Properties

Label 6036.2.a.g.1.6
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 1.6
Root \(-0.927807\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.92781 q^{5}\) \(+2.55035 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.92781 q^{5}\) \(+2.55035 q^{7}\) \(+1.00000 q^{9}\) \(+0.815289 q^{11}\) \(+5.13575 q^{13}\) \(-1.92781 q^{15}\) \(-6.73760 q^{17}\) \(-0.147315 q^{19}\) \(+2.55035 q^{21}\) \(-9.03100 q^{23}\) \(-1.28356 q^{25}\) \(+1.00000 q^{27}\) \(-7.65437 q^{29}\) \(-3.76735 q^{31}\) \(+0.815289 q^{33}\) \(-4.91658 q^{35}\) \(-4.31772 q^{37}\) \(+5.13575 q^{39}\) \(+10.2768 q^{41}\) \(+4.82692 q^{43}\) \(-1.92781 q^{45}\) \(+2.32723 q^{47}\) \(-0.495716 q^{49}\) \(-6.73760 q^{51}\) \(-10.7443 q^{53}\) \(-1.57172 q^{55}\) \(-0.147315 q^{57}\) \(-4.54599 q^{59}\) \(+2.14171 q^{61}\) \(+2.55035 q^{63}\) \(-9.90074 q^{65}\) \(-8.28920 q^{67}\) \(-9.03100 q^{69}\) \(-5.89873 q^{71}\) \(-3.28124 q^{73}\) \(-1.28356 q^{75}\) \(+2.07927 q^{77}\) \(+5.54238 q^{79}\) \(+1.00000 q^{81}\) \(-9.06785 q^{83}\) \(+12.9888 q^{85}\) \(-7.65437 q^{87}\) \(-0.924237 q^{89}\) \(+13.0980 q^{91}\) \(-3.76735 q^{93}\) \(+0.283995 q^{95}\) \(+14.2718 q^{97}\) \(+0.815289 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.92781 −0.862142 −0.431071 0.902318i \(-0.641864\pi\)
−0.431071 + 0.902318i \(0.641864\pi\)
\(6\) 0 0
\(7\) 2.55035 0.963942 0.481971 0.876187i \(-0.339921\pi\)
0.481971 + 0.876187i \(0.339921\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.815289 0.245819 0.122909 0.992418i \(-0.460778\pi\)
0.122909 + 0.992418i \(0.460778\pi\)
\(12\) 0 0
\(13\) 5.13575 1.42440 0.712201 0.701976i \(-0.247699\pi\)
0.712201 + 0.701976i \(0.247699\pi\)
\(14\) 0 0
\(15\) −1.92781 −0.497758
\(16\) 0 0
\(17\) −6.73760 −1.63411 −0.817054 0.576561i \(-0.804394\pi\)
−0.817054 + 0.576561i \(0.804394\pi\)
\(18\) 0 0
\(19\) −0.147315 −0.0337964 −0.0168982 0.999857i \(-0.505379\pi\)
−0.0168982 + 0.999857i \(0.505379\pi\)
\(20\) 0 0
\(21\) 2.55035 0.556532
\(22\) 0 0
\(23\) −9.03100 −1.88309 −0.941547 0.336881i \(-0.890628\pi\)
−0.941547 + 0.336881i \(0.890628\pi\)
\(24\) 0 0
\(25\) −1.28356 −0.256712
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −7.65437 −1.42138 −0.710690 0.703505i \(-0.751617\pi\)
−0.710690 + 0.703505i \(0.751617\pi\)
\(30\) 0 0
\(31\) −3.76735 −0.676636 −0.338318 0.941032i \(-0.609858\pi\)
−0.338318 + 0.941032i \(0.609858\pi\)
\(32\) 0 0
\(33\) 0.815289 0.141924
\(34\) 0 0
\(35\) −4.91658 −0.831054
\(36\) 0 0
\(37\) −4.31772 −0.709829 −0.354915 0.934899i \(-0.615490\pi\)
−0.354915 + 0.934899i \(0.615490\pi\)
\(38\) 0 0
\(39\) 5.13575 0.822378
\(40\) 0 0
\(41\) 10.2768 1.60497 0.802486 0.596670i \(-0.203510\pi\)
0.802486 + 0.596670i \(0.203510\pi\)
\(42\) 0 0
\(43\) 4.82692 0.736099 0.368050 0.929806i \(-0.380026\pi\)
0.368050 + 0.929806i \(0.380026\pi\)
\(44\) 0 0
\(45\) −1.92781 −0.287381
\(46\) 0 0
\(47\) 2.32723 0.339461 0.169731 0.985490i \(-0.445710\pi\)
0.169731 + 0.985490i \(0.445710\pi\)
\(48\) 0 0
\(49\) −0.495716 −0.0708165
\(50\) 0 0
\(51\) −6.73760 −0.943453
\(52\) 0 0
\(53\) −10.7443 −1.47585 −0.737925 0.674883i \(-0.764194\pi\)
−0.737925 + 0.674883i \(0.764194\pi\)
\(54\) 0 0
\(55\) −1.57172 −0.211931
\(56\) 0 0
\(57\) −0.147315 −0.0195124
\(58\) 0 0
\(59\) −4.54599 −0.591838 −0.295919 0.955213i \(-0.595626\pi\)
−0.295919 + 0.955213i \(0.595626\pi\)
\(60\) 0 0
\(61\) 2.14171 0.274218 0.137109 0.990556i \(-0.456219\pi\)
0.137109 + 0.990556i \(0.456219\pi\)
\(62\) 0 0
\(63\) 2.55035 0.321314
\(64\) 0 0
\(65\) −9.90074 −1.22804
\(66\) 0 0
\(67\) −8.28920 −1.01269 −0.506343 0.862332i \(-0.669003\pi\)
−0.506343 + 0.862332i \(0.669003\pi\)
\(68\) 0 0
\(69\) −9.03100 −1.08721
\(70\) 0 0
\(71\) −5.89873 −0.700050 −0.350025 0.936740i \(-0.613827\pi\)
−0.350025 + 0.936740i \(0.613827\pi\)
\(72\) 0 0
\(73\) −3.28124 −0.384040 −0.192020 0.981391i \(-0.561504\pi\)
−0.192020 + 0.981391i \(0.561504\pi\)
\(74\) 0 0
\(75\) −1.28356 −0.148213
\(76\) 0 0
\(77\) 2.07927 0.236955
\(78\) 0 0
\(79\) 5.54238 0.623567 0.311783 0.950153i \(-0.399074\pi\)
0.311783 + 0.950153i \(0.399074\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −9.06785 −0.995326 −0.497663 0.867370i \(-0.665808\pi\)
−0.497663 + 0.867370i \(0.665808\pi\)
\(84\) 0 0
\(85\) 12.9888 1.40883
\(86\) 0 0
\(87\) −7.65437 −0.820634
\(88\) 0 0
\(89\) −0.924237 −0.0979689 −0.0489844 0.998800i \(-0.515598\pi\)
−0.0489844 + 0.998800i \(0.515598\pi\)
\(90\) 0 0
\(91\) 13.0980 1.37304
\(92\) 0 0
\(93\) −3.76735 −0.390656
\(94\) 0 0
\(95\) 0.283995 0.0291373
\(96\) 0 0
\(97\) 14.2718 1.44908 0.724540 0.689233i \(-0.242052\pi\)
0.724540 + 0.689233i \(0.242052\pi\)
\(98\) 0 0
\(99\) 0.815289 0.0819396
\(100\) 0 0
\(101\) −0.709810 −0.0706287 −0.0353144 0.999376i \(-0.511243\pi\)
−0.0353144 + 0.999376i \(0.511243\pi\)
\(102\) 0 0
\(103\) 2.70600 0.266630 0.133315 0.991074i \(-0.457438\pi\)
0.133315 + 0.991074i \(0.457438\pi\)
\(104\) 0 0
\(105\) −4.91658 −0.479809
\(106\) 0 0
\(107\) −10.9377 −1.05739 −0.528695 0.848812i \(-0.677319\pi\)
−0.528695 + 0.848812i \(0.677319\pi\)
\(108\) 0 0
\(109\) −12.6426 −1.21094 −0.605471 0.795867i \(-0.707015\pi\)
−0.605471 + 0.795867i \(0.707015\pi\)
\(110\) 0 0
\(111\) −4.31772 −0.409820
\(112\) 0 0
\(113\) −9.77677 −0.919722 −0.459861 0.887991i \(-0.652101\pi\)
−0.459861 + 0.887991i \(0.652101\pi\)
\(114\) 0 0
\(115\) 17.4100 1.62349
\(116\) 0 0
\(117\) 5.13575 0.474800
\(118\) 0 0
\(119\) −17.1832 −1.57519
\(120\) 0 0
\(121\) −10.3353 −0.939573
\(122\) 0 0
\(123\) 10.2768 0.926632
\(124\) 0 0
\(125\) 12.1135 1.08346
\(126\) 0 0
\(127\) 12.5220 1.11115 0.555575 0.831466i \(-0.312498\pi\)
0.555575 + 0.831466i \(0.312498\pi\)
\(128\) 0 0
\(129\) 4.82692 0.424987
\(130\) 0 0
\(131\) 13.5402 1.18301 0.591505 0.806301i \(-0.298534\pi\)
0.591505 + 0.806301i \(0.298534\pi\)
\(132\) 0 0
\(133\) −0.375705 −0.0325778
\(134\) 0 0
\(135\) −1.92781 −0.165919
\(136\) 0 0
\(137\) 20.8882 1.78460 0.892301 0.451441i \(-0.149090\pi\)
0.892301 + 0.451441i \(0.149090\pi\)
\(138\) 0 0
\(139\) 3.30885 0.280653 0.140327 0.990105i \(-0.455185\pi\)
0.140327 + 0.990105i \(0.455185\pi\)
\(140\) 0 0
\(141\) 2.32723 0.195988
\(142\) 0 0
\(143\) 4.18712 0.350145
\(144\) 0 0
\(145\) 14.7561 1.22543
\(146\) 0 0
\(147\) −0.495716 −0.0408860
\(148\) 0 0
\(149\) 4.40642 0.360988 0.180494 0.983576i \(-0.442230\pi\)
0.180494 + 0.983576i \(0.442230\pi\)
\(150\) 0 0
\(151\) −13.5618 −1.10364 −0.551822 0.833962i \(-0.686067\pi\)
−0.551822 + 0.833962i \(0.686067\pi\)
\(152\) 0 0
\(153\) −6.73760 −0.544703
\(154\) 0 0
\(155\) 7.26273 0.583357
\(156\) 0 0
\(157\) 5.09542 0.406659 0.203330 0.979110i \(-0.434824\pi\)
0.203330 + 0.979110i \(0.434824\pi\)
\(158\) 0 0
\(159\) −10.7443 −0.852082
\(160\) 0 0
\(161\) −23.0322 −1.81519
\(162\) 0 0
\(163\) −14.3025 −1.12026 −0.560129 0.828405i \(-0.689249\pi\)
−0.560129 + 0.828405i \(0.689249\pi\)
\(164\) 0 0
\(165\) −1.57172 −0.122358
\(166\) 0 0
\(167\) 4.47377 0.346191 0.173095 0.984905i \(-0.444623\pi\)
0.173095 + 0.984905i \(0.444623\pi\)
\(168\) 0 0
\(169\) 13.3759 1.02892
\(170\) 0 0
\(171\) −0.147315 −0.0112655
\(172\) 0 0
\(173\) 23.8149 1.81061 0.905306 0.424759i \(-0.139641\pi\)
0.905306 + 0.424759i \(0.139641\pi\)
\(174\) 0 0
\(175\) −3.27352 −0.247455
\(176\) 0 0
\(177\) −4.54599 −0.341698
\(178\) 0 0
\(179\) −5.20420 −0.388980 −0.194490 0.980904i \(-0.562305\pi\)
−0.194490 + 0.980904i \(0.562305\pi\)
\(180\) 0 0
\(181\) 3.51871 0.261544 0.130772 0.991412i \(-0.458254\pi\)
0.130772 + 0.991412i \(0.458254\pi\)
\(182\) 0 0
\(183\) 2.14171 0.158320
\(184\) 0 0
\(185\) 8.32374 0.611973
\(186\) 0 0
\(187\) −5.49309 −0.401695
\(188\) 0 0
\(189\) 2.55035 0.185511
\(190\) 0 0
\(191\) −11.3466 −0.821009 −0.410505 0.911859i \(-0.634647\pi\)
−0.410505 + 0.911859i \(0.634647\pi\)
\(192\) 0 0
\(193\) −22.0003 −1.58361 −0.791806 0.610772i \(-0.790859\pi\)
−0.791806 + 0.610772i \(0.790859\pi\)
\(194\) 0 0
\(195\) −9.90074 −0.709007
\(196\) 0 0
\(197\) 4.72176 0.336412 0.168206 0.985752i \(-0.446203\pi\)
0.168206 + 0.985752i \(0.446203\pi\)
\(198\) 0 0
\(199\) −6.81490 −0.483096 −0.241548 0.970389i \(-0.577655\pi\)
−0.241548 + 0.970389i \(0.577655\pi\)
\(200\) 0 0
\(201\) −8.28920 −0.584675
\(202\) 0 0
\(203\) −19.5213 −1.37013
\(204\) 0 0
\(205\) −19.8118 −1.38371
\(206\) 0 0
\(207\) −9.03100 −0.627698
\(208\) 0 0
\(209\) −0.120104 −0.00830779
\(210\) 0 0
\(211\) −1.99499 −0.137341 −0.0686703 0.997639i \(-0.521876\pi\)
−0.0686703 + 0.997639i \(0.521876\pi\)
\(212\) 0 0
\(213\) −5.89873 −0.404174
\(214\) 0 0
\(215\) −9.30538 −0.634622
\(216\) 0 0
\(217\) −9.60807 −0.652238
\(218\) 0 0
\(219\) −3.28124 −0.221726
\(220\) 0 0
\(221\) −34.6027 −2.32763
\(222\) 0 0
\(223\) 12.7000 0.850453 0.425226 0.905087i \(-0.360194\pi\)
0.425226 + 0.905087i \(0.360194\pi\)
\(224\) 0 0
\(225\) −1.28356 −0.0855706
\(226\) 0 0
\(227\) 24.9423 1.65548 0.827741 0.561111i \(-0.189626\pi\)
0.827741 + 0.561111i \(0.189626\pi\)
\(228\) 0 0
\(229\) −21.1888 −1.40019 −0.700097 0.714048i \(-0.746860\pi\)
−0.700097 + 0.714048i \(0.746860\pi\)
\(230\) 0 0
\(231\) 2.07927 0.136806
\(232\) 0 0
\(233\) −4.00392 −0.262305 −0.131153 0.991362i \(-0.541868\pi\)
−0.131153 + 0.991362i \(0.541868\pi\)
\(234\) 0 0
\(235\) −4.48645 −0.292664
\(236\) 0 0
\(237\) 5.54238 0.360017
\(238\) 0 0
\(239\) −3.84871 −0.248952 −0.124476 0.992223i \(-0.539725\pi\)
−0.124476 + 0.992223i \(0.539725\pi\)
\(240\) 0 0
\(241\) −12.5810 −0.810416 −0.405208 0.914225i \(-0.632801\pi\)
−0.405208 + 0.914225i \(0.632801\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0.955645 0.0610539
\(246\) 0 0
\(247\) −0.756574 −0.0481396
\(248\) 0 0
\(249\) −9.06785 −0.574652
\(250\) 0 0
\(251\) −26.5150 −1.67361 −0.836806 0.547499i \(-0.815580\pi\)
−0.836806 + 0.547499i \(0.815580\pi\)
\(252\) 0 0
\(253\) −7.36288 −0.462900
\(254\) 0 0
\(255\) 12.9888 0.813390
\(256\) 0 0
\(257\) 7.40877 0.462147 0.231073 0.972936i \(-0.425776\pi\)
0.231073 + 0.972936i \(0.425776\pi\)
\(258\) 0 0
\(259\) −11.0117 −0.684234
\(260\) 0 0
\(261\) −7.65437 −0.473793
\(262\) 0 0
\(263\) −15.4882 −0.955041 −0.477521 0.878621i \(-0.658464\pi\)
−0.477521 + 0.878621i \(0.658464\pi\)
\(264\) 0 0
\(265\) 20.7130 1.27239
\(266\) 0 0
\(267\) −0.924237 −0.0565624
\(268\) 0 0
\(269\) 27.7858 1.69413 0.847064 0.531491i \(-0.178368\pi\)
0.847064 + 0.531491i \(0.178368\pi\)
\(270\) 0 0
\(271\) 1.45065 0.0881208 0.0440604 0.999029i \(-0.485971\pi\)
0.0440604 + 0.999029i \(0.485971\pi\)
\(272\) 0 0
\(273\) 13.0980 0.792725
\(274\) 0 0
\(275\) −1.04647 −0.0631046
\(276\) 0 0
\(277\) 4.80008 0.288409 0.144204 0.989548i \(-0.453938\pi\)
0.144204 + 0.989548i \(0.453938\pi\)
\(278\) 0 0
\(279\) −3.76735 −0.225545
\(280\) 0 0
\(281\) 13.8114 0.823916 0.411958 0.911203i \(-0.364845\pi\)
0.411958 + 0.911203i \(0.364845\pi\)
\(282\) 0 0
\(283\) −10.5213 −0.625427 −0.312713 0.949848i \(-0.601238\pi\)
−0.312713 + 0.949848i \(0.601238\pi\)
\(284\) 0 0
\(285\) 0.283995 0.0168224
\(286\) 0 0
\(287\) 26.2095 1.54710
\(288\) 0 0
\(289\) 28.3953 1.67031
\(290\) 0 0
\(291\) 14.2718 0.836626
\(292\) 0 0
\(293\) −21.2971 −1.24419 −0.622094 0.782943i \(-0.713718\pi\)
−0.622094 + 0.782943i \(0.713718\pi\)
\(294\) 0 0
\(295\) 8.76380 0.510248
\(296\) 0 0
\(297\) 0.815289 0.0473079
\(298\) 0 0
\(299\) −46.3810 −2.68228
\(300\) 0 0
\(301\) 12.3103 0.709557
\(302\) 0 0
\(303\) −0.709810 −0.0407775
\(304\) 0 0
\(305\) −4.12880 −0.236415
\(306\) 0 0
\(307\) −24.6983 −1.40961 −0.704803 0.709403i \(-0.748965\pi\)
−0.704803 + 0.709403i \(0.748965\pi\)
\(308\) 0 0
\(309\) 2.70600 0.153939
\(310\) 0 0
\(311\) −22.8450 −1.29542 −0.647711 0.761886i \(-0.724274\pi\)
−0.647711 + 0.761886i \(0.724274\pi\)
\(312\) 0 0
\(313\) 24.1946 1.36756 0.683780 0.729688i \(-0.260335\pi\)
0.683780 + 0.729688i \(0.260335\pi\)
\(314\) 0 0
\(315\) −4.91658 −0.277018
\(316\) 0 0
\(317\) −16.4658 −0.924812 −0.462406 0.886668i \(-0.653014\pi\)
−0.462406 + 0.886668i \(0.653014\pi\)
\(318\) 0 0
\(319\) −6.24052 −0.349402
\(320\) 0 0
\(321\) −10.9377 −0.610485
\(322\) 0 0
\(323\) 0.992550 0.0552270
\(324\) 0 0
\(325\) −6.59204 −0.365660
\(326\) 0 0
\(327\) −12.6426 −0.699138
\(328\) 0 0
\(329\) 5.93525 0.327221
\(330\) 0 0
\(331\) 6.48106 0.356231 0.178116 0.984010i \(-0.443000\pi\)
0.178116 + 0.984010i \(0.443000\pi\)
\(332\) 0 0
\(333\) −4.31772 −0.236610
\(334\) 0 0
\(335\) 15.9800 0.873079
\(336\) 0 0
\(337\) 1.21753 0.0663229 0.0331615 0.999450i \(-0.489442\pi\)
0.0331615 + 0.999450i \(0.489442\pi\)
\(338\) 0 0
\(339\) −9.77677 −0.531002
\(340\) 0 0
\(341\) −3.07148 −0.166330
\(342\) 0 0
\(343\) −19.1167 −1.03220
\(344\) 0 0
\(345\) 17.4100 0.937325
\(346\) 0 0
\(347\) −5.88896 −0.316136 −0.158068 0.987428i \(-0.550527\pi\)
−0.158068 + 0.987428i \(0.550527\pi\)
\(348\) 0 0
\(349\) −33.5403 −1.79537 −0.897685 0.440638i \(-0.854752\pi\)
−0.897685 + 0.440638i \(0.854752\pi\)
\(350\) 0 0
\(351\) 5.13575 0.274126
\(352\) 0 0
\(353\) 3.36963 0.179347 0.0896737 0.995971i \(-0.471418\pi\)
0.0896737 + 0.995971i \(0.471418\pi\)
\(354\) 0 0
\(355\) 11.3716 0.603542
\(356\) 0 0
\(357\) −17.1832 −0.909434
\(358\) 0 0
\(359\) 7.79905 0.411618 0.205809 0.978592i \(-0.434017\pi\)
0.205809 + 0.978592i \(0.434017\pi\)
\(360\) 0 0
\(361\) −18.9783 −0.998858
\(362\) 0 0
\(363\) −10.3353 −0.542463
\(364\) 0 0
\(365\) 6.32560 0.331097
\(366\) 0 0
\(367\) −27.9769 −1.46038 −0.730192 0.683242i \(-0.760569\pi\)
−0.730192 + 0.683242i \(0.760569\pi\)
\(368\) 0 0
\(369\) 10.2768 0.534991
\(370\) 0 0
\(371\) −27.4018 −1.42263
\(372\) 0 0
\(373\) 3.04578 0.157704 0.0788522 0.996886i \(-0.474874\pi\)
0.0788522 + 0.996886i \(0.474874\pi\)
\(374\) 0 0
\(375\) 12.1135 0.625538
\(376\) 0 0
\(377\) −39.3109 −2.02462
\(378\) 0 0
\(379\) 22.7816 1.17021 0.585106 0.810957i \(-0.301053\pi\)
0.585106 + 0.810957i \(0.301053\pi\)
\(380\) 0 0
\(381\) 12.5220 0.641523
\(382\) 0 0
\(383\) −2.41537 −0.123420 −0.0617098 0.998094i \(-0.519655\pi\)
−0.0617098 + 0.998094i \(0.519655\pi\)
\(384\) 0 0
\(385\) −4.00844 −0.204289
\(386\) 0 0
\(387\) 4.82692 0.245366
\(388\) 0 0
\(389\) 22.5608 1.14388 0.571940 0.820296i \(-0.306191\pi\)
0.571940 + 0.820296i \(0.306191\pi\)
\(390\) 0 0
\(391\) 60.8473 3.07718
\(392\) 0 0
\(393\) 13.5402 0.683011
\(394\) 0 0
\(395\) −10.6847 −0.537603
\(396\) 0 0
\(397\) −38.9416 −1.95442 −0.977211 0.212270i \(-0.931914\pi\)
−0.977211 + 0.212270i \(0.931914\pi\)
\(398\) 0 0
\(399\) −0.375705 −0.0188088
\(400\) 0 0
\(401\) −3.47161 −0.173364 −0.0866820 0.996236i \(-0.527626\pi\)
−0.0866820 + 0.996236i \(0.527626\pi\)
\(402\) 0 0
\(403\) −19.3482 −0.963802
\(404\) 0 0
\(405\) −1.92781 −0.0957935
\(406\) 0 0
\(407\) −3.52019 −0.174489
\(408\) 0 0
\(409\) 19.1612 0.947459 0.473729 0.880670i \(-0.342907\pi\)
0.473729 + 0.880670i \(0.342907\pi\)
\(410\) 0 0
\(411\) 20.8882 1.03034
\(412\) 0 0
\(413\) −11.5939 −0.570497
\(414\) 0 0
\(415\) 17.4811 0.858112
\(416\) 0 0
\(417\) 3.30885 0.162035
\(418\) 0 0
\(419\) 28.6911 1.40165 0.700825 0.713333i \(-0.252815\pi\)
0.700825 + 0.713333i \(0.252815\pi\)
\(420\) 0 0
\(421\) −5.64464 −0.275103 −0.137551 0.990495i \(-0.543923\pi\)
−0.137551 + 0.990495i \(0.543923\pi\)
\(422\) 0 0
\(423\) 2.32723 0.113154
\(424\) 0 0
\(425\) 8.64810 0.419495
\(426\) 0 0
\(427\) 5.46211 0.264330
\(428\) 0 0
\(429\) 4.18712 0.202156
\(430\) 0 0
\(431\) −3.97668 −0.191550 −0.0957749 0.995403i \(-0.530533\pi\)
−0.0957749 + 0.995403i \(0.530533\pi\)
\(432\) 0 0
\(433\) −7.32553 −0.352042 −0.176021 0.984386i \(-0.556323\pi\)
−0.176021 + 0.984386i \(0.556323\pi\)
\(434\) 0 0
\(435\) 14.7561 0.707503
\(436\) 0 0
\(437\) 1.33040 0.0636418
\(438\) 0 0
\(439\) −14.9099 −0.711609 −0.355804 0.934560i \(-0.615793\pi\)
−0.355804 + 0.934560i \(0.615793\pi\)
\(440\) 0 0
\(441\) −0.495716 −0.0236055
\(442\) 0 0
\(443\) −20.9461 −0.995179 −0.497589 0.867413i \(-0.665781\pi\)
−0.497589 + 0.867413i \(0.665781\pi\)
\(444\) 0 0
\(445\) 1.78175 0.0844631
\(446\) 0 0
\(447\) 4.40642 0.208417
\(448\) 0 0
\(449\) −33.4285 −1.57759 −0.788795 0.614657i \(-0.789295\pi\)
−0.788795 + 0.614657i \(0.789295\pi\)
\(450\) 0 0
\(451\) 8.37860 0.394533
\(452\) 0 0
\(453\) −13.5618 −0.637189
\(454\) 0 0
\(455\) −25.2504 −1.18375
\(456\) 0 0
\(457\) −1.67395 −0.0783040 −0.0391520 0.999233i \(-0.512466\pi\)
−0.0391520 + 0.999233i \(0.512466\pi\)
\(458\) 0 0
\(459\) −6.73760 −0.314484
\(460\) 0 0
\(461\) −30.5826 −1.42437 −0.712187 0.701990i \(-0.752295\pi\)
−0.712187 + 0.701990i \(0.752295\pi\)
\(462\) 0 0
\(463\) 29.6376 1.37738 0.688688 0.725058i \(-0.258187\pi\)
0.688688 + 0.725058i \(0.258187\pi\)
\(464\) 0 0
\(465\) 7.26273 0.336801
\(466\) 0 0
\(467\) 36.4831 1.68824 0.844118 0.536158i \(-0.180125\pi\)
0.844118 + 0.536158i \(0.180125\pi\)
\(468\) 0 0
\(469\) −21.1403 −0.976171
\(470\) 0 0
\(471\) 5.09542 0.234785
\(472\) 0 0
\(473\) 3.93534 0.180947
\(474\) 0 0
\(475\) 0.189087 0.00867593
\(476\) 0 0
\(477\) −10.7443 −0.491950
\(478\) 0 0
\(479\) −17.8729 −0.816633 −0.408316 0.912840i \(-0.633884\pi\)
−0.408316 + 0.912840i \(0.633884\pi\)
\(480\) 0 0
\(481\) −22.1747 −1.01108
\(482\) 0 0
\(483\) −23.0322 −1.04800
\(484\) 0 0
\(485\) −27.5132 −1.24931
\(486\) 0 0
\(487\) −18.4553 −0.836287 −0.418144 0.908381i \(-0.637319\pi\)
−0.418144 + 0.908381i \(0.637319\pi\)
\(488\) 0 0
\(489\) −14.3025 −0.646782
\(490\) 0 0
\(491\) −14.0191 −0.632672 −0.316336 0.948647i \(-0.602453\pi\)
−0.316336 + 0.948647i \(0.602453\pi\)
\(492\) 0 0
\(493\) 51.5721 2.32269
\(494\) 0 0
\(495\) −1.57172 −0.0706436
\(496\) 0 0
\(497\) −15.0438 −0.674808
\(498\) 0 0
\(499\) 11.9850 0.536522 0.268261 0.963346i \(-0.413551\pi\)
0.268261 + 0.963346i \(0.413551\pi\)
\(500\) 0 0
\(501\) 4.47377 0.199873
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 1.36838 0.0608920
\(506\) 0 0
\(507\) 13.3759 0.594047
\(508\) 0 0
\(509\) 7.99617 0.354424 0.177212 0.984173i \(-0.443292\pi\)
0.177212 + 0.984173i \(0.443292\pi\)
\(510\) 0 0
\(511\) −8.36832 −0.370193
\(512\) 0 0
\(513\) −0.147315 −0.00650412
\(514\) 0 0
\(515\) −5.21664 −0.229873
\(516\) 0 0
\(517\) 1.89736 0.0834460
\(518\) 0 0
\(519\) 23.8149 1.04536
\(520\) 0 0
\(521\) 35.7530 1.56637 0.783183 0.621791i \(-0.213595\pi\)
0.783183 + 0.621791i \(0.213595\pi\)
\(522\) 0 0
\(523\) −17.5812 −0.768771 −0.384385 0.923173i \(-0.625587\pi\)
−0.384385 + 0.923173i \(0.625587\pi\)
\(524\) 0 0
\(525\) −3.27352 −0.142868
\(526\) 0 0
\(527\) 25.3829 1.10570
\(528\) 0 0
\(529\) 58.5590 2.54605
\(530\) 0 0
\(531\) −4.54599 −0.197279
\(532\) 0 0
\(533\) 52.7793 2.28613
\(534\) 0 0
\(535\) 21.0858 0.911621
\(536\) 0 0
\(537\) −5.20420 −0.224578
\(538\) 0 0
\(539\) −0.404152 −0.0174080
\(540\) 0 0
\(541\) 5.55690 0.238910 0.119455 0.992840i \(-0.461885\pi\)
0.119455 + 0.992840i \(0.461885\pi\)
\(542\) 0 0
\(543\) 3.51871 0.151002
\(544\) 0 0
\(545\) 24.3725 1.04400
\(546\) 0 0
\(547\) 27.0807 1.15789 0.578943 0.815368i \(-0.303465\pi\)
0.578943 + 0.815368i \(0.303465\pi\)
\(548\) 0 0
\(549\) 2.14171 0.0914059
\(550\) 0 0
\(551\) 1.12760 0.0480375
\(552\) 0 0
\(553\) 14.1350 0.601082
\(554\) 0 0
\(555\) 8.32374 0.353323
\(556\) 0 0
\(557\) 33.7739 1.43104 0.715522 0.698590i \(-0.246189\pi\)
0.715522 + 0.698590i \(0.246189\pi\)
\(558\) 0 0
\(559\) 24.7899 1.04850
\(560\) 0 0
\(561\) −5.49309 −0.231919
\(562\) 0 0
\(563\) −33.7987 −1.42445 −0.712223 0.701953i \(-0.752312\pi\)
−0.712223 + 0.701953i \(0.752312\pi\)
\(564\) 0 0
\(565\) 18.8477 0.792930
\(566\) 0 0
\(567\) 2.55035 0.107105
\(568\) 0 0
\(569\) −14.5449 −0.609755 −0.304877 0.952392i \(-0.598616\pi\)
−0.304877 + 0.952392i \(0.598616\pi\)
\(570\) 0 0
\(571\) −5.66220 −0.236956 −0.118478 0.992957i \(-0.537801\pi\)
−0.118478 + 0.992957i \(0.537801\pi\)
\(572\) 0 0
\(573\) −11.3466 −0.474010
\(574\) 0 0
\(575\) 11.5918 0.483412
\(576\) 0 0
\(577\) −6.40675 −0.266716 −0.133358 0.991068i \(-0.542576\pi\)
−0.133358 + 0.991068i \(0.542576\pi\)
\(578\) 0 0
\(579\) −22.0003 −0.914299
\(580\) 0 0
\(581\) −23.1262 −0.959436
\(582\) 0 0
\(583\) −8.75975 −0.362792
\(584\) 0 0
\(585\) −9.90074 −0.409345
\(586\) 0 0
\(587\) 45.6470 1.88405 0.942027 0.335538i \(-0.108918\pi\)
0.942027 + 0.335538i \(0.108918\pi\)
\(588\) 0 0
\(589\) 0.554988 0.0228679
\(590\) 0 0
\(591\) 4.72176 0.194227
\(592\) 0 0
\(593\) −9.51930 −0.390911 −0.195455 0.980713i \(-0.562618\pi\)
−0.195455 + 0.980713i \(0.562618\pi\)
\(594\) 0 0
\(595\) 33.1260 1.35803
\(596\) 0 0
\(597\) −6.81490 −0.278915
\(598\) 0 0
\(599\) −13.4030 −0.547631 −0.273816 0.961782i \(-0.588286\pi\)
−0.273816 + 0.961782i \(0.588286\pi\)
\(600\) 0 0
\(601\) 3.95607 0.161371 0.0806856 0.996740i \(-0.474289\pi\)
0.0806856 + 0.996740i \(0.474289\pi\)
\(602\) 0 0
\(603\) −8.28920 −0.337562
\(604\) 0 0
\(605\) 19.9245 0.810045
\(606\) 0 0
\(607\) −9.14065 −0.371007 −0.185504 0.982644i \(-0.559392\pi\)
−0.185504 + 0.982644i \(0.559392\pi\)
\(608\) 0 0
\(609\) −19.5213 −0.791044
\(610\) 0 0
\(611\) 11.9521 0.483529
\(612\) 0 0
\(613\) −16.6762 −0.673544 −0.336772 0.941586i \(-0.609335\pi\)
−0.336772 + 0.941586i \(0.609335\pi\)
\(614\) 0 0
\(615\) −19.8118 −0.798888
\(616\) 0 0
\(617\) −17.5739 −0.707500 −0.353750 0.935340i \(-0.615094\pi\)
−0.353750 + 0.935340i \(0.615094\pi\)
\(618\) 0 0
\(619\) 42.1582 1.69448 0.847240 0.531210i \(-0.178262\pi\)
0.847240 + 0.531210i \(0.178262\pi\)
\(620\) 0 0
\(621\) −9.03100 −0.362402
\(622\) 0 0
\(623\) −2.35713 −0.0944363
\(624\) 0 0
\(625\) −16.9347 −0.677387
\(626\) 0 0
\(627\) −0.120104 −0.00479651
\(628\) 0 0
\(629\) 29.0911 1.15994
\(630\) 0 0
\(631\) 13.9570 0.555621 0.277811 0.960636i \(-0.410391\pi\)
0.277811 + 0.960636i \(0.410391\pi\)
\(632\) 0 0
\(633\) −1.99499 −0.0792936
\(634\) 0 0
\(635\) −24.1401 −0.957969
\(636\) 0 0
\(637\) −2.54587 −0.100871
\(638\) 0 0
\(639\) −5.89873 −0.233350
\(640\) 0 0
\(641\) 4.43588 0.175207 0.0876034 0.996155i \(-0.472079\pi\)
0.0876034 + 0.996155i \(0.472079\pi\)
\(642\) 0 0
\(643\) 30.4435 1.20057 0.600287 0.799785i \(-0.295053\pi\)
0.600287 + 0.799785i \(0.295053\pi\)
\(644\) 0 0
\(645\) −9.30538 −0.366399
\(646\) 0 0
\(647\) 39.0205 1.53405 0.767027 0.641615i \(-0.221735\pi\)
0.767027 + 0.641615i \(0.221735\pi\)
\(648\) 0 0
\(649\) −3.70630 −0.145485
\(650\) 0 0
\(651\) −9.60807 −0.376570
\(652\) 0 0
\(653\) 11.7006 0.457879 0.228939 0.973441i \(-0.426474\pi\)
0.228939 + 0.973441i \(0.426474\pi\)
\(654\) 0 0
\(655\) −26.1028 −1.01992
\(656\) 0 0
\(657\) −3.28124 −0.128013
\(658\) 0 0
\(659\) 24.8972 0.969858 0.484929 0.874554i \(-0.338845\pi\)
0.484929 + 0.874554i \(0.338845\pi\)
\(660\) 0 0
\(661\) 8.36955 0.325538 0.162769 0.986664i \(-0.447958\pi\)
0.162769 + 0.986664i \(0.447958\pi\)
\(662\) 0 0
\(663\) −34.6027 −1.34386
\(664\) 0 0
\(665\) 0.724287 0.0280866
\(666\) 0 0
\(667\) 69.1266 2.67659
\(668\) 0 0
\(669\) 12.7000 0.491009
\(670\) 0 0
\(671\) 1.74611 0.0674079
\(672\) 0 0
\(673\) −22.0651 −0.850548 −0.425274 0.905065i \(-0.639822\pi\)
−0.425274 + 0.905065i \(0.639822\pi\)
\(674\) 0 0
\(675\) −1.28356 −0.0494042
\(676\) 0 0
\(677\) 42.7514 1.64307 0.821536 0.570157i \(-0.193118\pi\)
0.821536 + 0.570157i \(0.193118\pi\)
\(678\) 0 0
\(679\) 36.3980 1.39683
\(680\) 0 0
\(681\) 24.9423 0.955792
\(682\) 0 0
\(683\) −22.5235 −0.861839 −0.430920 0.902390i \(-0.641811\pi\)
−0.430920 + 0.902390i \(0.641811\pi\)
\(684\) 0 0
\(685\) −40.2685 −1.53858
\(686\) 0 0
\(687\) −21.1888 −0.808402
\(688\) 0 0
\(689\) −55.1803 −2.10220
\(690\) 0 0
\(691\) −26.2795 −0.999718 −0.499859 0.866107i \(-0.666615\pi\)
−0.499859 + 0.866107i \(0.666615\pi\)
\(692\) 0 0
\(693\) 2.07927 0.0789850
\(694\) 0 0
\(695\) −6.37883 −0.241963
\(696\) 0 0
\(697\) −69.2413 −2.62270
\(698\) 0 0
\(699\) −4.00392 −0.151442
\(700\) 0 0
\(701\) −1.64347 −0.0620731 −0.0310365 0.999518i \(-0.509881\pi\)
−0.0310365 + 0.999518i \(0.509881\pi\)
\(702\) 0 0
\(703\) 0.636065 0.0239897
\(704\) 0 0
\(705\) −4.48645 −0.168970
\(706\) 0 0
\(707\) −1.81026 −0.0680820
\(708\) 0 0
\(709\) −25.2745 −0.949204 −0.474602 0.880200i \(-0.657408\pi\)
−0.474602 + 0.880200i \(0.657408\pi\)
\(710\) 0 0
\(711\) 5.54238 0.207856
\(712\) 0 0
\(713\) 34.0230 1.27417
\(714\) 0 0
\(715\) −8.07197 −0.301874
\(716\) 0 0
\(717\) −3.84871 −0.143733
\(718\) 0 0
\(719\) 28.5997 1.06659 0.533295 0.845929i \(-0.320954\pi\)
0.533295 + 0.845929i \(0.320954\pi\)
\(720\) 0 0
\(721\) 6.90124 0.257016
\(722\) 0 0
\(723\) −12.5810 −0.467894
\(724\) 0 0
\(725\) 9.82483 0.364885
\(726\) 0 0
\(727\) 20.3706 0.755505 0.377753 0.925907i \(-0.376697\pi\)
0.377753 + 0.925907i \(0.376697\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −32.5219 −1.20287
\(732\) 0 0
\(733\) 23.6257 0.872636 0.436318 0.899793i \(-0.356282\pi\)
0.436318 + 0.899793i \(0.356282\pi\)
\(734\) 0 0
\(735\) 0.955645 0.0352495
\(736\) 0 0
\(737\) −6.75809 −0.248937
\(738\) 0 0
\(739\) −18.9819 −0.698262 −0.349131 0.937074i \(-0.613523\pi\)
−0.349131 + 0.937074i \(0.613523\pi\)
\(740\) 0 0
\(741\) −0.756574 −0.0277934
\(742\) 0 0
\(743\) 40.7314 1.49429 0.747145 0.664661i \(-0.231424\pi\)
0.747145 + 0.664661i \(0.231424\pi\)
\(744\) 0 0
\(745\) −8.49473 −0.311223
\(746\) 0 0
\(747\) −9.06785 −0.331775
\(748\) 0 0
\(749\) −27.8950 −1.01926
\(750\) 0 0
\(751\) 0.300425 0.0109627 0.00548134 0.999985i \(-0.498255\pi\)
0.00548134 + 0.999985i \(0.498255\pi\)
\(752\) 0 0
\(753\) −26.5150 −0.966261
\(754\) 0 0
\(755\) 26.1446 0.951498
\(756\) 0 0
\(757\) −33.4251 −1.21486 −0.607429 0.794374i \(-0.707799\pi\)
−0.607429 + 0.794374i \(0.707799\pi\)
\(758\) 0 0
\(759\) −7.36288 −0.267256
\(760\) 0 0
\(761\) 53.8999 1.95387 0.976936 0.213534i \(-0.0684974\pi\)
0.976936 + 0.213534i \(0.0684974\pi\)
\(762\) 0 0
\(763\) −32.2431 −1.16728
\(764\) 0 0
\(765\) 12.9888 0.469611
\(766\) 0 0
\(767\) −23.3471 −0.843015
\(768\) 0 0
\(769\) −2.28947 −0.0825606 −0.0412803 0.999148i \(-0.513144\pi\)
−0.0412803 + 0.999148i \(0.513144\pi\)
\(770\) 0 0
\(771\) 7.40877 0.266820
\(772\) 0 0
\(773\) −13.4327 −0.483141 −0.241571 0.970383i \(-0.577663\pi\)
−0.241571 + 0.970383i \(0.577663\pi\)
\(774\) 0 0
\(775\) 4.83562 0.173700
\(776\) 0 0
\(777\) −11.0117 −0.395043
\(778\) 0 0
\(779\) −1.51393 −0.0542423
\(780\) 0 0
\(781\) −4.80917 −0.172086
\(782\) 0 0
\(783\) −7.65437 −0.273545
\(784\) 0 0
\(785\) −9.82300 −0.350598
\(786\) 0 0
\(787\) 2.95416 0.105305 0.0526523 0.998613i \(-0.483233\pi\)
0.0526523 + 0.998613i \(0.483233\pi\)
\(788\) 0 0
\(789\) −15.4882 −0.551393
\(790\) 0 0
\(791\) −24.9342 −0.886558
\(792\) 0 0
\(793\) 10.9993 0.390596
\(794\) 0 0
\(795\) 20.7130 0.734615
\(796\) 0 0
\(797\) 20.8737 0.739384 0.369692 0.929154i \(-0.379463\pi\)
0.369692 + 0.929154i \(0.379463\pi\)
\(798\) 0 0
\(799\) −15.6799 −0.554717
\(800\) 0 0
\(801\) −0.924237 −0.0326563
\(802\) 0 0
\(803\) −2.67516 −0.0944044
\(804\) 0 0
\(805\) 44.4017 1.56495
\(806\) 0 0
\(807\) 27.7858 0.978105
\(808\) 0 0
\(809\) −45.6461 −1.60483 −0.802416 0.596765i \(-0.796452\pi\)
−0.802416 + 0.596765i \(0.796452\pi\)
\(810\) 0 0
\(811\) 41.5251 1.45814 0.729071 0.684438i \(-0.239952\pi\)
0.729071 + 0.684438i \(0.239952\pi\)
\(812\) 0 0
\(813\) 1.45065 0.0508766
\(814\) 0 0
\(815\) 27.5725 0.965822
\(816\) 0 0
\(817\) −0.711079 −0.0248775
\(818\) 0 0
\(819\) 13.0980 0.457680
\(820\) 0 0
\(821\) −40.6283 −1.41794 −0.708969 0.705240i \(-0.750839\pi\)
−0.708969 + 0.705240i \(0.750839\pi\)
\(822\) 0 0
\(823\) 26.0319 0.907416 0.453708 0.891150i \(-0.350101\pi\)
0.453708 + 0.891150i \(0.350101\pi\)
\(824\) 0 0
\(825\) −1.04647 −0.0364334
\(826\) 0 0
\(827\) −16.5171 −0.574356 −0.287178 0.957877i \(-0.592717\pi\)
−0.287178 + 0.957877i \(0.592717\pi\)
\(828\) 0 0
\(829\) 13.2565 0.460416 0.230208 0.973141i \(-0.426059\pi\)
0.230208 + 0.973141i \(0.426059\pi\)
\(830\) 0 0
\(831\) 4.80008 0.166513
\(832\) 0 0
\(833\) 3.33994 0.115722
\(834\) 0 0
\(835\) −8.62456 −0.298465
\(836\) 0 0
\(837\) −3.76735 −0.130219
\(838\) 0 0
\(839\) 13.3887 0.462231 0.231115 0.972926i \(-0.425763\pi\)
0.231115 + 0.972926i \(0.425763\pi\)
\(840\) 0 0
\(841\) 29.5894 1.02032
\(842\) 0 0
\(843\) 13.8114 0.475688
\(844\) 0 0
\(845\) −25.7863 −0.887074
\(846\) 0 0
\(847\) −26.3586 −0.905694
\(848\) 0 0
\(849\) −10.5213 −0.361090
\(850\) 0 0
\(851\) 38.9934 1.33668
\(852\) 0 0
\(853\) −33.9570 −1.16267 −0.581334 0.813665i \(-0.697469\pi\)
−0.581334 + 0.813665i \(0.697469\pi\)
\(854\) 0 0
\(855\) 0.283995 0.00971243
\(856\) 0 0
\(857\) −39.0119 −1.33262 −0.666310 0.745675i \(-0.732127\pi\)
−0.666310 + 0.745675i \(0.732127\pi\)
\(858\) 0 0
\(859\) 31.4296 1.07236 0.536181 0.844103i \(-0.319866\pi\)
0.536181 + 0.844103i \(0.319866\pi\)
\(860\) 0 0
\(861\) 26.2095 0.893219
\(862\) 0 0
\(863\) −13.9943 −0.476371 −0.238185 0.971220i \(-0.576553\pi\)
−0.238185 + 0.971220i \(0.576553\pi\)
\(864\) 0 0
\(865\) −45.9105 −1.56100
\(866\) 0 0
\(867\) 28.3953 0.964354
\(868\) 0 0
\(869\) 4.51865 0.153285
\(870\) 0 0
\(871\) −42.5713 −1.44247
\(872\) 0 0
\(873\) 14.2718 0.483026
\(874\) 0 0
\(875\) 30.8936 1.04440
\(876\) 0 0
\(877\) 56.2593 1.89974 0.949870 0.312644i \(-0.101215\pi\)
0.949870 + 0.312644i \(0.101215\pi\)
\(878\) 0 0
\(879\) −21.2971 −0.718332
\(880\) 0 0
\(881\) −24.2590 −0.817306 −0.408653 0.912690i \(-0.634001\pi\)
−0.408653 + 0.912690i \(0.634001\pi\)
\(882\) 0 0
\(883\) 43.3317 1.45823 0.729115 0.684392i \(-0.239932\pi\)
0.729115 + 0.684392i \(0.239932\pi\)
\(884\) 0 0
\(885\) 8.76380 0.294592
\(886\) 0 0
\(887\) 6.72967 0.225960 0.112980 0.993597i \(-0.463960\pi\)
0.112980 + 0.993597i \(0.463960\pi\)
\(888\) 0 0
\(889\) 31.9356 1.07108
\(890\) 0 0
\(891\) 0.815289 0.0273132
\(892\) 0 0
\(893\) −0.342836 −0.0114726
\(894\) 0 0
\(895\) 10.0327 0.335356
\(896\) 0 0
\(897\) −46.3810 −1.54862
\(898\) 0 0
\(899\) 28.8367 0.961758
\(900\) 0 0
\(901\) 72.3911 2.41170
\(902\) 0 0
\(903\) 12.3103 0.409663
\(904\) 0 0
\(905\) −6.78339 −0.225488
\(906\) 0 0
\(907\) 10.1475 0.336943 0.168472 0.985707i \(-0.446117\pi\)
0.168472 + 0.985707i \(0.446117\pi\)
\(908\) 0 0
\(909\) −0.709810 −0.0235429
\(910\) 0 0
\(911\) 34.9128 1.15671 0.578356 0.815785i \(-0.303695\pi\)
0.578356 + 0.815785i \(0.303695\pi\)
\(912\) 0 0
\(913\) −7.39292 −0.244670
\(914\) 0 0
\(915\) −4.12880 −0.136494
\(916\) 0 0
\(917\) 34.5322 1.14035
\(918\) 0 0
\(919\) 31.6664 1.04458 0.522289 0.852768i \(-0.325078\pi\)
0.522289 + 0.852768i \(0.325078\pi\)
\(920\) 0 0
\(921\) −24.6983 −0.813836
\(922\) 0 0
\(923\) −30.2944 −0.997152
\(924\) 0 0
\(925\) 5.54205 0.182221
\(926\) 0 0
\(927\) 2.70600 0.0888766
\(928\) 0 0
\(929\) 7.15630 0.234791 0.117395 0.993085i \(-0.462546\pi\)
0.117395 + 0.993085i \(0.462546\pi\)
\(930\) 0 0
\(931\) 0.0730264 0.00239334
\(932\) 0 0
\(933\) −22.8450 −0.747912
\(934\) 0 0
\(935\) 10.5896 0.346318
\(936\) 0 0
\(937\) −1.23207 −0.0402500 −0.0201250 0.999797i \(-0.506406\pi\)
−0.0201250 + 0.999797i \(0.506406\pi\)
\(938\) 0 0
\(939\) 24.1946 0.789561
\(940\) 0 0
\(941\) −14.8516 −0.484148 −0.242074 0.970258i \(-0.577828\pi\)
−0.242074 + 0.970258i \(0.577828\pi\)
\(942\) 0 0
\(943\) −92.8102 −3.02232
\(944\) 0 0
\(945\) −4.91658 −0.159936
\(946\) 0 0
\(947\) 10.3321 0.335747 0.167874 0.985809i \(-0.446310\pi\)
0.167874 + 0.985809i \(0.446310\pi\)
\(948\) 0 0
\(949\) −16.8517 −0.547028
\(950\) 0 0
\(951\) −16.4658 −0.533940
\(952\) 0 0
\(953\) 7.17291 0.232353 0.116177 0.993229i \(-0.462936\pi\)
0.116177 + 0.993229i \(0.462936\pi\)
\(954\) 0 0
\(955\) 21.8740 0.707826
\(956\) 0 0
\(957\) −6.24052 −0.201727
\(958\) 0 0
\(959\) 53.2723 1.72025
\(960\) 0 0
\(961\) −16.8071 −0.542163
\(962\) 0 0
\(963\) −10.9377 −0.352464
\(964\) 0 0
\(965\) 42.4122 1.36530
\(966\) 0 0
\(967\) −25.2961 −0.813469 −0.406734 0.913546i \(-0.633333\pi\)
−0.406734 + 0.913546i \(0.633333\pi\)
\(968\) 0 0
\(969\) 0.992550 0.0318853
\(970\) 0 0
\(971\) 55.3044 1.77480 0.887401 0.460999i \(-0.152509\pi\)
0.887401 + 0.460999i \(0.152509\pi\)
\(972\) 0 0
\(973\) 8.43873 0.270533
\(974\) 0 0
\(975\) −6.59204 −0.211114
\(976\) 0 0
\(977\) −34.2648 −1.09623 −0.548114 0.836403i \(-0.684654\pi\)
−0.548114 + 0.836403i \(0.684654\pi\)
\(978\) 0 0
\(979\) −0.753520 −0.0240826
\(980\) 0 0
\(981\) −12.6426 −0.403648
\(982\) 0 0
\(983\) −24.4978 −0.781358 −0.390679 0.920527i \(-0.627760\pi\)
−0.390679 + 0.920527i \(0.627760\pi\)
\(984\) 0 0
\(985\) −9.10265 −0.290034
\(986\) 0 0
\(987\) 5.93525 0.188921
\(988\) 0 0
\(989\) −43.5920 −1.38614
\(990\) 0 0
\(991\) 14.3809 0.456826 0.228413 0.973564i \(-0.426646\pi\)
0.228413 + 0.973564i \(0.426646\pi\)
\(992\) 0 0
\(993\) 6.48106 0.205670
\(994\) 0 0
\(995\) 13.1378 0.416497
\(996\) 0 0
\(997\) 48.2956 1.52954 0.764768 0.644306i \(-0.222854\pi\)
0.764768 + 0.644306i \(0.222854\pi\)
\(998\) 0 0
\(999\) −4.31772 −0.136607
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 \(a_p\))