Properties

Label 8048.2.a.p.1.2
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.95007\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.950069 q^{3}\) \(-2.28693 q^{5}\) \(-2.71022 q^{7}\) \(-2.09737 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.950069 q^{3}\) \(-2.28693 q^{5}\) \(-2.71022 q^{7}\) \(-2.09737 q^{9}\) \(-1.36880 q^{11}\) \(-2.93079 q^{13}\) \(+2.17275 q^{15}\) \(-2.61287 q^{17}\) \(+7.79104 q^{19}\) \(+2.57490 q^{21}\) \(+2.61064 q^{23}\) \(+0.230071 q^{25}\) \(+4.84285 q^{27}\) \(-0.314480 q^{29}\) \(+7.95126 q^{31}\) \(+1.30046 q^{33}\) \(+6.19810 q^{35}\) \(-4.17299 q^{37}\) \(+2.78446 q^{39}\) \(+6.16482 q^{41}\) \(-0.457851 q^{43}\) \(+4.79655 q^{45}\) \(-7.67118 q^{47}\) \(+0.345296 q^{49}\) \(+2.48241 q^{51}\) \(+7.26306 q^{53}\) \(+3.13037 q^{55}\) \(-7.40203 q^{57}\) \(-0.217166 q^{59}\) \(+7.26694 q^{61}\) \(+5.68433 q^{63}\) \(+6.70253 q^{65}\) \(-10.1022 q^{67}\) \(-2.48029 q^{69}\) \(+16.5088 q^{71}\) \(+2.86838 q^{73}\) \(-0.218584 q^{75}\) \(+3.70976 q^{77}\) \(+16.0222 q^{79}\) \(+1.69106 q^{81}\) \(-12.5312 q^{83}\) \(+5.97547 q^{85}\) \(+0.298777 q^{87}\) \(-0.0952234 q^{89}\) \(+7.94310 q^{91}\) \(-7.55424 q^{93}\) \(-17.8176 q^{95}\) \(-9.27640 q^{97}\) \(+2.87089 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.950069 −0.548523 −0.274261 0.961655i \(-0.588433\pi\)
−0.274261 + 0.961655i \(0.588433\pi\)
\(4\) 0 0
\(5\) −2.28693 −1.02275 −0.511374 0.859358i \(-0.670863\pi\)
−0.511374 + 0.859358i \(0.670863\pi\)
\(6\) 0 0
\(7\) −2.71022 −1.02437 −0.512184 0.858876i \(-0.671163\pi\)
−0.512184 + 0.858876i \(0.671163\pi\)
\(8\) 0 0
\(9\) −2.09737 −0.699123
\(10\) 0 0
\(11\) −1.36880 −0.412710 −0.206355 0.978477i \(-0.566160\pi\)
−0.206355 + 0.978477i \(0.566160\pi\)
\(12\) 0 0
\(13\) −2.93079 −0.812856 −0.406428 0.913683i \(-0.633226\pi\)
−0.406428 + 0.913683i \(0.633226\pi\)
\(14\) 0 0
\(15\) 2.17275 0.561001
\(16\) 0 0
\(17\) −2.61287 −0.633715 −0.316857 0.948473i \(-0.602628\pi\)
−0.316857 + 0.948473i \(0.602628\pi\)
\(18\) 0 0
\(19\) 7.79104 1.78739 0.893694 0.448677i \(-0.148105\pi\)
0.893694 + 0.448677i \(0.148105\pi\)
\(20\) 0 0
\(21\) 2.57490 0.561888
\(22\) 0 0
\(23\) 2.61064 0.544356 0.272178 0.962247i \(-0.412256\pi\)
0.272178 + 0.962247i \(0.412256\pi\)
\(24\) 0 0
\(25\) 0.230071 0.0460143
\(26\) 0 0
\(27\) 4.84285 0.932007
\(28\) 0 0
\(29\) −0.314480 −0.0583974 −0.0291987 0.999574i \(-0.509296\pi\)
−0.0291987 + 0.999574i \(0.509296\pi\)
\(30\) 0 0
\(31\) 7.95126 1.42809 0.714044 0.700101i \(-0.246862\pi\)
0.714044 + 0.700101i \(0.246862\pi\)
\(32\) 0 0
\(33\) 1.30046 0.226381
\(34\) 0 0
\(35\) 6.19810 1.04767
\(36\) 0 0
\(37\) −4.17299 −0.686035 −0.343017 0.939329i \(-0.611449\pi\)
−0.343017 + 0.939329i \(0.611449\pi\)
\(38\) 0 0
\(39\) 2.78446 0.445870
\(40\) 0 0
\(41\) 6.16482 0.962783 0.481391 0.876506i \(-0.340132\pi\)
0.481391 + 0.876506i \(0.340132\pi\)
\(42\) 0 0
\(43\) −0.457851 −0.0698216 −0.0349108 0.999390i \(-0.511115\pi\)
−0.0349108 + 0.999390i \(0.511115\pi\)
\(44\) 0 0
\(45\) 4.79655 0.715027
\(46\) 0 0
\(47\) −7.67118 −1.11896 −0.559478 0.828845i \(-0.688998\pi\)
−0.559478 + 0.828845i \(0.688998\pi\)
\(48\) 0 0
\(49\) 0.345296 0.0493279
\(50\) 0 0
\(51\) 2.48241 0.347607
\(52\) 0 0
\(53\) 7.26306 0.997658 0.498829 0.866700i \(-0.333763\pi\)
0.498829 + 0.866700i \(0.333763\pi\)
\(54\) 0 0
\(55\) 3.13037 0.422099
\(56\) 0 0
\(57\) −7.40203 −0.980423
\(58\) 0 0
\(59\) −0.217166 −0.0282726 −0.0141363 0.999900i \(-0.504500\pi\)
−0.0141363 + 0.999900i \(0.504500\pi\)
\(60\) 0 0
\(61\) 7.26694 0.930436 0.465218 0.885196i \(-0.345976\pi\)
0.465218 + 0.885196i \(0.345976\pi\)
\(62\) 0 0
\(63\) 5.68433 0.716159
\(64\) 0 0
\(65\) 6.70253 0.831347
\(66\) 0 0
\(67\) −10.1022 −1.23418 −0.617091 0.786892i \(-0.711689\pi\)
−0.617091 + 0.786892i \(0.711689\pi\)
\(68\) 0 0
\(69\) −2.48029 −0.298592
\(70\) 0 0
\(71\) 16.5088 1.95924 0.979619 0.200863i \(-0.0643746\pi\)
0.979619 + 0.200863i \(0.0643746\pi\)
\(72\) 0 0
\(73\) 2.86838 0.335718 0.167859 0.985811i \(-0.446315\pi\)
0.167859 + 0.985811i \(0.446315\pi\)
\(74\) 0 0
\(75\) −0.218584 −0.0252399
\(76\) 0 0
\(77\) 3.70976 0.422767
\(78\) 0 0
\(79\) 16.0222 1.80264 0.901320 0.433153i \(-0.142599\pi\)
0.901320 + 0.433153i \(0.142599\pi\)
\(80\) 0 0
\(81\) 1.69106 0.187896
\(82\) 0 0
\(83\) −12.5312 −1.37548 −0.687741 0.725956i \(-0.741398\pi\)
−0.687741 + 0.725956i \(0.741398\pi\)
\(84\) 0 0
\(85\) 5.97547 0.648131
\(86\) 0 0
\(87\) 0.298777 0.0320323
\(88\) 0 0
\(89\) −0.0952234 −0.0100937 −0.00504683 0.999987i \(-0.501606\pi\)
−0.00504683 + 0.999987i \(0.501606\pi\)
\(90\) 0 0
\(91\) 7.94310 0.832663
\(92\) 0 0
\(93\) −7.55424 −0.783339
\(94\) 0 0
\(95\) −17.8176 −1.82805
\(96\) 0 0
\(97\) −9.27640 −0.941875 −0.470938 0.882167i \(-0.656084\pi\)
−0.470938 + 0.882167i \(0.656084\pi\)
\(98\) 0 0
\(99\) 2.87089 0.288535
\(100\) 0 0
\(101\) 8.77727 0.873371 0.436686 0.899614i \(-0.356152\pi\)
0.436686 + 0.899614i \(0.356152\pi\)
\(102\) 0 0
\(103\) −1.52475 −0.150238 −0.0751189 0.997175i \(-0.523934\pi\)
−0.0751189 + 0.997175i \(0.523934\pi\)
\(104\) 0 0
\(105\) −5.88862 −0.574670
\(106\) 0 0
\(107\) 17.6358 1.70492 0.852460 0.522792i \(-0.175110\pi\)
0.852460 + 0.522792i \(0.175110\pi\)
\(108\) 0 0
\(109\) −4.91427 −0.470702 −0.235351 0.971910i \(-0.575624\pi\)
−0.235351 + 0.971910i \(0.575624\pi\)
\(110\) 0 0
\(111\) 3.96462 0.376305
\(112\) 0 0
\(113\) 0.102880 0.00967811 0.00483905 0.999988i \(-0.498460\pi\)
0.00483905 + 0.999988i \(0.498460\pi\)
\(114\) 0 0
\(115\) −5.97037 −0.556740
\(116\) 0 0
\(117\) 6.14696 0.568286
\(118\) 0 0
\(119\) 7.08146 0.649157
\(120\) 0 0
\(121\) −9.12637 −0.829670
\(122\) 0 0
\(123\) −5.85700 −0.528108
\(124\) 0 0
\(125\) 10.9085 0.975687
\(126\) 0 0
\(127\) −14.7682 −1.31046 −0.655232 0.755428i \(-0.727429\pi\)
−0.655232 + 0.755428i \(0.727429\pi\)
\(128\) 0 0
\(129\) 0.434990 0.0382987
\(130\) 0 0
\(131\) −3.01646 −0.263549 −0.131775 0.991280i \(-0.542068\pi\)
−0.131775 + 0.991280i \(0.542068\pi\)
\(132\) 0 0
\(133\) −21.1154 −1.83094
\(134\) 0 0
\(135\) −11.0753 −0.953209
\(136\) 0 0
\(137\) 0.370190 0.0316275 0.0158137 0.999875i \(-0.494966\pi\)
0.0158137 + 0.999875i \(0.494966\pi\)
\(138\) 0 0
\(139\) −13.0944 −1.11065 −0.555324 0.831634i \(-0.687406\pi\)
−0.555324 + 0.831634i \(0.687406\pi\)
\(140\) 0 0
\(141\) 7.28815 0.613773
\(142\) 0 0
\(143\) 4.01168 0.335474
\(144\) 0 0
\(145\) 0.719195 0.0597259
\(146\) 0 0
\(147\) −0.328055 −0.0270575
\(148\) 0 0
\(149\) −5.61923 −0.460345 −0.230173 0.973150i \(-0.573929\pi\)
−0.230173 + 0.973150i \(0.573929\pi\)
\(150\) 0 0
\(151\) 6.99662 0.569377 0.284689 0.958620i \(-0.408110\pi\)
0.284689 + 0.958620i \(0.408110\pi\)
\(152\) 0 0
\(153\) 5.48016 0.443045
\(154\) 0 0
\(155\) −18.1840 −1.46058
\(156\) 0 0
\(157\) 10.5849 0.844764 0.422382 0.906418i \(-0.361194\pi\)
0.422382 + 0.906418i \(0.361194\pi\)
\(158\) 0 0
\(159\) −6.90041 −0.547238
\(160\) 0 0
\(161\) −7.07541 −0.557621
\(162\) 0 0
\(163\) 4.74396 0.371576 0.185788 0.982590i \(-0.440516\pi\)
0.185788 + 0.982590i \(0.440516\pi\)
\(164\) 0 0
\(165\) −2.97406 −0.231531
\(166\) 0 0
\(167\) −15.4650 −1.19672 −0.598360 0.801227i \(-0.704181\pi\)
−0.598360 + 0.801227i \(0.704181\pi\)
\(168\) 0 0
\(169\) −4.41045 −0.339265
\(170\) 0 0
\(171\) −16.3407 −1.24960
\(172\) 0 0
\(173\) −18.0030 −1.36874 −0.684372 0.729133i \(-0.739924\pi\)
−0.684372 + 0.729133i \(0.739924\pi\)
\(174\) 0 0
\(175\) −0.623544 −0.0471355
\(176\) 0 0
\(177\) 0.206322 0.0155081
\(178\) 0 0
\(179\) −22.6390 −1.69212 −0.846058 0.533092i \(-0.821030\pi\)
−0.846058 + 0.533092i \(0.821030\pi\)
\(180\) 0 0
\(181\) 2.97984 0.221490 0.110745 0.993849i \(-0.464676\pi\)
0.110745 + 0.993849i \(0.464676\pi\)
\(182\) 0 0
\(183\) −6.90409 −0.510365
\(184\) 0 0
\(185\) 9.54335 0.701641
\(186\) 0 0
\(187\) 3.57651 0.261541
\(188\) 0 0
\(189\) −13.1252 −0.954718
\(190\) 0 0
\(191\) −4.09564 −0.296350 −0.148175 0.988961i \(-0.547340\pi\)
−0.148175 + 0.988961i \(0.547340\pi\)
\(192\) 0 0
\(193\) −21.1708 −1.52391 −0.761955 0.647630i \(-0.775760\pi\)
−0.761955 + 0.647630i \(0.775760\pi\)
\(194\) 0 0
\(195\) −6.36787 −0.456013
\(196\) 0 0
\(197\) 18.5139 1.31906 0.659531 0.751677i \(-0.270755\pi\)
0.659531 + 0.751677i \(0.270755\pi\)
\(198\) 0 0
\(199\) 1.56711 0.111089 0.0555447 0.998456i \(-0.482310\pi\)
0.0555447 + 0.998456i \(0.482310\pi\)
\(200\) 0 0
\(201\) 9.59779 0.676976
\(202\) 0 0
\(203\) 0.852309 0.0598204
\(204\) 0 0
\(205\) −14.0985 −0.984685
\(206\) 0 0
\(207\) −5.47548 −0.380572
\(208\) 0 0
\(209\) −10.6644 −0.737673
\(210\) 0 0
\(211\) 22.8488 1.57298 0.786489 0.617604i \(-0.211897\pi\)
0.786489 + 0.617604i \(0.211897\pi\)
\(212\) 0 0
\(213\) −15.6845 −1.07469
\(214\) 0 0
\(215\) 1.04708 0.0714100
\(216\) 0 0
\(217\) −21.5497 −1.46289
\(218\) 0 0
\(219\) −2.72516 −0.184149
\(220\) 0 0
\(221\) 7.65779 0.515119
\(222\) 0 0
\(223\) −4.75557 −0.318457 −0.159228 0.987242i \(-0.550901\pi\)
−0.159228 + 0.987242i \(0.550901\pi\)
\(224\) 0 0
\(225\) −0.482545 −0.0321696
\(226\) 0 0
\(227\) 27.4709 1.82331 0.911655 0.410956i \(-0.134805\pi\)
0.911655 + 0.410956i \(0.134805\pi\)
\(228\) 0 0
\(229\) −4.52436 −0.298978 −0.149489 0.988763i \(-0.547763\pi\)
−0.149489 + 0.988763i \(0.547763\pi\)
\(230\) 0 0
\(231\) −3.52453 −0.231897
\(232\) 0 0
\(233\) −10.5567 −0.691594 −0.345797 0.938309i \(-0.612391\pi\)
−0.345797 + 0.938309i \(0.612391\pi\)
\(234\) 0 0
\(235\) 17.5435 1.14441
\(236\) 0 0
\(237\) −15.2222 −0.988789
\(238\) 0 0
\(239\) 28.3072 1.83104 0.915522 0.402269i \(-0.131778\pi\)
0.915522 + 0.402269i \(0.131778\pi\)
\(240\) 0 0
\(241\) −10.6922 −0.688748 −0.344374 0.938833i \(-0.611909\pi\)
−0.344374 + 0.938833i \(0.611909\pi\)
\(242\) 0 0
\(243\) −16.1352 −1.03507
\(244\) 0 0
\(245\) −0.789669 −0.0504501
\(246\) 0 0
\(247\) −22.8339 −1.45289
\(248\) 0 0
\(249\) 11.9055 0.754483
\(250\) 0 0
\(251\) 3.42359 0.216095 0.108048 0.994146i \(-0.465540\pi\)
0.108048 + 0.994146i \(0.465540\pi\)
\(252\) 0 0
\(253\) −3.57346 −0.224661
\(254\) 0 0
\(255\) −5.67711 −0.355514
\(256\) 0 0
\(257\) −11.2524 −0.701906 −0.350953 0.936393i \(-0.614142\pi\)
−0.350953 + 0.936393i \(0.614142\pi\)
\(258\) 0 0
\(259\) 11.3097 0.702751
\(260\) 0 0
\(261\) 0.659580 0.0408270
\(262\) 0 0
\(263\) −0.429180 −0.0264643 −0.0132322 0.999912i \(-0.504212\pi\)
−0.0132322 + 0.999912i \(0.504212\pi\)
\(264\) 0 0
\(265\) −16.6102 −1.02035
\(266\) 0 0
\(267\) 0.0904688 0.00553660
\(268\) 0 0
\(269\) 15.2320 0.928712 0.464356 0.885649i \(-0.346286\pi\)
0.464356 + 0.885649i \(0.346286\pi\)
\(270\) 0 0
\(271\) −17.7850 −1.08036 −0.540182 0.841548i \(-0.681645\pi\)
−0.540182 + 0.841548i \(0.681645\pi\)
\(272\) 0 0
\(273\) −7.54649 −0.456734
\(274\) 0 0
\(275\) −0.314923 −0.0189906
\(276\) 0 0
\(277\) 15.1882 0.912570 0.456285 0.889834i \(-0.349180\pi\)
0.456285 + 0.889834i \(0.349180\pi\)
\(278\) 0 0
\(279\) −16.6767 −0.998409
\(280\) 0 0
\(281\) 20.0885 1.19838 0.599191 0.800606i \(-0.295489\pi\)
0.599191 + 0.800606i \(0.295489\pi\)
\(282\) 0 0
\(283\) 1.63497 0.0971889 0.0485945 0.998819i \(-0.484526\pi\)
0.0485945 + 0.998819i \(0.484526\pi\)
\(284\) 0 0
\(285\) 16.9280 1.00273
\(286\) 0 0
\(287\) −16.7080 −0.986243
\(288\) 0 0
\(289\) −10.1729 −0.598405
\(290\) 0 0
\(291\) 8.81321 0.516640
\(292\) 0 0
\(293\) −10.1892 −0.595262 −0.297631 0.954681i \(-0.596196\pi\)
−0.297631 + 0.954681i \(0.596196\pi\)
\(294\) 0 0
\(295\) 0.496644 0.0289157
\(296\) 0 0
\(297\) −6.62892 −0.384649
\(298\) 0 0
\(299\) −7.65125 −0.442483
\(300\) 0 0
\(301\) 1.24088 0.0715230
\(302\) 0 0
\(303\) −8.33901 −0.479064
\(304\) 0 0
\(305\) −16.6190 −0.951602
\(306\) 0 0
\(307\) 16.3682 0.934184 0.467092 0.884209i \(-0.345302\pi\)
0.467092 + 0.884209i \(0.345302\pi\)
\(308\) 0 0
\(309\) 1.44861 0.0824088
\(310\) 0 0
\(311\) −6.98922 −0.396322 −0.198161 0.980169i \(-0.563497\pi\)
−0.198161 + 0.980169i \(0.563497\pi\)
\(312\) 0 0
\(313\) 2.22444 0.125733 0.0628665 0.998022i \(-0.479976\pi\)
0.0628665 + 0.998022i \(0.479976\pi\)
\(314\) 0 0
\(315\) −12.9997 −0.732450
\(316\) 0 0
\(317\) 3.49687 0.196404 0.0982019 0.995167i \(-0.468691\pi\)
0.0982019 + 0.995167i \(0.468691\pi\)
\(318\) 0 0
\(319\) 0.430461 0.0241012
\(320\) 0 0
\(321\) −16.7553 −0.935187
\(322\) 0 0
\(323\) −20.3570 −1.13269
\(324\) 0 0
\(325\) −0.674292 −0.0374030
\(326\) 0 0
\(327\) 4.66889 0.258190
\(328\) 0 0
\(329\) 20.7906 1.14622
\(330\) 0 0
\(331\) 13.8654 0.762112 0.381056 0.924552i \(-0.375561\pi\)
0.381056 + 0.924552i \(0.375561\pi\)
\(332\) 0 0
\(333\) 8.75229 0.479623
\(334\) 0 0
\(335\) 23.1031 1.26226
\(336\) 0 0
\(337\) −33.0259 −1.79903 −0.899517 0.436885i \(-0.856082\pi\)
−0.899517 + 0.436885i \(0.856082\pi\)
\(338\) 0 0
\(339\) −0.0977428 −0.00530866
\(340\) 0 0
\(341\) −10.8837 −0.589387
\(342\) 0 0
\(343\) 18.0357 0.973837
\(344\) 0 0
\(345\) 5.67226 0.305384
\(346\) 0 0
\(347\) 0.417829 0.0224302 0.0112151 0.999937i \(-0.496430\pi\)
0.0112151 + 0.999937i \(0.496430\pi\)
\(348\) 0 0
\(349\) −8.68607 −0.464955 −0.232477 0.972602i \(-0.574683\pi\)
−0.232477 + 0.972602i \(0.574683\pi\)
\(350\) 0 0
\(351\) −14.1934 −0.757588
\(352\) 0 0
\(353\) −9.09582 −0.484122 −0.242061 0.970261i \(-0.577823\pi\)
−0.242061 + 0.970261i \(0.577823\pi\)
\(354\) 0 0
\(355\) −37.7546 −2.00381
\(356\) 0 0
\(357\) −6.72788 −0.356077
\(358\) 0 0
\(359\) −5.51998 −0.291333 −0.145667 0.989334i \(-0.546533\pi\)
−0.145667 + 0.989334i \(0.546533\pi\)
\(360\) 0 0
\(361\) 41.7004 2.19476
\(362\) 0 0
\(363\) 8.67068 0.455093
\(364\) 0 0
\(365\) −6.55979 −0.343355
\(366\) 0 0
\(367\) −16.3639 −0.854188 −0.427094 0.904207i \(-0.640463\pi\)
−0.427094 + 0.904207i \(0.640463\pi\)
\(368\) 0 0
\(369\) −12.9299 −0.673104
\(370\) 0 0
\(371\) −19.6845 −1.02197
\(372\) 0 0
\(373\) −23.5721 −1.22051 −0.610257 0.792203i \(-0.708934\pi\)
−0.610257 + 0.792203i \(0.708934\pi\)
\(374\) 0 0
\(375\) −10.3638 −0.535186
\(376\) 0 0
\(377\) 0.921675 0.0474687
\(378\) 0 0
\(379\) 22.8307 1.17273 0.586367 0.810045i \(-0.300558\pi\)
0.586367 + 0.810045i \(0.300558\pi\)
\(380\) 0 0
\(381\) 14.0308 0.718819
\(382\) 0 0
\(383\) −21.8257 −1.11524 −0.557622 0.830095i \(-0.688286\pi\)
−0.557622 + 0.830095i \(0.688286\pi\)
\(384\) 0 0
\(385\) −8.48399 −0.432384
\(386\) 0 0
\(387\) 0.960283 0.0488139
\(388\) 0 0
\(389\) 29.7462 1.50819 0.754097 0.656763i \(-0.228075\pi\)
0.754097 + 0.656763i \(0.228075\pi\)
\(390\) 0 0
\(391\) −6.82127 −0.344967
\(392\) 0 0
\(393\) 2.86584 0.144563
\(394\) 0 0
\(395\) −36.6418 −1.84365
\(396\) 0 0
\(397\) 28.5561 1.43319 0.716595 0.697489i \(-0.245700\pi\)
0.716595 + 0.697489i \(0.245700\pi\)
\(398\) 0 0
\(399\) 20.0611 1.00431
\(400\) 0 0
\(401\) 13.9970 0.698975 0.349487 0.936941i \(-0.386356\pi\)
0.349487 + 0.936941i \(0.386356\pi\)
\(402\) 0 0
\(403\) −23.3035 −1.16083
\(404\) 0 0
\(405\) −3.86735 −0.192170
\(406\) 0 0
\(407\) 5.71200 0.283133
\(408\) 0 0
\(409\) −18.2429 −0.902055 −0.451028 0.892510i \(-0.648942\pi\)
−0.451028 + 0.892510i \(0.648942\pi\)
\(410\) 0 0
\(411\) −0.351706 −0.0173484
\(412\) 0 0
\(413\) 0.588567 0.0289615
\(414\) 0 0
\(415\) 28.6581 1.40677
\(416\) 0 0
\(417\) 12.4405 0.609216
\(418\) 0 0
\(419\) −9.78645 −0.478099 −0.239050 0.971007i \(-0.576836\pi\)
−0.239050 + 0.971007i \(0.576836\pi\)
\(420\) 0 0
\(421\) 2.26639 0.110457 0.0552286 0.998474i \(-0.482411\pi\)
0.0552286 + 0.998474i \(0.482411\pi\)
\(422\) 0 0
\(423\) 16.0893 0.782288
\(424\) 0 0
\(425\) −0.601147 −0.0291599
\(426\) 0 0
\(427\) −19.6950 −0.953109
\(428\) 0 0
\(429\) −3.81138 −0.184015
\(430\) 0 0
\(431\) −4.29790 −0.207023 −0.103511 0.994628i \(-0.533008\pi\)
−0.103511 + 0.994628i \(0.533008\pi\)
\(432\) 0 0
\(433\) −16.6114 −0.798292 −0.399146 0.916887i \(-0.630693\pi\)
−0.399146 + 0.916887i \(0.630693\pi\)
\(434\) 0 0
\(435\) −0.683284 −0.0327610
\(436\) 0 0
\(437\) 20.3396 0.972976
\(438\) 0 0
\(439\) 21.4863 1.02548 0.512742 0.858542i \(-0.328630\pi\)
0.512742 + 0.858542i \(0.328630\pi\)
\(440\) 0 0
\(441\) −0.724212 −0.0344863
\(442\) 0 0
\(443\) 19.6047 0.931447 0.465724 0.884930i \(-0.345794\pi\)
0.465724 + 0.884930i \(0.345794\pi\)
\(444\) 0 0
\(445\) 0.217770 0.0103233
\(446\) 0 0
\(447\) 5.33866 0.252510
\(448\) 0 0
\(449\) −35.1455 −1.65862 −0.829310 0.558789i \(-0.811266\pi\)
−0.829310 + 0.558789i \(0.811266\pi\)
\(450\) 0 0
\(451\) −8.43843 −0.397350
\(452\) 0 0
\(453\) −6.64728 −0.312316
\(454\) 0 0
\(455\) −18.1653 −0.851605
\(456\) 0 0
\(457\) −11.8432 −0.554002 −0.277001 0.960870i \(-0.589341\pi\)
−0.277001 + 0.960870i \(0.589341\pi\)
\(458\) 0 0
\(459\) −12.6538 −0.590627
\(460\) 0 0
\(461\) 17.1286 0.797756 0.398878 0.917004i \(-0.369400\pi\)
0.398878 + 0.917004i \(0.369400\pi\)
\(462\) 0 0
\(463\) 6.92218 0.321701 0.160850 0.986979i \(-0.448576\pi\)
0.160850 + 0.986979i \(0.448576\pi\)
\(464\) 0 0
\(465\) 17.2761 0.801158
\(466\) 0 0
\(467\) 32.6395 1.51038 0.755188 0.655508i \(-0.227545\pi\)
0.755188 + 0.655508i \(0.227545\pi\)
\(468\) 0 0
\(469\) 27.3792 1.26425
\(470\) 0 0
\(471\) −10.0563 −0.463372
\(472\) 0 0
\(473\) 0.626709 0.0288161
\(474\) 0 0
\(475\) 1.79250 0.0822454
\(476\) 0 0
\(477\) −15.2333 −0.697486
\(478\) 0 0
\(479\) −8.78005 −0.401171 −0.200585 0.979676i \(-0.564284\pi\)
−0.200585 + 0.979676i \(0.564284\pi\)
\(480\) 0 0
\(481\) 12.2302 0.557647
\(482\) 0 0
\(483\) 6.72213 0.305868
\(484\) 0 0
\(485\) 21.2145 0.963301
\(486\) 0 0
\(487\) 23.1617 1.04956 0.524779 0.851238i \(-0.324148\pi\)
0.524779 + 0.851238i \(0.324148\pi\)
\(488\) 0 0
\(489\) −4.50709 −0.203818
\(490\) 0 0
\(491\) −8.15363 −0.367968 −0.183984 0.982929i \(-0.558900\pi\)
−0.183984 + 0.982929i \(0.558900\pi\)
\(492\) 0 0
\(493\) 0.821696 0.0370073
\(494\) 0 0
\(495\) −6.56554 −0.295099
\(496\) 0 0
\(497\) −44.7426 −2.00698
\(498\) 0 0
\(499\) −30.6993 −1.37429 −0.687144 0.726521i \(-0.741136\pi\)
−0.687144 + 0.726521i \(0.741136\pi\)
\(500\) 0 0
\(501\) 14.6929 0.656428
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) −20.0731 −0.893239
\(506\) 0 0
\(507\) 4.19023 0.186095
\(508\) 0 0
\(509\) −6.39080 −0.283267 −0.141634 0.989919i \(-0.545235\pi\)
−0.141634 + 0.989919i \(0.545235\pi\)
\(510\) 0 0
\(511\) −7.77394 −0.343899
\(512\) 0 0
\(513\) 37.7309 1.66586
\(514\) 0 0
\(515\) 3.48700 0.153655
\(516\) 0 0
\(517\) 10.5003 0.461805
\(518\) 0 0
\(519\) 17.1041 0.750787
\(520\) 0 0
\(521\) −11.2745 −0.493944 −0.246972 0.969023i \(-0.579436\pi\)
−0.246972 + 0.969023i \(0.579436\pi\)
\(522\) 0 0
\(523\) −18.6154 −0.813993 −0.406996 0.913430i \(-0.633424\pi\)
−0.406996 + 0.913430i \(0.633424\pi\)
\(524\) 0 0
\(525\) 0.592410 0.0258549
\(526\) 0 0
\(527\) −20.7756 −0.905001
\(528\) 0 0
\(529\) −16.1846 −0.703676
\(530\) 0 0
\(531\) 0.455477 0.0197660
\(532\) 0 0
\(533\) −18.0678 −0.782604
\(534\) 0 0
\(535\) −40.3320 −1.74370
\(536\) 0 0
\(537\) 21.5086 0.928163
\(538\) 0 0
\(539\) −0.472642 −0.0203581
\(540\) 0 0
\(541\) −36.6446 −1.57547 −0.787736 0.616013i \(-0.788747\pi\)
−0.787736 + 0.616013i \(0.788747\pi\)
\(542\) 0 0
\(543\) −2.83105 −0.121492
\(544\) 0 0
\(545\) 11.2386 0.481409
\(546\) 0 0
\(547\) −19.4186 −0.830280 −0.415140 0.909758i \(-0.636267\pi\)
−0.415140 + 0.909758i \(0.636267\pi\)
\(548\) 0 0
\(549\) −15.2415 −0.650490
\(550\) 0 0
\(551\) −2.45013 −0.104379
\(552\) 0 0
\(553\) −43.4238 −1.84657
\(554\) 0 0
\(555\) −9.06684 −0.384866
\(556\) 0 0
\(557\) −35.6561 −1.51080 −0.755398 0.655266i \(-0.772556\pi\)
−0.755398 + 0.655266i \(0.772556\pi\)
\(558\) 0 0
\(559\) 1.34187 0.0567549
\(560\) 0 0
\(561\) −3.39793 −0.143461
\(562\) 0 0
\(563\) 34.0879 1.43663 0.718316 0.695717i \(-0.244913\pi\)
0.718316 + 0.695717i \(0.244913\pi\)
\(564\) 0 0
\(565\) −0.235279 −0.00989827
\(566\) 0 0
\(567\) −4.58316 −0.192475
\(568\) 0 0
\(569\) 13.0323 0.546342 0.273171 0.961965i \(-0.411927\pi\)
0.273171 + 0.961965i \(0.411927\pi\)
\(570\) 0 0
\(571\) −28.5710 −1.19566 −0.597829 0.801624i \(-0.703970\pi\)
−0.597829 + 0.801624i \(0.703970\pi\)
\(572\) 0 0
\(573\) 3.89114 0.162555
\(574\) 0 0
\(575\) 0.600634 0.0250482
\(576\) 0 0
\(577\) 40.1508 1.67150 0.835750 0.549110i \(-0.185033\pi\)
0.835750 + 0.549110i \(0.185033\pi\)
\(578\) 0 0
\(579\) 20.1137 0.835899
\(580\) 0 0
\(581\) 33.9624 1.40900
\(582\) 0 0
\(583\) −9.94172 −0.411744
\(584\) 0 0
\(585\) −14.0577 −0.581214
\(586\) 0 0
\(587\) 1.26390 0.0521666 0.0260833 0.999660i \(-0.491696\pi\)
0.0260833 + 0.999660i \(0.491696\pi\)
\(588\) 0 0
\(589\) 61.9486 2.55255
\(590\) 0 0
\(591\) −17.5895 −0.723535
\(592\) 0 0
\(593\) 0.473003 0.0194239 0.00971196 0.999953i \(-0.496909\pi\)
0.00971196 + 0.999953i \(0.496909\pi\)
\(594\) 0 0
\(595\) −16.1948 −0.663924
\(596\) 0 0
\(597\) −1.48886 −0.0609350
\(598\) 0 0
\(599\) −28.8689 −1.17955 −0.589775 0.807568i \(-0.700783\pi\)
−0.589775 + 0.807568i \(0.700783\pi\)
\(600\) 0 0
\(601\) 8.88531 0.362439 0.181220 0.983443i \(-0.441996\pi\)
0.181220 + 0.983443i \(0.441996\pi\)
\(602\) 0 0
\(603\) 21.1881 0.862845
\(604\) 0 0
\(605\) 20.8714 0.848544
\(606\) 0 0
\(607\) −28.6612 −1.16332 −0.581662 0.813431i \(-0.697597\pi\)
−0.581662 + 0.813431i \(0.697597\pi\)
\(608\) 0 0
\(609\) −0.809753 −0.0328128
\(610\) 0 0
\(611\) 22.4826 0.909550
\(612\) 0 0
\(613\) 46.9961 1.89815 0.949077 0.315043i \(-0.102019\pi\)
0.949077 + 0.315043i \(0.102019\pi\)
\(614\) 0 0
\(615\) 13.3946 0.540122
\(616\) 0 0
\(617\) −24.3030 −0.978401 −0.489201 0.872171i \(-0.662711\pi\)
−0.489201 + 0.872171i \(0.662711\pi\)
\(618\) 0 0
\(619\) −39.4552 −1.58584 −0.792920 0.609326i \(-0.791440\pi\)
−0.792920 + 0.609326i \(0.791440\pi\)
\(620\) 0 0
\(621\) 12.6429 0.507344
\(622\) 0 0
\(623\) 0.258077 0.0103396
\(624\) 0 0
\(625\) −26.0974 −1.04390
\(626\) 0 0
\(627\) 10.1319 0.404630
\(628\) 0 0
\(629\) 10.9035 0.434750
\(630\) 0 0
\(631\) −34.7457 −1.38320 −0.691602 0.722279i \(-0.743095\pi\)
−0.691602 + 0.722279i \(0.743095\pi\)
\(632\) 0 0
\(633\) −21.7080 −0.862814
\(634\) 0 0
\(635\) 33.7738 1.34027
\(636\) 0 0
\(637\) −1.01199 −0.0400965
\(638\) 0 0
\(639\) −34.6251 −1.36975
\(640\) 0 0
\(641\) −42.3173 −1.67143 −0.835716 0.549163i \(-0.814947\pi\)
−0.835716 + 0.549163i \(0.814947\pi\)
\(642\) 0 0
\(643\) 31.5672 1.24489 0.622444 0.782664i \(-0.286140\pi\)
0.622444 + 0.782664i \(0.286140\pi\)
\(644\) 0 0
\(645\) −0.994794 −0.0391700
\(646\) 0 0
\(647\) 45.6664 1.79533 0.897667 0.440675i \(-0.145261\pi\)
0.897667 + 0.440675i \(0.145261\pi\)
\(648\) 0 0
\(649\) 0.297258 0.0116684
\(650\) 0 0
\(651\) 20.4737 0.802426
\(652\) 0 0
\(653\) 7.15705 0.280077 0.140039 0.990146i \(-0.455277\pi\)
0.140039 + 0.990146i \(0.455277\pi\)
\(654\) 0 0
\(655\) 6.89844 0.269545
\(656\) 0 0
\(657\) −6.01605 −0.234708
\(658\) 0 0
\(659\) −12.1603 −0.473696 −0.236848 0.971547i \(-0.576114\pi\)
−0.236848 + 0.971547i \(0.576114\pi\)
\(660\) 0 0
\(661\) −15.2194 −0.591968 −0.295984 0.955193i \(-0.595647\pi\)
−0.295984 + 0.955193i \(0.595647\pi\)
\(662\) 0 0
\(663\) −7.27543 −0.282554
\(664\) 0 0
\(665\) 48.2896 1.87259
\(666\) 0 0
\(667\) −0.820994 −0.0317890
\(668\) 0 0
\(669\) 4.51812 0.174681
\(670\) 0 0
\(671\) −9.94702 −0.384001
\(672\) 0 0
\(673\) 34.9359 1.34668 0.673340 0.739333i \(-0.264859\pi\)
0.673340 + 0.739333i \(0.264859\pi\)
\(674\) 0 0
\(675\) 1.11420 0.0428856
\(676\) 0 0
\(677\) −17.6078 −0.676721 −0.338361 0.941016i \(-0.609872\pi\)
−0.338361 + 0.941016i \(0.609872\pi\)
\(678\) 0 0
\(679\) 25.1411 0.964826
\(680\) 0 0
\(681\) −26.0993 −1.00013
\(682\) 0 0
\(683\) 43.5075 1.66477 0.832385 0.554198i \(-0.186975\pi\)
0.832385 + 0.554198i \(0.186975\pi\)
\(684\) 0 0
\(685\) −0.846600 −0.0323469
\(686\) 0 0
\(687\) 4.29846 0.163996
\(688\) 0 0
\(689\) −21.2865 −0.810953
\(690\) 0 0
\(691\) 2.05256 0.0780829 0.0390415 0.999238i \(-0.487570\pi\)
0.0390415 + 0.999238i \(0.487570\pi\)
\(692\) 0 0
\(693\) −7.78074 −0.295566
\(694\) 0 0
\(695\) 29.9459 1.13591
\(696\) 0 0
\(697\) −16.1079 −0.610130
\(698\) 0 0
\(699\) 10.0296 0.379355
\(700\) 0 0
\(701\) −9.44349 −0.356676 −0.178338 0.983969i \(-0.557072\pi\)
−0.178338 + 0.983969i \(0.557072\pi\)
\(702\) 0 0
\(703\) −32.5119 −1.22621
\(704\) 0 0
\(705\) −16.6675 −0.627735
\(706\) 0 0
\(707\) −23.7883 −0.894653
\(708\) 0 0
\(709\) 15.9123 0.597598 0.298799 0.954316i \(-0.403414\pi\)
0.298799 + 0.954316i \(0.403414\pi\)
\(710\) 0 0
\(711\) −33.6045 −1.26027
\(712\) 0 0
\(713\) 20.7579 0.777389
\(714\) 0 0
\(715\) −9.17446 −0.343105
\(716\) 0 0
\(717\) −26.8938 −1.00437
\(718\) 0 0
\(719\) −24.9061 −0.928842 −0.464421 0.885615i \(-0.653737\pi\)
−0.464421 + 0.885615i \(0.653737\pi\)
\(720\) 0 0
\(721\) 4.13240 0.153899
\(722\) 0 0
\(723\) 10.1584 0.377794
\(724\) 0 0
\(725\) −0.0723528 −0.00268712
\(726\) 0 0
\(727\) −11.5573 −0.428636 −0.214318 0.976764i \(-0.568753\pi\)
−0.214318 + 0.976764i \(0.568753\pi\)
\(728\) 0 0
\(729\) 10.2563 0.379865
\(730\) 0 0
\(731\) 1.19631 0.0442470
\(732\) 0 0
\(733\) 11.9918 0.442926 0.221463 0.975169i \(-0.428917\pi\)
0.221463 + 0.975169i \(0.428917\pi\)
\(734\) 0 0
\(735\) 0.750240 0.0276730
\(736\) 0 0
\(737\) 13.8280 0.509359
\(738\) 0 0
\(739\) −48.3255 −1.77768 −0.888840 0.458217i \(-0.848488\pi\)
−0.888840 + 0.458217i \(0.848488\pi\)
\(740\) 0 0
\(741\) 21.6938 0.796942
\(742\) 0 0
\(743\) −40.3146 −1.47900 −0.739499 0.673158i \(-0.764937\pi\)
−0.739499 + 0.673158i \(0.764937\pi\)
\(744\) 0 0
\(745\) 12.8508 0.470817
\(746\) 0 0
\(747\) 26.2826 0.961632
\(748\) 0 0
\(749\) −47.7970 −1.74646
\(750\) 0 0
\(751\) 48.6091 1.77377 0.886885 0.461990i \(-0.152864\pi\)
0.886885 + 0.461990i \(0.152864\pi\)
\(752\) 0 0
\(753\) −3.25265 −0.118533
\(754\) 0 0
\(755\) −16.0008 −0.582330
\(756\) 0 0
\(757\) −44.8319 −1.62944 −0.814721 0.579853i \(-0.803110\pi\)
−0.814721 + 0.579853i \(0.803110\pi\)
\(758\) 0 0
\(759\) 3.39503 0.123232
\(760\) 0 0
\(761\) −31.4812 −1.14119 −0.570596 0.821231i \(-0.693288\pi\)
−0.570596 + 0.821231i \(0.693288\pi\)
\(762\) 0 0
\(763\) 13.3188 0.482171
\(764\) 0 0
\(765\) −12.5328 −0.453123
\(766\) 0 0
\(767\) 0.636468 0.0229815
\(768\) 0 0
\(769\) 30.6134 1.10395 0.551974 0.833861i \(-0.313875\pi\)
0.551974 + 0.833861i \(0.313875\pi\)
\(770\) 0 0
\(771\) 10.6906 0.385011
\(772\) 0 0
\(773\) 25.8605 0.930136 0.465068 0.885275i \(-0.346030\pi\)
0.465068 + 0.885275i \(0.346030\pi\)
\(774\) 0 0
\(775\) 1.82936 0.0657125
\(776\) 0 0
\(777\) −10.7450 −0.385475
\(778\) 0 0
\(779\) 48.0304 1.72087
\(780\) 0 0
\(781\) −22.5974 −0.808598
\(782\) 0 0
\(783\) −1.52298 −0.0544268
\(784\) 0 0
\(785\) −24.2069 −0.863981
\(786\) 0 0
\(787\) −31.7233 −1.13081 −0.565406 0.824813i \(-0.691281\pi\)
−0.565406 + 0.824813i \(0.691281\pi\)
\(788\) 0 0
\(789\) 0.407750 0.0145163
\(790\) 0 0
\(791\) −0.278827 −0.00991394
\(792\) 0 0
\(793\) −21.2979 −0.756311
\(794\) 0 0
\(795\) 15.7808 0.559687
\(796\) 0 0
\(797\) −55.1753 −1.95441 −0.977205 0.212296i \(-0.931906\pi\)
−0.977205 + 0.212296i \(0.931906\pi\)
\(798\) 0 0
\(799\) 20.0438 0.709099
\(800\) 0 0
\(801\) 0.199719 0.00705671
\(802\) 0 0
\(803\) −3.92625 −0.138554
\(804\) 0 0
\(805\) 16.1810 0.570306
\(806\) 0 0
\(807\) −14.4715 −0.509420
\(808\) 0 0
\(809\) −6.04923 −0.212680 −0.106340 0.994330i \(-0.533913\pi\)
−0.106340 + 0.994330i \(0.533913\pi\)
\(810\) 0 0
\(811\) 3.97693 0.139649 0.0698244 0.997559i \(-0.477756\pi\)
0.0698244 + 0.997559i \(0.477756\pi\)
\(812\) 0 0
\(813\) 16.8970 0.592604
\(814\) 0 0
\(815\) −10.8491 −0.380029
\(816\) 0 0
\(817\) −3.56714 −0.124798
\(818\) 0 0
\(819\) −16.6596 −0.582134
\(820\) 0 0
\(821\) 16.5562 0.577815 0.288907 0.957357i \(-0.406708\pi\)
0.288907 + 0.957357i \(0.406708\pi\)
\(822\) 0 0
\(823\) 29.9588 1.04430 0.522150 0.852854i \(-0.325130\pi\)
0.522150 + 0.852854i \(0.325130\pi\)
\(824\) 0 0
\(825\) 0.299198 0.0104168
\(826\) 0 0
\(827\) 39.4061 1.37029 0.685143 0.728409i \(-0.259740\pi\)
0.685143 + 0.728409i \(0.259740\pi\)
\(828\) 0 0
\(829\) 6.63817 0.230553 0.115277 0.993333i \(-0.463225\pi\)
0.115277 + 0.993333i \(0.463225\pi\)
\(830\) 0 0
\(831\) −14.4298 −0.500565
\(832\) 0 0
\(833\) −0.902214 −0.0312599
\(834\) 0 0
\(835\) 35.3675 1.22394
\(836\) 0 0
\(837\) 38.5068 1.33099
\(838\) 0 0
\(839\) 55.4839 1.91552 0.957759 0.287574i \(-0.0928486\pi\)
0.957759 + 0.287574i \(0.0928486\pi\)
\(840\) 0 0
\(841\) −28.9011 −0.996590
\(842\) 0 0
\(843\) −19.0855 −0.657340
\(844\) 0 0
\(845\) 10.0864 0.346983
\(846\) 0 0
\(847\) 24.7345 0.849887
\(848\) 0 0
\(849\) −1.55334 −0.0533103
\(850\) 0 0
\(851\) −10.8942 −0.373447
\(852\) 0 0
\(853\) −23.3264 −0.798680 −0.399340 0.916803i \(-0.630761\pi\)
−0.399340 + 0.916803i \(0.630761\pi\)
\(854\) 0 0
\(855\) 37.3701 1.27803
\(856\) 0 0
\(857\) 20.5822 0.703075 0.351537 0.936174i \(-0.385659\pi\)
0.351537 + 0.936174i \(0.385659\pi\)
\(858\) 0 0
\(859\) 45.7526 1.56106 0.780529 0.625120i \(-0.214950\pi\)
0.780529 + 0.625120i \(0.214950\pi\)
\(860\) 0 0
\(861\) 15.8738 0.540977
\(862\) 0 0
\(863\) −10.0848 −0.343290 −0.171645 0.985159i \(-0.554908\pi\)
−0.171645 + 0.985159i \(0.554908\pi\)
\(864\) 0 0
\(865\) 41.1717 1.39988
\(866\) 0 0
\(867\) 9.66495 0.328239
\(868\) 0 0
\(869\) −21.9313 −0.743968
\(870\) 0 0
\(871\) 29.6075 1.00321
\(872\) 0 0
\(873\) 19.4560 0.658487
\(874\) 0 0
\(875\) −29.5645 −0.999462
\(876\) 0 0
\(877\) 3.30564 0.111624 0.0558118 0.998441i \(-0.482225\pi\)
0.0558118 + 0.998441i \(0.482225\pi\)
\(878\) 0 0
\(879\) 9.68048 0.326515
\(880\) 0 0
\(881\) 8.30907 0.279940 0.139970 0.990156i \(-0.455299\pi\)
0.139970 + 0.990156i \(0.455299\pi\)
\(882\) 0 0
\(883\) −2.65895 −0.0894807 −0.0447403 0.998999i \(-0.514246\pi\)
−0.0447403 + 0.998999i \(0.514246\pi\)
\(884\) 0 0
\(885\) −0.471846 −0.0158609
\(886\) 0 0
\(887\) 21.5846 0.724740 0.362370 0.932034i \(-0.381968\pi\)
0.362370 + 0.932034i \(0.381968\pi\)
\(888\) 0 0
\(889\) 40.0250 1.34240
\(890\) 0 0
\(891\) −2.31474 −0.0775466
\(892\) 0 0
\(893\) −59.7665 −2.00001
\(894\) 0 0
\(895\) 51.7738 1.73061
\(896\) 0 0
\(897\) 7.26921 0.242712
\(898\) 0 0
\(899\) −2.50051 −0.0833967
\(900\) 0 0
\(901\) −18.9775 −0.632231
\(902\) 0 0
\(903\) −1.17892 −0.0392320
\(904\) 0 0
\(905\) −6.81470 −0.226528
\(906\) 0 0
\(907\) 5.95616 0.197771 0.0988855 0.995099i \(-0.468472\pi\)
0.0988855 + 0.995099i \(0.468472\pi\)
\(908\) 0 0
\(909\) −18.4092 −0.610594
\(910\) 0 0
\(911\) −14.9730 −0.496079 −0.248040 0.968750i \(-0.579786\pi\)
−0.248040 + 0.968750i \(0.579786\pi\)
\(912\) 0 0
\(913\) 17.1528 0.567676
\(914\) 0 0
\(915\) 15.7892 0.521975
\(916\) 0 0
\(917\) 8.17527 0.269971
\(918\) 0 0
\(919\) 21.4164 0.706463 0.353232 0.935536i \(-0.385083\pi\)
0.353232 + 0.935536i \(0.385083\pi\)
\(920\) 0 0
\(921\) −15.5509 −0.512421
\(922\) 0 0
\(923\) −48.3840 −1.59258
\(924\) 0 0
\(925\) −0.960085 −0.0315674
\(926\) 0 0
\(927\) 3.19796 0.105035
\(928\) 0 0
\(929\) −51.4153 −1.68688 −0.843441 0.537221i \(-0.819474\pi\)
−0.843441 + 0.537221i \(0.819474\pi\)
\(930\) 0 0
\(931\) 2.69021 0.0881682
\(932\) 0 0
\(933\) 6.64024 0.217392
\(934\) 0 0
\(935\) −8.17925 −0.267490
\(936\) 0 0
\(937\) −41.9350 −1.36996 −0.684979 0.728563i \(-0.740188\pi\)
−0.684979 + 0.728563i \(0.740188\pi\)
\(938\) 0 0
\(939\) −2.11337 −0.0689674
\(940\) 0 0
\(941\) −36.8467 −1.20117 −0.600585 0.799561i \(-0.705065\pi\)
−0.600585 + 0.799561i \(0.705065\pi\)
\(942\) 0 0
\(943\) 16.0941 0.524097
\(944\) 0 0
\(945\) 30.0165 0.976436
\(946\) 0 0
\(947\) −2.12177 −0.0689481 −0.0344741 0.999406i \(-0.510976\pi\)
−0.0344741 + 0.999406i \(0.510976\pi\)
\(948\) 0 0
\(949\) −8.40663 −0.272891
\(950\) 0 0
\(951\) −3.32227 −0.107732
\(952\) 0 0
\(953\) 13.5643 0.439391 0.219695 0.975569i \(-0.429494\pi\)
0.219695 + 0.975569i \(0.429494\pi\)
\(954\) 0 0
\(955\) 9.36645 0.303091
\(956\) 0 0
\(957\) −0.408968 −0.0132201
\(958\) 0 0
\(959\) −1.00330 −0.0323981
\(960\) 0 0
\(961\) 32.2225 1.03944
\(962\) 0 0
\(963\) −36.9889 −1.19195
\(964\) 0 0
\(965\) 48.4163 1.55858
\(966\) 0 0
\(967\) −5.95719 −0.191570 −0.0957851 0.995402i \(-0.530536\pi\)
−0.0957851 + 0.995402i \(0.530536\pi\)
\(968\) 0 0
\(969\) 19.3406 0.621308
\(970\) 0 0
\(971\) −12.1772 −0.390785 −0.195392 0.980725i \(-0.562598\pi\)
−0.195392 + 0.980725i \(0.562598\pi\)
\(972\) 0 0
\(973\) 35.4886 1.13771
\(974\) 0 0
\(975\) 0.640624 0.0205164
\(976\) 0 0
\(977\) 7.69439 0.246165 0.123083 0.992396i \(-0.460722\pi\)
0.123083 + 0.992396i \(0.460722\pi\)
\(978\) 0 0
\(979\) 0.130342 0.00416576
\(980\) 0 0
\(981\) 10.3070 0.329078
\(982\) 0 0
\(983\) 12.2144 0.389578 0.194789 0.980845i \(-0.437598\pi\)
0.194789 + 0.980845i \(0.437598\pi\)
\(984\) 0 0
\(985\) −42.3401 −1.34907
\(986\) 0 0
\(987\) −19.7525 −0.628729
\(988\) 0 0
\(989\) −1.19529 −0.0380079
\(990\) 0 0
\(991\) −2.35228 −0.0747227 −0.0373613 0.999302i \(-0.511895\pi\)
−0.0373613 + 0.999302i \(0.511895\pi\)
\(992\) 0 0
\(993\) −13.1731 −0.418036
\(994\) 0 0
\(995\) −3.58387 −0.113616
\(996\) 0 0
\(997\) 19.2415 0.609384 0.304692 0.952451i \(-0.401446\pi\)
0.304692 + 0.952451i \(0.401446\pi\)
\(998\) 0 0
\(999\) −20.2092 −0.639389
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 \(a_p\))