Properties

Label 6036.2.a.g.1.7
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 1.7
Root \(0.117275\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.882725 q^{5}\) \(-2.85663 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.882725 q^{5}\) \(-2.85663 q^{7}\) \(+1.00000 q^{9}\) \(+2.43664 q^{11}\) \(+1.92471 q^{13}\) \(-0.882725 q^{15}\) \(-2.82868 q^{17}\) \(+5.97479 q^{19}\) \(-2.85663 q^{21}\) \(-3.88140 q^{23}\) \(-4.22080 q^{25}\) \(+1.00000 q^{27}\) \(-6.73462 q^{29}\) \(+0.533408 q^{31}\) \(+2.43664 q^{33}\) \(+2.52162 q^{35}\) \(+3.20257 q^{37}\) \(+1.92471 q^{39}\) \(-2.13883 q^{41}\) \(-7.27961 q^{43}\) \(-0.882725 q^{45}\) \(-0.965205 q^{47}\) \(+1.16034 q^{49}\) \(-2.82868 q^{51}\) \(+11.3038 q^{53}\) \(-2.15089 q^{55}\) \(+5.97479 q^{57}\) \(-8.38597 q^{59}\) \(-4.72206 q^{61}\) \(-2.85663 q^{63}\) \(-1.69899 q^{65}\) \(+2.35883 q^{67}\) \(-3.88140 q^{69}\) \(-6.46064 q^{71}\) \(+11.4531 q^{73}\) \(-4.22080 q^{75}\) \(-6.96060 q^{77}\) \(-3.91208 q^{79}\) \(+1.00000 q^{81}\) \(-12.5325 q^{83}\) \(+2.49695 q^{85}\) \(-6.73462 q^{87}\) \(+14.9051 q^{89}\) \(-5.49820 q^{91}\) \(+0.533408 q^{93}\) \(-5.27410 q^{95}\) \(-9.34373 q^{97}\) \(+2.43664 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.882725 −0.394767 −0.197383 0.980326i \(-0.563244\pi\)
−0.197383 + 0.980326i \(0.563244\pi\)
\(6\) 0 0
\(7\) −2.85663 −1.07971 −0.539853 0.841760i \(-0.681520\pi\)
−0.539853 + 0.841760i \(0.681520\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.43664 0.734676 0.367338 0.930088i \(-0.380269\pi\)
0.367338 + 0.930088i \(0.380269\pi\)
\(12\) 0 0
\(13\) 1.92471 0.533819 0.266910 0.963722i \(-0.413997\pi\)
0.266910 + 0.963722i \(0.413997\pi\)
\(14\) 0 0
\(15\) −0.882725 −0.227919
\(16\) 0 0
\(17\) −2.82868 −0.686055 −0.343028 0.939325i \(-0.611452\pi\)
−0.343028 + 0.939325i \(0.611452\pi\)
\(18\) 0 0
\(19\) 5.97479 1.37071 0.685355 0.728209i \(-0.259647\pi\)
0.685355 + 0.728209i \(0.259647\pi\)
\(20\) 0 0
\(21\) −2.85663 −0.623368
\(22\) 0 0
\(23\) −3.88140 −0.809327 −0.404664 0.914466i \(-0.632611\pi\)
−0.404664 + 0.914466i \(0.632611\pi\)
\(24\) 0 0
\(25\) −4.22080 −0.844159
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.73462 −1.25059 −0.625294 0.780389i \(-0.715021\pi\)
−0.625294 + 0.780389i \(0.715021\pi\)
\(30\) 0 0
\(31\) 0.533408 0.0958028 0.0479014 0.998852i \(-0.484747\pi\)
0.0479014 + 0.998852i \(0.484747\pi\)
\(32\) 0 0
\(33\) 2.43664 0.424165
\(34\) 0 0
\(35\) 2.52162 0.426232
\(36\) 0 0
\(37\) 3.20257 0.526499 0.263249 0.964728i \(-0.415206\pi\)
0.263249 + 0.964728i \(0.415206\pi\)
\(38\) 0 0
\(39\) 1.92471 0.308201
\(40\) 0 0
\(41\) −2.13883 −0.334029 −0.167014 0.985954i \(-0.553413\pi\)
−0.167014 + 0.985954i \(0.553413\pi\)
\(42\) 0 0
\(43\) −7.27961 −1.11013 −0.555065 0.831807i \(-0.687307\pi\)
−0.555065 + 0.831807i \(0.687307\pi\)
\(44\) 0 0
\(45\) −0.882725 −0.131589
\(46\) 0 0
\(47\) −0.965205 −0.140790 −0.0703948 0.997519i \(-0.522426\pi\)
−0.0703948 + 0.997519i \(0.522426\pi\)
\(48\) 0 0
\(49\) 1.16034 0.165763
\(50\) 0 0
\(51\) −2.82868 −0.396094
\(52\) 0 0
\(53\) 11.3038 1.55269 0.776345 0.630308i \(-0.217071\pi\)
0.776345 + 0.630308i \(0.217071\pi\)
\(54\) 0 0
\(55\) −2.15089 −0.290026
\(56\) 0 0
\(57\) 5.97479 0.791380
\(58\) 0 0
\(59\) −8.38597 −1.09176 −0.545880 0.837863i \(-0.683805\pi\)
−0.545880 + 0.837863i \(0.683805\pi\)
\(60\) 0 0
\(61\) −4.72206 −0.604597 −0.302299 0.953213i \(-0.597754\pi\)
−0.302299 + 0.953213i \(0.597754\pi\)
\(62\) 0 0
\(63\) −2.85663 −0.359902
\(64\) 0 0
\(65\) −1.69899 −0.210734
\(66\) 0 0
\(67\) 2.35883 0.288177 0.144089 0.989565i \(-0.453975\pi\)
0.144089 + 0.989565i \(0.453975\pi\)
\(68\) 0 0
\(69\) −3.88140 −0.467265
\(70\) 0 0
\(71\) −6.46064 −0.766736 −0.383368 0.923596i \(-0.625236\pi\)
−0.383368 + 0.923596i \(0.625236\pi\)
\(72\) 0 0
\(73\) 11.4531 1.34048 0.670240 0.742144i \(-0.266191\pi\)
0.670240 + 0.742144i \(0.266191\pi\)
\(74\) 0 0
\(75\) −4.22080 −0.487376
\(76\) 0 0
\(77\) −6.96060 −0.793234
\(78\) 0 0
\(79\) −3.91208 −0.440143 −0.220072 0.975484i \(-0.570629\pi\)
−0.220072 + 0.975484i \(0.570629\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −12.5325 −1.37563 −0.687813 0.725888i \(-0.741429\pi\)
−0.687813 + 0.725888i \(0.741429\pi\)
\(84\) 0 0
\(85\) 2.49695 0.270832
\(86\) 0 0
\(87\) −6.73462 −0.722027
\(88\) 0 0
\(89\) 14.9051 1.57994 0.789971 0.613144i \(-0.210095\pi\)
0.789971 + 0.613144i \(0.210095\pi\)
\(90\) 0 0
\(91\) −5.49820 −0.576368
\(92\) 0 0
\(93\) 0.533408 0.0553118
\(94\) 0 0
\(95\) −5.27410 −0.541111
\(96\) 0 0
\(97\) −9.34373 −0.948712 −0.474356 0.880333i \(-0.657319\pi\)
−0.474356 + 0.880333i \(0.657319\pi\)
\(98\) 0 0
\(99\) 2.43664 0.244892
\(100\) 0 0
\(101\) 4.77150 0.474782 0.237391 0.971414i \(-0.423708\pi\)
0.237391 + 0.971414i \(0.423708\pi\)
\(102\) 0 0
\(103\) 1.35047 0.133065 0.0665327 0.997784i \(-0.478806\pi\)
0.0665327 + 0.997784i \(0.478806\pi\)
\(104\) 0 0
\(105\) 2.52162 0.246085
\(106\) 0 0
\(107\) 11.8653 1.14706 0.573532 0.819183i \(-0.305573\pi\)
0.573532 + 0.819183i \(0.305573\pi\)
\(108\) 0 0
\(109\) −2.24165 −0.214711 −0.107356 0.994221i \(-0.534238\pi\)
−0.107356 + 0.994221i \(0.534238\pi\)
\(110\) 0 0
\(111\) 3.20257 0.303974
\(112\) 0 0
\(113\) 5.76949 0.542748 0.271374 0.962474i \(-0.412522\pi\)
0.271374 + 0.962474i \(0.412522\pi\)
\(114\) 0 0
\(115\) 3.42621 0.319495
\(116\) 0 0
\(117\) 1.92471 0.177940
\(118\) 0 0
\(119\) 8.08049 0.740737
\(120\) 0 0
\(121\) −5.06276 −0.460251
\(122\) 0 0
\(123\) −2.13883 −0.192852
\(124\) 0 0
\(125\) 8.13943 0.728013
\(126\) 0 0
\(127\) 10.5810 0.938912 0.469456 0.882956i \(-0.344450\pi\)
0.469456 + 0.882956i \(0.344450\pi\)
\(128\) 0 0
\(129\) −7.27961 −0.640934
\(130\) 0 0
\(131\) −13.0718 −1.14209 −0.571046 0.820918i \(-0.693462\pi\)
−0.571046 + 0.820918i \(0.693462\pi\)
\(132\) 0 0
\(133\) −17.0678 −1.47996
\(134\) 0 0
\(135\) −0.882725 −0.0759729
\(136\) 0 0
\(137\) −18.9259 −1.61695 −0.808474 0.588532i \(-0.799706\pi\)
−0.808474 + 0.588532i \(0.799706\pi\)
\(138\) 0 0
\(139\) 9.86280 0.836552 0.418276 0.908320i \(-0.362634\pi\)
0.418276 + 0.908320i \(0.362634\pi\)
\(140\) 0 0
\(141\) −0.965205 −0.0812849
\(142\) 0 0
\(143\) 4.68984 0.392184
\(144\) 0 0
\(145\) 5.94482 0.493691
\(146\) 0 0
\(147\) 1.16034 0.0957036
\(148\) 0 0
\(149\) −14.3681 −1.17708 −0.588541 0.808468i \(-0.700297\pi\)
−0.588541 + 0.808468i \(0.700297\pi\)
\(150\) 0 0
\(151\) 3.21916 0.261971 0.130986 0.991384i \(-0.458186\pi\)
0.130986 + 0.991384i \(0.458186\pi\)
\(152\) 0 0
\(153\) −2.82868 −0.228685
\(154\) 0 0
\(155\) −0.470852 −0.0378198
\(156\) 0 0
\(157\) −10.3589 −0.826734 −0.413367 0.910564i \(-0.635647\pi\)
−0.413367 + 0.910564i \(0.635647\pi\)
\(158\) 0 0
\(159\) 11.3038 0.896446
\(160\) 0 0
\(161\) 11.0877 0.873835
\(162\) 0 0
\(163\) −8.00830 −0.627259 −0.313629 0.949546i \(-0.601545\pi\)
−0.313629 + 0.949546i \(0.601545\pi\)
\(164\) 0 0
\(165\) −2.15089 −0.167446
\(166\) 0 0
\(167\) −9.92715 −0.768186 −0.384093 0.923294i \(-0.625486\pi\)
−0.384093 + 0.923294i \(0.625486\pi\)
\(168\) 0 0
\(169\) −9.29548 −0.715037
\(170\) 0 0
\(171\) 5.97479 0.456903
\(172\) 0 0
\(173\) −15.5681 −1.18362 −0.591811 0.806077i \(-0.701587\pi\)
−0.591811 + 0.806077i \(0.701587\pi\)
\(174\) 0 0
\(175\) 12.0573 0.911443
\(176\) 0 0
\(177\) −8.38597 −0.630328
\(178\) 0 0
\(179\) 3.70146 0.276660 0.138330 0.990386i \(-0.455827\pi\)
0.138330 + 0.990386i \(0.455827\pi\)
\(180\) 0 0
\(181\) −24.7381 −1.83877 −0.919384 0.393360i \(-0.871312\pi\)
−0.919384 + 0.393360i \(0.871312\pi\)
\(182\) 0 0
\(183\) −4.72206 −0.349064
\(184\) 0 0
\(185\) −2.82699 −0.207844
\(186\) 0 0
\(187\) −6.89248 −0.504028
\(188\) 0 0
\(189\) −2.85663 −0.207789
\(190\) 0 0
\(191\) −13.0911 −0.947240 −0.473620 0.880729i \(-0.657053\pi\)
−0.473620 + 0.880729i \(0.657053\pi\)
\(192\) 0 0
\(193\) −5.85802 −0.421669 −0.210835 0.977522i \(-0.567618\pi\)
−0.210835 + 0.977522i \(0.567618\pi\)
\(194\) 0 0
\(195\) −1.69899 −0.121667
\(196\) 0 0
\(197\) −13.1264 −0.935220 −0.467610 0.883935i \(-0.654885\pi\)
−0.467610 + 0.883935i \(0.654885\pi\)
\(198\) 0 0
\(199\) −9.41618 −0.667495 −0.333748 0.942662i \(-0.608313\pi\)
−0.333748 + 0.942662i \(0.608313\pi\)
\(200\) 0 0
\(201\) 2.35883 0.166379
\(202\) 0 0
\(203\) 19.2383 1.35027
\(204\) 0 0
\(205\) 1.88800 0.131863
\(206\) 0 0
\(207\) −3.88140 −0.269776
\(208\) 0 0
\(209\) 14.5584 1.00703
\(210\) 0 0
\(211\) 8.03579 0.553207 0.276603 0.960984i \(-0.410791\pi\)
0.276603 + 0.960984i \(0.410791\pi\)
\(212\) 0 0
\(213\) −6.46064 −0.442675
\(214\) 0 0
\(215\) 6.42589 0.438242
\(216\) 0 0
\(217\) −1.52375 −0.103439
\(218\) 0 0
\(219\) 11.4531 0.773927
\(220\) 0 0
\(221\) −5.44439 −0.366230
\(222\) 0 0
\(223\) −17.9834 −1.20426 −0.602129 0.798399i \(-0.705681\pi\)
−0.602129 + 0.798399i \(0.705681\pi\)
\(224\) 0 0
\(225\) −4.22080 −0.281386
\(226\) 0 0
\(227\) −14.5752 −0.967388 −0.483694 0.875237i \(-0.660705\pi\)
−0.483694 + 0.875237i \(0.660705\pi\)
\(228\) 0 0
\(229\) −28.1053 −1.85725 −0.928624 0.371022i \(-0.879007\pi\)
−0.928624 + 0.371022i \(0.879007\pi\)
\(230\) 0 0
\(231\) −6.96060 −0.457974
\(232\) 0 0
\(233\) 1.44456 0.0946363 0.0473181 0.998880i \(-0.484933\pi\)
0.0473181 + 0.998880i \(0.484933\pi\)
\(234\) 0 0
\(235\) 0.852011 0.0555791
\(236\) 0 0
\(237\) −3.91208 −0.254117
\(238\) 0 0
\(239\) −10.8011 −0.698665 −0.349332 0.936999i \(-0.613592\pi\)
−0.349332 + 0.936999i \(0.613592\pi\)
\(240\) 0 0
\(241\) 17.0594 1.09889 0.549447 0.835529i \(-0.314838\pi\)
0.549447 + 0.835529i \(0.314838\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −1.02426 −0.0654379
\(246\) 0 0
\(247\) 11.4998 0.731712
\(248\) 0 0
\(249\) −12.5325 −0.794218
\(250\) 0 0
\(251\) −18.3563 −1.15864 −0.579320 0.815100i \(-0.696682\pi\)
−0.579320 + 0.815100i \(0.696682\pi\)
\(252\) 0 0
\(253\) −9.45758 −0.594593
\(254\) 0 0
\(255\) 2.49695 0.156365
\(256\) 0 0
\(257\) 21.6433 1.35007 0.675036 0.737785i \(-0.264128\pi\)
0.675036 + 0.737785i \(0.264128\pi\)
\(258\) 0 0
\(259\) −9.14855 −0.568463
\(260\) 0 0
\(261\) −6.73462 −0.416863
\(262\) 0 0
\(263\) 4.38202 0.270207 0.135103 0.990832i \(-0.456863\pi\)
0.135103 + 0.990832i \(0.456863\pi\)
\(264\) 0 0
\(265\) −9.97811 −0.612951
\(266\) 0 0
\(267\) 14.9051 0.912180
\(268\) 0 0
\(269\) 6.04760 0.368728 0.184364 0.982858i \(-0.440977\pi\)
0.184364 + 0.982858i \(0.440977\pi\)
\(270\) 0 0
\(271\) −20.9757 −1.27418 −0.637092 0.770788i \(-0.719863\pi\)
−0.637092 + 0.770788i \(0.719863\pi\)
\(272\) 0 0
\(273\) −5.49820 −0.332766
\(274\) 0 0
\(275\) −10.2846 −0.620184
\(276\) 0 0
\(277\) −16.9015 −1.01551 −0.507756 0.861501i \(-0.669525\pi\)
−0.507756 + 0.861501i \(0.669525\pi\)
\(278\) 0 0
\(279\) 0.533408 0.0319343
\(280\) 0 0
\(281\) −13.3651 −0.797296 −0.398648 0.917104i \(-0.630520\pi\)
−0.398648 + 0.917104i \(0.630520\pi\)
\(282\) 0 0
\(283\) −7.49433 −0.445492 −0.222746 0.974877i \(-0.571502\pi\)
−0.222746 + 0.974877i \(0.571502\pi\)
\(284\) 0 0
\(285\) −5.27410 −0.312410
\(286\) 0 0
\(287\) 6.10984 0.360653
\(288\) 0 0
\(289\) −8.99858 −0.529328
\(290\) 0 0
\(291\) −9.34373 −0.547739
\(292\) 0 0
\(293\) −32.6876 −1.90963 −0.954814 0.297203i \(-0.903946\pi\)
−0.954814 + 0.297203i \(0.903946\pi\)
\(294\) 0 0
\(295\) 7.40251 0.430991
\(296\) 0 0
\(297\) 2.43664 0.141388
\(298\) 0 0
\(299\) −7.47057 −0.432034
\(300\) 0 0
\(301\) 20.7952 1.19861
\(302\) 0 0
\(303\) 4.77150 0.274116
\(304\) 0 0
\(305\) 4.16828 0.238675
\(306\) 0 0
\(307\) 14.0085 0.799506 0.399753 0.916623i \(-0.369096\pi\)
0.399753 + 0.916623i \(0.369096\pi\)
\(308\) 0 0
\(309\) 1.35047 0.0768253
\(310\) 0 0
\(311\) −4.23519 −0.240156 −0.120078 0.992764i \(-0.538314\pi\)
−0.120078 + 0.992764i \(0.538314\pi\)
\(312\) 0 0
\(313\) 31.5070 1.78088 0.890441 0.455099i \(-0.150396\pi\)
0.890441 + 0.455099i \(0.150396\pi\)
\(314\) 0 0
\(315\) 2.52162 0.142077
\(316\) 0 0
\(317\) −14.4870 −0.813670 −0.406835 0.913502i \(-0.633368\pi\)
−0.406835 + 0.913502i \(0.633368\pi\)
\(318\) 0 0
\(319\) −16.4099 −0.918777
\(320\) 0 0
\(321\) 11.8653 0.662257
\(322\) 0 0
\(323\) −16.9007 −0.940383
\(324\) 0 0
\(325\) −8.12382 −0.450629
\(326\) 0 0
\(327\) −2.24165 −0.123964
\(328\) 0 0
\(329\) 2.75724 0.152011
\(330\) 0 0
\(331\) 17.0638 0.937910 0.468955 0.883222i \(-0.344631\pi\)
0.468955 + 0.883222i \(0.344631\pi\)
\(332\) 0 0
\(333\) 3.20257 0.175500
\(334\) 0 0
\(335\) −2.08220 −0.113763
\(336\) 0 0
\(337\) −15.6785 −0.854063 −0.427031 0.904237i \(-0.640441\pi\)
−0.427031 + 0.904237i \(0.640441\pi\)
\(338\) 0 0
\(339\) 5.76949 0.313356
\(340\) 0 0
\(341\) 1.29972 0.0703841
\(342\) 0 0
\(343\) 16.6817 0.900730
\(344\) 0 0
\(345\) 3.42621 0.184461
\(346\) 0 0
\(347\) 29.2873 1.57222 0.786111 0.618085i \(-0.212091\pi\)
0.786111 + 0.618085i \(0.212091\pi\)
\(348\) 0 0
\(349\) 20.5332 1.09912 0.549559 0.835455i \(-0.314796\pi\)
0.549559 + 0.835455i \(0.314796\pi\)
\(350\) 0 0
\(351\) 1.92471 0.102734
\(352\) 0 0
\(353\) −9.33420 −0.496809 −0.248405 0.968656i \(-0.579906\pi\)
−0.248405 + 0.968656i \(0.579906\pi\)
\(354\) 0 0
\(355\) 5.70297 0.302682
\(356\) 0 0
\(357\) 8.08049 0.427665
\(358\) 0 0
\(359\) −19.1808 −1.01232 −0.506162 0.862439i \(-0.668936\pi\)
−0.506162 + 0.862439i \(0.668936\pi\)
\(360\) 0 0
\(361\) 16.6981 0.878847
\(362\) 0 0
\(363\) −5.06276 −0.265726
\(364\) 0 0
\(365\) −10.1099 −0.529177
\(366\) 0 0
\(367\) 36.6243 1.91177 0.955887 0.293735i \(-0.0948983\pi\)
0.955887 + 0.293735i \(0.0948983\pi\)
\(368\) 0 0
\(369\) −2.13883 −0.111343
\(370\) 0 0
\(371\) −32.2907 −1.67645
\(372\) 0 0
\(373\) 13.0025 0.673242 0.336621 0.941640i \(-0.390716\pi\)
0.336621 + 0.941640i \(0.390716\pi\)
\(374\) 0 0
\(375\) 8.13943 0.420318
\(376\) 0 0
\(377\) −12.9622 −0.667588
\(378\) 0 0
\(379\) 14.5743 0.748632 0.374316 0.927301i \(-0.377877\pi\)
0.374316 + 0.927301i \(0.377877\pi\)
\(380\) 0 0
\(381\) 10.5810 0.542081
\(382\) 0 0
\(383\) −8.32014 −0.425139 −0.212570 0.977146i \(-0.568183\pi\)
−0.212570 + 0.977146i \(0.568183\pi\)
\(384\) 0 0
\(385\) 6.14429 0.313142
\(386\) 0 0
\(387\) −7.27961 −0.370043
\(388\) 0 0
\(389\) −4.05565 −0.205629 −0.102815 0.994701i \(-0.532785\pi\)
−0.102815 + 0.994701i \(0.532785\pi\)
\(390\) 0 0
\(391\) 10.9792 0.555243
\(392\) 0 0
\(393\) −13.0718 −0.659387
\(394\) 0 0
\(395\) 3.45329 0.173754
\(396\) 0 0
\(397\) −11.2905 −0.566654 −0.283327 0.959023i \(-0.591438\pi\)
−0.283327 + 0.959023i \(0.591438\pi\)
\(398\) 0 0
\(399\) −17.0678 −0.854457
\(400\) 0 0
\(401\) −16.0161 −0.799806 −0.399903 0.916557i \(-0.630956\pi\)
−0.399903 + 0.916557i \(0.630956\pi\)
\(402\) 0 0
\(403\) 1.02666 0.0511414
\(404\) 0 0
\(405\) −0.882725 −0.0438630
\(406\) 0 0
\(407\) 7.80352 0.386806
\(408\) 0 0
\(409\) 16.9702 0.839124 0.419562 0.907727i \(-0.362184\pi\)
0.419562 + 0.907727i \(0.362184\pi\)
\(410\) 0 0
\(411\) −18.9259 −0.933545
\(412\) 0 0
\(413\) 23.9556 1.17878
\(414\) 0 0
\(415\) 11.0628 0.543051
\(416\) 0 0
\(417\) 9.86280 0.482984
\(418\) 0 0
\(419\) −22.2427 −1.08663 −0.543314 0.839529i \(-0.682831\pi\)
−0.543314 + 0.839529i \(0.682831\pi\)
\(420\) 0 0
\(421\) −12.7430 −0.621056 −0.310528 0.950564i \(-0.600506\pi\)
−0.310528 + 0.950564i \(0.600506\pi\)
\(422\) 0 0
\(423\) −0.965205 −0.0469299
\(424\) 0 0
\(425\) 11.9393 0.579140
\(426\) 0 0
\(427\) 13.4892 0.652787
\(428\) 0 0
\(429\) 4.68984 0.226428
\(430\) 0 0
\(431\) −20.6029 −0.992405 −0.496203 0.868207i \(-0.665273\pi\)
−0.496203 + 0.868207i \(0.665273\pi\)
\(432\) 0 0
\(433\) 3.98986 0.191741 0.0958703 0.995394i \(-0.469437\pi\)
0.0958703 + 0.995394i \(0.469437\pi\)
\(434\) 0 0
\(435\) 5.94482 0.285032
\(436\) 0 0
\(437\) −23.1905 −1.10935
\(438\) 0 0
\(439\) 34.2107 1.63279 0.816394 0.577495i \(-0.195970\pi\)
0.816394 + 0.577495i \(0.195970\pi\)
\(440\) 0 0
\(441\) 1.16034 0.0552545
\(442\) 0 0
\(443\) −4.95750 −0.235538 −0.117769 0.993041i \(-0.537574\pi\)
−0.117769 + 0.993041i \(0.537574\pi\)
\(444\) 0 0
\(445\) −13.1572 −0.623709
\(446\) 0 0
\(447\) −14.3681 −0.679588
\(448\) 0 0
\(449\) 37.1327 1.75240 0.876200 0.481948i \(-0.160071\pi\)
0.876200 + 0.481948i \(0.160071\pi\)
\(450\) 0 0
\(451\) −5.21156 −0.245403
\(452\) 0 0
\(453\) 3.21916 0.151249
\(454\) 0 0
\(455\) 4.85340 0.227531
\(456\) 0 0
\(457\) 31.0058 1.45039 0.725196 0.688543i \(-0.241749\pi\)
0.725196 + 0.688543i \(0.241749\pi\)
\(458\) 0 0
\(459\) −2.82868 −0.132031
\(460\) 0 0
\(461\) 4.73747 0.220646 0.110323 0.993896i \(-0.464811\pi\)
0.110323 + 0.993896i \(0.464811\pi\)
\(462\) 0 0
\(463\) 38.1870 1.77470 0.887351 0.461094i \(-0.152543\pi\)
0.887351 + 0.461094i \(0.152543\pi\)
\(464\) 0 0
\(465\) −0.470852 −0.0218353
\(466\) 0 0
\(467\) 35.7460 1.65413 0.827063 0.562109i \(-0.190010\pi\)
0.827063 + 0.562109i \(0.190010\pi\)
\(468\) 0 0
\(469\) −6.73831 −0.311146
\(470\) 0 0
\(471\) −10.3589 −0.477315
\(472\) 0 0
\(473\) −17.7378 −0.815586
\(474\) 0 0
\(475\) −25.2184 −1.15710
\(476\) 0 0
\(477\) 11.3038 0.517563
\(478\) 0 0
\(479\) 23.3727 1.06793 0.533963 0.845508i \(-0.320702\pi\)
0.533963 + 0.845508i \(0.320702\pi\)
\(480\) 0 0
\(481\) 6.16402 0.281055
\(482\) 0 0
\(483\) 11.0877 0.504509
\(484\) 0 0
\(485\) 8.24794 0.374520
\(486\) 0 0
\(487\) −10.6405 −0.482166 −0.241083 0.970504i \(-0.577503\pi\)
−0.241083 + 0.970504i \(0.577503\pi\)
\(488\) 0 0
\(489\) −8.00830 −0.362148
\(490\) 0 0
\(491\) −9.36682 −0.422719 −0.211359 0.977408i \(-0.567789\pi\)
−0.211359 + 0.977408i \(0.567789\pi\)
\(492\) 0 0
\(493\) 19.0501 0.857973
\(494\) 0 0
\(495\) −2.15089 −0.0966752
\(496\) 0 0
\(497\) 18.4557 0.827849
\(498\) 0 0
\(499\) −2.71203 −0.121407 −0.0607037 0.998156i \(-0.519334\pi\)
−0.0607037 + 0.998156i \(0.519334\pi\)
\(500\) 0 0
\(501\) −9.92715 −0.443512
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −4.21193 −0.187428
\(506\) 0 0
\(507\) −9.29548 −0.412827
\(508\) 0 0
\(509\) −24.8305 −1.10059 −0.550296 0.834970i \(-0.685485\pi\)
−0.550296 + 0.834970i \(0.685485\pi\)
\(510\) 0 0
\(511\) −32.7172 −1.44732
\(512\) 0 0
\(513\) 5.97479 0.263793
\(514\) 0 0
\(515\) −1.19209 −0.0525298
\(516\) 0 0
\(517\) −2.35186 −0.103435
\(518\) 0 0
\(519\) −15.5681 −0.683364
\(520\) 0 0
\(521\) −5.29102 −0.231804 −0.115902 0.993261i \(-0.536976\pi\)
−0.115902 + 0.993261i \(0.536976\pi\)
\(522\) 0 0
\(523\) 41.4592 1.81289 0.906443 0.422329i \(-0.138787\pi\)
0.906443 + 0.422329i \(0.138787\pi\)
\(524\) 0 0
\(525\) 12.0573 0.526222
\(526\) 0 0
\(527\) −1.50884 −0.0657260
\(528\) 0 0
\(529\) −7.93476 −0.344990
\(530\) 0 0
\(531\) −8.38597 −0.363920
\(532\) 0 0
\(533\) −4.11663 −0.178311
\(534\) 0 0
\(535\) −10.4738 −0.452822
\(536\) 0 0
\(537\) 3.70146 0.159730
\(538\) 0 0
\(539\) 2.82735 0.121782
\(540\) 0 0
\(541\) −22.8495 −0.982378 −0.491189 0.871053i \(-0.663438\pi\)
−0.491189 + 0.871053i \(0.663438\pi\)
\(542\) 0 0
\(543\) −24.7381 −1.06161
\(544\) 0 0
\(545\) 1.97876 0.0847609
\(546\) 0 0
\(547\) −24.1153 −1.03110 −0.515549 0.856860i \(-0.672412\pi\)
−0.515549 + 0.856860i \(0.672412\pi\)
\(548\) 0 0
\(549\) −4.72206 −0.201532
\(550\) 0 0
\(551\) −40.2379 −1.71419
\(552\) 0 0
\(553\) 11.1754 0.475225
\(554\) 0 0
\(555\) −2.82699 −0.119999
\(556\) 0 0
\(557\) −3.30050 −0.139847 −0.0699233 0.997552i \(-0.522275\pi\)
−0.0699233 + 0.997552i \(0.522275\pi\)
\(558\) 0 0
\(559\) −14.0112 −0.592609
\(560\) 0 0
\(561\) −6.89248 −0.291001
\(562\) 0 0
\(563\) 17.4662 0.736114 0.368057 0.929803i \(-0.380023\pi\)
0.368057 + 0.929803i \(0.380023\pi\)
\(564\) 0 0
\(565\) −5.09288 −0.214259
\(566\) 0 0
\(567\) −2.85663 −0.119967
\(568\) 0 0
\(569\) 19.2414 0.806641 0.403321 0.915059i \(-0.367856\pi\)
0.403321 + 0.915059i \(0.367856\pi\)
\(570\) 0 0
\(571\) 34.2454 1.43312 0.716562 0.697523i \(-0.245715\pi\)
0.716562 + 0.697523i \(0.245715\pi\)
\(572\) 0 0
\(573\) −13.0911 −0.546889
\(574\) 0 0
\(575\) 16.3826 0.683201
\(576\) 0 0
\(577\) 39.2507 1.63403 0.817014 0.576618i \(-0.195628\pi\)
0.817014 + 0.576618i \(0.195628\pi\)
\(578\) 0 0
\(579\) −5.85802 −0.243451
\(580\) 0 0
\(581\) 35.8009 1.48527
\(582\) 0 0
\(583\) 27.5432 1.14072
\(584\) 0 0
\(585\) −1.69899 −0.0702447
\(586\) 0 0
\(587\) 17.9941 0.742695 0.371348 0.928494i \(-0.378896\pi\)
0.371348 + 0.928494i \(0.378896\pi\)
\(588\) 0 0
\(589\) 3.18700 0.131318
\(590\) 0 0
\(591\) −13.1264 −0.539950
\(592\) 0 0
\(593\) −27.8655 −1.14430 −0.572149 0.820150i \(-0.693890\pi\)
−0.572149 + 0.820150i \(0.693890\pi\)
\(594\) 0 0
\(595\) −7.13285 −0.292418
\(596\) 0 0
\(597\) −9.41618 −0.385379
\(598\) 0 0
\(599\) −4.42797 −0.180922 −0.0904610 0.995900i \(-0.528834\pi\)
−0.0904610 + 0.995900i \(0.528834\pi\)
\(600\) 0 0
\(601\) 11.7307 0.478506 0.239253 0.970957i \(-0.423097\pi\)
0.239253 + 0.970957i \(0.423097\pi\)
\(602\) 0 0
\(603\) 2.35883 0.0960591
\(604\) 0 0
\(605\) 4.46903 0.181692
\(606\) 0 0
\(607\) 31.8144 1.29131 0.645654 0.763630i \(-0.276585\pi\)
0.645654 + 0.763630i \(0.276585\pi\)
\(608\) 0 0
\(609\) 19.2383 0.779577
\(610\) 0 0
\(611\) −1.85774 −0.0751562
\(612\) 0 0
\(613\) −8.80960 −0.355816 −0.177908 0.984047i \(-0.556933\pi\)
−0.177908 + 0.984047i \(0.556933\pi\)
\(614\) 0 0
\(615\) 1.88800 0.0761314
\(616\) 0 0
\(617\) 16.7013 0.672369 0.336184 0.941796i \(-0.390863\pi\)
0.336184 + 0.941796i \(0.390863\pi\)
\(618\) 0 0
\(619\) 10.8816 0.437368 0.218684 0.975796i \(-0.429824\pi\)
0.218684 + 0.975796i \(0.429824\pi\)
\(620\) 0 0
\(621\) −3.88140 −0.155755
\(622\) 0 0
\(623\) −42.5785 −1.70587
\(624\) 0 0
\(625\) 13.9191 0.556764
\(626\) 0 0
\(627\) 14.5584 0.581408
\(628\) 0 0
\(629\) −9.05903 −0.361207
\(630\) 0 0
\(631\) −7.43646 −0.296041 −0.148020 0.988984i \(-0.547290\pi\)
−0.148020 + 0.988984i \(0.547290\pi\)
\(632\) 0 0
\(633\) 8.03579 0.319394
\(634\) 0 0
\(635\) −9.34012 −0.370651
\(636\) 0 0
\(637\) 2.23333 0.0884877
\(638\) 0 0
\(639\) −6.46064 −0.255579
\(640\) 0 0
\(641\) −24.5853 −0.971062 −0.485531 0.874219i \(-0.661374\pi\)
−0.485531 + 0.874219i \(0.661374\pi\)
\(642\) 0 0
\(643\) 27.9134 1.10080 0.550399 0.834902i \(-0.314476\pi\)
0.550399 + 0.834902i \(0.314476\pi\)
\(644\) 0 0
\(645\) 6.42589 0.253019
\(646\) 0 0
\(647\) 12.0352 0.473154 0.236577 0.971613i \(-0.423974\pi\)
0.236577 + 0.971613i \(0.423974\pi\)
\(648\) 0 0
\(649\) −20.4336 −0.802090
\(650\) 0 0
\(651\) −1.52375 −0.0597204
\(652\) 0 0
\(653\) 21.2680 0.832282 0.416141 0.909300i \(-0.363382\pi\)
0.416141 + 0.909300i \(0.363382\pi\)
\(654\) 0 0
\(655\) 11.5388 0.450860
\(656\) 0 0
\(657\) 11.4531 0.446827
\(658\) 0 0
\(659\) −30.6855 −1.19534 −0.597669 0.801743i \(-0.703906\pi\)
−0.597669 + 0.801743i \(0.703906\pi\)
\(660\) 0 0
\(661\) −2.72192 −0.105870 −0.0529352 0.998598i \(-0.516858\pi\)
−0.0529352 + 0.998598i \(0.516858\pi\)
\(662\) 0 0
\(663\) −5.44439 −0.211443
\(664\) 0 0
\(665\) 15.0661 0.584240
\(666\) 0 0
\(667\) 26.1397 1.01213
\(668\) 0 0
\(669\) −17.9834 −0.695278
\(670\) 0 0
\(671\) −11.5060 −0.444183
\(672\) 0 0
\(673\) 3.60459 0.138947 0.0694733 0.997584i \(-0.477868\pi\)
0.0694733 + 0.997584i \(0.477868\pi\)
\(674\) 0 0
\(675\) −4.22080 −0.162459
\(676\) 0 0
\(677\) 13.6457 0.524447 0.262223 0.965007i \(-0.415544\pi\)
0.262223 + 0.965007i \(0.415544\pi\)
\(678\) 0 0
\(679\) 26.6916 1.02433
\(680\) 0 0
\(681\) −14.5752 −0.558522
\(682\) 0 0
\(683\) 10.4370 0.399360 0.199680 0.979861i \(-0.436010\pi\)
0.199680 + 0.979861i \(0.436010\pi\)
\(684\) 0 0
\(685\) 16.7064 0.638317
\(686\) 0 0
\(687\) −28.1053 −1.07228
\(688\) 0 0
\(689\) 21.7565 0.828856
\(690\) 0 0
\(691\) 18.6888 0.710955 0.355478 0.934685i \(-0.384318\pi\)
0.355478 + 0.934685i \(0.384318\pi\)
\(692\) 0 0
\(693\) −6.96060 −0.264411
\(694\) 0 0
\(695\) −8.70615 −0.330243
\(696\) 0 0
\(697\) 6.05005 0.229162
\(698\) 0 0
\(699\) 1.44456 0.0546383
\(700\) 0 0
\(701\) 7.43350 0.280759 0.140380 0.990098i \(-0.455168\pi\)
0.140380 + 0.990098i \(0.455168\pi\)
\(702\) 0 0
\(703\) 19.1346 0.721677
\(704\) 0 0
\(705\) 0.852011 0.0320886
\(706\) 0 0
\(707\) −13.6304 −0.512625
\(708\) 0 0
\(709\) −8.76906 −0.329329 −0.164665 0.986350i \(-0.552654\pi\)
−0.164665 + 0.986350i \(0.552654\pi\)
\(710\) 0 0
\(711\) −3.91208 −0.146714
\(712\) 0 0
\(713\) −2.07037 −0.0775358
\(714\) 0 0
\(715\) −4.13984 −0.154821
\(716\) 0 0
\(717\) −10.8011 −0.403374
\(718\) 0 0
\(719\) 23.4746 0.875454 0.437727 0.899108i \(-0.355784\pi\)
0.437727 + 0.899108i \(0.355784\pi\)
\(720\) 0 0
\(721\) −3.85778 −0.143671
\(722\) 0 0
\(723\) 17.0594 0.634447
\(724\) 0 0
\(725\) 28.4255 1.05570
\(726\) 0 0
\(727\) 46.5560 1.72667 0.863333 0.504634i \(-0.168373\pi\)
0.863333 + 0.504634i \(0.168373\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 20.5917 0.761610
\(732\) 0 0
\(733\) −1.66488 −0.0614937 −0.0307468 0.999527i \(-0.509789\pi\)
−0.0307468 + 0.999527i \(0.509789\pi\)
\(734\) 0 0
\(735\) −1.02426 −0.0377806
\(736\) 0 0
\(737\) 5.74764 0.211717
\(738\) 0 0
\(739\) 22.5472 0.829412 0.414706 0.909955i \(-0.363884\pi\)
0.414706 + 0.909955i \(0.363884\pi\)
\(740\) 0 0
\(741\) 11.4998 0.422454
\(742\) 0 0
\(743\) −3.83847 −0.140820 −0.0704098 0.997518i \(-0.522431\pi\)
−0.0704098 + 0.997518i \(0.522431\pi\)
\(744\) 0 0
\(745\) 12.6831 0.464673
\(746\) 0 0
\(747\) −12.5325 −0.458542
\(748\) 0 0
\(749\) −33.8948 −1.23849
\(750\) 0 0
\(751\) −50.8035 −1.85385 −0.926923 0.375251i \(-0.877557\pi\)
−0.926923 + 0.375251i \(0.877557\pi\)
\(752\) 0 0
\(753\) −18.3563 −0.668942
\(754\) 0 0
\(755\) −2.84163 −0.103418
\(756\) 0 0
\(757\) −5.91138 −0.214853 −0.107426 0.994213i \(-0.534261\pi\)
−0.107426 + 0.994213i \(0.534261\pi\)
\(758\) 0 0
\(759\) −9.45758 −0.343289
\(760\) 0 0
\(761\) −16.7837 −0.608409 −0.304205 0.952607i \(-0.598391\pi\)
−0.304205 + 0.952607i \(0.598391\pi\)
\(762\) 0 0
\(763\) 6.40357 0.231825
\(764\) 0 0
\(765\) 2.49695 0.0902773
\(766\) 0 0
\(767\) −16.1406 −0.582803
\(768\) 0 0
\(769\) −20.6396 −0.744282 −0.372141 0.928176i \(-0.621376\pi\)
−0.372141 + 0.928176i \(0.621376\pi\)
\(770\) 0 0
\(771\) 21.6433 0.779464
\(772\) 0 0
\(773\) −38.6761 −1.39108 −0.695541 0.718487i \(-0.744835\pi\)
−0.695541 + 0.718487i \(0.744835\pi\)
\(774\) 0 0
\(775\) −2.25140 −0.0808729
\(776\) 0 0
\(777\) −9.14855 −0.328202
\(778\) 0 0
\(779\) −12.7790 −0.457857
\(780\) 0 0
\(781\) −15.7423 −0.563303
\(782\) 0 0
\(783\) −6.73462 −0.240676
\(784\) 0 0
\(785\) 9.14411 0.326367
\(786\) 0 0
\(787\) 22.6311 0.806712 0.403356 0.915043i \(-0.367844\pi\)
0.403356 + 0.915043i \(0.367844\pi\)
\(788\) 0 0
\(789\) 4.38202 0.156004
\(790\) 0 0
\(791\) −16.4813 −0.586008
\(792\) 0 0
\(793\) −9.08860 −0.322746
\(794\) 0 0
\(795\) −9.97811 −0.353887
\(796\) 0 0
\(797\) −51.4717 −1.82322 −0.911611 0.411054i \(-0.865161\pi\)
−0.911611 + 0.411054i \(0.865161\pi\)
\(798\) 0 0
\(799\) 2.73025 0.0965895
\(800\) 0 0
\(801\) 14.9051 0.526647
\(802\) 0 0
\(803\) 27.9071 0.984819
\(804\) 0 0
\(805\) −9.78741 −0.344961
\(806\) 0 0
\(807\) 6.04760 0.212885
\(808\) 0 0
\(809\) 2.73341 0.0961017 0.0480508 0.998845i \(-0.484699\pi\)
0.0480508 + 0.998845i \(0.484699\pi\)
\(810\) 0 0
\(811\) −2.04350 −0.0717571 −0.0358785 0.999356i \(-0.511423\pi\)
−0.0358785 + 0.999356i \(0.511423\pi\)
\(812\) 0 0
\(813\) −20.9757 −0.735651
\(814\) 0 0
\(815\) 7.06913 0.247621
\(816\) 0 0
\(817\) −43.4941 −1.52167
\(818\) 0 0
\(819\) −5.49820 −0.192123
\(820\) 0 0
\(821\) 6.34354 0.221391 0.110696 0.993854i \(-0.464692\pi\)
0.110696 + 0.993854i \(0.464692\pi\)
\(822\) 0 0
\(823\) −13.3451 −0.465182 −0.232591 0.972575i \(-0.574720\pi\)
−0.232591 + 0.972575i \(0.574720\pi\)
\(824\) 0 0
\(825\) −10.2846 −0.358063
\(826\) 0 0
\(827\) 36.2920 1.26200 0.630999 0.775784i \(-0.282645\pi\)
0.630999 + 0.775784i \(0.282645\pi\)
\(828\) 0 0
\(829\) 3.16316 0.109861 0.0549305 0.998490i \(-0.482506\pi\)
0.0549305 + 0.998490i \(0.482506\pi\)
\(830\) 0 0
\(831\) −16.9015 −0.586306
\(832\) 0 0
\(833\) −3.28224 −0.113723
\(834\) 0 0
\(835\) 8.76295 0.303254
\(836\) 0 0
\(837\) 0.533408 0.0184373
\(838\) 0 0
\(839\) 30.4924 1.05271 0.526357 0.850264i \(-0.323558\pi\)
0.526357 + 0.850264i \(0.323558\pi\)
\(840\) 0 0
\(841\) 16.3552 0.563971
\(842\) 0 0
\(843\) −13.3651 −0.460319
\(844\) 0 0
\(845\) 8.20535 0.282273
\(846\) 0 0
\(847\) 14.4624 0.496936
\(848\) 0 0
\(849\) −7.49433 −0.257205
\(850\) 0 0
\(851\) −12.4304 −0.426110
\(852\) 0 0
\(853\) 31.9933 1.09543 0.547714 0.836665i \(-0.315498\pi\)
0.547714 + 0.836665i \(0.315498\pi\)
\(854\) 0 0
\(855\) −5.27410 −0.180370
\(856\) 0 0
\(857\) −24.9200 −0.851251 −0.425626 0.904899i \(-0.639946\pi\)
−0.425626 + 0.904899i \(0.639946\pi\)
\(858\) 0 0
\(859\) 12.9699 0.442526 0.221263 0.975214i \(-0.428982\pi\)
0.221263 + 0.975214i \(0.428982\pi\)
\(860\) 0 0
\(861\) 6.10984 0.208223
\(862\) 0 0
\(863\) −11.2252 −0.382110 −0.191055 0.981579i \(-0.561191\pi\)
−0.191055 + 0.981579i \(0.561191\pi\)
\(864\) 0 0
\(865\) 13.7424 0.467254
\(866\) 0 0
\(867\) −8.99858 −0.305608
\(868\) 0 0
\(869\) −9.53234 −0.323363
\(870\) 0 0
\(871\) 4.54008 0.153835
\(872\) 0 0
\(873\) −9.34373 −0.316237
\(874\) 0 0
\(875\) −23.2514 −0.786039
\(876\) 0 0
\(877\) −26.2023 −0.884789 −0.442395 0.896820i \(-0.645871\pi\)
−0.442395 + 0.896820i \(0.645871\pi\)
\(878\) 0 0
\(879\) −32.6876 −1.10252
\(880\) 0 0
\(881\) −20.8166 −0.701328 −0.350664 0.936501i \(-0.614044\pi\)
−0.350664 + 0.936501i \(0.614044\pi\)
\(882\) 0 0
\(883\) −53.1311 −1.78801 −0.894003 0.448062i \(-0.852114\pi\)
−0.894003 + 0.448062i \(0.852114\pi\)
\(884\) 0 0
\(885\) 7.40251 0.248833
\(886\) 0 0
\(887\) −4.77782 −0.160424 −0.0802118 0.996778i \(-0.525560\pi\)
−0.0802118 + 0.996778i \(0.525560\pi\)
\(888\) 0 0
\(889\) −30.2260 −1.01375
\(890\) 0 0
\(891\) 2.43664 0.0816307
\(892\) 0 0
\(893\) −5.76690 −0.192982
\(894\) 0 0
\(895\) −3.26737 −0.109216
\(896\) 0 0
\(897\) −7.47057 −0.249435
\(898\) 0 0
\(899\) −3.59230 −0.119810
\(900\) 0 0
\(901\) −31.9747 −1.06523
\(902\) 0 0
\(903\) 20.7952 0.692019
\(904\) 0 0
\(905\) 21.8369 0.725885
\(906\) 0 0
\(907\) −10.9101 −0.362264 −0.181132 0.983459i \(-0.557976\pi\)
−0.181132 + 0.983459i \(0.557976\pi\)
\(908\) 0 0
\(909\) 4.77150 0.158261
\(910\) 0 0
\(911\) 17.2073 0.570104 0.285052 0.958512i \(-0.407989\pi\)
0.285052 + 0.958512i \(0.407989\pi\)
\(912\) 0 0
\(913\) −30.5374 −1.01064
\(914\) 0 0
\(915\) 4.16828 0.137799
\(916\) 0 0
\(917\) 37.3414 1.23312
\(918\) 0 0
\(919\) −53.7286 −1.77234 −0.886171 0.463358i \(-0.846644\pi\)
−0.886171 + 0.463358i \(0.846644\pi\)
\(920\) 0 0
\(921\) 14.0085 0.461595
\(922\) 0 0
\(923\) −12.4349 −0.409299
\(924\) 0 0
\(925\) −13.5174 −0.444449
\(926\) 0 0
\(927\) 1.35047 0.0443551
\(928\) 0 0
\(929\) 3.28437 0.107757 0.0538783 0.998548i \(-0.482842\pi\)
0.0538783 + 0.998548i \(0.482842\pi\)
\(930\) 0 0
\(931\) 6.93281 0.227214
\(932\) 0 0
\(933\) −4.23519 −0.138654
\(934\) 0 0
\(935\) 6.08417 0.198974
\(936\) 0 0
\(937\) −3.87143 −0.126474 −0.0632371 0.997999i \(-0.520142\pi\)
−0.0632371 + 0.997999i \(0.520142\pi\)
\(938\) 0 0
\(939\) 31.5070 1.02819
\(940\) 0 0
\(941\) −22.2231 −0.724451 −0.362225 0.932091i \(-0.617983\pi\)
−0.362225 + 0.932091i \(0.617983\pi\)
\(942\) 0 0
\(943\) 8.30164 0.270338
\(944\) 0 0
\(945\) 2.52162 0.0820283
\(946\) 0 0
\(947\) −17.3373 −0.563386 −0.281693 0.959505i \(-0.590896\pi\)
−0.281693 + 0.959505i \(0.590896\pi\)
\(948\) 0 0
\(949\) 22.0439 0.715575
\(950\) 0 0
\(951\) −14.4870 −0.469773
\(952\) 0 0
\(953\) −18.3243 −0.593583 −0.296791 0.954942i \(-0.595917\pi\)
−0.296791 + 0.954942i \(0.595917\pi\)
\(954\) 0 0
\(955\) 11.5559 0.373939
\(956\) 0 0
\(957\) −16.4099 −0.530456
\(958\) 0 0
\(959\) 54.0643 1.74583
\(960\) 0 0
\(961\) −30.7155 −0.990822
\(962\) 0 0
\(963\) 11.8653 0.382354
\(964\) 0 0
\(965\) 5.17102 0.166461
\(966\) 0 0
\(967\) 38.8684 1.24992 0.624962 0.780655i \(-0.285115\pi\)
0.624962 + 0.780655i \(0.285115\pi\)
\(968\) 0 0
\(969\) −16.9007 −0.542930
\(970\) 0 0
\(971\) −35.0772 −1.12568 −0.562841 0.826565i \(-0.690292\pi\)
−0.562841 + 0.826565i \(0.690292\pi\)
\(972\) 0 0
\(973\) −28.1744 −0.903230
\(974\) 0 0
\(975\) −8.12382 −0.260171
\(976\) 0 0
\(977\) 32.6016 1.04302 0.521509 0.853246i \(-0.325369\pi\)
0.521509 + 0.853246i \(0.325369\pi\)
\(978\) 0 0
\(979\) 36.3186 1.16075
\(980\) 0 0
\(981\) −2.24165 −0.0715704
\(982\) 0 0
\(983\) −52.6627 −1.67968 −0.839839 0.542836i \(-0.817351\pi\)
−0.839839 + 0.542836i \(0.817351\pi\)
\(984\) 0 0
\(985\) 11.5870 0.369194
\(986\) 0 0
\(987\) 2.75724 0.0877638
\(988\) 0 0
\(989\) 28.2550 0.898458
\(990\) 0 0
\(991\) −51.9623 −1.65064 −0.825319 0.564667i \(-0.809005\pi\)
−0.825319 + 0.564667i \(0.809005\pi\)
\(992\) 0 0
\(993\) 17.0638 0.541503
\(994\) 0 0
\(995\) 8.31190 0.263505
\(996\) 0 0
\(997\) 47.8628 1.51583 0.757916 0.652353i \(-0.226218\pi\)
0.757916 + 0.652353i \(0.226218\pi\)
\(998\) 0 0
\(999\) 3.20257 0.101325
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 \(a_p\))