Properties

Label 6036.2.a.g.1.2
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 1.2
Root \(-2.82901\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-3.82901 q^{5}\) \(+3.22079 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-3.82901 q^{5}\) \(+3.22079 q^{7}\) \(+1.00000 q^{9}\) \(+3.21987 q^{11}\) \(-3.97711 q^{13}\) \(-3.82901 q^{15}\) \(-2.27833 q^{17}\) \(+0.0375216 q^{19}\) \(+3.22079 q^{21}\) \(+1.29407 q^{23}\) \(+9.66131 q^{25}\) \(+1.00000 q^{27}\) \(-4.68621 q^{29}\) \(-4.65052 q^{31}\) \(+3.21987 q^{33}\) \(-12.3324 q^{35}\) \(-2.10968 q^{37}\) \(-3.97711 q^{39}\) \(-9.37784 q^{41}\) \(+10.1960 q^{43}\) \(-3.82901 q^{45}\) \(-9.03702 q^{47}\) \(+3.37347 q^{49}\) \(-2.27833 q^{51}\) \(-0.602797 q^{53}\) \(-12.3289 q^{55}\) \(+0.0375216 q^{57}\) \(+3.58965 q^{59}\) \(-3.24029 q^{61}\) \(+3.22079 q^{63}\) \(+15.2284 q^{65}\) \(+12.9269 q^{67}\) \(+1.29407 q^{69}\) \(-5.99438 q^{71}\) \(+0.896490 q^{73}\) \(+9.66131 q^{75}\) \(+10.3705 q^{77}\) \(+2.02321 q^{79}\) \(+1.00000 q^{81}\) \(+0.335149 q^{83}\) \(+8.72373 q^{85}\) \(-4.68621 q^{87}\) \(+6.96419 q^{89}\) \(-12.8094 q^{91}\) \(-4.65052 q^{93}\) \(-0.143670 q^{95}\) \(-5.63494 q^{97}\) \(+3.21987 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −3.82901 −1.71239 −0.856193 0.516657i \(-0.827176\pi\)
−0.856193 + 0.516657i \(0.827176\pi\)
\(6\) 0 0
\(7\) 3.22079 1.21734 0.608672 0.793422i \(-0.291703\pi\)
0.608672 + 0.793422i \(0.291703\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.21987 0.970826 0.485413 0.874285i \(-0.338669\pi\)
0.485413 + 0.874285i \(0.338669\pi\)
\(12\) 0 0
\(13\) −3.97711 −1.10305 −0.551526 0.834157i \(-0.685954\pi\)
−0.551526 + 0.834157i \(0.685954\pi\)
\(14\) 0 0
\(15\) −3.82901 −0.988646
\(16\) 0 0
\(17\) −2.27833 −0.552575 −0.276288 0.961075i \(-0.589104\pi\)
−0.276288 + 0.961075i \(0.589104\pi\)
\(18\) 0 0
\(19\) 0.0375216 0.00860804 0.00430402 0.999991i \(-0.498630\pi\)
0.00430402 + 0.999991i \(0.498630\pi\)
\(20\) 0 0
\(21\) 3.22079 0.702834
\(22\) 0 0
\(23\) 1.29407 0.269833 0.134917 0.990857i \(-0.456923\pi\)
0.134917 + 0.990857i \(0.456923\pi\)
\(24\) 0 0
\(25\) 9.66131 1.93226
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.68621 −0.870207 −0.435103 0.900380i \(-0.643288\pi\)
−0.435103 + 0.900380i \(0.643288\pi\)
\(30\) 0 0
\(31\) −4.65052 −0.835258 −0.417629 0.908618i \(-0.637139\pi\)
−0.417629 + 0.908618i \(0.637139\pi\)
\(32\) 0 0
\(33\) 3.21987 0.560507
\(34\) 0 0
\(35\) −12.3324 −2.08456
\(36\) 0 0
\(37\) −2.10968 −0.346830 −0.173415 0.984849i \(-0.555480\pi\)
−0.173415 + 0.984849i \(0.555480\pi\)
\(38\) 0 0
\(39\) −3.97711 −0.636848
\(40\) 0 0
\(41\) −9.37784 −1.46457 −0.732287 0.680997i \(-0.761547\pi\)
−0.732287 + 0.680997i \(0.761547\pi\)
\(42\) 0 0
\(43\) 10.1960 1.55488 0.777439 0.628958i \(-0.216518\pi\)
0.777439 + 0.628958i \(0.216518\pi\)
\(44\) 0 0
\(45\) −3.82901 −0.570795
\(46\) 0 0
\(47\) −9.03702 −1.31819 −0.659093 0.752062i \(-0.729060\pi\)
−0.659093 + 0.752062i \(0.729060\pi\)
\(48\) 0 0
\(49\) 3.37347 0.481925
\(50\) 0 0
\(51\) −2.27833 −0.319029
\(52\) 0 0
\(53\) −0.602797 −0.0828005 −0.0414002 0.999143i \(-0.513182\pi\)
−0.0414002 + 0.999143i \(0.513182\pi\)
\(54\) 0 0
\(55\) −12.3289 −1.66243
\(56\) 0 0
\(57\) 0.0375216 0.00496985
\(58\) 0 0
\(59\) 3.58965 0.467333 0.233667 0.972317i \(-0.424928\pi\)
0.233667 + 0.972317i \(0.424928\pi\)
\(60\) 0 0
\(61\) −3.24029 −0.414876 −0.207438 0.978248i \(-0.566513\pi\)
−0.207438 + 0.978248i \(0.566513\pi\)
\(62\) 0 0
\(63\) 3.22079 0.405781
\(64\) 0 0
\(65\) 15.2284 1.88885
\(66\) 0 0
\(67\) 12.9269 1.57927 0.789635 0.613577i \(-0.210270\pi\)
0.789635 + 0.613577i \(0.210270\pi\)
\(68\) 0 0
\(69\) 1.29407 0.155788
\(70\) 0 0
\(71\) −5.99438 −0.711402 −0.355701 0.934600i \(-0.615758\pi\)
−0.355701 + 0.934600i \(0.615758\pi\)
\(72\) 0 0
\(73\) 0.896490 0.104926 0.0524631 0.998623i \(-0.483293\pi\)
0.0524631 + 0.998623i \(0.483293\pi\)
\(74\) 0 0
\(75\) 9.66131 1.11559
\(76\) 0 0
\(77\) 10.3705 1.18183
\(78\) 0 0
\(79\) 2.02321 0.227629 0.113815 0.993502i \(-0.463693\pi\)
0.113815 + 0.993502i \(0.463693\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.335149 0.0367874 0.0183937 0.999831i \(-0.494145\pi\)
0.0183937 + 0.999831i \(0.494145\pi\)
\(84\) 0 0
\(85\) 8.72373 0.946222
\(86\) 0 0
\(87\) −4.68621 −0.502414
\(88\) 0 0
\(89\) 6.96419 0.738202 0.369101 0.929389i \(-0.379666\pi\)
0.369101 + 0.929389i \(0.379666\pi\)
\(90\) 0 0
\(91\) −12.8094 −1.34279
\(92\) 0 0
\(93\) −4.65052 −0.482236
\(94\) 0 0
\(95\) −0.143670 −0.0147403
\(96\) 0 0
\(97\) −5.63494 −0.572141 −0.286071 0.958209i \(-0.592349\pi\)
−0.286071 + 0.958209i \(0.592349\pi\)
\(98\) 0 0
\(99\) 3.21987 0.323609
\(100\) 0 0
\(101\) 0.592996 0.0590053 0.0295027 0.999565i \(-0.490608\pi\)
0.0295027 + 0.999565i \(0.490608\pi\)
\(102\) 0 0
\(103\) −8.58197 −0.845606 −0.422803 0.906222i \(-0.638954\pi\)
−0.422803 + 0.906222i \(0.638954\pi\)
\(104\) 0 0
\(105\) −12.3324 −1.20352
\(106\) 0 0
\(107\) −16.6553 −1.61013 −0.805064 0.593188i \(-0.797869\pi\)
−0.805064 + 0.593188i \(0.797869\pi\)
\(108\) 0 0
\(109\) 1.60814 0.154032 0.0770159 0.997030i \(-0.475461\pi\)
0.0770159 + 0.997030i \(0.475461\pi\)
\(110\) 0 0
\(111\) −2.10968 −0.200242
\(112\) 0 0
\(113\) 8.30402 0.781176 0.390588 0.920566i \(-0.372272\pi\)
0.390588 + 0.920566i \(0.372272\pi\)
\(114\) 0 0
\(115\) −4.95502 −0.462058
\(116\) 0 0
\(117\) −3.97711 −0.367684
\(118\) 0 0
\(119\) −7.33801 −0.672674
\(120\) 0 0
\(121\) −0.632465 −0.0574968
\(122\) 0 0
\(123\) −9.37784 −0.845572
\(124\) 0 0
\(125\) −17.8482 −1.59639
\(126\) 0 0
\(127\) −8.87450 −0.787484 −0.393742 0.919221i \(-0.628820\pi\)
−0.393742 + 0.919221i \(0.628820\pi\)
\(128\) 0 0
\(129\) 10.1960 0.897709
\(130\) 0 0
\(131\) −7.30235 −0.638009 −0.319005 0.947753i \(-0.603349\pi\)
−0.319005 + 0.947753i \(0.603349\pi\)
\(132\) 0 0
\(133\) 0.120849 0.0104789
\(134\) 0 0
\(135\) −3.82901 −0.329549
\(136\) 0 0
\(137\) −6.64349 −0.567591 −0.283796 0.958885i \(-0.591594\pi\)
−0.283796 + 0.958885i \(0.591594\pi\)
\(138\) 0 0
\(139\) −1.58350 −0.134311 −0.0671554 0.997743i \(-0.521392\pi\)
−0.0671554 + 0.997743i \(0.521392\pi\)
\(140\) 0 0
\(141\) −9.03702 −0.761055
\(142\) 0 0
\(143\) −12.8058 −1.07087
\(144\) 0 0
\(145\) 17.9435 1.49013
\(146\) 0 0
\(147\) 3.37347 0.278239
\(148\) 0 0
\(149\) 10.1028 0.827657 0.413829 0.910355i \(-0.364191\pi\)
0.413829 + 0.910355i \(0.364191\pi\)
\(150\) 0 0
\(151\) −1.88225 −0.153175 −0.0765875 0.997063i \(-0.524402\pi\)
−0.0765875 + 0.997063i \(0.524402\pi\)
\(152\) 0 0
\(153\) −2.27833 −0.184192
\(154\) 0 0
\(155\) 17.8069 1.43028
\(156\) 0 0
\(157\) −18.9549 −1.51276 −0.756381 0.654131i \(-0.773035\pi\)
−0.756381 + 0.654131i \(0.773035\pi\)
\(158\) 0 0
\(159\) −0.602797 −0.0478049
\(160\) 0 0
\(161\) 4.16794 0.328479
\(162\) 0 0
\(163\) −14.5057 −1.13617 −0.568086 0.822969i \(-0.692316\pi\)
−0.568086 + 0.822969i \(0.692316\pi\)
\(164\) 0 0
\(165\) −12.3289 −0.959803
\(166\) 0 0
\(167\) −20.4075 −1.57918 −0.789589 0.613636i \(-0.789706\pi\)
−0.789589 + 0.613636i \(0.789706\pi\)
\(168\) 0 0
\(169\) 2.81743 0.216725
\(170\) 0 0
\(171\) 0.0375216 0.00286935
\(172\) 0 0
\(173\) 5.65867 0.430221 0.215110 0.976590i \(-0.430989\pi\)
0.215110 + 0.976590i \(0.430989\pi\)
\(174\) 0 0
\(175\) 31.1170 2.35223
\(176\) 0 0
\(177\) 3.58965 0.269815
\(178\) 0 0
\(179\) 1.95966 0.146472 0.0732359 0.997315i \(-0.476667\pi\)
0.0732359 + 0.997315i \(0.476667\pi\)
\(180\) 0 0
\(181\) 14.2761 1.06113 0.530566 0.847644i \(-0.321980\pi\)
0.530566 + 0.847644i \(0.321980\pi\)
\(182\) 0 0
\(183\) −3.24029 −0.239529
\(184\) 0 0
\(185\) 8.07799 0.593906
\(186\) 0 0
\(187\) −7.33590 −0.536454
\(188\) 0 0
\(189\) 3.22079 0.234278
\(190\) 0 0
\(191\) −8.14830 −0.589590 −0.294795 0.955560i \(-0.595251\pi\)
−0.294795 + 0.955560i \(0.595251\pi\)
\(192\) 0 0
\(193\) 3.89931 0.280679 0.140339 0.990103i \(-0.455181\pi\)
0.140339 + 0.990103i \(0.455181\pi\)
\(194\) 0 0
\(195\) 15.2284 1.09053
\(196\) 0 0
\(197\) −2.27571 −0.162138 −0.0810690 0.996708i \(-0.525833\pi\)
−0.0810690 + 0.996708i \(0.525833\pi\)
\(198\) 0 0
\(199\) −1.79134 −0.126984 −0.0634922 0.997982i \(-0.520224\pi\)
−0.0634922 + 0.997982i \(0.520224\pi\)
\(200\) 0 0
\(201\) 12.9269 0.911792
\(202\) 0 0
\(203\) −15.0933 −1.05934
\(204\) 0 0
\(205\) 35.9078 2.50791
\(206\) 0 0
\(207\) 1.29407 0.0899443
\(208\) 0 0
\(209\) 0.120814 0.00835691
\(210\) 0 0
\(211\) 7.37064 0.507416 0.253708 0.967281i \(-0.418350\pi\)
0.253708 + 0.967281i \(0.418350\pi\)
\(212\) 0 0
\(213\) −5.99438 −0.410728
\(214\) 0 0
\(215\) −39.0406 −2.66255
\(216\) 0 0
\(217\) −14.9783 −1.01680
\(218\) 0 0
\(219\) 0.896490 0.0605792
\(220\) 0 0
\(221\) 9.06116 0.609520
\(222\) 0 0
\(223\) −5.17257 −0.346381 −0.173191 0.984888i \(-0.555408\pi\)
−0.173191 + 0.984888i \(0.555408\pi\)
\(224\) 0 0
\(225\) 9.66131 0.644088
\(226\) 0 0
\(227\) −19.4401 −1.29028 −0.645142 0.764063i \(-0.723202\pi\)
−0.645142 + 0.764063i \(0.723202\pi\)
\(228\) 0 0
\(229\) 1.94619 0.128608 0.0643040 0.997930i \(-0.479517\pi\)
0.0643040 + 0.997930i \(0.479517\pi\)
\(230\) 0 0
\(231\) 10.3705 0.682329
\(232\) 0 0
\(233\) −17.0762 −1.11870 −0.559348 0.828933i \(-0.688949\pi\)
−0.559348 + 0.828933i \(0.688949\pi\)
\(234\) 0 0
\(235\) 34.6028 2.25724
\(236\) 0 0
\(237\) 2.02321 0.131422
\(238\) 0 0
\(239\) −23.2634 −1.50478 −0.752391 0.658717i \(-0.771099\pi\)
−0.752391 + 0.658717i \(0.771099\pi\)
\(240\) 0 0
\(241\) −0.733843 −0.0472710 −0.0236355 0.999721i \(-0.507524\pi\)
−0.0236355 + 0.999721i \(0.507524\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −12.9171 −0.825241
\(246\) 0 0
\(247\) −0.149228 −0.00949512
\(248\) 0 0
\(249\) 0.335149 0.0212392
\(250\) 0 0
\(251\) −20.4878 −1.29318 −0.646590 0.762837i \(-0.723806\pi\)
−0.646590 + 0.762837i \(0.723806\pi\)
\(252\) 0 0
\(253\) 4.16674 0.261961
\(254\) 0 0
\(255\) 8.72373 0.546301
\(256\) 0 0
\(257\) 22.6875 1.41521 0.707604 0.706610i \(-0.249776\pi\)
0.707604 + 0.706610i \(0.249776\pi\)
\(258\) 0 0
\(259\) −6.79484 −0.422211
\(260\) 0 0
\(261\) −4.68621 −0.290069
\(262\) 0 0
\(263\) −17.5337 −1.08117 −0.540586 0.841289i \(-0.681797\pi\)
−0.540586 + 0.841289i \(0.681797\pi\)
\(264\) 0 0
\(265\) 2.30811 0.141786
\(266\) 0 0
\(267\) 6.96419 0.426201
\(268\) 0 0
\(269\) −22.2240 −1.35502 −0.677511 0.735513i \(-0.736941\pi\)
−0.677511 + 0.735513i \(0.736941\pi\)
\(270\) 0 0
\(271\) 26.9483 1.63699 0.818495 0.574513i \(-0.194809\pi\)
0.818495 + 0.574513i \(0.194809\pi\)
\(272\) 0 0
\(273\) −12.8094 −0.775262
\(274\) 0 0
\(275\) 31.1081 1.87589
\(276\) 0 0
\(277\) 19.2086 1.15413 0.577067 0.816697i \(-0.304197\pi\)
0.577067 + 0.816697i \(0.304197\pi\)
\(278\) 0 0
\(279\) −4.65052 −0.278419
\(280\) 0 0
\(281\) −12.1438 −0.724437 −0.362218 0.932093i \(-0.617980\pi\)
−0.362218 + 0.932093i \(0.617980\pi\)
\(282\) 0 0
\(283\) −29.3348 −1.74377 −0.871887 0.489708i \(-0.837103\pi\)
−0.871887 + 0.489708i \(0.837103\pi\)
\(284\) 0 0
\(285\) −0.143670 −0.00851030
\(286\) 0 0
\(287\) −30.2040 −1.78289
\(288\) 0 0
\(289\) −11.8092 −0.694661
\(290\) 0 0
\(291\) −5.63494 −0.330326
\(292\) 0 0
\(293\) −7.09482 −0.414484 −0.207242 0.978290i \(-0.566449\pi\)
−0.207242 + 0.978290i \(0.566449\pi\)
\(294\) 0 0
\(295\) −13.7448 −0.800254
\(296\) 0 0
\(297\) 3.21987 0.186836
\(298\) 0 0
\(299\) −5.14668 −0.297640
\(300\) 0 0
\(301\) 32.8392 1.89282
\(302\) 0 0
\(303\) 0.592996 0.0340668
\(304\) 0 0
\(305\) 12.4071 0.710428
\(306\) 0 0
\(307\) 13.6465 0.778847 0.389424 0.921059i \(-0.372674\pi\)
0.389424 + 0.921059i \(0.372674\pi\)
\(308\) 0 0
\(309\) −8.58197 −0.488211
\(310\) 0 0
\(311\) 16.9544 0.961396 0.480698 0.876886i \(-0.340383\pi\)
0.480698 + 0.876886i \(0.340383\pi\)
\(312\) 0 0
\(313\) −24.9576 −1.41068 −0.705342 0.708867i \(-0.749207\pi\)
−0.705342 + 0.708867i \(0.749207\pi\)
\(314\) 0 0
\(315\) −12.3324 −0.694854
\(316\) 0 0
\(317\) 27.4120 1.53961 0.769807 0.638277i \(-0.220352\pi\)
0.769807 + 0.638277i \(0.220352\pi\)
\(318\) 0 0
\(319\) −15.0890 −0.844819
\(320\) 0 0
\(321\) −16.6553 −0.929608
\(322\) 0 0
\(323\) −0.0854864 −0.00475659
\(324\) 0 0
\(325\) −38.4241 −2.13139
\(326\) 0 0
\(327\) 1.60814 0.0889303
\(328\) 0 0
\(329\) −29.1063 −1.60468
\(330\) 0 0
\(331\) 24.5608 1.34999 0.674993 0.737824i \(-0.264147\pi\)
0.674993 + 0.737824i \(0.264147\pi\)
\(332\) 0 0
\(333\) −2.10968 −0.115610
\(334\) 0 0
\(335\) −49.4972 −2.70432
\(336\) 0 0
\(337\) 5.00301 0.272531 0.136266 0.990672i \(-0.456490\pi\)
0.136266 + 0.990672i \(0.456490\pi\)
\(338\) 0 0
\(339\) 8.30402 0.451012
\(340\) 0 0
\(341\) −14.9741 −0.810890
\(342\) 0 0
\(343\) −11.6803 −0.630675
\(344\) 0 0
\(345\) −4.95502 −0.266769
\(346\) 0 0
\(347\) 6.16120 0.330751 0.165375 0.986231i \(-0.447116\pi\)
0.165375 + 0.986231i \(0.447116\pi\)
\(348\) 0 0
\(349\) −14.7991 −0.792179 −0.396089 0.918212i \(-0.629633\pi\)
−0.396089 + 0.918212i \(0.629633\pi\)
\(350\) 0 0
\(351\) −3.97711 −0.212283
\(352\) 0 0
\(353\) −10.9374 −0.582139 −0.291069 0.956702i \(-0.594011\pi\)
−0.291069 + 0.956702i \(0.594011\pi\)
\(354\) 0 0
\(355\) 22.9525 1.21819
\(356\) 0 0
\(357\) −7.33801 −0.388368
\(358\) 0 0
\(359\) −11.1133 −0.586537 −0.293269 0.956030i \(-0.594743\pi\)
−0.293269 + 0.956030i \(0.594743\pi\)
\(360\) 0 0
\(361\) −18.9986 −0.999926
\(362\) 0 0
\(363\) −0.632465 −0.0331958
\(364\) 0 0
\(365\) −3.43267 −0.179674
\(366\) 0 0
\(367\) 7.37225 0.384828 0.192414 0.981314i \(-0.438368\pi\)
0.192414 + 0.981314i \(0.438368\pi\)
\(368\) 0 0
\(369\) −9.37784 −0.488191
\(370\) 0 0
\(371\) −1.94148 −0.100797
\(372\) 0 0
\(373\) 31.2641 1.61879 0.809396 0.587263i \(-0.199795\pi\)
0.809396 + 0.587263i \(0.199795\pi\)
\(374\) 0 0
\(375\) −17.8482 −0.921678
\(376\) 0 0
\(377\) 18.6376 0.959884
\(378\) 0 0
\(379\) −25.1947 −1.29417 −0.647083 0.762420i \(-0.724011\pi\)
−0.647083 + 0.762420i \(0.724011\pi\)
\(380\) 0 0
\(381\) −8.87450 −0.454654
\(382\) 0 0
\(383\) 7.95689 0.406578 0.203289 0.979119i \(-0.434837\pi\)
0.203289 + 0.979119i \(0.434837\pi\)
\(384\) 0 0
\(385\) −39.7088 −2.02375
\(386\) 0 0
\(387\) 10.1960 0.518293
\(388\) 0 0
\(389\) −30.9458 −1.56902 −0.784508 0.620119i \(-0.787084\pi\)
−0.784508 + 0.620119i \(0.787084\pi\)
\(390\) 0 0
\(391\) −2.94832 −0.149103
\(392\) 0 0
\(393\) −7.30235 −0.368355
\(394\) 0 0
\(395\) −7.74690 −0.389789
\(396\) 0 0
\(397\) 2.32846 0.116862 0.0584310 0.998291i \(-0.481390\pi\)
0.0584310 + 0.998291i \(0.481390\pi\)
\(398\) 0 0
\(399\) 0.120849 0.00605002
\(400\) 0 0
\(401\) −17.3526 −0.866548 −0.433274 0.901262i \(-0.642642\pi\)
−0.433274 + 0.901262i \(0.642642\pi\)
\(402\) 0 0
\(403\) 18.4956 0.921334
\(404\) 0 0
\(405\) −3.82901 −0.190265
\(406\) 0 0
\(407\) −6.79289 −0.336711
\(408\) 0 0
\(409\) 4.41439 0.218277 0.109139 0.994027i \(-0.465191\pi\)
0.109139 + 0.994027i \(0.465191\pi\)
\(410\) 0 0
\(411\) −6.64349 −0.327699
\(412\) 0 0
\(413\) 11.5615 0.568905
\(414\) 0 0
\(415\) −1.28329 −0.0629943
\(416\) 0 0
\(417\) −1.58350 −0.0775444
\(418\) 0 0
\(419\) 11.6874 0.570966 0.285483 0.958384i \(-0.407846\pi\)
0.285483 + 0.958384i \(0.407846\pi\)
\(420\) 0 0
\(421\) −14.5203 −0.707677 −0.353839 0.935306i \(-0.615124\pi\)
−0.353839 + 0.935306i \(0.615124\pi\)
\(422\) 0 0
\(423\) −9.03702 −0.439395
\(424\) 0 0
\(425\) −22.0116 −1.06772
\(426\) 0 0
\(427\) −10.4363 −0.505047
\(428\) 0 0
\(429\) −12.8058 −0.618268
\(430\) 0 0
\(431\) −30.8625 −1.48659 −0.743297 0.668961i \(-0.766739\pi\)
−0.743297 + 0.668961i \(0.766739\pi\)
\(432\) 0 0
\(433\) −12.6824 −0.609478 −0.304739 0.952436i \(-0.598569\pi\)
−0.304739 + 0.952436i \(0.598569\pi\)
\(434\) 0 0
\(435\) 17.9435 0.860327
\(436\) 0 0
\(437\) 0.0485557 0.00232273
\(438\) 0 0
\(439\) −8.87354 −0.423511 −0.211756 0.977323i \(-0.567918\pi\)
−0.211756 + 0.977323i \(0.567918\pi\)
\(440\) 0 0
\(441\) 3.37347 0.160642
\(442\) 0 0
\(443\) −13.0293 −0.619041 −0.309521 0.950893i \(-0.600169\pi\)
−0.309521 + 0.950893i \(0.600169\pi\)
\(444\) 0 0
\(445\) −26.6659 −1.26409
\(446\) 0 0
\(447\) 10.1028 0.477848
\(448\) 0 0
\(449\) 1.23414 0.0582426 0.0291213 0.999576i \(-0.490729\pi\)
0.0291213 + 0.999576i \(0.490729\pi\)
\(450\) 0 0
\(451\) −30.1954 −1.42185
\(452\) 0 0
\(453\) −1.88225 −0.0884356
\(454\) 0 0
\(455\) 49.0475 2.29938
\(456\) 0 0
\(457\) 24.2156 1.13276 0.566378 0.824145i \(-0.308344\pi\)
0.566378 + 0.824145i \(0.308344\pi\)
\(458\) 0 0
\(459\) −2.27833 −0.106343
\(460\) 0 0
\(461\) −36.8704 −1.71723 −0.858613 0.512624i \(-0.828674\pi\)
−0.858613 + 0.512624i \(0.828674\pi\)
\(462\) 0 0
\(463\) 0.800018 0.0371800 0.0185900 0.999827i \(-0.494082\pi\)
0.0185900 + 0.999827i \(0.494082\pi\)
\(464\) 0 0
\(465\) 17.8069 0.825775
\(466\) 0 0
\(467\) −7.63578 −0.353342 −0.176671 0.984270i \(-0.556533\pi\)
−0.176671 + 0.984270i \(0.556533\pi\)
\(468\) 0 0
\(469\) 41.6348 1.92251
\(470\) 0 0
\(471\) −18.9549 −0.873394
\(472\) 0 0
\(473\) 32.8298 1.50952
\(474\) 0 0
\(475\) 0.362508 0.0166330
\(476\) 0 0
\(477\) −0.602797 −0.0276002
\(478\) 0 0
\(479\) 40.3555 1.84389 0.921945 0.387321i \(-0.126600\pi\)
0.921945 + 0.387321i \(0.126600\pi\)
\(480\) 0 0
\(481\) 8.39045 0.382571
\(482\) 0 0
\(483\) 4.16794 0.189648
\(484\) 0 0
\(485\) 21.5762 0.979726
\(486\) 0 0
\(487\) 24.7958 1.12361 0.561803 0.827271i \(-0.310108\pi\)
0.561803 + 0.827271i \(0.310108\pi\)
\(488\) 0 0
\(489\) −14.5057 −0.655970
\(490\) 0 0
\(491\) 37.3416 1.68520 0.842602 0.538537i \(-0.181023\pi\)
0.842602 + 0.538537i \(0.181023\pi\)
\(492\) 0 0
\(493\) 10.6767 0.480855
\(494\) 0 0
\(495\) −12.3289 −0.554143
\(496\) 0 0
\(497\) −19.3066 −0.866021
\(498\) 0 0
\(499\) 26.9940 1.20842 0.604208 0.796827i \(-0.293490\pi\)
0.604208 + 0.796827i \(0.293490\pi\)
\(500\) 0 0
\(501\) −20.4075 −0.911739
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −2.27059 −0.101040
\(506\) 0 0
\(507\) 2.81743 0.125127
\(508\) 0 0
\(509\) 16.8694 0.747725 0.373863 0.927484i \(-0.378033\pi\)
0.373863 + 0.927484i \(0.378033\pi\)
\(510\) 0 0
\(511\) 2.88741 0.127731
\(512\) 0 0
\(513\) 0.0375216 0.00165662
\(514\) 0 0
\(515\) 32.8604 1.44800
\(516\) 0 0
\(517\) −29.0980 −1.27973
\(518\) 0 0
\(519\) 5.65867 0.248388
\(520\) 0 0
\(521\) 13.9325 0.610393 0.305196 0.952289i \(-0.401278\pi\)
0.305196 + 0.952289i \(0.401278\pi\)
\(522\) 0 0
\(523\) −34.5959 −1.51277 −0.756387 0.654124i \(-0.773037\pi\)
−0.756387 + 0.654124i \(0.773037\pi\)
\(524\) 0 0
\(525\) 31.1170 1.35806
\(526\) 0 0
\(527\) 10.5954 0.461543
\(528\) 0 0
\(529\) −21.3254 −0.927190
\(530\) 0 0
\(531\) 3.58965 0.155778
\(532\) 0 0
\(533\) 37.2967 1.61550
\(534\) 0 0
\(535\) 63.7733 2.75716
\(536\) 0 0
\(537\) 1.95966 0.0845656
\(538\) 0 0
\(539\) 10.8621 0.467865
\(540\) 0 0
\(541\) 36.4723 1.56807 0.784034 0.620717i \(-0.213159\pi\)
0.784034 + 0.620717i \(0.213159\pi\)
\(542\) 0 0
\(543\) 14.2761 0.612644
\(544\) 0 0
\(545\) −6.15758 −0.263762
\(546\) 0 0
\(547\) 21.4727 0.918107 0.459053 0.888409i \(-0.348189\pi\)
0.459053 + 0.888409i \(0.348189\pi\)
\(548\) 0 0
\(549\) −3.24029 −0.138292
\(550\) 0 0
\(551\) −0.175834 −0.00749077
\(552\) 0 0
\(553\) 6.51634 0.277103
\(554\) 0 0
\(555\) 8.07799 0.342892
\(556\) 0 0
\(557\) 9.72148 0.411913 0.205956 0.978561i \(-0.433970\pi\)
0.205956 + 0.978561i \(0.433970\pi\)
\(558\) 0 0
\(559\) −40.5507 −1.71511
\(560\) 0 0
\(561\) −7.33590 −0.309722
\(562\) 0 0
\(563\) 21.5040 0.906285 0.453142 0.891438i \(-0.350303\pi\)
0.453142 + 0.891438i \(0.350303\pi\)
\(564\) 0 0
\(565\) −31.7962 −1.33767
\(566\) 0 0
\(567\) 3.22079 0.135260
\(568\) 0 0
\(569\) −31.1471 −1.30576 −0.652878 0.757463i \(-0.726439\pi\)
−0.652878 + 0.757463i \(0.726439\pi\)
\(570\) 0 0
\(571\) 30.5954 1.28038 0.640189 0.768218i \(-0.278856\pi\)
0.640189 + 0.768218i \(0.278856\pi\)
\(572\) 0 0
\(573\) −8.14830 −0.340400
\(574\) 0 0
\(575\) 12.5025 0.521388
\(576\) 0 0
\(577\) 19.3581 0.805887 0.402943 0.915225i \(-0.367987\pi\)
0.402943 + 0.915225i \(0.367987\pi\)
\(578\) 0 0
\(579\) 3.89931 0.162050
\(580\) 0 0
\(581\) 1.07945 0.0447829
\(582\) 0 0
\(583\) −1.94092 −0.0803849
\(584\) 0 0
\(585\) 15.2284 0.629617
\(586\) 0 0
\(587\) 5.16337 0.213115 0.106557 0.994307i \(-0.466017\pi\)
0.106557 + 0.994307i \(0.466017\pi\)
\(588\) 0 0
\(589\) −0.174495 −0.00718993
\(590\) 0 0
\(591\) −2.27571 −0.0936104
\(592\) 0 0
\(593\) −15.7080 −0.645052 −0.322526 0.946561i \(-0.604532\pi\)
−0.322526 + 0.946561i \(0.604532\pi\)
\(594\) 0 0
\(595\) 28.0973 1.15188
\(596\) 0 0
\(597\) −1.79134 −0.0733145
\(598\) 0 0
\(599\) 15.2564 0.623360 0.311680 0.950187i \(-0.399108\pi\)
0.311680 + 0.950187i \(0.399108\pi\)
\(600\) 0 0
\(601\) 7.48881 0.305475 0.152738 0.988267i \(-0.451191\pi\)
0.152738 + 0.988267i \(0.451191\pi\)
\(602\) 0 0
\(603\) 12.9269 0.526424
\(604\) 0 0
\(605\) 2.42171 0.0984566
\(606\) 0 0
\(607\) 6.86764 0.278749 0.139374 0.990240i \(-0.455491\pi\)
0.139374 + 0.990240i \(0.455491\pi\)
\(608\) 0 0
\(609\) −15.0933 −0.611611
\(610\) 0 0
\(611\) 35.9413 1.45403
\(612\) 0 0
\(613\) 5.68794 0.229734 0.114867 0.993381i \(-0.463356\pi\)
0.114867 + 0.993381i \(0.463356\pi\)
\(614\) 0 0
\(615\) 35.9078 1.44794
\(616\) 0 0
\(617\) 16.5248 0.665263 0.332632 0.943057i \(-0.392063\pi\)
0.332632 + 0.943057i \(0.392063\pi\)
\(618\) 0 0
\(619\) −32.3812 −1.30151 −0.650756 0.759287i \(-0.725548\pi\)
−0.650756 + 0.759287i \(0.725548\pi\)
\(620\) 0 0
\(621\) 1.29407 0.0519294
\(622\) 0 0
\(623\) 22.4302 0.898646
\(624\) 0 0
\(625\) 20.0344 0.801377
\(626\) 0 0
\(627\) 0.120814 0.00482486
\(628\) 0 0
\(629\) 4.80654 0.191649
\(630\) 0 0
\(631\) −5.33380 −0.212335 −0.106168 0.994348i \(-0.533858\pi\)
−0.106168 + 0.994348i \(0.533858\pi\)
\(632\) 0 0
\(633\) 7.37064 0.292957
\(634\) 0 0
\(635\) 33.9805 1.34848
\(636\) 0 0
\(637\) −13.4167 −0.531589
\(638\) 0 0
\(639\) −5.99438 −0.237134
\(640\) 0 0
\(641\) −0.285022 −0.0112577 −0.00562885 0.999984i \(-0.501792\pi\)
−0.00562885 + 0.999984i \(0.501792\pi\)
\(642\) 0 0
\(643\) 12.1657 0.479767 0.239883 0.970802i \(-0.422891\pi\)
0.239883 + 0.970802i \(0.422891\pi\)
\(644\) 0 0
\(645\) −39.0406 −1.53722
\(646\) 0 0
\(647\) 1.95350 0.0767999 0.0383999 0.999262i \(-0.487774\pi\)
0.0383999 + 0.999262i \(0.487774\pi\)
\(648\) 0 0
\(649\) 11.5582 0.453699
\(650\) 0 0
\(651\) −14.9783 −0.587047
\(652\) 0 0
\(653\) −4.87297 −0.190694 −0.0953471 0.995444i \(-0.530396\pi\)
−0.0953471 + 0.995444i \(0.530396\pi\)
\(654\) 0 0
\(655\) 27.9608 1.09252
\(656\) 0 0
\(657\) 0.896490 0.0349754
\(658\) 0 0
\(659\) −18.8365 −0.733764 −0.366882 0.930267i \(-0.619575\pi\)
−0.366882 + 0.930267i \(0.619575\pi\)
\(660\) 0 0
\(661\) 0.228625 0.00889248 0.00444624 0.999990i \(-0.498585\pi\)
0.00444624 + 0.999990i \(0.498585\pi\)
\(662\) 0 0
\(663\) 9.06116 0.351906
\(664\) 0 0
\(665\) −0.462732 −0.0179440
\(666\) 0 0
\(667\) −6.06430 −0.234811
\(668\) 0 0
\(669\) −5.17257 −0.199983
\(670\) 0 0
\(671\) −10.4333 −0.402773
\(672\) 0 0
\(673\) −27.4630 −1.05862 −0.529310 0.848428i \(-0.677549\pi\)
−0.529310 + 0.848428i \(0.677549\pi\)
\(674\) 0 0
\(675\) 9.66131 0.371864
\(676\) 0 0
\(677\) 9.07694 0.348855 0.174428 0.984670i \(-0.444192\pi\)
0.174428 + 0.984670i \(0.444192\pi\)
\(678\) 0 0
\(679\) −18.1489 −0.696492
\(680\) 0 0
\(681\) −19.4401 −0.744946
\(682\) 0 0
\(683\) −32.5554 −1.24570 −0.622849 0.782342i \(-0.714025\pi\)
−0.622849 + 0.782342i \(0.714025\pi\)
\(684\) 0 0
\(685\) 25.4380 0.971935
\(686\) 0 0
\(687\) 1.94619 0.0742518
\(688\) 0 0
\(689\) 2.39739 0.0913333
\(690\) 0 0
\(691\) 34.6163 1.31687 0.658434 0.752639i \(-0.271219\pi\)
0.658434 + 0.752639i \(0.271219\pi\)
\(692\) 0 0
\(693\) 10.3705 0.393943
\(694\) 0 0
\(695\) 6.06324 0.229992
\(696\) 0 0
\(697\) 21.3658 0.809287
\(698\) 0 0
\(699\) −17.0762 −0.645880
\(700\) 0 0
\(701\) 10.3569 0.391175 0.195588 0.980686i \(-0.437339\pi\)
0.195588 + 0.980686i \(0.437339\pi\)
\(702\) 0 0
\(703\) −0.0791586 −0.00298552
\(704\) 0 0
\(705\) 34.6028 1.30322
\(706\) 0 0
\(707\) 1.90992 0.0718298
\(708\) 0 0
\(709\) 42.4567 1.59450 0.797248 0.603652i \(-0.206288\pi\)
0.797248 + 0.603652i \(0.206288\pi\)
\(710\) 0 0
\(711\) 2.02321 0.0758764
\(712\) 0 0
\(713\) −6.01812 −0.225380
\(714\) 0 0
\(715\) 49.0334 1.83375
\(716\) 0 0
\(717\) −23.2634 −0.868786
\(718\) 0 0
\(719\) −7.08423 −0.264197 −0.132099 0.991237i \(-0.542172\pi\)
−0.132099 + 0.991237i \(0.542172\pi\)
\(720\) 0 0
\(721\) −27.6407 −1.02939
\(722\) 0 0
\(723\) −0.733843 −0.0272919
\(724\) 0 0
\(725\) −45.2749 −1.68147
\(726\) 0 0
\(727\) −35.8391 −1.32920 −0.664599 0.747200i \(-0.731398\pi\)
−0.664599 + 0.747200i \(0.731398\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −23.2299 −0.859187
\(732\) 0 0
\(733\) −8.06411 −0.297855 −0.148927 0.988848i \(-0.547582\pi\)
−0.148927 + 0.988848i \(0.547582\pi\)
\(734\) 0 0
\(735\) −12.9171 −0.476453
\(736\) 0 0
\(737\) 41.6228 1.53320
\(738\) 0 0
\(739\) −34.5458 −1.27079 −0.635394 0.772188i \(-0.719162\pi\)
−0.635394 + 0.772188i \(0.719162\pi\)
\(740\) 0 0
\(741\) −0.149228 −0.00548201
\(742\) 0 0
\(743\) −1.99681 −0.0732560 −0.0366280 0.999329i \(-0.511662\pi\)
−0.0366280 + 0.999329i \(0.511662\pi\)
\(744\) 0 0
\(745\) −38.6839 −1.41727
\(746\) 0 0
\(747\) 0.335149 0.0122625
\(748\) 0 0
\(749\) −53.6432 −1.96008
\(750\) 0 0
\(751\) 16.4344 0.599701 0.299851 0.953986i \(-0.403063\pi\)
0.299851 + 0.953986i \(0.403063\pi\)
\(752\) 0 0
\(753\) −20.4878 −0.746618
\(754\) 0 0
\(755\) 7.20714 0.262295
\(756\) 0 0
\(757\) 8.36051 0.303868 0.151934 0.988391i \(-0.451450\pi\)
0.151934 + 0.988391i \(0.451450\pi\)
\(758\) 0 0
\(759\) 4.16674 0.151243
\(760\) 0 0
\(761\) 36.3653 1.31824 0.659121 0.752037i \(-0.270929\pi\)
0.659121 + 0.752037i \(0.270929\pi\)
\(762\) 0 0
\(763\) 5.17947 0.187510
\(764\) 0 0
\(765\) 8.72373 0.315407
\(766\) 0 0
\(767\) −14.2765 −0.515493
\(768\) 0 0
\(769\) −29.9736 −1.08088 −0.540438 0.841384i \(-0.681742\pi\)
−0.540438 + 0.841384i \(0.681742\pi\)
\(770\) 0 0
\(771\) 22.6875 0.817070
\(772\) 0 0
\(773\) −3.71052 −0.133458 −0.0667291 0.997771i \(-0.521256\pi\)
−0.0667291 + 0.997771i \(0.521256\pi\)
\(774\) 0 0
\(775\) −44.9301 −1.61394
\(776\) 0 0
\(777\) −6.79484 −0.243764
\(778\) 0 0
\(779\) −0.351871 −0.0126071
\(780\) 0 0
\(781\) −19.3011 −0.690648
\(782\) 0 0
\(783\) −4.68621 −0.167471
\(784\) 0 0
\(785\) 72.5784 2.59043
\(786\) 0 0
\(787\) 25.1808 0.897599 0.448800 0.893632i \(-0.351852\pi\)
0.448800 + 0.893632i \(0.351852\pi\)
\(788\) 0 0
\(789\) −17.5337 −0.624215
\(790\) 0 0
\(791\) 26.7455 0.950960
\(792\) 0 0
\(793\) 12.8870 0.457630
\(794\) 0 0
\(795\) 2.30811 0.0818604
\(796\) 0 0
\(797\) −28.7617 −1.01879 −0.509396 0.860532i \(-0.670131\pi\)
−0.509396 + 0.860532i \(0.670131\pi\)
\(798\) 0 0
\(799\) 20.5893 0.728397
\(800\) 0 0
\(801\) 6.96419 0.246067
\(802\) 0 0
\(803\) 2.88658 0.101865
\(804\) 0 0
\(805\) −15.9591 −0.562483
\(806\) 0 0
\(807\) −22.2240 −0.782322
\(808\) 0 0
\(809\) 19.2338 0.676224 0.338112 0.941106i \(-0.390212\pi\)
0.338112 + 0.941106i \(0.390212\pi\)
\(810\) 0 0
\(811\) 50.6302 1.77787 0.888933 0.458037i \(-0.151447\pi\)
0.888933 + 0.458037i \(0.151447\pi\)
\(812\) 0 0
\(813\) 26.9483 0.945117
\(814\) 0 0
\(815\) 55.5424 1.94557
\(816\) 0 0
\(817\) 0.382571 0.0133844
\(818\) 0 0
\(819\) −12.8094 −0.447598
\(820\) 0 0
\(821\) 50.7685 1.77183 0.885916 0.463846i \(-0.153531\pi\)
0.885916 + 0.463846i \(0.153531\pi\)
\(822\) 0 0
\(823\) −14.6603 −0.511026 −0.255513 0.966806i \(-0.582244\pi\)
−0.255513 + 0.966806i \(0.582244\pi\)
\(824\) 0 0
\(825\) 31.1081 1.08305
\(826\) 0 0
\(827\) −11.0548 −0.384413 −0.192206 0.981355i \(-0.561564\pi\)
−0.192206 + 0.981355i \(0.561564\pi\)
\(828\) 0 0
\(829\) −35.6993 −1.23989 −0.619943 0.784647i \(-0.712844\pi\)
−0.619943 + 0.784647i \(0.712844\pi\)
\(830\) 0 0
\(831\) 19.2086 0.666339
\(832\) 0 0
\(833\) −7.68588 −0.266300
\(834\) 0 0
\(835\) 78.1404 2.70416
\(836\) 0 0
\(837\) −4.65052 −0.160745
\(838\) 0 0
\(839\) 4.10974 0.141884 0.0709420 0.997480i \(-0.477399\pi\)
0.0709420 + 0.997480i \(0.477399\pi\)
\(840\) 0 0
\(841\) −7.03946 −0.242740
\(842\) 0 0
\(843\) −12.1438 −0.418254
\(844\) 0 0
\(845\) −10.7880 −0.371117
\(846\) 0 0
\(847\) −2.03703 −0.0699933
\(848\) 0 0
\(849\) −29.3348 −1.00677
\(850\) 0 0
\(851\) −2.73008 −0.0935861
\(852\) 0 0
\(853\) −28.7630 −0.984827 −0.492413 0.870361i \(-0.663885\pi\)
−0.492413 + 0.870361i \(0.663885\pi\)
\(854\) 0 0
\(855\) −0.143670 −0.00491343
\(856\) 0 0
\(857\) 41.5457 1.41917 0.709587 0.704618i \(-0.248882\pi\)
0.709587 + 0.704618i \(0.248882\pi\)
\(858\) 0 0
\(859\) −31.6333 −1.07931 −0.539657 0.841885i \(-0.681446\pi\)
−0.539657 + 0.841885i \(0.681446\pi\)
\(860\) 0 0
\(861\) −30.2040 −1.02935
\(862\) 0 0
\(863\) 38.0934 1.29672 0.648358 0.761336i \(-0.275456\pi\)
0.648358 + 0.761336i \(0.275456\pi\)
\(864\) 0 0
\(865\) −21.6671 −0.736704
\(866\) 0 0
\(867\) −11.8092 −0.401062
\(868\) 0 0
\(869\) 6.51448 0.220988
\(870\) 0 0
\(871\) −51.4117 −1.74202
\(872\) 0 0
\(873\) −5.63494 −0.190714
\(874\) 0 0
\(875\) −57.4853 −1.94336
\(876\) 0 0
\(877\) 22.1667 0.748518 0.374259 0.927324i \(-0.377897\pi\)
0.374259 + 0.927324i \(0.377897\pi\)
\(878\) 0 0
\(879\) −7.09482 −0.239302
\(880\) 0 0
\(881\) 29.1275 0.981329 0.490665 0.871349i \(-0.336754\pi\)
0.490665 + 0.871349i \(0.336754\pi\)
\(882\) 0 0
\(883\) 14.6396 0.492662 0.246331 0.969186i \(-0.420775\pi\)
0.246331 + 0.969186i \(0.420775\pi\)
\(884\) 0 0
\(885\) −13.7448 −0.462027
\(886\) 0 0
\(887\) 54.3378 1.82449 0.912243 0.409650i \(-0.134349\pi\)
0.912243 + 0.409650i \(0.134349\pi\)
\(888\) 0 0
\(889\) −28.5829 −0.958639
\(890\) 0 0
\(891\) 3.21987 0.107870
\(892\) 0 0
\(893\) −0.339083 −0.0113470
\(894\) 0 0
\(895\) −7.50356 −0.250816
\(896\) 0 0
\(897\) −5.14668 −0.171843
\(898\) 0 0
\(899\) 21.7933 0.726847
\(900\) 0 0
\(901\) 1.37337 0.0457535
\(902\) 0 0
\(903\) 32.8392 1.09282
\(904\) 0 0
\(905\) −54.6632 −1.81706
\(906\) 0 0
\(907\) 26.5682 0.882183 0.441091 0.897462i \(-0.354591\pi\)
0.441091 + 0.897462i \(0.354591\pi\)
\(908\) 0 0
\(909\) 0.592996 0.0196684
\(910\) 0 0
\(911\) −45.5306 −1.50850 −0.754249 0.656589i \(-0.771999\pi\)
−0.754249 + 0.656589i \(0.771999\pi\)
\(912\) 0 0
\(913\) 1.07914 0.0357142
\(914\) 0 0
\(915\) 12.4071 0.410166
\(916\) 0 0
\(917\) −23.5193 −0.776677
\(918\) 0 0
\(919\) −26.3710 −0.869898 −0.434949 0.900455i \(-0.643234\pi\)
−0.434949 + 0.900455i \(0.643234\pi\)
\(920\) 0 0
\(921\) 13.6465 0.449668
\(922\) 0 0
\(923\) 23.8403 0.784714
\(924\) 0 0
\(925\) −20.3823 −0.670166
\(926\) 0 0
\(927\) −8.58197 −0.281869
\(928\) 0 0
\(929\) −6.15781 −0.202031 −0.101016 0.994885i \(-0.532209\pi\)
−0.101016 + 0.994885i \(0.532209\pi\)
\(930\) 0 0
\(931\) 0.126578 0.00414843
\(932\) 0 0
\(933\) 16.9544 0.555062
\(934\) 0 0
\(935\) 28.0892 0.918617
\(936\) 0 0
\(937\) −7.22212 −0.235936 −0.117968 0.993017i \(-0.537638\pi\)
−0.117968 + 0.993017i \(0.537638\pi\)
\(938\) 0 0
\(939\) −24.9576 −0.814459
\(940\) 0 0
\(941\) −10.5661 −0.344446 −0.172223 0.985058i \(-0.555095\pi\)
−0.172223 + 0.985058i \(0.555095\pi\)
\(942\) 0 0
\(943\) −12.1356 −0.395190
\(944\) 0 0
\(945\) −12.3324 −0.401174
\(946\) 0 0
\(947\) 20.4058 0.663100 0.331550 0.943438i \(-0.392428\pi\)
0.331550 + 0.943438i \(0.392428\pi\)
\(948\) 0 0
\(949\) −3.56544 −0.115739
\(950\) 0 0
\(951\) 27.4120 0.888897
\(952\) 0 0
\(953\) 30.2413 0.979613 0.489806 0.871831i \(-0.337067\pi\)
0.489806 + 0.871831i \(0.337067\pi\)
\(954\) 0 0
\(955\) 31.1999 1.00961
\(956\) 0 0
\(957\) −15.0890 −0.487757
\(958\) 0 0
\(959\) −21.3973 −0.690954
\(960\) 0 0
\(961\) −9.37266 −0.302344
\(962\) 0 0
\(963\) −16.6553 −0.536709
\(964\) 0 0
\(965\) −14.9305 −0.480630
\(966\) 0 0
\(967\) −38.2159 −1.22894 −0.614470 0.788940i \(-0.710630\pi\)
−0.614470 + 0.788940i \(0.710630\pi\)
\(968\) 0 0
\(969\) −0.0854864 −0.00274622
\(970\) 0 0
\(971\) 59.7778 1.91836 0.959180 0.282797i \(-0.0912622\pi\)
0.959180 + 0.282797i \(0.0912622\pi\)
\(972\) 0 0
\(973\) −5.10012 −0.163502
\(974\) 0 0
\(975\) −38.4241 −1.23056
\(976\) 0 0
\(977\) 6.74871 0.215910 0.107955 0.994156i \(-0.465570\pi\)
0.107955 + 0.994156i \(0.465570\pi\)
\(978\) 0 0
\(979\) 22.4237 0.716666
\(980\) 0 0
\(981\) 1.60814 0.0513439
\(982\) 0 0
\(983\) −36.4644 −1.16303 −0.581517 0.813534i \(-0.697541\pi\)
−0.581517 + 0.813534i \(0.697541\pi\)
\(984\) 0 0
\(985\) 8.71373 0.277643
\(986\) 0 0
\(987\) −29.1063 −0.926465
\(988\) 0 0
\(989\) 13.1944 0.419557
\(990\) 0 0
\(991\) −51.8622 −1.64746 −0.823729 0.566984i \(-0.808110\pi\)
−0.823729 + 0.566984i \(0.808110\pi\)
\(992\) 0 0
\(993\) 24.5608 0.779414
\(994\) 0 0
\(995\) 6.85905 0.217446
\(996\) 0 0
\(997\) −15.6529 −0.495732 −0.247866 0.968794i \(-0.579729\pi\)
−0.247866 + 0.968794i \(0.579729\pi\)
\(998\) 0 0
\(999\) −2.10968 −0.0667474
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 \(a_p\))