Properties

Label 6040.2.a.p.1.13
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-0.942024\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.942024 q^{3}\) \(+1.00000 q^{5}\) \(+1.85968 q^{7}\) \(-2.11259 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.942024 q^{3}\) \(+1.00000 q^{5}\) \(+1.85968 q^{7}\) \(-2.11259 q^{9}\) \(-5.46518 q^{11}\) \(-1.73017 q^{13}\) \(+0.942024 q^{15}\) \(+7.05540 q^{17}\) \(-0.773935 q^{19}\) \(+1.75186 q^{21}\) \(-3.81258 q^{23}\) \(+1.00000 q^{25}\) \(-4.81618 q^{27}\) \(-5.07852 q^{29}\) \(-3.44521 q^{31}\) \(-5.14833 q^{33}\) \(+1.85968 q^{35}\) \(+10.1557 q^{37}\) \(-1.62987 q^{39}\) \(+10.9597 q^{41}\) \(-11.4006 q^{43}\) \(-2.11259 q^{45}\) \(+4.80816 q^{47}\) \(-3.54160 q^{49}\) \(+6.64636 q^{51}\) \(-11.9347 q^{53}\) \(-5.46518 q^{55}\) \(-0.729066 q^{57}\) \(+9.86243 q^{59}\) \(-2.97110 q^{61}\) \(-3.92874 q^{63}\) \(-1.73017 q^{65}\) \(+1.49773 q^{67}\) \(-3.59154 q^{69}\) \(-4.03659 q^{71}\) \(-10.6541 q^{73}\) \(+0.942024 q^{75}\) \(-10.1635 q^{77}\) \(-6.78333 q^{79}\) \(+1.80081 q^{81}\) \(-8.89233 q^{83}\) \(+7.05540 q^{85}\) \(-4.78409 q^{87}\) \(+9.29643 q^{89}\) \(-3.21756 q^{91}\) \(-3.24547 q^{93}\) \(-0.773935 q^{95}\) \(-15.2342 q^{97}\) \(+11.5457 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.942024 0.543878 0.271939 0.962314i \(-0.412335\pi\)
0.271939 + 0.962314i \(0.412335\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.85968 0.702892 0.351446 0.936208i \(-0.385690\pi\)
0.351446 + 0.936208i \(0.385690\pi\)
\(8\) 0 0
\(9\) −2.11259 −0.704197
\(10\) 0 0
\(11\) −5.46518 −1.64781 −0.823907 0.566725i \(-0.808210\pi\)
−0.823907 + 0.566725i \(0.808210\pi\)
\(12\) 0 0
\(13\) −1.73017 −0.479864 −0.239932 0.970790i \(-0.577125\pi\)
−0.239932 + 0.970790i \(0.577125\pi\)
\(14\) 0 0
\(15\) 0.942024 0.243230
\(16\) 0 0
\(17\) 7.05540 1.71119 0.855593 0.517650i \(-0.173193\pi\)
0.855593 + 0.517650i \(0.173193\pi\)
\(18\) 0 0
\(19\) −0.773935 −0.177553 −0.0887765 0.996052i \(-0.528296\pi\)
−0.0887765 + 0.996052i \(0.528296\pi\)
\(20\) 0 0
\(21\) 1.75186 0.382288
\(22\) 0 0
\(23\) −3.81258 −0.794977 −0.397489 0.917607i \(-0.630118\pi\)
−0.397489 + 0.917607i \(0.630118\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.81618 −0.926875
\(28\) 0 0
\(29\) −5.07852 −0.943057 −0.471528 0.881851i \(-0.656298\pi\)
−0.471528 + 0.881851i \(0.656298\pi\)
\(30\) 0 0
\(31\) −3.44521 −0.618778 −0.309389 0.950936i \(-0.600125\pi\)
−0.309389 + 0.950936i \(0.600125\pi\)
\(32\) 0 0
\(33\) −5.14833 −0.896210
\(34\) 0 0
\(35\) 1.85968 0.314343
\(36\) 0 0
\(37\) 10.1557 1.66959 0.834793 0.550563i \(-0.185587\pi\)
0.834793 + 0.550563i \(0.185587\pi\)
\(38\) 0 0
\(39\) −1.62987 −0.260987
\(40\) 0 0
\(41\) 10.9597 1.71162 0.855812 0.517288i \(-0.173058\pi\)
0.855812 + 0.517288i \(0.173058\pi\)
\(42\) 0 0
\(43\) −11.4006 −1.73858 −0.869291 0.494300i \(-0.835424\pi\)
−0.869291 + 0.494300i \(0.835424\pi\)
\(44\) 0 0
\(45\) −2.11259 −0.314926
\(46\) 0 0
\(47\) 4.80816 0.701342 0.350671 0.936499i \(-0.385954\pi\)
0.350671 + 0.936499i \(0.385954\pi\)
\(48\) 0 0
\(49\) −3.54160 −0.505942
\(50\) 0 0
\(51\) 6.64636 0.930676
\(52\) 0 0
\(53\) −11.9347 −1.63936 −0.819678 0.572825i \(-0.805848\pi\)
−0.819678 + 0.572825i \(0.805848\pi\)
\(54\) 0 0
\(55\) −5.46518 −0.736925
\(56\) 0 0
\(57\) −0.729066 −0.0965671
\(58\) 0 0
\(59\) 9.86243 1.28398 0.641990 0.766713i \(-0.278109\pi\)
0.641990 + 0.766713i \(0.278109\pi\)
\(60\) 0 0
\(61\) −2.97110 −0.380410 −0.190205 0.981744i \(-0.560915\pi\)
−0.190205 + 0.981744i \(0.560915\pi\)
\(62\) 0 0
\(63\) −3.92874 −0.494974
\(64\) 0 0
\(65\) −1.73017 −0.214602
\(66\) 0 0
\(67\) 1.49773 0.182977 0.0914886 0.995806i \(-0.470838\pi\)
0.0914886 + 0.995806i \(0.470838\pi\)
\(68\) 0 0
\(69\) −3.59154 −0.432371
\(70\) 0 0
\(71\) −4.03659 −0.479055 −0.239527 0.970890i \(-0.576992\pi\)
−0.239527 + 0.970890i \(0.576992\pi\)
\(72\) 0 0
\(73\) −10.6541 −1.24697 −0.623484 0.781836i \(-0.714283\pi\)
−0.623484 + 0.781836i \(0.714283\pi\)
\(74\) 0 0
\(75\) 0.942024 0.108776
\(76\) 0 0
\(77\) −10.1635 −1.15824
\(78\) 0 0
\(79\) −6.78333 −0.763185 −0.381592 0.924331i \(-0.624624\pi\)
−0.381592 + 0.924331i \(0.624624\pi\)
\(80\) 0 0
\(81\) 1.80081 0.200090
\(82\) 0 0
\(83\) −8.89233 −0.976060 −0.488030 0.872827i \(-0.662284\pi\)
−0.488030 + 0.872827i \(0.662284\pi\)
\(84\) 0 0
\(85\) 7.05540 0.765265
\(86\) 0 0
\(87\) −4.78409 −0.512908
\(88\) 0 0
\(89\) 9.29643 0.985420 0.492710 0.870194i \(-0.336006\pi\)
0.492710 + 0.870194i \(0.336006\pi\)
\(90\) 0 0
\(91\) −3.21756 −0.337292
\(92\) 0 0
\(93\) −3.24547 −0.336540
\(94\) 0 0
\(95\) −0.773935 −0.0794041
\(96\) 0 0
\(97\) −15.2342 −1.54680 −0.773398 0.633920i \(-0.781445\pi\)
−0.773398 + 0.633920i \(0.781445\pi\)
\(98\) 0 0
\(99\) 11.5457 1.16038
\(100\) 0 0
\(101\) −14.9485 −1.48743 −0.743717 0.668494i \(-0.766939\pi\)
−0.743717 + 0.668494i \(0.766939\pi\)
\(102\) 0 0
\(103\) 14.6600 1.44449 0.722244 0.691638i \(-0.243111\pi\)
0.722244 + 0.691638i \(0.243111\pi\)
\(104\) 0 0
\(105\) 1.75186 0.170964
\(106\) 0 0
\(107\) −19.3707 −1.87264 −0.936320 0.351147i \(-0.885792\pi\)
−0.936320 + 0.351147i \(0.885792\pi\)
\(108\) 0 0
\(109\) −0.922013 −0.0883128 −0.0441564 0.999025i \(-0.514060\pi\)
−0.0441564 + 0.999025i \(0.514060\pi\)
\(110\) 0 0
\(111\) 9.56692 0.908052
\(112\) 0 0
\(113\) −8.59578 −0.808623 −0.404311 0.914621i \(-0.632489\pi\)
−0.404311 + 0.914621i \(0.632489\pi\)
\(114\) 0 0
\(115\) −3.81258 −0.355525
\(116\) 0 0
\(117\) 3.65515 0.337918
\(118\) 0 0
\(119\) 13.1208 1.20278
\(120\) 0 0
\(121\) 18.8682 1.71529
\(122\) 0 0
\(123\) 10.3243 0.930914
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −0.360098 −0.0319536 −0.0159768 0.999872i \(-0.505086\pi\)
−0.0159768 + 0.999872i \(0.505086\pi\)
\(128\) 0 0
\(129\) −10.7397 −0.945577
\(130\) 0 0
\(131\) −14.5951 −1.27518 −0.637590 0.770376i \(-0.720069\pi\)
−0.637590 + 0.770376i \(0.720069\pi\)
\(132\) 0 0
\(133\) −1.43927 −0.124801
\(134\) 0 0
\(135\) −4.81618 −0.414511
\(136\) 0 0
\(137\) −1.99895 −0.170782 −0.0853909 0.996348i \(-0.527214\pi\)
−0.0853909 + 0.996348i \(0.527214\pi\)
\(138\) 0 0
\(139\) −8.25356 −0.700058 −0.350029 0.936739i \(-0.613828\pi\)
−0.350029 + 0.936739i \(0.613828\pi\)
\(140\) 0 0
\(141\) 4.52940 0.381445
\(142\) 0 0
\(143\) 9.45571 0.790726
\(144\) 0 0
\(145\) −5.07852 −0.421748
\(146\) 0 0
\(147\) −3.33627 −0.275171
\(148\) 0 0
\(149\) −5.09019 −0.417005 −0.208502 0.978022i \(-0.566859\pi\)
−0.208502 + 0.978022i \(0.566859\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −14.9052 −1.20501
\(154\) 0 0
\(155\) −3.44521 −0.276726
\(156\) 0 0
\(157\) −22.3985 −1.78759 −0.893797 0.448473i \(-0.851968\pi\)
−0.893797 + 0.448473i \(0.851968\pi\)
\(158\) 0 0
\(159\) −11.2428 −0.891610
\(160\) 0 0
\(161\) −7.09017 −0.558783
\(162\) 0 0
\(163\) −11.7023 −0.916599 −0.458299 0.888798i \(-0.651541\pi\)
−0.458299 + 0.888798i \(0.651541\pi\)
\(164\) 0 0
\(165\) −5.14833 −0.400797
\(166\) 0 0
\(167\) −4.75896 −0.368260 −0.184130 0.982902i \(-0.558947\pi\)
−0.184130 + 0.982902i \(0.558947\pi\)
\(168\) 0 0
\(169\) −10.0065 −0.769731
\(170\) 0 0
\(171\) 1.63501 0.125032
\(172\) 0 0
\(173\) 12.4915 0.949711 0.474855 0.880064i \(-0.342500\pi\)
0.474855 + 0.880064i \(0.342500\pi\)
\(174\) 0 0
\(175\) 1.85968 0.140578
\(176\) 0 0
\(177\) 9.29065 0.698328
\(178\) 0 0
\(179\) 5.79891 0.433431 0.216715 0.976235i \(-0.430466\pi\)
0.216715 + 0.976235i \(0.430466\pi\)
\(180\) 0 0
\(181\) 20.4230 1.51803 0.759014 0.651074i \(-0.225681\pi\)
0.759014 + 0.651074i \(0.225681\pi\)
\(182\) 0 0
\(183\) −2.79885 −0.206897
\(184\) 0 0
\(185\) 10.1557 0.746662
\(186\) 0 0
\(187\) −38.5590 −2.81971
\(188\) 0 0
\(189\) −8.95655 −0.651493
\(190\) 0 0
\(191\) −12.6833 −0.917734 −0.458867 0.888505i \(-0.651745\pi\)
−0.458867 + 0.888505i \(0.651745\pi\)
\(192\) 0 0
\(193\) 2.96373 0.213334 0.106667 0.994295i \(-0.465982\pi\)
0.106667 + 0.994295i \(0.465982\pi\)
\(194\) 0 0
\(195\) −1.62987 −0.116717
\(196\) 0 0
\(197\) 7.41769 0.528488 0.264244 0.964456i \(-0.414878\pi\)
0.264244 + 0.964456i \(0.414878\pi\)
\(198\) 0 0
\(199\) 23.5540 1.66970 0.834851 0.550476i \(-0.185554\pi\)
0.834851 + 0.550476i \(0.185554\pi\)
\(200\) 0 0
\(201\) 1.41090 0.0995172
\(202\) 0 0
\(203\) −9.44441 −0.662867
\(204\) 0 0
\(205\) 10.9597 0.765461
\(206\) 0 0
\(207\) 8.05441 0.559820
\(208\) 0 0
\(209\) 4.22970 0.292574
\(210\) 0 0
\(211\) −1.35476 −0.0932656 −0.0466328 0.998912i \(-0.514849\pi\)
−0.0466328 + 0.998912i \(0.514849\pi\)
\(212\) 0 0
\(213\) −3.80256 −0.260547
\(214\) 0 0
\(215\) −11.4006 −0.777518
\(216\) 0 0
\(217\) −6.40698 −0.434934
\(218\) 0 0
\(219\) −10.0364 −0.678199
\(220\) 0 0
\(221\) −12.2071 −0.821136
\(222\) 0 0
\(223\) 12.0323 0.805743 0.402872 0.915257i \(-0.368012\pi\)
0.402872 + 0.915257i \(0.368012\pi\)
\(224\) 0 0
\(225\) −2.11259 −0.140839
\(226\) 0 0
\(227\) −18.3601 −1.21860 −0.609301 0.792939i \(-0.708550\pi\)
−0.609301 + 0.792939i \(0.708550\pi\)
\(228\) 0 0
\(229\) −2.16790 −0.143259 −0.0716294 0.997431i \(-0.522820\pi\)
−0.0716294 + 0.997431i \(0.522820\pi\)
\(230\) 0 0
\(231\) −9.57424 −0.629939
\(232\) 0 0
\(233\) 2.07658 0.136041 0.0680207 0.997684i \(-0.478332\pi\)
0.0680207 + 0.997684i \(0.478332\pi\)
\(234\) 0 0
\(235\) 4.80816 0.313650
\(236\) 0 0
\(237\) −6.39007 −0.415079
\(238\) 0 0
\(239\) −16.3456 −1.05731 −0.528654 0.848838i \(-0.677303\pi\)
−0.528654 + 0.848838i \(0.677303\pi\)
\(240\) 0 0
\(241\) −10.5561 −0.679981 −0.339990 0.940429i \(-0.610424\pi\)
−0.339990 + 0.940429i \(0.610424\pi\)
\(242\) 0 0
\(243\) 16.1450 1.03570
\(244\) 0 0
\(245\) −3.54160 −0.226264
\(246\) 0 0
\(247\) 1.33904 0.0852012
\(248\) 0 0
\(249\) −8.37679 −0.530857
\(250\) 0 0
\(251\) −3.88441 −0.245182 −0.122591 0.992457i \(-0.539120\pi\)
−0.122591 + 0.992457i \(0.539120\pi\)
\(252\) 0 0
\(253\) 20.8364 1.30997
\(254\) 0 0
\(255\) 6.64636 0.416211
\(256\) 0 0
\(257\) 23.6557 1.47560 0.737802 0.675017i \(-0.235864\pi\)
0.737802 + 0.675017i \(0.235864\pi\)
\(258\) 0 0
\(259\) 18.8863 1.17354
\(260\) 0 0
\(261\) 10.7288 0.664098
\(262\) 0 0
\(263\) −21.5604 −1.32947 −0.664737 0.747078i \(-0.731456\pi\)
−0.664737 + 0.747078i \(0.731456\pi\)
\(264\) 0 0
\(265\) −11.9347 −0.733142
\(266\) 0 0
\(267\) 8.75747 0.535948
\(268\) 0 0
\(269\) −27.1582 −1.65586 −0.827932 0.560829i \(-0.810483\pi\)
−0.827932 + 0.560829i \(0.810483\pi\)
\(270\) 0 0
\(271\) 21.5096 1.30661 0.653307 0.757093i \(-0.273381\pi\)
0.653307 + 0.757093i \(0.273381\pi\)
\(272\) 0 0
\(273\) −3.03102 −0.183446
\(274\) 0 0
\(275\) −5.46518 −0.329563
\(276\) 0 0
\(277\) 18.8380 1.13187 0.565933 0.824451i \(-0.308516\pi\)
0.565933 + 0.824451i \(0.308516\pi\)
\(278\) 0 0
\(279\) 7.27832 0.435742
\(280\) 0 0
\(281\) 23.0782 1.37673 0.688366 0.725364i \(-0.258328\pi\)
0.688366 + 0.725364i \(0.258328\pi\)
\(282\) 0 0
\(283\) −9.94744 −0.591314 −0.295657 0.955294i \(-0.595539\pi\)
−0.295657 + 0.955294i \(0.595539\pi\)
\(284\) 0 0
\(285\) −0.729066 −0.0431861
\(286\) 0 0
\(287\) 20.3816 1.20309
\(288\) 0 0
\(289\) 32.7787 1.92816
\(290\) 0 0
\(291\) −14.3510 −0.841269
\(292\) 0 0
\(293\) 2.76914 0.161775 0.0808875 0.996723i \(-0.474225\pi\)
0.0808875 + 0.996723i \(0.474225\pi\)
\(294\) 0 0
\(295\) 9.86243 0.574213
\(296\) 0 0
\(297\) 26.3213 1.52732
\(298\) 0 0
\(299\) 6.59642 0.381481
\(300\) 0 0
\(301\) −21.2015 −1.22204
\(302\) 0 0
\(303\) −14.0819 −0.808983
\(304\) 0 0
\(305\) −2.97110 −0.170125
\(306\) 0 0
\(307\) 26.2009 1.49537 0.747683 0.664056i \(-0.231166\pi\)
0.747683 + 0.664056i \(0.231166\pi\)
\(308\) 0 0
\(309\) 13.8100 0.785626
\(310\) 0 0
\(311\) −12.6108 −0.715093 −0.357546 0.933895i \(-0.616387\pi\)
−0.357546 + 0.933895i \(0.616387\pi\)
\(312\) 0 0
\(313\) 1.59498 0.0901534 0.0450767 0.998984i \(-0.485647\pi\)
0.0450767 + 0.998984i \(0.485647\pi\)
\(314\) 0 0
\(315\) −3.92874 −0.221359
\(316\) 0 0
\(317\) −0.542764 −0.0304847 −0.0152423 0.999884i \(-0.504852\pi\)
−0.0152423 + 0.999884i \(0.504852\pi\)
\(318\) 0 0
\(319\) 27.7550 1.55398
\(320\) 0 0
\(321\) −18.2477 −1.01849
\(322\) 0 0
\(323\) −5.46042 −0.303826
\(324\) 0 0
\(325\) −1.73017 −0.0959727
\(326\) 0 0
\(327\) −0.868559 −0.0480314
\(328\) 0 0
\(329\) 8.94163 0.492968
\(330\) 0 0
\(331\) 32.1664 1.76802 0.884012 0.467463i \(-0.154832\pi\)
0.884012 + 0.467463i \(0.154832\pi\)
\(332\) 0 0
\(333\) −21.4548 −1.17572
\(334\) 0 0
\(335\) 1.49773 0.0818299
\(336\) 0 0
\(337\) 12.6504 0.689111 0.344555 0.938766i \(-0.388030\pi\)
0.344555 + 0.938766i \(0.388030\pi\)
\(338\) 0 0
\(339\) −8.09743 −0.439792
\(340\) 0 0
\(341\) 18.8287 1.01963
\(342\) 0 0
\(343\) −19.6040 −1.05852
\(344\) 0 0
\(345\) −3.59154 −0.193362
\(346\) 0 0
\(347\) −12.2603 −0.658170 −0.329085 0.944300i \(-0.606740\pi\)
−0.329085 + 0.944300i \(0.606740\pi\)
\(348\) 0 0
\(349\) 24.8093 1.32801 0.664006 0.747727i \(-0.268855\pi\)
0.664006 + 0.747727i \(0.268855\pi\)
\(350\) 0 0
\(351\) 8.33283 0.444774
\(352\) 0 0
\(353\) 19.0626 1.01460 0.507301 0.861769i \(-0.330643\pi\)
0.507301 + 0.861769i \(0.330643\pi\)
\(354\) 0 0
\(355\) −4.03659 −0.214240
\(356\) 0 0
\(357\) 12.3601 0.654165
\(358\) 0 0
\(359\) −6.75013 −0.356258 −0.178129 0.984007i \(-0.557005\pi\)
−0.178129 + 0.984007i \(0.557005\pi\)
\(360\) 0 0
\(361\) −18.4010 −0.968475
\(362\) 0 0
\(363\) 17.7743 0.932908
\(364\) 0 0
\(365\) −10.6541 −0.557661
\(366\) 0 0
\(367\) −25.6322 −1.33799 −0.668995 0.743267i \(-0.733275\pi\)
−0.668995 + 0.743267i \(0.733275\pi\)
\(368\) 0 0
\(369\) −23.1534 −1.20532
\(370\) 0 0
\(371\) −22.1947 −1.15229
\(372\) 0 0
\(373\) 28.8673 1.49469 0.747346 0.664435i \(-0.231328\pi\)
0.747346 + 0.664435i \(0.231328\pi\)
\(374\) 0 0
\(375\) 0.942024 0.0486459
\(376\) 0 0
\(377\) 8.78671 0.452539
\(378\) 0 0
\(379\) 23.1364 1.18844 0.594218 0.804304i \(-0.297462\pi\)
0.594218 + 0.804304i \(0.297462\pi\)
\(380\) 0 0
\(381\) −0.339221 −0.0173788
\(382\) 0 0
\(383\) 31.0043 1.58424 0.792122 0.610362i \(-0.208976\pi\)
0.792122 + 0.610362i \(0.208976\pi\)
\(384\) 0 0
\(385\) −10.1635 −0.517979
\(386\) 0 0
\(387\) 24.0849 1.22430
\(388\) 0 0
\(389\) 17.9191 0.908535 0.454267 0.890865i \(-0.349901\pi\)
0.454267 + 0.890865i \(0.349901\pi\)
\(390\) 0 0
\(391\) −26.8992 −1.36035
\(392\) 0 0
\(393\) −13.7489 −0.693543
\(394\) 0 0
\(395\) −6.78333 −0.341307
\(396\) 0 0
\(397\) 3.93812 0.197648 0.0988242 0.995105i \(-0.468492\pi\)
0.0988242 + 0.995105i \(0.468492\pi\)
\(398\) 0 0
\(399\) −1.35583 −0.0678763
\(400\) 0 0
\(401\) −9.98027 −0.498391 −0.249195 0.968453i \(-0.580166\pi\)
−0.249195 + 0.968453i \(0.580166\pi\)
\(402\) 0 0
\(403\) 5.96081 0.296929
\(404\) 0 0
\(405\) 1.80081 0.0894828
\(406\) 0 0
\(407\) −55.5027 −2.75117
\(408\) 0 0
\(409\) 12.4497 0.615597 0.307798 0.951452i \(-0.400408\pi\)
0.307798 + 0.951452i \(0.400408\pi\)
\(410\) 0 0
\(411\) −1.88306 −0.0928844
\(412\) 0 0
\(413\) 18.3409 0.902499
\(414\) 0 0
\(415\) −8.89233 −0.436507
\(416\) 0 0
\(417\) −7.77506 −0.380746
\(418\) 0 0
\(419\) 8.67843 0.423969 0.211984 0.977273i \(-0.432007\pi\)
0.211984 + 0.977273i \(0.432007\pi\)
\(420\) 0 0
\(421\) −28.0069 −1.36497 −0.682485 0.730899i \(-0.739101\pi\)
−0.682485 + 0.730899i \(0.739101\pi\)
\(422\) 0 0
\(423\) −10.1577 −0.493883
\(424\) 0 0
\(425\) 7.05540 0.342237
\(426\) 0 0
\(427\) −5.52529 −0.267387
\(428\) 0 0
\(429\) 8.90751 0.430058
\(430\) 0 0
\(431\) 36.5263 1.75941 0.879705 0.475519i \(-0.157740\pi\)
0.879705 + 0.475519i \(0.157740\pi\)
\(432\) 0 0
\(433\) 4.40044 0.211472 0.105736 0.994394i \(-0.466280\pi\)
0.105736 + 0.994394i \(0.466280\pi\)
\(434\) 0 0
\(435\) −4.78409 −0.229379
\(436\) 0 0
\(437\) 2.95069 0.141151
\(438\) 0 0
\(439\) −37.3479 −1.78252 −0.891259 0.453494i \(-0.850177\pi\)
−0.891259 + 0.453494i \(0.850177\pi\)
\(440\) 0 0
\(441\) 7.48194 0.356283
\(442\) 0 0
\(443\) −29.6861 −1.41043 −0.705215 0.708994i \(-0.749149\pi\)
−0.705215 + 0.708994i \(0.749149\pi\)
\(444\) 0 0
\(445\) 9.29643 0.440693
\(446\) 0 0
\(447\) −4.79509 −0.226800
\(448\) 0 0
\(449\) −2.69250 −0.127067 −0.0635335 0.997980i \(-0.520237\pi\)
−0.0635335 + 0.997980i \(0.520237\pi\)
\(450\) 0 0
\(451\) −59.8969 −2.82044
\(452\) 0 0
\(453\) 0.942024 0.0442602
\(454\) 0 0
\(455\) −3.21756 −0.150842
\(456\) 0 0
\(457\) 9.46265 0.442644 0.221322 0.975201i \(-0.428963\pi\)
0.221322 + 0.975201i \(0.428963\pi\)
\(458\) 0 0
\(459\) −33.9801 −1.58606
\(460\) 0 0
\(461\) −22.9597 −1.06934 −0.534670 0.845061i \(-0.679564\pi\)
−0.534670 + 0.845061i \(0.679564\pi\)
\(462\) 0 0
\(463\) −9.78207 −0.454611 −0.227306 0.973823i \(-0.572992\pi\)
−0.227306 + 0.973823i \(0.572992\pi\)
\(464\) 0 0
\(465\) −3.24547 −0.150505
\(466\) 0 0
\(467\) −10.4773 −0.484830 −0.242415 0.970173i \(-0.577940\pi\)
−0.242415 + 0.970173i \(0.577940\pi\)
\(468\) 0 0
\(469\) 2.78530 0.128613
\(470\) 0 0
\(471\) −21.0999 −0.972233
\(472\) 0 0
\(473\) 62.3066 2.86486
\(474\) 0 0
\(475\) −0.773935 −0.0355106
\(476\) 0 0
\(477\) 25.2131 1.15443
\(478\) 0 0
\(479\) −32.9758 −1.50670 −0.753352 0.657617i \(-0.771565\pi\)
−0.753352 + 0.657617i \(0.771565\pi\)
\(480\) 0 0
\(481\) −17.5711 −0.801174
\(482\) 0 0
\(483\) −6.67911 −0.303910
\(484\) 0 0
\(485\) −15.2342 −0.691749
\(486\) 0 0
\(487\) −0.119256 −0.00540400 −0.00270200 0.999996i \(-0.500860\pi\)
−0.00270200 + 0.999996i \(0.500860\pi\)
\(488\) 0 0
\(489\) −11.0239 −0.498518
\(490\) 0 0
\(491\) −9.51914 −0.429593 −0.214796 0.976659i \(-0.568909\pi\)
−0.214796 + 0.976659i \(0.568909\pi\)
\(492\) 0 0
\(493\) −35.8310 −1.61375
\(494\) 0 0
\(495\) 11.5457 0.518940
\(496\) 0 0
\(497\) −7.50675 −0.336724
\(498\) 0 0
\(499\) −2.86759 −0.128371 −0.0641854 0.997938i \(-0.520445\pi\)
−0.0641854 + 0.997938i \(0.520445\pi\)
\(500\) 0 0
\(501\) −4.48306 −0.200288
\(502\) 0 0
\(503\) −31.4990 −1.40447 −0.702235 0.711946i \(-0.747814\pi\)
−0.702235 + 0.711946i \(0.747814\pi\)
\(504\) 0 0
\(505\) −14.9485 −0.665201
\(506\) 0 0
\(507\) −9.42637 −0.418640
\(508\) 0 0
\(509\) −26.2470 −1.16338 −0.581690 0.813411i \(-0.697608\pi\)
−0.581690 + 0.813411i \(0.697608\pi\)
\(510\) 0 0
\(511\) −19.8132 −0.876484
\(512\) 0 0
\(513\) 3.72741 0.164569
\(514\) 0 0
\(515\) 14.6600 0.645995
\(516\) 0 0
\(517\) −26.2775 −1.15568
\(518\) 0 0
\(519\) 11.7673 0.516527
\(520\) 0 0
\(521\) 17.7628 0.778202 0.389101 0.921195i \(-0.372786\pi\)
0.389101 + 0.921195i \(0.372786\pi\)
\(522\) 0 0
\(523\) 23.4991 1.02754 0.513771 0.857927i \(-0.328248\pi\)
0.513771 + 0.857927i \(0.328248\pi\)
\(524\) 0 0
\(525\) 1.75186 0.0764575
\(526\) 0 0
\(527\) −24.3073 −1.05884
\(528\) 0 0
\(529\) −8.46426 −0.368011
\(530\) 0 0
\(531\) −20.8353 −0.904174
\(532\) 0 0
\(533\) −18.9622 −0.821346
\(534\) 0 0
\(535\) −19.3707 −0.837470
\(536\) 0 0
\(537\) 5.46271 0.235733
\(538\) 0 0
\(539\) 19.3555 0.833699
\(540\) 0 0
\(541\) −24.8331 −1.06766 −0.533830 0.845592i \(-0.679248\pi\)
−0.533830 + 0.845592i \(0.679248\pi\)
\(542\) 0 0
\(543\) 19.2389 0.825622
\(544\) 0 0
\(545\) −0.922013 −0.0394947
\(546\) 0 0
\(547\) 9.12472 0.390145 0.195073 0.980789i \(-0.437506\pi\)
0.195073 + 0.980789i \(0.437506\pi\)
\(548\) 0 0
\(549\) 6.27672 0.267884
\(550\) 0 0
\(551\) 3.93044 0.167443
\(552\) 0 0
\(553\) −12.6148 −0.536437
\(554\) 0 0
\(555\) 9.56692 0.406093
\(556\) 0 0
\(557\) 41.4976 1.75831 0.879155 0.476536i \(-0.158108\pi\)
0.879155 + 0.476536i \(0.158108\pi\)
\(558\) 0 0
\(559\) 19.7251 0.834283
\(560\) 0 0
\(561\) −36.3235 −1.53358
\(562\) 0 0
\(563\) −20.4440 −0.861611 −0.430805 0.902445i \(-0.641770\pi\)
−0.430805 + 0.902445i \(0.641770\pi\)
\(564\) 0 0
\(565\) −8.59578 −0.361627
\(566\) 0 0
\(567\) 3.34892 0.140641
\(568\) 0 0
\(569\) 18.8637 0.790808 0.395404 0.918507i \(-0.370605\pi\)
0.395404 + 0.918507i \(0.370605\pi\)
\(570\) 0 0
\(571\) 33.0690 1.38389 0.691947 0.721948i \(-0.256753\pi\)
0.691947 + 0.721948i \(0.256753\pi\)
\(572\) 0 0
\(573\) −11.9480 −0.499135
\(574\) 0 0
\(575\) −3.81258 −0.158995
\(576\) 0 0
\(577\) −32.4593 −1.35130 −0.675648 0.737224i \(-0.736136\pi\)
−0.675648 + 0.737224i \(0.736136\pi\)
\(578\) 0 0
\(579\) 2.79191 0.116028
\(580\) 0 0
\(581\) −16.5369 −0.686065
\(582\) 0 0
\(583\) 65.2252 2.70135
\(584\) 0 0
\(585\) 3.65515 0.151122
\(586\) 0 0
\(587\) −39.1383 −1.61541 −0.807706 0.589586i \(-0.799291\pi\)
−0.807706 + 0.589586i \(0.799291\pi\)
\(588\) 0 0
\(589\) 2.66637 0.109866
\(590\) 0 0
\(591\) 6.98764 0.287433
\(592\) 0 0
\(593\) 4.16244 0.170931 0.0854655 0.996341i \(-0.472762\pi\)
0.0854655 + 0.996341i \(0.472762\pi\)
\(594\) 0 0
\(595\) 13.1208 0.537899
\(596\) 0 0
\(597\) 22.1885 0.908114
\(598\) 0 0
\(599\) −2.55066 −0.104217 −0.0521086 0.998641i \(-0.516594\pi\)
−0.0521086 + 0.998641i \(0.516594\pi\)
\(600\) 0 0
\(601\) −45.5984 −1.86000 −0.929999 0.367563i \(-0.880192\pi\)
−0.929999 + 0.367563i \(0.880192\pi\)
\(602\) 0 0
\(603\) −3.16409 −0.128852
\(604\) 0 0
\(605\) 18.8682 0.767101
\(606\) 0 0
\(607\) 3.73191 0.151473 0.0757367 0.997128i \(-0.475869\pi\)
0.0757367 + 0.997128i \(0.475869\pi\)
\(608\) 0 0
\(609\) −8.89686 −0.360519
\(610\) 0 0
\(611\) −8.31895 −0.336549
\(612\) 0 0
\(613\) 24.7399 0.999235 0.499618 0.866246i \(-0.333474\pi\)
0.499618 + 0.866246i \(0.333474\pi\)
\(614\) 0 0
\(615\) 10.3243 0.416317
\(616\) 0 0
\(617\) 10.2583 0.412984 0.206492 0.978448i \(-0.433795\pi\)
0.206492 + 0.978448i \(0.433795\pi\)
\(618\) 0 0
\(619\) 40.0207 1.60857 0.804284 0.594246i \(-0.202549\pi\)
0.804284 + 0.594246i \(0.202549\pi\)
\(620\) 0 0
\(621\) 18.3621 0.736845
\(622\) 0 0
\(623\) 17.2884 0.692644
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 3.98448 0.159125
\(628\) 0 0
\(629\) 71.6525 2.85697
\(630\) 0 0
\(631\) 11.8223 0.470637 0.235318 0.971918i \(-0.424387\pi\)
0.235318 + 0.971918i \(0.424387\pi\)
\(632\) 0 0
\(633\) −1.27622 −0.0507251
\(634\) 0 0
\(635\) −0.360098 −0.0142901
\(636\) 0 0
\(637\) 6.12758 0.242783
\(638\) 0 0
\(639\) 8.52765 0.337349
\(640\) 0 0
\(641\) −15.3260 −0.605341 −0.302670 0.953095i \(-0.597878\pi\)
−0.302670 + 0.953095i \(0.597878\pi\)
\(642\) 0 0
\(643\) −25.0979 −0.989765 −0.494883 0.868960i \(-0.664789\pi\)
−0.494883 + 0.868960i \(0.664789\pi\)
\(644\) 0 0
\(645\) −10.7397 −0.422875
\(646\) 0 0
\(647\) −16.2560 −0.639090 −0.319545 0.947571i \(-0.603530\pi\)
−0.319545 + 0.947571i \(0.603530\pi\)
\(648\) 0 0
\(649\) −53.9000 −2.11576
\(650\) 0 0
\(651\) −6.03554 −0.236551
\(652\) 0 0
\(653\) −48.2615 −1.88862 −0.944309 0.329059i \(-0.893268\pi\)
−0.944309 + 0.329059i \(0.893268\pi\)
\(654\) 0 0
\(655\) −14.5951 −0.570278
\(656\) 0 0
\(657\) 22.5077 0.878111
\(658\) 0 0
\(659\) 31.9498 1.24459 0.622294 0.782783i \(-0.286201\pi\)
0.622294 + 0.782783i \(0.286201\pi\)
\(660\) 0 0
\(661\) 22.5313 0.876364 0.438182 0.898886i \(-0.355623\pi\)
0.438182 + 0.898886i \(0.355623\pi\)
\(662\) 0 0
\(663\) −11.4993 −0.446598
\(664\) 0 0
\(665\) −1.43927 −0.0558125
\(666\) 0 0
\(667\) 19.3622 0.749709
\(668\) 0 0
\(669\) 11.3347 0.438226
\(670\) 0 0
\(671\) 16.2376 0.626845
\(672\) 0 0
\(673\) 26.7717 1.03197 0.515987 0.856597i \(-0.327425\pi\)
0.515987 + 0.856597i \(0.327425\pi\)
\(674\) 0 0
\(675\) −4.81618 −0.185375
\(676\) 0 0
\(677\) −41.9616 −1.61272 −0.806358 0.591427i \(-0.798565\pi\)
−0.806358 + 0.591427i \(0.798565\pi\)
\(678\) 0 0
\(679\) −28.3307 −1.08723
\(680\) 0 0
\(681\) −17.2957 −0.662771
\(682\) 0 0
\(683\) 30.6300 1.17202 0.586011 0.810303i \(-0.300697\pi\)
0.586011 + 0.810303i \(0.300697\pi\)
\(684\) 0 0
\(685\) −1.99895 −0.0763759
\(686\) 0 0
\(687\) −2.04221 −0.0779153
\(688\) 0 0
\(689\) 20.6491 0.786667
\(690\) 0 0
\(691\) −0.191722 −0.00729344 −0.00364672 0.999993i \(-0.501161\pi\)
−0.00364672 + 0.999993i \(0.501161\pi\)
\(692\) 0 0
\(693\) 21.4713 0.815626
\(694\) 0 0
\(695\) −8.25356 −0.313076
\(696\) 0 0
\(697\) 77.3253 2.92890
\(698\) 0 0
\(699\) 1.95619 0.0739899
\(700\) 0 0
\(701\) −13.1570 −0.496932 −0.248466 0.968641i \(-0.579926\pi\)
−0.248466 + 0.968641i \(0.579926\pi\)
\(702\) 0 0
\(703\) −7.85985 −0.296440
\(704\) 0 0
\(705\) 4.52940 0.170587
\(706\) 0 0
\(707\) −27.7995 −1.04551
\(708\) 0 0
\(709\) −22.0799 −0.829226 −0.414613 0.909998i \(-0.636083\pi\)
−0.414613 + 0.909998i \(0.636083\pi\)
\(710\) 0 0
\(711\) 14.3304 0.537432
\(712\) 0 0
\(713\) 13.1351 0.491915
\(714\) 0 0
\(715\) 9.45571 0.353623
\(716\) 0 0
\(717\) −15.3979 −0.575046
\(718\) 0 0
\(719\) −7.30618 −0.272475 −0.136237 0.990676i \(-0.543501\pi\)
−0.136237 + 0.990676i \(0.543501\pi\)
\(720\) 0 0
\(721\) 27.2628 1.01532
\(722\) 0 0
\(723\) −9.94414 −0.369826
\(724\) 0 0
\(725\) −5.07852 −0.188611
\(726\) 0 0
\(727\) 39.4806 1.46425 0.732127 0.681168i \(-0.238528\pi\)
0.732127 + 0.681168i \(0.238528\pi\)
\(728\) 0 0
\(729\) 9.80652 0.363205
\(730\) 0 0
\(731\) −80.4361 −2.97504
\(732\) 0 0
\(733\) 34.7787 1.28458 0.642290 0.766462i \(-0.277985\pi\)
0.642290 + 0.766462i \(0.277985\pi\)
\(734\) 0 0
\(735\) −3.33627 −0.123060
\(736\) 0 0
\(737\) −8.18538 −0.301512
\(738\) 0 0
\(739\) −31.3828 −1.15444 −0.577218 0.816590i \(-0.695862\pi\)
−0.577218 + 0.816590i \(0.695862\pi\)
\(740\) 0 0
\(741\) 1.26141 0.0463391
\(742\) 0 0
\(743\) −5.62389 −0.206320 −0.103160 0.994665i \(-0.532895\pi\)
−0.103160 + 0.994665i \(0.532895\pi\)
\(744\) 0 0
\(745\) −5.09019 −0.186490
\(746\) 0 0
\(747\) 18.7858 0.687338
\(748\) 0 0
\(749\) −36.0234 −1.31626
\(750\) 0 0
\(751\) −8.71183 −0.317899 −0.158950 0.987287i \(-0.550811\pi\)
−0.158950 + 0.987287i \(0.550811\pi\)
\(752\) 0 0
\(753\) −3.65921 −0.133349
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 6.94566 0.252444 0.126222 0.992002i \(-0.459715\pi\)
0.126222 + 0.992002i \(0.459715\pi\)
\(758\) 0 0
\(759\) 19.6284 0.712466
\(760\) 0 0
\(761\) 39.9711 1.44895 0.724476 0.689300i \(-0.242082\pi\)
0.724476 + 0.689300i \(0.242082\pi\)
\(762\) 0 0
\(763\) −1.71465 −0.0620744
\(764\) 0 0
\(765\) −14.9052 −0.538897
\(766\) 0 0
\(767\) −17.0637 −0.616135
\(768\) 0 0
\(769\) 6.04056 0.217828 0.108914 0.994051i \(-0.465263\pi\)
0.108914 + 0.994051i \(0.465263\pi\)
\(770\) 0 0
\(771\) 22.2843 0.802548
\(772\) 0 0
\(773\) 13.5620 0.487792 0.243896 0.969801i \(-0.421574\pi\)
0.243896 + 0.969801i \(0.421574\pi\)
\(774\) 0 0
\(775\) −3.44521 −0.123756
\(776\) 0 0
\(777\) 17.7914 0.638262
\(778\) 0 0
\(779\) −8.48213 −0.303904
\(780\) 0 0
\(781\) 22.0607 0.789393
\(782\) 0 0
\(783\) 24.4591 0.874096
\(784\) 0 0
\(785\) −22.3985 −0.799436
\(786\) 0 0
\(787\) 11.7846 0.420075 0.210038 0.977693i \(-0.432641\pi\)
0.210038 + 0.977693i \(0.432641\pi\)
\(788\) 0 0
\(789\) −20.3105 −0.723071
\(790\) 0 0
\(791\) −15.9854 −0.568375
\(792\) 0 0
\(793\) 5.14052 0.182545
\(794\) 0 0
\(795\) −11.2428 −0.398740
\(796\) 0 0
\(797\) 37.8658 1.34127 0.670637 0.741786i \(-0.266021\pi\)
0.670637 + 0.741786i \(0.266021\pi\)
\(798\) 0 0
\(799\) 33.9235 1.20013
\(800\) 0 0
\(801\) −19.6396 −0.693930
\(802\) 0 0
\(803\) 58.2266 2.05477
\(804\) 0 0
\(805\) −7.09017 −0.249895
\(806\) 0 0
\(807\) −25.5837 −0.900588
\(808\) 0 0
\(809\) −18.1249 −0.637238 −0.318619 0.947883i \(-0.603219\pi\)
−0.318619 + 0.947883i \(0.603219\pi\)
\(810\) 0 0
\(811\) −14.5280 −0.510145 −0.255073 0.966922i \(-0.582099\pi\)
−0.255073 + 0.966922i \(0.582099\pi\)
\(812\) 0 0
\(813\) 20.2625 0.710639
\(814\) 0 0
\(815\) −11.7023 −0.409915
\(816\) 0 0
\(817\) 8.82336 0.308690
\(818\) 0 0
\(819\) 6.79740 0.237520
\(820\) 0 0
\(821\) 2.80501 0.0978956 0.0489478 0.998801i \(-0.484413\pi\)
0.0489478 + 0.998801i \(0.484413\pi\)
\(822\) 0 0
\(823\) −37.0462 −1.29135 −0.645675 0.763612i \(-0.723424\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(824\) 0 0
\(825\) −5.14833 −0.179242
\(826\) 0 0
\(827\) 45.8953 1.59594 0.797968 0.602699i \(-0.205908\pi\)
0.797968 + 0.602699i \(0.205908\pi\)
\(828\) 0 0
\(829\) 17.1002 0.593914 0.296957 0.954891i \(-0.404028\pi\)
0.296957 + 0.954891i \(0.404028\pi\)
\(830\) 0 0
\(831\) 17.7459 0.615597
\(832\) 0 0
\(833\) −24.9874 −0.865761
\(834\) 0 0
\(835\) −4.75896 −0.164691
\(836\) 0 0
\(837\) 16.5928 0.573530
\(838\) 0 0
\(839\) 32.9731 1.13836 0.569178 0.822214i \(-0.307261\pi\)
0.569178 + 0.822214i \(0.307261\pi\)
\(840\) 0 0
\(841\) −3.20866 −0.110644
\(842\) 0 0
\(843\) 21.7402 0.748774
\(844\) 0 0
\(845\) −10.0065 −0.344234
\(846\) 0 0
\(847\) 35.0888 1.20566
\(848\) 0 0
\(849\) −9.37073 −0.321603
\(850\) 0 0
\(851\) −38.7194 −1.32728
\(852\) 0 0
\(853\) 30.0327 1.02830 0.514150 0.857701i \(-0.328108\pi\)
0.514150 + 0.857701i \(0.328108\pi\)
\(854\) 0 0
\(855\) 1.63501 0.0559161
\(856\) 0 0
\(857\) 9.27381 0.316787 0.158394 0.987376i \(-0.449368\pi\)
0.158394 + 0.987376i \(0.449368\pi\)
\(858\) 0 0
\(859\) 23.7216 0.809371 0.404686 0.914456i \(-0.367381\pi\)
0.404686 + 0.914456i \(0.367381\pi\)
\(860\) 0 0
\(861\) 19.1999 0.654332
\(862\) 0 0
\(863\) −8.52449 −0.290177 −0.145088 0.989419i \(-0.546347\pi\)
−0.145088 + 0.989419i \(0.546347\pi\)
\(864\) 0 0
\(865\) 12.4915 0.424724
\(866\) 0 0
\(867\) 30.8783 1.04868
\(868\) 0 0
\(869\) 37.0721 1.25759
\(870\) 0 0
\(871\) −2.59134 −0.0878041
\(872\) 0 0
\(873\) 32.1836 1.08925
\(874\) 0 0
\(875\) 1.85968 0.0628686
\(876\) 0 0
\(877\) 18.9338 0.639349 0.319675 0.947527i \(-0.396426\pi\)
0.319675 + 0.947527i \(0.396426\pi\)
\(878\) 0 0
\(879\) 2.60860 0.0879859
\(880\) 0 0
\(881\) 42.7275 1.43953 0.719763 0.694220i \(-0.244250\pi\)
0.719763 + 0.694220i \(0.244250\pi\)
\(882\) 0 0
\(883\) 9.46336 0.318467 0.159234 0.987241i \(-0.449098\pi\)
0.159234 + 0.987241i \(0.449098\pi\)
\(884\) 0 0
\(885\) 9.29065 0.312302
\(886\) 0 0
\(887\) −38.0558 −1.27779 −0.638895 0.769294i \(-0.720608\pi\)
−0.638895 + 0.769294i \(0.720608\pi\)
\(888\) 0 0
\(889\) −0.669667 −0.0224599
\(890\) 0 0
\(891\) −9.84173 −0.329711
\(892\) 0 0
\(893\) −3.72120 −0.124525
\(894\) 0 0
\(895\) 5.79891 0.193836
\(896\) 0 0
\(897\) 6.21399 0.207479
\(898\) 0 0
\(899\) 17.4966 0.583543
\(900\) 0 0
\(901\) −84.2040 −2.80524
\(902\) 0 0
\(903\) −19.9724 −0.664639
\(904\) 0 0
\(905\) 20.4230 0.678883
\(906\) 0 0
\(907\) −0.354493 −0.0117707 −0.00588537 0.999983i \(-0.501873\pi\)
−0.00588537 + 0.999983i \(0.501873\pi\)
\(908\) 0 0
\(909\) 31.5801 1.04745
\(910\) 0 0
\(911\) −25.1125 −0.832013 −0.416007 0.909362i \(-0.636571\pi\)
−0.416007 + 0.909362i \(0.636571\pi\)
\(912\) 0 0
\(913\) 48.5982 1.60836
\(914\) 0 0
\(915\) −2.79885 −0.0925271
\(916\) 0 0
\(917\) −27.1422 −0.896314
\(918\) 0 0
\(919\) −47.4338 −1.56470 −0.782349 0.622841i \(-0.785978\pi\)
−0.782349 + 0.622841i \(0.785978\pi\)
\(920\) 0 0
\(921\) 24.6819 0.813297
\(922\) 0 0
\(923\) 6.98399 0.229881
\(924\) 0 0
\(925\) 10.1557 0.333917
\(926\) 0 0
\(927\) −30.9705 −1.01720
\(928\) 0 0
\(929\) −0.518160 −0.0170003 −0.00850014 0.999964i \(-0.502706\pi\)
−0.00850014 + 0.999964i \(0.502706\pi\)
\(930\) 0 0
\(931\) 2.74097 0.0898316
\(932\) 0 0
\(933\) −11.8797 −0.388923
\(934\) 0 0
\(935\) −38.5590 −1.26101
\(936\) 0 0
\(937\) −34.4387 −1.12506 −0.562532 0.826776i \(-0.690173\pi\)
−0.562532 + 0.826776i \(0.690173\pi\)
\(938\) 0 0
\(939\) 1.50251 0.0490325
\(940\) 0 0
\(941\) −14.8006 −0.482485 −0.241242 0.970465i \(-0.577555\pi\)
−0.241242 + 0.970465i \(0.577555\pi\)
\(942\) 0 0
\(943\) −41.7848 −1.36070
\(944\) 0 0
\(945\) −8.95655 −0.291357
\(946\) 0 0
\(947\) 17.7019 0.575234 0.287617 0.957745i \(-0.407137\pi\)
0.287617 + 0.957745i \(0.407137\pi\)
\(948\) 0 0
\(949\) 18.4334 0.598375
\(950\) 0 0
\(951\) −0.511297 −0.0165799
\(952\) 0 0
\(953\) −44.6813 −1.44737 −0.723685 0.690130i \(-0.757553\pi\)
−0.723685 + 0.690130i \(0.757553\pi\)
\(954\) 0 0
\(955\) −12.6833 −0.410423
\(956\) 0 0
\(957\) 26.1459 0.845177
\(958\) 0 0
\(959\) −3.71740 −0.120041
\(960\) 0 0
\(961\) −19.1305 −0.617113
\(962\) 0 0
\(963\) 40.9224 1.31871
\(964\) 0 0
\(965\) 2.96373 0.0954059
\(966\) 0 0
\(967\) 18.1012 0.582094 0.291047 0.956709i \(-0.405996\pi\)
0.291047 + 0.956709i \(0.405996\pi\)
\(968\) 0 0
\(969\) −5.14385 −0.165244
\(970\) 0 0
\(971\) 16.1142 0.517131 0.258565 0.965994i \(-0.416750\pi\)
0.258565 + 0.965994i \(0.416750\pi\)
\(972\) 0 0
\(973\) −15.3490 −0.492065
\(974\) 0 0
\(975\) −1.62987 −0.0521975
\(976\) 0 0
\(977\) 57.1462 1.82827 0.914135 0.405411i \(-0.132871\pi\)
0.914135 + 0.405411i \(0.132871\pi\)
\(978\) 0 0
\(979\) −50.8067 −1.62379
\(980\) 0 0
\(981\) 1.94784 0.0621896
\(982\) 0 0
\(983\) −44.0265 −1.40423 −0.702113 0.712065i \(-0.747760\pi\)
−0.702113 + 0.712065i \(0.747760\pi\)
\(984\) 0 0
\(985\) 7.41769 0.236347
\(986\) 0 0
\(987\) 8.42323 0.268114
\(988\) 0 0
\(989\) 43.4658 1.38213
\(990\) 0 0
\(991\) 12.7478 0.404946 0.202473 0.979288i \(-0.435102\pi\)
0.202473 + 0.979288i \(0.435102\pi\)
\(992\) 0 0
\(993\) 30.3015 0.961590
\(994\) 0 0
\(995\) 23.5540 0.746713
\(996\) 0 0
\(997\) 28.1246 0.890715 0.445357 0.895353i \(-0.353077\pi\)
0.445357 + 0.895353i \(0.353077\pi\)
\(998\) 0 0
\(999\) −48.9117 −1.54750
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 \(a_p\))