Properties

Label 6040.2.a.p.1.2
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.2
Root \(3.31016\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.31016 q^{3}\) \(+1.00000 q^{5}\) \(-0.477457 q^{7}\) \(+7.95713 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.31016 q^{3}\) \(+1.00000 q^{5}\) \(-0.477457 q^{7}\) \(+7.95713 q^{9}\) \(+4.57039 q^{11}\) \(+2.86935 q^{13}\) \(-3.31016 q^{15}\) \(+7.02125 q^{17}\) \(-5.71822 q^{19}\) \(+1.58046 q^{21}\) \(-1.60378 q^{23}\) \(+1.00000 q^{25}\) \(-16.4089 q^{27}\) \(-8.07405 q^{29}\) \(-11.0218 q^{31}\) \(-15.1287 q^{33}\) \(-0.477457 q^{35}\) \(-2.92795 q^{37}\) \(-9.49800 q^{39}\) \(-5.80115 q^{41}\) \(-7.00093 q^{43}\) \(+7.95713 q^{45}\) \(+12.4002 q^{47}\) \(-6.77203 q^{49}\) \(-23.2414 q^{51}\) \(-0.250729 q^{53}\) \(+4.57039 q^{55}\) \(+18.9282 q^{57}\) \(+2.86948 q^{59}\) \(+2.93287 q^{61}\) \(-3.79919 q^{63}\) \(+2.86935 q^{65}\) \(+0.359307 q^{67}\) \(+5.30876 q^{69}\) \(+13.8626 q^{71}\) \(+6.69059 q^{73}\) \(-3.31016 q^{75}\) \(-2.18217 q^{77}\) \(-16.4177 q^{79}\) \(+30.4446 q^{81}\) \(+4.08016 q^{83}\) \(+7.02125 q^{85}\) \(+26.7264 q^{87}\) \(-2.51700 q^{89}\) \(-1.36999 q^{91}\) \(+36.4840 q^{93}\) \(-5.71822 q^{95}\) \(-13.1177 q^{97}\) \(+36.3672 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.31016 −1.91112 −0.955560 0.294797i \(-0.904748\pi\)
−0.955560 + 0.294797i \(0.904748\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.477457 −0.180462 −0.0902310 0.995921i \(-0.528761\pi\)
−0.0902310 + 0.995921i \(0.528761\pi\)
\(8\) 0 0
\(9\) 7.95713 2.65238
\(10\) 0 0
\(11\) 4.57039 1.37803 0.689013 0.724749i \(-0.258044\pi\)
0.689013 + 0.724749i \(0.258044\pi\)
\(12\) 0 0
\(13\) 2.86935 0.795815 0.397907 0.917426i \(-0.369737\pi\)
0.397907 + 0.917426i \(0.369737\pi\)
\(14\) 0 0
\(15\) −3.31016 −0.854679
\(16\) 0 0
\(17\) 7.02125 1.70290 0.851451 0.524433i \(-0.175723\pi\)
0.851451 + 0.524433i \(0.175723\pi\)
\(18\) 0 0
\(19\) −5.71822 −1.31185 −0.655925 0.754826i \(-0.727721\pi\)
−0.655925 + 0.754826i \(0.727721\pi\)
\(20\) 0 0
\(21\) 1.58046 0.344884
\(22\) 0 0
\(23\) −1.60378 −0.334411 −0.167205 0.985922i \(-0.553474\pi\)
−0.167205 + 0.985922i \(0.553474\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −16.4089 −3.15789
\(28\) 0 0
\(29\) −8.07405 −1.49931 −0.749657 0.661827i \(-0.769781\pi\)
−0.749657 + 0.661827i \(0.769781\pi\)
\(30\) 0 0
\(31\) −11.0218 −1.97958 −0.989789 0.142537i \(-0.954474\pi\)
−0.989789 + 0.142537i \(0.954474\pi\)
\(32\) 0 0
\(33\) −15.1287 −2.63357
\(34\) 0 0
\(35\) −0.477457 −0.0807050
\(36\) 0 0
\(37\) −2.92795 −0.481352 −0.240676 0.970606i \(-0.577369\pi\)
−0.240676 + 0.970606i \(0.577369\pi\)
\(38\) 0 0
\(39\) −9.49800 −1.52090
\(40\) 0 0
\(41\) −5.80115 −0.905988 −0.452994 0.891514i \(-0.649644\pi\)
−0.452994 + 0.891514i \(0.649644\pi\)
\(42\) 0 0
\(43\) −7.00093 −1.06763 −0.533816 0.845601i \(-0.679242\pi\)
−0.533816 + 0.845601i \(0.679242\pi\)
\(44\) 0 0
\(45\) 7.95713 1.18618
\(46\) 0 0
\(47\) 12.4002 1.80876 0.904378 0.426733i \(-0.140336\pi\)
0.904378 + 0.426733i \(0.140336\pi\)
\(48\) 0 0
\(49\) −6.77203 −0.967433
\(50\) 0 0
\(51\) −23.2414 −3.25445
\(52\) 0 0
\(53\) −0.250729 −0.0344402 −0.0172201 0.999852i \(-0.505482\pi\)
−0.0172201 + 0.999852i \(0.505482\pi\)
\(54\) 0 0
\(55\) 4.57039 0.616272
\(56\) 0 0
\(57\) 18.9282 2.50710
\(58\) 0 0
\(59\) 2.86948 0.373574 0.186787 0.982400i \(-0.440192\pi\)
0.186787 + 0.982400i \(0.440192\pi\)
\(60\) 0 0
\(61\) 2.93287 0.375515 0.187758 0.982215i \(-0.439878\pi\)
0.187758 + 0.982215i \(0.439878\pi\)
\(62\) 0 0
\(63\) −3.79919 −0.478653
\(64\) 0 0
\(65\) 2.86935 0.355899
\(66\) 0 0
\(67\) 0.359307 0.0438964 0.0219482 0.999759i \(-0.493013\pi\)
0.0219482 + 0.999759i \(0.493013\pi\)
\(68\) 0 0
\(69\) 5.30876 0.639099
\(70\) 0 0
\(71\) 13.8626 1.64518 0.822591 0.568633i \(-0.192528\pi\)
0.822591 + 0.568633i \(0.192528\pi\)
\(72\) 0 0
\(73\) 6.69059 0.783074 0.391537 0.920162i \(-0.371943\pi\)
0.391537 + 0.920162i \(0.371943\pi\)
\(74\) 0 0
\(75\) −3.31016 −0.382224
\(76\) 0 0
\(77\) −2.18217 −0.248681
\(78\) 0 0
\(79\) −16.4177 −1.84713 −0.923567 0.383438i \(-0.874740\pi\)
−0.923567 + 0.383438i \(0.874740\pi\)
\(80\) 0 0
\(81\) 30.4446 3.38273
\(82\) 0 0
\(83\) 4.08016 0.447856 0.223928 0.974606i \(-0.428112\pi\)
0.223928 + 0.974606i \(0.428112\pi\)
\(84\) 0 0
\(85\) 7.02125 0.761561
\(86\) 0 0
\(87\) 26.7264 2.86537
\(88\) 0 0
\(89\) −2.51700 −0.266802 −0.133401 0.991062i \(-0.542590\pi\)
−0.133401 + 0.991062i \(0.542590\pi\)
\(90\) 0 0
\(91\) −1.36999 −0.143614
\(92\) 0 0
\(93\) 36.4840 3.78321
\(94\) 0 0
\(95\) −5.71822 −0.586677
\(96\) 0 0
\(97\) −13.1177 −1.33190 −0.665948 0.745998i \(-0.731973\pi\)
−0.665948 + 0.745998i \(0.731973\pi\)
\(98\) 0 0
\(99\) 36.3672 3.65504
\(100\) 0 0
\(101\) −5.13472 −0.510924 −0.255462 0.966819i \(-0.582228\pi\)
−0.255462 + 0.966819i \(0.582228\pi\)
\(102\) 0 0
\(103\) −8.82746 −0.869796 −0.434898 0.900480i \(-0.643216\pi\)
−0.434898 + 0.900480i \(0.643216\pi\)
\(104\) 0 0
\(105\) 1.58046 0.154237
\(106\) 0 0
\(107\) −9.90023 −0.957092 −0.478546 0.878063i \(-0.658836\pi\)
−0.478546 + 0.878063i \(0.658836\pi\)
\(108\) 0 0
\(109\) −13.9578 −1.33691 −0.668455 0.743752i \(-0.733044\pi\)
−0.668455 + 0.743752i \(0.733044\pi\)
\(110\) 0 0
\(111\) 9.69197 0.919921
\(112\) 0 0
\(113\) 12.2709 1.15435 0.577173 0.816622i \(-0.304156\pi\)
0.577173 + 0.816622i \(0.304156\pi\)
\(114\) 0 0
\(115\) −1.60378 −0.149553
\(116\) 0 0
\(117\) 22.8318 2.11080
\(118\) 0 0
\(119\) −3.35235 −0.307309
\(120\) 0 0
\(121\) 9.88850 0.898954
\(122\) 0 0
\(123\) 19.2027 1.73145
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −0.370668 −0.0328915 −0.0164457 0.999865i \(-0.505235\pi\)
−0.0164457 + 0.999865i \(0.505235\pi\)
\(128\) 0 0
\(129\) 23.1742 2.04037
\(130\) 0 0
\(131\) −1.83804 −0.160591 −0.0802953 0.996771i \(-0.525586\pi\)
−0.0802953 + 0.996771i \(0.525586\pi\)
\(132\) 0 0
\(133\) 2.73021 0.236739
\(134\) 0 0
\(135\) −16.4089 −1.41225
\(136\) 0 0
\(137\) −16.3748 −1.39900 −0.699498 0.714635i \(-0.746593\pi\)
−0.699498 + 0.714635i \(0.746593\pi\)
\(138\) 0 0
\(139\) −12.2506 −1.03908 −0.519542 0.854445i \(-0.673897\pi\)
−0.519542 + 0.854445i \(0.673897\pi\)
\(140\) 0 0
\(141\) −41.0466 −3.45675
\(142\) 0 0
\(143\) 13.1141 1.09665
\(144\) 0 0
\(145\) −8.07405 −0.670513
\(146\) 0 0
\(147\) 22.4165 1.84888
\(148\) 0 0
\(149\) −8.94591 −0.732877 −0.366439 0.930442i \(-0.619423\pi\)
−0.366439 + 0.930442i \(0.619423\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) 55.8690 4.51674
\(154\) 0 0
\(155\) −11.0218 −0.885295
\(156\) 0 0
\(157\) 10.0682 0.803526 0.401763 0.915744i \(-0.368398\pi\)
0.401763 + 0.915744i \(0.368398\pi\)
\(158\) 0 0
\(159\) 0.829951 0.0658194
\(160\) 0 0
\(161\) 0.765736 0.0603484
\(162\) 0 0
\(163\) −7.23556 −0.566733 −0.283366 0.959012i \(-0.591451\pi\)
−0.283366 + 0.959012i \(0.591451\pi\)
\(164\) 0 0
\(165\) −15.1287 −1.17777
\(166\) 0 0
\(167\) 19.6561 1.52103 0.760516 0.649320i \(-0.224946\pi\)
0.760516 + 0.649320i \(0.224946\pi\)
\(168\) 0 0
\(169\) −4.76682 −0.366679
\(170\) 0 0
\(171\) −45.5007 −3.47952
\(172\) 0 0
\(173\) −22.8776 −1.73935 −0.869676 0.493622i \(-0.835673\pi\)
−0.869676 + 0.493622i \(0.835673\pi\)
\(174\) 0 0
\(175\) −0.477457 −0.0360924
\(176\) 0 0
\(177\) −9.49843 −0.713946
\(178\) 0 0
\(179\) 8.42748 0.629900 0.314950 0.949108i \(-0.398012\pi\)
0.314950 + 0.949108i \(0.398012\pi\)
\(180\) 0 0
\(181\) 1.21187 0.0900775 0.0450388 0.998985i \(-0.485659\pi\)
0.0450388 + 0.998985i \(0.485659\pi\)
\(182\) 0 0
\(183\) −9.70825 −0.717654
\(184\) 0 0
\(185\) −2.92795 −0.215267
\(186\) 0 0
\(187\) 32.0899 2.34664
\(188\) 0 0
\(189\) 7.83455 0.569879
\(190\) 0 0
\(191\) −12.1900 −0.882036 −0.441018 0.897498i \(-0.645383\pi\)
−0.441018 + 0.897498i \(0.645383\pi\)
\(192\) 0 0
\(193\) −5.35965 −0.385796 −0.192898 0.981219i \(-0.561789\pi\)
−0.192898 + 0.981219i \(0.561789\pi\)
\(194\) 0 0
\(195\) −9.49800 −0.680166
\(196\) 0 0
\(197\) −13.8689 −0.988117 −0.494059 0.869429i \(-0.664487\pi\)
−0.494059 + 0.869429i \(0.664487\pi\)
\(198\) 0 0
\(199\) −21.3390 −1.51268 −0.756342 0.654176i \(-0.773015\pi\)
−0.756342 + 0.654176i \(0.773015\pi\)
\(200\) 0 0
\(201\) −1.18936 −0.0838912
\(202\) 0 0
\(203\) 3.85501 0.270569
\(204\) 0 0
\(205\) −5.80115 −0.405170
\(206\) 0 0
\(207\) −12.7615 −0.886984
\(208\) 0 0
\(209\) −26.1345 −1.80776
\(210\) 0 0
\(211\) 7.12888 0.490772 0.245386 0.969425i \(-0.421085\pi\)
0.245386 + 0.969425i \(0.421085\pi\)
\(212\) 0 0
\(213\) −45.8872 −3.14414
\(214\) 0 0
\(215\) −7.00093 −0.477459
\(216\) 0 0
\(217\) 5.26245 0.357239
\(218\) 0 0
\(219\) −22.1469 −1.49655
\(220\) 0 0
\(221\) 20.1464 1.35520
\(222\) 0 0
\(223\) −2.28108 −0.152753 −0.0763763 0.997079i \(-0.524335\pi\)
−0.0763763 + 0.997079i \(0.524335\pi\)
\(224\) 0 0
\(225\) 7.95713 0.530476
\(226\) 0 0
\(227\) 17.9633 1.19227 0.596134 0.802885i \(-0.296703\pi\)
0.596134 + 0.802885i \(0.296703\pi\)
\(228\) 0 0
\(229\) 14.1077 0.932266 0.466133 0.884715i \(-0.345647\pi\)
0.466133 + 0.884715i \(0.345647\pi\)
\(230\) 0 0
\(231\) 7.22332 0.475259
\(232\) 0 0
\(233\) 26.2492 1.71964 0.859820 0.510598i \(-0.170576\pi\)
0.859820 + 0.510598i \(0.170576\pi\)
\(234\) 0 0
\(235\) 12.4002 0.808900
\(236\) 0 0
\(237\) 54.3451 3.53009
\(238\) 0 0
\(239\) −15.0090 −0.970849 −0.485425 0.874279i \(-0.661335\pi\)
−0.485425 + 0.874279i \(0.661335\pi\)
\(240\) 0 0
\(241\) 0.442366 0.0284953 0.0142476 0.999898i \(-0.495465\pi\)
0.0142476 + 0.999898i \(0.495465\pi\)
\(242\) 0 0
\(243\) −51.5497 −3.30691
\(244\) 0 0
\(245\) −6.77203 −0.432649
\(246\) 0 0
\(247\) −16.4076 −1.04399
\(248\) 0 0
\(249\) −13.5060 −0.855906
\(250\) 0 0
\(251\) 0.341253 0.0215397 0.0107699 0.999942i \(-0.496572\pi\)
0.0107699 + 0.999942i \(0.496572\pi\)
\(252\) 0 0
\(253\) −7.32990 −0.460827
\(254\) 0 0
\(255\) −23.2414 −1.45543
\(256\) 0 0
\(257\) 19.4223 1.21153 0.605764 0.795644i \(-0.292868\pi\)
0.605764 + 0.795644i \(0.292868\pi\)
\(258\) 0 0
\(259\) 1.39797 0.0868657
\(260\) 0 0
\(261\) −64.2463 −3.97675
\(262\) 0 0
\(263\) 11.3773 0.701554 0.350777 0.936459i \(-0.385918\pi\)
0.350777 + 0.936459i \(0.385918\pi\)
\(264\) 0 0
\(265\) −0.250729 −0.0154021
\(266\) 0 0
\(267\) 8.33167 0.509890
\(268\) 0 0
\(269\) 2.12272 0.129425 0.0647124 0.997904i \(-0.479387\pi\)
0.0647124 + 0.997904i \(0.479387\pi\)
\(270\) 0 0
\(271\) 10.8941 0.661770 0.330885 0.943671i \(-0.392653\pi\)
0.330885 + 0.943671i \(0.392653\pi\)
\(272\) 0 0
\(273\) 4.53489 0.274464
\(274\) 0 0
\(275\) 4.57039 0.275605
\(276\) 0 0
\(277\) −8.45475 −0.507997 −0.253998 0.967205i \(-0.581746\pi\)
−0.253998 + 0.967205i \(0.581746\pi\)
\(278\) 0 0
\(279\) −87.7022 −5.25059
\(280\) 0 0
\(281\) 31.7396 1.89343 0.946714 0.322075i \(-0.104380\pi\)
0.946714 + 0.322075i \(0.104380\pi\)
\(282\) 0 0
\(283\) −11.1546 −0.663070 −0.331535 0.943443i \(-0.607567\pi\)
−0.331535 + 0.943443i \(0.607567\pi\)
\(284\) 0 0
\(285\) 18.9282 1.12121
\(286\) 0 0
\(287\) 2.76980 0.163496
\(288\) 0 0
\(289\) 32.2979 1.89988
\(290\) 0 0
\(291\) 43.4215 2.54541
\(292\) 0 0
\(293\) 17.1225 1.00031 0.500154 0.865936i \(-0.333277\pi\)
0.500154 + 0.865936i \(0.333277\pi\)
\(294\) 0 0
\(295\) 2.86948 0.167068
\(296\) 0 0
\(297\) −74.9951 −4.35166
\(298\) 0 0
\(299\) −4.60180 −0.266129
\(300\) 0 0
\(301\) 3.34264 0.192667
\(302\) 0 0
\(303\) 16.9967 0.976437
\(304\) 0 0
\(305\) 2.93287 0.167935
\(306\) 0 0
\(307\) −26.2164 −1.49625 −0.748126 0.663557i \(-0.769046\pi\)
−0.748126 + 0.663557i \(0.769046\pi\)
\(308\) 0 0
\(309\) 29.2203 1.66228
\(310\) 0 0
\(311\) 7.64048 0.433252 0.216626 0.976255i \(-0.430495\pi\)
0.216626 + 0.976255i \(0.430495\pi\)
\(312\) 0 0
\(313\) −20.0333 −1.13235 −0.566175 0.824285i \(-0.691577\pi\)
−0.566175 + 0.824285i \(0.691577\pi\)
\(314\) 0 0
\(315\) −3.79919 −0.214060
\(316\) 0 0
\(317\) −21.8570 −1.22761 −0.613806 0.789457i \(-0.710362\pi\)
−0.613806 + 0.789457i \(0.710362\pi\)
\(318\) 0 0
\(319\) −36.9016 −2.06609
\(320\) 0 0
\(321\) 32.7713 1.82912
\(322\) 0 0
\(323\) −40.1491 −2.23395
\(324\) 0 0
\(325\) 2.86935 0.159163
\(326\) 0 0
\(327\) 46.2023 2.55500
\(328\) 0 0
\(329\) −5.92057 −0.326411
\(330\) 0 0
\(331\) 2.17211 0.119390 0.0596950 0.998217i \(-0.480987\pi\)
0.0596950 + 0.998217i \(0.480987\pi\)
\(332\) 0 0
\(333\) −23.2981 −1.27673
\(334\) 0 0
\(335\) 0.359307 0.0196310
\(336\) 0 0
\(337\) 17.7985 0.969547 0.484773 0.874640i \(-0.338902\pi\)
0.484773 + 0.874640i \(0.338902\pi\)
\(338\) 0 0
\(339\) −40.6185 −2.20609
\(340\) 0 0
\(341\) −50.3741 −2.72791
\(342\) 0 0
\(343\) 6.57556 0.355047
\(344\) 0 0
\(345\) 5.30876 0.285814
\(346\) 0 0
\(347\) 9.81221 0.526747 0.263373 0.964694i \(-0.415165\pi\)
0.263373 + 0.964694i \(0.415165\pi\)
\(348\) 0 0
\(349\) 10.2946 0.551056 0.275528 0.961293i \(-0.411147\pi\)
0.275528 + 0.961293i \(0.411147\pi\)
\(350\) 0 0
\(351\) −47.0829 −2.51310
\(352\) 0 0
\(353\) 16.4544 0.875780 0.437890 0.899029i \(-0.355726\pi\)
0.437890 + 0.899029i \(0.355726\pi\)
\(354\) 0 0
\(355\) 13.8626 0.735748
\(356\) 0 0
\(357\) 11.0968 0.587305
\(358\) 0 0
\(359\) −3.15583 −0.166558 −0.0832792 0.996526i \(-0.526539\pi\)
−0.0832792 + 0.996526i \(0.526539\pi\)
\(360\) 0 0
\(361\) 13.6981 0.720950
\(362\) 0 0
\(363\) −32.7325 −1.71801
\(364\) 0 0
\(365\) 6.69059 0.350201
\(366\) 0 0
\(367\) 10.8928 0.568599 0.284300 0.958735i \(-0.408239\pi\)
0.284300 + 0.958735i \(0.408239\pi\)
\(368\) 0 0
\(369\) −46.1606 −2.40302
\(370\) 0 0
\(371\) 0.119712 0.00621515
\(372\) 0 0
\(373\) −37.6287 −1.94834 −0.974169 0.225820i \(-0.927494\pi\)
−0.974169 + 0.225820i \(0.927494\pi\)
\(374\) 0 0
\(375\) −3.31016 −0.170936
\(376\) 0 0
\(377\) −23.1673 −1.19318
\(378\) 0 0
\(379\) −20.4558 −1.05075 −0.525373 0.850872i \(-0.676074\pi\)
−0.525373 + 0.850872i \(0.676074\pi\)
\(380\) 0 0
\(381\) 1.22697 0.0628595
\(382\) 0 0
\(383\) −10.2171 −0.522069 −0.261034 0.965330i \(-0.584064\pi\)
−0.261034 + 0.965330i \(0.584064\pi\)
\(384\) 0 0
\(385\) −2.18217 −0.111214
\(386\) 0 0
\(387\) −55.7073 −2.83176
\(388\) 0 0
\(389\) 4.13479 0.209642 0.104821 0.994491i \(-0.466573\pi\)
0.104821 + 0.994491i \(0.466573\pi\)
\(390\) 0 0
\(391\) −11.2605 −0.569469
\(392\) 0 0
\(393\) 6.08421 0.306908
\(394\) 0 0
\(395\) −16.4177 −0.826063
\(396\) 0 0
\(397\) 2.87821 0.144453 0.0722266 0.997388i \(-0.476990\pi\)
0.0722266 + 0.997388i \(0.476990\pi\)
\(398\) 0 0
\(399\) −9.03741 −0.452436
\(400\) 0 0
\(401\) −17.5295 −0.875381 −0.437691 0.899126i \(-0.644203\pi\)
−0.437691 + 0.899126i \(0.644203\pi\)
\(402\) 0 0
\(403\) −31.6255 −1.57538
\(404\) 0 0
\(405\) 30.4446 1.51280
\(406\) 0 0
\(407\) −13.3819 −0.663315
\(408\) 0 0
\(409\) −23.3765 −1.15589 −0.577946 0.816075i \(-0.696146\pi\)
−0.577946 + 0.816075i \(0.696146\pi\)
\(410\) 0 0
\(411\) 54.2032 2.67365
\(412\) 0 0
\(413\) −1.37005 −0.0674160
\(414\) 0 0
\(415\) 4.08016 0.200287
\(416\) 0 0
\(417\) 40.5515 1.98581
\(418\) 0 0
\(419\) 34.1445 1.66807 0.834033 0.551715i \(-0.186026\pi\)
0.834033 + 0.551715i \(0.186026\pi\)
\(420\) 0 0
\(421\) −17.1458 −0.835637 −0.417818 0.908531i \(-0.637205\pi\)
−0.417818 + 0.908531i \(0.637205\pi\)
\(422\) 0 0
\(423\) 98.6701 4.79750
\(424\) 0 0
\(425\) 7.02125 0.340581
\(426\) 0 0
\(427\) −1.40032 −0.0677662
\(428\) 0 0
\(429\) −43.4096 −2.09584
\(430\) 0 0
\(431\) −27.0734 −1.30408 −0.652040 0.758185i \(-0.726086\pi\)
−0.652040 + 0.758185i \(0.726086\pi\)
\(432\) 0 0
\(433\) −15.9416 −0.766106 −0.383053 0.923726i \(-0.625127\pi\)
−0.383053 + 0.923726i \(0.625127\pi\)
\(434\) 0 0
\(435\) 26.7264 1.28143
\(436\) 0 0
\(437\) 9.17076 0.438697
\(438\) 0 0
\(439\) 3.36694 0.160695 0.0803476 0.996767i \(-0.474397\pi\)
0.0803476 + 0.996767i \(0.474397\pi\)
\(440\) 0 0
\(441\) −53.8860 −2.56600
\(442\) 0 0
\(443\) −25.2415 −1.19926 −0.599629 0.800278i \(-0.704685\pi\)
−0.599629 + 0.800278i \(0.704685\pi\)
\(444\) 0 0
\(445\) −2.51700 −0.119317
\(446\) 0 0
\(447\) 29.6124 1.40062
\(448\) 0 0
\(449\) 19.5496 0.922603 0.461301 0.887243i \(-0.347383\pi\)
0.461301 + 0.887243i \(0.347383\pi\)
\(450\) 0 0
\(451\) −26.5135 −1.24847
\(452\) 0 0
\(453\) −3.31016 −0.155525
\(454\) 0 0
\(455\) −1.36999 −0.0642263
\(456\) 0 0
\(457\) 32.8315 1.53579 0.767897 0.640573i \(-0.221303\pi\)
0.767897 + 0.640573i \(0.221303\pi\)
\(458\) 0 0
\(459\) −115.211 −5.37758
\(460\) 0 0
\(461\) −15.1822 −0.707104 −0.353552 0.935415i \(-0.615026\pi\)
−0.353552 + 0.935415i \(0.615026\pi\)
\(462\) 0 0
\(463\) 3.15228 0.146499 0.0732494 0.997314i \(-0.476663\pi\)
0.0732494 + 0.997314i \(0.476663\pi\)
\(464\) 0 0
\(465\) 36.4840 1.69190
\(466\) 0 0
\(467\) −24.8132 −1.14822 −0.574108 0.818779i \(-0.694651\pi\)
−0.574108 + 0.818779i \(0.694651\pi\)
\(468\) 0 0
\(469\) −0.171554 −0.00792162
\(470\) 0 0
\(471\) −33.3272 −1.53563
\(472\) 0 0
\(473\) −31.9970 −1.47122
\(474\) 0 0
\(475\) −5.71822 −0.262370
\(476\) 0 0
\(477\) −1.99508 −0.0913486
\(478\) 0 0
\(479\) −3.81391 −0.174262 −0.0871309 0.996197i \(-0.527770\pi\)
−0.0871309 + 0.996197i \(0.527770\pi\)
\(480\) 0 0
\(481\) −8.40131 −0.383067
\(482\) 0 0
\(483\) −2.53471 −0.115333
\(484\) 0 0
\(485\) −13.1177 −0.595642
\(486\) 0 0
\(487\) 36.6581 1.66113 0.830567 0.556918i \(-0.188016\pi\)
0.830567 + 0.556918i \(0.188016\pi\)
\(488\) 0 0
\(489\) 23.9508 1.08309
\(490\) 0 0
\(491\) −0.660116 −0.0297906 −0.0148953 0.999889i \(-0.504742\pi\)
−0.0148953 + 0.999889i \(0.504742\pi\)
\(492\) 0 0
\(493\) −56.6899 −2.55319
\(494\) 0 0
\(495\) 36.3672 1.63459
\(496\) 0 0
\(497\) −6.61878 −0.296893
\(498\) 0 0
\(499\) 28.5930 1.28000 0.639999 0.768375i \(-0.278935\pi\)
0.639999 + 0.768375i \(0.278935\pi\)
\(500\) 0 0
\(501\) −65.0646 −2.90687
\(502\) 0 0
\(503\) −15.2567 −0.680265 −0.340132 0.940378i \(-0.610472\pi\)
−0.340132 + 0.940378i \(0.610472\pi\)
\(504\) 0 0
\(505\) −5.13472 −0.228492
\(506\) 0 0
\(507\) 15.7789 0.700767
\(508\) 0 0
\(509\) −11.0125 −0.488121 −0.244060 0.969760i \(-0.578480\pi\)
−0.244060 + 0.969760i \(0.578480\pi\)
\(510\) 0 0
\(511\) −3.19447 −0.141315
\(512\) 0 0
\(513\) 93.8297 4.14268
\(514\) 0 0
\(515\) −8.82746 −0.388984
\(516\) 0 0
\(517\) 56.6738 2.49251
\(518\) 0 0
\(519\) 75.7285 3.32411
\(520\) 0 0
\(521\) 13.2241 0.579358 0.289679 0.957124i \(-0.406451\pi\)
0.289679 + 0.957124i \(0.406451\pi\)
\(522\) 0 0
\(523\) 23.0224 1.00670 0.503350 0.864082i \(-0.332101\pi\)
0.503350 + 0.864082i \(0.332101\pi\)
\(524\) 0 0
\(525\) 1.58046 0.0689769
\(526\) 0 0
\(527\) −77.3870 −3.37103
\(528\) 0 0
\(529\) −20.4279 −0.888169
\(530\) 0 0
\(531\) 22.8328 0.990861
\(532\) 0 0
\(533\) −16.6455 −0.720999
\(534\) 0 0
\(535\) −9.90023 −0.428024
\(536\) 0 0
\(537\) −27.8963 −1.20381
\(538\) 0 0
\(539\) −30.9509 −1.33315
\(540\) 0 0
\(541\) −9.41992 −0.404994 −0.202497 0.979283i \(-0.564906\pi\)
−0.202497 + 0.979283i \(0.564906\pi\)
\(542\) 0 0
\(543\) −4.01148 −0.172149
\(544\) 0 0
\(545\) −13.9578 −0.597884
\(546\) 0 0
\(547\) −37.4340 −1.60056 −0.800280 0.599626i \(-0.795316\pi\)
−0.800280 + 0.599626i \(0.795316\pi\)
\(548\) 0 0
\(549\) 23.3372 0.996008
\(550\) 0 0
\(551\) 46.1692 1.96687
\(552\) 0 0
\(553\) 7.83874 0.333337
\(554\) 0 0
\(555\) 9.69197 0.411401
\(556\) 0 0
\(557\) −3.10073 −0.131382 −0.0656910 0.997840i \(-0.520925\pi\)
−0.0656910 + 0.997840i \(0.520925\pi\)
\(558\) 0 0
\(559\) −20.0881 −0.849637
\(560\) 0 0
\(561\) −106.222 −4.48472
\(562\) 0 0
\(563\) 21.6687 0.913229 0.456614 0.889665i \(-0.349062\pi\)
0.456614 + 0.889665i \(0.349062\pi\)
\(564\) 0 0
\(565\) 12.2709 0.516239
\(566\) 0 0
\(567\) −14.5360 −0.610454
\(568\) 0 0
\(569\) 34.0389 1.42698 0.713492 0.700663i \(-0.247112\pi\)
0.713492 + 0.700663i \(0.247112\pi\)
\(570\) 0 0
\(571\) −34.5849 −1.44733 −0.723666 0.690150i \(-0.757545\pi\)
−0.723666 + 0.690150i \(0.757545\pi\)
\(572\) 0 0
\(573\) 40.3507 1.68568
\(574\) 0 0
\(575\) −1.60378 −0.0668822
\(576\) 0 0
\(577\) 14.3184 0.596082 0.298041 0.954553i \(-0.403667\pi\)
0.298041 + 0.954553i \(0.403667\pi\)
\(578\) 0 0
\(579\) 17.7413 0.737302
\(580\) 0 0
\(581\) −1.94810 −0.0808209
\(582\) 0 0
\(583\) −1.14593 −0.0474595
\(584\) 0 0
\(585\) 22.8318 0.943979
\(586\) 0 0
\(587\) 47.3341 1.95369 0.976845 0.213950i \(-0.0686330\pi\)
0.976845 + 0.213950i \(0.0686330\pi\)
\(588\) 0 0
\(589\) 63.0253 2.59691
\(590\) 0 0
\(591\) 45.9082 1.88841
\(592\) 0 0
\(593\) 1.53057 0.0628529 0.0314264 0.999506i \(-0.489995\pi\)
0.0314264 + 0.999506i \(0.489995\pi\)
\(594\) 0 0
\(595\) −3.35235 −0.137433
\(596\) 0 0
\(597\) 70.6356 2.89092
\(598\) 0 0
\(599\) 24.7179 1.00995 0.504974 0.863135i \(-0.331502\pi\)
0.504974 + 0.863135i \(0.331502\pi\)
\(600\) 0 0
\(601\) −28.5283 −1.16369 −0.581846 0.813299i \(-0.697669\pi\)
−0.581846 + 0.813299i \(0.697669\pi\)
\(602\) 0 0
\(603\) 2.85906 0.116430
\(604\) 0 0
\(605\) 9.88850 0.402025
\(606\) 0 0
\(607\) 26.5748 1.07864 0.539319 0.842102i \(-0.318682\pi\)
0.539319 + 0.842102i \(0.318682\pi\)
\(608\) 0 0
\(609\) −12.7607 −0.517090
\(610\) 0 0
\(611\) 35.5805 1.43943
\(612\) 0 0
\(613\) −43.3039 −1.74903 −0.874514 0.485000i \(-0.838820\pi\)
−0.874514 + 0.485000i \(0.838820\pi\)
\(614\) 0 0
\(615\) 19.2027 0.774328
\(616\) 0 0
\(617\) −28.3610 −1.14177 −0.570886 0.821030i \(-0.693400\pi\)
−0.570886 + 0.821030i \(0.693400\pi\)
\(618\) 0 0
\(619\) −2.00072 −0.0804157 −0.0402078 0.999191i \(-0.512802\pi\)
−0.0402078 + 0.999191i \(0.512802\pi\)
\(620\) 0 0
\(621\) 26.3162 1.05603
\(622\) 0 0
\(623\) 1.20176 0.0481475
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 86.5094 3.45485
\(628\) 0 0
\(629\) −20.5579 −0.819695
\(630\) 0 0
\(631\) 3.47057 0.138161 0.0690806 0.997611i \(-0.477993\pi\)
0.0690806 + 0.997611i \(0.477993\pi\)
\(632\) 0 0
\(633\) −23.5977 −0.937924
\(634\) 0 0
\(635\) −0.370668 −0.0147095
\(636\) 0 0
\(637\) −19.4313 −0.769898
\(638\) 0 0
\(639\) 110.306 4.36365
\(640\) 0 0
\(641\) 1.06700 0.0421438 0.0210719 0.999778i \(-0.493292\pi\)
0.0210719 + 0.999778i \(0.493292\pi\)
\(642\) 0 0
\(643\) 3.05355 0.120420 0.0602101 0.998186i \(-0.480823\pi\)
0.0602101 + 0.998186i \(0.480823\pi\)
\(644\) 0 0
\(645\) 23.1742 0.912482
\(646\) 0 0
\(647\) −6.50100 −0.255581 −0.127790 0.991801i \(-0.540788\pi\)
−0.127790 + 0.991801i \(0.540788\pi\)
\(648\) 0 0
\(649\) 13.1147 0.514795
\(650\) 0 0
\(651\) −17.4195 −0.682726
\(652\) 0 0
\(653\) 42.7661 1.67357 0.836784 0.547534i \(-0.184433\pi\)
0.836784 + 0.547534i \(0.184433\pi\)
\(654\) 0 0
\(655\) −1.83804 −0.0718183
\(656\) 0 0
\(657\) 53.2379 2.07701
\(658\) 0 0
\(659\) −27.3064 −1.06371 −0.531853 0.846837i \(-0.678504\pi\)
−0.531853 + 0.846837i \(0.678504\pi\)
\(660\) 0 0
\(661\) 24.0143 0.934047 0.467024 0.884245i \(-0.345326\pi\)
0.467024 + 0.884245i \(0.345326\pi\)
\(662\) 0 0
\(663\) −66.6878 −2.58994
\(664\) 0 0
\(665\) 2.73021 0.105873
\(666\) 0 0
\(667\) 12.9490 0.501387
\(668\) 0 0
\(669\) 7.55074 0.291929
\(670\) 0 0
\(671\) 13.4044 0.517469
\(672\) 0 0
\(673\) −39.7984 −1.53412 −0.767058 0.641578i \(-0.778280\pi\)
−0.767058 + 0.641578i \(0.778280\pi\)
\(674\) 0 0
\(675\) −16.4089 −0.631578
\(676\) 0 0
\(677\) −4.22897 −0.162533 −0.0812663 0.996692i \(-0.525896\pi\)
−0.0812663 + 0.996692i \(0.525896\pi\)
\(678\) 0 0
\(679\) 6.26312 0.240357
\(680\) 0 0
\(681\) −59.4615 −2.27857
\(682\) 0 0
\(683\) −43.1761 −1.65209 −0.826044 0.563605i \(-0.809414\pi\)
−0.826044 + 0.563605i \(0.809414\pi\)
\(684\) 0 0
\(685\) −16.3748 −0.625650
\(686\) 0 0
\(687\) −46.6988 −1.78167
\(688\) 0 0
\(689\) −0.719429 −0.0274081
\(690\) 0 0
\(691\) 26.8640 1.02196 0.510978 0.859594i \(-0.329283\pi\)
0.510978 + 0.859594i \(0.329283\pi\)
\(692\) 0 0
\(693\) −17.3638 −0.659596
\(694\) 0 0
\(695\) −12.2506 −0.464692
\(696\) 0 0
\(697\) −40.7313 −1.54281
\(698\) 0 0
\(699\) −86.8888 −3.28644
\(700\) 0 0
\(701\) −11.3675 −0.429346 −0.214673 0.976686i \(-0.568869\pi\)
−0.214673 + 0.976686i \(0.568869\pi\)
\(702\) 0 0
\(703\) 16.7427 0.631461
\(704\) 0 0
\(705\) −41.0466 −1.54590
\(706\) 0 0
\(707\) 2.45161 0.0922024
\(708\) 0 0
\(709\) 6.65280 0.249851 0.124926 0.992166i \(-0.460131\pi\)
0.124926 + 0.992166i \(0.460131\pi\)
\(710\) 0 0
\(711\) −130.638 −4.89930
\(712\) 0 0
\(713\) 17.6766 0.661993
\(714\) 0 0
\(715\) 13.1141 0.490438
\(716\) 0 0
\(717\) 49.6820 1.85541
\(718\) 0 0
\(719\) −45.6899 −1.70394 −0.851972 0.523587i \(-0.824594\pi\)
−0.851972 + 0.523587i \(0.824594\pi\)
\(720\) 0 0
\(721\) 4.21474 0.156965
\(722\) 0 0
\(723\) −1.46430 −0.0544579
\(724\) 0 0
\(725\) −8.07405 −0.299863
\(726\) 0 0
\(727\) 16.1171 0.597752 0.298876 0.954292i \(-0.403388\pi\)
0.298876 + 0.954292i \(0.403388\pi\)
\(728\) 0 0
\(729\) 79.3037 2.93717
\(730\) 0 0
\(731\) −49.1553 −1.81807
\(732\) 0 0
\(733\) −32.2680 −1.19185 −0.595924 0.803041i \(-0.703214\pi\)
−0.595924 + 0.803041i \(0.703214\pi\)
\(734\) 0 0
\(735\) 22.4165 0.826845
\(736\) 0 0
\(737\) 1.64218 0.0604903
\(738\) 0 0
\(739\) −0.315945 −0.0116222 −0.00581110 0.999983i \(-0.501850\pi\)
−0.00581110 + 0.999983i \(0.501850\pi\)
\(740\) 0 0
\(741\) 54.3117 1.99519
\(742\) 0 0
\(743\) −12.5495 −0.460398 −0.230199 0.973144i \(-0.573938\pi\)
−0.230199 + 0.973144i \(0.573938\pi\)
\(744\) 0 0
\(745\) −8.94591 −0.327753
\(746\) 0 0
\(747\) 32.4664 1.18788
\(748\) 0 0
\(749\) 4.72694 0.172719
\(750\) 0 0
\(751\) −48.2774 −1.76167 −0.880834 0.473424i \(-0.843018\pi\)
−0.880834 + 0.473424i \(0.843018\pi\)
\(752\) 0 0
\(753\) −1.12960 −0.0411650
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −33.6955 −1.22468 −0.612342 0.790593i \(-0.709773\pi\)
−0.612342 + 0.790593i \(0.709773\pi\)
\(758\) 0 0
\(759\) 24.2631 0.880695
\(760\) 0 0
\(761\) 15.9571 0.578445 0.289222 0.957262i \(-0.406603\pi\)
0.289222 + 0.957262i \(0.406603\pi\)
\(762\) 0 0
\(763\) 6.66423 0.241261
\(764\) 0 0
\(765\) 55.8690 2.01995
\(766\) 0 0
\(767\) 8.23355 0.297296
\(768\) 0 0
\(769\) 21.3174 0.768724 0.384362 0.923182i \(-0.374421\pi\)
0.384362 + 0.923182i \(0.374421\pi\)
\(770\) 0 0
\(771\) −64.2908 −2.31538
\(772\) 0 0
\(773\) 12.5965 0.453065 0.226532 0.974004i \(-0.427261\pi\)
0.226532 + 0.974004i \(0.427261\pi\)
\(774\) 0 0
\(775\) −11.0218 −0.395916
\(776\) 0 0
\(777\) −4.62750 −0.166011
\(778\) 0 0
\(779\) 33.1723 1.18852
\(780\) 0 0
\(781\) 63.3573 2.26710
\(782\) 0 0
\(783\) 132.486 4.73467
\(784\) 0 0
\(785\) 10.0682 0.359348
\(786\) 0 0
\(787\) 23.3087 0.830867 0.415433 0.909624i \(-0.363630\pi\)
0.415433 + 0.909624i \(0.363630\pi\)
\(788\) 0 0
\(789\) −37.6606 −1.34075
\(790\) 0 0
\(791\) −5.85881 −0.208315
\(792\) 0 0
\(793\) 8.41543 0.298841
\(794\) 0 0
\(795\) 0.829951 0.0294353
\(796\) 0 0
\(797\) −24.2039 −0.857347 −0.428674 0.903459i \(-0.641019\pi\)
−0.428674 + 0.903459i \(0.641019\pi\)
\(798\) 0 0
\(799\) 87.0649 3.08013
\(800\) 0 0
\(801\) −20.0281 −0.707659
\(802\) 0 0
\(803\) 30.5786 1.07910
\(804\) 0 0
\(805\) 0.765736 0.0269886
\(806\) 0 0
\(807\) −7.02655 −0.247346
\(808\) 0 0
\(809\) −46.2509 −1.62610 −0.813048 0.582197i \(-0.802193\pi\)
−0.813048 + 0.582197i \(0.802193\pi\)
\(810\) 0 0
\(811\) 44.1204 1.54928 0.774639 0.632404i \(-0.217932\pi\)
0.774639 + 0.632404i \(0.217932\pi\)
\(812\) 0 0
\(813\) −36.0612 −1.26472
\(814\) 0 0
\(815\) −7.23556 −0.253451
\(816\) 0 0
\(817\) 40.0329 1.40057
\(818\) 0 0
\(819\) −10.9012 −0.380919
\(820\) 0 0
\(821\) 13.4583 0.469696 0.234848 0.972032i \(-0.424541\pi\)
0.234848 + 0.972032i \(0.424541\pi\)
\(822\) 0 0
\(823\) 29.8848 1.04172 0.520859 0.853643i \(-0.325612\pi\)
0.520859 + 0.853643i \(0.325612\pi\)
\(824\) 0 0
\(825\) −15.1287 −0.526714
\(826\) 0 0
\(827\) −37.7344 −1.31215 −0.656076 0.754695i \(-0.727785\pi\)
−0.656076 + 0.754695i \(0.727785\pi\)
\(828\) 0 0
\(829\) −9.46552 −0.328751 −0.164375 0.986398i \(-0.552561\pi\)
−0.164375 + 0.986398i \(0.552561\pi\)
\(830\) 0 0
\(831\) 27.9866 0.970843
\(832\) 0 0
\(833\) −47.5481 −1.64745
\(834\) 0 0
\(835\) 19.6561 0.680226
\(836\) 0 0
\(837\) 180.856 6.25130
\(838\) 0 0
\(839\) 7.77972 0.268586 0.134293 0.990942i \(-0.457124\pi\)
0.134293 + 0.990942i \(0.457124\pi\)
\(840\) 0 0
\(841\) 36.1903 1.24794
\(842\) 0 0
\(843\) −105.063 −3.61857
\(844\) 0 0
\(845\) −4.76682 −0.163984
\(846\) 0 0
\(847\) −4.72134 −0.162227
\(848\) 0 0
\(849\) 36.9234 1.26721
\(850\) 0 0
\(851\) 4.69578 0.160969
\(852\) 0 0
\(853\) −9.58721 −0.328260 −0.164130 0.986439i \(-0.552482\pi\)
−0.164130 + 0.986439i \(0.552482\pi\)
\(854\) 0 0
\(855\) −45.5007 −1.55609
\(856\) 0 0
\(857\) −48.6213 −1.66087 −0.830436 0.557115i \(-0.811908\pi\)
−0.830436 + 0.557115i \(0.811908\pi\)
\(858\) 0 0
\(859\) −42.2174 −1.44044 −0.720219 0.693747i \(-0.755959\pi\)
−0.720219 + 0.693747i \(0.755959\pi\)
\(860\) 0 0
\(861\) −9.16848 −0.312461
\(862\) 0 0
\(863\) 3.78023 0.128680 0.0643402 0.997928i \(-0.479506\pi\)
0.0643402 + 0.997928i \(0.479506\pi\)
\(864\) 0 0
\(865\) −22.8776 −0.777862
\(866\) 0 0
\(867\) −106.911 −3.63090
\(868\) 0 0
\(869\) −75.0353 −2.54540
\(870\) 0 0
\(871\) 1.03098 0.0349334
\(872\) 0 0
\(873\) −104.379 −3.53269
\(874\) 0 0
\(875\) −0.477457 −0.0161410
\(876\) 0 0
\(877\) −18.2569 −0.616491 −0.308246 0.951307i \(-0.599742\pi\)
−0.308246 + 0.951307i \(0.599742\pi\)
\(878\) 0 0
\(879\) −56.6782 −1.91171
\(880\) 0 0
\(881\) −16.1548 −0.544269 −0.272135 0.962259i \(-0.587730\pi\)
−0.272135 + 0.962259i \(0.587730\pi\)
\(882\) 0 0
\(883\) −44.0584 −1.48268 −0.741341 0.671128i \(-0.765810\pi\)
−0.741341 + 0.671128i \(0.765810\pi\)
\(884\) 0 0
\(885\) −9.49843 −0.319286
\(886\) 0 0
\(887\) 42.4081 1.42393 0.711963 0.702217i \(-0.247806\pi\)
0.711963 + 0.702217i \(0.247806\pi\)
\(888\) 0 0
\(889\) 0.176978 0.00593566
\(890\) 0 0
\(891\) 139.144 4.66149
\(892\) 0 0
\(893\) −70.9071 −2.37282
\(894\) 0 0
\(895\) 8.42748 0.281700
\(896\) 0 0
\(897\) 15.2327 0.508605
\(898\) 0 0
\(899\) 88.9908 2.96801
\(900\) 0 0
\(901\) −1.76043 −0.0586484
\(902\) 0 0
\(903\) −11.0647 −0.368209
\(904\) 0 0
\(905\) 1.21187 0.0402839
\(906\) 0 0
\(907\) −4.84139 −0.160756 −0.0803779 0.996764i \(-0.525613\pi\)
−0.0803779 + 0.996764i \(0.525613\pi\)
\(908\) 0 0
\(909\) −40.8577 −1.35516
\(910\) 0 0
\(911\) 41.8318 1.38595 0.692974 0.720963i \(-0.256300\pi\)
0.692974 + 0.720963i \(0.256300\pi\)
\(912\) 0 0
\(913\) 18.6479 0.617157
\(914\) 0 0
\(915\) −9.70825 −0.320945
\(916\) 0 0
\(917\) 0.877587 0.0289805
\(918\) 0 0
\(919\) 18.0845 0.596552 0.298276 0.954480i \(-0.403588\pi\)
0.298276 + 0.954480i \(0.403588\pi\)
\(920\) 0 0
\(921\) 86.7805 2.85951
\(922\) 0 0
\(923\) 39.7765 1.30926
\(924\) 0 0
\(925\) −2.92795 −0.0962704
\(926\) 0 0
\(927\) −70.2413 −2.30703
\(928\) 0 0
\(929\) 12.6937 0.416468 0.208234 0.978079i \(-0.433228\pi\)
0.208234 + 0.978079i \(0.433228\pi\)
\(930\) 0 0
\(931\) 38.7240 1.26913
\(932\) 0 0
\(933\) −25.2912 −0.827996
\(934\) 0 0
\(935\) 32.0899 1.04945
\(936\) 0 0
\(937\) −39.3640 −1.28597 −0.642983 0.765880i \(-0.722303\pi\)
−0.642983 + 0.765880i \(0.722303\pi\)
\(938\) 0 0
\(939\) 66.3134 2.16406
\(940\) 0 0
\(941\) −21.2284 −0.692025 −0.346012 0.938230i \(-0.612465\pi\)
−0.346012 + 0.938230i \(0.612465\pi\)
\(942\) 0 0
\(943\) 9.30376 0.302972
\(944\) 0 0
\(945\) 7.83455 0.254858
\(946\) 0 0
\(947\) 15.0570 0.489287 0.244644 0.969613i \(-0.421329\pi\)
0.244644 + 0.969613i \(0.421329\pi\)
\(948\) 0 0
\(949\) 19.1977 0.623182
\(950\) 0 0
\(951\) 72.3501 2.34611
\(952\) 0 0
\(953\) −1.98812 −0.0644014 −0.0322007 0.999481i \(-0.510252\pi\)
−0.0322007 + 0.999481i \(0.510252\pi\)
\(954\) 0 0
\(955\) −12.1900 −0.394459
\(956\) 0 0
\(957\) 122.150 3.94855
\(958\) 0 0
\(959\) 7.81828 0.252465
\(960\) 0 0
\(961\) 90.4807 2.91873
\(962\) 0 0
\(963\) −78.7775 −2.53857
\(964\) 0 0
\(965\) −5.35965 −0.172533
\(966\) 0 0
\(967\) −33.9801 −1.09273 −0.546364 0.837548i \(-0.683988\pi\)
−0.546364 + 0.837548i \(0.683988\pi\)
\(968\) 0 0
\(969\) 132.900 4.26935
\(970\) 0 0
\(971\) −3.13278 −0.100536 −0.0502678 0.998736i \(-0.516007\pi\)
−0.0502678 + 0.998736i \(0.516007\pi\)
\(972\) 0 0
\(973\) 5.84915 0.187515
\(974\) 0 0
\(975\) −9.49800 −0.304180
\(976\) 0 0
\(977\) 34.3665 1.09948 0.549740 0.835336i \(-0.314727\pi\)
0.549740 + 0.835336i \(0.314727\pi\)
\(978\) 0 0
\(979\) −11.5037 −0.367659
\(980\) 0 0
\(981\) −111.064 −3.54599
\(982\) 0 0
\(983\) −8.60360 −0.274412 −0.137206 0.990543i \(-0.543812\pi\)
−0.137206 + 0.990543i \(0.543812\pi\)
\(984\) 0 0
\(985\) −13.8689 −0.441900
\(986\) 0 0
\(987\) 19.5980 0.623811
\(988\) 0 0
\(989\) 11.2279 0.357028
\(990\) 0 0
\(991\) −17.2975 −0.549473 −0.274736 0.961520i \(-0.588591\pi\)
−0.274736 + 0.961520i \(0.588591\pi\)
\(992\) 0 0
\(993\) −7.19002 −0.228168
\(994\) 0 0
\(995\) −21.3390 −0.676493
\(996\) 0 0
\(997\) −42.2430 −1.33785 −0.668925 0.743330i \(-0.733245\pi\)
−0.668925 + 0.743330i \(0.733245\pi\)
\(998\) 0 0
\(999\) 48.0444 1.52006
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 \(a_p\))