Properties

Label 8016.2.a.bg.1.1
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.02595\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-4.02595 q^{5}\) \(-0.910115 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-4.02595 q^{5}\) \(-0.910115 q^{7}\) \(+1.00000 q^{9}\) \(+5.64943 q^{11}\) \(+6.43968 q^{13}\) \(+4.02595 q^{15}\) \(+3.30990 q^{17}\) \(-1.28987 q^{19}\) \(+0.910115 q^{21}\) \(+9.24783 q^{23}\) \(+11.2083 q^{25}\) \(-1.00000 q^{27}\) \(+2.90838 q^{29}\) \(+10.6281 q^{31}\) \(-5.64943 q^{33}\) \(+3.66408 q^{35}\) \(+3.18976 q^{37}\) \(-6.43968 q^{39}\) \(+1.79168 q^{41}\) \(-2.55965 q^{43}\) \(-4.02595 q^{45}\) \(-1.91679 q^{47}\) \(-6.17169 q^{49}\) \(-3.30990 q^{51}\) \(-6.55631 q^{53}\) \(-22.7443 q^{55}\) \(+1.28987 q^{57}\) \(+2.97385 q^{59}\) \(+8.34803 q^{61}\) \(-0.910115 q^{63}\) \(-25.9258 q^{65}\) \(-4.23967 q^{67}\) \(-9.24783 q^{69}\) \(-10.1160 q^{71}\) \(+1.27643 q^{73}\) \(-11.2083 q^{75}\) \(-5.14163 q^{77}\) \(+1.79214 q^{79}\) \(+1.00000 q^{81}\) \(-13.8633 q^{83}\) \(-13.3255 q^{85}\) \(-2.90838 q^{87}\) \(+5.45522 q^{89}\) \(-5.86085 q^{91}\) \(-10.6281 q^{93}\) \(+5.19293 q^{95}\) \(+13.0108 q^{97}\) \(+5.64943 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −4.02595 −1.80046 −0.900229 0.435416i \(-0.856601\pi\)
−0.900229 + 0.435416i \(0.856601\pi\)
\(6\) 0 0
\(7\) −0.910115 −0.343991 −0.171996 0.985098i \(-0.555021\pi\)
−0.171996 + 0.985098i \(0.555021\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.64943 1.70337 0.851683 0.524058i \(-0.175582\pi\)
0.851683 + 0.524058i \(0.175582\pi\)
\(12\) 0 0
\(13\) 6.43968 1.78605 0.893023 0.450011i \(-0.148580\pi\)
0.893023 + 0.450011i \(0.148580\pi\)
\(14\) 0 0
\(15\) 4.02595 1.03950
\(16\) 0 0
\(17\) 3.30990 0.802770 0.401385 0.915909i \(-0.368529\pi\)
0.401385 + 0.915909i \(0.368529\pi\)
\(18\) 0 0
\(19\) −1.28987 −0.295915 −0.147958 0.988994i \(-0.547270\pi\)
−0.147958 + 0.988994i \(0.547270\pi\)
\(20\) 0 0
\(21\) 0.910115 0.198603
\(22\) 0 0
\(23\) 9.24783 1.92830 0.964152 0.265349i \(-0.0854871\pi\)
0.964152 + 0.265349i \(0.0854871\pi\)
\(24\) 0 0
\(25\) 11.2083 2.24165
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.90838 0.540072 0.270036 0.962850i \(-0.412964\pi\)
0.270036 + 0.962850i \(0.412964\pi\)
\(30\) 0 0
\(31\) 10.6281 1.90886 0.954431 0.298432i \(-0.0964635\pi\)
0.954431 + 0.298432i \(0.0964635\pi\)
\(32\) 0 0
\(33\) −5.64943 −0.983439
\(34\) 0 0
\(35\) 3.66408 0.619342
\(36\) 0 0
\(37\) 3.18976 0.524393 0.262196 0.965015i \(-0.415553\pi\)
0.262196 + 0.965015i \(0.415553\pi\)
\(38\) 0 0
\(39\) −6.43968 −1.03117
\(40\) 0 0
\(41\) 1.79168 0.279813 0.139907 0.990165i \(-0.455320\pi\)
0.139907 + 0.990165i \(0.455320\pi\)
\(42\) 0 0
\(43\) −2.55965 −0.390344 −0.195172 0.980769i \(-0.562526\pi\)
−0.195172 + 0.980769i \(0.562526\pi\)
\(44\) 0 0
\(45\) −4.02595 −0.600153
\(46\) 0 0
\(47\) −1.91679 −0.279593 −0.139797 0.990180i \(-0.544645\pi\)
−0.139797 + 0.990180i \(0.544645\pi\)
\(48\) 0 0
\(49\) −6.17169 −0.881670
\(50\) 0 0
\(51\) −3.30990 −0.463479
\(52\) 0 0
\(53\) −6.55631 −0.900579 −0.450289 0.892883i \(-0.648679\pi\)
−0.450289 + 0.892883i \(0.648679\pi\)
\(54\) 0 0
\(55\) −22.7443 −3.06684
\(56\) 0 0
\(57\) 1.28987 0.170847
\(58\) 0 0
\(59\) 2.97385 0.387162 0.193581 0.981084i \(-0.437990\pi\)
0.193581 + 0.981084i \(0.437990\pi\)
\(60\) 0 0
\(61\) 8.34803 1.06886 0.534428 0.845214i \(-0.320527\pi\)
0.534428 + 0.845214i \(0.320527\pi\)
\(62\) 0 0
\(63\) −0.910115 −0.114664
\(64\) 0 0
\(65\) −25.9258 −3.21570
\(66\) 0 0
\(67\) −4.23967 −0.517959 −0.258979 0.965883i \(-0.583386\pi\)
−0.258979 + 0.965883i \(0.583386\pi\)
\(68\) 0 0
\(69\) −9.24783 −1.11331
\(70\) 0 0
\(71\) −10.1160 −1.20055 −0.600276 0.799793i \(-0.704943\pi\)
−0.600276 + 0.799793i \(0.704943\pi\)
\(72\) 0 0
\(73\) 1.27643 0.149395 0.0746974 0.997206i \(-0.476201\pi\)
0.0746974 + 0.997206i \(0.476201\pi\)
\(74\) 0 0
\(75\) −11.2083 −1.29422
\(76\) 0 0
\(77\) −5.14163 −0.585943
\(78\) 0 0
\(79\) 1.79214 0.201631 0.100816 0.994905i \(-0.467855\pi\)
0.100816 + 0.994905i \(0.467855\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.8633 −1.52169 −0.760846 0.648932i \(-0.775216\pi\)
−0.760846 + 0.648932i \(0.775216\pi\)
\(84\) 0 0
\(85\) −13.3255 −1.44535
\(86\) 0 0
\(87\) −2.90838 −0.311811
\(88\) 0 0
\(89\) 5.45522 0.578252 0.289126 0.957291i \(-0.406635\pi\)
0.289126 + 0.957291i \(0.406635\pi\)
\(90\) 0 0
\(91\) −5.86085 −0.614384
\(92\) 0 0
\(93\) −10.6281 −1.10208
\(94\) 0 0
\(95\) 5.19293 0.532783
\(96\) 0 0
\(97\) 13.0108 1.32105 0.660525 0.750804i \(-0.270334\pi\)
0.660525 + 0.750804i \(0.270334\pi\)
\(98\) 0 0
\(99\) 5.64943 0.567789
\(100\) 0 0
\(101\) 13.5075 1.34405 0.672023 0.740530i \(-0.265425\pi\)
0.672023 + 0.740530i \(0.265425\pi\)
\(102\) 0 0
\(103\) 2.77840 0.273763 0.136882 0.990587i \(-0.456292\pi\)
0.136882 + 0.990587i \(0.456292\pi\)
\(104\) 0 0
\(105\) −3.66408 −0.357577
\(106\) 0 0
\(107\) −3.24267 −0.313480 −0.156740 0.987640i \(-0.550099\pi\)
−0.156740 + 0.987640i \(0.550099\pi\)
\(108\) 0 0
\(109\) 9.99492 0.957339 0.478670 0.877995i \(-0.341119\pi\)
0.478670 + 0.877995i \(0.341119\pi\)
\(110\) 0 0
\(111\) −3.18976 −0.302758
\(112\) 0 0
\(113\) 12.1305 1.14114 0.570571 0.821249i \(-0.306722\pi\)
0.570571 + 0.821249i \(0.306722\pi\)
\(114\) 0 0
\(115\) −37.2313 −3.47183
\(116\) 0 0
\(117\) 6.43968 0.595349
\(118\) 0 0
\(119\) −3.01239 −0.276146
\(120\) 0 0
\(121\) 20.9160 1.90145
\(122\) 0 0
\(123\) −1.79168 −0.161550
\(124\) 0 0
\(125\) −24.9941 −2.23554
\(126\) 0 0
\(127\) −12.6803 −1.12520 −0.562599 0.826730i \(-0.690198\pi\)
−0.562599 + 0.826730i \(0.690198\pi\)
\(128\) 0 0
\(129\) 2.55965 0.225365
\(130\) 0 0
\(131\) −7.08979 −0.619438 −0.309719 0.950828i \(-0.600235\pi\)
−0.309719 + 0.950828i \(0.600235\pi\)
\(132\) 0 0
\(133\) 1.17393 0.101792
\(134\) 0 0
\(135\) 4.02595 0.346498
\(136\) 0 0
\(137\) 1.44562 0.123508 0.0617538 0.998091i \(-0.480331\pi\)
0.0617538 + 0.998091i \(0.480331\pi\)
\(138\) 0 0
\(139\) 19.4215 1.64731 0.823656 0.567089i \(-0.191931\pi\)
0.823656 + 0.567089i \(0.191931\pi\)
\(140\) 0 0
\(141\) 1.91679 0.161423
\(142\) 0 0
\(143\) 36.3805 3.04229
\(144\) 0 0
\(145\) −11.7090 −0.972378
\(146\) 0 0
\(147\) 6.17169 0.509032
\(148\) 0 0
\(149\) 10.6988 0.876482 0.438241 0.898858i \(-0.355602\pi\)
0.438241 + 0.898858i \(0.355602\pi\)
\(150\) 0 0
\(151\) −1.13414 −0.0922949 −0.0461474 0.998935i \(-0.514694\pi\)
−0.0461474 + 0.998935i \(0.514694\pi\)
\(152\) 0 0
\(153\) 3.30990 0.267590
\(154\) 0 0
\(155\) −42.7882 −3.43683
\(156\) 0 0
\(157\) −2.13747 −0.170589 −0.0852944 0.996356i \(-0.527183\pi\)
−0.0852944 + 0.996356i \(0.527183\pi\)
\(158\) 0 0
\(159\) 6.55631 0.519949
\(160\) 0 0
\(161\) −8.41658 −0.663320
\(162\) 0 0
\(163\) 8.75643 0.685857 0.342928 0.939362i \(-0.388581\pi\)
0.342928 + 0.939362i \(0.388581\pi\)
\(164\) 0 0
\(165\) 22.7443 1.77064
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 28.4695 2.18996
\(170\) 0 0
\(171\) −1.28987 −0.0986384
\(172\) 0 0
\(173\) 20.7771 1.57966 0.789829 0.613328i \(-0.210169\pi\)
0.789829 + 0.613328i \(0.210169\pi\)
\(174\) 0 0
\(175\) −10.2008 −0.771108
\(176\) 0 0
\(177\) −2.97385 −0.223528
\(178\) 0 0
\(179\) −20.6874 −1.54625 −0.773123 0.634256i \(-0.781307\pi\)
−0.773123 + 0.634256i \(0.781307\pi\)
\(180\) 0 0
\(181\) −10.6867 −0.794335 −0.397167 0.917746i \(-0.630007\pi\)
−0.397167 + 0.917746i \(0.630007\pi\)
\(182\) 0 0
\(183\) −8.34803 −0.617104
\(184\) 0 0
\(185\) −12.8418 −0.944148
\(186\) 0 0
\(187\) 18.6991 1.36741
\(188\) 0 0
\(189\) 0.910115 0.0662011
\(190\) 0 0
\(191\) −23.7568 −1.71898 −0.859489 0.511154i \(-0.829218\pi\)
−0.859489 + 0.511154i \(0.829218\pi\)
\(192\) 0 0
\(193\) 0.301545 0.0217057 0.0108528 0.999941i \(-0.496545\pi\)
0.0108528 + 0.999941i \(0.496545\pi\)
\(194\) 0 0
\(195\) 25.9258 1.85659
\(196\) 0 0
\(197\) −21.9860 −1.56644 −0.783218 0.621747i \(-0.786423\pi\)
−0.783218 + 0.621747i \(0.786423\pi\)
\(198\) 0 0
\(199\) 18.3274 1.29920 0.649598 0.760278i \(-0.274937\pi\)
0.649598 + 0.760278i \(0.274937\pi\)
\(200\) 0 0
\(201\) 4.23967 0.299044
\(202\) 0 0
\(203\) −2.64696 −0.185780
\(204\) 0 0
\(205\) −7.21321 −0.503792
\(206\) 0 0
\(207\) 9.24783 0.642768
\(208\) 0 0
\(209\) −7.28700 −0.504052
\(210\) 0 0
\(211\) −25.9537 −1.78673 −0.893363 0.449336i \(-0.851661\pi\)
−0.893363 + 0.449336i \(0.851661\pi\)
\(212\) 0 0
\(213\) 10.1160 0.693139
\(214\) 0 0
\(215\) 10.3050 0.702798
\(216\) 0 0
\(217\) −9.67279 −0.656631
\(218\) 0 0
\(219\) −1.27643 −0.0862531
\(220\) 0 0
\(221\) 21.3147 1.43378
\(222\) 0 0
\(223\) 23.8575 1.59761 0.798807 0.601588i \(-0.205465\pi\)
0.798807 + 0.601588i \(0.205465\pi\)
\(224\) 0 0
\(225\) 11.2083 0.747217
\(226\) 0 0
\(227\) −11.8006 −0.783233 −0.391616 0.920129i \(-0.628084\pi\)
−0.391616 + 0.920129i \(0.628084\pi\)
\(228\) 0 0
\(229\) 4.93628 0.326199 0.163099 0.986610i \(-0.447851\pi\)
0.163099 + 0.986610i \(0.447851\pi\)
\(230\) 0 0
\(231\) 5.14163 0.338294
\(232\) 0 0
\(233\) 20.2292 1.32526 0.662630 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(234\) 0 0
\(235\) 7.71692 0.503396
\(236\) 0 0
\(237\) −1.79214 −0.116412
\(238\) 0 0
\(239\) 9.31462 0.602513 0.301256 0.953543i \(-0.402594\pi\)
0.301256 + 0.953543i \(0.402594\pi\)
\(240\) 0 0
\(241\) −8.96831 −0.577700 −0.288850 0.957374i \(-0.593273\pi\)
−0.288850 + 0.957374i \(0.593273\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 24.8469 1.58741
\(246\) 0 0
\(247\) −8.30632 −0.528518
\(248\) 0 0
\(249\) 13.8633 0.878550
\(250\) 0 0
\(251\) −20.5794 −1.29896 −0.649480 0.760379i \(-0.725013\pi\)
−0.649480 + 0.760379i \(0.725013\pi\)
\(252\) 0 0
\(253\) 52.2449 3.28461
\(254\) 0 0
\(255\) 13.3255 0.834476
\(256\) 0 0
\(257\) −28.3369 −1.76761 −0.883803 0.467859i \(-0.845025\pi\)
−0.883803 + 0.467859i \(0.845025\pi\)
\(258\) 0 0
\(259\) −2.90304 −0.180386
\(260\) 0 0
\(261\) 2.90838 0.180024
\(262\) 0 0
\(263\) −21.9168 −1.35145 −0.675723 0.737156i \(-0.736168\pi\)
−0.675723 + 0.737156i \(0.736168\pi\)
\(264\) 0 0
\(265\) 26.3954 1.62146
\(266\) 0 0
\(267\) −5.45522 −0.333854
\(268\) 0 0
\(269\) 8.34233 0.508641 0.254320 0.967120i \(-0.418148\pi\)
0.254320 + 0.967120i \(0.418148\pi\)
\(270\) 0 0
\(271\) 5.97049 0.362681 0.181341 0.983420i \(-0.441956\pi\)
0.181341 + 0.983420i \(0.441956\pi\)
\(272\) 0 0
\(273\) 5.86085 0.354715
\(274\) 0 0
\(275\) 63.3202 3.81835
\(276\) 0 0
\(277\) −2.35540 −0.141522 −0.0707610 0.997493i \(-0.522543\pi\)
−0.0707610 + 0.997493i \(0.522543\pi\)
\(278\) 0 0
\(279\) 10.6281 0.636287
\(280\) 0 0
\(281\) −9.45133 −0.563819 −0.281909 0.959441i \(-0.590968\pi\)
−0.281909 + 0.959441i \(0.590968\pi\)
\(282\) 0 0
\(283\) −9.76734 −0.580608 −0.290304 0.956934i \(-0.593756\pi\)
−0.290304 + 0.956934i \(0.593756\pi\)
\(284\) 0 0
\(285\) −5.19293 −0.307603
\(286\) 0 0
\(287\) −1.63063 −0.0962532
\(288\) 0 0
\(289\) −6.04453 −0.355561
\(290\) 0 0
\(291\) −13.0108 −0.762709
\(292\) 0 0
\(293\) 1.86304 0.108840 0.0544200 0.998518i \(-0.482669\pi\)
0.0544200 + 0.998518i \(0.482669\pi\)
\(294\) 0 0
\(295\) −11.9726 −0.697069
\(296\) 0 0
\(297\) −5.64943 −0.327813
\(298\) 0 0
\(299\) 59.5530 3.44404
\(300\) 0 0
\(301\) 2.32958 0.134275
\(302\) 0 0
\(303\) −13.5075 −0.775986
\(304\) 0 0
\(305\) −33.6087 −1.92443
\(306\) 0 0
\(307\) −11.9878 −0.684178 −0.342089 0.939668i \(-0.611134\pi\)
−0.342089 + 0.939668i \(0.611134\pi\)
\(308\) 0 0
\(309\) −2.77840 −0.158057
\(310\) 0 0
\(311\) 7.72229 0.437891 0.218946 0.975737i \(-0.429738\pi\)
0.218946 + 0.975737i \(0.429738\pi\)
\(312\) 0 0
\(313\) −27.5266 −1.55590 −0.777949 0.628328i \(-0.783740\pi\)
−0.777949 + 0.628328i \(0.783740\pi\)
\(314\) 0 0
\(315\) 3.66408 0.206447
\(316\) 0 0
\(317\) −29.6703 −1.66645 −0.833225 0.552934i \(-0.813508\pi\)
−0.833225 + 0.552934i \(0.813508\pi\)
\(318\) 0 0
\(319\) 16.4307 0.919940
\(320\) 0 0
\(321\) 3.24267 0.180988
\(322\) 0 0
\(323\) −4.26933 −0.237552
\(324\) 0 0
\(325\) 72.1776 4.00369
\(326\) 0 0
\(327\) −9.99492 −0.552720
\(328\) 0 0
\(329\) 1.74450 0.0961776
\(330\) 0 0
\(331\) 9.06789 0.498416 0.249208 0.968450i \(-0.419830\pi\)
0.249208 + 0.968450i \(0.419830\pi\)
\(332\) 0 0
\(333\) 3.18976 0.174798
\(334\) 0 0
\(335\) 17.0687 0.932563
\(336\) 0 0
\(337\) 24.1926 1.31785 0.658927 0.752207i \(-0.271011\pi\)
0.658927 + 0.752207i \(0.271011\pi\)
\(338\) 0 0
\(339\) −12.1305 −0.658838
\(340\) 0 0
\(341\) 60.0426 3.25149
\(342\) 0 0
\(343\) 11.9878 0.647278
\(344\) 0 0
\(345\) 37.2313 2.00446
\(346\) 0 0
\(347\) −11.3260 −0.608011 −0.304006 0.952670i \(-0.598324\pi\)
−0.304006 + 0.952670i \(0.598324\pi\)
\(348\) 0 0
\(349\) −30.8336 −1.65048 −0.825241 0.564781i \(-0.808961\pi\)
−0.825241 + 0.564781i \(0.808961\pi\)
\(350\) 0 0
\(351\) −6.43968 −0.343725
\(352\) 0 0
\(353\) −29.5939 −1.57512 −0.787562 0.616236i \(-0.788657\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(354\) 0 0
\(355\) 40.7266 2.16155
\(356\) 0 0
\(357\) 3.01239 0.159433
\(358\) 0 0
\(359\) 11.0055 0.580847 0.290423 0.956898i \(-0.406204\pi\)
0.290423 + 0.956898i \(0.406204\pi\)
\(360\) 0 0
\(361\) −17.3362 −0.912434
\(362\) 0 0
\(363\) −20.9160 −1.09781
\(364\) 0 0
\(365\) −5.13884 −0.268979
\(366\) 0 0
\(367\) 22.8033 1.19032 0.595161 0.803606i \(-0.297088\pi\)
0.595161 + 0.803606i \(0.297088\pi\)
\(368\) 0 0
\(369\) 1.79168 0.0932711
\(370\) 0 0
\(371\) 5.96700 0.309791
\(372\) 0 0
\(373\) −6.84106 −0.354217 −0.177108 0.984191i \(-0.556674\pi\)
−0.177108 + 0.984191i \(0.556674\pi\)
\(374\) 0 0
\(375\) 24.9941 1.29069
\(376\) 0 0
\(377\) 18.7290 0.964593
\(378\) 0 0
\(379\) −16.7773 −0.861789 −0.430895 0.902402i \(-0.641802\pi\)
−0.430895 + 0.902402i \(0.641802\pi\)
\(380\) 0 0
\(381\) 12.6803 0.649633
\(382\) 0 0
\(383\) 17.9407 0.916726 0.458363 0.888765i \(-0.348436\pi\)
0.458363 + 0.888765i \(0.348436\pi\)
\(384\) 0 0
\(385\) 20.6999 1.05497
\(386\) 0 0
\(387\) −2.55965 −0.130115
\(388\) 0 0
\(389\) 15.8167 0.801939 0.400970 0.916091i \(-0.368673\pi\)
0.400970 + 0.916091i \(0.368673\pi\)
\(390\) 0 0
\(391\) 30.6094 1.54798
\(392\) 0 0
\(393\) 7.08979 0.357633
\(394\) 0 0
\(395\) −7.21506 −0.363029
\(396\) 0 0
\(397\) 3.10390 0.155781 0.0778903 0.996962i \(-0.475182\pi\)
0.0778903 + 0.996962i \(0.475182\pi\)
\(398\) 0 0
\(399\) −1.17393 −0.0587698
\(400\) 0 0
\(401\) 6.30176 0.314695 0.157348 0.987543i \(-0.449706\pi\)
0.157348 + 0.987543i \(0.449706\pi\)
\(402\) 0 0
\(403\) 68.4415 3.40931
\(404\) 0 0
\(405\) −4.02595 −0.200051
\(406\) 0 0
\(407\) 18.0203 0.893233
\(408\) 0 0
\(409\) 16.0912 0.795658 0.397829 0.917460i \(-0.369764\pi\)
0.397829 + 0.917460i \(0.369764\pi\)
\(410\) 0 0
\(411\) −1.44562 −0.0713071
\(412\) 0 0
\(413\) −2.70654 −0.133180
\(414\) 0 0
\(415\) 55.8129 2.73975
\(416\) 0 0
\(417\) −19.4215 −0.951076
\(418\) 0 0
\(419\) −28.0306 −1.36938 −0.684691 0.728833i \(-0.740063\pi\)
−0.684691 + 0.728833i \(0.740063\pi\)
\(420\) 0 0
\(421\) 3.41757 0.166562 0.0832811 0.996526i \(-0.473460\pi\)
0.0832811 + 0.996526i \(0.473460\pi\)
\(422\) 0 0
\(423\) −1.91679 −0.0931977
\(424\) 0 0
\(425\) 37.0983 1.79953
\(426\) 0 0
\(427\) −7.59767 −0.367677
\(428\) 0 0
\(429\) −36.3805 −1.75647
\(430\) 0 0
\(431\) −5.43379 −0.261737 −0.130868 0.991400i \(-0.541777\pi\)
−0.130868 + 0.991400i \(0.541777\pi\)
\(432\) 0 0
\(433\) 40.9533 1.96809 0.984044 0.177923i \(-0.0569378\pi\)
0.984044 + 0.177923i \(0.0569378\pi\)
\(434\) 0 0
\(435\) 11.7090 0.561402
\(436\) 0 0
\(437\) −11.9284 −0.570615
\(438\) 0 0
\(439\) 11.0418 0.526994 0.263497 0.964660i \(-0.415124\pi\)
0.263497 + 0.964660i \(0.415124\pi\)
\(440\) 0 0
\(441\) −6.17169 −0.293890
\(442\) 0 0
\(443\) 2.25699 0.107233 0.0536164 0.998562i \(-0.482925\pi\)
0.0536164 + 0.998562i \(0.482925\pi\)
\(444\) 0 0
\(445\) −21.9624 −1.04112
\(446\) 0 0
\(447\) −10.6988 −0.506037
\(448\) 0 0
\(449\) −34.4263 −1.62468 −0.812339 0.583185i \(-0.801806\pi\)
−0.812339 + 0.583185i \(0.801806\pi\)
\(450\) 0 0
\(451\) 10.1220 0.476624
\(452\) 0 0
\(453\) 1.13414 0.0532865
\(454\) 0 0
\(455\) 23.5955 1.10617
\(456\) 0 0
\(457\) 5.47846 0.256271 0.128136 0.991757i \(-0.459101\pi\)
0.128136 + 0.991757i \(0.459101\pi\)
\(458\) 0 0
\(459\) −3.30990 −0.154493
\(460\) 0 0
\(461\) 21.7152 1.01138 0.505689 0.862716i \(-0.331238\pi\)
0.505689 + 0.862716i \(0.331238\pi\)
\(462\) 0 0
\(463\) −4.49087 −0.208709 −0.104354 0.994540i \(-0.533278\pi\)
−0.104354 + 0.994540i \(0.533278\pi\)
\(464\) 0 0
\(465\) 42.7882 1.98425
\(466\) 0 0
\(467\) −0.0664030 −0.00307277 −0.00153638 0.999999i \(-0.500489\pi\)
−0.00153638 + 0.999999i \(0.500489\pi\)
\(468\) 0 0
\(469\) 3.85859 0.178173
\(470\) 0 0
\(471\) 2.13747 0.0984895
\(472\) 0 0
\(473\) −14.4606 −0.664898
\(474\) 0 0
\(475\) −14.4571 −0.663339
\(476\) 0 0
\(477\) −6.55631 −0.300193
\(478\) 0 0
\(479\) −28.4840 −1.30147 −0.650733 0.759307i \(-0.725538\pi\)
−0.650733 + 0.759307i \(0.725538\pi\)
\(480\) 0 0
\(481\) 20.5410 0.936589
\(482\) 0 0
\(483\) 8.41658 0.382968
\(484\) 0 0
\(485\) −52.3810 −2.37850
\(486\) 0 0
\(487\) 39.2150 1.77700 0.888502 0.458873i \(-0.151747\pi\)
0.888502 + 0.458873i \(0.151747\pi\)
\(488\) 0 0
\(489\) −8.75643 −0.395980
\(490\) 0 0
\(491\) −25.5329 −1.15228 −0.576141 0.817350i \(-0.695442\pi\)
−0.576141 + 0.817350i \(0.695442\pi\)
\(492\) 0 0
\(493\) 9.62645 0.433554
\(494\) 0 0
\(495\) −22.7443 −1.02228
\(496\) 0 0
\(497\) 9.20675 0.412979
\(498\) 0 0
\(499\) −25.9599 −1.16212 −0.581061 0.813860i \(-0.697362\pi\)
−0.581061 + 0.813860i \(0.697362\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 34.3605 1.53206 0.766030 0.642805i \(-0.222230\pi\)
0.766030 + 0.642805i \(0.222230\pi\)
\(504\) 0 0
\(505\) −54.3805 −2.41990
\(506\) 0 0
\(507\) −28.4695 −1.26437
\(508\) 0 0
\(509\) 18.1390 0.803998 0.401999 0.915640i \(-0.368315\pi\)
0.401999 + 0.915640i \(0.368315\pi\)
\(510\) 0 0
\(511\) −1.16170 −0.0513905
\(512\) 0 0
\(513\) 1.28987 0.0569489
\(514\) 0 0
\(515\) −11.1857 −0.492900
\(516\) 0 0
\(517\) −10.8288 −0.476250
\(518\) 0 0
\(519\) −20.7771 −0.912016
\(520\) 0 0
\(521\) −18.7860 −0.823031 −0.411515 0.911403i \(-0.635000\pi\)
−0.411515 + 0.911403i \(0.635000\pi\)
\(522\) 0 0
\(523\) 2.94829 0.128920 0.0644600 0.997920i \(-0.479468\pi\)
0.0644600 + 0.997920i \(0.479468\pi\)
\(524\) 0 0
\(525\) 10.2008 0.445200
\(526\) 0 0
\(527\) 35.1780 1.53238
\(528\) 0 0
\(529\) 62.5223 2.71836
\(530\) 0 0
\(531\) 2.97385 0.129054
\(532\) 0 0
\(533\) 11.5378 0.499759
\(534\) 0 0
\(535\) 13.0548 0.564409
\(536\) 0 0
\(537\) 20.6874 0.892726
\(538\) 0 0
\(539\) −34.8665 −1.50181
\(540\) 0 0
\(541\) 11.9263 0.512751 0.256375 0.966577i \(-0.417472\pi\)
0.256375 + 0.966577i \(0.417472\pi\)
\(542\) 0 0
\(543\) 10.6867 0.458609
\(544\) 0 0
\(545\) −40.2390 −1.72365
\(546\) 0 0
\(547\) 8.94329 0.382387 0.191194 0.981552i \(-0.438764\pi\)
0.191194 + 0.981552i \(0.438764\pi\)
\(548\) 0 0
\(549\) 8.34803 0.356285
\(550\) 0 0
\(551\) −3.75141 −0.159816
\(552\) 0 0
\(553\) −1.63105 −0.0693594
\(554\) 0 0
\(555\) 12.8418 0.545104
\(556\) 0 0
\(557\) −38.5579 −1.63375 −0.816876 0.576814i \(-0.804296\pi\)
−0.816876 + 0.576814i \(0.804296\pi\)
\(558\) 0 0
\(559\) −16.4834 −0.697172
\(560\) 0 0
\(561\) −18.6991 −0.789475
\(562\) 0 0
\(563\) −10.8490 −0.457232 −0.228616 0.973517i \(-0.573420\pi\)
−0.228616 + 0.973517i \(0.573420\pi\)
\(564\) 0 0
\(565\) −48.8368 −2.05458
\(566\) 0 0
\(567\) −0.910115 −0.0382212
\(568\) 0 0
\(569\) −2.09232 −0.0877148 −0.0438574 0.999038i \(-0.513965\pi\)
−0.0438574 + 0.999038i \(0.513965\pi\)
\(570\) 0 0
\(571\) 20.2241 0.846352 0.423176 0.906047i \(-0.360915\pi\)
0.423176 + 0.906047i \(0.360915\pi\)
\(572\) 0 0
\(573\) 23.7568 0.992453
\(574\) 0 0
\(575\) 103.652 4.32259
\(576\) 0 0
\(577\) 31.9254 1.32907 0.664536 0.747256i \(-0.268629\pi\)
0.664536 + 0.747256i \(0.268629\pi\)
\(578\) 0 0
\(579\) −0.301545 −0.0125318
\(580\) 0 0
\(581\) 12.6172 0.523449
\(582\) 0 0
\(583\) −37.0394 −1.53402
\(584\) 0 0
\(585\) −25.9258 −1.07190
\(586\) 0 0
\(587\) −20.2855 −0.837274 −0.418637 0.908154i \(-0.637492\pi\)
−0.418637 + 0.908154i \(0.637492\pi\)
\(588\) 0 0
\(589\) −13.7088 −0.564862
\(590\) 0 0
\(591\) 21.9860 0.904382
\(592\) 0 0
\(593\) 15.1257 0.621139 0.310570 0.950551i \(-0.399480\pi\)
0.310570 + 0.950551i \(0.399480\pi\)
\(594\) 0 0
\(595\) 12.1277 0.497189
\(596\) 0 0
\(597\) −18.3274 −0.750091
\(598\) 0 0
\(599\) −29.7919 −1.21727 −0.608633 0.793452i \(-0.708282\pi\)
−0.608633 + 0.793452i \(0.708282\pi\)
\(600\) 0 0
\(601\) −26.0228 −1.06149 −0.530746 0.847531i \(-0.678088\pi\)
−0.530746 + 0.847531i \(0.678088\pi\)
\(602\) 0 0
\(603\) −4.23967 −0.172653
\(604\) 0 0
\(605\) −84.2068 −3.42349
\(606\) 0 0
\(607\) −2.81543 −0.114275 −0.0571373 0.998366i \(-0.518197\pi\)
−0.0571373 + 0.998366i \(0.518197\pi\)
\(608\) 0 0
\(609\) 2.64696 0.107260
\(610\) 0 0
\(611\) −12.3435 −0.499366
\(612\) 0 0
\(613\) −20.9337 −0.845504 −0.422752 0.906245i \(-0.638936\pi\)
−0.422752 + 0.906245i \(0.638936\pi\)
\(614\) 0 0
\(615\) 7.21321 0.290865
\(616\) 0 0
\(617\) 17.3534 0.698623 0.349312 0.937007i \(-0.386415\pi\)
0.349312 + 0.937007i \(0.386415\pi\)
\(618\) 0 0
\(619\) −20.9527 −0.842159 −0.421079 0.907024i \(-0.638349\pi\)
−0.421079 + 0.907024i \(0.638349\pi\)
\(620\) 0 0
\(621\) −9.24783 −0.371102
\(622\) 0 0
\(623\) −4.96488 −0.198914
\(624\) 0 0
\(625\) 44.5838 1.78335
\(626\) 0 0
\(627\) 7.28700 0.291015
\(628\) 0 0
\(629\) 10.5578 0.420967
\(630\) 0 0
\(631\) −16.6037 −0.660983 −0.330492 0.943809i \(-0.607215\pi\)
−0.330492 + 0.943809i \(0.607215\pi\)
\(632\) 0 0
\(633\) 25.9537 1.03157
\(634\) 0 0
\(635\) 51.0504 2.02587
\(636\) 0 0
\(637\) −39.7437 −1.57470
\(638\) 0 0
\(639\) −10.1160 −0.400184
\(640\) 0 0
\(641\) 23.1161 0.913033 0.456516 0.889715i \(-0.349097\pi\)
0.456516 + 0.889715i \(0.349097\pi\)
\(642\) 0 0
\(643\) 7.04889 0.277981 0.138991 0.990294i \(-0.455614\pi\)
0.138991 + 0.990294i \(0.455614\pi\)
\(644\) 0 0
\(645\) −10.3050 −0.405761
\(646\) 0 0
\(647\) 15.6485 0.615206 0.307603 0.951515i \(-0.400473\pi\)
0.307603 + 0.951515i \(0.400473\pi\)
\(648\) 0 0
\(649\) 16.8005 0.659478
\(650\) 0 0
\(651\) 9.67279 0.379106
\(652\) 0 0
\(653\) −32.5382 −1.27332 −0.636658 0.771146i \(-0.719684\pi\)
−0.636658 + 0.771146i \(0.719684\pi\)
\(654\) 0 0
\(655\) 28.5431 1.11527
\(656\) 0 0
\(657\) 1.27643 0.0497983
\(658\) 0 0
\(659\) 7.89404 0.307508 0.153754 0.988109i \(-0.450864\pi\)
0.153754 + 0.988109i \(0.450864\pi\)
\(660\) 0 0
\(661\) −9.82653 −0.382208 −0.191104 0.981570i \(-0.561207\pi\)
−0.191104 + 0.981570i \(0.561207\pi\)
\(662\) 0 0
\(663\) −21.3147 −0.827795
\(664\) 0 0
\(665\) −4.72616 −0.183273
\(666\) 0 0
\(667\) 26.8962 1.04142
\(668\) 0 0
\(669\) −23.8575 −0.922382
\(670\) 0 0
\(671\) 47.1616 1.82065
\(672\) 0 0
\(673\) −12.2177 −0.470959 −0.235480 0.971879i \(-0.575666\pi\)
−0.235480 + 0.971879i \(0.575666\pi\)
\(674\) 0 0
\(675\) −11.2083 −0.431406
\(676\) 0 0
\(677\) −17.9900 −0.691413 −0.345706 0.938343i \(-0.612361\pi\)
−0.345706 + 0.938343i \(0.612361\pi\)
\(678\) 0 0
\(679\) −11.8414 −0.454430
\(680\) 0 0
\(681\) 11.8006 0.452200
\(682\) 0 0
\(683\) −38.4906 −1.47280 −0.736401 0.676545i \(-0.763476\pi\)
−0.736401 + 0.676545i \(0.763476\pi\)
\(684\) 0 0
\(685\) −5.81999 −0.222370
\(686\) 0 0
\(687\) −4.93628 −0.188331
\(688\) 0 0
\(689\) −42.2206 −1.60848
\(690\) 0 0
\(691\) −17.2590 −0.656565 −0.328283 0.944580i \(-0.606470\pi\)
−0.328283 + 0.944580i \(0.606470\pi\)
\(692\) 0 0
\(693\) −5.14163 −0.195314
\(694\) 0 0
\(695\) −78.1901 −2.96592
\(696\) 0 0
\(697\) 5.93028 0.224626
\(698\) 0 0
\(699\) −20.2292 −0.765139
\(700\) 0 0
\(701\) −27.5288 −1.03975 −0.519874 0.854243i \(-0.674021\pi\)
−0.519874 + 0.854243i \(0.674021\pi\)
\(702\) 0 0
\(703\) −4.11436 −0.155176
\(704\) 0 0
\(705\) −7.71692 −0.290636
\(706\) 0 0
\(707\) −12.2934 −0.462340
\(708\) 0 0
\(709\) 44.1421 1.65779 0.828895 0.559404i \(-0.188970\pi\)
0.828895 + 0.559404i \(0.188970\pi\)
\(710\) 0 0
\(711\) 1.79214 0.0672104
\(712\) 0 0
\(713\) 98.2868 3.68087
\(714\) 0 0
\(715\) −146.466 −5.47752
\(716\) 0 0
\(717\) −9.31462 −0.347861
\(718\) 0 0
\(719\) −20.3261 −0.758037 −0.379018 0.925389i \(-0.623738\pi\)
−0.379018 + 0.925389i \(0.623738\pi\)
\(720\) 0 0
\(721\) −2.52866 −0.0941722
\(722\) 0 0
\(723\) 8.96831 0.333535
\(724\) 0 0
\(725\) 32.5979 1.21065
\(726\) 0 0
\(727\) −42.3208 −1.56959 −0.784796 0.619754i \(-0.787233\pi\)
−0.784796 + 0.619754i \(0.787233\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −8.47221 −0.313356
\(732\) 0 0
\(733\) −16.9178 −0.624874 −0.312437 0.949938i \(-0.601145\pi\)
−0.312437 + 0.949938i \(0.601145\pi\)
\(734\) 0 0
\(735\) −24.8469 −0.916492
\(736\) 0 0
\(737\) −23.9517 −0.882273
\(738\) 0 0
\(739\) −7.57315 −0.278583 −0.139291 0.990251i \(-0.544482\pi\)
−0.139291 + 0.990251i \(0.544482\pi\)
\(740\) 0 0
\(741\) 8.30632 0.305140
\(742\) 0 0
\(743\) 43.7667 1.60565 0.802823 0.596218i \(-0.203330\pi\)
0.802823 + 0.596218i \(0.203330\pi\)
\(744\) 0 0
\(745\) −43.0729 −1.57807
\(746\) 0 0
\(747\) −13.8633 −0.507231
\(748\) 0 0
\(749\) 2.95120 0.107834
\(750\) 0 0
\(751\) −34.8474 −1.27160 −0.635800 0.771854i \(-0.719330\pi\)
−0.635800 + 0.771854i \(0.719330\pi\)
\(752\) 0 0
\(753\) 20.5794 0.749954
\(754\) 0 0
\(755\) 4.56598 0.166173
\(756\) 0 0
\(757\) 8.95171 0.325356 0.162678 0.986679i \(-0.447987\pi\)
0.162678 + 0.986679i \(0.447987\pi\)
\(758\) 0 0
\(759\) −52.2449 −1.89637
\(760\) 0 0
\(761\) 1.90648 0.0691098 0.0345549 0.999403i \(-0.488999\pi\)
0.0345549 + 0.999403i \(0.488999\pi\)
\(762\) 0 0
\(763\) −9.09652 −0.329316
\(764\) 0 0
\(765\) −13.3255 −0.481785
\(766\) 0 0
\(767\) 19.1506 0.691489
\(768\) 0 0
\(769\) 43.7489 1.57763 0.788813 0.614633i \(-0.210696\pi\)
0.788813 + 0.614633i \(0.210696\pi\)
\(770\) 0 0
\(771\) 28.3369 1.02053
\(772\) 0 0
\(773\) 48.8809 1.75812 0.879062 0.476708i \(-0.158170\pi\)
0.879062 + 0.476708i \(0.158170\pi\)
\(774\) 0 0
\(775\) 119.122 4.27900
\(776\) 0 0
\(777\) 2.90304 0.104146
\(778\) 0 0
\(779\) −2.31102 −0.0828010
\(780\) 0 0
\(781\) −57.1498 −2.04498
\(782\) 0 0
\(783\) −2.90838 −0.103937
\(784\) 0 0
\(785\) 8.60535 0.307138
\(786\) 0 0
\(787\) −47.8888 −1.70705 −0.853525 0.521052i \(-0.825540\pi\)
−0.853525 + 0.521052i \(0.825540\pi\)
\(788\) 0 0
\(789\) 21.9168 0.780258
\(790\) 0 0
\(791\) −11.0401 −0.392542
\(792\) 0 0
\(793\) 53.7586 1.90903
\(794\) 0 0
\(795\) −26.3954 −0.936148
\(796\) 0 0
\(797\) 46.4221 1.64436 0.822178 0.569231i \(-0.192759\pi\)
0.822178 + 0.569231i \(0.192759\pi\)
\(798\) 0 0
\(799\) −6.34441 −0.224449
\(800\) 0 0
\(801\) 5.45522 0.192751
\(802\) 0 0
\(803\) 7.21109 0.254474
\(804\) 0 0
\(805\) 33.8847 1.19428
\(806\) 0 0
\(807\) −8.34233 −0.293664
\(808\) 0 0
\(809\) −20.3954 −0.717065 −0.358533 0.933517i \(-0.616723\pi\)
−0.358533 + 0.933517i \(0.616723\pi\)
\(810\) 0 0
\(811\) 27.1993 0.955097 0.477549 0.878605i \(-0.341525\pi\)
0.477549 + 0.878605i \(0.341525\pi\)
\(812\) 0 0
\(813\) −5.97049 −0.209394
\(814\) 0 0
\(815\) −35.2529 −1.23486
\(816\) 0 0
\(817\) 3.30161 0.115509
\(818\) 0 0
\(819\) −5.86085 −0.204795
\(820\) 0 0
\(821\) 53.9559 1.88308 0.941538 0.336908i \(-0.109381\pi\)
0.941538 + 0.336908i \(0.109381\pi\)
\(822\) 0 0
\(823\) 20.3519 0.709421 0.354711 0.934976i \(-0.384579\pi\)
0.354711 + 0.934976i \(0.384579\pi\)
\(824\) 0 0
\(825\) −63.3202 −2.20453
\(826\) 0 0
\(827\) 38.5345 1.33998 0.669988 0.742372i \(-0.266299\pi\)
0.669988 + 0.742372i \(0.266299\pi\)
\(828\) 0 0
\(829\) 26.7280 0.928302 0.464151 0.885756i \(-0.346360\pi\)
0.464151 + 0.885756i \(0.346360\pi\)
\(830\) 0 0
\(831\) 2.35540 0.0817077
\(832\) 0 0
\(833\) −20.4277 −0.707778
\(834\) 0 0
\(835\) −4.02595 −0.139324
\(836\) 0 0
\(837\) −10.6281 −0.367361
\(838\) 0 0
\(839\) 14.9538 0.516261 0.258131 0.966110i \(-0.416893\pi\)
0.258131 + 0.966110i \(0.416893\pi\)
\(840\) 0 0
\(841\) −20.5413 −0.708322
\(842\) 0 0
\(843\) 9.45133 0.325521
\(844\) 0 0
\(845\) −114.617 −3.94293
\(846\) 0 0
\(847\) −19.0360 −0.654084
\(848\) 0 0
\(849\) 9.76734 0.335214
\(850\) 0 0
\(851\) 29.4983 1.01119
\(852\) 0 0
\(853\) 3.85973 0.132155 0.0660773 0.997815i \(-0.478952\pi\)
0.0660773 + 0.997815i \(0.478952\pi\)
\(854\) 0 0
\(855\) 5.19293 0.177594
\(856\) 0 0
\(857\) 20.1803 0.689347 0.344674 0.938723i \(-0.387990\pi\)
0.344674 + 0.938723i \(0.387990\pi\)
\(858\) 0 0
\(859\) 5.19182 0.177143 0.0885713 0.996070i \(-0.471770\pi\)
0.0885713 + 0.996070i \(0.471770\pi\)
\(860\) 0 0
\(861\) 1.63063 0.0555718
\(862\) 0 0
\(863\) 24.6739 0.839908 0.419954 0.907545i \(-0.362046\pi\)
0.419954 + 0.907545i \(0.362046\pi\)
\(864\) 0 0
\(865\) −83.6477 −2.84411
\(866\) 0 0
\(867\) 6.04453 0.205283
\(868\) 0 0
\(869\) 10.1246 0.343452
\(870\) 0 0
\(871\) −27.3021 −0.925098
\(872\) 0 0
\(873\) 13.0108 0.440350
\(874\) 0 0
\(875\) 22.7475 0.769007
\(876\) 0 0
\(877\) −21.5120 −0.726409 −0.363205 0.931709i \(-0.618317\pi\)
−0.363205 + 0.931709i \(0.618317\pi\)
\(878\) 0 0
\(879\) −1.86304 −0.0628388
\(880\) 0 0
\(881\) 7.28798 0.245538 0.122769 0.992435i \(-0.460823\pi\)
0.122769 + 0.992435i \(0.460823\pi\)
\(882\) 0 0
\(883\) −46.9312 −1.57936 −0.789681 0.613517i \(-0.789754\pi\)
−0.789681 + 0.613517i \(0.789754\pi\)
\(884\) 0 0
\(885\) 11.9726 0.402453
\(886\) 0 0
\(887\) 14.7405 0.494939 0.247469 0.968896i \(-0.420401\pi\)
0.247469 + 0.968896i \(0.420401\pi\)
\(888\) 0 0
\(889\) 11.5406 0.387058
\(890\) 0 0
\(891\) 5.64943 0.189263
\(892\) 0 0
\(893\) 2.47241 0.0827359
\(894\) 0 0
\(895\) 83.2863 2.78395
\(896\) 0 0
\(897\) −59.5530 −1.98842
\(898\) 0 0
\(899\) 30.9105 1.03092
\(900\) 0 0
\(901\) −21.7008 −0.722958
\(902\) 0 0
\(903\) −2.32958 −0.0775236
\(904\) 0 0
\(905\) 43.0240 1.43017
\(906\) 0 0
\(907\) −49.1909 −1.63336 −0.816678 0.577093i \(-0.804187\pi\)
−0.816678 + 0.577093i \(0.804187\pi\)
\(908\) 0 0
\(909\) 13.5075 0.448016
\(910\) 0 0
\(911\) 24.1824 0.801198 0.400599 0.916254i \(-0.368802\pi\)
0.400599 + 0.916254i \(0.368802\pi\)
\(912\) 0 0
\(913\) −78.3196 −2.59200
\(914\) 0 0
\(915\) 33.6087 1.11107
\(916\) 0 0
\(917\) 6.45253 0.213081
\(918\) 0 0
\(919\) 47.1032 1.55379 0.776895 0.629630i \(-0.216793\pi\)
0.776895 + 0.629630i \(0.216793\pi\)
\(920\) 0 0
\(921\) 11.9878 0.395010
\(922\) 0 0
\(923\) −65.1440 −2.14424
\(924\) 0 0
\(925\) 35.7516 1.17551
\(926\) 0 0
\(927\) 2.77840 0.0912545
\(928\) 0 0
\(929\) −23.7341 −0.778690 −0.389345 0.921092i \(-0.627299\pi\)
−0.389345 + 0.921092i \(0.627299\pi\)
\(930\) 0 0
\(931\) 7.96065 0.260900
\(932\) 0 0
\(933\) −7.72229 −0.252817
\(934\) 0 0
\(935\) −75.2814 −2.46197
\(936\) 0 0
\(937\) 49.3550 1.61236 0.806179 0.591672i \(-0.201532\pi\)
0.806179 + 0.591672i \(0.201532\pi\)
\(938\) 0 0
\(939\) 27.5266 0.898298
\(940\) 0 0
\(941\) −11.4267 −0.372499 −0.186249 0.982502i \(-0.559633\pi\)
−0.186249 + 0.982502i \(0.559633\pi\)
\(942\) 0 0
\(943\) 16.5691 0.539565
\(944\) 0 0
\(945\) −3.66408 −0.119192
\(946\) 0 0
\(947\) 34.8099 1.13117 0.565585 0.824690i \(-0.308650\pi\)
0.565585 + 0.824690i \(0.308650\pi\)
\(948\) 0 0
\(949\) 8.21980 0.266826
\(950\) 0 0
\(951\) 29.6703 0.962126
\(952\) 0 0
\(953\) −55.3657 −1.79347 −0.896736 0.442566i \(-0.854068\pi\)
−0.896736 + 0.442566i \(0.854068\pi\)
\(954\) 0 0
\(955\) 95.6435 3.09495
\(956\) 0 0
\(957\) −16.4307 −0.531128
\(958\) 0 0
\(959\) −1.31568 −0.0424855
\(960\) 0 0
\(961\) 81.9564 2.64375
\(962\) 0 0
\(963\) −3.24267 −0.104493
\(964\) 0 0
\(965\) −1.21400 −0.0390801
\(966\) 0 0
\(967\) −41.9967 −1.35052 −0.675261 0.737579i \(-0.735969\pi\)
−0.675261 + 0.737579i \(0.735969\pi\)
\(968\) 0 0
\(969\) 4.26933 0.137151
\(970\) 0 0
\(971\) 1.16677 0.0374435 0.0187218 0.999825i \(-0.494040\pi\)
0.0187218 + 0.999825i \(0.494040\pi\)
\(972\) 0 0
\(973\) −17.6758 −0.566661
\(974\) 0 0
\(975\) −72.1776 −2.31153
\(976\) 0 0
\(977\) −52.0060 −1.66382 −0.831909 0.554912i \(-0.812752\pi\)
−0.831909 + 0.554912i \(0.812752\pi\)
\(978\) 0 0
\(979\) 30.8189 0.984975
\(980\) 0 0
\(981\) 9.99492 0.319113
\(982\) 0 0
\(983\) −16.8873 −0.538622 −0.269311 0.963053i \(-0.586796\pi\)
−0.269311 + 0.963053i \(0.586796\pi\)
\(984\) 0 0
\(985\) 88.5144 2.82030
\(986\) 0 0
\(987\) −1.74450 −0.0555281
\(988\) 0 0
\(989\) −23.6712 −0.752702
\(990\) 0 0
\(991\) 18.8021 0.597269 0.298634 0.954368i \(-0.403469\pi\)
0.298634 + 0.954368i \(0.403469\pi\)
\(992\) 0 0
\(993\) −9.06789 −0.287761
\(994\) 0 0
\(995\) −73.7853 −2.33915
\(996\) 0 0
\(997\) 1.11330 0.0352587 0.0176294 0.999845i \(-0.494388\pi\)
0.0176294 + 0.999845i \(0.494388\pi\)
\(998\) 0 0
\(999\) −3.18976 −0.100919
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 \(a_p\))