Properties

Label 6040.2.a.p.1.12
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 1.12
Root \(-0.815820\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.815820 q^{3}\) \(+1.00000 q^{5}\) \(-2.49382 q^{7}\) \(-2.33444 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.815820 q^{3}\) \(+1.00000 q^{5}\) \(-2.49382 q^{7}\) \(-2.33444 q^{9}\) \(+1.48661 q^{11}\) \(+5.26621 q^{13}\) \(+0.815820 q^{15}\) \(+1.04575 q^{17}\) \(-7.39355 q^{19}\) \(-2.03450 q^{21}\) \(+0.0259902 q^{23}\) \(+1.00000 q^{25}\) \(-4.35194 q^{27}\) \(+6.30898 q^{29}\) \(-8.70155 q^{31}\) \(+1.21281 q^{33}\) \(-2.49382 q^{35}\) \(+0.895610 q^{37}\) \(+4.29628 q^{39}\) \(+3.52055 q^{41}\) \(-8.45857 q^{43}\) \(-2.33444 q^{45}\) \(-4.55300 q^{47}\) \(-0.780881 q^{49}\) \(+0.853142 q^{51}\) \(-4.01326 q^{53}\) \(+1.48661 q^{55}\) \(-6.03180 q^{57}\) \(+4.73895 q^{59}\) \(-8.15857 q^{61}\) \(+5.82166 q^{63}\) \(+5.26621 q^{65}\) \(-8.54928 q^{67}\) \(+0.0212033 q^{69}\) \(-2.24512 q^{71}\) \(-6.46490 q^{73}\) \(+0.815820 q^{75}\) \(-3.70734 q^{77}\) \(+15.6805 q^{79}\) \(+3.45292 q^{81}\) \(+13.6215 q^{83}\) \(+1.04575 q^{85}\) \(+5.14699 q^{87}\) \(-1.61193 q^{89}\) \(-13.1330 q^{91}\) \(-7.09890 q^{93}\) \(-7.39355 q^{95}\) \(-4.71034 q^{97}\) \(-3.47041 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.815820 0.471014 0.235507 0.971873i \(-0.424325\pi\)
0.235507 + 0.971873i \(0.424325\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.49382 −0.942574 −0.471287 0.881980i \(-0.656210\pi\)
−0.471287 + 0.881980i \(0.656210\pi\)
\(8\) 0 0
\(9\) −2.33444 −0.778146
\(10\) 0 0
\(11\) 1.48661 0.448231 0.224115 0.974563i \(-0.428051\pi\)
0.224115 + 0.974563i \(0.428051\pi\)
\(12\) 0 0
\(13\) 5.26621 1.46058 0.730292 0.683135i \(-0.239384\pi\)
0.730292 + 0.683135i \(0.239384\pi\)
\(14\) 0 0
\(15\) 0.815820 0.210644
\(16\) 0 0
\(17\) 1.04575 0.253631 0.126816 0.991926i \(-0.459524\pi\)
0.126816 + 0.991926i \(0.459524\pi\)
\(18\) 0 0
\(19\) −7.39355 −1.69620 −0.848098 0.529839i \(-0.822252\pi\)
−0.848098 + 0.529839i \(0.822252\pi\)
\(20\) 0 0
\(21\) −2.03450 −0.443965
\(22\) 0 0
\(23\) 0.0259902 0.00541933 0.00270967 0.999996i \(-0.499137\pi\)
0.00270967 + 0.999996i \(0.499137\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.35194 −0.837531
\(28\) 0 0
\(29\) 6.30898 1.17155 0.585774 0.810474i \(-0.300790\pi\)
0.585774 + 0.810474i \(0.300790\pi\)
\(30\) 0 0
\(31\) −8.70155 −1.56284 −0.781422 0.624003i \(-0.785505\pi\)
−0.781422 + 0.624003i \(0.785505\pi\)
\(32\) 0 0
\(33\) 1.21281 0.211123
\(34\) 0 0
\(35\) −2.49382 −0.421532
\(36\) 0 0
\(37\) 0.895610 0.147237 0.0736187 0.997286i \(-0.476545\pi\)
0.0736187 + 0.997286i \(0.476545\pi\)
\(38\) 0 0
\(39\) 4.29628 0.687955
\(40\) 0 0
\(41\) 3.52055 0.549817 0.274908 0.961470i \(-0.411352\pi\)
0.274908 + 0.961470i \(0.411352\pi\)
\(42\) 0 0
\(43\) −8.45857 −1.28992 −0.644960 0.764216i \(-0.723126\pi\)
−0.644960 + 0.764216i \(0.723126\pi\)
\(44\) 0 0
\(45\) −2.33444 −0.347998
\(46\) 0 0
\(47\) −4.55300 −0.664123 −0.332062 0.943258i \(-0.607744\pi\)
−0.332062 + 0.943258i \(0.607744\pi\)
\(48\) 0 0
\(49\) −0.780881 −0.111554
\(50\) 0 0
\(51\) 0.853142 0.119464
\(52\) 0 0
\(53\) −4.01326 −0.551263 −0.275632 0.961263i \(-0.588887\pi\)
−0.275632 + 0.961263i \(0.588887\pi\)
\(54\) 0 0
\(55\) 1.48661 0.200455
\(56\) 0 0
\(57\) −6.03180 −0.798932
\(58\) 0 0
\(59\) 4.73895 0.616958 0.308479 0.951231i \(-0.400180\pi\)
0.308479 + 0.951231i \(0.400180\pi\)
\(60\) 0 0
\(61\) −8.15857 −1.04460 −0.522299 0.852763i \(-0.674925\pi\)
−0.522299 + 0.852763i \(0.674925\pi\)
\(62\) 0 0
\(63\) 5.82166 0.733460
\(64\) 0 0
\(65\) 5.26621 0.653193
\(66\) 0 0
\(67\) −8.54928 −1.04446 −0.522231 0.852804i \(-0.674900\pi\)
−0.522231 + 0.852804i \(0.674900\pi\)
\(68\) 0 0
\(69\) 0.0212033 0.00255258
\(70\) 0 0
\(71\) −2.24512 −0.266446 −0.133223 0.991086i \(-0.542533\pi\)
−0.133223 + 0.991086i \(0.542533\pi\)
\(72\) 0 0
\(73\) −6.46490 −0.756659 −0.378329 0.925671i \(-0.623501\pi\)
−0.378329 + 0.925671i \(0.623501\pi\)
\(74\) 0 0
\(75\) 0.815820 0.0942027
\(76\) 0 0
\(77\) −3.70734 −0.422490
\(78\) 0 0
\(79\) 15.6805 1.76420 0.882100 0.471063i \(-0.156130\pi\)
0.882100 + 0.471063i \(0.156130\pi\)
\(80\) 0 0
\(81\) 3.45292 0.383658
\(82\) 0 0
\(83\) 13.6215 1.49515 0.747577 0.664176i \(-0.231217\pi\)
0.747577 + 0.664176i \(0.231217\pi\)
\(84\) 0 0
\(85\) 1.04575 0.113427
\(86\) 0 0
\(87\) 5.14699 0.551816
\(88\) 0 0
\(89\) −1.61193 −0.170864 −0.0854322 0.996344i \(-0.527227\pi\)
−0.0854322 + 0.996344i \(0.527227\pi\)
\(90\) 0 0
\(91\) −13.1330 −1.37671
\(92\) 0 0
\(93\) −7.09890 −0.736121
\(94\) 0 0
\(95\) −7.39355 −0.758562
\(96\) 0 0
\(97\) −4.71034 −0.478262 −0.239131 0.970987i \(-0.576863\pi\)
−0.239131 + 0.970987i \(0.576863\pi\)
\(98\) 0 0
\(99\) −3.47041 −0.348789
\(100\) 0 0
\(101\) 2.90267 0.288826 0.144413 0.989517i \(-0.453871\pi\)
0.144413 + 0.989517i \(0.453871\pi\)
\(102\) 0 0
\(103\) −16.0372 −1.58019 −0.790094 0.612985i \(-0.789969\pi\)
−0.790094 + 0.612985i \(0.789969\pi\)
\(104\) 0 0
\(105\) −2.03450 −0.198547
\(106\) 0 0
\(107\) 15.6986 1.51764 0.758821 0.651299i \(-0.225776\pi\)
0.758821 + 0.651299i \(0.225776\pi\)
\(108\) 0 0
\(109\) 9.46068 0.906169 0.453085 0.891468i \(-0.350324\pi\)
0.453085 + 0.891468i \(0.350324\pi\)
\(110\) 0 0
\(111\) 0.730657 0.0693509
\(112\) 0 0
\(113\) −10.8741 −1.02295 −0.511473 0.859300i \(-0.670900\pi\)
−0.511473 + 0.859300i \(0.670900\pi\)
\(114\) 0 0
\(115\) 0.0259902 0.00242360
\(116\) 0 0
\(117\) −12.2936 −1.13655
\(118\) 0 0
\(119\) −2.60790 −0.239066
\(120\) 0 0
\(121\) −8.78998 −0.799089
\(122\) 0 0
\(123\) 2.87213 0.258971
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.83300 −0.606331 −0.303165 0.952938i \(-0.598043\pi\)
−0.303165 + 0.952938i \(0.598043\pi\)
\(128\) 0 0
\(129\) −6.90067 −0.607570
\(130\) 0 0
\(131\) −16.3567 −1.42909 −0.714544 0.699591i \(-0.753366\pi\)
−0.714544 + 0.699591i \(0.753366\pi\)
\(132\) 0 0
\(133\) 18.4382 1.59879
\(134\) 0 0
\(135\) −4.35194 −0.374555
\(136\) 0 0
\(137\) −14.8708 −1.27050 −0.635250 0.772307i \(-0.719103\pi\)
−0.635250 + 0.772307i \(0.719103\pi\)
\(138\) 0 0
\(139\) 17.4615 1.48106 0.740531 0.672022i \(-0.234574\pi\)
0.740531 + 0.672022i \(0.234574\pi\)
\(140\) 0 0
\(141\) −3.71443 −0.312811
\(142\) 0 0
\(143\) 7.82882 0.654679
\(144\) 0 0
\(145\) 6.30898 0.523933
\(146\) 0 0
\(147\) −0.637058 −0.0525437
\(148\) 0 0
\(149\) 17.5804 1.44024 0.720121 0.693849i \(-0.244086\pi\)
0.720121 + 0.693849i \(0.244086\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −2.44123 −0.197362
\(154\) 0 0
\(155\) −8.70155 −0.698925
\(156\) 0 0
\(157\) −6.44378 −0.514270 −0.257135 0.966376i \(-0.582778\pi\)
−0.257135 + 0.966376i \(0.582778\pi\)
\(158\) 0 0
\(159\) −3.27409 −0.259652
\(160\) 0 0
\(161\) −0.0648148 −0.00510812
\(162\) 0 0
\(163\) −24.4787 −1.91732 −0.958659 0.284558i \(-0.908153\pi\)
−0.958659 + 0.284558i \(0.908153\pi\)
\(164\) 0 0
\(165\) 1.21281 0.0944170
\(166\) 0 0
\(167\) −4.35235 −0.336795 −0.168397 0.985719i \(-0.553859\pi\)
−0.168397 + 0.985719i \(0.553859\pi\)
\(168\) 0 0
\(169\) 14.7330 1.13331
\(170\) 0 0
\(171\) 17.2598 1.31989
\(172\) 0 0
\(173\) 15.3263 1.16524 0.582618 0.812746i \(-0.302028\pi\)
0.582618 + 0.812746i \(0.302028\pi\)
\(174\) 0 0
\(175\) −2.49382 −0.188515
\(176\) 0 0
\(177\) 3.86613 0.290596
\(178\) 0 0
\(179\) −5.48802 −0.410194 −0.205097 0.978742i \(-0.565751\pi\)
−0.205097 + 0.978742i \(0.565751\pi\)
\(180\) 0 0
\(181\) −18.5589 −1.37947 −0.689734 0.724062i \(-0.742273\pi\)
−0.689734 + 0.724062i \(0.742273\pi\)
\(182\) 0 0
\(183\) −6.65592 −0.492020
\(184\) 0 0
\(185\) 0.895610 0.0658466
\(186\) 0 0
\(187\) 1.55462 0.113685
\(188\) 0 0
\(189\) 10.8529 0.789435
\(190\) 0 0
\(191\) −11.3552 −0.821633 −0.410816 0.911718i \(-0.634756\pi\)
−0.410816 + 0.911718i \(0.634756\pi\)
\(192\) 0 0
\(193\) −6.49585 −0.467581 −0.233791 0.972287i \(-0.575113\pi\)
−0.233791 + 0.972287i \(0.575113\pi\)
\(194\) 0 0
\(195\) 4.29628 0.307663
\(196\) 0 0
\(197\) −22.2838 −1.58765 −0.793827 0.608143i \(-0.791915\pi\)
−0.793827 + 0.608143i \(0.791915\pi\)
\(198\) 0 0
\(199\) −22.6010 −1.60214 −0.801072 0.598568i \(-0.795736\pi\)
−0.801072 + 0.598568i \(0.795736\pi\)
\(200\) 0 0
\(201\) −6.97467 −0.491955
\(202\) 0 0
\(203\) −15.7334 −1.10427
\(204\) 0 0
\(205\) 3.52055 0.245886
\(206\) 0 0
\(207\) −0.0606726 −0.00421703
\(208\) 0 0
\(209\) −10.9913 −0.760287
\(210\) 0 0
\(211\) −11.2261 −0.772834 −0.386417 0.922324i \(-0.626287\pi\)
−0.386417 + 0.922324i \(0.626287\pi\)
\(212\) 0 0
\(213\) −1.83161 −0.125500
\(214\) 0 0
\(215\) −8.45857 −0.576870
\(216\) 0 0
\(217\) 21.7001 1.47310
\(218\) 0 0
\(219\) −5.27419 −0.356397
\(220\) 0 0
\(221\) 5.50713 0.370450
\(222\) 0 0
\(223\) 1.96676 0.131704 0.0658519 0.997829i \(-0.479024\pi\)
0.0658519 + 0.997829i \(0.479024\pi\)
\(224\) 0 0
\(225\) −2.33444 −0.155629
\(226\) 0 0
\(227\) 16.7316 1.11052 0.555259 0.831678i \(-0.312619\pi\)
0.555259 + 0.831678i \(0.312619\pi\)
\(228\) 0 0
\(229\) 9.09161 0.600790 0.300395 0.953815i \(-0.402881\pi\)
0.300395 + 0.953815i \(0.402881\pi\)
\(230\) 0 0
\(231\) −3.02452 −0.198999
\(232\) 0 0
\(233\) −26.3161 −1.72402 −0.862012 0.506888i \(-0.830796\pi\)
−0.862012 + 0.506888i \(0.830796\pi\)
\(234\) 0 0
\(235\) −4.55300 −0.297005
\(236\) 0 0
\(237\) 12.7925 0.830962
\(238\) 0 0
\(239\) −17.5753 −1.13685 −0.568425 0.822735i \(-0.692447\pi\)
−0.568425 + 0.822735i \(0.692447\pi\)
\(240\) 0 0
\(241\) −20.8207 −1.34118 −0.670588 0.741830i \(-0.733958\pi\)
−0.670588 + 0.741830i \(0.733958\pi\)
\(242\) 0 0
\(243\) 15.8728 1.01824
\(244\) 0 0
\(245\) −0.780881 −0.0498887
\(246\) 0 0
\(247\) −38.9360 −2.47744
\(248\) 0 0
\(249\) 11.1127 0.704238
\(250\) 0 0
\(251\) −14.5478 −0.918248 −0.459124 0.888372i \(-0.651837\pi\)
−0.459124 + 0.888372i \(0.651837\pi\)
\(252\) 0 0
\(253\) 0.0386374 0.00242911
\(254\) 0 0
\(255\) 0.853142 0.0534258
\(256\) 0 0
\(257\) −0.407814 −0.0254388 −0.0127194 0.999919i \(-0.504049\pi\)
−0.0127194 + 0.999919i \(0.504049\pi\)
\(258\) 0 0
\(259\) −2.23349 −0.138782
\(260\) 0 0
\(261\) −14.7279 −0.911636
\(262\) 0 0
\(263\) 22.5215 1.38873 0.694367 0.719621i \(-0.255685\pi\)
0.694367 + 0.719621i \(0.255685\pi\)
\(264\) 0 0
\(265\) −4.01326 −0.246532
\(266\) 0 0
\(267\) −1.31505 −0.0804795
\(268\) 0 0
\(269\) −3.40350 −0.207515 −0.103757 0.994603i \(-0.533087\pi\)
−0.103757 + 0.994603i \(0.533087\pi\)
\(270\) 0 0
\(271\) −16.5424 −1.00488 −0.502439 0.864613i \(-0.667564\pi\)
−0.502439 + 0.864613i \(0.667564\pi\)
\(272\) 0 0
\(273\) −10.7141 −0.648448
\(274\) 0 0
\(275\) 1.48661 0.0896461
\(276\) 0 0
\(277\) 13.7340 0.825194 0.412597 0.910914i \(-0.364622\pi\)
0.412597 + 0.910914i \(0.364622\pi\)
\(278\) 0 0
\(279\) 20.3132 1.21612
\(280\) 0 0
\(281\) −21.3283 −1.27234 −0.636170 0.771549i \(-0.719482\pi\)
−0.636170 + 0.771549i \(0.719482\pi\)
\(282\) 0 0
\(283\) 10.4259 0.619753 0.309876 0.950777i \(-0.399712\pi\)
0.309876 + 0.950777i \(0.399712\pi\)
\(284\) 0 0
\(285\) −6.03180 −0.357293
\(286\) 0 0
\(287\) −8.77959 −0.518243
\(288\) 0 0
\(289\) −15.9064 −0.935671
\(290\) 0 0
\(291\) −3.84278 −0.225268
\(292\) 0 0
\(293\) 27.0198 1.57851 0.789256 0.614064i \(-0.210466\pi\)
0.789256 + 0.614064i \(0.210466\pi\)
\(294\) 0 0
\(295\) 4.73895 0.275912
\(296\) 0 0
\(297\) −6.46965 −0.375407
\(298\) 0 0
\(299\) 0.136870 0.00791539
\(300\) 0 0
\(301\) 21.0941 1.21584
\(302\) 0 0
\(303\) 2.36805 0.136041
\(304\) 0 0
\(305\) −8.15857 −0.467158
\(306\) 0 0
\(307\) −8.62153 −0.492057 −0.246028 0.969263i \(-0.579126\pi\)
−0.246028 + 0.969263i \(0.579126\pi\)
\(308\) 0 0
\(309\) −13.0834 −0.744291
\(310\) 0 0
\(311\) −26.2623 −1.48920 −0.744599 0.667512i \(-0.767359\pi\)
−0.744599 + 0.667512i \(0.767359\pi\)
\(312\) 0 0
\(313\) 20.6476 1.16707 0.583535 0.812088i \(-0.301669\pi\)
0.583535 + 0.812088i \(0.301669\pi\)
\(314\) 0 0
\(315\) 5.82166 0.328013
\(316\) 0 0
\(317\) −5.14134 −0.288766 −0.144383 0.989522i \(-0.546120\pi\)
−0.144383 + 0.989522i \(0.546120\pi\)
\(318\) 0 0
\(319\) 9.37902 0.525124
\(320\) 0 0
\(321\) 12.8072 0.714830
\(322\) 0 0
\(323\) −7.73179 −0.430208
\(324\) 0 0
\(325\) 5.26621 0.292117
\(326\) 0 0
\(327\) 7.71821 0.426818
\(328\) 0 0
\(329\) 11.3543 0.625985
\(330\) 0 0
\(331\) 22.6710 1.24611 0.623055 0.782178i \(-0.285891\pi\)
0.623055 + 0.782178i \(0.285891\pi\)
\(332\) 0 0
\(333\) −2.09075 −0.114572
\(334\) 0 0
\(335\) −8.54928 −0.467097
\(336\) 0 0
\(337\) −8.13975 −0.443401 −0.221700 0.975115i \(-0.571161\pi\)
−0.221700 + 0.975115i \(0.571161\pi\)
\(338\) 0 0
\(339\) −8.87127 −0.481821
\(340\) 0 0
\(341\) −12.9358 −0.700515
\(342\) 0 0
\(343\) 19.4041 1.04772
\(344\) 0 0
\(345\) 0.0212033 0.00114155
\(346\) 0 0
\(347\) 32.4079 1.73975 0.869874 0.493275i \(-0.164200\pi\)
0.869874 + 0.493275i \(0.164200\pi\)
\(348\) 0 0
\(349\) −35.3292 −1.89113 −0.945563 0.325438i \(-0.894488\pi\)
−0.945563 + 0.325438i \(0.894488\pi\)
\(350\) 0 0
\(351\) −22.9182 −1.22328
\(352\) 0 0
\(353\) 36.5765 1.94677 0.973386 0.229171i \(-0.0736015\pi\)
0.973386 + 0.229171i \(0.0736015\pi\)
\(354\) 0 0
\(355\) −2.24512 −0.119158
\(356\) 0 0
\(357\) −2.12758 −0.112603
\(358\) 0 0
\(359\) 14.0125 0.739554 0.369777 0.929121i \(-0.379434\pi\)
0.369777 + 0.929121i \(0.379434\pi\)
\(360\) 0 0
\(361\) 35.6646 1.87708
\(362\) 0 0
\(363\) −7.17104 −0.376382
\(364\) 0 0
\(365\) −6.46490 −0.338388
\(366\) 0 0
\(367\) −24.4215 −1.27479 −0.637395 0.770537i \(-0.719988\pi\)
−0.637395 + 0.770537i \(0.719988\pi\)
\(368\) 0 0
\(369\) −8.21850 −0.427838
\(370\) 0 0
\(371\) 10.0083 0.519606
\(372\) 0 0
\(373\) −0.764317 −0.0395748 −0.0197874 0.999804i \(-0.506299\pi\)
−0.0197874 + 0.999804i \(0.506299\pi\)
\(374\) 0 0
\(375\) 0.815820 0.0421287
\(376\) 0 0
\(377\) 33.2244 1.71115
\(378\) 0 0
\(379\) −28.6707 −1.47271 −0.736357 0.676593i \(-0.763456\pi\)
−0.736357 + 0.676593i \(0.763456\pi\)
\(380\) 0 0
\(381\) −5.57450 −0.285590
\(382\) 0 0
\(383\) −11.3882 −0.581910 −0.290955 0.956737i \(-0.593973\pi\)
−0.290955 + 0.956737i \(0.593973\pi\)
\(384\) 0 0
\(385\) −3.70734 −0.188943
\(386\) 0 0
\(387\) 19.7460 1.00375
\(388\) 0 0
\(389\) −32.8184 −1.66396 −0.831980 0.554806i \(-0.812793\pi\)
−0.831980 + 0.554806i \(0.812793\pi\)
\(390\) 0 0
\(391\) 0.0271792 0.00137451
\(392\) 0 0
\(393\) −13.3441 −0.673120
\(394\) 0 0
\(395\) 15.6805 0.788974
\(396\) 0 0
\(397\) 31.4177 1.57681 0.788405 0.615156i \(-0.210907\pi\)
0.788405 + 0.615156i \(0.210907\pi\)
\(398\) 0 0
\(399\) 15.0422 0.753052
\(400\) 0 0
\(401\) 13.9941 0.698834 0.349417 0.936967i \(-0.386380\pi\)
0.349417 + 0.936967i \(0.386380\pi\)
\(402\) 0 0
\(403\) −45.8242 −2.28267
\(404\) 0 0
\(405\) 3.45292 0.171577
\(406\) 0 0
\(407\) 1.33143 0.0659963
\(408\) 0 0
\(409\) 28.3104 1.39986 0.699929 0.714213i \(-0.253215\pi\)
0.699929 + 0.714213i \(0.253215\pi\)
\(410\) 0 0
\(411\) −12.1319 −0.598422
\(412\) 0 0
\(413\) −11.8181 −0.581529
\(414\) 0 0
\(415\) 13.6215 0.668653
\(416\) 0 0
\(417\) 14.2454 0.697600
\(418\) 0 0
\(419\) 36.3234 1.77452 0.887258 0.461274i \(-0.152607\pi\)
0.887258 + 0.461274i \(0.152607\pi\)
\(420\) 0 0
\(421\) 26.2898 1.28128 0.640642 0.767840i \(-0.278668\pi\)
0.640642 + 0.767840i \(0.278668\pi\)
\(422\) 0 0
\(423\) 10.6287 0.516785
\(424\) 0 0
\(425\) 1.04575 0.0507262
\(426\) 0 0
\(427\) 20.3460 0.984610
\(428\) 0 0
\(429\) 6.38690 0.308363
\(430\) 0 0
\(431\) −27.8740 −1.34264 −0.671321 0.741167i \(-0.734273\pi\)
−0.671321 + 0.741167i \(0.734273\pi\)
\(432\) 0 0
\(433\) −5.44329 −0.261588 −0.130794 0.991410i \(-0.541753\pi\)
−0.130794 + 0.991410i \(0.541753\pi\)
\(434\) 0 0
\(435\) 5.14699 0.246779
\(436\) 0 0
\(437\) −0.192160 −0.00919226
\(438\) 0 0
\(439\) 1.84567 0.0880890 0.0440445 0.999030i \(-0.485976\pi\)
0.0440445 + 0.999030i \(0.485976\pi\)
\(440\) 0 0
\(441\) 1.82292 0.0868057
\(442\) 0 0
\(443\) 25.4715 1.21019 0.605094 0.796154i \(-0.293136\pi\)
0.605094 + 0.796154i \(0.293136\pi\)
\(444\) 0 0
\(445\) −1.61193 −0.0764129
\(446\) 0 0
\(447\) 14.3424 0.678373
\(448\) 0 0
\(449\) 3.83174 0.180831 0.0904156 0.995904i \(-0.471180\pi\)
0.0904156 + 0.995904i \(0.471180\pi\)
\(450\) 0 0
\(451\) 5.23369 0.246445
\(452\) 0 0
\(453\) 0.815820 0.0383305
\(454\) 0 0
\(455\) −13.1330 −0.615683
\(456\) 0 0
\(457\) 0.439109 0.0205407 0.0102703 0.999947i \(-0.496731\pi\)
0.0102703 + 0.999947i \(0.496731\pi\)
\(458\) 0 0
\(459\) −4.55103 −0.212424
\(460\) 0 0
\(461\) −10.8733 −0.506422 −0.253211 0.967411i \(-0.581487\pi\)
−0.253211 + 0.967411i \(0.581487\pi\)
\(462\) 0 0
\(463\) 18.1320 0.842664 0.421332 0.906907i \(-0.361563\pi\)
0.421332 + 0.906907i \(0.361563\pi\)
\(464\) 0 0
\(465\) −7.09890 −0.329203
\(466\) 0 0
\(467\) −6.62096 −0.306381 −0.153191 0.988197i \(-0.548955\pi\)
−0.153191 + 0.988197i \(0.548955\pi\)
\(468\) 0 0
\(469\) 21.3203 0.984482
\(470\) 0 0
\(471\) −5.25696 −0.242228
\(472\) 0 0
\(473\) −12.5746 −0.578181
\(474\) 0 0
\(475\) −7.39355 −0.339239
\(476\) 0 0
\(477\) 9.36870 0.428963
\(478\) 0 0
\(479\) −8.44168 −0.385710 −0.192855 0.981227i \(-0.561775\pi\)
−0.192855 + 0.981227i \(0.561775\pi\)
\(480\) 0 0
\(481\) 4.71647 0.215053
\(482\) 0 0
\(483\) −0.0528772 −0.00240600
\(484\) 0 0
\(485\) −4.71034 −0.213885
\(486\) 0 0
\(487\) 19.2073 0.870366 0.435183 0.900342i \(-0.356684\pi\)
0.435183 + 0.900342i \(0.356684\pi\)
\(488\) 0 0
\(489\) −19.9702 −0.903083
\(490\) 0 0
\(491\) 24.0758 1.08653 0.543263 0.839563i \(-0.317189\pi\)
0.543263 + 0.839563i \(0.317189\pi\)
\(492\) 0 0
\(493\) 6.59761 0.297141
\(494\) 0 0
\(495\) −3.47041 −0.155983
\(496\) 0 0
\(497\) 5.59891 0.251145
\(498\) 0 0
\(499\) −42.2199 −1.89002 −0.945011 0.327037i \(-0.893950\pi\)
−0.945011 + 0.327037i \(0.893950\pi\)
\(500\) 0 0
\(501\) −3.55073 −0.158635
\(502\) 0 0
\(503\) 10.0451 0.447888 0.223944 0.974602i \(-0.428107\pi\)
0.223944 + 0.974602i \(0.428107\pi\)
\(504\) 0 0
\(505\) 2.90267 0.129167
\(506\) 0 0
\(507\) 12.0195 0.533803
\(508\) 0 0
\(509\) −9.94121 −0.440636 −0.220318 0.975428i \(-0.570710\pi\)
−0.220318 + 0.975428i \(0.570710\pi\)
\(510\) 0 0
\(511\) 16.1223 0.713207
\(512\) 0 0
\(513\) 32.1763 1.42062
\(514\) 0 0
\(515\) −16.0372 −0.706682
\(516\) 0 0
\(517\) −6.76855 −0.297680
\(518\) 0 0
\(519\) 12.5035 0.548842
\(520\) 0 0
\(521\) 33.7158 1.47711 0.738557 0.674191i \(-0.235508\pi\)
0.738557 + 0.674191i \(0.235508\pi\)
\(522\) 0 0
\(523\) 1.08746 0.0475513 0.0237757 0.999717i \(-0.492431\pi\)
0.0237757 + 0.999717i \(0.492431\pi\)
\(524\) 0 0
\(525\) −2.03450 −0.0887930
\(526\) 0 0
\(527\) −9.09963 −0.396386
\(528\) 0 0
\(529\) −22.9993 −0.999971
\(530\) 0 0
\(531\) −11.0628 −0.480084
\(532\) 0 0
\(533\) 18.5399 0.803054
\(534\) 0 0
\(535\) 15.6986 0.678710
\(536\) 0 0
\(537\) −4.47723 −0.193207
\(538\) 0 0
\(539\) −1.16087 −0.0500021
\(540\) 0 0
\(541\) 34.8695 1.49916 0.749579 0.661915i \(-0.230256\pi\)
0.749579 + 0.661915i \(0.230256\pi\)
\(542\) 0 0
\(543\) −15.1407 −0.649749
\(544\) 0 0
\(545\) 9.46068 0.405251
\(546\) 0 0
\(547\) −18.3571 −0.784895 −0.392447 0.919774i \(-0.628372\pi\)
−0.392447 + 0.919774i \(0.628372\pi\)
\(548\) 0 0
\(549\) 19.0457 0.812849
\(550\) 0 0
\(551\) −46.6458 −1.98718
\(552\) 0 0
\(553\) −39.1044 −1.66289
\(554\) 0 0
\(555\) 0.730657 0.0310146
\(556\) 0 0
\(557\) −0.866545 −0.0367167 −0.0183583 0.999831i \(-0.505844\pi\)
−0.0183583 + 0.999831i \(0.505844\pi\)
\(558\) 0 0
\(559\) −44.5446 −1.88404
\(560\) 0 0
\(561\) 1.26829 0.0535473
\(562\) 0 0
\(563\) 34.6019 1.45830 0.729148 0.684356i \(-0.239917\pi\)
0.729148 + 0.684356i \(0.239917\pi\)
\(564\) 0 0
\(565\) −10.8741 −0.457475
\(566\) 0 0
\(567\) −8.61094 −0.361626
\(568\) 0 0
\(569\) −28.0389 −1.17545 −0.587725 0.809061i \(-0.699976\pi\)
−0.587725 + 0.809061i \(0.699976\pi\)
\(570\) 0 0
\(571\) 19.7871 0.828064 0.414032 0.910262i \(-0.364120\pi\)
0.414032 + 0.910262i \(0.364120\pi\)
\(572\) 0 0
\(573\) −9.26378 −0.387000
\(574\) 0 0
\(575\) 0.0259902 0.00108387
\(576\) 0 0
\(577\) 30.1597 1.25557 0.627783 0.778388i \(-0.283963\pi\)
0.627783 + 0.778388i \(0.283963\pi\)
\(578\) 0 0
\(579\) −5.29944 −0.220237
\(580\) 0 0
\(581\) −33.9695 −1.40929
\(582\) 0 0
\(583\) −5.96616 −0.247093
\(584\) 0 0
\(585\) −12.2936 −0.508280
\(586\) 0 0
\(587\) −9.49212 −0.391782 −0.195891 0.980626i \(-0.562760\pi\)
−0.195891 + 0.980626i \(0.562760\pi\)
\(588\) 0 0
\(589\) 64.3353 2.65089
\(590\) 0 0
\(591\) −18.1796 −0.747807
\(592\) 0 0
\(593\) 5.21125 0.214000 0.107000 0.994259i \(-0.465875\pi\)
0.107000 + 0.994259i \(0.465875\pi\)
\(594\) 0 0
\(595\) −2.60790 −0.106914
\(596\) 0 0
\(597\) −18.4384 −0.754631
\(598\) 0 0
\(599\) −38.0809 −1.55594 −0.777971 0.628300i \(-0.783751\pi\)
−0.777971 + 0.628300i \(0.783751\pi\)
\(600\) 0 0
\(601\) −16.8393 −0.686890 −0.343445 0.939173i \(-0.611594\pi\)
−0.343445 + 0.939173i \(0.611594\pi\)
\(602\) 0 0
\(603\) 19.9578 0.812743
\(604\) 0 0
\(605\) −8.78998 −0.357364
\(606\) 0 0
\(607\) −32.8649 −1.33395 −0.666974 0.745081i \(-0.732411\pi\)
−0.666974 + 0.745081i \(0.732411\pi\)
\(608\) 0 0
\(609\) −12.8357 −0.520127
\(610\) 0 0
\(611\) −23.9771 −0.970008
\(612\) 0 0
\(613\) −6.55646 −0.264813 −0.132406 0.991196i \(-0.542270\pi\)
−0.132406 + 0.991196i \(0.542270\pi\)
\(614\) 0 0
\(615\) 2.87213 0.115815
\(616\) 0 0
\(617\) −30.2120 −1.21629 −0.608144 0.793827i \(-0.708086\pi\)
−0.608144 + 0.793827i \(0.708086\pi\)
\(618\) 0 0
\(619\) 32.5398 1.30789 0.653943 0.756544i \(-0.273114\pi\)
0.653943 + 0.756544i \(0.273114\pi\)
\(620\) 0 0
\(621\) −0.113108 −0.00453886
\(622\) 0 0
\(623\) 4.01986 0.161052
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −8.96695 −0.358106
\(628\) 0 0
\(629\) 0.936583 0.0373440
\(630\) 0 0
\(631\) 13.9013 0.553402 0.276701 0.960956i \(-0.410759\pi\)
0.276701 + 0.960956i \(0.410759\pi\)
\(632\) 0 0
\(633\) −9.15844 −0.364015
\(634\) 0 0
\(635\) −6.83300 −0.271159
\(636\) 0 0
\(637\) −4.11229 −0.162935
\(638\) 0 0
\(639\) 5.24108 0.207334
\(640\) 0 0
\(641\) 34.0600 1.34529 0.672645 0.739965i \(-0.265158\pi\)
0.672645 + 0.739965i \(0.265158\pi\)
\(642\) 0 0
\(643\) 12.1253 0.478176 0.239088 0.970998i \(-0.423152\pi\)
0.239088 + 0.970998i \(0.423152\pi\)
\(644\) 0 0
\(645\) −6.90067 −0.271713
\(646\) 0 0
\(647\) −8.82321 −0.346876 −0.173438 0.984845i \(-0.555488\pi\)
−0.173438 + 0.984845i \(0.555488\pi\)
\(648\) 0 0
\(649\) 7.04498 0.276540
\(650\) 0 0
\(651\) 17.7033 0.693849
\(652\) 0 0
\(653\) −30.1111 −1.17834 −0.589169 0.808010i \(-0.700545\pi\)
−0.589169 + 0.808010i \(0.700545\pi\)
\(654\) 0 0
\(655\) −16.3567 −0.639107
\(656\) 0 0
\(657\) 15.0919 0.588791
\(658\) 0 0
\(659\) 50.7203 1.97578 0.987891 0.155151i \(-0.0495865\pi\)
0.987891 + 0.155151i \(0.0495865\pi\)
\(660\) 0 0
\(661\) 10.0303 0.390135 0.195068 0.980790i \(-0.437507\pi\)
0.195068 + 0.980790i \(0.437507\pi\)
\(662\) 0 0
\(663\) 4.49282 0.174487
\(664\) 0 0
\(665\) 18.4382 0.715001
\(666\) 0 0
\(667\) 0.163972 0.00634902
\(668\) 0 0
\(669\) 1.60452 0.0620343
\(670\) 0 0
\(671\) −12.1286 −0.468221
\(672\) 0 0
\(673\) 36.7156 1.41528 0.707641 0.706572i \(-0.249759\pi\)
0.707641 + 0.706572i \(0.249759\pi\)
\(674\) 0 0
\(675\) −4.35194 −0.167506
\(676\) 0 0
\(677\) 12.0158 0.461806 0.230903 0.972977i \(-0.425832\pi\)
0.230903 + 0.972977i \(0.425832\pi\)
\(678\) 0 0
\(679\) 11.7467 0.450797
\(680\) 0 0
\(681\) 13.6500 0.523069
\(682\) 0 0
\(683\) 1.66763 0.0638100 0.0319050 0.999491i \(-0.489843\pi\)
0.0319050 + 0.999491i \(0.489843\pi\)
\(684\) 0 0
\(685\) −14.8708 −0.568185
\(686\) 0 0
\(687\) 7.41711 0.282980
\(688\) 0 0
\(689\) −21.1346 −0.805166
\(690\) 0 0
\(691\) −29.8533 −1.13567 −0.567837 0.823141i \(-0.692220\pi\)
−0.567837 + 0.823141i \(0.692220\pi\)
\(692\) 0 0
\(693\) 8.65455 0.328759
\(694\) 0 0
\(695\) 17.4615 0.662351
\(696\) 0 0
\(697\) 3.68160 0.139451
\(698\) 0 0
\(699\) −21.4692 −0.812039
\(700\) 0 0
\(701\) −28.6608 −1.08250 −0.541251 0.840861i \(-0.682049\pi\)
−0.541251 + 0.840861i \(0.682049\pi\)
\(702\) 0 0
\(703\) −6.62174 −0.249744
\(704\) 0 0
\(705\) −3.71443 −0.139893
\(706\) 0 0
\(707\) −7.23872 −0.272240
\(708\) 0 0
\(709\) −41.6945 −1.56587 −0.782935 0.622103i \(-0.786278\pi\)
−0.782935 + 0.622103i \(0.786278\pi\)
\(710\) 0 0
\(711\) −36.6053 −1.37280
\(712\) 0 0
\(713\) −0.226155 −0.00846958
\(714\) 0 0
\(715\) 7.82882 0.292781
\(716\) 0 0
\(717\) −14.3383 −0.535472
\(718\) 0 0
\(719\) 40.3489 1.50476 0.752380 0.658730i \(-0.228906\pi\)
0.752380 + 0.658730i \(0.228906\pi\)
\(720\) 0 0
\(721\) 39.9937 1.48944
\(722\) 0 0
\(723\) −16.9859 −0.631712
\(724\) 0 0
\(725\) 6.30898 0.234310
\(726\) 0 0
\(727\) −44.7788 −1.66076 −0.830378 0.557201i \(-0.811875\pi\)
−0.830378 + 0.557201i \(0.811875\pi\)
\(728\) 0 0
\(729\) 2.59057 0.0959470
\(730\) 0 0
\(731\) −8.84553 −0.327164
\(732\) 0 0
\(733\) −28.6441 −1.05800 −0.528998 0.848623i \(-0.677432\pi\)
−0.528998 + 0.848623i \(0.677432\pi\)
\(734\) 0 0
\(735\) −0.637058 −0.0234983
\(736\) 0 0
\(737\) −12.7095 −0.468159
\(738\) 0 0
\(739\) 16.7894 0.617608 0.308804 0.951126i \(-0.400071\pi\)
0.308804 + 0.951126i \(0.400071\pi\)
\(740\) 0 0
\(741\) −31.7647 −1.16691
\(742\) 0 0
\(743\) −26.6824 −0.978882 −0.489441 0.872036i \(-0.662799\pi\)
−0.489441 + 0.872036i \(0.662799\pi\)
\(744\) 0 0
\(745\) 17.5804 0.644096
\(746\) 0 0
\(747\) −31.7985 −1.16345
\(748\) 0 0
\(749\) −39.1495 −1.43049
\(750\) 0 0
\(751\) −31.8648 −1.16276 −0.581382 0.813631i \(-0.697488\pi\)
−0.581382 + 0.813631i \(0.697488\pi\)
\(752\) 0 0
\(753\) −11.8684 −0.432508
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −49.0643 −1.78327 −0.891636 0.452753i \(-0.850442\pi\)
−0.891636 + 0.452753i \(0.850442\pi\)
\(758\) 0 0
\(759\) 0.0315211 0.00114414
\(760\) 0 0
\(761\) −33.1581 −1.20198 −0.600991 0.799256i \(-0.705227\pi\)
−0.600991 + 0.799256i \(0.705227\pi\)
\(762\) 0 0
\(763\) −23.5932 −0.854131
\(764\) 0 0
\(765\) −2.44123 −0.0882630
\(766\) 0 0
\(767\) 24.9563 0.901120
\(768\) 0 0
\(769\) −30.3930 −1.09600 −0.548000 0.836478i \(-0.684611\pi\)
−0.548000 + 0.836478i \(0.684611\pi\)
\(770\) 0 0
\(771\) −0.332703 −0.0119820
\(772\) 0 0
\(773\) 19.7199 0.709275 0.354637 0.935004i \(-0.384604\pi\)
0.354637 + 0.935004i \(0.384604\pi\)
\(774\) 0 0
\(775\) −8.70155 −0.312569
\(776\) 0 0
\(777\) −1.82212 −0.0653683
\(778\) 0 0
\(779\) −26.0293 −0.932597
\(780\) 0 0
\(781\) −3.33762 −0.119429
\(782\) 0 0
\(783\) −27.4563 −0.981209
\(784\) 0 0
\(785\) −6.44378 −0.229988
\(786\) 0 0
\(787\) 2.88388 0.102799 0.0513996 0.998678i \(-0.483632\pi\)
0.0513996 + 0.998678i \(0.483632\pi\)
\(788\) 0 0
\(789\) 18.3735 0.654113
\(790\) 0 0
\(791\) 27.1179 0.964201
\(792\) 0 0
\(793\) −42.9647 −1.52572
\(794\) 0 0
\(795\) −3.27409 −0.116120
\(796\) 0 0
\(797\) 45.4239 1.60900 0.804498 0.593955i \(-0.202434\pi\)
0.804498 + 0.593955i \(0.202434\pi\)
\(798\) 0 0
\(799\) −4.76129 −0.168442
\(800\) 0 0
\(801\) 3.76295 0.132957
\(802\) 0 0
\(803\) −9.61080 −0.339158
\(804\) 0 0
\(805\) −0.0648148 −0.00228442
\(806\) 0 0
\(807\) −2.77664 −0.0977423
\(808\) 0 0
\(809\) −3.54331 −0.124576 −0.0622880 0.998058i \(-0.519840\pi\)
−0.0622880 + 0.998058i \(0.519840\pi\)
\(810\) 0 0
\(811\) 14.4017 0.505712 0.252856 0.967504i \(-0.418630\pi\)
0.252856 + 0.967504i \(0.418630\pi\)
\(812\) 0 0
\(813\) −13.4956 −0.473311
\(814\) 0 0
\(815\) −24.4787 −0.857450
\(816\) 0 0
\(817\) 62.5388 2.18796
\(818\) 0 0
\(819\) 30.6581 1.07128
\(820\) 0 0
\(821\) −45.0725 −1.57304 −0.786520 0.617565i \(-0.788119\pi\)
−0.786520 + 0.617565i \(0.788119\pi\)
\(822\) 0 0
\(823\) 14.9721 0.521894 0.260947 0.965353i \(-0.415965\pi\)
0.260947 + 0.965353i \(0.415965\pi\)
\(824\) 0 0
\(825\) 1.21281 0.0422245
\(826\) 0 0
\(827\) 17.7163 0.616058 0.308029 0.951377i \(-0.400331\pi\)
0.308029 + 0.951377i \(0.400331\pi\)
\(828\) 0 0
\(829\) 49.3964 1.71561 0.857803 0.513978i \(-0.171829\pi\)
0.857803 + 0.513978i \(0.171829\pi\)
\(830\) 0 0
\(831\) 11.2044 0.388678
\(832\) 0 0
\(833\) −0.816605 −0.0282937
\(834\) 0 0
\(835\) −4.35235 −0.150619
\(836\) 0 0
\(837\) 37.8686 1.30893
\(838\) 0 0
\(839\) 34.1615 1.17939 0.589693 0.807627i \(-0.299249\pi\)
0.589693 + 0.807627i \(0.299249\pi\)
\(840\) 0 0
\(841\) 10.8033 0.372527
\(842\) 0 0
\(843\) −17.4000 −0.599289
\(844\) 0 0
\(845\) 14.7330 0.506830
\(846\) 0 0
\(847\) 21.9206 0.753201
\(848\) 0 0
\(849\) 8.50562 0.291912
\(850\) 0 0
\(851\) 0.0232771 0.000797929 0
\(852\) 0 0
\(853\) −27.5569 −0.943531 −0.471765 0.881724i \(-0.656383\pi\)
−0.471765 + 0.881724i \(0.656383\pi\)
\(854\) 0 0
\(855\) 17.2598 0.590272
\(856\) 0 0
\(857\) 53.2308 1.81833 0.909165 0.416437i \(-0.136721\pi\)
0.909165 + 0.416437i \(0.136721\pi\)
\(858\) 0 0
\(859\) 20.7430 0.707741 0.353870 0.935294i \(-0.384865\pi\)
0.353870 + 0.935294i \(0.384865\pi\)
\(860\) 0 0
\(861\) −7.16256 −0.244100
\(862\) 0 0
\(863\) −14.9469 −0.508800 −0.254400 0.967099i \(-0.581878\pi\)
−0.254400 + 0.967099i \(0.581878\pi\)
\(864\) 0 0
\(865\) 15.3263 0.521110
\(866\) 0 0
\(867\) −12.9768 −0.440714
\(868\) 0 0
\(869\) 23.3109 0.790768
\(870\) 0 0
\(871\) −45.0223 −1.52552
\(872\) 0 0
\(873\) 10.9960 0.372158
\(874\) 0 0
\(875\) −2.49382 −0.0843064
\(876\) 0 0
\(877\) 29.0485 0.980897 0.490449 0.871470i \(-0.336833\pi\)
0.490449 + 0.871470i \(0.336833\pi\)
\(878\) 0 0
\(879\) 22.0433 0.743501
\(880\) 0 0
\(881\) 9.34637 0.314887 0.157444 0.987528i \(-0.449675\pi\)
0.157444 + 0.987528i \(0.449675\pi\)
\(882\) 0 0
\(883\) 43.2527 1.45557 0.727784 0.685806i \(-0.240550\pi\)
0.727784 + 0.685806i \(0.240550\pi\)
\(884\) 0 0
\(885\) 3.86613 0.129958
\(886\) 0 0
\(887\) −46.4026 −1.55805 −0.779023 0.626996i \(-0.784284\pi\)
−0.779023 + 0.626996i \(0.784284\pi\)
\(888\) 0 0
\(889\) 17.0402 0.571512
\(890\) 0 0
\(891\) 5.13315 0.171967
\(892\) 0 0
\(893\) 33.6628 1.12648
\(894\) 0 0
\(895\) −5.48802 −0.183444
\(896\) 0 0
\(897\) 0.111661 0.00372826
\(898\) 0 0
\(899\) −54.8979 −1.83095
\(900\) 0 0
\(901\) −4.19685 −0.139817
\(902\) 0 0
\(903\) 17.2090 0.572679
\(904\) 0 0
\(905\) −18.5589 −0.616917
\(906\) 0 0
\(907\) 2.55941 0.0849838 0.0424919 0.999097i \(-0.486470\pi\)
0.0424919 + 0.999097i \(0.486470\pi\)
\(908\) 0 0
\(909\) −6.77610 −0.224749
\(910\) 0 0
\(911\) 57.4927 1.90482 0.952410 0.304820i \(-0.0985964\pi\)
0.952410 + 0.304820i \(0.0985964\pi\)
\(912\) 0 0
\(913\) 20.2499 0.670173
\(914\) 0 0
\(915\) −6.65592 −0.220038
\(916\) 0 0
\(917\) 40.7905 1.34702
\(918\) 0 0
\(919\) 35.4036 1.16786 0.583929 0.811805i \(-0.301515\pi\)
0.583929 + 0.811805i \(0.301515\pi\)
\(920\) 0 0
\(921\) −7.03361 −0.231765
\(922\) 0 0
\(923\) −11.8233 −0.389167
\(924\) 0 0
\(925\) 0.895610 0.0294475
\(926\) 0 0
\(927\) 37.4378 1.22962
\(928\) 0 0
\(929\) 49.6502 1.62897 0.814486 0.580184i \(-0.197019\pi\)
0.814486 + 0.580184i \(0.197019\pi\)
\(930\) 0 0
\(931\) 5.77348 0.189218
\(932\) 0 0
\(933\) −21.4253 −0.701432
\(934\) 0 0
\(935\) 1.55462 0.0508416
\(936\) 0 0
\(937\) 25.4318 0.830821 0.415410 0.909634i \(-0.363638\pi\)
0.415410 + 0.909634i \(0.363638\pi\)
\(938\) 0 0
\(939\) 16.8447 0.549706
\(940\) 0 0
\(941\) −8.10387 −0.264179 −0.132089 0.991238i \(-0.542169\pi\)
−0.132089 + 0.991238i \(0.542169\pi\)
\(942\) 0 0
\(943\) 0.0914997 0.00297964
\(944\) 0 0
\(945\) 10.8529 0.353046
\(946\) 0 0
\(947\) −18.2598 −0.593362 −0.296681 0.954977i \(-0.595880\pi\)
−0.296681 + 0.954977i \(0.595880\pi\)
\(948\) 0 0
\(949\) −34.0455 −1.10516
\(950\) 0 0
\(951\) −4.19440 −0.136013
\(952\) 0 0
\(953\) 17.2527 0.558871 0.279435 0.960164i \(-0.409853\pi\)
0.279435 + 0.960164i \(0.409853\pi\)
\(954\) 0 0
\(955\) −11.3552 −0.367445
\(956\) 0 0
\(957\) 7.65158 0.247341
\(958\) 0 0
\(959\) 37.0851 1.19754
\(960\) 0 0
\(961\) 44.7170 1.44248
\(962\) 0 0
\(963\) −36.6475 −1.18095
\(964\) 0 0
\(965\) −6.49585 −0.209109
\(966\) 0 0
\(967\) −14.1667 −0.455572 −0.227786 0.973711i \(-0.573149\pi\)
−0.227786 + 0.973711i \(0.573149\pi\)
\(968\) 0 0
\(969\) −6.30774 −0.202634
\(970\) 0 0
\(971\) −22.0791 −0.708553 −0.354276 0.935141i \(-0.615273\pi\)
−0.354276 + 0.935141i \(0.615273\pi\)
\(972\) 0 0
\(973\) −43.5457 −1.39601
\(974\) 0 0
\(975\) 4.29628 0.137591
\(976\) 0 0
\(977\) 47.7424 1.52742 0.763708 0.645562i \(-0.223377\pi\)
0.763708 + 0.645562i \(0.223377\pi\)
\(978\) 0 0
\(979\) −2.39632 −0.0765867
\(980\) 0 0
\(981\) −22.0854 −0.705132
\(982\) 0 0
\(983\) −5.77646 −0.184240 −0.0921202 0.995748i \(-0.529364\pi\)
−0.0921202 + 0.995748i \(0.529364\pi\)
\(984\) 0 0
\(985\) −22.2838 −0.710021
\(986\) 0 0
\(987\) 9.26309 0.294848
\(988\) 0 0
\(989\) −0.219840 −0.00699051
\(990\) 0 0
\(991\) 49.6709 1.57785 0.788924 0.614491i \(-0.210639\pi\)
0.788924 + 0.614491i \(0.210639\pi\)
\(992\) 0 0
\(993\) 18.4954 0.586935
\(994\) 0 0
\(995\) −22.6010 −0.716500
\(996\) 0 0
\(997\) 38.2765 1.21223 0.606114 0.795378i \(-0.292727\pi\)
0.606114 + 0.795378i \(0.292727\pi\)
\(998\) 0 0
\(999\) −3.89764 −0.123316
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 \(a_p\))