Properties

Label 8020.2.a.c.1.10
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.42561 q^{3}\) \(-1.00000 q^{5}\) \(-3.82644 q^{7}\) \(-0.967639 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.42561 q^{3}\) \(-1.00000 q^{5}\) \(-3.82644 q^{7}\) \(-0.967639 q^{9}\) \(+2.52224 q^{11}\) \(+7.13963 q^{13}\) \(+1.42561 q^{15}\) \(-6.37964 q^{17}\) \(-4.40687 q^{19}\) \(+5.45500 q^{21}\) \(+1.00931 q^{23}\) \(+1.00000 q^{25}\) \(+5.65630 q^{27}\) \(+2.93809 q^{29}\) \(-4.16374 q^{31}\) \(-3.59573 q^{33}\) \(+3.82644 q^{35}\) \(-11.7415 q^{37}\) \(-10.1783 q^{39}\) \(+1.67600 q^{41}\) \(+9.49358 q^{43}\) \(+0.967639 q^{45}\) \(+9.50027 q^{47}\) \(+7.64162 q^{49}\) \(+9.09487 q^{51}\) \(+5.55872 q^{53}\) \(-2.52224 q^{55}\) \(+6.28247 q^{57}\) \(+5.03660 q^{59}\) \(-6.50125 q^{61}\) \(+3.70261 q^{63}\) \(-7.13963 q^{65}\) \(-10.7038 q^{67}\) \(-1.43888 q^{69}\) \(+16.2918 q^{71}\) \(+4.97205 q^{73}\) \(-1.42561 q^{75}\) \(-9.65120 q^{77}\) \(-5.11619 q^{79}\) \(-5.16076 q^{81}\) \(-1.92072 q^{83}\) \(+6.37964 q^{85}\) \(-4.18857 q^{87}\) \(-16.4866 q^{89}\) \(-27.3194 q^{91}\) \(+5.93586 q^{93}\) \(+4.40687 q^{95}\) \(+13.7260 q^{97}\) \(-2.44062 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.42561 −0.823076 −0.411538 0.911393i \(-0.635008\pi\)
−0.411538 + 0.911393i \(0.635008\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −3.82644 −1.44626 −0.723129 0.690713i \(-0.757297\pi\)
−0.723129 + 0.690713i \(0.757297\pi\)
\(8\) 0 0
\(9\) −0.967639 −0.322546
\(10\) 0 0
\(11\) 2.52224 0.760485 0.380242 0.924887i \(-0.375841\pi\)
0.380242 + 0.924887i \(0.375841\pi\)
\(12\) 0 0
\(13\) 7.13963 1.98018 0.990089 0.140442i \(-0.0448525\pi\)
0.990089 + 0.140442i \(0.0448525\pi\)
\(14\) 0 0
\(15\) 1.42561 0.368091
\(16\) 0 0
\(17\) −6.37964 −1.54729 −0.773645 0.633619i \(-0.781569\pi\)
−0.773645 + 0.633619i \(0.781569\pi\)
\(18\) 0 0
\(19\) −4.40687 −1.01100 −0.505502 0.862825i \(-0.668693\pi\)
−0.505502 + 0.862825i \(0.668693\pi\)
\(20\) 0 0
\(21\) 5.45500 1.19038
\(22\) 0 0
\(23\) 1.00931 0.210456 0.105228 0.994448i \(-0.466443\pi\)
0.105228 + 0.994448i \(0.466443\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.65630 1.08856
\(28\) 0 0
\(29\) 2.93809 0.545590 0.272795 0.962072i \(-0.412052\pi\)
0.272795 + 0.962072i \(0.412052\pi\)
\(30\) 0 0
\(31\) −4.16374 −0.747830 −0.373915 0.927463i \(-0.621985\pi\)
−0.373915 + 0.927463i \(0.621985\pi\)
\(32\) 0 0
\(33\) −3.59573 −0.625936
\(34\) 0 0
\(35\) 3.82644 0.646786
\(36\) 0 0
\(37\) −11.7415 −1.93029 −0.965147 0.261708i \(-0.915714\pi\)
−0.965147 + 0.261708i \(0.915714\pi\)
\(38\) 0 0
\(39\) −10.1783 −1.62984
\(40\) 0 0
\(41\) 1.67600 0.261748 0.130874 0.991399i \(-0.458222\pi\)
0.130874 + 0.991399i \(0.458222\pi\)
\(42\) 0 0
\(43\) 9.49358 1.44776 0.723879 0.689927i \(-0.242358\pi\)
0.723879 + 0.689927i \(0.242358\pi\)
\(44\) 0 0
\(45\) 0.967639 0.144247
\(46\) 0 0
\(47\) 9.50027 1.38576 0.692878 0.721055i \(-0.256342\pi\)
0.692878 + 0.721055i \(0.256342\pi\)
\(48\) 0 0
\(49\) 7.64162 1.09166
\(50\) 0 0
\(51\) 9.09487 1.27354
\(52\) 0 0
\(53\) 5.55872 0.763549 0.381775 0.924255i \(-0.375313\pi\)
0.381775 + 0.924255i \(0.375313\pi\)
\(54\) 0 0
\(55\) −2.52224 −0.340099
\(56\) 0 0
\(57\) 6.28247 0.832133
\(58\) 0 0
\(59\) 5.03660 0.655709 0.327855 0.944728i \(-0.393674\pi\)
0.327855 + 0.944728i \(0.393674\pi\)
\(60\) 0 0
\(61\) −6.50125 −0.832400 −0.416200 0.909273i \(-0.636638\pi\)
−0.416200 + 0.909273i \(0.636638\pi\)
\(62\) 0 0
\(63\) 3.70261 0.466485
\(64\) 0 0
\(65\) −7.13963 −0.885562
\(66\) 0 0
\(67\) −10.7038 −1.30767 −0.653836 0.756636i \(-0.726841\pi\)
−0.653836 + 0.756636i \(0.726841\pi\)
\(68\) 0 0
\(69\) −1.43888 −0.173221
\(70\) 0 0
\(71\) 16.2918 1.93348 0.966738 0.255769i \(-0.0823286\pi\)
0.966738 + 0.255769i \(0.0823286\pi\)
\(72\) 0 0
\(73\) 4.97205 0.581934 0.290967 0.956733i \(-0.406023\pi\)
0.290967 + 0.956733i \(0.406023\pi\)
\(74\) 0 0
\(75\) −1.42561 −0.164615
\(76\) 0 0
\(77\) −9.65120 −1.09986
\(78\) 0 0
\(79\) −5.11619 −0.575617 −0.287808 0.957688i \(-0.592927\pi\)
−0.287808 + 0.957688i \(0.592927\pi\)
\(80\) 0 0
\(81\) −5.16076 −0.573417
\(82\) 0 0
\(83\) −1.92072 −0.210826 −0.105413 0.994429i \(-0.533617\pi\)
−0.105413 + 0.994429i \(0.533617\pi\)
\(84\) 0 0
\(85\) 6.37964 0.691969
\(86\) 0 0
\(87\) −4.18857 −0.449062
\(88\) 0 0
\(89\) −16.4866 −1.74757 −0.873787 0.486308i \(-0.838343\pi\)
−0.873787 + 0.486308i \(0.838343\pi\)
\(90\) 0 0
\(91\) −27.3194 −2.86385
\(92\) 0 0
\(93\) 5.93586 0.615520
\(94\) 0 0
\(95\) 4.40687 0.452135
\(96\) 0 0
\(97\) 13.7260 1.39366 0.696832 0.717234i \(-0.254592\pi\)
0.696832 + 0.717234i \(0.254592\pi\)
\(98\) 0 0
\(99\) −2.44062 −0.245292
\(100\) 0 0
\(101\) −3.05617 −0.304100 −0.152050 0.988373i \(-0.548587\pi\)
−0.152050 + 0.988373i \(0.548587\pi\)
\(102\) 0 0
\(103\) 9.88073 0.973577 0.486788 0.873520i \(-0.338168\pi\)
0.486788 + 0.873520i \(0.338168\pi\)
\(104\) 0 0
\(105\) −5.45500 −0.532354
\(106\) 0 0
\(107\) 8.34543 0.806783 0.403391 0.915028i \(-0.367831\pi\)
0.403391 + 0.915028i \(0.367831\pi\)
\(108\) 0 0
\(109\) 8.17421 0.782947 0.391474 0.920189i \(-0.371965\pi\)
0.391474 + 0.920189i \(0.371965\pi\)
\(110\) 0 0
\(111\) 16.7388 1.58878
\(112\) 0 0
\(113\) 10.7614 1.01235 0.506175 0.862431i \(-0.331059\pi\)
0.506175 + 0.862431i \(0.331059\pi\)
\(114\) 0 0
\(115\) −1.00931 −0.0941189
\(116\) 0 0
\(117\) −6.90859 −0.638699
\(118\) 0 0
\(119\) 24.4113 2.23778
\(120\) 0 0
\(121\) −4.63829 −0.421663
\(122\) 0 0
\(123\) −2.38933 −0.215438
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −7.22352 −0.640984 −0.320492 0.947251i \(-0.603848\pi\)
−0.320492 + 0.947251i \(0.603848\pi\)
\(128\) 0 0
\(129\) −13.5341 −1.19161
\(130\) 0 0
\(131\) 13.7818 1.20412 0.602059 0.798452i \(-0.294347\pi\)
0.602059 + 0.798452i \(0.294347\pi\)
\(132\) 0 0
\(133\) 16.8626 1.46217
\(134\) 0 0
\(135\) −5.65630 −0.486817
\(136\) 0 0
\(137\) −1.52083 −0.129934 −0.0649668 0.997887i \(-0.520694\pi\)
−0.0649668 + 0.997887i \(0.520694\pi\)
\(138\) 0 0
\(139\) 2.77428 0.235311 0.117656 0.993054i \(-0.462462\pi\)
0.117656 + 0.993054i \(0.462462\pi\)
\(140\) 0 0
\(141\) −13.5437 −1.14058
\(142\) 0 0
\(143\) 18.0079 1.50589
\(144\) 0 0
\(145\) −2.93809 −0.243995
\(146\) 0 0
\(147\) −10.8940 −0.898519
\(148\) 0 0
\(149\) −19.2544 −1.57738 −0.788689 0.614792i \(-0.789240\pi\)
−0.788689 + 0.614792i \(0.789240\pi\)
\(150\) 0 0
\(151\) 13.9250 1.13320 0.566600 0.823993i \(-0.308259\pi\)
0.566600 + 0.823993i \(0.308259\pi\)
\(152\) 0 0
\(153\) 6.17319 0.499073
\(154\) 0 0
\(155\) 4.16374 0.334440
\(156\) 0 0
\(157\) 8.34856 0.666288 0.333144 0.942876i \(-0.391891\pi\)
0.333144 + 0.942876i \(0.391891\pi\)
\(158\) 0 0
\(159\) −7.92456 −0.628459
\(160\) 0 0
\(161\) −3.86207 −0.304374
\(162\) 0 0
\(163\) 8.93608 0.699928 0.349964 0.936763i \(-0.386194\pi\)
0.349964 + 0.936763i \(0.386194\pi\)
\(164\) 0 0
\(165\) 3.59573 0.279927
\(166\) 0 0
\(167\) 10.9435 0.846832 0.423416 0.905935i \(-0.360831\pi\)
0.423416 + 0.905935i \(0.360831\pi\)
\(168\) 0 0
\(169\) 37.9743 2.92110
\(170\) 0 0
\(171\) 4.26426 0.326096
\(172\) 0 0
\(173\) −5.17402 −0.393373 −0.196687 0.980466i \(-0.563018\pi\)
−0.196687 + 0.980466i \(0.563018\pi\)
\(174\) 0 0
\(175\) −3.82644 −0.289251
\(176\) 0 0
\(177\) −7.18022 −0.539699
\(178\) 0 0
\(179\) −24.7530 −1.85013 −0.925064 0.379811i \(-0.875989\pi\)
−0.925064 + 0.379811i \(0.875989\pi\)
\(180\) 0 0
\(181\) −3.83998 −0.285424 −0.142712 0.989764i \(-0.545582\pi\)
−0.142712 + 0.989764i \(0.545582\pi\)
\(182\) 0 0
\(183\) 9.26824 0.685128
\(184\) 0 0
\(185\) 11.7415 0.863254
\(186\) 0 0
\(187\) −16.0910 −1.17669
\(188\) 0 0
\(189\) −21.6435 −1.57433
\(190\) 0 0
\(191\) 8.31951 0.601979 0.300989 0.953627i \(-0.402683\pi\)
0.300989 + 0.953627i \(0.402683\pi\)
\(192\) 0 0
\(193\) −21.0278 −1.51361 −0.756806 0.653639i \(-0.773241\pi\)
−0.756806 + 0.653639i \(0.773241\pi\)
\(194\) 0 0
\(195\) 10.1783 0.728885
\(196\) 0 0
\(197\) −26.1768 −1.86502 −0.932510 0.361145i \(-0.882386\pi\)
−0.932510 + 0.361145i \(0.882386\pi\)
\(198\) 0 0
\(199\) −13.6712 −0.969127 −0.484563 0.874756i \(-0.661022\pi\)
−0.484563 + 0.874756i \(0.661022\pi\)
\(200\) 0 0
\(201\) 15.2594 1.07631
\(202\) 0 0
\(203\) −11.2424 −0.789064
\(204\) 0 0
\(205\) −1.67600 −0.117057
\(206\) 0 0
\(207\) −0.976650 −0.0678819
\(208\) 0 0
\(209\) −11.1152 −0.768853
\(210\) 0 0
\(211\) 10.1118 0.696127 0.348063 0.937471i \(-0.386839\pi\)
0.348063 + 0.937471i \(0.386839\pi\)
\(212\) 0 0
\(213\) −23.2257 −1.59140
\(214\) 0 0
\(215\) −9.49358 −0.647457
\(216\) 0 0
\(217\) 15.9323 1.08155
\(218\) 0 0
\(219\) −7.08819 −0.478976
\(220\) 0 0
\(221\) −45.5483 −3.06391
\(222\) 0 0
\(223\) −2.15048 −0.144007 −0.0720033 0.997404i \(-0.522939\pi\)
−0.0720033 + 0.997404i \(0.522939\pi\)
\(224\) 0 0
\(225\) −0.967639 −0.0645093
\(226\) 0 0
\(227\) 3.18146 0.211161 0.105580 0.994411i \(-0.466330\pi\)
0.105580 + 0.994411i \(0.466330\pi\)
\(228\) 0 0
\(229\) −20.2860 −1.34054 −0.670268 0.742119i \(-0.733821\pi\)
−0.670268 + 0.742119i \(0.733821\pi\)
\(230\) 0 0
\(231\) 13.7588 0.905265
\(232\) 0 0
\(233\) −21.3700 −1.39999 −0.699996 0.714147i \(-0.746815\pi\)
−0.699996 + 0.714147i \(0.746815\pi\)
\(234\) 0 0
\(235\) −9.50027 −0.619729
\(236\) 0 0
\(237\) 7.29369 0.473776
\(238\) 0 0
\(239\) −30.4733 −1.97116 −0.985578 0.169223i \(-0.945874\pi\)
−0.985578 + 0.169223i \(0.945874\pi\)
\(240\) 0 0
\(241\) −15.2679 −0.983492 −0.491746 0.870739i \(-0.663641\pi\)
−0.491746 + 0.870739i \(0.663641\pi\)
\(242\) 0 0
\(243\) −9.61169 −0.616590
\(244\) 0 0
\(245\) −7.64162 −0.488205
\(246\) 0 0
\(247\) −31.4634 −2.00197
\(248\) 0 0
\(249\) 2.73820 0.173526
\(250\) 0 0
\(251\) −16.8775 −1.06530 −0.532648 0.846337i \(-0.678803\pi\)
−0.532648 + 0.846337i \(0.678803\pi\)
\(252\) 0 0
\(253\) 2.54573 0.160049
\(254\) 0 0
\(255\) −9.09487 −0.569543
\(256\) 0 0
\(257\) 5.33868 0.333017 0.166509 0.986040i \(-0.446751\pi\)
0.166509 + 0.986040i \(0.446751\pi\)
\(258\) 0 0
\(259\) 44.9282 2.79170
\(260\) 0 0
\(261\) −2.84301 −0.175978
\(262\) 0 0
\(263\) 16.3133 1.00592 0.502960 0.864310i \(-0.332244\pi\)
0.502960 + 0.864310i \(0.332244\pi\)
\(264\) 0 0
\(265\) −5.55872 −0.341470
\(266\) 0 0
\(267\) 23.5034 1.43839
\(268\) 0 0
\(269\) −6.27216 −0.382420 −0.191210 0.981549i \(-0.561241\pi\)
−0.191210 + 0.981549i \(0.561241\pi\)
\(270\) 0 0
\(271\) 24.4756 1.48679 0.743393 0.668855i \(-0.233215\pi\)
0.743393 + 0.668855i \(0.233215\pi\)
\(272\) 0 0
\(273\) 38.9467 2.35716
\(274\) 0 0
\(275\) 2.52224 0.152097
\(276\) 0 0
\(277\) −6.12014 −0.367724 −0.183862 0.982952i \(-0.558860\pi\)
−0.183862 + 0.982952i \(0.558860\pi\)
\(278\) 0 0
\(279\) 4.02900 0.241210
\(280\) 0 0
\(281\) −10.7234 −0.639705 −0.319852 0.947467i \(-0.603633\pi\)
−0.319852 + 0.947467i \(0.603633\pi\)
\(282\) 0 0
\(283\) −17.9150 −1.06494 −0.532470 0.846449i \(-0.678736\pi\)
−0.532470 + 0.846449i \(0.678736\pi\)
\(284\) 0 0
\(285\) −6.28247 −0.372141
\(286\) 0 0
\(287\) −6.41313 −0.378555
\(288\) 0 0
\(289\) 23.6998 1.39411
\(290\) 0 0
\(291\) −19.5679 −1.14709
\(292\) 0 0
\(293\) 23.8503 1.39335 0.696675 0.717387i \(-0.254662\pi\)
0.696675 + 0.717387i \(0.254662\pi\)
\(294\) 0 0
\(295\) −5.03660 −0.293242
\(296\) 0 0
\(297\) 14.2666 0.827830
\(298\) 0 0
\(299\) 7.20612 0.416741
\(300\) 0 0
\(301\) −36.3266 −2.09383
\(302\) 0 0
\(303\) 4.35690 0.250297
\(304\) 0 0
\(305\) 6.50125 0.372260
\(306\) 0 0
\(307\) −28.1123 −1.60446 −0.802228 0.597018i \(-0.796352\pi\)
−0.802228 + 0.597018i \(0.796352\pi\)
\(308\) 0 0
\(309\) −14.0861 −0.801328
\(310\) 0 0
\(311\) −18.6160 −1.05562 −0.527809 0.849363i \(-0.676986\pi\)
−0.527809 + 0.849363i \(0.676986\pi\)
\(312\) 0 0
\(313\) −8.33454 −0.471096 −0.235548 0.971863i \(-0.575689\pi\)
−0.235548 + 0.971863i \(0.575689\pi\)
\(314\) 0 0
\(315\) −3.70261 −0.208619
\(316\) 0 0
\(317\) 15.7243 0.883164 0.441582 0.897221i \(-0.354417\pi\)
0.441582 + 0.897221i \(0.354417\pi\)
\(318\) 0 0
\(319\) 7.41058 0.414913
\(320\) 0 0
\(321\) −11.8973 −0.664043
\(322\) 0 0
\(323\) 28.1142 1.56432
\(324\) 0 0
\(325\) 7.13963 0.396036
\(326\) 0 0
\(327\) −11.6532 −0.644425
\(328\) 0 0
\(329\) −36.3522 −2.00416
\(330\) 0 0
\(331\) −17.8283 −0.979934 −0.489967 0.871741i \(-0.662991\pi\)
−0.489967 + 0.871741i \(0.662991\pi\)
\(332\) 0 0
\(333\) 11.3616 0.622609
\(334\) 0 0
\(335\) 10.7038 0.584809
\(336\) 0 0
\(337\) −26.5384 −1.44564 −0.722819 0.691038i \(-0.757154\pi\)
−0.722819 + 0.691038i \(0.757154\pi\)
\(338\) 0 0
\(339\) −15.3416 −0.833240
\(340\) 0 0
\(341\) −10.5020 −0.568713
\(342\) 0 0
\(343\) −2.45513 −0.132565
\(344\) 0 0
\(345\) 1.43888 0.0774670
\(346\) 0 0
\(347\) 18.1241 0.972950 0.486475 0.873694i \(-0.338282\pi\)
0.486475 + 0.873694i \(0.338282\pi\)
\(348\) 0 0
\(349\) 27.1814 1.45499 0.727493 0.686115i \(-0.240686\pi\)
0.727493 + 0.686115i \(0.240686\pi\)
\(350\) 0 0
\(351\) 40.3839 2.15553
\(352\) 0 0
\(353\) 15.6912 0.835158 0.417579 0.908641i \(-0.362879\pi\)
0.417579 + 0.908641i \(0.362879\pi\)
\(354\) 0 0
\(355\) −16.2918 −0.864677
\(356\) 0 0
\(357\) −34.8010 −1.84186
\(358\) 0 0
\(359\) −18.7331 −0.988695 −0.494347 0.869265i \(-0.664593\pi\)
−0.494347 + 0.869265i \(0.664593\pi\)
\(360\) 0 0
\(361\) 0.420464 0.0221297
\(362\) 0 0
\(363\) 6.61239 0.347061
\(364\) 0 0
\(365\) −4.97205 −0.260249
\(366\) 0 0
\(367\) 17.1258 0.893960 0.446980 0.894544i \(-0.352499\pi\)
0.446980 + 0.894544i \(0.352499\pi\)
\(368\) 0 0
\(369\) −1.62177 −0.0844258
\(370\) 0 0
\(371\) −21.2701 −1.10429
\(372\) 0 0
\(373\) −4.06658 −0.210559 −0.105280 0.994443i \(-0.533574\pi\)
−0.105280 + 0.994443i \(0.533574\pi\)
\(374\) 0 0
\(375\) 1.42561 0.0736181
\(376\) 0 0
\(377\) 20.9769 1.08037
\(378\) 0 0
\(379\) −17.7387 −0.911177 −0.455588 0.890191i \(-0.650571\pi\)
−0.455588 + 0.890191i \(0.650571\pi\)
\(380\) 0 0
\(381\) 10.2979 0.527578
\(382\) 0 0
\(383\) −28.7273 −1.46790 −0.733949 0.679205i \(-0.762325\pi\)
−0.733949 + 0.679205i \(0.762325\pi\)
\(384\) 0 0
\(385\) 9.65120 0.491871
\(386\) 0 0
\(387\) −9.18636 −0.466969
\(388\) 0 0
\(389\) −32.9678 −1.67153 −0.835766 0.549086i \(-0.814976\pi\)
−0.835766 + 0.549086i \(0.814976\pi\)
\(390\) 0 0
\(391\) −6.43905 −0.325637
\(392\) 0 0
\(393\) −19.6474 −0.991080
\(394\) 0 0
\(395\) 5.11619 0.257424
\(396\) 0 0
\(397\) −0.434718 −0.0218179 −0.0109089 0.999940i \(-0.503472\pi\)
−0.0109089 + 0.999940i \(0.503472\pi\)
\(398\) 0 0
\(399\) −24.0395 −1.20348
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −29.7276 −1.48084
\(404\) 0 0
\(405\) 5.16076 0.256440
\(406\) 0 0
\(407\) −29.6150 −1.46796
\(408\) 0 0
\(409\) −23.1892 −1.14663 −0.573316 0.819334i \(-0.694343\pi\)
−0.573316 + 0.819334i \(0.694343\pi\)
\(410\) 0 0
\(411\) 2.16811 0.106945
\(412\) 0 0
\(413\) −19.2722 −0.948325
\(414\) 0 0
\(415\) 1.92072 0.0942845
\(416\) 0 0
\(417\) −3.95504 −0.193679
\(418\) 0 0
\(419\) 8.75794 0.427853 0.213927 0.976850i \(-0.431375\pi\)
0.213927 + 0.976850i \(0.431375\pi\)
\(420\) 0 0
\(421\) 30.2112 1.47240 0.736201 0.676763i \(-0.236618\pi\)
0.736201 + 0.676763i \(0.236618\pi\)
\(422\) 0 0
\(423\) −9.19283 −0.446971
\(424\) 0 0
\(425\) −6.37964 −0.309458
\(426\) 0 0
\(427\) 24.8766 1.20386
\(428\) 0 0
\(429\) −25.6722 −1.23947
\(430\) 0 0
\(431\) −15.0159 −0.723292 −0.361646 0.932316i \(-0.617785\pi\)
−0.361646 + 0.932316i \(0.617785\pi\)
\(432\) 0 0
\(433\) 12.3453 0.593277 0.296639 0.954990i \(-0.404134\pi\)
0.296639 + 0.954990i \(0.404134\pi\)
\(434\) 0 0
\(435\) 4.18857 0.200827
\(436\) 0 0
\(437\) −4.44790 −0.212772
\(438\) 0 0
\(439\) 4.98867 0.238096 0.119048 0.992888i \(-0.462016\pi\)
0.119048 + 0.992888i \(0.462016\pi\)
\(440\) 0 0
\(441\) −7.39434 −0.352111
\(442\) 0 0
\(443\) −14.6749 −0.697223 −0.348612 0.937267i \(-0.613347\pi\)
−0.348612 + 0.937267i \(0.613347\pi\)
\(444\) 0 0
\(445\) 16.4866 0.781539
\(446\) 0 0
\(447\) 27.4492 1.29830
\(448\) 0 0
\(449\) 25.1113 1.18508 0.592538 0.805543i \(-0.298126\pi\)
0.592538 + 0.805543i \(0.298126\pi\)
\(450\) 0 0
\(451\) 4.22729 0.199055
\(452\) 0 0
\(453\) −19.8516 −0.932709
\(454\) 0 0
\(455\) 27.3194 1.28075
\(456\) 0 0
\(457\) 14.4500 0.675944 0.337972 0.941156i \(-0.390259\pi\)
0.337972 + 0.941156i \(0.390259\pi\)
\(458\) 0 0
\(459\) −36.0852 −1.68431
\(460\) 0 0
\(461\) −3.75446 −0.174863 −0.0874313 0.996171i \(-0.527866\pi\)
−0.0874313 + 0.996171i \(0.527866\pi\)
\(462\) 0 0
\(463\) −0.405427 −0.0188418 −0.00942089 0.999956i \(-0.502999\pi\)
−0.00942089 + 0.999956i \(0.502999\pi\)
\(464\) 0 0
\(465\) −5.93586 −0.275269
\(466\) 0 0
\(467\) 2.43678 0.112761 0.0563804 0.998409i \(-0.482044\pi\)
0.0563804 + 0.998409i \(0.482044\pi\)
\(468\) 0 0
\(469\) 40.9573 1.89123
\(470\) 0 0
\(471\) −11.9018 −0.548405
\(472\) 0 0
\(473\) 23.9451 1.10100
\(474\) 0 0
\(475\) −4.40687 −0.202201
\(476\) 0 0
\(477\) −5.37884 −0.246280
\(478\) 0 0
\(479\) 18.0431 0.824408 0.412204 0.911091i \(-0.364759\pi\)
0.412204 + 0.911091i \(0.364759\pi\)
\(480\) 0 0
\(481\) −83.8301 −3.82233
\(482\) 0 0
\(483\) 5.50580 0.250523
\(484\) 0 0
\(485\) −13.7260 −0.623266
\(486\) 0 0
\(487\) 27.7589 1.25788 0.628938 0.777455i \(-0.283490\pi\)
0.628938 + 0.777455i \(0.283490\pi\)
\(488\) 0 0
\(489\) −12.7394 −0.576093
\(490\) 0 0
\(491\) −34.5678 −1.56002 −0.780011 0.625765i \(-0.784787\pi\)
−0.780011 + 0.625765i \(0.784787\pi\)
\(492\) 0 0
\(493\) −18.7440 −0.844186
\(494\) 0 0
\(495\) 2.44062 0.109698
\(496\) 0 0
\(497\) −62.3394 −2.79630
\(498\) 0 0
\(499\) −17.4337 −0.780440 −0.390220 0.920722i \(-0.627601\pi\)
−0.390220 + 0.920722i \(0.627601\pi\)
\(500\) 0 0
\(501\) −15.6011 −0.697006
\(502\) 0 0
\(503\) 0.906638 0.0404250 0.0202125 0.999796i \(-0.493566\pi\)
0.0202125 + 0.999796i \(0.493566\pi\)
\(504\) 0 0
\(505\) 3.05617 0.135998
\(506\) 0 0
\(507\) −54.1366 −2.40429
\(508\) 0 0
\(509\) 10.0622 0.445998 0.222999 0.974819i \(-0.428415\pi\)
0.222999 + 0.974819i \(0.428415\pi\)
\(510\) 0 0
\(511\) −19.0252 −0.841626
\(512\) 0 0
\(513\) −24.9266 −1.10053
\(514\) 0 0
\(515\) −9.88073 −0.435397
\(516\) 0 0
\(517\) 23.9620 1.05385
\(518\) 0 0
\(519\) 7.37613 0.323776
\(520\) 0 0
\(521\) −36.0100 −1.57763 −0.788814 0.614632i \(-0.789305\pi\)
−0.788814 + 0.614632i \(0.789305\pi\)
\(522\) 0 0
\(523\) 28.4576 1.24436 0.622181 0.782873i \(-0.286247\pi\)
0.622181 + 0.782873i \(0.286247\pi\)
\(524\) 0 0
\(525\) 5.45500 0.238076
\(526\) 0 0
\(527\) 26.5632 1.15711
\(528\) 0 0
\(529\) −21.9813 −0.955708
\(530\) 0 0
\(531\) −4.87361 −0.211497
\(532\) 0 0
\(533\) 11.9661 0.518307
\(534\) 0 0
\(535\) −8.34543 −0.360804
\(536\) 0 0
\(537\) 35.2881 1.52280
\(538\) 0 0
\(539\) 19.2740 0.830191
\(540\) 0 0
\(541\) −30.8044 −1.32438 −0.662192 0.749334i \(-0.730374\pi\)
−0.662192 + 0.749334i \(0.730374\pi\)
\(542\) 0 0
\(543\) 5.47431 0.234925
\(544\) 0 0
\(545\) −8.17421 −0.350145
\(546\) 0 0
\(547\) −17.3332 −0.741113 −0.370556 0.928810i \(-0.620833\pi\)
−0.370556 + 0.928810i \(0.620833\pi\)
\(548\) 0 0
\(549\) 6.29086 0.268488
\(550\) 0 0
\(551\) −12.9478 −0.551594
\(552\) 0 0
\(553\) 19.5768 0.832490
\(554\) 0 0
\(555\) −16.7388 −0.710523
\(556\) 0 0
\(557\) −11.8944 −0.503984 −0.251992 0.967729i \(-0.581086\pi\)
−0.251992 + 0.967729i \(0.581086\pi\)
\(558\) 0 0
\(559\) 67.7807 2.86682
\(560\) 0 0
\(561\) 22.9395 0.968505
\(562\) 0 0
\(563\) −22.8529 −0.963136 −0.481568 0.876409i \(-0.659933\pi\)
−0.481568 + 0.876409i \(0.659933\pi\)
\(564\) 0 0
\(565\) −10.7614 −0.452736
\(566\) 0 0
\(567\) 19.7473 0.829309
\(568\) 0 0
\(569\) −35.2331 −1.47705 −0.738524 0.674227i \(-0.764477\pi\)
−0.738524 + 0.674227i \(0.764477\pi\)
\(570\) 0 0
\(571\) 27.3222 1.14340 0.571699 0.820463i \(-0.306284\pi\)
0.571699 + 0.820463i \(0.306284\pi\)
\(572\) 0 0
\(573\) −11.8604 −0.495474
\(574\) 0 0
\(575\) 1.00931 0.0420912
\(576\) 0 0
\(577\) 24.5717 1.02293 0.511466 0.859304i \(-0.329103\pi\)
0.511466 + 0.859304i \(0.329103\pi\)
\(578\) 0 0
\(579\) 29.9774 1.24582
\(580\) 0 0
\(581\) 7.34952 0.304909
\(582\) 0 0
\(583\) 14.0204 0.580667
\(584\) 0 0
\(585\) 6.90859 0.285635
\(586\) 0 0
\(587\) 2.68394 0.110778 0.0553890 0.998465i \(-0.482360\pi\)
0.0553890 + 0.998465i \(0.482360\pi\)
\(588\) 0 0
\(589\) 18.3490 0.756059
\(590\) 0 0
\(591\) 37.3179 1.53505
\(592\) 0 0
\(593\) −22.3433 −0.917529 −0.458764 0.888558i \(-0.651708\pi\)
−0.458764 + 0.888558i \(0.651708\pi\)
\(594\) 0 0
\(595\) −24.4113 −1.00077
\(596\) 0 0
\(597\) 19.4898 0.797665
\(598\) 0 0
\(599\) −14.9922 −0.612565 −0.306282 0.951941i \(-0.599085\pi\)
−0.306282 + 0.951941i \(0.599085\pi\)
\(600\) 0 0
\(601\) −15.4886 −0.631793 −0.315896 0.948794i \(-0.602305\pi\)
−0.315896 + 0.948794i \(0.602305\pi\)
\(602\) 0 0
\(603\) 10.3574 0.421785
\(604\) 0 0
\(605\) 4.63829 0.188573
\(606\) 0 0
\(607\) 32.6772 1.32633 0.663164 0.748474i \(-0.269213\pi\)
0.663164 + 0.748474i \(0.269213\pi\)
\(608\) 0 0
\(609\) 16.0273 0.649459
\(610\) 0 0
\(611\) 67.8284 2.74404
\(612\) 0 0
\(613\) −41.9453 −1.69415 −0.847077 0.531471i \(-0.821640\pi\)
−0.847077 + 0.531471i \(0.821640\pi\)
\(614\) 0 0
\(615\) 2.38933 0.0963469
\(616\) 0 0
\(617\) 19.5582 0.787383 0.393692 0.919243i \(-0.371198\pi\)
0.393692 + 0.919243i \(0.371198\pi\)
\(618\) 0 0
\(619\) 27.6626 1.11185 0.555926 0.831232i \(-0.312364\pi\)
0.555926 + 0.831232i \(0.312364\pi\)
\(620\) 0 0
\(621\) 5.70898 0.229093
\(622\) 0 0
\(623\) 63.0849 2.52744
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 15.8459 0.632824
\(628\) 0 0
\(629\) 74.9067 2.98672
\(630\) 0 0
\(631\) 18.7228 0.745342 0.372671 0.927964i \(-0.378442\pi\)
0.372671 + 0.927964i \(0.378442\pi\)
\(632\) 0 0
\(633\) −14.4155 −0.572965
\(634\) 0 0
\(635\) 7.22352 0.286657
\(636\) 0 0
\(637\) 54.5584 2.16168
\(638\) 0 0
\(639\) −15.7645 −0.623636
\(640\) 0 0
\(641\) 46.0681 1.81958 0.909789 0.415070i \(-0.136243\pi\)
0.909789 + 0.415070i \(0.136243\pi\)
\(642\) 0 0
\(643\) 2.44079 0.0962552 0.0481276 0.998841i \(-0.484675\pi\)
0.0481276 + 0.998841i \(0.484675\pi\)
\(644\) 0 0
\(645\) 13.5341 0.532906
\(646\) 0 0
\(647\) −38.1979 −1.50171 −0.750857 0.660465i \(-0.770359\pi\)
−0.750857 + 0.660465i \(0.770359\pi\)
\(648\) 0 0
\(649\) 12.7035 0.498657
\(650\) 0 0
\(651\) −22.7132 −0.890201
\(652\) 0 0
\(653\) −14.0090 −0.548216 −0.274108 0.961699i \(-0.588383\pi\)
−0.274108 + 0.961699i \(0.588383\pi\)
\(654\) 0 0
\(655\) −13.7818 −0.538498
\(656\) 0 0
\(657\) −4.81115 −0.187701
\(658\) 0 0
\(659\) −4.04132 −0.157428 −0.0787138 0.996897i \(-0.525081\pi\)
−0.0787138 + 0.996897i \(0.525081\pi\)
\(660\) 0 0
\(661\) −27.8755 −1.08423 −0.542115 0.840304i \(-0.682376\pi\)
−0.542115 + 0.840304i \(0.682376\pi\)
\(662\) 0 0
\(663\) 64.9340 2.52183
\(664\) 0 0
\(665\) −16.8626 −0.653903
\(666\) 0 0
\(667\) 2.96545 0.114823
\(668\) 0 0
\(669\) 3.06574 0.118528
\(670\) 0 0
\(671\) −16.3977 −0.633027
\(672\) 0 0
\(673\) −19.3480 −0.745809 −0.372905 0.927870i \(-0.621638\pi\)
−0.372905 + 0.927870i \(0.621638\pi\)
\(674\) 0 0
\(675\) 5.65630 0.217711
\(676\) 0 0
\(677\) 30.6933 1.17964 0.589820 0.807535i \(-0.299199\pi\)
0.589820 + 0.807535i \(0.299199\pi\)
\(678\) 0 0
\(679\) −52.5217 −2.01560
\(680\) 0 0
\(681\) −4.53552 −0.173801
\(682\) 0 0
\(683\) −6.40544 −0.245097 −0.122549 0.992463i \(-0.539107\pi\)
−0.122549 + 0.992463i \(0.539107\pi\)
\(684\) 0 0
\(685\) 1.52083 0.0581080
\(686\) 0 0
\(687\) 28.9199 1.10336
\(688\) 0 0
\(689\) 39.6872 1.51196
\(690\) 0 0
\(691\) −43.2323 −1.64463 −0.822317 0.569030i \(-0.807319\pi\)
−0.822317 + 0.569030i \(0.807319\pi\)
\(692\) 0 0
\(693\) 9.33888 0.354755
\(694\) 0 0
\(695\) −2.77428 −0.105234
\(696\) 0 0
\(697\) −10.6923 −0.405000
\(698\) 0 0
\(699\) 30.4652 1.15230
\(700\) 0 0
\(701\) −0.538908 −0.0203543 −0.0101771 0.999948i \(-0.503240\pi\)
−0.0101771 + 0.999948i \(0.503240\pi\)
\(702\) 0 0
\(703\) 51.7433 1.95154
\(704\) 0 0
\(705\) 13.5437 0.510084
\(706\) 0 0
\(707\) 11.6942 0.439807
\(708\) 0 0
\(709\) 33.0003 1.23935 0.619676 0.784858i \(-0.287264\pi\)
0.619676 + 0.784858i \(0.287264\pi\)
\(710\) 0 0
\(711\) 4.95063 0.185663
\(712\) 0 0
\(713\) −4.20251 −0.157385
\(714\) 0 0
\(715\) −18.0079 −0.673457
\(716\) 0 0
\(717\) 43.4430 1.62241
\(718\) 0 0
\(719\) 19.4337 0.724754 0.362377 0.932032i \(-0.381965\pi\)
0.362377 + 0.932032i \(0.381965\pi\)
\(720\) 0 0
\(721\) −37.8080 −1.40804
\(722\) 0 0
\(723\) 21.7661 0.809489
\(724\) 0 0
\(725\) 2.93809 0.109118
\(726\) 0 0
\(727\) −2.10647 −0.0781246 −0.0390623 0.999237i \(-0.512437\pi\)
−0.0390623 + 0.999237i \(0.512437\pi\)
\(728\) 0 0
\(729\) 29.1848 1.08092
\(730\) 0 0
\(731\) −60.5656 −2.24010
\(732\) 0 0
\(733\) −4.03179 −0.148918 −0.0744588 0.997224i \(-0.523723\pi\)
−0.0744588 + 0.997224i \(0.523723\pi\)
\(734\) 0 0
\(735\) 10.8940 0.401830
\(736\) 0 0
\(737\) −26.9975 −0.994465
\(738\) 0 0
\(739\) 31.2105 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(740\) 0 0
\(741\) 44.8545 1.64777
\(742\) 0 0
\(743\) −23.8418 −0.874670 −0.437335 0.899299i \(-0.644078\pi\)
−0.437335 + 0.899299i \(0.644078\pi\)
\(744\) 0 0
\(745\) 19.2544 0.705425
\(746\) 0 0
\(747\) 1.85856 0.0680013
\(748\) 0 0
\(749\) −31.9333 −1.16682
\(750\) 0 0
\(751\) −34.3344 −1.25288 −0.626441 0.779469i \(-0.715489\pi\)
−0.626441 + 0.779469i \(0.715489\pi\)
\(752\) 0 0
\(753\) 24.0607 0.876819
\(754\) 0 0
\(755\) −13.9250 −0.506782
\(756\) 0 0
\(757\) −14.7732 −0.536942 −0.268471 0.963288i \(-0.586518\pi\)
−0.268471 + 0.963288i \(0.586518\pi\)
\(758\) 0 0
\(759\) −3.62922 −0.131732
\(760\) 0 0
\(761\) 36.1973 1.31215 0.656075 0.754695i \(-0.272215\pi\)
0.656075 + 0.754695i \(0.272215\pi\)
\(762\) 0 0
\(763\) −31.2781 −1.13234
\(764\) 0 0
\(765\) −6.17319 −0.223192
\(766\) 0 0
\(767\) 35.9595 1.29842
\(768\) 0 0
\(769\) −36.2936 −1.30878 −0.654390 0.756157i \(-0.727074\pi\)
−0.654390 + 0.756157i \(0.727074\pi\)
\(770\) 0 0
\(771\) −7.61086 −0.274099
\(772\) 0 0
\(773\) 25.4127 0.914030 0.457015 0.889459i \(-0.348919\pi\)
0.457015 + 0.889459i \(0.348919\pi\)
\(774\) 0 0
\(775\) −4.16374 −0.149566
\(776\) 0 0
\(777\) −64.0500 −2.29778
\(778\) 0 0
\(779\) −7.38593 −0.264628
\(780\) 0 0
\(781\) 41.0918 1.47038
\(782\) 0 0
\(783\) 16.6187 0.593905
\(784\) 0 0
\(785\) −8.34856 −0.297973
\(786\) 0 0
\(787\) 6.08274 0.216826 0.108413 0.994106i \(-0.465423\pi\)
0.108413 + 0.994106i \(0.465423\pi\)
\(788\) 0 0
\(789\) −23.2564 −0.827948
\(790\) 0 0
\(791\) −41.1779 −1.46412
\(792\) 0 0
\(793\) −46.4165 −1.64830
\(794\) 0 0
\(795\) 7.92456 0.281055
\(796\) 0 0
\(797\) −22.1851 −0.785837 −0.392919 0.919573i \(-0.628535\pi\)
−0.392919 + 0.919573i \(0.628535\pi\)
\(798\) 0 0
\(799\) −60.6083 −2.14417
\(800\) 0 0
\(801\) 15.9531 0.563674
\(802\) 0 0
\(803\) 12.5407 0.442552
\(804\) 0 0
\(805\) 3.86207 0.136120
\(806\) 0 0
\(807\) 8.94164 0.314761
\(808\) 0 0
\(809\) 1.60973 0.0565951 0.0282975 0.999600i \(-0.490991\pi\)
0.0282975 + 0.999600i \(0.490991\pi\)
\(810\) 0 0
\(811\) −20.4204 −0.717057 −0.358528 0.933519i \(-0.616721\pi\)
−0.358528 + 0.933519i \(0.616721\pi\)
\(812\) 0 0
\(813\) −34.8926 −1.22374
\(814\) 0 0
\(815\) −8.93608 −0.313017
\(816\) 0 0
\(817\) −41.8369 −1.46369
\(818\) 0 0
\(819\) 26.4353 0.923724
\(820\) 0 0
\(821\) −28.6127 −0.998590 −0.499295 0.866432i \(-0.666408\pi\)
−0.499295 + 0.866432i \(0.666408\pi\)
\(822\) 0 0
\(823\) −38.9332 −1.35713 −0.678563 0.734542i \(-0.737397\pi\)
−0.678563 + 0.734542i \(0.737397\pi\)
\(824\) 0 0
\(825\) −3.59573 −0.125187
\(826\) 0 0
\(827\) 21.6386 0.752448 0.376224 0.926529i \(-0.377222\pi\)
0.376224 + 0.926529i \(0.377222\pi\)
\(828\) 0 0
\(829\) −8.99005 −0.312237 −0.156119 0.987738i \(-0.549898\pi\)
−0.156119 + 0.987738i \(0.549898\pi\)
\(830\) 0 0
\(831\) 8.72493 0.302664
\(832\) 0 0
\(833\) −48.7508 −1.68912
\(834\) 0 0
\(835\) −10.9435 −0.378715
\(836\) 0 0
\(837\) −23.5514 −0.814054
\(838\) 0 0
\(839\) 2.55082 0.0880640 0.0440320 0.999030i \(-0.485980\pi\)
0.0440320 + 0.999030i \(0.485980\pi\)
\(840\) 0 0
\(841\) −20.3676 −0.702331
\(842\) 0 0
\(843\) 15.2874 0.526526
\(844\) 0 0
\(845\) −37.9743 −1.30636
\(846\) 0 0
\(847\) 17.7481 0.609833
\(848\) 0 0
\(849\) 25.5399 0.876526
\(850\) 0 0
\(851\) −11.8509 −0.406242
\(852\) 0 0
\(853\) −5.78746 −0.198159 −0.0990795 0.995080i \(-0.531590\pi\)
−0.0990795 + 0.995080i \(0.531590\pi\)
\(854\) 0 0
\(855\) −4.26426 −0.145834
\(856\) 0 0
\(857\) 0.883123 0.0301669 0.0150834 0.999886i \(-0.495199\pi\)
0.0150834 + 0.999886i \(0.495199\pi\)
\(858\) 0 0
\(859\) −22.8753 −0.780494 −0.390247 0.920710i \(-0.627610\pi\)
−0.390247 + 0.920710i \(0.627610\pi\)
\(860\) 0 0
\(861\) 9.14261 0.311579
\(862\) 0 0
\(863\) 32.2492 1.09778 0.548888 0.835896i \(-0.315051\pi\)
0.548888 + 0.835896i \(0.315051\pi\)
\(864\) 0 0
\(865\) 5.17402 0.175922
\(866\) 0 0
\(867\) −33.7866 −1.14745
\(868\) 0 0
\(869\) −12.9043 −0.437748
\(870\) 0 0
\(871\) −76.4209 −2.58942
\(872\) 0 0
\(873\) −13.2818 −0.449521
\(874\) 0 0
\(875\) 3.82644 0.129357
\(876\) 0 0
\(877\) 22.5615 0.761849 0.380925 0.924606i \(-0.375606\pi\)
0.380925 + 0.924606i \(0.375606\pi\)
\(878\) 0 0
\(879\) −34.0012 −1.14683
\(880\) 0 0
\(881\) −21.0899 −0.710535 −0.355268 0.934765i \(-0.615610\pi\)
−0.355268 + 0.934765i \(0.615610\pi\)
\(882\) 0 0
\(883\) 33.1474 1.11550 0.557749 0.830009i \(-0.311665\pi\)
0.557749 + 0.830009i \(0.311665\pi\)
\(884\) 0 0
\(885\) 7.18022 0.241361
\(886\) 0 0
\(887\) −29.2731 −0.982895 −0.491448 0.870907i \(-0.663532\pi\)
−0.491448 + 0.870907i \(0.663532\pi\)
\(888\) 0 0
\(889\) 27.6404 0.927028
\(890\) 0 0
\(891\) −13.0167 −0.436075
\(892\) 0 0
\(893\) −41.8664 −1.40101
\(894\) 0 0
\(895\) 24.7530 0.827402
\(896\) 0 0
\(897\) −10.2731 −0.343009
\(898\) 0 0
\(899\) −12.2335 −0.408009
\(900\) 0 0
\(901\) −35.4626 −1.18143
\(902\) 0 0
\(903\) 51.7875 1.72338
\(904\) 0 0
\(905\) 3.83998 0.127645
\(906\) 0 0
\(907\) 44.7814 1.48694 0.743471 0.668768i \(-0.233178\pi\)
0.743471 + 0.668768i \(0.233178\pi\)
\(908\) 0 0
\(909\) 2.95727 0.0980863
\(910\) 0 0
\(911\) −14.6694 −0.486020 −0.243010 0.970024i \(-0.578135\pi\)
−0.243010 + 0.970024i \(0.578135\pi\)
\(912\) 0 0
\(913\) −4.84452 −0.160330
\(914\) 0 0
\(915\) −9.26824 −0.306398
\(916\) 0 0
\(917\) −52.7350 −1.74146
\(918\) 0 0
\(919\) 14.7674 0.487130 0.243565 0.969885i \(-0.421683\pi\)
0.243565 + 0.969885i \(0.421683\pi\)
\(920\) 0 0
\(921\) 40.0772 1.32059
\(922\) 0 0
\(923\) 116.317 3.82863
\(924\) 0 0
\(925\) −11.7415 −0.386059
\(926\) 0 0
\(927\) −9.56098 −0.314024
\(928\) 0 0
\(929\) −13.1126 −0.430210 −0.215105 0.976591i \(-0.569009\pi\)
−0.215105 + 0.976591i \(0.569009\pi\)
\(930\) 0 0
\(931\) −33.6756 −1.10367
\(932\) 0 0
\(933\) 26.5392 0.868853
\(934\) 0 0
\(935\) 16.0910 0.526232
\(936\) 0 0
\(937\) 15.9260 0.520279 0.260140 0.965571i \(-0.416231\pi\)
0.260140 + 0.965571i \(0.416231\pi\)
\(938\) 0 0
\(939\) 11.8818 0.387748
\(940\) 0 0
\(941\) −22.8474 −0.744803 −0.372401 0.928072i \(-0.621465\pi\)
−0.372401 + 0.928072i \(0.621465\pi\)
\(942\) 0 0
\(943\) 1.69161 0.0550865
\(944\) 0 0
\(945\) 21.6435 0.704063
\(946\) 0 0
\(947\) 43.7130 1.42048 0.710241 0.703959i \(-0.248586\pi\)
0.710241 + 0.703959i \(0.248586\pi\)
\(948\) 0 0
\(949\) 35.4986 1.15233
\(950\) 0 0
\(951\) −22.4167 −0.726911
\(952\) 0 0
\(953\) −16.6640 −0.539799 −0.269900 0.962888i \(-0.586991\pi\)
−0.269900 + 0.962888i \(0.586991\pi\)
\(954\) 0 0
\(955\) −8.31951 −0.269213
\(956\) 0 0
\(957\) −10.5646 −0.341505
\(958\) 0 0
\(959\) 5.81937 0.187917
\(960\) 0 0
\(961\) −13.6633 −0.440751
\(962\) 0 0
\(963\) −8.07536 −0.260225
\(964\) 0 0
\(965\) 21.0278 0.676908
\(966\) 0 0
\(967\) −10.9323 −0.351558 −0.175779 0.984430i \(-0.556244\pi\)
−0.175779 + 0.984430i \(0.556244\pi\)
\(968\) 0 0
\(969\) −40.0799 −1.28755
\(970\) 0 0
\(971\) −18.0693 −0.579871 −0.289935 0.957046i \(-0.593634\pi\)
−0.289935 + 0.957046i \(0.593634\pi\)
\(972\) 0 0
\(973\) −10.6156 −0.340321
\(974\) 0 0
\(975\) −10.1783 −0.325967
\(976\) 0 0
\(977\) −17.9420 −0.574015 −0.287007 0.957928i \(-0.592660\pi\)
−0.287007 + 0.957928i \(0.592660\pi\)
\(978\) 0 0
\(979\) −41.5832 −1.32900
\(980\) 0 0
\(981\) −7.90969 −0.252537
\(982\) 0 0
\(983\) −37.4902 −1.19575 −0.597876 0.801589i \(-0.703988\pi\)
−0.597876 + 0.801589i \(0.703988\pi\)
\(984\) 0 0
\(985\) 26.1768 0.834062
\(986\) 0 0
\(987\) 51.8240 1.64958
\(988\) 0 0
\(989\) 9.58199 0.304689
\(990\) 0 0
\(991\) 4.59427 0.145942 0.0729708 0.997334i \(-0.476752\pi\)
0.0729708 + 0.997334i \(0.476752\pi\)
\(992\) 0 0
\(993\) 25.4162 0.806560
\(994\) 0 0
\(995\) 13.6712 0.433407
\(996\) 0 0
\(997\) 45.5362 1.44215 0.721073 0.692859i \(-0.243649\pi\)
0.721073 + 0.692859i \(0.243649\pi\)
\(998\) 0 0
\(999\) −66.4136 −2.10123
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 \(a_p\))