Properties

Label 6040.2.a.p.1.6
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 1.6
Root \(1.90812\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.90812 q^{3}\) \(+1.00000 q^{5}\) \(+1.15158 q^{7}\) \(+0.640908 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.90812 q^{3}\) \(+1.00000 q^{5}\) \(+1.15158 q^{7}\) \(+0.640908 q^{9}\) \(+4.77254 q^{11}\) \(+3.49113 q^{13}\) \(-1.90812 q^{15}\) \(-7.78011 q^{17}\) \(+1.91284 q^{19}\) \(-2.19736 q^{21}\) \(-6.30459 q^{23}\) \(+1.00000 q^{25}\) \(+4.50142 q^{27}\) \(-0.185654 q^{29}\) \(-9.77853 q^{31}\) \(-9.10657 q^{33}\) \(+1.15158 q^{35}\) \(+9.42468 q^{37}\) \(-6.66148 q^{39}\) \(-3.34035 q^{41}\) \(-1.84412 q^{43}\) \(+0.640908 q^{45}\) \(-1.21211 q^{47}\) \(-5.67385 q^{49}\) \(+14.8454 q^{51}\) \(-0.503670 q^{53}\) \(+4.77254 q^{55}\) \(-3.64993 q^{57}\) \(-14.1409 q^{59}\) \(-7.19463 q^{61}\) \(+0.738059 q^{63}\) \(+3.49113 q^{65}\) \(+1.44963 q^{67}\) \(+12.0299 q^{69}\) \(-12.3875 q^{71}\) \(+5.53104 q^{73}\) \(-1.90812 q^{75}\) \(+5.49599 q^{77}\) \(-8.71646 q^{79}\) \(-10.5120 q^{81}\) \(-5.43959 q^{83}\) \(-7.78011 q^{85}\) \(+0.354249 q^{87}\) \(+1.98863 q^{89}\) \(+4.02033 q^{91}\) \(+18.6586 q^{93}\) \(+1.91284 q^{95}\) \(+16.0631 q^{97}\) \(+3.05876 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.90812 −1.10165 −0.550826 0.834620i \(-0.685687\pi\)
−0.550826 + 0.834620i \(0.685687\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.15158 0.435258 0.217629 0.976032i \(-0.430168\pi\)
0.217629 + 0.976032i \(0.430168\pi\)
\(8\) 0 0
\(9\) 0.640908 0.213636
\(10\) 0 0
\(11\) 4.77254 1.43898 0.719488 0.694505i \(-0.244377\pi\)
0.719488 + 0.694505i \(0.244377\pi\)
\(12\) 0 0
\(13\) 3.49113 0.968265 0.484132 0.874995i \(-0.339135\pi\)
0.484132 + 0.874995i \(0.339135\pi\)
\(14\) 0 0
\(15\) −1.90812 −0.492674
\(16\) 0 0
\(17\) −7.78011 −1.88695 −0.943477 0.331439i \(-0.892466\pi\)
−0.943477 + 0.331439i \(0.892466\pi\)
\(18\) 0 0
\(19\) 1.91284 0.438836 0.219418 0.975631i \(-0.429584\pi\)
0.219418 + 0.975631i \(0.429584\pi\)
\(20\) 0 0
\(21\) −2.19736 −0.479503
\(22\) 0 0
\(23\) −6.30459 −1.31460 −0.657299 0.753630i \(-0.728301\pi\)
−0.657299 + 0.753630i \(0.728301\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 4.50142 0.866299
\(28\) 0 0
\(29\) −0.185654 −0.0344750 −0.0172375 0.999851i \(-0.505487\pi\)
−0.0172375 + 0.999851i \(0.505487\pi\)
\(30\) 0 0
\(31\) −9.77853 −1.75628 −0.878138 0.478408i \(-0.841214\pi\)
−0.878138 + 0.478408i \(0.841214\pi\)
\(32\) 0 0
\(33\) −9.10657 −1.58525
\(34\) 0 0
\(35\) 1.15158 0.194653
\(36\) 0 0
\(37\) 9.42468 1.54941 0.774704 0.632324i \(-0.217899\pi\)
0.774704 + 0.632324i \(0.217899\pi\)
\(38\) 0 0
\(39\) −6.66148 −1.06669
\(40\) 0 0
\(41\) −3.34035 −0.521675 −0.260838 0.965383i \(-0.583999\pi\)
−0.260838 + 0.965383i \(0.583999\pi\)
\(42\) 0 0
\(43\) −1.84412 −0.281226 −0.140613 0.990065i \(-0.544907\pi\)
−0.140613 + 0.990065i \(0.544907\pi\)
\(44\) 0 0
\(45\) 0.640908 0.0955409
\(46\) 0 0
\(47\) −1.21211 −0.176805 −0.0884024 0.996085i \(-0.528176\pi\)
−0.0884024 + 0.996085i \(0.528176\pi\)
\(48\) 0 0
\(49\) −5.67385 −0.810550
\(50\) 0 0
\(51\) 14.8454 2.07877
\(52\) 0 0
\(53\) −0.503670 −0.0691844 −0.0345922 0.999402i \(-0.511013\pi\)
−0.0345922 + 0.999402i \(0.511013\pi\)
\(54\) 0 0
\(55\) 4.77254 0.643530
\(56\) 0 0
\(57\) −3.64993 −0.483445
\(58\) 0 0
\(59\) −14.1409 −1.84099 −0.920495 0.390754i \(-0.872214\pi\)
−0.920495 + 0.390754i \(0.872214\pi\)
\(60\) 0 0
\(61\) −7.19463 −0.921178 −0.460589 0.887614i \(-0.652362\pi\)
−0.460589 + 0.887614i \(0.652362\pi\)
\(62\) 0 0
\(63\) 0.738059 0.0929867
\(64\) 0 0
\(65\) 3.49113 0.433021
\(66\) 0 0
\(67\) 1.44963 0.177101 0.0885505 0.996072i \(-0.471777\pi\)
0.0885505 + 0.996072i \(0.471777\pi\)
\(68\) 0 0
\(69\) 12.0299 1.44823
\(70\) 0 0
\(71\) −12.3875 −1.47013 −0.735064 0.677998i \(-0.762848\pi\)
−0.735064 + 0.677998i \(0.762848\pi\)
\(72\) 0 0
\(73\) 5.53104 0.647359 0.323680 0.946167i \(-0.395080\pi\)
0.323680 + 0.946167i \(0.395080\pi\)
\(74\) 0 0
\(75\) −1.90812 −0.220330
\(76\) 0 0
\(77\) 5.49599 0.626326
\(78\) 0 0
\(79\) −8.71646 −0.980679 −0.490339 0.871532i \(-0.663127\pi\)
−0.490339 + 0.871532i \(0.663127\pi\)
\(80\) 0 0
\(81\) −10.5120 −1.16800
\(82\) 0 0
\(83\) −5.43959 −0.597072 −0.298536 0.954398i \(-0.596498\pi\)
−0.298536 + 0.954398i \(0.596498\pi\)
\(84\) 0 0
\(85\) −7.78011 −0.843871
\(86\) 0 0
\(87\) 0.354249 0.0379795
\(88\) 0 0
\(89\) 1.98863 0.210794 0.105397 0.994430i \(-0.466389\pi\)
0.105397 + 0.994430i \(0.466389\pi\)
\(90\) 0 0
\(91\) 4.02033 0.421445
\(92\) 0 0
\(93\) 18.6586 1.93480
\(94\) 0 0
\(95\) 1.91284 0.196254
\(96\) 0 0
\(97\) 16.0631 1.63096 0.815481 0.578783i \(-0.196472\pi\)
0.815481 + 0.578783i \(0.196472\pi\)
\(98\) 0 0
\(99\) 3.05876 0.307417
\(100\) 0 0
\(101\) −5.80780 −0.577898 −0.288949 0.957345i \(-0.593306\pi\)
−0.288949 + 0.957345i \(0.593306\pi\)
\(102\) 0 0
\(103\) 16.2606 1.60221 0.801103 0.598526i \(-0.204247\pi\)
0.801103 + 0.598526i \(0.204247\pi\)
\(104\) 0 0
\(105\) −2.19736 −0.214440
\(106\) 0 0
\(107\) 10.4039 1.00578 0.502889 0.864351i \(-0.332270\pi\)
0.502889 + 0.864351i \(0.332270\pi\)
\(108\) 0 0
\(109\) 8.68259 0.831641 0.415821 0.909447i \(-0.363494\pi\)
0.415821 + 0.909447i \(0.363494\pi\)
\(110\) 0 0
\(111\) −17.9834 −1.70691
\(112\) 0 0
\(113\) −7.72969 −0.727148 −0.363574 0.931565i \(-0.618444\pi\)
−0.363574 + 0.931565i \(0.618444\pi\)
\(114\) 0 0
\(115\) −6.30459 −0.587906
\(116\) 0 0
\(117\) 2.23749 0.206856
\(118\) 0 0
\(119\) −8.95945 −0.821312
\(120\) 0 0
\(121\) 11.7772 1.07065
\(122\) 0 0
\(123\) 6.37378 0.574704
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −14.9015 −1.32229 −0.661145 0.750258i \(-0.729929\pi\)
−0.661145 + 0.750258i \(0.729929\pi\)
\(128\) 0 0
\(129\) 3.51880 0.309813
\(130\) 0 0
\(131\) 15.9332 1.39209 0.696047 0.717996i \(-0.254940\pi\)
0.696047 + 0.717996i \(0.254940\pi\)
\(132\) 0 0
\(133\) 2.20280 0.191007
\(134\) 0 0
\(135\) 4.50142 0.387421
\(136\) 0 0
\(137\) 0.648293 0.0553874 0.0276937 0.999616i \(-0.491184\pi\)
0.0276937 + 0.999616i \(0.491184\pi\)
\(138\) 0 0
\(139\) 2.77102 0.235035 0.117518 0.993071i \(-0.462506\pi\)
0.117518 + 0.993071i \(0.462506\pi\)
\(140\) 0 0
\(141\) 2.31285 0.194777
\(142\) 0 0
\(143\) 16.6616 1.39331
\(144\) 0 0
\(145\) −0.185654 −0.0154177
\(146\) 0 0
\(147\) 10.8264 0.892944
\(148\) 0 0
\(149\) 7.92025 0.648852 0.324426 0.945911i \(-0.394829\pi\)
0.324426 + 0.945911i \(0.394829\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −4.98633 −0.403121
\(154\) 0 0
\(155\) −9.77853 −0.785430
\(156\) 0 0
\(157\) 6.40941 0.511527 0.255763 0.966739i \(-0.417673\pi\)
0.255763 + 0.966739i \(0.417673\pi\)
\(158\) 0 0
\(159\) 0.961061 0.0762171
\(160\) 0 0
\(161\) −7.26026 −0.572189
\(162\) 0 0
\(163\) −18.7773 −1.47075 −0.735374 0.677662i \(-0.762993\pi\)
−0.735374 + 0.677662i \(0.762993\pi\)
\(164\) 0 0
\(165\) −9.10657 −0.708945
\(166\) 0 0
\(167\) −8.35575 −0.646587 −0.323294 0.946299i \(-0.604790\pi\)
−0.323294 + 0.946299i \(0.604790\pi\)
\(168\) 0 0
\(169\) −0.812022 −0.0624632
\(170\) 0 0
\(171\) 1.22596 0.0937512
\(172\) 0 0
\(173\) 11.9231 0.906498 0.453249 0.891384i \(-0.350265\pi\)
0.453249 + 0.891384i \(0.350265\pi\)
\(174\) 0 0
\(175\) 1.15158 0.0870516
\(176\) 0 0
\(177\) 26.9825 2.02813
\(178\) 0 0
\(179\) −18.9922 −1.41954 −0.709771 0.704433i \(-0.751201\pi\)
−0.709771 + 0.704433i \(0.751201\pi\)
\(180\) 0 0
\(181\) 6.88300 0.511609 0.255805 0.966728i \(-0.417660\pi\)
0.255805 + 0.966728i \(0.417660\pi\)
\(182\) 0 0
\(183\) 13.7282 1.01482
\(184\) 0 0
\(185\) 9.42468 0.692916
\(186\) 0 0
\(187\) −37.1309 −2.71528
\(188\) 0 0
\(189\) 5.18377 0.377064
\(190\) 0 0
\(191\) −19.3701 −1.40157 −0.700787 0.713370i \(-0.747168\pi\)
−0.700787 + 0.713370i \(0.747168\pi\)
\(192\) 0 0
\(193\) −12.2516 −0.881890 −0.440945 0.897534i \(-0.645357\pi\)
−0.440945 + 0.897534i \(0.645357\pi\)
\(194\) 0 0
\(195\) −6.66148 −0.477038
\(196\) 0 0
\(197\) −6.80002 −0.484482 −0.242241 0.970216i \(-0.577882\pi\)
−0.242241 + 0.970216i \(0.577882\pi\)
\(198\) 0 0
\(199\) 4.40229 0.312070 0.156035 0.987752i \(-0.450129\pi\)
0.156035 + 0.987752i \(0.450129\pi\)
\(200\) 0 0
\(201\) −2.76607 −0.195104
\(202\) 0 0
\(203\) −0.213796 −0.0150055
\(204\) 0 0
\(205\) −3.34035 −0.233300
\(206\) 0 0
\(207\) −4.04066 −0.280845
\(208\) 0 0
\(209\) 9.12913 0.631475
\(210\) 0 0
\(211\) 0.143515 0.00987997 0.00493999 0.999988i \(-0.498428\pi\)
0.00493999 + 0.999988i \(0.498428\pi\)
\(212\) 0 0
\(213\) 23.6368 1.61957
\(214\) 0 0
\(215\) −1.84412 −0.125768
\(216\) 0 0
\(217\) −11.2608 −0.764433
\(218\) 0 0
\(219\) −10.5539 −0.713164
\(220\) 0 0
\(221\) −27.1614 −1.82707
\(222\) 0 0
\(223\) −19.0197 −1.27365 −0.636827 0.771007i \(-0.719753\pi\)
−0.636827 + 0.771007i \(0.719753\pi\)
\(224\) 0 0
\(225\) 0.640908 0.0427272
\(226\) 0 0
\(227\) 11.7645 0.780837 0.390419 0.920637i \(-0.372330\pi\)
0.390419 + 0.920637i \(0.372330\pi\)
\(228\) 0 0
\(229\) 21.6927 1.43349 0.716746 0.697334i \(-0.245630\pi\)
0.716746 + 0.697334i \(0.245630\pi\)
\(230\) 0 0
\(231\) −10.4870 −0.689993
\(232\) 0 0
\(233\) 8.17820 0.535772 0.267886 0.963451i \(-0.413675\pi\)
0.267886 + 0.963451i \(0.413675\pi\)
\(234\) 0 0
\(235\) −1.21211 −0.0790695
\(236\) 0 0
\(237\) 16.6320 1.08037
\(238\) 0 0
\(239\) −20.1698 −1.30467 −0.652337 0.757929i \(-0.726211\pi\)
−0.652337 + 0.757929i \(0.726211\pi\)
\(240\) 0 0
\(241\) 17.9815 1.15829 0.579145 0.815224i \(-0.303386\pi\)
0.579145 + 0.815224i \(0.303386\pi\)
\(242\) 0 0
\(243\) 6.55378 0.420425
\(244\) 0 0
\(245\) −5.67385 −0.362489
\(246\) 0 0
\(247\) 6.67798 0.424910
\(248\) 0 0
\(249\) 10.3794 0.657766
\(250\) 0 0
\(251\) −4.51640 −0.285072 −0.142536 0.989790i \(-0.545526\pi\)
−0.142536 + 0.989790i \(0.545526\pi\)
\(252\) 0 0
\(253\) −30.0889 −1.89167
\(254\) 0 0
\(255\) 14.8454 0.929652
\(256\) 0 0
\(257\) −3.17303 −0.197928 −0.0989639 0.995091i \(-0.531553\pi\)
−0.0989639 + 0.995091i \(0.531553\pi\)
\(258\) 0 0
\(259\) 10.8533 0.674392
\(260\) 0 0
\(261\) −0.118987 −0.00736510
\(262\) 0 0
\(263\) −4.14288 −0.255461 −0.127730 0.991809i \(-0.540769\pi\)
−0.127730 + 0.991809i \(0.540769\pi\)
\(264\) 0 0
\(265\) −0.503670 −0.0309402
\(266\) 0 0
\(267\) −3.79454 −0.232222
\(268\) 0 0
\(269\) −23.4001 −1.42673 −0.713363 0.700794i \(-0.752829\pi\)
−0.713363 + 0.700794i \(0.752829\pi\)
\(270\) 0 0
\(271\) −23.3117 −1.41609 −0.708043 0.706170i \(-0.750422\pi\)
−0.708043 + 0.706170i \(0.750422\pi\)
\(272\) 0 0
\(273\) −7.67126 −0.464285
\(274\) 0 0
\(275\) 4.77254 0.287795
\(276\) 0 0
\(277\) 5.61214 0.337201 0.168600 0.985684i \(-0.446075\pi\)
0.168600 + 0.985684i \(0.446075\pi\)
\(278\) 0 0
\(279\) −6.26713 −0.375204
\(280\) 0 0
\(281\) −18.9155 −1.12840 −0.564201 0.825637i \(-0.690816\pi\)
−0.564201 + 0.825637i \(0.690816\pi\)
\(282\) 0 0
\(283\) −17.8090 −1.05863 −0.529317 0.848424i \(-0.677552\pi\)
−0.529317 + 0.848424i \(0.677552\pi\)
\(284\) 0 0
\(285\) −3.64993 −0.216203
\(286\) 0 0
\(287\) −3.84670 −0.227063
\(288\) 0 0
\(289\) 43.5301 2.56059
\(290\) 0 0
\(291\) −30.6503 −1.79675
\(292\) 0 0
\(293\) −19.9853 −1.16756 −0.583778 0.811913i \(-0.698426\pi\)
−0.583778 + 0.811913i \(0.698426\pi\)
\(294\) 0 0
\(295\) −14.1409 −0.823316
\(296\) 0 0
\(297\) 21.4832 1.24658
\(298\) 0 0
\(299\) −22.0101 −1.27288
\(300\) 0 0
\(301\) −2.12366 −0.122406
\(302\) 0 0
\(303\) 11.0820 0.636642
\(304\) 0 0
\(305\) −7.19463 −0.411963
\(306\) 0 0
\(307\) 4.11533 0.234874 0.117437 0.993080i \(-0.462532\pi\)
0.117437 + 0.993080i \(0.462532\pi\)
\(308\) 0 0
\(309\) −31.0272 −1.76507
\(310\) 0 0
\(311\) 18.5633 1.05263 0.526315 0.850289i \(-0.323573\pi\)
0.526315 + 0.850289i \(0.323573\pi\)
\(312\) 0 0
\(313\) −19.2697 −1.08919 −0.544595 0.838699i \(-0.683317\pi\)
−0.544595 + 0.838699i \(0.683317\pi\)
\(314\) 0 0
\(315\) 0.738059 0.0415849
\(316\) 0 0
\(317\) 14.6002 0.820029 0.410014 0.912079i \(-0.365524\pi\)
0.410014 + 0.912079i \(0.365524\pi\)
\(318\) 0 0
\(319\) −0.886040 −0.0496087
\(320\) 0 0
\(321\) −19.8518 −1.10802
\(322\) 0 0
\(323\) −14.8821 −0.828064
\(324\) 0 0
\(325\) 3.49113 0.193653
\(326\) 0 0
\(327\) −16.5674 −0.916179
\(328\) 0 0
\(329\) −1.39585 −0.0769557
\(330\) 0 0
\(331\) −23.4749 −1.29029 −0.645147 0.764058i \(-0.723204\pi\)
−0.645147 + 0.764058i \(0.723204\pi\)
\(332\) 0 0
\(333\) 6.04035 0.331009
\(334\) 0 0
\(335\) 1.44963 0.0792020
\(336\) 0 0
\(337\) −6.72634 −0.366407 −0.183203 0.983075i \(-0.558647\pi\)
−0.183203 + 0.983075i \(0.558647\pi\)
\(338\) 0 0
\(339\) 14.7491 0.801064
\(340\) 0 0
\(341\) −46.6684 −2.52724
\(342\) 0 0
\(343\) −14.5950 −0.788057
\(344\) 0 0
\(345\) 12.0299 0.647667
\(346\) 0 0
\(347\) −1.14897 −0.0616800 −0.0308400 0.999524i \(-0.509818\pi\)
−0.0308400 + 0.999524i \(0.509818\pi\)
\(348\) 0 0
\(349\) −23.7212 −1.26977 −0.634885 0.772607i \(-0.718952\pi\)
−0.634885 + 0.772607i \(0.718952\pi\)
\(350\) 0 0
\(351\) 15.7150 0.838807
\(352\) 0 0
\(353\) −21.8193 −1.16133 −0.580663 0.814144i \(-0.697207\pi\)
−0.580663 + 0.814144i \(0.697207\pi\)
\(354\) 0 0
\(355\) −12.3875 −0.657461
\(356\) 0 0
\(357\) 17.0957 0.904799
\(358\) 0 0
\(359\) −7.32958 −0.386841 −0.193420 0.981116i \(-0.561958\pi\)
−0.193420 + 0.981116i \(0.561958\pi\)
\(360\) 0 0
\(361\) −15.3410 −0.807423
\(362\) 0 0
\(363\) −22.4722 −1.17948
\(364\) 0 0
\(365\) 5.53104 0.289508
\(366\) 0 0
\(367\) 35.8361 1.87063 0.935315 0.353817i \(-0.115117\pi\)
0.935315 + 0.353817i \(0.115117\pi\)
\(368\) 0 0
\(369\) −2.14086 −0.111449
\(370\) 0 0
\(371\) −0.580019 −0.0301131
\(372\) 0 0
\(373\) −1.19833 −0.0620473 −0.0310237 0.999519i \(-0.509877\pi\)
−0.0310237 + 0.999519i \(0.509877\pi\)
\(374\) 0 0
\(375\) −1.90812 −0.0985347
\(376\) 0 0
\(377\) −0.648141 −0.0333810
\(378\) 0 0
\(379\) −21.6068 −1.10986 −0.554932 0.831895i \(-0.687256\pi\)
−0.554932 + 0.831895i \(0.687256\pi\)
\(380\) 0 0
\(381\) 28.4337 1.45670
\(382\) 0 0
\(383\) 29.7618 1.52076 0.760378 0.649481i \(-0.225014\pi\)
0.760378 + 0.649481i \(0.225014\pi\)
\(384\) 0 0
\(385\) 5.49599 0.280101
\(386\) 0 0
\(387\) −1.18191 −0.0600800
\(388\) 0 0
\(389\) 28.8316 1.46182 0.730909 0.682475i \(-0.239096\pi\)
0.730909 + 0.682475i \(0.239096\pi\)
\(390\) 0 0
\(391\) 49.0504 2.48058
\(392\) 0 0
\(393\) −30.4025 −1.53360
\(394\) 0 0
\(395\) −8.71646 −0.438573
\(396\) 0 0
\(397\) −0.653539 −0.0328002 −0.0164001 0.999866i \(-0.505221\pi\)
−0.0164001 + 0.999866i \(0.505221\pi\)
\(398\) 0 0
\(399\) −4.20320 −0.210423
\(400\) 0 0
\(401\) −15.7068 −0.784359 −0.392179 0.919889i \(-0.628279\pi\)
−0.392179 + 0.919889i \(0.628279\pi\)
\(402\) 0 0
\(403\) −34.1381 −1.70054
\(404\) 0 0
\(405\) −10.5120 −0.522344
\(406\) 0 0
\(407\) 44.9797 2.22956
\(408\) 0 0
\(409\) 31.8387 1.57432 0.787160 0.616748i \(-0.211550\pi\)
0.787160 + 0.616748i \(0.211550\pi\)
\(410\) 0 0
\(411\) −1.23702 −0.0610176
\(412\) 0 0
\(413\) −16.2845 −0.801306
\(414\) 0 0
\(415\) −5.43959 −0.267019
\(416\) 0 0
\(417\) −5.28743 −0.258927
\(418\) 0 0
\(419\) −29.6514 −1.44857 −0.724284 0.689502i \(-0.757829\pi\)
−0.724284 + 0.689502i \(0.757829\pi\)
\(420\) 0 0
\(421\) −28.2695 −1.37777 −0.688886 0.724870i \(-0.741900\pi\)
−0.688886 + 0.724870i \(0.741900\pi\)
\(422\) 0 0
\(423\) −0.776852 −0.0377718
\(424\) 0 0
\(425\) −7.78011 −0.377391
\(426\) 0 0
\(427\) −8.28522 −0.400950
\(428\) 0 0
\(429\) −31.7922 −1.53494
\(430\) 0 0
\(431\) 18.1568 0.874580 0.437290 0.899321i \(-0.355938\pi\)
0.437290 + 0.899321i \(0.355938\pi\)
\(432\) 0 0
\(433\) 14.0694 0.676134 0.338067 0.941122i \(-0.390227\pi\)
0.338067 + 0.941122i \(0.390227\pi\)
\(434\) 0 0
\(435\) 0.354249 0.0169849
\(436\) 0 0
\(437\) −12.0597 −0.576893
\(438\) 0 0
\(439\) 5.94867 0.283914 0.141957 0.989873i \(-0.454660\pi\)
0.141957 + 0.989873i \(0.454660\pi\)
\(440\) 0 0
\(441\) −3.63642 −0.173163
\(442\) 0 0
\(443\) −20.8504 −0.990631 −0.495315 0.868713i \(-0.664947\pi\)
−0.495315 + 0.868713i \(0.664947\pi\)
\(444\) 0 0
\(445\) 1.98863 0.0942701
\(446\) 0 0
\(447\) −15.1128 −0.714809
\(448\) 0 0
\(449\) −0.972773 −0.0459080 −0.0229540 0.999737i \(-0.507307\pi\)
−0.0229540 + 0.999737i \(0.507307\pi\)
\(450\) 0 0
\(451\) −15.9420 −0.750678
\(452\) 0 0
\(453\) −1.90812 −0.0896511
\(454\) 0 0
\(455\) 4.02033 0.188476
\(456\) 0 0
\(457\) −0.139601 −0.00653026 −0.00326513 0.999995i \(-0.501039\pi\)
−0.00326513 + 0.999995i \(0.501039\pi\)
\(458\) 0 0
\(459\) −35.0216 −1.63467
\(460\) 0 0
\(461\) 39.7094 1.84945 0.924725 0.380636i \(-0.124295\pi\)
0.924725 + 0.380636i \(0.124295\pi\)
\(462\) 0 0
\(463\) −39.2427 −1.82376 −0.911880 0.410456i \(-0.865370\pi\)
−0.911880 + 0.410456i \(0.865370\pi\)
\(464\) 0 0
\(465\) 18.6586 0.865270
\(466\) 0 0
\(467\) 13.0241 0.602682 0.301341 0.953516i \(-0.402566\pi\)
0.301341 + 0.953516i \(0.402566\pi\)
\(468\) 0 0
\(469\) 1.66938 0.0770847
\(470\) 0 0
\(471\) −12.2299 −0.563524
\(472\) 0 0
\(473\) −8.80115 −0.404677
\(474\) 0 0
\(475\) 1.91284 0.0877673
\(476\) 0 0
\(477\) −0.322806 −0.0147803
\(478\) 0 0
\(479\) −24.7172 −1.12936 −0.564680 0.825310i \(-0.691000\pi\)
−0.564680 + 0.825310i \(0.691000\pi\)
\(480\) 0 0
\(481\) 32.9028 1.50024
\(482\) 0 0
\(483\) 13.8534 0.630353
\(484\) 0 0
\(485\) 16.0631 0.729389
\(486\) 0 0
\(487\) −39.0981 −1.77170 −0.885852 0.463968i \(-0.846425\pi\)
−0.885852 + 0.463968i \(0.846425\pi\)
\(488\) 0 0
\(489\) 35.8292 1.62025
\(490\) 0 0
\(491\) 23.0824 1.04169 0.520847 0.853650i \(-0.325616\pi\)
0.520847 + 0.853650i \(0.325616\pi\)
\(492\) 0 0
\(493\) 1.44441 0.0650528
\(494\) 0 0
\(495\) 3.05876 0.137481
\(496\) 0 0
\(497\) −14.2653 −0.639885
\(498\) 0 0
\(499\) 8.73690 0.391117 0.195559 0.980692i \(-0.437348\pi\)
0.195559 + 0.980692i \(0.437348\pi\)
\(500\) 0 0
\(501\) 15.9437 0.712314
\(502\) 0 0
\(503\) 16.8938 0.753255 0.376628 0.926365i \(-0.377084\pi\)
0.376628 + 0.926365i \(0.377084\pi\)
\(504\) 0 0
\(505\) −5.80780 −0.258444
\(506\) 0 0
\(507\) 1.54943 0.0688127
\(508\) 0 0
\(509\) −9.18885 −0.407289 −0.203644 0.979045i \(-0.565279\pi\)
−0.203644 + 0.979045i \(0.565279\pi\)
\(510\) 0 0
\(511\) 6.36946 0.281768
\(512\) 0 0
\(513\) 8.61052 0.380164
\(514\) 0 0
\(515\) 16.2606 0.716529
\(516\) 0 0
\(517\) −5.78486 −0.254418
\(518\) 0 0
\(519\) −22.7507 −0.998644
\(520\) 0 0
\(521\) 27.4061 1.20068 0.600342 0.799743i \(-0.295031\pi\)
0.600342 + 0.799743i \(0.295031\pi\)
\(522\) 0 0
\(523\) 3.95352 0.172875 0.0864377 0.996257i \(-0.472452\pi\)
0.0864377 + 0.996257i \(0.472452\pi\)
\(524\) 0 0
\(525\) −2.19736 −0.0959005
\(526\) 0 0
\(527\) 76.0780 3.31401
\(528\) 0 0
\(529\) 16.7478 0.728166
\(530\) 0 0
\(531\) −9.06302 −0.393302
\(532\) 0 0
\(533\) −11.6616 −0.505120
\(534\) 0 0
\(535\) 10.4039 0.449798
\(536\) 0 0
\(537\) 36.2393 1.56384
\(538\) 0 0
\(539\) −27.0787 −1.16636
\(540\) 0 0
\(541\) −0.912930 −0.0392499 −0.0196250 0.999807i \(-0.506247\pi\)
−0.0196250 + 0.999807i \(0.506247\pi\)
\(542\) 0 0
\(543\) −13.1336 −0.563615
\(544\) 0 0
\(545\) 8.68259 0.371921
\(546\) 0 0
\(547\) 14.9716 0.640141 0.320070 0.947394i \(-0.396293\pi\)
0.320070 + 0.947394i \(0.396293\pi\)
\(548\) 0 0
\(549\) −4.61109 −0.196797
\(550\) 0 0
\(551\) −0.355126 −0.0151289
\(552\) 0 0
\(553\) −10.0377 −0.426848
\(554\) 0 0
\(555\) −17.9834 −0.763352
\(556\) 0 0
\(557\) 43.1682 1.82909 0.914547 0.404479i \(-0.132547\pi\)
0.914547 + 0.404479i \(0.132547\pi\)
\(558\) 0 0
\(559\) −6.43807 −0.272301
\(560\) 0 0
\(561\) 70.8501 2.99129
\(562\) 0 0
\(563\) −45.3966 −1.91324 −0.956618 0.291344i \(-0.905898\pi\)
−0.956618 + 0.291344i \(0.905898\pi\)
\(564\) 0 0
\(565\) −7.72969 −0.325190
\(566\) 0 0
\(567\) −12.1054 −0.508379
\(568\) 0 0
\(569\) −33.3868 −1.39965 −0.699824 0.714315i \(-0.746738\pi\)
−0.699824 + 0.714315i \(0.746738\pi\)
\(570\) 0 0
\(571\) 8.12756 0.340128 0.170064 0.985433i \(-0.445603\pi\)
0.170064 + 0.985433i \(0.445603\pi\)
\(572\) 0 0
\(573\) 36.9605 1.54405
\(574\) 0 0
\(575\) −6.30459 −0.262919
\(576\) 0 0
\(577\) −0.873789 −0.0363763 −0.0181882 0.999835i \(-0.505790\pi\)
−0.0181882 + 0.999835i \(0.505790\pi\)
\(578\) 0 0
\(579\) 23.3775 0.971535
\(580\) 0 0
\(581\) −6.26415 −0.259881
\(582\) 0 0
\(583\) −2.40379 −0.0995547
\(584\) 0 0
\(585\) 2.23749 0.0925089
\(586\) 0 0
\(587\) 36.0685 1.48871 0.744353 0.667787i \(-0.232758\pi\)
0.744353 + 0.667787i \(0.232758\pi\)
\(588\) 0 0
\(589\) −18.7048 −0.770717
\(590\) 0 0
\(591\) 12.9752 0.533730
\(592\) 0 0
\(593\) −44.1750 −1.81405 −0.907025 0.421076i \(-0.861653\pi\)
−0.907025 + 0.421076i \(0.861653\pi\)
\(594\) 0 0
\(595\) −8.95945 −0.367302
\(596\) 0 0
\(597\) −8.40008 −0.343792
\(598\) 0 0
\(599\) −7.51214 −0.306938 −0.153469 0.988153i \(-0.549045\pi\)
−0.153469 + 0.988153i \(0.549045\pi\)
\(600\) 0 0
\(601\) −35.3318 −1.44122 −0.720608 0.693343i \(-0.756137\pi\)
−0.720608 + 0.693343i \(0.756137\pi\)
\(602\) 0 0
\(603\) 0.929082 0.0378352
\(604\) 0 0
\(605\) 11.7772 0.478810
\(606\) 0 0
\(607\) 1.71787 0.0697261 0.0348631 0.999392i \(-0.488900\pi\)
0.0348631 + 0.999392i \(0.488900\pi\)
\(608\) 0 0
\(609\) 0.407947 0.0165309
\(610\) 0 0
\(611\) −4.23164 −0.171194
\(612\) 0 0
\(613\) −2.78026 −0.112294 −0.0561469 0.998423i \(-0.517882\pi\)
−0.0561469 + 0.998423i \(0.517882\pi\)
\(614\) 0 0
\(615\) 6.37378 0.257016
\(616\) 0 0
\(617\) −33.1898 −1.33617 −0.668086 0.744084i \(-0.732886\pi\)
−0.668086 + 0.744084i \(0.732886\pi\)
\(618\) 0 0
\(619\) 12.9037 0.518642 0.259321 0.965791i \(-0.416501\pi\)
0.259321 + 0.965791i \(0.416501\pi\)
\(620\) 0 0
\(621\) −28.3796 −1.13883
\(622\) 0 0
\(623\) 2.29007 0.0917499
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −17.4194 −0.695665
\(628\) 0 0
\(629\) −73.3250 −2.92366
\(630\) 0 0
\(631\) −23.9375 −0.952936 −0.476468 0.879192i \(-0.658083\pi\)
−0.476468 + 0.879192i \(0.658083\pi\)
\(632\) 0 0
\(633\) −0.273843 −0.0108843
\(634\) 0 0
\(635\) −14.9015 −0.591346
\(636\) 0 0
\(637\) −19.8082 −0.784828
\(638\) 0 0
\(639\) −7.93925 −0.314072
\(640\) 0 0
\(641\) 3.44753 0.136169 0.0680845 0.997680i \(-0.478311\pi\)
0.0680845 + 0.997680i \(0.478311\pi\)
\(642\) 0 0
\(643\) 8.44353 0.332980 0.166490 0.986043i \(-0.446757\pi\)
0.166490 + 0.986043i \(0.446757\pi\)
\(644\) 0 0
\(645\) 3.51880 0.138553
\(646\) 0 0
\(647\) 0.116748 0.00458986 0.00229493 0.999997i \(-0.499270\pi\)
0.00229493 + 0.999997i \(0.499270\pi\)
\(648\) 0 0
\(649\) −67.4881 −2.64914
\(650\) 0 0
\(651\) 21.4869 0.842139
\(652\) 0 0
\(653\) 14.8110 0.579600 0.289800 0.957087i \(-0.406411\pi\)
0.289800 + 0.957087i \(0.406411\pi\)
\(654\) 0 0
\(655\) 15.9332 0.622563
\(656\) 0 0
\(657\) 3.54489 0.138299
\(658\) 0 0
\(659\) 39.6137 1.54313 0.771564 0.636151i \(-0.219475\pi\)
0.771564 + 0.636151i \(0.219475\pi\)
\(660\) 0 0
\(661\) 0.763064 0.0296797 0.0148399 0.999890i \(-0.495276\pi\)
0.0148399 + 0.999890i \(0.495276\pi\)
\(662\) 0 0
\(663\) 51.8270 2.01280
\(664\) 0 0
\(665\) 2.20280 0.0854209
\(666\) 0 0
\(667\) 1.17047 0.0453208
\(668\) 0 0
\(669\) 36.2918 1.40312
\(670\) 0 0
\(671\) −34.3367 −1.32555
\(672\) 0 0
\(673\) −12.7674 −0.492146 −0.246073 0.969251i \(-0.579140\pi\)
−0.246073 + 0.969251i \(0.579140\pi\)
\(674\) 0 0
\(675\) 4.50142 0.173260
\(676\) 0 0
\(677\) −16.6653 −0.640499 −0.320250 0.947333i \(-0.603767\pi\)
−0.320250 + 0.947333i \(0.603767\pi\)
\(678\) 0 0
\(679\) 18.4980 0.709889
\(680\) 0 0
\(681\) −22.4480 −0.860210
\(682\) 0 0
\(683\) 4.96758 0.190079 0.0950395 0.995474i \(-0.469702\pi\)
0.0950395 + 0.995474i \(0.469702\pi\)
\(684\) 0 0
\(685\) 0.648293 0.0247700
\(686\) 0 0
\(687\) −41.3922 −1.57921
\(688\) 0 0
\(689\) −1.75838 −0.0669888
\(690\) 0 0
\(691\) −45.1073 −1.71596 −0.857982 0.513680i \(-0.828282\pi\)
−0.857982 + 0.513680i \(0.828282\pi\)
\(692\) 0 0
\(693\) 3.52242 0.133806
\(694\) 0 0
\(695\) 2.77102 0.105111
\(696\) 0 0
\(697\) 25.9883 0.984377
\(698\) 0 0
\(699\) −15.6050 −0.590234
\(700\) 0 0
\(701\) −20.1108 −0.759573 −0.379786 0.925074i \(-0.624003\pi\)
−0.379786 + 0.925074i \(0.624003\pi\)
\(702\) 0 0
\(703\) 18.0279 0.679937
\(704\) 0 0
\(705\) 2.31285 0.0871070
\(706\) 0 0
\(707\) −6.68817 −0.251535
\(708\) 0 0
\(709\) −31.3240 −1.17640 −0.588199 0.808716i \(-0.700163\pi\)
−0.588199 + 0.808716i \(0.700163\pi\)
\(710\) 0 0
\(711\) −5.58645 −0.209508
\(712\) 0 0
\(713\) 61.6496 2.30879
\(714\) 0 0
\(715\) 16.6616 0.623107
\(716\) 0 0
\(717\) 38.4862 1.43730
\(718\) 0 0
\(719\) −30.0942 −1.12233 −0.561163 0.827706i \(-0.689646\pi\)
−0.561163 + 0.827706i \(0.689646\pi\)
\(720\) 0 0
\(721\) 18.7255 0.697373
\(722\) 0 0
\(723\) −34.3108 −1.27603
\(724\) 0 0
\(725\) −0.185654 −0.00689500
\(726\) 0 0
\(727\) 31.0306 1.15086 0.575430 0.817851i \(-0.304835\pi\)
0.575430 + 0.817851i \(0.304835\pi\)
\(728\) 0 0
\(729\) 19.0305 0.704834
\(730\) 0 0
\(731\) 14.3475 0.530660
\(732\) 0 0
\(733\) 17.0809 0.630897 0.315448 0.948943i \(-0.397845\pi\)
0.315448 + 0.948943i \(0.397845\pi\)
\(734\) 0 0
\(735\) 10.8264 0.399337
\(736\) 0 0
\(737\) 6.91844 0.254844
\(738\) 0 0
\(739\) −5.00537 −0.184125 −0.0920627 0.995753i \(-0.529346\pi\)
−0.0920627 + 0.995753i \(0.529346\pi\)
\(740\) 0 0
\(741\) −12.7424 −0.468103
\(742\) 0 0
\(743\) −0.484143 −0.0177615 −0.00888074 0.999961i \(-0.502827\pi\)
−0.00888074 + 0.999961i \(0.502827\pi\)
\(744\) 0 0
\(745\) 7.92025 0.290175
\(746\) 0 0
\(747\) −3.48627 −0.127556
\(748\) 0 0
\(749\) 11.9809 0.437773
\(750\) 0 0
\(751\) −7.69016 −0.280618 −0.140309 0.990108i \(-0.544810\pi\)
−0.140309 + 0.990108i \(0.544810\pi\)
\(752\) 0 0
\(753\) 8.61781 0.314050
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 20.2578 0.736283 0.368141 0.929770i \(-0.379994\pi\)
0.368141 + 0.929770i \(0.379994\pi\)
\(758\) 0 0
\(759\) 57.4131 2.08397
\(760\) 0 0
\(761\) 5.25858 0.190623 0.0953117 0.995447i \(-0.469615\pi\)
0.0953117 + 0.995447i \(0.469615\pi\)
\(762\) 0 0
\(763\) 9.99874 0.361979
\(764\) 0 0
\(765\) −4.98633 −0.180281
\(766\) 0 0
\(767\) −49.3677 −1.78257
\(768\) 0 0
\(769\) −27.3986 −0.988018 −0.494009 0.869457i \(-0.664469\pi\)
−0.494009 + 0.869457i \(0.664469\pi\)
\(770\) 0 0
\(771\) 6.05450 0.218048
\(772\) 0 0
\(773\) −24.1021 −0.866892 −0.433446 0.901180i \(-0.642702\pi\)
−0.433446 + 0.901180i \(0.642702\pi\)
\(774\) 0 0
\(775\) −9.77853 −0.351255
\(776\) 0 0
\(777\) −20.7094 −0.742945
\(778\) 0 0
\(779\) −6.38957 −0.228930
\(780\) 0 0
\(781\) −59.1199 −2.11548
\(782\) 0 0
\(783\) −0.835706 −0.0298657
\(784\) 0 0
\(785\) 6.40941 0.228762
\(786\) 0 0
\(787\) 22.8459 0.814367 0.407183 0.913346i \(-0.366511\pi\)
0.407183 + 0.913346i \(0.366511\pi\)
\(788\) 0 0
\(789\) 7.90509 0.281429
\(790\) 0 0
\(791\) −8.90139 −0.316497
\(792\) 0 0
\(793\) −25.1174 −0.891944
\(794\) 0 0
\(795\) 0.961061 0.0340853
\(796\) 0 0
\(797\) 14.3708 0.509039 0.254519 0.967068i \(-0.418083\pi\)
0.254519 + 0.967068i \(0.418083\pi\)
\(798\) 0 0
\(799\) 9.43036 0.333622
\(800\) 0 0
\(801\) 1.27453 0.0450332
\(802\) 0 0
\(803\) 26.3971 0.931534
\(804\) 0 0
\(805\) −7.26026 −0.255891
\(806\) 0 0
\(807\) 44.6500 1.57176
\(808\) 0 0
\(809\) −3.50159 −0.123109 −0.0615547 0.998104i \(-0.519606\pi\)
−0.0615547 + 0.998104i \(0.519606\pi\)
\(810\) 0 0
\(811\) −23.0733 −0.810214 −0.405107 0.914269i \(-0.632766\pi\)
−0.405107 + 0.914269i \(0.632766\pi\)
\(812\) 0 0
\(813\) 44.4815 1.56003
\(814\) 0 0
\(815\) −18.7773 −0.657738
\(816\) 0 0
\(817\) −3.52752 −0.123412
\(818\) 0 0
\(819\) 2.57666 0.0900358
\(820\) 0 0
\(821\) −4.92514 −0.171889 −0.0859443 0.996300i \(-0.527391\pi\)
−0.0859443 + 0.996300i \(0.527391\pi\)
\(822\) 0 0
\(823\) 20.5252 0.715465 0.357733 0.933824i \(-0.383550\pi\)
0.357733 + 0.933824i \(0.383550\pi\)
\(824\) 0 0
\(825\) −9.10657 −0.317050
\(826\) 0 0
\(827\) −23.6420 −0.822112 −0.411056 0.911610i \(-0.634840\pi\)
−0.411056 + 0.911610i \(0.634840\pi\)
\(828\) 0 0
\(829\) 5.90235 0.204997 0.102499 0.994733i \(-0.467316\pi\)
0.102499 + 0.994733i \(0.467316\pi\)
\(830\) 0 0
\(831\) −10.7086 −0.371478
\(832\) 0 0
\(833\) 44.1432 1.52947
\(834\) 0 0
\(835\) −8.35575 −0.289163
\(836\) 0 0
\(837\) −44.0173 −1.52146
\(838\) 0 0
\(839\) 26.7355 0.923011 0.461505 0.887137i \(-0.347309\pi\)
0.461505 + 0.887137i \(0.347309\pi\)
\(840\) 0 0
\(841\) −28.9655 −0.998811
\(842\) 0 0
\(843\) 36.0929 1.24311
\(844\) 0 0
\(845\) −0.812022 −0.0279344
\(846\) 0 0
\(847\) 13.5624 0.466009
\(848\) 0 0
\(849\) 33.9816 1.16625
\(850\) 0 0
\(851\) −59.4187 −2.03685
\(852\) 0 0
\(853\) −41.1209 −1.40795 −0.703976 0.710224i \(-0.748594\pi\)
−0.703976 + 0.710224i \(0.748594\pi\)
\(854\) 0 0
\(855\) 1.22596 0.0419268
\(856\) 0 0
\(857\) 32.4116 1.10716 0.553580 0.832796i \(-0.313261\pi\)
0.553580 + 0.832796i \(0.313261\pi\)
\(858\) 0 0
\(859\) 5.88089 0.200653 0.100327 0.994955i \(-0.468011\pi\)
0.100327 + 0.994955i \(0.468011\pi\)
\(860\) 0 0
\(861\) 7.33994 0.250145
\(862\) 0 0
\(863\) 8.70645 0.296371 0.148185 0.988960i \(-0.452657\pi\)
0.148185 + 0.988960i \(0.452657\pi\)
\(864\) 0 0
\(865\) 11.9231 0.405398
\(866\) 0 0
\(867\) −83.0605 −2.82088
\(868\) 0 0
\(869\) −41.5997 −1.41117
\(870\) 0 0
\(871\) 5.06086 0.171481
\(872\) 0 0
\(873\) 10.2950 0.348432
\(874\) 0 0
\(875\) 1.15158 0.0389307
\(876\) 0 0
\(877\) 35.3638 1.19415 0.597075 0.802186i \(-0.296330\pi\)
0.597075 + 0.802186i \(0.296330\pi\)
\(878\) 0 0
\(879\) 38.1343 1.28624
\(880\) 0 0
\(881\) −10.1564 −0.342178 −0.171089 0.985256i \(-0.554729\pi\)
−0.171089 + 0.985256i \(0.554729\pi\)
\(882\) 0 0
\(883\) 20.1784 0.679059 0.339529 0.940595i \(-0.389732\pi\)
0.339529 + 0.940595i \(0.389732\pi\)
\(884\) 0 0
\(885\) 26.9825 0.907007
\(886\) 0 0
\(887\) 31.1471 1.04582 0.522909 0.852389i \(-0.324847\pi\)
0.522909 + 0.852389i \(0.324847\pi\)
\(888\) 0 0
\(889\) −17.1603 −0.575538
\(890\) 0 0
\(891\) −50.1688 −1.68072
\(892\) 0 0
\(893\) −2.31858 −0.0775883
\(894\) 0 0
\(895\) −18.9922 −0.634838
\(896\) 0 0
\(897\) 41.9979 1.40227
\(898\) 0 0
\(899\) 1.81542 0.0605476
\(900\) 0 0
\(901\) 3.91861 0.130548
\(902\) 0 0
\(903\) 4.05219 0.134849
\(904\) 0 0
\(905\) 6.88300 0.228799
\(906\) 0 0
\(907\) 50.1859 1.66640 0.833198 0.552975i \(-0.186508\pi\)
0.833198 + 0.552975i \(0.186508\pi\)
\(908\) 0 0
\(909\) −3.72226 −0.123460
\(910\) 0 0
\(911\) −15.9822 −0.529513 −0.264757 0.964315i \(-0.585292\pi\)
−0.264757 + 0.964315i \(0.585292\pi\)
\(912\) 0 0
\(913\) −25.9607 −0.859173
\(914\) 0 0
\(915\) 13.7282 0.453840
\(916\) 0 0
\(917\) 18.3485 0.605920
\(918\) 0 0
\(919\) 28.9576 0.955224 0.477612 0.878571i \(-0.341502\pi\)
0.477612 + 0.878571i \(0.341502\pi\)
\(920\) 0 0
\(921\) −7.85252 −0.258749
\(922\) 0 0
\(923\) −43.2464 −1.42347
\(924\) 0 0
\(925\) 9.42468 0.309882
\(926\) 0 0
\(927\) 10.4216 0.342289
\(928\) 0 0
\(929\) 13.9893 0.458973 0.229486 0.973312i \(-0.426295\pi\)
0.229486 + 0.973312i \(0.426295\pi\)
\(930\) 0 0
\(931\) −10.8532 −0.355699
\(932\) 0 0
\(933\) −35.4210 −1.15963
\(934\) 0 0
\(935\) −37.1309 −1.21431
\(936\) 0 0
\(937\) −40.0484 −1.30832 −0.654162 0.756354i \(-0.726979\pi\)
−0.654162 + 0.756354i \(0.726979\pi\)
\(938\) 0 0
\(939\) 36.7689 1.19991
\(940\) 0 0
\(941\) −0.759012 −0.0247431 −0.0123715 0.999923i \(-0.503938\pi\)
−0.0123715 + 0.999923i \(0.503938\pi\)
\(942\) 0 0
\(943\) 21.0595 0.685793
\(944\) 0 0
\(945\) 5.18377 0.168628
\(946\) 0 0
\(947\) −10.8394 −0.352234 −0.176117 0.984369i \(-0.556354\pi\)
−0.176117 + 0.984369i \(0.556354\pi\)
\(948\) 0 0
\(949\) 19.3096 0.626815
\(950\) 0 0
\(951\) −27.8589 −0.903386
\(952\) 0 0
\(953\) 24.6328 0.797936 0.398968 0.916965i \(-0.369368\pi\)
0.398968 + 0.916965i \(0.369368\pi\)
\(954\) 0 0
\(955\) −19.3701 −0.626803
\(956\) 0 0
\(957\) 1.69067 0.0546515
\(958\) 0 0
\(959\) 0.746564 0.0241078
\(960\) 0 0
\(961\) 64.6196 2.08450
\(962\) 0 0
\(963\) 6.66791 0.214870
\(964\) 0 0
\(965\) −12.2516 −0.394393
\(966\) 0 0
\(967\) −5.46203 −0.175647 −0.0878236 0.996136i \(-0.527991\pi\)
−0.0878236 + 0.996136i \(0.527991\pi\)
\(968\) 0 0
\(969\) 28.3968 0.912238
\(970\) 0 0
\(971\) 34.7957 1.11665 0.558324 0.829623i \(-0.311444\pi\)
0.558324 + 0.829623i \(0.311444\pi\)
\(972\) 0 0
\(973\) 3.19107 0.102301
\(974\) 0 0
\(975\) −6.66148 −0.213338
\(976\) 0 0
\(977\) 56.3630 1.80321 0.901606 0.432558i \(-0.142389\pi\)
0.901606 + 0.432558i \(0.142389\pi\)
\(978\) 0 0
\(979\) 9.49082 0.303328
\(980\) 0 0
\(981\) 5.56474 0.177669
\(982\) 0 0
\(983\) 3.05597 0.0974703 0.0487351 0.998812i \(-0.484481\pi\)
0.0487351 + 0.998812i \(0.484481\pi\)
\(984\) 0 0
\(985\) −6.80002 −0.216667
\(986\) 0 0
\(987\) 2.66344 0.0847783
\(988\) 0 0
\(989\) 11.6264 0.369699
\(990\) 0 0
\(991\) −0.706158 −0.0224318 −0.0112159 0.999937i \(-0.503570\pi\)
−0.0112159 + 0.999937i \(0.503570\pi\)
\(992\) 0 0
\(993\) 44.7927 1.42145
\(994\) 0 0
\(995\) 4.40229 0.139562
\(996\) 0 0
\(997\) 16.6064 0.525931 0.262966 0.964805i \(-0.415299\pi\)
0.262966 + 0.964805i \(0.415299\pi\)
\(998\) 0 0
\(999\) 42.4245 1.34225
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 \(a_p\))