Properties

Label 4005.2.a.p.1.7
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.66289\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.66289 q^{2} +0.765209 q^{4} +1.00000 q^{5} -1.19579 q^{7} -2.05332 q^{8} +O(q^{10})\) \(q+1.66289 q^{2} +0.765209 q^{4} +1.00000 q^{5} -1.19579 q^{7} -2.05332 q^{8} +1.66289 q^{10} +1.71622 q^{11} -6.71750 q^{13} -1.98846 q^{14} -4.94487 q^{16} -0.198198 q^{17} +5.88536 q^{19} +0.765209 q^{20} +2.85388 q^{22} +5.52172 q^{23} +1.00000 q^{25} -11.1705 q^{26} -0.915025 q^{28} -9.07040 q^{29} +2.91047 q^{31} -4.11614 q^{32} -0.329581 q^{34} -1.19579 q^{35} +1.00129 q^{37} +9.78671 q^{38} -2.05332 q^{40} -9.69562 q^{41} -6.27832 q^{43} +1.31326 q^{44} +9.18202 q^{46} -4.24748 q^{47} -5.57010 q^{49} +1.66289 q^{50} -5.14029 q^{52} -8.93237 q^{53} +1.71622 q^{55} +2.45534 q^{56} -15.0831 q^{58} -3.20445 q^{59} -10.8563 q^{61} +4.83979 q^{62} +3.04505 q^{64} -6.71750 q^{65} +15.0366 q^{67} -0.151663 q^{68} -1.98846 q^{70} -3.52924 q^{71} -3.36638 q^{73} +1.66503 q^{74} +4.50353 q^{76} -2.05223 q^{77} -5.21235 q^{79} -4.94487 q^{80} -16.1228 q^{82} -11.4175 q^{83} -0.198198 q^{85} -10.4402 q^{86} -3.52395 q^{88} -1.00000 q^{89} +8.03269 q^{91} +4.22526 q^{92} -7.06310 q^{94} +5.88536 q^{95} -12.3533 q^{97} -9.26247 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.66289 1.17584 0.587921 0.808918i \(-0.299947\pi\)
0.587921 + 0.808918i \(0.299947\pi\)
\(3\) 0 0
\(4\) 0.765209 0.382604
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.19579 −0.451964 −0.225982 0.974131i \(-0.572559\pi\)
−0.225982 + 0.974131i \(0.572559\pi\)
\(8\) −2.05332 −0.725960
\(9\) 0 0
\(10\) 1.66289 0.525853
\(11\) 1.71622 0.517459 0.258729 0.965950i \(-0.416696\pi\)
0.258729 + 0.965950i \(0.416696\pi\)
\(12\) 0 0
\(13\) −6.71750 −1.86310 −0.931550 0.363614i \(-0.881543\pi\)
−0.931550 + 0.363614i \(0.881543\pi\)
\(14\) −1.98846 −0.531439
\(15\) 0 0
\(16\) −4.94487 −1.23622
\(17\) −0.198198 −0.0480700 −0.0240350 0.999711i \(-0.507651\pi\)
−0.0240350 + 0.999711i \(0.507651\pi\)
\(18\) 0 0
\(19\) 5.88536 1.35019 0.675097 0.737729i \(-0.264102\pi\)
0.675097 + 0.737729i \(0.264102\pi\)
\(20\) 0.765209 0.171106
\(21\) 0 0
\(22\) 2.85388 0.608449
\(23\) 5.52172 1.15136 0.575679 0.817676i \(-0.304738\pi\)
0.575679 + 0.817676i \(0.304738\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −11.1705 −2.19071
\(27\) 0 0
\(28\) −0.915025 −0.172924
\(29\) −9.07040 −1.68433 −0.842165 0.539219i \(-0.818719\pi\)
−0.842165 + 0.539219i \(0.818719\pi\)
\(30\) 0 0
\(31\) 2.91047 0.522735 0.261368 0.965239i \(-0.415827\pi\)
0.261368 + 0.965239i \(0.415827\pi\)
\(32\) −4.11614 −0.727638
\(33\) 0 0
\(34\) −0.329581 −0.0565227
\(35\) −1.19579 −0.202125
\(36\) 0 0
\(37\) 1.00129 0.164610 0.0823052 0.996607i \(-0.473772\pi\)
0.0823052 + 0.996607i \(0.473772\pi\)
\(38\) 9.78671 1.58761
\(39\) 0 0
\(40\) −2.05332 −0.324659
\(41\) −9.69562 −1.51420 −0.757101 0.653298i \(-0.773385\pi\)
−0.757101 + 0.653298i \(0.773385\pi\)
\(42\) 0 0
\(43\) −6.27832 −0.957435 −0.478718 0.877969i \(-0.658898\pi\)
−0.478718 + 0.877969i \(0.658898\pi\)
\(44\) 1.31326 0.197982
\(45\) 0 0
\(46\) 9.18202 1.35381
\(47\) −4.24748 −0.619559 −0.309780 0.950808i \(-0.600255\pi\)
−0.309780 + 0.950808i \(0.600255\pi\)
\(48\) 0 0
\(49\) −5.57010 −0.795728
\(50\) 1.66289 0.235168
\(51\) 0 0
\(52\) −5.14029 −0.712830
\(53\) −8.93237 −1.22696 −0.613478 0.789712i \(-0.710230\pi\)
−0.613478 + 0.789712i \(0.710230\pi\)
\(54\) 0 0
\(55\) 1.71622 0.231415
\(56\) 2.45534 0.328108
\(57\) 0 0
\(58\) −15.0831 −1.98051
\(59\) −3.20445 −0.417184 −0.208592 0.978003i \(-0.566888\pi\)
−0.208592 + 0.978003i \(0.566888\pi\)
\(60\) 0 0
\(61\) −10.8563 −1.39001 −0.695004 0.719006i \(-0.744598\pi\)
−0.695004 + 0.719006i \(0.744598\pi\)
\(62\) 4.83979 0.614654
\(63\) 0 0
\(64\) 3.04505 0.380632
\(65\) −6.71750 −0.833204
\(66\) 0 0
\(67\) 15.0366 1.83701 0.918505 0.395409i \(-0.129397\pi\)
0.918505 + 0.395409i \(0.129397\pi\)
\(68\) −0.151663 −0.0183918
\(69\) 0 0
\(70\) −1.98846 −0.237667
\(71\) −3.52924 −0.418843 −0.209422 0.977825i \(-0.567158\pi\)
−0.209422 + 0.977825i \(0.567158\pi\)
\(72\) 0 0
\(73\) −3.36638 −0.394004 −0.197002 0.980403i \(-0.563121\pi\)
−0.197002 + 0.980403i \(0.563121\pi\)
\(74\) 1.66503 0.193556
\(75\) 0 0
\(76\) 4.50353 0.516590
\(77\) −2.05223 −0.233873
\(78\) 0 0
\(79\) −5.21235 −0.586435 −0.293217 0.956046i \(-0.594726\pi\)
−0.293217 + 0.956046i \(0.594726\pi\)
\(80\) −4.94487 −0.552854
\(81\) 0 0
\(82\) −16.1228 −1.78046
\(83\) −11.4175 −1.25323 −0.626616 0.779328i \(-0.715560\pi\)
−0.626616 + 0.779328i \(0.715560\pi\)
\(84\) 0 0
\(85\) −0.198198 −0.0214976
\(86\) −10.4402 −1.12579
\(87\) 0 0
\(88\) −3.52395 −0.375654
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) 8.03269 0.842055
\(92\) 4.22526 0.440514
\(93\) 0 0
\(94\) −7.06310 −0.728504
\(95\) 5.88536 0.603825
\(96\) 0 0
\(97\) −12.3533 −1.25429 −0.627145 0.778903i \(-0.715777\pi\)
−0.627145 + 0.778903i \(0.715777\pi\)
\(98\) −9.26247 −0.935651
\(99\) 0 0
\(100\) 0.765209 0.0765209
\(101\) 13.8431 1.37744 0.688719 0.725029i \(-0.258174\pi\)
0.688719 + 0.725029i \(0.258174\pi\)
\(102\) 0 0
\(103\) −2.82296 −0.278155 −0.139077 0.990282i \(-0.544414\pi\)
−0.139077 + 0.990282i \(0.544414\pi\)
\(104\) 13.7932 1.35254
\(105\) 0 0
\(106\) −14.8536 −1.44271
\(107\) −14.4241 −1.39443 −0.697214 0.716863i \(-0.745577\pi\)
−0.697214 + 0.716863i \(0.745577\pi\)
\(108\) 0 0
\(109\) −11.2682 −1.07929 −0.539647 0.841892i \(-0.681442\pi\)
−0.539647 + 0.841892i \(0.681442\pi\)
\(110\) 2.85388 0.272107
\(111\) 0 0
\(112\) 5.91301 0.558727
\(113\) 6.97824 0.656458 0.328229 0.944598i \(-0.393548\pi\)
0.328229 + 0.944598i \(0.393548\pi\)
\(114\) 0 0
\(115\) 5.52172 0.514903
\(116\) −6.94075 −0.644432
\(117\) 0 0
\(118\) −5.32866 −0.490543
\(119\) 0.237002 0.0217259
\(120\) 0 0
\(121\) −8.05460 −0.732237
\(122\) −18.0529 −1.63443
\(123\) 0 0
\(124\) 2.22711 0.200001
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 12.7488 1.13127 0.565636 0.824655i \(-0.308631\pi\)
0.565636 + 0.824655i \(0.308631\pi\)
\(128\) 13.2959 1.17520
\(129\) 0 0
\(130\) −11.1705 −0.979716
\(131\) −14.2498 −1.24501 −0.622505 0.782616i \(-0.713885\pi\)
−0.622505 + 0.782616i \(0.713885\pi\)
\(132\) 0 0
\(133\) −7.03763 −0.610240
\(134\) 25.0042 2.16003
\(135\) 0 0
\(136\) 0.406964 0.0348969
\(137\) −12.5956 −1.07611 −0.538055 0.842909i \(-0.680841\pi\)
−0.538055 + 0.842909i \(0.680841\pi\)
\(138\) 0 0
\(139\) 20.2156 1.71466 0.857330 0.514766i \(-0.172121\pi\)
0.857330 + 0.514766i \(0.172121\pi\)
\(140\) −0.915025 −0.0773338
\(141\) 0 0
\(142\) −5.86874 −0.492493
\(143\) −11.5287 −0.964077
\(144\) 0 0
\(145\) −9.07040 −0.753256
\(146\) −5.59792 −0.463287
\(147\) 0 0
\(148\) 0.766192 0.0629806
\(149\) 21.1805 1.73518 0.867588 0.497283i \(-0.165669\pi\)
0.867588 + 0.497283i \(0.165669\pi\)
\(150\) 0 0
\(151\) 6.83007 0.555824 0.277912 0.960607i \(-0.410358\pi\)
0.277912 + 0.960607i \(0.410358\pi\)
\(152\) −12.0846 −0.980187
\(153\) 0 0
\(154\) −3.41263 −0.274998
\(155\) 2.91047 0.233774
\(156\) 0 0
\(157\) 8.11228 0.647430 0.323715 0.946155i \(-0.395068\pi\)
0.323715 + 0.946155i \(0.395068\pi\)
\(158\) −8.66757 −0.689555
\(159\) 0 0
\(160\) −4.11614 −0.325409
\(161\) −6.60279 −0.520373
\(162\) 0 0
\(163\) 0.775772 0.0607632 0.0303816 0.999538i \(-0.490328\pi\)
0.0303816 + 0.999538i \(0.490328\pi\)
\(164\) −7.41917 −0.579340
\(165\) 0 0
\(166\) −18.9860 −1.47360
\(167\) 8.31329 0.643302 0.321651 0.946858i \(-0.395762\pi\)
0.321651 + 0.946858i \(0.395762\pi\)
\(168\) 0 0
\(169\) 32.1248 2.47114
\(170\) −0.329581 −0.0252777
\(171\) 0 0
\(172\) −4.80423 −0.366319
\(173\) −2.84871 −0.216584 −0.108292 0.994119i \(-0.534538\pi\)
−0.108292 + 0.994119i \(0.534538\pi\)
\(174\) 0 0
\(175\) −1.19579 −0.0903929
\(176\) −8.48647 −0.639692
\(177\) 0 0
\(178\) −1.66289 −0.124639
\(179\) 11.2580 0.841461 0.420730 0.907186i \(-0.361774\pi\)
0.420730 + 0.907186i \(0.361774\pi\)
\(180\) 0 0
\(181\) 6.89728 0.512671 0.256336 0.966588i \(-0.417485\pi\)
0.256336 + 0.966588i \(0.417485\pi\)
\(182\) 13.3575 0.990123
\(183\) 0 0
\(184\) −11.3379 −0.835839
\(185\) 1.00129 0.0736160
\(186\) 0 0
\(187\) −0.340150 −0.0248742
\(188\) −3.25021 −0.237046
\(189\) 0 0
\(190\) 9.78671 0.710003
\(191\) 14.6743 1.06179 0.530897 0.847436i \(-0.321855\pi\)
0.530897 + 0.847436i \(0.321855\pi\)
\(192\) 0 0
\(193\) −11.6706 −0.840068 −0.420034 0.907508i \(-0.637982\pi\)
−0.420034 + 0.907508i \(0.637982\pi\)
\(194\) −20.5422 −1.47485
\(195\) 0 0
\(196\) −4.26229 −0.304449
\(197\) −13.1956 −0.940147 −0.470074 0.882627i \(-0.655773\pi\)
−0.470074 + 0.882627i \(0.655773\pi\)
\(198\) 0 0
\(199\) 10.1226 0.717575 0.358788 0.933419i \(-0.383190\pi\)
0.358788 + 0.933419i \(0.383190\pi\)
\(200\) −2.05332 −0.145192
\(201\) 0 0
\(202\) 23.0195 1.61965
\(203\) 10.8463 0.761258
\(204\) 0 0
\(205\) −9.69562 −0.677172
\(206\) −4.69428 −0.327066
\(207\) 0 0
\(208\) 33.2172 2.30320
\(209\) 10.1005 0.698669
\(210\) 0 0
\(211\) 12.8961 0.887802 0.443901 0.896076i \(-0.353594\pi\)
0.443901 + 0.896076i \(0.353594\pi\)
\(212\) −6.83513 −0.469438
\(213\) 0 0
\(214\) −23.9857 −1.63963
\(215\) −6.27832 −0.428178
\(216\) 0 0
\(217\) −3.48029 −0.236258
\(218\) −18.7377 −1.26908
\(219\) 0 0
\(220\) 1.31326 0.0885402
\(221\) 1.33139 0.0895592
\(222\) 0 0
\(223\) 11.2759 0.755090 0.377545 0.925991i \(-0.376768\pi\)
0.377545 + 0.925991i \(0.376768\pi\)
\(224\) 4.92202 0.328866
\(225\) 0 0
\(226\) 11.6041 0.771891
\(227\) −5.26072 −0.349167 −0.174583 0.984642i \(-0.555858\pi\)
−0.174583 + 0.984642i \(0.555858\pi\)
\(228\) 0 0
\(229\) 27.7381 1.83298 0.916492 0.400054i \(-0.131008\pi\)
0.916492 + 0.400054i \(0.131008\pi\)
\(230\) 9.18202 0.605444
\(231\) 0 0
\(232\) 18.6245 1.22276
\(233\) −12.9676 −0.849533 −0.424766 0.905303i \(-0.639644\pi\)
−0.424766 + 0.905303i \(0.639644\pi\)
\(234\) 0 0
\(235\) −4.24748 −0.277075
\(236\) −2.45207 −0.159616
\(237\) 0 0
\(238\) 0.394109 0.0255463
\(239\) 2.84490 0.184021 0.0920106 0.995758i \(-0.470671\pi\)
0.0920106 + 0.995758i \(0.470671\pi\)
\(240\) 0 0
\(241\) 15.4580 0.995736 0.497868 0.867253i \(-0.334116\pi\)
0.497868 + 0.867253i \(0.334116\pi\)
\(242\) −13.3939 −0.860995
\(243\) 0 0
\(244\) −8.30735 −0.531823
\(245\) −5.57010 −0.355860
\(246\) 0 0
\(247\) −39.5349 −2.51555
\(248\) −5.97613 −0.379485
\(249\) 0 0
\(250\) 1.66289 0.105171
\(251\) −15.5422 −0.981016 −0.490508 0.871437i \(-0.663189\pi\)
−0.490508 + 0.871437i \(0.663189\pi\)
\(252\) 0 0
\(253\) 9.47646 0.595780
\(254\) 21.1999 1.33020
\(255\) 0 0
\(256\) 16.0195 1.00122
\(257\) 18.4372 1.15008 0.575040 0.818125i \(-0.304986\pi\)
0.575040 + 0.818125i \(0.304986\pi\)
\(258\) 0 0
\(259\) −1.19732 −0.0743980
\(260\) −5.14029 −0.318787
\(261\) 0 0
\(262\) −23.6959 −1.46394
\(263\) −1.37018 −0.0844891 −0.0422445 0.999107i \(-0.513451\pi\)
−0.0422445 + 0.999107i \(0.513451\pi\)
\(264\) 0 0
\(265\) −8.93237 −0.548711
\(266\) −11.7028 −0.717545
\(267\) 0 0
\(268\) 11.5061 0.702848
\(269\) −12.6384 −0.770580 −0.385290 0.922796i \(-0.625899\pi\)
−0.385290 + 0.922796i \(0.625899\pi\)
\(270\) 0 0
\(271\) −12.8509 −0.780635 −0.390317 0.920680i \(-0.627635\pi\)
−0.390317 + 0.920680i \(0.627635\pi\)
\(272\) 0.980063 0.0594250
\(273\) 0 0
\(274\) −20.9450 −1.26534
\(275\) 1.71622 0.103492
\(276\) 0 0
\(277\) −25.5069 −1.53256 −0.766279 0.642508i \(-0.777894\pi\)
−0.766279 + 0.642508i \(0.777894\pi\)
\(278\) 33.6163 2.01617
\(279\) 0 0
\(280\) 2.45534 0.146734
\(281\) 10.0582 0.600022 0.300011 0.953936i \(-0.403010\pi\)
0.300011 + 0.953936i \(0.403010\pi\)
\(282\) 0 0
\(283\) −11.8405 −0.703848 −0.351924 0.936029i \(-0.614472\pi\)
−0.351924 + 0.936029i \(0.614472\pi\)
\(284\) −2.70060 −0.160251
\(285\) 0 0
\(286\) −19.1710 −1.13360
\(287\) 11.5939 0.684365
\(288\) 0 0
\(289\) −16.9607 −0.997689
\(290\) −15.0831 −0.885710
\(291\) 0 0
\(292\) −2.57598 −0.150748
\(293\) −19.8376 −1.15893 −0.579463 0.814999i \(-0.696738\pi\)
−0.579463 + 0.814999i \(0.696738\pi\)
\(294\) 0 0
\(295\) −3.20445 −0.186570
\(296\) −2.05596 −0.119500
\(297\) 0 0
\(298\) 35.2209 2.04029
\(299\) −37.0921 −2.14509
\(300\) 0 0
\(301\) 7.50753 0.432727
\(302\) 11.3577 0.653561
\(303\) 0 0
\(304\) −29.1024 −1.66913
\(305\) −10.8563 −0.621631
\(306\) 0 0
\(307\) −3.32228 −0.189613 −0.0948064 0.995496i \(-0.530223\pi\)
−0.0948064 + 0.995496i \(0.530223\pi\)
\(308\) −1.57038 −0.0894808
\(309\) 0 0
\(310\) 4.83979 0.274882
\(311\) −10.8962 −0.617869 −0.308934 0.951083i \(-0.599972\pi\)
−0.308934 + 0.951083i \(0.599972\pi\)
\(312\) 0 0
\(313\) 3.60276 0.203640 0.101820 0.994803i \(-0.467533\pi\)
0.101820 + 0.994803i \(0.467533\pi\)
\(314\) 13.4898 0.761276
\(315\) 0 0
\(316\) −3.98853 −0.224372
\(317\) −8.70500 −0.488921 −0.244461 0.969659i \(-0.578611\pi\)
−0.244461 + 0.969659i \(0.578611\pi\)
\(318\) 0 0
\(319\) −15.5668 −0.871571
\(320\) 3.04505 0.170224
\(321\) 0 0
\(322\) −10.9797 −0.611876
\(323\) −1.16647 −0.0649039
\(324\) 0 0
\(325\) −6.71750 −0.372620
\(326\) 1.29003 0.0714479
\(327\) 0 0
\(328\) 19.9083 1.09925
\(329\) 5.07908 0.280019
\(330\) 0 0
\(331\) −28.9163 −1.58938 −0.794691 0.607014i \(-0.792367\pi\)
−0.794691 + 0.607014i \(0.792367\pi\)
\(332\) −8.73676 −0.479492
\(333\) 0 0
\(334\) 13.8241 0.756421
\(335\) 15.0366 0.821536
\(336\) 0 0
\(337\) −3.14680 −0.171417 −0.0857085 0.996320i \(-0.527315\pi\)
−0.0857085 + 0.996320i \(0.527315\pi\)
\(338\) 53.4201 2.90567
\(339\) 0 0
\(340\) −0.151663 −0.00822506
\(341\) 4.99499 0.270494
\(342\) 0 0
\(343\) 15.0311 0.811605
\(344\) 12.8914 0.695060
\(345\) 0 0
\(346\) −4.73710 −0.254668
\(347\) 15.4128 0.827405 0.413702 0.910412i \(-0.364235\pi\)
0.413702 + 0.910412i \(0.364235\pi\)
\(348\) 0 0
\(349\) 20.5617 1.10064 0.550322 0.834952i \(-0.314505\pi\)
0.550322 + 0.834952i \(0.314505\pi\)
\(350\) −1.98846 −0.106288
\(351\) 0 0
\(352\) −7.06418 −0.376522
\(353\) −33.5463 −1.78549 −0.892745 0.450563i \(-0.851223\pi\)
−0.892745 + 0.450563i \(0.851223\pi\)
\(354\) 0 0
\(355\) −3.52924 −0.187312
\(356\) −0.765209 −0.0405560
\(357\) 0 0
\(358\) 18.7208 0.989425
\(359\) 17.2671 0.911321 0.455660 0.890154i \(-0.349403\pi\)
0.455660 + 0.890154i \(0.349403\pi\)
\(360\) 0 0
\(361\) 15.6375 0.823024
\(362\) 11.4694 0.602820
\(363\) 0 0
\(364\) 6.14668 0.322174
\(365\) −3.36638 −0.176204
\(366\) 0 0
\(367\) 12.8203 0.669215 0.334608 0.942358i \(-0.391396\pi\)
0.334608 + 0.942358i \(0.391396\pi\)
\(368\) −27.3042 −1.42333
\(369\) 0 0
\(370\) 1.66503 0.0865608
\(371\) 10.6812 0.554540
\(372\) 0 0
\(373\) 23.0233 1.19210 0.596051 0.802947i \(-0.296736\pi\)
0.596051 + 0.802947i \(0.296736\pi\)
\(374\) −0.565633 −0.0292482
\(375\) 0 0
\(376\) 8.72146 0.449775
\(377\) 60.9304 3.13808
\(378\) 0 0
\(379\) −3.39286 −0.174279 −0.0871397 0.996196i \(-0.527773\pi\)
−0.0871397 + 0.996196i \(0.527773\pi\)
\(380\) 4.50353 0.231026
\(381\) 0 0
\(382\) 24.4017 1.24850
\(383\) 20.1762 1.03096 0.515479 0.856902i \(-0.327614\pi\)
0.515479 + 0.856902i \(0.327614\pi\)
\(384\) 0 0
\(385\) −2.05223 −0.104591
\(386\) −19.4069 −0.987787
\(387\) 0 0
\(388\) −9.45287 −0.479897
\(389\) 7.30763 0.370512 0.185256 0.982690i \(-0.440689\pi\)
0.185256 + 0.982690i \(0.440689\pi\)
\(390\) 0 0
\(391\) −1.09439 −0.0553458
\(392\) 11.4372 0.577667
\(393\) 0 0
\(394\) −21.9428 −1.10546
\(395\) −5.21235 −0.262262
\(396\) 0 0
\(397\) −23.5261 −1.18074 −0.590372 0.807131i \(-0.701019\pi\)
−0.590372 + 0.807131i \(0.701019\pi\)
\(398\) 16.8329 0.843755
\(399\) 0 0
\(400\) −4.94487 −0.247244
\(401\) 25.2928 1.26306 0.631531 0.775351i \(-0.282427\pi\)
0.631531 + 0.775351i \(0.282427\pi\)
\(402\) 0 0
\(403\) −19.5511 −0.973908
\(404\) 10.5928 0.527013
\(405\) 0 0
\(406\) 18.0361 0.895119
\(407\) 1.71842 0.0851790
\(408\) 0 0
\(409\) −15.0516 −0.744252 −0.372126 0.928182i \(-0.621371\pi\)
−0.372126 + 0.928182i \(0.621371\pi\)
\(410\) −16.1228 −0.796247
\(411\) 0 0
\(412\) −2.16016 −0.106423
\(413\) 3.83184 0.188552
\(414\) 0 0
\(415\) −11.4175 −0.560462
\(416\) 27.6502 1.35566
\(417\) 0 0
\(418\) 16.7961 0.821525
\(419\) −16.8945 −0.825352 −0.412676 0.910878i \(-0.635406\pi\)
−0.412676 + 0.910878i \(0.635406\pi\)
\(420\) 0 0
\(421\) 30.0518 1.46464 0.732319 0.680962i \(-0.238438\pi\)
0.732319 + 0.680962i \(0.238438\pi\)
\(422\) 21.4448 1.04391
\(423\) 0 0
\(424\) 18.3411 0.890720
\(425\) −0.198198 −0.00961400
\(426\) 0 0
\(427\) 12.9818 0.628234
\(428\) −11.0374 −0.533514
\(429\) 0 0
\(430\) −10.4402 −0.503470
\(431\) −30.4221 −1.46538 −0.732690 0.680562i \(-0.761736\pi\)
−0.732690 + 0.680562i \(0.761736\pi\)
\(432\) 0 0
\(433\) −3.56731 −0.171434 −0.0857169 0.996320i \(-0.527318\pi\)
−0.0857169 + 0.996320i \(0.527318\pi\)
\(434\) −5.78735 −0.277802
\(435\) 0 0
\(436\) −8.62249 −0.412942
\(437\) 32.4973 1.55456
\(438\) 0 0
\(439\) 26.6626 1.27254 0.636269 0.771467i \(-0.280477\pi\)
0.636269 + 0.771467i \(0.280477\pi\)
\(440\) −3.52395 −0.167998
\(441\) 0 0
\(442\) 2.21396 0.105308
\(443\) −28.8940 −1.37280 −0.686398 0.727226i \(-0.740809\pi\)
−0.686398 + 0.727226i \(0.740809\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) 18.7506 0.887867
\(447\) 0 0
\(448\) −3.64123 −0.172032
\(449\) 0.202083 0.00953690 0.00476845 0.999989i \(-0.498482\pi\)
0.00476845 + 0.999989i \(0.498482\pi\)
\(450\) 0 0
\(451\) −16.6398 −0.783537
\(452\) 5.33981 0.251164
\(453\) 0 0
\(454\) −8.74801 −0.410565
\(455\) 8.03269 0.376578
\(456\) 0 0
\(457\) 31.8993 1.49219 0.746094 0.665841i \(-0.231927\pi\)
0.746094 + 0.665841i \(0.231927\pi\)
\(458\) 46.1254 2.15530
\(459\) 0 0
\(460\) 4.22526 0.197004
\(461\) −14.8233 −0.690390 −0.345195 0.938531i \(-0.612187\pi\)
−0.345195 + 0.938531i \(0.612187\pi\)
\(462\) 0 0
\(463\) −15.0952 −0.701532 −0.350766 0.936463i \(-0.614079\pi\)
−0.350766 + 0.936463i \(0.614079\pi\)
\(464\) 44.8520 2.08220
\(465\) 0 0
\(466\) −21.5636 −0.998916
\(467\) −26.4862 −1.22564 −0.612818 0.790224i \(-0.709964\pi\)
−0.612818 + 0.790224i \(0.709964\pi\)
\(468\) 0 0
\(469\) −17.9805 −0.830264
\(470\) −7.06310 −0.325797
\(471\) 0 0
\(472\) 6.57978 0.302859
\(473\) −10.7750 −0.495433
\(474\) 0 0
\(475\) 5.88536 0.270039
\(476\) 0.181356 0.00831244
\(477\) 0 0
\(478\) 4.73076 0.216380
\(479\) 38.6539 1.76614 0.883071 0.469240i \(-0.155472\pi\)
0.883071 + 0.469240i \(0.155472\pi\)
\(480\) 0 0
\(481\) −6.72614 −0.306685
\(482\) 25.7050 1.17083
\(483\) 0 0
\(484\) −6.16345 −0.280157
\(485\) −12.3533 −0.560936
\(486\) 0 0
\(487\) 43.2894 1.96163 0.980814 0.194946i \(-0.0624531\pi\)
0.980814 + 0.194946i \(0.0624531\pi\)
\(488\) 22.2915 1.00909
\(489\) 0 0
\(490\) −9.26247 −0.418436
\(491\) −6.88098 −0.310534 −0.155267 0.987873i \(-0.549624\pi\)
−0.155267 + 0.987873i \(0.549624\pi\)
\(492\) 0 0
\(493\) 1.79773 0.0809658
\(494\) −65.7423 −2.95788
\(495\) 0 0
\(496\) −14.3919 −0.646215
\(497\) 4.22021 0.189302
\(498\) 0 0
\(499\) 7.61190 0.340756 0.170378 0.985379i \(-0.445501\pi\)
0.170378 + 0.985379i \(0.445501\pi\)
\(500\) 0.765209 0.0342212
\(501\) 0 0
\(502\) −25.8450 −1.15352
\(503\) 1.51948 0.0677503 0.0338752 0.999426i \(-0.489215\pi\)
0.0338752 + 0.999426i \(0.489215\pi\)
\(504\) 0 0
\(505\) 13.8431 0.616009
\(506\) 15.7583 0.700543
\(507\) 0 0
\(508\) 9.75549 0.432830
\(509\) −0.581726 −0.0257845 −0.0128923 0.999917i \(-0.504104\pi\)
−0.0128923 + 0.999917i \(0.504104\pi\)
\(510\) 0 0
\(511\) 4.02546 0.178076
\(512\) 0.0469310 0.00207408
\(513\) 0 0
\(514\) 30.6590 1.35231
\(515\) −2.82296 −0.124395
\(516\) 0 0
\(517\) −7.28960 −0.320596
\(518\) −1.99102 −0.0874803
\(519\) 0 0
\(520\) 13.7932 0.604872
\(521\) −24.8734 −1.08972 −0.544862 0.838526i \(-0.683418\pi\)
−0.544862 + 0.838526i \(0.683418\pi\)
\(522\) 0 0
\(523\) 3.87994 0.169658 0.0848290 0.996396i \(-0.472966\pi\)
0.0848290 + 0.996396i \(0.472966\pi\)
\(524\) −10.9041 −0.476346
\(525\) 0 0
\(526\) −2.27847 −0.0993458
\(527\) −0.576848 −0.0251279
\(528\) 0 0
\(529\) 7.48935 0.325624
\(530\) −14.8536 −0.645198
\(531\) 0 0
\(532\) −5.38525 −0.233480
\(533\) 65.1304 2.82111
\(534\) 0 0
\(535\) −14.4241 −0.623607
\(536\) −30.8750 −1.33360
\(537\) 0 0
\(538\) −21.0164 −0.906080
\(539\) −9.55949 −0.411756
\(540\) 0 0
\(541\) −2.04133 −0.0877634 −0.0438817 0.999037i \(-0.513972\pi\)
−0.0438817 + 0.999037i \(0.513972\pi\)
\(542\) −21.3696 −0.917903
\(543\) 0 0
\(544\) 0.815810 0.0349776
\(545\) −11.2682 −0.482675
\(546\) 0 0
\(547\) −2.56220 −0.109552 −0.0547760 0.998499i \(-0.517444\pi\)
−0.0547760 + 0.998499i \(0.517444\pi\)
\(548\) −9.63823 −0.411725
\(549\) 0 0
\(550\) 2.85388 0.121690
\(551\) −53.3826 −2.27417
\(552\) 0 0
\(553\) 6.23285 0.265048
\(554\) −42.4151 −1.80205
\(555\) 0 0
\(556\) 15.4691 0.656037
\(557\) −17.4626 −0.739913 −0.369957 0.929049i \(-0.620627\pi\)
−0.369957 + 0.929049i \(0.620627\pi\)
\(558\) 0 0
\(559\) 42.1746 1.78380
\(560\) 5.91301 0.249870
\(561\) 0 0
\(562\) 16.7257 0.705531
\(563\) −28.7597 −1.21208 −0.606039 0.795435i \(-0.707243\pi\)
−0.606039 + 0.795435i \(0.707243\pi\)
\(564\) 0 0
\(565\) 6.97824 0.293577
\(566\) −19.6895 −0.827613
\(567\) 0 0
\(568\) 7.24667 0.304063
\(569\) −15.4946 −0.649566 −0.324783 0.945789i \(-0.605291\pi\)
−0.324783 + 0.945789i \(0.605291\pi\)
\(570\) 0 0
\(571\) −5.95093 −0.249039 −0.124519 0.992217i \(-0.539739\pi\)
−0.124519 + 0.992217i \(0.539739\pi\)
\(572\) −8.82185 −0.368860
\(573\) 0 0
\(574\) 19.2794 0.804706
\(575\) 5.52172 0.230271
\(576\) 0 0
\(577\) −16.1544 −0.672517 −0.336258 0.941770i \(-0.609162\pi\)
−0.336258 + 0.941770i \(0.609162\pi\)
\(578\) −28.2038 −1.17312
\(579\) 0 0
\(580\) −6.94075 −0.288199
\(581\) 13.6529 0.566416
\(582\) 0 0
\(583\) −15.3299 −0.634899
\(584\) 6.91226 0.286031
\(585\) 0 0
\(586\) −32.9878 −1.36271
\(587\) −11.3500 −0.468467 −0.234233 0.972180i \(-0.575258\pi\)
−0.234233 + 0.972180i \(0.575258\pi\)
\(588\) 0 0
\(589\) 17.1291 0.705794
\(590\) −5.32866 −0.219377
\(591\) 0 0
\(592\) −4.95123 −0.203494
\(593\) −41.0239 −1.68465 −0.842325 0.538970i \(-0.818814\pi\)
−0.842325 + 0.538970i \(0.818814\pi\)
\(594\) 0 0
\(595\) 0.237002 0.00971614
\(596\) 16.2075 0.663886
\(597\) 0 0
\(598\) −61.6802 −2.52229
\(599\) 27.9781 1.14316 0.571578 0.820548i \(-0.306331\pi\)
0.571578 + 0.820548i \(0.306331\pi\)
\(600\) 0 0
\(601\) 12.6344 0.515367 0.257683 0.966229i \(-0.417041\pi\)
0.257683 + 0.966229i \(0.417041\pi\)
\(602\) 12.4842 0.508818
\(603\) 0 0
\(604\) 5.22643 0.212660
\(605\) −8.05460 −0.327466
\(606\) 0 0
\(607\) −14.4981 −0.588459 −0.294229 0.955735i \(-0.595063\pi\)
−0.294229 + 0.955735i \(0.595063\pi\)
\(608\) −24.2250 −0.982452
\(609\) 0 0
\(610\) −18.0529 −0.730940
\(611\) 28.5325 1.15430
\(612\) 0 0
\(613\) −14.5975 −0.589589 −0.294794 0.955561i \(-0.595251\pi\)
−0.294794 + 0.955561i \(0.595251\pi\)
\(614\) −5.52460 −0.222955
\(615\) 0 0
\(616\) 4.21389 0.169782
\(617\) −16.4323 −0.661541 −0.330771 0.943711i \(-0.607309\pi\)
−0.330771 + 0.943711i \(0.607309\pi\)
\(618\) 0 0
\(619\) 29.9391 1.20335 0.601677 0.798740i \(-0.294500\pi\)
0.601677 + 0.798740i \(0.294500\pi\)
\(620\) 2.22711 0.0894431
\(621\) 0 0
\(622\) −18.1193 −0.726516
\(623\) 1.19579 0.0479081
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 5.99100 0.239448
\(627\) 0 0
\(628\) 6.20758 0.247710
\(629\) −0.198453 −0.00791282
\(630\) 0 0
\(631\) −17.8242 −0.709571 −0.354786 0.934948i \(-0.615446\pi\)
−0.354786 + 0.934948i \(0.615446\pi\)
\(632\) 10.7026 0.425728
\(633\) 0 0
\(634\) −14.4755 −0.574894
\(635\) 12.7488 0.505920
\(636\) 0 0
\(637\) 37.4171 1.48252
\(638\) −25.8858 −1.02483
\(639\) 0 0
\(640\) 13.2959 0.525565
\(641\) −8.57421 −0.338661 −0.169330 0.985559i \(-0.554160\pi\)
−0.169330 + 0.985559i \(0.554160\pi\)
\(642\) 0 0
\(643\) 1.12722 0.0444531 0.0222266 0.999753i \(-0.492924\pi\)
0.0222266 + 0.999753i \(0.492924\pi\)
\(644\) −5.05251 −0.199097
\(645\) 0 0
\(646\) −1.93971 −0.0763167
\(647\) −3.85176 −0.151428 −0.0757141 0.997130i \(-0.524124\pi\)
−0.0757141 + 0.997130i \(0.524124\pi\)
\(648\) 0 0
\(649\) −5.49953 −0.215875
\(650\) −11.1705 −0.438142
\(651\) 0 0
\(652\) 0.593628 0.0232483
\(653\) 27.7221 1.08485 0.542426 0.840104i \(-0.317506\pi\)
0.542426 + 0.840104i \(0.317506\pi\)
\(654\) 0 0
\(655\) −14.2498 −0.556786
\(656\) 47.9436 1.87188
\(657\) 0 0
\(658\) 8.44596 0.329258
\(659\) 15.6657 0.610249 0.305125 0.952312i \(-0.401302\pi\)
0.305125 + 0.952312i \(0.401302\pi\)
\(660\) 0 0
\(661\) 45.3528 1.76402 0.882009 0.471233i \(-0.156191\pi\)
0.882009 + 0.471233i \(0.156191\pi\)
\(662\) −48.0847 −1.86886
\(663\) 0 0
\(664\) 23.4438 0.909796
\(665\) −7.03763 −0.272907
\(666\) 0 0
\(667\) −50.0842 −1.93927
\(668\) 6.36140 0.246130
\(669\) 0 0
\(670\) 25.0042 0.965997
\(671\) −18.6318 −0.719272
\(672\) 0 0
\(673\) 45.0019 1.73470 0.867348 0.497702i \(-0.165823\pi\)
0.867348 + 0.497702i \(0.165823\pi\)
\(674\) −5.23278 −0.201559
\(675\) 0 0
\(676\) 24.5822 0.945469
\(677\) −9.10467 −0.349921 −0.174960 0.984575i \(-0.555980\pi\)
−0.174960 + 0.984575i \(0.555980\pi\)
\(678\) 0 0
\(679\) 14.7719 0.566894
\(680\) 0.406964 0.0156064
\(681\) 0 0
\(682\) 8.30613 0.318058
\(683\) 16.3302 0.624856 0.312428 0.949941i \(-0.398858\pi\)
0.312428 + 0.949941i \(0.398858\pi\)
\(684\) 0 0
\(685\) −12.5956 −0.481251
\(686\) 24.9952 0.954320
\(687\) 0 0
\(688\) 31.0455 1.18360
\(689\) 60.0032 2.28594
\(690\) 0 0
\(691\) −9.41243 −0.358066 −0.179033 0.983843i \(-0.557297\pi\)
−0.179033 + 0.983843i \(0.557297\pi\)
\(692\) −2.17986 −0.0828659
\(693\) 0 0
\(694\) 25.6299 0.972897
\(695\) 20.2156 0.766820
\(696\) 0 0
\(697\) 1.92165 0.0727877
\(698\) 34.1919 1.29418
\(699\) 0 0
\(700\) −0.915025 −0.0345847
\(701\) 19.5729 0.739257 0.369628 0.929180i \(-0.379485\pi\)
0.369628 + 0.929180i \(0.379485\pi\)
\(702\) 0 0
\(703\) 5.89293 0.222256
\(704\) 5.22597 0.196961
\(705\) 0 0
\(706\) −55.7839 −2.09945
\(707\) −16.5533 −0.622553
\(708\) 0 0
\(709\) 20.6409 0.775187 0.387593 0.921830i \(-0.373307\pi\)
0.387593 + 0.921830i \(0.373307\pi\)
\(710\) −5.86874 −0.220250
\(711\) 0 0
\(712\) 2.05332 0.0769516
\(713\) 16.0708 0.601855
\(714\) 0 0
\(715\) −11.5287 −0.431148
\(716\) 8.61470 0.321946
\(717\) 0 0
\(718\) 28.7133 1.07157
\(719\) −1.99007 −0.0742169 −0.0371085 0.999311i \(-0.511815\pi\)
−0.0371085 + 0.999311i \(0.511815\pi\)
\(720\) 0 0
\(721\) 3.37566 0.125716
\(722\) 26.0034 0.967746
\(723\) 0 0
\(724\) 5.27786 0.196150
\(725\) −9.07040 −0.336866
\(726\) 0 0
\(727\) 22.1638 0.822009 0.411005 0.911633i \(-0.365178\pi\)
0.411005 + 0.911633i \(0.365178\pi\)
\(728\) −16.4937 −0.611298
\(729\) 0 0
\(730\) −5.59792 −0.207188
\(731\) 1.24435 0.0460239
\(732\) 0 0
\(733\) 25.4198 0.938903 0.469452 0.882958i \(-0.344452\pi\)
0.469452 + 0.882958i \(0.344452\pi\)
\(734\) 21.3188 0.786891
\(735\) 0 0
\(736\) −22.7282 −0.837771
\(737\) 25.8060 0.950577
\(738\) 0 0
\(739\) −22.8759 −0.841502 −0.420751 0.907176i \(-0.638233\pi\)
−0.420751 + 0.907176i \(0.638233\pi\)
\(740\) 0.766192 0.0281658
\(741\) 0 0
\(742\) 17.7617 0.652052
\(743\) −33.2907 −1.22132 −0.610658 0.791894i \(-0.709095\pi\)
−0.610658 + 0.791894i \(0.709095\pi\)
\(744\) 0 0
\(745\) 21.1805 0.775994
\(746\) 38.2852 1.40172
\(747\) 0 0
\(748\) −0.260286 −0.00951699
\(749\) 17.2481 0.630232
\(750\) 0 0
\(751\) −28.3081 −1.03298 −0.516488 0.856294i \(-0.672761\pi\)
−0.516488 + 0.856294i \(0.672761\pi\)
\(752\) 21.0033 0.765910
\(753\) 0 0
\(754\) 101.321 3.68988
\(755\) 6.83007 0.248572
\(756\) 0 0
\(757\) −32.0207 −1.16381 −0.581906 0.813256i \(-0.697693\pi\)
−0.581906 + 0.813256i \(0.697693\pi\)
\(758\) −5.64196 −0.204925
\(759\) 0 0
\(760\) −12.0846 −0.438353
\(761\) −8.64233 −0.313284 −0.156642 0.987655i \(-0.550067\pi\)
−0.156642 + 0.987655i \(0.550067\pi\)
\(762\) 0 0
\(763\) 13.4743 0.487802
\(764\) 11.2289 0.406247
\(765\) 0 0
\(766\) 33.5509 1.21224
\(767\) 21.5259 0.777255
\(768\) 0 0
\(769\) −40.1270 −1.44702 −0.723509 0.690315i \(-0.757472\pi\)
−0.723509 + 0.690315i \(0.757472\pi\)
\(770\) −3.41263 −0.122983
\(771\) 0 0
\(772\) −8.93044 −0.321414
\(773\) 2.23597 0.0804221 0.0402111 0.999191i \(-0.487197\pi\)
0.0402111 + 0.999191i \(0.487197\pi\)
\(774\) 0 0
\(775\) 2.91047 0.104547
\(776\) 25.3654 0.910564
\(777\) 0 0
\(778\) 12.1518 0.435663
\(779\) −57.0622 −2.04447
\(780\) 0 0
\(781\) −6.05693 −0.216734
\(782\) −1.81986 −0.0650779
\(783\) 0 0
\(784\) 27.5434 0.983694
\(785\) 8.11228 0.289540
\(786\) 0 0
\(787\) −8.85057 −0.315489 −0.157744 0.987480i \(-0.550422\pi\)
−0.157744 + 0.987480i \(0.550422\pi\)
\(788\) −10.0974 −0.359704
\(789\) 0 0
\(790\) −8.66757 −0.308378
\(791\) −8.34448 −0.296696
\(792\) 0 0
\(793\) 72.9273 2.58972
\(794\) −39.1214 −1.38837
\(795\) 0 0
\(796\) 7.74593 0.274547
\(797\) 9.35770 0.331467 0.165733 0.986171i \(-0.447001\pi\)
0.165733 + 0.986171i \(0.447001\pi\)
\(798\) 0 0
\(799\) 0.841842 0.0297822
\(800\) −4.11614 −0.145528
\(801\) 0 0
\(802\) 42.0592 1.48516
\(803\) −5.77743 −0.203881
\(804\) 0 0
\(805\) −6.60279 −0.232718
\(806\) −32.5113 −1.14516
\(807\) 0 0
\(808\) −28.4243 −0.999964
\(809\) 11.3616 0.399452 0.199726 0.979852i \(-0.435995\pi\)
0.199726 + 0.979852i \(0.435995\pi\)
\(810\) 0 0
\(811\) −0.473846 −0.0166390 −0.00831950 0.999965i \(-0.502648\pi\)
−0.00831950 + 0.999965i \(0.502648\pi\)
\(812\) 8.29964 0.291260
\(813\) 0 0
\(814\) 2.85755 0.100157
\(815\) 0.775772 0.0271741
\(816\) 0 0
\(817\) −36.9502 −1.29272
\(818\) −25.0291 −0.875122
\(819\) 0 0
\(820\) −7.41917 −0.259089
\(821\) 20.7434 0.723950 0.361975 0.932188i \(-0.382103\pi\)
0.361975 + 0.932188i \(0.382103\pi\)
\(822\) 0 0
\(823\) −1.18591 −0.0413381 −0.0206691 0.999786i \(-0.506580\pi\)
−0.0206691 + 0.999786i \(0.506580\pi\)
\(824\) 5.79646 0.201929
\(825\) 0 0
\(826\) 6.37193 0.221708
\(827\) 3.91986 0.136307 0.0681535 0.997675i \(-0.478289\pi\)
0.0681535 + 0.997675i \(0.478289\pi\)
\(828\) 0 0
\(829\) −22.6555 −0.786858 −0.393429 0.919355i \(-0.628711\pi\)
−0.393429 + 0.919355i \(0.628711\pi\)
\(830\) −18.9860 −0.659015
\(831\) 0 0
\(832\) −20.4551 −0.709154
\(833\) 1.10398 0.0382507
\(834\) 0 0
\(835\) 8.31329 0.287693
\(836\) 7.72903 0.267314
\(837\) 0 0
\(838\) −28.0938 −0.970484
\(839\) 19.8509 0.685330 0.342665 0.939458i \(-0.388670\pi\)
0.342665 + 0.939458i \(0.388670\pi\)
\(840\) 0 0
\(841\) 53.2721 1.83697
\(842\) 49.9730 1.72218
\(843\) 0 0
\(844\) 9.86818 0.339677
\(845\) 32.1248 1.10513
\(846\) 0 0
\(847\) 9.63158 0.330945
\(848\) 44.1694 1.51678
\(849\) 0 0
\(850\) −0.329581 −0.0113045
\(851\) 5.52881 0.189525
\(852\) 0 0
\(853\) 24.6566 0.844224 0.422112 0.906544i \(-0.361289\pi\)
0.422112 + 0.906544i \(0.361289\pi\)
\(854\) 21.5874 0.738704
\(855\) 0 0
\(856\) 29.6173 1.01230
\(857\) −38.0292 −1.29905 −0.649526 0.760339i \(-0.725033\pi\)
−0.649526 + 0.760339i \(0.725033\pi\)
\(858\) 0 0
\(859\) 2.74130 0.0935321 0.0467660 0.998906i \(-0.485108\pi\)
0.0467660 + 0.998906i \(0.485108\pi\)
\(860\) −4.80423 −0.163823
\(861\) 0 0
\(862\) −50.5887 −1.72306
\(863\) 55.9189 1.90350 0.951750 0.306874i \(-0.0992831\pi\)
0.951750 + 0.306874i \(0.0992831\pi\)
\(864\) 0 0
\(865\) −2.84871 −0.0968592
\(866\) −5.93204 −0.201579
\(867\) 0 0
\(868\) −2.66315 −0.0903932
\(869\) −8.94551 −0.303456
\(870\) 0 0
\(871\) −101.008 −3.42253
\(872\) 23.1372 0.783524
\(873\) 0 0
\(874\) 54.0395 1.82791
\(875\) −1.19579 −0.0404249
\(876\) 0 0
\(877\) 8.89562 0.300384 0.150192 0.988657i \(-0.452011\pi\)
0.150192 + 0.988657i \(0.452011\pi\)
\(878\) 44.3371 1.49630
\(879\) 0 0
\(880\) −8.48647 −0.286079
\(881\) −36.7358 −1.23766 −0.618831 0.785524i \(-0.712393\pi\)
−0.618831 + 0.785524i \(0.712393\pi\)
\(882\) 0 0
\(883\) −32.5930 −1.09684 −0.548422 0.836202i \(-0.684771\pi\)
−0.548422 + 0.836202i \(0.684771\pi\)
\(884\) 1.01879 0.0342658
\(885\) 0 0
\(886\) −48.0476 −1.61419
\(887\) −17.7696 −0.596646 −0.298323 0.954465i \(-0.596427\pi\)
−0.298323 + 0.954465i \(0.596427\pi\)
\(888\) 0 0
\(889\) −15.2448 −0.511295
\(890\) −1.66289 −0.0557403
\(891\) 0 0
\(892\) 8.62842 0.288901
\(893\) −24.9980 −0.836525
\(894\) 0 0
\(895\) 11.2580 0.376313
\(896\) −15.8990 −0.531149
\(897\) 0 0
\(898\) 0.336043 0.0112139
\(899\) −26.3991 −0.880459
\(900\) 0 0
\(901\) 1.77038 0.0589798
\(902\) −27.6702 −0.921315
\(903\) 0 0
\(904\) −14.3286 −0.476562
\(905\) 6.89728 0.229273
\(906\) 0 0
\(907\) 34.2038 1.13572 0.567860 0.823125i \(-0.307772\pi\)
0.567860 + 0.823125i \(0.307772\pi\)
\(908\) −4.02555 −0.133593
\(909\) 0 0
\(910\) 13.3575 0.442797
\(911\) 4.05202 0.134249 0.0671246 0.997745i \(-0.478617\pi\)
0.0671246 + 0.997745i \(0.478617\pi\)
\(912\) 0 0
\(913\) −19.5949 −0.648495
\(914\) 53.0451 1.75458
\(915\) 0 0
\(916\) 21.2254 0.701307
\(917\) 17.0397 0.562700
\(918\) 0 0
\(919\) 28.2709 0.932571 0.466285 0.884634i \(-0.345592\pi\)
0.466285 + 0.884634i \(0.345592\pi\)
\(920\) −11.3379 −0.373799
\(921\) 0 0
\(922\) −24.6495 −0.811790
\(923\) 23.7076 0.780347
\(924\) 0 0
\(925\) 1.00129 0.0329221
\(926\) −25.1016 −0.824890
\(927\) 0 0
\(928\) 37.3350 1.22558
\(929\) 36.5851 1.20032 0.600159 0.799881i \(-0.295104\pi\)
0.600159 + 0.799881i \(0.295104\pi\)
\(930\) 0 0
\(931\) −32.7820 −1.07439
\(932\) −9.92289 −0.325035
\(933\) 0 0
\(934\) −44.0437 −1.44115
\(935\) −0.340150 −0.0111241
\(936\) 0 0
\(937\) 27.3092 0.892153 0.446076 0.894995i \(-0.352821\pi\)
0.446076 + 0.894995i \(0.352821\pi\)
\(938\) −29.8997 −0.976259
\(939\) 0 0
\(940\) −3.25021 −0.106010
\(941\) 22.8368 0.744457 0.372228 0.928141i \(-0.378594\pi\)
0.372228 + 0.928141i \(0.378594\pi\)
\(942\) 0 0
\(943\) −53.5365 −1.74339
\(944\) 15.8456 0.515731
\(945\) 0 0
\(946\) −17.9176 −0.582551
\(947\) −9.04038 −0.293773 −0.146887 0.989153i \(-0.546925\pi\)
−0.146887 + 0.989153i \(0.546925\pi\)
\(948\) 0 0
\(949\) 22.6136 0.734070
\(950\) 9.78671 0.317523
\(951\) 0 0
\(952\) −0.486642 −0.0157722
\(953\) 34.7105 1.12438 0.562192 0.827007i \(-0.309958\pi\)
0.562192 + 0.827007i \(0.309958\pi\)
\(954\) 0 0
\(955\) 14.6743 0.474849
\(956\) 2.17694 0.0704073
\(957\) 0 0
\(958\) 64.2772 2.07670
\(959\) 15.0616 0.486364
\(960\) 0 0
\(961\) −22.5292 −0.726748
\(962\) −11.1848 −0.360614
\(963\) 0 0
\(964\) 11.8286 0.380973
\(965\) −11.6706 −0.375690
\(966\) 0 0
\(967\) −48.0870 −1.54637 −0.773187 0.634178i \(-0.781339\pi\)
−0.773187 + 0.634178i \(0.781339\pi\)
\(968\) 16.5387 0.531574
\(969\) 0 0
\(970\) −20.5422 −0.659572
\(971\) −60.5323 −1.94257 −0.971287 0.237912i \(-0.923537\pi\)
−0.971287 + 0.237912i \(0.923537\pi\)
\(972\) 0 0
\(973\) −24.1735 −0.774966
\(974\) 71.9855 2.30656
\(975\) 0 0
\(976\) 53.6831 1.71835
\(977\) 34.0996 1.09094 0.545472 0.838129i \(-0.316351\pi\)
0.545472 + 0.838129i \(0.316351\pi\)
\(978\) 0 0
\(979\) −1.71622 −0.0548505
\(980\) −4.26229 −0.136154
\(981\) 0 0
\(982\) −11.4423 −0.365139
\(983\) 38.6982 1.23428 0.617141 0.786853i \(-0.288291\pi\)
0.617141 + 0.786853i \(0.288291\pi\)
\(984\) 0 0
\(985\) −13.1956 −0.420447
\(986\) 2.98943 0.0952030
\(987\) 0 0
\(988\) −30.2525 −0.962459
\(989\) −34.6671 −1.10235
\(990\) 0 0
\(991\) −5.87602 −0.186658 −0.0933290 0.995635i \(-0.529751\pi\)
−0.0933290 + 0.995635i \(0.529751\pi\)
\(992\) −11.9799 −0.380362
\(993\) 0 0
\(994\) 7.01775 0.222590
\(995\) 10.1226 0.320909
\(996\) 0 0
\(997\) −42.1823 −1.33593 −0.667963 0.744195i \(-0.732834\pi\)
−0.667963 + 0.744195i \(0.732834\pi\)
\(998\) 12.6578 0.400675
\(999\) 0 0
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 \(a_p\))