Properties

Label 6003.2.a.t.1.9
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.06922 q^{2} -0.856774 q^{4} +0.420836 q^{5} +1.13415 q^{7} +3.05451 q^{8} +O(q^{10})\) \(q-1.06922 q^{2} -0.856774 q^{4} +0.420836 q^{5} +1.13415 q^{7} +3.05451 q^{8} -0.449966 q^{10} -2.91779 q^{11} -1.70064 q^{13} -1.21266 q^{14} -1.55239 q^{16} +0.536110 q^{17} +0.585904 q^{19} -0.360562 q^{20} +3.11976 q^{22} +1.00000 q^{23} -4.82290 q^{25} +1.81835 q^{26} -0.971713 q^{28} +1.00000 q^{29} +7.49962 q^{31} -4.44918 q^{32} -0.573218 q^{34} +0.477293 q^{35} -1.22414 q^{37} -0.626459 q^{38} +1.28545 q^{40} +12.2002 q^{41} -2.78460 q^{43} +2.49989 q^{44} -1.06922 q^{46} +0.180494 q^{47} -5.71370 q^{49} +5.15673 q^{50} +1.45706 q^{52} -11.0675 q^{53} -1.22791 q^{55} +3.46429 q^{56} -1.06922 q^{58} -5.86452 q^{59} +12.1083 q^{61} -8.01872 q^{62} +7.86192 q^{64} -0.715690 q^{65} -14.3374 q^{67} -0.459325 q^{68} -0.510330 q^{70} +13.2457 q^{71} -4.56789 q^{73} +1.30887 q^{74} -0.501988 q^{76} -3.30923 q^{77} -6.89701 q^{79} -0.653302 q^{80} -13.0447 q^{82} -8.57178 q^{83} +0.225614 q^{85} +2.97734 q^{86} -8.91244 q^{88} +2.75169 q^{89} -1.92878 q^{91} -0.856774 q^{92} -0.192988 q^{94} +0.246570 q^{95} -7.28509 q^{97} +6.10918 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06922 −0.756051 −0.378025 0.925795i \(-0.623397\pi\)
−0.378025 + 0.925795i \(0.623397\pi\)
\(3\) 0 0
\(4\) −0.856774 −0.428387
\(5\) 0.420836 0.188204 0.0941019 0.995563i \(-0.470002\pi\)
0.0941019 + 0.995563i \(0.470002\pi\)
\(6\) 0 0
\(7\) 1.13415 0.428670 0.214335 0.976760i \(-0.431242\pi\)
0.214335 + 0.976760i \(0.431242\pi\)
\(8\) 3.05451 1.07993
\(9\) 0 0
\(10\) −0.449966 −0.142292
\(11\) −2.91779 −0.879748 −0.439874 0.898059i \(-0.644977\pi\)
−0.439874 + 0.898059i \(0.644977\pi\)
\(12\) 0 0
\(13\) −1.70064 −0.471672 −0.235836 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(14\) −1.21266 −0.324096
\(15\) 0 0
\(16\) −1.55239 −0.388097
\(17\) 0.536110 0.130026 0.0650128 0.997884i \(-0.479291\pi\)
0.0650128 + 0.997884i \(0.479291\pi\)
\(18\) 0 0
\(19\) 0.585904 0.134416 0.0672078 0.997739i \(-0.478591\pi\)
0.0672078 + 0.997739i \(0.478591\pi\)
\(20\) −0.360562 −0.0806240
\(21\) 0 0
\(22\) 3.11976 0.665134
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.82290 −0.964579
\(26\) 1.81835 0.356608
\(27\) 0 0
\(28\) −0.971713 −0.183637
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 7.49962 1.34697 0.673486 0.739200i \(-0.264796\pi\)
0.673486 + 0.739200i \(0.264796\pi\)
\(32\) −4.44918 −0.786512
\(33\) 0 0
\(34\) −0.573218 −0.0983060
\(35\) 0.477293 0.0806772
\(36\) 0 0
\(37\) −1.22414 −0.201247 −0.100623 0.994925i \(-0.532084\pi\)
−0.100623 + 0.994925i \(0.532084\pi\)
\(38\) −0.626459 −0.101625
\(39\) 0 0
\(40\) 1.28545 0.203247
\(41\) 12.2002 1.90535 0.952676 0.303987i \(-0.0983179\pi\)
0.952676 + 0.303987i \(0.0983179\pi\)
\(42\) 0 0
\(43\) −2.78460 −0.424647 −0.212324 0.977199i \(-0.568103\pi\)
−0.212324 + 0.977199i \(0.568103\pi\)
\(44\) 2.49989 0.376873
\(45\) 0 0
\(46\) −1.06922 −0.157648
\(47\) 0.180494 0.0263278 0.0131639 0.999913i \(-0.495810\pi\)
0.0131639 + 0.999913i \(0.495810\pi\)
\(48\) 0 0
\(49\) −5.71370 −0.816242
\(50\) 5.15673 0.729271
\(51\) 0 0
\(52\) 1.45706 0.202058
\(53\) −11.0675 −1.52023 −0.760116 0.649787i \(-0.774858\pi\)
−0.760116 + 0.649787i \(0.774858\pi\)
\(54\) 0 0
\(55\) −1.22791 −0.165572
\(56\) 3.46429 0.462935
\(57\) 0 0
\(58\) −1.06922 −0.140395
\(59\) −5.86452 −0.763496 −0.381748 0.924266i \(-0.624678\pi\)
−0.381748 + 0.924266i \(0.624678\pi\)
\(60\) 0 0
\(61\) 12.1083 1.55031 0.775153 0.631773i \(-0.217673\pi\)
0.775153 + 0.631773i \(0.217673\pi\)
\(62\) −8.01872 −1.01838
\(63\) 0 0
\(64\) 7.86192 0.982740
\(65\) −0.715690 −0.0887705
\(66\) 0 0
\(67\) −14.3374 −1.75159 −0.875794 0.482686i \(-0.839661\pi\)
−0.875794 + 0.482686i \(0.839661\pi\)
\(68\) −0.459325 −0.0557013
\(69\) 0 0
\(70\) −0.510330 −0.0609961
\(71\) 13.2457 1.57198 0.785988 0.618242i \(-0.212155\pi\)
0.785988 + 0.618242i \(0.212155\pi\)
\(72\) 0 0
\(73\) −4.56789 −0.534632 −0.267316 0.963609i \(-0.586137\pi\)
−0.267316 + 0.963609i \(0.586137\pi\)
\(74\) 1.30887 0.152153
\(75\) 0 0
\(76\) −0.501988 −0.0575819
\(77\) −3.30923 −0.377121
\(78\) 0 0
\(79\) −6.89701 −0.775974 −0.387987 0.921665i \(-0.626829\pi\)
−0.387987 + 0.921665i \(0.626829\pi\)
\(80\) −0.653302 −0.0730414
\(81\) 0 0
\(82\) −13.0447 −1.44054
\(83\) −8.57178 −0.940875 −0.470438 0.882433i \(-0.655904\pi\)
−0.470438 + 0.882433i \(0.655904\pi\)
\(84\) 0 0
\(85\) 0.225614 0.0244713
\(86\) 2.97734 0.321055
\(87\) 0 0
\(88\) −8.91244 −0.950069
\(89\) 2.75169 0.291678 0.145839 0.989308i \(-0.453412\pi\)
0.145839 + 0.989308i \(0.453412\pi\)
\(90\) 0 0
\(91\) −1.92878 −0.202192
\(92\) −0.856774 −0.0893249
\(93\) 0 0
\(94\) −0.192988 −0.0199052
\(95\) 0.246570 0.0252975
\(96\) 0 0
\(97\) −7.28509 −0.739689 −0.369844 0.929094i \(-0.620589\pi\)
−0.369844 + 0.929094i \(0.620589\pi\)
\(98\) 6.10918 0.617121
\(99\) 0 0
\(100\) 4.13213 0.413213
\(101\) −7.18183 −0.714618 −0.357309 0.933986i \(-0.616306\pi\)
−0.357309 + 0.933986i \(0.616306\pi\)
\(102\) 0 0
\(103\) 3.02471 0.298034 0.149017 0.988835i \(-0.452389\pi\)
0.149017 + 0.988835i \(0.452389\pi\)
\(104\) −5.19462 −0.509374
\(105\) 0 0
\(106\) 11.8335 1.14937
\(107\) 9.61926 0.929929 0.464965 0.885329i \(-0.346067\pi\)
0.464965 + 0.885329i \(0.346067\pi\)
\(108\) 0 0
\(109\) 10.0908 0.966521 0.483261 0.875477i \(-0.339452\pi\)
0.483261 + 0.875477i \(0.339452\pi\)
\(110\) 1.31291 0.125181
\(111\) 0 0
\(112\) −1.76065 −0.166366
\(113\) 6.82687 0.642218 0.321109 0.947042i \(-0.395944\pi\)
0.321109 + 0.947042i \(0.395944\pi\)
\(114\) 0 0
\(115\) 0.420836 0.0392432
\(116\) −0.856774 −0.0795495
\(117\) 0 0
\(118\) 6.27045 0.577242
\(119\) 0.608031 0.0557381
\(120\) 0 0
\(121\) −2.48647 −0.226043
\(122\) −12.9464 −1.17211
\(123\) 0 0
\(124\) −6.42548 −0.577025
\(125\) −4.13383 −0.369741
\(126\) 0 0
\(127\) −5.53291 −0.490967 −0.245483 0.969401i \(-0.578947\pi\)
−0.245483 + 0.969401i \(0.578947\pi\)
\(128\) 0.492261 0.0435101
\(129\) 0 0
\(130\) 0.765229 0.0671150
\(131\) 13.4974 1.17927 0.589637 0.807668i \(-0.299271\pi\)
0.589637 + 0.807668i \(0.299271\pi\)
\(132\) 0 0
\(133\) 0.664505 0.0576199
\(134\) 15.3298 1.32429
\(135\) 0 0
\(136\) 1.63755 0.140419
\(137\) 5.83987 0.498934 0.249467 0.968383i \(-0.419745\pi\)
0.249467 + 0.968383i \(0.419745\pi\)
\(138\) 0 0
\(139\) −22.3348 −1.89442 −0.947208 0.320619i \(-0.896109\pi\)
−0.947208 + 0.320619i \(0.896109\pi\)
\(140\) −0.408932 −0.0345611
\(141\) 0 0
\(142\) −14.1625 −1.18849
\(143\) 4.96211 0.414953
\(144\) 0 0
\(145\) 0.420836 0.0349486
\(146\) 4.88407 0.404209
\(147\) 0 0
\(148\) 1.04881 0.0862116
\(149\) −0.856186 −0.0701415 −0.0350707 0.999385i \(-0.511166\pi\)
−0.0350707 + 0.999385i \(0.511166\pi\)
\(150\) 0 0
\(151\) −5.82116 −0.473720 −0.236860 0.971544i \(-0.576118\pi\)
−0.236860 + 0.971544i \(0.576118\pi\)
\(152\) 1.78965 0.145160
\(153\) 0 0
\(154\) 3.53828 0.285123
\(155\) 3.15611 0.253505
\(156\) 0 0
\(157\) −1.59058 −0.126942 −0.0634709 0.997984i \(-0.520217\pi\)
−0.0634709 + 0.997984i \(0.520217\pi\)
\(158\) 7.37440 0.586676
\(159\) 0 0
\(160\) −1.87238 −0.148024
\(161\) 1.13415 0.0893838
\(162\) 0 0
\(163\) −9.80469 −0.767963 −0.383981 0.923341i \(-0.625447\pi\)
−0.383981 + 0.923341i \(0.625447\pi\)
\(164\) −10.4528 −0.816228
\(165\) 0 0
\(166\) 9.16510 0.711349
\(167\) 16.2385 1.25658 0.628288 0.777981i \(-0.283756\pi\)
0.628288 + 0.777981i \(0.283756\pi\)
\(168\) 0 0
\(169\) −10.1078 −0.777525
\(170\) −0.241231 −0.0185016
\(171\) 0 0
\(172\) 2.38577 0.181913
\(173\) −14.2547 −1.08376 −0.541881 0.840455i \(-0.682288\pi\)
−0.541881 + 0.840455i \(0.682288\pi\)
\(174\) 0 0
\(175\) −5.46991 −0.413486
\(176\) 4.52955 0.341428
\(177\) 0 0
\(178\) −2.94215 −0.220524
\(179\) 0.143629 0.0107353 0.00536766 0.999986i \(-0.498291\pi\)
0.00536766 + 0.999986i \(0.498291\pi\)
\(180\) 0 0
\(181\) −11.6508 −0.865997 −0.432998 0.901395i \(-0.642544\pi\)
−0.432998 + 0.901395i \(0.642544\pi\)
\(182\) 2.06229 0.152867
\(183\) 0 0
\(184\) 3.05451 0.225182
\(185\) −0.515161 −0.0378754
\(186\) 0 0
\(187\) −1.56426 −0.114390
\(188\) −0.154643 −0.0112785
\(189\) 0 0
\(190\) −0.263637 −0.0191262
\(191\) 26.1784 1.89420 0.947100 0.320939i \(-0.103998\pi\)
0.947100 + 0.320939i \(0.103998\pi\)
\(192\) 0 0
\(193\) 7.02480 0.505656 0.252828 0.967511i \(-0.418639\pi\)
0.252828 + 0.967511i \(0.418639\pi\)
\(194\) 7.78934 0.559242
\(195\) 0 0
\(196\) 4.89535 0.349668
\(197\) 3.74205 0.266610 0.133305 0.991075i \(-0.457441\pi\)
0.133305 + 0.991075i \(0.457441\pi\)
\(198\) 0 0
\(199\) 13.8087 0.978875 0.489437 0.872038i \(-0.337202\pi\)
0.489437 + 0.872038i \(0.337202\pi\)
\(200\) −14.7316 −1.04168
\(201\) 0 0
\(202\) 7.67893 0.540288
\(203\) 1.13415 0.0796020
\(204\) 0 0
\(205\) 5.13429 0.358594
\(206\) −3.23407 −0.225329
\(207\) 0 0
\(208\) 2.64005 0.183055
\(209\) −1.70955 −0.118252
\(210\) 0 0
\(211\) 5.17516 0.356273 0.178136 0.984006i \(-0.442993\pi\)
0.178136 + 0.984006i \(0.442993\pi\)
\(212\) 9.48231 0.651248
\(213\) 0 0
\(214\) −10.2851 −0.703074
\(215\) −1.17186 −0.0799202
\(216\) 0 0
\(217\) 8.50572 0.577406
\(218\) −10.7892 −0.730739
\(219\) 0 0
\(220\) 1.05205 0.0709289
\(221\) −0.911728 −0.0613295
\(222\) 0 0
\(223\) −12.8518 −0.860617 −0.430308 0.902682i \(-0.641595\pi\)
−0.430308 + 0.902682i \(0.641595\pi\)
\(224\) −5.04606 −0.337154
\(225\) 0 0
\(226\) −7.29941 −0.485550
\(227\) −12.5847 −0.835278 −0.417639 0.908613i \(-0.637142\pi\)
−0.417639 + 0.908613i \(0.637142\pi\)
\(228\) 0 0
\(229\) 19.4879 1.28779 0.643897 0.765112i \(-0.277316\pi\)
0.643897 + 0.765112i \(0.277316\pi\)
\(230\) −0.449966 −0.0296699
\(231\) 0 0
\(232\) 3.05451 0.200539
\(233\) −11.0040 −0.720893 −0.360446 0.932780i \(-0.617376\pi\)
−0.360446 + 0.932780i \(0.617376\pi\)
\(234\) 0 0
\(235\) 0.0759586 0.00495499
\(236\) 5.02457 0.327072
\(237\) 0 0
\(238\) −0.650117 −0.0421408
\(239\) 9.61008 0.621625 0.310812 0.950471i \(-0.399399\pi\)
0.310812 + 0.950471i \(0.399399\pi\)
\(240\) 0 0
\(241\) −5.96508 −0.384244 −0.192122 0.981371i \(-0.561537\pi\)
−0.192122 + 0.981371i \(0.561537\pi\)
\(242\) 2.65858 0.170900
\(243\) 0 0
\(244\) −10.3741 −0.664131
\(245\) −2.40453 −0.153620
\(246\) 0 0
\(247\) −0.996411 −0.0634001
\(248\) 22.9077 1.45464
\(249\) 0 0
\(250\) 4.41997 0.279543
\(251\) −9.33642 −0.589310 −0.294655 0.955604i \(-0.595205\pi\)
−0.294655 + 0.955604i \(0.595205\pi\)
\(252\) 0 0
\(253\) −2.91779 −0.183440
\(254\) 5.91589 0.371196
\(255\) 0 0
\(256\) −16.2502 −1.01564
\(257\) 27.9492 1.74342 0.871711 0.490021i \(-0.163011\pi\)
0.871711 + 0.490021i \(0.163011\pi\)
\(258\) 0 0
\(259\) −1.38836 −0.0862685
\(260\) 0.613185 0.0380281
\(261\) 0 0
\(262\) −14.4317 −0.891591
\(263\) −27.8535 −1.71752 −0.858760 0.512379i \(-0.828764\pi\)
−0.858760 + 0.512379i \(0.828764\pi\)
\(264\) 0 0
\(265\) −4.65759 −0.286113
\(266\) −0.710501 −0.0435636
\(267\) 0 0
\(268\) 12.2839 0.750357
\(269\) 8.33222 0.508025 0.254012 0.967201i \(-0.418250\pi\)
0.254012 + 0.967201i \(0.418250\pi\)
\(270\) 0 0
\(271\) −25.0222 −1.51999 −0.759995 0.649929i \(-0.774799\pi\)
−0.759995 + 0.649929i \(0.774799\pi\)
\(272\) −0.832251 −0.0504626
\(273\) 0 0
\(274\) −6.24409 −0.377219
\(275\) 14.0722 0.848587
\(276\) 0 0
\(277\) −17.5910 −1.05694 −0.528469 0.848952i \(-0.677234\pi\)
−0.528469 + 0.848952i \(0.677234\pi\)
\(278\) 23.8808 1.43228
\(279\) 0 0
\(280\) 1.45790 0.0871260
\(281\) 2.63805 0.157373 0.0786864 0.996899i \(-0.474927\pi\)
0.0786864 + 0.996899i \(0.474927\pi\)
\(282\) 0 0
\(283\) −16.9340 −1.00662 −0.503312 0.864105i \(-0.667885\pi\)
−0.503312 + 0.864105i \(0.667885\pi\)
\(284\) −11.3486 −0.673414
\(285\) 0 0
\(286\) −5.30558 −0.313725
\(287\) 13.8369 0.816767
\(288\) 0 0
\(289\) −16.7126 −0.983093
\(290\) −0.449966 −0.0264229
\(291\) 0 0
\(292\) 3.91365 0.229029
\(293\) 4.73836 0.276818 0.138409 0.990375i \(-0.455801\pi\)
0.138409 + 0.990375i \(0.455801\pi\)
\(294\) 0 0
\(295\) −2.46800 −0.143693
\(296\) −3.73914 −0.217333
\(297\) 0 0
\(298\) 0.915449 0.0530305
\(299\) −1.70064 −0.0983504
\(300\) 0 0
\(301\) −3.15816 −0.182034
\(302\) 6.22409 0.358156
\(303\) 0 0
\(304\) −0.909552 −0.0521664
\(305\) 5.09561 0.291774
\(306\) 0 0
\(307\) −34.0679 −1.94436 −0.972178 0.234243i \(-0.924739\pi\)
−0.972178 + 0.234243i \(0.924739\pi\)
\(308\) 2.83526 0.161554
\(309\) 0 0
\(310\) −3.37457 −0.191663
\(311\) −3.97157 −0.225207 −0.112604 0.993640i \(-0.535919\pi\)
−0.112604 + 0.993640i \(0.535919\pi\)
\(312\) 0 0
\(313\) 21.4087 1.21009 0.605045 0.796192i \(-0.293155\pi\)
0.605045 + 0.796192i \(0.293155\pi\)
\(314\) 1.70067 0.0959744
\(315\) 0 0
\(316\) 5.90918 0.332417
\(317\) −28.2785 −1.58828 −0.794140 0.607735i \(-0.792078\pi\)
−0.794140 + 0.607735i \(0.792078\pi\)
\(318\) 0 0
\(319\) −2.91779 −0.163365
\(320\) 3.30858 0.184955
\(321\) 0 0
\(322\) −1.21266 −0.0675787
\(323\) 0.314109 0.0174775
\(324\) 0 0
\(325\) 8.20200 0.454965
\(326\) 10.4833 0.580619
\(327\) 0 0
\(328\) 37.2657 2.05765
\(329\) 0.204708 0.0112859
\(330\) 0 0
\(331\) −17.6922 −0.972450 −0.486225 0.873834i \(-0.661627\pi\)
−0.486225 + 0.873834i \(0.661627\pi\)
\(332\) 7.34408 0.403059
\(333\) 0 0
\(334\) −17.3625 −0.950035
\(335\) −6.03368 −0.329655
\(336\) 0 0
\(337\) −19.4660 −1.06038 −0.530191 0.847878i \(-0.677880\pi\)
−0.530191 + 0.847878i \(0.677880\pi\)
\(338\) 10.8075 0.587849
\(339\) 0 0
\(340\) −0.193301 −0.0104832
\(341\) −21.8823 −1.18500
\(342\) 0 0
\(343\) −14.4193 −0.778568
\(344\) −8.50559 −0.458591
\(345\) 0 0
\(346\) 15.2413 0.819379
\(347\) −7.18999 −0.385979 −0.192989 0.981201i \(-0.561818\pi\)
−0.192989 + 0.981201i \(0.561818\pi\)
\(348\) 0 0
\(349\) 19.0083 1.01749 0.508746 0.860917i \(-0.330109\pi\)
0.508746 + 0.860917i \(0.330109\pi\)
\(350\) 5.84852 0.312616
\(351\) 0 0
\(352\) 12.9818 0.691932
\(353\) −3.18574 −0.169560 −0.0847799 0.996400i \(-0.527019\pi\)
−0.0847799 + 0.996400i \(0.527019\pi\)
\(354\) 0 0
\(355\) 5.57427 0.295852
\(356\) −2.35758 −0.124951
\(357\) 0 0
\(358\) −0.153571 −0.00811645
\(359\) 10.3826 0.547973 0.273986 0.961734i \(-0.411658\pi\)
0.273986 + 0.961734i \(0.411658\pi\)
\(360\) 0 0
\(361\) −18.6567 −0.981932
\(362\) 12.4572 0.654737
\(363\) 0 0
\(364\) 1.65253 0.0866163
\(365\) −1.92234 −0.100620
\(366\) 0 0
\(367\) 2.15378 0.112426 0.0562132 0.998419i \(-0.482097\pi\)
0.0562132 + 0.998419i \(0.482097\pi\)
\(368\) −1.55239 −0.0809239
\(369\) 0 0
\(370\) 0.550820 0.0286357
\(371\) −12.5522 −0.651678
\(372\) 0 0
\(373\) 10.6902 0.553517 0.276758 0.960940i \(-0.410740\pi\)
0.276758 + 0.960940i \(0.410740\pi\)
\(374\) 1.67253 0.0864846
\(375\) 0 0
\(376\) 0.551323 0.0284323
\(377\) −1.70064 −0.0875873
\(378\) 0 0
\(379\) 9.12577 0.468759 0.234380 0.972145i \(-0.424694\pi\)
0.234380 + 0.972145i \(0.424694\pi\)
\(380\) −0.211255 −0.0108371
\(381\) 0 0
\(382\) −27.9904 −1.43211
\(383\) −11.0898 −0.566663 −0.283332 0.959022i \(-0.591440\pi\)
−0.283332 + 0.959022i \(0.591440\pi\)
\(384\) 0 0
\(385\) −1.39264 −0.0709757
\(386\) −7.51104 −0.382302
\(387\) 0 0
\(388\) 6.24168 0.316873
\(389\) −7.52137 −0.381349 −0.190674 0.981653i \(-0.561067\pi\)
−0.190674 + 0.981653i \(0.561067\pi\)
\(390\) 0 0
\(391\) 0.536110 0.0271122
\(392\) −17.4526 −0.881487
\(393\) 0 0
\(394\) −4.00106 −0.201571
\(395\) −2.90251 −0.146041
\(396\) 0 0
\(397\) 7.78635 0.390786 0.195393 0.980725i \(-0.437402\pi\)
0.195393 + 0.980725i \(0.437402\pi\)
\(398\) −14.7645 −0.740079
\(399\) 0 0
\(400\) 7.48702 0.374351
\(401\) −29.2302 −1.45968 −0.729842 0.683616i \(-0.760406\pi\)
−0.729842 + 0.683616i \(0.760406\pi\)
\(402\) 0 0
\(403\) −12.7541 −0.635329
\(404\) 6.15320 0.306133
\(405\) 0 0
\(406\) −1.21266 −0.0601831
\(407\) 3.57178 0.177047
\(408\) 0 0
\(409\) −13.3398 −0.659611 −0.329806 0.944049i \(-0.606983\pi\)
−0.329806 + 0.944049i \(0.606983\pi\)
\(410\) −5.48967 −0.271116
\(411\) 0 0
\(412\) −2.59149 −0.127674
\(413\) −6.65127 −0.327288
\(414\) 0 0
\(415\) −3.60732 −0.177076
\(416\) 7.56645 0.370976
\(417\) 0 0
\(418\) 1.82788 0.0894045
\(419\) −28.6408 −1.39919 −0.699597 0.714537i \(-0.746637\pi\)
−0.699597 + 0.714537i \(0.746637\pi\)
\(420\) 0 0
\(421\) −35.9225 −1.75075 −0.875377 0.483441i \(-0.839387\pi\)
−0.875377 + 0.483441i \(0.839387\pi\)
\(422\) −5.53337 −0.269360
\(423\) 0 0
\(424\) −33.8057 −1.64175
\(425\) −2.58560 −0.125420
\(426\) 0 0
\(427\) 13.7327 0.664570
\(428\) −8.24154 −0.398370
\(429\) 0 0
\(430\) 1.25297 0.0604238
\(431\) −27.2374 −1.31198 −0.655989 0.754770i \(-0.727748\pi\)
−0.655989 + 0.754770i \(0.727748\pi\)
\(432\) 0 0
\(433\) −23.7658 −1.14211 −0.571057 0.820910i \(-0.693466\pi\)
−0.571057 + 0.820910i \(0.693466\pi\)
\(434\) −9.09446 −0.436548
\(435\) 0 0
\(436\) −8.64552 −0.414045
\(437\) 0.585904 0.0280276
\(438\) 0 0
\(439\) 27.4214 1.30875 0.654377 0.756169i \(-0.272931\pi\)
0.654377 + 0.756169i \(0.272931\pi\)
\(440\) −3.75068 −0.178807
\(441\) 0 0
\(442\) 0.974836 0.0463682
\(443\) −24.9966 −1.18763 −0.593813 0.804603i \(-0.702378\pi\)
−0.593813 + 0.804603i \(0.702378\pi\)
\(444\) 0 0
\(445\) 1.15801 0.0548950
\(446\) 13.7413 0.650670
\(447\) 0 0
\(448\) 8.91663 0.421271
\(449\) −19.5495 −0.922598 −0.461299 0.887245i \(-0.652616\pi\)
−0.461299 + 0.887245i \(0.652616\pi\)
\(450\) 0 0
\(451\) −35.5977 −1.67623
\(452\) −5.84909 −0.275118
\(453\) 0 0
\(454\) 13.4558 0.631512
\(455\) −0.811703 −0.0380532
\(456\) 0 0
\(457\) −11.7789 −0.550995 −0.275498 0.961302i \(-0.588843\pi\)
−0.275498 + 0.961302i \(0.588843\pi\)
\(458\) −20.8368 −0.973638
\(459\) 0 0
\(460\) −0.360562 −0.0168113
\(461\) 2.35402 0.109638 0.0548189 0.998496i \(-0.482542\pi\)
0.0548189 + 0.998496i \(0.482542\pi\)
\(462\) 0 0
\(463\) 33.5600 1.55967 0.779833 0.625988i \(-0.215304\pi\)
0.779833 + 0.625988i \(0.215304\pi\)
\(464\) −1.55239 −0.0720679
\(465\) 0 0
\(466\) 11.7656 0.545032
\(467\) 17.2653 0.798945 0.399472 0.916745i \(-0.369193\pi\)
0.399472 + 0.916745i \(0.369193\pi\)
\(468\) 0 0
\(469\) −16.2608 −0.750852
\(470\) −0.0812163 −0.00374623
\(471\) 0 0
\(472\) −17.9133 −0.824525
\(473\) 8.12489 0.373583
\(474\) 0 0
\(475\) −2.82576 −0.129655
\(476\) −0.520945 −0.0238775
\(477\) 0 0
\(478\) −10.2753 −0.469980
\(479\) −31.1558 −1.42354 −0.711771 0.702411i \(-0.752107\pi\)
−0.711771 + 0.702411i \(0.752107\pi\)
\(480\) 0 0
\(481\) 2.08181 0.0949226
\(482\) 6.37796 0.290508
\(483\) 0 0
\(484\) 2.13035 0.0968339
\(485\) −3.06583 −0.139212
\(486\) 0 0
\(487\) 13.4246 0.608326 0.304163 0.952620i \(-0.401623\pi\)
0.304163 + 0.952620i \(0.401623\pi\)
\(488\) 36.9849 1.67423
\(489\) 0 0
\(490\) 2.57097 0.116144
\(491\) −4.34995 −0.196310 −0.0981552 0.995171i \(-0.531294\pi\)
−0.0981552 + 0.995171i \(0.531294\pi\)
\(492\) 0 0
\(493\) 0.536110 0.0241452
\(494\) 1.06538 0.0479337
\(495\) 0 0
\(496\) −11.6423 −0.522756
\(497\) 15.0227 0.673858
\(498\) 0 0
\(499\) −34.3267 −1.53668 −0.768338 0.640044i \(-0.778916\pi\)
−0.768338 + 0.640044i \(0.778916\pi\)
\(500\) 3.54176 0.158392
\(501\) 0 0
\(502\) 9.98266 0.445548
\(503\) 35.4539 1.58081 0.790406 0.612584i \(-0.209870\pi\)
0.790406 + 0.612584i \(0.209870\pi\)
\(504\) 0 0
\(505\) −3.02237 −0.134494
\(506\) 3.11976 0.138690
\(507\) 0 0
\(508\) 4.74046 0.210324
\(509\) −11.3342 −0.502378 −0.251189 0.967938i \(-0.580822\pi\)
−0.251189 + 0.967938i \(0.580822\pi\)
\(510\) 0 0
\(511\) −5.18069 −0.229180
\(512\) 16.3905 0.724363
\(513\) 0 0
\(514\) −29.8837 −1.31812
\(515\) 1.27291 0.0560910
\(516\) 0 0
\(517\) −0.526646 −0.0231619
\(518\) 1.48446 0.0652234
\(519\) 0 0
\(520\) −2.18609 −0.0958662
\(521\) 13.6651 0.598679 0.299339 0.954147i \(-0.403234\pi\)
0.299339 + 0.954147i \(0.403234\pi\)
\(522\) 0 0
\(523\) 4.43578 0.193963 0.0969816 0.995286i \(-0.469081\pi\)
0.0969816 + 0.995286i \(0.469081\pi\)
\(524\) −11.5642 −0.505186
\(525\) 0 0
\(526\) 29.7814 1.29853
\(527\) 4.02062 0.175141
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 4.97997 0.216316
\(531\) 0 0
\(532\) −0.569331 −0.0246836
\(533\) −20.7481 −0.898702
\(534\) 0 0
\(535\) 4.04814 0.175016
\(536\) −43.7936 −1.89160
\(537\) 0 0
\(538\) −8.90896 −0.384092
\(539\) 16.6714 0.718088
\(540\) 0 0
\(541\) −43.6790 −1.87791 −0.938954 0.344044i \(-0.888203\pi\)
−0.938954 + 0.344044i \(0.888203\pi\)
\(542\) 26.7542 1.14919
\(543\) 0 0
\(544\) −2.38525 −0.102267
\(545\) 4.24657 0.181903
\(546\) 0 0
\(547\) −22.1181 −0.945702 −0.472851 0.881142i \(-0.656775\pi\)
−0.472851 + 0.881142i \(0.656775\pi\)
\(548\) −5.00345 −0.213737
\(549\) 0 0
\(550\) −15.0463 −0.641575
\(551\) 0.585904 0.0249604
\(552\) 0 0
\(553\) −7.82226 −0.332637
\(554\) 18.8086 0.799099
\(555\) 0 0
\(556\) 19.1359 0.811544
\(557\) 4.37611 0.185422 0.0927108 0.995693i \(-0.470447\pi\)
0.0927108 + 0.995693i \(0.470447\pi\)
\(558\) 0 0
\(559\) 4.73560 0.200294
\(560\) −0.740945 −0.0313106
\(561\) 0 0
\(562\) −2.82065 −0.118982
\(563\) −11.8239 −0.498318 −0.249159 0.968463i \(-0.580154\pi\)
−0.249159 + 0.968463i \(0.580154\pi\)
\(564\) 0 0
\(565\) 2.87300 0.120868
\(566\) 18.1062 0.761058
\(567\) 0 0
\(568\) 40.4592 1.69763
\(569\) −38.5706 −1.61696 −0.808482 0.588521i \(-0.799710\pi\)
−0.808482 + 0.588521i \(0.799710\pi\)
\(570\) 0 0
\(571\) 23.5913 0.987264 0.493632 0.869671i \(-0.335669\pi\)
0.493632 + 0.869671i \(0.335669\pi\)
\(572\) −4.25141 −0.177760
\(573\) 0 0
\(574\) −14.7947 −0.617517
\(575\) −4.82290 −0.201129
\(576\) 0 0
\(577\) 1.28918 0.0536692 0.0268346 0.999640i \(-0.491457\pi\)
0.0268346 + 0.999640i \(0.491457\pi\)
\(578\) 17.8694 0.743269
\(579\) 0 0
\(580\) −0.360562 −0.0149715
\(581\) −9.72172 −0.403325
\(582\) 0 0
\(583\) 32.2926 1.33742
\(584\) −13.9527 −0.577366
\(585\) 0 0
\(586\) −5.06634 −0.209288
\(587\) 7.18244 0.296451 0.148226 0.988954i \(-0.452644\pi\)
0.148226 + 0.988954i \(0.452644\pi\)
\(588\) 0 0
\(589\) 4.39406 0.181054
\(590\) 2.63883 0.108639
\(591\) 0 0
\(592\) 1.90034 0.0781034
\(593\) −29.1976 −1.19900 −0.599502 0.800373i \(-0.704635\pi\)
−0.599502 + 0.800373i \(0.704635\pi\)
\(594\) 0 0
\(595\) 0.255881 0.0104901
\(596\) 0.733558 0.0300477
\(597\) 0 0
\(598\) 1.81835 0.0743579
\(599\) 4.66540 0.190623 0.0953115 0.995448i \(-0.469615\pi\)
0.0953115 + 0.995448i \(0.469615\pi\)
\(600\) 0 0
\(601\) 25.9769 1.05962 0.529810 0.848117i \(-0.322263\pi\)
0.529810 + 0.848117i \(0.322263\pi\)
\(602\) 3.37676 0.137627
\(603\) 0 0
\(604\) 4.98742 0.202935
\(605\) −1.04640 −0.0425422
\(606\) 0 0
\(607\) −14.6632 −0.595162 −0.297581 0.954697i \(-0.596180\pi\)
−0.297581 + 0.954697i \(0.596180\pi\)
\(608\) −2.60680 −0.105720
\(609\) 0 0
\(610\) −5.44831 −0.220596
\(611\) −0.306956 −0.0124181
\(612\) 0 0
\(613\) −15.1212 −0.610741 −0.305371 0.952234i \(-0.598780\pi\)
−0.305371 + 0.952234i \(0.598780\pi\)
\(614\) 36.4260 1.47003
\(615\) 0 0
\(616\) −10.1081 −0.407266
\(617\) 8.37624 0.337215 0.168607 0.985683i \(-0.446073\pi\)
0.168607 + 0.985683i \(0.446073\pi\)
\(618\) 0 0
\(619\) 24.4794 0.983912 0.491956 0.870620i \(-0.336282\pi\)
0.491956 + 0.870620i \(0.336282\pi\)
\(620\) −2.70408 −0.108598
\(621\) 0 0
\(622\) 4.24648 0.170268
\(623\) 3.12084 0.125034
\(624\) 0 0
\(625\) 22.3748 0.894993
\(626\) −22.8905 −0.914889
\(627\) 0 0
\(628\) 1.36276 0.0543802
\(629\) −0.656272 −0.0261673
\(630\) 0 0
\(631\) −19.8813 −0.791463 −0.395731 0.918366i \(-0.629509\pi\)
−0.395731 + 0.918366i \(0.629509\pi\)
\(632\) −21.0670 −0.838000
\(633\) 0 0
\(634\) 30.2359 1.20082
\(635\) −2.32845 −0.0924018
\(636\) 0 0
\(637\) 9.71693 0.384999
\(638\) 3.11976 0.123512
\(639\) 0 0
\(640\) 0.207161 0.00818876
\(641\) −30.4724 −1.20359 −0.601793 0.798652i \(-0.705547\pi\)
−0.601793 + 0.798652i \(0.705547\pi\)
\(642\) 0 0
\(643\) 16.0989 0.634879 0.317440 0.948278i \(-0.397177\pi\)
0.317440 + 0.948278i \(0.397177\pi\)
\(644\) −0.971713 −0.0382909
\(645\) 0 0
\(646\) −0.335851 −0.0132139
\(647\) 26.4180 1.03860 0.519299 0.854593i \(-0.326193\pi\)
0.519299 + 0.854593i \(0.326193\pi\)
\(648\) 0 0
\(649\) 17.1115 0.671684
\(650\) −8.76972 −0.343977
\(651\) 0 0
\(652\) 8.40041 0.328985
\(653\) −29.0738 −1.13775 −0.568873 0.822425i \(-0.692621\pi\)
−0.568873 + 0.822425i \(0.692621\pi\)
\(654\) 0 0
\(655\) 5.68020 0.221944
\(656\) −18.9395 −0.739462
\(657\) 0 0
\(658\) −0.218878 −0.00853275
\(659\) −22.7601 −0.886607 −0.443303 0.896372i \(-0.646194\pi\)
−0.443303 + 0.896372i \(0.646194\pi\)
\(660\) 0 0
\(661\) 35.5742 1.38368 0.691838 0.722053i \(-0.256801\pi\)
0.691838 + 0.722053i \(0.256801\pi\)
\(662\) 18.9168 0.735222
\(663\) 0 0
\(664\) −26.1826 −1.01608
\(665\) 0.279648 0.0108443
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −13.9128 −0.538301
\(669\) 0 0
\(670\) 6.45132 0.249236
\(671\) −35.3295 −1.36388
\(672\) 0 0
\(673\) −45.9525 −1.77134 −0.885669 0.464318i \(-0.846300\pi\)
−0.885669 + 0.464318i \(0.846300\pi\)
\(674\) 20.8134 0.801703
\(675\) 0 0
\(676\) 8.66013 0.333082
\(677\) 48.5051 1.86420 0.932102 0.362196i \(-0.117973\pi\)
0.932102 + 0.362196i \(0.117973\pi\)
\(678\) 0 0
\(679\) −8.26241 −0.317082
\(680\) 0.689142 0.0264274
\(681\) 0 0
\(682\) 23.3970 0.895917
\(683\) −1.90270 −0.0728048 −0.0364024 0.999337i \(-0.511590\pi\)
−0.0364024 + 0.999337i \(0.511590\pi\)
\(684\) 0 0
\(685\) 2.45763 0.0939012
\(686\) 15.4173 0.588637
\(687\) 0 0
\(688\) 4.32278 0.164805
\(689\) 18.8217 0.717051
\(690\) 0 0
\(691\) 4.71656 0.179426 0.0897132 0.995968i \(-0.471405\pi\)
0.0897132 + 0.995968i \(0.471405\pi\)
\(692\) 12.2130 0.464270
\(693\) 0 0
\(694\) 7.68766 0.291820
\(695\) −9.39931 −0.356536
\(696\) 0 0
\(697\) 6.54065 0.247745
\(698\) −20.3240 −0.769276
\(699\) 0 0
\(700\) 4.68647 0.177132
\(701\) −21.6293 −0.816926 −0.408463 0.912775i \(-0.633935\pi\)
−0.408463 + 0.912775i \(0.633935\pi\)
\(702\) 0 0
\(703\) −0.717227 −0.0270507
\(704\) −22.9395 −0.864564
\(705\) 0 0
\(706\) 3.40625 0.128196
\(707\) −8.14529 −0.306335
\(708\) 0 0
\(709\) −9.74667 −0.366044 −0.183022 0.983109i \(-0.558588\pi\)
−0.183022 + 0.983109i \(0.558588\pi\)
\(710\) −5.96011 −0.223679
\(711\) 0 0
\(712\) 8.40507 0.314993
\(713\) 7.49962 0.280863
\(714\) 0 0
\(715\) 2.08824 0.0780957
\(716\) −0.123058 −0.00459888
\(717\) 0 0
\(718\) −11.1013 −0.414295
\(719\) 24.3097 0.906599 0.453300 0.891358i \(-0.350247\pi\)
0.453300 + 0.891358i \(0.350247\pi\)
\(720\) 0 0
\(721\) 3.43049 0.127758
\(722\) 19.9481 0.742391
\(723\) 0 0
\(724\) 9.98210 0.370982
\(725\) −4.82290 −0.179118
\(726\) 0 0
\(727\) 1.84325 0.0683625 0.0341812 0.999416i \(-0.489118\pi\)
0.0341812 + 0.999416i \(0.489118\pi\)
\(728\) −5.89150 −0.218353
\(729\) 0 0
\(730\) 2.05540 0.0760736
\(731\) −1.49285 −0.0552151
\(732\) 0 0
\(733\) −16.7848 −0.619961 −0.309981 0.950743i \(-0.600323\pi\)
−0.309981 + 0.950743i \(0.600323\pi\)
\(734\) −2.30286 −0.0850001
\(735\) 0 0
\(736\) −4.44918 −0.163999
\(737\) 41.8335 1.54096
\(738\) 0 0
\(739\) 43.0787 1.58467 0.792337 0.610083i \(-0.208864\pi\)
0.792337 + 0.610083i \(0.208864\pi\)
\(740\) 0.441377 0.0162253
\(741\) 0 0
\(742\) 13.4210 0.492701
\(743\) 0.629086 0.0230789 0.0115395 0.999933i \(-0.496327\pi\)
0.0115395 + 0.999933i \(0.496327\pi\)
\(744\) 0 0
\(745\) −0.360314 −0.0132009
\(746\) −11.4301 −0.418487
\(747\) 0 0
\(748\) 1.34022 0.0490031
\(749\) 10.9097 0.398633
\(750\) 0 0
\(751\) 32.3302 1.17975 0.589873 0.807496i \(-0.299178\pi\)
0.589873 + 0.807496i \(0.299178\pi\)
\(752\) −0.280198 −0.0102178
\(753\) 0 0
\(754\) 1.81835 0.0662205
\(755\) −2.44976 −0.0891558
\(756\) 0 0
\(757\) 41.8728 1.52189 0.760946 0.648815i \(-0.224735\pi\)
0.760946 + 0.648815i \(0.224735\pi\)
\(758\) −9.75744 −0.354406
\(759\) 0 0
\(760\) 0.753151 0.0273196
\(761\) 22.7021 0.822950 0.411475 0.911421i \(-0.365014\pi\)
0.411475 + 0.911421i \(0.365014\pi\)
\(762\) 0 0
\(763\) 11.4445 0.414318
\(764\) −22.4289 −0.811451
\(765\) 0 0
\(766\) 11.8574 0.428426
\(767\) 9.97343 0.360120
\(768\) 0 0
\(769\) −39.9953 −1.44227 −0.721134 0.692795i \(-0.756379\pi\)
−0.721134 + 0.692795i \(0.756379\pi\)
\(770\) 1.48904 0.0536612
\(771\) 0 0
\(772\) −6.01867 −0.216617
\(773\) 6.67792 0.240188 0.120094 0.992763i \(-0.461680\pi\)
0.120094 + 0.992763i \(0.461680\pi\)
\(774\) 0 0
\(775\) −36.1699 −1.29926
\(776\) −22.2524 −0.798815
\(777\) 0 0
\(778\) 8.04198 0.288319
\(779\) 7.14815 0.256109
\(780\) 0 0
\(781\) −38.6482 −1.38294
\(782\) −0.573218 −0.0204982
\(783\) 0 0
\(784\) 8.86988 0.316782
\(785\) −0.669372 −0.0238909
\(786\) 0 0
\(787\) 26.5400 0.946048 0.473024 0.881050i \(-0.343162\pi\)
0.473024 + 0.881050i \(0.343162\pi\)
\(788\) −3.20609 −0.114212
\(789\) 0 0
\(790\) 3.10342 0.110415
\(791\) 7.74272 0.275299
\(792\) 0 0
\(793\) −20.5918 −0.731237
\(794\) −8.32530 −0.295454
\(795\) 0 0
\(796\) −11.8310 −0.419337
\(797\) 31.8075 1.12668 0.563340 0.826225i \(-0.309516\pi\)
0.563340 + 0.826225i \(0.309516\pi\)
\(798\) 0 0
\(799\) 0.0967648 0.00342329
\(800\) 21.4580 0.758653
\(801\) 0 0
\(802\) 31.2534 1.10360
\(803\) 13.3282 0.470341
\(804\) 0 0
\(805\) 0.477293 0.0168224
\(806\) 13.6369 0.480341
\(807\) 0 0
\(808\) −21.9370 −0.771740
\(809\) −17.4024 −0.611836 −0.305918 0.952058i \(-0.598963\pi\)
−0.305918 + 0.952058i \(0.598963\pi\)
\(810\) 0 0
\(811\) 48.5297 1.70411 0.852055 0.523452i \(-0.175356\pi\)
0.852055 + 0.523452i \(0.175356\pi\)
\(812\) −0.971713 −0.0341005
\(813\) 0 0
\(814\) −3.81901 −0.133856
\(815\) −4.12617 −0.144533
\(816\) 0 0
\(817\) −1.63151 −0.0570793
\(818\) 14.2632 0.498700
\(819\) 0 0
\(820\) −4.39893 −0.153617
\(821\) −21.8969 −0.764207 −0.382103 0.924120i \(-0.624800\pi\)
−0.382103 + 0.924120i \(0.624800\pi\)
\(822\) 0 0
\(823\) −12.2048 −0.425433 −0.212717 0.977114i \(-0.568231\pi\)
−0.212717 + 0.977114i \(0.568231\pi\)
\(824\) 9.23902 0.321856
\(825\) 0 0
\(826\) 7.11165 0.247446
\(827\) −36.2068 −1.25903 −0.629516 0.776987i \(-0.716747\pi\)
−0.629516 + 0.776987i \(0.716747\pi\)
\(828\) 0 0
\(829\) −2.38205 −0.0827320 −0.0413660 0.999144i \(-0.513171\pi\)
−0.0413660 + 0.999144i \(0.513171\pi\)
\(830\) 3.85701 0.133879
\(831\) 0 0
\(832\) −13.3703 −0.463531
\(833\) −3.06317 −0.106132
\(834\) 0 0
\(835\) 6.83377 0.236492
\(836\) 1.46470 0.0506576
\(837\) 0 0
\(838\) 30.6232 1.05786
\(839\) −52.3933 −1.80882 −0.904408 0.426668i \(-0.859687\pi\)
−0.904408 + 0.426668i \(0.859687\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 38.4089 1.32366
\(843\) 0 0
\(844\) −4.43394 −0.152623
\(845\) −4.25374 −0.146333
\(846\) 0 0
\(847\) −2.82004 −0.0968978
\(848\) 17.1810 0.589998
\(849\) 0 0
\(850\) 2.76457 0.0948240
\(851\) −1.22414 −0.0419629
\(852\) 0 0
\(853\) −12.3989 −0.424529 −0.212265 0.977212i \(-0.568084\pi\)
−0.212265 + 0.977212i \(0.568084\pi\)
\(854\) −14.6832 −0.502448
\(855\) 0 0
\(856\) 29.3822 1.00426
\(857\) −11.3105 −0.386359 −0.193179 0.981163i \(-0.561880\pi\)
−0.193179 + 0.981163i \(0.561880\pi\)
\(858\) 0 0
\(859\) −27.2778 −0.930706 −0.465353 0.885125i \(-0.654073\pi\)
−0.465353 + 0.885125i \(0.654073\pi\)
\(860\) 1.00402 0.0342368
\(861\) 0 0
\(862\) 29.1227 0.991923
\(863\) 26.0532 0.886863 0.443431 0.896308i \(-0.353761\pi\)
0.443431 + 0.896308i \(0.353761\pi\)
\(864\) 0 0
\(865\) −5.99888 −0.203968
\(866\) 25.4109 0.863496
\(867\) 0 0
\(868\) −7.28748 −0.247353
\(869\) 20.1240 0.682662
\(870\) 0 0
\(871\) 24.3827 0.826175
\(872\) 30.8224 1.04378
\(873\) 0 0
\(874\) −0.626459 −0.0211903
\(875\) −4.68840 −0.158497
\(876\) 0 0
\(877\) −53.0592 −1.79168 −0.895841 0.444375i \(-0.853426\pi\)
−0.895841 + 0.444375i \(0.853426\pi\)
\(878\) −29.3195 −0.989484
\(879\) 0 0
\(880\) 1.90620 0.0642580
\(881\) 40.1909 1.35406 0.677032 0.735953i \(-0.263266\pi\)
0.677032 + 0.735953i \(0.263266\pi\)
\(882\) 0 0
\(883\) 20.1420 0.677833 0.338916 0.940816i \(-0.389940\pi\)
0.338916 + 0.940816i \(0.389940\pi\)
\(884\) 0.781145 0.0262728
\(885\) 0 0
\(886\) 26.7268 0.897906
\(887\) −28.3924 −0.953325 −0.476662 0.879086i \(-0.658154\pi\)
−0.476662 + 0.879086i \(0.658154\pi\)
\(888\) 0 0
\(889\) −6.27517 −0.210463
\(890\) −1.23816 −0.0415034
\(891\) 0 0
\(892\) 11.0110 0.368677
\(893\) 0.105752 0.00353887
\(894\) 0 0
\(895\) 0.0604443 0.00202043
\(896\) 0.558299 0.0186515
\(897\) 0 0
\(898\) 20.9027 0.697531
\(899\) 7.49962 0.250126
\(900\) 0 0
\(901\) −5.93337 −0.197669
\(902\) 38.0617 1.26732
\(903\) 0 0
\(904\) 20.8528 0.693553
\(905\) −4.90308 −0.162984
\(906\) 0 0
\(907\) −24.3598 −0.808854 −0.404427 0.914570i \(-0.632529\pi\)
−0.404427 + 0.914570i \(0.632529\pi\)
\(908\) 10.7823 0.357822
\(909\) 0 0
\(910\) 0.867887 0.0287702
\(911\) −33.0626 −1.09541 −0.547707 0.836670i \(-0.684499\pi\)
−0.547707 + 0.836670i \(0.684499\pi\)
\(912\) 0 0
\(913\) 25.0107 0.827733
\(914\) 12.5942 0.416580
\(915\) 0 0
\(916\) −16.6967 −0.551675
\(917\) 15.3081 0.505519
\(918\) 0 0
\(919\) 47.7236 1.57426 0.787128 0.616789i \(-0.211567\pi\)
0.787128 + 0.616789i \(0.211567\pi\)
\(920\) 1.28545 0.0423800
\(921\) 0 0
\(922\) −2.51696 −0.0828918
\(923\) −22.5261 −0.741457
\(924\) 0 0
\(925\) 5.90389 0.194119
\(926\) −35.8829 −1.17919
\(927\) 0 0
\(928\) −4.44918 −0.146052
\(929\) −21.6699 −0.710968 −0.355484 0.934682i \(-0.615684\pi\)
−0.355484 + 0.934682i \(0.615684\pi\)
\(930\) 0 0
\(931\) −3.34768 −0.109716
\(932\) 9.42790 0.308821
\(933\) 0 0
\(934\) −18.4604 −0.604043
\(935\) −0.658297 −0.0215286
\(936\) 0 0
\(937\) 11.3492 0.370764 0.185382 0.982667i \(-0.440648\pi\)
0.185382 + 0.982667i \(0.440648\pi\)
\(938\) 17.3863 0.567683
\(939\) 0 0
\(940\) −0.0650794 −0.00212266
\(941\) 12.8107 0.417618 0.208809 0.977956i \(-0.433041\pi\)
0.208809 + 0.977956i \(0.433041\pi\)
\(942\) 0 0
\(943\) 12.2002 0.397293
\(944\) 9.10403 0.296311
\(945\) 0 0
\(946\) −8.68727 −0.282448
\(947\) −17.0001 −0.552428 −0.276214 0.961096i \(-0.589080\pi\)
−0.276214 + 0.961096i \(0.589080\pi\)
\(948\) 0 0
\(949\) 7.76834 0.252171
\(950\) 3.02135 0.0980255
\(951\) 0 0
\(952\) 1.85724 0.0601934
\(953\) −36.4300 −1.18008 −0.590042 0.807373i \(-0.700889\pi\)
−0.590042 + 0.807373i \(0.700889\pi\)
\(954\) 0 0
\(955\) 11.0168 0.356495
\(956\) −8.23367 −0.266296
\(957\) 0 0
\(958\) 33.3123 1.07627
\(959\) 6.62331 0.213878
\(960\) 0 0
\(961\) 25.2443 0.814332
\(962\) −2.22591 −0.0717663
\(963\) 0 0
\(964\) 5.11072 0.164605
\(965\) 2.95629 0.0951664
\(966\) 0 0
\(967\) −23.2204 −0.746719 −0.373359 0.927687i \(-0.621794\pi\)
−0.373359 + 0.927687i \(0.621794\pi\)
\(968\) −7.59497 −0.244111
\(969\) 0 0
\(970\) 3.27804 0.105252
\(971\) 25.4051 0.815289 0.407644 0.913141i \(-0.366350\pi\)
0.407644 + 0.913141i \(0.366350\pi\)
\(972\) 0 0
\(973\) −25.3311 −0.812079
\(974\) −14.3538 −0.459926
\(975\) 0 0
\(976\) −18.7968 −0.601670
\(977\) −35.6930 −1.14192 −0.570961 0.820978i \(-0.693429\pi\)
−0.570961 + 0.820978i \(0.693429\pi\)
\(978\) 0 0
\(979\) −8.02886 −0.256604
\(980\) 2.06014 0.0658088
\(981\) 0 0
\(982\) 4.65104 0.148421
\(983\) 30.1919 0.962973 0.481486 0.876454i \(-0.340097\pi\)
0.481486 + 0.876454i \(0.340097\pi\)
\(984\) 0 0
\(985\) 1.57479 0.0501770
\(986\) −0.573218 −0.0182550
\(987\) 0 0
\(988\) 0.853699 0.0271598
\(989\) −2.78460 −0.0885451
\(990\) 0 0
\(991\) −18.5980 −0.590784 −0.295392 0.955376i \(-0.595450\pi\)
−0.295392 + 0.955376i \(0.595450\pi\)
\(992\) −33.3672 −1.05941
\(993\) 0 0
\(994\) −16.0625 −0.509471
\(995\) 5.81122 0.184228
\(996\) 0 0
\(997\) −57.0452 −1.80664 −0.903319 0.428969i \(-0.858877\pi\)
−0.903319 + 0.428969i \(0.858877\pi\)
\(998\) 36.7027 1.16181
\(999\) 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 \(a_p\))