Properties

Label 8015.2.a.l.1.29
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.29
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.348082 q^{2} +1.65091 q^{3} -1.87884 q^{4} -1.00000 q^{5} -0.574652 q^{6} -1.00000 q^{7} +1.35015 q^{8} -0.274499 q^{9} +O(q^{10})\) \(q-0.348082 q^{2} +1.65091 q^{3} -1.87884 q^{4} -1.00000 q^{5} -0.574652 q^{6} -1.00000 q^{7} +1.35015 q^{8} -0.274499 q^{9} +0.348082 q^{10} -2.76949 q^{11} -3.10179 q^{12} -4.02564 q^{13} +0.348082 q^{14} -1.65091 q^{15} +3.28771 q^{16} -1.29135 q^{17} +0.0955480 q^{18} -4.23831 q^{19} +1.87884 q^{20} -1.65091 q^{21} +0.964009 q^{22} +9.13506 q^{23} +2.22898 q^{24} +1.00000 q^{25} +1.40125 q^{26} -5.40590 q^{27} +1.87884 q^{28} -0.484842 q^{29} +0.574652 q^{30} +1.36515 q^{31} -3.84470 q^{32} -4.57218 q^{33} +0.449496 q^{34} +1.00000 q^{35} +0.515739 q^{36} -8.84752 q^{37} +1.47528 q^{38} -6.64597 q^{39} -1.35015 q^{40} -9.64385 q^{41} +0.574652 q^{42} -12.3731 q^{43} +5.20342 q^{44} +0.274499 q^{45} -3.17975 q^{46} +10.7001 q^{47} +5.42772 q^{48} +1.00000 q^{49} -0.348082 q^{50} -2.13191 q^{51} +7.56353 q^{52} +12.4788 q^{53} +1.88170 q^{54} +2.76949 q^{55} -1.35015 q^{56} -6.99707 q^{57} +0.168765 q^{58} +3.92402 q^{59} +3.10179 q^{60} -13.6963 q^{61} -0.475182 q^{62} +0.274499 q^{63} -5.23716 q^{64} +4.02564 q^{65} +1.59149 q^{66} -10.4416 q^{67} +2.42624 q^{68} +15.0812 q^{69} -0.348082 q^{70} +13.1062 q^{71} -0.370615 q^{72} -7.82705 q^{73} +3.07966 q^{74} +1.65091 q^{75} +7.96311 q^{76} +2.76949 q^{77} +2.31334 q^{78} +9.94054 q^{79} -3.28771 q^{80} -8.10115 q^{81} +3.35685 q^{82} +1.57206 q^{83} +3.10179 q^{84} +1.29135 q^{85} +4.30686 q^{86} -0.800430 q^{87} -3.73924 q^{88} -5.68848 q^{89} -0.0955480 q^{90} +4.02564 q^{91} -17.1633 q^{92} +2.25373 q^{93} -3.72450 q^{94} +4.23831 q^{95} -6.34725 q^{96} +2.95243 q^{97} -0.348082 q^{98} +0.760221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.348082 −0.246131 −0.123066 0.992399i \(-0.539273\pi\)
−0.123066 + 0.992399i \(0.539273\pi\)
\(3\) 1.65091 0.953153 0.476576 0.879133i \(-0.341878\pi\)
0.476576 + 0.879133i \(0.341878\pi\)
\(4\) −1.87884 −0.939419
\(5\) −1.00000 −0.447214
\(6\) −0.574652 −0.234601
\(7\) −1.00000 −0.377964
\(8\) 1.35015 0.477351
\(9\) −0.274499 −0.0914995
\(10\) 0.348082 0.110073
\(11\) −2.76949 −0.835032 −0.417516 0.908669i \(-0.637099\pi\)
−0.417516 + 0.908669i \(0.637099\pi\)
\(12\) −3.10179 −0.895410
\(13\) −4.02564 −1.11651 −0.558256 0.829669i \(-0.688529\pi\)
−0.558256 + 0.829669i \(0.688529\pi\)
\(14\) 0.348082 0.0930288
\(15\) −1.65091 −0.426263
\(16\) 3.28771 0.821928
\(17\) −1.29135 −0.313199 −0.156600 0.987662i \(-0.550053\pi\)
−0.156600 + 0.987662i \(0.550053\pi\)
\(18\) 0.0955480 0.0225209
\(19\) −4.23831 −0.972336 −0.486168 0.873865i \(-0.661606\pi\)
−0.486168 + 0.873865i \(0.661606\pi\)
\(20\) 1.87884 0.420121
\(21\) −1.65091 −0.360258
\(22\) 0.964009 0.205527
\(23\) 9.13506 1.90479 0.952396 0.304863i \(-0.0986107\pi\)
0.952396 + 0.304863i \(0.0986107\pi\)
\(24\) 2.22898 0.454989
\(25\) 1.00000 0.200000
\(26\) 1.40125 0.274808
\(27\) −5.40590 −1.04037
\(28\) 1.87884 0.355067
\(29\) −0.484842 −0.0900329 −0.0450164 0.998986i \(-0.514334\pi\)
−0.0450164 + 0.998986i \(0.514334\pi\)
\(30\) 0.574652 0.104917
\(31\) 1.36515 0.245187 0.122594 0.992457i \(-0.460879\pi\)
0.122594 + 0.992457i \(0.460879\pi\)
\(32\) −3.84470 −0.679654
\(33\) −4.57218 −0.795914
\(34\) 0.449496 0.0770880
\(35\) 1.00000 0.169031
\(36\) 0.515739 0.0859564
\(37\) −8.84752 −1.45452 −0.727262 0.686360i \(-0.759208\pi\)
−0.727262 + 0.686360i \(0.759208\pi\)
\(38\) 1.47528 0.239322
\(39\) −6.64597 −1.06421
\(40\) −1.35015 −0.213478
\(41\) −9.64385 −1.50612 −0.753058 0.657954i \(-0.771422\pi\)
−0.753058 + 0.657954i \(0.771422\pi\)
\(42\) 0.574652 0.0886707
\(43\) −12.3731 −1.88688 −0.943442 0.331538i \(-0.892432\pi\)
−0.943442 + 0.331538i \(0.892432\pi\)
\(44\) 5.20342 0.784446
\(45\) 0.274499 0.0409198
\(46\) −3.17975 −0.468829
\(47\) 10.7001 1.56076 0.780382 0.625303i \(-0.215025\pi\)
0.780382 + 0.625303i \(0.215025\pi\)
\(48\) 5.42772 0.783424
\(49\) 1.00000 0.142857
\(50\) −0.348082 −0.0492262
\(51\) −2.13191 −0.298527
\(52\) 7.56353 1.04887
\(53\) 12.4788 1.71409 0.857047 0.515238i \(-0.172297\pi\)
0.857047 + 0.515238i \(0.172297\pi\)
\(54\) 1.88170 0.256066
\(55\) 2.76949 0.373438
\(56\) −1.35015 −0.180422
\(57\) −6.99707 −0.926785
\(58\) 0.168765 0.0221599
\(59\) 3.92402 0.510864 0.255432 0.966827i \(-0.417782\pi\)
0.255432 + 0.966827i \(0.417782\pi\)
\(60\) 3.10179 0.400440
\(61\) −13.6963 −1.75364 −0.876819 0.480821i \(-0.840339\pi\)
−0.876819 + 0.480821i \(0.840339\pi\)
\(62\) −0.475182 −0.0603482
\(63\) 0.274499 0.0345836
\(64\) −5.23716 −0.654645
\(65\) 4.02564 0.499319
\(66\) 1.59149 0.195899
\(67\) −10.4416 −1.27564 −0.637821 0.770185i \(-0.720164\pi\)
−0.637821 + 0.770185i \(0.720164\pi\)
\(68\) 2.42624 0.294225
\(69\) 15.0812 1.81556
\(70\) −0.348082 −0.0416037
\(71\) 13.1062 1.55542 0.777709 0.628625i \(-0.216382\pi\)
0.777709 + 0.628625i \(0.216382\pi\)
\(72\) −0.370615 −0.0436774
\(73\) −7.82705 −0.916087 −0.458044 0.888930i \(-0.651450\pi\)
−0.458044 + 0.888930i \(0.651450\pi\)
\(74\) 3.07966 0.358004
\(75\) 1.65091 0.190631
\(76\) 7.96311 0.913431
\(77\) 2.76949 0.315613
\(78\) 2.31334 0.261934
\(79\) 9.94054 1.11840 0.559199 0.829034i \(-0.311109\pi\)
0.559199 + 0.829034i \(0.311109\pi\)
\(80\) −3.28771 −0.367578
\(81\) −8.10115 −0.900128
\(82\) 3.35685 0.370702
\(83\) 1.57206 0.172556 0.0862779 0.996271i \(-0.472503\pi\)
0.0862779 + 0.996271i \(0.472503\pi\)
\(84\) 3.10179 0.338433
\(85\) 1.29135 0.140067
\(86\) 4.30686 0.464421
\(87\) −0.800430 −0.0858151
\(88\) −3.73924 −0.398604
\(89\) −5.68848 −0.602977 −0.301489 0.953470i \(-0.597484\pi\)
−0.301489 + 0.953470i \(0.597484\pi\)
\(90\) −0.0955480 −0.0100716
\(91\) 4.02564 0.422002
\(92\) −17.1633 −1.78940
\(93\) 2.25373 0.233701
\(94\) −3.72450 −0.384153
\(95\) 4.23831 0.434842
\(96\) −6.34725 −0.647814
\(97\) 2.95243 0.299774 0.149887 0.988703i \(-0.452109\pi\)
0.149887 + 0.988703i \(0.452109\pi\)
\(98\) −0.348082 −0.0351616
\(99\) 0.760221 0.0764051
\(100\) −1.87884 −0.187884
\(101\) 0.473144 0.0470796 0.0235398 0.999723i \(-0.492506\pi\)
0.0235398 + 0.999723i \(0.492506\pi\)
\(102\) 0.742078 0.0734767
\(103\) −1.18387 −0.116650 −0.0583249 0.998298i \(-0.518576\pi\)
−0.0583249 + 0.998298i \(0.518576\pi\)
\(104\) −5.43523 −0.532969
\(105\) 1.65091 0.161112
\(106\) −4.34364 −0.421892
\(107\) −4.14838 −0.401039 −0.200520 0.979690i \(-0.564263\pi\)
−0.200520 + 0.979690i \(0.564263\pi\)
\(108\) 10.1568 0.977340
\(109\) −8.68527 −0.831898 −0.415949 0.909388i \(-0.636551\pi\)
−0.415949 + 0.909388i \(0.636551\pi\)
\(110\) −0.964009 −0.0919147
\(111\) −14.6065 −1.38638
\(112\) −3.28771 −0.310660
\(113\) 0.771176 0.0725461 0.0362731 0.999342i \(-0.488451\pi\)
0.0362731 + 0.999342i \(0.488451\pi\)
\(114\) 2.43555 0.228110
\(115\) −9.13506 −0.851849
\(116\) 0.910940 0.0845786
\(117\) 1.10503 0.102160
\(118\) −1.36588 −0.125739
\(119\) 1.29135 0.118378
\(120\) −2.22898 −0.203477
\(121\) −3.32993 −0.302721
\(122\) 4.76745 0.431625
\(123\) −15.9211 −1.43556
\(124\) −2.56489 −0.230334
\(125\) −1.00000 −0.0894427
\(126\) −0.0955480 −0.00851209
\(127\) 2.21935 0.196936 0.0984678 0.995140i \(-0.468606\pi\)
0.0984678 + 0.995140i \(0.468606\pi\)
\(128\) 9.51236 0.840782
\(129\) −20.4269 −1.79849
\(130\) −1.40125 −0.122898
\(131\) 6.04214 0.527904 0.263952 0.964536i \(-0.414974\pi\)
0.263952 + 0.964536i \(0.414974\pi\)
\(132\) 8.59038 0.747697
\(133\) 4.23831 0.367508
\(134\) 3.63452 0.313975
\(135\) 5.40590 0.465266
\(136\) −1.74352 −0.149506
\(137\) 1.56342 0.133572 0.0667858 0.997767i \(-0.478726\pi\)
0.0667858 + 0.997767i \(0.478726\pi\)
\(138\) −5.24948 −0.446865
\(139\) 17.8864 1.51710 0.758552 0.651612i \(-0.225907\pi\)
0.758552 + 0.651612i \(0.225907\pi\)
\(140\) −1.87884 −0.158791
\(141\) 17.6648 1.48765
\(142\) −4.56203 −0.382837
\(143\) 11.1490 0.932324
\(144\) −0.902473 −0.0752061
\(145\) 0.484842 0.0402639
\(146\) 2.72446 0.225478
\(147\) 1.65091 0.136165
\(148\) 16.6231 1.36641
\(149\) 20.1590 1.65149 0.825743 0.564046i \(-0.190756\pi\)
0.825743 + 0.564046i \(0.190756\pi\)
\(150\) −0.574652 −0.0469201
\(151\) −7.72037 −0.628275 −0.314137 0.949378i \(-0.601715\pi\)
−0.314137 + 0.949378i \(0.601715\pi\)
\(152\) −5.72237 −0.464146
\(153\) 0.354474 0.0286576
\(154\) −0.964009 −0.0776821
\(155\) −1.36515 −0.109651
\(156\) 12.4867 0.999736
\(157\) −0.968004 −0.0772551 −0.0386276 0.999254i \(-0.512299\pi\)
−0.0386276 + 0.999254i \(0.512299\pi\)
\(158\) −3.46012 −0.275272
\(159\) 20.6014 1.63379
\(160\) 3.84470 0.303950
\(161\) −9.13506 −0.719944
\(162\) 2.81987 0.221550
\(163\) 15.3470 1.20207 0.601037 0.799221i \(-0.294755\pi\)
0.601037 + 0.799221i \(0.294755\pi\)
\(164\) 18.1192 1.41488
\(165\) 4.57218 0.355943
\(166\) −0.547205 −0.0424714
\(167\) 22.2761 1.72377 0.861886 0.507101i \(-0.169283\pi\)
0.861886 + 0.507101i \(0.169283\pi\)
\(168\) −2.22898 −0.171970
\(169\) 3.20579 0.246599
\(170\) −0.449496 −0.0344748
\(171\) 1.16341 0.0889683
\(172\) 23.2471 1.77258
\(173\) 6.47862 0.492560 0.246280 0.969199i \(-0.420792\pi\)
0.246280 + 0.969199i \(0.420792\pi\)
\(174\) 0.278615 0.0211218
\(175\) −1.00000 −0.0755929
\(176\) −9.10529 −0.686337
\(177\) 6.47820 0.486931
\(178\) 1.98006 0.148411
\(179\) 5.31716 0.397423 0.198712 0.980058i \(-0.436324\pi\)
0.198712 + 0.980058i \(0.436324\pi\)
\(180\) −0.515739 −0.0384409
\(181\) 14.6112 1.08604 0.543022 0.839719i \(-0.317280\pi\)
0.543022 + 0.839719i \(0.317280\pi\)
\(182\) −1.40125 −0.103868
\(183\) −22.6114 −1.67149
\(184\) 12.3337 0.909255
\(185\) 8.84752 0.650483
\(186\) −0.784483 −0.0575211
\(187\) 3.57639 0.261531
\(188\) −20.1037 −1.46621
\(189\) 5.40590 0.393221
\(190\) −1.47528 −0.107028
\(191\) −10.9499 −0.792307 −0.396153 0.918184i \(-0.629655\pi\)
−0.396153 + 0.918184i \(0.629655\pi\)
\(192\) −8.64607 −0.623976
\(193\) 5.06928 0.364895 0.182447 0.983216i \(-0.441598\pi\)
0.182447 + 0.983216i \(0.441598\pi\)
\(194\) −1.02769 −0.0737838
\(195\) 6.64597 0.475928
\(196\) −1.87884 −0.134203
\(197\) −24.0532 −1.71372 −0.856858 0.515552i \(-0.827587\pi\)
−0.856858 + 0.515552i \(0.827587\pi\)
\(198\) −0.264619 −0.0188057
\(199\) 23.5440 1.66899 0.834495 0.551016i \(-0.185760\pi\)
0.834495 + 0.551016i \(0.185760\pi\)
\(200\) 1.35015 0.0954703
\(201\) −17.2381 −1.21588
\(202\) −0.164693 −0.0115877
\(203\) 0.484842 0.0340292
\(204\) 4.00551 0.280442
\(205\) 9.64385 0.673556
\(206\) 0.412083 0.0287112
\(207\) −2.50756 −0.174288
\(208\) −13.2352 −0.917693
\(209\) 11.7380 0.811932
\(210\) −0.574652 −0.0396547
\(211\) −9.38463 −0.646064 −0.323032 0.946388i \(-0.604702\pi\)
−0.323032 + 0.946388i \(0.604702\pi\)
\(212\) −23.4456 −1.61025
\(213\) 21.6371 1.48255
\(214\) 1.44398 0.0987082
\(215\) 12.3731 0.843840
\(216\) −7.29880 −0.496620
\(217\) −1.36515 −0.0926721
\(218\) 3.02319 0.204756
\(219\) −12.9218 −0.873171
\(220\) −5.20342 −0.350815
\(221\) 5.19852 0.349690
\(222\) 5.08424 0.341232
\(223\) 29.4379 1.97131 0.985654 0.168780i \(-0.0539828\pi\)
0.985654 + 0.168780i \(0.0539828\pi\)
\(224\) 3.84470 0.256885
\(225\) −0.274499 −0.0182999
\(226\) −0.268432 −0.0178559
\(227\) 28.2046 1.87201 0.936004 0.351990i \(-0.114495\pi\)
0.936004 + 0.351990i \(0.114495\pi\)
\(228\) 13.1464 0.870639
\(229\) 1.00000 0.0660819
\(230\) 3.17975 0.209667
\(231\) 4.57218 0.300827
\(232\) −0.654611 −0.0429773
\(233\) −19.5505 −1.28080 −0.640399 0.768042i \(-0.721231\pi\)
−0.640399 + 0.768042i \(0.721231\pi\)
\(234\) −0.384642 −0.0251448
\(235\) −10.7001 −0.697995
\(236\) −7.37260 −0.479915
\(237\) 16.4109 1.06600
\(238\) −0.449496 −0.0291365
\(239\) −23.5780 −1.52513 −0.762567 0.646910i \(-0.776061\pi\)
−0.762567 + 0.646910i \(0.776061\pi\)
\(240\) −5.42772 −0.350358
\(241\) 14.1632 0.912332 0.456166 0.889895i \(-0.349222\pi\)
0.456166 + 0.889895i \(0.349222\pi\)
\(242\) 1.15909 0.0745090
\(243\) 2.84343 0.182406
\(244\) 25.7332 1.64740
\(245\) −1.00000 −0.0638877
\(246\) 5.54185 0.353336
\(247\) 17.0619 1.08562
\(248\) 1.84316 0.117041
\(249\) 2.59533 0.164472
\(250\) 0.348082 0.0220146
\(251\) −3.95246 −0.249477 −0.124738 0.992190i \(-0.539809\pi\)
−0.124738 + 0.992190i \(0.539809\pi\)
\(252\) −0.515739 −0.0324885
\(253\) −25.2995 −1.59056
\(254\) −0.772516 −0.0484720
\(255\) 2.13191 0.133505
\(256\) 7.16323 0.447702
\(257\) −16.3399 −1.01925 −0.509627 0.860395i \(-0.670217\pi\)
−0.509627 + 0.860395i \(0.670217\pi\)
\(258\) 7.11024 0.442664
\(259\) 8.84752 0.549758
\(260\) −7.56353 −0.469070
\(261\) 0.133088 0.00823797
\(262\) −2.10316 −0.129934
\(263\) 22.4664 1.38534 0.692669 0.721256i \(-0.256435\pi\)
0.692669 + 0.721256i \(0.256435\pi\)
\(264\) −6.17314 −0.379931
\(265\) −12.4788 −0.766566
\(266\) −1.47528 −0.0904552
\(267\) −9.39116 −0.574730
\(268\) 19.6180 1.19836
\(269\) 30.7419 1.87437 0.937183 0.348838i \(-0.113424\pi\)
0.937183 + 0.348838i \(0.113424\pi\)
\(270\) −1.88170 −0.114516
\(271\) 8.13752 0.494319 0.247160 0.968975i \(-0.420503\pi\)
0.247160 + 0.968975i \(0.420503\pi\)
\(272\) −4.24560 −0.257427
\(273\) 6.64597 0.402232
\(274\) −0.544196 −0.0328761
\(275\) −2.76949 −0.167006
\(276\) −28.3351 −1.70557
\(277\) −4.84689 −0.291221 −0.145611 0.989342i \(-0.546515\pi\)
−0.145611 + 0.989342i \(0.546515\pi\)
\(278\) −6.22593 −0.373407
\(279\) −0.374730 −0.0224345
\(280\) 1.35015 0.0806871
\(281\) 25.3066 1.50967 0.754833 0.655916i \(-0.227718\pi\)
0.754833 + 0.655916i \(0.227718\pi\)
\(282\) −6.14881 −0.366156
\(283\) −15.6441 −0.929943 −0.464971 0.885326i \(-0.653935\pi\)
−0.464971 + 0.885326i \(0.653935\pi\)
\(284\) −24.6244 −1.46119
\(285\) 6.99707 0.414471
\(286\) −3.88076 −0.229474
\(287\) 9.64385 0.569259
\(288\) 1.05537 0.0621880
\(289\) −15.3324 −0.901906
\(290\) −0.168765 −0.00991020
\(291\) 4.87420 0.285731
\(292\) 14.7058 0.860590
\(293\) 22.6165 1.32127 0.660636 0.750707i \(-0.270287\pi\)
0.660636 + 0.750707i \(0.270287\pi\)
\(294\) −0.574652 −0.0335144
\(295\) −3.92402 −0.228465
\(296\) −11.9455 −0.694319
\(297\) 14.9716 0.868739
\(298\) −7.01697 −0.406482
\(299\) −36.7745 −2.12672
\(300\) −3.10179 −0.179082
\(301\) 12.3731 0.713175
\(302\) 2.68732 0.154638
\(303\) 0.781117 0.0448740
\(304\) −13.9344 −0.799190
\(305\) 13.6963 0.784251
\(306\) −0.123386 −0.00705352
\(307\) −23.2243 −1.32548 −0.662741 0.748849i \(-0.730607\pi\)
−0.662741 + 0.748849i \(0.730607\pi\)
\(308\) −5.20342 −0.296493
\(309\) −1.95446 −0.111185
\(310\) 0.475182 0.0269885
\(311\) 10.9287 0.619709 0.309854 0.950784i \(-0.399720\pi\)
0.309854 + 0.950784i \(0.399720\pi\)
\(312\) −8.97308 −0.508001
\(313\) −20.9893 −1.18639 −0.593193 0.805060i \(-0.702133\pi\)
−0.593193 + 0.805060i \(0.702133\pi\)
\(314\) 0.336945 0.0190149
\(315\) −0.274499 −0.0154662
\(316\) −18.6767 −1.05064
\(317\) −10.7214 −0.602176 −0.301088 0.953596i \(-0.597350\pi\)
−0.301088 + 0.953596i \(0.597350\pi\)
\(318\) −7.17096 −0.402127
\(319\) 1.34276 0.0751804
\(320\) 5.23716 0.292766
\(321\) −6.84860 −0.382252
\(322\) 3.17975 0.177201
\(323\) 5.47316 0.304535
\(324\) 15.2208 0.845598
\(325\) −4.02564 −0.223302
\(326\) −5.34203 −0.295868
\(327\) −14.3386 −0.792926
\(328\) −13.0207 −0.718947
\(329\) −10.7001 −0.589913
\(330\) −1.59149 −0.0876087
\(331\) 20.1848 1.10946 0.554728 0.832032i \(-0.312822\pi\)
0.554728 + 0.832032i \(0.312822\pi\)
\(332\) −2.95364 −0.162102
\(333\) 2.42863 0.133088
\(334\) −7.75389 −0.424274
\(335\) 10.4416 0.570484
\(336\) −5.42772 −0.296106
\(337\) 21.0178 1.14491 0.572457 0.819935i \(-0.305990\pi\)
0.572457 + 0.819935i \(0.305990\pi\)
\(338\) −1.11588 −0.0606957
\(339\) 1.27314 0.0691476
\(340\) −2.42624 −0.131582
\(341\) −3.78076 −0.204739
\(342\) −0.404962 −0.0218979
\(343\) −1.00000 −0.0539949
\(344\) −16.7056 −0.900707
\(345\) −15.0812 −0.811942
\(346\) −2.25509 −0.121234
\(347\) −23.0999 −1.24007 −0.620034 0.784575i \(-0.712881\pi\)
−0.620034 + 0.784575i \(0.712881\pi\)
\(348\) 1.50388 0.0806164
\(349\) 2.64085 0.141362 0.0706808 0.997499i \(-0.477483\pi\)
0.0706808 + 0.997499i \(0.477483\pi\)
\(350\) 0.348082 0.0186058
\(351\) 21.7622 1.16158
\(352\) 10.6479 0.567533
\(353\) 6.94384 0.369583 0.184792 0.982778i \(-0.440839\pi\)
0.184792 + 0.982778i \(0.440839\pi\)
\(354\) −2.25494 −0.119849
\(355\) −13.1062 −0.695604
\(356\) 10.6877 0.566449
\(357\) 2.13191 0.112832
\(358\) −1.85081 −0.0978182
\(359\) 4.41837 0.233193 0.116596 0.993179i \(-0.462802\pi\)
0.116596 + 0.993179i \(0.462802\pi\)
\(360\) 0.370615 0.0195331
\(361\) −1.03670 −0.0545633
\(362\) −5.08590 −0.267309
\(363\) −5.49741 −0.288539
\(364\) −7.56353 −0.396437
\(365\) 7.82705 0.409687
\(366\) 7.87063 0.411404
\(367\) −22.0409 −1.15053 −0.575264 0.817968i \(-0.695101\pi\)
−0.575264 + 0.817968i \(0.695101\pi\)
\(368\) 30.0335 1.56560
\(369\) 2.64722 0.137809
\(370\) −3.07966 −0.160104
\(371\) −12.4788 −0.647867
\(372\) −4.23440 −0.219543
\(373\) −17.1784 −0.889466 −0.444733 0.895663i \(-0.646701\pi\)
−0.444733 + 0.895663i \(0.646701\pi\)
\(374\) −1.24488 −0.0643710
\(375\) −1.65091 −0.0852526
\(376\) 14.4467 0.745033
\(377\) 1.95180 0.100523
\(378\) −1.88170 −0.0967840
\(379\) 29.5824 1.51955 0.759774 0.650187i \(-0.225310\pi\)
0.759774 + 0.650187i \(0.225310\pi\)
\(380\) −7.96311 −0.408499
\(381\) 3.66395 0.187710
\(382\) 3.81146 0.195011
\(383\) 12.9784 0.663163 0.331581 0.943427i \(-0.392418\pi\)
0.331581 + 0.943427i \(0.392418\pi\)
\(384\) 15.7040 0.801394
\(385\) −2.76949 −0.141146
\(386\) −1.76452 −0.0898119
\(387\) 3.39640 0.172649
\(388\) −5.54715 −0.281614
\(389\) −27.7396 −1.40645 −0.703226 0.710966i \(-0.748258\pi\)
−0.703226 + 0.710966i \(0.748258\pi\)
\(390\) −2.31334 −0.117141
\(391\) −11.7966 −0.596579
\(392\) 1.35015 0.0681931
\(393\) 9.97502 0.503173
\(394\) 8.37247 0.421799
\(395\) −9.94054 −0.500163
\(396\) −1.42833 −0.0717764
\(397\) −2.49561 −0.125251 −0.0626256 0.998037i \(-0.519947\pi\)
−0.0626256 + 0.998037i \(0.519947\pi\)
\(398\) −8.19524 −0.410790
\(399\) 6.99707 0.350292
\(400\) 3.28771 0.164386
\(401\) −30.2728 −1.51175 −0.755876 0.654714i \(-0.772789\pi\)
−0.755876 + 0.654714i \(0.772789\pi\)
\(402\) 6.00027 0.299266
\(403\) −5.49559 −0.273755
\(404\) −0.888961 −0.0442275
\(405\) 8.10115 0.402550
\(406\) −0.168765 −0.00837565
\(407\) 24.5031 1.21457
\(408\) −2.87840 −0.142502
\(409\) −21.9112 −1.08344 −0.541720 0.840559i \(-0.682227\pi\)
−0.541720 + 0.840559i \(0.682227\pi\)
\(410\) −3.35685 −0.165783
\(411\) 2.58106 0.127314
\(412\) 2.22429 0.109583
\(413\) −3.92402 −0.193088
\(414\) 0.872837 0.0428976
\(415\) −1.57206 −0.0771693
\(416\) 15.4774 0.758841
\(417\) 29.5288 1.44603
\(418\) −4.08577 −0.199842
\(419\) 30.5775 1.49381 0.746903 0.664933i \(-0.231540\pi\)
0.746903 + 0.664933i \(0.231540\pi\)
\(420\) −3.10179 −0.151352
\(421\) 29.5723 1.44126 0.720632 0.693317i \(-0.243852\pi\)
0.720632 + 0.693317i \(0.243852\pi\)
\(422\) 3.26662 0.159017
\(423\) −2.93715 −0.142809
\(424\) 16.8483 0.818225
\(425\) −1.29135 −0.0626398
\(426\) −7.53149 −0.364902
\(427\) 13.6963 0.662813
\(428\) 7.79414 0.376744
\(429\) 18.4059 0.888647
\(430\) −4.30686 −0.207695
\(431\) −17.8640 −0.860477 −0.430238 0.902715i \(-0.641571\pi\)
−0.430238 + 0.902715i \(0.641571\pi\)
\(432\) −17.7731 −0.855106
\(433\) −3.26672 −0.156989 −0.0784943 0.996915i \(-0.525011\pi\)
−0.0784943 + 0.996915i \(0.525011\pi\)
\(434\) 0.475182 0.0228095
\(435\) 0.800430 0.0383777
\(436\) 16.3182 0.781501
\(437\) −38.7173 −1.85210
\(438\) 4.49783 0.214915
\(439\) −15.6021 −0.744646 −0.372323 0.928103i \(-0.621439\pi\)
−0.372323 + 0.928103i \(0.621439\pi\)
\(440\) 3.73924 0.178261
\(441\) −0.274499 −0.0130714
\(442\) −1.80951 −0.0860697
\(443\) −10.3872 −0.493511 −0.246756 0.969078i \(-0.579364\pi\)
−0.246756 + 0.969078i \(0.579364\pi\)
\(444\) 27.4432 1.30240
\(445\) 5.68848 0.269660
\(446\) −10.2468 −0.485200
\(447\) 33.2806 1.57412
\(448\) 5.23716 0.247432
\(449\) 18.1077 0.854554 0.427277 0.904121i \(-0.359473\pi\)
0.427277 + 0.904121i \(0.359473\pi\)
\(450\) 0.0955480 0.00450418
\(451\) 26.7085 1.25766
\(452\) −1.44892 −0.0681513
\(453\) −12.7456 −0.598842
\(454\) −9.81752 −0.460759
\(455\) −4.02564 −0.188725
\(456\) −9.44712 −0.442402
\(457\) −7.66039 −0.358338 −0.179169 0.983818i \(-0.557341\pi\)
−0.179169 + 0.983818i \(0.557341\pi\)
\(458\) −0.348082 −0.0162648
\(459\) 6.98092 0.325842
\(460\) 17.1633 0.800244
\(461\) −2.52525 −0.117612 −0.0588062 0.998269i \(-0.518729\pi\)
−0.0588062 + 0.998269i \(0.518729\pi\)
\(462\) −1.59149 −0.0740429
\(463\) −4.10660 −0.190850 −0.0954249 0.995437i \(-0.530421\pi\)
−0.0954249 + 0.995437i \(0.530421\pi\)
\(464\) −1.59402 −0.0740006
\(465\) −2.25373 −0.104514
\(466\) 6.80519 0.315244
\(467\) 10.3398 0.478467 0.239234 0.970962i \(-0.423104\pi\)
0.239234 + 0.970962i \(0.423104\pi\)
\(468\) −2.07618 −0.0959714
\(469\) 10.4416 0.482147
\(470\) 3.72450 0.171798
\(471\) −1.59809 −0.0736359
\(472\) 5.29803 0.243862
\(473\) 34.2672 1.57561
\(474\) −5.71235 −0.262377
\(475\) −4.23831 −0.194467
\(476\) −2.42624 −0.111207
\(477\) −3.42541 −0.156839
\(478\) 8.20707 0.375383
\(479\) 20.6515 0.943591 0.471796 0.881708i \(-0.343606\pi\)
0.471796 + 0.881708i \(0.343606\pi\)
\(480\) 6.34725 0.289711
\(481\) 35.6170 1.62399
\(482\) −4.92995 −0.224553
\(483\) −15.0812 −0.686217
\(484\) 6.25640 0.284382
\(485\) −2.95243 −0.134063
\(486\) −0.989746 −0.0448958
\(487\) 4.55842 0.206562 0.103281 0.994652i \(-0.467066\pi\)
0.103281 + 0.994652i \(0.467066\pi\)
\(488\) −18.4922 −0.837102
\(489\) 25.3366 1.14576
\(490\) 0.348082 0.0157247
\(491\) 5.08849 0.229641 0.114820 0.993386i \(-0.463371\pi\)
0.114820 + 0.993386i \(0.463371\pi\)
\(492\) 29.9132 1.34859
\(493\) 0.626102 0.0281982
\(494\) −5.93895 −0.267206
\(495\) −0.760221 −0.0341694
\(496\) 4.48821 0.201526
\(497\) −13.1062 −0.587893
\(498\) −0.903386 −0.0404817
\(499\) 44.2008 1.97870 0.989349 0.145564i \(-0.0464998\pi\)
0.989349 + 0.145564i \(0.0464998\pi\)
\(500\) 1.87884 0.0840242
\(501\) 36.7757 1.64302
\(502\) 1.37578 0.0614040
\(503\) 20.1739 0.899509 0.449754 0.893152i \(-0.351512\pi\)
0.449754 + 0.893152i \(0.351512\pi\)
\(504\) 0.370615 0.0165085
\(505\) −0.473144 −0.0210546
\(506\) 8.80628 0.391487
\(507\) 5.29246 0.235047
\(508\) −4.16981 −0.185005
\(509\) −17.6989 −0.784489 −0.392245 0.919861i \(-0.628301\pi\)
−0.392245 + 0.919861i \(0.628301\pi\)
\(510\) −0.742078 −0.0328598
\(511\) 7.82705 0.346249
\(512\) −21.5181 −0.950975
\(513\) 22.9119 1.01158
\(514\) 5.68762 0.250870
\(515\) 1.18387 0.0521674
\(516\) 38.3789 1.68954
\(517\) −29.6337 −1.30329
\(518\) −3.07966 −0.135313
\(519\) 10.6956 0.469485
\(520\) 5.43523 0.238351
\(521\) 23.3969 1.02504 0.512518 0.858677i \(-0.328713\pi\)
0.512518 + 0.858677i \(0.328713\pi\)
\(522\) −0.0463257 −0.00202762
\(523\) −40.2731 −1.76102 −0.880510 0.474028i \(-0.842800\pi\)
−0.880510 + 0.474028i \(0.842800\pi\)
\(524\) −11.3522 −0.495923
\(525\) −1.65091 −0.0720516
\(526\) −7.82014 −0.340975
\(527\) −1.76288 −0.0767924
\(528\) −15.0320 −0.654184
\(529\) 60.4494 2.62823
\(530\) 4.34364 0.188676
\(531\) −1.07714 −0.0467438
\(532\) −7.96311 −0.345244
\(533\) 38.8227 1.68160
\(534\) 3.26889 0.141459
\(535\) 4.14838 0.179350
\(536\) −14.0977 −0.608929
\(537\) 8.77815 0.378805
\(538\) −10.7007 −0.461340
\(539\) −2.76949 −0.119290
\(540\) −10.1568 −0.437080
\(541\) −36.4197 −1.56580 −0.782902 0.622145i \(-0.786261\pi\)
−0.782902 + 0.622145i \(0.786261\pi\)
\(542\) −2.83252 −0.121667
\(543\) 24.1218 1.03517
\(544\) 4.96486 0.212867
\(545\) 8.68527 0.372036
\(546\) −2.31334 −0.0990019
\(547\) −27.8495 −1.19076 −0.595380 0.803445i \(-0.702998\pi\)
−0.595380 + 0.803445i \(0.702998\pi\)
\(548\) −2.93741 −0.125480
\(549\) 3.75963 0.160457
\(550\) 0.964009 0.0411055
\(551\) 2.05491 0.0875422
\(552\) 20.3619 0.866659
\(553\) −9.94054 −0.422715
\(554\) 1.68712 0.0716786
\(555\) 14.6065 0.620010
\(556\) −33.6057 −1.42520
\(557\) −13.4272 −0.568928 −0.284464 0.958687i \(-0.591816\pi\)
−0.284464 + 0.958687i \(0.591816\pi\)
\(558\) 0.130437 0.00552183
\(559\) 49.8098 2.10673
\(560\) 3.28771 0.138931
\(561\) 5.90429 0.249279
\(562\) −8.80878 −0.371576
\(563\) −3.77083 −0.158922 −0.0794608 0.996838i \(-0.525320\pi\)
−0.0794608 + 0.996838i \(0.525320\pi\)
\(564\) −33.1894 −1.39752
\(565\) −0.771176 −0.0324436
\(566\) 5.44541 0.228888
\(567\) 8.10115 0.340217
\(568\) 17.6954 0.742481
\(569\) −19.7635 −0.828531 −0.414265 0.910156i \(-0.635961\pi\)
−0.414265 + 0.910156i \(0.635961\pi\)
\(570\) −2.43555 −0.102014
\(571\) −2.38240 −0.0997003 −0.0498501 0.998757i \(-0.515874\pi\)
−0.0498501 + 0.998757i \(0.515874\pi\)
\(572\) −20.9471 −0.875843
\(573\) −18.0773 −0.755189
\(574\) −3.35685 −0.140112
\(575\) 9.13506 0.380958
\(576\) 1.43759 0.0598997
\(577\) 25.7501 1.07199 0.535996 0.844221i \(-0.319936\pi\)
0.535996 + 0.844221i \(0.319936\pi\)
\(578\) 5.33693 0.221987
\(579\) 8.36892 0.347801
\(580\) −0.910940 −0.0378247
\(581\) −1.57206 −0.0652200
\(582\) −1.69662 −0.0703272
\(583\) −34.5599 −1.43132
\(584\) −10.5677 −0.437296
\(585\) −1.10503 −0.0456875
\(586\) −7.87240 −0.325206
\(587\) 11.5931 0.478499 0.239250 0.970958i \(-0.423099\pi\)
0.239250 + 0.970958i \(0.423099\pi\)
\(588\) −3.10179 −0.127916
\(589\) −5.78591 −0.238404
\(590\) 1.36588 0.0562324
\(591\) −39.7096 −1.63343
\(592\) −29.0881 −1.19551
\(593\) 11.2336 0.461310 0.230655 0.973036i \(-0.425913\pi\)
0.230655 + 0.973036i \(0.425913\pi\)
\(594\) −5.21134 −0.213824
\(595\) −1.29135 −0.0529403
\(596\) −37.8754 −1.55144
\(597\) 38.8690 1.59080
\(598\) 12.8005 0.523453
\(599\) −33.4577 −1.36705 −0.683523 0.729929i \(-0.739553\pi\)
−0.683523 + 0.729929i \(0.739553\pi\)
\(600\) 2.22898 0.0909978
\(601\) 5.22694 0.213211 0.106606 0.994301i \(-0.466002\pi\)
0.106606 + 0.994301i \(0.466002\pi\)
\(602\) −4.30686 −0.175535
\(603\) 2.86620 0.116721
\(604\) 14.5053 0.590214
\(605\) 3.32993 0.135381
\(606\) −0.271893 −0.0110449
\(607\) 25.8435 1.04896 0.524478 0.851424i \(-0.324261\pi\)
0.524478 + 0.851424i \(0.324261\pi\)
\(608\) 16.2950 0.660851
\(609\) 0.800430 0.0324351
\(610\) −4.76745 −0.193028
\(611\) −43.0746 −1.74261
\(612\) −0.666000 −0.0269215
\(613\) 13.2598 0.535559 0.267779 0.963480i \(-0.413710\pi\)
0.267779 + 0.963480i \(0.413710\pi\)
\(614\) 8.08396 0.326242
\(615\) 15.9211 0.642002
\(616\) 3.73924 0.150658
\(617\) 13.4081 0.539789 0.269895 0.962890i \(-0.413011\pi\)
0.269895 + 0.962890i \(0.413011\pi\)
\(618\) 0.680311 0.0273661
\(619\) −13.1842 −0.529919 −0.264959 0.964260i \(-0.585359\pi\)
−0.264959 + 0.964260i \(0.585359\pi\)
\(620\) 2.56489 0.103008
\(621\) −49.3832 −1.98168
\(622\) −3.80408 −0.152530
\(623\) 5.68848 0.227904
\(624\) −21.8500 −0.874702
\(625\) 1.00000 0.0400000
\(626\) 7.30600 0.292006
\(627\) 19.3783 0.773895
\(628\) 1.81872 0.0725750
\(629\) 11.4253 0.455556
\(630\) 0.0955480 0.00380672
\(631\) 10.9698 0.436701 0.218351 0.975870i \(-0.429932\pi\)
0.218351 + 0.975870i \(0.429932\pi\)
\(632\) 13.4213 0.533869
\(633\) −15.4932 −0.615798
\(634\) 3.73194 0.148214
\(635\) −2.21935 −0.0880723
\(636\) −38.7066 −1.53482
\(637\) −4.02564 −0.159502
\(638\) −0.467392 −0.0185042
\(639\) −3.59763 −0.142320
\(640\) −9.51236 −0.376009
\(641\) 27.0601 1.06881 0.534405 0.845229i \(-0.320536\pi\)
0.534405 + 0.845229i \(0.320536\pi\)
\(642\) 2.38388 0.0940840
\(643\) −17.1305 −0.675562 −0.337781 0.941225i \(-0.609676\pi\)
−0.337781 + 0.941225i \(0.609676\pi\)
\(644\) 17.1633 0.676329
\(645\) 20.4269 0.804309
\(646\) −1.90511 −0.0749554
\(647\) −20.6424 −0.811537 −0.405769 0.913976i \(-0.632996\pi\)
−0.405769 + 0.913976i \(0.632996\pi\)
\(648\) −10.9378 −0.429678
\(649\) −10.8675 −0.426588
\(650\) 1.40125 0.0549617
\(651\) −2.25373 −0.0883307
\(652\) −28.8346 −1.12925
\(653\) 30.3111 1.18617 0.593083 0.805141i \(-0.297911\pi\)
0.593083 + 0.805141i \(0.297911\pi\)
\(654\) 4.99101 0.195164
\(655\) −6.04214 −0.236086
\(656\) −31.7062 −1.23792
\(657\) 2.14852 0.0838216
\(658\) 3.72450 0.145196
\(659\) 10.2551 0.399483 0.199741 0.979849i \(-0.435990\pi\)
0.199741 + 0.979849i \(0.435990\pi\)
\(660\) −8.59038 −0.334380
\(661\) −11.1029 −0.431852 −0.215926 0.976410i \(-0.569277\pi\)
−0.215926 + 0.976410i \(0.569277\pi\)
\(662\) −7.02596 −0.273072
\(663\) 8.58229 0.333308
\(664\) 2.12252 0.0823698
\(665\) −4.23831 −0.164355
\(666\) −0.845363 −0.0327572
\(667\) −4.42906 −0.171494
\(668\) −41.8531 −1.61935
\(669\) 48.5993 1.87896
\(670\) −3.63452 −0.140414
\(671\) 37.9319 1.46434
\(672\) 6.34725 0.244851
\(673\) −22.5170 −0.867968 −0.433984 0.900921i \(-0.642893\pi\)
−0.433984 + 0.900921i \(0.642893\pi\)
\(674\) −7.31593 −0.281799
\(675\) −5.40590 −0.208073
\(676\) −6.02316 −0.231660
\(677\) −46.7821 −1.79798 −0.898990 0.437969i \(-0.855698\pi\)
−0.898990 + 0.437969i \(0.855698\pi\)
\(678\) −0.443158 −0.0170194
\(679\) −2.95243 −0.113304
\(680\) 1.74352 0.0668611
\(681\) 46.5633 1.78431
\(682\) 1.31601 0.0503927
\(683\) 32.6186 1.24812 0.624058 0.781378i \(-0.285483\pi\)
0.624058 + 0.781378i \(0.285483\pi\)
\(684\) −2.18586 −0.0835785
\(685\) −1.56342 −0.0597350
\(686\) 0.348082 0.0132898
\(687\) 1.65091 0.0629861
\(688\) −40.6793 −1.55088
\(689\) −50.2351 −1.91381
\(690\) 5.24948 0.199844
\(691\) −35.6236 −1.35519 −0.677593 0.735437i \(-0.736977\pi\)
−0.677593 + 0.735437i \(0.736977\pi\)
\(692\) −12.1723 −0.462721
\(693\) −0.760221 −0.0288784
\(694\) 8.04066 0.305219
\(695\) −17.8864 −0.678470
\(696\) −1.08070 −0.0409640
\(697\) 12.4536 0.471714
\(698\) −0.919233 −0.0347935
\(699\) −32.2762 −1.22080
\(700\) 1.87884 0.0710134
\(701\) −0.386601 −0.0146017 −0.00730086 0.999973i \(-0.502324\pi\)
−0.00730086 + 0.999973i \(0.502324\pi\)
\(702\) −7.57503 −0.285901
\(703\) 37.4986 1.41429
\(704\) 14.5043 0.546649
\(705\) −17.6648 −0.665296
\(706\) −2.41702 −0.0909659
\(707\) −0.473144 −0.0177944
\(708\) −12.1715 −0.457433
\(709\) −15.4126 −0.578833 −0.289416 0.957203i \(-0.593461\pi\)
−0.289416 + 0.957203i \(0.593461\pi\)
\(710\) 4.56203 0.171210
\(711\) −2.72866 −0.102333
\(712\) −7.68032 −0.287832
\(713\) 12.4707 0.467031
\(714\) −0.742078 −0.0277716
\(715\) −11.1490 −0.416948
\(716\) −9.99009 −0.373347
\(717\) −38.9251 −1.45369
\(718\) −1.53795 −0.0573959
\(719\) 27.9198 1.04123 0.520617 0.853790i \(-0.325702\pi\)
0.520617 + 0.853790i \(0.325702\pi\)
\(720\) 0.902473 0.0336332
\(721\) 1.18387 0.0440895
\(722\) 0.360858 0.0134297
\(723\) 23.3822 0.869592
\(724\) −27.4521 −1.02025
\(725\) −0.484842 −0.0180066
\(726\) 1.91355 0.0710185
\(727\) −8.61249 −0.319420 −0.159710 0.987164i \(-0.551056\pi\)
−0.159710 + 0.987164i \(0.551056\pi\)
\(728\) 5.43523 0.201443
\(729\) 28.9977 1.07399
\(730\) −2.72446 −0.100837
\(731\) 15.9781 0.590970
\(732\) 42.4832 1.57023
\(733\) −8.06399 −0.297850 −0.148925 0.988848i \(-0.547581\pi\)
−0.148925 + 0.988848i \(0.547581\pi\)
\(734\) 7.67205 0.283181
\(735\) −1.65091 −0.0608947
\(736\) −35.1216 −1.29460
\(737\) 28.9178 1.06520
\(738\) −0.921451 −0.0339191
\(739\) 3.33275 0.122597 0.0612986 0.998119i \(-0.480476\pi\)
0.0612986 + 0.998119i \(0.480476\pi\)
\(740\) −16.6231 −0.611076
\(741\) 28.1677 1.03477
\(742\) 4.34364 0.159460
\(743\) 11.6989 0.429189 0.214595 0.976703i \(-0.431157\pi\)
0.214595 + 0.976703i \(0.431157\pi\)
\(744\) 3.04288 0.111558
\(745\) −20.1590 −0.738567
\(746\) 5.97950 0.218925
\(747\) −0.431528 −0.0157888
\(748\) −6.71946 −0.245688
\(749\) 4.14838 0.151579
\(750\) 0.574652 0.0209833
\(751\) 2.68295 0.0979024 0.0489512 0.998801i \(-0.484412\pi\)
0.0489512 + 0.998801i \(0.484412\pi\)
\(752\) 35.1787 1.28284
\(753\) −6.52515 −0.237790
\(754\) −0.679386 −0.0247418
\(755\) 7.72037 0.280973
\(756\) −10.1568 −0.369400
\(757\) 44.6271 1.62200 0.811000 0.585046i \(-0.198924\pi\)
0.811000 + 0.585046i \(0.198924\pi\)
\(758\) −10.2971 −0.374008
\(759\) −41.7671 −1.51605
\(760\) 5.72237 0.207572
\(761\) −5.35138 −0.193987 −0.0969937 0.995285i \(-0.530923\pi\)
−0.0969937 + 0.995285i \(0.530923\pi\)
\(762\) −1.27535 −0.0462012
\(763\) 8.68527 0.314428
\(764\) 20.5731 0.744308
\(765\) −0.354474 −0.0128161
\(766\) −4.51753 −0.163225
\(767\) −15.7967 −0.570386
\(768\) 11.8258 0.426728
\(769\) 6.87169 0.247800 0.123900 0.992295i \(-0.460460\pi\)
0.123900 + 0.992295i \(0.460460\pi\)
\(770\) 0.964009 0.0347405
\(771\) −26.9757 −0.971505
\(772\) −9.52436 −0.342789
\(773\) −32.8170 −1.18035 −0.590174 0.807276i \(-0.700941\pi\)
−0.590174 + 0.807276i \(0.700941\pi\)
\(774\) −1.18223 −0.0424943
\(775\) 1.36515 0.0490375
\(776\) 3.98624 0.143098
\(777\) 14.6065 0.524004
\(778\) 9.65564 0.346172
\(779\) 40.8737 1.46445
\(780\) −12.4867 −0.447096
\(781\) −36.2974 −1.29882
\(782\) 4.10618 0.146837
\(783\) 2.62101 0.0936671
\(784\) 3.28771 0.117418
\(785\) 0.968004 0.0345495
\(786\) −3.47212 −0.123847
\(787\) −24.5404 −0.874771 −0.437386 0.899274i \(-0.644096\pi\)
−0.437386 + 0.899274i \(0.644096\pi\)
\(788\) 45.1920 1.60990
\(789\) 37.0900 1.32044
\(790\) 3.46012 0.123106
\(791\) −0.771176 −0.0274199
\(792\) 1.02642 0.0364721
\(793\) 55.1366 1.95796
\(794\) 0.868677 0.0308282
\(795\) −20.6014 −0.730655
\(796\) −44.2354 −1.56788
\(797\) −6.43383 −0.227898 −0.113949 0.993487i \(-0.536350\pi\)
−0.113949 + 0.993487i \(0.536350\pi\)
\(798\) −2.43555 −0.0862177
\(799\) −13.8175 −0.488830
\(800\) −3.84470 −0.135931
\(801\) 1.56148 0.0551721
\(802\) 10.5374 0.372089
\(803\) 21.6769 0.764963
\(804\) 32.3876 1.14222
\(805\) 9.13506 0.321969
\(806\) 1.91291 0.0673795
\(807\) 50.7521 1.78656
\(808\) 0.638817 0.0224735
\(809\) 5.05570 0.177749 0.0888744 0.996043i \(-0.471673\pi\)
0.0888744 + 0.996043i \(0.471673\pi\)
\(810\) −2.81987 −0.0990800
\(811\) −16.4271 −0.576833 −0.288416 0.957505i \(-0.593129\pi\)
−0.288416 + 0.957505i \(0.593129\pi\)
\(812\) −0.910940 −0.0319677
\(813\) 13.4343 0.471162
\(814\) −8.52910 −0.298945
\(815\) −15.3470 −0.537584
\(816\) −7.00910 −0.245367
\(817\) 52.4412 1.83468
\(818\) 7.62689 0.266668
\(819\) −1.10503 −0.0386130
\(820\) −18.1192 −0.632751
\(821\) 9.33738 0.325877 0.162938 0.986636i \(-0.447903\pi\)
0.162938 + 0.986636i \(0.447903\pi\)
\(822\) −0.898419 −0.0313360
\(823\) 10.5883 0.369083 0.184542 0.982825i \(-0.440920\pi\)
0.184542 + 0.982825i \(0.440920\pi\)
\(824\) −1.59840 −0.0556830
\(825\) −4.57218 −0.159183
\(826\) 1.36588 0.0475251
\(827\) 12.2458 0.425829 0.212914 0.977071i \(-0.431704\pi\)
0.212914 + 0.977071i \(0.431704\pi\)
\(828\) 4.71130 0.163729
\(829\) −14.2996 −0.496645 −0.248322 0.968677i \(-0.579879\pi\)
−0.248322 + 0.968677i \(0.579879\pi\)
\(830\) 0.547205 0.0189938
\(831\) −8.00178 −0.277579
\(832\) 21.0829 0.730919
\(833\) −1.29135 −0.0447427
\(834\) −10.2785 −0.355914
\(835\) −22.2761 −0.770895
\(836\) −22.0537 −0.762745
\(837\) −7.37984 −0.255085
\(838\) −10.6435 −0.367672
\(839\) 44.0677 1.52139 0.760693 0.649112i \(-0.224859\pi\)
0.760693 + 0.649112i \(0.224859\pi\)
\(840\) 2.22898 0.0769072
\(841\) −28.7649 −0.991894
\(842\) −10.2936 −0.354740
\(843\) 41.7789 1.43894
\(844\) 17.6322 0.606926
\(845\) −3.20579 −0.110282
\(846\) 1.02237 0.0351498
\(847\) 3.32993 0.114418
\(848\) 41.0267 1.40886
\(849\) −25.8269 −0.886378
\(850\) 0.449496 0.0154176
\(851\) −80.8227 −2.77057
\(852\) −40.6527 −1.39274
\(853\) 41.8305 1.43225 0.716125 0.697972i \(-0.245914\pi\)
0.716125 + 0.697972i \(0.245914\pi\)
\(854\) −4.76745 −0.163139
\(855\) −1.16341 −0.0397878
\(856\) −5.60095 −0.191437
\(857\) −42.3877 −1.44793 −0.723967 0.689834i \(-0.757683\pi\)
−0.723967 + 0.689834i \(0.757683\pi\)
\(858\) −6.40677 −0.218724
\(859\) 44.3753 1.51407 0.757034 0.653376i \(-0.226648\pi\)
0.757034 + 0.653376i \(0.226648\pi\)
\(860\) −23.2471 −0.792720
\(861\) 15.9211 0.542590
\(862\) 6.21812 0.211790
\(863\) 11.8987 0.405038 0.202519 0.979278i \(-0.435087\pi\)
0.202519 + 0.979278i \(0.435087\pi\)
\(864\) 20.7841 0.707088
\(865\) −6.47862 −0.220280
\(866\) 1.13709 0.0386398
\(867\) −25.3124 −0.859655
\(868\) 2.56489 0.0870580
\(869\) −27.5302 −0.933898
\(870\) −0.278615 −0.00944594
\(871\) 42.0340 1.42427
\(872\) −11.7265 −0.397108
\(873\) −0.810439 −0.0274292
\(874\) 13.4768 0.455859
\(875\) 1.00000 0.0338062
\(876\) 24.2779 0.820274
\(877\) 11.9095 0.402154 0.201077 0.979575i \(-0.435556\pi\)
0.201077 + 0.979575i \(0.435556\pi\)
\(878\) 5.43079 0.183280
\(879\) 37.3378 1.25937
\(880\) 9.10529 0.306939
\(881\) −4.97365 −0.167567 −0.0837833 0.996484i \(-0.526700\pi\)
−0.0837833 + 0.996484i \(0.526700\pi\)
\(882\) 0.0955480 0.00321727
\(883\) −13.4365 −0.452176 −0.226088 0.974107i \(-0.572594\pi\)
−0.226088 + 0.974107i \(0.572594\pi\)
\(884\) −9.76719 −0.328506
\(885\) −6.47820 −0.217762
\(886\) 3.61560 0.121468
\(887\) 52.7196 1.77015 0.885075 0.465449i \(-0.154107\pi\)
0.885075 + 0.465449i \(0.154107\pi\)
\(888\) −19.7210 −0.661792
\(889\) −2.21935 −0.0744347
\(890\) −1.98006 −0.0663716
\(891\) 22.4361 0.751636
\(892\) −55.3091 −1.85188
\(893\) −45.3502 −1.51759
\(894\) −11.5844 −0.387440
\(895\) −5.31716 −0.177733
\(896\) −9.51236 −0.317786
\(897\) −60.7113 −2.02709
\(898\) −6.30295 −0.210332
\(899\) −0.661880 −0.0220749
\(900\) 0.515739 0.0171913
\(901\) −16.1145 −0.536853
\(902\) −9.29676 −0.309548
\(903\) 20.4269 0.679765
\(904\) 1.04121 0.0346300
\(905\) −14.6112 −0.485693
\(906\) 4.43652 0.147394
\(907\) −46.6533 −1.54910 −0.774548 0.632515i \(-0.782023\pi\)
−0.774548 + 0.632515i \(0.782023\pi\)
\(908\) −52.9920 −1.75860
\(909\) −0.129877 −0.00430776
\(910\) 1.40125 0.0464511
\(911\) −50.0716 −1.65895 −0.829473 0.558546i \(-0.811359\pi\)
−0.829473 + 0.558546i \(0.811359\pi\)
\(912\) −23.0044 −0.761751
\(913\) −4.35380 −0.144090
\(914\) 2.66644 0.0881981
\(915\) 22.6114 0.747511
\(916\) −1.87884 −0.0620786
\(917\) −6.04214 −0.199529
\(918\) −2.42993 −0.0801997
\(919\) 6.62344 0.218487 0.109244 0.994015i \(-0.465157\pi\)
0.109244 + 0.994015i \(0.465157\pi\)
\(920\) −12.3337 −0.406631
\(921\) −38.3412 −1.26339
\(922\) 0.878992 0.0289481
\(923\) −52.7608 −1.73664
\(924\) −8.59038 −0.282603
\(925\) −8.84752 −0.290905
\(926\) 1.42943 0.0469741
\(927\) 0.324970 0.0106734
\(928\) 1.86407 0.0611912
\(929\) −19.3548 −0.635010 −0.317505 0.948257i \(-0.602845\pi\)
−0.317505 + 0.948257i \(0.602845\pi\)
\(930\) 0.784483 0.0257242
\(931\) −4.23831 −0.138905
\(932\) 36.7323 1.20321
\(933\) 18.0423 0.590677
\(934\) −3.59909 −0.117766
\(935\) −3.57639 −0.116960
\(936\) 1.49196 0.0487664
\(937\) −0.983655 −0.0321346 −0.0160673 0.999871i \(-0.505115\pi\)
−0.0160673 + 0.999871i \(0.505115\pi\)
\(938\) −3.63452 −0.118671
\(939\) −34.6514 −1.13081
\(940\) 20.1037 0.655710
\(941\) 33.0903 1.07871 0.539357 0.842077i \(-0.318667\pi\)
0.539357 + 0.842077i \(0.318667\pi\)
\(942\) 0.556265 0.0181241
\(943\) −88.0972 −2.86884
\(944\) 12.9011 0.419894
\(945\) −5.40590 −0.175854
\(946\) −11.9278 −0.387806
\(947\) 54.3380 1.76575 0.882874 0.469610i \(-0.155606\pi\)
0.882874 + 0.469610i \(0.155606\pi\)
\(948\) −30.8335 −1.00142
\(949\) 31.5089 1.02282
\(950\) 1.47528 0.0478644
\(951\) −17.7001 −0.573965
\(952\) 1.74352 0.0565080
\(953\) −9.83560 −0.318606 −0.159303 0.987230i \(-0.550925\pi\)
−0.159303 + 0.987230i \(0.550925\pi\)
\(954\) 1.19232 0.0386029
\(955\) 10.9499 0.354330
\(956\) 44.2992 1.43274
\(957\) 2.21678 0.0716584
\(958\) −7.18841 −0.232247
\(959\) −1.56342 −0.0504853
\(960\) 8.64607 0.279051
\(961\) −29.1364 −0.939883
\(962\) −12.3976 −0.399715
\(963\) 1.13873 0.0366949
\(964\) −26.6104 −0.857062
\(965\) −5.06928 −0.163186
\(966\) 5.24948 0.168899
\(967\) 5.11383 0.164450 0.0822248 0.996614i \(-0.473797\pi\)
0.0822248 + 0.996614i \(0.473797\pi\)
\(968\) −4.49592 −0.144504
\(969\) 9.03568 0.290268
\(970\) 1.02769 0.0329971
\(971\) −38.3252 −1.22991 −0.614957 0.788561i \(-0.710827\pi\)
−0.614957 + 0.788561i \(0.710827\pi\)
\(972\) −5.34234 −0.171356
\(973\) −17.8864 −0.573412
\(974\) −1.58670 −0.0508412
\(975\) −6.64597 −0.212841
\(976\) −45.0297 −1.44136
\(977\) 6.08843 0.194786 0.0973930 0.995246i \(-0.468950\pi\)
0.0973930 + 0.995246i \(0.468950\pi\)
\(978\) −8.81921 −0.282007
\(979\) 15.7542 0.503506
\(980\) 1.87884 0.0600173
\(981\) 2.38410 0.0761183
\(982\) −1.77121 −0.0565217
\(983\) 50.7106 1.61742 0.808708 0.588210i \(-0.200167\pi\)
0.808708 + 0.588210i \(0.200167\pi\)
\(984\) −21.4960 −0.685266
\(985\) 24.0532 0.766397
\(986\) −0.217935 −0.00694046
\(987\) −17.6648 −0.562278
\(988\) −32.0566 −1.01986
\(989\) −113.029 −3.59412
\(990\) 0.264619 0.00841015
\(991\) 14.7178 0.467525 0.233763 0.972294i \(-0.424896\pi\)
0.233763 + 0.972294i \(0.424896\pi\)
\(992\) −5.24858 −0.166642
\(993\) 33.3232 1.05748
\(994\) 4.56203 0.144699
\(995\) −23.5440 −0.746395
\(996\) −4.87620 −0.154508
\(997\) −9.38007 −0.297070 −0.148535 0.988907i \(-0.547456\pi\)
−0.148535 + 0.988907i \(0.547456\pi\)
\(998\) −15.3855 −0.487019
\(999\) 47.8288 1.51324
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 \(a_p\))