Properties

Label 4030.2.a.f.1.4
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 1
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4418197.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.59064\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.252625 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.252625 q^{6} -1.23948 q^{7} +1.00000 q^{8} -2.93618 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.252625 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.252625 q^{6} -1.23948 q^{7} +1.00000 q^{8} -2.93618 q^{9} -1.00000 q^{10} +4.08674 q^{11} -0.252625 q^{12} +1.00000 q^{13} -1.23948 q^{14} +0.252625 q^{15} +1.00000 q^{16} -1.06781 q^{17} -2.93618 q^{18} -8.14236 q^{19} -1.00000 q^{20} +0.313125 q^{21} +4.08674 q^{22} +6.59643 q^{23} -0.252625 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.49963 q^{27} -1.23948 q^{28} -1.85322 q^{29} +0.252625 q^{30} -1.00000 q^{31} +1.00000 q^{32} -1.03241 q^{33} -1.06781 q^{34} +1.23948 q^{35} -2.93618 q^{36} -0.537878 q^{37} -8.14236 q^{38} -0.252625 q^{39} -1.00000 q^{40} -0.693843 q^{41} +0.313125 q^{42} -12.5556 q^{43} +4.08674 q^{44} +2.93618 q^{45} +6.59643 q^{46} +6.79817 q^{47} -0.252625 q^{48} -5.46368 q^{49} +1.00000 q^{50} +0.269755 q^{51} +1.00000 q^{52} -11.4271 q^{53} +1.49963 q^{54} -4.08674 q^{55} -1.23948 q^{56} +2.05697 q^{57} -1.85322 q^{58} +4.92227 q^{59} +0.252625 q^{60} +4.53622 q^{61} -1.00000 q^{62} +3.63935 q^{63} +1.00000 q^{64} -1.00000 q^{65} -1.03241 q^{66} -7.82519 q^{67} -1.06781 q^{68} -1.66643 q^{69} +1.23948 q^{70} +2.45442 q^{71} -2.93618 q^{72} -14.2626 q^{73} -0.537878 q^{74} -0.252625 q^{75} -8.14236 q^{76} -5.06544 q^{77} -0.252625 q^{78} +0.819624 q^{79} -1.00000 q^{80} +8.42970 q^{81} -0.693843 q^{82} -16.3989 q^{83} +0.313125 q^{84} +1.06781 q^{85} -12.5556 q^{86} +0.468169 q^{87} +4.08674 q^{88} +9.66762 q^{89} +2.93618 q^{90} -1.23948 q^{91} +6.59643 q^{92} +0.252625 q^{93} +6.79817 q^{94} +8.14236 q^{95} -0.252625 q^{96} -4.14428 q^{97} -5.46368 q^{98} -11.9994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.252625 −0.145853 −0.0729266 0.997337i \(-0.523234\pi\)
−0.0729266 + 0.997337i \(0.523234\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.252625 −0.103134
\(7\) −1.23948 −0.468481 −0.234240 0.972179i \(-0.575260\pi\)
−0.234240 + 0.972179i \(0.575260\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.93618 −0.978727
\(10\) −1.00000 −0.316228
\(11\) 4.08674 1.23220 0.616099 0.787669i \(-0.288712\pi\)
0.616099 + 0.787669i \(0.288712\pi\)
\(12\) −0.252625 −0.0729266
\(13\) 1.00000 0.277350
\(14\) −1.23948 −0.331266
\(15\) 0.252625 0.0652276
\(16\) 1.00000 0.250000
\(17\) −1.06781 −0.258981 −0.129491 0.991581i \(-0.541334\pi\)
−0.129491 + 0.991581i \(0.541334\pi\)
\(18\) −2.93618 −0.692064
\(19\) −8.14236 −1.86798 −0.933992 0.357293i \(-0.883700\pi\)
−0.933992 + 0.357293i \(0.883700\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0.313125 0.0683294
\(22\) 4.08674 0.871295
\(23\) 6.59643 1.37545 0.687725 0.725971i \(-0.258609\pi\)
0.687725 + 0.725971i \(0.258609\pi\)
\(24\) −0.252625 −0.0515669
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 1.49963 0.288604
\(28\) −1.23948 −0.234240
\(29\) −1.85322 −0.344134 −0.172067 0.985085i \(-0.555044\pi\)
−0.172067 + 0.985085i \(0.555044\pi\)
\(30\) 0.252625 0.0461229
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −1.03241 −0.179720
\(34\) −1.06781 −0.183127
\(35\) 1.23948 0.209511
\(36\) −2.93618 −0.489363
\(37\) −0.537878 −0.0884266 −0.0442133 0.999022i \(-0.514078\pi\)
−0.0442133 + 0.999022i \(0.514078\pi\)
\(38\) −8.14236 −1.32086
\(39\) −0.252625 −0.0404524
\(40\) −1.00000 −0.158114
\(41\) −0.693843 −0.108360 −0.0541800 0.998531i \(-0.517254\pi\)
−0.0541800 + 0.998531i \(0.517254\pi\)
\(42\) 0.313125 0.0483162
\(43\) −12.5556 −1.91471 −0.957356 0.288912i \(-0.906707\pi\)
−0.957356 + 0.288912i \(0.906707\pi\)
\(44\) 4.08674 0.616099
\(45\) 2.93618 0.437700
\(46\) 6.59643 0.972591
\(47\) 6.79817 0.991614 0.495807 0.868433i \(-0.334872\pi\)
0.495807 + 0.868433i \(0.334872\pi\)
\(48\) −0.252625 −0.0364633
\(49\) −5.46368 −0.780526
\(50\) 1.00000 0.141421
\(51\) 0.269755 0.0377733
\(52\) 1.00000 0.138675
\(53\) −11.4271 −1.56963 −0.784817 0.619727i \(-0.787243\pi\)
−0.784817 + 0.619727i \(0.787243\pi\)
\(54\) 1.49963 0.204074
\(55\) −4.08674 −0.551056
\(56\) −1.23948 −0.165633
\(57\) 2.05697 0.272452
\(58\) −1.85322 −0.243339
\(59\) 4.92227 0.640825 0.320413 0.947278i \(-0.396178\pi\)
0.320413 + 0.947278i \(0.396178\pi\)
\(60\) 0.252625 0.0326138
\(61\) 4.53622 0.580803 0.290402 0.956905i \(-0.406211\pi\)
0.290402 + 0.956905i \(0.406211\pi\)
\(62\) −1.00000 −0.127000
\(63\) 3.63935 0.458514
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −1.03241 −0.127081
\(67\) −7.82519 −0.955999 −0.478000 0.878360i \(-0.658638\pi\)
−0.478000 + 0.878360i \(0.658638\pi\)
\(68\) −1.06781 −0.129491
\(69\) −1.66643 −0.200614
\(70\) 1.23948 0.148147
\(71\) 2.45442 0.291286 0.145643 0.989337i \(-0.453475\pi\)
0.145643 + 0.989337i \(0.453475\pi\)
\(72\) −2.93618 −0.346032
\(73\) −14.2626 −1.66931 −0.834654 0.550775i \(-0.814332\pi\)
−0.834654 + 0.550775i \(0.814332\pi\)
\(74\) −0.537878 −0.0625270
\(75\) −0.252625 −0.0291707
\(76\) −8.14236 −0.933992
\(77\) −5.06544 −0.577261
\(78\) −0.252625 −0.0286042
\(79\) 0.819624 0.0922149 0.0461074 0.998936i \(-0.485318\pi\)
0.0461074 + 0.998936i \(0.485318\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.42970 0.936633
\(82\) −0.693843 −0.0766221
\(83\) −16.3989 −1.80001 −0.900005 0.435880i \(-0.856437\pi\)
−0.900005 + 0.435880i \(0.856437\pi\)
\(84\) 0.313125 0.0341647
\(85\) 1.06781 0.115820
\(86\) −12.5556 −1.35391
\(87\) 0.468169 0.0501930
\(88\) 4.08674 0.435648
\(89\) 9.66762 1.02477 0.512383 0.858757i \(-0.328763\pi\)
0.512383 + 0.858757i \(0.328763\pi\)
\(90\) 2.93618 0.309501
\(91\) −1.23948 −0.129933
\(92\) 6.59643 0.687725
\(93\) 0.252625 0.0261960
\(94\) 6.79817 0.701177
\(95\) 8.14236 0.835388
\(96\) −0.252625 −0.0257835
\(97\) −4.14428 −0.420788 −0.210394 0.977617i \(-0.567475\pi\)
−0.210394 + 0.977617i \(0.567475\pi\)
\(98\) −5.46368 −0.551915
\(99\) −11.9994 −1.20599
\(100\) 1.00000 0.100000
\(101\) −6.09882 −0.606855 −0.303428 0.952854i \(-0.598131\pi\)
−0.303428 + 0.952854i \(0.598131\pi\)
\(102\) 0.269755 0.0267097
\(103\) 4.89812 0.482626 0.241313 0.970447i \(-0.422422\pi\)
0.241313 + 0.970447i \(0.422422\pi\)
\(104\) 1.00000 0.0980581
\(105\) −0.313125 −0.0305578
\(106\) −11.4271 −1.10990
\(107\) 7.34568 0.710134 0.355067 0.934841i \(-0.384458\pi\)
0.355067 + 0.934841i \(0.384458\pi\)
\(108\) 1.49963 0.144302
\(109\) −19.2327 −1.84216 −0.921081 0.389370i \(-0.872693\pi\)
−0.921081 + 0.389370i \(0.872693\pi\)
\(110\) −4.08674 −0.389655
\(111\) 0.135882 0.0128973
\(112\) −1.23948 −0.117120
\(113\) −16.4569 −1.54813 −0.774065 0.633106i \(-0.781780\pi\)
−0.774065 + 0.633106i \(0.781780\pi\)
\(114\) 2.05697 0.192652
\(115\) −6.59643 −0.615120
\(116\) −1.85322 −0.172067
\(117\) −2.93618 −0.271450
\(118\) 4.92227 0.453132
\(119\) 1.32353 0.121328
\(120\) 0.252625 0.0230614
\(121\) 5.70143 0.518311
\(122\) 4.53622 0.410690
\(123\) 0.175282 0.0158047
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 3.63935 0.324219
\(127\) −17.7965 −1.57918 −0.789590 0.613635i \(-0.789707\pi\)
−0.789590 + 0.613635i \(0.789707\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.17186 0.279267
\(130\) −1.00000 −0.0877058
\(131\) −7.32944 −0.640376 −0.320188 0.947354i \(-0.603746\pi\)
−0.320188 + 0.947354i \(0.603746\pi\)
\(132\) −1.03241 −0.0898601
\(133\) 10.0923 0.875114
\(134\) −7.82519 −0.675994
\(135\) −1.49963 −0.129068
\(136\) −1.06781 −0.0915637
\(137\) 17.0050 1.45283 0.726417 0.687254i \(-0.241184\pi\)
0.726417 + 0.687254i \(0.241184\pi\)
\(138\) −1.66643 −0.141856
\(139\) 6.80321 0.577040 0.288520 0.957474i \(-0.406837\pi\)
0.288520 + 0.957474i \(0.406837\pi\)
\(140\) 1.23948 0.104755
\(141\) −1.71739 −0.144630
\(142\) 2.45442 0.205971
\(143\) 4.08674 0.341750
\(144\) −2.93618 −0.244682
\(145\) 1.85322 0.153901
\(146\) −14.2626 −1.18038
\(147\) 1.38026 0.113842
\(148\) −0.537878 −0.0442133
\(149\) −10.7988 −0.884671 −0.442336 0.896850i \(-0.645850\pi\)
−0.442336 + 0.896850i \(0.645850\pi\)
\(150\) −0.252625 −0.0206268
\(151\) −1.77076 −0.144102 −0.0720511 0.997401i \(-0.522954\pi\)
−0.0720511 + 0.997401i \(0.522954\pi\)
\(152\) −8.14236 −0.660432
\(153\) 3.13527 0.253472
\(154\) −5.06544 −0.408185
\(155\) 1.00000 0.0803219
\(156\) −0.252625 −0.0202262
\(157\) 22.1053 1.76420 0.882099 0.471064i \(-0.156130\pi\)
0.882099 + 0.471064i \(0.156130\pi\)
\(158\) 0.819624 0.0652058
\(159\) 2.88678 0.228936
\(160\) −1.00000 −0.0790569
\(161\) −8.17616 −0.644372
\(162\) 8.42970 0.662300
\(163\) −17.9197 −1.40358 −0.701788 0.712385i \(-0.747615\pi\)
−0.701788 + 0.712385i \(0.747615\pi\)
\(164\) −0.693843 −0.0541800
\(165\) 1.03241 0.0803733
\(166\) −16.3989 −1.27280
\(167\) 12.0670 0.933775 0.466887 0.884317i \(-0.345375\pi\)
0.466887 + 0.884317i \(0.345375\pi\)
\(168\) 0.313125 0.0241581
\(169\) 1.00000 0.0769231
\(170\) 1.06781 0.0818970
\(171\) 23.9074 1.82825
\(172\) −12.5556 −0.957356
\(173\) 21.4481 1.63067 0.815335 0.578989i \(-0.196553\pi\)
0.815335 + 0.578989i \(0.196553\pi\)
\(174\) 0.468169 0.0354918
\(175\) −1.23948 −0.0936961
\(176\) 4.08674 0.308049
\(177\) −1.24349 −0.0934664
\(178\) 9.66762 0.724619
\(179\) −18.8075 −1.40574 −0.702871 0.711318i \(-0.748099\pi\)
−0.702871 + 0.711318i \(0.748099\pi\)
\(180\) 2.93618 0.218850
\(181\) −19.2383 −1.42997 −0.714986 0.699138i \(-0.753567\pi\)
−0.714986 + 0.699138i \(0.753567\pi\)
\(182\) −1.23948 −0.0918766
\(183\) −1.14596 −0.0847120
\(184\) 6.59643 0.486295
\(185\) 0.537878 0.0395456
\(186\) 0.252625 0.0185234
\(187\) −4.36385 −0.319116
\(188\) 6.79817 0.495807
\(189\) −1.85877 −0.135205
\(190\) 8.14236 0.590709
\(191\) 3.25410 0.235458 0.117729 0.993046i \(-0.462439\pi\)
0.117729 + 0.993046i \(0.462439\pi\)
\(192\) −0.252625 −0.0182317
\(193\) 4.75236 0.342082 0.171041 0.985264i \(-0.445287\pi\)
0.171041 + 0.985264i \(0.445287\pi\)
\(194\) −4.14428 −0.297542
\(195\) 0.252625 0.0180909
\(196\) −5.46368 −0.390263
\(197\) −20.7562 −1.47882 −0.739410 0.673255i \(-0.764896\pi\)
−0.739410 + 0.673255i \(0.764896\pi\)
\(198\) −11.9994 −0.852760
\(199\) −12.6687 −0.898057 −0.449028 0.893517i \(-0.648230\pi\)
−0.449028 + 0.893517i \(0.648230\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.97684 0.139436
\(202\) −6.09882 −0.429111
\(203\) 2.29703 0.161220
\(204\) 0.269755 0.0188866
\(205\) 0.693843 0.0484601
\(206\) 4.89812 0.341268
\(207\) −19.3683 −1.34619
\(208\) 1.00000 0.0693375
\(209\) −33.2757 −2.30173
\(210\) −0.313125 −0.0216077
\(211\) 5.59342 0.385067 0.192534 0.981290i \(-0.438330\pi\)
0.192534 + 0.981290i \(0.438330\pi\)
\(212\) −11.4271 −0.784817
\(213\) −0.620049 −0.0424851
\(214\) 7.34568 0.502140
\(215\) 12.5556 0.856285
\(216\) 1.49963 0.102037
\(217\) 1.23948 0.0841416
\(218\) −19.2327 −1.30261
\(219\) 3.60309 0.243474
\(220\) −4.08674 −0.275528
\(221\) −1.06781 −0.0718285
\(222\) 0.135882 0.00911977
\(223\) 25.1249 1.68249 0.841243 0.540657i \(-0.181824\pi\)
0.841243 + 0.540657i \(0.181824\pi\)
\(224\) −1.23948 −0.0828164
\(225\) −2.93618 −0.195745
\(226\) −16.4569 −1.09469
\(227\) 13.2454 0.879131 0.439565 0.898211i \(-0.355132\pi\)
0.439565 + 0.898211i \(0.355132\pi\)
\(228\) 2.05697 0.136226
\(229\) −6.93174 −0.458063 −0.229031 0.973419i \(-0.573556\pi\)
−0.229031 + 0.973419i \(0.573556\pi\)
\(230\) −6.59643 −0.434956
\(231\) 1.27966 0.0841954
\(232\) −1.85322 −0.121670
\(233\) −21.5947 −1.41471 −0.707357 0.706856i \(-0.750113\pi\)
−0.707357 + 0.706856i \(0.750113\pi\)
\(234\) −2.93618 −0.191944
\(235\) −6.79817 −0.443463
\(236\) 4.92227 0.320413
\(237\) −0.207058 −0.0134498
\(238\) 1.32353 0.0857916
\(239\) −20.6583 −1.33628 −0.668139 0.744037i \(-0.732909\pi\)
−0.668139 + 0.744037i \(0.732909\pi\)
\(240\) 0.252625 0.0163069
\(241\) −21.7353 −1.40010 −0.700048 0.714096i \(-0.746838\pi\)
−0.700048 + 0.714096i \(0.746838\pi\)
\(242\) 5.70143 0.366502
\(243\) −6.62844 −0.425215
\(244\) 4.53622 0.290402
\(245\) 5.46368 0.349062
\(246\) 0.175282 0.0111756
\(247\) −8.14236 −0.518086
\(248\) −1.00000 −0.0635001
\(249\) 4.14277 0.262537
\(250\) −1.00000 −0.0632456
\(251\) 12.7871 0.807117 0.403558 0.914954i \(-0.367773\pi\)
0.403558 + 0.914954i \(0.367773\pi\)
\(252\) 3.63935 0.229257
\(253\) 26.9579 1.69483
\(254\) −17.7965 −1.11665
\(255\) −0.269755 −0.0168927
\(256\) 1.00000 0.0625000
\(257\) −6.88832 −0.429681 −0.214841 0.976649i \(-0.568923\pi\)
−0.214841 + 0.976649i \(0.568923\pi\)
\(258\) 3.17186 0.197472
\(259\) 0.666690 0.0414261
\(260\) −1.00000 −0.0620174
\(261\) 5.44138 0.336813
\(262\) −7.32944 −0.452814
\(263\) 17.9601 1.10747 0.553733 0.832694i \(-0.313203\pi\)
0.553733 + 0.832694i \(0.313203\pi\)
\(264\) −1.03241 −0.0635407
\(265\) 11.4271 0.701962
\(266\) 10.0923 0.618799
\(267\) −2.44229 −0.149465
\(268\) −7.82519 −0.478000
\(269\) 3.72219 0.226946 0.113473 0.993541i \(-0.463802\pi\)
0.113473 + 0.993541i \(0.463802\pi\)
\(270\) −1.49963 −0.0912645
\(271\) 3.22237 0.195745 0.0978726 0.995199i \(-0.468796\pi\)
0.0978726 + 0.995199i \(0.468796\pi\)
\(272\) −1.06781 −0.0647453
\(273\) 0.313125 0.0189512
\(274\) 17.0050 1.02731
\(275\) 4.08674 0.246440
\(276\) −1.66643 −0.100307
\(277\) 24.9074 1.49654 0.748271 0.663394i \(-0.230884\pi\)
0.748271 + 0.663394i \(0.230884\pi\)
\(278\) 6.80321 0.408029
\(279\) 2.93618 0.175785
\(280\) 1.23948 0.0740733
\(281\) 18.3523 1.09481 0.547403 0.836869i \(-0.315616\pi\)
0.547403 + 0.836869i \(0.315616\pi\)
\(282\) −1.71739 −0.102269
\(283\) −9.33022 −0.554624 −0.277312 0.960780i \(-0.589444\pi\)
−0.277312 + 0.960780i \(0.589444\pi\)
\(284\) 2.45442 0.145643
\(285\) −2.05697 −0.121844
\(286\) 4.08674 0.241654
\(287\) 0.860006 0.0507646
\(288\) −2.93618 −0.173016
\(289\) −15.8598 −0.932929
\(290\) 1.85322 0.108825
\(291\) 1.04695 0.0613733
\(292\) −14.2626 −0.834654
\(293\) 21.5474 1.25881 0.629406 0.777077i \(-0.283298\pi\)
0.629406 + 0.777077i \(0.283298\pi\)
\(294\) 1.38026 0.0804987
\(295\) −4.92227 −0.286586
\(296\) −0.537878 −0.0312635
\(297\) 6.12859 0.355617
\(298\) −10.7988 −0.625557
\(299\) 6.59643 0.381481
\(300\) −0.252625 −0.0145853
\(301\) 15.5625 0.897005
\(302\) −1.77076 −0.101896
\(303\) 1.54072 0.0885118
\(304\) −8.14236 −0.466996
\(305\) −4.53622 −0.259743
\(306\) 3.13527 0.179232
\(307\) 15.4675 0.882779 0.441389 0.897316i \(-0.354486\pi\)
0.441389 + 0.897316i \(0.354486\pi\)
\(308\) −5.06544 −0.288630
\(309\) −1.23739 −0.0703926
\(310\) 1.00000 0.0567962
\(311\) −20.4847 −1.16158 −0.580789 0.814054i \(-0.697256\pi\)
−0.580789 + 0.814054i \(0.697256\pi\)
\(312\) −0.252625 −0.0143021
\(313\) 25.7248 1.45405 0.727026 0.686610i \(-0.240902\pi\)
0.727026 + 0.686610i \(0.240902\pi\)
\(314\) 22.1053 1.24748
\(315\) −3.63935 −0.205054
\(316\) 0.819624 0.0461074
\(317\) −0.411304 −0.0231011 −0.0115506 0.999933i \(-0.503677\pi\)
−0.0115506 + 0.999933i \(0.503677\pi\)
\(318\) 2.88678 0.161882
\(319\) −7.57361 −0.424041
\(320\) −1.00000 −0.0559017
\(321\) −1.85570 −0.103575
\(322\) −8.17616 −0.455640
\(323\) 8.69446 0.483773
\(324\) 8.42970 0.468316
\(325\) 1.00000 0.0554700
\(326\) −17.9197 −0.992479
\(327\) 4.85868 0.268685
\(328\) −0.693843 −0.0383110
\(329\) −8.42621 −0.464552
\(330\) 1.03241 0.0568325
\(331\) −19.5537 −1.07477 −0.537383 0.843338i \(-0.680587\pi\)
−0.537383 + 0.843338i \(0.680587\pi\)
\(332\) −16.3989 −0.900005
\(333\) 1.57931 0.0865455
\(334\) 12.0670 0.660278
\(335\) 7.82519 0.427536
\(336\) 0.313125 0.0170824
\(337\) −24.8159 −1.35181 −0.675904 0.736989i \(-0.736247\pi\)
−0.675904 + 0.736989i \(0.736247\pi\)
\(338\) 1.00000 0.0543928
\(339\) 4.15742 0.225800
\(340\) 1.06781 0.0579100
\(341\) −4.08674 −0.221309
\(342\) 23.9074 1.29277
\(343\) 15.4485 0.834142
\(344\) −12.5556 −0.676953
\(345\) 1.66643 0.0897173
\(346\) 21.4481 1.15306
\(347\) −12.2109 −0.655518 −0.327759 0.944761i \(-0.606293\pi\)
−0.327759 + 0.944761i \(0.606293\pi\)
\(348\) 0.468169 0.0250965
\(349\) 31.9548 1.71050 0.855249 0.518217i \(-0.173404\pi\)
0.855249 + 0.518217i \(0.173404\pi\)
\(350\) −1.23948 −0.0662531
\(351\) 1.49963 0.0800443
\(352\) 4.08674 0.217824
\(353\) 23.4863 1.25005 0.625024 0.780606i \(-0.285089\pi\)
0.625024 + 0.780606i \(0.285089\pi\)
\(354\) −1.24349 −0.0660908
\(355\) −2.45442 −0.130267
\(356\) 9.66762 0.512383
\(357\) −0.334357 −0.0176960
\(358\) −18.8075 −0.994009
\(359\) −4.71759 −0.248985 −0.124493 0.992221i \(-0.539730\pi\)
−0.124493 + 0.992221i \(0.539730\pi\)
\(360\) 2.93618 0.154750
\(361\) 47.2980 2.48937
\(362\) −19.2383 −1.01114
\(363\) −1.44032 −0.0755974
\(364\) −1.23948 −0.0649666
\(365\) 14.2626 0.746537
\(366\) −1.14596 −0.0599005
\(367\) −2.37279 −0.123859 −0.0619294 0.998081i \(-0.519725\pi\)
−0.0619294 + 0.998081i \(0.519725\pi\)
\(368\) 6.59643 0.343863
\(369\) 2.03725 0.106055
\(370\) 0.537878 0.0279629
\(371\) 14.1637 0.735343
\(372\) 0.252625 0.0130980
\(373\) −14.2652 −0.738623 −0.369312 0.929306i \(-0.620406\pi\)
−0.369312 + 0.929306i \(0.620406\pi\)
\(374\) −4.36385 −0.225649
\(375\) 0.252625 0.0130455
\(376\) 6.79817 0.350589
\(377\) −1.85322 −0.0954455
\(378\) −1.85877 −0.0956046
\(379\) 26.9056 1.38205 0.691023 0.722832i \(-0.257160\pi\)
0.691023 + 0.722832i \(0.257160\pi\)
\(380\) 8.14236 0.417694
\(381\) 4.49584 0.230329
\(382\) 3.25410 0.166494
\(383\) 32.3812 1.65460 0.827301 0.561759i \(-0.189875\pi\)
0.827301 + 0.561759i \(0.189875\pi\)
\(384\) −0.252625 −0.0128917
\(385\) 5.06544 0.258159
\(386\) 4.75236 0.241889
\(387\) 36.8655 1.87398
\(388\) −4.14428 −0.210394
\(389\) 7.42585 0.376506 0.188253 0.982121i \(-0.439718\pi\)
0.188253 + 0.982121i \(0.439718\pi\)
\(390\) 0.252625 0.0127922
\(391\) −7.04371 −0.356216
\(392\) −5.46368 −0.275958
\(393\) 1.85160 0.0934009
\(394\) −20.7562 −1.04568
\(395\) −0.819624 −0.0412398
\(396\) −11.9994 −0.602993
\(397\) −0.532290 −0.0267149 −0.0133574 0.999911i \(-0.504252\pi\)
−0.0133574 + 0.999911i \(0.504252\pi\)
\(398\) −12.6687 −0.635022
\(399\) −2.54957 −0.127638
\(400\) 1.00000 0.0500000
\(401\) 5.08171 0.253768 0.126884 0.991918i \(-0.459502\pi\)
0.126884 + 0.991918i \(0.459502\pi\)
\(402\) 1.97684 0.0985959
\(403\) −1.00000 −0.0498135
\(404\) −6.09882 −0.303428
\(405\) −8.42970 −0.418875
\(406\) 2.29703 0.114000
\(407\) −2.19817 −0.108959
\(408\) 0.269755 0.0133549
\(409\) −11.9445 −0.590617 −0.295308 0.955402i \(-0.595422\pi\)
−0.295308 + 0.955402i \(0.595422\pi\)
\(410\) 0.693843 0.0342664
\(411\) −4.29589 −0.211901
\(412\) 4.89812 0.241313
\(413\) −6.10107 −0.300214
\(414\) −19.3683 −0.951901
\(415\) 16.3989 0.804989
\(416\) 1.00000 0.0490290
\(417\) −1.71866 −0.0841632
\(418\) −33.2757 −1.62757
\(419\) 29.6890 1.45040 0.725200 0.688538i \(-0.241747\pi\)
0.725200 + 0.688538i \(0.241747\pi\)
\(420\) −0.313125 −0.0152789
\(421\) −8.84383 −0.431022 −0.215511 0.976501i \(-0.569142\pi\)
−0.215511 + 0.976501i \(0.569142\pi\)
\(422\) 5.59342 0.272284
\(423\) −19.9606 −0.970520
\(424\) −11.4271 −0.554950
\(425\) −1.06781 −0.0517962
\(426\) −0.620049 −0.0300415
\(427\) −5.62256 −0.272095
\(428\) 7.34568 0.355067
\(429\) −1.03241 −0.0498454
\(430\) 12.5556 0.605485
\(431\) −27.1853 −1.30947 −0.654734 0.755860i \(-0.727219\pi\)
−0.654734 + 0.755860i \(0.727219\pi\)
\(432\) 1.49963 0.0721510
\(433\) 28.8950 1.38860 0.694301 0.719684i \(-0.255713\pi\)
0.694301 + 0.719684i \(0.255713\pi\)
\(434\) 1.23948 0.0594971
\(435\) −0.468169 −0.0224470
\(436\) −19.2327 −0.921081
\(437\) −53.7105 −2.56932
\(438\) 3.60309 0.172162
\(439\) −27.7820 −1.32596 −0.662981 0.748636i \(-0.730709\pi\)
−0.662981 + 0.748636i \(0.730709\pi\)
\(440\) −4.08674 −0.194828
\(441\) 16.0424 0.763922
\(442\) −1.06781 −0.0507904
\(443\) 14.8814 0.707036 0.353518 0.935428i \(-0.384985\pi\)
0.353518 + 0.935428i \(0.384985\pi\)
\(444\) 0.135882 0.00644865
\(445\) −9.66762 −0.458289
\(446\) 25.1249 1.18970
\(447\) 2.72805 0.129032
\(448\) −1.23948 −0.0585601
\(449\) 6.47878 0.305753 0.152876 0.988245i \(-0.451146\pi\)
0.152876 + 0.988245i \(0.451146\pi\)
\(450\) −2.93618 −0.138413
\(451\) −2.83555 −0.133521
\(452\) −16.4569 −0.774065
\(453\) 0.447338 0.0210178
\(454\) 13.2454 0.621639
\(455\) 1.23948 0.0581079
\(456\) 2.05697 0.0963262
\(457\) 4.98112 0.233007 0.116504 0.993190i \(-0.462831\pi\)
0.116504 + 0.993190i \(0.462831\pi\)
\(458\) −6.93174 −0.323899
\(459\) −1.60131 −0.0747430
\(460\) −6.59643 −0.307560
\(461\) −18.0686 −0.841539 −0.420769 0.907168i \(-0.638240\pi\)
−0.420769 + 0.907168i \(0.638240\pi\)
\(462\) 1.27966 0.0595351
\(463\) −0.522460 −0.0242808 −0.0121404 0.999926i \(-0.503865\pi\)
−0.0121404 + 0.999926i \(0.503865\pi\)
\(464\) −1.85322 −0.0860334
\(465\) −0.252625 −0.0117152
\(466\) −21.5947 −1.00035
\(467\) 8.97422 0.415277 0.207639 0.978206i \(-0.433422\pi\)
0.207639 + 0.978206i \(0.433422\pi\)
\(468\) −2.93618 −0.135725
\(469\) 9.69919 0.447867
\(470\) −6.79817 −0.313576
\(471\) −5.58437 −0.257314
\(472\) 4.92227 0.226566
\(473\) −51.3115 −2.35930
\(474\) −0.207058 −0.00951048
\(475\) −8.14236 −0.373597
\(476\) 1.32353 0.0606638
\(477\) 33.5521 1.53624
\(478\) −20.6583 −0.944891
\(479\) 11.3765 0.519805 0.259902 0.965635i \(-0.416310\pi\)
0.259902 + 0.965635i \(0.416310\pi\)
\(480\) 0.252625 0.0115307
\(481\) −0.537878 −0.0245251
\(482\) −21.7353 −0.990018
\(483\) 2.06551 0.0939838
\(484\) 5.70143 0.259156
\(485\) 4.14428 0.188182
\(486\) −6.62844 −0.300672
\(487\) 5.50411 0.249415 0.124707 0.992194i \(-0.460201\pi\)
0.124707 + 0.992194i \(0.460201\pi\)
\(488\) 4.53622 0.205345
\(489\) 4.52696 0.204716
\(490\) 5.46368 0.246824
\(491\) −39.8235 −1.79721 −0.898604 0.438761i \(-0.855418\pi\)
−0.898604 + 0.438761i \(0.855418\pi\)
\(492\) 0.175282 0.00790233
\(493\) 1.97888 0.0891241
\(494\) −8.14236 −0.366342
\(495\) 11.9994 0.539333
\(496\) −1.00000 −0.0449013
\(497\) −3.04221 −0.136462
\(498\) 4.14277 0.185642
\(499\) −12.4798 −0.558675 −0.279337 0.960193i \(-0.590115\pi\)
−0.279337 + 0.960193i \(0.590115\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −3.04844 −0.136194
\(502\) 12.7871 0.570718
\(503\) −25.0994 −1.11913 −0.559563 0.828788i \(-0.689031\pi\)
−0.559563 + 0.828788i \(0.689031\pi\)
\(504\) 3.63935 0.162109
\(505\) 6.09882 0.271394
\(506\) 26.9579 1.19842
\(507\) −0.252625 −0.0112195
\(508\) −17.7965 −0.789590
\(509\) −29.1914 −1.29389 −0.646944 0.762538i \(-0.723953\pi\)
−0.646944 + 0.762538i \(0.723953\pi\)
\(510\) −0.269755 −0.0119450
\(511\) 17.6782 0.782038
\(512\) 1.00000 0.0441942
\(513\) −12.2105 −0.539108
\(514\) −6.88832 −0.303831
\(515\) −4.89812 −0.215837
\(516\) 3.17186 0.139633
\(517\) 27.7823 1.22186
\(518\) 0.666690 0.0292927
\(519\) −5.41834 −0.237839
\(520\) −1.00000 −0.0438529
\(521\) 23.9008 1.04711 0.523557 0.851991i \(-0.324605\pi\)
0.523557 + 0.851991i \(0.324605\pi\)
\(522\) 5.44138 0.238163
\(523\) −14.9556 −0.653963 −0.326982 0.945031i \(-0.606032\pi\)
−0.326982 + 0.945031i \(0.606032\pi\)
\(524\) −7.32944 −0.320188
\(525\) 0.313125 0.0136659
\(526\) 17.9601 0.783097
\(527\) 1.06781 0.0465144
\(528\) −1.03241 −0.0449300
\(529\) 20.5129 0.891865
\(530\) 11.4271 0.496362
\(531\) −14.4527 −0.627193
\(532\) 10.0923 0.437557
\(533\) −0.693843 −0.0300537
\(534\) −2.44229 −0.105688
\(535\) −7.34568 −0.317581
\(536\) −7.82519 −0.337997
\(537\) 4.75126 0.205032
\(538\) 3.72219 0.160475
\(539\) −22.3286 −0.961762
\(540\) −1.49963 −0.0645338
\(541\) 26.1527 1.12439 0.562196 0.827004i \(-0.309957\pi\)
0.562196 + 0.827004i \(0.309957\pi\)
\(542\) 3.22237 0.138413
\(543\) 4.86009 0.208566
\(544\) −1.06781 −0.0457818
\(545\) 19.2327 0.823840
\(546\) 0.313125 0.0134005
\(547\) 17.1760 0.734392 0.367196 0.930144i \(-0.380318\pi\)
0.367196 + 0.930144i \(0.380318\pi\)
\(548\) 17.0050 0.726417
\(549\) −13.3192 −0.568448
\(550\) 4.08674 0.174259
\(551\) 15.0895 0.642836
\(552\) −1.66643 −0.0709278
\(553\) −1.01591 −0.0432009
\(554\) 24.9074 1.05821
\(555\) −0.135882 −0.00576785
\(556\) 6.80321 0.288520
\(557\) −12.7916 −0.541999 −0.270999 0.962580i \(-0.587354\pi\)
−0.270999 + 0.962580i \(0.587354\pi\)
\(558\) 2.93618 0.124298
\(559\) −12.5556 −0.531045
\(560\) 1.23948 0.0523777
\(561\) 1.10242 0.0465441
\(562\) 18.3523 0.774145
\(563\) 14.3652 0.605423 0.302711 0.953082i \(-0.402108\pi\)
0.302711 + 0.953082i \(0.402108\pi\)
\(564\) −1.71739 −0.0723151
\(565\) 16.4569 0.692345
\(566\) −9.33022 −0.392178
\(567\) −10.4485 −0.438794
\(568\) 2.45442 0.102985
\(569\) −22.5054 −0.943475 −0.471737 0.881739i \(-0.656373\pi\)
−0.471737 + 0.881739i \(0.656373\pi\)
\(570\) −2.05697 −0.0861568
\(571\) 22.2032 0.929176 0.464588 0.885527i \(-0.346202\pi\)
0.464588 + 0.885527i \(0.346202\pi\)
\(572\) 4.08674 0.170875
\(573\) −0.822067 −0.0343423
\(574\) 0.860006 0.0358960
\(575\) 6.59643 0.275090
\(576\) −2.93618 −0.122341
\(577\) 9.89301 0.411852 0.205926 0.978568i \(-0.433979\pi\)
0.205926 + 0.978568i \(0.433979\pi\)
\(578\) −15.8598 −0.659680
\(579\) −1.20057 −0.0498938
\(580\) 1.85322 0.0769506
\(581\) 20.3261 0.843270
\(582\) 1.04695 0.0433974
\(583\) −46.6996 −1.93410
\(584\) −14.2626 −0.590189
\(585\) 2.93618 0.121396
\(586\) 21.5474 0.890114
\(587\) −15.4613 −0.638155 −0.319078 0.947729i \(-0.603373\pi\)
−0.319078 + 0.947729i \(0.603373\pi\)
\(588\) 1.38026 0.0569211
\(589\) 8.14236 0.335500
\(590\) −4.92227 −0.202647
\(591\) 5.24355 0.215691
\(592\) −0.537878 −0.0221066
\(593\) 37.1204 1.52435 0.762177 0.647369i \(-0.224131\pi\)
0.762177 + 0.647369i \(0.224131\pi\)
\(594\) 6.12859 0.251459
\(595\) −1.32353 −0.0542594
\(596\) −10.7988 −0.442336
\(597\) 3.20042 0.130985
\(598\) 6.59643 0.269748
\(599\) −0.998753 −0.0408079 −0.0204040 0.999792i \(-0.506495\pi\)
−0.0204040 + 0.999792i \(0.506495\pi\)
\(600\) −0.252625 −0.0103134
\(601\) −24.7299 −1.00875 −0.504377 0.863484i \(-0.668278\pi\)
−0.504377 + 0.863484i \(0.668278\pi\)
\(602\) 15.5625 0.634278
\(603\) 22.9762 0.935662
\(604\) −1.77076 −0.0720511
\(605\) −5.70143 −0.231796
\(606\) 1.54072 0.0625873
\(607\) −32.7085 −1.32760 −0.663798 0.747912i \(-0.731056\pi\)
−0.663798 + 0.747912i \(0.731056\pi\)
\(608\) −8.14236 −0.330216
\(609\) −0.580288 −0.0235145
\(610\) −4.53622 −0.183666
\(611\) 6.79817 0.275024
\(612\) 3.13527 0.126736
\(613\) −14.3331 −0.578910 −0.289455 0.957192i \(-0.593474\pi\)
−0.289455 + 0.957192i \(0.593474\pi\)
\(614\) 15.4675 0.624219
\(615\) −0.175282 −0.00706806
\(616\) −5.06544 −0.204092
\(617\) 10.3893 0.418256 0.209128 0.977888i \(-0.432938\pi\)
0.209128 + 0.977888i \(0.432938\pi\)
\(618\) −1.23739 −0.0497751
\(619\) −16.4954 −0.663005 −0.331503 0.943454i \(-0.607556\pi\)
−0.331503 + 0.943454i \(0.607556\pi\)
\(620\) 1.00000 0.0401610
\(621\) 9.89220 0.396960
\(622\) −20.4847 −0.821360
\(623\) −11.9828 −0.480083
\(624\) −0.252625 −0.0101131
\(625\) 1.00000 0.0400000
\(626\) 25.7248 1.02817
\(627\) 8.40628 0.335714
\(628\) 22.1053 0.882099
\(629\) 0.574350 0.0229008
\(630\) −3.63935 −0.144995
\(631\) −11.7825 −0.469053 −0.234527 0.972110i \(-0.575354\pi\)
−0.234527 + 0.972110i \(0.575354\pi\)
\(632\) 0.819624 0.0326029
\(633\) −1.41304 −0.0561633
\(634\) −0.411304 −0.0163350
\(635\) 17.7965 0.706231
\(636\) 2.88678 0.114468
\(637\) −5.46368 −0.216479
\(638\) −7.57361 −0.299842
\(639\) −7.20663 −0.285090
\(640\) −1.00000 −0.0395285
\(641\) 37.2059 1.46954 0.734772 0.678314i \(-0.237289\pi\)
0.734772 + 0.678314i \(0.237289\pi\)
\(642\) −1.85570 −0.0732388
\(643\) 22.9318 0.904343 0.452171 0.891931i \(-0.350650\pi\)
0.452171 + 0.891931i \(0.350650\pi\)
\(644\) −8.17616 −0.322186
\(645\) −3.17186 −0.124892
\(646\) 8.69446 0.342079
\(647\) 7.39363 0.290674 0.145337 0.989382i \(-0.453573\pi\)
0.145337 + 0.989382i \(0.453573\pi\)
\(648\) 8.42970 0.331150
\(649\) 20.1160 0.789623
\(650\) 1.00000 0.0392232
\(651\) −0.313125 −0.0122723
\(652\) −17.9197 −0.701788
\(653\) 1.32955 0.0520292 0.0260146 0.999662i \(-0.491718\pi\)
0.0260146 + 0.999662i \(0.491718\pi\)
\(654\) 4.85868 0.189989
\(655\) 7.32944 0.286385
\(656\) −0.693843 −0.0270900
\(657\) 41.8775 1.63380
\(658\) −8.42621 −0.328488
\(659\) −17.5624 −0.684136 −0.342068 0.939675i \(-0.611127\pi\)
−0.342068 + 0.939675i \(0.611127\pi\)
\(660\) 1.03241 0.0401866
\(661\) 45.0340 1.75162 0.875810 0.482657i \(-0.160328\pi\)
0.875810 + 0.482657i \(0.160328\pi\)
\(662\) −19.5537 −0.759974
\(663\) 0.269755 0.0104764
\(664\) −16.3989 −0.636400
\(665\) −10.0923 −0.391363
\(666\) 1.57931 0.0611969
\(667\) −12.2246 −0.473339
\(668\) 12.0670 0.466887
\(669\) −6.34718 −0.245396
\(670\) 7.82519 0.302314
\(671\) 18.5383 0.715664
\(672\) 0.313125 0.0120790
\(673\) 35.5859 1.37173 0.685867 0.727727i \(-0.259423\pi\)
0.685867 + 0.727727i \(0.259423\pi\)
\(674\) −24.8159 −0.955873
\(675\) 1.49963 0.0577208
\(676\) 1.00000 0.0384615
\(677\) −11.3157 −0.434899 −0.217449 0.976072i \(-0.569774\pi\)
−0.217449 + 0.976072i \(0.569774\pi\)
\(678\) 4.15742 0.159665
\(679\) 5.13676 0.197131
\(680\) 1.06781 0.0409485
\(681\) −3.34613 −0.128224
\(682\) −4.08674 −0.156489
\(683\) −36.7408 −1.40585 −0.702924 0.711265i \(-0.748123\pi\)
−0.702924 + 0.711265i \(0.748123\pi\)
\(684\) 23.9074 0.914123
\(685\) −17.0050 −0.649727
\(686\) 15.4485 0.589827
\(687\) 1.75113 0.0668099
\(688\) −12.5556 −0.478678
\(689\) −11.4271 −0.435338
\(690\) 1.66643 0.0634397
\(691\) 0.889761 0.0338481 0.0169241 0.999857i \(-0.494613\pi\)
0.0169241 + 0.999857i \(0.494613\pi\)
\(692\) 21.4481 0.815335
\(693\) 14.8731 0.564980
\(694\) −12.2109 −0.463521
\(695\) −6.80321 −0.258060
\(696\) 0.468169 0.0177459
\(697\) 0.740890 0.0280632
\(698\) 31.9548 1.20951
\(699\) 5.45536 0.206341
\(700\) −1.23948 −0.0468481
\(701\) 8.29197 0.313183 0.156592 0.987663i \(-0.449949\pi\)
0.156592 + 0.987663i \(0.449949\pi\)
\(702\) 1.49963 0.0565999
\(703\) 4.37959 0.165180
\(704\) 4.08674 0.154025
\(705\) 1.71739 0.0646806
\(706\) 23.4863 0.883917
\(707\) 7.55938 0.284300
\(708\) −1.24349 −0.0467332
\(709\) 20.9812 0.787964 0.393982 0.919118i \(-0.371097\pi\)
0.393982 + 0.919118i \(0.371097\pi\)
\(710\) −2.45442 −0.0921128
\(711\) −2.40656 −0.0902532
\(712\) 9.66762 0.362309
\(713\) −6.59643 −0.247038
\(714\) −0.334357 −0.0125130
\(715\) −4.08674 −0.152835
\(716\) −18.8075 −0.702871
\(717\) 5.21882 0.194900
\(718\) −4.71759 −0.176059
\(719\) −34.7957 −1.29766 −0.648829 0.760934i \(-0.724741\pi\)
−0.648829 + 0.760934i \(0.724741\pi\)
\(720\) 2.93618 0.109425
\(721\) −6.07114 −0.226101
\(722\) 47.2980 1.76025
\(723\) 5.49090 0.204209
\(724\) −19.2383 −0.714986
\(725\) −1.85322 −0.0688267
\(726\) −1.44032 −0.0534555
\(727\) 41.1678 1.52683 0.763415 0.645909i \(-0.223521\pi\)
0.763415 + 0.645909i \(0.223521\pi\)
\(728\) −1.23948 −0.0459383
\(729\) −23.6146 −0.874614
\(730\) 14.2626 0.527881
\(731\) 13.4070 0.495874
\(732\) −1.14596 −0.0423560
\(733\) 47.7243 1.76274 0.881368 0.472431i \(-0.156623\pi\)
0.881368 + 0.472431i \(0.156623\pi\)
\(734\) −2.37279 −0.0875814
\(735\) −1.38026 −0.0509118
\(736\) 6.59643 0.243148
\(737\) −31.9795 −1.17798
\(738\) 2.03725 0.0749921
\(739\) −31.0167 −1.14097 −0.570485 0.821308i \(-0.693245\pi\)
−0.570485 + 0.821308i \(0.693245\pi\)
\(740\) 0.537878 0.0197728
\(741\) 2.05697 0.0755645
\(742\) 14.1637 0.519966
\(743\) 25.5923 0.938891 0.469446 0.882961i \(-0.344454\pi\)
0.469446 + 0.882961i \(0.344454\pi\)
\(744\) 0.252625 0.00926169
\(745\) 10.7988 0.395637
\(746\) −14.2652 −0.522285
\(747\) 48.1500 1.76172
\(748\) −4.36385 −0.159558
\(749\) −9.10484 −0.332684
\(750\) 0.252625 0.00922457
\(751\) −18.1625 −0.662759 −0.331379 0.943498i \(-0.607514\pi\)
−0.331379 + 0.943498i \(0.607514\pi\)
\(752\) 6.79817 0.247904
\(753\) −3.23035 −0.117721
\(754\) −1.85322 −0.0674902
\(755\) 1.77076 0.0644445
\(756\) −1.85877 −0.0676026
\(757\) 49.7137 1.80687 0.903437 0.428721i \(-0.141036\pi\)
0.903437 + 0.428721i \(0.141036\pi\)
\(758\) 26.9056 0.977255
\(759\) −6.81024 −0.247196
\(760\) 8.14236 0.295354
\(761\) −42.8571 −1.55357 −0.776784 0.629767i \(-0.783150\pi\)
−0.776784 + 0.629767i \(0.783150\pi\)
\(762\) 4.49584 0.162867
\(763\) 23.8387 0.863017
\(764\) 3.25410 0.117729
\(765\) −3.13527 −0.113356
\(766\) 32.3812 1.16998
\(767\) 4.92227 0.177733
\(768\) −0.252625 −0.00911583
\(769\) −4.05252 −0.146138 −0.0730689 0.997327i \(-0.523279\pi\)
−0.0730689 + 0.997327i \(0.523279\pi\)
\(770\) 5.06544 0.182546
\(771\) 1.74016 0.0626704
\(772\) 4.75236 0.171041
\(773\) −42.4579 −1.52711 −0.763553 0.645745i \(-0.776547\pi\)
−0.763553 + 0.645745i \(0.776547\pi\)
\(774\) 36.8655 1.32510
\(775\) −1.00000 −0.0359211
\(776\) −4.14428 −0.148771
\(777\) −0.168423 −0.00604214
\(778\) 7.42585 0.266230
\(779\) 5.64951 0.202415
\(780\) 0.252625 0.00904544
\(781\) 10.0306 0.358922
\(782\) −7.04371 −0.251883
\(783\) −2.77914 −0.0993183
\(784\) −5.46368 −0.195132
\(785\) −22.1053 −0.788974
\(786\) 1.85160 0.0660444
\(787\) −42.3030 −1.50794 −0.753970 0.656908i \(-0.771864\pi\)
−0.753970 + 0.656908i \(0.771864\pi\)
\(788\) −20.7562 −0.739410
\(789\) −4.53717 −0.161528
\(790\) −0.819624 −0.0291609
\(791\) 20.3980 0.725269
\(792\) −11.9994 −0.426380
\(793\) 4.53622 0.161086
\(794\) −0.532290 −0.0188903
\(795\) −2.88678 −0.102383
\(796\) −12.6687 −0.449028
\(797\) 30.6478 1.08560 0.542800 0.839862i \(-0.317364\pi\)
0.542800 + 0.839862i \(0.317364\pi\)
\(798\) −2.54957 −0.0902539
\(799\) −7.25913 −0.256809
\(800\) 1.00000 0.0353553
\(801\) −28.3859 −1.00297
\(802\) 5.08171 0.179441
\(803\) −58.2874 −2.05692
\(804\) 1.97684 0.0697178
\(805\) 8.17616 0.288172
\(806\) −1.00000 −0.0352235
\(807\) −0.940321 −0.0331009
\(808\) −6.09882 −0.214556
\(809\) 31.8304 1.11910 0.559548 0.828798i \(-0.310975\pi\)
0.559548 + 0.828798i \(0.310975\pi\)
\(810\) −8.42970 −0.296189
\(811\) −28.4738 −0.999850 −0.499925 0.866069i \(-0.666639\pi\)
−0.499925 + 0.866069i \(0.666639\pi\)
\(812\) 2.29703 0.0806099
\(813\) −0.814053 −0.0285501
\(814\) −2.19817 −0.0770457
\(815\) 17.9197 0.627699
\(816\) 0.269755 0.00944332
\(817\) 102.232 3.57665
\(818\) −11.9445 −0.417629
\(819\) 3.63935 0.127169
\(820\) 0.693843 0.0242300
\(821\) −21.3139 −0.743860 −0.371930 0.928261i \(-0.621304\pi\)
−0.371930 + 0.928261i \(0.621304\pi\)
\(822\) −4.29589 −0.149836
\(823\) 51.4546 1.79359 0.896797 0.442442i \(-0.145888\pi\)
0.896797 + 0.442442i \(0.145888\pi\)
\(824\) 4.89812 0.170634
\(825\) −1.03241 −0.0359440
\(826\) −6.10107 −0.212283
\(827\) 49.3955 1.71765 0.858825 0.512269i \(-0.171195\pi\)
0.858825 + 0.512269i \(0.171195\pi\)
\(828\) −19.3683 −0.673095
\(829\) −32.0823 −1.11426 −0.557132 0.830424i \(-0.688098\pi\)
−0.557132 + 0.830424i \(0.688098\pi\)
\(830\) 16.3989 0.569213
\(831\) −6.29224 −0.218275
\(832\) 1.00000 0.0346688
\(833\) 5.83416 0.202142
\(834\) −1.71866 −0.0595124
\(835\) −12.0670 −0.417597
\(836\) −33.2757 −1.15086
\(837\) −1.49963 −0.0518348
\(838\) 29.6890 1.02559
\(839\) −9.12410 −0.314999 −0.157500 0.987519i \(-0.550343\pi\)
−0.157500 + 0.987519i \(0.550343\pi\)
\(840\) −0.313125 −0.0108038
\(841\) −25.5656 −0.881572
\(842\) −8.84383 −0.304778
\(843\) −4.63626 −0.159681
\(844\) 5.59342 0.192534
\(845\) −1.00000 −0.0344010
\(846\) −19.9606 −0.686261
\(847\) −7.06682 −0.242819
\(848\) −11.4271 −0.392409
\(849\) 2.35705 0.0808937
\(850\) −1.06781 −0.0366255
\(851\) −3.54807 −0.121626
\(852\) −0.620049 −0.0212425
\(853\) −13.8725 −0.474986 −0.237493 0.971389i \(-0.576326\pi\)
−0.237493 + 0.971389i \(0.576326\pi\)
\(854\) −5.62256 −0.192400
\(855\) −23.9074 −0.817617
\(856\) 7.34568 0.251070
\(857\) −9.35314 −0.319497 −0.159749 0.987158i \(-0.551068\pi\)
−0.159749 + 0.987158i \(0.551068\pi\)
\(858\) −1.03241 −0.0352460
\(859\) 10.8291 0.369483 0.184742 0.982787i \(-0.440855\pi\)
0.184742 + 0.982787i \(0.440855\pi\)
\(860\) 12.5556 0.428143
\(861\) −0.217259 −0.00740418
\(862\) −27.1853 −0.925933
\(863\) 1.57292 0.0535428 0.0267714 0.999642i \(-0.491477\pi\)
0.0267714 + 0.999642i \(0.491477\pi\)
\(864\) 1.49963 0.0510184
\(865\) −21.4481 −0.729258
\(866\) 28.8950 0.981890
\(867\) 4.00658 0.136071
\(868\) 1.23948 0.0420708
\(869\) 3.34959 0.113627
\(870\) −0.468169 −0.0158724
\(871\) −7.82519 −0.265146
\(872\) −19.2327 −0.651303
\(873\) 12.1683 0.411836
\(874\) −53.7105 −1.81678
\(875\) 1.23948 0.0419022
\(876\) 3.60309 0.121737
\(877\) 18.5215 0.625427 0.312713 0.949847i \(-0.398762\pi\)
0.312713 + 0.949847i \(0.398762\pi\)
\(878\) −27.7820 −0.937596
\(879\) −5.44341 −0.183602
\(880\) −4.08674 −0.137764
\(881\) 37.0775 1.24917 0.624587 0.780956i \(-0.285267\pi\)
0.624587 + 0.780956i \(0.285267\pi\)
\(882\) 16.0424 0.540174
\(883\) −7.31224 −0.246076 −0.123038 0.992402i \(-0.539264\pi\)
−0.123038 + 0.992402i \(0.539264\pi\)
\(884\) −1.06781 −0.0359142
\(885\) 1.24349 0.0417995
\(886\) 14.8814 0.499950
\(887\) −45.9674 −1.54343 −0.771717 0.635967i \(-0.780602\pi\)
−0.771717 + 0.635967i \(0.780602\pi\)
\(888\) 0.135882 0.00455989
\(889\) 22.0584 0.739815
\(890\) −9.66762 −0.324059
\(891\) 34.4500 1.15412
\(892\) 25.1249 0.841243
\(893\) −55.3531 −1.85232
\(894\) 2.72805 0.0912396
\(895\) 18.8075 0.628667
\(896\) −1.23948 −0.0414082
\(897\) −1.66643 −0.0556403
\(898\) 6.47878 0.216200
\(899\) 1.85322 0.0618082
\(900\) −2.93618 −0.0978727
\(901\) 12.2019 0.406506
\(902\) −2.83555 −0.0944136
\(903\) −3.93147 −0.130831
\(904\) −16.4569 −0.547347
\(905\) 19.2383 0.639503
\(906\) 0.447338 0.0148618
\(907\) −35.1358 −1.16667 −0.583333 0.812233i \(-0.698252\pi\)
−0.583333 + 0.812233i \(0.698252\pi\)
\(908\) 13.2454 0.439565
\(909\) 17.9072 0.593946
\(910\) 1.23948 0.0410885
\(911\) −24.2580 −0.803703 −0.401851 0.915705i \(-0.631633\pi\)
−0.401851 + 0.915705i \(0.631633\pi\)
\(912\) 2.05697 0.0681129
\(913\) −67.0179 −2.21797
\(914\) 4.98112 0.164761
\(915\) 1.14596 0.0378844
\(916\) −6.93174 −0.229031
\(917\) 9.08471 0.300004
\(918\) −1.60131 −0.0528513
\(919\) −47.9168 −1.58063 −0.790315 0.612701i \(-0.790083\pi\)
−0.790315 + 0.612701i \(0.790083\pi\)
\(920\) −6.59643 −0.217478
\(921\) −3.90749 −0.128756
\(922\) −18.0686 −0.595058
\(923\) 2.45442 0.0807883
\(924\) 1.27966 0.0420977
\(925\) −0.537878 −0.0176853
\(926\) −0.522460 −0.0171691
\(927\) −14.3818 −0.472359
\(928\) −1.85322 −0.0608348
\(929\) 5.33547 0.175051 0.0875256 0.996162i \(-0.472104\pi\)
0.0875256 + 0.996162i \(0.472104\pi\)
\(930\) −0.252625 −0.00828391
\(931\) 44.4873 1.45801
\(932\) −21.5947 −0.707357
\(933\) 5.17494 0.169420
\(934\) 8.97422 0.293645
\(935\) 4.36385 0.142713
\(936\) −2.93618 −0.0959721
\(937\) −32.1668 −1.05084 −0.525422 0.850842i \(-0.676092\pi\)
−0.525422 + 0.850842i \(0.676092\pi\)
\(938\) 9.69919 0.316690
\(939\) −6.49874 −0.212078
\(940\) −6.79817 −0.221732
\(941\) 29.3481 0.956721 0.478360 0.878164i \(-0.341231\pi\)
0.478360 + 0.878164i \(0.341231\pi\)
\(942\) −5.58437 −0.181949
\(943\) −4.57688 −0.149044
\(944\) 4.92227 0.160206
\(945\) 1.85877 0.0604656
\(946\) −51.3115 −1.66828
\(947\) 14.7608 0.479663 0.239831 0.970815i \(-0.422908\pi\)
0.239831 + 0.970815i \(0.422908\pi\)
\(948\) −0.207058 −0.00672492
\(949\) −14.2626 −0.462983
\(950\) −8.14236 −0.264173
\(951\) 0.103906 0.00336938
\(952\) 1.32353 0.0428958
\(953\) 39.9727 1.29484 0.647421 0.762132i \(-0.275847\pi\)
0.647421 + 0.762132i \(0.275847\pi\)
\(954\) 33.5521 1.08629
\(955\) −3.25410 −0.105300
\(956\) −20.6583 −0.668139
\(957\) 1.91329 0.0618477
\(958\) 11.3765 0.367557
\(959\) −21.0774 −0.680625
\(960\) 0.252625 0.00815345
\(961\) 1.00000 0.0322581
\(962\) −0.537878 −0.0173419
\(963\) −21.5682 −0.695027
\(964\) −21.7353 −0.700048
\(965\) −4.75236 −0.152984
\(966\) 2.06551 0.0664566
\(967\) 32.8199 1.05542 0.527709 0.849425i \(-0.323051\pi\)
0.527709 + 0.849425i \(0.323051\pi\)
\(968\) 5.70143 0.183251
\(969\) −2.19644 −0.0705599
\(970\) 4.14428 0.133065
\(971\) −30.7539 −0.986940 −0.493470 0.869763i \(-0.664272\pi\)
−0.493470 + 0.869763i \(0.664272\pi\)
\(972\) −6.62844 −0.212607
\(973\) −8.43246 −0.270332
\(974\) 5.50411 0.176363
\(975\) −0.252625 −0.00809049
\(976\) 4.53622 0.145201
\(977\) 40.3591 1.29120 0.645601 0.763675i \(-0.276607\pi\)
0.645601 + 0.763675i \(0.276607\pi\)
\(978\) 4.52696 0.144756
\(979\) 39.5090 1.26271
\(980\) 5.46368 0.174531
\(981\) 56.4708 1.80297
\(982\) −39.8235 −1.27082
\(983\) −33.6357 −1.07281 −0.536407 0.843960i \(-0.680219\pi\)
−0.536407 + 0.843960i \(0.680219\pi\)
\(984\) 0.175282 0.00558779
\(985\) 20.7562 0.661349
\(986\) 1.97888 0.0630203
\(987\) 2.12867 0.0677564
\(988\) −8.14236 −0.259043
\(989\) −82.8222 −2.63359
\(990\) 11.9994 0.381366
\(991\) −31.0175 −0.985303 −0.492652 0.870227i \(-0.663972\pi\)
−0.492652 + 0.870227i \(0.663972\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 4.93975 0.156758
\(994\) −3.04221 −0.0964932
\(995\) 12.6687 0.401623
\(996\) 4.14277 0.131269
\(997\) 23.5340 0.745330 0.372665 0.927966i \(-0.378444\pi\)
0.372665 + 0.927966i \(0.378444\pi\)
\(998\) −12.4798 −0.395043
\(999\) −0.806617 −0.0255202
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 \(a_p\))