Properties

Label 8007.2.a.j.1.13
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.78864 q^{2} -1.00000 q^{3} +1.19923 q^{4} -3.68881 q^{5} +1.78864 q^{6} +4.99843 q^{7} +1.43229 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.78864 q^{2} -1.00000 q^{3} +1.19923 q^{4} -3.68881 q^{5} +1.78864 q^{6} +4.99843 q^{7} +1.43229 q^{8} +1.00000 q^{9} +6.59796 q^{10} +6.42178 q^{11} -1.19923 q^{12} +0.498319 q^{13} -8.94039 q^{14} +3.68881 q^{15} -4.96031 q^{16} +1.00000 q^{17} -1.78864 q^{18} -6.09004 q^{19} -4.42373 q^{20} -4.99843 q^{21} -11.4862 q^{22} -0.523686 q^{23} -1.43229 q^{24} +8.60735 q^{25} -0.891313 q^{26} -1.00000 q^{27} +5.99427 q^{28} -5.30029 q^{29} -6.59796 q^{30} +11.1068 q^{31} +6.00762 q^{32} -6.42178 q^{33} -1.78864 q^{34} -18.4383 q^{35} +1.19923 q^{36} +8.07574 q^{37} +10.8929 q^{38} -0.498319 q^{39} -5.28345 q^{40} +10.3622 q^{41} +8.94039 q^{42} +9.75318 q^{43} +7.70118 q^{44} -3.68881 q^{45} +0.936685 q^{46} -0.340550 q^{47} +4.96031 q^{48} +17.9843 q^{49} -15.3954 q^{50} -1.00000 q^{51} +0.597599 q^{52} -6.33403 q^{53} +1.78864 q^{54} -23.6887 q^{55} +7.15921 q^{56} +6.09004 q^{57} +9.48030 q^{58} +2.65352 q^{59} +4.42373 q^{60} +0.558687 q^{61} -19.8660 q^{62} +4.99843 q^{63} -0.824845 q^{64} -1.83821 q^{65} +11.4862 q^{66} -2.80896 q^{67} +1.19923 q^{68} +0.523686 q^{69} +32.9794 q^{70} -7.18263 q^{71} +1.43229 q^{72} +8.94140 q^{73} -14.4446 q^{74} -8.60735 q^{75} -7.30336 q^{76} +32.0988 q^{77} +0.891313 q^{78} +16.9055 q^{79} +18.2977 q^{80} +1.00000 q^{81} -18.5343 q^{82} +5.45638 q^{83} -5.99427 q^{84} -3.68881 q^{85} -17.4449 q^{86} +5.30029 q^{87} +9.19785 q^{88} -1.05029 q^{89} +6.59796 q^{90} +2.49082 q^{91} -0.628019 q^{92} -11.1068 q^{93} +0.609121 q^{94} +22.4650 q^{95} -6.00762 q^{96} -4.64699 q^{97} -32.1675 q^{98} +6.42178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q + 5q^{2} - 64q^{3} + 77q^{4} - 3q^{5} - 5q^{6} + 5q^{7} + 18q^{8} + 64q^{9} + O(q^{10}) \) \( 64q + 5q^{2} - 64q^{3} + 77q^{4} - 3q^{5} - 5q^{6} + 5q^{7} + 18q^{8} + 64q^{9} + 12q^{10} - 7q^{11} - 77q^{12} + 24q^{13} - 14q^{14} + 3q^{15} + 103q^{16} + 64q^{17} + 5q^{18} + 26q^{19} - 24q^{20} - 5q^{21} + 25q^{22} + 20q^{23} - 18q^{24} + 141q^{25} + 9q^{26} - 64q^{27} + 14q^{28} + 5q^{29} - 12q^{30} + 11q^{31} + 31q^{32} + 7q^{33} + 5q^{34} - 3q^{35} + 77q^{36} + 50q^{37} + 8q^{38} - 24q^{39} + 28q^{40} - 9q^{41} + 14q^{42} + 59q^{43} - 6q^{44} - 3q^{45} + 11q^{47} - 103q^{48} + 163q^{49} + 20q^{50} - 64q^{51} + 65q^{52} + 39q^{53} - 5q^{54} + 35q^{55} - 34q^{56} - 26q^{57} - 27q^{58} - 65q^{59} + 24q^{60} + 15q^{61} + 18q^{62} + 5q^{63} + 152q^{64} + 49q^{65} - 25q^{66} + 56q^{67} + 77q^{68} - 20q^{69} + 28q^{70} - 18q^{71} + 18q^{72} + 37q^{73} - 76q^{74} - 141q^{75} + 30q^{76} + 80q^{77} - 9q^{78} + 20q^{79} - 144q^{80} + 64q^{81} + 27q^{82} + 3q^{83} - 14q^{84} - 3q^{85} + 12q^{86} - 5q^{87} + 108q^{88} + 42q^{89} + 12q^{90} + 25q^{91} + 18q^{92} - 11q^{93} + 60q^{94} + 42q^{95} - 31q^{96} + 72q^{97} + 18q^{98} - 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78864 −1.26476 −0.632379 0.774659i \(-0.717922\pi\)
−0.632379 + 0.774659i \(0.717922\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.19923 0.599614
\(5\) −3.68881 −1.64969 −0.824844 0.565361i \(-0.808737\pi\)
−0.824844 + 0.565361i \(0.808737\pi\)
\(6\) 1.78864 0.730209
\(7\) 4.99843 1.88923 0.944615 0.328180i \(-0.106435\pi\)
0.944615 + 0.328180i \(0.106435\pi\)
\(8\) 1.43229 0.506391
\(9\) 1.00000 0.333333
\(10\) 6.59796 2.08646
\(11\) 6.42178 1.93624 0.968119 0.250489i \(-0.0805914\pi\)
0.968119 + 0.250489i \(0.0805914\pi\)
\(12\) −1.19923 −0.346188
\(13\) 0.498319 0.138209 0.0691045 0.997609i \(-0.477986\pi\)
0.0691045 + 0.997609i \(0.477986\pi\)
\(14\) −8.94039 −2.38942
\(15\) 3.68881 0.952448
\(16\) −4.96031 −1.24008
\(17\) 1.00000 0.242536
\(18\) −1.78864 −0.421586
\(19\) −6.09004 −1.39715 −0.698576 0.715536i \(-0.746183\pi\)
−0.698576 + 0.715536i \(0.746183\pi\)
\(20\) −4.42373 −0.989177
\(21\) −4.99843 −1.09075
\(22\) −11.4862 −2.44887
\(23\) −0.523686 −0.109196 −0.0545980 0.998508i \(-0.517388\pi\)
−0.0545980 + 0.998508i \(0.517388\pi\)
\(24\) −1.43229 −0.292365
\(25\) 8.60735 1.72147
\(26\) −0.891313 −0.174801
\(27\) −1.00000 −0.192450
\(28\) 5.99427 1.13281
\(29\) −5.30029 −0.984239 −0.492119 0.870528i \(-0.663778\pi\)
−0.492119 + 0.870528i \(0.663778\pi\)
\(30\) −6.59796 −1.20462
\(31\) 11.1068 1.99484 0.997419 0.0717957i \(-0.0228729\pi\)
0.997419 + 0.0717957i \(0.0228729\pi\)
\(32\) 6.00762 1.06201
\(33\) −6.42178 −1.11789
\(34\) −1.78864 −0.306749
\(35\) −18.4383 −3.11664
\(36\) 1.19923 0.199871
\(37\) 8.07574 1.32764 0.663822 0.747891i \(-0.268933\pi\)
0.663822 + 0.747891i \(0.268933\pi\)
\(38\) 10.8929 1.76706
\(39\) −0.498319 −0.0797949
\(40\) −5.28345 −0.835387
\(41\) 10.3622 1.61831 0.809154 0.587596i \(-0.199926\pi\)
0.809154 + 0.587596i \(0.199926\pi\)
\(42\) 8.94039 1.37953
\(43\) 9.75318 1.48735 0.743673 0.668543i \(-0.233082\pi\)
0.743673 + 0.668543i \(0.233082\pi\)
\(44\) 7.70118 1.16100
\(45\) −3.68881 −0.549896
\(46\) 0.936685 0.138107
\(47\) −0.340550 −0.0496743 −0.0248371 0.999692i \(-0.507907\pi\)
−0.0248371 + 0.999692i \(0.507907\pi\)
\(48\) 4.96031 0.715959
\(49\) 17.9843 2.56919
\(50\) −15.3954 −2.17724
\(51\) −1.00000 −0.140028
\(52\) 0.597599 0.0828721
\(53\) −6.33403 −0.870046 −0.435023 0.900419i \(-0.643260\pi\)
−0.435023 + 0.900419i \(0.643260\pi\)
\(54\) 1.78864 0.243403
\(55\) −23.6887 −3.19419
\(56\) 7.15921 0.956689
\(57\) 6.09004 0.806646
\(58\) 9.48030 1.24482
\(59\) 2.65352 0.345459 0.172730 0.984969i \(-0.444741\pi\)
0.172730 + 0.984969i \(0.444741\pi\)
\(60\) 4.42373 0.571101
\(61\) 0.558687 0.0715326 0.0357663 0.999360i \(-0.488613\pi\)
0.0357663 + 0.999360i \(0.488613\pi\)
\(62\) −19.8660 −2.52299
\(63\) 4.99843 0.629743
\(64\) −0.824845 −0.103106
\(65\) −1.83821 −0.228002
\(66\) 11.4862 1.41386
\(67\) −2.80896 −0.343170 −0.171585 0.985169i \(-0.554889\pi\)
−0.171585 + 0.985169i \(0.554889\pi\)
\(68\) 1.19923 0.145428
\(69\) 0.523686 0.0630444
\(70\) 32.9794 3.94180
\(71\) −7.18263 −0.852421 −0.426211 0.904624i \(-0.640152\pi\)
−0.426211 + 0.904624i \(0.640152\pi\)
\(72\) 1.43229 0.168797
\(73\) 8.94140 1.04651 0.523256 0.852176i \(-0.324717\pi\)
0.523256 + 0.852176i \(0.324717\pi\)
\(74\) −14.4446 −1.67915
\(75\) −8.60735 −0.993891
\(76\) −7.30336 −0.837752
\(77\) 32.0988 3.65800
\(78\) 0.891313 0.100921
\(79\) 16.9055 1.90202 0.951010 0.309159i \(-0.100047\pi\)
0.951010 + 0.309159i \(0.100047\pi\)
\(80\) 18.2977 2.04574
\(81\) 1.00000 0.111111
\(82\) −18.5343 −2.04677
\(83\) 5.45638 0.598916 0.299458 0.954110i \(-0.403194\pi\)
0.299458 + 0.954110i \(0.403194\pi\)
\(84\) −5.99427 −0.654028
\(85\) −3.68881 −0.400108
\(86\) −17.4449 −1.88113
\(87\) 5.30029 0.568251
\(88\) 9.19785 0.980494
\(89\) −1.05029 −0.111330 −0.0556650 0.998450i \(-0.517728\pi\)
−0.0556650 + 0.998450i \(0.517728\pi\)
\(90\) 6.59796 0.695486
\(91\) 2.49082 0.261108
\(92\) −0.628019 −0.0654755
\(93\) −11.1068 −1.15172
\(94\) 0.609121 0.0628260
\(95\) 22.4650 2.30486
\(96\) −6.00762 −0.613150
\(97\) −4.64699 −0.471830 −0.235915 0.971774i \(-0.575809\pi\)
−0.235915 + 0.971774i \(0.575809\pi\)
\(98\) −32.1675 −3.24941
\(99\) 6.42178 0.645413
\(100\) 10.3222 1.03222
\(101\) −9.92040 −0.987117 −0.493558 0.869713i \(-0.664304\pi\)
−0.493558 + 0.869713i \(0.664304\pi\)
\(102\) 1.78864 0.177102
\(103\) −6.29664 −0.620427 −0.310213 0.950667i \(-0.600400\pi\)
−0.310213 + 0.950667i \(0.600400\pi\)
\(104\) 0.713738 0.0699878
\(105\) 18.4383 1.79939
\(106\) 11.3293 1.10040
\(107\) −6.10636 −0.590324 −0.295162 0.955447i \(-0.595374\pi\)
−0.295162 + 0.955447i \(0.595374\pi\)
\(108\) −1.19923 −0.115396
\(109\) −8.69436 −0.832768 −0.416384 0.909189i \(-0.636703\pi\)
−0.416384 + 0.909189i \(0.636703\pi\)
\(110\) 42.3706 4.03988
\(111\) −8.07574 −0.766515
\(112\) −24.7938 −2.34279
\(113\) 17.0902 1.60771 0.803853 0.594828i \(-0.202780\pi\)
0.803853 + 0.594828i \(0.202780\pi\)
\(114\) −10.8929 −1.02021
\(115\) 1.93178 0.180139
\(116\) −6.35626 −0.590164
\(117\) 0.498319 0.0460696
\(118\) −4.74620 −0.436923
\(119\) 4.99843 0.458206
\(120\) 5.28345 0.482311
\(121\) 30.2392 2.74902
\(122\) −0.999290 −0.0904715
\(123\) −10.3622 −0.934331
\(124\) 13.3196 1.19613
\(125\) −13.3068 −1.19020
\(126\) −8.94039 −0.796473
\(127\) −0.669840 −0.0594387 −0.0297193 0.999558i \(-0.509461\pi\)
−0.0297193 + 0.999558i \(0.509461\pi\)
\(128\) −10.5399 −0.931603
\(129\) −9.75318 −0.858720
\(130\) 3.28789 0.288367
\(131\) 7.07731 0.618347 0.309174 0.951006i \(-0.399948\pi\)
0.309174 + 0.951006i \(0.399948\pi\)
\(132\) −7.70118 −0.670302
\(133\) −30.4407 −2.63954
\(134\) 5.02422 0.434027
\(135\) 3.68881 0.317483
\(136\) 1.43229 0.122818
\(137\) 12.8025 1.09379 0.546896 0.837201i \(-0.315809\pi\)
0.546896 + 0.837201i \(0.315809\pi\)
\(138\) −0.936685 −0.0797359
\(139\) 6.91581 0.586592 0.293296 0.956022i \(-0.405248\pi\)
0.293296 + 0.956022i \(0.405248\pi\)
\(140\) −22.1117 −1.86878
\(141\) 0.340550 0.0286795
\(142\) 12.8471 1.07811
\(143\) 3.20010 0.267605
\(144\) −4.96031 −0.413359
\(145\) 19.5518 1.62369
\(146\) −15.9929 −1.32358
\(147\) −17.9843 −1.48332
\(148\) 9.68466 0.796074
\(149\) 16.5982 1.35977 0.679887 0.733317i \(-0.262029\pi\)
0.679887 + 0.733317i \(0.262029\pi\)
\(150\) 15.3954 1.25703
\(151\) −9.60086 −0.781307 −0.390653 0.920538i \(-0.627751\pi\)
−0.390653 + 0.920538i \(0.627751\pi\)
\(152\) −8.72271 −0.707505
\(153\) 1.00000 0.0808452
\(154\) −57.4132 −4.62649
\(155\) −40.9709 −3.29086
\(156\) −0.597599 −0.0478462
\(157\) −1.00000 −0.0798087
\(158\) −30.2379 −2.40560
\(159\) 6.33403 0.502321
\(160\) −22.1610 −1.75198
\(161\) −2.61761 −0.206296
\(162\) −1.78864 −0.140529
\(163\) 11.3561 0.889481 0.444740 0.895660i \(-0.353296\pi\)
0.444740 + 0.895660i \(0.353296\pi\)
\(164\) 12.4267 0.970361
\(165\) 23.6887 1.84417
\(166\) −9.75949 −0.757484
\(167\) −8.19440 −0.634102 −0.317051 0.948409i \(-0.602693\pi\)
−0.317051 + 0.948409i \(0.602693\pi\)
\(168\) −7.15921 −0.552345
\(169\) −12.7517 −0.980898
\(170\) 6.59796 0.506040
\(171\) −6.09004 −0.465717
\(172\) 11.6963 0.891834
\(173\) −3.38489 −0.257349 −0.128674 0.991687i \(-0.541072\pi\)
−0.128674 + 0.991687i \(0.541072\pi\)
\(174\) −9.48030 −0.718700
\(175\) 43.0232 3.25225
\(176\) −31.8540 −2.40109
\(177\) −2.65352 −0.199451
\(178\) 1.87858 0.140806
\(179\) −18.5579 −1.38708 −0.693540 0.720418i \(-0.743950\pi\)
−0.693540 + 0.720418i \(0.743950\pi\)
\(180\) −4.42373 −0.329726
\(181\) 10.4065 0.773509 0.386754 0.922183i \(-0.373596\pi\)
0.386754 + 0.922183i \(0.373596\pi\)
\(182\) −4.45517 −0.330239
\(183\) −0.558687 −0.0412994
\(184\) −0.750070 −0.0552959
\(185\) −29.7899 −2.19020
\(186\) 19.8660 1.45665
\(187\) 6.42178 0.469607
\(188\) −0.408397 −0.0297854
\(189\) −4.99843 −0.363583
\(190\) −40.1818 −2.91510
\(191\) −1.94279 −0.140576 −0.0702878 0.997527i \(-0.522392\pi\)
−0.0702878 + 0.997527i \(0.522392\pi\)
\(192\) 0.824845 0.0595280
\(193\) −16.9622 −1.22097 −0.610485 0.792028i \(-0.709025\pi\)
−0.610485 + 0.792028i \(0.709025\pi\)
\(194\) 8.31178 0.596751
\(195\) 1.83821 0.131637
\(196\) 21.5673 1.54052
\(197\) −25.5899 −1.82320 −0.911602 0.411075i \(-0.865153\pi\)
−0.911602 + 0.411075i \(0.865153\pi\)
\(198\) −11.4862 −0.816292
\(199\) 17.1968 1.21905 0.609525 0.792767i \(-0.291360\pi\)
0.609525 + 0.792767i \(0.291360\pi\)
\(200\) 12.3282 0.871737
\(201\) 2.80896 0.198129
\(202\) 17.7440 1.24846
\(203\) −26.4931 −1.85945
\(204\) −1.19923 −0.0839628
\(205\) −38.2243 −2.66970
\(206\) 11.2624 0.784690
\(207\) −0.523686 −0.0363987
\(208\) −2.47182 −0.171390
\(209\) −39.1089 −2.70522
\(210\) −32.9794 −2.27580
\(211\) −4.38406 −0.301811 −0.150905 0.988548i \(-0.548219\pi\)
−0.150905 + 0.988548i \(0.548219\pi\)
\(212\) −7.59595 −0.521692
\(213\) 7.18263 0.492146
\(214\) 10.9221 0.746618
\(215\) −35.9777 −2.45366
\(216\) −1.43229 −0.0974550
\(217\) 55.5166 3.76871
\(218\) 15.5511 1.05325
\(219\) −8.94140 −0.604204
\(220\) −28.4082 −1.91528
\(221\) 0.498319 0.0335206
\(222\) 14.4446 0.969457
\(223\) 10.5981 0.709703 0.354852 0.934923i \(-0.384531\pi\)
0.354852 + 0.934923i \(0.384531\pi\)
\(224\) 30.0287 2.00638
\(225\) 8.60735 0.573823
\(226\) −30.5681 −2.03336
\(227\) 15.6722 1.04020 0.520100 0.854106i \(-0.325895\pi\)
0.520100 + 0.854106i \(0.325895\pi\)
\(228\) 7.30336 0.483677
\(229\) −26.1823 −1.73018 −0.865088 0.501620i \(-0.832737\pi\)
−0.865088 + 0.501620i \(0.832737\pi\)
\(230\) −3.45526 −0.227833
\(231\) −32.0988 −2.11195
\(232\) −7.59155 −0.498410
\(233\) 8.14008 0.533275 0.266637 0.963797i \(-0.414087\pi\)
0.266637 + 0.963797i \(0.414087\pi\)
\(234\) −0.891313 −0.0582670
\(235\) 1.25622 0.0819471
\(236\) 3.18218 0.207142
\(237\) −16.9055 −1.09813
\(238\) −8.94039 −0.579520
\(239\) −13.8131 −0.893496 −0.446748 0.894660i \(-0.647418\pi\)
−0.446748 + 0.894660i \(0.647418\pi\)
\(240\) −18.2977 −1.18111
\(241\) 27.6965 1.78409 0.892045 0.451946i \(-0.149270\pi\)
0.892045 + 0.451946i \(0.149270\pi\)
\(242\) −54.0871 −3.47685
\(243\) −1.00000 −0.0641500
\(244\) 0.669994 0.0428920
\(245\) −66.3409 −4.23836
\(246\) 18.5343 1.18170
\(247\) −3.03479 −0.193099
\(248\) 15.9081 1.01017
\(249\) −5.45638 −0.345784
\(250\) 23.8011 1.50531
\(251\) −4.06052 −0.256298 −0.128149 0.991755i \(-0.540904\pi\)
−0.128149 + 0.991755i \(0.540904\pi\)
\(252\) 5.99427 0.377603
\(253\) −3.36299 −0.211430
\(254\) 1.19810 0.0751756
\(255\) 3.68881 0.231002
\(256\) 20.5017 1.28136
\(257\) −29.5186 −1.84132 −0.920660 0.390366i \(-0.872349\pi\)
−0.920660 + 0.390366i \(0.872349\pi\)
\(258\) 17.4449 1.08607
\(259\) 40.3660 2.50822
\(260\) −2.20443 −0.136713
\(261\) −5.30029 −0.328080
\(262\) −12.6587 −0.782060
\(263\) −6.79580 −0.419047 −0.209523 0.977804i \(-0.567191\pi\)
−0.209523 + 0.977804i \(0.567191\pi\)
\(264\) −9.19785 −0.566089
\(265\) 23.3651 1.43530
\(266\) 54.4474 3.33838
\(267\) 1.05029 0.0642764
\(268\) −3.36859 −0.205769
\(269\) −23.1537 −1.41171 −0.705853 0.708358i \(-0.749436\pi\)
−0.705853 + 0.708358i \(0.749436\pi\)
\(270\) −6.59796 −0.401539
\(271\) −6.38779 −0.388030 −0.194015 0.980999i \(-0.562151\pi\)
−0.194015 + 0.980999i \(0.562151\pi\)
\(272\) −4.96031 −0.300763
\(273\) −2.49082 −0.150751
\(274\) −22.8991 −1.38338
\(275\) 55.2745 3.33318
\(276\) 0.628019 0.0378023
\(277\) −7.67985 −0.461437 −0.230719 0.973021i \(-0.574108\pi\)
−0.230719 + 0.973021i \(0.574108\pi\)
\(278\) −12.3699 −0.741897
\(279\) 11.1068 0.664946
\(280\) −26.4090 −1.57824
\(281\) −8.61923 −0.514180 −0.257090 0.966387i \(-0.582764\pi\)
−0.257090 + 0.966387i \(0.582764\pi\)
\(282\) −0.609121 −0.0362726
\(283\) −1.38010 −0.0820383 −0.0410192 0.999158i \(-0.513060\pi\)
−0.0410192 + 0.999158i \(0.513060\pi\)
\(284\) −8.61362 −0.511124
\(285\) −22.4650 −1.33071
\(286\) −5.72382 −0.338456
\(287\) 51.7949 3.05736
\(288\) 6.00762 0.354002
\(289\) 1.00000 0.0588235
\(290\) −34.9711 −2.05357
\(291\) 4.64699 0.272411
\(292\) 10.7228 0.627503
\(293\) −24.4425 −1.42795 −0.713974 0.700172i \(-0.753106\pi\)
−0.713974 + 0.700172i \(0.753106\pi\)
\(294\) 32.1675 1.87605
\(295\) −9.78836 −0.569900
\(296\) 11.5668 0.672307
\(297\) −6.42178 −0.372629
\(298\) −29.6881 −1.71979
\(299\) −0.260963 −0.0150919
\(300\) −10.3222 −0.595951
\(301\) 48.7506 2.80994
\(302\) 17.1725 0.988164
\(303\) 9.92040 0.569912
\(304\) 30.2085 1.73258
\(305\) −2.06089 −0.118006
\(306\) −1.78864 −0.102250
\(307\) −23.1189 −1.31946 −0.659732 0.751501i \(-0.729330\pi\)
−0.659732 + 0.751501i \(0.729330\pi\)
\(308\) 38.4938 2.19339
\(309\) 6.29664 0.358204
\(310\) 73.2821 4.16214
\(311\) 21.6190 1.22590 0.612951 0.790121i \(-0.289982\pi\)
0.612951 + 0.790121i \(0.289982\pi\)
\(312\) −0.713738 −0.0404074
\(313\) 20.4821 1.15771 0.578857 0.815429i \(-0.303499\pi\)
0.578857 + 0.815429i \(0.303499\pi\)
\(314\) 1.78864 0.100939
\(315\) −18.4383 −1.03888
\(316\) 20.2736 1.14048
\(317\) 4.01241 0.225359 0.112680 0.993631i \(-0.464057\pi\)
0.112680 + 0.993631i \(0.464057\pi\)
\(318\) −11.3293 −0.635315
\(319\) −34.0373 −1.90572
\(320\) 3.04270 0.170092
\(321\) 6.10636 0.340824
\(322\) 4.68196 0.260915
\(323\) −6.09004 −0.338859
\(324\) 1.19923 0.0666238
\(325\) 4.28921 0.237922
\(326\) −20.3120 −1.12498
\(327\) 8.69436 0.480799
\(328\) 14.8417 0.819497
\(329\) −1.70222 −0.0938462
\(330\) −42.3706 −2.33243
\(331\) 11.6058 0.637911 0.318956 0.947770i \(-0.396668\pi\)
0.318956 + 0.947770i \(0.396668\pi\)
\(332\) 6.54345 0.359118
\(333\) 8.07574 0.442548
\(334\) 14.6568 0.801985
\(335\) 10.3617 0.566123
\(336\) 24.7938 1.35261
\(337\) −10.0710 −0.548601 −0.274301 0.961644i \(-0.588446\pi\)
−0.274301 + 0.961644i \(0.588446\pi\)
\(338\) 22.8081 1.24060
\(339\) −17.0902 −0.928210
\(340\) −4.42373 −0.239911
\(341\) 71.3254 3.86248
\(342\) 10.8929 0.589020
\(343\) 54.9045 2.96456
\(344\) 13.9694 0.753179
\(345\) −1.93178 −0.104003
\(346\) 6.05435 0.325484
\(347\) 13.7175 0.736393 0.368197 0.929748i \(-0.379975\pi\)
0.368197 + 0.929748i \(0.379975\pi\)
\(348\) 6.35626 0.340731
\(349\) −19.1623 −1.02573 −0.512866 0.858468i \(-0.671416\pi\)
−0.512866 + 0.858468i \(0.671416\pi\)
\(350\) −76.9531 −4.11331
\(351\) −0.498319 −0.0265983
\(352\) 38.5796 2.05630
\(353\) 6.53268 0.347700 0.173850 0.984772i \(-0.444379\pi\)
0.173850 + 0.984772i \(0.444379\pi\)
\(354\) 4.74620 0.252258
\(355\) 26.4954 1.40623
\(356\) −1.25953 −0.0667551
\(357\) −4.99843 −0.264545
\(358\) 33.1933 1.75432
\(359\) 7.77596 0.410399 0.205200 0.978720i \(-0.434216\pi\)
0.205200 + 0.978720i \(0.434216\pi\)
\(360\) −5.28345 −0.278462
\(361\) 18.0886 0.952033
\(362\) −18.6135 −0.978302
\(363\) −30.2392 −1.58715
\(364\) 2.98706 0.156564
\(365\) −32.9831 −1.72642
\(366\) 0.999290 0.0522337
\(367\) −2.99896 −0.156545 −0.0782723 0.996932i \(-0.524940\pi\)
−0.0782723 + 0.996932i \(0.524940\pi\)
\(368\) 2.59764 0.135411
\(369\) 10.3622 0.539436
\(370\) 53.2834 2.77007
\(371\) −31.6602 −1.64372
\(372\) −13.3196 −0.690588
\(373\) −23.0479 −1.19337 −0.596687 0.802474i \(-0.703516\pi\)
−0.596687 + 0.802474i \(0.703516\pi\)
\(374\) −11.4862 −0.593939
\(375\) 13.3068 0.687162
\(376\) −0.487766 −0.0251546
\(377\) −2.64124 −0.136031
\(378\) 8.94039 0.459844
\(379\) 31.2737 1.60642 0.803212 0.595694i \(-0.203123\pi\)
0.803212 + 0.595694i \(0.203123\pi\)
\(380\) 26.9407 1.38203
\(381\) 0.669840 0.0343169
\(382\) 3.47496 0.177794
\(383\) 2.40636 0.122959 0.0614796 0.998108i \(-0.480418\pi\)
0.0614796 + 0.998108i \(0.480418\pi\)
\(384\) 10.5399 0.537861
\(385\) −118.407 −6.03456
\(386\) 30.3393 1.54423
\(387\) 9.75318 0.495782
\(388\) −5.57280 −0.282916
\(389\) 6.22776 0.315760 0.157880 0.987458i \(-0.449534\pi\)
0.157880 + 0.987458i \(0.449534\pi\)
\(390\) −3.28789 −0.166489
\(391\) −0.523686 −0.0264839
\(392\) 25.7588 1.30102
\(393\) −7.07731 −0.357003
\(394\) 45.7710 2.30591
\(395\) −62.3614 −3.13774
\(396\) 7.70118 0.386999
\(397\) −4.81061 −0.241437 −0.120719 0.992687i \(-0.538520\pi\)
−0.120719 + 0.992687i \(0.538520\pi\)
\(398\) −30.7589 −1.54180
\(399\) 30.4407 1.52394
\(400\) −42.6951 −2.13475
\(401\) 32.2728 1.61163 0.805813 0.592171i \(-0.201729\pi\)
0.805813 + 0.592171i \(0.201729\pi\)
\(402\) −5.02422 −0.250585
\(403\) 5.53473 0.275704
\(404\) −11.8968 −0.591890
\(405\) −3.68881 −0.183299
\(406\) 47.3867 2.35176
\(407\) 51.8606 2.57064
\(408\) −1.43229 −0.0709089
\(409\) −26.5320 −1.31192 −0.655962 0.754794i \(-0.727737\pi\)
−0.655962 + 0.754794i \(0.727737\pi\)
\(410\) 68.3695 3.37653
\(411\) −12.8025 −0.631501
\(412\) −7.55112 −0.372017
\(413\) 13.2635 0.652652
\(414\) 0.936685 0.0460355
\(415\) −20.1276 −0.988024
\(416\) 2.99371 0.146779
\(417\) −6.91581 −0.338669
\(418\) 69.9517 3.42145
\(419\) −29.2525 −1.42908 −0.714539 0.699596i \(-0.753363\pi\)
−0.714539 + 0.699596i \(0.753363\pi\)
\(420\) 22.1117 1.07894
\(421\) 25.1079 1.22368 0.611841 0.790981i \(-0.290429\pi\)
0.611841 + 0.790981i \(0.290429\pi\)
\(422\) 7.84149 0.381718
\(423\) −0.340550 −0.0165581
\(424\) −9.07217 −0.440584
\(425\) 8.60735 0.417518
\(426\) −12.8471 −0.622446
\(427\) 2.79256 0.135142
\(428\) −7.32293 −0.353967
\(429\) −3.20010 −0.154502
\(430\) 64.3511 3.10328
\(431\) 6.49029 0.312626 0.156313 0.987708i \(-0.450039\pi\)
0.156313 + 0.987708i \(0.450039\pi\)
\(432\) 4.96031 0.238653
\(433\) −34.7770 −1.67128 −0.835638 0.549281i \(-0.814902\pi\)
−0.835638 + 0.549281i \(0.814902\pi\)
\(434\) −99.2991 −4.76651
\(435\) −19.5518 −0.937436
\(436\) −10.4265 −0.499340
\(437\) 3.18927 0.152563
\(438\) 15.9929 0.764172
\(439\) −33.4638 −1.59714 −0.798570 0.601902i \(-0.794410\pi\)
−0.798570 + 0.601902i \(0.794410\pi\)
\(440\) −33.9292 −1.61751
\(441\) 17.9843 0.856397
\(442\) −0.891313 −0.0423954
\(443\) 12.4743 0.592671 0.296335 0.955084i \(-0.404235\pi\)
0.296335 + 0.955084i \(0.404235\pi\)
\(444\) −9.68466 −0.459614
\(445\) 3.87431 0.183660
\(446\) −18.9562 −0.897604
\(447\) −16.5982 −0.785066
\(448\) −4.12293 −0.194790
\(449\) 27.9597 1.31950 0.659751 0.751485i \(-0.270662\pi\)
0.659751 + 0.751485i \(0.270662\pi\)
\(450\) −15.3954 −0.725748
\(451\) 66.5439 3.13343
\(452\) 20.4950 0.964004
\(453\) 9.60086 0.451088
\(454\) −28.0319 −1.31560
\(455\) −9.18815 −0.430747
\(456\) 8.72271 0.408478
\(457\) −9.07744 −0.424625 −0.212312 0.977202i \(-0.568099\pi\)
−0.212312 + 0.977202i \(0.568099\pi\)
\(458\) 46.8307 2.18825
\(459\) −1.00000 −0.0466760
\(460\) 2.31665 0.108014
\(461\) −14.1094 −0.657140 −0.328570 0.944480i \(-0.606567\pi\)
−0.328570 + 0.944480i \(0.606567\pi\)
\(462\) 57.4132 2.67110
\(463\) 0.164941 0.00766544 0.00383272 0.999993i \(-0.498780\pi\)
0.00383272 + 0.999993i \(0.498780\pi\)
\(464\) 26.2911 1.22053
\(465\) 40.9709 1.89998
\(466\) −14.5597 −0.674464
\(467\) 31.5513 1.46002 0.730010 0.683436i \(-0.239515\pi\)
0.730010 + 0.683436i \(0.239515\pi\)
\(468\) 0.597599 0.0276240
\(469\) −14.0404 −0.648326
\(470\) −2.24693 −0.103643
\(471\) 1.00000 0.0460776
\(472\) 3.80062 0.174938
\(473\) 62.6328 2.87986
\(474\) 30.2379 1.38887
\(475\) −52.4191 −2.40515
\(476\) 5.99427 0.274747
\(477\) −6.33403 −0.290015
\(478\) 24.7067 1.13006
\(479\) 11.0714 0.505863 0.252931 0.967484i \(-0.418605\pi\)
0.252931 + 0.967484i \(0.418605\pi\)
\(480\) 22.1610 1.01151
\(481\) 4.02430 0.183492
\(482\) −49.5391 −2.25644
\(483\) 2.61761 0.119105
\(484\) 36.2638 1.64835
\(485\) 17.1419 0.778372
\(486\) 1.78864 0.0811343
\(487\) 25.9356 1.17525 0.587626 0.809133i \(-0.300063\pi\)
0.587626 + 0.809133i \(0.300063\pi\)
\(488\) 0.800202 0.0362235
\(489\) −11.3561 −0.513542
\(490\) 118.660 5.36050
\(491\) −36.4550 −1.64519 −0.822595 0.568628i \(-0.807474\pi\)
−0.822595 + 0.568628i \(0.807474\pi\)
\(492\) −12.4267 −0.560238
\(493\) −5.30029 −0.238713
\(494\) 5.42814 0.244223
\(495\) −23.6887 −1.06473
\(496\) −55.0931 −2.47375
\(497\) −35.9019 −1.61042
\(498\) 9.75949 0.437333
\(499\) 27.4277 1.22783 0.613917 0.789370i \(-0.289593\pi\)
0.613917 + 0.789370i \(0.289593\pi\)
\(500\) −15.9579 −0.713661
\(501\) 8.19440 0.366099
\(502\) 7.26281 0.324155
\(503\) −14.1495 −0.630897 −0.315448 0.948943i \(-0.602155\pi\)
−0.315448 + 0.948943i \(0.602155\pi\)
\(504\) 7.15921 0.318896
\(505\) 36.5945 1.62843
\(506\) 6.01518 0.267407
\(507\) 12.7517 0.566322
\(508\) −0.803292 −0.0356403
\(509\) −30.0441 −1.33168 −0.665842 0.746093i \(-0.731927\pi\)
−0.665842 + 0.746093i \(0.731927\pi\)
\(510\) −6.59796 −0.292162
\(511\) 44.6930 1.97710
\(512\) −15.5904 −0.689007
\(513\) 6.09004 0.268882
\(514\) 52.7981 2.32883
\(515\) 23.2271 1.02351
\(516\) −11.6963 −0.514901
\(517\) −2.18694 −0.0961813
\(518\) −72.2003 −3.17230
\(519\) 3.38489 0.148580
\(520\) −2.63285 −0.115458
\(521\) −35.4315 −1.55228 −0.776141 0.630559i \(-0.782826\pi\)
−0.776141 + 0.630559i \(0.782826\pi\)
\(522\) 9.48030 0.414942
\(523\) −10.3511 −0.452623 −0.226312 0.974055i \(-0.572667\pi\)
−0.226312 + 0.974055i \(0.572667\pi\)
\(524\) 8.48731 0.370770
\(525\) −43.0232 −1.87769
\(526\) 12.1552 0.529993
\(527\) 11.1068 0.483819
\(528\) 31.8540 1.38627
\(529\) −22.7258 −0.988076
\(530\) −41.7917 −1.81531
\(531\) 2.65352 0.115153
\(532\) −36.5053 −1.58271
\(533\) 5.16370 0.223665
\(534\) −1.87858 −0.0812941
\(535\) 22.5252 0.973851
\(536\) −4.02325 −0.173778
\(537\) 18.5579 0.800831
\(538\) 41.4136 1.78547
\(539\) 115.491 4.97457
\(540\) 4.42373 0.190367
\(541\) 41.4031 1.78006 0.890029 0.455903i \(-0.150684\pi\)
0.890029 + 0.455903i \(0.150684\pi\)
\(542\) 11.4254 0.490765
\(543\) −10.4065 −0.446586
\(544\) 6.00762 0.257575
\(545\) 32.0719 1.37381
\(546\) 4.45517 0.190664
\(547\) 0.323912 0.0138495 0.00692474 0.999976i \(-0.497796\pi\)
0.00692474 + 0.999976i \(0.497796\pi\)
\(548\) 15.3531 0.655854
\(549\) 0.558687 0.0238442
\(550\) −98.8661 −4.21566
\(551\) 32.2790 1.37513
\(552\) 0.750070 0.0319251
\(553\) 84.5012 3.59336
\(554\) 13.7365 0.583607
\(555\) 29.7899 1.26451
\(556\) 8.29364 0.351729
\(557\) 41.1175 1.74220 0.871102 0.491102i \(-0.163406\pi\)
0.871102 + 0.491102i \(0.163406\pi\)
\(558\) −19.8660 −0.840997
\(559\) 4.86020 0.205564
\(560\) 91.4596 3.86487
\(561\) −6.42178 −0.271128
\(562\) 15.4167 0.650314
\(563\) −12.9058 −0.543916 −0.271958 0.962309i \(-0.587671\pi\)
−0.271958 + 0.962309i \(0.587671\pi\)
\(564\) 0.408397 0.0171966
\(565\) −63.0424 −2.65221
\(566\) 2.46850 0.103759
\(567\) 4.99843 0.209914
\(568\) −10.2876 −0.431659
\(569\) −28.6992 −1.20313 −0.601566 0.798823i \(-0.705456\pi\)
−0.601566 + 0.798823i \(0.705456\pi\)
\(570\) 40.1818 1.68303
\(571\) 37.3400 1.56263 0.781316 0.624136i \(-0.214549\pi\)
0.781316 + 0.624136i \(0.214549\pi\)
\(572\) 3.83765 0.160460
\(573\) 1.94279 0.0811614
\(574\) −92.6424 −3.86682
\(575\) −4.50754 −0.187978
\(576\) −0.824845 −0.0343685
\(577\) −7.67580 −0.319548 −0.159774 0.987154i \(-0.551077\pi\)
−0.159774 + 0.987154i \(0.551077\pi\)
\(578\) −1.78864 −0.0743976
\(579\) 16.9622 0.704927
\(580\) 23.4471 0.973586
\(581\) 27.2734 1.13149
\(582\) −8.31178 −0.344534
\(583\) −40.6757 −1.68462
\(584\) 12.8067 0.529944
\(585\) −1.83821 −0.0760005
\(586\) 43.7189 1.80601
\(587\) 16.5758 0.684156 0.342078 0.939672i \(-0.388869\pi\)
0.342078 + 0.939672i \(0.388869\pi\)
\(588\) −21.5673 −0.889422
\(589\) −67.6408 −2.78709
\(590\) 17.5078 0.720786
\(591\) 25.5899 1.05263
\(592\) −40.0582 −1.64638
\(593\) 12.4162 0.509873 0.254936 0.966958i \(-0.417945\pi\)
0.254936 + 0.966958i \(0.417945\pi\)
\(594\) 11.4862 0.471286
\(595\) −18.4383 −0.755896
\(596\) 19.9050 0.815340
\(597\) −17.1968 −0.703819
\(598\) 0.466768 0.0190876
\(599\) 17.3062 0.707113 0.353556 0.935413i \(-0.384972\pi\)
0.353556 + 0.935413i \(0.384972\pi\)
\(600\) −12.3282 −0.503297
\(601\) −35.7423 −1.45796 −0.728979 0.684536i \(-0.760005\pi\)
−0.728979 + 0.684536i \(0.760005\pi\)
\(602\) −87.1973 −3.55389
\(603\) −2.80896 −0.114390
\(604\) −11.5136 −0.468483
\(605\) −111.547 −4.53503
\(606\) −17.7440 −0.720801
\(607\) 2.96323 0.120274 0.0601369 0.998190i \(-0.480846\pi\)
0.0601369 + 0.998190i \(0.480846\pi\)
\(608\) −36.5867 −1.48378
\(609\) 26.4931 1.07356
\(610\) 3.68619 0.149250
\(611\) −0.169703 −0.00686543
\(612\) 1.19923 0.0484760
\(613\) −8.10755 −0.327461 −0.163730 0.986505i \(-0.552353\pi\)
−0.163730 + 0.986505i \(0.552353\pi\)
\(614\) 41.3513 1.66880
\(615\) 38.2243 1.54135
\(616\) 45.9748 1.85238
\(617\) −15.1282 −0.609039 −0.304520 0.952506i \(-0.598496\pi\)
−0.304520 + 0.952506i \(0.598496\pi\)
\(618\) −11.2624 −0.453041
\(619\) 22.7058 0.912625 0.456312 0.889820i \(-0.349170\pi\)
0.456312 + 0.889820i \(0.349170\pi\)
\(620\) −49.1335 −1.97325
\(621\) 0.523686 0.0210148
\(622\) −38.6686 −1.55047
\(623\) −5.24978 −0.210328
\(624\) 2.47182 0.0989519
\(625\) 6.04968 0.241987
\(626\) −36.6350 −1.46423
\(627\) 39.1089 1.56186
\(628\) −1.19923 −0.0478544
\(629\) 8.07574 0.322001
\(630\) 32.9794 1.31393
\(631\) −27.7112 −1.10316 −0.551582 0.834120i \(-0.685976\pi\)
−0.551582 + 0.834120i \(0.685976\pi\)
\(632\) 24.2136 0.963166
\(633\) 4.38406 0.174251
\(634\) −7.17675 −0.285025
\(635\) 2.47092 0.0980553
\(636\) 7.59595 0.301199
\(637\) 8.96194 0.355085
\(638\) 60.8804 2.41028
\(639\) −7.18263 −0.284140
\(640\) 38.8797 1.53685
\(641\) −27.7653 −1.09666 −0.548332 0.836261i \(-0.684737\pi\)
−0.548332 + 0.836261i \(0.684737\pi\)
\(642\) −10.9221 −0.431060
\(643\) 34.3396 1.35422 0.677111 0.735881i \(-0.263232\pi\)
0.677111 + 0.735881i \(0.263232\pi\)
\(644\) −3.13911 −0.123698
\(645\) 35.9777 1.41662
\(646\) 10.8929 0.428575
\(647\) −5.68618 −0.223547 −0.111773 0.993734i \(-0.535653\pi\)
−0.111773 + 0.993734i \(0.535653\pi\)
\(648\) 1.43229 0.0562657
\(649\) 17.0403 0.668892
\(650\) −7.67184 −0.300914
\(651\) −55.5166 −2.17587
\(652\) 13.6186 0.533345
\(653\) 19.2310 0.752569 0.376284 0.926504i \(-0.377202\pi\)
0.376284 + 0.926504i \(0.377202\pi\)
\(654\) −15.5511 −0.608095
\(655\) −26.1069 −1.02008
\(656\) −51.3999 −2.00683
\(657\) 8.94140 0.348837
\(658\) 3.04465 0.118693
\(659\) −16.6730 −0.649488 −0.324744 0.945802i \(-0.605278\pi\)
−0.324744 + 0.945802i \(0.605278\pi\)
\(660\) 28.4082 1.10579
\(661\) 26.0439 1.01299 0.506496 0.862242i \(-0.330941\pi\)
0.506496 + 0.862242i \(0.330941\pi\)
\(662\) −20.7586 −0.806804
\(663\) −0.498319 −0.0193531
\(664\) 7.81512 0.303285
\(665\) 112.290 4.35442
\(666\) −14.4446 −0.559716
\(667\) 2.77569 0.107475
\(668\) −9.82696 −0.380216
\(669\) −10.5981 −0.409747
\(670\) −18.5334 −0.716009
\(671\) 3.58777 0.138504
\(672\) −30.0287 −1.15838
\(673\) −33.6384 −1.29666 −0.648332 0.761358i \(-0.724533\pi\)
−0.648332 + 0.761358i \(0.724533\pi\)
\(674\) 18.0133 0.693848
\(675\) −8.60735 −0.331297
\(676\) −15.2922 −0.588161
\(677\) 2.88919 0.111040 0.0555202 0.998458i \(-0.482318\pi\)
0.0555202 + 0.998458i \(0.482318\pi\)
\(678\) 30.5681 1.17396
\(679\) −23.2276 −0.891395
\(680\) −5.28345 −0.202611
\(681\) −15.6722 −0.600559
\(682\) −127.575 −4.88511
\(683\) 4.92486 0.188445 0.0942223 0.995551i \(-0.469964\pi\)
0.0942223 + 0.995551i \(0.469964\pi\)
\(684\) −7.30336 −0.279251
\(685\) −47.2261 −1.80442
\(686\) −98.2042 −3.74946
\(687\) 26.1823 0.998917
\(688\) −48.3788 −1.84442
\(689\) −3.15637 −0.120248
\(690\) 3.45526 0.131539
\(691\) 33.1752 1.26204 0.631022 0.775765i \(-0.282636\pi\)
0.631022 + 0.775765i \(0.282636\pi\)
\(692\) −4.05926 −0.154310
\(693\) 32.0988 1.21933
\(694\) −24.5356 −0.931360
\(695\) −25.5111 −0.967693
\(696\) 7.59155 0.287757
\(697\) 10.3622 0.392497
\(698\) 34.2744 1.29730
\(699\) −8.14008 −0.307886
\(700\) 51.5947 1.95010
\(701\) 2.79468 0.105554 0.0527769 0.998606i \(-0.483193\pi\)
0.0527769 + 0.998606i \(0.483193\pi\)
\(702\) 0.891313 0.0336405
\(703\) −49.1816 −1.85492
\(704\) −5.29697 −0.199637
\(705\) −1.25622 −0.0473122
\(706\) −11.6846 −0.439756
\(707\) −49.5865 −1.86489
\(708\) −3.18218 −0.119594
\(709\) −31.9364 −1.19940 −0.599699 0.800226i \(-0.704713\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(710\) −47.3907 −1.77854
\(711\) 16.9055 0.634007
\(712\) −1.50431 −0.0563765
\(713\) −5.81647 −0.217828
\(714\) 8.94039 0.334586
\(715\) −11.8046 −0.441465
\(716\) −22.2551 −0.831713
\(717\) 13.8131 0.515860
\(718\) −13.9084 −0.519056
\(719\) −10.7154 −0.399618 −0.199809 0.979835i \(-0.564032\pi\)
−0.199809 + 0.979835i \(0.564032\pi\)
\(720\) 18.2977 0.681913
\(721\) −31.4734 −1.17213
\(722\) −32.3540 −1.20409
\(723\) −27.6965 −1.03005
\(724\) 12.4798 0.463807
\(725\) −45.6214 −1.69434
\(726\) 54.0871 2.00736
\(727\) −35.2447 −1.30715 −0.653577 0.756860i \(-0.726732\pi\)
−0.653577 + 0.756860i \(0.726732\pi\)
\(728\) 3.56757 0.132223
\(729\) 1.00000 0.0370370
\(730\) 58.9949 2.18350
\(731\) 9.75318 0.360734
\(732\) −0.669994 −0.0247637
\(733\) −6.36318 −0.235029 −0.117515 0.993071i \(-0.537493\pi\)
−0.117515 + 0.993071i \(0.537493\pi\)
\(734\) 5.36406 0.197991
\(735\) 66.3409 2.44702
\(736\) −3.14610 −0.115967
\(737\) −18.0385 −0.664458
\(738\) −18.5343 −0.682257
\(739\) 31.9258 1.17441 0.587204 0.809439i \(-0.300229\pi\)
0.587204 + 0.809439i \(0.300229\pi\)
\(740\) −35.7249 −1.31327
\(741\) 3.03479 0.111486
\(742\) 56.6287 2.07891
\(743\) 7.72069 0.283244 0.141622 0.989921i \(-0.454768\pi\)
0.141622 + 0.989921i \(0.454768\pi\)
\(744\) −15.9081 −0.583221
\(745\) −61.2275 −2.24320
\(746\) 41.2243 1.50933
\(747\) 5.45638 0.199639
\(748\) 7.70118 0.281583
\(749\) −30.5222 −1.11526
\(750\) −23.8011 −0.869094
\(751\) 19.9841 0.729231 0.364616 0.931158i \(-0.381200\pi\)
0.364616 + 0.931158i \(0.381200\pi\)
\(752\) 1.68923 0.0615999
\(753\) 4.06052 0.147974
\(754\) 4.72422 0.172046
\(755\) 35.4158 1.28891
\(756\) −5.99427 −0.218009
\(757\) −25.1730 −0.914929 −0.457464 0.889228i \(-0.651242\pi\)
−0.457464 + 0.889228i \(0.651242\pi\)
\(758\) −55.9374 −2.03174
\(759\) 3.36299 0.122069
\(760\) 32.1764 1.16716
\(761\) −12.6032 −0.456866 −0.228433 0.973560i \(-0.573360\pi\)
−0.228433 + 0.973560i \(0.573360\pi\)
\(762\) −1.19810 −0.0434027
\(763\) −43.4582 −1.57329
\(764\) −2.32985 −0.0842912
\(765\) −3.68881 −0.133369
\(766\) −4.30410 −0.155514
\(767\) 1.32230 0.0477456
\(768\) −20.5017 −0.739793
\(769\) −41.4989 −1.49649 −0.748244 0.663423i \(-0.769103\pi\)
−0.748244 + 0.663423i \(0.769103\pi\)
\(770\) 211.787 7.63226
\(771\) 29.5186 1.06309
\(772\) −20.3416 −0.732111
\(773\) 50.8582 1.82924 0.914622 0.404311i \(-0.132489\pi\)
0.914622 + 0.404311i \(0.132489\pi\)
\(774\) −17.4449 −0.627045
\(775\) 95.6000 3.43405
\(776\) −6.65583 −0.238930
\(777\) −40.3660 −1.44812
\(778\) −11.1392 −0.399360
\(779\) −63.1064 −2.26102
\(780\) 2.20443 0.0789313
\(781\) −46.1253 −1.65049
\(782\) 0.936685 0.0334958
\(783\) 5.30029 0.189417
\(784\) −89.2078 −3.18599
\(785\) 3.68881 0.131659
\(786\) 12.6587 0.451523
\(787\) 3.12825 0.111510 0.0557550 0.998444i \(-0.482243\pi\)
0.0557550 + 0.998444i \(0.482243\pi\)
\(788\) −30.6881 −1.09322
\(789\) 6.79580 0.241937
\(790\) 111.542 3.96848
\(791\) 85.4240 3.03733
\(792\) 9.19785 0.326831
\(793\) 0.278405 0.00988644
\(794\) 8.60444 0.305360
\(795\) −23.3651 −0.828673
\(796\) 20.6229 0.730960
\(797\) 22.1524 0.784679 0.392339 0.919820i \(-0.371666\pi\)
0.392339 + 0.919820i \(0.371666\pi\)
\(798\) −54.4474 −1.92742
\(799\) −0.340550 −0.0120478
\(800\) 51.7097 1.82821
\(801\) −1.05029 −0.0371100
\(802\) −57.7243 −2.03832
\(803\) 57.4197 2.02630
\(804\) 3.36859 0.118801
\(805\) 9.65587 0.340325
\(806\) −9.89963 −0.348700
\(807\) 23.1537 0.815049
\(808\) −14.2089 −0.499867
\(809\) −6.13956 −0.215855 −0.107928 0.994159i \(-0.534422\pi\)
−0.107928 + 0.994159i \(0.534422\pi\)
\(810\) 6.59796 0.231829
\(811\) 23.8867 0.838776 0.419388 0.907807i \(-0.362245\pi\)
0.419388 + 0.907807i \(0.362245\pi\)
\(812\) −31.7713 −1.11496
\(813\) 6.38779 0.224029
\(814\) −92.7599 −3.25123
\(815\) −41.8906 −1.46737
\(816\) 4.96031 0.173646
\(817\) −59.3973 −2.07805
\(818\) 47.4562 1.65927
\(819\) 2.49082 0.0870361
\(820\) −45.8397 −1.60079
\(821\) 3.73180 0.130241 0.0651203 0.997877i \(-0.479257\pi\)
0.0651203 + 0.997877i \(0.479257\pi\)
\(822\) 22.8991 0.798697
\(823\) −8.79021 −0.306407 −0.153204 0.988195i \(-0.548959\pi\)
−0.153204 + 0.988195i \(0.548959\pi\)
\(824\) −9.01862 −0.314179
\(825\) −55.2745 −1.92441
\(826\) −23.7235 −0.825448
\(827\) 33.8786 1.17807 0.589037 0.808106i \(-0.299507\pi\)
0.589037 + 0.808106i \(0.299507\pi\)
\(828\) −0.628019 −0.0218252
\(829\) −6.89122 −0.239342 −0.119671 0.992814i \(-0.538184\pi\)
−0.119671 + 0.992814i \(0.538184\pi\)
\(830\) 36.0010 1.24961
\(831\) 7.67985 0.266411
\(832\) −0.411036 −0.0142501
\(833\) 17.9843 0.623120
\(834\) 12.3699 0.428334
\(835\) 30.2276 1.04607
\(836\) −46.9005 −1.62209
\(837\) −11.1068 −0.383907
\(838\) 52.3221 1.80744
\(839\) −19.5207 −0.673930 −0.336965 0.941517i \(-0.609400\pi\)
−0.336965 + 0.941517i \(0.609400\pi\)
\(840\) 26.4090 0.911196
\(841\) −0.906939 −0.0312738
\(842\) −44.9089 −1.54766
\(843\) 8.61923 0.296862
\(844\) −5.25749 −0.180970
\(845\) 47.0386 1.61818
\(846\) 0.609121 0.0209420
\(847\) 151.149 5.19353
\(848\) 31.4187 1.07892
\(849\) 1.38010 0.0473648
\(850\) −15.3954 −0.528059
\(851\) −4.22915 −0.144973
\(852\) 8.61362 0.295098
\(853\) −41.7096 −1.42811 −0.714054 0.700090i \(-0.753143\pi\)
−0.714054 + 0.700090i \(0.753143\pi\)
\(854\) −4.99488 −0.170921
\(855\) 22.4650 0.768288
\(856\) −8.74608 −0.298935
\(857\) −30.3859 −1.03796 −0.518981 0.854786i \(-0.673688\pi\)
−0.518981 + 0.854786i \(0.673688\pi\)
\(858\) 5.72382 0.195408
\(859\) −12.0865 −0.412385 −0.206192 0.978511i \(-0.566107\pi\)
−0.206192 + 0.978511i \(0.566107\pi\)
\(860\) −43.1455 −1.47125
\(861\) −51.7949 −1.76517
\(862\) −11.6088 −0.395397
\(863\) 43.9719 1.49682 0.748410 0.663236i \(-0.230817\pi\)
0.748410 + 0.663236i \(0.230817\pi\)
\(864\) −6.00762 −0.204383
\(865\) 12.4862 0.424545
\(866\) 62.2035 2.11376
\(867\) −1.00000 −0.0339618
\(868\) 66.5771 2.25977
\(869\) 108.564 3.68277
\(870\) 34.9711 1.18563
\(871\) −1.39976 −0.0474291
\(872\) −12.4528 −0.421706
\(873\) −4.64699 −0.157277
\(874\) −5.70445 −0.192956
\(875\) −66.5133 −2.24856
\(876\) −10.7228 −0.362289
\(877\) 15.6894 0.529795 0.264897 0.964277i \(-0.414662\pi\)
0.264897 + 0.964277i \(0.414662\pi\)
\(878\) 59.8546 2.02000
\(879\) 24.4425 0.824426
\(880\) 117.503 3.96104
\(881\) −16.2523 −0.547555 −0.273777 0.961793i \(-0.588273\pi\)
−0.273777 + 0.961793i \(0.588273\pi\)
\(882\) −32.1675 −1.08314
\(883\) 4.96920 0.167227 0.0836135 0.996498i \(-0.473354\pi\)
0.0836135 + 0.996498i \(0.473354\pi\)
\(884\) 0.597599 0.0200994
\(885\) 9.78836 0.329032
\(886\) −22.3120 −0.749586
\(887\) −1.73078 −0.0581138 −0.0290569 0.999578i \(-0.509250\pi\)
−0.0290569 + 0.999578i \(0.509250\pi\)
\(888\) −11.5668 −0.388157
\(889\) −3.34815 −0.112293
\(890\) −6.92973 −0.232285
\(891\) 6.42178 0.215138
\(892\) 12.7096 0.425548
\(893\) 2.07396 0.0694025
\(894\) 29.6881 0.992918
\(895\) 68.4565 2.28825
\(896\) −52.6829 −1.76001
\(897\) 0.260963 0.00871329
\(898\) −50.0099 −1.66885
\(899\) −58.8692 −1.96340
\(900\) 10.3222 0.344073
\(901\) −6.33403 −0.211017
\(902\) −119.023 −3.96304
\(903\) −48.7506 −1.62232
\(904\) 24.4781 0.814128
\(905\) −38.3876 −1.27605
\(906\) −17.1725 −0.570517
\(907\) −30.3560 −1.00796 −0.503978 0.863717i \(-0.668131\pi\)
−0.503978 + 0.863717i \(0.668131\pi\)
\(908\) 18.7945 0.623718
\(909\) −9.92040 −0.329039
\(910\) 16.4343 0.544791
\(911\) 17.0157 0.563755 0.281877 0.959450i \(-0.409043\pi\)
0.281877 + 0.959450i \(0.409043\pi\)
\(912\) −30.2085 −1.00030
\(913\) 35.0397 1.15964
\(914\) 16.2363 0.537048
\(915\) 2.06089 0.0681310
\(916\) −31.3986 −1.03744
\(917\) 35.3754 1.16820
\(918\) 1.78864 0.0590339
\(919\) −31.5392 −1.04038 −0.520190 0.854050i \(-0.674139\pi\)
−0.520190 + 0.854050i \(0.674139\pi\)
\(920\) 2.76687 0.0912210
\(921\) 23.1189 0.761793
\(922\) 25.2366 0.831124
\(923\) −3.57924 −0.117812
\(924\) −38.4938 −1.26635
\(925\) 69.5107 2.28550
\(926\) −0.295019 −0.00969493
\(927\) −6.29664 −0.206809
\(928\) −31.8421 −1.04527
\(929\) −1.41769 −0.0465131 −0.0232565 0.999730i \(-0.507403\pi\)
−0.0232565 + 0.999730i \(0.507403\pi\)
\(930\) −73.2821 −2.40302
\(931\) −109.525 −3.58955
\(932\) 9.76183 0.319759
\(933\) −21.6190 −0.707775
\(934\) −56.4339 −1.84657
\(935\) −23.6887 −0.774705
\(936\) 0.713738 0.0233293
\(937\) −24.0410 −0.785385 −0.392693 0.919670i \(-0.628456\pi\)
−0.392693 + 0.919670i \(0.628456\pi\)
\(938\) 25.1132 0.819976
\(939\) −20.4821 −0.668407
\(940\) 1.50650 0.0491366
\(941\) −3.88309 −0.126585 −0.0632925 0.997995i \(-0.520160\pi\)
−0.0632925 + 0.997995i \(0.520160\pi\)
\(942\) −1.78864 −0.0582770
\(943\) −5.42655 −0.176713
\(944\) −13.1623 −0.428396
\(945\) 18.4383 0.599798
\(946\) −112.027 −3.64232
\(947\) 41.3097 1.34239 0.671193 0.741283i \(-0.265782\pi\)
0.671193 + 0.741283i \(0.265782\pi\)
\(948\) −20.2736 −0.658456
\(949\) 4.45567 0.144637
\(950\) 93.7589 3.04194
\(951\) −4.01241 −0.130111
\(952\) 7.15921 0.232031
\(953\) 52.6727 1.70624 0.853118 0.521719i \(-0.174709\pi\)
0.853118 + 0.521719i \(0.174709\pi\)
\(954\) 11.3293 0.366799
\(955\) 7.16660 0.231906
\(956\) −16.5651 −0.535753
\(957\) 34.0373 1.10027
\(958\) −19.8026 −0.639795
\(959\) 63.9925 2.06643
\(960\) −3.04270 −0.0982027
\(961\) 92.3608 2.97938
\(962\) −7.19801 −0.232073
\(963\) −6.10636 −0.196775
\(964\) 33.2145 1.06977
\(965\) 62.5706 2.01422
\(966\) −4.68196 −0.150639
\(967\) 9.06672 0.291566 0.145783 0.989317i \(-0.453430\pi\)
0.145783 + 0.989317i \(0.453430\pi\)
\(968\) 43.3114 1.39208
\(969\) 6.09004 0.195640
\(970\) −30.6606 −0.984453
\(971\) −22.9332 −0.735960 −0.367980 0.929834i \(-0.619950\pi\)
−0.367980 + 0.929834i \(0.619950\pi\)
\(972\) −1.19923 −0.0384653
\(973\) 34.5682 1.10821
\(974\) −46.3893 −1.48641
\(975\) −4.28921 −0.137365
\(976\) −2.77126 −0.0887059
\(977\) 57.0979 1.82672 0.913361 0.407150i \(-0.133477\pi\)
0.913361 + 0.407150i \(0.133477\pi\)
\(978\) 20.3120 0.649507
\(979\) −6.74470 −0.215561
\(980\) −79.5579 −2.54138
\(981\) −8.69436 −0.277589
\(982\) 65.2048 2.08077
\(983\) −21.0500 −0.671390 −0.335695 0.941971i \(-0.608971\pi\)
−0.335695 + 0.941971i \(0.608971\pi\)
\(984\) −14.8417 −0.473137
\(985\) 94.3963 3.00772
\(986\) 9.48030 0.301914
\(987\) 1.70222 0.0541821
\(988\) −3.63940 −0.115785
\(989\) −5.10760 −0.162412
\(990\) 42.3706 1.34663
\(991\) −37.0232 −1.17608 −0.588040 0.808832i \(-0.700100\pi\)
−0.588040 + 0.808832i \(0.700100\pi\)
\(992\) 66.7254 2.11853
\(993\) −11.6058 −0.368298
\(994\) 64.2155 2.03679
\(995\) −63.4359 −2.01105
\(996\) −6.54345 −0.207337
\(997\) 56.2009 1.77990 0.889950 0.456058i \(-0.150739\pi\)
0.889950 + 0.456058i \(0.150739\pi\)
\(998\) −49.0583 −1.55291
\(999\) −8.07574 −0.255505
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 \(a_p\))