Properties

Label 6027.2.a.y.1.5
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.762978\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.76298 q^{2} -1.00000 q^{3} +1.10809 q^{4} -3.51322 q^{5} -1.76298 q^{6} -1.57241 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.76298 q^{2} -1.00000 q^{3} +1.10809 q^{4} -3.51322 q^{5} -1.76298 q^{6} -1.57241 q^{8} +1.00000 q^{9} -6.19372 q^{10} -0.153259 q^{11} -1.10809 q^{12} +2.35241 q^{13} +3.51322 q^{15} -4.98832 q^{16} -2.14700 q^{17} +1.76298 q^{18} -1.53924 q^{19} -3.89296 q^{20} -0.270193 q^{22} -3.30805 q^{23} +1.57241 q^{24} +7.34269 q^{25} +4.14724 q^{26} -1.00000 q^{27} -4.53129 q^{29} +6.19372 q^{30} +0.462221 q^{31} -5.64946 q^{32} +0.153259 q^{33} -3.78511 q^{34} +1.10809 q^{36} -7.31083 q^{37} -2.71365 q^{38} -2.35241 q^{39} +5.52423 q^{40} -1.00000 q^{41} +3.68806 q^{43} -0.169825 q^{44} -3.51322 q^{45} -5.83202 q^{46} +0.200461 q^{47} +4.98832 q^{48} +12.9450 q^{50} +2.14700 q^{51} +2.60668 q^{52} -8.09875 q^{53} -1.76298 q^{54} +0.538433 q^{55} +1.53924 q^{57} -7.98856 q^{58} -0.519212 q^{59} +3.89296 q^{60} -2.10590 q^{61} +0.814885 q^{62} +0.0167549 q^{64} -8.26451 q^{65} +0.270193 q^{66} +14.3401 q^{67} -2.37907 q^{68} +3.30805 q^{69} +5.11775 q^{71} -1.57241 q^{72} +6.70809 q^{73} -12.8888 q^{74} -7.34269 q^{75} -1.70562 q^{76} -4.14724 q^{78} -2.88889 q^{79} +17.5250 q^{80} +1.00000 q^{81} -1.76298 q^{82} +0.349683 q^{83} +7.54287 q^{85} +6.50196 q^{86} +4.53129 q^{87} +0.240987 q^{88} +1.87138 q^{89} -6.19372 q^{90} -3.66562 q^{92} -0.462221 q^{93} +0.353409 q^{94} +5.40770 q^{95} +5.64946 q^{96} -9.30390 q^{97} -0.153259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.76298 1.24661 0.623307 0.781977i \(-0.285789\pi\)
0.623307 + 0.781977i \(0.285789\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.10809 0.554046
\(5\) −3.51322 −1.57116 −0.785579 0.618761i \(-0.787635\pi\)
−0.785579 + 0.618761i \(0.787635\pi\)
\(6\) −1.76298 −0.719733
\(7\) 0 0
\(8\) −1.57241 −0.555933
\(9\) 1.00000 0.333333
\(10\) −6.19372 −1.95863
\(11\) −0.153259 −0.0462094 −0.0231047 0.999733i \(-0.507355\pi\)
−0.0231047 + 0.999733i \(0.507355\pi\)
\(12\) −1.10809 −0.319878
\(13\) 2.35241 0.652440 0.326220 0.945294i \(-0.394225\pi\)
0.326220 + 0.945294i \(0.394225\pi\)
\(14\) 0 0
\(15\) 3.51322 0.907108
\(16\) −4.98832 −1.24708
\(17\) −2.14700 −0.520724 −0.260362 0.965511i \(-0.583842\pi\)
−0.260362 + 0.965511i \(0.583842\pi\)
\(18\) 1.76298 0.415538
\(19\) −1.53924 −0.353127 −0.176563 0.984289i \(-0.556498\pi\)
−0.176563 + 0.984289i \(0.556498\pi\)
\(20\) −3.89296 −0.870493
\(21\) 0 0
\(22\) −0.270193 −0.0576053
\(23\) −3.30805 −0.689776 −0.344888 0.938644i \(-0.612083\pi\)
−0.344888 + 0.938644i \(0.612083\pi\)
\(24\) 1.57241 0.320968
\(25\) 7.34269 1.46854
\(26\) 4.14724 0.813341
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −4.53129 −0.841439 −0.420719 0.907191i \(-0.638222\pi\)
−0.420719 + 0.907191i \(0.638222\pi\)
\(30\) 6.19372 1.13081
\(31\) 0.462221 0.0830173 0.0415086 0.999138i \(-0.486784\pi\)
0.0415086 + 0.999138i \(0.486784\pi\)
\(32\) −5.64946 −0.998693
\(33\) 0.153259 0.0266790
\(34\) −3.78511 −0.649142
\(35\) 0 0
\(36\) 1.10809 0.184682
\(37\) −7.31083 −1.20189 −0.600946 0.799289i \(-0.705210\pi\)
−0.600946 + 0.799289i \(0.705210\pi\)
\(38\) −2.71365 −0.440213
\(39\) −2.35241 −0.376686
\(40\) 5.52423 0.873458
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 3.68806 0.562423 0.281212 0.959646i \(-0.409264\pi\)
0.281212 + 0.959646i \(0.409264\pi\)
\(44\) −0.169825 −0.0256021
\(45\) −3.51322 −0.523719
\(46\) −5.83202 −0.859884
\(47\) 0.200461 0.0292403 0.0146201 0.999893i \(-0.495346\pi\)
0.0146201 + 0.999893i \(0.495346\pi\)
\(48\) 4.98832 0.720001
\(49\) 0 0
\(50\) 12.9450 1.83070
\(51\) 2.14700 0.300640
\(52\) 2.60668 0.361482
\(53\) −8.09875 −1.11245 −0.556224 0.831032i \(-0.687751\pi\)
−0.556224 + 0.831032i \(0.687751\pi\)
\(54\) −1.76298 −0.239911
\(55\) 0.538433 0.0726023
\(56\) 0 0
\(57\) 1.53924 0.203878
\(58\) −7.98856 −1.04895
\(59\) −0.519212 −0.0675956 −0.0337978 0.999429i \(-0.510760\pi\)
−0.0337978 + 0.999429i \(0.510760\pi\)
\(60\) 3.89296 0.502580
\(61\) −2.10590 −0.269633 −0.134816 0.990871i \(-0.543044\pi\)
−0.134816 + 0.990871i \(0.543044\pi\)
\(62\) 0.814885 0.103490
\(63\) 0 0
\(64\) 0.0167549 0.00209436
\(65\) −8.26451 −1.02509
\(66\) 0.270193 0.0332584
\(67\) 14.3401 1.75192 0.875958 0.482387i \(-0.160230\pi\)
0.875958 + 0.482387i \(0.160230\pi\)
\(68\) −2.37907 −0.288505
\(69\) 3.30805 0.398242
\(70\) 0 0
\(71\) 5.11775 0.607365 0.303682 0.952773i \(-0.401784\pi\)
0.303682 + 0.952773i \(0.401784\pi\)
\(72\) −1.57241 −0.185311
\(73\) 6.70809 0.785123 0.392561 0.919726i \(-0.371589\pi\)
0.392561 + 0.919726i \(0.371589\pi\)
\(74\) −12.8888 −1.49830
\(75\) −7.34269 −0.847860
\(76\) −1.70562 −0.195648
\(77\) 0 0
\(78\) −4.14724 −0.469582
\(79\) −2.88889 −0.325026 −0.162513 0.986706i \(-0.551960\pi\)
−0.162513 + 0.986706i \(0.551960\pi\)
\(80\) 17.5250 1.95936
\(81\) 1.00000 0.111111
\(82\) −1.76298 −0.194688
\(83\) 0.349683 0.0383827 0.0191913 0.999816i \(-0.493891\pi\)
0.0191913 + 0.999816i \(0.493891\pi\)
\(84\) 0 0
\(85\) 7.54287 0.818140
\(86\) 6.50196 0.701125
\(87\) 4.53129 0.485805
\(88\) 0.240987 0.0256893
\(89\) 1.87138 0.198366 0.0991831 0.995069i \(-0.468377\pi\)
0.0991831 + 0.995069i \(0.468377\pi\)
\(90\) −6.19372 −0.652876
\(91\) 0 0
\(92\) −3.66562 −0.382168
\(93\) −0.462221 −0.0479300
\(94\) 0.353409 0.0364514
\(95\) 5.40770 0.554818
\(96\) 5.64946 0.576596
\(97\) −9.30390 −0.944668 −0.472334 0.881420i \(-0.656588\pi\)
−0.472334 + 0.881420i \(0.656588\pi\)
\(98\) 0 0
\(99\) −0.153259 −0.0154031
\(100\) 8.13637 0.813637
\(101\) 15.8760 1.57972 0.789858 0.613289i \(-0.210154\pi\)
0.789858 + 0.613289i \(0.210154\pi\)
\(102\) 3.78511 0.374782
\(103\) 18.7078 1.84333 0.921667 0.387981i \(-0.126827\pi\)
0.921667 + 0.387981i \(0.126827\pi\)
\(104\) −3.69896 −0.362713
\(105\) 0 0
\(106\) −14.2779 −1.38679
\(107\) 6.80514 0.657877 0.328939 0.944351i \(-0.393309\pi\)
0.328939 + 0.944351i \(0.393309\pi\)
\(108\) −1.10809 −0.106626
\(109\) 14.4970 1.38856 0.694280 0.719705i \(-0.255723\pi\)
0.694280 + 0.719705i \(0.255723\pi\)
\(110\) 0.949245 0.0905070
\(111\) 7.31083 0.693913
\(112\) 0 0
\(113\) 10.9043 1.02579 0.512896 0.858451i \(-0.328573\pi\)
0.512896 + 0.858451i \(0.328573\pi\)
\(114\) 2.71365 0.254157
\(115\) 11.6219 1.08375
\(116\) −5.02108 −0.466195
\(117\) 2.35241 0.217480
\(118\) −0.915359 −0.0842656
\(119\) 0 0
\(120\) −5.52423 −0.504291
\(121\) −10.9765 −0.997865
\(122\) −3.71265 −0.336128
\(123\) 1.00000 0.0901670
\(124\) 0.512183 0.0459954
\(125\) −8.23036 −0.736146
\(126\) 0 0
\(127\) −2.69248 −0.238919 −0.119459 0.992839i \(-0.538116\pi\)
−0.119459 + 0.992839i \(0.538116\pi\)
\(128\) 11.3285 1.00130
\(129\) −3.68806 −0.324715
\(130\) −14.5701 −1.27789
\(131\) −14.1990 −1.24057 −0.620287 0.784375i \(-0.712984\pi\)
−0.620287 + 0.784375i \(0.712984\pi\)
\(132\) 0.169825 0.0147814
\(133\) 0 0
\(134\) 25.2812 2.18396
\(135\) 3.51322 0.302369
\(136\) 3.37597 0.289487
\(137\) −9.57507 −0.818054 −0.409027 0.912522i \(-0.634132\pi\)
−0.409027 + 0.912522i \(0.634132\pi\)
\(138\) 5.83202 0.496454
\(139\) 18.0900 1.53438 0.767189 0.641421i \(-0.221655\pi\)
0.767189 + 0.641421i \(0.221655\pi\)
\(140\) 0 0
\(141\) −0.200461 −0.0168819
\(142\) 9.02247 0.757149
\(143\) −0.360528 −0.0301489
\(144\) −4.98832 −0.415693
\(145\) 15.9194 1.32203
\(146\) 11.8262 0.978745
\(147\) 0 0
\(148\) −8.10107 −0.665904
\(149\) 7.52984 0.616868 0.308434 0.951246i \(-0.400195\pi\)
0.308434 + 0.951246i \(0.400195\pi\)
\(150\) −12.9450 −1.05695
\(151\) 7.18861 0.585000 0.292500 0.956265i \(-0.405513\pi\)
0.292500 + 0.956265i \(0.405513\pi\)
\(152\) 2.42033 0.196315
\(153\) −2.14700 −0.173575
\(154\) 0 0
\(155\) −1.62388 −0.130433
\(156\) −2.60668 −0.208702
\(157\) 21.9904 1.75503 0.877513 0.479554i \(-0.159201\pi\)
0.877513 + 0.479554i \(0.159201\pi\)
\(158\) −5.09306 −0.405182
\(159\) 8.09875 0.642273
\(160\) 19.8478 1.56910
\(161\) 0 0
\(162\) 1.76298 0.138513
\(163\) −8.91625 −0.698374 −0.349187 0.937053i \(-0.613542\pi\)
−0.349187 + 0.937053i \(0.613542\pi\)
\(164\) −1.10809 −0.0865274
\(165\) −0.538433 −0.0419169
\(166\) 0.616483 0.0478483
\(167\) 3.01514 0.233318 0.116659 0.993172i \(-0.462781\pi\)
0.116659 + 0.993172i \(0.462781\pi\)
\(168\) 0 0
\(169\) −7.46619 −0.574322
\(170\) 13.2979 1.01990
\(171\) −1.53924 −0.117709
\(172\) 4.08671 0.311608
\(173\) 2.42150 0.184103 0.0920516 0.995754i \(-0.470658\pi\)
0.0920516 + 0.995754i \(0.470658\pi\)
\(174\) 7.98856 0.605611
\(175\) 0 0
\(176\) 0.764505 0.0576268
\(177\) 0.519212 0.0390263
\(178\) 3.29921 0.247286
\(179\) 17.7746 1.32854 0.664268 0.747495i \(-0.268744\pi\)
0.664268 + 0.747495i \(0.268744\pi\)
\(180\) −3.89296 −0.290164
\(181\) 18.9450 1.40817 0.704087 0.710114i \(-0.251356\pi\)
0.704087 + 0.710114i \(0.251356\pi\)
\(182\) 0 0
\(183\) 2.10590 0.155672
\(184\) 5.20163 0.383469
\(185\) 25.6845 1.88836
\(186\) −0.814885 −0.0597502
\(187\) 0.329048 0.0240623
\(188\) 0.222130 0.0162005
\(189\) 0 0
\(190\) 9.53365 0.691644
\(191\) −9.12762 −0.660451 −0.330226 0.943902i \(-0.607125\pi\)
−0.330226 + 0.943902i \(0.607125\pi\)
\(192\) −0.0167549 −0.00120918
\(193\) −15.0315 −1.08199 −0.540996 0.841025i \(-0.681953\pi\)
−0.540996 + 0.841025i \(0.681953\pi\)
\(194\) −16.4026 −1.17764
\(195\) 8.26451 0.591834
\(196\) 0 0
\(197\) 6.19254 0.441200 0.220600 0.975364i \(-0.429198\pi\)
0.220600 + 0.975364i \(0.429198\pi\)
\(198\) −0.270193 −0.0192018
\(199\) −20.8642 −1.47903 −0.739513 0.673143i \(-0.764944\pi\)
−0.739513 + 0.673143i \(0.764944\pi\)
\(200\) −11.5457 −0.816408
\(201\) −14.3401 −1.01147
\(202\) 27.9890 1.96930
\(203\) 0 0
\(204\) 2.37907 0.166568
\(205\) 3.51322 0.245374
\(206\) 32.9814 2.29793
\(207\) −3.30805 −0.229925
\(208\) −11.7345 −0.813644
\(209\) 0.235903 0.0163178
\(210\) 0 0
\(211\) 15.0775 1.03798 0.518989 0.854781i \(-0.326309\pi\)
0.518989 + 0.854781i \(0.326309\pi\)
\(212\) −8.97416 −0.616348
\(213\) −5.11775 −0.350662
\(214\) 11.9973 0.820119
\(215\) −12.9569 −0.883656
\(216\) 1.57241 0.106989
\(217\) 0 0
\(218\) 25.5579 1.73100
\(219\) −6.70809 −0.453291
\(220\) 0.596633 0.0402250
\(221\) −5.05062 −0.339741
\(222\) 12.8888 0.865042
\(223\) −6.22227 −0.416674 −0.208337 0.978057i \(-0.566805\pi\)
−0.208337 + 0.978057i \(0.566805\pi\)
\(224\) 0 0
\(225\) 7.34269 0.489512
\(226\) 19.2241 1.27877
\(227\) −22.2786 −1.47868 −0.739340 0.673332i \(-0.764862\pi\)
−0.739340 + 0.673332i \(0.764862\pi\)
\(228\) 1.70562 0.112958
\(229\) −22.3029 −1.47382 −0.736910 0.675991i \(-0.763716\pi\)
−0.736910 + 0.675991i \(0.763716\pi\)
\(230\) 20.4891 1.35101
\(231\) 0 0
\(232\) 7.12506 0.467783
\(233\) 9.54073 0.625034 0.312517 0.949912i \(-0.398828\pi\)
0.312517 + 0.949912i \(0.398828\pi\)
\(234\) 4.14724 0.271114
\(235\) −0.704264 −0.0459411
\(236\) −0.575334 −0.0374510
\(237\) 2.88889 0.187654
\(238\) 0 0
\(239\) 7.33462 0.474437 0.237219 0.971456i \(-0.423764\pi\)
0.237219 + 0.971456i \(0.423764\pi\)
\(240\) −17.5250 −1.13124
\(241\) 10.6267 0.684524 0.342262 0.939605i \(-0.388807\pi\)
0.342262 + 0.939605i \(0.388807\pi\)
\(242\) −19.3513 −1.24395
\(243\) −1.00000 −0.0641500
\(244\) −2.33353 −0.149389
\(245\) 0 0
\(246\) 1.76298 0.112403
\(247\) −3.62093 −0.230394
\(248\) −0.726803 −0.0461520
\(249\) −0.349683 −0.0221602
\(250\) −14.5099 −0.917689
\(251\) −24.9505 −1.57486 −0.787432 0.616401i \(-0.788590\pi\)
−0.787432 + 0.616401i \(0.788590\pi\)
\(252\) 0 0
\(253\) 0.506989 0.0318741
\(254\) −4.74678 −0.297840
\(255\) −7.54287 −0.472353
\(256\) 19.9383 1.24615
\(257\) −16.9251 −1.05576 −0.527880 0.849319i \(-0.677013\pi\)
−0.527880 + 0.849319i \(0.677013\pi\)
\(258\) −6.50196 −0.404795
\(259\) 0 0
\(260\) −9.15783 −0.567945
\(261\) −4.53129 −0.280480
\(262\) −25.0326 −1.54652
\(263\) 8.88776 0.548043 0.274021 0.961724i \(-0.411646\pi\)
0.274021 + 0.961724i \(0.411646\pi\)
\(264\) −0.240987 −0.0148317
\(265\) 28.4527 1.74783
\(266\) 0 0
\(267\) −1.87138 −0.114527
\(268\) 15.8901 0.970642
\(269\) 1.00992 0.0615760 0.0307880 0.999526i \(-0.490198\pi\)
0.0307880 + 0.999526i \(0.490198\pi\)
\(270\) 6.19372 0.376938
\(271\) 5.34824 0.324882 0.162441 0.986718i \(-0.448063\pi\)
0.162441 + 0.986718i \(0.448063\pi\)
\(272\) 10.7099 0.649384
\(273\) 0 0
\(274\) −16.8806 −1.01980
\(275\) −1.12533 −0.0678602
\(276\) 3.66562 0.220645
\(277\) 22.6002 1.35792 0.678958 0.734177i \(-0.262432\pi\)
0.678958 + 0.734177i \(0.262432\pi\)
\(278\) 31.8924 1.91278
\(279\) 0.462221 0.0276724
\(280\) 0 0
\(281\) 22.8887 1.36542 0.682712 0.730688i \(-0.260800\pi\)
0.682712 + 0.730688i \(0.260800\pi\)
\(282\) −0.353409 −0.0210452
\(283\) 5.82600 0.346320 0.173160 0.984894i \(-0.444602\pi\)
0.173160 + 0.984894i \(0.444602\pi\)
\(284\) 5.67093 0.336508
\(285\) −5.40770 −0.320324
\(286\) −0.635603 −0.0375840
\(287\) 0 0
\(288\) −5.64946 −0.332898
\(289\) −12.3904 −0.728847
\(290\) 28.0655 1.64806
\(291\) 9.30390 0.545404
\(292\) 7.43318 0.434994
\(293\) −14.4075 −0.841695 −0.420848 0.907131i \(-0.638267\pi\)
−0.420848 + 0.907131i \(0.638267\pi\)
\(294\) 0 0
\(295\) 1.82410 0.106203
\(296\) 11.4957 0.668172
\(297\) 0.153259 0.00889300
\(298\) 13.2749 0.768996
\(299\) −7.78188 −0.450038
\(300\) −8.13637 −0.469753
\(301\) 0 0
\(302\) 12.6734 0.729270
\(303\) −15.8760 −0.912050
\(304\) 7.67824 0.440377
\(305\) 7.39848 0.423635
\(306\) −3.78511 −0.216381
\(307\) 28.0043 1.59829 0.799145 0.601139i \(-0.205286\pi\)
0.799145 + 0.601139i \(0.205286\pi\)
\(308\) 0 0
\(309\) −18.7078 −1.06425
\(310\) −2.86287 −0.162600
\(311\) −5.44438 −0.308723 −0.154361 0.988014i \(-0.549332\pi\)
−0.154361 + 0.988014i \(0.549332\pi\)
\(312\) 3.69896 0.209412
\(313\) −10.2875 −0.581487 −0.290743 0.956801i \(-0.593903\pi\)
−0.290743 + 0.956801i \(0.593903\pi\)
\(314\) 38.7686 2.18784
\(315\) 0 0
\(316\) −3.20116 −0.180079
\(317\) −6.28867 −0.353207 −0.176603 0.984282i \(-0.556511\pi\)
−0.176603 + 0.984282i \(0.556511\pi\)
\(318\) 14.2779 0.800666
\(319\) 0.694461 0.0388824
\(320\) −0.0588636 −0.00329058
\(321\) −6.80514 −0.379826
\(322\) 0 0
\(323\) 3.30476 0.183882
\(324\) 1.10809 0.0615606
\(325\) 17.2730 0.958132
\(326\) −15.7191 −0.870603
\(327\) −14.4970 −0.801686
\(328\) 1.57241 0.0868221
\(329\) 0 0
\(330\) −0.949245 −0.0522542
\(331\) −10.4513 −0.574455 −0.287227 0.957862i \(-0.592734\pi\)
−0.287227 + 0.957862i \(0.592734\pi\)
\(332\) 0.387480 0.0212657
\(333\) −7.31083 −0.400631
\(334\) 5.31562 0.290858
\(335\) −50.3797 −2.75254
\(336\) 0 0
\(337\) 20.2234 1.10164 0.550819 0.834625i \(-0.314316\pi\)
0.550819 + 0.834625i \(0.314316\pi\)
\(338\) −13.1627 −0.715958
\(339\) −10.9043 −0.592242
\(340\) 8.35820 0.453287
\(341\) −0.0708396 −0.00383618
\(342\) −2.71365 −0.146738
\(343\) 0 0
\(344\) −5.79916 −0.312670
\(345\) −11.6219 −0.625702
\(346\) 4.26905 0.229506
\(347\) −27.0279 −1.45093 −0.725466 0.688258i \(-0.758376\pi\)
−0.725466 + 0.688258i \(0.758376\pi\)
\(348\) 5.02108 0.269158
\(349\) 3.37370 0.180590 0.0902950 0.995915i \(-0.471219\pi\)
0.0902950 + 0.995915i \(0.471219\pi\)
\(350\) 0 0
\(351\) −2.35241 −0.125562
\(352\) 0.865832 0.0461490
\(353\) 5.94112 0.316214 0.158107 0.987422i \(-0.449461\pi\)
0.158107 + 0.987422i \(0.449461\pi\)
\(354\) 0.915359 0.0486508
\(355\) −17.9797 −0.954266
\(356\) 2.07366 0.109904
\(357\) 0 0
\(358\) 31.3362 1.65617
\(359\) 29.5196 1.55798 0.778991 0.627035i \(-0.215732\pi\)
0.778991 + 0.627035i \(0.215732\pi\)
\(360\) 5.52423 0.291153
\(361\) −16.6307 −0.875301
\(362\) 33.3997 1.75545
\(363\) 10.9765 0.576117
\(364\) 0 0
\(365\) −23.5670 −1.23355
\(366\) 3.71265 0.194063
\(367\) 36.7303 1.91731 0.958653 0.284577i \(-0.0918532\pi\)
0.958653 + 0.284577i \(0.0918532\pi\)
\(368\) 16.5016 0.860205
\(369\) −1.00000 −0.0520579
\(370\) 45.2812 2.35406
\(371\) 0 0
\(372\) −0.512183 −0.0265554
\(373\) 3.94562 0.204296 0.102148 0.994769i \(-0.467428\pi\)
0.102148 + 0.994769i \(0.467428\pi\)
\(374\) 0.580104 0.0299964
\(375\) 8.23036 0.425014
\(376\) −0.315208 −0.0162556
\(377\) −10.6594 −0.548988
\(378\) 0 0
\(379\) 18.5735 0.954057 0.477029 0.878888i \(-0.341714\pi\)
0.477029 + 0.878888i \(0.341714\pi\)
\(380\) 5.99222 0.307395
\(381\) 2.69248 0.137940
\(382\) −16.0918 −0.823327
\(383\) −32.0391 −1.63712 −0.818560 0.574421i \(-0.805227\pi\)
−0.818560 + 0.574421i \(0.805227\pi\)
\(384\) −11.3285 −0.578103
\(385\) 0 0
\(386\) −26.5002 −1.34883
\(387\) 3.68806 0.187474
\(388\) −10.3096 −0.523389
\(389\) 6.04608 0.306549 0.153274 0.988184i \(-0.451018\pi\)
0.153274 + 0.988184i \(0.451018\pi\)
\(390\) 14.5701 0.737788
\(391\) 7.10238 0.359183
\(392\) 0 0
\(393\) 14.1990 0.716246
\(394\) 10.9173 0.550006
\(395\) 10.1493 0.510667
\(396\) −0.169825 −0.00853404
\(397\) −12.0690 −0.605725 −0.302862 0.953034i \(-0.597942\pi\)
−0.302862 + 0.953034i \(0.597942\pi\)
\(398\) −36.7832 −1.84377
\(399\) 0 0
\(400\) −36.6276 −1.83138
\(401\) −12.2878 −0.613625 −0.306813 0.951770i \(-0.599262\pi\)
−0.306813 + 0.951770i \(0.599262\pi\)
\(402\) −25.2812 −1.26091
\(403\) 1.08733 0.0541638
\(404\) 17.5920 0.875235
\(405\) −3.51322 −0.174573
\(406\) 0 0
\(407\) 1.12045 0.0555387
\(408\) −3.37597 −0.167136
\(409\) −10.8267 −0.535344 −0.267672 0.963510i \(-0.586254\pi\)
−0.267672 + 0.963510i \(0.586254\pi\)
\(410\) 6.19372 0.305886
\(411\) 9.57507 0.472303
\(412\) 20.7300 1.02129
\(413\) 0 0
\(414\) −5.83202 −0.286628
\(415\) −1.22851 −0.0603052
\(416\) −13.2898 −0.651587
\(417\) −18.0900 −0.885873
\(418\) 0.415892 0.0203420
\(419\) 6.22595 0.304157 0.152079 0.988368i \(-0.451403\pi\)
0.152079 + 0.988368i \(0.451403\pi\)
\(420\) 0 0
\(421\) 15.7312 0.766692 0.383346 0.923605i \(-0.374772\pi\)
0.383346 + 0.923605i \(0.374772\pi\)
\(422\) 26.5813 1.29396
\(423\) 0.200461 0.00974677
\(424\) 12.7346 0.618447
\(425\) −15.7647 −0.764702
\(426\) −9.02247 −0.437140
\(427\) 0 0
\(428\) 7.54071 0.364494
\(429\) 0.360528 0.0174065
\(430\) −22.8428 −1.10158
\(431\) 3.48632 0.167930 0.0839652 0.996469i \(-0.473242\pi\)
0.0839652 + 0.996469i \(0.473242\pi\)
\(432\) 4.98832 0.240000
\(433\) 4.30477 0.206874 0.103437 0.994636i \(-0.467016\pi\)
0.103437 + 0.994636i \(0.467016\pi\)
\(434\) 0 0
\(435\) −15.9194 −0.763276
\(436\) 16.0640 0.769326
\(437\) 5.09190 0.243578
\(438\) −11.8262 −0.565078
\(439\) −15.4484 −0.737314 −0.368657 0.929566i \(-0.620182\pi\)
−0.368657 + 0.929566i \(0.620182\pi\)
\(440\) −0.846640 −0.0403620
\(441\) 0 0
\(442\) −8.90412 −0.423526
\(443\) 26.4331 1.25587 0.627936 0.778265i \(-0.283900\pi\)
0.627936 + 0.778265i \(0.283900\pi\)
\(444\) 8.10107 0.384460
\(445\) −6.57457 −0.311665
\(446\) −10.9697 −0.519432
\(447\) −7.52984 −0.356149
\(448\) 0 0
\(449\) −24.3795 −1.15054 −0.575271 0.817963i \(-0.695103\pi\)
−0.575271 + 0.817963i \(0.695103\pi\)
\(450\) 12.9450 0.610233
\(451\) 0.153259 0.00721669
\(452\) 12.0830 0.568336
\(453\) −7.18861 −0.337750
\(454\) −39.2766 −1.84334
\(455\) 0 0
\(456\) −2.42033 −0.113342
\(457\) 2.04659 0.0957355 0.0478678 0.998854i \(-0.484757\pi\)
0.0478678 + 0.998854i \(0.484757\pi\)
\(458\) −39.3196 −1.83728
\(459\) 2.14700 0.100213
\(460\) 12.8781 0.600446
\(461\) 9.05983 0.421958 0.210979 0.977491i \(-0.432335\pi\)
0.210979 + 0.977491i \(0.432335\pi\)
\(462\) 0 0
\(463\) 34.2073 1.58975 0.794874 0.606775i \(-0.207537\pi\)
0.794874 + 0.606775i \(0.207537\pi\)
\(464\) 22.6035 1.04934
\(465\) 1.62388 0.0753057
\(466\) 16.8201 0.779176
\(467\) −18.2381 −0.843961 −0.421980 0.906605i \(-0.638665\pi\)
−0.421980 + 0.906605i \(0.638665\pi\)
\(468\) 2.60668 0.120494
\(469\) 0 0
\(470\) −1.24160 −0.0572708
\(471\) −21.9904 −1.01326
\(472\) 0.816416 0.0375786
\(473\) −0.565229 −0.0259892
\(474\) 5.09306 0.233932
\(475\) −11.3022 −0.518580
\(476\) 0 0
\(477\) −8.09875 −0.370816
\(478\) 12.9308 0.591440
\(479\) −17.6864 −0.808110 −0.404055 0.914735i \(-0.632400\pi\)
−0.404055 + 0.914735i \(0.632400\pi\)
\(480\) −19.8478 −0.905923
\(481\) −17.1980 −0.784163
\(482\) 18.7346 0.853337
\(483\) 0 0
\(484\) −12.1630 −0.552863
\(485\) 32.6866 1.48422
\(486\) −1.76298 −0.0799703
\(487\) −36.2629 −1.64323 −0.821615 0.570043i \(-0.806927\pi\)
−0.821615 + 0.570043i \(0.806927\pi\)
\(488\) 3.31135 0.149898
\(489\) 8.91625 0.403207
\(490\) 0 0
\(491\) −36.2157 −1.63439 −0.817195 0.576361i \(-0.804472\pi\)
−0.817195 + 0.576361i \(0.804472\pi\)
\(492\) 1.10809 0.0499566
\(493\) 9.72867 0.438157
\(494\) −6.38362 −0.287212
\(495\) 0.538433 0.0242008
\(496\) −2.30570 −0.103529
\(497\) 0 0
\(498\) −0.616483 −0.0276253
\(499\) −5.27117 −0.235970 −0.117985 0.993015i \(-0.537643\pi\)
−0.117985 + 0.993015i \(0.537643\pi\)
\(500\) −9.11999 −0.407858
\(501\) −3.01514 −0.134706
\(502\) −43.9873 −1.96325
\(503\) 8.59294 0.383140 0.191570 0.981479i \(-0.438642\pi\)
0.191570 + 0.981479i \(0.438642\pi\)
\(504\) 0 0
\(505\) −55.7757 −2.48198
\(506\) 0.893811 0.0397347
\(507\) 7.46619 0.331585
\(508\) −2.98351 −0.132372
\(509\) 35.7148 1.58303 0.791515 0.611150i \(-0.209293\pi\)
0.791515 + 0.611150i \(0.209293\pi\)
\(510\) −13.2979 −0.588842
\(511\) 0 0
\(512\) 12.4939 0.552157
\(513\) 1.53924 0.0679593
\(514\) −29.8386 −1.31613
\(515\) −65.7246 −2.89617
\(516\) −4.08671 −0.179907
\(517\) −0.0307226 −0.00135118
\(518\) 0 0
\(519\) −2.42150 −0.106292
\(520\) 12.9952 0.569879
\(521\) −4.85721 −0.212798 −0.106399 0.994324i \(-0.533932\pi\)
−0.106399 + 0.994324i \(0.533932\pi\)
\(522\) −7.98856 −0.349650
\(523\) −13.7918 −0.603073 −0.301537 0.953455i \(-0.597500\pi\)
−0.301537 + 0.953455i \(0.597500\pi\)
\(524\) −15.7338 −0.687335
\(525\) 0 0
\(526\) 15.6689 0.683197
\(527\) −0.992387 −0.0432291
\(528\) −0.764505 −0.0332708
\(529\) −12.0568 −0.524209
\(530\) 50.1614 2.17887
\(531\) −0.519212 −0.0225319
\(532\) 0 0
\(533\) −2.35241 −0.101894
\(534\) −3.29921 −0.142771
\(535\) −23.9079 −1.03363
\(536\) −22.5485 −0.973948
\(537\) −17.7746 −0.767030
\(538\) 1.78047 0.0767615
\(539\) 0 0
\(540\) 3.89296 0.167527
\(541\) 13.9611 0.600235 0.300117 0.953902i \(-0.402974\pi\)
0.300117 + 0.953902i \(0.402974\pi\)
\(542\) 9.42882 0.405003
\(543\) −18.9450 −0.813010
\(544\) 12.1294 0.520043
\(545\) −50.9311 −2.18165
\(546\) 0 0
\(547\) 37.3982 1.59903 0.799516 0.600644i \(-0.205089\pi\)
0.799516 + 0.600644i \(0.205089\pi\)
\(548\) −10.6101 −0.453239
\(549\) −2.10590 −0.0898775
\(550\) −1.98394 −0.0845955
\(551\) 6.97476 0.297135
\(552\) −5.20163 −0.221396
\(553\) 0 0
\(554\) 39.8437 1.69280
\(555\) −25.6845 −1.09025
\(556\) 20.0454 0.850116
\(557\) 1.73041 0.0733200 0.0366600 0.999328i \(-0.488328\pi\)
0.0366600 + 0.999328i \(0.488328\pi\)
\(558\) 0.814885 0.0344968
\(559\) 8.67581 0.366948
\(560\) 0 0
\(561\) −0.329048 −0.0138924
\(562\) 40.3522 1.70216
\(563\) 9.87388 0.416134 0.208067 0.978115i \(-0.433283\pi\)
0.208067 + 0.978115i \(0.433283\pi\)
\(564\) −0.222130 −0.00935334
\(565\) −38.3092 −1.61168
\(566\) 10.2711 0.431727
\(567\) 0 0
\(568\) −8.04722 −0.337654
\(569\) 36.4363 1.52749 0.763744 0.645519i \(-0.223359\pi\)
0.763744 + 0.645519i \(0.223359\pi\)
\(570\) −9.53365 −0.399321
\(571\) −29.8704 −1.25004 −0.625019 0.780610i \(-0.714909\pi\)
−0.625019 + 0.780610i \(0.714909\pi\)
\(572\) −0.399498 −0.0167038
\(573\) 9.12762 0.381312
\(574\) 0 0
\(575\) −24.2900 −1.01296
\(576\) 0.0167549 0.000698121 0
\(577\) 20.4964 0.853277 0.426638 0.904422i \(-0.359698\pi\)
0.426638 + 0.904422i \(0.359698\pi\)
\(578\) −21.8440 −0.908590
\(579\) 15.0315 0.624688
\(580\) 17.6401 0.732467
\(581\) 0 0
\(582\) 16.4026 0.679909
\(583\) 1.24121 0.0514056
\(584\) −10.5479 −0.436475
\(585\) −8.26451 −0.341695
\(586\) −25.4001 −1.04927
\(587\) 5.59113 0.230771 0.115385 0.993321i \(-0.463190\pi\)
0.115385 + 0.993321i \(0.463190\pi\)
\(588\) 0 0
\(589\) −0.711470 −0.0293156
\(590\) 3.21585 0.132395
\(591\) −6.19254 −0.254727
\(592\) 36.4687 1.49886
\(593\) −7.14936 −0.293589 −0.146794 0.989167i \(-0.546896\pi\)
−0.146794 + 0.989167i \(0.546896\pi\)
\(594\) 0.270193 0.0110861
\(595\) 0 0
\(596\) 8.34375 0.341773
\(597\) 20.8642 0.853916
\(598\) −13.7193 −0.561023
\(599\) 32.9077 1.34457 0.672287 0.740291i \(-0.265312\pi\)
0.672287 + 0.740291i \(0.265312\pi\)
\(600\) 11.5457 0.471353
\(601\) −40.7143 −1.66077 −0.830386 0.557188i \(-0.811880\pi\)
−0.830386 + 0.557188i \(0.811880\pi\)
\(602\) 0 0
\(603\) 14.3401 0.583972
\(604\) 7.96563 0.324117
\(605\) 38.5629 1.56780
\(606\) −27.9890 −1.13697
\(607\) −6.02578 −0.244579 −0.122289 0.992494i \(-0.539024\pi\)
−0.122289 + 0.992494i \(0.539024\pi\)
\(608\) 8.69590 0.352665
\(609\) 0 0
\(610\) 13.0433 0.528110
\(611\) 0.471567 0.0190775
\(612\) −2.37907 −0.0961683
\(613\) 12.1435 0.490471 0.245235 0.969464i \(-0.421135\pi\)
0.245235 + 0.969464i \(0.421135\pi\)
\(614\) 49.3710 1.99245
\(615\) −3.51322 −0.141667
\(616\) 0 0
\(617\) 31.7612 1.27866 0.639329 0.768933i \(-0.279212\pi\)
0.639329 + 0.768933i \(0.279212\pi\)
\(618\) −32.9814 −1.32671
\(619\) 13.2321 0.531842 0.265921 0.963995i \(-0.414324\pi\)
0.265921 + 0.963995i \(0.414324\pi\)
\(620\) −1.79941 −0.0722660
\(621\) 3.30805 0.132747
\(622\) −9.59832 −0.384858
\(623\) 0 0
\(624\) 11.7345 0.469758
\(625\) −7.79840 −0.311936
\(626\) −18.1367 −0.724889
\(627\) −0.235903 −0.00942107
\(628\) 24.3674 0.972364
\(629\) 15.6963 0.625854
\(630\) 0 0
\(631\) 4.27005 0.169988 0.0849940 0.996381i \(-0.472913\pi\)
0.0849940 + 0.996381i \(0.472913\pi\)
\(632\) 4.54254 0.180693
\(633\) −15.0775 −0.599277
\(634\) −11.0868 −0.440312
\(635\) 9.45926 0.375379
\(636\) 8.97416 0.355849
\(637\) 0 0
\(638\) 1.22432 0.0484713
\(639\) 5.11775 0.202455
\(640\) −39.7993 −1.57321
\(641\) −30.8242 −1.21748 −0.608741 0.793369i \(-0.708325\pi\)
−0.608741 + 0.793369i \(0.708325\pi\)
\(642\) −11.9973 −0.473496
\(643\) −40.6982 −1.60498 −0.802490 0.596666i \(-0.796492\pi\)
−0.802490 + 0.596666i \(0.796492\pi\)
\(644\) 0 0
\(645\) 12.9569 0.510179
\(646\) 5.82621 0.229229
\(647\) −2.71221 −0.106628 −0.0533141 0.998578i \(-0.516978\pi\)
−0.0533141 + 0.998578i \(0.516978\pi\)
\(648\) −1.57241 −0.0617703
\(649\) 0.0795740 0.00312355
\(650\) 30.4519 1.19442
\(651\) 0 0
\(652\) −9.88002 −0.386931
\(653\) 28.3292 1.10861 0.554303 0.832315i \(-0.312985\pi\)
0.554303 + 0.832315i \(0.312985\pi\)
\(654\) −25.5579 −0.999393
\(655\) 49.8843 1.94914
\(656\) 4.98832 0.194761
\(657\) 6.70809 0.261708
\(658\) 0 0
\(659\) 19.3189 0.752559 0.376279 0.926506i \(-0.377203\pi\)
0.376279 + 0.926506i \(0.377203\pi\)
\(660\) −0.596633 −0.0232239
\(661\) −17.0248 −0.662188 −0.331094 0.943598i \(-0.607418\pi\)
−0.331094 + 0.943598i \(0.607418\pi\)
\(662\) −18.4254 −0.716123
\(663\) 5.05062 0.196150
\(664\) −0.549846 −0.0213382
\(665\) 0 0
\(666\) −12.8888 −0.499432
\(667\) 14.9897 0.580404
\(668\) 3.34105 0.129269
\(669\) 6.22227 0.240567
\(670\) −88.8183 −3.43135
\(671\) 0.322748 0.0124596
\(672\) 0 0
\(673\) −49.7452 −1.91754 −0.958768 0.284190i \(-0.908275\pi\)
−0.958768 + 0.284190i \(0.908275\pi\)
\(674\) 35.6534 1.37332
\(675\) −7.34269 −0.282620
\(676\) −8.27322 −0.318201
\(677\) 29.5251 1.13474 0.567372 0.823462i \(-0.307960\pi\)
0.567372 + 0.823462i \(0.307960\pi\)
\(678\) −19.2241 −0.738296
\(679\) 0 0
\(680\) −11.8605 −0.454830
\(681\) 22.2786 0.853717
\(682\) −0.124889 −0.00478223
\(683\) −22.1250 −0.846589 −0.423294 0.905992i \(-0.639126\pi\)
−0.423294 + 0.905992i \(0.639126\pi\)
\(684\) −1.70562 −0.0652161
\(685\) 33.6393 1.28529
\(686\) 0 0
\(687\) 22.3029 0.850911
\(688\) −18.3972 −0.701386
\(689\) −19.0516 −0.725806
\(690\) −20.4891 −0.780008
\(691\) 46.6462 1.77450 0.887252 0.461285i \(-0.152611\pi\)
0.887252 + 0.461285i \(0.152611\pi\)
\(692\) 2.68324 0.102002
\(693\) 0 0
\(694\) −47.6495 −1.80875
\(695\) −63.5542 −2.41075
\(696\) −7.12506 −0.270075
\(697\) 2.14700 0.0813234
\(698\) 5.94776 0.225126
\(699\) −9.54073 −0.360864
\(700\) 0 0
\(701\) −37.0007 −1.39750 −0.698748 0.715368i \(-0.746259\pi\)
−0.698748 + 0.715368i \(0.746259\pi\)
\(702\) −4.14724 −0.156527
\(703\) 11.2532 0.424421
\(704\) −0.00256784 −9.67793e−5 0
\(705\) 0.704264 0.0265241
\(706\) 10.4741 0.394197
\(707\) 0 0
\(708\) 0.575334 0.0216224
\(709\) 20.1599 0.757123 0.378561 0.925576i \(-0.376419\pi\)
0.378561 + 0.925576i \(0.376419\pi\)
\(710\) −31.6979 −1.18960
\(711\) −2.88889 −0.108342
\(712\) −2.94259 −0.110278
\(713\) −1.52905 −0.0572633
\(714\) 0 0
\(715\) 1.26661 0.0473686
\(716\) 19.6959 0.736069
\(717\) −7.33462 −0.273917
\(718\) 52.0423 1.94220
\(719\) 41.6127 1.55189 0.775946 0.630799i \(-0.217273\pi\)
0.775946 + 0.630799i \(0.217273\pi\)
\(720\) 17.5250 0.653119
\(721\) 0 0
\(722\) −29.3196 −1.09116
\(723\) −10.6267 −0.395210
\(724\) 20.9928 0.780193
\(725\) −33.2718 −1.23568
\(726\) 19.3513 0.718196
\(727\) 13.1809 0.488853 0.244427 0.969668i \(-0.421400\pi\)
0.244427 + 0.969668i \(0.421400\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −41.5480 −1.53776
\(731\) −7.91826 −0.292867
\(732\) 2.33353 0.0862497
\(733\) 46.8015 1.72865 0.864327 0.502930i \(-0.167745\pi\)
0.864327 + 0.502930i \(0.167745\pi\)
\(734\) 64.7547 2.39014
\(735\) 0 0
\(736\) 18.6887 0.688875
\(737\) −2.19775 −0.0809550
\(738\) −1.76298 −0.0648961
\(739\) 26.0375 0.957807 0.478903 0.877868i \(-0.341034\pi\)
0.478903 + 0.877868i \(0.341034\pi\)
\(740\) 28.4608 1.04624
\(741\) 3.62093 0.133018
\(742\) 0 0
\(743\) 23.6043 0.865956 0.432978 0.901404i \(-0.357463\pi\)
0.432978 + 0.901404i \(0.357463\pi\)
\(744\) 0.726803 0.0266459
\(745\) −26.4539 −0.969197
\(746\) 6.95604 0.254679
\(747\) 0.349683 0.0127942
\(748\) 0.364615 0.0133316
\(749\) 0 0
\(750\) 14.5099 0.529828
\(751\) −5.74126 −0.209502 −0.104751 0.994498i \(-0.533405\pi\)
−0.104751 + 0.994498i \(0.533405\pi\)
\(752\) −0.999965 −0.0364650
\(753\) 24.9505 0.909248
\(754\) −18.7923 −0.684376
\(755\) −25.2551 −0.919128
\(756\) 0 0
\(757\) −34.2154 −1.24358 −0.621791 0.783183i \(-0.713595\pi\)
−0.621791 + 0.783183i \(0.713595\pi\)
\(758\) 32.7447 1.18934
\(759\) −0.506989 −0.0184025
\(760\) −8.50314 −0.308441
\(761\) 20.5043 0.743280 0.371640 0.928377i \(-0.378796\pi\)
0.371640 + 0.928377i \(0.378796\pi\)
\(762\) 4.74678 0.171958
\(763\) 0 0
\(764\) −10.1142 −0.365920
\(765\) 7.54287 0.272713
\(766\) −56.4842 −2.04086
\(767\) −1.22140 −0.0441021
\(768\) −19.9383 −0.719462
\(769\) 5.59555 0.201781 0.100890 0.994898i \(-0.467831\pi\)
0.100890 + 0.994898i \(0.467831\pi\)
\(770\) 0 0
\(771\) 16.9251 0.609544
\(772\) −16.6563 −0.599473
\(773\) 14.0158 0.504114 0.252057 0.967712i \(-0.418893\pi\)
0.252057 + 0.967712i \(0.418893\pi\)
\(774\) 6.50196 0.233708
\(775\) 3.39394 0.121914
\(776\) 14.6296 0.525172
\(777\) 0 0
\(778\) 10.6591 0.382148
\(779\) 1.53924 0.0551491
\(780\) 9.15783 0.327903
\(781\) −0.784342 −0.0280659
\(782\) 12.5213 0.447762
\(783\) 4.53129 0.161935
\(784\) 0 0
\(785\) −77.2570 −2.75742
\(786\) 25.0326 0.892882
\(787\) −0.00890650 −0.000317482 0 −0.000158741 1.00000i \(-0.500051\pi\)
−0.000158741 1.00000i \(0.500051\pi\)
\(788\) 6.86190 0.244445
\(789\) −8.88776 −0.316413
\(790\) 17.8930 0.636605
\(791\) 0 0
\(792\) 0.240987 0.00856310
\(793\) −4.95393 −0.175919
\(794\) −21.2774 −0.755105
\(795\) −28.4527 −1.00911
\(796\) −23.1195 −0.819448
\(797\) −47.0451 −1.66642 −0.833211 0.552954i \(-0.813500\pi\)
−0.833211 + 0.552954i \(0.813500\pi\)
\(798\) 0 0
\(799\) −0.430391 −0.0152261
\(800\) −41.4822 −1.46662
\(801\) 1.87138 0.0661221
\(802\) −21.6632 −0.764953
\(803\) −1.02808 −0.0362800
\(804\) −15.8901 −0.560400
\(805\) 0 0
\(806\) 1.91694 0.0675213
\(807\) −1.00992 −0.0355509
\(808\) −24.9636 −0.878216
\(809\) −19.5973 −0.689006 −0.344503 0.938785i \(-0.611953\pi\)
−0.344503 + 0.938785i \(0.611953\pi\)
\(810\) −6.19372 −0.217625
\(811\) −19.1670 −0.673046 −0.336523 0.941675i \(-0.609251\pi\)
−0.336523 + 0.941675i \(0.609251\pi\)
\(812\) 0 0
\(813\) −5.34824 −0.187571
\(814\) 1.97533 0.0692354
\(815\) 31.3247 1.09726
\(816\) −10.7099 −0.374922
\(817\) −5.67682 −0.198607
\(818\) −19.0872 −0.667367
\(819\) 0 0
\(820\) 3.89296 0.135948
\(821\) −26.7619 −0.933996 −0.466998 0.884258i \(-0.654665\pi\)
−0.466998 + 0.884258i \(0.654665\pi\)
\(822\) 16.8806 0.588780
\(823\) −49.8669 −1.73825 −0.869125 0.494592i \(-0.835317\pi\)
−0.869125 + 0.494592i \(0.835317\pi\)
\(824\) −29.4164 −1.02477
\(825\) 1.12533 0.0391791
\(826\) 0 0
\(827\) 11.5217 0.400650 0.200325 0.979729i \(-0.435800\pi\)
0.200325 + 0.979729i \(0.435800\pi\)
\(828\) −3.66562 −0.127389
\(829\) 36.8850 1.28107 0.640535 0.767929i \(-0.278713\pi\)
0.640535 + 0.767929i \(0.278713\pi\)
\(830\) −2.16584 −0.0751773
\(831\) −22.6002 −0.783993
\(832\) 0.0394144 0.00136645
\(833\) 0 0
\(834\) −31.8924 −1.10434
\(835\) −10.5928 −0.366580
\(836\) 0.261403 0.00904080
\(837\) −0.462221 −0.0159767
\(838\) 10.9762 0.379167
\(839\) −20.8081 −0.718377 −0.359188 0.933265i \(-0.616946\pi\)
−0.359188 + 0.933265i \(0.616946\pi\)
\(840\) 0 0
\(841\) −8.46745 −0.291981
\(842\) 27.7338 0.955769
\(843\) −22.8887 −0.788328
\(844\) 16.7073 0.575087
\(845\) 26.2303 0.902351
\(846\) 0.353409 0.0121505
\(847\) 0 0
\(848\) 40.3991 1.38731
\(849\) −5.82600 −0.199948
\(850\) −27.7929 −0.953289
\(851\) 24.1846 0.829037
\(852\) −5.67093 −0.194283
\(853\) 46.0297 1.57603 0.788014 0.615658i \(-0.211110\pi\)
0.788014 + 0.615658i \(0.211110\pi\)
\(854\) 0 0
\(855\) 5.40770 0.184939
\(856\) −10.7005 −0.365735
\(857\) −8.16902 −0.279048 −0.139524 0.990219i \(-0.544557\pi\)
−0.139524 + 0.990219i \(0.544557\pi\)
\(858\) 0.635603 0.0216991
\(859\) −19.6237 −0.669551 −0.334776 0.942298i \(-0.608661\pi\)
−0.334776 + 0.942298i \(0.608661\pi\)
\(860\) −14.3575 −0.489586
\(861\) 0 0
\(862\) 6.14631 0.209344
\(863\) −38.9104 −1.32452 −0.662262 0.749272i \(-0.730403\pi\)
−0.662262 + 0.749272i \(0.730403\pi\)
\(864\) 5.64946 0.192199
\(865\) −8.50725 −0.289255
\(866\) 7.58922 0.257892
\(867\) 12.3904 0.420800
\(868\) 0 0
\(869\) 0.442750 0.0150193
\(870\) −28.0655 −0.951510
\(871\) 33.7336 1.14302
\(872\) −22.7953 −0.771946
\(873\) −9.30390 −0.314889
\(874\) 8.97690 0.303648
\(875\) 0 0
\(876\) −7.43318 −0.251144
\(877\) −30.9324 −1.04451 −0.522256 0.852789i \(-0.674909\pi\)
−0.522256 + 0.852789i \(0.674909\pi\)
\(878\) −27.2353 −0.919145
\(879\) 14.4075 0.485953
\(880\) −2.68587 −0.0905407
\(881\) 36.6380 1.23437 0.617183 0.786819i \(-0.288274\pi\)
0.617183 + 0.786819i \(0.288274\pi\)
\(882\) 0 0
\(883\) −7.63457 −0.256924 −0.128462 0.991714i \(-0.541004\pi\)
−0.128462 + 0.991714i \(0.541004\pi\)
\(884\) −5.59654 −0.188232
\(885\) −1.82410 −0.0613165
\(886\) 46.6009 1.56559
\(887\) 6.73740 0.226220 0.113110 0.993582i \(-0.463919\pi\)
0.113110 + 0.993582i \(0.463919\pi\)
\(888\) −11.4957 −0.385769
\(889\) 0 0
\(890\) −11.5908 −0.388525
\(891\) −0.153259 −0.00513438
\(892\) −6.89485 −0.230857
\(893\) −0.308559 −0.0103255
\(894\) −13.2749 −0.443980
\(895\) −62.4460 −2.08734
\(896\) 0 0
\(897\) 7.78188 0.259829
\(898\) −42.9806 −1.43428
\(899\) −2.09445 −0.0698539
\(900\) 8.13637 0.271212
\(901\) 17.3880 0.579279
\(902\) 0.270193 0.00899643
\(903\) 0 0
\(904\) −17.1461 −0.570272
\(905\) −66.5580 −2.21246
\(906\) −12.6734 −0.421044
\(907\) 25.4475 0.844969 0.422485 0.906370i \(-0.361158\pi\)
0.422485 + 0.906370i \(0.361158\pi\)
\(908\) −24.6867 −0.819257
\(909\) 15.8760 0.526572
\(910\) 0 0
\(911\) −52.3981 −1.73603 −0.868013 0.496541i \(-0.834603\pi\)
−0.868013 + 0.496541i \(0.834603\pi\)
\(912\) −7.67824 −0.254252
\(913\) −0.0535921 −0.00177364
\(914\) 3.60810 0.119345
\(915\) −7.39848 −0.244586
\(916\) −24.7137 −0.816564
\(917\) 0 0
\(918\) 3.78511 0.124927
\(919\) 39.4875 1.30257 0.651286 0.758833i \(-0.274230\pi\)
0.651286 + 0.758833i \(0.274230\pi\)
\(920\) −18.2744 −0.602490
\(921\) −28.0043 −0.922773
\(922\) 15.9723 0.526019
\(923\) 12.0390 0.396269
\(924\) 0 0
\(925\) −53.6811 −1.76502
\(926\) 60.3067 1.98180
\(927\) 18.7078 0.614445
\(928\) 25.5993 0.840339
\(929\) −6.33471 −0.207835 −0.103917 0.994586i \(-0.533138\pi\)
−0.103917 + 0.994586i \(0.533138\pi\)
\(930\) 2.86287 0.0938771
\(931\) 0 0
\(932\) 10.5720 0.346297
\(933\) 5.44438 0.178241
\(934\) −32.1534 −1.05209
\(935\) −1.15601 −0.0378057
\(936\) −3.69896 −0.120904
\(937\) −11.7911 −0.385198 −0.192599 0.981278i \(-0.561692\pi\)
−0.192599 + 0.981278i \(0.561692\pi\)
\(938\) 0 0
\(939\) 10.2875 0.335721
\(940\) −0.780389 −0.0254535
\(941\) 46.3405 1.51066 0.755329 0.655345i \(-0.227477\pi\)
0.755329 + 0.655345i \(0.227477\pi\)
\(942\) −38.7686 −1.26315
\(943\) 3.30805 0.107725
\(944\) 2.58999 0.0842970
\(945\) 0 0
\(946\) −0.996486 −0.0323985
\(947\) −44.0358 −1.43097 −0.715485 0.698628i \(-0.753794\pi\)
−0.715485 + 0.698628i \(0.753794\pi\)
\(948\) 3.20116 0.103969
\(949\) 15.7802 0.512245
\(950\) −19.9255 −0.646469
\(951\) 6.28867 0.203924
\(952\) 0 0
\(953\) 42.4278 1.37437 0.687185 0.726482i \(-0.258846\pi\)
0.687185 + 0.726482i \(0.258846\pi\)
\(954\) −14.2779 −0.462265
\(955\) 32.0673 1.03767
\(956\) 8.12743 0.262860
\(957\) −0.694461 −0.0224487
\(958\) −31.1806 −1.00740
\(959\) 0 0
\(960\) 0.0588636 0.00189982
\(961\) −30.7864 −0.993108
\(962\) −30.3198 −0.977548
\(963\) 6.80514 0.219292
\(964\) 11.7753 0.379258
\(965\) 52.8089 1.69998
\(966\) 0 0
\(967\) 46.9193 1.50882 0.754412 0.656401i \(-0.227922\pi\)
0.754412 + 0.656401i \(0.227922\pi\)
\(968\) 17.2596 0.554746
\(969\) −3.30476 −0.106164
\(970\) 57.6258 1.85025
\(971\) 50.5664 1.62275 0.811376 0.584525i \(-0.198719\pi\)
0.811376 + 0.584525i \(0.198719\pi\)
\(972\) −1.10809 −0.0355421
\(973\) 0 0
\(974\) −63.9308 −2.04847
\(975\) −17.2730 −0.553178
\(976\) 10.5049 0.336253
\(977\) 41.0155 1.31220 0.656101 0.754673i \(-0.272205\pi\)
0.656101 + 0.754673i \(0.272205\pi\)
\(978\) 15.7191 0.502643
\(979\) −0.286807 −0.00916638
\(980\) 0 0
\(981\) 14.4970 0.462854
\(982\) −63.8474 −2.03745
\(983\) −7.15597 −0.228240 −0.114120 0.993467i \(-0.536405\pi\)
−0.114120 + 0.993467i \(0.536405\pi\)
\(984\) −1.57241 −0.0501268
\(985\) −21.7557 −0.693195
\(986\) 17.1514 0.546213
\(987\) 0 0
\(988\) −4.01232 −0.127649
\(989\) −12.2003 −0.387946
\(990\) 0.949245 0.0301690
\(991\) −0.649041 −0.0206175 −0.0103087 0.999947i \(-0.503281\pi\)
−0.0103087 + 0.999947i \(0.503281\pi\)
\(992\) −2.61130 −0.0829088
\(993\) 10.4513 0.331662
\(994\) 0 0
\(995\) 73.3005 2.32378
\(996\) −0.387480 −0.0122778
\(997\) 29.1089 0.921887 0.460944 0.887429i \(-0.347511\pi\)
0.460944 + 0.887429i \(0.347511\pi\)
\(998\) −9.29296 −0.294164
\(999\) 7.31083 0.231304
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 \(a_p\))