Properties

Label 6027.2.a.bm.1.5
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
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: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.63508\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.63508 q^{2} +1.00000 q^{3} +0.673497 q^{4} +1.18651 q^{5} -1.63508 q^{6} +2.16894 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.63508 q^{2} +1.00000 q^{3} +0.673497 q^{4} +1.18651 q^{5} -1.63508 q^{6} +2.16894 q^{8} +1.00000 q^{9} -1.94005 q^{10} +6.03827 q^{11} +0.673497 q^{12} -6.76120 q^{13} +1.18651 q^{15} -4.89340 q^{16} +2.16841 q^{17} -1.63508 q^{18} -0.190732 q^{19} +0.799112 q^{20} -9.87308 q^{22} +1.56671 q^{23} +2.16894 q^{24} -3.59219 q^{25} +11.0551 q^{26} +1.00000 q^{27} -1.86469 q^{29} -1.94005 q^{30} -4.59985 q^{31} +3.66322 q^{32} +6.03827 q^{33} -3.54554 q^{34} +0.673497 q^{36} -9.75991 q^{37} +0.311862 q^{38} -6.76120 q^{39} +2.57348 q^{40} +1.00000 q^{41} -3.27874 q^{43} +4.06676 q^{44} +1.18651 q^{45} -2.56169 q^{46} +7.29761 q^{47} -4.89340 q^{48} +5.87353 q^{50} +2.16841 q^{51} -4.55365 q^{52} -8.09108 q^{53} -1.63508 q^{54} +7.16449 q^{55} -0.190732 q^{57} +3.04892 q^{58} -6.53265 q^{59} +0.799112 q^{60} -2.90591 q^{61} +7.52114 q^{62} +3.79712 q^{64} -8.02225 q^{65} -9.87308 q^{66} -10.5427 q^{67} +1.46042 q^{68} +1.56671 q^{69} -15.0801 q^{71} +2.16894 q^{72} +1.12356 q^{73} +15.9583 q^{74} -3.59219 q^{75} -0.128457 q^{76} +11.0551 q^{78} -13.1347 q^{79} -5.80607 q^{80} +1.00000 q^{81} -1.63508 q^{82} -6.13893 q^{83} +2.57285 q^{85} +5.36102 q^{86} -1.86469 q^{87} +13.0967 q^{88} +8.62339 q^{89} -1.94005 q^{90} +1.05517 q^{92} -4.59985 q^{93} -11.9322 q^{94} -0.226306 q^{95} +3.66322 q^{96} -6.82744 q^{97} +6.03827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63508 −1.15618 −0.578089 0.815974i \(-0.696201\pi\)
−0.578089 + 0.815974i \(0.696201\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.673497 0.336748
\(5\) 1.18651 0.530624 0.265312 0.964163i \(-0.414525\pi\)
0.265312 + 0.964163i \(0.414525\pi\)
\(6\) −1.63508 −0.667520
\(7\) 0 0
\(8\) 2.16894 0.766837
\(9\) 1.00000 0.333333
\(10\) −1.94005 −0.613496
\(11\) 6.03827 1.82061 0.910304 0.413940i \(-0.135848\pi\)
0.910304 + 0.413940i \(0.135848\pi\)
\(12\) 0.673497 0.194422
\(13\) −6.76120 −1.87522 −0.937610 0.347690i \(-0.886966\pi\)
−0.937610 + 0.347690i \(0.886966\pi\)
\(14\) 0 0
\(15\) 1.18651 0.306356
\(16\) −4.89340 −1.22335
\(17\) 2.16841 0.525917 0.262959 0.964807i \(-0.415302\pi\)
0.262959 + 0.964807i \(0.415302\pi\)
\(18\) −1.63508 −0.385393
\(19\) −0.190732 −0.0437569 −0.0218784 0.999761i \(-0.506965\pi\)
−0.0218784 + 0.999761i \(0.506965\pi\)
\(20\) 0.799112 0.178687
\(21\) 0 0
\(22\) −9.87308 −2.10495
\(23\) 1.56671 0.326681 0.163340 0.986570i \(-0.447773\pi\)
0.163340 + 0.986570i \(0.447773\pi\)
\(24\) 2.16894 0.442734
\(25\) −3.59219 −0.718438
\(26\) 11.0551 2.16809
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.86469 −0.346264 −0.173132 0.984899i \(-0.555389\pi\)
−0.173132 + 0.984899i \(0.555389\pi\)
\(30\) −1.94005 −0.354202
\(31\) −4.59985 −0.826158 −0.413079 0.910695i \(-0.635547\pi\)
−0.413079 + 0.910695i \(0.635547\pi\)
\(32\) 3.66322 0.647572
\(33\) 6.03827 1.05113
\(34\) −3.54554 −0.608054
\(35\) 0 0
\(36\) 0.673497 0.112249
\(37\) −9.75991 −1.60452 −0.802259 0.596976i \(-0.796369\pi\)
−0.802259 + 0.596976i \(0.796369\pi\)
\(38\) 0.311862 0.0505907
\(39\) −6.76120 −1.08266
\(40\) 2.57348 0.406903
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −3.27874 −0.500003 −0.250002 0.968245i \(-0.580431\pi\)
−0.250002 + 0.968245i \(0.580431\pi\)
\(44\) 4.06676 0.613087
\(45\) 1.18651 0.176875
\(46\) −2.56169 −0.377701
\(47\) 7.29761 1.06447 0.532233 0.846598i \(-0.321353\pi\)
0.532233 + 0.846598i \(0.321353\pi\)
\(48\) −4.89340 −0.706301
\(49\) 0 0
\(50\) 5.87353 0.830642
\(51\) 2.16841 0.303639
\(52\) −4.55365 −0.631477
\(53\) −8.09108 −1.11140 −0.555698 0.831384i \(-0.687549\pi\)
−0.555698 + 0.831384i \(0.687549\pi\)
\(54\) −1.63508 −0.222507
\(55\) 7.16449 0.966059
\(56\) 0 0
\(57\) −0.190732 −0.0252630
\(58\) 3.04892 0.400343
\(59\) −6.53265 −0.850478 −0.425239 0.905081i \(-0.639810\pi\)
−0.425239 + 0.905081i \(0.639810\pi\)
\(60\) 0.799112 0.103165
\(61\) −2.90591 −0.372063 −0.186032 0.982544i \(-0.559563\pi\)
−0.186032 + 0.982544i \(0.559563\pi\)
\(62\) 7.52114 0.955186
\(63\) 0 0
\(64\) 3.79712 0.474640
\(65\) −8.02225 −0.995037
\(66\) −9.87308 −1.21529
\(67\) −10.5427 −1.28800 −0.643999 0.765027i \(-0.722726\pi\)
−0.643999 + 0.765027i \(0.722726\pi\)
\(68\) 1.46042 0.177102
\(69\) 1.56671 0.188609
\(70\) 0 0
\(71\) −15.0801 −1.78968 −0.894841 0.446384i \(-0.852712\pi\)
−0.894841 + 0.446384i \(0.852712\pi\)
\(72\) 2.16894 0.255612
\(73\) 1.12356 0.131503 0.0657516 0.997836i \(-0.479056\pi\)
0.0657516 + 0.997836i \(0.479056\pi\)
\(74\) 15.9583 1.85511
\(75\) −3.59219 −0.414790
\(76\) −0.128457 −0.0147351
\(77\) 0 0
\(78\) 11.0551 1.25175
\(79\) −13.1347 −1.47776 −0.738882 0.673834i \(-0.764646\pi\)
−0.738882 + 0.673834i \(0.764646\pi\)
\(80\) −5.80607 −0.649139
\(81\) 1.00000 0.111111
\(82\) −1.63508 −0.180565
\(83\) −6.13893 −0.673835 −0.336918 0.941534i \(-0.609384\pi\)
−0.336918 + 0.941534i \(0.609384\pi\)
\(84\) 0 0
\(85\) 2.57285 0.279065
\(86\) 5.36102 0.578093
\(87\) −1.86469 −0.199916
\(88\) 13.0967 1.39611
\(89\) 8.62339 0.914077 0.457039 0.889447i \(-0.348910\pi\)
0.457039 + 0.889447i \(0.348910\pi\)
\(90\) −1.94005 −0.204499
\(91\) 0 0
\(92\) 1.05517 0.110009
\(93\) −4.59985 −0.476983
\(94\) −11.9322 −1.23071
\(95\) −0.226306 −0.0232185
\(96\) 3.66322 0.373876
\(97\) −6.82744 −0.693221 −0.346611 0.938009i \(-0.612667\pi\)
−0.346611 + 0.938009i \(0.612667\pi\)
\(98\) 0 0
\(99\) 6.03827 0.606869
\(100\) −2.41933 −0.241933
\(101\) −6.63595 −0.660302 −0.330151 0.943928i \(-0.607100\pi\)
−0.330151 + 0.943928i \(0.607100\pi\)
\(102\) −3.54554 −0.351060
\(103\) 12.2443 1.20647 0.603233 0.797565i \(-0.293879\pi\)
0.603233 + 0.797565i \(0.293879\pi\)
\(104\) −14.6647 −1.43799
\(105\) 0 0
\(106\) 13.2296 1.28497
\(107\) 6.76869 0.654354 0.327177 0.944963i \(-0.393903\pi\)
0.327177 + 0.944963i \(0.393903\pi\)
\(108\) 0.673497 0.0648073
\(109\) −9.13962 −0.875417 −0.437709 0.899117i \(-0.644210\pi\)
−0.437709 + 0.899117i \(0.644210\pi\)
\(110\) −11.7145 −1.11694
\(111\) −9.75991 −0.926369
\(112\) 0 0
\(113\) 3.30804 0.311194 0.155597 0.987821i \(-0.450270\pi\)
0.155597 + 0.987821i \(0.450270\pi\)
\(114\) 0.311862 0.0292086
\(115\) 1.85892 0.173345
\(116\) −1.25586 −0.116604
\(117\) −6.76120 −0.625073
\(118\) 10.6814 0.983305
\(119\) 0 0
\(120\) 2.57348 0.234925
\(121\) 25.4608 2.31461
\(122\) 4.75140 0.430171
\(123\) 1.00000 0.0901670
\(124\) −3.09799 −0.278207
\(125\) −10.1947 −0.911845
\(126\) 0 0
\(127\) −15.8127 −1.40315 −0.701573 0.712597i \(-0.747519\pi\)
−0.701573 + 0.712597i \(0.747519\pi\)
\(128\) −13.5350 −1.19634
\(129\) −3.27874 −0.288677
\(130\) 13.1170 1.15044
\(131\) −1.88985 −0.165117 −0.0825584 0.996586i \(-0.526309\pi\)
−0.0825584 + 0.996586i \(0.526309\pi\)
\(132\) 4.06676 0.353966
\(133\) 0 0
\(134\) 17.2382 1.48915
\(135\) 1.18651 0.102119
\(136\) 4.70317 0.403293
\(137\) −0.0721484 −0.00616405 −0.00308203 0.999995i \(-0.500981\pi\)
−0.00308203 + 0.999995i \(0.500981\pi\)
\(138\) −2.56169 −0.218066
\(139\) 12.1969 1.03453 0.517266 0.855825i \(-0.326950\pi\)
0.517266 + 0.855825i \(0.326950\pi\)
\(140\) 0 0
\(141\) 7.29761 0.614569
\(142\) 24.6573 2.06919
\(143\) −40.8260 −3.41404
\(144\) −4.89340 −0.407783
\(145\) −2.21248 −0.183736
\(146\) −1.83712 −0.152041
\(147\) 0 0
\(148\) −6.57326 −0.540319
\(149\) 22.1052 1.81093 0.905465 0.424421i \(-0.139522\pi\)
0.905465 + 0.424421i \(0.139522\pi\)
\(150\) 5.87353 0.479571
\(151\) −21.6238 −1.75972 −0.879859 0.475234i \(-0.842363\pi\)
−0.879859 + 0.475234i \(0.842363\pi\)
\(152\) −0.413686 −0.0335544
\(153\) 2.16841 0.175306
\(154\) 0 0
\(155\) −5.45778 −0.438380
\(156\) −4.55365 −0.364583
\(157\) −2.96167 −0.236367 −0.118183 0.992992i \(-0.537707\pi\)
−0.118183 + 0.992992i \(0.537707\pi\)
\(158\) 21.4763 1.70856
\(159\) −8.09108 −0.641665
\(160\) 4.34646 0.343618
\(161\) 0 0
\(162\) −1.63508 −0.128464
\(163\) −10.6953 −0.837720 −0.418860 0.908051i \(-0.637570\pi\)
−0.418860 + 0.908051i \(0.637570\pi\)
\(164\) 0.673497 0.0525913
\(165\) 7.16449 0.557754
\(166\) 10.0377 0.779074
\(167\) 4.18953 0.324196 0.162098 0.986775i \(-0.448174\pi\)
0.162098 + 0.986775i \(0.448174\pi\)
\(168\) 0 0
\(169\) 32.7138 2.51645
\(170\) −4.20682 −0.322649
\(171\) −0.190732 −0.0145856
\(172\) −2.20822 −0.168375
\(173\) 8.24573 0.626911 0.313455 0.949603i \(-0.398513\pi\)
0.313455 + 0.949603i \(0.398513\pi\)
\(174\) 3.04892 0.231138
\(175\) 0 0
\(176\) −29.5477 −2.22724
\(177\) −6.53265 −0.491024
\(178\) −14.1000 −1.05684
\(179\) −0.0995296 −0.00743919 −0.00371959 0.999993i \(-0.501184\pi\)
−0.00371959 + 0.999993i \(0.501184\pi\)
\(180\) 0.799112 0.0595623
\(181\) −0.598347 −0.0444748 −0.0222374 0.999753i \(-0.507079\pi\)
−0.0222374 + 0.999753i \(0.507079\pi\)
\(182\) 0 0
\(183\) −2.90591 −0.214811
\(184\) 3.39810 0.250511
\(185\) −11.5802 −0.851397
\(186\) 7.52114 0.551477
\(187\) 13.0935 0.957490
\(188\) 4.91492 0.358457
\(189\) 0 0
\(190\) 0.370028 0.0268447
\(191\) 6.09259 0.440844 0.220422 0.975405i \(-0.429256\pi\)
0.220422 + 0.975405i \(0.429256\pi\)
\(192\) 3.79712 0.274033
\(193\) 8.47368 0.609949 0.304974 0.952361i \(-0.401352\pi\)
0.304974 + 0.952361i \(0.401352\pi\)
\(194\) 11.1634 0.801487
\(195\) −8.02225 −0.574485
\(196\) 0 0
\(197\) −3.03721 −0.216392 −0.108196 0.994130i \(-0.534507\pi\)
−0.108196 + 0.994130i \(0.534507\pi\)
\(198\) −9.87308 −0.701649
\(199\) 10.6476 0.754790 0.377395 0.926052i \(-0.376820\pi\)
0.377395 + 0.926052i \(0.376820\pi\)
\(200\) −7.79125 −0.550925
\(201\) −10.5427 −0.743626
\(202\) 10.8503 0.763427
\(203\) 0 0
\(204\) 1.46042 0.102250
\(205\) 1.18651 0.0828696
\(206\) −20.0204 −1.39489
\(207\) 1.56671 0.108894
\(208\) 33.0852 2.29405
\(209\) −1.15169 −0.0796641
\(210\) 0 0
\(211\) 1.16029 0.0798776 0.0399388 0.999202i \(-0.487284\pi\)
0.0399388 + 0.999202i \(0.487284\pi\)
\(212\) −5.44932 −0.374261
\(213\) −15.0801 −1.03327
\(214\) −11.0674 −0.756550
\(215\) −3.89027 −0.265314
\(216\) 2.16894 0.147578
\(217\) 0 0
\(218\) 14.9440 1.01214
\(219\) 1.12356 0.0759234
\(220\) 4.82526 0.325319
\(221\) −14.6611 −0.986211
\(222\) 15.9583 1.07105
\(223\) −1.73694 −0.116314 −0.0581571 0.998307i \(-0.518522\pi\)
−0.0581571 + 0.998307i \(0.518522\pi\)
\(224\) 0 0
\(225\) −3.59219 −0.239479
\(226\) −5.40892 −0.359796
\(227\) 2.94864 0.195708 0.0978541 0.995201i \(-0.468802\pi\)
0.0978541 + 0.995201i \(0.468802\pi\)
\(228\) −0.128457 −0.00850729
\(229\) 25.2145 1.66622 0.833110 0.553108i \(-0.186558\pi\)
0.833110 + 0.553108i \(0.186558\pi\)
\(230\) −3.03948 −0.200418
\(231\) 0 0
\(232\) −4.04440 −0.265528
\(233\) −0.291334 −0.0190859 −0.00954297 0.999954i \(-0.503038\pi\)
−0.00954297 + 0.999954i \(0.503038\pi\)
\(234\) 11.0551 0.722696
\(235\) 8.65870 0.564831
\(236\) −4.39972 −0.286397
\(237\) −13.1347 −0.853188
\(238\) 0 0
\(239\) −24.8353 −1.60646 −0.803232 0.595667i \(-0.796888\pi\)
−0.803232 + 0.595667i \(0.796888\pi\)
\(240\) −5.80607 −0.374780
\(241\) 7.18194 0.462630 0.231315 0.972879i \(-0.425697\pi\)
0.231315 + 0.972879i \(0.425697\pi\)
\(242\) −41.6304 −2.67611
\(243\) 1.00000 0.0641500
\(244\) −1.95712 −0.125292
\(245\) 0 0
\(246\) −1.63508 −0.104249
\(247\) 1.28958 0.0820537
\(248\) −9.97682 −0.633529
\(249\) −6.13893 −0.389039
\(250\) 16.6692 1.05426
\(251\) −5.47716 −0.345715 −0.172858 0.984947i \(-0.555300\pi\)
−0.172858 + 0.984947i \(0.555300\pi\)
\(252\) 0 0
\(253\) 9.46020 0.594758
\(254\) 25.8550 1.62229
\(255\) 2.57285 0.161118
\(256\) 14.5367 0.908543
\(257\) 22.7771 1.42080 0.710399 0.703800i \(-0.248515\pi\)
0.710399 + 0.703800i \(0.248515\pi\)
\(258\) 5.36102 0.333762
\(259\) 0 0
\(260\) −5.40296 −0.335077
\(261\) −1.86469 −0.115421
\(262\) 3.09006 0.190905
\(263\) 30.4246 1.87606 0.938032 0.346549i \(-0.112647\pi\)
0.938032 + 0.346549i \(0.112647\pi\)
\(264\) 13.0967 0.806044
\(265\) −9.60017 −0.589734
\(266\) 0 0
\(267\) 8.62339 0.527743
\(268\) −7.10048 −0.433731
\(269\) −8.54145 −0.520781 −0.260391 0.965503i \(-0.583851\pi\)
−0.260391 + 0.965503i \(0.583851\pi\)
\(270\) −1.94005 −0.118067
\(271\) 14.8801 0.903902 0.451951 0.892043i \(-0.350728\pi\)
0.451951 + 0.892043i \(0.350728\pi\)
\(272\) −10.6109 −0.643381
\(273\) 0 0
\(274\) 0.117969 0.00712674
\(275\) −21.6906 −1.30799
\(276\) 1.05517 0.0635139
\(277\) −17.9250 −1.07701 −0.538504 0.842623i \(-0.681010\pi\)
−0.538504 + 0.842623i \(0.681010\pi\)
\(278\) −19.9430 −1.19610
\(279\) −4.59985 −0.275386
\(280\) 0 0
\(281\) 8.08764 0.482468 0.241234 0.970467i \(-0.422448\pi\)
0.241234 + 0.970467i \(0.422448\pi\)
\(282\) −11.9322 −0.710552
\(283\) −27.1588 −1.61443 −0.807213 0.590261i \(-0.799025\pi\)
−0.807213 + 0.590261i \(0.799025\pi\)
\(284\) −10.1564 −0.602673
\(285\) −0.226306 −0.0134052
\(286\) 66.7539 3.94724
\(287\) 0 0
\(288\) 3.66322 0.215857
\(289\) −12.2980 −0.723411
\(290\) 3.61758 0.212432
\(291\) −6.82744 −0.400231
\(292\) 0.756716 0.0442835
\(293\) 18.4774 1.07946 0.539730 0.841838i \(-0.318527\pi\)
0.539730 + 0.841838i \(0.318527\pi\)
\(294\) 0 0
\(295\) −7.75107 −0.451285
\(296\) −21.1687 −1.23040
\(297\) 6.03827 0.350376
\(298\) −36.1439 −2.09376
\(299\) −10.5928 −0.612598
\(300\) −2.41933 −0.139680
\(301\) 0 0
\(302\) 35.3567 2.03455
\(303\) −6.63595 −0.381226
\(304\) 0.933326 0.0535299
\(305\) −3.44789 −0.197426
\(306\) −3.54554 −0.202685
\(307\) −25.7014 −1.46686 −0.733429 0.679766i \(-0.762081\pi\)
−0.733429 + 0.679766i \(0.762081\pi\)
\(308\) 0 0
\(309\) 12.2443 0.696553
\(310\) 8.92393 0.506845
\(311\) 12.2010 0.691855 0.345928 0.938261i \(-0.387564\pi\)
0.345928 + 0.938261i \(0.387564\pi\)
\(312\) −14.6647 −0.830223
\(313\) 13.5275 0.764617 0.382309 0.924035i \(-0.375129\pi\)
0.382309 + 0.924035i \(0.375129\pi\)
\(314\) 4.84257 0.273282
\(315\) 0 0
\(316\) −8.84615 −0.497635
\(317\) −25.3356 −1.42299 −0.711495 0.702691i \(-0.751982\pi\)
−0.711495 + 0.702691i \(0.751982\pi\)
\(318\) 13.2296 0.741879
\(319\) −11.2595 −0.630411
\(320\) 4.50533 0.251855
\(321\) 6.76869 0.377791
\(322\) 0 0
\(323\) −0.413585 −0.0230125
\(324\) 0.673497 0.0374165
\(325\) 24.2875 1.34723
\(326\) 17.4877 0.968554
\(327\) −9.13962 −0.505422
\(328\) 2.16894 0.119760
\(329\) 0 0
\(330\) −11.7145 −0.644864
\(331\) −14.6290 −0.804083 −0.402041 0.915621i \(-0.631699\pi\)
−0.402041 + 0.915621i \(0.631699\pi\)
\(332\) −4.13455 −0.226913
\(333\) −9.75991 −0.534840
\(334\) −6.85023 −0.374828
\(335\) −12.5091 −0.683443
\(336\) 0 0
\(337\) −22.0068 −1.19879 −0.599394 0.800454i \(-0.704592\pi\)
−0.599394 + 0.800454i \(0.704592\pi\)
\(338\) −53.4898 −2.90946
\(339\) 3.30804 0.179668
\(340\) 1.73281 0.0939746
\(341\) −27.7752 −1.50411
\(342\) 0.311862 0.0168636
\(343\) 0 0
\(344\) −7.11140 −0.383421
\(345\) 1.85892 0.100081
\(346\) −13.4824 −0.724821
\(347\) −1.86868 −0.100316 −0.0501579 0.998741i \(-0.515972\pi\)
−0.0501579 + 0.998741i \(0.515972\pi\)
\(348\) −1.25586 −0.0673212
\(349\) −22.4885 −1.20378 −0.601891 0.798579i \(-0.705586\pi\)
−0.601891 + 0.798579i \(0.705586\pi\)
\(350\) 0 0
\(351\) −6.76120 −0.360886
\(352\) 22.1195 1.17898
\(353\) −17.1123 −0.910797 −0.455398 0.890288i \(-0.650503\pi\)
−0.455398 + 0.890288i \(0.650503\pi\)
\(354\) 10.6814 0.567711
\(355\) −17.8928 −0.949649
\(356\) 5.80782 0.307814
\(357\) 0 0
\(358\) 0.162739 0.00860103
\(359\) 13.8490 0.730922 0.365461 0.930827i \(-0.380911\pi\)
0.365461 + 0.930827i \(0.380911\pi\)
\(360\) 2.57348 0.135634
\(361\) −18.9636 −0.998085
\(362\) 0.978348 0.0514208
\(363\) 25.4608 1.33634
\(364\) 0 0
\(365\) 1.33312 0.0697788
\(366\) 4.75140 0.248359
\(367\) 27.1366 1.41652 0.708260 0.705952i \(-0.249481\pi\)
0.708260 + 0.705952i \(0.249481\pi\)
\(368\) −7.66651 −0.399645
\(369\) 1.00000 0.0520579
\(370\) 18.9347 0.984366
\(371\) 0 0
\(372\) −3.09799 −0.160623
\(373\) −12.9137 −0.668647 −0.334324 0.942458i \(-0.608508\pi\)
−0.334324 + 0.942458i \(0.608508\pi\)
\(374\) −21.4089 −1.10703
\(375\) −10.1947 −0.526454
\(376\) 15.8281 0.816272
\(377\) 12.6075 0.649321
\(378\) 0 0
\(379\) 15.2859 0.785185 0.392592 0.919713i \(-0.371578\pi\)
0.392592 + 0.919713i \(0.371578\pi\)
\(380\) −0.152416 −0.00781878
\(381\) −15.8127 −0.810107
\(382\) −9.96189 −0.509695
\(383\) −31.5671 −1.61301 −0.806503 0.591231i \(-0.798642\pi\)
−0.806503 + 0.591231i \(0.798642\pi\)
\(384\) −13.5350 −0.690708
\(385\) 0 0
\(386\) −13.8552 −0.705210
\(387\) −3.27874 −0.166668
\(388\) −4.59826 −0.233441
\(389\) 10.7554 0.545320 0.272660 0.962110i \(-0.412097\pi\)
0.272660 + 0.962110i \(0.412097\pi\)
\(390\) 13.1170 0.664207
\(391\) 3.39727 0.171807
\(392\) 0 0
\(393\) −1.88985 −0.0953303
\(394\) 4.96610 0.250188
\(395\) −15.5844 −0.784138
\(396\) 4.06676 0.204362
\(397\) −30.7767 −1.54464 −0.772320 0.635233i \(-0.780904\pi\)
−0.772320 + 0.635233i \(0.780904\pi\)
\(398\) −17.4097 −0.872672
\(399\) 0 0
\(400\) 17.5780 0.878900
\(401\) 19.3013 0.963863 0.481931 0.876209i \(-0.339935\pi\)
0.481931 + 0.876209i \(0.339935\pi\)
\(402\) 17.2382 0.859764
\(403\) 31.1005 1.54923
\(404\) −4.46929 −0.222356
\(405\) 1.18651 0.0589583
\(406\) 0 0
\(407\) −58.9330 −2.92120
\(408\) 4.70317 0.232841
\(409\) 32.8122 1.62246 0.811229 0.584729i \(-0.198799\pi\)
0.811229 + 0.584729i \(0.198799\pi\)
\(410\) −1.94005 −0.0958120
\(411\) −0.0721484 −0.00355882
\(412\) 8.24649 0.406275
\(413\) 0 0
\(414\) −2.56169 −0.125900
\(415\) −7.28392 −0.357553
\(416\) −24.7678 −1.21434
\(417\) 12.1969 0.597287
\(418\) 1.88311 0.0921059
\(419\) 12.5559 0.613398 0.306699 0.951807i \(-0.400775\pi\)
0.306699 + 0.951807i \(0.400775\pi\)
\(420\) 0 0
\(421\) 3.98056 0.194001 0.0970004 0.995284i \(-0.469075\pi\)
0.0970004 + 0.995284i \(0.469075\pi\)
\(422\) −1.89717 −0.0923528
\(423\) 7.29761 0.354822
\(424\) −17.5491 −0.852260
\(425\) −7.78935 −0.377839
\(426\) 24.6573 1.19465
\(427\) 0 0
\(428\) 4.55869 0.220353
\(429\) −40.8260 −1.97110
\(430\) 6.36091 0.306750
\(431\) 15.1697 0.730698 0.365349 0.930871i \(-0.380950\pi\)
0.365349 + 0.930871i \(0.380950\pi\)
\(432\) −4.89340 −0.235434
\(433\) 23.7096 1.13941 0.569706 0.821849i \(-0.307057\pi\)
0.569706 + 0.821849i \(0.307057\pi\)
\(434\) 0 0
\(435\) −2.21248 −0.106080
\(436\) −6.15551 −0.294795
\(437\) −0.298821 −0.0142945
\(438\) −1.83712 −0.0877809
\(439\) −26.8746 −1.28265 −0.641327 0.767267i \(-0.721616\pi\)
−0.641327 + 0.767267i \(0.721616\pi\)
\(440\) 15.5394 0.740810
\(441\) 0 0
\(442\) 23.9721 1.14024
\(443\) 34.7765 1.65228 0.826142 0.563462i \(-0.190531\pi\)
0.826142 + 0.563462i \(0.190531\pi\)
\(444\) −6.57326 −0.311953
\(445\) 10.2318 0.485032
\(446\) 2.84004 0.134480
\(447\) 22.1052 1.04554
\(448\) 0 0
\(449\) 31.7289 1.49738 0.748690 0.662921i \(-0.230683\pi\)
0.748690 + 0.662921i \(0.230683\pi\)
\(450\) 5.87353 0.276881
\(451\) 6.03827 0.284331
\(452\) 2.22795 0.104794
\(453\) −21.6238 −1.01597
\(454\) −4.82127 −0.226274
\(455\) 0 0
\(456\) −0.413686 −0.0193726
\(457\) 0.596013 0.0278803 0.0139401 0.999903i \(-0.495563\pi\)
0.0139401 + 0.999903i \(0.495563\pi\)
\(458\) −41.2278 −1.92645
\(459\) 2.16841 0.101213
\(460\) 1.25197 0.0583736
\(461\) −2.14488 −0.0998972 −0.0499486 0.998752i \(-0.515906\pi\)
−0.0499486 + 0.998752i \(0.515906\pi\)
\(462\) 0 0
\(463\) 21.6912 1.00807 0.504037 0.863682i \(-0.331847\pi\)
0.504037 + 0.863682i \(0.331847\pi\)
\(464\) 9.12466 0.423602
\(465\) −5.45778 −0.253099
\(466\) 0.476356 0.0220667
\(467\) −36.2250 −1.67629 −0.838147 0.545444i \(-0.816361\pi\)
−0.838147 + 0.545444i \(0.816361\pi\)
\(468\) −4.55365 −0.210492
\(469\) 0 0
\(470\) −14.1577 −0.653046
\(471\) −2.96167 −0.136466
\(472\) −14.1689 −0.652178
\(473\) −19.7979 −0.910310
\(474\) 21.4763 0.986437
\(475\) 0.685144 0.0314366
\(476\) 0 0
\(477\) −8.09108 −0.370465
\(478\) 40.6078 1.85736
\(479\) 33.6997 1.53978 0.769888 0.638179i \(-0.220312\pi\)
0.769888 + 0.638179i \(0.220312\pi\)
\(480\) 4.34646 0.198388
\(481\) 65.9887 3.00882
\(482\) −11.7431 −0.534882
\(483\) 0 0
\(484\) 17.1477 0.779442
\(485\) −8.10084 −0.367840
\(486\) −1.63508 −0.0741689
\(487\) −16.0359 −0.726658 −0.363329 0.931661i \(-0.618360\pi\)
−0.363329 + 0.931661i \(0.618360\pi\)
\(488\) −6.30274 −0.285312
\(489\) −10.6953 −0.483658
\(490\) 0 0
\(491\) 9.67196 0.436490 0.218245 0.975894i \(-0.429967\pi\)
0.218245 + 0.975894i \(0.429967\pi\)
\(492\) 0.673497 0.0303636
\(493\) −4.04342 −0.182106
\(494\) −2.10856 −0.0948687
\(495\) 7.16449 0.322020
\(496\) 22.5089 1.01068
\(497\) 0 0
\(498\) 10.0377 0.449799
\(499\) −7.79437 −0.348924 −0.174462 0.984664i \(-0.555819\pi\)
−0.174462 + 0.984664i \(0.555819\pi\)
\(500\) −6.86612 −0.307062
\(501\) 4.18953 0.187175
\(502\) 8.95561 0.399709
\(503\) −31.0481 −1.38437 −0.692184 0.721721i \(-0.743351\pi\)
−0.692184 + 0.721721i \(0.743351\pi\)
\(504\) 0 0
\(505\) −7.87364 −0.350372
\(506\) −15.4682 −0.687646
\(507\) 32.7138 1.45287
\(508\) −10.6498 −0.472507
\(509\) 2.77977 0.123211 0.0616056 0.998101i \(-0.480378\pi\)
0.0616056 + 0.998101i \(0.480378\pi\)
\(510\) −4.20682 −0.186281
\(511\) 0 0
\(512\) 3.30140 0.145902
\(513\) −0.190732 −0.00842101
\(514\) −37.2425 −1.64269
\(515\) 14.5280 0.640180
\(516\) −2.20822 −0.0972116
\(517\) 44.0650 1.93797
\(518\) 0 0
\(519\) 8.24573 0.361947
\(520\) −17.3998 −0.763031
\(521\) −9.59805 −0.420498 −0.210249 0.977648i \(-0.567428\pi\)
−0.210249 + 0.977648i \(0.567428\pi\)
\(522\) 3.04892 0.133448
\(523\) −18.8288 −0.823324 −0.411662 0.911337i \(-0.635052\pi\)
−0.411662 + 0.911337i \(0.635052\pi\)
\(524\) −1.27281 −0.0556028
\(525\) 0 0
\(526\) −49.7468 −2.16906
\(527\) −9.97438 −0.434491
\(528\) −29.5477 −1.28590
\(529\) −20.5454 −0.893280
\(530\) 15.6971 0.681837
\(531\) −6.53265 −0.283493
\(532\) 0 0
\(533\) −6.76120 −0.292860
\(534\) −14.1000 −0.610165
\(535\) 8.03113 0.347216
\(536\) −22.8665 −0.987684
\(537\) −0.0995296 −0.00429502
\(538\) 13.9660 0.602116
\(539\) 0 0
\(540\) 0.799112 0.0343883
\(541\) 42.8223 1.84108 0.920538 0.390653i \(-0.127751\pi\)
0.920538 + 0.390653i \(0.127751\pi\)
\(542\) −24.3302 −1.04507
\(543\) −0.598347 −0.0256775
\(544\) 7.94338 0.340570
\(545\) −10.8443 −0.464518
\(546\) 0 0
\(547\) −37.0730 −1.58513 −0.792564 0.609789i \(-0.791254\pi\)
−0.792564 + 0.609789i \(0.791254\pi\)
\(548\) −0.0485917 −0.00207573
\(549\) −2.90591 −0.124021
\(550\) 35.4660 1.51227
\(551\) 0.355655 0.0151514
\(552\) 3.39810 0.144633
\(553\) 0 0
\(554\) 29.3088 1.24521
\(555\) −11.5802 −0.491554
\(556\) 8.21461 0.348377
\(557\) −15.5614 −0.659359 −0.329679 0.944093i \(-0.606941\pi\)
−0.329679 + 0.944093i \(0.606941\pi\)
\(558\) 7.52114 0.318395
\(559\) 22.1682 0.937616
\(560\) 0 0
\(561\) 13.0935 0.552807
\(562\) −13.2240 −0.557819
\(563\) 29.6009 1.24753 0.623765 0.781612i \(-0.285602\pi\)
0.623765 + 0.781612i \(0.285602\pi\)
\(564\) 4.91492 0.206955
\(565\) 3.92503 0.165127
\(566\) 44.4070 1.86656
\(567\) 0 0
\(568\) −32.7080 −1.37240
\(569\) −3.87808 −0.162577 −0.0812887 0.996691i \(-0.525904\pi\)
−0.0812887 + 0.996691i \(0.525904\pi\)
\(570\) 0.370028 0.0154988
\(571\) 8.99096 0.376260 0.188130 0.982144i \(-0.439757\pi\)
0.188130 + 0.982144i \(0.439757\pi\)
\(572\) −27.4962 −1.14967
\(573\) 6.09259 0.254522
\(574\) 0 0
\(575\) −5.62790 −0.234700
\(576\) 3.79712 0.158213
\(577\) −2.57684 −0.107275 −0.0536376 0.998560i \(-0.517082\pi\)
−0.0536376 + 0.998560i \(0.517082\pi\)
\(578\) 20.1082 0.836392
\(579\) 8.47368 0.352154
\(580\) −1.49010 −0.0618728
\(581\) 0 0
\(582\) 11.1634 0.462739
\(583\) −48.8562 −2.02342
\(584\) 2.43694 0.100841
\(585\) −8.02225 −0.331679
\(586\) −30.2120 −1.24805
\(587\) −0.220807 −0.00911369 −0.00455684 0.999990i \(-0.501450\pi\)
−0.00455684 + 0.999990i \(0.501450\pi\)
\(588\) 0 0
\(589\) 0.877338 0.0361501
\(590\) 12.6736 0.521765
\(591\) −3.03721 −0.124934
\(592\) 47.7591 1.96289
\(593\) 39.2367 1.61126 0.805630 0.592420i \(-0.201827\pi\)
0.805630 + 0.592420i \(0.201827\pi\)
\(594\) −9.87308 −0.405097
\(595\) 0 0
\(596\) 14.8878 0.609828
\(597\) 10.6476 0.435778
\(598\) 17.3201 0.708273
\(599\) −15.9137 −0.650216 −0.325108 0.945677i \(-0.605401\pi\)
−0.325108 + 0.945677i \(0.605401\pi\)
\(600\) −7.79125 −0.318077
\(601\) −17.8588 −0.728474 −0.364237 0.931306i \(-0.618670\pi\)
−0.364237 + 0.931306i \(0.618670\pi\)
\(602\) 0 0
\(603\) −10.5427 −0.429333
\(604\) −14.5635 −0.592582
\(605\) 30.2095 1.22819
\(606\) 10.8503 0.440765
\(607\) 21.8339 0.886209 0.443105 0.896470i \(-0.353877\pi\)
0.443105 + 0.896470i \(0.353877\pi\)
\(608\) −0.698693 −0.0283357
\(609\) 0 0
\(610\) 5.63759 0.228259
\(611\) −49.3406 −1.99611
\(612\) 1.46042 0.0590340
\(613\) −43.8002 −1.76907 −0.884537 0.466470i \(-0.845526\pi\)
−0.884537 + 0.466470i \(0.845526\pi\)
\(614\) 42.0240 1.69595
\(615\) 1.18651 0.0478448
\(616\) 0 0
\(617\) −43.8427 −1.76504 −0.882521 0.470274i \(-0.844155\pi\)
−0.882521 + 0.470274i \(0.844155\pi\)
\(618\) −20.0204 −0.805340
\(619\) −15.8048 −0.635250 −0.317625 0.948216i \(-0.602885\pi\)
−0.317625 + 0.948216i \(0.602885\pi\)
\(620\) −3.67580 −0.147624
\(621\) 1.56671 0.0628698
\(622\) −19.9496 −0.799908
\(623\) 0 0
\(624\) 33.0852 1.32447
\(625\) 5.86476 0.234591
\(626\) −22.1185 −0.884034
\(627\) −1.15169 −0.0459941
\(628\) −1.99467 −0.0795961
\(629\) −21.1635 −0.843844
\(630\) 0 0
\(631\) 9.99857 0.398037 0.199018 0.979996i \(-0.436225\pi\)
0.199018 + 0.979996i \(0.436225\pi\)
\(632\) −28.4883 −1.13321
\(633\) 1.16029 0.0461174
\(634\) 41.4258 1.64523
\(635\) −18.7619 −0.744544
\(636\) −5.44932 −0.216080
\(637\) 0 0
\(638\) 18.4102 0.728867
\(639\) −15.0801 −0.596561
\(640\) −16.0595 −0.634807
\(641\) 15.8669 0.626706 0.313353 0.949637i \(-0.398548\pi\)
0.313353 + 0.949637i \(0.398548\pi\)
\(642\) −11.0674 −0.436794
\(643\) 13.4252 0.529439 0.264720 0.964325i \(-0.414721\pi\)
0.264720 + 0.964325i \(0.414721\pi\)
\(644\) 0 0
\(645\) −3.89027 −0.153179
\(646\) 0.676246 0.0266066
\(647\) 10.4724 0.411713 0.205857 0.978582i \(-0.434002\pi\)
0.205857 + 0.978582i \(0.434002\pi\)
\(648\) 2.16894 0.0852041
\(649\) −39.4459 −1.54839
\(650\) −39.7121 −1.55764
\(651\) 0 0
\(652\) −7.20325 −0.282101
\(653\) −31.6074 −1.23689 −0.618447 0.785826i \(-0.712238\pi\)
−0.618447 + 0.785826i \(0.712238\pi\)
\(654\) 14.9440 0.584358
\(655\) −2.24233 −0.0876150
\(656\) −4.89340 −0.191055
\(657\) 1.12356 0.0438344
\(658\) 0 0
\(659\) −47.0497 −1.83280 −0.916398 0.400269i \(-0.868917\pi\)
−0.916398 + 0.400269i \(0.868917\pi\)
\(660\) 4.82526 0.187823
\(661\) 8.28359 0.322194 0.161097 0.986939i \(-0.448497\pi\)
0.161097 + 0.986939i \(0.448497\pi\)
\(662\) 23.9196 0.929663
\(663\) −14.6611 −0.569389
\(664\) −13.3150 −0.516722
\(665\) 0 0
\(666\) 15.9583 0.618370
\(667\) −2.92142 −0.113118
\(668\) 2.82164 0.109172
\(669\) −1.73694 −0.0671540
\(670\) 20.4534 0.790182
\(671\) −17.5467 −0.677381
\(672\) 0 0
\(673\) −36.5082 −1.40729 −0.703643 0.710554i \(-0.748445\pi\)
−0.703643 + 0.710554i \(0.748445\pi\)
\(674\) 35.9830 1.38601
\(675\) −3.59219 −0.138263
\(676\) 22.0327 0.847410
\(677\) −25.6242 −0.984817 −0.492408 0.870364i \(-0.663883\pi\)
−0.492408 + 0.870364i \(0.663883\pi\)
\(678\) −5.40892 −0.207728
\(679\) 0 0
\(680\) 5.58036 0.213997
\(681\) 2.94864 0.112992
\(682\) 45.4147 1.73902
\(683\) 1.57119 0.0601199 0.0300599 0.999548i \(-0.490430\pi\)
0.0300599 + 0.999548i \(0.490430\pi\)
\(684\) −0.128457 −0.00491168
\(685\) −0.0856049 −0.00327080
\(686\) 0 0
\(687\) 25.2145 0.961992
\(688\) 16.0442 0.611679
\(689\) 54.7054 2.08411
\(690\) −3.03948 −0.115711
\(691\) −51.8594 −1.97283 −0.986413 0.164285i \(-0.947468\pi\)
−0.986413 + 0.164285i \(0.947468\pi\)
\(692\) 5.55347 0.211111
\(693\) 0 0
\(694\) 3.05544 0.115983
\(695\) 14.4718 0.548948
\(696\) −4.04440 −0.153303
\(697\) 2.16841 0.0821345
\(698\) 36.7706 1.39179
\(699\) −0.291334 −0.0110193
\(700\) 0 0
\(701\) −18.2912 −0.690850 −0.345425 0.938446i \(-0.612265\pi\)
−0.345425 + 0.938446i \(0.612265\pi\)
\(702\) 11.0551 0.417249
\(703\) 1.86152 0.0702087
\(704\) 22.9280 0.864133
\(705\) 8.65870 0.326106
\(706\) 27.9801 1.05304
\(707\) 0 0
\(708\) −4.39972 −0.165351
\(709\) 26.7300 1.00387 0.501934 0.864906i \(-0.332622\pi\)
0.501934 + 0.864906i \(0.332622\pi\)
\(710\) 29.2562 1.09796
\(711\) −13.1347 −0.492588
\(712\) 18.7036 0.700948
\(713\) −7.20662 −0.269890
\(714\) 0 0
\(715\) −48.4405 −1.81157
\(716\) −0.0670328 −0.00250513
\(717\) −24.8353 −0.927492
\(718\) −22.6443 −0.845076
\(719\) −26.6398 −0.993497 −0.496748 0.867895i \(-0.665473\pi\)
−0.496748 + 0.867895i \(0.665473\pi\)
\(720\) −5.80607 −0.216380
\(721\) 0 0
\(722\) 31.0071 1.15396
\(723\) 7.18194 0.267099
\(724\) −0.402985 −0.0149768
\(725\) 6.69831 0.248769
\(726\) −41.6304 −1.54505
\(727\) 10.5021 0.389503 0.194751 0.980853i \(-0.437610\pi\)
0.194751 + 0.980853i \(0.437610\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.17976 −0.0806767
\(731\) −7.10967 −0.262961
\(732\) −1.95712 −0.0723372
\(733\) −47.4356 −1.75207 −0.876037 0.482244i \(-0.839822\pi\)
−0.876037 + 0.482244i \(0.839822\pi\)
\(734\) −44.3706 −1.63775
\(735\) 0 0
\(736\) 5.73919 0.211549
\(737\) −63.6598 −2.34494
\(738\) −1.63508 −0.0601882
\(739\) 1.56904 0.0577181 0.0288591 0.999583i \(-0.490813\pi\)
0.0288591 + 0.999583i \(0.490813\pi\)
\(740\) −7.79926 −0.286706
\(741\) 1.28958 0.0473737
\(742\) 0 0
\(743\) −27.4416 −1.00674 −0.503368 0.864072i \(-0.667906\pi\)
−0.503368 + 0.864072i \(0.667906\pi\)
\(744\) −9.97682 −0.365768
\(745\) 26.2281 0.960924
\(746\) 21.1150 0.773075
\(747\) −6.13893 −0.224612
\(748\) 8.81841 0.322433
\(749\) 0 0
\(750\) 16.6692 0.608675
\(751\) 6.36454 0.232245 0.116123 0.993235i \(-0.462953\pi\)
0.116123 + 0.993235i \(0.462953\pi\)
\(752\) −35.7101 −1.30221
\(753\) −5.47716 −0.199599
\(754\) −20.6144 −0.750731
\(755\) −25.6569 −0.933750
\(756\) 0 0
\(757\) −52.1059 −1.89382 −0.946911 0.321495i \(-0.895815\pi\)
−0.946911 + 0.321495i \(0.895815\pi\)
\(758\) −24.9937 −0.907814
\(759\) 9.46020 0.343384
\(760\) −0.490844 −0.0178048
\(761\) −10.4650 −0.379355 −0.189677 0.981846i \(-0.560744\pi\)
−0.189677 + 0.981846i \(0.560744\pi\)
\(762\) 25.8550 0.936628
\(763\) 0 0
\(764\) 4.10334 0.148454
\(765\) 2.57285 0.0930215
\(766\) 51.6149 1.86492
\(767\) 44.1685 1.59483
\(768\) 14.5367 0.524548
\(769\) 53.8129 1.94054 0.970272 0.242019i \(-0.0778096\pi\)
0.970272 + 0.242019i \(0.0778096\pi\)
\(770\) 0 0
\(771\) 22.7771 0.820298
\(772\) 5.70700 0.205399
\(773\) 41.3159 1.48603 0.743015 0.669274i \(-0.233395\pi\)
0.743015 + 0.669274i \(0.233395\pi\)
\(774\) 5.36102 0.192698
\(775\) 16.5235 0.593543
\(776\) −14.8083 −0.531588
\(777\) 0 0
\(778\) −17.5860 −0.630488
\(779\) −0.190732 −0.00683367
\(780\) −5.40296 −0.193457
\(781\) −91.0580 −3.25831
\(782\) −5.55481 −0.198640
\(783\) −1.86469 −0.0666385
\(784\) 0 0
\(785\) −3.51405 −0.125422
\(786\) 3.09006 0.110219
\(787\) −43.4359 −1.54832 −0.774161 0.632989i \(-0.781828\pi\)
−0.774161 + 0.632989i \(0.781828\pi\)
\(788\) −2.04555 −0.0728698
\(789\) 30.4246 1.08315
\(790\) 25.4818 0.906604
\(791\) 0 0
\(792\) 13.0967 0.465370
\(793\) 19.6474 0.697700
\(794\) 50.3225 1.78588
\(795\) −9.60017 −0.340483
\(796\) 7.17114 0.254174
\(797\) −20.4671 −0.724983 −0.362492 0.931987i \(-0.618074\pi\)
−0.362492 + 0.931987i \(0.618074\pi\)
\(798\) 0 0
\(799\) 15.8242 0.559821
\(800\) −13.1590 −0.465240
\(801\) 8.62339 0.304692
\(802\) −31.5593 −1.11440
\(803\) 6.78438 0.239416
\(804\) −7.10048 −0.250415
\(805\) 0 0
\(806\) −50.8519 −1.79118
\(807\) −8.54145 −0.300673
\(808\) −14.3930 −0.506344
\(809\) 17.9052 0.629515 0.314757 0.949172i \(-0.398077\pi\)
0.314757 + 0.949172i \(0.398077\pi\)
\(810\) −1.94005 −0.0681663
\(811\) 28.0013 0.983259 0.491629 0.870805i \(-0.336401\pi\)
0.491629 + 0.870805i \(0.336401\pi\)
\(812\) 0 0
\(813\) 14.8801 0.521868
\(814\) 96.3603 3.37743
\(815\) −12.6901 −0.444515
\(816\) −10.6109 −0.371456
\(817\) 0.625360 0.0218786
\(818\) −53.6506 −1.87585
\(819\) 0 0
\(820\) 0.799112 0.0279062
\(821\) 20.8566 0.727901 0.363950 0.931418i \(-0.381428\pi\)
0.363950 + 0.931418i \(0.381428\pi\)
\(822\) 0.117969 0.00411463
\(823\) −2.92738 −0.102042 −0.0510209 0.998698i \(-0.516248\pi\)
−0.0510209 + 0.998698i \(0.516248\pi\)
\(824\) 26.5572 0.925162
\(825\) −21.6906 −0.755170
\(826\) 0 0
\(827\) 31.8673 1.10814 0.554068 0.832471i \(-0.313075\pi\)
0.554068 + 0.832471i \(0.313075\pi\)
\(828\) 1.05517 0.0366697
\(829\) −31.9250 −1.10880 −0.554401 0.832250i \(-0.687052\pi\)
−0.554401 + 0.832250i \(0.687052\pi\)
\(830\) 11.9098 0.413396
\(831\) −17.9250 −0.621811
\(832\) −25.6731 −0.890054
\(833\) 0 0
\(834\) −19.9430 −0.690571
\(835\) 4.97093 0.172026
\(836\) −0.775660 −0.0268268
\(837\) −4.59985 −0.158994
\(838\) −20.5300 −0.709198
\(839\) −49.2274 −1.69952 −0.849760 0.527170i \(-0.823253\pi\)
−0.849760 + 0.527170i \(0.823253\pi\)
\(840\) 0 0
\(841\) −25.5229 −0.880101
\(842\) −6.50855 −0.224300
\(843\) 8.08764 0.278553
\(844\) 0.781451 0.0268987
\(845\) 38.8153 1.33529
\(846\) −11.9322 −0.410237
\(847\) 0 0
\(848\) 39.5929 1.35962
\(849\) −27.1588 −0.932089
\(850\) 12.7362 0.436849
\(851\) −15.2909 −0.524165
\(852\) −10.1564 −0.347953
\(853\) 17.9981 0.616242 0.308121 0.951347i \(-0.400300\pi\)
0.308121 + 0.951347i \(0.400300\pi\)
\(854\) 0 0
\(855\) −0.226306 −0.00773949
\(856\) 14.6809 0.501783
\(857\) 42.5590 1.45379 0.726894 0.686749i \(-0.240963\pi\)
0.726894 + 0.686749i \(0.240963\pi\)
\(858\) 66.7539 2.27894
\(859\) −9.46509 −0.322945 −0.161472 0.986877i \(-0.551624\pi\)
−0.161472 + 0.986877i \(0.551624\pi\)
\(860\) −2.62008 −0.0893441
\(861\) 0 0
\(862\) −24.8037 −0.844818
\(863\) 35.0039 1.19155 0.595773 0.803153i \(-0.296846\pi\)
0.595773 + 0.803153i \(0.296846\pi\)
\(864\) 3.66322 0.124625
\(865\) 9.78365 0.332654
\(866\) −38.7672 −1.31736
\(867\) −12.2980 −0.417661
\(868\) 0 0
\(869\) −79.3107 −2.69043
\(870\) 3.61758 0.122647
\(871\) 71.2814 2.41528
\(872\) −19.8233 −0.671302
\(873\) −6.82744 −0.231074
\(874\) 0.488597 0.0165270
\(875\) 0 0
\(876\) 0.756716 0.0255671
\(877\) 31.0315 1.04786 0.523929 0.851762i \(-0.324466\pi\)
0.523929 + 0.851762i \(0.324466\pi\)
\(878\) 43.9422 1.48298
\(879\) 18.4774 0.623226
\(880\) −35.0587 −1.18183
\(881\) −5.51668 −0.185862 −0.0929309 0.995673i \(-0.529624\pi\)
−0.0929309 + 0.995673i \(0.529624\pi\)
\(882\) 0 0
\(883\) 13.3820 0.450341 0.225170 0.974319i \(-0.427706\pi\)
0.225170 + 0.974319i \(0.427706\pi\)
\(884\) −9.87419 −0.332105
\(885\) −7.75107 −0.260549
\(886\) −56.8625 −1.91033
\(887\) 39.4172 1.32350 0.661750 0.749725i \(-0.269814\pi\)
0.661750 + 0.749725i \(0.269814\pi\)
\(888\) −21.1687 −0.710374
\(889\) 0 0
\(890\) −16.7298 −0.560783
\(891\) 6.03827 0.202290
\(892\) −1.16982 −0.0391686
\(893\) −1.39189 −0.0465777
\(894\) −36.1439 −1.20883
\(895\) −0.118093 −0.00394741
\(896\) 0 0
\(897\) −10.5928 −0.353684
\(898\) −51.8794 −1.73124
\(899\) 8.57729 0.286069
\(900\) −2.41933 −0.0806442
\(901\) −17.5448 −0.584503
\(902\) −9.87308 −0.328738
\(903\) 0 0
\(904\) 7.17495 0.238635
\(905\) −0.709947 −0.0235994
\(906\) 35.3567 1.17465
\(907\) −37.2578 −1.23712 −0.618562 0.785736i \(-0.712285\pi\)
−0.618562 + 0.785736i \(0.712285\pi\)
\(908\) 1.98590 0.0659044
\(909\) −6.63595 −0.220101
\(910\) 0 0
\(911\) −14.0722 −0.466233 −0.233116 0.972449i \(-0.574892\pi\)
−0.233116 + 0.972449i \(0.574892\pi\)
\(912\) 0.933326 0.0309055
\(913\) −37.0686 −1.22679
\(914\) −0.974530 −0.0322346
\(915\) −3.44789 −0.113984
\(916\) 16.9819 0.561097
\(917\) 0 0
\(918\) −3.54554 −0.117020
\(919\) 33.2871 1.09804 0.549020 0.835809i \(-0.315001\pi\)
0.549020 + 0.835809i \(0.315001\pi\)
\(920\) 4.03188 0.132927
\(921\) −25.7014 −0.846891
\(922\) 3.50706 0.115499
\(923\) 101.960 3.35605
\(924\) 0 0
\(925\) 35.0594 1.15275
\(926\) −35.4669 −1.16551
\(927\) 12.2443 0.402155
\(928\) −6.83077 −0.224231
\(929\) −49.8856 −1.63669 −0.818346 0.574726i \(-0.805109\pi\)
−0.818346 + 0.574726i \(0.805109\pi\)
\(930\) 8.92393 0.292627
\(931\) 0 0
\(932\) −0.196213 −0.00642716
\(933\) 12.2010 0.399443
\(934\) 59.2309 1.93810
\(935\) 15.5356 0.508067
\(936\) −14.6647 −0.479329
\(937\) −10.0550 −0.328481 −0.164241 0.986420i \(-0.552517\pi\)
−0.164241 + 0.986420i \(0.552517\pi\)
\(938\) 0 0
\(939\) 13.5275 0.441452
\(940\) 5.83161 0.190206
\(941\) −0.902873 −0.0294328 −0.0147164 0.999892i \(-0.504685\pi\)
−0.0147164 + 0.999892i \(0.504685\pi\)
\(942\) 4.84257 0.157779
\(943\) 1.56671 0.0510190
\(944\) 31.9668 1.04043
\(945\) 0 0
\(946\) 32.3713 1.05248
\(947\) 8.29979 0.269707 0.134853 0.990866i \(-0.456944\pi\)
0.134853 + 0.990866i \(0.456944\pi\)
\(948\) −8.84615 −0.287310
\(949\) −7.59663 −0.246597
\(950\) −1.12027 −0.0363463
\(951\) −25.3356 −0.821564
\(952\) 0 0
\(953\) 15.6761 0.507799 0.253899 0.967231i \(-0.418287\pi\)
0.253899 + 0.967231i \(0.418287\pi\)
\(954\) 13.2296 0.428324
\(955\) 7.22893 0.233923
\(956\) −16.7265 −0.540974
\(957\) −11.2595 −0.363968
\(958\) −55.1017 −1.78026
\(959\) 0 0
\(960\) 4.50533 0.145409
\(961\) −9.84135 −0.317463
\(962\) −107.897 −3.47874
\(963\) 6.76869 0.218118
\(964\) 4.83701 0.155790
\(965\) 10.0541 0.323654
\(966\) 0 0
\(967\) −15.4670 −0.497385 −0.248693 0.968582i \(-0.580001\pi\)
−0.248693 + 0.968582i \(0.580001\pi\)
\(968\) 55.2229 1.77493
\(969\) −0.413585 −0.0132863
\(970\) 13.2455 0.425289
\(971\) −23.3623 −0.749731 −0.374865 0.927079i \(-0.622311\pi\)
−0.374865 + 0.927079i \(0.622311\pi\)
\(972\) 0.673497 0.0216024
\(973\) 0 0
\(974\) 26.2201 0.840146
\(975\) 24.2875 0.777823
\(976\) 14.2197 0.455163
\(977\) −46.8664 −1.49939 −0.749695 0.661784i \(-0.769800\pi\)
−0.749695 + 0.661784i \(0.769800\pi\)
\(978\) 17.4877 0.559195
\(979\) 52.0704 1.66418
\(980\) 0 0
\(981\) −9.13962 −0.291806
\(982\) −15.8145 −0.504660
\(983\) −32.4502 −1.03500 −0.517501 0.855683i \(-0.673137\pi\)
−0.517501 + 0.855683i \(0.673137\pi\)
\(984\) 2.16894 0.0691434
\(985\) −3.60369 −0.114823
\(986\) 6.61132 0.210547
\(987\) 0 0
\(988\) 0.868525 0.0276315
\(989\) −5.13683 −0.163342
\(990\) −11.7145 −0.372312
\(991\) −43.7943 −1.39117 −0.695586 0.718443i \(-0.744855\pi\)
−0.695586 + 0.718443i \(0.744855\pi\)
\(992\) −16.8503 −0.534997
\(993\) −14.6290 −0.464238
\(994\) 0 0
\(995\) 12.6335 0.400510
\(996\) −4.13455 −0.131008
\(997\) 13.6442 0.432116 0.216058 0.976381i \(-0.430680\pi\)
0.216058 + 0.976381i \(0.430680\pi\)
\(998\) 12.7445 0.403419
\(999\) −9.75991 −0.308790
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 \(a_p\))