Properties

Label 6027.2.a.bc.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 8
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: \(8\)
Coefficient field: 8.8.7457527933.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.70360\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.23115 q^{2} +1.00000 q^{3} +2.97801 q^{4} -0.893036 q^{5} -2.23115 q^{6} -2.18209 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.23115 q^{2} +1.00000 q^{3} +2.97801 q^{4} -0.893036 q^{5} -2.23115 q^{6} -2.18209 q^{8} +1.00000 q^{9} +1.99249 q^{10} -3.03213 q^{11} +2.97801 q^{12} -1.02235 q^{13} -0.893036 q^{15} -1.08747 q^{16} -0.590534 q^{17} -2.23115 q^{18} -3.50700 q^{19} -2.65947 q^{20} +6.76512 q^{22} -0.556191 q^{23} -2.18209 q^{24} -4.20249 q^{25} +2.28100 q^{26} +1.00000 q^{27} +7.89796 q^{29} +1.99249 q^{30} +1.28393 q^{31} +6.79048 q^{32} -3.03213 q^{33} +1.31757 q^{34} +2.97801 q^{36} -11.5424 q^{37} +7.82463 q^{38} -1.02235 q^{39} +1.94868 q^{40} +1.00000 q^{41} -5.76153 q^{43} -9.02971 q^{44} -0.893036 q^{45} +1.24094 q^{46} +0.229519 q^{47} -1.08747 q^{48} +9.37636 q^{50} -0.590534 q^{51} -3.04456 q^{52} +8.54823 q^{53} -2.23115 q^{54} +2.70780 q^{55} -3.50700 q^{57} -17.6215 q^{58} -10.6811 q^{59} -2.65947 q^{60} -8.09457 q^{61} -2.86464 q^{62} -12.9756 q^{64} +0.912992 q^{65} +6.76512 q^{66} +8.13979 q^{67} -1.75862 q^{68} -0.556191 q^{69} +1.38924 q^{71} -2.18209 q^{72} +10.7543 q^{73} +25.7528 q^{74} -4.20249 q^{75} -10.4439 q^{76} +2.28100 q^{78} +4.67035 q^{79} +0.971148 q^{80} +1.00000 q^{81} -2.23115 q^{82} +3.22689 q^{83} +0.527368 q^{85} +12.8548 q^{86} +7.89796 q^{87} +6.61637 q^{88} +15.9423 q^{89} +1.99249 q^{90} -1.65634 q^{92} +1.28393 q^{93} -0.512091 q^{94} +3.13188 q^{95} +6.79048 q^{96} +5.16775 q^{97} -3.03213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23115 −1.57766 −0.788829 0.614612i \(-0.789312\pi\)
−0.788829 + 0.614612i \(0.789312\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.97801 1.48901
\(5\) −0.893036 −0.399378 −0.199689 0.979859i \(-0.563993\pi\)
−0.199689 + 0.979859i \(0.563993\pi\)
\(6\) −2.23115 −0.910862
\(7\) 0 0
\(8\) −2.18209 −0.771485
\(9\) 1.00000 0.333333
\(10\) 1.99249 0.630082
\(11\) −3.03213 −0.914220 −0.457110 0.889410i \(-0.651116\pi\)
−0.457110 + 0.889410i \(0.651116\pi\)
\(12\) 2.97801 0.859678
\(13\) −1.02235 −0.283548 −0.141774 0.989899i \(-0.545281\pi\)
−0.141774 + 0.989899i \(0.545281\pi\)
\(14\) 0 0
\(15\) −0.893036 −0.230581
\(16\) −1.08747 −0.271867
\(17\) −0.590534 −0.143226 −0.0716128 0.997433i \(-0.522815\pi\)
−0.0716128 + 0.997433i \(0.522815\pi\)
\(18\) −2.23115 −0.525886
\(19\) −3.50700 −0.804561 −0.402281 0.915516i \(-0.631782\pi\)
−0.402281 + 0.915516i \(0.631782\pi\)
\(20\) −2.65947 −0.594676
\(21\) 0 0
\(22\) 6.76512 1.44233
\(23\) −0.556191 −0.115974 −0.0579870 0.998317i \(-0.518468\pi\)
−0.0579870 + 0.998317i \(0.518468\pi\)
\(24\) −2.18209 −0.445417
\(25\) −4.20249 −0.840497
\(26\) 2.28100 0.447342
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 7.89796 1.46661 0.733307 0.679898i \(-0.237976\pi\)
0.733307 + 0.679898i \(0.237976\pi\)
\(30\) 1.99249 0.363778
\(31\) 1.28393 0.230601 0.115300 0.993331i \(-0.463217\pi\)
0.115300 + 0.993331i \(0.463217\pi\)
\(32\) 6.79048 1.20040
\(33\) −3.03213 −0.527825
\(34\) 1.31757 0.225961
\(35\) 0 0
\(36\) 2.97801 0.496335
\(37\) −11.5424 −1.89756 −0.948779 0.315940i \(-0.897680\pi\)
−0.948779 + 0.315940i \(0.897680\pi\)
\(38\) 7.82463 1.26932
\(39\) −1.02235 −0.163706
\(40\) 1.94868 0.308114
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −5.76153 −0.878625 −0.439313 0.898334i \(-0.644778\pi\)
−0.439313 + 0.898334i \(0.644778\pi\)
\(44\) −9.02971 −1.36128
\(45\) −0.893036 −0.133126
\(46\) 1.24094 0.182967
\(47\) 0.229519 0.0334788 0.0167394 0.999860i \(-0.494671\pi\)
0.0167394 + 0.999860i \(0.494671\pi\)
\(48\) −1.08747 −0.156962
\(49\) 0 0
\(50\) 9.37636 1.32602
\(51\) −0.590534 −0.0826913
\(52\) −3.04456 −0.422205
\(53\) 8.54823 1.17419 0.587095 0.809518i \(-0.300271\pi\)
0.587095 + 0.809518i \(0.300271\pi\)
\(54\) −2.23115 −0.303621
\(55\) 2.70780 0.365119
\(56\) 0 0
\(57\) −3.50700 −0.464514
\(58\) −17.6215 −2.31382
\(59\) −10.6811 −1.39056 −0.695282 0.718737i \(-0.744721\pi\)
−0.695282 + 0.718737i \(0.744721\pi\)
\(60\) −2.65947 −0.343336
\(61\) −8.09457 −1.03640 −0.518202 0.855258i \(-0.673398\pi\)
−0.518202 + 0.855258i \(0.673398\pi\)
\(62\) −2.86464 −0.363809
\(63\) 0 0
\(64\) −12.9756 −1.62195
\(65\) 0.912992 0.113243
\(66\) 6.76512 0.832728
\(67\) 8.13979 0.994434 0.497217 0.867626i \(-0.334355\pi\)
0.497217 + 0.867626i \(0.334355\pi\)
\(68\) −1.75862 −0.213264
\(69\) −0.556191 −0.0669576
\(70\) 0 0
\(71\) 1.38924 0.164873 0.0824363 0.996596i \(-0.473730\pi\)
0.0824363 + 0.996596i \(0.473730\pi\)
\(72\) −2.18209 −0.257162
\(73\) 10.7543 1.25869 0.629345 0.777126i \(-0.283323\pi\)
0.629345 + 0.777126i \(0.283323\pi\)
\(74\) 25.7528 2.99370
\(75\) −4.20249 −0.485261
\(76\) −10.4439 −1.19800
\(77\) 0 0
\(78\) 2.28100 0.258273
\(79\) 4.67035 0.525456 0.262728 0.964870i \(-0.415378\pi\)
0.262728 + 0.964870i \(0.415378\pi\)
\(80\) 0.971148 0.108578
\(81\) 1.00000 0.111111
\(82\) −2.23115 −0.246389
\(83\) 3.22689 0.354197 0.177099 0.984193i \(-0.443329\pi\)
0.177099 + 0.984193i \(0.443329\pi\)
\(84\) 0 0
\(85\) 0.527368 0.0572011
\(86\) 12.8548 1.38617
\(87\) 7.89796 0.846750
\(88\) 6.61637 0.705307
\(89\) 15.9423 1.68989 0.844943 0.534857i \(-0.179634\pi\)
0.844943 + 0.534857i \(0.179634\pi\)
\(90\) 1.99249 0.210027
\(91\) 0 0
\(92\) −1.65634 −0.172686
\(93\) 1.28393 0.133138
\(94\) −0.512091 −0.0528182
\(95\) 3.13188 0.321324
\(96\) 6.79048 0.693050
\(97\) 5.16775 0.524706 0.262353 0.964972i \(-0.415502\pi\)
0.262353 + 0.964972i \(0.415502\pi\)
\(98\) 0 0
\(99\) −3.03213 −0.304740
\(100\) −12.5151 −1.25151
\(101\) 10.6304 1.05776 0.528881 0.848696i \(-0.322612\pi\)
0.528881 + 0.848696i \(0.322612\pi\)
\(102\) 1.31757 0.130459
\(103\) −3.93822 −0.388044 −0.194022 0.980997i \(-0.562153\pi\)
−0.194022 + 0.980997i \(0.562153\pi\)
\(104\) 2.23085 0.218753
\(105\) 0 0
\(106\) −19.0724 −1.85247
\(107\) −10.8000 −1.04408 −0.522039 0.852922i \(-0.674828\pi\)
−0.522039 + 0.852922i \(0.674828\pi\)
\(108\) 2.97801 0.286559
\(109\) −13.7396 −1.31601 −0.658007 0.753012i \(-0.728600\pi\)
−0.658007 + 0.753012i \(0.728600\pi\)
\(110\) −6.04149 −0.576034
\(111\) −11.5424 −1.09556
\(112\) 0 0
\(113\) 2.87693 0.270638 0.135319 0.990802i \(-0.456794\pi\)
0.135319 + 0.990802i \(0.456794\pi\)
\(114\) 7.82463 0.732844
\(115\) 0.496699 0.0463174
\(116\) 23.5202 2.18380
\(117\) −1.02235 −0.0945160
\(118\) 23.8312 2.19384
\(119\) 0 0
\(120\) 1.94868 0.177890
\(121\) −1.80621 −0.164201
\(122\) 18.0602 1.63509
\(123\) 1.00000 0.0901670
\(124\) 3.82356 0.343366
\(125\) 8.21815 0.735054
\(126\) 0 0
\(127\) −7.93950 −0.704517 −0.352258 0.935903i \(-0.614586\pi\)
−0.352258 + 0.935903i \(0.614586\pi\)
\(128\) 15.3695 1.35849
\(129\) −5.76153 −0.507274
\(130\) −2.03702 −0.178658
\(131\) 1.91414 0.167239 0.0836195 0.996498i \(-0.473352\pi\)
0.0836195 + 0.996498i \(0.473352\pi\)
\(132\) −9.02971 −0.785935
\(133\) 0 0
\(134\) −18.1611 −1.56888
\(135\) −0.893036 −0.0768603
\(136\) 1.28860 0.110496
\(137\) 10.9420 0.934842 0.467421 0.884035i \(-0.345183\pi\)
0.467421 + 0.884035i \(0.345183\pi\)
\(138\) 1.24094 0.105636
\(139\) 20.5931 1.74668 0.873341 0.487109i \(-0.161949\pi\)
0.873341 + 0.487109i \(0.161949\pi\)
\(140\) 0 0
\(141\) 0.229519 0.0193290
\(142\) −3.09960 −0.260112
\(143\) 3.09988 0.259225
\(144\) −1.08747 −0.0906223
\(145\) −7.05316 −0.585733
\(146\) −23.9943 −1.98578
\(147\) 0 0
\(148\) −34.3734 −2.82548
\(149\) 3.25543 0.266695 0.133347 0.991069i \(-0.457427\pi\)
0.133347 + 0.991069i \(0.457427\pi\)
\(150\) 9.37636 0.765577
\(151\) 12.0406 0.979852 0.489926 0.871764i \(-0.337024\pi\)
0.489926 + 0.871764i \(0.337024\pi\)
\(152\) 7.65258 0.620706
\(153\) −0.590534 −0.0477418
\(154\) 0 0
\(155\) −1.14660 −0.0920969
\(156\) −3.04456 −0.243760
\(157\) 0.580260 0.0463098 0.0231549 0.999732i \(-0.492629\pi\)
0.0231549 + 0.999732i \(0.492629\pi\)
\(158\) −10.4202 −0.828990
\(159\) 8.54823 0.677919
\(160\) −6.06414 −0.479412
\(161\) 0 0
\(162\) −2.23115 −0.175295
\(163\) 11.9654 0.937204 0.468602 0.883409i \(-0.344758\pi\)
0.468602 + 0.883409i \(0.344758\pi\)
\(164\) 2.97801 0.232544
\(165\) 2.70780 0.210802
\(166\) −7.19967 −0.558802
\(167\) −16.9933 −1.31498 −0.657490 0.753463i \(-0.728382\pi\)
−0.657490 + 0.753463i \(0.728382\pi\)
\(168\) 0 0
\(169\) −11.9548 −0.919601
\(170\) −1.17664 −0.0902438
\(171\) −3.50700 −0.268187
\(172\) −17.1579 −1.30828
\(173\) 3.00321 0.228330 0.114165 0.993462i \(-0.463581\pi\)
0.114165 + 0.993462i \(0.463581\pi\)
\(174\) −17.6215 −1.33588
\(175\) 0 0
\(176\) 3.29734 0.248546
\(177\) −10.6811 −0.802843
\(178\) −35.5697 −2.66606
\(179\) 10.3399 0.772844 0.386422 0.922322i \(-0.373711\pi\)
0.386422 + 0.922322i \(0.373711\pi\)
\(180\) −2.65947 −0.198225
\(181\) −9.54059 −0.709146 −0.354573 0.935028i \(-0.615374\pi\)
−0.354573 + 0.935028i \(0.615374\pi\)
\(182\) 0 0
\(183\) −8.09457 −0.598368
\(184\) 1.21366 0.0894721
\(185\) 10.3078 0.757843
\(186\) −2.86464 −0.210046
\(187\) 1.79057 0.130940
\(188\) 0.683511 0.0498502
\(189\) 0 0
\(190\) −6.98768 −0.506939
\(191\) 3.85532 0.278961 0.139480 0.990225i \(-0.455457\pi\)
0.139480 + 0.990225i \(0.455457\pi\)
\(192\) −12.9756 −0.936434
\(193\) 12.2524 0.881949 0.440975 0.897520i \(-0.354633\pi\)
0.440975 + 0.897520i \(0.354633\pi\)
\(194\) −11.5300 −0.827806
\(195\) 0.912992 0.0653807
\(196\) 0 0
\(197\) 20.0578 1.42906 0.714529 0.699606i \(-0.246641\pi\)
0.714529 + 0.699606i \(0.246641\pi\)
\(198\) 6.76512 0.480776
\(199\) −8.76302 −0.621194 −0.310597 0.950542i \(-0.600529\pi\)
−0.310597 + 0.950542i \(0.600529\pi\)
\(200\) 9.17019 0.648431
\(201\) 8.13979 0.574137
\(202\) −23.7179 −1.66879
\(203\) 0 0
\(204\) −1.75862 −0.123128
\(205\) −0.893036 −0.0623724
\(206\) 8.78674 0.612201
\(207\) −0.556191 −0.0386580
\(208\) 1.11177 0.0770873
\(209\) 10.6337 0.735546
\(210\) 0 0
\(211\) 21.8898 1.50696 0.753478 0.657473i \(-0.228375\pi\)
0.753478 + 0.657473i \(0.228375\pi\)
\(212\) 25.4567 1.74838
\(213\) 1.38924 0.0951892
\(214\) 24.0964 1.64720
\(215\) 5.14525 0.350903
\(216\) −2.18209 −0.148472
\(217\) 0 0
\(218\) 30.6550 2.07622
\(219\) 10.7543 0.726705
\(220\) 8.06386 0.543665
\(221\) 0.603730 0.0406113
\(222\) 25.7528 1.72841
\(223\) 19.0053 1.27269 0.636343 0.771406i \(-0.280446\pi\)
0.636343 + 0.771406i \(0.280446\pi\)
\(224\) 0 0
\(225\) −4.20249 −0.280166
\(226\) −6.41884 −0.426975
\(227\) 14.7021 0.975814 0.487907 0.872896i \(-0.337761\pi\)
0.487907 + 0.872896i \(0.337761\pi\)
\(228\) −10.4439 −0.691664
\(229\) 22.7562 1.50377 0.751886 0.659293i \(-0.229144\pi\)
0.751886 + 0.659293i \(0.229144\pi\)
\(230\) −1.10821 −0.0730731
\(231\) 0 0
\(232\) −17.2340 −1.13147
\(233\) −27.3282 −1.79033 −0.895164 0.445737i \(-0.852942\pi\)
−0.895164 + 0.445737i \(0.852942\pi\)
\(234\) 2.28100 0.149114
\(235\) −0.204969 −0.0133707
\(236\) −31.8085 −2.07056
\(237\) 4.67035 0.303372
\(238\) 0 0
\(239\) −12.5731 −0.813286 −0.406643 0.913587i \(-0.633301\pi\)
−0.406643 + 0.913587i \(0.633301\pi\)
\(240\) 0.971148 0.0626873
\(241\) 4.30351 0.277214 0.138607 0.990347i \(-0.455738\pi\)
0.138607 + 0.990347i \(0.455738\pi\)
\(242\) 4.02992 0.259053
\(243\) 1.00000 0.0641500
\(244\) −24.1057 −1.54321
\(245\) 0 0
\(246\) −2.23115 −0.142253
\(247\) 3.58537 0.228132
\(248\) −2.80165 −0.177905
\(249\) 3.22689 0.204496
\(250\) −18.3359 −1.15966
\(251\) −12.7442 −0.804408 −0.402204 0.915550i \(-0.631756\pi\)
−0.402204 + 0.915550i \(0.631756\pi\)
\(252\) 0 0
\(253\) 1.68644 0.106026
\(254\) 17.7142 1.11149
\(255\) 0.527368 0.0330251
\(256\) −8.34043 −0.521277
\(257\) −15.3531 −0.957701 −0.478850 0.877897i \(-0.658946\pi\)
−0.478850 + 0.877897i \(0.658946\pi\)
\(258\) 12.8548 0.800306
\(259\) 0 0
\(260\) 2.71890 0.168619
\(261\) 7.89796 0.488871
\(262\) −4.27072 −0.263846
\(263\) 4.70180 0.289925 0.144963 0.989437i \(-0.453694\pi\)
0.144963 + 0.989437i \(0.453694\pi\)
\(264\) 6.61637 0.407209
\(265\) −7.63388 −0.468946
\(266\) 0 0
\(267\) 15.9423 0.975656
\(268\) 24.2404 1.48072
\(269\) −17.8058 −1.08564 −0.542818 0.839850i \(-0.682643\pi\)
−0.542818 + 0.839850i \(0.682643\pi\)
\(270\) 1.99249 0.121259
\(271\) −5.15229 −0.312980 −0.156490 0.987680i \(-0.550018\pi\)
−0.156490 + 0.987680i \(0.550018\pi\)
\(272\) 0.642187 0.0389383
\(273\) 0 0
\(274\) −24.4133 −1.47486
\(275\) 12.7425 0.768400
\(276\) −1.65634 −0.0997002
\(277\) −8.01369 −0.481496 −0.240748 0.970588i \(-0.577393\pi\)
−0.240748 + 0.970588i \(0.577393\pi\)
\(278\) −45.9462 −2.75567
\(279\) 1.28393 0.0768670
\(280\) 0 0
\(281\) 4.98277 0.297247 0.148624 0.988894i \(-0.452516\pi\)
0.148624 + 0.988894i \(0.452516\pi\)
\(282\) −0.512091 −0.0304946
\(283\) 6.83872 0.406520 0.203260 0.979125i \(-0.434846\pi\)
0.203260 + 0.979125i \(0.434846\pi\)
\(284\) 4.13717 0.245496
\(285\) 3.13188 0.185516
\(286\) −6.91629 −0.408969
\(287\) 0 0
\(288\) 6.79048 0.400133
\(289\) −16.6513 −0.979486
\(290\) 15.7366 0.924087
\(291\) 5.16775 0.302939
\(292\) 32.0263 1.87420
\(293\) 23.1644 1.35328 0.676639 0.736315i \(-0.263436\pi\)
0.676639 + 0.736315i \(0.263436\pi\)
\(294\) 0 0
\(295\) 9.53863 0.555361
\(296\) 25.1865 1.46394
\(297\) −3.03213 −0.175942
\(298\) −7.26333 −0.420754
\(299\) 0.568620 0.0328842
\(300\) −12.5151 −0.722557
\(301\) 0 0
\(302\) −26.8644 −1.54587
\(303\) 10.6304 0.610699
\(304\) 3.81375 0.218734
\(305\) 7.22875 0.413917
\(306\) 1.31757 0.0753203
\(307\) −16.0121 −0.913857 −0.456929 0.889503i \(-0.651051\pi\)
−0.456929 + 0.889503i \(0.651051\pi\)
\(308\) 0 0
\(309\) −3.93822 −0.224037
\(310\) 2.55823 0.145297
\(311\) −20.7107 −1.17440 −0.587198 0.809443i \(-0.699769\pi\)
−0.587198 + 0.809443i \(0.699769\pi\)
\(312\) 2.23085 0.126297
\(313\) 18.5447 1.04821 0.524105 0.851653i \(-0.324400\pi\)
0.524105 + 0.851653i \(0.324400\pi\)
\(314\) −1.29464 −0.0730610
\(315\) 0 0
\(316\) 13.9084 0.782407
\(317\) 20.6683 1.16085 0.580425 0.814314i \(-0.302887\pi\)
0.580425 + 0.814314i \(0.302887\pi\)
\(318\) −19.0724 −1.06952
\(319\) −23.9476 −1.34081
\(320\) 11.5877 0.647771
\(321\) −10.8000 −0.602798
\(322\) 0 0
\(323\) 2.07100 0.115234
\(324\) 2.97801 0.165445
\(325\) 4.29640 0.238321
\(326\) −26.6966 −1.47859
\(327\) −13.7396 −0.759801
\(328\) −2.18209 −0.120486
\(329\) 0 0
\(330\) −6.04149 −0.332573
\(331\) 3.75882 0.206603 0.103302 0.994650i \(-0.467059\pi\)
0.103302 + 0.994650i \(0.467059\pi\)
\(332\) 9.60972 0.527402
\(333\) −11.5424 −0.632519
\(334\) 37.9145 2.07459
\(335\) −7.26913 −0.397155
\(336\) 0 0
\(337\) −26.8704 −1.46373 −0.731863 0.681452i \(-0.761349\pi\)
−0.731863 + 0.681452i \(0.761349\pi\)
\(338\) 26.6729 1.45082
\(339\) 2.87693 0.156253
\(340\) 1.57051 0.0851728
\(341\) −3.89304 −0.210820
\(342\) 7.82463 0.423108
\(343\) 0 0
\(344\) 12.5722 0.677846
\(345\) 0.496699 0.0267414
\(346\) −6.70059 −0.360226
\(347\) −21.4572 −1.15188 −0.575941 0.817491i \(-0.695364\pi\)
−0.575941 + 0.817491i \(0.695364\pi\)
\(348\) 23.5202 1.26082
\(349\) 26.1532 1.39995 0.699974 0.714168i \(-0.253195\pi\)
0.699974 + 0.714168i \(0.253195\pi\)
\(350\) 0 0
\(351\) −1.02235 −0.0545688
\(352\) −20.5896 −1.09743
\(353\) −3.71713 −0.197843 −0.0989216 0.995095i \(-0.531539\pi\)
−0.0989216 + 0.995095i \(0.531539\pi\)
\(354\) 23.8312 1.26661
\(355\) −1.24064 −0.0658464
\(356\) 47.4765 2.51625
\(357\) 0 0
\(358\) −23.0699 −1.21928
\(359\) 13.2589 0.699776 0.349888 0.936792i \(-0.386220\pi\)
0.349888 + 0.936792i \(0.386220\pi\)
\(360\) 1.94868 0.102705
\(361\) −6.70095 −0.352681
\(362\) 21.2864 1.11879
\(363\) −1.80621 −0.0948015
\(364\) 0 0
\(365\) −9.60393 −0.502693
\(366\) 18.0602 0.944021
\(367\) −19.4105 −1.01322 −0.506610 0.862175i \(-0.669102\pi\)
−0.506610 + 0.862175i \(0.669102\pi\)
\(368\) 0.604840 0.0315295
\(369\) 1.00000 0.0520579
\(370\) −22.9982 −1.19562
\(371\) 0 0
\(372\) 3.82356 0.198243
\(373\) 19.8031 1.02536 0.512682 0.858579i \(-0.328652\pi\)
0.512682 + 0.858579i \(0.328652\pi\)
\(374\) −3.99503 −0.206578
\(375\) 8.21815 0.424384
\(376\) −0.500831 −0.0258284
\(377\) −8.07445 −0.415855
\(378\) 0 0
\(379\) 10.4729 0.537955 0.268977 0.963147i \(-0.413314\pi\)
0.268977 + 0.963147i \(0.413314\pi\)
\(380\) 9.32677 0.478453
\(381\) −7.93950 −0.406753
\(382\) −8.60178 −0.440105
\(383\) 17.9568 0.917552 0.458776 0.888552i \(-0.348288\pi\)
0.458776 + 0.888552i \(0.348288\pi\)
\(384\) 15.3695 0.784322
\(385\) 0 0
\(386\) −27.3370 −1.39141
\(387\) −5.76153 −0.292875
\(388\) 15.3896 0.781290
\(389\) 31.2703 1.58547 0.792733 0.609569i \(-0.208657\pi\)
0.792733 + 0.609569i \(0.208657\pi\)
\(390\) −2.03702 −0.103148
\(391\) 0.328450 0.0166104
\(392\) 0 0
\(393\) 1.91414 0.0965555
\(394\) −44.7519 −2.25457
\(395\) −4.17079 −0.209855
\(396\) −9.02971 −0.453760
\(397\) 29.4827 1.47969 0.739846 0.672776i \(-0.234898\pi\)
0.739846 + 0.672776i \(0.234898\pi\)
\(398\) 19.5516 0.980032
\(399\) 0 0
\(400\) 4.57007 0.228503
\(401\) −11.3149 −0.565040 −0.282520 0.959261i \(-0.591170\pi\)
−0.282520 + 0.959261i \(0.591170\pi\)
\(402\) −18.1611 −0.905791
\(403\) −1.31262 −0.0653864
\(404\) 31.6574 1.57501
\(405\) −0.893036 −0.0443753
\(406\) 0 0
\(407\) 34.9980 1.73479
\(408\) 1.28860 0.0637951
\(409\) 18.9256 0.935812 0.467906 0.883778i \(-0.345009\pi\)
0.467906 + 0.883778i \(0.345009\pi\)
\(410\) 1.99249 0.0984023
\(411\) 10.9420 0.539731
\(412\) −11.7281 −0.577800
\(413\) 0 0
\(414\) 1.24094 0.0609891
\(415\) −2.88173 −0.141459
\(416\) −6.94222 −0.340370
\(417\) 20.5931 1.00845
\(418\) −23.7253 −1.16044
\(419\) 11.2826 0.551193 0.275597 0.961273i \(-0.411125\pi\)
0.275597 + 0.961273i \(0.411125\pi\)
\(420\) 0 0
\(421\) 1.47063 0.0716742 0.0358371 0.999358i \(-0.488590\pi\)
0.0358371 + 0.999358i \(0.488590\pi\)
\(422\) −48.8393 −2.37746
\(423\) 0.229519 0.0111596
\(424\) −18.6530 −0.905870
\(425\) 2.48171 0.120381
\(426\) −3.09960 −0.150176
\(427\) 0 0
\(428\) −32.1626 −1.55464
\(429\) 3.09988 0.149664
\(430\) −11.4798 −0.553606
\(431\) −4.90425 −0.236229 −0.118115 0.993000i \(-0.537685\pi\)
−0.118115 + 0.993000i \(0.537685\pi\)
\(432\) −1.08747 −0.0523208
\(433\) −9.20606 −0.442415 −0.221207 0.975227i \(-0.571000\pi\)
−0.221207 + 0.975227i \(0.571000\pi\)
\(434\) 0 0
\(435\) −7.05316 −0.338173
\(436\) −40.9166 −1.95955
\(437\) 1.95056 0.0933081
\(438\) −23.9943 −1.14649
\(439\) −24.0382 −1.14728 −0.573641 0.819107i \(-0.694470\pi\)
−0.573641 + 0.819107i \(0.694470\pi\)
\(440\) −5.90865 −0.281684
\(441\) 0 0
\(442\) −1.34701 −0.0640708
\(443\) −22.3474 −1.06176 −0.530878 0.847448i \(-0.678138\pi\)
−0.530878 + 0.847448i \(0.678138\pi\)
\(444\) −34.3734 −1.63129
\(445\) −14.2371 −0.674903
\(446\) −42.4035 −2.00786
\(447\) 3.25543 0.153976
\(448\) 0 0
\(449\) 15.0846 0.711886 0.355943 0.934508i \(-0.384160\pi\)
0.355943 + 0.934508i \(0.384160\pi\)
\(450\) 9.37636 0.442006
\(451\) −3.03213 −0.142777
\(452\) 8.56752 0.402982
\(453\) 12.0406 0.565718
\(454\) −32.8026 −1.53950
\(455\) 0 0
\(456\) 7.65258 0.358365
\(457\) −11.9480 −0.558905 −0.279453 0.960160i \(-0.590153\pi\)
−0.279453 + 0.960160i \(0.590153\pi\)
\(458\) −50.7724 −2.37244
\(459\) −0.590534 −0.0275638
\(460\) 1.47918 0.0689669
\(461\) −8.73937 −0.407033 −0.203517 0.979071i \(-0.565237\pi\)
−0.203517 + 0.979071i \(0.565237\pi\)
\(462\) 0 0
\(463\) −32.3911 −1.50534 −0.752670 0.658398i \(-0.771235\pi\)
−0.752670 + 0.658398i \(0.771235\pi\)
\(464\) −8.58877 −0.398724
\(465\) −1.14660 −0.0531722
\(466\) 60.9731 2.82453
\(467\) 0.327510 0.0151553 0.00757767 0.999971i \(-0.497588\pi\)
0.00757767 + 0.999971i \(0.497588\pi\)
\(468\) −3.04456 −0.140735
\(469\) 0 0
\(470\) 0.457316 0.0210944
\(471\) 0.580260 0.0267370
\(472\) 23.3072 1.07280
\(473\) 17.4697 0.803257
\(474\) −10.4202 −0.478617
\(475\) 14.7381 0.676231
\(476\) 0 0
\(477\) 8.54823 0.391397
\(478\) 28.0524 1.28309
\(479\) −5.82212 −0.266020 −0.133010 0.991115i \(-0.542464\pi\)
−0.133010 + 0.991115i \(0.542464\pi\)
\(480\) −6.06414 −0.276789
\(481\) 11.8003 0.538049
\(482\) −9.60177 −0.437349
\(483\) 0 0
\(484\) −5.37892 −0.244496
\(485\) −4.61499 −0.209556
\(486\) −2.23115 −0.101207
\(487\) −24.5314 −1.11162 −0.555811 0.831309i \(-0.687592\pi\)
−0.555811 + 0.831309i \(0.687592\pi\)
\(488\) 17.6631 0.799570
\(489\) 11.9654 0.541095
\(490\) 0 0
\(491\) 21.0462 0.949801 0.474900 0.880040i \(-0.342484\pi\)
0.474900 + 0.880040i \(0.342484\pi\)
\(492\) 2.97801 0.134259
\(493\) −4.66401 −0.210057
\(494\) −7.99948 −0.359914
\(495\) 2.70780 0.121706
\(496\) −1.39623 −0.0626928
\(497\) 0 0
\(498\) −7.19967 −0.322625
\(499\) 21.4488 0.960181 0.480090 0.877219i \(-0.340604\pi\)
0.480090 + 0.877219i \(0.340604\pi\)
\(500\) 24.4738 1.09450
\(501\) −16.9933 −0.759204
\(502\) 28.4342 1.26908
\(503\) 33.1070 1.47617 0.738084 0.674708i \(-0.235731\pi\)
0.738084 + 0.674708i \(0.235731\pi\)
\(504\) 0 0
\(505\) −9.49330 −0.422446
\(506\) −3.76270 −0.167272
\(507\) −11.9548 −0.530932
\(508\) −23.6439 −1.04903
\(509\) 13.7852 0.611018 0.305509 0.952189i \(-0.401173\pi\)
0.305509 + 0.952189i \(0.401173\pi\)
\(510\) −1.17664 −0.0521023
\(511\) 0 0
\(512\) −12.1303 −0.536090
\(513\) −3.50700 −0.154838
\(514\) 34.2550 1.51092
\(515\) 3.51697 0.154976
\(516\) −17.1579 −0.755335
\(517\) −0.695932 −0.0306070
\(518\) 0 0
\(519\) 3.00321 0.131826
\(520\) −1.99223 −0.0873651
\(521\) 27.8521 1.22022 0.610112 0.792315i \(-0.291124\pi\)
0.610112 + 0.792315i \(0.291124\pi\)
\(522\) −17.6215 −0.771272
\(523\) 25.6651 1.12226 0.561128 0.827729i \(-0.310367\pi\)
0.561128 + 0.827729i \(0.310367\pi\)
\(524\) 5.70033 0.249020
\(525\) 0 0
\(526\) −10.4904 −0.457403
\(527\) −0.758205 −0.0330279
\(528\) 3.29734 0.143498
\(529\) −22.6907 −0.986550
\(530\) 17.0323 0.739836
\(531\) −10.6811 −0.463521
\(532\) 0 0
\(533\) −1.02235 −0.0442827
\(534\) −35.5697 −1.53925
\(535\) 9.64481 0.416981
\(536\) −17.7617 −0.767190
\(537\) 10.3399 0.446202
\(538\) 39.7273 1.71276
\(539\) 0 0
\(540\) −2.65947 −0.114445
\(541\) −24.9672 −1.07342 −0.536711 0.843766i \(-0.680333\pi\)
−0.536711 + 0.843766i \(0.680333\pi\)
\(542\) 11.4955 0.493775
\(543\) −9.54059 −0.409426
\(544\) −4.01001 −0.171928
\(545\) 12.2699 0.525587
\(546\) 0 0
\(547\) 0.176971 0.00756675 0.00378338 0.999993i \(-0.498796\pi\)
0.00378338 + 0.999993i \(0.498796\pi\)
\(548\) 32.5855 1.39198
\(549\) −8.09457 −0.345468
\(550\) −28.4303 −1.21227
\(551\) −27.6981 −1.17998
\(552\) 1.21366 0.0516567
\(553\) 0 0
\(554\) 17.8797 0.759636
\(555\) 10.3078 0.437541
\(556\) 61.3264 2.60082
\(557\) 28.8231 1.22127 0.610636 0.791911i \(-0.290914\pi\)
0.610636 + 0.791911i \(0.290914\pi\)
\(558\) −2.86464 −0.121270
\(559\) 5.89028 0.249132
\(560\) 0 0
\(561\) 1.79057 0.0755981
\(562\) −11.1173 −0.468954
\(563\) 28.9563 1.22036 0.610181 0.792262i \(-0.291097\pi\)
0.610181 + 0.792262i \(0.291097\pi\)
\(564\) 0.683511 0.0287810
\(565\) −2.56920 −0.108087
\(566\) −15.2582 −0.641350
\(567\) 0 0
\(568\) −3.03144 −0.127197
\(569\) 2.87743 0.120628 0.0603140 0.998179i \(-0.480790\pi\)
0.0603140 + 0.998179i \(0.480790\pi\)
\(570\) −6.98768 −0.292682
\(571\) −23.6968 −0.991680 −0.495840 0.868414i \(-0.665140\pi\)
−0.495840 + 0.868414i \(0.665140\pi\)
\(572\) 9.23149 0.385988
\(573\) 3.85532 0.161058
\(574\) 0 0
\(575\) 2.33739 0.0974758
\(576\) −12.9756 −0.540650
\(577\) 25.8656 1.07680 0.538399 0.842690i \(-0.319029\pi\)
0.538399 + 0.842690i \(0.319029\pi\)
\(578\) 37.1514 1.54530
\(579\) 12.2524 0.509194
\(580\) −21.0044 −0.872160
\(581\) 0 0
\(582\) −11.5300 −0.477934
\(583\) −25.9193 −1.07347
\(584\) −23.4667 −0.971060
\(585\) 0.912992 0.0377476
\(586\) −51.6831 −2.13501
\(587\) 42.3285 1.74708 0.873542 0.486750i \(-0.161818\pi\)
0.873542 + 0.486750i \(0.161818\pi\)
\(588\) 0 0
\(589\) −4.50275 −0.185533
\(590\) −21.2821 −0.876170
\(591\) 20.0578 0.825067
\(592\) 12.5520 0.515883
\(593\) 32.3171 1.32711 0.663553 0.748129i \(-0.269048\pi\)
0.663553 + 0.748129i \(0.269048\pi\)
\(594\) 6.76512 0.277576
\(595\) 0 0
\(596\) 9.69470 0.397110
\(597\) −8.76302 −0.358647
\(598\) −1.26868 −0.0518800
\(599\) −34.5668 −1.41236 −0.706181 0.708032i \(-0.749583\pi\)
−0.706181 + 0.708032i \(0.749583\pi\)
\(600\) 9.17019 0.374372
\(601\) 21.2165 0.865439 0.432720 0.901529i \(-0.357554\pi\)
0.432720 + 0.901529i \(0.357554\pi\)
\(602\) 0 0
\(603\) 8.13979 0.331478
\(604\) 35.8571 1.45900
\(605\) 1.61301 0.0655783
\(606\) −23.7179 −0.963474
\(607\) −14.5087 −0.588890 −0.294445 0.955668i \(-0.595135\pi\)
−0.294445 + 0.955668i \(0.595135\pi\)
\(608\) −23.8142 −0.965793
\(609\) 0 0
\(610\) −16.1284 −0.653020
\(611\) −0.234648 −0.00949285
\(612\) −1.75862 −0.0710879
\(613\) −32.3488 −1.30656 −0.653278 0.757118i \(-0.726607\pi\)
−0.653278 + 0.757118i \(0.726607\pi\)
\(614\) 35.7253 1.44175
\(615\) −0.893036 −0.0360107
\(616\) 0 0
\(617\) 0.742674 0.0298989 0.0149495 0.999888i \(-0.495241\pi\)
0.0149495 + 0.999888i \(0.495241\pi\)
\(618\) 8.78674 0.353455
\(619\) 26.3539 1.05925 0.529627 0.848231i \(-0.322332\pi\)
0.529627 + 0.848231i \(0.322332\pi\)
\(620\) −3.41458 −0.137133
\(621\) −0.556191 −0.0223192
\(622\) 46.2086 1.85280
\(623\) 0 0
\(624\) 1.11177 0.0445064
\(625\) 13.6733 0.546933
\(626\) −41.3760 −1.65372
\(627\) 10.6337 0.424668
\(628\) 1.72802 0.0689556
\(629\) 6.81618 0.271779
\(630\) 0 0
\(631\) −20.2431 −0.805867 −0.402933 0.915229i \(-0.632009\pi\)
−0.402933 + 0.915229i \(0.632009\pi\)
\(632\) −10.1911 −0.405381
\(633\) 21.8898 0.870042
\(634\) −46.1141 −1.83142
\(635\) 7.09026 0.281368
\(636\) 25.4567 1.00943
\(637\) 0 0
\(638\) 53.4306 2.11534
\(639\) 1.38924 0.0549575
\(640\) −13.7255 −0.542549
\(641\) 18.2442 0.720604 0.360302 0.932836i \(-0.382674\pi\)
0.360302 + 0.932836i \(0.382674\pi\)
\(642\) 24.0964 0.951010
\(643\) −16.3210 −0.643637 −0.321819 0.946801i \(-0.604294\pi\)
−0.321819 + 0.946801i \(0.604294\pi\)
\(644\) 0 0
\(645\) 5.14525 0.202594
\(646\) −4.62071 −0.181799
\(647\) 47.4111 1.86392 0.931962 0.362556i \(-0.118096\pi\)
0.931962 + 0.362556i \(0.118096\pi\)
\(648\) −2.18209 −0.0857205
\(649\) 32.3865 1.27128
\(650\) −9.58589 −0.375990
\(651\) 0 0
\(652\) 35.6332 1.39550
\(653\) −16.4495 −0.643720 −0.321860 0.946787i \(-0.604308\pi\)
−0.321860 + 0.946787i \(0.604308\pi\)
\(654\) 30.6550 1.19871
\(655\) −1.70940 −0.0667916
\(656\) −1.08747 −0.0424585
\(657\) 10.7543 0.419563
\(658\) 0 0
\(659\) 19.4662 0.758297 0.379148 0.925336i \(-0.376217\pi\)
0.379148 + 0.925336i \(0.376217\pi\)
\(660\) 8.06386 0.313885
\(661\) 29.5252 1.14840 0.574198 0.818716i \(-0.305314\pi\)
0.574198 + 0.818716i \(0.305314\pi\)
\(662\) −8.38648 −0.325950
\(663\) 0.603730 0.0234469
\(664\) −7.04136 −0.273258
\(665\) 0 0
\(666\) 25.7528 0.997900
\(667\) −4.39278 −0.170089
\(668\) −50.6062 −1.95801
\(669\) 19.0053 0.734786
\(670\) 16.2185 0.626575
\(671\) 24.5438 0.947502
\(672\) 0 0
\(673\) 26.0433 1.00390 0.501948 0.864898i \(-0.332617\pi\)
0.501948 + 0.864898i \(0.332617\pi\)
\(674\) 59.9519 2.30926
\(675\) −4.20249 −0.161754
\(676\) −35.6016 −1.36929
\(677\) 1.23438 0.0474410 0.0237205 0.999719i \(-0.492449\pi\)
0.0237205 + 0.999719i \(0.492449\pi\)
\(678\) −6.41884 −0.246514
\(679\) 0 0
\(680\) −1.15076 −0.0441298
\(681\) 14.7021 0.563386
\(682\) 8.68595 0.332602
\(683\) −9.24065 −0.353584 −0.176792 0.984248i \(-0.556572\pi\)
−0.176792 + 0.984248i \(0.556572\pi\)
\(684\) −10.4439 −0.399332
\(685\) −9.77164 −0.373355
\(686\) 0 0
\(687\) 22.7562 0.868203
\(688\) 6.26548 0.238869
\(689\) −8.73926 −0.332939
\(690\) −1.10821 −0.0421888
\(691\) 12.5139 0.476051 0.238026 0.971259i \(-0.423500\pi\)
0.238026 + 0.971259i \(0.423500\pi\)
\(692\) 8.94359 0.339984
\(693\) 0 0
\(694\) 47.8741 1.81728
\(695\) −18.3904 −0.697586
\(696\) −17.2340 −0.653254
\(697\) −0.590534 −0.0223681
\(698\) −58.3516 −2.20864
\(699\) −27.3282 −1.03365
\(700\) 0 0
\(701\) −26.7565 −1.01058 −0.505289 0.862950i \(-0.668614\pi\)
−0.505289 + 0.862950i \(0.668614\pi\)
\(702\) 2.28100 0.0860910
\(703\) 40.4792 1.52670
\(704\) 39.3437 1.48282
\(705\) −0.204969 −0.00771958
\(706\) 8.29347 0.312129
\(707\) 0 0
\(708\) −31.8085 −1.19544
\(709\) 25.9800 0.975698 0.487849 0.872928i \(-0.337782\pi\)
0.487849 + 0.872928i \(0.337782\pi\)
\(710\) 2.76805 0.103883
\(711\) 4.67035 0.175152
\(712\) −34.7876 −1.30372
\(713\) −0.714112 −0.0267437
\(714\) 0 0
\(715\) −2.76831 −0.103529
\(716\) 30.7925 1.15077
\(717\) −12.5731 −0.469551
\(718\) −29.5824 −1.10401
\(719\) −23.7887 −0.887169 −0.443585 0.896232i \(-0.646293\pi\)
−0.443585 + 0.896232i \(0.646293\pi\)
\(720\) 0.971148 0.0361926
\(721\) 0 0
\(722\) 14.9508 0.556411
\(723\) 4.30351 0.160049
\(724\) −28.4120 −1.05592
\(725\) −33.1911 −1.23268
\(726\) 4.02992 0.149564
\(727\) −34.9164 −1.29498 −0.647489 0.762074i \(-0.724181\pi\)
−0.647489 + 0.762074i \(0.724181\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 21.4278 0.793078
\(731\) 3.40238 0.125842
\(732\) −24.1057 −0.890974
\(733\) −1.49359 −0.0551670 −0.0275835 0.999620i \(-0.508781\pi\)
−0.0275835 + 0.999620i \(0.508781\pi\)
\(734\) 43.3077 1.59852
\(735\) 0 0
\(736\) −3.77680 −0.139215
\(737\) −24.6809 −0.909132
\(738\) −2.23115 −0.0821296
\(739\) 35.3095 1.29888 0.649440 0.760413i \(-0.275003\pi\)
0.649440 + 0.760413i \(0.275003\pi\)
\(740\) 30.6967 1.12843
\(741\) 3.58537 0.131712
\(742\) 0 0
\(743\) 20.1868 0.740582 0.370291 0.928916i \(-0.379258\pi\)
0.370291 + 0.928916i \(0.379258\pi\)
\(744\) −2.80165 −0.102714
\(745\) −2.90721 −0.106512
\(746\) −44.1835 −1.61767
\(747\) 3.22689 0.118066
\(748\) 5.33235 0.194970
\(749\) 0 0
\(750\) −18.3359 −0.669532
\(751\) 43.9665 1.60436 0.802180 0.597083i \(-0.203674\pi\)
0.802180 + 0.597083i \(0.203674\pi\)
\(752\) −0.249595 −0.00910179
\(753\) −12.7442 −0.464425
\(754\) 18.0153 0.656078
\(755\) −10.7527 −0.391331
\(756\) 0 0
\(757\) 17.4722 0.635040 0.317520 0.948252i \(-0.397150\pi\)
0.317520 + 0.948252i \(0.397150\pi\)
\(758\) −23.3665 −0.848709
\(759\) 1.68644 0.0612140
\(760\) −6.83403 −0.247896
\(761\) −8.70835 −0.315677 −0.157839 0.987465i \(-0.550453\pi\)
−0.157839 + 0.987465i \(0.550453\pi\)
\(762\) 17.7142 0.641717
\(763\) 0 0
\(764\) 11.4812 0.415375
\(765\) 0.527368 0.0190670
\(766\) −40.0643 −1.44758
\(767\) 10.9198 0.394292
\(768\) −8.34043 −0.300959
\(769\) −18.9265 −0.682507 −0.341253 0.939971i \(-0.610851\pi\)
−0.341253 + 0.939971i \(0.610851\pi\)
\(770\) 0 0
\(771\) −15.3531 −0.552929
\(772\) 36.4879 1.31323
\(773\) 32.6886 1.17573 0.587864 0.808960i \(-0.299969\pi\)
0.587864 + 0.808960i \(0.299969\pi\)
\(774\) 12.8548 0.462057
\(775\) −5.39570 −0.193819
\(776\) −11.2765 −0.404802
\(777\) 0 0
\(778\) −69.7686 −2.50132
\(779\) −3.50700 −0.125651
\(780\) 2.71890 0.0973523
\(781\) −4.21235 −0.150730
\(782\) −0.732820 −0.0262056
\(783\) 7.89796 0.282250
\(784\) 0 0
\(785\) −0.518193 −0.0184951
\(786\) −4.27072 −0.152332
\(787\) 54.7501 1.95163 0.975814 0.218601i \(-0.0701494\pi\)
0.975814 + 0.218601i \(0.0701494\pi\)
\(788\) 59.7323 2.12788
\(789\) 4.70180 0.167388
\(790\) 9.30565 0.331080
\(791\) 0 0
\(792\) 6.61637 0.235102
\(793\) 8.27546 0.293870
\(794\) −65.7801 −2.33445
\(795\) −7.63388 −0.270746
\(796\) −26.0964 −0.924962
\(797\) 44.9819 1.59334 0.796671 0.604414i \(-0.206593\pi\)
0.796671 + 0.604414i \(0.206593\pi\)
\(798\) 0 0
\(799\) −0.135539 −0.00479502
\(800\) −28.5369 −1.00893
\(801\) 15.9423 0.563295
\(802\) 25.2452 0.891439
\(803\) −32.6082 −1.15072
\(804\) 24.2404 0.854893
\(805\) 0 0
\(806\) 2.92865 0.103157
\(807\) −17.8058 −0.626792
\(808\) −23.1964 −0.816046
\(809\) 11.9297 0.419425 0.209713 0.977763i \(-0.432747\pi\)
0.209713 + 0.977763i \(0.432747\pi\)
\(810\) 1.99249 0.0700091
\(811\) 6.14692 0.215848 0.107924 0.994159i \(-0.465580\pi\)
0.107924 + 0.994159i \(0.465580\pi\)
\(812\) 0 0
\(813\) −5.15229 −0.180699
\(814\) −78.0857 −2.73690
\(815\) −10.6856 −0.374299
\(816\) 0.642187 0.0224810
\(817\) 20.2057 0.706908
\(818\) −42.2258 −1.47639
\(819\) 0 0
\(820\) −2.65947 −0.0928728
\(821\) 28.1002 0.980702 0.490351 0.871525i \(-0.336869\pi\)
0.490351 + 0.871525i \(0.336869\pi\)
\(822\) −24.4133 −0.851511
\(823\) 10.2799 0.358334 0.179167 0.983819i \(-0.442660\pi\)
0.179167 + 0.983819i \(0.442660\pi\)
\(824\) 8.59354 0.299370
\(825\) 12.7425 0.443636
\(826\) 0 0
\(827\) −42.5878 −1.48092 −0.740462 0.672098i \(-0.765393\pi\)
−0.740462 + 0.672098i \(0.765393\pi\)
\(828\) −1.65634 −0.0575620
\(829\) −15.6799 −0.544586 −0.272293 0.962214i \(-0.587782\pi\)
−0.272293 + 0.962214i \(0.587782\pi\)
\(830\) 6.42956 0.223173
\(831\) −8.01369 −0.277992
\(832\) 13.2656 0.459901
\(833\) 0 0
\(834\) −45.9462 −1.59099
\(835\) 15.1756 0.525174
\(836\) 31.6672 1.09523
\(837\) 1.28393 0.0443792
\(838\) −25.1732 −0.869595
\(839\) 46.4057 1.60210 0.801052 0.598595i \(-0.204274\pi\)
0.801052 + 0.598595i \(0.204274\pi\)
\(840\) 0 0
\(841\) 33.3777 1.15096
\(842\) −3.28119 −0.113077
\(843\) 4.98277 0.171616
\(844\) 65.1881 2.24387
\(845\) 10.6761 0.367268
\(846\) −0.512091 −0.0176061
\(847\) 0 0
\(848\) −9.29593 −0.319224
\(849\) 6.83872 0.234704
\(850\) −5.53706 −0.189920
\(851\) 6.41978 0.220067
\(852\) 4.13717 0.141737
\(853\) 23.0031 0.787611 0.393805 0.919194i \(-0.371158\pi\)
0.393805 + 0.919194i \(0.371158\pi\)
\(854\) 0 0
\(855\) 3.13188 0.107108
\(856\) 23.5666 0.805489
\(857\) −4.92156 −0.168117 −0.0840587 0.996461i \(-0.526788\pi\)
−0.0840587 + 0.996461i \(0.526788\pi\)
\(858\) −6.91629 −0.236118
\(859\) 7.76979 0.265102 0.132551 0.991176i \(-0.457683\pi\)
0.132551 + 0.991176i \(0.457683\pi\)
\(860\) 15.3226 0.522497
\(861\) 0 0
\(862\) 10.9421 0.372689
\(863\) −12.3757 −0.421274 −0.210637 0.977564i \(-0.567554\pi\)
−0.210637 + 0.977564i \(0.567554\pi\)
\(864\) 6.79048 0.231017
\(865\) −2.68197 −0.0911898
\(866\) 20.5401 0.697980
\(867\) −16.6513 −0.565507
\(868\) 0 0
\(869\) −14.1611 −0.480382
\(870\) 15.7366 0.533522
\(871\) −8.32169 −0.281970
\(872\) 29.9810 1.01528
\(873\) 5.16775 0.174902
\(874\) −4.35199 −0.147208
\(875\) 0 0
\(876\) 32.0263 1.08207
\(877\) −31.0076 −1.04705 −0.523526 0.852010i \(-0.675384\pi\)
−0.523526 + 0.852010i \(0.675384\pi\)
\(878\) 53.6328 1.81002
\(879\) 23.1644 0.781315
\(880\) −2.94464 −0.0992639
\(881\) 49.0117 1.65125 0.825624 0.564221i \(-0.190824\pi\)
0.825624 + 0.564221i \(0.190824\pi\)
\(882\) 0 0
\(883\) 52.3902 1.76307 0.881535 0.472119i \(-0.156511\pi\)
0.881535 + 0.472119i \(0.156511\pi\)
\(884\) 1.79792 0.0604705
\(885\) 9.53863 0.320638
\(886\) 49.8603 1.67509
\(887\) 49.6047 1.66556 0.832781 0.553603i \(-0.186747\pi\)
0.832781 + 0.553603i \(0.186747\pi\)
\(888\) 25.1865 0.845204
\(889\) 0 0
\(890\) 31.7650 1.06477
\(891\) −3.03213 −0.101580
\(892\) 56.5979 1.89504
\(893\) −0.804924 −0.0269358
\(894\) −7.26333 −0.242922
\(895\) −9.23395 −0.308657
\(896\) 0 0
\(897\) 0.568620 0.0189857
\(898\) −33.6559 −1.12311
\(899\) 10.1404 0.338202
\(900\) −12.5151 −0.417169
\(901\) −5.04802 −0.168174
\(902\) 6.76512 0.225254
\(903\) 0 0
\(904\) −6.27771 −0.208793
\(905\) 8.52009 0.283217
\(906\) −26.8644 −0.892509
\(907\) 1.69849 0.0563974 0.0281987 0.999602i \(-0.491023\pi\)
0.0281987 + 0.999602i \(0.491023\pi\)
\(908\) 43.7831 1.45299
\(909\) 10.6304 0.352587
\(910\) 0 0
\(911\) −7.66674 −0.254010 −0.127005 0.991902i \(-0.540537\pi\)
−0.127005 + 0.991902i \(0.540537\pi\)
\(912\) 3.81375 0.126286
\(913\) −9.78434 −0.323814
\(914\) 26.6578 0.881761
\(915\) 7.22875 0.238975
\(916\) 67.7682 2.23913
\(917\) 0 0
\(918\) 1.31757 0.0434862
\(919\) 29.6626 0.978480 0.489240 0.872149i \(-0.337274\pi\)
0.489240 + 0.872149i \(0.337274\pi\)
\(920\) −1.08384 −0.0357332
\(921\) −16.0121 −0.527616
\(922\) 19.4988 0.642159
\(923\) −1.42029 −0.0467493
\(924\) 0 0
\(925\) 48.5068 1.59489
\(926\) 72.2692 2.37491
\(927\) −3.93822 −0.129348
\(928\) 53.6309 1.76052
\(929\) −46.0046 −1.50936 −0.754681 0.656091i \(-0.772209\pi\)
−0.754681 + 0.656091i \(0.772209\pi\)
\(930\) 2.55823 0.0838875
\(931\) 0 0
\(932\) −81.3836 −2.66581
\(933\) −20.7107 −0.678038
\(934\) −0.730722 −0.0239100
\(935\) −1.59905 −0.0522944
\(936\) 2.23085 0.0729176
\(937\) 21.8284 0.713102 0.356551 0.934276i \(-0.383953\pi\)
0.356551 + 0.934276i \(0.383953\pi\)
\(938\) 0 0
\(939\) 18.5447 0.605185
\(940\) −0.610400 −0.0199091
\(941\) −27.7442 −0.904435 −0.452217 0.891908i \(-0.649367\pi\)
−0.452217 + 0.891908i \(0.649367\pi\)
\(942\) −1.29464 −0.0421818
\(943\) −0.556191 −0.0181121
\(944\) 11.6154 0.378049
\(945\) 0 0
\(946\) −38.9774 −1.26727
\(947\) −12.5298 −0.407163 −0.203581 0.979058i \(-0.565258\pi\)
−0.203581 + 0.979058i \(0.565258\pi\)
\(948\) 13.9084 0.451723
\(949\) −10.9946 −0.356899
\(950\) −32.8829 −1.06686
\(951\) 20.6683 0.670217
\(952\) 0 0
\(953\) −21.2076 −0.686981 −0.343491 0.939156i \(-0.611609\pi\)
−0.343491 + 0.939156i \(0.611609\pi\)
\(954\) −19.0724 −0.617490
\(955\) −3.44294 −0.111411
\(956\) −37.4428 −1.21099
\(957\) −23.9476 −0.774116
\(958\) 12.9900 0.419688
\(959\) 0 0
\(960\) 11.5877 0.373991
\(961\) −29.3515 −0.946823
\(962\) −26.3283 −0.848857
\(963\) −10.8000 −0.348026
\(964\) 12.8159 0.412773
\(965\) −10.9419 −0.352231
\(966\) 0 0
\(967\) −15.6750 −0.504073 −0.252037 0.967718i \(-0.581100\pi\)
−0.252037 + 0.967718i \(0.581100\pi\)
\(968\) 3.94131 0.126679
\(969\) 2.07100 0.0665302
\(970\) 10.2967 0.330608
\(971\) −32.1713 −1.03243 −0.516214 0.856460i \(-0.672659\pi\)
−0.516214 + 0.856460i \(0.672659\pi\)
\(972\) 2.97801 0.0955198
\(973\) 0 0
\(974\) 54.7330 1.75376
\(975\) 4.29640 0.137595
\(976\) 8.80259 0.281764
\(977\) −21.8155 −0.697940 −0.348970 0.937134i \(-0.613468\pi\)
−0.348970 + 0.937134i \(0.613468\pi\)
\(978\) −26.6966 −0.853663
\(979\) −48.3392 −1.54493
\(980\) 0 0
\(981\) −13.7396 −0.438671
\(982\) −46.9571 −1.49846
\(983\) 42.4637 1.35438 0.677191 0.735808i \(-0.263197\pi\)
0.677191 + 0.735808i \(0.263197\pi\)
\(984\) −2.18209 −0.0695624
\(985\) −17.9123 −0.570734
\(986\) 10.4061 0.331397
\(987\) 0 0
\(988\) 10.6773 0.339689
\(989\) 3.20451 0.101898
\(990\) −6.04149 −0.192011
\(991\) −60.9054 −1.93473 −0.967363 0.253396i \(-0.918452\pi\)
−0.967363 + 0.253396i \(0.918452\pi\)
\(992\) 8.71851 0.276813
\(993\) 3.75882 0.119283
\(994\) 0 0
\(995\) 7.82569 0.248091
\(996\) 9.60972 0.304496
\(997\) 19.4303 0.615363 0.307681 0.951489i \(-0.400447\pi\)
0.307681 + 0.951489i \(0.400447\pi\)
\(998\) −47.8554 −1.51484
\(999\) −11.5424 −0.365185
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 \(a_p\))