Properties

Label 6027.2.a.bo.1.18
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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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: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.95065 q^{2} +1.00000 q^{3} +1.80504 q^{4} +2.46699 q^{5} +1.95065 q^{6} -0.380308 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.95065 q^{2} +1.00000 q^{3} +1.80504 q^{4} +2.46699 q^{5} +1.95065 q^{6} -0.380308 q^{8} +1.00000 q^{9} +4.81223 q^{10} +3.40967 q^{11} +1.80504 q^{12} +3.78591 q^{13} +2.46699 q^{15} -4.35192 q^{16} -7.48620 q^{17} +1.95065 q^{18} +1.93227 q^{19} +4.45300 q^{20} +6.65108 q^{22} -1.38797 q^{23} -0.380308 q^{24} +1.08602 q^{25} +7.38498 q^{26} +1.00000 q^{27} +4.33428 q^{29} +4.81223 q^{30} +10.1756 q^{31} -7.72845 q^{32} +3.40967 q^{33} -14.6030 q^{34} +1.80504 q^{36} +8.77161 q^{37} +3.76918 q^{38} +3.78591 q^{39} -0.938215 q^{40} -1.00000 q^{41} -5.71076 q^{43} +6.15458 q^{44} +2.46699 q^{45} -2.70744 q^{46} +4.34350 q^{47} -4.35192 q^{48} +2.11845 q^{50} -7.48620 q^{51} +6.83369 q^{52} +4.49496 q^{53} +1.95065 q^{54} +8.41161 q^{55} +1.93227 q^{57} +8.45467 q^{58} +9.48620 q^{59} +4.45300 q^{60} -12.7058 q^{61} +19.8490 q^{62} -6.37167 q^{64} +9.33978 q^{65} +6.65108 q^{66} +8.88133 q^{67} -13.5129 q^{68} -1.38797 q^{69} +16.4496 q^{71} -0.380308 q^{72} -0.523059 q^{73} +17.1103 q^{74} +1.08602 q^{75} +3.48781 q^{76} +7.38498 q^{78} -11.0022 q^{79} -10.7361 q^{80} +1.00000 q^{81} -1.95065 q^{82} +14.1159 q^{83} -18.4684 q^{85} -11.1397 q^{86} +4.33428 q^{87} -1.29673 q^{88} -18.8161 q^{89} +4.81223 q^{90} -2.50533 q^{92} +10.1756 q^{93} +8.47265 q^{94} +4.76688 q^{95} -7.72845 q^{96} -8.05622 q^{97} +3.40967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.95065 1.37932 0.689659 0.724134i \(-0.257760\pi\)
0.689659 + 0.724134i \(0.257760\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.80504 0.902518
\(5\) 2.46699 1.10327 0.551635 0.834086i \(-0.314004\pi\)
0.551635 + 0.834086i \(0.314004\pi\)
\(6\) 1.95065 0.796349
\(7\) 0 0
\(8\) −0.380308 −0.134459
\(9\) 1.00000 0.333333
\(10\) 4.81223 1.52176
\(11\) 3.40967 1.02805 0.514027 0.857774i \(-0.328153\pi\)
0.514027 + 0.857774i \(0.328153\pi\)
\(12\) 1.80504 0.521069
\(13\) 3.78591 1.05002 0.525011 0.851096i \(-0.324061\pi\)
0.525011 + 0.851096i \(0.324061\pi\)
\(14\) 0 0
\(15\) 2.46699 0.636973
\(16\) −4.35192 −1.08798
\(17\) −7.48620 −1.81567 −0.907835 0.419327i \(-0.862266\pi\)
−0.907835 + 0.419327i \(0.862266\pi\)
\(18\) 1.95065 0.459773
\(19\) 1.93227 0.443293 0.221646 0.975127i \(-0.428857\pi\)
0.221646 + 0.975127i \(0.428857\pi\)
\(20\) 4.45300 0.995720
\(21\) 0 0
\(22\) 6.65108 1.41801
\(23\) −1.38797 −0.289412 −0.144706 0.989475i \(-0.546224\pi\)
−0.144706 + 0.989475i \(0.546224\pi\)
\(24\) −0.380308 −0.0776301
\(25\) 1.08602 0.217204
\(26\) 7.38498 1.44831
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.33428 0.804856 0.402428 0.915452i \(-0.368166\pi\)
0.402428 + 0.915452i \(0.368166\pi\)
\(30\) 4.81223 0.878588
\(31\) 10.1756 1.82759 0.913795 0.406175i \(-0.133138\pi\)
0.913795 + 0.406175i \(0.133138\pi\)
\(32\) −7.72845 −1.36621
\(33\) 3.40967 0.593548
\(34\) −14.6030 −2.50439
\(35\) 0 0
\(36\) 1.80504 0.300839
\(37\) 8.77161 1.44204 0.721022 0.692913i \(-0.243673\pi\)
0.721022 + 0.692913i \(0.243673\pi\)
\(38\) 3.76918 0.611441
\(39\) 3.78591 0.606230
\(40\) −0.938215 −0.148345
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −5.71076 −0.870883 −0.435442 0.900217i \(-0.643408\pi\)
−0.435442 + 0.900217i \(0.643408\pi\)
\(44\) 6.15458 0.927838
\(45\) 2.46699 0.367757
\(46\) −2.70744 −0.399191
\(47\) 4.34350 0.633565 0.316782 0.948498i \(-0.397398\pi\)
0.316782 + 0.948498i \(0.397398\pi\)
\(48\) −4.35192 −0.628145
\(49\) 0 0
\(50\) 2.11845 0.299593
\(51\) −7.48620 −1.04828
\(52\) 6.83369 0.947662
\(53\) 4.49496 0.617430 0.308715 0.951155i \(-0.400101\pi\)
0.308715 + 0.951155i \(0.400101\pi\)
\(54\) 1.95065 0.265450
\(55\) 8.41161 1.13422
\(56\) 0 0
\(57\) 1.93227 0.255935
\(58\) 8.45467 1.11015
\(59\) 9.48620 1.23500 0.617499 0.786571i \(-0.288146\pi\)
0.617499 + 0.786571i \(0.288146\pi\)
\(60\) 4.45300 0.574879
\(61\) −12.7058 −1.62681 −0.813404 0.581699i \(-0.802388\pi\)
−0.813404 + 0.581699i \(0.802388\pi\)
\(62\) 19.8490 2.52083
\(63\) 0 0
\(64\) −6.37167 −0.796459
\(65\) 9.33978 1.15846
\(66\) 6.65108 0.818691
\(67\) 8.88133 1.08503 0.542514 0.840047i \(-0.317473\pi\)
0.542514 + 0.840047i \(0.317473\pi\)
\(68\) −13.5129 −1.63867
\(69\) −1.38797 −0.167092
\(70\) 0 0
\(71\) 16.4496 1.95221 0.976106 0.217294i \(-0.0697230\pi\)
0.976106 + 0.217294i \(0.0697230\pi\)
\(72\) −0.380308 −0.0448198
\(73\) −0.523059 −0.0612195 −0.0306097 0.999531i \(-0.509745\pi\)
−0.0306097 + 0.999531i \(0.509745\pi\)
\(74\) 17.1103 1.98904
\(75\) 1.08602 0.125403
\(76\) 3.48781 0.400079
\(77\) 0 0
\(78\) 7.38498 0.836184
\(79\) −11.0022 −1.23784 −0.618922 0.785452i \(-0.712430\pi\)
−0.618922 + 0.785452i \(0.712430\pi\)
\(80\) −10.7361 −1.20033
\(81\) 1.00000 0.111111
\(82\) −1.95065 −0.215413
\(83\) 14.1159 1.54942 0.774709 0.632318i \(-0.217896\pi\)
0.774709 + 0.632318i \(0.217896\pi\)
\(84\) 0 0
\(85\) −18.4684 −2.00317
\(86\) −11.1397 −1.20122
\(87\) 4.33428 0.464684
\(88\) −1.29673 −0.138232
\(89\) −18.8161 −1.99450 −0.997251 0.0740962i \(-0.976393\pi\)
−0.997251 + 0.0740962i \(0.976393\pi\)
\(90\) 4.81223 0.507253
\(91\) 0 0
\(92\) −2.50533 −0.261199
\(93\) 10.1756 1.05516
\(94\) 8.47265 0.873887
\(95\) 4.76688 0.489071
\(96\) −7.72845 −0.788782
\(97\) −8.05622 −0.817985 −0.408993 0.912538i \(-0.634120\pi\)
−0.408993 + 0.912538i \(0.634120\pi\)
\(98\) 0 0
\(99\) 3.40967 0.342685
\(100\) 1.96030 0.196030
\(101\) −19.1657 −1.90706 −0.953529 0.301302i \(-0.902579\pi\)
−0.953529 + 0.301302i \(0.902579\pi\)
\(102\) −14.6030 −1.44591
\(103\) −15.3244 −1.50996 −0.754979 0.655749i \(-0.772353\pi\)
−0.754979 + 0.655749i \(0.772353\pi\)
\(104\) −1.43981 −0.141185
\(105\) 0 0
\(106\) 8.76810 0.851633
\(107\) 8.53803 0.825403 0.412701 0.910866i \(-0.364585\pi\)
0.412701 + 0.910866i \(0.364585\pi\)
\(108\) 1.80504 0.173690
\(109\) 14.3317 1.37273 0.686366 0.727256i \(-0.259205\pi\)
0.686366 + 0.727256i \(0.259205\pi\)
\(110\) 16.4081 1.56445
\(111\) 8.77161 0.832564
\(112\) 0 0
\(113\) 0.0125194 0.00117773 0.000588865 1.00000i \(-0.499813\pi\)
0.000588865 1.00000i \(0.499813\pi\)
\(114\) 3.76918 0.353016
\(115\) −3.42410 −0.319299
\(116\) 7.82353 0.726397
\(117\) 3.78591 0.350007
\(118\) 18.5043 1.70346
\(119\) 0 0
\(120\) −0.938215 −0.0856469
\(121\) 0.625868 0.0568971
\(122\) −24.7845 −2.24389
\(123\) −1.00000 −0.0901670
\(124\) 18.3673 1.64943
\(125\) −9.65573 −0.863635
\(126\) 0 0
\(127\) −2.83107 −0.251217 −0.125608 0.992080i \(-0.540088\pi\)
−0.125608 + 0.992080i \(0.540088\pi\)
\(128\) 3.02801 0.267641
\(129\) −5.71076 −0.502805
\(130\) 18.2186 1.59788
\(131\) −8.54530 −0.746607 −0.373303 0.927709i \(-0.621775\pi\)
−0.373303 + 0.927709i \(0.621775\pi\)
\(132\) 6.15458 0.535687
\(133\) 0 0
\(134\) 17.3244 1.49660
\(135\) 2.46699 0.212324
\(136\) 2.84706 0.244134
\(137\) −3.47348 −0.296760 −0.148380 0.988930i \(-0.547406\pi\)
−0.148380 + 0.988930i \(0.547406\pi\)
\(138\) −2.70744 −0.230473
\(139\) 2.23775 0.189804 0.0949018 0.995487i \(-0.469746\pi\)
0.0949018 + 0.995487i \(0.469746\pi\)
\(140\) 0 0
\(141\) 4.34350 0.365789
\(142\) 32.0875 2.69272
\(143\) 12.9087 1.07948
\(144\) −4.35192 −0.362660
\(145\) 10.6926 0.887973
\(146\) −1.02031 −0.0844411
\(147\) 0 0
\(148\) 15.8331 1.30147
\(149\) 8.91994 0.730750 0.365375 0.930860i \(-0.380941\pi\)
0.365375 + 0.930860i \(0.380941\pi\)
\(150\) 2.11845 0.172970
\(151\) −11.9438 −0.971974 −0.485987 0.873966i \(-0.661540\pi\)
−0.485987 + 0.873966i \(0.661540\pi\)
\(152\) −0.734858 −0.0596048
\(153\) −7.48620 −0.605223
\(154\) 0 0
\(155\) 25.1031 2.01633
\(156\) 6.83369 0.547133
\(157\) −17.3359 −1.38356 −0.691778 0.722110i \(-0.743172\pi\)
−0.691778 + 0.722110i \(0.743172\pi\)
\(158\) −21.4614 −1.70738
\(159\) 4.49496 0.356474
\(160\) −19.0660 −1.50730
\(161\) 0 0
\(162\) 1.95065 0.153258
\(163\) −1.43399 −0.112319 −0.0561593 0.998422i \(-0.517885\pi\)
−0.0561593 + 0.998422i \(0.517885\pi\)
\(164\) −1.80504 −0.140950
\(165\) 8.41161 0.654843
\(166\) 27.5351 2.13714
\(167\) −16.8506 −1.30394 −0.651971 0.758244i \(-0.726058\pi\)
−0.651971 + 0.758244i \(0.726058\pi\)
\(168\) 0 0
\(169\) 1.33308 0.102544
\(170\) −36.0253 −2.76301
\(171\) 1.93227 0.147764
\(172\) −10.3081 −0.785987
\(173\) −2.36949 −0.180149 −0.0900744 0.995935i \(-0.528710\pi\)
−0.0900744 + 0.995935i \(0.528710\pi\)
\(174\) 8.45467 0.640947
\(175\) 0 0
\(176\) −14.8386 −1.11850
\(177\) 9.48620 0.713027
\(178\) −36.7036 −2.75105
\(179\) −12.3125 −0.920279 −0.460139 0.887847i \(-0.652201\pi\)
−0.460139 + 0.887847i \(0.652201\pi\)
\(180\) 4.45300 0.331907
\(181\) 24.0143 1.78497 0.892483 0.451080i \(-0.148961\pi\)
0.892483 + 0.451080i \(0.148961\pi\)
\(182\) 0 0
\(183\) −12.7058 −0.939238
\(184\) 0.527856 0.0389141
\(185\) 21.6394 1.59096
\(186\) 19.8490 1.45540
\(187\) −25.5255 −1.86661
\(188\) 7.84017 0.571803
\(189\) 0 0
\(190\) 9.29851 0.674585
\(191\) 10.0853 0.729747 0.364873 0.931057i \(-0.381112\pi\)
0.364873 + 0.931057i \(0.381112\pi\)
\(192\) −6.37167 −0.459836
\(193\) 4.38437 0.315594 0.157797 0.987472i \(-0.449561\pi\)
0.157797 + 0.987472i \(0.449561\pi\)
\(194\) −15.7149 −1.12826
\(195\) 9.33978 0.668835
\(196\) 0 0
\(197\) −5.57135 −0.396942 −0.198471 0.980107i \(-0.563598\pi\)
−0.198471 + 0.980107i \(0.563598\pi\)
\(198\) 6.65108 0.472672
\(199\) −19.2500 −1.36460 −0.682300 0.731072i \(-0.739020\pi\)
−0.682300 + 0.731072i \(0.739020\pi\)
\(200\) −0.413023 −0.0292051
\(201\) 8.88133 0.626441
\(202\) −37.3856 −2.63044
\(203\) 0 0
\(204\) −13.5129 −0.946089
\(205\) −2.46699 −0.172302
\(206\) −29.8925 −2.08271
\(207\) −1.38797 −0.0964705
\(208\) −16.4760 −1.14240
\(209\) 6.58840 0.455729
\(210\) 0 0
\(211\) −5.16241 −0.355395 −0.177698 0.984085i \(-0.556865\pi\)
−0.177698 + 0.984085i \(0.556865\pi\)
\(212\) 8.11356 0.557242
\(213\) 16.4496 1.12711
\(214\) 16.6547 1.13849
\(215\) −14.0884 −0.960819
\(216\) −0.380308 −0.0258767
\(217\) 0 0
\(218\) 27.9562 1.89343
\(219\) −0.523059 −0.0353451
\(220\) 15.1833 1.02366
\(221\) −28.3420 −1.90649
\(222\) 17.1103 1.14837
\(223\) 5.91934 0.396388 0.198194 0.980163i \(-0.436492\pi\)
0.198194 + 0.980163i \(0.436492\pi\)
\(224\) 0 0
\(225\) 1.08602 0.0724014
\(226\) 0.0244210 0.00162446
\(227\) −24.0214 −1.59435 −0.797177 0.603746i \(-0.793674\pi\)
−0.797177 + 0.603746i \(0.793674\pi\)
\(228\) 3.48781 0.230986
\(229\) −5.99435 −0.396118 −0.198059 0.980190i \(-0.563464\pi\)
−0.198059 + 0.980190i \(0.563464\pi\)
\(230\) −6.67922 −0.440415
\(231\) 0 0
\(232\) −1.64836 −0.108220
\(233\) 16.8529 1.10407 0.552035 0.833821i \(-0.313851\pi\)
0.552035 + 0.833821i \(0.313851\pi\)
\(234\) 7.38498 0.482771
\(235\) 10.7154 0.698993
\(236\) 17.1229 1.11461
\(237\) −11.0022 −0.714670
\(238\) 0 0
\(239\) 1.05568 0.0682864 0.0341432 0.999417i \(-0.489130\pi\)
0.0341432 + 0.999417i \(0.489130\pi\)
\(240\) −10.7361 −0.693014
\(241\) 29.7927 1.91911 0.959557 0.281515i \(-0.0908368\pi\)
0.959557 + 0.281515i \(0.0908368\pi\)
\(242\) 1.22085 0.0784791
\(243\) 1.00000 0.0641500
\(244\) −22.9344 −1.46822
\(245\) 0 0
\(246\) −1.95065 −0.124369
\(247\) 7.31538 0.465467
\(248\) −3.86986 −0.245737
\(249\) 14.1159 0.894557
\(250\) −18.8350 −1.19123
\(251\) 16.0282 1.01169 0.505845 0.862624i \(-0.331181\pi\)
0.505845 + 0.862624i \(0.331181\pi\)
\(252\) 0 0
\(253\) −4.73252 −0.297531
\(254\) −5.52243 −0.346508
\(255\) −18.4684 −1.15653
\(256\) 18.6499 1.16562
\(257\) −3.41486 −0.213013 −0.106507 0.994312i \(-0.533967\pi\)
−0.106507 + 0.994312i \(0.533967\pi\)
\(258\) −11.1397 −0.693527
\(259\) 0 0
\(260\) 16.8586 1.04553
\(261\) 4.33428 0.268285
\(262\) −16.6689 −1.02981
\(263\) −6.96532 −0.429500 −0.214750 0.976669i \(-0.568894\pi\)
−0.214750 + 0.976669i \(0.568894\pi\)
\(264\) −1.29673 −0.0798080
\(265\) 11.0890 0.681192
\(266\) 0 0
\(267\) −18.8161 −1.15153
\(268\) 16.0311 0.979256
\(269\) 7.67353 0.467863 0.233932 0.972253i \(-0.424841\pi\)
0.233932 + 0.972253i \(0.424841\pi\)
\(270\) 4.81223 0.292863
\(271\) −28.1522 −1.71013 −0.855063 0.518525i \(-0.826481\pi\)
−0.855063 + 0.518525i \(0.826481\pi\)
\(272\) 32.5793 1.97541
\(273\) 0 0
\(274\) −6.77555 −0.409326
\(275\) 3.70297 0.223298
\(276\) −2.50533 −0.150803
\(277\) 4.85108 0.291473 0.145737 0.989323i \(-0.453445\pi\)
0.145737 + 0.989323i \(0.453445\pi\)
\(278\) 4.36507 0.261800
\(279\) 10.1756 0.609197
\(280\) 0 0
\(281\) −13.4939 −0.804977 −0.402489 0.915425i \(-0.631855\pi\)
−0.402489 + 0.915425i \(0.631855\pi\)
\(282\) 8.47265 0.504539
\(283\) −3.39249 −0.201662 −0.100831 0.994904i \(-0.532150\pi\)
−0.100831 + 0.994904i \(0.532150\pi\)
\(284\) 29.6922 1.76191
\(285\) 4.76688 0.282365
\(286\) 25.1803 1.48895
\(287\) 0 0
\(288\) −7.72845 −0.455403
\(289\) 39.0432 2.29666
\(290\) 20.8576 1.22480
\(291\) −8.05622 −0.472264
\(292\) −0.944140 −0.0552516
\(293\) 19.8814 1.16148 0.580742 0.814088i \(-0.302763\pi\)
0.580742 + 0.814088i \(0.302763\pi\)
\(294\) 0 0
\(295\) 23.4023 1.36254
\(296\) −3.33592 −0.193896
\(297\) 3.40967 0.197849
\(298\) 17.3997 1.00794
\(299\) −5.25472 −0.303888
\(300\) 1.96030 0.113178
\(301\) 0 0
\(302\) −23.2982 −1.34066
\(303\) −19.1657 −1.10104
\(304\) −8.40907 −0.482293
\(305\) −31.3450 −1.79481
\(306\) −14.6030 −0.834795
\(307\) 20.5502 1.17286 0.586431 0.809999i \(-0.300533\pi\)
0.586431 + 0.809999i \(0.300533\pi\)
\(308\) 0 0
\(309\) −15.3244 −0.871774
\(310\) 48.9673 2.78115
\(311\) −7.09527 −0.402336 −0.201168 0.979557i \(-0.564474\pi\)
−0.201168 + 0.979557i \(0.564474\pi\)
\(312\) −1.43981 −0.0815133
\(313\) −10.8328 −0.612308 −0.306154 0.951982i \(-0.599042\pi\)
−0.306154 + 0.951982i \(0.599042\pi\)
\(314\) −33.8163 −1.90836
\(315\) 0 0
\(316\) −19.8594 −1.11718
\(317\) 15.8780 0.891799 0.445900 0.895083i \(-0.352884\pi\)
0.445900 + 0.895083i \(0.352884\pi\)
\(318\) 8.76810 0.491690
\(319\) 14.7785 0.827436
\(320\) −15.7188 −0.878709
\(321\) 8.53803 0.476547
\(322\) 0 0
\(323\) −14.4653 −0.804873
\(324\) 1.80504 0.100280
\(325\) 4.11157 0.228069
\(326\) −2.79721 −0.154923
\(327\) 14.3317 0.792548
\(328\) 0.380308 0.0209990
\(329\) 0 0
\(330\) 16.4081 0.903237
\(331\) 8.57678 0.471423 0.235711 0.971823i \(-0.424258\pi\)
0.235711 + 0.971823i \(0.424258\pi\)
\(332\) 25.4796 1.39838
\(333\) 8.77161 0.480681
\(334\) −32.8697 −1.79855
\(335\) 21.9101 1.19708
\(336\) 0 0
\(337\) −11.6799 −0.636247 −0.318123 0.948049i \(-0.603053\pi\)
−0.318123 + 0.948049i \(0.603053\pi\)
\(338\) 2.60037 0.141441
\(339\) 0.0125194 0.000679963 0
\(340\) −33.3360 −1.80790
\(341\) 34.6954 1.87886
\(342\) 3.76918 0.203814
\(343\) 0 0
\(344\) 2.17185 0.117098
\(345\) −3.42410 −0.184347
\(346\) −4.62204 −0.248483
\(347\) −8.68399 −0.466181 −0.233091 0.972455i \(-0.574884\pi\)
−0.233091 + 0.972455i \(0.574884\pi\)
\(348\) 7.82353 0.419385
\(349\) −18.9911 −1.01657 −0.508284 0.861189i \(-0.669720\pi\)
−0.508284 + 0.861189i \(0.669720\pi\)
\(350\) 0 0
\(351\) 3.78591 0.202077
\(352\) −26.3515 −1.40454
\(353\) 11.8748 0.632030 0.316015 0.948754i \(-0.397655\pi\)
0.316015 + 0.948754i \(0.397655\pi\)
\(354\) 18.5043 0.983490
\(355\) 40.5810 2.15382
\(356\) −33.9637 −1.80007
\(357\) 0 0
\(358\) −24.0174 −1.26936
\(359\) −30.1157 −1.58944 −0.794722 0.606973i \(-0.792384\pi\)
−0.794722 + 0.606973i \(0.792384\pi\)
\(360\) −0.938215 −0.0494483
\(361\) −15.2663 −0.803492
\(362\) 46.8434 2.46204
\(363\) 0.625868 0.0328495
\(364\) 0 0
\(365\) −1.29038 −0.0675416
\(366\) −24.7845 −1.29551
\(367\) 4.88812 0.255158 0.127579 0.991828i \(-0.459279\pi\)
0.127579 + 0.991828i \(0.459279\pi\)
\(368\) 6.04033 0.314874
\(369\) −1.00000 −0.0520579
\(370\) 42.2110 2.19444
\(371\) 0 0
\(372\) 18.3673 0.952300
\(373\) −15.8244 −0.819358 −0.409679 0.912230i \(-0.634359\pi\)
−0.409679 + 0.912230i \(0.634359\pi\)
\(374\) −49.7913 −2.57465
\(375\) −9.65573 −0.498620
\(376\) −1.65187 −0.0851886
\(377\) 16.4092 0.845116
\(378\) 0 0
\(379\) 13.5020 0.693549 0.346774 0.937949i \(-0.387277\pi\)
0.346774 + 0.937949i \(0.387277\pi\)
\(380\) 8.60438 0.441395
\(381\) −2.83107 −0.145040
\(382\) 19.6729 1.00655
\(383\) 25.0776 1.28140 0.640702 0.767790i \(-0.278643\pi\)
0.640702 + 0.767790i \(0.278643\pi\)
\(384\) 3.02801 0.154523
\(385\) 0 0
\(386\) 8.55238 0.435305
\(387\) −5.71076 −0.290294
\(388\) −14.5418 −0.738246
\(389\) −34.0257 −1.72517 −0.862585 0.505912i \(-0.831156\pi\)
−0.862585 + 0.505912i \(0.831156\pi\)
\(390\) 18.2186 0.922536
\(391\) 10.3906 0.525476
\(392\) 0 0
\(393\) −8.54530 −0.431054
\(394\) −10.8677 −0.547509
\(395\) −27.1423 −1.36568
\(396\) 6.15458 0.309279
\(397\) 2.33249 0.117064 0.0585321 0.998286i \(-0.481358\pi\)
0.0585321 + 0.998286i \(0.481358\pi\)
\(398\) −37.5501 −1.88222
\(399\) 0 0
\(400\) −4.72627 −0.236314
\(401\) −1.65085 −0.0824396 −0.0412198 0.999150i \(-0.513124\pi\)
−0.0412198 + 0.999150i \(0.513124\pi\)
\(402\) 17.3244 0.864061
\(403\) 38.5238 1.91901
\(404\) −34.5947 −1.72115
\(405\) 2.46699 0.122586
\(406\) 0 0
\(407\) 29.9083 1.48250
\(408\) 2.84706 0.140951
\(409\) −9.18226 −0.454033 −0.227017 0.973891i \(-0.572897\pi\)
−0.227017 + 0.973891i \(0.572897\pi\)
\(410\) −4.81223 −0.237659
\(411\) −3.47348 −0.171334
\(412\) −27.6611 −1.36276
\(413\) 0 0
\(414\) −2.70744 −0.133064
\(415\) 34.8236 1.70943
\(416\) −29.2592 −1.43455
\(417\) 2.23775 0.109583
\(418\) 12.8517 0.628595
\(419\) 3.34417 0.163374 0.0816868 0.996658i \(-0.473969\pi\)
0.0816868 + 0.996658i \(0.473969\pi\)
\(420\) 0 0
\(421\) 21.9541 1.06998 0.534988 0.844860i \(-0.320316\pi\)
0.534988 + 0.844860i \(0.320316\pi\)
\(422\) −10.0701 −0.490203
\(423\) 4.34350 0.211188
\(424\) −1.70947 −0.0830193
\(425\) −8.13016 −0.394371
\(426\) 32.0875 1.55464
\(427\) 0 0
\(428\) 15.4115 0.744941
\(429\) 12.9087 0.623238
\(430\) −27.4815 −1.32527
\(431\) 9.23239 0.444709 0.222354 0.974966i \(-0.428626\pi\)
0.222354 + 0.974966i \(0.428626\pi\)
\(432\) −4.35192 −0.209382
\(433\) −17.2047 −0.826807 −0.413403 0.910548i \(-0.635660\pi\)
−0.413403 + 0.910548i \(0.635660\pi\)
\(434\) 0 0
\(435\) 10.6926 0.512672
\(436\) 25.8693 1.23892
\(437\) −2.68193 −0.128294
\(438\) −1.02031 −0.0487521
\(439\) −40.7622 −1.94548 −0.972738 0.231907i \(-0.925503\pi\)
−0.972738 + 0.231907i \(0.925503\pi\)
\(440\) −3.19901 −0.152507
\(441\) 0 0
\(442\) −55.2854 −2.62966
\(443\) 15.9825 0.759350 0.379675 0.925120i \(-0.376036\pi\)
0.379675 + 0.925120i \(0.376036\pi\)
\(444\) 15.8331 0.751404
\(445\) −46.4190 −2.20047
\(446\) 11.5466 0.546745
\(447\) 8.91994 0.421899
\(448\) 0 0
\(449\) 27.3328 1.28991 0.644957 0.764218i \(-0.276875\pi\)
0.644957 + 0.764218i \(0.276875\pi\)
\(450\) 2.11845 0.0998645
\(451\) −3.40967 −0.160555
\(452\) 0.0225980 0.00106292
\(453\) −11.9438 −0.561169
\(454\) −46.8572 −2.19912
\(455\) 0 0
\(456\) −0.734858 −0.0344129
\(457\) 30.3192 1.41827 0.709136 0.705072i \(-0.249085\pi\)
0.709136 + 0.705072i \(0.249085\pi\)
\(458\) −11.6929 −0.546373
\(459\) −7.48620 −0.349426
\(460\) −6.18062 −0.288173
\(461\) −14.9967 −0.698465 −0.349232 0.937036i \(-0.613558\pi\)
−0.349232 + 0.937036i \(0.613558\pi\)
\(462\) 0 0
\(463\) −18.4478 −0.857343 −0.428671 0.903461i \(-0.641018\pi\)
−0.428671 + 0.903461i \(0.641018\pi\)
\(464\) −18.8624 −0.875667
\(465\) 25.1031 1.16413
\(466\) 32.8741 1.52286
\(467\) 14.8885 0.688957 0.344478 0.938794i \(-0.388056\pi\)
0.344478 + 0.938794i \(0.388056\pi\)
\(468\) 6.83369 0.315887
\(469\) 0 0
\(470\) 20.9019 0.964133
\(471\) −17.3359 −0.798797
\(472\) −3.60768 −0.166057
\(473\) −19.4718 −0.895316
\(474\) −21.4614 −0.985757
\(475\) 2.09848 0.0962850
\(476\) 0 0
\(477\) 4.49496 0.205810
\(478\) 2.05927 0.0941886
\(479\) 20.8298 0.951736 0.475868 0.879517i \(-0.342134\pi\)
0.475868 + 0.879517i \(0.342134\pi\)
\(480\) −19.0660 −0.870239
\(481\) 33.2085 1.51418
\(482\) 58.1150 2.64707
\(483\) 0 0
\(484\) 1.12971 0.0513506
\(485\) −19.8746 −0.902459
\(486\) 1.95065 0.0884833
\(487\) −34.9111 −1.58197 −0.790986 0.611834i \(-0.790432\pi\)
−0.790986 + 0.611834i \(0.790432\pi\)
\(488\) 4.83211 0.218740
\(489\) −1.43399 −0.0648472
\(490\) 0 0
\(491\) −29.0789 −1.31231 −0.656156 0.754625i \(-0.727819\pi\)
−0.656156 + 0.754625i \(0.727819\pi\)
\(492\) −1.80504 −0.0813773
\(493\) −32.4473 −1.46135
\(494\) 14.2698 0.642026
\(495\) 8.41161 0.378074
\(496\) −44.2834 −1.98838
\(497\) 0 0
\(498\) 27.5351 1.23388
\(499\) 6.60144 0.295521 0.147760 0.989023i \(-0.452794\pi\)
0.147760 + 0.989023i \(0.452794\pi\)
\(500\) −17.4289 −0.779446
\(501\) −16.8506 −0.752831
\(502\) 31.2654 1.39544
\(503\) −32.6788 −1.45708 −0.728539 0.685005i \(-0.759800\pi\)
−0.728539 + 0.685005i \(0.759800\pi\)
\(504\) 0 0
\(505\) −47.2815 −2.10400
\(506\) −9.23149 −0.410390
\(507\) 1.33308 0.0592040
\(508\) −5.11018 −0.226728
\(509\) −30.5152 −1.35256 −0.676281 0.736644i \(-0.736409\pi\)
−0.676281 + 0.736644i \(0.736409\pi\)
\(510\) −36.0253 −1.59523
\(511\) 0 0
\(512\) 30.3235 1.34012
\(513\) 1.93227 0.0853117
\(514\) −6.66120 −0.293813
\(515\) −37.8051 −1.66589
\(516\) −10.3081 −0.453790
\(517\) 14.8099 0.651339
\(518\) 0 0
\(519\) −2.36949 −0.104009
\(520\) −3.55199 −0.155765
\(521\) −18.8954 −0.827820 −0.413910 0.910318i \(-0.635837\pi\)
−0.413910 + 0.910318i \(0.635837\pi\)
\(522\) 8.45467 0.370051
\(523\) −9.39131 −0.410653 −0.205327 0.978694i \(-0.565826\pi\)
−0.205327 + 0.978694i \(0.565826\pi\)
\(524\) −15.4246 −0.673826
\(525\) 0 0
\(526\) −13.5869 −0.592417
\(527\) −76.1765 −3.31830
\(528\) −14.8386 −0.645768
\(529\) −21.0735 −0.916241
\(530\) 21.6308 0.939581
\(531\) 9.48620 0.411666
\(532\) 0 0
\(533\) −3.78591 −0.163986
\(534\) −36.7036 −1.58832
\(535\) 21.0632 0.910642
\(536\) −3.37764 −0.145892
\(537\) −12.3125 −0.531323
\(538\) 14.9684 0.645332
\(539\) 0 0
\(540\) 4.45300 0.191626
\(541\) 7.79461 0.335116 0.167558 0.985862i \(-0.446412\pi\)
0.167558 + 0.985862i \(0.446412\pi\)
\(542\) −54.9151 −2.35881
\(543\) 24.0143 1.03055
\(544\) 57.8567 2.48059
\(545\) 35.3562 1.51449
\(546\) 0 0
\(547\) 32.8239 1.40345 0.701725 0.712448i \(-0.252414\pi\)
0.701725 + 0.712448i \(0.252414\pi\)
\(548\) −6.26976 −0.267831
\(549\) −12.7058 −0.542270
\(550\) 7.22321 0.307999
\(551\) 8.37500 0.356787
\(552\) 0.527856 0.0224671
\(553\) 0 0
\(554\) 9.46276 0.402034
\(555\) 21.6394 0.918543
\(556\) 4.03922 0.171301
\(557\) −8.23895 −0.349096 −0.174548 0.984649i \(-0.555846\pi\)
−0.174548 + 0.984649i \(0.555846\pi\)
\(558\) 19.8490 0.840276
\(559\) −21.6204 −0.914446
\(560\) 0 0
\(561\) −25.5255 −1.07769
\(562\) −26.3218 −1.11032
\(563\) −2.24259 −0.0945137 −0.0472569 0.998883i \(-0.515048\pi\)
−0.0472569 + 0.998883i \(0.515048\pi\)
\(564\) 7.84017 0.330131
\(565\) 0.0308853 0.00129935
\(566\) −6.61756 −0.278157
\(567\) 0 0
\(568\) −6.25593 −0.262493
\(569\) −22.0558 −0.924625 −0.462313 0.886717i \(-0.652980\pi\)
−0.462313 + 0.886717i \(0.652980\pi\)
\(570\) 9.29851 0.389472
\(571\) −22.8597 −0.956650 −0.478325 0.878183i \(-0.658756\pi\)
−0.478325 + 0.878183i \(0.658756\pi\)
\(572\) 23.3007 0.974249
\(573\) 10.0853 0.421319
\(574\) 0 0
\(575\) −1.50736 −0.0628614
\(576\) −6.37167 −0.265486
\(577\) −6.08498 −0.253321 −0.126660 0.991946i \(-0.540426\pi\)
−0.126660 + 0.991946i \(0.540426\pi\)
\(578\) 76.1596 3.16782
\(579\) 4.38437 0.182208
\(580\) 19.3005 0.801412
\(581\) 0 0
\(582\) −15.7149 −0.651402
\(583\) 15.3263 0.634752
\(584\) 0.198924 0.00823152
\(585\) 9.33978 0.386152
\(586\) 38.7816 1.60205
\(587\) 9.48311 0.391410 0.195705 0.980663i \(-0.437301\pi\)
0.195705 + 0.980663i \(0.437301\pi\)
\(588\) 0 0
\(589\) 19.6620 0.810158
\(590\) 45.6498 1.87937
\(591\) −5.57135 −0.229175
\(592\) −38.1733 −1.56891
\(593\) 26.7188 1.09721 0.548604 0.836082i \(-0.315160\pi\)
0.548604 + 0.836082i \(0.315160\pi\)
\(594\) 6.65108 0.272897
\(595\) 0 0
\(596\) 16.1008 0.659514
\(597\) −19.2500 −0.787852
\(598\) −10.2501 −0.419159
\(599\) −10.9319 −0.446667 −0.223333 0.974742i \(-0.571694\pi\)
−0.223333 + 0.974742i \(0.571694\pi\)
\(600\) −0.413023 −0.0168616
\(601\) 31.5604 1.28738 0.643688 0.765288i \(-0.277403\pi\)
0.643688 + 0.765288i \(0.277403\pi\)
\(602\) 0 0
\(603\) 8.88133 0.361676
\(604\) −21.5590 −0.877224
\(605\) 1.54401 0.0627728
\(606\) −37.3856 −1.51868
\(607\) −24.8257 −1.00765 −0.503823 0.863807i \(-0.668074\pi\)
−0.503823 + 0.863807i \(0.668074\pi\)
\(608\) −14.9334 −0.605631
\(609\) 0 0
\(610\) −61.1431 −2.47561
\(611\) 16.4441 0.665256
\(612\) −13.5129 −0.546225
\(613\) −17.3856 −0.702198 −0.351099 0.936338i \(-0.614192\pi\)
−0.351099 + 0.936338i \(0.614192\pi\)
\(614\) 40.0862 1.61775
\(615\) −2.46699 −0.0994785
\(616\) 0 0
\(617\) 37.7106 1.51817 0.759085 0.650992i \(-0.225647\pi\)
0.759085 + 0.650992i \(0.225647\pi\)
\(618\) −29.8925 −1.20245
\(619\) −30.7411 −1.23559 −0.617794 0.786340i \(-0.711974\pi\)
−0.617794 + 0.786340i \(0.711974\pi\)
\(620\) 45.3119 1.81977
\(621\) −1.38797 −0.0556973
\(622\) −13.8404 −0.554949
\(623\) 0 0
\(624\) −16.4760 −0.659566
\(625\) −29.2507 −1.17003
\(626\) −21.1311 −0.844567
\(627\) 6.58840 0.263115
\(628\) −31.2919 −1.24868
\(629\) −65.6660 −2.61827
\(630\) 0 0
\(631\) 2.48516 0.0989325 0.0494663 0.998776i \(-0.484248\pi\)
0.0494663 + 0.998776i \(0.484248\pi\)
\(632\) 4.18423 0.166440
\(633\) −5.16241 −0.205188
\(634\) 30.9725 1.23007
\(635\) −6.98421 −0.277160
\(636\) 8.11356 0.321724
\(637\) 0 0
\(638\) 28.8277 1.14130
\(639\) 16.4496 0.650737
\(640\) 7.47006 0.295280
\(641\) −3.47852 −0.137393 −0.0686967 0.997638i \(-0.521884\pi\)
−0.0686967 + 0.997638i \(0.521884\pi\)
\(642\) 16.6547 0.657309
\(643\) 6.66666 0.262907 0.131454 0.991322i \(-0.458036\pi\)
0.131454 + 0.991322i \(0.458036\pi\)
\(644\) 0 0
\(645\) −14.0884 −0.554729
\(646\) −28.2168 −1.11018
\(647\) −12.7615 −0.501707 −0.250853 0.968025i \(-0.580711\pi\)
−0.250853 + 0.968025i \(0.580711\pi\)
\(648\) −0.380308 −0.0149399
\(649\) 32.3448 1.26965
\(650\) 8.02023 0.314579
\(651\) 0 0
\(652\) −2.58840 −0.101369
\(653\) −48.3605 −1.89249 −0.946247 0.323445i \(-0.895159\pi\)
−0.946247 + 0.323445i \(0.895159\pi\)
\(654\) 27.9562 1.09317
\(655\) −21.0811 −0.823708
\(656\) 4.35192 0.169914
\(657\) −0.523059 −0.0204065
\(658\) 0 0
\(659\) −31.3864 −1.22264 −0.611320 0.791383i \(-0.709361\pi\)
−0.611320 + 0.791383i \(0.709361\pi\)
\(660\) 15.1833 0.591008
\(661\) −27.8855 −1.08462 −0.542310 0.840178i \(-0.682450\pi\)
−0.542310 + 0.840178i \(0.682450\pi\)
\(662\) 16.7303 0.650242
\(663\) −28.3420 −1.10071
\(664\) −5.36838 −0.208334
\(665\) 0 0
\(666\) 17.1103 0.663012
\(667\) −6.01585 −0.232935
\(668\) −30.4160 −1.17683
\(669\) 5.91934 0.228855
\(670\) 42.7390 1.65115
\(671\) −43.3226 −1.67245
\(672\) 0 0
\(673\) −19.8350 −0.764583 −0.382291 0.924042i \(-0.624865\pi\)
−0.382291 + 0.924042i \(0.624865\pi\)
\(674\) −22.7835 −0.877586
\(675\) 1.08602 0.0418009
\(676\) 2.40625 0.0925481
\(677\) 3.64538 0.140103 0.0700517 0.997543i \(-0.477684\pi\)
0.0700517 + 0.997543i \(0.477684\pi\)
\(678\) 0.0244210 0.000937885 0
\(679\) 0 0
\(680\) 7.02367 0.269345
\(681\) −24.0214 −0.920500
\(682\) 67.6787 2.59155
\(683\) 39.2949 1.50358 0.751790 0.659403i \(-0.229191\pi\)
0.751790 + 0.659403i \(0.229191\pi\)
\(684\) 3.48781 0.133360
\(685\) −8.56903 −0.327406
\(686\) 0 0
\(687\) −5.99435 −0.228699
\(688\) 24.8528 0.947503
\(689\) 17.0175 0.648315
\(690\) −6.67922 −0.254274
\(691\) −0.957556 −0.0364272 −0.0182136 0.999834i \(-0.505798\pi\)
−0.0182136 + 0.999834i \(0.505798\pi\)
\(692\) −4.27701 −0.162588
\(693\) 0 0
\(694\) −16.9394 −0.643012
\(695\) 5.52050 0.209405
\(696\) −1.64836 −0.0624811
\(697\) 7.48620 0.283560
\(698\) −37.0449 −1.40217
\(699\) 16.8529 0.637435
\(700\) 0 0
\(701\) 30.4024 1.14828 0.574141 0.818757i \(-0.305336\pi\)
0.574141 + 0.818757i \(0.305336\pi\)
\(702\) 7.38498 0.278728
\(703\) 16.9491 0.639247
\(704\) −21.7253 −0.818803
\(705\) 10.7154 0.403564
\(706\) 23.1635 0.871770
\(707\) 0 0
\(708\) 17.1229 0.643519
\(709\) 48.6578 1.82738 0.913691 0.406410i \(-0.133220\pi\)
0.913691 + 0.406410i \(0.133220\pi\)
\(710\) 79.1594 2.97080
\(711\) −11.0022 −0.412615
\(712\) 7.15592 0.268179
\(713\) −14.1234 −0.528926
\(714\) 0 0
\(715\) 31.8456 1.19096
\(716\) −22.2245 −0.830568
\(717\) 1.05568 0.0394252
\(718\) −58.7451 −2.19235
\(719\) 1.65328 0.0616570 0.0308285 0.999525i \(-0.490185\pi\)
0.0308285 + 0.999525i \(0.490185\pi\)
\(720\) −10.7361 −0.400112
\(721\) 0 0
\(722\) −29.7793 −1.10827
\(723\) 29.7927 1.10800
\(724\) 43.3466 1.61096
\(725\) 4.70712 0.174818
\(726\) 1.22085 0.0453099
\(727\) 32.4853 1.20481 0.602407 0.798189i \(-0.294208\pi\)
0.602407 + 0.798189i \(0.294208\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.51708 −0.0931613
\(731\) 42.7519 1.58124
\(732\) −22.9344 −0.847679
\(733\) 18.1869 0.671750 0.335875 0.941907i \(-0.390968\pi\)
0.335875 + 0.941907i \(0.390968\pi\)
\(734\) 9.53501 0.351944
\(735\) 0 0
\(736\) 10.7269 0.395397
\(737\) 30.2824 1.11547
\(738\) −1.95065 −0.0718044
\(739\) −12.5060 −0.460042 −0.230021 0.973186i \(-0.573880\pi\)
−0.230021 + 0.973186i \(0.573880\pi\)
\(740\) 39.0599 1.43587
\(741\) 7.31538 0.268737
\(742\) 0 0
\(743\) 13.6638 0.501277 0.250639 0.968081i \(-0.419359\pi\)
0.250639 + 0.968081i \(0.419359\pi\)
\(744\) −3.86986 −0.141876
\(745\) 22.0054 0.806214
\(746\) −30.8679 −1.13015
\(747\) 14.1159 0.516473
\(748\) −46.0744 −1.68465
\(749\) 0 0
\(750\) −18.8350 −0.687755
\(751\) −25.4172 −0.927487 −0.463743 0.885970i \(-0.653494\pi\)
−0.463743 + 0.885970i \(0.653494\pi\)
\(752\) −18.9026 −0.689305
\(753\) 16.0282 0.584100
\(754\) 32.0086 1.16568
\(755\) −29.4652 −1.07235
\(756\) 0 0
\(757\) 38.3522 1.39393 0.696967 0.717103i \(-0.254532\pi\)
0.696967 + 0.717103i \(0.254532\pi\)
\(758\) 26.3376 0.956624
\(759\) −4.73252 −0.171780
\(760\) −1.81288 −0.0657602
\(761\) 3.94762 0.143101 0.0715506 0.997437i \(-0.477205\pi\)
0.0715506 + 0.997437i \(0.477205\pi\)
\(762\) −5.52243 −0.200056
\(763\) 0 0
\(764\) 18.2043 0.658609
\(765\) −18.4684 −0.667725
\(766\) 48.9176 1.76746
\(767\) 35.9139 1.29677
\(768\) 18.6499 0.672971
\(769\) 39.2114 1.41400 0.707000 0.707214i \(-0.250048\pi\)
0.707000 + 0.707214i \(0.250048\pi\)
\(770\) 0 0
\(771\) −3.41486 −0.122983
\(772\) 7.91395 0.284829
\(773\) 12.5429 0.451137 0.225569 0.974227i \(-0.427576\pi\)
0.225569 + 0.974227i \(0.427576\pi\)
\(774\) −11.1397 −0.400408
\(775\) 11.0509 0.396960
\(776\) 3.06385 0.109986
\(777\) 0 0
\(778\) −66.3722 −2.37956
\(779\) −1.93227 −0.0692307
\(780\) 16.8586 0.603635
\(781\) 56.0879 2.00698
\(782\) 20.2685 0.724798
\(783\) 4.33428 0.154895
\(784\) 0 0
\(785\) −42.7675 −1.52644
\(786\) −16.6689 −0.594560
\(787\) −40.8000 −1.45436 −0.727182 0.686445i \(-0.759170\pi\)
−0.727182 + 0.686445i \(0.759170\pi\)
\(788\) −10.0565 −0.358247
\(789\) −6.96532 −0.247972
\(790\) −52.9451 −1.88370
\(791\) 0 0
\(792\) −1.29673 −0.0460772
\(793\) −48.1029 −1.70818
\(794\) 4.54987 0.161469
\(795\) 11.0890 0.393287
\(796\) −34.7470 −1.23158
\(797\) 22.4983 0.796930 0.398465 0.917184i \(-0.369543\pi\)
0.398465 + 0.917184i \(0.369543\pi\)
\(798\) 0 0
\(799\) −32.5163 −1.15034
\(800\) −8.39326 −0.296746
\(801\) −18.8161 −0.664834
\(802\) −3.22023 −0.113710
\(803\) −1.78346 −0.0629370
\(804\) 16.0311 0.565374
\(805\) 0 0
\(806\) 75.1465 2.64692
\(807\) 7.67353 0.270121
\(808\) 7.28887 0.256422
\(809\) 32.3502 1.13737 0.568686 0.822555i \(-0.307452\pi\)
0.568686 + 0.822555i \(0.307452\pi\)
\(810\) 4.81223 0.169084
\(811\) −41.8941 −1.47110 −0.735551 0.677469i \(-0.763077\pi\)
−0.735551 + 0.677469i \(0.763077\pi\)
\(812\) 0 0
\(813\) −28.1522 −0.987341
\(814\) 58.3406 2.04484
\(815\) −3.53763 −0.123918
\(816\) 32.5793 1.14050
\(817\) −11.0347 −0.386056
\(818\) −17.9114 −0.626256
\(819\) 0 0
\(820\) −4.45300 −0.155505
\(821\) −38.7515 −1.35244 −0.676219 0.736701i \(-0.736383\pi\)
−0.676219 + 0.736701i \(0.736383\pi\)
\(822\) −6.77555 −0.236324
\(823\) 38.8323 1.35361 0.676804 0.736163i \(-0.263364\pi\)
0.676804 + 0.736163i \(0.263364\pi\)
\(824\) 5.82799 0.203028
\(825\) 3.70297 0.128921
\(826\) 0 0
\(827\) 12.4060 0.431397 0.215699 0.976460i \(-0.430797\pi\)
0.215699 + 0.976460i \(0.430797\pi\)
\(828\) −2.50533 −0.0870664
\(829\) −21.5753 −0.749341 −0.374670 0.927158i \(-0.622244\pi\)
−0.374670 + 0.927158i \(0.622244\pi\)
\(830\) 67.9287 2.35784
\(831\) 4.85108 0.168282
\(832\) −24.1225 −0.836298
\(833\) 0 0
\(834\) 4.36507 0.151150
\(835\) −41.5703 −1.43860
\(836\) 11.8923 0.411304
\(837\) 10.1756 0.351720
\(838\) 6.52331 0.225344
\(839\) 9.21299 0.318068 0.159034 0.987273i \(-0.449162\pi\)
0.159034 + 0.987273i \(0.449162\pi\)
\(840\) 0 0
\(841\) −10.2140 −0.352207
\(842\) 42.8247 1.47584
\(843\) −13.4939 −0.464754
\(844\) −9.31834 −0.320750
\(845\) 3.28868 0.113134
\(846\) 8.47265 0.291296
\(847\) 0 0
\(848\) −19.5617 −0.671752
\(849\) −3.39249 −0.116430
\(850\) −15.8591 −0.543963
\(851\) −12.1747 −0.417344
\(852\) 29.6922 1.01724
\(853\) 12.8696 0.440646 0.220323 0.975427i \(-0.429289\pi\)
0.220323 + 0.975427i \(0.429289\pi\)
\(854\) 0 0
\(855\) 4.76688 0.163024
\(856\) −3.24709 −0.110983
\(857\) −0.400158 −0.0136691 −0.00683457 0.999977i \(-0.502176\pi\)
−0.00683457 + 0.999977i \(0.502176\pi\)
\(858\) 25.1803 0.859643
\(859\) −28.9248 −0.986902 −0.493451 0.869774i \(-0.664265\pi\)
−0.493451 + 0.869774i \(0.664265\pi\)
\(860\) −25.4300 −0.867156
\(861\) 0 0
\(862\) 18.0092 0.613394
\(863\) −10.5621 −0.359540 −0.179770 0.983709i \(-0.557535\pi\)
−0.179770 + 0.983709i \(0.557535\pi\)
\(864\) −7.72845 −0.262927
\(865\) −5.84550 −0.198753
\(866\) −33.5604 −1.14043
\(867\) 39.0432 1.32598
\(868\) 0 0
\(869\) −37.5139 −1.27257
\(870\) 20.8576 0.707137
\(871\) 33.6239 1.13930
\(872\) −5.45048 −0.184577
\(873\) −8.05622 −0.272662
\(874\) −5.23150 −0.176958
\(875\) 0 0
\(876\) −0.944140 −0.0318995
\(877\) 1.53055 0.0516830 0.0258415 0.999666i \(-0.491773\pi\)
0.0258415 + 0.999666i \(0.491773\pi\)
\(878\) −79.5129 −2.68343
\(879\) 19.8814 0.670583
\(880\) −36.6067 −1.23401
\(881\) 8.25921 0.278260 0.139130 0.990274i \(-0.455569\pi\)
0.139130 + 0.990274i \(0.455569\pi\)
\(882\) 0 0
\(883\) 16.5389 0.556578 0.278289 0.960497i \(-0.410233\pi\)
0.278289 + 0.960497i \(0.410233\pi\)
\(884\) −51.1584 −1.72064
\(885\) 23.4023 0.786661
\(886\) 31.1762 1.04738
\(887\) 28.9877 0.973310 0.486655 0.873594i \(-0.338217\pi\)
0.486655 + 0.873594i \(0.338217\pi\)
\(888\) −3.33592 −0.111946
\(889\) 0 0
\(890\) −90.5473 −3.03515
\(891\) 3.40967 0.114228
\(892\) 10.6846 0.357747
\(893\) 8.39281 0.280855
\(894\) 17.3997 0.581932
\(895\) −30.3747 −1.01532
\(896\) 0 0
\(897\) −5.25472 −0.175450
\(898\) 53.3167 1.77920
\(899\) 44.1039 1.47095
\(900\) 1.96030 0.0653435
\(901\) −33.6502 −1.12105
\(902\) −6.65108 −0.221457
\(903\) 0 0
\(904\) −0.00476125 −0.000158357 0
\(905\) 59.2429 1.96930
\(906\) −23.2982 −0.774031
\(907\) −4.20847 −0.139740 −0.0698700 0.997556i \(-0.522258\pi\)
−0.0698700 + 0.997556i \(0.522258\pi\)
\(908\) −43.3594 −1.43893
\(909\) −19.1657 −0.635686
\(910\) 0 0
\(911\) −45.2126 −1.49796 −0.748980 0.662593i \(-0.769456\pi\)
−0.748980 + 0.662593i \(0.769456\pi\)
\(912\) −8.40907 −0.278452
\(913\) 48.1305 1.59289
\(914\) 59.1421 1.95625
\(915\) −31.3450 −1.03623
\(916\) −10.8200 −0.357504
\(917\) 0 0
\(918\) −14.6030 −0.481969
\(919\) −39.1541 −1.29158 −0.645788 0.763517i \(-0.723471\pi\)
−0.645788 + 0.763517i \(0.723471\pi\)
\(920\) 1.30221 0.0429327
\(921\) 20.5502 0.677152
\(922\) −29.2533 −0.963405
\(923\) 62.2768 2.04986
\(924\) 0 0
\(925\) 9.52614 0.313218
\(926\) −35.9852 −1.18255
\(927\) −15.3244 −0.503319
\(928\) −33.4973 −1.09960
\(929\) 13.0337 0.427621 0.213811 0.976875i \(-0.431412\pi\)
0.213811 + 0.976875i \(0.431412\pi\)
\(930\) 48.9673 1.60570
\(931\) 0 0
\(932\) 30.4201 0.996442
\(933\) −7.09527 −0.232289
\(934\) 29.0422 0.950290
\(935\) −62.9710 −2.05937
\(936\) −1.43981 −0.0470617
\(937\) −27.4537 −0.896874 −0.448437 0.893815i \(-0.648019\pi\)
−0.448437 + 0.893815i \(0.648019\pi\)
\(938\) 0 0
\(939\) −10.8328 −0.353516
\(940\) 19.3416 0.630853
\(941\) 52.6685 1.71694 0.858472 0.512861i \(-0.171414\pi\)
0.858472 + 0.512861i \(0.171414\pi\)
\(942\) −33.8163 −1.10179
\(943\) 1.38797 0.0451985
\(944\) −41.2832 −1.34365
\(945\) 0 0
\(946\) −37.9827 −1.23492
\(947\) −35.1078 −1.14085 −0.570425 0.821350i \(-0.693221\pi\)
−0.570425 + 0.821350i \(0.693221\pi\)
\(948\) −19.8594 −0.645002
\(949\) −1.98025 −0.0642817
\(950\) 4.09340 0.132808
\(951\) 15.8780 0.514880
\(952\) 0 0
\(953\) 19.7506 0.639784 0.319892 0.947454i \(-0.396353\pi\)
0.319892 + 0.947454i \(0.396353\pi\)
\(954\) 8.76810 0.283878
\(955\) 24.8803 0.805107
\(956\) 1.90554 0.0616297
\(957\) 14.7785 0.477721
\(958\) 40.6316 1.31275
\(959\) 0 0
\(960\) −15.7188 −0.507323
\(961\) 72.5427 2.34009
\(962\) 64.7781 2.08853
\(963\) 8.53803 0.275134
\(964\) 53.7768 1.73203
\(965\) 10.8162 0.348186
\(966\) 0 0
\(967\) 15.7402 0.506171 0.253085 0.967444i \(-0.418555\pi\)
0.253085 + 0.967444i \(0.418555\pi\)
\(968\) −0.238023 −0.00765034
\(969\) −14.4653 −0.464694
\(970\) −38.7684 −1.24478
\(971\) −16.8101 −0.539462 −0.269731 0.962936i \(-0.586935\pi\)
−0.269731 + 0.962936i \(0.586935\pi\)
\(972\) 1.80504 0.0578965
\(973\) 0 0
\(974\) −68.0993 −2.18204
\(975\) 4.11157 0.131676
\(976\) 55.2945 1.76993
\(977\) 4.71491 0.150843 0.0754217 0.997152i \(-0.475970\pi\)
0.0754217 + 0.997152i \(0.475970\pi\)
\(978\) −2.79721 −0.0894448
\(979\) −64.1567 −2.05046
\(980\) 0 0
\(981\) 14.3317 0.457578
\(982\) −56.7228 −1.81010
\(983\) 24.6443 0.786032 0.393016 0.919532i \(-0.371432\pi\)
0.393016 + 0.919532i \(0.371432\pi\)
\(984\) 0.380308 0.0121238
\(985\) −13.7444 −0.437934
\(986\) −63.2933 −2.01567
\(987\) 0 0
\(988\) 13.2045 0.420092
\(989\) 7.92636 0.252044
\(990\) 16.4081 0.521484
\(991\) 0.939287 0.0298374 0.0149187 0.999889i \(-0.495251\pi\)
0.0149187 + 0.999889i \(0.495251\pi\)
\(992\) −78.6416 −2.49687
\(993\) 8.57678 0.272176
\(994\) 0 0
\(995\) −47.4896 −1.50552
\(996\) 25.4796 0.807353
\(997\) −20.4352 −0.647188 −0.323594 0.946196i \(-0.604891\pi\)
−0.323594 + 0.946196i \(0.604891\pi\)
\(998\) 12.8771 0.407617
\(999\) 8.77161 0.277521
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 \(a_p\))