Properties

Label 6027.2.a.u.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 4
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: \(4\)
Coefficient field: 4.4.8468.1
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 \(-1.89122\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.89122 q^{2} +1.00000 q^{3} +1.57671 q^{4} +1.57671 q^{5} -1.89122 q^{6} +0.800530 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.89122 q^{2} +1.00000 q^{3} +1.57671 q^{4} +1.57671 q^{5} -1.89122 q^{6} +0.800530 q^{8} +1.00000 q^{9} -2.98191 q^{10} +1.66740 q^{11} +1.57671 q^{12} +5.04464 q^{13} +1.57671 q^{15} -4.66740 q^{16} -6.35915 q^{17} -1.89122 q^{18} -0.691750 q^{19} +2.48602 q^{20} -3.15343 q^{22} +8.82708 q^{23} +0.800530 q^{24} -2.51398 q^{25} -9.54053 q^{26} +1.00000 q^{27} -6.64931 q^{29} -2.98191 q^{30} -2.35915 q^{31} +7.22603 q^{32} +1.66740 q^{33} +12.0266 q^{34} +1.57671 q^{36} +9.02655 q^{37} +1.30825 q^{38} +5.04464 q^{39} +1.26221 q^{40} +1.00000 q^{41} -9.96021 q^{43} +2.62901 q^{44} +1.57671 q^{45} -16.6940 q^{46} +1.33621 q^{47} -4.66740 q^{48} +4.75448 q^{50} -6.35915 q^{51} +7.95395 q^{52} +1.66115 q^{53} -1.89122 q^{54} +2.62901 q^{55} -0.691750 q^{57} +12.5753 q^{58} +12.0266 q^{59} +2.48602 q^{60} +11.9602 q^{61} +4.46168 q^{62} -4.33120 q^{64} +7.95395 q^{65} -3.15343 q^{66} -0.870922 q^{67} -10.0266 q^{68} +8.82708 q^{69} -10.8961 q^{71} +0.800530 q^{72} +2.79427 q^{73} -17.0712 q^{74} -2.51398 q^{75} -1.09069 q^{76} -9.54053 q^{78} +12.2463 q^{79} -7.35915 q^{80} +1.00000 q^{81} -1.89122 q^{82} +2.62901 q^{83} -10.0266 q^{85} +18.8369 q^{86} -6.64931 q^{87} +1.33481 q^{88} +12.7183 q^{89} -2.98191 q^{90} +13.9178 q^{92} -2.35915 q^{93} -2.52706 q^{94} -1.09069 q^{95} +7.22603 q^{96} +3.21198 q^{97} +1.66740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + O(q^{10}) \) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + 5q^{10} - 5q^{11} + 3q^{12} + 5q^{13} + 3q^{15} - 7q^{16} - 5q^{17} + q^{18} + 6q^{19} + 15q^{20} - 6q^{22} + 3q^{23} + 3q^{24} - 5q^{25} - q^{26} + 4q^{27} + 2q^{29} + 5q^{30} + 11q^{31} - 3q^{32} - 5q^{33} + 16q^{34} + 3q^{36} + 4q^{37} + 14q^{38} + 5q^{39} + 7q^{40} + 4q^{41} - 19q^{43} + 3q^{45} - 23q^{46} + 4q^{47} - 7q^{48} + 12q^{50} - 5q^{51} + 25q^{52} + 9q^{53} + q^{54} + 6q^{57} + 25q^{58} + 16q^{59} + 15q^{60} + 27q^{61} + 20q^{62} - 7q^{64} + 25q^{65} - 6q^{66} - 13q^{67} - 8q^{68} + 3q^{69} + q^{71} + 3q^{72} + 25q^{73} - 21q^{74} - 5q^{75} + 4q^{76} - q^{78} - q^{79} - 9q^{80} + 4q^{81} + q^{82} - 8q^{85} + 16q^{86} + 2q^{87} - 18q^{88} + 10q^{89} + 5q^{90} + 15q^{92} + 11q^{93} - 13q^{94} + 4q^{95} - 3q^{96} - 15q^{97} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89122 −1.33729 −0.668647 0.743580i \(-0.733126\pi\)
−0.668647 + 0.743580i \(0.733126\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.57671 0.788356
\(5\) 1.57671 0.705127 0.352564 0.935788i \(-0.385310\pi\)
0.352564 + 0.935788i \(0.385310\pi\)
\(6\) −1.89122 −0.772087
\(7\) 0 0
\(8\) 0.800530 0.283030
\(9\) 1.00000 0.333333
\(10\) −2.98191 −0.942963
\(11\) 1.66740 0.502741 0.251370 0.967891i \(-0.419119\pi\)
0.251370 + 0.967891i \(0.419119\pi\)
\(12\) 1.57671 0.455158
\(13\) 5.04464 1.39913 0.699566 0.714568i \(-0.253377\pi\)
0.699566 + 0.714568i \(0.253377\pi\)
\(14\) 0 0
\(15\) 1.57671 0.407105
\(16\) −4.66740 −1.16685
\(17\) −6.35915 −1.54232 −0.771160 0.636641i \(-0.780323\pi\)
−0.771160 + 0.636641i \(0.780323\pi\)
\(18\) −1.89122 −0.445765
\(19\) −0.691750 −0.158698 −0.0793491 0.996847i \(-0.525284\pi\)
−0.0793491 + 0.996847i \(0.525284\pi\)
\(20\) 2.48602 0.555891
\(21\) 0 0
\(22\) −3.15343 −0.672312
\(23\) 8.82708 1.84057 0.920287 0.391244i \(-0.127955\pi\)
0.920287 + 0.391244i \(0.127955\pi\)
\(24\) 0.800530 0.163407
\(25\) −2.51398 −0.502796
\(26\) −9.54053 −1.87105
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.64931 −1.23475 −0.617373 0.786670i \(-0.711803\pi\)
−0.617373 + 0.786670i \(0.711803\pi\)
\(30\) −2.98191 −0.544420
\(31\) −2.35915 −0.423716 −0.211858 0.977300i \(-0.567951\pi\)
−0.211858 + 0.977300i \(0.567951\pi\)
\(32\) 7.22603 1.27739
\(33\) 1.66740 0.290258
\(34\) 12.0266 2.06254
\(35\) 0 0
\(36\) 1.57671 0.262785
\(37\) 9.02655 1.48396 0.741978 0.670424i \(-0.233888\pi\)
0.741978 + 0.670424i \(0.233888\pi\)
\(38\) 1.30825 0.212226
\(39\) 5.04464 0.807790
\(40\) 1.26221 0.199572
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −9.96021 −1.51892 −0.759459 0.650555i \(-0.774536\pi\)
−0.759459 + 0.650555i \(0.774536\pi\)
\(44\) 2.62901 0.396339
\(45\) 1.57671 0.235042
\(46\) −16.6940 −2.46139
\(47\) 1.33621 0.194906 0.0974528 0.995240i \(-0.468930\pi\)
0.0974528 + 0.995240i \(0.468930\pi\)
\(48\) −4.66740 −0.673682
\(49\) 0 0
\(50\) 4.75448 0.672386
\(51\) −6.35915 −0.890459
\(52\) 7.95395 1.10302
\(53\) 1.66115 0.228176 0.114088 0.993471i \(-0.463605\pi\)
0.114088 + 0.993471i \(0.463605\pi\)
\(54\) −1.89122 −0.257362
\(55\) 2.62901 0.354496
\(56\) 0 0
\(57\) −0.691750 −0.0916245
\(58\) 12.5753 1.65122
\(59\) 12.0266 1.56572 0.782862 0.622195i \(-0.213759\pi\)
0.782862 + 0.622195i \(0.213759\pi\)
\(60\) 2.48602 0.320944
\(61\) 11.9602 1.53135 0.765674 0.643229i \(-0.222406\pi\)
0.765674 + 0.643229i \(0.222406\pi\)
\(62\) 4.46168 0.566633
\(63\) 0 0
\(64\) −4.33120 −0.541400
\(65\) 7.95395 0.986567
\(66\) −3.15343 −0.388160
\(67\) −0.870922 −0.106400 −0.0532000 0.998584i \(-0.516942\pi\)
−0.0532000 + 0.998584i \(0.516942\pi\)
\(68\) −10.0266 −1.21590
\(69\) 8.82708 1.06266
\(70\) 0 0
\(71\) −10.8961 −1.29313 −0.646563 0.762860i \(-0.723794\pi\)
−0.646563 + 0.762860i \(0.723794\pi\)
\(72\) 0.800530 0.0943433
\(73\) 2.79427 0.327045 0.163522 0.986540i \(-0.447714\pi\)
0.163522 + 0.986540i \(0.447714\pi\)
\(74\) −17.0712 −1.98449
\(75\) −2.51398 −0.290289
\(76\) −1.09069 −0.125111
\(77\) 0 0
\(78\) −9.54053 −1.08025
\(79\) 12.2463 1.37782 0.688910 0.724847i \(-0.258090\pi\)
0.688910 + 0.724847i \(0.258090\pi\)
\(80\) −7.35915 −0.822778
\(81\) 1.00000 0.111111
\(82\) −1.89122 −0.208850
\(83\) 2.62901 0.288572 0.144286 0.989536i \(-0.453911\pi\)
0.144286 + 0.989536i \(0.453911\pi\)
\(84\) 0 0
\(85\) −10.0266 −1.08753
\(86\) 18.8369 2.03124
\(87\) −6.64931 −0.712881
\(88\) 1.33481 0.142291
\(89\) 12.7183 1.34814 0.674069 0.738669i \(-0.264545\pi\)
0.674069 + 0.738669i \(0.264545\pi\)
\(90\) −2.98191 −0.314321
\(91\) 0 0
\(92\) 13.9178 1.45103
\(93\) −2.35915 −0.244633
\(94\) −2.52706 −0.260646
\(95\) −1.09069 −0.111902
\(96\) 7.22603 0.737503
\(97\) 3.21198 0.326128 0.163064 0.986616i \(-0.447862\pi\)
0.163064 + 0.986616i \(0.447862\pi\)
\(98\) 0 0
\(99\) 1.66740 0.167580
\(100\) −3.96382 −0.396382
\(101\) 7.97425 0.793468 0.396734 0.917934i \(-0.370144\pi\)
0.396734 + 0.917934i \(0.370144\pi\)
\(102\) 12.0266 1.19081
\(103\) 6.34246 0.624941 0.312471 0.949927i \(-0.398843\pi\)
0.312471 + 0.949927i \(0.398843\pi\)
\(104\) 4.03839 0.395997
\(105\) 0 0
\(106\) −3.14159 −0.305138
\(107\) −11.2401 −1.08662 −0.543309 0.839533i \(-0.682829\pi\)
−0.543309 + 0.839533i \(0.682829\pi\)
\(108\) 1.57671 0.151719
\(109\) −7.48963 −0.717377 −0.358688 0.933457i \(-0.616776\pi\)
−0.358688 + 0.933457i \(0.616776\pi\)
\(110\) −4.97204 −0.474066
\(111\) 9.02655 0.856763
\(112\) 0 0
\(113\) 15.3348 1.44258 0.721289 0.692635i \(-0.243550\pi\)
0.721289 + 0.692635i \(0.243550\pi\)
\(114\) 1.30825 0.122529
\(115\) 13.9178 1.29784
\(116\) −10.4841 −0.973420
\(117\) 5.04464 0.466378
\(118\) −22.7449 −2.09383
\(119\) 0 0
\(120\) 1.26221 0.115223
\(121\) −8.21977 −0.747252
\(122\) −22.6194 −2.04786
\(123\) 1.00000 0.0901670
\(124\) −3.71970 −0.334039
\(125\) −11.8474 −1.05966
\(126\) 0 0
\(127\) −15.4241 −1.36867 −0.684334 0.729169i \(-0.739907\pi\)
−0.684334 + 0.729169i \(0.739907\pi\)
\(128\) −6.26080 −0.553382
\(129\) −9.96021 −0.876948
\(130\) −15.0427 −1.31933
\(131\) 15.9345 1.39220 0.696100 0.717945i \(-0.254917\pi\)
0.696100 + 0.717945i \(0.254917\pi\)
\(132\) 2.62901 0.228826
\(133\) 0 0
\(134\) 1.64710 0.142288
\(135\) 1.57671 0.135702
\(136\) −5.09069 −0.436523
\(137\) 3.13313 0.267681 0.133841 0.991003i \(-0.457269\pi\)
0.133841 + 0.991003i \(0.457269\pi\)
\(138\) −16.6940 −1.42108
\(139\) 12.9192 1.09579 0.547895 0.836547i \(-0.315429\pi\)
0.547895 + 0.836547i \(0.315429\pi\)
\(140\) 0 0
\(141\) 1.33621 0.112529
\(142\) 20.6069 1.72929
\(143\) 8.41145 0.703401
\(144\) −4.66740 −0.388950
\(145\) −10.4841 −0.870653
\(146\) −5.28458 −0.437355
\(147\) 0 0
\(148\) 14.2323 1.16989
\(149\) 17.0545 1.39716 0.698580 0.715532i \(-0.253816\pi\)
0.698580 + 0.715532i \(0.253816\pi\)
\(150\) 4.75448 0.388202
\(151\) −4.62901 −0.376704 −0.188352 0.982102i \(-0.560315\pi\)
−0.188352 + 0.982102i \(0.560315\pi\)
\(152\) −0.553766 −0.0449164
\(153\) −6.35915 −0.514107
\(154\) 0 0
\(155\) −3.71970 −0.298774
\(156\) 7.95395 0.636826
\(157\) −18.4380 −1.47151 −0.735757 0.677246i \(-0.763173\pi\)
−0.735757 + 0.677246i \(0.763173\pi\)
\(158\) −23.1605 −1.84255
\(159\) 1.66115 0.131737
\(160\) 11.3934 0.900725
\(161\) 0 0
\(162\) −1.89122 −0.148588
\(163\) −17.6019 −1.37868 −0.689342 0.724436i \(-0.742100\pi\)
−0.689342 + 0.724436i \(0.742100\pi\)
\(164\) 1.57671 0.123121
\(165\) 2.62901 0.204669
\(166\) −4.97204 −0.385906
\(167\) 0.255948 0.0198059 0.00990294 0.999951i \(-0.496848\pi\)
0.00990294 + 0.999951i \(0.496848\pi\)
\(168\) 0 0
\(169\) 12.4484 0.957572
\(170\) 18.9624 1.45435
\(171\) −0.691750 −0.0528994
\(172\) −15.7044 −1.19745
\(173\) −21.9173 −1.66634 −0.833172 0.553014i \(-0.813478\pi\)
−0.833172 + 0.553014i \(0.813478\pi\)
\(174\) 12.5753 0.953332
\(175\) 0 0
\(176\) −7.78244 −0.586623
\(177\) 12.0266 0.903971
\(178\) −24.0531 −1.80286
\(179\) 15.5685 1.16364 0.581822 0.813316i \(-0.302340\pi\)
0.581822 + 0.813316i \(0.302340\pi\)
\(180\) 2.48602 0.185297
\(181\) 22.5707 1.67767 0.838833 0.544388i \(-0.183238\pi\)
0.838833 + 0.544388i \(0.183238\pi\)
\(182\) 0 0
\(183\) 11.9602 0.884124
\(184\) 7.06634 0.520938
\(185\) 14.2323 1.04638
\(186\) 4.46168 0.327146
\(187\) −10.6033 −0.775388
\(188\) 2.10681 0.153655
\(189\) 0 0
\(190\) 2.06273 0.149647
\(191\) 20.0797 1.45291 0.726457 0.687212i \(-0.241166\pi\)
0.726457 + 0.687212i \(0.241166\pi\)
\(192\) −4.33120 −0.312577
\(193\) 2.56628 0.184725 0.0923624 0.995725i \(-0.470558\pi\)
0.0923624 + 0.995725i \(0.470558\pi\)
\(194\) −6.07457 −0.436129
\(195\) 7.95395 0.569595
\(196\) 0 0
\(197\) 25.4241 1.81139 0.905696 0.423928i \(-0.139349\pi\)
0.905696 + 0.423928i \(0.139349\pi\)
\(198\) −3.15343 −0.224104
\(199\) −15.8215 −1.12156 −0.560778 0.827966i \(-0.689498\pi\)
−0.560778 + 0.827966i \(0.689498\pi\)
\(200\) −2.01251 −0.142306
\(201\) −0.870922 −0.0614301
\(202\) −15.0811 −1.06110
\(203\) 0 0
\(204\) −10.0266 −0.701999
\(205\) 1.57671 0.110122
\(206\) −11.9950 −0.835731
\(207\) 8.82708 0.613525
\(208\) −23.5454 −1.63258
\(209\) −1.15343 −0.0797841
\(210\) 0 0
\(211\) 5.63262 0.387766 0.193883 0.981025i \(-0.437892\pi\)
0.193883 + 0.981025i \(0.437892\pi\)
\(212\) 2.61915 0.179884
\(213\) −10.8961 −0.746587
\(214\) 21.2574 1.45313
\(215\) −15.7044 −1.07103
\(216\) 0.800530 0.0544691
\(217\) 0 0
\(218\) 14.1645 0.959344
\(219\) 2.79427 0.188819
\(220\) 4.14520 0.279469
\(221\) −32.0797 −2.15791
\(222\) −17.0712 −1.14574
\(223\) 14.7909 0.990472 0.495236 0.868758i \(-0.335082\pi\)
0.495236 + 0.868758i \(0.335082\pi\)
\(224\) 0 0
\(225\) −2.51398 −0.167599
\(226\) −29.0015 −1.92915
\(227\) 5.41298 0.359272 0.179636 0.983733i \(-0.442508\pi\)
0.179636 + 0.983733i \(0.442508\pi\)
\(228\) −1.09069 −0.0722327
\(229\) −0.527059 −0.0348290 −0.0174145 0.999848i \(-0.505543\pi\)
−0.0174145 + 0.999848i \(0.505543\pi\)
\(230\) −26.3216 −1.73559
\(231\) 0 0
\(232\) −5.32297 −0.349470
\(233\) −16.7449 −1.09699 −0.548496 0.836153i \(-0.684799\pi\)
−0.548496 + 0.836153i \(0.684799\pi\)
\(234\) −9.54053 −0.623684
\(235\) 2.10681 0.137433
\(236\) 18.9624 1.23435
\(237\) 12.2463 0.795484
\(238\) 0 0
\(239\) 1.42690 0.0922982 0.0461491 0.998935i \(-0.485305\pi\)
0.0461491 + 0.998935i \(0.485305\pi\)
\(240\) −7.35915 −0.475031
\(241\) −12.8767 −0.829464 −0.414732 0.909944i \(-0.636125\pi\)
−0.414732 + 0.909944i \(0.636125\pi\)
\(242\) 15.5454 0.999295
\(243\) 1.00000 0.0641500
\(244\) 18.8578 1.20725
\(245\) 0 0
\(246\) −1.89122 −0.120580
\(247\) −3.48963 −0.222040
\(248\) −1.88857 −0.119924
\(249\) 2.62901 0.166607
\(250\) 22.4060 1.41708
\(251\) 20.8104 1.31354 0.656770 0.754091i \(-0.271922\pi\)
0.656770 + 0.754091i \(0.271922\pi\)
\(252\) 0 0
\(253\) 14.7183 0.925332
\(254\) 29.1704 1.83031
\(255\) −10.0266 −0.627887
\(256\) 20.5030 1.28143
\(257\) 24.4388 1.52445 0.762226 0.647311i \(-0.224107\pi\)
0.762226 + 0.647311i \(0.224107\pi\)
\(258\) 18.8369 1.17274
\(259\) 0 0
\(260\) 12.5411 0.777766
\(261\) −6.64931 −0.411582
\(262\) −30.1356 −1.86178
\(263\) −15.0147 −0.925847 −0.462924 0.886398i \(-0.653200\pi\)
−0.462924 + 0.886398i \(0.653200\pi\)
\(264\) 1.33481 0.0821516
\(265\) 2.61915 0.160893
\(266\) 0 0
\(267\) 12.7183 0.778348
\(268\) −1.37319 −0.0838811
\(269\) −4.84598 −0.295465 −0.147732 0.989027i \(-0.547197\pi\)
−0.147732 + 0.989027i \(0.547197\pi\)
\(270\) −2.98191 −0.181473
\(271\) −15.3411 −0.931903 −0.465952 0.884810i \(-0.654288\pi\)
−0.465952 + 0.884810i \(0.654288\pi\)
\(272\) 29.6807 1.79966
\(273\) 0 0
\(274\) −5.92543 −0.357968
\(275\) −4.19181 −0.252776
\(276\) 13.9178 0.837752
\(277\) −4.75741 −0.285845 −0.142923 0.989734i \(-0.545650\pi\)
−0.142923 + 0.989734i \(0.545650\pi\)
\(278\) −24.4330 −1.46539
\(279\) −2.35915 −0.141239
\(280\) 0 0
\(281\) −29.6242 −1.76723 −0.883617 0.468210i \(-0.844899\pi\)
−0.883617 + 0.468210i \(0.844899\pi\)
\(282\) −2.52706 −0.150484
\(283\) 4.78176 0.284246 0.142123 0.989849i \(-0.454607\pi\)
0.142123 + 0.989849i \(0.454607\pi\)
\(284\) −17.1800 −1.01944
\(285\) −1.09069 −0.0646069
\(286\) −15.9079 −0.940654
\(287\) 0 0
\(288\) 7.22603 0.425798
\(289\) 23.4388 1.37875
\(290\) 19.8277 1.16432
\(291\) 3.21198 0.188290
\(292\) 4.40576 0.257828
\(293\) −15.6380 −0.913584 −0.456792 0.889573i \(-0.651002\pi\)
−0.456792 + 0.889573i \(0.651002\pi\)
\(294\) 0 0
\(295\) 18.9624 1.10403
\(296\) 7.22603 0.420004
\(297\) 1.66740 0.0967525
\(298\) −32.2538 −1.86841
\(299\) 44.5295 2.57521
\(300\) −3.96382 −0.228851
\(301\) 0 0
\(302\) 8.75448 0.503764
\(303\) 7.97425 0.458109
\(304\) 3.22867 0.185177
\(305\) 18.8578 1.07980
\(306\) 12.0266 0.687512
\(307\) 21.2711 1.21401 0.607003 0.794699i \(-0.292372\pi\)
0.607003 + 0.794699i \(0.292372\pi\)
\(308\) 0 0
\(309\) 6.34246 0.360810
\(310\) 7.03478 0.399549
\(311\) −2.85031 −0.161626 −0.0808131 0.996729i \(-0.525752\pi\)
−0.0808131 + 0.996729i \(0.525752\pi\)
\(312\) 4.03839 0.228629
\(313\) 13.3306 0.753492 0.376746 0.926317i \(-0.377043\pi\)
0.376746 + 0.926317i \(0.377043\pi\)
\(314\) 34.8703 1.96785
\(315\) 0 0
\(316\) 19.3089 1.08621
\(317\) 8.50980 0.477958 0.238979 0.971025i \(-0.423187\pi\)
0.238979 + 0.971025i \(0.423187\pi\)
\(318\) −3.14159 −0.176172
\(319\) −11.0871 −0.620757
\(320\) −6.82905 −0.381756
\(321\) −11.2401 −0.627359
\(322\) 0 0
\(323\) 4.39894 0.244764
\(324\) 1.57671 0.0875951
\(325\) −12.6821 −0.703478
\(326\) 33.2890 1.84371
\(327\) −7.48963 −0.414178
\(328\) 0.800530 0.0442019
\(329\) 0 0
\(330\) −4.97204 −0.273702
\(331\) −29.9173 −1.64441 −0.822203 0.569195i \(-0.807255\pi\)
−0.822203 + 0.569195i \(0.807255\pi\)
\(332\) 4.14520 0.227497
\(333\) 9.02655 0.494652
\(334\) −0.484055 −0.0264863
\(335\) −1.37319 −0.0750256
\(336\) 0 0
\(337\) −6.71161 −0.365605 −0.182802 0.983150i \(-0.558517\pi\)
−0.182802 + 0.983150i \(0.558517\pi\)
\(338\) −23.5427 −1.28056
\(339\) 15.3348 0.832872
\(340\) −15.8090 −0.857363
\(341\) −3.93366 −0.213019
\(342\) 1.30825 0.0707421
\(343\) 0 0
\(344\) −7.97345 −0.429899
\(345\) 13.9178 0.749308
\(346\) 41.4505 2.22839
\(347\) 34.5656 1.85558 0.927788 0.373107i \(-0.121708\pi\)
0.927788 + 0.373107i \(0.121708\pi\)
\(348\) −10.4841 −0.562004
\(349\) −9.95211 −0.532724 −0.266362 0.963873i \(-0.585822\pi\)
−0.266362 + 0.963873i \(0.585822\pi\)
\(350\) 0 0
\(351\) 5.04464 0.269263
\(352\) 12.0487 0.642198
\(353\) 7.57739 0.403304 0.201652 0.979457i \(-0.435369\pi\)
0.201652 + 0.979457i \(0.435369\pi\)
\(354\) −22.7449 −1.20888
\(355\) −17.1800 −0.911819
\(356\) 20.0531 1.06281
\(357\) 0 0
\(358\) −29.4434 −1.55613
\(359\) −6.47307 −0.341635 −0.170818 0.985303i \(-0.554641\pi\)
−0.170818 + 0.985303i \(0.554641\pi\)
\(360\) 1.26221 0.0665241
\(361\) −18.5215 −0.974815
\(362\) −42.6861 −2.24353
\(363\) −8.21977 −0.431426
\(364\) 0 0
\(365\) 4.40576 0.230608
\(366\) −22.6194 −1.18233
\(367\) 11.1250 0.580722 0.290361 0.956917i \(-0.406225\pi\)
0.290361 + 0.956917i \(0.406225\pi\)
\(368\) −41.1996 −2.14768
\(369\) 1.00000 0.0520579
\(370\) −26.9164 −1.39932
\(371\) 0 0
\(372\) −3.71970 −0.192858
\(373\) −25.1437 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(374\) 20.0531 1.03692
\(375\) −11.8474 −0.611796
\(376\) 1.06967 0.0551641
\(377\) −33.5434 −1.72757
\(378\) 0 0
\(379\) −24.8289 −1.27537 −0.637686 0.770296i \(-0.720108\pi\)
−0.637686 + 0.770296i \(0.720108\pi\)
\(380\) −1.71970 −0.0882190
\(381\) −15.4241 −0.790200
\(382\) −37.9751 −1.94297
\(383\) 18.1410 0.926962 0.463481 0.886107i \(-0.346600\pi\)
0.463481 + 0.886107i \(0.346600\pi\)
\(384\) −6.26080 −0.319495
\(385\) 0 0
\(386\) −4.85340 −0.247032
\(387\) −9.96021 −0.506306
\(388\) 5.06438 0.257105
\(389\) −28.8703 −1.46378 −0.731892 0.681421i \(-0.761362\pi\)
−0.731892 + 0.681421i \(0.761362\pi\)
\(390\) −15.0427 −0.761716
\(391\) −56.1328 −2.83876
\(392\) 0 0
\(393\) 15.9345 0.803787
\(394\) −48.0826 −2.42236
\(395\) 19.3089 0.971538
\(396\) 2.62901 0.132113
\(397\) −26.5988 −1.33495 −0.667477 0.744630i \(-0.732626\pi\)
−0.667477 + 0.744630i \(0.732626\pi\)
\(398\) 29.9220 1.49985
\(399\) 0 0
\(400\) 11.7337 0.586687
\(401\) 7.07665 0.353391 0.176695 0.984266i \(-0.443459\pi\)
0.176695 + 0.984266i \(0.443459\pi\)
\(402\) 1.64710 0.0821501
\(403\) −11.9011 −0.592835
\(404\) 12.5731 0.625535
\(405\) 1.57671 0.0783475
\(406\) 0 0
\(407\) 15.0509 0.746046
\(408\) −5.09069 −0.252027
\(409\) 9.14019 0.451953 0.225977 0.974133i \(-0.427443\pi\)
0.225977 + 0.974133i \(0.427443\pi\)
\(410\) −2.98191 −0.147266
\(411\) 3.13313 0.154546
\(412\) 10.0002 0.492676
\(413\) 0 0
\(414\) −16.6940 −0.820463
\(415\) 4.14520 0.203480
\(416\) 36.4527 1.78724
\(417\) 12.9192 0.632655
\(418\) 2.18138 0.106695
\(419\) 23.3208 1.13929 0.569647 0.821890i \(-0.307080\pi\)
0.569647 + 0.821890i \(0.307080\pi\)
\(420\) 0 0
\(421\) −7.23309 −0.352519 −0.176260 0.984344i \(-0.556400\pi\)
−0.176260 + 0.984344i \(0.556400\pi\)
\(422\) −10.6525 −0.518557
\(423\) 1.33621 0.0649685
\(424\) 1.32980 0.0645806
\(425\) 15.9868 0.775472
\(426\) 20.6069 0.998406
\(427\) 0 0
\(428\) −17.7224 −0.856642
\(429\) 8.41145 0.406109
\(430\) 29.7005 1.43228
\(431\) 9.75308 0.469790 0.234895 0.972021i \(-0.424525\pi\)
0.234895 + 0.972021i \(0.424525\pi\)
\(432\) −4.66740 −0.224561
\(433\) −14.8459 −0.713446 −0.356723 0.934210i \(-0.616106\pi\)
−0.356723 + 0.934210i \(0.616106\pi\)
\(434\) 0 0
\(435\) −10.4841 −0.502672
\(436\) −11.8090 −0.565548
\(437\) −6.10613 −0.292096
\(438\) −5.28458 −0.252507
\(439\) 0.686453 0.0327626 0.0163813 0.999866i \(-0.494785\pi\)
0.0163813 + 0.999866i \(0.494785\pi\)
\(440\) 2.10460 0.100333
\(441\) 0 0
\(442\) 60.6697 2.88576
\(443\) 14.2413 0.676625 0.338313 0.941034i \(-0.390144\pi\)
0.338313 + 0.941034i \(0.390144\pi\)
\(444\) 14.2323 0.675434
\(445\) 20.0531 0.950609
\(446\) −27.9729 −1.32455
\(447\) 17.0545 0.806651
\(448\) 0 0
\(449\) 21.0517 0.993492 0.496746 0.867896i \(-0.334528\pi\)
0.496746 + 0.867896i \(0.334528\pi\)
\(450\) 4.75448 0.224129
\(451\) 1.66740 0.0785149
\(452\) 24.1786 1.13726
\(453\) −4.62901 −0.217490
\(454\) −10.2371 −0.480453
\(455\) 0 0
\(456\) −0.553766 −0.0259325
\(457\) −29.4366 −1.37699 −0.688493 0.725243i \(-0.741728\pi\)
−0.688493 + 0.725243i \(0.741728\pi\)
\(458\) 0.996784 0.0465767
\(459\) −6.35915 −0.296820
\(460\) 21.9443 1.02316
\(461\) −12.8388 −0.597961 −0.298980 0.954259i \(-0.596647\pi\)
−0.298980 + 0.954259i \(0.596647\pi\)
\(462\) 0 0
\(463\) −12.2308 −0.568411 −0.284206 0.958763i \(-0.591730\pi\)
−0.284206 + 0.958763i \(0.591730\pi\)
\(464\) 31.0350 1.44076
\(465\) −3.71970 −0.172497
\(466\) 31.6682 1.46700
\(467\) 22.4867 1.04056 0.520280 0.853996i \(-0.325827\pi\)
0.520280 + 0.853996i \(0.325827\pi\)
\(468\) 7.95395 0.367672
\(469\) 0 0
\(470\) −3.98445 −0.183789
\(471\) −18.4380 −0.849579
\(472\) 9.62761 0.443147
\(473\) −16.6077 −0.763622
\(474\) −23.1605 −1.06380
\(475\) 1.73904 0.0797928
\(476\) 0 0
\(477\) 1.66115 0.0760586
\(478\) −2.69857 −0.123430
\(479\) −0.0510288 −0.00233156 −0.00116578 0.999999i \(-0.500371\pi\)
−0.00116578 + 0.999999i \(0.500371\pi\)
\(480\) 11.3934 0.520034
\(481\) 45.5358 2.07625
\(482\) 24.3527 1.10924
\(483\) 0 0
\(484\) −12.9602 −0.589101
\(485\) 5.06438 0.229961
\(486\) −1.89122 −0.0857875
\(487\) 21.9309 0.993782 0.496891 0.867813i \(-0.334475\pi\)
0.496891 + 0.867813i \(0.334475\pi\)
\(488\) 9.57450 0.433417
\(489\) −17.6019 −0.795984
\(490\) 0 0
\(491\) −22.7657 −1.02740 −0.513701 0.857969i \(-0.671726\pi\)
−0.513701 + 0.857969i \(0.671726\pi\)
\(492\) 1.57671 0.0710837
\(493\) 42.2840 1.90438
\(494\) 6.59966 0.296933
\(495\) 2.62901 0.118165
\(496\) 11.0111 0.494414
\(497\) 0 0
\(498\) −4.97204 −0.222803
\(499\) 25.0730 1.12242 0.561210 0.827673i \(-0.310336\pi\)
0.561210 + 0.827673i \(0.310336\pi\)
\(500\) −18.6799 −0.835391
\(501\) 0.255948 0.0114349
\(502\) −39.3570 −1.75659
\(503\) 29.4448 1.31288 0.656440 0.754378i \(-0.272061\pi\)
0.656440 + 0.754378i \(0.272061\pi\)
\(504\) 0 0
\(505\) 12.5731 0.559496
\(506\) −27.8355 −1.23744
\(507\) 12.4484 0.552855
\(508\) −24.3194 −1.07900
\(509\) −8.94477 −0.396470 −0.198235 0.980155i \(-0.563521\pi\)
−0.198235 + 0.980155i \(0.563521\pi\)
\(510\) 18.9624 0.839670
\(511\) 0 0
\(512\) −26.2540 −1.16027
\(513\) −0.691750 −0.0305415
\(514\) −46.2192 −2.03864
\(515\) 10.0002 0.440663
\(516\) −15.7044 −0.691347
\(517\) 2.22799 0.0979870
\(518\) 0 0
\(519\) −21.9173 −0.962064
\(520\) 6.36738 0.279228
\(521\) 1.13578 0.0497592 0.0248796 0.999690i \(-0.492080\pi\)
0.0248796 + 0.999690i \(0.492080\pi\)
\(522\) 12.5753 0.550406
\(523\) −24.2249 −1.05928 −0.529640 0.848223i \(-0.677673\pi\)
−0.529640 + 0.848223i \(0.677673\pi\)
\(524\) 25.1241 1.09755
\(525\) 0 0
\(526\) 28.3961 1.23813
\(527\) 15.0022 0.653506
\(528\) −7.78244 −0.338687
\(529\) 54.9174 2.38771
\(530\) −4.95339 −0.215161
\(531\) 12.0266 0.521908
\(532\) 0 0
\(533\) 5.04464 0.218508
\(534\) −24.0531 −1.04088
\(535\) −17.7224 −0.766204
\(536\) −0.697199 −0.0301144
\(537\) 15.5685 0.671830
\(538\) 9.16482 0.395123
\(539\) 0 0
\(540\) 2.48602 0.106981
\(541\) 15.5016 0.666464 0.333232 0.942845i \(-0.391861\pi\)
0.333232 + 0.942845i \(0.391861\pi\)
\(542\) 29.0133 1.24623
\(543\) 22.5707 0.968601
\(544\) −45.9514 −1.97015
\(545\) −11.8090 −0.505842
\(546\) 0 0
\(547\) 33.5952 1.43643 0.718213 0.695823i \(-0.244960\pi\)
0.718213 + 0.695823i \(0.244960\pi\)
\(548\) 4.94004 0.211028
\(549\) 11.9602 0.510449
\(550\) 7.92764 0.338036
\(551\) 4.59966 0.195952
\(552\) 7.06634 0.300764
\(553\) 0 0
\(554\) 8.99731 0.382259
\(555\) 14.2323 0.604127
\(556\) 20.3698 0.863873
\(557\) 12.7050 0.538327 0.269164 0.963094i \(-0.413253\pi\)
0.269164 + 0.963094i \(0.413253\pi\)
\(558\) 4.46168 0.188878
\(559\) −50.2457 −2.12517
\(560\) 0 0
\(561\) −10.6033 −0.447670
\(562\) 56.0260 2.36331
\(563\) 17.0531 0.718703 0.359351 0.933202i \(-0.382998\pi\)
0.359351 + 0.933202i \(0.382998\pi\)
\(564\) 2.10681 0.0887128
\(565\) 24.1786 1.01720
\(566\) −9.04336 −0.380121
\(567\) 0 0
\(568\) −8.72263 −0.365994
\(569\) 28.0319 1.17516 0.587578 0.809167i \(-0.300081\pi\)
0.587578 + 0.809167i \(0.300081\pi\)
\(570\) 2.06273 0.0863985
\(571\) −30.4034 −1.27234 −0.636170 0.771549i \(-0.719482\pi\)
−0.636170 + 0.771549i \(0.719482\pi\)
\(572\) 13.2624 0.554531
\(573\) 20.0797 0.838840
\(574\) 0 0
\(575\) −22.1911 −0.925433
\(576\) −4.33120 −0.180467
\(577\) −32.6653 −1.35987 −0.679937 0.733271i \(-0.737993\pi\)
−0.679937 + 0.733271i \(0.737993\pi\)
\(578\) −44.3280 −1.84380
\(579\) 2.56628 0.106651
\(580\) −16.5303 −0.686385
\(581\) 0 0
\(582\) −6.07457 −0.251799
\(583\) 2.76980 0.114713
\(584\) 2.23690 0.0925635
\(585\) 7.95395 0.328856
\(586\) 29.5750 1.22173
\(587\) −4.70346 −0.194132 −0.0970662 0.995278i \(-0.530946\pi\)
−0.0970662 + 0.995278i \(0.530946\pi\)
\(588\) 0 0
\(589\) 1.63194 0.0672430
\(590\) −35.8621 −1.47642
\(591\) 25.4241 1.04581
\(592\) −42.1306 −1.73156
\(593\) −22.8333 −0.937653 −0.468826 0.883290i \(-0.655323\pi\)
−0.468826 + 0.883290i \(0.655323\pi\)
\(594\) −3.15343 −0.129387
\(595\) 0 0
\(596\) 26.8901 1.10146
\(597\) −15.8215 −0.647531
\(598\) −84.2151 −3.44381
\(599\) −28.2078 −1.15254 −0.576269 0.817260i \(-0.695492\pi\)
−0.576269 + 0.817260i \(0.695492\pi\)
\(600\) −2.01251 −0.0821605
\(601\) 46.0212 1.87724 0.938622 0.344948i \(-0.112103\pi\)
0.938622 + 0.344948i \(0.112103\pi\)
\(602\) 0 0
\(603\) −0.870922 −0.0354667
\(604\) −7.29863 −0.296977
\(605\) −12.9602 −0.526908
\(606\) −15.0811 −0.612626
\(607\) 48.3754 1.96350 0.981748 0.190188i \(-0.0609098\pi\)
0.981748 + 0.190188i \(0.0609098\pi\)
\(608\) −4.99860 −0.202720
\(609\) 0 0
\(610\) −35.6643 −1.44400
\(611\) 6.74068 0.272699
\(612\) −10.0266 −0.405299
\(613\) 30.5767 1.23498 0.617490 0.786579i \(-0.288150\pi\)
0.617490 + 0.786579i \(0.288150\pi\)
\(614\) −40.2283 −1.62348
\(615\) 1.57671 0.0635792
\(616\) 0 0
\(617\) 38.6874 1.55750 0.778748 0.627336i \(-0.215855\pi\)
0.778748 + 0.627336i \(0.215855\pi\)
\(618\) −11.9950 −0.482509
\(619\) −0.413942 −0.0166377 −0.00831886 0.999965i \(-0.502648\pi\)
−0.00831886 + 0.999965i \(0.502648\pi\)
\(620\) −5.86491 −0.235540
\(621\) 8.82708 0.354219
\(622\) 5.39056 0.216142
\(623\) 0 0
\(624\) −23.5454 −0.942570
\(625\) −6.11003 −0.244401
\(626\) −25.2112 −1.00764
\(627\) −1.15343 −0.0460634
\(628\) −29.0714 −1.16008
\(629\) −57.4012 −2.28874
\(630\) 0 0
\(631\) 2.84144 0.113116 0.0565580 0.998399i \(-0.481987\pi\)
0.0565580 + 0.998399i \(0.481987\pi\)
\(632\) 9.80355 0.389964
\(633\) 5.63262 0.223877
\(634\) −16.0939 −0.639171
\(635\) −24.3194 −0.965085
\(636\) 2.61915 0.103856
\(637\) 0 0
\(638\) 20.9681 0.830135
\(639\) −10.8961 −0.431042
\(640\) −9.87149 −0.390205
\(641\) −9.25354 −0.365493 −0.182746 0.983160i \(-0.558499\pi\)
−0.182746 + 0.983160i \(0.558499\pi\)
\(642\) 21.2574 0.838964
\(643\) −8.80165 −0.347103 −0.173552 0.984825i \(-0.555524\pi\)
−0.173552 + 0.984825i \(0.555524\pi\)
\(644\) 0 0
\(645\) −15.7044 −0.618360
\(646\) −8.31936 −0.327321
\(647\) 30.1439 1.18508 0.592540 0.805541i \(-0.298125\pi\)
0.592540 + 0.805541i \(0.298125\pi\)
\(648\) 0.800530 0.0314478
\(649\) 20.0531 0.787153
\(650\) 23.9847 0.940757
\(651\) 0 0
\(652\) −27.7531 −1.08689
\(653\) 3.42858 0.134171 0.0670854 0.997747i \(-0.478630\pi\)
0.0670854 + 0.997747i \(0.478630\pi\)
\(654\) 14.1645 0.553877
\(655\) 25.1241 0.981679
\(656\) −4.66740 −0.182231
\(657\) 2.79427 0.109015
\(658\) 0 0
\(659\) 5.84806 0.227808 0.113904 0.993492i \(-0.463664\pi\)
0.113904 + 0.993492i \(0.463664\pi\)
\(660\) 4.14520 0.161352
\(661\) 10.8716 0.422856 0.211428 0.977394i \(-0.432189\pi\)
0.211428 + 0.977394i \(0.432189\pi\)
\(662\) 56.5803 2.19905
\(663\) −32.0797 −1.24587
\(664\) 2.10460 0.0816745
\(665\) 0 0
\(666\) −17.0712 −0.661496
\(667\) −58.6940 −2.27264
\(668\) 0.403557 0.0156141
\(669\) 14.7909 0.571849
\(670\) 2.59701 0.100331
\(671\) 19.9425 0.769871
\(672\) 0 0
\(673\) 22.8775 0.881865 0.440932 0.897540i \(-0.354648\pi\)
0.440932 + 0.897540i \(0.354648\pi\)
\(674\) 12.6931 0.488921
\(675\) −2.51398 −0.0967630
\(676\) 19.6276 0.754908
\(677\) 16.2635 0.625055 0.312528 0.949909i \(-0.398824\pi\)
0.312528 + 0.949909i \(0.398824\pi\)
\(678\) −29.0015 −1.11380
\(679\) 0 0
\(680\) −8.02655 −0.307804
\(681\) 5.41298 0.207426
\(682\) 7.43941 0.284870
\(683\) 7.01794 0.268534 0.134267 0.990945i \(-0.457132\pi\)
0.134267 + 0.990945i \(0.457132\pi\)
\(684\) −1.09069 −0.0417036
\(685\) 4.94004 0.188749
\(686\) 0 0
\(687\) −0.527059 −0.0201085
\(688\) 46.4883 1.77235
\(689\) 8.37989 0.319248
\(690\) −26.3216 −1.00205
\(691\) −47.3364 −1.80076 −0.900381 0.435102i \(-0.856712\pi\)
−0.900381 + 0.435102i \(0.856712\pi\)
\(692\) −34.5573 −1.31367
\(693\) 0 0
\(694\) −65.3711 −2.48145
\(695\) 20.3698 0.772672
\(696\) −5.32297 −0.201767
\(697\) −6.35915 −0.240870
\(698\) 18.8216 0.712409
\(699\) −16.7449 −0.633349
\(700\) 0 0
\(701\) 2.65268 0.100190 0.0500952 0.998744i \(-0.484048\pi\)
0.0500952 + 0.998744i \(0.484048\pi\)
\(702\) −9.54053 −0.360084
\(703\) −6.24412 −0.235501
\(704\) −7.22185 −0.272184
\(705\) 2.10681 0.0793471
\(706\) −14.3305 −0.539336
\(707\) 0 0
\(708\) 18.9624 0.712651
\(709\) −28.8201 −1.08236 −0.541181 0.840906i \(-0.682023\pi\)
−0.541181 + 0.840906i \(0.682023\pi\)
\(710\) 32.4911 1.21937
\(711\) 12.2463 0.459273
\(712\) 10.1814 0.381563
\(713\) −20.8244 −0.779881
\(714\) 0 0
\(715\) 13.2624 0.495987
\(716\) 24.5470 0.917366
\(717\) 1.42690 0.0532884
\(718\) 12.2420 0.456867
\(719\) −23.3900 −0.872300 −0.436150 0.899874i \(-0.643658\pi\)
−0.436150 + 0.899874i \(0.643658\pi\)
\(720\) −7.35915 −0.274259
\(721\) 0 0
\(722\) 35.0282 1.30361
\(723\) −12.8767 −0.478891
\(724\) 35.5875 1.32260
\(725\) 16.7162 0.620825
\(726\) 15.5454 0.576943
\(727\) −24.6218 −0.913172 −0.456586 0.889679i \(-0.650928\pi\)
−0.456586 + 0.889679i \(0.650928\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −8.33227 −0.308391
\(731\) 63.3385 2.34266
\(732\) 18.8578 0.697005
\(733\) 47.1181 1.74035 0.870174 0.492744i \(-0.164006\pi\)
0.870174 + 0.492744i \(0.164006\pi\)
\(734\) −21.0399 −0.776596
\(735\) 0 0
\(736\) 63.7847 2.35114
\(737\) −1.45218 −0.0534916
\(738\) −1.89122 −0.0696168
\(739\) −2.83767 −0.104385 −0.0521927 0.998637i \(-0.516621\pi\)
−0.0521927 + 0.998637i \(0.516621\pi\)
\(740\) 22.4402 0.824919
\(741\) −3.48963 −0.128195
\(742\) 0 0
\(743\) −15.6763 −0.575108 −0.287554 0.957764i \(-0.592842\pi\)
−0.287554 + 0.957764i \(0.592842\pi\)
\(744\) −1.88857 −0.0692384
\(745\) 26.8901 0.985176
\(746\) 47.5522 1.74101
\(747\) 2.62901 0.0961906
\(748\) −16.7183 −0.611282
\(749\) 0 0
\(750\) 22.4060 0.818152
\(751\) −26.2001 −0.956056 −0.478028 0.878345i \(-0.658648\pi\)
−0.478028 + 0.878345i \(0.658648\pi\)
\(752\) −6.23661 −0.227426
\(753\) 20.8104 0.758373
\(754\) 63.4380 2.31028
\(755\) −7.29863 −0.265624
\(756\) 0 0
\(757\) 36.9359 1.34246 0.671228 0.741251i \(-0.265767\pi\)
0.671228 + 0.741251i \(0.265767\pi\)
\(758\) 46.9568 1.70555
\(759\) 14.7183 0.534241
\(760\) −0.873130 −0.0316717
\(761\) 4.64085 0.168231 0.0841153 0.996456i \(-0.473194\pi\)
0.0841153 + 0.996456i \(0.473194\pi\)
\(762\) 29.1704 1.05673
\(763\) 0 0
\(764\) 31.6599 1.14541
\(765\) −10.0266 −0.362511
\(766\) −34.3086 −1.23962
\(767\) 60.6697 2.19066
\(768\) 20.5030 0.739837
\(769\) 37.9759 1.36944 0.684722 0.728804i \(-0.259923\pi\)
0.684722 + 0.728804i \(0.259923\pi\)
\(770\) 0 0
\(771\) 24.4388 0.880142
\(772\) 4.04629 0.145629
\(773\) 35.0191 1.25955 0.629775 0.776777i \(-0.283147\pi\)
0.629775 + 0.776777i \(0.283147\pi\)
\(774\) 18.8369 0.677080
\(775\) 5.93086 0.213043
\(776\) 2.57129 0.0923039
\(777\) 0 0
\(778\) 54.6001 1.95751
\(779\) −0.691750 −0.0247845
\(780\) 12.5411 0.449043
\(781\) −18.1681 −0.650107
\(782\) 106.159 3.79625
\(783\) −6.64931 −0.237627
\(784\) 0 0
\(785\) −29.0714 −1.03760
\(786\) −30.1356 −1.07490
\(787\) −30.4583 −1.08572 −0.542861 0.839823i \(-0.682659\pi\)
−0.542861 + 0.839823i \(0.682659\pi\)
\(788\) 40.0865 1.42802
\(789\) −15.0147 −0.534538
\(790\) −36.5174 −1.29923
\(791\) 0 0
\(792\) 1.33481 0.0474302
\(793\) 60.3350 2.14256
\(794\) 50.3041 1.78523
\(795\) 2.61915 0.0928917
\(796\) −24.9460 −0.884186
\(797\) −14.9234 −0.528612 −0.264306 0.964439i \(-0.585143\pi\)
−0.264306 + 0.964439i \(0.585143\pi\)
\(798\) 0 0
\(799\) −8.49714 −0.300607
\(800\) −18.1661 −0.642267
\(801\) 12.7183 0.449379
\(802\) −13.3835 −0.472588
\(803\) 4.65918 0.164419
\(804\) −1.37319 −0.0484288
\(805\) 0 0
\(806\) 22.5076 0.792795
\(807\) −4.84598 −0.170587
\(808\) 6.38363 0.224575
\(809\) 40.8287 1.43546 0.717730 0.696321i \(-0.245181\pi\)
0.717730 + 0.696321i \(0.245181\pi\)
\(810\) −2.98191 −0.104774
\(811\) −11.4066 −0.400540 −0.200270 0.979741i \(-0.564182\pi\)
−0.200270 + 0.979741i \(0.564182\pi\)
\(812\) 0 0
\(813\) −15.3411 −0.538035
\(814\) −28.4646 −0.997682
\(815\) −27.7531 −0.972148
\(816\) 29.6807 1.03903
\(817\) 6.88997 0.241050
\(818\) −17.2861 −0.604395
\(819\) 0 0
\(820\) 2.48602 0.0868157
\(821\) 42.0952 1.46913 0.734567 0.678536i \(-0.237385\pi\)
0.734567 + 0.678536i \(0.237385\pi\)
\(822\) −5.92543 −0.206673
\(823\) −17.7641 −0.619217 −0.309608 0.950864i \(-0.600198\pi\)
−0.309608 + 0.950864i \(0.600198\pi\)
\(824\) 5.07733 0.176877
\(825\) −4.19181 −0.145940
\(826\) 0 0
\(827\) −24.3092 −0.845313 −0.422657 0.906290i \(-0.638902\pi\)
−0.422657 + 0.906290i \(0.638902\pi\)
\(828\) 13.9178 0.483676
\(829\) −20.3379 −0.706364 −0.353182 0.935555i \(-0.614900\pi\)
−0.353182 + 0.935555i \(0.614900\pi\)
\(830\) −7.83949 −0.272113
\(831\) −4.75741 −0.165033
\(832\) −21.8494 −0.757490
\(833\) 0 0
\(834\) −24.4330 −0.846046
\(835\) 0.403557 0.0139657
\(836\) −1.81862 −0.0628983
\(837\) −2.35915 −0.0815442
\(838\) −44.1047 −1.52357
\(839\) −7.52649 −0.259843 −0.129922 0.991524i \(-0.541473\pi\)
−0.129922 + 0.991524i \(0.541473\pi\)
\(840\) 0 0
\(841\) 15.2134 0.524599
\(842\) 13.6794 0.471422
\(843\) −29.6242 −1.02031
\(844\) 8.88103 0.305698
\(845\) 19.6276 0.675210
\(846\) −2.52706 −0.0868821
\(847\) 0 0
\(848\) −7.75324 −0.266247
\(849\) 4.78176 0.164110
\(850\) −30.2345 −1.03703
\(851\) 79.6782 2.73133
\(852\) −17.1800 −0.588576
\(853\) 30.5664 1.04657 0.523286 0.852157i \(-0.324706\pi\)
0.523286 + 0.852157i \(0.324706\pi\)
\(854\) 0 0
\(855\) −1.09069 −0.0373008
\(856\) −8.99801 −0.307546
\(857\) −23.2562 −0.794415 −0.397208 0.917729i \(-0.630021\pi\)
−0.397208 + 0.917729i \(0.630021\pi\)
\(858\) −15.9079 −0.543087
\(859\) 15.2284 0.519585 0.259792 0.965664i \(-0.416346\pi\)
0.259792 + 0.965664i \(0.416346\pi\)
\(860\) −24.7613 −0.844354
\(861\) 0 0
\(862\) −18.4452 −0.628247
\(863\) −31.1449 −1.06019 −0.530093 0.847940i \(-0.677843\pi\)
−0.530093 + 0.847940i \(0.677843\pi\)
\(864\) 7.22603 0.245834
\(865\) −34.5573 −1.17498
\(866\) 28.0768 0.954088
\(867\) 23.4388 0.796024
\(868\) 0 0
\(869\) 20.4196 0.692686
\(870\) 19.8277 0.672220
\(871\) −4.39349 −0.148868
\(872\) −5.99567 −0.203039
\(873\) 3.21198 0.108709
\(874\) 11.5480 0.390618
\(875\) 0 0
\(876\) 4.40576 0.148857
\(877\) 11.7539 0.396901 0.198450 0.980111i \(-0.436409\pi\)
0.198450 + 0.980111i \(0.436409\pi\)
\(878\) −1.29823 −0.0438132
\(879\) −15.6380 −0.527458
\(880\) −12.2707 −0.413644
\(881\) 47.4654 1.59915 0.799575 0.600567i \(-0.205058\pi\)
0.799575 + 0.600567i \(0.205058\pi\)
\(882\) 0 0
\(883\) 10.4218 0.350720 0.175360 0.984504i \(-0.443891\pi\)
0.175360 + 0.984504i \(0.443891\pi\)
\(884\) −50.5804 −1.70120
\(885\) 18.9624 0.637415
\(886\) −26.9335 −0.904847
\(887\) 4.31114 0.144754 0.0723769 0.997377i \(-0.476942\pi\)
0.0723769 + 0.997377i \(0.476942\pi\)
\(888\) 7.22603 0.242490
\(889\) 0 0
\(890\) −37.9248 −1.27124
\(891\) 1.66740 0.0558601
\(892\) 23.3210 0.780845
\(893\) −0.924320 −0.0309312
\(894\) −32.2538 −1.07873
\(895\) 24.5470 0.820517
\(896\) 0 0
\(897\) 44.5295 1.48680
\(898\) −39.8134 −1.32859
\(899\) 15.6867 0.523182
\(900\) −3.96382 −0.132127
\(901\) −10.5635 −0.351921
\(902\) −3.15343 −0.104998
\(903\) 0 0
\(904\) 12.2760 0.408293
\(905\) 35.5875 1.18297
\(906\) 8.75448 0.290848
\(907\) −7.31924 −0.243031 −0.121516 0.992590i \(-0.538775\pi\)
−0.121516 + 0.992590i \(0.538775\pi\)
\(908\) 8.53472 0.283235
\(909\) 7.97425 0.264489
\(910\) 0 0
\(911\) −13.5987 −0.450543 −0.225272 0.974296i \(-0.572327\pi\)
−0.225272 + 0.974296i \(0.572327\pi\)
\(912\) 3.22867 0.106912
\(913\) 4.38363 0.145077
\(914\) 55.6711 1.84144
\(915\) 18.8578 0.623420
\(916\) −0.831020 −0.0274577
\(917\) 0 0
\(918\) 12.0266 0.396935
\(919\) −21.2143 −0.699797 −0.349898 0.936788i \(-0.613784\pi\)
−0.349898 + 0.936788i \(0.613784\pi\)
\(920\) 11.1416 0.367327
\(921\) 21.2711 0.700907
\(922\) 24.2809 0.799650
\(923\) −54.9668 −1.80926
\(924\) 0 0
\(925\) −22.6926 −0.746127
\(926\) 23.1310 0.760133
\(927\) 6.34246 0.208314
\(928\) −48.0481 −1.57726
\(929\) −30.5044 −1.00082 −0.500408 0.865790i \(-0.666817\pi\)
−0.500408 + 0.865790i \(0.666817\pi\)
\(930\) 7.03478 0.230680
\(931\) 0 0
\(932\) −26.4018 −0.864821
\(933\) −2.85031 −0.0933150
\(934\) −42.5273 −1.39154
\(935\) −16.7183 −0.546747
\(936\) 4.03839 0.131999
\(937\) 21.5636 0.704452 0.352226 0.935915i \(-0.385425\pi\)
0.352226 + 0.935915i \(0.385425\pi\)
\(938\) 0 0
\(939\) 13.3306 0.435029
\(940\) 3.32184 0.108346
\(941\) −21.3467 −0.695883 −0.347942 0.937516i \(-0.613119\pi\)
−0.347942 + 0.937516i \(0.613119\pi\)
\(942\) 34.8703 1.13614
\(943\) 8.82708 0.287449
\(944\) −56.1328 −1.82697
\(945\) 0 0
\(946\) 31.4088 1.02119
\(947\) 40.6083 1.31959 0.659795 0.751445i \(-0.270643\pi\)
0.659795 + 0.751445i \(0.270643\pi\)
\(948\) 19.3089 0.627125
\(949\) 14.0961 0.457579
\(950\) −3.28891 −0.106706
\(951\) 8.50980 0.275949
\(952\) 0 0
\(953\) 13.4968 0.437206 0.218603 0.975814i \(-0.429850\pi\)
0.218603 + 0.975814i \(0.429850\pi\)
\(954\) −3.14159 −0.101713
\(955\) 31.6599 1.02449
\(956\) 2.24980 0.0727639
\(957\) −11.0871 −0.358394
\(958\) 0.0965066 0.00311799
\(959\) 0 0
\(960\) −6.82905 −0.220407
\(961\) −25.4344 −0.820465
\(962\) −86.1181 −2.77656
\(963\) −11.2401 −0.362206
\(964\) −20.3029 −0.653913
\(965\) 4.04629 0.130255
\(966\) 0 0
\(967\) −26.7592 −0.860517 −0.430259 0.902706i \(-0.641578\pi\)
−0.430259 + 0.902706i \(0.641578\pi\)
\(968\) −6.58017 −0.211495
\(969\) 4.39894 0.141314
\(970\) −9.57785 −0.307526
\(971\) −37.6519 −1.20831 −0.604153 0.796868i \(-0.706489\pi\)
−0.604153 + 0.796868i \(0.706489\pi\)
\(972\) 1.57671 0.0505731
\(973\) 0 0
\(974\) −41.4761 −1.32898
\(975\) −12.6821 −0.406153
\(976\) −55.8231 −1.78685
\(977\) 48.0278 1.53654 0.768272 0.640124i \(-0.221117\pi\)
0.768272 + 0.640124i \(0.221117\pi\)
\(978\) 33.2890 1.06446
\(979\) 21.2065 0.677764
\(980\) 0 0
\(981\) −7.48963 −0.239126
\(982\) 43.0550 1.37394
\(983\) −21.5525 −0.687417 −0.343708 0.939076i \(-0.611683\pi\)
−0.343708 + 0.939076i \(0.611683\pi\)
\(984\) 0.800530 0.0255200
\(985\) 40.0865 1.27726
\(986\) −79.9683 −2.54671
\(987\) 0 0
\(988\) −5.50214 −0.175047
\(989\) −87.9196 −2.79568
\(990\) −4.97204 −0.158022
\(991\) 3.92823 0.124784 0.0623922 0.998052i \(-0.480127\pi\)
0.0623922 + 0.998052i \(0.480127\pi\)
\(992\) −17.0473 −0.541252
\(993\) −29.9173 −0.949398
\(994\) 0 0
\(995\) −24.9460 −0.790840
\(996\) 4.14520 0.131346
\(997\) −51.0675 −1.61732 −0.808662 0.588273i \(-0.799808\pi\)
−0.808662 + 0.588273i \(0.799808\pi\)
\(998\) −47.4185 −1.50101
\(999\) 9.02655 0.285588
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 \(a_p\))