Properties

Label 8027.2.a.f.1.18
Level 8027
Weight 2
Character 8027.1
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 176
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(176\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.32771 q^{2} -1.02581 q^{3} +3.41824 q^{4} +4.27433 q^{5} +2.38779 q^{6} +1.70170 q^{7} -3.30124 q^{8} -1.94772 q^{9} +O(q^{10})\) \(q-2.32771 q^{2} -1.02581 q^{3} +3.41824 q^{4} +4.27433 q^{5} +2.38779 q^{6} +1.70170 q^{7} -3.30124 q^{8} -1.94772 q^{9} -9.94939 q^{10} +2.00974 q^{11} -3.50646 q^{12} +1.61811 q^{13} -3.96106 q^{14} -4.38464 q^{15} +0.847868 q^{16} -6.17530 q^{17} +4.53372 q^{18} +4.28930 q^{19} +14.6107 q^{20} -1.74562 q^{21} -4.67809 q^{22} +1.00000 q^{23} +3.38644 q^{24} +13.2699 q^{25} -3.76649 q^{26} +5.07541 q^{27} +5.81681 q^{28} +0.608216 q^{29} +10.2062 q^{30} +5.38009 q^{31} +4.62890 q^{32} -2.06161 q^{33} +14.3743 q^{34} +7.27362 q^{35} -6.65776 q^{36} +1.89650 q^{37} -9.98424 q^{38} -1.65987 q^{39} -14.1106 q^{40} -5.00330 q^{41} +4.06329 q^{42} +9.86830 q^{43} +6.86976 q^{44} -8.32518 q^{45} -2.32771 q^{46} -8.33383 q^{47} -0.869750 q^{48} -4.10422 q^{49} -30.8884 q^{50} +6.33467 q^{51} +5.53107 q^{52} -12.1363 q^{53} -11.8141 q^{54} +8.59028 q^{55} -5.61772 q^{56} -4.40000 q^{57} -1.41575 q^{58} +13.2643 q^{59} -14.9877 q^{60} -1.11954 q^{61} -12.5233 q^{62} -3.31443 q^{63} -12.4705 q^{64} +6.91632 q^{65} +4.79882 q^{66} +5.17780 q^{67} -21.1086 q^{68} -1.02581 q^{69} -16.9309 q^{70} -9.04501 q^{71} +6.42989 q^{72} +11.1757 q^{73} -4.41451 q^{74} -13.6123 q^{75} +14.6618 q^{76} +3.41997 q^{77} +3.86369 q^{78} -7.67606 q^{79} +3.62406 q^{80} +0.636753 q^{81} +11.6462 q^{82} +0.460957 q^{83} -5.96693 q^{84} -26.3952 q^{85} -22.9705 q^{86} -0.623913 q^{87} -6.63464 q^{88} +8.95569 q^{89} +19.3786 q^{90} +2.75353 q^{91} +3.41824 q^{92} -5.51894 q^{93} +19.3987 q^{94} +18.3339 q^{95} -4.74836 q^{96} +12.0748 q^{97} +9.55344 q^{98} -3.91440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32771 −1.64594 −0.822970 0.568085i \(-0.807685\pi\)
−0.822970 + 0.568085i \(0.807685\pi\)
\(3\) −1.02581 −0.592251 −0.296125 0.955149i \(-0.595695\pi\)
−0.296125 + 0.955149i \(0.595695\pi\)
\(4\) 3.41824 1.70912
\(5\) 4.27433 1.91154 0.955768 0.294121i \(-0.0950269\pi\)
0.955768 + 0.294121i \(0.0950269\pi\)
\(6\) 2.38779 0.974809
\(7\) 1.70170 0.643182 0.321591 0.946879i \(-0.395782\pi\)
0.321591 + 0.946879i \(0.395782\pi\)
\(8\) −3.30124 −1.16717
\(9\) −1.94772 −0.649239
\(10\) −9.94939 −3.14627
\(11\) 2.00974 0.605959 0.302980 0.952997i \(-0.402019\pi\)
0.302980 + 0.952997i \(0.402019\pi\)
\(12\) −3.50646 −1.01223
\(13\) 1.61811 0.448782 0.224391 0.974499i \(-0.427961\pi\)
0.224391 + 0.974499i \(0.427961\pi\)
\(14\) −3.96106 −1.05864
\(15\) −4.38464 −1.13211
\(16\) 0.847868 0.211967
\(17\) −6.17530 −1.49773 −0.748865 0.662723i \(-0.769401\pi\)
−0.748865 + 0.662723i \(0.769401\pi\)
\(18\) 4.53372 1.06861
\(19\) 4.28930 0.984032 0.492016 0.870586i \(-0.336260\pi\)
0.492016 + 0.870586i \(0.336260\pi\)
\(20\) 14.6107 3.26704
\(21\) −1.74562 −0.380925
\(22\) −4.67809 −0.997372
\(23\) 1.00000 0.208514
\(24\) 3.38644 0.691255
\(25\) 13.2699 2.65397
\(26\) −3.76649 −0.738669
\(27\) 5.07541 0.976763
\(28\) 5.81681 1.09927
\(29\) 0.608216 0.112943 0.0564714 0.998404i \(-0.482015\pi\)
0.0564714 + 0.998404i \(0.482015\pi\)
\(30\) 10.2062 1.86338
\(31\) 5.38009 0.966292 0.483146 0.875540i \(-0.339494\pi\)
0.483146 + 0.875540i \(0.339494\pi\)
\(32\) 4.62890 0.818281
\(33\) −2.06161 −0.358880
\(34\) 14.3743 2.46517
\(35\) 7.27362 1.22947
\(36\) −6.65776 −1.10963
\(37\) 1.89650 0.311783 0.155892 0.987774i \(-0.450175\pi\)
0.155892 + 0.987774i \(0.450175\pi\)
\(38\) −9.98424 −1.61966
\(39\) −1.65987 −0.265792
\(40\) −14.1106 −2.23108
\(41\) −5.00330 −0.781384 −0.390692 0.920521i \(-0.627764\pi\)
−0.390692 + 0.920521i \(0.627764\pi\)
\(42\) 4.06329 0.626980
\(43\) 9.86830 1.50490 0.752451 0.658648i \(-0.228872\pi\)
0.752451 + 0.658648i \(0.228872\pi\)
\(44\) 6.86976 1.03566
\(45\) −8.32518 −1.24104
\(46\) −2.32771 −0.343202
\(47\) −8.33383 −1.21561 −0.607807 0.794085i \(-0.707951\pi\)
−0.607807 + 0.794085i \(0.707951\pi\)
\(48\) −0.869750 −0.125538
\(49\) −4.10422 −0.586317
\(50\) −30.8884 −4.36828
\(51\) 6.33467 0.887031
\(52\) 5.53107 0.767022
\(53\) −12.1363 −1.66705 −0.833526 0.552480i \(-0.813681\pi\)
−0.833526 + 0.552480i \(0.813681\pi\)
\(54\) −11.8141 −1.60769
\(55\) 8.59028 1.15831
\(56\) −5.61772 −0.750700
\(57\) −4.40000 −0.582794
\(58\) −1.41575 −0.185897
\(59\) 13.2643 1.72687 0.863435 0.504460i \(-0.168308\pi\)
0.863435 + 0.504460i \(0.168308\pi\)
\(60\) −14.9877 −1.93491
\(61\) −1.11954 −0.143342 −0.0716712 0.997428i \(-0.522833\pi\)
−0.0716712 + 0.997428i \(0.522833\pi\)
\(62\) −12.5233 −1.59046
\(63\) −3.31443 −0.417579
\(64\) −12.4705 −1.55881
\(65\) 6.91632 0.857863
\(66\) 4.79882 0.590694
\(67\) 5.17780 0.632569 0.316285 0.948664i \(-0.397565\pi\)
0.316285 + 0.948664i \(0.397565\pi\)
\(68\) −21.1086 −2.55980
\(69\) −1.02581 −0.123493
\(70\) −16.9309 −2.02363
\(71\) −9.04501 −1.07345 −0.536723 0.843759i \(-0.680338\pi\)
−0.536723 + 0.843759i \(0.680338\pi\)
\(72\) 6.42989 0.757770
\(73\) 11.1757 1.30802 0.654008 0.756488i \(-0.273086\pi\)
0.654008 + 0.756488i \(0.273086\pi\)
\(74\) −4.41451 −0.513176
\(75\) −13.6123 −1.57182
\(76\) 14.6618 1.68183
\(77\) 3.41997 0.389742
\(78\) 3.86369 0.437477
\(79\) −7.67606 −0.863624 −0.431812 0.901964i \(-0.642126\pi\)
−0.431812 + 0.901964i \(0.642126\pi\)
\(80\) 3.62406 0.405183
\(81\) 0.636753 0.0707504
\(82\) 11.6462 1.28611
\(83\) 0.460957 0.0505966 0.0252983 0.999680i \(-0.491946\pi\)
0.0252983 + 0.999680i \(0.491946\pi\)
\(84\) −5.96693 −0.651046
\(85\) −26.3952 −2.86296
\(86\) −22.9705 −2.47698
\(87\) −0.623913 −0.0668905
\(88\) −6.63464 −0.707255
\(89\) 8.95569 0.949301 0.474651 0.880174i \(-0.342574\pi\)
0.474651 + 0.880174i \(0.342574\pi\)
\(90\) 19.3786 2.04268
\(91\) 2.75353 0.288649
\(92\) 3.41824 0.356376
\(93\) −5.51894 −0.572287
\(94\) 19.3987 2.00083
\(95\) 18.3339 1.88101
\(96\) −4.74836 −0.484628
\(97\) 12.0748 1.22601 0.613007 0.790078i \(-0.289960\pi\)
0.613007 + 0.790078i \(0.289960\pi\)
\(98\) 9.55344 0.965043
\(99\) −3.91440 −0.393412
\(100\) 45.3595 4.53595
\(101\) 1.50920 0.150171 0.0750853 0.997177i \(-0.476077\pi\)
0.0750853 + 0.997177i \(0.476077\pi\)
\(102\) −14.7453 −1.46000
\(103\) −10.6660 −1.05095 −0.525474 0.850810i \(-0.676112\pi\)
−0.525474 + 0.850810i \(0.676112\pi\)
\(104\) −5.34177 −0.523803
\(105\) −7.46134 −0.728152
\(106\) 28.2498 2.74387
\(107\) 5.01926 0.485230 0.242615 0.970123i \(-0.421995\pi\)
0.242615 + 0.970123i \(0.421995\pi\)
\(108\) 17.3490 1.66940
\(109\) −9.42712 −0.902954 −0.451477 0.892283i \(-0.649103\pi\)
−0.451477 + 0.892283i \(0.649103\pi\)
\(110\) −19.9957 −1.90651
\(111\) −1.94545 −0.184654
\(112\) 1.44282 0.136333
\(113\) 16.2427 1.52798 0.763990 0.645228i \(-0.223238\pi\)
0.763990 + 0.645228i \(0.223238\pi\)
\(114\) 10.2419 0.959244
\(115\) 4.27433 0.398583
\(116\) 2.07903 0.193033
\(117\) −3.15162 −0.291367
\(118\) −30.8756 −2.84232
\(119\) −10.5085 −0.963312
\(120\) 14.4748 1.32136
\(121\) −6.96095 −0.632814
\(122\) 2.60596 0.235933
\(123\) 5.13243 0.462775
\(124\) 18.3904 1.65151
\(125\) 35.3481 3.16163
\(126\) 7.71503 0.687310
\(127\) −14.1448 −1.25515 −0.627575 0.778556i \(-0.715952\pi\)
−0.627575 + 0.778556i \(0.715952\pi\)
\(128\) 19.7698 1.74742
\(129\) −10.1230 −0.891279
\(130\) −16.0992 −1.41199
\(131\) −6.85130 −0.598601 −0.299300 0.954159i \(-0.596753\pi\)
−0.299300 + 0.954159i \(0.596753\pi\)
\(132\) −7.04706 −0.613368
\(133\) 7.29909 0.632912
\(134\) −12.0524 −1.04117
\(135\) 21.6940 1.86712
\(136\) 20.3862 1.74810
\(137\) 11.5482 0.986633 0.493317 0.869850i \(-0.335784\pi\)
0.493317 + 0.869850i \(0.335784\pi\)
\(138\) 2.38779 0.203262
\(139\) 11.0022 0.933197 0.466598 0.884469i \(-0.345479\pi\)
0.466598 + 0.884469i \(0.345479\pi\)
\(140\) 24.8629 2.10130
\(141\) 8.54891 0.719948
\(142\) 21.0542 1.76683
\(143\) 3.25197 0.271944
\(144\) −1.65141 −0.137617
\(145\) 2.59971 0.215894
\(146\) −26.0138 −2.15292
\(147\) 4.21014 0.347247
\(148\) 6.48270 0.532874
\(149\) 11.2261 0.919682 0.459841 0.888001i \(-0.347906\pi\)
0.459841 + 0.888001i \(0.347906\pi\)
\(150\) 31.6856 2.58712
\(151\) 7.28367 0.592737 0.296368 0.955074i \(-0.404224\pi\)
0.296368 + 0.955074i \(0.404224\pi\)
\(152\) −14.1600 −1.14853
\(153\) 12.0277 0.972385
\(154\) −7.96070 −0.641492
\(155\) 22.9962 1.84710
\(156\) −5.67382 −0.454269
\(157\) 11.7311 0.936246 0.468123 0.883663i \(-0.344930\pi\)
0.468123 + 0.883663i \(0.344930\pi\)
\(158\) 17.8676 1.42147
\(159\) 12.4495 0.987313
\(160\) 19.7854 1.56417
\(161\) 1.70170 0.134113
\(162\) −1.48218 −0.116451
\(163\) 7.53172 0.589930 0.294965 0.955508i \(-0.404692\pi\)
0.294965 + 0.955508i \(0.404692\pi\)
\(164\) −17.1025 −1.33548
\(165\) −8.81198 −0.686012
\(166\) −1.07297 −0.0832789
\(167\) 16.9939 1.31503 0.657515 0.753441i \(-0.271607\pi\)
0.657515 + 0.753441i \(0.271607\pi\)
\(168\) 5.76271 0.444603
\(169\) −10.3817 −0.798595
\(170\) 61.4405 4.71227
\(171\) −8.35434 −0.638872
\(172\) 33.7322 2.57205
\(173\) 6.48923 0.493367 0.246683 0.969096i \(-0.420659\pi\)
0.246683 + 0.969096i \(0.420659\pi\)
\(174\) 1.45229 0.110098
\(175\) 22.5813 1.70699
\(176\) 1.70399 0.128443
\(177\) −13.6067 −1.02274
\(178\) −20.8463 −1.56249
\(179\) −14.4878 −1.08287 −0.541435 0.840743i \(-0.682119\pi\)
−0.541435 + 0.840743i \(0.682119\pi\)
\(180\) −28.4574 −2.12109
\(181\) 12.0057 0.892379 0.446190 0.894938i \(-0.352781\pi\)
0.446190 + 0.894938i \(0.352781\pi\)
\(182\) −6.40942 −0.475098
\(183\) 1.14843 0.0848946
\(184\) −3.30124 −0.243371
\(185\) 8.10627 0.595985
\(186\) 12.8465 0.941950
\(187\) −12.4107 −0.907563
\(188\) −28.4870 −2.07763
\(189\) 8.63682 0.628236
\(190\) −42.6759 −3.09604
\(191\) −22.3997 −1.62079 −0.810393 0.585887i \(-0.800746\pi\)
−0.810393 + 0.585887i \(0.800746\pi\)
\(192\) 12.7923 0.923206
\(193\) −13.6594 −0.983222 −0.491611 0.870815i \(-0.663592\pi\)
−0.491611 + 0.870815i \(0.663592\pi\)
\(194\) −28.1067 −2.01794
\(195\) −7.09482 −0.508070
\(196\) −14.0292 −1.00209
\(197\) −9.60206 −0.684118 −0.342059 0.939678i \(-0.611124\pi\)
−0.342059 + 0.939678i \(0.611124\pi\)
\(198\) 9.11160 0.647533
\(199\) 13.0056 0.921945 0.460972 0.887414i \(-0.347501\pi\)
0.460972 + 0.887414i \(0.347501\pi\)
\(200\) −43.8070 −3.09763
\(201\) −5.31143 −0.374640
\(202\) −3.51297 −0.247172
\(203\) 1.03500 0.0726428
\(204\) 21.6534 1.51604
\(205\) −21.3857 −1.49364
\(206\) 24.8273 1.72980
\(207\) −1.94772 −0.135376
\(208\) 1.37194 0.0951270
\(209\) 8.62037 0.596283
\(210\) 17.3678 1.19849
\(211\) −14.3769 −0.989748 −0.494874 0.868965i \(-0.664786\pi\)
−0.494874 + 0.868965i \(0.664786\pi\)
\(212\) −41.4848 −2.84919
\(213\) 9.27845 0.635749
\(214\) −11.6834 −0.798660
\(215\) 42.1803 2.87667
\(216\) −16.7552 −1.14004
\(217\) 9.15529 0.621501
\(218\) 21.9436 1.48621
\(219\) −11.4641 −0.774673
\(220\) 29.3636 1.97969
\(221\) −9.99229 −0.672154
\(222\) 4.52844 0.303929
\(223\) 24.7345 1.65635 0.828174 0.560471i \(-0.189380\pi\)
0.828174 + 0.560471i \(0.189380\pi\)
\(224\) 7.87699 0.526304
\(225\) −25.8459 −1.72306
\(226\) −37.8082 −2.51496
\(227\) −14.2027 −0.942667 −0.471333 0.881955i \(-0.656227\pi\)
−0.471333 + 0.881955i \(0.656227\pi\)
\(228\) −15.0402 −0.996064
\(229\) −5.01020 −0.331083 −0.165542 0.986203i \(-0.552937\pi\)
−0.165542 + 0.986203i \(0.552937\pi\)
\(230\) −9.94939 −0.656043
\(231\) −3.50823 −0.230825
\(232\) −2.00787 −0.131823
\(233\) −17.8985 −1.17257 −0.586285 0.810105i \(-0.699410\pi\)
−0.586285 + 0.810105i \(0.699410\pi\)
\(234\) 7.33605 0.479572
\(235\) −35.6215 −2.32369
\(236\) 45.3407 2.95143
\(237\) 7.87416 0.511482
\(238\) 24.4607 1.58555
\(239\) 17.4463 1.12851 0.564255 0.825600i \(-0.309163\pi\)
0.564255 + 0.825600i \(0.309163\pi\)
\(240\) −3.71759 −0.239970
\(241\) 6.26578 0.403614 0.201807 0.979425i \(-0.435319\pi\)
0.201807 + 0.979425i \(0.435319\pi\)
\(242\) 16.2031 1.04157
\(243\) −15.8794 −1.01867
\(244\) −3.82685 −0.244989
\(245\) −17.5428 −1.12077
\(246\) −11.9468 −0.761700
\(247\) 6.94054 0.441616
\(248\) −17.7610 −1.12782
\(249\) −0.472853 −0.0299659
\(250\) −82.2800 −5.20385
\(251\) 24.6239 1.55425 0.777123 0.629349i \(-0.216678\pi\)
0.777123 + 0.629349i \(0.216678\pi\)
\(252\) −11.3295 −0.713691
\(253\) 2.00974 0.126351
\(254\) 32.9251 2.06590
\(255\) 27.0764 1.69559
\(256\) −21.0775 −1.31735
\(257\) 6.79868 0.424090 0.212045 0.977260i \(-0.431988\pi\)
0.212045 + 0.977260i \(0.431988\pi\)
\(258\) 23.5634 1.46699
\(259\) 3.22728 0.200533
\(260\) 23.6416 1.46619
\(261\) −1.18463 −0.0733269
\(262\) 15.9478 0.985261
\(263\) −4.80455 −0.296261 −0.148131 0.988968i \(-0.547326\pi\)
−0.148131 + 0.988968i \(0.547326\pi\)
\(264\) 6.80587 0.418872
\(265\) −51.8746 −3.18663
\(266\) −16.9902 −1.04173
\(267\) −9.18682 −0.562224
\(268\) 17.6990 1.08114
\(269\) 16.2703 0.992018 0.496009 0.868317i \(-0.334798\pi\)
0.496009 + 0.868317i \(0.334798\pi\)
\(270\) −50.4972 −3.07316
\(271\) 14.1453 0.859264 0.429632 0.903004i \(-0.358643\pi\)
0.429632 + 0.903004i \(0.358643\pi\)
\(272\) −5.23584 −0.317469
\(273\) −2.82460 −0.170952
\(274\) −26.8810 −1.62394
\(275\) 26.6689 1.60820
\(276\) −3.50646 −0.211064
\(277\) −3.49890 −0.210228 −0.105114 0.994460i \(-0.533521\pi\)
−0.105114 + 0.994460i \(0.533521\pi\)
\(278\) −25.6100 −1.53599
\(279\) −10.4789 −0.627354
\(280\) −24.0120 −1.43499
\(281\) −27.0853 −1.61577 −0.807887 0.589338i \(-0.799389\pi\)
−0.807887 + 0.589338i \(0.799389\pi\)
\(282\) −19.8994 −1.18499
\(283\) 32.2220 1.91540 0.957699 0.287772i \(-0.0929147\pi\)
0.957699 + 0.287772i \(0.0929147\pi\)
\(284\) −30.9180 −1.83464
\(285\) −18.8070 −1.11403
\(286\) −7.56965 −0.447603
\(287\) −8.51411 −0.502572
\(288\) −9.01578 −0.531260
\(289\) 21.1343 1.24319
\(290\) −6.05138 −0.355349
\(291\) −12.3865 −0.726108
\(292\) 38.2012 2.23555
\(293\) 12.3090 0.719099 0.359549 0.933126i \(-0.382930\pi\)
0.359549 + 0.933126i \(0.382930\pi\)
\(294\) −9.80000 −0.571547
\(295\) 56.6961 3.30098
\(296\) −6.26082 −0.363903
\(297\) 10.2002 0.591878
\(298\) −26.1312 −1.51374
\(299\) 1.61811 0.0935776
\(300\) −46.5302 −2.68642
\(301\) 16.7929 0.967925
\(302\) −16.9543 −0.975609
\(303\) −1.54815 −0.0889386
\(304\) 3.63676 0.208582
\(305\) −4.78528 −0.274004
\(306\) −27.9971 −1.60049
\(307\) 19.4108 1.10783 0.553916 0.832572i \(-0.313133\pi\)
0.553916 + 0.832572i \(0.313133\pi\)
\(308\) 11.6903 0.666115
\(309\) 10.9412 0.622425
\(310\) −53.5286 −3.04022
\(311\) −11.1369 −0.631514 −0.315757 0.948840i \(-0.602258\pi\)
−0.315757 + 0.948840i \(0.602258\pi\)
\(312\) 5.47963 0.310223
\(313\) −1.19380 −0.0674775 −0.0337387 0.999431i \(-0.510741\pi\)
−0.0337387 + 0.999431i \(0.510741\pi\)
\(314\) −27.3067 −1.54100
\(315\) −14.1669 −0.798217
\(316\) −26.2386 −1.47604
\(317\) 10.3650 0.582155 0.291077 0.956700i \(-0.405986\pi\)
0.291077 + 0.956700i \(0.405986\pi\)
\(318\) −28.9789 −1.62506
\(319\) 1.22236 0.0684388
\(320\) −53.3028 −2.97972
\(321\) −5.14880 −0.287378
\(322\) −3.96106 −0.220741
\(323\) −26.4877 −1.47381
\(324\) 2.17657 0.120921
\(325\) 21.4720 1.19105
\(326\) −17.5317 −0.970989
\(327\) 9.67042 0.534775
\(328\) 16.5171 0.912005
\(329\) −14.1817 −0.781861
\(330\) 20.5117 1.12913
\(331\) 5.14683 0.282895 0.141448 0.989946i \(-0.454824\pi\)
0.141448 + 0.989946i \(0.454824\pi\)
\(332\) 1.57566 0.0864756
\(333\) −3.69385 −0.202422
\(334\) −39.5570 −2.16446
\(335\) 22.1316 1.20918
\(336\) −1.48005 −0.0807435
\(337\) −14.3182 −0.779964 −0.389982 0.920823i \(-0.627519\pi\)
−0.389982 + 0.920823i \(0.627519\pi\)
\(338\) 24.1657 1.31444
\(339\) −16.6618 −0.904947
\(340\) −90.2251 −4.89314
\(341\) 10.8126 0.585533
\(342\) 19.4465 1.05155
\(343\) −18.8960 −1.02029
\(344\) −32.5777 −1.75647
\(345\) −4.38464 −0.236061
\(346\) −15.1050 −0.812052
\(347\) 7.02408 0.377072 0.188536 0.982066i \(-0.439626\pi\)
0.188536 + 0.982066i \(0.439626\pi\)
\(348\) −2.13268 −0.114324
\(349\) −1.00000 −0.0535288
\(350\) −52.5627 −2.80960
\(351\) 8.21256 0.438354
\(352\) 9.30287 0.495845
\(353\) −1.94258 −0.103393 −0.0516965 0.998663i \(-0.516463\pi\)
−0.0516965 + 0.998663i \(0.516463\pi\)
\(354\) 31.6724 1.68337
\(355\) −38.6613 −2.05193
\(356\) 30.6127 1.62247
\(357\) 10.7797 0.570522
\(358\) 33.7234 1.78234
\(359\) 21.8606 1.15376 0.576879 0.816830i \(-0.304271\pi\)
0.576879 + 0.816830i \(0.304271\pi\)
\(360\) 27.4834 1.44850
\(361\) −0.601929 −0.0316805
\(362\) −27.9459 −1.46880
\(363\) 7.14060 0.374784
\(364\) 9.41222 0.493334
\(365\) 47.7685 2.50032
\(366\) −2.67322 −0.139731
\(367\) −17.8826 −0.933462 −0.466731 0.884399i \(-0.654568\pi\)
−0.466731 + 0.884399i \(0.654568\pi\)
\(368\) 0.847868 0.0441982
\(369\) 9.74501 0.507305
\(370\) −18.8691 −0.980955
\(371\) −20.6524 −1.07222
\(372\) −18.8650 −0.978106
\(373\) −4.41097 −0.228391 −0.114196 0.993458i \(-0.536429\pi\)
−0.114196 + 0.993458i \(0.536429\pi\)
\(374\) 28.8886 1.49379
\(375\) −36.2603 −1.87248
\(376\) 27.5120 1.41882
\(377\) 0.984159 0.0506868
\(378\) −20.1040 −1.03404
\(379\) 27.0213 1.38799 0.693995 0.719980i \(-0.255849\pi\)
0.693995 + 0.719980i \(0.255849\pi\)
\(380\) 62.6694 3.21487
\(381\) 14.5099 0.743364
\(382\) 52.1400 2.66772
\(383\) −34.4391 −1.75976 −0.879879 0.475197i \(-0.842377\pi\)
−0.879879 + 0.475197i \(0.842377\pi\)
\(384\) −20.2801 −1.03491
\(385\) 14.6181 0.745006
\(386\) 31.7950 1.61832
\(387\) −19.2207 −0.977041
\(388\) 41.2746 2.09540
\(389\) −17.6612 −0.895458 −0.447729 0.894169i \(-0.647767\pi\)
−0.447729 + 0.894169i \(0.647767\pi\)
\(390\) 16.5147 0.836253
\(391\) −6.17530 −0.312298
\(392\) 13.5490 0.684330
\(393\) 7.02812 0.354522
\(394\) 22.3508 1.12602
\(395\) −32.8100 −1.65085
\(396\) −13.3804 −0.672388
\(397\) 15.5929 0.782585 0.391292 0.920266i \(-0.372028\pi\)
0.391292 + 0.920266i \(0.372028\pi\)
\(398\) −30.2733 −1.51747
\(399\) −7.48747 −0.374842
\(400\) 11.2511 0.562554
\(401\) 23.8802 1.19252 0.596259 0.802792i \(-0.296653\pi\)
0.596259 + 0.802792i \(0.296653\pi\)
\(402\) 12.3635 0.616634
\(403\) 8.70556 0.433655
\(404\) 5.15879 0.256659
\(405\) 2.72169 0.135242
\(406\) −2.40918 −0.119566
\(407\) 3.81148 0.188928
\(408\) −20.9123 −1.03531
\(409\) −13.8778 −0.686212 −0.343106 0.939297i \(-0.611479\pi\)
−0.343106 + 0.939297i \(0.611479\pi\)
\(410\) 49.7798 2.45845
\(411\) −11.8463 −0.584334
\(412\) −36.4588 −1.79619
\(413\) 22.5719 1.11069
\(414\) 4.53372 0.222820
\(415\) 1.97028 0.0967172
\(416\) 7.49005 0.367230
\(417\) −11.2862 −0.552686
\(418\) −20.0657 −0.981446
\(419\) −27.1245 −1.32512 −0.662559 0.749010i \(-0.730530\pi\)
−0.662559 + 0.749010i \(0.730530\pi\)
\(420\) −25.5046 −1.24450
\(421\) −26.7887 −1.30560 −0.652800 0.757531i \(-0.726406\pi\)
−0.652800 + 0.757531i \(0.726406\pi\)
\(422\) 33.4653 1.62907
\(423\) 16.2319 0.789224
\(424\) 40.0650 1.94573
\(425\) −81.9453 −3.97493
\(426\) −21.5975 −1.04640
\(427\) −1.90512 −0.0921952
\(428\) 17.1570 0.829316
\(429\) −3.33590 −0.161059
\(430\) −98.1836 −4.73483
\(431\) 29.2686 1.40982 0.704909 0.709297i \(-0.250988\pi\)
0.704909 + 0.709297i \(0.250988\pi\)
\(432\) 4.30328 0.207042
\(433\) −26.6150 −1.27903 −0.639517 0.768777i \(-0.720866\pi\)
−0.639517 + 0.768777i \(0.720866\pi\)
\(434\) −21.3109 −1.02295
\(435\) −2.66681 −0.127864
\(436\) −32.2241 −1.54326
\(437\) 4.28930 0.205185
\(438\) 26.6851 1.27507
\(439\) 4.97431 0.237411 0.118705 0.992930i \(-0.462126\pi\)
0.118705 + 0.992930i \(0.462126\pi\)
\(440\) −28.3586 −1.35194
\(441\) 7.99386 0.380660
\(442\) 23.2592 1.10633
\(443\) −40.2880 −1.91414 −0.957071 0.289853i \(-0.906394\pi\)
−0.957071 + 0.289853i \(0.906394\pi\)
\(444\) −6.65000 −0.315595
\(445\) 38.2795 1.81462
\(446\) −57.5749 −2.72625
\(447\) −11.5159 −0.544682
\(448\) −21.2210 −1.00260
\(449\) −29.6619 −1.39983 −0.699915 0.714226i \(-0.746779\pi\)
−0.699915 + 0.714226i \(0.746779\pi\)
\(450\) 60.1618 2.83606
\(451\) −10.0553 −0.473487
\(452\) 55.5212 2.61150
\(453\) −7.47165 −0.351049
\(454\) 33.0598 1.55157
\(455\) 11.7695 0.551762
\(456\) 14.5255 0.680217
\(457\) 20.0955 0.940028 0.470014 0.882659i \(-0.344249\pi\)
0.470014 + 0.882659i \(0.344249\pi\)
\(458\) 11.6623 0.544943
\(459\) −31.3422 −1.46293
\(460\) 14.6107 0.681225
\(461\) −15.2847 −0.711880 −0.355940 0.934509i \(-0.615839\pi\)
−0.355940 + 0.934509i \(0.615839\pi\)
\(462\) 8.16616 0.379924
\(463\) −18.5771 −0.863351 −0.431676 0.902029i \(-0.642078\pi\)
−0.431676 + 0.902029i \(0.642078\pi\)
\(464\) 0.515687 0.0239402
\(465\) −23.5897 −1.09395
\(466\) 41.6626 1.92998
\(467\) 36.3534 1.68224 0.841118 0.540852i \(-0.181898\pi\)
0.841118 + 0.540852i \(0.181898\pi\)
\(468\) −10.7730 −0.497981
\(469\) 8.81106 0.406857
\(470\) 82.9165 3.82465
\(471\) −12.0339 −0.554492
\(472\) −43.7888 −2.01554
\(473\) 19.8327 0.911909
\(474\) −18.3288 −0.841869
\(475\) 56.9184 2.61159
\(476\) −35.9205 −1.64641
\(477\) 23.6381 1.08232
\(478\) −40.6100 −1.85746
\(479\) −16.6557 −0.761018 −0.380509 0.924777i \(-0.624251\pi\)
−0.380509 + 0.924777i \(0.624251\pi\)
\(480\) −20.2960 −0.926383
\(481\) 3.06875 0.139923
\(482\) −14.5849 −0.664325
\(483\) −1.74562 −0.0794283
\(484\) −23.7942 −1.08155
\(485\) 51.6118 2.34357
\(486\) 36.9627 1.67666
\(487\) 21.6123 0.979345 0.489672 0.871907i \(-0.337116\pi\)
0.489672 + 0.871907i \(0.337116\pi\)
\(488\) 3.69587 0.167304
\(489\) −7.72610 −0.349386
\(490\) 40.8345 1.84471
\(491\) −26.6400 −1.20225 −0.601123 0.799156i \(-0.705280\pi\)
−0.601123 + 0.799156i \(0.705280\pi\)
\(492\) 17.5438 0.790938
\(493\) −3.75591 −0.169158
\(494\) −16.1556 −0.726874
\(495\) −16.7314 −0.752022
\(496\) 4.56160 0.204822
\(497\) −15.3919 −0.690420
\(498\) 1.10067 0.0493220
\(499\) −22.1313 −0.990732 −0.495366 0.868684i \(-0.664966\pi\)
−0.495366 + 0.868684i \(0.664966\pi\)
\(500\) 120.828 5.40359
\(501\) −17.4325 −0.778828
\(502\) −57.3173 −2.55819
\(503\) −24.3122 −1.08403 −0.542013 0.840370i \(-0.682338\pi\)
−0.542013 + 0.840370i \(0.682338\pi\)
\(504\) 10.9417 0.487384
\(505\) 6.45079 0.287057
\(506\) −4.67809 −0.207966
\(507\) 10.6497 0.472968
\(508\) −48.3503 −2.14520
\(509\) 16.9018 0.749158 0.374579 0.927195i \(-0.377787\pi\)
0.374579 + 0.927195i \(0.377787\pi\)
\(510\) −63.0261 −2.79084
\(511\) 19.0177 0.841292
\(512\) 9.52273 0.420849
\(513\) 21.7699 0.961166
\(514\) −15.8254 −0.698026
\(515\) −45.5898 −2.00893
\(516\) −34.6028 −1.52330
\(517\) −16.7488 −0.736612
\(518\) −7.51217 −0.330066
\(519\) −6.65670 −0.292197
\(520\) −22.8324 −1.00127
\(521\) 27.6484 1.21130 0.605650 0.795731i \(-0.292913\pi\)
0.605650 + 0.795731i \(0.292913\pi\)
\(522\) 2.75748 0.120692
\(523\) 25.4626 1.11340 0.556701 0.830713i \(-0.312067\pi\)
0.556701 + 0.830713i \(0.312067\pi\)
\(524\) −23.4194 −1.02308
\(525\) −23.1641 −1.01096
\(526\) 11.1836 0.487628
\(527\) −33.2236 −1.44724
\(528\) −1.74797 −0.0760707
\(529\) 1.00000 0.0434783
\(530\) 120.749 5.24500
\(531\) −25.8352 −1.12115
\(532\) 24.9500 1.08172
\(533\) −8.09587 −0.350671
\(534\) 21.3843 0.925388
\(535\) 21.4539 0.927535
\(536\) −17.0932 −0.738313
\(537\) 14.8617 0.641330
\(538\) −37.8725 −1.63280
\(539\) −8.24841 −0.355284
\(540\) 74.1551 3.19113
\(541\) 17.6280 0.757887 0.378943 0.925420i \(-0.376288\pi\)
0.378943 + 0.925420i \(0.376288\pi\)
\(542\) −32.9261 −1.41430
\(543\) −12.3156 −0.528512
\(544\) −28.5848 −1.22556
\(545\) −40.2946 −1.72603
\(546\) 6.57484 0.281377
\(547\) 0.0364265 0.00155749 0.000778743 1.00000i \(-0.499752\pi\)
0.000778743 1.00000i \(0.499752\pi\)
\(548\) 39.4746 1.68627
\(549\) 2.18055 0.0930635
\(550\) −62.0776 −2.64700
\(551\) 2.60882 0.111139
\(552\) 3.38644 0.144137
\(553\) −13.0623 −0.555467
\(554\) 8.14442 0.346023
\(555\) −8.31548 −0.352972
\(556\) 37.6082 1.59494
\(557\) −9.67931 −0.410126 −0.205063 0.978749i \(-0.565740\pi\)
−0.205063 + 0.978749i \(0.565740\pi\)
\(558\) 24.3918 1.03259
\(559\) 15.9680 0.675373
\(560\) 6.16707 0.260606
\(561\) 12.7310 0.537505
\(562\) 63.0467 2.65947
\(563\) −6.93225 −0.292160 −0.146080 0.989273i \(-0.546666\pi\)
−0.146080 + 0.989273i \(0.546666\pi\)
\(564\) 29.2222 1.23048
\(565\) 69.4264 2.92079
\(566\) −75.0034 −3.15263
\(567\) 1.08356 0.0455054
\(568\) 29.8598 1.25289
\(569\) 45.7594 1.91833 0.959167 0.282840i \(-0.0912766\pi\)
0.959167 + 0.282840i \(0.0912766\pi\)
\(570\) 43.7773 1.83363
\(571\) −23.5660 −0.986208 −0.493104 0.869970i \(-0.664138\pi\)
−0.493104 + 0.869970i \(0.664138\pi\)
\(572\) 11.1160 0.464784
\(573\) 22.9778 0.959912
\(574\) 19.8184 0.827203
\(575\) 13.2699 0.553391
\(576\) 24.2889 1.01204
\(577\) 44.5555 1.85487 0.927435 0.373984i \(-0.122009\pi\)
0.927435 + 0.373984i \(0.122009\pi\)
\(578\) −49.1945 −2.04622
\(579\) 14.0119 0.582314
\(580\) 8.88643 0.368989
\(581\) 0.784410 0.0325428
\(582\) 28.8321 1.19513
\(583\) −24.3908 −1.01017
\(584\) −36.8937 −1.52667
\(585\) −13.4710 −0.556958
\(586\) −28.6518 −1.18359
\(587\) −0.704570 −0.0290807 −0.0145404 0.999894i \(-0.504629\pi\)
−0.0145404 + 0.999894i \(0.504629\pi\)
\(588\) 14.3913 0.593486
\(589\) 23.0768 0.950862
\(590\) −131.972 −5.43321
\(591\) 9.84987 0.405170
\(592\) 1.60798 0.0660877
\(593\) 39.4417 1.61968 0.809839 0.586653i \(-0.199555\pi\)
0.809839 + 0.586653i \(0.199555\pi\)
\(594\) −23.7432 −0.974196
\(595\) −44.9167 −1.84141
\(596\) 38.3736 1.57184
\(597\) −13.3413 −0.546022
\(598\) −3.76649 −0.154023
\(599\) −22.5458 −0.921196 −0.460598 0.887609i \(-0.652365\pi\)
−0.460598 + 0.887609i \(0.652365\pi\)
\(600\) 44.9376 1.83457
\(601\) 18.0719 0.737166 0.368583 0.929595i \(-0.379843\pi\)
0.368583 + 0.929595i \(0.379843\pi\)
\(602\) −39.0890 −1.59315
\(603\) −10.0849 −0.410689
\(604\) 24.8973 1.01306
\(605\) −29.7534 −1.20965
\(606\) 3.60364 0.146388
\(607\) −4.73812 −0.192315 −0.0961573 0.995366i \(-0.530655\pi\)
−0.0961573 + 0.995366i \(0.530655\pi\)
\(608\) 19.8547 0.805215
\(609\) −1.06171 −0.0430228
\(610\) 11.1387 0.450994
\(611\) −13.4850 −0.545546
\(612\) 41.1136 1.66192
\(613\) −11.0776 −0.447420 −0.223710 0.974656i \(-0.571817\pi\)
−0.223710 + 0.974656i \(0.571817\pi\)
\(614\) −45.1827 −1.82343
\(615\) 21.9377 0.884612
\(616\) −11.2902 −0.454893
\(617\) −46.8859 −1.88756 −0.943778 0.330579i \(-0.892756\pi\)
−0.943778 + 0.330579i \(0.892756\pi\)
\(618\) −25.4680 −1.02447
\(619\) −22.0795 −0.887451 −0.443725 0.896163i \(-0.646343\pi\)
−0.443725 + 0.896163i \(0.646343\pi\)
\(620\) 78.6066 3.15692
\(621\) 5.07541 0.203669
\(622\) 25.9234 1.03943
\(623\) 15.2399 0.610573
\(624\) −1.40735 −0.0563390
\(625\) 84.7398 3.38959
\(626\) 2.77882 0.111064
\(627\) −8.84285 −0.353149
\(628\) 40.0998 1.60015
\(629\) −11.7115 −0.466967
\(630\) 32.9765 1.31382
\(631\) 42.2089 1.68031 0.840154 0.542348i \(-0.182464\pi\)
0.840154 + 0.542348i \(0.182464\pi\)
\(632\) 25.3405 1.00799
\(633\) 14.7480 0.586179
\(634\) −24.1266 −0.958192
\(635\) −60.4596 −2.39926
\(636\) 42.5555 1.68743
\(637\) −6.64107 −0.263129
\(638\) −2.84529 −0.112646
\(639\) 17.6171 0.696922
\(640\) 84.5028 3.34026
\(641\) 28.4238 1.12267 0.561337 0.827587i \(-0.310287\pi\)
0.561337 + 0.827587i \(0.310287\pi\)
\(642\) 11.9849 0.473007
\(643\) −2.51831 −0.0993126 −0.0496563 0.998766i \(-0.515813\pi\)
−0.0496563 + 0.998766i \(0.515813\pi\)
\(644\) 5.81681 0.229214
\(645\) −43.2689 −1.70371
\(646\) 61.6557 2.42581
\(647\) 42.1876 1.65857 0.829283 0.558829i \(-0.188749\pi\)
0.829283 + 0.558829i \(0.188749\pi\)
\(648\) −2.10208 −0.0825774
\(649\) 26.6579 1.04641
\(650\) −49.9807 −1.96040
\(651\) −9.39157 −0.368085
\(652\) 25.7452 1.00826
\(653\) 11.2829 0.441534 0.220767 0.975327i \(-0.429144\pi\)
0.220767 + 0.975327i \(0.429144\pi\)
\(654\) −22.5099 −0.880208
\(655\) −29.2847 −1.14425
\(656\) −4.24214 −0.165628
\(657\) −21.7671 −0.849215
\(658\) 33.0108 1.28690
\(659\) −41.5918 −1.62018 −0.810092 0.586302i \(-0.800583\pi\)
−0.810092 + 0.586302i \(0.800583\pi\)
\(660\) −30.1214 −1.17247
\(661\) 20.7577 0.807380 0.403690 0.914896i \(-0.367727\pi\)
0.403690 + 0.914896i \(0.367727\pi\)
\(662\) −11.9803 −0.465629
\(663\) 10.2502 0.398084
\(664\) −1.52173 −0.0590546
\(665\) 31.1987 1.20983
\(666\) 8.59822 0.333174
\(667\) 0.608216 0.0235502
\(668\) 58.0893 2.24754
\(669\) −25.3729 −0.980973
\(670\) −51.5160 −1.99024
\(671\) −2.24998 −0.0868596
\(672\) −8.08028 −0.311704
\(673\) −4.93686 −0.190302 −0.0951509 0.995463i \(-0.530333\pi\)
−0.0951509 + 0.995463i \(0.530333\pi\)
\(674\) 33.3287 1.28377
\(675\) 67.3500 2.59230
\(676\) −35.4872 −1.36489
\(677\) −9.42202 −0.362118 −0.181059 0.983472i \(-0.557952\pi\)
−0.181059 + 0.983472i \(0.557952\pi\)
\(678\) 38.7840 1.48949
\(679\) 20.5477 0.788550
\(680\) 87.1371 3.34156
\(681\) 14.5693 0.558295
\(682\) −25.1685 −0.963753
\(683\) 9.24765 0.353852 0.176926 0.984224i \(-0.443385\pi\)
0.176926 + 0.984224i \(0.443385\pi\)
\(684\) −28.5571 −1.09191
\(685\) 49.3610 1.88598
\(686\) 43.9845 1.67934
\(687\) 5.13950 0.196084
\(688\) 8.36702 0.318989
\(689\) −19.6379 −0.748143
\(690\) 10.2062 0.388542
\(691\) −49.8540 −1.89654 −0.948268 0.317470i \(-0.897167\pi\)
−0.948268 + 0.317470i \(0.897167\pi\)
\(692\) 22.1817 0.843222
\(693\) −6.66114 −0.253036
\(694\) −16.3500 −0.620638
\(695\) 47.0271 1.78384
\(696\) 2.05969 0.0780723
\(697\) 30.8969 1.17030
\(698\) 2.32771 0.0881051
\(699\) 18.3604 0.694456
\(700\) 77.1882 2.91744
\(701\) −32.1548 −1.21447 −0.607235 0.794522i \(-0.707722\pi\)
−0.607235 + 0.794522i \(0.707722\pi\)
\(702\) −19.1165 −0.721504
\(703\) 8.13467 0.306805
\(704\) −25.0624 −0.944574
\(705\) 36.5408 1.37621
\(706\) 4.52176 0.170179
\(707\) 2.56820 0.0965870
\(708\) −46.5108 −1.74798
\(709\) 7.32416 0.275065 0.137532 0.990497i \(-0.456083\pi\)
0.137532 + 0.990497i \(0.456083\pi\)
\(710\) 89.9923 3.37735
\(711\) 14.9508 0.560698
\(712\) −29.5649 −1.10799
\(713\) 5.38009 0.201486
\(714\) −25.0920 −0.939046
\(715\) 13.9000 0.519830
\(716\) −49.5227 −1.85075
\(717\) −17.8966 −0.668361
\(718\) −50.8851 −1.89902
\(719\) −28.8645 −1.07646 −0.538232 0.842797i \(-0.680908\pi\)
−0.538232 + 0.842797i \(0.680908\pi\)
\(720\) −7.05865 −0.263060
\(721\) −18.1503 −0.675951
\(722\) 1.40112 0.0521442
\(723\) −6.42749 −0.239041
\(724\) 41.0384 1.52518
\(725\) 8.07094 0.299747
\(726\) −16.6213 −0.616873
\(727\) 4.45516 0.165233 0.0826164 0.996581i \(-0.473672\pi\)
0.0826164 + 0.996581i \(0.473672\pi\)
\(728\) −9.09008 −0.336901
\(729\) 14.3790 0.532555
\(730\) −111.191 −4.11538
\(731\) −60.9397 −2.25394
\(732\) 3.92562 0.145095
\(733\) 11.8779 0.438721 0.219360 0.975644i \(-0.429603\pi\)
0.219360 + 0.975644i \(0.429603\pi\)
\(734\) 41.6254 1.53642
\(735\) 17.9955 0.663775
\(736\) 4.62890 0.170623
\(737\) 10.4060 0.383311
\(738\) −22.6836 −0.834994
\(739\) −6.82724 −0.251144 −0.125572 0.992085i \(-0.540077\pi\)
−0.125572 + 0.992085i \(0.540077\pi\)
\(740\) 27.7092 1.01861
\(741\) −7.11967 −0.261547
\(742\) 48.0727 1.76481
\(743\) −0.685788 −0.0251591 −0.0125796 0.999921i \(-0.504004\pi\)
−0.0125796 + 0.999921i \(0.504004\pi\)
\(744\) 18.2194 0.667954
\(745\) 47.9842 1.75800
\(746\) 10.2675 0.375918
\(747\) −0.897814 −0.0328493
\(748\) −42.4228 −1.55113
\(749\) 8.54127 0.312091
\(750\) 84.4035 3.08198
\(751\) 42.7148 1.55869 0.779343 0.626598i \(-0.215553\pi\)
0.779343 + 0.626598i \(0.215553\pi\)
\(752\) −7.06599 −0.257670
\(753\) −25.2594 −0.920503
\(754\) −2.29084 −0.0834274
\(755\) 31.1328 1.13304
\(756\) 29.5227 1.07373
\(757\) 31.7729 1.15481 0.577404 0.816459i \(-0.304066\pi\)
0.577404 + 0.816459i \(0.304066\pi\)
\(758\) −62.8977 −2.28455
\(759\) −2.06161 −0.0748316
\(760\) −60.5245 −2.19546
\(761\) 39.1843 1.42043 0.710215 0.703985i \(-0.248598\pi\)
0.710215 + 0.703985i \(0.248598\pi\)
\(762\) −33.7748 −1.22353
\(763\) −16.0421 −0.580764
\(764\) −76.5675 −2.77011
\(765\) 51.4104 1.85875
\(766\) 80.1644 2.89646
\(767\) 21.4631 0.774989
\(768\) 21.6215 0.780200
\(769\) 24.4316 0.881027 0.440514 0.897746i \(-0.354796\pi\)
0.440514 + 0.897746i \(0.354796\pi\)
\(770\) −34.0266 −1.22623
\(771\) −6.97414 −0.251168
\(772\) −46.6909 −1.68044
\(773\) −10.8754 −0.391160 −0.195580 0.980688i \(-0.562659\pi\)
−0.195580 + 0.980688i \(0.562659\pi\)
\(774\) 44.7401 1.60815
\(775\) 71.3930 2.56451
\(776\) −39.8620 −1.43096
\(777\) −3.31057 −0.118766
\(778\) 41.1101 1.47387
\(779\) −21.4606 −0.768907
\(780\) −24.2518 −0.868352
\(781\) −18.1781 −0.650464
\(782\) 14.3743 0.514024
\(783\) 3.08695 0.110318
\(784\) −3.47984 −0.124280
\(785\) 50.1426 1.78967
\(786\) −16.3594 −0.583521
\(787\) 13.2611 0.472706 0.236353 0.971667i \(-0.424048\pi\)
0.236353 + 0.971667i \(0.424048\pi\)
\(788\) −32.8221 −1.16924
\(789\) 4.92855 0.175461
\(790\) 76.3721 2.71720
\(791\) 27.6401 0.982769
\(792\) 12.9224 0.459177
\(793\) −1.81154 −0.0643295
\(794\) −36.2957 −1.28809
\(795\) 53.2134 1.88728
\(796\) 44.4563 1.57571
\(797\) −47.0003 −1.66483 −0.832417 0.554149i \(-0.813044\pi\)
−0.832417 + 0.554149i \(0.813044\pi\)
\(798\) 17.4287 0.616968
\(799\) 51.4639 1.82066
\(800\) 61.4248 2.17169
\(801\) −17.4432 −0.616324
\(802\) −55.5861 −1.96281
\(803\) 22.4602 0.792604
\(804\) −18.1557 −0.640303
\(805\) 7.27362 0.256361
\(806\) −20.2640 −0.713769
\(807\) −16.6902 −0.587523
\(808\) −4.98222 −0.175274
\(809\) −13.7566 −0.483658 −0.241829 0.970319i \(-0.577747\pi\)
−0.241829 + 0.970319i \(0.577747\pi\)
\(810\) −6.33531 −0.222600
\(811\) −3.44967 −0.121134 −0.0605672 0.998164i \(-0.519291\pi\)
−0.0605672 + 0.998164i \(0.519291\pi\)
\(812\) 3.53788 0.124155
\(813\) −14.5103 −0.508900
\(814\) −8.87201 −0.310964
\(815\) 32.1930 1.12767
\(816\) 5.37097 0.188021
\(817\) 42.3281 1.48087
\(818\) 32.3034 1.12946
\(819\) −5.36310 −0.187402
\(820\) −73.1015 −2.55281
\(821\) 6.01932 0.210076 0.105038 0.994468i \(-0.466504\pi\)
0.105038 + 0.994468i \(0.466504\pi\)
\(822\) 27.5747 0.961779
\(823\) −10.2270 −0.356490 −0.178245 0.983986i \(-0.557042\pi\)
−0.178245 + 0.983986i \(0.557042\pi\)
\(824\) 35.2109 1.22663
\(825\) −27.3572 −0.952456
\(826\) −52.5409 −1.82813
\(827\) −11.2946 −0.392751 −0.196376 0.980529i \(-0.562917\pi\)
−0.196376 + 0.980529i \(0.562917\pi\)
\(828\) −6.65776 −0.231373
\(829\) 45.1632 1.56858 0.784291 0.620394i \(-0.213027\pi\)
0.784291 + 0.620394i \(0.213027\pi\)
\(830\) −4.58624 −0.159191
\(831\) 3.58920 0.124508
\(832\) −20.1786 −0.699566
\(833\) 25.3448 0.878145
\(834\) 26.2710 0.909689
\(835\) 72.6376 2.51373
\(836\) 29.4665 1.01912
\(837\) 27.3061 0.943838
\(838\) 63.1379 2.18106
\(839\) 25.8740 0.893270 0.446635 0.894716i \(-0.352622\pi\)
0.446635 + 0.894716i \(0.352622\pi\)
\(840\) 24.6317 0.849874
\(841\) −28.6301 −0.987244
\(842\) 62.3562 2.14894
\(843\) 27.7843 0.956943
\(844\) −49.1437 −1.69160
\(845\) −44.3749 −1.52654
\(846\) −37.7833 −1.29902
\(847\) −11.8454 −0.407014
\(848\) −10.2900 −0.353360
\(849\) −33.0536 −1.13440
\(850\) 190.745 6.54250
\(851\) 1.89650 0.0650113
\(852\) 31.7159 1.08657
\(853\) −11.6416 −0.398599 −0.199300 0.979939i \(-0.563867\pi\)
−0.199300 + 0.979939i \(0.563867\pi\)
\(854\) 4.43457 0.151748
\(855\) −35.7092 −1.22123
\(856\) −16.5698 −0.566344
\(857\) 51.6165 1.76319 0.881593 0.472010i \(-0.156471\pi\)
0.881593 + 0.472010i \(0.156471\pi\)
\(858\) 7.76501 0.265093
\(859\) −38.2249 −1.30422 −0.652109 0.758125i \(-0.726116\pi\)
−0.652109 + 0.758125i \(0.726116\pi\)
\(860\) 144.182 4.91658
\(861\) 8.73384 0.297649
\(862\) −68.1288 −2.32048
\(863\) 7.79497 0.265344 0.132672 0.991160i \(-0.457644\pi\)
0.132672 + 0.991160i \(0.457644\pi\)
\(864\) 23.4935 0.799267
\(865\) 27.7371 0.943089
\(866\) 61.9520 2.10521
\(867\) −21.6797 −0.736282
\(868\) 31.2949 1.06222
\(869\) −15.4269 −0.523321
\(870\) 6.20756 0.210456
\(871\) 8.37824 0.283886
\(872\) 31.1212 1.05390
\(873\) −23.5184 −0.795976
\(874\) −9.98424 −0.337722
\(875\) 60.1517 2.03350
\(876\) −39.1871 −1.32401
\(877\) 21.4478 0.724242 0.362121 0.932131i \(-0.382053\pi\)
0.362121 + 0.932131i \(0.382053\pi\)
\(878\) −11.5788 −0.390764
\(879\) −12.6267 −0.425887
\(880\) 7.28342 0.245524
\(881\) −8.51828 −0.286988 −0.143494 0.989651i \(-0.545834\pi\)
−0.143494 + 0.989651i \(0.545834\pi\)
\(882\) −18.6074 −0.626544
\(883\) 34.6783 1.16702 0.583509 0.812106i \(-0.301679\pi\)
0.583509 + 0.812106i \(0.301679\pi\)
\(884\) −34.1560 −1.14879
\(885\) −58.1594 −1.95501
\(886\) 93.7789 3.15056
\(887\) −33.8190 −1.13553 −0.567766 0.823190i \(-0.692192\pi\)
−0.567766 + 0.823190i \(0.692192\pi\)
\(888\) 6.42240 0.215522
\(889\) −24.0702 −0.807290
\(890\) −89.1037 −2.98676
\(891\) 1.27971 0.0428718
\(892\) 84.5485 2.83089
\(893\) −35.7463 −1.19620
\(894\) 26.8056 0.896514
\(895\) −61.9256 −2.06994
\(896\) 33.6423 1.12391
\(897\) −1.65987 −0.0554214
\(898\) 69.0442 2.30404
\(899\) 3.27225 0.109136
\(900\) −88.3475 −2.94492
\(901\) 74.9454 2.49679
\(902\) 23.4059 0.779331
\(903\) −17.2263 −0.573254
\(904\) −53.6210 −1.78341
\(905\) 51.3164 1.70582
\(906\) 17.3918 0.577805
\(907\) 50.3773 1.67275 0.836376 0.548156i \(-0.184670\pi\)
0.836376 + 0.548156i \(0.184670\pi\)
\(908\) −48.5482 −1.61113
\(909\) −2.93949 −0.0974966
\(910\) −27.3960 −0.908167
\(911\) −9.70175 −0.321433 −0.160717 0.987001i \(-0.551381\pi\)
−0.160717 + 0.987001i \(0.551381\pi\)
\(912\) −3.73062 −0.123533
\(913\) 0.926403 0.0306595
\(914\) −46.7765 −1.54723
\(915\) 4.90878 0.162279
\(916\) −17.1260 −0.565860
\(917\) −11.6588 −0.385009
\(918\) 72.9555 2.40789
\(919\) −55.0373 −1.81551 −0.907756 0.419498i \(-0.862206\pi\)
−0.907756 + 0.419498i \(0.862206\pi\)
\(920\) −14.1106 −0.465212
\(921\) −19.9118 −0.656115
\(922\) 35.5784 1.17171
\(923\) −14.6358 −0.481743
\(924\) −11.9920 −0.394507
\(925\) 25.1663 0.827464
\(926\) 43.2421 1.42102
\(927\) 20.7743 0.682317
\(928\) 2.81537 0.0924190
\(929\) 14.9212 0.489548 0.244774 0.969580i \(-0.421286\pi\)
0.244774 + 0.969580i \(0.421286\pi\)
\(930\) 54.9101 1.80057
\(931\) −17.6042 −0.576955
\(932\) −61.1813 −2.00406
\(933\) 11.4243 0.374014
\(934\) −84.6203 −2.76886
\(935\) −53.0475 −1.73484
\(936\) 10.4043 0.340074
\(937\) 20.7962 0.679382 0.339691 0.940537i \(-0.389677\pi\)
0.339691 + 0.940537i \(0.389677\pi\)
\(938\) −20.5096 −0.669662
\(939\) 1.22461 0.0399636
\(940\) −121.763 −3.97146
\(941\) −25.7833 −0.840510 −0.420255 0.907406i \(-0.638059\pi\)
−0.420255 + 0.907406i \(0.638059\pi\)
\(942\) 28.0114 0.912661
\(943\) −5.00330 −0.162930
\(944\) 11.2464 0.366040
\(945\) 36.9166 1.20090
\(946\) −46.1648 −1.50095
\(947\) −37.5575 −1.22046 −0.610228 0.792226i \(-0.708922\pi\)
−0.610228 + 0.792226i \(0.708922\pi\)
\(948\) 26.9158 0.874183
\(949\) 18.0835 0.587014
\(950\) −132.489 −4.29853
\(951\) −10.6325 −0.344782
\(952\) 34.6911 1.12435
\(953\) 6.96993 0.225778 0.112889 0.993608i \(-0.463990\pi\)
0.112889 + 0.993608i \(0.463990\pi\)
\(954\) −55.0227 −1.78143
\(955\) −95.7436 −3.09819
\(956\) 59.6357 1.92876
\(957\) −1.25390 −0.0405329
\(958\) 38.7696 1.25259
\(959\) 19.6516 0.634584
\(960\) 54.6785 1.76474
\(961\) −2.05468 −0.0662799
\(962\) −7.14315 −0.230304
\(963\) −9.77610 −0.315030
\(964\) 21.4179 0.689825
\(965\) −58.3845 −1.87947
\(966\) 4.06329 0.130734
\(967\) 24.8235 0.798271 0.399135 0.916892i \(-0.369310\pi\)
0.399135 + 0.916892i \(0.369310\pi\)
\(968\) 22.9798 0.738599
\(969\) 27.1713 0.872868
\(970\) −120.137 −3.85737
\(971\) −25.9555 −0.832952 −0.416476 0.909147i \(-0.636735\pi\)
−0.416476 + 0.909147i \(0.636735\pi\)
\(972\) −54.2796 −1.74102
\(973\) 18.7225 0.600215
\(974\) −50.3071 −1.61194
\(975\) −22.0262 −0.705403
\(976\) −0.949222 −0.0303839
\(977\) 9.32928 0.298470 0.149235 0.988802i \(-0.452319\pi\)
0.149235 + 0.988802i \(0.452319\pi\)
\(978\) 17.9841 0.575069
\(979\) 17.9986 0.575238
\(980\) −59.9653 −1.91552
\(981\) 18.3614 0.586233
\(982\) 62.0102 1.97883
\(983\) 15.4183 0.491766 0.245883 0.969299i \(-0.420922\pi\)
0.245883 + 0.969299i \(0.420922\pi\)
\(984\) −16.9434 −0.540136
\(985\) −41.0423 −1.30772
\(986\) 8.74268 0.278424
\(987\) 14.5477 0.463058
\(988\) 23.7244 0.754774
\(989\) 9.86830 0.313794
\(990\) 38.9459 1.23778
\(991\) 11.2765 0.358211 0.179105 0.983830i \(-0.442680\pi\)
0.179105 + 0.983830i \(0.442680\pi\)
\(992\) 24.9039 0.790698
\(993\) −5.27966 −0.167545
\(994\) 35.8278 1.13639
\(995\) 55.5903 1.76233
\(996\) −1.61632 −0.0512152
\(997\) 12.1855 0.385919 0.192959 0.981207i \(-0.438191\pi\)
0.192959 + 0.981207i \(0.438191\pi\)
\(998\) 51.5152 1.63068
\(999\) 9.62553 0.304538
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 \(a_p\))