Properties

Label 8027.2.a.f.1.10
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 1.10
Character \(\chi\) = 8027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.59269 q^{2} +0.175910 q^{3} +4.72203 q^{4} +3.23280 q^{5} -0.456079 q^{6} +2.53654 q^{7} -7.05738 q^{8} -2.96906 q^{9} +O(q^{10})\) \(q-2.59269 q^{2} +0.175910 q^{3} +4.72203 q^{4} +3.23280 q^{5} -0.456079 q^{6} +2.53654 q^{7} -7.05738 q^{8} -2.96906 q^{9} -8.38164 q^{10} +5.30695 q^{11} +0.830651 q^{12} -5.29312 q^{13} -6.57644 q^{14} +0.568680 q^{15} +8.85352 q^{16} +2.29833 q^{17} +7.69784 q^{18} -3.46792 q^{19} +15.2654 q^{20} +0.446201 q^{21} -13.7593 q^{22} +1.00000 q^{23} -1.24146 q^{24} +5.45098 q^{25} +13.7234 q^{26} -1.05001 q^{27} +11.9776 q^{28} -8.54620 q^{29} -1.47441 q^{30} +5.22128 q^{31} -8.83965 q^{32} +0.933545 q^{33} -5.95884 q^{34} +8.20011 q^{35} -14.0200 q^{36} +9.38807 q^{37} +8.99124 q^{38} -0.931112 q^{39} -22.8151 q^{40} +12.6328 q^{41} -1.15686 q^{42} -3.98512 q^{43} +25.0596 q^{44} -9.59836 q^{45} -2.59269 q^{46} -2.42572 q^{47} +1.55742 q^{48} -0.565990 q^{49} -14.1327 q^{50} +0.404298 q^{51} -24.9943 q^{52} +7.85499 q^{53} +2.72236 q^{54} +17.1563 q^{55} -17.9013 q^{56} -0.610041 q^{57} +22.1576 q^{58} +2.47534 q^{59} +2.68533 q^{60} -13.0307 q^{61} -13.5371 q^{62} -7.53111 q^{63} +5.21143 q^{64} -17.1116 q^{65} -2.42039 q^{66} +7.45338 q^{67} +10.8528 q^{68} +0.175910 q^{69} -21.2603 q^{70} -3.92447 q^{71} +20.9537 q^{72} -13.8239 q^{73} -24.3403 q^{74} +0.958881 q^{75} -16.3756 q^{76} +13.4613 q^{77} +2.41408 q^{78} +1.45457 q^{79} +28.6216 q^{80} +8.72246 q^{81} -32.7528 q^{82} +6.69824 q^{83} +2.10698 q^{84} +7.43002 q^{85} +10.3322 q^{86} -1.50336 q^{87} -37.4532 q^{88} +15.8078 q^{89} +24.8855 q^{90} -13.4262 q^{91} +4.72203 q^{92} +0.918474 q^{93} +6.28913 q^{94} -11.2111 q^{95} -1.55498 q^{96} +11.9373 q^{97} +1.46743 q^{98} -15.7566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + O(q^{10}) \) \( 176q + 19q^{2} + 22q^{3} + 203q^{4} + 28q^{5} + 9q^{6} + 30q^{7} + 51q^{8} + 204q^{9} + 18q^{10} + 11q^{11} + 46q^{12} + 87q^{13} - 6q^{14} + 29q^{15} + 257q^{16} + 14q^{17} + 72q^{18} + 34q^{19} + 45q^{20} + 23q^{21} + 62q^{22} + 176q^{23} + 33q^{24} + 272q^{25} + 31q^{26} + 82q^{27} + 80q^{28} + 75q^{29} - 30q^{30} + 73q^{31} + 71q^{32} + 30q^{33} + 23q^{34} + 44q^{35} + 264q^{36} + 236q^{37} - 21q^{38} + 17q^{39} + 43q^{40} + 51q^{41} + 38q^{42} + 51q^{43} + 12q^{44} + 127q^{45} + 19q^{46} + 45q^{47} + 61q^{48} + 268q^{49} + 55q^{50} - 3q^{51} + 166q^{52} + 63q^{53} - 32q^{54} + 11q^{55} - 9q^{56} + 72q^{57} + 98q^{58} + 95q^{59} - 7q^{60} + 73q^{61} + 12q^{62} + 19q^{63} + 365q^{64} + 19q^{65} - 28q^{66} + 138q^{67} + 16q^{68} + 22q^{69} + 100q^{70} + 85q^{71} + 129q^{72} + 118q^{73} - 21q^{74} - 12q^{75} + 52q^{76} + 75q^{77} + 97q^{78} + 74q^{79} + 8q^{80} + 280q^{81} + 67q^{82} + 10q^{83} - 51q^{84} + 169q^{85} - 39q^{86} - 6q^{87} + 159q^{88} + 38q^{89} + 22q^{90} + 90q^{91} + 203q^{92} + 230q^{93} + 63q^{94} + 30q^{95} + 107q^{96} + 161q^{97} + 58q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59269 −1.83331 −0.916654 0.399682i \(-0.869120\pi\)
−0.916654 + 0.399682i \(0.869120\pi\)
\(3\) 0.175910 0.101562 0.0507808 0.998710i \(-0.483829\pi\)
0.0507808 + 0.998710i \(0.483829\pi\)
\(4\) 4.72203 2.36102
\(5\) 3.23280 1.44575 0.722876 0.690978i \(-0.242820\pi\)
0.722876 + 0.690978i \(0.242820\pi\)
\(6\) −0.456079 −0.186193
\(7\) 2.53654 0.958720 0.479360 0.877618i \(-0.340869\pi\)
0.479360 + 0.877618i \(0.340869\pi\)
\(8\) −7.05738 −2.49516
\(9\) −2.96906 −0.989685
\(10\) −8.38164 −2.65051
\(11\) 5.30695 1.60011 0.800053 0.599929i \(-0.204804\pi\)
0.800053 + 0.599929i \(0.204804\pi\)
\(12\) 0.830651 0.239788
\(13\) −5.29312 −1.46805 −0.734024 0.679123i \(-0.762360\pi\)
−0.734024 + 0.679123i \(0.762360\pi\)
\(14\) −6.57644 −1.75763
\(15\) 0.568680 0.146833
\(16\) 8.85352 2.21338
\(17\) 2.29833 0.557426 0.278713 0.960374i \(-0.410092\pi\)
0.278713 + 0.960374i \(0.410092\pi\)
\(18\) 7.69784 1.81440
\(19\) −3.46792 −0.795596 −0.397798 0.917473i \(-0.630225\pi\)
−0.397798 + 0.917473i \(0.630225\pi\)
\(20\) 15.2654 3.41344
\(21\) 0.446201 0.0973691
\(22\) −13.7593 −2.93349
\(23\) 1.00000 0.208514
\(24\) −1.24146 −0.253412
\(25\) 5.45098 1.09020
\(26\) 13.7234 2.69138
\(27\) −1.05001 −0.202075
\(28\) 11.9776 2.26355
\(29\) −8.54620 −1.58699 −0.793495 0.608577i \(-0.791741\pi\)
−0.793495 + 0.608577i \(0.791741\pi\)
\(30\) −1.47441 −0.269189
\(31\) 5.22128 0.937769 0.468885 0.883259i \(-0.344656\pi\)
0.468885 + 0.883259i \(0.344656\pi\)
\(32\) −8.83965 −1.56264
\(33\) 0.933545 0.162509
\(34\) −5.95884 −1.02193
\(35\) 8.20011 1.38607
\(36\) −14.0200 −2.33666
\(37\) 9.38807 1.54339 0.771694 0.635994i \(-0.219410\pi\)
0.771694 + 0.635994i \(0.219410\pi\)
\(38\) 8.99124 1.45857
\(39\) −0.931112 −0.149097
\(40\) −22.8151 −3.60738
\(41\) 12.6328 1.97291 0.986454 0.164040i \(-0.0524527\pi\)
0.986454 + 0.164040i \(0.0524527\pi\)
\(42\) −1.15686 −0.178507
\(43\) −3.98512 −0.607725 −0.303862 0.952716i \(-0.598276\pi\)
−0.303862 + 0.952716i \(0.598276\pi\)
\(44\) 25.0596 3.77788
\(45\) −9.59836 −1.43084
\(46\) −2.59269 −0.382271
\(47\) −2.42572 −0.353827 −0.176914 0.984226i \(-0.556611\pi\)
−0.176914 + 0.984226i \(0.556611\pi\)
\(48\) 1.55742 0.224794
\(49\) −0.565990 −0.0808557
\(50\) −14.1327 −1.99867
\(51\) 0.404298 0.0566130
\(52\) −24.9943 −3.46609
\(53\) 7.85499 1.07897 0.539483 0.841996i \(-0.318620\pi\)
0.539483 + 0.841996i \(0.318620\pi\)
\(54\) 2.72236 0.370466
\(55\) 17.1563 2.31336
\(56\) −17.9013 −2.39216
\(57\) −0.610041 −0.0808019
\(58\) 22.1576 2.90944
\(59\) 2.47534 0.322262 0.161131 0.986933i \(-0.448486\pi\)
0.161131 + 0.986933i \(0.448486\pi\)
\(60\) 2.68533 0.346674
\(61\) −13.0307 −1.66841 −0.834206 0.551453i \(-0.814074\pi\)
−0.834206 + 0.551453i \(0.814074\pi\)
\(62\) −13.5371 −1.71922
\(63\) −7.53111 −0.948831
\(64\) 5.21143 0.651428
\(65\) −17.1116 −2.12243
\(66\) −2.42039 −0.297929
\(67\) 7.45338 0.910576 0.455288 0.890344i \(-0.349536\pi\)
0.455288 + 0.890344i \(0.349536\pi\)
\(68\) 10.8528 1.31609
\(69\) 0.175910 0.0211770
\(70\) −21.2603 −2.54109
\(71\) −3.92447 −0.465749 −0.232874 0.972507i \(-0.574813\pi\)
−0.232874 + 0.972507i \(0.574813\pi\)
\(72\) 20.9537 2.46942
\(73\) −13.8239 −1.61797 −0.808985 0.587830i \(-0.799982\pi\)
−0.808985 + 0.587830i \(0.799982\pi\)
\(74\) −24.3403 −2.82951
\(75\) 0.958881 0.110722
\(76\) −16.3756 −1.87841
\(77\) 13.4613 1.53405
\(78\) 2.41408 0.273341
\(79\) 1.45457 0.163652 0.0818262 0.996647i \(-0.473925\pi\)
0.0818262 + 0.996647i \(0.473925\pi\)
\(80\) 28.6216 3.20000
\(81\) 8.72246 0.969162
\(82\) −32.7528 −3.61695
\(83\) 6.69824 0.735228 0.367614 0.929979i \(-0.380175\pi\)
0.367614 + 0.929979i \(0.380175\pi\)
\(84\) 2.10698 0.229890
\(85\) 7.43002 0.805899
\(86\) 10.3322 1.11415
\(87\) −1.50336 −0.161177
\(88\) −37.4532 −3.99252
\(89\) 15.8078 1.67562 0.837810 0.545962i \(-0.183836\pi\)
0.837810 + 0.545962i \(0.183836\pi\)
\(90\) 24.8855 2.62317
\(91\) −13.4262 −1.40745
\(92\) 4.72203 0.492306
\(93\) 0.918474 0.0952413
\(94\) 6.28913 0.648674
\(95\) −11.2111 −1.15023
\(96\) −1.55498 −0.158705
\(97\) 11.9373 1.21205 0.606023 0.795447i \(-0.292764\pi\)
0.606023 + 0.795447i \(0.292764\pi\)
\(98\) 1.46743 0.148233
\(99\) −15.7566 −1.58360
\(100\) 25.7397 2.57397
\(101\) −4.49752 −0.447520 −0.223760 0.974644i \(-0.571833\pi\)
−0.223760 + 0.974644i \(0.571833\pi\)
\(102\) −1.04822 −0.103789
\(103\) 6.36534 0.627195 0.313598 0.949556i \(-0.398466\pi\)
0.313598 + 0.949556i \(0.398466\pi\)
\(104\) 37.3556 3.66302
\(105\) 1.44248 0.140771
\(106\) −20.3656 −1.97808
\(107\) −11.3893 −1.10105 −0.550525 0.834819i \(-0.685572\pi\)
−0.550525 + 0.834819i \(0.685572\pi\)
\(108\) −4.95820 −0.477103
\(109\) 9.00556 0.862576 0.431288 0.902214i \(-0.358059\pi\)
0.431288 + 0.902214i \(0.358059\pi\)
\(110\) −44.4810 −4.24109
\(111\) 1.65145 0.156749
\(112\) 22.4573 2.12201
\(113\) −12.8681 −1.21053 −0.605263 0.796025i \(-0.706932\pi\)
−0.605263 + 0.796025i \(0.706932\pi\)
\(114\) 1.58165 0.148135
\(115\) 3.23280 0.301460
\(116\) −40.3554 −3.74691
\(117\) 15.7156 1.45291
\(118\) −6.41779 −0.590805
\(119\) 5.82978 0.534415
\(120\) −4.01339 −0.366371
\(121\) 17.1638 1.56034
\(122\) 33.7846 3.05871
\(123\) 2.22223 0.200371
\(124\) 24.6550 2.21409
\(125\) 1.45794 0.130402
\(126\) 19.5258 1.73950
\(127\) 11.0793 0.983133 0.491566 0.870840i \(-0.336424\pi\)
0.491566 + 0.870840i \(0.336424\pi\)
\(128\) 4.16770 0.368376
\(129\) −0.701021 −0.0617214
\(130\) 44.3650 3.89107
\(131\) 17.7650 1.55214 0.776068 0.630649i \(-0.217211\pi\)
0.776068 + 0.630649i \(0.217211\pi\)
\(132\) 4.40823 0.383687
\(133\) −8.79650 −0.762754
\(134\) −19.3243 −1.66937
\(135\) −3.39449 −0.292151
\(136\) −16.2202 −1.39087
\(137\) −14.4118 −1.23129 −0.615644 0.788025i \(-0.711104\pi\)
−0.615644 + 0.788025i \(0.711104\pi\)
\(138\) −0.456079 −0.0388240
\(139\) −4.54714 −0.385683 −0.192842 0.981230i \(-0.561770\pi\)
−0.192842 + 0.981230i \(0.561770\pi\)
\(140\) 38.7212 3.27254
\(141\) −0.426707 −0.0359352
\(142\) 10.1749 0.853860
\(143\) −28.0904 −2.34903
\(144\) −26.2866 −2.19055
\(145\) −27.6281 −2.29439
\(146\) 35.8411 2.96623
\(147\) −0.0995631 −0.00821182
\(148\) 44.3307 3.64396
\(149\) −23.0896 −1.89158 −0.945789 0.324783i \(-0.894709\pi\)
−0.945789 + 0.324783i \(0.894709\pi\)
\(150\) −2.48608 −0.202987
\(151\) −7.98078 −0.649467 −0.324733 0.945806i \(-0.605275\pi\)
−0.324733 + 0.945806i \(0.605275\pi\)
\(152\) 24.4744 1.98514
\(153\) −6.82386 −0.551676
\(154\) −34.9009 −2.81239
\(155\) 16.8793 1.35578
\(156\) −4.39674 −0.352021
\(157\) 20.5567 1.64061 0.820303 0.571929i \(-0.193805\pi\)
0.820303 + 0.571929i \(0.193805\pi\)
\(158\) −3.77126 −0.300025
\(159\) 1.38177 0.109581
\(160\) −28.5768 −2.25920
\(161\) 2.53654 0.199907
\(162\) −22.6146 −1.77677
\(163\) 12.3571 0.967883 0.483942 0.875100i \(-0.339205\pi\)
0.483942 + 0.875100i \(0.339205\pi\)
\(164\) 59.6523 4.65807
\(165\) 3.01796 0.234948
\(166\) −17.3665 −1.34790
\(167\) 14.0043 1.08368 0.541841 0.840481i \(-0.317727\pi\)
0.541841 + 0.840481i \(0.317727\pi\)
\(168\) −3.14901 −0.242951
\(169\) 15.0172 1.15517
\(170\) −19.2637 −1.47746
\(171\) 10.2965 0.787389
\(172\) −18.8178 −1.43485
\(173\) −3.15493 −0.239865 −0.119933 0.992782i \(-0.538268\pi\)
−0.119933 + 0.992782i \(0.538268\pi\)
\(174\) 3.89774 0.295487
\(175\) 13.8266 1.04519
\(176\) 46.9852 3.54164
\(177\) 0.435436 0.0327294
\(178\) −40.9846 −3.07193
\(179\) 15.3675 1.14862 0.574312 0.818637i \(-0.305270\pi\)
0.574312 + 0.818637i \(0.305270\pi\)
\(180\) −45.3237 −3.37823
\(181\) −1.71861 −0.127743 −0.0638717 0.997958i \(-0.520345\pi\)
−0.0638717 + 0.997958i \(0.520345\pi\)
\(182\) 34.8099 2.58028
\(183\) −2.29223 −0.169446
\(184\) −7.05738 −0.520277
\(185\) 30.3497 2.23136
\(186\) −2.38132 −0.174607
\(187\) 12.1971 0.891941
\(188\) −11.4543 −0.835392
\(189\) −2.66340 −0.193734
\(190\) 29.0669 2.10873
\(191\) 20.4084 1.47670 0.738351 0.674416i \(-0.235605\pi\)
0.738351 + 0.674416i \(0.235605\pi\)
\(192\) 0.916741 0.0661600
\(193\) 8.25880 0.594481 0.297241 0.954803i \(-0.403934\pi\)
0.297241 + 0.954803i \(0.403934\pi\)
\(194\) −30.9496 −2.22205
\(195\) −3.01010 −0.215558
\(196\) −2.67262 −0.190902
\(197\) −1.27985 −0.0911852 −0.0455926 0.998960i \(-0.514518\pi\)
−0.0455926 + 0.998960i \(0.514518\pi\)
\(198\) 40.8521 2.90323
\(199\) 26.9308 1.90908 0.954539 0.298088i \(-0.0963487\pi\)
0.954539 + 0.298088i \(0.0963487\pi\)
\(200\) −38.4697 −2.72022
\(201\) 1.31112 0.0924794
\(202\) 11.6607 0.820442
\(203\) −21.6777 −1.52148
\(204\) 1.90911 0.133664
\(205\) 40.8392 2.85233
\(206\) −16.5033 −1.14984
\(207\) −2.96906 −0.206364
\(208\) −46.8628 −3.24935
\(209\) −18.4041 −1.27304
\(210\) −3.73990 −0.258077
\(211\) 18.0657 1.24369 0.621847 0.783139i \(-0.286382\pi\)
0.621847 + 0.783139i \(0.286382\pi\)
\(212\) 37.0915 2.54746
\(213\) −0.690352 −0.0473021
\(214\) 29.5290 2.01856
\(215\) −12.8831 −0.878619
\(216\) 7.41035 0.504211
\(217\) 13.2440 0.899058
\(218\) −23.3486 −1.58137
\(219\) −2.43176 −0.164323
\(220\) 81.0126 5.46187
\(221\) −12.1653 −0.818328
\(222\) −4.28170 −0.287369
\(223\) 17.3104 1.15919 0.579595 0.814904i \(-0.303211\pi\)
0.579595 + 0.814904i \(0.303211\pi\)
\(224\) −22.4221 −1.49814
\(225\) −16.1843 −1.07895
\(226\) 33.3629 2.21927
\(227\) −0.257651 −0.0171009 −0.00855045 0.999963i \(-0.502722\pi\)
−0.00855045 + 0.999963i \(0.502722\pi\)
\(228\) −2.88063 −0.190775
\(229\) 1.74044 0.115012 0.0575058 0.998345i \(-0.481685\pi\)
0.0575058 + 0.998345i \(0.481685\pi\)
\(230\) −8.38164 −0.552669
\(231\) 2.36797 0.155801
\(232\) 60.3138 3.95979
\(233\) 7.55104 0.494685 0.247343 0.968928i \(-0.420443\pi\)
0.247343 + 0.968928i \(0.420443\pi\)
\(234\) −40.7456 −2.66362
\(235\) −7.84186 −0.511546
\(236\) 11.6886 0.760866
\(237\) 0.255874 0.0166208
\(238\) −15.1148 −0.979748
\(239\) 15.1585 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(240\) 5.03482 0.324996
\(241\) −11.2210 −0.722809 −0.361405 0.932409i \(-0.617703\pi\)
−0.361405 + 0.932409i \(0.617703\pi\)
\(242\) −44.5003 −2.86059
\(243\) 4.68441 0.300505
\(244\) −61.5315 −3.93915
\(245\) −1.82973 −0.116897
\(246\) −5.76154 −0.367342
\(247\) 18.3561 1.16797
\(248\) −36.8485 −2.33988
\(249\) 1.17829 0.0746708
\(250\) −3.77998 −0.239067
\(251\) −23.0807 −1.45684 −0.728422 0.685129i \(-0.759746\pi\)
−0.728422 + 0.685129i \(0.759746\pi\)
\(252\) −35.5622 −2.24021
\(253\) 5.30695 0.333645
\(254\) −28.7253 −1.80238
\(255\) 1.30701 0.0818483
\(256\) −21.2284 −1.32678
\(257\) 30.9575 1.93108 0.965538 0.260264i \(-0.0838095\pi\)
0.965538 + 0.260264i \(0.0838095\pi\)
\(258\) 1.81753 0.113154
\(259\) 23.8132 1.47968
\(260\) −80.8015 −5.01110
\(261\) 25.3741 1.57062
\(262\) −46.0591 −2.84554
\(263\) 13.8789 0.855810 0.427905 0.903824i \(-0.359252\pi\)
0.427905 + 0.903824i \(0.359252\pi\)
\(264\) −6.58838 −0.405487
\(265\) 25.3936 1.55992
\(266\) 22.8066 1.39836
\(267\) 2.78074 0.170178
\(268\) 35.1951 2.14988
\(269\) −6.99772 −0.426659 −0.213329 0.976980i \(-0.568431\pi\)
−0.213329 + 0.976980i \(0.568431\pi\)
\(270\) 8.80084 0.535602
\(271\) −3.13129 −0.190212 −0.0951062 0.995467i \(-0.530319\pi\)
−0.0951062 + 0.995467i \(0.530319\pi\)
\(272\) 20.3483 1.23379
\(273\) −2.36180 −0.142943
\(274\) 37.3654 2.25733
\(275\) 28.9281 1.74443
\(276\) 0.830651 0.0499993
\(277\) −19.4257 −1.16718 −0.583590 0.812049i \(-0.698352\pi\)
−0.583590 + 0.812049i \(0.698352\pi\)
\(278\) 11.7893 0.707076
\(279\) −15.5023 −0.928097
\(280\) −57.8712 −3.45847
\(281\) 11.5559 0.689365 0.344682 0.938719i \(-0.387987\pi\)
0.344682 + 0.938719i \(0.387987\pi\)
\(282\) 1.10632 0.0658804
\(283\) 15.8417 0.941689 0.470844 0.882216i \(-0.343949\pi\)
0.470844 + 0.882216i \(0.343949\pi\)
\(284\) −18.5315 −1.09964
\(285\) −1.97214 −0.116819
\(286\) 72.8296 4.30650
\(287\) 32.0435 1.89147
\(288\) 26.2454 1.54653
\(289\) −11.7177 −0.689276
\(290\) 71.6312 4.20633
\(291\) 2.09988 0.123097
\(292\) −65.2770 −3.82005
\(293\) 4.41479 0.257915 0.128957 0.991650i \(-0.458837\pi\)
0.128957 + 0.991650i \(0.458837\pi\)
\(294\) 0.258136 0.0150548
\(295\) 8.00228 0.465911
\(296\) −66.2551 −3.85100
\(297\) −5.57238 −0.323342
\(298\) 59.8642 3.46784
\(299\) −5.29312 −0.306109
\(300\) 4.52787 0.261416
\(301\) −10.1084 −0.582638
\(302\) 20.6917 1.19067
\(303\) −0.791157 −0.0454508
\(304\) −30.7033 −1.76096
\(305\) −42.1257 −2.41211
\(306\) 17.6921 1.01139
\(307\) 32.0835 1.83110 0.915550 0.402204i \(-0.131756\pi\)
0.915550 + 0.402204i \(0.131756\pi\)
\(308\) 63.5646 3.62193
\(309\) 1.11972 0.0636989
\(310\) −43.7629 −2.48556
\(311\) −4.65407 −0.263908 −0.131954 0.991256i \(-0.542125\pi\)
−0.131954 + 0.991256i \(0.542125\pi\)
\(312\) 6.57121 0.372021
\(313\) −23.7613 −1.34307 −0.671534 0.740974i \(-0.734364\pi\)
−0.671534 + 0.740974i \(0.734364\pi\)
\(314\) −53.2972 −3.00774
\(315\) −24.3466 −1.37177
\(316\) 6.86854 0.386386
\(317\) −7.81222 −0.438778 −0.219389 0.975637i \(-0.570406\pi\)
−0.219389 + 0.975637i \(0.570406\pi\)
\(318\) −3.58250 −0.200896
\(319\) −45.3543 −2.53935
\(320\) 16.8475 0.941803
\(321\) −2.00350 −0.111824
\(322\) −6.57644 −0.366491
\(323\) −7.97041 −0.443486
\(324\) 41.1877 2.28821
\(325\) −28.8527 −1.60046
\(326\) −32.0381 −1.77443
\(327\) 1.58417 0.0876045
\(328\) −89.1542 −4.92272
\(329\) −6.15292 −0.339222
\(330\) −7.82463 −0.430732
\(331\) 5.44931 0.299521 0.149761 0.988722i \(-0.452150\pi\)
0.149761 + 0.988722i \(0.452150\pi\)
\(332\) 31.6293 1.73588
\(333\) −27.8737 −1.52747
\(334\) −36.3087 −1.98672
\(335\) 24.0953 1.31647
\(336\) 3.95045 0.215515
\(337\) −28.3777 −1.54583 −0.772916 0.634508i \(-0.781203\pi\)
−0.772916 + 0.634508i \(0.781203\pi\)
\(338\) −38.9348 −2.11778
\(339\) −2.26362 −0.122943
\(340\) 35.0848 1.90274
\(341\) 27.7091 1.50053
\(342\) −26.6955 −1.44353
\(343\) −19.1914 −1.03624
\(344\) 28.1245 1.51637
\(345\) 0.568680 0.0306167
\(346\) 8.17976 0.439747
\(347\) 17.5063 0.939786 0.469893 0.882723i \(-0.344292\pi\)
0.469893 + 0.882723i \(0.344292\pi\)
\(348\) −7.09891 −0.380542
\(349\) −1.00000 −0.0535288
\(350\) −35.8481 −1.91616
\(351\) 5.55786 0.296657
\(352\) −46.9116 −2.50040
\(353\) −5.20548 −0.277059 −0.138530 0.990358i \(-0.544238\pi\)
−0.138530 + 0.990358i \(0.544238\pi\)
\(354\) −1.12895 −0.0600031
\(355\) −12.6870 −0.673357
\(356\) 74.6448 3.95616
\(357\) 1.02552 0.0542760
\(358\) −39.8432 −2.10578
\(359\) −19.8325 −1.04672 −0.523359 0.852112i \(-0.675321\pi\)
−0.523359 + 0.852112i \(0.675321\pi\)
\(360\) 67.7392 3.57017
\(361\) −6.97352 −0.367027
\(362\) 4.45582 0.234193
\(363\) 3.01927 0.158471
\(364\) −63.3989 −3.32301
\(365\) −44.6900 −2.33918
\(366\) 5.94304 0.310647
\(367\) 1.83519 0.0957960 0.0478980 0.998852i \(-0.484748\pi\)
0.0478980 + 0.998852i \(0.484748\pi\)
\(368\) 8.85352 0.461522
\(369\) −37.5074 −1.95256
\(370\) −78.6874 −4.09076
\(371\) 19.9245 1.03443
\(372\) 4.33706 0.224866
\(373\) 24.0662 1.24610 0.623050 0.782182i \(-0.285893\pi\)
0.623050 + 0.782182i \(0.285893\pi\)
\(374\) −31.6233 −1.63520
\(375\) 0.256466 0.0132438
\(376\) 17.1192 0.882856
\(377\) 45.2361 2.32978
\(378\) 6.90536 0.355174
\(379\) −1.26215 −0.0648323 −0.0324161 0.999474i \(-0.510320\pi\)
−0.0324161 + 0.999474i \(0.510320\pi\)
\(380\) −52.9391 −2.71572
\(381\) 1.94896 0.0998485
\(382\) −52.9127 −2.70725
\(383\) −15.1001 −0.771577 −0.385788 0.922587i \(-0.626070\pi\)
−0.385788 + 0.922587i \(0.626070\pi\)
\(384\) 0.733139 0.0374128
\(385\) 43.5176 2.21786
\(386\) −21.4125 −1.08987
\(387\) 11.8320 0.601456
\(388\) 56.3682 2.86166
\(389\) −12.3806 −0.627720 −0.313860 0.949469i \(-0.601622\pi\)
−0.313860 + 0.949469i \(0.601622\pi\)
\(390\) 7.80424 0.395183
\(391\) 2.29833 0.116231
\(392\) 3.99440 0.201748
\(393\) 3.12504 0.157637
\(394\) 3.31824 0.167171
\(395\) 4.70234 0.236601
\(396\) −74.4034 −3.73891
\(397\) −5.24230 −0.263103 −0.131552 0.991309i \(-0.541996\pi\)
−0.131552 + 0.991309i \(0.541996\pi\)
\(398\) −69.8233 −3.49992
\(399\) −1.54739 −0.0774664
\(400\) 48.2604 2.41302
\(401\) −29.1741 −1.45689 −0.728443 0.685106i \(-0.759756\pi\)
−0.728443 + 0.685106i \(0.759756\pi\)
\(402\) −3.39933 −0.169543
\(403\) −27.6369 −1.37669
\(404\) −21.2374 −1.05660
\(405\) 28.1980 1.40117
\(406\) 56.2036 2.78934
\(407\) 49.8220 2.46959
\(408\) −2.85328 −0.141259
\(409\) −16.1404 −0.798090 −0.399045 0.916931i \(-0.630658\pi\)
−0.399045 + 0.916931i \(0.630658\pi\)
\(410\) −105.883 −5.22920
\(411\) −2.53518 −0.125051
\(412\) 30.0573 1.48082
\(413\) 6.27879 0.308959
\(414\) 7.69784 0.378328
\(415\) 21.6541 1.06296
\(416\) 46.7894 2.29404
\(417\) −0.799886 −0.0391706
\(418\) 47.7161 2.33387
\(419\) −29.7775 −1.45473 −0.727364 0.686252i \(-0.759255\pi\)
−0.727364 + 0.686252i \(0.759255\pi\)
\(420\) 6.81143 0.332364
\(421\) 32.4816 1.58306 0.791528 0.611133i \(-0.209286\pi\)
0.791528 + 0.611133i \(0.209286\pi\)
\(422\) −46.8387 −2.28007
\(423\) 7.20209 0.350178
\(424\) −55.4357 −2.69219
\(425\) 12.5281 0.607704
\(426\) 1.78987 0.0867193
\(427\) −33.0529 −1.59954
\(428\) −53.7808 −2.59960
\(429\) −4.94137 −0.238572
\(430\) 33.4018 1.61078
\(431\) −18.6525 −0.898459 −0.449230 0.893416i \(-0.648302\pi\)
−0.449230 + 0.893416i \(0.648302\pi\)
\(432\) −9.29632 −0.447270
\(433\) 39.5864 1.90240 0.951201 0.308572i \(-0.0998512\pi\)
0.951201 + 0.308572i \(0.0998512\pi\)
\(434\) −34.3374 −1.64825
\(435\) −4.86006 −0.233022
\(436\) 42.5245 2.03656
\(437\) −3.46792 −0.165893
\(438\) 6.30480 0.301255
\(439\) −10.9755 −0.523832 −0.261916 0.965091i \(-0.584354\pi\)
−0.261916 + 0.965091i \(0.584354\pi\)
\(440\) −121.079 −5.77219
\(441\) 1.68045 0.0800217
\(442\) 31.5409 1.50025
\(443\) −33.5263 −1.59288 −0.796442 0.604715i \(-0.793287\pi\)
−0.796442 + 0.604715i \(0.793287\pi\)
\(444\) 7.79821 0.370087
\(445\) 51.1033 2.42253
\(446\) −44.8805 −2.12515
\(447\) −4.06169 −0.192111
\(448\) 13.2190 0.624538
\(449\) −9.26977 −0.437468 −0.218734 0.975785i \(-0.570193\pi\)
−0.218734 + 0.975785i \(0.570193\pi\)
\(450\) 41.9608 1.97805
\(451\) 67.0415 3.15686
\(452\) −60.7634 −2.85807
\(453\) −1.40390 −0.0659608
\(454\) 0.668009 0.0313512
\(455\) −43.4042 −2.03482
\(456\) 4.30529 0.201614
\(457\) −1.67842 −0.0785134 −0.0392567 0.999229i \(-0.512499\pi\)
−0.0392567 + 0.999229i \(0.512499\pi\)
\(458\) −4.51242 −0.210851
\(459\) −2.41328 −0.112642
\(460\) 15.2654 0.711752
\(461\) 26.5704 1.23751 0.618753 0.785585i \(-0.287638\pi\)
0.618753 + 0.785585i \(0.287638\pi\)
\(462\) −6.13940 −0.285631
\(463\) −12.6709 −0.588868 −0.294434 0.955672i \(-0.595131\pi\)
−0.294434 + 0.955672i \(0.595131\pi\)
\(464\) −75.6639 −3.51261
\(465\) 2.96924 0.137695
\(466\) −19.5775 −0.906910
\(467\) 16.2456 0.751756 0.375878 0.926669i \(-0.377341\pi\)
0.375878 + 0.926669i \(0.377341\pi\)
\(468\) 74.2095 3.43033
\(469\) 18.9058 0.872987
\(470\) 20.3315 0.937822
\(471\) 3.61613 0.166623
\(472\) −17.4694 −0.804095
\(473\) −21.1488 −0.972424
\(474\) −0.663400 −0.0304710
\(475\) −18.9036 −0.867356
\(476\) 27.5284 1.26176
\(477\) −23.3219 −1.06784
\(478\) −39.3013 −1.79760
\(479\) −37.6739 −1.72136 −0.860681 0.509144i \(-0.829962\pi\)
−0.860681 + 0.509144i \(0.829962\pi\)
\(480\) −5.02694 −0.229447
\(481\) −49.6922 −2.26577
\(482\) 29.0926 1.32513
\(483\) 0.446201 0.0203029
\(484\) 81.0478 3.68399
\(485\) 38.5908 1.75232
\(486\) −12.1452 −0.550918
\(487\) 7.83577 0.355073 0.177536 0.984114i \(-0.443187\pi\)
0.177536 + 0.984114i \(0.443187\pi\)
\(488\) 91.9627 4.16296
\(489\) 2.17373 0.0982997
\(490\) 4.74392 0.214308
\(491\) 32.9341 1.48630 0.743148 0.669127i \(-0.233332\pi\)
0.743148 + 0.669127i \(0.233332\pi\)
\(492\) 10.4934 0.473080
\(493\) −19.6420 −0.884629
\(494\) −47.5917 −2.14125
\(495\) −50.9380 −2.28949
\(496\) 46.2267 2.07564
\(497\) −9.95455 −0.446523
\(498\) −3.05493 −0.136895
\(499\) −10.1013 −0.452198 −0.226099 0.974104i \(-0.572597\pi\)
−0.226099 + 0.974104i \(0.572597\pi\)
\(500\) 6.88443 0.307881
\(501\) 2.46349 0.110060
\(502\) 59.8411 2.67084
\(503\) 38.1479 1.70093 0.850465 0.526031i \(-0.176321\pi\)
0.850465 + 0.526031i \(0.176321\pi\)
\(504\) 53.1499 2.36749
\(505\) −14.5396 −0.647003
\(506\) −13.7593 −0.611674
\(507\) 2.64167 0.117320
\(508\) 52.3170 2.32119
\(509\) 17.2125 0.762930 0.381465 0.924383i \(-0.375420\pi\)
0.381465 + 0.924383i \(0.375420\pi\)
\(510\) −3.38868 −0.150053
\(511\) −35.0649 −1.55118
\(512\) 46.7032 2.06401
\(513\) 3.64137 0.160770
\(514\) −80.2631 −3.54025
\(515\) 20.5779 0.906768
\(516\) −3.31024 −0.145725
\(517\) −12.8732 −0.566162
\(518\) −61.7401 −2.71270
\(519\) −0.554983 −0.0243611
\(520\) 120.763 5.29581
\(521\) −13.1711 −0.577037 −0.288518 0.957474i \(-0.593163\pi\)
−0.288518 + 0.957474i \(0.593163\pi\)
\(522\) −65.7872 −2.87943
\(523\) 39.3267 1.71964 0.859819 0.510599i \(-0.170576\pi\)
0.859819 + 0.510599i \(0.170576\pi\)
\(524\) 83.8869 3.66462
\(525\) 2.43223 0.106151
\(526\) −35.9837 −1.56896
\(527\) 12.0002 0.522737
\(528\) 8.26515 0.359695
\(529\) 1.00000 0.0434783
\(530\) −65.8377 −2.85981
\(531\) −7.34943 −0.318938
\(532\) −41.5374 −1.80087
\(533\) −66.8668 −2.89632
\(534\) −7.20959 −0.311989
\(535\) −36.8195 −1.59184
\(536\) −52.6013 −2.27203
\(537\) 2.70330 0.116656
\(538\) 18.1429 0.782196
\(539\) −3.00368 −0.129378
\(540\) −16.0289 −0.689773
\(541\) 3.97101 0.170727 0.0853636 0.996350i \(-0.472795\pi\)
0.0853636 + 0.996350i \(0.472795\pi\)
\(542\) 8.11846 0.348718
\(543\) −0.302320 −0.0129738
\(544\) −20.3164 −0.871059
\(545\) 29.1132 1.24707
\(546\) 6.12341 0.262058
\(547\) 44.0248 1.88236 0.941182 0.337900i \(-0.109716\pi\)
0.941182 + 0.337900i \(0.109716\pi\)
\(548\) −68.0532 −2.90709
\(549\) 38.6889 1.65120
\(550\) −75.0016 −3.19808
\(551\) 29.6376 1.26260
\(552\) −1.24146 −0.0528401
\(553\) 3.68958 0.156897
\(554\) 50.3649 2.13980
\(555\) 5.33881 0.226620
\(556\) −21.4717 −0.910604
\(557\) −42.4833 −1.80008 −0.900038 0.435812i \(-0.856461\pi\)
−0.900038 + 0.435812i \(0.856461\pi\)
\(558\) 40.1925 1.70149
\(559\) 21.0937 0.892169
\(560\) 72.5998 3.06790
\(561\) 2.14559 0.0905869
\(562\) −29.9607 −1.26382
\(563\) 3.73885 0.157574 0.0787870 0.996891i \(-0.474895\pi\)
0.0787870 + 0.996891i \(0.474895\pi\)
\(564\) −2.01493 −0.0848437
\(565\) −41.5999 −1.75012
\(566\) −41.0725 −1.72640
\(567\) 22.1248 0.929155
\(568\) 27.6965 1.16212
\(569\) −19.7972 −0.829942 −0.414971 0.909835i \(-0.636208\pi\)
−0.414971 + 0.909835i \(0.636208\pi\)
\(570\) 5.11314 0.214166
\(571\) 10.8234 0.452946 0.226473 0.974017i \(-0.427281\pi\)
0.226473 + 0.974017i \(0.427281\pi\)
\(572\) −132.644 −5.54611
\(573\) 3.59004 0.149976
\(574\) −83.0787 −3.46764
\(575\) 5.45098 0.227322
\(576\) −15.4730 −0.644709
\(577\) 31.6089 1.31590 0.657948 0.753063i \(-0.271424\pi\)
0.657948 + 0.753063i \(0.271424\pi\)
\(578\) 30.3803 1.26366
\(579\) 1.45280 0.0603764
\(580\) −130.461 −5.41710
\(581\) 16.9903 0.704878
\(582\) −5.44434 −0.225675
\(583\) 41.6861 1.72646
\(584\) 97.5607 4.03709
\(585\) 50.8053 2.10054
\(586\) −11.4462 −0.472837
\(587\) −43.1552 −1.78121 −0.890604 0.454780i \(-0.849718\pi\)
−0.890604 + 0.454780i \(0.849718\pi\)
\(588\) −0.470140 −0.0193882
\(589\) −18.1070 −0.746085
\(590\) −20.7474 −0.854157
\(591\) −0.225137 −0.00926091
\(592\) 83.1174 3.41610
\(593\) −2.72270 −0.111808 −0.0559040 0.998436i \(-0.517804\pi\)
−0.0559040 + 0.998436i \(0.517804\pi\)
\(594\) 14.4474 0.592786
\(595\) 18.8465 0.772632
\(596\) −109.030 −4.46604
\(597\) 4.73740 0.193889
\(598\) 13.7234 0.561192
\(599\) −17.0076 −0.694912 −0.347456 0.937696i \(-0.612954\pi\)
−0.347456 + 0.937696i \(0.612954\pi\)
\(600\) −6.76718 −0.276269
\(601\) −5.13132 −0.209311 −0.104656 0.994509i \(-0.533374\pi\)
−0.104656 + 0.994509i \(0.533374\pi\)
\(602\) 26.2079 1.06815
\(603\) −22.1295 −0.901183
\(604\) −37.6855 −1.53340
\(605\) 55.4870 2.25587
\(606\) 2.05122 0.0833253
\(607\) −27.1784 −1.10314 −0.551568 0.834130i \(-0.685970\pi\)
−0.551568 + 0.834130i \(0.685970\pi\)
\(608\) 30.6552 1.24323
\(609\) −3.81332 −0.154524
\(610\) 109.219 4.42214
\(611\) 12.8396 0.519436
\(612\) −32.2225 −1.30252
\(613\) 34.6808 1.40075 0.700373 0.713777i \(-0.253017\pi\)
0.700373 + 0.713777i \(0.253017\pi\)
\(614\) −83.1824 −3.35697
\(615\) 7.18401 0.289687
\(616\) −95.0013 −3.82771
\(617\) 18.7244 0.753816 0.376908 0.926251i \(-0.376987\pi\)
0.376908 + 0.926251i \(0.376987\pi\)
\(618\) −2.90310 −0.116780
\(619\) −3.41941 −0.137438 −0.0687189 0.997636i \(-0.521891\pi\)
−0.0687189 + 0.997636i \(0.521891\pi\)
\(620\) 79.7048 3.20102
\(621\) −1.05001 −0.0421356
\(622\) 12.0666 0.483825
\(623\) 40.0970 1.60645
\(624\) −8.24362 −0.330009
\(625\) −22.5417 −0.901668
\(626\) 61.6056 2.46225
\(627\) −3.23746 −0.129292
\(628\) 97.0696 3.87350
\(629\) 21.5768 0.860325
\(630\) 63.1231 2.51488
\(631\) 7.66016 0.304946 0.152473 0.988308i \(-0.451276\pi\)
0.152473 + 0.988308i \(0.451276\pi\)
\(632\) −10.2655 −0.408339
\(633\) 3.17793 0.126311
\(634\) 20.2546 0.804415
\(635\) 35.8173 1.42137
\(636\) 6.52476 0.258724
\(637\) 2.99585 0.118700
\(638\) 117.590 4.65541
\(639\) 11.6520 0.460945
\(640\) 13.4733 0.532580
\(641\) −32.4635 −1.28223 −0.641115 0.767445i \(-0.721528\pi\)
−0.641115 + 0.767445i \(0.721528\pi\)
\(642\) 5.19444 0.205008
\(643\) −23.6973 −0.934532 −0.467266 0.884117i \(-0.654761\pi\)
−0.467266 + 0.884117i \(0.654761\pi\)
\(644\) 11.9776 0.471983
\(645\) −2.26626 −0.0892338
\(646\) 20.6648 0.813045
\(647\) 8.69439 0.341812 0.170906 0.985287i \(-0.445331\pi\)
0.170906 + 0.985287i \(0.445331\pi\)
\(648\) −61.5577 −2.41821
\(649\) 13.1365 0.515654
\(650\) 74.8061 2.93414
\(651\) 2.32974 0.0913097
\(652\) 58.3506 2.28519
\(653\) 19.3883 0.758724 0.379362 0.925248i \(-0.376144\pi\)
0.379362 + 0.925248i \(0.376144\pi\)
\(654\) −4.10725 −0.160606
\(655\) 57.4307 2.24400
\(656\) 111.844 4.36679
\(657\) 41.0440 1.60128
\(658\) 15.9526 0.621897
\(659\) −44.0571 −1.71622 −0.858110 0.513466i \(-0.828361\pi\)
−0.858110 + 0.513466i \(0.828361\pi\)
\(660\) 14.2509 0.554716
\(661\) 4.81955 0.187459 0.0937293 0.995598i \(-0.470121\pi\)
0.0937293 + 0.995598i \(0.470121\pi\)
\(662\) −14.1284 −0.549115
\(663\) −2.14000 −0.0831107
\(664\) −47.2720 −1.83451
\(665\) −28.4373 −1.10275
\(666\) 72.2678 2.80032
\(667\) −8.54620 −0.330910
\(668\) 66.1286 2.55859
\(669\) 3.04507 0.117729
\(670\) −62.4716 −2.41349
\(671\) −69.1534 −2.66964
\(672\) −3.94426 −0.152153
\(673\) −21.5639 −0.831226 −0.415613 0.909542i \(-0.636433\pi\)
−0.415613 + 0.909542i \(0.636433\pi\)
\(674\) 73.5746 2.83399
\(675\) −5.72361 −0.220302
\(676\) 70.9115 2.72737
\(677\) −3.86572 −0.148572 −0.0742859 0.997237i \(-0.523668\pi\)
−0.0742859 + 0.997237i \(0.523668\pi\)
\(678\) 5.86886 0.225392
\(679\) 30.2793 1.16201
\(680\) −52.4365 −2.01085
\(681\) −0.0453233 −0.00173679
\(682\) −71.8410 −2.75093
\(683\) −40.6051 −1.55371 −0.776855 0.629680i \(-0.783186\pi\)
−0.776855 + 0.629680i \(0.783186\pi\)
\(684\) 48.6202 1.85904
\(685\) −46.5906 −1.78014
\(686\) 49.7573 1.89974
\(687\) 0.306160 0.0116807
\(688\) −35.2823 −1.34512
\(689\) −41.5775 −1.58398
\(690\) −1.47441 −0.0561299
\(691\) 21.5402 0.819426 0.409713 0.912214i \(-0.365629\pi\)
0.409713 + 0.912214i \(0.365629\pi\)
\(692\) −14.8977 −0.566325
\(693\) −39.9673 −1.51823
\(694\) −45.3883 −1.72292
\(695\) −14.7000 −0.557602
\(696\) 10.6098 0.402163
\(697\) 29.0342 1.09975
\(698\) 2.59269 0.0981347
\(699\) 1.32830 0.0502410
\(700\) 65.2897 2.46772
\(701\) 45.3565 1.71309 0.856546 0.516071i \(-0.172606\pi\)
0.856546 + 0.516071i \(0.172606\pi\)
\(702\) −14.4098 −0.543863
\(703\) −32.5571 −1.22791
\(704\) 27.6568 1.04236
\(705\) −1.37946 −0.0519534
\(706\) 13.4962 0.507935
\(707\) −11.4081 −0.429046
\(708\) 2.05614 0.0772747
\(709\) −50.5314 −1.89775 −0.948873 0.315658i \(-0.897775\pi\)
−0.948873 + 0.315658i \(0.897775\pi\)
\(710\) 32.8935 1.23447
\(711\) −4.31871 −0.161964
\(712\) −111.561 −4.18094
\(713\) 5.22128 0.195538
\(714\) −2.65884 −0.0995047
\(715\) −90.8105 −3.39612
\(716\) 72.5660 2.71192
\(717\) 2.66653 0.0995833
\(718\) 51.4194 1.91896
\(719\) 7.97915 0.297572 0.148786 0.988869i \(-0.452463\pi\)
0.148786 + 0.988869i \(0.452463\pi\)
\(720\) −84.9792 −3.16699
\(721\) 16.1459 0.601305
\(722\) 18.0802 0.672874
\(723\) −1.97389 −0.0734096
\(724\) −8.11533 −0.301604
\(725\) −46.5852 −1.73013
\(726\) −7.82803 −0.290525
\(727\) 47.7961 1.77266 0.886329 0.463056i \(-0.153247\pi\)
0.886329 + 0.463056i \(0.153247\pi\)
\(728\) 94.7537 3.51181
\(729\) −25.3433 −0.938642
\(730\) 115.867 4.28844
\(731\) −9.15910 −0.338761
\(732\) −10.8240 −0.400066
\(733\) 6.50357 0.240215 0.120107 0.992761i \(-0.461676\pi\)
0.120107 + 0.992761i \(0.461676\pi\)
\(734\) −4.75807 −0.175623
\(735\) −0.321867 −0.0118723
\(736\) −8.83965 −0.325834
\(737\) 39.5548 1.45702
\(738\) 97.2450 3.57964
\(739\) 15.4770 0.569332 0.284666 0.958627i \(-0.408117\pi\)
0.284666 + 0.958627i \(0.408117\pi\)
\(740\) 143.312 5.26827
\(741\) 3.22902 0.118621
\(742\) −51.6579 −1.89642
\(743\) 36.3789 1.33461 0.667307 0.744783i \(-0.267447\pi\)
0.667307 + 0.744783i \(0.267447\pi\)
\(744\) −6.48202 −0.237642
\(745\) −74.6442 −2.73475
\(746\) −62.3962 −2.28449
\(747\) −19.8875 −0.727644
\(748\) 57.5951 2.10589
\(749\) −28.8895 −1.05560
\(750\) −0.664935 −0.0242800
\(751\) −4.14915 −0.151405 −0.0757024 0.997130i \(-0.524120\pi\)
−0.0757024 + 0.997130i \(0.524120\pi\)
\(752\) −21.4761 −0.783154
\(753\) −4.06012 −0.147959
\(754\) −117.283 −4.27120
\(755\) −25.8002 −0.938967
\(756\) −12.5767 −0.457409
\(757\) 44.8811 1.63123 0.815617 0.578593i \(-0.196398\pi\)
0.815617 + 0.578593i \(0.196398\pi\)
\(758\) 3.27236 0.118857
\(759\) 0.933545 0.0338855
\(760\) 79.1209 2.87002
\(761\) −22.8383 −0.827887 −0.413944 0.910302i \(-0.635849\pi\)
−0.413944 + 0.910302i \(0.635849\pi\)
\(762\) −5.05306 −0.183053
\(763\) 22.8429 0.826969
\(764\) 96.3693 3.48652
\(765\) −22.0602 −0.797587
\(766\) 39.1497 1.41454
\(767\) −13.1023 −0.473096
\(768\) −3.73428 −0.134749
\(769\) 45.9753 1.65791 0.828955 0.559315i \(-0.188936\pi\)
0.828955 + 0.559315i \(0.188936\pi\)
\(770\) −112.828 −4.06602
\(771\) 5.44572 0.196123
\(772\) 38.9983 1.40358
\(773\) 30.3509 1.09164 0.545822 0.837901i \(-0.316217\pi\)
0.545822 + 0.837901i \(0.316217\pi\)
\(774\) −30.6768 −1.10265
\(775\) 28.4611 1.02235
\(776\) −84.2458 −3.02425
\(777\) 4.18897 0.150278
\(778\) 32.0990 1.15080
\(779\) −43.8095 −1.56964
\(780\) −14.2138 −0.508935
\(781\) −20.8270 −0.745248
\(782\) −5.95884 −0.213088
\(783\) 8.97364 0.320692
\(784\) −5.01100 −0.178964
\(785\) 66.4558 2.37191
\(786\) −8.10225 −0.288998
\(787\) −9.53022 −0.339716 −0.169858 0.985469i \(-0.554331\pi\)
−0.169858 + 0.985469i \(0.554331\pi\)
\(788\) −6.04347 −0.215290
\(789\) 2.44143 0.0869174
\(790\) −12.1917 −0.433762
\(791\) −32.6403 −1.16056
\(792\) 111.201 3.95134
\(793\) 68.9732 2.44931
\(794\) 13.5916 0.482349
\(795\) 4.46698 0.158428
\(796\) 127.168 4.50736
\(797\) −5.71014 −0.202263 −0.101132 0.994873i \(-0.532246\pi\)
−0.101132 + 0.994873i \(0.532246\pi\)
\(798\) 4.01190 0.142020
\(799\) −5.57509 −0.197233
\(800\) −48.1848 −1.70359
\(801\) −46.9341 −1.65834
\(802\) 75.6394 2.67092
\(803\) −73.3630 −2.58892
\(804\) 6.19116 0.218345
\(805\) 8.20011 0.289016
\(806\) 71.6538 2.52390
\(807\) −1.23097 −0.0433321
\(808\) 31.7407 1.11663
\(809\) −6.76993 −0.238018 −0.119009 0.992893i \(-0.537972\pi\)
−0.119009 + 0.992893i \(0.537972\pi\)
\(810\) −73.1085 −2.56877
\(811\) −6.68482 −0.234736 −0.117368 0.993088i \(-0.537446\pi\)
−0.117368 + 0.993088i \(0.537446\pi\)
\(812\) −102.363 −3.59224
\(813\) −0.550824 −0.0193183
\(814\) −129.173 −4.52751
\(815\) 39.9480 1.39932
\(816\) 3.57946 0.125306
\(817\) 13.8201 0.483503
\(818\) 41.8470 1.46315
\(819\) 39.8631 1.39293
\(820\) 192.844 6.73440
\(821\) 42.8550 1.49565 0.747825 0.663895i \(-0.231098\pi\)
0.747825 + 0.663895i \(0.231098\pi\)
\(822\) 6.57294 0.229258
\(823\) −55.2803 −1.92695 −0.963476 0.267795i \(-0.913705\pi\)
−0.963476 + 0.267795i \(0.913705\pi\)
\(824\) −44.9226 −1.56495
\(825\) 5.08874 0.177167
\(826\) −16.2789 −0.566417
\(827\) 5.62064 0.195449 0.0977244 0.995214i \(-0.468844\pi\)
0.0977244 + 0.995214i \(0.468844\pi\)
\(828\) −14.0200 −0.487228
\(829\) −7.23925 −0.251430 −0.125715 0.992066i \(-0.540122\pi\)
−0.125715 + 0.992066i \(0.540122\pi\)
\(830\) −56.1422 −1.94873
\(831\) −3.41717 −0.118540
\(832\) −27.5847 −0.956329
\(833\) −1.30083 −0.0450710
\(834\) 2.07385 0.0718117
\(835\) 45.2730 1.56674
\(836\) −86.9047 −3.00566
\(837\) −5.48242 −0.189500
\(838\) 77.2039 2.66696
\(839\) 55.5398 1.91745 0.958724 0.284339i \(-0.0917740\pi\)
0.958724 + 0.284339i \(0.0917740\pi\)
\(840\) −10.1801 −0.351247
\(841\) 44.0376 1.51854
\(842\) −84.2146 −2.90223
\(843\) 2.03279 0.0700129
\(844\) 85.3068 2.93638
\(845\) 48.5475 1.67008
\(846\) −18.6728 −0.641984
\(847\) 43.5365 1.49593
\(848\) 69.5443 2.38816
\(849\) 2.78670 0.0956393
\(850\) −32.4815 −1.11411
\(851\) 9.38807 0.321819
\(852\) −3.25986 −0.111681
\(853\) −5.48135 −0.187678 −0.0938389 0.995587i \(-0.529914\pi\)
−0.0938389 + 0.995587i \(0.529914\pi\)
\(854\) 85.6958 2.93245
\(855\) 33.2863 1.13837
\(856\) 80.3789 2.74729
\(857\) −29.3810 −1.00363 −0.501817 0.864974i \(-0.667335\pi\)
−0.501817 + 0.864974i \(0.667335\pi\)
\(858\) 12.8114 0.437375
\(859\) −7.37326 −0.251572 −0.125786 0.992057i \(-0.540145\pi\)
−0.125786 + 0.992057i \(0.540145\pi\)
\(860\) −60.8343 −2.07443
\(861\) 5.63676 0.192100
\(862\) 48.3601 1.64715
\(863\) −37.9220 −1.29088 −0.645440 0.763811i \(-0.723326\pi\)
−0.645440 + 0.763811i \(0.723326\pi\)
\(864\) 9.28177 0.315772
\(865\) −10.1993 −0.346785
\(866\) −102.635 −3.48769
\(867\) −2.06126 −0.0700039
\(868\) 62.5384 2.12269
\(869\) 7.71936 0.261861
\(870\) 12.6006 0.427201
\(871\) −39.4517 −1.33677
\(872\) −63.5557 −2.15227
\(873\) −35.4424 −1.19954
\(874\) 8.99124 0.304133
\(875\) 3.69811 0.125019
\(876\) −11.4829 −0.387970
\(877\) 58.8995 1.98889 0.994447 0.105235i \(-0.0335594\pi\)
0.994447 + 0.105235i \(0.0335594\pi\)
\(878\) 28.4560 0.960344
\(879\) 0.776605 0.0261942
\(880\) 151.894 5.12034
\(881\) −14.0544 −0.473504 −0.236752 0.971570i \(-0.576083\pi\)
−0.236752 + 0.971570i \(0.576083\pi\)
\(882\) −4.35690 −0.146704
\(883\) 50.0721 1.68506 0.842530 0.538650i \(-0.181065\pi\)
0.842530 + 0.538650i \(0.181065\pi\)
\(884\) −57.4450 −1.93209
\(885\) 1.40768 0.0473186
\(886\) 86.9233 2.92024
\(887\) −39.1700 −1.31520 −0.657599 0.753368i \(-0.728428\pi\)
−0.657599 + 0.753368i \(0.728428\pi\)
\(888\) −11.6549 −0.391114
\(889\) 28.1032 0.942549
\(890\) −132.495 −4.44124
\(891\) 46.2897 1.55076
\(892\) 81.7403 2.73687
\(893\) 8.41220 0.281504
\(894\) 10.5307 0.352199
\(895\) 49.6802 1.66062
\(896\) 10.5715 0.353170
\(897\) −0.931112 −0.0310889
\(898\) 24.0336 0.802013
\(899\) −44.6221 −1.48823
\(900\) −76.4226 −2.54742
\(901\) 18.0533 0.601444
\(902\) −173.818 −5.78750
\(903\) −1.77816 −0.0591736
\(904\) 90.8149 3.02046
\(905\) −5.55592 −0.184685
\(906\) 3.63987 0.120926
\(907\) −47.9227 −1.59125 −0.795623 0.605792i \(-0.792856\pi\)
−0.795623 + 0.605792i \(0.792856\pi\)
\(908\) −1.21664 −0.0403755
\(909\) 13.3534 0.442904
\(910\) 112.534 3.73045
\(911\) −46.2741 −1.53313 −0.766565 0.642167i \(-0.778036\pi\)
−0.766565 + 0.642167i \(0.778036\pi\)
\(912\) −5.40101 −0.178845
\(913\) 35.5473 1.17644
\(914\) 4.35163 0.143939
\(915\) −7.41031 −0.244977
\(916\) 8.21841 0.271544
\(917\) 45.0616 1.48806
\(918\) 6.25687 0.206508
\(919\) 12.0186 0.396458 0.198229 0.980156i \(-0.436481\pi\)
0.198229 + 0.980156i \(0.436481\pi\)
\(920\) −22.8151 −0.752191
\(921\) 5.64379 0.185969
\(922\) −68.8887 −2.26873
\(923\) 20.7727 0.683742
\(924\) 11.1816 0.367848
\(925\) 51.1742 1.68260
\(926\) 32.8517 1.07958
\(927\) −18.8990 −0.620726
\(928\) 75.5455 2.47990
\(929\) −3.65244 −0.119833 −0.0599164 0.998203i \(-0.519083\pi\)
−0.0599164 + 0.998203i \(0.519083\pi\)
\(930\) −7.69831 −0.252438
\(931\) 1.96281 0.0643284
\(932\) 35.6563 1.16796
\(933\) −0.818696 −0.0268029
\(934\) −42.1197 −1.37820
\(935\) 39.4308 1.28952
\(936\) −110.911 −3.62523
\(937\) −0.787379 −0.0257226 −0.0128613 0.999917i \(-0.504094\pi\)
−0.0128613 + 0.999917i \(0.504094\pi\)
\(938\) −49.0168 −1.60045
\(939\) −4.17984 −0.136404
\(940\) −37.0295 −1.20777
\(941\) 22.5297 0.734447 0.367224 0.930133i \(-0.380308\pi\)
0.367224 + 0.930133i \(0.380308\pi\)
\(942\) −9.37550 −0.305470
\(943\) 12.6328 0.411380
\(944\) 21.9155 0.713288
\(945\) −8.61023 −0.280091
\(946\) 54.8323 1.78275
\(947\) 33.7184 1.09570 0.547850 0.836576i \(-0.315446\pi\)
0.547850 + 0.836576i \(0.315446\pi\)
\(948\) 1.20824 0.0392419
\(949\) 73.1718 2.37526
\(950\) 49.0111 1.59013
\(951\) −1.37424 −0.0445629
\(952\) −41.1430 −1.33345
\(953\) −3.85626 −0.124916 −0.0624582 0.998048i \(-0.519894\pi\)
−0.0624582 + 0.998048i \(0.519894\pi\)
\(954\) 60.4665 1.95767
\(955\) 65.9763 2.13494
\(956\) 71.5789 2.31503
\(957\) −7.97826 −0.257901
\(958\) 97.6766 3.15579
\(959\) −36.5562 −1.18046
\(960\) 2.96364 0.0956510
\(961\) −3.73825 −0.120589
\(962\) 128.836 4.15385
\(963\) 33.8156 1.08969
\(964\) −52.9860 −1.70656
\(965\) 26.6990 0.859472
\(966\) −1.15686 −0.0372214
\(967\) −7.05723 −0.226945 −0.113473 0.993541i \(-0.536197\pi\)
−0.113473 + 0.993541i \(0.536197\pi\)
\(968\) −121.131 −3.89330
\(969\) −1.40207 −0.0450411
\(970\) −100.054 −3.21254
\(971\) −8.62231 −0.276703 −0.138351 0.990383i \(-0.544180\pi\)
−0.138351 + 0.990383i \(0.544180\pi\)
\(972\) 22.1199 0.709497
\(973\) −11.5340 −0.369762
\(974\) −20.3157 −0.650957
\(975\) −5.07548 −0.162545
\(976\) −115.368 −3.69283
\(977\) 9.03507 0.289058 0.144529 0.989501i \(-0.453833\pi\)
0.144529 + 0.989501i \(0.453833\pi\)
\(978\) −5.63581 −0.180213
\(979\) 83.8911 2.68117
\(980\) −8.64004 −0.275996
\(981\) −26.7380 −0.853679
\(982\) −85.3879 −2.72484
\(983\) 13.6514 0.435412 0.217706 0.976014i \(-0.430143\pi\)
0.217706 + 0.976014i \(0.430143\pi\)
\(984\) −15.6831 −0.499959
\(985\) −4.13748 −0.131831
\(986\) 50.9255 1.62180
\(987\) −1.08236 −0.0344518
\(988\) 86.6783 2.75760
\(989\) −3.98512 −0.126719
\(990\) 132.066 4.19735
\(991\) −31.4355 −0.998581 −0.499291 0.866435i \(-0.666406\pi\)
−0.499291 + 0.866435i \(0.666406\pi\)
\(992\) −46.1543 −1.46540
\(993\) 0.958587 0.0304198
\(994\) 25.8090 0.818613
\(995\) 87.0620 2.76005
\(996\) 5.56390 0.176299
\(997\) 12.7209 0.402875 0.201437 0.979501i \(-0.435439\pi\)
0.201437 + 0.979501i \(0.435439\pi\)
\(998\) 26.1896 0.829017
\(999\) −9.85761 −0.311881
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 \(a_p\))