Properties

Label 8041.2.a.g.1.13
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.10431 q^{2} -0.209589 q^{3} +2.42810 q^{4} +1.85985 q^{5} +0.441039 q^{6} +3.06120 q^{7} -0.900860 q^{8} -2.95607 q^{9} +O(q^{10})\) \(q-2.10431 q^{2} -0.209589 q^{3} +2.42810 q^{4} +1.85985 q^{5} +0.441039 q^{6} +3.06120 q^{7} -0.900860 q^{8} -2.95607 q^{9} -3.91370 q^{10} -1.00000 q^{11} -0.508903 q^{12} +0.726479 q^{13} -6.44170 q^{14} -0.389804 q^{15} -2.96052 q^{16} +1.00000 q^{17} +6.22048 q^{18} +5.08340 q^{19} +4.51592 q^{20} -0.641592 q^{21} +2.10431 q^{22} -7.62725 q^{23} +0.188810 q^{24} -1.54095 q^{25} -1.52874 q^{26} +1.24833 q^{27} +7.43290 q^{28} +0.475914 q^{29} +0.820267 q^{30} -10.6680 q^{31} +8.03156 q^{32} +0.209589 q^{33} -2.10431 q^{34} +5.69338 q^{35} -7.17765 q^{36} +1.04893 q^{37} -10.6970 q^{38} -0.152262 q^{39} -1.67547 q^{40} +9.14621 q^{41} +1.35011 q^{42} +1.00000 q^{43} -2.42810 q^{44} -5.49786 q^{45} +16.0501 q^{46} -5.27026 q^{47} +0.620492 q^{48} +2.37094 q^{49} +3.24262 q^{50} -0.209589 q^{51} +1.76397 q^{52} +9.59866 q^{53} -2.62686 q^{54} -1.85985 q^{55} -2.75771 q^{56} -1.06542 q^{57} -1.00147 q^{58} -4.55358 q^{59} -0.946485 q^{60} +2.60439 q^{61} +22.4487 q^{62} -9.04912 q^{63} -10.9798 q^{64} +1.35115 q^{65} -0.441039 q^{66} -0.886767 q^{67} +2.42810 q^{68} +1.59858 q^{69} -11.9806 q^{70} -7.16694 q^{71} +2.66301 q^{72} +1.47020 q^{73} -2.20726 q^{74} +0.322965 q^{75} +12.3430 q^{76} -3.06120 q^{77} +0.320406 q^{78} +1.82931 q^{79} -5.50614 q^{80} +8.60658 q^{81} -19.2464 q^{82} -17.7224 q^{83} -1.55785 q^{84} +1.85985 q^{85} -2.10431 q^{86} -0.0997461 q^{87} +0.900860 q^{88} +2.12582 q^{89} +11.5692 q^{90} +2.22390 q^{91} -18.5197 q^{92} +2.23589 q^{93} +11.0902 q^{94} +9.45437 q^{95} -1.68332 q^{96} -9.30338 q^{97} -4.98917 q^{98} +2.95607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10431 −1.48797 −0.743984 0.668197i \(-0.767066\pi\)
−0.743984 + 0.668197i \(0.767066\pi\)
\(3\) −0.209589 −0.121006 −0.0605030 0.998168i \(-0.519270\pi\)
−0.0605030 + 0.998168i \(0.519270\pi\)
\(4\) 2.42810 1.21405
\(5\) 1.85985 0.831752 0.415876 0.909421i \(-0.363475\pi\)
0.415876 + 0.909421i \(0.363475\pi\)
\(6\) 0.441039 0.180053
\(7\) 3.06120 1.15702 0.578512 0.815674i \(-0.303634\pi\)
0.578512 + 0.815674i \(0.303634\pi\)
\(8\) −0.900860 −0.318502
\(9\) −2.95607 −0.985358
\(10\) −3.91370 −1.23762
\(11\) −1.00000 −0.301511
\(12\) −0.508903 −0.146908
\(13\) 0.726479 0.201489 0.100745 0.994912i \(-0.467878\pi\)
0.100745 + 0.994912i \(0.467878\pi\)
\(14\) −6.44170 −1.72162
\(15\) −0.389804 −0.100647
\(16\) −2.96052 −0.740130
\(17\) 1.00000 0.242536
\(18\) 6.22048 1.46618
\(19\) 5.08340 1.16621 0.583105 0.812396i \(-0.301837\pi\)
0.583105 + 0.812396i \(0.301837\pi\)
\(20\) 4.51592 1.00979
\(21\) −0.641592 −0.140007
\(22\) 2.10431 0.448640
\(23\) −7.62725 −1.59039 −0.795196 0.606353i \(-0.792632\pi\)
−0.795196 + 0.606353i \(0.792632\pi\)
\(24\) 0.188810 0.0385407
\(25\) −1.54095 −0.308189
\(26\) −1.52874 −0.299810
\(27\) 1.24833 0.240240
\(28\) 7.43290 1.40469
\(29\) 0.475914 0.0883750 0.0441875 0.999023i \(-0.485930\pi\)
0.0441875 + 0.999023i \(0.485930\pi\)
\(30\) 0.820267 0.149760
\(31\) −10.6680 −1.91603 −0.958013 0.286725i \(-0.907433\pi\)
−0.958013 + 0.286725i \(0.907433\pi\)
\(32\) 8.03156 1.41979
\(33\) 0.209589 0.0364847
\(34\) −2.10431 −0.360885
\(35\) 5.69338 0.962357
\(36\) −7.17765 −1.19627
\(37\) 1.04893 0.172442 0.0862212 0.996276i \(-0.472521\pi\)
0.0862212 + 0.996276i \(0.472521\pi\)
\(38\) −10.6970 −1.73529
\(39\) −0.152262 −0.0243814
\(40\) −1.67547 −0.264915
\(41\) 9.14621 1.42840 0.714199 0.699943i \(-0.246791\pi\)
0.714199 + 0.699943i \(0.246791\pi\)
\(42\) 1.35011 0.208326
\(43\) 1.00000 0.152499
\(44\) −2.42810 −0.366050
\(45\) −5.49786 −0.819573
\(46\) 16.0501 2.36645
\(47\) −5.27026 −0.768747 −0.384373 0.923178i \(-0.625582\pi\)
−0.384373 + 0.923178i \(0.625582\pi\)
\(48\) 0.620492 0.0895603
\(49\) 2.37094 0.338705
\(50\) 3.24262 0.458576
\(51\) −0.209589 −0.0293483
\(52\) 1.76397 0.244618
\(53\) 9.59866 1.31848 0.659239 0.751934i \(-0.270879\pi\)
0.659239 + 0.751934i \(0.270879\pi\)
\(54\) −2.62686 −0.357470
\(55\) −1.85985 −0.250783
\(56\) −2.75771 −0.368514
\(57\) −1.06542 −0.141119
\(58\) −1.00147 −0.131499
\(59\) −4.55358 −0.592826 −0.296413 0.955060i \(-0.595790\pi\)
−0.296413 + 0.955060i \(0.595790\pi\)
\(60\) −0.946485 −0.122191
\(61\) 2.60439 0.333458 0.166729 0.986003i \(-0.446680\pi\)
0.166729 + 0.986003i \(0.446680\pi\)
\(62\) 22.4487 2.85099
\(63\) −9.04912 −1.14008
\(64\) −10.9798 −1.37248
\(65\) 1.35115 0.167589
\(66\) −0.441039 −0.0542881
\(67\) −0.886767 −0.108336 −0.0541679 0.998532i \(-0.517251\pi\)
−0.0541679 + 0.998532i \(0.517251\pi\)
\(68\) 2.42810 0.294451
\(69\) 1.59858 0.192447
\(70\) −11.9806 −1.43196
\(71\) −7.16694 −0.850559 −0.425280 0.905062i \(-0.639824\pi\)
−0.425280 + 0.905062i \(0.639824\pi\)
\(72\) 2.66301 0.313838
\(73\) 1.47020 0.172074 0.0860372 0.996292i \(-0.472580\pi\)
0.0860372 + 0.996292i \(0.472580\pi\)
\(74\) −2.20726 −0.256589
\(75\) 0.322965 0.0372928
\(76\) 12.3430 1.41584
\(77\) −3.06120 −0.348856
\(78\) 0.320406 0.0362788
\(79\) 1.82931 0.205814 0.102907 0.994691i \(-0.467186\pi\)
0.102907 + 0.994691i \(0.467186\pi\)
\(80\) −5.50614 −0.615605
\(81\) 8.60658 0.956287
\(82\) −19.2464 −2.12541
\(83\) −17.7224 −1.94528 −0.972641 0.232314i \(-0.925370\pi\)
−0.972641 + 0.232314i \(0.925370\pi\)
\(84\) −1.55785 −0.169976
\(85\) 1.85985 0.201729
\(86\) −2.10431 −0.226913
\(87\) −0.0997461 −0.0106939
\(88\) 0.900860 0.0960320
\(89\) 2.12582 0.225337 0.112668 0.993633i \(-0.464060\pi\)
0.112668 + 0.993633i \(0.464060\pi\)
\(90\) 11.5692 1.21950
\(91\) 2.22390 0.233128
\(92\) −18.5197 −1.93082
\(93\) 2.23589 0.231851
\(94\) 11.0902 1.14387
\(95\) 9.45437 0.969998
\(96\) −1.68332 −0.171804
\(97\) −9.30338 −0.944615 −0.472307 0.881434i \(-0.656579\pi\)
−0.472307 + 0.881434i \(0.656579\pi\)
\(98\) −4.98917 −0.503983
\(99\) 2.95607 0.297096
\(100\) −3.74158 −0.374158
\(101\) −3.23826 −0.322218 −0.161109 0.986937i \(-0.551507\pi\)
−0.161109 + 0.986937i \(0.551507\pi\)
\(102\) 0.441039 0.0436693
\(103\) 11.4940 1.13254 0.566270 0.824220i \(-0.308386\pi\)
0.566270 + 0.824220i \(0.308386\pi\)
\(104\) −0.654456 −0.0641747
\(105\) −1.19327 −0.116451
\(106\) −20.1985 −1.96185
\(107\) −5.62193 −0.543492 −0.271746 0.962369i \(-0.587601\pi\)
−0.271746 + 0.962369i \(0.587601\pi\)
\(108\) 3.03106 0.291664
\(109\) −2.26945 −0.217373 −0.108687 0.994076i \(-0.534665\pi\)
−0.108687 + 0.994076i \(0.534665\pi\)
\(110\) 3.91370 0.373157
\(111\) −0.219843 −0.0208666
\(112\) −9.06274 −0.856349
\(113\) −18.1614 −1.70848 −0.854240 0.519879i \(-0.825977\pi\)
−0.854240 + 0.519879i \(0.825977\pi\)
\(114\) 2.24197 0.209980
\(115\) −14.1856 −1.32281
\(116\) 1.15557 0.107292
\(117\) −2.14753 −0.198539
\(118\) 9.58212 0.882106
\(119\) 3.06120 0.280620
\(120\) 0.351159 0.0320563
\(121\) 1.00000 0.0909091
\(122\) −5.48043 −0.496175
\(123\) −1.91694 −0.172845
\(124\) −25.9030 −2.32615
\(125\) −12.1652 −1.08809
\(126\) 19.0421 1.69641
\(127\) 17.9353 1.59150 0.795751 0.605624i \(-0.207076\pi\)
0.795751 + 0.605624i \(0.207076\pi\)
\(128\) 7.04177 0.622411
\(129\) −0.209589 −0.0184533
\(130\) −2.84322 −0.249367
\(131\) 14.2150 1.24197 0.620984 0.783823i \(-0.286733\pi\)
0.620984 + 0.783823i \(0.286733\pi\)
\(132\) 0.508903 0.0442943
\(133\) 15.5613 1.34933
\(134\) 1.86603 0.161200
\(135\) 2.32170 0.199820
\(136\) −0.900860 −0.0772481
\(137\) 21.9278 1.87342 0.936709 0.350110i \(-0.113856\pi\)
0.936709 + 0.350110i \(0.113856\pi\)
\(138\) −3.36391 −0.286355
\(139\) 11.3640 0.963878 0.481939 0.876205i \(-0.339933\pi\)
0.481939 + 0.876205i \(0.339933\pi\)
\(140\) 13.8241 1.16835
\(141\) 1.10459 0.0930230
\(142\) 15.0814 1.26561
\(143\) −0.726479 −0.0607513
\(144\) 8.75152 0.729293
\(145\) 0.885130 0.0735060
\(146\) −3.09376 −0.256041
\(147\) −0.496921 −0.0409854
\(148\) 2.54690 0.209354
\(149\) −18.1750 −1.48896 −0.744478 0.667647i \(-0.767302\pi\)
−0.744478 + 0.667647i \(0.767302\pi\)
\(150\) −0.679617 −0.0554905
\(151\) −11.9923 −0.975923 −0.487962 0.872865i \(-0.662259\pi\)
−0.487962 + 0.872865i \(0.662259\pi\)
\(152\) −4.57943 −0.371440
\(153\) −2.95607 −0.238984
\(154\) 6.44170 0.519087
\(155\) −19.8409 −1.59366
\(156\) −0.369707 −0.0296003
\(157\) −13.6774 −1.09158 −0.545790 0.837922i \(-0.683770\pi\)
−0.545790 + 0.837922i \(0.683770\pi\)
\(158\) −3.84944 −0.306245
\(159\) −2.01177 −0.159544
\(160\) 14.9375 1.18092
\(161\) −23.3485 −1.84012
\(162\) −18.1109 −1.42293
\(163\) −24.9541 −1.95456 −0.977280 0.211954i \(-0.932017\pi\)
−0.977280 + 0.211954i \(0.932017\pi\)
\(164\) 22.2079 1.73415
\(165\) 0.389804 0.0303462
\(166\) 37.2933 2.89452
\(167\) −12.5385 −0.970259 −0.485130 0.874442i \(-0.661228\pi\)
−0.485130 + 0.874442i \(0.661228\pi\)
\(168\) 0.577985 0.0445925
\(169\) −12.4722 −0.959402
\(170\) −3.91370 −0.300167
\(171\) −15.0269 −1.14913
\(172\) 2.42810 0.185141
\(173\) 1.09101 0.0829482 0.0414741 0.999140i \(-0.486795\pi\)
0.0414741 + 0.999140i \(0.486795\pi\)
\(174\) 0.209896 0.0159122
\(175\) −4.71714 −0.356582
\(176\) 2.96052 0.223158
\(177\) 0.954379 0.0717355
\(178\) −4.47338 −0.335294
\(179\) −23.9875 −1.79291 −0.896454 0.443138i \(-0.853865\pi\)
−0.896454 + 0.443138i \(0.853865\pi\)
\(180\) −13.3494 −0.995003
\(181\) 15.9868 1.18829 0.594144 0.804359i \(-0.297491\pi\)
0.594144 + 0.804359i \(0.297491\pi\)
\(182\) −4.67976 −0.346887
\(183\) −0.545850 −0.0403504
\(184\) 6.87108 0.506543
\(185\) 1.95085 0.143429
\(186\) −4.70499 −0.344987
\(187\) −1.00000 −0.0731272
\(188\) −12.7967 −0.933298
\(189\) 3.82137 0.277964
\(190\) −19.8949 −1.44333
\(191\) −14.3508 −1.03839 −0.519193 0.854657i \(-0.673768\pi\)
−0.519193 + 0.854657i \(0.673768\pi\)
\(192\) 2.30125 0.166078
\(193\) −9.82795 −0.707431 −0.353716 0.935353i \(-0.615082\pi\)
−0.353716 + 0.935353i \(0.615082\pi\)
\(194\) 19.5771 1.40556
\(195\) −0.283185 −0.0202793
\(196\) 5.75688 0.411205
\(197\) −24.1837 −1.72302 −0.861510 0.507741i \(-0.830481\pi\)
−0.861510 + 0.507741i \(0.830481\pi\)
\(198\) −6.22048 −0.442070
\(199\) −15.7433 −1.11601 −0.558007 0.829836i \(-0.688434\pi\)
−0.558007 + 0.829836i \(0.688434\pi\)
\(200\) 1.38818 0.0981589
\(201\) 0.185856 0.0131093
\(202\) 6.81428 0.479451
\(203\) 1.45687 0.102252
\(204\) −0.508903 −0.0356303
\(205\) 17.0106 1.18807
\(206\) −24.1870 −1.68519
\(207\) 22.5467 1.56710
\(208\) −2.15076 −0.149128
\(209\) −5.08340 −0.351626
\(210\) 2.51100 0.173275
\(211\) 24.9140 1.71515 0.857577 0.514356i \(-0.171969\pi\)
0.857577 + 0.514356i \(0.171969\pi\)
\(212\) 23.3065 1.60070
\(213\) 1.50211 0.102923
\(214\) 11.8303 0.808699
\(215\) 1.85985 0.126841
\(216\) −1.12457 −0.0765170
\(217\) −32.6568 −2.21689
\(218\) 4.77561 0.323445
\(219\) −0.308138 −0.0208220
\(220\) −4.51592 −0.304463
\(221\) 0.726479 0.0488683
\(222\) 0.462617 0.0310488
\(223\) −22.3146 −1.49429 −0.747147 0.664659i \(-0.768577\pi\)
−0.747147 + 0.664659i \(0.768577\pi\)
\(224\) 24.5862 1.64274
\(225\) 4.55515 0.303677
\(226\) 38.2171 2.54216
\(227\) −8.06731 −0.535446 −0.267723 0.963496i \(-0.586271\pi\)
−0.267723 + 0.963496i \(0.586271\pi\)
\(228\) −2.58695 −0.171325
\(229\) 25.1328 1.66083 0.830413 0.557149i \(-0.188105\pi\)
0.830413 + 0.557149i \(0.188105\pi\)
\(230\) 29.8508 1.96830
\(231\) 0.641592 0.0422137
\(232\) −0.428731 −0.0281476
\(233\) 19.3852 1.26997 0.634983 0.772526i \(-0.281007\pi\)
0.634983 + 0.772526i \(0.281007\pi\)
\(234\) 4.51905 0.295420
\(235\) −9.80191 −0.639406
\(236\) −11.0566 −0.719721
\(237\) −0.383404 −0.0249047
\(238\) −6.44170 −0.417553
\(239\) −10.9713 −0.709672 −0.354836 0.934929i \(-0.615463\pi\)
−0.354836 + 0.934929i \(0.615463\pi\)
\(240\) 1.15402 0.0744919
\(241\) −9.37694 −0.604022 −0.302011 0.953305i \(-0.597658\pi\)
−0.302011 + 0.953305i \(0.597658\pi\)
\(242\) −2.10431 −0.135270
\(243\) −5.54882 −0.355957
\(244\) 6.32373 0.404835
\(245\) 4.40959 0.281718
\(246\) 4.03383 0.257188
\(247\) 3.69298 0.234979
\(248\) 9.61035 0.610258
\(249\) 3.71441 0.235391
\(250\) 25.5993 1.61904
\(251\) −12.8414 −0.810545 −0.405272 0.914196i \(-0.632823\pi\)
−0.405272 + 0.914196i \(0.632823\pi\)
\(252\) −21.9722 −1.38412
\(253\) 7.62725 0.479521
\(254\) −37.7414 −2.36811
\(255\) −0.389804 −0.0244105
\(256\) 7.14159 0.446350
\(257\) 25.2799 1.57692 0.788460 0.615086i \(-0.210879\pi\)
0.788460 + 0.615086i \(0.210879\pi\)
\(258\) 0.441039 0.0274579
\(259\) 3.21097 0.199520
\(260\) 3.28072 0.203462
\(261\) −1.40684 −0.0870809
\(262\) −29.9126 −1.84801
\(263\) 7.18575 0.443093 0.221546 0.975150i \(-0.428890\pi\)
0.221546 + 0.975150i \(0.428890\pi\)
\(264\) −0.188810 −0.0116204
\(265\) 17.8521 1.09665
\(266\) −32.7457 −2.00777
\(267\) −0.445548 −0.0272671
\(268\) −2.15316 −0.131525
\(269\) −24.9386 −1.52053 −0.760266 0.649612i \(-0.774931\pi\)
−0.760266 + 0.649612i \(0.774931\pi\)
\(270\) −4.88557 −0.297326
\(271\) −11.3104 −0.687059 −0.343530 0.939142i \(-0.611623\pi\)
−0.343530 + 0.939142i \(0.611623\pi\)
\(272\) −2.96052 −0.179508
\(273\) −0.466104 −0.0282099
\(274\) −46.1428 −2.78759
\(275\) 1.54095 0.0929226
\(276\) 3.88153 0.233641
\(277\) −4.30358 −0.258577 −0.129288 0.991607i \(-0.541269\pi\)
−0.129288 + 0.991607i \(0.541269\pi\)
\(278\) −23.9132 −1.43422
\(279\) 31.5353 1.88797
\(280\) −5.12894 −0.306513
\(281\) 16.2400 0.968797 0.484399 0.874847i \(-0.339038\pi\)
0.484399 + 0.874847i \(0.339038\pi\)
\(282\) −2.32439 −0.138415
\(283\) 24.9247 1.48162 0.740809 0.671716i \(-0.234442\pi\)
0.740809 + 0.671716i \(0.234442\pi\)
\(284\) −17.4021 −1.03262
\(285\) −1.98153 −0.117376
\(286\) 1.52874 0.0903960
\(287\) 27.9984 1.65269
\(288\) −23.7419 −1.39900
\(289\) 1.00000 0.0588235
\(290\) −1.86258 −0.109375
\(291\) 1.94988 0.114304
\(292\) 3.56981 0.208907
\(293\) 11.7128 0.684270 0.342135 0.939651i \(-0.388850\pi\)
0.342135 + 0.939651i \(0.388850\pi\)
\(294\) 1.04567 0.0609850
\(295\) −8.46899 −0.493084
\(296\) −0.944935 −0.0549232
\(297\) −1.24833 −0.0724352
\(298\) 38.2458 2.21552
\(299\) −5.54104 −0.320447
\(300\) 0.784192 0.0452753
\(301\) 3.06120 0.176445
\(302\) 25.2356 1.45214
\(303\) 0.678702 0.0389904
\(304\) −15.0495 −0.863148
\(305\) 4.84378 0.277354
\(306\) 6.22048 0.355601
\(307\) −3.88930 −0.221974 −0.110987 0.993822i \(-0.535401\pi\)
−0.110987 + 0.993822i \(0.535401\pi\)
\(308\) −7.43290 −0.423529
\(309\) −2.40902 −0.137044
\(310\) 41.7513 2.37131
\(311\) −0.0197684 −0.00112097 −0.000560483 1.00000i \(-0.500178\pi\)
−0.000560483 1.00000i \(0.500178\pi\)
\(312\) 0.137167 0.00776553
\(313\) 14.3009 0.808334 0.404167 0.914685i \(-0.367561\pi\)
0.404167 + 0.914685i \(0.367561\pi\)
\(314\) 28.7815 1.62424
\(315\) −16.8300 −0.948266
\(316\) 4.44177 0.249869
\(317\) −17.7457 −0.996696 −0.498348 0.866977i \(-0.666060\pi\)
−0.498348 + 0.866977i \(0.666060\pi\)
\(318\) 4.23338 0.237396
\(319\) −0.475914 −0.0266461
\(320\) −20.4209 −1.14156
\(321\) 1.17829 0.0657658
\(322\) 49.1324 2.73804
\(323\) 5.08340 0.282848
\(324\) 20.8977 1.16098
\(325\) −1.11947 −0.0620968
\(326\) 52.5111 2.90832
\(327\) 0.475650 0.0263035
\(328\) −8.23945 −0.454948
\(329\) −16.1333 −0.889458
\(330\) −0.820267 −0.0451542
\(331\) 34.1665 1.87796 0.938980 0.343971i \(-0.111772\pi\)
0.938980 + 0.343971i \(0.111772\pi\)
\(332\) −43.0317 −2.36167
\(333\) −3.10070 −0.169917
\(334\) 26.3849 1.44372
\(335\) −1.64926 −0.0901085
\(336\) 1.89945 0.103623
\(337\) 31.0467 1.69122 0.845611 0.533799i \(-0.179236\pi\)
0.845611 + 0.533799i \(0.179236\pi\)
\(338\) 26.2454 1.42756
\(339\) 3.80642 0.206736
\(340\) 4.51592 0.244910
\(341\) 10.6680 0.577704
\(342\) 31.6212 1.70988
\(343\) −14.1705 −0.765134
\(344\) −0.900860 −0.0485711
\(345\) 2.97313 0.160068
\(346\) −2.29583 −0.123424
\(347\) −23.0547 −1.23764 −0.618820 0.785533i \(-0.712389\pi\)
−0.618820 + 0.785533i \(0.712389\pi\)
\(348\) −0.242194 −0.0129830
\(349\) 8.70542 0.465990 0.232995 0.972478i \(-0.425147\pi\)
0.232995 + 0.972478i \(0.425147\pi\)
\(350\) 9.92631 0.530584
\(351\) 0.906883 0.0484058
\(352\) −8.03156 −0.428084
\(353\) −29.9037 −1.59161 −0.795807 0.605551i \(-0.792953\pi\)
−0.795807 + 0.605551i \(0.792953\pi\)
\(354\) −2.00830 −0.106740
\(355\) −13.3295 −0.707454
\(356\) 5.16172 0.273570
\(357\) −0.641592 −0.0339567
\(358\) 50.4770 2.66779
\(359\) −7.30953 −0.385782 −0.192891 0.981220i \(-0.561786\pi\)
−0.192891 + 0.981220i \(0.561786\pi\)
\(360\) 4.95280 0.261036
\(361\) 6.84091 0.360048
\(362\) −33.6411 −1.76813
\(363\) −0.209589 −0.0110006
\(364\) 5.39985 0.283029
\(365\) 2.73436 0.143123
\(366\) 1.14864 0.0600402
\(367\) −1.63849 −0.0855283 −0.0427642 0.999085i \(-0.513616\pi\)
−0.0427642 + 0.999085i \(0.513616\pi\)
\(368\) 22.5806 1.17710
\(369\) −27.0369 −1.40748
\(370\) −4.10518 −0.213418
\(371\) 29.3834 1.52551
\(372\) 5.42897 0.281479
\(373\) −33.5333 −1.73629 −0.868143 0.496314i \(-0.834686\pi\)
−0.868143 + 0.496314i \(0.834686\pi\)
\(374\) 2.10431 0.108811
\(375\) 2.54969 0.131665
\(376\) 4.74776 0.244847
\(377\) 0.345742 0.0178066
\(378\) −8.04133 −0.413602
\(379\) 22.6981 1.16592 0.582961 0.812500i \(-0.301894\pi\)
0.582961 + 0.812500i \(0.301894\pi\)
\(380\) 22.9562 1.17763
\(381\) −3.75904 −0.192581
\(382\) 30.1984 1.54509
\(383\) 23.8050 1.21638 0.608189 0.793792i \(-0.291896\pi\)
0.608189 + 0.793792i \(0.291896\pi\)
\(384\) −1.47588 −0.0753155
\(385\) −5.69338 −0.290161
\(386\) 20.6810 1.05264
\(387\) −2.95607 −0.150266
\(388\) −22.5896 −1.14681
\(389\) −6.16831 −0.312746 −0.156373 0.987698i \(-0.549980\pi\)
−0.156373 + 0.987698i \(0.549980\pi\)
\(390\) 0.595907 0.0301749
\(391\) −7.62725 −0.385727
\(392\) −2.13588 −0.107878
\(393\) −2.97930 −0.150286
\(394\) 50.8900 2.56380
\(395\) 3.40226 0.171186
\(396\) 7.17765 0.360690
\(397\) 10.5844 0.531217 0.265609 0.964081i \(-0.414427\pi\)
0.265609 + 0.964081i \(0.414427\pi\)
\(398\) 33.1288 1.66059
\(399\) −3.26147 −0.163278
\(400\) 4.56200 0.228100
\(401\) 16.9699 0.847439 0.423719 0.905794i \(-0.360724\pi\)
0.423719 + 0.905794i \(0.360724\pi\)
\(402\) −0.391099 −0.0195062
\(403\) −7.75007 −0.386058
\(404\) −7.86282 −0.391190
\(405\) 16.0070 0.795393
\(406\) −3.06569 −0.152148
\(407\) −1.04893 −0.0519933
\(408\) 0.188810 0.00934748
\(409\) 19.3687 0.957722 0.478861 0.877891i \(-0.341050\pi\)
0.478861 + 0.877891i \(0.341050\pi\)
\(410\) −35.7955 −1.76782
\(411\) −4.59581 −0.226695
\(412\) 27.9087 1.37496
\(413\) −13.9394 −0.685914
\(414\) −47.4452 −2.33180
\(415\) −32.9610 −1.61799
\(416\) 5.83477 0.286073
\(417\) −2.38176 −0.116635
\(418\) 10.6970 0.523208
\(419\) 12.8405 0.627300 0.313650 0.949539i \(-0.398448\pi\)
0.313650 + 0.949539i \(0.398448\pi\)
\(420\) −2.89738 −0.141378
\(421\) −8.41148 −0.409950 −0.204975 0.978767i \(-0.565711\pi\)
−0.204975 + 0.978767i \(0.565711\pi\)
\(422\) −52.4268 −2.55209
\(423\) 15.5793 0.757490
\(424\) −8.64705 −0.419938
\(425\) −1.54095 −0.0747469
\(426\) −3.16090 −0.153146
\(427\) 7.97255 0.385819
\(428\) −13.6506 −0.659827
\(429\) 0.152262 0.00735127
\(430\) −3.91370 −0.188735
\(431\) 2.22092 0.106978 0.0534889 0.998568i \(-0.482966\pi\)
0.0534889 + 0.998568i \(0.482966\pi\)
\(432\) −3.69569 −0.177809
\(433\) −26.8548 −1.29056 −0.645279 0.763947i \(-0.723259\pi\)
−0.645279 + 0.763947i \(0.723259\pi\)
\(434\) 68.7199 3.29866
\(435\) −0.185513 −0.00889467
\(436\) −5.51045 −0.263903
\(437\) −38.7723 −1.85473
\(438\) 0.648417 0.0309825
\(439\) 34.8981 1.66560 0.832799 0.553576i \(-0.186737\pi\)
0.832799 + 0.553576i \(0.186737\pi\)
\(440\) 1.67547 0.0798747
\(441\) −7.00866 −0.333746
\(442\) −1.52874 −0.0727145
\(443\) 3.60254 0.171162 0.0855808 0.996331i \(-0.472725\pi\)
0.0855808 + 0.996331i \(0.472725\pi\)
\(444\) −0.533801 −0.0253331
\(445\) 3.95372 0.187424
\(446\) 46.9567 2.22346
\(447\) 3.80928 0.180173
\(448\) −33.6114 −1.58799
\(449\) 29.3958 1.38728 0.693638 0.720324i \(-0.256007\pi\)
0.693638 + 0.720324i \(0.256007\pi\)
\(450\) −9.58543 −0.451861
\(451\) −9.14621 −0.430678
\(452\) −44.0977 −2.07418
\(453\) 2.51346 0.118093
\(454\) 16.9761 0.796727
\(455\) 4.13612 0.193904
\(456\) 0.959796 0.0449465
\(457\) 2.15091 0.100615 0.0503076 0.998734i \(-0.483980\pi\)
0.0503076 + 0.998734i \(0.483980\pi\)
\(458\) −52.8872 −2.47126
\(459\) 1.24833 0.0582668
\(460\) −34.4440 −1.60596
\(461\) 2.81724 0.131212 0.0656060 0.997846i \(-0.479102\pi\)
0.0656060 + 0.997846i \(0.479102\pi\)
\(462\) −1.35011 −0.0628126
\(463\) −24.8398 −1.15441 −0.577203 0.816601i \(-0.695856\pi\)
−0.577203 + 0.816601i \(0.695856\pi\)
\(464\) −1.40895 −0.0654090
\(465\) 4.15842 0.192842
\(466\) −40.7924 −1.88967
\(467\) 5.89652 0.272859 0.136429 0.990650i \(-0.456437\pi\)
0.136429 + 0.990650i \(0.456437\pi\)
\(468\) −5.21441 −0.241036
\(469\) −2.71457 −0.125347
\(470\) 20.6262 0.951416
\(471\) 2.86664 0.132088
\(472\) 4.10214 0.188816
\(473\) −1.00000 −0.0459800
\(474\) 0.806799 0.0370575
\(475\) −7.83324 −0.359414
\(476\) 7.43290 0.340687
\(477\) −28.3743 −1.29917
\(478\) 23.0869 1.05597
\(479\) 20.7757 0.949267 0.474634 0.880183i \(-0.342581\pi\)
0.474634 + 0.880183i \(0.342581\pi\)
\(480\) −3.13074 −0.142898
\(481\) 0.762023 0.0347453
\(482\) 19.7319 0.898765
\(483\) 4.89358 0.222666
\(484\) 2.42810 0.110368
\(485\) −17.3029 −0.785685
\(486\) 11.6764 0.529653
\(487\) −30.8034 −1.39584 −0.697918 0.716178i \(-0.745890\pi\)
−0.697918 + 0.716178i \(0.745890\pi\)
\(488\) −2.34619 −0.106207
\(489\) 5.23010 0.236514
\(490\) −9.27913 −0.419188
\(491\) −2.60810 −0.117702 −0.0588510 0.998267i \(-0.518744\pi\)
−0.0588510 + 0.998267i \(0.518744\pi\)
\(492\) −4.65453 −0.209843
\(493\) 0.475914 0.0214341
\(494\) −7.77117 −0.349641
\(495\) 5.49786 0.247110
\(496\) 31.5828 1.41811
\(497\) −21.9394 −0.984118
\(498\) −7.81625 −0.350254
\(499\) 3.35149 0.150033 0.0750166 0.997182i \(-0.476099\pi\)
0.0750166 + 0.997182i \(0.476099\pi\)
\(500\) −29.5384 −1.32100
\(501\) 2.62793 0.117407
\(502\) 27.0223 1.20607
\(503\) −7.95554 −0.354720 −0.177360 0.984146i \(-0.556756\pi\)
−0.177360 + 0.984146i \(0.556756\pi\)
\(504\) 8.15199 0.363119
\(505\) −6.02268 −0.268006
\(506\) −16.0501 −0.713512
\(507\) 2.61404 0.116093
\(508\) 43.5488 1.93217
\(509\) −7.86486 −0.348604 −0.174302 0.984692i \(-0.555767\pi\)
−0.174302 + 0.984692i \(0.555767\pi\)
\(510\) 0.820267 0.0363220
\(511\) 4.50058 0.199094
\(512\) −29.1116 −1.28657
\(513\) 6.34573 0.280171
\(514\) −53.1967 −2.34641
\(515\) 21.3772 0.941993
\(516\) −0.508903 −0.0224032
\(517\) 5.27026 0.231786
\(518\) −6.75686 −0.296880
\(519\) −0.228664 −0.0100372
\(520\) −1.21719 −0.0533774
\(521\) 28.9324 1.26755 0.633777 0.773516i \(-0.281504\pi\)
0.633777 + 0.773516i \(0.281504\pi\)
\(522\) 2.96041 0.129574
\(523\) −26.3748 −1.15329 −0.576645 0.816995i \(-0.695638\pi\)
−0.576645 + 0.816995i \(0.695638\pi\)
\(524\) 34.5154 1.50781
\(525\) 0.988659 0.0431486
\(526\) −15.1210 −0.659308
\(527\) −10.6680 −0.464705
\(528\) −0.620492 −0.0270034
\(529\) 35.1749 1.52934
\(530\) −37.5663 −1.63178
\(531\) 13.4607 0.584145
\(532\) 37.7844 1.63816
\(533\) 6.64454 0.287807
\(534\) 0.937570 0.0405726
\(535\) −10.4560 −0.452050
\(536\) 0.798853 0.0345052
\(537\) 5.02750 0.216953
\(538\) 52.4784 2.26250
\(539\) −2.37094 −0.102123
\(540\) 5.63733 0.242592
\(541\) −14.7050 −0.632217 −0.316109 0.948723i \(-0.602376\pi\)
−0.316109 + 0.948723i \(0.602376\pi\)
\(542\) 23.8006 1.02232
\(543\) −3.35065 −0.143790
\(544\) 8.03156 0.344350
\(545\) −4.22084 −0.180801
\(546\) 0.980825 0.0419754
\(547\) 29.2320 1.24987 0.624935 0.780677i \(-0.285125\pi\)
0.624935 + 0.780677i \(0.285125\pi\)
\(548\) 53.2429 2.27442
\(549\) −7.69876 −0.328575
\(550\) −3.24262 −0.138266
\(551\) 2.41926 0.103064
\(552\) −1.44010 −0.0612947
\(553\) 5.59990 0.238132
\(554\) 9.05605 0.384755
\(555\) −0.408876 −0.0173558
\(556\) 27.5929 1.17020
\(557\) −35.9213 −1.52204 −0.761018 0.648731i \(-0.775300\pi\)
−0.761018 + 0.648731i \(0.775300\pi\)
\(558\) −66.3600 −2.80924
\(559\) 0.726479 0.0307268
\(560\) −16.8554 −0.712270
\(561\) 0.209589 0.00884884
\(562\) −34.1739 −1.44154
\(563\) −5.57095 −0.234788 −0.117394 0.993085i \(-0.537454\pi\)
−0.117394 + 0.993085i \(0.537454\pi\)
\(564\) 2.68205 0.112935
\(565\) −33.7775 −1.42103
\(566\) −52.4491 −2.20460
\(567\) 26.3465 1.10645
\(568\) 6.45641 0.270905
\(569\) −40.2830 −1.68875 −0.844376 0.535751i \(-0.820029\pi\)
−0.844376 + 0.535751i \(0.820029\pi\)
\(570\) 4.16974 0.174651
\(571\) 9.87248 0.413150 0.206575 0.978431i \(-0.433768\pi\)
0.206575 + 0.978431i \(0.433768\pi\)
\(572\) −1.76397 −0.0737552
\(573\) 3.00776 0.125651
\(574\) −58.9171 −2.45915
\(575\) 11.7532 0.490141
\(576\) 32.4571 1.35238
\(577\) 12.0904 0.503331 0.251665 0.967814i \(-0.419022\pi\)
0.251665 + 0.967814i \(0.419022\pi\)
\(578\) −2.10431 −0.0875276
\(579\) 2.05983 0.0856035
\(580\) 2.14919 0.0892401
\(581\) −54.2517 −2.25074
\(582\) −4.10315 −0.170081
\(583\) −9.59866 −0.397536
\(584\) −1.32445 −0.0548060
\(585\) −3.99408 −0.165135
\(586\) −24.6474 −1.01817
\(587\) 0.254444 0.0105020 0.00525101 0.999986i \(-0.498329\pi\)
0.00525101 + 0.999986i \(0.498329\pi\)
\(588\) −1.20658 −0.0497583
\(589\) −54.2296 −2.23449
\(590\) 17.8213 0.733693
\(591\) 5.06864 0.208496
\(592\) −3.10537 −0.127630
\(593\) −15.7293 −0.645925 −0.322963 0.946412i \(-0.604679\pi\)
−0.322963 + 0.946412i \(0.604679\pi\)
\(594\) 2.62686 0.107781
\(595\) 5.69338 0.233406
\(596\) −44.1308 −1.80767
\(597\) 3.29962 0.135045
\(598\) 11.6600 0.476815
\(599\) −42.0469 −1.71799 −0.858995 0.511984i \(-0.828911\pi\)
−0.858995 + 0.511984i \(0.828911\pi\)
\(600\) −0.290946 −0.0118778
\(601\) 12.3967 0.505671 0.252836 0.967509i \(-0.418637\pi\)
0.252836 + 0.967509i \(0.418637\pi\)
\(602\) −6.44170 −0.262544
\(603\) 2.62135 0.106750
\(604\) −29.1187 −1.18482
\(605\) 1.85985 0.0756138
\(606\) −1.42820 −0.0580165
\(607\) 24.4949 0.994216 0.497108 0.867689i \(-0.334395\pi\)
0.497108 + 0.867689i \(0.334395\pi\)
\(608\) 40.8276 1.65578
\(609\) −0.305343 −0.0123731
\(610\) −10.1928 −0.412694
\(611\) −3.82874 −0.154894
\(612\) −7.17765 −0.290139
\(613\) −29.1142 −1.17591 −0.587955 0.808894i \(-0.700067\pi\)
−0.587955 + 0.808894i \(0.700067\pi\)
\(614\) 8.18429 0.330291
\(615\) −3.56523 −0.143764
\(616\) 2.75771 0.111111
\(617\) −27.3730 −1.10200 −0.550998 0.834507i \(-0.685753\pi\)
−0.550998 + 0.834507i \(0.685753\pi\)
\(618\) 5.06931 0.203918
\(619\) −4.06787 −0.163501 −0.0817507 0.996653i \(-0.526051\pi\)
−0.0817507 + 0.996653i \(0.526051\pi\)
\(620\) −48.1757 −1.93478
\(621\) −9.52129 −0.382076
\(622\) 0.0415989 0.00166796
\(623\) 6.50757 0.260720
\(624\) 0.450775 0.0180454
\(625\) −14.9208 −0.596830
\(626\) −30.0934 −1.20278
\(627\) 1.06542 0.0425489
\(628\) −33.2103 −1.32523
\(629\) 1.04893 0.0418234
\(630\) 35.4156 1.41099
\(631\) 13.4205 0.534261 0.267130 0.963660i \(-0.413925\pi\)
0.267130 + 0.963660i \(0.413925\pi\)
\(632\) −1.64796 −0.0655522
\(633\) −5.22170 −0.207544
\(634\) 37.3423 1.48305
\(635\) 33.3571 1.32373
\(636\) −4.88479 −0.193694
\(637\) 1.72244 0.0682454
\(638\) 1.00147 0.0396485
\(639\) 21.1860 0.838105
\(640\) 13.0967 0.517691
\(641\) −26.5729 −1.04957 −0.524784 0.851236i \(-0.675854\pi\)
−0.524784 + 0.851236i \(0.675854\pi\)
\(642\) −2.47949 −0.0978575
\(643\) −19.1280 −0.754334 −0.377167 0.926145i \(-0.623102\pi\)
−0.377167 + 0.926145i \(0.623102\pi\)
\(644\) −56.6926 −2.23400
\(645\) −0.389804 −0.0153485
\(646\) −10.6970 −0.420869
\(647\) −1.93466 −0.0760592 −0.0380296 0.999277i \(-0.512108\pi\)
−0.0380296 + 0.999277i \(0.512108\pi\)
\(648\) −7.75332 −0.304579
\(649\) 4.55358 0.178744
\(650\) 2.35570 0.0923981
\(651\) 6.84450 0.268257
\(652\) −60.5912 −2.37294
\(653\) 24.9418 0.976050 0.488025 0.872830i \(-0.337718\pi\)
0.488025 + 0.872830i \(0.337718\pi\)
\(654\) −1.00091 −0.0391388
\(655\) 26.4377 1.03301
\(656\) −27.0776 −1.05720
\(657\) −4.34603 −0.169555
\(658\) 33.9494 1.32349
\(659\) −23.4304 −0.912721 −0.456360 0.889795i \(-0.650847\pi\)
−0.456360 + 0.889795i \(0.650847\pi\)
\(660\) 0.946485 0.0368419
\(661\) −23.9191 −0.930346 −0.465173 0.885220i \(-0.654008\pi\)
−0.465173 + 0.885220i \(0.654008\pi\)
\(662\) −71.8967 −2.79435
\(663\) −0.152262 −0.00591336
\(664\) 15.9654 0.619576
\(665\) 28.9417 1.12231
\(666\) 6.52482 0.252832
\(667\) −3.62991 −0.140551
\(668\) −30.4448 −1.17794
\(669\) 4.67688 0.180819
\(670\) 3.47054 0.134079
\(671\) −2.60439 −0.100541
\(672\) −5.15299 −0.198781
\(673\) −16.2822 −0.627632 −0.313816 0.949484i \(-0.601607\pi\)
−0.313816 + 0.949484i \(0.601607\pi\)
\(674\) −65.3318 −2.51649
\(675\) −1.92360 −0.0740395
\(676\) −30.2839 −1.16476
\(677\) −35.5011 −1.36442 −0.682209 0.731157i \(-0.738981\pi\)
−0.682209 + 0.731157i \(0.738981\pi\)
\(678\) −8.00987 −0.307617
\(679\) −28.4795 −1.09294
\(680\) −1.67547 −0.0642512
\(681\) 1.69082 0.0647922
\(682\) −22.4487 −0.859605
\(683\) 25.4482 0.973750 0.486875 0.873472i \(-0.338137\pi\)
0.486875 + 0.873472i \(0.338137\pi\)
\(684\) −36.4868 −1.39511
\(685\) 40.7825 1.55822
\(686\) 29.8190 1.13850
\(687\) −5.26756 −0.200970
\(688\) −2.96052 −0.112869
\(689\) 6.97323 0.265659
\(690\) −6.25638 −0.238176
\(691\) −34.8708 −1.32655 −0.663274 0.748376i \(-0.730834\pi\)
−0.663274 + 0.748376i \(0.730834\pi\)
\(692\) 2.64909 0.100703
\(693\) 9.04912 0.343748
\(694\) 48.5141 1.84157
\(695\) 21.1353 0.801707
\(696\) 0.0898573 0.00340603
\(697\) 9.14621 0.346437
\(698\) −18.3189 −0.693379
\(699\) −4.06292 −0.153674
\(700\) −11.4537 −0.432909
\(701\) −11.8474 −0.447469 −0.223735 0.974650i \(-0.571825\pi\)
−0.223735 + 0.974650i \(0.571825\pi\)
\(702\) −1.90836 −0.0720263
\(703\) 5.33211 0.201104
\(704\) 10.9798 0.413818
\(705\) 2.05437 0.0773720
\(706\) 62.9265 2.36827
\(707\) −9.91294 −0.372815
\(708\) 2.31733 0.0870906
\(709\) 2.45662 0.0922601 0.0461301 0.998935i \(-0.485311\pi\)
0.0461301 + 0.998935i \(0.485311\pi\)
\(710\) 28.0493 1.05267
\(711\) −5.40759 −0.202800
\(712\) −1.91507 −0.0717702
\(713\) 81.3673 3.04723
\(714\) 1.35011 0.0505265
\(715\) −1.35115 −0.0505300
\(716\) −58.2440 −2.17668
\(717\) 2.29945 0.0858746
\(718\) 15.3815 0.574032
\(719\) −42.7323 −1.59364 −0.796822 0.604213i \(-0.793487\pi\)
−0.796822 + 0.604213i \(0.793487\pi\)
\(720\) 16.2765 0.606591
\(721\) 35.1855 1.31038
\(722\) −14.3954 −0.535740
\(723\) 1.96530 0.0730903
\(724\) 38.8175 1.44264
\(725\) −0.733358 −0.0272362
\(726\) 0.441039 0.0163685
\(727\) −3.92497 −0.145569 −0.0727845 0.997348i \(-0.523189\pi\)
−0.0727845 + 0.997348i \(0.523189\pi\)
\(728\) −2.00342 −0.0742517
\(729\) −24.6568 −0.913214
\(730\) −5.75394 −0.212963
\(731\) 1.00000 0.0369863
\(732\) −1.32538 −0.0489875
\(733\) 23.0735 0.852240 0.426120 0.904667i \(-0.359880\pi\)
0.426120 + 0.904667i \(0.359880\pi\)
\(734\) 3.44788 0.127263
\(735\) −0.924200 −0.0340896
\(736\) −61.2587 −2.25803
\(737\) 0.886767 0.0326645
\(738\) 56.8938 2.09429
\(739\) 8.54317 0.314266 0.157133 0.987577i \(-0.449775\pi\)
0.157133 + 0.987577i \(0.449775\pi\)
\(740\) 4.73686 0.174130
\(741\) −0.774007 −0.0284339
\(742\) −61.8317 −2.26991
\(743\) 23.5082 0.862434 0.431217 0.902248i \(-0.358084\pi\)
0.431217 + 0.902248i \(0.358084\pi\)
\(744\) −2.01422 −0.0738449
\(745\) −33.8029 −1.23844
\(746\) 70.5642 2.58354
\(747\) 52.3886 1.91680
\(748\) −2.42810 −0.0887802
\(749\) −17.2098 −0.628833
\(750\) −5.36532 −0.195914
\(751\) −35.1019 −1.28089 −0.640443 0.768006i \(-0.721249\pi\)
−0.640443 + 0.768006i \(0.721249\pi\)
\(752\) 15.6027 0.568973
\(753\) 2.69142 0.0980808
\(754\) −0.727546 −0.0264957
\(755\) −22.3040 −0.811726
\(756\) 9.27868 0.337462
\(757\) −16.8333 −0.611818 −0.305909 0.952061i \(-0.598960\pi\)
−0.305909 + 0.952061i \(0.598960\pi\)
\(758\) −47.7637 −1.73486
\(759\) −1.59858 −0.0580249
\(760\) −8.51706 −0.308946
\(761\) −11.5439 −0.418468 −0.209234 0.977866i \(-0.567097\pi\)
−0.209234 + 0.977866i \(0.567097\pi\)
\(762\) 7.91017 0.286555
\(763\) −6.94722 −0.251506
\(764\) −34.8452 −1.26065
\(765\) −5.49786 −0.198776
\(766\) −50.0930 −1.80993
\(767\) −3.30808 −0.119448
\(768\) −1.49680 −0.0540110
\(769\) −1.20619 −0.0434963 −0.0217482 0.999763i \(-0.506923\pi\)
−0.0217482 + 0.999763i \(0.506923\pi\)
\(770\) 11.9806 0.431751
\(771\) −5.29839 −0.190817
\(772\) −23.8633 −0.858858
\(773\) −22.1529 −0.796785 −0.398393 0.917215i \(-0.630432\pi\)
−0.398393 + 0.917215i \(0.630432\pi\)
\(774\) 6.22048 0.223591
\(775\) 16.4388 0.590499
\(776\) 8.38103 0.300862
\(777\) −0.672983 −0.0241431
\(778\) 12.9800 0.465356
\(779\) 46.4938 1.66581
\(780\) −0.687602 −0.0246201
\(781\) 7.16694 0.256453
\(782\) 16.0501 0.573949
\(783\) 0.594095 0.0212312
\(784\) −7.01921 −0.250686
\(785\) −25.4380 −0.907923
\(786\) 6.26935 0.223620
\(787\) 27.4664 0.979073 0.489537 0.871983i \(-0.337166\pi\)
0.489537 + 0.871983i \(0.337166\pi\)
\(788\) −58.7206 −2.09184
\(789\) −1.50605 −0.0536169
\(790\) −7.15939 −0.254720
\(791\) −55.5956 −1.97675
\(792\) −2.66301 −0.0946258
\(793\) 1.89204 0.0671882
\(794\) −22.2729 −0.790435
\(795\) −3.74160 −0.132701
\(796\) −38.2264 −1.35490
\(797\) 49.6969 1.76036 0.880178 0.474644i \(-0.157423\pi\)
0.880178 + 0.474644i \(0.157423\pi\)
\(798\) 6.86313 0.242952
\(799\) −5.27026 −0.186448
\(800\) −12.3762 −0.437565
\(801\) −6.28409 −0.222037
\(802\) −35.7100 −1.26096
\(803\) −1.47020 −0.0518824
\(804\) 0.451278 0.0159154
\(805\) −43.4248 −1.53052
\(806\) 16.3085 0.574443
\(807\) 5.22684 0.183994
\(808\) 2.91721 0.102627
\(809\) −18.9120 −0.664910 −0.332455 0.943119i \(-0.607877\pi\)
−0.332455 + 0.943119i \(0.607877\pi\)
\(810\) −33.6836 −1.18352
\(811\) −51.6228 −1.81272 −0.906362 0.422503i \(-0.861152\pi\)
−0.906362 + 0.422503i \(0.861152\pi\)
\(812\) 3.53742 0.124139
\(813\) 2.37054 0.0831384
\(814\) 2.20726 0.0773645
\(815\) −46.4110 −1.62571
\(816\) 0.620492 0.0217216
\(817\) 5.08340 0.177846
\(818\) −40.7577 −1.42506
\(819\) −6.57400 −0.229714
\(820\) 41.3035 1.44238
\(821\) 5.00103 0.174537 0.0872685 0.996185i \(-0.472186\pi\)
0.0872685 + 0.996185i \(0.472186\pi\)
\(822\) 9.67100 0.337315
\(823\) −22.9405 −0.799654 −0.399827 0.916591i \(-0.630930\pi\)
−0.399827 + 0.916591i \(0.630930\pi\)
\(824\) −10.3545 −0.360716
\(825\) −0.322965 −0.0112442
\(826\) 29.3328 1.02062
\(827\) −25.9968 −0.903998 −0.451999 0.892019i \(-0.649289\pi\)
−0.451999 + 0.892019i \(0.649289\pi\)
\(828\) 54.7457 1.90255
\(829\) −38.2718 −1.32924 −0.664618 0.747184i \(-0.731406\pi\)
−0.664618 + 0.747184i \(0.731406\pi\)
\(830\) 69.3600 2.40752
\(831\) 0.901981 0.0312894
\(832\) −7.97661 −0.276539
\(833\) 2.37094 0.0821480
\(834\) 5.01194 0.173549
\(835\) −23.3198 −0.807015
\(836\) −12.3430 −0.426892
\(837\) −13.3171 −0.460307
\(838\) −27.0204 −0.933403
\(839\) −23.7885 −0.821272 −0.410636 0.911799i \(-0.634693\pi\)
−0.410636 + 0.911799i \(0.634693\pi\)
\(840\) 1.07497 0.0370899
\(841\) −28.7735 −0.992190
\(842\) 17.7003 0.609993
\(843\) −3.40372 −0.117230
\(844\) 60.4939 2.08228
\(845\) −23.1965 −0.797984
\(846\) −32.7836 −1.12712
\(847\) 3.06120 0.105184
\(848\) −28.4171 −0.975846
\(849\) −5.22393 −0.179285
\(850\) 3.24262 0.111221
\(851\) −8.00042 −0.274251
\(852\) 3.64728 0.124954
\(853\) −27.9994 −0.958683 −0.479341 0.877629i \(-0.659124\pi\)
−0.479341 + 0.877629i \(0.659124\pi\)
\(854\) −16.7767 −0.574086
\(855\) −27.9478 −0.955795
\(856\) 5.06457 0.173103
\(857\) 44.5600 1.52214 0.761071 0.648669i \(-0.224674\pi\)
0.761071 + 0.648669i \(0.224674\pi\)
\(858\) −0.320406 −0.0109385
\(859\) 24.2499 0.827395 0.413698 0.910414i \(-0.364237\pi\)
0.413698 + 0.910414i \(0.364237\pi\)
\(860\) 4.51592 0.153991
\(861\) −5.86814 −0.199986
\(862\) −4.67349 −0.159180
\(863\) 17.7838 0.605367 0.302684 0.953091i \(-0.402117\pi\)
0.302684 + 0.953091i \(0.402117\pi\)
\(864\) 10.0260 0.341092
\(865\) 2.02912 0.0689923
\(866\) 56.5106 1.92031
\(867\) −0.209589 −0.00711800
\(868\) −79.2941 −2.69142
\(869\) −1.82931 −0.0620553
\(870\) 0.390376 0.0132350
\(871\) −0.644218 −0.0218285
\(872\) 2.04445 0.0692339
\(873\) 27.5015 0.930783
\(874\) 81.5888 2.75978
\(875\) −37.2401 −1.25894
\(876\) −0.748191 −0.0252790
\(877\) 6.70924 0.226555 0.113277 0.993563i \(-0.463865\pi\)
0.113277 + 0.993563i \(0.463865\pi\)
\(878\) −73.4363 −2.47836
\(879\) −2.45487 −0.0828008
\(880\) 5.50614 0.185612
\(881\) −42.0653 −1.41721 −0.708607 0.705603i \(-0.750676\pi\)
−0.708607 + 0.705603i \(0.750676\pi\)
\(882\) 14.7484 0.496603
\(883\) −17.4690 −0.587878 −0.293939 0.955824i \(-0.594966\pi\)
−0.293939 + 0.955824i \(0.594966\pi\)
\(884\) 1.76397 0.0593286
\(885\) 1.77500 0.0596661
\(886\) −7.58084 −0.254683
\(887\) 16.7046 0.560886 0.280443 0.959871i \(-0.409519\pi\)
0.280443 + 0.959871i \(0.409519\pi\)
\(888\) 0.198048 0.00664604
\(889\) 54.9036 1.84141
\(890\) −8.31983 −0.278881
\(891\) −8.60658 −0.288331
\(892\) −54.1820 −1.81415
\(893\) −26.7908 −0.896521
\(894\) −8.01589 −0.268091
\(895\) −44.6132 −1.49125
\(896\) 21.5563 0.720144
\(897\) 1.16134 0.0387760
\(898\) −61.8578 −2.06422
\(899\) −5.07704 −0.169329
\(900\) 11.0604 0.368679
\(901\) 9.59866 0.319778
\(902\) 19.2464 0.640836
\(903\) −0.641592 −0.0213509
\(904\) 16.3609 0.544154
\(905\) 29.7331 0.988360
\(906\) −5.28909 −0.175718
\(907\) 44.2942 1.47077 0.735383 0.677652i \(-0.237002\pi\)
0.735383 + 0.677652i \(0.237002\pi\)
\(908\) −19.5883 −0.650059
\(909\) 9.57252 0.317500
\(910\) −8.70367 −0.288524
\(911\) 30.6099 1.01415 0.507076 0.861901i \(-0.330726\pi\)
0.507076 + 0.861901i \(0.330726\pi\)
\(912\) 3.15421 0.104446
\(913\) 17.7224 0.586525
\(914\) −4.52616 −0.149712
\(915\) −1.01520 −0.0335615
\(916\) 61.0251 2.01633
\(917\) 43.5148 1.43699
\(918\) −2.62686 −0.0866992
\(919\) 25.9137 0.854813 0.427406 0.904060i \(-0.359427\pi\)
0.427406 + 0.904060i \(0.359427\pi\)
\(920\) 12.7792 0.421318
\(921\) 0.815154 0.0268602
\(922\) −5.92833 −0.195239
\(923\) −5.20664 −0.171379
\(924\) 1.55785 0.0512496
\(925\) −1.61634 −0.0531449
\(926\) 52.2706 1.71772
\(927\) −33.9772 −1.11596
\(928\) 3.82233 0.125474
\(929\) −37.7538 −1.23866 −0.619330 0.785131i \(-0.712596\pi\)
−0.619330 + 0.785131i \(0.712596\pi\)
\(930\) −8.75059 −0.286943
\(931\) 12.0524 0.395002
\(932\) 47.0692 1.54180
\(933\) 0.00414324 0.000135644 0
\(934\) −12.4081 −0.406005
\(935\) −1.85985 −0.0608237
\(936\) 1.93462 0.0632350
\(937\) 25.4574 0.831658 0.415829 0.909443i \(-0.363491\pi\)
0.415829 + 0.909443i \(0.363491\pi\)
\(938\) 5.71229 0.186513
\(939\) −2.99730 −0.0978133
\(940\) −23.8000 −0.776272
\(941\) −20.6450 −0.673009 −0.336505 0.941682i \(-0.609245\pi\)
−0.336505 + 0.941682i \(0.609245\pi\)
\(942\) −6.03228 −0.196542
\(943\) −69.7604 −2.27171
\(944\) 13.4810 0.438768
\(945\) 7.10719 0.231197
\(946\) 2.10431 0.0684169
\(947\) −7.33040 −0.238206 −0.119103 0.992882i \(-0.538002\pi\)
−0.119103 + 0.992882i \(0.538002\pi\)
\(948\) −0.930944 −0.0302356
\(949\) 1.06807 0.0346711
\(950\) 16.4835 0.534796
\(951\) 3.71929 0.120606
\(952\) −2.75771 −0.0893779
\(953\) 44.4936 1.44129 0.720645 0.693304i \(-0.243846\pi\)
0.720645 + 0.693304i \(0.243846\pi\)
\(954\) 59.7083 1.93313
\(955\) −26.6904 −0.863680
\(956\) −26.6394 −0.861579
\(957\) 0.0997461 0.00322433
\(958\) −43.7185 −1.41248
\(959\) 67.1253 2.16759
\(960\) 4.27998 0.138136
\(961\) 82.8058 2.67116
\(962\) −1.60353 −0.0516999
\(963\) 16.6188 0.535534
\(964\) −22.7682 −0.733313
\(965\) −18.2785 −0.588407
\(966\) −10.2976 −0.331320
\(967\) 51.4774 1.65540 0.827701 0.561169i \(-0.189648\pi\)
0.827701 + 0.561169i \(0.189648\pi\)
\(968\) −0.900860 −0.0289547
\(969\) −1.06542 −0.0342263
\(970\) 36.4106 1.16907
\(971\) −39.3219 −1.26190 −0.630950 0.775824i \(-0.717335\pi\)
−0.630950 + 0.775824i \(0.717335\pi\)
\(972\) −13.4731 −0.432150
\(973\) 34.7873 1.11523
\(974\) 64.8198 2.07696
\(975\) 0.234627 0.00751409
\(976\) −7.71035 −0.246802
\(977\) −47.9157 −1.53296 −0.766479 0.642269i \(-0.777993\pi\)
−0.766479 + 0.642269i \(0.777993\pi\)
\(978\) −11.0057 −0.351925
\(979\) −2.12582 −0.0679416
\(980\) 10.7069 0.342021
\(981\) 6.70865 0.214191
\(982\) 5.48825 0.175137
\(983\) 25.4630 0.812143 0.406072 0.913841i \(-0.366898\pi\)
0.406072 + 0.913841i \(0.366898\pi\)
\(984\) 1.72690 0.0550514
\(985\) −44.9782 −1.43312
\(986\) −1.00147 −0.0318932
\(987\) 3.38136 0.107630
\(988\) 8.96694 0.285276
\(989\) −7.62725 −0.242532
\(990\) −11.5692 −0.367693
\(991\) −22.1820 −0.704636 −0.352318 0.935880i \(-0.614606\pi\)
−0.352318 + 0.935880i \(0.614606\pi\)
\(992\) −85.6806 −2.72036
\(993\) −7.16091 −0.227245
\(994\) 46.1673 1.46434
\(995\) −29.2803 −0.928247
\(996\) 9.01896 0.285777
\(997\) 40.4539 1.28119 0.640594 0.767880i \(-0.278688\pi\)
0.640594 + 0.767880i \(0.278688\pi\)
\(998\) −7.05256 −0.223245
\(999\) 1.30940 0.0414276
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 \(a_p\))