Properties

Label 6025.2.a.h.1.9
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.28632\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.28632 q^{2} +0.126224 q^{3} -0.345373 q^{4} +0.162365 q^{6} -1.03110 q^{7} -3.01691 q^{8} -2.98407 q^{9} +O(q^{10})\) \(q+1.28632 q^{2} +0.126224 q^{3} -0.345373 q^{4} +0.162365 q^{6} -1.03110 q^{7} -3.01691 q^{8} -2.98407 q^{9} +0.227935 q^{11} -0.0435945 q^{12} -3.38088 q^{13} -1.32633 q^{14} -3.18997 q^{16} -7.12130 q^{17} -3.83847 q^{18} +3.40112 q^{19} -0.130150 q^{21} +0.293198 q^{22} -6.91488 q^{23} -0.380807 q^{24} -4.34890 q^{26} -0.755335 q^{27} +0.356115 q^{28} +0.569431 q^{29} +4.93697 q^{31} +1.93048 q^{32} +0.0287710 q^{33} -9.16030 q^{34} +1.03062 q^{36} +5.37832 q^{37} +4.37494 q^{38} -0.426749 q^{39} +10.7559 q^{41} -0.167415 q^{42} +0.910247 q^{43} -0.0787228 q^{44} -8.89477 q^{46} +8.50333 q^{47} -0.402652 q^{48} -5.93683 q^{49} -0.898882 q^{51} +1.16766 q^{52} +7.76696 q^{53} -0.971605 q^{54} +3.11074 q^{56} +0.429304 q^{57} +0.732472 q^{58} +11.2505 q^{59} -3.65450 q^{61} +6.35054 q^{62} +3.07688 q^{63} +8.86317 q^{64} +0.0370088 q^{66} +12.0694 q^{67} +2.45951 q^{68} -0.872826 q^{69} -9.48630 q^{71} +9.00266 q^{72} +7.10488 q^{73} +6.91825 q^{74} -1.17466 q^{76} -0.235024 q^{77} -0.548937 q^{78} +0.366201 q^{79} +8.85686 q^{81} +13.8356 q^{82} -17.8030 q^{83} +0.0449504 q^{84} +1.17087 q^{86} +0.0718760 q^{87} -0.687660 q^{88} -7.54236 q^{89} +3.48603 q^{91} +2.38822 q^{92} +0.623166 q^{93} +10.9380 q^{94} +0.243674 q^{96} +7.85505 q^{97} -7.63668 q^{98} -0.680174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + O(q^{10}) \) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + 22q^{11} + 7q^{12} + 5q^{13} + 6q^{14} + 15q^{16} + 4q^{17} + q^{18} - 6q^{19} - 14q^{21} + 12q^{22} - 32q^{23} - 15q^{24} + 8q^{26} + 5q^{27} + 11q^{28} + 6q^{29} + 8q^{31} - q^{32} + 24q^{33} - 19q^{34} - 8q^{36} + 8q^{37} + 10q^{38} + 31q^{39} - q^{41} + 49q^{42} + 2q^{43} + 42q^{44} - 25q^{46} - 34q^{47} + 49q^{48} - 9q^{49} - 3q^{51} + 41q^{52} - 5q^{53} - 40q^{54} + q^{56} + 22q^{57} + 33q^{58} + 26q^{59} - 26q^{61} + 17q^{62} + 4q^{63} + 13q^{64} - 2q^{66} - 6q^{67} + 35q^{68} - 2q^{69} + 94q^{71} - 17q^{72} + 22q^{73} + 26q^{74} - 20q^{76} + 7q^{77} - 54q^{78} + 9q^{79} + 4q^{81} - 15q^{82} + 8q^{83} + 2q^{84} + 9q^{86} - 4q^{87} - 6q^{88} - 3q^{89} - 20q^{91} - 36q^{92} - 12q^{93} + 48q^{94} - 23q^{96} + 29q^{97} - 28q^{98} + 36q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28632 0.909568 0.454784 0.890602i \(-0.349717\pi\)
0.454784 + 0.890602i \(0.349717\pi\)
\(3\) 0.126224 0.0728757 0.0364378 0.999336i \(-0.488399\pi\)
0.0364378 + 0.999336i \(0.488399\pi\)
\(4\) −0.345373 −0.172687
\(5\) 0 0
\(6\) 0.162365 0.0662853
\(7\) −1.03110 −0.389720 −0.194860 0.980831i \(-0.562425\pi\)
−0.194860 + 0.980831i \(0.562425\pi\)
\(8\) −3.01691 −1.06664
\(9\) −2.98407 −0.994689
\(10\) 0 0
\(11\) 0.227935 0.0687251 0.0343625 0.999409i \(-0.489060\pi\)
0.0343625 + 0.999409i \(0.489060\pi\)
\(12\) −0.0435945 −0.0125847
\(13\) −3.38088 −0.937686 −0.468843 0.883281i \(-0.655329\pi\)
−0.468843 + 0.883281i \(0.655329\pi\)
\(14\) −1.32633 −0.354477
\(15\) 0 0
\(16\) −3.18997 −0.797493
\(17\) −7.12130 −1.72717 −0.863585 0.504203i \(-0.831786\pi\)
−0.863585 + 0.504203i \(0.831786\pi\)
\(18\) −3.83847 −0.904737
\(19\) 3.40112 0.780270 0.390135 0.920758i \(-0.372428\pi\)
0.390135 + 0.920758i \(0.372428\pi\)
\(20\) 0 0
\(21\) −0.130150 −0.0284011
\(22\) 0.293198 0.0625101
\(23\) −6.91488 −1.44185 −0.720926 0.693012i \(-0.756283\pi\)
−0.720926 + 0.693012i \(0.756283\pi\)
\(24\) −0.380807 −0.0777319
\(25\) 0 0
\(26\) −4.34890 −0.852889
\(27\) −0.755335 −0.145364
\(28\) 0.356115 0.0672995
\(29\) 0.569431 0.105741 0.0528703 0.998601i \(-0.483163\pi\)
0.0528703 + 0.998601i \(0.483163\pi\)
\(30\) 0 0
\(31\) 4.93697 0.886706 0.443353 0.896347i \(-0.353789\pi\)
0.443353 + 0.896347i \(0.353789\pi\)
\(32\) 1.93048 0.341264
\(33\) 0.0287710 0.00500838
\(34\) −9.16030 −1.57098
\(35\) 0 0
\(36\) 1.03062 0.171770
\(37\) 5.37832 0.884190 0.442095 0.896968i \(-0.354235\pi\)
0.442095 + 0.896968i \(0.354235\pi\)
\(38\) 4.37494 0.709709
\(39\) −0.426749 −0.0683345
\(40\) 0 0
\(41\) 10.7559 1.67979 0.839897 0.542747i \(-0.182616\pi\)
0.839897 + 0.542747i \(0.182616\pi\)
\(42\) −0.167415 −0.0258327
\(43\) 0.910247 0.138811 0.0694057 0.997589i \(-0.477890\pi\)
0.0694057 + 0.997589i \(0.477890\pi\)
\(44\) −0.0787228 −0.0118679
\(45\) 0 0
\(46\) −8.89477 −1.31146
\(47\) 8.50333 1.24034 0.620169 0.784468i \(-0.287064\pi\)
0.620169 + 0.784468i \(0.287064\pi\)
\(48\) −0.402652 −0.0581178
\(49\) −5.93683 −0.848118
\(50\) 0 0
\(51\) −0.898882 −0.125869
\(52\) 1.16766 0.161926
\(53\) 7.76696 1.06687 0.533437 0.845840i \(-0.320900\pi\)
0.533437 + 0.845840i \(0.320900\pi\)
\(54\) −0.971605 −0.132219
\(55\) 0 0
\(56\) 3.11074 0.415690
\(57\) 0.429304 0.0568627
\(58\) 0.732472 0.0961783
\(59\) 11.2505 1.46468 0.732342 0.680937i \(-0.238427\pi\)
0.732342 + 0.680937i \(0.238427\pi\)
\(60\) 0 0
\(61\) −3.65450 −0.467910 −0.233955 0.972247i \(-0.575167\pi\)
−0.233955 + 0.972247i \(0.575167\pi\)
\(62\) 6.35054 0.806519
\(63\) 3.07688 0.387650
\(64\) 8.86317 1.10790
\(65\) 0 0
\(66\) 0.0370088 0.00455546
\(67\) 12.0694 1.47451 0.737257 0.675613i \(-0.236121\pi\)
0.737257 + 0.675613i \(0.236121\pi\)
\(68\) 2.45951 0.298259
\(69\) −0.872826 −0.105076
\(70\) 0 0
\(71\) −9.48630 −1.12582 −0.562908 0.826519i \(-0.690318\pi\)
−0.562908 + 0.826519i \(0.690318\pi\)
\(72\) 9.00266 1.06097
\(73\) 7.10488 0.831563 0.415782 0.909464i \(-0.363508\pi\)
0.415782 + 0.909464i \(0.363508\pi\)
\(74\) 6.91825 0.804231
\(75\) 0 0
\(76\) −1.17466 −0.134742
\(77\) −0.235024 −0.0267835
\(78\) −0.548937 −0.0621548
\(79\) 0.366201 0.0412008 0.0206004 0.999788i \(-0.493442\pi\)
0.0206004 + 0.999788i \(0.493442\pi\)
\(80\) 0 0
\(81\) 8.85686 0.984096
\(82\) 13.8356 1.52789
\(83\) −17.8030 −1.95413 −0.977067 0.212932i \(-0.931699\pi\)
−0.977067 + 0.212932i \(0.931699\pi\)
\(84\) 0.0449504 0.00490449
\(85\) 0 0
\(86\) 1.17087 0.126258
\(87\) 0.0718760 0.00770592
\(88\) −0.687660 −0.0733048
\(89\) −7.54236 −0.799489 −0.399744 0.916627i \(-0.630901\pi\)
−0.399744 + 0.916627i \(0.630901\pi\)
\(90\) 0 0
\(91\) 3.48603 0.365435
\(92\) 2.38822 0.248989
\(93\) 0.623166 0.0646193
\(94\) 10.9380 1.12817
\(95\) 0 0
\(96\) 0.243674 0.0248699
\(97\) 7.85505 0.797560 0.398780 0.917047i \(-0.369434\pi\)
0.398780 + 0.917047i \(0.369434\pi\)
\(98\) −7.63668 −0.771421
\(99\) −0.680174 −0.0683601
\(100\) 0 0
\(101\) 17.4801 1.73933 0.869666 0.493640i \(-0.164334\pi\)
0.869666 + 0.493640i \(0.164334\pi\)
\(102\) −1.15625 −0.114486
\(103\) −6.10361 −0.601407 −0.300703 0.953718i \(-0.597221\pi\)
−0.300703 + 0.953718i \(0.597221\pi\)
\(104\) 10.1998 1.00017
\(105\) 0 0
\(106\) 9.99081 0.970394
\(107\) −7.86203 −0.760051 −0.380026 0.924976i \(-0.624085\pi\)
−0.380026 + 0.924976i \(0.624085\pi\)
\(108\) 0.260873 0.0251025
\(109\) −4.17241 −0.399644 −0.199822 0.979832i \(-0.564036\pi\)
−0.199822 + 0.979832i \(0.564036\pi\)
\(110\) 0 0
\(111\) 0.678875 0.0644359
\(112\) 3.28919 0.310799
\(113\) −3.62203 −0.340732 −0.170366 0.985381i \(-0.554495\pi\)
−0.170366 + 0.985381i \(0.554495\pi\)
\(114\) 0.552224 0.0517205
\(115\) 0 0
\(116\) −0.196666 −0.0182600
\(117\) 10.0888 0.932706
\(118\) 14.4717 1.33223
\(119\) 7.34279 0.673113
\(120\) 0 0
\(121\) −10.9480 −0.995277
\(122\) −4.70086 −0.425596
\(123\) 1.35766 0.122416
\(124\) −1.70510 −0.153122
\(125\) 0 0
\(126\) 3.95786 0.352594
\(127\) −13.5446 −1.20189 −0.600943 0.799292i \(-0.705208\pi\)
−0.600943 + 0.799292i \(0.705208\pi\)
\(128\) 7.53993 0.666442
\(129\) 0.114895 0.0101160
\(130\) 0 0
\(131\) 1.03003 0.0899942 0.0449971 0.998987i \(-0.485672\pi\)
0.0449971 + 0.998987i \(0.485672\pi\)
\(132\) −0.00993673 −0.000864881 0
\(133\) −3.50690 −0.304087
\(134\) 15.5252 1.34117
\(135\) 0 0
\(136\) 21.4843 1.84226
\(137\) 11.5780 0.989180 0.494590 0.869127i \(-0.335318\pi\)
0.494590 + 0.869127i \(0.335318\pi\)
\(138\) −1.12274 −0.0955736
\(139\) 0.110960 0.00941151 0.00470575 0.999989i \(-0.498502\pi\)
0.00470575 + 0.999989i \(0.498502\pi\)
\(140\) 0 0
\(141\) 1.07333 0.0903904
\(142\) −12.2024 −1.02401
\(143\) −0.770621 −0.0644425
\(144\) 9.51909 0.793257
\(145\) 0 0
\(146\) 9.13917 0.756363
\(147\) −0.749372 −0.0618072
\(148\) −1.85753 −0.152688
\(149\) −19.5413 −1.60089 −0.800443 0.599409i \(-0.795402\pi\)
−0.800443 + 0.599409i \(0.795402\pi\)
\(150\) 0 0
\(151\) 17.7745 1.44647 0.723233 0.690604i \(-0.242655\pi\)
0.723233 + 0.690604i \(0.242655\pi\)
\(152\) −10.2609 −0.832266
\(153\) 21.2505 1.71800
\(154\) −0.302317 −0.0243614
\(155\) 0 0
\(156\) 0.147388 0.0118005
\(157\) −6.98884 −0.557770 −0.278885 0.960325i \(-0.589965\pi\)
−0.278885 + 0.960325i \(0.589965\pi\)
\(158\) 0.471053 0.0374749
\(159\) 0.980379 0.0777491
\(160\) 0 0
\(161\) 7.12995 0.561918
\(162\) 11.3928 0.895102
\(163\) 8.87693 0.695295 0.347647 0.937625i \(-0.386981\pi\)
0.347647 + 0.937625i \(0.386981\pi\)
\(164\) −3.71481 −0.290078
\(165\) 0 0
\(166\) −22.9004 −1.77742
\(167\) −4.85435 −0.375641 −0.187820 0.982203i \(-0.560142\pi\)
−0.187820 + 0.982203i \(0.560142\pi\)
\(168\) 0.392651 0.0302937
\(169\) −1.56968 −0.120745
\(170\) 0 0
\(171\) −10.1492 −0.776126
\(172\) −0.314375 −0.0239709
\(173\) 13.5277 1.02849 0.514247 0.857642i \(-0.328072\pi\)
0.514247 + 0.857642i \(0.328072\pi\)
\(174\) 0.0924558 0.00700905
\(175\) 0 0
\(176\) −0.727107 −0.0548077
\(177\) 1.42008 0.106740
\(178\) −9.70191 −0.727189
\(179\) −10.4800 −0.783310 −0.391655 0.920112i \(-0.628097\pi\)
−0.391655 + 0.920112i \(0.628097\pi\)
\(180\) 0 0
\(181\) −8.82686 −0.656095 −0.328048 0.944661i \(-0.606391\pi\)
−0.328048 + 0.944661i \(0.606391\pi\)
\(182\) 4.48416 0.332388
\(183\) −0.461286 −0.0340993
\(184\) 20.8616 1.53793
\(185\) 0 0
\(186\) 0.801593 0.0587756
\(187\) −1.62320 −0.118700
\(188\) −2.93682 −0.214190
\(189\) 0.778827 0.0566514
\(190\) 0 0
\(191\) −3.25920 −0.235827 −0.117914 0.993024i \(-0.537621\pi\)
−0.117914 + 0.993024i \(0.537621\pi\)
\(192\) 1.11875 0.0807386
\(193\) −16.9658 −1.22123 −0.610613 0.791929i \(-0.709077\pi\)
−0.610613 + 0.791929i \(0.709077\pi\)
\(194\) 10.1041 0.725434
\(195\) 0 0
\(196\) 2.05042 0.146459
\(197\) 18.5572 1.32214 0.661072 0.750322i \(-0.270102\pi\)
0.661072 + 0.750322i \(0.270102\pi\)
\(198\) −0.874924 −0.0621781
\(199\) −19.6484 −1.39284 −0.696420 0.717634i \(-0.745225\pi\)
−0.696420 + 0.717634i \(0.745225\pi\)
\(200\) 0 0
\(201\) 1.52345 0.107456
\(202\) 22.4850 1.58204
\(203\) −0.587141 −0.0412092
\(204\) 0.310450 0.0217358
\(205\) 0 0
\(206\) −7.85121 −0.547020
\(207\) 20.6345 1.43419
\(208\) 10.7849 0.747798
\(209\) 0.775235 0.0536241
\(210\) 0 0
\(211\) −8.18657 −0.563587 −0.281794 0.959475i \(-0.590929\pi\)
−0.281794 + 0.959475i \(0.590929\pi\)
\(212\) −2.68250 −0.184235
\(213\) −1.19740 −0.0820446
\(214\) −10.1131 −0.691318
\(215\) 0 0
\(216\) 2.27878 0.155051
\(217\) −5.09052 −0.345567
\(218\) −5.36706 −0.363503
\(219\) 0.896809 0.0606007
\(220\) 0 0
\(221\) 24.0762 1.61954
\(222\) 0.873252 0.0586088
\(223\) −15.5070 −1.03843 −0.519213 0.854645i \(-0.673775\pi\)
−0.519213 + 0.854645i \(0.673775\pi\)
\(224\) −1.99053 −0.132998
\(225\) 0 0
\(226\) −4.65910 −0.309919
\(227\) 27.1128 1.79954 0.899769 0.436366i \(-0.143735\pi\)
0.899769 + 0.436366i \(0.143735\pi\)
\(228\) −0.148270 −0.00981944
\(229\) 8.10947 0.535889 0.267944 0.963434i \(-0.413656\pi\)
0.267944 + 0.963434i \(0.413656\pi\)
\(230\) 0 0
\(231\) −0.0296658 −0.00195187
\(232\) −1.71792 −0.112787
\(233\) 4.34697 0.284780 0.142390 0.989811i \(-0.454521\pi\)
0.142390 + 0.989811i \(0.454521\pi\)
\(234\) 12.9774 0.848359
\(235\) 0 0
\(236\) −3.88561 −0.252932
\(237\) 0.0462235 0.00300254
\(238\) 9.44520 0.612241
\(239\) 18.3619 1.18773 0.593867 0.804563i \(-0.297601\pi\)
0.593867 + 0.804563i \(0.297601\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −14.0827 −0.905272
\(243\) 3.38396 0.217081
\(244\) 1.26217 0.0808019
\(245\) 0 0
\(246\) 1.74639 0.111346
\(247\) −11.4988 −0.731649
\(248\) −14.8944 −0.945795
\(249\) −2.24717 −0.142409
\(250\) 0 0
\(251\) 12.3629 0.780337 0.390169 0.920743i \(-0.372417\pi\)
0.390169 + 0.920743i \(0.372417\pi\)
\(252\) −1.06267 −0.0669420
\(253\) −1.57614 −0.0990914
\(254\) −17.4227 −1.09320
\(255\) 0 0
\(256\) −8.02755 −0.501722
\(257\) 12.1589 0.758452 0.379226 0.925304i \(-0.376190\pi\)
0.379226 + 0.925304i \(0.376190\pi\)
\(258\) 0.147793 0.00920116
\(259\) −5.54560 −0.344587
\(260\) 0 0
\(261\) −1.69922 −0.105179
\(262\) 1.32495 0.0818558
\(263\) 5.76048 0.355207 0.177603 0.984102i \(-0.443166\pi\)
0.177603 + 0.984102i \(0.443166\pi\)
\(264\) −0.0867994 −0.00534213
\(265\) 0 0
\(266\) −4.51101 −0.276588
\(267\) −0.952030 −0.0582633
\(268\) −4.16846 −0.254629
\(269\) 14.4585 0.881551 0.440776 0.897617i \(-0.354703\pi\)
0.440776 + 0.897617i \(0.354703\pi\)
\(270\) 0 0
\(271\) 6.81638 0.414065 0.207033 0.978334i \(-0.433619\pi\)
0.207033 + 0.978334i \(0.433619\pi\)
\(272\) 22.7167 1.37741
\(273\) 0.440022 0.0266313
\(274\) 14.8931 0.899726
\(275\) 0 0
\(276\) 0.301451 0.0181452
\(277\) 25.1323 1.51005 0.755027 0.655693i \(-0.227624\pi\)
0.755027 + 0.655693i \(0.227624\pi\)
\(278\) 0.142730 0.00856040
\(279\) −14.7323 −0.881997
\(280\) 0 0
\(281\) −6.03331 −0.359917 −0.179959 0.983674i \(-0.557596\pi\)
−0.179959 + 0.983674i \(0.557596\pi\)
\(282\) 1.38064 0.0822162
\(283\) 3.47423 0.206521 0.103261 0.994654i \(-0.467072\pi\)
0.103261 + 0.994654i \(0.467072\pi\)
\(284\) 3.27631 0.194414
\(285\) 0 0
\(286\) −0.991267 −0.0586148
\(287\) −11.0905 −0.654649
\(288\) −5.76069 −0.339452
\(289\) 33.7130 1.98312
\(290\) 0 0
\(291\) 0.991499 0.0581227
\(292\) −2.45384 −0.143600
\(293\) 19.7300 1.15264 0.576321 0.817224i \(-0.304488\pi\)
0.576321 + 0.817224i \(0.304488\pi\)
\(294\) −0.963935 −0.0562178
\(295\) 0 0
\(296\) −16.2259 −0.943111
\(297\) −0.172167 −0.00999017
\(298\) −25.1364 −1.45611
\(299\) 23.3783 1.35200
\(300\) 0 0
\(301\) −0.938558 −0.0540976
\(302\) 22.8637 1.31566
\(303\) 2.20641 0.126755
\(304\) −10.8495 −0.622260
\(305\) 0 0
\(306\) 27.3349 1.56263
\(307\) 0.0265060 0.00151278 0.000756388 1.00000i \(-0.499759\pi\)
0.000756388 1.00000i \(0.499759\pi\)
\(308\) 0.0811712 0.00462516
\(309\) −0.770424 −0.0438279
\(310\) 0 0
\(311\) 21.2822 1.20680 0.603400 0.797439i \(-0.293812\pi\)
0.603400 + 0.797439i \(0.293812\pi\)
\(312\) 1.28746 0.0728882
\(313\) −10.6916 −0.604323 −0.302161 0.953257i \(-0.597708\pi\)
−0.302161 + 0.953257i \(0.597708\pi\)
\(314\) −8.98990 −0.507329
\(315\) 0 0
\(316\) −0.126476 −0.00711484
\(317\) 2.07826 0.116727 0.0583633 0.998295i \(-0.481412\pi\)
0.0583633 + 0.998295i \(0.481412\pi\)
\(318\) 1.26108 0.0707181
\(319\) 0.129793 0.00726703
\(320\) 0 0
\(321\) −0.992380 −0.0553892
\(322\) 9.17141 0.511103
\(323\) −24.2204 −1.34766
\(324\) −3.05892 −0.169940
\(325\) 0 0
\(326\) 11.4186 0.632418
\(327\) −0.526659 −0.0291243
\(328\) −32.4496 −1.79173
\(329\) −8.76780 −0.483384
\(330\) 0 0
\(331\) −28.1272 −1.54601 −0.773006 0.634399i \(-0.781248\pi\)
−0.773006 + 0.634399i \(0.781248\pi\)
\(332\) 6.14869 0.337453
\(333\) −16.0493 −0.879494
\(334\) −6.24426 −0.341671
\(335\) 0 0
\(336\) 0.415175 0.0226497
\(337\) −23.5835 −1.28468 −0.642338 0.766422i \(-0.722035\pi\)
−0.642338 + 0.766422i \(0.722035\pi\)
\(338\) −2.01911 −0.109825
\(339\) −0.457188 −0.0248311
\(340\) 0 0
\(341\) 1.12531 0.0609389
\(342\) −13.0551 −0.705940
\(343\) 13.3392 0.720249
\(344\) −2.74613 −0.148061
\(345\) 0 0
\(346\) 17.4010 0.935484
\(347\) 21.8697 1.17403 0.587013 0.809578i \(-0.300304\pi\)
0.587013 + 0.809578i \(0.300304\pi\)
\(348\) −0.0248241 −0.00133071
\(349\) 18.8525 1.00915 0.504575 0.863368i \(-0.331649\pi\)
0.504575 + 0.863368i \(0.331649\pi\)
\(350\) 0 0
\(351\) 2.55369 0.136306
\(352\) 0.440025 0.0234534
\(353\) 11.3768 0.605526 0.302763 0.953066i \(-0.402091\pi\)
0.302763 + 0.953066i \(0.402091\pi\)
\(354\) 1.82668 0.0970871
\(355\) 0 0
\(356\) 2.60493 0.138061
\(357\) 0.926839 0.0490535
\(358\) −13.4806 −0.712473
\(359\) −0.146567 −0.00773548 −0.00386774 0.999993i \(-0.501231\pi\)
−0.00386774 + 0.999993i \(0.501231\pi\)
\(360\) 0 0
\(361\) −7.43238 −0.391178
\(362\) −11.3542 −0.596763
\(363\) −1.38191 −0.0725315
\(364\) −1.20398 −0.0631058
\(365\) 0 0
\(366\) −0.593363 −0.0310156
\(367\) −32.6647 −1.70508 −0.852541 0.522660i \(-0.824940\pi\)
−0.852541 + 0.522660i \(0.824940\pi\)
\(368\) 22.0583 1.14987
\(369\) −32.0964 −1.67087
\(370\) 0 0
\(371\) −8.00852 −0.415782
\(372\) −0.215225 −0.0111589
\(373\) 17.7530 0.919218 0.459609 0.888121i \(-0.347990\pi\)
0.459609 + 0.888121i \(0.347990\pi\)
\(374\) −2.08795 −0.107966
\(375\) 0 0
\(376\) −25.6538 −1.32299
\(377\) −1.92517 −0.0991515
\(378\) 1.00182 0.0515282
\(379\) −4.82435 −0.247810 −0.123905 0.992294i \(-0.539542\pi\)
−0.123905 + 0.992294i \(0.539542\pi\)
\(380\) 0 0
\(381\) −1.70965 −0.0875882
\(382\) −4.19238 −0.214501
\(383\) −14.7127 −0.751783 −0.375892 0.926664i \(-0.622664\pi\)
−0.375892 + 0.926664i \(0.622664\pi\)
\(384\) 0.951722 0.0485674
\(385\) 0 0
\(386\) −21.8235 −1.11079
\(387\) −2.71624 −0.138074
\(388\) −2.71293 −0.137728
\(389\) 4.90322 0.248603 0.124301 0.992244i \(-0.460331\pi\)
0.124301 + 0.992244i \(0.460331\pi\)
\(390\) 0 0
\(391\) 49.2430 2.49032
\(392\) 17.9109 0.904635
\(393\) 0.130015 0.00655839
\(394\) 23.8705 1.20258
\(395\) 0 0
\(396\) 0.234914 0.0118049
\(397\) 14.8959 0.747606 0.373803 0.927508i \(-0.378054\pi\)
0.373803 + 0.927508i \(0.378054\pi\)
\(398\) −25.2742 −1.26688
\(399\) −0.442656 −0.0221605
\(400\) 0 0
\(401\) 6.72128 0.335645 0.167822 0.985817i \(-0.446327\pi\)
0.167822 + 0.985817i \(0.446327\pi\)
\(402\) 1.95965 0.0977386
\(403\) −16.6913 −0.831452
\(404\) −6.03715 −0.300360
\(405\) 0 0
\(406\) −0.755253 −0.0374826
\(407\) 1.22591 0.0607660
\(408\) 2.71184 0.134256
\(409\) −2.59935 −0.128529 −0.0642647 0.997933i \(-0.520470\pi\)
−0.0642647 + 0.997933i \(0.520470\pi\)
\(410\) 0 0
\(411\) 1.46143 0.0720871
\(412\) 2.10803 0.103855
\(413\) −11.6004 −0.570817
\(414\) 26.5426 1.30450
\(415\) 0 0
\(416\) −6.52672 −0.319999
\(417\) 0.0140059 0.000685870 0
\(418\) 0.997203 0.0487748
\(419\) −13.1622 −0.643018 −0.321509 0.946907i \(-0.604190\pi\)
−0.321509 + 0.946907i \(0.604190\pi\)
\(420\) 0 0
\(421\) −6.53715 −0.318601 −0.159301 0.987230i \(-0.550924\pi\)
−0.159301 + 0.987230i \(0.550924\pi\)
\(422\) −10.5306 −0.512620
\(423\) −25.3745 −1.23375
\(424\) −23.4322 −1.13797
\(425\) 0 0
\(426\) −1.54025 −0.0746251
\(427\) 3.76816 0.182354
\(428\) 2.71534 0.131251
\(429\) −0.0972711 −0.00469629
\(430\) 0 0
\(431\) 10.8319 0.521755 0.260878 0.965372i \(-0.415988\pi\)
0.260878 + 0.965372i \(0.415988\pi\)
\(432\) 2.40950 0.115927
\(433\) 25.6037 1.23044 0.615218 0.788357i \(-0.289068\pi\)
0.615218 + 0.788357i \(0.289068\pi\)
\(434\) −6.54805 −0.314317
\(435\) 0 0
\(436\) 1.44104 0.0690132
\(437\) −23.5183 −1.12503
\(438\) 1.15359 0.0551205
\(439\) 14.6842 0.700839 0.350419 0.936593i \(-0.386039\pi\)
0.350419 + 0.936593i \(0.386039\pi\)
\(440\) 0 0
\(441\) 17.7159 0.843614
\(442\) 30.9698 1.47308
\(443\) 15.2687 0.725436 0.362718 0.931899i \(-0.381849\pi\)
0.362718 + 0.931899i \(0.381849\pi\)
\(444\) −0.234465 −0.0111272
\(445\) 0 0
\(446\) −19.9470 −0.944518
\(447\) −2.46659 −0.116666
\(448\) −9.13883 −0.431769
\(449\) 31.2160 1.47317 0.736587 0.676343i \(-0.236436\pi\)
0.736587 + 0.676343i \(0.236436\pi\)
\(450\) 0 0
\(451\) 2.45165 0.115444
\(452\) 1.25095 0.0588399
\(453\) 2.24357 0.105412
\(454\) 34.8758 1.63680
\(455\) 0 0
\(456\) −1.29517 −0.0606519
\(457\) −9.43632 −0.441412 −0.220706 0.975340i \(-0.570836\pi\)
−0.220706 + 0.975340i \(0.570836\pi\)
\(458\) 10.4314 0.487427
\(459\) 5.37897 0.251069
\(460\) 0 0
\(461\) 8.65525 0.403115 0.201557 0.979477i \(-0.435400\pi\)
0.201557 + 0.979477i \(0.435400\pi\)
\(462\) −0.0381598 −0.00177536
\(463\) 12.5415 0.582853 0.291426 0.956593i \(-0.405870\pi\)
0.291426 + 0.956593i \(0.405870\pi\)
\(464\) −1.81647 −0.0843274
\(465\) 0 0
\(466\) 5.59161 0.259026
\(467\) 5.28477 0.244550 0.122275 0.992496i \(-0.460981\pi\)
0.122275 + 0.992496i \(0.460981\pi\)
\(468\) −3.48439 −0.161066
\(469\) −12.4448 −0.574647
\(470\) 0 0
\(471\) −0.882161 −0.0406479
\(472\) −33.9416 −1.56229
\(473\) 0.207477 0.00953982
\(474\) 0.0594583 0.00273101
\(475\) 0 0
\(476\) −2.53601 −0.116238
\(477\) −23.1771 −1.06121
\(478\) 23.6194 1.08032
\(479\) −29.0596 −1.32777 −0.663884 0.747835i \(-0.731093\pi\)
−0.663884 + 0.747835i \(0.731093\pi\)
\(480\) 0 0
\(481\) −18.1834 −0.829093
\(482\) 1.28632 0.0585904
\(483\) 0.899973 0.0409502
\(484\) 3.78116 0.171871
\(485\) 0 0
\(486\) 4.35286 0.197450
\(487\) 36.2854 1.64425 0.822124 0.569309i \(-0.192789\pi\)
0.822124 + 0.569309i \(0.192789\pi\)
\(488\) 11.0253 0.499091
\(489\) 1.12048 0.0506701
\(490\) 0 0
\(491\) −3.99282 −0.180193 −0.0900967 0.995933i \(-0.528718\pi\)
−0.0900967 + 0.995933i \(0.528718\pi\)
\(492\) −0.468899 −0.0211396
\(493\) −4.05509 −0.182632
\(494\) −14.7911 −0.665484
\(495\) 0 0
\(496\) −15.7488 −0.707142
\(497\) 9.78134 0.438753
\(498\) −2.89059 −0.129530
\(499\) 9.25262 0.414204 0.207102 0.978319i \(-0.433597\pi\)
0.207102 + 0.978319i \(0.433597\pi\)
\(500\) 0 0
\(501\) −0.612737 −0.0273751
\(502\) 15.9026 0.709769
\(503\) −30.0225 −1.33864 −0.669319 0.742975i \(-0.733414\pi\)
−0.669319 + 0.742975i \(0.733414\pi\)
\(504\) −9.28266 −0.413482
\(505\) 0 0
\(506\) −2.02743 −0.0901303
\(507\) −0.198132 −0.00879934
\(508\) 4.67793 0.207550
\(509\) 8.01192 0.355122 0.177561 0.984110i \(-0.443179\pi\)
0.177561 + 0.984110i \(0.443179\pi\)
\(510\) 0 0
\(511\) −7.32586 −0.324077
\(512\) −25.4059 −1.12279
\(513\) −2.56898 −0.113423
\(514\) 15.6403 0.689864
\(515\) 0 0
\(516\) −0.0396818 −0.00174689
\(517\) 1.93821 0.0852423
\(518\) −7.13343 −0.313425
\(519\) 1.70753 0.0749521
\(520\) 0 0
\(521\) −10.1940 −0.446608 −0.223304 0.974749i \(-0.571684\pi\)
−0.223304 + 0.974749i \(0.571684\pi\)
\(522\) −2.18575 −0.0956675
\(523\) 41.0217 1.79375 0.896877 0.442281i \(-0.145830\pi\)
0.896877 + 0.442281i \(0.145830\pi\)
\(524\) −0.355745 −0.0155408
\(525\) 0 0
\(526\) 7.40984 0.323084
\(527\) −35.1577 −1.53149
\(528\) −0.0917786 −0.00399415
\(529\) 24.8156 1.07894
\(530\) 0 0
\(531\) −33.5721 −1.45691
\(532\) 1.21119 0.0525118
\(533\) −36.3644 −1.57512
\(534\) −1.22462 −0.0529944
\(535\) 0 0
\(536\) −36.4123 −1.57277
\(537\) −1.32283 −0.0570842
\(538\) 18.5983 0.801831
\(539\) −1.35321 −0.0582870
\(540\) 0 0
\(541\) −25.9044 −1.11372 −0.556858 0.830608i \(-0.687993\pi\)
−0.556858 + 0.830608i \(0.687993\pi\)
\(542\) 8.76806 0.376620
\(543\) −1.11416 −0.0478134
\(544\) −13.7476 −0.589422
\(545\) 0 0
\(546\) 0.566010 0.0242230
\(547\) 43.6488 1.86629 0.933145 0.359501i \(-0.117053\pi\)
0.933145 + 0.359501i \(0.117053\pi\)
\(548\) −3.99875 −0.170818
\(549\) 10.9053 0.465425
\(550\) 0 0
\(551\) 1.93670 0.0825063
\(552\) 2.63324 0.112078
\(553\) −0.377591 −0.0160568
\(554\) 32.3283 1.37350
\(555\) 0 0
\(556\) −0.0383227 −0.00162524
\(557\) −22.1122 −0.936925 −0.468463 0.883483i \(-0.655192\pi\)
−0.468463 + 0.883483i \(0.655192\pi\)
\(558\) −18.9504 −0.802236
\(559\) −3.07743 −0.130162
\(560\) 0 0
\(561\) −0.204887 −0.00865033
\(562\) −7.76078 −0.327369
\(563\) −19.0461 −0.802697 −0.401348 0.915925i \(-0.631458\pi\)
−0.401348 + 0.915925i \(0.631458\pi\)
\(564\) −0.370699 −0.0156092
\(565\) 0 0
\(566\) 4.46898 0.187845
\(567\) −9.13233 −0.383522
\(568\) 28.6193 1.20084
\(569\) −24.1421 −1.01209 −0.506045 0.862507i \(-0.668893\pi\)
−0.506045 + 0.862507i \(0.668893\pi\)
\(570\) 0 0
\(571\) −37.2649 −1.55949 −0.779745 0.626098i \(-0.784651\pi\)
−0.779745 + 0.626098i \(0.784651\pi\)
\(572\) 0.266152 0.0111284
\(573\) −0.411390 −0.0171861
\(574\) −14.2659 −0.595447
\(575\) 0 0
\(576\) −26.4483 −1.10201
\(577\) 6.94471 0.289112 0.144556 0.989497i \(-0.453825\pi\)
0.144556 + 0.989497i \(0.453825\pi\)
\(578\) 43.3658 1.80378
\(579\) −2.14150 −0.0889977
\(580\) 0 0
\(581\) 18.3567 0.761565
\(582\) 1.27539 0.0528665
\(583\) 1.77036 0.0733209
\(584\) −21.4348 −0.886977
\(585\) 0 0
\(586\) 25.3792 1.04841
\(587\) 33.6812 1.39017 0.695085 0.718927i \(-0.255367\pi\)
0.695085 + 0.718927i \(0.255367\pi\)
\(588\) 0.258813 0.0106733
\(589\) 16.7912 0.691871
\(590\) 0 0
\(591\) 2.34237 0.0963522
\(592\) −17.1567 −0.705135
\(593\) 25.1034 1.03087 0.515437 0.856927i \(-0.327630\pi\)
0.515437 + 0.856927i \(0.327630\pi\)
\(594\) −0.221463 −0.00908673
\(595\) 0 0
\(596\) 6.74905 0.276452
\(597\) −2.48011 −0.101504
\(598\) 30.0721 1.22974
\(599\) −5.93752 −0.242601 −0.121300 0.992616i \(-0.538706\pi\)
−0.121300 + 0.992616i \(0.538706\pi\)
\(600\) 0 0
\(601\) −29.7235 −1.21245 −0.606223 0.795294i \(-0.707316\pi\)
−0.606223 + 0.795294i \(0.707316\pi\)
\(602\) −1.20729 −0.0492054
\(603\) −36.0159 −1.46668
\(604\) −6.13883 −0.249785
\(605\) 0 0
\(606\) 2.83816 0.115292
\(607\) −16.5792 −0.672929 −0.336464 0.941696i \(-0.609231\pi\)
−0.336464 + 0.941696i \(0.609231\pi\)
\(608\) 6.56580 0.266279
\(609\) −0.0741115 −0.00300315
\(610\) 0 0
\(611\) −28.7487 −1.16305
\(612\) −7.33934 −0.296675
\(613\) −39.4836 −1.59473 −0.797364 0.603499i \(-0.793773\pi\)
−0.797364 + 0.603499i \(0.793773\pi\)
\(614\) 0.0340952 0.00137597
\(615\) 0 0
\(616\) 0.709047 0.0285683
\(617\) −38.4323 −1.54723 −0.773613 0.633658i \(-0.781553\pi\)
−0.773613 + 0.633658i \(0.781553\pi\)
\(618\) −0.991014 −0.0398644
\(619\) 14.9244 0.599861 0.299931 0.953961i \(-0.403036\pi\)
0.299931 + 0.953961i \(0.403036\pi\)
\(620\) 0 0
\(621\) 5.22305 0.209594
\(622\) 27.3757 1.09767
\(623\) 7.77695 0.311577
\(624\) 1.36132 0.0544963
\(625\) 0 0
\(626\) −13.7528 −0.549672
\(627\) 0.0978535 0.00390789
\(628\) 2.41376 0.0963195
\(629\) −38.3006 −1.52715
\(630\) 0 0
\(631\) 30.8867 1.22958 0.614791 0.788690i \(-0.289241\pi\)
0.614791 + 0.788690i \(0.289241\pi\)
\(632\) −1.10479 −0.0439464
\(633\) −1.03334 −0.0410718
\(634\) 2.67331 0.106171
\(635\) 0 0
\(636\) −0.338597 −0.0134262
\(637\) 20.0717 0.795269
\(638\) 0.166956 0.00660986
\(639\) 28.3077 1.11984
\(640\) 0 0
\(641\) 31.6649 1.25069 0.625344 0.780349i \(-0.284959\pi\)
0.625344 + 0.780349i \(0.284959\pi\)
\(642\) −1.27652 −0.0503803
\(643\) 17.2630 0.680786 0.340393 0.940283i \(-0.389440\pi\)
0.340393 + 0.940283i \(0.389440\pi\)
\(644\) −2.46249 −0.0970359
\(645\) 0 0
\(646\) −31.1553 −1.22579
\(647\) −35.2693 −1.38658 −0.693289 0.720659i \(-0.743839\pi\)
−0.693289 + 0.720659i \(0.743839\pi\)
\(648\) −26.7203 −1.04967
\(649\) 2.56437 0.100661
\(650\) 0 0
\(651\) −0.642548 −0.0251834
\(652\) −3.06586 −0.120068
\(653\) 38.0371 1.48851 0.744253 0.667898i \(-0.232806\pi\)
0.744253 + 0.667898i \(0.232806\pi\)
\(654\) −0.677454 −0.0264905
\(655\) 0 0
\(656\) −34.3111 −1.33962
\(657\) −21.2014 −0.827147
\(658\) −11.2782 −0.439671
\(659\) −7.14619 −0.278376 −0.139188 0.990266i \(-0.544449\pi\)
−0.139188 + 0.990266i \(0.544449\pi\)
\(660\) 0 0
\(661\) 33.6588 1.30917 0.654587 0.755986i \(-0.272842\pi\)
0.654587 + 0.755986i \(0.272842\pi\)
\(662\) −36.1807 −1.40620
\(663\) 3.03901 0.118025
\(664\) 53.7100 2.08435
\(665\) 0 0
\(666\) −20.6445 −0.799960
\(667\) −3.93754 −0.152462
\(668\) 1.67656 0.0648682
\(669\) −1.95736 −0.0756759
\(670\) 0 0
\(671\) −0.832989 −0.0321572
\(672\) −0.251253 −0.00969229
\(673\) 4.10894 0.158388 0.0791939 0.996859i \(-0.474765\pi\)
0.0791939 + 0.996859i \(0.474765\pi\)
\(674\) −30.3360 −1.16850
\(675\) 0 0
\(676\) 0.542126 0.0208510
\(677\) 26.3822 1.01395 0.506976 0.861960i \(-0.330763\pi\)
0.506976 + 0.861960i \(0.330763\pi\)
\(678\) −0.588092 −0.0225855
\(679\) −8.09936 −0.310825
\(680\) 0 0
\(681\) 3.42229 0.131143
\(682\) 1.44751 0.0554281
\(683\) 18.1548 0.694676 0.347338 0.937740i \(-0.387086\pi\)
0.347338 + 0.937740i \(0.387086\pi\)
\(684\) 3.50525 0.134027
\(685\) 0 0
\(686\) 17.1585 0.655115
\(687\) 1.02361 0.0390532
\(688\) −2.90366 −0.110701
\(689\) −26.2591 −1.00039
\(690\) 0 0
\(691\) 28.1899 1.07239 0.536196 0.844093i \(-0.319861\pi\)
0.536196 + 0.844093i \(0.319861\pi\)
\(692\) −4.67212 −0.177607
\(693\) 0.701329 0.0266413
\(694\) 28.1315 1.06786
\(695\) 0 0
\(696\) −0.216843 −0.00821942
\(697\) −76.5962 −2.90129
\(698\) 24.2504 0.917890
\(699\) 0.548694 0.0207535
\(700\) 0 0
\(701\) 39.3669 1.48687 0.743434 0.668809i \(-0.233196\pi\)
0.743434 + 0.668809i \(0.233196\pi\)
\(702\) 3.28487 0.123980
\(703\) 18.2923 0.689907
\(704\) 2.02023 0.0761402
\(705\) 0 0
\(706\) 14.6342 0.550766
\(707\) −18.0237 −0.677853
\(708\) −0.490458 −0.0184326
\(709\) 48.4112 1.81812 0.909060 0.416664i \(-0.136801\pi\)
0.909060 + 0.416664i \(0.136801\pi\)
\(710\) 0 0
\(711\) −1.09277 −0.0409820
\(712\) 22.7546 0.852765
\(713\) −34.1386 −1.27850
\(714\) 1.19221 0.0446175
\(715\) 0 0
\(716\) 3.61950 0.135267
\(717\) 2.31772 0.0865569
\(718\) −0.188532 −0.00703595
\(719\) −10.8564 −0.404877 −0.202438 0.979295i \(-0.564887\pi\)
−0.202438 + 0.979295i \(0.564887\pi\)
\(720\) 0 0
\(721\) 6.29345 0.234380
\(722\) −9.56045 −0.355803
\(723\) 0.126224 0.00469433
\(724\) 3.04856 0.113299
\(725\) 0 0
\(726\) −1.77758 −0.0659723
\(727\) 37.5110 1.39121 0.695604 0.718426i \(-0.255137\pi\)
0.695604 + 0.718426i \(0.255137\pi\)
\(728\) −10.5170 −0.389787
\(729\) −26.1434 −0.968276
\(730\) 0 0
\(731\) −6.48215 −0.239751
\(732\) 0.159316 0.00588849
\(733\) 1.31177 0.0484512 0.0242256 0.999707i \(-0.492288\pi\)
0.0242256 + 0.999707i \(0.492288\pi\)
\(734\) −42.0173 −1.55089
\(735\) 0 0
\(736\) −13.3491 −0.492053
\(737\) 2.75105 0.101336
\(738\) −41.2863 −1.51977
\(739\) 52.6696 1.93748 0.968742 0.248072i \(-0.0797969\pi\)
0.968742 + 0.248072i \(0.0797969\pi\)
\(740\) 0 0
\(741\) −1.45142 −0.0533194
\(742\) −10.3015 −0.378182
\(743\) −44.6512 −1.63809 −0.819046 0.573728i \(-0.805497\pi\)
−0.819046 + 0.573728i \(0.805497\pi\)
\(744\) −1.88003 −0.0689254
\(745\) 0 0
\(746\) 22.8362 0.836091
\(747\) 53.1254 1.94376
\(748\) 0.560609 0.0204979
\(749\) 8.10656 0.296207
\(750\) 0 0
\(751\) −30.0001 −1.09472 −0.547360 0.836897i \(-0.684367\pi\)
−0.547360 + 0.836897i \(0.684367\pi\)
\(752\) −27.1254 −0.989160
\(753\) 1.56049 0.0568676
\(754\) −2.47640 −0.0901850
\(755\) 0 0
\(756\) −0.268986 −0.00978294
\(757\) −10.8998 −0.396160 −0.198080 0.980186i \(-0.563471\pi\)
−0.198080 + 0.980186i \(0.563471\pi\)
\(758\) −6.20568 −0.225400
\(759\) −0.198948 −0.00722135
\(760\) 0 0
\(761\) 54.3944 1.97180 0.985898 0.167348i \(-0.0535203\pi\)
0.985898 + 0.167348i \(0.0535203\pi\)
\(762\) −2.19917 −0.0796674
\(763\) 4.30218 0.155749
\(764\) 1.12564 0.0407242
\(765\) 0 0
\(766\) −18.9253 −0.683798
\(767\) −38.0364 −1.37341
\(768\) −1.01327 −0.0365633
\(769\) −16.9359 −0.610723 −0.305361 0.952237i \(-0.598777\pi\)
−0.305361 + 0.952237i \(0.598777\pi\)
\(770\) 0 0
\(771\) 1.53475 0.0552727
\(772\) 5.85954 0.210890
\(773\) 29.5026 1.06113 0.530567 0.847643i \(-0.321979\pi\)
0.530567 + 0.847643i \(0.321979\pi\)
\(774\) −3.49396 −0.125588
\(775\) 0 0
\(776\) −23.6980 −0.850707
\(777\) −0.699989 −0.0251120
\(778\) 6.30712 0.226121
\(779\) 36.5822 1.31069
\(780\) 0 0
\(781\) −2.16226 −0.0773718
\(782\) 63.3423 2.26512
\(783\) −0.430111 −0.0153709
\(784\) 18.9383 0.676368
\(785\) 0 0
\(786\) 0.167241 0.00596530
\(787\) 5.96992 0.212805 0.106402 0.994323i \(-0.466067\pi\)
0.106402 + 0.994323i \(0.466067\pi\)
\(788\) −6.40916 −0.228317
\(789\) 0.727113 0.0258859
\(790\) 0 0
\(791\) 3.73468 0.132790
\(792\) 2.05202 0.0729154
\(793\) 12.3554 0.438753
\(794\) 19.1610 0.679998
\(795\) 0 0
\(796\) 6.78605 0.240525
\(797\) −19.1226 −0.677357 −0.338679 0.940902i \(-0.609980\pi\)
−0.338679 + 0.940902i \(0.609980\pi\)
\(798\) −0.569399 −0.0201565
\(799\) −60.5548 −2.14227
\(800\) 0 0
\(801\) 22.5069 0.795243
\(802\) 8.64573 0.305291
\(803\) 1.61945 0.0571492
\(804\) −0.526161 −0.0185563
\(805\) 0 0
\(806\) −21.4704 −0.756262
\(807\) 1.82502 0.0642436
\(808\) −52.7358 −1.85524
\(809\) 34.3768 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(810\) 0 0
\(811\) 18.2250 0.639967 0.319984 0.947423i \(-0.396323\pi\)
0.319984 + 0.947423i \(0.396323\pi\)
\(812\) 0.202783 0.00711629
\(813\) 0.860393 0.0301753
\(814\) 1.57691 0.0552708
\(815\) 0 0
\(816\) 2.86741 0.100379
\(817\) 3.09586 0.108310
\(818\) −3.34360 −0.116906
\(819\) −10.4025 −0.363494
\(820\) 0 0
\(821\) 36.2130 1.26384 0.631920 0.775033i \(-0.282267\pi\)
0.631920 + 0.775033i \(0.282267\pi\)
\(822\) 1.87987 0.0655681
\(823\) 42.2212 1.47174 0.735869 0.677124i \(-0.236774\pi\)
0.735869 + 0.677124i \(0.236774\pi\)
\(824\) 18.4140 0.641483
\(825\) 0 0
\(826\) −14.9218 −0.519196
\(827\) −15.1566 −0.527048 −0.263524 0.964653i \(-0.584885\pi\)
−0.263524 + 0.964653i \(0.584885\pi\)
\(828\) −7.12660 −0.247666
\(829\) −3.49294 −0.121315 −0.0606575 0.998159i \(-0.519320\pi\)
−0.0606575 + 0.998159i \(0.519320\pi\)
\(830\) 0 0
\(831\) 3.17231 0.110046
\(832\) −29.9653 −1.03886
\(833\) 42.2780 1.46484
\(834\) 0.0180161 0.000623845 0
\(835\) 0 0
\(836\) −0.267746 −0.00926017
\(837\) −3.72907 −0.128895
\(838\) −16.9309 −0.584868
\(839\) −28.5020 −0.983999 −0.491999 0.870596i \(-0.663734\pi\)
−0.491999 + 0.870596i \(0.663734\pi\)
\(840\) 0 0
\(841\) −28.6757 −0.988819
\(842\) −8.40889 −0.289789
\(843\) −0.761550 −0.0262292
\(844\) 2.82743 0.0973240
\(845\) 0 0
\(846\) −32.6398 −1.12218
\(847\) 11.2886 0.387879
\(848\) −24.7764 −0.850824
\(849\) 0.438532 0.0150504
\(850\) 0 0
\(851\) −37.1904 −1.27487
\(852\) 0.413551 0.0141680
\(853\) −5.52236 −0.189082 −0.0945410 0.995521i \(-0.530138\pi\)
−0.0945410 + 0.995521i \(0.530138\pi\)
\(854\) 4.84707 0.165863
\(855\) 0 0
\(856\) 23.7190 0.810700
\(857\) 17.0172 0.581298 0.290649 0.956830i \(-0.406129\pi\)
0.290649 + 0.956830i \(0.406129\pi\)
\(858\) −0.125122 −0.00427160
\(859\) −1.16642 −0.0397979 −0.0198989 0.999802i \(-0.506334\pi\)
−0.0198989 + 0.999802i \(0.506334\pi\)
\(860\) 0 0
\(861\) −1.39989 −0.0477080
\(862\) 13.9333 0.474572
\(863\) 8.50057 0.289363 0.144681 0.989478i \(-0.453784\pi\)
0.144681 + 0.989478i \(0.453784\pi\)
\(864\) −1.45816 −0.0496077
\(865\) 0 0
\(866\) 32.9346 1.11916
\(867\) 4.25540 0.144521
\(868\) 1.75813 0.0596749
\(869\) 0.0834701 0.00283153
\(870\) 0 0
\(871\) −40.8052 −1.38263
\(872\) 12.5878 0.426275
\(873\) −23.4400 −0.793324
\(874\) −30.2522 −1.02329
\(875\) 0 0
\(876\) −0.309734 −0.0104649
\(877\) −7.37310 −0.248972 −0.124486 0.992221i \(-0.539728\pi\)
−0.124486 + 0.992221i \(0.539728\pi\)
\(878\) 18.8886 0.637460
\(879\) 2.49041 0.0839995
\(880\) 0 0
\(881\) −48.8726 −1.64656 −0.823279 0.567637i \(-0.807858\pi\)
−0.823279 + 0.567637i \(0.807858\pi\)
\(882\) 22.7884 0.767324
\(883\) 26.8006 0.901911 0.450956 0.892546i \(-0.351083\pi\)
0.450956 + 0.892546i \(0.351083\pi\)
\(884\) −8.31529 −0.279674
\(885\) 0 0
\(886\) 19.6404 0.659833
\(887\) 3.15346 0.105883 0.0529414 0.998598i \(-0.483140\pi\)
0.0529414 + 0.998598i \(0.483140\pi\)
\(888\) −2.04810 −0.0687298
\(889\) 13.9658 0.468399
\(890\) 0 0
\(891\) 2.01879 0.0676320
\(892\) 5.35571 0.179322
\(893\) 28.9208 0.967799
\(894\) −3.17283 −0.106115
\(895\) 0 0
\(896\) −7.77443 −0.259726
\(897\) 2.95092 0.0985282
\(898\) 40.1538 1.33995
\(899\) 2.81126 0.0937609
\(900\) 0 0
\(901\) −55.3109 −1.84267
\(902\) 3.15362 0.105004
\(903\) −0.118469 −0.00394240
\(904\) 10.9273 0.363438
\(905\) 0 0
\(906\) 2.88596 0.0958795
\(907\) 25.7319 0.854414 0.427207 0.904154i \(-0.359498\pi\)
0.427207 + 0.904154i \(0.359498\pi\)
\(908\) −9.36404 −0.310756
\(909\) −52.1617 −1.73010
\(910\) 0 0
\(911\) 10.3710 0.343606 0.171803 0.985131i \(-0.445041\pi\)
0.171803 + 0.985131i \(0.445041\pi\)
\(912\) −1.36947 −0.0453476
\(913\) −4.05793 −0.134298
\(914\) −12.1381 −0.401494
\(915\) 0 0
\(916\) −2.80079 −0.0925409
\(917\) −1.06207 −0.0350725
\(918\) 6.91909 0.228364
\(919\) −33.5553 −1.10689 −0.553444 0.832887i \(-0.686687\pi\)
−0.553444 + 0.832887i \(0.686687\pi\)
\(920\) 0 0
\(921\) 0.00334570 0.000110244 0
\(922\) 11.1334 0.366660
\(923\) 32.0720 1.05566
\(924\) 0.0102458 0.000337062 0
\(925\) 0 0
\(926\) 16.1324 0.530144
\(927\) 18.2136 0.598213
\(928\) 1.09928 0.0360855
\(929\) 11.6222 0.381314 0.190657 0.981657i \(-0.438938\pi\)
0.190657 + 0.981657i \(0.438938\pi\)
\(930\) 0 0
\(931\) −20.1919 −0.661762
\(932\) −1.50133 −0.0491777
\(933\) 2.68633 0.0879464
\(934\) 6.79792 0.222435
\(935\) 0 0
\(936\) −30.4369 −0.994860
\(937\) −46.3339 −1.51366 −0.756831 0.653611i \(-0.773253\pi\)
−0.756831 + 0.653611i \(0.773253\pi\)
\(938\) −16.0080 −0.522681
\(939\) −1.34954 −0.0440404
\(940\) 0 0
\(941\) −7.22995 −0.235690 −0.117845 0.993032i \(-0.537599\pi\)
−0.117845 + 0.993032i \(0.537599\pi\)
\(942\) −1.13474 −0.0369720
\(943\) −74.3759 −2.42201
\(944\) −35.8886 −1.16807
\(945\) 0 0
\(946\) 0.266883 0.00867711
\(947\) −30.3453 −0.986091 −0.493045 0.870004i \(-0.664116\pi\)
−0.493045 + 0.870004i \(0.664116\pi\)
\(948\) −0.0159644 −0.000518498 0
\(949\) −24.0207 −0.779745
\(950\) 0 0
\(951\) 0.262327 0.00850653
\(952\) −22.1525 −0.717967
\(953\) −4.89634 −0.158608 −0.0793040 0.996850i \(-0.525270\pi\)
−0.0793040 + 0.996850i \(0.525270\pi\)
\(954\) −29.8133 −0.965240
\(955\) 0 0
\(956\) −6.34172 −0.205106
\(957\) 0.0163831 0.000529590 0
\(958\) −37.3801 −1.20770
\(959\) −11.9382 −0.385503
\(960\) 0 0
\(961\) −6.62631 −0.213752
\(962\) −23.3898 −0.754116
\(963\) 23.4608 0.756015
\(964\) −0.345373 −0.0111237
\(965\) 0 0
\(966\) 1.15766 0.0372470
\(967\) −25.6038 −0.823363 −0.411681 0.911328i \(-0.635058\pi\)
−0.411681 + 0.911328i \(0.635058\pi\)
\(968\) 33.0292 1.06160
\(969\) −3.05720 −0.0982116
\(970\) 0 0
\(971\) 19.2440 0.617570 0.308785 0.951132i \(-0.400078\pi\)
0.308785 + 0.951132i \(0.400078\pi\)
\(972\) −1.16873 −0.0374870
\(973\) −0.114411 −0.00366785
\(974\) 46.6747 1.49555
\(975\) 0 0
\(976\) 11.6577 0.373155
\(977\) −14.0956 −0.450957 −0.225479 0.974248i \(-0.572395\pi\)
−0.225479 + 0.974248i \(0.572395\pi\)
\(978\) 1.44131 0.0460879
\(979\) −1.71917 −0.0549449
\(980\) 0 0
\(981\) 12.4507 0.397521
\(982\) −5.13606 −0.163898
\(983\) 50.6189 1.61449 0.807246 0.590216i \(-0.200957\pi\)
0.807246 + 0.590216i \(0.200957\pi\)
\(984\) −4.09593 −0.130574
\(985\) 0 0
\(986\) −5.21615 −0.166116
\(987\) −1.10671 −0.0352270
\(988\) 3.97137 0.126346
\(989\) −6.29425 −0.200145
\(990\) 0 0
\(991\) 15.7226 0.499444 0.249722 0.968318i \(-0.419661\pi\)
0.249722 + 0.968318i \(0.419661\pi\)
\(992\) 9.53074 0.302601
\(993\) −3.55034 −0.112667
\(994\) 12.5820 0.399076
\(995\) 0 0
\(996\) 0.776114 0.0245921
\(997\) 9.08507 0.287727 0.143864 0.989598i \(-0.454047\pi\)
0.143864 + 0.989598i \(0.454047\pi\)
\(998\) 11.9019 0.376747
\(999\) −4.06243 −0.128530
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 \(a_p\))