Properties

Label 6039.2.a.j.1.2
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.54331\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.54331 q^{2}\) \(+4.46845 q^{4}\) \(-0.329781 q^{5}\) \(+0.595463 q^{7}\) \(-6.27804 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.54331 q^{2}\) \(+4.46845 q^{4}\) \(-0.329781 q^{5}\) \(+0.595463 q^{7}\) \(-6.27804 q^{8}\) \(+0.838736 q^{10}\) \(+1.00000 q^{11}\) \(+0.0829823 q^{13}\) \(-1.51445 q^{14}\) \(+7.03014 q^{16}\) \(-6.96049 q^{17}\) \(+1.08146 q^{19}\) \(-1.47361 q^{20}\) \(-2.54331 q^{22}\) \(-3.20203 q^{23}\) \(-4.89124 q^{25}\) \(-0.211050 q^{26}\) \(+2.66080 q^{28}\) \(-8.72957 q^{29}\) \(-3.05943 q^{31}\) \(-5.32378 q^{32}\) \(+17.7027 q^{34}\) \(-0.196372 q^{35}\) \(-5.63463 q^{37}\) \(-2.75050 q^{38}\) \(+2.07038 q^{40}\) \(+0.0715670 q^{41}\) \(+11.3684 q^{43}\) \(+4.46845 q^{44}\) \(+8.14377 q^{46}\) \(-11.2549 q^{47}\) \(-6.64542 q^{49}\) \(+12.4400 q^{50}\) \(+0.370802 q^{52}\) \(+8.24041 q^{53}\) \(-0.329781 q^{55}\) \(-3.73835 q^{56}\) \(+22.2021 q^{58}\) \(+0.674261 q^{59}\) \(+1.00000 q^{61}\) \(+7.78108 q^{62}\) \(-0.520247 q^{64}\) \(-0.0273660 q^{65}\) \(+0.140859 q^{67}\) \(-31.1026 q^{68}\) \(+0.499437 q^{70}\) \(+12.8499 q^{71}\) \(-1.10649 q^{73}\) \(+14.3306 q^{74}\) \(+4.83247 q^{76}\) \(+0.595463 q^{77}\) \(+14.9245 q^{79}\) \(-2.31841 q^{80}\) \(-0.182017 q^{82}\) \(+1.08794 q^{83}\) \(+2.29543 q^{85}\) \(-28.9134 q^{86}\) \(-6.27804 q^{88}\) \(+1.53437 q^{89}\) \(+0.0494129 q^{91}\) \(-14.3081 q^{92}\) \(+28.6246 q^{94}\) \(-0.356646 q^{95}\) \(-8.74805 q^{97}\) \(+16.9014 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54331 −1.79840 −0.899198 0.437543i \(-0.855849\pi\)
−0.899198 + 0.437543i \(0.855849\pi\)
\(3\) 0 0
\(4\) 4.46845 2.23422
\(5\) −0.329781 −0.147482 −0.0737412 0.997277i \(-0.523494\pi\)
−0.0737412 + 0.997277i \(0.523494\pi\)
\(6\) 0 0
\(7\) 0.595463 0.225064 0.112532 0.993648i \(-0.464104\pi\)
0.112532 + 0.993648i \(0.464104\pi\)
\(8\) −6.27804 −2.21962
\(9\) 0 0
\(10\) 0.838736 0.265232
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 0.0829823 0.0230152 0.0115076 0.999934i \(-0.496337\pi\)
0.0115076 + 0.999934i \(0.496337\pi\)
\(14\) −1.51445 −0.404754
\(15\) 0 0
\(16\) 7.03014 1.75754
\(17\) −6.96049 −1.68817 −0.844083 0.536213i \(-0.819854\pi\)
−0.844083 + 0.536213i \(0.819854\pi\)
\(18\) 0 0
\(19\) 1.08146 0.248105 0.124052 0.992276i \(-0.460411\pi\)
0.124052 + 0.992276i \(0.460411\pi\)
\(20\) −1.47361 −0.329509
\(21\) 0 0
\(22\) −2.54331 −0.542237
\(23\) −3.20203 −0.667669 −0.333835 0.942632i \(-0.608343\pi\)
−0.333835 + 0.942632i \(0.608343\pi\)
\(24\) 0 0
\(25\) −4.89124 −0.978249
\(26\) −0.211050 −0.0413903
\(27\) 0 0
\(28\) 2.66080 0.502844
\(29\) −8.72957 −1.62104 −0.810521 0.585710i \(-0.800816\pi\)
−0.810521 + 0.585710i \(0.800816\pi\)
\(30\) 0 0
\(31\) −3.05943 −0.549489 −0.274745 0.961517i \(-0.588593\pi\)
−0.274745 + 0.961517i \(0.588593\pi\)
\(32\) −5.32378 −0.941119
\(33\) 0 0
\(34\) 17.7027 3.03599
\(35\) −0.196372 −0.0331930
\(36\) 0 0
\(37\) −5.63463 −0.926328 −0.463164 0.886273i \(-0.653286\pi\)
−0.463164 + 0.886273i \(0.653286\pi\)
\(38\) −2.75050 −0.446190
\(39\) 0 0
\(40\) 2.07038 0.327355
\(41\) 0.0715670 0.0111769 0.00558844 0.999984i \(-0.498221\pi\)
0.00558844 + 0.999984i \(0.498221\pi\)
\(42\) 0 0
\(43\) 11.3684 1.73366 0.866831 0.498603i \(-0.166153\pi\)
0.866831 + 0.498603i \(0.166153\pi\)
\(44\) 4.46845 0.673644
\(45\) 0 0
\(46\) 8.14377 1.20073
\(47\) −11.2549 −1.64169 −0.820845 0.571151i \(-0.806497\pi\)
−0.820845 + 0.571151i \(0.806497\pi\)
\(48\) 0 0
\(49\) −6.64542 −0.949346
\(50\) 12.4400 1.75928
\(51\) 0 0
\(52\) 0.370802 0.0514210
\(53\) 8.24041 1.13191 0.565954 0.824437i \(-0.308508\pi\)
0.565954 + 0.824437i \(0.308508\pi\)
\(54\) 0 0
\(55\) −0.329781 −0.0444676
\(56\) −3.73835 −0.499557
\(57\) 0 0
\(58\) 22.2021 2.91527
\(59\) 0.674261 0.0877813 0.0438907 0.999036i \(-0.486025\pi\)
0.0438907 + 0.999036i \(0.486025\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 7.78108 0.988199
\(63\) 0 0
\(64\) −0.520247 −0.0650309
\(65\) −0.0273660 −0.00339433
\(66\) 0 0
\(67\) 0.140859 0.0172087 0.00860433 0.999963i \(-0.497261\pi\)
0.00860433 + 0.999963i \(0.497261\pi\)
\(68\) −31.1026 −3.77174
\(69\) 0 0
\(70\) 0.499437 0.0596941
\(71\) 12.8499 1.52500 0.762500 0.646988i \(-0.223972\pi\)
0.762500 + 0.646988i \(0.223972\pi\)
\(72\) 0 0
\(73\) −1.10649 −0.129505 −0.0647527 0.997901i \(-0.520626\pi\)
−0.0647527 + 0.997901i \(0.520626\pi\)
\(74\) 14.3306 1.66590
\(75\) 0 0
\(76\) 4.83247 0.554322
\(77\) 0.595463 0.0678594
\(78\) 0 0
\(79\) 14.9245 1.67913 0.839567 0.543256i \(-0.182809\pi\)
0.839567 + 0.543256i \(0.182809\pi\)
\(80\) −2.31841 −0.259206
\(81\) 0 0
\(82\) −0.182017 −0.0201005
\(83\) 1.08794 0.119417 0.0597087 0.998216i \(-0.480983\pi\)
0.0597087 + 0.998216i \(0.480983\pi\)
\(84\) 0 0
\(85\) 2.29543 0.248975
\(86\) −28.9134 −3.11781
\(87\) 0 0
\(88\) −6.27804 −0.669242
\(89\) 1.53437 0.162642 0.0813212 0.996688i \(-0.474086\pi\)
0.0813212 + 0.996688i \(0.474086\pi\)
\(90\) 0 0
\(91\) 0.0494129 0.00517988
\(92\) −14.3081 −1.49172
\(93\) 0 0
\(94\) 28.6246 2.95241
\(95\) −0.356646 −0.0365911
\(96\) 0 0
\(97\) −8.74805 −0.888230 −0.444115 0.895970i \(-0.646482\pi\)
−0.444115 + 0.895970i \(0.646482\pi\)
\(98\) 16.9014 1.70730
\(99\) 0 0
\(100\) −21.8563 −2.18563
\(101\) −9.88085 −0.983181 −0.491590 0.870827i \(-0.663584\pi\)
−0.491590 + 0.870827i \(0.663584\pi\)
\(102\) 0 0
\(103\) −7.23771 −0.713153 −0.356577 0.934266i \(-0.616056\pi\)
−0.356577 + 0.934266i \(0.616056\pi\)
\(104\) −0.520967 −0.0510850
\(105\) 0 0
\(106\) −20.9580 −2.03562
\(107\) 16.9166 1.63539 0.817695 0.575652i \(-0.195252\pi\)
0.817695 + 0.575652i \(0.195252\pi\)
\(108\) 0 0
\(109\) 5.79446 0.555008 0.277504 0.960724i \(-0.410493\pi\)
0.277504 + 0.960724i \(0.410493\pi\)
\(110\) 0.838736 0.0799704
\(111\) 0 0
\(112\) 4.18619 0.395558
\(113\) 12.3271 1.15964 0.579818 0.814746i \(-0.303124\pi\)
0.579818 + 0.814746i \(0.303124\pi\)
\(114\) 0 0
\(115\) 1.05597 0.0984695
\(116\) −39.0077 −3.62177
\(117\) 0 0
\(118\) −1.71486 −0.157865
\(119\) −4.14471 −0.379945
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −2.54331 −0.230261
\(123\) 0 0
\(124\) −13.6709 −1.22768
\(125\) 3.26194 0.291757
\(126\) 0 0
\(127\) −7.99339 −0.709299 −0.354649 0.934999i \(-0.615400\pi\)
−0.354649 + 0.934999i \(0.615400\pi\)
\(128\) 11.9707 1.05807
\(129\) 0 0
\(130\) 0.0696003 0.00610435
\(131\) 15.8726 1.38680 0.693398 0.720555i \(-0.256113\pi\)
0.693398 + 0.720555i \(0.256113\pi\)
\(132\) 0 0
\(133\) 0.643972 0.0558395
\(134\) −0.358249 −0.0309480
\(135\) 0 0
\(136\) 43.6982 3.74709
\(137\) 16.9666 1.44956 0.724778 0.688983i \(-0.241942\pi\)
0.724778 + 0.688983i \(0.241942\pi\)
\(138\) 0 0
\(139\) 15.7351 1.33463 0.667315 0.744775i \(-0.267443\pi\)
0.667315 + 0.744775i \(0.267443\pi\)
\(140\) −0.877480 −0.0741606
\(141\) 0 0
\(142\) −32.6813 −2.74255
\(143\) 0.0829823 0.00693933
\(144\) 0 0
\(145\) 2.87885 0.239075
\(146\) 2.81416 0.232902
\(147\) 0 0
\(148\) −25.1781 −2.06963
\(149\) 15.3791 1.25990 0.629950 0.776635i \(-0.283075\pi\)
0.629950 + 0.776635i \(0.283075\pi\)
\(150\) 0 0
\(151\) 16.5708 1.34851 0.674257 0.738497i \(-0.264464\pi\)
0.674257 + 0.738497i \(0.264464\pi\)
\(152\) −6.78948 −0.550699
\(153\) 0 0
\(154\) −1.51445 −0.122038
\(155\) 1.00894 0.0810400
\(156\) 0 0
\(157\) −6.06333 −0.483907 −0.241953 0.970288i \(-0.577788\pi\)
−0.241953 + 0.970288i \(0.577788\pi\)
\(158\) −37.9576 −3.01975
\(159\) 0 0
\(160\) 1.75568 0.138799
\(161\) −1.90669 −0.150268
\(162\) 0 0
\(163\) 17.8621 1.39907 0.699535 0.714598i \(-0.253390\pi\)
0.699535 + 0.714598i \(0.253390\pi\)
\(164\) 0.319793 0.0249717
\(165\) 0 0
\(166\) −2.76698 −0.214759
\(167\) −21.2052 −1.64091 −0.820455 0.571711i \(-0.806280\pi\)
−0.820455 + 0.571711i \(0.806280\pi\)
\(168\) 0 0
\(169\) −12.9931 −0.999470
\(170\) −5.83801 −0.447755
\(171\) 0 0
\(172\) 50.7990 3.87339
\(173\) −2.96793 −0.225647 −0.112824 0.993615i \(-0.535990\pi\)
−0.112824 + 0.993615i \(0.535990\pi\)
\(174\) 0 0
\(175\) −2.91256 −0.220169
\(176\) 7.03014 0.529917
\(177\) 0 0
\(178\) −3.90237 −0.292495
\(179\) −1.16838 −0.0873291 −0.0436646 0.999046i \(-0.513903\pi\)
−0.0436646 + 0.999046i \(0.513903\pi\)
\(180\) 0 0
\(181\) −11.0228 −0.819318 −0.409659 0.912239i \(-0.634352\pi\)
−0.409659 + 0.912239i \(0.634352\pi\)
\(182\) −0.125673 −0.00931548
\(183\) 0 0
\(184\) 20.1025 1.48197
\(185\) 1.85819 0.136617
\(186\) 0 0
\(187\) −6.96049 −0.509001
\(188\) −50.2918 −3.66790
\(189\) 0 0
\(190\) 0.907063 0.0658052
\(191\) 15.3640 1.11170 0.555849 0.831283i \(-0.312393\pi\)
0.555849 + 0.831283i \(0.312393\pi\)
\(192\) 0 0
\(193\) −11.1185 −0.800324 −0.400162 0.916444i \(-0.631046\pi\)
−0.400162 + 0.916444i \(0.631046\pi\)
\(194\) 22.2490 1.59739
\(195\) 0 0
\(196\) −29.6947 −2.12105
\(197\) 17.7144 1.26210 0.631050 0.775742i \(-0.282624\pi\)
0.631050 + 0.775742i \(0.282624\pi\)
\(198\) 0 0
\(199\) 24.5173 1.73798 0.868992 0.494826i \(-0.164768\pi\)
0.868992 + 0.494826i \(0.164768\pi\)
\(200\) 30.7074 2.17134
\(201\) 0 0
\(202\) 25.1301 1.76815
\(203\) −5.19814 −0.364838
\(204\) 0 0
\(205\) −0.0236014 −0.00164839
\(206\) 18.4078 1.28253
\(207\) 0 0
\(208\) 0.583378 0.0404500
\(209\) 1.08146 0.0748064
\(210\) 0 0
\(211\) 9.34349 0.643232 0.321616 0.946870i \(-0.395774\pi\)
0.321616 + 0.946870i \(0.395774\pi\)
\(212\) 36.8219 2.52894
\(213\) 0 0
\(214\) −43.0243 −2.94108
\(215\) −3.74907 −0.255685
\(216\) 0 0
\(217\) −1.82178 −0.123670
\(218\) −14.7371 −0.998124
\(219\) 0 0
\(220\) −1.47361 −0.0993507
\(221\) −0.577597 −0.0388534
\(222\) 0 0
\(223\) −23.8528 −1.59730 −0.798652 0.601793i \(-0.794453\pi\)
−0.798652 + 0.601793i \(0.794453\pi\)
\(224\) −3.17011 −0.211812
\(225\) 0 0
\(226\) −31.3517 −2.08548
\(227\) −4.98647 −0.330964 −0.165482 0.986213i \(-0.552918\pi\)
−0.165482 + 0.986213i \(0.552918\pi\)
\(228\) 0 0
\(229\) 0.915859 0.0605217 0.0302608 0.999542i \(-0.490366\pi\)
0.0302608 + 0.999542i \(0.490366\pi\)
\(230\) −2.68566 −0.177087
\(231\) 0 0
\(232\) 54.8046 3.59810
\(233\) −7.32305 −0.479749 −0.239875 0.970804i \(-0.577106\pi\)
−0.239875 + 0.970804i \(0.577106\pi\)
\(234\) 0 0
\(235\) 3.71164 0.242120
\(236\) 3.01290 0.196123
\(237\) 0 0
\(238\) 10.5413 0.683292
\(239\) 24.5442 1.58763 0.793817 0.608157i \(-0.208091\pi\)
0.793817 + 0.608157i \(0.208091\pi\)
\(240\) 0 0
\(241\) 18.3505 1.18206 0.591031 0.806649i \(-0.298721\pi\)
0.591031 + 0.806649i \(0.298721\pi\)
\(242\) −2.54331 −0.163490
\(243\) 0 0
\(244\) 4.46845 0.286063
\(245\) 2.19153 0.140012
\(246\) 0 0
\(247\) 0.0897424 0.00571017
\(248\) 19.2072 1.21966
\(249\) 0 0
\(250\) −8.29614 −0.524694
\(251\) −2.34673 −0.148125 −0.0740623 0.997254i \(-0.523596\pi\)
−0.0740623 + 0.997254i \(0.523596\pi\)
\(252\) 0 0
\(253\) −3.20203 −0.201310
\(254\) 20.3297 1.27560
\(255\) 0 0
\(256\) −29.4048 −1.83780
\(257\) 2.07933 0.129705 0.0648527 0.997895i \(-0.479342\pi\)
0.0648527 + 0.997895i \(0.479342\pi\)
\(258\) 0 0
\(259\) −3.35522 −0.208483
\(260\) −0.122283 −0.00758370
\(261\) 0 0
\(262\) −40.3690 −2.49401
\(263\) 24.1181 1.48718 0.743591 0.668634i \(-0.233121\pi\)
0.743591 + 0.668634i \(0.233121\pi\)
\(264\) 0 0
\(265\) −2.71753 −0.166936
\(266\) −1.63782 −0.100421
\(267\) 0 0
\(268\) 0.629421 0.0384480
\(269\) 13.9942 0.853243 0.426622 0.904430i \(-0.359704\pi\)
0.426622 + 0.904430i \(0.359704\pi\)
\(270\) 0 0
\(271\) −24.2791 −1.47485 −0.737426 0.675428i \(-0.763959\pi\)
−0.737426 + 0.675428i \(0.763959\pi\)
\(272\) −48.9332 −2.96701
\(273\) 0 0
\(274\) −43.1514 −2.60687
\(275\) −4.89124 −0.294953
\(276\) 0 0
\(277\) −16.3119 −0.980085 −0.490043 0.871699i \(-0.663019\pi\)
−0.490043 + 0.871699i \(0.663019\pi\)
\(278\) −40.0192 −2.40019
\(279\) 0 0
\(280\) 1.23283 0.0736759
\(281\) −13.7085 −0.817778 −0.408889 0.912584i \(-0.634084\pi\)
−0.408889 + 0.912584i \(0.634084\pi\)
\(282\) 0 0
\(283\) 31.0223 1.84409 0.922043 0.387087i \(-0.126519\pi\)
0.922043 + 0.387087i \(0.126519\pi\)
\(284\) 57.4190 3.40719
\(285\) 0 0
\(286\) −0.211050 −0.0124797
\(287\) 0.0426155 0.00251551
\(288\) 0 0
\(289\) 31.4484 1.84990
\(290\) −7.32181 −0.429951
\(291\) 0 0
\(292\) −4.94431 −0.289344
\(293\) −4.76769 −0.278531 −0.139266 0.990255i \(-0.544474\pi\)
−0.139266 + 0.990255i \(0.544474\pi\)
\(294\) 0 0
\(295\) −0.222358 −0.0129462
\(296\) 35.3745 2.05610
\(297\) 0 0
\(298\) −39.1138 −2.26580
\(299\) −0.265712 −0.0153665
\(300\) 0 0
\(301\) 6.76945 0.390185
\(302\) −42.1448 −2.42516
\(303\) 0 0
\(304\) 7.60284 0.436053
\(305\) −0.329781 −0.0188832
\(306\) 0 0
\(307\) −9.09194 −0.518905 −0.259452 0.965756i \(-0.583542\pi\)
−0.259452 + 0.965756i \(0.583542\pi\)
\(308\) 2.66080 0.151613
\(309\) 0 0
\(310\) −2.56605 −0.145742
\(311\) −0.130155 −0.00738041 −0.00369020 0.999993i \(-0.501175\pi\)
−0.00369020 + 0.999993i \(0.501175\pi\)
\(312\) 0 0
\(313\) −18.8073 −1.06305 −0.531526 0.847042i \(-0.678381\pi\)
−0.531526 + 0.847042i \(0.678381\pi\)
\(314\) 15.4210 0.870255
\(315\) 0 0
\(316\) 66.6892 3.75156
\(317\) −21.5314 −1.20932 −0.604661 0.796483i \(-0.706692\pi\)
−0.604661 + 0.796483i \(0.706692\pi\)
\(318\) 0 0
\(319\) −8.72957 −0.488762
\(320\) 0.171568 0.00959092
\(321\) 0 0
\(322\) 4.84931 0.270242
\(323\) −7.52751 −0.418842
\(324\) 0 0
\(325\) −0.405887 −0.0225146
\(326\) −45.4290 −2.51608
\(327\) 0 0
\(328\) −0.449301 −0.0248085
\(329\) −6.70186 −0.369485
\(330\) 0 0
\(331\) −5.77423 −0.317380 −0.158690 0.987328i \(-0.550727\pi\)
−0.158690 + 0.987328i \(0.550727\pi\)
\(332\) 4.86142 0.266805
\(333\) 0 0
\(334\) 53.9316 2.95100
\(335\) −0.0464526 −0.00253797
\(336\) 0 0
\(337\) −16.2916 −0.887462 −0.443731 0.896160i \(-0.646345\pi\)
−0.443731 + 0.896160i \(0.646345\pi\)
\(338\) 33.0456 1.79744
\(339\) 0 0
\(340\) 10.2570 0.556266
\(341\) −3.05943 −0.165677
\(342\) 0 0
\(343\) −8.12535 −0.438728
\(344\) −71.3712 −3.84808
\(345\) 0 0
\(346\) 7.54837 0.405803
\(347\) 18.5188 0.994143 0.497072 0.867710i \(-0.334409\pi\)
0.497072 + 0.867710i \(0.334409\pi\)
\(348\) 0 0
\(349\) 9.92712 0.531387 0.265693 0.964058i \(-0.414399\pi\)
0.265693 + 0.964058i \(0.414399\pi\)
\(350\) 7.40755 0.395950
\(351\) 0 0
\(352\) −5.32378 −0.283758
\(353\) −14.8318 −0.789415 −0.394707 0.918807i \(-0.629154\pi\)
−0.394707 + 0.918807i \(0.629154\pi\)
\(354\) 0 0
\(355\) −4.23764 −0.224911
\(356\) 6.85623 0.363380
\(357\) 0 0
\(358\) 2.97157 0.157052
\(359\) −27.5857 −1.45592 −0.727959 0.685621i \(-0.759531\pi\)
−0.727959 + 0.685621i \(0.759531\pi\)
\(360\) 0 0
\(361\) −17.8304 −0.938444
\(362\) 28.0344 1.47346
\(363\) 0 0
\(364\) 0.220799 0.0115730
\(365\) 0.364900 0.0190998
\(366\) 0 0
\(367\) −25.3367 −1.32256 −0.661281 0.750138i \(-0.729987\pi\)
−0.661281 + 0.750138i \(0.729987\pi\)
\(368\) −22.5107 −1.17345
\(369\) 0 0
\(370\) −4.72597 −0.245692
\(371\) 4.90686 0.254752
\(372\) 0 0
\(373\) 22.9549 1.18856 0.594281 0.804258i \(-0.297437\pi\)
0.594281 + 0.804258i \(0.297437\pi\)
\(374\) 17.7027 0.915385
\(375\) 0 0
\(376\) 70.6585 3.64393
\(377\) −0.724400 −0.0373085
\(378\) 0 0
\(379\) −2.82059 −0.144884 −0.0724420 0.997373i \(-0.523079\pi\)
−0.0724420 + 0.997373i \(0.523079\pi\)
\(380\) −1.59365 −0.0817527
\(381\) 0 0
\(382\) −39.0754 −1.99927
\(383\) −25.6130 −1.30876 −0.654382 0.756164i \(-0.727071\pi\)
−0.654382 + 0.756164i \(0.727071\pi\)
\(384\) 0 0
\(385\) −0.196372 −0.0100081
\(386\) 28.2777 1.43930
\(387\) 0 0
\(388\) −39.0902 −1.98450
\(389\) 2.02580 0.102712 0.0513562 0.998680i \(-0.483646\pi\)
0.0513562 + 0.998680i \(0.483646\pi\)
\(390\) 0 0
\(391\) 22.2877 1.12714
\(392\) 41.7203 2.10719
\(393\) 0 0
\(394\) −45.0533 −2.26975
\(395\) −4.92180 −0.247643
\(396\) 0 0
\(397\) 1.07995 0.0542011 0.0271006 0.999633i \(-0.491373\pi\)
0.0271006 + 0.999633i \(0.491373\pi\)
\(398\) −62.3552 −3.12558
\(399\) 0 0
\(400\) −34.3861 −1.71931
\(401\) −3.50052 −0.174807 −0.0874037 0.996173i \(-0.527857\pi\)
−0.0874037 + 0.996173i \(0.527857\pi\)
\(402\) 0 0
\(403\) −0.253878 −0.0126466
\(404\) −44.1521 −2.19665
\(405\) 0 0
\(406\) 13.2205 0.656123
\(407\) −5.63463 −0.279298
\(408\) 0 0
\(409\) −27.1693 −1.34344 −0.671719 0.740806i \(-0.734444\pi\)
−0.671719 + 0.740806i \(0.734444\pi\)
\(410\) 0.0600258 0.00296446
\(411\) 0 0
\(412\) −32.3414 −1.59334
\(413\) 0.401498 0.0197564
\(414\) 0 0
\(415\) −0.358783 −0.0176120
\(416\) −0.441779 −0.0216600
\(417\) 0 0
\(418\) −2.75050 −0.134531
\(419\) 15.6757 0.765810 0.382905 0.923788i \(-0.374924\pi\)
0.382905 + 0.923788i \(0.374924\pi\)
\(420\) 0 0
\(421\) −1.40707 −0.0685762 −0.0342881 0.999412i \(-0.510916\pi\)
−0.0342881 + 0.999412i \(0.510916\pi\)
\(422\) −23.7634 −1.15679
\(423\) 0 0
\(424\) −51.7337 −2.51241
\(425\) 34.0454 1.65145
\(426\) 0 0
\(427\) 0.595463 0.0288165
\(428\) 75.5910 3.65383
\(429\) 0 0
\(430\) 9.53507 0.459822
\(431\) 23.5382 1.13379 0.566897 0.823789i \(-0.308144\pi\)
0.566897 + 0.823789i \(0.308144\pi\)
\(432\) 0 0
\(433\) 29.2710 1.40668 0.703338 0.710856i \(-0.251692\pi\)
0.703338 + 0.710856i \(0.251692\pi\)
\(434\) 4.63335 0.222408
\(435\) 0 0
\(436\) 25.8922 1.24001
\(437\) −3.46288 −0.165652
\(438\) 0 0
\(439\) −17.0691 −0.814664 −0.407332 0.913280i \(-0.633541\pi\)
−0.407332 + 0.913280i \(0.633541\pi\)
\(440\) 2.07038 0.0987014
\(441\) 0 0
\(442\) 1.46901 0.0698738
\(443\) 32.9257 1.56435 0.782173 0.623061i \(-0.214111\pi\)
0.782173 + 0.623061i \(0.214111\pi\)
\(444\) 0 0
\(445\) −0.506004 −0.0239869
\(446\) 60.6653 2.87258
\(447\) 0 0
\(448\) −0.309788 −0.0146361
\(449\) 30.7700 1.45213 0.726064 0.687627i \(-0.241348\pi\)
0.726064 + 0.687627i \(0.241348\pi\)
\(450\) 0 0
\(451\) 0.0715670 0.00336996
\(452\) 55.0831 2.59089
\(453\) 0 0
\(454\) 12.6822 0.595204
\(455\) −0.0162954 −0.000763942 0
\(456\) 0 0
\(457\) −11.8994 −0.556632 −0.278316 0.960490i \(-0.589776\pi\)
−0.278316 + 0.960490i \(0.589776\pi\)
\(458\) −2.32932 −0.108842
\(459\) 0 0
\(460\) 4.71854 0.220003
\(461\) −9.53778 −0.444218 −0.222109 0.975022i \(-0.571294\pi\)
−0.222109 + 0.975022i \(0.571294\pi\)
\(462\) 0 0
\(463\) 22.8038 1.05978 0.529890 0.848066i \(-0.322233\pi\)
0.529890 + 0.848066i \(0.322233\pi\)
\(464\) −61.3701 −2.84904
\(465\) 0 0
\(466\) 18.6248 0.862778
\(467\) −41.0776 −1.90084 −0.950422 0.310962i \(-0.899349\pi\)
−0.950422 + 0.310962i \(0.899349\pi\)
\(468\) 0 0
\(469\) 0.0838763 0.00387305
\(470\) −9.43986 −0.435428
\(471\) 0 0
\(472\) −4.23304 −0.194842
\(473\) 11.3684 0.522719
\(474\) 0 0
\(475\) −5.28970 −0.242708
\(476\) −18.5204 −0.848883
\(477\) 0 0
\(478\) −62.4237 −2.85519
\(479\) 11.8369 0.540841 0.270421 0.962742i \(-0.412837\pi\)
0.270421 + 0.962742i \(0.412837\pi\)
\(480\) 0 0
\(481\) −0.467575 −0.0213196
\(482\) −46.6712 −2.12581
\(483\) 0 0
\(484\) 4.46845 0.203111
\(485\) 2.88494 0.130998
\(486\) 0 0
\(487\) 23.2203 1.05221 0.526105 0.850420i \(-0.323652\pi\)
0.526105 + 0.850420i \(0.323652\pi\)
\(488\) −6.27804 −0.284194
\(489\) 0 0
\(490\) −5.57376 −0.251797
\(491\) 10.6561 0.480901 0.240451 0.970661i \(-0.422705\pi\)
0.240451 + 0.970661i \(0.422705\pi\)
\(492\) 0 0
\(493\) 60.7621 2.73659
\(494\) −0.228243 −0.0102691
\(495\) 0 0
\(496\) −21.5082 −0.965747
\(497\) 7.65163 0.343223
\(498\) 0 0
\(499\) 41.6152 1.86295 0.931475 0.363804i \(-0.118522\pi\)
0.931475 + 0.363804i \(0.118522\pi\)
\(500\) 14.5758 0.651851
\(501\) 0 0
\(502\) 5.96848 0.266386
\(503\) −31.7709 −1.41660 −0.708298 0.705914i \(-0.750537\pi\)
−0.708298 + 0.705914i \(0.750537\pi\)
\(504\) 0 0
\(505\) 3.25851 0.145002
\(506\) 8.14377 0.362035
\(507\) 0 0
\(508\) −35.7181 −1.58473
\(509\) −29.3708 −1.30184 −0.650920 0.759147i \(-0.725617\pi\)
−0.650920 + 0.759147i \(0.725617\pi\)
\(510\) 0 0
\(511\) −0.658877 −0.0291470
\(512\) 50.8442 2.24702
\(513\) 0 0
\(514\) −5.28840 −0.233261
\(515\) 2.38686 0.105178
\(516\) 0 0
\(517\) −11.2549 −0.494988
\(518\) 8.53338 0.374935
\(519\) 0 0
\(520\) 0.171805 0.00753414
\(521\) 3.61714 0.158470 0.0792350 0.996856i \(-0.474752\pi\)
0.0792350 + 0.996856i \(0.474752\pi\)
\(522\) 0 0
\(523\) −21.7716 −0.952004 −0.476002 0.879444i \(-0.657914\pi\)
−0.476002 + 0.879444i \(0.657914\pi\)
\(524\) 70.9259 3.09841
\(525\) 0 0
\(526\) −61.3398 −2.67454
\(527\) 21.2951 0.927629
\(528\) 0 0
\(529\) −12.7470 −0.554218
\(530\) 6.91153 0.300218
\(531\) 0 0
\(532\) 2.87756 0.124758
\(533\) 0.00593879 0.000257238 0
\(534\) 0 0
\(535\) −5.57877 −0.241191
\(536\) −0.884319 −0.0381967
\(537\) 0 0
\(538\) −35.5917 −1.53447
\(539\) −6.64542 −0.286239
\(540\) 0 0
\(541\) 39.5580 1.70073 0.850366 0.526191i \(-0.176380\pi\)
0.850366 + 0.526191i \(0.176380\pi\)
\(542\) 61.7494 2.65236
\(543\) 0 0
\(544\) 37.0561 1.58877
\(545\) −1.91090 −0.0818540
\(546\) 0 0
\(547\) 22.9213 0.980046 0.490023 0.871710i \(-0.336988\pi\)
0.490023 + 0.871710i \(0.336988\pi\)
\(548\) 75.8144 3.23863
\(549\) 0 0
\(550\) 12.4400 0.530442
\(551\) −9.44072 −0.402188
\(552\) 0 0
\(553\) 8.88697 0.377913
\(554\) 41.4862 1.76258
\(555\) 0 0
\(556\) 70.3113 2.98186
\(557\) −4.36360 −0.184892 −0.0924458 0.995718i \(-0.529468\pi\)
−0.0924458 + 0.995718i \(0.529468\pi\)
\(558\) 0 0
\(559\) 0.943374 0.0399005
\(560\) −1.38053 −0.0583378
\(561\) 0 0
\(562\) 34.8649 1.47069
\(563\) −7.88133 −0.332158 −0.166079 0.986112i \(-0.553111\pi\)
−0.166079 + 0.986112i \(0.553111\pi\)
\(564\) 0 0
\(565\) −4.06524 −0.171026
\(566\) −78.8995 −3.31640
\(567\) 0 0
\(568\) −80.6721 −3.38493
\(569\) −19.5591 −0.819961 −0.409980 0.912094i \(-0.634464\pi\)
−0.409980 + 0.912094i \(0.634464\pi\)
\(570\) 0 0
\(571\) 37.0732 1.55147 0.775733 0.631061i \(-0.217380\pi\)
0.775733 + 0.631061i \(0.217380\pi\)
\(572\) 0.370802 0.0155040
\(573\) 0 0
\(574\) −0.108385 −0.00452389
\(575\) 15.6619 0.653147
\(576\) 0 0
\(577\) 20.2481 0.842941 0.421471 0.906842i \(-0.361514\pi\)
0.421471 + 0.906842i \(0.361514\pi\)
\(578\) −79.9831 −3.32686
\(579\) 0 0
\(580\) 12.8640 0.534147
\(581\) 0.647830 0.0268765
\(582\) 0 0
\(583\) 8.24041 0.341283
\(584\) 6.94662 0.287453
\(585\) 0 0
\(586\) 12.1257 0.500910
\(587\) 14.4483 0.596343 0.298172 0.954512i \(-0.403623\pi\)
0.298172 + 0.954512i \(0.403623\pi\)
\(588\) 0 0
\(589\) −3.30866 −0.136331
\(590\) 0.565527 0.0232824
\(591\) 0 0
\(592\) −39.6123 −1.62805
\(593\) 14.6070 0.599839 0.299920 0.953964i \(-0.403040\pi\)
0.299920 + 0.953964i \(0.403040\pi\)
\(594\) 0 0
\(595\) 1.36685 0.0560353
\(596\) 68.7205 2.81490
\(597\) 0 0
\(598\) 0.675789 0.0276351
\(599\) −3.38693 −0.138386 −0.0691932 0.997603i \(-0.522042\pi\)
−0.0691932 + 0.997603i \(0.522042\pi\)
\(600\) 0 0
\(601\) 25.0307 1.02102 0.510512 0.859871i \(-0.329456\pi\)
0.510512 + 0.859871i \(0.329456\pi\)
\(602\) −17.2168 −0.701706
\(603\) 0 0
\(604\) 74.0459 3.01288
\(605\) −0.329781 −0.0134075
\(606\) 0 0
\(607\) 41.4522 1.68249 0.841246 0.540652i \(-0.181822\pi\)
0.841246 + 0.540652i \(0.181822\pi\)
\(608\) −5.75747 −0.233496
\(609\) 0 0
\(610\) 0.838736 0.0339594
\(611\) −0.933954 −0.0377837
\(612\) 0 0
\(613\) −22.4905 −0.908383 −0.454191 0.890904i \(-0.650072\pi\)
−0.454191 + 0.890904i \(0.650072\pi\)
\(614\) 23.1237 0.933195
\(615\) 0 0
\(616\) −3.73835 −0.150622
\(617\) −19.0197 −0.765703 −0.382851 0.923810i \(-0.625058\pi\)
−0.382851 + 0.923810i \(0.625058\pi\)
\(618\) 0 0
\(619\) −19.8223 −0.796727 −0.398364 0.917228i \(-0.630422\pi\)
−0.398364 + 0.917228i \(0.630422\pi\)
\(620\) 4.50840 0.181062
\(621\) 0 0
\(622\) 0.331025 0.0132729
\(623\) 0.913658 0.0366050
\(624\) 0 0
\(625\) 23.3805 0.935220
\(626\) 47.8329 1.91179
\(627\) 0 0
\(628\) −27.0937 −1.08116
\(629\) 39.2198 1.56380
\(630\) 0 0
\(631\) −8.96489 −0.356886 −0.178443 0.983950i \(-0.557106\pi\)
−0.178443 + 0.983950i \(0.557106\pi\)
\(632\) −93.6965 −3.72704
\(633\) 0 0
\(634\) 54.7611 2.17484
\(635\) 2.63607 0.104609
\(636\) 0 0
\(637\) −0.551453 −0.0218494
\(638\) 22.2021 0.878988
\(639\) 0 0
\(640\) −3.94771 −0.156047
\(641\) 2.96210 0.116996 0.0584980 0.998288i \(-0.481369\pi\)
0.0584980 + 0.998288i \(0.481369\pi\)
\(642\) 0 0
\(643\) 30.3611 1.19733 0.598663 0.801001i \(-0.295699\pi\)
0.598663 + 0.801001i \(0.295699\pi\)
\(644\) −8.51995 −0.335733
\(645\) 0 0
\(646\) 19.1448 0.753243
\(647\) −44.6983 −1.75727 −0.878636 0.477491i \(-0.841546\pi\)
−0.878636 + 0.477491i \(0.841546\pi\)
\(648\) 0 0
\(649\) 0.674261 0.0264671
\(650\) 1.03230 0.0404901
\(651\) 0 0
\(652\) 79.8161 3.12584
\(653\) 21.4840 0.840733 0.420366 0.907355i \(-0.361902\pi\)
0.420366 + 0.907355i \(0.361902\pi\)
\(654\) 0 0
\(655\) −5.23448 −0.204528
\(656\) 0.503126 0.0196438
\(657\) 0 0
\(658\) 17.0449 0.664481
\(659\) 26.1584 1.01899 0.509493 0.860475i \(-0.329833\pi\)
0.509493 + 0.860475i \(0.329833\pi\)
\(660\) 0 0
\(661\) 49.2767 1.91664 0.958320 0.285697i \(-0.0922249\pi\)
0.958320 + 0.285697i \(0.0922249\pi\)
\(662\) 14.6857 0.570775
\(663\) 0 0
\(664\) −6.83016 −0.265061
\(665\) −0.212370 −0.00823534
\(666\) 0 0
\(667\) 27.9523 1.08232
\(668\) −94.7545 −3.66616
\(669\) 0 0
\(670\) 0.118143 0.00456428
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −7.96941 −0.307198 −0.153599 0.988133i \(-0.549086\pi\)
−0.153599 + 0.988133i \(0.549086\pi\)
\(674\) 41.4348 1.59601
\(675\) 0 0
\(676\) −58.0591 −2.23304
\(677\) −13.0772 −0.502596 −0.251298 0.967910i \(-0.580857\pi\)
−0.251298 + 0.967910i \(0.580857\pi\)
\(678\) 0 0
\(679\) −5.20914 −0.199909
\(680\) −14.4108 −0.552630
\(681\) 0 0
\(682\) 7.78108 0.297953
\(683\) −29.5060 −1.12902 −0.564508 0.825427i \(-0.690934\pi\)
−0.564508 + 0.825427i \(0.690934\pi\)
\(684\) 0 0
\(685\) −5.59526 −0.213784
\(686\) 20.6653 0.789006
\(687\) 0 0
\(688\) 79.9213 3.04697
\(689\) 0.683809 0.0260510
\(690\) 0 0
\(691\) 1.06947 0.0406846 0.0203423 0.999793i \(-0.493524\pi\)
0.0203423 + 0.999793i \(0.493524\pi\)
\(692\) −13.2620 −0.504147
\(693\) 0 0
\(694\) −47.0992 −1.78786
\(695\) −5.18912 −0.196835
\(696\) 0 0
\(697\) −0.498141 −0.0188684
\(698\) −25.2478 −0.955643
\(699\) 0 0
\(700\) −13.0146 −0.491906
\(701\) 2.52697 0.0954424 0.0477212 0.998861i \(-0.484804\pi\)
0.0477212 + 0.998861i \(0.484804\pi\)
\(702\) 0 0
\(703\) −6.09365 −0.229826
\(704\) −0.520247 −0.0196076
\(705\) 0 0
\(706\) 37.7218 1.41968
\(707\) −5.88368 −0.221279
\(708\) 0 0
\(709\) −8.02051 −0.301217 −0.150608 0.988594i \(-0.548123\pi\)
−0.150608 + 0.988594i \(0.548123\pi\)
\(710\) 10.7777 0.404478
\(711\) 0 0
\(712\) −9.63281 −0.361005
\(713\) 9.79637 0.366877
\(714\) 0 0
\(715\) −0.0273660 −0.00102343
\(716\) −5.22087 −0.195113
\(717\) 0 0
\(718\) 70.1591 2.61831
\(719\) 17.4383 0.650339 0.325170 0.945656i \(-0.394579\pi\)
0.325170 + 0.945656i \(0.394579\pi\)
\(720\) 0 0
\(721\) −4.30979 −0.160505
\(722\) 45.3484 1.68769
\(723\) 0 0
\(724\) −49.2548 −1.83054
\(725\) 42.6985 1.58578
\(726\) 0 0
\(727\) −21.4232 −0.794541 −0.397271 0.917701i \(-0.630043\pi\)
−0.397271 + 0.917701i \(0.630043\pi\)
\(728\) −0.310217 −0.0114974
\(729\) 0 0
\(730\) −0.928057 −0.0343489
\(731\) −79.1294 −2.92671
\(732\) 0 0
\(733\) 24.8791 0.918929 0.459464 0.888196i \(-0.348041\pi\)
0.459464 + 0.888196i \(0.348041\pi\)
\(734\) 64.4391 2.37849
\(735\) 0 0
\(736\) 17.0469 0.628356
\(737\) 0.140859 0.00518861
\(738\) 0 0
\(739\) −3.44825 −0.126846 −0.0634230 0.997987i \(-0.520202\pi\)
−0.0634230 + 0.997987i \(0.520202\pi\)
\(740\) 8.30325 0.305233
\(741\) 0 0
\(742\) −12.4797 −0.458144
\(743\) 18.1232 0.664874 0.332437 0.943125i \(-0.392129\pi\)
0.332437 + 0.943125i \(0.392129\pi\)
\(744\) 0 0
\(745\) −5.07171 −0.185813
\(746\) −58.3816 −2.13750
\(747\) 0 0
\(748\) −31.1026 −1.13722
\(749\) 10.0732 0.368067
\(750\) 0 0
\(751\) 12.9982 0.474310 0.237155 0.971472i \(-0.423785\pi\)
0.237155 + 0.971472i \(0.423785\pi\)
\(752\) −79.1233 −2.88533
\(753\) 0 0
\(754\) 1.84238 0.0670954
\(755\) −5.46474 −0.198882
\(756\) 0 0
\(757\) −16.0448 −0.583158 −0.291579 0.956547i \(-0.594181\pi\)
−0.291579 + 0.956547i \(0.594181\pi\)
\(758\) 7.17365 0.260559
\(759\) 0 0
\(760\) 2.23904 0.0812185
\(761\) −40.4165 −1.46510 −0.732549 0.680714i \(-0.761670\pi\)
−0.732549 + 0.680714i \(0.761670\pi\)
\(762\) 0 0
\(763\) 3.45039 0.124912
\(764\) 68.6532 2.48379
\(765\) 0 0
\(766\) 65.1419 2.35367
\(767\) 0.0559518 0.00202030
\(768\) 0 0
\(769\) 25.1456 0.906774 0.453387 0.891314i \(-0.350216\pi\)
0.453387 + 0.891314i \(0.350216\pi\)
\(770\) 0.499437 0.0179984
\(771\) 0 0
\(772\) −49.6822 −1.78810
\(773\) 16.3560 0.588284 0.294142 0.955762i \(-0.404966\pi\)
0.294142 + 0.955762i \(0.404966\pi\)
\(774\) 0 0
\(775\) 14.9644 0.537537
\(776\) 54.9206 1.97154
\(777\) 0 0
\(778\) −5.15226 −0.184717
\(779\) 0.0773971 0.00277304
\(780\) 0 0
\(781\) 12.8499 0.459805
\(782\) −56.6846 −2.02704
\(783\) 0 0
\(784\) −46.7183 −1.66851
\(785\) 1.99957 0.0713677
\(786\) 0 0
\(787\) 28.0304 0.999175 0.499588 0.866263i \(-0.333485\pi\)
0.499588 + 0.866263i \(0.333485\pi\)
\(788\) 79.1560 2.81981
\(789\) 0 0
\(790\) 12.5177 0.445359
\(791\) 7.34034 0.260992
\(792\) 0 0
\(793\) 0.0829823 0.00294679
\(794\) −2.74665 −0.0974751
\(795\) 0 0
\(796\) 109.554 3.88305
\(797\) 35.6574 1.26305 0.631525 0.775356i \(-0.282429\pi\)
0.631525 + 0.775356i \(0.282429\pi\)
\(798\) 0 0
\(799\) 78.3393 2.77144
\(800\) 26.0399 0.920649
\(801\) 0 0
\(802\) 8.90292 0.314373
\(803\) −1.10649 −0.0390473
\(804\) 0 0
\(805\) 0.628790 0.0221619
\(806\) 0.645692 0.0227435
\(807\) 0 0
\(808\) 62.0324 2.18229
\(809\) −13.6655 −0.480452 −0.240226 0.970717i \(-0.577222\pi\)
−0.240226 + 0.970717i \(0.577222\pi\)
\(810\) 0 0
\(811\) 47.8791 1.68126 0.840631 0.541608i \(-0.182184\pi\)
0.840631 + 0.541608i \(0.182184\pi\)
\(812\) −23.2276 −0.815130
\(813\) 0 0
\(814\) 14.3306 0.502289
\(815\) −5.89059 −0.206338
\(816\) 0 0
\(817\) 12.2945 0.430130
\(818\) 69.1002 2.41603
\(819\) 0 0
\(820\) −0.105462 −0.00368288
\(821\) −8.04263 −0.280690 −0.140345 0.990103i \(-0.544821\pi\)
−0.140345 + 0.990103i \(0.544821\pi\)
\(822\) 0 0
\(823\) 12.4433 0.433745 0.216872 0.976200i \(-0.430414\pi\)
0.216872 + 0.976200i \(0.430414\pi\)
\(824\) 45.4387 1.58293
\(825\) 0 0
\(826\) −1.02114 −0.0355298
\(827\) −12.2012 −0.424278 −0.212139 0.977240i \(-0.568043\pi\)
−0.212139 + 0.977240i \(0.568043\pi\)
\(828\) 0 0
\(829\) −21.1707 −0.735288 −0.367644 0.929967i \(-0.619835\pi\)
−0.367644 + 0.929967i \(0.619835\pi\)
\(830\) 0.912497 0.0316732
\(831\) 0 0
\(832\) −0.0431713 −0.00149670
\(833\) 46.2554 1.60265
\(834\) 0 0
\(835\) 6.99307 0.242005
\(836\) 4.83247 0.167134
\(837\) 0 0
\(838\) −39.8683 −1.37723
\(839\) 39.8488 1.37573 0.687867 0.725837i \(-0.258547\pi\)
0.687867 + 0.725837i \(0.258547\pi\)
\(840\) 0 0
\(841\) 47.2055 1.62777
\(842\) 3.57861 0.123327
\(843\) 0 0
\(844\) 41.7509 1.43713
\(845\) 4.28488 0.147404
\(846\) 0 0
\(847\) 0.595463 0.0204604
\(848\) 57.9313 1.98937
\(849\) 0 0
\(850\) −86.5883 −2.96995
\(851\) 18.0423 0.618481
\(852\) 0 0
\(853\) 47.3637 1.62170 0.810851 0.585252i \(-0.199005\pi\)
0.810851 + 0.585252i \(0.199005\pi\)
\(854\) −1.51445 −0.0518234
\(855\) 0 0
\(856\) −106.203 −3.62995
\(857\) −0.0360945 −0.00123297 −0.000616483 1.00000i \(-0.500196\pi\)
−0.000616483 1.00000i \(0.500196\pi\)
\(858\) 0 0
\(859\) −6.64544 −0.226740 −0.113370 0.993553i \(-0.536164\pi\)
−0.113370 + 0.993553i \(0.536164\pi\)
\(860\) −16.7525 −0.571257
\(861\) 0 0
\(862\) −59.8650 −2.03901
\(863\) −29.7608 −1.01307 −0.506535 0.862219i \(-0.669074\pi\)
−0.506535 + 0.862219i \(0.669074\pi\)
\(864\) 0 0
\(865\) 0.978765 0.0332790
\(866\) −74.4454 −2.52976
\(867\) 0 0
\(868\) −8.14052 −0.276307
\(869\) 14.9245 0.506278
\(870\) 0 0
\(871\) 0.0116888 0.000396060 0
\(872\) −36.3779 −1.23191
\(873\) 0 0
\(874\) 8.80719 0.297908
\(875\) 1.94237 0.0656640
\(876\) 0 0
\(877\) −16.7597 −0.565934 −0.282967 0.959130i \(-0.591319\pi\)
−0.282967 + 0.959130i \(0.591319\pi\)
\(878\) 43.4121 1.46509
\(879\) 0 0
\(880\) −2.31841 −0.0781534
\(881\) −24.3345 −0.819851 −0.409925 0.912119i \(-0.634445\pi\)
−0.409925 + 0.912119i \(0.634445\pi\)
\(882\) 0 0
\(883\) 26.7278 0.899461 0.449731 0.893164i \(-0.351520\pi\)
0.449731 + 0.893164i \(0.351520\pi\)
\(884\) −2.58096 −0.0868072
\(885\) 0 0
\(886\) −83.7404 −2.81331
\(887\) −42.4352 −1.42484 −0.712418 0.701756i \(-0.752400\pi\)
−0.712418 + 0.701756i \(0.752400\pi\)
\(888\) 0 0
\(889\) −4.75977 −0.159638
\(890\) 1.28693 0.0431379
\(891\) 0 0
\(892\) −106.585 −3.56874
\(893\) −12.1717 −0.407311
\(894\) 0 0
\(895\) 0.385311 0.0128795
\(896\) 7.12812 0.238134
\(897\) 0 0
\(898\) −78.2579 −2.61150
\(899\) 26.7075 0.890745
\(900\) 0 0
\(901\) −57.3573 −1.91085
\(902\) −0.182017 −0.00606052
\(903\) 0 0
\(904\) −77.3901 −2.57396
\(905\) 3.63511 0.120835
\(906\) 0 0
\(907\) −7.59234 −0.252100 −0.126050 0.992024i \(-0.540230\pi\)
−0.126050 + 0.992024i \(0.540230\pi\)
\(908\) −22.2818 −0.739448
\(909\) 0 0
\(910\) 0.0414444 0.00137387
\(911\) 30.6962 1.01701 0.508505 0.861059i \(-0.330198\pi\)
0.508505 + 0.861059i \(0.330198\pi\)
\(912\) 0 0
\(913\) 1.08794 0.0360057
\(914\) 30.2640 1.00104
\(915\) 0 0
\(916\) 4.09247 0.135219
\(917\) 9.45155 0.312118
\(918\) 0 0
\(919\) −47.5570 −1.56876 −0.784380 0.620281i \(-0.787019\pi\)
−0.784380 + 0.620281i \(0.787019\pi\)
\(920\) −6.62941 −0.218565
\(921\) 0 0
\(922\) 24.2576 0.798880
\(923\) 1.06631 0.0350981
\(924\) 0 0
\(925\) 27.5604 0.906180
\(926\) −57.9972 −1.90590
\(927\) 0 0
\(928\) 46.4743 1.52559
\(929\) 24.6228 0.807847 0.403923 0.914793i \(-0.367646\pi\)
0.403923 + 0.914793i \(0.367646\pi\)
\(930\) 0 0
\(931\) −7.18678 −0.235537
\(932\) −32.7227 −1.07187
\(933\) 0 0
\(934\) 104.473 3.41847
\(935\) 2.29543 0.0750687
\(936\) 0 0
\(937\) 13.4835 0.440487 0.220244 0.975445i \(-0.429315\pi\)
0.220244 + 0.975445i \(0.429315\pi\)
\(938\) −0.213324 −0.00696527
\(939\) 0 0
\(940\) 16.5853 0.540951
\(941\) 51.2951 1.67217 0.836086 0.548598i \(-0.184838\pi\)
0.836086 + 0.548598i \(0.184838\pi\)
\(942\) 0 0
\(943\) −0.229160 −0.00746246
\(944\) 4.74015 0.154279
\(945\) 0 0
\(946\) −28.9134 −0.940054
\(947\) −36.6121 −1.18973 −0.594867 0.803824i \(-0.702795\pi\)
−0.594867 + 0.803824i \(0.702795\pi\)
\(948\) 0 0
\(949\) −0.0918195 −0.00298059
\(950\) 13.4534 0.436485
\(951\) 0 0
\(952\) 26.0207 0.843336
\(953\) 34.3089 1.11137 0.555687 0.831392i \(-0.312455\pi\)
0.555687 + 0.831392i \(0.312455\pi\)
\(954\) 0 0
\(955\) −5.06675 −0.163956
\(956\) 109.675 3.54713
\(957\) 0 0
\(958\) −30.1049 −0.972646
\(959\) 10.1030 0.326243
\(960\) 0 0
\(961\) −21.6399 −0.698062
\(962\) 1.18919 0.0383410
\(963\) 0 0
\(964\) 81.9984 2.64099
\(965\) 3.66665 0.118034
\(966\) 0 0
\(967\) 35.6507 1.14645 0.573225 0.819398i \(-0.305692\pi\)
0.573225 + 0.819398i \(0.305692\pi\)
\(968\) −6.27804 −0.201784
\(969\) 0 0
\(970\) −7.33730 −0.235587
\(971\) −2.45087 −0.0786520 −0.0393260 0.999226i \(-0.512521\pi\)
−0.0393260 + 0.999226i \(0.512521\pi\)
\(972\) 0 0
\(973\) 9.36965 0.300377
\(974\) −59.0564 −1.89229
\(975\) 0 0
\(976\) 7.03014 0.225029
\(977\) 36.7003 1.17415 0.587073 0.809534i \(-0.300280\pi\)
0.587073 + 0.809534i \(0.300280\pi\)
\(978\) 0 0
\(979\) 1.53437 0.0490385
\(980\) 9.79275 0.312818
\(981\) 0 0
\(982\) −27.1017 −0.864851
\(983\) 34.5193 1.10099 0.550497 0.834837i \(-0.314438\pi\)
0.550497 + 0.834837i \(0.314438\pi\)
\(984\) 0 0
\(985\) −5.84187 −0.186138
\(986\) −154.537 −4.92146
\(987\) 0 0
\(988\) 0.401009 0.0127578
\(989\) −36.4019 −1.15751
\(990\) 0 0
\(991\) −36.6557 −1.16441 −0.582204 0.813043i \(-0.697809\pi\)
−0.582204 + 0.813043i \(0.697809\pi\)
\(992\) 16.2877 0.517135
\(993\) 0 0
\(994\) −19.4605 −0.617250
\(995\) −8.08533 −0.256322
\(996\) 0 0
\(997\) 17.8981 0.566840 0.283420 0.958996i \(-0.408531\pi\)
0.283420 + 0.958996i \(0.408531\pi\)
\(998\) −105.840 −3.35032
\(999\) 0 0
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 \(a_p\))