Properties

Label 4030.2.a.n.1.3
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
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 1.3
Root \(1.54913\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.54913 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.54913 q^{6} -2.44745 q^{7} +1.00000 q^{8} -0.600186 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.54913 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.54913 q^{6} -2.44745 q^{7} +1.00000 q^{8} -0.600186 q^{9} -1.00000 q^{10} -5.54556 q^{11} -1.54913 q^{12} -1.00000 q^{13} -2.44745 q^{14} +1.54913 q^{15} +1.00000 q^{16} +2.34210 q^{17} -0.600186 q^{18} +4.05227 q^{19} -1.00000 q^{20} +3.79143 q^{21} -5.54556 q^{22} -9.12289 q^{23} -1.54913 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.57717 q^{27} -2.44745 q^{28} -6.24163 q^{29} +1.54913 q^{30} -1.00000 q^{31} +1.00000 q^{32} +8.59082 q^{33} +2.34210 q^{34} +2.44745 q^{35} -0.600186 q^{36} -5.94196 q^{37} +4.05227 q^{38} +1.54913 q^{39} -1.00000 q^{40} +7.55244 q^{41} +3.79143 q^{42} +1.44624 q^{43} -5.54556 q^{44} +0.600186 q^{45} -9.12289 q^{46} +10.0998 q^{47} -1.54913 q^{48} -1.00997 q^{49} +1.00000 q^{50} -3.62822 q^{51} -1.00000 q^{52} -4.83126 q^{53} +5.57717 q^{54} +5.54556 q^{55} -2.44745 q^{56} -6.27750 q^{57} -6.24163 q^{58} +3.28367 q^{59} +1.54913 q^{60} -0.864407 q^{61} -1.00000 q^{62} +1.46893 q^{63} +1.00000 q^{64} +1.00000 q^{65} +8.59082 q^{66} -1.53132 q^{67} +2.34210 q^{68} +14.1326 q^{69} +2.44745 q^{70} +12.8137 q^{71} -0.600186 q^{72} -3.86412 q^{73} -5.94196 q^{74} -1.54913 q^{75} +4.05227 q^{76} +13.5725 q^{77} +1.54913 q^{78} +12.9284 q^{79} -1.00000 q^{80} -6.83922 q^{81} +7.55244 q^{82} +15.0039 q^{83} +3.79143 q^{84} -2.34210 q^{85} +1.44624 q^{86} +9.66912 q^{87} -5.54556 q^{88} -17.7702 q^{89} +0.600186 q^{90} +2.44745 q^{91} -9.12289 q^{92} +1.54913 q^{93} +10.0998 q^{94} -4.05227 q^{95} -1.54913 q^{96} -15.2244 q^{97} -1.00997 q^{98} +3.32837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - q^{3} + 8q^{4} - 8q^{5} - q^{6} + q^{7} + 8q^{8} + 9q^{9} - 8q^{10} + 4q^{11} - q^{12} - 8q^{13} + q^{14} + q^{15} + 8q^{16} - 5q^{17} + 9q^{18} + 2q^{19} - 8q^{20} + 17q^{21} + 4q^{22} + 4q^{23} - q^{24} + 8q^{25} - 8q^{26} + 11q^{27} + q^{28} + 11q^{29} + q^{30} - 8q^{31} + 8q^{32} + 10q^{33} - 5q^{34} - q^{35} + 9q^{36} + 19q^{37} + 2q^{38} + q^{39} - 8q^{40} + 10q^{41} + 17q^{42} + 19q^{43} + 4q^{44} - 9q^{45} + 4q^{46} + 11q^{47} - q^{48} + 11q^{49} + 8q^{50} + 7q^{51} - 8q^{52} + 8q^{53} + 11q^{54} - 4q^{55} + q^{56} - 11q^{57} + 11q^{58} + 28q^{59} + q^{60} - 12q^{61} - 8q^{62} + 20q^{63} + 8q^{64} + 8q^{65} + 10q^{66} + 24q^{67} - 5q^{68} + 30q^{69} - q^{70} + 18q^{71} + 9q^{72} - 3q^{73} + 19q^{74} - q^{75} + 2q^{76} - 7q^{77} + q^{78} + 22q^{79} - 8q^{80} + 24q^{81} + 10q^{82} + 17q^{83} + 17q^{84} + 5q^{85} + 19q^{86} + 11q^{87} + 4q^{88} + 17q^{89} - 9q^{90} - q^{91} + 4q^{92} + q^{93} + 11q^{94} - 2q^{95} - q^{96} - 24q^{97} + 11q^{98} + 23q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.54913 −0.894392 −0.447196 0.894436i \(-0.647577\pi\)
−0.447196 + 0.894436i \(0.647577\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.54913 −0.632431
\(7\) −2.44745 −0.925050 −0.462525 0.886606i \(-0.653056\pi\)
−0.462525 + 0.886606i \(0.653056\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.600186 −0.200062
\(10\) −1.00000 −0.316228
\(11\) −5.54556 −1.67205 −0.836025 0.548691i \(-0.815126\pi\)
−0.836025 + 0.548691i \(0.815126\pi\)
\(12\) −1.54913 −0.447196
\(13\) −1.00000 −0.277350
\(14\) −2.44745 −0.654109
\(15\) 1.54913 0.399984
\(16\) 1.00000 0.250000
\(17\) 2.34210 0.568042 0.284021 0.958818i \(-0.408331\pi\)
0.284021 + 0.958818i \(0.408331\pi\)
\(18\) −0.600186 −0.141465
\(19\) 4.05227 0.929654 0.464827 0.885402i \(-0.346117\pi\)
0.464827 + 0.885402i \(0.346117\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.79143 0.827358
\(22\) −5.54556 −1.18232
\(23\) −9.12289 −1.90225 −0.951127 0.308801i \(-0.900072\pi\)
−0.951127 + 0.308801i \(0.900072\pi\)
\(24\) −1.54913 −0.316215
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 5.57717 1.07333
\(28\) −2.44745 −0.462525
\(29\) −6.24163 −1.15904 −0.579521 0.814957i \(-0.696760\pi\)
−0.579521 + 0.814957i \(0.696760\pi\)
\(30\) 1.54913 0.282832
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) 8.59082 1.49547
\(34\) 2.34210 0.401666
\(35\) 2.44745 0.413695
\(36\) −0.600186 −0.100031
\(37\) −5.94196 −0.976853 −0.488426 0.872605i \(-0.662429\pi\)
−0.488426 + 0.872605i \(0.662429\pi\)
\(38\) 4.05227 0.657364
\(39\) 1.54913 0.248060
\(40\) −1.00000 −0.158114
\(41\) 7.55244 1.17949 0.589746 0.807588i \(-0.299228\pi\)
0.589746 + 0.807588i \(0.299228\pi\)
\(42\) 3.79143 0.585030
\(43\) 1.44624 0.220549 0.110275 0.993901i \(-0.464827\pi\)
0.110275 + 0.993901i \(0.464827\pi\)
\(44\) −5.54556 −0.836025
\(45\) 0.600186 0.0894705
\(46\) −9.12289 −1.34510
\(47\) 10.0998 1.47320 0.736600 0.676329i \(-0.236430\pi\)
0.736600 + 0.676329i \(0.236430\pi\)
\(48\) −1.54913 −0.223598
\(49\) −1.00997 −0.144282
\(50\) 1.00000 0.141421
\(51\) −3.62822 −0.508053
\(52\) −1.00000 −0.138675
\(53\) −4.83126 −0.663625 −0.331812 0.943345i \(-0.607660\pi\)
−0.331812 + 0.943345i \(0.607660\pi\)
\(54\) 5.57717 0.758956
\(55\) 5.54556 0.747764
\(56\) −2.44745 −0.327055
\(57\) −6.27750 −0.831475
\(58\) −6.24163 −0.819566
\(59\) 3.28367 0.427497 0.213749 0.976889i \(-0.431433\pi\)
0.213749 + 0.976889i \(0.431433\pi\)
\(60\) 1.54913 0.199992
\(61\) −0.864407 −0.110676 −0.0553380 0.998468i \(-0.517624\pi\)
−0.0553380 + 0.998468i \(0.517624\pi\)
\(62\) −1.00000 −0.127000
\(63\) 1.46893 0.185067
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 8.59082 1.05746
\(67\) −1.53132 −0.187081 −0.0935405 0.995615i \(-0.529818\pi\)
−0.0935405 + 0.995615i \(0.529818\pi\)
\(68\) 2.34210 0.284021
\(69\) 14.1326 1.70136
\(70\) 2.44745 0.292527
\(71\) 12.8137 1.52071 0.760356 0.649507i \(-0.225025\pi\)
0.760356 + 0.649507i \(0.225025\pi\)
\(72\) −0.600186 −0.0707326
\(73\) −3.86412 −0.452261 −0.226130 0.974097i \(-0.572608\pi\)
−0.226130 + 0.974097i \(0.572608\pi\)
\(74\) −5.94196 −0.690739
\(75\) −1.54913 −0.178878
\(76\) 4.05227 0.464827
\(77\) 13.5725 1.54673
\(78\) 1.54913 0.175405
\(79\) 12.9284 1.45456 0.727282 0.686339i \(-0.240783\pi\)
0.727282 + 0.686339i \(0.240783\pi\)
\(80\) −1.00000 −0.111803
\(81\) −6.83922 −0.759913
\(82\) 7.55244 0.834027
\(83\) 15.0039 1.64689 0.823447 0.567394i \(-0.192048\pi\)
0.823447 + 0.567394i \(0.192048\pi\)
\(84\) 3.79143 0.413679
\(85\) −2.34210 −0.254036
\(86\) 1.44624 0.155952
\(87\) 9.66912 1.03664
\(88\) −5.54556 −0.591159
\(89\) −17.7702 −1.88364 −0.941821 0.336116i \(-0.890887\pi\)
−0.941821 + 0.336116i \(0.890887\pi\)
\(90\) 0.600186 0.0632652
\(91\) 2.44745 0.256563
\(92\) −9.12289 −0.951127
\(93\) 1.54913 0.160638
\(94\) 10.0998 1.04171
\(95\) −4.05227 −0.415754
\(96\) −1.54913 −0.158108
\(97\) −15.2244 −1.54580 −0.772901 0.634527i \(-0.781195\pi\)
−0.772901 + 0.634527i \(0.781195\pi\)
\(98\) −1.00997 −0.102023
\(99\) 3.32837 0.334514
\(100\) 1.00000 0.100000
\(101\) 5.00777 0.498292 0.249146 0.968466i \(-0.419850\pi\)
0.249146 + 0.968466i \(0.419850\pi\)
\(102\) −3.62822 −0.359247
\(103\) 15.2753 1.50512 0.752560 0.658524i \(-0.228819\pi\)
0.752560 + 0.658524i \(0.228819\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −3.79143 −0.370006
\(106\) −4.83126 −0.469254
\(107\) 18.7916 1.81665 0.908327 0.418261i \(-0.137360\pi\)
0.908327 + 0.418261i \(0.137360\pi\)
\(108\) 5.57717 0.536663
\(109\) −2.05689 −0.197015 −0.0985074 0.995136i \(-0.531407\pi\)
−0.0985074 + 0.995136i \(0.531407\pi\)
\(110\) 5.54556 0.528749
\(111\) 9.20489 0.873690
\(112\) −2.44745 −0.231263
\(113\) −16.9106 −1.59082 −0.795408 0.606074i \(-0.792744\pi\)
−0.795408 + 0.606074i \(0.792744\pi\)
\(114\) −6.27750 −0.587942
\(115\) 9.12289 0.850714
\(116\) −6.24163 −0.579521
\(117\) 0.600186 0.0554872
\(118\) 3.28367 0.302286
\(119\) −5.73217 −0.525467
\(120\) 1.54913 0.141416
\(121\) 19.7533 1.79575
\(122\) −0.864407 −0.0782597
\(123\) −11.6997 −1.05493
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) 1.46893 0.130862
\(127\) −14.7356 −1.30757 −0.653787 0.756679i \(-0.726821\pi\)
−0.653787 + 0.756679i \(0.726821\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.24042 −0.197258
\(130\) 1.00000 0.0877058
\(131\) 14.9000 1.30182 0.650910 0.759155i \(-0.274388\pi\)
0.650910 + 0.759155i \(0.274388\pi\)
\(132\) 8.59082 0.747735
\(133\) −9.91773 −0.859976
\(134\) −1.53132 −0.132286
\(135\) −5.57717 −0.480006
\(136\) 2.34210 0.200833
\(137\) 15.7314 1.34402 0.672011 0.740541i \(-0.265431\pi\)
0.672011 + 0.740541i \(0.265431\pi\)
\(138\) 14.1326 1.20304
\(139\) 10.4165 0.883519 0.441759 0.897134i \(-0.354355\pi\)
0.441759 + 0.897134i \(0.354355\pi\)
\(140\) 2.44745 0.206848
\(141\) −15.6459 −1.31762
\(142\) 12.8137 1.07531
\(143\) 5.54556 0.463743
\(144\) −0.600186 −0.0500155
\(145\) 6.24163 0.518339
\(146\) −3.86412 −0.319797
\(147\) 1.56458 0.129045
\(148\) −5.94196 −0.488426
\(149\) 21.9458 1.79787 0.898934 0.438083i \(-0.144342\pi\)
0.898934 + 0.438083i \(0.144342\pi\)
\(150\) −1.54913 −0.126486
\(151\) −21.9433 −1.78572 −0.892862 0.450331i \(-0.851306\pi\)
−0.892862 + 0.450331i \(0.851306\pi\)
\(152\) 4.05227 0.328682
\(153\) −1.40569 −0.113644
\(154\) 13.5725 1.09370
\(155\) 1.00000 0.0803219
\(156\) 1.54913 0.124030
\(157\) 5.98154 0.477379 0.238689 0.971096i \(-0.423282\pi\)
0.238689 + 0.971096i \(0.423282\pi\)
\(158\) 12.9284 1.02853
\(159\) 7.48427 0.593541
\(160\) −1.00000 −0.0790569
\(161\) 22.3278 1.75968
\(162\) −6.83922 −0.537340
\(163\) −9.29991 −0.728425 −0.364213 0.931316i \(-0.618662\pi\)
−0.364213 + 0.931316i \(0.618662\pi\)
\(164\) 7.55244 0.589746
\(165\) −8.59082 −0.668794
\(166\) 15.0039 1.16453
\(167\) 7.25922 0.561735 0.280868 0.959747i \(-0.409378\pi\)
0.280868 + 0.959747i \(0.409378\pi\)
\(168\) 3.79143 0.292515
\(169\) 1.00000 0.0769231
\(170\) −2.34210 −0.179631
\(171\) −2.43211 −0.185988
\(172\) 1.44624 0.110275
\(173\) 4.11152 0.312593 0.156296 0.987710i \(-0.450044\pi\)
0.156296 + 0.987710i \(0.450044\pi\)
\(174\) 9.66912 0.733014
\(175\) −2.44745 −0.185010
\(176\) −5.54556 −0.418013
\(177\) −5.08684 −0.382350
\(178\) −17.7702 −1.33194
\(179\) 1.25592 0.0938719 0.0469360 0.998898i \(-0.485054\pi\)
0.0469360 + 0.998898i \(0.485054\pi\)
\(180\) 0.600186 0.0447352
\(181\) 15.0542 1.11897 0.559484 0.828841i \(-0.310999\pi\)
0.559484 + 0.828841i \(0.310999\pi\)
\(182\) 2.44745 0.181417
\(183\) 1.33908 0.0989878
\(184\) −9.12289 −0.672548
\(185\) 5.94196 0.436862
\(186\) 1.54913 0.113588
\(187\) −12.9883 −0.949795
\(188\) 10.0998 0.736600
\(189\) −13.6499 −0.992881
\(190\) −4.05227 −0.293982
\(191\) 11.3609 0.822043 0.411022 0.911626i \(-0.365172\pi\)
0.411022 + 0.911626i \(0.365172\pi\)
\(192\) −1.54913 −0.111799
\(193\) −21.2055 −1.52640 −0.763202 0.646161i \(-0.776374\pi\)
−0.763202 + 0.646161i \(0.776374\pi\)
\(194\) −15.2244 −1.09305
\(195\) −1.54913 −0.110936
\(196\) −1.00997 −0.0721410
\(197\) 17.0707 1.21624 0.608119 0.793846i \(-0.291924\pi\)
0.608119 + 0.793846i \(0.291924\pi\)
\(198\) 3.32837 0.236537
\(199\) 2.56114 0.181555 0.0907773 0.995871i \(-0.471065\pi\)
0.0907773 + 0.995871i \(0.471065\pi\)
\(200\) 1.00000 0.0707107
\(201\) 2.37222 0.167324
\(202\) 5.00777 0.352346
\(203\) 15.2761 1.07217
\(204\) −3.62822 −0.254026
\(205\) −7.55244 −0.527485
\(206\) 15.2753 1.06428
\(207\) 5.47543 0.380569
\(208\) −1.00000 −0.0693375
\(209\) −22.4721 −1.55443
\(210\) −3.79143 −0.261634
\(211\) −14.2991 −0.984390 −0.492195 0.870485i \(-0.663805\pi\)
−0.492195 + 0.870485i \(0.663805\pi\)
\(212\) −4.83126 −0.331812
\(213\) −19.8502 −1.36011
\(214\) 18.7916 1.28457
\(215\) −1.44624 −0.0986327
\(216\) 5.57717 0.379478
\(217\) 2.44745 0.166144
\(218\) −2.05689 −0.139310
\(219\) 5.98603 0.404498
\(220\) 5.54556 0.373882
\(221\) −2.34210 −0.157547
\(222\) 9.20489 0.617792
\(223\) −2.46758 −0.165242 −0.0826208 0.996581i \(-0.526329\pi\)
−0.0826208 + 0.996581i \(0.526329\pi\)
\(224\) −2.44745 −0.163527
\(225\) −0.600186 −0.0400124
\(226\) −16.9106 −1.12488
\(227\) −26.1082 −1.73287 −0.866433 0.499294i \(-0.833593\pi\)
−0.866433 + 0.499294i \(0.833593\pi\)
\(228\) −6.27750 −0.415738
\(229\) −6.36309 −0.420485 −0.210243 0.977649i \(-0.567425\pi\)
−0.210243 + 0.977649i \(0.567425\pi\)
\(230\) 9.12289 0.601545
\(231\) −21.0256 −1.38338
\(232\) −6.24163 −0.409783
\(233\) −13.3530 −0.874786 −0.437393 0.899271i \(-0.644098\pi\)
−0.437393 + 0.899271i \(0.644098\pi\)
\(234\) 0.600186 0.0392354
\(235\) −10.0998 −0.658835
\(236\) 3.28367 0.213749
\(237\) −20.0279 −1.30095
\(238\) −5.73217 −0.371562
\(239\) 14.8652 0.961551 0.480776 0.876844i \(-0.340355\pi\)
0.480776 + 0.876844i \(0.340355\pi\)
\(240\) 1.54913 0.0999961
\(241\) −10.7130 −0.690086 −0.345043 0.938587i \(-0.612136\pi\)
−0.345043 + 0.938587i \(0.612136\pi\)
\(242\) 19.7533 1.26979
\(243\) −6.13664 −0.393666
\(244\) −0.864407 −0.0553380
\(245\) 1.00997 0.0645249
\(246\) −11.6997 −0.745948
\(247\) −4.05227 −0.257840
\(248\) −1.00000 −0.0635001
\(249\) −23.2431 −1.47297
\(250\) −1.00000 −0.0632456
\(251\) −24.9380 −1.57407 −0.787036 0.616908i \(-0.788385\pi\)
−0.787036 + 0.616908i \(0.788385\pi\)
\(252\) 1.46893 0.0925337
\(253\) 50.5916 3.18066
\(254\) −14.7356 −0.924594
\(255\) 3.62822 0.227208
\(256\) 1.00000 0.0625000
\(257\) 10.7059 0.667816 0.333908 0.942606i \(-0.391633\pi\)
0.333908 + 0.942606i \(0.391633\pi\)
\(258\) −2.24042 −0.139482
\(259\) 14.5427 0.903638
\(260\) 1.00000 0.0620174
\(261\) 3.74614 0.231880
\(262\) 14.9000 0.920525
\(263\) 7.82206 0.482329 0.241165 0.970484i \(-0.422471\pi\)
0.241165 + 0.970484i \(0.422471\pi\)
\(264\) 8.59082 0.528728
\(265\) 4.83126 0.296782
\(266\) −9.91773 −0.608095
\(267\) 27.5285 1.68471
\(268\) −1.53132 −0.0935405
\(269\) 8.95435 0.545956 0.272978 0.962020i \(-0.411991\pi\)
0.272978 + 0.962020i \(0.411991\pi\)
\(270\) −5.57717 −0.339416
\(271\) −5.63277 −0.342167 −0.171083 0.985257i \(-0.554727\pi\)
−0.171083 + 0.985257i \(0.554727\pi\)
\(272\) 2.34210 0.142011
\(273\) −3.79143 −0.229468
\(274\) 15.7314 0.950367
\(275\) −5.54556 −0.334410
\(276\) 14.1326 0.850681
\(277\) 24.6756 1.48261 0.741305 0.671168i \(-0.234207\pi\)
0.741305 + 0.671168i \(0.234207\pi\)
\(278\) 10.4165 0.624742
\(279\) 0.600186 0.0359322
\(280\) 2.44745 0.146263
\(281\) 3.10065 0.184969 0.0924845 0.995714i \(-0.470519\pi\)
0.0924845 + 0.995714i \(0.470519\pi\)
\(282\) −15.6459 −0.931697
\(283\) 3.09939 0.184240 0.0921199 0.995748i \(-0.470636\pi\)
0.0921199 + 0.995748i \(0.470636\pi\)
\(284\) 12.8137 0.760356
\(285\) 6.27750 0.371847
\(286\) 5.54556 0.327916
\(287\) −18.4842 −1.09109
\(288\) −0.600186 −0.0353663
\(289\) −11.5146 −0.677328
\(290\) 6.24163 0.366521
\(291\) 23.5846 1.38255
\(292\) −3.86412 −0.226130
\(293\) −12.9052 −0.753932 −0.376966 0.926227i \(-0.623033\pi\)
−0.376966 + 0.926227i \(0.623033\pi\)
\(294\) 1.56458 0.0912484
\(295\) −3.28367 −0.191183
\(296\) −5.94196 −0.345370
\(297\) −30.9285 −1.79466
\(298\) 21.9458 1.27129
\(299\) 9.12289 0.527590
\(300\) −1.54913 −0.0894392
\(301\) −3.53960 −0.204019
\(302\) −21.9433 −1.26270
\(303\) −7.75771 −0.445669
\(304\) 4.05227 0.232413
\(305\) 0.864407 0.0494958
\(306\) −1.40569 −0.0803582
\(307\) −27.1174 −1.54767 −0.773835 0.633387i \(-0.781664\pi\)
−0.773835 + 0.633387i \(0.781664\pi\)
\(308\) 13.5725 0.773365
\(309\) −23.6635 −1.34617
\(310\) 1.00000 0.0567962
\(311\) 15.0204 0.851729 0.425865 0.904787i \(-0.359970\pi\)
0.425865 + 0.904787i \(0.359970\pi\)
\(312\) 1.54913 0.0877024
\(313\) 22.4506 1.26898 0.634492 0.772929i \(-0.281209\pi\)
0.634492 + 0.772929i \(0.281209\pi\)
\(314\) 5.98154 0.337558
\(315\) −1.46893 −0.0827647
\(316\) 12.9284 0.727282
\(317\) −20.4469 −1.14841 −0.574207 0.818710i \(-0.694690\pi\)
−0.574207 + 0.818710i \(0.694690\pi\)
\(318\) 7.48427 0.419697
\(319\) 34.6134 1.93798
\(320\) −1.00000 −0.0559017
\(321\) −29.1107 −1.62480
\(322\) 22.3278 1.24428
\(323\) 9.49080 0.528082
\(324\) −6.83922 −0.379957
\(325\) −1.00000 −0.0554700
\(326\) −9.29991 −0.515074
\(327\) 3.18640 0.176209
\(328\) 7.55244 0.417014
\(329\) −24.7187 −1.36278
\(330\) −8.59082 −0.472909
\(331\) 16.0603 0.882755 0.441377 0.897322i \(-0.354490\pi\)
0.441377 + 0.897322i \(0.354490\pi\)
\(332\) 15.0039 0.823447
\(333\) 3.56628 0.195431
\(334\) 7.25922 0.397207
\(335\) 1.53132 0.0836652
\(336\) 3.79143 0.206840
\(337\) −20.8945 −1.13820 −0.569098 0.822270i \(-0.692708\pi\)
−0.569098 + 0.822270i \(0.692708\pi\)
\(338\) 1.00000 0.0543928
\(339\) 26.1968 1.42281
\(340\) −2.34210 −0.127018
\(341\) 5.54556 0.300309
\(342\) −2.43211 −0.131514
\(343\) 19.6040 1.05852
\(344\) 1.44624 0.0779760
\(345\) −14.1326 −0.760872
\(346\) 4.11152 0.221037
\(347\) 4.36732 0.234450 0.117225 0.993105i \(-0.462600\pi\)
0.117225 + 0.993105i \(0.462600\pi\)
\(348\) 9.66912 0.518319
\(349\) 27.9147 1.49424 0.747121 0.664688i \(-0.231436\pi\)
0.747121 + 0.664688i \(0.231436\pi\)
\(350\) −2.44745 −0.130822
\(351\) −5.57717 −0.297687
\(352\) −5.54556 −0.295580
\(353\) 20.6711 1.10021 0.550107 0.835094i \(-0.314587\pi\)
0.550107 + 0.835094i \(0.314587\pi\)
\(354\) −5.08684 −0.270363
\(355\) −12.8137 −0.680083
\(356\) −17.7702 −0.941821
\(357\) 8.87990 0.469974
\(358\) 1.25592 0.0663775
\(359\) −3.07167 −0.162117 −0.0810583 0.996709i \(-0.525830\pi\)
−0.0810583 + 0.996709i \(0.525830\pi\)
\(360\) 0.600186 0.0316326
\(361\) −2.57913 −0.135744
\(362\) 15.0542 0.791230
\(363\) −30.6005 −1.60611
\(364\) 2.44745 0.128281
\(365\) 3.86412 0.202257
\(366\) 1.33908 0.0699949
\(367\) 1.81266 0.0946199 0.0473099 0.998880i \(-0.484935\pi\)
0.0473099 + 0.998880i \(0.484935\pi\)
\(368\) −9.12289 −0.475563
\(369\) −4.53287 −0.235972
\(370\) 5.94196 0.308908
\(371\) 11.8243 0.613886
\(372\) 1.54913 0.0803188
\(373\) −20.8441 −1.07927 −0.539633 0.841900i \(-0.681437\pi\)
−0.539633 + 0.841900i \(0.681437\pi\)
\(374\) −12.9883 −0.671606
\(375\) 1.54913 0.0799969
\(376\) 10.0998 0.520855
\(377\) 6.24163 0.321460
\(378\) −13.6499 −0.702073
\(379\) 32.8527 1.68753 0.843766 0.536711i \(-0.180334\pi\)
0.843766 + 0.536711i \(0.180334\pi\)
\(380\) −4.05227 −0.207877
\(381\) 22.8274 1.16948
\(382\) 11.3609 0.581272
\(383\) 10.0122 0.511602 0.255801 0.966729i \(-0.417661\pi\)
0.255801 + 0.966729i \(0.417661\pi\)
\(384\) −1.54913 −0.0790539
\(385\) −13.5725 −0.691719
\(386\) −21.2055 −1.07933
\(387\) −0.868013 −0.0441236
\(388\) −15.2244 −0.772901
\(389\) 35.4099 1.79535 0.897675 0.440657i \(-0.145255\pi\)
0.897675 + 0.440657i \(0.145255\pi\)
\(390\) −1.54913 −0.0784434
\(391\) −21.3667 −1.08056
\(392\) −1.00997 −0.0510114
\(393\) −23.0821 −1.16434
\(394\) 17.0707 0.860011
\(395\) −12.9284 −0.650501
\(396\) 3.32837 0.167257
\(397\) 6.88727 0.345662 0.172831 0.984951i \(-0.444709\pi\)
0.172831 + 0.984951i \(0.444709\pi\)
\(398\) 2.56114 0.128379
\(399\) 15.3639 0.769156
\(400\) 1.00000 0.0500000
\(401\) 2.69010 0.134337 0.0671686 0.997742i \(-0.478603\pi\)
0.0671686 + 0.997742i \(0.478603\pi\)
\(402\) 2.37222 0.118316
\(403\) 1.00000 0.0498135
\(404\) 5.00777 0.249146
\(405\) 6.83922 0.339843
\(406\) 15.2761 0.758140
\(407\) 32.9515 1.63335
\(408\) −3.62822 −0.179624
\(409\) 11.3839 0.562897 0.281449 0.959576i \(-0.409185\pi\)
0.281449 + 0.959576i \(0.409185\pi\)
\(410\) −7.55244 −0.372988
\(411\) −24.3700 −1.20208
\(412\) 15.2753 0.752560
\(413\) −8.03663 −0.395457
\(414\) 5.47543 0.269103
\(415\) −15.0039 −0.736513
\(416\) −1.00000 −0.0490290
\(417\) −16.1366 −0.790212
\(418\) −22.4721 −1.09915
\(419\) 23.0761 1.12734 0.563670 0.826000i \(-0.309389\pi\)
0.563670 + 0.826000i \(0.309389\pi\)
\(420\) −3.79143 −0.185003
\(421\) 29.0039 1.41357 0.706783 0.707431i \(-0.250146\pi\)
0.706783 + 0.707431i \(0.250146\pi\)
\(422\) −14.2991 −0.696069
\(423\) −6.06173 −0.294731
\(424\) −4.83126 −0.234627
\(425\) 2.34210 0.113608
\(426\) −19.8502 −0.961745
\(427\) 2.11560 0.102381
\(428\) 18.7916 0.908327
\(429\) −8.59082 −0.414769
\(430\) −1.44624 −0.0697438
\(431\) 10.1033 0.486661 0.243331 0.969943i \(-0.421760\pi\)
0.243331 + 0.969943i \(0.421760\pi\)
\(432\) 5.57717 0.268332
\(433\) −26.3104 −1.26440 −0.632199 0.774806i \(-0.717847\pi\)
−0.632199 + 0.774806i \(0.717847\pi\)
\(434\) 2.44745 0.117482
\(435\) −9.66912 −0.463599
\(436\) −2.05689 −0.0985074
\(437\) −36.9684 −1.76844
\(438\) 5.98603 0.286024
\(439\) 15.8154 0.754827 0.377414 0.926045i \(-0.376813\pi\)
0.377414 + 0.926045i \(0.376813\pi\)
\(440\) 5.54556 0.264374
\(441\) 0.606173 0.0288654
\(442\) −2.34210 −0.111402
\(443\) −10.2929 −0.489029 −0.244514 0.969646i \(-0.578629\pi\)
−0.244514 + 0.969646i \(0.578629\pi\)
\(444\) 9.20489 0.436845
\(445\) 17.7702 0.842390
\(446\) −2.46758 −0.116843
\(447\) −33.9969 −1.60800
\(448\) −2.44745 −0.115631
\(449\) −6.92180 −0.326660 −0.163330 0.986572i \(-0.552223\pi\)
−0.163330 + 0.986572i \(0.552223\pi\)
\(450\) −0.600186 −0.0282930
\(451\) −41.8825 −1.97217
\(452\) −16.9106 −0.795408
\(453\) 33.9932 1.59714
\(454\) −26.1082 −1.22532
\(455\) −2.44745 −0.114738
\(456\) −6.27750 −0.293971
\(457\) 12.2905 0.574925 0.287463 0.957792i \(-0.407188\pi\)
0.287463 + 0.957792i \(0.407188\pi\)
\(458\) −6.36309 −0.297328
\(459\) 13.0623 0.609695
\(460\) 9.12289 0.425357
\(461\) −13.7756 −0.641594 −0.320797 0.947148i \(-0.603951\pi\)
−0.320797 + 0.947148i \(0.603951\pi\)
\(462\) −21.0256 −0.978200
\(463\) −15.2867 −0.710434 −0.355217 0.934784i \(-0.615593\pi\)
−0.355217 + 0.934784i \(0.615593\pi\)
\(464\) −6.24163 −0.289760
\(465\) −1.54913 −0.0718393
\(466\) −13.3530 −0.618567
\(467\) −23.5599 −1.09022 −0.545110 0.838364i \(-0.683512\pi\)
−0.545110 + 0.838364i \(0.683512\pi\)
\(468\) 0.600186 0.0277436
\(469\) 3.74784 0.173059
\(470\) −10.0998 −0.465867
\(471\) −9.26620 −0.426964
\(472\) 3.28367 0.151143
\(473\) −8.02021 −0.368770
\(474\) −20.0279 −0.919911
\(475\) 4.05227 0.185931
\(476\) −5.73217 −0.262734
\(477\) 2.89966 0.132766
\(478\) 14.8652 0.679919
\(479\) 25.1565 1.14943 0.574715 0.818353i \(-0.305113\pi\)
0.574715 + 0.818353i \(0.305113\pi\)
\(480\) 1.54913 0.0707079
\(481\) 5.94196 0.270930
\(482\) −10.7130 −0.487965
\(483\) −34.5888 −1.57384
\(484\) 19.7533 0.897876
\(485\) 15.2244 0.691303
\(486\) −6.13664 −0.278364
\(487\) 0.268264 0.0121562 0.00607809 0.999982i \(-0.498065\pi\)
0.00607809 + 0.999982i \(0.498065\pi\)
\(488\) −0.864407 −0.0391299
\(489\) 14.4068 0.651498
\(490\) 1.00997 0.0456260
\(491\) −26.8444 −1.21147 −0.605736 0.795666i \(-0.707121\pi\)
−0.605736 + 0.795666i \(0.707121\pi\)
\(492\) −11.6997 −0.527465
\(493\) −14.6185 −0.658384
\(494\) −4.05227 −0.182320
\(495\) −3.32837 −0.149599
\(496\) −1.00000 −0.0449013
\(497\) −31.3610 −1.40673
\(498\) −23.2431 −1.04155
\(499\) 11.7989 0.528190 0.264095 0.964497i \(-0.414927\pi\)
0.264095 + 0.964497i \(0.414927\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −11.2455 −0.502412
\(502\) −24.9380 −1.11304
\(503\) −7.35983 −0.328159 −0.164079 0.986447i \(-0.552465\pi\)
−0.164079 + 0.986447i \(0.552465\pi\)
\(504\) 1.46893 0.0654312
\(505\) −5.00777 −0.222843
\(506\) 50.5916 2.24907
\(507\) −1.54913 −0.0687994
\(508\) −14.7356 −0.653787
\(509\) 25.4475 1.12794 0.563971 0.825794i \(-0.309273\pi\)
0.563971 + 0.825794i \(0.309273\pi\)
\(510\) 3.62822 0.160660
\(511\) 9.45724 0.418364
\(512\) 1.00000 0.0441942
\(513\) 22.6002 0.997822
\(514\) 10.7059 0.472217
\(515\) −15.2753 −0.673110
\(516\) −2.24042 −0.0986289
\(517\) −56.0088 −2.46326
\(518\) 14.5427 0.638969
\(519\) −6.36929 −0.279581
\(520\) 1.00000 0.0438529
\(521\) −24.5340 −1.07486 −0.537428 0.843310i \(-0.680604\pi\)
−0.537428 + 0.843310i \(0.680604\pi\)
\(522\) 3.74614 0.163964
\(523\) −3.66146 −0.160105 −0.0800523 0.996791i \(-0.525509\pi\)
−0.0800523 + 0.996791i \(0.525509\pi\)
\(524\) 14.9000 0.650910
\(525\) 3.79143 0.165472
\(526\) 7.82206 0.341058
\(527\) −2.34210 −0.102023
\(528\) 8.59082 0.373867
\(529\) 60.2271 2.61857
\(530\) 4.83126 0.209857
\(531\) −1.97081 −0.0855260
\(532\) −9.91773 −0.429988
\(533\) −7.55244 −0.327132
\(534\) 27.5285 1.19127
\(535\) −18.7916 −0.812432
\(536\) −1.53132 −0.0661431
\(537\) −1.94559 −0.0839583
\(538\) 8.95435 0.386049
\(539\) 5.60088 0.241247
\(540\) −5.57717 −0.240003
\(541\) −32.2617 −1.38704 −0.693519 0.720439i \(-0.743940\pi\)
−0.693519 + 0.720439i \(0.743940\pi\)
\(542\) −5.63277 −0.241948
\(543\) −23.3209 −1.00080
\(544\) 2.34210 0.100417
\(545\) 2.05689 0.0881077
\(546\) −3.79143 −0.162258
\(547\) −38.0510 −1.62694 −0.813471 0.581605i \(-0.802425\pi\)
−0.813471 + 0.581605i \(0.802425\pi\)
\(548\) 15.7314 0.672011
\(549\) 0.518805 0.0221421
\(550\) −5.54556 −0.236464
\(551\) −25.2928 −1.07751
\(552\) 14.1326 0.601522
\(553\) −31.6418 −1.34554
\(554\) 24.6756 1.04836
\(555\) −9.20489 −0.390726
\(556\) 10.4165 0.441759
\(557\) 0.793849 0.0336365 0.0168182 0.999859i \(-0.494646\pi\)
0.0168182 + 0.999859i \(0.494646\pi\)
\(558\) 0.600186 0.0254079
\(559\) −1.44624 −0.0611694
\(560\) 2.44745 0.103424
\(561\) 20.1205 0.849490
\(562\) 3.10065 0.130793
\(563\) −26.3962 −1.11247 −0.556234 0.831026i \(-0.687754\pi\)
−0.556234 + 0.831026i \(0.687754\pi\)
\(564\) −15.6459 −0.658810
\(565\) 16.9106 0.711435
\(566\) 3.09939 0.130277
\(567\) 16.7387 0.702958
\(568\) 12.8137 0.537653
\(569\) −10.5573 −0.442585 −0.221293 0.975207i \(-0.571028\pi\)
−0.221293 + 0.975207i \(0.571028\pi\)
\(570\) 6.27750 0.262936
\(571\) −5.29402 −0.221548 −0.110774 0.993846i \(-0.535333\pi\)
−0.110774 + 0.993846i \(0.535333\pi\)
\(572\) 5.54556 0.231872
\(573\) −17.5995 −0.735229
\(574\) −18.4842 −0.771517
\(575\) −9.12289 −0.380451
\(576\) −0.600186 −0.0250078
\(577\) −19.0055 −0.791208 −0.395604 0.918421i \(-0.629465\pi\)
−0.395604 + 0.918421i \(0.629465\pi\)
\(578\) −11.5146 −0.478943
\(579\) 32.8501 1.36520
\(580\) 6.24163 0.259170
\(581\) −36.7214 −1.52346
\(582\) 23.5846 0.977613
\(583\) 26.7921 1.10961
\(584\) −3.86412 −0.159898
\(585\) −0.600186 −0.0248146
\(586\) −12.9052 −0.533110
\(587\) 13.8163 0.570260 0.285130 0.958489i \(-0.407963\pi\)
0.285130 + 0.958489i \(0.407963\pi\)
\(588\) 1.56458 0.0645224
\(589\) −4.05227 −0.166971
\(590\) −3.28367 −0.135187
\(591\) −26.4448 −1.08779
\(592\) −5.94196 −0.244213
\(593\) −6.01761 −0.247114 −0.123557 0.992337i \(-0.539430\pi\)
−0.123557 + 0.992337i \(0.539430\pi\)
\(594\) −30.9285 −1.26901
\(595\) 5.73217 0.234996
\(596\) 21.9458 0.898934
\(597\) −3.96755 −0.162381
\(598\) 9.12289 0.373063
\(599\) 20.8331 0.851217 0.425609 0.904907i \(-0.360060\pi\)
0.425609 + 0.904907i \(0.360060\pi\)
\(600\) −1.54913 −0.0632431
\(601\) 5.12603 0.209095 0.104547 0.994520i \(-0.466661\pi\)
0.104547 + 0.994520i \(0.466661\pi\)
\(602\) −3.53960 −0.144263
\(603\) 0.919079 0.0374278
\(604\) −21.9433 −0.892862
\(605\) −19.7533 −0.803085
\(606\) −7.75771 −0.315135
\(607\) 13.4816 0.547202 0.273601 0.961843i \(-0.411785\pi\)
0.273601 + 0.961843i \(0.411785\pi\)
\(608\) 4.05227 0.164341
\(609\) −23.6647 −0.958942
\(610\) 0.864407 0.0349988
\(611\) −10.0998 −0.408592
\(612\) −1.40569 −0.0568218
\(613\) −26.0503 −1.05216 −0.526081 0.850435i \(-0.676339\pi\)
−0.526081 + 0.850435i \(0.676339\pi\)
\(614\) −27.1174 −1.09437
\(615\) 11.6997 0.471779
\(616\) 13.5725 0.546852
\(617\) 6.49390 0.261435 0.130717 0.991420i \(-0.458272\pi\)
0.130717 + 0.991420i \(0.458272\pi\)
\(618\) −23.6635 −0.951885
\(619\) 6.55089 0.263303 0.131651 0.991296i \(-0.457972\pi\)
0.131651 + 0.991296i \(0.457972\pi\)
\(620\) 1.00000 0.0401610
\(621\) −50.8799 −2.04174
\(622\) 15.0204 0.602264
\(623\) 43.4918 1.74246
\(624\) 1.54913 0.0620150
\(625\) 1.00000 0.0400000
\(626\) 22.4506 0.897307
\(627\) 34.8123 1.39027
\(628\) 5.98154 0.238689
\(629\) −13.9167 −0.554894
\(630\) −1.46893 −0.0585235
\(631\) 48.2402 1.92041 0.960205 0.279296i \(-0.0901011\pi\)
0.960205 + 0.279296i \(0.0901011\pi\)
\(632\) 12.9284 0.514266
\(633\) 22.1512 0.880431
\(634\) −20.4469 −0.812051
\(635\) 14.7356 0.584765
\(636\) 7.48427 0.296771
\(637\) 1.00997 0.0400166
\(638\) 34.6134 1.37036
\(639\) −7.69063 −0.304237
\(640\) −1.00000 −0.0395285
\(641\) −37.7946 −1.49280 −0.746398 0.665499i \(-0.768219\pi\)
−0.746398 + 0.665499i \(0.768219\pi\)
\(642\) −29.1107 −1.14891
\(643\) −22.2650 −0.878044 −0.439022 0.898476i \(-0.644675\pi\)
−0.439022 + 0.898476i \(0.644675\pi\)
\(644\) 22.3278 0.879840
\(645\) 2.24042 0.0882163
\(646\) 9.49080 0.373411
\(647\) −3.79210 −0.149083 −0.0745414 0.997218i \(-0.523749\pi\)
−0.0745414 + 0.997218i \(0.523749\pi\)
\(648\) −6.83922 −0.268670
\(649\) −18.2098 −0.714797
\(650\) −1.00000 −0.0392232
\(651\) −3.79143 −0.148598
\(652\) −9.29991 −0.364213
\(653\) 23.8419 0.933005 0.466502 0.884520i \(-0.345514\pi\)
0.466502 + 0.884520i \(0.345514\pi\)
\(654\) 3.18640 0.124598
\(655\) −14.9000 −0.582191
\(656\) 7.55244 0.294873
\(657\) 2.31919 0.0904802
\(658\) −24.7187 −0.963634
\(659\) 15.2769 0.595102 0.297551 0.954706i \(-0.403830\pi\)
0.297551 + 0.954706i \(0.403830\pi\)
\(660\) −8.59082 −0.334397
\(661\) 37.6856 1.46580 0.732901 0.680336i \(-0.238166\pi\)
0.732901 + 0.680336i \(0.238166\pi\)
\(662\) 16.0603 0.624202
\(663\) 3.62822 0.140908
\(664\) 15.0039 0.582265
\(665\) 9.91773 0.384593
\(666\) 3.56628 0.138191
\(667\) 56.9417 2.20479
\(668\) 7.25922 0.280868
\(669\) 3.82262 0.147791
\(670\) 1.53132 0.0591602
\(671\) 4.79362 0.185056
\(672\) 3.79143 0.146258
\(673\) −44.6599 −1.72151 −0.860757 0.509016i \(-0.830009\pi\)
−0.860757 + 0.509016i \(0.830009\pi\)
\(674\) −20.8945 −0.804826
\(675\) 5.57717 0.214665
\(676\) 1.00000 0.0384615
\(677\) −10.0628 −0.386745 −0.193373 0.981125i \(-0.561943\pi\)
−0.193373 + 0.981125i \(0.561943\pi\)
\(678\) 26.1968 1.00608
\(679\) 37.2610 1.42994
\(680\) −2.34210 −0.0898153
\(681\) 40.4452 1.54986
\(682\) 5.54556 0.212351
\(683\) −24.7628 −0.947521 −0.473761 0.880654i \(-0.657104\pi\)
−0.473761 + 0.880654i \(0.657104\pi\)
\(684\) −2.43211 −0.0929942
\(685\) −15.7314 −0.601065
\(686\) 19.6040 0.748486
\(687\) 9.85728 0.376079
\(688\) 1.44624 0.0551374
\(689\) 4.83126 0.184056
\(690\) −14.1326 −0.538018
\(691\) −7.20138 −0.273954 −0.136977 0.990574i \(-0.543739\pi\)
−0.136977 + 0.990574i \(0.543739\pi\)
\(692\) 4.11152 0.156296
\(693\) −8.14603 −0.309442
\(694\) 4.36732 0.165781
\(695\) −10.4165 −0.395122
\(696\) 9.66912 0.366507
\(697\) 17.6885 0.670002
\(698\) 27.9147 1.05659
\(699\) 20.6856 0.782402
\(700\) −2.44745 −0.0925050
\(701\) −46.3871 −1.75202 −0.876008 0.482297i \(-0.839803\pi\)
−0.876008 + 0.482297i \(0.839803\pi\)
\(702\) −5.57717 −0.210497
\(703\) −24.0784 −0.908135
\(704\) −5.54556 −0.209006
\(705\) 15.6459 0.589257
\(706\) 20.6711 0.777969
\(707\) −12.2563 −0.460945
\(708\) −5.08684 −0.191175
\(709\) 18.3704 0.689913 0.344957 0.938619i \(-0.387894\pi\)
0.344957 + 0.938619i \(0.387894\pi\)
\(710\) −12.8137 −0.480891
\(711\) −7.75947 −0.291003
\(712\) −17.7702 −0.665968
\(713\) 9.12289 0.341655
\(714\) 8.87990 0.332322
\(715\) −5.54556 −0.207392
\(716\) 1.25592 0.0469360
\(717\) −23.0282 −0.860004
\(718\) −3.07167 −0.114634
\(719\) −30.9378 −1.15378 −0.576892 0.816820i \(-0.695735\pi\)
−0.576892 + 0.816820i \(0.695735\pi\)
\(720\) 0.600186 0.0223676
\(721\) −37.3856 −1.39231
\(722\) −2.57913 −0.0959854
\(723\) 16.5959 0.617208
\(724\) 15.0542 0.559484
\(725\) −6.24163 −0.231808
\(726\) −30.6005 −1.13569
\(727\) −8.12584 −0.301371 −0.150685 0.988582i \(-0.548148\pi\)
−0.150685 + 0.988582i \(0.548148\pi\)
\(728\) 2.44745 0.0907086
\(729\) 30.0241 1.11200
\(730\) 3.86412 0.143017
\(731\) 3.38723 0.125281
\(732\) 1.33908 0.0494939
\(733\) 43.1005 1.59195 0.795977 0.605326i \(-0.206957\pi\)
0.795977 + 0.605326i \(0.206957\pi\)
\(734\) 1.81266 0.0669064
\(735\) −1.56458 −0.0577106
\(736\) −9.12289 −0.336274
\(737\) 8.49205 0.312809
\(738\) −4.53287 −0.166857
\(739\) −16.2253 −0.596858 −0.298429 0.954432i \(-0.596463\pi\)
−0.298429 + 0.954432i \(0.596463\pi\)
\(740\) 5.94196 0.218431
\(741\) 6.27750 0.230610
\(742\) 11.8243 0.434083
\(743\) 43.4806 1.59515 0.797573 0.603222i \(-0.206117\pi\)
0.797573 + 0.603222i \(0.206117\pi\)
\(744\) 1.54913 0.0567940
\(745\) −21.9458 −0.804031
\(746\) −20.8441 −0.763156
\(747\) −9.00514 −0.329481
\(748\) −12.9883 −0.474898
\(749\) −45.9916 −1.68050
\(750\) 1.54913 0.0565663
\(751\) −45.4236 −1.65753 −0.828765 0.559597i \(-0.810956\pi\)
−0.828765 + 0.559597i \(0.810956\pi\)
\(752\) 10.0998 0.368300
\(753\) 38.6323 1.40784
\(754\) 6.24163 0.227307
\(755\) 21.9433 0.798600
\(756\) −13.6499 −0.496440
\(757\) −2.00646 −0.0729260 −0.0364630 0.999335i \(-0.511609\pi\)
−0.0364630 + 0.999335i \(0.511609\pi\)
\(758\) 32.8527 1.19327
\(759\) −78.3731 −2.84476
\(760\) −4.05227 −0.146991
\(761\) 12.2864 0.445382 0.222691 0.974889i \(-0.428516\pi\)
0.222691 + 0.974889i \(0.428516\pi\)
\(762\) 22.8274 0.826950
\(763\) 5.03415 0.182249
\(764\) 11.3609 0.411022
\(765\) 1.40569 0.0508230
\(766\) 10.0122 0.361757
\(767\) −3.28367 −0.118566
\(768\) −1.54913 −0.0558995
\(769\) 21.1263 0.761834 0.380917 0.924609i \(-0.375608\pi\)
0.380917 + 0.924609i \(0.375608\pi\)
\(770\) −13.5725 −0.489119
\(771\) −16.5849 −0.597290
\(772\) −21.2055 −0.763202
\(773\) −18.4904 −0.665054 −0.332527 0.943094i \(-0.607901\pi\)
−0.332527 + 0.943094i \(0.607901\pi\)
\(774\) −0.868013 −0.0312001
\(775\) −1.00000 −0.0359211
\(776\) −15.2244 −0.546523
\(777\) −22.5285 −0.808207
\(778\) 35.4099 1.26950
\(779\) 30.6045 1.09652
\(780\) −1.54913 −0.0554679
\(781\) −71.0594 −2.54271
\(782\) −21.3667 −0.764071
\(783\) −34.8106 −1.24403
\(784\) −1.00997 −0.0360705
\(785\) −5.98154 −0.213490
\(786\) −23.0821 −0.823311
\(787\) −25.0132 −0.891626 −0.445813 0.895126i \(-0.647085\pi\)
−0.445813 + 0.895126i \(0.647085\pi\)
\(788\) 17.0707 0.608119
\(789\) −12.1174 −0.431392
\(790\) −12.9284 −0.459973
\(791\) 41.3879 1.47159
\(792\) 3.32837 0.118269
\(793\) 0.864407 0.0306960
\(794\) 6.88727 0.244420
\(795\) −7.48427 −0.265440
\(796\) 2.56114 0.0907773
\(797\) 30.0470 1.06432 0.532160 0.846644i \(-0.321380\pi\)
0.532160 + 0.846644i \(0.321380\pi\)
\(798\) 15.3639 0.543876
\(799\) 23.6546 0.836840
\(800\) 1.00000 0.0353553
\(801\) 10.6655 0.376845
\(802\) 2.69010 0.0949907
\(803\) 21.4287 0.756203
\(804\) 2.37222 0.0836619
\(805\) −22.3278 −0.786953
\(806\) 1.00000 0.0352235
\(807\) −13.8715 −0.488299
\(808\) 5.00777 0.176173
\(809\) 11.2101 0.394127 0.197063 0.980391i \(-0.436860\pi\)
0.197063 + 0.980391i \(0.436860\pi\)
\(810\) 6.83922 0.240306
\(811\) 48.2767 1.69522 0.847611 0.530617i \(-0.178040\pi\)
0.847611 + 0.530617i \(0.178040\pi\)
\(812\) 15.2761 0.536086
\(813\) 8.72592 0.306031
\(814\) 32.9515 1.15495
\(815\) 9.29991 0.325762
\(816\) −3.62822 −0.127013
\(817\) 5.86055 0.205035
\(818\) 11.3839 0.398028
\(819\) −1.46893 −0.0513285
\(820\) −7.55244 −0.263743
\(821\) −23.6880 −0.826716 −0.413358 0.910569i \(-0.635644\pi\)
−0.413358 + 0.910569i \(0.635644\pi\)
\(822\) −24.3700 −0.850001
\(823\) −27.8310 −0.970127 −0.485063 0.874479i \(-0.661203\pi\)
−0.485063 + 0.874479i \(0.661203\pi\)
\(824\) 15.2753 0.532140
\(825\) 8.59082 0.299094
\(826\) −8.03663 −0.279630
\(827\) −22.4245 −0.779776 −0.389888 0.920862i \(-0.627486\pi\)
−0.389888 + 0.920862i \(0.627486\pi\)
\(828\) 5.47543 0.190284
\(829\) −32.2365 −1.11962 −0.559810 0.828621i \(-0.689126\pi\)
−0.559810 + 0.828621i \(0.689126\pi\)
\(830\) −15.0039 −0.520793
\(831\) −38.2257 −1.32604
\(832\) −1.00000 −0.0346688
\(833\) −2.36546 −0.0819583
\(834\) −16.1366 −0.558765
\(835\) −7.25922 −0.251216
\(836\) −22.4721 −0.777214
\(837\) −5.57717 −0.192775
\(838\) 23.0761 0.797150
\(839\) −26.2444 −0.906057 −0.453028 0.891496i \(-0.649656\pi\)
−0.453028 + 0.891496i \(0.649656\pi\)
\(840\) −3.79143 −0.130817
\(841\) 9.95796 0.343378
\(842\) 29.0039 0.999542
\(843\) −4.80331 −0.165435
\(844\) −14.2991 −0.492195
\(845\) −1.00000 −0.0344010
\(846\) −6.06173 −0.208407
\(847\) −48.3452 −1.66116
\(848\) −4.83126 −0.165906
\(849\) −4.80137 −0.164783
\(850\) 2.34210 0.0803333
\(851\) 54.2079 1.85822
\(852\) −19.8502 −0.680057
\(853\) 14.8053 0.506923 0.253461 0.967345i \(-0.418431\pi\)
0.253461 + 0.967345i \(0.418431\pi\)
\(854\) 2.11560 0.0723942
\(855\) 2.43211 0.0831766
\(856\) 18.7916 0.642284
\(857\) −2.42749 −0.0829214 −0.0414607 0.999140i \(-0.513201\pi\)
−0.0414607 + 0.999140i \(0.513201\pi\)
\(858\) −8.59082 −0.293286
\(859\) 9.65169 0.329312 0.164656 0.986351i \(-0.447349\pi\)
0.164656 + 0.986351i \(0.447349\pi\)
\(860\) −1.44624 −0.0493163
\(861\) 28.6346 0.975863
\(862\) 10.1033 0.344121
\(863\) 35.2153 1.19874 0.599371 0.800471i \(-0.295417\pi\)
0.599371 + 0.800471i \(0.295417\pi\)
\(864\) 5.57717 0.189739
\(865\) −4.11152 −0.139796
\(866\) −26.3104 −0.894064
\(867\) 17.8376 0.605797
\(868\) 2.44745 0.0830720
\(869\) −71.6955 −2.43210
\(870\) −9.66912 −0.327814
\(871\) 1.53132 0.0518869
\(872\) −2.05689 −0.0696552
\(873\) 9.13746 0.309256
\(874\) −36.9684 −1.25047
\(875\) 2.44745 0.0827390
\(876\) 5.98603 0.202249
\(877\) −35.2460 −1.19017 −0.595087 0.803662i \(-0.702882\pi\)
−0.595087 + 0.803662i \(0.702882\pi\)
\(878\) 15.8154 0.533744
\(879\) 19.9919 0.674311
\(880\) 5.54556 0.186941
\(881\) 0.188805 0.00636099 0.00318050 0.999995i \(-0.498988\pi\)
0.00318050 + 0.999995i \(0.498988\pi\)
\(882\) 0.606173 0.0204109
\(883\) −0.00355519 −0.000119642 0 −5.98209e−5 1.00000i \(-0.500019\pi\)
−5.98209e−5 1.00000i \(0.500019\pi\)
\(884\) −2.34210 −0.0787733
\(885\) 5.08684 0.170992
\(886\) −10.2929 −0.345796
\(887\) −32.2186 −1.08180 −0.540898 0.841088i \(-0.681916\pi\)
−0.540898 + 0.841088i \(0.681916\pi\)
\(888\) 9.20489 0.308896
\(889\) 36.0647 1.20957
\(890\) 17.7702 0.595660
\(891\) 37.9273 1.27061
\(892\) −2.46758 −0.0826208
\(893\) 40.9269 1.36957
\(894\) −33.9969 −1.13703
\(895\) −1.25592 −0.0419808
\(896\) −2.44745 −0.0817637
\(897\) −14.1326 −0.471873
\(898\) −6.92180 −0.230983
\(899\) 6.24163 0.208170
\(900\) −0.600186 −0.0200062
\(901\) −11.3153 −0.376967
\(902\) −41.8825 −1.39454
\(903\) 5.48332 0.182473
\(904\) −16.9106 −0.562439
\(905\) −15.0542 −0.500418
\(906\) 33.9932 1.12935
\(907\) −7.35645 −0.244267 −0.122133 0.992514i \(-0.538974\pi\)
−0.122133 + 0.992514i \(0.538974\pi\)
\(908\) −26.1082 −0.866433
\(909\) −3.00560 −0.0996893
\(910\) −2.44745 −0.0811323
\(911\) −34.1287 −1.13073 −0.565367 0.824839i \(-0.691266\pi\)
−0.565367 + 0.824839i \(0.691266\pi\)
\(912\) −6.27750 −0.207869
\(913\) −83.2051 −2.75369
\(914\) 12.2905 0.406534
\(915\) −1.33908 −0.0442687
\(916\) −6.36309 −0.210243
\(917\) −36.4671 −1.20425
\(918\) 13.0623 0.431119
\(919\) −28.7039 −0.946853 −0.473426 0.880833i \(-0.656983\pi\)
−0.473426 + 0.880833i \(0.656983\pi\)
\(920\) 9.12289 0.300773
\(921\) 42.0084 1.38422
\(922\) −13.7756 −0.453675
\(923\) −12.8137 −0.421770
\(924\) −21.0256 −0.691692
\(925\) −5.94196 −0.195371
\(926\) −15.2867 −0.502353
\(927\) −9.16802 −0.301117
\(928\) −6.24163 −0.204892
\(929\) 54.6399 1.79268 0.896339 0.443370i \(-0.146217\pi\)
0.896339 + 0.443370i \(0.146217\pi\)
\(930\) −1.54913 −0.0507981
\(931\) −4.09268 −0.134132
\(932\) −13.3530 −0.437393
\(933\) −23.2686 −0.761780
\(934\) −23.5599 −0.770902
\(935\) 12.9883 0.424761
\(936\) 0.600186 0.0196177
\(937\) 57.9889 1.89441 0.947207 0.320622i \(-0.103892\pi\)
0.947207 + 0.320622i \(0.103892\pi\)
\(938\) 3.74784 0.122371
\(939\) −34.7790 −1.13497
\(940\) −10.0998 −0.329418
\(941\) 14.5839 0.475420 0.237710 0.971336i \(-0.423603\pi\)
0.237710 + 0.971336i \(0.423603\pi\)
\(942\) −9.26620 −0.301909
\(943\) −68.9001 −2.24369
\(944\) 3.28367 0.106874
\(945\) 13.6499 0.444030
\(946\) −8.02021 −0.260760
\(947\) 37.8031 1.22843 0.614217 0.789137i \(-0.289472\pi\)
0.614217 + 0.789137i \(0.289472\pi\)
\(948\) −20.0279 −0.650475
\(949\) 3.86412 0.125435
\(950\) 4.05227 0.131473
\(951\) 31.6750 1.02713
\(952\) −5.73217 −0.185781
\(953\) 18.8531 0.610712 0.305356 0.952238i \(-0.401225\pi\)
0.305356 + 0.952238i \(0.401225\pi\)
\(954\) 2.89966 0.0938799
\(955\) −11.3609 −0.367629
\(956\) 14.8652 0.480776
\(957\) −53.6207 −1.73331
\(958\) 25.1565 0.812770
\(959\) −38.5018 −1.24329
\(960\) 1.54913 0.0499981
\(961\) 1.00000 0.0322581
\(962\) 5.94196 0.191577
\(963\) −11.2785 −0.363443
\(964\) −10.7130 −0.345043
\(965\) 21.2055 0.682628
\(966\) −34.5888 −1.11288
\(967\) 53.9544 1.73506 0.867528 0.497388i \(-0.165707\pi\)
0.867528 + 0.497388i \(0.165707\pi\)
\(968\) 19.7533 0.634894
\(969\) −14.7025 −0.472313
\(970\) 15.2244 0.488825
\(971\) −0.904696 −0.0290331 −0.0145165 0.999895i \(-0.504621\pi\)
−0.0145165 + 0.999895i \(0.504621\pi\)
\(972\) −6.13664 −0.196833
\(973\) −25.4940 −0.817299
\(974\) 0.268264 0.00859572
\(975\) 1.54913 0.0496120
\(976\) −0.864407 −0.0276690
\(977\) −32.9236 −1.05332 −0.526659 0.850076i \(-0.676556\pi\)
−0.526659 + 0.850076i \(0.676556\pi\)
\(978\) 14.4068 0.460679
\(979\) 98.5460 3.14954
\(980\) 1.00997 0.0322624
\(981\) 1.23452 0.0394152
\(982\) −26.8444 −0.856640
\(983\) −30.7336 −0.980250 −0.490125 0.871652i \(-0.663049\pi\)
−0.490125 + 0.871652i \(0.663049\pi\)
\(984\) −11.6997 −0.372974
\(985\) −17.0707 −0.543919
\(986\) −14.6185 −0.465548
\(987\) 38.2925 1.21886
\(988\) −4.05227 −0.128920
\(989\) −13.1939 −0.419541
\(990\) −3.32837 −0.105783
\(991\) −7.36808 −0.234055 −0.117027 0.993129i \(-0.537337\pi\)
−0.117027 + 0.993129i \(0.537337\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −24.8796 −0.789529
\(994\) −31.3610 −0.994712
\(995\) −2.56114 −0.0811937
\(996\) −23.2431 −0.736484
\(997\) −16.2999 −0.516223 −0.258111 0.966115i \(-0.583100\pi\)
−0.258111 + 0.966115i \(0.583100\pi\)
\(998\) 11.7989 0.373487
\(999\) −33.1393 −1.04848
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 \(a_p\))