Properties

Label 6040.2.a.l.1.3
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.10984\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.57672 q^{3} +1.00000 q^{5} -0.208807 q^{7} -0.513952 q^{9} +O(q^{10})\) \(q-1.57672 q^{3} +1.00000 q^{5} -0.208807 q^{7} -0.513952 q^{9} -0.616299 q^{11} -3.24227 q^{13} -1.57672 q^{15} +1.94776 q^{17} +1.81681 q^{19} +0.329230 q^{21} -1.42747 q^{23} +1.00000 q^{25} +5.54052 q^{27} -4.26518 q^{29} +6.21450 q^{31} +0.971732 q^{33} -0.208807 q^{35} +4.31510 q^{37} +5.11215 q^{39} +1.53452 q^{41} -1.84534 q^{43} -0.513952 q^{45} -4.09784 q^{47} -6.95640 q^{49} -3.07107 q^{51} +10.8297 q^{53} -0.616299 q^{55} -2.86460 q^{57} +8.06057 q^{59} -11.1832 q^{61} +0.107317 q^{63} -3.24227 q^{65} +5.24700 q^{67} +2.25071 q^{69} +8.10268 q^{71} -1.11838 q^{73} -1.57672 q^{75} +0.128687 q^{77} -7.47039 q^{79} -7.19400 q^{81} -13.6712 q^{83} +1.94776 q^{85} +6.72499 q^{87} -13.1975 q^{89} +0.677008 q^{91} -9.79853 q^{93} +1.81681 q^{95} +9.40168 q^{97} +0.316748 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{5} - 2q^{7} - 3q^{9} + O(q^{10}) \) \( 9q + 9q^{5} - 2q^{7} - 3q^{9} - 6q^{11} - 9q^{13} - 2q^{17} - 10q^{19} - 9q^{21} - 6q^{23} + 9q^{25} + 12q^{27} - 6q^{29} + 9q^{31} - 11q^{33} - 2q^{35} - 12q^{37} - 3q^{39} - 20q^{41} + q^{43} - 3q^{45} + 22q^{47} - 29q^{49} + 2q^{51} - 35q^{53} - 6q^{55} - 20q^{57} + 14q^{59} - 22q^{61} - 12q^{63} - 9q^{65} + 4q^{67} + 5q^{69} - 22q^{71} - 34q^{73} - 5q^{77} + 8q^{79} - 31q^{81} - 3q^{83} - 2q^{85} - 5q^{89} - 7q^{91} - 21q^{93} - 10q^{95} - 33q^{97} - 15q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.57672 −0.910320 −0.455160 0.890410i \(-0.650418\pi\)
−0.455160 + 0.890410i \(0.650418\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.208807 −0.0789215 −0.0394608 0.999221i \(-0.512564\pi\)
−0.0394608 + 0.999221i \(0.512564\pi\)
\(8\) 0 0
\(9\) −0.513952 −0.171317
\(10\) 0 0
\(11\) −0.616299 −0.185821 −0.0929106 0.995674i \(-0.529617\pi\)
−0.0929106 + 0.995674i \(0.529617\pi\)
\(12\) 0 0
\(13\) −3.24227 −0.899244 −0.449622 0.893219i \(-0.648441\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(14\) 0 0
\(15\) −1.57672 −0.407107
\(16\) 0 0
\(17\) 1.94776 0.472401 0.236201 0.971704i \(-0.424098\pi\)
0.236201 + 0.971704i \(0.424098\pi\)
\(18\) 0 0
\(19\) 1.81681 0.416805 0.208402 0.978043i \(-0.433174\pi\)
0.208402 + 0.978043i \(0.433174\pi\)
\(20\) 0 0
\(21\) 0.329230 0.0718438
\(22\) 0 0
\(23\) −1.42747 −0.297647 −0.148824 0.988864i \(-0.547549\pi\)
−0.148824 + 0.988864i \(0.547549\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.54052 1.06627
\(28\) 0 0
\(29\) −4.26518 −0.792023 −0.396012 0.918245i \(-0.629606\pi\)
−0.396012 + 0.918245i \(0.629606\pi\)
\(30\) 0 0
\(31\) 6.21450 1.11616 0.558079 0.829788i \(-0.311539\pi\)
0.558079 + 0.829788i \(0.311539\pi\)
\(32\) 0 0
\(33\) 0.971732 0.169157
\(34\) 0 0
\(35\) −0.208807 −0.0352948
\(36\) 0 0
\(37\) 4.31510 0.709397 0.354699 0.934981i \(-0.384583\pi\)
0.354699 + 0.934981i \(0.384583\pi\)
\(38\) 0 0
\(39\) 5.11215 0.818600
\(40\) 0 0
\(41\) 1.53452 0.239652 0.119826 0.992795i \(-0.461766\pi\)
0.119826 + 0.992795i \(0.461766\pi\)
\(42\) 0 0
\(43\) −1.84534 −0.281412 −0.140706 0.990051i \(-0.544937\pi\)
−0.140706 + 0.990051i \(0.544937\pi\)
\(44\) 0 0
\(45\) −0.513952 −0.0766155
\(46\) 0 0
\(47\) −4.09784 −0.597732 −0.298866 0.954295i \(-0.596608\pi\)
−0.298866 + 0.954295i \(0.596608\pi\)
\(48\) 0 0
\(49\) −6.95640 −0.993771
\(50\) 0 0
\(51\) −3.07107 −0.430036
\(52\) 0 0
\(53\) 10.8297 1.48757 0.743785 0.668419i \(-0.233029\pi\)
0.743785 + 0.668419i \(0.233029\pi\)
\(54\) 0 0
\(55\) −0.616299 −0.0831018
\(56\) 0 0
\(57\) −2.86460 −0.379426
\(58\) 0 0
\(59\) 8.06057 1.04940 0.524699 0.851288i \(-0.324178\pi\)
0.524699 + 0.851288i \(0.324178\pi\)
\(60\) 0 0
\(61\) −11.1832 −1.43187 −0.715933 0.698169i \(-0.753998\pi\)
−0.715933 + 0.698169i \(0.753998\pi\)
\(62\) 0 0
\(63\) 0.107317 0.0135206
\(64\) 0 0
\(65\) −3.24227 −0.402154
\(66\) 0 0
\(67\) 5.24700 0.641023 0.320511 0.947245i \(-0.396145\pi\)
0.320511 + 0.947245i \(0.396145\pi\)
\(68\) 0 0
\(69\) 2.25071 0.270954
\(70\) 0 0
\(71\) 8.10268 0.961611 0.480805 0.876827i \(-0.340344\pi\)
0.480805 + 0.876827i \(0.340344\pi\)
\(72\) 0 0
\(73\) −1.11838 −0.130896 −0.0654480 0.997856i \(-0.520848\pi\)
−0.0654480 + 0.997856i \(0.520848\pi\)
\(74\) 0 0
\(75\) −1.57672 −0.182064
\(76\) 0 0
\(77\) 0.128687 0.0146653
\(78\) 0 0
\(79\) −7.47039 −0.840484 −0.420242 0.907412i \(-0.638055\pi\)
−0.420242 + 0.907412i \(0.638055\pi\)
\(80\) 0 0
\(81\) −7.19400 −0.799333
\(82\) 0 0
\(83\) −13.6712 −1.50061 −0.750305 0.661092i \(-0.770093\pi\)
−0.750305 + 0.661092i \(0.770093\pi\)
\(84\) 0 0
\(85\) 1.94776 0.211264
\(86\) 0 0
\(87\) 6.72499 0.720995
\(88\) 0 0
\(89\) −13.1975 −1.39893 −0.699467 0.714665i \(-0.746579\pi\)
−0.699467 + 0.714665i \(0.746579\pi\)
\(90\) 0 0
\(91\) 0.677008 0.0709697
\(92\) 0 0
\(93\) −9.79853 −1.01606
\(94\) 0 0
\(95\) 1.81681 0.186401
\(96\) 0 0
\(97\) 9.40168 0.954596 0.477298 0.878741i \(-0.341616\pi\)
0.477298 + 0.878741i \(0.341616\pi\)
\(98\) 0 0
\(99\) 0.316748 0.0318344
\(100\) 0 0
\(101\) −13.2614 −1.31956 −0.659781 0.751458i \(-0.729351\pi\)
−0.659781 + 0.751458i \(0.729351\pi\)
\(102\) 0 0
\(103\) 1.44604 0.142483 0.0712415 0.997459i \(-0.477304\pi\)
0.0712415 + 0.997459i \(0.477304\pi\)
\(104\) 0 0
\(105\) 0.329230 0.0321295
\(106\) 0 0
\(107\) 10.7757 1.04173 0.520865 0.853639i \(-0.325610\pi\)
0.520865 + 0.853639i \(0.325610\pi\)
\(108\) 0 0
\(109\) 5.75641 0.551364 0.275682 0.961249i \(-0.411096\pi\)
0.275682 + 0.961249i \(0.411096\pi\)
\(110\) 0 0
\(111\) −6.80370 −0.645779
\(112\) 0 0
\(113\) −5.46809 −0.514394 −0.257197 0.966359i \(-0.582799\pi\)
−0.257197 + 0.966359i \(0.582799\pi\)
\(114\) 0 0
\(115\) −1.42747 −0.133112
\(116\) 0 0
\(117\) 1.66637 0.154056
\(118\) 0 0
\(119\) −0.406705 −0.0372826
\(120\) 0 0
\(121\) −10.6202 −0.965470
\(122\) 0 0
\(123\) −2.41951 −0.218160
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −7.43210 −0.659492 −0.329746 0.944070i \(-0.606963\pi\)
−0.329746 + 0.944070i \(0.606963\pi\)
\(128\) 0 0
\(129\) 2.90958 0.256175
\(130\) 0 0
\(131\) 7.40484 0.646964 0.323482 0.946234i \(-0.395146\pi\)
0.323482 + 0.946234i \(0.395146\pi\)
\(132\) 0 0
\(133\) −0.379362 −0.0328949
\(134\) 0 0
\(135\) 5.54052 0.476852
\(136\) 0 0
\(137\) −17.9623 −1.53462 −0.767312 0.641273i \(-0.778406\pi\)
−0.767312 + 0.641273i \(0.778406\pi\)
\(138\) 0 0
\(139\) −2.74094 −0.232483 −0.116242 0.993221i \(-0.537085\pi\)
−0.116242 + 0.993221i \(0.537085\pi\)
\(140\) 0 0
\(141\) 6.46115 0.544127
\(142\) 0 0
\(143\) 1.99821 0.167099
\(144\) 0 0
\(145\) −4.26518 −0.354204
\(146\) 0 0
\(147\) 10.9683 0.904650
\(148\) 0 0
\(149\) −17.6431 −1.44538 −0.722689 0.691174i \(-0.757094\pi\)
−0.722689 + 0.691174i \(0.757094\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) −1.00106 −0.0809305
\(154\) 0 0
\(155\) 6.21450 0.499161
\(156\) 0 0
\(157\) −3.25706 −0.259942 −0.129971 0.991518i \(-0.541488\pi\)
−0.129971 + 0.991518i \(0.541488\pi\)
\(158\) 0 0
\(159\) −17.0754 −1.35416
\(160\) 0 0
\(161\) 0.298064 0.0234908
\(162\) 0 0
\(163\) −7.69472 −0.602697 −0.301348 0.953514i \(-0.597437\pi\)
−0.301348 + 0.953514i \(0.597437\pi\)
\(164\) 0 0
\(165\) 0.971732 0.0756492
\(166\) 0 0
\(167\) 20.9172 1.61862 0.809311 0.587381i \(-0.199841\pi\)
0.809311 + 0.587381i \(0.199841\pi\)
\(168\) 0 0
\(169\) −2.48769 −0.191361
\(170\) 0 0
\(171\) −0.933754 −0.0714060
\(172\) 0 0
\(173\) −14.4578 −1.09921 −0.549605 0.835425i \(-0.685222\pi\)
−0.549605 + 0.835425i \(0.685222\pi\)
\(174\) 0 0
\(175\) −0.208807 −0.0157843
\(176\) 0 0
\(177\) −12.7093 −0.955287
\(178\) 0 0
\(179\) −8.11436 −0.606496 −0.303248 0.952912i \(-0.598071\pi\)
−0.303248 + 0.952912i \(0.598071\pi\)
\(180\) 0 0
\(181\) 22.6472 1.68335 0.841676 0.539983i \(-0.181569\pi\)
0.841676 + 0.539983i \(0.181569\pi\)
\(182\) 0 0
\(183\) 17.6328 1.30346
\(184\) 0 0
\(185\) 4.31510 0.317252
\(186\) 0 0
\(187\) −1.20040 −0.0877822
\(188\) 0 0
\(189\) −1.15690 −0.0841519
\(190\) 0 0
\(191\) 3.36141 0.243223 0.121611 0.992578i \(-0.461194\pi\)
0.121611 + 0.992578i \(0.461194\pi\)
\(192\) 0 0
\(193\) 3.99457 0.287535 0.143768 0.989611i \(-0.454078\pi\)
0.143768 + 0.989611i \(0.454078\pi\)
\(194\) 0 0
\(195\) 5.11215 0.366089
\(196\) 0 0
\(197\) 15.4145 1.09823 0.549117 0.835745i \(-0.314964\pi\)
0.549117 + 0.835745i \(0.314964\pi\)
\(198\) 0 0
\(199\) 4.61808 0.327367 0.163683 0.986513i \(-0.447662\pi\)
0.163683 + 0.986513i \(0.447662\pi\)
\(200\) 0 0
\(201\) −8.27305 −0.583536
\(202\) 0 0
\(203\) 0.890597 0.0625077
\(204\) 0 0
\(205\) 1.53452 0.107175
\(206\) 0 0
\(207\) 0.733649 0.0509921
\(208\) 0 0
\(209\) −1.11970 −0.0774512
\(210\) 0 0
\(211\) −0.713130 −0.0490939 −0.0245470 0.999699i \(-0.507814\pi\)
−0.0245470 + 0.999699i \(0.507814\pi\)
\(212\) 0 0
\(213\) −12.7757 −0.875374
\(214\) 0 0
\(215\) −1.84534 −0.125851
\(216\) 0 0
\(217\) −1.29763 −0.0880888
\(218\) 0 0
\(219\) 1.76337 0.119157
\(220\) 0 0
\(221\) −6.31516 −0.424804
\(222\) 0 0
\(223\) 3.64969 0.244401 0.122201 0.992505i \(-0.461005\pi\)
0.122201 + 0.992505i \(0.461005\pi\)
\(224\) 0 0
\(225\) −0.513952 −0.0342635
\(226\) 0 0
\(227\) 5.20840 0.345694 0.172847 0.984949i \(-0.444703\pi\)
0.172847 + 0.984949i \(0.444703\pi\)
\(228\) 0 0
\(229\) 5.13516 0.339341 0.169670 0.985501i \(-0.445730\pi\)
0.169670 + 0.985501i \(0.445730\pi\)
\(230\) 0 0
\(231\) −0.202904 −0.0133501
\(232\) 0 0
\(233\) 2.78606 0.182521 0.0912605 0.995827i \(-0.470910\pi\)
0.0912605 + 0.995827i \(0.470910\pi\)
\(234\) 0 0
\(235\) −4.09784 −0.267314
\(236\) 0 0
\(237\) 11.7787 0.765110
\(238\) 0 0
\(239\) −13.6225 −0.881167 −0.440584 0.897712i \(-0.645229\pi\)
−0.440584 + 0.897712i \(0.645229\pi\)
\(240\) 0 0
\(241\) −28.6786 −1.84735 −0.923677 0.383173i \(-0.874831\pi\)
−0.923677 + 0.383173i \(0.874831\pi\)
\(242\) 0 0
\(243\) −5.27864 −0.338625
\(244\) 0 0
\(245\) −6.95640 −0.444428
\(246\) 0 0
\(247\) −5.89059 −0.374809
\(248\) 0 0
\(249\) 21.5557 1.36604
\(250\) 0 0
\(251\) −6.32430 −0.399186 −0.199593 0.979879i \(-0.563962\pi\)
−0.199593 + 0.979879i \(0.563962\pi\)
\(252\) 0 0
\(253\) 0.879746 0.0553092
\(254\) 0 0
\(255\) −3.07107 −0.192318
\(256\) 0 0
\(257\) −22.1344 −1.38071 −0.690354 0.723472i \(-0.742545\pi\)
−0.690354 + 0.723472i \(0.742545\pi\)
\(258\) 0 0
\(259\) −0.901021 −0.0559867
\(260\) 0 0
\(261\) 2.19210 0.135687
\(262\) 0 0
\(263\) −9.72503 −0.599671 −0.299836 0.953991i \(-0.596932\pi\)
−0.299836 + 0.953991i \(0.596932\pi\)
\(264\) 0 0
\(265\) 10.8297 0.665261
\(266\) 0 0
\(267\) 20.8088 1.27348
\(268\) 0 0
\(269\) −0.848837 −0.0517545 −0.0258773 0.999665i \(-0.508238\pi\)
−0.0258773 + 0.999665i \(0.508238\pi\)
\(270\) 0 0
\(271\) −3.31253 −0.201222 −0.100611 0.994926i \(-0.532080\pi\)
−0.100611 + 0.994926i \(0.532080\pi\)
\(272\) 0 0
\(273\) −1.06745 −0.0646051
\(274\) 0 0
\(275\) −0.616299 −0.0371643
\(276\) 0 0
\(277\) −21.1085 −1.26829 −0.634144 0.773215i \(-0.718647\pi\)
−0.634144 + 0.773215i \(0.718647\pi\)
\(278\) 0 0
\(279\) −3.19396 −0.191217
\(280\) 0 0
\(281\) −6.31579 −0.376768 −0.188384 0.982095i \(-0.560325\pi\)
−0.188384 + 0.982095i \(0.560325\pi\)
\(282\) 0 0
\(283\) 13.7968 0.820134 0.410067 0.912055i \(-0.365505\pi\)
0.410067 + 0.912055i \(0.365505\pi\)
\(284\) 0 0
\(285\) −2.86460 −0.169684
\(286\) 0 0
\(287\) −0.320418 −0.0189137
\(288\) 0 0
\(289\) −13.2062 −0.776837
\(290\) 0 0
\(291\) −14.8238 −0.868988
\(292\) 0 0
\(293\) −0.0503915 −0.00294390 −0.00147195 0.999999i \(-0.500469\pi\)
−0.00147195 + 0.999999i \(0.500469\pi\)
\(294\) 0 0
\(295\) 8.06057 0.469305
\(296\) 0 0
\(297\) −3.41462 −0.198136
\(298\) 0 0
\(299\) 4.62823 0.267657
\(300\) 0 0
\(301\) 0.385319 0.0222094
\(302\) 0 0
\(303\) 20.9096 1.20122
\(304\) 0 0
\(305\) −11.1832 −0.640350
\(306\) 0 0
\(307\) −29.5064 −1.68402 −0.842008 0.539464i \(-0.818627\pi\)
−0.842008 + 0.539464i \(0.818627\pi\)
\(308\) 0 0
\(309\) −2.28001 −0.129705
\(310\) 0 0
\(311\) −15.6955 −0.890012 −0.445006 0.895528i \(-0.646798\pi\)
−0.445006 + 0.895528i \(0.646798\pi\)
\(312\) 0 0
\(313\) 19.2491 1.08803 0.544013 0.839077i \(-0.316904\pi\)
0.544013 + 0.839077i \(0.316904\pi\)
\(314\) 0 0
\(315\) 0.107317 0.00604661
\(316\) 0 0
\(317\) −8.23495 −0.462521 −0.231260 0.972892i \(-0.574285\pi\)
−0.231260 + 0.972892i \(0.574285\pi\)
\(318\) 0 0
\(319\) 2.62863 0.147175
\(320\) 0 0
\(321\) −16.9903 −0.948307
\(322\) 0 0
\(323\) 3.53871 0.196899
\(324\) 0 0
\(325\) −3.24227 −0.179849
\(326\) 0 0
\(327\) −9.07625 −0.501918
\(328\) 0 0
\(329\) 0.855657 0.0471739
\(330\) 0 0
\(331\) 8.87968 0.488072 0.244036 0.969766i \(-0.421529\pi\)
0.244036 + 0.969766i \(0.421529\pi\)
\(332\) 0 0
\(333\) −2.21775 −0.121532
\(334\) 0 0
\(335\) 5.24700 0.286674
\(336\) 0 0
\(337\) 16.6349 0.906159 0.453080 0.891470i \(-0.350325\pi\)
0.453080 + 0.891470i \(0.350325\pi\)
\(338\) 0 0
\(339\) 8.62165 0.468264
\(340\) 0 0
\(341\) −3.82999 −0.207406
\(342\) 0 0
\(343\) 2.91419 0.157351
\(344\) 0 0
\(345\) 2.25071 0.121174
\(346\) 0 0
\(347\) 24.2974 1.30435 0.652176 0.758068i \(-0.273856\pi\)
0.652176 + 0.758068i \(0.273856\pi\)
\(348\) 0 0
\(349\) −12.5363 −0.671051 −0.335525 0.942031i \(-0.608914\pi\)
−0.335525 + 0.942031i \(0.608914\pi\)
\(350\) 0 0
\(351\) −17.9639 −0.958840
\(352\) 0 0
\(353\) −18.4445 −0.981703 −0.490852 0.871243i \(-0.663314\pi\)
−0.490852 + 0.871243i \(0.663314\pi\)
\(354\) 0 0
\(355\) 8.10268 0.430045
\(356\) 0 0
\(357\) 0.641260 0.0339391
\(358\) 0 0
\(359\) 12.0751 0.637300 0.318650 0.947873i \(-0.396771\pi\)
0.318650 + 0.947873i \(0.396771\pi\)
\(360\) 0 0
\(361\) −15.6992 −0.826274
\(362\) 0 0
\(363\) 16.7450 0.878887
\(364\) 0 0
\(365\) −1.11838 −0.0585385
\(366\) 0 0
\(367\) −11.7726 −0.614523 −0.307262 0.951625i \(-0.599413\pi\)
−0.307262 + 0.951625i \(0.599413\pi\)
\(368\) 0 0
\(369\) −0.788669 −0.0410565
\(370\) 0 0
\(371\) −2.26131 −0.117401
\(372\) 0 0
\(373\) −1.70761 −0.0884168 −0.0442084 0.999022i \(-0.514077\pi\)
−0.0442084 + 0.999022i \(0.514077\pi\)
\(374\) 0 0
\(375\) −1.57672 −0.0814215
\(376\) 0 0
\(377\) 13.8289 0.712222
\(378\) 0 0
\(379\) 7.29129 0.374528 0.187264 0.982310i \(-0.440038\pi\)
0.187264 + 0.982310i \(0.440038\pi\)
\(380\) 0 0
\(381\) 11.7183 0.600349
\(382\) 0 0
\(383\) 13.6210 0.696002 0.348001 0.937494i \(-0.386861\pi\)
0.348001 + 0.937494i \(0.386861\pi\)
\(384\) 0 0
\(385\) 0.128687 0.00655852
\(386\) 0 0
\(387\) 0.948416 0.0482107
\(388\) 0 0
\(389\) −22.8664 −1.15937 −0.579685 0.814841i \(-0.696824\pi\)
−0.579685 + 0.814841i \(0.696824\pi\)
\(390\) 0 0
\(391\) −2.78036 −0.140609
\(392\) 0 0
\(393\) −11.6754 −0.588944
\(394\) 0 0
\(395\) −7.47039 −0.375876
\(396\) 0 0
\(397\) −3.92578 −0.197029 −0.0985146 0.995136i \(-0.531409\pi\)
−0.0985146 + 0.995136i \(0.531409\pi\)
\(398\) 0 0
\(399\) 0.598148 0.0299449
\(400\) 0 0
\(401\) 23.5785 1.17745 0.588727 0.808332i \(-0.299629\pi\)
0.588727 + 0.808332i \(0.299629\pi\)
\(402\) 0 0
\(403\) −20.1491 −1.00370
\(404\) 0 0
\(405\) −7.19400 −0.357473
\(406\) 0 0
\(407\) −2.65939 −0.131821
\(408\) 0 0
\(409\) −31.4830 −1.55673 −0.778367 0.627810i \(-0.783952\pi\)
−0.778367 + 0.627810i \(0.783952\pi\)
\(410\) 0 0
\(411\) 28.3216 1.39700
\(412\) 0 0
\(413\) −1.68310 −0.0828200
\(414\) 0 0
\(415\) −13.6712 −0.671093
\(416\) 0 0
\(417\) 4.32169 0.211634
\(418\) 0 0
\(419\) 4.50972 0.220314 0.110157 0.993914i \(-0.464865\pi\)
0.110157 + 0.993914i \(0.464865\pi\)
\(420\) 0 0
\(421\) −27.7864 −1.35423 −0.677113 0.735879i \(-0.736769\pi\)
−0.677113 + 0.735879i \(0.736769\pi\)
\(422\) 0 0
\(423\) 2.10609 0.102402
\(424\) 0 0
\(425\) 1.94776 0.0944802
\(426\) 0 0
\(427\) 2.33513 0.113005
\(428\) 0 0
\(429\) −3.15062 −0.152113
\(430\) 0 0
\(431\) −27.0231 −1.30166 −0.650829 0.759225i \(-0.725578\pi\)
−0.650829 + 0.759225i \(0.725578\pi\)
\(432\) 0 0
\(433\) −30.9410 −1.48693 −0.743464 0.668775i \(-0.766819\pi\)
−0.743464 + 0.668775i \(0.766819\pi\)
\(434\) 0 0
\(435\) 6.72499 0.322439
\(436\) 0 0
\(437\) −2.59343 −0.124061
\(438\) 0 0
\(439\) −36.2431 −1.72979 −0.864895 0.501952i \(-0.832615\pi\)
−0.864895 + 0.501952i \(0.832615\pi\)
\(440\) 0 0
\(441\) 3.57526 0.170250
\(442\) 0 0
\(443\) −25.3711 −1.20542 −0.602709 0.797961i \(-0.705912\pi\)
−0.602709 + 0.797961i \(0.705912\pi\)
\(444\) 0 0
\(445\) −13.1975 −0.625622
\(446\) 0 0
\(447\) 27.8182 1.31576
\(448\) 0 0
\(449\) 18.9558 0.894580 0.447290 0.894389i \(-0.352389\pi\)
0.447290 + 0.894389i \(0.352389\pi\)
\(450\) 0 0
\(451\) −0.945723 −0.0445323
\(452\) 0 0
\(453\) 1.57672 0.0740808
\(454\) 0 0
\(455\) 0.677008 0.0317386
\(456\) 0 0
\(457\) −14.2217 −0.665265 −0.332632 0.943057i \(-0.607937\pi\)
−0.332632 + 0.943057i \(0.607937\pi\)
\(458\) 0 0
\(459\) 10.7916 0.503709
\(460\) 0 0
\(461\) −24.0031 −1.11794 −0.558969 0.829189i \(-0.688803\pi\)
−0.558969 + 0.829189i \(0.688803\pi\)
\(462\) 0 0
\(463\) −11.8075 −0.548743 −0.274372 0.961624i \(-0.588470\pi\)
−0.274372 + 0.961624i \(0.588470\pi\)
\(464\) 0 0
\(465\) −9.79853 −0.454396
\(466\) 0 0
\(467\) −4.03966 −0.186933 −0.0934667 0.995622i \(-0.529795\pi\)
−0.0934667 + 0.995622i \(0.529795\pi\)
\(468\) 0 0
\(469\) −1.09561 −0.0505905
\(470\) 0 0
\(471\) 5.13547 0.236630
\(472\) 0 0
\(473\) 1.13728 0.0522923
\(474\) 0 0
\(475\) 1.81681 0.0833610
\(476\) 0 0
\(477\) −5.56593 −0.254847
\(478\) 0 0
\(479\) −24.1312 −1.10258 −0.551291 0.834313i \(-0.685864\pi\)
−0.551291 + 0.834313i \(0.685864\pi\)
\(480\) 0 0
\(481\) −13.9907 −0.637921
\(482\) 0 0
\(483\) −0.469964 −0.0213841
\(484\) 0 0
\(485\) 9.40168 0.426908
\(486\) 0 0
\(487\) 18.0591 0.818334 0.409167 0.912460i \(-0.365819\pi\)
0.409167 + 0.912460i \(0.365819\pi\)
\(488\) 0 0
\(489\) 12.1324 0.548647
\(490\) 0 0
\(491\) −19.3288 −0.872295 −0.436148 0.899875i \(-0.643657\pi\)
−0.436148 + 0.899875i \(0.643657\pi\)
\(492\) 0 0
\(493\) −8.30754 −0.374153
\(494\) 0 0
\(495\) 0.316748 0.0142368
\(496\) 0 0
\(497\) −1.69189 −0.0758918
\(498\) 0 0
\(499\) 5.06467 0.226726 0.113363 0.993554i \(-0.463838\pi\)
0.113363 + 0.993554i \(0.463838\pi\)
\(500\) 0 0
\(501\) −32.9806 −1.47346
\(502\) 0 0
\(503\) −28.2555 −1.25985 −0.629925 0.776656i \(-0.716915\pi\)
−0.629925 + 0.776656i \(0.716915\pi\)
\(504\) 0 0
\(505\) −13.2614 −0.590126
\(506\) 0 0
\(507\) 3.92239 0.174199
\(508\) 0 0
\(509\) 31.2474 1.38502 0.692508 0.721410i \(-0.256506\pi\)
0.692508 + 0.721410i \(0.256506\pi\)
\(510\) 0 0
\(511\) 0.233524 0.0103305
\(512\) 0 0
\(513\) 10.0661 0.444428
\(514\) 0 0
\(515\) 1.44604 0.0637203
\(516\) 0 0
\(517\) 2.52550 0.111071
\(518\) 0 0
\(519\) 22.7960 1.00063
\(520\) 0 0
\(521\) 16.0452 0.702954 0.351477 0.936196i \(-0.385679\pi\)
0.351477 + 0.936196i \(0.385679\pi\)
\(522\) 0 0
\(523\) −3.44740 −0.150744 −0.0753722 0.997155i \(-0.524015\pi\)
−0.0753722 + 0.997155i \(0.524015\pi\)
\(524\) 0 0
\(525\) 0.329230 0.0143688
\(526\) 0 0
\(527\) 12.1044 0.527274
\(528\) 0 0
\(529\) −20.9623 −0.911406
\(530\) 0 0
\(531\) −4.14275 −0.179780
\(532\) 0 0
\(533\) −4.97532 −0.215505
\(534\) 0 0
\(535\) 10.7757 0.465876
\(536\) 0 0
\(537\) 12.7941 0.552106
\(538\) 0 0
\(539\) 4.28723 0.184664
\(540\) 0 0
\(541\) −21.3423 −0.917578 −0.458789 0.888545i \(-0.651717\pi\)
−0.458789 + 0.888545i \(0.651717\pi\)
\(542\) 0 0
\(543\) −35.7083 −1.53239
\(544\) 0 0
\(545\) 5.75641 0.246578
\(546\) 0 0
\(547\) 31.9664 1.36679 0.683393 0.730050i \(-0.260503\pi\)
0.683393 + 0.730050i \(0.260503\pi\)
\(548\) 0 0
\(549\) 5.74764 0.245303
\(550\) 0 0
\(551\) −7.74902 −0.330119
\(552\) 0 0
\(553\) 1.55987 0.0663323
\(554\) 0 0
\(555\) −6.80370 −0.288801
\(556\) 0 0
\(557\) 29.5091 1.25034 0.625171 0.780488i \(-0.285029\pi\)
0.625171 + 0.780488i \(0.285029\pi\)
\(558\) 0 0
\(559\) 5.98309 0.253058
\(560\) 0 0
\(561\) 1.89270 0.0799099
\(562\) 0 0
\(563\) −47.0845 −1.98438 −0.992188 0.124748i \(-0.960188\pi\)
−0.992188 + 0.124748i \(0.960188\pi\)
\(564\) 0 0
\(565\) −5.46809 −0.230044
\(566\) 0 0
\(567\) 1.50215 0.0630846
\(568\) 0 0
\(569\) −12.8848 −0.540158 −0.270079 0.962838i \(-0.587050\pi\)
−0.270079 + 0.962838i \(0.587050\pi\)
\(570\) 0 0
\(571\) −40.7747 −1.70637 −0.853183 0.521611i \(-0.825331\pi\)
−0.853183 + 0.521611i \(0.825331\pi\)
\(572\) 0 0
\(573\) −5.30000 −0.221411
\(574\) 0 0
\(575\) −1.42747 −0.0595294
\(576\) 0 0
\(577\) 44.8273 1.86618 0.933091 0.359639i \(-0.117100\pi\)
0.933091 + 0.359639i \(0.117100\pi\)
\(578\) 0 0
\(579\) −6.29832 −0.261749
\(580\) 0 0
\(581\) 2.85464 0.118430
\(582\) 0 0
\(583\) −6.67432 −0.276422
\(584\) 0 0
\(585\) 1.66637 0.0688960
\(586\) 0 0
\(587\) 19.2724 0.795455 0.397728 0.917504i \(-0.369799\pi\)
0.397728 + 0.917504i \(0.369799\pi\)
\(588\) 0 0
\(589\) 11.2906 0.465220
\(590\) 0 0
\(591\) −24.3043 −0.999745
\(592\) 0 0
\(593\) 14.6610 0.602055 0.301027 0.953616i \(-0.402670\pi\)
0.301027 + 0.953616i \(0.402670\pi\)
\(594\) 0 0
\(595\) −0.406705 −0.0166733
\(596\) 0 0
\(597\) −7.28142 −0.298009
\(598\) 0 0
\(599\) 12.0961 0.494232 0.247116 0.968986i \(-0.420517\pi\)
0.247116 + 0.968986i \(0.420517\pi\)
\(600\) 0 0
\(601\) 12.0154 0.490117 0.245059 0.969508i \(-0.421193\pi\)
0.245059 + 0.969508i \(0.421193\pi\)
\(602\) 0 0
\(603\) −2.69671 −0.109818
\(604\) 0 0
\(605\) −10.6202 −0.431772
\(606\) 0 0
\(607\) −22.7414 −0.923047 −0.461523 0.887128i \(-0.652697\pi\)
−0.461523 + 0.887128i \(0.652697\pi\)
\(608\) 0 0
\(609\) −1.40422 −0.0569020
\(610\) 0 0
\(611\) 13.2863 0.537506
\(612\) 0 0
\(613\) 17.0718 0.689522 0.344761 0.938690i \(-0.387960\pi\)
0.344761 + 0.938690i \(0.387960\pi\)
\(614\) 0 0
\(615\) −2.41951 −0.0975639
\(616\) 0 0
\(617\) −34.6057 −1.39317 −0.696587 0.717473i \(-0.745299\pi\)
−0.696587 + 0.717473i \(0.745299\pi\)
\(618\) 0 0
\(619\) −30.1899 −1.21344 −0.606718 0.794917i \(-0.707514\pi\)
−0.606718 + 0.794917i \(0.707514\pi\)
\(620\) 0 0
\(621\) −7.90890 −0.317373
\(622\) 0 0
\(623\) 2.75573 0.110406
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 1.76545 0.0705054
\(628\) 0 0
\(629\) 8.40477 0.335120
\(630\) 0 0
\(631\) −44.2735 −1.76250 −0.881251 0.472649i \(-0.843298\pi\)
−0.881251 + 0.472649i \(0.843298\pi\)
\(632\) 0 0
\(633\) 1.12441 0.0446912
\(634\) 0 0
\(635\) −7.43210 −0.294934
\(636\) 0 0
\(637\) 22.5545 0.893643
\(638\) 0 0
\(639\) −4.16439 −0.164741
\(640\) 0 0
\(641\) 32.3085 1.27611 0.638055 0.769991i \(-0.279739\pi\)
0.638055 + 0.769991i \(0.279739\pi\)
\(642\) 0 0
\(643\) −0.498956 −0.0196769 −0.00983845 0.999952i \(-0.503132\pi\)
−0.00983845 + 0.999952i \(0.503132\pi\)
\(644\) 0 0
\(645\) 2.90958 0.114565
\(646\) 0 0
\(647\) 39.2668 1.54374 0.771869 0.635781i \(-0.219322\pi\)
0.771869 + 0.635781i \(0.219322\pi\)
\(648\) 0 0
\(649\) −4.96773 −0.195000
\(650\) 0 0
\(651\) 2.04600 0.0801890
\(652\) 0 0
\(653\) 23.0748 0.902987 0.451493 0.892274i \(-0.350891\pi\)
0.451493 + 0.892274i \(0.350891\pi\)
\(654\) 0 0
\(655\) 7.40484 0.289331
\(656\) 0 0
\(657\) 0.574792 0.0224248
\(658\) 0 0
\(659\) 36.2100 1.41054 0.705271 0.708938i \(-0.250825\pi\)
0.705271 + 0.708938i \(0.250825\pi\)
\(660\) 0 0
\(661\) 39.4735 1.53534 0.767670 0.640846i \(-0.221416\pi\)
0.767670 + 0.640846i \(0.221416\pi\)
\(662\) 0 0
\(663\) 9.95725 0.386707
\(664\) 0 0
\(665\) −0.379362 −0.0147110
\(666\) 0 0
\(667\) 6.08839 0.235743
\(668\) 0 0
\(669\) −5.75454 −0.222483
\(670\) 0 0
\(671\) 6.89222 0.266071
\(672\) 0 0
\(673\) 13.5574 0.522598 0.261299 0.965258i \(-0.415849\pi\)
0.261299 + 0.965258i \(0.415849\pi\)
\(674\) 0 0
\(675\) 5.54052 0.213255
\(676\) 0 0
\(677\) −41.1325 −1.58085 −0.790426 0.612558i \(-0.790141\pi\)
−0.790426 + 0.612558i \(0.790141\pi\)
\(678\) 0 0
\(679\) −1.96313 −0.0753382
\(680\) 0 0
\(681\) −8.21219 −0.314692
\(682\) 0 0
\(683\) 19.1400 0.732371 0.366186 0.930542i \(-0.380664\pi\)
0.366186 + 0.930542i \(0.380664\pi\)
\(684\) 0 0
\(685\) −17.9623 −0.686305
\(686\) 0 0
\(687\) −8.09671 −0.308909
\(688\) 0 0
\(689\) −35.1127 −1.33769
\(690\) 0 0
\(691\) 7.34560 0.279440 0.139720 0.990191i \(-0.455380\pi\)
0.139720 + 0.990191i \(0.455380\pi\)
\(692\) 0 0
\(693\) −0.0661392 −0.00251242
\(694\) 0 0
\(695\) −2.74094 −0.103970
\(696\) 0 0
\(697\) 2.98887 0.113212
\(698\) 0 0
\(699\) −4.39284 −0.166153
\(700\) 0 0
\(701\) −27.2689 −1.02993 −0.514966 0.857210i \(-0.672196\pi\)
−0.514966 + 0.857210i \(0.672196\pi\)
\(702\) 0 0
\(703\) 7.83971 0.295680
\(704\) 0 0
\(705\) 6.46115 0.243341
\(706\) 0 0
\(707\) 2.76908 0.104142
\(708\) 0 0
\(709\) 8.89231 0.333958 0.166979 0.985960i \(-0.446599\pi\)
0.166979 + 0.985960i \(0.446599\pi\)
\(710\) 0 0
\(711\) 3.83942 0.143990
\(712\) 0 0
\(713\) −8.87098 −0.332221
\(714\) 0 0
\(715\) 1.99821 0.0747288
\(716\) 0 0
\(717\) 21.4789 0.802144
\(718\) 0 0
\(719\) −21.7533 −0.811260 −0.405630 0.914037i \(-0.632948\pi\)
−0.405630 + 0.914037i \(0.632948\pi\)
\(720\) 0 0
\(721\) −0.301944 −0.0112450
\(722\) 0 0
\(723\) 45.2182 1.68168
\(724\) 0 0
\(725\) −4.26518 −0.158405
\(726\) 0 0
\(727\) 9.99766 0.370793 0.185396 0.982664i \(-0.440643\pi\)
0.185396 + 0.982664i \(0.440643\pi\)
\(728\) 0 0
\(729\) 29.9049 1.10759
\(730\) 0 0
\(731\) −3.59428 −0.132939
\(732\) 0 0
\(733\) 26.6425 0.984061 0.492031 0.870578i \(-0.336255\pi\)
0.492031 + 0.870578i \(0.336255\pi\)
\(734\) 0 0
\(735\) 10.9683 0.404572
\(736\) 0 0
\(737\) −3.23372 −0.119116
\(738\) 0 0
\(739\) 47.9446 1.76367 0.881835 0.471558i \(-0.156308\pi\)
0.881835 + 0.471558i \(0.156308\pi\)
\(740\) 0 0
\(741\) 9.28782 0.341196
\(742\) 0 0
\(743\) −20.8792 −0.765983 −0.382992 0.923752i \(-0.625106\pi\)
−0.382992 + 0.923752i \(0.625106\pi\)
\(744\) 0 0
\(745\) −17.6431 −0.646392
\(746\) 0 0
\(747\) 7.02635 0.257081
\(748\) 0 0
\(749\) −2.25004 −0.0822148
\(750\) 0 0
\(751\) 3.44860 0.125841 0.0629207 0.998019i \(-0.479958\pi\)
0.0629207 + 0.998019i \(0.479958\pi\)
\(752\) 0 0
\(753\) 9.97166 0.363387
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) 2.99315 0.108788 0.0543940 0.998520i \(-0.482677\pi\)
0.0543940 + 0.998520i \(0.482677\pi\)
\(758\) 0 0
\(759\) −1.38711 −0.0503490
\(760\) 0 0
\(761\) −24.5750 −0.890844 −0.445422 0.895321i \(-0.646946\pi\)
−0.445422 + 0.895321i \(0.646946\pi\)
\(762\) 0 0
\(763\) −1.20198 −0.0435145
\(764\) 0 0
\(765\) −1.00106 −0.0361932
\(766\) 0 0
\(767\) −26.1345 −0.943664
\(768\) 0 0
\(769\) −37.2537 −1.34340 −0.671702 0.740822i \(-0.734436\pi\)
−0.671702 + 0.740822i \(0.734436\pi\)
\(770\) 0 0
\(771\) 34.8998 1.25689
\(772\) 0 0
\(773\) 21.3887 0.769299 0.384649 0.923063i \(-0.374322\pi\)
0.384649 + 0.923063i \(0.374322\pi\)
\(774\) 0 0
\(775\) 6.21450 0.223231
\(776\) 0 0
\(777\) 1.42066 0.0509658
\(778\) 0 0
\(779\) 2.78793 0.0998879
\(780\) 0 0
\(781\) −4.99368 −0.178688
\(782\) 0 0
\(783\) −23.6313 −0.844514
\(784\) 0 0
\(785\) −3.25706 −0.116249
\(786\) 0 0
\(787\) 30.1181 1.07359 0.536797 0.843711i \(-0.319634\pi\)
0.536797 + 0.843711i \(0.319634\pi\)
\(788\) 0 0
\(789\) 15.3337 0.545893
\(790\) 0 0
\(791\) 1.14177 0.0405968
\(792\) 0 0
\(793\) 36.2590 1.28760
\(794\) 0 0
\(795\) −17.0754 −0.605601
\(796\) 0 0
\(797\) −17.1673 −0.608099 −0.304049 0.952656i \(-0.598339\pi\)
−0.304049 + 0.952656i \(0.598339\pi\)
\(798\) 0 0
\(799\) −7.98161 −0.282369
\(800\) 0 0
\(801\) 6.78289 0.239662
\(802\) 0 0
\(803\) 0.689255 0.0243233
\(804\) 0 0
\(805\) 0.298064 0.0105054
\(806\) 0 0
\(807\) 1.33838 0.0471132
\(808\) 0 0
\(809\) −14.1584 −0.497784 −0.248892 0.968531i \(-0.580066\pi\)
−0.248892 + 0.968531i \(0.580066\pi\)
\(810\) 0 0
\(811\) 21.0139 0.737897 0.368948 0.929450i \(-0.379718\pi\)
0.368948 + 0.929450i \(0.379718\pi\)
\(812\) 0 0
\(813\) 5.22294 0.183176
\(814\) 0 0
\(815\) −7.69472 −0.269534
\(816\) 0 0
\(817\) −3.35263 −0.117294
\(818\) 0 0
\(819\) −0.347950 −0.0121583
\(820\) 0 0
\(821\) −34.3762 −1.19974 −0.599869 0.800098i \(-0.704781\pi\)
−0.599869 + 0.800098i \(0.704781\pi\)
\(822\) 0 0
\(823\) 28.5373 0.994749 0.497375 0.867536i \(-0.334297\pi\)
0.497375 + 0.867536i \(0.334297\pi\)
\(824\) 0 0
\(825\) 0.971732 0.0338314
\(826\) 0 0
\(827\) −31.2311 −1.08601 −0.543005 0.839729i \(-0.682714\pi\)
−0.543005 + 0.839729i \(0.682714\pi\)
\(828\) 0 0
\(829\) 13.1885 0.458056 0.229028 0.973420i \(-0.426445\pi\)
0.229028 + 0.973420i \(0.426445\pi\)
\(830\) 0 0
\(831\) 33.2822 1.15455
\(832\) 0 0
\(833\) −13.5494 −0.469459
\(834\) 0 0
\(835\) 20.9172 0.723870
\(836\) 0 0
\(837\) 34.4316 1.19013
\(838\) 0 0
\(839\) 7.03792 0.242976 0.121488 0.992593i \(-0.461233\pi\)
0.121488 + 0.992593i \(0.461233\pi\)
\(840\) 0 0
\(841\) −10.8083 −0.372699
\(842\) 0 0
\(843\) 9.95823 0.342980
\(844\) 0 0
\(845\) −2.48769 −0.0855791
\(846\) 0 0
\(847\) 2.21756 0.0761964
\(848\) 0 0
\(849\) −21.7537 −0.746584
\(850\) 0 0
\(851\) −6.15965 −0.211150
\(852\) 0 0
\(853\) 2.21589 0.0758705 0.0379353 0.999280i \(-0.487922\pi\)
0.0379353 + 0.999280i \(0.487922\pi\)
\(854\) 0 0
\(855\) −0.933754 −0.0319337
\(856\) 0 0
\(857\) −0.678188 −0.0231665 −0.0115832 0.999933i \(-0.503687\pi\)
−0.0115832 + 0.999933i \(0.503687\pi\)
\(858\) 0 0
\(859\) 12.2532 0.418073 0.209036 0.977908i \(-0.432967\pi\)
0.209036 + 0.977908i \(0.432967\pi\)
\(860\) 0 0
\(861\) 0.505209 0.0172175
\(862\) 0 0
\(863\) −46.7632 −1.59184 −0.795920 0.605402i \(-0.793012\pi\)
−0.795920 + 0.605402i \(0.793012\pi\)
\(864\) 0 0
\(865\) −14.4578 −0.491582
\(866\) 0 0
\(867\) 20.8225 0.707170
\(868\) 0 0
\(869\) 4.60400 0.156180
\(870\) 0 0
\(871\) −17.0122 −0.576436
\(872\) 0 0
\(873\) −4.83202 −0.163539
\(874\) 0 0
\(875\) −0.208807 −0.00705895
\(876\) 0 0
\(877\) 21.3470 0.720838 0.360419 0.932791i \(-0.382634\pi\)
0.360419 + 0.932791i \(0.382634\pi\)
\(878\) 0 0
\(879\) 0.0794533 0.00267989
\(880\) 0 0
\(881\) −40.7670 −1.37348 −0.686738 0.726905i \(-0.740958\pi\)
−0.686738 + 0.726905i \(0.740958\pi\)
\(882\) 0 0
\(883\) 34.0744 1.14669 0.573347 0.819313i \(-0.305645\pi\)
0.573347 + 0.819313i \(0.305645\pi\)
\(884\) 0 0
\(885\) −12.7093 −0.427217
\(886\) 0 0
\(887\) −33.3868 −1.12102 −0.560510 0.828148i \(-0.689395\pi\)
−0.560510 + 0.828148i \(0.689395\pi\)
\(888\) 0 0
\(889\) 1.55187 0.0520481
\(890\) 0 0
\(891\) 4.43366 0.148533
\(892\) 0 0
\(893\) −7.44500 −0.249137
\(894\) 0 0
\(895\) −8.11436 −0.271233
\(896\) 0 0
\(897\) −7.29742 −0.243654
\(898\) 0 0
\(899\) −26.5059 −0.884023
\(900\) 0 0
\(901\) 21.0936 0.702729
\(902\) 0 0
\(903\) −0.607541 −0.0202177
\(904\) 0 0
\(905\) 22.6472 0.752818
\(906\) 0 0
\(907\) 30.3554 1.00794 0.503968 0.863723i \(-0.331873\pi\)
0.503968 + 0.863723i \(0.331873\pi\)
\(908\) 0 0
\(909\) 6.81574 0.226064
\(910\) 0 0
\(911\) 47.3403 1.56845 0.784227 0.620474i \(-0.213060\pi\)
0.784227 + 0.620474i \(0.213060\pi\)
\(912\) 0 0
\(913\) 8.42556 0.278845
\(914\) 0 0
\(915\) 17.6328 0.582923
\(916\) 0 0
\(917\) −1.54618 −0.0510594
\(918\) 0 0
\(919\) 6.15031 0.202880 0.101440 0.994842i \(-0.467655\pi\)
0.101440 + 0.994842i \(0.467655\pi\)
\(920\) 0 0
\(921\) 46.5233 1.53299
\(922\) 0 0
\(923\) −26.2711 −0.864723
\(924\) 0 0
\(925\) 4.31510 0.141879
\(926\) 0 0
\(927\) −0.743198 −0.0244098
\(928\) 0 0
\(929\) 35.7758 1.17377 0.586883 0.809672i \(-0.300355\pi\)
0.586883 + 0.809672i \(0.300355\pi\)
\(930\) 0 0
\(931\) −12.6385 −0.414209
\(932\) 0 0
\(933\) 24.7475 0.810196
\(934\) 0 0
\(935\) −1.20040 −0.0392574
\(936\) 0 0
\(937\) 6.49148 0.212067 0.106034 0.994363i \(-0.466185\pi\)
0.106034 + 0.994363i \(0.466185\pi\)
\(938\) 0 0
\(939\) −30.3505 −0.990452
\(940\) 0 0
\(941\) 48.9031 1.59420 0.797098 0.603850i \(-0.206367\pi\)
0.797098 + 0.603850i \(0.206367\pi\)
\(942\) 0 0
\(943\) −2.19047 −0.0713316
\(944\) 0 0
\(945\) −1.15690 −0.0376339
\(946\) 0 0
\(947\) 23.8981 0.776585 0.388292 0.921536i \(-0.373065\pi\)
0.388292 + 0.921536i \(0.373065\pi\)
\(948\) 0 0
\(949\) 3.62608 0.117707
\(950\) 0 0
\(951\) 12.9842 0.421042
\(952\) 0 0
\(953\) −44.3409 −1.43634 −0.718172 0.695866i \(-0.755021\pi\)
−0.718172 + 0.695866i \(0.755021\pi\)
\(954\) 0 0
\(955\) 3.36141 0.108773
\(956\) 0 0
\(957\) −4.14461 −0.133976
\(958\) 0 0
\(959\) 3.75065 0.121115
\(960\) 0 0
\(961\) 7.62001 0.245807
\(962\) 0 0
\(963\) −5.53821 −0.178466
\(964\) 0 0
\(965\) 3.99457 0.128590
\(966\) 0 0
\(967\) 43.2516 1.39088 0.695440 0.718585i \(-0.255210\pi\)
0.695440 + 0.718585i \(0.255210\pi\)
\(968\) 0 0
\(969\) −5.57956 −0.179241
\(970\) 0 0
\(971\) −48.3956 −1.55309 −0.776544 0.630062i \(-0.783029\pi\)
−0.776544 + 0.630062i \(0.783029\pi\)
\(972\) 0 0
\(973\) 0.572326 0.0183479
\(974\) 0 0
\(975\) 5.11215 0.163720
\(976\) 0 0
\(977\) −4.81703 −0.154110 −0.0770552 0.997027i \(-0.524552\pi\)
−0.0770552 + 0.997027i \(0.524552\pi\)
\(978\) 0 0
\(979\) 8.13362 0.259952
\(980\) 0 0
\(981\) −2.95852 −0.0944583
\(982\) 0 0
\(983\) −0.128226 −0.00408979 −0.00204490 0.999998i \(-0.500651\pi\)
−0.00204490 + 0.999998i \(0.500651\pi\)
\(984\) 0 0
\(985\) 15.4145 0.491146
\(986\) 0 0
\(987\) −1.34913 −0.0429433
\(988\) 0 0
\(989\) 2.63416 0.0837614
\(990\) 0 0
\(991\) 10.3265 0.328033 0.164016 0.986458i \(-0.447555\pi\)
0.164016 + 0.986458i \(0.447555\pi\)
\(992\) 0 0
\(993\) −14.0008 −0.444301
\(994\) 0 0
\(995\) 4.61808 0.146403
\(996\) 0 0
\(997\) 49.1178 1.55558 0.777789 0.628526i \(-0.216341\pi\)
0.777789 + 0.628526i \(0.216341\pi\)
\(998\) 0 0
\(999\) 23.9079 0.756412
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 \(a_p\))