Properties

Label 8048.2.a.v.1.15
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.0730681 q^{3} -4.10981 q^{5} +1.52145 q^{7} -2.99466 q^{9} +O(q^{10})\) \(q+0.0730681 q^{3} -4.10981 q^{5} +1.52145 q^{7} -2.99466 q^{9} -0.141296 q^{11} +5.15872 q^{13} -0.300296 q^{15} -0.728702 q^{17} -4.77534 q^{19} +0.111169 q^{21} +3.29945 q^{23} +11.8905 q^{25} -0.438018 q^{27} +5.05296 q^{29} -6.69716 q^{31} -0.0103242 q^{33} -6.25287 q^{35} +0.889403 q^{37} +0.376938 q^{39} -3.88933 q^{41} -10.3047 q^{43} +12.3075 q^{45} +10.1280 q^{47} -4.68519 q^{49} -0.0532449 q^{51} -5.37737 q^{53} +0.580698 q^{55} -0.348925 q^{57} +10.8751 q^{59} +2.06054 q^{61} -4.55623 q^{63} -21.2014 q^{65} -0.840216 q^{67} +0.241084 q^{69} +3.16133 q^{71} +1.65463 q^{73} +0.868819 q^{75} -0.214974 q^{77} +15.3526 q^{79} +8.95198 q^{81} +4.48134 q^{83} +2.99483 q^{85} +0.369210 q^{87} +9.40735 q^{89} +7.84874 q^{91} -0.489349 q^{93} +19.6258 q^{95} +3.59608 q^{97} +0.423132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

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
\(3\) 0.0730681 0.0421859 0.0210929 0.999778i \(-0.493285\pi\)
0.0210929 + 0.999778i \(0.493285\pi\)
\(4\) 0 0
\(5\) −4.10981 −1.83796 −0.918981 0.394301i \(-0.870987\pi\)
−0.918981 + 0.394301i \(0.870987\pi\)
\(6\) 0 0
\(7\) 1.52145 0.575054 0.287527 0.957773i \(-0.407167\pi\)
0.287527 + 0.957773i \(0.407167\pi\)
\(8\) 0 0
\(9\) −2.99466 −0.998220
\(10\) 0 0
\(11\) −0.141296 −0.0426022 −0.0213011 0.999773i \(-0.506781\pi\)
−0.0213011 + 0.999773i \(0.506781\pi\)
\(12\) 0 0
\(13\) 5.15872 1.43077 0.715386 0.698729i \(-0.246251\pi\)
0.715386 + 0.698729i \(0.246251\pi\)
\(14\) 0 0
\(15\) −0.300296 −0.0775361
\(16\) 0 0
\(17\) −0.728702 −0.176736 −0.0883681 0.996088i \(-0.528165\pi\)
−0.0883681 + 0.996088i \(0.528165\pi\)
\(18\) 0 0
\(19\) −4.77534 −1.09554 −0.547770 0.836629i \(-0.684523\pi\)
−0.547770 + 0.836629i \(0.684523\pi\)
\(20\) 0 0
\(21\) 0.111169 0.0242592
\(22\) 0 0
\(23\) 3.29945 0.687982 0.343991 0.938973i \(-0.388221\pi\)
0.343991 + 0.938973i \(0.388221\pi\)
\(24\) 0 0
\(25\) 11.8905 2.37811
\(26\) 0 0
\(27\) −0.438018 −0.0842967
\(28\) 0 0
\(29\) 5.05296 0.938311 0.469156 0.883116i \(-0.344558\pi\)
0.469156 + 0.883116i \(0.344558\pi\)
\(30\) 0 0
\(31\) −6.69716 −1.20285 −0.601423 0.798931i \(-0.705399\pi\)
−0.601423 + 0.798931i \(0.705399\pi\)
\(32\) 0 0
\(33\) −0.0103242 −0.00179721
\(34\) 0 0
\(35\) −6.25287 −1.05693
\(36\) 0 0
\(37\) 0.889403 0.146217 0.0731084 0.997324i \(-0.476708\pi\)
0.0731084 + 0.997324i \(0.476708\pi\)
\(38\) 0 0
\(39\) 0.376938 0.0603584
\(40\) 0 0
\(41\) −3.88933 −0.607411 −0.303705 0.952766i \(-0.598224\pi\)
−0.303705 + 0.952766i \(0.598224\pi\)
\(42\) 0 0
\(43\) −10.3047 −1.57146 −0.785729 0.618571i \(-0.787712\pi\)
−0.785729 + 0.618571i \(0.787712\pi\)
\(44\) 0 0
\(45\) 12.3075 1.83469
\(46\) 0 0
\(47\) 10.1280 1.47732 0.738661 0.674077i \(-0.235458\pi\)
0.738661 + 0.674077i \(0.235458\pi\)
\(48\) 0 0
\(49\) −4.68519 −0.669313
\(50\) 0 0
\(51\) −0.0532449 −0.00745577
\(52\) 0 0
\(53\) −5.37737 −0.738638 −0.369319 0.929303i \(-0.620409\pi\)
−0.369319 + 0.929303i \(0.620409\pi\)
\(54\) 0 0
\(55\) 0.580698 0.0783013
\(56\) 0 0
\(57\) −0.348925 −0.0462163
\(58\) 0 0
\(59\) 10.8751 1.41581 0.707906 0.706307i \(-0.249640\pi\)
0.707906 + 0.706307i \(0.249640\pi\)
\(60\) 0 0
\(61\) 2.06054 0.263825 0.131912 0.991261i \(-0.457888\pi\)
0.131912 + 0.991261i \(0.457888\pi\)
\(62\) 0 0
\(63\) −4.55623 −0.574031
\(64\) 0 0
\(65\) −21.2014 −2.62971
\(66\) 0 0
\(67\) −0.840216 −0.102649 −0.0513244 0.998682i \(-0.516344\pi\)
−0.0513244 + 0.998682i \(0.516344\pi\)
\(68\) 0 0
\(69\) 0.241084 0.0290231
\(70\) 0 0
\(71\) 3.16133 0.375180 0.187590 0.982247i \(-0.439932\pi\)
0.187590 + 0.982247i \(0.439932\pi\)
\(72\) 0 0
\(73\) 1.65463 0.193660 0.0968299 0.995301i \(-0.469130\pi\)
0.0968299 + 0.995301i \(0.469130\pi\)
\(74\) 0 0
\(75\) 0.868819 0.100323
\(76\) 0 0
\(77\) −0.214974 −0.0244986
\(78\) 0 0
\(79\) 15.3526 1.72731 0.863653 0.504086i \(-0.168171\pi\)
0.863653 + 0.504086i \(0.168171\pi\)
\(80\) 0 0
\(81\) 8.95198 0.994664
\(82\) 0 0
\(83\) 4.48134 0.491891 0.245945 0.969284i \(-0.420902\pi\)
0.245945 + 0.969284i \(0.420902\pi\)
\(84\) 0 0
\(85\) 2.99483 0.324835
\(86\) 0 0
\(87\) 0.369210 0.0395835
\(88\) 0 0
\(89\) 9.40735 0.997177 0.498589 0.866839i \(-0.333852\pi\)
0.498589 + 0.866839i \(0.333852\pi\)
\(90\) 0 0
\(91\) 7.84874 0.822771
\(92\) 0 0
\(93\) −0.489349 −0.0507431
\(94\) 0 0
\(95\) 19.6258 2.01356
\(96\) 0 0
\(97\) 3.59608 0.365127 0.182563 0.983194i \(-0.441561\pi\)
0.182563 + 0.983194i \(0.441561\pi\)
\(98\) 0 0
\(99\) 0.423132 0.0425264
\(100\) 0 0
\(101\) 2.53397 0.252140 0.126070 0.992021i \(-0.459764\pi\)
0.126070 + 0.992021i \(0.459764\pi\)
\(102\) 0 0
\(103\) −4.92495 −0.485270 −0.242635 0.970118i \(-0.578012\pi\)
−0.242635 + 0.970118i \(0.578012\pi\)
\(104\) 0 0
\(105\) −0.456885 −0.0445874
\(106\) 0 0
\(107\) 14.2378 1.37642 0.688210 0.725511i \(-0.258397\pi\)
0.688210 + 0.725511i \(0.258397\pi\)
\(108\) 0 0
\(109\) −17.8156 −1.70643 −0.853215 0.521560i \(-0.825350\pi\)
−0.853215 + 0.521560i \(0.825350\pi\)
\(110\) 0 0
\(111\) 0.0649869 0.00616829
\(112\) 0 0
\(113\) 20.4837 1.92694 0.963472 0.267808i \(-0.0862994\pi\)
0.963472 + 0.267808i \(0.0862994\pi\)
\(114\) 0 0
\(115\) −13.5601 −1.26449
\(116\) 0 0
\(117\) −15.4486 −1.42823
\(118\) 0 0
\(119\) −1.10868 −0.101633
\(120\) 0 0
\(121\) −10.9800 −0.998185
\(122\) 0 0
\(123\) −0.284186 −0.0256242
\(124\) 0 0
\(125\) −28.3188 −2.53291
\(126\) 0 0
\(127\) −5.92105 −0.525408 −0.262704 0.964876i \(-0.584614\pi\)
−0.262704 + 0.964876i \(0.584614\pi\)
\(128\) 0 0
\(129\) −0.752948 −0.0662933
\(130\) 0 0
\(131\) −9.91998 −0.866713 −0.433356 0.901223i \(-0.642671\pi\)
−0.433356 + 0.901223i \(0.642671\pi\)
\(132\) 0 0
\(133\) −7.26545 −0.629994
\(134\) 0 0
\(135\) 1.80017 0.154934
\(136\) 0 0
\(137\) −7.38820 −0.631216 −0.315608 0.948890i \(-0.602209\pi\)
−0.315608 + 0.948890i \(0.602209\pi\)
\(138\) 0 0
\(139\) 8.65267 0.733910 0.366955 0.930239i \(-0.380400\pi\)
0.366955 + 0.930239i \(0.380400\pi\)
\(140\) 0 0
\(141\) 0.740034 0.0623221
\(142\) 0 0
\(143\) −0.728905 −0.0609541
\(144\) 0 0
\(145\) −20.7667 −1.72458
\(146\) 0 0
\(147\) −0.342338 −0.0282355
\(148\) 0 0
\(149\) −6.04411 −0.495152 −0.247576 0.968868i \(-0.579634\pi\)
−0.247576 + 0.968868i \(0.579634\pi\)
\(150\) 0 0
\(151\) −17.6839 −1.43909 −0.719546 0.694445i \(-0.755650\pi\)
−0.719546 + 0.694445i \(0.755650\pi\)
\(152\) 0 0
\(153\) 2.18222 0.176422
\(154\) 0 0
\(155\) 27.5241 2.21079
\(156\) 0 0
\(157\) −17.6441 −1.40815 −0.704076 0.710125i \(-0.748638\pi\)
−0.704076 + 0.710125i \(0.748638\pi\)
\(158\) 0 0
\(159\) −0.392914 −0.0311601
\(160\) 0 0
\(161\) 5.01994 0.395627
\(162\) 0 0
\(163\) 8.29214 0.649491 0.324745 0.945801i \(-0.394721\pi\)
0.324745 + 0.945801i \(0.394721\pi\)
\(164\) 0 0
\(165\) 0.0424305 0.00330321
\(166\) 0 0
\(167\) 5.51612 0.426850 0.213425 0.976959i \(-0.431538\pi\)
0.213425 + 0.976959i \(0.431538\pi\)
\(168\) 0 0
\(169\) 13.6124 1.04711
\(170\) 0 0
\(171\) 14.3005 1.09359
\(172\) 0 0
\(173\) −17.2594 −1.31221 −0.656103 0.754672i \(-0.727796\pi\)
−0.656103 + 0.754672i \(0.727796\pi\)
\(174\) 0 0
\(175\) 18.0909 1.36754
\(176\) 0 0
\(177\) 0.794619 0.0597273
\(178\) 0 0
\(179\) −19.4972 −1.45729 −0.728643 0.684893i \(-0.759849\pi\)
−0.728643 + 0.684893i \(0.759849\pi\)
\(180\) 0 0
\(181\) −15.6670 −1.16452 −0.582261 0.813002i \(-0.697832\pi\)
−0.582261 + 0.813002i \(0.697832\pi\)
\(182\) 0 0
\(183\) 0.150560 0.0111297
\(184\) 0 0
\(185\) −3.65528 −0.268741
\(186\) 0 0
\(187\) 0.102962 0.00752936
\(188\) 0 0
\(189\) −0.666423 −0.0484751
\(190\) 0 0
\(191\) −2.96938 −0.214857 −0.107428 0.994213i \(-0.534262\pi\)
−0.107428 + 0.994213i \(0.534262\pi\)
\(192\) 0 0
\(193\) 0.575182 0.0414025 0.0207012 0.999786i \(-0.493410\pi\)
0.0207012 + 0.999786i \(0.493410\pi\)
\(194\) 0 0
\(195\) −1.54914 −0.110936
\(196\) 0 0
\(197\) 10.5996 0.755190 0.377595 0.925971i \(-0.376751\pi\)
0.377595 + 0.925971i \(0.376751\pi\)
\(198\) 0 0
\(199\) −8.21873 −0.582611 −0.291305 0.956630i \(-0.594090\pi\)
−0.291305 + 0.956630i \(0.594090\pi\)
\(200\) 0 0
\(201\) −0.0613930 −0.00433033
\(202\) 0 0
\(203\) 7.68783 0.539580
\(204\) 0 0
\(205\) 15.9844 1.11640
\(206\) 0 0
\(207\) −9.88073 −0.686758
\(208\) 0 0
\(209\) 0.674735 0.0466724
\(210\) 0 0
\(211\) −5.30392 −0.365137 −0.182568 0.983193i \(-0.558441\pi\)
−0.182568 + 0.983193i \(0.558441\pi\)
\(212\) 0 0
\(213\) 0.230992 0.0158273
\(214\) 0 0
\(215\) 42.3505 2.88828
\(216\) 0 0
\(217\) −10.1894 −0.691702
\(218\) 0 0
\(219\) 0.120901 0.00816971
\(220\) 0 0
\(221\) −3.75917 −0.252869
\(222\) 0 0
\(223\) 15.0828 1.01002 0.505009 0.863114i \(-0.331489\pi\)
0.505009 + 0.863114i \(0.331489\pi\)
\(224\) 0 0
\(225\) −35.6081 −2.37388
\(226\) 0 0
\(227\) −19.3241 −1.28259 −0.641293 0.767296i \(-0.721602\pi\)
−0.641293 + 0.767296i \(0.721602\pi\)
\(228\) 0 0
\(229\) −14.6934 −0.970965 −0.485482 0.874246i \(-0.661356\pi\)
−0.485482 + 0.874246i \(0.661356\pi\)
\(230\) 0 0
\(231\) −0.0157078 −0.00103349
\(232\) 0 0
\(233\) −24.7379 −1.62064 −0.810318 0.585990i \(-0.800706\pi\)
−0.810318 + 0.585990i \(0.800706\pi\)
\(234\) 0 0
\(235\) −41.6242 −2.71526
\(236\) 0 0
\(237\) 1.12179 0.0728679
\(238\) 0 0
\(239\) −13.5630 −0.877320 −0.438660 0.898653i \(-0.644547\pi\)
−0.438660 + 0.898653i \(0.644547\pi\)
\(240\) 0 0
\(241\) −12.5435 −0.808000 −0.404000 0.914759i \(-0.632380\pi\)
−0.404000 + 0.914759i \(0.632380\pi\)
\(242\) 0 0
\(243\) 1.96816 0.126257
\(244\) 0 0
\(245\) 19.2552 1.23017
\(246\) 0 0
\(247\) −24.6347 −1.56747
\(248\) 0 0
\(249\) 0.327443 0.0207508
\(250\) 0 0
\(251\) 1.66001 0.104779 0.0523895 0.998627i \(-0.483316\pi\)
0.0523895 + 0.998627i \(0.483316\pi\)
\(252\) 0 0
\(253\) −0.466197 −0.0293096
\(254\) 0 0
\(255\) 0.218826 0.0137034
\(256\) 0 0
\(257\) 23.4693 1.46397 0.731986 0.681320i \(-0.238594\pi\)
0.731986 + 0.681320i \(0.238594\pi\)
\(258\) 0 0
\(259\) 1.35318 0.0840826
\(260\) 0 0
\(261\) −15.1319 −0.936641
\(262\) 0 0
\(263\) −23.7494 −1.46445 −0.732225 0.681063i \(-0.761518\pi\)
−0.732225 + 0.681063i \(0.761518\pi\)
\(264\) 0 0
\(265\) 22.1000 1.35759
\(266\) 0 0
\(267\) 0.687377 0.0420668
\(268\) 0 0
\(269\) −26.1291 −1.59312 −0.796560 0.604559i \(-0.793349\pi\)
−0.796560 + 0.604559i \(0.793349\pi\)
\(270\) 0 0
\(271\) 2.72457 0.165506 0.0827530 0.996570i \(-0.473629\pi\)
0.0827530 + 0.996570i \(0.473629\pi\)
\(272\) 0 0
\(273\) 0.573492 0.0347093
\(274\) 0 0
\(275\) −1.68008 −0.101313
\(276\) 0 0
\(277\) −20.6569 −1.24115 −0.620577 0.784146i \(-0.713101\pi\)
−0.620577 + 0.784146i \(0.713101\pi\)
\(278\) 0 0
\(279\) 20.0557 1.20071
\(280\) 0 0
\(281\) −14.5258 −0.866539 −0.433270 0.901264i \(-0.642640\pi\)
−0.433270 + 0.901264i \(0.642640\pi\)
\(282\) 0 0
\(283\) 12.4114 0.737783 0.368892 0.929472i \(-0.379737\pi\)
0.368892 + 0.929472i \(0.379737\pi\)
\(284\) 0 0
\(285\) 1.43402 0.0849438
\(286\) 0 0
\(287\) −5.91742 −0.349294
\(288\) 0 0
\(289\) −16.4690 −0.968764
\(290\) 0 0
\(291\) 0.262759 0.0154032
\(292\) 0 0
\(293\) 27.6191 1.61352 0.806762 0.590876i \(-0.201218\pi\)
0.806762 + 0.590876i \(0.201218\pi\)
\(294\) 0 0
\(295\) −44.6944 −2.60221
\(296\) 0 0
\(297\) 0.0618901 0.00359123
\(298\) 0 0
\(299\) 17.0209 0.984346
\(300\) 0 0
\(301\) −15.6781 −0.903674
\(302\) 0 0
\(303\) 0.185153 0.0106367
\(304\) 0 0
\(305\) −8.46842 −0.484900
\(306\) 0 0
\(307\) −27.7198 −1.58205 −0.791025 0.611783i \(-0.790452\pi\)
−0.791025 + 0.611783i \(0.790452\pi\)
\(308\) 0 0
\(309\) −0.359857 −0.0204715
\(310\) 0 0
\(311\) −26.7891 −1.51907 −0.759536 0.650466i \(-0.774574\pi\)
−0.759536 + 0.650466i \(0.774574\pi\)
\(312\) 0 0
\(313\) 32.2082 1.82051 0.910257 0.414043i \(-0.135884\pi\)
0.910257 + 0.414043i \(0.135884\pi\)
\(314\) 0 0
\(315\) 18.7252 1.05505
\(316\) 0 0
\(317\) 5.60285 0.314687 0.157344 0.987544i \(-0.449707\pi\)
0.157344 + 0.987544i \(0.449707\pi\)
\(318\) 0 0
\(319\) −0.713961 −0.0399741
\(320\) 0 0
\(321\) 1.04033 0.0580655
\(322\) 0 0
\(323\) 3.47980 0.193622
\(324\) 0 0
\(325\) 61.3400 3.40253
\(326\) 0 0
\(327\) −1.30175 −0.0719872
\(328\) 0 0
\(329\) 15.4093 0.849541
\(330\) 0 0
\(331\) 6.98909 0.384155 0.192078 0.981380i \(-0.438477\pi\)
0.192078 + 0.981380i \(0.438477\pi\)
\(332\) 0 0
\(333\) −2.66346 −0.145957
\(334\) 0 0
\(335\) 3.45313 0.188665
\(336\) 0 0
\(337\) −6.65743 −0.362653 −0.181327 0.983423i \(-0.558039\pi\)
−0.181327 + 0.983423i \(0.558039\pi\)
\(338\) 0 0
\(339\) 1.49670 0.0812898
\(340\) 0 0
\(341\) 0.946280 0.0512439
\(342\) 0 0
\(343\) −17.7784 −0.959945
\(344\) 0 0
\(345\) −0.990810 −0.0533434
\(346\) 0 0
\(347\) 22.7192 1.21963 0.609814 0.792545i \(-0.291244\pi\)
0.609814 + 0.792545i \(0.291244\pi\)
\(348\) 0 0
\(349\) −26.8265 −1.43599 −0.717995 0.696049i \(-0.754940\pi\)
−0.717995 + 0.696049i \(0.754940\pi\)
\(350\) 0 0
\(351\) −2.25961 −0.120609
\(352\) 0 0
\(353\) −22.8463 −1.21598 −0.607992 0.793943i \(-0.708025\pi\)
−0.607992 + 0.793943i \(0.708025\pi\)
\(354\) 0 0
\(355\) −12.9925 −0.689568
\(356\) 0 0
\(357\) −0.0810094 −0.00428747
\(358\) 0 0
\(359\) 0.532684 0.0281140 0.0140570 0.999901i \(-0.495525\pi\)
0.0140570 + 0.999901i \(0.495525\pi\)
\(360\) 0 0
\(361\) 3.80392 0.200206
\(362\) 0 0
\(363\) −0.802290 −0.0421093
\(364\) 0 0
\(365\) −6.80022 −0.355940
\(366\) 0 0
\(367\) 18.7563 0.979072 0.489536 0.871983i \(-0.337166\pi\)
0.489536 + 0.871983i \(0.337166\pi\)
\(368\) 0 0
\(369\) 11.6472 0.606330
\(370\) 0 0
\(371\) −8.18139 −0.424757
\(372\) 0 0
\(373\) −0.686733 −0.0355577 −0.0177788 0.999842i \(-0.505659\pi\)
−0.0177788 + 0.999842i \(0.505659\pi\)
\(374\) 0 0
\(375\) −2.06920 −0.106853
\(376\) 0 0
\(377\) 26.0668 1.34251
\(378\) 0 0
\(379\) −17.5577 −0.901879 −0.450939 0.892555i \(-0.648911\pi\)
−0.450939 + 0.892555i \(0.648911\pi\)
\(380\) 0 0
\(381\) −0.432639 −0.0221648
\(382\) 0 0
\(383\) 28.1269 1.43722 0.718609 0.695414i \(-0.244779\pi\)
0.718609 + 0.695414i \(0.244779\pi\)
\(384\) 0 0
\(385\) 0.883503 0.0450275
\(386\) 0 0
\(387\) 30.8592 1.56866
\(388\) 0 0
\(389\) −28.6249 −1.45134 −0.725669 0.688043i \(-0.758470\pi\)
−0.725669 + 0.688043i \(0.758470\pi\)
\(390\) 0 0
\(391\) −2.40431 −0.121591
\(392\) 0 0
\(393\) −0.724834 −0.0365630
\(394\) 0 0
\(395\) −63.0964 −3.17473
\(396\) 0 0
\(397\) −26.0198 −1.30590 −0.652949 0.757402i \(-0.726468\pi\)
−0.652949 + 0.757402i \(0.726468\pi\)
\(398\) 0 0
\(399\) −0.530872 −0.0265769
\(400\) 0 0
\(401\) 27.3587 1.36623 0.683115 0.730311i \(-0.260625\pi\)
0.683115 + 0.730311i \(0.260625\pi\)
\(402\) 0 0
\(403\) −34.5488 −1.72100
\(404\) 0 0
\(405\) −36.7909 −1.82816
\(406\) 0 0
\(407\) −0.125669 −0.00622917
\(408\) 0 0
\(409\) −4.25359 −0.210326 −0.105163 0.994455i \(-0.533537\pi\)
−0.105163 + 0.994455i \(0.533537\pi\)
\(410\) 0 0
\(411\) −0.539841 −0.0266284
\(412\) 0 0
\(413\) 16.5459 0.814168
\(414\) 0 0
\(415\) −18.4174 −0.904077
\(416\) 0 0
\(417\) 0.632234 0.0309606
\(418\) 0 0
\(419\) −22.9112 −1.11929 −0.559643 0.828734i \(-0.689062\pi\)
−0.559643 + 0.828734i \(0.689062\pi\)
\(420\) 0 0
\(421\) −20.2561 −0.987224 −0.493612 0.869682i \(-0.664324\pi\)
−0.493612 + 0.869682i \(0.664324\pi\)
\(422\) 0 0
\(423\) −30.3300 −1.47469
\(424\) 0 0
\(425\) −8.66466 −0.420298
\(426\) 0 0
\(427\) 3.13501 0.151714
\(428\) 0 0
\(429\) −0.0532597 −0.00257140
\(430\) 0 0
\(431\) 32.2661 1.55421 0.777103 0.629374i \(-0.216689\pi\)
0.777103 + 0.629374i \(0.216689\pi\)
\(432\) 0 0
\(433\) −12.3984 −0.595831 −0.297916 0.954592i \(-0.596291\pi\)
−0.297916 + 0.954592i \(0.596291\pi\)
\(434\) 0 0
\(435\) −1.51738 −0.0727530
\(436\) 0 0
\(437\) −15.7560 −0.753712
\(438\) 0 0
\(439\) 23.4324 1.11837 0.559183 0.829044i \(-0.311115\pi\)
0.559183 + 0.829044i \(0.311115\pi\)
\(440\) 0 0
\(441\) 14.0306 0.668122
\(442\) 0 0
\(443\) 16.6583 0.791459 0.395729 0.918367i \(-0.370492\pi\)
0.395729 + 0.918367i \(0.370492\pi\)
\(444\) 0 0
\(445\) −38.6624 −1.83277
\(446\) 0 0
\(447\) −0.441631 −0.0208884
\(448\) 0 0
\(449\) −38.2161 −1.80353 −0.901765 0.432227i \(-0.857728\pi\)
−0.901765 + 0.432227i \(0.857728\pi\)
\(450\) 0 0
\(451\) 0.549545 0.0258771
\(452\) 0 0
\(453\) −1.29213 −0.0607093
\(454\) 0 0
\(455\) −32.2568 −1.51222
\(456\) 0 0
\(457\) 12.3565 0.578013 0.289006 0.957327i \(-0.406675\pi\)
0.289006 + 0.957327i \(0.406675\pi\)
\(458\) 0 0
\(459\) 0.319185 0.0148983
\(460\) 0 0
\(461\) 2.87272 0.133796 0.0668979 0.997760i \(-0.478690\pi\)
0.0668979 + 0.997760i \(0.478690\pi\)
\(462\) 0 0
\(463\) −17.2179 −0.800184 −0.400092 0.916475i \(-0.631022\pi\)
−0.400092 + 0.916475i \(0.631022\pi\)
\(464\) 0 0
\(465\) 2.01113 0.0932640
\(466\) 0 0
\(467\) 24.2286 1.12117 0.560583 0.828098i \(-0.310577\pi\)
0.560583 + 0.828098i \(0.310577\pi\)
\(468\) 0 0
\(469\) −1.27835 −0.0590286
\(470\) 0 0
\(471\) −1.28922 −0.0594041
\(472\) 0 0
\(473\) 1.45601 0.0669476
\(474\) 0 0
\(475\) −56.7814 −2.60531
\(476\) 0 0
\(477\) 16.1034 0.737323
\(478\) 0 0
\(479\) 6.90956 0.315706 0.157853 0.987463i \(-0.449543\pi\)
0.157853 + 0.987463i \(0.449543\pi\)
\(480\) 0 0
\(481\) 4.58818 0.209203
\(482\) 0 0
\(483\) 0.366798 0.0166899
\(484\) 0 0
\(485\) −14.7792 −0.671090
\(486\) 0 0
\(487\) 33.2651 1.50738 0.753692 0.657228i \(-0.228271\pi\)
0.753692 + 0.657228i \(0.228271\pi\)
\(488\) 0 0
\(489\) 0.605891 0.0273993
\(490\) 0 0
\(491\) −20.7578 −0.936785 −0.468393 0.883520i \(-0.655167\pi\)
−0.468393 + 0.883520i \(0.655167\pi\)
\(492\) 0 0
\(493\) −3.68210 −0.165834
\(494\) 0 0
\(495\) −1.73899 −0.0781620
\(496\) 0 0
\(497\) 4.80980 0.215749
\(498\) 0 0
\(499\) −15.4688 −0.692481 −0.346240 0.938146i \(-0.612542\pi\)
−0.346240 + 0.938146i \(0.612542\pi\)
\(500\) 0 0
\(501\) 0.403053 0.0180071
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −10.4141 −0.463424
\(506\) 0 0
\(507\) 0.994633 0.0441732
\(508\) 0 0
\(509\) −13.7838 −0.610956 −0.305478 0.952199i \(-0.598816\pi\)
−0.305478 + 0.952199i \(0.598816\pi\)
\(510\) 0 0
\(511\) 2.51744 0.111365
\(512\) 0 0
\(513\) 2.09169 0.0923503
\(514\) 0 0
\(515\) 20.2406 0.891908
\(516\) 0 0
\(517\) −1.43104 −0.0629372
\(518\) 0 0
\(519\) −1.26111 −0.0553565
\(520\) 0 0
\(521\) 7.46908 0.327226 0.163613 0.986525i \(-0.447685\pi\)
0.163613 + 0.986525i \(0.447685\pi\)
\(522\) 0 0
\(523\) 9.98612 0.436663 0.218331 0.975875i \(-0.429939\pi\)
0.218331 + 0.975875i \(0.429939\pi\)
\(524\) 0 0
\(525\) 1.32186 0.0576909
\(526\) 0 0
\(527\) 4.88024 0.212587
\(528\) 0 0
\(529\) −12.1136 −0.526680
\(530\) 0 0
\(531\) −32.5671 −1.41329
\(532\) 0 0
\(533\) −20.0640 −0.869066
\(534\) 0 0
\(535\) −58.5147 −2.52981
\(536\) 0 0
\(537\) −1.42462 −0.0614769
\(538\) 0 0
\(539\) 0.661997 0.0285142
\(540\) 0 0
\(541\) −32.9816 −1.41799 −0.708996 0.705213i \(-0.750852\pi\)
−0.708996 + 0.705213i \(0.750852\pi\)
\(542\) 0 0
\(543\) −1.14476 −0.0491264
\(544\) 0 0
\(545\) 73.2189 3.13635
\(546\) 0 0
\(547\) 29.2017 1.24857 0.624287 0.781195i \(-0.285390\pi\)
0.624287 + 0.781195i \(0.285390\pi\)
\(548\) 0 0
\(549\) −6.17061 −0.263355
\(550\) 0 0
\(551\) −24.1296 −1.02796
\(552\) 0 0
\(553\) 23.3583 0.993295
\(554\) 0 0
\(555\) −0.267084 −0.0113371
\(556\) 0 0
\(557\) −3.99891 −0.169439 −0.0847197 0.996405i \(-0.526999\pi\)
−0.0847197 + 0.996405i \(0.526999\pi\)
\(558\) 0 0
\(559\) −53.1593 −2.24840
\(560\) 0 0
\(561\) 0.00752327 0.000317633 0
\(562\) 0 0
\(563\) 18.3964 0.775315 0.387657 0.921804i \(-0.373284\pi\)
0.387657 + 0.921804i \(0.373284\pi\)
\(564\) 0 0
\(565\) −84.1841 −3.54165
\(566\) 0 0
\(567\) 13.6200 0.571986
\(568\) 0 0
\(569\) 34.6703 1.45346 0.726728 0.686926i \(-0.241040\pi\)
0.726728 + 0.686926i \(0.241040\pi\)
\(570\) 0 0
\(571\) −8.27969 −0.346494 −0.173247 0.984878i \(-0.555426\pi\)
−0.173247 + 0.984878i \(0.555426\pi\)
\(572\) 0 0
\(573\) −0.216967 −0.00906392
\(574\) 0 0
\(575\) 39.2322 1.63610
\(576\) 0 0
\(577\) −4.92315 −0.204953 −0.102477 0.994735i \(-0.532677\pi\)
−0.102477 + 0.994735i \(0.532677\pi\)
\(578\) 0 0
\(579\) 0.0420274 0.00174660
\(580\) 0 0
\(581\) 6.81813 0.282864
\(582\) 0 0
\(583\) 0.759798 0.0314676
\(584\) 0 0
\(585\) 63.4909 2.62503
\(586\) 0 0
\(587\) 9.75924 0.402807 0.201403 0.979508i \(-0.435450\pi\)
0.201403 + 0.979508i \(0.435450\pi\)
\(588\) 0 0
\(589\) 31.9813 1.31777
\(590\) 0 0
\(591\) 0.774492 0.0318583
\(592\) 0 0
\(593\) 28.1136 1.15449 0.577244 0.816572i \(-0.304128\pi\)
0.577244 + 0.816572i \(0.304128\pi\)
\(594\) 0 0
\(595\) 4.55648 0.186798
\(596\) 0 0
\(597\) −0.600527 −0.0245779
\(598\) 0 0
\(599\) −2.03151 −0.0830054 −0.0415027 0.999138i \(-0.513215\pi\)
−0.0415027 + 0.999138i \(0.513215\pi\)
\(600\) 0 0
\(601\) 26.8019 1.09327 0.546637 0.837370i \(-0.315908\pi\)
0.546637 + 0.837370i \(0.315908\pi\)
\(602\) 0 0
\(603\) 2.51616 0.102466
\(604\) 0 0
\(605\) 45.1259 1.83463
\(606\) 0 0
\(607\) −23.7433 −0.963711 −0.481856 0.876251i \(-0.660037\pi\)
−0.481856 + 0.876251i \(0.660037\pi\)
\(608\) 0 0
\(609\) 0.561735 0.0227626
\(610\) 0 0
\(611\) 52.2476 2.11371
\(612\) 0 0
\(613\) 12.3499 0.498809 0.249404 0.968399i \(-0.419765\pi\)
0.249404 + 0.968399i \(0.419765\pi\)
\(614\) 0 0
\(615\) 1.16795 0.0470962
\(616\) 0 0
\(617\) −40.9551 −1.64879 −0.824395 0.566015i \(-0.808484\pi\)
−0.824395 + 0.566015i \(0.808484\pi\)
\(618\) 0 0
\(619\) −33.2176 −1.33513 −0.667564 0.744553i \(-0.732663\pi\)
−0.667564 + 0.744553i \(0.732663\pi\)
\(620\) 0 0
\(621\) −1.44522 −0.0579946
\(622\) 0 0
\(623\) 14.3128 0.573431
\(624\) 0 0
\(625\) 56.9322 2.27729
\(626\) 0 0
\(627\) 0.0493016 0.00196892
\(628\) 0 0
\(629\) −0.648110 −0.0258418
\(630\) 0 0
\(631\) 32.5839 1.29715 0.648573 0.761153i \(-0.275366\pi\)
0.648573 + 0.761153i \(0.275366\pi\)
\(632\) 0 0
\(633\) −0.387547 −0.0154036
\(634\) 0 0
\(635\) 24.3344 0.965680
\(636\) 0 0
\(637\) −24.1696 −0.957634
\(638\) 0 0
\(639\) −9.46710 −0.374513
\(640\) 0 0
\(641\) 24.5080 0.968007 0.484003 0.875066i \(-0.339182\pi\)
0.484003 + 0.875066i \(0.339182\pi\)
\(642\) 0 0
\(643\) 42.0710 1.65912 0.829559 0.558419i \(-0.188592\pi\)
0.829559 + 0.558419i \(0.188592\pi\)
\(644\) 0 0
\(645\) 3.09447 0.121845
\(646\) 0 0
\(647\) 16.7124 0.657033 0.328517 0.944498i \(-0.393451\pi\)
0.328517 + 0.944498i \(0.393451\pi\)
\(648\) 0 0
\(649\) −1.53660 −0.0603167
\(650\) 0 0
\(651\) −0.744520 −0.0291800
\(652\) 0 0
\(653\) −22.4510 −0.878577 −0.439288 0.898346i \(-0.644769\pi\)
−0.439288 + 0.898346i \(0.644769\pi\)
\(654\) 0 0
\(655\) 40.7692 1.59299
\(656\) 0 0
\(657\) −4.95506 −0.193315
\(658\) 0 0
\(659\) −49.5169 −1.92890 −0.964452 0.264260i \(-0.914872\pi\)
−0.964452 + 0.264260i \(0.914872\pi\)
\(660\) 0 0
\(661\) −19.5166 −0.759109 −0.379554 0.925169i \(-0.623923\pi\)
−0.379554 + 0.925169i \(0.623923\pi\)
\(662\) 0 0
\(663\) −0.274676 −0.0106675
\(664\) 0 0
\(665\) 29.8596 1.15791
\(666\) 0 0
\(667\) 16.6720 0.645541
\(668\) 0 0
\(669\) 1.10207 0.0426084
\(670\) 0 0
\(671\) −0.291145 −0.0112395
\(672\) 0 0
\(673\) −2.03282 −0.0783595 −0.0391797 0.999232i \(-0.512474\pi\)
−0.0391797 + 0.999232i \(0.512474\pi\)
\(674\) 0 0
\(675\) −5.20827 −0.200467
\(676\) 0 0
\(677\) 26.7787 1.02919 0.514595 0.857433i \(-0.327942\pi\)
0.514595 + 0.857433i \(0.327942\pi\)
\(678\) 0 0
\(679\) 5.47126 0.209968
\(680\) 0 0
\(681\) −1.41197 −0.0541070
\(682\) 0 0
\(683\) −13.8120 −0.528500 −0.264250 0.964454i \(-0.585124\pi\)
−0.264250 + 0.964454i \(0.585124\pi\)
\(684\) 0 0
\(685\) 30.3641 1.16015
\(686\) 0 0
\(687\) −1.07362 −0.0409610
\(688\) 0 0
\(689\) −27.7403 −1.05682
\(690\) 0 0
\(691\) 12.6835 0.482504 0.241252 0.970462i \(-0.422442\pi\)
0.241252 + 0.970462i \(0.422442\pi\)
\(692\) 0 0
\(693\) 0.643775 0.0244550
\(694\) 0 0
\(695\) −35.5608 −1.34890
\(696\) 0 0
\(697\) 2.83416 0.107352
\(698\) 0 0
\(699\) −1.80755 −0.0683679
\(700\) 0 0
\(701\) −15.4620 −0.583992 −0.291996 0.956419i \(-0.594319\pi\)
−0.291996 + 0.956419i \(0.594319\pi\)
\(702\) 0 0
\(703\) −4.24720 −0.160186
\(704\) 0 0
\(705\) −3.04140 −0.114546
\(706\) 0 0
\(707\) 3.85531 0.144994
\(708\) 0 0
\(709\) −25.8423 −0.970527 −0.485263 0.874368i \(-0.661276\pi\)
−0.485263 + 0.874368i \(0.661276\pi\)
\(710\) 0 0
\(711\) −45.9759 −1.72423
\(712\) 0 0
\(713\) −22.0969 −0.827537
\(714\) 0 0
\(715\) 2.99566 0.112031
\(716\) 0 0
\(717\) −0.991025 −0.0370105
\(718\) 0 0
\(719\) 0.741955 0.0276703 0.0138351 0.999904i \(-0.495596\pi\)
0.0138351 + 0.999904i \(0.495596\pi\)
\(720\) 0 0
\(721\) −7.49307 −0.279057
\(722\) 0 0
\(723\) −0.916532 −0.0340862
\(724\) 0 0
\(725\) 60.0824 2.23140
\(726\) 0 0
\(727\) −11.5068 −0.426765 −0.213382 0.976969i \(-0.568448\pi\)
−0.213382 + 0.976969i \(0.568448\pi\)
\(728\) 0 0
\(729\) −26.7121 −0.989338
\(730\) 0 0
\(731\) 7.50909 0.277734
\(732\) 0 0
\(733\) 28.6560 1.05843 0.529217 0.848486i \(-0.322486\pi\)
0.529217 + 0.848486i \(0.322486\pi\)
\(734\) 0 0
\(735\) 1.40694 0.0518959
\(736\) 0 0
\(737\) 0.118719 0.00437307
\(738\) 0 0
\(739\) 12.4543 0.458140 0.229070 0.973410i \(-0.426431\pi\)
0.229070 + 0.973410i \(0.426431\pi\)
\(740\) 0 0
\(741\) −1.80001 −0.0661250
\(742\) 0 0
\(743\) 29.9540 1.09891 0.549453 0.835525i \(-0.314836\pi\)
0.549453 + 0.835525i \(0.314836\pi\)
\(744\) 0 0
\(745\) 24.8401 0.910072
\(746\) 0 0
\(747\) −13.4201 −0.491015
\(748\) 0 0
\(749\) 21.6621 0.791516
\(750\) 0 0
\(751\) 41.4823 1.51371 0.756856 0.653582i \(-0.226734\pi\)
0.756856 + 0.653582i \(0.226734\pi\)
\(752\) 0 0
\(753\) 0.121294 0.00442019
\(754\) 0 0
\(755\) 72.6773 2.64500
\(756\) 0 0
\(757\) 27.8676 1.01287 0.506433 0.862279i \(-0.330964\pi\)
0.506433 + 0.862279i \(0.330964\pi\)
\(758\) 0 0
\(759\) −0.0340641 −0.00123645
\(760\) 0 0
\(761\) 26.3231 0.954210 0.477105 0.878846i \(-0.341686\pi\)
0.477105 + 0.878846i \(0.341686\pi\)
\(762\) 0 0
\(763\) −27.1056 −0.981289
\(764\) 0 0
\(765\) −8.96849 −0.324257
\(766\) 0 0
\(767\) 56.1014 2.02570
\(768\) 0 0
\(769\) −11.6606 −0.420494 −0.210247 0.977648i \(-0.567427\pi\)
−0.210247 + 0.977648i \(0.567427\pi\)
\(770\) 0 0
\(771\) 1.71485 0.0617589
\(772\) 0 0
\(773\) −5.19436 −0.186828 −0.0934141 0.995627i \(-0.529778\pi\)
−0.0934141 + 0.995627i \(0.529778\pi\)
\(774\) 0 0
\(775\) −79.6329 −2.86050
\(776\) 0 0
\(777\) 0.0988744 0.00354710
\(778\) 0 0
\(779\) 18.5729 0.665442
\(780\) 0 0
\(781\) −0.446682 −0.0159835
\(782\) 0 0
\(783\) −2.21329 −0.0790965
\(784\) 0 0
\(785\) 72.5138 2.58813
\(786\) 0 0
\(787\) −30.1729 −1.07555 −0.537774 0.843089i \(-0.680735\pi\)
−0.537774 + 0.843089i \(0.680735\pi\)
\(788\) 0 0
\(789\) −1.73532 −0.0617791
\(790\) 0 0
\(791\) 31.1649 1.10810
\(792\) 0 0
\(793\) 10.6297 0.377473
\(794\) 0 0
\(795\) 1.61480 0.0572711
\(796\) 0 0
\(797\) −37.8145 −1.33946 −0.669729 0.742605i \(-0.733590\pi\)
−0.669729 + 0.742605i \(0.733590\pi\)
\(798\) 0 0
\(799\) −7.38031 −0.261096
\(800\) 0 0
\(801\) −28.1718 −0.995403
\(802\) 0 0
\(803\) −0.233792 −0.00825034
\(804\) 0 0
\(805\) −20.6310 −0.727148
\(806\) 0 0
\(807\) −1.90920 −0.0672072
\(808\) 0 0
\(809\) −22.6375 −0.795893 −0.397947 0.917409i \(-0.630277\pi\)
−0.397947 + 0.917409i \(0.630277\pi\)
\(810\) 0 0
\(811\) −17.4411 −0.612440 −0.306220 0.951961i \(-0.599064\pi\)
−0.306220 + 0.951961i \(0.599064\pi\)
\(812\) 0 0
\(813\) 0.199079 0.00698202
\(814\) 0 0
\(815\) −34.0791 −1.19374
\(816\) 0 0
\(817\) 49.2087 1.72159
\(818\) 0 0
\(819\) −23.5043 −0.821307
\(820\) 0 0
\(821\) −52.3011 −1.82532 −0.912660 0.408720i \(-0.865975\pi\)
−0.912660 + 0.408720i \(0.865975\pi\)
\(822\) 0 0
\(823\) −18.3400 −0.639293 −0.319647 0.947537i \(-0.603564\pi\)
−0.319647 + 0.947537i \(0.603564\pi\)
\(824\) 0 0
\(825\) −0.122760 −0.00427396
\(826\) 0 0
\(827\) 20.4391 0.710738 0.355369 0.934726i \(-0.384355\pi\)
0.355369 + 0.934726i \(0.384355\pi\)
\(828\) 0 0
\(829\) −31.9572 −1.10992 −0.554959 0.831878i \(-0.687266\pi\)
−0.554959 + 0.831878i \(0.687266\pi\)
\(830\) 0 0
\(831\) −1.50936 −0.0523591
\(832\) 0 0
\(833\) 3.41411 0.118292
\(834\) 0 0
\(835\) −22.6702 −0.784535
\(836\) 0 0
\(837\) 2.93348 0.101396
\(838\) 0 0
\(839\) −5.32138 −0.183715 −0.0918573 0.995772i \(-0.529280\pi\)
−0.0918573 + 0.995772i \(0.529280\pi\)
\(840\) 0 0
\(841\) −3.46760 −0.119572
\(842\) 0 0
\(843\) −1.06138 −0.0365557
\(844\) 0 0
\(845\) −55.9444 −1.92455
\(846\) 0 0
\(847\) −16.7056 −0.574010
\(848\) 0 0
\(849\) 0.906880 0.0311240
\(850\) 0 0
\(851\) 2.93454 0.100595
\(852\) 0 0
\(853\) 20.3101 0.695405 0.347702 0.937605i \(-0.386962\pi\)
0.347702 + 0.937605i \(0.386962\pi\)
\(854\) 0 0
\(855\) −58.7725 −2.00998
\(856\) 0 0
\(857\) −25.7179 −0.878506 −0.439253 0.898363i \(-0.644757\pi\)
−0.439253 + 0.898363i \(0.644757\pi\)
\(858\) 0 0
\(859\) 32.0127 1.09226 0.546130 0.837700i \(-0.316100\pi\)
0.546130 + 0.837700i \(0.316100\pi\)
\(860\) 0 0
\(861\) −0.432374 −0.0147353
\(862\) 0 0
\(863\) 4.70980 0.160324 0.0801618 0.996782i \(-0.474456\pi\)
0.0801618 + 0.996782i \(0.474456\pi\)
\(864\) 0 0
\(865\) 70.9327 2.41178
\(866\) 0 0
\(867\) −1.20336 −0.0408682
\(868\) 0 0
\(869\) −2.16926 −0.0735871
\(870\) 0 0
\(871\) −4.33444 −0.146867
\(872\) 0 0
\(873\) −10.7690 −0.364477
\(874\) 0 0
\(875\) −43.0856 −1.45656
\(876\) 0 0
\(877\) 34.8968 1.17838 0.589191 0.807994i \(-0.299447\pi\)
0.589191 + 0.807994i \(0.299447\pi\)
\(878\) 0 0
\(879\) 2.01807 0.0680679
\(880\) 0 0
\(881\) 15.0888 0.508356 0.254178 0.967157i \(-0.418195\pi\)
0.254178 + 0.967157i \(0.418195\pi\)
\(882\) 0 0
\(883\) −20.0939 −0.676215 −0.338108 0.941107i \(-0.609787\pi\)
−0.338108 + 0.941107i \(0.609787\pi\)
\(884\) 0 0
\(885\) −3.26573 −0.109776
\(886\) 0 0
\(887\) 13.3512 0.448289 0.224144 0.974556i \(-0.428041\pi\)
0.224144 + 0.974556i \(0.428041\pi\)
\(888\) 0 0
\(889\) −9.00858 −0.302138
\(890\) 0 0
\(891\) −1.26488 −0.0423749
\(892\) 0 0
\(893\) −48.3648 −1.61846
\(894\) 0 0
\(895\) 80.1297 2.67844
\(896\) 0 0
\(897\) 1.24369 0.0415255
\(898\) 0 0
\(899\) −33.8405 −1.12864
\(900\) 0 0
\(901\) 3.91850 0.130544
\(902\) 0 0
\(903\) −1.14557 −0.0381223
\(904\) 0 0
\(905\) 64.3885 2.14035
\(906\) 0 0
\(907\) 28.2979 0.939617 0.469809 0.882768i \(-0.344323\pi\)
0.469809 + 0.882768i \(0.344323\pi\)
\(908\) 0 0
\(909\) −7.58839 −0.251691
\(910\) 0 0
\(911\) 11.4782 0.380289 0.190145 0.981756i \(-0.439104\pi\)
0.190145 + 0.981756i \(0.439104\pi\)
\(912\) 0 0
\(913\) −0.633193 −0.0209556
\(914\) 0 0
\(915\) −0.618771 −0.0204559
\(916\) 0 0
\(917\) −15.0928 −0.498407
\(918\) 0 0
\(919\) −10.2410 −0.337821 −0.168910 0.985631i \(-0.554025\pi\)
−0.168910 + 0.985631i \(0.554025\pi\)
\(920\) 0 0
\(921\) −2.02543 −0.0667402
\(922\) 0 0
\(923\) 16.3084 0.536798
\(924\) 0 0
\(925\) 10.5755 0.347720
\(926\) 0 0
\(927\) 14.7486 0.484406
\(928\) 0 0
\(929\) −39.8486 −1.30739 −0.653696 0.756758i \(-0.726782\pi\)
−0.653696 + 0.756758i \(0.726782\pi\)
\(930\) 0 0
\(931\) 22.3734 0.733258
\(932\) 0 0
\(933\) −1.95743 −0.0640833
\(934\) 0 0
\(935\) −0.423156 −0.0138387
\(936\) 0 0
\(937\) −30.7233 −1.00368 −0.501842 0.864959i \(-0.667344\pi\)
−0.501842 + 0.864959i \(0.667344\pi\)
\(938\) 0 0
\(939\) 2.35339 0.0768000
\(940\) 0 0
\(941\) −33.5974 −1.09524 −0.547622 0.836726i \(-0.684467\pi\)
−0.547622 + 0.836726i \(0.684467\pi\)
\(942\) 0 0
\(943\) −12.8326 −0.417888
\(944\) 0 0
\(945\) 2.73887 0.0890955
\(946\) 0 0
\(947\) −44.7905 −1.45549 −0.727747 0.685845i \(-0.759433\pi\)
−0.727747 + 0.685845i \(0.759433\pi\)
\(948\) 0 0
\(949\) 8.53578 0.277083
\(950\) 0 0
\(951\) 0.409389 0.0132754
\(952\) 0 0
\(953\) 42.3911 1.37318 0.686591 0.727044i \(-0.259106\pi\)
0.686591 + 0.727044i \(0.259106\pi\)
\(954\) 0 0
\(955\) 12.2036 0.394899
\(956\) 0 0
\(957\) −0.0521678 −0.00168634
\(958\) 0 0
\(959\) −11.2408 −0.362984
\(960\) 0 0
\(961\) 13.8520 0.446839
\(962\) 0 0
\(963\) −42.6374 −1.37397
\(964\) 0 0
\(965\) −2.36389 −0.0760963
\(966\) 0 0
\(967\) 34.5556 1.11123 0.555617 0.831438i \(-0.312482\pi\)
0.555617 + 0.831438i \(0.312482\pi\)
\(968\) 0 0
\(969\) 0.254263 0.00816809
\(970\) 0 0
\(971\) 25.3833 0.814590 0.407295 0.913297i \(-0.366472\pi\)
0.407295 + 0.913297i \(0.366472\pi\)
\(972\) 0 0
\(973\) 13.1646 0.422038
\(974\) 0 0
\(975\) 4.48199 0.143539
\(976\) 0 0
\(977\) −9.73604 −0.311484 −0.155742 0.987798i \(-0.549777\pi\)
−0.155742 + 0.987798i \(0.549777\pi\)
\(978\) 0 0
\(979\) −1.32922 −0.0424820
\(980\) 0 0
\(981\) 53.3518 1.70339
\(982\) 0 0
\(983\) −25.0925 −0.800325 −0.400162 0.916444i \(-0.631046\pi\)
−0.400162 + 0.916444i \(0.631046\pi\)
\(984\) 0 0
\(985\) −43.5623 −1.38801
\(986\) 0 0
\(987\) 1.12593 0.0358386
\(988\) 0 0
\(989\) −33.9999 −1.08114
\(990\) 0 0
\(991\) −12.5639 −0.399104 −0.199552 0.979887i \(-0.563949\pi\)
−0.199552 + 0.979887i \(0.563949\pi\)
\(992\) 0 0
\(993\) 0.510680 0.0162059
\(994\) 0 0
\(995\) 33.7774 1.07082
\(996\) 0 0
\(997\) 33.0261 1.04595 0.522974 0.852349i \(-0.324823\pi\)
0.522974 + 0.852349i \(0.324823\pi\)
\(998\) 0 0
\(999\) −0.389575 −0.0123256
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 \(a_p\))