Properties

Label 6004.2.a.g.1.20
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.41351 q^{3} -0.774385 q^{5} -1.47209 q^{7} -1.00198 q^{9} +O(q^{10})\) \(q+1.41351 q^{3} -0.774385 q^{5} -1.47209 q^{7} -1.00198 q^{9} +1.39960 q^{11} -0.835705 q^{13} -1.09460 q^{15} +6.36245 q^{17} +1.00000 q^{19} -2.08083 q^{21} -2.70029 q^{23} -4.40033 q^{25} -5.65685 q^{27} -6.34850 q^{29} +8.44981 q^{31} +1.97835 q^{33} +1.13997 q^{35} -5.59928 q^{37} -1.18128 q^{39} +8.34120 q^{41} +2.34849 q^{43} +0.775916 q^{45} -13.0033 q^{47} -4.83294 q^{49} +8.99342 q^{51} +6.78665 q^{53} -1.08383 q^{55} +1.41351 q^{57} -9.23753 q^{59} -5.97256 q^{61} +1.47501 q^{63} +0.647158 q^{65} -0.612758 q^{67} -3.81690 q^{69} -2.89595 q^{71} +3.61320 q^{73} -6.21993 q^{75} -2.06034 q^{77} -1.00000 q^{79} -4.99011 q^{81} -9.51099 q^{83} -4.92699 q^{85} -8.97369 q^{87} +1.80314 q^{89} +1.23024 q^{91} +11.9439 q^{93} -0.774385 q^{95} -11.7277 q^{97} -1.40237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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
\(3\) 1.41351 0.816093 0.408046 0.912961i \(-0.366210\pi\)
0.408046 + 0.912961i \(0.366210\pi\)
\(4\) 0 0
\(5\) −0.774385 −0.346315 −0.173158 0.984894i \(-0.555397\pi\)
−0.173158 + 0.984894i \(0.555397\pi\)
\(6\) 0 0
\(7\) −1.47209 −0.556400 −0.278200 0.960523i \(-0.589738\pi\)
−0.278200 + 0.960523i \(0.589738\pi\)
\(8\) 0 0
\(9\) −1.00198 −0.333992
\(10\) 0 0
\(11\) 1.39960 0.421995 0.210998 0.977487i \(-0.432329\pi\)
0.210998 + 0.977487i \(0.432329\pi\)
\(12\) 0 0
\(13\) −0.835705 −0.231783 −0.115891 0.993262i \(-0.536972\pi\)
−0.115891 + 0.993262i \(0.536972\pi\)
\(14\) 0 0
\(15\) −1.09460 −0.282626
\(16\) 0 0
\(17\) 6.36245 1.54312 0.771561 0.636156i \(-0.219476\pi\)
0.771561 + 0.636156i \(0.219476\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −2.08083 −0.454074
\(22\) 0 0
\(23\) −2.70029 −0.563050 −0.281525 0.959554i \(-0.590840\pi\)
−0.281525 + 0.959554i \(0.590840\pi\)
\(24\) 0 0
\(25\) −4.40033 −0.880066
\(26\) 0 0
\(27\) −5.65685 −1.08866
\(28\) 0 0
\(29\) −6.34850 −1.17889 −0.589443 0.807810i \(-0.700653\pi\)
−0.589443 + 0.807810i \(0.700653\pi\)
\(30\) 0 0
\(31\) 8.44981 1.51763 0.758815 0.651306i \(-0.225779\pi\)
0.758815 + 0.651306i \(0.225779\pi\)
\(32\) 0 0
\(33\) 1.97835 0.344387
\(34\) 0 0
\(35\) 1.13997 0.192690
\(36\) 0 0
\(37\) −5.59928 −0.920516 −0.460258 0.887785i \(-0.652243\pi\)
−0.460258 + 0.887785i \(0.652243\pi\)
\(38\) 0 0
\(39\) −1.18128 −0.189156
\(40\) 0 0
\(41\) 8.34120 1.30268 0.651338 0.758788i \(-0.274208\pi\)
0.651338 + 0.758788i \(0.274208\pi\)
\(42\) 0 0
\(43\) 2.34849 0.358141 0.179071 0.983836i \(-0.442691\pi\)
0.179071 + 0.983836i \(0.442691\pi\)
\(44\) 0 0
\(45\) 0.775916 0.115667
\(46\) 0 0
\(47\) −13.0033 −1.89672 −0.948360 0.317196i \(-0.897259\pi\)
−0.948360 + 0.317196i \(0.897259\pi\)
\(48\) 0 0
\(49\) −4.83294 −0.690420
\(50\) 0 0
\(51\) 8.99342 1.25933
\(52\) 0 0
\(53\) 6.78665 0.932219 0.466109 0.884727i \(-0.345655\pi\)
0.466109 + 0.884727i \(0.345655\pi\)
\(54\) 0 0
\(55\) −1.08383 −0.146143
\(56\) 0 0
\(57\) 1.41351 0.187225
\(58\) 0 0
\(59\) −9.23753 −1.20262 −0.601312 0.799014i \(-0.705355\pi\)
−0.601312 + 0.799014i \(0.705355\pi\)
\(60\) 0 0
\(61\) −5.97256 −0.764707 −0.382354 0.924016i \(-0.624886\pi\)
−0.382354 + 0.924016i \(0.624886\pi\)
\(62\) 0 0
\(63\) 1.47501 0.185833
\(64\) 0 0
\(65\) 0.647158 0.0802700
\(66\) 0 0
\(67\) −0.612758 −0.0748603 −0.0374301 0.999299i \(-0.511917\pi\)
−0.0374301 + 0.999299i \(0.511917\pi\)
\(68\) 0 0
\(69\) −3.81690 −0.459501
\(70\) 0 0
\(71\) −2.89595 −0.343686 −0.171843 0.985124i \(-0.554972\pi\)
−0.171843 + 0.985124i \(0.554972\pi\)
\(72\) 0 0
\(73\) 3.61320 0.422893 0.211447 0.977390i \(-0.432183\pi\)
0.211447 + 0.977390i \(0.432183\pi\)
\(74\) 0 0
\(75\) −6.21993 −0.718215
\(76\) 0 0
\(77\) −2.06034 −0.234798
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −4.99011 −0.554457
\(82\) 0 0
\(83\) −9.51099 −1.04397 −0.521983 0.852956i \(-0.674808\pi\)
−0.521983 + 0.852956i \(0.674808\pi\)
\(84\) 0 0
\(85\) −4.92699 −0.534407
\(86\) 0 0
\(87\) −8.97369 −0.962080
\(88\) 0 0
\(89\) 1.80314 0.191133 0.0955663 0.995423i \(-0.469534\pi\)
0.0955663 + 0.995423i \(0.469534\pi\)
\(90\) 0 0
\(91\) 1.23024 0.128964
\(92\) 0 0
\(93\) 11.9439 1.23853
\(94\) 0 0
\(95\) −0.774385 −0.0794502
\(96\) 0 0
\(97\) −11.7277 −1.19077 −0.595386 0.803440i \(-0.703001\pi\)
−0.595386 + 0.803440i \(0.703001\pi\)
\(98\) 0 0
\(99\) −1.40237 −0.140943
\(100\) 0 0
\(101\) −3.05786 −0.304269 −0.152134 0.988360i \(-0.548615\pi\)
−0.152134 + 0.988360i \(0.548615\pi\)
\(102\) 0 0
\(103\) 15.1125 1.48908 0.744541 0.667576i \(-0.232668\pi\)
0.744541 + 0.667576i \(0.232668\pi\)
\(104\) 0 0
\(105\) 1.61136 0.157253
\(106\) 0 0
\(107\) 11.1798 1.08079 0.540395 0.841411i \(-0.318275\pi\)
0.540395 + 0.841411i \(0.318275\pi\)
\(108\) 0 0
\(109\) 15.4747 1.48221 0.741103 0.671391i \(-0.234303\pi\)
0.741103 + 0.671391i \(0.234303\pi\)
\(110\) 0 0
\(111\) −7.91466 −0.751226
\(112\) 0 0
\(113\) −8.23795 −0.774961 −0.387480 0.921878i \(-0.626655\pi\)
−0.387480 + 0.921878i \(0.626655\pi\)
\(114\) 0 0
\(115\) 2.09107 0.194993
\(116\) 0 0
\(117\) 0.837358 0.0774138
\(118\) 0 0
\(119\) −9.36613 −0.858592
\(120\) 0 0
\(121\) −9.04112 −0.821920
\(122\) 0 0
\(123\) 11.7904 1.06310
\(124\) 0 0
\(125\) 7.27947 0.651096
\(126\) 0 0
\(127\) −14.0740 −1.24887 −0.624435 0.781077i \(-0.714671\pi\)
−0.624435 + 0.781077i \(0.714671\pi\)
\(128\) 0 0
\(129\) 3.31962 0.292276
\(130\) 0 0
\(131\) 20.7337 1.81151 0.905757 0.423797i \(-0.139303\pi\)
0.905757 + 0.423797i \(0.139303\pi\)
\(132\) 0 0
\(133\) −1.47209 −0.127647
\(134\) 0 0
\(135\) 4.38058 0.377020
\(136\) 0 0
\(137\) −4.82954 −0.412616 −0.206308 0.978487i \(-0.566145\pi\)
−0.206308 + 0.978487i \(0.566145\pi\)
\(138\) 0 0
\(139\) −13.7093 −1.16281 −0.581404 0.813615i \(-0.697496\pi\)
−0.581404 + 0.813615i \(0.697496\pi\)
\(140\) 0 0
\(141\) −18.3803 −1.54790
\(142\) 0 0
\(143\) −1.16965 −0.0978113
\(144\) 0 0
\(145\) 4.91618 0.408266
\(146\) 0 0
\(147\) −6.83143 −0.563446
\(148\) 0 0
\(149\) 3.69242 0.302495 0.151247 0.988496i \(-0.451671\pi\)
0.151247 + 0.988496i \(0.451671\pi\)
\(150\) 0 0
\(151\) −18.1346 −1.47577 −0.737887 0.674924i \(-0.764176\pi\)
−0.737887 + 0.674924i \(0.764176\pi\)
\(152\) 0 0
\(153\) −6.37503 −0.515391
\(154\) 0 0
\(155\) −6.54340 −0.525579
\(156\) 0 0
\(157\) −9.90415 −0.790438 −0.395219 0.918587i \(-0.629331\pi\)
−0.395219 + 0.918587i \(0.629331\pi\)
\(158\) 0 0
\(159\) 9.59303 0.760777
\(160\) 0 0
\(161\) 3.97509 0.313281
\(162\) 0 0
\(163\) 5.76671 0.451684 0.225842 0.974164i \(-0.427487\pi\)
0.225842 + 0.974164i \(0.427487\pi\)
\(164\) 0 0
\(165\) −1.53201 −0.119267
\(166\) 0 0
\(167\) −5.40558 −0.418297 −0.209148 0.977884i \(-0.567069\pi\)
−0.209148 + 0.977884i \(0.567069\pi\)
\(168\) 0 0
\(169\) −12.3016 −0.946277
\(170\) 0 0
\(171\) −1.00198 −0.0766231
\(172\) 0 0
\(173\) 0.553258 0.0420634 0.0210317 0.999779i \(-0.493305\pi\)
0.0210317 + 0.999779i \(0.493305\pi\)
\(174\) 0 0
\(175\) 6.47770 0.489668
\(176\) 0 0
\(177\) −13.0574 −0.981453
\(178\) 0 0
\(179\) −11.7371 −0.877274 −0.438637 0.898664i \(-0.644539\pi\)
−0.438637 + 0.898664i \(0.644539\pi\)
\(180\) 0 0
\(181\) −25.3407 −1.88356 −0.941780 0.336229i \(-0.890848\pi\)
−0.941780 + 0.336229i \(0.890848\pi\)
\(182\) 0 0
\(183\) −8.44229 −0.624072
\(184\) 0 0
\(185\) 4.33600 0.318789
\(186\) 0 0
\(187\) 8.90488 0.651190
\(188\) 0 0
\(189\) 8.32742 0.605731
\(190\) 0 0
\(191\) −21.2615 −1.53843 −0.769215 0.638990i \(-0.779352\pi\)
−0.769215 + 0.638990i \(0.779352\pi\)
\(192\) 0 0
\(193\) 12.0245 0.865543 0.432772 0.901504i \(-0.357536\pi\)
0.432772 + 0.901504i \(0.357536\pi\)
\(194\) 0 0
\(195\) 0.914767 0.0655078
\(196\) 0 0
\(197\) −8.64779 −0.616129 −0.308065 0.951365i \(-0.599681\pi\)
−0.308065 + 0.951365i \(0.599681\pi\)
\(198\) 0 0
\(199\) −20.4299 −1.44824 −0.724118 0.689677i \(-0.757753\pi\)
−0.724118 + 0.689677i \(0.757753\pi\)
\(200\) 0 0
\(201\) −0.866142 −0.0610929
\(202\) 0 0
\(203\) 9.34559 0.655932
\(204\) 0 0
\(205\) −6.45930 −0.451137
\(206\) 0 0
\(207\) 2.70563 0.188054
\(208\) 0 0
\(209\) 1.39960 0.0968123
\(210\) 0 0
\(211\) 11.9071 0.819720 0.409860 0.912148i \(-0.365577\pi\)
0.409860 + 0.912148i \(0.365577\pi\)
\(212\) 0 0
\(213\) −4.09347 −0.280480
\(214\) 0 0
\(215\) −1.81863 −0.124030
\(216\) 0 0
\(217\) −12.4389 −0.844409
\(218\) 0 0
\(219\) 5.10731 0.345120
\(220\) 0 0
\(221\) −5.31714 −0.357669
\(222\) 0 0
\(223\) −26.7338 −1.79023 −0.895115 0.445836i \(-0.852907\pi\)
−0.895115 + 0.445836i \(0.852907\pi\)
\(224\) 0 0
\(225\) 4.40903 0.293935
\(226\) 0 0
\(227\) 0.425128 0.0282167 0.0141084 0.999900i \(-0.495509\pi\)
0.0141084 + 0.999900i \(0.495509\pi\)
\(228\) 0 0
\(229\) −28.0592 −1.85421 −0.927103 0.374808i \(-0.877709\pi\)
−0.927103 + 0.374808i \(0.877709\pi\)
\(230\) 0 0
\(231\) −2.91232 −0.191617
\(232\) 0 0
\(233\) 8.00268 0.524273 0.262137 0.965031i \(-0.415573\pi\)
0.262137 + 0.965031i \(0.415573\pi\)
\(234\) 0 0
\(235\) 10.0695 0.656863
\(236\) 0 0
\(237\) −1.41351 −0.0918176
\(238\) 0 0
\(239\) 7.62206 0.493030 0.246515 0.969139i \(-0.420715\pi\)
0.246515 + 0.969139i \(0.420715\pi\)
\(240\) 0 0
\(241\) 13.2953 0.856428 0.428214 0.903677i \(-0.359143\pi\)
0.428214 + 0.903677i \(0.359143\pi\)
\(242\) 0 0
\(243\) 9.91697 0.636174
\(244\) 0 0
\(245\) 3.74255 0.239103
\(246\) 0 0
\(247\) −0.835705 −0.0531747
\(248\) 0 0
\(249\) −13.4439 −0.851974
\(250\) 0 0
\(251\) −19.7163 −1.24448 −0.622241 0.782826i \(-0.713778\pi\)
−0.622241 + 0.782826i \(0.713778\pi\)
\(252\) 0 0
\(253\) −3.77933 −0.237604
\(254\) 0 0
\(255\) −6.96437 −0.436126
\(256\) 0 0
\(257\) −13.0729 −0.815465 −0.407733 0.913101i \(-0.633680\pi\)
−0.407733 + 0.913101i \(0.633680\pi\)
\(258\) 0 0
\(259\) 8.24267 0.512175
\(260\) 0 0
\(261\) 6.36105 0.393739
\(262\) 0 0
\(263\) −19.2542 −1.18726 −0.593632 0.804736i \(-0.702307\pi\)
−0.593632 + 0.804736i \(0.702307\pi\)
\(264\) 0 0
\(265\) −5.25548 −0.322842
\(266\) 0 0
\(267\) 2.54877 0.155982
\(268\) 0 0
\(269\) −4.44576 −0.271063 −0.135531 0.990773i \(-0.543274\pi\)
−0.135531 + 0.990773i \(0.543274\pi\)
\(270\) 0 0
\(271\) 18.4799 1.12257 0.561286 0.827622i \(-0.310307\pi\)
0.561286 + 0.827622i \(0.310307\pi\)
\(272\) 0 0
\(273\) 1.73896 0.105247
\(274\) 0 0
\(275\) −6.15870 −0.371383
\(276\) 0 0
\(277\) −28.2490 −1.69732 −0.848658 0.528942i \(-0.822589\pi\)
−0.848658 + 0.528942i \(0.822589\pi\)
\(278\) 0 0
\(279\) −8.46652 −0.506877
\(280\) 0 0
\(281\) 2.95595 0.176337 0.0881686 0.996106i \(-0.471899\pi\)
0.0881686 + 0.996106i \(0.471899\pi\)
\(282\) 0 0
\(283\) −0.626007 −0.0372123 −0.0186061 0.999827i \(-0.505923\pi\)
−0.0186061 + 0.999827i \(0.505923\pi\)
\(284\) 0 0
\(285\) −1.09460 −0.0648388
\(286\) 0 0
\(287\) −12.2790 −0.724808
\(288\) 0 0
\(289\) 23.4808 1.38122
\(290\) 0 0
\(291\) −16.5773 −0.971780
\(292\) 0 0
\(293\) 30.3828 1.77498 0.887491 0.460825i \(-0.152446\pi\)
0.887491 + 0.460825i \(0.152446\pi\)
\(294\) 0 0
\(295\) 7.15340 0.416487
\(296\) 0 0
\(297\) −7.91733 −0.459410
\(298\) 0 0
\(299\) 2.25665 0.130505
\(300\) 0 0
\(301\) −3.45720 −0.199270
\(302\) 0 0
\(303\) −4.32234 −0.248312
\(304\) 0 0
\(305\) 4.62506 0.264830
\(306\) 0 0
\(307\) 19.2374 1.09794 0.548969 0.835842i \(-0.315020\pi\)
0.548969 + 0.835842i \(0.315020\pi\)
\(308\) 0 0
\(309\) 21.3618 1.21523
\(310\) 0 0
\(311\) −14.8570 −0.842462 −0.421231 0.906953i \(-0.638402\pi\)
−0.421231 + 0.906953i \(0.638402\pi\)
\(312\) 0 0
\(313\) 11.9584 0.675929 0.337964 0.941159i \(-0.390262\pi\)
0.337964 + 0.941159i \(0.390262\pi\)
\(314\) 0 0
\(315\) −1.14222 −0.0643569
\(316\) 0 0
\(317\) −24.6436 −1.38412 −0.692062 0.721838i \(-0.743298\pi\)
−0.692062 + 0.721838i \(0.743298\pi\)
\(318\) 0 0
\(319\) −8.88535 −0.497484
\(320\) 0 0
\(321\) 15.8028 0.882025
\(322\) 0 0
\(323\) 6.36245 0.354016
\(324\) 0 0
\(325\) 3.67738 0.203984
\(326\) 0 0
\(327\) 21.8737 1.20962
\(328\) 0 0
\(329\) 19.1420 1.05533
\(330\) 0 0
\(331\) −32.4370 −1.78290 −0.891450 0.453120i \(-0.850311\pi\)
−0.891450 + 0.453120i \(0.850311\pi\)
\(332\) 0 0
\(333\) 5.61035 0.307445
\(334\) 0 0
\(335\) 0.474510 0.0259253
\(336\) 0 0
\(337\) 8.30322 0.452305 0.226153 0.974092i \(-0.427385\pi\)
0.226153 + 0.974092i \(0.427385\pi\)
\(338\) 0 0
\(339\) −11.6445 −0.632440
\(340\) 0 0
\(341\) 11.8263 0.640433
\(342\) 0 0
\(343\) 17.4192 0.940549
\(344\) 0 0
\(345\) 2.95575 0.159132
\(346\) 0 0
\(347\) 16.5566 0.888807 0.444403 0.895827i \(-0.353416\pi\)
0.444403 + 0.895827i \(0.353416\pi\)
\(348\) 0 0
\(349\) 9.19901 0.492412 0.246206 0.969218i \(-0.420816\pi\)
0.246206 + 0.969218i \(0.420816\pi\)
\(350\) 0 0
\(351\) 4.72746 0.252333
\(352\) 0 0
\(353\) −5.47278 −0.291287 −0.145643 0.989337i \(-0.546525\pi\)
−0.145643 + 0.989337i \(0.546525\pi\)
\(354\) 0 0
\(355\) 2.24258 0.119024
\(356\) 0 0
\(357\) −13.2392 −0.700691
\(358\) 0 0
\(359\) 0.379156 0.0200111 0.0100055 0.999950i \(-0.496815\pi\)
0.0100055 + 0.999950i \(0.496815\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −12.7798 −0.670763
\(364\) 0 0
\(365\) −2.79801 −0.146454
\(366\) 0 0
\(367\) 28.8330 1.50507 0.752535 0.658552i \(-0.228831\pi\)
0.752535 + 0.658552i \(0.228831\pi\)
\(368\) 0 0
\(369\) −8.35769 −0.435084
\(370\) 0 0
\(371\) −9.99060 −0.518686
\(372\) 0 0
\(373\) −3.11790 −0.161439 −0.0807193 0.996737i \(-0.525722\pi\)
−0.0807193 + 0.996737i \(0.525722\pi\)
\(374\) 0 0
\(375\) 10.2896 0.531355
\(376\) 0 0
\(377\) 5.30547 0.273246
\(378\) 0 0
\(379\) 27.0258 1.38822 0.694112 0.719867i \(-0.255797\pi\)
0.694112 + 0.719867i \(0.255797\pi\)
\(380\) 0 0
\(381\) −19.8939 −1.01919
\(382\) 0 0
\(383\) 25.3908 1.29741 0.648704 0.761041i \(-0.275311\pi\)
0.648704 + 0.761041i \(0.275311\pi\)
\(384\) 0 0
\(385\) 1.59550 0.0813141
\(386\) 0 0
\(387\) −2.35313 −0.119616
\(388\) 0 0
\(389\) 25.9565 1.31605 0.658023 0.752998i \(-0.271393\pi\)
0.658023 + 0.752998i \(0.271393\pi\)
\(390\) 0 0
\(391\) −17.1805 −0.868854
\(392\) 0 0
\(393\) 29.3074 1.47836
\(394\) 0 0
\(395\) 0.774385 0.0389635
\(396\) 0 0
\(397\) 2.53535 0.127246 0.0636228 0.997974i \(-0.479735\pi\)
0.0636228 + 0.997974i \(0.479735\pi\)
\(398\) 0 0
\(399\) −2.08083 −0.104172
\(400\) 0 0
\(401\) 0.882963 0.0440931 0.0220465 0.999757i \(-0.492982\pi\)
0.0220465 + 0.999757i \(0.492982\pi\)
\(402\) 0 0
\(403\) −7.06155 −0.351761
\(404\) 0 0
\(405\) 3.86427 0.192017
\(406\) 0 0
\(407\) −7.83675 −0.388453
\(408\) 0 0
\(409\) −28.3123 −1.39995 −0.699976 0.714166i \(-0.746806\pi\)
−0.699976 + 0.714166i \(0.746806\pi\)
\(410\) 0 0
\(411\) −6.82663 −0.336733
\(412\) 0 0
\(413\) 13.5985 0.669139
\(414\) 0 0
\(415\) 7.36517 0.361542
\(416\) 0 0
\(417\) −19.3783 −0.948960
\(418\) 0 0
\(419\) 18.3791 0.897878 0.448939 0.893562i \(-0.351802\pi\)
0.448939 + 0.893562i \(0.351802\pi\)
\(420\) 0 0
\(421\) 26.3246 1.28298 0.641492 0.767129i \(-0.278316\pi\)
0.641492 + 0.767129i \(0.278316\pi\)
\(422\) 0 0
\(423\) 13.0290 0.633490
\(424\) 0 0
\(425\) −27.9969 −1.35805
\(426\) 0 0
\(427\) 8.79217 0.425483
\(428\) 0 0
\(429\) −1.65332 −0.0798231
\(430\) 0 0
\(431\) −40.1995 −1.93634 −0.968172 0.250287i \(-0.919475\pi\)
−0.968172 + 0.250287i \(0.919475\pi\)
\(432\) 0 0
\(433\) −4.80403 −0.230867 −0.115434 0.993315i \(-0.536826\pi\)
−0.115434 + 0.993315i \(0.536826\pi\)
\(434\) 0 0
\(435\) 6.94909 0.333183
\(436\) 0 0
\(437\) −2.70029 −0.129172
\(438\) 0 0
\(439\) −13.5989 −0.649041 −0.324520 0.945879i \(-0.605203\pi\)
−0.324520 + 0.945879i \(0.605203\pi\)
\(440\) 0 0
\(441\) 4.84249 0.230595
\(442\) 0 0
\(443\) −23.9050 −1.13576 −0.567881 0.823111i \(-0.692236\pi\)
−0.567881 + 0.823111i \(0.692236\pi\)
\(444\) 0 0
\(445\) −1.39633 −0.0661922
\(446\) 0 0
\(447\) 5.21928 0.246864
\(448\) 0 0
\(449\) 16.2670 0.767685 0.383843 0.923399i \(-0.374601\pi\)
0.383843 + 0.923399i \(0.374601\pi\)
\(450\) 0 0
\(451\) 11.6743 0.549723
\(452\) 0 0
\(453\) −25.6335 −1.20437
\(454\) 0 0
\(455\) −0.952677 −0.0446622
\(456\) 0 0
\(457\) 39.2972 1.83825 0.919123 0.393971i \(-0.128899\pi\)
0.919123 + 0.393971i \(0.128899\pi\)
\(458\) 0 0
\(459\) −35.9915 −1.67994
\(460\) 0 0
\(461\) 1.40539 0.0654555 0.0327278 0.999464i \(-0.489581\pi\)
0.0327278 + 0.999464i \(0.489581\pi\)
\(462\) 0 0
\(463\) 21.8190 1.01402 0.507008 0.861941i \(-0.330751\pi\)
0.507008 + 0.861941i \(0.330751\pi\)
\(464\) 0 0
\(465\) −9.24919 −0.428921
\(466\) 0 0
\(467\) 12.2835 0.568411 0.284205 0.958763i \(-0.408270\pi\)
0.284205 + 0.958763i \(0.408270\pi\)
\(468\) 0 0
\(469\) 0.902037 0.0416522
\(470\) 0 0
\(471\) −13.9997 −0.645070
\(472\) 0 0
\(473\) 3.28694 0.151134
\(474\) 0 0
\(475\) −4.40033 −0.201901
\(476\) 0 0
\(477\) −6.80007 −0.311354
\(478\) 0 0
\(479\) 11.8810 0.542857 0.271429 0.962459i \(-0.412504\pi\)
0.271429 + 0.962459i \(0.412504\pi\)
\(480\) 0 0
\(481\) 4.67935 0.213360
\(482\) 0 0
\(483\) 5.61884 0.255666
\(484\) 0 0
\(485\) 9.08178 0.412383
\(486\) 0 0
\(487\) −20.3298 −0.921229 −0.460615 0.887600i \(-0.652371\pi\)
−0.460615 + 0.887600i \(0.652371\pi\)
\(488\) 0 0
\(489\) 8.15133 0.368616
\(490\) 0 0
\(491\) −15.7077 −0.708880 −0.354440 0.935079i \(-0.615328\pi\)
−0.354440 + 0.935079i \(0.615328\pi\)
\(492\) 0 0
\(493\) −40.3920 −1.81916
\(494\) 0 0
\(495\) 1.08597 0.0488108
\(496\) 0 0
\(497\) 4.26311 0.191227
\(498\) 0 0
\(499\) 0.223546 0.0100073 0.00500365 0.999987i \(-0.498407\pi\)
0.00500365 + 0.999987i \(0.498407\pi\)
\(500\) 0 0
\(501\) −7.64087 −0.341369
\(502\) 0 0
\(503\) 25.7343 1.14744 0.573719 0.819052i \(-0.305500\pi\)
0.573719 + 0.819052i \(0.305500\pi\)
\(504\) 0 0
\(505\) 2.36796 0.105373
\(506\) 0 0
\(507\) −17.3885 −0.772250
\(508\) 0 0
\(509\) −4.59995 −0.203889 −0.101945 0.994790i \(-0.532506\pi\)
−0.101945 + 0.994790i \(0.532506\pi\)
\(510\) 0 0
\(511\) −5.31897 −0.235297
\(512\) 0 0
\(513\) −5.65685 −0.249756
\(514\) 0 0
\(515\) −11.7029 −0.515692
\(516\) 0 0
\(517\) −18.1994 −0.800407
\(518\) 0 0
\(519\) 0.782038 0.0343276
\(520\) 0 0
\(521\) 7.57999 0.332085 0.166043 0.986119i \(-0.446901\pi\)
0.166043 + 0.986119i \(0.446901\pi\)
\(522\) 0 0
\(523\) −9.70634 −0.424429 −0.212214 0.977223i \(-0.568068\pi\)
−0.212214 + 0.977223i \(0.568068\pi\)
\(524\) 0 0
\(525\) 9.15632 0.399615
\(526\) 0 0
\(527\) 53.7615 2.34189
\(528\) 0 0
\(529\) −15.7084 −0.682975
\(530\) 0 0
\(531\) 9.25580 0.401667
\(532\) 0 0
\(533\) −6.97078 −0.301938
\(534\) 0 0
\(535\) −8.65746 −0.374294
\(536\) 0 0
\(537\) −16.5906 −0.715937
\(538\) 0 0
\(539\) −6.76418 −0.291354
\(540\) 0 0
\(541\) 38.3492 1.64876 0.824381 0.566035i \(-0.191523\pi\)
0.824381 + 0.566035i \(0.191523\pi\)
\(542\) 0 0
\(543\) −35.8195 −1.53716
\(544\) 0 0
\(545\) −11.9834 −0.513311
\(546\) 0 0
\(547\) 20.3424 0.869779 0.434890 0.900484i \(-0.356787\pi\)
0.434890 + 0.900484i \(0.356787\pi\)
\(548\) 0 0
\(549\) 5.98437 0.255406
\(550\) 0 0
\(551\) −6.34850 −0.270455
\(552\) 0 0
\(553\) 1.47209 0.0625998
\(554\) 0 0
\(555\) 6.12899 0.260161
\(556\) 0 0
\(557\) −10.0353 −0.425210 −0.212605 0.977138i \(-0.568195\pi\)
−0.212605 + 0.977138i \(0.568195\pi\)
\(558\) 0 0
\(559\) −1.96264 −0.0830110
\(560\) 0 0
\(561\) 12.5872 0.531431
\(562\) 0 0
\(563\) −30.7118 −1.29435 −0.647173 0.762343i \(-0.724049\pi\)
−0.647173 + 0.762343i \(0.724049\pi\)
\(564\) 0 0
\(565\) 6.37934 0.268381
\(566\) 0 0
\(567\) 7.34591 0.308499
\(568\) 0 0
\(569\) 7.40944 0.310620 0.155310 0.987866i \(-0.450362\pi\)
0.155310 + 0.987866i \(0.450362\pi\)
\(570\) 0 0
\(571\) 36.2464 1.51686 0.758431 0.651753i \(-0.225966\pi\)
0.758431 + 0.651753i \(0.225966\pi\)
\(572\) 0 0
\(573\) −30.0535 −1.25550
\(574\) 0 0
\(575\) 11.8822 0.495521
\(576\) 0 0
\(577\) −35.1738 −1.46430 −0.732152 0.681141i \(-0.761484\pi\)
−0.732152 + 0.681141i \(0.761484\pi\)
\(578\) 0 0
\(579\) 16.9968 0.706364
\(580\) 0 0
\(581\) 14.0011 0.580863
\(582\) 0 0
\(583\) 9.49860 0.393392
\(584\) 0 0
\(585\) −0.648437 −0.0268096
\(586\) 0 0
\(587\) −25.4899 −1.05208 −0.526040 0.850460i \(-0.676324\pi\)
−0.526040 + 0.850460i \(0.676324\pi\)
\(588\) 0 0
\(589\) 8.44981 0.348168
\(590\) 0 0
\(591\) −12.2238 −0.502819
\(592\) 0 0
\(593\) −45.7445 −1.87850 −0.939252 0.343229i \(-0.888479\pi\)
−0.939252 + 0.343229i \(0.888479\pi\)
\(594\) 0 0
\(595\) 7.25299 0.297344
\(596\) 0 0
\(597\) −28.8779 −1.18189
\(598\) 0 0
\(599\) 31.7399 1.29686 0.648429 0.761275i \(-0.275426\pi\)
0.648429 + 0.761275i \(0.275426\pi\)
\(600\) 0 0
\(601\) 22.3510 0.911717 0.455859 0.890052i \(-0.349332\pi\)
0.455859 + 0.890052i \(0.349332\pi\)
\(602\) 0 0
\(603\) 0.613969 0.0250028
\(604\) 0 0
\(605\) 7.00131 0.284644
\(606\) 0 0
\(607\) 7.53011 0.305638 0.152819 0.988254i \(-0.451165\pi\)
0.152819 + 0.988254i \(0.451165\pi\)
\(608\) 0 0
\(609\) 13.2101 0.535301
\(610\) 0 0
\(611\) 10.8669 0.439627
\(612\) 0 0
\(613\) −30.9095 −1.24842 −0.624211 0.781256i \(-0.714580\pi\)
−0.624211 + 0.781256i \(0.714580\pi\)
\(614\) 0 0
\(615\) −9.13031 −0.368170
\(616\) 0 0
\(617\) 23.2291 0.935170 0.467585 0.883948i \(-0.345124\pi\)
0.467585 + 0.883948i \(0.345124\pi\)
\(618\) 0 0
\(619\) 21.2358 0.853541 0.426770 0.904360i \(-0.359651\pi\)
0.426770 + 0.904360i \(0.359651\pi\)
\(620\) 0 0
\(621\) 15.2752 0.612971
\(622\) 0 0
\(623\) −2.65439 −0.106346
\(624\) 0 0
\(625\) 16.3645 0.654581
\(626\) 0 0
\(627\) 1.97835 0.0790078
\(628\) 0 0
\(629\) −35.6251 −1.42047
\(630\) 0 0
\(631\) 4.55045 0.181151 0.0905754 0.995890i \(-0.471129\pi\)
0.0905754 + 0.995890i \(0.471129\pi\)
\(632\) 0 0
\(633\) 16.8309 0.668968
\(634\) 0 0
\(635\) 10.8987 0.432503
\(636\) 0 0
\(637\) 4.03891 0.160028
\(638\) 0 0
\(639\) 2.90168 0.114789
\(640\) 0 0
\(641\) 6.74444 0.266389 0.133195 0.991090i \(-0.457476\pi\)
0.133195 + 0.991090i \(0.457476\pi\)
\(642\) 0 0
\(643\) −19.5024 −0.769101 −0.384550 0.923104i \(-0.625644\pi\)
−0.384550 + 0.923104i \(0.625644\pi\)
\(644\) 0 0
\(645\) −2.57066 −0.101220
\(646\) 0 0
\(647\) 14.2044 0.558431 0.279216 0.960228i \(-0.409926\pi\)
0.279216 + 0.960228i \(0.409926\pi\)
\(648\) 0 0
\(649\) −12.9288 −0.507501
\(650\) 0 0
\(651\) −17.5826 −0.689116
\(652\) 0 0
\(653\) −13.6061 −0.532448 −0.266224 0.963911i \(-0.585776\pi\)
−0.266224 + 0.963911i \(0.585776\pi\)
\(654\) 0 0
\(655\) −16.0559 −0.627355
\(656\) 0 0
\(657\) −3.62034 −0.141243
\(658\) 0 0
\(659\) −4.41489 −0.171980 −0.0859898 0.996296i \(-0.527405\pi\)
−0.0859898 + 0.996296i \(0.527405\pi\)
\(660\) 0 0
\(661\) −2.65776 −0.103375 −0.0516874 0.998663i \(-0.516460\pi\)
−0.0516874 + 0.998663i \(0.516460\pi\)
\(662\) 0 0
\(663\) −7.51585 −0.291891
\(664\) 0 0
\(665\) 1.13997 0.0442061
\(666\) 0 0
\(667\) 17.1428 0.663772
\(668\) 0 0
\(669\) −37.7887 −1.46099
\(670\) 0 0
\(671\) −8.35918 −0.322703
\(672\) 0 0
\(673\) 36.6678 1.41344 0.706721 0.707493i \(-0.250174\pi\)
0.706721 + 0.707493i \(0.250174\pi\)
\(674\) 0 0
\(675\) 24.8920 0.958094
\(676\) 0 0
\(677\) 25.3390 0.973857 0.486929 0.873442i \(-0.338117\pi\)
0.486929 + 0.873442i \(0.338117\pi\)
\(678\) 0 0
\(679\) 17.2643 0.662545
\(680\) 0 0
\(681\) 0.600924 0.0230275
\(682\) 0 0
\(683\) 13.2600 0.507381 0.253691 0.967285i \(-0.418355\pi\)
0.253691 + 0.967285i \(0.418355\pi\)
\(684\) 0 0
\(685\) 3.73993 0.142895
\(686\) 0 0
\(687\) −39.6621 −1.51320
\(688\) 0 0
\(689\) −5.67164 −0.216072
\(690\) 0 0
\(691\) 16.2345 0.617589 0.308794 0.951129i \(-0.400074\pi\)
0.308794 + 0.951129i \(0.400074\pi\)
\(692\) 0 0
\(693\) 2.06442 0.0784207
\(694\) 0 0
\(695\) 10.6163 0.402699
\(696\) 0 0
\(697\) 53.0705 2.01019
\(698\) 0 0
\(699\) 11.3119 0.427856
\(700\) 0 0
\(701\) −30.1937 −1.14040 −0.570201 0.821506i \(-0.693135\pi\)
−0.570201 + 0.821506i \(0.693135\pi\)
\(702\) 0 0
\(703\) −5.59928 −0.211181
\(704\) 0 0
\(705\) 14.2334 0.536062
\(706\) 0 0
\(707\) 4.50147 0.169295
\(708\) 0 0
\(709\) −14.9202 −0.560341 −0.280170 0.959950i \(-0.590391\pi\)
−0.280170 + 0.959950i \(0.590391\pi\)
\(710\) 0 0
\(711\) 1.00198 0.0375771
\(712\) 0 0
\(713\) −22.8169 −0.854501
\(714\) 0 0
\(715\) 0.905761 0.0338736
\(716\) 0 0
\(717\) 10.7739 0.402358
\(718\) 0 0
\(719\) 43.8157 1.63405 0.817024 0.576603i \(-0.195622\pi\)
0.817024 + 0.576603i \(0.195622\pi\)
\(720\) 0 0
\(721\) −22.2471 −0.828525
\(722\) 0 0
\(723\) 18.7932 0.698925
\(724\) 0 0
\(725\) 27.9355 1.03750
\(726\) 0 0
\(727\) 26.5631 0.985172 0.492586 0.870264i \(-0.336052\pi\)
0.492586 + 0.870264i \(0.336052\pi\)
\(728\) 0 0
\(729\) 28.9881 1.07363
\(730\) 0 0
\(731\) 14.9421 0.552655
\(732\) 0 0
\(733\) 46.0462 1.70075 0.850377 0.526174i \(-0.176374\pi\)
0.850377 + 0.526174i \(0.176374\pi\)
\(734\) 0 0
\(735\) 5.29015 0.195130
\(736\) 0 0
\(737\) −0.857615 −0.0315907
\(738\) 0 0
\(739\) −8.31308 −0.305801 −0.152901 0.988242i \(-0.548861\pi\)
−0.152901 + 0.988242i \(0.548861\pi\)
\(740\) 0 0
\(741\) −1.18128 −0.0433955
\(742\) 0 0
\(743\) 24.6836 0.905553 0.452777 0.891624i \(-0.350434\pi\)
0.452777 + 0.891624i \(0.350434\pi\)
\(744\) 0 0
\(745\) −2.85935 −0.104759
\(746\) 0 0
\(747\) 9.52980 0.348677
\(748\) 0 0
\(749\) −16.4577 −0.601351
\(750\) 0 0
\(751\) 44.0857 1.60871 0.804355 0.594149i \(-0.202511\pi\)
0.804355 + 0.594149i \(0.202511\pi\)
\(752\) 0 0
\(753\) −27.8693 −1.01561
\(754\) 0 0
\(755\) 14.0432 0.511083
\(756\) 0 0
\(757\) 38.0793 1.38401 0.692007 0.721891i \(-0.256727\pi\)
0.692007 + 0.721891i \(0.256727\pi\)
\(758\) 0 0
\(759\) −5.34213 −0.193907
\(760\) 0 0
\(761\) −25.0722 −0.908866 −0.454433 0.890781i \(-0.650158\pi\)
−0.454433 + 0.890781i \(0.650158\pi\)
\(762\) 0 0
\(763\) −22.7802 −0.824699
\(764\) 0 0
\(765\) 4.93673 0.178488
\(766\) 0 0
\(767\) 7.71985 0.278748
\(768\) 0 0
\(769\) −32.9005 −1.18642 −0.593211 0.805047i \(-0.702140\pi\)
−0.593211 + 0.805047i \(0.702140\pi\)
\(770\) 0 0
\(771\) −18.4787 −0.665495
\(772\) 0 0
\(773\) −20.3011 −0.730178 −0.365089 0.930973i \(-0.618961\pi\)
−0.365089 + 0.930973i \(0.618961\pi\)
\(774\) 0 0
\(775\) −37.1819 −1.33561
\(776\) 0 0
\(777\) 11.6511 0.417982
\(778\) 0 0
\(779\) 8.34120 0.298854
\(780\) 0 0
\(781\) −4.05317 −0.145034
\(782\) 0 0
\(783\) 35.9125 1.28341
\(784\) 0 0
\(785\) 7.66963 0.273741
\(786\) 0 0
\(787\) 53.2127 1.89683 0.948415 0.317032i \(-0.102686\pi\)
0.948415 + 0.317032i \(0.102686\pi\)
\(788\) 0 0
\(789\) −27.2161 −0.968918
\(790\) 0 0
\(791\) 12.1270 0.431188
\(792\) 0 0
\(793\) 4.99130 0.177246
\(794\) 0 0
\(795\) −7.42870 −0.263469
\(796\) 0 0
\(797\) −48.2952 −1.71070 −0.855352 0.518048i \(-0.826659\pi\)
−0.855352 + 0.518048i \(0.826659\pi\)
\(798\) 0 0
\(799\) −82.7326 −2.92687
\(800\) 0 0
\(801\) −1.80671 −0.0638368
\(802\) 0 0
\(803\) 5.05703 0.178459
\(804\) 0 0
\(805\) −3.07825 −0.108494
\(806\) 0 0
\(807\) −6.28415 −0.221213
\(808\) 0 0
\(809\) −9.56100 −0.336147 −0.168073 0.985774i \(-0.553755\pi\)
−0.168073 + 0.985774i \(0.553755\pi\)
\(810\) 0 0
\(811\) 12.4095 0.435756 0.217878 0.975976i \(-0.430087\pi\)
0.217878 + 0.975976i \(0.430087\pi\)
\(812\) 0 0
\(813\) 26.1215 0.916122
\(814\) 0 0
\(815\) −4.46566 −0.156425
\(816\) 0 0
\(817\) 2.34849 0.0821632
\(818\) 0 0
\(819\) −1.23267 −0.0430730
\(820\) 0 0
\(821\) −49.0777 −1.71282 −0.856412 0.516292i \(-0.827312\pi\)
−0.856412 + 0.516292i \(0.827312\pi\)
\(822\) 0 0
\(823\) 10.0206 0.349298 0.174649 0.984631i \(-0.444121\pi\)
0.174649 + 0.984631i \(0.444121\pi\)
\(824\) 0 0
\(825\) −8.70541 −0.303083
\(826\) 0 0
\(827\) −5.35349 −0.186159 −0.0930796 0.995659i \(-0.529671\pi\)
−0.0930796 + 0.995659i \(0.529671\pi\)
\(828\) 0 0
\(829\) 25.5264 0.886569 0.443285 0.896381i \(-0.353813\pi\)
0.443285 + 0.896381i \(0.353813\pi\)
\(830\) 0 0
\(831\) −39.9303 −1.38517
\(832\) 0 0
\(833\) −30.7493 −1.06540
\(834\) 0 0
\(835\) 4.18600 0.144863
\(836\) 0 0
\(837\) −47.7993 −1.65219
\(838\) 0 0
\(839\) −13.4699 −0.465032 −0.232516 0.972593i \(-0.574696\pi\)
−0.232516 + 0.972593i \(0.574696\pi\)
\(840\) 0 0
\(841\) 11.3034 0.389772
\(842\) 0 0
\(843\) 4.17828 0.143908
\(844\) 0 0
\(845\) 9.52617 0.327710
\(846\) 0 0
\(847\) 13.3094 0.457316
\(848\) 0 0
\(849\) −0.884870 −0.0303687
\(850\) 0 0
\(851\) 15.1197 0.518296
\(852\) 0 0
\(853\) −51.7172 −1.77076 −0.885382 0.464864i \(-0.846103\pi\)
−0.885382 + 0.464864i \(0.846103\pi\)
\(854\) 0 0
\(855\) 0.775916 0.0265358
\(856\) 0 0
\(857\) −29.5215 −1.00843 −0.504217 0.863577i \(-0.668219\pi\)
−0.504217 + 0.863577i \(0.668219\pi\)
\(858\) 0 0
\(859\) 10.6645 0.363869 0.181934 0.983311i \(-0.441764\pi\)
0.181934 + 0.983311i \(0.441764\pi\)
\(860\) 0 0
\(861\) −17.3566 −0.591511
\(862\) 0 0
\(863\) 38.7388 1.31869 0.659343 0.751843i \(-0.270835\pi\)
0.659343 + 0.751843i \(0.270835\pi\)
\(864\) 0 0
\(865\) −0.428434 −0.0145672
\(866\) 0 0
\(867\) 33.1904 1.12721
\(868\) 0 0
\(869\) −1.39960 −0.0474782
\(870\) 0 0
\(871\) 0.512085 0.0173513
\(872\) 0 0
\(873\) 11.7509 0.397709
\(874\) 0 0
\(875\) −10.7161 −0.362269
\(876\) 0 0
\(877\) 15.7011 0.530187 0.265094 0.964223i \(-0.414597\pi\)
0.265094 + 0.964223i \(0.414597\pi\)
\(878\) 0 0
\(879\) 42.9465 1.44855
\(880\) 0 0
\(881\) −29.7452 −1.00214 −0.501071 0.865406i \(-0.667060\pi\)
−0.501071 + 0.865406i \(0.667060\pi\)
\(882\) 0 0
\(883\) 26.5309 0.892836 0.446418 0.894825i \(-0.352700\pi\)
0.446418 + 0.894825i \(0.352700\pi\)
\(884\) 0 0
\(885\) 10.1114 0.339892
\(886\) 0 0
\(887\) −54.2772 −1.82245 −0.911226 0.411907i \(-0.864863\pi\)
−0.911226 + 0.411907i \(0.864863\pi\)
\(888\) 0 0
\(889\) 20.7183 0.694870
\(890\) 0 0
\(891\) −6.98415 −0.233978
\(892\) 0 0
\(893\) −13.0033 −0.435137
\(894\) 0 0
\(895\) 9.08905 0.303814
\(896\) 0 0
\(897\) 3.18981 0.106504
\(898\) 0 0
\(899\) −53.6436 −1.78911
\(900\) 0 0
\(901\) 43.1798 1.43853
\(902\) 0 0
\(903\) −4.88680 −0.162622
\(904\) 0 0
\(905\) 19.6235 0.652306
\(906\) 0 0
\(907\) −20.8919 −0.693704 −0.346852 0.937920i \(-0.612749\pi\)
−0.346852 + 0.937920i \(0.612749\pi\)
\(908\) 0 0
\(909\) 3.06391 0.101624
\(910\) 0 0
\(911\) −13.5884 −0.450203 −0.225102 0.974335i \(-0.572271\pi\)
−0.225102 + 0.974335i \(0.572271\pi\)
\(912\) 0 0
\(913\) −13.3116 −0.440549
\(914\) 0 0
\(915\) 6.53758 0.216126
\(916\) 0 0
\(917\) −30.5220 −1.00793
\(918\) 0 0
\(919\) 56.3308 1.85818 0.929090 0.369853i \(-0.120592\pi\)
0.929090 + 0.369853i \(0.120592\pi\)
\(920\) 0 0
\(921\) 27.1924 0.896020
\(922\) 0 0
\(923\) 2.42016 0.0796606
\(924\) 0 0
\(925\) 24.6387 0.810114
\(926\) 0 0
\(927\) −15.1424 −0.497342
\(928\) 0 0
\(929\) −27.8760 −0.914583 −0.457291 0.889317i \(-0.651180\pi\)
−0.457291 + 0.889317i \(0.651180\pi\)
\(930\) 0 0
\(931\) −4.83294 −0.158393
\(932\) 0 0
\(933\) −21.0006 −0.687528
\(934\) 0 0
\(935\) −6.89581 −0.225517
\(936\) 0 0
\(937\) −2.95785 −0.0966288 −0.0483144 0.998832i \(-0.515385\pi\)
−0.0483144 + 0.998832i \(0.515385\pi\)
\(938\) 0 0
\(939\) 16.9034 0.551621
\(940\) 0 0
\(941\) 33.1216 1.07973 0.539867 0.841750i \(-0.318475\pi\)
0.539867 + 0.841750i \(0.318475\pi\)
\(942\) 0 0
\(943\) −22.5237 −0.733472
\(944\) 0 0
\(945\) −6.44863 −0.209774
\(946\) 0 0
\(947\) 7.44438 0.241910 0.120955 0.992658i \(-0.461404\pi\)
0.120955 + 0.992658i \(0.461404\pi\)
\(948\) 0 0
\(949\) −3.01957 −0.0980194
\(950\) 0 0
\(951\) −34.8341 −1.12957
\(952\) 0 0
\(953\) −35.0640 −1.13584 −0.567918 0.823085i \(-0.692251\pi\)
−0.567918 + 0.823085i \(0.692251\pi\)
\(954\) 0 0
\(955\) 16.4646 0.532782
\(956\) 0 0
\(957\) −12.5596 −0.405993
\(958\) 0 0
\(959\) 7.10955 0.229579
\(960\) 0 0
\(961\) 40.3992 1.30320
\(962\) 0 0
\(963\) −11.2019 −0.360976
\(964\) 0 0
\(965\) −9.31160 −0.299751
\(966\) 0 0
\(967\) −33.1678 −1.06660 −0.533301 0.845925i \(-0.679049\pi\)
−0.533301 + 0.845925i \(0.679049\pi\)
\(968\) 0 0
\(969\) 8.99342 0.288910
\(970\) 0 0
\(971\) −5.16827 −0.165858 −0.0829288 0.996555i \(-0.526427\pi\)
−0.0829288 + 0.996555i \(0.526427\pi\)
\(972\) 0 0
\(973\) 20.1814 0.646986
\(974\) 0 0
\(975\) 5.19803 0.166470
\(976\) 0 0
\(977\) −17.8373 −0.570665 −0.285333 0.958429i \(-0.592104\pi\)
−0.285333 + 0.958429i \(0.592104\pi\)
\(978\) 0 0
\(979\) 2.52368 0.0806570
\(980\) 0 0
\(981\) −15.5053 −0.495046
\(982\) 0 0
\(983\) 30.6358 0.977131 0.488566 0.872527i \(-0.337520\pi\)
0.488566 + 0.872527i \(0.337520\pi\)
\(984\) 0 0
\(985\) 6.69672 0.213375
\(986\) 0 0
\(987\) 27.0575 0.861251
\(988\) 0 0
\(989\) −6.34160 −0.201651
\(990\) 0 0
\(991\) 0.890956 0.0283021 0.0141511 0.999900i \(-0.495495\pi\)
0.0141511 + 0.999900i \(0.495495\pi\)
\(992\) 0 0
\(993\) −45.8502 −1.45501
\(994\) 0 0
\(995\) 15.8206 0.501546
\(996\) 0 0
\(997\) −21.0416 −0.666394 −0.333197 0.942857i \(-0.608127\pi\)
−0.333197 + 0.942857i \(0.608127\pi\)
\(998\) 0 0
\(999\) 31.6743 1.00213
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 \(a_p\))