Properties

Label 8020.2.a.c.1.1
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.10189 q^{3}\) \(-1.00000 q^{5}\) \(+1.97262 q^{7}\) \(+6.62170 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.10189 q^{3}\) \(-1.00000 q^{5}\) \(+1.97262 q^{7}\) \(+6.62170 q^{9}\) \(+0.185891 q^{11}\) \(+5.99884 q^{13}\) \(+3.10189 q^{15}\) \(-1.15817 q^{17}\) \(+2.61335 q^{19}\) \(-6.11884 q^{21}\) \(-0.915400 q^{23}\) \(+1.00000 q^{25}\) \(-11.2341 q^{27}\) \(-5.92842 q^{29}\) \(+1.52735 q^{31}\) \(-0.576612 q^{33}\) \(-1.97262 q^{35}\) \(-4.46101 q^{37}\) \(-18.6077 q^{39}\) \(-9.05750 q^{41}\) \(+1.79219 q^{43}\) \(-6.62170 q^{45}\) \(-4.47790 q^{47}\) \(-3.10878 q^{49}\) \(+3.59252 q^{51}\) \(-12.0796 q^{53}\) \(-0.185891 q^{55}\) \(-8.10633 q^{57}\) \(-1.16916 q^{59}\) \(+9.27981 q^{61}\) \(+13.0621 q^{63}\) \(-5.99884 q^{65}\) \(+12.9087 q^{67}\) \(+2.83947 q^{69}\) \(-4.83239 q^{71}\) \(+3.01365 q^{73}\) \(-3.10189 q^{75}\) \(+0.366691 q^{77}\) \(+6.21687 q^{79}\) \(+14.9818 q^{81}\) \(-9.34234 q^{83}\) \(+1.15817 q^{85}\) \(+18.3893 q^{87}\) \(-17.4169 q^{89}\) \(+11.8334 q^{91}\) \(-4.73766 q^{93}\) \(-2.61335 q^{95}\) \(+4.82293 q^{97}\) \(+1.23091 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.10189 −1.79088 −0.895438 0.445187i \(-0.853137\pi\)
−0.895438 + 0.445187i \(0.853137\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.97262 0.745579 0.372790 0.927916i \(-0.378401\pi\)
0.372790 + 0.927916i \(0.378401\pi\)
\(8\) 0 0
\(9\) 6.62170 2.20723
\(10\) 0 0
\(11\) 0.185891 0.0560482 0.0280241 0.999607i \(-0.491078\pi\)
0.0280241 + 0.999607i \(0.491078\pi\)
\(12\) 0 0
\(13\) 5.99884 1.66378 0.831889 0.554942i \(-0.187259\pi\)
0.831889 + 0.554942i \(0.187259\pi\)
\(14\) 0 0
\(15\) 3.10189 0.800904
\(16\) 0 0
\(17\) −1.15817 −0.280898 −0.140449 0.990088i \(-0.544855\pi\)
−0.140449 + 0.990088i \(0.544855\pi\)
\(18\) 0 0
\(19\) 2.61335 0.599545 0.299772 0.954011i \(-0.403089\pi\)
0.299772 + 0.954011i \(0.403089\pi\)
\(20\) 0 0
\(21\) −6.11884 −1.33524
\(22\) 0 0
\(23\) −0.915400 −0.190874 −0.0954370 0.995435i \(-0.530425\pi\)
−0.0954370 + 0.995435i \(0.530425\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −11.2341 −2.16201
\(28\) 0 0
\(29\) −5.92842 −1.10088 −0.550440 0.834875i \(-0.685540\pi\)
−0.550440 + 0.834875i \(0.685540\pi\)
\(30\) 0 0
\(31\) 1.52735 0.274320 0.137160 0.990549i \(-0.456203\pi\)
0.137160 + 0.990549i \(0.456203\pi\)
\(32\) 0 0
\(33\) −0.576612 −0.100375
\(34\) 0 0
\(35\) −1.97262 −0.333433
\(36\) 0 0
\(37\) −4.46101 −0.733386 −0.366693 0.930342i \(-0.619510\pi\)
−0.366693 + 0.930342i \(0.619510\pi\)
\(38\) 0 0
\(39\) −18.6077 −2.97962
\(40\) 0 0
\(41\) −9.05750 −1.41454 −0.707272 0.706942i \(-0.750074\pi\)
−0.707272 + 0.706942i \(0.750074\pi\)
\(42\) 0 0
\(43\) 1.79219 0.273306 0.136653 0.990619i \(-0.456365\pi\)
0.136653 + 0.990619i \(0.456365\pi\)
\(44\) 0 0
\(45\) −6.62170 −0.987105
\(46\) 0 0
\(47\) −4.47790 −0.653169 −0.326585 0.945168i \(-0.605898\pi\)
−0.326585 + 0.945168i \(0.605898\pi\)
\(48\) 0 0
\(49\) −3.10878 −0.444112
\(50\) 0 0
\(51\) 3.59252 0.503054
\(52\) 0 0
\(53\) −12.0796 −1.65925 −0.829627 0.558318i \(-0.811447\pi\)
−0.829627 + 0.558318i \(0.811447\pi\)
\(54\) 0 0
\(55\) −0.185891 −0.0250655
\(56\) 0 0
\(57\) −8.10633 −1.07371
\(58\) 0 0
\(59\) −1.16916 −0.152212 −0.0761058 0.997100i \(-0.524249\pi\)
−0.0761058 + 0.997100i \(0.524249\pi\)
\(60\) 0 0
\(61\) 9.27981 1.18816 0.594079 0.804407i \(-0.297517\pi\)
0.594079 + 0.804407i \(0.297517\pi\)
\(62\) 0 0
\(63\) 13.0621 1.64567
\(64\) 0 0
\(65\) −5.99884 −0.744064
\(66\) 0 0
\(67\) 12.9087 1.57705 0.788527 0.615001i \(-0.210844\pi\)
0.788527 + 0.615001i \(0.210844\pi\)
\(68\) 0 0
\(69\) 2.83947 0.341832
\(70\) 0 0
\(71\) −4.83239 −0.573499 −0.286750 0.958006i \(-0.592575\pi\)
−0.286750 + 0.958006i \(0.592575\pi\)
\(72\) 0 0
\(73\) 3.01365 0.352721 0.176360 0.984326i \(-0.443568\pi\)
0.176360 + 0.984326i \(0.443568\pi\)
\(74\) 0 0
\(75\) −3.10189 −0.358175
\(76\) 0 0
\(77\) 0.366691 0.0417884
\(78\) 0 0
\(79\) 6.21687 0.699453 0.349727 0.936852i \(-0.386275\pi\)
0.349727 + 0.936852i \(0.386275\pi\)
\(80\) 0 0
\(81\) 14.9818 1.66465
\(82\) 0 0
\(83\) −9.34234 −1.02545 −0.512727 0.858551i \(-0.671365\pi\)
−0.512727 + 0.858551i \(0.671365\pi\)
\(84\) 0 0
\(85\) 1.15817 0.125622
\(86\) 0 0
\(87\) 18.3893 1.97154
\(88\) 0 0
\(89\) −17.4169 −1.84619 −0.923096 0.384569i \(-0.874350\pi\)
−0.923096 + 0.384569i \(0.874350\pi\)
\(90\) 0 0
\(91\) 11.8334 1.24048
\(92\) 0 0
\(93\) −4.73766 −0.491272
\(94\) 0 0
\(95\) −2.61335 −0.268125
\(96\) 0 0
\(97\) 4.82293 0.489694 0.244847 0.969562i \(-0.421262\pi\)
0.244847 + 0.969562i \(0.421262\pi\)
\(98\) 0 0
\(99\) 1.23091 0.123711
\(100\) 0 0
\(101\) 0.282599 0.0281197 0.0140598 0.999901i \(-0.495524\pi\)
0.0140598 + 0.999901i \(0.495524\pi\)
\(102\) 0 0
\(103\) −5.60175 −0.551957 −0.275979 0.961164i \(-0.589002\pi\)
−0.275979 + 0.961164i \(0.589002\pi\)
\(104\) 0 0
\(105\) 6.11884 0.597137
\(106\) 0 0
\(107\) 19.7182 1.90623 0.953116 0.302605i \(-0.0978562\pi\)
0.953116 + 0.302605i \(0.0978562\pi\)
\(108\) 0 0
\(109\) 1.92431 0.184315 0.0921576 0.995744i \(-0.470624\pi\)
0.0921576 + 0.995744i \(0.470624\pi\)
\(110\) 0 0
\(111\) 13.8376 1.31340
\(112\) 0 0
\(113\) 7.77312 0.731234 0.365617 0.930765i \(-0.380858\pi\)
0.365617 + 0.930765i \(0.380858\pi\)
\(114\) 0 0
\(115\) 0.915400 0.0853615
\(116\) 0 0
\(117\) 39.7225 3.67235
\(118\) 0 0
\(119\) −2.28463 −0.209432
\(120\) 0 0
\(121\) −10.9654 −0.996859
\(122\) 0 0
\(123\) 28.0953 2.53327
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.234435 0.0208028 0.0104014 0.999946i \(-0.496689\pi\)
0.0104014 + 0.999946i \(0.496689\pi\)
\(128\) 0 0
\(129\) −5.55916 −0.489457
\(130\) 0 0
\(131\) 4.81052 0.420297 0.210149 0.977669i \(-0.432605\pi\)
0.210149 + 0.977669i \(0.432605\pi\)
\(132\) 0 0
\(133\) 5.15515 0.447008
\(134\) 0 0
\(135\) 11.2341 0.966878
\(136\) 0 0
\(137\) −15.7908 −1.34910 −0.674550 0.738229i \(-0.735663\pi\)
−0.674550 + 0.738229i \(0.735663\pi\)
\(138\) 0 0
\(139\) −8.36842 −0.709800 −0.354900 0.934904i \(-0.615485\pi\)
−0.354900 + 0.934904i \(0.615485\pi\)
\(140\) 0 0
\(141\) 13.8899 1.16974
\(142\) 0 0
\(143\) 1.11513 0.0932517
\(144\) 0 0
\(145\) 5.92842 0.492328
\(146\) 0 0
\(147\) 9.64309 0.795348
\(148\) 0 0
\(149\) −10.4799 −0.858546 −0.429273 0.903175i \(-0.641230\pi\)
−0.429273 + 0.903175i \(0.641230\pi\)
\(150\) 0 0
\(151\) −14.4639 −1.17705 −0.588526 0.808478i \(-0.700292\pi\)
−0.588526 + 0.808478i \(0.700292\pi\)
\(152\) 0 0
\(153\) −7.66908 −0.620009
\(154\) 0 0
\(155\) −1.52735 −0.122679
\(156\) 0 0
\(157\) −1.19408 −0.0952980 −0.0476490 0.998864i \(-0.515173\pi\)
−0.0476490 + 0.998864i \(0.515173\pi\)
\(158\) 0 0
\(159\) 37.4694 2.97152
\(160\) 0 0
\(161\) −1.80573 −0.142312
\(162\) 0 0
\(163\) −0.455128 −0.0356484 −0.0178242 0.999841i \(-0.505674\pi\)
−0.0178242 + 0.999841i \(0.505674\pi\)
\(164\) 0 0
\(165\) 0.576612 0.0448892
\(166\) 0 0
\(167\) −1.62963 −0.126105 −0.0630524 0.998010i \(-0.520084\pi\)
−0.0630524 + 0.998010i \(0.520084\pi\)
\(168\) 0 0
\(169\) 22.9861 1.76816
\(170\) 0 0
\(171\) 17.3049 1.32334
\(172\) 0 0
\(173\) −14.8042 −1.12554 −0.562771 0.826613i \(-0.690265\pi\)
−0.562771 + 0.826613i \(0.690265\pi\)
\(174\) 0 0
\(175\) 1.97262 0.149116
\(176\) 0 0
\(177\) 3.62660 0.272592
\(178\) 0 0
\(179\) 7.43781 0.555928 0.277964 0.960591i \(-0.410340\pi\)
0.277964 + 0.960591i \(0.410340\pi\)
\(180\) 0 0
\(181\) −13.8852 −1.03208 −0.516038 0.856565i \(-0.672594\pi\)
−0.516038 + 0.856565i \(0.672594\pi\)
\(182\) 0 0
\(183\) −28.7849 −2.12784
\(184\) 0 0
\(185\) 4.46101 0.327980
\(186\) 0 0
\(187\) −0.215294 −0.0157438
\(188\) 0 0
\(189\) −22.1606 −1.61195
\(190\) 0 0
\(191\) 11.1009 0.803231 0.401616 0.915808i \(-0.368449\pi\)
0.401616 + 0.915808i \(0.368449\pi\)
\(192\) 0 0
\(193\) 4.90003 0.352712 0.176356 0.984326i \(-0.443569\pi\)
0.176356 + 0.984326i \(0.443569\pi\)
\(194\) 0 0
\(195\) 18.6077 1.33253
\(196\) 0 0
\(197\) 9.43054 0.671898 0.335949 0.941880i \(-0.390943\pi\)
0.335949 + 0.941880i \(0.390943\pi\)
\(198\) 0 0
\(199\) 8.03587 0.569648 0.284824 0.958580i \(-0.408065\pi\)
0.284824 + 0.958580i \(0.408065\pi\)
\(200\) 0 0
\(201\) −40.0414 −2.82431
\(202\) 0 0
\(203\) −11.6945 −0.820793
\(204\) 0 0
\(205\) 9.05750 0.632603
\(206\) 0 0
\(207\) −6.06150 −0.421304
\(208\) 0 0
\(209\) 0.485798 0.0336034
\(210\) 0 0
\(211\) −19.5735 −1.34750 −0.673748 0.738961i \(-0.735317\pi\)
−0.673748 + 0.738961i \(0.735317\pi\)
\(212\) 0 0
\(213\) 14.9895 1.02707
\(214\) 0 0
\(215\) −1.79219 −0.122226
\(216\) 0 0
\(217\) 3.01287 0.204527
\(218\) 0 0
\(219\) −9.34799 −0.631679
\(220\) 0 0
\(221\) −6.94770 −0.467353
\(222\) 0 0
\(223\) −6.78366 −0.454268 −0.227134 0.973864i \(-0.572935\pi\)
−0.227134 + 0.973864i \(0.572935\pi\)
\(224\) 0 0
\(225\) 6.62170 0.441447
\(226\) 0 0
\(227\) 20.8382 1.38308 0.691541 0.722337i \(-0.256932\pi\)
0.691541 + 0.722337i \(0.256932\pi\)
\(228\) 0 0
\(229\) −4.23931 −0.280142 −0.140071 0.990141i \(-0.544733\pi\)
−0.140071 + 0.990141i \(0.544733\pi\)
\(230\) 0 0
\(231\) −1.13743 −0.0748377
\(232\) 0 0
\(233\) 0.201662 0.0132113 0.00660565 0.999978i \(-0.497897\pi\)
0.00660565 + 0.999978i \(0.497897\pi\)
\(234\) 0 0
\(235\) 4.47790 0.292106
\(236\) 0 0
\(237\) −19.2840 −1.25263
\(238\) 0 0
\(239\) −18.8098 −1.21670 −0.608351 0.793668i \(-0.708169\pi\)
−0.608351 + 0.793668i \(0.708169\pi\)
\(240\) 0 0
\(241\) −6.32279 −0.407286 −0.203643 0.979045i \(-0.565278\pi\)
−0.203643 + 0.979045i \(0.565278\pi\)
\(242\) 0 0
\(243\) −12.7696 −0.819172
\(244\) 0 0
\(245\) 3.10878 0.198613
\(246\) 0 0
\(247\) 15.6771 0.997510
\(248\) 0 0
\(249\) 28.9789 1.83646
\(250\) 0 0
\(251\) 14.8817 0.939322 0.469661 0.882847i \(-0.344376\pi\)
0.469661 + 0.882847i \(0.344376\pi\)
\(252\) 0 0
\(253\) −0.170164 −0.0106981
\(254\) 0 0
\(255\) −3.59252 −0.224973
\(256\) 0 0
\(257\) 0.743600 0.0463845 0.0231923 0.999731i \(-0.492617\pi\)
0.0231923 + 0.999731i \(0.492617\pi\)
\(258\) 0 0
\(259\) −8.79987 −0.546798
\(260\) 0 0
\(261\) −39.2562 −2.42990
\(262\) 0 0
\(263\) 7.29543 0.449855 0.224928 0.974375i \(-0.427785\pi\)
0.224928 + 0.974375i \(0.427785\pi\)
\(264\) 0 0
\(265\) 12.0796 0.742041
\(266\) 0 0
\(267\) 54.0254 3.30630
\(268\) 0 0
\(269\) 22.1052 1.34778 0.673889 0.738833i \(-0.264623\pi\)
0.673889 + 0.738833i \(0.264623\pi\)
\(270\) 0 0
\(271\) −16.5100 −1.00291 −0.501456 0.865183i \(-0.667202\pi\)
−0.501456 + 0.865183i \(0.667202\pi\)
\(272\) 0 0
\(273\) −36.7059 −2.22154
\(274\) 0 0
\(275\) 0.185891 0.0112096
\(276\) 0 0
\(277\) 0.738435 0.0443682 0.0221841 0.999754i \(-0.492938\pi\)
0.0221841 + 0.999754i \(0.492938\pi\)
\(278\) 0 0
\(279\) 10.1136 0.605488
\(280\) 0 0
\(281\) −4.15931 −0.248124 −0.124062 0.992274i \(-0.539592\pi\)
−0.124062 + 0.992274i \(0.539592\pi\)
\(282\) 0 0
\(283\) 4.32278 0.256963 0.128481 0.991712i \(-0.458990\pi\)
0.128481 + 0.991712i \(0.458990\pi\)
\(284\) 0 0
\(285\) 8.10633 0.480178
\(286\) 0 0
\(287\) −17.8670 −1.05465
\(288\) 0 0
\(289\) −15.6586 −0.921096
\(290\) 0 0
\(291\) −14.9602 −0.876981
\(292\) 0 0
\(293\) 32.2955 1.88672 0.943361 0.331769i \(-0.107645\pi\)
0.943361 + 0.331769i \(0.107645\pi\)
\(294\) 0 0
\(295\) 1.16916 0.0680711
\(296\) 0 0
\(297\) −2.08832 −0.121176
\(298\) 0 0
\(299\) −5.49134 −0.317572
\(300\) 0 0
\(301\) 3.53530 0.203771
\(302\) 0 0
\(303\) −0.876590 −0.0503588
\(304\) 0 0
\(305\) −9.27981 −0.531361
\(306\) 0 0
\(307\) 1.40664 0.0802814 0.0401407 0.999194i \(-0.487219\pi\)
0.0401407 + 0.999194i \(0.487219\pi\)
\(308\) 0 0
\(309\) 17.3760 0.988487
\(310\) 0 0
\(311\) −16.6181 −0.942323 −0.471162 0.882047i \(-0.656165\pi\)
−0.471162 + 0.882047i \(0.656165\pi\)
\(312\) 0 0
\(313\) −8.97109 −0.507076 −0.253538 0.967325i \(-0.581594\pi\)
−0.253538 + 0.967325i \(0.581594\pi\)
\(314\) 0 0
\(315\) −13.0621 −0.735965
\(316\) 0 0
\(317\) −27.1399 −1.52433 −0.762166 0.647382i \(-0.775864\pi\)
−0.762166 + 0.647382i \(0.775864\pi\)
\(318\) 0 0
\(319\) −1.10204 −0.0617023
\(320\) 0 0
\(321\) −61.1637 −3.41382
\(322\) 0 0
\(323\) −3.02672 −0.168411
\(324\) 0 0
\(325\) 5.99884 0.332756
\(326\) 0 0
\(327\) −5.96898 −0.330085
\(328\) 0 0
\(329\) −8.83319 −0.486990
\(330\) 0 0
\(331\) 23.2415 1.27747 0.638734 0.769428i \(-0.279459\pi\)
0.638734 + 0.769428i \(0.279459\pi\)
\(332\) 0 0
\(333\) −29.5395 −1.61876
\(334\) 0 0
\(335\) −12.9087 −0.705280
\(336\) 0 0
\(337\) 14.1771 0.772279 0.386139 0.922440i \(-0.373808\pi\)
0.386139 + 0.922440i \(0.373808\pi\)
\(338\) 0 0
\(339\) −24.1113 −1.30955
\(340\) 0 0
\(341\) 0.283920 0.0153751
\(342\) 0 0
\(343\) −19.9408 −1.07670
\(344\) 0 0
\(345\) −2.83947 −0.152872
\(346\) 0 0
\(347\) 5.11881 0.274792 0.137396 0.990516i \(-0.456127\pi\)
0.137396 + 0.990516i \(0.456127\pi\)
\(348\) 0 0
\(349\) 2.91019 0.155779 0.0778894 0.996962i \(-0.475182\pi\)
0.0778894 + 0.996962i \(0.475182\pi\)
\(350\) 0 0
\(351\) −67.3916 −3.59710
\(352\) 0 0
\(353\) 15.4289 0.821198 0.410599 0.911816i \(-0.365320\pi\)
0.410599 + 0.911816i \(0.365320\pi\)
\(354\) 0 0
\(355\) 4.83239 0.256477
\(356\) 0 0
\(357\) 7.08667 0.375067
\(358\) 0 0
\(359\) −20.9945 −1.10805 −0.554024 0.832501i \(-0.686908\pi\)
−0.554024 + 0.832501i \(0.686908\pi\)
\(360\) 0 0
\(361\) −12.1704 −0.640546
\(362\) 0 0
\(363\) 34.0136 1.78525
\(364\) 0 0
\(365\) −3.01365 −0.157742
\(366\) 0 0
\(367\) 9.41327 0.491369 0.245684 0.969350i \(-0.420987\pi\)
0.245684 + 0.969350i \(0.420987\pi\)
\(368\) 0 0
\(369\) −59.9761 −3.12223
\(370\) 0 0
\(371\) −23.8283 −1.23711
\(372\) 0 0
\(373\) −10.6443 −0.551143 −0.275571 0.961281i \(-0.588867\pi\)
−0.275571 + 0.961281i \(0.588867\pi\)
\(374\) 0 0
\(375\) 3.10189 0.160181
\(376\) 0 0
\(377\) −35.5636 −1.83162
\(378\) 0 0
\(379\) −16.9872 −0.872573 −0.436286 0.899808i \(-0.643706\pi\)
−0.436286 + 0.899808i \(0.643706\pi\)
\(380\) 0 0
\(381\) −0.727192 −0.0372552
\(382\) 0 0
\(383\) 5.60790 0.286550 0.143275 0.989683i \(-0.454237\pi\)
0.143275 + 0.989683i \(0.454237\pi\)
\(384\) 0 0
\(385\) −0.366691 −0.0186883
\(386\) 0 0
\(387\) 11.8673 0.603251
\(388\) 0 0
\(389\) 13.2801 0.673326 0.336663 0.941625i \(-0.390702\pi\)
0.336663 + 0.941625i \(0.390702\pi\)
\(390\) 0 0
\(391\) 1.06019 0.0536162
\(392\) 0 0
\(393\) −14.9217 −0.752700
\(394\) 0 0
\(395\) −6.21687 −0.312805
\(396\) 0 0
\(397\) −17.0017 −0.853292 −0.426646 0.904419i \(-0.640305\pi\)
−0.426646 + 0.904419i \(0.640305\pi\)
\(398\) 0 0
\(399\) −15.9907 −0.800536
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) 9.16231 0.456407
\(404\) 0 0
\(405\) −14.9818 −0.744454
\(406\) 0 0
\(407\) −0.829261 −0.0411049
\(408\) 0 0
\(409\) 2.95348 0.146040 0.0730202 0.997330i \(-0.476736\pi\)
0.0730202 + 0.997330i \(0.476736\pi\)
\(410\) 0 0
\(411\) 48.9813 2.41607
\(412\) 0 0
\(413\) −2.30631 −0.113486
\(414\) 0 0
\(415\) 9.34234 0.458597
\(416\) 0 0
\(417\) 25.9579 1.27116
\(418\) 0 0
\(419\) −11.5570 −0.564598 −0.282299 0.959326i \(-0.591097\pi\)
−0.282299 + 0.959326i \(0.591097\pi\)
\(420\) 0 0
\(421\) −31.0211 −1.51187 −0.755937 0.654644i \(-0.772818\pi\)
−0.755937 + 0.654644i \(0.772818\pi\)
\(422\) 0 0
\(423\) −29.6513 −1.44170
\(424\) 0 0
\(425\) −1.15817 −0.0561797
\(426\) 0 0
\(427\) 18.3055 0.885866
\(428\) 0 0
\(429\) −3.45900 −0.167002
\(430\) 0 0
\(431\) −3.74633 −0.180454 −0.0902272 0.995921i \(-0.528759\pi\)
−0.0902272 + 0.995921i \(0.528759\pi\)
\(432\) 0 0
\(433\) −32.0977 −1.54252 −0.771258 0.636523i \(-0.780372\pi\)
−0.771258 + 0.636523i \(0.780372\pi\)
\(434\) 0 0
\(435\) −18.3893 −0.881699
\(436\) 0 0
\(437\) −2.39226 −0.114437
\(438\) 0 0
\(439\) −12.6297 −0.602782 −0.301391 0.953501i \(-0.597451\pi\)
−0.301391 + 0.953501i \(0.597451\pi\)
\(440\) 0 0
\(441\) −20.5854 −0.980258
\(442\) 0 0
\(443\) 4.97080 0.236170 0.118085 0.993004i \(-0.462325\pi\)
0.118085 + 0.993004i \(0.462325\pi\)
\(444\) 0 0
\(445\) 17.4169 0.825642
\(446\) 0 0
\(447\) 32.5074 1.53755
\(448\) 0 0
\(449\) 13.8969 0.655833 0.327917 0.944707i \(-0.393653\pi\)
0.327917 + 0.944707i \(0.393653\pi\)
\(450\) 0 0
\(451\) −1.68371 −0.0792826
\(452\) 0 0
\(453\) 44.8653 2.10795
\(454\) 0 0
\(455\) −11.8334 −0.554759
\(456\) 0 0
\(457\) −19.1624 −0.896379 −0.448190 0.893939i \(-0.647931\pi\)
−0.448190 + 0.893939i \(0.647931\pi\)
\(458\) 0 0
\(459\) 13.0111 0.607304
\(460\) 0 0
\(461\) −34.8438 −1.62284 −0.811420 0.584464i \(-0.801305\pi\)
−0.811420 + 0.584464i \(0.801305\pi\)
\(462\) 0 0
\(463\) 22.7936 1.05931 0.529655 0.848213i \(-0.322321\pi\)
0.529655 + 0.848213i \(0.322321\pi\)
\(464\) 0 0
\(465\) 4.73766 0.219704
\(466\) 0 0
\(467\) −15.7097 −0.726957 −0.363478 0.931603i \(-0.618411\pi\)
−0.363478 + 0.931603i \(0.618411\pi\)
\(468\) 0 0
\(469\) 25.4640 1.17582
\(470\) 0 0
\(471\) 3.70390 0.170667
\(472\) 0 0
\(473\) 0.333151 0.0153183
\(474\) 0 0
\(475\) 2.61335 0.119909
\(476\) 0 0
\(477\) −79.9872 −3.66236
\(478\) 0 0
\(479\) 20.2742 0.926351 0.463176 0.886267i \(-0.346710\pi\)
0.463176 + 0.886267i \(0.346710\pi\)
\(480\) 0 0
\(481\) −26.7609 −1.22019
\(482\) 0 0
\(483\) 5.60118 0.254863
\(484\) 0 0
\(485\) −4.82293 −0.218998
\(486\) 0 0
\(487\) −23.0295 −1.04357 −0.521784 0.853078i \(-0.674733\pi\)
−0.521784 + 0.853078i \(0.674733\pi\)
\(488\) 0 0
\(489\) 1.41176 0.0638419
\(490\) 0 0
\(491\) −32.6056 −1.47147 −0.735735 0.677269i \(-0.763163\pi\)
−0.735735 + 0.677269i \(0.763163\pi\)
\(492\) 0 0
\(493\) 6.86614 0.309235
\(494\) 0 0
\(495\) −1.23091 −0.0553254
\(496\) 0 0
\(497\) −9.53246 −0.427589
\(498\) 0 0
\(499\) −5.04163 −0.225694 −0.112847 0.993612i \(-0.535997\pi\)
−0.112847 + 0.993612i \(0.535997\pi\)
\(500\) 0 0
\(501\) 5.05494 0.225838
\(502\) 0 0
\(503\) 10.9995 0.490445 0.245223 0.969467i \(-0.421139\pi\)
0.245223 + 0.969467i \(0.421139\pi\)
\(504\) 0 0
\(505\) −0.282599 −0.0125755
\(506\) 0 0
\(507\) −71.3002 −3.16655
\(508\) 0 0
\(509\) 37.1759 1.64779 0.823897 0.566739i \(-0.191795\pi\)
0.823897 + 0.566739i \(0.191795\pi\)
\(510\) 0 0
\(511\) 5.94477 0.262981
\(512\) 0 0
\(513\) −29.3587 −1.29622
\(514\) 0 0
\(515\) 5.60175 0.246843
\(516\) 0 0
\(517\) −0.832401 −0.0366089
\(518\) 0 0
\(519\) 45.9209 2.01570
\(520\) 0 0
\(521\) −19.8544 −0.869837 −0.434919 0.900470i \(-0.643223\pi\)
−0.434919 + 0.900470i \(0.643223\pi\)
\(522\) 0 0
\(523\) −3.93838 −0.172213 −0.0861066 0.996286i \(-0.527443\pi\)
−0.0861066 + 0.996286i \(0.527443\pi\)
\(524\) 0 0
\(525\) −6.11884 −0.267048
\(526\) 0 0
\(527\) −1.76893 −0.0770559
\(528\) 0 0
\(529\) −22.1620 −0.963567
\(530\) 0 0
\(531\) −7.74183 −0.335967
\(532\) 0 0
\(533\) −54.3345 −2.35349
\(534\) 0 0
\(535\) −19.7182 −0.852493
\(536\) 0 0
\(537\) −23.0712 −0.995598
\(538\) 0 0
\(539\) −0.577894 −0.0248916
\(540\) 0 0
\(541\) 13.0238 0.559939 0.279969 0.960009i \(-0.409676\pi\)
0.279969 + 0.960009i \(0.409676\pi\)
\(542\) 0 0
\(543\) 43.0702 1.84832
\(544\) 0 0
\(545\) −1.92431 −0.0824283
\(546\) 0 0
\(547\) 20.3242 0.869002 0.434501 0.900671i \(-0.356925\pi\)
0.434501 + 0.900671i \(0.356925\pi\)
\(548\) 0 0
\(549\) 61.4482 2.62254
\(550\) 0 0
\(551\) −15.4931 −0.660026
\(552\) 0 0
\(553\) 12.2635 0.521498
\(554\) 0 0
\(555\) −13.8376 −0.587372
\(556\) 0 0
\(557\) −2.39829 −0.101619 −0.0508094 0.998708i \(-0.516180\pi\)
−0.0508094 + 0.998708i \(0.516180\pi\)
\(558\) 0 0
\(559\) 10.7510 0.454721
\(560\) 0 0
\(561\) 0.667817 0.0281953
\(562\) 0 0
\(563\) −3.83710 −0.161715 −0.0808573 0.996726i \(-0.525766\pi\)
−0.0808573 + 0.996726i \(0.525766\pi\)
\(564\) 0 0
\(565\) −7.77312 −0.327018
\(566\) 0 0
\(567\) 29.5534 1.24113
\(568\) 0 0
\(569\) −15.1032 −0.633160 −0.316580 0.948566i \(-0.602535\pi\)
−0.316580 + 0.948566i \(0.602535\pi\)
\(570\) 0 0
\(571\) −6.96447 −0.291454 −0.145727 0.989325i \(-0.546552\pi\)
−0.145727 + 0.989325i \(0.546552\pi\)
\(572\) 0 0
\(573\) −34.4337 −1.43849
\(574\) 0 0
\(575\) −0.915400 −0.0381748
\(576\) 0 0
\(577\) 23.3917 0.973811 0.486906 0.873455i \(-0.338126\pi\)
0.486906 + 0.873455i \(0.338126\pi\)
\(578\) 0 0
\(579\) −15.1993 −0.631663
\(580\) 0 0
\(581\) −18.4289 −0.764558
\(582\) 0 0
\(583\) −2.24548 −0.0929982
\(584\) 0 0
\(585\) −39.7225 −1.64232
\(586\) 0 0
\(587\) 5.99646 0.247501 0.123750 0.992313i \(-0.460508\pi\)
0.123750 + 0.992313i \(0.460508\pi\)
\(588\) 0 0
\(589\) 3.99150 0.164467
\(590\) 0 0
\(591\) −29.2525 −1.20329
\(592\) 0 0
\(593\) 12.7066 0.521798 0.260899 0.965366i \(-0.415981\pi\)
0.260899 + 0.965366i \(0.415981\pi\)
\(594\) 0 0
\(595\) 2.28463 0.0936608
\(596\) 0 0
\(597\) −24.9264 −1.02017
\(598\) 0 0
\(599\) −39.7648 −1.62475 −0.812373 0.583139i \(-0.801824\pi\)
−0.812373 + 0.583139i \(0.801824\pi\)
\(600\) 0 0
\(601\) 39.7160 1.62005 0.810026 0.586394i \(-0.199453\pi\)
0.810026 + 0.586394i \(0.199453\pi\)
\(602\) 0 0
\(603\) 85.4778 3.48093
\(604\) 0 0
\(605\) 10.9654 0.445809
\(606\) 0 0
\(607\) 31.1461 1.26418 0.632091 0.774894i \(-0.282197\pi\)
0.632091 + 0.774894i \(0.282197\pi\)
\(608\) 0 0
\(609\) 36.2750 1.46994
\(610\) 0 0
\(611\) −26.8622 −1.08673
\(612\) 0 0
\(613\) 33.5549 1.35527 0.677635 0.735398i \(-0.263005\pi\)
0.677635 + 0.735398i \(0.263005\pi\)
\(614\) 0 0
\(615\) −28.0953 −1.13291
\(616\) 0 0
\(617\) −15.6154 −0.628653 −0.314326 0.949315i \(-0.601779\pi\)
−0.314326 + 0.949315i \(0.601779\pi\)
\(618\) 0 0
\(619\) 30.4666 1.22456 0.612279 0.790642i \(-0.290253\pi\)
0.612279 + 0.790642i \(0.290253\pi\)
\(620\) 0 0
\(621\) 10.2837 0.412671
\(622\) 0 0
\(623\) −34.3570 −1.37648
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −1.50689 −0.0601795
\(628\) 0 0
\(629\) 5.16663 0.206007
\(630\) 0 0
\(631\) −27.8821 −1.10997 −0.554984 0.831861i \(-0.687275\pi\)
−0.554984 + 0.831861i \(0.687275\pi\)
\(632\) 0 0
\(633\) 60.7148 2.41320
\(634\) 0 0
\(635\) −0.234435 −0.00930328
\(636\) 0 0
\(637\) −18.6491 −0.738903
\(638\) 0 0
\(639\) −31.9986 −1.26585
\(640\) 0 0
\(641\) −28.9800 −1.14464 −0.572320 0.820031i \(-0.693956\pi\)
−0.572320 + 0.820031i \(0.693956\pi\)
\(642\) 0 0
\(643\) −25.7800 −1.01667 −0.508333 0.861161i \(-0.669738\pi\)
−0.508333 + 0.861161i \(0.669738\pi\)
\(644\) 0 0
\(645\) 5.55916 0.218892
\(646\) 0 0
\(647\) 10.2704 0.403772 0.201886 0.979409i \(-0.435293\pi\)
0.201886 + 0.979409i \(0.435293\pi\)
\(648\) 0 0
\(649\) −0.217336 −0.00853119
\(650\) 0 0
\(651\) −9.34559 −0.366282
\(652\) 0 0
\(653\) −36.2398 −1.41817 −0.709087 0.705121i \(-0.750892\pi\)
−0.709087 + 0.705121i \(0.750892\pi\)
\(654\) 0 0
\(655\) −4.81052 −0.187963
\(656\) 0 0
\(657\) 19.9555 0.778537
\(658\) 0 0
\(659\) 19.2951 0.751630 0.375815 0.926695i \(-0.377363\pi\)
0.375815 + 0.926695i \(0.377363\pi\)
\(660\) 0 0
\(661\) −24.5310 −0.954147 −0.477074 0.878863i \(-0.658302\pi\)
−0.477074 + 0.878863i \(0.658302\pi\)
\(662\) 0 0
\(663\) 21.5510 0.836970
\(664\) 0 0
\(665\) −5.15515 −0.199908
\(666\) 0 0
\(667\) 5.42687 0.210129
\(668\) 0 0
\(669\) 21.0421 0.813536
\(670\) 0 0
\(671\) 1.72503 0.0665941
\(672\) 0 0
\(673\) −27.7957 −1.07145 −0.535724 0.844393i \(-0.679961\pi\)
−0.535724 + 0.844393i \(0.679961\pi\)
\(674\) 0 0
\(675\) −11.2341 −0.432401
\(676\) 0 0
\(677\) −20.4172 −0.784697 −0.392349 0.919817i \(-0.628337\pi\)
−0.392349 + 0.919817i \(0.628337\pi\)
\(678\) 0 0
\(679\) 9.51379 0.365106
\(680\) 0 0
\(681\) −64.6379 −2.47693
\(682\) 0 0
\(683\) 19.3296 0.739627 0.369813 0.929106i \(-0.379422\pi\)
0.369813 + 0.929106i \(0.379422\pi\)
\(684\) 0 0
\(685\) 15.7908 0.603336
\(686\) 0 0
\(687\) 13.1499 0.501699
\(688\) 0 0
\(689\) −72.4633 −2.76063
\(690\) 0 0
\(691\) −36.8036 −1.40007 −0.700037 0.714106i \(-0.746833\pi\)
−0.700037 + 0.714106i \(0.746833\pi\)
\(692\) 0 0
\(693\) 2.42812 0.0922367
\(694\) 0 0
\(695\) 8.36842 0.317432
\(696\) 0 0
\(697\) 10.4902 0.397343
\(698\) 0 0
\(699\) −0.625532 −0.0236598
\(700\) 0 0
\(701\) −19.1881 −0.724725 −0.362363 0.932037i \(-0.618030\pi\)
−0.362363 + 0.932037i \(0.618030\pi\)
\(702\) 0 0
\(703\) −11.6582 −0.439698
\(704\) 0 0
\(705\) −13.8899 −0.523126
\(706\) 0 0
\(707\) 0.557460 0.0209654
\(708\) 0 0
\(709\) 18.1262 0.680742 0.340371 0.940291i \(-0.389447\pi\)
0.340371 + 0.940291i \(0.389447\pi\)
\(710\) 0 0
\(711\) 41.1663 1.54386
\(712\) 0 0
\(713\) −1.39813 −0.0523605
\(714\) 0 0
\(715\) −1.11513 −0.0417034
\(716\) 0 0
\(717\) 58.3458 2.17896
\(718\) 0 0
\(719\) 20.6737 0.770997 0.385499 0.922708i \(-0.374029\pi\)
0.385499 + 0.922708i \(0.374029\pi\)
\(720\) 0 0
\(721\) −11.0501 −0.411528
\(722\) 0 0
\(723\) 19.6126 0.729399
\(724\) 0 0
\(725\) −5.92842 −0.220176
\(726\) 0 0
\(727\) −13.5398 −0.502164 −0.251082 0.967966i \(-0.580786\pi\)
−0.251082 + 0.967966i \(0.580786\pi\)
\(728\) 0 0
\(729\) −5.33556 −0.197613
\(730\) 0 0
\(731\) −2.07566 −0.0767712
\(732\) 0 0
\(733\) −14.4540 −0.533871 −0.266936 0.963714i \(-0.586011\pi\)
−0.266936 + 0.963714i \(0.586011\pi\)
\(734\) 0 0
\(735\) −9.64309 −0.355691
\(736\) 0 0
\(737\) 2.39961 0.0883909
\(738\) 0 0
\(739\) −5.56089 −0.204561 −0.102280 0.994756i \(-0.532614\pi\)
−0.102280 + 0.994756i \(0.532614\pi\)
\(740\) 0 0
\(741\) −48.6286 −1.78642
\(742\) 0 0
\(743\) 46.8370 1.71828 0.859142 0.511737i \(-0.170998\pi\)
0.859142 + 0.511737i \(0.170998\pi\)
\(744\) 0 0
\(745\) 10.4799 0.383954
\(746\) 0 0
\(747\) −61.8622 −2.26342
\(748\) 0 0
\(749\) 38.8965 1.42125
\(750\) 0 0
\(751\) −44.7896 −1.63440 −0.817199 0.576356i \(-0.804474\pi\)
−0.817199 + 0.576356i \(0.804474\pi\)
\(752\) 0 0
\(753\) −46.1612 −1.68221
\(754\) 0 0
\(755\) 14.4639 0.526394
\(756\) 0 0
\(757\) 31.9019 1.15949 0.579746 0.814797i \(-0.303152\pi\)
0.579746 + 0.814797i \(0.303152\pi\)
\(758\) 0 0
\(759\) 0.527830 0.0191590
\(760\) 0 0
\(761\) 2.52380 0.0914878 0.0457439 0.998953i \(-0.485434\pi\)
0.0457439 + 0.998953i \(0.485434\pi\)
\(762\) 0 0
\(763\) 3.79592 0.137422
\(764\) 0 0
\(765\) 7.66908 0.277276
\(766\) 0 0
\(767\) −7.01360 −0.253247
\(768\) 0 0
\(769\) −44.9644 −1.62146 −0.810729 0.585422i \(-0.800929\pi\)
−0.810729 + 0.585422i \(0.800929\pi\)
\(770\) 0 0
\(771\) −2.30656 −0.0830689
\(772\) 0 0
\(773\) 26.7131 0.960803 0.480402 0.877049i \(-0.340491\pi\)
0.480402 + 0.877049i \(0.340491\pi\)
\(774\) 0 0
\(775\) 1.52735 0.0548639
\(776\) 0 0
\(777\) 27.2962 0.979246
\(778\) 0 0
\(779\) −23.6705 −0.848082
\(780\) 0 0
\(781\) −0.898297 −0.0321436
\(782\) 0 0
\(783\) 66.6005 2.38011
\(784\) 0 0
\(785\) 1.19408 0.0426186
\(786\) 0 0
\(787\) −4.04080 −0.144039 −0.0720195 0.997403i \(-0.522944\pi\)
−0.0720195 + 0.997403i \(0.522944\pi\)
\(788\) 0 0
\(789\) −22.6296 −0.805635
\(790\) 0 0
\(791\) 15.3334 0.545193
\(792\) 0 0
\(793\) 55.6681 1.97683
\(794\) 0 0
\(795\) −37.4694 −1.32890
\(796\) 0 0
\(797\) 51.1792 1.81286 0.906430 0.422356i \(-0.138797\pi\)
0.906430 + 0.422356i \(0.138797\pi\)
\(798\) 0 0
\(799\) 5.18619 0.183474
\(800\) 0 0
\(801\) −115.330 −4.07498
\(802\) 0 0
\(803\) 0.560209 0.0197694
\(804\) 0 0
\(805\) 1.80573 0.0636437
\(806\) 0 0
\(807\) −68.5678 −2.41370
\(808\) 0 0
\(809\) −0.745105 −0.0261965 −0.0130982 0.999914i \(-0.504169\pi\)
−0.0130982 + 0.999914i \(0.504169\pi\)
\(810\) 0 0
\(811\) 26.9104 0.944954 0.472477 0.881343i \(-0.343360\pi\)
0.472477 + 0.881343i \(0.343360\pi\)
\(812\) 0 0
\(813\) 51.2122 1.79609
\(814\) 0 0
\(815\) 0.455128 0.0159425
\(816\) 0 0
\(817\) 4.68362 0.163859
\(818\) 0 0
\(819\) 78.3573 2.73803
\(820\) 0 0
\(821\) 51.6654 1.80313 0.901567 0.432639i \(-0.142418\pi\)
0.901567 + 0.432639i \(0.142418\pi\)
\(822\) 0 0
\(823\) −33.5710 −1.17021 −0.585106 0.810957i \(-0.698947\pi\)
−0.585106 + 0.810957i \(0.698947\pi\)
\(824\) 0 0
\(825\) −0.576612 −0.0200751
\(826\) 0 0
\(827\) 34.2714 1.19173 0.595867 0.803083i \(-0.296809\pi\)
0.595867 + 0.803083i \(0.296809\pi\)
\(828\) 0 0
\(829\) 44.2439 1.53665 0.768327 0.640057i \(-0.221089\pi\)
0.768327 + 0.640057i \(0.221089\pi\)
\(830\) 0 0
\(831\) −2.29054 −0.0794580
\(832\) 0 0
\(833\) 3.60051 0.124750
\(834\) 0 0
\(835\) 1.62963 0.0563958
\(836\) 0 0
\(837\) −17.1584 −0.593081
\(838\) 0 0
\(839\) −33.2835 −1.14908 −0.574538 0.818478i \(-0.694818\pi\)
−0.574538 + 0.818478i \(0.694818\pi\)
\(840\) 0 0
\(841\) 6.14613 0.211936
\(842\) 0 0
\(843\) 12.9017 0.444358
\(844\) 0 0
\(845\) −22.9861 −0.790745
\(846\) 0 0
\(847\) −21.6306 −0.743237
\(848\) 0 0
\(849\) −13.4088 −0.460188
\(850\) 0 0
\(851\) 4.08361 0.139984
\(852\) 0 0
\(853\) −1.89277 −0.0648071 −0.0324035 0.999475i \(-0.510316\pi\)
−0.0324035 + 0.999475i \(0.510316\pi\)
\(854\) 0 0
\(855\) −17.3049 −0.591814
\(856\) 0 0
\(857\) 10.6471 0.363700 0.181850 0.983326i \(-0.441792\pi\)
0.181850 + 0.983326i \(0.441792\pi\)
\(858\) 0 0
\(859\) −10.5542 −0.360106 −0.180053 0.983657i \(-0.557627\pi\)
−0.180053 + 0.983657i \(0.557627\pi\)
\(860\) 0 0
\(861\) 55.4214 1.88875
\(862\) 0 0
\(863\) −22.0399 −0.750247 −0.375124 0.926975i \(-0.622400\pi\)
−0.375124 + 0.926975i \(0.622400\pi\)
\(864\) 0 0
\(865\) 14.8042 0.503357
\(866\) 0 0
\(867\) 48.5713 1.64957
\(868\) 0 0
\(869\) 1.15566 0.0392031
\(870\) 0 0
\(871\) 77.4374 2.62387
\(872\) 0 0
\(873\) 31.9360 1.08087
\(874\) 0 0
\(875\) −1.97262 −0.0666866
\(876\) 0 0
\(877\) −57.3912 −1.93796 −0.968982 0.247133i \(-0.920512\pi\)
−0.968982 + 0.247133i \(0.920512\pi\)
\(878\) 0 0
\(879\) −100.177 −3.37888
\(880\) 0 0
\(881\) −18.6979 −0.629947 −0.314973 0.949100i \(-0.601996\pi\)
−0.314973 + 0.949100i \(0.601996\pi\)
\(882\) 0 0
\(883\) −26.8895 −0.904903 −0.452451 0.891789i \(-0.649450\pi\)
−0.452451 + 0.891789i \(0.649450\pi\)
\(884\) 0 0
\(885\) −3.62660 −0.121907
\(886\) 0 0
\(887\) 22.3004 0.748775 0.374387 0.927272i \(-0.377853\pi\)
0.374387 + 0.927272i \(0.377853\pi\)
\(888\) 0 0
\(889\) 0.462451 0.0155101
\(890\) 0 0
\(891\) 2.78499 0.0933005
\(892\) 0 0
\(893\) −11.7023 −0.391604
\(894\) 0 0
\(895\) −7.43781 −0.248619
\(896\) 0 0
\(897\) 17.0335 0.568732
\(898\) 0 0
\(899\) −9.05475 −0.301993
\(900\) 0 0
\(901\) 13.9902 0.466082
\(902\) 0 0
\(903\) −10.9661 −0.364929
\(904\) 0 0
\(905\) 13.8852 0.461559
\(906\) 0 0
\(907\) −34.7322 −1.15326 −0.576631 0.817005i \(-0.695633\pi\)
−0.576631 + 0.817005i \(0.695633\pi\)
\(908\) 0 0
\(909\) 1.87129 0.0620667
\(910\) 0 0
\(911\) 44.5643 1.47648 0.738241 0.674537i \(-0.235657\pi\)
0.738241 + 0.674537i \(0.235657\pi\)
\(912\) 0 0
\(913\) −1.73665 −0.0574749
\(914\) 0 0
\(915\) 28.7849 0.951601
\(916\) 0 0
\(917\) 9.48932 0.313365
\(918\) 0 0
\(919\) −4.73926 −0.156334 −0.0781669 0.996940i \(-0.524907\pi\)
−0.0781669 + 0.996940i \(0.524907\pi\)
\(920\) 0 0
\(921\) −4.36325 −0.143774
\(922\) 0 0
\(923\) −28.9887 −0.954176
\(924\) 0 0
\(925\) −4.46101 −0.146677
\(926\) 0 0
\(927\) −37.0931 −1.21830
\(928\) 0 0
\(929\) 25.5550 0.838433 0.419216 0.907886i \(-0.362305\pi\)
0.419216 + 0.907886i \(0.362305\pi\)
\(930\) 0 0
\(931\) −8.12435 −0.266265
\(932\) 0 0
\(933\) 51.5473 1.68758
\(934\) 0 0
\(935\) 0.215294 0.00704086
\(936\) 0 0
\(937\) −4.24355 −0.138631 −0.0693153 0.997595i \(-0.522081\pi\)
−0.0693153 + 0.997595i \(0.522081\pi\)
\(938\) 0 0
\(939\) 27.8273 0.908110
\(940\) 0 0
\(941\) −24.1928 −0.788664 −0.394332 0.918968i \(-0.629024\pi\)
−0.394332 + 0.918968i \(0.629024\pi\)
\(942\) 0 0
\(943\) 8.29123 0.270000
\(944\) 0 0
\(945\) 22.1606 0.720885
\(946\) 0 0
\(947\) −0.205536 −0.00667902 −0.00333951 0.999994i \(-0.501063\pi\)
−0.00333951 + 0.999994i \(0.501063\pi\)
\(948\) 0 0
\(949\) 18.0784 0.586849
\(950\) 0 0
\(951\) 84.1851 2.72989
\(952\) 0 0
\(953\) 3.60112 0.116652 0.0583259 0.998298i \(-0.481424\pi\)
0.0583259 + 0.998298i \(0.481424\pi\)
\(954\) 0 0
\(955\) −11.1009 −0.359216
\(956\) 0 0
\(957\) 3.41840 0.110501
\(958\) 0 0
\(959\) −31.1492 −1.00586
\(960\) 0 0
\(961\) −28.6672 −0.924749
\(962\) 0 0
\(963\) 130.568 4.20750
\(964\) 0 0
\(965\) −4.90003 −0.157737
\(966\) 0 0
\(967\) −43.2378 −1.39044 −0.695218 0.718799i \(-0.744692\pi\)
−0.695218 + 0.718799i \(0.744692\pi\)
\(968\) 0 0
\(969\) 9.38854 0.301603
\(970\) 0 0
\(971\) 21.6240 0.693947 0.346974 0.937875i \(-0.387209\pi\)
0.346974 + 0.937875i \(0.387209\pi\)
\(972\) 0 0
\(973\) −16.5077 −0.529212
\(974\) 0 0
\(975\) −18.6077 −0.595924
\(976\) 0 0
\(977\) 31.0512 0.993415 0.496708 0.867918i \(-0.334542\pi\)
0.496708 + 0.867918i \(0.334542\pi\)
\(978\) 0 0
\(979\) −3.23765 −0.103476
\(980\) 0 0
\(981\) 12.7422 0.406827
\(982\) 0 0
\(983\) 34.1386 1.08885 0.544427 0.838808i \(-0.316747\pi\)
0.544427 + 0.838808i \(0.316747\pi\)
\(984\) 0 0
\(985\) −9.43054 −0.300482
\(986\) 0 0
\(987\) 27.3996 0.872137
\(988\) 0 0
\(989\) −1.64057 −0.0521670
\(990\) 0 0
\(991\) −45.6659 −1.45062 −0.725312 0.688420i \(-0.758305\pi\)
−0.725312 + 0.688420i \(0.758305\pi\)
\(992\) 0 0
\(993\) −72.0924 −2.28778
\(994\) 0 0
\(995\) −8.03587 −0.254754
\(996\) 0 0
\(997\) −8.30234 −0.262938 −0.131469 0.991320i \(-0.541969\pi\)
−0.131469 + 0.991320i \(0.541969\pi\)
\(998\) 0 0
\(999\) 50.1155 1.58559
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 \(a_p\))