Properties

Label 6040.2.a.p.1.18
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(-2.11583\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.11583 q^{3}\) \(+1.00000 q^{5}\) \(-4.51128 q^{7}\) \(+1.47674 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.11583 q^{3}\) \(+1.00000 q^{5}\) \(-4.51128 q^{7}\) \(+1.47674 q^{9}\) \(+3.71984 q^{11}\) \(+2.26860 q^{13}\) \(+2.11583 q^{15}\) \(-7.69906 q^{17}\) \(-3.28730 q^{19}\) \(-9.54511 q^{21}\) \(+3.96341 q^{23}\) \(+1.00000 q^{25}\) \(-3.22296 q^{27}\) \(-10.2241 q^{29}\) \(+7.05701 q^{31}\) \(+7.87054 q^{33}\) \(-4.51128 q^{35}\) \(-2.55251 q^{37}\) \(+4.79996 q^{39}\) \(-1.38725 q^{41}\) \(+2.98163 q^{43}\) \(+1.47674 q^{45}\) \(+1.63223 q^{47}\) \(+13.3517 q^{49}\) \(-16.2899 q^{51}\) \(-11.1634 q^{53}\) \(+3.71984 q^{55}\) \(-6.95538 q^{57}\) \(-8.02460 q^{59}\) \(-8.37952 q^{61}\) \(-6.66198 q^{63}\) \(+2.26860 q^{65}\) \(+2.46579 q^{67}\) \(+8.38590 q^{69}\) \(-13.4850 q^{71}\) \(+7.06681 q^{73}\) \(+2.11583 q^{75}\) \(-16.7812 q^{77}\) \(-7.66667 q^{79}\) \(-11.2495 q^{81}\) \(-6.35179 q^{83}\) \(-7.69906 q^{85}\) \(-21.6324 q^{87}\) \(+15.7665 q^{89}\) \(-10.2343 q^{91}\) \(+14.9314 q^{93}\) \(-3.28730 q^{95}\) \(+5.64835 q^{97}\) \(+5.49322 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.11583 1.22158 0.610788 0.791794i \(-0.290853\pi\)
0.610788 + 0.791794i \(0.290853\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.51128 −1.70510 −0.852552 0.522642i \(-0.824947\pi\)
−0.852552 + 0.522642i \(0.824947\pi\)
\(8\) 0 0
\(9\) 1.47674 0.492246
\(10\) 0 0
\(11\) 3.71984 1.12157 0.560786 0.827960i \(-0.310499\pi\)
0.560786 + 0.827960i \(0.310499\pi\)
\(12\) 0 0
\(13\) 2.26860 0.629195 0.314598 0.949225i \(-0.398130\pi\)
0.314598 + 0.949225i \(0.398130\pi\)
\(14\) 0 0
\(15\) 2.11583 0.546305
\(16\) 0 0
\(17\) −7.69906 −1.86730 −0.933648 0.358192i \(-0.883393\pi\)
−0.933648 + 0.358192i \(0.883393\pi\)
\(18\) 0 0
\(19\) −3.28730 −0.754159 −0.377080 0.926181i \(-0.623072\pi\)
−0.377080 + 0.926181i \(0.623072\pi\)
\(20\) 0 0
\(21\) −9.54511 −2.08291
\(22\) 0 0
\(23\) 3.96341 0.826427 0.413214 0.910634i \(-0.364406\pi\)
0.413214 + 0.910634i \(0.364406\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −3.22296 −0.620260
\(28\) 0 0
\(29\) −10.2241 −1.89856 −0.949280 0.314431i \(-0.898186\pi\)
−0.949280 + 0.314431i \(0.898186\pi\)
\(30\) 0 0
\(31\) 7.05701 1.26748 0.633738 0.773548i \(-0.281520\pi\)
0.633738 + 0.773548i \(0.281520\pi\)
\(32\) 0 0
\(33\) 7.87054 1.37009
\(34\) 0 0
\(35\) −4.51128 −0.762546
\(36\) 0 0
\(37\) −2.55251 −0.419630 −0.209815 0.977741i \(-0.567286\pi\)
−0.209815 + 0.977741i \(0.567286\pi\)
\(38\) 0 0
\(39\) 4.79996 0.768609
\(40\) 0 0
\(41\) −1.38725 −0.216652 −0.108326 0.994115i \(-0.534549\pi\)
−0.108326 + 0.994115i \(0.534549\pi\)
\(42\) 0 0
\(43\) 2.98163 0.454694 0.227347 0.973814i \(-0.426995\pi\)
0.227347 + 0.973814i \(0.426995\pi\)
\(44\) 0 0
\(45\) 1.47674 0.220139
\(46\) 0 0
\(47\) 1.63223 0.238085 0.119043 0.992889i \(-0.462017\pi\)
0.119043 + 0.992889i \(0.462017\pi\)
\(48\) 0 0
\(49\) 13.3517 1.90738
\(50\) 0 0
\(51\) −16.2899 −2.28104
\(52\) 0 0
\(53\) −11.1634 −1.53341 −0.766706 0.641999i \(-0.778105\pi\)
−0.766706 + 0.641999i \(0.778105\pi\)
\(54\) 0 0
\(55\) 3.71984 0.501583
\(56\) 0 0
\(57\) −6.95538 −0.921262
\(58\) 0 0
\(59\) −8.02460 −1.04471 −0.522357 0.852727i \(-0.674947\pi\)
−0.522357 + 0.852727i \(0.674947\pi\)
\(60\) 0 0
\(61\) −8.37952 −1.07289 −0.536444 0.843936i \(-0.680233\pi\)
−0.536444 + 0.843936i \(0.680233\pi\)
\(62\) 0 0
\(63\) −6.66198 −0.839331
\(64\) 0 0
\(65\) 2.26860 0.281385
\(66\) 0 0
\(67\) 2.46579 0.301244 0.150622 0.988591i \(-0.451872\pi\)
0.150622 + 0.988591i \(0.451872\pi\)
\(68\) 0 0
\(69\) 8.38590 1.00954
\(70\) 0 0
\(71\) −13.4850 −1.60037 −0.800186 0.599752i \(-0.795266\pi\)
−0.800186 + 0.599752i \(0.795266\pi\)
\(72\) 0 0
\(73\) 7.06681 0.827107 0.413554 0.910480i \(-0.364287\pi\)
0.413554 + 0.910480i \(0.364287\pi\)
\(74\) 0 0
\(75\) 2.11583 0.244315
\(76\) 0 0
\(77\) −16.7812 −1.91240
\(78\) 0 0
\(79\) −7.66667 −0.862568 −0.431284 0.902216i \(-0.641939\pi\)
−0.431284 + 0.902216i \(0.641939\pi\)
\(80\) 0 0
\(81\) −11.2495 −1.24994
\(82\) 0 0
\(83\) −6.35179 −0.697200 −0.348600 0.937272i \(-0.613343\pi\)
−0.348600 + 0.937272i \(0.613343\pi\)
\(84\) 0 0
\(85\) −7.69906 −0.835080
\(86\) 0 0
\(87\) −21.6324 −2.31923
\(88\) 0 0
\(89\) 15.7665 1.67125 0.835624 0.549302i \(-0.185106\pi\)
0.835624 + 0.549302i \(0.185106\pi\)
\(90\) 0 0
\(91\) −10.2343 −1.07284
\(92\) 0 0
\(93\) 14.9314 1.54832
\(94\) 0 0
\(95\) −3.28730 −0.337270
\(96\) 0 0
\(97\) 5.64835 0.573503 0.286752 0.958005i \(-0.407425\pi\)
0.286752 + 0.958005i \(0.407425\pi\)
\(98\) 0 0
\(99\) 5.49322 0.552090
\(100\) 0 0
\(101\) 3.05229 0.303714 0.151857 0.988402i \(-0.451475\pi\)
0.151857 + 0.988402i \(0.451475\pi\)
\(102\) 0 0
\(103\) −11.9624 −1.17869 −0.589343 0.807883i \(-0.700613\pi\)
−0.589343 + 0.807883i \(0.700613\pi\)
\(104\) 0 0
\(105\) −9.54511 −0.931507
\(106\) 0 0
\(107\) 0.500824 0.0484165 0.0242083 0.999707i \(-0.492294\pi\)
0.0242083 + 0.999707i \(0.492294\pi\)
\(108\) 0 0
\(109\) −1.51650 −0.145255 −0.0726274 0.997359i \(-0.523138\pi\)
−0.0726274 + 0.997359i \(0.523138\pi\)
\(110\) 0 0
\(111\) −5.40068 −0.512609
\(112\) 0 0
\(113\) 9.30075 0.874941 0.437470 0.899233i \(-0.355874\pi\)
0.437470 + 0.899233i \(0.355874\pi\)
\(114\) 0 0
\(115\) 3.96341 0.369590
\(116\) 0 0
\(117\) 3.35012 0.309719
\(118\) 0 0
\(119\) 34.7326 3.18394
\(120\) 0 0
\(121\) 2.83718 0.257926
\(122\) 0 0
\(123\) −2.93518 −0.264656
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −0.747438 −0.0663244 −0.0331622 0.999450i \(-0.510558\pi\)
−0.0331622 + 0.999450i \(0.510558\pi\)
\(128\) 0 0
\(129\) 6.30863 0.555443
\(130\) 0 0
\(131\) −18.1581 −1.58648 −0.793241 0.608907i \(-0.791608\pi\)
−0.793241 + 0.608907i \(0.791608\pi\)
\(132\) 0 0
\(133\) 14.8300 1.28592
\(134\) 0 0
\(135\) −3.22296 −0.277389
\(136\) 0 0
\(137\) −4.31717 −0.368841 −0.184420 0.982847i \(-0.559041\pi\)
−0.184420 + 0.982847i \(0.559041\pi\)
\(138\) 0 0
\(139\) −18.7431 −1.58977 −0.794885 0.606761i \(-0.792469\pi\)
−0.794885 + 0.606761i \(0.792469\pi\)
\(140\) 0 0
\(141\) 3.45353 0.290839
\(142\) 0 0
\(143\) 8.43880 0.705688
\(144\) 0 0
\(145\) −10.2241 −0.849062
\(146\) 0 0
\(147\) 28.2499 2.33001
\(148\) 0 0
\(149\) −9.08849 −0.744558 −0.372279 0.928121i \(-0.621424\pi\)
−0.372279 + 0.928121i \(0.621424\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −11.3695 −0.919169
\(154\) 0 0
\(155\) 7.05701 0.566833
\(156\) 0 0
\(157\) 2.99321 0.238884 0.119442 0.992841i \(-0.461889\pi\)
0.119442 + 0.992841i \(0.461889\pi\)
\(158\) 0 0
\(159\) −23.6199 −1.87318
\(160\) 0 0
\(161\) −17.8800 −1.40915
\(162\) 0 0
\(163\) 18.1281 1.41990 0.709950 0.704252i \(-0.248717\pi\)
0.709950 + 0.704252i \(0.248717\pi\)
\(164\) 0 0
\(165\) 7.87054 0.612721
\(166\) 0 0
\(167\) −6.32933 −0.489779 −0.244889 0.969551i \(-0.578752\pi\)
−0.244889 + 0.969551i \(0.578752\pi\)
\(168\) 0 0
\(169\) −7.85347 −0.604113
\(170\) 0 0
\(171\) −4.85449 −0.371232
\(172\) 0 0
\(173\) 18.6860 1.42067 0.710335 0.703863i \(-0.248543\pi\)
0.710335 + 0.703863i \(0.248543\pi\)
\(174\) 0 0
\(175\) −4.51128 −0.341021
\(176\) 0 0
\(177\) −16.9787 −1.27620
\(178\) 0 0
\(179\) −21.0915 −1.57645 −0.788227 0.615384i \(-0.789001\pi\)
−0.788227 + 0.615384i \(0.789001\pi\)
\(180\) 0 0
\(181\) 22.1118 1.64355 0.821777 0.569809i \(-0.192983\pi\)
0.821777 + 0.569809i \(0.192983\pi\)
\(182\) 0 0
\(183\) −17.7296 −1.31061
\(184\) 0 0
\(185\) −2.55251 −0.187664
\(186\) 0 0
\(187\) −28.6392 −2.09431
\(188\) 0 0
\(189\) 14.5397 1.05761
\(190\) 0 0
\(191\) 0.215454 0.0155897 0.00779485 0.999970i \(-0.497519\pi\)
0.00779485 + 0.999970i \(0.497519\pi\)
\(192\) 0 0
\(193\) 27.0769 1.94904 0.974519 0.224304i \(-0.0720108\pi\)
0.974519 + 0.224304i \(0.0720108\pi\)
\(194\) 0 0
\(195\) 4.79996 0.343733
\(196\) 0 0
\(197\) 16.1435 1.15018 0.575090 0.818090i \(-0.304967\pi\)
0.575090 + 0.818090i \(0.304967\pi\)
\(198\) 0 0
\(199\) −2.66452 −0.188883 −0.0944413 0.995530i \(-0.530106\pi\)
−0.0944413 + 0.995530i \(0.530106\pi\)
\(200\) 0 0
\(201\) 5.21720 0.367993
\(202\) 0 0
\(203\) 46.1236 3.23724
\(204\) 0 0
\(205\) −1.38725 −0.0968896
\(206\) 0 0
\(207\) 5.85291 0.406806
\(208\) 0 0
\(209\) −12.2282 −0.845845
\(210\) 0 0
\(211\) −15.8509 −1.09122 −0.545612 0.838038i \(-0.683703\pi\)
−0.545612 + 0.838038i \(0.683703\pi\)
\(212\) 0 0
\(213\) −28.5319 −1.95497
\(214\) 0 0
\(215\) 2.98163 0.203346
\(216\) 0 0
\(217\) −31.8362 −2.16118
\(218\) 0 0
\(219\) 14.9522 1.01037
\(220\) 0 0
\(221\) −17.4660 −1.17489
\(222\) 0 0
\(223\) −24.8927 −1.66694 −0.833470 0.552564i \(-0.813649\pi\)
−0.833470 + 0.552564i \(0.813649\pi\)
\(224\) 0 0
\(225\) 1.47674 0.0984492
\(226\) 0 0
\(227\) 8.14663 0.540711 0.270355 0.962761i \(-0.412859\pi\)
0.270355 + 0.962761i \(0.412859\pi\)
\(228\) 0 0
\(229\) −24.1896 −1.59850 −0.799248 0.601002i \(-0.794768\pi\)
−0.799248 + 0.601002i \(0.794768\pi\)
\(230\) 0 0
\(231\) −35.5062 −2.33614
\(232\) 0 0
\(233\) −14.1813 −0.929046 −0.464523 0.885561i \(-0.653774\pi\)
−0.464523 + 0.885561i \(0.653774\pi\)
\(234\) 0 0
\(235\) 1.63223 0.106475
\(236\) 0 0
\(237\) −16.2214 −1.05369
\(238\) 0 0
\(239\) −10.9426 −0.707815 −0.353907 0.935280i \(-0.615147\pi\)
−0.353907 + 0.935280i \(0.615147\pi\)
\(240\) 0 0
\(241\) −10.5175 −0.677489 −0.338745 0.940878i \(-0.610002\pi\)
−0.338745 + 0.940878i \(0.610002\pi\)
\(242\) 0 0
\(243\) −14.1331 −0.906636
\(244\) 0 0
\(245\) 13.3517 0.853007
\(246\) 0 0
\(247\) −7.45757 −0.474514
\(248\) 0 0
\(249\) −13.4393 −0.851682
\(250\) 0 0
\(251\) 17.2694 1.09003 0.545016 0.838425i \(-0.316523\pi\)
0.545016 + 0.838425i \(0.316523\pi\)
\(252\) 0 0
\(253\) 14.7432 0.926899
\(254\) 0 0
\(255\) −16.2899 −1.02011
\(256\) 0 0
\(257\) 14.6380 0.913090 0.456545 0.889700i \(-0.349087\pi\)
0.456545 + 0.889700i \(0.349087\pi\)
\(258\) 0 0
\(259\) 11.5151 0.715513
\(260\) 0 0
\(261\) −15.0983 −0.934559
\(262\) 0 0
\(263\) 10.6848 0.658851 0.329426 0.944182i \(-0.393145\pi\)
0.329426 + 0.944182i \(0.393145\pi\)
\(264\) 0 0
\(265\) −11.1634 −0.685762
\(266\) 0 0
\(267\) 33.3593 2.04155
\(268\) 0 0
\(269\) −14.8756 −0.906979 −0.453490 0.891262i \(-0.649821\pi\)
−0.453490 + 0.891262i \(0.649821\pi\)
\(270\) 0 0
\(271\) −19.5627 −1.18835 −0.594176 0.804335i \(-0.702522\pi\)
−0.594176 + 0.804335i \(0.702522\pi\)
\(272\) 0 0
\(273\) −21.6540 −1.31056
\(274\) 0 0
\(275\) 3.71984 0.224315
\(276\) 0 0
\(277\) −31.1190 −1.86976 −0.934881 0.354962i \(-0.884494\pi\)
−0.934881 + 0.354962i \(0.884494\pi\)
\(278\) 0 0
\(279\) 10.4214 0.623910
\(280\) 0 0
\(281\) 16.0160 0.955434 0.477717 0.878514i \(-0.341464\pi\)
0.477717 + 0.878514i \(0.341464\pi\)
\(282\) 0 0
\(283\) −14.7988 −0.879697 −0.439848 0.898072i \(-0.644968\pi\)
−0.439848 + 0.898072i \(0.644968\pi\)
\(284\) 0 0
\(285\) −6.95538 −0.412001
\(286\) 0 0
\(287\) 6.25827 0.369414
\(288\) 0 0
\(289\) 42.2755 2.48679
\(290\) 0 0
\(291\) 11.9510 0.700577
\(292\) 0 0
\(293\) 2.05226 0.119894 0.0599471 0.998202i \(-0.480907\pi\)
0.0599471 + 0.998202i \(0.480907\pi\)
\(294\) 0 0
\(295\) −8.02460 −0.467210
\(296\) 0 0
\(297\) −11.9889 −0.695666
\(298\) 0 0
\(299\) 8.99137 0.519984
\(300\) 0 0
\(301\) −13.4510 −0.775302
\(302\) 0 0
\(303\) 6.45813 0.371010
\(304\) 0 0
\(305\) −8.37952 −0.479810
\(306\) 0 0
\(307\) −1.00621 −0.0574276 −0.0287138 0.999588i \(-0.509141\pi\)
−0.0287138 + 0.999588i \(0.509141\pi\)
\(308\) 0 0
\(309\) −25.3103 −1.43985
\(310\) 0 0
\(311\) −5.83367 −0.330797 −0.165399 0.986227i \(-0.552891\pi\)
−0.165399 + 0.986227i \(0.552891\pi\)
\(312\) 0 0
\(313\) −16.6990 −0.943883 −0.471941 0.881630i \(-0.656447\pi\)
−0.471941 + 0.881630i \(0.656447\pi\)
\(314\) 0 0
\(315\) −6.66198 −0.375360
\(316\) 0 0
\(317\) −15.4986 −0.870491 −0.435245 0.900312i \(-0.643338\pi\)
−0.435245 + 0.900312i \(0.643338\pi\)
\(318\) 0 0
\(319\) −38.0318 −2.12937
\(320\) 0 0
\(321\) 1.05966 0.0591444
\(322\) 0 0
\(323\) 25.3092 1.40824
\(324\) 0 0
\(325\) 2.26860 0.125839
\(326\) 0 0
\(327\) −3.20867 −0.177440
\(328\) 0 0
\(329\) −7.36346 −0.405961
\(330\) 0 0
\(331\) 23.4348 1.28810 0.644048 0.764985i \(-0.277254\pi\)
0.644048 + 0.764985i \(0.277254\pi\)
\(332\) 0 0
\(333\) −3.76939 −0.206561
\(334\) 0 0
\(335\) 2.46579 0.134721
\(336\) 0 0
\(337\) 30.6211 1.66804 0.834018 0.551737i \(-0.186035\pi\)
0.834018 + 0.551737i \(0.186035\pi\)
\(338\) 0 0
\(339\) 19.6788 1.06881
\(340\) 0 0
\(341\) 26.2509 1.42157
\(342\) 0 0
\(343\) −28.6542 −1.54718
\(344\) 0 0
\(345\) 8.38590 0.451481
\(346\) 0 0
\(347\) 18.6948 1.00359 0.501795 0.864987i \(-0.332673\pi\)
0.501795 + 0.864987i \(0.332673\pi\)
\(348\) 0 0
\(349\) 14.3654 0.768960 0.384480 0.923133i \(-0.374381\pi\)
0.384480 + 0.923133i \(0.374381\pi\)
\(350\) 0 0
\(351\) −7.31160 −0.390264
\(352\) 0 0
\(353\) 2.65807 0.141475 0.0707373 0.997495i \(-0.477465\pi\)
0.0707373 + 0.997495i \(0.477465\pi\)
\(354\) 0 0
\(355\) −13.4850 −0.715708
\(356\) 0 0
\(357\) 73.4884 3.88942
\(358\) 0 0
\(359\) −19.5446 −1.03152 −0.515762 0.856732i \(-0.672491\pi\)
−0.515762 + 0.856732i \(0.672491\pi\)
\(360\) 0 0
\(361\) −8.19363 −0.431244
\(362\) 0 0
\(363\) 6.00300 0.315076
\(364\) 0 0
\(365\) 7.06681 0.369894
\(366\) 0 0
\(367\) −8.69577 −0.453916 −0.226958 0.973905i \(-0.572878\pi\)
−0.226958 + 0.973905i \(0.572878\pi\)
\(368\) 0 0
\(369\) −2.04860 −0.106646
\(370\) 0 0
\(371\) 50.3613 2.61463
\(372\) 0 0
\(373\) 15.8358 0.819946 0.409973 0.912098i \(-0.365538\pi\)
0.409973 + 0.912098i \(0.365538\pi\)
\(374\) 0 0
\(375\) 2.11583 0.109261
\(376\) 0 0
\(377\) −23.1943 −1.19457
\(378\) 0 0
\(379\) 15.4450 0.793359 0.396679 0.917957i \(-0.370162\pi\)
0.396679 + 0.917957i \(0.370162\pi\)
\(380\) 0 0
\(381\) −1.58145 −0.0810203
\(382\) 0 0
\(383\) 19.9134 1.01753 0.508764 0.860906i \(-0.330102\pi\)
0.508764 + 0.860906i \(0.330102\pi\)
\(384\) 0 0
\(385\) −16.7812 −0.855251
\(386\) 0 0
\(387\) 4.40309 0.223822
\(388\) 0 0
\(389\) −25.5704 −1.29647 −0.648236 0.761439i \(-0.724493\pi\)
−0.648236 + 0.761439i \(0.724493\pi\)
\(390\) 0 0
\(391\) −30.5145 −1.54318
\(392\) 0 0
\(393\) −38.4195 −1.93801
\(394\) 0 0
\(395\) −7.66667 −0.385752
\(396\) 0 0
\(397\) 11.8759 0.596032 0.298016 0.954561i \(-0.403675\pi\)
0.298016 + 0.954561i \(0.403675\pi\)
\(398\) 0 0
\(399\) 31.3777 1.57085
\(400\) 0 0
\(401\) 6.94490 0.346812 0.173406 0.984850i \(-0.444523\pi\)
0.173406 + 0.984850i \(0.444523\pi\)
\(402\) 0 0
\(403\) 16.0095 0.797490
\(404\) 0 0
\(405\) −11.2495 −0.558990
\(406\) 0 0
\(407\) −9.49492 −0.470645
\(408\) 0 0
\(409\) −5.90345 −0.291907 −0.145953 0.989291i \(-0.546625\pi\)
−0.145953 + 0.989291i \(0.546625\pi\)
\(410\) 0 0
\(411\) −9.13441 −0.450567
\(412\) 0 0
\(413\) 36.2012 1.78135
\(414\) 0 0
\(415\) −6.35179 −0.311797
\(416\) 0 0
\(417\) −39.6572 −1.94202
\(418\) 0 0
\(419\) 3.26629 0.159569 0.0797844 0.996812i \(-0.474577\pi\)
0.0797844 + 0.996812i \(0.474577\pi\)
\(420\) 0 0
\(421\) −6.48828 −0.316219 −0.158110 0.987422i \(-0.550540\pi\)
−0.158110 + 0.987422i \(0.550540\pi\)
\(422\) 0 0
\(423\) 2.41038 0.117197
\(424\) 0 0
\(425\) −7.69906 −0.373459
\(426\) 0 0
\(427\) 37.8024 1.82939
\(428\) 0 0
\(429\) 17.8551 0.862051
\(430\) 0 0
\(431\) −0.668692 −0.0322098 −0.0161049 0.999870i \(-0.505127\pi\)
−0.0161049 + 0.999870i \(0.505127\pi\)
\(432\) 0 0
\(433\) 33.8543 1.62693 0.813466 0.581612i \(-0.197578\pi\)
0.813466 + 0.581612i \(0.197578\pi\)
\(434\) 0 0
\(435\) −21.6324 −1.03719
\(436\) 0 0
\(437\) −13.0289 −0.623258
\(438\) 0 0
\(439\) 27.3622 1.30592 0.652962 0.757390i \(-0.273526\pi\)
0.652962 + 0.757390i \(0.273526\pi\)
\(440\) 0 0
\(441\) 19.7169 0.938901
\(442\) 0 0
\(443\) −6.14659 −0.292033 −0.146017 0.989282i \(-0.546645\pi\)
−0.146017 + 0.989282i \(0.546645\pi\)
\(444\) 0 0
\(445\) 15.7665 0.747405
\(446\) 0 0
\(447\) −19.2297 −0.909534
\(448\) 0 0
\(449\) 10.5378 0.497310 0.248655 0.968592i \(-0.420011\pi\)
0.248655 + 0.968592i \(0.420011\pi\)
\(450\) 0 0
\(451\) −5.16034 −0.242991
\(452\) 0 0
\(453\) 2.11583 0.0994104
\(454\) 0 0
\(455\) −10.2343 −0.479790
\(456\) 0 0
\(457\) 39.1421 1.83099 0.915495 0.402329i \(-0.131799\pi\)
0.915495 + 0.402329i \(0.131799\pi\)
\(458\) 0 0
\(459\) 24.8138 1.15821
\(460\) 0 0
\(461\) −31.6505 −1.47411 −0.737055 0.675833i \(-0.763784\pi\)
−0.737055 + 0.675833i \(0.763784\pi\)
\(462\) 0 0
\(463\) −21.9119 −1.01833 −0.509167 0.860668i \(-0.670046\pi\)
−0.509167 + 0.860668i \(0.670046\pi\)
\(464\) 0 0
\(465\) 14.9314 0.692429
\(466\) 0 0
\(467\) −0.317363 −0.0146858 −0.00734290 0.999973i \(-0.502337\pi\)
−0.00734290 + 0.999973i \(0.502337\pi\)
\(468\) 0 0
\(469\) −11.1239 −0.513653
\(470\) 0 0
\(471\) 6.33312 0.291815
\(472\) 0 0
\(473\) 11.0912 0.509973
\(474\) 0 0
\(475\) −3.28730 −0.150832
\(476\) 0 0
\(477\) −16.4854 −0.754815
\(478\) 0 0
\(479\) 23.8213 1.08842 0.544211 0.838948i \(-0.316829\pi\)
0.544211 + 0.838948i \(0.316829\pi\)
\(480\) 0 0
\(481\) −5.79061 −0.264029
\(482\) 0 0
\(483\) −37.8311 −1.72138
\(484\) 0 0
\(485\) 5.64835 0.256478
\(486\) 0 0
\(487\) 34.4937 1.56306 0.781529 0.623869i \(-0.214440\pi\)
0.781529 + 0.623869i \(0.214440\pi\)
\(488\) 0 0
\(489\) 38.3559 1.73451
\(490\) 0 0
\(491\) 13.9461 0.629379 0.314690 0.949195i \(-0.398100\pi\)
0.314690 + 0.949195i \(0.398100\pi\)
\(492\) 0 0
\(493\) 78.7156 3.54517
\(494\) 0 0
\(495\) 5.49322 0.246902
\(496\) 0 0
\(497\) 60.8345 2.72880
\(498\) 0 0
\(499\) 29.5897 1.32462 0.662309 0.749231i \(-0.269577\pi\)
0.662309 + 0.749231i \(0.269577\pi\)
\(500\) 0 0
\(501\) −13.3918 −0.598301
\(502\) 0 0
\(503\) 2.51914 0.112323 0.0561615 0.998422i \(-0.482114\pi\)
0.0561615 + 0.998422i \(0.482114\pi\)
\(504\) 0 0
\(505\) 3.05229 0.135825
\(506\) 0 0
\(507\) −16.6166 −0.737970
\(508\) 0 0
\(509\) −11.0469 −0.489645 −0.244823 0.969568i \(-0.578730\pi\)
−0.244823 + 0.969568i \(0.578730\pi\)
\(510\) 0 0
\(511\) −31.8804 −1.41030
\(512\) 0 0
\(513\) 10.5949 0.467775
\(514\) 0 0
\(515\) −11.9624 −0.527125
\(516\) 0 0
\(517\) 6.07164 0.267030
\(518\) 0 0
\(519\) 39.5364 1.73546
\(520\) 0 0
\(521\) 26.7746 1.17302 0.586508 0.809944i \(-0.300502\pi\)
0.586508 + 0.809944i \(0.300502\pi\)
\(522\) 0 0
\(523\) −7.20878 −0.315218 −0.157609 0.987502i \(-0.550379\pi\)
−0.157609 + 0.987502i \(0.550379\pi\)
\(524\) 0 0
\(525\) −9.54511 −0.416583
\(526\) 0 0
\(527\) −54.3323 −2.36675
\(528\) 0 0
\(529\) −7.29141 −0.317018
\(530\) 0 0
\(531\) −11.8502 −0.514256
\(532\) 0 0
\(533\) −3.14711 −0.136316
\(534\) 0 0
\(535\) 0.500824 0.0216525
\(536\) 0 0
\(537\) −44.6261 −1.92576
\(538\) 0 0
\(539\) 49.6660 2.13927
\(540\) 0 0
\(541\) 11.7310 0.504356 0.252178 0.967681i \(-0.418853\pi\)
0.252178 + 0.967681i \(0.418853\pi\)
\(542\) 0 0
\(543\) 46.7847 2.00773
\(544\) 0 0
\(545\) −1.51650 −0.0649599
\(546\) 0 0
\(547\) −6.27482 −0.268292 −0.134146 0.990962i \(-0.542829\pi\)
−0.134146 + 0.990962i \(0.542829\pi\)
\(548\) 0 0
\(549\) −12.3744 −0.528125
\(550\) 0 0
\(551\) 33.6096 1.43182
\(552\) 0 0
\(553\) 34.5865 1.47077
\(554\) 0 0
\(555\) −5.40068 −0.229246
\(556\) 0 0
\(557\) −38.9052 −1.64847 −0.824234 0.566249i \(-0.808394\pi\)
−0.824234 + 0.566249i \(0.808394\pi\)
\(558\) 0 0
\(559\) 6.76411 0.286092
\(560\) 0 0
\(561\) −60.5958 −2.55836
\(562\) 0 0
\(563\) −20.3855 −0.859147 −0.429574 0.903032i \(-0.641336\pi\)
−0.429574 + 0.903032i \(0.641336\pi\)
\(564\) 0 0
\(565\) 9.30075 0.391285
\(566\) 0 0
\(567\) 50.7495 2.13128
\(568\) 0 0
\(569\) 5.93510 0.248812 0.124406 0.992231i \(-0.460297\pi\)
0.124406 + 0.992231i \(0.460297\pi\)
\(570\) 0 0
\(571\) −37.5842 −1.57285 −0.786424 0.617687i \(-0.788070\pi\)
−0.786424 + 0.617687i \(0.788070\pi\)
\(572\) 0 0
\(573\) 0.455864 0.0190440
\(574\) 0 0
\(575\) 3.96341 0.165285
\(576\) 0 0
\(577\) 39.2644 1.63460 0.817299 0.576214i \(-0.195471\pi\)
0.817299 + 0.576214i \(0.195471\pi\)
\(578\) 0 0
\(579\) 57.2901 2.38090
\(580\) 0 0
\(581\) 28.6547 1.18880
\(582\) 0 0
\(583\) −41.5260 −1.71983
\(584\) 0 0
\(585\) 3.35012 0.138510
\(586\) 0 0
\(587\) −26.4387 −1.09124 −0.545620 0.838033i \(-0.683706\pi\)
−0.545620 + 0.838033i \(0.683706\pi\)
\(588\) 0 0
\(589\) −23.1985 −0.955879
\(590\) 0 0
\(591\) 34.1570 1.40503
\(592\) 0 0
\(593\) −33.3619 −1.37001 −0.685004 0.728539i \(-0.740200\pi\)
−0.685004 + 0.728539i \(0.740200\pi\)
\(594\) 0 0
\(595\) 34.7326 1.42390
\(596\) 0 0
\(597\) −5.63767 −0.230734
\(598\) 0 0
\(599\) 5.06454 0.206932 0.103466 0.994633i \(-0.467007\pi\)
0.103466 + 0.994633i \(0.467007\pi\)
\(600\) 0 0
\(601\) 29.8712 1.21847 0.609236 0.792989i \(-0.291476\pi\)
0.609236 + 0.792989i \(0.291476\pi\)
\(602\) 0 0
\(603\) 3.64133 0.148286
\(604\) 0 0
\(605\) 2.83718 0.115348
\(606\) 0 0
\(607\) −22.3573 −0.907454 −0.453727 0.891141i \(-0.649906\pi\)
−0.453727 + 0.891141i \(0.649906\pi\)
\(608\) 0 0
\(609\) 97.5898 3.95454
\(610\) 0 0
\(611\) 3.70287 0.149802
\(612\) 0 0
\(613\) −1.00997 −0.0407925 −0.0203963 0.999792i \(-0.506493\pi\)
−0.0203963 + 0.999792i \(0.506493\pi\)
\(614\) 0 0
\(615\) −2.93518 −0.118358
\(616\) 0 0
\(617\) −6.62854 −0.266855 −0.133427 0.991059i \(-0.542598\pi\)
−0.133427 + 0.991059i \(0.542598\pi\)
\(618\) 0 0
\(619\) 7.77867 0.312651 0.156326 0.987706i \(-0.450035\pi\)
0.156326 + 0.987706i \(0.450035\pi\)
\(620\) 0 0
\(621\) −12.7739 −0.512600
\(622\) 0 0
\(623\) −71.1272 −2.84965
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −25.8729 −1.03326
\(628\) 0 0
\(629\) 19.6519 0.783573
\(630\) 0 0
\(631\) 39.7921 1.58410 0.792050 0.610457i \(-0.209014\pi\)
0.792050 + 0.610457i \(0.209014\pi\)
\(632\) 0 0
\(633\) −33.5379 −1.33301
\(634\) 0 0
\(635\) −0.747438 −0.0296612
\(636\) 0 0
\(637\) 30.2896 1.20012
\(638\) 0 0
\(639\) −19.9138 −0.787777
\(640\) 0 0
\(641\) −8.02688 −0.317043 −0.158521 0.987356i \(-0.550673\pi\)
−0.158521 + 0.987356i \(0.550673\pi\)
\(642\) 0 0
\(643\) −47.8178 −1.88575 −0.942876 0.333144i \(-0.891890\pi\)
−0.942876 + 0.333144i \(0.891890\pi\)
\(644\) 0 0
\(645\) 6.30863 0.248402
\(646\) 0 0
\(647\) −27.2488 −1.07126 −0.535631 0.844452i \(-0.679926\pi\)
−0.535631 + 0.844452i \(0.679926\pi\)
\(648\) 0 0
\(649\) −29.8502 −1.17172
\(650\) 0 0
\(651\) −67.3599 −2.64004
\(652\) 0 0
\(653\) −15.3195 −0.599498 −0.299749 0.954018i \(-0.596903\pi\)
−0.299749 + 0.954018i \(0.596903\pi\)
\(654\) 0 0
\(655\) −18.1581 −0.709497
\(656\) 0 0
\(657\) 10.4358 0.407140
\(658\) 0 0
\(659\) −17.0052 −0.662428 −0.331214 0.943556i \(-0.607458\pi\)
−0.331214 + 0.943556i \(0.607458\pi\)
\(660\) 0 0
\(661\) −6.99978 −0.272260 −0.136130 0.990691i \(-0.543466\pi\)
−0.136130 + 0.990691i \(0.543466\pi\)
\(662\) 0 0
\(663\) −36.9552 −1.43522
\(664\) 0 0
\(665\) 14.8300 0.575081
\(666\) 0 0
\(667\) −40.5221 −1.56902
\(668\) 0 0
\(669\) −52.6688 −2.03629
\(670\) 0 0
\(671\) −31.1704 −1.20332
\(672\) 0 0
\(673\) −21.0099 −0.809872 −0.404936 0.914345i \(-0.632706\pi\)
−0.404936 + 0.914345i \(0.632706\pi\)
\(674\) 0 0
\(675\) −3.22296 −0.124052
\(676\) 0 0
\(677\) 44.8381 1.72327 0.861635 0.507529i \(-0.169441\pi\)
0.861635 + 0.507529i \(0.169441\pi\)
\(678\) 0 0
\(679\) −25.4813 −0.977883
\(680\) 0 0
\(681\) 17.2369 0.660519
\(682\) 0 0
\(683\) 34.9167 1.33605 0.668025 0.744139i \(-0.267140\pi\)
0.668025 + 0.744139i \(0.267140\pi\)
\(684\) 0 0
\(685\) −4.31717 −0.164951
\(686\) 0 0
\(687\) −51.1811 −1.95268
\(688\) 0 0
\(689\) −25.3252 −0.964815
\(690\) 0 0
\(691\) −14.4494 −0.549680 −0.274840 0.961490i \(-0.588625\pi\)
−0.274840 + 0.961490i \(0.588625\pi\)
\(692\) 0 0
\(693\) −24.7815 −0.941371
\(694\) 0 0
\(695\) −18.7431 −0.710966
\(696\) 0 0
\(697\) 10.6805 0.404553
\(698\) 0 0
\(699\) −30.0052 −1.13490
\(700\) 0 0
\(701\) 46.8408 1.76915 0.884577 0.466395i \(-0.154447\pi\)
0.884577 + 0.466395i \(0.154447\pi\)
\(702\) 0 0
\(703\) 8.39087 0.316468
\(704\) 0 0
\(705\) 3.45353 0.130067
\(706\) 0 0
\(707\) −13.7698 −0.517865
\(708\) 0 0
\(709\) −23.0134 −0.864285 −0.432143 0.901805i \(-0.642242\pi\)
−0.432143 + 0.901805i \(0.642242\pi\)
\(710\) 0 0
\(711\) −11.3217 −0.424595
\(712\) 0 0
\(713\) 27.9698 1.04748
\(714\) 0 0
\(715\) 8.43880 0.315593
\(716\) 0 0
\(717\) −23.1526 −0.864649
\(718\) 0 0
\(719\) 23.9939 0.894821 0.447410 0.894329i \(-0.352346\pi\)
0.447410 + 0.894329i \(0.352346\pi\)
\(720\) 0 0
\(721\) 53.9656 2.00978
\(722\) 0 0
\(723\) −22.2532 −0.827604
\(724\) 0 0
\(725\) −10.2241 −0.379712
\(726\) 0 0
\(727\) −24.6362 −0.913705 −0.456853 0.889542i \(-0.651023\pi\)
−0.456853 + 0.889542i \(0.651023\pi\)
\(728\) 0 0
\(729\) 3.84523 0.142416
\(730\) 0 0
\(731\) −22.9558 −0.849049
\(732\) 0 0
\(733\) −39.4171 −1.45590 −0.727951 0.685629i \(-0.759527\pi\)
−0.727951 + 0.685629i \(0.759527\pi\)
\(734\) 0 0
\(735\) 28.2499 1.04201
\(736\) 0 0
\(737\) 9.17234 0.337868
\(738\) 0 0
\(739\) 5.81176 0.213789 0.106895 0.994270i \(-0.465909\pi\)
0.106895 + 0.994270i \(0.465909\pi\)
\(740\) 0 0
\(741\) −15.7789 −0.579654
\(742\) 0 0
\(743\) 32.5844 1.19541 0.597703 0.801717i \(-0.296080\pi\)
0.597703 + 0.801717i \(0.296080\pi\)
\(744\) 0 0
\(745\) −9.08849 −0.332976
\(746\) 0 0
\(747\) −9.37993 −0.343194
\(748\) 0 0
\(749\) −2.25936 −0.0825552
\(750\) 0 0
\(751\) −16.8692 −0.615567 −0.307784 0.951456i \(-0.599587\pi\)
−0.307784 + 0.951456i \(0.599587\pi\)
\(752\) 0 0
\(753\) 36.5390 1.33156
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 15.3523 0.557989 0.278995 0.960293i \(-0.409999\pi\)
0.278995 + 0.960293i \(0.409999\pi\)
\(758\) 0 0
\(759\) 31.1942 1.13228
\(760\) 0 0
\(761\) 22.9605 0.832316 0.416158 0.909292i \(-0.363376\pi\)
0.416158 + 0.909292i \(0.363376\pi\)
\(762\) 0 0
\(763\) 6.84138 0.247675
\(764\) 0 0
\(765\) −11.3695 −0.411065
\(766\) 0 0
\(767\) −18.2046 −0.657329
\(768\) 0 0
\(769\) −3.65769 −0.131900 −0.0659498 0.997823i \(-0.521008\pi\)
−0.0659498 + 0.997823i \(0.521008\pi\)
\(770\) 0 0
\(771\) 30.9714 1.11541
\(772\) 0 0
\(773\) 42.8739 1.54207 0.771033 0.636795i \(-0.219740\pi\)
0.771033 + 0.636795i \(0.219740\pi\)
\(774\) 0 0
\(775\) 7.05701 0.253495
\(776\) 0 0
\(777\) 24.3640 0.874053
\(778\) 0 0
\(779\) 4.56031 0.163390
\(780\) 0 0
\(781\) −50.1619 −1.79493
\(782\) 0 0
\(783\) 32.9518 1.17760
\(784\) 0 0
\(785\) 2.99321 0.106832
\(786\) 0 0
\(787\) 43.3175 1.54410 0.772050 0.635562i \(-0.219231\pi\)
0.772050 + 0.635562i \(0.219231\pi\)
\(788\) 0 0
\(789\) 22.6072 0.804836
\(790\) 0 0
\(791\) −41.9583 −1.49187
\(792\) 0 0
\(793\) −19.0097 −0.675056
\(794\) 0 0
\(795\) −23.6199 −0.837710
\(796\) 0 0
\(797\) −5.70540 −0.202096 −0.101048 0.994882i \(-0.532220\pi\)
−0.101048 + 0.994882i \(0.532220\pi\)
\(798\) 0 0
\(799\) −12.5666 −0.444576
\(800\) 0 0
\(801\) 23.2830 0.822665
\(802\) 0 0
\(803\) 26.2874 0.927661
\(804\) 0 0
\(805\) −17.8800 −0.630189
\(806\) 0 0
\(807\) −31.4742 −1.10794
\(808\) 0 0
\(809\) −12.6999 −0.446505 −0.223253 0.974761i \(-0.571668\pi\)
−0.223253 + 0.974761i \(0.571668\pi\)
\(810\) 0 0
\(811\) 14.4283 0.506645 0.253322 0.967382i \(-0.418477\pi\)
0.253322 + 0.967382i \(0.418477\pi\)
\(812\) 0 0
\(813\) −41.3914 −1.45166
\(814\) 0 0
\(815\) 18.1281 0.634999
\(816\) 0 0
\(817\) −9.80153 −0.342912
\(818\) 0 0
\(819\) −15.1133 −0.528103
\(820\) 0 0
\(821\) 14.2371 0.496877 0.248438 0.968648i \(-0.420083\pi\)
0.248438 + 0.968648i \(0.420083\pi\)
\(822\) 0 0
\(823\) 12.7627 0.444881 0.222441 0.974946i \(-0.428598\pi\)
0.222441 + 0.974946i \(0.428598\pi\)
\(824\) 0 0
\(825\) 7.87054 0.274017
\(826\) 0 0
\(827\) −1.46999 −0.0511165 −0.0255583 0.999673i \(-0.508136\pi\)
−0.0255583 + 0.999673i \(0.508136\pi\)
\(828\) 0 0
\(829\) −45.2360 −1.57111 −0.785556 0.618791i \(-0.787623\pi\)
−0.785556 + 0.618791i \(0.787623\pi\)
\(830\) 0 0
\(831\) −65.8426 −2.28405
\(832\) 0 0
\(833\) −102.795 −3.56165
\(834\) 0 0
\(835\) −6.32933 −0.219036
\(836\) 0 0
\(837\) −22.7445 −0.786164
\(838\) 0 0
\(839\) 54.1876 1.87076 0.935382 0.353638i \(-0.115056\pi\)
0.935382 + 0.353638i \(0.115056\pi\)
\(840\) 0 0
\(841\) 75.5314 2.60453
\(842\) 0 0
\(843\) 33.8871 1.16713
\(844\) 0 0
\(845\) −7.85347 −0.270168
\(846\) 0 0
\(847\) −12.7993 −0.439790
\(848\) 0 0
\(849\) −31.3117 −1.07462
\(850\) 0 0
\(851\) −10.1166 −0.346794
\(852\) 0 0
\(853\) 20.2809 0.694404 0.347202 0.937790i \(-0.387132\pi\)
0.347202 + 0.937790i \(0.387132\pi\)
\(854\) 0 0
\(855\) −4.85449 −0.166020
\(856\) 0 0
\(857\) 1.85067 0.0632177 0.0316088 0.999500i \(-0.489937\pi\)
0.0316088 + 0.999500i \(0.489937\pi\)
\(858\) 0 0
\(859\) −28.6235 −0.976621 −0.488310 0.872670i \(-0.662387\pi\)
−0.488310 + 0.872670i \(0.662387\pi\)
\(860\) 0 0
\(861\) 13.2414 0.451267
\(862\) 0 0
\(863\) 1.61741 0.0550571 0.0275286 0.999621i \(-0.491236\pi\)
0.0275286 + 0.999621i \(0.491236\pi\)
\(864\) 0 0
\(865\) 18.6860 0.635343
\(866\) 0 0
\(867\) 89.4478 3.03781
\(868\) 0 0
\(869\) −28.5188 −0.967433
\(870\) 0 0
\(871\) 5.59388 0.189542
\(872\) 0 0
\(873\) 8.34113 0.282305
\(874\) 0 0
\(875\) −4.51128 −0.152509
\(876\) 0 0
\(877\) 17.4195 0.588216 0.294108 0.955772i \(-0.404977\pi\)
0.294108 + 0.955772i \(0.404977\pi\)
\(878\) 0 0
\(879\) 4.34223 0.146460
\(880\) 0 0
\(881\) 37.6771 1.26937 0.634687 0.772770i \(-0.281129\pi\)
0.634687 + 0.772770i \(0.281129\pi\)
\(882\) 0 0
\(883\) −57.6986 −1.94171 −0.970855 0.239666i \(-0.922962\pi\)
−0.970855 + 0.239666i \(0.922962\pi\)
\(884\) 0 0
\(885\) −16.9787 −0.570732
\(886\) 0 0
\(887\) −36.7674 −1.23453 −0.617264 0.786756i \(-0.711759\pi\)
−0.617264 + 0.786756i \(0.711759\pi\)
\(888\) 0 0
\(889\) 3.37191 0.113090
\(890\) 0 0
\(891\) −41.8461 −1.40190
\(892\) 0 0
\(893\) −5.36564 −0.179554
\(894\) 0 0
\(895\) −21.0915 −0.705012
\(896\) 0 0
\(897\) 19.0242 0.635200
\(898\) 0 0
\(899\) −72.1513 −2.40638
\(900\) 0 0
\(901\) 85.9477 2.86333
\(902\) 0 0
\(903\) −28.4600 −0.947089
\(904\) 0 0
\(905\) 22.1118 0.735020
\(906\) 0 0
\(907\) −12.9585 −0.430281 −0.215140 0.976583i \(-0.569021\pi\)
−0.215140 + 0.976583i \(0.569021\pi\)
\(908\) 0 0
\(909\) 4.50744 0.149502
\(910\) 0 0
\(911\) −59.6576 −1.97654 −0.988272 0.152705i \(-0.951202\pi\)
−0.988272 + 0.152705i \(0.951202\pi\)
\(912\) 0 0
\(913\) −23.6276 −0.781960
\(914\) 0 0
\(915\) −17.7296 −0.586124
\(916\) 0 0
\(917\) 81.9164 2.70512
\(918\) 0 0
\(919\) 0.534704 0.0176382 0.00881912 0.999961i \(-0.497193\pi\)
0.00881912 + 0.999961i \(0.497193\pi\)
\(920\) 0 0
\(921\) −2.12897 −0.0701521
\(922\) 0 0
\(923\) −30.5919 −1.00695
\(924\) 0 0
\(925\) −2.55251 −0.0839260
\(926\) 0 0
\(927\) −17.6653 −0.580204
\(928\) 0 0
\(929\) 8.84060 0.290051 0.145025 0.989428i \(-0.453674\pi\)
0.145025 + 0.989428i \(0.453674\pi\)
\(930\) 0 0
\(931\) −43.8910 −1.43847
\(932\) 0 0
\(933\) −12.3431 −0.404094
\(934\) 0 0
\(935\) −28.6392 −0.936603
\(936\) 0 0
\(937\) 24.1659 0.789466 0.394733 0.918796i \(-0.370837\pi\)
0.394733 + 0.918796i \(0.370837\pi\)
\(938\) 0 0
\(939\) −35.3322 −1.15302
\(940\) 0 0
\(941\) −35.4887 −1.15690 −0.578449 0.815718i \(-0.696342\pi\)
−0.578449 + 0.815718i \(0.696342\pi\)
\(942\) 0 0
\(943\) −5.49823 −0.179047
\(944\) 0 0
\(945\) 14.5397 0.472977
\(946\) 0 0
\(947\) 13.5918 0.441676 0.220838 0.975311i \(-0.429121\pi\)
0.220838 + 0.975311i \(0.429121\pi\)
\(948\) 0 0
\(949\) 16.0317 0.520412
\(950\) 0 0
\(951\) −32.7925 −1.06337
\(952\) 0 0
\(953\) −59.5249 −1.92820 −0.964100 0.265540i \(-0.914450\pi\)
−0.964100 + 0.265540i \(0.914450\pi\)
\(954\) 0 0
\(955\) 0.215454 0.00697192
\(956\) 0 0
\(957\) −80.4689 −2.60119
\(958\) 0 0
\(959\) 19.4760 0.628913
\(960\) 0 0
\(961\) 18.8014 0.606496
\(962\) 0 0
\(963\) 0.739586 0.0238328
\(964\) 0 0
\(965\) 27.0769 0.871637
\(966\) 0 0
\(967\) 14.6334 0.470579 0.235290 0.971925i \(-0.424396\pi\)
0.235290 + 0.971925i \(0.424396\pi\)
\(968\) 0 0
\(969\) 53.5499 1.72027
\(970\) 0 0
\(971\) 49.4747 1.58772 0.793859 0.608101i \(-0.208069\pi\)
0.793859 + 0.608101i \(0.208069\pi\)
\(972\) 0 0
\(973\) 84.5555 2.71072
\(974\) 0 0
\(975\) 4.79996 0.153722
\(976\) 0 0
\(977\) −34.5230 −1.10449 −0.552244 0.833683i \(-0.686228\pi\)
−0.552244 + 0.833683i \(0.686228\pi\)
\(978\) 0 0
\(979\) 58.6489 1.87443
\(980\) 0 0
\(981\) −2.23948 −0.0715011
\(982\) 0 0
\(983\) −57.0839 −1.82069 −0.910347 0.413847i \(-0.864185\pi\)
−0.910347 + 0.413847i \(0.864185\pi\)
\(984\) 0 0
\(985\) 16.1435 0.514376
\(986\) 0 0
\(987\) −15.5798 −0.495911
\(988\) 0 0
\(989\) 11.8174 0.375772
\(990\) 0 0
\(991\) 24.4457 0.776543 0.388272 0.921545i \(-0.373072\pi\)
0.388272 + 0.921545i \(0.373072\pi\)
\(992\) 0 0
\(993\) 49.5842 1.57351
\(994\) 0 0
\(995\) −2.66452 −0.0844709
\(996\) 0 0
\(997\) −11.9859 −0.379596 −0.189798 0.981823i \(-0.560783\pi\)
−0.189798 + 0.981823i \(0.560783\pi\)
\(998\) 0 0
\(999\) 8.22664 0.260280
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 \(a_p\))