Properties

Label 8040.2.a.t.1.2
Level 8040
Weight 2
Character 8040.1
Self dual Yes
Analytic conductor 64.200
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1997232251\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.51692\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(-0.274078 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(-0.274078 q^{7}\) \(+1.00000 q^{9}\) \(-4.75091 q^{11}\) \(-2.11982 q^{13}\) \(-1.00000 q^{15}\) \(+3.21588 q^{17}\) \(-1.31998 q^{19}\) \(-0.274078 q^{21}\) \(-4.76957 q^{23}\) \(+1.00000 q^{25}\) \(+1.00000 q^{27}\) \(-6.42263 q^{29}\) \(+3.56282 q^{31}\) \(-4.75091 q^{33}\) \(+0.274078 q^{35}\) \(+9.24113 q^{37}\) \(-2.11982 q^{39}\) \(-1.56282 q^{41}\) \(+2.64975 q^{43}\) \(-1.00000 q^{45}\) \(+7.55397 q^{47}\) \(-6.92488 q^{49}\) \(+3.21588 q^{51}\) \(-12.6509 q^{53}\) \(+4.75091 q^{55}\) \(-1.31998 q^{57}\) \(+11.9312 q^{59}\) \(+5.61957 q^{61}\) \(-0.274078 q^{63}\) \(+2.11982 q^{65}\) \(+1.00000 q^{67}\) \(-4.76957 q^{69}\) \(+5.03912 q^{71}\) \(+0.416872 q^{73}\) \(+1.00000 q^{75}\) \(+1.30212 q^{77}\) \(+15.6884 q^{79}\) \(+1.00000 q^{81}\) \(-8.57594 q^{83}\) \(-3.21588 q^{85}\) \(-6.42263 q^{87}\) \(+6.86302 q^{89}\) \(+0.580996 q^{91}\) \(+3.56282 q^{93}\) \(+1.31998 q^{95}\) \(-11.2626 q^{97}\) \(-4.75091 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut 7q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 23q^{37} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 13q^{53} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut q^{65} \) \(\mathstrut +\mathstrut 7q^{67} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 25q^{79} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 29q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut q^{87} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut +\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 9q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.274078 −0.103592 −0.0517958 0.998658i \(-0.516494\pi\)
−0.0517958 + 0.998658i \(0.516494\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.75091 −1.43245 −0.716227 0.697867i \(-0.754133\pi\)
−0.716227 + 0.697867i \(0.754133\pi\)
\(12\) 0 0
\(13\) −2.11982 −0.587933 −0.293966 0.955816i \(-0.594975\pi\)
−0.293966 + 0.955816i \(0.594975\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 3.21588 0.779964 0.389982 0.920822i \(-0.372481\pi\)
0.389982 + 0.920822i \(0.372481\pi\)
\(18\) 0 0
\(19\) −1.31998 −0.302824 −0.151412 0.988471i \(-0.548382\pi\)
−0.151412 + 0.988471i \(0.548382\pi\)
\(20\) 0 0
\(21\) −0.274078 −0.0598086
\(22\) 0 0
\(23\) −4.76957 −0.994524 −0.497262 0.867600i \(-0.665661\pi\)
−0.497262 + 0.867600i \(0.665661\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.42263 −1.19265 −0.596326 0.802742i \(-0.703373\pi\)
−0.596326 + 0.802742i \(0.703373\pi\)
\(30\) 0 0
\(31\) 3.56282 0.639901 0.319951 0.947434i \(-0.396334\pi\)
0.319951 + 0.947434i \(0.396334\pi\)
\(32\) 0 0
\(33\) −4.75091 −0.827028
\(34\) 0 0
\(35\) 0.274078 0.0463276
\(36\) 0 0
\(37\) 9.24113 1.51923 0.759616 0.650372i \(-0.225387\pi\)
0.759616 + 0.650372i \(0.225387\pi\)
\(38\) 0 0
\(39\) −2.11982 −0.339443
\(40\) 0 0
\(41\) −1.56282 −0.244071 −0.122036 0.992526i \(-0.538942\pi\)
−0.122036 + 0.992526i \(0.538942\pi\)
\(42\) 0 0
\(43\) 2.64975 0.404083 0.202041 0.979377i \(-0.435242\pi\)
0.202041 + 0.979377i \(0.435242\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 7.55397 1.10186 0.550930 0.834551i \(-0.314273\pi\)
0.550930 + 0.834551i \(0.314273\pi\)
\(48\) 0 0
\(49\) −6.92488 −0.989269
\(50\) 0 0
\(51\) 3.21588 0.450313
\(52\) 0 0
\(53\) −12.6509 −1.73774 −0.868868 0.495043i \(-0.835152\pi\)
−0.868868 + 0.495043i \(0.835152\pi\)
\(54\) 0 0
\(55\) 4.75091 0.640613
\(56\) 0 0
\(57\) −1.31998 −0.174835
\(58\) 0 0
\(59\) 11.9312 1.55331 0.776657 0.629923i \(-0.216914\pi\)
0.776657 + 0.629923i \(0.216914\pi\)
\(60\) 0 0
\(61\) 5.61957 0.719512 0.359756 0.933046i \(-0.382860\pi\)
0.359756 + 0.933046i \(0.382860\pi\)
\(62\) 0 0
\(63\) −0.274078 −0.0345305
\(64\) 0 0
\(65\) 2.11982 0.262932
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) −4.76957 −0.574189
\(70\) 0 0
\(71\) 5.03912 0.598033 0.299017 0.954248i \(-0.403341\pi\)
0.299017 + 0.954248i \(0.403341\pi\)
\(72\) 0 0
\(73\) 0.416872 0.0487912 0.0243956 0.999702i \(-0.492234\pi\)
0.0243956 + 0.999702i \(0.492234\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 1.30212 0.148390
\(78\) 0 0
\(79\) 15.6884 1.76508 0.882541 0.470235i \(-0.155831\pi\)
0.882541 + 0.470235i \(0.155831\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −8.57594 −0.941331 −0.470666 0.882312i \(-0.655986\pi\)
−0.470666 + 0.882312i \(0.655986\pi\)
\(84\) 0 0
\(85\) −3.21588 −0.348811
\(86\) 0 0
\(87\) −6.42263 −0.688578
\(88\) 0 0
\(89\) 6.86302 0.727479 0.363739 0.931501i \(-0.381500\pi\)
0.363739 + 0.931501i \(0.381500\pi\)
\(90\) 0 0
\(91\) 0.580996 0.0609049
\(92\) 0 0
\(93\) 3.56282 0.369447
\(94\) 0 0
\(95\) 1.31998 0.135427
\(96\) 0 0
\(97\) −11.2626 −1.14354 −0.571772 0.820413i \(-0.693744\pi\)
−0.571772 + 0.820413i \(0.693744\pi\)
\(98\) 0 0
\(99\) −4.75091 −0.477485
\(100\) 0 0
\(101\) 11.7316 1.16734 0.583670 0.811991i \(-0.301616\pi\)
0.583670 + 0.811991i \(0.301616\pi\)
\(102\) 0 0
\(103\) 5.29950 0.522175 0.261088 0.965315i \(-0.415919\pi\)
0.261088 + 0.965315i \(0.415919\pi\)
\(104\) 0 0
\(105\) 0.274078 0.0267472
\(106\) 0 0
\(107\) 7.02493 0.679126 0.339563 0.940583i \(-0.389721\pi\)
0.339563 + 0.940583i \(0.389721\pi\)
\(108\) 0 0
\(109\) 9.86380 0.944781 0.472390 0.881389i \(-0.343391\pi\)
0.472390 + 0.881389i \(0.343391\pi\)
\(110\) 0 0
\(111\) 9.24113 0.877129
\(112\) 0 0
\(113\) −0.546353 −0.0513966 −0.0256983 0.999670i \(-0.508181\pi\)
−0.0256983 + 0.999670i \(0.508181\pi\)
\(114\) 0 0
\(115\) 4.76957 0.444765
\(116\) 0 0
\(117\) −2.11982 −0.195978
\(118\) 0 0
\(119\) −0.881400 −0.0807978
\(120\) 0 0
\(121\) 11.5712 1.05192
\(122\) 0 0
\(123\) −1.56282 −0.140915
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 7.53111 0.668278 0.334139 0.942524i \(-0.391554\pi\)
0.334139 + 0.942524i \(0.391554\pi\)
\(128\) 0 0
\(129\) 2.64975 0.233297
\(130\) 0 0
\(131\) −12.9151 −1.12840 −0.564200 0.825638i \(-0.690815\pi\)
−0.564200 + 0.825638i \(0.690815\pi\)
\(132\) 0 0
\(133\) 0.361776 0.0313700
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 3.99615 0.341414 0.170707 0.985322i \(-0.445395\pi\)
0.170707 + 0.985322i \(0.445395\pi\)
\(138\) 0 0
\(139\) −2.03032 −0.172210 −0.0861048 0.996286i \(-0.527442\pi\)
−0.0861048 + 0.996286i \(0.527442\pi\)
\(140\) 0 0
\(141\) 7.55397 0.636159
\(142\) 0 0
\(143\) 10.0711 0.842187
\(144\) 0 0
\(145\) 6.42263 0.533370
\(146\) 0 0
\(147\) −6.92488 −0.571155
\(148\) 0 0
\(149\) 3.32105 0.272071 0.136036 0.990704i \(-0.456564\pi\)
0.136036 + 0.990704i \(0.456564\pi\)
\(150\) 0 0
\(151\) −14.6664 −1.19354 −0.596769 0.802413i \(-0.703549\pi\)
−0.596769 + 0.802413i \(0.703549\pi\)
\(152\) 0 0
\(153\) 3.21588 0.259988
\(154\) 0 0
\(155\) −3.56282 −0.286172
\(156\) 0 0
\(157\) 1.11832 0.0892518 0.0446259 0.999004i \(-0.485790\pi\)
0.0446259 + 0.999004i \(0.485790\pi\)
\(158\) 0 0
\(159\) −12.6509 −1.00328
\(160\) 0 0
\(161\) 1.30723 0.103024
\(162\) 0 0
\(163\) 1.93177 0.151308 0.0756538 0.997134i \(-0.475896\pi\)
0.0756538 + 0.997134i \(0.475896\pi\)
\(164\) 0 0
\(165\) 4.75091 0.369858
\(166\) 0 0
\(167\) 6.84403 0.529607 0.264803 0.964302i \(-0.414693\pi\)
0.264803 + 0.964302i \(0.414693\pi\)
\(168\) 0 0
\(169\) −8.50636 −0.654335
\(170\) 0 0
\(171\) −1.31998 −0.100941
\(172\) 0 0
\(173\) 4.23895 0.322282 0.161141 0.986931i \(-0.448483\pi\)
0.161141 + 0.986931i \(0.448483\pi\)
\(174\) 0 0
\(175\) −0.274078 −0.0207183
\(176\) 0 0
\(177\) 11.9312 0.896807
\(178\) 0 0
\(179\) 17.5435 1.31126 0.655631 0.755081i \(-0.272403\pi\)
0.655631 + 0.755081i \(0.272403\pi\)
\(180\) 0 0
\(181\) 17.5358 1.30342 0.651712 0.758467i \(-0.274051\pi\)
0.651712 + 0.758467i \(0.274051\pi\)
\(182\) 0 0
\(183\) 5.61957 0.415410
\(184\) 0 0
\(185\) −9.24113 −0.679421
\(186\) 0 0
\(187\) −15.2783 −1.11726
\(188\) 0 0
\(189\) −0.274078 −0.0199362
\(190\) 0 0
\(191\) 21.2082 1.53457 0.767285 0.641306i \(-0.221607\pi\)
0.767285 + 0.641306i \(0.221607\pi\)
\(192\) 0 0
\(193\) 15.2523 1.09789 0.548943 0.835860i \(-0.315030\pi\)
0.548943 + 0.835860i \(0.315030\pi\)
\(194\) 0 0
\(195\) 2.11982 0.151804
\(196\) 0 0
\(197\) −14.0688 −1.00236 −0.501180 0.865343i \(-0.667101\pi\)
−0.501180 + 0.865343i \(0.667101\pi\)
\(198\) 0 0
\(199\) 13.2706 0.940728 0.470364 0.882472i \(-0.344123\pi\)
0.470364 + 0.882472i \(0.344123\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) 1.76030 0.123549
\(204\) 0 0
\(205\) 1.56282 0.109152
\(206\) 0 0
\(207\) −4.76957 −0.331508
\(208\) 0 0
\(209\) 6.27110 0.433781
\(210\) 0 0
\(211\) −3.60376 −0.248093 −0.124047 0.992276i \(-0.539587\pi\)
−0.124047 + 0.992276i \(0.539587\pi\)
\(212\) 0 0
\(213\) 5.03912 0.345275
\(214\) 0 0
\(215\) −2.64975 −0.180711
\(216\) 0 0
\(217\) −0.976489 −0.0662884
\(218\) 0 0
\(219\) 0.416872 0.0281696
\(220\) 0 0
\(221\) −6.81708 −0.458567
\(222\) 0 0
\(223\) 10.1472 0.679507 0.339754 0.940514i \(-0.389656\pi\)
0.339754 + 0.940514i \(0.389656\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −2.42806 −0.161156 −0.0805781 0.996748i \(-0.525677\pi\)
−0.0805781 + 0.996748i \(0.525677\pi\)
\(228\) 0 0
\(229\) 0.696447 0.0460225 0.0230113 0.999735i \(-0.492675\pi\)
0.0230113 + 0.999735i \(0.492675\pi\)
\(230\) 0 0
\(231\) 1.30212 0.0856731
\(232\) 0 0
\(233\) 24.1181 1.58003 0.790016 0.613087i \(-0.210072\pi\)
0.790016 + 0.613087i \(0.210072\pi\)
\(234\) 0 0
\(235\) −7.55397 −0.492767
\(236\) 0 0
\(237\) 15.6884 1.01907
\(238\) 0 0
\(239\) −7.52635 −0.486839 −0.243420 0.969921i \(-0.578269\pi\)
−0.243420 + 0.969921i \(0.578269\pi\)
\(240\) 0 0
\(241\) −8.96980 −0.577795 −0.288898 0.957360i \(-0.593289\pi\)
−0.288898 + 0.957360i \(0.593289\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 6.92488 0.442414
\(246\) 0 0
\(247\) 2.79812 0.178040
\(248\) 0 0
\(249\) −8.57594 −0.543478
\(250\) 0 0
\(251\) −3.03755 −0.191729 −0.0958644 0.995394i \(-0.530562\pi\)
−0.0958644 + 0.995394i \(0.530562\pi\)
\(252\) 0 0
\(253\) 22.6598 1.42461
\(254\) 0 0
\(255\) −3.21588 −0.201386
\(256\) 0 0
\(257\) −3.68721 −0.230002 −0.115001 0.993365i \(-0.536687\pi\)
−0.115001 + 0.993365i \(0.536687\pi\)
\(258\) 0 0
\(259\) −2.53279 −0.157380
\(260\) 0 0
\(261\) −6.42263 −0.397551
\(262\) 0 0
\(263\) 0.242711 0.0149662 0.00748309 0.999972i \(-0.497618\pi\)
0.00748309 + 0.999972i \(0.497618\pi\)
\(264\) 0 0
\(265\) 12.6509 0.777139
\(266\) 0 0
\(267\) 6.86302 0.420010
\(268\) 0 0
\(269\) −28.3909 −1.73102 −0.865512 0.500888i \(-0.833007\pi\)
−0.865512 + 0.500888i \(0.833007\pi\)
\(270\) 0 0
\(271\) 2.93780 0.178459 0.0892294 0.996011i \(-0.471560\pi\)
0.0892294 + 0.996011i \(0.471560\pi\)
\(272\) 0 0
\(273\) 0.580996 0.0351635
\(274\) 0 0
\(275\) −4.75091 −0.286491
\(276\) 0 0
\(277\) 3.37127 0.202560 0.101280 0.994858i \(-0.467706\pi\)
0.101280 + 0.994858i \(0.467706\pi\)
\(278\) 0 0
\(279\) 3.56282 0.213300
\(280\) 0 0
\(281\) −5.98422 −0.356989 −0.178494 0.983941i \(-0.557123\pi\)
−0.178494 + 0.983941i \(0.557123\pi\)
\(282\) 0 0
\(283\) 17.8711 1.06233 0.531164 0.847269i \(-0.321755\pi\)
0.531164 + 0.847269i \(0.321755\pi\)
\(284\) 0 0
\(285\) 1.31998 0.0781887
\(286\) 0 0
\(287\) 0.428334 0.0252837
\(288\) 0 0
\(289\) −6.65814 −0.391655
\(290\) 0 0
\(291\) −11.2626 −0.660225
\(292\) 0 0
\(293\) −21.8762 −1.27802 −0.639009 0.769199i \(-0.720655\pi\)
−0.639009 + 0.769199i \(0.720655\pi\)
\(294\) 0 0
\(295\) −11.9312 −0.694663
\(296\) 0 0
\(297\) −4.75091 −0.275676
\(298\) 0 0
\(299\) 10.1106 0.584713
\(300\) 0 0
\(301\) −0.726237 −0.0418596
\(302\) 0 0
\(303\) 11.7316 0.673964
\(304\) 0 0
\(305\) −5.61957 −0.321775
\(306\) 0 0
\(307\) −19.4125 −1.10793 −0.553966 0.832539i \(-0.686886\pi\)
−0.553966 + 0.832539i \(0.686886\pi\)
\(308\) 0 0
\(309\) 5.29950 0.301478
\(310\) 0 0
\(311\) 32.7827 1.85894 0.929469 0.368899i \(-0.120265\pi\)
0.929469 + 0.368899i \(0.120265\pi\)
\(312\) 0 0
\(313\) 28.0757 1.58693 0.793467 0.608613i \(-0.208274\pi\)
0.793467 + 0.608613i \(0.208274\pi\)
\(314\) 0 0
\(315\) 0.274078 0.0154425
\(316\) 0 0
\(317\) −0.862332 −0.0484334 −0.0242167 0.999707i \(-0.507709\pi\)
−0.0242167 + 0.999707i \(0.507709\pi\)
\(318\) 0 0
\(319\) 30.5133 1.70842
\(320\) 0 0
\(321\) 7.02493 0.392093
\(322\) 0 0
\(323\) −4.24488 −0.236192
\(324\) 0 0
\(325\) −2.11982 −0.117587
\(326\) 0 0
\(327\) 9.86380 0.545469
\(328\) 0 0
\(329\) −2.07037 −0.114143
\(330\) 0 0
\(331\) 12.9261 0.710484 0.355242 0.934774i \(-0.384398\pi\)
0.355242 + 0.934774i \(0.384398\pi\)
\(332\) 0 0
\(333\) 9.24113 0.506411
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) 12.4358 0.677422 0.338711 0.940890i \(-0.390009\pi\)
0.338711 + 0.940890i \(0.390009\pi\)
\(338\) 0 0
\(339\) −0.546353 −0.0296738
\(340\) 0 0
\(341\) −16.9266 −0.916629
\(342\) 0 0
\(343\) 3.81650 0.206072
\(344\) 0 0
\(345\) 4.76957 0.256785
\(346\) 0 0
\(347\) −11.5517 −0.620125 −0.310063 0.950716i \(-0.600350\pi\)
−0.310063 + 0.950716i \(0.600350\pi\)
\(348\) 0 0
\(349\) −8.12813 −0.435089 −0.217544 0.976050i \(-0.569805\pi\)
−0.217544 + 0.976050i \(0.569805\pi\)
\(350\) 0 0
\(351\) −2.11982 −0.113148
\(352\) 0 0
\(353\) 6.13851 0.326720 0.163360 0.986567i \(-0.447767\pi\)
0.163360 + 0.986567i \(0.447767\pi\)
\(354\) 0 0
\(355\) −5.03912 −0.267449
\(356\) 0 0
\(357\) −0.881400 −0.0466486
\(358\) 0 0
\(359\) 1.73600 0.0916223 0.0458112 0.998950i \(-0.485413\pi\)
0.0458112 + 0.998950i \(0.485413\pi\)
\(360\) 0 0
\(361\) −17.2577 −0.908298
\(362\) 0 0
\(363\) 11.5712 0.607329
\(364\) 0 0
\(365\) −0.416872 −0.0218201
\(366\) 0 0
\(367\) 19.8185 1.03452 0.517260 0.855829i \(-0.326952\pi\)
0.517260 + 0.855829i \(0.326952\pi\)
\(368\) 0 0
\(369\) −1.56282 −0.0813571
\(370\) 0 0
\(371\) 3.46733 0.180015
\(372\) 0 0
\(373\) 12.2367 0.633594 0.316797 0.948493i \(-0.397393\pi\)
0.316797 + 0.948493i \(0.397393\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 13.6148 0.701199
\(378\) 0 0
\(379\) 10.5061 0.539662 0.269831 0.962908i \(-0.413032\pi\)
0.269831 + 0.962908i \(0.413032\pi\)
\(380\) 0 0
\(381\) 7.53111 0.385831
\(382\) 0 0
\(383\) −16.0500 −0.820117 −0.410059 0.912059i \(-0.634492\pi\)
−0.410059 + 0.912059i \(0.634492\pi\)
\(384\) 0 0
\(385\) −1.30212 −0.0663621
\(386\) 0 0
\(387\) 2.64975 0.134694
\(388\) 0 0
\(389\) 4.65662 0.236100 0.118050 0.993008i \(-0.462336\pi\)
0.118050 + 0.993008i \(0.462336\pi\)
\(390\) 0 0
\(391\) −15.3383 −0.775693
\(392\) 0 0
\(393\) −12.9151 −0.651483
\(394\) 0 0
\(395\) −15.6884 −0.789369
\(396\) 0 0
\(397\) 8.51888 0.427551 0.213775 0.976883i \(-0.431424\pi\)
0.213775 + 0.976883i \(0.431424\pi\)
\(398\) 0 0
\(399\) 0.361776 0.0181115
\(400\) 0 0
\(401\) 5.21350 0.260350 0.130175 0.991491i \(-0.458446\pi\)
0.130175 + 0.991491i \(0.458446\pi\)
\(402\) 0 0
\(403\) −7.55254 −0.376219
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −43.9038 −2.17623
\(408\) 0 0
\(409\) −7.37518 −0.364679 −0.182340 0.983236i \(-0.558367\pi\)
−0.182340 + 0.983236i \(0.558367\pi\)
\(410\) 0 0
\(411\) 3.99615 0.197116
\(412\) 0 0
\(413\) −3.27009 −0.160910
\(414\) 0 0
\(415\) 8.57594 0.420976
\(416\) 0 0
\(417\) −2.03032 −0.0994252
\(418\) 0 0
\(419\) −13.6802 −0.668320 −0.334160 0.942516i \(-0.608453\pi\)
−0.334160 + 0.942516i \(0.608453\pi\)
\(420\) 0 0
\(421\) −20.9999 −1.02347 −0.511736 0.859143i \(-0.670997\pi\)
−0.511736 + 0.859143i \(0.670997\pi\)
\(422\) 0 0
\(423\) 7.55397 0.367287
\(424\) 0 0
\(425\) 3.21588 0.155993
\(426\) 0 0
\(427\) −1.54020 −0.0745354
\(428\) 0 0
\(429\) 10.0711 0.486237
\(430\) 0 0
\(431\) 11.8306 0.569861 0.284930 0.958548i \(-0.408030\pi\)
0.284930 + 0.958548i \(0.408030\pi\)
\(432\) 0 0
\(433\) −13.6077 −0.653944 −0.326972 0.945034i \(-0.606028\pi\)
−0.326972 + 0.945034i \(0.606028\pi\)
\(434\) 0 0
\(435\) 6.42263 0.307941
\(436\) 0 0
\(437\) 6.29572 0.301165
\(438\) 0 0
\(439\) 16.8746 0.805381 0.402691 0.915336i \(-0.368075\pi\)
0.402691 + 0.915336i \(0.368075\pi\)
\(440\) 0 0
\(441\) −6.92488 −0.329756
\(442\) 0 0
\(443\) −37.5322 −1.78321 −0.891604 0.452817i \(-0.850419\pi\)
−0.891604 + 0.452817i \(0.850419\pi\)
\(444\) 0 0
\(445\) −6.86302 −0.325338
\(446\) 0 0
\(447\) 3.32105 0.157080
\(448\) 0 0
\(449\) 35.4315 1.67211 0.836057 0.548643i \(-0.184855\pi\)
0.836057 + 0.548643i \(0.184855\pi\)
\(450\) 0 0
\(451\) 7.42482 0.349621
\(452\) 0 0
\(453\) −14.6664 −0.689089
\(454\) 0 0
\(455\) −0.580996 −0.0272375
\(456\) 0 0
\(457\) 13.6692 0.639416 0.319708 0.947516i \(-0.396415\pi\)
0.319708 + 0.947516i \(0.396415\pi\)
\(458\) 0 0
\(459\) 3.21588 0.150104
\(460\) 0 0
\(461\) 20.9521 0.975837 0.487919 0.872889i \(-0.337756\pi\)
0.487919 + 0.872889i \(0.337756\pi\)
\(462\) 0 0
\(463\) 1.41264 0.0656508 0.0328254 0.999461i \(-0.489549\pi\)
0.0328254 + 0.999461i \(0.489549\pi\)
\(464\) 0 0
\(465\) −3.56282 −0.165222
\(466\) 0 0
\(467\) −16.2423 −0.751603 −0.375801 0.926700i \(-0.622632\pi\)
−0.375801 + 0.926700i \(0.622632\pi\)
\(468\) 0 0
\(469\) −0.274078 −0.0126557
\(470\) 0 0
\(471\) 1.11832 0.0515296
\(472\) 0 0
\(473\) −12.5887 −0.578830
\(474\) 0 0
\(475\) −1.31998 −0.0605647
\(476\) 0 0
\(477\) −12.6509 −0.579245
\(478\) 0 0
\(479\) −13.6332 −0.622917 −0.311459 0.950260i \(-0.600818\pi\)
−0.311459 + 0.950260i \(0.600818\pi\)
\(480\) 0 0
\(481\) −19.5895 −0.893206
\(482\) 0 0
\(483\) 1.30723 0.0594811
\(484\) 0 0
\(485\) 11.2626 0.511408
\(486\) 0 0
\(487\) 34.3246 1.55540 0.777699 0.628637i \(-0.216387\pi\)
0.777699 + 0.628637i \(0.216387\pi\)
\(488\) 0 0
\(489\) 1.93177 0.0873575
\(490\) 0 0
\(491\) −11.6081 −0.523865 −0.261933 0.965086i \(-0.584360\pi\)
−0.261933 + 0.965086i \(0.584360\pi\)
\(492\) 0 0
\(493\) −20.6544 −0.930226
\(494\) 0 0
\(495\) 4.75091 0.213538
\(496\) 0 0
\(497\) −1.38111 −0.0619512
\(498\) 0 0
\(499\) 43.5861 1.95118 0.975592 0.219591i \(-0.0704724\pi\)
0.975592 + 0.219591i \(0.0704724\pi\)
\(500\) 0 0
\(501\) 6.84403 0.305769
\(502\) 0 0
\(503\) 5.84233 0.260497 0.130248 0.991481i \(-0.458423\pi\)
0.130248 + 0.991481i \(0.458423\pi\)
\(504\) 0 0
\(505\) −11.7316 −0.522050
\(506\) 0 0
\(507\) −8.50636 −0.377781
\(508\) 0 0
\(509\) −19.4123 −0.860435 −0.430217 0.902725i \(-0.641563\pi\)
−0.430217 + 0.902725i \(0.641563\pi\)
\(510\) 0 0
\(511\) −0.114255 −0.00505436
\(512\) 0 0
\(513\) −1.31998 −0.0582784
\(514\) 0 0
\(515\) −5.29950 −0.233524
\(516\) 0 0
\(517\) −35.8883 −1.57836
\(518\) 0 0
\(519\) 4.23895 0.186069
\(520\) 0 0
\(521\) −43.9104 −1.92375 −0.961875 0.273491i \(-0.911822\pi\)
−0.961875 + 0.273491i \(0.911822\pi\)
\(522\) 0 0
\(523\) 15.9649 0.698096 0.349048 0.937105i \(-0.386505\pi\)
0.349048 + 0.937105i \(0.386505\pi\)
\(524\) 0 0
\(525\) −0.274078 −0.0119617
\(526\) 0 0
\(527\) 11.4576 0.499100
\(528\) 0 0
\(529\) −0.251210 −0.0109222
\(530\) 0 0
\(531\) 11.9312 0.517772
\(532\) 0 0
\(533\) 3.31290 0.143498
\(534\) 0 0
\(535\) −7.02493 −0.303714
\(536\) 0 0
\(537\) 17.5435 0.757058
\(538\) 0 0
\(539\) 32.8995 1.41708
\(540\) 0 0
\(541\) 21.4941 0.924103 0.462051 0.886853i \(-0.347114\pi\)
0.462051 + 0.886853i \(0.347114\pi\)
\(542\) 0 0
\(543\) 17.5358 0.752532
\(544\) 0 0
\(545\) −9.86380 −0.422519
\(546\) 0 0
\(547\) −2.28962 −0.0978970 −0.0489485 0.998801i \(-0.515587\pi\)
−0.0489485 + 0.998801i \(0.515587\pi\)
\(548\) 0 0
\(549\) 5.61957 0.239837
\(550\) 0 0
\(551\) 8.47772 0.361163
\(552\) 0 0
\(553\) −4.29984 −0.182848
\(554\) 0 0
\(555\) −9.24113 −0.392264
\(556\) 0 0
\(557\) −4.50372 −0.190829 −0.0954144 0.995438i \(-0.530418\pi\)
−0.0954144 + 0.995438i \(0.530418\pi\)
\(558\) 0 0
\(559\) −5.61699 −0.237573
\(560\) 0 0
\(561\) −15.2783 −0.645052
\(562\) 0 0
\(563\) −19.8701 −0.837425 −0.418712 0.908119i \(-0.637518\pi\)
−0.418712 + 0.908119i \(0.637518\pi\)
\(564\) 0 0
\(565\) 0.546353 0.0229853
\(566\) 0 0
\(567\) −0.274078 −0.0115102
\(568\) 0 0
\(569\) 13.7633 0.576988 0.288494 0.957482i \(-0.406845\pi\)
0.288494 + 0.957482i \(0.406845\pi\)
\(570\) 0 0
\(571\) −4.68946 −0.196248 −0.0981239 0.995174i \(-0.531284\pi\)
−0.0981239 + 0.995174i \(0.531284\pi\)
\(572\) 0 0
\(573\) 21.2082 0.885985
\(574\) 0 0
\(575\) −4.76957 −0.198905
\(576\) 0 0
\(577\) 31.8293 1.32507 0.662536 0.749030i \(-0.269480\pi\)
0.662536 + 0.749030i \(0.269480\pi\)
\(578\) 0 0
\(579\) 15.2523 0.633865
\(580\) 0 0
\(581\) 2.35047 0.0975140
\(582\) 0 0
\(583\) 60.1034 2.48923
\(584\) 0 0
\(585\) 2.11982 0.0876438
\(586\) 0 0
\(587\) 19.6046 0.809167 0.404584 0.914501i \(-0.367416\pi\)
0.404584 + 0.914501i \(0.367416\pi\)
\(588\) 0 0
\(589\) −4.70284 −0.193777
\(590\) 0 0
\(591\) −14.0688 −0.578713
\(592\) 0 0
\(593\) 18.5848 0.763185 0.381593 0.924331i \(-0.375376\pi\)
0.381593 + 0.924331i \(0.375376\pi\)
\(594\) 0 0
\(595\) 0.881400 0.0361339
\(596\) 0 0
\(597\) 13.2706 0.543130
\(598\) 0 0
\(599\) 42.2678 1.72701 0.863507 0.504337i \(-0.168263\pi\)
0.863507 + 0.504337i \(0.168263\pi\)
\(600\) 0 0
\(601\) −19.3968 −0.791211 −0.395606 0.918420i \(-0.629465\pi\)
−0.395606 + 0.918420i \(0.629465\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) −11.5712 −0.470435
\(606\) 0 0
\(607\) −12.5784 −0.510540 −0.255270 0.966870i \(-0.582164\pi\)
−0.255270 + 0.966870i \(0.582164\pi\)
\(608\) 0 0
\(609\) 1.76030 0.0713309
\(610\) 0 0
\(611\) −16.0131 −0.647820
\(612\) 0 0
\(613\) −17.8994 −0.722950 −0.361475 0.932382i \(-0.617727\pi\)
−0.361475 + 0.932382i \(0.617727\pi\)
\(614\) 0 0
\(615\) 1.56282 0.0630189
\(616\) 0 0
\(617\) −14.9521 −0.601949 −0.300974 0.953632i \(-0.597312\pi\)
−0.300974 + 0.953632i \(0.597312\pi\)
\(618\) 0 0
\(619\) 12.6389 0.508001 0.254000 0.967204i \(-0.418254\pi\)
0.254000 + 0.967204i \(0.418254\pi\)
\(620\) 0 0
\(621\) −4.76957 −0.191396
\(622\) 0 0
\(623\) −1.88100 −0.0753607
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 6.27110 0.250444
\(628\) 0 0
\(629\) 29.7183 1.18495
\(630\) 0 0
\(631\) 1.95655 0.0778891 0.0389446 0.999241i \(-0.487600\pi\)
0.0389446 + 0.999241i \(0.487600\pi\)
\(632\) 0 0
\(633\) −3.60376 −0.143237
\(634\) 0 0
\(635\) −7.53111 −0.298863
\(636\) 0 0
\(637\) 14.6795 0.581623
\(638\) 0 0
\(639\) 5.03912 0.199344
\(640\) 0 0
\(641\) −15.6620 −0.618611 −0.309306 0.950963i \(-0.600097\pi\)
−0.309306 + 0.950963i \(0.600097\pi\)
\(642\) 0 0
\(643\) 31.8842 1.25739 0.628695 0.777652i \(-0.283589\pi\)
0.628695 + 0.777652i \(0.283589\pi\)
\(644\) 0 0
\(645\) −2.64975 −0.104334
\(646\) 0 0
\(647\) 27.7142 1.08956 0.544779 0.838580i \(-0.316614\pi\)
0.544779 + 0.838580i \(0.316614\pi\)
\(648\) 0 0
\(649\) −56.6843 −2.22505
\(650\) 0 0
\(651\) −0.976489 −0.0382716
\(652\) 0 0
\(653\) −29.2711 −1.14547 −0.572733 0.819742i \(-0.694117\pi\)
−0.572733 + 0.819742i \(0.694117\pi\)
\(654\) 0 0
\(655\) 12.9151 0.504636
\(656\) 0 0
\(657\) 0.416872 0.0162637
\(658\) 0 0
\(659\) −28.8923 −1.12549 −0.562743 0.826632i \(-0.690254\pi\)
−0.562743 + 0.826632i \(0.690254\pi\)
\(660\) 0 0
\(661\) −32.5189 −1.26484 −0.632419 0.774627i \(-0.717938\pi\)
−0.632419 + 0.774627i \(0.717938\pi\)
\(662\) 0 0
\(663\) −6.81708 −0.264754
\(664\) 0 0
\(665\) −0.361776 −0.0140291
\(666\) 0 0
\(667\) 30.6332 1.18612
\(668\) 0 0
\(669\) 10.1472 0.392314
\(670\) 0 0
\(671\) −26.6981 −1.03067
\(672\) 0 0
\(673\) 42.9155 1.65427 0.827136 0.562002i \(-0.189969\pi\)
0.827136 + 0.562002i \(0.189969\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 19.9407 0.766382 0.383191 0.923669i \(-0.374825\pi\)
0.383191 + 0.923669i \(0.374825\pi\)
\(678\) 0 0
\(679\) 3.08683 0.118462
\(680\) 0 0
\(681\) −2.42806 −0.0930435
\(682\) 0 0
\(683\) 29.7954 1.14009 0.570045 0.821613i \(-0.306926\pi\)
0.570045 + 0.821613i \(0.306926\pi\)
\(684\) 0 0
\(685\) −3.99615 −0.152685
\(686\) 0 0
\(687\) 0.696447 0.0265711
\(688\) 0 0
\(689\) 26.8177 1.02167
\(690\) 0 0
\(691\) −48.5139 −1.84556 −0.922779 0.385330i \(-0.874088\pi\)
−0.922779 + 0.385330i \(0.874088\pi\)
\(692\) 0 0
\(693\) 1.30212 0.0494634
\(694\) 0 0
\(695\) 2.03032 0.0770145
\(696\) 0 0
\(697\) −5.02583 −0.190367
\(698\) 0 0
\(699\) 24.1181 0.912232
\(700\) 0 0
\(701\) 51.7582 1.95488 0.977440 0.211214i \(-0.0677417\pi\)
0.977440 + 0.211214i \(0.0677417\pi\)
\(702\) 0 0
\(703\) −12.1981 −0.460059
\(704\) 0 0
\(705\) −7.55397 −0.284499
\(706\) 0 0
\(707\) −3.21537 −0.120927
\(708\) 0 0
\(709\) −26.0615 −0.978760 −0.489380 0.872071i \(-0.662777\pi\)
−0.489380 + 0.872071i \(0.662777\pi\)
\(710\) 0 0
\(711\) 15.6884 0.588361
\(712\) 0 0
\(713\) −16.9931 −0.636397
\(714\) 0 0
\(715\) −10.0711 −0.376637
\(716\) 0 0
\(717\) −7.52635 −0.281077
\(718\) 0 0
\(719\) 13.0431 0.486425 0.243213 0.969973i \(-0.421799\pi\)
0.243213 + 0.969973i \(0.421799\pi\)
\(720\) 0 0
\(721\) −1.45247 −0.0540930
\(722\) 0 0
\(723\) −8.96980 −0.333590
\(724\) 0 0
\(725\) −6.42263 −0.238530
\(726\) 0 0
\(727\) −1.65637 −0.0614315 −0.0307157 0.999528i \(-0.509779\pi\)
−0.0307157 + 0.999528i \(0.509779\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.52126 0.315170
\(732\) 0 0
\(733\) −35.7746 −1.32137 −0.660683 0.750665i \(-0.729733\pi\)
−0.660683 + 0.750665i \(0.729733\pi\)
\(734\) 0 0
\(735\) 6.92488 0.255428
\(736\) 0 0
\(737\) −4.75091 −0.175002
\(738\) 0 0
\(739\) 43.9936 1.61833 0.809165 0.587581i \(-0.199920\pi\)
0.809165 + 0.587581i \(0.199920\pi\)
\(740\) 0 0
\(741\) 2.79812 0.102791
\(742\) 0 0
\(743\) 25.2341 0.925751 0.462875 0.886423i \(-0.346818\pi\)
0.462875 + 0.886423i \(0.346818\pi\)
\(744\) 0 0
\(745\) −3.32105 −0.121674
\(746\) 0 0
\(747\) −8.57594 −0.313777
\(748\) 0 0
\(749\) −1.92538 −0.0703517
\(750\) 0 0
\(751\) −29.4931 −1.07622 −0.538109 0.842875i \(-0.680861\pi\)
−0.538109 + 0.842875i \(0.680861\pi\)
\(752\) 0 0
\(753\) −3.03755 −0.110695
\(754\) 0 0
\(755\) 14.6664 0.533766
\(756\) 0 0
\(757\) 16.9847 0.617318 0.308659 0.951173i \(-0.400120\pi\)
0.308659 + 0.951173i \(0.400120\pi\)
\(758\) 0 0
\(759\) 22.6598 0.822499
\(760\) 0 0
\(761\) −45.0408 −1.63273 −0.816364 0.577538i \(-0.804014\pi\)
−0.816364 + 0.577538i \(0.804014\pi\)
\(762\) 0 0
\(763\) −2.70345 −0.0978714
\(764\) 0 0
\(765\) −3.21588 −0.116270
\(766\) 0 0
\(767\) −25.2921 −0.913244
\(768\) 0 0
\(769\) −24.3584 −0.878387 −0.439194 0.898392i \(-0.644736\pi\)
−0.439194 + 0.898392i \(0.644736\pi\)
\(770\) 0 0
\(771\) −3.68721 −0.132792
\(772\) 0 0
\(773\) 24.1670 0.869227 0.434614 0.900617i \(-0.356885\pi\)
0.434614 + 0.900617i \(0.356885\pi\)
\(774\) 0 0
\(775\) 3.56282 0.127980
\(776\) 0 0
\(777\) −2.53279 −0.0908632
\(778\) 0 0
\(779\) 2.06289 0.0739106
\(780\) 0 0
\(781\) −23.9404 −0.856655
\(782\) 0 0
\(783\) −6.42263 −0.229526
\(784\) 0 0
\(785\) −1.11832 −0.0399146
\(786\) 0 0
\(787\) −10.0855 −0.359508 −0.179754 0.983712i \(-0.557530\pi\)
−0.179754 + 0.983712i \(0.557530\pi\)
\(788\) 0 0
\(789\) 0.242711 0.00864073
\(790\) 0 0
\(791\) 0.149743 0.00532426
\(792\) 0 0
\(793\) −11.9125 −0.423025
\(794\) 0 0
\(795\) 12.6509 0.448682
\(796\) 0 0
\(797\) 34.3548 1.21691 0.608454 0.793589i \(-0.291790\pi\)
0.608454 + 0.793589i \(0.291790\pi\)
\(798\) 0 0
\(799\) 24.2926 0.859412
\(800\) 0 0
\(801\) 6.86302 0.242493
\(802\) 0 0
\(803\) −1.98052 −0.0698912
\(804\) 0 0
\(805\) −1.30723 −0.0460739
\(806\) 0 0
\(807\) −28.3909 −0.999407
\(808\) 0 0
\(809\) 10.1064 0.355322 0.177661 0.984092i \(-0.443147\pi\)
0.177661 + 0.984092i \(0.443147\pi\)
\(810\) 0 0
\(811\) 38.2166 1.34197 0.670983 0.741473i \(-0.265873\pi\)
0.670983 + 0.741473i \(0.265873\pi\)
\(812\) 0 0
\(813\) 2.93780 0.103033
\(814\) 0 0
\(815\) −1.93177 −0.0676668
\(816\) 0 0
\(817\) −3.49761 −0.122366
\(818\) 0 0
\(819\) 0.580996 0.0203016
\(820\) 0 0
\(821\) 48.9304 1.70768 0.853841 0.520534i \(-0.174267\pi\)
0.853841 + 0.520534i \(0.174267\pi\)
\(822\) 0 0
\(823\) −44.0331 −1.53490 −0.767449 0.641110i \(-0.778474\pi\)
−0.767449 + 0.641110i \(0.778474\pi\)
\(824\) 0 0
\(825\) −4.75091 −0.165406
\(826\) 0 0
\(827\) −0.996143 −0.0346393 −0.0173196 0.999850i \(-0.505513\pi\)
−0.0173196 + 0.999850i \(0.505513\pi\)
\(828\) 0 0
\(829\) −18.1697 −0.631060 −0.315530 0.948916i \(-0.602182\pi\)
−0.315530 + 0.948916i \(0.602182\pi\)
\(830\) 0 0
\(831\) 3.37127 0.116948
\(832\) 0 0
\(833\) −22.2696 −0.771594
\(834\) 0 0
\(835\) −6.84403 −0.236847
\(836\) 0 0
\(837\) 3.56282 0.123149
\(838\) 0 0
\(839\) 22.2280 0.767395 0.383698 0.923459i \(-0.374650\pi\)
0.383698 + 0.923459i \(0.374650\pi\)
\(840\) 0 0
\(841\) 12.2501 0.422418
\(842\) 0 0
\(843\) −5.98422 −0.206108
\(844\) 0 0
\(845\) 8.50636 0.292628
\(846\) 0 0
\(847\) −3.17140 −0.108971
\(848\) 0 0
\(849\) 17.8711 0.613335
\(850\) 0 0
\(851\) −44.0762 −1.51091
\(852\) 0 0
\(853\) 10.8813 0.372568 0.186284 0.982496i \(-0.440356\pi\)
0.186284 + 0.982496i \(0.440356\pi\)
\(854\) 0 0
\(855\) 1.31998 0.0451423
\(856\) 0 0
\(857\) 2.23751 0.0764320 0.0382160 0.999270i \(-0.487832\pi\)
0.0382160 + 0.999270i \(0.487832\pi\)
\(858\) 0 0
\(859\) 21.2351 0.724532 0.362266 0.932075i \(-0.382003\pi\)
0.362266 + 0.932075i \(0.382003\pi\)
\(860\) 0 0
\(861\) 0.428334 0.0145976
\(862\) 0 0
\(863\) −36.3874 −1.23864 −0.619321 0.785138i \(-0.712592\pi\)
−0.619321 + 0.785138i \(0.712592\pi\)
\(864\) 0 0
\(865\) −4.23895 −0.144129
\(866\) 0 0
\(867\) −6.65814 −0.226122
\(868\) 0 0
\(869\) −74.5342 −2.52840
\(870\) 0 0
\(871\) −2.11982 −0.0718274
\(872\) 0 0
\(873\) −11.2626 −0.381181
\(874\) 0 0
\(875\) 0.274078 0.00926552
\(876\) 0 0
\(877\) −12.3253 −0.416195 −0.208097 0.978108i \(-0.566727\pi\)
−0.208097 + 0.978108i \(0.566727\pi\)
\(878\) 0 0
\(879\) −21.8762 −0.737864
\(880\) 0 0
\(881\) −43.3712 −1.46121 −0.730606 0.682800i \(-0.760762\pi\)
−0.730606 + 0.682800i \(0.760762\pi\)
\(882\) 0 0
\(883\) 8.88396 0.298969 0.149485 0.988764i \(-0.452239\pi\)
0.149485 + 0.988764i \(0.452239\pi\)
\(884\) 0 0
\(885\) −11.9312 −0.401064
\(886\) 0 0
\(887\) −3.87622 −0.130151 −0.0650754 0.997880i \(-0.520729\pi\)
−0.0650754 + 0.997880i \(0.520729\pi\)
\(888\) 0 0
\(889\) −2.06411 −0.0692280
\(890\) 0 0
\(891\) −4.75091 −0.159162
\(892\) 0 0
\(893\) −9.97107 −0.333669
\(894\) 0 0
\(895\) −17.5435 −0.586415
\(896\) 0 0
\(897\) 10.1106 0.337584
\(898\) 0 0
\(899\) −22.8827 −0.763179
\(900\) 0 0
\(901\) −40.6838 −1.35537
\(902\) 0 0
\(903\) −0.726237 −0.0241676
\(904\) 0 0
\(905\) −17.5358 −0.582909
\(906\) 0 0
\(907\) 32.1024 1.06594 0.532972 0.846133i \(-0.321075\pi\)
0.532972 + 0.846133i \(0.321075\pi\)
\(908\) 0 0
\(909\) 11.7316 0.389113
\(910\) 0 0
\(911\) −24.9479 −0.826562 −0.413281 0.910603i \(-0.635617\pi\)
−0.413281 + 0.910603i \(0.635617\pi\)
\(912\) 0 0
\(913\) 40.7435 1.34841
\(914\) 0 0
\(915\) −5.61957 −0.185777
\(916\) 0 0
\(917\) 3.53975 0.116893
\(918\) 0 0
\(919\) 11.6271 0.383541 0.191771 0.981440i \(-0.438577\pi\)
0.191771 + 0.981440i \(0.438577\pi\)
\(920\) 0 0
\(921\) −19.4125 −0.639665
\(922\) 0 0
\(923\) −10.6820 −0.351603
\(924\) 0 0
\(925\) 9.24113 0.303846
\(926\) 0 0
\(927\) 5.29950 0.174058
\(928\) 0 0
\(929\) −37.1907 −1.22019 −0.610094 0.792329i \(-0.708868\pi\)
−0.610094 + 0.792329i \(0.708868\pi\)
\(930\) 0 0
\(931\) 9.14069 0.299574
\(932\) 0 0
\(933\) 32.7827 1.07326
\(934\) 0 0
\(935\) 15.2783 0.499655
\(936\) 0 0
\(937\) −35.7860 −1.16908 −0.584538 0.811366i \(-0.698724\pi\)
−0.584538 + 0.811366i \(0.698724\pi\)
\(938\) 0 0
\(939\) 28.0757 0.916217
\(940\) 0 0
\(941\) −44.5118 −1.45104 −0.725521 0.688200i \(-0.758401\pi\)
−0.725521 + 0.688200i \(0.758401\pi\)
\(942\) 0 0
\(943\) 7.45397 0.242735
\(944\) 0 0
\(945\) 0.274078 0.00891575
\(946\) 0 0
\(947\) −5.21198 −0.169366 −0.0846832 0.996408i \(-0.526988\pi\)
−0.0846832 + 0.996408i \(0.526988\pi\)
\(948\) 0 0
\(949\) −0.883695 −0.0286859
\(950\) 0 0
\(951\) −0.862332 −0.0279630
\(952\) 0 0
\(953\) 26.9135 0.871814 0.435907 0.899992i \(-0.356428\pi\)
0.435907 + 0.899992i \(0.356428\pi\)
\(954\) 0 0
\(955\) −21.2082 −0.686281
\(956\) 0 0
\(957\) 30.5133 0.986356
\(958\) 0 0
\(959\) −1.09526 −0.0353677
\(960\) 0 0
\(961\) −18.3063 −0.590527
\(962\) 0 0
\(963\) 7.02493 0.226375
\(964\) 0 0
\(965\) −15.2523 −0.490990
\(966\) 0 0
\(967\) 37.7612 1.21432 0.607159 0.794581i \(-0.292309\pi\)
0.607159 + 0.794581i \(0.292309\pi\)
\(968\) 0 0
\(969\) −4.24488 −0.136365
\(970\) 0 0
\(971\) 11.1654 0.358316 0.179158 0.983820i \(-0.442663\pi\)
0.179158 + 0.983820i \(0.442663\pi\)
\(972\) 0 0
\(973\) 0.556466 0.0178395
\(974\) 0 0
\(975\) −2.11982 −0.0678886
\(976\) 0 0
\(977\) 34.1644 1.09302 0.546508 0.837454i \(-0.315957\pi\)
0.546508 + 0.837454i \(0.315957\pi\)
\(978\) 0 0
\(979\) −32.6056 −1.04208
\(980\) 0 0
\(981\) 9.86380 0.314927
\(982\) 0 0
\(983\) −5.53628 −0.176580 −0.0882899 0.996095i \(-0.528140\pi\)
−0.0882899 + 0.996095i \(0.528140\pi\)
\(984\) 0 0
\(985\) 14.0688 0.448269
\(986\) 0 0
\(987\) −2.07037 −0.0659008
\(988\) 0 0
\(989\) −12.6382 −0.401870
\(990\) 0 0
\(991\) 0.895489 0.0284462 0.0142231 0.999899i \(-0.495473\pi\)
0.0142231 + 0.999899i \(0.495473\pi\)
\(992\) 0 0
\(993\) 12.9261 0.410198
\(994\) 0 0
\(995\) −13.2706 −0.420706
\(996\) 0 0
\(997\) 23.5066 0.744461 0.372230 0.928140i \(-0.378593\pi\)
0.372230 + 0.928140i \(0.378593\pi\)
\(998\) 0 0
\(999\) 9.24113 0.292376
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 \(a_p\))