Properties

Label 6040.2.a.p.1.14
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 1.14
Root \(-1.62033\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.62033 q^{3}\) \(+1.00000 q^{5}\) \(+1.05807 q^{7}\) \(-0.374546 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.62033 q^{3}\) \(+1.00000 q^{5}\) \(+1.05807 q^{7}\) \(-0.374546 q^{9}\) \(+1.92929 q^{11}\) \(-5.16563 q^{13}\) \(+1.62033 q^{15}\) \(-0.487306 q^{17}\) \(+3.35387 q^{19}\) \(+1.71442 q^{21}\) \(-8.10261 q^{23}\) \(+1.00000 q^{25}\) \(-5.46786 q^{27}\) \(-5.06662 q^{29}\) \(-9.15516 q^{31}\) \(+3.12608 q^{33}\) \(+1.05807 q^{35}\) \(-2.78935 q^{37}\) \(-8.36999 q^{39}\) \(-9.74056 q^{41}\) \(+9.98299 q^{43}\) \(-0.374546 q^{45}\) \(-12.5870 q^{47}\) \(-5.88048 q^{49}\) \(-0.789594 q^{51}\) \(-8.21593 q^{53}\) \(+1.92929 q^{55}\) \(+5.43436 q^{57}\) \(+6.65236 q^{59}\) \(+7.66930 q^{61}\) \(-0.396297 q^{63}\) \(-5.16563 q^{65}\) \(+13.0551 q^{67}\) \(-13.1289 q^{69}\) \(-15.2608 q^{71}\) \(-5.43519 q^{73}\) \(+1.62033 q^{75}\) \(+2.04133 q^{77}\) \(+11.2081 q^{79}\) \(-7.73608 q^{81}\) \(+5.38477 q^{83}\) \(-0.487306 q^{85}\) \(-8.20958 q^{87}\) \(-5.15799 q^{89}\) \(-5.46561 q^{91}\) \(-14.8343 q^{93}\) \(+3.35387 q^{95}\) \(-4.23953 q^{97}\) \(-0.722609 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.62033 0.935495 0.467748 0.883862i \(-0.345066\pi\)
0.467748 + 0.883862i \(0.345066\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.05807 0.399914 0.199957 0.979805i \(-0.435920\pi\)
0.199957 + 0.979805i \(0.435920\pi\)
\(8\) 0 0
\(9\) −0.374546 −0.124849
\(10\) 0 0
\(11\) 1.92929 0.581704 0.290852 0.956768i \(-0.406061\pi\)
0.290852 + 0.956768i \(0.406061\pi\)
\(12\) 0 0
\(13\) −5.16563 −1.43269 −0.716343 0.697748i \(-0.754186\pi\)
−0.716343 + 0.697748i \(0.754186\pi\)
\(14\) 0 0
\(15\) 1.62033 0.418366
\(16\) 0 0
\(17\) −0.487306 −0.118189 −0.0590945 0.998252i \(-0.518821\pi\)
−0.0590945 + 0.998252i \(0.518821\pi\)
\(18\) 0 0
\(19\) 3.35387 0.769430 0.384715 0.923035i \(-0.374300\pi\)
0.384715 + 0.923035i \(0.374300\pi\)
\(20\) 0 0
\(21\) 1.71442 0.374118
\(22\) 0 0
\(23\) −8.10261 −1.68951 −0.844755 0.535153i \(-0.820254\pi\)
−0.844755 + 0.535153i \(0.820254\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.46786 −1.05229
\(28\) 0 0
\(29\) −5.06662 −0.940848 −0.470424 0.882440i \(-0.655899\pi\)
−0.470424 + 0.882440i \(0.655899\pi\)
\(30\) 0 0
\(31\) −9.15516 −1.64431 −0.822157 0.569260i \(-0.807230\pi\)
−0.822157 + 0.569260i \(0.807230\pi\)
\(32\) 0 0
\(33\) 3.12608 0.544181
\(34\) 0 0
\(35\) 1.05807 0.178847
\(36\) 0 0
\(37\) −2.78935 −0.458566 −0.229283 0.973360i \(-0.573638\pi\)
−0.229283 + 0.973360i \(0.573638\pi\)
\(38\) 0 0
\(39\) −8.36999 −1.34027
\(40\) 0 0
\(41\) −9.74056 −1.52122 −0.760610 0.649209i \(-0.775100\pi\)
−0.760610 + 0.649209i \(0.775100\pi\)
\(42\) 0 0
\(43\) 9.98299 1.52239 0.761196 0.648522i \(-0.224613\pi\)
0.761196 + 0.648522i \(0.224613\pi\)
\(44\) 0 0
\(45\) −0.374546 −0.0558341
\(46\) 0 0
\(47\) −12.5870 −1.83600 −0.918001 0.396578i \(-0.870198\pi\)
−0.918001 + 0.396578i \(0.870198\pi\)
\(48\) 0 0
\(49\) −5.88048 −0.840069
\(50\) 0 0
\(51\) −0.789594 −0.110565
\(52\) 0 0
\(53\) −8.21593 −1.12855 −0.564273 0.825589i \(-0.690843\pi\)
−0.564273 + 0.825589i \(0.690843\pi\)
\(54\) 0 0
\(55\) 1.92929 0.260146
\(56\) 0 0
\(57\) 5.43436 0.719798
\(58\) 0 0
\(59\) 6.65236 0.866064 0.433032 0.901379i \(-0.357444\pi\)
0.433032 + 0.901379i \(0.357444\pi\)
\(60\) 0 0
\(61\) 7.66930 0.981954 0.490977 0.871173i \(-0.336640\pi\)
0.490977 + 0.871173i \(0.336640\pi\)
\(62\) 0 0
\(63\) −0.396297 −0.0499288
\(64\) 0 0
\(65\) −5.16563 −0.640717
\(66\) 0 0
\(67\) 13.0551 1.59493 0.797465 0.603365i \(-0.206174\pi\)
0.797465 + 0.603365i \(0.206174\pi\)
\(68\) 0 0
\(69\) −13.1289 −1.58053
\(70\) 0 0
\(71\) −15.2608 −1.81112 −0.905562 0.424215i \(-0.860550\pi\)
−0.905562 + 0.424215i \(0.860550\pi\)
\(72\) 0 0
\(73\) −5.43519 −0.636141 −0.318071 0.948067i \(-0.603035\pi\)
−0.318071 + 0.948067i \(0.603035\pi\)
\(74\) 0 0
\(75\) 1.62033 0.187099
\(76\) 0 0
\(77\) 2.04133 0.232631
\(78\) 0 0
\(79\) 11.2081 1.26100 0.630502 0.776187i \(-0.282849\pi\)
0.630502 + 0.776187i \(0.282849\pi\)
\(80\) 0 0
\(81\) −7.73608 −0.859564
\(82\) 0 0
\(83\) 5.38477 0.591055 0.295528 0.955334i \(-0.404505\pi\)
0.295528 + 0.955334i \(0.404505\pi\)
\(84\) 0 0
\(85\) −0.487306 −0.0528557
\(86\) 0 0
\(87\) −8.20958 −0.880159
\(88\) 0 0
\(89\) −5.15799 −0.546746 −0.273373 0.961908i \(-0.588139\pi\)
−0.273373 + 0.961908i \(0.588139\pi\)
\(90\) 0 0
\(91\) −5.46561 −0.572951
\(92\) 0 0
\(93\) −14.8343 −1.53825
\(94\) 0 0
\(95\) 3.35387 0.344100
\(96\) 0 0
\(97\) −4.23953 −0.430459 −0.215230 0.976563i \(-0.569050\pi\)
−0.215230 + 0.976563i \(0.569050\pi\)
\(98\) 0 0
\(99\) −0.722609 −0.0726250
\(100\) 0 0
\(101\) 13.8470 1.37783 0.688913 0.724844i \(-0.258088\pi\)
0.688913 + 0.724844i \(0.258088\pi\)
\(102\) 0 0
\(103\) 5.25202 0.517497 0.258748 0.965945i \(-0.416690\pi\)
0.258748 + 0.965945i \(0.416690\pi\)
\(104\) 0 0
\(105\) 1.71442 0.167310
\(106\) 0 0
\(107\) 17.4722 1.68910 0.844551 0.535474i \(-0.179867\pi\)
0.844551 + 0.535474i \(0.179867\pi\)
\(108\) 0 0
\(109\) −8.11212 −0.777000 −0.388500 0.921449i \(-0.627007\pi\)
−0.388500 + 0.921449i \(0.627007\pi\)
\(110\) 0 0
\(111\) −4.51966 −0.428987
\(112\) 0 0
\(113\) 14.1787 1.33382 0.666909 0.745139i \(-0.267617\pi\)
0.666909 + 0.745139i \(0.267617\pi\)
\(114\) 0 0
\(115\) −8.10261 −0.755572
\(116\) 0 0
\(117\) 1.93477 0.178869
\(118\) 0 0
\(119\) −0.515605 −0.0472654
\(120\) 0 0
\(121\) −7.27783 −0.661621
\(122\) 0 0
\(123\) −15.7829 −1.42309
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 15.4839 1.37397 0.686986 0.726670i \(-0.258933\pi\)
0.686986 + 0.726670i \(0.258933\pi\)
\(128\) 0 0
\(129\) 16.1757 1.42419
\(130\) 0 0
\(131\) 4.38247 0.382898 0.191449 0.981503i \(-0.438681\pi\)
0.191449 + 0.981503i \(0.438681\pi\)
\(132\) 0 0
\(133\) 3.54864 0.307706
\(134\) 0 0
\(135\) −5.46786 −0.470599
\(136\) 0 0
\(137\) −0.547672 −0.0467908 −0.0233954 0.999726i \(-0.507448\pi\)
−0.0233954 + 0.999726i \(0.507448\pi\)
\(138\) 0 0
\(139\) −9.56779 −0.811529 −0.405764 0.913978i \(-0.632995\pi\)
−0.405764 + 0.913978i \(0.632995\pi\)
\(140\) 0 0
\(141\) −20.3950 −1.71757
\(142\) 0 0
\(143\) −9.96600 −0.833399
\(144\) 0 0
\(145\) −5.06662 −0.420760
\(146\) 0 0
\(147\) −9.52829 −0.785880
\(148\) 0 0
\(149\) −16.6102 −1.36076 −0.680380 0.732860i \(-0.738185\pi\)
−0.680380 + 0.732860i \(0.738185\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) 0.182519 0.0147558
\(154\) 0 0
\(155\) −9.15516 −0.735360
\(156\) 0 0
\(157\) −5.64640 −0.450632 −0.225316 0.974286i \(-0.572341\pi\)
−0.225316 + 0.974286i \(0.572341\pi\)
\(158\) 0 0
\(159\) −13.3125 −1.05575
\(160\) 0 0
\(161\) −8.57315 −0.675659
\(162\) 0 0
\(163\) −20.8024 −1.62937 −0.814686 0.579902i \(-0.803091\pi\)
−0.814686 + 0.579902i \(0.803091\pi\)
\(164\) 0 0
\(165\) 3.12608 0.243365
\(166\) 0 0
\(167\) −6.69428 −0.518019 −0.259010 0.965875i \(-0.583396\pi\)
−0.259010 + 0.965875i \(0.583396\pi\)
\(168\) 0 0
\(169\) 13.6837 1.05259
\(170\) 0 0
\(171\) −1.25618 −0.0960624
\(172\) 0 0
\(173\) 4.00866 0.304773 0.152387 0.988321i \(-0.451304\pi\)
0.152387 + 0.988321i \(0.451304\pi\)
\(174\) 0 0
\(175\) 1.05807 0.0799828
\(176\) 0 0
\(177\) 10.7790 0.810199
\(178\) 0 0
\(179\) −9.16408 −0.684955 −0.342478 0.939526i \(-0.611266\pi\)
−0.342478 + 0.939526i \(0.611266\pi\)
\(180\) 0 0
\(181\) 6.65788 0.494877 0.247438 0.968904i \(-0.420411\pi\)
0.247438 + 0.968904i \(0.420411\pi\)
\(182\) 0 0
\(183\) 12.4268 0.918613
\(184\) 0 0
\(185\) −2.78935 −0.205077
\(186\) 0 0
\(187\) −0.940156 −0.0687510
\(188\) 0 0
\(189\) −5.78540 −0.420826
\(190\) 0 0
\(191\) 4.25377 0.307792 0.153896 0.988087i \(-0.450818\pi\)
0.153896 + 0.988087i \(0.450818\pi\)
\(192\) 0 0
\(193\) 12.2128 0.879100 0.439550 0.898218i \(-0.355138\pi\)
0.439550 + 0.898218i \(0.355138\pi\)
\(194\) 0 0
\(195\) −8.36999 −0.599388
\(196\) 0 0
\(197\) 15.0139 1.06970 0.534848 0.844948i \(-0.320369\pi\)
0.534848 + 0.844948i \(0.320369\pi\)
\(198\) 0 0
\(199\) 2.41316 0.171064 0.0855320 0.996335i \(-0.472741\pi\)
0.0855320 + 0.996335i \(0.472741\pi\)
\(200\) 0 0
\(201\) 21.1535 1.49205
\(202\) 0 0
\(203\) −5.36086 −0.376258
\(204\) 0 0
\(205\) −9.74056 −0.680310
\(206\) 0 0
\(207\) 3.03480 0.210933
\(208\) 0 0
\(209\) 6.47059 0.447580
\(210\) 0 0
\(211\) −7.95842 −0.547880 −0.273940 0.961747i \(-0.588327\pi\)
−0.273940 + 0.961747i \(0.588327\pi\)
\(212\) 0 0
\(213\) −24.7275 −1.69430
\(214\) 0 0
\(215\) 9.98299 0.680834
\(216\) 0 0
\(217\) −9.68682 −0.657584
\(218\) 0 0
\(219\) −8.80678 −0.595107
\(220\) 0 0
\(221\) 2.51724 0.169328
\(222\) 0 0
\(223\) −11.9357 −0.799273 −0.399637 0.916674i \(-0.630864\pi\)
−0.399637 + 0.916674i \(0.630864\pi\)
\(224\) 0 0
\(225\) −0.374546 −0.0249697
\(226\) 0 0
\(227\) 14.6193 0.970314 0.485157 0.874427i \(-0.338762\pi\)
0.485157 + 0.874427i \(0.338762\pi\)
\(228\) 0 0
\(229\) 28.7403 1.89921 0.949605 0.313449i \(-0.101485\pi\)
0.949605 + 0.313449i \(0.101485\pi\)
\(230\) 0 0
\(231\) 3.30762 0.217626
\(232\) 0 0
\(233\) 20.8455 1.36564 0.682819 0.730588i \(-0.260754\pi\)
0.682819 + 0.730588i \(0.260754\pi\)
\(234\) 0 0
\(235\) −12.5870 −0.821085
\(236\) 0 0
\(237\) 18.1607 1.17966
\(238\) 0 0
\(239\) −6.77335 −0.438131 −0.219066 0.975710i \(-0.570301\pi\)
−0.219066 + 0.975710i \(0.570301\pi\)
\(240\) 0 0
\(241\) −26.8706 −1.73089 −0.865445 0.501003i \(-0.832964\pi\)
−0.865445 + 0.501003i \(0.832964\pi\)
\(242\) 0 0
\(243\) 3.86863 0.248173
\(244\) 0 0
\(245\) −5.88048 −0.375690
\(246\) 0 0
\(247\) −17.3248 −1.10235
\(248\) 0 0
\(249\) 8.72508 0.552929
\(250\) 0 0
\(251\) −7.71524 −0.486982 −0.243491 0.969903i \(-0.578293\pi\)
−0.243491 + 0.969903i \(0.578293\pi\)
\(252\) 0 0
\(253\) −15.6323 −0.982794
\(254\) 0 0
\(255\) −0.789594 −0.0494463
\(256\) 0 0
\(257\) 8.39666 0.523769 0.261884 0.965099i \(-0.415656\pi\)
0.261884 + 0.965099i \(0.415656\pi\)
\(258\) 0 0
\(259\) −2.95134 −0.183387
\(260\) 0 0
\(261\) 1.89768 0.117464
\(262\) 0 0
\(263\) −12.7351 −0.785280 −0.392640 0.919692i \(-0.628438\pi\)
−0.392640 + 0.919692i \(0.628438\pi\)
\(264\) 0 0
\(265\) −8.21593 −0.504701
\(266\) 0 0
\(267\) −8.35762 −0.511478
\(268\) 0 0
\(269\) 31.5442 1.92328 0.961641 0.274312i \(-0.0884502\pi\)
0.961641 + 0.274312i \(0.0884502\pi\)
\(270\) 0 0
\(271\) −2.06355 −0.125352 −0.0626760 0.998034i \(-0.519963\pi\)
−0.0626760 + 0.998034i \(0.519963\pi\)
\(272\) 0 0
\(273\) −8.85606 −0.535993
\(274\) 0 0
\(275\) 1.92929 0.116341
\(276\) 0 0
\(277\) −5.06936 −0.304588 −0.152294 0.988335i \(-0.548666\pi\)
−0.152294 + 0.988335i \(0.548666\pi\)
\(278\) 0 0
\(279\) 3.42903 0.205291
\(280\) 0 0
\(281\) −14.6303 −0.872771 −0.436385 0.899760i \(-0.643742\pi\)
−0.436385 + 0.899760i \(0.643742\pi\)
\(282\) 0 0
\(283\) −1.03291 −0.0614004 −0.0307002 0.999529i \(-0.509774\pi\)
−0.0307002 + 0.999529i \(0.509774\pi\)
\(284\) 0 0
\(285\) 5.43436 0.321904
\(286\) 0 0
\(287\) −10.3062 −0.608357
\(288\) 0 0
\(289\) −16.7625 −0.986031
\(290\) 0 0
\(291\) −6.86942 −0.402693
\(292\) 0 0
\(293\) 31.5619 1.84387 0.921934 0.387347i \(-0.126609\pi\)
0.921934 + 0.387347i \(0.126609\pi\)
\(294\) 0 0
\(295\) 6.65236 0.387316
\(296\) 0 0
\(297\) −10.5491 −0.612121
\(298\) 0 0
\(299\) 41.8550 2.42054
\(300\) 0 0
\(301\) 10.5627 0.608826
\(302\) 0 0
\(303\) 22.4366 1.28895
\(304\) 0 0
\(305\) 7.66930 0.439143
\(306\) 0 0
\(307\) −30.1225 −1.71918 −0.859592 0.510981i \(-0.829282\pi\)
−0.859592 + 0.510981i \(0.829282\pi\)
\(308\) 0 0
\(309\) 8.50998 0.484116
\(310\) 0 0
\(311\) −1.91311 −0.108482 −0.0542412 0.998528i \(-0.517274\pi\)
−0.0542412 + 0.998528i \(0.517274\pi\)
\(312\) 0 0
\(313\) 13.5815 0.767671 0.383835 0.923402i \(-0.374603\pi\)
0.383835 + 0.923402i \(0.374603\pi\)
\(314\) 0 0
\(315\) −0.396297 −0.0223288
\(316\) 0 0
\(317\) −19.9547 −1.12077 −0.560384 0.828233i \(-0.689346\pi\)
−0.560384 + 0.828233i \(0.689346\pi\)
\(318\) 0 0
\(319\) −9.77500 −0.547295
\(320\) 0 0
\(321\) 28.3107 1.58015
\(322\) 0 0
\(323\) −1.63436 −0.0909382
\(324\) 0 0
\(325\) −5.16563 −0.286537
\(326\) 0 0
\(327\) −13.1443 −0.726880
\(328\) 0 0
\(329\) −13.3180 −0.734243
\(330\) 0 0
\(331\) −4.00780 −0.220289 −0.110144 0.993916i \(-0.535131\pi\)
−0.110144 + 0.993916i \(0.535131\pi\)
\(332\) 0 0
\(333\) 1.04474 0.0572514
\(334\) 0 0
\(335\) 13.0551 0.713275
\(336\) 0 0
\(337\) 24.3401 1.32589 0.662946 0.748668i \(-0.269306\pi\)
0.662946 + 0.748668i \(0.269306\pi\)
\(338\) 0 0
\(339\) 22.9741 1.24778
\(340\) 0 0
\(341\) −17.6630 −0.956504
\(342\) 0 0
\(343\) −13.6285 −0.735869
\(344\) 0 0
\(345\) −13.1289 −0.706834
\(346\) 0 0
\(347\) −18.8504 −1.01194 −0.505972 0.862550i \(-0.668866\pi\)
−0.505972 + 0.862550i \(0.668866\pi\)
\(348\) 0 0
\(349\) 0.618813 0.0331243 0.0165621 0.999863i \(-0.494728\pi\)
0.0165621 + 0.999863i \(0.494728\pi\)
\(350\) 0 0
\(351\) 28.2449 1.50760
\(352\) 0 0
\(353\) −0.350929 −0.0186780 −0.00933902 0.999956i \(-0.502973\pi\)
−0.00933902 + 0.999956i \(0.502973\pi\)
\(354\) 0 0
\(355\) −15.2608 −0.809959
\(356\) 0 0
\(357\) −0.835448 −0.0442166
\(358\) 0 0
\(359\) 4.27830 0.225800 0.112900 0.993606i \(-0.463986\pi\)
0.112900 + 0.993606i \(0.463986\pi\)
\(360\) 0 0
\(361\) −7.75156 −0.407977
\(362\) 0 0
\(363\) −11.7925 −0.618943
\(364\) 0 0
\(365\) −5.43519 −0.284491
\(366\) 0 0
\(367\) −11.7862 −0.615236 −0.307618 0.951510i \(-0.599532\pi\)
−0.307618 + 0.951510i \(0.599532\pi\)
\(368\) 0 0
\(369\) 3.64829 0.189922
\(370\) 0 0
\(371\) −8.69305 −0.451321
\(372\) 0 0
\(373\) −9.07310 −0.469787 −0.234894 0.972021i \(-0.575474\pi\)
−0.234894 + 0.972021i \(0.575474\pi\)
\(374\) 0 0
\(375\) 1.62033 0.0836732
\(376\) 0 0
\(377\) 26.1723 1.34794
\(378\) 0 0
\(379\) 36.6842 1.88434 0.942169 0.335137i \(-0.108783\pi\)
0.942169 + 0.335137i \(0.108783\pi\)
\(380\) 0 0
\(381\) 25.0889 1.28534
\(382\) 0 0
\(383\) −16.2004 −0.827804 −0.413902 0.910321i \(-0.635834\pi\)
−0.413902 + 0.910321i \(0.635834\pi\)
\(384\) 0 0
\(385\) 2.04133 0.104036
\(386\) 0 0
\(387\) −3.73909 −0.190069
\(388\) 0 0
\(389\) 1.40557 0.0712654 0.0356327 0.999365i \(-0.488655\pi\)
0.0356327 + 0.999365i \(0.488655\pi\)
\(390\) 0 0
\(391\) 3.94845 0.199682
\(392\) 0 0
\(393\) 7.10103 0.358199
\(394\) 0 0
\(395\) 11.2081 0.563938
\(396\) 0 0
\(397\) −21.7209 −1.09014 −0.545071 0.838390i \(-0.683497\pi\)
−0.545071 + 0.838390i \(0.683497\pi\)
\(398\) 0 0
\(399\) 5.74995 0.287857
\(400\) 0 0
\(401\) −28.3974 −1.41810 −0.709050 0.705158i \(-0.750876\pi\)
−0.709050 + 0.705158i \(0.750876\pi\)
\(402\) 0 0
\(403\) 47.2921 2.35579
\(404\) 0 0
\(405\) −7.73608 −0.384409
\(406\) 0 0
\(407\) −5.38147 −0.266750
\(408\) 0 0
\(409\) 4.09142 0.202308 0.101154 0.994871i \(-0.467747\pi\)
0.101154 + 0.994871i \(0.467747\pi\)
\(410\) 0 0
\(411\) −0.887407 −0.0437726
\(412\) 0 0
\(413\) 7.03868 0.346351
\(414\) 0 0
\(415\) 5.38477 0.264328
\(416\) 0 0
\(417\) −15.5029 −0.759181
\(418\) 0 0
\(419\) 36.7408 1.79490 0.897452 0.441113i \(-0.145416\pi\)
0.897452 + 0.441113i \(0.145416\pi\)
\(420\) 0 0
\(421\) −0.763792 −0.0372250 −0.0186125 0.999827i \(-0.505925\pi\)
−0.0186125 + 0.999827i \(0.505925\pi\)
\(422\) 0 0
\(423\) 4.71441 0.229223
\(424\) 0 0
\(425\) −0.487306 −0.0236378
\(426\) 0 0
\(427\) 8.11468 0.392697
\(428\) 0 0
\(429\) −16.1482 −0.779641
\(430\) 0 0
\(431\) −8.83835 −0.425728 −0.212864 0.977082i \(-0.568279\pi\)
−0.212864 + 0.977082i \(0.568279\pi\)
\(432\) 0 0
\(433\) −13.9829 −0.671977 −0.335989 0.941866i \(-0.609070\pi\)
−0.335989 + 0.941866i \(0.609070\pi\)
\(434\) 0 0
\(435\) −8.20958 −0.393619
\(436\) 0 0
\(437\) −27.1751 −1.29996
\(438\) 0 0
\(439\) 21.3954 1.02115 0.510573 0.859834i \(-0.329433\pi\)
0.510573 + 0.859834i \(0.329433\pi\)
\(440\) 0 0
\(441\) 2.20251 0.104882
\(442\) 0 0
\(443\) −32.5148 −1.54482 −0.772412 0.635121i \(-0.780950\pi\)
−0.772412 + 0.635121i \(0.780950\pi\)
\(444\) 0 0
\(445\) −5.15799 −0.244512
\(446\) 0 0
\(447\) −26.9139 −1.27298
\(448\) 0 0
\(449\) −25.6289 −1.20950 −0.604751 0.796414i \(-0.706727\pi\)
−0.604751 + 0.796414i \(0.706727\pi\)
\(450\) 0 0
\(451\) −18.7924 −0.884899
\(452\) 0 0
\(453\) 1.62033 0.0761295
\(454\) 0 0
\(455\) −5.46561 −0.256232
\(456\) 0 0
\(457\) 13.4164 0.627591 0.313796 0.949491i \(-0.398399\pi\)
0.313796 + 0.949491i \(0.398399\pi\)
\(458\) 0 0
\(459\) 2.66452 0.124369
\(460\) 0 0
\(461\) −7.58177 −0.353118 −0.176559 0.984290i \(-0.556497\pi\)
−0.176559 + 0.984290i \(0.556497\pi\)
\(462\) 0 0
\(463\) 29.1496 1.35470 0.677348 0.735663i \(-0.263129\pi\)
0.677348 + 0.735663i \(0.263129\pi\)
\(464\) 0 0
\(465\) −14.8343 −0.687926
\(466\) 0 0
\(467\) −27.0796 −1.25309 −0.626547 0.779384i \(-0.715532\pi\)
−0.626547 + 0.779384i \(0.715532\pi\)
\(468\) 0 0
\(469\) 13.8132 0.637835
\(470\) 0 0
\(471\) −9.14901 −0.421564
\(472\) 0 0
\(473\) 19.2601 0.885581
\(474\) 0 0
\(475\) 3.35387 0.153886
\(476\) 0 0
\(477\) 3.07725 0.140897
\(478\) 0 0
\(479\) 13.1467 0.600688 0.300344 0.953831i \(-0.402898\pi\)
0.300344 + 0.953831i \(0.402898\pi\)
\(480\) 0 0
\(481\) 14.4087 0.656982
\(482\) 0 0
\(483\) −13.8913 −0.632076
\(484\) 0 0
\(485\) −4.23953 −0.192507
\(486\) 0 0
\(487\) −37.0442 −1.67863 −0.839317 0.543642i \(-0.817045\pi\)
−0.839317 + 0.543642i \(0.817045\pi\)
\(488\) 0 0
\(489\) −33.7067 −1.52427
\(490\) 0 0
\(491\) −38.9757 −1.75895 −0.879475 0.475945i \(-0.842106\pi\)
−0.879475 + 0.475945i \(0.842106\pi\)
\(492\) 0 0
\(493\) 2.46900 0.111198
\(494\) 0 0
\(495\) −0.722609 −0.0324789
\(496\) 0 0
\(497\) −16.1470 −0.724293
\(498\) 0 0
\(499\) 40.6445 1.81950 0.909749 0.415160i \(-0.136274\pi\)
0.909749 + 0.415160i \(0.136274\pi\)
\(500\) 0 0
\(501\) −10.8469 −0.484604
\(502\) 0 0
\(503\) −19.3969 −0.864863 −0.432432 0.901667i \(-0.642344\pi\)
−0.432432 + 0.901667i \(0.642344\pi\)
\(504\) 0 0
\(505\) 13.8470 0.616183
\(506\) 0 0
\(507\) 22.1720 0.984694
\(508\) 0 0
\(509\) −8.63101 −0.382563 −0.191281 0.981535i \(-0.561264\pi\)
−0.191281 + 0.981535i \(0.561264\pi\)
\(510\) 0 0
\(511\) −5.75083 −0.254402
\(512\) 0 0
\(513\) −18.3385 −0.809664
\(514\) 0 0
\(515\) 5.25202 0.231432
\(516\) 0 0
\(517\) −24.2840 −1.06801
\(518\) 0 0
\(519\) 6.49534 0.285114
\(520\) 0 0
\(521\) −15.2056 −0.666168 −0.333084 0.942897i \(-0.608089\pi\)
−0.333084 + 0.942897i \(0.608089\pi\)
\(522\) 0 0
\(523\) −13.5883 −0.594176 −0.297088 0.954850i \(-0.596015\pi\)
−0.297088 + 0.954850i \(0.596015\pi\)
\(524\) 0 0
\(525\) 1.71442 0.0748235
\(526\) 0 0
\(527\) 4.46136 0.194340
\(528\) 0 0
\(529\) 42.6523 1.85445
\(530\) 0 0
\(531\) −2.49162 −0.108127
\(532\) 0 0
\(533\) 50.3161 2.17943
\(534\) 0 0
\(535\) 17.4722 0.755390
\(536\) 0 0
\(537\) −14.8488 −0.640772
\(538\) 0 0
\(539\) −11.3452 −0.488671
\(540\) 0 0
\(541\) 15.0953 0.648998 0.324499 0.945886i \(-0.394804\pi\)
0.324499 + 0.945886i \(0.394804\pi\)
\(542\) 0 0
\(543\) 10.7879 0.462955
\(544\) 0 0
\(545\) −8.11212 −0.347485
\(546\) 0 0
\(547\) 9.21865 0.394161 0.197080 0.980387i \(-0.436854\pi\)
0.197080 + 0.980387i \(0.436854\pi\)
\(548\) 0 0
\(549\) −2.87251 −0.122596
\(550\) 0 0
\(551\) −16.9928 −0.723917
\(552\) 0 0
\(553\) 11.8589 0.504293
\(554\) 0 0
\(555\) −4.51966 −0.191849
\(556\) 0 0
\(557\) −13.4618 −0.570395 −0.285198 0.958469i \(-0.592059\pi\)
−0.285198 + 0.958469i \(0.592059\pi\)
\(558\) 0 0
\(559\) −51.5684 −2.18111
\(560\) 0 0
\(561\) −1.52336 −0.0643162
\(562\) 0 0
\(563\) 24.4598 1.03086 0.515428 0.856933i \(-0.327633\pi\)
0.515428 + 0.856933i \(0.327633\pi\)
\(564\) 0 0
\(565\) 14.1787 0.596502
\(566\) 0 0
\(567\) −8.18533 −0.343752
\(568\) 0 0
\(569\) 18.4196 0.772190 0.386095 0.922459i \(-0.373824\pi\)
0.386095 + 0.922459i \(0.373824\pi\)
\(570\) 0 0
\(571\) −5.05481 −0.211537 −0.105769 0.994391i \(-0.533730\pi\)
−0.105769 + 0.994391i \(0.533730\pi\)
\(572\) 0 0
\(573\) 6.89248 0.287938
\(574\) 0 0
\(575\) −8.10261 −0.337902
\(576\) 0 0
\(577\) −0.547146 −0.0227780 −0.0113890 0.999935i \(-0.503625\pi\)
−0.0113890 + 0.999935i \(0.503625\pi\)
\(578\) 0 0
\(579\) 19.7888 0.822394
\(580\) 0 0
\(581\) 5.69748 0.236371
\(582\) 0 0
\(583\) −15.8509 −0.656479
\(584\) 0 0
\(585\) 1.93477 0.0799927
\(586\) 0 0
\(587\) −33.9726 −1.40220 −0.701101 0.713062i \(-0.747308\pi\)
−0.701101 + 0.713062i \(0.747308\pi\)
\(588\) 0 0
\(589\) −30.7052 −1.26519
\(590\) 0 0
\(591\) 24.3274 1.00070
\(592\) 0 0
\(593\) −11.8796 −0.487838 −0.243919 0.969796i \(-0.578433\pi\)
−0.243919 + 0.969796i \(0.578433\pi\)
\(594\) 0 0
\(595\) −0.515605 −0.0211377
\(596\) 0 0
\(597\) 3.91010 0.160030
\(598\) 0 0
\(599\) −40.2211 −1.64339 −0.821695 0.569928i \(-0.806971\pi\)
−0.821695 + 0.569928i \(0.806971\pi\)
\(600\) 0 0
\(601\) 6.72967 0.274509 0.137254 0.990536i \(-0.456172\pi\)
0.137254 + 0.990536i \(0.456172\pi\)
\(602\) 0 0
\(603\) −4.88973 −0.199125
\(604\) 0 0
\(605\) −7.27783 −0.295886
\(606\) 0 0
\(607\) 36.1292 1.46644 0.733220 0.679992i \(-0.238017\pi\)
0.733220 + 0.679992i \(0.238017\pi\)
\(608\) 0 0
\(609\) −8.68633 −0.351988
\(610\) 0 0
\(611\) 65.0197 2.63042
\(612\) 0 0
\(613\) 1.52315 0.0615193 0.0307597 0.999527i \(-0.490207\pi\)
0.0307597 + 0.999527i \(0.490207\pi\)
\(614\) 0 0
\(615\) −15.7829 −0.636427
\(616\) 0 0
\(617\) 37.8055 1.52199 0.760996 0.648757i \(-0.224711\pi\)
0.760996 + 0.648757i \(0.224711\pi\)
\(618\) 0 0
\(619\) 17.0988 0.687258 0.343629 0.939105i \(-0.388344\pi\)
0.343629 + 0.939105i \(0.388344\pi\)
\(620\) 0 0
\(621\) 44.3039 1.77786
\(622\) 0 0
\(623\) −5.45753 −0.218651
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 10.4845 0.418709
\(628\) 0 0
\(629\) 1.35927 0.0541975
\(630\) 0 0
\(631\) −18.8960 −0.752237 −0.376119 0.926572i \(-0.622741\pi\)
−0.376119 + 0.926572i \(0.622741\pi\)
\(632\) 0 0
\(633\) −12.8952 −0.512539
\(634\) 0 0
\(635\) 15.4839 0.614459
\(636\) 0 0
\(637\) 30.3764 1.20356
\(638\) 0 0
\(639\) 5.71587 0.226116
\(640\) 0 0
\(641\) 6.55954 0.259086 0.129543 0.991574i \(-0.458649\pi\)
0.129543 + 0.991574i \(0.458649\pi\)
\(642\) 0 0
\(643\) 4.52213 0.178335 0.0891677 0.996017i \(-0.471579\pi\)
0.0891677 + 0.996017i \(0.471579\pi\)
\(644\) 0 0
\(645\) 16.1757 0.636917
\(646\) 0 0
\(647\) −0.878452 −0.0345355 −0.0172678 0.999851i \(-0.505497\pi\)
−0.0172678 + 0.999851i \(0.505497\pi\)
\(648\) 0 0
\(649\) 12.8344 0.503792
\(650\) 0 0
\(651\) −15.6958 −0.615167
\(652\) 0 0
\(653\) 0.791423 0.0309708 0.0154854 0.999880i \(-0.495071\pi\)
0.0154854 + 0.999880i \(0.495071\pi\)
\(654\) 0 0
\(655\) 4.38247 0.171237
\(656\) 0 0
\(657\) 2.03573 0.0794214
\(658\) 0 0
\(659\) −37.9841 −1.47965 −0.739825 0.672799i \(-0.765092\pi\)
−0.739825 + 0.672799i \(0.765092\pi\)
\(660\) 0 0
\(661\) −28.2021 −1.09694 −0.548468 0.836172i \(-0.684789\pi\)
−0.548468 + 0.836172i \(0.684789\pi\)
\(662\) 0 0
\(663\) 4.07875 0.158405
\(664\) 0 0
\(665\) 3.54864 0.137610
\(666\) 0 0
\(667\) 41.0529 1.58957
\(668\) 0 0
\(669\) −19.3397 −0.747716
\(670\) 0 0
\(671\) 14.7963 0.571206
\(672\) 0 0
\(673\) 22.6005 0.871186 0.435593 0.900144i \(-0.356539\pi\)
0.435593 + 0.900144i \(0.356539\pi\)
\(674\) 0 0
\(675\) −5.46786 −0.210458
\(676\) 0 0
\(677\) 43.7202 1.68031 0.840153 0.542350i \(-0.182465\pi\)
0.840153 + 0.542350i \(0.182465\pi\)
\(678\) 0 0
\(679\) −4.48573 −0.172147
\(680\) 0 0
\(681\) 23.6879 0.907724
\(682\) 0 0
\(683\) −43.8848 −1.67920 −0.839602 0.543202i \(-0.817212\pi\)
−0.839602 + 0.543202i \(0.817212\pi\)
\(684\) 0 0
\(685\) −0.547672 −0.0209255
\(686\) 0 0
\(687\) 46.5686 1.77670
\(688\) 0 0
\(689\) 42.4404 1.61685
\(690\) 0 0
\(691\) −44.1231 −1.67852 −0.839262 0.543728i \(-0.817012\pi\)
−0.839262 + 0.543728i \(0.817012\pi\)
\(692\) 0 0
\(693\) −0.764573 −0.0290437
\(694\) 0 0
\(695\) −9.56779 −0.362927
\(696\) 0 0
\(697\) 4.74663 0.179792
\(698\) 0 0
\(699\) 33.7766 1.27755
\(700\) 0 0
\(701\) 0.284789 0.0107563 0.00537816 0.999986i \(-0.498288\pi\)
0.00537816 + 0.999986i \(0.498288\pi\)
\(702\) 0 0
\(703\) −9.35512 −0.352835
\(704\) 0 0
\(705\) −20.3950 −0.768121
\(706\) 0 0
\(707\) 14.6511 0.551012
\(708\) 0 0
\(709\) −7.91058 −0.297088 −0.148544 0.988906i \(-0.547459\pi\)
−0.148544 + 0.988906i \(0.547459\pi\)
\(710\) 0 0
\(711\) −4.19794 −0.157435
\(712\) 0 0
\(713\) 74.1806 2.77809
\(714\) 0 0
\(715\) −9.96600 −0.372707
\(716\) 0 0
\(717\) −10.9750 −0.409870
\(718\) 0 0
\(719\) 17.8141 0.664355 0.332177 0.943217i \(-0.392217\pi\)
0.332177 + 0.943217i \(0.392217\pi\)
\(720\) 0 0
\(721\) 5.55702 0.206954
\(722\) 0 0
\(723\) −43.5392 −1.61924
\(724\) 0 0
\(725\) −5.06662 −0.188170
\(726\) 0 0
\(727\) −38.6237 −1.43247 −0.716237 0.697857i \(-0.754137\pi\)
−0.716237 + 0.697857i \(0.754137\pi\)
\(728\) 0 0
\(729\) 29.4767 1.09173
\(730\) 0 0
\(731\) −4.86477 −0.179930
\(732\) 0 0
\(733\) 49.8329 1.84062 0.920310 0.391190i \(-0.127936\pi\)
0.920310 + 0.391190i \(0.127936\pi\)
\(734\) 0 0
\(735\) −9.52829 −0.351456
\(736\) 0 0
\(737\) 25.1871 0.927777
\(738\) 0 0
\(739\) −4.20167 −0.154561 −0.0772805 0.997009i \(-0.524624\pi\)
−0.0772805 + 0.997009i \(0.524624\pi\)
\(740\) 0 0
\(741\) −28.0719 −1.03125
\(742\) 0 0
\(743\) −1.08102 −0.0396589 −0.0198294 0.999803i \(-0.506312\pi\)
−0.0198294 + 0.999803i \(0.506312\pi\)
\(744\) 0 0
\(745\) −16.6102 −0.608550
\(746\) 0 0
\(747\) −2.01684 −0.0737925
\(748\) 0 0
\(749\) 18.4869 0.675496
\(750\) 0 0
\(751\) −1.04193 −0.0380206 −0.0190103 0.999819i \(-0.506052\pi\)
−0.0190103 + 0.999819i \(0.506052\pi\)
\(752\) 0 0
\(753\) −12.5012 −0.455569
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −13.0957 −0.475970 −0.237985 0.971269i \(-0.576487\pi\)
−0.237985 + 0.971269i \(0.576487\pi\)
\(758\) 0 0
\(759\) −25.3294 −0.919400
\(760\) 0 0
\(761\) −25.5784 −0.927218 −0.463609 0.886040i \(-0.653446\pi\)
−0.463609 + 0.886040i \(0.653446\pi\)
\(762\) 0 0
\(763\) −8.58321 −0.310733
\(764\) 0 0
\(765\) 0.182519 0.00659897
\(766\) 0 0
\(767\) −34.3636 −1.24080
\(768\) 0 0
\(769\) −10.4246 −0.375920 −0.187960 0.982177i \(-0.560188\pi\)
−0.187960 + 0.982177i \(0.560188\pi\)
\(770\) 0 0
\(771\) 13.6053 0.489983
\(772\) 0 0
\(773\) 34.0719 1.22548 0.612740 0.790285i \(-0.290067\pi\)
0.612740 + 0.790285i \(0.290067\pi\)
\(774\) 0 0
\(775\) −9.15516 −0.328863
\(776\) 0 0
\(777\) −4.78212 −0.171558
\(778\) 0 0
\(779\) −32.6686 −1.17047
\(780\) 0 0
\(781\) −29.4425 −1.05354
\(782\) 0 0
\(783\) 27.7036 0.990046
\(784\) 0 0
\(785\) −5.64640 −0.201529
\(786\) 0 0
\(787\) 39.5791 1.41084 0.705421 0.708789i \(-0.250758\pi\)
0.705421 + 0.708789i \(0.250758\pi\)
\(788\) 0 0
\(789\) −20.6350 −0.734626
\(790\) 0 0
\(791\) 15.0021 0.533413
\(792\) 0 0
\(793\) −39.6168 −1.40683
\(794\) 0 0
\(795\) −13.3125 −0.472145
\(796\) 0 0
\(797\) 9.87979 0.349960 0.174980 0.984572i \(-0.444014\pi\)
0.174980 + 0.984572i \(0.444014\pi\)
\(798\) 0 0
\(799\) 6.13372 0.216995
\(800\) 0 0
\(801\) 1.93190 0.0682605
\(802\) 0 0
\(803\) −10.4861 −0.370046
\(804\) 0 0
\(805\) −8.57315 −0.302164
\(806\) 0 0
\(807\) 51.1118 1.79922
\(808\) 0 0
\(809\) −34.8718 −1.22603 −0.613013 0.790073i \(-0.710043\pi\)
−0.613013 + 0.790073i \(0.710043\pi\)
\(810\) 0 0
\(811\) −25.4689 −0.894333 −0.447166 0.894451i \(-0.647567\pi\)
−0.447166 + 0.894451i \(0.647567\pi\)
\(812\) 0 0
\(813\) −3.34363 −0.117266
\(814\) 0 0
\(815\) −20.8024 −0.728678
\(816\) 0 0
\(817\) 33.4816 1.17137
\(818\) 0 0
\(819\) 2.04712 0.0715323
\(820\) 0 0
\(821\) −19.7225 −0.688321 −0.344160 0.938911i \(-0.611836\pi\)
−0.344160 + 0.938911i \(0.611836\pi\)
\(822\) 0 0
\(823\) −19.4552 −0.678166 −0.339083 0.940756i \(-0.610117\pi\)
−0.339083 + 0.940756i \(0.610117\pi\)
\(824\) 0 0
\(825\) 3.12608 0.108836
\(826\) 0 0
\(827\) −3.60716 −0.125433 −0.0627166 0.998031i \(-0.519976\pi\)
−0.0627166 + 0.998031i \(0.519976\pi\)
\(828\) 0 0
\(829\) −4.84485 −0.168269 −0.0841343 0.996454i \(-0.526812\pi\)
−0.0841343 + 0.996454i \(0.526812\pi\)
\(830\) 0 0
\(831\) −8.21400 −0.284941
\(832\) 0 0
\(833\) 2.86559 0.0992869
\(834\) 0 0
\(835\) −6.69428 −0.231665
\(836\) 0 0
\(837\) 50.0591 1.73030
\(838\) 0 0
\(839\) −45.9800 −1.58741 −0.793704 0.608305i \(-0.791850\pi\)
−0.793704 + 0.608305i \(0.791850\pi\)
\(840\) 0 0
\(841\) −3.32933 −0.114805
\(842\) 0 0
\(843\) −23.7059 −0.816473
\(844\) 0 0
\(845\) 13.6837 0.470733
\(846\) 0 0
\(847\) −7.70047 −0.264591
\(848\) 0 0
\(849\) −1.67366 −0.0574398
\(850\) 0 0
\(851\) 22.6010 0.774753
\(852\) 0 0
\(853\) 35.5200 1.21618 0.608091 0.793867i \(-0.291935\pi\)
0.608091 + 0.793867i \(0.291935\pi\)
\(854\) 0 0
\(855\) −1.25618 −0.0429604
\(856\) 0 0
\(857\) −26.8202 −0.916162 −0.458081 0.888910i \(-0.651463\pi\)
−0.458081 + 0.888910i \(0.651463\pi\)
\(858\) 0 0
\(859\) 40.7804 1.39141 0.695705 0.718327i \(-0.255092\pi\)
0.695705 + 0.718327i \(0.255092\pi\)
\(860\) 0 0
\(861\) −16.6994 −0.569115
\(862\) 0 0
\(863\) −28.0998 −0.956530 −0.478265 0.878216i \(-0.658734\pi\)
−0.478265 + 0.878216i \(0.658734\pi\)
\(864\) 0 0
\(865\) 4.00866 0.136299
\(866\) 0 0
\(867\) −27.1608 −0.922428
\(868\) 0 0
\(869\) 21.6236 0.733531
\(870\) 0 0
\(871\) −67.4376 −2.28504
\(872\) 0 0
\(873\) 1.58790 0.0537423
\(874\) 0 0
\(875\) 1.05807 0.0357694
\(876\) 0 0
\(877\) 26.8497 0.906651 0.453326 0.891345i \(-0.350237\pi\)
0.453326 + 0.891345i \(0.350237\pi\)
\(878\) 0 0
\(879\) 51.1406 1.72493
\(880\) 0 0
\(881\) −7.85386 −0.264603 −0.132302 0.991210i \(-0.542237\pi\)
−0.132302 + 0.991210i \(0.542237\pi\)
\(882\) 0 0
\(883\) 25.0492 0.842971 0.421486 0.906835i \(-0.361509\pi\)
0.421486 + 0.906835i \(0.361509\pi\)
\(884\) 0 0
\(885\) 10.7790 0.362332
\(886\) 0 0
\(887\) 9.18602 0.308436 0.154218 0.988037i \(-0.450714\pi\)
0.154218 + 0.988037i \(0.450714\pi\)
\(888\) 0 0
\(889\) 16.3831 0.549471
\(890\) 0 0
\(891\) −14.9252 −0.500012
\(892\) 0 0
\(893\) −42.2151 −1.41268
\(894\) 0 0
\(895\) −9.16408 −0.306321
\(896\) 0 0
\(897\) 67.8188 2.26440
\(898\) 0 0
\(899\) 46.3857 1.54705
\(900\) 0 0
\(901\) 4.00367 0.133382
\(902\) 0 0
\(903\) 17.1151 0.569553
\(904\) 0 0
\(905\) 6.65788 0.221316
\(906\) 0 0
\(907\) 38.0734 1.26421 0.632103 0.774884i \(-0.282192\pi\)
0.632103 + 0.774884i \(0.282192\pi\)
\(908\) 0 0
\(909\) −5.18634 −0.172020
\(910\) 0 0
\(911\) 39.5816 1.31140 0.655699 0.755023i \(-0.272374\pi\)
0.655699 + 0.755023i \(0.272374\pi\)
\(912\) 0 0
\(913\) 10.3888 0.343819
\(914\) 0 0
\(915\) 12.4268 0.410816
\(916\) 0 0
\(917\) 4.63697 0.153126
\(918\) 0 0
\(919\) −50.9239 −1.67982 −0.839912 0.542722i \(-0.817394\pi\)
−0.839912 + 0.542722i \(0.817394\pi\)
\(920\) 0 0
\(921\) −48.8083 −1.60829
\(922\) 0 0
\(923\) 78.8316 2.59477
\(924\) 0 0
\(925\) −2.78935 −0.0917133
\(926\) 0 0
\(927\) −1.96712 −0.0646088
\(928\) 0 0
\(929\) −38.6584 −1.26834 −0.634171 0.773193i \(-0.718658\pi\)
−0.634171 + 0.773193i \(0.718658\pi\)
\(930\) 0 0
\(931\) −19.7224 −0.646374
\(932\) 0 0
\(933\) −3.09986 −0.101485
\(934\) 0 0
\(935\) −0.940156 −0.0307464
\(936\) 0 0
\(937\) 32.9374 1.07602 0.538009 0.842939i \(-0.319177\pi\)
0.538009 + 0.842939i \(0.319177\pi\)
\(938\) 0 0
\(939\) 22.0064 0.718152
\(940\) 0 0
\(941\) 3.09564 0.100915 0.0504575 0.998726i \(-0.483932\pi\)
0.0504575 + 0.998726i \(0.483932\pi\)
\(942\) 0 0
\(943\) 78.9240 2.57012
\(944\) 0 0
\(945\) −5.78540 −0.188199
\(946\) 0 0
\(947\) −42.0061 −1.36502 −0.682508 0.730878i \(-0.739111\pi\)
−0.682508 + 0.730878i \(0.739111\pi\)
\(948\) 0 0
\(949\) 28.0762 0.911391
\(950\) 0 0
\(951\) −32.3331 −1.04847
\(952\) 0 0
\(953\) 39.6327 1.28383 0.641915 0.766776i \(-0.278140\pi\)
0.641915 + 0.766776i \(0.278140\pi\)
\(954\) 0 0
\(955\) 4.25377 0.137649
\(956\) 0 0
\(957\) −15.8387 −0.511992
\(958\) 0 0
\(959\) −0.579477 −0.0187123
\(960\) 0 0
\(961\) 52.8169 1.70377
\(962\) 0 0
\(963\) −6.54415 −0.210882
\(964\) 0 0
\(965\) 12.2128 0.393145
\(966\) 0 0
\(967\) −12.1740 −0.391490 −0.195745 0.980655i \(-0.562713\pi\)
−0.195745 + 0.980655i \(0.562713\pi\)
\(968\) 0 0
\(969\) −2.64819 −0.0850723
\(970\) 0 0
\(971\) −49.8589 −1.60005 −0.800024 0.599968i \(-0.795180\pi\)
−0.800024 + 0.599968i \(0.795180\pi\)
\(972\) 0 0
\(973\) −10.1234 −0.324542
\(974\) 0 0
\(975\) −8.36999 −0.268054
\(976\) 0 0
\(977\) 0.957118 0.0306209 0.0153105 0.999883i \(-0.495126\pi\)
0.0153105 + 0.999883i \(0.495126\pi\)
\(978\) 0 0
\(979\) −9.95127 −0.318044
\(980\) 0 0
\(981\) 3.03836 0.0970074
\(982\) 0 0
\(983\) −24.3977 −0.778165 −0.389082 0.921203i \(-0.627208\pi\)
−0.389082 + 0.921203i \(0.627208\pi\)
\(984\) 0 0
\(985\) 15.0139 0.478383
\(986\) 0 0
\(987\) −21.5794 −0.686881
\(988\) 0 0
\(989\) −80.8883 −2.57210
\(990\) 0 0
\(991\) −37.0031 −1.17544 −0.587721 0.809064i \(-0.699975\pi\)
−0.587721 + 0.809064i \(0.699975\pi\)
\(992\) 0 0
\(993\) −6.49394 −0.206079
\(994\) 0 0
\(995\) 2.41316 0.0765022
\(996\) 0 0
\(997\) 15.3519 0.486199 0.243100 0.970001i \(-0.421836\pi\)
0.243100 + 0.970001i \(0.421836\pi\)
\(998\) 0 0
\(999\) 15.2518 0.482545
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 \(a_p\))