Properties

Label 8048.2.a.v.1.17
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.596863 q^{3}\) \(+3.74289 q^{5}\) \(-1.10831 q^{7}\) \(-2.64375 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.596863 q^{3}\) \(+3.74289 q^{5}\) \(-1.10831 q^{7}\) \(-2.64375 q^{9}\) \(+4.05435 q^{11}\) \(-6.28166 q^{13}\) \(+2.23399 q^{15}\) \(+3.42667 q^{17}\) \(-4.55414 q^{19}\) \(-0.661511 q^{21}\) \(+7.12930 q^{23}\) \(+9.00922 q^{25}\) \(-3.36855 q^{27}\) \(-7.58996 q^{29}\) \(-10.1526 q^{31}\) \(+2.41989 q^{33}\) \(-4.14829 q^{35}\) \(-10.9132 q^{37}\) \(-3.74929 q^{39}\) \(+4.41002 q^{41}\) \(-9.01601 q^{43}\) \(-9.89528 q^{45}\) \(-0.789928 q^{47}\) \(-5.77164 q^{49}\) \(+2.04525 q^{51}\) \(-12.5917 q^{53}\) \(+15.1750 q^{55}\) \(-2.71820 q^{57}\) \(-3.67098 q^{59}\) \(-12.4825 q^{61}\) \(+2.93010 q^{63}\) \(-23.5116 q^{65}\) \(+8.33923 q^{67}\) \(+4.25522 q^{69}\) \(+16.5483 q^{71}\) \(+13.9080 q^{73}\) \(+5.37727 q^{75}\) \(-4.49349 q^{77}\) \(-1.08841 q^{79}\) \(+5.92070 q^{81}\) \(+8.85350 q^{83}\) \(+12.8256 q^{85}\) \(-4.53017 q^{87}\) \(-13.8450 q^{89}\) \(+6.96204 q^{91}\) \(-6.05974 q^{93}\) \(-17.0456 q^{95}\) \(+7.23701 q^{97}\) \(-10.7187 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.596863 0.344599 0.172300 0.985045i \(-0.444880\pi\)
0.172300 + 0.985045i \(0.444880\pi\)
\(4\) 0 0
\(5\) 3.74289 1.67387 0.836936 0.547301i \(-0.184345\pi\)
0.836936 + 0.547301i \(0.184345\pi\)
\(6\) 0 0
\(7\) −1.10831 −0.418903 −0.209451 0.977819i \(-0.567168\pi\)
−0.209451 + 0.977819i \(0.567168\pi\)
\(8\) 0 0
\(9\) −2.64375 −0.881251
\(10\) 0 0
\(11\) 4.05435 1.22243 0.611216 0.791464i \(-0.290681\pi\)
0.611216 + 0.791464i \(0.290681\pi\)
\(12\) 0 0
\(13\) −6.28166 −1.74222 −0.871110 0.491088i \(-0.836599\pi\)
−0.871110 + 0.491088i \(0.836599\pi\)
\(14\) 0 0
\(15\) 2.23399 0.576815
\(16\) 0 0
\(17\) 3.42667 0.831089 0.415545 0.909573i \(-0.363591\pi\)
0.415545 + 0.909573i \(0.363591\pi\)
\(18\) 0 0
\(19\) −4.55414 −1.04479 −0.522395 0.852704i \(-0.674961\pi\)
−0.522395 + 0.852704i \(0.674961\pi\)
\(20\) 0 0
\(21\) −0.661511 −0.144353
\(22\) 0 0
\(23\) 7.12930 1.48656 0.743281 0.668980i \(-0.233269\pi\)
0.743281 + 0.668980i \(0.233269\pi\)
\(24\) 0 0
\(25\) 9.00922 1.80184
\(26\) 0 0
\(27\) −3.36855 −0.648278
\(28\) 0 0
\(29\) −7.58996 −1.40942 −0.704710 0.709495i \(-0.748923\pi\)
−0.704710 + 0.709495i \(0.748923\pi\)
\(30\) 0 0
\(31\) −10.1526 −1.82347 −0.911735 0.410779i \(-0.865257\pi\)
−0.911735 + 0.410779i \(0.865257\pi\)
\(32\) 0 0
\(33\) 2.41989 0.421249
\(34\) 0 0
\(35\) −4.14829 −0.701189
\(36\) 0 0
\(37\) −10.9132 −1.79413 −0.897063 0.441902i \(-0.854304\pi\)
−0.897063 + 0.441902i \(0.854304\pi\)
\(38\) 0 0
\(39\) −3.74929 −0.600368
\(40\) 0 0
\(41\) 4.41002 0.688730 0.344365 0.938836i \(-0.388094\pi\)
0.344365 + 0.938836i \(0.388094\pi\)
\(42\) 0 0
\(43\) −9.01601 −1.37493 −0.687464 0.726218i \(-0.741276\pi\)
−0.687464 + 0.726218i \(0.741276\pi\)
\(44\) 0 0
\(45\) −9.89528 −1.47510
\(46\) 0 0
\(47\) −0.789928 −0.115223 −0.0576115 0.998339i \(-0.518348\pi\)
−0.0576115 + 0.998339i \(0.518348\pi\)
\(48\) 0 0
\(49\) −5.77164 −0.824521
\(50\) 0 0
\(51\) 2.04525 0.286393
\(52\) 0 0
\(53\) −12.5917 −1.72960 −0.864799 0.502117i \(-0.832555\pi\)
−0.864799 + 0.502117i \(0.832555\pi\)
\(54\) 0 0
\(55\) 15.1750 2.04620
\(56\) 0 0
\(57\) −2.71820 −0.360034
\(58\) 0 0
\(59\) −3.67098 −0.477921 −0.238961 0.971029i \(-0.576807\pi\)
−0.238961 + 0.971029i \(0.576807\pi\)
\(60\) 0 0
\(61\) −12.4825 −1.59823 −0.799113 0.601181i \(-0.794697\pi\)
−0.799113 + 0.601181i \(0.794697\pi\)
\(62\) 0 0
\(63\) 2.93010 0.369158
\(64\) 0 0
\(65\) −23.5116 −2.91625
\(66\) 0 0
\(67\) 8.33923 1.01880 0.509400 0.860530i \(-0.329867\pi\)
0.509400 + 0.860530i \(0.329867\pi\)
\(68\) 0 0
\(69\) 4.25522 0.512268
\(70\) 0 0
\(71\) 16.5483 1.96392 0.981961 0.189084i \(-0.0605517\pi\)
0.981961 + 0.189084i \(0.0605517\pi\)
\(72\) 0 0
\(73\) 13.9080 1.62780 0.813902 0.581002i \(-0.197339\pi\)
0.813902 + 0.581002i \(0.197339\pi\)
\(74\) 0 0
\(75\) 5.37727 0.620914
\(76\) 0 0
\(77\) −4.49349 −0.512080
\(78\) 0 0
\(79\) −1.08841 −0.122456 −0.0612280 0.998124i \(-0.519502\pi\)
−0.0612280 + 0.998124i \(0.519502\pi\)
\(80\) 0 0
\(81\) 5.92070 0.657855
\(82\) 0 0
\(83\) 8.85350 0.971798 0.485899 0.874015i \(-0.338492\pi\)
0.485899 + 0.874015i \(0.338492\pi\)
\(84\) 0 0
\(85\) 12.8256 1.39114
\(86\) 0 0
\(87\) −4.53017 −0.485685
\(88\) 0 0
\(89\) −13.8450 −1.46757 −0.733784 0.679383i \(-0.762248\pi\)
−0.733784 + 0.679383i \(0.762248\pi\)
\(90\) 0 0
\(91\) 6.96204 0.729820
\(92\) 0 0
\(93\) −6.05974 −0.628366
\(94\) 0 0
\(95\) −17.0456 −1.74884
\(96\) 0 0
\(97\) 7.23701 0.734807 0.367403 0.930062i \(-0.380247\pi\)
0.367403 + 0.930062i \(0.380247\pi\)
\(98\) 0 0
\(99\) −10.7187 −1.07727
\(100\) 0 0
\(101\) −12.3018 −1.22407 −0.612036 0.790830i \(-0.709649\pi\)
−0.612036 + 0.790830i \(0.709649\pi\)
\(102\) 0 0
\(103\) 4.52046 0.445414 0.222707 0.974885i \(-0.428511\pi\)
0.222707 + 0.974885i \(0.428511\pi\)
\(104\) 0 0
\(105\) −2.47596 −0.241629
\(106\) 0 0
\(107\) −16.6723 −1.61177 −0.805886 0.592071i \(-0.798310\pi\)
−0.805886 + 0.592071i \(0.798310\pi\)
\(108\) 0 0
\(109\) −2.13728 −0.204714 −0.102357 0.994748i \(-0.532638\pi\)
−0.102357 + 0.994748i \(0.532638\pi\)
\(110\) 0 0
\(111\) −6.51372 −0.618255
\(112\) 0 0
\(113\) 3.98985 0.375334 0.187667 0.982233i \(-0.439907\pi\)
0.187667 + 0.982233i \(0.439907\pi\)
\(114\) 0 0
\(115\) 26.6842 2.48831
\(116\) 0 0
\(117\) 16.6072 1.53533
\(118\) 0 0
\(119\) −3.79782 −0.348145
\(120\) 0 0
\(121\) 5.43776 0.494342
\(122\) 0 0
\(123\) 2.63218 0.237336
\(124\) 0 0
\(125\) 15.0061 1.34218
\(126\) 0 0
\(127\) 10.6610 0.946008 0.473004 0.881060i \(-0.343170\pi\)
0.473004 + 0.881060i \(0.343170\pi\)
\(128\) 0 0
\(129\) −5.38132 −0.473799
\(130\) 0 0
\(131\) 8.97324 0.783996 0.391998 0.919966i \(-0.371784\pi\)
0.391998 + 0.919966i \(0.371784\pi\)
\(132\) 0 0
\(133\) 5.04740 0.437665
\(134\) 0 0
\(135\) −12.6081 −1.08513
\(136\) 0 0
\(137\) −15.1837 −1.29723 −0.648614 0.761117i \(-0.724651\pi\)
−0.648614 + 0.761117i \(0.724651\pi\)
\(138\) 0 0
\(139\) 11.0272 0.935315 0.467657 0.883910i \(-0.345098\pi\)
0.467657 + 0.883910i \(0.345098\pi\)
\(140\) 0 0
\(141\) −0.471479 −0.0397057
\(142\) 0 0
\(143\) −25.4681 −2.12975
\(144\) 0 0
\(145\) −28.4084 −2.35919
\(146\) 0 0
\(147\) −3.44488 −0.284129
\(148\) 0 0
\(149\) 5.53804 0.453694 0.226847 0.973930i \(-0.427158\pi\)
0.226847 + 0.973930i \(0.427158\pi\)
\(150\) 0 0
\(151\) 7.05565 0.574181 0.287090 0.957903i \(-0.407312\pi\)
0.287090 + 0.957903i \(0.407312\pi\)
\(152\) 0 0
\(153\) −9.05927 −0.732398
\(154\) 0 0
\(155\) −38.0002 −3.05225
\(156\) 0 0
\(157\) −14.7281 −1.17543 −0.587714 0.809069i \(-0.699972\pi\)
−0.587714 + 0.809069i \(0.699972\pi\)
\(158\) 0 0
\(159\) −7.51551 −0.596018
\(160\) 0 0
\(161\) −7.90149 −0.622724
\(162\) 0 0
\(163\) −12.3357 −0.966206 −0.483103 0.875563i \(-0.660490\pi\)
−0.483103 + 0.875563i \(0.660490\pi\)
\(164\) 0 0
\(165\) 9.05739 0.705117
\(166\) 0 0
\(167\) −8.22308 −0.636321 −0.318160 0.948037i \(-0.603065\pi\)
−0.318160 + 0.948037i \(0.603065\pi\)
\(168\) 0 0
\(169\) 26.4593 2.03533
\(170\) 0 0
\(171\) 12.0400 0.920723
\(172\) 0 0
\(173\) −4.10789 −0.312317 −0.156158 0.987732i \(-0.549911\pi\)
−0.156158 + 0.987732i \(0.549911\pi\)
\(174\) 0 0
\(175\) −9.98503 −0.754797
\(176\) 0 0
\(177\) −2.19107 −0.164691
\(178\) 0 0
\(179\) −11.4420 −0.855218 −0.427609 0.903964i \(-0.640644\pi\)
−0.427609 + 0.903964i \(0.640644\pi\)
\(180\) 0 0
\(181\) −2.82949 −0.210315 −0.105157 0.994456i \(-0.533535\pi\)
−0.105157 + 0.994456i \(0.533535\pi\)
\(182\) 0 0
\(183\) −7.45037 −0.550747
\(184\) 0 0
\(185\) −40.8471 −3.00314
\(186\) 0 0
\(187\) 13.8929 1.01595
\(188\) 0 0
\(189\) 3.73340 0.271565
\(190\) 0 0
\(191\) 11.8684 0.858770 0.429385 0.903122i \(-0.358730\pi\)
0.429385 + 0.903122i \(0.358730\pi\)
\(192\) 0 0
\(193\) 2.58302 0.185930 0.0929649 0.995669i \(-0.470366\pi\)
0.0929649 + 0.995669i \(0.470366\pi\)
\(194\) 0 0
\(195\) −14.0332 −1.00494
\(196\) 0 0
\(197\) 16.0693 1.14489 0.572444 0.819944i \(-0.305995\pi\)
0.572444 + 0.819944i \(0.305995\pi\)
\(198\) 0 0
\(199\) −18.5167 −1.31261 −0.656305 0.754495i \(-0.727882\pi\)
−0.656305 + 0.754495i \(0.727882\pi\)
\(200\) 0 0
\(201\) 4.97738 0.351077
\(202\) 0 0
\(203\) 8.41204 0.590410
\(204\) 0 0
\(205\) 16.5062 1.15285
\(206\) 0 0
\(207\) −18.8481 −1.31003
\(208\) 0 0
\(209\) −18.4641 −1.27719
\(210\) 0 0
\(211\) −12.0114 −0.826900 −0.413450 0.910527i \(-0.635676\pi\)
−0.413450 + 0.910527i \(0.635676\pi\)
\(212\) 0 0
\(213\) 9.87707 0.676766
\(214\) 0 0
\(215\) −33.7459 −2.30145
\(216\) 0 0
\(217\) 11.2523 0.763856
\(218\) 0 0
\(219\) 8.30115 0.560940
\(220\) 0 0
\(221\) −21.5252 −1.44794
\(222\) 0 0
\(223\) 4.53206 0.303489 0.151745 0.988420i \(-0.451511\pi\)
0.151745 + 0.988420i \(0.451511\pi\)
\(224\) 0 0
\(225\) −23.8182 −1.58788
\(226\) 0 0
\(227\) −8.77728 −0.582568 −0.291284 0.956637i \(-0.594083\pi\)
−0.291284 + 0.956637i \(0.594083\pi\)
\(228\) 0 0
\(229\) −21.7649 −1.43827 −0.719133 0.694873i \(-0.755461\pi\)
−0.719133 + 0.694873i \(0.755461\pi\)
\(230\) 0 0
\(231\) −2.68200 −0.176462
\(232\) 0 0
\(233\) 15.4379 1.01137 0.505685 0.862718i \(-0.331240\pi\)
0.505685 + 0.862718i \(0.331240\pi\)
\(234\) 0 0
\(235\) −2.95662 −0.192868
\(236\) 0 0
\(237\) −0.649634 −0.0421983
\(238\) 0 0
\(239\) −5.89595 −0.381377 −0.190689 0.981651i \(-0.561072\pi\)
−0.190689 + 0.981651i \(0.561072\pi\)
\(240\) 0 0
\(241\) 17.6126 1.13453 0.567264 0.823536i \(-0.308002\pi\)
0.567264 + 0.823536i \(0.308002\pi\)
\(242\) 0 0
\(243\) 13.6395 0.874974
\(244\) 0 0
\(245\) −21.6026 −1.38014
\(246\) 0 0
\(247\) 28.6075 1.82025
\(248\) 0 0
\(249\) 5.28433 0.334881
\(250\) 0 0
\(251\) 18.2226 1.15020 0.575101 0.818082i \(-0.304963\pi\)
0.575101 + 0.818082i \(0.304963\pi\)
\(252\) 0 0
\(253\) 28.9047 1.81722
\(254\) 0 0
\(255\) 7.65515 0.479384
\(256\) 0 0
\(257\) 2.00865 0.125296 0.0626479 0.998036i \(-0.480045\pi\)
0.0626479 + 0.998036i \(0.480045\pi\)
\(258\) 0 0
\(259\) 12.0953 0.751564
\(260\) 0 0
\(261\) 20.0660 1.24205
\(262\) 0 0
\(263\) 26.0383 1.60559 0.802794 0.596256i \(-0.203346\pi\)
0.802794 + 0.596256i \(0.203346\pi\)
\(264\) 0 0
\(265\) −47.1292 −2.89513
\(266\) 0 0
\(267\) −8.26358 −0.505723
\(268\) 0 0
\(269\) 25.7113 1.56764 0.783822 0.620985i \(-0.213267\pi\)
0.783822 + 0.620985i \(0.213267\pi\)
\(270\) 0 0
\(271\) 22.3375 1.35691 0.678453 0.734644i \(-0.262651\pi\)
0.678453 + 0.734644i \(0.262651\pi\)
\(272\) 0 0
\(273\) 4.15539 0.251496
\(274\) 0 0
\(275\) 36.5266 2.20263
\(276\) 0 0
\(277\) 12.0231 0.722396 0.361198 0.932489i \(-0.382368\pi\)
0.361198 + 0.932489i \(0.382368\pi\)
\(278\) 0 0
\(279\) 26.8411 1.60694
\(280\) 0 0
\(281\) −0.165606 −0.00987924 −0.00493962 0.999988i \(-0.501572\pi\)
−0.00493962 + 0.999988i \(0.501572\pi\)
\(282\) 0 0
\(283\) 9.10918 0.541484 0.270742 0.962652i \(-0.412731\pi\)
0.270742 + 0.962652i \(0.412731\pi\)
\(284\) 0 0
\(285\) −10.1739 −0.602650
\(286\) 0 0
\(287\) −4.88768 −0.288511
\(288\) 0 0
\(289\) −5.25794 −0.309291
\(290\) 0 0
\(291\) 4.31950 0.253214
\(292\) 0 0
\(293\) −4.00724 −0.234105 −0.117053 0.993126i \(-0.537345\pi\)
−0.117053 + 0.993126i \(0.537345\pi\)
\(294\) 0 0
\(295\) −13.7401 −0.799979
\(296\) 0 0
\(297\) −13.6573 −0.792476
\(298\) 0 0
\(299\) −44.7838 −2.58992
\(300\) 0 0
\(301\) 9.99255 0.575961
\(302\) 0 0
\(303\) −7.34248 −0.421814
\(304\) 0 0
\(305\) −46.7208 −2.67522
\(306\) 0 0
\(307\) 5.30062 0.302522 0.151261 0.988494i \(-0.451667\pi\)
0.151261 + 0.988494i \(0.451667\pi\)
\(308\) 0 0
\(309\) 2.69809 0.153489
\(310\) 0 0
\(311\) −11.9719 −0.678862 −0.339431 0.940631i \(-0.610235\pi\)
−0.339431 + 0.940631i \(0.610235\pi\)
\(312\) 0 0
\(313\) −19.9937 −1.13011 −0.565056 0.825053i \(-0.691145\pi\)
−0.565056 + 0.825053i \(0.691145\pi\)
\(314\) 0 0
\(315\) 10.9671 0.617924
\(316\) 0 0
\(317\) −9.46272 −0.531479 −0.265740 0.964045i \(-0.585616\pi\)
−0.265740 + 0.964045i \(0.585616\pi\)
\(318\) 0 0
\(319\) −30.7724 −1.72292
\(320\) 0 0
\(321\) −9.95108 −0.555415
\(322\) 0 0
\(323\) −15.6055 −0.868314
\(324\) 0 0
\(325\) −56.5929 −3.13921
\(326\) 0 0
\(327\) −1.27567 −0.0705444
\(328\) 0 0
\(329\) 0.875487 0.0482672
\(330\) 0 0
\(331\) −12.7619 −0.701459 −0.350730 0.936477i \(-0.614066\pi\)
−0.350730 + 0.936477i \(0.614066\pi\)
\(332\) 0 0
\(333\) 28.8519 1.58108
\(334\) 0 0
\(335\) 31.2128 1.70534
\(336\) 0 0
\(337\) 5.84959 0.318648 0.159324 0.987226i \(-0.449069\pi\)
0.159324 + 0.987226i \(0.449069\pi\)
\(338\) 0 0
\(339\) 2.38140 0.129340
\(340\) 0 0
\(341\) −41.1624 −2.22907
\(342\) 0 0
\(343\) 14.1550 0.764296
\(344\) 0 0
\(345\) 15.9268 0.857470
\(346\) 0 0
\(347\) 10.7771 0.578548 0.289274 0.957246i \(-0.406586\pi\)
0.289274 + 0.957246i \(0.406586\pi\)
\(348\) 0 0
\(349\) 7.48714 0.400777 0.200389 0.979716i \(-0.435780\pi\)
0.200389 + 0.979716i \(0.435780\pi\)
\(350\) 0 0
\(351\) 21.1601 1.12944
\(352\) 0 0
\(353\) −18.8339 −1.00243 −0.501215 0.865323i \(-0.667113\pi\)
−0.501215 + 0.865323i \(0.667113\pi\)
\(354\) 0 0
\(355\) 61.9385 3.28735
\(356\) 0 0
\(357\) −2.26678 −0.119971
\(358\) 0 0
\(359\) 19.4047 1.02414 0.512070 0.858944i \(-0.328879\pi\)
0.512070 + 0.858944i \(0.328879\pi\)
\(360\) 0 0
\(361\) 1.74015 0.0915867
\(362\) 0 0
\(363\) 3.24560 0.170350
\(364\) 0 0
\(365\) 52.0560 2.72473
\(366\) 0 0
\(367\) 10.7684 0.562108 0.281054 0.959692i \(-0.409316\pi\)
0.281054 + 0.959692i \(0.409316\pi\)
\(368\) 0 0
\(369\) −11.6590 −0.606944
\(370\) 0 0
\(371\) 13.9555 0.724533
\(372\) 0 0
\(373\) −12.6677 −0.655910 −0.327955 0.944693i \(-0.606359\pi\)
−0.327955 + 0.944693i \(0.606359\pi\)
\(374\) 0 0
\(375\) 8.95658 0.462516
\(376\) 0 0
\(377\) 47.6776 2.45552
\(378\) 0 0
\(379\) −27.0510 −1.38952 −0.694759 0.719243i \(-0.744489\pi\)
−0.694759 + 0.719243i \(0.744489\pi\)
\(380\) 0 0
\(381\) 6.36314 0.325993
\(382\) 0 0
\(383\) −25.0428 −1.27963 −0.639813 0.768531i \(-0.720988\pi\)
−0.639813 + 0.768531i \(0.720988\pi\)
\(384\) 0 0
\(385\) −16.8186 −0.857156
\(386\) 0 0
\(387\) 23.8361 1.21166
\(388\) 0 0
\(389\) 15.2476 0.773085 0.386543 0.922272i \(-0.373669\pi\)
0.386543 + 0.922272i \(0.373669\pi\)
\(390\) 0 0
\(391\) 24.4297 1.23546
\(392\) 0 0
\(393\) 5.35580 0.270164
\(394\) 0 0
\(395\) −4.07381 −0.204976
\(396\) 0 0
\(397\) 11.9551 0.600007 0.300004 0.953938i \(-0.403012\pi\)
0.300004 + 0.953938i \(0.403012\pi\)
\(398\) 0 0
\(399\) 3.01261 0.150819
\(400\) 0 0
\(401\) −4.83325 −0.241361 −0.120680 0.992691i \(-0.538508\pi\)
−0.120680 + 0.992691i \(0.538508\pi\)
\(402\) 0 0
\(403\) 63.7755 3.17689
\(404\) 0 0
\(405\) 22.1605 1.10117
\(406\) 0 0
\(407\) −44.2461 −2.19320
\(408\) 0 0
\(409\) −18.7528 −0.927264 −0.463632 0.886028i \(-0.653454\pi\)
−0.463632 + 0.886028i \(0.653454\pi\)
\(410\) 0 0
\(411\) −9.06258 −0.447024
\(412\) 0 0
\(413\) 4.06859 0.200202
\(414\) 0 0
\(415\) 33.1377 1.62666
\(416\) 0 0
\(417\) 6.58173 0.322309
\(418\) 0 0
\(419\) 6.75926 0.330211 0.165106 0.986276i \(-0.447203\pi\)
0.165106 + 0.986276i \(0.447203\pi\)
\(420\) 0 0
\(421\) −23.9070 −1.16515 −0.582577 0.812775i \(-0.697956\pi\)
−0.582577 + 0.812775i \(0.697956\pi\)
\(422\) 0 0
\(423\) 2.08838 0.101540
\(424\) 0 0
\(425\) 30.8716 1.49749
\(426\) 0 0
\(427\) 13.8346 0.669501
\(428\) 0 0
\(429\) −15.2010 −0.733909
\(430\) 0 0
\(431\) −22.0435 −1.06180 −0.530899 0.847435i \(-0.678146\pi\)
−0.530899 + 0.847435i \(0.678146\pi\)
\(432\) 0 0
\(433\) 7.78620 0.374181 0.187090 0.982343i \(-0.440094\pi\)
0.187090 + 0.982343i \(0.440094\pi\)
\(434\) 0 0
\(435\) −16.9559 −0.812974
\(436\) 0 0
\(437\) −32.4678 −1.55314
\(438\) 0 0
\(439\) −15.7303 −0.750766 −0.375383 0.926870i \(-0.622489\pi\)
−0.375383 + 0.926870i \(0.622489\pi\)
\(440\) 0 0
\(441\) 15.2588 0.726610
\(442\) 0 0
\(443\) 16.1674 0.768135 0.384068 0.923305i \(-0.374523\pi\)
0.384068 + 0.923305i \(0.374523\pi\)
\(444\) 0 0
\(445\) −51.8204 −2.45652
\(446\) 0 0
\(447\) 3.30546 0.156343
\(448\) 0 0
\(449\) 37.0269 1.74741 0.873703 0.486460i \(-0.161712\pi\)
0.873703 + 0.486460i \(0.161712\pi\)
\(450\) 0 0
\(451\) 17.8798 0.841926
\(452\) 0 0
\(453\) 4.21126 0.197862
\(454\) 0 0
\(455\) 26.0582 1.22163
\(456\) 0 0
\(457\) 0.144604 0.00676429 0.00338214 0.999994i \(-0.498923\pi\)
0.00338214 + 0.999994i \(0.498923\pi\)
\(458\) 0 0
\(459\) −11.5429 −0.538777
\(460\) 0 0
\(461\) −6.52018 −0.303675 −0.151837 0.988405i \(-0.548519\pi\)
−0.151837 + 0.988405i \(0.548519\pi\)
\(462\) 0 0
\(463\) −26.2598 −1.22039 −0.610197 0.792250i \(-0.708910\pi\)
−0.610197 + 0.792250i \(0.708910\pi\)
\(464\) 0 0
\(465\) −22.6810 −1.05180
\(466\) 0 0
\(467\) −26.3872 −1.22105 −0.610527 0.791996i \(-0.709042\pi\)
−0.610527 + 0.791996i \(0.709042\pi\)
\(468\) 0 0
\(469\) −9.24247 −0.426778
\(470\) 0 0
\(471\) −8.79064 −0.405052
\(472\) 0 0
\(473\) −36.5541 −1.68076
\(474\) 0 0
\(475\) −41.0292 −1.88255
\(476\) 0 0
\(477\) 33.2893 1.52421
\(478\) 0 0
\(479\) −22.9251 −1.04747 −0.523736 0.851880i \(-0.675462\pi\)
−0.523736 + 0.851880i \(0.675462\pi\)
\(480\) 0 0
\(481\) 68.5533 3.12576
\(482\) 0 0
\(483\) −4.71611 −0.214590
\(484\) 0 0
\(485\) 27.0873 1.22997
\(486\) 0 0
\(487\) −9.95964 −0.451314 −0.225657 0.974207i \(-0.572453\pi\)
−0.225657 + 0.974207i \(0.572453\pi\)
\(488\) 0 0
\(489\) −7.36272 −0.332954
\(490\) 0 0
\(491\) 3.65342 0.164877 0.0824384 0.996596i \(-0.473729\pi\)
0.0824384 + 0.996596i \(0.473729\pi\)
\(492\) 0 0
\(493\) −26.0083 −1.17135
\(494\) 0 0
\(495\) −40.1189 −1.80321
\(496\) 0 0
\(497\) −18.3407 −0.822692
\(498\) 0 0
\(499\) −27.8117 −1.24502 −0.622511 0.782611i \(-0.713887\pi\)
−0.622511 + 0.782611i \(0.713887\pi\)
\(500\) 0 0
\(501\) −4.90805 −0.219276
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −46.0442 −2.04894
\(506\) 0 0
\(507\) 15.7926 0.701373
\(508\) 0 0
\(509\) −1.97937 −0.0877341 −0.0438671 0.999037i \(-0.513968\pi\)
−0.0438671 + 0.999037i \(0.513968\pi\)
\(510\) 0 0
\(511\) −15.4144 −0.681891
\(512\) 0 0
\(513\) 15.3408 0.677314
\(514\) 0 0
\(515\) 16.9196 0.745565
\(516\) 0 0
\(517\) −3.20265 −0.140852
\(518\) 0 0
\(519\) −2.45185 −0.107624
\(520\) 0 0
\(521\) −7.35762 −0.322343 −0.161172 0.986926i \(-0.551527\pi\)
−0.161172 + 0.986926i \(0.551527\pi\)
\(522\) 0 0
\(523\) −7.94830 −0.347555 −0.173778 0.984785i \(-0.555597\pi\)
−0.173778 + 0.984785i \(0.555597\pi\)
\(524\) 0 0
\(525\) −5.95970 −0.260103
\(526\) 0 0
\(527\) −34.7898 −1.51547
\(528\) 0 0
\(529\) 27.8269 1.20986
\(530\) 0 0
\(531\) 9.70517 0.421169
\(532\) 0 0
\(533\) −27.7023 −1.19992
\(534\) 0 0
\(535\) −62.4026 −2.69790
\(536\) 0 0
\(537\) −6.82933 −0.294707
\(538\) 0 0
\(539\) −23.4003 −1.00792
\(540\) 0 0
\(541\) −19.4451 −0.836009 −0.418005 0.908445i \(-0.637270\pi\)
−0.418005 + 0.908445i \(0.637270\pi\)
\(542\) 0 0
\(543\) −1.68882 −0.0724742
\(544\) 0 0
\(545\) −7.99961 −0.342666
\(546\) 0 0
\(547\) −13.4460 −0.574907 −0.287454 0.957795i \(-0.592809\pi\)
−0.287454 + 0.957795i \(0.592809\pi\)
\(548\) 0 0
\(549\) 33.0008 1.40844
\(550\) 0 0
\(551\) 34.5657 1.47255
\(552\) 0 0
\(553\) 1.20630 0.0512972
\(554\) 0 0
\(555\) −24.3801 −1.03488
\(556\) 0 0
\(557\) −20.3211 −0.861032 −0.430516 0.902583i \(-0.641668\pi\)
−0.430516 + 0.902583i \(0.641668\pi\)
\(558\) 0 0
\(559\) 56.6355 2.39543
\(560\) 0 0
\(561\) 8.29217 0.350096
\(562\) 0 0
\(563\) 16.8840 0.711576 0.355788 0.934567i \(-0.384212\pi\)
0.355788 + 0.934567i \(0.384212\pi\)
\(564\) 0 0
\(565\) 14.9336 0.628260
\(566\) 0 0
\(567\) −6.56198 −0.275577
\(568\) 0 0
\(569\) 14.8114 0.620928 0.310464 0.950585i \(-0.399516\pi\)
0.310464 + 0.950585i \(0.399516\pi\)
\(570\) 0 0
\(571\) −20.4136 −0.854284 −0.427142 0.904185i \(-0.640480\pi\)
−0.427142 + 0.904185i \(0.640480\pi\)
\(572\) 0 0
\(573\) 7.08384 0.295931
\(574\) 0 0
\(575\) 64.2294 2.67855
\(576\) 0 0
\(577\) 4.09712 0.170565 0.0852827 0.996357i \(-0.472821\pi\)
0.0852827 + 0.996357i \(0.472821\pi\)
\(578\) 0 0
\(579\) 1.54171 0.0640712
\(580\) 0 0
\(581\) −9.81244 −0.407089
\(582\) 0 0
\(583\) −51.0511 −2.11432
\(584\) 0 0
\(585\) 62.1588 2.56995
\(586\) 0 0
\(587\) −12.5359 −0.517412 −0.258706 0.965956i \(-0.583296\pi\)
−0.258706 + 0.965956i \(0.583296\pi\)
\(588\) 0 0
\(589\) 46.2365 1.90514
\(590\) 0 0
\(591\) 9.59116 0.394528
\(592\) 0 0
\(593\) 17.2115 0.706793 0.353396 0.935474i \(-0.385027\pi\)
0.353396 + 0.935474i \(0.385027\pi\)
\(594\) 0 0
\(595\) −14.2148 −0.582751
\(596\) 0 0
\(597\) −11.0519 −0.452325
\(598\) 0 0
\(599\) −6.04421 −0.246960 −0.123480 0.992347i \(-0.539405\pi\)
−0.123480 + 0.992347i \(0.539405\pi\)
\(600\) 0 0
\(601\) 43.0009 1.75404 0.877021 0.480452i \(-0.159527\pi\)
0.877021 + 0.480452i \(0.159527\pi\)
\(602\) 0 0
\(603\) −22.0469 −0.897818
\(604\) 0 0
\(605\) 20.3529 0.827465
\(606\) 0 0
\(607\) −9.34473 −0.379291 −0.189645 0.981853i \(-0.560734\pi\)
−0.189645 + 0.981853i \(0.560734\pi\)
\(608\) 0 0
\(609\) 5.02084 0.203455
\(610\) 0 0
\(611\) 4.96207 0.200744
\(612\) 0 0
\(613\) 23.2822 0.940360 0.470180 0.882570i \(-0.344189\pi\)
0.470180 + 0.882570i \(0.344189\pi\)
\(614\) 0 0
\(615\) 9.85196 0.397270
\(616\) 0 0
\(617\) −32.8413 −1.32214 −0.661071 0.750324i \(-0.729898\pi\)
−0.661071 + 0.750324i \(0.729898\pi\)
\(618\) 0 0
\(619\) −9.26759 −0.372496 −0.186248 0.982503i \(-0.559633\pi\)
−0.186248 + 0.982503i \(0.559633\pi\)
\(620\) 0 0
\(621\) −24.0154 −0.963705
\(622\) 0 0
\(623\) 15.3446 0.614768
\(624\) 0 0
\(625\) 11.1200 0.444800
\(626\) 0 0
\(627\) −11.0205 −0.440117
\(628\) 0 0
\(629\) −37.3961 −1.49108
\(630\) 0 0
\(631\) 7.74843 0.308460 0.154230 0.988035i \(-0.450710\pi\)
0.154230 + 0.988035i \(0.450710\pi\)
\(632\) 0 0
\(633\) −7.16917 −0.284949
\(634\) 0 0
\(635\) 39.9028 1.58349
\(636\) 0 0
\(637\) 36.2555 1.43650
\(638\) 0 0
\(639\) −43.7496 −1.73071
\(640\) 0 0
\(641\) −29.2774 −1.15639 −0.578193 0.815900i \(-0.696242\pi\)
−0.578193 + 0.815900i \(0.696242\pi\)
\(642\) 0 0
\(643\) 24.5922 0.969824 0.484912 0.874563i \(-0.338852\pi\)
0.484912 + 0.874563i \(0.338852\pi\)
\(644\) 0 0
\(645\) −20.1417 −0.793079
\(646\) 0 0
\(647\) 22.5557 0.886758 0.443379 0.896334i \(-0.353780\pi\)
0.443379 + 0.896334i \(0.353780\pi\)
\(648\) 0 0
\(649\) −14.8835 −0.584227
\(650\) 0 0
\(651\) 6.71609 0.263224
\(652\) 0 0
\(653\) 7.45203 0.291621 0.145810 0.989313i \(-0.453421\pi\)
0.145810 + 0.989313i \(0.453421\pi\)
\(654\) 0 0
\(655\) 33.5858 1.31231
\(656\) 0 0
\(657\) −36.7692 −1.43450
\(658\) 0 0
\(659\) −1.23818 −0.0482326 −0.0241163 0.999709i \(-0.507677\pi\)
−0.0241163 + 0.999709i \(0.507677\pi\)
\(660\) 0 0
\(661\) 38.7457 1.50703 0.753517 0.657428i \(-0.228356\pi\)
0.753517 + 0.657428i \(0.228356\pi\)
\(662\) 0 0
\(663\) −12.8476 −0.498959
\(664\) 0 0
\(665\) 18.8919 0.732595
\(666\) 0 0
\(667\) −54.1111 −2.09519
\(668\) 0 0
\(669\) 2.70502 0.104582
\(670\) 0 0
\(671\) −50.6086 −1.95372
\(672\) 0 0
\(673\) −2.29534 −0.0884788 −0.0442394 0.999021i \(-0.514086\pi\)
−0.0442394 + 0.999021i \(0.514086\pi\)
\(674\) 0 0
\(675\) −30.3480 −1.16810
\(676\) 0 0
\(677\) 30.9949 1.19123 0.595615 0.803270i \(-0.296908\pi\)
0.595615 + 0.803270i \(0.296908\pi\)
\(678\) 0 0
\(679\) −8.02086 −0.307812
\(680\) 0 0
\(681\) −5.23884 −0.200753
\(682\) 0 0
\(683\) 12.6566 0.484290 0.242145 0.970240i \(-0.422149\pi\)
0.242145 + 0.970240i \(0.422149\pi\)
\(684\) 0 0
\(685\) −56.8308 −2.17139
\(686\) 0 0
\(687\) −12.9907 −0.495625
\(688\) 0 0
\(689\) 79.0966 3.01334
\(690\) 0 0
\(691\) 47.5327 1.80823 0.904114 0.427291i \(-0.140532\pi\)
0.904114 + 0.427291i \(0.140532\pi\)
\(692\) 0 0
\(693\) 11.8797 0.451271
\(694\) 0 0
\(695\) 41.2736 1.56560
\(696\) 0 0
\(697\) 15.1117 0.572396
\(698\) 0 0
\(699\) 9.21431 0.348517
\(700\) 0 0
\(701\) −41.1521 −1.55429 −0.777147 0.629319i \(-0.783334\pi\)
−0.777147 + 0.629319i \(0.783334\pi\)
\(702\) 0 0
\(703\) 49.7004 1.87449
\(704\) 0 0
\(705\) −1.76470 −0.0664623
\(706\) 0 0
\(707\) 13.6342 0.512767
\(708\) 0 0
\(709\) 5.55047 0.208452 0.104226 0.994554i \(-0.466763\pi\)
0.104226 + 0.994554i \(0.466763\pi\)
\(710\) 0 0
\(711\) 2.87750 0.107915
\(712\) 0 0
\(713\) −72.3813 −2.71070
\(714\) 0 0
\(715\) −95.3242 −3.56492
\(716\) 0 0
\(717\) −3.51908 −0.131422
\(718\) 0 0
\(719\) −14.0126 −0.522583 −0.261291 0.965260i \(-0.584148\pi\)
−0.261291 + 0.965260i \(0.584148\pi\)
\(720\) 0 0
\(721\) −5.01007 −0.186585
\(722\) 0 0
\(723\) 10.5123 0.390958
\(724\) 0 0
\(725\) −68.3796 −2.53956
\(726\) 0 0
\(727\) 0.112833 0.00418476 0.00209238 0.999998i \(-0.499334\pi\)
0.00209238 + 0.999998i \(0.499334\pi\)
\(728\) 0 0
\(729\) −9.62118 −0.356340
\(730\) 0 0
\(731\) −30.8949 −1.14269
\(732\) 0 0
\(733\) 22.0094 0.812935 0.406467 0.913665i \(-0.366760\pi\)
0.406467 + 0.913665i \(0.366760\pi\)
\(734\) 0 0
\(735\) −12.8938 −0.475596
\(736\) 0 0
\(737\) 33.8102 1.24541
\(738\) 0 0
\(739\) 4.05841 0.149291 0.0746455 0.997210i \(-0.476217\pi\)
0.0746455 + 0.997210i \(0.476217\pi\)
\(740\) 0 0
\(741\) 17.0748 0.627258
\(742\) 0 0
\(743\) −18.6795 −0.685283 −0.342642 0.939466i \(-0.611322\pi\)
−0.342642 + 0.939466i \(0.611322\pi\)
\(744\) 0 0
\(745\) 20.7283 0.759426
\(746\) 0 0
\(747\) −23.4065 −0.856398
\(748\) 0 0
\(749\) 18.4781 0.675175
\(750\) 0 0
\(751\) 37.8836 1.38239 0.691196 0.722667i \(-0.257084\pi\)
0.691196 + 0.722667i \(0.257084\pi\)
\(752\) 0 0
\(753\) 10.8764 0.396359
\(754\) 0 0
\(755\) 26.4085 0.961105
\(756\) 0 0
\(757\) −26.3896 −0.959146 −0.479573 0.877502i \(-0.659208\pi\)
−0.479573 + 0.877502i \(0.659208\pi\)
\(758\) 0 0
\(759\) 17.2521 0.626213
\(760\) 0 0
\(761\) 47.4889 1.72147 0.860736 0.509052i \(-0.170004\pi\)
0.860736 + 0.509052i \(0.170004\pi\)
\(762\) 0 0
\(763\) 2.36878 0.0857554
\(764\) 0 0
\(765\) −33.9078 −1.22594
\(766\) 0 0
\(767\) 23.0599 0.832644
\(768\) 0 0
\(769\) −22.1250 −0.797849 −0.398924 0.916984i \(-0.630616\pi\)
−0.398924 + 0.916984i \(0.630616\pi\)
\(770\) 0 0
\(771\) 1.19889 0.0431769
\(772\) 0 0
\(773\) −4.70020 −0.169054 −0.0845272 0.996421i \(-0.526938\pi\)
−0.0845272 + 0.996421i \(0.526938\pi\)
\(774\) 0 0
\(775\) −91.4675 −3.28561
\(776\) 0 0
\(777\) 7.21923 0.258988
\(778\) 0 0
\(779\) −20.0838 −0.719578
\(780\) 0 0
\(781\) 67.0926 2.40076
\(782\) 0 0
\(783\) 25.5672 0.913696
\(784\) 0 0
\(785\) −55.1255 −1.96751
\(786\) 0 0
\(787\) 5.97274 0.212905 0.106453 0.994318i \(-0.466051\pi\)
0.106453 + 0.994318i \(0.466051\pi\)
\(788\) 0 0
\(789\) 15.5413 0.553284
\(790\) 0 0
\(791\) −4.42200 −0.157228
\(792\) 0 0
\(793\) 78.4111 2.78446
\(794\) 0 0
\(795\) −28.1297 −0.997658
\(796\) 0 0
\(797\) −13.7237 −0.486120 −0.243060 0.970011i \(-0.578151\pi\)
−0.243060 + 0.970011i \(0.578151\pi\)
\(798\) 0 0
\(799\) −2.70682 −0.0957605
\(800\) 0 0
\(801\) 36.6028 1.29330
\(802\) 0 0
\(803\) 56.3878 1.98988
\(804\) 0 0
\(805\) −29.5744 −1.04236
\(806\) 0 0
\(807\) 15.3461 0.540209
\(808\) 0 0
\(809\) −44.2563 −1.55597 −0.777985 0.628283i \(-0.783758\pi\)
−0.777985 + 0.628283i \(0.783758\pi\)
\(810\) 0 0
\(811\) −47.3816 −1.66379 −0.831896 0.554932i \(-0.812744\pi\)
−0.831896 + 0.554932i \(0.812744\pi\)
\(812\) 0 0
\(813\) 13.3324 0.467589
\(814\) 0 0
\(815\) −46.1712 −1.61730
\(816\) 0 0
\(817\) 41.0601 1.43651
\(818\) 0 0
\(819\) −18.4059 −0.643155
\(820\) 0 0
\(821\) −11.7955 −0.411666 −0.205833 0.978587i \(-0.565990\pi\)
−0.205833 + 0.978587i \(0.565990\pi\)
\(822\) 0 0
\(823\) −2.96953 −0.103511 −0.0517557 0.998660i \(-0.516482\pi\)
−0.0517557 + 0.998660i \(0.516482\pi\)
\(824\) 0 0
\(825\) 21.8014 0.759026
\(826\) 0 0
\(827\) −23.7782 −0.826850 −0.413425 0.910538i \(-0.635668\pi\)
−0.413425 + 0.910538i \(0.635668\pi\)
\(828\) 0 0
\(829\) −14.6100 −0.507426 −0.253713 0.967280i \(-0.581652\pi\)
−0.253713 + 0.967280i \(0.581652\pi\)
\(830\) 0 0
\(831\) 7.17613 0.248937
\(832\) 0 0
\(833\) −19.7775 −0.685250
\(834\) 0 0
\(835\) −30.7781 −1.06512
\(836\) 0 0
\(837\) 34.1997 1.18211
\(838\) 0 0
\(839\) 22.2987 0.769836 0.384918 0.922951i \(-0.374230\pi\)
0.384918 + 0.922951i \(0.374230\pi\)
\(840\) 0 0
\(841\) 28.6075 0.986465
\(842\) 0 0
\(843\) −0.0988443 −0.00340438
\(844\) 0 0
\(845\) 99.0342 3.40688
\(846\) 0 0
\(847\) −6.02674 −0.207081
\(848\) 0 0
\(849\) 5.43693 0.186595
\(850\) 0 0
\(851\) −77.8038 −2.66708
\(852\) 0 0
\(853\) 25.6780 0.879199 0.439599 0.898194i \(-0.355120\pi\)
0.439599 + 0.898194i \(0.355120\pi\)
\(854\) 0 0
\(855\) 45.0644 1.54117
\(856\) 0 0
\(857\) −0.639804 −0.0218553 −0.0109276 0.999940i \(-0.503478\pi\)
−0.0109276 + 0.999940i \(0.503478\pi\)
\(858\) 0 0
\(859\) −15.2690 −0.520973 −0.260486 0.965478i \(-0.583883\pi\)
−0.260486 + 0.965478i \(0.583883\pi\)
\(860\) 0 0
\(861\) −2.91728 −0.0994206
\(862\) 0 0
\(863\) −9.05247 −0.308150 −0.154075 0.988059i \(-0.549240\pi\)
−0.154075 + 0.988059i \(0.549240\pi\)
\(864\) 0 0
\(865\) −15.3754 −0.522778
\(866\) 0 0
\(867\) −3.13827 −0.106581
\(868\) 0 0
\(869\) −4.41281 −0.149694
\(870\) 0 0
\(871\) −52.3843 −1.77497
\(872\) 0 0
\(873\) −19.1329 −0.647549
\(874\) 0 0
\(875\) −16.6314 −0.562245
\(876\) 0 0
\(877\) −20.7534 −0.700793 −0.350397 0.936601i \(-0.613953\pi\)
−0.350397 + 0.936601i \(0.613953\pi\)
\(878\) 0 0
\(879\) −2.39177 −0.0806725
\(880\) 0 0
\(881\) −31.1931 −1.05092 −0.525461 0.850818i \(-0.676107\pi\)
−0.525461 + 0.850818i \(0.676107\pi\)
\(882\) 0 0
\(883\) −11.1829 −0.376333 −0.188167 0.982137i \(-0.560255\pi\)
−0.188167 + 0.982137i \(0.560255\pi\)
\(884\) 0 0
\(885\) −8.20095 −0.275672
\(886\) 0 0
\(887\) 9.12495 0.306386 0.153193 0.988196i \(-0.451044\pi\)
0.153193 + 0.988196i \(0.451044\pi\)
\(888\) 0 0
\(889\) −11.8157 −0.396285
\(890\) 0 0
\(891\) 24.0046 0.804184
\(892\) 0 0
\(893\) 3.59744 0.120384
\(894\) 0 0
\(895\) −42.8263 −1.43152
\(896\) 0 0
\(897\) −26.7298 −0.892483
\(898\) 0 0
\(899\) 77.0582 2.57003
\(900\) 0 0
\(901\) −43.1475 −1.43745
\(902\) 0 0
\(903\) 5.96419 0.198476
\(904\) 0 0
\(905\) −10.5905 −0.352039
\(906\) 0 0
\(907\) −43.2911 −1.43746 −0.718728 0.695291i \(-0.755275\pi\)
−0.718728 + 0.695291i \(0.755275\pi\)
\(908\) 0 0
\(909\) 32.5229 1.07872
\(910\) 0 0
\(911\) 5.88679 0.195038 0.0975190 0.995234i \(-0.468909\pi\)
0.0975190 + 0.995234i \(0.468909\pi\)
\(912\) 0 0
\(913\) 35.8952 1.18796
\(914\) 0 0
\(915\) −27.8859 −0.921880
\(916\) 0 0
\(917\) −9.94515 −0.328418
\(918\) 0 0
\(919\) 52.5637 1.73392 0.866958 0.498380i \(-0.166072\pi\)
0.866958 + 0.498380i \(0.166072\pi\)
\(920\) 0 0
\(921\) 3.16374 0.104249
\(922\) 0 0
\(923\) −103.951 −3.42158
\(924\) 0 0
\(925\) −98.3199 −3.23274
\(926\) 0 0
\(927\) −11.9510 −0.392521
\(928\) 0 0
\(929\) 38.5702 1.26545 0.632724 0.774378i \(-0.281937\pi\)
0.632724 + 0.774378i \(0.281937\pi\)
\(930\) 0 0
\(931\) 26.2848 0.861451
\(932\) 0 0
\(933\) −7.14557 −0.233935
\(934\) 0 0
\(935\) 51.9997 1.70057
\(936\) 0 0
\(937\) 48.6182 1.58829 0.794144 0.607729i \(-0.207919\pi\)
0.794144 + 0.607729i \(0.207919\pi\)
\(938\) 0 0
\(939\) −11.9335 −0.389436
\(940\) 0 0
\(941\) 30.3489 0.989346 0.494673 0.869079i \(-0.335288\pi\)
0.494673 + 0.869079i \(0.335288\pi\)
\(942\) 0 0
\(943\) 31.4404 1.02384
\(944\) 0 0
\(945\) 13.9737 0.454565
\(946\) 0 0
\(947\) −50.4765 −1.64027 −0.820133 0.572172i \(-0.806101\pi\)
−0.820133 + 0.572172i \(0.806101\pi\)
\(948\) 0 0
\(949\) −87.3651 −2.83599
\(950\) 0 0
\(951\) −5.64795 −0.183147
\(952\) 0 0
\(953\) 5.77733 0.187146 0.0935731 0.995612i \(-0.470171\pi\)
0.0935731 + 0.995612i \(0.470171\pi\)
\(954\) 0 0
\(955\) 44.4223 1.43747
\(956\) 0 0
\(957\) −18.3669 −0.593717
\(958\) 0 0
\(959\) 16.8282 0.543412
\(960\) 0 0
\(961\) 72.0763 2.32504
\(962\) 0 0
\(963\) 44.0774 1.42038
\(964\) 0 0
\(965\) 9.66795 0.311222
\(966\) 0 0
\(967\) 12.2393 0.393588 0.196794 0.980445i \(-0.436947\pi\)
0.196794 + 0.980445i \(0.436947\pi\)
\(968\) 0 0
\(969\) −9.31436 −0.299220
\(970\) 0 0
\(971\) 12.9154 0.414476 0.207238 0.978291i \(-0.433553\pi\)
0.207238 + 0.978291i \(0.433553\pi\)
\(972\) 0 0
\(973\) −12.2216 −0.391806
\(974\) 0 0
\(975\) −33.7782 −1.08177
\(976\) 0 0
\(977\) 17.5065 0.560084 0.280042 0.959988i \(-0.409652\pi\)
0.280042 + 0.959988i \(0.409652\pi\)
\(978\) 0 0
\(979\) −56.1325 −1.79400
\(980\) 0 0
\(981\) 5.65045 0.180405
\(982\) 0 0
\(983\) −7.14983 −0.228044 −0.114022 0.993478i \(-0.536373\pi\)
−0.114022 + 0.993478i \(0.536373\pi\)
\(984\) 0 0
\(985\) 60.1455 1.91640
\(986\) 0 0
\(987\) 0.522546 0.0166328
\(988\) 0 0
\(989\) −64.2778 −2.04392
\(990\) 0 0
\(991\) −42.8989 −1.36273 −0.681364 0.731945i \(-0.738613\pi\)
−0.681364 + 0.731945i \(0.738613\pi\)
\(992\) 0 0
\(993\) −7.61713 −0.241722
\(994\) 0 0
\(995\) −69.3058 −2.19714
\(996\) 0 0
\(997\) −32.1968 −1.01968 −0.509842 0.860268i \(-0.670296\pi\)
−0.509842 + 0.860268i \(0.670296\pi\)
\(998\) 0 0
\(999\) 36.7618 1.16309
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 \(a_p\))