Properties

Label 8040.2.a.t.1.6
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 1.6
Root \(-2.84959\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(+4.47701 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(+4.47701 q^{7}\) \(+1.00000 q^{9}\) \(+3.66054 q^{11}\) \(+3.81438 q^{13}\) \(-1.00000 q^{15}\) \(-6.96978 q^{17}\) \(-0.0738657 q^{19}\) \(+4.47701 q^{21}\) \(-7.13234 q^{23}\) \(+1.00000 q^{25}\) \(+1.00000 q^{27}\) \(+0.538723 q^{29}\) \(+2.70128 q^{31}\) \(+3.66054 q^{33}\) \(-4.47701 q^{35}\) \(+8.36592 q^{37}\) \(+3.81438 q^{39}\) \(-0.701282 q^{41}\) \(+10.9467 q^{43}\) \(-1.00000 q^{45}\) \(+2.26292 q^{47}\) \(+13.0436 q^{49}\) \(-6.96978 q^{51}\) \(+1.74875 q^{53}\) \(-3.66054 q^{55}\) \(-0.0738657 q^{57}\) \(+0.807367 q^{59}\) \(-4.46218 q^{61}\) \(+4.47701 q^{63}\) \(-3.81438 q^{65}\) \(+1.00000 q^{67}\) \(-7.13234 q^{69}\) \(-4.11630 q^{71}\) \(-1.83177 q^{73}\) \(+1.00000 q^{75}\) \(+16.3883 q^{77}\) \(+4.17995 q^{79}\) \(+1.00000 q^{81}\) \(+3.56198 q^{83}\) \(+6.96978 q^{85}\) \(+0.538723 q^{87}\) \(+8.57170 q^{89}\) \(+17.0770 q^{91}\) \(+2.70128 q^{93}\) \(+0.0738657 q^{95}\) \(+9.19906 q^{97}\) \(+3.66054 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut 7q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 23q^{37} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 13q^{53} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut q^{65} \) \(\mathstrut +\mathstrut 7q^{67} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 25q^{79} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 29q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut q^{87} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut +\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 9q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(7\) 4.47701 1.69215 0.846075 0.533063i \(-0.178959\pi\)
0.846075 + 0.533063i \(0.178959\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.66054 1.10369 0.551847 0.833945i \(-0.313923\pi\)
0.551847 + 0.833945i \(0.313923\pi\)
\(12\) 0 0
\(13\) 3.81438 1.05792 0.528959 0.848648i \(-0.322583\pi\)
0.528959 + 0.848648i \(0.322583\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −6.96978 −1.69042 −0.845210 0.534434i \(-0.820525\pi\)
−0.845210 + 0.534434i \(0.820525\pi\)
\(18\) 0 0
\(19\) −0.0738657 −0.0169459 −0.00847297 0.999964i \(-0.502697\pi\)
−0.00847297 + 0.999964i \(0.502697\pi\)
\(20\) 0 0
\(21\) 4.47701 0.976964
\(22\) 0 0
\(23\) −7.13234 −1.48720 −0.743598 0.668627i \(-0.766882\pi\)
−0.743598 + 0.668627i \(0.766882\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.538723 0.100038 0.0500192 0.998748i \(-0.484072\pi\)
0.0500192 + 0.998748i \(0.484072\pi\)
\(30\) 0 0
\(31\) 2.70128 0.485165 0.242582 0.970131i \(-0.422006\pi\)
0.242582 + 0.970131i \(0.422006\pi\)
\(32\) 0 0
\(33\) 3.66054 0.637218
\(34\) 0 0
\(35\) −4.47701 −0.756753
\(36\) 0 0
\(37\) 8.36592 1.37535 0.687674 0.726020i \(-0.258632\pi\)
0.687674 + 0.726020i \(0.258632\pi\)
\(38\) 0 0
\(39\) 3.81438 0.610789
\(40\) 0 0
\(41\) −0.701282 −0.109522 −0.0547609 0.998499i \(-0.517440\pi\)
−0.0547609 + 0.998499i \(0.517440\pi\)
\(42\) 0 0
\(43\) 10.9467 1.66936 0.834679 0.550737i \(-0.185653\pi\)
0.834679 + 0.550737i \(0.185653\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 2.26292 0.330081 0.165040 0.986287i \(-0.447225\pi\)
0.165040 + 0.986287i \(0.447225\pi\)
\(48\) 0 0
\(49\) 13.0436 1.86337
\(50\) 0 0
\(51\) −6.96978 −0.975964
\(52\) 0 0
\(53\) 1.74875 0.240209 0.120105 0.992761i \(-0.461677\pi\)
0.120105 + 0.992761i \(0.461677\pi\)
\(54\) 0 0
\(55\) −3.66054 −0.493587
\(56\) 0 0
\(57\) −0.0738657 −0.00978375
\(58\) 0 0
\(59\) 0.807367 0.105110 0.0525551 0.998618i \(-0.483263\pi\)
0.0525551 + 0.998618i \(0.483263\pi\)
\(60\) 0 0
\(61\) −4.46218 −0.571324 −0.285662 0.958330i \(-0.592213\pi\)
−0.285662 + 0.958330i \(0.592213\pi\)
\(62\) 0 0
\(63\) 4.47701 0.564050
\(64\) 0 0
\(65\) −3.81438 −0.473115
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) −7.13234 −0.858633
\(70\) 0 0
\(71\) −4.11630 −0.488515 −0.244257 0.969710i \(-0.578544\pi\)
−0.244257 + 0.969710i \(0.578544\pi\)
\(72\) 0 0
\(73\) −1.83177 −0.214392 −0.107196 0.994238i \(-0.534187\pi\)
−0.107196 + 0.994238i \(0.534187\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 16.3883 1.86762
\(78\) 0 0
\(79\) 4.17995 0.470281 0.235141 0.971961i \(-0.424445\pi\)
0.235141 + 0.971961i \(0.424445\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.56198 0.390978 0.195489 0.980706i \(-0.437371\pi\)
0.195489 + 0.980706i \(0.437371\pi\)
\(84\) 0 0
\(85\) 6.96978 0.755979
\(86\) 0 0
\(87\) 0.538723 0.0577572
\(88\) 0 0
\(89\) 8.57170 0.908598 0.454299 0.890849i \(-0.349890\pi\)
0.454299 + 0.890849i \(0.349890\pi\)
\(90\) 0 0
\(91\) 17.0770 1.79016
\(92\) 0 0
\(93\) 2.70128 0.280110
\(94\) 0 0
\(95\) 0.0738657 0.00757846
\(96\) 0 0
\(97\) 9.19906 0.934023 0.467012 0.884251i \(-0.345331\pi\)
0.467012 + 0.884251i \(0.345331\pi\)
\(98\) 0 0
\(99\) 3.66054 0.367898
\(100\) 0 0
\(101\) 0.553173 0.0550428 0.0275214 0.999621i \(-0.491239\pi\)
0.0275214 + 0.999621i \(0.491239\pi\)
\(102\) 0 0
\(103\) −8.79837 −0.866930 −0.433465 0.901170i \(-0.642709\pi\)
−0.433465 + 0.901170i \(0.642709\pi\)
\(104\) 0 0
\(105\) −4.47701 −0.436911
\(106\) 0 0
\(107\) −17.3544 −1.67772 −0.838858 0.544350i \(-0.816776\pi\)
−0.838858 + 0.544350i \(0.816776\pi\)
\(108\) 0 0
\(109\) 5.89757 0.564885 0.282443 0.959284i \(-0.408855\pi\)
0.282443 + 0.959284i \(0.408855\pi\)
\(110\) 0 0
\(111\) 8.36592 0.794058
\(112\) 0 0
\(113\) 14.1199 1.32829 0.664146 0.747603i \(-0.268795\pi\)
0.664146 + 0.747603i \(0.268795\pi\)
\(114\) 0 0
\(115\) 7.13234 0.665094
\(116\) 0 0
\(117\) 3.81438 0.352639
\(118\) 0 0
\(119\) −31.2038 −2.86045
\(120\) 0 0
\(121\) 2.39956 0.218142
\(122\) 0 0
\(123\) −0.701282 −0.0632324
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 1.15524 0.102511 0.0512556 0.998686i \(-0.483678\pi\)
0.0512556 + 0.998686i \(0.483678\pi\)
\(128\) 0 0
\(129\) 10.9467 0.963804
\(130\) 0 0
\(131\) −11.2772 −0.985298 −0.492649 0.870228i \(-0.663971\pi\)
−0.492649 + 0.870228i \(0.663971\pi\)
\(132\) 0 0
\(133\) −0.330697 −0.0286751
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 16.9837 1.45102 0.725509 0.688213i \(-0.241604\pi\)
0.725509 + 0.688213i \(0.241604\pi\)
\(138\) 0 0
\(139\) 13.1266 1.11338 0.556692 0.830719i \(-0.312070\pi\)
0.556692 + 0.830719i \(0.312070\pi\)
\(140\) 0 0
\(141\) 2.26292 0.190572
\(142\) 0 0
\(143\) 13.9627 1.16762
\(144\) 0 0
\(145\) −0.538723 −0.0447385
\(146\) 0 0
\(147\) 13.0436 1.07582
\(148\) 0 0
\(149\) 11.3420 0.929170 0.464585 0.885529i \(-0.346204\pi\)
0.464585 + 0.885529i \(0.346204\pi\)
\(150\) 0 0
\(151\) −10.0048 −0.814183 −0.407091 0.913387i \(-0.633457\pi\)
−0.407091 + 0.913387i \(0.633457\pi\)
\(152\) 0 0
\(153\) −6.96978 −0.563473
\(154\) 0 0
\(155\) −2.70128 −0.216972
\(156\) 0 0
\(157\) −11.3646 −0.906992 −0.453496 0.891258i \(-0.649823\pi\)
−0.453496 + 0.891258i \(0.649823\pi\)
\(158\) 0 0
\(159\) 1.74875 0.138685
\(160\) 0 0
\(161\) −31.9316 −2.51656
\(162\) 0 0
\(163\) −18.0171 −1.41121 −0.705604 0.708607i \(-0.749324\pi\)
−0.705604 + 0.708607i \(0.749324\pi\)
\(164\) 0 0
\(165\) −3.66054 −0.284973
\(166\) 0 0
\(167\) 4.40114 0.340570 0.170285 0.985395i \(-0.445531\pi\)
0.170285 + 0.985395i \(0.445531\pi\)
\(168\) 0 0
\(169\) 1.54946 0.119189
\(170\) 0 0
\(171\) −0.0738657 −0.00564865
\(172\) 0 0
\(173\) 10.7769 0.819350 0.409675 0.912232i \(-0.365642\pi\)
0.409675 + 0.912232i \(0.365642\pi\)
\(174\) 0 0
\(175\) 4.47701 0.338430
\(176\) 0 0
\(177\) 0.807367 0.0606854
\(178\) 0 0
\(179\) 11.8254 0.883870 0.441935 0.897047i \(-0.354292\pi\)
0.441935 + 0.897047i \(0.354292\pi\)
\(180\) 0 0
\(181\) −7.20241 −0.535351 −0.267675 0.963509i \(-0.586256\pi\)
−0.267675 + 0.963509i \(0.586256\pi\)
\(182\) 0 0
\(183\) −4.46218 −0.329854
\(184\) 0 0
\(185\) −8.36592 −0.615074
\(186\) 0 0
\(187\) −25.5132 −1.86571
\(188\) 0 0
\(189\) 4.47701 0.325655
\(190\) 0 0
\(191\) −16.1036 −1.16522 −0.582608 0.812753i \(-0.697968\pi\)
−0.582608 + 0.812753i \(0.697968\pi\)
\(192\) 0 0
\(193\) −11.7082 −0.842774 −0.421387 0.906881i \(-0.638457\pi\)
−0.421387 + 0.906881i \(0.638457\pi\)
\(194\) 0 0
\(195\) −3.81438 −0.273153
\(196\) 0 0
\(197\) 2.23632 0.159331 0.0796655 0.996822i \(-0.474615\pi\)
0.0796655 + 0.996822i \(0.474615\pi\)
\(198\) 0 0
\(199\) −21.7620 −1.54266 −0.771332 0.636433i \(-0.780409\pi\)
−0.771332 + 0.636433i \(0.780409\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) 2.41187 0.169280
\(204\) 0 0
\(205\) 0.701282 0.0489796
\(206\) 0 0
\(207\) −7.13234 −0.495732
\(208\) 0 0
\(209\) −0.270388 −0.0187032
\(210\) 0 0
\(211\) −0.840526 −0.0578642 −0.0289321 0.999581i \(-0.509211\pi\)
−0.0289321 + 0.999581i \(0.509211\pi\)
\(212\) 0 0
\(213\) −4.11630 −0.282044
\(214\) 0 0
\(215\) −10.9467 −0.746560
\(216\) 0 0
\(217\) 12.0937 0.820971
\(218\) 0 0
\(219\) −1.83177 −0.123779
\(220\) 0 0
\(221\) −26.5854 −1.78832
\(222\) 0 0
\(223\) 12.0649 0.807927 0.403964 0.914775i \(-0.367632\pi\)
0.403964 + 0.914775i \(0.367632\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 21.4614 1.42444 0.712222 0.701954i \(-0.247689\pi\)
0.712222 + 0.701954i \(0.247689\pi\)
\(228\) 0 0
\(229\) 3.73690 0.246941 0.123471 0.992348i \(-0.460598\pi\)
0.123471 + 0.992348i \(0.460598\pi\)
\(230\) 0 0
\(231\) 16.3883 1.07827
\(232\) 0 0
\(233\) −23.9633 −1.56989 −0.784945 0.619566i \(-0.787309\pi\)
−0.784945 + 0.619566i \(0.787309\pi\)
\(234\) 0 0
\(235\) −2.26292 −0.147617
\(236\) 0 0
\(237\) 4.17995 0.271517
\(238\) 0 0
\(239\) −4.11678 −0.266293 −0.133146 0.991096i \(-0.542508\pi\)
−0.133146 + 0.991096i \(0.542508\pi\)
\(240\) 0 0
\(241\) −24.3695 −1.56978 −0.784888 0.619638i \(-0.787279\pi\)
−0.784888 + 0.619638i \(0.787279\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −13.0436 −0.833326
\(246\) 0 0
\(247\) −0.281751 −0.0179274
\(248\) 0 0
\(249\) 3.56198 0.225731
\(250\) 0 0
\(251\) 21.5904 1.36277 0.681387 0.731924i \(-0.261377\pi\)
0.681387 + 0.731924i \(0.261377\pi\)
\(252\) 0 0
\(253\) −26.1082 −1.64141
\(254\) 0 0
\(255\) 6.96978 0.436465
\(256\) 0 0
\(257\) 20.1990 1.25998 0.629989 0.776604i \(-0.283059\pi\)
0.629989 + 0.776604i \(0.283059\pi\)
\(258\) 0 0
\(259\) 37.4543 2.32730
\(260\) 0 0
\(261\) 0.538723 0.0333461
\(262\) 0 0
\(263\) −2.28006 −0.140594 −0.0702972 0.997526i \(-0.522395\pi\)
−0.0702972 + 0.997526i \(0.522395\pi\)
\(264\) 0 0
\(265\) −1.74875 −0.107425
\(266\) 0 0
\(267\) 8.57170 0.524579
\(268\) 0 0
\(269\) 3.40768 0.207770 0.103885 0.994589i \(-0.466873\pi\)
0.103885 + 0.994589i \(0.466873\pi\)
\(270\) 0 0
\(271\) 31.2376 1.89755 0.948776 0.315951i \(-0.102323\pi\)
0.948776 + 0.315951i \(0.102323\pi\)
\(272\) 0 0
\(273\) 17.0770 1.03355
\(274\) 0 0
\(275\) 3.66054 0.220739
\(276\) 0 0
\(277\) 14.8526 0.892404 0.446202 0.894932i \(-0.352776\pi\)
0.446202 + 0.894932i \(0.352776\pi\)
\(278\) 0 0
\(279\) 2.70128 0.161722
\(280\) 0 0
\(281\) −9.64114 −0.575142 −0.287571 0.957759i \(-0.592848\pi\)
−0.287571 + 0.957759i \(0.592848\pi\)
\(282\) 0 0
\(283\) −13.4963 −0.802269 −0.401135 0.916019i \(-0.631384\pi\)
−0.401135 + 0.916019i \(0.631384\pi\)
\(284\) 0 0
\(285\) 0.0738657 0.00437542
\(286\) 0 0
\(287\) −3.13965 −0.185327
\(288\) 0 0
\(289\) 31.5778 1.85752
\(290\) 0 0
\(291\) 9.19906 0.539258
\(292\) 0 0
\(293\) 26.4275 1.54391 0.771957 0.635675i \(-0.219278\pi\)
0.771957 + 0.635675i \(0.219278\pi\)
\(294\) 0 0
\(295\) −0.807367 −0.0470067
\(296\) 0 0
\(297\) 3.66054 0.212406
\(298\) 0 0
\(299\) −27.2054 −1.57333
\(300\) 0 0
\(301\) 49.0085 2.82481
\(302\) 0 0
\(303\) 0.553173 0.0317790
\(304\) 0 0
\(305\) 4.46218 0.255504
\(306\) 0 0
\(307\) −12.9674 −0.740089 −0.370045 0.929014i \(-0.620658\pi\)
−0.370045 + 0.929014i \(0.620658\pi\)
\(308\) 0 0
\(309\) −8.79837 −0.500522
\(310\) 0 0
\(311\) 12.8951 0.731212 0.365606 0.930770i \(-0.380862\pi\)
0.365606 + 0.930770i \(0.380862\pi\)
\(312\) 0 0
\(313\) −0.760285 −0.0429739 −0.0214869 0.999769i \(-0.506840\pi\)
−0.0214869 + 0.999769i \(0.506840\pi\)
\(314\) 0 0
\(315\) −4.47701 −0.252251
\(316\) 0 0
\(317\) −20.9773 −1.17820 −0.589102 0.808059i \(-0.700518\pi\)
−0.589102 + 0.808059i \(0.700518\pi\)
\(318\) 0 0
\(319\) 1.97202 0.110412
\(320\) 0 0
\(321\) −17.3544 −0.968630
\(322\) 0 0
\(323\) 0.514827 0.0286458
\(324\) 0 0
\(325\) 3.81438 0.211583
\(326\) 0 0
\(327\) 5.89757 0.326137
\(328\) 0 0
\(329\) 10.1311 0.558546
\(330\) 0 0
\(331\) 14.2592 0.783757 0.391879 0.920017i \(-0.371825\pi\)
0.391879 + 0.920017i \(0.371825\pi\)
\(332\) 0 0
\(333\) 8.36592 0.458449
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) 2.54691 0.138739 0.0693695 0.997591i \(-0.477901\pi\)
0.0693695 + 0.997591i \(0.477901\pi\)
\(338\) 0 0
\(339\) 14.1199 0.766890
\(340\) 0 0
\(341\) 9.88815 0.535474
\(342\) 0 0
\(343\) 27.0573 1.46096
\(344\) 0 0
\(345\) 7.13234 0.383992
\(346\) 0 0
\(347\) −29.2444 −1.56992 −0.784960 0.619547i \(-0.787316\pi\)
−0.784960 + 0.619547i \(0.787316\pi\)
\(348\) 0 0
\(349\) 4.54414 0.243242 0.121621 0.992577i \(-0.461191\pi\)
0.121621 + 0.992577i \(0.461191\pi\)
\(350\) 0 0
\(351\) 3.81438 0.203596
\(352\) 0 0
\(353\) −23.3749 −1.24412 −0.622059 0.782970i \(-0.713704\pi\)
−0.622059 + 0.782970i \(0.713704\pi\)
\(354\) 0 0
\(355\) 4.11630 0.218470
\(356\) 0 0
\(357\) −31.2038 −1.65148
\(358\) 0 0
\(359\) −31.2550 −1.64958 −0.824788 0.565442i \(-0.808706\pi\)
−0.824788 + 0.565442i \(0.808706\pi\)
\(360\) 0 0
\(361\) −18.9945 −0.999713
\(362\) 0 0
\(363\) 2.39956 0.125944
\(364\) 0 0
\(365\) 1.83177 0.0958791
\(366\) 0 0
\(367\) −4.48696 −0.234218 −0.117109 0.993119i \(-0.537363\pi\)
−0.117109 + 0.993119i \(0.537363\pi\)
\(368\) 0 0
\(369\) −0.701282 −0.0365073
\(370\) 0 0
\(371\) 7.82917 0.406470
\(372\) 0 0
\(373\) 5.35029 0.277027 0.138514 0.990361i \(-0.455768\pi\)
0.138514 + 0.990361i \(0.455768\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 2.05489 0.105832
\(378\) 0 0
\(379\) 20.3794 1.04682 0.523409 0.852082i \(-0.324660\pi\)
0.523409 + 0.852082i \(0.324660\pi\)
\(380\) 0 0
\(381\) 1.15524 0.0591848
\(382\) 0 0
\(383\) 13.9367 0.712131 0.356065 0.934461i \(-0.384118\pi\)
0.356065 + 0.934461i \(0.384118\pi\)
\(384\) 0 0
\(385\) −16.3883 −0.835224
\(386\) 0 0
\(387\) 10.9467 0.556453
\(388\) 0 0
\(389\) −6.34967 −0.321941 −0.160971 0.986959i \(-0.551462\pi\)
−0.160971 + 0.986959i \(0.551462\pi\)
\(390\) 0 0
\(391\) 49.7108 2.51398
\(392\) 0 0
\(393\) −11.2772 −0.568862
\(394\) 0 0
\(395\) −4.17995 −0.210316
\(396\) 0 0
\(397\) −22.1296 −1.11065 −0.555325 0.831633i \(-0.687406\pi\)
−0.555325 + 0.831633i \(0.687406\pi\)
\(398\) 0 0
\(399\) −0.330697 −0.0165556
\(400\) 0 0
\(401\) 6.79478 0.339315 0.169658 0.985503i \(-0.445734\pi\)
0.169658 + 0.985503i \(0.445734\pi\)
\(402\) 0 0
\(403\) 10.3037 0.513264
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 30.6238 1.51796
\(408\) 0 0
\(409\) −7.68364 −0.379932 −0.189966 0.981791i \(-0.560838\pi\)
−0.189966 + 0.981791i \(0.560838\pi\)
\(410\) 0 0
\(411\) 16.9837 0.837746
\(412\) 0 0
\(413\) 3.61459 0.177862
\(414\) 0 0
\(415\) −3.56198 −0.174851
\(416\) 0 0
\(417\) 13.1266 0.642813
\(418\) 0 0
\(419\) 27.4364 1.34036 0.670179 0.742200i \(-0.266217\pi\)
0.670179 + 0.742200i \(0.266217\pi\)
\(420\) 0 0
\(421\) −0.859225 −0.0418761 −0.0209380 0.999781i \(-0.506665\pi\)
−0.0209380 + 0.999781i \(0.506665\pi\)
\(422\) 0 0
\(423\) 2.26292 0.110027
\(424\) 0 0
\(425\) −6.96978 −0.338084
\(426\) 0 0
\(427\) −19.9772 −0.966766
\(428\) 0 0
\(429\) 13.9627 0.674124
\(430\) 0 0
\(431\) 34.8375 1.67806 0.839032 0.544082i \(-0.183122\pi\)
0.839032 + 0.544082i \(0.183122\pi\)
\(432\) 0 0
\(433\) −21.1636 −1.01706 −0.508529 0.861045i \(-0.669810\pi\)
−0.508529 + 0.861045i \(0.669810\pi\)
\(434\) 0 0
\(435\) −0.538723 −0.0258298
\(436\) 0 0
\(437\) 0.526835 0.0252019
\(438\) 0 0
\(439\) 35.1116 1.67579 0.837893 0.545835i \(-0.183787\pi\)
0.837893 + 0.545835i \(0.183787\pi\)
\(440\) 0 0
\(441\) 13.0436 0.621125
\(442\) 0 0
\(443\) −0.532835 −0.0253158 −0.0126579 0.999920i \(-0.504029\pi\)
−0.0126579 + 0.999920i \(0.504029\pi\)
\(444\) 0 0
\(445\) −8.57170 −0.406337
\(446\) 0 0
\(447\) 11.3420 0.536456
\(448\) 0 0
\(449\) 7.04264 0.332363 0.166181 0.986095i \(-0.446856\pi\)
0.166181 + 0.986095i \(0.446856\pi\)
\(450\) 0 0
\(451\) −2.56707 −0.120879
\(452\) 0 0
\(453\) −10.0048 −0.470069
\(454\) 0 0
\(455\) −17.0770 −0.800582
\(456\) 0 0
\(457\) 8.31756 0.389079 0.194540 0.980895i \(-0.437679\pi\)
0.194540 + 0.980895i \(0.437679\pi\)
\(458\) 0 0
\(459\) −6.96978 −0.325321
\(460\) 0 0
\(461\) 23.0483 1.07347 0.536733 0.843752i \(-0.319658\pi\)
0.536733 + 0.843752i \(0.319658\pi\)
\(462\) 0 0
\(463\) 14.8080 0.688186 0.344093 0.938936i \(-0.388186\pi\)
0.344093 + 0.938936i \(0.388186\pi\)
\(464\) 0 0
\(465\) −2.70128 −0.125269
\(466\) 0 0
\(467\) 40.1110 1.85611 0.928057 0.372438i \(-0.121478\pi\)
0.928057 + 0.372438i \(0.121478\pi\)
\(468\) 0 0
\(469\) 4.47701 0.206729
\(470\) 0 0
\(471\) −11.3646 −0.523652
\(472\) 0 0
\(473\) 40.0709 1.84246
\(474\) 0 0
\(475\) −0.0738657 −0.00338919
\(476\) 0 0
\(477\) 1.74875 0.0800697
\(478\) 0 0
\(479\) −26.8175 −1.22532 −0.612662 0.790345i \(-0.709901\pi\)
−0.612662 + 0.790345i \(0.709901\pi\)
\(480\) 0 0
\(481\) 31.9107 1.45500
\(482\) 0 0
\(483\) −31.9316 −1.45294
\(484\) 0 0
\(485\) −9.19906 −0.417708
\(486\) 0 0
\(487\) 37.0018 1.67671 0.838355 0.545124i \(-0.183517\pi\)
0.838355 + 0.545124i \(0.183517\pi\)
\(488\) 0 0
\(489\) −18.0171 −0.814761
\(490\) 0 0
\(491\) 8.43305 0.380578 0.190289 0.981728i \(-0.439057\pi\)
0.190289 + 0.981728i \(0.439057\pi\)
\(492\) 0 0
\(493\) −3.75478 −0.169107
\(494\) 0 0
\(495\) −3.66054 −0.164529
\(496\) 0 0
\(497\) −18.4287 −0.826640
\(498\) 0 0
\(499\) −17.9648 −0.804214 −0.402107 0.915593i \(-0.631722\pi\)
−0.402107 + 0.915593i \(0.631722\pi\)
\(500\) 0 0
\(501\) 4.40114 0.196628
\(502\) 0 0
\(503\) −16.6984 −0.744546 −0.372273 0.928123i \(-0.621421\pi\)
−0.372273 + 0.928123i \(0.621421\pi\)
\(504\) 0 0
\(505\) −0.553173 −0.0246159
\(506\) 0 0
\(507\) 1.54946 0.0688138
\(508\) 0 0
\(509\) 20.9368 0.928006 0.464003 0.885834i \(-0.346413\pi\)
0.464003 + 0.885834i \(0.346413\pi\)
\(510\) 0 0
\(511\) −8.20084 −0.362784
\(512\) 0 0
\(513\) −0.0738657 −0.00326125
\(514\) 0 0
\(515\) 8.79837 0.387703
\(516\) 0 0
\(517\) 8.28351 0.364308
\(518\) 0 0
\(519\) 10.7769 0.473052
\(520\) 0 0
\(521\) −3.56844 −0.156336 −0.0781681 0.996940i \(-0.524907\pi\)
−0.0781681 + 0.996940i \(0.524907\pi\)
\(522\) 0 0
\(523\) −11.4821 −0.502077 −0.251039 0.967977i \(-0.580772\pi\)
−0.251039 + 0.967977i \(0.580772\pi\)
\(524\) 0 0
\(525\) 4.47701 0.195393
\(526\) 0 0
\(527\) −18.8273 −0.820132
\(528\) 0 0
\(529\) 27.8703 1.21175
\(530\) 0 0
\(531\) 0.807367 0.0350367
\(532\) 0 0
\(533\) −2.67495 −0.115865
\(534\) 0 0
\(535\) 17.3544 0.750298
\(536\) 0 0
\(537\) 11.8254 0.510303
\(538\) 0 0
\(539\) 47.7467 2.05660
\(540\) 0 0
\(541\) −33.6718 −1.44766 −0.723832 0.689977i \(-0.757621\pi\)
−0.723832 + 0.689977i \(0.757621\pi\)
\(542\) 0 0
\(543\) −7.20241 −0.309085
\(544\) 0 0
\(545\) −5.89757 −0.252624
\(546\) 0 0
\(547\) −37.7650 −1.61472 −0.807358 0.590062i \(-0.799103\pi\)
−0.807358 + 0.590062i \(0.799103\pi\)
\(548\) 0 0
\(549\) −4.46218 −0.190441
\(550\) 0 0
\(551\) −0.0397931 −0.00169525
\(552\) 0 0
\(553\) 18.7137 0.795787
\(554\) 0 0
\(555\) −8.36592 −0.355113
\(556\) 0 0
\(557\) −32.3987 −1.37278 −0.686388 0.727236i \(-0.740805\pi\)
−0.686388 + 0.727236i \(0.740805\pi\)
\(558\) 0 0
\(559\) 41.7549 1.76604
\(560\) 0 0
\(561\) −25.5132 −1.07717
\(562\) 0 0
\(563\) 45.1969 1.90482 0.952411 0.304818i \(-0.0985956\pi\)
0.952411 + 0.304818i \(0.0985956\pi\)
\(564\) 0 0
\(565\) −14.1199 −0.594031
\(566\) 0 0
\(567\) 4.47701 0.188017
\(568\) 0 0
\(569\) −26.9752 −1.13086 −0.565429 0.824797i \(-0.691290\pi\)
−0.565429 + 0.824797i \(0.691290\pi\)
\(570\) 0 0
\(571\) −19.6813 −0.823639 −0.411819 0.911266i \(-0.635107\pi\)
−0.411819 + 0.911266i \(0.635107\pi\)
\(572\) 0 0
\(573\) −16.1036 −0.672738
\(574\) 0 0
\(575\) −7.13234 −0.297439
\(576\) 0 0
\(577\) 35.2013 1.46545 0.732724 0.680526i \(-0.238248\pi\)
0.732724 + 0.680526i \(0.238248\pi\)
\(578\) 0 0
\(579\) −11.7082 −0.486576
\(580\) 0 0
\(581\) 15.9470 0.661593
\(582\) 0 0
\(583\) 6.40137 0.265118
\(584\) 0 0
\(585\) −3.81438 −0.157705
\(586\) 0 0
\(587\) −36.4737 −1.50543 −0.752715 0.658346i \(-0.771256\pi\)
−0.752715 + 0.658346i \(0.771256\pi\)
\(588\) 0 0
\(589\) −0.199532 −0.00822157
\(590\) 0 0
\(591\) 2.23632 0.0919897
\(592\) 0 0
\(593\) −8.44653 −0.346857 −0.173429 0.984846i \(-0.555485\pi\)
−0.173429 + 0.984846i \(0.555485\pi\)
\(594\) 0 0
\(595\) 31.2038 1.27923
\(596\) 0 0
\(597\) −21.7620 −0.890658
\(598\) 0 0
\(599\) 1.24306 0.0507899 0.0253949 0.999677i \(-0.491916\pi\)
0.0253949 + 0.999677i \(0.491916\pi\)
\(600\) 0 0
\(601\) −22.9241 −0.935092 −0.467546 0.883969i \(-0.654862\pi\)
−0.467546 + 0.883969i \(0.654862\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) −2.39956 −0.0975561
\(606\) 0 0
\(607\) 18.8576 0.765405 0.382703 0.923872i \(-0.374993\pi\)
0.382703 + 0.923872i \(0.374993\pi\)
\(608\) 0 0
\(609\) 2.41187 0.0977339
\(610\) 0 0
\(611\) 8.63162 0.349198
\(612\) 0 0
\(613\) −31.9288 −1.28959 −0.644797 0.764354i \(-0.723058\pi\)
−0.644797 + 0.764354i \(0.723058\pi\)
\(614\) 0 0
\(615\) 0.701282 0.0282784
\(616\) 0 0
\(617\) 27.1641 1.09358 0.546792 0.837268i \(-0.315849\pi\)
0.546792 + 0.837268i \(0.315849\pi\)
\(618\) 0 0
\(619\) 15.1831 0.610260 0.305130 0.952311i \(-0.401300\pi\)
0.305130 + 0.952311i \(0.401300\pi\)
\(620\) 0 0
\(621\) −7.13234 −0.286211
\(622\) 0 0
\(623\) 38.3756 1.53748
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.270388 −0.0107983
\(628\) 0 0
\(629\) −58.3086 −2.32492
\(630\) 0 0
\(631\) −17.9740 −0.715532 −0.357766 0.933811i \(-0.616461\pi\)
−0.357766 + 0.933811i \(0.616461\pi\)
\(632\) 0 0
\(633\) −0.840526 −0.0334079
\(634\) 0 0
\(635\) −1.15524 −0.0458444
\(636\) 0 0
\(637\) 49.7533 1.97130
\(638\) 0 0
\(639\) −4.11630 −0.162838
\(640\) 0 0
\(641\) −16.9647 −0.670066 −0.335033 0.942206i \(-0.608747\pi\)
−0.335033 + 0.942206i \(0.608747\pi\)
\(642\) 0 0
\(643\) −40.4544 −1.59536 −0.797682 0.603078i \(-0.793941\pi\)
−0.797682 + 0.603078i \(0.793941\pi\)
\(644\) 0 0
\(645\) −10.9467 −0.431026
\(646\) 0 0
\(647\) 43.7214 1.71887 0.859433 0.511248i \(-0.170817\pi\)
0.859433 + 0.511248i \(0.170817\pi\)
\(648\) 0 0
\(649\) 2.95540 0.116010
\(650\) 0 0
\(651\) 12.0937 0.473988
\(652\) 0 0
\(653\) 15.0713 0.589785 0.294892 0.955531i \(-0.404716\pi\)
0.294892 + 0.955531i \(0.404716\pi\)
\(654\) 0 0
\(655\) 11.2772 0.440639
\(656\) 0 0
\(657\) −1.83177 −0.0714640
\(658\) 0 0
\(659\) 6.37351 0.248277 0.124138 0.992265i \(-0.460383\pi\)
0.124138 + 0.992265i \(0.460383\pi\)
\(660\) 0 0
\(661\) 9.83983 0.382725 0.191362 0.981519i \(-0.438709\pi\)
0.191362 + 0.981519i \(0.438709\pi\)
\(662\) 0 0
\(663\) −26.5854 −1.03249
\(664\) 0 0
\(665\) 0.330697 0.0128239
\(666\) 0 0
\(667\) −3.84236 −0.148777
\(668\) 0 0
\(669\) 12.0649 0.466457
\(670\) 0 0
\(671\) −16.3340 −0.630567
\(672\) 0 0
\(673\) 17.1468 0.660961 0.330481 0.943813i \(-0.392789\pi\)
0.330481 + 0.943813i \(0.392789\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) −12.5118 −0.480869 −0.240434 0.970665i \(-0.577290\pi\)
−0.240434 + 0.970665i \(0.577290\pi\)
\(678\) 0 0
\(679\) 41.1843 1.58051
\(680\) 0 0
\(681\) 21.4614 0.822403
\(682\) 0 0
\(683\) −38.7594 −1.48309 −0.741543 0.670905i \(-0.765906\pi\)
−0.741543 + 0.670905i \(0.765906\pi\)
\(684\) 0 0
\(685\) −16.9837 −0.648915
\(686\) 0 0
\(687\) 3.73690 0.142572
\(688\) 0 0
\(689\) 6.67038 0.254121
\(690\) 0 0
\(691\) −39.2097 −1.49161 −0.745804 0.666166i \(-0.767934\pi\)
−0.745804 + 0.666166i \(0.767934\pi\)
\(692\) 0 0
\(693\) 16.3883 0.622539
\(694\) 0 0
\(695\) −13.1266 −0.497921
\(696\) 0 0
\(697\) 4.88778 0.185138
\(698\) 0 0
\(699\) −23.9633 −0.906376
\(700\) 0 0
\(701\) −17.3206 −0.654192 −0.327096 0.944991i \(-0.606070\pi\)
−0.327096 + 0.944991i \(0.606070\pi\)
\(702\) 0 0
\(703\) −0.617954 −0.0233066
\(704\) 0 0
\(705\) −2.26292 −0.0852264
\(706\) 0 0
\(707\) 2.47656 0.0931407
\(708\) 0 0
\(709\) −24.6689 −0.926459 −0.463230 0.886238i \(-0.653309\pi\)
−0.463230 + 0.886238i \(0.653309\pi\)
\(710\) 0 0
\(711\) 4.17995 0.156760
\(712\) 0 0
\(713\) −19.2665 −0.721534
\(714\) 0 0
\(715\) −13.9627 −0.522175
\(716\) 0 0
\(717\) −4.11678 −0.153744
\(718\) 0 0
\(719\) 24.4993 0.913668 0.456834 0.889552i \(-0.348983\pi\)
0.456834 + 0.889552i \(0.348983\pi\)
\(720\) 0 0
\(721\) −39.3904 −1.46698
\(722\) 0 0
\(723\) −24.3695 −0.906310
\(724\) 0 0
\(725\) 0.538723 0.0200077
\(726\) 0 0
\(727\) 11.8303 0.438763 0.219381 0.975639i \(-0.429596\pi\)
0.219381 + 0.975639i \(0.429596\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −76.2962 −2.82192
\(732\) 0 0
\(733\) 7.80437 0.288261 0.144130 0.989559i \(-0.453962\pi\)
0.144130 + 0.989559i \(0.453962\pi\)
\(734\) 0 0
\(735\) −13.0436 −0.481121
\(736\) 0 0
\(737\) 3.66054 0.134838
\(738\) 0 0
\(739\) 7.20240 0.264945 0.132472 0.991187i \(-0.457708\pi\)
0.132472 + 0.991187i \(0.457708\pi\)
\(740\) 0 0
\(741\) −0.281751 −0.0103504
\(742\) 0 0
\(743\) 13.1180 0.481252 0.240626 0.970618i \(-0.422647\pi\)
0.240626 + 0.970618i \(0.422647\pi\)
\(744\) 0 0
\(745\) −11.3420 −0.415537
\(746\) 0 0
\(747\) 3.56198 0.130326
\(748\) 0 0
\(749\) −77.6960 −2.83895
\(750\) 0 0
\(751\) 41.7499 1.52347 0.761737 0.647886i \(-0.224347\pi\)
0.761737 + 0.647886i \(0.224347\pi\)
\(752\) 0 0
\(753\) 21.5904 0.786798
\(754\) 0 0
\(755\) 10.0048 0.364114
\(756\) 0 0
\(757\) −4.48623 −0.163055 −0.0815275 0.996671i \(-0.525980\pi\)
−0.0815275 + 0.996671i \(0.525980\pi\)
\(758\) 0 0
\(759\) −26.1082 −0.947668
\(760\) 0 0
\(761\) 19.4036 0.703380 0.351690 0.936117i \(-0.385607\pi\)
0.351690 + 0.936117i \(0.385607\pi\)
\(762\) 0 0
\(763\) 26.4035 0.955871
\(764\) 0 0
\(765\) 6.96978 0.251993
\(766\) 0 0
\(767\) 3.07960 0.111198
\(768\) 0 0
\(769\) −27.3437 −0.986040 −0.493020 0.870018i \(-0.664107\pi\)
−0.493020 + 0.870018i \(0.664107\pi\)
\(770\) 0 0
\(771\) 20.1990 0.727449
\(772\) 0 0
\(773\) −5.16057 −0.185613 −0.0928064 0.995684i \(-0.529584\pi\)
−0.0928064 + 0.995684i \(0.529584\pi\)
\(774\) 0 0
\(775\) 2.70128 0.0970329
\(776\) 0 0
\(777\) 37.4543 1.34367
\(778\) 0 0
\(779\) 0.0518006 0.00185595
\(780\) 0 0
\(781\) −15.0679 −0.539171
\(782\) 0 0
\(783\) 0.538723 0.0192524
\(784\) 0 0
\(785\) 11.3646 0.405619
\(786\) 0 0
\(787\) −42.7502 −1.52388 −0.761939 0.647648i \(-0.775753\pi\)
−0.761939 + 0.647648i \(0.775753\pi\)
\(788\) 0 0
\(789\) −2.28006 −0.0811723
\(790\) 0 0
\(791\) 63.2151 2.24767
\(792\) 0 0
\(793\) −17.0204 −0.604414
\(794\) 0 0
\(795\) −1.74875 −0.0620217
\(796\) 0 0
\(797\) 37.6597 1.33398 0.666988 0.745069i \(-0.267583\pi\)
0.666988 + 0.745069i \(0.267583\pi\)
\(798\) 0 0
\(799\) −15.7720 −0.557975
\(800\) 0 0
\(801\) 8.57170 0.302866
\(802\) 0 0
\(803\) −6.70526 −0.236623
\(804\) 0 0
\(805\) 31.9316 1.12544
\(806\) 0 0
\(807\) 3.40768 0.119956
\(808\) 0 0
\(809\) −18.2412 −0.641328 −0.320664 0.947193i \(-0.603906\pi\)
−0.320664 + 0.947193i \(0.603906\pi\)
\(810\) 0 0
\(811\) 36.8070 1.29247 0.646235 0.763139i \(-0.276343\pi\)
0.646235 + 0.763139i \(0.276343\pi\)
\(812\) 0 0
\(813\) 31.2376 1.09555
\(814\) 0 0
\(815\) 18.0171 0.631111
\(816\) 0 0
\(817\) −0.808586 −0.0282889
\(818\) 0 0
\(819\) 17.0770 0.596719
\(820\) 0 0
\(821\) −26.9488 −0.940520 −0.470260 0.882528i \(-0.655840\pi\)
−0.470260 + 0.882528i \(0.655840\pi\)
\(822\) 0 0
\(823\) 25.8314 0.900425 0.450213 0.892921i \(-0.351348\pi\)
0.450213 + 0.892921i \(0.351348\pi\)
\(824\) 0 0
\(825\) 3.66054 0.127444
\(826\) 0 0
\(827\) −24.9623 −0.868023 −0.434012 0.900907i \(-0.642902\pi\)
−0.434012 + 0.900907i \(0.642902\pi\)
\(828\) 0 0
\(829\) 16.4174 0.570201 0.285100 0.958498i \(-0.407973\pi\)
0.285100 + 0.958498i \(0.407973\pi\)
\(830\) 0 0
\(831\) 14.8526 0.515230
\(832\) 0 0
\(833\) −90.9112 −3.14988
\(834\) 0 0
\(835\) −4.40114 −0.152308
\(836\) 0 0
\(837\) 2.70128 0.0933700
\(838\) 0 0
\(839\) 28.9631 0.999917 0.499958 0.866049i \(-0.333349\pi\)
0.499958 + 0.866049i \(0.333349\pi\)
\(840\) 0 0
\(841\) −28.7098 −0.989992
\(842\) 0 0
\(843\) −9.64114 −0.332059
\(844\) 0 0
\(845\) −1.54946 −0.0533029
\(846\) 0 0
\(847\) 10.7429 0.369129
\(848\) 0 0
\(849\) −13.4963 −0.463190
\(850\) 0 0
\(851\) −59.6685 −2.04541
\(852\) 0 0
\(853\) −45.4968 −1.55778 −0.778890 0.627160i \(-0.784217\pi\)
−0.778890 + 0.627160i \(0.784217\pi\)
\(854\) 0 0
\(855\) 0.0738657 0.00252615
\(856\) 0 0
\(857\) 42.5589 1.45378 0.726892 0.686752i \(-0.240964\pi\)
0.726892 + 0.686752i \(0.240964\pi\)
\(858\) 0 0
\(859\) −30.1818 −1.02979 −0.514895 0.857253i \(-0.672169\pi\)
−0.514895 + 0.857253i \(0.672169\pi\)
\(860\) 0 0
\(861\) −3.13965 −0.106999
\(862\) 0 0
\(863\) −36.4846 −1.24195 −0.620974 0.783831i \(-0.713263\pi\)
−0.620974 + 0.783831i \(0.713263\pi\)
\(864\) 0 0
\(865\) −10.7769 −0.366424
\(866\) 0 0
\(867\) 31.5778 1.07244
\(868\) 0 0
\(869\) 15.3009 0.519047
\(870\) 0 0
\(871\) 3.81438 0.129245
\(872\) 0 0
\(873\) 9.19906 0.311341
\(874\) 0 0
\(875\) −4.47701 −0.151351
\(876\) 0 0
\(877\) 22.9030 0.773381 0.386690 0.922210i \(-0.373618\pi\)
0.386690 + 0.922210i \(0.373618\pi\)
\(878\) 0 0
\(879\) 26.4275 0.891379
\(880\) 0 0
\(881\) −23.0167 −0.775453 −0.387727 0.921774i \(-0.626740\pi\)
−0.387727 + 0.921774i \(0.626740\pi\)
\(882\) 0 0
\(883\) −46.6121 −1.56862 −0.784311 0.620367i \(-0.786983\pi\)
−0.784311 + 0.620367i \(0.786983\pi\)
\(884\) 0 0
\(885\) −0.807367 −0.0271393
\(886\) 0 0
\(887\) −36.0137 −1.20922 −0.604612 0.796520i \(-0.706672\pi\)
−0.604612 + 0.796520i \(0.706672\pi\)
\(888\) 0 0
\(889\) 5.17203 0.173464
\(890\) 0 0
\(891\) 3.66054 0.122633
\(892\) 0 0
\(893\) −0.167152 −0.00559353
\(894\) 0 0
\(895\) −11.8254 −0.395279
\(896\) 0 0
\(897\) −27.2054 −0.908362
\(898\) 0 0
\(899\) 1.45524 0.0485351
\(900\) 0 0
\(901\) −12.1884 −0.406054
\(902\) 0 0
\(903\) 49.0085 1.63090
\(904\) 0 0
\(905\) 7.20241 0.239416
\(906\) 0 0
\(907\) −10.5074 −0.348892 −0.174446 0.984667i \(-0.555813\pi\)
−0.174446 + 0.984667i \(0.555813\pi\)
\(908\) 0 0
\(909\) 0.553173 0.0183476
\(910\) 0 0
\(911\) −18.6783 −0.618841 −0.309420 0.950925i \(-0.600135\pi\)
−0.309420 + 0.950925i \(0.600135\pi\)
\(912\) 0 0
\(913\) 13.0388 0.431520
\(914\) 0 0
\(915\) 4.46218 0.147515
\(916\) 0 0
\(917\) −50.4883 −1.66727
\(918\) 0 0
\(919\) 30.8738 1.01843 0.509216 0.860639i \(-0.329935\pi\)
0.509216 + 0.860639i \(0.329935\pi\)
\(920\) 0 0
\(921\) −12.9674 −0.427291
\(922\) 0 0
\(923\) −15.7011 −0.516808
\(924\) 0 0
\(925\) 8.36592 0.275070
\(926\) 0 0
\(927\) −8.79837 −0.288977
\(928\) 0 0
\(929\) −0.907452 −0.0297725 −0.0148863 0.999889i \(-0.504739\pi\)
−0.0148863 + 0.999889i \(0.504739\pi\)
\(930\) 0 0
\(931\) −0.963476 −0.0315766
\(932\) 0 0
\(933\) 12.8951 0.422165
\(934\) 0 0
\(935\) 25.5132 0.834370
\(936\) 0 0
\(937\) −18.5306 −0.605368 −0.302684 0.953091i \(-0.597883\pi\)
−0.302684 + 0.953091i \(0.597883\pi\)
\(938\) 0 0
\(939\) −0.760285 −0.0248110
\(940\) 0 0
\(941\) −46.1583 −1.50472 −0.752359 0.658753i \(-0.771084\pi\)
−0.752359 + 0.658753i \(0.771084\pi\)
\(942\) 0 0
\(943\) 5.00178 0.162880
\(944\) 0 0
\(945\) −4.47701 −0.145637
\(946\) 0 0
\(947\) 46.9021 1.52411 0.762057 0.647509i \(-0.224189\pi\)
0.762057 + 0.647509i \(0.224189\pi\)
\(948\) 0 0
\(949\) −6.98705 −0.226809
\(950\) 0 0
\(951\) −20.9773 −0.680236
\(952\) 0 0
\(953\) 4.84102 0.156816 0.0784081 0.996921i \(-0.475016\pi\)
0.0784081 + 0.996921i \(0.475016\pi\)
\(954\) 0 0
\(955\) 16.1036 0.521100
\(956\) 0 0
\(957\) 1.97202 0.0637463
\(958\) 0 0
\(959\) 76.0363 2.45534
\(960\) 0 0
\(961\) −23.7031 −0.764615
\(962\) 0 0
\(963\) −17.3544 −0.559239
\(964\) 0 0
\(965\) 11.7082 0.376900
\(966\) 0 0
\(967\) 14.9492 0.480734 0.240367 0.970682i \(-0.422732\pi\)
0.240367 + 0.970682i \(0.422732\pi\)
\(968\) 0 0
\(969\) 0.514827 0.0165386
\(970\) 0 0
\(971\) −6.32963 −0.203127 −0.101564 0.994829i \(-0.532385\pi\)
−0.101564 + 0.994829i \(0.532385\pi\)
\(972\) 0 0
\(973\) 58.7680 1.88401
\(974\) 0 0
\(975\) 3.81438 0.122158
\(976\) 0 0
\(977\) −23.5643 −0.753890 −0.376945 0.926236i \(-0.623025\pi\)
−0.376945 + 0.926236i \(0.623025\pi\)
\(978\) 0 0
\(979\) 31.3770 1.00281
\(980\) 0 0
\(981\) 5.89757 0.188295
\(982\) 0 0
\(983\) 8.61381 0.274738 0.137369 0.990520i \(-0.456135\pi\)
0.137369 + 0.990520i \(0.456135\pi\)
\(984\) 0 0
\(985\) −2.23632 −0.0712549
\(986\) 0 0
\(987\) 10.1311 0.322477
\(988\) 0 0
\(989\) −78.0757 −2.48266
\(990\) 0 0
\(991\) −59.6434 −1.89464 −0.947318 0.320295i \(-0.896218\pi\)
−0.947318 + 0.320295i \(0.896218\pi\)
\(992\) 0 0
\(993\) 14.2592 0.452503
\(994\) 0 0
\(995\) 21.7620 0.689900
\(996\) 0 0
\(997\) −49.7555 −1.57577 −0.787887 0.615820i \(-0.788825\pi\)
−0.787887 + 0.615820i \(0.788825\pi\)
\(998\) 0 0
\(999\) 8.36592 0.264686
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 \(a_p\))