Properties

Label 8001.2.a.u.1.15
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(2.40246\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.40246 q^{2}\) \(+3.77179 q^{4}\) \(+0.666645 q^{5}\) \(+1.00000 q^{7}\) \(+4.25666 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.40246 q^{2}\) \(+3.77179 q^{4}\) \(+0.666645 q^{5}\) \(+1.00000 q^{7}\) \(+4.25666 q^{8}\) \(+1.60159 q^{10}\) \(+5.05203 q^{11}\) \(+5.76961 q^{13}\) \(+2.40246 q^{14}\) \(+2.68284 q^{16}\) \(+0.396381 q^{17}\) \(+3.56828 q^{19}\) \(+2.51445 q^{20}\) \(+12.1373 q^{22}\) \(+4.24325 q^{23}\) \(-4.55558 q^{25}\) \(+13.8612 q^{26}\) \(+3.77179 q^{28}\) \(-0.519685 q^{29}\) \(+3.84273 q^{31}\) \(-2.06791 q^{32}\) \(+0.952288 q^{34}\) \(+0.666645 q^{35}\) \(-7.00515 q^{37}\) \(+8.57264 q^{38}\) \(+2.83768 q^{40}\) \(-3.06775 q^{41}\) \(-4.79677 q^{43}\) \(+19.0552 q^{44}\) \(+10.1942 q^{46}\) \(-11.2665 q^{47}\) \(+1.00000 q^{49}\) \(-10.9446 q^{50}\) \(+21.7618 q^{52}\) \(+1.29111 q^{53}\) \(+3.36791 q^{55}\) \(+4.25666 q^{56}\) \(-1.24852 q^{58}\) \(+1.96260 q^{59}\) \(-9.45403 q^{61}\) \(+9.23199 q^{62}\) \(-10.3337 q^{64}\) \(+3.84628 q^{65}\) \(-8.88556 q^{67}\) \(+1.49507 q^{68}\) \(+1.60159 q^{70}\) \(+8.51845 q^{71}\) \(-6.50942 q^{73}\) \(-16.8296 q^{74}\) \(+13.4588 q^{76}\) \(+5.05203 q^{77}\) \(+14.8928 q^{79}\) \(+1.78850 q^{80}\) \(-7.37013 q^{82}\) \(-13.6579 q^{83}\) \(+0.264246 q^{85}\) \(-11.5240 q^{86}\) \(+21.5047 q^{88}\) \(+12.6023 q^{89}\) \(+5.76961 q^{91}\) \(+16.0047 q^{92}\) \(-27.0673 q^{94}\) \(+2.37878 q^{95}\) \(+9.21904 q^{97}\) \(+2.40246 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.40246 1.69879 0.849396 0.527755i \(-0.176966\pi\)
0.849396 + 0.527755i \(0.176966\pi\)
\(3\) 0 0
\(4\) 3.77179 1.88590
\(5\) 0.666645 0.298133 0.149066 0.988827i \(-0.452373\pi\)
0.149066 + 0.988827i \(0.452373\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 4.25666 1.50496
\(9\) 0 0
\(10\) 1.60159 0.506466
\(11\) 5.05203 1.52324 0.761622 0.648022i \(-0.224403\pi\)
0.761622 + 0.648022i \(0.224403\pi\)
\(12\) 0 0
\(13\) 5.76961 1.60020 0.800101 0.599866i \(-0.204779\pi\)
0.800101 + 0.599866i \(0.204779\pi\)
\(14\) 2.40246 0.642083
\(15\) 0 0
\(16\) 2.68284 0.670710
\(17\) 0.396381 0.0961366 0.0480683 0.998844i \(-0.484693\pi\)
0.0480683 + 0.998844i \(0.484693\pi\)
\(18\) 0 0
\(19\) 3.56828 0.818620 0.409310 0.912395i \(-0.365769\pi\)
0.409310 + 0.912395i \(0.365769\pi\)
\(20\) 2.51445 0.562248
\(21\) 0 0
\(22\) 12.1373 2.58768
\(23\) 4.24325 0.884780 0.442390 0.896823i \(-0.354131\pi\)
0.442390 + 0.896823i \(0.354131\pi\)
\(24\) 0 0
\(25\) −4.55558 −0.911117
\(26\) 13.8612 2.71841
\(27\) 0 0
\(28\) 3.77179 0.712802
\(29\) −0.519685 −0.0965030 −0.0482515 0.998835i \(-0.515365\pi\)
−0.0482515 + 0.998835i \(0.515365\pi\)
\(30\) 0 0
\(31\) 3.84273 0.690175 0.345087 0.938571i \(-0.387849\pi\)
0.345087 + 0.938571i \(0.387849\pi\)
\(32\) −2.06791 −0.365558
\(33\) 0 0
\(34\) 0.952288 0.163316
\(35\) 0.666645 0.112684
\(36\) 0 0
\(37\) −7.00515 −1.15164 −0.575820 0.817577i \(-0.695317\pi\)
−0.575820 + 0.817577i \(0.695317\pi\)
\(38\) 8.57264 1.39067
\(39\) 0 0
\(40\) 2.83768 0.448677
\(41\) −3.06775 −0.479102 −0.239551 0.970884i \(-0.577000\pi\)
−0.239551 + 0.970884i \(0.577000\pi\)
\(42\) 0 0
\(43\) −4.79677 −0.731501 −0.365750 0.930713i \(-0.619188\pi\)
−0.365750 + 0.930713i \(0.619188\pi\)
\(44\) 19.0552 2.87268
\(45\) 0 0
\(46\) 10.1942 1.50306
\(47\) −11.2665 −1.64339 −0.821696 0.569926i \(-0.806972\pi\)
−0.821696 + 0.569926i \(0.806972\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −10.9446 −1.54780
\(51\) 0 0
\(52\) 21.7618 3.01781
\(53\) 1.29111 0.177348 0.0886740 0.996061i \(-0.471737\pi\)
0.0886740 + 0.996061i \(0.471737\pi\)
\(54\) 0 0
\(55\) 3.36791 0.454129
\(56\) 4.25666 0.568820
\(57\) 0 0
\(58\) −1.24852 −0.163939
\(59\) 1.96260 0.255509 0.127755 0.991806i \(-0.459223\pi\)
0.127755 + 0.991806i \(0.459223\pi\)
\(60\) 0 0
\(61\) −9.45403 −1.21046 −0.605232 0.796049i \(-0.706920\pi\)
−0.605232 + 0.796049i \(0.706920\pi\)
\(62\) 9.23199 1.17246
\(63\) 0 0
\(64\) −10.3337 −1.29172
\(65\) 3.84628 0.477073
\(66\) 0 0
\(67\) −8.88556 −1.08554 −0.542772 0.839880i \(-0.682625\pi\)
−0.542772 + 0.839880i \(0.682625\pi\)
\(68\) 1.49507 0.181304
\(69\) 0 0
\(70\) 1.60159 0.191426
\(71\) 8.51845 1.01095 0.505477 0.862840i \(-0.331317\pi\)
0.505477 + 0.862840i \(0.331317\pi\)
\(72\) 0 0
\(73\) −6.50942 −0.761870 −0.380935 0.924602i \(-0.624398\pi\)
−0.380935 + 0.924602i \(0.624398\pi\)
\(74\) −16.8296 −1.95640
\(75\) 0 0
\(76\) 13.4588 1.54383
\(77\) 5.05203 0.575732
\(78\) 0 0
\(79\) 14.8928 1.67557 0.837783 0.546004i \(-0.183852\pi\)
0.837783 + 0.546004i \(0.183852\pi\)
\(80\) 1.78850 0.199961
\(81\) 0 0
\(82\) −7.37013 −0.813894
\(83\) −13.6579 −1.49915 −0.749575 0.661919i \(-0.769742\pi\)
−0.749575 + 0.661919i \(0.769742\pi\)
\(84\) 0 0
\(85\) 0.264246 0.0286615
\(86\) −11.5240 −1.24267
\(87\) 0 0
\(88\) 21.5047 2.29241
\(89\) 12.6023 1.33585 0.667923 0.744231i \(-0.267184\pi\)
0.667923 + 0.744231i \(0.267184\pi\)
\(90\) 0 0
\(91\) 5.76961 0.604819
\(92\) 16.0047 1.66860
\(93\) 0 0
\(94\) −27.0673 −2.79178
\(95\) 2.37878 0.244058
\(96\) 0 0
\(97\) 9.21904 0.936052 0.468026 0.883715i \(-0.344965\pi\)
0.468026 + 0.883715i \(0.344965\pi\)
\(98\) 2.40246 0.242685
\(99\) 0 0
\(100\) −17.1827 −1.71827
\(101\) −5.22301 −0.519709 −0.259855 0.965648i \(-0.583675\pi\)
−0.259855 + 0.965648i \(0.583675\pi\)
\(102\) 0 0
\(103\) −1.04722 −0.103185 −0.0515926 0.998668i \(-0.516430\pi\)
−0.0515926 + 0.998668i \(0.516430\pi\)
\(104\) 24.5592 2.40823
\(105\) 0 0
\(106\) 3.10184 0.301277
\(107\) −15.4399 −1.49263 −0.746317 0.665590i \(-0.768180\pi\)
−0.746317 + 0.665590i \(0.768180\pi\)
\(108\) 0 0
\(109\) 8.22589 0.787897 0.393949 0.919132i \(-0.371109\pi\)
0.393949 + 0.919132i \(0.371109\pi\)
\(110\) 8.09126 0.771471
\(111\) 0 0
\(112\) 2.68284 0.253505
\(113\) 2.61402 0.245906 0.122953 0.992412i \(-0.460764\pi\)
0.122953 + 0.992412i \(0.460764\pi\)
\(114\) 0 0
\(115\) 2.82875 0.263782
\(116\) −1.96014 −0.181995
\(117\) 0 0
\(118\) 4.71506 0.434057
\(119\) 0.396381 0.0363362
\(120\) 0 0
\(121\) 14.5230 1.32027
\(122\) −22.7129 −2.05633
\(123\) 0 0
\(124\) 14.4940 1.30160
\(125\) −6.37019 −0.569767
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −20.6905 −1.82880
\(129\) 0 0
\(130\) 9.24052 0.810447
\(131\) −14.8530 −1.29771 −0.648855 0.760912i \(-0.724752\pi\)
−0.648855 + 0.760912i \(0.724752\pi\)
\(132\) 0 0
\(133\) 3.56828 0.309409
\(134\) −21.3472 −1.84411
\(135\) 0 0
\(136\) 1.68726 0.144681
\(137\) 20.4969 1.75117 0.875583 0.483068i \(-0.160478\pi\)
0.875583 + 0.483068i \(0.160478\pi\)
\(138\) 0 0
\(139\) −3.53740 −0.300039 −0.150019 0.988683i \(-0.547934\pi\)
−0.150019 + 0.988683i \(0.547934\pi\)
\(140\) 2.51445 0.212510
\(141\) 0 0
\(142\) 20.4652 1.71740
\(143\) 29.1482 2.43750
\(144\) 0 0
\(145\) −0.346445 −0.0287707
\(146\) −15.6386 −1.29426
\(147\) 0 0
\(148\) −26.4220 −2.17187
\(149\) 19.9965 1.63817 0.819087 0.573669i \(-0.194480\pi\)
0.819087 + 0.573669i \(0.194480\pi\)
\(150\) 0 0
\(151\) 18.2975 1.48903 0.744516 0.667605i \(-0.232680\pi\)
0.744516 + 0.667605i \(0.232680\pi\)
\(152\) 15.1889 1.23199
\(153\) 0 0
\(154\) 12.1373 0.978049
\(155\) 2.56174 0.205764
\(156\) 0 0
\(157\) −23.8970 −1.90718 −0.953592 0.301100i \(-0.902646\pi\)
−0.953592 + 0.301100i \(0.902646\pi\)
\(158\) 35.7792 2.84644
\(159\) 0 0
\(160\) −1.37856 −0.108985
\(161\) 4.24325 0.334415
\(162\) 0 0
\(163\) −14.7857 −1.15810 −0.579051 0.815291i \(-0.696577\pi\)
−0.579051 + 0.815291i \(0.696577\pi\)
\(164\) −11.5709 −0.903536
\(165\) 0 0
\(166\) −32.8125 −2.54675
\(167\) −21.2454 −1.64402 −0.822010 0.569474i \(-0.807147\pi\)
−0.822010 + 0.569474i \(0.807147\pi\)
\(168\) 0 0
\(169\) 20.2884 1.56064
\(170\) 0.634839 0.0486899
\(171\) 0 0
\(172\) −18.0924 −1.37954
\(173\) 8.03384 0.610802 0.305401 0.952224i \(-0.401210\pi\)
0.305401 + 0.952224i \(0.401210\pi\)
\(174\) 0 0
\(175\) −4.55558 −0.344370
\(176\) 13.5538 1.02165
\(177\) 0 0
\(178\) 30.2766 2.26932
\(179\) 18.5927 1.38968 0.694840 0.719164i \(-0.255475\pi\)
0.694840 + 0.719164i \(0.255475\pi\)
\(180\) 0 0
\(181\) 10.8782 0.808569 0.404284 0.914633i \(-0.367521\pi\)
0.404284 + 0.914633i \(0.367521\pi\)
\(182\) 13.8612 1.02746
\(183\) 0 0
\(184\) 18.0621 1.33155
\(185\) −4.66995 −0.343342
\(186\) 0 0
\(187\) 2.00253 0.146439
\(188\) −42.4950 −3.09927
\(189\) 0 0
\(190\) 5.71491 0.414603
\(191\) −19.0877 −1.38114 −0.690570 0.723266i \(-0.742640\pi\)
−0.690570 + 0.723266i \(0.742640\pi\)
\(192\) 0 0
\(193\) −16.5306 −1.18990 −0.594951 0.803762i \(-0.702828\pi\)
−0.594951 + 0.803762i \(0.702828\pi\)
\(194\) 22.1483 1.59016
\(195\) 0 0
\(196\) 3.77179 0.269414
\(197\) 26.3357 1.87634 0.938169 0.346178i \(-0.112521\pi\)
0.938169 + 0.346178i \(0.112521\pi\)
\(198\) 0 0
\(199\) −0.679810 −0.0481905 −0.0240952 0.999710i \(-0.507670\pi\)
−0.0240952 + 0.999710i \(0.507670\pi\)
\(200\) −19.3916 −1.37119
\(201\) 0 0
\(202\) −12.5481 −0.882878
\(203\) −0.519685 −0.0364747
\(204\) 0 0
\(205\) −2.04510 −0.142836
\(206\) −2.51589 −0.175290
\(207\) 0 0
\(208\) 15.4789 1.07327
\(209\) 18.0271 1.24696
\(210\) 0 0
\(211\) 17.0443 1.17338 0.586688 0.809813i \(-0.300432\pi\)
0.586688 + 0.809813i \(0.300432\pi\)
\(212\) 4.86981 0.334460
\(213\) 0 0
\(214\) −37.0938 −2.53568
\(215\) −3.19775 −0.218084
\(216\) 0 0
\(217\) 3.84273 0.260862
\(218\) 19.7623 1.33847
\(219\) 0 0
\(220\) 12.7031 0.856441
\(221\) 2.28696 0.153838
\(222\) 0 0
\(223\) −20.7478 −1.38938 −0.694689 0.719311i \(-0.744458\pi\)
−0.694689 + 0.719311i \(0.744458\pi\)
\(224\) −2.06791 −0.138168
\(225\) 0 0
\(226\) 6.28006 0.417744
\(227\) 10.9843 0.729051 0.364525 0.931193i \(-0.381231\pi\)
0.364525 + 0.931193i \(0.381231\pi\)
\(228\) 0 0
\(229\) −3.69557 −0.244210 −0.122105 0.992517i \(-0.538964\pi\)
−0.122105 + 0.992517i \(0.538964\pi\)
\(230\) 6.79594 0.448111
\(231\) 0 0
\(232\) −2.21212 −0.145233
\(233\) 27.0298 1.77078 0.885389 0.464851i \(-0.153892\pi\)
0.885389 + 0.464851i \(0.153892\pi\)
\(234\) 0 0
\(235\) −7.51078 −0.489949
\(236\) 7.40253 0.481864
\(237\) 0 0
\(238\) 0.952288 0.0617277
\(239\) −2.63505 −0.170447 −0.0852235 0.996362i \(-0.527160\pi\)
−0.0852235 + 0.996362i \(0.527160\pi\)
\(240\) 0 0
\(241\) 16.8404 1.08478 0.542392 0.840125i \(-0.317519\pi\)
0.542392 + 0.840125i \(0.317519\pi\)
\(242\) 34.8908 2.24287
\(243\) 0 0
\(244\) −35.6587 −2.28281
\(245\) 0.666645 0.0425904
\(246\) 0 0
\(247\) 20.5876 1.30996
\(248\) 16.3572 1.03868
\(249\) 0 0
\(250\) −15.3041 −0.967916
\(251\) 22.7185 1.43398 0.716990 0.697083i \(-0.245519\pi\)
0.716990 + 0.697083i \(0.245519\pi\)
\(252\) 0 0
\(253\) 21.4370 1.34774
\(254\) 2.40246 0.150743
\(255\) 0 0
\(256\) −29.0406 −1.81504
\(257\) 16.8856 1.05330 0.526648 0.850084i \(-0.323449\pi\)
0.526648 + 0.850084i \(0.323449\pi\)
\(258\) 0 0
\(259\) −7.00515 −0.435279
\(260\) 14.5074 0.899710
\(261\) 0 0
\(262\) −35.6836 −2.20454
\(263\) 14.4874 0.893334 0.446667 0.894700i \(-0.352611\pi\)
0.446667 + 0.894700i \(0.352611\pi\)
\(264\) 0 0
\(265\) 0.860714 0.0528733
\(266\) 8.57264 0.525622
\(267\) 0 0
\(268\) −33.5145 −2.04722
\(269\) −19.0894 −1.16390 −0.581952 0.813223i \(-0.697711\pi\)
−0.581952 + 0.813223i \(0.697711\pi\)
\(270\) 0 0
\(271\) −12.5847 −0.764467 −0.382234 0.924066i \(-0.624845\pi\)
−0.382234 + 0.924066i \(0.624845\pi\)
\(272\) 1.06343 0.0644798
\(273\) 0 0
\(274\) 49.2428 2.97487
\(275\) −23.0149 −1.38785
\(276\) 0 0
\(277\) −23.5452 −1.41470 −0.707348 0.706866i \(-0.750108\pi\)
−0.707348 + 0.706866i \(0.750108\pi\)
\(278\) −8.49845 −0.509703
\(279\) 0 0
\(280\) 2.83768 0.169584
\(281\) 17.3606 1.03565 0.517824 0.855487i \(-0.326742\pi\)
0.517824 + 0.855487i \(0.326742\pi\)
\(282\) 0 0
\(283\) −28.0114 −1.66511 −0.832554 0.553945i \(-0.813122\pi\)
−0.832554 + 0.553945i \(0.813122\pi\)
\(284\) 32.1298 1.90655
\(285\) 0 0
\(286\) 70.0273 4.14080
\(287\) −3.06775 −0.181083
\(288\) 0 0
\(289\) −16.8429 −0.990758
\(290\) −0.832320 −0.0488755
\(291\) 0 0
\(292\) −24.5522 −1.43681
\(293\) −22.0696 −1.28932 −0.644661 0.764469i \(-0.723001\pi\)
−0.644661 + 0.764469i \(0.723001\pi\)
\(294\) 0 0
\(295\) 1.30836 0.0761756
\(296\) −29.8185 −1.73317
\(297\) 0 0
\(298\) 48.0406 2.78292
\(299\) 24.4819 1.41583
\(300\) 0 0
\(301\) −4.79677 −0.276481
\(302\) 43.9590 2.52956
\(303\) 0 0
\(304\) 9.57313 0.549057
\(305\) −6.30249 −0.360879
\(306\) 0 0
\(307\) −17.8522 −1.01888 −0.509439 0.860507i \(-0.670147\pi\)
−0.509439 + 0.860507i \(0.670147\pi\)
\(308\) 19.0552 1.08577
\(309\) 0 0
\(310\) 6.15447 0.349550
\(311\) 15.7490 0.893045 0.446522 0.894772i \(-0.352662\pi\)
0.446522 + 0.894772i \(0.352662\pi\)
\(312\) 0 0
\(313\) −15.8596 −0.896439 −0.448219 0.893924i \(-0.647942\pi\)
−0.448219 + 0.893924i \(0.647942\pi\)
\(314\) −57.4114 −3.23991
\(315\) 0 0
\(316\) 56.1724 3.15994
\(317\) −28.1773 −1.58259 −0.791296 0.611433i \(-0.790593\pi\)
−0.791296 + 0.611433i \(0.790593\pi\)
\(318\) 0 0
\(319\) −2.62546 −0.146998
\(320\) −6.88894 −0.385103
\(321\) 0 0
\(322\) 10.1942 0.568102
\(323\) 1.41440 0.0786993
\(324\) 0 0
\(325\) −26.2839 −1.45797
\(326\) −35.5219 −1.96738
\(327\) 0 0
\(328\) −13.0583 −0.721026
\(329\) −11.2665 −0.621144
\(330\) 0 0
\(331\) −27.8507 −1.53081 −0.765406 0.643547i \(-0.777462\pi\)
−0.765406 + 0.643547i \(0.777462\pi\)
\(332\) −51.5148 −2.82724
\(333\) 0 0
\(334\) −51.0412 −2.79285
\(335\) −5.92352 −0.323636
\(336\) 0 0
\(337\) −7.64516 −0.416458 −0.208229 0.978080i \(-0.566770\pi\)
−0.208229 + 0.978080i \(0.566770\pi\)
\(338\) 48.7419 2.65121
\(339\) 0 0
\(340\) 0.996680 0.0540526
\(341\) 19.4136 1.05130
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −20.4182 −1.10088
\(345\) 0 0
\(346\) 19.3010 1.03763
\(347\) −22.1004 −1.18641 −0.593205 0.805052i \(-0.702137\pi\)
−0.593205 + 0.805052i \(0.702137\pi\)
\(348\) 0 0
\(349\) 7.12427 0.381353 0.190677 0.981653i \(-0.438932\pi\)
0.190677 + 0.981653i \(0.438932\pi\)
\(350\) −10.9446 −0.585013
\(351\) 0 0
\(352\) −10.4471 −0.556833
\(353\) 14.0285 0.746662 0.373331 0.927698i \(-0.378216\pi\)
0.373331 + 0.927698i \(0.378216\pi\)
\(354\) 0 0
\(355\) 5.67878 0.301399
\(356\) 47.5334 2.51927
\(357\) 0 0
\(358\) 44.6680 2.36078
\(359\) −6.03937 −0.318746 −0.159373 0.987218i \(-0.550947\pi\)
−0.159373 + 0.987218i \(0.550947\pi\)
\(360\) 0 0
\(361\) −6.26736 −0.329861
\(362\) 26.1343 1.37359
\(363\) 0 0
\(364\) 21.7618 1.14063
\(365\) −4.33948 −0.227139
\(366\) 0 0
\(367\) −12.6586 −0.660775 −0.330387 0.943845i \(-0.607179\pi\)
−0.330387 + 0.943845i \(0.607179\pi\)
\(368\) 11.3840 0.593431
\(369\) 0 0
\(370\) −11.2194 −0.583267
\(371\) 1.29111 0.0670312
\(372\) 0 0
\(373\) 16.3249 0.845269 0.422635 0.906300i \(-0.361105\pi\)
0.422635 + 0.906300i \(0.361105\pi\)
\(374\) 4.81099 0.248770
\(375\) 0 0
\(376\) −47.9577 −2.47323
\(377\) −2.99838 −0.154424
\(378\) 0 0
\(379\) 16.1793 0.831074 0.415537 0.909576i \(-0.363594\pi\)
0.415537 + 0.909576i \(0.363594\pi\)
\(380\) 8.97226 0.460267
\(381\) 0 0
\(382\) −45.8574 −2.34627
\(383\) 14.1963 0.725399 0.362699 0.931906i \(-0.381855\pi\)
0.362699 + 0.931906i \(0.381855\pi\)
\(384\) 0 0
\(385\) 3.36791 0.171645
\(386\) −39.7141 −2.02140
\(387\) 0 0
\(388\) 34.7723 1.76530
\(389\) −1.32405 −0.0671318 −0.0335659 0.999437i \(-0.510686\pi\)
−0.0335659 + 0.999437i \(0.510686\pi\)
\(390\) 0 0
\(391\) 1.68195 0.0850597
\(392\) 4.25666 0.214994
\(393\) 0 0
\(394\) 63.2702 3.18751
\(395\) 9.92819 0.499541
\(396\) 0 0
\(397\) −33.9588 −1.70434 −0.852172 0.523262i \(-0.824715\pi\)
−0.852172 + 0.523262i \(0.824715\pi\)
\(398\) −1.63321 −0.0818656
\(399\) 0 0
\(400\) −12.2219 −0.611095
\(401\) 3.27288 0.163440 0.0817198 0.996655i \(-0.473959\pi\)
0.0817198 + 0.996655i \(0.473959\pi\)
\(402\) 0 0
\(403\) 22.1710 1.10442
\(404\) −19.7001 −0.980118
\(405\) 0 0
\(406\) −1.24852 −0.0619630
\(407\) −35.3902 −1.75423
\(408\) 0 0
\(409\) 7.93648 0.392434 0.196217 0.980561i \(-0.437134\pi\)
0.196217 + 0.980561i \(0.437134\pi\)
\(410\) −4.91326 −0.242649
\(411\) 0 0
\(412\) −3.94988 −0.194597
\(413\) 1.96260 0.0965733
\(414\) 0 0
\(415\) −9.10498 −0.446946
\(416\) −11.9310 −0.584966
\(417\) 0 0
\(418\) 43.3092 2.11832
\(419\) 21.1144 1.03151 0.515754 0.856737i \(-0.327512\pi\)
0.515754 + 0.856737i \(0.327512\pi\)
\(420\) 0 0
\(421\) −30.0789 −1.46596 −0.732978 0.680252i \(-0.761870\pi\)
−0.732978 + 0.680252i \(0.761870\pi\)
\(422\) 40.9481 1.99332
\(423\) 0 0
\(424\) 5.49582 0.266901
\(425\) −1.80575 −0.0875916
\(426\) 0 0
\(427\) −9.45403 −0.457513
\(428\) −58.2362 −2.81495
\(429\) 0 0
\(430\) −7.68244 −0.370480
\(431\) 16.0258 0.771938 0.385969 0.922512i \(-0.373867\pi\)
0.385969 + 0.922512i \(0.373867\pi\)
\(432\) 0 0
\(433\) 7.23386 0.347637 0.173819 0.984778i \(-0.444389\pi\)
0.173819 + 0.984778i \(0.444389\pi\)
\(434\) 9.23199 0.443150
\(435\) 0 0
\(436\) 31.0264 1.48589
\(437\) 15.1411 0.724298
\(438\) 0 0
\(439\) −10.4196 −0.497300 −0.248650 0.968593i \(-0.579987\pi\)
−0.248650 + 0.968593i \(0.579987\pi\)
\(440\) 14.3360 0.683444
\(441\) 0 0
\(442\) 5.49433 0.261339
\(443\) 9.43052 0.448057 0.224029 0.974583i \(-0.428079\pi\)
0.224029 + 0.974583i \(0.428079\pi\)
\(444\) 0 0
\(445\) 8.40129 0.398259
\(446\) −49.8457 −2.36026
\(447\) 0 0
\(448\) −10.3337 −0.488223
\(449\) 6.74268 0.318207 0.159103 0.987262i \(-0.449140\pi\)
0.159103 + 0.987262i \(0.449140\pi\)
\(450\) 0 0
\(451\) −15.4983 −0.729788
\(452\) 9.85954 0.463754
\(453\) 0 0
\(454\) 26.3892 1.23851
\(455\) 3.84628 0.180316
\(456\) 0 0
\(457\) 5.04899 0.236182 0.118091 0.993003i \(-0.462323\pi\)
0.118091 + 0.993003i \(0.462323\pi\)
\(458\) −8.87844 −0.414862
\(459\) 0 0
\(460\) 10.6694 0.497466
\(461\) 12.8408 0.598056 0.299028 0.954244i \(-0.403338\pi\)
0.299028 + 0.954244i \(0.403338\pi\)
\(462\) 0 0
\(463\) −7.31274 −0.339852 −0.169926 0.985457i \(-0.554353\pi\)
−0.169926 + 0.985457i \(0.554353\pi\)
\(464\) −1.39423 −0.0647256
\(465\) 0 0
\(466\) 64.9378 3.00818
\(467\) 20.4933 0.948317 0.474159 0.880439i \(-0.342752\pi\)
0.474159 + 0.880439i \(0.342752\pi\)
\(468\) 0 0
\(469\) −8.88556 −0.410297
\(470\) −18.0443 −0.832322
\(471\) 0 0
\(472\) 8.35412 0.384530
\(473\) −24.2334 −1.11425
\(474\) 0 0
\(475\) −16.2556 −0.745858
\(476\) 1.49507 0.0685263
\(477\) 0 0
\(478\) −6.33058 −0.289554
\(479\) −42.2742 −1.93156 −0.965778 0.259371i \(-0.916485\pi\)
−0.965778 + 0.259371i \(0.916485\pi\)
\(480\) 0 0
\(481\) −40.4170 −1.84286
\(482\) 40.4583 1.84282
\(483\) 0 0
\(484\) 54.7777 2.48989
\(485\) 6.14583 0.279068
\(486\) 0 0
\(487\) 11.3695 0.515202 0.257601 0.966251i \(-0.417068\pi\)
0.257601 + 0.966251i \(0.417068\pi\)
\(488\) −40.2426 −1.82170
\(489\) 0 0
\(490\) 1.60159 0.0723523
\(491\) 8.86723 0.400172 0.200086 0.979778i \(-0.435878\pi\)
0.200086 + 0.979778i \(0.435878\pi\)
\(492\) 0 0
\(493\) −0.205993 −0.00927747
\(494\) 49.4608 2.22534
\(495\) 0 0
\(496\) 10.3094 0.462907
\(497\) 8.51845 0.382105
\(498\) 0 0
\(499\) 4.93677 0.221000 0.110500 0.993876i \(-0.464755\pi\)
0.110500 + 0.993876i \(0.464755\pi\)
\(500\) −24.0270 −1.07452
\(501\) 0 0
\(502\) 54.5802 2.43604
\(503\) −23.9458 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(504\) 0 0
\(505\) −3.48190 −0.154942
\(506\) 51.5015 2.28952
\(507\) 0 0
\(508\) 3.77179 0.167346
\(509\) 21.1558 0.937716 0.468858 0.883273i \(-0.344666\pi\)
0.468858 + 0.883273i \(0.344666\pi\)
\(510\) 0 0
\(511\) −6.50942 −0.287960
\(512\) −28.3877 −1.25457
\(513\) 0 0
\(514\) 40.5669 1.78933
\(515\) −0.698122 −0.0307629
\(516\) 0 0
\(517\) −56.9188 −2.50329
\(518\) −16.8296 −0.739449
\(519\) 0 0
\(520\) 16.3723 0.717973
\(521\) −28.8671 −1.26469 −0.632346 0.774686i \(-0.717908\pi\)
−0.632346 + 0.774686i \(0.717908\pi\)
\(522\) 0 0
\(523\) 13.2821 0.580785 0.290393 0.956908i \(-0.406214\pi\)
0.290393 + 0.956908i \(0.406214\pi\)
\(524\) −56.0223 −2.44735
\(525\) 0 0
\(526\) 34.8054 1.51759
\(527\) 1.52319 0.0663510
\(528\) 0 0
\(529\) −4.99479 −0.217165
\(530\) 2.06783 0.0898207
\(531\) 0 0
\(532\) 13.4588 0.583514
\(533\) −17.6997 −0.766659
\(534\) 0 0
\(535\) −10.2930 −0.445004
\(536\) −37.8228 −1.63370
\(537\) 0 0
\(538\) −45.8616 −1.97723
\(539\) 5.05203 0.217606
\(540\) 0 0
\(541\) 35.5192 1.52709 0.763545 0.645754i \(-0.223457\pi\)
0.763545 + 0.645754i \(0.223457\pi\)
\(542\) −30.2342 −1.29867
\(543\) 0 0
\(544\) −0.819679 −0.0351435
\(545\) 5.48375 0.234898
\(546\) 0 0
\(547\) −1.19586 −0.0511314 −0.0255657 0.999673i \(-0.508139\pi\)
−0.0255657 + 0.999673i \(0.508139\pi\)
\(548\) 77.3100 3.30252
\(549\) 0 0
\(550\) −55.2924 −2.35767
\(551\) −1.85438 −0.0789993
\(552\) 0 0
\(553\) 14.8928 0.633304
\(554\) −56.5664 −2.40327
\(555\) 0 0
\(556\) −13.3424 −0.565842
\(557\) −0.640333 −0.0271318 −0.0135659 0.999908i \(-0.504318\pi\)
−0.0135659 + 0.999908i \(0.504318\pi\)
\(558\) 0 0
\(559\) −27.6755 −1.17055
\(560\) 1.78850 0.0755781
\(561\) 0 0
\(562\) 41.7081 1.75935
\(563\) −0.399140 −0.0168217 −0.00841086 0.999965i \(-0.502677\pi\)
−0.00841086 + 0.999965i \(0.502677\pi\)
\(564\) 0 0
\(565\) 1.74262 0.0733127
\(566\) −67.2962 −2.82867
\(567\) 0 0
\(568\) 36.2601 1.52144
\(569\) 10.0883 0.422924 0.211462 0.977386i \(-0.432177\pi\)
0.211462 + 0.977386i \(0.432177\pi\)
\(570\) 0 0
\(571\) 5.05274 0.211451 0.105725 0.994395i \(-0.466284\pi\)
0.105725 + 0.994395i \(0.466284\pi\)
\(572\) 109.941 4.59687
\(573\) 0 0
\(574\) −7.37013 −0.307623
\(575\) −19.3305 −0.806138
\(576\) 0 0
\(577\) −16.5648 −0.689601 −0.344800 0.938676i \(-0.612053\pi\)
−0.344800 + 0.938676i \(0.612053\pi\)
\(578\) −40.4643 −1.68309
\(579\) 0 0
\(580\) −1.30672 −0.0542586
\(581\) −13.6579 −0.566626
\(582\) 0 0
\(583\) 6.52273 0.270144
\(584\) −27.7084 −1.14658
\(585\) 0 0
\(586\) −53.0213 −2.19029
\(587\) 15.6730 0.646896 0.323448 0.946246i \(-0.395158\pi\)
0.323448 + 0.946246i \(0.395158\pi\)
\(588\) 0 0
\(589\) 13.7119 0.564991
\(590\) 3.14328 0.129407
\(591\) 0 0
\(592\) −18.7937 −0.772417
\(593\) −2.34319 −0.0962235 −0.0481117 0.998842i \(-0.515320\pi\)
−0.0481117 + 0.998842i \(0.515320\pi\)
\(594\) 0 0
\(595\) 0.264246 0.0108330
\(596\) 75.4225 3.08943
\(597\) 0 0
\(598\) 58.8167 2.40519
\(599\) 19.0363 0.777802 0.388901 0.921280i \(-0.372855\pi\)
0.388901 + 0.921280i \(0.372855\pi\)
\(600\) 0 0
\(601\) 23.0581 0.940560 0.470280 0.882517i \(-0.344153\pi\)
0.470280 + 0.882517i \(0.344153\pi\)
\(602\) −11.5240 −0.469684
\(603\) 0 0
\(604\) 69.0145 2.80816
\(605\) 9.68168 0.393616
\(606\) 0 0
\(607\) 16.5040 0.669878 0.334939 0.942240i \(-0.391284\pi\)
0.334939 + 0.942240i \(0.391284\pi\)
\(608\) −7.37887 −0.299253
\(609\) 0 0
\(610\) −15.1414 −0.613059
\(611\) −65.0034 −2.62976
\(612\) 0 0
\(613\) −13.9856 −0.564872 −0.282436 0.959286i \(-0.591142\pi\)
−0.282436 + 0.959286i \(0.591142\pi\)
\(614\) −42.8891 −1.73086
\(615\) 0 0
\(616\) 21.5047 0.866451
\(617\) −43.4723 −1.75013 −0.875064 0.484007i \(-0.839181\pi\)
−0.875064 + 0.484007i \(0.839181\pi\)
\(618\) 0 0
\(619\) 40.2578 1.61810 0.809049 0.587741i \(-0.199983\pi\)
0.809049 + 0.587741i \(0.199983\pi\)
\(620\) 9.66235 0.388049
\(621\) 0 0
\(622\) 37.8363 1.51710
\(623\) 12.6023 0.504902
\(624\) 0 0
\(625\) 18.5313 0.741251
\(626\) −38.1020 −1.52286
\(627\) 0 0
\(628\) −90.1344 −3.59675
\(629\) −2.77671 −0.110715
\(630\) 0 0
\(631\) 0.191328 0.00761664 0.00380832 0.999993i \(-0.498788\pi\)
0.00380832 + 0.999993i \(0.498788\pi\)
\(632\) 63.3933 2.52165
\(633\) 0 0
\(634\) −67.6946 −2.68850
\(635\) 0.666645 0.0264550
\(636\) 0 0
\(637\) 5.76961 0.228600
\(638\) −6.30756 −0.249719
\(639\) 0 0
\(640\) −13.7932 −0.545226
\(641\) −16.7190 −0.660361 −0.330181 0.943918i \(-0.607110\pi\)
−0.330181 + 0.943918i \(0.607110\pi\)
\(642\) 0 0
\(643\) −27.9484 −1.10218 −0.551088 0.834447i \(-0.685787\pi\)
−0.551088 + 0.834447i \(0.685787\pi\)
\(644\) 16.0047 0.630673
\(645\) 0 0
\(646\) 3.39803 0.133694
\(647\) 20.8215 0.818578 0.409289 0.912405i \(-0.365777\pi\)
0.409289 + 0.912405i \(0.365777\pi\)
\(648\) 0 0
\(649\) 9.91512 0.389202
\(650\) −63.1460 −2.47679
\(651\) 0 0
\(652\) −55.7685 −2.18406
\(653\) −4.58740 −0.179519 −0.0897594 0.995963i \(-0.528610\pi\)
−0.0897594 + 0.995963i \(0.528610\pi\)
\(654\) 0 0
\(655\) −9.90167 −0.386890
\(656\) −8.23028 −0.321338
\(657\) 0 0
\(658\) −27.0673 −1.05519
\(659\) 12.5704 0.489674 0.244837 0.969564i \(-0.421266\pi\)
0.244837 + 0.969564i \(0.421266\pi\)
\(660\) 0 0
\(661\) 25.8123 1.00398 0.501991 0.864873i \(-0.332601\pi\)
0.501991 + 0.864873i \(0.332601\pi\)
\(662\) −66.9101 −2.60053
\(663\) 0 0
\(664\) −58.1370 −2.25615
\(665\) 2.37878 0.0922451
\(666\) 0 0
\(667\) −2.20515 −0.0853839
\(668\) −80.1333 −3.10045
\(669\) 0 0
\(670\) −14.2310 −0.549791
\(671\) −47.7620 −1.84383
\(672\) 0 0
\(673\) −46.6132 −1.79681 −0.898403 0.439172i \(-0.855272\pi\)
−0.898403 + 0.439172i \(0.855272\pi\)
\(674\) −18.3672 −0.707476
\(675\) 0 0
\(676\) 76.5235 2.94321
\(677\) 15.3276 0.589087 0.294544 0.955638i \(-0.404832\pi\)
0.294544 + 0.955638i \(0.404832\pi\)
\(678\) 0 0
\(679\) 9.21904 0.353794
\(680\) 1.12480 0.0431342
\(681\) 0 0
\(682\) 46.6403 1.78595
\(683\) −1.55964 −0.0596778 −0.0298389 0.999555i \(-0.509499\pi\)
−0.0298389 + 0.999555i \(0.509499\pi\)
\(684\) 0 0
\(685\) 13.6641 0.522080
\(686\) 2.40246 0.0917262
\(687\) 0 0
\(688\) −12.8690 −0.490625
\(689\) 7.44921 0.283792
\(690\) 0 0
\(691\) −13.6905 −0.520810 −0.260405 0.965499i \(-0.583856\pi\)
−0.260405 + 0.965499i \(0.583856\pi\)
\(692\) 30.3020 1.15191
\(693\) 0 0
\(694\) −53.0951 −2.01546
\(695\) −2.35819 −0.0894514
\(696\) 0 0
\(697\) −1.21600 −0.0460592
\(698\) 17.1157 0.647840
\(699\) 0 0
\(700\) −17.1827 −0.649446
\(701\) −35.3818 −1.33635 −0.668176 0.744003i \(-0.732925\pi\)
−0.668176 + 0.744003i \(0.732925\pi\)
\(702\) 0 0
\(703\) −24.9964 −0.942756
\(704\) −52.2063 −1.96760
\(705\) 0 0
\(706\) 33.7028 1.26842
\(707\) −5.22301 −0.196432
\(708\) 0 0
\(709\) 2.44584 0.0918554 0.0459277 0.998945i \(-0.485376\pi\)
0.0459277 + 0.998945i \(0.485376\pi\)
\(710\) 13.6430 0.512014
\(711\) 0 0
\(712\) 53.6438 2.01039
\(713\) 16.3057 0.610653
\(714\) 0 0
\(715\) 19.4315 0.726698
\(716\) 70.1277 2.62079
\(717\) 0 0
\(718\) −14.5093 −0.541483
\(719\) 14.0093 0.522459 0.261229 0.965277i \(-0.415872\pi\)
0.261229 + 0.965277i \(0.415872\pi\)
\(720\) 0 0
\(721\) −1.04722 −0.0390004
\(722\) −15.0571 −0.560366
\(723\) 0 0
\(724\) 41.0303 1.52488
\(725\) 2.36747 0.0879255
\(726\) 0 0
\(727\) 5.51126 0.204401 0.102201 0.994764i \(-0.467412\pi\)
0.102201 + 0.994764i \(0.467412\pi\)
\(728\) 24.5592 0.910226
\(729\) 0 0
\(730\) −10.4254 −0.385861
\(731\) −1.90135 −0.0703240
\(732\) 0 0
\(733\) −7.42286 −0.274170 −0.137085 0.990559i \(-0.543773\pi\)
−0.137085 + 0.990559i \(0.543773\pi\)
\(734\) −30.4118 −1.12252
\(735\) 0 0
\(736\) −8.77465 −0.323438
\(737\) −44.8901 −1.65355
\(738\) 0 0
\(739\) 31.5583 1.16089 0.580445 0.814299i \(-0.302879\pi\)
0.580445 + 0.814299i \(0.302879\pi\)
\(740\) −17.6141 −0.647507
\(741\) 0 0
\(742\) 3.10184 0.113872
\(743\) 34.9462 1.28205 0.641027 0.767519i \(-0.278509\pi\)
0.641027 + 0.767519i \(0.278509\pi\)
\(744\) 0 0
\(745\) 13.3306 0.488394
\(746\) 39.2198 1.43594
\(747\) 0 0
\(748\) 7.55313 0.276170
\(749\) −15.4399 −0.564163
\(750\) 0 0
\(751\) 47.6101 1.73732 0.868659 0.495410i \(-0.164982\pi\)
0.868659 + 0.495410i \(0.164982\pi\)
\(752\) −30.2263 −1.10224
\(753\) 0 0
\(754\) −7.20347 −0.262335
\(755\) 12.1980 0.443929
\(756\) 0 0
\(757\) −7.55653 −0.274647 −0.137323 0.990526i \(-0.543850\pi\)
−0.137323 + 0.990526i \(0.543850\pi\)
\(758\) 38.8700 1.41182
\(759\) 0 0
\(760\) 10.1256 0.367296
\(761\) 2.24334 0.0813209 0.0406605 0.999173i \(-0.487054\pi\)
0.0406605 + 0.999173i \(0.487054\pi\)
\(762\) 0 0
\(763\) 8.22589 0.297797
\(764\) −71.9950 −2.60469
\(765\) 0 0
\(766\) 34.1061 1.23230
\(767\) 11.3234 0.408866
\(768\) 0 0
\(769\) −31.4607 −1.13450 −0.567250 0.823546i \(-0.691993\pi\)
−0.567250 + 0.823546i \(0.691993\pi\)
\(770\) 8.09126 0.291589
\(771\) 0 0
\(772\) −62.3501 −2.24403
\(773\) −7.68396 −0.276373 −0.138186 0.990406i \(-0.544127\pi\)
−0.138186 + 0.990406i \(0.544127\pi\)
\(774\) 0 0
\(775\) −17.5059 −0.628830
\(776\) 39.2423 1.40872
\(777\) 0 0
\(778\) −3.18096 −0.114043
\(779\) −10.9466 −0.392202
\(780\) 0 0
\(781\) 43.0354 1.53993
\(782\) 4.04080 0.144499
\(783\) 0 0
\(784\) 2.68284 0.0958157
\(785\) −15.9308 −0.568595
\(786\) 0 0
\(787\) −4.63829 −0.165337 −0.0826686 0.996577i \(-0.526344\pi\)
−0.0826686 + 0.996577i \(0.526344\pi\)
\(788\) 99.3326 3.53858
\(789\) 0 0
\(790\) 23.8520 0.848617
\(791\) 2.61402 0.0929438
\(792\) 0 0
\(793\) −54.5461 −1.93699
\(794\) −81.5845 −2.89533
\(795\) 0 0
\(796\) −2.56410 −0.0908823
\(797\) −50.7223 −1.79668 −0.898338 0.439304i \(-0.855225\pi\)
−0.898338 + 0.439304i \(0.855225\pi\)
\(798\) 0 0
\(799\) −4.46584 −0.157990
\(800\) 9.42052 0.333066
\(801\) 0 0
\(802\) 7.86294 0.277650
\(803\) −32.8858 −1.16051
\(804\) 0 0
\(805\) 2.82875 0.0997002
\(806\) 53.2650 1.87618
\(807\) 0 0
\(808\) −22.2326 −0.782139
\(809\) 8.25319 0.290167 0.145083 0.989419i \(-0.453655\pi\)
0.145083 + 0.989419i \(0.453655\pi\)
\(810\) 0 0
\(811\) −42.5309 −1.49346 −0.746731 0.665127i \(-0.768378\pi\)
−0.746731 + 0.665127i \(0.768378\pi\)
\(812\) −1.96014 −0.0687876
\(813\) 0 0
\(814\) −85.0234 −2.98007
\(815\) −9.85679 −0.345268
\(816\) 0 0
\(817\) −17.1162 −0.598821
\(818\) 19.0670 0.666664
\(819\) 0 0
\(820\) −7.71369 −0.269374
\(821\) −34.7449 −1.21260 −0.606302 0.795235i \(-0.707348\pi\)
−0.606302 + 0.795235i \(0.707348\pi\)
\(822\) 0 0
\(823\) 6.45981 0.225175 0.112587 0.993642i \(-0.464086\pi\)
0.112587 + 0.993642i \(0.464086\pi\)
\(824\) −4.45764 −0.155289
\(825\) 0 0
\(826\) 4.71506 0.164058
\(827\) 32.2022 1.11978 0.559889 0.828567i \(-0.310844\pi\)
0.559889 + 0.828567i \(0.310844\pi\)
\(828\) 0 0
\(829\) 17.8107 0.618593 0.309296 0.950966i \(-0.399906\pi\)
0.309296 + 0.950966i \(0.399906\pi\)
\(830\) −21.8743 −0.759269
\(831\) 0 0
\(832\) −59.6216 −2.06701
\(833\) 0.396381 0.0137338
\(834\) 0 0
\(835\) −14.1632 −0.490136
\(836\) 67.9943 2.35163
\(837\) 0 0
\(838\) 50.7265 1.75232
\(839\) −11.6047 −0.400639 −0.200319 0.979731i \(-0.564198\pi\)
−0.200319 + 0.979731i \(0.564198\pi\)
\(840\) 0 0
\(841\) −28.7299 −0.990687
\(842\) −72.2633 −2.49036
\(843\) 0 0
\(844\) 64.2875 2.21287
\(845\) 13.5251 0.465279
\(846\) 0 0
\(847\) 14.5230 0.499016
\(848\) 3.46385 0.118949
\(849\) 0 0
\(850\) −4.33823 −0.148800
\(851\) −29.7246 −1.01895
\(852\) 0 0
\(853\) 34.3397 1.17577 0.587884 0.808945i \(-0.299961\pi\)
0.587884 + 0.808945i \(0.299961\pi\)
\(854\) −22.7129 −0.777219
\(855\) 0 0
\(856\) −65.7225 −2.24635
\(857\) −14.3054 −0.488664 −0.244332 0.969692i \(-0.578569\pi\)
−0.244332 + 0.969692i \(0.578569\pi\)
\(858\) 0 0
\(859\) −49.4636 −1.68768 −0.843838 0.536597i \(-0.819709\pi\)
−0.843838 + 0.536597i \(0.819709\pi\)
\(860\) −12.0612 −0.411285
\(861\) 0 0
\(862\) 38.5014 1.31136
\(863\) 39.0263 1.32847 0.664235 0.747524i \(-0.268757\pi\)
0.664235 + 0.747524i \(0.268757\pi\)
\(864\) 0 0
\(865\) 5.35572 0.182100
\(866\) 17.3790 0.590564
\(867\) 0 0
\(868\) 14.4940 0.491958
\(869\) 75.2386 2.55229
\(870\) 0 0
\(871\) −51.2662 −1.73709
\(872\) 35.0148 1.18575
\(873\) 0 0
\(874\) 36.3759 1.23043
\(875\) −6.37019 −0.215352
\(876\) 0 0
\(877\) −32.8794 −1.11026 −0.555129 0.831764i \(-0.687331\pi\)
−0.555129 + 0.831764i \(0.687331\pi\)
\(878\) −25.0326 −0.844809
\(879\) 0 0
\(880\) 9.03557 0.304589
\(881\) 23.5044 0.791884 0.395942 0.918275i \(-0.370418\pi\)
0.395942 + 0.918275i \(0.370418\pi\)
\(882\) 0 0
\(883\) 3.78292 0.127305 0.0636527 0.997972i \(-0.479725\pi\)
0.0636527 + 0.997972i \(0.479725\pi\)
\(884\) 8.62596 0.290122
\(885\) 0 0
\(886\) 22.6564 0.761156
\(887\) −16.0603 −0.539253 −0.269627 0.962965i \(-0.586900\pi\)
−0.269627 + 0.962965i \(0.586900\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 20.1837 0.676560
\(891\) 0 0
\(892\) −78.2565 −2.62022
\(893\) −40.2021 −1.34531
\(894\) 0 0
\(895\) 12.3947 0.414309
\(896\) −20.6905 −0.691222
\(897\) 0 0
\(898\) 16.1990 0.540567
\(899\) −1.99701 −0.0666040
\(900\) 0 0
\(901\) 0.511773 0.0170496
\(902\) −37.2341 −1.23976
\(903\) 0 0
\(904\) 11.1270 0.370078
\(905\) 7.25189 0.241061
\(906\) 0 0
\(907\) −3.13873 −0.104220 −0.0521099 0.998641i \(-0.516595\pi\)
−0.0521099 + 0.998641i \(0.516595\pi\)
\(908\) 41.4304 1.37491
\(909\) 0 0
\(910\) 9.24052 0.306320
\(911\) −5.56286 −0.184306 −0.0921530 0.995745i \(-0.529375\pi\)
−0.0921530 + 0.995745i \(0.529375\pi\)
\(912\) 0 0
\(913\) −69.0001 −2.28357
\(914\) 12.1300 0.401224
\(915\) 0 0
\(916\) −13.9389 −0.460555
\(917\) −14.8530 −0.490488
\(918\) 0 0
\(919\) −55.9312 −1.84500 −0.922501 0.385995i \(-0.873858\pi\)
−0.922501 + 0.385995i \(0.873858\pi\)
\(920\) 12.0410 0.396980
\(921\) 0 0
\(922\) 30.8494 1.01597
\(923\) 49.1481 1.61773
\(924\) 0 0
\(925\) 31.9126 1.04928
\(926\) −17.5685 −0.577338
\(927\) 0 0
\(928\) 1.07466 0.0352774
\(929\) −15.0146 −0.492612 −0.246306 0.969192i \(-0.579217\pi\)
−0.246306 + 0.969192i \(0.579217\pi\)
\(930\) 0 0
\(931\) 3.56828 0.116946
\(932\) 101.951 3.33950
\(933\) 0 0
\(934\) 49.2343 1.61099
\(935\) 1.33498 0.0436584
\(936\) 0 0
\(937\) 6.36422 0.207910 0.103955 0.994582i \(-0.466850\pi\)
0.103955 + 0.994582i \(0.466850\pi\)
\(938\) −21.3472 −0.697010
\(939\) 0 0
\(940\) −28.3291 −0.923994
\(941\) 40.4525 1.31871 0.659357 0.751830i \(-0.270829\pi\)
0.659357 + 0.751830i \(0.270829\pi\)
\(942\) 0 0
\(943\) −13.0172 −0.423899
\(944\) 5.26535 0.171372
\(945\) 0 0
\(946\) −58.2197 −1.89289
\(947\) 48.6835 1.58200 0.791000 0.611816i \(-0.209561\pi\)
0.791000 + 0.611816i \(0.209561\pi\)
\(948\) 0 0
\(949\) −37.5568 −1.21915
\(950\) −39.0534 −1.26706
\(951\) 0 0
\(952\) 1.68726 0.0546844
\(953\) −2.87131 −0.0930110 −0.0465055 0.998918i \(-0.514809\pi\)
−0.0465055 + 0.998918i \(0.514809\pi\)
\(954\) 0 0
\(955\) −12.7247 −0.411763
\(956\) −9.93885 −0.321445
\(957\) 0 0
\(958\) −101.562 −3.28131
\(959\) 20.4969 0.661878
\(960\) 0 0
\(961\) −16.2334 −0.523659
\(962\) −97.1000 −3.13063
\(963\) 0 0
\(964\) 63.5185 2.04579
\(965\) −11.0201 −0.354749
\(966\) 0 0
\(967\) 45.1711 1.45261 0.726303 0.687375i \(-0.241237\pi\)
0.726303 + 0.687375i \(0.241237\pi\)
\(968\) 61.8193 1.98695
\(969\) 0 0
\(970\) 14.7651 0.474079
\(971\) 30.5373 0.979990 0.489995 0.871725i \(-0.336999\pi\)
0.489995 + 0.871725i \(0.336999\pi\)
\(972\) 0 0
\(973\) −3.53740 −0.113404
\(974\) 27.3147 0.875221
\(975\) 0 0
\(976\) −25.3637 −0.811871
\(977\) 51.3484 1.64278 0.821391 0.570365i \(-0.193198\pi\)
0.821391 + 0.570365i \(0.193198\pi\)
\(978\) 0 0
\(979\) 63.6674 2.03482
\(980\) 2.51445 0.0803211
\(981\) 0 0
\(982\) 21.3031 0.679810
\(983\) −17.9373 −0.572111 −0.286055 0.958213i \(-0.592344\pi\)
−0.286055 + 0.958213i \(0.592344\pi\)
\(984\) 0 0
\(985\) 17.5565 0.559398
\(986\) −0.494890 −0.0157605
\(987\) 0 0
\(988\) 77.6521 2.47044
\(989\) −20.3539 −0.647217
\(990\) 0 0
\(991\) 1.31878 0.0418924 0.0209462 0.999781i \(-0.493332\pi\)
0.0209462 + 0.999781i \(0.493332\pi\)
\(992\) −7.94641 −0.252299
\(993\) 0 0
\(994\) 20.4652 0.649116
\(995\) −0.453193 −0.0143672
\(996\) 0 0
\(997\) −4.64514 −0.147113 −0.0735565 0.997291i \(-0.523435\pi\)
−0.0735565 + 0.997291i \(0.523435\pi\)
\(998\) 11.8604 0.375433
\(999\) 0 0
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 \(a_p\))