Properties

Label 4031.2.a.c.1.15
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.55145 q^{2}\) \(+0.350675 q^{3}\) \(+0.406987 q^{4}\) \(-2.80587 q^{5}\) \(-0.544053 q^{6}\) \(-3.32540 q^{7}\) \(+2.47147 q^{8}\) \(-2.87703 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.55145 q^{2}\) \(+0.350675 q^{3}\) \(+0.406987 q^{4}\) \(-2.80587 q^{5}\) \(-0.544053 q^{6}\) \(-3.32540 q^{7}\) \(+2.47147 q^{8}\) \(-2.87703 q^{9}\) \(+4.35316 q^{10}\) \(-3.82247 q^{11}\) \(+0.142720 q^{12}\) \(+0.682868 q^{13}\) \(+5.15918 q^{14}\) \(-0.983948 q^{15}\) \(-4.64834 q^{16}\) \(+2.91413 q^{17}\) \(+4.46355 q^{18}\) \(+4.20224 q^{19}\) \(-1.14195 q^{20}\) \(-1.16613 q^{21}\) \(+5.93036 q^{22}\) \(+2.71492 q^{23}\) \(+0.866683 q^{24}\) \(+2.87291 q^{25}\) \(-1.05943 q^{26}\) \(-2.06092 q^{27}\) \(-1.35339 q^{28}\) \(-1.00000 q^{29}\) \(+1.52654 q^{30}\) \(+2.51179 q^{31}\) \(+2.26870 q^{32}\) \(-1.34044 q^{33}\) \(-4.52112 q^{34}\) \(+9.33063 q^{35}\) \(-1.17091 q^{36}\) \(-2.72784 q^{37}\) \(-6.51956 q^{38}\) \(+0.239465 q^{39}\) \(-6.93464 q^{40}\) \(+5.25069 q^{41}\) \(+1.80919 q^{42}\) \(+7.56996 q^{43}\) \(-1.55570 q^{44}\) \(+8.07257 q^{45}\) \(-4.21205 q^{46}\) \(+6.67214 q^{47}\) \(-1.63005 q^{48}\) \(+4.05826 q^{49}\) \(-4.45717 q^{50}\) \(+1.02191 q^{51}\) \(+0.277919 q^{52}\) \(-0.715752 q^{53}\) \(+3.19741 q^{54}\) \(+10.7254 q^{55}\) \(-8.21863 q^{56}\) \(+1.47362 q^{57}\) \(+1.55145 q^{58}\) \(-1.54046 q^{59}\) \(-0.400454 q^{60}\) \(+4.04596 q^{61}\) \(-3.89691 q^{62}\) \(+9.56726 q^{63}\) \(+5.77691 q^{64}\) \(-1.91604 q^{65}\) \(+2.07963 q^{66}\) \(-7.46543 q^{67}\) \(+1.18601 q^{68}\) \(+0.952053 q^{69}\) \(-14.4760 q^{70}\) \(+3.18730 q^{71}\) \(-7.11050 q^{72}\) \(+7.53899 q^{73}\) \(+4.23210 q^{74}\) \(+1.00746 q^{75}\) \(+1.71026 q^{76}\) \(+12.7112 q^{77}\) \(-0.371516 q^{78}\) \(-10.7323 q^{79}\) \(+13.0426 q^{80}\) \(+7.90837 q^{81}\) \(-8.14617 q^{82}\) \(+4.35926 q^{83}\) \(-0.474601 q^{84}\) \(-8.17668 q^{85}\) \(-11.7444 q^{86}\) \(-0.350675 q^{87}\) \(-9.44714 q^{88}\) \(+9.22015 q^{89}\) \(-12.5242 q^{90}\) \(-2.27081 q^{91}\) \(+1.10494 q^{92}\) \(+0.880820 q^{93}\) \(-10.3515 q^{94}\) \(-11.7909 q^{95}\) \(+0.795574 q^{96}\) \(-17.8047 q^{97}\) \(-6.29617 q^{98}\) \(+10.9974 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55145 −1.09704 −0.548519 0.836138i \(-0.684808\pi\)
−0.548519 + 0.836138i \(0.684808\pi\)
\(3\) 0.350675 0.202462 0.101231 0.994863i \(-0.467722\pi\)
0.101231 + 0.994863i \(0.467722\pi\)
\(4\) 0.406987 0.203494
\(5\) −2.80587 −1.25482 −0.627412 0.778688i \(-0.715886\pi\)
−0.627412 + 0.778688i \(0.715886\pi\)
\(6\) −0.544053 −0.222109
\(7\) −3.32540 −1.25688 −0.628441 0.777857i \(-0.716307\pi\)
−0.628441 + 0.777857i \(0.716307\pi\)
\(8\) 2.47147 0.873798
\(9\) −2.87703 −0.959009
\(10\) 4.35316 1.37659
\(11\) −3.82247 −1.15252 −0.576259 0.817267i \(-0.695488\pi\)
−0.576259 + 0.817267i \(0.695488\pi\)
\(12\) 0.142720 0.0411997
\(13\) 0.682868 0.189394 0.0946968 0.995506i \(-0.469812\pi\)
0.0946968 + 0.995506i \(0.469812\pi\)
\(14\) 5.15918 1.37885
\(15\) −0.983948 −0.254054
\(16\) −4.64834 −1.16208
\(17\) 2.91413 0.706781 0.353390 0.935476i \(-0.385029\pi\)
0.353390 + 0.935476i \(0.385029\pi\)
\(18\) 4.46355 1.05207
\(19\) 4.20224 0.964060 0.482030 0.876155i \(-0.339900\pi\)
0.482030 + 0.876155i \(0.339900\pi\)
\(20\) −1.14195 −0.255349
\(21\) −1.16613 −0.254471
\(22\) 5.93036 1.26436
\(23\) 2.71492 0.566100 0.283050 0.959105i \(-0.408654\pi\)
0.283050 + 0.959105i \(0.408654\pi\)
\(24\) 0.866683 0.176911
\(25\) 2.87291 0.574582
\(26\) −1.05943 −0.207772
\(27\) −2.06092 −0.396625
\(28\) −1.35339 −0.255767
\(29\) −1.00000 −0.185695
\(30\) 1.52654 0.278707
\(31\) 2.51179 0.451131 0.225565 0.974228i \(-0.427577\pi\)
0.225565 + 0.974228i \(0.427577\pi\)
\(32\) 2.26870 0.401053
\(33\) −1.34044 −0.233341
\(34\) −4.52112 −0.775366
\(35\) 9.33063 1.57716
\(36\) −1.17091 −0.195152
\(37\) −2.72784 −0.448455 −0.224227 0.974537i \(-0.571986\pi\)
−0.224227 + 0.974537i \(0.571986\pi\)
\(38\) −6.51956 −1.05761
\(39\) 0.239465 0.0383450
\(40\) −6.93464 −1.09646
\(41\) 5.25069 0.820020 0.410010 0.912081i \(-0.365525\pi\)
0.410010 + 0.912081i \(0.365525\pi\)
\(42\) 1.80919 0.279164
\(43\) 7.56996 1.15441 0.577204 0.816600i \(-0.304144\pi\)
0.577204 + 0.816600i \(0.304144\pi\)
\(44\) −1.55570 −0.234530
\(45\) 8.07257 1.20339
\(46\) −4.21205 −0.621033
\(47\) 6.67214 0.973232 0.486616 0.873616i \(-0.338231\pi\)
0.486616 + 0.873616i \(0.338231\pi\)
\(48\) −1.63005 −0.235278
\(49\) 4.05826 0.579751
\(50\) −4.45717 −0.630339
\(51\) 1.02191 0.143096
\(52\) 0.277919 0.0385404
\(53\) −0.715752 −0.0983161 −0.0491581 0.998791i \(-0.515654\pi\)
−0.0491581 + 0.998791i \(0.515654\pi\)
\(54\) 3.19741 0.435113
\(55\) 10.7254 1.44621
\(56\) −8.21863 −1.09826
\(57\) 1.47362 0.195186
\(58\) 1.55145 0.203715
\(59\) −1.54046 −0.200551 −0.100275 0.994960i \(-0.531972\pi\)
−0.100275 + 0.994960i \(0.531972\pi\)
\(60\) −0.400454 −0.0516984
\(61\) 4.04596 0.518032 0.259016 0.965873i \(-0.416602\pi\)
0.259016 + 0.965873i \(0.416602\pi\)
\(62\) −3.89691 −0.494908
\(63\) 9.56726 1.20536
\(64\) 5.77691 0.722114
\(65\) −1.91604 −0.237656
\(66\) 2.07963 0.255984
\(67\) −7.46543 −0.912048 −0.456024 0.889967i \(-0.650727\pi\)
−0.456024 + 0.889967i \(0.650727\pi\)
\(68\) 1.18601 0.143825
\(69\) 0.952053 0.114614
\(70\) −14.4760 −1.73021
\(71\) 3.18730 0.378263 0.189131 0.981952i \(-0.439433\pi\)
0.189131 + 0.981952i \(0.439433\pi\)
\(72\) −7.11050 −0.837980
\(73\) 7.53899 0.882372 0.441186 0.897416i \(-0.354558\pi\)
0.441186 + 0.897416i \(0.354558\pi\)
\(74\) 4.23210 0.491972
\(75\) 1.00746 0.116331
\(76\) 1.71026 0.196180
\(77\) 12.7112 1.44858
\(78\) −0.371516 −0.0420660
\(79\) −10.7323 −1.20748 −0.603739 0.797182i \(-0.706323\pi\)
−0.603739 + 0.797182i \(0.706323\pi\)
\(80\) 13.0426 1.45821
\(81\) 7.90837 0.878708
\(82\) −8.14617 −0.899594
\(83\) 4.35926 0.478491 0.239246 0.970959i \(-0.423100\pi\)
0.239246 + 0.970959i \(0.423100\pi\)
\(84\) −0.474601 −0.0517832
\(85\) −8.17668 −0.886885
\(86\) −11.7444 −1.26643
\(87\) −0.350675 −0.0375963
\(88\) −9.44714 −1.00707
\(89\) 9.22015 0.977333 0.488667 0.872471i \(-0.337483\pi\)
0.488667 + 0.872471i \(0.337483\pi\)
\(90\) −12.5242 −1.32016
\(91\) −2.27081 −0.238045
\(92\) 1.10494 0.115198
\(93\) 0.880820 0.0913368
\(94\) −10.3515 −1.06767
\(95\) −11.7909 −1.20973
\(96\) 0.795574 0.0811979
\(97\) −17.8047 −1.80780 −0.903898 0.427747i \(-0.859307\pi\)
−0.903898 + 0.427747i \(0.859307\pi\)
\(98\) −6.29617 −0.636010
\(99\) 10.9974 1.10528
\(100\) 1.16924 0.116924
\(101\) −2.76335 −0.274964 −0.137482 0.990504i \(-0.543901\pi\)
−0.137482 + 0.990504i \(0.543901\pi\)
\(102\) −1.58544 −0.156982
\(103\) −11.6156 −1.14452 −0.572259 0.820073i \(-0.693933\pi\)
−0.572259 + 0.820073i \(0.693933\pi\)
\(104\) 1.68769 0.165492
\(105\) 3.27202 0.319316
\(106\) 1.11045 0.107857
\(107\) −16.1174 −1.55813 −0.779064 0.626944i \(-0.784305\pi\)
−0.779064 + 0.626944i \(0.784305\pi\)
\(108\) −0.838770 −0.0807106
\(109\) 17.8945 1.71398 0.856990 0.515333i \(-0.172332\pi\)
0.856990 + 0.515333i \(0.172332\pi\)
\(110\) −16.6398 −1.58655
\(111\) −0.956585 −0.0907950
\(112\) 15.4576 1.46060
\(113\) 4.06640 0.382535 0.191267 0.981538i \(-0.438740\pi\)
0.191267 + 0.981538i \(0.438740\pi\)
\(114\) −2.28624 −0.214126
\(115\) −7.61771 −0.710355
\(116\) −0.406987 −0.0377878
\(117\) −1.96463 −0.181630
\(118\) 2.38994 0.220012
\(119\) −9.69064 −0.888340
\(120\) −2.43180 −0.221992
\(121\) 3.61129 0.328299
\(122\) −6.27709 −0.568301
\(123\) 1.84128 0.166023
\(124\) 1.02227 0.0918022
\(125\) 5.96833 0.533824
\(126\) −14.8431 −1.32233
\(127\) 14.7589 1.30964 0.654821 0.755784i \(-0.272744\pi\)
0.654821 + 0.755784i \(0.272744\pi\)
\(128\) −13.5000 −1.19324
\(129\) 2.65459 0.233724
\(130\) 2.97263 0.260717
\(131\) 8.69323 0.759531 0.379765 0.925083i \(-0.376005\pi\)
0.379765 + 0.925083i \(0.376005\pi\)
\(132\) −0.545543 −0.0474834
\(133\) −13.9741 −1.21171
\(134\) 11.5822 1.00055
\(135\) 5.78269 0.497694
\(136\) 7.20220 0.617584
\(137\) −15.1191 −1.29171 −0.645854 0.763461i \(-0.723499\pi\)
−0.645854 + 0.763461i \(0.723499\pi\)
\(138\) −1.47706 −0.125736
\(139\) −1.00000 −0.0848189
\(140\) 3.79745 0.320943
\(141\) 2.33975 0.197043
\(142\) −4.94492 −0.414969
\(143\) −2.61024 −0.218280
\(144\) 13.3734 1.11445
\(145\) 2.80587 0.233015
\(146\) −11.6963 −0.967996
\(147\) 1.42313 0.117378
\(148\) −1.11020 −0.0912576
\(149\) −2.81214 −0.230379 −0.115190 0.993344i \(-0.536748\pi\)
−0.115190 + 0.993344i \(0.536748\pi\)
\(150\) −1.56302 −0.127620
\(151\) −4.90219 −0.398934 −0.199467 0.979905i \(-0.563921\pi\)
−0.199467 + 0.979905i \(0.563921\pi\)
\(152\) 10.3857 0.842394
\(153\) −8.38404 −0.677809
\(154\) −19.7208 −1.58915
\(155\) −7.04776 −0.566089
\(156\) 0.0974590 0.00780296
\(157\) −11.8804 −0.948162 −0.474081 0.880481i \(-0.657220\pi\)
−0.474081 + 0.880481i \(0.657220\pi\)
\(158\) 16.6506 1.32465
\(159\) −0.250996 −0.0199053
\(160\) −6.36567 −0.503250
\(161\) −9.02818 −0.711520
\(162\) −12.2694 −0.963976
\(163\) −2.69216 −0.210866 −0.105433 0.994426i \(-0.533623\pi\)
−0.105433 + 0.994426i \(0.533623\pi\)
\(164\) 2.13696 0.166869
\(165\) 3.76111 0.292802
\(166\) −6.76317 −0.524924
\(167\) −4.68479 −0.362520 −0.181260 0.983435i \(-0.558018\pi\)
−0.181260 + 0.983435i \(0.558018\pi\)
\(168\) −2.88207 −0.222356
\(169\) −12.5337 −0.964130
\(170\) 12.6857 0.972947
\(171\) −12.0900 −0.924543
\(172\) 3.08088 0.234915
\(173\) 2.09648 0.159392 0.0796961 0.996819i \(-0.474605\pi\)
0.0796961 + 0.996819i \(0.474605\pi\)
\(174\) 0.544053 0.0412445
\(175\) −9.55357 −0.722182
\(176\) 17.7681 1.33932
\(177\) −0.540200 −0.0406039
\(178\) −14.3046 −1.07217
\(179\) 9.18320 0.686384 0.343192 0.939265i \(-0.388492\pi\)
0.343192 + 0.939265i \(0.388492\pi\)
\(180\) 3.28543 0.244882
\(181\) 10.5343 0.783006 0.391503 0.920177i \(-0.371955\pi\)
0.391503 + 0.920177i \(0.371955\pi\)
\(182\) 3.52304 0.261145
\(183\) 1.41882 0.104882
\(184\) 6.70985 0.494657
\(185\) 7.65397 0.562731
\(186\) −1.36655 −0.100200
\(187\) −11.1392 −0.814578
\(188\) 2.71548 0.198046
\(189\) 6.85339 0.498511
\(190\) 18.2930 1.32712
\(191\) 4.95181 0.358301 0.179150 0.983822i \(-0.442665\pi\)
0.179150 + 0.983822i \(0.442665\pi\)
\(192\) 2.02582 0.146201
\(193\) 2.74857 0.197846 0.0989231 0.995095i \(-0.468460\pi\)
0.0989231 + 0.995095i \(0.468460\pi\)
\(194\) 27.6231 1.98322
\(195\) −0.671907 −0.0481162
\(196\) 1.65166 0.117976
\(197\) 7.83508 0.558226 0.279113 0.960258i \(-0.409960\pi\)
0.279113 + 0.960258i \(0.409960\pi\)
\(198\) −17.0618 −1.21253
\(199\) −8.05143 −0.570751 −0.285376 0.958416i \(-0.592118\pi\)
−0.285376 + 0.958416i \(0.592118\pi\)
\(200\) 7.10033 0.502069
\(201\) −2.61794 −0.184655
\(202\) 4.28720 0.301646
\(203\) 3.32540 0.233397
\(204\) 0.415905 0.0291192
\(205\) −14.7328 −1.02898
\(206\) 18.0210 1.25558
\(207\) −7.81089 −0.542895
\(208\) −3.17420 −0.220091
\(209\) −16.0629 −1.11110
\(210\) −5.07636 −0.350302
\(211\) −1.98324 −0.136532 −0.0682659 0.997667i \(-0.521747\pi\)
−0.0682659 + 0.997667i \(0.521747\pi\)
\(212\) −0.291302 −0.0200067
\(213\) 1.11770 0.0765838
\(214\) 25.0053 1.70933
\(215\) −21.2403 −1.44858
\(216\) −5.09352 −0.346570
\(217\) −8.35269 −0.567018
\(218\) −27.7623 −1.88030
\(219\) 2.64373 0.178647
\(220\) 4.36508 0.294294
\(221\) 1.98997 0.133860
\(222\) 1.48409 0.0996056
\(223\) 7.39797 0.495405 0.247702 0.968836i \(-0.420325\pi\)
0.247702 + 0.968836i \(0.420325\pi\)
\(224\) −7.54431 −0.504076
\(225\) −8.26545 −0.551030
\(226\) −6.30881 −0.419655
\(227\) −13.2342 −0.878386 −0.439193 0.898393i \(-0.644736\pi\)
−0.439193 + 0.898393i \(0.644736\pi\)
\(228\) 0.599744 0.0397190
\(229\) −0.461974 −0.0305281 −0.0152640 0.999883i \(-0.504859\pi\)
−0.0152640 + 0.999883i \(0.504859\pi\)
\(230\) 11.8185 0.779287
\(231\) 4.45750 0.293282
\(232\) −2.47147 −0.162260
\(233\) 2.25945 0.148021 0.0740107 0.997257i \(-0.476420\pi\)
0.0740107 + 0.997257i \(0.476420\pi\)
\(234\) 3.04802 0.199255
\(235\) −18.7212 −1.22123
\(236\) −0.626948 −0.0408108
\(237\) −3.76354 −0.244468
\(238\) 15.0345 0.974543
\(239\) 30.0187 1.94175 0.970873 0.239593i \(-0.0770141\pi\)
0.970873 + 0.239593i \(0.0770141\pi\)
\(240\) 4.57372 0.295232
\(241\) −14.8413 −0.956014 −0.478007 0.878356i \(-0.658641\pi\)
−0.478007 + 0.878356i \(0.658641\pi\)
\(242\) −5.60272 −0.360156
\(243\) 8.95604 0.574530
\(244\) 1.64665 0.105416
\(245\) −11.3870 −0.727486
\(246\) −2.85665 −0.182134
\(247\) 2.86958 0.182587
\(248\) 6.20782 0.394197
\(249\) 1.52868 0.0968763
\(250\) −9.25955 −0.585626
\(251\) −12.3814 −0.781507 −0.390754 0.920495i \(-0.627786\pi\)
−0.390754 + 0.920495i \(0.627786\pi\)
\(252\) 3.89375 0.245283
\(253\) −10.3777 −0.652440
\(254\) −22.8977 −1.43673
\(255\) −2.86735 −0.179561
\(256\) 9.39065 0.586916
\(257\) −17.0022 −1.06057 −0.530284 0.847820i \(-0.677915\pi\)
−0.530284 + 0.847820i \(0.677915\pi\)
\(258\) −4.11846 −0.256404
\(259\) 9.07116 0.563654
\(260\) −0.779804 −0.0483614
\(261\) 2.87703 0.178084
\(262\) −13.4871 −0.833234
\(263\) 15.3799 0.948363 0.474182 0.880427i \(-0.342744\pi\)
0.474182 + 0.880427i \(0.342744\pi\)
\(264\) −3.31287 −0.203893
\(265\) 2.00831 0.123369
\(266\) 21.6801 1.32929
\(267\) 3.23327 0.197873
\(268\) −3.03834 −0.185596
\(269\) −11.1763 −0.681430 −0.340715 0.940167i \(-0.610669\pi\)
−0.340715 + 0.940167i \(0.610669\pi\)
\(270\) −8.97153 −0.545990
\(271\) −25.8034 −1.56745 −0.783723 0.621111i \(-0.786682\pi\)
−0.783723 + 0.621111i \(0.786682\pi\)
\(272\) −13.5459 −0.821339
\(273\) −0.796314 −0.0481951
\(274\) 23.4564 1.41705
\(275\) −10.9816 −0.662217
\(276\) 0.387473 0.0233231
\(277\) 21.8613 1.31352 0.656761 0.754099i \(-0.271926\pi\)
0.656761 + 0.754099i \(0.271926\pi\)
\(278\) 1.55145 0.0930496
\(279\) −7.22649 −0.432638
\(280\) 23.0604 1.37812
\(281\) 14.7721 0.881232 0.440616 0.897696i \(-0.354760\pi\)
0.440616 + 0.897696i \(0.354760\pi\)
\(282\) −3.63000 −0.216163
\(283\) 9.30807 0.553307 0.276654 0.960970i \(-0.410775\pi\)
0.276654 + 0.960970i \(0.410775\pi\)
\(284\) 1.29719 0.0769740
\(285\) −4.13479 −0.244924
\(286\) 4.04966 0.239461
\(287\) −17.4606 −1.03067
\(288\) −6.52710 −0.384613
\(289\) −8.50784 −0.500461
\(290\) −4.35316 −0.255626
\(291\) −6.24367 −0.366010
\(292\) 3.06827 0.179557
\(293\) −15.9406 −0.931258 −0.465629 0.884980i \(-0.654172\pi\)
−0.465629 + 0.884980i \(0.654172\pi\)
\(294\) −2.20791 −0.128768
\(295\) 4.32233 0.251656
\(296\) −6.74179 −0.391859
\(297\) 7.87782 0.457118
\(298\) 4.36288 0.252735
\(299\) 1.85393 0.107216
\(300\) 0.410022 0.0236726
\(301\) −25.1731 −1.45096
\(302\) 7.60548 0.437646
\(303\) −0.969038 −0.0556698
\(304\) −19.5334 −1.12032
\(305\) −11.3524 −0.650039
\(306\) 13.0074 0.743583
\(307\) 9.76356 0.557236 0.278618 0.960402i \(-0.410124\pi\)
0.278618 + 0.960402i \(0.410124\pi\)
\(308\) 5.17331 0.294777
\(309\) −4.07329 −0.231722
\(310\) 10.9342 0.621022
\(311\) −11.9926 −0.680040 −0.340020 0.940418i \(-0.610434\pi\)
−0.340020 + 0.940418i \(0.610434\pi\)
\(312\) 0.591831 0.0335058
\(313\) 9.75494 0.551382 0.275691 0.961246i \(-0.411093\pi\)
0.275691 + 0.961246i \(0.411093\pi\)
\(314\) 18.4319 1.04017
\(315\) −26.8445 −1.51252
\(316\) −4.36791 −0.245714
\(317\) 25.8018 1.44917 0.724587 0.689184i \(-0.242031\pi\)
0.724587 + 0.689184i \(0.242031\pi\)
\(318\) 0.389407 0.0218369
\(319\) 3.82247 0.214017
\(320\) −16.2093 −0.906125
\(321\) −5.65196 −0.315462
\(322\) 14.0067 0.780565
\(323\) 12.2459 0.681379
\(324\) 3.21860 0.178811
\(325\) 1.96182 0.108822
\(326\) 4.17674 0.231328
\(327\) 6.27514 0.347016
\(328\) 12.9769 0.716532
\(329\) −22.1875 −1.22324
\(330\) −5.83516 −0.321215
\(331\) −12.7650 −0.701627 −0.350814 0.936445i \(-0.614095\pi\)
−0.350814 + 0.936445i \(0.614095\pi\)
\(332\) 1.77416 0.0973699
\(333\) 7.84808 0.430072
\(334\) 7.26821 0.397699
\(335\) 20.9470 1.14446
\(336\) 5.42057 0.295716
\(337\) −19.3249 −1.05270 −0.526348 0.850269i \(-0.676439\pi\)
−0.526348 + 0.850269i \(0.676439\pi\)
\(338\) 19.4454 1.05769
\(339\) 1.42598 0.0774488
\(340\) −3.32780 −0.180475
\(341\) −9.60124 −0.519936
\(342\) 18.7569 1.01426
\(343\) 9.78245 0.528203
\(344\) 18.7090 1.00872
\(345\) −2.67134 −0.143820
\(346\) −3.25257 −0.174859
\(347\) 30.1874 1.62054 0.810271 0.586055i \(-0.199320\pi\)
0.810271 + 0.586055i \(0.199320\pi\)
\(348\) −0.142720 −0.00765060
\(349\) −17.2574 −0.923767 −0.461883 0.886941i \(-0.652826\pi\)
−0.461883 + 0.886941i \(0.652826\pi\)
\(350\) 14.8219 0.792261
\(351\) −1.40734 −0.0751182
\(352\) −8.67203 −0.462221
\(353\) 16.1406 0.859077 0.429538 0.903049i \(-0.358676\pi\)
0.429538 + 0.903049i \(0.358676\pi\)
\(354\) 0.838092 0.0445441
\(355\) −8.94315 −0.474653
\(356\) 3.75248 0.198881
\(357\) −3.39826 −0.179855
\(358\) −14.2472 −0.752990
\(359\) 3.96669 0.209354 0.104677 0.994506i \(-0.466619\pi\)
0.104677 + 0.994506i \(0.466619\pi\)
\(360\) 19.9511 1.05152
\(361\) −1.34116 −0.0705874
\(362\) −16.3434 −0.858988
\(363\) 1.26639 0.0664680
\(364\) −0.924190 −0.0484407
\(365\) −21.1534 −1.10722
\(366\) −2.20122 −0.115059
\(367\) −26.9004 −1.40419 −0.702094 0.712085i \(-0.747751\pi\)
−0.702094 + 0.712085i \(0.747751\pi\)
\(368\) −12.6199 −0.657855
\(369\) −15.1064 −0.786407
\(370\) −11.8747 −0.617338
\(371\) 2.38016 0.123572
\(372\) 0.358483 0.0185865
\(373\) 26.4384 1.36893 0.684465 0.729046i \(-0.260036\pi\)
0.684465 + 0.729046i \(0.260036\pi\)
\(374\) 17.2819 0.893623
\(375\) 2.09294 0.108079
\(376\) 16.4900 0.850408
\(377\) −0.682868 −0.0351695
\(378\) −10.6327 −0.546885
\(379\) 5.64307 0.289865 0.144932 0.989442i \(-0.453704\pi\)
0.144932 + 0.989442i \(0.453704\pi\)
\(380\) −4.79876 −0.246171
\(381\) 5.17558 0.265153
\(382\) −7.68247 −0.393070
\(383\) 11.4307 0.584079 0.292040 0.956406i \(-0.405666\pi\)
0.292040 + 0.956406i \(0.405666\pi\)
\(384\) −4.73409 −0.241586
\(385\) −35.6661 −1.81771
\(386\) −4.26426 −0.217045
\(387\) −21.7790 −1.10709
\(388\) −7.24630 −0.367875
\(389\) −32.7769 −1.66185 −0.830927 0.556382i \(-0.812189\pi\)
−0.830927 + 0.556382i \(0.812189\pi\)
\(390\) 1.04243 0.0527854
\(391\) 7.91163 0.400108
\(392\) 10.0299 0.506586
\(393\) 3.04849 0.153776
\(394\) −12.1557 −0.612395
\(395\) 30.1134 1.51517
\(396\) 4.47578 0.224916
\(397\) −10.2491 −0.514390 −0.257195 0.966360i \(-0.582798\pi\)
−0.257195 + 0.966360i \(0.582798\pi\)
\(398\) 12.4914 0.626136
\(399\) −4.90037 −0.245325
\(400\) −13.3543 −0.667713
\(401\) −23.7630 −1.18667 −0.593333 0.804957i \(-0.702188\pi\)
−0.593333 + 0.804957i \(0.702188\pi\)
\(402\) 4.06159 0.202574
\(403\) 1.71522 0.0854412
\(404\) −1.12465 −0.0559534
\(405\) −22.1899 −1.10262
\(406\) −5.15918 −0.256046
\(407\) 10.4271 0.516852
\(408\) 2.52563 0.125037
\(409\) −5.32203 −0.263158 −0.131579 0.991306i \(-0.542005\pi\)
−0.131579 + 0.991306i \(0.542005\pi\)
\(410\) 22.8571 1.12883
\(411\) −5.30187 −0.261522
\(412\) −4.72740 −0.232902
\(413\) 5.12264 0.252069
\(414\) 12.1182 0.595576
\(415\) −12.2315 −0.600422
\(416\) 1.54922 0.0759568
\(417\) −0.350675 −0.0171726
\(418\) 24.9208 1.21892
\(419\) 28.9917 1.41634 0.708168 0.706043i \(-0.249522\pi\)
0.708168 + 0.706043i \(0.249522\pi\)
\(420\) 1.33167 0.0649788
\(421\) −13.6625 −0.665871 −0.332936 0.942950i \(-0.608039\pi\)
−0.332936 + 0.942950i \(0.608039\pi\)
\(422\) 3.07689 0.149781
\(423\) −19.1959 −0.933338
\(424\) −1.76896 −0.0859085
\(425\) 8.37204 0.406104
\(426\) −1.73406 −0.0840154
\(427\) −13.4544 −0.651105
\(428\) −6.55958 −0.317069
\(429\) −0.915346 −0.0441933
\(430\) 32.9533 1.58915
\(431\) 32.7563 1.57782 0.788908 0.614511i \(-0.210647\pi\)
0.788908 + 0.614511i \(0.210647\pi\)
\(432\) 9.57987 0.460912
\(433\) −16.0628 −0.771931 −0.385965 0.922513i \(-0.626132\pi\)
−0.385965 + 0.922513i \(0.626132\pi\)
\(434\) 12.9588 0.622040
\(435\) 0.983948 0.0471767
\(436\) 7.28282 0.348784
\(437\) 11.4087 0.545754
\(438\) −4.10161 −0.195982
\(439\) 39.2799 1.87473 0.937365 0.348349i \(-0.113258\pi\)
0.937365 + 0.348349i \(0.113258\pi\)
\(440\) 26.5075 1.26369
\(441\) −11.6757 −0.555987
\(442\) −3.08733 −0.146849
\(443\) −12.2292 −0.581028 −0.290514 0.956871i \(-0.593826\pi\)
−0.290514 + 0.956871i \(0.593826\pi\)
\(444\) −0.389318 −0.0184762
\(445\) −25.8705 −1.22638
\(446\) −11.4776 −0.543478
\(447\) −0.986145 −0.0466430
\(448\) −19.2105 −0.907611
\(449\) 40.8373 1.92723 0.963615 0.267294i \(-0.0861296\pi\)
0.963615 + 0.267294i \(0.0861296\pi\)
\(450\) 12.8234 0.604501
\(451\) −20.0706 −0.945088
\(452\) 1.65497 0.0778434
\(453\) −1.71907 −0.0807690
\(454\) 20.5322 0.963624
\(455\) 6.37159 0.298705
\(456\) 3.64201 0.170553
\(457\) −24.6290 −1.15210 −0.576049 0.817415i \(-0.695406\pi\)
−0.576049 + 0.817415i \(0.695406\pi\)
\(458\) 0.716728 0.0334905
\(459\) −6.00580 −0.280327
\(460\) −3.10031 −0.144553
\(461\) 21.4532 0.999177 0.499588 0.866263i \(-0.333485\pi\)
0.499588 + 0.866263i \(0.333485\pi\)
\(462\) −6.91558 −0.321742
\(463\) −24.6768 −1.14683 −0.573415 0.819265i \(-0.694382\pi\)
−0.573415 + 0.819265i \(0.694382\pi\)
\(464\) 4.64834 0.215794
\(465\) −2.47147 −0.114612
\(466\) −3.50541 −0.162385
\(467\) −18.5112 −0.856594 −0.428297 0.903638i \(-0.640886\pi\)
−0.428297 + 0.903638i \(0.640886\pi\)
\(468\) −0.799580 −0.0369606
\(469\) 24.8255 1.14634
\(470\) 29.0449 1.33974
\(471\) −4.16617 −0.191967
\(472\) −3.80721 −0.175241
\(473\) −28.9360 −1.33048
\(474\) 5.83893 0.268191
\(475\) 12.0727 0.553932
\(476\) −3.94397 −0.180771
\(477\) 2.05924 0.0942861
\(478\) −46.5724 −2.13017
\(479\) −33.9491 −1.55117 −0.775587 0.631241i \(-0.782546\pi\)
−0.775587 + 0.631241i \(0.782546\pi\)
\(480\) −2.23228 −0.101889
\(481\) −1.86276 −0.0849344
\(482\) 23.0255 1.04878
\(483\) −3.16595 −0.144056
\(484\) 1.46975 0.0668067
\(485\) 49.9578 2.26847
\(486\) −13.8948 −0.630281
\(487\) −19.2546 −0.872509 −0.436254 0.899823i \(-0.643695\pi\)
−0.436254 + 0.899823i \(0.643695\pi\)
\(488\) 9.99949 0.452656
\(489\) −0.944070 −0.0426923
\(490\) 17.6662 0.798080
\(491\) 5.25042 0.236948 0.118474 0.992957i \(-0.462200\pi\)
0.118474 + 0.992957i \(0.462200\pi\)
\(492\) 0.749379 0.0337846
\(493\) −2.91413 −0.131246
\(494\) −4.45200 −0.200305
\(495\) −30.8572 −1.38693
\(496\) −11.6756 −0.524252
\(497\) −10.5990 −0.475431
\(498\) −2.37167 −0.106277
\(499\) −20.5863 −0.921570 −0.460785 0.887512i \(-0.652432\pi\)
−0.460785 + 0.887512i \(0.652432\pi\)
\(500\) 2.42904 0.108630
\(501\) −1.64284 −0.0733966
\(502\) 19.2091 0.857344
\(503\) −19.8253 −0.883965 −0.441982 0.897024i \(-0.645725\pi\)
−0.441982 + 0.897024i \(0.645725\pi\)
\(504\) 23.6452 1.05324
\(505\) 7.75361 0.345031
\(506\) 16.1004 0.715752
\(507\) −4.39525 −0.195200
\(508\) 6.00669 0.266504
\(509\) 6.68879 0.296475 0.148238 0.988952i \(-0.452640\pi\)
0.148238 + 0.988952i \(0.452640\pi\)
\(510\) 4.44855 0.196985
\(511\) −25.0701 −1.10904
\(512\) 12.4308 0.549370
\(513\) −8.66050 −0.382370
\(514\) 26.3780 1.16348
\(515\) 32.5919 1.43617
\(516\) 1.08039 0.0475613
\(517\) −25.5041 −1.12167
\(518\) −14.0734 −0.618350
\(519\) 0.735181 0.0322709
\(520\) −4.73545 −0.207663
\(521\) −32.2542 −1.41308 −0.706540 0.707673i \(-0.749745\pi\)
−0.706540 + 0.707673i \(0.749745\pi\)
\(522\) −4.46355 −0.195364
\(523\) −28.2310 −1.23445 −0.617227 0.786785i \(-0.711744\pi\)
−0.617227 + 0.786785i \(0.711744\pi\)
\(524\) 3.53803 0.154560
\(525\) −3.35019 −0.146214
\(526\) −23.8610 −1.04039
\(527\) 7.31968 0.318850
\(528\) 6.23083 0.271162
\(529\) −15.6292 −0.679531
\(530\) −3.11578 −0.135341
\(531\) 4.43195 0.192330
\(532\) −5.68729 −0.246575
\(533\) 3.58553 0.155307
\(534\) −5.01625 −0.217074
\(535\) 45.2234 1.95518
\(536\) −18.4506 −0.796946
\(537\) 3.22031 0.138967
\(538\) 17.3394 0.747554
\(539\) −15.5126 −0.668174
\(540\) 2.35348 0.101278
\(541\) 8.83992 0.380058 0.190029 0.981778i \(-0.439142\pi\)
0.190029 + 0.981778i \(0.439142\pi\)
\(542\) 40.0326 1.71955
\(543\) 3.69410 0.158529
\(544\) 6.61128 0.283456
\(545\) −50.2096 −2.15074
\(546\) 1.23544 0.0528719
\(547\) 25.5225 1.09127 0.545633 0.838024i \(-0.316289\pi\)
0.545633 + 0.838024i \(0.316289\pi\)
\(548\) −6.15326 −0.262854
\(549\) −11.6403 −0.496798
\(550\) 17.0374 0.726477
\(551\) −4.20224 −0.179022
\(552\) 2.35297 0.100149
\(553\) 35.6891 1.51766
\(554\) −33.9167 −1.44098
\(555\) 2.68405 0.113932
\(556\) −0.406987 −0.0172601
\(557\) 4.84318 0.205212 0.102606 0.994722i \(-0.467282\pi\)
0.102606 + 0.994722i \(0.467282\pi\)
\(558\) 11.2115 0.474621
\(559\) 5.16929 0.218638
\(560\) −43.3719 −1.83280
\(561\) −3.90623 −0.164921
\(562\) −22.9182 −0.966746
\(563\) −18.8352 −0.793809 −0.396904 0.917860i \(-0.629916\pi\)
−0.396904 + 0.917860i \(0.629916\pi\)
\(564\) 0.952248 0.0400969
\(565\) −11.4098 −0.480014
\(566\) −14.4410 −0.606999
\(567\) −26.2985 −1.10443
\(568\) 7.87732 0.330525
\(569\) −2.33201 −0.0977631 −0.0488816 0.998805i \(-0.515566\pi\)
−0.0488816 + 0.998805i \(0.515566\pi\)
\(570\) 6.41490 0.268691
\(571\) −37.3353 −1.56243 −0.781216 0.624260i \(-0.785400\pi\)
−0.781216 + 0.624260i \(0.785400\pi\)
\(572\) −1.06234 −0.0444185
\(573\) 1.73647 0.0725423
\(574\) 27.0892 1.13068
\(575\) 7.79972 0.325271
\(576\) −16.6203 −0.692514
\(577\) −20.9917 −0.873897 −0.436949 0.899486i \(-0.643941\pi\)
−0.436949 + 0.899486i \(0.643941\pi\)
\(578\) 13.1995 0.549025
\(579\) 0.963853 0.0400564
\(580\) 1.14195 0.0474170
\(581\) −14.4963 −0.601407
\(582\) 9.68672 0.401527
\(583\) 2.73594 0.113311
\(584\) 18.6324 0.771015
\(585\) 5.51250 0.227914
\(586\) 24.7309 1.02163
\(587\) −13.3654 −0.551650 −0.275825 0.961208i \(-0.588951\pi\)
−0.275825 + 0.961208i \(0.588951\pi\)
\(588\) 0.579195 0.0238856
\(589\) 10.5551 0.434917
\(590\) −6.70587 −0.276076
\(591\) 2.74756 0.113020
\(592\) 12.6799 0.521142
\(593\) 9.02449 0.370592 0.185296 0.982683i \(-0.440676\pi\)
0.185296 + 0.982683i \(0.440676\pi\)
\(594\) −12.2220 −0.501476
\(595\) 27.1907 1.11471
\(596\) −1.14450 −0.0468807
\(597\) −2.82343 −0.115555
\(598\) −2.87628 −0.117620
\(599\) 11.5226 0.470802 0.235401 0.971898i \(-0.424360\pi\)
0.235401 + 0.971898i \(0.424360\pi\)
\(600\) 2.48990 0.101650
\(601\) −21.9151 −0.893935 −0.446967 0.894550i \(-0.647496\pi\)
−0.446967 + 0.894550i \(0.647496\pi\)
\(602\) 39.0548 1.59175
\(603\) 21.4783 0.874662
\(604\) −1.99513 −0.0811805
\(605\) −10.1328 −0.411957
\(606\) 1.50341 0.0610719
\(607\) −22.5695 −0.916068 −0.458034 0.888935i \(-0.651446\pi\)
−0.458034 + 0.888935i \(0.651446\pi\)
\(608\) 9.53361 0.386639
\(609\) 1.16613 0.0472540
\(610\) 17.6127 0.713118
\(611\) 4.55619 0.184324
\(612\) −3.41220 −0.137930
\(613\) 33.9013 1.36926 0.684630 0.728890i \(-0.259964\pi\)
0.684630 + 0.728890i \(0.259964\pi\)
\(614\) −15.1476 −0.611309
\(615\) −5.16640 −0.208329
\(616\) 31.4155 1.26577
\(617\) 20.3914 0.820926 0.410463 0.911877i \(-0.365367\pi\)
0.410463 + 0.911877i \(0.365367\pi\)
\(618\) 6.31950 0.254207
\(619\) −8.65709 −0.347958 −0.173979 0.984749i \(-0.555662\pi\)
−0.173979 + 0.984749i \(0.555662\pi\)
\(620\) −2.86835 −0.115196
\(621\) −5.59524 −0.224529
\(622\) 18.6059 0.746031
\(623\) −30.6606 −1.22839
\(624\) −1.11311 −0.0445601
\(625\) −31.1109 −1.24444
\(626\) −15.1343 −0.604887
\(627\) −5.63287 −0.224955
\(628\) −4.83518 −0.192945
\(629\) −7.94929 −0.316959
\(630\) 41.6478 1.65929
\(631\) −25.1540 −1.00136 −0.500682 0.865631i \(-0.666917\pi\)
−0.500682 + 0.865631i \(0.666917\pi\)
\(632\) −26.5246 −1.05509
\(633\) −0.695471 −0.0276425
\(634\) −40.0301 −1.58980
\(635\) −41.4116 −1.64337
\(636\) −0.102152 −0.00405060
\(637\) 2.77126 0.109801
\(638\) −5.93036 −0.234785
\(639\) −9.16994 −0.362757
\(640\) 37.8791 1.49730
\(641\) 16.3829 0.647087 0.323543 0.946213i \(-0.395126\pi\)
0.323543 + 0.946213i \(0.395126\pi\)
\(642\) 8.76872 0.346074
\(643\) 22.0943 0.871313 0.435657 0.900113i \(-0.356516\pi\)
0.435657 + 0.900113i \(0.356516\pi\)
\(644\) −3.67435 −0.144790
\(645\) −7.44845 −0.293282
\(646\) −18.9988 −0.747500
\(647\) 13.7729 0.541468 0.270734 0.962654i \(-0.412734\pi\)
0.270734 + 0.962654i \(0.412734\pi\)
\(648\) 19.5453 0.767813
\(649\) 5.88837 0.231139
\(650\) −3.04366 −0.119382
\(651\) −2.92908 −0.114800
\(652\) −1.09567 −0.0429099
\(653\) −10.3941 −0.406754 −0.203377 0.979101i \(-0.565192\pi\)
−0.203377 + 0.979101i \(0.565192\pi\)
\(654\) −9.73554 −0.380690
\(655\) −24.3921 −0.953077
\(656\) −24.4070 −0.952932
\(657\) −21.6899 −0.846203
\(658\) 34.4228 1.34194
\(659\) −12.1426 −0.473009 −0.236504 0.971630i \(-0.576002\pi\)
−0.236504 + 0.971630i \(0.576002\pi\)
\(660\) 1.53072 0.0595833
\(661\) −30.1150 −1.17134 −0.585669 0.810551i \(-0.699168\pi\)
−0.585669 + 0.810551i \(0.699168\pi\)
\(662\) 19.8042 0.769712
\(663\) 0.697831 0.0271015
\(664\) 10.7738 0.418105
\(665\) 39.2096 1.52048
\(666\) −12.1759 −0.471806
\(667\) −2.71492 −0.105122
\(668\) −1.90665 −0.0737705
\(669\) 2.59428 0.100301
\(670\) −32.4982 −1.25552
\(671\) −15.4656 −0.597042
\(672\) −2.64560 −0.102056
\(673\) 14.1911 0.547025 0.273513 0.961868i \(-0.411814\pi\)
0.273513 + 0.961868i \(0.411814\pi\)
\(674\) 29.9816 1.15485
\(675\) −5.92085 −0.227894
\(676\) −5.10105 −0.196194
\(677\) 7.71599 0.296550 0.148275 0.988946i \(-0.452628\pi\)
0.148275 + 0.988946i \(0.452628\pi\)
\(678\) −2.21234 −0.0849643
\(679\) 59.2078 2.27219
\(680\) −20.2085 −0.774959
\(681\) −4.64091 −0.177840
\(682\) 14.8958 0.570390
\(683\) −46.6393 −1.78460 −0.892302 0.451439i \(-0.850911\pi\)
−0.892302 + 0.451439i \(0.850911\pi\)
\(684\) −4.92046 −0.188139
\(685\) 42.4221 1.62087
\(686\) −15.1770 −0.579459
\(687\) −0.162002 −0.00618078
\(688\) −35.1877 −1.34152
\(689\) −0.488765 −0.0186204
\(690\) 4.14444 0.157776
\(691\) 7.64777 0.290935 0.145467 0.989363i \(-0.453531\pi\)
0.145467 + 0.989363i \(0.453531\pi\)
\(692\) 0.853239 0.0324353
\(693\) −36.5706 −1.38920
\(694\) −46.8341 −1.77780
\(695\) 2.80587 0.106433
\(696\) −0.866683 −0.0328515
\(697\) 15.3012 0.579574
\(698\) 26.7739 1.01341
\(699\) 0.792331 0.0299687
\(700\) −3.88818 −0.146959
\(701\) −31.8255 −1.20203 −0.601017 0.799236i \(-0.705238\pi\)
−0.601017 + 0.799236i \(0.705238\pi\)
\(702\) 2.18341 0.0824076
\(703\) −11.4631 −0.432337
\(704\) −22.0821 −0.832249
\(705\) −6.56504 −0.247254
\(706\) −25.0413 −0.942440
\(707\) 9.18924 0.345597
\(708\) −0.219855 −0.00826264
\(709\) −36.6723 −1.37726 −0.688628 0.725115i \(-0.741787\pi\)
−0.688628 + 0.725115i \(0.741787\pi\)
\(710\) 13.8748 0.520712
\(711\) 30.8771 1.15798
\(712\) 22.7874 0.853992
\(713\) 6.81930 0.255385
\(714\) 5.27222 0.197308
\(715\) 7.32401 0.273902
\(716\) 3.73744 0.139675
\(717\) 10.5268 0.393130
\(718\) −6.15411 −0.229669
\(719\) 25.2100 0.940175 0.470088 0.882620i \(-0.344222\pi\)
0.470088 + 0.882620i \(0.344222\pi\)
\(720\) −37.5240 −1.39844
\(721\) 38.6264 1.43852
\(722\) 2.08074 0.0774371
\(723\) −5.20447 −0.193556
\(724\) 4.28731 0.159337
\(725\) −2.87291 −0.106697
\(726\) −1.96473 −0.0729180
\(727\) 12.4930 0.463341 0.231670 0.972794i \(-0.425581\pi\)
0.231670 + 0.972794i \(0.425581\pi\)
\(728\) −5.61224 −0.208004
\(729\) −20.5845 −0.762387
\(730\) 32.8184 1.21466
\(731\) 22.0599 0.815914
\(732\) 0.577440 0.0213428
\(733\) 21.3731 0.789434 0.394717 0.918803i \(-0.370843\pi\)
0.394717 + 0.918803i \(0.370843\pi\)
\(734\) 41.7345 1.54045
\(735\) −3.99311 −0.147288
\(736\) 6.15932 0.227036
\(737\) 28.5364 1.05115
\(738\) 23.4367 0.862718
\(739\) −2.40609 −0.0885093 −0.0442547 0.999020i \(-0.514091\pi\)
−0.0442547 + 0.999020i \(0.514091\pi\)
\(740\) 3.11507 0.114512
\(741\) 1.00629 0.0369669
\(742\) −3.69269 −0.135563
\(743\) 22.5879 0.828669 0.414334 0.910125i \(-0.364014\pi\)
0.414334 + 0.910125i \(0.364014\pi\)
\(744\) 2.17693 0.0798100
\(745\) 7.89049 0.289085
\(746\) −41.0178 −1.50177
\(747\) −12.5417 −0.458878
\(748\) −4.53351 −0.165761
\(749\) 53.5968 1.95838
\(750\) −3.24709 −0.118567
\(751\) −37.0373 −1.35151 −0.675755 0.737126i \(-0.736182\pi\)
−0.675755 + 0.737126i \(0.736182\pi\)
\(752\) −31.0144 −1.13098
\(753\) −4.34184 −0.158226
\(754\) 1.05943 0.0385823
\(755\) 13.7549 0.500592
\(756\) 2.78924 0.101444
\(757\) 36.6217 1.33104 0.665520 0.746380i \(-0.268210\pi\)
0.665520 + 0.746380i \(0.268210\pi\)
\(758\) −8.75492 −0.317993
\(759\) −3.63919 −0.132094
\(760\) −29.1410 −1.05706
\(761\) 22.7761 0.825634 0.412817 0.910814i \(-0.364545\pi\)
0.412817 + 0.910814i \(0.364545\pi\)
\(762\) −8.02963 −0.290883
\(763\) −59.5062 −2.15427
\(764\) 2.01532 0.0729119
\(765\) 23.5245 0.850531
\(766\) −17.7341 −0.640758
\(767\) −1.05193 −0.0379831
\(768\) 3.29306 0.118828
\(769\) 9.60357 0.346313 0.173157 0.984894i \(-0.444603\pi\)
0.173157 + 0.984894i \(0.444603\pi\)
\(770\) 55.3340 1.99410
\(771\) −5.96223 −0.214725
\(772\) 1.11863 0.0402604
\(773\) −25.8298 −0.929032 −0.464516 0.885565i \(-0.653772\pi\)
−0.464516 + 0.885565i \(0.653772\pi\)
\(774\) 33.7890 1.21452
\(775\) 7.21615 0.259212
\(776\) −44.0039 −1.57965
\(777\) 3.18102 0.114119
\(778\) 50.8516 1.82312
\(779\) 22.0647 0.790549
\(780\) −0.273457 −0.00979134
\(781\) −12.1834 −0.435955
\(782\) −12.2745 −0.438934
\(783\) 2.06092 0.0736514
\(784\) −18.8642 −0.673720
\(785\) 33.3350 1.18978
\(786\) −4.72957 −0.168698
\(787\) 52.1260 1.85809 0.929046 0.369963i \(-0.120630\pi\)
0.929046 + 0.369963i \(0.120630\pi\)
\(788\) 3.18877 0.113595
\(789\) 5.39333 0.192008
\(790\) −46.7194 −1.66220
\(791\) −13.5224 −0.480801
\(792\) 27.1797 0.965788
\(793\) 2.76286 0.0981120
\(794\) 15.9010 0.564306
\(795\) 0.704263 0.0249776
\(796\) −3.27683 −0.116144
\(797\) 6.38007 0.225994 0.112997 0.993595i \(-0.463955\pi\)
0.112997 + 0.993595i \(0.463955\pi\)
\(798\) 7.60266 0.269131
\(799\) 19.4435 0.687862
\(800\) 6.51776 0.230438
\(801\) −26.5266 −0.937272
\(802\) 36.8670 1.30182
\(803\) −28.8176 −1.01695
\(804\) −1.06547 −0.0375761
\(805\) 25.3319 0.892832
\(806\) −2.66107 −0.0937323
\(807\) −3.91924 −0.137964
\(808\) −6.82956 −0.240263
\(809\) 30.2008 1.06180 0.530902 0.847433i \(-0.321853\pi\)
0.530902 + 0.847433i \(0.321853\pi\)
\(810\) 34.4264 1.20962
\(811\) 34.1849 1.20039 0.600197 0.799852i \(-0.295089\pi\)
0.600197 + 0.799852i \(0.295089\pi\)
\(812\) 1.35339 0.0474948
\(813\) −9.04860 −0.317348
\(814\) −16.1771 −0.567007
\(815\) 7.55384 0.264600
\(816\) −4.75019 −0.166290
\(817\) 31.8108 1.11292
\(818\) 8.25685 0.288694
\(819\) 6.53318 0.228288
\(820\) −5.99604 −0.209391
\(821\) 31.6474 1.10450 0.552251 0.833678i \(-0.313769\pi\)
0.552251 + 0.833678i \(0.313769\pi\)
\(822\) 8.22557 0.286900
\(823\) −10.2327 −0.356690 −0.178345 0.983968i \(-0.557074\pi\)
−0.178345 + 0.983968i \(0.557074\pi\)
\(824\) −28.7076 −1.00008
\(825\) −3.85098 −0.134074
\(826\) −7.94751 −0.276529
\(827\) −13.5749 −0.472044 −0.236022 0.971748i \(-0.575844\pi\)
−0.236022 + 0.971748i \(0.575844\pi\)
\(828\) −3.17893 −0.110476
\(829\) 1.92847 0.0669784 0.0334892 0.999439i \(-0.489338\pi\)
0.0334892 + 0.999439i \(0.489338\pi\)
\(830\) 18.9766 0.658686
\(831\) 7.66622 0.265938
\(832\) 3.94487 0.136764
\(833\) 11.8263 0.409757
\(834\) 0.544053 0.0188390
\(835\) 13.1449 0.454899
\(836\) −6.53741 −0.226101
\(837\) −5.17661 −0.178930
\(838\) −44.9791 −1.55378
\(839\) 26.7842 0.924694 0.462347 0.886699i \(-0.347007\pi\)
0.462347 + 0.886699i \(0.347007\pi\)
\(840\) 8.08670 0.279018
\(841\) 1.00000 0.0344828
\(842\) 21.1967 0.730487
\(843\) 5.18021 0.178416
\(844\) −0.807152 −0.0277833
\(845\) 35.1679 1.20981
\(846\) 29.7815 1.02391
\(847\) −12.0090 −0.412633
\(848\) 3.32706 0.114252
\(849\) 3.26410 0.112024
\(850\) −12.9888 −0.445512
\(851\) −7.40587 −0.253870
\(852\) 0.454891 0.0155843
\(853\) −49.7999 −1.70511 −0.852557 0.522634i \(-0.824950\pi\)
−0.852557 + 0.522634i \(0.824950\pi\)
\(854\) 20.8738 0.714288
\(855\) 33.9229 1.16014
\(856\) −39.8338 −1.36149
\(857\) 43.8420 1.49761 0.748806 0.662789i \(-0.230627\pi\)
0.748806 + 0.662789i \(0.230627\pi\)
\(858\) 1.42011 0.0484818
\(859\) −44.7687 −1.52749 −0.763744 0.645519i \(-0.776641\pi\)
−0.763744 + 0.645519i \(0.776641\pi\)
\(860\) −8.64455 −0.294777
\(861\) −6.12300 −0.208671
\(862\) −50.8197 −1.73093
\(863\) 2.95384 0.100550 0.0502749 0.998735i \(-0.483990\pi\)
0.0502749 + 0.998735i \(0.483990\pi\)
\(864\) −4.67561 −0.159067
\(865\) −5.88244 −0.200009
\(866\) 24.9206 0.846838
\(867\) −2.98348 −0.101324
\(868\) −3.39944 −0.115384
\(869\) 41.0239 1.39164
\(870\) −1.52654 −0.0517546
\(871\) −5.09791 −0.172736
\(872\) 44.2257 1.49767
\(873\) 51.2247 1.73369
\(874\) −17.7001 −0.598713
\(875\) −19.8471 −0.670954
\(876\) 1.07596 0.0363535
\(877\) −15.3677 −0.518931 −0.259466 0.965752i \(-0.583546\pi\)
−0.259466 + 0.965752i \(0.583546\pi\)
\(878\) −60.9407 −2.05665
\(879\) −5.58995 −0.188544
\(880\) −49.8551 −1.68061
\(881\) 49.4609 1.66638 0.833190 0.552987i \(-0.186512\pi\)
0.833190 + 0.552987i \(0.186512\pi\)
\(882\) 18.1143 0.609939
\(883\) 14.2953 0.481074 0.240537 0.970640i \(-0.422677\pi\)
0.240537 + 0.970640i \(0.422677\pi\)
\(884\) 0.809892 0.0272396
\(885\) 1.51573 0.0509508
\(886\) 18.9730 0.637410
\(887\) −3.34807 −0.112417 −0.0562087 0.998419i \(-0.517901\pi\)
−0.0562087 + 0.998419i \(0.517901\pi\)
\(888\) −2.36418 −0.0793365
\(889\) −49.0793 −1.64607
\(890\) 40.1368 1.34539
\(891\) −30.2295 −1.01273
\(892\) 3.01088 0.100812
\(893\) 28.0380 0.938255
\(894\) 1.52995 0.0511692
\(895\) −25.7669 −0.861291
\(896\) 44.8927 1.49976
\(897\) 0.650127 0.0217071
\(898\) −63.3569 −2.11425
\(899\) −2.51179 −0.0837729
\(900\) −3.36393 −0.112131
\(901\) −2.08580 −0.0694880
\(902\) 31.1385 1.03680
\(903\) −8.82758 −0.293763
\(904\) 10.0500 0.334258
\(905\) −29.5578 −0.982534
\(906\) 2.66705 0.0886067
\(907\) 6.53410 0.216961 0.108481 0.994099i \(-0.465401\pi\)
0.108481 + 0.994099i \(0.465401\pi\)
\(908\) −5.38616 −0.178746
\(909\) 7.95024 0.263693
\(910\) −9.88519 −0.327691
\(911\) −20.3177 −0.673154 −0.336577 0.941656i \(-0.609269\pi\)
−0.336577 + 0.941656i \(0.609269\pi\)
\(912\) −6.84988 −0.226822
\(913\) −16.6632 −0.551470
\(914\) 38.2106 1.26390
\(915\) −3.98101 −0.131608
\(916\) −0.188017 −0.00621227
\(917\) −28.9084 −0.954640
\(918\) 9.31769 0.307529
\(919\) 10.9398 0.360870 0.180435 0.983587i \(-0.442250\pi\)
0.180435 + 0.983587i \(0.442250\pi\)
\(920\) −18.8270 −0.620707
\(921\) 3.42383 0.112819
\(922\) −33.2836 −1.09614
\(923\) 2.17650 0.0716405
\(924\) 1.81415 0.0596811
\(925\) −7.83685 −0.257674
\(926\) 38.2848 1.25812
\(927\) 33.4184 1.09760
\(928\) −2.26870 −0.0744736
\(929\) −19.3792 −0.635810 −0.317905 0.948123i \(-0.602979\pi\)
−0.317905 + 0.948123i \(0.602979\pi\)
\(930\) 3.83435 0.125733
\(931\) 17.0538 0.558915
\(932\) 0.919566 0.0301214
\(933\) −4.20551 −0.137682
\(934\) 28.7191 0.939717
\(935\) 31.2551 1.02215
\(936\) −4.85554 −0.158708
\(937\) −6.13718 −0.200493 −0.100247 0.994963i \(-0.531963\pi\)
−0.100247 + 0.994963i \(0.531963\pi\)
\(938\) −38.5155 −1.25758
\(939\) 3.42081 0.111634
\(940\) −7.61928 −0.248513
\(941\) 11.5877 0.377749 0.188874 0.982001i \(-0.439516\pi\)
0.188874 + 0.982001i \(0.439516\pi\)
\(942\) 6.46358 0.210595
\(943\) 14.2552 0.464213
\(944\) 7.16058 0.233057
\(945\) −19.2297 −0.625543
\(946\) 44.8926 1.45958
\(947\) −20.3808 −0.662286 −0.331143 0.943581i \(-0.607434\pi\)
−0.331143 + 0.943581i \(0.607434\pi\)
\(948\) −1.53171 −0.0497477
\(949\) 5.14814 0.167116
\(950\) −18.7301 −0.607685
\(951\) 9.04803 0.293403
\(952\) −23.9502 −0.776230
\(953\) −42.9792 −1.39223 −0.696117 0.717928i \(-0.745091\pi\)
−0.696117 + 0.717928i \(0.745091\pi\)
\(954\) −3.19480 −0.103435
\(955\) −13.8941 −0.449604
\(956\) 12.2172 0.395133
\(957\) 1.34044 0.0433304
\(958\) 52.6702 1.70170
\(959\) 50.2769 1.62352
\(960\) −5.68418 −0.183456
\(961\) −24.6909 −0.796481
\(962\) 2.88997 0.0931763
\(963\) 46.3702 1.49426
\(964\) −6.04023 −0.194543
\(965\) −7.71213 −0.248262
\(966\) 4.91181 0.158035
\(967\) 40.5274 1.30327 0.651636 0.758531i \(-0.274083\pi\)
0.651636 + 0.758531i \(0.274083\pi\)
\(968\) 8.92520 0.286867
\(969\) 4.29432 0.137953
\(970\) −77.5068 −2.48859
\(971\) 21.7713 0.698674 0.349337 0.936997i \(-0.386407\pi\)
0.349337 + 0.936997i \(0.386407\pi\)
\(972\) 3.64499 0.116913
\(973\) 3.32540 0.106607
\(974\) 29.8725 0.957176
\(975\) 0.687960 0.0220324
\(976\) −18.8070 −0.601997
\(977\) 4.53355 0.145041 0.0725205 0.997367i \(-0.476896\pi\)
0.0725205 + 0.997367i \(0.476896\pi\)
\(978\) 1.46468 0.0468351
\(979\) −35.2437 −1.12639
\(980\) −4.63434 −0.148039
\(981\) −51.4829 −1.64372
\(982\) −8.14574 −0.259941
\(983\) 27.9410 0.891179 0.445590 0.895237i \(-0.352994\pi\)
0.445590 + 0.895237i \(0.352994\pi\)
\(984\) 4.55068 0.145071
\(985\) −21.9842 −0.700475
\(986\) 4.52112 0.143982
\(987\) −7.78060 −0.247659
\(988\) 1.16788 0.0371553
\(989\) 20.5518 0.653510
\(990\) 47.8732 1.52151
\(991\) −34.5666 −1.09805 −0.549023 0.835807i \(-0.685000\pi\)
−0.549023 + 0.835807i \(0.685000\pi\)
\(992\) 5.69849 0.180927
\(993\) −4.47636 −0.142053
\(994\) 16.4438 0.521566
\(995\) 22.5913 0.716192
\(996\) 0.622154 0.0197137
\(997\) 21.2031 0.671509 0.335754 0.941950i \(-0.391009\pi\)
0.335754 + 0.941950i \(0.391009\pi\)
\(998\) 31.9386 1.01100
\(999\) 5.62188 0.177868
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 \(a_p\))