Properties

Label 6018.2.a.p.1.3
Level 6018
Weight 2
Character 6018.1
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 5
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1668357.1
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 1.3
Root \(1.24777\)
Character \(\chi\) = 6018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.08688 q^{5}\) \(-1.00000 q^{6}\) \(-1.24777 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-1.08688 q^{5}\) \(-1.00000 q^{6}\) \(-1.24777 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+1.08688 q^{10}\) \(-1.58865 q^{11}\) \(+1.00000 q^{12}\) \(-3.49933 q^{13}\) \(+1.24777 q^{14}\) \(-1.08688 q^{15}\) \(+1.00000 q^{16}\) \(-1.00000 q^{17}\) \(-1.00000 q^{18}\) \(+3.42776 q^{19}\) \(-1.08688 q^{20}\) \(-1.24777 q^{21}\) \(+1.58865 q^{22}\) \(+1.76754 q^{23}\) \(-1.00000 q^{24}\) \(-3.81868 q^{25}\) \(+3.49933 q^{26}\) \(+1.00000 q^{27}\) \(-1.24777 q^{28}\) \(+6.53238 q^{29}\) \(+1.08688 q^{30}\) \(+1.05627 q^{31}\) \(-1.00000 q^{32}\) \(-1.58865 q^{33}\) \(+1.00000 q^{34}\) \(+1.35618 q^{35}\) \(+1.00000 q^{36}\) \(-5.65400 q^{37}\) \(-3.42776 q^{38}\) \(-3.49933 q^{39}\) \(+1.08688 q^{40}\) \(-0.263080 q^{41}\) \(+1.24777 q^{42}\) \(+4.90177 q^{43}\) \(-1.58865 q^{44}\) \(-1.08688 q^{45}\) \(-1.76754 q^{46}\) \(-7.04190 q^{47}\) \(+1.00000 q^{48}\) \(-5.44307 q^{49}\) \(+3.81868 q^{50}\) \(-1.00000 q^{51}\) \(-3.49933 q^{52}\) \(+8.92088 q^{53}\) \(-1.00000 q^{54}\) \(+1.72667 q^{55}\) \(+1.24777 q^{56}\) \(+3.42776 q^{57}\) \(-6.53238 q^{58}\) \(-1.00000 q^{59}\) \(-1.08688 q^{60}\) \(+2.97847 q^{61}\) \(-1.05627 q^{62}\) \(-1.24777 q^{63}\) \(+1.00000 q^{64}\) \(+3.80337 q^{65}\) \(+1.58865 q^{66}\) \(+1.69459 q^{67}\) \(-1.00000 q^{68}\) \(+1.76754 q^{69}\) \(-1.35618 q^{70}\) \(-3.41002 q^{71}\) \(-1.00000 q^{72}\) \(-2.04835 q^{73}\) \(+5.65400 q^{74}\) \(-3.81868 q^{75}\) \(+3.42776 q^{76}\) \(+1.98227 q^{77}\) \(+3.49933 q^{78}\) \(-13.9437 q^{79}\) \(-1.08688 q^{80}\) \(+1.00000 q^{81}\) \(+0.263080 q^{82}\) \(-7.00506 q^{83}\) \(-1.24777 q^{84}\) \(+1.08688 q^{85}\) \(-4.90177 q^{86}\) \(+6.53238 q^{87}\) \(+1.58865 q^{88}\) \(+2.56073 q^{89}\) \(+1.08688 q^{90}\) \(+4.36637 q^{91}\) \(+1.76754 q^{92}\) \(+1.05627 q^{93}\) \(+7.04190 q^{94}\) \(-3.72558 q^{95}\) \(-1.00000 q^{96}\) \(+5.85172 q^{97}\) \(+5.44307 q^{98}\) \(-1.58865 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(5q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 5q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 5q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 19q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 5q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 5q^{36} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 19q^{58} \) \(\mathstrut -\mathstrut 5q^{59} \) \(\mathstrut -\mathstrut q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 5q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 5q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 5q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 19q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut +\mathstrut 19q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 22q^{94} \) \(\mathstrut +\mathstrut q^{95} \) \(\mathstrut -\mathstrut 5q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 12q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.08688 −0.486070 −0.243035 0.970018i \(-0.578143\pi\)
−0.243035 + 0.970018i \(0.578143\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.24777 −0.471613 −0.235807 0.971800i \(-0.575773\pi\)
−0.235807 + 0.971800i \(0.575773\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.08688 0.343703
\(11\) −1.58865 −0.478995 −0.239497 0.970897i \(-0.576983\pi\)
−0.239497 + 0.970897i \(0.576983\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.49933 −0.970541 −0.485270 0.874364i \(-0.661279\pi\)
−0.485270 + 0.874364i \(0.661279\pi\)
\(14\) 1.24777 0.333481
\(15\) −1.08688 −0.280632
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 3.42776 0.786382 0.393191 0.919457i \(-0.371371\pi\)
0.393191 + 0.919457i \(0.371371\pi\)
\(20\) −1.08688 −0.243035
\(21\) −1.24777 −0.272286
\(22\) 1.58865 0.338700
\(23\) 1.76754 0.368557 0.184279 0.982874i \(-0.441005\pi\)
0.184279 + 0.982874i \(0.441005\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.81868 −0.763736
\(26\) 3.49933 0.686276
\(27\) 1.00000 0.192450
\(28\) −1.24777 −0.235807
\(29\) 6.53238 1.21303 0.606516 0.795071i \(-0.292567\pi\)
0.606516 + 0.795071i \(0.292567\pi\)
\(30\) 1.08688 0.198437
\(31\) 1.05627 0.189711 0.0948556 0.995491i \(-0.469761\pi\)
0.0948556 + 0.995491i \(0.469761\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.58865 −0.276548
\(34\) 1.00000 0.171499
\(35\) 1.35618 0.229237
\(36\) 1.00000 0.166667
\(37\) −5.65400 −0.929512 −0.464756 0.885439i \(-0.653858\pi\)
−0.464756 + 0.885439i \(0.653858\pi\)
\(38\) −3.42776 −0.556056
\(39\) −3.49933 −0.560342
\(40\) 1.08688 0.171852
\(41\) −0.263080 −0.0410861 −0.0205431 0.999789i \(-0.506540\pi\)
−0.0205431 + 0.999789i \(0.506540\pi\)
\(42\) 1.24777 0.192535
\(43\) 4.90177 0.747513 0.373757 0.927527i \(-0.378069\pi\)
0.373757 + 0.927527i \(0.378069\pi\)
\(44\) −1.58865 −0.239497
\(45\) −1.08688 −0.162023
\(46\) −1.76754 −0.260609
\(47\) −7.04190 −1.02717 −0.513583 0.858040i \(-0.671682\pi\)
−0.513583 + 0.858040i \(0.671682\pi\)
\(48\) 1.00000 0.144338
\(49\) −5.44307 −0.777581
\(50\) 3.81868 0.540043
\(51\) −1.00000 −0.140028
\(52\) −3.49933 −0.485270
\(53\) 8.92088 1.22538 0.612688 0.790325i \(-0.290088\pi\)
0.612688 + 0.790325i \(0.290088\pi\)
\(54\) −1.00000 −0.136083
\(55\) 1.72667 0.232825
\(56\) 1.24777 0.166740
\(57\) 3.42776 0.454018
\(58\) −6.53238 −0.857743
\(59\) −1.00000 −0.130189
\(60\) −1.08688 −0.140316
\(61\) 2.97847 0.381354 0.190677 0.981653i \(-0.438932\pi\)
0.190677 + 0.981653i \(0.438932\pi\)
\(62\) −1.05627 −0.134146
\(63\) −1.24777 −0.157204
\(64\) 1.00000 0.125000
\(65\) 3.80337 0.471750
\(66\) 1.58865 0.195549
\(67\) 1.69459 0.207028 0.103514 0.994628i \(-0.466991\pi\)
0.103514 + 0.994628i \(0.466991\pi\)
\(68\) −1.00000 −0.121268
\(69\) 1.76754 0.212787
\(70\) −1.35618 −0.162095
\(71\) −3.41002 −0.404695 −0.202348 0.979314i \(-0.564857\pi\)
−0.202348 + 0.979314i \(0.564857\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.04835 −0.239741 −0.119871 0.992790i \(-0.538248\pi\)
−0.119871 + 0.992790i \(0.538248\pi\)
\(74\) 5.65400 0.657264
\(75\) −3.81868 −0.440943
\(76\) 3.42776 0.393191
\(77\) 1.98227 0.225900
\(78\) 3.49933 0.396222
\(79\) −13.9437 −1.56879 −0.784393 0.620264i \(-0.787025\pi\)
−0.784393 + 0.620264i \(0.787025\pi\)
\(80\) −1.08688 −0.121517
\(81\) 1.00000 0.111111
\(82\) 0.263080 0.0290523
\(83\) −7.00506 −0.768905 −0.384453 0.923145i \(-0.625610\pi\)
−0.384453 + 0.923145i \(0.625610\pi\)
\(84\) −1.24777 −0.136143
\(85\) 1.08688 0.117889
\(86\) −4.90177 −0.528572
\(87\) 6.53238 0.700344
\(88\) 1.58865 0.169350
\(89\) 2.56073 0.271436 0.135718 0.990747i \(-0.456666\pi\)
0.135718 + 0.990747i \(0.456666\pi\)
\(90\) 1.08688 0.114568
\(91\) 4.36637 0.457720
\(92\) 1.76754 0.184279
\(93\) 1.05627 0.109530
\(94\) 7.04190 0.726316
\(95\) −3.72558 −0.382236
\(96\) −1.00000 −0.102062
\(97\) 5.85172 0.594153 0.297076 0.954854i \(-0.403988\pi\)
0.297076 + 0.954854i \(0.403988\pi\)
\(98\) 5.44307 0.549833
\(99\) −1.58865 −0.159665
\(100\) −3.81868 −0.381868
\(101\) 12.6294 1.25668 0.628339 0.777940i \(-0.283735\pi\)
0.628339 + 0.777940i \(0.283735\pi\)
\(102\) 1.00000 0.0990148
\(103\) 19.1684 1.88872 0.944360 0.328914i \(-0.106683\pi\)
0.944360 + 0.328914i \(0.106683\pi\)
\(104\) 3.49933 0.343138
\(105\) 1.35618 0.132350
\(106\) −8.92088 −0.866472
\(107\) 18.4199 1.78072 0.890361 0.455255i \(-0.150452\pi\)
0.890361 + 0.455255i \(0.150452\pi\)
\(108\) 1.00000 0.0962250
\(109\) 0.567118 0.0543200 0.0271600 0.999631i \(-0.491354\pi\)
0.0271600 + 0.999631i \(0.491354\pi\)
\(110\) −1.72667 −0.164632
\(111\) −5.65400 −0.536654
\(112\) −1.24777 −0.117903
\(113\) 2.30294 0.216643 0.108321 0.994116i \(-0.465452\pi\)
0.108321 + 0.994116i \(0.465452\pi\)
\(114\) −3.42776 −0.321039
\(115\) −1.92111 −0.179144
\(116\) 6.53238 0.606516
\(117\) −3.49933 −0.323514
\(118\) 1.00000 0.0920575
\(119\) 1.24777 0.114383
\(120\) 1.08688 0.0992185
\(121\) −8.47621 −0.770564
\(122\) −2.97847 −0.269658
\(123\) −0.263080 −0.0237211
\(124\) 1.05627 0.0948556
\(125\) 9.58489 0.857299
\(126\) 1.24777 0.111160
\(127\) −12.6195 −1.11980 −0.559899 0.828561i \(-0.689160\pi\)
−0.559899 + 0.828561i \(0.689160\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.90177 0.431577
\(130\) −3.80337 −0.333578
\(131\) 11.3817 0.994422 0.497211 0.867630i \(-0.334358\pi\)
0.497211 + 0.867630i \(0.334358\pi\)
\(132\) −1.58865 −0.138274
\(133\) −4.27706 −0.370868
\(134\) −1.69459 −0.146391
\(135\) −1.08688 −0.0935441
\(136\) 1.00000 0.0857493
\(137\) 11.5144 0.983742 0.491871 0.870668i \(-0.336313\pi\)
0.491871 + 0.870668i \(0.336313\pi\)
\(138\) −1.76754 −0.150463
\(139\) −10.0793 −0.854918 −0.427459 0.904035i \(-0.640591\pi\)
−0.427459 + 0.904035i \(0.640591\pi\)
\(140\) 1.35618 0.114618
\(141\) −7.04190 −0.593035
\(142\) 3.41002 0.286163
\(143\) 5.55920 0.464884
\(144\) 1.00000 0.0833333
\(145\) −7.09994 −0.589618
\(146\) 2.04835 0.169523
\(147\) −5.44307 −0.448937
\(148\) −5.65400 −0.464756
\(149\) 3.14073 0.257298 0.128649 0.991690i \(-0.458936\pi\)
0.128649 + 0.991690i \(0.458936\pi\)
\(150\) 3.81868 0.311794
\(151\) −2.68202 −0.218260 −0.109130 0.994028i \(-0.534806\pi\)
−0.109130 + 0.994028i \(0.534806\pi\)
\(152\) −3.42776 −0.278028
\(153\) −1.00000 −0.0808452
\(154\) −1.98227 −0.159736
\(155\) −1.14804 −0.0922128
\(156\) −3.49933 −0.280171
\(157\) 24.7992 1.97919 0.989595 0.143878i \(-0.0459573\pi\)
0.989595 + 0.143878i \(0.0459573\pi\)
\(158\) 13.9437 1.10930
\(159\) 8.92088 0.707471
\(160\) 1.08688 0.0859258
\(161\) −2.20548 −0.173816
\(162\) −1.00000 −0.0785674
\(163\) −1.67796 −0.131428 −0.0657138 0.997839i \(-0.520932\pi\)
−0.0657138 + 0.997839i \(0.520932\pi\)
\(164\) −0.263080 −0.0205431
\(165\) 1.72667 0.134421
\(166\) 7.00506 0.543698
\(167\) 17.5555 1.35849 0.679244 0.733912i \(-0.262308\pi\)
0.679244 + 0.733912i \(0.262308\pi\)
\(168\) 1.24777 0.0962676
\(169\) −0.754655 −0.0580504
\(170\) −1.08688 −0.0833602
\(171\) 3.42776 0.262127
\(172\) 4.90177 0.373757
\(173\) 22.5221 1.71233 0.856163 0.516706i \(-0.172842\pi\)
0.856163 + 0.516706i \(0.172842\pi\)
\(174\) −6.53238 −0.495218
\(175\) 4.76484 0.360188
\(176\) −1.58865 −0.119749
\(177\) −1.00000 −0.0751646
\(178\) −2.56073 −0.191934
\(179\) 0.971809 0.0726364 0.0363182 0.999340i \(-0.488437\pi\)
0.0363182 + 0.999340i \(0.488437\pi\)
\(180\) −1.08688 −0.0810116
\(181\) 7.46723 0.555035 0.277517 0.960721i \(-0.410488\pi\)
0.277517 + 0.960721i \(0.410488\pi\)
\(182\) −4.36637 −0.323657
\(183\) 2.97847 0.220175
\(184\) −1.76754 −0.130305
\(185\) 6.14525 0.451808
\(186\) −1.05627 −0.0774493
\(187\) 1.58865 0.116173
\(188\) −7.04190 −0.513583
\(189\) −1.24777 −0.0907620
\(190\) 3.72558 0.270282
\(191\) −19.4441 −1.40693 −0.703463 0.710732i \(-0.748364\pi\)
−0.703463 + 0.710732i \(0.748364\pi\)
\(192\) 1.00000 0.0721688
\(193\) 4.96696 0.357529 0.178765 0.983892i \(-0.442790\pi\)
0.178765 + 0.983892i \(0.442790\pi\)
\(194\) −5.85172 −0.420129
\(195\) 3.80337 0.272365
\(196\) −5.44307 −0.388791
\(197\) 10.2631 0.731214 0.365607 0.930769i \(-0.380861\pi\)
0.365607 + 0.930769i \(0.380861\pi\)
\(198\) 1.58865 0.112900
\(199\) 11.9743 0.848835 0.424417 0.905467i \(-0.360479\pi\)
0.424417 + 0.905467i \(0.360479\pi\)
\(200\) 3.81868 0.270022
\(201\) 1.69459 0.119527
\(202\) −12.6294 −0.888605
\(203\) −8.15091 −0.572082
\(204\) −1.00000 −0.0700140
\(205\) 0.285937 0.0199707
\(206\) −19.1684 −1.33553
\(207\) 1.76754 0.122852
\(208\) −3.49933 −0.242635
\(209\) −5.44549 −0.376673
\(210\) −1.35618 −0.0935855
\(211\) 0.298820 0.0205716 0.0102858 0.999947i \(-0.496726\pi\)
0.0102858 + 0.999947i \(0.496726\pi\)
\(212\) 8.92088 0.612688
\(213\) −3.41002 −0.233651
\(214\) −18.4199 −1.25916
\(215\) −5.32766 −0.363344
\(216\) −1.00000 −0.0680414
\(217\) −1.31798 −0.0894703
\(218\) −0.567118 −0.0384101
\(219\) −2.04835 −0.138415
\(220\) 1.72667 0.116412
\(221\) 3.49933 0.235391
\(222\) 5.65400 0.379472
\(223\) 22.6580 1.51729 0.758645 0.651504i \(-0.225862\pi\)
0.758645 + 0.651504i \(0.225862\pi\)
\(224\) 1.24777 0.0833702
\(225\) −3.81868 −0.254579
\(226\) −2.30294 −0.153189
\(227\) −21.7085 −1.44085 −0.720424 0.693534i \(-0.756053\pi\)
−0.720424 + 0.693534i \(0.756053\pi\)
\(228\) 3.42776 0.227009
\(229\) 2.56949 0.169796 0.0848982 0.996390i \(-0.472943\pi\)
0.0848982 + 0.996390i \(0.472943\pi\)
\(230\) 1.92111 0.126674
\(231\) 1.98227 0.130423
\(232\) −6.53238 −0.428872
\(233\) −5.23889 −0.343211 −0.171606 0.985166i \(-0.554895\pi\)
−0.171606 + 0.985166i \(0.554895\pi\)
\(234\) 3.49933 0.228759
\(235\) 7.65373 0.499274
\(236\) −1.00000 −0.0650945
\(237\) −13.9437 −0.905739
\(238\) −1.24777 −0.0808810
\(239\) −7.38807 −0.477894 −0.238947 0.971033i \(-0.576802\pi\)
−0.238947 + 0.971033i \(0.576802\pi\)
\(240\) −1.08688 −0.0701581
\(241\) −23.1478 −1.49108 −0.745541 0.666460i \(-0.767809\pi\)
−0.745541 + 0.666460i \(0.767809\pi\)
\(242\) 8.47621 0.544871
\(243\) 1.00000 0.0641500
\(244\) 2.97847 0.190677
\(245\) 5.91599 0.377959
\(246\) 0.263080 0.0167733
\(247\) −11.9949 −0.763216
\(248\) −1.05627 −0.0670730
\(249\) −7.00506 −0.443928
\(250\) −9.58489 −0.606202
\(251\) 19.9514 1.25932 0.629662 0.776870i \(-0.283194\pi\)
0.629662 + 0.776870i \(0.283194\pi\)
\(252\) −1.24777 −0.0786022
\(253\) −2.80799 −0.176537
\(254\) 12.6195 0.791816
\(255\) 1.08688 0.0680634
\(256\) 1.00000 0.0625000
\(257\) 21.6923 1.35313 0.676564 0.736384i \(-0.263468\pi\)
0.676564 + 0.736384i \(0.263468\pi\)
\(258\) −4.90177 −0.305171
\(259\) 7.05490 0.438370
\(260\) 3.80337 0.235875
\(261\) 6.53238 0.404344
\(262\) −11.3817 −0.703162
\(263\) 23.4791 1.44778 0.723892 0.689913i \(-0.242351\pi\)
0.723892 + 0.689913i \(0.242351\pi\)
\(264\) 1.58865 0.0977744
\(265\) −9.69596 −0.595618
\(266\) 4.27706 0.262243
\(267\) 2.56073 0.156714
\(268\) 1.69459 0.103514
\(269\) −18.4264 −1.12348 −0.561740 0.827314i \(-0.689868\pi\)
−0.561740 + 0.827314i \(0.689868\pi\)
\(270\) 1.08688 0.0661457
\(271\) 4.78257 0.290521 0.145260 0.989393i \(-0.453598\pi\)
0.145260 + 0.989393i \(0.453598\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 4.36637 0.264265
\(274\) −11.5144 −0.695611
\(275\) 6.06653 0.365826
\(276\) 1.76754 0.106393
\(277\) 11.4444 0.687627 0.343814 0.939038i \(-0.388281\pi\)
0.343814 + 0.939038i \(0.388281\pi\)
\(278\) 10.0793 0.604518
\(279\) 1.05627 0.0632371
\(280\) −1.35618 −0.0810474
\(281\) 24.7173 1.47451 0.737254 0.675615i \(-0.236122\pi\)
0.737254 + 0.675615i \(0.236122\pi\)
\(282\) 7.04190 0.419339
\(283\) 11.3884 0.676972 0.338486 0.940971i \(-0.390085\pi\)
0.338486 + 0.940971i \(0.390085\pi\)
\(284\) −3.41002 −0.202348
\(285\) −3.72558 −0.220684
\(286\) −5.55920 −0.328723
\(287\) 0.328263 0.0193768
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 7.09994 0.416923
\(291\) 5.85172 0.343034
\(292\) −2.04835 −0.119871
\(293\) 4.39572 0.256800 0.128400 0.991722i \(-0.459016\pi\)
0.128400 + 0.991722i \(0.459016\pi\)
\(294\) 5.44307 0.317446
\(295\) 1.08688 0.0632809
\(296\) 5.65400 0.328632
\(297\) −1.58865 −0.0921826
\(298\) −3.14073 −0.181937
\(299\) −6.18521 −0.357700
\(300\) −3.81868 −0.220472
\(301\) −6.11629 −0.352537
\(302\) 2.68202 0.154333
\(303\) 12.6294 0.725543
\(304\) 3.42776 0.196595
\(305\) −3.23726 −0.185365
\(306\) 1.00000 0.0571662
\(307\) −2.47798 −0.141426 −0.0707129 0.997497i \(-0.522527\pi\)
−0.0707129 + 0.997497i \(0.522527\pi\)
\(308\) 1.98227 0.112950
\(309\) 19.1684 1.09045
\(310\) 1.14804 0.0652043
\(311\) 4.05650 0.230023 0.115012 0.993364i \(-0.463309\pi\)
0.115012 + 0.993364i \(0.463309\pi\)
\(312\) 3.49933 0.198111
\(313\) 6.30146 0.356179 0.178090 0.984014i \(-0.443008\pi\)
0.178090 + 0.984014i \(0.443008\pi\)
\(314\) −24.7992 −1.39950
\(315\) 1.35618 0.0764123
\(316\) −13.9437 −0.784393
\(317\) 17.0586 0.958108 0.479054 0.877785i \(-0.340980\pi\)
0.479054 + 0.877785i \(0.340980\pi\)
\(318\) −8.92088 −0.500258
\(319\) −10.3776 −0.581036
\(320\) −1.08688 −0.0607587
\(321\) 18.4199 1.02810
\(322\) 2.20548 0.122907
\(323\) −3.42776 −0.190726
\(324\) 1.00000 0.0555556
\(325\) 13.3628 0.741237
\(326\) 1.67796 0.0929334
\(327\) 0.567118 0.0313617
\(328\) 0.263080 0.0145261
\(329\) 8.78668 0.484425
\(330\) −1.72667 −0.0950503
\(331\) 5.78371 0.317901 0.158951 0.987287i \(-0.449189\pi\)
0.158951 + 0.987287i \(0.449189\pi\)
\(332\) −7.00506 −0.384453
\(333\) −5.65400 −0.309837
\(334\) −17.5555 −0.960596
\(335\) −1.84183 −0.100630
\(336\) −1.24777 −0.0680715
\(337\) −15.2489 −0.830659 −0.415329 0.909671i \(-0.636334\pi\)
−0.415329 + 0.909671i \(0.636334\pi\)
\(338\) 0.754655 0.0410478
\(339\) 2.30294 0.125079
\(340\) 1.08688 0.0589446
\(341\) −1.67803 −0.0908706
\(342\) −3.42776 −0.185352
\(343\) 15.5261 0.838331
\(344\) −4.90177 −0.264286
\(345\) −1.92111 −0.103429
\(346\) −22.5221 −1.21080
\(347\) 15.3513 0.824103 0.412051 0.911161i \(-0.364812\pi\)
0.412051 + 0.911161i \(0.364812\pi\)
\(348\) 6.53238 0.350172
\(349\) 19.4089 1.03893 0.519467 0.854490i \(-0.326130\pi\)
0.519467 + 0.854490i \(0.326130\pi\)
\(350\) −4.76484 −0.254691
\(351\) −3.49933 −0.186781
\(352\) 1.58865 0.0846751
\(353\) −8.51189 −0.453042 −0.226521 0.974006i \(-0.572735\pi\)
−0.226521 + 0.974006i \(0.572735\pi\)
\(354\) 1.00000 0.0531494
\(355\) 3.70630 0.196710
\(356\) 2.56073 0.135718
\(357\) 1.24777 0.0660390
\(358\) −0.971809 −0.0513617
\(359\) 6.28008 0.331450 0.165725 0.986172i \(-0.447004\pi\)
0.165725 + 0.986172i \(0.447004\pi\)
\(360\) 1.08688 0.0572838
\(361\) −7.25047 −0.381604
\(362\) −7.46723 −0.392469
\(363\) −8.47621 −0.444885
\(364\) 4.36637 0.228860
\(365\) 2.22632 0.116531
\(366\) −2.97847 −0.155687
\(367\) −6.36236 −0.332113 −0.166056 0.986116i \(-0.553103\pi\)
−0.166056 + 0.986116i \(0.553103\pi\)
\(368\) 1.76754 0.0921393
\(369\) −0.263080 −0.0136954
\(370\) −6.14525 −0.319476
\(371\) −11.1312 −0.577904
\(372\) 1.05627 0.0547649
\(373\) −8.37898 −0.433847 −0.216924 0.976189i \(-0.569602\pi\)
−0.216924 + 0.976189i \(0.569602\pi\)
\(374\) −1.58865 −0.0821469
\(375\) 9.58489 0.494962
\(376\) 7.04190 0.363158
\(377\) −22.8590 −1.17730
\(378\) 1.24777 0.0641784
\(379\) 16.4736 0.846192 0.423096 0.906085i \(-0.360943\pi\)
0.423096 + 0.906085i \(0.360943\pi\)
\(380\) −3.72558 −0.191118
\(381\) −12.6195 −0.646515
\(382\) 19.4441 0.994847
\(383\) 29.4135 1.50296 0.751479 0.659757i \(-0.229341\pi\)
0.751479 + 0.659757i \(0.229341\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −2.15449 −0.109803
\(386\) −4.96696 −0.252811
\(387\) 4.90177 0.249171
\(388\) 5.85172 0.297076
\(389\) −11.0075 −0.558104 −0.279052 0.960276i \(-0.590020\pi\)
−0.279052 + 0.960276i \(0.590020\pi\)
\(390\) −3.80337 −0.192591
\(391\) −1.76754 −0.0893882
\(392\) 5.44307 0.274916
\(393\) 11.3817 0.574130
\(394\) −10.2631 −0.517046
\(395\) 15.1552 0.762539
\(396\) −1.58865 −0.0798324
\(397\) −10.9319 −0.548659 −0.274329 0.961636i \(-0.588456\pi\)
−0.274329 + 0.961636i \(0.588456\pi\)
\(398\) −11.9743 −0.600217
\(399\) −4.27706 −0.214121
\(400\) −3.81868 −0.190934
\(401\) −16.0447 −0.801234 −0.400617 0.916246i \(-0.631204\pi\)
−0.400617 + 0.916246i \(0.631204\pi\)
\(402\) −1.69459 −0.0845187
\(403\) −3.69623 −0.184122
\(404\) 12.6294 0.628339
\(405\) −1.08688 −0.0540077
\(406\) 8.15091 0.404523
\(407\) 8.98220 0.445231
\(408\) 1.00000 0.0495074
\(409\) −34.4158 −1.70175 −0.850876 0.525367i \(-0.823928\pi\)
−0.850876 + 0.525367i \(0.823928\pi\)
\(410\) −0.285937 −0.0141214
\(411\) 11.5144 0.567964
\(412\) 19.1684 0.944360
\(413\) 1.24777 0.0613988
\(414\) −1.76754 −0.0868697
\(415\) 7.61369 0.373742
\(416\) 3.49933 0.171569
\(417\) −10.0793 −0.493587
\(418\) 5.44549 0.266348
\(419\) −30.4667 −1.48840 −0.744198 0.667959i \(-0.767168\pi\)
−0.744198 + 0.667959i \(0.767168\pi\)
\(420\) 1.35618 0.0661750
\(421\) −35.3614 −1.72341 −0.861704 0.507411i \(-0.830603\pi\)
−0.861704 + 0.507411i \(0.830603\pi\)
\(422\) −0.298820 −0.0145463
\(423\) −7.04190 −0.342389
\(424\) −8.92088 −0.433236
\(425\) 3.81868 0.185233
\(426\) 3.41002 0.165216
\(427\) −3.71645 −0.179852
\(428\) 18.4199 0.890361
\(429\) 5.55920 0.268401
\(430\) 5.32766 0.256923
\(431\) 37.8294 1.82218 0.911089 0.412210i \(-0.135243\pi\)
0.911089 + 0.412210i \(0.135243\pi\)
\(432\) 1.00000 0.0481125
\(433\) 23.4830 1.12852 0.564262 0.825596i \(-0.309161\pi\)
0.564262 + 0.825596i \(0.309161\pi\)
\(434\) 1.31798 0.0632651
\(435\) −7.09994 −0.340416
\(436\) 0.567118 0.0271600
\(437\) 6.05869 0.289827
\(438\) 2.04835 0.0978740
\(439\) −11.4651 −0.547201 −0.273601 0.961843i \(-0.588215\pi\)
−0.273601 + 0.961843i \(0.588215\pi\)
\(440\) −1.72667 −0.0823160
\(441\) −5.44307 −0.259194
\(442\) −3.49933 −0.166446
\(443\) −3.17547 −0.150871 −0.0754355 0.997151i \(-0.524035\pi\)
−0.0754355 + 0.997151i \(0.524035\pi\)
\(444\) −5.65400 −0.268327
\(445\) −2.78321 −0.131937
\(446\) −22.6580 −1.07289
\(447\) 3.14073 0.148551
\(448\) −1.24777 −0.0589516
\(449\) −1.50463 −0.0710080 −0.0355040 0.999370i \(-0.511304\pi\)
−0.0355040 + 0.999370i \(0.511304\pi\)
\(450\) 3.81868 0.180014
\(451\) 0.417940 0.0196800
\(452\) 2.30294 0.108321
\(453\) −2.68202 −0.126012
\(454\) 21.7085 1.01883
\(455\) −4.74574 −0.222484
\(456\) −3.42776 −0.160520
\(457\) 4.28245 0.200325 0.100162 0.994971i \(-0.468064\pi\)
0.100162 + 0.994971i \(0.468064\pi\)
\(458\) −2.56949 −0.120064
\(459\) −1.00000 −0.0466760
\(460\) −1.92111 −0.0895722
\(461\) −25.6090 −1.19273 −0.596365 0.802713i \(-0.703389\pi\)
−0.596365 + 0.802713i \(0.703389\pi\)
\(462\) −1.98227 −0.0922233
\(463\) −22.8439 −1.06165 −0.530823 0.847483i \(-0.678117\pi\)
−0.530823 + 0.847483i \(0.678117\pi\)
\(464\) 6.53238 0.303258
\(465\) −1.14804 −0.0532391
\(466\) 5.23889 0.242687
\(467\) 15.5653 0.720278 0.360139 0.932899i \(-0.382729\pi\)
0.360139 + 0.932899i \(0.382729\pi\)
\(468\) −3.49933 −0.161757
\(469\) −2.11447 −0.0976370
\(470\) −7.65373 −0.353040
\(471\) 24.7992 1.14269
\(472\) 1.00000 0.0460287
\(473\) −7.78718 −0.358055
\(474\) 13.9437 0.640454
\(475\) −13.0895 −0.600588
\(476\) 1.24777 0.0571915
\(477\) 8.92088 0.408459
\(478\) 7.38807 0.337922
\(479\) −20.7173 −0.946596 −0.473298 0.880902i \(-0.656937\pi\)
−0.473298 + 0.880902i \(0.656937\pi\)
\(480\) 1.08688 0.0496093
\(481\) 19.7852 0.902130
\(482\) 23.1478 1.05435
\(483\) −2.20548 −0.100353
\(484\) −8.47621 −0.385282
\(485\) −6.36015 −0.288800
\(486\) −1.00000 −0.0453609
\(487\) 15.5679 0.705448 0.352724 0.935727i \(-0.385255\pi\)
0.352724 + 0.935727i \(0.385255\pi\)
\(488\) −2.97847 −0.134829
\(489\) −1.67796 −0.0758798
\(490\) −5.91599 −0.267257
\(491\) 31.4196 1.41795 0.708973 0.705235i \(-0.249159\pi\)
0.708973 + 0.705235i \(0.249159\pi\)
\(492\) −0.263080 −0.0118605
\(493\) −6.53238 −0.294204
\(494\) 11.9949 0.539675
\(495\) 1.72667 0.0776082
\(496\) 1.05627 0.0474278
\(497\) 4.25493 0.190860
\(498\) 7.00506 0.313904
\(499\) 21.7979 0.975806 0.487903 0.872898i \(-0.337762\pi\)
0.487903 + 0.872898i \(0.337762\pi\)
\(500\) 9.58489 0.428649
\(501\) 17.5555 0.784324
\(502\) −19.9514 −0.890476
\(503\) −23.4545 −1.04579 −0.522893 0.852398i \(-0.675147\pi\)
−0.522893 + 0.852398i \(0.675147\pi\)
\(504\) 1.24777 0.0555801
\(505\) −13.7268 −0.610832
\(506\) 2.80799 0.124830
\(507\) −0.754655 −0.0335154
\(508\) −12.6195 −0.559899
\(509\) −25.4825 −1.12949 −0.564746 0.825265i \(-0.691026\pi\)
−0.564746 + 0.825265i \(0.691026\pi\)
\(510\) −1.08688 −0.0481281
\(511\) 2.55587 0.113065
\(512\) −1.00000 −0.0441942
\(513\) 3.42776 0.151339
\(514\) −21.6923 −0.956806
\(515\) −20.8339 −0.918049
\(516\) 4.90177 0.215789
\(517\) 11.1871 0.492007
\(518\) −7.05490 −0.309975
\(519\) 22.5221 0.988612
\(520\) −3.80337 −0.166789
\(521\) 14.4675 0.633831 0.316916 0.948454i \(-0.397353\pi\)
0.316916 + 0.948454i \(0.397353\pi\)
\(522\) −6.53238 −0.285914
\(523\) −25.9563 −1.13499 −0.567495 0.823377i \(-0.692087\pi\)
−0.567495 + 0.823377i \(0.692087\pi\)
\(524\) 11.3817 0.497211
\(525\) 4.76484 0.207955
\(526\) −23.4791 −1.02374
\(527\) −1.05627 −0.0460117
\(528\) −1.58865 −0.0691369
\(529\) −19.8758 −0.864166
\(530\) 9.69596 0.421166
\(531\) −1.00000 −0.0433963
\(532\) −4.27706 −0.185434
\(533\) 0.920604 0.0398758
\(534\) −2.56073 −0.110813
\(535\) −20.0203 −0.865555
\(536\) −1.69459 −0.0731953
\(537\) 0.971809 0.0419366
\(538\) 18.4264 0.794420
\(539\) 8.64710 0.372457
\(540\) −1.08688 −0.0467721
\(541\) 38.0841 1.63736 0.818681 0.574249i \(-0.194706\pi\)
0.818681 + 0.574249i \(0.194706\pi\)
\(542\) −4.78257 −0.205429
\(543\) 7.46723 0.320450
\(544\) 1.00000 0.0428746
\(545\) −0.616392 −0.0264033
\(546\) −4.36637 −0.186863
\(547\) −22.6929 −0.970277 −0.485139 0.874437i \(-0.661231\pi\)
−0.485139 + 0.874437i \(0.661231\pi\)
\(548\) 11.5144 0.491871
\(549\) 2.97847 0.127118
\(550\) −6.06653 −0.258678
\(551\) 22.3914 0.953906
\(552\) −1.76754 −0.0752314
\(553\) 17.3985 0.739860
\(554\) −11.4444 −0.486226
\(555\) 6.14525 0.260851
\(556\) −10.0793 −0.427459
\(557\) −19.3892 −0.821545 −0.410773 0.911738i \(-0.634741\pi\)
−0.410773 + 0.911738i \(0.634741\pi\)
\(558\) −1.05627 −0.0447154
\(559\) −17.1529 −0.725492
\(560\) 1.35618 0.0573092
\(561\) 1.58865 0.0670727
\(562\) −24.7173 −1.04264
\(563\) 27.4649 1.15751 0.578753 0.815503i \(-0.303540\pi\)
0.578753 + 0.815503i \(0.303540\pi\)
\(564\) −7.04190 −0.296517
\(565\) −2.50303 −0.105303
\(566\) −11.3884 −0.478692
\(567\) −1.24777 −0.0524015
\(568\) 3.41002 0.143081
\(569\) −30.6953 −1.28682 −0.643408 0.765524i \(-0.722480\pi\)
−0.643408 + 0.765524i \(0.722480\pi\)
\(570\) 3.72558 0.156047
\(571\) 7.37235 0.308523 0.154262 0.988030i \(-0.450700\pi\)
0.154262 + 0.988030i \(0.450700\pi\)
\(572\) 5.55920 0.232442
\(573\) −19.4441 −0.812289
\(574\) −0.328263 −0.0137014
\(575\) −6.74966 −0.281480
\(576\) 1.00000 0.0416667
\(577\) 4.25420 0.177105 0.0885523 0.996072i \(-0.471776\pi\)
0.0885523 + 0.996072i \(0.471776\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 4.96696 0.206420
\(580\) −7.09994 −0.294809
\(581\) 8.74071 0.362626
\(582\) −5.85172 −0.242562
\(583\) −14.1721 −0.586949
\(584\) 2.04835 0.0847614
\(585\) 3.80337 0.157250
\(586\) −4.39572 −0.181585
\(587\) −6.17387 −0.254823 −0.127411 0.991850i \(-0.540667\pi\)
−0.127411 + 0.991850i \(0.540667\pi\)
\(588\) −5.44307 −0.224468
\(589\) 3.62063 0.149185
\(590\) −1.08688 −0.0447463
\(591\) 10.2631 0.422167
\(592\) −5.65400 −0.232378
\(593\) 31.2741 1.28427 0.642136 0.766590i \(-0.278048\pi\)
0.642136 + 0.766590i \(0.278048\pi\)
\(594\) 1.58865 0.0651829
\(595\) −1.35618 −0.0555981
\(596\) 3.14073 0.128649
\(597\) 11.9743 0.490075
\(598\) 6.18521 0.252932
\(599\) 24.1012 0.984748 0.492374 0.870384i \(-0.336129\pi\)
0.492374 + 0.870384i \(0.336129\pi\)
\(600\) 3.81868 0.155897
\(601\) −8.87445 −0.361996 −0.180998 0.983483i \(-0.557933\pi\)
−0.180998 + 0.983483i \(0.557933\pi\)
\(602\) 6.11629 0.249281
\(603\) 1.69459 0.0690092
\(604\) −2.68202 −0.109130
\(605\) 9.21266 0.374548
\(606\) −12.6294 −0.513036
\(607\) 7.30188 0.296374 0.148187 0.988959i \(-0.452656\pi\)
0.148187 + 0.988959i \(0.452656\pi\)
\(608\) −3.42776 −0.139014
\(609\) −8.15091 −0.330292
\(610\) 3.23726 0.131073
\(611\) 24.6420 0.996907
\(612\) −1.00000 −0.0404226
\(613\) 24.3518 0.983561 0.491781 0.870719i \(-0.336346\pi\)
0.491781 + 0.870719i \(0.336346\pi\)
\(614\) 2.47798 0.100003
\(615\) 0.285937 0.0115301
\(616\) −1.98227 −0.0798678
\(617\) 34.1199 1.37362 0.686808 0.726839i \(-0.259011\pi\)
0.686808 + 0.726839i \(0.259011\pi\)
\(618\) −19.1684 −0.771067
\(619\) −40.6829 −1.63518 −0.817592 0.575798i \(-0.804691\pi\)
−0.817592 + 0.575798i \(0.804691\pi\)
\(620\) −1.14804 −0.0461064
\(621\) 1.76754 0.0709288
\(622\) −4.05650 −0.162651
\(623\) −3.19520 −0.128013
\(624\) −3.49933 −0.140086
\(625\) 8.67574 0.347030
\(626\) −6.30146 −0.251857
\(627\) −5.44549 −0.217472
\(628\) 24.7992 0.989595
\(629\) 5.65400 0.225440
\(630\) −1.35618 −0.0540316
\(631\) 33.9858 1.35295 0.676477 0.736464i \(-0.263506\pi\)
0.676477 + 0.736464i \(0.263506\pi\)
\(632\) 13.9437 0.554649
\(633\) 0.298820 0.0118770
\(634\) −17.0586 −0.677485
\(635\) 13.7159 0.544299
\(636\) 8.92088 0.353736
\(637\) 19.0471 0.754674
\(638\) 10.3776 0.410854
\(639\) −3.41002 −0.134898
\(640\) 1.08688 0.0429629
\(641\) 49.3913 1.95084 0.975420 0.220353i \(-0.0707209\pi\)
0.975420 + 0.220353i \(0.0707209\pi\)
\(642\) −18.4199 −0.726977
\(643\) −37.4159 −1.47554 −0.737769 0.675054i \(-0.764120\pi\)
−0.737769 + 0.675054i \(0.764120\pi\)
\(644\) −2.20548 −0.0869082
\(645\) −5.32766 −0.209776
\(646\) 3.42776 0.134863
\(647\) −43.5462 −1.71198 −0.855989 0.516994i \(-0.827051\pi\)
−0.855989 + 0.516994i \(0.827051\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 1.58865 0.0623598
\(650\) −13.3628 −0.524134
\(651\) −1.31798 −0.0516557
\(652\) −1.67796 −0.0657138
\(653\) 12.4268 0.486299 0.243150 0.969989i \(-0.421819\pi\)
0.243150 + 0.969989i \(0.421819\pi\)
\(654\) −0.567118 −0.0221761
\(655\) −12.3706 −0.483358
\(656\) −0.263080 −0.0102715
\(657\) −2.04835 −0.0799138
\(658\) −8.78668 −0.342540
\(659\) 16.8280 0.655525 0.327763 0.944760i \(-0.393705\pi\)
0.327763 + 0.944760i \(0.393705\pi\)
\(660\) 1.72667 0.0672107
\(661\) −0.718490 −0.0279460 −0.0139730 0.999902i \(-0.504448\pi\)
−0.0139730 + 0.999902i \(0.504448\pi\)
\(662\) −5.78371 −0.224790
\(663\) 3.49933 0.135903
\(664\) 7.00506 0.271849
\(665\) 4.64867 0.180268
\(666\) 5.65400 0.219088
\(667\) 11.5462 0.447072
\(668\) 17.5555 0.679244
\(669\) 22.6580 0.876008
\(670\) 1.84183 0.0711560
\(671\) −4.73174 −0.182667
\(672\) 1.24777 0.0481338
\(673\) 24.2378 0.934297 0.467148 0.884179i \(-0.345281\pi\)
0.467148 + 0.884179i \(0.345281\pi\)
\(674\) 15.2489 0.587364
\(675\) −3.81868 −0.146981
\(676\) −0.754655 −0.0290252
\(677\) 14.3196 0.550346 0.275173 0.961395i \(-0.411265\pi\)
0.275173 + 0.961395i \(0.411265\pi\)
\(678\) −2.30294 −0.0884440
\(679\) −7.30161 −0.280210
\(680\) −1.08688 −0.0416801
\(681\) −21.7085 −0.831873
\(682\) 1.67803 0.0642553
\(683\) 20.3479 0.778590 0.389295 0.921113i \(-0.372719\pi\)
0.389295 + 0.921113i \(0.372719\pi\)
\(684\) 3.42776 0.131064
\(685\) −12.5148 −0.478167
\(686\) −15.5261 −0.592789
\(687\) 2.56949 0.0980320
\(688\) 4.90177 0.186878
\(689\) −31.2171 −1.18928
\(690\) 1.92111 0.0731354
\(691\) −22.5023 −0.856028 −0.428014 0.903772i \(-0.640787\pi\)
−0.428014 + 0.903772i \(0.640787\pi\)
\(692\) 22.5221 0.856163
\(693\) 1.98227 0.0753000
\(694\) −15.3513 −0.582729
\(695\) 10.9551 0.415550
\(696\) −6.53238 −0.247609
\(697\) 0.263080 0.00996485
\(698\) −19.4089 −0.734638
\(699\) −5.23889 −0.198153
\(700\) 4.76484 0.180094
\(701\) −19.9927 −0.755113 −0.377556 0.925987i \(-0.623236\pi\)
−0.377556 + 0.925987i \(0.623236\pi\)
\(702\) 3.49933 0.132074
\(703\) −19.3806 −0.730952
\(704\) −1.58865 −0.0598743
\(705\) 7.65373 0.288256
\(706\) 8.51189 0.320349
\(707\) −15.7587 −0.592665
\(708\) −1.00000 −0.0375823
\(709\) 12.3461 0.463666 0.231833 0.972756i \(-0.425528\pi\)
0.231833 + 0.972756i \(0.425528\pi\)
\(710\) −3.70630 −0.139095
\(711\) −13.9437 −0.522929
\(712\) −2.56073 −0.0959672
\(713\) 1.86699 0.0699194
\(714\) −1.24777 −0.0466967
\(715\) −6.04221 −0.225966
\(716\) 0.971809 0.0363182
\(717\) −7.38807 −0.275913
\(718\) −6.28008 −0.234371
\(719\) 11.1568 0.416079 0.208040 0.978120i \(-0.433292\pi\)
0.208040 + 0.978120i \(0.433292\pi\)
\(720\) −1.08688 −0.0405058
\(721\) −23.9178 −0.890745
\(722\) 7.25047 0.269834
\(723\) −23.1478 −0.860877
\(724\) 7.46723 0.277517
\(725\) −24.9451 −0.926437
\(726\) 8.47621 0.314582
\(727\) 39.2816 1.45687 0.728436 0.685114i \(-0.240247\pi\)
0.728436 + 0.685114i \(0.240247\pi\)
\(728\) −4.36637 −0.161828
\(729\) 1.00000 0.0370370
\(730\) −2.22632 −0.0823999
\(731\) −4.90177 −0.181299
\(732\) 2.97847 0.110088
\(733\) −25.5761 −0.944674 −0.472337 0.881418i \(-0.656589\pi\)
−0.472337 + 0.881418i \(0.656589\pi\)
\(734\) 6.36236 0.234839
\(735\) 5.91599 0.218214
\(736\) −1.76754 −0.0651523
\(737\) −2.69211 −0.0991651
\(738\) 0.263080 0.00968409
\(739\) 26.8591 0.988027 0.494014 0.869454i \(-0.335529\pi\)
0.494014 + 0.869454i \(0.335529\pi\)
\(740\) 6.14525 0.225904
\(741\) −11.9949 −0.440643
\(742\) 11.1312 0.408640
\(743\) 41.3809 1.51812 0.759059 0.651022i \(-0.225659\pi\)
0.759059 + 0.651022i \(0.225659\pi\)
\(744\) −1.05627 −0.0387246
\(745\) −3.41361 −0.125065
\(746\) 8.37898 0.306776
\(747\) −7.00506 −0.256302
\(748\) 1.58865 0.0580866
\(749\) −22.9839 −0.839812
\(750\) −9.58489 −0.349991
\(751\) 45.8273 1.67226 0.836130 0.548531i \(-0.184813\pi\)
0.836130 + 0.548531i \(0.184813\pi\)
\(752\) −7.04190 −0.256792
\(753\) 19.9514 0.727071
\(754\) 22.8590 0.832475
\(755\) 2.91505 0.106089
\(756\) −1.24777 −0.0453810
\(757\) −29.7711 −1.08205 −0.541025 0.841006i \(-0.681964\pi\)
−0.541025 + 0.841006i \(0.681964\pi\)
\(758\) −16.4736 −0.598348
\(759\) −2.80799 −0.101924
\(760\) 3.72558 0.135141
\(761\) 1.65420 0.0599645 0.0299823 0.999550i \(-0.490455\pi\)
0.0299823 + 0.999550i \(0.490455\pi\)
\(762\) 12.6195 0.457155
\(763\) −0.707633 −0.0256180
\(764\) −19.4441 −0.703463
\(765\) 1.08688 0.0392964
\(766\) −29.4135 −1.06275
\(767\) 3.49933 0.126354
\(768\) 1.00000 0.0360844
\(769\) −3.49990 −0.126210 −0.0631048 0.998007i \(-0.520100\pi\)
−0.0631048 + 0.998007i \(0.520100\pi\)
\(770\) 2.15449 0.0776426
\(771\) 21.6923 0.781229
\(772\) 4.96696 0.178765
\(773\) −42.4792 −1.52787 −0.763936 0.645292i \(-0.776736\pi\)
−0.763936 + 0.645292i \(0.776736\pi\)
\(774\) −4.90177 −0.176191
\(775\) −4.03355 −0.144889
\(776\) −5.85172 −0.210065
\(777\) 7.05490 0.253093
\(778\) 11.0075 0.394639
\(779\) −0.901773 −0.0323094
\(780\) 3.80337 0.136183
\(781\) 5.41732 0.193847
\(782\) 1.76754 0.0632070
\(783\) 6.53238 0.233448
\(784\) −5.44307 −0.194395
\(785\) −26.9539 −0.962024
\(786\) −11.3817 −0.405971
\(787\) −11.2027 −0.399333 −0.199666 0.979864i \(-0.563986\pi\)
−0.199666 + 0.979864i \(0.563986\pi\)
\(788\) 10.2631 0.365607
\(789\) 23.4791 0.835879
\(790\) −15.1552 −0.539196
\(791\) −2.87354 −0.102171
\(792\) 1.58865 0.0564501
\(793\) −10.4227 −0.370120
\(794\) 10.9319 0.387960
\(795\) −9.69596 −0.343880
\(796\) 11.9743 0.424417
\(797\) 42.4937 1.50520 0.752601 0.658476i \(-0.228799\pi\)
0.752601 + 0.658476i \(0.228799\pi\)
\(798\) 4.27706 0.151406
\(799\) 7.04190 0.249124
\(800\) 3.81868 0.135011
\(801\) 2.56073 0.0904788
\(802\) 16.0447 0.566558
\(803\) 3.25410 0.114835
\(804\) 1.69459 0.0597637
\(805\) 2.39710 0.0844868
\(806\) 3.69623 0.130194
\(807\) −18.4264 −0.648641
\(808\) −12.6294 −0.444302
\(809\) −38.1848 −1.34251 −0.671253 0.741228i \(-0.734244\pi\)
−0.671253 + 0.741228i \(0.734244\pi\)
\(810\) 1.08688 0.0381892
\(811\) −25.3406 −0.889829 −0.444915 0.895573i \(-0.646766\pi\)
−0.444915 + 0.895573i \(0.646766\pi\)
\(812\) −8.15091 −0.286041
\(813\) 4.78257 0.167732
\(814\) −8.98220 −0.314826
\(815\) 1.82374 0.0638830
\(816\) −1.00000 −0.0350070
\(817\) 16.8021 0.587831
\(818\) 34.4158 1.20332
\(819\) 4.36637 0.152573
\(820\) 0.285937 0.00998536
\(821\) −29.7403 −1.03795 −0.518973 0.854791i \(-0.673685\pi\)
−0.518973 + 0.854791i \(0.673685\pi\)
\(822\) −11.5144 −0.401611
\(823\) 14.7604 0.514517 0.257258 0.966343i \(-0.417181\pi\)
0.257258 + 0.966343i \(0.417181\pi\)
\(824\) −19.1684 −0.667763
\(825\) 6.06653 0.211210
\(826\) −1.24777 −0.0434155
\(827\) 19.1358 0.665416 0.332708 0.943030i \(-0.392038\pi\)
0.332708 + 0.943030i \(0.392038\pi\)
\(828\) 1.76754 0.0614262
\(829\) 43.0528 1.49529 0.747643 0.664100i \(-0.231185\pi\)
0.747643 + 0.664100i \(0.231185\pi\)
\(830\) −7.61369 −0.264275
\(831\) 11.4444 0.397002
\(832\) −3.49933 −0.121318
\(833\) 5.44307 0.188591
\(834\) 10.0793 0.349019
\(835\) −19.0808 −0.660320
\(836\) −5.44549 −0.188336
\(837\) 1.05627 0.0365099
\(838\) 30.4667 1.05246
\(839\) 26.3976 0.911347 0.455674 0.890147i \(-0.349398\pi\)
0.455674 + 0.890147i \(0.349398\pi\)
\(840\) −1.35618 −0.0467928
\(841\) 13.6720 0.471447
\(842\) 35.3614 1.21863
\(843\) 24.7173 0.851308
\(844\) 0.298820 0.0102858
\(845\) 0.820223 0.0282165
\(846\) 7.04190 0.242105
\(847\) 10.5764 0.363408
\(848\) 8.92088 0.306344
\(849\) 11.3884 0.390850
\(850\) −3.81868 −0.130980
\(851\) −9.99366 −0.342578
\(852\) −3.41002 −0.116826
\(853\) 21.8260 0.747308 0.373654 0.927568i \(-0.378105\pi\)
0.373654 + 0.927568i \(0.378105\pi\)
\(854\) 3.71645 0.127174
\(855\) −3.72558 −0.127412
\(856\) −18.4199 −0.629581
\(857\) 19.6925 0.672683 0.336341 0.941740i \(-0.390810\pi\)
0.336341 + 0.941740i \(0.390810\pi\)
\(858\) −5.55920 −0.189788
\(859\) −17.9205 −0.611438 −0.305719 0.952122i \(-0.598897\pi\)
−0.305719 + 0.952122i \(0.598897\pi\)
\(860\) −5.32766 −0.181672
\(861\) 0.328263 0.0111872
\(862\) −37.8294 −1.28847
\(863\) 29.5703 1.00658 0.503292 0.864116i \(-0.332122\pi\)
0.503292 + 0.864116i \(0.332122\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −24.4790 −0.832310
\(866\) −23.4830 −0.797986
\(867\) 1.00000 0.0339618
\(868\) −1.31798 −0.0447351
\(869\) 22.1515 0.751440
\(870\) 7.09994 0.240711
\(871\) −5.92995 −0.200929
\(872\) −0.567118 −0.0192050
\(873\) 5.85172 0.198051
\(874\) −6.05869 −0.204938
\(875\) −11.9597 −0.404313
\(876\) −2.04835 −0.0692074
\(877\) −25.8551 −0.873064 −0.436532 0.899689i \(-0.643793\pi\)
−0.436532 + 0.899689i \(0.643793\pi\)
\(878\) 11.4651 0.386930
\(879\) 4.39572 0.148264
\(880\) 1.72667 0.0582062
\(881\) 29.0764 0.979608 0.489804 0.871833i \(-0.337068\pi\)
0.489804 + 0.871833i \(0.337068\pi\)
\(882\) 5.44307 0.183278
\(883\) −22.2971 −0.750356 −0.375178 0.926953i \(-0.622418\pi\)
−0.375178 + 0.926953i \(0.622418\pi\)
\(884\) 3.49933 0.117695
\(885\) 1.08688 0.0365352
\(886\) 3.17547 0.106682
\(887\) −53.7133 −1.80352 −0.901758 0.432242i \(-0.857723\pi\)
−0.901758 + 0.432242i \(0.857723\pi\)
\(888\) 5.65400 0.189736
\(889\) 15.7462 0.528111
\(890\) 2.78321 0.0932935
\(891\) −1.58865 −0.0532216
\(892\) 22.6580 0.758645
\(893\) −24.1379 −0.807745
\(894\) −3.14073 −0.105042
\(895\) −1.05624 −0.0353063
\(896\) 1.24777 0.0416851
\(897\) −6.18521 −0.206518
\(898\) 1.50463 0.0502102
\(899\) 6.89994 0.230126
\(900\) −3.81868 −0.127289
\(901\) −8.92088 −0.297197
\(902\) −0.417940 −0.0139159
\(903\) −6.11629 −0.203537
\(904\) −2.30294 −0.0765947
\(905\) −8.11602 −0.269786
\(906\) 2.68202 0.0891042
\(907\) 27.1098 0.900165 0.450083 0.892987i \(-0.351395\pi\)
0.450083 + 0.892987i \(0.351395\pi\)
\(908\) −21.7085 −0.720424
\(909\) 12.6294 0.418892
\(910\) 4.74574 0.157320
\(911\) −27.5099 −0.911445 −0.455722 0.890122i \(-0.650619\pi\)
−0.455722 + 0.890122i \(0.650619\pi\)
\(912\) 3.42776 0.113504
\(913\) 11.1286 0.368302
\(914\) −4.28245 −0.141651
\(915\) −3.23726 −0.107020
\(916\) 2.56949 0.0848982
\(917\) −14.2017 −0.468982
\(918\) 1.00000 0.0330049
\(919\) −20.4183 −0.673537 −0.336769 0.941587i \(-0.609334\pi\)
−0.336769 + 0.941587i \(0.609334\pi\)
\(920\) 1.92111 0.0633371
\(921\) −2.47798 −0.0816523
\(922\) 25.6090 0.843388
\(923\) 11.9328 0.392773
\(924\) 1.98227 0.0652117
\(925\) 21.5908 0.709902
\(926\) 22.8439 0.750697
\(927\) 19.1684 0.629573
\(928\) −6.53238 −0.214436
\(929\) 16.5047 0.541501 0.270751 0.962650i \(-0.412728\pi\)
0.270751 + 0.962650i \(0.412728\pi\)
\(930\) 1.14804 0.0376457
\(931\) −18.6575 −0.611476
\(932\) −5.23889 −0.171606
\(933\) 4.05650 0.132804
\(934\) −15.5653 −0.509314
\(935\) −1.72667 −0.0564683
\(936\) 3.49933 0.114379
\(937\) 49.2423 1.60868 0.804338 0.594171i \(-0.202520\pi\)
0.804338 + 0.594171i \(0.202520\pi\)
\(938\) 2.11447 0.0690398
\(939\) 6.30146 0.205640
\(940\) 7.65373 0.249637
\(941\) 53.6543 1.74908 0.874540 0.484953i \(-0.161163\pi\)
0.874540 + 0.484953i \(0.161163\pi\)
\(942\) −24.7992 −0.808001
\(943\) −0.465003 −0.0151426
\(944\) −1.00000 −0.0325472
\(945\) 1.35618 0.0441166
\(946\) 7.78718 0.253183
\(947\) −50.0273 −1.62567 −0.812834 0.582495i \(-0.802076\pi\)
−0.812834 + 0.582495i \(0.802076\pi\)
\(948\) −13.9437 −0.452869
\(949\) 7.16787 0.232679
\(950\) 13.0895 0.424680
\(951\) 17.0586 0.553164
\(952\) −1.24777 −0.0404405
\(953\) −17.4501 −0.565265 −0.282633 0.959228i \(-0.591208\pi\)
−0.282633 + 0.959228i \(0.591208\pi\)
\(954\) −8.92088 −0.288824
\(955\) 21.1335 0.683864
\(956\) −7.38807 −0.238947
\(957\) −10.3776 −0.335461
\(958\) 20.7173 0.669345
\(959\) −14.3673 −0.463946
\(960\) −1.08688 −0.0350790
\(961\) −29.8843 −0.964010
\(962\) −19.7852 −0.637902
\(963\) 18.4199 0.593574
\(964\) −23.1478 −0.745541
\(965\) −5.39851 −0.173784
\(966\) 2.20548 0.0709602
\(967\) 41.7301 1.34195 0.670975 0.741480i \(-0.265876\pi\)
0.670975 + 0.741480i \(0.265876\pi\)
\(968\) 8.47621 0.272436
\(969\) −3.42776 −0.110115
\(970\) 6.36015 0.204212
\(971\) 17.9956 0.577507 0.288754 0.957403i \(-0.406759\pi\)
0.288754 + 0.957403i \(0.406759\pi\)
\(972\) 1.00000 0.0320750
\(973\) 12.5767 0.403191
\(974\) −15.5679 −0.498827
\(975\) 13.3628 0.427954
\(976\) 2.97847 0.0953386
\(977\) −29.7319 −0.951208 −0.475604 0.879660i \(-0.657770\pi\)
−0.475604 + 0.879660i \(0.657770\pi\)
\(978\) 1.67796 0.0536551
\(979\) −4.06808 −0.130017
\(980\) 5.91599 0.188979
\(981\) 0.567118 0.0181067
\(982\) −31.4196 −1.00264
\(983\) −29.0181 −0.925534 −0.462767 0.886480i \(-0.653143\pi\)
−0.462767 + 0.886480i \(0.653143\pi\)
\(984\) 0.263080 0.00838667
\(985\) −11.1548 −0.355421
\(986\) 6.53238 0.208033
\(987\) 8.78668 0.279683
\(988\) −11.9949 −0.381608
\(989\) 8.66407 0.275501
\(990\) −1.72667 −0.0548773
\(991\) 36.5247 1.16025 0.580123 0.814529i \(-0.303005\pi\)
0.580123 + 0.814529i \(0.303005\pi\)
\(992\) −1.05627 −0.0335365
\(993\) 5.78371 0.183540
\(994\) −4.25493 −0.134958
\(995\) −13.0147 −0.412593
\(996\) −7.00506 −0.221964
\(997\) 33.3766 1.05705 0.528524 0.848918i \(-0.322746\pi\)
0.528524 + 0.848918i \(0.322746\pi\)
\(998\) −21.7979 −0.689999
\(999\) −5.65400 −0.178885
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 \(a_p\))