Properties

Label 8042.2.a.a.1.10
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.36999 q^{3}\) \(+1.00000 q^{4}\) \(+1.57394 q^{5}\) \(-2.36999 q^{6}\) \(+1.59393 q^{7}\) \(+1.00000 q^{8}\) \(+2.61687 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.36999 q^{3}\) \(+1.00000 q^{4}\) \(+1.57394 q^{5}\) \(-2.36999 q^{6}\) \(+1.59393 q^{7}\) \(+1.00000 q^{8}\) \(+2.61687 q^{9}\) \(+1.57394 q^{10}\) \(-1.45522 q^{11}\) \(-2.36999 q^{12}\) \(+1.08958 q^{13}\) \(+1.59393 q^{14}\) \(-3.73022 q^{15}\) \(+1.00000 q^{16}\) \(-1.26543 q^{17}\) \(+2.61687 q^{18}\) \(+2.02440 q^{19}\) \(+1.57394 q^{20}\) \(-3.77760 q^{21}\) \(-1.45522 q^{22}\) \(-3.02412 q^{23}\) \(-2.36999 q^{24}\) \(-2.52272 q^{25}\) \(+1.08958 q^{26}\) \(+0.908022 q^{27}\) \(+1.59393 q^{28}\) \(-2.01834 q^{29}\) \(-3.73022 q^{30}\) \(-6.74478 q^{31}\) \(+1.00000 q^{32}\) \(+3.44885 q^{33}\) \(-1.26543 q^{34}\) \(+2.50874 q^{35}\) \(+2.61687 q^{36}\) \(+1.22529 q^{37}\) \(+2.02440 q^{38}\) \(-2.58230 q^{39}\) \(+1.57394 q^{40}\) \(+1.59789 q^{41}\) \(-3.77760 q^{42}\) \(+0.188669 q^{43}\) \(-1.45522 q^{44}\) \(+4.11878 q^{45}\) \(-3.02412 q^{46}\) \(-3.24332 q^{47}\) \(-2.36999 q^{48}\) \(-4.45939 q^{49}\) \(-2.52272 q^{50}\) \(+2.99907 q^{51}\) \(+1.08958 q^{52}\) \(-4.65195 q^{53}\) \(+0.908022 q^{54}\) \(-2.29042 q^{55}\) \(+1.59393 q^{56}\) \(-4.79781 q^{57}\) \(-2.01834 q^{58}\) \(-2.64062 q^{59}\) \(-3.73022 q^{60}\) \(-15.4282 q^{61}\) \(-6.74478 q^{62}\) \(+4.17110 q^{63}\) \(+1.00000 q^{64}\) \(+1.71493 q^{65}\) \(+3.44885 q^{66}\) \(-5.82549 q^{67}\) \(-1.26543 q^{68}\) \(+7.16714 q^{69}\) \(+2.50874 q^{70}\) \(+11.2978 q^{71}\) \(+2.61687 q^{72}\) \(-8.57257 q^{73}\) \(+1.22529 q^{74}\) \(+5.97884 q^{75}\) \(+2.02440 q^{76}\) \(-2.31951 q^{77}\) \(-2.58230 q^{78}\) \(+7.53323 q^{79}\) \(+1.57394 q^{80}\) \(-10.0026 q^{81}\) \(+1.59789 q^{82}\) \(-4.74304 q^{83}\) \(-3.77760 q^{84}\) \(-1.99171 q^{85}\) \(+0.188669 q^{86}\) \(+4.78344 q^{87}\) \(-1.45522 q^{88}\) \(-0.722253 q^{89}\) \(+4.11878 q^{90}\) \(+1.73672 q^{91}\) \(-3.02412 q^{92}\) \(+15.9851 q^{93}\) \(-3.24332 q^{94}\) \(+3.18627 q^{95}\) \(-2.36999 q^{96}\) \(+7.32169 q^{97}\) \(-4.45939 q^{98}\) \(-3.80810 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.36999 −1.36832 −0.684158 0.729334i \(-0.739830\pi\)
−0.684158 + 0.729334i \(0.739830\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.57394 0.703886 0.351943 0.936021i \(-0.385521\pi\)
0.351943 + 0.936021i \(0.385521\pi\)
\(6\) −2.36999 −0.967546
\(7\) 1.59393 0.602448 0.301224 0.953553i \(-0.402605\pi\)
0.301224 + 0.953553i \(0.402605\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.61687 0.872289
\(10\) 1.57394 0.497722
\(11\) −1.45522 −0.438764 −0.219382 0.975639i \(-0.570404\pi\)
−0.219382 + 0.975639i \(0.570404\pi\)
\(12\) −2.36999 −0.684158
\(13\) 1.08958 0.302196 0.151098 0.988519i \(-0.451719\pi\)
0.151098 + 0.988519i \(0.451719\pi\)
\(14\) 1.59393 0.425995
\(15\) −3.73022 −0.963138
\(16\) 1.00000 0.250000
\(17\) −1.26543 −0.306913 −0.153456 0.988155i \(-0.549040\pi\)
−0.153456 + 0.988155i \(0.549040\pi\)
\(18\) 2.61687 0.616802
\(19\) 2.02440 0.464428 0.232214 0.972665i \(-0.425403\pi\)
0.232214 + 0.972665i \(0.425403\pi\)
\(20\) 1.57394 0.351943
\(21\) −3.77760 −0.824340
\(22\) −1.45522 −0.310253
\(23\) −3.02412 −0.630572 −0.315286 0.948997i \(-0.602100\pi\)
−0.315286 + 0.948997i \(0.602100\pi\)
\(24\) −2.36999 −0.483773
\(25\) −2.52272 −0.504545
\(26\) 1.08958 0.213685
\(27\) 0.908022 0.174749
\(28\) 1.59393 0.301224
\(29\) −2.01834 −0.374796 −0.187398 0.982284i \(-0.560005\pi\)
−0.187398 + 0.982284i \(0.560005\pi\)
\(30\) −3.73022 −0.681042
\(31\) −6.74478 −1.21140 −0.605699 0.795694i \(-0.707106\pi\)
−0.605699 + 0.795694i \(0.707106\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.44885 0.600368
\(34\) −1.26543 −0.217020
\(35\) 2.50874 0.424055
\(36\) 2.61687 0.436145
\(37\) 1.22529 0.201437 0.100718 0.994915i \(-0.467886\pi\)
0.100718 + 0.994915i \(0.467886\pi\)
\(38\) 2.02440 0.328400
\(39\) −2.58230 −0.413500
\(40\) 1.57394 0.248861
\(41\) 1.59789 0.249549 0.124774 0.992185i \(-0.460179\pi\)
0.124774 + 0.992185i \(0.460179\pi\)
\(42\) −3.77760 −0.582896
\(43\) 0.188669 0.0287718 0.0143859 0.999897i \(-0.495421\pi\)
0.0143859 + 0.999897i \(0.495421\pi\)
\(44\) −1.45522 −0.219382
\(45\) 4.11878 0.613992
\(46\) −3.02412 −0.445882
\(47\) −3.24332 −0.473086 −0.236543 0.971621i \(-0.576014\pi\)
−0.236543 + 0.971621i \(0.576014\pi\)
\(48\) −2.36999 −0.342079
\(49\) −4.45939 −0.637056
\(50\) −2.52272 −0.356767
\(51\) 2.99907 0.419954
\(52\) 1.08958 0.151098
\(53\) −4.65195 −0.638995 −0.319498 0.947587i \(-0.603514\pi\)
−0.319498 + 0.947587i \(0.603514\pi\)
\(54\) 0.908022 0.123566
\(55\) −2.29042 −0.308840
\(56\) 1.59393 0.212998
\(57\) −4.79781 −0.635485
\(58\) −2.01834 −0.265021
\(59\) −2.64062 −0.343780 −0.171890 0.985116i \(-0.554987\pi\)
−0.171890 + 0.985116i \(0.554987\pi\)
\(60\) −3.73022 −0.481569
\(61\) −15.4282 −1.97537 −0.987686 0.156448i \(-0.949996\pi\)
−0.987686 + 0.156448i \(0.949996\pi\)
\(62\) −6.74478 −0.856587
\(63\) 4.17110 0.525509
\(64\) 1.00000 0.125000
\(65\) 1.71493 0.212711
\(66\) 3.44885 0.424524
\(67\) −5.82549 −0.711696 −0.355848 0.934544i \(-0.615808\pi\)
−0.355848 + 0.934544i \(0.615808\pi\)
\(68\) −1.26543 −0.153456
\(69\) 7.16714 0.862822
\(70\) 2.50874 0.299852
\(71\) 11.2978 1.34080 0.670400 0.742000i \(-0.266122\pi\)
0.670400 + 0.742000i \(0.266122\pi\)
\(72\) 2.61687 0.308401
\(73\) −8.57257 −1.00334 −0.501672 0.865058i \(-0.667282\pi\)
−0.501672 + 0.865058i \(0.667282\pi\)
\(74\) 1.22529 0.142437
\(75\) 5.97884 0.690377
\(76\) 2.02440 0.232214
\(77\) −2.31951 −0.264333
\(78\) −2.58230 −0.292388
\(79\) 7.53323 0.847554 0.423777 0.905767i \(-0.360704\pi\)
0.423777 + 0.905767i \(0.360704\pi\)
\(80\) 1.57394 0.175971
\(81\) −10.0026 −1.11140
\(82\) 1.59789 0.176458
\(83\) −4.74304 −0.520616 −0.260308 0.965526i \(-0.583824\pi\)
−0.260308 + 0.965526i \(0.583824\pi\)
\(84\) −3.77760 −0.412170
\(85\) −1.99171 −0.216031
\(86\) 0.188669 0.0203447
\(87\) 4.78344 0.512839
\(88\) −1.45522 −0.155126
\(89\) −0.722253 −0.0765586 −0.0382793 0.999267i \(-0.512188\pi\)
−0.0382793 + 0.999267i \(0.512188\pi\)
\(90\) 4.11878 0.434158
\(91\) 1.73672 0.182057
\(92\) −3.02412 −0.315286
\(93\) 15.9851 1.65757
\(94\) −3.24332 −0.334522
\(95\) 3.18627 0.326905
\(96\) −2.36999 −0.241886
\(97\) 7.32169 0.743405 0.371703 0.928352i \(-0.378774\pi\)
0.371703 + 0.928352i \(0.378774\pi\)
\(98\) −4.45939 −0.450467
\(99\) −3.80810 −0.382729
\(100\) −2.52272 −0.252272
\(101\) 8.46910 0.842707 0.421353 0.906897i \(-0.361555\pi\)
0.421353 + 0.906897i \(0.361555\pi\)
\(102\) 2.99907 0.296952
\(103\) 12.6629 1.24772 0.623858 0.781538i \(-0.285564\pi\)
0.623858 + 0.781538i \(0.285564\pi\)
\(104\) 1.08958 0.106842
\(105\) −5.94570 −0.580241
\(106\) −4.65195 −0.451838
\(107\) −9.20169 −0.889561 −0.444781 0.895640i \(-0.646718\pi\)
−0.444781 + 0.895640i \(0.646718\pi\)
\(108\) 0.908022 0.0873745
\(109\) 5.30425 0.508055 0.254027 0.967197i \(-0.418245\pi\)
0.254027 + 0.967197i \(0.418245\pi\)
\(110\) −2.29042 −0.218383
\(111\) −2.90393 −0.275629
\(112\) 1.59393 0.150612
\(113\) −6.07270 −0.571272 −0.285636 0.958338i \(-0.592205\pi\)
−0.285636 + 0.958338i \(0.592205\pi\)
\(114\) −4.79781 −0.449356
\(115\) −4.75977 −0.443851
\(116\) −2.01834 −0.187398
\(117\) 2.85129 0.263602
\(118\) −2.64062 −0.243089
\(119\) −2.01701 −0.184899
\(120\) −3.73022 −0.340521
\(121\) −8.88235 −0.807486
\(122\) −15.4282 −1.39680
\(123\) −3.78699 −0.341461
\(124\) −6.74478 −0.605699
\(125\) −11.8403 −1.05903
\(126\) 4.17110 0.371591
\(127\) 13.7667 1.22160 0.610798 0.791787i \(-0.290849\pi\)
0.610798 + 0.791787i \(0.290849\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.447145 −0.0393689
\(130\) 1.71493 0.150410
\(131\) −4.95814 −0.433195 −0.216597 0.976261i \(-0.569496\pi\)
−0.216597 + 0.976261i \(0.569496\pi\)
\(132\) 3.44885 0.300184
\(133\) 3.22674 0.279794
\(134\) −5.82549 −0.503245
\(135\) 1.42917 0.123003
\(136\) −1.26543 −0.108510
\(137\) −9.81564 −0.838607 −0.419303 0.907846i \(-0.637726\pi\)
−0.419303 + 0.907846i \(0.637726\pi\)
\(138\) 7.16714 0.610107
\(139\) 1.27239 0.107923 0.0539613 0.998543i \(-0.482815\pi\)
0.0539613 + 0.998543i \(0.482815\pi\)
\(140\) 2.50874 0.212027
\(141\) 7.68664 0.647331
\(142\) 11.2978 0.948089
\(143\) −1.58558 −0.132593
\(144\) 2.61687 0.218072
\(145\) −3.17673 −0.263813
\(146\) −8.57257 −0.709471
\(147\) 10.5687 0.871694
\(148\) 1.22529 0.100718
\(149\) −16.1054 −1.31940 −0.659702 0.751528i \(-0.729317\pi\)
−0.659702 + 0.751528i \(0.729317\pi\)
\(150\) 5.97884 0.488170
\(151\) 9.18990 0.747863 0.373932 0.927456i \(-0.378009\pi\)
0.373932 + 0.927456i \(0.378009\pi\)
\(152\) 2.02440 0.164200
\(153\) −3.31147 −0.267717
\(154\) −2.31951 −0.186911
\(155\) −10.6158 −0.852685
\(156\) −2.58230 −0.206750
\(157\) −11.1585 −0.890543 −0.445271 0.895396i \(-0.646893\pi\)
−0.445271 + 0.895396i \(0.646893\pi\)
\(158\) 7.53323 0.599311
\(159\) 11.0251 0.874347
\(160\) 1.57394 0.124431
\(161\) −4.82023 −0.379887
\(162\) −10.0026 −0.785879
\(163\) −6.20270 −0.485833 −0.242916 0.970047i \(-0.578104\pi\)
−0.242916 + 0.970047i \(0.578104\pi\)
\(164\) 1.59789 0.124774
\(165\) 5.42827 0.422590
\(166\) −4.74304 −0.368131
\(167\) −23.0755 −1.78564 −0.892818 0.450418i \(-0.851275\pi\)
−0.892818 + 0.450418i \(0.851275\pi\)
\(168\) −3.77760 −0.291448
\(169\) −11.8128 −0.908678
\(170\) −1.99171 −0.152757
\(171\) 5.29758 0.405116
\(172\) 0.188669 0.0143859
\(173\) −2.50660 −0.190573 −0.0952866 0.995450i \(-0.530377\pi\)
−0.0952866 + 0.995450i \(0.530377\pi\)
\(174\) 4.78344 0.362632
\(175\) −4.02104 −0.303962
\(176\) −1.45522 −0.109691
\(177\) 6.25826 0.470400
\(178\) −0.722253 −0.0541351
\(179\) 14.6526 1.09519 0.547593 0.836745i \(-0.315544\pi\)
0.547593 + 0.836745i \(0.315544\pi\)
\(180\) 4.11878 0.306996
\(181\) 17.2563 1.28265 0.641327 0.767268i \(-0.278384\pi\)
0.641327 + 0.767268i \(0.278384\pi\)
\(182\) 1.73672 0.128734
\(183\) 36.5646 2.70293
\(184\) −3.02412 −0.222941
\(185\) 1.92853 0.141788
\(186\) 15.9851 1.17208
\(187\) 1.84148 0.134662
\(188\) −3.24332 −0.236543
\(189\) 1.44732 0.105277
\(190\) 3.18627 0.231156
\(191\) 18.3904 1.33068 0.665342 0.746539i \(-0.268286\pi\)
0.665342 + 0.746539i \(0.268286\pi\)
\(192\) −2.36999 −0.171040
\(193\) −6.51055 −0.468639 −0.234320 0.972160i \(-0.575286\pi\)
−0.234320 + 0.972160i \(0.575286\pi\)
\(194\) 7.32169 0.525667
\(195\) −4.06438 −0.291056
\(196\) −4.45939 −0.318528
\(197\) 13.5903 0.968266 0.484133 0.874994i \(-0.339135\pi\)
0.484133 + 0.874994i \(0.339135\pi\)
\(198\) −3.80810 −0.270630
\(199\) −13.7842 −0.977135 −0.488568 0.872526i \(-0.662480\pi\)
−0.488568 + 0.872526i \(0.662480\pi\)
\(200\) −2.52272 −0.178384
\(201\) 13.8064 0.973826
\(202\) 8.46910 0.595884
\(203\) −3.21709 −0.225795
\(204\) 2.99907 0.209977
\(205\) 2.51498 0.175654
\(206\) 12.6629 0.882269
\(207\) −7.91371 −0.550041
\(208\) 1.08958 0.0755490
\(209\) −2.94593 −0.203774
\(210\) −5.94570 −0.410292
\(211\) −9.53853 −0.656659 −0.328330 0.944563i \(-0.606486\pi\)
−0.328330 + 0.944563i \(0.606486\pi\)
\(212\) −4.65195 −0.319498
\(213\) −26.7757 −1.83464
\(214\) −9.20169 −0.629015
\(215\) 0.296954 0.0202521
\(216\) 0.908022 0.0617831
\(217\) −10.7507 −0.729804
\(218\) 5.30425 0.359249
\(219\) 20.3169 1.37289
\(220\) −2.29042 −0.154420
\(221\) −1.37879 −0.0927478
\(222\) −2.90393 −0.194899
\(223\) 12.7731 0.855347 0.427673 0.903933i \(-0.359333\pi\)
0.427673 + 0.903933i \(0.359333\pi\)
\(224\) 1.59393 0.106499
\(225\) −6.60164 −0.440109
\(226\) −6.07270 −0.403950
\(227\) 19.9844 1.32641 0.663206 0.748437i \(-0.269195\pi\)
0.663206 + 0.748437i \(0.269195\pi\)
\(228\) −4.79781 −0.317742
\(229\) −11.6113 −0.767294 −0.383647 0.923480i \(-0.625332\pi\)
−0.383647 + 0.923480i \(0.625332\pi\)
\(230\) −4.75977 −0.313850
\(231\) 5.49722 0.361691
\(232\) −2.01834 −0.132510
\(233\) 24.2822 1.59078 0.795392 0.606096i \(-0.207265\pi\)
0.795392 + 0.606096i \(0.207265\pi\)
\(234\) 2.85129 0.186395
\(235\) −5.10477 −0.332999
\(236\) −2.64062 −0.171890
\(237\) −17.8537 −1.15972
\(238\) −2.01701 −0.130743
\(239\) −19.6722 −1.27249 −0.636245 0.771487i \(-0.719513\pi\)
−0.636245 + 0.771487i \(0.719513\pi\)
\(240\) −3.73022 −0.240785
\(241\) 8.85103 0.570145 0.285072 0.958506i \(-0.407982\pi\)
0.285072 + 0.958506i \(0.407982\pi\)
\(242\) −8.88235 −0.570979
\(243\) 20.9820 1.34600
\(244\) −15.4282 −0.987686
\(245\) −7.01880 −0.448415
\(246\) −3.78699 −0.241450
\(247\) 2.20575 0.140348
\(248\) −6.74478 −0.428294
\(249\) 11.2410 0.712367
\(250\) −11.8403 −0.748846
\(251\) 0.989008 0.0624256 0.0312128 0.999513i \(-0.490063\pi\)
0.0312128 + 0.999513i \(0.490063\pi\)
\(252\) 4.17110 0.262755
\(253\) 4.40074 0.276672
\(254\) 13.7667 0.863798
\(255\) 4.72034 0.295599
\(256\) 1.00000 0.0625000
\(257\) 14.9999 0.935669 0.467834 0.883816i \(-0.345034\pi\)
0.467834 + 0.883816i \(0.345034\pi\)
\(258\) −0.447145 −0.0278380
\(259\) 1.95303 0.121355
\(260\) 1.71493 0.106356
\(261\) −5.28172 −0.326930
\(262\) −4.95814 −0.306315
\(263\) 18.3854 1.13369 0.566846 0.823824i \(-0.308164\pi\)
0.566846 + 0.823824i \(0.308164\pi\)
\(264\) 3.44885 0.212262
\(265\) −7.32188 −0.449779
\(266\) 3.22674 0.197844
\(267\) 1.71173 0.104756
\(268\) −5.82549 −0.355848
\(269\) 13.0813 0.797582 0.398791 0.917042i \(-0.369430\pi\)
0.398791 + 0.917042i \(0.369430\pi\)
\(270\) 1.42917 0.0869765
\(271\) −9.28426 −0.563979 −0.281989 0.959418i \(-0.590994\pi\)
−0.281989 + 0.959418i \(0.590994\pi\)
\(272\) −1.26543 −0.0767282
\(273\) −4.11601 −0.249112
\(274\) −9.81564 −0.592984
\(275\) 3.67111 0.221376
\(276\) 7.16714 0.431411
\(277\) −17.5260 −1.05304 −0.526518 0.850164i \(-0.676503\pi\)
−0.526518 + 0.850164i \(0.676503\pi\)
\(278\) 1.27239 0.0763129
\(279\) −17.6502 −1.05669
\(280\) 2.50874 0.149926
\(281\) −28.0768 −1.67492 −0.837461 0.546498i \(-0.815961\pi\)
−0.837461 + 0.546498i \(0.815961\pi\)
\(282\) 7.68664 0.457732
\(283\) −16.4120 −0.975593 −0.487796 0.872957i \(-0.662199\pi\)
−0.487796 + 0.872957i \(0.662199\pi\)
\(284\) 11.2978 0.670400
\(285\) −7.55144 −0.447309
\(286\) −1.58558 −0.0937572
\(287\) 2.54692 0.150340
\(288\) 2.61687 0.154200
\(289\) −15.3987 −0.905805
\(290\) −3.17673 −0.186544
\(291\) −17.3524 −1.01721
\(292\) −8.57257 −0.501672
\(293\) −9.15821 −0.535029 −0.267514 0.963554i \(-0.586202\pi\)
−0.267514 + 0.963554i \(0.586202\pi\)
\(294\) 10.5687 0.616381
\(295\) −4.15617 −0.241982
\(296\) 1.22529 0.0712186
\(297\) −1.32137 −0.0766735
\(298\) −16.1054 −0.932959
\(299\) −3.29503 −0.190556
\(300\) 5.97884 0.345188
\(301\) 0.300726 0.0173335
\(302\) 9.18990 0.528819
\(303\) −20.0717 −1.15309
\(304\) 2.02440 0.116107
\(305\) −24.2829 −1.39044
\(306\) −3.31147 −0.189304
\(307\) 14.8303 0.846409 0.423204 0.906034i \(-0.360905\pi\)
0.423204 + 0.906034i \(0.360905\pi\)
\(308\) −2.31951 −0.132166
\(309\) −30.0111 −1.70727
\(310\) −10.6158 −0.602940
\(311\) 25.6635 1.45524 0.727622 0.685978i \(-0.240625\pi\)
0.727622 + 0.685978i \(0.240625\pi\)
\(312\) −2.58230 −0.146194
\(313\) 15.9469 0.901372 0.450686 0.892683i \(-0.351179\pi\)
0.450686 + 0.892683i \(0.351179\pi\)
\(314\) −11.1585 −0.629709
\(315\) 6.56504 0.369898
\(316\) 7.53323 0.423777
\(317\) −3.76227 −0.211310 −0.105655 0.994403i \(-0.533694\pi\)
−0.105655 + 0.994403i \(0.533694\pi\)
\(318\) 11.0251 0.618257
\(319\) 2.93711 0.164447
\(320\) 1.57394 0.0879857
\(321\) 21.8079 1.21720
\(322\) −4.82023 −0.268621
\(323\) −2.56174 −0.142539
\(324\) −10.0026 −0.555700
\(325\) −2.74872 −0.152471
\(326\) −6.20270 −0.343536
\(327\) −12.5710 −0.695180
\(328\) 1.59789 0.0882288
\(329\) −5.16961 −0.285010
\(330\) 5.42827 0.298816
\(331\) −15.4315 −0.848194 −0.424097 0.905617i \(-0.639408\pi\)
−0.424097 + 0.905617i \(0.639408\pi\)
\(332\) −4.74304 −0.260308
\(333\) 3.20642 0.175711
\(334\) −23.0755 −1.26264
\(335\) −9.16894 −0.500953
\(336\) −3.77760 −0.206085
\(337\) −17.5762 −0.957438 −0.478719 0.877968i \(-0.658899\pi\)
−0.478719 + 0.877968i \(0.658899\pi\)
\(338\) −11.8128 −0.642532
\(339\) 14.3923 0.781681
\(340\) −1.99171 −0.108016
\(341\) 9.81510 0.531517
\(342\) 5.29758 0.286460
\(343\) −18.2655 −0.986242
\(344\) 0.188669 0.0101724
\(345\) 11.2806 0.607328
\(346\) −2.50660 −0.134756
\(347\) −3.30225 −0.177274 −0.0886371 0.996064i \(-0.528251\pi\)
−0.0886371 + 0.996064i \(0.528251\pi\)
\(348\) 4.78344 0.256420
\(349\) −3.24409 −0.173652 −0.0868261 0.996223i \(-0.527672\pi\)
−0.0868261 + 0.996223i \(0.527672\pi\)
\(350\) −4.02104 −0.214934
\(351\) 0.989366 0.0528084
\(352\) −1.45522 −0.0775632
\(353\) −6.94052 −0.369407 −0.184703 0.982794i \(-0.559132\pi\)
−0.184703 + 0.982794i \(0.559132\pi\)
\(354\) 6.25826 0.332623
\(355\) 17.7820 0.943770
\(356\) −0.722253 −0.0382793
\(357\) 4.78030 0.253000
\(358\) 14.6526 0.774413
\(359\) −25.3192 −1.33630 −0.668148 0.744028i \(-0.732913\pi\)
−0.668148 + 0.744028i \(0.732913\pi\)
\(360\) 4.11878 0.217079
\(361\) −14.9018 −0.784306
\(362\) 17.2563 0.906974
\(363\) 21.0511 1.10490
\(364\) 1.73672 0.0910287
\(365\) −13.4927 −0.706239
\(366\) 36.5646 1.91126
\(367\) −29.5013 −1.53995 −0.769977 0.638072i \(-0.779732\pi\)
−0.769977 + 0.638072i \(0.779732\pi\)
\(368\) −3.02412 −0.157643
\(369\) 4.18147 0.217679
\(370\) 1.92853 0.100260
\(371\) −7.41488 −0.384962
\(372\) 15.9851 0.828787
\(373\) −29.0522 −1.50427 −0.752134 0.659011i \(-0.770975\pi\)
−0.752134 + 0.659011i \(0.770975\pi\)
\(374\) 1.84148 0.0952206
\(375\) 28.0614 1.44908
\(376\) −3.24332 −0.167261
\(377\) −2.19915 −0.113262
\(378\) 1.44732 0.0744422
\(379\) 3.19572 0.164153 0.0820767 0.996626i \(-0.473845\pi\)
0.0820767 + 0.996626i \(0.473845\pi\)
\(380\) 3.18627 0.163452
\(381\) −32.6269 −1.67153
\(382\) 18.3904 0.940935
\(383\) 5.19416 0.265409 0.132705 0.991156i \(-0.457634\pi\)
0.132705 + 0.991156i \(0.457634\pi\)
\(384\) −2.36999 −0.120943
\(385\) −3.65076 −0.186060
\(386\) −6.51055 −0.331378
\(387\) 0.493723 0.0250973
\(388\) 7.32169 0.371703
\(389\) 37.6167 1.90724 0.953620 0.301012i \(-0.0973245\pi\)
0.953620 + 0.301012i \(0.0973245\pi\)
\(390\) −4.06438 −0.205808
\(391\) 3.82682 0.193531
\(392\) −4.45939 −0.225233
\(393\) 11.7508 0.592747
\(394\) 13.5903 0.684668
\(395\) 11.8568 0.596581
\(396\) −3.80810 −0.191364
\(397\) −27.9068 −1.40060 −0.700302 0.713847i \(-0.746951\pi\)
−0.700302 + 0.713847i \(0.746951\pi\)
\(398\) −13.7842 −0.690939
\(399\) −7.64736 −0.382847
\(400\) −2.52272 −0.126136
\(401\) 17.7271 0.885249 0.442624 0.896707i \(-0.354048\pi\)
0.442624 + 0.896707i \(0.354048\pi\)
\(402\) 13.8064 0.688599
\(403\) −7.34899 −0.366079
\(404\) 8.46910 0.421353
\(405\) −15.7435 −0.782299
\(406\) −3.21709 −0.159661
\(407\) −1.78306 −0.0883831
\(408\) 2.99907 0.148476
\(409\) −9.57326 −0.473367 −0.236684 0.971587i \(-0.576061\pi\)
−0.236684 + 0.971587i \(0.576061\pi\)
\(410\) 2.51498 0.124206
\(411\) 23.2630 1.14748
\(412\) 12.6629 0.623858
\(413\) −4.20897 −0.207110
\(414\) −7.91371 −0.388938
\(415\) −7.46524 −0.366454
\(416\) 1.08958 0.0534212
\(417\) −3.01555 −0.147672
\(418\) −2.94593 −0.144090
\(419\) −15.7393 −0.768916 −0.384458 0.923142i \(-0.625612\pi\)
−0.384458 + 0.923142i \(0.625612\pi\)
\(420\) −5.94570 −0.290121
\(421\) −34.8963 −1.70074 −0.850370 0.526185i \(-0.823622\pi\)
−0.850370 + 0.526185i \(0.823622\pi\)
\(422\) −9.53853 −0.464328
\(423\) −8.48733 −0.412668
\(424\) −4.65195 −0.225919
\(425\) 3.19234 0.154851
\(426\) −26.7757 −1.29729
\(427\) −24.5914 −1.19006
\(428\) −9.20169 −0.444781
\(429\) 3.75781 0.181429
\(430\) 0.296954 0.0143204
\(431\) −32.7475 −1.57739 −0.788696 0.614783i \(-0.789244\pi\)
−0.788696 + 0.614783i \(0.789244\pi\)
\(432\) 0.908022 0.0436872
\(433\) 36.1285 1.73623 0.868113 0.496367i \(-0.165333\pi\)
0.868113 + 0.496367i \(0.165333\pi\)
\(434\) −10.7507 −0.516050
\(435\) 7.52884 0.360980
\(436\) 5.30425 0.254027
\(437\) −6.12201 −0.292856
\(438\) 20.3169 0.970781
\(439\) −1.93567 −0.0923846 −0.0461923 0.998933i \(-0.514709\pi\)
−0.0461923 + 0.998933i \(0.514709\pi\)
\(440\) −2.29042 −0.109191
\(441\) −11.6696 −0.555697
\(442\) −1.37879 −0.0655826
\(443\) 11.9595 0.568213 0.284106 0.958793i \(-0.408303\pi\)
0.284106 + 0.958793i \(0.408303\pi\)
\(444\) −2.90393 −0.137814
\(445\) −1.13678 −0.0538885
\(446\) 12.7731 0.604821
\(447\) 38.1696 1.80536
\(448\) 1.59393 0.0753061
\(449\) −26.6005 −1.25536 −0.627678 0.778473i \(-0.715994\pi\)
−0.627678 + 0.778473i \(0.715994\pi\)
\(450\) −6.60164 −0.311204
\(451\) −2.32527 −0.109493
\(452\) −6.07270 −0.285636
\(453\) −21.7800 −1.02331
\(454\) 19.9844 0.937914
\(455\) 2.73348 0.128148
\(456\) −4.79781 −0.224678
\(457\) 4.75305 0.222338 0.111169 0.993802i \(-0.464540\pi\)
0.111169 + 0.993802i \(0.464540\pi\)
\(458\) −11.6113 −0.542559
\(459\) −1.14904 −0.0536327
\(460\) −4.75977 −0.221925
\(461\) −4.08028 −0.190038 −0.0950188 0.995475i \(-0.530291\pi\)
−0.0950188 + 0.995475i \(0.530291\pi\)
\(462\) 5.49722 0.255754
\(463\) 4.31122 0.200359 0.100180 0.994969i \(-0.468058\pi\)
0.100180 + 0.994969i \(0.468058\pi\)
\(464\) −2.01834 −0.0936989
\(465\) 25.1595 1.16674
\(466\) 24.2822 1.12485
\(467\) −32.5024 −1.50403 −0.752017 0.659144i \(-0.770919\pi\)
−0.752017 + 0.659144i \(0.770919\pi\)
\(468\) 2.85129 0.131801
\(469\) −9.28541 −0.428760
\(470\) −5.10477 −0.235466
\(471\) 26.4455 1.21854
\(472\) −2.64062 −0.121545
\(473\) −0.274555 −0.0126240
\(474\) −17.8537 −0.820047
\(475\) −5.10700 −0.234325
\(476\) −2.01701 −0.0924495
\(477\) −12.1735 −0.557388
\(478\) −19.6722 −0.899786
\(479\) 11.7102 0.535055 0.267527 0.963550i \(-0.413793\pi\)
0.267527 + 0.963550i \(0.413793\pi\)
\(480\) −3.73022 −0.170260
\(481\) 1.33506 0.0608733
\(482\) 8.85103 0.403153
\(483\) 11.4239 0.519806
\(484\) −8.88235 −0.403743
\(485\) 11.5239 0.523272
\(486\) 20.9820 0.951765
\(487\) −26.8841 −1.21824 −0.609118 0.793080i \(-0.708476\pi\)
−0.609118 + 0.793080i \(0.708476\pi\)
\(488\) −15.4282 −0.698400
\(489\) 14.7004 0.664773
\(490\) −7.01880 −0.317077
\(491\) −20.7525 −0.936545 −0.468273 0.883584i \(-0.655123\pi\)
−0.468273 + 0.883584i \(0.655123\pi\)
\(492\) −3.78699 −0.170731
\(493\) 2.55407 0.115030
\(494\) 2.20575 0.0992413
\(495\) −5.99371 −0.269397
\(496\) −6.74478 −0.302849
\(497\) 18.0079 0.807763
\(498\) 11.2410 0.503720
\(499\) 15.4767 0.692831 0.346415 0.938081i \(-0.387399\pi\)
0.346415 + 0.938081i \(0.387399\pi\)
\(500\) −11.8403 −0.529514
\(501\) 54.6888 2.44331
\(502\) 0.989008 0.0441416
\(503\) −19.8746 −0.886164 −0.443082 0.896481i \(-0.646115\pi\)
−0.443082 + 0.896481i \(0.646115\pi\)
\(504\) 4.17110 0.185796
\(505\) 13.3298 0.593169
\(506\) 4.40074 0.195637
\(507\) 27.9963 1.24336
\(508\) 13.7667 0.610798
\(509\) −16.7878 −0.744105 −0.372052 0.928212i \(-0.621346\pi\)
−0.372052 + 0.928212i \(0.621346\pi\)
\(510\) 4.72034 0.209020
\(511\) −13.6641 −0.604463
\(512\) 1.00000 0.0441942
\(513\) 1.83820 0.0811584
\(514\) 14.9999 0.661618
\(515\) 19.9307 0.878250
\(516\) −0.447145 −0.0196845
\(517\) 4.71972 0.207573
\(518\) 1.95303 0.0858111
\(519\) 5.94062 0.260764
\(520\) 1.71493 0.0752048
\(521\) −2.48079 −0.108685 −0.0543426 0.998522i \(-0.517306\pi\)
−0.0543426 + 0.998522i \(0.517306\pi\)
\(522\) −5.28172 −0.231175
\(523\) 32.2891 1.41190 0.705952 0.708260i \(-0.250519\pi\)
0.705952 + 0.708260i \(0.250519\pi\)
\(524\) −4.95814 −0.216597
\(525\) 9.52984 0.415917
\(526\) 18.3854 0.801641
\(527\) 8.53507 0.371793
\(528\) 3.44885 0.150092
\(529\) −13.8547 −0.602379
\(530\) −7.32188 −0.318042
\(531\) −6.91016 −0.299875
\(532\) 3.22674 0.139897
\(533\) 1.74103 0.0754126
\(534\) 1.71173 0.0740740
\(535\) −14.4829 −0.626149
\(536\) −5.82549 −0.251623
\(537\) −34.7265 −1.49856
\(538\) 13.0813 0.563976
\(539\) 6.48937 0.279517
\(540\) 1.42917 0.0615016
\(541\) −7.29027 −0.313433 −0.156717 0.987644i \(-0.550091\pi\)
−0.156717 + 0.987644i \(0.550091\pi\)
\(542\) −9.28426 −0.398793
\(543\) −40.8974 −1.75508
\(544\) −1.26543 −0.0542550
\(545\) 8.34855 0.357613
\(546\) −4.11601 −0.176149
\(547\) 11.3262 0.484275 0.242138 0.970242i \(-0.422151\pi\)
0.242138 + 0.970242i \(0.422151\pi\)
\(548\) −9.81564 −0.419303
\(549\) −40.3734 −1.72310
\(550\) 3.67111 0.156537
\(551\) −4.08591 −0.174066
\(552\) 7.16714 0.305054
\(553\) 12.0074 0.510608
\(554\) −17.5260 −0.744608
\(555\) −4.57060 −0.194011
\(556\) 1.27239 0.0539613
\(557\) −19.2760 −0.816752 −0.408376 0.912814i \(-0.633905\pi\)
−0.408376 + 0.912814i \(0.633905\pi\)
\(558\) −17.6502 −0.747192
\(559\) 0.205571 0.00869473
\(560\) 2.50874 0.106014
\(561\) −4.36429 −0.184260
\(562\) −28.0768 −1.18435
\(563\) −22.3783 −0.943131 −0.471566 0.881831i \(-0.656311\pi\)
−0.471566 + 0.881831i \(0.656311\pi\)
\(564\) 7.68664 0.323666
\(565\) −9.55805 −0.402110
\(566\) −16.4120 −0.689848
\(567\) −15.9434 −0.669562
\(568\) 11.2978 0.474045
\(569\) 40.9996 1.71879 0.859397 0.511309i \(-0.170839\pi\)
0.859397 + 0.511309i \(0.170839\pi\)
\(570\) −7.55144 −0.316295
\(571\) 28.2362 1.18165 0.590824 0.806800i \(-0.298803\pi\)
0.590824 + 0.806800i \(0.298803\pi\)
\(572\) −1.58558 −0.0662963
\(573\) −43.5851 −1.82080
\(574\) 2.54692 0.106307
\(575\) 7.62902 0.318152
\(576\) 2.61687 0.109036
\(577\) −31.6393 −1.31716 −0.658581 0.752510i \(-0.728843\pi\)
−0.658581 + 0.752510i \(0.728843\pi\)
\(578\) −15.3987 −0.640501
\(579\) 15.4300 0.641247
\(580\) −3.17673 −0.131907
\(581\) −7.56006 −0.313644
\(582\) −17.3524 −0.719278
\(583\) 6.76959 0.280368
\(584\) −8.57257 −0.354736
\(585\) 4.48775 0.185546
\(586\) −9.15821 −0.378322
\(587\) −26.8560 −1.10846 −0.554232 0.832362i \(-0.686988\pi\)
−0.554232 + 0.832362i \(0.686988\pi\)
\(588\) 10.5687 0.435847
\(589\) −13.6541 −0.562607
\(590\) −4.15617 −0.171107
\(591\) −32.2088 −1.32489
\(592\) 1.22529 0.0503592
\(593\) −20.2072 −0.829810 −0.414905 0.909865i \(-0.636185\pi\)
−0.414905 + 0.909865i \(0.636185\pi\)
\(594\) −1.32137 −0.0542164
\(595\) −3.17465 −0.130148
\(596\) −16.1054 −0.659702
\(597\) 32.6684 1.33703
\(598\) −3.29503 −0.134744
\(599\) −36.4067 −1.48754 −0.743769 0.668437i \(-0.766964\pi\)
−0.743769 + 0.668437i \(0.766964\pi\)
\(600\) 5.97884 0.244085
\(601\) −20.0267 −0.816907 −0.408453 0.912779i \(-0.633932\pi\)
−0.408453 + 0.912779i \(0.633932\pi\)
\(602\) 0.300726 0.0122567
\(603\) −15.2445 −0.620805
\(604\) 9.18990 0.373932
\(605\) −13.9803 −0.568378
\(606\) −20.0717 −0.815357
\(607\) −7.65184 −0.310579 −0.155289 0.987869i \(-0.549631\pi\)
−0.155289 + 0.987869i \(0.549631\pi\)
\(608\) 2.02440 0.0821001
\(609\) 7.62447 0.308959
\(610\) −24.2829 −0.983187
\(611\) −3.53386 −0.142965
\(612\) −3.31147 −0.133858
\(613\) 22.0456 0.890414 0.445207 0.895428i \(-0.353130\pi\)
0.445207 + 0.895428i \(0.353130\pi\)
\(614\) 14.8303 0.598501
\(615\) −5.96048 −0.240350
\(616\) −2.31951 −0.0934557
\(617\) −38.3564 −1.54417 −0.772086 0.635518i \(-0.780786\pi\)
−0.772086 + 0.635518i \(0.780786\pi\)
\(618\) −30.0111 −1.20722
\(619\) −36.7028 −1.47521 −0.737606 0.675232i \(-0.764044\pi\)
−0.737606 + 0.675232i \(0.764044\pi\)
\(620\) −10.6158 −0.426343
\(621\) −2.74597 −0.110192
\(622\) 25.6635 1.02901
\(623\) −1.15122 −0.0461226
\(624\) −2.58230 −0.103375
\(625\) −6.02224 −0.240889
\(626\) 15.9469 0.637366
\(627\) 6.98184 0.278828
\(628\) −11.1585 −0.445271
\(629\) −1.55052 −0.0618235
\(630\) 6.56504 0.261558
\(631\) 17.5818 0.699919 0.349960 0.936765i \(-0.386195\pi\)
0.349960 + 0.936765i \(0.386195\pi\)
\(632\) 7.53323 0.299656
\(633\) 22.6062 0.898517
\(634\) −3.76227 −0.149419
\(635\) 21.6679 0.859863
\(636\) 11.0251 0.437174
\(637\) −4.85888 −0.192516
\(638\) 2.93711 0.116281
\(639\) 29.5648 1.16957
\(640\) 1.57394 0.0622153
\(641\) 23.2445 0.918101 0.459050 0.888410i \(-0.348190\pi\)
0.459050 + 0.888410i \(0.348190\pi\)
\(642\) 21.8079 0.860691
\(643\) −12.4072 −0.489291 −0.244645 0.969613i \(-0.578672\pi\)
−0.244645 + 0.969613i \(0.578672\pi\)
\(644\) −4.82023 −0.189944
\(645\) −0.703778 −0.0277112
\(646\) −2.56174 −0.100790
\(647\) 41.4121 1.62808 0.814039 0.580811i \(-0.197264\pi\)
0.814039 + 0.580811i \(0.197264\pi\)
\(648\) −10.0026 −0.392940
\(649\) 3.84268 0.150838
\(650\) −2.74872 −0.107814
\(651\) 25.4791 0.998603
\(652\) −6.20270 −0.242916
\(653\) 32.3478 1.26587 0.632933 0.774206i \(-0.281851\pi\)
0.632933 + 0.774206i \(0.281851\pi\)
\(654\) −12.5710 −0.491566
\(655\) −7.80380 −0.304920
\(656\) 1.59789 0.0623872
\(657\) −22.4333 −0.875206
\(658\) −5.16961 −0.201533
\(659\) 42.9015 1.67120 0.835602 0.549335i \(-0.185119\pi\)
0.835602 + 0.549335i \(0.185119\pi\)
\(660\) 5.42827 0.211295
\(661\) −23.9138 −0.930140 −0.465070 0.885274i \(-0.653971\pi\)
−0.465070 + 0.885274i \(0.653971\pi\)
\(662\) −15.4315 −0.599764
\(663\) 3.26773 0.126908
\(664\) −4.74304 −0.184066
\(665\) 5.07869 0.196943
\(666\) 3.20642 0.124246
\(667\) 6.10369 0.236336
\(668\) −23.0755 −0.892818
\(669\) −30.2720 −1.17038
\(670\) −9.16894 −0.354227
\(671\) 22.4513 0.866722
\(672\) −3.77760 −0.145724
\(673\) 38.1793 1.47170 0.735852 0.677142i \(-0.236782\pi\)
0.735852 + 0.677142i \(0.236782\pi\)
\(674\) −17.5762 −0.677011
\(675\) −2.29069 −0.0881687
\(676\) −11.8128 −0.454339
\(677\) −28.3519 −1.08965 −0.544825 0.838550i \(-0.683404\pi\)
−0.544825 + 0.838550i \(0.683404\pi\)
\(678\) 14.3923 0.552732
\(679\) 11.6703 0.447863
\(680\) −1.99171 −0.0763787
\(681\) −47.3629 −1.81495
\(682\) 9.81510 0.375840
\(683\) 40.9899 1.56844 0.784218 0.620485i \(-0.213064\pi\)
0.784218 + 0.620485i \(0.213064\pi\)
\(684\) 5.29758 0.202558
\(685\) −15.4492 −0.590283
\(686\) −18.2655 −0.697378
\(687\) 27.5186 1.04990
\(688\) 0.188669 0.00719295
\(689\) −5.06869 −0.193102
\(690\) 11.2806 0.429446
\(691\) 9.83019 0.373958 0.186979 0.982364i \(-0.440130\pi\)
0.186979 + 0.982364i \(0.440130\pi\)
\(692\) −2.50660 −0.0952866
\(693\) −6.06985 −0.230574
\(694\) −3.30225 −0.125352
\(695\) 2.00266 0.0759652
\(696\) 4.78344 0.181316
\(697\) −2.02202 −0.0765896
\(698\) −3.24409 −0.122791
\(699\) −57.5488 −2.17669
\(700\) −4.02104 −0.151981
\(701\) 51.0308 1.92741 0.963704 0.266973i \(-0.0860236\pi\)
0.963704 + 0.266973i \(0.0860236\pi\)
\(702\) 0.989366 0.0373412
\(703\) 2.48047 0.0935529
\(704\) −1.45522 −0.0548455
\(705\) 12.0983 0.455647
\(706\) −6.94052 −0.261210
\(707\) 13.4991 0.507687
\(708\) 6.25826 0.235200
\(709\) 24.2127 0.909326 0.454663 0.890663i \(-0.349760\pi\)
0.454663 + 0.890663i \(0.349760\pi\)
\(710\) 17.7820 0.667346
\(711\) 19.7135 0.739312
\(712\) −0.722253 −0.0270676
\(713\) 20.3970 0.763873
\(714\) 4.78030 0.178898
\(715\) −2.49560 −0.0933301
\(716\) 14.6526 0.547593
\(717\) 46.6230 1.74117
\(718\) −25.3192 −0.944904
\(719\) 7.56756 0.282222 0.141111 0.989994i \(-0.454933\pi\)
0.141111 + 0.989994i \(0.454933\pi\)
\(720\) 4.11878 0.153498
\(721\) 20.1838 0.751685
\(722\) −14.9018 −0.554588
\(723\) −20.9769 −0.780139
\(724\) 17.2563 0.641327
\(725\) 5.09171 0.189101
\(726\) 21.0511 0.781280
\(727\) −18.4701 −0.685019 −0.342509 0.939514i \(-0.611277\pi\)
−0.342509 + 0.939514i \(0.611277\pi\)
\(728\) 1.73672 0.0643670
\(729\) −19.7195 −0.730351
\(730\) −13.4927 −0.499387
\(731\) −0.238749 −0.00883044
\(732\) 36.5646 1.35147
\(733\) −29.2011 −1.07857 −0.539284 0.842124i \(-0.681305\pi\)
−0.539284 + 0.842124i \(0.681305\pi\)
\(734\) −29.5013 −1.08891
\(735\) 16.6345 0.613573
\(736\) −3.02412 −0.111470
\(737\) 8.47734 0.312267
\(738\) 4.18147 0.153922
\(739\) 5.37525 0.197732 0.0988659 0.995101i \(-0.468479\pi\)
0.0988659 + 0.995101i \(0.468479\pi\)
\(740\) 1.92853 0.0708942
\(741\) −5.22761 −0.192041
\(742\) −7.41488 −0.272209
\(743\) −12.9288 −0.474312 −0.237156 0.971472i \(-0.576215\pi\)
−0.237156 + 0.971472i \(0.576215\pi\)
\(744\) 15.9851 0.586041
\(745\) −25.3488 −0.928709
\(746\) −29.0522 −1.06368
\(747\) −12.4119 −0.454128
\(748\) 1.84148 0.0673311
\(749\) −14.6668 −0.535915
\(750\) 28.0614 1.02466
\(751\) −8.67100 −0.316409 −0.158205 0.987406i \(-0.550571\pi\)
−0.158205 + 0.987406i \(0.550571\pi\)
\(752\) −3.24332 −0.118272
\(753\) −2.34394 −0.0854180
\(754\) −2.19915 −0.0800882
\(755\) 14.4643 0.526410
\(756\) 1.44732 0.0526386
\(757\) 39.6710 1.44187 0.720933 0.693005i \(-0.243713\pi\)
0.720933 + 0.693005i \(0.243713\pi\)
\(758\) 3.19572 0.116074
\(759\) −10.4297 −0.378575
\(760\) 3.18627 0.115578
\(761\) 38.1915 1.38444 0.692220 0.721686i \(-0.256633\pi\)
0.692220 + 0.721686i \(0.256633\pi\)
\(762\) −32.6269 −1.18195
\(763\) 8.45460 0.306077
\(764\) 18.3904 0.665342
\(765\) −5.21205 −0.188442
\(766\) 5.19416 0.187673
\(767\) −2.87718 −0.103889
\(768\) −2.36999 −0.0855198
\(769\) −25.9183 −0.934637 −0.467318 0.884089i \(-0.654780\pi\)
−0.467318 + 0.884089i \(0.654780\pi\)
\(770\) −3.65076 −0.131564
\(771\) −35.5497 −1.28029
\(772\) −6.51055 −0.234320
\(773\) −15.6243 −0.561966 −0.280983 0.959713i \(-0.590660\pi\)
−0.280983 + 0.959713i \(0.590660\pi\)
\(774\) 0.493723 0.0177465
\(775\) 17.0152 0.611204
\(776\) 7.32169 0.262833
\(777\) −4.62866 −0.166052
\(778\) 37.6167 1.34862
\(779\) 3.23476 0.115897
\(780\) −4.06438 −0.145528
\(781\) −16.4407 −0.588295
\(782\) 3.82682 0.136847
\(783\) −1.83269 −0.0654952
\(784\) −4.45939 −0.159264
\(785\) −17.5627 −0.626840
\(786\) 11.7508 0.419136
\(787\) 36.3232 1.29478 0.647392 0.762157i \(-0.275860\pi\)
0.647392 + 0.762157i \(0.275860\pi\)
\(788\) 13.5903 0.484133
\(789\) −43.5732 −1.55125
\(790\) 11.8568 0.421847
\(791\) −9.67946 −0.344162
\(792\) −3.80810 −0.135315
\(793\) −16.8103 −0.596950
\(794\) −27.9068 −0.990376
\(795\) 17.3528 0.615441
\(796\) −13.7842 −0.488568
\(797\) 11.7487 0.416160 0.208080 0.978112i \(-0.433279\pi\)
0.208080 + 0.978112i \(0.433279\pi\)
\(798\) −7.64736 −0.270714
\(799\) 4.10420 0.145196
\(800\) −2.52272 −0.0891918
\(801\) −1.89004 −0.0667812
\(802\) 17.7271 0.625965
\(803\) 12.4749 0.440231
\(804\) 13.8064 0.486913
\(805\) −7.58673 −0.267397
\(806\) −7.34899 −0.258857
\(807\) −31.0026 −1.09134
\(808\) 8.46910 0.297942
\(809\) −32.4310 −1.14021 −0.570106 0.821571i \(-0.693098\pi\)
−0.570106 + 0.821571i \(0.693098\pi\)
\(810\) −15.7435 −0.553169
\(811\) −14.5762 −0.511840 −0.255920 0.966698i \(-0.582378\pi\)
−0.255920 + 0.966698i \(0.582378\pi\)
\(812\) −3.21709 −0.112898
\(813\) 22.0036 0.771701
\(814\) −1.78306 −0.0624963
\(815\) −9.76265 −0.341971
\(816\) 2.99907 0.104988
\(817\) 0.381942 0.0133624
\(818\) −9.57326 −0.334721
\(819\) 4.54476 0.158807
\(820\) 2.51498 0.0878268
\(821\) 1.87768 0.0655314 0.0327657 0.999463i \(-0.489568\pi\)
0.0327657 + 0.999463i \(0.489568\pi\)
\(822\) 23.2630 0.811390
\(823\) 21.5499 0.751182 0.375591 0.926785i \(-0.377440\pi\)
0.375591 + 0.926785i \(0.377440\pi\)
\(824\) 12.6629 0.441134
\(825\) −8.70050 −0.302913
\(826\) −4.20897 −0.146449
\(827\) −19.2726 −0.670175 −0.335088 0.942187i \(-0.608766\pi\)
−0.335088 + 0.942187i \(0.608766\pi\)
\(828\) −7.91371 −0.275021
\(829\) −23.9777 −0.832778 −0.416389 0.909186i \(-0.636705\pi\)
−0.416389 + 0.909186i \(0.636705\pi\)
\(830\) −7.46524 −0.259122
\(831\) 41.5365 1.44089
\(832\) 1.08958 0.0377745
\(833\) 5.64306 0.195521
\(834\) −3.01555 −0.104420
\(835\) −36.3194 −1.25688
\(836\) −2.94593 −0.101887
\(837\) −6.12441 −0.211690
\(838\) −15.7393 −0.543706
\(839\) 6.37702 0.220159 0.110080 0.993923i \(-0.464889\pi\)
0.110080 + 0.993923i \(0.464889\pi\)
\(840\) −5.94570 −0.205146
\(841\) −24.9263 −0.859528
\(842\) −34.8963 −1.20261
\(843\) 66.5418 2.29182
\(844\) −9.53853 −0.328330
\(845\) −18.5926 −0.639605
\(846\) −8.48733 −0.291800
\(847\) −14.1578 −0.486469
\(848\) −4.65195 −0.159749
\(849\) 38.8964 1.33492
\(850\) 3.19234 0.109496
\(851\) −3.70542 −0.127020
\(852\) −26.7757 −0.917319
\(853\) 18.7988 0.643659 0.321829 0.946798i \(-0.395702\pi\)
0.321829 + 0.946798i \(0.395702\pi\)
\(854\) −24.5914 −0.841499
\(855\) 8.33805 0.285155
\(856\) −9.20169 −0.314507
\(857\) −1.74194 −0.0595035 −0.0297518 0.999557i \(-0.509472\pi\)
−0.0297518 + 0.999557i \(0.509472\pi\)
\(858\) 3.75781 0.128289
\(859\) 47.8082 1.63120 0.815598 0.578619i \(-0.196408\pi\)
0.815598 + 0.578619i \(0.196408\pi\)
\(860\) 0.296954 0.0101260
\(861\) −6.03619 −0.205713
\(862\) −32.7475 −1.11539
\(863\) −4.25556 −0.144861 −0.0724305 0.997373i \(-0.523076\pi\)
−0.0724305 + 0.997373i \(0.523076\pi\)
\(864\) 0.908022 0.0308915
\(865\) −3.94523 −0.134142
\(866\) 36.1285 1.22770
\(867\) 36.4948 1.23943
\(868\) −10.7507 −0.364902
\(869\) −10.9625 −0.371876
\(870\) 7.52884 0.255251
\(871\) −6.34735 −0.215072
\(872\) 5.30425 0.179625
\(873\) 19.1599 0.648464
\(874\) −6.12201 −0.207080
\(875\) −18.8726 −0.638010
\(876\) 20.3169 0.686446
\(877\) 20.0559 0.677240 0.338620 0.940923i \(-0.390040\pi\)
0.338620 + 0.940923i \(0.390040\pi\)
\(878\) −1.93567 −0.0653258
\(879\) 21.7049 0.732088
\(880\) −2.29042 −0.0772099
\(881\) 28.4515 0.958555 0.479278 0.877663i \(-0.340899\pi\)
0.479278 + 0.877663i \(0.340899\pi\)
\(882\) −11.6696 −0.392937
\(883\) 35.8629 1.20688 0.603441 0.797408i \(-0.293796\pi\)
0.603441 + 0.797408i \(0.293796\pi\)
\(884\) −1.37879 −0.0463739
\(885\) 9.85010 0.331108
\(886\) 11.9595 0.401787
\(887\) 33.4678 1.12374 0.561869 0.827226i \(-0.310082\pi\)
0.561869 + 0.827226i \(0.310082\pi\)
\(888\) −2.90393 −0.0974496
\(889\) 21.9431 0.735948
\(890\) −1.13678 −0.0381049
\(891\) 14.5559 0.487643
\(892\) 12.7731 0.427673
\(893\) −6.56576 −0.219715
\(894\) 38.1696 1.27658
\(895\) 23.0622 0.770885
\(896\) 1.59393 0.0532494
\(897\) 7.80919 0.260741
\(898\) −26.6005 −0.887670
\(899\) 13.6132 0.454027
\(900\) −6.60164 −0.220055
\(901\) 5.88674 0.196116
\(902\) −2.32527 −0.0774232
\(903\) −0.712718 −0.0237178
\(904\) −6.07270 −0.201975
\(905\) 27.1604 0.902842
\(906\) −21.7800 −0.723592
\(907\) 20.4980 0.680623 0.340312 0.940313i \(-0.389467\pi\)
0.340312 + 0.940313i \(0.389467\pi\)
\(908\) 19.9844 0.663206
\(909\) 22.1625 0.735084
\(910\) 2.73348 0.0906141
\(911\) 47.6928 1.58013 0.790067 0.613021i \(-0.210046\pi\)
0.790067 + 0.613021i \(0.210046\pi\)
\(912\) −4.79781 −0.158871
\(913\) 6.90214 0.228427
\(914\) 4.75305 0.157217
\(915\) 57.5504 1.90256
\(916\) −11.6113 −0.383647
\(917\) −7.90292 −0.260978
\(918\) −1.14904 −0.0379240
\(919\) −15.1264 −0.498975 −0.249487 0.968378i \(-0.580262\pi\)
−0.249487 + 0.968378i \(0.580262\pi\)
\(920\) −4.75977 −0.156925
\(921\) −35.1477 −1.15815
\(922\) −4.08028 −0.134377
\(923\) 12.3099 0.405184
\(924\) 5.49722 0.180845
\(925\) −3.09107 −0.101634
\(926\) 4.31122 0.141675
\(927\) 33.1372 1.08837
\(928\) −2.01834 −0.0662552
\(929\) −6.35714 −0.208571 −0.104285 0.994547i \(-0.533256\pi\)
−0.104285 + 0.994547i \(0.533256\pi\)
\(930\) 25.1595 0.825012
\(931\) −9.02758 −0.295867
\(932\) 24.2822 0.795392
\(933\) −60.8224 −1.99124
\(934\) −32.5024 −1.06351
\(935\) 2.89837 0.0947868
\(936\) 2.85129 0.0931975
\(937\) −32.8472 −1.07307 −0.536536 0.843877i \(-0.680267\pi\)
−0.536536 + 0.843877i \(0.680267\pi\)
\(938\) −9.28541 −0.303179
\(939\) −37.7940 −1.23336
\(940\) −5.10477 −0.166499
\(941\) 41.6656 1.35826 0.679130 0.734018i \(-0.262357\pi\)
0.679130 + 0.734018i \(0.262357\pi\)
\(942\) 26.4455 0.861641
\(943\) −4.83221 −0.157358
\(944\) −2.64062 −0.0859450
\(945\) 2.27799 0.0741031
\(946\) −0.274555 −0.00892654
\(947\) 48.8264 1.58665 0.793323 0.608801i \(-0.208349\pi\)
0.793323 + 0.608801i \(0.208349\pi\)
\(948\) −17.8537 −0.579861
\(949\) −9.34053 −0.303206
\(950\) −5.10700 −0.165693
\(951\) 8.91655 0.289139
\(952\) −2.01701 −0.0653717
\(953\) −36.6982 −1.18877 −0.594386 0.804180i \(-0.702605\pi\)
−0.594386 + 0.804180i \(0.702605\pi\)
\(954\) −12.1735 −0.394133
\(955\) 28.9453 0.936649
\(956\) −19.6722 −0.636245
\(957\) −6.96094 −0.225015
\(958\) 11.7102 0.378341
\(959\) −15.6454 −0.505217
\(960\) −3.73022 −0.120392
\(961\) 14.4920 0.467484
\(962\) 1.33506 0.0430439
\(963\) −24.0796 −0.775954
\(964\) 8.85103 0.285072
\(965\) −10.2472 −0.329869
\(966\) 11.4239 0.367558
\(967\) 24.8447 0.798952 0.399476 0.916744i \(-0.369192\pi\)
0.399476 + 0.916744i \(0.369192\pi\)
\(968\) −8.88235 −0.285489
\(969\) 6.07130 0.195038
\(970\) 11.5239 0.370009
\(971\) 47.3468 1.51943 0.759715 0.650256i \(-0.225339\pi\)
0.759715 + 0.650256i \(0.225339\pi\)
\(972\) 20.9820 0.672999
\(973\) 2.02810 0.0650178
\(974\) −26.8841 −0.861423
\(975\) 6.51444 0.208629
\(976\) −15.4282 −0.493843
\(977\) −56.3957 −1.80426 −0.902129 0.431467i \(-0.857996\pi\)
−0.902129 + 0.431467i \(0.857996\pi\)
\(978\) 14.7004 0.470066
\(979\) 1.05103 0.0335912
\(980\) −7.01880 −0.224207
\(981\) 13.8805 0.443171
\(982\) −20.7525 −0.662237
\(983\) −11.0927 −0.353804 −0.176902 0.984228i \(-0.556608\pi\)
−0.176902 + 0.984228i \(0.556608\pi\)
\(984\) −3.78699 −0.120725
\(985\) 21.3902 0.681549
\(986\) 2.55407 0.0813382
\(987\) 12.2519 0.389984
\(988\) 2.20575 0.0701742
\(989\) −0.570559 −0.0181427
\(990\) −5.99371 −0.190493
\(991\) 24.1386 0.766787 0.383393 0.923585i \(-0.374755\pi\)
0.383393 + 0.923585i \(0.374755\pi\)
\(992\) −6.74478 −0.214147
\(993\) 36.5726 1.16060
\(994\) 18.0079 0.571175
\(995\) −21.6954 −0.687791
\(996\) 11.2410 0.356184
\(997\) 21.7831 0.689878 0.344939 0.938625i \(-0.387900\pi\)
0.344939 + 0.938625i \(0.387900\pi\)
\(998\) 15.4767 0.489905
\(999\) 1.11259 0.0352008
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 \(a_p\))