Properties

Label 8023.2.a.c.1.8
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70672 q^{2}\) \(-0.0191468 q^{3}\) \(+5.32634 q^{4}\) \(+0.870977 q^{5}\) \(+0.0518250 q^{6}\) \(-3.03945 q^{7}\) \(-9.00349 q^{8}\) \(-2.99963 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70672 q^{2}\) \(-0.0191468 q^{3}\) \(+5.32634 q^{4}\) \(+0.870977 q^{5}\) \(+0.0518250 q^{6}\) \(-3.03945 q^{7}\) \(-9.00349 q^{8}\) \(-2.99963 q^{9}\) \(-2.35749 q^{10}\) \(-3.59310 q^{11}\) \(-0.101982 q^{12}\) \(-5.77445 q^{13}\) \(+8.22694 q^{14}\) \(-0.0166764 q^{15}\) \(+13.7173 q^{16}\) \(-3.74142 q^{17}\) \(+8.11917 q^{18}\) \(+6.69279 q^{19}\) \(+4.63912 q^{20}\) \(+0.0581956 q^{21}\) \(+9.72554 q^{22}\) \(+5.05288 q^{23}\) \(+0.172388 q^{24}\) \(-4.24140 q^{25}\) \(+15.6298 q^{26}\) \(+0.114874 q^{27}\) \(-16.1891 q^{28}\) \(+5.40420 q^{29}\) \(+0.0451384 q^{30}\) \(+1.79712 q^{31}\) \(-19.1218 q^{32}\) \(+0.0687964 q^{33}\) \(+10.1270 q^{34}\) \(-2.64729 q^{35}\) \(-15.9771 q^{36}\) \(+5.63669 q^{37}\) \(-18.1155 q^{38}\) \(+0.110562 q^{39}\) \(-7.84183 q^{40}\) \(+2.08926 q^{41}\) \(-0.157519 q^{42}\) \(-3.83798 q^{43}\) \(-19.1381 q^{44}\) \(-2.61261 q^{45}\) \(-13.6767 q^{46}\) \(-2.15769 q^{47}\) \(-0.262641 q^{48}\) \(+2.23823 q^{49}\) \(+11.4803 q^{50}\) \(+0.0716362 q^{51}\) \(-30.7567 q^{52}\) \(+7.27647 q^{53}\) \(-0.310931 q^{54}\) \(-3.12951 q^{55}\) \(+27.3656 q^{56}\) \(-0.128145 q^{57}\) \(-14.6277 q^{58}\) \(+2.34252 q^{59}\) \(-0.0888242 q^{60}\) \(+4.67760 q^{61}\) \(-4.86431 q^{62}\) \(+9.11722 q^{63}\) \(+24.3229 q^{64}\) \(-5.02941 q^{65}\) \(-0.186213 q^{66}\) \(+10.3912 q^{67}\) \(-19.9281 q^{68}\) \(-0.0967464 q^{69}\) \(+7.16547 q^{70}\) \(-1.00000 q^{71}\) \(+27.0072 q^{72}\) \(+14.0439 q^{73}\) \(-15.2570 q^{74}\) \(+0.0812091 q^{75}\) \(+35.6481 q^{76}\) \(+10.9210 q^{77}\) \(-0.299261 q^{78}\) \(-1.41032 q^{79}\) \(+11.9474 q^{80}\) \(+8.99670 q^{81}\) \(-5.65506 q^{82}\) \(-13.1146 q^{83}\) \(+0.309970 q^{84}\) \(-3.25869 q^{85}\) \(+10.3883 q^{86}\) \(-0.103473 q^{87}\) \(+32.3505 q^{88}\) \(+10.5583 q^{89}\) \(+7.07161 q^{90}\) \(+17.5511 q^{91}\) \(+26.9134 q^{92}\) \(-0.0344091 q^{93}\) \(+5.84026 q^{94}\) \(+5.82926 q^{95}\) \(+0.366121 q^{96}\) \(+2.32124 q^{97}\) \(-6.05827 q^{98}\) \(+10.7780 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70672 −1.91394 −0.956971 0.290184i \(-0.906283\pi\)
−0.956971 + 0.290184i \(0.906283\pi\)
\(3\) −0.0191468 −0.0110544 −0.00552720 0.999985i \(-0.501759\pi\)
−0.00552720 + 0.999985i \(0.501759\pi\)
\(4\) 5.32634 2.66317
\(5\) 0.870977 0.389513 0.194756 0.980852i \(-0.437608\pi\)
0.194756 + 0.980852i \(0.437608\pi\)
\(6\) 0.0518250 0.0211575
\(7\) −3.03945 −1.14880 −0.574401 0.818574i \(-0.694765\pi\)
−0.574401 + 0.818574i \(0.694765\pi\)
\(8\) −9.00349 −3.18321
\(9\) −2.99963 −0.999878
\(10\) −2.35749 −0.745504
\(11\) −3.59310 −1.08336 −0.541681 0.840584i \(-0.682212\pi\)
−0.541681 + 0.840584i \(0.682212\pi\)
\(12\) −0.101982 −0.0294398
\(13\) −5.77445 −1.60154 −0.800772 0.598970i \(-0.795577\pi\)
−0.800772 + 0.598970i \(0.795577\pi\)
\(14\) 8.22694 2.19874
\(15\) −0.0166764 −0.00430583
\(16\) 13.7173 3.42931
\(17\) −3.74142 −0.907429 −0.453714 0.891147i \(-0.649901\pi\)
−0.453714 + 0.891147i \(0.649901\pi\)
\(18\) 8.11917 1.91371
\(19\) 6.69279 1.53543 0.767715 0.640791i \(-0.221394\pi\)
0.767715 + 0.640791i \(0.221394\pi\)
\(20\) 4.63912 1.03734
\(21\) 0.0581956 0.0126993
\(22\) 9.72554 2.07349
\(23\) 5.05288 1.05360 0.526799 0.849990i \(-0.323392\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(24\) 0.172388 0.0351885
\(25\) −4.24140 −0.848280
\(26\) 15.6298 3.06526
\(27\) 0.114874 0.0221074
\(28\) −16.1891 −3.05946
\(29\) 5.40420 1.00353 0.501767 0.865003i \(-0.332683\pi\)
0.501767 + 0.865003i \(0.332683\pi\)
\(30\) 0.0451384 0.00824110
\(31\) 1.79712 0.322773 0.161386 0.986891i \(-0.448403\pi\)
0.161386 + 0.986891i \(0.448403\pi\)
\(32\) −19.1218 −3.38029
\(33\) 0.0687964 0.0119759
\(34\) 10.1270 1.73677
\(35\) −2.64729 −0.447473
\(36\) −15.9771 −2.66285
\(37\) 5.63669 0.926666 0.463333 0.886184i \(-0.346653\pi\)
0.463333 + 0.886184i \(0.346653\pi\)
\(38\) −18.1155 −2.93872
\(39\) 0.110562 0.0177041
\(40\) −7.84183 −1.23990
\(41\) 2.08926 0.326288 0.163144 0.986602i \(-0.447836\pi\)
0.163144 + 0.986602i \(0.447836\pi\)
\(42\) −0.157519 −0.0243057
\(43\) −3.83798 −0.585286 −0.292643 0.956222i \(-0.594535\pi\)
−0.292643 + 0.956222i \(0.594535\pi\)
\(44\) −19.1381 −2.88518
\(45\) −2.61261 −0.389465
\(46\) −13.6767 −2.01653
\(47\) −2.15769 −0.314731 −0.157365 0.987540i \(-0.550300\pi\)
−0.157365 + 0.987540i \(0.550300\pi\)
\(48\) −0.262641 −0.0379090
\(49\) 2.23823 0.319747
\(50\) 11.4803 1.62356
\(51\) 0.0716362 0.0100311
\(52\) −30.7567 −4.26519
\(53\) 7.27647 0.999500 0.499750 0.866170i \(-0.333425\pi\)
0.499750 + 0.866170i \(0.333425\pi\)
\(54\) −0.310931 −0.0423123
\(55\) −3.12951 −0.421983
\(56\) 27.3656 3.65688
\(57\) −0.128145 −0.0169732
\(58\) −14.6277 −1.92071
\(59\) 2.34252 0.304971 0.152485 0.988306i \(-0.451272\pi\)
0.152485 + 0.988306i \(0.451272\pi\)
\(60\) −0.0888242 −0.0114672
\(61\) 4.67760 0.598905 0.299453 0.954111i \(-0.403196\pi\)
0.299453 + 0.954111i \(0.403196\pi\)
\(62\) −4.86431 −0.617769
\(63\) 9.11722 1.14866
\(64\) 24.3229 3.04037
\(65\) −5.02941 −0.623821
\(66\) −0.186213 −0.0229212
\(67\) 10.3912 1.26949 0.634744 0.772722i \(-0.281105\pi\)
0.634744 + 0.772722i \(0.281105\pi\)
\(68\) −19.9281 −2.41664
\(69\) −0.0967464 −0.0116469
\(70\) 7.16547 0.856437
\(71\) −1.00000 −0.118678
\(72\) 27.0072 3.18283
\(73\) 14.0439 1.64371 0.821857 0.569695i \(-0.192938\pi\)
0.821857 + 0.569695i \(0.192938\pi\)
\(74\) −15.2570 −1.77358
\(75\) 0.0812091 0.00937722
\(76\) 35.6481 4.08912
\(77\) 10.9210 1.24457
\(78\) −0.299261 −0.0338846
\(79\) −1.41032 −0.158674 −0.0793368 0.996848i \(-0.525280\pi\)
−0.0793368 + 0.996848i \(0.525280\pi\)
\(80\) 11.9474 1.33576
\(81\) 8.99670 0.999633
\(82\) −5.65506 −0.624496
\(83\) −13.1146 −1.43951 −0.719756 0.694227i \(-0.755746\pi\)
−0.719756 + 0.694227i \(0.755746\pi\)
\(84\) 0.309970 0.0338205
\(85\) −3.25869 −0.353455
\(86\) 10.3883 1.12020
\(87\) −0.103473 −0.0110935
\(88\) 32.3505 3.44857
\(89\) 10.5583 1.11918 0.559591 0.828769i \(-0.310958\pi\)
0.559591 + 0.828769i \(0.310958\pi\)
\(90\) 7.07161 0.745413
\(91\) 17.5511 1.83986
\(92\) 26.9134 2.80591
\(93\) −0.0344091 −0.00356806
\(94\) 5.84026 0.602376
\(95\) 5.82926 0.598069
\(96\) 0.366121 0.0373671
\(97\) 2.32124 0.235686 0.117843 0.993032i \(-0.462402\pi\)
0.117843 + 0.993032i \(0.462402\pi\)
\(98\) −6.05827 −0.611978
\(99\) 10.7780 1.08323
\(100\) −22.5912 −2.25912
\(101\) 9.13572 0.909038 0.454519 0.890737i \(-0.349811\pi\)
0.454519 + 0.890737i \(0.349811\pi\)
\(102\) −0.193899 −0.0191989
\(103\) −7.50397 −0.739388 −0.369694 0.929154i \(-0.620538\pi\)
−0.369694 + 0.929154i \(0.620538\pi\)
\(104\) 51.9902 5.09806
\(105\) 0.0506870 0.00494654
\(106\) −19.6954 −1.91299
\(107\) −1.76571 −0.170698 −0.0853489 0.996351i \(-0.527200\pi\)
−0.0853489 + 0.996351i \(0.527200\pi\)
\(108\) 0.611856 0.0588759
\(109\) 7.18422 0.688124 0.344062 0.938947i \(-0.388197\pi\)
0.344062 + 0.938947i \(0.388197\pi\)
\(110\) 8.47072 0.807651
\(111\) −0.107924 −0.0102437
\(112\) −41.6929 −3.93961
\(113\) −1.00000 −0.0940721
\(114\) 0.346854 0.0324858
\(115\) 4.40094 0.410390
\(116\) 28.7846 2.67258
\(117\) 17.3212 1.60135
\(118\) −6.34056 −0.583696
\(119\) 11.3719 1.04246
\(120\) 0.150146 0.0137064
\(121\) 1.91040 0.173673
\(122\) −12.6610 −1.14627
\(123\) −0.0400026 −0.00360692
\(124\) 9.57210 0.859600
\(125\) −8.04904 −0.719928
\(126\) −24.6778 −2.19847
\(127\) 1.86070 0.165111 0.0825554 0.996586i \(-0.473692\pi\)
0.0825554 + 0.996586i \(0.473692\pi\)
\(128\) −27.5918 −2.43879
\(129\) 0.0734849 0.00646998
\(130\) 13.6132 1.19396
\(131\) −15.5210 −1.35607 −0.678037 0.735028i \(-0.737169\pi\)
−0.678037 + 0.735028i \(0.737169\pi\)
\(132\) 0.366433 0.0318939
\(133\) −20.3424 −1.76391
\(134\) −28.1261 −2.42973
\(135\) 0.100052 0.00861113
\(136\) 33.6859 2.88854
\(137\) −21.4363 −1.83142 −0.915712 0.401836i \(-0.868372\pi\)
−0.915712 + 0.401836i \(0.868372\pi\)
\(138\) 0.261866 0.0222915
\(139\) 6.68471 0.566990 0.283495 0.958974i \(-0.408506\pi\)
0.283495 + 0.958974i \(0.408506\pi\)
\(140\) −14.1004 −1.19170
\(141\) 0.0413127 0.00347916
\(142\) 2.70672 0.227143
\(143\) 20.7482 1.73505
\(144\) −41.1467 −3.42890
\(145\) 4.70693 0.390889
\(146\) −38.0129 −3.14597
\(147\) −0.0428549 −0.00353461
\(148\) 30.0230 2.46787
\(149\) −15.0295 −1.23126 −0.615630 0.788035i \(-0.711099\pi\)
−0.615630 + 0.788035i \(0.711099\pi\)
\(150\) −0.219810 −0.0179474
\(151\) 21.4359 1.74443 0.872213 0.489126i \(-0.162684\pi\)
0.872213 + 0.489126i \(0.162684\pi\)
\(152\) −60.2584 −4.88760
\(153\) 11.2229 0.907318
\(154\) −29.5602 −2.38203
\(155\) 1.56525 0.125724
\(156\) 0.588891 0.0471490
\(157\) −24.1743 −1.92932 −0.964659 0.263500i \(-0.915123\pi\)
−0.964659 + 0.263500i \(0.915123\pi\)
\(158\) 3.81735 0.303692
\(159\) −0.139321 −0.0110489
\(160\) −16.6547 −1.31667
\(161\) −15.3580 −1.21038
\(162\) −24.3516 −1.91324
\(163\) 22.4650 1.75960 0.879799 0.475346i \(-0.157677\pi\)
0.879799 + 0.475346i \(0.157677\pi\)
\(164\) 11.1281 0.868962
\(165\) 0.0599200 0.00466477
\(166\) 35.4975 2.75514
\(167\) −22.1461 −1.71372 −0.856860 0.515550i \(-0.827588\pi\)
−0.856860 + 0.515550i \(0.827588\pi\)
\(168\) −0.523963 −0.0404246
\(169\) 20.3442 1.56494
\(170\) 8.82038 0.676492
\(171\) −20.0759 −1.53524
\(172\) −20.4424 −1.55872
\(173\) 17.4539 1.32699 0.663497 0.748179i \(-0.269071\pi\)
0.663497 + 0.748179i \(0.269071\pi\)
\(174\) 0.280072 0.0212322
\(175\) 12.8915 0.974506
\(176\) −49.2875 −3.71519
\(177\) −0.0448518 −0.00337126
\(178\) −28.5785 −2.14205
\(179\) 9.11157 0.681031 0.340515 0.940239i \(-0.389398\pi\)
0.340515 + 0.940239i \(0.389398\pi\)
\(180\) −13.9157 −1.03721
\(181\) −3.03403 −0.225518 −0.112759 0.993622i \(-0.535969\pi\)
−0.112759 + 0.993622i \(0.535969\pi\)
\(182\) −47.5060 −3.52138
\(183\) −0.0895609 −0.00662053
\(184\) −45.4936 −3.35383
\(185\) 4.90943 0.360948
\(186\) 0.0931359 0.00682906
\(187\) 13.4433 0.983074
\(188\) −11.4926 −0.838182
\(189\) −0.349152 −0.0253971
\(190\) −15.7782 −1.14467
\(191\) −9.51203 −0.688266 −0.344133 0.938921i \(-0.611827\pi\)
−0.344133 + 0.938921i \(0.611827\pi\)
\(192\) −0.465706 −0.0336094
\(193\) 9.10434 0.655345 0.327672 0.944791i \(-0.393736\pi\)
0.327672 + 0.944791i \(0.393736\pi\)
\(194\) −6.28294 −0.451089
\(195\) 0.0962969 0.00689597
\(196\) 11.9216 0.851542
\(197\) 9.99320 0.711986 0.355993 0.934489i \(-0.384143\pi\)
0.355993 + 0.934489i \(0.384143\pi\)
\(198\) −29.1730 −2.07324
\(199\) 10.7795 0.764136 0.382068 0.924134i \(-0.375212\pi\)
0.382068 + 0.924134i \(0.375212\pi\)
\(200\) 38.1874 2.70026
\(201\) −0.198958 −0.0140334
\(202\) −24.7278 −1.73985
\(203\) −16.4258 −1.15286
\(204\) 0.381559 0.0267145
\(205\) 1.81970 0.127093
\(206\) 20.3112 1.41515
\(207\) −15.1568 −1.05347
\(208\) −79.2096 −5.49219
\(209\) −24.0479 −1.66343
\(210\) −0.137196 −0.00946740
\(211\) −17.0183 −1.17159 −0.585795 0.810459i \(-0.699218\pi\)
−0.585795 + 0.810459i \(0.699218\pi\)
\(212\) 38.7570 2.66184
\(213\) 0.0191468 0.00131192
\(214\) 4.77929 0.326706
\(215\) −3.34279 −0.227976
\(216\) −1.03426 −0.0703727
\(217\) −5.46226 −0.370802
\(218\) −19.4457 −1.31703
\(219\) −0.268895 −0.0181703
\(220\) −16.6689 −1.12381
\(221\) 21.6047 1.45329
\(222\) 0.292121 0.0196059
\(223\) −10.1801 −0.681708 −0.340854 0.940116i \(-0.610716\pi\)
−0.340854 + 0.940116i \(0.610716\pi\)
\(224\) 58.1197 3.88329
\(225\) 12.7226 0.848176
\(226\) 2.70672 0.180048
\(227\) −3.70955 −0.246211 −0.123106 0.992394i \(-0.539285\pi\)
−0.123106 + 0.992394i \(0.539285\pi\)
\(228\) −0.682546 −0.0452027
\(229\) 2.73934 0.181020 0.0905102 0.995896i \(-0.471150\pi\)
0.0905102 + 0.995896i \(0.471150\pi\)
\(230\) −11.9121 −0.785462
\(231\) −0.209103 −0.0137580
\(232\) −48.6566 −3.19446
\(233\) −17.8643 −1.17033 −0.585165 0.810915i \(-0.698970\pi\)
−0.585165 + 0.810915i \(0.698970\pi\)
\(234\) −46.8837 −3.06489
\(235\) −1.87929 −0.122592
\(236\) 12.4771 0.812189
\(237\) 0.0270031 0.00175404
\(238\) −30.7805 −1.99520
\(239\) −13.1300 −0.849310 −0.424655 0.905355i \(-0.639605\pi\)
−0.424655 + 0.905355i \(0.639605\pi\)
\(240\) −0.228754 −0.0147660
\(241\) −7.96526 −0.513088 −0.256544 0.966533i \(-0.582584\pi\)
−0.256544 + 0.966533i \(0.582584\pi\)
\(242\) −5.17093 −0.332400
\(243\) −0.516879 −0.0331578
\(244\) 24.9145 1.59499
\(245\) 1.94945 0.124546
\(246\) 0.108276 0.00690343
\(247\) −38.6471 −2.45906
\(248\) −16.1804 −1.02746
\(249\) 0.251102 0.0159129
\(250\) 21.7865 1.37790
\(251\) −5.49554 −0.346875 −0.173438 0.984845i \(-0.555488\pi\)
−0.173438 + 0.984845i \(0.555488\pi\)
\(252\) 48.5615 3.05909
\(253\) −18.1555 −1.14143
\(254\) −5.03641 −0.316012
\(255\) 0.0623935 0.00390723
\(256\) 26.0375 1.62734
\(257\) −10.6605 −0.664983 −0.332491 0.943106i \(-0.607889\pi\)
−0.332491 + 0.943106i \(0.607889\pi\)
\(258\) −0.198903 −0.0123832
\(259\) −17.1324 −1.06456
\(260\) −26.7884 −1.66134
\(261\) −16.2106 −1.00341
\(262\) 42.0110 2.59545
\(263\) 15.3488 0.946445 0.473222 0.880943i \(-0.343091\pi\)
0.473222 + 0.880943i \(0.343091\pi\)
\(264\) −0.619407 −0.0381219
\(265\) 6.33764 0.389318
\(266\) 55.0611 3.37601
\(267\) −0.202158 −0.0123719
\(268\) 55.3472 3.38087
\(269\) −9.48596 −0.578369 −0.289185 0.957273i \(-0.593384\pi\)
−0.289185 + 0.957273i \(0.593384\pi\)
\(270\) −0.270814 −0.0164812
\(271\) −15.6593 −0.951234 −0.475617 0.879653i \(-0.657775\pi\)
−0.475617 + 0.879653i \(0.657775\pi\)
\(272\) −51.3221 −3.11186
\(273\) −0.336047 −0.0203385
\(274\) 58.0220 3.50524
\(275\) 15.2398 0.918994
\(276\) −0.515304 −0.0310177
\(277\) −26.7052 −1.60456 −0.802281 0.596946i \(-0.796381\pi\)
−0.802281 + 0.596946i \(0.796381\pi\)
\(278\) −18.0936 −1.08518
\(279\) −5.39071 −0.322733
\(280\) 23.8348 1.42440
\(281\) 1.82146 0.108659 0.0543297 0.998523i \(-0.482698\pi\)
0.0543297 + 0.998523i \(0.482698\pi\)
\(282\) −0.111822 −0.00665890
\(283\) −3.03336 −0.180314 −0.0901571 0.995928i \(-0.528737\pi\)
−0.0901571 + 0.995928i \(0.528737\pi\)
\(284\) −5.32634 −0.316060
\(285\) −0.111612 −0.00661130
\(286\) −56.1596 −3.32079
\(287\) −6.35020 −0.374841
\(288\) 57.3585 3.37988
\(289\) −3.00175 −0.176573
\(290\) −12.7403 −0.748139
\(291\) −0.0444442 −0.00260536
\(292\) 74.8026 4.37749
\(293\) −27.5871 −1.61166 −0.805828 0.592150i \(-0.798279\pi\)
−0.805828 + 0.592150i \(0.798279\pi\)
\(294\) 0.115996 0.00676504
\(295\) 2.04028 0.118790
\(296\) −50.7499 −2.94978
\(297\) −0.412753 −0.0239504
\(298\) 40.6806 2.35656
\(299\) −29.1776 −1.68738
\(300\) 0.432548 0.0249732
\(301\) 11.6653 0.672378
\(302\) −58.0209 −3.33873
\(303\) −0.174919 −0.0100489
\(304\) 91.8067 5.26547
\(305\) 4.07408 0.233281
\(306\) −30.3773 −1.73655
\(307\) −8.28799 −0.473021 −0.236510 0.971629i \(-0.576004\pi\)
−0.236510 + 0.971629i \(0.576004\pi\)
\(308\) 58.1693 3.31450
\(309\) 0.143677 0.00817349
\(310\) −4.23670 −0.240629
\(311\) 20.7945 1.17915 0.589575 0.807714i \(-0.299295\pi\)
0.589575 + 0.807714i \(0.299295\pi\)
\(312\) −0.995444 −0.0563559
\(313\) 1.21920 0.0689135 0.0344568 0.999406i \(-0.489030\pi\)
0.0344568 + 0.999406i \(0.489030\pi\)
\(314\) 65.4331 3.69260
\(315\) 7.94089 0.447418
\(316\) −7.51186 −0.422575
\(317\) −11.2070 −0.629450 −0.314725 0.949183i \(-0.601912\pi\)
−0.314725 + 0.949183i \(0.601912\pi\)
\(318\) 0.377103 0.0211469
\(319\) −19.4178 −1.08719
\(320\) 21.1847 1.18426
\(321\) 0.0338077 0.00188696
\(322\) 41.5697 2.31659
\(323\) −25.0405 −1.39329
\(324\) 47.9195 2.66220
\(325\) 24.4917 1.35856
\(326\) −60.8066 −3.36777
\(327\) −0.137555 −0.00760679
\(328\) −18.8107 −1.03865
\(329\) 6.55817 0.361564
\(330\) −0.162187 −0.00892809
\(331\) 33.6414 1.84910 0.924549 0.381064i \(-0.124442\pi\)
0.924549 + 0.381064i \(0.124442\pi\)
\(332\) −69.8528 −3.83367
\(333\) −16.9080 −0.926553
\(334\) 59.9434 3.27996
\(335\) 9.05050 0.494482
\(336\) 0.798284 0.0435499
\(337\) 26.0447 1.41874 0.709371 0.704835i \(-0.248979\pi\)
0.709371 + 0.704835i \(0.248979\pi\)
\(338\) −55.0662 −2.99520
\(339\) 0.0191468 0.00103991
\(340\) −17.3569 −0.941311
\(341\) −6.45725 −0.349680
\(342\) 54.3399 2.93836
\(343\) 14.4731 0.781476
\(344\) 34.5552 1.86309
\(345\) −0.0842638 −0.00453661
\(346\) −47.2428 −2.53979
\(347\) 12.9155 0.693342 0.346671 0.937987i \(-0.387312\pi\)
0.346671 + 0.937987i \(0.387312\pi\)
\(348\) −0.551132 −0.0295438
\(349\) −1.80159 −0.0964369 −0.0482184 0.998837i \(-0.515354\pi\)
−0.0482184 + 0.998837i \(0.515354\pi\)
\(350\) −34.8937 −1.86515
\(351\) −0.663331 −0.0354060
\(352\) 68.7067 3.66208
\(353\) 22.1581 1.17936 0.589679 0.807637i \(-0.299254\pi\)
0.589679 + 0.807637i \(0.299254\pi\)
\(354\) 0.121401 0.00645240
\(355\) −0.870977 −0.0462266
\(356\) 56.2374 2.98058
\(357\) −0.217734 −0.0115237
\(358\) −24.6625 −1.30345
\(359\) −19.8543 −1.04787 −0.523934 0.851759i \(-0.675536\pi\)
−0.523934 + 0.851759i \(0.675536\pi\)
\(360\) 23.5226 1.23975
\(361\) 25.7934 1.35755
\(362\) 8.21229 0.431628
\(363\) −0.0365780 −0.00191985
\(364\) 93.4833 4.89986
\(365\) 12.2319 0.640247
\(366\) 0.242416 0.0126713
\(367\) 6.45293 0.336840 0.168420 0.985715i \(-0.446133\pi\)
0.168420 + 0.985715i \(0.446133\pi\)
\(368\) 69.3117 3.61312
\(369\) −6.26702 −0.326248
\(370\) −13.2885 −0.690834
\(371\) −22.1164 −1.14823
\(372\) −0.183275 −0.00950236
\(373\) −6.53623 −0.338433 −0.169217 0.985579i \(-0.554124\pi\)
−0.169217 + 0.985579i \(0.554124\pi\)
\(374\) −36.3874 −1.88155
\(375\) 0.154113 0.00795837
\(376\) 19.4267 1.00186
\(377\) −31.2062 −1.60720
\(378\) 0.945058 0.0486085
\(379\) −14.6164 −0.750792 −0.375396 0.926865i \(-0.622493\pi\)
−0.375396 + 0.926865i \(0.622493\pi\)
\(380\) 31.0486 1.59276
\(381\) −0.0356265 −0.00182520
\(382\) 25.7464 1.31730
\(383\) −15.7867 −0.806665 −0.403332 0.915054i \(-0.632148\pi\)
−0.403332 + 0.915054i \(0.632148\pi\)
\(384\) 0.528294 0.0269594
\(385\) 9.51198 0.484775
\(386\) −24.6429 −1.25429
\(387\) 11.5125 0.585215
\(388\) 12.3637 0.627672
\(389\) 8.20744 0.416133 0.208067 0.978115i \(-0.433283\pi\)
0.208067 + 0.978115i \(0.433283\pi\)
\(390\) −0.260649 −0.0131985
\(391\) −18.9050 −0.956066
\(392\) −20.1519 −1.01782
\(393\) 0.297177 0.0149906
\(394\) −27.0488 −1.36270
\(395\) −1.22836 −0.0618053
\(396\) 57.4073 2.88483
\(397\) −8.43733 −0.423457 −0.211729 0.977328i \(-0.567909\pi\)
−0.211729 + 0.977328i \(0.567909\pi\)
\(398\) −29.1770 −1.46251
\(399\) 0.389490 0.0194989
\(400\) −58.1804 −2.90902
\(401\) −5.60049 −0.279675 −0.139838 0.990174i \(-0.544658\pi\)
−0.139838 + 0.990174i \(0.544658\pi\)
\(402\) 0.538524 0.0268592
\(403\) −10.3774 −0.516935
\(404\) 48.6600 2.42092
\(405\) 7.83592 0.389370
\(406\) 44.4600 2.20651
\(407\) −20.2532 −1.00391
\(408\) −0.644976 −0.0319311
\(409\) −14.2337 −0.703811 −0.351905 0.936036i \(-0.614466\pi\)
−0.351905 + 0.936036i \(0.614466\pi\)
\(410\) −4.92542 −0.243249
\(411\) 0.410435 0.0202453
\(412\) −39.9687 −1.96912
\(413\) −7.11997 −0.350351
\(414\) 41.0252 2.01628
\(415\) −11.4225 −0.560708
\(416\) 110.418 5.41368
\(417\) −0.127991 −0.00626773
\(418\) 65.0909 3.18370
\(419\) 2.75702 0.134689 0.0673447 0.997730i \(-0.478547\pi\)
0.0673447 + 0.997730i \(0.478547\pi\)
\(420\) 0.269976 0.0131735
\(421\) 28.2291 1.37580 0.687900 0.725805i \(-0.258533\pi\)
0.687900 + 0.725805i \(0.258533\pi\)
\(422\) 46.0639 2.24236
\(423\) 6.47227 0.314692
\(424\) −65.5136 −3.18162
\(425\) 15.8689 0.769753
\(426\) −0.0518250 −0.00251093
\(427\) −14.2173 −0.688024
\(428\) −9.40479 −0.454598
\(429\) −0.397261 −0.0191799
\(430\) 9.04800 0.436334
\(431\) −18.3722 −0.884959 −0.442480 0.896779i \(-0.645901\pi\)
−0.442480 + 0.896779i \(0.645901\pi\)
\(432\) 1.57575 0.0758133
\(433\) 25.1084 1.20663 0.603317 0.797501i \(-0.293845\pi\)
0.603317 + 0.797501i \(0.293845\pi\)
\(434\) 14.7848 0.709694
\(435\) −0.0901225 −0.00432104
\(436\) 38.2657 1.83259
\(437\) 33.8179 1.61773
\(438\) 0.727824 0.0347768
\(439\) 5.85340 0.279367 0.139684 0.990196i \(-0.455391\pi\)
0.139684 + 0.990196i \(0.455391\pi\)
\(440\) 28.1765 1.34326
\(441\) −6.71387 −0.319708
\(442\) −58.4778 −2.78150
\(443\) 1.64491 0.0781519 0.0390760 0.999236i \(-0.487559\pi\)
0.0390760 + 0.999236i \(0.487559\pi\)
\(444\) −0.574843 −0.0272808
\(445\) 9.19608 0.435936
\(446\) 27.5546 1.30475
\(447\) 0.287766 0.0136108
\(448\) −73.9283 −3.49278
\(449\) 12.3635 0.583471 0.291735 0.956499i \(-0.405767\pi\)
0.291735 + 0.956499i \(0.405767\pi\)
\(450\) −34.4367 −1.62336
\(451\) −7.50694 −0.353488
\(452\) −5.32634 −0.250530
\(453\) −0.410428 −0.0192836
\(454\) 10.0407 0.471234
\(455\) 15.2866 0.716647
\(456\) 1.15375 0.0540295
\(457\) −25.4522 −1.19060 −0.595302 0.803502i \(-0.702968\pi\)
−0.595302 + 0.803502i \(0.702968\pi\)
\(458\) −7.41462 −0.346462
\(459\) −0.429791 −0.0200609
\(460\) 23.4409 1.09294
\(461\) −39.1010 −1.82112 −0.910559 0.413380i \(-0.864348\pi\)
−0.910559 + 0.413380i \(0.864348\pi\)
\(462\) 0.565983 0.0263319
\(463\) 10.6904 0.496827 0.248414 0.968654i \(-0.420091\pi\)
0.248414 + 0.968654i \(0.420091\pi\)
\(464\) 74.1307 3.44143
\(465\) −0.0299695 −0.00138980
\(466\) 48.3537 2.23994
\(467\) −5.67525 −0.262619 −0.131310 0.991341i \(-0.541918\pi\)
−0.131310 + 0.991341i \(0.541918\pi\)
\(468\) 92.2588 4.26466
\(469\) −31.5835 −1.45839
\(470\) 5.08673 0.234633
\(471\) 0.462860 0.0213274
\(472\) −21.0909 −0.970787
\(473\) 13.7903 0.634077
\(474\) −0.0730899 −0.00335713
\(475\) −28.3868 −1.30247
\(476\) 60.5704 2.77624
\(477\) −21.8267 −0.999378
\(478\) 35.5393 1.62553
\(479\) −29.7070 −1.35735 −0.678674 0.734440i \(-0.737445\pi\)
−0.678674 + 0.734440i \(0.737445\pi\)
\(480\) 0.318883 0.0145550
\(481\) −32.5488 −1.48410
\(482\) 21.5598 0.982020
\(483\) 0.294055 0.0133800
\(484\) 10.1755 0.462521
\(485\) 2.02174 0.0918026
\(486\) 1.39905 0.0634620
\(487\) 3.48301 0.157830 0.0789151 0.996881i \(-0.474854\pi\)
0.0789151 + 0.996881i \(0.474854\pi\)
\(488\) −42.1147 −1.90644
\(489\) −0.430133 −0.0194513
\(490\) −5.27661 −0.238373
\(491\) −1.50232 −0.0677987 −0.0338993 0.999425i \(-0.510793\pi\)
−0.0338993 + 0.999425i \(0.510793\pi\)
\(492\) −0.213068 −0.00960584
\(493\) −20.2194 −0.910635
\(494\) 104.607 4.70649
\(495\) 9.38738 0.421932
\(496\) 24.6516 1.10689
\(497\) 3.03945 0.136338
\(498\) −0.679663 −0.0304564
\(499\) 7.63426 0.341756 0.170878 0.985292i \(-0.445340\pi\)
0.170878 + 0.985292i \(0.445340\pi\)
\(500\) −42.8720 −1.91729
\(501\) 0.424027 0.0189441
\(502\) 14.8749 0.663899
\(503\) −14.7350 −0.657003 −0.328502 0.944503i \(-0.606544\pi\)
−0.328502 + 0.944503i \(0.606544\pi\)
\(504\) −82.0868 −3.65644
\(505\) 7.95700 0.354082
\(506\) 49.1420 2.18463
\(507\) −0.389526 −0.0172995
\(508\) 9.91075 0.439719
\(509\) 22.9002 1.01503 0.507516 0.861642i \(-0.330564\pi\)
0.507516 + 0.861642i \(0.330564\pi\)
\(510\) −0.168882 −0.00747821
\(511\) −42.6856 −1.88830
\(512\) −15.2926 −0.675843
\(513\) 0.768824 0.0339444
\(514\) 28.8550 1.27274
\(515\) −6.53578 −0.288001
\(516\) 0.391406 0.0172307
\(517\) 7.75279 0.340967
\(518\) 46.3727 2.03750
\(519\) −0.334186 −0.0146691
\(520\) 45.2822 1.98576
\(521\) 18.5688 0.813514 0.406757 0.913536i \(-0.366660\pi\)
0.406757 + 0.913536i \(0.366660\pi\)
\(522\) 43.8776 1.92047
\(523\) 29.5702 1.29301 0.646507 0.762908i \(-0.276229\pi\)
0.646507 + 0.762908i \(0.276229\pi\)
\(524\) −82.6701 −3.61146
\(525\) −0.246831 −0.0107726
\(526\) −41.5448 −1.81144
\(527\) −6.72380 −0.292893
\(528\) 0.943697 0.0410692
\(529\) 2.53161 0.110070
\(530\) −17.1542 −0.745132
\(531\) −7.02671 −0.304933
\(532\) −108.350 −4.69759
\(533\) −12.0643 −0.522565
\(534\) 0.547186 0.0236791
\(535\) −1.53789 −0.0664889
\(536\) −93.5572 −4.04105
\(537\) −0.174457 −0.00752838
\(538\) 25.6759 1.10696
\(539\) −8.04220 −0.346402
\(540\) 0.532913 0.0229329
\(541\) 3.51792 0.151247 0.0756236 0.997136i \(-0.475905\pi\)
0.0756236 + 0.997136i \(0.475905\pi\)
\(542\) 42.3853 1.82061
\(543\) 0.0580919 0.00249296
\(544\) 71.5429 3.06737
\(545\) 6.25729 0.268033
\(546\) 0.909586 0.0389267
\(547\) −38.3009 −1.63763 −0.818814 0.574059i \(-0.805368\pi\)
−0.818814 + 0.574059i \(0.805368\pi\)
\(548\) −114.177 −4.87740
\(549\) −14.0311 −0.598832
\(550\) −41.2499 −1.75890
\(551\) 36.1691 1.54086
\(552\) 0.871055 0.0370746
\(553\) 4.28659 0.182285
\(554\) 72.2837 3.07104
\(555\) −0.0939996 −0.00399006
\(556\) 35.6051 1.50999
\(557\) 19.5749 0.829414 0.414707 0.909955i \(-0.363884\pi\)
0.414707 + 0.909955i \(0.363884\pi\)
\(558\) 14.5912 0.617693
\(559\) 22.1622 0.937361
\(560\) −36.3135 −1.53453
\(561\) −0.257396 −0.0108673
\(562\) −4.93019 −0.207968
\(563\) 10.0518 0.423634 0.211817 0.977309i \(-0.432062\pi\)
0.211817 + 0.977309i \(0.432062\pi\)
\(564\) 0.220046 0.00926560
\(565\) −0.870977 −0.0366423
\(566\) 8.21045 0.345111
\(567\) −27.3450 −1.14838
\(568\) 9.00349 0.377778
\(569\) 33.7209 1.41366 0.706828 0.707386i \(-0.250126\pi\)
0.706828 + 0.707386i \(0.250126\pi\)
\(570\) 0.302101 0.0126536
\(571\) 11.0748 0.463465 0.231732 0.972780i \(-0.425561\pi\)
0.231732 + 0.972780i \(0.425561\pi\)
\(572\) 110.512 4.62074
\(573\) 0.182125 0.00760837
\(574\) 17.1882 0.717423
\(575\) −21.4313 −0.893747
\(576\) −72.9599 −3.04000
\(577\) −16.8628 −0.702008 −0.351004 0.936374i \(-0.614160\pi\)
−0.351004 + 0.936374i \(0.614160\pi\)
\(578\) 8.12489 0.337951
\(579\) −0.174319 −0.00724444
\(580\) 25.0707 1.04101
\(581\) 39.8611 1.65372
\(582\) 0.120298 0.00498652
\(583\) −26.1451 −1.08282
\(584\) −126.444 −5.23229
\(585\) 15.0864 0.623745
\(586\) 74.6706 3.08461
\(587\) −25.7797 −1.06404 −0.532021 0.846731i \(-0.678567\pi\)
−0.532021 + 0.846731i \(0.678567\pi\)
\(588\) −0.228260 −0.00941328
\(589\) 12.0278 0.495595
\(590\) −5.52248 −0.227357
\(591\) −0.191337 −0.00787057
\(592\) 77.3199 3.17783
\(593\) 32.2514 1.32441 0.662203 0.749324i \(-0.269621\pi\)
0.662203 + 0.749324i \(0.269621\pi\)
\(594\) 1.11721 0.0458396
\(595\) 9.90462 0.406050
\(596\) −80.0521 −3.27906
\(597\) −0.206392 −0.00844706
\(598\) 78.9756 3.22955
\(599\) 17.2427 0.704519 0.352260 0.935902i \(-0.385413\pi\)
0.352260 + 0.935902i \(0.385413\pi\)
\(600\) −0.731165 −0.0298497
\(601\) 5.11099 0.208481 0.104241 0.994552i \(-0.466759\pi\)
0.104241 + 0.994552i \(0.466759\pi\)
\(602\) −31.5748 −1.28689
\(603\) −31.1698 −1.26933
\(604\) 114.175 4.64571
\(605\) 1.66392 0.0676478
\(606\) 0.473458 0.0192329
\(607\) 12.1784 0.494306 0.247153 0.968977i \(-0.420505\pi\)
0.247153 + 0.968977i \(0.420505\pi\)
\(608\) −127.978 −5.19020
\(609\) 0.314500 0.0127442
\(610\) −11.0274 −0.446486
\(611\) 12.4594 0.504055
\(612\) 59.7770 2.41634
\(613\) −46.0533 −1.86007 −0.930037 0.367467i \(-0.880225\pi\)
−0.930037 + 0.367467i \(0.880225\pi\)
\(614\) 22.4333 0.905334
\(615\) −0.0348414 −0.00140494
\(616\) −98.3275 −3.96173
\(617\) −29.9243 −1.20471 −0.602354 0.798229i \(-0.705770\pi\)
−0.602354 + 0.798229i \(0.705770\pi\)
\(618\) −0.388893 −0.0156436
\(619\) −13.5477 −0.544527 −0.272263 0.962223i \(-0.587772\pi\)
−0.272263 + 0.962223i \(0.587772\pi\)
\(620\) 8.33708 0.334825
\(621\) 0.580443 0.0232924
\(622\) −56.2850 −2.25682
\(623\) −32.0915 −1.28572
\(624\) 1.51661 0.0607129
\(625\) 14.1965 0.567859
\(626\) −3.30005 −0.131896
\(627\) 0.460439 0.0183882
\(628\) −128.761 −5.13811
\(629\) −21.0892 −0.840883
\(630\) −21.4938 −0.856333
\(631\) 25.5043 1.01531 0.507656 0.861560i \(-0.330512\pi\)
0.507656 + 0.861560i \(0.330512\pi\)
\(632\) 12.6978 0.505092
\(633\) 0.325846 0.0129512
\(634\) 30.3344 1.20473
\(635\) 1.62063 0.0643128
\(636\) −0.742071 −0.0294250
\(637\) −12.9245 −0.512089
\(638\) 52.5587 2.08082
\(639\) 2.99963 0.118664
\(640\) −24.0318 −0.949941
\(641\) 28.3366 1.11923 0.559615 0.828753i \(-0.310949\pi\)
0.559615 + 0.828753i \(0.310949\pi\)
\(642\) −0.0915080 −0.00361153
\(643\) 0.987473 0.0389421 0.0194711 0.999810i \(-0.493802\pi\)
0.0194711 + 0.999810i \(0.493802\pi\)
\(644\) −81.8018 −3.22344
\(645\) 0.0640036 0.00252014
\(646\) 67.7778 2.66668
\(647\) 6.72189 0.264265 0.132132 0.991232i \(-0.457818\pi\)
0.132132 + 0.991232i \(0.457818\pi\)
\(648\) −81.0017 −3.18205
\(649\) −8.41693 −0.330393
\(650\) −66.2923 −2.60020
\(651\) 0.104585 0.00409899
\(652\) 119.657 4.68611
\(653\) 10.3910 0.406630 0.203315 0.979113i \(-0.434828\pi\)
0.203315 + 0.979113i \(0.434828\pi\)
\(654\) 0.372322 0.0145590
\(655\) −13.5184 −0.528208
\(656\) 28.6590 1.11894
\(657\) −42.1265 −1.64351
\(658\) −17.7511 −0.692011
\(659\) −8.51494 −0.331695 −0.165847 0.986151i \(-0.553036\pi\)
−0.165847 + 0.986151i \(0.553036\pi\)
\(660\) 0.319155 0.0124231
\(661\) 10.9715 0.426743 0.213371 0.976971i \(-0.431556\pi\)
0.213371 + 0.976971i \(0.431556\pi\)
\(662\) −91.0579 −3.53906
\(663\) −0.413659 −0.0160652
\(664\) 118.077 4.58228
\(665\) −17.7177 −0.687064
\(666\) 45.7653 1.77337
\(667\) 27.3068 1.05732
\(668\) −117.958 −4.56393
\(669\) 0.194915 0.00753586
\(670\) −24.4972 −0.946409
\(671\) −16.8071 −0.648831
\(672\) −1.11281 −0.0429274
\(673\) 38.8310 1.49682 0.748412 0.663234i \(-0.230817\pi\)
0.748412 + 0.663234i \(0.230817\pi\)
\(674\) −70.4956 −2.71539
\(675\) −0.487225 −0.0187533
\(676\) 108.360 4.16771
\(677\) 16.0646 0.617411 0.308706 0.951158i \(-0.400104\pi\)
0.308706 + 0.951158i \(0.400104\pi\)
\(678\) −0.0518250 −0.00199033
\(679\) −7.05527 −0.270757
\(680\) 29.3396 1.12512
\(681\) 0.0710259 0.00272172
\(682\) 17.4780 0.669267
\(683\) −30.3031 −1.15952 −0.579758 0.814789i \(-0.696853\pi\)
−0.579758 + 0.814789i \(0.696853\pi\)
\(684\) −106.931 −4.08862
\(685\) −18.6705 −0.713362
\(686\) −39.1748 −1.49570
\(687\) −0.0524494 −0.00200107
\(688\) −52.6465 −2.00713
\(689\) −42.0176 −1.60074
\(690\) 0.228079 0.00868281
\(691\) −2.01000 −0.0764641 −0.0382320 0.999269i \(-0.512173\pi\)
−0.0382320 + 0.999269i \(0.512173\pi\)
\(692\) 92.9654 3.53401
\(693\) −32.7591 −1.24442
\(694\) −34.9588 −1.32702
\(695\) 5.82223 0.220850
\(696\) 0.931617 0.0353129
\(697\) −7.81682 −0.296083
\(698\) 4.87640 0.184575
\(699\) 0.342044 0.0129373
\(700\) 68.6646 2.59528
\(701\) −33.1146 −1.25072 −0.625360 0.780336i \(-0.715048\pi\)
−0.625360 + 0.780336i \(0.715048\pi\)
\(702\) 1.79545 0.0677650
\(703\) 37.7252 1.42283
\(704\) −87.3949 −3.29382
\(705\) 0.0359824 0.00135518
\(706\) −59.9759 −2.25722
\(707\) −27.7675 −1.04430
\(708\) −0.238896 −0.00897826
\(709\) −13.9956 −0.525614 −0.262807 0.964848i \(-0.584648\pi\)
−0.262807 + 0.964848i \(0.584648\pi\)
\(710\) 2.35749 0.0884751
\(711\) 4.23045 0.158654
\(712\) −95.0620 −3.56260
\(713\) 9.08065 0.340073
\(714\) 0.589346 0.0220557
\(715\) 18.0712 0.675824
\(716\) 48.5314 1.81370
\(717\) 0.251397 0.00938861
\(718\) 53.7400 2.00556
\(719\) 3.72624 0.138965 0.0694827 0.997583i \(-0.477865\pi\)
0.0694827 + 0.997583i \(0.477865\pi\)
\(720\) −35.8379 −1.33560
\(721\) 22.8079 0.849411
\(722\) −69.8155 −2.59826
\(723\) 0.152509 0.00567187
\(724\) −16.1603 −0.600593
\(725\) −22.9214 −0.851278
\(726\) 0.0990066 0.00367448
\(727\) 44.3658 1.64544 0.822718 0.568450i \(-0.192457\pi\)
0.822718 + 0.568450i \(0.192457\pi\)
\(728\) −158.021 −5.85666
\(729\) −26.9802 −0.999267
\(730\) −33.1084 −1.22540
\(731\) 14.3595 0.531106
\(732\) −0.477032 −0.0176316
\(733\) −14.6686 −0.541798 −0.270899 0.962608i \(-0.587321\pi\)
−0.270899 + 0.962608i \(0.587321\pi\)
\(734\) −17.4663 −0.644693
\(735\) −0.0373256 −0.00137678
\(736\) −96.6203 −3.56147
\(737\) −37.3367 −1.37532
\(738\) 16.9631 0.624420
\(739\) −35.7985 −1.31687 −0.658435 0.752638i \(-0.728781\pi\)
−0.658435 + 0.752638i \(0.728781\pi\)
\(740\) 26.1493 0.961267
\(741\) 0.739968 0.0271834
\(742\) 59.8631 2.19764
\(743\) −20.6388 −0.757166 −0.378583 0.925567i \(-0.623589\pi\)
−0.378583 + 0.925567i \(0.623589\pi\)
\(744\) 0.309802 0.0113579
\(745\) −13.0903 −0.479592
\(746\) 17.6918 0.647742
\(747\) 39.3389 1.43934
\(748\) 71.6038 2.61809
\(749\) 5.36678 0.196098
\(750\) −0.417142 −0.0152319
\(751\) 50.0216 1.82531 0.912657 0.408727i \(-0.134027\pi\)
0.912657 + 0.408727i \(0.134027\pi\)
\(752\) −29.5975 −1.07931
\(753\) 0.105222 0.00383450
\(754\) 84.4666 3.07609
\(755\) 18.6701 0.679476
\(756\) −1.85970 −0.0676368
\(757\) 40.8599 1.48508 0.742540 0.669802i \(-0.233621\pi\)
0.742540 + 0.669802i \(0.233621\pi\)
\(758\) 39.5624 1.43697
\(759\) 0.347620 0.0126178
\(760\) −52.4837 −1.90378
\(761\) −50.2049 −1.81993 −0.909963 0.414690i \(-0.863890\pi\)
−0.909963 + 0.414690i \(0.863890\pi\)
\(762\) 0.0964310 0.00349333
\(763\) −21.8361 −0.790518
\(764\) −50.6643 −1.83297
\(765\) 9.77489 0.353412
\(766\) 42.7303 1.54391
\(767\) −13.5268 −0.488423
\(768\) −0.498534 −0.0179893
\(769\) −19.5198 −0.703901 −0.351950 0.936019i \(-0.614481\pi\)
−0.351950 + 0.936019i \(0.614481\pi\)
\(770\) −25.7463 −0.927832
\(771\) 0.204114 0.00735098
\(772\) 48.4928 1.74530
\(773\) 5.00052 0.179856 0.0899281 0.995948i \(-0.471336\pi\)
0.0899281 + 0.995948i \(0.471336\pi\)
\(774\) −31.1612 −1.12007
\(775\) −7.62232 −0.273802
\(776\) −20.8992 −0.750239
\(777\) 0.328030 0.0117680
\(778\) −22.2152 −0.796455
\(779\) 13.9830 0.500993
\(780\) 0.512911 0.0183651
\(781\) 3.59310 0.128571
\(782\) 51.1705 1.82985
\(783\) 0.620799 0.0221856
\(784\) 30.7024 1.09651
\(785\) −21.0552 −0.751494
\(786\) −0.804374 −0.0286911
\(787\) 41.8463 1.49166 0.745830 0.666137i \(-0.232053\pi\)
0.745830 + 0.666137i \(0.232053\pi\)
\(788\) 53.2272 1.89614
\(789\) −0.293879 −0.0104624
\(790\) 3.32482 0.118292
\(791\) 3.03945 0.108070
\(792\) −97.0396 −3.44815
\(793\) −27.0105 −0.959172
\(794\) 22.8375 0.810472
\(795\) −0.121345 −0.00430367
\(796\) 57.4151 2.03502
\(797\) −21.0571 −0.745882 −0.372941 0.927855i \(-0.621651\pi\)
−0.372941 + 0.927855i \(0.621651\pi\)
\(798\) −1.05424 −0.0373198
\(799\) 8.07282 0.285596
\(800\) 81.1033 2.86743
\(801\) −31.6712 −1.11905
\(802\) 15.1590 0.535282
\(803\) −50.4612 −1.78074
\(804\) −1.05972 −0.0373734
\(805\) −13.3764 −0.471457
\(806\) 28.0887 0.989383
\(807\) 0.181625 0.00639352
\(808\) −82.2533 −2.89366
\(809\) 34.8418 1.22497 0.612487 0.790481i \(-0.290169\pi\)
0.612487 + 0.790481i \(0.290169\pi\)
\(810\) −21.2096 −0.745231
\(811\) −14.9088 −0.523520 −0.261760 0.965133i \(-0.584303\pi\)
−0.261760 + 0.965133i \(0.584303\pi\)
\(812\) −87.4893 −3.07027
\(813\) 0.299825 0.0105153
\(814\) 54.8198 1.92143
\(815\) 19.5665 0.685386
\(816\) 0.982652 0.0343997
\(817\) −25.6868 −0.898666
\(818\) 38.5266 1.34705
\(819\) −52.6469 −1.83963
\(820\) 9.69235 0.338471
\(821\) −14.5154 −0.506592 −0.253296 0.967389i \(-0.581515\pi\)
−0.253296 + 0.967389i \(0.581515\pi\)
\(822\) −1.11093 −0.0387483
\(823\) −25.5346 −0.890081 −0.445040 0.895510i \(-0.646811\pi\)
−0.445040 + 0.895510i \(0.646811\pi\)
\(824\) 67.5619 2.35363
\(825\) −0.291793 −0.0101589
\(826\) 19.2718 0.670551
\(827\) 25.1087 0.873115 0.436558 0.899676i \(-0.356197\pi\)
0.436558 + 0.899676i \(0.356197\pi\)
\(828\) −80.7303 −2.80557
\(829\) 14.9955 0.520814 0.260407 0.965499i \(-0.416143\pi\)
0.260407 + 0.965499i \(0.416143\pi\)
\(830\) 30.9175 1.07316
\(831\) 0.511319 0.0177375
\(832\) −140.452 −4.86928
\(833\) −8.37417 −0.290148
\(834\) 0.346435 0.0119961
\(835\) −19.2888 −0.667515
\(836\) −128.087 −4.42999
\(837\) 0.206442 0.00713568
\(838\) −7.46250 −0.257788
\(839\) −2.13871 −0.0738366 −0.0369183 0.999318i \(-0.511754\pi\)
−0.0369183 + 0.999318i \(0.511754\pi\)
\(840\) −0.456360 −0.0157459
\(841\) 0.205332 0.00708042
\(842\) −76.4083 −2.63320
\(843\) −0.0348751 −0.00120116
\(844\) −90.6455 −3.12015
\(845\) 17.7193 0.609564
\(846\) −17.5186 −0.602303
\(847\) −5.80656 −0.199516
\(848\) 99.8132 3.42760
\(849\) 0.0580790 0.00199326
\(850\) −42.9526 −1.47326
\(851\) 28.4815 0.976334
\(852\) 0.101982 0.00349386
\(853\) −3.08877 −0.105758 −0.0528788 0.998601i \(-0.516840\pi\)
−0.0528788 + 0.998601i \(0.516840\pi\)
\(854\) 38.4823 1.31684
\(855\) −17.4856 −0.597996
\(856\) 15.8976 0.543368
\(857\) −34.0894 −1.16447 −0.582236 0.813020i \(-0.697822\pi\)
−0.582236 + 0.813020i \(0.697822\pi\)
\(858\) 1.07527 0.0367093
\(859\) 36.6353 1.24998 0.624991 0.780632i \(-0.285103\pi\)
0.624991 + 0.780632i \(0.285103\pi\)
\(860\) −17.8049 −0.607140
\(861\) 0.121586 0.00414364
\(862\) 49.7285 1.69376
\(863\) −29.2272 −0.994905 −0.497452 0.867491i \(-0.665731\pi\)
−0.497452 + 0.867491i \(0.665731\pi\)
\(864\) −2.19659 −0.0747296
\(865\) 15.2019 0.516881
\(866\) −67.9615 −2.30943
\(867\) 0.0574737 0.00195191
\(868\) −29.0939 −0.987511
\(869\) 5.06743 0.171901
\(870\) 0.243937 0.00827022
\(871\) −60.0035 −2.03314
\(872\) −64.6831 −2.19045
\(873\) −6.96286 −0.235657
\(874\) −91.5355 −3.09624
\(875\) 24.4646 0.827056
\(876\) −1.43223 −0.0483905
\(877\) −20.0518 −0.677100 −0.338550 0.940948i \(-0.609936\pi\)
−0.338550 + 0.940948i \(0.609936\pi\)
\(878\) −15.8435 −0.534693
\(879\) 0.528204 0.0178159
\(880\) −42.9283 −1.44711
\(881\) 17.0122 0.573155 0.286578 0.958057i \(-0.407482\pi\)
0.286578 + 0.958057i \(0.407482\pi\)
\(882\) 18.1726 0.611903
\(883\) 40.1020 1.34954 0.674770 0.738028i \(-0.264243\pi\)
0.674770 + 0.738028i \(0.264243\pi\)
\(884\) 115.074 3.87035
\(885\) −0.0390648 −0.00131315
\(886\) −4.45231 −0.149578
\(887\) −49.1718 −1.65103 −0.825513 0.564383i \(-0.809114\pi\)
−0.825513 + 0.564383i \(0.809114\pi\)
\(888\) 0.971696 0.0326080
\(889\) −5.65551 −0.189680
\(890\) −24.8912 −0.834356
\(891\) −32.3261 −1.08296
\(892\) −54.2225 −1.81550
\(893\) −14.4409 −0.483247
\(894\) −0.778901 −0.0260504
\(895\) 7.93597 0.265270
\(896\) 83.8638 2.80169
\(897\) 0.558657 0.0186530
\(898\) −33.4646 −1.11673
\(899\) 9.71201 0.323914
\(900\) 67.7652 2.25884
\(901\) −27.2244 −0.906975
\(902\) 20.3192 0.676556
\(903\) −0.223353 −0.00743273
\(904\) 9.00349 0.299452
\(905\) −2.64257 −0.0878421
\(906\) 1.11091 0.0369076
\(907\) 47.3010 1.57060 0.785302 0.619113i \(-0.212508\pi\)
0.785302 + 0.619113i \(0.212508\pi\)
\(908\) −19.7583 −0.655703
\(909\) −27.4038 −0.908927
\(910\) −41.3766 −1.37162
\(911\) 9.15601 0.303352 0.151676 0.988430i \(-0.451533\pi\)
0.151676 + 0.988430i \(0.451533\pi\)
\(912\) −1.75780 −0.0582066
\(913\) 47.1221 1.55951
\(914\) 68.8921 2.27875
\(915\) −0.0780054 −0.00257878
\(916\) 14.5906 0.482088
\(917\) 47.1752 1.55786
\(918\) 1.16332 0.0383954
\(919\) 39.0468 1.28804 0.644018 0.765011i \(-0.277266\pi\)
0.644018 + 0.765011i \(0.277266\pi\)
\(920\) −39.6238 −1.30636
\(921\) 0.158688 0.00522896
\(922\) 105.836 3.48551
\(923\) 5.77445 0.190068
\(924\) −1.11375 −0.0366398
\(925\) −23.9075 −0.786072
\(926\) −28.9361 −0.950898
\(927\) 22.5092 0.739298
\(928\) −103.338 −3.39224
\(929\) 11.0530 0.362636 0.181318 0.983425i \(-0.441964\pi\)
0.181318 + 0.983425i \(0.441964\pi\)
\(930\) 0.0811192 0.00266000
\(931\) 14.9800 0.490950
\(932\) −95.1514 −3.11679
\(933\) −0.398148 −0.0130348
\(934\) 15.3613 0.502638
\(935\) 11.7088 0.382920
\(936\) −155.951 −5.09743
\(937\) −2.28724 −0.0747209 −0.0373605 0.999302i \(-0.511895\pi\)
−0.0373605 + 0.999302i \(0.511895\pi\)
\(938\) 85.4878 2.79128
\(939\) −0.0233438 −0.000761797 0
\(940\) −10.0098 −0.326483
\(941\) −39.7887 −1.29708 −0.648538 0.761183i \(-0.724619\pi\)
−0.648538 + 0.761183i \(0.724619\pi\)
\(942\) −1.25283 −0.0408195
\(943\) 10.5568 0.343777
\(944\) 32.1330 1.04584
\(945\) −0.304103 −0.00989248
\(946\) −37.3264 −1.21359
\(947\) 2.27351 0.0738792 0.0369396 0.999317i \(-0.488239\pi\)
0.0369396 + 0.999317i \(0.488239\pi\)
\(948\) 0.143828 0.00467131
\(949\) −81.0957 −2.63248
\(950\) 76.8351 2.49286
\(951\) 0.214579 0.00695819
\(952\) −102.386 −3.31836
\(953\) 41.8786 1.35658 0.678291 0.734794i \(-0.262721\pi\)
0.678291 + 0.734794i \(0.262721\pi\)
\(954\) 59.0789 1.91275
\(955\) −8.28476 −0.268088
\(956\) −69.9350 −2.26186
\(957\) 0.371789 0.0120182
\(958\) 80.4086 2.59788
\(959\) 65.1543 2.10394
\(960\) −0.405619 −0.0130913
\(961\) −27.7703 −0.895818
\(962\) 88.1005 2.84047
\(963\) 5.29649 0.170677
\(964\) −42.4257 −1.36644
\(965\) 7.92967 0.255265
\(966\) −0.795926 −0.0256085
\(967\) −8.74919 −0.281355 −0.140677 0.990055i \(-0.544928\pi\)
−0.140677 + 0.990055i \(0.544928\pi\)
\(968\) −17.2003 −0.552838
\(969\) 0.479446 0.0154020
\(970\) −5.47230 −0.175705
\(971\) −13.0245 −0.417975 −0.208987 0.977918i \(-0.567017\pi\)
−0.208987 + 0.977918i \(0.567017\pi\)
\(972\) −2.75307 −0.0883049
\(973\) −20.3178 −0.651359
\(974\) −9.42754 −0.302078
\(975\) −0.468938 −0.0150180
\(976\) 64.1638 2.05383
\(977\) −19.6210 −0.627732 −0.313866 0.949467i \(-0.601624\pi\)
−0.313866 + 0.949467i \(0.601624\pi\)
\(978\) 1.16425 0.0372286
\(979\) −37.9373 −1.21248
\(980\) 10.3834 0.331686
\(981\) −21.5500 −0.688040
\(982\) 4.06636 0.129763
\(983\) −24.0656 −0.767573 −0.383787 0.923422i \(-0.625380\pi\)
−0.383787 + 0.923422i \(0.625380\pi\)
\(984\) 0.360163 0.0114816
\(985\) 8.70384 0.277327
\(986\) 54.7283 1.74290
\(987\) −0.125568 −0.00399687
\(988\) −205.848 −6.54889
\(989\) −19.3929 −0.616657
\(990\) −25.4090 −0.807552
\(991\) −35.1652 −1.11706 −0.558529 0.829485i \(-0.688634\pi\)
−0.558529 + 0.829485i \(0.688634\pi\)
\(992\) −34.3643 −1.09107
\(993\) −0.644124 −0.0204406
\(994\) −8.22694 −0.260943
\(995\) 9.38866 0.297640
\(996\) 1.33746 0.0423789
\(997\) −52.0092 −1.64715 −0.823574 0.567209i \(-0.808023\pi\)
−0.823574 + 0.567209i \(0.808023\pi\)
\(998\) −20.6638 −0.654102
\(999\) 0.647507 0.0204862
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 \(a_p\))