Properties

Label 8015.2.a.l.1.14
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.76681 q^{2}\) \(+2.93332 q^{3}\) \(+1.12163 q^{4}\) \(-1.00000 q^{5}\) \(-5.18264 q^{6}\) \(-1.00000 q^{7}\) \(+1.55191 q^{8}\) \(+5.60439 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.76681 q^{2}\) \(+2.93332 q^{3}\) \(+1.12163 q^{4}\) \(-1.00000 q^{5}\) \(-5.18264 q^{6}\) \(-1.00000 q^{7}\) \(+1.55191 q^{8}\) \(+5.60439 q^{9}\) \(+1.76681 q^{10}\) \(+5.57251 q^{11}\) \(+3.29012 q^{12}\) \(+2.46065 q^{13}\) \(+1.76681 q^{14}\) \(-2.93332 q^{15}\) \(-4.98520 q^{16}\) \(+6.99936 q^{17}\) \(-9.90191 q^{18}\) \(-7.29290 q^{19}\) \(-1.12163 q^{20}\) \(-2.93332 q^{21}\) \(-9.84559 q^{22}\) \(+7.80740 q^{23}\) \(+4.55225 q^{24}\) \(+1.00000 q^{25}\) \(-4.34751 q^{26}\) \(+7.63951 q^{27}\) \(-1.12163 q^{28}\) \(-0.282924 q^{29}\) \(+5.18264 q^{30}\) \(+9.08665 q^{31}\) \(+5.70412 q^{32}\) \(+16.3460 q^{33}\) \(-12.3666 q^{34}\) \(+1.00000 q^{35}\) \(+6.28607 q^{36}\) \(+3.25443 q^{37}\) \(+12.8852 q^{38}\) \(+7.21787 q^{39}\) \(-1.55191 q^{40}\) \(+5.90197 q^{41}\) \(+5.18264 q^{42}\) \(-7.89879 q^{43}\) \(+6.25032 q^{44}\) \(-5.60439 q^{45}\) \(-13.7942 q^{46}\) \(+6.99295 q^{47}\) \(-14.6232 q^{48}\) \(+1.00000 q^{49}\) \(-1.76681 q^{50}\) \(+20.5314 q^{51}\) \(+2.75995 q^{52}\) \(-9.58756 q^{53}\) \(-13.4976 q^{54}\) \(-5.57251 q^{55}\) \(-1.55191 q^{56}\) \(-21.3924 q^{57}\) \(+0.499874 q^{58}\) \(-2.15310 q^{59}\) \(-3.29012 q^{60}\) \(+4.50495 q^{61}\) \(-16.0544 q^{62}\) \(-5.60439 q^{63}\) \(-0.107708 q^{64}\) \(-2.46065 q^{65}\) \(-28.8803 q^{66}\) \(-8.61501 q^{67}\) \(+7.85073 q^{68}\) \(+22.9016 q^{69}\) \(-1.76681 q^{70}\) \(+14.1801 q^{71}\) \(+8.69750 q^{72}\) \(-12.7551 q^{73}\) \(-5.74998 q^{74}\) \(+2.93332 q^{75}\) \(-8.17997 q^{76}\) \(-5.57251 q^{77}\) \(-12.7526 q^{78}\) \(-10.9668 q^{79}\) \(+4.98520 q^{80}\) \(+5.59598 q^{81}\) \(-10.4277 q^{82}\) \(-0.554755 q^{83}\) \(-3.29012 q^{84}\) \(-6.99936 q^{85}\) \(+13.9557 q^{86}\) \(-0.829907 q^{87}\) \(+8.64802 q^{88}\) \(+11.4222 q^{89}\) \(+9.90191 q^{90}\) \(-2.46065 q^{91}\) \(+8.75705 q^{92}\) \(+26.6541 q^{93}\) \(-12.3553 q^{94}\) \(+7.29290 q^{95}\) \(+16.7320 q^{96}\) \(+9.69786 q^{97}\) \(-1.76681 q^{98}\) \(+31.2305 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76681 −1.24933 −0.624663 0.780894i \(-0.714764\pi\)
−0.624663 + 0.780894i \(0.714764\pi\)
\(3\) 2.93332 1.69356 0.846778 0.531947i \(-0.178540\pi\)
0.846778 + 0.531947i \(0.178540\pi\)
\(4\) 1.12163 0.560817
\(5\) −1.00000 −0.447214
\(6\) −5.18264 −2.11580
\(7\) −1.00000 −0.377964
\(8\) 1.55191 0.548683
\(9\) 5.60439 1.86813
\(10\) 1.76681 0.558716
\(11\) 5.57251 1.68017 0.840087 0.542452i \(-0.182504\pi\)
0.840087 + 0.542452i \(0.182504\pi\)
\(12\) 3.29012 0.949775
\(13\) 2.46065 0.682461 0.341230 0.939980i \(-0.389156\pi\)
0.341230 + 0.939980i \(0.389156\pi\)
\(14\) 1.76681 0.472201
\(15\) −2.93332 −0.757381
\(16\) −4.98520 −1.24630
\(17\) 6.99936 1.69759 0.848797 0.528719i \(-0.177327\pi\)
0.848797 + 0.528719i \(0.177327\pi\)
\(18\) −9.90191 −2.33390
\(19\) −7.29290 −1.67311 −0.836553 0.547886i \(-0.815433\pi\)
−0.836553 + 0.547886i \(0.815433\pi\)
\(20\) −1.12163 −0.250805
\(21\) −2.93332 −0.640104
\(22\) −9.84559 −2.09909
\(23\) 7.80740 1.62795 0.813977 0.580896i \(-0.197298\pi\)
0.813977 + 0.580896i \(0.197298\pi\)
\(24\) 4.55225 0.929224
\(25\) 1.00000 0.200000
\(26\) −4.34751 −0.852616
\(27\) 7.63951 1.47022
\(28\) −1.12163 −0.211969
\(29\) −0.282924 −0.0525376 −0.0262688 0.999655i \(-0.508363\pi\)
−0.0262688 + 0.999655i \(0.508363\pi\)
\(30\) 5.18264 0.946216
\(31\) 9.08665 1.63201 0.816005 0.578044i \(-0.196184\pi\)
0.816005 + 0.578044i \(0.196184\pi\)
\(32\) 5.70412 1.00835
\(33\) 16.3460 2.84547
\(34\) −12.3666 −2.12085
\(35\) 1.00000 0.169031
\(36\) 6.28607 1.04768
\(37\) 3.25443 0.535026 0.267513 0.963554i \(-0.413798\pi\)
0.267513 + 0.963554i \(0.413798\pi\)
\(38\) 12.8852 2.09026
\(39\) 7.21787 1.15578
\(40\) −1.55191 −0.245378
\(41\) 5.90197 0.921733 0.460866 0.887470i \(-0.347539\pi\)
0.460866 + 0.887470i \(0.347539\pi\)
\(42\) 5.18264 0.799699
\(43\) −7.89879 −1.20455 −0.602277 0.798287i \(-0.705740\pi\)
−0.602277 + 0.798287i \(0.705740\pi\)
\(44\) 6.25032 0.942271
\(45\) −5.60439 −0.835453
\(46\) −13.7942 −2.03385
\(47\) 6.99295 1.02003 0.510014 0.860166i \(-0.329640\pi\)
0.510014 + 0.860166i \(0.329640\pi\)
\(48\) −14.6232 −2.11068
\(49\) 1.00000 0.142857
\(50\) −1.76681 −0.249865
\(51\) 20.5314 2.87497
\(52\) 2.75995 0.382736
\(53\) −9.58756 −1.31695 −0.658476 0.752602i \(-0.728799\pi\)
−0.658476 + 0.752602i \(0.728799\pi\)
\(54\) −13.4976 −1.83679
\(55\) −5.57251 −0.751397
\(56\) −1.55191 −0.207383
\(57\) −21.3924 −2.83350
\(58\) 0.499874 0.0656367
\(59\) −2.15310 −0.280310 −0.140155 0.990130i \(-0.544760\pi\)
−0.140155 + 0.990130i \(0.544760\pi\)
\(60\) −3.29012 −0.424752
\(61\) 4.50495 0.576800 0.288400 0.957510i \(-0.406877\pi\)
0.288400 + 0.957510i \(0.406877\pi\)
\(62\) −16.0544 −2.03891
\(63\) −5.60439 −0.706086
\(64\) −0.107708 −0.0134635
\(65\) −2.46065 −0.305206
\(66\) −28.8803 −3.55492
\(67\) −8.61501 −1.05249 −0.526245 0.850333i \(-0.676401\pi\)
−0.526245 + 0.850333i \(0.676401\pi\)
\(68\) 7.85073 0.952040
\(69\) 22.9016 2.75703
\(70\) −1.76681 −0.211175
\(71\) 14.1801 1.68287 0.841434 0.540359i \(-0.181712\pi\)
0.841434 + 0.540359i \(0.181712\pi\)
\(72\) 8.69750 1.02501
\(73\) −12.7551 −1.49287 −0.746436 0.665457i \(-0.768237\pi\)
−0.746436 + 0.665457i \(0.768237\pi\)
\(74\) −5.74998 −0.668422
\(75\) 2.93332 0.338711
\(76\) −8.17997 −0.938307
\(77\) −5.57251 −0.635046
\(78\) −12.7526 −1.44395
\(79\) −10.9668 −1.23386 −0.616930 0.787018i \(-0.711624\pi\)
−0.616930 + 0.787018i \(0.711624\pi\)
\(80\) 4.98520 0.557363
\(81\) 5.59598 0.621776
\(82\) −10.4277 −1.15155
\(83\) −0.554755 −0.0608922 −0.0304461 0.999536i \(-0.509693\pi\)
−0.0304461 + 0.999536i \(0.509693\pi\)
\(84\) −3.29012 −0.358981
\(85\) −6.99936 −0.759187
\(86\) 13.9557 1.50488
\(87\) −0.829907 −0.0889754
\(88\) 8.64802 0.921882
\(89\) 11.4222 1.21075 0.605374 0.795941i \(-0.293023\pi\)
0.605374 + 0.795941i \(0.293023\pi\)
\(90\) 9.90191 1.04375
\(91\) −2.46065 −0.257946
\(92\) 8.75705 0.912985
\(93\) 26.6541 2.76390
\(94\) −12.3553 −1.27435
\(95\) 7.29290 0.748236
\(96\) 16.7320 1.70770
\(97\) 9.69786 0.984668 0.492334 0.870406i \(-0.336144\pi\)
0.492334 + 0.870406i \(0.336144\pi\)
\(98\) −1.76681 −0.178475
\(99\) 31.2305 3.13878
\(100\) 1.12163 0.112163
\(101\) −3.30049 −0.328411 −0.164206 0.986426i \(-0.552506\pi\)
−0.164206 + 0.986426i \(0.552506\pi\)
\(102\) −36.2752 −3.59178
\(103\) −11.3910 −1.12239 −0.561193 0.827685i \(-0.689657\pi\)
−0.561193 + 0.827685i \(0.689657\pi\)
\(104\) 3.81870 0.374454
\(105\) 2.93332 0.286263
\(106\) 16.9394 1.64530
\(107\) 14.6507 1.41634 0.708168 0.706044i \(-0.249522\pi\)
0.708168 + 0.706044i \(0.249522\pi\)
\(108\) 8.56873 0.824527
\(109\) −6.01512 −0.576144 −0.288072 0.957609i \(-0.593014\pi\)
−0.288072 + 0.957609i \(0.593014\pi\)
\(110\) 9.84559 0.938740
\(111\) 9.54631 0.906096
\(112\) 4.98520 0.471058
\(113\) −10.9393 −1.02908 −0.514539 0.857467i \(-0.672037\pi\)
−0.514539 + 0.857467i \(0.672037\pi\)
\(114\) 37.7965 3.53996
\(115\) −7.80740 −0.728044
\(116\) −0.317337 −0.0294640
\(117\) 13.7904 1.27492
\(118\) 3.80413 0.350199
\(119\) −6.99936 −0.641630
\(120\) −4.55225 −0.415562
\(121\) 20.0528 1.82299
\(122\) −7.95942 −0.720612
\(123\) 17.3124 1.56101
\(124\) 10.1919 0.915260
\(125\) −1.00000 −0.0894427
\(126\) 9.90191 0.882132
\(127\) −0.0780272 −0.00692380 −0.00346190 0.999994i \(-0.501102\pi\)
−0.00346190 + 0.999994i \(0.501102\pi\)
\(128\) −11.2179 −0.991535
\(129\) −23.1697 −2.03998
\(130\) 4.34751 0.381302
\(131\) −11.7880 −1.02992 −0.514960 0.857214i \(-0.672193\pi\)
−0.514960 + 0.857214i \(0.672193\pi\)
\(132\) 18.3342 1.59579
\(133\) 7.29290 0.632375
\(134\) 15.2211 1.31490
\(135\) −7.63951 −0.657504
\(136\) 10.8624 0.931441
\(137\) 2.46593 0.210679 0.105339 0.994436i \(-0.466407\pi\)
0.105339 + 0.994436i \(0.466407\pi\)
\(138\) −40.4629 −3.44443
\(139\) 12.0994 1.02626 0.513129 0.858312i \(-0.328486\pi\)
0.513129 + 0.858312i \(0.328486\pi\)
\(140\) 1.12163 0.0947954
\(141\) 20.5126 1.72747
\(142\) −25.0536 −2.10245
\(143\) 13.7120 1.14665
\(144\) −27.9390 −2.32825
\(145\) 0.282924 0.0234955
\(146\) 22.5359 1.86509
\(147\) 2.93332 0.241936
\(148\) 3.65029 0.300052
\(149\) −2.35083 −0.192588 −0.0962938 0.995353i \(-0.530699\pi\)
−0.0962938 + 0.995353i \(0.530699\pi\)
\(150\) −5.18264 −0.423161
\(151\) −11.8960 −0.968086 −0.484043 0.875044i \(-0.660832\pi\)
−0.484043 + 0.875044i \(0.660832\pi\)
\(152\) −11.3179 −0.918004
\(153\) 39.2271 3.17132
\(154\) 9.84559 0.793380
\(155\) −9.08665 −0.729857
\(156\) 8.09582 0.648184
\(157\) −16.0234 −1.27880 −0.639402 0.768873i \(-0.720818\pi\)
−0.639402 + 0.768873i \(0.720818\pi\)
\(158\) 19.3763 1.54149
\(159\) −28.1234 −2.23033
\(160\) −5.70412 −0.450950
\(161\) −7.80740 −0.615309
\(162\) −9.88707 −0.776801
\(163\) 2.75757 0.215989 0.107995 0.994151i \(-0.465557\pi\)
0.107995 + 0.994151i \(0.465557\pi\)
\(164\) 6.61985 0.516924
\(165\) −16.3460 −1.27253
\(166\) 0.980149 0.0760743
\(167\) −22.0299 −1.70472 −0.852361 0.522953i \(-0.824830\pi\)
−0.852361 + 0.522953i \(0.824830\pi\)
\(168\) −4.55225 −0.351214
\(169\) −6.94522 −0.534248
\(170\) 12.3666 0.948473
\(171\) −40.8722 −3.12558
\(172\) −8.85955 −0.675535
\(173\) 23.7596 1.80641 0.903206 0.429207i \(-0.141207\pi\)
0.903206 + 0.429207i \(0.141207\pi\)
\(174\) 1.46629 0.111159
\(175\) −1.00000 −0.0755929
\(176\) −27.7801 −2.09400
\(177\) −6.31574 −0.474720
\(178\) −20.1809 −1.51262
\(179\) 11.5524 0.863467 0.431734 0.902001i \(-0.357902\pi\)
0.431734 + 0.902001i \(0.357902\pi\)
\(180\) −6.28607 −0.468536
\(181\) −25.8028 −1.91791 −0.958953 0.283565i \(-0.908483\pi\)
−0.958953 + 0.283565i \(0.908483\pi\)
\(182\) 4.34751 0.322259
\(183\) 13.2145 0.976843
\(184\) 12.1164 0.893231
\(185\) −3.25443 −0.239271
\(186\) −47.0928 −3.45301
\(187\) 39.0040 2.85225
\(188\) 7.84354 0.572049
\(189\) −7.63951 −0.555692
\(190\) −12.8852 −0.934791
\(191\) 27.0255 1.95549 0.977747 0.209786i \(-0.0672768\pi\)
0.977747 + 0.209786i \(0.0672768\pi\)
\(192\) −0.315942 −0.0228012
\(193\) −8.88805 −0.639776 −0.319888 0.947455i \(-0.603645\pi\)
−0.319888 + 0.947455i \(0.603645\pi\)
\(194\) −17.1343 −1.23017
\(195\) −7.21787 −0.516883
\(196\) 1.12163 0.0801168
\(197\) −18.1670 −1.29435 −0.647173 0.762343i \(-0.724049\pi\)
−0.647173 + 0.762343i \(0.724049\pi\)
\(198\) −55.1785 −3.92136
\(199\) −20.1135 −1.42581 −0.712904 0.701262i \(-0.752620\pi\)
−0.712904 + 0.701262i \(0.752620\pi\)
\(200\) 1.55191 0.109737
\(201\) −25.2706 −1.78245
\(202\) 5.83136 0.410293
\(203\) 0.282924 0.0198574
\(204\) 23.0287 1.61233
\(205\) −5.90197 −0.412211
\(206\) 20.1257 1.40223
\(207\) 43.7557 3.04123
\(208\) −12.2668 −0.850551
\(209\) −40.6398 −2.81111
\(210\) −5.18264 −0.357636
\(211\) 25.6863 1.76832 0.884160 0.467183i \(-0.154731\pi\)
0.884160 + 0.467183i \(0.154731\pi\)
\(212\) −10.7537 −0.738570
\(213\) 41.5948 2.85003
\(214\) −25.8851 −1.76947
\(215\) 7.89879 0.538693
\(216\) 11.8558 0.806686
\(217\) −9.08665 −0.616842
\(218\) 10.6276 0.719793
\(219\) −37.4148 −2.52826
\(220\) −6.25032 −0.421396
\(221\) 17.2230 1.15854
\(222\) −16.8666 −1.13201
\(223\) 3.72658 0.249550 0.124775 0.992185i \(-0.460179\pi\)
0.124775 + 0.992185i \(0.460179\pi\)
\(224\) −5.70412 −0.381122
\(225\) 5.60439 0.373626
\(226\) 19.3276 1.28566
\(227\) 10.1304 0.672379 0.336189 0.941794i \(-0.390862\pi\)
0.336189 + 0.941794i \(0.390862\pi\)
\(228\) −23.9945 −1.58907
\(229\) 1.00000 0.0660819
\(230\) 13.7942 0.909564
\(231\) −16.3460 −1.07549
\(232\) −0.439072 −0.0288265
\(233\) 1.22517 0.0802634 0.0401317 0.999194i \(-0.487222\pi\)
0.0401317 + 0.999194i \(0.487222\pi\)
\(234\) −24.3651 −1.59280
\(235\) −6.99295 −0.456170
\(236\) −2.41499 −0.157203
\(237\) −32.1691 −2.08961
\(238\) 12.3666 0.801606
\(239\) −25.2747 −1.63489 −0.817443 0.576009i \(-0.804609\pi\)
−0.817443 + 0.576009i \(0.804609\pi\)
\(240\) 14.6232 0.943925
\(241\) −2.54854 −0.164166 −0.0820831 0.996625i \(-0.526157\pi\)
−0.0820831 + 0.996625i \(0.526157\pi\)
\(242\) −35.4297 −2.27750
\(243\) −6.50369 −0.417212
\(244\) 5.05291 0.323480
\(245\) −1.00000 −0.0638877
\(246\) −30.5878 −1.95021
\(247\) −17.9453 −1.14183
\(248\) 14.1017 0.895456
\(249\) −1.62728 −0.103124
\(250\) 1.76681 0.111743
\(251\) 4.34906 0.274510 0.137255 0.990536i \(-0.456172\pi\)
0.137255 + 0.990536i \(0.456172\pi\)
\(252\) −6.28607 −0.395985
\(253\) 43.5068 2.73525
\(254\) 0.137860 0.00865009
\(255\) −20.5314 −1.28573
\(256\) 20.0354 1.25221
\(257\) 16.0884 1.00356 0.501782 0.864994i \(-0.332678\pi\)
0.501782 + 0.864994i \(0.332678\pi\)
\(258\) 40.9366 2.54860
\(259\) −3.25443 −0.202221
\(260\) −2.75995 −0.171165
\(261\) −1.58561 −0.0981471
\(262\) 20.8272 1.28671
\(263\) 15.1036 0.931330 0.465665 0.884961i \(-0.345815\pi\)
0.465665 + 0.884961i \(0.345815\pi\)
\(264\) 25.3674 1.56126
\(265\) 9.58756 0.588959
\(266\) −12.8852 −0.790043
\(267\) 33.5049 2.05047
\(268\) −9.66289 −0.590255
\(269\) −21.9389 −1.33764 −0.668820 0.743424i \(-0.733200\pi\)
−0.668820 + 0.743424i \(0.733200\pi\)
\(270\) 13.4976 0.821437
\(271\) −21.9172 −1.33138 −0.665689 0.746230i \(-0.731862\pi\)
−0.665689 + 0.746230i \(0.731862\pi\)
\(272\) −34.8932 −2.11571
\(273\) −7.21787 −0.436845
\(274\) −4.35685 −0.263207
\(275\) 5.57251 0.336035
\(276\) 25.6873 1.54619
\(277\) −1.46742 −0.0881685 −0.0440843 0.999028i \(-0.514037\pi\)
−0.0440843 + 0.999028i \(0.514037\pi\)
\(278\) −21.3774 −1.28213
\(279\) 50.9251 3.04881
\(280\) 1.55191 0.0927443
\(281\) 9.73542 0.580766 0.290383 0.956910i \(-0.406217\pi\)
0.290383 + 0.956910i \(0.406217\pi\)
\(282\) −36.2420 −2.15818
\(283\) −4.69544 −0.279115 −0.139558 0.990214i \(-0.544568\pi\)
−0.139558 + 0.990214i \(0.544568\pi\)
\(284\) 15.9049 0.943782
\(285\) 21.3924 1.26718
\(286\) −24.2265 −1.43254
\(287\) −5.90197 −0.348382
\(288\) 31.9681 1.88374
\(289\) 31.9911 1.88183
\(290\) −0.499874 −0.0293536
\(291\) 28.4470 1.66759
\(292\) −14.3066 −0.837229
\(293\) 19.8129 1.15748 0.578740 0.815512i \(-0.303545\pi\)
0.578740 + 0.815512i \(0.303545\pi\)
\(294\) −5.18264 −0.302258
\(295\) 2.15310 0.125358
\(296\) 5.05059 0.293559
\(297\) 42.5712 2.47023
\(298\) 4.15348 0.240605
\(299\) 19.2112 1.11101
\(300\) 3.29012 0.189955
\(301\) 7.89879 0.455279
\(302\) 21.0181 1.20946
\(303\) −9.68141 −0.556182
\(304\) 36.3566 2.08519
\(305\) −4.50495 −0.257953
\(306\) −69.3071 −3.96202
\(307\) −22.2882 −1.27206 −0.636028 0.771666i \(-0.719424\pi\)
−0.636028 + 0.771666i \(0.719424\pi\)
\(308\) −6.25032 −0.356145
\(309\) −33.4134 −1.90082
\(310\) 16.0544 0.911830
\(311\) −8.81128 −0.499642 −0.249821 0.968292i \(-0.580372\pi\)
−0.249821 + 0.968292i \(0.580372\pi\)
\(312\) 11.2015 0.634159
\(313\) 17.5808 0.993724 0.496862 0.867829i \(-0.334485\pi\)
0.496862 + 0.867829i \(0.334485\pi\)
\(314\) 28.3103 1.59764
\(315\) 5.60439 0.315771
\(316\) −12.3007 −0.691970
\(317\) −24.6180 −1.38269 −0.691343 0.722526i \(-0.742981\pi\)
−0.691343 + 0.722526i \(0.742981\pi\)
\(318\) 49.6888 2.78641
\(319\) −1.57660 −0.0882724
\(320\) 0.107708 0.00602106
\(321\) 42.9752 2.39864
\(322\) 13.7942 0.768722
\(323\) −51.0457 −2.84026
\(324\) 6.27665 0.348703
\(325\) 2.46065 0.136492
\(326\) −4.87211 −0.269841
\(327\) −17.6443 −0.975732
\(328\) 9.15932 0.505739
\(329\) −6.99295 −0.385534
\(330\) 28.8803 1.58981
\(331\) 17.0015 0.934484 0.467242 0.884129i \(-0.345248\pi\)
0.467242 + 0.884129i \(0.345248\pi\)
\(332\) −0.622232 −0.0341494
\(333\) 18.2391 0.999497
\(334\) 38.9227 2.12976
\(335\) 8.61501 0.470688
\(336\) 14.6232 0.797762
\(337\) −6.26804 −0.341442 −0.170721 0.985319i \(-0.554610\pi\)
−0.170721 + 0.985319i \(0.554610\pi\)
\(338\) 12.2709 0.667450
\(339\) −32.0884 −1.74280
\(340\) −7.85073 −0.425765
\(341\) 50.6354 2.74206
\(342\) 72.2137 3.90487
\(343\) −1.00000 −0.0539949
\(344\) −12.2582 −0.660918
\(345\) −22.9016 −1.23298
\(346\) −41.9789 −2.25680
\(347\) 11.0320 0.592230 0.296115 0.955152i \(-0.404309\pi\)
0.296115 + 0.955152i \(0.404309\pi\)
\(348\) −0.930853 −0.0498989
\(349\) −23.9723 −1.28321 −0.641603 0.767037i \(-0.721730\pi\)
−0.641603 + 0.767037i \(0.721730\pi\)
\(350\) 1.76681 0.0944402
\(351\) 18.7981 1.00337
\(352\) 31.7862 1.69421
\(353\) −14.6943 −0.782101 −0.391051 0.920369i \(-0.627888\pi\)
−0.391051 + 0.920369i \(0.627888\pi\)
\(354\) 11.1587 0.593081
\(355\) −14.1801 −0.752602
\(356\) 12.8115 0.679009
\(357\) −20.5314 −1.08664
\(358\) −20.4110 −1.07875
\(359\) 8.60763 0.454294 0.227147 0.973861i \(-0.427060\pi\)
0.227147 + 0.973861i \(0.427060\pi\)
\(360\) −8.69750 −0.458398
\(361\) 34.1864 1.79929
\(362\) 45.5887 2.39609
\(363\) 58.8215 3.08733
\(364\) −2.75995 −0.144660
\(365\) 12.7551 0.667633
\(366\) −23.3476 −1.22040
\(367\) −0.831519 −0.0434049 −0.0217025 0.999764i \(-0.506909\pi\)
−0.0217025 + 0.999764i \(0.506909\pi\)
\(368\) −38.9215 −2.02892
\(369\) 33.0769 1.72192
\(370\) 5.74998 0.298927
\(371\) 9.58756 0.497761
\(372\) 29.8961 1.55004
\(373\) 9.85102 0.510066 0.255033 0.966932i \(-0.417914\pi\)
0.255033 + 0.966932i \(0.417914\pi\)
\(374\) −68.9128 −3.56340
\(375\) −2.93332 −0.151476
\(376\) 10.8524 0.559671
\(377\) −0.696176 −0.0358549
\(378\) 13.4976 0.694241
\(379\) 4.68612 0.240710 0.120355 0.992731i \(-0.461597\pi\)
0.120355 + 0.992731i \(0.461597\pi\)
\(380\) 8.17997 0.419624
\(381\) −0.228879 −0.0117258
\(382\) −47.7490 −2.44305
\(383\) 20.9263 1.06928 0.534641 0.845079i \(-0.320447\pi\)
0.534641 + 0.845079i \(0.320447\pi\)
\(384\) −32.9058 −1.67922
\(385\) 5.57251 0.284001
\(386\) 15.7035 0.799289
\(387\) −44.2678 −2.25026
\(388\) 10.8775 0.552219
\(389\) 12.4828 0.632905 0.316452 0.948608i \(-0.397508\pi\)
0.316452 + 0.948608i \(0.397508\pi\)
\(390\) 12.7526 0.645755
\(391\) 54.6468 2.76361
\(392\) 1.55191 0.0783832
\(393\) −34.5779 −1.74423
\(394\) 32.0978 1.61706
\(395\) 10.9668 0.551799
\(396\) 35.0292 1.76028
\(397\) 23.1029 1.15950 0.579751 0.814794i \(-0.303150\pi\)
0.579751 + 0.814794i \(0.303150\pi\)
\(398\) 35.5368 1.78130
\(399\) 21.3924 1.07096
\(400\) −4.98520 −0.249260
\(401\) −0.559463 −0.0279382 −0.0139691 0.999902i \(-0.504447\pi\)
−0.0139691 + 0.999902i \(0.504447\pi\)
\(402\) 44.6485 2.22686
\(403\) 22.3590 1.11378
\(404\) −3.70195 −0.184179
\(405\) −5.59598 −0.278067
\(406\) −0.499874 −0.0248083
\(407\) 18.1354 0.898936
\(408\) 31.8628 1.57745
\(409\) 17.5238 0.866498 0.433249 0.901274i \(-0.357367\pi\)
0.433249 + 0.901274i \(0.357367\pi\)
\(410\) 10.4277 0.514987
\(411\) 7.23338 0.356796
\(412\) −12.7765 −0.629453
\(413\) 2.15310 0.105947
\(414\) −77.3082 −3.79949
\(415\) 0.554755 0.0272318
\(416\) 14.0358 0.688162
\(417\) 35.4915 1.73802
\(418\) 71.8029 3.51200
\(419\) −30.6310 −1.49642 −0.748210 0.663462i \(-0.769086\pi\)
−0.748210 + 0.663462i \(0.769086\pi\)
\(420\) 3.29012 0.160541
\(421\) −4.02979 −0.196400 −0.0981999 0.995167i \(-0.531308\pi\)
−0.0981999 + 0.995167i \(0.531308\pi\)
\(422\) −45.3830 −2.20921
\(423\) 39.1912 1.90554
\(424\) −14.8790 −0.722589
\(425\) 6.99936 0.339519
\(426\) −73.4904 −3.56062
\(427\) −4.50495 −0.218010
\(428\) 16.4327 0.794306
\(429\) 40.2216 1.94192
\(430\) −13.9557 −0.673003
\(431\) −24.0938 −1.16056 −0.580279 0.814418i \(-0.697056\pi\)
−0.580279 + 0.814418i \(0.697056\pi\)
\(432\) −38.0845 −1.83234
\(433\) 6.12482 0.294340 0.147170 0.989111i \(-0.452984\pi\)
0.147170 + 0.989111i \(0.452984\pi\)
\(434\) 16.0544 0.770637
\(435\) 0.829907 0.0397910
\(436\) −6.74677 −0.323112
\(437\) −56.9386 −2.72374
\(438\) 66.1051 3.15862
\(439\) −10.8531 −0.517990 −0.258995 0.965879i \(-0.583391\pi\)
−0.258995 + 0.965879i \(0.583391\pi\)
\(440\) −8.64802 −0.412278
\(441\) 5.60439 0.266876
\(442\) −30.4298 −1.44740
\(443\) 16.6982 0.793354 0.396677 0.917958i \(-0.370163\pi\)
0.396677 + 0.917958i \(0.370163\pi\)
\(444\) 10.7075 0.508154
\(445\) −11.4222 −0.541463
\(446\) −6.58417 −0.311770
\(447\) −6.89575 −0.326158
\(448\) 0.107708 0.00508872
\(449\) 13.9150 0.656691 0.328345 0.944558i \(-0.393509\pi\)
0.328345 + 0.944558i \(0.393509\pi\)
\(450\) −9.90191 −0.466781
\(451\) 32.8888 1.54867
\(452\) −12.2698 −0.577125
\(453\) −34.8949 −1.63951
\(454\) −17.8986 −0.840021
\(455\) 2.46065 0.115357
\(456\) −33.1991 −1.55469
\(457\) 23.5948 1.10372 0.551859 0.833937i \(-0.313919\pi\)
0.551859 + 0.833937i \(0.313919\pi\)
\(458\) −1.76681 −0.0825578
\(459\) 53.4717 2.49584
\(460\) −8.75705 −0.408299
\(461\) 7.28675 0.339378 0.169689 0.985498i \(-0.445724\pi\)
0.169689 + 0.985498i \(0.445724\pi\)
\(462\) 28.8803 1.34363
\(463\) −2.00582 −0.0932182 −0.0466091 0.998913i \(-0.514842\pi\)
−0.0466091 + 0.998913i \(0.514842\pi\)
\(464\) 1.41043 0.0654777
\(465\) −26.6541 −1.23605
\(466\) −2.16465 −0.100275
\(467\) −13.6741 −0.632760 −0.316380 0.948632i \(-0.602468\pi\)
−0.316380 + 0.948632i \(0.602468\pi\)
\(468\) 15.4678 0.715000
\(469\) 8.61501 0.397804
\(470\) 12.3553 0.569905
\(471\) −47.0017 −2.16572
\(472\) −3.34142 −0.153801
\(473\) −44.0160 −2.02386
\(474\) 56.8369 2.61061
\(475\) −7.29290 −0.334621
\(476\) −7.85073 −0.359837
\(477\) −53.7324 −2.46024
\(478\) 44.6558 2.04251
\(479\) −15.8846 −0.725787 −0.362893 0.931831i \(-0.618211\pi\)
−0.362893 + 0.931831i \(0.618211\pi\)
\(480\) −16.7320 −0.763709
\(481\) 8.00801 0.365134
\(482\) 4.50280 0.205097
\(483\) −22.9016 −1.04206
\(484\) 22.4920 1.02236
\(485\) −9.69786 −0.440357
\(486\) 11.4908 0.521234
\(487\) 35.2183 1.59589 0.797947 0.602727i \(-0.205919\pi\)
0.797947 + 0.602727i \(0.205919\pi\)
\(488\) 6.99128 0.316480
\(489\) 8.08884 0.365790
\(490\) 1.76681 0.0798166
\(491\) 0.185421 0.00836795 0.00418398 0.999991i \(-0.498668\pi\)
0.00418398 + 0.999991i \(0.498668\pi\)
\(492\) 19.4182 0.875439
\(493\) −1.98029 −0.0891876
\(494\) 31.7059 1.42652
\(495\) −31.2305 −1.40371
\(496\) −45.2988 −2.03398
\(497\) −14.1801 −0.636065
\(498\) 2.87509 0.128836
\(499\) 15.3955 0.689199 0.344599 0.938750i \(-0.388015\pi\)
0.344599 + 0.938750i \(0.388015\pi\)
\(500\) −1.12163 −0.0501610
\(501\) −64.6207 −2.88704
\(502\) −7.68398 −0.342953
\(503\) −12.4786 −0.556394 −0.278197 0.960524i \(-0.589737\pi\)
−0.278197 + 0.960524i \(0.589737\pi\)
\(504\) −8.69750 −0.387417
\(505\) 3.30049 0.146870
\(506\) −76.8684 −3.41722
\(507\) −20.3726 −0.904778
\(508\) −0.0875181 −0.00388299
\(509\) 23.9865 1.06318 0.531592 0.847001i \(-0.321594\pi\)
0.531592 + 0.847001i \(0.321594\pi\)
\(510\) 36.2752 1.60629
\(511\) 12.7551 0.564253
\(512\) −12.9630 −0.572890
\(513\) −55.7142 −2.45984
\(514\) −28.4251 −1.25378
\(515\) 11.3910 0.501946
\(516\) −25.9879 −1.14406
\(517\) 38.9683 1.71382
\(518\) 5.74998 0.252640
\(519\) 69.6947 3.05926
\(520\) −3.81870 −0.167461
\(521\) 2.06211 0.0903427 0.0451713 0.998979i \(-0.485617\pi\)
0.0451713 + 0.998979i \(0.485617\pi\)
\(522\) 2.80149 0.122618
\(523\) −16.8449 −0.736577 −0.368288 0.929712i \(-0.620056\pi\)
−0.368288 + 0.929712i \(0.620056\pi\)
\(524\) −13.2218 −0.577597
\(525\) −2.93332 −0.128021
\(526\) −26.6853 −1.16354
\(527\) 63.6007 2.77049
\(528\) −81.4880 −3.54631
\(529\) 37.9555 1.65024
\(530\) −16.9394 −0.735802
\(531\) −12.0668 −0.523655
\(532\) 8.17997 0.354647
\(533\) 14.5227 0.629046
\(534\) −59.1970 −2.56171
\(535\) −14.6507 −0.633405
\(536\) −13.3697 −0.577483
\(537\) 33.8869 1.46233
\(538\) 38.7620 1.67115
\(539\) 5.57251 0.240025
\(540\) −8.56873 −0.368740
\(541\) −2.13928 −0.0919747 −0.0459874 0.998942i \(-0.514643\pi\)
−0.0459874 + 0.998942i \(0.514643\pi\)
\(542\) 38.7237 1.66333
\(543\) −75.6879 −3.24808
\(544\) 39.9252 1.71178
\(545\) 6.01512 0.257660
\(546\) 12.7526 0.545763
\(547\) −38.9611 −1.66585 −0.832927 0.553382i \(-0.813337\pi\)
−0.832927 + 0.553382i \(0.813337\pi\)
\(548\) 2.76588 0.118152
\(549\) 25.2475 1.07754
\(550\) −9.84559 −0.419817
\(551\) 2.06334 0.0879011
\(552\) 35.5412 1.51274
\(553\) 10.9668 0.466355
\(554\) 2.59265 0.110151
\(555\) −9.54631 −0.405218
\(556\) 13.5711 0.575543
\(557\) 24.3258 1.03072 0.515359 0.856974i \(-0.327658\pi\)
0.515359 + 0.856974i \(0.327658\pi\)
\(558\) −89.9752 −3.80895
\(559\) −19.4361 −0.822060
\(560\) −4.98520 −0.210663
\(561\) 114.411 4.83045
\(562\) −17.2007 −0.725567
\(563\) 33.5731 1.41494 0.707469 0.706744i \(-0.249837\pi\)
0.707469 + 0.706744i \(0.249837\pi\)
\(564\) 23.0076 0.968796
\(565\) 10.9393 0.460218
\(566\) 8.29598 0.348706
\(567\) −5.59598 −0.235009
\(568\) 22.0062 0.923361
\(569\) −7.83718 −0.328552 −0.164276 0.986414i \(-0.552529\pi\)
−0.164276 + 0.986414i \(0.552529\pi\)
\(570\) −37.7965 −1.58312
\(571\) −27.0736 −1.13299 −0.566497 0.824064i \(-0.691702\pi\)
−0.566497 + 0.824064i \(0.691702\pi\)
\(572\) 15.3798 0.643063
\(573\) 79.2744 3.31174
\(574\) 10.4277 0.435243
\(575\) 7.80740 0.325591
\(576\) −0.603637 −0.0251515
\(577\) 4.95258 0.206179 0.103089 0.994672i \(-0.467127\pi\)
0.103089 + 0.994672i \(0.467127\pi\)
\(578\) −56.5223 −2.35102
\(579\) −26.0715 −1.08350
\(580\) 0.317337 0.0131767
\(581\) 0.554755 0.0230151
\(582\) −50.2605 −2.08337
\(583\) −53.4267 −2.21271
\(584\) −19.7948 −0.819113
\(585\) −13.7904 −0.570163
\(586\) −35.0057 −1.44607
\(587\) 23.0449 0.951163 0.475581 0.879672i \(-0.342238\pi\)
0.475581 + 0.879672i \(0.342238\pi\)
\(588\) 3.29012 0.135682
\(589\) −66.2681 −2.73053
\(590\) −3.80413 −0.156614
\(591\) −53.2897 −2.19205
\(592\) −16.2240 −0.666803
\(593\) 13.5697 0.557242 0.278621 0.960401i \(-0.410123\pi\)
0.278621 + 0.960401i \(0.410123\pi\)
\(594\) −75.2154 −3.08613
\(595\) 6.99936 0.286946
\(596\) −2.63677 −0.108006
\(597\) −58.9994 −2.41468
\(598\) −33.9427 −1.38802
\(599\) −33.6379 −1.37441 −0.687203 0.726465i \(-0.741162\pi\)
−0.687203 + 0.726465i \(0.741162\pi\)
\(600\) 4.55225 0.185845
\(601\) 38.3161 1.56295 0.781474 0.623938i \(-0.214468\pi\)
0.781474 + 0.623938i \(0.214468\pi\)
\(602\) −13.9557 −0.568792
\(603\) −48.2818 −1.96619
\(604\) −13.3430 −0.542919
\(605\) −20.0528 −0.815264
\(606\) 17.1053 0.694854
\(607\) 3.05677 0.124071 0.0620353 0.998074i \(-0.480241\pi\)
0.0620353 + 0.998074i \(0.480241\pi\)
\(608\) −41.5996 −1.68709
\(609\) 0.829907 0.0336295
\(610\) 7.95942 0.322267
\(611\) 17.2072 0.696128
\(612\) 43.9985 1.77853
\(613\) 19.0380 0.768936 0.384468 0.923138i \(-0.374385\pi\)
0.384468 + 0.923138i \(0.374385\pi\)
\(614\) 39.3791 1.58921
\(615\) −17.3124 −0.698103
\(616\) −8.64802 −0.348439
\(617\) −1.04915 −0.0422371 −0.0211185 0.999777i \(-0.506723\pi\)
−0.0211185 + 0.999777i \(0.506723\pi\)
\(618\) 59.0353 2.37475
\(619\) 2.01296 0.0809076 0.0404538 0.999181i \(-0.487120\pi\)
0.0404538 + 0.999181i \(0.487120\pi\)
\(620\) −10.1919 −0.409317
\(621\) 59.6447 2.39346
\(622\) 15.5679 0.624216
\(623\) −11.4222 −0.457620
\(624\) −35.9826 −1.44046
\(625\) 1.00000 0.0400000
\(626\) −31.0620 −1.24149
\(627\) −119.210 −4.76077
\(628\) −17.9724 −0.717175
\(629\) 22.7790 0.908257
\(630\) −9.90191 −0.394502
\(631\) −19.6968 −0.784117 −0.392059 0.919940i \(-0.628237\pi\)
−0.392059 + 0.919940i \(0.628237\pi\)
\(632\) −17.0195 −0.676998
\(633\) 75.3463 2.99475
\(634\) 43.4955 1.72743
\(635\) 0.0780272 0.00309642
\(636\) −31.5442 −1.25081
\(637\) 2.46065 0.0974944
\(638\) 2.78555 0.110281
\(639\) 79.4708 3.14381
\(640\) 11.2179 0.443428
\(641\) −8.70703 −0.343907 −0.171954 0.985105i \(-0.555008\pi\)
−0.171954 + 0.985105i \(0.555008\pi\)
\(642\) −75.9293 −2.99669
\(643\) 17.7885 0.701511 0.350756 0.936467i \(-0.385925\pi\)
0.350756 + 0.936467i \(0.385925\pi\)
\(644\) −8.75705 −0.345076
\(645\) 23.1697 0.912306
\(646\) 90.1882 3.54841
\(647\) −31.1355 −1.22406 −0.612032 0.790833i \(-0.709648\pi\)
−0.612032 + 0.790833i \(0.709648\pi\)
\(648\) 8.68445 0.341158
\(649\) −11.9982 −0.470969
\(650\) −4.34751 −0.170523
\(651\) −26.6541 −1.04466
\(652\) 3.09298 0.121131
\(653\) −11.9099 −0.466069 −0.233035 0.972468i \(-0.574866\pi\)
−0.233035 + 0.972468i \(0.574866\pi\)
\(654\) 31.1742 1.21901
\(655\) 11.7880 0.460594
\(656\) −29.4225 −1.14876
\(657\) −71.4845 −2.78888
\(658\) 12.3553 0.481658
\(659\) −12.2728 −0.478079 −0.239040 0.971010i \(-0.576833\pi\)
−0.239040 + 0.971010i \(0.576833\pi\)
\(660\) −18.3342 −0.713658
\(661\) 21.5059 0.836481 0.418240 0.908336i \(-0.362647\pi\)
0.418240 + 0.908336i \(0.362647\pi\)
\(662\) −30.0384 −1.16748
\(663\) 50.5205 1.96205
\(664\) −0.860929 −0.0334105
\(665\) −7.29290 −0.282807
\(666\) −32.2251 −1.24870
\(667\) −2.20890 −0.0855289
\(668\) −24.7095 −0.956038
\(669\) 10.9313 0.422627
\(670\) −15.2211 −0.588043
\(671\) 25.1039 0.969125
\(672\) −16.7320 −0.645452
\(673\) −15.2023 −0.586006 −0.293003 0.956111i \(-0.594655\pi\)
−0.293003 + 0.956111i \(0.594655\pi\)
\(674\) 11.0745 0.426572
\(675\) 7.63951 0.294045
\(676\) −7.79000 −0.299615
\(677\) 28.2617 1.08618 0.543092 0.839673i \(-0.317253\pi\)
0.543092 + 0.839673i \(0.317253\pi\)
\(678\) 56.6942 2.17733
\(679\) −9.69786 −0.372170
\(680\) −10.8624 −0.416553
\(681\) 29.7158 1.13871
\(682\) −89.4634 −3.42573
\(683\) −21.5966 −0.826372 −0.413186 0.910647i \(-0.635584\pi\)
−0.413186 + 0.910647i \(0.635584\pi\)
\(684\) −45.8437 −1.75288
\(685\) −2.46593 −0.0942185
\(686\) 1.76681 0.0674573
\(687\) 2.93332 0.111913
\(688\) 39.3771 1.50124
\(689\) −23.5916 −0.898768
\(690\) 40.4629 1.54040
\(691\) 2.53457 0.0964197 0.0482098 0.998837i \(-0.484648\pi\)
0.0482098 + 0.998837i \(0.484648\pi\)
\(692\) 26.6496 1.01307
\(693\) −31.2305 −1.18635
\(694\) −19.4916 −0.739889
\(695\) −12.0994 −0.458957
\(696\) −1.28794 −0.0488193
\(697\) 41.3100 1.56473
\(698\) 42.3546 1.60314
\(699\) 3.59381 0.135931
\(700\) −1.12163 −0.0423938
\(701\) −34.1597 −1.29019 −0.645097 0.764100i \(-0.723183\pi\)
−0.645097 + 0.764100i \(0.723183\pi\)
\(702\) −33.2128 −1.25354
\(703\) −23.7343 −0.895155
\(704\) −0.600203 −0.0226210
\(705\) −20.5126 −0.772549
\(706\) 25.9622 0.977100
\(707\) 3.30049 0.124128
\(708\) −7.08396 −0.266231
\(709\) −32.1055 −1.20575 −0.602875 0.797836i \(-0.705978\pi\)
−0.602875 + 0.797836i \(0.705978\pi\)
\(710\) 25.0536 0.940245
\(711\) −61.4621 −2.30501
\(712\) 17.7262 0.664317
\(713\) 70.9431 2.65684
\(714\) 36.2752 1.35756
\(715\) −13.7120 −0.512799
\(716\) 12.9576 0.484247
\(717\) −74.1390 −2.76877
\(718\) −15.2081 −0.567561
\(719\) 8.31992 0.310280 0.155140 0.987892i \(-0.450417\pi\)
0.155140 + 0.987892i \(0.450417\pi\)
\(720\) 27.9390 1.04123
\(721\) 11.3910 0.424222
\(722\) −60.4011 −2.24790
\(723\) −7.47570 −0.278024
\(724\) −28.9413 −1.07560
\(725\) −0.282924 −0.0105075
\(726\) −103.927 −3.85708
\(727\) 9.85286 0.365422 0.182711 0.983167i \(-0.441513\pi\)
0.182711 + 0.983167i \(0.441513\pi\)
\(728\) −3.81870 −0.141530
\(729\) −35.8654 −1.32835
\(730\) −22.5359 −0.834091
\(731\) −55.2865 −2.04484
\(732\) 14.8218 0.547830
\(733\) 18.2883 0.675494 0.337747 0.941237i \(-0.390335\pi\)
0.337747 + 0.941237i \(0.390335\pi\)
\(734\) 1.46914 0.0542270
\(735\) −2.93332 −0.108197
\(736\) 44.5343 1.64156
\(737\) −48.0072 −1.76837
\(738\) −58.4408 −2.15124
\(739\) 33.3823 1.22799 0.613994 0.789311i \(-0.289562\pi\)
0.613994 + 0.789311i \(0.289562\pi\)
\(740\) −3.65029 −0.134187
\(741\) −52.6392 −1.93375
\(742\) −16.9394 −0.621866
\(743\) −11.9424 −0.438123 −0.219062 0.975711i \(-0.570300\pi\)
−0.219062 + 0.975711i \(0.570300\pi\)
\(744\) 41.3647 1.51650
\(745\) 2.35083 0.0861278
\(746\) −17.4049 −0.637239
\(747\) −3.10906 −0.113755
\(748\) 43.7482 1.59959
\(749\) −14.6507 −0.535325
\(750\) 5.18264 0.189243
\(751\) −8.69916 −0.317437 −0.158718 0.987324i \(-0.550736\pi\)
−0.158718 + 0.987324i \(0.550736\pi\)
\(752\) −34.8613 −1.27126
\(753\) 12.7572 0.464898
\(754\) 1.23001 0.0447944
\(755\) 11.8960 0.432941
\(756\) −8.56873 −0.311642
\(757\) −19.9289 −0.724327 −0.362164 0.932115i \(-0.617962\pi\)
−0.362164 + 0.932115i \(0.617962\pi\)
\(758\) −8.27950 −0.300725
\(759\) 127.619 4.63229
\(760\) 11.3179 0.410544
\(761\) −22.0167 −0.798104 −0.399052 0.916928i \(-0.630661\pi\)
−0.399052 + 0.916928i \(0.630661\pi\)
\(762\) 0.404387 0.0146494
\(763\) 6.01512 0.217762
\(764\) 30.3127 1.09668
\(765\) −39.2271 −1.41826
\(766\) −36.9728 −1.33588
\(767\) −5.29802 −0.191300
\(768\) 58.7704 2.12069
\(769\) 10.3014 0.371477 0.185738 0.982599i \(-0.440532\pi\)
0.185738 + 0.982599i \(0.440532\pi\)
\(770\) −9.84559 −0.354810
\(771\) 47.1923 1.69959
\(772\) −9.96914 −0.358797
\(773\) 1.42750 0.0513435 0.0256717 0.999670i \(-0.491828\pi\)
0.0256717 + 0.999670i \(0.491828\pi\)
\(774\) 78.2131 2.81131
\(775\) 9.08665 0.326402
\(776\) 15.0502 0.540270
\(777\) −9.54631 −0.342472
\(778\) −22.0549 −0.790705
\(779\) −43.0425 −1.54216
\(780\) −8.09582 −0.289877
\(781\) 79.0187 2.82751
\(782\) −96.5508 −3.45265
\(783\) −2.16140 −0.0772421
\(784\) −4.98520 −0.178043
\(785\) 16.0234 0.571898
\(786\) 61.0928 2.17911
\(787\) 53.7310 1.91530 0.957652 0.287927i \(-0.0929660\pi\)
0.957652 + 0.287927i \(0.0929660\pi\)
\(788\) −20.3768 −0.725892
\(789\) 44.3039 1.57726
\(790\) −19.3763 −0.689377
\(791\) 10.9393 0.388955
\(792\) 48.4669 1.72219
\(793\) 11.0851 0.393643
\(794\) −40.8185 −1.44860
\(795\) 28.1234 0.997434
\(796\) −22.5600 −0.799618
\(797\) −38.5582 −1.36580 −0.682900 0.730512i \(-0.739282\pi\)
−0.682900 + 0.730512i \(0.739282\pi\)
\(798\) −37.7965 −1.33798
\(799\) 48.9462 1.73159
\(800\) 5.70412 0.201671
\(801\) 64.0143 2.26183
\(802\) 0.988467 0.0349040
\(803\) −71.0779 −2.50829
\(804\) −28.3444 −0.999629
\(805\) 7.80740 0.275175
\(806\) −39.5043 −1.39148
\(807\) −64.3540 −2.26537
\(808\) −5.12206 −0.180194
\(809\) 8.74409 0.307426 0.153713 0.988116i \(-0.450877\pi\)
0.153713 + 0.988116i \(0.450877\pi\)
\(810\) 9.88707 0.347396
\(811\) −6.36588 −0.223536 −0.111768 0.993734i \(-0.535651\pi\)
−0.111768 + 0.993734i \(0.535651\pi\)
\(812\) 0.317337 0.0111364
\(813\) −64.2903 −2.25476
\(814\) −32.0418 −1.12307
\(815\) −2.75757 −0.0965934
\(816\) −102.353 −3.58308
\(817\) 57.6051 2.01535
\(818\) −30.9614 −1.08254
\(819\) −13.7904 −0.481876
\(820\) −6.61985 −0.231175
\(821\) −28.5401 −0.996057 −0.498028 0.867161i \(-0.665942\pi\)
−0.498028 + 0.867161i \(0.665942\pi\)
\(822\) −12.7800 −0.445755
\(823\) 29.1255 1.01525 0.507626 0.861578i \(-0.330523\pi\)
0.507626 + 0.861578i \(0.330523\pi\)
\(824\) −17.6777 −0.615833
\(825\) 16.3460 0.569093
\(826\) −3.80413 −0.132363
\(827\) −31.5453 −1.09694 −0.548468 0.836172i \(-0.684789\pi\)
−0.548468 + 0.836172i \(0.684789\pi\)
\(828\) 49.0779 1.70557
\(829\) 21.9470 0.762251 0.381126 0.924523i \(-0.375537\pi\)
0.381126 + 0.924523i \(0.375537\pi\)
\(830\) −0.980149 −0.0340215
\(831\) −4.30441 −0.149318
\(832\) −0.265031 −0.00918830
\(833\) 6.99936 0.242513
\(834\) −62.7068 −2.17136
\(835\) 22.0299 0.762375
\(836\) −45.5830 −1.57652
\(837\) 69.4175 2.39942
\(838\) 54.1192 1.86952
\(839\) 13.1665 0.454558 0.227279 0.973830i \(-0.427017\pi\)
0.227279 + 0.973830i \(0.427017\pi\)
\(840\) 4.55225 0.157068
\(841\) −28.9200 −0.997240
\(842\) 7.11989 0.245368
\(843\) 28.5571 0.983560
\(844\) 28.8107 0.991705
\(845\) 6.94522 0.238923
\(846\) −69.2436 −2.38064
\(847\) −20.0528 −0.689024
\(848\) 47.7959 1.64132
\(849\) −13.7733 −0.472697
\(850\) −12.3666 −0.424170
\(851\) 25.4087 0.870998
\(852\) 46.6542 1.59835
\(853\) 9.97282 0.341463 0.170731 0.985318i \(-0.445387\pi\)
0.170731 + 0.985318i \(0.445387\pi\)
\(854\) 7.95942 0.272366
\(855\) 40.8722 1.39780
\(856\) 22.7366 0.777119
\(857\) −13.1891 −0.450533 −0.225266 0.974297i \(-0.572325\pi\)
−0.225266 + 0.974297i \(0.572325\pi\)
\(858\) −71.0642 −2.42609
\(859\) 1.16310 0.0396844 0.0198422 0.999803i \(-0.493684\pi\)
0.0198422 + 0.999803i \(0.493684\pi\)
\(860\) 8.85955 0.302108
\(861\) −17.3124 −0.590005
\(862\) 42.5693 1.44992
\(863\) 55.1620 1.87774 0.938868 0.344278i \(-0.111876\pi\)
0.938868 + 0.344278i \(0.111876\pi\)
\(864\) 43.5766 1.48251
\(865\) −23.7596 −0.807852
\(866\) −10.8214 −0.367727
\(867\) 93.8401 3.18698
\(868\) −10.1919 −0.345936
\(869\) −61.1125 −2.07310
\(870\) −1.46629 −0.0497120
\(871\) −21.1985 −0.718283
\(872\) −9.33492 −0.316120
\(873\) 54.3505 1.83949
\(874\) 100.600 3.40284
\(875\) 1.00000 0.0338062
\(876\) −41.9658 −1.41789
\(877\) −8.97353 −0.303015 −0.151507 0.988456i \(-0.548413\pi\)
−0.151507 + 0.988456i \(0.548413\pi\)
\(878\) 19.1754 0.647139
\(879\) 58.1175 1.96026
\(880\) 27.7801 0.936467
\(881\) 52.7878 1.77847 0.889233 0.457454i \(-0.151239\pi\)
0.889233 + 0.457454i \(0.151239\pi\)
\(882\) −9.90191 −0.333415
\(883\) 7.46113 0.251087 0.125544 0.992088i \(-0.459933\pi\)
0.125544 + 0.992088i \(0.459933\pi\)
\(884\) 19.3179 0.649730
\(885\) 6.31574 0.212301
\(886\) −29.5026 −0.991158
\(887\) 5.05704 0.169799 0.0848995 0.996390i \(-0.472943\pi\)
0.0848995 + 0.996390i \(0.472943\pi\)
\(888\) 14.8150 0.497159
\(889\) 0.0780272 0.00261695
\(890\) 20.1809 0.676464
\(891\) 31.1837 1.04469
\(892\) 4.17986 0.139952
\(893\) −50.9989 −1.70661
\(894\) 12.1835 0.407478
\(895\) −11.5524 −0.386154
\(896\) 11.2179 0.374765
\(897\) 56.3528 1.88156
\(898\) −24.5853 −0.820421
\(899\) −2.57083 −0.0857420
\(900\) 6.28607 0.209536
\(901\) −67.1068 −2.23565
\(902\) −58.1084 −1.93480
\(903\) 23.1697 0.771039
\(904\) −16.9767 −0.564638
\(905\) 25.8028 0.857714
\(906\) 61.6529 2.04828
\(907\) −21.4264 −0.711453 −0.355726 0.934590i \(-0.615767\pi\)
−0.355726 + 0.934590i \(0.615767\pi\)
\(908\) 11.3626 0.377082
\(909\) −18.4972 −0.613514
\(910\) −4.34751 −0.144118
\(911\) 11.2098 0.371398 0.185699 0.982607i \(-0.440545\pi\)
0.185699 + 0.982607i \(0.440545\pi\)
\(912\) 106.646 3.53139
\(913\) −3.09138 −0.102310
\(914\) −41.6877 −1.37891
\(915\) −13.2145 −0.436857
\(916\) 1.12163 0.0370599
\(917\) 11.7880 0.389273
\(918\) −94.4745 −3.11812
\(919\) 33.1011 1.09191 0.545953 0.837816i \(-0.316168\pi\)
0.545953 + 0.837816i \(0.316168\pi\)
\(920\) −12.1164 −0.399465
\(921\) −65.3785 −2.15430
\(922\) −12.8743 −0.423994
\(923\) 34.8922 1.14849
\(924\) −18.3342 −0.603151
\(925\) 3.25443 0.107005
\(926\) 3.54391 0.116460
\(927\) −63.8394 −2.09676
\(928\) −1.61383 −0.0529766
\(929\) 20.2164 0.663278 0.331639 0.943406i \(-0.392398\pi\)
0.331639 + 0.943406i \(0.392398\pi\)
\(930\) 47.0928 1.54423
\(931\) −7.29290 −0.239015
\(932\) 1.37419 0.0450131
\(933\) −25.8463 −0.846171
\(934\) 24.1595 0.790524
\(935\) −39.0040 −1.27557
\(936\) 21.4015 0.699529
\(937\) 1.88144 0.0614639 0.0307319 0.999528i \(-0.490216\pi\)
0.0307319 + 0.999528i \(0.490216\pi\)
\(938\) −15.2211 −0.496987
\(939\) 51.5701 1.68293
\(940\) −7.84354 −0.255828
\(941\) −16.9898 −0.553851 −0.276925 0.960891i \(-0.589316\pi\)
−0.276925 + 0.960891i \(0.589316\pi\)
\(942\) 83.0433 2.70570
\(943\) 46.0790 1.50054
\(944\) 10.7337 0.349351
\(945\) 7.63951 0.248513
\(946\) 77.7682 2.52846
\(947\) 19.4492 0.632013 0.316007 0.948757i \(-0.397658\pi\)
0.316007 + 0.948757i \(0.397658\pi\)
\(948\) −36.0820 −1.17189
\(949\) −31.3858 −1.01883
\(950\) 12.8852 0.418051
\(951\) −72.2127 −2.34166
\(952\) −10.8624 −0.352051
\(953\) 15.6168 0.505877 0.252939 0.967482i \(-0.418603\pi\)
0.252939 + 0.967482i \(0.418603\pi\)
\(954\) 94.9351 3.07364
\(955\) −27.0255 −0.874524
\(956\) −28.3490 −0.916873
\(957\) −4.62466 −0.149494
\(958\) 28.0652 0.906745
\(959\) −2.46593 −0.0796292
\(960\) 0.315942 0.0101970
\(961\) 51.5672 1.66346
\(962\) −14.1487 −0.456172
\(963\) 82.1082 2.64590
\(964\) −2.85853 −0.0920672
\(965\) 8.88805 0.286116
\(966\) 40.4629 1.30187
\(967\) 6.17907 0.198705 0.0993527 0.995052i \(-0.468323\pi\)
0.0993527 + 0.995052i \(0.468323\pi\)
\(968\) 31.1202 1.00024
\(969\) −149.733 −4.81013
\(970\) 17.1343 0.550150
\(971\) −42.0542 −1.34958 −0.674791 0.738008i \(-0.735766\pi\)
−0.674791 + 0.738008i \(0.735766\pi\)
\(972\) −7.29476 −0.233980
\(973\) −12.0994 −0.387889
\(974\) −62.2243 −1.99379
\(975\) 7.21787 0.231157
\(976\) −22.4581 −0.718867
\(977\) −1.79994 −0.0575851 −0.0287925 0.999585i \(-0.509166\pi\)
−0.0287925 + 0.999585i \(0.509166\pi\)
\(978\) −14.2915 −0.456991
\(979\) 63.6502 2.03427
\(980\) −1.12163 −0.0358293
\(981\) −33.7111 −1.07631
\(982\) −0.327605 −0.0104543
\(983\) 3.13320 0.0999336 0.0499668 0.998751i \(-0.484088\pi\)
0.0499668 + 0.998751i \(0.484088\pi\)
\(984\) 26.8672 0.856496
\(985\) 18.1670 0.578849
\(986\) 3.49880 0.111424
\(987\) −20.5126 −0.652923
\(988\) −20.1280 −0.640358
\(989\) −61.6690 −1.96096
\(990\) 55.1785 1.75369
\(991\) 8.04171 0.255453 0.127727 0.991809i \(-0.459232\pi\)
0.127727 + 0.991809i \(0.459232\pi\)
\(992\) 51.8313 1.64565
\(993\) 49.8708 1.58260
\(994\) 25.0536 0.794652
\(995\) 20.1135 0.637641
\(996\) −1.82521 −0.0578339
\(997\) 36.6604 1.16105 0.580523 0.814244i \(-0.302848\pi\)
0.580523 + 0.814244i \(0.302848\pi\)
\(998\) −27.2011 −0.861035
\(999\) 24.8623 0.786607
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 \(a_p\))