Properties

Label 8002.2.a.d.1.4
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.09800 q^{3}\) \(+1.00000 q^{4}\) \(-2.64538 q^{5}\) \(-3.09800 q^{6}\) \(+3.07801 q^{7}\) \(+1.00000 q^{8}\) \(+6.59762 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.09800 q^{3}\) \(+1.00000 q^{4}\) \(-2.64538 q^{5}\) \(-3.09800 q^{6}\) \(+3.07801 q^{7}\) \(+1.00000 q^{8}\) \(+6.59762 q^{9}\) \(-2.64538 q^{10}\) \(-2.21532 q^{11}\) \(-3.09800 q^{12}\) \(+3.83880 q^{13}\) \(+3.07801 q^{14}\) \(+8.19540 q^{15}\) \(+1.00000 q^{16}\) \(+3.02764 q^{17}\) \(+6.59762 q^{18}\) \(-1.43150 q^{19}\) \(-2.64538 q^{20}\) \(-9.53568 q^{21}\) \(-2.21532 q^{22}\) \(-1.68937 q^{23}\) \(-3.09800 q^{24}\) \(+1.99804 q^{25}\) \(+3.83880 q^{26}\) \(-11.1454 q^{27}\) \(+3.07801 q^{28}\) \(-10.1345 q^{29}\) \(+8.19540 q^{30}\) \(-6.75644 q^{31}\) \(+1.00000 q^{32}\) \(+6.86307 q^{33}\) \(+3.02764 q^{34}\) \(-8.14251 q^{35}\) \(+6.59762 q^{36}\) \(+1.29634 q^{37}\) \(-1.43150 q^{38}\) \(-11.8926 q^{39}\) \(-2.64538 q^{40}\) \(-0.898028 q^{41}\) \(-9.53568 q^{42}\) \(-1.79099 q^{43}\) \(-2.21532 q^{44}\) \(-17.4532 q^{45}\) \(-1.68937 q^{46}\) \(+6.29459 q^{47}\) \(-3.09800 q^{48}\) \(+2.47415 q^{49}\) \(+1.99804 q^{50}\) \(-9.37962 q^{51}\) \(+3.83880 q^{52}\) \(+1.20789 q^{53}\) \(-11.1454 q^{54}\) \(+5.86037 q^{55}\) \(+3.07801 q^{56}\) \(+4.43478 q^{57}\) \(-10.1345 q^{58}\) \(+5.14420 q^{59}\) \(+8.19540 q^{60}\) \(-3.71458 q^{61}\) \(-6.75644 q^{62}\) \(+20.3075 q^{63}\) \(+1.00000 q^{64}\) \(-10.1551 q^{65}\) \(+6.86307 q^{66}\) \(+12.9871 q^{67}\) \(+3.02764 q^{68}\) \(+5.23367 q^{69}\) \(-8.14251 q^{70}\) \(+4.67918 q^{71}\) \(+6.59762 q^{72}\) \(+0.143405 q^{73}\) \(+1.29634 q^{74}\) \(-6.18994 q^{75}\) \(-1.43150 q^{76}\) \(-6.81878 q^{77}\) \(-11.8926 q^{78}\) \(+9.02266 q^{79}\) \(-2.64538 q^{80}\) \(+14.7357 q^{81}\) \(-0.898028 q^{82}\) \(+1.16562 q^{83}\) \(-9.53568 q^{84}\) \(-8.00925 q^{85}\) \(-1.79099 q^{86}\) \(+31.3967 q^{87}\) \(-2.21532 q^{88}\) \(-15.4087 q^{89}\) \(-17.4532 q^{90}\) \(+11.8159 q^{91}\) \(-1.68937 q^{92}\) \(+20.9315 q^{93}\) \(+6.29459 q^{94}\) \(+3.78685 q^{95}\) \(-3.09800 q^{96}\) \(+8.67297 q^{97}\) \(+2.47415 q^{98}\) \(-14.6158 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.09800 −1.78863 −0.894316 0.447435i \(-0.852337\pi\)
−0.894316 + 0.447435i \(0.852337\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.64538 −1.18305 −0.591525 0.806286i \(-0.701474\pi\)
−0.591525 + 0.806286i \(0.701474\pi\)
\(6\) −3.09800 −1.26475
\(7\) 3.07801 1.16338 0.581689 0.813411i \(-0.302392\pi\)
0.581689 + 0.813411i \(0.302392\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.59762 2.19921
\(10\) −2.64538 −0.836543
\(11\) −2.21532 −0.667944 −0.333972 0.942583i \(-0.608389\pi\)
−0.333972 + 0.942583i \(0.608389\pi\)
\(12\) −3.09800 −0.894316
\(13\) 3.83880 1.06469 0.532346 0.846527i \(-0.321311\pi\)
0.532346 + 0.846527i \(0.321311\pi\)
\(14\) 3.07801 0.822633
\(15\) 8.19540 2.11604
\(16\) 1.00000 0.250000
\(17\) 3.02764 0.734310 0.367155 0.930160i \(-0.380332\pi\)
0.367155 + 0.930160i \(0.380332\pi\)
\(18\) 6.59762 1.55507
\(19\) −1.43150 −0.328408 −0.164204 0.986426i \(-0.552505\pi\)
−0.164204 + 0.986426i \(0.552505\pi\)
\(20\) −2.64538 −0.591525
\(21\) −9.53568 −2.08086
\(22\) −2.21532 −0.472308
\(23\) −1.68937 −0.352258 −0.176129 0.984367i \(-0.556358\pi\)
−0.176129 + 0.984367i \(0.556358\pi\)
\(24\) −3.09800 −0.632377
\(25\) 1.99804 0.399609
\(26\) 3.83880 0.752851
\(27\) −11.1454 −2.14494
\(28\) 3.07801 0.581689
\(29\) −10.1345 −1.88193 −0.940963 0.338508i \(-0.890078\pi\)
−0.940963 + 0.338508i \(0.890078\pi\)
\(30\) 8.19540 1.49627
\(31\) −6.75644 −1.21349 −0.606746 0.794895i \(-0.707526\pi\)
−0.606746 + 0.794895i \(0.707526\pi\)
\(32\) 1.00000 0.176777
\(33\) 6.86307 1.19471
\(34\) 3.02764 0.519235
\(35\) −8.14251 −1.37634
\(36\) 6.59762 1.09960
\(37\) 1.29634 0.213118 0.106559 0.994306i \(-0.466017\pi\)
0.106559 + 0.994306i \(0.466017\pi\)
\(38\) −1.43150 −0.232219
\(39\) −11.8926 −1.90434
\(40\) −2.64538 −0.418272
\(41\) −0.898028 −0.140248 −0.0701242 0.997538i \(-0.522340\pi\)
−0.0701242 + 0.997538i \(0.522340\pi\)
\(42\) −9.53568 −1.47139
\(43\) −1.79099 −0.273124 −0.136562 0.990632i \(-0.543605\pi\)
−0.136562 + 0.990632i \(0.543605\pi\)
\(44\) −2.21532 −0.333972
\(45\) −17.4532 −2.60177
\(46\) −1.68937 −0.249084
\(47\) 6.29459 0.918160 0.459080 0.888395i \(-0.348179\pi\)
0.459080 + 0.888395i \(0.348179\pi\)
\(48\) −3.09800 −0.447158
\(49\) 2.47415 0.353450
\(50\) 1.99804 0.282566
\(51\) −9.37962 −1.31341
\(52\) 3.83880 0.532346
\(53\) 1.20789 0.165916 0.0829582 0.996553i \(-0.473563\pi\)
0.0829582 + 0.996553i \(0.473563\pi\)
\(54\) −11.1454 −1.51670
\(55\) 5.86037 0.790212
\(56\) 3.07801 0.411316
\(57\) 4.43478 0.587401
\(58\) −10.1345 −1.33072
\(59\) 5.14420 0.669717 0.334859 0.942268i \(-0.391311\pi\)
0.334859 + 0.942268i \(0.391311\pi\)
\(60\) 8.19540 1.05802
\(61\) −3.71458 −0.475603 −0.237802 0.971314i \(-0.576427\pi\)
−0.237802 + 0.971314i \(0.576427\pi\)
\(62\) −6.75644 −0.858069
\(63\) 20.3075 2.55851
\(64\) 1.00000 0.125000
\(65\) −10.1551 −1.25958
\(66\) 6.86307 0.844785
\(67\) 12.9871 1.58663 0.793314 0.608812i \(-0.208354\pi\)
0.793314 + 0.608812i \(0.208354\pi\)
\(68\) 3.02764 0.367155
\(69\) 5.23367 0.630059
\(70\) −8.14251 −0.973216
\(71\) 4.67918 0.555317 0.277658 0.960680i \(-0.410442\pi\)
0.277658 + 0.960680i \(0.410442\pi\)
\(72\) 6.59762 0.777537
\(73\) 0.143405 0.0167842 0.00839212 0.999965i \(-0.497329\pi\)
0.00839212 + 0.999965i \(0.497329\pi\)
\(74\) 1.29634 0.150697
\(75\) −6.18994 −0.714753
\(76\) −1.43150 −0.164204
\(77\) −6.81878 −0.777072
\(78\) −11.8926 −1.34657
\(79\) 9.02266 1.01513 0.507564 0.861614i \(-0.330546\pi\)
0.507564 + 0.861614i \(0.330546\pi\)
\(80\) −2.64538 −0.295763
\(81\) 14.7357 1.63730
\(82\) −0.898028 −0.0991706
\(83\) 1.16562 0.127944 0.0639719 0.997952i \(-0.479623\pi\)
0.0639719 + 0.997952i \(0.479623\pi\)
\(84\) −9.53568 −1.04043
\(85\) −8.00925 −0.868725
\(86\) −1.79099 −0.193128
\(87\) 31.3967 3.36608
\(88\) −2.21532 −0.236154
\(89\) −15.4087 −1.63332 −0.816658 0.577122i \(-0.804176\pi\)
−0.816658 + 0.577122i \(0.804176\pi\)
\(90\) −17.4532 −1.83973
\(91\) 11.8159 1.23864
\(92\) −1.68937 −0.176129
\(93\) 20.9315 2.17049
\(94\) 6.29459 0.649237
\(95\) 3.78685 0.388523
\(96\) −3.09800 −0.316189
\(97\) 8.67297 0.880607 0.440303 0.897849i \(-0.354871\pi\)
0.440303 + 0.897849i \(0.354871\pi\)
\(98\) 2.47415 0.249927
\(99\) −14.6158 −1.46895
\(100\) 1.99804 0.199804
\(101\) −9.91404 −0.986484 −0.493242 0.869892i \(-0.664188\pi\)
−0.493242 + 0.869892i \(0.664188\pi\)
\(102\) −9.37962 −0.928721
\(103\) 9.76468 0.962142 0.481071 0.876682i \(-0.340248\pi\)
0.481071 + 0.876682i \(0.340248\pi\)
\(104\) 3.83880 0.376425
\(105\) 25.2255 2.46176
\(106\) 1.20789 0.117321
\(107\) −3.26718 −0.315850 −0.157925 0.987451i \(-0.550480\pi\)
−0.157925 + 0.987451i \(0.550480\pi\)
\(108\) −11.1454 −1.07247
\(109\) −1.78608 −0.171076 −0.0855379 0.996335i \(-0.527261\pi\)
−0.0855379 + 0.996335i \(0.527261\pi\)
\(110\) 5.86037 0.558764
\(111\) −4.01608 −0.381189
\(112\) 3.07801 0.290845
\(113\) 3.16696 0.297923 0.148961 0.988843i \(-0.452407\pi\)
0.148961 + 0.988843i \(0.452407\pi\)
\(114\) 4.43478 0.415355
\(115\) 4.46902 0.416739
\(116\) −10.1345 −0.940963
\(117\) 25.3269 2.34148
\(118\) 5.14420 0.473562
\(119\) 9.31910 0.854280
\(120\) 8.19540 0.748134
\(121\) −6.09236 −0.553851
\(122\) −3.71458 −0.336302
\(123\) 2.78209 0.250853
\(124\) −6.75644 −0.606746
\(125\) 7.94132 0.710293
\(126\) 20.3075 1.80914
\(127\) −6.81761 −0.604965 −0.302482 0.953155i \(-0.597815\pi\)
−0.302482 + 0.953155i \(0.597815\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.54849 0.488518
\(130\) −10.1551 −0.890661
\(131\) −8.77340 −0.766536 −0.383268 0.923637i \(-0.625201\pi\)
−0.383268 + 0.923637i \(0.625201\pi\)
\(132\) 6.86307 0.597353
\(133\) −4.40616 −0.382062
\(134\) 12.9871 1.12192
\(135\) 29.4839 2.53757
\(136\) 3.02764 0.259618
\(137\) 3.48026 0.297339 0.148669 0.988887i \(-0.452501\pi\)
0.148669 + 0.988887i \(0.452501\pi\)
\(138\) 5.23367 0.445519
\(139\) −8.89572 −0.754525 −0.377262 0.926106i \(-0.623135\pi\)
−0.377262 + 0.926106i \(0.623135\pi\)
\(140\) −8.14251 −0.688168
\(141\) −19.5006 −1.64225
\(142\) 4.67918 0.392668
\(143\) −8.50417 −0.711155
\(144\) 6.59762 0.549802
\(145\) 26.8096 2.22641
\(146\) 0.143405 0.0118683
\(147\) −7.66491 −0.632191
\(148\) 1.29634 0.106559
\(149\) −0.764322 −0.0626157 −0.0313078 0.999510i \(-0.509967\pi\)
−0.0313078 + 0.999510i \(0.509967\pi\)
\(150\) −6.18994 −0.505407
\(151\) 17.3450 1.41152 0.705758 0.708453i \(-0.250606\pi\)
0.705758 + 0.708453i \(0.250606\pi\)
\(152\) −1.43150 −0.116110
\(153\) 19.9752 1.61490
\(154\) −6.81878 −0.549473
\(155\) 17.8734 1.43562
\(156\) −11.8926 −0.952171
\(157\) −15.4446 −1.23262 −0.616308 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(158\) 9.02266 0.717804
\(159\) −3.74205 −0.296764
\(160\) −2.64538 −0.209136
\(161\) −5.19989 −0.409809
\(162\) 14.7357 1.15775
\(163\) −14.3399 −1.12319 −0.561595 0.827412i \(-0.689812\pi\)
−0.561595 + 0.827412i \(0.689812\pi\)
\(164\) −0.898028 −0.0701242
\(165\) −18.1554 −1.41340
\(166\) 1.16562 0.0904700
\(167\) −3.33399 −0.257992 −0.128996 0.991645i \(-0.541175\pi\)
−0.128996 + 0.991645i \(0.541175\pi\)
\(168\) −9.53568 −0.735694
\(169\) 1.73639 0.133569
\(170\) −8.00925 −0.614282
\(171\) −9.44446 −0.722236
\(172\) −1.79099 −0.136562
\(173\) −18.9082 −1.43756 −0.718781 0.695237i \(-0.755300\pi\)
−0.718781 + 0.695237i \(0.755300\pi\)
\(174\) 31.3967 2.38017
\(175\) 6.15000 0.464896
\(176\) −2.21532 −0.166986
\(177\) −15.9367 −1.19788
\(178\) −15.4087 −1.15493
\(179\) −4.73487 −0.353901 −0.176950 0.984220i \(-0.556623\pi\)
−0.176950 + 0.984220i \(0.556623\pi\)
\(180\) −17.4532 −1.30089
\(181\) −14.5692 −1.08292 −0.541462 0.840725i \(-0.682129\pi\)
−0.541462 + 0.840725i \(0.682129\pi\)
\(182\) 11.8159 0.875850
\(183\) 11.5078 0.850679
\(184\) −1.68937 −0.124542
\(185\) −3.42932 −0.252129
\(186\) 20.9315 1.53477
\(187\) −6.70718 −0.490478
\(188\) 6.29459 0.459080
\(189\) −34.3057 −2.49538
\(190\) 3.78685 0.274727
\(191\) −12.7519 −0.922693 −0.461347 0.887220i \(-0.652634\pi\)
−0.461347 + 0.887220i \(0.652634\pi\)
\(192\) −3.09800 −0.223579
\(193\) 19.8366 1.42787 0.713936 0.700211i \(-0.246911\pi\)
0.713936 + 0.700211i \(0.246911\pi\)
\(194\) 8.67297 0.622683
\(195\) 31.4605 2.25293
\(196\) 2.47415 0.176725
\(197\) 13.0385 0.928952 0.464476 0.885586i \(-0.346243\pi\)
0.464476 + 0.885586i \(0.346243\pi\)
\(198\) −14.6158 −1.03870
\(199\) −15.4703 −1.09666 −0.548331 0.836262i \(-0.684737\pi\)
−0.548331 + 0.836262i \(0.684737\pi\)
\(200\) 1.99804 0.141283
\(201\) −40.2341 −2.83790
\(202\) −9.91404 −0.697549
\(203\) −31.1940 −2.18939
\(204\) −9.37962 −0.656705
\(205\) 2.37563 0.165921
\(206\) 9.76468 0.680337
\(207\) −11.1458 −0.774687
\(208\) 3.83880 0.266173
\(209\) 3.17122 0.219358
\(210\) 25.2255 1.74073
\(211\) 19.2436 1.32478 0.662391 0.749158i \(-0.269542\pi\)
0.662391 + 0.749158i \(0.269542\pi\)
\(212\) 1.20789 0.0829582
\(213\) −14.4961 −0.993258
\(214\) −3.26718 −0.223340
\(215\) 4.73785 0.323119
\(216\) −11.1454 −0.758350
\(217\) −20.7964 −1.41175
\(218\) −1.78608 −0.120969
\(219\) −0.444268 −0.0300208
\(220\) 5.86037 0.395106
\(221\) 11.6225 0.781814
\(222\) −4.01608 −0.269541
\(223\) 5.47567 0.366678 0.183339 0.983050i \(-0.441309\pi\)
0.183339 + 0.983050i \(0.441309\pi\)
\(224\) 3.07801 0.205658
\(225\) 13.1823 0.878822
\(226\) 3.16696 0.210663
\(227\) −4.52193 −0.300131 −0.150066 0.988676i \(-0.547949\pi\)
−0.150066 + 0.988676i \(0.547949\pi\)
\(228\) 4.43478 0.293700
\(229\) −0.880741 −0.0582010 −0.0291005 0.999576i \(-0.509264\pi\)
−0.0291005 + 0.999576i \(0.509264\pi\)
\(230\) 4.46902 0.294679
\(231\) 21.1246 1.38990
\(232\) −10.1345 −0.665362
\(233\) 23.6779 1.55119 0.775596 0.631229i \(-0.217449\pi\)
0.775596 + 0.631229i \(0.217449\pi\)
\(234\) 25.3269 1.65567
\(235\) −16.6516 −1.08623
\(236\) 5.14420 0.334859
\(237\) −27.9522 −1.81569
\(238\) 9.31910 0.604067
\(239\) −6.06478 −0.392298 −0.196149 0.980574i \(-0.562844\pi\)
−0.196149 + 0.980574i \(0.562844\pi\)
\(240\) 8.19540 0.529011
\(241\) −18.2169 −1.17346 −0.586728 0.809784i \(-0.699584\pi\)
−0.586728 + 0.809784i \(0.699584\pi\)
\(242\) −6.09236 −0.391631
\(243\) −12.2150 −0.783591
\(244\) −3.71458 −0.237802
\(245\) −6.54506 −0.418149
\(246\) 2.78209 0.177380
\(247\) −5.49523 −0.349653
\(248\) −6.75644 −0.429034
\(249\) −3.61111 −0.228845
\(250\) 7.94132 0.502253
\(251\) −16.1799 −1.02126 −0.510632 0.859800i \(-0.670588\pi\)
−0.510632 + 0.859800i \(0.670588\pi\)
\(252\) 20.3075 1.27925
\(253\) 3.74249 0.235288
\(254\) −6.81761 −0.427775
\(255\) 24.8127 1.55383
\(256\) 1.00000 0.0625000
\(257\) −20.5296 −1.28060 −0.640301 0.768124i \(-0.721191\pi\)
−0.640301 + 0.768124i \(0.721191\pi\)
\(258\) 5.54849 0.345434
\(259\) 3.99016 0.247936
\(260\) −10.1551 −0.629792
\(261\) −66.8635 −4.13874
\(262\) −8.77340 −0.542023
\(263\) 14.9555 0.922193 0.461096 0.887350i \(-0.347456\pi\)
0.461096 + 0.887350i \(0.347456\pi\)
\(264\) 6.86307 0.422393
\(265\) −3.19533 −0.196288
\(266\) −4.40616 −0.270159
\(267\) 47.7361 2.92140
\(268\) 12.9871 0.793314
\(269\) −19.7665 −1.20519 −0.602593 0.798049i \(-0.705866\pi\)
−0.602593 + 0.798049i \(0.705866\pi\)
\(270\) 29.4839 1.79433
\(271\) 6.34465 0.385410 0.192705 0.981257i \(-0.438274\pi\)
0.192705 + 0.981257i \(0.438274\pi\)
\(272\) 3.02764 0.183577
\(273\) −36.6056 −2.21547
\(274\) 3.48026 0.210250
\(275\) −4.42631 −0.266916
\(276\) 5.23367 0.315030
\(277\) 2.95981 0.177838 0.0889189 0.996039i \(-0.471659\pi\)
0.0889189 + 0.996039i \(0.471659\pi\)
\(278\) −8.89572 −0.533530
\(279\) −44.5764 −2.66872
\(280\) −8.14251 −0.486608
\(281\) −3.84944 −0.229638 −0.114819 0.993386i \(-0.536629\pi\)
−0.114819 + 0.993386i \(0.536629\pi\)
\(282\) −19.5006 −1.16125
\(283\) 5.16757 0.307180 0.153590 0.988135i \(-0.450916\pi\)
0.153590 + 0.988135i \(0.450916\pi\)
\(284\) 4.67918 0.277658
\(285\) −11.7317 −0.694925
\(286\) −8.50417 −0.502862
\(287\) −2.76414 −0.163162
\(288\) 6.59762 0.388768
\(289\) −7.83342 −0.460789
\(290\) 26.8096 1.57431
\(291\) −26.8689 −1.57508
\(292\) 0.143405 0.00839212
\(293\) −17.0851 −0.998121 −0.499060 0.866567i \(-0.666321\pi\)
−0.499060 + 0.866567i \(0.666321\pi\)
\(294\) −7.66491 −0.447027
\(295\) −13.6084 −0.792309
\(296\) 1.29634 0.0753484
\(297\) 24.6907 1.43270
\(298\) −0.764322 −0.0442760
\(299\) −6.48515 −0.375046
\(300\) −6.18994 −0.357377
\(301\) −5.51269 −0.317746
\(302\) 17.3450 0.998093
\(303\) 30.7137 1.76446
\(304\) −1.43150 −0.0821019
\(305\) 9.82648 0.562662
\(306\) 19.9752 1.14191
\(307\) 0.190275 0.0108596 0.00542978 0.999985i \(-0.498272\pi\)
0.00542978 + 0.999985i \(0.498272\pi\)
\(308\) −6.81878 −0.388536
\(309\) −30.2510 −1.72092
\(310\) 17.8734 1.01514
\(311\) −17.7303 −1.00539 −0.502695 0.864464i \(-0.667658\pi\)
−0.502695 + 0.864464i \(0.667658\pi\)
\(312\) −11.8926 −0.673287
\(313\) 30.6130 1.73035 0.865175 0.501470i \(-0.167207\pi\)
0.865175 + 0.501470i \(0.167207\pi\)
\(314\) −15.4446 −0.871591
\(315\) −53.7212 −3.02685
\(316\) 9.02266 0.507564
\(317\) −31.6948 −1.78016 −0.890080 0.455804i \(-0.849352\pi\)
−0.890080 + 0.455804i \(0.849352\pi\)
\(318\) −3.74205 −0.209843
\(319\) 22.4511 1.25702
\(320\) −2.64538 −0.147881
\(321\) 10.1217 0.564940
\(322\) −5.19989 −0.289779
\(323\) −4.33405 −0.241153
\(324\) 14.7357 0.818651
\(325\) 7.67009 0.425460
\(326\) −14.3399 −0.794215
\(327\) 5.53329 0.305992
\(328\) −0.898028 −0.0495853
\(329\) 19.3748 1.06817
\(330\) −18.1554 −0.999424
\(331\) 25.3499 1.39336 0.696678 0.717384i \(-0.254661\pi\)
0.696678 + 0.717384i \(0.254661\pi\)
\(332\) 1.16562 0.0639719
\(333\) 8.55278 0.468689
\(334\) −3.33399 −0.182428
\(335\) −34.3559 −1.87706
\(336\) −9.53568 −0.520214
\(337\) −29.2304 −1.59228 −0.796140 0.605113i \(-0.793128\pi\)
−0.796140 + 0.605113i \(0.793128\pi\)
\(338\) 1.73639 0.0944474
\(339\) −9.81126 −0.532874
\(340\) −8.00925 −0.434363
\(341\) 14.9677 0.810545
\(342\) −9.44446 −0.510698
\(343\) −13.9306 −0.752183
\(344\) −1.79099 −0.0965638
\(345\) −13.8450 −0.745392
\(346\) −18.9082 −1.01651
\(347\) −7.35068 −0.394605 −0.197303 0.980343i \(-0.563218\pi\)
−0.197303 + 0.980343i \(0.563218\pi\)
\(348\) 31.3967 1.68304
\(349\) −2.43187 −0.130175 −0.0650876 0.997880i \(-0.520733\pi\)
−0.0650876 + 0.997880i \(0.520733\pi\)
\(350\) 6.15000 0.328731
\(351\) −42.7851 −2.28370
\(352\) −2.21532 −0.118077
\(353\) −1.05006 −0.0558890 −0.0279445 0.999609i \(-0.508896\pi\)
−0.0279445 + 0.999609i \(0.508896\pi\)
\(354\) −15.9367 −0.847028
\(355\) −12.3782 −0.656968
\(356\) −15.4087 −0.816658
\(357\) −28.8706 −1.52799
\(358\) −4.73487 −0.250246
\(359\) −8.54944 −0.451222 −0.225611 0.974217i \(-0.572438\pi\)
−0.225611 + 0.974217i \(0.572438\pi\)
\(360\) −17.4532 −0.919865
\(361\) −16.9508 −0.892148
\(362\) −14.5692 −0.765742
\(363\) 18.8741 0.990635
\(364\) 11.8159 0.619320
\(365\) −0.379360 −0.0198566
\(366\) 11.5078 0.601521
\(367\) −10.4636 −0.546197 −0.273099 0.961986i \(-0.588049\pi\)
−0.273099 + 0.961986i \(0.588049\pi\)
\(368\) −1.68937 −0.0880644
\(369\) −5.92484 −0.308435
\(370\) −3.42932 −0.178282
\(371\) 3.71790 0.193024
\(372\) 20.9315 1.08525
\(373\) 14.8133 0.767002 0.383501 0.923540i \(-0.374718\pi\)
0.383501 + 0.923540i \(0.374718\pi\)
\(374\) −6.70718 −0.346820
\(375\) −24.6022 −1.27045
\(376\) 6.29459 0.324618
\(377\) −38.9043 −2.00367
\(378\) −34.3057 −1.76450
\(379\) −14.6830 −0.754215 −0.377108 0.926169i \(-0.623081\pi\)
−0.377108 + 0.926169i \(0.623081\pi\)
\(380\) 3.78685 0.194261
\(381\) 21.1210 1.08206
\(382\) −12.7519 −0.652443
\(383\) −6.26003 −0.319872 −0.159936 0.987127i \(-0.551129\pi\)
−0.159936 + 0.987127i \(0.551129\pi\)
\(384\) −3.09800 −0.158094
\(385\) 18.0383 0.919315
\(386\) 19.8366 1.00966
\(387\) −11.8163 −0.600655
\(388\) 8.67297 0.440303
\(389\) −3.62073 −0.183578 −0.0917892 0.995778i \(-0.529259\pi\)
−0.0917892 + 0.995778i \(0.529259\pi\)
\(390\) 31.4605 1.59306
\(391\) −5.11479 −0.258666
\(392\) 2.47415 0.124963
\(393\) 27.1800 1.37105
\(394\) 13.0385 0.656869
\(395\) −23.8684 −1.20095
\(396\) −14.6158 −0.734473
\(397\) 22.6882 1.13869 0.569343 0.822100i \(-0.307198\pi\)
0.569343 + 0.822100i \(0.307198\pi\)
\(398\) −15.4703 −0.775457
\(399\) 13.6503 0.683369
\(400\) 1.99804 0.0999022
\(401\) 9.17077 0.457966 0.228983 0.973430i \(-0.426460\pi\)
0.228983 + 0.973430i \(0.426460\pi\)
\(402\) −40.2341 −2.00669
\(403\) −25.9366 −1.29200
\(404\) −9.91404 −0.493242
\(405\) −38.9816 −1.93701
\(406\) −31.1940 −1.54813
\(407\) −2.87182 −0.142351
\(408\) −9.37962 −0.464361
\(409\) −10.1575 −0.502257 −0.251129 0.967954i \(-0.580802\pi\)
−0.251129 + 0.967954i \(0.580802\pi\)
\(410\) 2.37563 0.117324
\(411\) −10.7819 −0.531830
\(412\) 9.76468 0.481071
\(413\) 15.8339 0.779135
\(414\) −11.1458 −0.547786
\(415\) −3.08352 −0.151364
\(416\) 3.83880 0.188213
\(417\) 27.5590 1.34957
\(418\) 3.17122 0.155110
\(419\) −18.3235 −0.895160 −0.447580 0.894244i \(-0.647714\pi\)
−0.447580 + 0.894244i \(0.647714\pi\)
\(420\) 25.2255 1.23088
\(421\) 4.48495 0.218583 0.109291 0.994010i \(-0.465142\pi\)
0.109291 + 0.994010i \(0.465142\pi\)
\(422\) 19.2436 0.936763
\(423\) 41.5293 2.01922
\(424\) 1.20789 0.0586603
\(425\) 6.04935 0.293437
\(426\) −14.4961 −0.702339
\(427\) −11.4335 −0.553306
\(428\) −3.26718 −0.157925
\(429\) 26.3459 1.27199
\(430\) 4.73785 0.228480
\(431\) 17.7456 0.854774 0.427387 0.904069i \(-0.359434\pi\)
0.427387 + 0.904069i \(0.359434\pi\)
\(432\) −11.1454 −0.536235
\(433\) −22.9322 −1.10205 −0.551026 0.834488i \(-0.685764\pi\)
−0.551026 + 0.834488i \(0.685764\pi\)
\(434\) −20.7964 −0.998259
\(435\) −83.0561 −3.98224
\(436\) −1.78608 −0.0855379
\(437\) 2.41832 0.115684
\(438\) −0.444268 −0.0212279
\(439\) 4.53752 0.216564 0.108282 0.994120i \(-0.465465\pi\)
0.108282 + 0.994120i \(0.465465\pi\)
\(440\) 5.86037 0.279382
\(441\) 16.3235 0.777308
\(442\) 11.6225 0.552826
\(443\) 8.15917 0.387654 0.193827 0.981036i \(-0.437910\pi\)
0.193827 + 0.981036i \(0.437910\pi\)
\(444\) −4.01608 −0.190595
\(445\) 40.7618 1.93230
\(446\) 5.47567 0.259281
\(447\) 2.36787 0.111996
\(448\) 3.07801 0.145422
\(449\) −15.4823 −0.730653 −0.365327 0.930879i \(-0.619043\pi\)
−0.365327 + 0.930879i \(0.619043\pi\)
\(450\) 13.1823 0.621421
\(451\) 1.98942 0.0936781
\(452\) 3.16696 0.148961
\(453\) −53.7349 −2.52468
\(454\) −4.52193 −0.212225
\(455\) −31.2575 −1.46537
\(456\) 4.43478 0.207678
\(457\) 3.48455 0.163000 0.0815002 0.996673i \(-0.474029\pi\)
0.0815002 + 0.996673i \(0.474029\pi\)
\(458\) −0.880741 −0.0411543
\(459\) −33.7443 −1.57505
\(460\) 4.46902 0.208369
\(461\) 23.8020 1.10857 0.554284 0.832327i \(-0.312992\pi\)
0.554284 + 0.832327i \(0.312992\pi\)
\(462\) 21.1246 0.982805
\(463\) 30.6752 1.42560 0.712798 0.701369i \(-0.247428\pi\)
0.712798 + 0.701369i \(0.247428\pi\)
\(464\) −10.1345 −0.470482
\(465\) −55.3717 −2.56780
\(466\) 23.6779 1.09686
\(467\) 10.9114 0.504921 0.252461 0.967607i \(-0.418760\pi\)
0.252461 + 0.967607i \(0.418760\pi\)
\(468\) 25.3269 1.17074
\(469\) 39.9745 1.84585
\(470\) −16.6516 −0.768080
\(471\) 47.8475 2.20470
\(472\) 5.14420 0.236781
\(473\) 3.96762 0.182431
\(474\) −27.9522 −1.28389
\(475\) −2.86019 −0.131235
\(476\) 9.31910 0.427140
\(477\) 7.96920 0.364884
\(478\) −6.06478 −0.277397
\(479\) 16.6553 0.760999 0.380500 0.924781i \(-0.375752\pi\)
0.380500 + 0.924781i \(0.375752\pi\)
\(480\) 8.19540 0.374067
\(481\) 4.97641 0.226905
\(482\) −18.2169 −0.829759
\(483\) 16.1093 0.732997
\(484\) −6.09236 −0.276925
\(485\) −22.9433 −1.04180
\(486\) −12.2150 −0.554083
\(487\) −6.46773 −0.293081 −0.146540 0.989205i \(-0.546814\pi\)
−0.146540 + 0.989205i \(0.546814\pi\)
\(488\) −3.71458 −0.168151
\(489\) 44.4251 2.00897
\(490\) −6.54506 −0.295676
\(491\) −19.4399 −0.877312 −0.438656 0.898655i \(-0.644545\pi\)
−0.438656 + 0.898655i \(0.644545\pi\)
\(492\) 2.78209 0.125426
\(493\) −30.6835 −1.38192
\(494\) −5.49523 −0.247242
\(495\) 38.6645 1.73784
\(496\) −6.75644 −0.303373
\(497\) 14.4026 0.646044
\(498\) −3.61111 −0.161818
\(499\) 1.83225 0.0820226 0.0410113 0.999159i \(-0.486942\pi\)
0.0410113 + 0.999159i \(0.486942\pi\)
\(500\) 7.94132 0.355147
\(501\) 10.3287 0.461452
\(502\) −16.1799 −0.722142
\(503\) 20.7889 0.926932 0.463466 0.886115i \(-0.346606\pi\)
0.463466 + 0.886115i \(0.346606\pi\)
\(504\) 20.3075 0.904570
\(505\) 26.2264 1.16706
\(506\) 3.74249 0.166374
\(507\) −5.37935 −0.238905
\(508\) −6.81761 −0.302482
\(509\) 8.26477 0.366330 0.183165 0.983082i \(-0.441366\pi\)
0.183165 + 0.983082i \(0.441366\pi\)
\(510\) 24.8127 1.09872
\(511\) 0.441401 0.0195264
\(512\) 1.00000 0.0441942
\(513\) 15.9546 0.704414
\(514\) −20.5296 −0.905523
\(515\) −25.8313 −1.13826
\(516\) 5.54849 0.244259
\(517\) −13.9445 −0.613279
\(518\) 3.99016 0.175318
\(519\) 58.5776 2.57127
\(520\) −10.1551 −0.445330
\(521\) 18.5716 0.813635 0.406818 0.913509i \(-0.366638\pi\)
0.406818 + 0.913509i \(0.366638\pi\)
\(522\) −66.8635 −2.92653
\(523\) 34.7737 1.52055 0.760275 0.649601i \(-0.225064\pi\)
0.760275 + 0.649601i \(0.225064\pi\)
\(524\) −8.77340 −0.383268
\(525\) −19.0527 −0.831528
\(526\) 14.9555 0.652089
\(527\) −20.4560 −0.891079
\(528\) 6.86307 0.298677
\(529\) −20.1460 −0.875915
\(530\) −3.19533 −0.138796
\(531\) 33.9394 1.47285
\(532\) −4.40616 −0.191031
\(533\) −3.44735 −0.149321
\(534\) 47.7361 2.06574
\(535\) 8.64294 0.373667
\(536\) 12.9871 0.560958
\(537\) 14.6686 0.632998
\(538\) −19.7665 −0.852196
\(539\) −5.48103 −0.236085
\(540\) 29.4839 1.26879
\(541\) 30.7539 1.32221 0.661107 0.750292i \(-0.270087\pi\)
0.661107 + 0.750292i \(0.270087\pi\)
\(542\) 6.34465 0.272526
\(543\) 45.1356 1.93695
\(544\) 3.02764 0.129809
\(545\) 4.72488 0.202391
\(546\) −36.6056 −1.56657
\(547\) 1.70461 0.0728840 0.0364420 0.999336i \(-0.488398\pi\)
0.0364420 + 0.999336i \(0.488398\pi\)
\(548\) 3.48026 0.148669
\(549\) −24.5074 −1.04595
\(550\) −4.42631 −0.188738
\(551\) 14.5075 0.618039
\(552\) 5.23367 0.222760
\(553\) 27.7718 1.18098
\(554\) 2.95981 0.125750
\(555\) 10.6241 0.450966
\(556\) −8.89572 −0.377262
\(557\) −10.6522 −0.451349 −0.225675 0.974203i \(-0.572459\pi\)
−0.225675 + 0.974203i \(0.572459\pi\)
\(558\) −44.5764 −1.88707
\(559\) −6.87526 −0.290792
\(560\) −8.14251 −0.344084
\(561\) 20.7789 0.877285
\(562\) −3.84944 −0.162379
\(563\) −43.3181 −1.82564 −0.912820 0.408362i \(-0.866100\pi\)
−0.912820 + 0.408362i \(0.866100\pi\)
\(564\) −19.5006 −0.821125
\(565\) −8.37783 −0.352458
\(566\) 5.16757 0.217209
\(567\) 45.3567 1.90480
\(568\) 4.67918 0.196334
\(569\) 13.8179 0.579277 0.289639 0.957136i \(-0.406465\pi\)
0.289639 + 0.957136i \(0.406465\pi\)
\(570\) −11.7317 −0.491386
\(571\) −8.70415 −0.364257 −0.182129 0.983275i \(-0.558299\pi\)
−0.182129 + 0.983275i \(0.558299\pi\)
\(572\) −8.50417 −0.355577
\(573\) 39.5053 1.65036
\(574\) −2.76414 −0.115373
\(575\) −3.37543 −0.140765
\(576\) 6.59762 0.274901
\(577\) −34.0580 −1.41785 −0.708926 0.705283i \(-0.750820\pi\)
−0.708926 + 0.705283i \(0.750820\pi\)
\(578\) −7.83342 −0.325827
\(579\) −61.4540 −2.55394
\(580\) 26.8096 1.11321
\(581\) 3.58780 0.148847
\(582\) −26.8689 −1.11375
\(583\) −2.67586 −0.110823
\(584\) 0.143405 0.00593413
\(585\) −66.9994 −2.77009
\(586\) −17.0851 −0.705778
\(587\) −18.7402 −0.773492 −0.386746 0.922186i \(-0.626401\pi\)
−0.386746 + 0.922186i \(0.626401\pi\)
\(588\) −7.66491 −0.316096
\(589\) 9.67182 0.398520
\(590\) −13.6084 −0.560247
\(591\) −40.3932 −1.66155
\(592\) 1.29634 0.0532794
\(593\) 27.5562 1.13160 0.565798 0.824544i \(-0.308568\pi\)
0.565798 + 0.824544i \(0.308568\pi\)
\(594\) 24.6907 1.01307
\(595\) −24.6526 −1.01066
\(596\) −0.764322 −0.0313078
\(597\) 47.9271 1.96152
\(598\) −6.48515 −0.265197
\(599\) −8.96083 −0.366130 −0.183065 0.983101i \(-0.558602\pi\)
−0.183065 + 0.983101i \(0.558602\pi\)
\(600\) −6.18994 −0.252703
\(601\) −29.3653 −1.19783 −0.598917 0.800811i \(-0.704402\pi\)
−0.598917 + 0.800811i \(0.704402\pi\)
\(602\) −5.51269 −0.224680
\(603\) 85.6840 3.48932
\(604\) 17.3450 0.705758
\(605\) 16.1166 0.655233
\(606\) 30.7137 1.24766
\(607\) −9.28330 −0.376797 −0.188399 0.982093i \(-0.560330\pi\)
−0.188399 + 0.982093i \(0.560330\pi\)
\(608\) −1.43150 −0.0580548
\(609\) 96.6392 3.91602
\(610\) 9.82648 0.397862
\(611\) 24.1637 0.977557
\(612\) 19.9752 0.807449
\(613\) 4.85967 0.196280 0.0981402 0.995173i \(-0.468711\pi\)
0.0981402 + 0.995173i \(0.468711\pi\)
\(614\) 0.190275 0.00767886
\(615\) −7.35970 −0.296772
\(616\) −6.81878 −0.274736
\(617\) −24.5197 −0.987128 −0.493564 0.869710i \(-0.664306\pi\)
−0.493564 + 0.869710i \(0.664306\pi\)
\(618\) −30.2510 −1.21687
\(619\) −47.8048 −1.92144 −0.960718 0.277528i \(-0.910485\pi\)
−0.960718 + 0.277528i \(0.910485\pi\)
\(620\) 17.8734 0.717812
\(621\) 18.8287 0.755571
\(622\) −17.7303 −0.710919
\(623\) −47.4281 −1.90017
\(624\) −11.8926 −0.476086
\(625\) −30.9980 −1.23992
\(626\) 30.6130 1.22354
\(627\) −9.82445 −0.392351
\(628\) −15.4446 −0.616308
\(629\) 3.92486 0.156494
\(630\) −53.7212 −2.14030
\(631\) −40.4150 −1.60890 −0.804449 0.594022i \(-0.797539\pi\)
−0.804449 + 0.594022i \(0.797539\pi\)
\(632\) 9.02266 0.358902
\(633\) −59.6166 −2.36955
\(634\) −31.6948 −1.25876
\(635\) 18.0352 0.715704
\(636\) −3.74205 −0.148382
\(637\) 9.49776 0.376315
\(638\) 22.4511 0.888849
\(639\) 30.8715 1.22126
\(640\) −2.64538 −0.104568
\(641\) −46.6431 −1.84229 −0.921146 0.389217i \(-0.872746\pi\)
−0.921146 + 0.389217i \(0.872746\pi\)
\(642\) 10.1217 0.399473
\(643\) 33.0587 1.30371 0.651855 0.758344i \(-0.273991\pi\)
0.651855 + 0.758344i \(0.273991\pi\)
\(644\) −5.19989 −0.204904
\(645\) −14.6779 −0.577941
\(646\) −4.33405 −0.170521
\(647\) −20.8734 −0.820618 −0.410309 0.911947i \(-0.634579\pi\)
−0.410309 + 0.911947i \(0.634579\pi\)
\(648\) 14.7357 0.578873
\(649\) −11.3960 −0.447334
\(650\) 7.67009 0.300846
\(651\) 64.4273 2.52510
\(652\) −14.3399 −0.561595
\(653\) 11.1065 0.434632 0.217316 0.976101i \(-0.430270\pi\)
0.217316 + 0.976101i \(0.430270\pi\)
\(654\) 5.53329 0.216369
\(655\) 23.2090 0.906850
\(656\) −0.898028 −0.0350621
\(657\) 0.946129 0.0369120
\(658\) 19.3748 0.755308
\(659\) −27.0585 −1.05405 −0.527026 0.849849i \(-0.676693\pi\)
−0.527026 + 0.849849i \(0.676693\pi\)
\(660\) −18.1554 −0.706699
\(661\) 9.69117 0.376943 0.188471 0.982079i \(-0.439647\pi\)
0.188471 + 0.982079i \(0.439647\pi\)
\(662\) 25.3499 0.985252
\(663\) −36.0065 −1.39838
\(664\) 1.16562 0.0452350
\(665\) 11.6560 0.451999
\(666\) 8.55278 0.331414
\(667\) 17.1209 0.662923
\(668\) −3.33399 −0.128996
\(669\) −16.9636 −0.655852
\(670\) −34.3559 −1.32728
\(671\) 8.22898 0.317676
\(672\) −9.53568 −0.367847
\(673\) −30.9230 −1.19199 −0.595996 0.802987i \(-0.703243\pi\)
−0.595996 + 0.802987i \(0.703243\pi\)
\(674\) −29.2304 −1.12591
\(675\) −22.2691 −0.857136
\(676\) 1.73639 0.0667844
\(677\) −39.9586 −1.53573 −0.767867 0.640610i \(-0.778682\pi\)
−0.767867 + 0.640610i \(0.778682\pi\)
\(678\) −9.81126 −0.376799
\(679\) 26.6955 1.02448
\(680\) −8.00925 −0.307141
\(681\) 14.0090 0.536825
\(682\) 14.9677 0.573142
\(683\) −27.0331 −1.03439 −0.517197 0.855867i \(-0.673024\pi\)
−0.517197 + 0.855867i \(0.673024\pi\)
\(684\) −9.44446 −0.361118
\(685\) −9.20662 −0.351767
\(686\) −13.9306 −0.531874
\(687\) 2.72854 0.104100
\(688\) −1.79099 −0.0682809
\(689\) 4.63685 0.176650
\(690\) −13.8450 −0.527072
\(691\) 21.2382 0.807941 0.403970 0.914772i \(-0.367630\pi\)
0.403970 + 0.914772i \(0.367630\pi\)
\(692\) −18.9082 −0.718781
\(693\) −44.9877 −1.70894
\(694\) −7.35068 −0.279028
\(695\) 23.5326 0.892641
\(696\) 31.3967 1.19009
\(697\) −2.71890 −0.102986
\(698\) −2.43187 −0.0920478
\(699\) −73.3543 −2.77451
\(700\) 6.15000 0.232448
\(701\) 1.88429 0.0711687 0.0355844 0.999367i \(-0.488671\pi\)
0.0355844 + 0.999367i \(0.488671\pi\)
\(702\) −42.7851 −1.61482
\(703\) −1.85571 −0.0699895
\(704\) −2.21532 −0.0834930
\(705\) 51.5866 1.94286
\(706\) −1.05006 −0.0395195
\(707\) −30.5155 −1.14765
\(708\) −15.9367 −0.598939
\(709\) 5.99391 0.225106 0.112553 0.993646i \(-0.464097\pi\)
0.112553 + 0.993646i \(0.464097\pi\)
\(710\) −12.3782 −0.464546
\(711\) 59.5280 2.23248
\(712\) −15.4087 −0.577465
\(713\) 11.4141 0.427462
\(714\) −28.8706 −1.08045
\(715\) 22.4968 0.841332
\(716\) −4.73487 −0.176950
\(717\) 18.7887 0.701677
\(718\) −8.54944 −0.319062
\(719\) −35.1656 −1.31146 −0.655729 0.754997i \(-0.727638\pi\)
−0.655729 + 0.754997i \(0.727638\pi\)
\(720\) −17.4532 −0.650443
\(721\) 30.0558 1.11934
\(722\) −16.9508 −0.630844
\(723\) 56.4361 2.09888
\(724\) −14.5692 −0.541462
\(725\) −20.2491 −0.752034
\(726\) 18.8741 0.700485
\(727\) 36.5475 1.35547 0.677736 0.735306i \(-0.262961\pi\)
0.677736 + 0.735306i \(0.262961\pi\)
\(728\) 11.8159 0.437925
\(729\) −6.36511 −0.235745
\(730\) −0.379360 −0.0140407
\(731\) −5.42247 −0.200557
\(732\) 11.5078 0.425339
\(733\) −10.3520 −0.382359 −0.191179 0.981555i \(-0.561231\pi\)
−0.191179 + 0.981555i \(0.561231\pi\)
\(734\) −10.4636 −0.386220
\(735\) 20.2766 0.747914
\(736\) −1.68937 −0.0622709
\(737\) −28.7706 −1.05978
\(738\) −5.92484 −0.218097
\(739\) 4.25377 0.156477 0.0782387 0.996935i \(-0.475070\pi\)
0.0782387 + 0.996935i \(0.475070\pi\)
\(740\) −3.42932 −0.126064
\(741\) 17.0242 0.625401
\(742\) 3.71790 0.136488
\(743\) −10.4303 −0.382649 −0.191325 0.981527i \(-0.561278\pi\)
−0.191325 + 0.981527i \(0.561278\pi\)
\(744\) 20.9315 0.767385
\(745\) 2.02192 0.0740775
\(746\) 14.8133 0.542352
\(747\) 7.69034 0.281375
\(748\) −6.70718 −0.245239
\(749\) −10.0564 −0.367454
\(750\) −24.6022 −0.898346
\(751\) −24.0984 −0.879362 −0.439681 0.898154i \(-0.644908\pi\)
−0.439681 + 0.898154i \(0.644908\pi\)
\(752\) 6.29459 0.229540
\(753\) 50.1252 1.82666
\(754\) −38.9043 −1.41681
\(755\) −45.8842 −1.66990
\(756\) −34.3057 −1.24769
\(757\) −42.6798 −1.55123 −0.775613 0.631209i \(-0.782559\pi\)
−0.775613 + 0.631209i \(0.782559\pi\)
\(758\) −14.6830 −0.533311
\(759\) −11.5942 −0.420844
\(760\) 3.78685 0.137364
\(761\) 2.50128 0.0906712 0.0453356 0.998972i \(-0.485564\pi\)
0.0453356 + 0.998972i \(0.485564\pi\)
\(762\) 21.1210 0.765132
\(763\) −5.49759 −0.199026
\(764\) −12.7519 −0.461347
\(765\) −52.8420 −1.91051
\(766\) −6.26003 −0.226184
\(767\) 19.7475 0.713043
\(768\) −3.09800 −0.111790
\(769\) 21.7036 0.782651 0.391326 0.920252i \(-0.372017\pi\)
0.391326 + 0.920252i \(0.372017\pi\)
\(770\) 18.0383 0.650054
\(771\) 63.6008 2.29053
\(772\) 19.8366 0.713936
\(773\) −29.8572 −1.07389 −0.536944 0.843618i \(-0.680421\pi\)
−0.536944 + 0.843618i \(0.680421\pi\)
\(774\) −11.8163 −0.424727
\(775\) −13.4997 −0.484922
\(776\) 8.67297 0.311342
\(777\) −12.3615 −0.443467
\(778\) −3.62073 −0.129810
\(779\) 1.28552 0.0460587
\(780\) 31.4605 1.12647
\(781\) −10.3659 −0.370921
\(782\) −5.11479 −0.182905
\(783\) 112.953 4.03662
\(784\) 2.47415 0.0883624
\(785\) 40.8569 1.45825
\(786\) 27.1800 0.969479
\(787\) −13.7826 −0.491295 −0.245648 0.969359i \(-0.579001\pi\)
−0.245648 + 0.969359i \(0.579001\pi\)
\(788\) 13.0385 0.464476
\(789\) −46.3320 −1.64946
\(790\) −23.8684 −0.849198
\(791\) 9.74794 0.346597
\(792\) −14.6158 −0.519351
\(793\) −14.2595 −0.506371
\(794\) 22.6882 0.805173
\(795\) 9.89914 0.351086
\(796\) −15.4703 −0.548331
\(797\) −26.9481 −0.954551 −0.477276 0.878754i \(-0.658376\pi\)
−0.477276 + 0.878754i \(0.658376\pi\)
\(798\) 13.6503 0.483215
\(799\) 19.0577 0.674213
\(800\) 1.99804 0.0706415
\(801\) −101.661 −3.59200
\(802\) 9.17077 0.323831
\(803\) −0.317687 −0.0112109
\(804\) −40.2341 −1.41895
\(805\) 13.7557 0.484825
\(806\) −25.9366 −0.913579
\(807\) 61.2367 2.15564
\(808\) −9.91404 −0.348775
\(809\) −11.2677 −0.396152 −0.198076 0.980187i \(-0.563469\pi\)
−0.198076 + 0.980187i \(0.563469\pi\)
\(810\) −38.9816 −1.36967
\(811\) −50.8623 −1.78602 −0.893008 0.450041i \(-0.851409\pi\)
−0.893008 + 0.450041i \(0.851409\pi\)
\(812\) −31.1940 −1.09470
\(813\) −19.6558 −0.689357
\(814\) −2.87182 −0.100657
\(815\) 37.9346 1.32879
\(816\) −9.37962 −0.328353
\(817\) 2.56380 0.0896959
\(818\) −10.1575 −0.355150
\(819\) 77.9566 2.72402
\(820\) 2.37563 0.0829605
\(821\) −10.9553 −0.382342 −0.191171 0.981557i \(-0.561229\pi\)
−0.191171 + 0.981557i \(0.561229\pi\)
\(822\) −10.7819 −0.376061
\(823\) 12.0717 0.420793 0.210396 0.977616i \(-0.432525\pi\)
0.210396 + 0.977616i \(0.432525\pi\)
\(824\) 9.76468 0.340169
\(825\) 13.7127 0.477415
\(826\) 15.8339 0.550931
\(827\) 17.0181 0.591778 0.295889 0.955222i \(-0.404384\pi\)
0.295889 + 0.955222i \(0.404384\pi\)
\(828\) −11.1458 −0.387343
\(829\) −8.16156 −0.283463 −0.141731 0.989905i \(-0.545267\pi\)
−0.141731 + 0.989905i \(0.545267\pi\)
\(830\) −3.08352 −0.107031
\(831\) −9.16950 −0.318086
\(832\) 3.83880 0.133086
\(833\) 7.49082 0.259541
\(834\) 27.5590 0.954288
\(835\) 8.81967 0.305217
\(836\) 3.17122 0.109679
\(837\) 75.3034 2.60287
\(838\) −18.3235 −0.632974
\(839\) −42.1621 −1.45560 −0.727799 0.685791i \(-0.759457\pi\)
−0.727799 + 0.685791i \(0.759457\pi\)
\(840\) 25.2255 0.870363
\(841\) 73.7078 2.54165
\(842\) 4.48495 0.154561
\(843\) 11.9256 0.410738
\(844\) 19.2436 0.662391
\(845\) −4.59342 −0.158019
\(846\) 41.5293 1.42781
\(847\) −18.7523 −0.644338
\(848\) 1.20789 0.0414791
\(849\) −16.0091 −0.549432
\(850\) 6.04935 0.207491
\(851\) −2.19000 −0.0750723
\(852\) −14.4961 −0.496629
\(853\) −55.9138 −1.91445 −0.957225 0.289343i \(-0.906563\pi\)
−0.957225 + 0.289343i \(0.906563\pi\)
\(854\) −11.4335 −0.391247
\(855\) 24.9842 0.854442
\(856\) −3.26718 −0.111670
\(857\) −5.65385 −0.193132 −0.0965659 0.995327i \(-0.530786\pi\)
−0.0965659 + 0.995327i \(0.530786\pi\)
\(858\) 26.3459 0.899436
\(859\) −26.3075 −0.897601 −0.448800 0.893632i \(-0.648149\pi\)
−0.448800 + 0.893632i \(0.648149\pi\)
\(860\) 4.73785 0.161559
\(861\) 8.56331 0.291837
\(862\) 17.7456 0.604416
\(863\) 57.3154 1.95104 0.975519 0.219916i \(-0.0705783\pi\)
0.975519 + 0.219916i \(0.0705783\pi\)
\(864\) −11.1454 −0.379175
\(865\) 50.0193 1.70071
\(866\) −22.9322 −0.779269
\(867\) 24.2679 0.824183
\(868\) −20.7964 −0.705876
\(869\) −19.9881 −0.678049
\(870\) −83.0561 −2.81587
\(871\) 49.8549 1.68927
\(872\) −1.78608 −0.0604845
\(873\) 57.2210 1.93664
\(874\) 2.41832 0.0818010
\(875\) 24.4435 0.826340
\(876\) −0.444268 −0.0150104
\(877\) −52.0205 −1.75661 −0.878303 0.478104i \(-0.841324\pi\)
−0.878303 + 0.478104i \(0.841324\pi\)
\(878\) 4.53752 0.153134
\(879\) 52.9296 1.78527
\(880\) 5.86037 0.197553
\(881\) −22.0343 −0.742354 −0.371177 0.928562i \(-0.621046\pi\)
−0.371177 + 0.928562i \(0.621046\pi\)
\(882\) 16.3235 0.549640
\(883\) −2.90552 −0.0977785 −0.0488892 0.998804i \(-0.515568\pi\)
−0.0488892 + 0.998804i \(0.515568\pi\)
\(884\) 11.6225 0.390907
\(885\) 42.1587 1.41715
\(886\) 8.15917 0.274113
\(887\) −23.4956 −0.788904 −0.394452 0.918917i \(-0.629066\pi\)
−0.394452 + 0.918917i \(0.629066\pi\)
\(888\) −4.01608 −0.134771
\(889\) −20.9847 −0.703803
\(890\) 40.7618 1.36634
\(891\) −32.6443 −1.09363
\(892\) 5.47567 0.183339
\(893\) −9.01067 −0.301531
\(894\) 2.36787 0.0791934
\(895\) 12.5255 0.418682
\(896\) 3.07801 0.102829
\(897\) 20.0910 0.670819
\(898\) −15.4823 −0.516650
\(899\) 68.4731 2.28370
\(900\) 13.1823 0.439411
\(901\) 3.65705 0.121834
\(902\) 1.98942 0.0662404
\(903\) 17.0783 0.568331
\(904\) 3.16696 0.105332
\(905\) 38.5412 1.28115
\(906\) −53.7349 −1.78522
\(907\) −6.20579 −0.206060 −0.103030 0.994678i \(-0.532854\pi\)
−0.103030 + 0.994678i \(0.532854\pi\)
\(908\) −4.52193 −0.150066
\(909\) −65.4090 −2.16948
\(910\) −31.2575 −1.03618
\(911\) −39.2928 −1.30183 −0.650914 0.759152i \(-0.725614\pi\)
−0.650914 + 0.759152i \(0.725614\pi\)
\(912\) 4.43478 0.146850
\(913\) −2.58223 −0.0854594
\(914\) 3.48455 0.115259
\(915\) −30.4424 −1.00640
\(916\) −0.880741 −0.0291005
\(917\) −27.0046 −0.891771
\(918\) −33.7443 −1.11373
\(919\) 55.1648 1.81972 0.909859 0.414918i \(-0.136190\pi\)
0.909859 + 0.414918i \(0.136190\pi\)
\(920\) 4.46902 0.147339
\(921\) −0.589472 −0.0194237
\(922\) 23.8020 0.783877
\(923\) 17.9624 0.591241
\(924\) 21.1246 0.694948
\(925\) 2.59015 0.0851636
\(926\) 30.6752 1.00805
\(927\) 64.4236 2.11595
\(928\) −10.1345 −0.332681
\(929\) 5.13054 0.168328 0.0841638 0.996452i \(-0.473178\pi\)
0.0841638 + 0.996452i \(0.473178\pi\)
\(930\) −55.3717 −1.81571
\(931\) −3.54173 −0.116076
\(932\) 23.6779 0.775596
\(933\) 54.9284 1.79827
\(934\) 10.9114 0.357033
\(935\) 17.7431 0.580260
\(936\) 25.3269 0.827837
\(937\) −17.4365 −0.569625 −0.284813 0.958583i \(-0.591931\pi\)
−0.284813 + 0.958583i \(0.591931\pi\)
\(938\) 39.9745 1.30521
\(939\) −94.8392 −3.09496
\(940\) −16.6516 −0.543115
\(941\) −17.8110 −0.580621 −0.290310 0.956933i \(-0.593759\pi\)
−0.290310 + 0.956933i \(0.593759\pi\)
\(942\) 47.8475 1.55896
\(943\) 1.51710 0.0494036
\(944\) 5.14420 0.167429
\(945\) 90.7518 2.95216
\(946\) 3.96762 0.128998
\(947\) 15.2834 0.496642 0.248321 0.968678i \(-0.420121\pi\)
0.248321 + 0.968678i \(0.420121\pi\)
\(948\) −27.9522 −0.907846
\(949\) 0.550502 0.0178700
\(950\) −2.86019 −0.0927969
\(951\) 98.1907 3.18405
\(952\) 9.31910 0.302034
\(953\) −7.31737 −0.237033 −0.118516 0.992952i \(-0.537814\pi\)
−0.118516 + 0.992952i \(0.537814\pi\)
\(954\) 7.96920 0.258012
\(955\) 33.7336 1.09159
\(956\) −6.06478 −0.196149
\(957\) −69.5537 −2.24835
\(958\) 16.6553 0.538108
\(959\) 10.7123 0.345918
\(960\) 8.19540 0.264505
\(961\) 14.6495 0.472565
\(962\) 4.97641 0.160446
\(963\) −21.5556 −0.694620
\(964\) −18.2169 −0.586728
\(965\) −52.4755 −1.68925
\(966\) 16.1093 0.518307
\(967\) 14.8093 0.476236 0.238118 0.971236i \(-0.423469\pi\)
0.238118 + 0.971236i \(0.423469\pi\)
\(968\) −6.09236 −0.195816
\(969\) 13.4269 0.431334
\(970\) −22.9433 −0.736666
\(971\) 38.0877 1.22229 0.611147 0.791517i \(-0.290709\pi\)
0.611147 + 0.791517i \(0.290709\pi\)
\(972\) −12.2150 −0.391796
\(973\) −27.3811 −0.877798
\(974\) −6.46773 −0.207239
\(975\) −23.7620 −0.760992
\(976\) −3.71458 −0.118901
\(977\) 27.3417 0.874738 0.437369 0.899282i \(-0.355910\pi\)
0.437369 + 0.899282i \(0.355910\pi\)
\(978\) 44.4251 1.42056
\(979\) 34.1352 1.09096
\(980\) −6.54506 −0.209074
\(981\) −11.7839 −0.376231
\(982\) −19.4399 −0.620353
\(983\) −36.3702 −1.16003 −0.580015 0.814606i \(-0.696953\pi\)
−0.580015 + 0.814606i \(0.696953\pi\)
\(984\) 2.78209 0.0886899
\(985\) −34.4917 −1.09900
\(986\) −30.6835 −0.977163
\(987\) −60.0232 −1.91056
\(988\) −5.49523 −0.174827
\(989\) 3.02564 0.0962098
\(990\) 38.6645 1.22884
\(991\) 10.9382 0.347464 0.173732 0.984793i \(-0.444417\pi\)
0.173732 + 0.984793i \(0.444417\pi\)
\(992\) −6.75644 −0.214517
\(993\) −78.5340 −2.49220
\(994\) 14.4026 0.456822
\(995\) 40.9249 1.29741
\(996\) −3.61111 −0.114422
\(997\) −19.0585 −0.603589 −0.301795 0.953373i \(-0.597586\pi\)
−0.301795 + 0.953373i \(0.597586\pi\)
\(998\) 1.83225 0.0579987
\(999\) −14.4483 −0.457124
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 \(a_p\))