Properties

Label 8002.2.a.d.1.12
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 1.12
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.62997 q^{3}\) \(+1.00000 q^{4}\) \(-0.133179 q^{5}\) \(-2.62997 q^{6}\) \(-2.98290 q^{7}\) \(+1.00000 q^{8}\) \(+3.91674 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.62997 q^{3}\) \(+1.00000 q^{4}\) \(-0.133179 q^{5}\) \(-2.62997 q^{6}\) \(-2.98290 q^{7}\) \(+1.00000 q^{8}\) \(+3.91674 q^{9}\) \(-0.133179 q^{10}\) \(-3.21116 q^{11}\) \(-2.62997 q^{12}\) \(+6.39878 q^{13}\) \(-2.98290 q^{14}\) \(+0.350258 q^{15}\) \(+1.00000 q^{16}\) \(-3.30489 q^{17}\) \(+3.91674 q^{18}\) \(+4.41196 q^{19}\) \(-0.133179 q^{20}\) \(+7.84493 q^{21}\) \(-3.21116 q^{22}\) \(-1.70409 q^{23}\) \(-2.62997 q^{24}\) \(-4.98226 q^{25}\) \(+6.39878 q^{26}\) \(-2.41100 q^{27}\) \(-2.98290 q^{28}\) \(-4.05713 q^{29}\) \(+0.350258 q^{30}\) \(+9.35394 q^{31}\) \(+1.00000 q^{32}\) \(+8.44527 q^{33}\) \(-3.30489 q^{34}\) \(+0.397260 q^{35}\) \(+3.91674 q^{36}\) \(-11.1712 q^{37}\) \(+4.41196 q^{38}\) \(-16.8286 q^{39}\) \(-0.133179 q^{40}\) \(-9.01963 q^{41}\) \(+7.84493 q^{42}\) \(+7.51380 q^{43}\) \(-3.21116 q^{44}\) \(-0.521629 q^{45}\) \(-1.70409 q^{46}\) \(+7.66372 q^{47}\) \(-2.62997 q^{48}\) \(+1.89767 q^{49}\) \(-4.98226 q^{50}\) \(+8.69175 q^{51}\) \(+6.39878 q^{52}\) \(-3.41893 q^{53}\) \(-2.41100 q^{54}\) \(+0.427661 q^{55}\) \(-2.98290 q^{56}\) \(-11.6033 q^{57}\) \(-4.05713 q^{58}\) \(+6.87216 q^{59}\) \(+0.350258 q^{60}\) \(+12.8840 q^{61}\) \(+9.35394 q^{62}\) \(-11.6832 q^{63}\) \(+1.00000 q^{64}\) \(-0.852185 q^{65}\) \(+8.44527 q^{66}\) \(+6.96556 q^{67}\) \(-3.30489 q^{68}\) \(+4.48170 q^{69}\) \(+0.397260 q^{70}\) \(-3.36425 q^{71}\) \(+3.91674 q^{72}\) \(+8.97955 q^{73}\) \(-11.1712 q^{74}\) \(+13.1032 q^{75}\) \(+4.41196 q^{76}\) \(+9.57857 q^{77}\) \(-16.8286 q^{78}\) \(-6.45762 q^{79}\) \(-0.133179 q^{80}\) \(-5.40936 q^{81}\) \(-9.01963 q^{82}\) \(-2.50616 q^{83}\) \(+7.84493 q^{84}\) \(+0.440142 q^{85}\) \(+7.51380 q^{86}\) \(+10.6701 q^{87}\) \(-3.21116 q^{88}\) \(+6.26390 q^{89}\) \(-0.521629 q^{90}\) \(-19.0869 q^{91}\) \(-1.70409 q^{92}\) \(-24.6006 q^{93}\) \(+7.66372 q^{94}\) \(-0.587583 q^{95}\) \(-2.62997 q^{96}\) \(+4.35742 q^{97}\) \(+1.89767 q^{98}\) \(-12.5773 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.62997 −1.51841 −0.759207 0.650849i \(-0.774413\pi\)
−0.759207 + 0.650849i \(0.774413\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.133179 −0.0595596 −0.0297798 0.999556i \(-0.509481\pi\)
−0.0297798 + 0.999556i \(0.509481\pi\)
\(6\) −2.62997 −1.07368
\(7\) −2.98290 −1.12743 −0.563714 0.825970i \(-0.690628\pi\)
−0.563714 + 0.825970i \(0.690628\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.91674 1.30558
\(10\) −0.133179 −0.0421150
\(11\) −3.21116 −0.968203 −0.484101 0.875012i \(-0.660853\pi\)
−0.484101 + 0.875012i \(0.660853\pi\)
\(12\) −2.62997 −0.759207
\(13\) 6.39878 1.77470 0.887351 0.461095i \(-0.152543\pi\)
0.887351 + 0.461095i \(0.152543\pi\)
\(14\) −2.98290 −0.797212
\(15\) 0.350258 0.0904361
\(16\) 1.00000 0.250000
\(17\) −3.30489 −0.801553 −0.400776 0.916176i \(-0.631260\pi\)
−0.400776 + 0.916176i \(0.631260\pi\)
\(18\) 3.91674 0.923185
\(19\) 4.41196 1.01217 0.506087 0.862482i \(-0.331091\pi\)
0.506087 + 0.862482i \(0.331091\pi\)
\(20\) −0.133179 −0.0297798
\(21\) 7.84493 1.71190
\(22\) −3.21116 −0.684623
\(23\) −1.70409 −0.355327 −0.177663 0.984091i \(-0.556854\pi\)
−0.177663 + 0.984091i \(0.556854\pi\)
\(24\) −2.62997 −0.536840
\(25\) −4.98226 −0.996453
\(26\) 6.39878 1.25490
\(27\) −2.41100 −0.463998
\(28\) −2.98290 −0.563714
\(29\) −4.05713 −0.753390 −0.376695 0.926337i \(-0.622939\pi\)
−0.376695 + 0.926337i \(0.622939\pi\)
\(30\) 0.350258 0.0639480
\(31\) 9.35394 1.68002 0.840009 0.542573i \(-0.182550\pi\)
0.840009 + 0.542573i \(0.182550\pi\)
\(32\) 1.00000 0.176777
\(33\) 8.44527 1.47013
\(34\) −3.30489 −0.566783
\(35\) 0.397260 0.0671492
\(36\) 3.91674 0.652790
\(37\) −11.1712 −1.83653 −0.918267 0.395961i \(-0.870411\pi\)
−0.918267 + 0.395961i \(0.870411\pi\)
\(38\) 4.41196 0.715715
\(39\) −16.8286 −2.69473
\(40\) −0.133179 −0.0210575
\(41\) −9.01963 −1.40863 −0.704315 0.709888i \(-0.748746\pi\)
−0.704315 + 0.709888i \(0.748746\pi\)
\(42\) 7.84493 1.21050
\(43\) 7.51380 1.14584 0.572922 0.819610i \(-0.305810\pi\)
0.572922 + 0.819610i \(0.305810\pi\)
\(44\) −3.21116 −0.484101
\(45\) −0.521629 −0.0777599
\(46\) −1.70409 −0.251254
\(47\) 7.66372 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(48\) −2.62997 −0.379603
\(49\) 1.89767 0.271095
\(50\) −4.98226 −0.704598
\(51\) 8.69175 1.21709
\(52\) 6.39878 0.887351
\(53\) −3.41893 −0.469626 −0.234813 0.972041i \(-0.575448\pi\)
−0.234813 + 0.972041i \(0.575448\pi\)
\(54\) −2.41100 −0.328096
\(55\) 0.427661 0.0576658
\(56\) −2.98290 −0.398606
\(57\) −11.6033 −1.53690
\(58\) −4.05713 −0.532727
\(59\) 6.87216 0.894679 0.447339 0.894364i \(-0.352372\pi\)
0.447339 + 0.894364i \(0.352372\pi\)
\(60\) 0.350258 0.0452181
\(61\) 12.8840 1.64963 0.824813 0.565405i \(-0.191280\pi\)
0.824813 + 0.565405i \(0.191280\pi\)
\(62\) 9.35394 1.18795
\(63\) −11.6832 −1.47195
\(64\) 1.00000 0.125000
\(65\) −0.852185 −0.105701
\(66\) 8.44527 1.03954
\(67\) 6.96556 0.850978 0.425489 0.904964i \(-0.360102\pi\)
0.425489 + 0.904964i \(0.360102\pi\)
\(68\) −3.30489 −0.400776
\(69\) 4.48170 0.539533
\(70\) 0.397260 0.0474817
\(71\) −3.36425 −0.399263 −0.199632 0.979871i \(-0.563975\pi\)
−0.199632 + 0.979871i \(0.563975\pi\)
\(72\) 3.91674 0.461592
\(73\) 8.97955 1.05098 0.525488 0.850801i \(-0.323883\pi\)
0.525488 + 0.850801i \(0.323883\pi\)
\(74\) −11.1712 −1.29863
\(75\) 13.1032 1.51303
\(76\) 4.41196 0.506087
\(77\) 9.57857 1.09158
\(78\) −16.8286 −1.90546
\(79\) −6.45762 −0.726539 −0.363269 0.931684i \(-0.618340\pi\)
−0.363269 + 0.931684i \(0.618340\pi\)
\(80\) −0.133179 −0.0148899
\(81\) −5.40936 −0.601040
\(82\) −9.01963 −0.996051
\(83\) −2.50616 −0.275087 −0.137543 0.990496i \(-0.543921\pi\)
−0.137543 + 0.990496i \(0.543921\pi\)
\(84\) 7.84493 0.855952
\(85\) 0.440142 0.0477402
\(86\) 7.51380 0.810234
\(87\) 10.6701 1.14396
\(88\) −3.21116 −0.342311
\(89\) 6.26390 0.663972 0.331986 0.943284i \(-0.392281\pi\)
0.331986 + 0.943284i \(0.392281\pi\)
\(90\) −0.521629 −0.0549845
\(91\) −19.0869 −2.00085
\(92\) −1.70409 −0.177663
\(93\) −24.6006 −2.55096
\(94\) 7.66372 0.790452
\(95\) −0.587583 −0.0602847
\(96\) −2.62997 −0.268420
\(97\) 4.35742 0.442429 0.221215 0.975225i \(-0.428998\pi\)
0.221215 + 0.975225i \(0.428998\pi\)
\(98\) 1.89767 0.191693
\(99\) −12.5773 −1.26407
\(100\) −4.98226 −0.498226
\(101\) −5.87049 −0.584135 −0.292068 0.956398i \(-0.594343\pi\)
−0.292068 + 0.956398i \(0.594343\pi\)
\(102\) 8.69175 0.860612
\(103\) 2.77219 0.273152 0.136576 0.990630i \(-0.456390\pi\)
0.136576 + 0.990630i \(0.456390\pi\)
\(104\) 6.39878 0.627452
\(105\) −1.04478 −0.101960
\(106\) −3.41893 −0.332076
\(107\) 4.07490 0.393936 0.196968 0.980410i \(-0.436891\pi\)
0.196968 + 0.980410i \(0.436891\pi\)
\(108\) −2.41100 −0.231999
\(109\) 12.3408 1.18203 0.591015 0.806661i \(-0.298727\pi\)
0.591015 + 0.806661i \(0.298727\pi\)
\(110\) 0.427661 0.0407759
\(111\) 29.3799 2.78862
\(112\) −2.98290 −0.281857
\(113\) −10.3693 −0.975458 −0.487729 0.872995i \(-0.662175\pi\)
−0.487729 + 0.872995i \(0.662175\pi\)
\(114\) −11.6033 −1.08675
\(115\) 0.226949 0.0211631
\(116\) −4.05713 −0.376695
\(117\) 25.0624 2.31702
\(118\) 6.87216 0.632633
\(119\) 9.85813 0.903693
\(120\) 0.350258 0.0319740
\(121\) −0.688423 −0.0625839
\(122\) 12.8840 1.16646
\(123\) 23.7214 2.13888
\(124\) 9.35394 0.840009
\(125\) 1.32943 0.118908
\(126\) −11.6832 −1.04083
\(127\) 4.89366 0.434242 0.217121 0.976145i \(-0.430333\pi\)
0.217121 + 0.976145i \(0.430333\pi\)
\(128\) 1.00000 0.0883883
\(129\) −19.7611 −1.73987
\(130\) −0.852185 −0.0747416
\(131\) −15.7955 −1.38006 −0.690029 0.723781i \(-0.742402\pi\)
−0.690029 + 0.723781i \(0.742402\pi\)
\(132\) 8.44527 0.735066
\(133\) −13.1604 −1.14115
\(134\) 6.96556 0.601732
\(135\) 0.321096 0.0276355
\(136\) −3.30489 −0.283392
\(137\) −10.6305 −0.908226 −0.454113 0.890944i \(-0.650044\pi\)
−0.454113 + 0.890944i \(0.650044\pi\)
\(138\) 4.48170 0.381508
\(139\) 7.14185 0.605764 0.302882 0.953028i \(-0.402051\pi\)
0.302882 + 0.953028i \(0.402051\pi\)
\(140\) 0.397260 0.0335746
\(141\) −20.1553 −1.69739
\(142\) −3.36425 −0.282322
\(143\) −20.5475 −1.71827
\(144\) 3.91674 0.326395
\(145\) 0.540326 0.0448716
\(146\) 8.97955 0.743153
\(147\) −4.99080 −0.411635
\(148\) −11.1712 −0.918267
\(149\) 3.29780 0.270166 0.135083 0.990834i \(-0.456870\pi\)
0.135083 + 0.990834i \(0.456870\pi\)
\(150\) 13.1032 1.06987
\(151\) −4.60869 −0.375050 −0.187525 0.982260i \(-0.560047\pi\)
−0.187525 + 0.982260i \(0.560047\pi\)
\(152\) 4.41196 0.357858
\(153\) −12.9444 −1.04649
\(154\) 9.57857 0.771863
\(155\) −1.24575 −0.100061
\(156\) −16.8286 −1.34737
\(157\) −19.9945 −1.59573 −0.797867 0.602833i \(-0.794038\pi\)
−0.797867 + 0.602833i \(0.794038\pi\)
\(158\) −6.45762 −0.513740
\(159\) 8.99168 0.713087
\(160\) −0.133179 −0.0105288
\(161\) 5.08312 0.400606
\(162\) −5.40936 −0.424999
\(163\) 8.64548 0.677166 0.338583 0.940936i \(-0.390052\pi\)
0.338583 + 0.940936i \(0.390052\pi\)
\(164\) −9.01963 −0.704315
\(165\) −1.12473 −0.0875605
\(166\) −2.50616 −0.194516
\(167\) −1.48837 −0.115173 −0.0575866 0.998341i \(-0.518341\pi\)
−0.0575866 + 0.998341i \(0.518341\pi\)
\(168\) 7.84493 0.605249
\(169\) 27.9444 2.14957
\(170\) 0.440142 0.0337574
\(171\) 17.2805 1.32147
\(172\) 7.51380 0.572922
\(173\) −22.2013 −1.68793 −0.843965 0.536398i \(-0.819785\pi\)
−0.843965 + 0.536398i \(0.819785\pi\)
\(174\) 10.6701 0.808900
\(175\) 14.8616 1.12343
\(176\) −3.21116 −0.242051
\(177\) −18.0736 −1.35849
\(178\) 6.26390 0.469499
\(179\) 15.6212 1.16758 0.583792 0.811903i \(-0.301568\pi\)
0.583792 + 0.811903i \(0.301568\pi\)
\(180\) −0.521629 −0.0388799
\(181\) 20.7058 1.53905 0.769526 0.638615i \(-0.220492\pi\)
0.769526 + 0.638615i \(0.220492\pi\)
\(182\) −19.0869 −1.41481
\(183\) −33.8845 −2.50482
\(184\) −1.70409 −0.125627
\(185\) 1.48777 0.109383
\(186\) −24.6006 −1.80380
\(187\) 10.6125 0.776065
\(188\) 7.66372 0.558934
\(189\) 7.19177 0.523125
\(190\) −0.587583 −0.0426277
\(191\) −10.5596 −0.764067 −0.382034 0.924148i \(-0.624776\pi\)
−0.382034 + 0.924148i \(0.624776\pi\)
\(192\) −2.62997 −0.189802
\(193\) −24.0218 −1.72912 −0.864562 0.502526i \(-0.832404\pi\)
−0.864562 + 0.502526i \(0.832404\pi\)
\(194\) 4.35742 0.312845
\(195\) 2.24122 0.160497
\(196\) 1.89767 0.135548
\(197\) −9.67603 −0.689388 −0.344694 0.938715i \(-0.612017\pi\)
−0.344694 + 0.938715i \(0.612017\pi\)
\(198\) −12.5773 −0.893830
\(199\) −19.0908 −1.35331 −0.676656 0.736300i \(-0.736571\pi\)
−0.676656 + 0.736300i \(0.736571\pi\)
\(200\) −4.98226 −0.352299
\(201\) −18.3192 −1.29214
\(202\) −5.87049 −0.413046
\(203\) 12.1020 0.849393
\(204\) 8.69175 0.608544
\(205\) 1.20123 0.0838974
\(206\) 2.77219 0.193147
\(207\) −6.67447 −0.463908
\(208\) 6.39878 0.443675
\(209\) −14.1675 −0.979989
\(210\) −1.04478 −0.0720968
\(211\) −6.74610 −0.464421 −0.232210 0.972666i \(-0.574596\pi\)
−0.232210 + 0.972666i \(0.574596\pi\)
\(212\) −3.41893 −0.234813
\(213\) 8.84788 0.606247
\(214\) 4.07490 0.278555
\(215\) −1.00068 −0.0682460
\(216\) −2.41100 −0.164048
\(217\) −27.9018 −1.89410
\(218\) 12.3408 0.835821
\(219\) −23.6159 −1.59582
\(220\) 0.427661 0.0288329
\(221\) −21.1472 −1.42252
\(222\) 29.3799 1.97185
\(223\) −9.99394 −0.669244 −0.334622 0.942352i \(-0.608609\pi\)
−0.334622 + 0.942352i \(0.608609\pi\)
\(224\) −2.98290 −0.199303
\(225\) −19.5142 −1.30095
\(226\) −10.3693 −0.689753
\(227\) −26.2775 −1.74410 −0.872051 0.489416i \(-0.837210\pi\)
−0.872051 + 0.489416i \(0.837210\pi\)
\(228\) −11.6033 −0.768450
\(229\) −8.88024 −0.586823 −0.293412 0.955986i \(-0.594791\pi\)
−0.293412 + 0.955986i \(0.594791\pi\)
\(230\) 0.226949 0.0149646
\(231\) −25.1913 −1.65747
\(232\) −4.05713 −0.266363
\(233\) −14.2979 −0.936687 −0.468343 0.883547i \(-0.655149\pi\)
−0.468343 + 0.883547i \(0.655149\pi\)
\(234\) 25.0624 1.63838
\(235\) −1.02065 −0.0665798
\(236\) 6.87216 0.447339
\(237\) 16.9833 1.10319
\(238\) 9.85813 0.639008
\(239\) 0.234563 0.0151726 0.00758631 0.999971i \(-0.497585\pi\)
0.00758631 + 0.999971i \(0.497585\pi\)
\(240\) 0.350258 0.0226090
\(241\) −18.6942 −1.20420 −0.602101 0.798420i \(-0.705670\pi\)
−0.602101 + 0.798420i \(0.705670\pi\)
\(242\) −0.688423 −0.0442535
\(243\) 21.4595 1.37663
\(244\) 12.8840 0.824813
\(245\) −0.252730 −0.0161463
\(246\) 23.7214 1.51242
\(247\) 28.2312 1.79631
\(248\) 9.35394 0.593976
\(249\) 6.59112 0.417695
\(250\) 1.32943 0.0840806
\(251\) −16.5827 −1.04669 −0.523344 0.852122i \(-0.675316\pi\)
−0.523344 + 0.852122i \(0.675316\pi\)
\(252\) −11.6832 −0.735974
\(253\) 5.47211 0.344028
\(254\) 4.89366 0.307056
\(255\) −1.15756 −0.0724893
\(256\) 1.00000 0.0625000
\(257\) −0.577994 −0.0360543 −0.0180271 0.999837i \(-0.505739\pi\)
−0.0180271 + 0.999837i \(0.505739\pi\)
\(258\) −19.7611 −1.23027
\(259\) 33.3225 2.07056
\(260\) −0.852185 −0.0528503
\(261\) −15.8907 −0.983611
\(262\) −15.7955 −0.975849
\(263\) −9.09976 −0.561115 −0.280558 0.959837i \(-0.590519\pi\)
−0.280558 + 0.959837i \(0.590519\pi\)
\(264\) 8.44527 0.519770
\(265\) 0.455331 0.0279707
\(266\) −13.1604 −0.806918
\(267\) −16.4739 −1.00818
\(268\) 6.96556 0.425489
\(269\) 6.92422 0.422177 0.211089 0.977467i \(-0.432299\pi\)
0.211089 + 0.977467i \(0.432299\pi\)
\(270\) 0.321096 0.0195413
\(271\) 3.32939 0.202246 0.101123 0.994874i \(-0.467756\pi\)
0.101123 + 0.994874i \(0.467756\pi\)
\(272\) −3.30489 −0.200388
\(273\) 50.1979 3.03812
\(274\) −10.6305 −0.642212
\(275\) 15.9989 0.964768
\(276\) 4.48170 0.269767
\(277\) 0.190648 0.0114549 0.00572747 0.999984i \(-0.498177\pi\)
0.00572747 + 0.999984i \(0.498177\pi\)
\(278\) 7.14185 0.428340
\(279\) 36.6370 2.19340
\(280\) 0.397260 0.0237408
\(281\) −8.34937 −0.498081 −0.249041 0.968493i \(-0.580115\pi\)
−0.249041 + 0.968493i \(0.580115\pi\)
\(282\) −20.1553 −1.20023
\(283\) −12.0914 −0.718758 −0.359379 0.933192i \(-0.617011\pi\)
−0.359379 + 0.933192i \(0.617011\pi\)
\(284\) −3.36425 −0.199632
\(285\) 1.54532 0.0915371
\(286\) −20.5475 −1.21500
\(287\) 26.9046 1.58813
\(288\) 3.91674 0.230796
\(289\) −6.07773 −0.357514
\(290\) 0.540326 0.0317290
\(291\) −11.4599 −0.671791
\(292\) 8.97955 0.525488
\(293\) 22.0633 1.28895 0.644477 0.764624i \(-0.277075\pi\)
0.644477 + 0.764624i \(0.277075\pi\)
\(294\) −4.99080 −0.291070
\(295\) −0.915230 −0.0532867
\(296\) −11.1712 −0.649313
\(297\) 7.74213 0.449244
\(298\) 3.29780 0.191036
\(299\) −10.9041 −0.630599
\(300\) 13.1032 0.756514
\(301\) −22.4129 −1.29186
\(302\) −4.60869 −0.265200
\(303\) 15.4392 0.886959
\(304\) 4.41196 0.253044
\(305\) −1.71588 −0.0982511
\(306\) −12.9444 −0.739981
\(307\) 5.65068 0.322501 0.161251 0.986913i \(-0.448447\pi\)
0.161251 + 0.986913i \(0.448447\pi\)
\(308\) 9.57857 0.545790
\(309\) −7.29077 −0.414757
\(310\) −1.24575 −0.0707539
\(311\) −17.5752 −0.996597 −0.498299 0.867006i \(-0.666042\pi\)
−0.498299 + 0.867006i \(0.666042\pi\)
\(312\) −16.8286 −0.952732
\(313\) −10.6930 −0.604403 −0.302201 0.953244i \(-0.597722\pi\)
−0.302201 + 0.953244i \(0.597722\pi\)
\(314\) −19.9945 −1.12835
\(315\) 1.55597 0.0876687
\(316\) −6.45762 −0.363269
\(317\) 7.51322 0.421985 0.210992 0.977488i \(-0.432331\pi\)
0.210992 + 0.977488i \(0.432331\pi\)
\(318\) 8.99168 0.504228
\(319\) 13.0281 0.729434
\(320\) −0.133179 −0.00744495
\(321\) −10.7169 −0.598158
\(322\) 5.08312 0.283271
\(323\) −14.5810 −0.811311
\(324\) −5.40936 −0.300520
\(325\) −31.8804 −1.76841
\(326\) 8.64548 0.478829
\(327\) −32.4558 −1.79481
\(328\) −9.01963 −0.498026
\(329\) −22.8601 −1.26032
\(330\) −1.12473 −0.0619146
\(331\) −1.19105 −0.0654659 −0.0327330 0.999464i \(-0.510421\pi\)
−0.0327330 + 0.999464i \(0.510421\pi\)
\(332\) −2.50616 −0.137543
\(333\) −43.7547 −2.39774
\(334\) −1.48837 −0.0814398
\(335\) −0.927668 −0.0506839
\(336\) 7.84493 0.427976
\(337\) −15.7956 −0.860441 −0.430220 0.902724i \(-0.641564\pi\)
−0.430220 + 0.902724i \(0.641564\pi\)
\(338\) 27.9444 1.51997
\(339\) 27.2709 1.48115
\(340\) 0.440142 0.0238701
\(341\) −30.0370 −1.62660
\(342\) 17.2805 0.934424
\(343\) 15.2197 0.821788
\(344\) 7.51380 0.405117
\(345\) −0.596870 −0.0321344
\(346\) −22.2013 −1.19355
\(347\) −29.3425 −1.57519 −0.787593 0.616196i \(-0.788673\pi\)
−0.787593 + 0.616196i \(0.788673\pi\)
\(348\) 10.6701 0.571979
\(349\) −11.1330 −0.595936 −0.297968 0.954576i \(-0.596309\pi\)
−0.297968 + 0.954576i \(0.596309\pi\)
\(350\) 14.8616 0.794384
\(351\) −15.4275 −0.823458
\(352\) −3.21116 −0.171156
\(353\) −11.1144 −0.591559 −0.295780 0.955256i \(-0.595579\pi\)
−0.295780 + 0.955256i \(0.595579\pi\)
\(354\) −18.0736 −0.960599
\(355\) 0.448049 0.0237800
\(356\) 6.26390 0.331986
\(357\) −25.9266 −1.37218
\(358\) 15.6212 0.825606
\(359\) 26.5411 1.40078 0.700392 0.713758i \(-0.253009\pi\)
0.700392 + 0.713758i \(0.253009\pi\)
\(360\) −0.521629 −0.0274923
\(361\) 0.465431 0.0244964
\(362\) 20.7058 1.08827
\(363\) 1.81053 0.0950283
\(364\) −19.0869 −1.00042
\(365\) −1.19589 −0.0625958
\(366\) −33.8845 −1.77117
\(367\) 16.7371 0.873668 0.436834 0.899542i \(-0.356100\pi\)
0.436834 + 0.899542i \(0.356100\pi\)
\(368\) −1.70409 −0.0888317
\(369\) −35.3276 −1.83908
\(370\) 1.48777 0.0773457
\(371\) 10.1983 0.529470
\(372\) −24.6006 −1.27548
\(373\) −20.5677 −1.06496 −0.532478 0.846444i \(-0.678739\pi\)
−0.532478 + 0.846444i \(0.678739\pi\)
\(374\) 10.6125 0.548761
\(375\) −3.49636 −0.180551
\(376\) 7.66372 0.395226
\(377\) −25.9607 −1.33704
\(378\) 7.19177 0.369905
\(379\) 6.19803 0.318371 0.159186 0.987249i \(-0.449113\pi\)
0.159186 + 0.987249i \(0.449113\pi\)
\(380\) −0.587583 −0.0301423
\(381\) −12.8702 −0.659359
\(382\) −10.5596 −0.540277
\(383\) −0.542879 −0.0277398 −0.0138699 0.999904i \(-0.504415\pi\)
−0.0138699 + 0.999904i \(0.504415\pi\)
\(384\) −2.62997 −0.134210
\(385\) −1.27567 −0.0650140
\(386\) −24.0218 −1.22268
\(387\) 29.4296 1.49599
\(388\) 4.35742 0.221215
\(389\) −21.7112 −1.10080 −0.550401 0.834901i \(-0.685525\pi\)
−0.550401 + 0.834901i \(0.685525\pi\)
\(390\) 2.24122 0.113489
\(391\) 5.63182 0.284813
\(392\) 1.89767 0.0958466
\(393\) 41.5417 2.09550
\(394\) −9.67603 −0.487471
\(395\) 0.860021 0.0432724
\(396\) −12.5773 −0.632033
\(397\) 32.2232 1.61724 0.808618 0.588334i \(-0.200216\pi\)
0.808618 + 0.588334i \(0.200216\pi\)
\(398\) −19.0908 −0.956935
\(399\) 34.6115 1.73274
\(400\) −4.98226 −0.249113
\(401\) 34.0790 1.70182 0.850912 0.525308i \(-0.176050\pi\)
0.850912 + 0.525308i \(0.176050\pi\)
\(402\) −18.3192 −0.913679
\(403\) 59.8538 2.98153
\(404\) −5.87049 −0.292068
\(405\) 0.720415 0.0357977
\(406\) 12.1020 0.600612
\(407\) 35.8726 1.77814
\(408\) 8.69175 0.430306
\(409\) −4.18983 −0.207174 −0.103587 0.994620i \(-0.533032\pi\)
−0.103587 + 0.994620i \(0.533032\pi\)
\(410\) 1.20123 0.0593244
\(411\) 27.9579 1.37906
\(412\) 2.77219 0.136576
\(413\) −20.4989 −1.00869
\(414\) −6.67447 −0.328032
\(415\) 0.333768 0.0163841
\(416\) 6.39878 0.313726
\(417\) −18.7828 −0.919800
\(418\) −14.1675 −0.692957
\(419\) 17.5670 0.858203 0.429101 0.903256i \(-0.358830\pi\)
0.429101 + 0.903256i \(0.358830\pi\)
\(420\) −1.04478 −0.0509801
\(421\) −25.4373 −1.23974 −0.619869 0.784705i \(-0.712814\pi\)
−0.619869 + 0.784705i \(0.712814\pi\)
\(422\) −6.74610 −0.328395
\(423\) 30.0168 1.45947
\(424\) −3.41893 −0.166038
\(425\) 16.4658 0.798709
\(426\) 8.84788 0.428681
\(427\) −38.4316 −1.85984
\(428\) 4.07490 0.196968
\(429\) 54.0394 2.60905
\(430\) −1.00068 −0.0482572
\(431\) −7.70426 −0.371101 −0.185551 0.982635i \(-0.559407\pi\)
−0.185551 + 0.982635i \(0.559407\pi\)
\(432\) −2.41100 −0.115999
\(433\) 33.2194 1.59642 0.798211 0.602378i \(-0.205780\pi\)
0.798211 + 0.602378i \(0.205780\pi\)
\(434\) −27.9018 −1.33933
\(435\) −1.42104 −0.0681337
\(436\) 12.3408 0.591015
\(437\) −7.51838 −0.359653
\(438\) −23.6159 −1.12841
\(439\) −40.5548 −1.93558 −0.967788 0.251767i \(-0.918988\pi\)
−0.967788 + 0.251767i \(0.918988\pi\)
\(440\) 0.427661 0.0203879
\(441\) 7.43267 0.353937
\(442\) −21.1472 −1.00587
\(443\) −20.2385 −0.961558 −0.480779 0.876842i \(-0.659646\pi\)
−0.480779 + 0.876842i \(0.659646\pi\)
\(444\) 29.3799 1.39431
\(445\) −0.834221 −0.0395459
\(446\) −9.99394 −0.473227
\(447\) −8.67311 −0.410224
\(448\) −2.98290 −0.140929
\(449\) 7.57351 0.357416 0.178708 0.983902i \(-0.442808\pi\)
0.178708 + 0.983902i \(0.442808\pi\)
\(450\) −19.5142 −0.919910
\(451\) 28.9635 1.36384
\(452\) −10.3693 −0.487729
\(453\) 12.1207 0.569481
\(454\) −26.2775 −1.23327
\(455\) 2.54198 0.119170
\(456\) −11.6033 −0.543376
\(457\) −0.569802 −0.0266542 −0.0133271 0.999911i \(-0.504242\pi\)
−0.0133271 + 0.999911i \(0.504242\pi\)
\(458\) −8.88024 −0.414947
\(459\) 7.96809 0.371919
\(460\) 0.226949 0.0105816
\(461\) 3.89924 0.181606 0.0908028 0.995869i \(-0.471057\pi\)
0.0908028 + 0.995869i \(0.471057\pi\)
\(462\) −25.1913 −1.17201
\(463\) 30.2977 1.40806 0.704028 0.710173i \(-0.251383\pi\)
0.704028 + 0.710173i \(0.251383\pi\)
\(464\) −4.05713 −0.188347
\(465\) 3.27629 0.151934
\(466\) −14.2979 −0.662338
\(467\) −18.0191 −0.833825 −0.416913 0.908947i \(-0.636888\pi\)
−0.416913 + 0.908947i \(0.636888\pi\)
\(468\) 25.0624 1.15851
\(469\) −20.7775 −0.959417
\(470\) −1.02065 −0.0470790
\(471\) 52.5849 2.42299
\(472\) 6.87216 0.316317
\(473\) −24.1280 −1.10941
\(474\) 16.9833 0.780071
\(475\) −21.9816 −1.00858
\(476\) 9.85813 0.451847
\(477\) −13.3911 −0.613135
\(478\) 0.234563 0.0107287
\(479\) −7.99029 −0.365086 −0.182543 0.983198i \(-0.558433\pi\)
−0.182543 + 0.983198i \(0.558433\pi\)
\(480\) 0.350258 0.0159870
\(481\) −71.4821 −3.25930
\(482\) −18.6942 −0.851500
\(483\) −13.3684 −0.608285
\(484\) −0.688423 −0.0312920
\(485\) −0.580319 −0.0263509
\(486\) 21.4595 0.973421
\(487\) 21.1513 0.958455 0.479228 0.877691i \(-0.340917\pi\)
0.479228 + 0.877691i \(0.340917\pi\)
\(488\) 12.8840 0.583231
\(489\) −22.7374 −1.02822
\(490\) −0.252730 −0.0114172
\(491\) 35.1515 1.58637 0.793183 0.608983i \(-0.208422\pi\)
0.793183 + 0.608983i \(0.208422\pi\)
\(492\) 23.7214 1.06944
\(493\) 13.4083 0.603881
\(494\) 28.2312 1.27018
\(495\) 1.67504 0.0752873
\(496\) 9.35394 0.420004
\(497\) 10.0352 0.450141
\(498\) 6.59112 0.295355
\(499\) 11.9801 0.536303 0.268152 0.963377i \(-0.413587\pi\)
0.268152 + 0.963377i \(0.413587\pi\)
\(500\) 1.32943 0.0594540
\(501\) 3.91436 0.174881
\(502\) −16.5827 −0.740120
\(503\) −34.3504 −1.53161 −0.765805 0.643073i \(-0.777659\pi\)
−0.765805 + 0.643073i \(0.777659\pi\)
\(504\) −11.6832 −0.520413
\(505\) 0.781828 0.0347909
\(506\) 5.47211 0.243265
\(507\) −73.4929 −3.26393
\(508\) 4.89366 0.217121
\(509\) 5.95234 0.263833 0.131916 0.991261i \(-0.457887\pi\)
0.131916 + 0.991261i \(0.457887\pi\)
\(510\) −1.15756 −0.0512577
\(511\) −26.7851 −1.18490
\(512\) 1.00000 0.0441942
\(513\) −10.6373 −0.469647
\(514\) −0.577994 −0.0254942
\(515\) −0.369198 −0.0162688
\(516\) −19.7611 −0.869933
\(517\) −24.6095 −1.08232
\(518\) 33.3225 1.46411
\(519\) 58.3886 2.56298
\(520\) −0.852185 −0.0373708
\(521\) −4.23233 −0.185422 −0.0927109 0.995693i \(-0.529553\pi\)
−0.0927109 + 0.995693i \(0.529553\pi\)
\(522\) −15.8907 −0.695518
\(523\) 25.0692 1.09620 0.548100 0.836413i \(-0.315351\pi\)
0.548100 + 0.836413i \(0.315351\pi\)
\(524\) −15.7955 −0.690029
\(525\) −39.0855 −1.70583
\(526\) −9.09976 −0.396768
\(527\) −30.9137 −1.34662
\(528\) 8.44527 0.367533
\(529\) −20.0961 −0.873743
\(530\) 0.455331 0.0197783
\(531\) 26.9165 1.16808
\(532\) −13.1604 −0.570577
\(533\) −57.7146 −2.49990
\(534\) −16.4739 −0.712894
\(535\) −0.542693 −0.0234627
\(536\) 6.96556 0.300866
\(537\) −41.0833 −1.77288
\(538\) 6.92422 0.298524
\(539\) −6.09372 −0.262475
\(540\) 0.321096 0.0138178
\(541\) 44.6416 1.91929 0.959646 0.281212i \(-0.0907364\pi\)
0.959646 + 0.281212i \(0.0907364\pi\)
\(542\) 3.32939 0.143010
\(543\) −54.4557 −2.33692
\(544\) −3.30489 −0.141696
\(545\) −1.64353 −0.0704012
\(546\) 50.1979 2.14827
\(547\) −19.2707 −0.823957 −0.411978 0.911194i \(-0.635162\pi\)
−0.411978 + 0.911194i \(0.635162\pi\)
\(548\) −10.6305 −0.454113
\(549\) 50.4633 2.15372
\(550\) 15.9989 0.682194
\(551\) −17.8999 −0.762562
\(552\) 4.48170 0.190754
\(553\) 19.2624 0.819120
\(554\) 0.190648 0.00809986
\(555\) −3.91280 −0.166089
\(556\) 7.14185 0.302882
\(557\) −17.2624 −0.731430 −0.365715 0.930727i \(-0.619175\pi\)
−0.365715 + 0.930727i \(0.619175\pi\)
\(558\) 36.6370 1.55097
\(559\) 48.0791 2.03353
\(560\) 0.397260 0.0167873
\(561\) −27.9106 −1.17839
\(562\) −8.34937 −0.352197
\(563\) −3.14065 −0.132363 −0.0661813 0.997808i \(-0.521082\pi\)
−0.0661813 + 0.997808i \(0.521082\pi\)
\(564\) −20.1553 −0.848693
\(565\) 1.38097 0.0580979
\(566\) −12.0914 −0.508238
\(567\) 16.1355 0.677629
\(568\) −3.36425 −0.141161
\(569\) 10.3020 0.431881 0.215941 0.976406i \(-0.430718\pi\)
0.215941 + 0.976406i \(0.430718\pi\)
\(570\) 1.54532 0.0647265
\(571\) −35.0932 −1.46860 −0.734301 0.678824i \(-0.762490\pi\)
−0.734301 + 0.678824i \(0.762490\pi\)
\(572\) −20.5475 −0.859135
\(573\) 27.7715 1.16017
\(574\) 26.9046 1.12298
\(575\) 8.49022 0.354066
\(576\) 3.91674 0.163198
\(577\) 15.4046 0.641303 0.320651 0.947197i \(-0.396098\pi\)
0.320651 + 0.947197i \(0.396098\pi\)
\(578\) −6.07773 −0.252800
\(579\) 63.1765 2.62553
\(580\) 0.540326 0.0224358
\(581\) 7.47561 0.310140
\(582\) −11.4599 −0.475028
\(583\) 10.9787 0.454693
\(584\) 8.97955 0.371576
\(585\) −3.33779 −0.138001
\(586\) 22.0633 0.911428
\(587\) −45.9000 −1.89450 −0.947248 0.320502i \(-0.896148\pi\)
−0.947248 + 0.320502i \(0.896148\pi\)
\(588\) −4.99080 −0.205817
\(589\) 41.2693 1.70047
\(590\) −0.915230 −0.0376794
\(591\) 25.4477 1.04678
\(592\) −11.1712 −0.459134
\(593\) 3.55411 0.145950 0.0729749 0.997334i \(-0.476751\pi\)
0.0729749 + 0.997334i \(0.476751\pi\)
\(594\) 7.74213 0.317663
\(595\) −1.31290 −0.0538236
\(596\) 3.29780 0.135083
\(597\) 50.2082 2.05489
\(598\) −10.9041 −0.445901
\(599\) −47.5119 −1.94128 −0.970642 0.240529i \(-0.922679\pi\)
−0.970642 + 0.240529i \(0.922679\pi\)
\(600\) 13.1032 0.534936
\(601\) −42.2330 −1.72272 −0.861360 0.507995i \(-0.830387\pi\)
−0.861360 + 0.507995i \(0.830387\pi\)
\(602\) −22.4129 −0.913481
\(603\) 27.2823 1.11102
\(604\) −4.60869 −0.187525
\(605\) 0.0916837 0.00372747
\(606\) 15.4392 0.627175
\(607\) −43.1107 −1.74981 −0.874904 0.484296i \(-0.839076\pi\)
−0.874904 + 0.484296i \(0.839076\pi\)
\(608\) 4.41196 0.178929
\(609\) −31.8279 −1.28973
\(610\) −1.71588 −0.0694740
\(611\) 49.0384 1.98388
\(612\) −12.9444 −0.523246
\(613\) −20.2861 −0.819348 −0.409674 0.912232i \(-0.634358\pi\)
−0.409674 + 0.912232i \(0.634358\pi\)
\(614\) 5.65068 0.228043
\(615\) −3.15919 −0.127391
\(616\) 9.57857 0.385932
\(617\) 22.0173 0.886384 0.443192 0.896427i \(-0.353846\pi\)
0.443192 + 0.896427i \(0.353846\pi\)
\(618\) −7.29077 −0.293278
\(619\) 26.6371 1.07063 0.535317 0.844651i \(-0.320192\pi\)
0.535317 + 0.844651i \(0.320192\pi\)
\(620\) −1.24575 −0.0500306
\(621\) 4.10856 0.164871
\(622\) −17.5752 −0.704701
\(623\) −18.6845 −0.748581
\(624\) −16.8286 −0.673683
\(625\) 24.7343 0.989371
\(626\) −10.6930 −0.427377
\(627\) 37.2602 1.48803
\(628\) −19.9945 −0.797867
\(629\) 36.9196 1.47208
\(630\) 1.55597 0.0619911
\(631\) −23.0720 −0.918482 −0.459241 0.888312i \(-0.651879\pi\)
−0.459241 + 0.888312i \(0.651879\pi\)
\(632\) −6.45762 −0.256870
\(633\) 17.7421 0.705183
\(634\) 7.51322 0.298388
\(635\) −0.651734 −0.0258633
\(636\) 8.99168 0.356543
\(637\) 12.1427 0.481113
\(638\) 13.0281 0.515788
\(639\) −13.1769 −0.521270
\(640\) −0.133179 −0.00526438
\(641\) −4.86034 −0.191972 −0.0959860 0.995383i \(-0.530600\pi\)
−0.0959860 + 0.995383i \(0.530600\pi\)
\(642\) −10.7169 −0.422961
\(643\) −29.0047 −1.14384 −0.571918 0.820311i \(-0.693800\pi\)
−0.571918 + 0.820311i \(0.693800\pi\)
\(644\) 5.08312 0.200303
\(645\) 2.63177 0.103626
\(646\) −14.5810 −0.573683
\(647\) −43.7061 −1.71826 −0.859132 0.511754i \(-0.828996\pi\)
−0.859132 + 0.511754i \(0.828996\pi\)
\(648\) −5.40936 −0.212500
\(649\) −22.0676 −0.866230
\(650\) −31.8804 −1.25045
\(651\) 73.3810 2.87603
\(652\) 8.64548 0.338583
\(653\) −23.7803 −0.930593 −0.465297 0.885155i \(-0.654052\pi\)
−0.465297 + 0.885155i \(0.654052\pi\)
\(654\) −32.4558 −1.26912
\(655\) 2.10363 0.0821958
\(656\) −9.01963 −0.352157
\(657\) 35.1706 1.37213
\(658\) −22.8601 −0.891178
\(659\) 29.1985 1.13741 0.568705 0.822541i \(-0.307444\pi\)
0.568705 + 0.822541i \(0.307444\pi\)
\(660\) −1.12473 −0.0437802
\(661\) −32.6219 −1.26884 −0.634422 0.772987i \(-0.718762\pi\)
−0.634422 + 0.772987i \(0.718762\pi\)
\(662\) −1.19105 −0.0462914
\(663\) 55.6166 2.15997
\(664\) −2.50616 −0.0972578
\(665\) 1.75270 0.0679667
\(666\) −43.7547 −1.69546
\(667\) 6.91370 0.267700
\(668\) −1.48837 −0.0575866
\(669\) 26.2838 1.01619
\(670\) −0.927668 −0.0358389
\(671\) −41.3726 −1.59717
\(672\) 7.84493 0.302625
\(673\) −37.4977 −1.44543 −0.722715 0.691146i \(-0.757106\pi\)
−0.722715 + 0.691146i \(0.757106\pi\)
\(674\) −15.7956 −0.608423
\(675\) 12.0123 0.462352
\(676\) 27.9444 1.07478
\(677\) −22.8796 −0.879333 −0.439667 0.898161i \(-0.644903\pi\)
−0.439667 + 0.898161i \(0.644903\pi\)
\(678\) 27.2709 1.04733
\(679\) −12.9977 −0.498807
\(680\) 0.440142 0.0168787
\(681\) 69.1091 2.64827
\(682\) −30.0370 −1.15018
\(683\) 2.77870 0.106324 0.0531621 0.998586i \(-0.483070\pi\)
0.0531621 + 0.998586i \(0.483070\pi\)
\(684\) 17.2805 0.660737
\(685\) 1.41576 0.0540936
\(686\) 15.2197 0.581092
\(687\) 23.3548 0.891040
\(688\) 7.51380 0.286461
\(689\) −21.8770 −0.833446
\(690\) −0.596870 −0.0227224
\(691\) −7.68775 −0.292456 −0.146228 0.989251i \(-0.546713\pi\)
−0.146228 + 0.989251i \(0.546713\pi\)
\(692\) −22.2013 −0.843965
\(693\) 37.5168 1.42514
\(694\) −29.3425 −1.11382
\(695\) −0.951147 −0.0360791
\(696\) 10.6701 0.404450
\(697\) 29.8088 1.12909
\(698\) −11.1330 −0.421391
\(699\) 37.6031 1.42228
\(700\) 14.8616 0.561715
\(701\) −29.7679 −1.12432 −0.562159 0.827029i \(-0.690029\pi\)
−0.562159 + 0.827029i \(0.690029\pi\)
\(702\) −15.4275 −0.582273
\(703\) −49.2870 −1.85889
\(704\) −3.21116 −0.121025
\(705\) 2.68428 0.101096
\(706\) −11.1144 −0.418296
\(707\) 17.5111 0.658571
\(708\) −18.0736 −0.679246
\(709\) 3.74967 0.140822 0.0704109 0.997518i \(-0.477569\pi\)
0.0704109 + 0.997518i \(0.477569\pi\)
\(710\) 0.448049 0.0168150
\(711\) −25.2928 −0.948555
\(712\) 6.26390 0.234749
\(713\) −15.9399 −0.596955
\(714\) −25.9266 −0.970278
\(715\) 2.73651 0.102340
\(716\) 15.6212 0.583792
\(717\) −0.616894 −0.0230383
\(718\) 26.5411 0.990504
\(719\) 38.2410 1.42615 0.713074 0.701089i \(-0.247302\pi\)
0.713074 + 0.701089i \(0.247302\pi\)
\(720\) −0.521629 −0.0194400
\(721\) −8.26915 −0.307959
\(722\) 0.465431 0.0173216
\(723\) 49.1653 1.82848
\(724\) 20.7058 0.769526
\(725\) 20.2137 0.750717
\(726\) 1.81053 0.0671951
\(727\) 21.0432 0.780450 0.390225 0.920720i \(-0.372397\pi\)
0.390225 + 0.920720i \(0.372397\pi\)
\(728\) −19.0869 −0.707407
\(729\) −40.2097 −1.48925
\(730\) −1.19589 −0.0442619
\(731\) −24.8323 −0.918454
\(732\) −33.8845 −1.25241
\(733\) 51.3367 1.89616 0.948082 0.318025i \(-0.103020\pi\)
0.948082 + 0.318025i \(0.103020\pi\)
\(734\) 16.7371 0.617777
\(735\) 0.664672 0.0245168
\(736\) −1.70409 −0.0628135
\(737\) −22.3675 −0.823919
\(738\) −35.3276 −1.30043
\(739\) −41.4344 −1.52419 −0.762094 0.647467i \(-0.775829\pi\)
−0.762094 + 0.647467i \(0.775829\pi\)
\(740\) 1.48777 0.0546916
\(741\) −74.2472 −2.72754
\(742\) 10.1983 0.374392
\(743\) −4.65789 −0.170881 −0.0854406 0.996343i \(-0.527230\pi\)
−0.0854406 + 0.996343i \(0.527230\pi\)
\(744\) −24.6006 −0.901901
\(745\) −0.439198 −0.0160910
\(746\) −20.5677 −0.753038
\(747\) −9.81598 −0.359148
\(748\) 10.6125 0.388033
\(749\) −12.1550 −0.444134
\(750\) −3.49636 −0.127669
\(751\) 44.7500 1.63295 0.816476 0.577380i \(-0.195925\pi\)
0.816476 + 0.577380i \(0.195925\pi\)
\(752\) 7.66372 0.279467
\(753\) 43.6119 1.58931
\(754\) −25.9607 −0.945432
\(755\) 0.613783 0.0223378
\(756\) 7.19177 0.261562
\(757\) −18.1450 −0.659490 −0.329745 0.944070i \(-0.606963\pi\)
−0.329745 + 0.944070i \(0.606963\pi\)
\(758\) 6.19803 0.225122
\(759\) −14.3915 −0.522378
\(760\) −0.587583 −0.0213139
\(761\) 3.29321 0.119379 0.0596894 0.998217i \(-0.480989\pi\)
0.0596894 + 0.998217i \(0.480989\pi\)
\(762\) −12.8702 −0.466237
\(763\) −36.8112 −1.33265
\(764\) −10.5596 −0.382034
\(765\) 1.72392 0.0623286
\(766\) −0.542879 −0.0196150
\(767\) 43.9734 1.58779
\(768\) −2.62997 −0.0949009
\(769\) 31.6709 1.14208 0.571042 0.820921i \(-0.306540\pi\)
0.571042 + 0.820921i \(0.306540\pi\)
\(770\) −1.27567 −0.0459719
\(771\) 1.52011 0.0547453
\(772\) −24.0218 −0.864562
\(773\) 25.2491 0.908147 0.454074 0.890964i \(-0.349970\pi\)
0.454074 + 0.890964i \(0.349970\pi\)
\(774\) 29.4296 1.05783
\(775\) −46.6038 −1.67406
\(776\) 4.35742 0.156422
\(777\) −87.6373 −3.14397
\(778\) −21.7112 −0.778384
\(779\) −39.7943 −1.42578
\(780\) 2.24122 0.0802486
\(781\) 10.8032 0.386567
\(782\) 5.63182 0.201393
\(783\) 9.78175 0.349571
\(784\) 1.89767 0.0677738
\(785\) 2.66285 0.0950413
\(786\) 41.5417 1.48174
\(787\) 19.7923 0.705521 0.352760 0.935714i \(-0.385243\pi\)
0.352760 + 0.935714i \(0.385243\pi\)
\(788\) −9.67603 −0.344694
\(789\) 23.9321 0.852005
\(790\) 0.860021 0.0305982
\(791\) 30.9304 1.09976
\(792\) −12.5773 −0.446915
\(793\) 82.4418 2.92760
\(794\) 32.2232 1.14356
\(795\) −1.19751 −0.0424712
\(796\) −19.0908 −0.676656
\(797\) 15.6704 0.555075 0.277538 0.960715i \(-0.410482\pi\)
0.277538 + 0.960715i \(0.410482\pi\)
\(798\) 34.6115 1.22524
\(799\) −25.3277 −0.896030
\(800\) −4.98226 −0.176150
\(801\) 24.5341 0.866869
\(802\) 34.0790 1.20337
\(803\) −28.8348 −1.01756
\(804\) −18.3192 −0.646069
\(805\) −0.676966 −0.0238599
\(806\) 59.8538 2.10826
\(807\) −18.2105 −0.641039
\(808\) −5.87049 −0.206523
\(809\) 33.4793 1.17707 0.588534 0.808472i \(-0.299705\pi\)
0.588534 + 0.808472i \(0.299705\pi\)
\(810\) 0.720415 0.0253128
\(811\) 30.9366 1.08633 0.543166 0.839626i \(-0.317226\pi\)
0.543166 + 0.839626i \(0.317226\pi\)
\(812\) 12.1020 0.424697
\(813\) −8.75620 −0.307093
\(814\) 35.8726 1.25733
\(815\) −1.15140 −0.0403318
\(816\) 8.69175 0.304272
\(817\) 33.1506 1.15979
\(818\) −4.18983 −0.146494
\(819\) −74.7584 −2.61227
\(820\) 1.20123 0.0419487
\(821\) −6.18660 −0.215914 −0.107957 0.994156i \(-0.534431\pi\)
−0.107957 + 0.994156i \(0.534431\pi\)
\(822\) 27.9579 0.975144
\(823\) −12.3996 −0.432224 −0.216112 0.976369i \(-0.569338\pi\)
−0.216112 + 0.976369i \(0.569338\pi\)
\(824\) 2.77219 0.0965737
\(825\) −42.0765 −1.46492
\(826\) −20.4989 −0.713249
\(827\) 34.1205 1.18649 0.593243 0.805023i \(-0.297847\pi\)
0.593243 + 0.805023i \(0.297847\pi\)
\(828\) −6.67447 −0.231954
\(829\) −11.9221 −0.414070 −0.207035 0.978334i \(-0.566381\pi\)
−0.207035 + 0.978334i \(0.566381\pi\)
\(830\) 0.333768 0.0115853
\(831\) −0.501399 −0.0173933
\(832\) 6.39878 0.221838
\(833\) −6.27157 −0.217297
\(834\) −18.7828 −0.650397
\(835\) 0.198220 0.00685967
\(836\) −14.1675 −0.489995
\(837\) −22.5524 −0.779525
\(838\) 17.5670 0.606841
\(839\) 31.2257 1.07803 0.539016 0.842296i \(-0.318796\pi\)
0.539016 + 0.842296i \(0.318796\pi\)
\(840\) −1.04478 −0.0360484
\(841\) −12.5397 −0.432404
\(842\) −25.4373 −0.876628
\(843\) 21.9586 0.756294
\(844\) −6.74610 −0.232210
\(845\) −3.72161 −0.128027
\(846\) 30.0168 1.03200
\(847\) 2.05349 0.0705589
\(848\) −3.41893 −0.117407
\(849\) 31.7999 1.09137
\(850\) 16.4658 0.564773
\(851\) 19.0367 0.652570
\(852\) 8.84788 0.303123
\(853\) −31.4513 −1.07687 −0.538437 0.842666i \(-0.680985\pi\)
−0.538437 + 0.842666i \(0.680985\pi\)
\(854\) −38.4316 −1.31510
\(855\) −2.30141 −0.0787065
\(856\) 4.07490 0.139277
\(857\) 42.9199 1.46612 0.733059 0.680165i \(-0.238092\pi\)
0.733059 + 0.680165i \(0.238092\pi\)
\(858\) 54.0394 1.84487
\(859\) −35.7822 −1.22087 −0.610437 0.792065i \(-0.709006\pi\)
−0.610437 + 0.792065i \(0.709006\pi\)
\(860\) −1.00068 −0.0341230
\(861\) −70.7583 −2.41144
\(862\) −7.70426 −0.262408
\(863\) −10.4621 −0.356136 −0.178068 0.984018i \(-0.556985\pi\)
−0.178068 + 0.984018i \(0.556985\pi\)
\(864\) −2.41100 −0.0820240
\(865\) 2.95675 0.100532
\(866\) 33.2194 1.12884
\(867\) 15.9842 0.542853
\(868\) −27.9018 −0.947050
\(869\) 20.7365 0.703437
\(870\) −1.42104 −0.0481778
\(871\) 44.5711 1.51023
\(872\) 12.3408 0.417911
\(873\) 17.0669 0.577627
\(874\) −7.51838 −0.254313
\(875\) −3.96555 −0.134060
\(876\) −23.6159 −0.797909
\(877\) −36.6331 −1.23701 −0.618506 0.785780i \(-0.712262\pi\)
−0.618506 + 0.785780i \(0.712262\pi\)
\(878\) −40.5548 −1.36866
\(879\) −58.0259 −1.95717
\(880\) 0.427661 0.0144164
\(881\) −6.11592 −0.206050 −0.103025 0.994679i \(-0.532852\pi\)
−0.103025 + 0.994679i \(0.532852\pi\)
\(882\) 7.43267 0.250271
\(883\) −12.4748 −0.419812 −0.209906 0.977722i \(-0.567316\pi\)
−0.209906 + 0.977722i \(0.567316\pi\)
\(884\) −21.1472 −0.711258
\(885\) 2.40703 0.0809113
\(886\) −20.2385 −0.679924
\(887\) −2.96844 −0.0996705 −0.0498353 0.998757i \(-0.515870\pi\)
−0.0498353 + 0.998757i \(0.515870\pi\)
\(888\) 29.3799 0.985926
\(889\) −14.5973 −0.489577
\(890\) −0.834221 −0.0279632
\(891\) 17.3703 0.581928
\(892\) −9.99394 −0.334622
\(893\) 33.8120 1.13148
\(894\) −8.67311 −0.290072
\(895\) −2.08042 −0.0695408
\(896\) −2.98290 −0.0996515
\(897\) 28.6774 0.957511
\(898\) 7.57351 0.252731
\(899\) −37.9501 −1.26571
\(900\) −19.5142 −0.650475
\(901\) 11.2992 0.376430
\(902\) 28.9635 0.964379
\(903\) 58.9452 1.96157
\(904\) −10.3693 −0.344877
\(905\) −2.75759 −0.0916654
\(906\) 12.1207 0.402684
\(907\) −31.0898 −1.03232 −0.516160 0.856492i \(-0.672639\pi\)
−0.516160 + 0.856492i \(0.672639\pi\)
\(908\) −26.2775 −0.872051
\(909\) −22.9932 −0.762636
\(910\) 2.54198 0.0842658
\(911\) 40.8917 1.35480 0.677401 0.735614i \(-0.263106\pi\)
0.677401 + 0.735614i \(0.263106\pi\)
\(912\) −11.6033 −0.384225
\(913\) 8.04769 0.266340
\(914\) −0.569802 −0.0188474
\(915\) 4.51272 0.149186
\(916\) −8.88024 −0.293412
\(917\) 47.1163 1.55592
\(918\) 7.96809 0.262986
\(919\) −3.20026 −0.105567 −0.0527834 0.998606i \(-0.516809\pi\)
−0.0527834 + 0.998606i \(0.516809\pi\)
\(920\) 0.226949 0.00748230
\(921\) −14.8611 −0.489690
\(922\) 3.89924 0.128415
\(923\) −21.5271 −0.708573
\(924\) −25.1913 −0.828734
\(925\) 55.6579 1.83002
\(926\) 30.2977 0.995646
\(927\) 10.8579 0.356622
\(928\) −4.05713 −0.133182
\(929\) 34.4417 1.12999 0.564997 0.825093i \(-0.308877\pi\)
0.564997 + 0.825093i \(0.308877\pi\)
\(930\) 3.27629 0.107434
\(931\) 8.37244 0.274395
\(932\) −14.2979 −0.468343
\(933\) 46.2222 1.51325
\(934\) −18.0191 −0.589604
\(935\) −1.41337 −0.0462221
\(936\) 25.0624 0.819189
\(937\) 2.20212 0.0719402 0.0359701 0.999353i \(-0.488548\pi\)
0.0359701 + 0.999353i \(0.488548\pi\)
\(938\) −20.7775 −0.678410
\(939\) 28.1222 0.917733
\(940\) −1.02065 −0.0332899
\(941\) −1.34998 −0.0440082 −0.0220041 0.999758i \(-0.507005\pi\)
−0.0220041 + 0.999758i \(0.507005\pi\)
\(942\) 52.5849 1.71331
\(943\) 15.3702 0.500524
\(944\) 6.87216 0.223670
\(945\) −0.957796 −0.0311571
\(946\) −24.1280 −0.784471
\(947\) 5.09719 0.165637 0.0828183 0.996565i \(-0.473608\pi\)
0.0828183 + 0.996565i \(0.473608\pi\)
\(948\) 16.9833 0.551593
\(949\) 57.4581 1.86517
\(950\) −21.9816 −0.713176
\(951\) −19.7595 −0.640747
\(952\) 9.85813 0.319504
\(953\) −36.0854 −1.16892 −0.584460 0.811422i \(-0.698694\pi\)
−0.584460 + 0.811422i \(0.698694\pi\)
\(954\) −13.3911 −0.433552
\(955\) 1.40632 0.0455075
\(956\) 0.234563 0.00758631
\(957\) −34.2635 −1.10758
\(958\) −7.99029 −0.258155
\(959\) 31.7097 1.02396
\(960\) 0.350258 0.0113045
\(961\) 56.4962 1.82246
\(962\) −71.4821 −2.30467
\(963\) 15.9603 0.514315
\(964\) −18.6942 −0.602101
\(965\) 3.19920 0.102986
\(966\) −13.3684 −0.430123
\(967\) −35.7635 −1.15008 −0.575039 0.818126i \(-0.695013\pi\)
−0.575039 + 0.818126i \(0.695013\pi\)
\(968\) −0.688423 −0.0221268
\(969\) 38.3477 1.23191
\(970\) −0.580319 −0.0186329
\(971\) 26.4057 0.847400 0.423700 0.905802i \(-0.360731\pi\)
0.423700 + 0.905802i \(0.360731\pi\)
\(972\) 21.4595 0.688313
\(973\) −21.3034 −0.682955
\(974\) 21.1513 0.677730
\(975\) 83.8445 2.68517
\(976\) 12.8840 0.412407
\(977\) 11.2346 0.359428 0.179714 0.983719i \(-0.442483\pi\)
0.179714 + 0.983719i \(0.442483\pi\)
\(978\) −22.7374 −0.727061
\(979\) −20.1144 −0.642859
\(980\) −0.252730 −0.00807316
\(981\) 48.3355 1.54324
\(982\) 35.1515 1.12173
\(983\) −40.6174 −1.29549 −0.647746 0.761856i \(-0.724288\pi\)
−0.647746 + 0.761856i \(0.724288\pi\)
\(984\) 23.7214 0.756209
\(985\) 1.28865 0.0410597
\(986\) 13.4083 0.427009
\(987\) 60.1213 1.91368
\(988\) 28.2312 0.898154
\(989\) −12.8042 −0.407149
\(990\) 1.67504 0.0532362
\(991\) −10.5683 −0.335712 −0.167856 0.985811i \(-0.553684\pi\)
−0.167856 + 0.985811i \(0.553684\pi\)
\(992\) 9.35394 0.296988
\(993\) 3.13242 0.0994044
\(994\) 10.0352 0.318297
\(995\) 2.54250 0.0806027
\(996\) 6.59112 0.208848
\(997\) 10.1443 0.321274 0.160637 0.987014i \(-0.448645\pi\)
0.160637 + 0.987014i \(0.448645\pi\)
\(998\) 11.9801 0.379224
\(999\) 26.9338 0.852148
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 \(a_p\))