Properties

Label 8007.2.a.e.1.3
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60999 q^{2}\) \(+1.00000 q^{3}\) \(+4.81203 q^{4}\) \(-2.83562 q^{5}\) \(-2.60999 q^{6}\) \(+1.53827 q^{7}\) \(-7.33937 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60999 q^{2}\) \(+1.00000 q^{3}\) \(+4.81203 q^{4}\) \(-2.83562 q^{5}\) \(-2.60999 q^{6}\) \(+1.53827 q^{7}\) \(-7.33937 q^{8}\) \(+1.00000 q^{9}\) \(+7.40094 q^{10}\) \(-5.14470 q^{11}\) \(+4.81203 q^{12}\) \(-5.76308 q^{13}\) \(-4.01487 q^{14}\) \(-2.83562 q^{15}\) \(+9.53161 q^{16}\) \(-1.00000 q^{17}\) \(-2.60999 q^{18}\) \(+7.46231 q^{19}\) \(-13.6451 q^{20}\) \(+1.53827 q^{21}\) \(+13.4276 q^{22}\) \(+3.10447 q^{23}\) \(-7.33937 q^{24}\) \(+3.04076 q^{25}\) \(+15.0416 q^{26}\) \(+1.00000 q^{27}\) \(+7.40221 q^{28}\) \(+3.18309 q^{29}\) \(+7.40094 q^{30}\) \(+2.43358 q^{31}\) \(-10.1986 q^{32}\) \(-5.14470 q^{33}\) \(+2.60999 q^{34}\) \(-4.36196 q^{35}\) \(+4.81203 q^{36}\) \(-8.32995 q^{37}\) \(-19.4765 q^{38}\) \(-5.76308 q^{39}\) \(+20.8117 q^{40}\) \(-1.09141 q^{41}\) \(-4.01487 q^{42}\) \(+3.70310 q^{43}\) \(-24.7565 q^{44}\) \(-2.83562 q^{45}\) \(-8.10264 q^{46}\) \(-1.15137 q^{47}\) \(+9.53161 q^{48}\) \(-4.63372 q^{49}\) \(-7.93635 q^{50}\) \(-1.00000 q^{51}\) \(-27.7322 q^{52}\) \(-3.51007 q^{53}\) \(-2.60999 q^{54}\) \(+14.5884 q^{55}\) \(-11.2899 q^{56}\) \(+7.46231 q^{57}\) \(-8.30782 q^{58}\) \(+11.8360 q^{59}\) \(-13.6451 q^{60}\) \(+0.108053 q^{61}\) \(-6.35161 q^{62}\) \(+1.53827 q^{63}\) \(+7.55507 q^{64}\) \(+16.3419 q^{65}\) \(+13.4276 q^{66}\) \(+12.6485 q^{67}\) \(-4.81203 q^{68}\) \(+3.10447 q^{69}\) \(+11.3847 q^{70}\) \(+0.363136 q^{71}\) \(-7.33937 q^{72}\) \(+8.47199 q^{73}\) \(+21.7411 q^{74}\) \(+3.04076 q^{75}\) \(+35.9089 q^{76}\) \(-7.91394 q^{77}\) \(+15.0416 q^{78}\) \(+2.26541 q^{79}\) \(-27.0280 q^{80}\) \(+1.00000 q^{81}\) \(+2.84858 q^{82}\) \(-2.62989 q^{83}\) \(+7.40221 q^{84}\) \(+2.83562 q^{85}\) \(-9.66505 q^{86}\) \(+3.18309 q^{87}\) \(+37.7589 q^{88}\) \(+3.19988 q^{89}\) \(+7.40094 q^{90}\) \(-8.86518 q^{91}\) \(+14.9388 q^{92}\) \(+2.43358 q^{93}\) \(+3.00506 q^{94}\) \(-21.1603 q^{95}\) \(-10.1986 q^{96}\) \(+9.70271 q^{97}\) \(+12.0940 q^{98}\) \(-5.14470 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60999 −1.84554 −0.922770 0.385351i \(-0.874080\pi\)
−0.922770 + 0.385351i \(0.874080\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.81203 2.40602
\(5\) −2.83562 −1.26813 −0.634065 0.773280i \(-0.718615\pi\)
−0.634065 + 0.773280i \(0.718615\pi\)
\(6\) −2.60999 −1.06552
\(7\) 1.53827 0.581412 0.290706 0.956812i \(-0.406110\pi\)
0.290706 + 0.956812i \(0.406110\pi\)
\(8\) −7.33937 −2.59486
\(9\) 1.00000 0.333333
\(10\) 7.40094 2.34038
\(11\) −5.14470 −1.55118 −0.775592 0.631234i \(-0.782549\pi\)
−0.775592 + 0.631234i \(0.782549\pi\)
\(12\) 4.81203 1.38911
\(13\) −5.76308 −1.59839 −0.799196 0.601070i \(-0.794741\pi\)
−0.799196 + 0.601070i \(0.794741\pi\)
\(14\) −4.01487 −1.07302
\(15\) −2.83562 −0.732155
\(16\) 9.53161 2.38290
\(17\) −1.00000 −0.242536
\(18\) −2.60999 −0.615180
\(19\) 7.46231 1.71197 0.855986 0.516999i \(-0.172951\pi\)
0.855986 + 0.516999i \(0.172951\pi\)
\(20\) −13.6451 −3.05114
\(21\) 1.53827 0.335678
\(22\) 13.4276 2.86277
\(23\) 3.10447 0.647327 0.323664 0.946172i \(-0.395085\pi\)
0.323664 + 0.946172i \(0.395085\pi\)
\(24\) −7.33937 −1.49814
\(25\) 3.04076 0.608152
\(26\) 15.0416 2.94990
\(27\) 1.00000 0.192450
\(28\) 7.40221 1.39889
\(29\) 3.18309 0.591085 0.295542 0.955330i \(-0.404500\pi\)
0.295542 + 0.955330i \(0.404500\pi\)
\(30\) 7.40094 1.35122
\(31\) 2.43358 0.437084 0.218542 0.975828i \(-0.429870\pi\)
0.218542 + 0.975828i \(0.429870\pi\)
\(32\) −10.1986 −1.80288
\(33\) −5.14470 −0.895577
\(34\) 2.60999 0.447609
\(35\) −4.36196 −0.737305
\(36\) 4.81203 0.802006
\(37\) −8.32995 −1.36944 −0.684718 0.728809i \(-0.740074\pi\)
−0.684718 + 0.728809i \(0.740074\pi\)
\(38\) −19.4765 −3.15951
\(39\) −5.76308 −0.922832
\(40\) 20.8117 3.29062
\(41\) −1.09141 −0.170450 −0.0852251 0.996362i \(-0.527161\pi\)
−0.0852251 + 0.996362i \(0.527161\pi\)
\(42\) −4.01487 −0.619507
\(43\) 3.70310 0.564718 0.282359 0.959309i \(-0.408883\pi\)
0.282359 + 0.959309i \(0.408883\pi\)
\(44\) −24.7565 −3.73218
\(45\) −2.83562 −0.422710
\(46\) −8.10264 −1.19467
\(47\) −1.15137 −0.167944 −0.0839722 0.996468i \(-0.526761\pi\)
−0.0839722 + 0.996468i \(0.526761\pi\)
\(48\) 9.53161 1.37577
\(49\) −4.63372 −0.661960
\(50\) −7.93635 −1.12237
\(51\) −1.00000 −0.140028
\(52\) −27.7322 −3.84576
\(53\) −3.51007 −0.482145 −0.241073 0.970507i \(-0.577499\pi\)
−0.241073 + 0.970507i \(0.577499\pi\)
\(54\) −2.60999 −0.355174
\(55\) 14.5884 1.96710
\(56\) −11.2899 −1.50868
\(57\) 7.46231 0.988407
\(58\) −8.30782 −1.09087
\(59\) 11.8360 1.54092 0.770458 0.637491i \(-0.220028\pi\)
0.770458 + 0.637491i \(0.220028\pi\)
\(60\) −13.6451 −1.76158
\(61\) 0.108053 0.0138348 0.00691741 0.999976i \(-0.497798\pi\)
0.00691741 + 0.999976i \(0.497798\pi\)
\(62\) −6.35161 −0.806656
\(63\) 1.53827 0.193804
\(64\) 7.55507 0.944384
\(65\) 16.3419 2.02697
\(66\) 13.4276 1.65282
\(67\) 12.6485 1.54526 0.772632 0.634854i \(-0.218940\pi\)
0.772632 + 0.634854i \(0.218940\pi\)
\(68\) −4.81203 −0.583545
\(69\) 3.10447 0.373735
\(70\) 11.3847 1.36073
\(71\) 0.363136 0.0430963 0.0215482 0.999768i \(-0.493140\pi\)
0.0215482 + 0.999768i \(0.493140\pi\)
\(72\) −7.33937 −0.864954
\(73\) 8.47199 0.991571 0.495786 0.868445i \(-0.334880\pi\)
0.495786 + 0.868445i \(0.334880\pi\)
\(74\) 21.7411 2.52735
\(75\) 3.04076 0.351117
\(76\) 35.9089 4.11903
\(77\) −7.91394 −0.901877
\(78\) 15.0416 1.70312
\(79\) 2.26541 0.254879 0.127439 0.991846i \(-0.459324\pi\)
0.127439 + 0.991846i \(0.459324\pi\)
\(80\) −27.0280 −3.02183
\(81\) 1.00000 0.111111
\(82\) 2.84858 0.314573
\(83\) −2.62989 −0.288668 −0.144334 0.989529i \(-0.546104\pi\)
−0.144334 + 0.989529i \(0.546104\pi\)
\(84\) 7.40221 0.807648
\(85\) 2.83562 0.307567
\(86\) −9.66505 −1.04221
\(87\) 3.18309 0.341263
\(88\) 37.7589 4.02511
\(89\) 3.19988 0.339187 0.169593 0.985514i \(-0.445755\pi\)
0.169593 + 0.985514i \(0.445755\pi\)
\(90\) 7.40094 0.780128
\(91\) −8.86518 −0.929324
\(92\) 14.9388 1.55748
\(93\) 2.43358 0.252351
\(94\) 3.00506 0.309948
\(95\) −21.1603 −2.17100
\(96\) −10.1986 −1.04089
\(97\) 9.70271 0.985160 0.492580 0.870267i \(-0.336054\pi\)
0.492580 + 0.870267i \(0.336054\pi\)
\(98\) 12.0940 1.22167
\(99\) −5.14470 −0.517061
\(100\) 14.6322 1.46322
\(101\) 5.05721 0.503211 0.251605 0.967830i \(-0.419041\pi\)
0.251605 + 0.967830i \(0.419041\pi\)
\(102\) 2.60999 0.258427
\(103\) 9.12966 0.899572 0.449786 0.893136i \(-0.351500\pi\)
0.449786 + 0.893136i \(0.351500\pi\)
\(104\) 42.2974 4.14760
\(105\) −4.36196 −0.425683
\(106\) 9.16124 0.889818
\(107\) −5.83628 −0.564214 −0.282107 0.959383i \(-0.591033\pi\)
−0.282107 + 0.959383i \(0.591033\pi\)
\(108\) 4.81203 0.463038
\(109\) 14.9628 1.43318 0.716590 0.697494i \(-0.245702\pi\)
0.716590 + 0.697494i \(0.245702\pi\)
\(110\) −38.0756 −3.63037
\(111\) −8.32995 −0.790644
\(112\) 14.6622 1.38545
\(113\) −18.2850 −1.72011 −0.860055 0.510201i \(-0.829571\pi\)
−0.860055 + 0.510201i \(0.829571\pi\)
\(114\) −19.4765 −1.82414
\(115\) −8.80312 −0.820895
\(116\) 15.3171 1.42216
\(117\) −5.76308 −0.532797
\(118\) −30.8918 −2.84382
\(119\) −1.53827 −0.141013
\(120\) 20.8117 1.89984
\(121\) 15.4679 1.40617
\(122\) −0.282018 −0.0255327
\(123\) −1.09141 −0.0984095
\(124\) 11.7105 1.05163
\(125\) 5.55567 0.496914
\(126\) −4.01487 −0.357673
\(127\) −18.4156 −1.63412 −0.817059 0.576554i \(-0.804397\pi\)
−0.817059 + 0.576554i \(0.804397\pi\)
\(128\) 0.678611 0.0599813
\(129\) 3.70310 0.326040
\(130\) −42.6523 −3.74085
\(131\) −13.5949 −1.18779 −0.593897 0.804541i \(-0.702411\pi\)
−0.593897 + 0.804541i \(0.702411\pi\)
\(132\) −24.7565 −2.15477
\(133\) 11.4791 0.995360
\(134\) −33.0125 −2.85185
\(135\) −2.83562 −0.244052
\(136\) 7.33937 0.629346
\(137\) −5.01134 −0.428147 −0.214074 0.976818i \(-0.568673\pi\)
−0.214074 + 0.976818i \(0.568673\pi\)
\(138\) −8.10264 −0.689742
\(139\) −7.14731 −0.606227 −0.303113 0.952955i \(-0.598026\pi\)
−0.303113 + 0.952955i \(0.598026\pi\)
\(140\) −20.9899 −1.77397
\(141\) −1.15137 −0.0969627
\(142\) −0.947780 −0.0795360
\(143\) 29.6493 2.47940
\(144\) 9.53161 0.794301
\(145\) −9.02604 −0.749572
\(146\) −22.1118 −1.82998
\(147\) −4.63372 −0.382183
\(148\) −40.0840 −3.29488
\(149\) −6.22325 −0.509829 −0.254914 0.966964i \(-0.582047\pi\)
−0.254914 + 0.966964i \(0.582047\pi\)
\(150\) −7.93635 −0.648000
\(151\) −1.69421 −0.137873 −0.0689363 0.997621i \(-0.521961\pi\)
−0.0689363 + 0.997621i \(0.521961\pi\)
\(152\) −54.7687 −4.44233
\(153\) −1.00000 −0.0808452
\(154\) 20.6553 1.66445
\(155\) −6.90072 −0.554279
\(156\) −27.7322 −2.22035
\(157\) 1.00000 0.0798087
\(158\) −5.91270 −0.470389
\(159\) −3.51007 −0.278367
\(160\) 28.9195 2.28628
\(161\) 4.77552 0.376364
\(162\) −2.60999 −0.205060
\(163\) −6.60248 −0.517146 −0.258573 0.965992i \(-0.583252\pi\)
−0.258573 + 0.965992i \(0.583252\pi\)
\(164\) −5.25192 −0.410106
\(165\) 14.5884 1.13571
\(166\) 6.86397 0.532748
\(167\) −0.195685 −0.0151425 −0.00757127 0.999971i \(-0.502410\pi\)
−0.00757127 + 0.999971i \(0.502410\pi\)
\(168\) −11.2899 −0.871038
\(169\) 20.2131 1.55486
\(170\) −7.40094 −0.567626
\(171\) 7.46231 0.570657
\(172\) 17.8194 1.35872
\(173\) 16.0672 1.22156 0.610782 0.791798i \(-0.290855\pi\)
0.610782 + 0.791798i \(0.290855\pi\)
\(174\) −8.30782 −0.629814
\(175\) 4.67751 0.353587
\(176\) −49.0372 −3.69632
\(177\) 11.8360 0.889648
\(178\) −8.35165 −0.625983
\(179\) −1.44212 −0.107789 −0.0538947 0.998547i \(-0.517164\pi\)
−0.0538947 + 0.998547i \(0.517164\pi\)
\(180\) −13.6451 −1.01705
\(181\) −9.39990 −0.698689 −0.349344 0.936994i \(-0.613596\pi\)
−0.349344 + 0.936994i \(0.613596\pi\)
\(182\) 23.1380 1.71510
\(183\) 0.108053 0.00798753
\(184\) −22.7849 −1.67972
\(185\) 23.6206 1.73662
\(186\) −6.35161 −0.465723
\(187\) 5.14470 0.376217
\(188\) −5.54042 −0.404077
\(189\) 1.53827 0.111893
\(190\) 55.2281 4.00667
\(191\) 10.1320 0.733129 0.366565 0.930393i \(-0.380534\pi\)
0.366565 + 0.930393i \(0.380534\pi\)
\(192\) 7.55507 0.545240
\(193\) −22.4580 −1.61656 −0.808281 0.588796i \(-0.799602\pi\)
−0.808281 + 0.588796i \(0.799602\pi\)
\(194\) −25.3239 −1.81815
\(195\) 16.3419 1.17027
\(196\) −22.2976 −1.59269
\(197\) 24.3674 1.73611 0.868053 0.496471i \(-0.165371\pi\)
0.868053 + 0.496471i \(0.165371\pi\)
\(198\) 13.4276 0.954258
\(199\) −5.49168 −0.389295 −0.194648 0.980873i \(-0.562356\pi\)
−0.194648 + 0.980873i \(0.562356\pi\)
\(200\) −22.3173 −1.57807
\(201\) 12.6485 0.892159
\(202\) −13.1992 −0.928696
\(203\) 4.89645 0.343664
\(204\) −4.81203 −0.336910
\(205\) 3.09484 0.216153
\(206\) −23.8283 −1.66020
\(207\) 3.10447 0.215776
\(208\) −54.9315 −3.80881
\(209\) −38.3913 −2.65558
\(210\) 11.3847 0.785616
\(211\) −22.3895 −1.54136 −0.770678 0.637225i \(-0.780082\pi\)
−0.770678 + 0.637225i \(0.780082\pi\)
\(212\) −16.8906 −1.16005
\(213\) 0.363136 0.0248817
\(214\) 15.2326 1.04128
\(215\) −10.5006 −0.716135
\(216\) −7.33937 −0.499381
\(217\) 3.74351 0.254126
\(218\) −39.0528 −2.64499
\(219\) 8.47199 0.572484
\(220\) 70.2000 4.73288
\(221\) 5.76308 0.387667
\(222\) 21.7411 1.45916
\(223\) −25.1735 −1.68574 −0.842871 0.538115i \(-0.819137\pi\)
−0.842871 + 0.538115i \(0.819137\pi\)
\(224\) −15.6882 −1.04822
\(225\) 3.04076 0.202717
\(226\) 47.7237 3.17453
\(227\) −1.56993 −0.104200 −0.0520999 0.998642i \(-0.516591\pi\)
−0.0520999 + 0.998642i \(0.516591\pi\)
\(228\) 35.9089 2.37812
\(229\) 11.5907 0.765937 0.382968 0.923761i \(-0.374902\pi\)
0.382968 + 0.923761i \(0.374902\pi\)
\(230\) 22.9760 1.51499
\(231\) −7.91394 −0.520699
\(232\) −23.3619 −1.53378
\(233\) −24.9761 −1.63624 −0.818119 0.575049i \(-0.804983\pi\)
−0.818119 + 0.575049i \(0.804983\pi\)
\(234\) 15.0416 0.983299
\(235\) 3.26485 0.212975
\(236\) 56.9553 3.70747
\(237\) 2.26541 0.147154
\(238\) 4.01487 0.260245
\(239\) 23.9646 1.55014 0.775072 0.631873i \(-0.217714\pi\)
0.775072 + 0.631873i \(0.217714\pi\)
\(240\) −27.0280 −1.74465
\(241\) 7.24733 0.466841 0.233421 0.972376i \(-0.425008\pi\)
0.233421 + 0.972376i \(0.425008\pi\)
\(242\) −40.3710 −2.59515
\(243\) 1.00000 0.0641500
\(244\) 0.519957 0.0332868
\(245\) 13.1395 0.839451
\(246\) 2.84858 0.181619
\(247\) −43.0059 −2.73640
\(248\) −17.8610 −1.13417
\(249\) −2.62989 −0.166662
\(250\) −14.5002 −0.917074
\(251\) −5.10578 −0.322274 −0.161137 0.986932i \(-0.551516\pi\)
−0.161137 + 0.986932i \(0.551516\pi\)
\(252\) 7.40221 0.466296
\(253\) −15.9716 −1.00412
\(254\) 48.0644 3.01583
\(255\) 2.83562 0.177574
\(256\) −16.8813 −1.05508
\(257\) −23.2465 −1.45008 −0.725038 0.688709i \(-0.758178\pi\)
−0.725038 + 0.688709i \(0.758178\pi\)
\(258\) −9.66505 −0.601720
\(259\) −12.8137 −0.796206
\(260\) 78.6380 4.87692
\(261\) 3.18309 0.197028
\(262\) 35.4826 2.19212
\(263\) 10.3425 0.637744 0.318872 0.947798i \(-0.396696\pi\)
0.318872 + 0.947798i \(0.396696\pi\)
\(264\) 37.7589 2.32390
\(265\) 9.95323 0.611422
\(266\) −29.9602 −1.83698
\(267\) 3.19988 0.195830
\(268\) 60.8652 3.71793
\(269\) 22.9266 1.39786 0.698929 0.715191i \(-0.253660\pi\)
0.698929 + 0.715191i \(0.253660\pi\)
\(270\) 7.40094 0.450407
\(271\) −6.62942 −0.402709 −0.201354 0.979518i \(-0.564534\pi\)
−0.201354 + 0.979518i \(0.564534\pi\)
\(272\) −9.53161 −0.577939
\(273\) −8.86518 −0.536545
\(274\) 13.0795 0.790163
\(275\) −15.6438 −0.943356
\(276\) 14.9388 0.899212
\(277\) −5.35349 −0.321660 −0.160830 0.986982i \(-0.551417\pi\)
−0.160830 + 0.986982i \(0.551417\pi\)
\(278\) 18.6544 1.11882
\(279\) 2.43358 0.145695
\(280\) 32.0140 1.91320
\(281\) −8.55418 −0.510300 −0.255150 0.966902i \(-0.582125\pi\)
−0.255150 + 0.966902i \(0.582125\pi\)
\(282\) 3.00506 0.178949
\(283\) −19.2640 −1.14512 −0.572562 0.819862i \(-0.694050\pi\)
−0.572562 + 0.819862i \(0.694050\pi\)
\(284\) 1.74742 0.103690
\(285\) −21.1603 −1.25343
\(286\) −77.3844 −4.57583
\(287\) −1.67889 −0.0991018
\(288\) −10.1986 −0.600960
\(289\) 1.00000 0.0588235
\(290\) 23.5578 1.38336
\(291\) 9.70271 0.568783
\(292\) 40.7675 2.38574
\(293\) −22.0816 −1.29002 −0.645010 0.764174i \(-0.723147\pi\)
−0.645010 + 0.764174i \(0.723147\pi\)
\(294\) 12.0940 0.705334
\(295\) −33.5624 −1.95408
\(296\) 61.1366 3.55349
\(297\) −5.14470 −0.298526
\(298\) 16.2426 0.940909
\(299\) −17.8913 −1.03468
\(300\) 14.6322 0.844793
\(301\) 5.69637 0.328333
\(302\) 4.42186 0.254449
\(303\) 5.05721 0.290529
\(304\) 71.1278 4.07946
\(305\) −0.306399 −0.0175443
\(306\) 2.60999 0.149203
\(307\) −8.90379 −0.508166 −0.254083 0.967182i \(-0.581774\pi\)
−0.254083 + 0.967182i \(0.581774\pi\)
\(308\) −38.0821 −2.16993
\(309\) 9.12966 0.519368
\(310\) 18.0108 1.02294
\(311\) −6.89073 −0.390738 −0.195369 0.980730i \(-0.562590\pi\)
−0.195369 + 0.980730i \(0.562590\pi\)
\(312\) 42.2974 2.39462
\(313\) −21.8193 −1.23330 −0.616649 0.787238i \(-0.711510\pi\)
−0.616649 + 0.787238i \(0.711510\pi\)
\(314\) −2.60999 −0.147290
\(315\) −4.36196 −0.245768
\(316\) 10.9012 0.613243
\(317\) 33.8159 1.89929 0.949646 0.313325i \(-0.101443\pi\)
0.949646 + 0.313325i \(0.101443\pi\)
\(318\) 9.16124 0.513737
\(319\) −16.3760 −0.916881
\(320\) −21.4233 −1.19760
\(321\) −5.83628 −0.325749
\(322\) −12.4640 −0.694594
\(323\) −7.46231 −0.415214
\(324\) 4.81203 0.267335
\(325\) −17.5242 −0.972065
\(326\) 17.2324 0.954414
\(327\) 14.9628 0.827447
\(328\) 8.01030 0.442295
\(329\) −1.77112 −0.0976448
\(330\) −38.0756 −2.09599
\(331\) 7.59780 0.417613 0.208806 0.977957i \(-0.433042\pi\)
0.208806 + 0.977957i \(0.433042\pi\)
\(332\) −12.6551 −0.694539
\(333\) −8.32995 −0.456478
\(334\) 0.510735 0.0279462
\(335\) −35.8665 −1.95960
\(336\) 14.6622 0.799888
\(337\) −15.9663 −0.869740 −0.434870 0.900493i \(-0.643206\pi\)
−0.434870 + 0.900493i \(0.643206\pi\)
\(338\) −52.7560 −2.86955
\(339\) −18.2850 −0.993106
\(340\) 13.6451 0.740010
\(341\) −12.5200 −0.677998
\(342\) −19.4765 −1.05317
\(343\) −17.8958 −0.966283
\(344\) −27.1784 −1.46536
\(345\) −8.80312 −0.473944
\(346\) −41.9351 −2.25445
\(347\) 25.9387 1.39246 0.696230 0.717819i \(-0.254859\pi\)
0.696230 + 0.717819i \(0.254859\pi\)
\(348\) 15.3171 0.821084
\(349\) 17.1167 0.916234 0.458117 0.888892i \(-0.348524\pi\)
0.458117 + 0.888892i \(0.348524\pi\)
\(350\) −12.2082 −0.652558
\(351\) −5.76308 −0.307611
\(352\) 52.4688 2.79660
\(353\) −18.2325 −0.970417 −0.485208 0.874399i \(-0.661256\pi\)
−0.485208 + 0.874399i \(0.661256\pi\)
\(354\) −30.8918 −1.64188
\(355\) −1.02972 −0.0546517
\(356\) 15.3979 0.816089
\(357\) −1.53827 −0.0814139
\(358\) 3.76393 0.198930
\(359\) 1.35313 0.0714156 0.0357078 0.999362i \(-0.488631\pi\)
0.0357078 + 0.999362i \(0.488631\pi\)
\(360\) 20.8117 1.09687
\(361\) 36.6861 1.93085
\(362\) 24.5336 1.28946
\(363\) 15.4679 0.811854
\(364\) −42.6596 −2.23597
\(365\) −24.0234 −1.25744
\(366\) −0.282018 −0.0147413
\(367\) −17.0472 −0.889854 −0.444927 0.895567i \(-0.646770\pi\)
−0.444927 + 0.895567i \(0.646770\pi\)
\(368\) 29.5906 1.54252
\(369\) −1.09141 −0.0568167
\(370\) −61.6495 −3.20500
\(371\) −5.39944 −0.280325
\(372\) 11.7105 0.607160
\(373\) 30.1820 1.56277 0.781383 0.624052i \(-0.214515\pi\)
0.781383 + 0.624052i \(0.214515\pi\)
\(374\) −13.4276 −0.694324
\(375\) 5.55567 0.286893
\(376\) 8.45032 0.435792
\(377\) −18.3444 −0.944785
\(378\) −4.01487 −0.206502
\(379\) 27.2270 1.39856 0.699279 0.714849i \(-0.253504\pi\)
0.699279 + 0.714849i \(0.253504\pi\)
\(380\) −101.824 −5.22347
\(381\) −18.4156 −0.943459
\(382\) −26.4445 −1.35302
\(383\) −8.42505 −0.430500 −0.215250 0.976559i \(-0.569057\pi\)
−0.215250 + 0.976559i \(0.569057\pi\)
\(384\) 0.678611 0.0346302
\(385\) 22.4409 1.14370
\(386\) 58.6151 2.98343
\(387\) 3.70310 0.188239
\(388\) 46.6898 2.37031
\(389\) −29.2099 −1.48100 −0.740500 0.672056i \(-0.765411\pi\)
−0.740500 + 0.672056i \(0.765411\pi\)
\(390\) −42.6523 −2.15978
\(391\) −3.10447 −0.157000
\(392\) 34.0086 1.71770
\(393\) −13.5949 −0.685774
\(394\) −63.5987 −3.20405
\(395\) −6.42386 −0.323219
\(396\) −24.7565 −1.24406
\(397\) 23.1857 1.16366 0.581828 0.813312i \(-0.302338\pi\)
0.581828 + 0.813312i \(0.302338\pi\)
\(398\) 14.3332 0.718460
\(399\) 11.4791 0.574672
\(400\) 28.9833 1.44917
\(401\) −22.6713 −1.13215 −0.566076 0.824353i \(-0.691539\pi\)
−0.566076 + 0.824353i \(0.691539\pi\)
\(402\) −33.0125 −1.64652
\(403\) −14.0249 −0.698631
\(404\) 24.3355 1.21073
\(405\) −2.83562 −0.140903
\(406\) −12.7797 −0.634245
\(407\) 42.8551 2.12425
\(408\) 7.33937 0.363353
\(409\) 14.7707 0.730365 0.365183 0.930936i \(-0.381007\pi\)
0.365183 + 0.930936i \(0.381007\pi\)
\(410\) −8.07749 −0.398919
\(411\) −5.01134 −0.247191
\(412\) 43.9322 2.16439
\(413\) 18.2070 0.895907
\(414\) −8.10264 −0.398223
\(415\) 7.45737 0.366068
\(416\) 58.7755 2.88171
\(417\) −7.14731 −0.350005
\(418\) 100.201 4.90099
\(419\) −27.0745 −1.32267 −0.661337 0.750089i \(-0.730011\pi\)
−0.661337 + 0.750089i \(0.730011\pi\)
\(420\) −20.9899 −1.02420
\(421\) −9.56721 −0.466277 −0.233139 0.972443i \(-0.574900\pi\)
−0.233139 + 0.972443i \(0.574900\pi\)
\(422\) 58.4363 2.84463
\(423\) −1.15137 −0.0559814
\(424\) 25.7617 1.25110
\(425\) −3.04076 −0.147499
\(426\) −0.947780 −0.0459201
\(427\) 0.166215 0.00804372
\(428\) −28.0844 −1.35751
\(429\) 29.6493 1.43148
\(430\) 27.4064 1.32166
\(431\) −39.9714 −1.92536 −0.962678 0.270648i \(-0.912762\pi\)
−0.962678 + 0.270648i \(0.912762\pi\)
\(432\) 9.53161 0.458590
\(433\) −34.4056 −1.65343 −0.826713 0.562623i \(-0.809792\pi\)
−0.826713 + 0.562623i \(0.809792\pi\)
\(434\) −9.77050 −0.468999
\(435\) −9.02604 −0.432765
\(436\) 72.0017 3.44826
\(437\) 23.1665 1.10821
\(438\) −22.1118 −1.05654
\(439\) −30.7055 −1.46549 −0.732746 0.680502i \(-0.761762\pi\)
−0.732746 + 0.680502i \(0.761762\pi\)
\(440\) −107.070 −5.10436
\(441\) −4.63372 −0.220653
\(442\) −15.0416 −0.715455
\(443\) 16.4766 0.782825 0.391412 0.920215i \(-0.371987\pi\)
0.391412 + 0.920215i \(0.371987\pi\)
\(444\) −40.0840 −1.90230
\(445\) −9.07366 −0.430133
\(446\) 65.7025 3.11111
\(447\) −6.22325 −0.294350
\(448\) 11.6217 0.549076
\(449\) 22.6297 1.06796 0.533982 0.845496i \(-0.320695\pi\)
0.533982 + 0.845496i \(0.320695\pi\)
\(450\) −7.93635 −0.374123
\(451\) 5.61499 0.264400
\(452\) −87.9882 −4.13861
\(453\) −1.69421 −0.0796008
\(454\) 4.09749 0.192305
\(455\) 25.1383 1.17850
\(456\) −54.7687 −2.56478
\(457\) −15.3551 −0.718282 −0.359141 0.933283i \(-0.616930\pi\)
−0.359141 + 0.933283i \(0.616930\pi\)
\(458\) −30.2516 −1.41357
\(459\) −1.00000 −0.0466760
\(460\) −42.3609 −1.97509
\(461\) 8.46443 0.394228 0.197114 0.980381i \(-0.436843\pi\)
0.197114 + 0.980381i \(0.436843\pi\)
\(462\) 20.6553 0.960970
\(463\) 3.61812 0.168148 0.0840740 0.996460i \(-0.473207\pi\)
0.0840740 + 0.996460i \(0.473207\pi\)
\(464\) 30.3399 1.40850
\(465\) −6.90072 −0.320013
\(466\) 65.1873 3.01974
\(467\) 20.4696 0.947218 0.473609 0.880735i \(-0.342951\pi\)
0.473609 + 0.880735i \(0.342951\pi\)
\(468\) −27.7322 −1.28192
\(469\) 19.4569 0.898435
\(470\) −8.52121 −0.393054
\(471\) 1.00000 0.0460776
\(472\) −86.8689 −3.99846
\(473\) −19.0513 −0.875981
\(474\) −5.91270 −0.271579
\(475\) 22.6911 1.04114
\(476\) −7.40221 −0.339280
\(477\) −3.51007 −0.160715
\(478\) −62.5474 −2.86085
\(479\) 19.5025 0.891094 0.445547 0.895259i \(-0.353009\pi\)
0.445547 + 0.895259i \(0.353009\pi\)
\(480\) 28.9195 1.31999
\(481\) 48.0062 2.18889
\(482\) −18.9154 −0.861574
\(483\) 4.77552 0.217294
\(484\) 74.4321 3.38328
\(485\) −27.5132 −1.24931
\(486\) −2.60999 −0.118391
\(487\) 33.8528 1.53402 0.767009 0.641636i \(-0.221744\pi\)
0.767009 + 0.641636i \(0.221744\pi\)
\(488\) −0.793044 −0.0358994
\(489\) −6.60248 −0.298574
\(490\) −34.2939 −1.54924
\(491\) −15.0058 −0.677201 −0.338601 0.940930i \(-0.609954\pi\)
−0.338601 + 0.940930i \(0.609954\pi\)
\(492\) −5.25192 −0.236775
\(493\) −3.18309 −0.143359
\(494\) 112.245 5.05014
\(495\) 14.5884 0.655701
\(496\) 23.1959 1.04153
\(497\) 0.558601 0.0250567
\(498\) 6.86397 0.307582
\(499\) −19.1435 −0.856979 −0.428489 0.903547i \(-0.640954\pi\)
−0.428489 + 0.903547i \(0.640954\pi\)
\(500\) 26.7341 1.19558
\(501\) −0.195685 −0.00874255
\(502\) 13.3260 0.594770
\(503\) −12.2645 −0.546846 −0.273423 0.961894i \(-0.588156\pi\)
−0.273423 + 0.961894i \(0.588156\pi\)
\(504\) −11.2899 −0.502894
\(505\) −14.3403 −0.638136
\(506\) 41.6856 1.85315
\(507\) 20.2131 0.897697
\(508\) −88.6164 −3.93172
\(509\) −18.7065 −0.829153 −0.414576 0.910014i \(-0.636070\pi\)
−0.414576 + 0.910014i \(0.636070\pi\)
\(510\) −7.40094 −0.327719
\(511\) 13.0322 0.576511
\(512\) 42.7028 1.88721
\(513\) 7.46231 0.329469
\(514\) 60.6731 2.67617
\(515\) −25.8883 −1.14077
\(516\) 17.8194 0.784458
\(517\) 5.92344 0.260513
\(518\) 33.4436 1.46943
\(519\) 16.0672 0.705271
\(520\) −119.940 −5.25970
\(521\) 9.61955 0.421440 0.210720 0.977546i \(-0.432419\pi\)
0.210720 + 0.977546i \(0.432419\pi\)
\(522\) −8.30782 −0.363623
\(523\) 20.0133 0.875121 0.437560 0.899189i \(-0.355843\pi\)
0.437560 + 0.899189i \(0.355843\pi\)
\(524\) −65.4193 −2.85785
\(525\) 4.67751 0.204143
\(526\) −26.9937 −1.17698
\(527\) −2.43358 −0.106008
\(528\) −49.0372 −2.13407
\(529\) −13.3622 −0.580967
\(530\) −25.9778 −1.12840
\(531\) 11.8360 0.513639
\(532\) 55.2376 2.39485
\(533\) 6.28991 0.272446
\(534\) −8.35165 −0.361411
\(535\) 16.5495 0.715497
\(536\) −92.8324 −4.00975
\(537\) −1.44212 −0.0622322
\(538\) −59.8381 −2.57980
\(539\) 23.8391 1.02682
\(540\) −13.6451 −0.587192
\(541\) −6.96291 −0.299359 −0.149679 0.988735i \(-0.547824\pi\)
−0.149679 + 0.988735i \(0.547824\pi\)
\(542\) 17.3027 0.743215
\(543\) −9.39990 −0.403388
\(544\) 10.1986 0.437262
\(545\) −42.4290 −1.81746
\(546\) 23.1380 0.990216
\(547\) 25.4701 1.08902 0.544511 0.838754i \(-0.316715\pi\)
0.544511 + 0.838754i \(0.316715\pi\)
\(548\) −24.1147 −1.03013
\(549\) 0.108053 0.00461161
\(550\) 40.8301 1.74100
\(551\) 23.7532 1.01192
\(552\) −22.7849 −0.969790
\(553\) 3.48482 0.148190
\(554\) 13.9725 0.593636
\(555\) 23.6206 1.00264
\(556\) −34.3931 −1.45859
\(557\) 23.4048 0.991692 0.495846 0.868411i \(-0.334858\pi\)
0.495846 + 0.868411i \(0.334858\pi\)
\(558\) −6.35161 −0.268885
\(559\) −21.3413 −0.902640
\(560\) −41.5765 −1.75693
\(561\) 5.14470 0.217209
\(562\) 22.3263 0.941779
\(563\) −7.34508 −0.309558 −0.154779 0.987949i \(-0.549467\pi\)
−0.154779 + 0.987949i \(0.549467\pi\)
\(564\) −5.54042 −0.233294
\(565\) 51.8494 2.18132
\(566\) 50.2787 2.11337
\(567\) 1.53827 0.0646013
\(568\) −2.66519 −0.111829
\(569\) 7.08977 0.297219 0.148609 0.988896i \(-0.452520\pi\)
0.148609 + 0.988896i \(0.452520\pi\)
\(570\) 55.2281 2.31325
\(571\) −15.5033 −0.648791 −0.324396 0.945922i \(-0.605161\pi\)
−0.324396 + 0.945922i \(0.605161\pi\)
\(572\) 142.674 5.96548
\(573\) 10.1320 0.423272
\(574\) 4.38188 0.182896
\(575\) 9.43996 0.393674
\(576\) 7.55507 0.314795
\(577\) 19.7041 0.820293 0.410147 0.912020i \(-0.365478\pi\)
0.410147 + 0.912020i \(0.365478\pi\)
\(578\) −2.60999 −0.108561
\(579\) −22.4580 −0.933323
\(580\) −43.4336 −1.80348
\(581\) −4.04548 −0.167835
\(582\) −25.3239 −1.04971
\(583\) 18.0582 0.747896
\(584\) −62.1791 −2.57299
\(585\) 16.3419 0.675656
\(586\) 57.6327 2.38079
\(587\) −30.1098 −1.24277 −0.621383 0.783507i \(-0.713429\pi\)
−0.621383 + 0.783507i \(0.713429\pi\)
\(588\) −22.2976 −0.919539
\(589\) 18.1601 0.748275
\(590\) 87.5976 3.60633
\(591\) 24.3674 1.00234
\(592\) −79.3978 −3.26323
\(593\) −25.8882 −1.06310 −0.531551 0.847026i \(-0.678391\pi\)
−0.531551 + 0.847026i \(0.678391\pi\)
\(594\) 13.4276 0.550941
\(595\) 4.36196 0.178823
\(596\) −29.9465 −1.22666
\(597\) −5.49168 −0.224760
\(598\) 46.6962 1.90955
\(599\) 35.9348 1.46826 0.734128 0.679011i \(-0.237591\pi\)
0.734128 + 0.679011i \(0.237591\pi\)
\(600\) −22.3173 −0.911099
\(601\) −43.2076 −1.76248 −0.881238 0.472673i \(-0.843289\pi\)
−0.881238 + 0.472673i \(0.843289\pi\)
\(602\) −14.8675 −0.605952
\(603\) 12.6485 0.515088
\(604\) −8.15258 −0.331724
\(605\) −43.8611 −1.78321
\(606\) −13.1992 −0.536183
\(607\) −41.0049 −1.66434 −0.832168 0.554524i \(-0.812900\pi\)
−0.832168 + 0.554524i \(0.812900\pi\)
\(608\) −76.1053 −3.08648
\(609\) 4.89645 0.198414
\(610\) 0.799697 0.0323788
\(611\) 6.63543 0.268441
\(612\) −4.81203 −0.194515
\(613\) −10.0742 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(614\) 23.2388 0.937840
\(615\) 3.09484 0.124796
\(616\) 58.0833 2.34024
\(617\) 37.0303 1.49078 0.745391 0.666628i \(-0.232263\pi\)
0.745391 + 0.666628i \(0.232263\pi\)
\(618\) −23.8283 −0.958514
\(619\) −23.3925 −0.940226 −0.470113 0.882606i \(-0.655787\pi\)
−0.470113 + 0.882606i \(0.655787\pi\)
\(620\) −33.2065 −1.33360
\(621\) 3.10447 0.124578
\(622\) 17.9847 0.721122
\(623\) 4.92228 0.197207
\(624\) −54.9315 −2.19902
\(625\) −30.9576 −1.23830
\(626\) 56.9480 2.27610
\(627\) −38.3913 −1.53320
\(628\) 4.81203 0.192021
\(629\) 8.32995 0.332137
\(630\) 11.3847 0.453575
\(631\) −40.2195 −1.60111 −0.800556 0.599258i \(-0.795462\pi\)
−0.800556 + 0.599258i \(0.795462\pi\)
\(632\) −16.6267 −0.661375
\(633\) −22.3895 −0.889902
\(634\) −88.2592 −3.50522
\(635\) 52.2197 2.07227
\(636\) −16.8906 −0.669755
\(637\) 26.7045 1.05807
\(638\) 42.7412 1.69214
\(639\) 0.363136 0.0143654
\(640\) −1.92428 −0.0760640
\(641\) −3.83723 −0.151562 −0.0757808 0.997124i \(-0.524145\pi\)
−0.0757808 + 0.997124i \(0.524145\pi\)
\(642\) 15.2326 0.601183
\(643\) −44.6730 −1.76173 −0.880865 0.473368i \(-0.843038\pi\)
−0.880865 + 0.473368i \(0.843038\pi\)
\(644\) 22.9800 0.905538
\(645\) −10.5006 −0.413461
\(646\) 19.4765 0.766294
\(647\) 25.3616 0.997067 0.498534 0.866870i \(-0.333872\pi\)
0.498534 + 0.866870i \(0.333872\pi\)
\(648\) −7.33937 −0.288318
\(649\) −60.8926 −2.39025
\(650\) 45.7378 1.79399
\(651\) 3.74351 0.146720
\(652\) −31.7714 −1.24426
\(653\) −2.41837 −0.0946382 −0.0473191 0.998880i \(-0.515068\pi\)
−0.0473191 + 0.998880i \(0.515068\pi\)
\(654\) −39.0528 −1.52709
\(655\) 38.5501 1.50628
\(656\) −10.4029 −0.406166
\(657\) 8.47199 0.330524
\(658\) 4.62259 0.180207
\(659\) 50.4800 1.96642 0.983210 0.182477i \(-0.0584116\pi\)
0.983210 + 0.182477i \(0.0584116\pi\)
\(660\) 70.2000 2.73253
\(661\) −27.6724 −1.07633 −0.538166 0.842839i \(-0.680883\pi\)
−0.538166 + 0.842839i \(0.680883\pi\)
\(662\) −19.8302 −0.770721
\(663\) 5.76308 0.223820
\(664\) 19.3017 0.749053
\(665\) −32.5503 −1.26225
\(666\) 21.7411 0.842449
\(667\) 9.88181 0.382625
\(668\) −0.941642 −0.0364332
\(669\) −25.1735 −0.973264
\(670\) 93.6111 3.61651
\(671\) −0.555902 −0.0214603
\(672\) −15.6882 −0.605187
\(673\) −9.62601 −0.371055 −0.185528 0.982639i \(-0.559399\pi\)
−0.185528 + 0.982639i \(0.559399\pi\)
\(674\) 41.6719 1.60514
\(675\) 3.04076 0.117039
\(676\) 97.2663 3.74101
\(677\) 14.5655 0.559798 0.279899 0.960029i \(-0.409699\pi\)
0.279899 + 0.960029i \(0.409699\pi\)
\(678\) 47.7237 1.83282
\(679\) 14.9254 0.572784
\(680\) −20.8117 −0.798092
\(681\) −1.56993 −0.0601598
\(682\) 32.6771 1.25127
\(683\) −26.7340 −1.02295 −0.511474 0.859299i \(-0.670900\pi\)
−0.511474 + 0.859299i \(0.670900\pi\)
\(684\) 35.9089 1.37301
\(685\) 14.2103 0.542946
\(686\) 46.7079 1.78331
\(687\) 11.5907 0.442214
\(688\) 35.2965 1.34567
\(689\) 20.2288 0.770657
\(690\) 22.9760 0.874682
\(691\) 9.52737 0.362438 0.181219 0.983443i \(-0.441996\pi\)
0.181219 + 0.983443i \(0.441996\pi\)
\(692\) 77.3158 2.93911
\(693\) −7.91394 −0.300626
\(694\) −67.6996 −2.56984
\(695\) 20.2671 0.768774
\(696\) −23.3619 −0.885530
\(697\) 1.09141 0.0413403
\(698\) −44.6743 −1.69095
\(699\) −24.9761 −0.944683
\(700\) 22.5084 0.850736
\(701\) 11.6998 0.441894 0.220947 0.975286i \(-0.429085\pi\)
0.220947 + 0.975286i \(0.429085\pi\)
\(702\) 15.0416 0.567708
\(703\) −62.1607 −2.34443
\(704\) −38.8685 −1.46491
\(705\) 3.26485 0.122961
\(706\) 47.5865 1.79094
\(707\) 7.77935 0.292573
\(708\) 56.9553 2.14051
\(709\) 20.2296 0.759740 0.379870 0.925040i \(-0.375969\pi\)
0.379870 + 0.925040i \(0.375969\pi\)
\(710\) 2.68755 0.100862
\(711\) 2.26541 0.0849597
\(712\) −23.4851 −0.880143
\(713\) 7.55499 0.282936
\(714\) 4.01487 0.150253
\(715\) −84.0743 −3.14420
\(716\) −6.93955 −0.259343
\(717\) 23.9646 0.894976
\(718\) −3.53166 −0.131800
\(719\) −23.8743 −0.890360 −0.445180 0.895441i \(-0.646860\pi\)
−0.445180 + 0.895441i \(0.646860\pi\)
\(720\) −27.0280 −1.00728
\(721\) 14.0439 0.523022
\(722\) −95.7502 −3.56345
\(723\) 7.24733 0.269531
\(724\) −45.2326 −1.68106
\(725\) 9.67901 0.359469
\(726\) −40.3710 −1.49831
\(727\) −8.06820 −0.299233 −0.149617 0.988744i \(-0.547804\pi\)
−0.149617 + 0.988744i \(0.547804\pi\)
\(728\) 65.0649 2.41147
\(729\) 1.00000 0.0370370
\(730\) 62.7007 2.32066
\(731\) −3.70310 −0.136964
\(732\) 0.519957 0.0192181
\(733\) −4.09338 −0.151192 −0.0755962 0.997139i \(-0.524086\pi\)
−0.0755962 + 0.997139i \(0.524086\pi\)
\(734\) 44.4929 1.64226
\(735\) 13.1395 0.484658
\(736\) −31.6614 −1.16705
\(737\) −65.0729 −2.39699
\(738\) 2.84858 0.104858
\(739\) 22.2495 0.818462 0.409231 0.912431i \(-0.365797\pi\)
0.409231 + 0.912431i \(0.365797\pi\)
\(740\) 113.663 4.17834
\(741\) −43.0059 −1.57986
\(742\) 14.0925 0.517351
\(743\) 14.9272 0.547625 0.273812 0.961783i \(-0.411715\pi\)
0.273812 + 0.961783i \(0.411715\pi\)
\(744\) −17.8610 −0.654814
\(745\) 17.6468 0.646529
\(746\) −78.7747 −2.88415
\(747\) −2.62989 −0.0962226
\(748\) 24.7565 0.905186
\(749\) −8.97778 −0.328041
\(750\) −14.5002 −0.529473
\(751\) −27.1988 −0.992498 −0.496249 0.868180i \(-0.665290\pi\)
−0.496249 + 0.868180i \(0.665290\pi\)
\(752\) −10.9744 −0.400195
\(753\) −5.10578 −0.186065
\(754\) 47.8787 1.74364
\(755\) 4.80413 0.174840
\(756\) 7.40221 0.269216
\(757\) 38.8350 1.41148 0.705741 0.708469i \(-0.250614\pi\)
0.705741 + 0.708469i \(0.250614\pi\)
\(758\) −71.0622 −2.58110
\(759\) −15.9716 −0.579731
\(760\) 155.303 5.63345
\(761\) −14.2772 −0.517549 −0.258774 0.965938i \(-0.583319\pi\)
−0.258774 + 0.965938i \(0.583319\pi\)
\(762\) 48.0644 1.74119
\(763\) 23.0169 0.833268
\(764\) 48.7558 1.76392
\(765\) 2.83562 0.102522
\(766\) 21.9893 0.794504
\(767\) −68.2119 −2.46299
\(768\) −16.8813 −0.609152
\(769\) −12.8623 −0.463828 −0.231914 0.972736i \(-0.574499\pi\)
−0.231914 + 0.972736i \(0.574499\pi\)
\(770\) −58.5706 −2.11074
\(771\) −23.2465 −0.837202
\(772\) −108.069 −3.88948
\(773\) −42.6196 −1.53292 −0.766459 0.642293i \(-0.777983\pi\)
−0.766459 + 0.642293i \(0.777983\pi\)
\(774\) −9.66505 −0.347403
\(775\) 7.39993 0.265813
\(776\) −71.2118 −2.55635
\(777\) −12.8137 −0.459689
\(778\) 76.2375 2.73325
\(779\) −8.14447 −0.291806
\(780\) 78.6380 2.81569
\(781\) −1.86822 −0.0668503
\(782\) 8.10264 0.289750
\(783\) 3.18309 0.113754
\(784\) −44.1668 −1.57739
\(785\) −2.83562 −0.101208
\(786\) 35.4826 1.26562
\(787\) −27.7398 −0.988819 −0.494409 0.869229i \(-0.664616\pi\)
−0.494409 + 0.869229i \(0.664616\pi\)
\(788\) 117.257 4.17710
\(789\) 10.3425 0.368202
\(790\) 16.7662 0.596514
\(791\) −28.1273 −1.00009
\(792\) 37.7589 1.34170
\(793\) −0.622721 −0.0221135
\(794\) −60.5144 −2.14757
\(795\) 9.95323 0.353005
\(796\) −26.4262 −0.936651
\(797\) 15.8699 0.562142 0.281071 0.959687i \(-0.409310\pi\)
0.281071 + 0.959687i \(0.409310\pi\)
\(798\) −29.9602 −1.06058
\(799\) 1.15137 0.0407325
\(800\) −31.0116 −1.09642
\(801\) 3.19988 0.113062
\(802\) 59.1719 2.08943
\(803\) −43.5858 −1.53811
\(804\) 60.8652 2.14655
\(805\) −13.5416 −0.477278
\(806\) 36.6049 1.28935
\(807\) 22.9266 0.807054
\(808\) −37.1167 −1.30576
\(809\) −13.1493 −0.462303 −0.231152 0.972918i \(-0.574249\pi\)
−0.231152 + 0.972918i \(0.574249\pi\)
\(810\) 7.40094 0.260043
\(811\) 28.7883 1.01089 0.505446 0.862858i \(-0.331328\pi\)
0.505446 + 0.862858i \(0.331328\pi\)
\(812\) 23.5619 0.826860
\(813\) −6.62942 −0.232504
\(814\) −111.851 −3.92038
\(815\) 18.7221 0.655808
\(816\) −9.53161 −0.333673
\(817\) 27.6337 0.966780
\(818\) −38.5514 −1.34792
\(819\) −8.86518 −0.309775
\(820\) 14.8925 0.520068
\(821\) 31.0064 1.08213 0.541066 0.840980i \(-0.318021\pi\)
0.541066 + 0.840980i \(0.318021\pi\)
\(822\) 13.0795 0.456201
\(823\) 13.5514 0.472372 0.236186 0.971708i \(-0.424102\pi\)
0.236186 + 0.971708i \(0.424102\pi\)
\(824\) −67.0060 −2.33426
\(825\) −15.6438 −0.544647
\(826\) −47.5200 −1.65343
\(827\) −37.2520 −1.29538 −0.647689 0.761905i \(-0.724264\pi\)
−0.647689 + 0.761905i \(0.724264\pi\)
\(828\) 14.9388 0.519160
\(829\) 0.955146 0.0331736 0.0165868 0.999862i \(-0.494720\pi\)
0.0165868 + 0.999862i \(0.494720\pi\)
\(830\) −19.4636 −0.675593
\(831\) −5.35349 −0.185710
\(832\) −43.5405 −1.50950
\(833\) 4.63372 0.160549
\(834\) 18.6544 0.645948
\(835\) 0.554888 0.0192027
\(836\) −184.740 −6.38938
\(837\) 2.43358 0.0841168
\(838\) 70.6640 2.44105
\(839\) −32.5469 −1.12364 −0.561822 0.827258i \(-0.689899\pi\)
−0.561822 + 0.827258i \(0.689899\pi\)
\(840\) 32.0140 1.10459
\(841\) −18.8679 −0.650619
\(842\) 24.9703 0.860534
\(843\) −8.55418 −0.294622
\(844\) −107.739 −3.70853
\(845\) −57.3169 −1.97176
\(846\) 3.00506 0.103316
\(847\) 23.7938 0.817565
\(848\) −33.4566 −1.14890
\(849\) −19.2640 −0.661137
\(850\) 7.93635 0.272214
\(851\) −25.8601 −0.886473
\(852\) 1.74742 0.0598657
\(853\) −56.0334 −1.91855 −0.959274 0.282479i \(-0.908843\pi\)
−0.959274 + 0.282479i \(0.908843\pi\)
\(854\) −0.433820 −0.0148450
\(855\) −21.1603 −0.723667
\(856\) 42.8346 1.46406
\(857\) −12.4530 −0.425387 −0.212693 0.977119i \(-0.568224\pi\)
−0.212693 + 0.977119i \(0.568224\pi\)
\(858\) −77.3844 −2.64186
\(859\) −44.6702 −1.52413 −0.762065 0.647501i \(-0.775814\pi\)
−0.762065 + 0.647501i \(0.775814\pi\)
\(860\) −50.5292 −1.72303
\(861\) −1.67889 −0.0572164
\(862\) 104.325 3.55332
\(863\) 29.8007 1.01443 0.507214 0.861820i \(-0.330675\pi\)
0.507214 + 0.861820i \(0.330675\pi\)
\(864\) −10.1986 −0.346964
\(865\) −45.5605 −1.54910
\(866\) 89.7981 3.05146
\(867\) 1.00000 0.0339618
\(868\) 18.0139 0.611431
\(869\) −11.6549 −0.395364
\(870\) 23.5578 0.798686
\(871\) −72.8946 −2.46994
\(872\) −109.818 −3.71890
\(873\) 9.70271 0.328387
\(874\) −60.4644 −2.04524
\(875\) 8.54612 0.288912
\(876\) 40.7675 1.37741
\(877\) −9.01730 −0.304493 −0.152246 0.988343i \(-0.548651\pi\)
−0.152246 + 0.988343i \(0.548651\pi\)
\(878\) 80.1409 2.70463
\(879\) −22.0816 −0.744794
\(880\) 139.051 4.68741
\(881\) −38.0780 −1.28288 −0.641440 0.767173i \(-0.721663\pi\)
−0.641440 + 0.767173i \(0.721663\pi\)
\(882\) 12.0940 0.407225
\(883\) −12.3661 −0.416153 −0.208077 0.978113i \(-0.566720\pi\)
−0.208077 + 0.978113i \(0.566720\pi\)
\(884\) 27.7322 0.932734
\(885\) −33.5624 −1.12819
\(886\) −43.0036 −1.44473
\(887\) −3.37861 −0.113443 −0.0567213 0.998390i \(-0.518065\pi\)
−0.0567213 + 0.998390i \(0.518065\pi\)
\(888\) 61.1366 2.05161
\(889\) −28.3282 −0.950096
\(890\) 23.6821 0.793827
\(891\) −5.14470 −0.172354
\(892\) −121.136 −4.05593
\(893\) −8.59187 −0.287516
\(894\) 16.2426 0.543234
\(895\) 4.08932 0.136691
\(896\) 1.04389 0.0348738
\(897\) −17.8913 −0.597375
\(898\) −59.0634 −1.97097
\(899\) 7.74630 0.258354
\(900\) 14.6322 0.487741
\(901\) 3.51007 0.116937
\(902\) −14.6551 −0.487960
\(903\) 5.69637 0.189563
\(904\) 134.201 4.46345
\(905\) 26.6546 0.886028
\(906\) 4.42186 0.146906
\(907\) 30.7818 1.02209 0.511047 0.859553i \(-0.329258\pi\)
0.511047 + 0.859553i \(0.329258\pi\)
\(908\) −7.55455 −0.250707
\(909\) 5.05721 0.167737
\(910\) −65.6107 −2.17497
\(911\) −46.8287 −1.55150 −0.775752 0.631038i \(-0.782629\pi\)
−0.775752 + 0.631038i \(0.782629\pi\)
\(912\) 71.1278 2.35528
\(913\) 13.5300 0.447777
\(914\) 40.0766 1.32562
\(915\) −0.306399 −0.0101292
\(916\) 55.7750 1.84286
\(917\) −20.9127 −0.690598
\(918\) 2.60999 0.0861424
\(919\) 34.8807 1.15061 0.575303 0.817940i \(-0.304884\pi\)
0.575303 + 0.817940i \(0.304884\pi\)
\(920\) 64.6094 2.13011
\(921\) −8.90379 −0.293390
\(922\) −22.0921 −0.727563
\(923\) −2.09278 −0.0688848
\(924\) −38.0821 −1.25281
\(925\) −25.3294 −0.832825
\(926\) −9.44324 −0.310324
\(927\) 9.12966 0.299857
\(928\) −32.4631 −1.06565
\(929\) 16.5301 0.542336 0.271168 0.962532i \(-0.412590\pi\)
0.271168 + 0.962532i \(0.412590\pi\)
\(930\) 18.0108 0.590597
\(931\) −34.5783 −1.13326
\(932\) −120.186 −3.93682
\(933\) −6.89073 −0.225592
\(934\) −53.4253 −1.74813
\(935\) −14.5884 −0.477092
\(936\) 42.2974 1.38253
\(937\) 34.2602 1.11923 0.559616 0.828752i \(-0.310949\pi\)
0.559616 + 0.828752i \(0.310949\pi\)
\(938\) −50.7822 −1.65810
\(939\) −21.8193 −0.712045
\(940\) 15.7106 0.512422
\(941\) −39.3180 −1.28173 −0.640864 0.767654i \(-0.721424\pi\)
−0.640864 + 0.767654i \(0.721424\pi\)
\(942\) −2.60999 −0.0850380
\(943\) −3.38827 −0.110337
\(944\) 112.816 3.67185
\(945\) −4.36196 −0.141894
\(946\) 49.7237 1.61666
\(947\) −6.28453 −0.204220 −0.102110 0.994773i \(-0.532559\pi\)
−0.102110 + 0.994773i \(0.532559\pi\)
\(948\) 10.9012 0.354056
\(949\) −48.8248 −1.58492
\(950\) −59.2235 −1.92146
\(951\) 33.8159 1.09656
\(952\) 11.2899 0.365909
\(953\) −17.1216 −0.554624 −0.277312 0.960780i \(-0.589444\pi\)
−0.277312 + 0.960780i \(0.589444\pi\)
\(954\) 9.16124 0.296606
\(955\) −28.7307 −0.929702
\(956\) 115.319 3.72967
\(957\) −16.3760 −0.529362
\(958\) −50.9014 −1.64455
\(959\) −7.70879 −0.248930
\(960\) −21.4233 −0.691435
\(961\) −25.0777 −0.808958
\(962\) −125.296 −4.03969
\(963\) −5.83628 −0.188071
\(964\) 34.8744 1.12323
\(965\) 63.6825 2.05001
\(966\) −12.4640 −0.401024
\(967\) 43.3991 1.39562 0.697810 0.716283i \(-0.254158\pi\)
0.697810 + 0.716283i \(0.254158\pi\)
\(968\) −113.525 −3.64882
\(969\) −7.46231 −0.239724
\(970\) 71.8092 2.30565
\(971\) −58.5134 −1.87778 −0.938892 0.344211i \(-0.888147\pi\)
−0.938892 + 0.344211i \(0.888147\pi\)
\(972\) 4.81203 0.154346
\(973\) −10.9945 −0.352467
\(974\) −88.3555 −2.83109
\(975\) −17.5242 −0.561222
\(976\) 1.02992 0.0329670
\(977\) 0.264856 0.00847350 0.00423675 0.999991i \(-0.498651\pi\)
0.00423675 + 0.999991i \(0.498651\pi\)
\(978\) 17.2324 0.551031
\(979\) −16.4624 −0.526141
\(980\) 63.2277 2.01973
\(981\) 14.9628 0.477727
\(982\) 39.1649 1.24980
\(983\) −29.3955 −0.937569 −0.468785 0.883312i \(-0.655308\pi\)
−0.468785 + 0.883312i \(0.655308\pi\)
\(984\) 8.01030 0.255359
\(985\) −69.0968 −2.20161
\(986\) 8.30782 0.264575
\(987\) −1.77112 −0.0563752
\(988\) −206.946 −6.58383
\(989\) 11.4962 0.365557
\(990\) −38.0756 −1.21012
\(991\) 51.4409 1.63407 0.817037 0.576586i \(-0.195615\pi\)
0.817037 + 0.576586i \(0.195615\pi\)
\(992\) −24.8192 −0.788010
\(993\) 7.59780 0.241109
\(994\) −1.45794 −0.0462431
\(995\) 15.5723 0.493677
\(996\) −12.6551 −0.400993
\(997\) 17.1842 0.544228 0.272114 0.962265i \(-0.412277\pi\)
0.272114 + 0.962265i \(0.412277\pi\)
\(998\) 49.9642 1.58159
\(999\) −8.32995 −0.263548
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 \(a_p\))