Properties

Label 8007.2.a.j.1.1
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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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: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.81598 q^{2}\) \(-1.00000 q^{3}\) \(+5.92975 q^{4}\) \(-4.24598 q^{5}\) \(+2.81598 q^{6}\) \(+0.0516498 q^{7}\) \(-11.0661 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.81598 q^{2}\) \(-1.00000 q^{3}\) \(+5.92975 q^{4}\) \(-4.24598 q^{5}\) \(+2.81598 q^{6}\) \(+0.0516498 q^{7}\) \(-11.0661 q^{8}\) \(+1.00000 q^{9}\) \(+11.9566 q^{10}\) \(-4.06087 q^{11}\) \(-5.92975 q^{12}\) \(-4.35985 q^{13}\) \(-0.145445 q^{14}\) \(+4.24598 q^{15}\) \(+19.3024 q^{16}\) \(+1.00000 q^{17}\) \(-2.81598 q^{18}\) \(-5.28010 q^{19}\) \(-25.1776 q^{20}\) \(-0.0516498 q^{21}\) \(+11.4353 q^{22}\) \(+6.73037 q^{23}\) \(+11.0661 q^{24}\) \(+13.0284 q^{25}\) \(+12.2772 q^{26}\) \(-1.00000 q^{27}\) \(+0.306270 q^{28}\) \(+6.81104 q^{29}\) \(-11.9566 q^{30}\) \(+5.25753 q^{31}\) \(-32.2230 q^{32}\) \(+4.06087 q^{33}\) \(-2.81598 q^{34}\) \(-0.219304 q^{35}\) \(+5.92975 q^{36}\) \(+10.7233 q^{37}\) \(+14.8687 q^{38}\) \(+4.35985 q^{39}\) \(+46.9865 q^{40}\) \(-5.37399 q^{41}\) \(+0.145445 q^{42}\) \(+7.06168 q^{43}\) \(-24.0799 q^{44}\) \(-4.24598 q^{45}\) \(-18.9526 q^{46}\) \(-6.72574 q^{47}\) \(-19.3024 q^{48}\) \(-6.99733 q^{49}\) \(-36.6877 q^{50}\) \(-1.00000 q^{51}\) \(-25.8528 q^{52}\) \(+6.76745 q^{53}\) \(+2.81598 q^{54}\) \(+17.2424 q^{55}\) \(-0.571562 q^{56}\) \(+5.28010 q^{57}\) \(-19.1798 q^{58}\) \(-4.71390 q^{59}\) \(+25.1776 q^{60}\) \(-12.2611 q^{61}\) \(-14.8051 q^{62}\) \(+0.0516498 q^{63}\) \(+52.1346 q^{64}\) \(+18.5118 q^{65}\) \(-11.4353 q^{66}\) \(-6.89514 q^{67}\) \(+5.92975 q^{68}\) \(-6.73037 q^{69}\) \(+0.617557 q^{70}\) \(-3.50032 q^{71}\) \(-11.0661 q^{72}\) \(+2.03623 q^{73}\) \(-30.1967 q^{74}\) \(-13.0284 q^{75}\) \(-31.3097 q^{76}\) \(-0.209743 q^{77}\) \(-12.2772 q^{78}\) \(-14.8058 q^{79}\) \(-81.9577 q^{80}\) \(+1.00000 q^{81}\) \(+15.1331 q^{82}\) \(-7.14336 q^{83}\) \(-0.306270 q^{84}\) \(-4.24598 q^{85}\) \(-19.8855 q^{86}\) \(-6.81104 q^{87}\) \(+44.9380 q^{88}\) \(+2.78938 q^{89}\) \(+11.9566 q^{90}\) \(-0.225185 q^{91}\) \(+39.9094 q^{92}\) \(-5.25753 q^{93}\) \(+18.9396 q^{94}\) \(+22.4192 q^{95}\) \(+32.2230 q^{96}\) \(+8.30804 q^{97}\) \(+19.7044 q^{98}\) \(-4.06087 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81598 −1.99120 −0.995600 0.0937098i \(-0.970127\pi\)
−0.995600 + 0.0937098i \(0.970127\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.92975 2.96487
\(5\) −4.24598 −1.89886 −0.949431 0.313976i \(-0.898339\pi\)
−0.949431 + 0.313976i \(0.898339\pi\)
\(6\) 2.81598 1.14962
\(7\) 0.0516498 0.0195218 0.00976090 0.999952i \(-0.496893\pi\)
0.00976090 + 0.999952i \(0.496893\pi\)
\(8\) −11.0661 −3.91246
\(9\) 1.00000 0.333333
\(10\) 11.9566 3.78101
\(11\) −4.06087 −1.22440 −0.612199 0.790704i \(-0.709715\pi\)
−0.612199 + 0.790704i \(0.709715\pi\)
\(12\) −5.92975 −1.71177
\(13\) −4.35985 −1.20920 −0.604602 0.796528i \(-0.706668\pi\)
−0.604602 + 0.796528i \(0.706668\pi\)
\(14\) −0.145445 −0.0388718
\(15\) 4.24598 1.09631
\(16\) 19.3024 4.82560
\(17\) 1.00000 0.242536
\(18\) −2.81598 −0.663733
\(19\) −5.28010 −1.21134 −0.605669 0.795717i \(-0.707094\pi\)
−0.605669 + 0.795717i \(0.707094\pi\)
\(20\) −25.1776 −5.62989
\(21\) −0.0516498 −0.0112709
\(22\) 11.4353 2.43802
\(23\) 6.73037 1.40338 0.701689 0.712483i \(-0.252429\pi\)
0.701689 + 0.712483i \(0.252429\pi\)
\(24\) 11.0661 2.25886
\(25\) 13.0284 2.60568
\(26\) 12.2772 2.40777
\(27\) −1.00000 −0.192450
\(28\) 0.306270 0.0578797
\(29\) 6.81104 1.26478 0.632389 0.774651i \(-0.282074\pi\)
0.632389 + 0.774651i \(0.282074\pi\)
\(30\) −11.9566 −2.18297
\(31\) 5.25753 0.944280 0.472140 0.881523i \(-0.343482\pi\)
0.472140 + 0.881523i \(0.343482\pi\)
\(32\) −32.2230 −5.69628
\(33\) 4.06087 0.706906
\(34\) −2.81598 −0.482937
\(35\) −0.219304 −0.0370692
\(36\) 5.92975 0.988291
\(37\) 10.7233 1.76290 0.881451 0.472275i \(-0.156567\pi\)
0.881451 + 0.472275i \(0.156567\pi\)
\(38\) 14.8687 2.41201
\(39\) 4.35985 0.698134
\(40\) 46.9865 7.42921
\(41\) −5.37399 −0.839276 −0.419638 0.907691i \(-0.637843\pi\)
−0.419638 + 0.907691i \(0.637843\pi\)
\(42\) 0.145445 0.0224426
\(43\) 7.06168 1.07690 0.538448 0.842659i \(-0.319011\pi\)
0.538448 + 0.842659i \(0.319011\pi\)
\(44\) −24.0799 −3.63019
\(45\) −4.24598 −0.632954
\(46\) −18.9526 −2.79441
\(47\) −6.72574 −0.981051 −0.490525 0.871427i \(-0.663195\pi\)
−0.490525 + 0.871427i \(0.663195\pi\)
\(48\) −19.3024 −2.78606
\(49\) −6.99733 −0.999619
\(50\) −36.6877 −5.18842
\(51\) −1.00000 −0.140028
\(52\) −25.8528 −3.58514
\(53\) 6.76745 0.929580 0.464790 0.885421i \(-0.346130\pi\)
0.464790 + 0.885421i \(0.346130\pi\)
\(54\) 2.81598 0.383206
\(55\) 17.2424 2.32496
\(56\) −0.571562 −0.0763781
\(57\) 5.28010 0.699366
\(58\) −19.1798 −2.51843
\(59\) −4.71390 −0.613698 −0.306849 0.951758i \(-0.599275\pi\)
−0.306849 + 0.951758i \(0.599275\pi\)
\(60\) 25.1776 3.25042
\(61\) −12.2611 −1.56987 −0.784936 0.619577i \(-0.787304\pi\)
−0.784936 + 0.619577i \(0.787304\pi\)
\(62\) −14.8051 −1.88025
\(63\) 0.0516498 0.00650726
\(64\) 52.1346 6.51683
\(65\) 18.5118 2.29611
\(66\) −11.4353 −1.40759
\(67\) −6.89514 −0.842375 −0.421188 0.906974i \(-0.638387\pi\)
−0.421188 + 0.906974i \(0.638387\pi\)
\(68\) 5.92975 0.719088
\(69\) −6.73037 −0.810241
\(70\) 0.617557 0.0738121
\(71\) −3.50032 −0.415411 −0.207706 0.978191i \(-0.566600\pi\)
−0.207706 + 0.978191i \(0.566600\pi\)
\(72\) −11.0661 −1.30415
\(73\) 2.03623 0.238323 0.119162 0.992875i \(-0.461979\pi\)
0.119162 + 0.992875i \(0.461979\pi\)
\(74\) −30.1967 −3.51029
\(75\) −13.0284 −1.50439
\(76\) −31.3097 −3.59146
\(77\) −0.209743 −0.0239024
\(78\) −12.2772 −1.39012
\(79\) −14.8058 −1.66578 −0.832892 0.553435i \(-0.813317\pi\)
−0.832892 + 0.553435i \(0.813317\pi\)
\(80\) −81.9577 −9.16315
\(81\) 1.00000 0.111111
\(82\) 15.1331 1.67117
\(83\) −7.14336 −0.784085 −0.392043 0.919947i \(-0.628231\pi\)
−0.392043 + 0.919947i \(0.628231\pi\)
\(84\) −0.306270 −0.0334168
\(85\) −4.24598 −0.460542
\(86\) −19.8855 −2.14431
\(87\) −6.81104 −0.730220
\(88\) 44.9380 4.79040
\(89\) 2.78938 0.295674 0.147837 0.989012i \(-0.452769\pi\)
0.147837 + 0.989012i \(0.452769\pi\)
\(90\) 11.9566 1.26034
\(91\) −0.225185 −0.0236058
\(92\) 39.9094 4.16084
\(93\) −5.25753 −0.545180
\(94\) 18.9396 1.95347
\(95\) 22.4192 2.30016
\(96\) 32.2230 3.28875
\(97\) 8.30804 0.843554 0.421777 0.906700i \(-0.361407\pi\)
0.421777 + 0.906700i \(0.361407\pi\)
\(98\) 19.7044 1.99044
\(99\) −4.06087 −0.408133
\(100\) 77.2550 7.72550
\(101\) −12.2751 −1.22141 −0.610707 0.791857i \(-0.709115\pi\)
−0.610707 + 0.791857i \(0.709115\pi\)
\(102\) 2.81598 0.278824
\(103\) −14.2913 −1.40816 −0.704079 0.710121i \(-0.748640\pi\)
−0.704079 + 0.710121i \(0.748640\pi\)
\(104\) 48.2465 4.73096
\(105\) 0.219304 0.0214019
\(106\) −19.0570 −1.85098
\(107\) −3.76324 −0.363806 −0.181903 0.983316i \(-0.558226\pi\)
−0.181903 + 0.983316i \(0.558226\pi\)
\(108\) −5.92975 −0.570590
\(109\) −12.3326 −1.18125 −0.590623 0.806948i \(-0.701118\pi\)
−0.590623 + 0.806948i \(0.701118\pi\)
\(110\) −48.5542 −4.62946
\(111\) −10.7233 −1.01781
\(112\) 0.996966 0.0942044
\(113\) −1.49671 −0.140799 −0.0703993 0.997519i \(-0.522427\pi\)
−0.0703993 + 0.997519i \(0.522427\pi\)
\(114\) −14.8687 −1.39258
\(115\) −28.5770 −2.66482
\(116\) 40.3877 3.74991
\(117\) −4.35985 −0.403068
\(118\) 13.2743 1.22199
\(119\) 0.0516498 0.00473473
\(120\) −46.9865 −4.28926
\(121\) 5.49065 0.499150
\(122\) 34.5270 3.12593
\(123\) 5.37399 0.484557
\(124\) 31.1758 2.79967
\(125\) −34.0884 −3.04896
\(126\) −0.145445 −0.0129573
\(127\) 3.34745 0.297038 0.148519 0.988910i \(-0.452549\pi\)
0.148519 + 0.988910i \(0.452549\pi\)
\(128\) −82.3640 −7.28002
\(129\) −7.06168 −0.621746
\(130\) −52.1290 −4.57202
\(131\) −11.9733 −1.04611 −0.523056 0.852298i \(-0.675208\pi\)
−0.523056 + 0.852298i \(0.675208\pi\)
\(132\) 24.0799 2.09589
\(133\) −0.272716 −0.0236475
\(134\) 19.4166 1.67734
\(135\) 4.24598 0.365436
\(136\) −11.0661 −0.948910
\(137\) 6.15761 0.526080 0.263040 0.964785i \(-0.415275\pi\)
0.263040 + 0.964785i \(0.415275\pi\)
\(138\) 18.9526 1.61335
\(139\) −10.9488 −0.928661 −0.464331 0.885662i \(-0.653705\pi\)
−0.464331 + 0.885662i \(0.653705\pi\)
\(140\) −1.30042 −0.109905
\(141\) 6.72574 0.566410
\(142\) 9.85683 0.827167
\(143\) 17.7048 1.48055
\(144\) 19.3024 1.60853
\(145\) −28.9196 −2.40164
\(146\) −5.73399 −0.474549
\(147\) 6.99733 0.577130
\(148\) 63.5866 5.22678
\(149\) 12.8346 1.05145 0.525727 0.850653i \(-0.323793\pi\)
0.525727 + 0.850653i \(0.323793\pi\)
\(150\) 36.6877 2.99554
\(151\) −2.07020 −0.168470 −0.0842352 0.996446i \(-0.526845\pi\)
−0.0842352 + 0.996446i \(0.526845\pi\)
\(152\) 58.4301 4.73931
\(153\) 1.00000 0.0808452
\(154\) 0.590633 0.0475945
\(155\) −22.3234 −1.79306
\(156\) 25.8528 2.06988
\(157\) −1.00000 −0.0798087
\(158\) 41.6929 3.31691
\(159\) −6.76745 −0.536693
\(160\) 136.819 10.8165
\(161\) 0.347622 0.0273965
\(162\) −2.81598 −0.221244
\(163\) −12.7043 −0.995079 −0.497539 0.867441i \(-0.665763\pi\)
−0.497539 + 0.867441i \(0.665763\pi\)
\(164\) −31.8664 −2.48835
\(165\) −17.2424 −1.34232
\(166\) 20.1156 1.56127
\(167\) 19.0944 1.47757 0.738783 0.673943i \(-0.235401\pi\)
0.738783 + 0.673943i \(0.235401\pi\)
\(168\) 0.571562 0.0440969
\(169\) 6.00828 0.462175
\(170\) 11.9566 0.917030
\(171\) −5.28010 −0.403779
\(172\) 41.8740 3.19286
\(173\) −12.2680 −0.932716 −0.466358 0.884596i \(-0.654434\pi\)
−0.466358 + 0.884596i \(0.654434\pi\)
\(174\) 19.1798 1.45401
\(175\) 0.672914 0.0508675
\(176\) −78.3846 −5.90846
\(177\) 4.71390 0.354319
\(178\) −7.85484 −0.588745
\(179\) −11.5661 −0.864489 −0.432244 0.901757i \(-0.642278\pi\)
−0.432244 + 0.901757i \(0.642278\pi\)
\(180\) −25.1776 −1.87663
\(181\) 4.00986 0.298051 0.149025 0.988833i \(-0.452386\pi\)
0.149025 + 0.988833i \(0.452386\pi\)
\(182\) 0.634118 0.0470039
\(183\) 12.2611 0.906366
\(184\) −74.4789 −5.49066
\(185\) −45.5310 −3.34751
\(186\) 14.8051 1.08556
\(187\) −4.06087 −0.296960
\(188\) −39.8820 −2.90869
\(189\) −0.0516498 −0.00375697
\(190\) −63.1321 −4.58008
\(191\) 4.51279 0.326534 0.163267 0.986582i \(-0.447797\pi\)
0.163267 + 0.986582i \(0.447797\pi\)
\(192\) −52.1346 −3.76249
\(193\) 8.27853 0.595902 0.297951 0.954581i \(-0.403697\pi\)
0.297951 + 0.954581i \(0.403697\pi\)
\(194\) −23.3953 −1.67968
\(195\) −18.5118 −1.32566
\(196\) −41.4924 −2.96374
\(197\) −8.36548 −0.596015 −0.298008 0.954563i \(-0.596322\pi\)
−0.298008 + 0.954563i \(0.596322\pi\)
\(198\) 11.4353 0.812673
\(199\) 11.6725 0.827444 0.413722 0.910403i \(-0.364229\pi\)
0.413722 + 0.910403i \(0.364229\pi\)
\(200\) −144.173 −10.1946
\(201\) 6.89514 0.486346
\(202\) 34.5663 2.43208
\(203\) 0.351789 0.0246907
\(204\) −5.92975 −0.415165
\(205\) 22.8179 1.59367
\(206\) 40.2439 2.80392
\(207\) 6.73037 0.467793
\(208\) −84.1556 −5.83514
\(209\) 21.4418 1.48316
\(210\) −0.617557 −0.0426155
\(211\) −12.9686 −0.892792 −0.446396 0.894835i \(-0.647293\pi\)
−0.446396 + 0.894835i \(0.647293\pi\)
\(212\) 40.1293 2.75609
\(213\) 3.50032 0.239838
\(214\) 10.5972 0.724411
\(215\) −29.9838 −2.04488
\(216\) 11.0661 0.752952
\(217\) 0.271550 0.0184340
\(218\) 34.7283 2.35210
\(219\) −2.03623 −0.137596
\(220\) 102.243 6.89322
\(221\) −4.35985 −0.293275
\(222\) 30.1967 2.02667
\(223\) 11.7529 0.787030 0.393515 0.919318i \(-0.371259\pi\)
0.393515 + 0.919318i \(0.371259\pi\)
\(224\) −1.66431 −0.111202
\(225\) 13.0284 0.868559
\(226\) 4.21471 0.280358
\(227\) −19.9116 −1.32158 −0.660788 0.750572i \(-0.729778\pi\)
−0.660788 + 0.750572i \(0.729778\pi\)
\(228\) 31.3097 2.07353
\(229\) −5.43413 −0.359097 −0.179549 0.983749i \(-0.557464\pi\)
−0.179549 + 0.983749i \(0.557464\pi\)
\(230\) 80.4724 5.30619
\(231\) 0.209743 0.0138001
\(232\) −75.3716 −4.94839
\(233\) −27.2094 −1.78254 −0.891272 0.453468i \(-0.850186\pi\)
−0.891272 + 0.453468i \(0.850186\pi\)
\(234\) 12.2772 0.802589
\(235\) 28.5574 1.86288
\(236\) −27.9523 −1.81954
\(237\) 14.8058 0.961741
\(238\) −0.145445 −0.00942779
\(239\) −0.173199 −0.0112033 −0.00560165 0.999984i \(-0.501783\pi\)
−0.00560165 + 0.999984i \(0.501783\pi\)
\(240\) 81.9577 5.29035
\(241\) 17.4422 1.12355 0.561775 0.827290i \(-0.310119\pi\)
0.561775 + 0.827290i \(0.310119\pi\)
\(242\) −15.4616 −0.993908
\(243\) −1.00000 −0.0641500
\(244\) −72.7052 −4.65447
\(245\) 29.7106 1.89814
\(246\) −15.1331 −0.964848
\(247\) 23.0204 1.46476
\(248\) −58.1803 −3.69445
\(249\) 7.14336 0.452692
\(250\) 95.9923 6.07109
\(251\) 20.9588 1.32291 0.661454 0.749986i \(-0.269940\pi\)
0.661454 + 0.749986i \(0.269940\pi\)
\(252\) 0.306270 0.0192932
\(253\) −27.3311 −1.71829
\(254\) −9.42636 −0.591462
\(255\) 4.24598 0.265894
\(256\) 127.666 7.97914
\(257\) −5.27856 −0.329268 −0.164634 0.986355i \(-0.552644\pi\)
−0.164634 + 0.986355i \(0.552644\pi\)
\(258\) 19.8855 1.23802
\(259\) 0.553857 0.0344150
\(260\) 109.771 6.80768
\(261\) 6.81104 0.421593
\(262\) 33.7166 2.08302
\(263\) 17.8038 1.09783 0.548915 0.835878i \(-0.315041\pi\)
0.548915 + 0.835878i \(0.315041\pi\)
\(264\) −44.9380 −2.76574
\(265\) −28.7345 −1.76514
\(266\) 0.767963 0.0470869
\(267\) −2.78938 −0.170707
\(268\) −40.8864 −2.49754
\(269\) 6.92771 0.422390 0.211195 0.977444i \(-0.432265\pi\)
0.211195 + 0.977444i \(0.432265\pi\)
\(270\) −11.9566 −0.727656
\(271\) −5.74026 −0.348696 −0.174348 0.984684i \(-0.555782\pi\)
−0.174348 + 0.984684i \(0.555782\pi\)
\(272\) 19.3024 1.17038
\(273\) 0.225185 0.0136288
\(274\) −17.3397 −1.04753
\(275\) −52.9066 −3.19039
\(276\) −39.9094 −2.40226
\(277\) 6.71496 0.403463 0.201731 0.979441i \(-0.435343\pi\)
0.201731 + 0.979441i \(0.435343\pi\)
\(278\) 30.8315 1.84915
\(279\) 5.25753 0.314760
\(280\) 2.42684 0.145032
\(281\) 3.50732 0.209229 0.104615 0.994513i \(-0.466639\pi\)
0.104615 + 0.994513i \(0.466639\pi\)
\(282\) −18.9396 −1.12783
\(283\) −0.290625 −0.0172759 −0.00863793 0.999963i \(-0.502750\pi\)
−0.00863793 + 0.999963i \(0.502750\pi\)
\(284\) −20.7560 −1.23164
\(285\) −22.4192 −1.32800
\(286\) −49.8563 −2.94806
\(287\) −0.277566 −0.0163842
\(288\) −32.2230 −1.89876
\(289\) 1.00000 0.0588235
\(290\) 81.4369 4.78214
\(291\) −8.30804 −0.487026
\(292\) 12.0743 0.706598
\(293\) 22.2072 1.29736 0.648679 0.761062i \(-0.275322\pi\)
0.648679 + 0.761062i \(0.275322\pi\)
\(294\) −19.7044 −1.14918
\(295\) 20.0152 1.16533
\(296\) −118.665 −6.89728
\(297\) 4.06087 0.235635
\(298\) −36.1421 −2.09365
\(299\) −29.3434 −1.69697
\(300\) −77.2550 −4.46032
\(301\) 0.364734 0.0210229
\(302\) 5.82964 0.335458
\(303\) 12.2751 0.705184
\(304\) −101.919 −5.84544
\(305\) 52.0604 2.98097
\(306\) −2.81598 −0.160979
\(307\) 11.4221 0.651893 0.325947 0.945388i \(-0.394317\pi\)
0.325947 + 0.945388i \(0.394317\pi\)
\(308\) −1.24372 −0.0708677
\(309\) 14.2913 0.813001
\(310\) 62.8622 3.57034
\(311\) −11.0051 −0.624041 −0.312020 0.950075i \(-0.601006\pi\)
−0.312020 + 0.950075i \(0.601006\pi\)
\(312\) −48.2465 −2.73142
\(313\) 4.22402 0.238756 0.119378 0.992849i \(-0.461910\pi\)
0.119378 + 0.992849i \(0.461910\pi\)
\(314\) 2.81598 0.158915
\(315\) −0.219304 −0.0123564
\(316\) −87.7948 −4.93884
\(317\) 20.5233 1.15270 0.576351 0.817202i \(-0.304476\pi\)
0.576351 + 0.817202i \(0.304476\pi\)
\(318\) 19.0570 1.06866
\(319\) −27.6587 −1.54859
\(320\) −221.363 −12.3746
\(321\) 3.76324 0.210044
\(322\) −0.978897 −0.0545518
\(323\) −5.28010 −0.293793
\(324\) 5.92975 0.329430
\(325\) −56.8018 −3.15080
\(326\) 35.7751 1.98140
\(327\) 12.3326 0.681993
\(328\) 59.4691 3.28363
\(329\) −0.347383 −0.0191519
\(330\) 48.5542 2.67282
\(331\) −7.92050 −0.435350 −0.217675 0.976021i \(-0.569847\pi\)
−0.217675 + 0.976021i \(0.569847\pi\)
\(332\) −42.3583 −2.32471
\(333\) 10.7233 0.587634
\(334\) −53.7694 −2.94213
\(335\) 29.2766 1.59955
\(336\) −0.996966 −0.0543890
\(337\) −15.1205 −0.823666 −0.411833 0.911259i \(-0.635111\pi\)
−0.411833 + 0.911259i \(0.635111\pi\)
\(338\) −16.9192 −0.920283
\(339\) 1.49671 0.0812901
\(340\) −25.1776 −1.36545
\(341\) −21.3501 −1.15617
\(342\) 14.8687 0.804005
\(343\) −0.722960 −0.0390361
\(344\) −78.1452 −4.21331
\(345\) 28.5770 1.53854
\(346\) 34.5463 1.85722
\(347\) 27.3094 1.46604 0.733022 0.680205i \(-0.238109\pi\)
0.733022 + 0.680205i \(0.238109\pi\)
\(348\) −40.3877 −2.16501
\(349\) −15.7609 −0.843660 −0.421830 0.906675i \(-0.638612\pi\)
−0.421830 + 0.906675i \(0.638612\pi\)
\(350\) −1.89491 −0.101287
\(351\) 4.35985 0.232711
\(352\) 130.854 6.97452
\(353\) 15.0661 0.801885 0.400943 0.916103i \(-0.368683\pi\)
0.400943 + 0.916103i \(0.368683\pi\)
\(354\) −13.2743 −0.705519
\(355\) 14.8623 0.788809
\(356\) 16.5403 0.876635
\(357\) −0.0516498 −0.00273360
\(358\) 32.5698 1.72137
\(359\) −16.5372 −0.872801 −0.436401 0.899753i \(-0.643747\pi\)
−0.436401 + 0.899753i \(0.643747\pi\)
\(360\) 46.9865 2.47640
\(361\) 8.87945 0.467340
\(362\) −11.2917 −0.593478
\(363\) −5.49065 −0.288185
\(364\) −1.33529 −0.0699883
\(365\) −8.64581 −0.452543
\(366\) −34.5270 −1.80476
\(367\) −13.6569 −0.712882 −0.356441 0.934318i \(-0.616010\pi\)
−0.356441 + 0.934318i \(0.616010\pi\)
\(368\) 129.912 6.77215
\(369\) −5.37399 −0.279759
\(370\) 128.215 6.66556
\(371\) 0.349537 0.0181471
\(372\) −31.1758 −1.61639
\(373\) −12.6906 −0.657095 −0.328548 0.944487i \(-0.606559\pi\)
−0.328548 + 0.944487i \(0.606559\pi\)
\(374\) 11.4353 0.591307
\(375\) 34.0884 1.76032
\(376\) 74.4277 3.83832
\(377\) −29.6951 −1.52938
\(378\) 0.145445 0.00748088
\(379\) −0.568417 −0.0291976 −0.0145988 0.999893i \(-0.504647\pi\)
−0.0145988 + 0.999893i \(0.504647\pi\)
\(380\) 132.940 6.81969
\(381\) −3.34745 −0.171495
\(382\) −12.7079 −0.650194
\(383\) 15.4097 0.787400 0.393700 0.919239i \(-0.371195\pi\)
0.393700 + 0.919239i \(0.371195\pi\)
\(384\) 82.3640 4.20312
\(385\) 0.890566 0.0453874
\(386\) −23.3122 −1.18656
\(387\) 7.06168 0.358965
\(388\) 49.2646 2.50103
\(389\) 27.5426 1.39646 0.698232 0.715872i \(-0.253970\pi\)
0.698232 + 0.715872i \(0.253970\pi\)
\(390\) 52.1290 2.63965
\(391\) 6.73037 0.340369
\(392\) 77.4331 3.91096
\(393\) 11.9733 0.603973
\(394\) 23.5570 1.18679
\(395\) 62.8653 3.16309
\(396\) −24.0799 −1.21006
\(397\) −3.02548 −0.151845 −0.0759223 0.997114i \(-0.524190\pi\)
−0.0759223 + 0.997114i \(0.524190\pi\)
\(398\) −32.8696 −1.64761
\(399\) 0.272716 0.0136529
\(400\) 251.479 12.5740
\(401\) −6.83885 −0.341516 −0.170758 0.985313i \(-0.554622\pi\)
−0.170758 + 0.985313i \(0.554622\pi\)
\(402\) −19.4166 −0.968411
\(403\) −22.9220 −1.14183
\(404\) −72.7880 −3.62134
\(405\) −4.24598 −0.210985
\(406\) −0.990631 −0.0491642
\(407\) −43.5460 −2.15849
\(408\) 11.0661 0.547853
\(409\) −13.4382 −0.664476 −0.332238 0.943196i \(-0.607804\pi\)
−0.332238 + 0.943196i \(0.607804\pi\)
\(410\) −64.2547 −3.17331
\(411\) −6.15761 −0.303733
\(412\) −84.7435 −4.17501
\(413\) −0.243472 −0.0119805
\(414\) −18.9526 −0.931469
\(415\) 30.3306 1.48887
\(416\) 140.488 6.88797
\(417\) 10.9488 0.536163
\(418\) −60.3797 −2.95327
\(419\) −19.0390 −0.930115 −0.465057 0.885281i \(-0.653966\pi\)
−0.465057 + 0.885281i \(0.653966\pi\)
\(420\) 1.30042 0.0634540
\(421\) −28.6901 −1.39827 −0.699135 0.714990i \(-0.746431\pi\)
−0.699135 + 0.714990i \(0.746431\pi\)
\(422\) 36.5192 1.77773
\(423\) −6.72574 −0.327017
\(424\) −74.8892 −3.63694
\(425\) 13.0284 0.631970
\(426\) −9.85683 −0.477565
\(427\) −0.633283 −0.0306467
\(428\) −22.3151 −1.07864
\(429\) −17.7048 −0.854794
\(430\) 84.4337 4.07176
\(431\) 4.24230 0.204344 0.102172 0.994767i \(-0.467421\pi\)
0.102172 + 0.994767i \(0.467421\pi\)
\(432\) −19.3024 −0.928688
\(433\) −7.33968 −0.352723 −0.176361 0.984325i \(-0.556433\pi\)
−0.176361 + 0.984325i \(0.556433\pi\)
\(434\) −0.764681 −0.0367059
\(435\) 28.9196 1.38659
\(436\) −73.1290 −3.50225
\(437\) −35.5370 −1.69997
\(438\) 5.73399 0.273981
\(439\) −9.64569 −0.460363 −0.230182 0.973148i \(-0.573932\pi\)
−0.230182 + 0.973148i \(0.573932\pi\)
\(440\) −190.806 −9.09631
\(441\) −6.99733 −0.333206
\(442\) 12.2772 0.583969
\(443\) 12.1552 0.577512 0.288756 0.957403i \(-0.406758\pi\)
0.288756 + 0.957403i \(0.406758\pi\)
\(444\) −63.5866 −3.01768
\(445\) −11.8437 −0.561443
\(446\) −33.0958 −1.56713
\(447\) −12.8346 −0.607057
\(448\) 2.69274 0.127220
\(449\) 25.4215 1.19971 0.599857 0.800107i \(-0.295224\pi\)
0.599857 + 0.800107i \(0.295224\pi\)
\(450\) −36.6877 −1.72947
\(451\) 21.8231 1.02761
\(452\) −8.87511 −0.417450
\(453\) 2.07020 0.0972664
\(454\) 56.0706 2.63152
\(455\) 0.956133 0.0448242
\(456\) −58.4301 −2.73624
\(457\) 18.1994 0.851330 0.425665 0.904881i \(-0.360040\pi\)
0.425665 + 0.904881i \(0.360040\pi\)
\(458\) 15.3024 0.715034
\(459\) −1.00000 −0.0466760
\(460\) −169.455 −7.90086
\(461\) −0.589374 −0.0274499 −0.0137249 0.999906i \(-0.504369\pi\)
−0.0137249 + 0.999906i \(0.504369\pi\)
\(462\) −0.590633 −0.0274787
\(463\) −33.1737 −1.54171 −0.770856 0.637010i \(-0.780171\pi\)
−0.770856 + 0.637010i \(0.780171\pi\)
\(464\) 131.469 6.10332
\(465\) 22.3234 1.03522
\(466\) 76.6210 3.54940
\(467\) −22.1450 −1.02475 −0.512375 0.858762i \(-0.671234\pi\)
−0.512375 + 0.858762i \(0.671234\pi\)
\(468\) −25.8528 −1.19505
\(469\) −0.356133 −0.0164447
\(470\) −80.4171 −3.70936
\(471\) 1.00000 0.0460776
\(472\) 52.1645 2.40107
\(473\) −28.6765 −1.31855
\(474\) −41.6929 −1.91502
\(475\) −68.7912 −3.15636
\(476\) 0.306270 0.0140379
\(477\) 6.76745 0.309860
\(478\) 0.487725 0.0223080
\(479\) −0.471722 −0.0215535 −0.0107768 0.999942i \(-0.503430\pi\)
−0.0107768 + 0.999942i \(0.503430\pi\)
\(480\) −136.819 −6.24488
\(481\) −46.7520 −2.13171
\(482\) −49.1168 −2.23721
\(483\) −0.347622 −0.0158174
\(484\) 32.5582 1.47992
\(485\) −35.2758 −1.60179
\(486\) 2.81598 0.127735
\(487\) −12.5418 −0.568325 −0.284163 0.958776i \(-0.591716\pi\)
−0.284163 + 0.958776i \(0.591716\pi\)
\(488\) 135.682 6.14205
\(489\) 12.7043 0.574509
\(490\) −83.6644 −3.77957
\(491\) 34.7159 1.56671 0.783353 0.621577i \(-0.213508\pi\)
0.783353 + 0.621577i \(0.213508\pi\)
\(492\) 31.8664 1.43665
\(493\) 6.81104 0.306754
\(494\) −64.8251 −2.91662
\(495\) 17.2424 0.774988
\(496\) 101.483 4.55672
\(497\) −0.180791 −0.00810957
\(498\) −20.1156 −0.901400
\(499\) 3.18817 0.142722 0.0713610 0.997451i \(-0.477266\pi\)
0.0713610 + 0.997451i \(0.477266\pi\)
\(500\) −202.136 −9.03978
\(501\) −19.0944 −0.853073
\(502\) −59.0196 −2.63417
\(503\) 14.9017 0.664433 0.332217 0.943203i \(-0.392203\pi\)
0.332217 + 0.943203i \(0.392203\pi\)
\(504\) −0.571562 −0.0254594
\(505\) 52.1197 2.31930
\(506\) 76.9640 3.42147
\(507\) −6.00828 −0.266837
\(508\) 19.8495 0.880681
\(509\) −37.5932 −1.66629 −0.833145 0.553055i \(-0.813462\pi\)
−0.833145 + 0.553055i \(0.813462\pi\)
\(510\) −11.9566 −0.529448
\(511\) 0.105171 0.00465249
\(512\) −194.778 −8.60804
\(513\) 5.28010 0.233122
\(514\) 14.8643 0.655637
\(515\) 60.6804 2.67390
\(516\) −41.8740 −1.84340
\(517\) 27.3124 1.20120
\(518\) −1.55965 −0.0685271
\(519\) 12.2680 0.538504
\(520\) −204.854 −8.98344
\(521\) −30.5592 −1.33882 −0.669412 0.742891i \(-0.733454\pi\)
−0.669412 + 0.742891i \(0.733454\pi\)
\(522\) −19.1798 −0.839475
\(523\) 5.01460 0.219273 0.109637 0.993972i \(-0.465031\pi\)
0.109637 + 0.993972i \(0.465031\pi\)
\(524\) −70.9987 −3.10159
\(525\) −0.672914 −0.0293684
\(526\) −50.1352 −2.18600
\(527\) 5.25753 0.229022
\(528\) 78.3846 3.41125
\(529\) 22.2978 0.969472
\(530\) 80.9157 3.51475
\(531\) −4.71390 −0.204566
\(532\) −1.61714 −0.0701118
\(533\) 23.4298 1.01486
\(534\) 7.85484 0.339912
\(535\) 15.9787 0.690818
\(536\) 76.3022 3.29575
\(537\) 11.5661 0.499113
\(538\) −19.5083 −0.841062
\(539\) 28.4152 1.22393
\(540\) 25.1776 1.08347
\(541\) −2.26237 −0.0972668 −0.0486334 0.998817i \(-0.515487\pi\)
−0.0486334 + 0.998817i \(0.515487\pi\)
\(542\) 16.1645 0.694324
\(543\) −4.00986 −0.172080
\(544\) −32.2230 −1.38155
\(545\) 52.3639 2.24302
\(546\) −0.634118 −0.0271377
\(547\) −15.0800 −0.644774 −0.322387 0.946608i \(-0.604485\pi\)
−0.322387 + 0.946608i \(0.604485\pi\)
\(548\) 36.5131 1.55976
\(549\) −12.2611 −0.523291
\(550\) 148.984 6.35269
\(551\) −35.9630 −1.53207
\(552\) 74.4789 3.17003
\(553\) −0.764718 −0.0325191
\(554\) −18.9092 −0.803375
\(555\) 45.5310 1.93268
\(556\) −64.9233 −2.75336
\(557\) 1.98612 0.0841546 0.0420773 0.999114i \(-0.486602\pi\)
0.0420773 + 0.999114i \(0.486602\pi\)
\(558\) −14.8051 −0.626750
\(559\) −30.7878 −1.30219
\(560\) −4.23310 −0.178881
\(561\) 4.06087 0.171450
\(562\) −9.87654 −0.416617
\(563\) −13.9777 −0.589089 −0.294544 0.955638i \(-0.595168\pi\)
−0.294544 + 0.955638i \(0.595168\pi\)
\(564\) 39.8820 1.67933
\(565\) 6.35501 0.267357
\(566\) 0.818394 0.0343997
\(567\) 0.0516498 0.00216909
\(568\) 38.7349 1.62528
\(569\) −8.09275 −0.339266 −0.169633 0.985507i \(-0.554258\pi\)
−0.169633 + 0.985507i \(0.554258\pi\)
\(570\) 63.1321 2.64431
\(571\) −31.7412 −1.32833 −0.664164 0.747587i \(-0.731212\pi\)
−0.664164 + 0.747587i \(0.731212\pi\)
\(572\) 104.985 4.38964
\(573\) −4.51279 −0.188525
\(574\) 0.781620 0.0326242
\(575\) 87.6858 3.65675
\(576\) 52.1346 2.17228
\(577\) −9.72273 −0.404763 −0.202381 0.979307i \(-0.564868\pi\)
−0.202381 + 0.979307i \(0.564868\pi\)
\(578\) −2.81598 −0.117129
\(579\) −8.27853 −0.344044
\(580\) −171.486 −7.12056
\(581\) −0.368953 −0.0153068
\(582\) 23.3953 0.969765
\(583\) −27.4817 −1.13818
\(584\) −22.5331 −0.932428
\(585\) 18.5118 0.765371
\(586\) −62.5351 −2.58330
\(587\) 13.2141 0.545402 0.272701 0.962099i \(-0.412083\pi\)
0.272701 + 0.962099i \(0.412083\pi\)
\(588\) 41.4924 1.71112
\(589\) −27.7603 −1.14384
\(590\) −56.3623 −2.32040
\(591\) 8.36548 0.344110
\(592\) 206.986 8.50707
\(593\) 24.9497 1.02456 0.512281 0.858818i \(-0.328801\pi\)
0.512281 + 0.858818i \(0.328801\pi\)
\(594\) −11.4353 −0.469197
\(595\) −0.219304 −0.00899060
\(596\) 76.1061 3.11743
\(597\) −11.6725 −0.477725
\(598\) 82.6304 3.37901
\(599\) 26.9894 1.10276 0.551378 0.834255i \(-0.314102\pi\)
0.551378 + 0.834255i \(0.314102\pi\)
\(600\) 144.173 5.88585
\(601\) −48.0430 −1.95972 −0.979858 0.199697i \(-0.936004\pi\)
−0.979858 + 0.199697i \(0.936004\pi\)
\(602\) −1.02708 −0.0418608
\(603\) −6.89514 −0.280792
\(604\) −12.2758 −0.499494
\(605\) −23.3132 −0.947818
\(606\) −34.5663 −1.40416
\(607\) −31.8990 −1.29474 −0.647371 0.762175i \(-0.724132\pi\)
−0.647371 + 0.762175i \(0.724132\pi\)
\(608\) 170.141 6.90012
\(609\) −0.351789 −0.0142552
\(610\) −146.601 −5.93571
\(611\) 29.3232 1.18629
\(612\) 5.92975 0.239696
\(613\) −32.4981 −1.31258 −0.656292 0.754507i \(-0.727876\pi\)
−0.656292 + 0.754507i \(0.727876\pi\)
\(614\) −32.1644 −1.29805
\(615\) −22.8179 −0.920106
\(616\) 2.32104 0.0935172
\(617\) −36.2237 −1.45831 −0.729156 0.684348i \(-0.760087\pi\)
−0.729156 + 0.684348i \(0.760087\pi\)
\(618\) −40.2439 −1.61885
\(619\) −33.7377 −1.35603 −0.678015 0.735048i \(-0.737160\pi\)
−0.678015 + 0.735048i \(0.737160\pi\)
\(620\) −132.372 −5.31619
\(621\) −6.73037 −0.270080
\(622\) 30.9901 1.24259
\(623\) 0.144071 0.00577208
\(624\) 84.1556 3.36892
\(625\) 79.5969 3.18388
\(626\) −11.8948 −0.475411
\(627\) −21.4418 −0.856303
\(628\) −5.92975 −0.236623
\(629\) 10.7233 0.427567
\(630\) 0.617557 0.0246040
\(631\) 14.6574 0.583503 0.291752 0.956494i \(-0.405762\pi\)
0.291752 + 0.956494i \(0.405762\pi\)
\(632\) 163.843 6.51731
\(633\) 12.9686 0.515454
\(634\) −57.7931 −2.29526
\(635\) −14.2132 −0.564035
\(636\) −40.1293 −1.59123
\(637\) 30.5073 1.20874
\(638\) 77.8865 3.08355
\(639\) −3.50032 −0.138470
\(640\) 349.716 13.8238
\(641\) 21.1802 0.836566 0.418283 0.908317i \(-0.362632\pi\)
0.418283 + 0.908317i \(0.362632\pi\)
\(642\) −10.5972 −0.418239
\(643\) 15.4097 0.607699 0.303849 0.952720i \(-0.401728\pi\)
0.303849 + 0.952720i \(0.401728\pi\)
\(644\) 2.06131 0.0812271
\(645\) 29.9838 1.18061
\(646\) 14.8687 0.585000
\(647\) −26.9858 −1.06092 −0.530461 0.847709i \(-0.677981\pi\)
−0.530461 + 0.847709i \(0.677981\pi\)
\(648\) −11.0661 −0.434717
\(649\) 19.1425 0.751411
\(650\) 159.953 6.27386
\(651\) −0.271550 −0.0106429
\(652\) −75.3334 −2.95028
\(653\) 47.0120 1.83972 0.919861 0.392245i \(-0.128301\pi\)
0.919861 + 0.392245i \(0.128301\pi\)
\(654\) −34.7283 −1.35798
\(655\) 50.8385 1.98642
\(656\) −103.731 −4.05002
\(657\) 2.03623 0.0794410
\(658\) 0.978225 0.0381352
\(659\) 3.75131 0.146130 0.0730652 0.997327i \(-0.476722\pi\)
0.0730652 + 0.997327i \(0.476722\pi\)
\(660\) −102.243 −3.97980
\(661\) 40.6523 1.58119 0.790595 0.612340i \(-0.209772\pi\)
0.790595 + 0.612340i \(0.209772\pi\)
\(662\) 22.3040 0.866869
\(663\) 4.35985 0.169322
\(664\) 79.0491 3.06770
\(665\) 1.15795 0.0449033
\(666\) −30.1967 −1.17010
\(667\) 45.8408 1.77496
\(668\) 113.225 4.38080
\(669\) −11.7529 −0.454392
\(670\) −82.4425 −3.18503
\(671\) 49.7907 1.92215
\(672\) 1.66431 0.0642023
\(673\) 34.9762 1.34823 0.674117 0.738625i \(-0.264524\pi\)
0.674117 + 0.738625i \(0.264524\pi\)
\(674\) 42.5790 1.64008
\(675\) −13.0284 −0.501463
\(676\) 35.6276 1.37029
\(677\) 7.88983 0.303231 0.151615 0.988440i \(-0.451552\pi\)
0.151615 + 0.988440i \(0.451552\pi\)
\(678\) −4.21471 −0.161865
\(679\) 0.429109 0.0164677
\(680\) 46.9865 1.80185
\(681\) 19.9116 0.763013
\(682\) 60.1216 2.30217
\(683\) −30.4180 −1.16391 −0.581955 0.813221i \(-0.697712\pi\)
−0.581955 + 0.813221i \(0.697712\pi\)
\(684\) −31.3097 −1.19715
\(685\) −26.1451 −0.998954
\(686\) 2.03584 0.0777287
\(687\) 5.43413 0.207325
\(688\) 136.307 5.19667
\(689\) −29.5050 −1.12405
\(690\) −80.4724 −3.06353
\(691\) 14.7414 0.560787 0.280394 0.959885i \(-0.409535\pi\)
0.280394 + 0.959885i \(0.409535\pi\)
\(692\) −72.7459 −2.76538
\(693\) −0.209743 −0.00796748
\(694\) −76.9027 −2.91919
\(695\) 46.4882 1.76340
\(696\) 75.3716 2.85695
\(697\) −5.37399 −0.203554
\(698\) 44.3823 1.67990
\(699\) 27.2094 1.02915
\(700\) 3.99021 0.150816
\(701\) −47.7801 −1.80463 −0.902314 0.431079i \(-0.858133\pi\)
−0.902314 + 0.431079i \(0.858133\pi\)
\(702\) −12.2772 −0.463375
\(703\) −56.6202 −2.13547
\(704\) −211.712 −7.97919
\(705\) −28.5574 −1.07553
\(706\) −42.4257 −1.59671
\(707\) −0.634005 −0.0238442
\(708\) 27.9523 1.05051
\(709\) 20.2838 0.761773 0.380886 0.924622i \(-0.375619\pi\)
0.380886 + 0.924622i \(0.375619\pi\)
\(710\) −41.8519 −1.57068
\(711\) −14.8058 −0.555261
\(712\) −30.8675 −1.15681
\(713\) 35.3851 1.32518
\(714\) 0.145445 0.00544314
\(715\) −75.1742 −2.81136
\(716\) −68.5839 −2.56310
\(717\) 0.173199 0.00646823
\(718\) 46.5685 1.73792
\(719\) −20.7115 −0.772409 −0.386204 0.922413i \(-0.626214\pi\)
−0.386204 + 0.922413i \(0.626214\pi\)
\(720\) −81.9577 −3.05438
\(721\) −0.738140 −0.0274898
\(722\) −25.0044 −0.930566
\(723\) −17.4422 −0.648682
\(724\) 23.7775 0.883682
\(725\) 88.7368 3.29560
\(726\) 15.4616 0.573833
\(727\) 3.59014 0.133151 0.0665755 0.997781i \(-0.478793\pi\)
0.0665755 + 0.997781i \(0.478793\pi\)
\(728\) 2.49192 0.0923568
\(729\) 1.00000 0.0370370
\(730\) 24.3464 0.901102
\(731\) 7.06168 0.261186
\(732\) 72.7052 2.68726
\(733\) −35.9031 −1.32611 −0.663055 0.748571i \(-0.730740\pi\)
−0.663055 + 0.748571i \(0.730740\pi\)
\(734\) 38.4575 1.41949
\(735\) −29.7106 −1.09589
\(736\) −216.873 −7.99404
\(737\) 28.0002 1.03140
\(738\) 15.1331 0.557056
\(739\) 9.36547 0.344514 0.172257 0.985052i \(-0.444894\pi\)
0.172257 + 0.985052i \(0.444894\pi\)
\(740\) −269.988 −9.92494
\(741\) −23.0204 −0.845677
\(742\) −0.984291 −0.0361344
\(743\) −11.8837 −0.435969 −0.217985 0.975952i \(-0.569948\pi\)
−0.217985 + 0.975952i \(0.569948\pi\)
\(744\) 58.1803 2.13299
\(745\) −54.4956 −1.99657
\(746\) 35.7365 1.30841
\(747\) −7.14336 −0.261362
\(748\) −24.0799 −0.880449
\(749\) −0.194371 −0.00710215
\(750\) −95.9923 −3.50514
\(751\) −14.9055 −0.543908 −0.271954 0.962310i \(-0.587670\pi\)
−0.271954 + 0.962310i \(0.587670\pi\)
\(752\) −129.823 −4.73416
\(753\) −20.9588 −0.763781
\(754\) 83.6208 3.04529
\(755\) 8.79003 0.319902
\(756\) −0.306270 −0.0111389
\(757\) 42.6578 1.55042 0.775212 0.631701i \(-0.217643\pi\)
0.775212 + 0.631701i \(0.217643\pi\)
\(758\) 1.60065 0.0581383
\(759\) 27.3311 0.992057
\(760\) −248.093 −8.99929
\(761\) 10.5539 0.382579 0.191290 0.981534i \(-0.438733\pi\)
0.191290 + 0.981534i \(0.438733\pi\)
\(762\) 9.42636 0.341481
\(763\) −0.636975 −0.0230600
\(764\) 26.7597 0.968132
\(765\) −4.24598 −0.153514
\(766\) −43.3935 −1.56787
\(767\) 20.5519 0.742086
\(768\) −127.666 −4.60676
\(769\) 29.1358 1.05066 0.525331 0.850898i \(-0.323941\pi\)
0.525331 + 0.850898i \(0.323941\pi\)
\(770\) −2.50782 −0.0903754
\(771\) 5.27856 0.190103
\(772\) 49.0896 1.76677
\(773\) 41.7734 1.50249 0.751243 0.660026i \(-0.229455\pi\)
0.751243 + 0.660026i \(0.229455\pi\)
\(774\) −19.8855 −0.714771
\(775\) 68.4971 2.46049
\(776\) −91.9375 −3.30037
\(777\) −0.553857 −0.0198695
\(778\) −77.5594 −2.78064
\(779\) 28.3752 1.01665
\(780\) −109.771 −3.93042
\(781\) 14.2143 0.508629
\(782\) −18.9526 −0.677743
\(783\) −6.81104 −0.243407
\(784\) −135.065 −4.82376
\(785\) 4.24598 0.151546
\(786\) −33.7166 −1.20263
\(787\) 44.8476 1.59864 0.799322 0.600903i \(-0.205192\pi\)
0.799322 + 0.600903i \(0.205192\pi\)
\(788\) −49.6052 −1.76711
\(789\) −17.8038 −0.633832
\(790\) −177.027 −6.29835
\(791\) −0.0773048 −0.00274864
\(792\) 44.9380 1.59680
\(793\) 53.4565 1.89830
\(794\) 8.51969 0.302353
\(795\) 28.7345 1.01911
\(796\) 69.2152 2.45327
\(797\) −51.7523 −1.83316 −0.916581 0.399849i \(-0.869062\pi\)
−0.916581 + 0.399849i \(0.869062\pi\)
\(798\) −0.767963 −0.0271856
\(799\) −6.72574 −0.237940
\(800\) −419.814 −14.8427
\(801\) 2.78938 0.0985579
\(802\) 19.2581 0.680026
\(803\) −8.26887 −0.291802
\(804\) 40.8864 1.44195
\(805\) −1.47600 −0.0520221
\(806\) 64.5480 2.27361
\(807\) −6.92771 −0.243867
\(808\) 135.837 4.77873
\(809\) −2.21921 −0.0780234 −0.0390117 0.999239i \(-0.512421\pi\)
−0.0390117 + 0.999239i \(0.512421\pi\)
\(810\) 11.9566 0.420112
\(811\) 36.0095 1.26447 0.632233 0.774779i \(-0.282139\pi\)
0.632233 + 0.774779i \(0.282139\pi\)
\(812\) 2.08602 0.0732049
\(813\) 5.74026 0.201320
\(814\) 122.625 4.29799
\(815\) 53.9423 1.88952
\(816\) −19.3024 −0.675720
\(817\) −37.2864 −1.30448
\(818\) 37.8417 1.32310
\(819\) −0.225185 −0.00786861
\(820\) 135.304 4.72503
\(821\) 35.9993 1.25639 0.628193 0.778058i \(-0.283795\pi\)
0.628193 + 0.778058i \(0.283795\pi\)
\(822\) 17.3397 0.604792
\(823\) 25.4428 0.886880 0.443440 0.896304i \(-0.353758\pi\)
0.443440 + 0.896304i \(0.353758\pi\)
\(824\) 158.148 5.50936
\(825\) 52.9066 1.84197
\(826\) 0.685613 0.0238555
\(827\) −12.3700 −0.430145 −0.215073 0.976598i \(-0.568999\pi\)
−0.215073 + 0.976598i \(0.568999\pi\)
\(828\) 39.9094 1.38695
\(829\) 50.1470 1.74168 0.870839 0.491568i \(-0.163576\pi\)
0.870839 + 0.491568i \(0.163576\pi\)
\(830\) −85.4104 −2.96464
\(831\) −6.71496 −0.232939
\(832\) −227.299 −7.88018
\(833\) −6.99733 −0.242443
\(834\) −30.8315 −1.06761
\(835\) −81.0744 −2.80569
\(836\) 127.144 4.39738
\(837\) −5.25753 −0.181727
\(838\) 53.6134 1.85204
\(839\) −32.6743 −1.12804 −0.564021 0.825761i \(-0.690746\pi\)
−0.564021 + 0.825761i \(0.690746\pi\)
\(840\) −2.42684 −0.0837340
\(841\) 17.3903 0.599664
\(842\) 80.7908 2.78423
\(843\) −3.50732 −0.120798
\(844\) −76.9003 −2.64702
\(845\) −25.5110 −0.877607
\(846\) 18.9396 0.651156
\(847\) 0.283591 0.00974431
\(848\) 130.628 4.48579
\(849\) 0.290625 0.00997422
\(850\) −36.6877 −1.25838
\(851\) 72.1719 2.47402
\(852\) 20.7560 0.711089
\(853\) −8.75886 −0.299898 −0.149949 0.988694i \(-0.547911\pi\)
−0.149949 + 0.988694i \(0.547911\pi\)
\(854\) 1.78331 0.0610237
\(855\) 22.4192 0.766721
\(856\) 41.6444 1.42338
\(857\) −21.1405 −0.722145 −0.361072 0.932538i \(-0.617589\pi\)
−0.361072 + 0.932538i \(0.617589\pi\)
\(858\) 49.8563 1.70207
\(859\) 39.8728 1.36044 0.680220 0.733008i \(-0.261884\pi\)
0.680220 + 0.733008i \(0.261884\pi\)
\(860\) −177.796 −6.06280
\(861\) 0.277566 0.00945941
\(862\) −11.9462 −0.406890
\(863\) −27.4924 −0.935851 −0.467926 0.883768i \(-0.654999\pi\)
−0.467926 + 0.883768i \(0.654999\pi\)
\(864\) 32.2230 1.09625
\(865\) 52.0896 1.77110
\(866\) 20.6684 0.702341
\(867\) −1.00000 −0.0339618
\(868\) 1.61023 0.0546546
\(869\) 60.1245 2.03958
\(870\) −81.4369 −2.76097
\(871\) 30.0618 1.01860
\(872\) 136.473 4.62157
\(873\) 8.30804 0.281185
\(874\) 100.072 3.38497
\(875\) −1.76066 −0.0595212
\(876\) −12.0743 −0.407954
\(877\) −57.4522 −1.94002 −0.970012 0.243058i \(-0.921849\pi\)
−0.970012 + 0.243058i \(0.921849\pi\)
\(878\) 27.1621 0.916675
\(879\) −22.2072 −0.749031
\(880\) 332.820 11.2193
\(881\) −3.37088 −0.113568 −0.0567839 0.998386i \(-0.518085\pi\)
−0.0567839 + 0.998386i \(0.518085\pi\)
\(882\) 19.7044 0.663480
\(883\) 13.7375 0.462304 0.231152 0.972918i \(-0.425751\pi\)
0.231152 + 0.972918i \(0.425751\pi\)
\(884\) −25.8528 −0.869524
\(885\) −20.0152 −0.672802
\(886\) −34.2288 −1.14994
\(887\) 43.4992 1.46056 0.730280 0.683148i \(-0.239390\pi\)
0.730280 + 0.683148i \(0.239390\pi\)
\(888\) 118.665 3.98214
\(889\) 0.172895 0.00579872
\(890\) 33.3515 1.11795
\(891\) −4.06087 −0.136044
\(892\) 69.6915 2.33344
\(893\) 35.5126 1.18838
\(894\) 36.1421 1.20877
\(895\) 49.1093 1.64154
\(896\) −4.25409 −0.142119
\(897\) 29.3434 0.979747
\(898\) −71.5864 −2.38887
\(899\) 35.8092 1.19431
\(900\) 77.2550 2.57517
\(901\) 6.76745 0.225456
\(902\) −61.4534 −2.04617
\(903\) −0.364734 −0.0121376
\(904\) 16.5627 0.550868
\(905\) −17.0258 −0.565957
\(906\) −5.82964 −0.193677
\(907\) 22.3081 0.740729 0.370365 0.928886i \(-0.379233\pi\)
0.370365 + 0.928886i \(0.379233\pi\)
\(908\) −118.071 −3.91831
\(909\) −12.2751 −0.407138
\(910\) −2.69245 −0.0892540
\(911\) 42.5098 1.40841 0.704206 0.709996i \(-0.251303\pi\)
0.704206 + 0.709996i \(0.251303\pi\)
\(912\) 101.919 3.37486
\(913\) 29.0082 0.960033
\(914\) −51.2490 −1.69517
\(915\) −52.0604 −1.72106
\(916\) −32.2230 −1.06468
\(917\) −0.618419 −0.0204220
\(918\) 2.81598 0.0929412
\(919\) 37.9202 1.25087 0.625436 0.780275i \(-0.284921\pi\)
0.625436 + 0.780275i \(0.284921\pi\)
\(920\) 316.236 10.4260
\(921\) −11.4221 −0.376371
\(922\) 1.65967 0.0546582
\(923\) 15.2609 0.502317
\(924\) 1.24372 0.0409155
\(925\) 139.707 4.59355
\(926\) 93.4165 3.06986
\(927\) −14.2913 −0.469386
\(928\) −219.472 −7.20453
\(929\) −14.5891 −0.478654 −0.239327 0.970939i \(-0.576927\pi\)
−0.239327 + 0.970939i \(0.576927\pi\)
\(930\) −62.8622 −2.06133
\(931\) 36.9466 1.21088
\(932\) −161.345 −5.28502
\(933\) 11.0051 0.360290
\(934\) 62.3600 2.04048
\(935\) 17.2424 0.563886
\(936\) 48.2465 1.57699
\(937\) 8.61972 0.281594 0.140797 0.990038i \(-0.455034\pi\)
0.140797 + 0.990038i \(0.455034\pi\)
\(938\) 1.00286 0.0327446
\(939\) −4.22402 −0.137846
\(940\) 169.338 5.52320
\(941\) −4.65283 −0.151678 −0.0758390 0.997120i \(-0.524163\pi\)
−0.0758390 + 0.997120i \(0.524163\pi\)
\(942\) −2.81598 −0.0917496
\(943\) −36.1689 −1.17782
\(944\) −90.9897 −2.96146
\(945\) 0.219304 0.00713397
\(946\) 80.7526 2.62549
\(947\) −41.2712 −1.34113 −0.670567 0.741849i \(-0.733949\pi\)
−0.670567 + 0.741849i \(0.733949\pi\)
\(948\) 87.7948 2.85144
\(949\) −8.87767 −0.288181
\(950\) 193.715 6.28493
\(951\) −20.5233 −0.665513
\(952\) −0.571562 −0.0185244
\(953\) 28.4766 0.922447 0.461224 0.887284i \(-0.347411\pi\)
0.461224 + 0.887284i \(0.347411\pi\)
\(954\) −19.0570 −0.616993
\(955\) −19.1612 −0.620043
\(956\) −1.02703 −0.0332164
\(957\) 27.6587 0.894080
\(958\) 1.32836 0.0429173
\(959\) 0.318040 0.0102700
\(960\) 221.363 7.14445
\(961\) −3.35838 −0.108335
\(962\) 131.653 4.24466
\(963\) −3.76324 −0.121269
\(964\) 103.428 3.33118
\(965\) −35.1505 −1.13153
\(966\) 0.978897 0.0314955
\(967\) −31.3993 −1.00973 −0.504867 0.863197i \(-0.668459\pi\)
−0.504867 + 0.863197i \(0.668459\pi\)
\(968\) −60.7601 −1.95290
\(969\) 5.28010 0.169621
\(970\) 99.3360 3.18949
\(971\) −19.6048 −0.629149 −0.314574 0.949233i \(-0.601862\pi\)
−0.314574 + 0.949233i \(0.601862\pi\)
\(972\) −5.92975 −0.190197
\(973\) −0.565501 −0.0181291
\(974\) 35.3176 1.13165
\(975\) 56.8018 1.81911
\(976\) −236.669 −7.57558
\(977\) −26.1525 −0.836693 −0.418347 0.908287i \(-0.637390\pi\)
−0.418347 + 0.908287i \(0.637390\pi\)
\(978\) −35.7751 −1.14396
\(979\) −11.3273 −0.362022
\(980\) 176.176 5.62774
\(981\) −12.3326 −0.393749
\(982\) −97.7593 −3.11962
\(983\) 32.2084 1.02729 0.513645 0.858003i \(-0.328295\pi\)
0.513645 + 0.858003i \(0.328295\pi\)
\(984\) −59.4691 −1.89581
\(985\) 35.5197 1.13175
\(986\) −19.1798 −0.610808
\(987\) 0.347383 0.0110573
\(988\) 136.505 4.34281
\(989\) 47.5277 1.51129
\(990\) −48.5542 −1.54315
\(991\) 50.1843 1.59416 0.797079 0.603876i \(-0.206378\pi\)
0.797079 + 0.603876i \(0.206378\pi\)
\(992\) −169.414 −5.37889
\(993\) 7.92050 0.251349
\(994\) 0.509103 0.0161478
\(995\) −49.5614 −1.57120
\(996\) 42.3583 1.34217
\(997\) −17.9517 −0.568537 −0.284268 0.958745i \(-0.591751\pi\)
−0.284268 + 0.958745i \(0.591751\pi\)
\(998\) −8.97782 −0.284188
\(999\) −10.7233 −0.339271
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 \(a_p\))