Properties

Label 8007.2.a.e.1.19
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
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: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.756159 q^{2}\) \(+1.00000 q^{3}\) \(-1.42822 q^{4}\) \(-3.23827 q^{5}\) \(-0.756159 q^{6}\) \(+4.69700 q^{7}\) \(+2.59228 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.756159 q^{2}\) \(+1.00000 q^{3}\) \(-1.42822 q^{4}\) \(-3.23827 q^{5}\) \(-0.756159 q^{6}\) \(+4.69700 q^{7}\) \(+2.59228 q^{8}\) \(+1.00000 q^{9}\) \(+2.44865 q^{10}\) \(+3.89444 q^{11}\) \(-1.42822 q^{12}\) \(+0.979560 q^{13}\) \(-3.55168 q^{14}\) \(-3.23827 q^{15}\) \(+0.896267 q^{16}\) \(-1.00000 q^{17}\) \(-0.756159 q^{18}\) \(-4.21016 q^{19}\) \(+4.62497 q^{20}\) \(+4.69700 q^{21}\) \(-2.94482 q^{22}\) \(-3.94172 q^{23}\) \(+2.59228 q^{24}\) \(+5.48638 q^{25}\) \(-0.740704 q^{26}\) \(+1.00000 q^{27}\) \(-6.70836 q^{28}\) \(+5.35490 q^{29}\) \(+2.44865 q^{30}\) \(-3.41929 q^{31}\) \(-5.86229 q^{32}\) \(+3.89444 q^{33}\) \(+0.756159 q^{34}\) \(-15.2101 q^{35}\) \(-1.42822 q^{36}\) \(-9.92936 q^{37}\) \(+3.18355 q^{38}\) \(+0.979560 q^{39}\) \(-8.39451 q^{40}\) \(-2.77702 q^{41}\) \(-3.55168 q^{42}\) \(+8.94697 q^{43}\) \(-5.56213 q^{44}\) \(-3.23827 q^{45}\) \(+2.98057 q^{46}\) \(-7.88353 q^{47}\) \(+0.896267 q^{48}\) \(+15.0618 q^{49}\) \(-4.14858 q^{50}\) \(-1.00000 q^{51}\) \(-1.39903 q^{52}\) \(-12.9229 q^{53}\) \(-0.756159 q^{54}\) \(-12.6113 q^{55}\) \(+12.1760 q^{56}\) \(-4.21016 q^{57}\) \(-4.04916 q^{58}\) \(-8.38870 q^{59}\) \(+4.62497 q^{60}\) \(-2.01800 q^{61}\) \(+2.58553 q^{62}\) \(+4.69700 q^{63}\) \(+2.64029 q^{64}\) \(-3.17208 q^{65}\) \(-2.94482 q^{66}\) \(-9.85675 q^{67}\) \(+1.42822 q^{68}\) \(-3.94172 q^{69}\) \(+11.5013 q^{70}\) \(+3.35982 q^{71}\) \(+2.59228 q^{72}\) \(-4.43641 q^{73}\) \(+7.50818 q^{74}\) \(+5.48638 q^{75}\) \(+6.01305 q^{76}\) \(+18.2922 q^{77}\) \(-0.740704 q^{78}\) \(-7.68352 q^{79}\) \(-2.90235 q^{80}\) \(+1.00000 q^{81}\) \(+2.09987 q^{82}\) \(+1.36491 q^{83}\) \(-6.70836 q^{84}\) \(+3.23827 q^{85}\) \(-6.76534 q^{86}\) \(+5.35490 q^{87}\) \(+10.0955 q^{88}\) \(+11.2296 q^{89}\) \(+2.44865 q^{90}\) \(+4.60099 q^{91}\) \(+5.62965 q^{92}\) \(-3.41929 q^{93}\) \(+5.96120 q^{94}\) \(+13.6336 q^{95}\) \(-5.86229 q^{96}\) \(-9.58636 q^{97}\) \(-11.3891 q^{98}\) \(+3.89444 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.756159 −0.534685 −0.267343 0.963602i \(-0.586146\pi\)
−0.267343 + 0.963602i \(0.586146\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.42822 −0.714112
\(5\) −3.23827 −1.44820 −0.724099 0.689696i \(-0.757744\pi\)
−0.724099 + 0.689696i \(0.757744\pi\)
\(6\) −0.756159 −0.308701
\(7\) 4.69700 1.77530 0.887650 0.460520i \(-0.152337\pi\)
0.887650 + 0.460520i \(0.152337\pi\)
\(8\) 2.59228 0.916510
\(9\) 1.00000 0.333333
\(10\) 2.44865 0.774330
\(11\) 3.89444 1.17422 0.587109 0.809508i \(-0.300266\pi\)
0.587109 + 0.809508i \(0.300266\pi\)
\(12\) −1.42822 −0.412292
\(13\) 0.979560 0.271681 0.135841 0.990731i \(-0.456627\pi\)
0.135841 + 0.990731i \(0.456627\pi\)
\(14\) −3.55168 −0.949227
\(15\) −3.23827 −0.836117
\(16\) 0.896267 0.224067
\(17\) −1.00000 −0.242536
\(18\) −0.756159 −0.178228
\(19\) −4.21016 −0.965878 −0.482939 0.875654i \(-0.660431\pi\)
−0.482939 + 0.875654i \(0.660431\pi\)
\(20\) 4.62497 1.03417
\(21\) 4.69700 1.02497
\(22\) −2.94482 −0.627838
\(23\) −3.94172 −0.821905 −0.410952 0.911657i \(-0.634804\pi\)
−0.410952 + 0.911657i \(0.634804\pi\)
\(24\) 2.59228 0.529148
\(25\) 5.48638 1.09728
\(26\) −0.740704 −0.145264
\(27\) 1.00000 0.192450
\(28\) −6.70836 −1.26776
\(29\) 5.35490 0.994380 0.497190 0.867642i \(-0.334365\pi\)
0.497190 + 0.867642i \(0.334365\pi\)
\(30\) 2.44865 0.447060
\(31\) −3.41929 −0.614122 −0.307061 0.951690i \(-0.599346\pi\)
−0.307061 + 0.951690i \(0.599346\pi\)
\(32\) −5.86229 −1.03632
\(33\) 3.89444 0.677936
\(34\) 0.756159 0.129680
\(35\) −15.2101 −2.57098
\(36\) −1.42822 −0.238037
\(37\) −9.92936 −1.63238 −0.816188 0.577786i \(-0.803917\pi\)
−0.816188 + 0.577786i \(0.803917\pi\)
\(38\) 3.18355 0.516441
\(39\) 0.979560 0.156855
\(40\) −8.39451 −1.32729
\(41\) −2.77702 −0.433697 −0.216848 0.976205i \(-0.569578\pi\)
−0.216848 + 0.976205i \(0.569578\pi\)
\(42\) −3.55168 −0.548036
\(43\) 8.94697 1.36440 0.682200 0.731165i \(-0.261023\pi\)
0.682200 + 0.731165i \(0.261023\pi\)
\(44\) −5.56213 −0.838523
\(45\) −3.23827 −0.482732
\(46\) 2.98057 0.439460
\(47\) −7.88353 −1.14993 −0.574965 0.818178i \(-0.694984\pi\)
−0.574965 + 0.818178i \(0.694984\pi\)
\(48\) 0.896267 0.129365
\(49\) 15.0618 2.15169
\(50\) −4.14858 −0.586697
\(51\) −1.00000 −0.140028
\(52\) −1.39903 −0.194011
\(53\) −12.9229 −1.77510 −0.887551 0.460710i \(-0.847595\pi\)
−0.887551 + 0.460710i \(0.847595\pi\)
\(54\) −0.756159 −0.102900
\(55\) −12.6113 −1.70050
\(56\) 12.1760 1.62708
\(57\) −4.21016 −0.557650
\(58\) −4.04916 −0.531681
\(59\) −8.38870 −1.09212 −0.546058 0.837748i \(-0.683872\pi\)
−0.546058 + 0.837748i \(0.683872\pi\)
\(60\) 4.62497 0.597081
\(61\) −2.01800 −0.258379 −0.129189 0.991620i \(-0.541237\pi\)
−0.129189 + 0.991620i \(0.541237\pi\)
\(62\) 2.58553 0.328362
\(63\) 4.69700 0.591766
\(64\) 2.64029 0.330036
\(65\) −3.17208 −0.393448
\(66\) −2.94482 −0.362482
\(67\) −9.85675 −1.20419 −0.602097 0.798423i \(-0.705668\pi\)
−0.602097 + 0.798423i \(0.705668\pi\)
\(68\) 1.42822 0.173197
\(69\) −3.94172 −0.474527
\(70\) 11.5013 1.37467
\(71\) 3.35982 0.398737 0.199369 0.979925i \(-0.436111\pi\)
0.199369 + 0.979925i \(0.436111\pi\)
\(72\) 2.59228 0.305503
\(73\) −4.43641 −0.519242 −0.259621 0.965711i \(-0.583598\pi\)
−0.259621 + 0.965711i \(0.583598\pi\)
\(74\) 7.50818 0.872808
\(75\) 5.48638 0.633513
\(76\) 6.01305 0.689744
\(77\) 18.2922 2.08459
\(78\) −0.740704 −0.0838682
\(79\) −7.68352 −0.864464 −0.432232 0.901763i \(-0.642274\pi\)
−0.432232 + 0.901763i \(0.642274\pi\)
\(80\) −2.90235 −0.324493
\(81\) 1.00000 0.111111
\(82\) 2.09987 0.231891
\(83\) 1.36491 0.149818 0.0749089 0.997190i \(-0.476133\pi\)
0.0749089 + 0.997190i \(0.476133\pi\)
\(84\) −6.70836 −0.731942
\(85\) 3.23827 0.351239
\(86\) −6.76534 −0.729525
\(87\) 5.35490 0.574106
\(88\) 10.0955 1.07618
\(89\) 11.2296 1.19034 0.595168 0.803601i \(-0.297086\pi\)
0.595168 + 0.803601i \(0.297086\pi\)
\(90\) 2.44865 0.258110
\(91\) 4.60099 0.482315
\(92\) 5.62965 0.586932
\(93\) −3.41929 −0.354564
\(94\) 5.96120 0.614851
\(95\) 13.6336 1.39878
\(96\) −5.86229 −0.598317
\(97\) −9.58636 −0.973347 −0.486674 0.873584i \(-0.661790\pi\)
−0.486674 + 0.873584i \(0.661790\pi\)
\(98\) −11.3891 −1.15048
\(99\) 3.89444 0.391406
\(100\) −7.83577 −0.783577
\(101\) −9.91835 −0.986913 −0.493456 0.869771i \(-0.664267\pi\)
−0.493456 + 0.869771i \(0.664267\pi\)
\(102\) 0.756159 0.0748709
\(103\) 15.4652 1.52384 0.761918 0.647674i \(-0.224258\pi\)
0.761918 + 0.647674i \(0.224258\pi\)
\(104\) 2.53930 0.248999
\(105\) −15.2101 −1.48436
\(106\) 9.77180 0.949121
\(107\) 3.10496 0.300168 0.150084 0.988673i \(-0.452046\pi\)
0.150084 + 0.988673i \(0.452046\pi\)
\(108\) −1.42822 −0.137431
\(109\) 16.2718 1.55856 0.779278 0.626678i \(-0.215586\pi\)
0.779278 + 0.626678i \(0.215586\pi\)
\(110\) 9.53612 0.909233
\(111\) −9.92936 −0.942453
\(112\) 4.20977 0.397785
\(113\) −21.1316 −1.98790 −0.993949 0.109842i \(-0.964966\pi\)
−0.993949 + 0.109842i \(0.964966\pi\)
\(114\) 3.18355 0.298167
\(115\) 12.7643 1.19028
\(116\) −7.64799 −0.710098
\(117\) 0.979560 0.0905604
\(118\) 6.34319 0.583938
\(119\) −4.69700 −0.430573
\(120\) −8.39451 −0.766310
\(121\) 4.16669 0.378790
\(122\) 1.52593 0.138151
\(123\) −2.77702 −0.250395
\(124\) 4.88350 0.438552
\(125\) −1.57503 −0.140875
\(126\) −3.55168 −0.316409
\(127\) −5.92498 −0.525757 −0.262879 0.964829i \(-0.584672\pi\)
−0.262879 + 0.964829i \(0.584672\pi\)
\(128\) 9.72809 0.859850
\(129\) 8.94697 0.787737
\(130\) 2.39860 0.210371
\(131\) −1.70352 −0.148837 −0.0744186 0.997227i \(-0.523710\pi\)
−0.0744186 + 0.997227i \(0.523710\pi\)
\(132\) −5.56213 −0.484122
\(133\) −19.7751 −1.71472
\(134\) 7.45327 0.643865
\(135\) −3.23827 −0.278706
\(136\) −2.59228 −0.222286
\(137\) −10.5268 −0.899367 −0.449684 0.893188i \(-0.648463\pi\)
−0.449684 + 0.893188i \(0.648463\pi\)
\(138\) 2.98057 0.253723
\(139\) 13.2214 1.12143 0.560714 0.828009i \(-0.310527\pi\)
0.560714 + 0.828009i \(0.310527\pi\)
\(140\) 21.7235 1.83597
\(141\) −7.88353 −0.663913
\(142\) −2.54056 −0.213199
\(143\) 3.81484 0.319013
\(144\) 0.896267 0.0746889
\(145\) −17.3406 −1.44006
\(146\) 3.35463 0.277631
\(147\) 15.0618 1.24228
\(148\) 14.1813 1.16570
\(149\) 1.29815 0.106349 0.0531744 0.998585i \(-0.483066\pi\)
0.0531744 + 0.998585i \(0.483066\pi\)
\(150\) −4.14858 −0.338730
\(151\) 24.2497 1.97341 0.986706 0.162516i \(-0.0519609\pi\)
0.986706 + 0.162516i \(0.0519609\pi\)
\(152\) −10.9139 −0.885237
\(153\) −1.00000 −0.0808452
\(154\) −13.8318 −1.11460
\(155\) 11.0726 0.889370
\(156\) −1.39903 −0.112012
\(157\) 1.00000 0.0798087
\(158\) 5.80997 0.462216
\(159\) −12.9229 −1.02486
\(160\) 18.9837 1.50079
\(161\) −18.5142 −1.45913
\(162\) −0.756159 −0.0594095
\(163\) −17.3444 −1.35852 −0.679258 0.733900i \(-0.737698\pi\)
−0.679258 + 0.733900i \(0.737698\pi\)
\(164\) 3.96620 0.309708
\(165\) −12.6113 −0.981785
\(166\) −1.03209 −0.0801054
\(167\) −13.2331 −1.02401 −0.512003 0.858984i \(-0.671096\pi\)
−0.512003 + 0.858984i \(0.671096\pi\)
\(168\) 12.1760 0.939395
\(169\) −12.0405 −0.926189
\(170\) −2.44865 −0.187803
\(171\) −4.21016 −0.321959
\(172\) −12.7783 −0.974334
\(173\) −12.4883 −0.949465 −0.474732 0.880130i \(-0.657455\pi\)
−0.474732 + 0.880130i \(0.657455\pi\)
\(174\) −4.04916 −0.306966
\(175\) 25.7695 1.94799
\(176\) 3.49046 0.263103
\(177\) −8.38870 −0.630533
\(178\) −8.49137 −0.636455
\(179\) −22.5928 −1.68867 −0.844333 0.535819i \(-0.820003\pi\)
−0.844333 + 0.535819i \(0.820003\pi\)
\(180\) 4.62497 0.344725
\(181\) 12.5309 0.931411 0.465706 0.884940i \(-0.345801\pi\)
0.465706 + 0.884940i \(0.345801\pi\)
\(182\) −3.47908 −0.257887
\(183\) −2.01800 −0.149175
\(184\) −10.2180 −0.753284
\(185\) 32.1539 2.36400
\(186\) 2.58553 0.189580
\(187\) −3.89444 −0.284790
\(188\) 11.2594 0.821179
\(189\) 4.69700 0.341656
\(190\) −10.3092 −0.747908
\(191\) 7.14709 0.517145 0.258573 0.965992i \(-0.416748\pi\)
0.258573 + 0.965992i \(0.416748\pi\)
\(192\) 2.64029 0.190546
\(193\) −5.78891 −0.416695 −0.208347 0.978055i \(-0.566808\pi\)
−0.208347 + 0.978055i \(0.566808\pi\)
\(194\) 7.24881 0.520435
\(195\) −3.17208 −0.227157
\(196\) −21.5116 −1.53654
\(197\) −18.9138 −1.34756 −0.673778 0.738934i \(-0.735329\pi\)
−0.673778 + 0.738934i \(0.735329\pi\)
\(198\) −2.94482 −0.209279
\(199\) 19.4854 1.38128 0.690640 0.723198i \(-0.257329\pi\)
0.690640 + 0.723198i \(0.257329\pi\)
\(200\) 14.2222 1.00566
\(201\) −9.85675 −0.695241
\(202\) 7.49985 0.527688
\(203\) 25.1520 1.76532
\(204\) 1.42822 0.0999956
\(205\) 8.99272 0.628079
\(206\) −11.6942 −0.814773
\(207\) −3.94172 −0.273968
\(208\) 0.877947 0.0608747
\(209\) −16.3962 −1.13415
\(210\) 11.5013 0.793665
\(211\) 24.1833 1.66485 0.832424 0.554140i \(-0.186953\pi\)
0.832424 + 0.554140i \(0.186953\pi\)
\(212\) 18.4568 1.26762
\(213\) 3.35982 0.230211
\(214\) −2.34785 −0.160496
\(215\) −28.9727 −1.97592
\(216\) 2.59228 0.176383
\(217\) −16.0604 −1.09025
\(218\) −12.3041 −0.833338
\(219\) −4.43641 −0.299785
\(220\) 18.0117 1.21435
\(221\) −0.979560 −0.0658923
\(222\) 7.50818 0.503916
\(223\) 0.326609 0.0218713 0.0109357 0.999940i \(-0.496519\pi\)
0.0109357 + 0.999940i \(0.496519\pi\)
\(224\) −27.5352 −1.83977
\(225\) 5.48638 0.365759
\(226\) 15.9789 1.06290
\(227\) 12.6504 0.839637 0.419818 0.907608i \(-0.362094\pi\)
0.419818 + 0.907608i \(0.362094\pi\)
\(228\) 6.01305 0.398224
\(229\) 21.6181 1.42856 0.714282 0.699858i \(-0.246753\pi\)
0.714282 + 0.699858i \(0.246753\pi\)
\(230\) −9.65187 −0.636426
\(231\) 18.2922 1.20354
\(232\) 13.8814 0.911360
\(233\) 13.5577 0.888196 0.444098 0.895978i \(-0.353524\pi\)
0.444098 + 0.895978i \(0.353524\pi\)
\(234\) −0.740704 −0.0484213
\(235\) 25.5290 1.66533
\(236\) 11.9809 0.779892
\(237\) −7.68352 −0.499098
\(238\) 3.55168 0.230221
\(239\) 27.1640 1.75709 0.878547 0.477655i \(-0.158513\pi\)
0.878547 + 0.477655i \(0.158513\pi\)
\(240\) −2.90235 −0.187346
\(241\) −8.08544 −0.520829 −0.260415 0.965497i \(-0.583859\pi\)
−0.260415 + 0.965497i \(0.583859\pi\)
\(242\) −3.15068 −0.202533
\(243\) 1.00000 0.0641500
\(244\) 2.88215 0.184511
\(245\) −48.7742 −3.11607
\(246\) 2.09987 0.133883
\(247\) −4.12411 −0.262411
\(248\) −8.86376 −0.562849
\(249\) 1.36491 0.0864974
\(250\) 1.19097 0.0753236
\(251\) −6.95982 −0.439300 −0.219650 0.975579i \(-0.570492\pi\)
−0.219650 + 0.975579i \(0.570492\pi\)
\(252\) −6.70836 −0.422587
\(253\) −15.3508 −0.965096
\(254\) 4.48023 0.281115
\(255\) 3.23827 0.202788
\(256\) −12.6366 −0.789785
\(257\) −24.2037 −1.50978 −0.754892 0.655849i \(-0.772311\pi\)
−0.754892 + 0.655849i \(0.772311\pi\)
\(258\) −6.76534 −0.421191
\(259\) −46.6382 −2.89796
\(260\) 4.53044 0.280966
\(261\) 5.35490 0.331460
\(262\) 1.28813 0.0795810
\(263\) −17.4276 −1.07463 −0.537316 0.843381i \(-0.680562\pi\)
−0.537316 + 0.843381i \(0.680562\pi\)
\(264\) 10.0955 0.621335
\(265\) 41.8479 2.57070
\(266\) 14.9532 0.916837
\(267\) 11.2296 0.687241
\(268\) 14.0776 0.859928
\(269\) 22.6669 1.38202 0.691011 0.722844i \(-0.257166\pi\)
0.691011 + 0.722844i \(0.257166\pi\)
\(270\) 2.44865 0.149020
\(271\) −29.4442 −1.78861 −0.894305 0.447458i \(-0.852330\pi\)
−0.894305 + 0.447458i \(0.852330\pi\)
\(272\) −0.896267 −0.0543442
\(273\) 4.60099 0.278465
\(274\) 7.95996 0.480879
\(275\) 21.3664 1.28844
\(276\) 5.62965 0.338865
\(277\) −2.94976 −0.177234 −0.0886170 0.996066i \(-0.528245\pi\)
−0.0886170 + 0.996066i \(0.528245\pi\)
\(278\) −9.99752 −0.599611
\(279\) −3.41929 −0.204707
\(280\) −39.4290 −2.35633
\(281\) −9.09540 −0.542586 −0.271293 0.962497i \(-0.587451\pi\)
−0.271293 + 0.962497i \(0.587451\pi\)
\(282\) 5.96120 0.354984
\(283\) −15.3680 −0.913532 −0.456766 0.889587i \(-0.650992\pi\)
−0.456766 + 0.889587i \(0.650992\pi\)
\(284\) −4.79857 −0.284743
\(285\) 13.6336 0.807587
\(286\) −2.88463 −0.170572
\(287\) −13.0436 −0.769942
\(288\) −5.86229 −0.345439
\(289\) 1.00000 0.0588235
\(290\) 13.1123 0.769979
\(291\) −9.58636 −0.561962
\(292\) 6.33618 0.370797
\(293\) −14.1378 −0.825941 −0.412970 0.910744i \(-0.635509\pi\)
−0.412970 + 0.910744i \(0.635509\pi\)
\(294\) −11.3891 −0.664227
\(295\) 27.1648 1.58160
\(296\) −25.7397 −1.49609
\(297\) 3.89444 0.225979
\(298\) −0.981610 −0.0568632
\(299\) −3.86115 −0.223296
\(300\) −7.83577 −0.452399
\(301\) 42.0239 2.42222
\(302\) −18.3366 −1.05515
\(303\) −9.91835 −0.569794
\(304\) −3.77343 −0.216421
\(305\) 6.53483 0.374183
\(306\) 0.756159 0.0432268
\(307\) 19.6604 1.12208 0.561038 0.827790i \(-0.310402\pi\)
0.561038 + 0.827790i \(0.310402\pi\)
\(308\) −26.1253 −1.48863
\(309\) 15.4652 0.879787
\(310\) −8.37263 −0.475533
\(311\) −12.1890 −0.691173 −0.345587 0.938387i \(-0.612320\pi\)
−0.345587 + 0.938387i \(0.612320\pi\)
\(312\) 2.53930 0.143759
\(313\) −2.03715 −0.115147 −0.0575734 0.998341i \(-0.518336\pi\)
−0.0575734 + 0.998341i \(0.518336\pi\)
\(314\) −0.756159 −0.0426725
\(315\) −15.2101 −0.856995
\(316\) 10.9738 0.617323
\(317\) −28.1589 −1.58156 −0.790782 0.612098i \(-0.790326\pi\)
−0.790782 + 0.612098i \(0.790326\pi\)
\(318\) 9.77180 0.547975
\(319\) 20.8544 1.16762
\(320\) −8.54996 −0.477957
\(321\) 3.10496 0.173302
\(322\) 13.9997 0.780174
\(323\) 4.21016 0.234260
\(324\) −1.42822 −0.0793457
\(325\) 5.37424 0.298109
\(326\) 13.1151 0.726378
\(327\) 16.2718 0.899833
\(328\) −7.19881 −0.397488
\(329\) −37.0289 −2.04147
\(330\) 9.53612 0.524946
\(331\) −16.6225 −0.913654 −0.456827 0.889556i \(-0.651014\pi\)
−0.456827 + 0.889556i \(0.651014\pi\)
\(332\) −1.94939 −0.106987
\(333\) −9.92936 −0.544126
\(334\) 10.0063 0.547521
\(335\) 31.9188 1.74391
\(336\) 4.20977 0.229662
\(337\) 15.8170 0.861606 0.430803 0.902446i \(-0.358230\pi\)
0.430803 + 0.902446i \(0.358230\pi\)
\(338\) 9.10451 0.495220
\(339\) −21.1316 −1.14771
\(340\) −4.62497 −0.250824
\(341\) −13.3162 −0.721114
\(342\) 3.18355 0.172147
\(343\) 37.8663 2.04459
\(344\) 23.1931 1.25049
\(345\) 12.7643 0.687209
\(346\) 9.44311 0.507665
\(347\) −33.5002 −1.79838 −0.899192 0.437554i \(-0.855845\pi\)
−0.899192 + 0.437554i \(0.855845\pi\)
\(348\) −7.64799 −0.409976
\(349\) 21.2186 1.13581 0.567904 0.823095i \(-0.307755\pi\)
0.567904 + 0.823095i \(0.307755\pi\)
\(350\) −19.4859 −1.04156
\(351\) 0.979560 0.0522851
\(352\) −22.8303 −1.21686
\(353\) 11.3408 0.603612 0.301806 0.953369i \(-0.402411\pi\)
0.301806 + 0.953369i \(0.402411\pi\)
\(354\) 6.34319 0.337137
\(355\) −10.8800 −0.577450
\(356\) −16.0384 −0.850032
\(357\) −4.69700 −0.248592
\(358\) 17.0838 0.902905
\(359\) −5.53738 −0.292252 −0.146126 0.989266i \(-0.546680\pi\)
−0.146126 + 0.989266i \(0.546680\pi\)
\(360\) −8.39451 −0.442429
\(361\) −1.27453 −0.0670806
\(362\) −9.47533 −0.498012
\(363\) 4.16669 0.218694
\(364\) −6.57125 −0.344427
\(365\) 14.3663 0.751965
\(366\) 1.52593 0.0797616
\(367\) −32.3581 −1.68908 −0.844540 0.535493i \(-0.820126\pi\)
−0.844540 + 0.535493i \(0.820126\pi\)
\(368\) −3.53283 −0.184162
\(369\) −2.77702 −0.144566
\(370\) −24.3135 −1.26400
\(371\) −60.6990 −3.15134
\(372\) 4.88350 0.253198
\(373\) 12.0439 0.623609 0.311805 0.950146i \(-0.399067\pi\)
0.311805 + 0.950146i \(0.399067\pi\)
\(374\) 2.94482 0.152273
\(375\) −1.57503 −0.0813340
\(376\) −20.4363 −1.05392
\(377\) 5.24545 0.270154
\(378\) −3.55168 −0.182679
\(379\) 20.0098 1.02784 0.513918 0.857840i \(-0.328194\pi\)
0.513918 + 0.857840i \(0.328194\pi\)
\(380\) −19.4719 −0.998886
\(381\) −5.92498 −0.303546
\(382\) −5.40434 −0.276510
\(383\) 30.0836 1.53720 0.768600 0.639729i \(-0.220953\pi\)
0.768600 + 0.639729i \(0.220953\pi\)
\(384\) 9.72809 0.496435
\(385\) −59.2350 −3.01890
\(386\) 4.37734 0.222801
\(387\) 8.94697 0.454800
\(388\) 13.6915 0.695078
\(389\) 32.8468 1.66540 0.832700 0.553724i \(-0.186794\pi\)
0.832700 + 0.553724i \(0.186794\pi\)
\(390\) 2.39860 0.121458
\(391\) 3.94172 0.199341
\(392\) 39.0445 1.97204
\(393\) −1.70352 −0.0859312
\(394\) 14.3019 0.720518
\(395\) 24.8813 1.25191
\(396\) −5.56213 −0.279508
\(397\) −24.3792 −1.22355 −0.611777 0.791030i \(-0.709545\pi\)
−0.611777 + 0.791030i \(0.709545\pi\)
\(398\) −14.7340 −0.738551
\(399\) −19.7751 −0.989995
\(400\) 4.91726 0.245863
\(401\) 0.373064 0.0186299 0.00931495 0.999957i \(-0.497035\pi\)
0.00931495 + 0.999957i \(0.497035\pi\)
\(402\) 7.45327 0.371735
\(403\) −3.34940 −0.166845
\(404\) 14.1656 0.704766
\(405\) −3.23827 −0.160911
\(406\) −19.0189 −0.943892
\(407\) −38.6693 −1.91677
\(408\) −2.59228 −0.128337
\(409\) 25.0079 1.23656 0.618279 0.785958i \(-0.287830\pi\)
0.618279 + 0.785958i \(0.287830\pi\)
\(410\) −6.79993 −0.335825
\(411\) −10.5268 −0.519250
\(412\) −22.0878 −1.08819
\(413\) −39.4017 −1.93883
\(414\) 2.98057 0.146487
\(415\) −4.41993 −0.216966
\(416\) −5.74246 −0.281547
\(417\) 13.2214 0.647457
\(418\) 12.3982 0.606414
\(419\) 9.91758 0.484505 0.242253 0.970213i \(-0.422114\pi\)
0.242253 + 0.970213i \(0.422114\pi\)
\(420\) 21.7235 1.06000
\(421\) −19.2406 −0.937728 −0.468864 0.883270i \(-0.655336\pi\)
−0.468864 + 0.883270i \(0.655336\pi\)
\(422\) −18.2864 −0.890169
\(423\) −7.88353 −0.383310
\(424\) −33.4999 −1.62690
\(425\) −5.48638 −0.266128
\(426\) −2.54056 −0.123090
\(427\) −9.47855 −0.458699
\(428\) −4.43458 −0.214353
\(429\) 3.81484 0.184182
\(430\) 21.9080 1.05650
\(431\) −28.0512 −1.35118 −0.675589 0.737279i \(-0.736111\pi\)
−0.675589 + 0.737279i \(0.736111\pi\)
\(432\) 0.896267 0.0431217
\(433\) −33.7257 −1.62076 −0.810378 0.585908i \(-0.800738\pi\)
−0.810378 + 0.585908i \(0.800738\pi\)
\(434\) 12.1442 0.582941
\(435\) −17.3406 −0.831419
\(436\) −23.2398 −1.11298
\(437\) 16.5953 0.793859
\(438\) 3.35463 0.160291
\(439\) 10.9830 0.524190 0.262095 0.965042i \(-0.415587\pi\)
0.262095 + 0.965042i \(0.415587\pi\)
\(440\) −32.6919 −1.55853
\(441\) 15.0618 0.717229
\(442\) 0.740704 0.0352317
\(443\) −27.2641 −1.29536 −0.647678 0.761914i \(-0.724260\pi\)
−0.647678 + 0.761914i \(0.724260\pi\)
\(444\) 14.1813 0.673017
\(445\) −36.3645 −1.72384
\(446\) −0.246968 −0.0116943
\(447\) 1.29815 0.0614005
\(448\) 12.4014 0.585913
\(449\) −24.0886 −1.13681 −0.568405 0.822749i \(-0.692439\pi\)
−0.568405 + 0.822749i \(0.692439\pi\)
\(450\) −4.14858 −0.195566
\(451\) −10.8149 −0.509255
\(452\) 30.1807 1.41958
\(453\) 24.2497 1.13935
\(454\) −9.56572 −0.448942
\(455\) −14.8993 −0.698488
\(456\) −10.9139 −0.511092
\(457\) 25.3801 1.18723 0.593615 0.804749i \(-0.297700\pi\)
0.593615 + 0.804749i \(0.297700\pi\)
\(458\) −16.3467 −0.763832
\(459\) −1.00000 −0.0466760
\(460\) −18.2303 −0.849993
\(461\) 26.8287 1.24954 0.624769 0.780809i \(-0.285193\pi\)
0.624769 + 0.780809i \(0.285193\pi\)
\(462\) −13.8318 −0.643514
\(463\) −41.6174 −1.93413 −0.967063 0.254536i \(-0.918077\pi\)
−0.967063 + 0.254536i \(0.918077\pi\)
\(464\) 4.79942 0.222808
\(465\) 11.0726 0.513478
\(466\) −10.2518 −0.474905
\(467\) 16.6046 0.768370 0.384185 0.923256i \(-0.374482\pi\)
0.384185 + 0.923256i \(0.374482\pi\)
\(468\) −1.39903 −0.0646702
\(469\) −46.2972 −2.13780
\(470\) −19.3040 −0.890426
\(471\) 1.00000 0.0460776
\(472\) −21.7459 −1.00093
\(473\) 34.8435 1.60210
\(474\) 5.80997 0.266861
\(475\) −23.0985 −1.05983
\(476\) 6.70836 0.307477
\(477\) −12.9229 −0.591700
\(478\) −20.5403 −0.939493
\(479\) 16.0186 0.731908 0.365954 0.930633i \(-0.380743\pi\)
0.365954 + 0.930633i \(0.380743\pi\)
\(480\) 18.9837 0.866481
\(481\) −9.72641 −0.443486
\(482\) 6.11388 0.278480
\(483\) −18.5142 −0.842427
\(484\) −5.95096 −0.270498
\(485\) 31.0432 1.40960
\(486\) −0.756159 −0.0343001
\(487\) −16.7536 −0.759177 −0.379589 0.925155i \(-0.623934\pi\)
−0.379589 + 0.925155i \(0.623934\pi\)
\(488\) −5.23123 −0.236807
\(489\) −17.3444 −0.784339
\(490\) 36.8811 1.66612
\(491\) −37.8794 −1.70948 −0.854738 0.519060i \(-0.826282\pi\)
−0.854738 + 0.519060i \(0.826282\pi\)
\(492\) 3.96620 0.178810
\(493\) −5.35490 −0.241173
\(494\) 3.11848 0.140307
\(495\) −12.6113 −0.566834
\(496\) −3.06459 −0.137604
\(497\) 15.7811 0.707878
\(498\) −1.03209 −0.0462489
\(499\) −28.0543 −1.25588 −0.627941 0.778261i \(-0.716102\pi\)
−0.627941 + 0.778261i \(0.716102\pi\)
\(500\) 2.24949 0.100600
\(501\) −13.2331 −0.591210
\(502\) 5.26274 0.234887
\(503\) −27.0301 −1.20521 −0.602605 0.798039i \(-0.705871\pi\)
−0.602605 + 0.798039i \(0.705871\pi\)
\(504\) 12.1760 0.542360
\(505\) 32.1183 1.42924
\(506\) 11.6076 0.516023
\(507\) −12.0405 −0.534736
\(508\) 8.46220 0.375449
\(509\) −7.87173 −0.348908 −0.174454 0.984665i \(-0.555816\pi\)
−0.174454 + 0.984665i \(0.555816\pi\)
\(510\) −2.44865 −0.108428
\(511\) −20.8378 −0.921810
\(512\) −9.90093 −0.437563
\(513\) −4.21016 −0.185883
\(514\) 18.3018 0.807260
\(515\) −50.0806 −2.20682
\(516\) −12.7783 −0.562532
\(517\) −30.7020 −1.35027
\(518\) 35.2659 1.54950
\(519\) −12.4883 −0.548174
\(520\) −8.22292 −0.360599
\(521\) −26.7389 −1.17145 −0.585727 0.810509i \(-0.699191\pi\)
−0.585727 + 0.810509i \(0.699191\pi\)
\(522\) −4.04916 −0.177227
\(523\) −27.7586 −1.21380 −0.606900 0.794778i \(-0.707587\pi\)
−0.606900 + 0.794778i \(0.707587\pi\)
\(524\) 2.43300 0.106286
\(525\) 25.7695 1.12467
\(526\) 13.1780 0.574590
\(527\) 3.41929 0.148946
\(528\) 3.49046 0.151903
\(529\) −7.46287 −0.324473
\(530\) −31.6437 −1.37451
\(531\) −8.38870 −0.364038
\(532\) 28.2433 1.22450
\(533\) −2.72025 −0.117827
\(534\) −8.49137 −0.367458
\(535\) −10.0547 −0.434703
\(536\) −25.5515 −1.10366
\(537\) −22.5928 −0.974951
\(538\) −17.1398 −0.738947
\(539\) 58.6574 2.52655
\(540\) 4.62497 0.199027
\(541\) −4.21585 −0.181254 −0.0906268 0.995885i \(-0.528887\pi\)
−0.0906268 + 0.995885i \(0.528887\pi\)
\(542\) 22.2645 0.956344
\(543\) 12.5309 0.537751
\(544\) 5.86229 0.251343
\(545\) −52.6925 −2.25710
\(546\) −3.47908 −0.148891
\(547\) −33.5163 −1.43305 −0.716526 0.697560i \(-0.754269\pi\)
−0.716526 + 0.697560i \(0.754269\pi\)
\(548\) 15.0347 0.642248
\(549\) −2.01800 −0.0861262
\(550\) −16.1564 −0.688911
\(551\) −22.5450 −0.960450
\(552\) −10.2180 −0.434909
\(553\) −36.0895 −1.53468
\(554\) 2.23049 0.0947644
\(555\) 32.1539 1.36486
\(556\) −18.8832 −0.800825
\(557\) 8.12590 0.344305 0.172153 0.985070i \(-0.444928\pi\)
0.172153 + 0.985070i \(0.444928\pi\)
\(558\) 2.58553 0.109454
\(559\) 8.76410 0.370682
\(560\) −13.6324 −0.576072
\(561\) −3.89444 −0.164424
\(562\) 6.87757 0.290113
\(563\) −45.3402 −1.91086 −0.955431 0.295214i \(-0.904609\pi\)
−0.955431 + 0.295214i \(0.904609\pi\)
\(564\) 11.2594 0.474108
\(565\) 68.4299 2.87887
\(566\) 11.6206 0.488452
\(567\) 4.69700 0.197255
\(568\) 8.70960 0.365447
\(569\) −33.5291 −1.40561 −0.702806 0.711382i \(-0.748070\pi\)
−0.702806 + 0.711382i \(0.748070\pi\)
\(570\) −10.3092 −0.431805
\(571\) 32.0347 1.34061 0.670305 0.742085i \(-0.266163\pi\)
0.670305 + 0.742085i \(0.266163\pi\)
\(572\) −5.44844 −0.227811
\(573\) 7.14709 0.298574
\(574\) 9.86307 0.411677
\(575\) −21.6258 −0.901856
\(576\) 2.64029 0.110012
\(577\) −20.9015 −0.870141 −0.435070 0.900396i \(-0.643277\pi\)
−0.435070 + 0.900396i \(0.643277\pi\)
\(578\) −0.756159 −0.0314521
\(579\) −5.78891 −0.240579
\(580\) 24.7663 1.02836
\(581\) 6.41096 0.265972
\(582\) 7.24881 0.300473
\(583\) −50.3276 −2.08436
\(584\) −11.5004 −0.475891
\(585\) −3.17208 −0.131149
\(586\) 10.6904 0.441618
\(587\) 44.6166 1.84152 0.920761 0.390127i \(-0.127569\pi\)
0.920761 + 0.390127i \(0.127569\pi\)
\(588\) −21.5116 −0.887124
\(589\) 14.3958 0.593167
\(590\) −20.5410 −0.845658
\(591\) −18.9138 −0.778011
\(592\) −8.89936 −0.365761
\(593\) −5.89702 −0.242162 −0.121081 0.992643i \(-0.538636\pi\)
−0.121081 + 0.992643i \(0.538636\pi\)
\(594\) −2.94482 −0.120827
\(595\) 15.2101 0.623555
\(596\) −1.85405 −0.0759449
\(597\) 19.4854 0.797483
\(598\) 2.91964 0.119393
\(599\) 23.4220 0.956998 0.478499 0.878088i \(-0.341181\pi\)
0.478499 + 0.878088i \(0.341181\pi\)
\(600\) 14.2222 0.580621
\(601\) 1.21096 0.0493960 0.0246980 0.999695i \(-0.492138\pi\)
0.0246980 + 0.999695i \(0.492138\pi\)
\(602\) −31.7768 −1.29513
\(603\) −9.85675 −0.401398
\(604\) −34.6340 −1.40924
\(605\) −13.4929 −0.548563
\(606\) 7.49985 0.304661
\(607\) 28.5422 1.15849 0.579245 0.815153i \(-0.303347\pi\)
0.579245 + 0.815153i \(0.303347\pi\)
\(608\) 24.6812 1.00095
\(609\) 25.1520 1.01921
\(610\) −4.94137 −0.200070
\(611\) −7.72239 −0.312414
\(612\) 1.42822 0.0577325
\(613\) 11.3302 0.457621 0.228811 0.973471i \(-0.426516\pi\)
0.228811 + 0.973471i \(0.426516\pi\)
\(614\) −14.8664 −0.599958
\(615\) 8.99272 0.362621
\(616\) 47.4186 1.91055
\(617\) 17.3290 0.697640 0.348820 0.937190i \(-0.386582\pi\)
0.348820 + 0.937190i \(0.386582\pi\)
\(618\) −11.6942 −0.470409
\(619\) 23.0361 0.925901 0.462950 0.886384i \(-0.346791\pi\)
0.462950 + 0.886384i \(0.346791\pi\)
\(620\) −15.8141 −0.635109
\(621\) −3.94172 −0.158176
\(622\) 9.21680 0.369560
\(623\) 52.7454 2.11320
\(624\) 0.877947 0.0351460
\(625\) −22.3315 −0.893262
\(626\) 1.54041 0.0615673
\(627\) −16.3962 −0.654803
\(628\) −1.42822 −0.0569923
\(629\) 9.92936 0.395910
\(630\) 11.5013 0.458223
\(631\) −44.3553 −1.76576 −0.882878 0.469603i \(-0.844397\pi\)
−0.882878 + 0.469603i \(0.844397\pi\)
\(632\) −19.9179 −0.792290
\(633\) 24.1833 0.961200
\(634\) 21.2926 0.845639
\(635\) 19.1867 0.761400
\(636\) 18.4568 0.731861
\(637\) 14.7539 0.584573
\(638\) −15.7692 −0.624310
\(639\) 3.35982 0.132912
\(640\) −31.5022 −1.24523
\(641\) 31.8725 1.25889 0.629443 0.777046i \(-0.283283\pi\)
0.629443 + 0.777046i \(0.283283\pi\)
\(642\) −2.34785 −0.0926621
\(643\) 38.1630 1.50500 0.752501 0.658591i \(-0.228847\pi\)
0.752501 + 0.658591i \(0.228847\pi\)
\(644\) 26.4425 1.04198
\(645\) −28.9727 −1.14080
\(646\) −3.18355 −0.125255
\(647\) 3.87212 0.152229 0.0761144 0.997099i \(-0.475749\pi\)
0.0761144 + 0.997099i \(0.475749\pi\)
\(648\) 2.59228 0.101834
\(649\) −32.6693 −1.28238
\(650\) −4.06378 −0.159395
\(651\) −16.0604 −0.629456
\(652\) 24.7716 0.970131
\(653\) −31.7973 −1.24432 −0.622162 0.782889i \(-0.713745\pi\)
−0.622162 + 0.782889i \(0.713745\pi\)
\(654\) −12.3041 −0.481128
\(655\) 5.51645 0.215546
\(656\) −2.48895 −0.0971771
\(657\) −4.43641 −0.173081
\(658\) 27.9998 1.09154
\(659\) 2.74720 0.107016 0.0535079 0.998567i \(-0.482960\pi\)
0.0535079 + 0.998567i \(0.482960\pi\)
\(660\) 18.0117 0.701104
\(661\) −0.404631 −0.0157383 −0.00786916 0.999969i \(-0.502505\pi\)
−0.00786916 + 0.999969i \(0.502505\pi\)
\(662\) 12.5692 0.488517
\(663\) −0.979560 −0.0380430
\(664\) 3.53822 0.137310
\(665\) 64.0372 2.48326
\(666\) 7.50818 0.290936
\(667\) −21.1075 −0.817286
\(668\) 18.8998 0.731254
\(669\) 0.326609 0.0126274
\(670\) −24.1357 −0.932443
\(671\) −7.85899 −0.303393
\(672\) −27.5352 −1.06219
\(673\) −14.4775 −0.558068 −0.279034 0.960281i \(-0.590014\pi\)
−0.279034 + 0.960281i \(0.590014\pi\)
\(674\) −11.9602 −0.460688
\(675\) 5.48638 0.211171
\(676\) 17.1965 0.661402
\(677\) 34.7629 1.33605 0.668023 0.744141i \(-0.267141\pi\)
0.668023 + 0.744141i \(0.267141\pi\)
\(678\) 15.9789 0.613666
\(679\) −45.0271 −1.72798
\(680\) 8.39451 0.321915
\(681\) 12.6504 0.484765
\(682\) 10.0692 0.385569
\(683\) 30.2203 1.15635 0.578173 0.815914i \(-0.303766\pi\)
0.578173 + 0.815914i \(0.303766\pi\)
\(684\) 6.01305 0.229915
\(685\) 34.0887 1.30246
\(686\) −28.6330 −1.09321
\(687\) 21.6181 0.824782
\(688\) 8.01887 0.305717
\(689\) −12.6588 −0.482261
\(690\) −9.65187 −0.367440
\(691\) 11.6763 0.444188 0.222094 0.975025i \(-0.428711\pi\)
0.222094 + 0.975025i \(0.428711\pi\)
\(692\) 17.8360 0.678024
\(693\) 18.2922 0.694863
\(694\) 25.3315 0.961570
\(695\) −42.8146 −1.62405
\(696\) 13.8814 0.526174
\(697\) 2.77702 0.105187
\(698\) −16.0447 −0.607300
\(699\) 13.5577 0.512800
\(700\) −36.8046 −1.39108
\(701\) 44.7658 1.69078 0.845390 0.534150i \(-0.179368\pi\)
0.845390 + 0.534150i \(0.179368\pi\)
\(702\) −0.740704 −0.0279561
\(703\) 41.8042 1.57668
\(704\) 10.2825 0.387535
\(705\) 25.5290 0.961477
\(706\) −8.57548 −0.322742
\(707\) −46.5865 −1.75207
\(708\) 11.9809 0.450271
\(709\) 32.3427 1.21465 0.607327 0.794452i \(-0.292242\pi\)
0.607327 + 0.794452i \(0.292242\pi\)
\(710\) 8.22701 0.308754
\(711\) −7.68352 −0.288155
\(712\) 29.1103 1.09095
\(713\) 13.4779 0.504750
\(714\) 3.55168 0.132918
\(715\) −12.3535 −0.461994
\(716\) 32.2676 1.20590
\(717\) 27.1640 1.01446
\(718\) 4.18714 0.156263
\(719\) −35.7331 −1.33262 −0.666310 0.745675i \(-0.732127\pi\)
−0.666310 + 0.745675i \(0.732127\pi\)
\(720\) −2.90235 −0.108164
\(721\) 72.6403 2.70526
\(722\) 0.963749 0.0358670
\(723\) −8.08544 −0.300701
\(724\) −17.8969 −0.665132
\(725\) 29.3790 1.09111
\(726\) −3.15068 −0.116933
\(727\) 38.0941 1.41283 0.706417 0.707796i \(-0.250310\pi\)
0.706417 + 0.707796i \(0.250310\pi\)
\(728\) 11.9271 0.442047
\(729\) 1.00000 0.0370370
\(730\) −10.8632 −0.402065
\(731\) −8.94697 −0.330916
\(732\) 2.88215 0.106528
\(733\) 37.7330 1.39370 0.696850 0.717217i \(-0.254584\pi\)
0.696850 + 0.717217i \(0.254584\pi\)
\(734\) 24.4679 0.903126
\(735\) −48.7742 −1.79906
\(736\) 23.1075 0.851753
\(737\) −38.3866 −1.41399
\(738\) 2.09987 0.0772971
\(739\) 1.49855 0.0551249 0.0275624 0.999620i \(-0.491225\pi\)
0.0275624 + 0.999620i \(0.491225\pi\)
\(740\) −45.9230 −1.68816
\(741\) −4.12411 −0.151503
\(742\) 45.8981 1.68497
\(743\) 34.4765 1.26482 0.632410 0.774634i \(-0.282066\pi\)
0.632410 + 0.774634i \(0.282066\pi\)
\(744\) −8.86376 −0.324961
\(745\) −4.20377 −0.154014
\(746\) −9.10711 −0.333435
\(747\) 1.36491 0.0499393
\(748\) 5.56213 0.203372
\(749\) 14.5840 0.532888
\(750\) 1.19097 0.0434881
\(751\) −51.7670 −1.88901 −0.944503 0.328504i \(-0.893456\pi\)
−0.944503 + 0.328504i \(0.893456\pi\)
\(752\) −7.06575 −0.257661
\(753\) −6.95982 −0.253630
\(754\) −3.96640 −0.144448
\(755\) −78.5270 −2.85789
\(756\) −6.70836 −0.243981
\(757\) −9.06994 −0.329652 −0.164826 0.986323i \(-0.552706\pi\)
−0.164826 + 0.986323i \(0.552706\pi\)
\(758\) −15.1306 −0.549569
\(759\) −15.3508 −0.557198
\(760\) 35.3422 1.28200
\(761\) −25.0993 −0.909850 −0.454925 0.890530i \(-0.650334\pi\)
−0.454925 + 0.890530i \(0.650334\pi\)
\(762\) 4.48023 0.162302
\(763\) 76.4287 2.76690
\(764\) −10.2076 −0.369300
\(765\) 3.23827 0.117080
\(766\) −22.7480 −0.821919
\(767\) −8.21723 −0.296707
\(768\) −12.6366 −0.455983
\(769\) −12.2855 −0.443025 −0.221512 0.975158i \(-0.571099\pi\)
−0.221512 + 0.975158i \(0.571099\pi\)
\(770\) 44.7911 1.61416
\(771\) −24.2037 −0.871675
\(772\) 8.26786 0.297567
\(773\) 31.5706 1.13552 0.567758 0.823195i \(-0.307811\pi\)
0.567758 + 0.823195i \(0.307811\pi\)
\(774\) −6.76534 −0.243175
\(775\) −18.7595 −0.673861
\(776\) −24.8506 −0.892083
\(777\) −46.6382 −1.67314
\(778\) −24.8374 −0.890465
\(779\) 11.6917 0.418898
\(780\) 4.53044 0.162216
\(781\) 13.0846 0.468205
\(782\) −2.98057 −0.106585
\(783\) 5.35490 0.191369
\(784\) 13.4994 0.482122
\(785\) −3.23827 −0.115579
\(786\) 1.28813 0.0459461
\(787\) 51.2075 1.82535 0.912676 0.408685i \(-0.134012\pi\)
0.912676 + 0.408685i \(0.134012\pi\)
\(788\) 27.0132 0.962305
\(789\) −17.4276 −0.620439
\(790\) −18.8142 −0.669380
\(791\) −99.2554 −3.52911
\(792\) 10.0955 0.358728
\(793\) −1.97675 −0.0701966
\(794\) 18.4345 0.654217
\(795\) 41.8479 1.48419
\(796\) −27.8294 −0.986389
\(797\) −40.2223 −1.42475 −0.712374 0.701800i \(-0.752380\pi\)
−0.712374 + 0.701800i \(0.752380\pi\)
\(798\) 14.9532 0.529336
\(799\) 7.88353 0.278899
\(800\) −32.1627 −1.13712
\(801\) 11.2296 0.396779
\(802\) −0.282096 −0.00996114
\(803\) −17.2773 −0.609704
\(804\) 14.0776 0.496480
\(805\) 59.9541 2.11310
\(806\) 2.53268 0.0892098
\(807\) 22.6669 0.797911
\(808\) −25.7112 −0.904516
\(809\) 18.3783 0.646147 0.323074 0.946374i \(-0.395284\pi\)
0.323074 + 0.946374i \(0.395284\pi\)
\(810\) 2.44865 0.0860367
\(811\) 12.1831 0.427807 0.213904 0.976855i \(-0.431382\pi\)
0.213904 + 0.976855i \(0.431382\pi\)
\(812\) −35.9226 −1.26064
\(813\) −29.4442 −1.03265
\(814\) 29.2402 1.02487
\(815\) 56.1657 1.96740
\(816\) −0.896267 −0.0313756
\(817\) −37.6682 −1.31784
\(818\) −18.9099 −0.661170
\(819\) 4.60099 0.160772
\(820\) −12.8436 −0.448518
\(821\) 21.8930 0.764071 0.382035 0.924148i \(-0.375223\pi\)
0.382035 + 0.924148i \(0.375223\pi\)
\(822\) 7.95996 0.277635
\(823\) 3.73740 0.130278 0.0651388 0.997876i \(-0.479251\pi\)
0.0651388 + 0.997876i \(0.479251\pi\)
\(824\) 40.0903 1.39661
\(825\) 21.3664 0.743882
\(826\) 29.7940 1.03666
\(827\) 23.0393 0.801155 0.400577 0.916263i \(-0.368810\pi\)
0.400577 + 0.916263i \(0.368810\pi\)
\(828\) 5.62965 0.195644
\(829\) 6.03791 0.209705 0.104853 0.994488i \(-0.466563\pi\)
0.104853 + 0.994488i \(0.466563\pi\)
\(830\) 3.34217 0.116008
\(831\) −2.94976 −0.102326
\(832\) 2.58632 0.0896646
\(833\) −15.0618 −0.521861
\(834\) −9.99752 −0.346186
\(835\) 42.8522 1.48296
\(836\) 23.4175 0.809911
\(837\) −3.41929 −0.118188
\(838\) −7.49927 −0.259058
\(839\) 28.7538 0.992691 0.496346 0.868125i \(-0.334675\pi\)
0.496346 + 0.868125i \(0.334675\pi\)
\(840\) −39.4290 −1.36043
\(841\) −0.325020 −0.0112076
\(842\) 14.5489 0.501389
\(843\) −9.09540 −0.313262
\(844\) −34.5391 −1.18889
\(845\) 38.9902 1.34131
\(846\) 5.96120 0.204950
\(847\) 19.5709 0.672465
\(848\) −11.5824 −0.397741
\(849\) −15.3680 −0.527428
\(850\) 4.14858 0.142295
\(851\) 39.1387 1.34166
\(852\) −4.79857 −0.164396
\(853\) −22.6825 −0.776633 −0.388316 0.921526i \(-0.626943\pi\)
−0.388316 + 0.921526i \(0.626943\pi\)
\(854\) 7.16729 0.245260
\(855\) 13.6336 0.466260
\(856\) 8.04894 0.275107
\(857\) 1.22525 0.0418539 0.0209269 0.999781i \(-0.493338\pi\)
0.0209269 + 0.999781i \(0.493338\pi\)
\(858\) −2.88463 −0.0984796
\(859\) 0.633833 0.0216261 0.0108130 0.999942i \(-0.496558\pi\)
0.0108130 + 0.999942i \(0.496558\pi\)
\(860\) 41.3795 1.41103
\(861\) −13.0436 −0.444526
\(862\) 21.2112 0.722455
\(863\) −37.0724 −1.26196 −0.630979 0.775800i \(-0.717347\pi\)
−0.630979 + 0.775800i \(0.717347\pi\)
\(864\) −5.86229 −0.199439
\(865\) 40.4403 1.37501
\(866\) 25.5020 0.866594
\(867\) 1.00000 0.0339618
\(868\) 22.9378 0.778560
\(869\) −29.9230 −1.01507
\(870\) 13.1123 0.444547
\(871\) −9.65528 −0.327157
\(872\) 42.1811 1.42843
\(873\) −9.58636 −0.324449
\(874\) −12.5487 −0.424465
\(875\) −7.39790 −0.250095
\(876\) 6.33618 0.214080
\(877\) 4.67672 0.157922 0.0789608 0.996878i \(-0.474840\pi\)
0.0789608 + 0.996878i \(0.474840\pi\)
\(878\) −8.30489 −0.280276
\(879\) −14.1378 −0.476857
\(880\) −11.3030 −0.381026
\(881\) 42.6505 1.43693 0.718466 0.695562i \(-0.244844\pi\)
0.718466 + 0.695562i \(0.244844\pi\)
\(882\) −11.3891 −0.383492
\(883\) −22.0463 −0.741917 −0.370959 0.928649i \(-0.620971\pi\)
−0.370959 + 0.928649i \(0.620971\pi\)
\(884\) 1.39903 0.0470545
\(885\) 27.1648 0.913136
\(886\) 20.6160 0.692608
\(887\) 15.3039 0.513853 0.256927 0.966431i \(-0.417290\pi\)
0.256927 + 0.966431i \(0.417290\pi\)
\(888\) −25.7397 −0.863768
\(889\) −27.8296 −0.933376
\(890\) 27.4973 0.921713
\(891\) 3.89444 0.130469
\(892\) −0.466470 −0.0156186
\(893\) 33.1909 1.11069
\(894\) −0.981610 −0.0328300
\(895\) 73.1616 2.44552
\(896\) 45.6929 1.52649
\(897\) −3.86115 −0.128920
\(898\) 18.2148 0.607836
\(899\) −18.3099 −0.610671
\(900\) −7.83577 −0.261192
\(901\) 12.9229 0.430525
\(902\) 8.17781 0.272291
\(903\) 42.0239 1.39847
\(904\) −54.7792 −1.82193
\(905\) −40.5783 −1.34887
\(906\) −18.3366 −0.609194
\(907\) −9.19825 −0.305423 −0.152711 0.988271i \(-0.548801\pi\)
−0.152711 + 0.988271i \(0.548801\pi\)
\(908\) −18.0676 −0.599594
\(909\) −9.91835 −0.328971
\(910\) 11.2662 0.373471
\(911\) −1.93728 −0.0641850 −0.0320925 0.999485i \(-0.510217\pi\)
−0.0320925 + 0.999485i \(0.510217\pi\)
\(912\) −3.77343 −0.124951
\(913\) 5.31555 0.175919
\(914\) −19.1914 −0.634795
\(915\) 6.53483 0.216035
\(916\) −30.8755 −1.02015
\(917\) −8.00143 −0.264230
\(918\) 0.756159 0.0249570
\(919\) −22.1104 −0.729355 −0.364677 0.931134i \(-0.618821\pi\)
−0.364677 + 0.931134i \(0.618821\pi\)
\(920\) 33.0888 1.09090
\(921\) 19.6604 0.647831
\(922\) −20.2868 −0.668110
\(923\) 3.29115 0.108329
\(924\) −26.1253 −0.859461
\(925\) −54.4762 −1.79117
\(926\) 31.4694 1.03415
\(927\) 15.4652 0.507945
\(928\) −31.3920 −1.03049
\(929\) 8.65867 0.284082 0.142041 0.989861i \(-0.454634\pi\)
0.142041 + 0.989861i \(0.454634\pi\)
\(930\) −8.37263 −0.274549
\(931\) −63.4127 −2.07827
\(932\) −19.3635 −0.634271
\(933\) −12.1890 −0.399049
\(934\) −12.5557 −0.410836
\(935\) 12.6113 0.412432
\(936\) 2.53930 0.0829995
\(937\) 37.2436 1.21669 0.608347 0.793671i \(-0.291833\pi\)
0.608347 + 0.793671i \(0.291833\pi\)
\(938\) 35.0080 1.14305
\(939\) −2.03715 −0.0664800
\(940\) −36.4611 −1.18923
\(941\) 5.93547 0.193491 0.0967455 0.995309i \(-0.469157\pi\)
0.0967455 + 0.995309i \(0.469157\pi\)
\(942\) −0.756159 −0.0246370
\(943\) 10.9462 0.356458
\(944\) −7.51851 −0.244707
\(945\) −15.2101 −0.494786
\(946\) −26.3472 −0.856622
\(947\) −20.3241 −0.660445 −0.330223 0.943903i \(-0.607124\pi\)
−0.330223 + 0.943903i \(0.607124\pi\)
\(948\) 10.9738 0.356412
\(949\) −4.34573 −0.141068
\(950\) 17.4662 0.566678
\(951\) −28.1589 −0.913116
\(952\) −12.1760 −0.394625
\(953\) 13.1630 0.426391 0.213195 0.977010i \(-0.431613\pi\)
0.213195 + 0.977010i \(0.431613\pi\)
\(954\) 9.77180 0.316374
\(955\) −23.1442 −0.748929
\(956\) −38.7963 −1.25476
\(957\) 20.8544 0.674126
\(958\) −12.1126 −0.391341
\(959\) −49.4445 −1.59665
\(960\) −8.54996 −0.275949
\(961\) −19.3085 −0.622854
\(962\) 7.35471 0.237125
\(963\) 3.10496 0.100056
\(964\) 11.5478 0.371930
\(965\) 18.7460 0.603457
\(966\) 13.9997 0.450434
\(967\) 9.50860 0.305776 0.152888 0.988244i \(-0.451143\pi\)
0.152888 + 0.988244i \(0.451143\pi\)
\(968\) 10.8012 0.347165
\(969\) 4.21016 0.135250
\(970\) −23.4736 −0.753692
\(971\) −40.5746 −1.30210 −0.651050 0.759035i \(-0.725671\pi\)
−0.651050 + 0.759035i \(0.725671\pi\)
\(972\) −1.42822 −0.0458103
\(973\) 62.1011 1.99087
\(974\) 12.6684 0.405921
\(975\) 5.37424 0.172113
\(976\) −1.80867 −0.0578940
\(977\) −0.335819 −0.0107438 −0.00537190 0.999986i \(-0.501710\pi\)
−0.00537190 + 0.999986i \(0.501710\pi\)
\(978\) 13.1151 0.419375
\(979\) 43.7331 1.39771
\(980\) 69.6604 2.22522
\(981\) 16.2718 0.519519
\(982\) 28.6429 0.914032
\(983\) −42.2232 −1.34671 −0.673356 0.739319i \(-0.735148\pi\)
−0.673356 + 0.739319i \(0.735148\pi\)
\(984\) −7.19881 −0.229490
\(985\) 61.2481 1.95153
\(986\) 4.04916 0.128952
\(987\) −37.0289 −1.17864
\(988\) 5.89015 0.187390
\(989\) −35.2664 −1.12141
\(990\) 9.53612 0.303078
\(991\) 10.8371 0.344253 0.172127 0.985075i \(-0.444936\pi\)
0.172127 + 0.985075i \(0.444936\pi\)
\(992\) 20.0448 0.636424
\(993\) −16.6225 −0.527498
\(994\) −11.9330 −0.378492
\(995\) −63.0988 −2.00037
\(996\) −1.94939 −0.0617688
\(997\) −52.3527 −1.65803 −0.829013 0.559229i \(-0.811097\pi\)
−0.829013 + 0.559229i \(0.811097\pi\)
\(998\) 21.2135 0.671502
\(999\) −9.92936 −0.314151
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 \(a_p\))