Properties

Label 4009.2.a.c.1.14
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.08320 q^{2}\) \(+2.50442 q^{3}\) \(+2.33972 q^{4}\) \(-4.26568 q^{5}\) \(-5.21720 q^{6}\) \(-3.89477 q^{7}\) \(-0.707698 q^{8}\) \(+3.27211 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.08320 q^{2}\) \(+2.50442 q^{3}\) \(+2.33972 q^{4}\) \(-4.26568 q^{5}\) \(-5.21720 q^{6}\) \(-3.89477 q^{7}\) \(-0.707698 q^{8}\) \(+3.27211 q^{9}\) \(+8.88625 q^{10}\) \(-0.717906 q^{11}\) \(+5.85963 q^{12}\) \(+1.36066 q^{13}\) \(+8.11358 q^{14}\) \(-10.6830 q^{15}\) \(-3.20516 q^{16}\) \(+1.14117 q^{17}\) \(-6.81646 q^{18}\) \(+1.00000 q^{19}\) \(-9.98048 q^{20}\) \(-9.75414 q^{21}\) \(+1.49554 q^{22}\) \(+3.32840 q^{23}\) \(-1.77237 q^{24}\) \(+13.1960 q^{25}\) \(-2.83452 q^{26}\) \(+0.681482 q^{27}\) \(-9.11266 q^{28}\) \(+8.60525 q^{29}\) \(+22.2549 q^{30}\) \(-1.36901 q^{31}\) \(+8.09238 q^{32}\) \(-1.79794 q^{33}\) \(-2.37729 q^{34}\) \(+16.6138 q^{35}\) \(+7.65582 q^{36}\) \(-0.348108 q^{37}\) \(-2.08320 q^{38}\) \(+3.40766 q^{39}\) \(+3.01881 q^{40}\) \(-3.19719 q^{41}\) \(+20.3198 q^{42}\) \(+9.29999 q^{43}\) \(-1.67970 q^{44}\) \(-13.9578 q^{45}\) \(-6.93371 q^{46}\) \(-9.35756 q^{47}\) \(-8.02706 q^{48}\) \(+8.16924 q^{49}\) \(-27.4899 q^{50}\) \(+2.85798 q^{51}\) \(+3.18356 q^{52}\) \(-9.83068 q^{53}\) \(-1.41966 q^{54}\) \(+3.06236 q^{55}\) \(+2.75632 q^{56}\) \(+2.50442 q^{57}\) \(-17.9265 q^{58}\) \(-1.11151 q^{59}\) \(-24.9953 q^{60}\) \(-0.418657 q^{61}\) \(+2.85192 q^{62}\) \(-12.7441 q^{63}\) \(-10.4477 q^{64}\) \(-5.80413 q^{65}\) \(+3.74546 q^{66}\) \(+5.87719 q^{67}\) \(+2.67003 q^{68}\) \(+8.33570 q^{69}\) \(-34.6099 q^{70}\) \(-10.3544 q^{71}\) \(-2.31567 q^{72}\) \(+11.0662 q^{73}\) \(+0.725179 q^{74}\) \(+33.0483 q^{75}\) \(+2.33972 q^{76}\) \(+2.79608 q^{77}\) \(-7.09883 q^{78}\) \(+10.0203 q^{79}\) \(+13.6722 q^{80}\) \(-8.10962 q^{81}\) \(+6.66037 q^{82}\) \(+1.29356 q^{83}\) \(-22.8219 q^{84}\) \(-4.86788 q^{85}\) \(-19.3737 q^{86}\) \(+21.5512 q^{87}\) \(+0.508061 q^{88}\) \(+11.1348 q^{89}\) \(+29.0768 q^{90}\) \(-5.29945 q^{91}\) \(+7.78751 q^{92}\) \(-3.42857 q^{93}\) \(+19.4937 q^{94}\) \(-4.26568 q^{95}\) \(+20.2667 q^{96}\) \(-5.00956 q^{97}\) \(-17.0182 q^{98}\) \(-2.34907 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08320 −1.47304 −0.736522 0.676414i \(-0.763533\pi\)
−0.736522 + 0.676414i \(0.763533\pi\)
\(3\) 2.50442 1.44593 0.722963 0.690886i \(-0.242780\pi\)
0.722963 + 0.690886i \(0.242780\pi\)
\(4\) 2.33972 1.16986
\(5\) −4.26568 −1.90767 −0.953834 0.300333i \(-0.902902\pi\)
−0.953834 + 0.300333i \(0.902902\pi\)
\(6\) −5.21720 −2.12991
\(7\) −3.89477 −1.47209 −0.736043 0.676935i \(-0.763308\pi\)
−0.736043 + 0.676935i \(0.763308\pi\)
\(8\) −0.707698 −0.250209
\(9\) 3.27211 1.09070
\(10\) 8.88625 2.81008
\(11\) −0.717906 −0.216457 −0.108228 0.994126i \(-0.534518\pi\)
−0.108228 + 0.994126i \(0.534518\pi\)
\(12\) 5.85963 1.69153
\(13\) 1.36066 0.377379 0.188689 0.982037i \(-0.439576\pi\)
0.188689 + 0.982037i \(0.439576\pi\)
\(14\) 8.11358 2.16845
\(15\) −10.6830 −2.75835
\(16\) −3.20516 −0.801290
\(17\) 1.14117 0.276776 0.138388 0.990378i \(-0.455808\pi\)
0.138388 + 0.990378i \(0.455808\pi\)
\(18\) −6.81646 −1.60665
\(19\) 1.00000 0.229416
\(20\) −9.98048 −2.23170
\(21\) −9.75414 −2.12853
\(22\) 1.49554 0.318851
\(23\) 3.32840 0.694019 0.347009 0.937862i \(-0.387197\pi\)
0.347009 + 0.937862i \(0.387197\pi\)
\(24\) −1.77237 −0.361784
\(25\) 13.1960 2.63920
\(26\) −2.83452 −0.555896
\(27\) 0.681482 0.131151
\(28\) −9.11266 −1.72213
\(29\) 8.60525 1.59796 0.798978 0.601361i \(-0.205375\pi\)
0.798978 + 0.601361i \(0.205375\pi\)
\(30\) 22.2549 4.06317
\(31\) −1.36901 −0.245881 −0.122941 0.992414i \(-0.539232\pi\)
−0.122941 + 0.992414i \(0.539232\pi\)
\(32\) 8.09238 1.43054
\(33\) −1.79794 −0.312981
\(34\) −2.37729 −0.407703
\(35\) 16.6138 2.80825
\(36\) 7.65582 1.27597
\(37\) −0.348108 −0.0572287 −0.0286143 0.999591i \(-0.509109\pi\)
−0.0286143 + 0.999591i \(0.509109\pi\)
\(38\) −2.08320 −0.337939
\(39\) 3.40766 0.545662
\(40\) 3.01881 0.477316
\(41\) −3.19719 −0.499316 −0.249658 0.968334i \(-0.580318\pi\)
−0.249658 + 0.968334i \(0.580318\pi\)
\(42\) 20.3198 3.13541
\(43\) 9.29999 1.41823 0.709117 0.705090i \(-0.249094\pi\)
0.709117 + 0.705090i \(0.249094\pi\)
\(44\) −1.67970 −0.253224
\(45\) −13.9578 −2.08070
\(46\) −6.93371 −1.02232
\(47\) −9.35756 −1.36494 −0.682470 0.730913i \(-0.739094\pi\)
−0.682470 + 0.730913i \(0.739094\pi\)
\(48\) −8.02706 −1.15861
\(49\) 8.16924 1.16703
\(50\) −27.4899 −3.88766
\(51\) 2.85798 0.400197
\(52\) 3.18356 0.441480
\(53\) −9.83068 −1.35035 −0.675174 0.737658i \(-0.735931\pi\)
−0.675174 + 0.737658i \(0.735931\pi\)
\(54\) −1.41966 −0.193192
\(55\) 3.06236 0.412928
\(56\) 2.75632 0.368329
\(57\) 2.50442 0.331718
\(58\) −17.9265 −2.35386
\(59\) −1.11151 −0.144706 −0.0723528 0.997379i \(-0.523051\pi\)
−0.0723528 + 0.997379i \(0.523051\pi\)
\(60\) −24.9953 −3.22688
\(61\) −0.418657 −0.0536036 −0.0268018 0.999641i \(-0.508532\pi\)
−0.0268018 + 0.999641i \(0.508532\pi\)
\(62\) 2.85192 0.362194
\(63\) −12.7441 −1.60561
\(64\) −10.4477 −1.30596
\(65\) −5.80413 −0.719914
\(66\) 3.74546 0.461034
\(67\) 5.87719 0.718013 0.359007 0.933335i \(-0.383116\pi\)
0.359007 + 0.933335i \(0.383116\pi\)
\(68\) 2.67003 0.323788
\(69\) 8.33570 1.00350
\(70\) −34.6099 −4.13668
\(71\) −10.3544 −1.22885 −0.614423 0.788977i \(-0.710611\pi\)
−0.614423 + 0.788977i \(0.710611\pi\)
\(72\) −2.31567 −0.272904
\(73\) 11.0662 1.29520 0.647602 0.761979i \(-0.275772\pi\)
0.647602 + 0.761979i \(0.275772\pi\)
\(74\) 0.725179 0.0843003
\(75\) 33.0483 3.81609
\(76\) 2.33972 0.268384
\(77\) 2.79608 0.318643
\(78\) −7.09883 −0.803784
\(79\) 10.0203 1.12737 0.563687 0.825989i \(-0.309382\pi\)
0.563687 + 0.825989i \(0.309382\pi\)
\(80\) 13.6722 1.52860
\(81\) −8.10962 −0.901069
\(82\) 6.66037 0.735515
\(83\) 1.29356 0.141987 0.0709936 0.997477i \(-0.477383\pi\)
0.0709936 + 0.997477i \(0.477383\pi\)
\(84\) −22.8219 −2.49008
\(85\) −4.86788 −0.527996
\(86\) −19.3737 −2.08912
\(87\) 21.5512 2.31053
\(88\) 0.508061 0.0541595
\(89\) 11.1348 1.18029 0.590145 0.807297i \(-0.299070\pi\)
0.590145 + 0.807297i \(0.299070\pi\)
\(90\) 29.0768 3.06497
\(91\) −5.29945 −0.555534
\(92\) 7.78751 0.811904
\(93\) −3.42857 −0.355526
\(94\) 19.4937 2.01062
\(95\) −4.26568 −0.437649
\(96\) 20.2667 2.06846
\(97\) −5.00956 −0.508644 −0.254322 0.967120i \(-0.581852\pi\)
−0.254322 + 0.967120i \(0.581852\pi\)
\(98\) −17.0182 −1.71909
\(99\) −2.34907 −0.236090
\(100\) 30.8749 3.08749
\(101\) −4.94851 −0.492395 −0.246197 0.969220i \(-0.579181\pi\)
−0.246197 + 0.969220i \(0.579181\pi\)
\(102\) −5.95374 −0.589508
\(103\) −4.69978 −0.463083 −0.231542 0.972825i \(-0.574377\pi\)
−0.231542 + 0.972825i \(0.574377\pi\)
\(104\) −0.962935 −0.0944236
\(105\) 41.6080 4.06052
\(106\) 20.4793 1.98912
\(107\) −6.63349 −0.641284 −0.320642 0.947200i \(-0.603899\pi\)
−0.320642 + 0.947200i \(0.603899\pi\)
\(108\) 1.59447 0.153428
\(109\) −2.35326 −0.225401 −0.112701 0.993629i \(-0.535950\pi\)
−0.112701 + 0.993629i \(0.535950\pi\)
\(110\) −6.37950 −0.608261
\(111\) −0.871809 −0.0827484
\(112\) 12.4834 1.17957
\(113\) 4.42555 0.416320 0.208160 0.978095i \(-0.433252\pi\)
0.208160 + 0.978095i \(0.433252\pi\)
\(114\) −5.21720 −0.488636
\(115\) −14.1979 −1.32396
\(116\) 20.1339 1.86938
\(117\) 4.45223 0.411609
\(118\) 2.31549 0.213158
\(119\) −4.44461 −0.407437
\(120\) 7.56037 0.690164
\(121\) −10.4846 −0.953146
\(122\) 0.872147 0.0789604
\(123\) −8.00709 −0.721975
\(124\) −3.20309 −0.287646
\(125\) −34.9615 −3.12705
\(126\) 26.5485 2.36513
\(127\) −16.9923 −1.50782 −0.753912 0.656976i \(-0.771835\pi\)
−0.753912 + 0.656976i \(0.771835\pi\)
\(128\) 5.57991 0.493199
\(129\) 23.2911 2.05066
\(130\) 12.0912 1.06046
\(131\) 2.74282 0.239641 0.119820 0.992796i \(-0.461768\pi\)
0.119820 + 0.992796i \(0.461768\pi\)
\(132\) −4.20667 −0.366143
\(133\) −3.89477 −0.337719
\(134\) −12.2434 −1.05767
\(135\) −2.90698 −0.250193
\(136\) −0.807607 −0.0692517
\(137\) −3.22948 −0.275914 −0.137957 0.990438i \(-0.544053\pi\)
−0.137957 + 0.990438i \(0.544053\pi\)
\(138\) −17.3649 −1.47820
\(139\) −12.4364 −1.05484 −0.527421 0.849604i \(-0.676841\pi\)
−0.527421 + 0.849604i \(0.676841\pi\)
\(140\) 38.8717 3.28526
\(141\) −23.4352 −1.97360
\(142\) 21.5704 1.81014
\(143\) −0.976825 −0.0816862
\(144\) −10.4876 −0.873970
\(145\) −36.7072 −3.04837
\(146\) −23.0532 −1.90789
\(147\) 20.4592 1.68745
\(148\) −0.814475 −0.0669494
\(149\) −3.07642 −0.252030 −0.126015 0.992028i \(-0.540219\pi\)
−0.126015 + 0.992028i \(0.540219\pi\)
\(150\) −68.8462 −5.62127
\(151\) 6.65967 0.541956 0.270978 0.962586i \(-0.412653\pi\)
0.270978 + 0.962586i \(0.412653\pi\)
\(152\) −0.707698 −0.0574019
\(153\) 3.73405 0.301880
\(154\) −5.82479 −0.469375
\(155\) 5.83975 0.469060
\(156\) 7.97296 0.638347
\(157\) 11.6680 0.931208 0.465604 0.884993i \(-0.345837\pi\)
0.465604 + 0.884993i \(0.345837\pi\)
\(158\) −20.8743 −1.66067
\(159\) −24.6201 −1.95250
\(160\) −34.5195 −2.72900
\(161\) −12.9633 −1.02165
\(162\) 16.8939 1.32731
\(163\) −12.9478 −1.01415 −0.507077 0.861901i \(-0.669274\pi\)
−0.507077 + 0.861901i \(0.669274\pi\)
\(164\) −7.48051 −0.584130
\(165\) 7.66942 0.597064
\(166\) −2.69475 −0.209153
\(167\) −9.79314 −0.757816 −0.378908 0.925434i \(-0.623700\pi\)
−0.378908 + 0.925434i \(0.623700\pi\)
\(168\) 6.90298 0.532577
\(169\) −11.1486 −0.857585
\(170\) 10.1408 0.777761
\(171\) 3.27211 0.250225
\(172\) 21.7593 1.65913
\(173\) 10.9902 0.835572 0.417786 0.908545i \(-0.362806\pi\)
0.417786 + 0.908545i \(0.362806\pi\)
\(174\) −44.8953 −3.40351
\(175\) −51.3954 −3.88513
\(176\) 2.30100 0.173445
\(177\) −2.78367 −0.209234
\(178\) −23.1961 −1.73862
\(179\) −8.06631 −0.602904 −0.301452 0.953481i \(-0.597471\pi\)
−0.301452 + 0.953481i \(0.597471\pi\)
\(180\) −32.6572 −2.43413
\(181\) −5.27084 −0.391779 −0.195889 0.980626i \(-0.562759\pi\)
−0.195889 + 0.980626i \(0.562759\pi\)
\(182\) 11.0398 0.818326
\(183\) −1.04849 −0.0775069
\(184\) −2.35550 −0.173650
\(185\) 1.48492 0.109173
\(186\) 7.14240 0.523706
\(187\) −0.819257 −0.0599100
\(188\) −21.8940 −1.59679
\(189\) −2.65422 −0.193066
\(190\) 8.88625 0.644677
\(191\) −21.2805 −1.53981 −0.769903 0.638162i \(-0.779695\pi\)
−0.769903 + 0.638162i \(0.779695\pi\)
\(192\) −26.1654 −1.88833
\(193\) 21.6556 1.55881 0.779404 0.626522i \(-0.215522\pi\)
0.779404 + 0.626522i \(0.215522\pi\)
\(194\) 10.4359 0.749255
\(195\) −14.5360 −1.04094
\(196\) 19.1137 1.36527
\(197\) −4.59309 −0.327244 −0.163622 0.986523i \(-0.552318\pi\)
−0.163622 + 0.986523i \(0.552318\pi\)
\(198\) 4.89358 0.347772
\(199\) 27.3740 1.94049 0.970247 0.242119i \(-0.0778423\pi\)
0.970247 + 0.242119i \(0.0778423\pi\)
\(200\) −9.33878 −0.660352
\(201\) 14.7189 1.03819
\(202\) 10.3087 0.725319
\(203\) −33.5155 −2.35233
\(204\) 6.68686 0.468174
\(205\) 13.6382 0.952530
\(206\) 9.79057 0.682142
\(207\) 10.8909 0.756969
\(208\) −4.36113 −0.302390
\(209\) −0.717906 −0.0496586
\(210\) −86.6777 −5.98133
\(211\) 1.00000 0.0688428
\(212\) −23.0010 −1.57972
\(213\) −25.9318 −1.77682
\(214\) 13.8189 0.944639
\(215\) −39.6707 −2.70552
\(216\) −0.482283 −0.0328152
\(217\) 5.33198 0.361958
\(218\) 4.90230 0.332026
\(219\) 27.7145 1.87277
\(220\) 7.16505 0.483067
\(221\) 1.55275 0.104449
\(222\) 1.81615 0.121892
\(223\) 10.1143 0.677305 0.338653 0.940911i \(-0.390029\pi\)
0.338653 + 0.940911i \(0.390029\pi\)
\(224\) −31.5180 −2.10588
\(225\) 43.1788 2.87859
\(226\) −9.21929 −0.613258
\(227\) −28.2840 −1.87728 −0.938639 0.344901i \(-0.887912\pi\)
−0.938639 + 0.344901i \(0.887912\pi\)
\(228\) 5.85963 0.388064
\(229\) 7.62003 0.503546 0.251773 0.967786i \(-0.418986\pi\)
0.251773 + 0.967786i \(0.418986\pi\)
\(230\) 29.5770 1.95025
\(231\) 7.00256 0.460734
\(232\) −6.08992 −0.399823
\(233\) −22.4303 −1.46946 −0.734730 0.678360i \(-0.762691\pi\)
−0.734730 + 0.678360i \(0.762691\pi\)
\(234\) −9.27487 −0.606317
\(235\) 39.9163 2.60385
\(236\) −2.60061 −0.169285
\(237\) 25.0951 1.63010
\(238\) 9.25901 0.600173
\(239\) −8.70037 −0.562780 −0.281390 0.959593i \(-0.590795\pi\)
−0.281390 + 0.959593i \(0.590795\pi\)
\(240\) 34.2408 2.21024
\(241\) −13.4256 −0.864816 −0.432408 0.901678i \(-0.642336\pi\)
−0.432408 + 0.901678i \(0.642336\pi\)
\(242\) 21.8415 1.40403
\(243\) −22.3543 −1.43403
\(244\) −0.979540 −0.0627086
\(245\) −34.8473 −2.22632
\(246\) 16.6804 1.06350
\(247\) 1.36066 0.0865766
\(248\) 0.968845 0.0615217
\(249\) 3.23963 0.205303
\(250\) 72.8317 4.60628
\(251\) −21.8720 −1.38055 −0.690273 0.723549i \(-0.742510\pi\)
−0.690273 + 0.723549i \(0.742510\pi\)
\(252\) −29.8176 −1.87834
\(253\) −2.38948 −0.150225
\(254\) 35.3984 2.22109
\(255\) −12.1912 −0.763444
\(256\) 9.27137 0.579460
\(257\) −2.90751 −0.181365 −0.0906826 0.995880i \(-0.528905\pi\)
−0.0906826 + 0.995880i \(0.528905\pi\)
\(258\) −48.5199 −3.02072
\(259\) 1.35580 0.0842455
\(260\) −13.5800 −0.842197
\(261\) 28.1573 1.74290
\(262\) −5.71383 −0.353002
\(263\) −18.0713 −1.11432 −0.557161 0.830405i \(-0.688109\pi\)
−0.557161 + 0.830405i \(0.688109\pi\)
\(264\) 1.27240 0.0783106
\(265\) 41.9345 2.57602
\(266\) 8.11358 0.497476
\(267\) 27.8863 1.70661
\(268\) 13.7510 0.839974
\(269\) 0.426291 0.0259914 0.0129957 0.999916i \(-0.495863\pi\)
0.0129957 + 0.999916i \(0.495863\pi\)
\(270\) 6.05582 0.368545
\(271\) −23.1458 −1.40601 −0.703004 0.711186i \(-0.748158\pi\)
−0.703004 + 0.711186i \(0.748158\pi\)
\(272\) −3.65765 −0.221777
\(273\) −13.2720 −0.803261
\(274\) 6.72766 0.406433
\(275\) −9.47349 −0.571273
\(276\) 19.5032 1.17395
\(277\) 13.7558 0.826509 0.413254 0.910616i \(-0.364392\pi\)
0.413254 + 0.910616i \(0.364392\pi\)
\(278\) 25.9075 1.55383
\(279\) −4.47955 −0.268184
\(280\) −11.7576 −0.702650
\(281\) 26.4252 1.57639 0.788196 0.615424i \(-0.211015\pi\)
0.788196 + 0.615424i \(0.211015\pi\)
\(282\) 48.8203 2.90721
\(283\) 18.6998 1.11159 0.555795 0.831319i \(-0.312414\pi\)
0.555795 + 0.831319i \(0.312414\pi\)
\(284\) −24.2265 −1.43758
\(285\) −10.6830 −0.632809
\(286\) 2.03492 0.120327
\(287\) 12.4523 0.735036
\(288\) 26.4792 1.56030
\(289\) −15.6977 −0.923395
\(290\) 76.4685 4.49038
\(291\) −12.5460 −0.735462
\(292\) 25.8918 1.51521
\(293\) −28.9577 −1.69173 −0.845864 0.533399i \(-0.820914\pi\)
−0.845864 + 0.533399i \(0.820914\pi\)
\(294\) −42.6206 −2.48568
\(295\) 4.74132 0.276050
\(296\) 0.246356 0.0143191
\(297\) −0.489240 −0.0283886
\(298\) 6.40879 0.371251
\(299\) 4.52881 0.261908
\(300\) 77.3237 4.46428
\(301\) −36.2213 −2.08776
\(302\) −13.8734 −0.798325
\(303\) −12.3931 −0.711967
\(304\) −3.20516 −0.183828
\(305\) 1.78586 0.102258
\(306\) −7.77877 −0.444683
\(307\) −0.0823094 −0.00469764 −0.00234882 0.999997i \(-0.500748\pi\)
−0.00234882 + 0.999997i \(0.500748\pi\)
\(308\) 6.54204 0.372767
\(309\) −11.7702 −0.669584
\(310\) −12.1654 −0.690946
\(311\) 15.6210 0.885786 0.442893 0.896574i \(-0.353952\pi\)
0.442893 + 0.896574i \(0.353952\pi\)
\(312\) −2.41159 −0.136530
\(313\) −13.9639 −0.789287 −0.394644 0.918834i \(-0.629132\pi\)
−0.394644 + 0.918834i \(0.629132\pi\)
\(314\) −24.3068 −1.37171
\(315\) 54.3623 3.06297
\(316\) 23.4447 1.31887
\(317\) −20.2316 −1.13632 −0.568161 0.822917i \(-0.692345\pi\)
−0.568161 + 0.822917i \(0.692345\pi\)
\(318\) 51.2886 2.87612
\(319\) −6.17777 −0.345888
\(320\) 44.5666 2.49135
\(321\) −16.6130 −0.927249
\(322\) 27.0052 1.50494
\(323\) 1.14117 0.0634967
\(324\) −18.9742 −1.05412
\(325\) 17.9552 0.995978
\(326\) 26.9729 1.49389
\(327\) −5.89354 −0.325914
\(328\) 2.26264 0.124933
\(329\) 36.4456 2.00931
\(330\) −15.9769 −0.879501
\(331\) 1.62526 0.0893323 0.0446662 0.999002i \(-0.485778\pi\)
0.0446662 + 0.999002i \(0.485778\pi\)
\(332\) 3.02658 0.166105
\(333\) −1.13905 −0.0624195
\(334\) 20.4011 1.11630
\(335\) −25.0702 −1.36973
\(336\) 31.2636 1.70557
\(337\) 10.4019 0.566629 0.283315 0.959027i \(-0.408566\pi\)
0.283315 + 0.959027i \(0.408566\pi\)
\(338\) 23.2248 1.26326
\(339\) 11.0834 0.601969
\(340\) −11.3895 −0.617681
\(341\) 0.982820 0.0532227
\(342\) −6.81646 −0.368592
\(343\) −4.55393 −0.245889
\(344\) −6.58158 −0.354855
\(345\) −35.5574 −1.91435
\(346\) −22.8949 −1.23083
\(347\) −13.4195 −0.720397 −0.360199 0.932876i \(-0.617291\pi\)
−0.360199 + 0.932876i \(0.617291\pi\)
\(348\) 50.4236 2.70299
\(349\) −28.8807 −1.54595 −0.772973 0.634439i \(-0.781231\pi\)
−0.772973 + 0.634439i \(0.781231\pi\)
\(350\) 107.067 5.72296
\(351\) 0.927264 0.0494937
\(352\) −5.80957 −0.309651
\(353\) 22.1950 1.18132 0.590661 0.806920i \(-0.298867\pi\)
0.590661 + 0.806920i \(0.298867\pi\)
\(354\) 5.79895 0.308211
\(355\) 44.1687 2.34423
\(356\) 26.0524 1.38077
\(357\) −11.1312 −0.589124
\(358\) 16.8037 0.888104
\(359\) −22.5884 −1.19217 −0.596084 0.802922i \(-0.703277\pi\)
−0.596084 + 0.802922i \(0.703277\pi\)
\(360\) 9.87789 0.520610
\(361\) 1.00000 0.0526316
\(362\) 10.9802 0.577107
\(363\) −26.2579 −1.37818
\(364\) −12.3992 −0.649896
\(365\) −47.2050 −2.47082
\(366\) 2.18422 0.114171
\(367\) 11.3655 0.593277 0.296638 0.954990i \(-0.404134\pi\)
0.296638 + 0.954990i \(0.404134\pi\)
\(368\) −10.6680 −0.556110
\(369\) −10.4615 −0.544606
\(370\) −3.09338 −0.160817
\(371\) 38.2883 1.98783
\(372\) −8.02189 −0.415916
\(373\) 34.8016 1.80196 0.900980 0.433862i \(-0.142849\pi\)
0.900980 + 0.433862i \(0.142849\pi\)
\(374\) 1.70667 0.0882500
\(375\) −87.5582 −4.52149
\(376\) 6.62233 0.341520
\(377\) 11.7088 0.603034
\(378\) 5.52926 0.284394
\(379\) 29.2686 1.50343 0.751714 0.659489i \(-0.229227\pi\)
0.751714 + 0.659489i \(0.229227\pi\)
\(380\) −9.98048 −0.511988
\(381\) −42.5559 −2.18020
\(382\) 44.3316 2.26820
\(383\) 15.6258 0.798443 0.399222 0.916854i \(-0.369280\pi\)
0.399222 + 0.916854i \(0.369280\pi\)
\(384\) 13.9744 0.713130
\(385\) −11.9272 −0.607865
\(386\) −45.1130 −2.29619
\(387\) 30.4306 1.54687
\(388\) −11.7210 −0.595042
\(389\) 35.8233 1.81631 0.908156 0.418631i \(-0.137490\pi\)
0.908156 + 0.418631i \(0.137490\pi\)
\(390\) 30.2813 1.53335
\(391\) 3.79828 0.192087
\(392\) −5.78136 −0.292003
\(393\) 6.86916 0.346503
\(394\) 9.56831 0.482044
\(395\) −42.7434 −2.15066
\(396\) −5.49616 −0.276192
\(397\) −22.2129 −1.11483 −0.557417 0.830233i \(-0.688208\pi\)
−0.557417 + 0.830233i \(0.688208\pi\)
\(398\) −57.0255 −2.85843
\(399\) −9.75414 −0.488318
\(400\) −42.2953 −2.11476
\(401\) 30.8386 1.54001 0.770003 0.638041i \(-0.220255\pi\)
0.770003 + 0.638041i \(0.220255\pi\)
\(402\) −30.6625 −1.52931
\(403\) −1.86275 −0.0927904
\(404\) −11.5781 −0.576032
\(405\) 34.5930 1.71894
\(406\) 69.8194 3.46508
\(407\) 0.249909 0.0123875
\(408\) −2.02259 −0.100133
\(409\) 35.6269 1.76164 0.880819 0.473453i \(-0.156993\pi\)
0.880819 + 0.473453i \(0.156993\pi\)
\(410\) −28.4110 −1.40312
\(411\) −8.08798 −0.398951
\(412\) −10.9962 −0.541742
\(413\) 4.32906 0.213019
\(414\) −22.6879 −1.11505
\(415\) −5.51793 −0.270865
\(416\) 11.0110 0.539857
\(417\) −31.1460 −1.52523
\(418\) 1.49554 0.0731493
\(419\) −16.9440 −0.827770 −0.413885 0.910329i \(-0.635828\pi\)
−0.413885 + 0.910329i \(0.635828\pi\)
\(420\) 97.3509 4.75024
\(421\) −19.9914 −0.974319 −0.487160 0.873313i \(-0.661967\pi\)
−0.487160 + 0.873313i \(0.661967\pi\)
\(422\) −2.08320 −0.101409
\(423\) −30.6190 −1.48875
\(424\) 6.95715 0.337869
\(425\) 15.0589 0.730466
\(426\) 54.0212 2.61734
\(427\) 1.63057 0.0789090
\(428\) −15.5205 −0.750211
\(429\) −2.44638 −0.118112
\(430\) 82.6420 3.98535
\(431\) −3.35013 −0.161370 −0.0806850 0.996740i \(-0.525711\pi\)
−0.0806850 + 0.996740i \(0.525711\pi\)
\(432\) −2.18426 −0.105090
\(433\) 21.6782 1.04179 0.520895 0.853621i \(-0.325598\pi\)
0.520895 + 0.853621i \(0.325598\pi\)
\(434\) −11.1076 −0.533180
\(435\) −91.9303 −4.40772
\(436\) −5.50596 −0.263687
\(437\) 3.32840 0.159219
\(438\) −57.7348 −2.75867
\(439\) −33.0035 −1.57517 −0.787585 0.616206i \(-0.788669\pi\)
−0.787585 + 0.616206i \(0.788669\pi\)
\(440\) −2.16722 −0.103318
\(441\) 26.7307 1.27289
\(442\) −3.23469 −0.153858
\(443\) −27.9772 −1.32924 −0.664619 0.747183i \(-0.731406\pi\)
−0.664619 + 0.747183i \(0.731406\pi\)
\(444\) −2.03979 −0.0968040
\(445\) −47.4976 −2.25160
\(446\) −21.0702 −0.997701
\(447\) −7.70464 −0.364417
\(448\) 40.6915 1.92249
\(449\) 3.53561 0.166856 0.0834279 0.996514i \(-0.473413\pi\)
0.0834279 + 0.996514i \(0.473413\pi\)
\(450\) −89.9500 −4.24028
\(451\) 2.29528 0.108080
\(452\) 10.3545 0.487036
\(453\) 16.6786 0.783628
\(454\) 58.9213 2.76531
\(455\) 22.6058 1.05977
\(456\) −1.77237 −0.0829989
\(457\) 11.9057 0.556926 0.278463 0.960447i \(-0.410175\pi\)
0.278463 + 0.960447i \(0.410175\pi\)
\(458\) −15.8740 −0.741745
\(459\) 0.777690 0.0362995
\(460\) −33.2190 −1.54884
\(461\) 17.7625 0.827284 0.413642 0.910440i \(-0.364257\pi\)
0.413642 + 0.910440i \(0.364257\pi\)
\(462\) −14.5877 −0.678682
\(463\) −7.23358 −0.336173 −0.168086 0.985772i \(-0.553759\pi\)
−0.168086 + 0.985772i \(0.553759\pi\)
\(464\) −27.5812 −1.28042
\(465\) 14.6252 0.678226
\(466\) 46.7268 2.16458
\(467\) 16.7818 0.776569 0.388285 0.921540i \(-0.373068\pi\)
0.388285 + 0.921540i \(0.373068\pi\)
\(468\) 10.4170 0.481524
\(469\) −22.8903 −1.05698
\(470\) −83.1536 −3.83559
\(471\) 29.2216 1.34646
\(472\) 0.786610 0.0362067
\(473\) −6.67652 −0.306987
\(474\) −52.2780 −2.40121
\(475\) 13.1960 0.605474
\(476\) −10.3991 −0.476644
\(477\) −32.1671 −1.47283
\(478\) 18.1246 0.829000
\(479\) 3.34578 0.152873 0.0764363 0.997074i \(-0.475646\pi\)
0.0764363 + 0.997074i \(0.475646\pi\)
\(480\) −86.4512 −3.94594
\(481\) −0.473657 −0.0215969
\(482\) 27.9681 1.27391
\(483\) −32.4656 −1.47724
\(484\) −24.5310 −1.11505
\(485\) 21.3692 0.970325
\(486\) 46.5685 2.11239
\(487\) −0.173122 −0.00784489 −0.00392244 0.999992i \(-0.501249\pi\)
−0.00392244 + 0.999992i \(0.501249\pi\)
\(488\) 0.296283 0.0134121
\(489\) −32.4268 −1.46639
\(490\) 72.5939 3.27946
\(491\) −3.39523 −0.153224 −0.0766122 0.997061i \(-0.524410\pi\)
−0.0766122 + 0.997061i \(0.524410\pi\)
\(492\) −18.7343 −0.844609
\(493\) 9.82010 0.442275
\(494\) −2.83452 −0.127531
\(495\) 10.0204 0.450382
\(496\) 4.38789 0.197022
\(497\) 40.3282 1.80897
\(498\) −6.74879 −0.302420
\(499\) −10.9801 −0.491537 −0.245768 0.969329i \(-0.579040\pi\)
−0.245768 + 0.969329i \(0.579040\pi\)
\(500\) −81.8000 −3.65821
\(501\) −24.5261 −1.09575
\(502\) 45.5637 2.03361
\(503\) −14.7808 −0.659044 −0.329522 0.944148i \(-0.606888\pi\)
−0.329522 + 0.944148i \(0.606888\pi\)
\(504\) 9.01899 0.401738
\(505\) 21.1087 0.939326
\(506\) 4.97776 0.221288
\(507\) −27.9208 −1.24001
\(508\) −39.7572 −1.76394
\(509\) 0.220794 0.00978650 0.00489325 0.999988i \(-0.498442\pi\)
0.00489325 + 0.999988i \(0.498442\pi\)
\(510\) 25.3967 1.12459
\(511\) −43.1004 −1.90665
\(512\) −30.4739 −1.34677
\(513\) 0.681482 0.0300882
\(514\) 6.05691 0.267159
\(515\) 20.0477 0.883409
\(516\) 54.4945 2.39899
\(517\) 6.71785 0.295451
\(518\) −2.82441 −0.124097
\(519\) 27.5242 1.20818
\(520\) 4.10757 0.180129
\(521\) −14.6300 −0.640954 −0.320477 0.947256i \(-0.603843\pi\)
−0.320477 + 0.947256i \(0.603843\pi\)
\(522\) −58.6574 −2.56736
\(523\) 23.2970 1.01871 0.509353 0.860558i \(-0.329885\pi\)
0.509353 + 0.860558i \(0.329885\pi\)
\(524\) 6.41741 0.280346
\(525\) −128.716 −5.61761
\(526\) 37.6460 1.64144
\(527\) −1.56228 −0.0680539
\(528\) 5.76268 0.250788
\(529\) −11.9218 −0.518338
\(530\) −87.3579 −3.79459
\(531\) −3.63697 −0.157831
\(532\) −9.11266 −0.395084
\(533\) −4.35028 −0.188431
\(534\) −58.0927 −2.51392
\(535\) 28.2963 1.22336
\(536\) −4.15928 −0.179653
\(537\) −20.2014 −0.871755
\(538\) −0.888050 −0.0382865
\(539\) −5.86475 −0.252613
\(540\) −6.80151 −0.292691
\(541\) −27.5243 −1.18336 −0.591681 0.806172i \(-0.701535\pi\)
−0.591681 + 0.806172i \(0.701535\pi\)
\(542\) 48.2173 2.07111
\(543\) −13.2004 −0.566483
\(544\) 9.23482 0.395940
\(545\) 10.0382 0.429991
\(546\) 27.6483 1.18324
\(547\) −36.1302 −1.54482 −0.772408 0.635126i \(-0.780948\pi\)
−0.772408 + 0.635126i \(0.780948\pi\)
\(548\) −7.55608 −0.322780
\(549\) −1.36989 −0.0584656
\(550\) 19.7352 0.841510
\(551\) 8.60525 0.366596
\(552\) −5.89916 −0.251085
\(553\) −39.0268 −1.65959
\(554\) −28.6562 −1.21748
\(555\) 3.71886 0.157857
\(556\) −29.0977 −1.23402
\(557\) −39.2333 −1.66237 −0.831184 0.555997i \(-0.812337\pi\)
−0.831184 + 0.555997i \(0.812337\pi\)
\(558\) 9.33180 0.395046
\(559\) 12.6541 0.535212
\(560\) −53.2500 −2.25022
\(561\) −2.05176 −0.0866254
\(562\) −55.0489 −2.32210
\(563\) 15.1668 0.639206 0.319603 0.947552i \(-0.396451\pi\)
0.319603 + 0.947552i \(0.396451\pi\)
\(564\) −54.8318 −2.30884
\(565\) −18.8780 −0.794202
\(566\) −38.9555 −1.63742
\(567\) 31.5851 1.32645
\(568\) 7.32781 0.307468
\(569\) −38.4545 −1.61210 −0.806049 0.591849i \(-0.798398\pi\)
−0.806049 + 0.591849i \(0.798398\pi\)
\(570\) 22.2549 0.932155
\(571\) −36.8816 −1.54345 −0.771723 0.635959i \(-0.780605\pi\)
−0.771723 + 0.635959i \(0.780605\pi\)
\(572\) −2.28549 −0.0955613
\(573\) −53.2953 −2.22645
\(574\) −25.9406 −1.08274
\(575\) 43.9215 1.83165
\(576\) −34.1861 −1.42442
\(577\) −27.1309 −1.12947 −0.564736 0.825272i \(-0.691022\pi\)
−0.564736 + 0.825272i \(0.691022\pi\)
\(578\) 32.7015 1.36020
\(579\) 54.2348 2.25392
\(580\) −85.8845 −3.56616
\(581\) −5.03814 −0.209017
\(582\) 26.1359 1.08337
\(583\) 7.05751 0.292292
\(584\) −7.83155 −0.324072
\(585\) −18.9918 −0.785213
\(586\) 60.3247 2.49199
\(587\) 21.0774 0.869958 0.434979 0.900441i \(-0.356756\pi\)
0.434979 + 0.900441i \(0.356756\pi\)
\(588\) 47.8687 1.97407
\(589\) −1.36901 −0.0564090
\(590\) −9.87712 −0.406634
\(591\) −11.5030 −0.473171
\(592\) 1.11574 0.0458567
\(593\) 39.6201 1.62700 0.813502 0.581562i \(-0.197558\pi\)
0.813502 + 0.581562i \(0.197558\pi\)
\(594\) 1.01918 0.0418176
\(595\) 18.9593 0.777255
\(596\) −7.19795 −0.294840
\(597\) 68.5560 2.80581
\(598\) −9.43441 −0.385802
\(599\) −45.4804 −1.85828 −0.929139 0.369731i \(-0.879450\pi\)
−0.929139 + 0.369731i \(0.879450\pi\)
\(600\) −23.3882 −0.954820
\(601\) 4.90388 0.200034 0.100017 0.994986i \(-0.468110\pi\)
0.100017 + 0.994986i \(0.468110\pi\)
\(602\) 75.4562 3.07537
\(603\) 19.2308 0.783140
\(604\) 15.5817 0.634012
\(605\) 44.7240 1.81829
\(606\) 25.8174 1.04876
\(607\) 5.95518 0.241713 0.120857 0.992670i \(-0.461436\pi\)
0.120857 + 0.992670i \(0.461436\pi\)
\(608\) 8.09238 0.328189
\(609\) −83.9368 −3.40129
\(610\) −3.72030 −0.150630
\(611\) −12.7324 −0.515100
\(612\) 8.73662 0.353157
\(613\) −19.2455 −0.777320 −0.388660 0.921381i \(-0.627062\pi\)
−0.388660 + 0.921381i \(0.627062\pi\)
\(614\) 0.171467 0.00691984
\(615\) 34.1557 1.37729
\(616\) −1.97878 −0.0797273
\(617\) 18.8192 0.757633 0.378816 0.925472i \(-0.376331\pi\)
0.378816 + 0.925472i \(0.376331\pi\)
\(618\) 24.5197 0.986327
\(619\) −1.82633 −0.0734064 −0.0367032 0.999326i \(-0.511686\pi\)
−0.0367032 + 0.999326i \(0.511686\pi\)
\(620\) 13.6634 0.548734
\(621\) 2.26824 0.0910214
\(622\) −32.5417 −1.30480
\(623\) −43.3677 −1.73749
\(624\) −10.9221 −0.437233
\(625\) 83.1544 3.32618
\(626\) 29.0896 1.16265
\(627\) −1.79794 −0.0718027
\(628\) 27.2998 1.08938
\(629\) −0.397252 −0.0158395
\(630\) −113.248 −4.51189
\(631\) 8.07679 0.321532 0.160766 0.986993i \(-0.448604\pi\)
0.160766 + 0.986993i \(0.448604\pi\)
\(632\) −7.09136 −0.282079
\(633\) 2.50442 0.0995417
\(634\) 42.1465 1.67385
\(635\) 72.4837 2.87643
\(636\) −57.6042 −2.28415
\(637\) 11.1155 0.440414
\(638\) 12.8695 0.509509
\(639\) −33.8809 −1.34031
\(640\) −23.8021 −0.940860
\(641\) −45.9378 −1.81443 −0.907216 0.420664i \(-0.861797\pi\)
−0.907216 + 0.420664i \(0.861797\pi\)
\(642\) 34.6083 1.36588
\(643\) 32.1642 1.26843 0.634216 0.773156i \(-0.281323\pi\)
0.634216 + 0.773156i \(0.281323\pi\)
\(644\) −30.3306 −1.19519
\(645\) −99.3521 −3.91199
\(646\) −2.37729 −0.0935334
\(647\) 45.2590 1.77931 0.889657 0.456630i \(-0.150944\pi\)
0.889657 + 0.456630i \(0.150944\pi\)
\(648\) 5.73916 0.225456
\(649\) 0.797957 0.0313225
\(650\) −37.4044 −1.46712
\(651\) 13.3535 0.523365
\(652\) −30.2943 −1.18642
\(653\) 28.9430 1.13263 0.566314 0.824190i \(-0.308369\pi\)
0.566314 + 0.824190i \(0.308369\pi\)
\(654\) 12.2774 0.480085
\(655\) −11.7000 −0.457155
\(656\) 10.2475 0.400097
\(657\) 36.2099 1.41268
\(658\) −75.9233 −2.95980
\(659\) −18.1301 −0.706248 −0.353124 0.935577i \(-0.614881\pi\)
−0.353124 + 0.935577i \(0.614881\pi\)
\(660\) 17.9443 0.698480
\(661\) 4.80886 0.187043 0.0935215 0.995617i \(-0.470188\pi\)
0.0935215 + 0.995617i \(0.470188\pi\)
\(662\) −3.38574 −0.131590
\(663\) 3.88873 0.151026
\(664\) −0.915453 −0.0355265
\(665\) 16.6138 0.644257
\(666\) 2.37287 0.0919467
\(667\) 28.6417 1.10901
\(668\) −22.9132 −0.886538
\(669\) 25.3305 0.979334
\(670\) 52.2262 2.01767
\(671\) 0.300557 0.0116029
\(672\) −78.9342 −3.04495
\(673\) −45.6346 −1.75909 −0.879543 0.475820i \(-0.842152\pi\)
−0.879543 + 0.475820i \(0.842152\pi\)
\(674\) −21.6693 −0.834669
\(675\) 8.99283 0.346134
\(676\) −26.0846 −1.00325
\(677\) −17.6007 −0.676451 −0.338225 0.941065i \(-0.609827\pi\)
−0.338225 + 0.941065i \(0.609827\pi\)
\(678\) −23.0890 −0.886727
\(679\) 19.5111 0.748767
\(680\) 3.44499 0.132109
\(681\) −70.8351 −2.71441
\(682\) −2.04741 −0.0783994
\(683\) 8.30785 0.317891 0.158946 0.987287i \(-0.449191\pi\)
0.158946 + 0.987287i \(0.449191\pi\)
\(684\) 7.65582 0.292727
\(685\) 13.7759 0.526352
\(686\) 9.48674 0.362205
\(687\) 19.0837 0.728090
\(688\) −29.8079 −1.13642
\(689\) −13.3762 −0.509593
\(690\) 74.0731 2.81992
\(691\) 22.4090 0.852477 0.426238 0.904611i \(-0.359838\pi\)
0.426238 + 0.904611i \(0.359838\pi\)
\(692\) 25.7140 0.977501
\(693\) 9.14909 0.347545
\(694\) 27.9555 1.06118
\(695\) 53.0497 2.01229
\(696\) −15.2517 −0.578114
\(697\) −3.64855 −0.138199
\(698\) 60.1642 2.27725
\(699\) −56.1750 −2.12473
\(700\) −120.251 −4.54505
\(701\) 11.7052 0.442100 0.221050 0.975262i \(-0.429052\pi\)
0.221050 + 0.975262i \(0.429052\pi\)
\(702\) −1.93168 −0.0729064
\(703\) −0.348108 −0.0131292
\(704\) 7.50048 0.282685
\(705\) 99.9672 3.76498
\(706\) −46.2367 −1.74014
\(707\) 19.2733 0.724847
\(708\) −6.51301 −0.244774
\(709\) −35.8423 −1.34609 −0.673043 0.739603i \(-0.735013\pi\)
−0.673043 + 0.739603i \(0.735013\pi\)
\(710\) −92.0122 −3.45315
\(711\) 32.7876 1.22963
\(712\) −7.88011 −0.295319
\(713\) −4.55661 −0.170646
\(714\) 23.1884 0.867806
\(715\) 4.16682 0.155830
\(716\) −18.8729 −0.705313
\(717\) −21.7894 −0.813739
\(718\) 47.0560 1.75612
\(719\) −51.6705 −1.92698 −0.963492 0.267737i \(-0.913724\pi\)
−0.963492 + 0.267737i \(0.913724\pi\)
\(720\) 44.7369 1.66724
\(721\) 18.3046 0.681698
\(722\) −2.08320 −0.0775286
\(723\) −33.6232 −1.25046
\(724\) −12.3323 −0.458326
\(725\) 113.555 4.21732
\(726\) 54.7003 2.03012
\(727\) −12.9863 −0.481634 −0.240817 0.970571i \(-0.577415\pi\)
−0.240817 + 0.970571i \(0.577415\pi\)
\(728\) 3.75041 0.139000
\(729\) −31.6557 −1.17243
\(730\) 98.3373 3.63963
\(731\) 10.6129 0.392533
\(732\) −2.45318 −0.0906721
\(733\) −10.8703 −0.401505 −0.200753 0.979642i \(-0.564339\pi\)
−0.200753 + 0.979642i \(0.564339\pi\)
\(734\) −23.6767 −0.873923
\(735\) −87.2723 −3.21909
\(736\) 26.9346 0.992824
\(737\) −4.21927 −0.155419
\(738\) 21.7935 0.802229
\(739\) −33.7667 −1.24213 −0.621063 0.783760i \(-0.713299\pi\)
−0.621063 + 0.783760i \(0.713299\pi\)
\(740\) 3.47429 0.127717
\(741\) 3.40766 0.125183
\(742\) −79.7620 −2.92816
\(743\) 7.36333 0.270135 0.135067 0.990836i \(-0.456875\pi\)
0.135067 + 0.990836i \(0.456875\pi\)
\(744\) 2.42639 0.0889559
\(745\) 13.1230 0.480790
\(746\) −72.4987 −2.65436
\(747\) 4.23269 0.154866
\(748\) −1.91683 −0.0700862
\(749\) 25.8359 0.944024
\(750\) 182.401 6.66035
\(751\) −8.65055 −0.315663 −0.157832 0.987466i \(-0.550450\pi\)
−0.157832 + 0.987466i \(0.550450\pi\)
\(752\) 29.9925 1.09371
\(753\) −54.7766 −1.99617
\(754\) −24.3918 −0.888296
\(755\) −28.4080 −1.03387
\(756\) −6.21011 −0.225860
\(757\) −23.9176 −0.869299 −0.434650 0.900600i \(-0.643128\pi\)
−0.434650 + 0.900600i \(0.643128\pi\)
\(758\) −60.9724 −2.21462
\(759\) −5.98425 −0.217215
\(760\) 3.01881 0.109504
\(761\) 2.80990 0.101859 0.0509294 0.998702i \(-0.483782\pi\)
0.0509294 + 0.998702i \(0.483782\pi\)
\(762\) 88.6523 3.21153
\(763\) 9.16540 0.331810
\(764\) −49.7904 −1.80135
\(765\) −15.9283 −0.575887
\(766\) −32.5517 −1.17614
\(767\) −1.51238 −0.0546088
\(768\) 23.2194 0.837857
\(769\) −13.8811 −0.500564 −0.250282 0.968173i \(-0.580523\pi\)
−0.250282 + 0.968173i \(0.580523\pi\)
\(770\) 24.8467 0.895412
\(771\) −7.28161 −0.262241
\(772\) 50.6681 1.82358
\(773\) 24.3274 0.874994 0.437497 0.899220i \(-0.355865\pi\)
0.437497 + 0.899220i \(0.355865\pi\)
\(774\) −63.3930 −2.27861
\(775\) −18.0654 −0.648930
\(776\) 3.54526 0.127267
\(777\) 3.39550 0.121813
\(778\) −74.6270 −2.67551
\(779\) −3.19719 −0.114551
\(780\) −34.0101 −1.21776
\(781\) 7.43352 0.265992
\(782\) −7.91258 −0.282953
\(783\) 5.86432 0.209574
\(784\) −26.1837 −0.935133
\(785\) −49.7719 −1.77644
\(786\) −14.3098 −0.510414
\(787\) 21.8086 0.777392 0.388696 0.921366i \(-0.372926\pi\)
0.388696 + 0.921366i \(0.372926\pi\)
\(788\) −10.7465 −0.382829
\(789\) −45.2580 −1.61123
\(790\) 89.0431 3.16801
\(791\) −17.2365 −0.612859
\(792\) 1.66243 0.0590719
\(793\) −0.569650 −0.0202289
\(794\) 46.2739 1.64220
\(795\) 105.022 3.72473
\(796\) 64.0475 2.27010
\(797\) −31.3673 −1.11109 −0.555544 0.831487i \(-0.687490\pi\)
−0.555544 + 0.831487i \(0.687490\pi\)
\(798\) 20.3198 0.719313
\(799\) −10.6786 −0.377782
\(800\) 106.787 3.77549
\(801\) 36.4344 1.28735
\(802\) −64.2429 −2.26850
\(803\) −7.94452 −0.280356
\(804\) 34.4382 1.21454
\(805\) 55.2974 1.94898
\(806\) 3.88049 0.136684
\(807\) 1.06761 0.0375817
\(808\) 3.50205 0.123202
\(809\) −7.49622 −0.263553 −0.131776 0.991279i \(-0.542068\pi\)
−0.131776 + 0.991279i \(0.542068\pi\)
\(810\) −72.0641 −2.53208
\(811\) −8.05207 −0.282746 −0.141373 0.989956i \(-0.545152\pi\)
−0.141373 + 0.989956i \(0.545152\pi\)
\(812\) −78.4168 −2.75189
\(813\) −57.9668 −2.03298
\(814\) −0.520610 −0.0182474
\(815\) 55.2313 1.93467
\(816\) −9.16028 −0.320674
\(817\) 9.29999 0.325365
\(818\) −74.2180 −2.59497
\(819\) −17.3404 −0.605923
\(820\) 31.9094 1.11433
\(821\) 3.45632 0.120627 0.0603133 0.998179i \(-0.480790\pi\)
0.0603133 + 0.998179i \(0.480790\pi\)
\(822\) 16.8489 0.587672
\(823\) 14.6503 0.510678 0.255339 0.966852i \(-0.417813\pi\)
0.255339 + 0.966852i \(0.417813\pi\)
\(824\) 3.32602 0.115868
\(825\) −23.7256 −0.826019
\(826\) −9.01829 −0.313786
\(827\) −9.58314 −0.333239 −0.166619 0.986021i \(-0.553285\pi\)
−0.166619 + 0.986021i \(0.553285\pi\)
\(828\) 25.4816 0.885546
\(829\) −21.4262 −0.744162 −0.372081 0.928200i \(-0.621356\pi\)
−0.372081 + 0.928200i \(0.621356\pi\)
\(830\) 11.4949 0.398995
\(831\) 34.4504 1.19507
\(832\) −14.2158 −0.492843
\(833\) 9.32253 0.323007
\(834\) 64.8833 2.24672
\(835\) 41.7744 1.44566
\(836\) −1.67970 −0.0580936
\(837\) −0.932955 −0.0322476
\(838\) 35.2978 1.21934
\(839\) 28.6087 0.987681 0.493841 0.869552i \(-0.335593\pi\)
0.493841 + 0.869552i \(0.335593\pi\)
\(840\) −29.4459 −1.01598
\(841\) 45.0504 1.55346
\(842\) 41.6460 1.43522
\(843\) 66.1797 2.27935
\(844\) 2.33972 0.0805364
\(845\) 47.5564 1.63599
\(846\) 63.7854 2.19299
\(847\) 40.8352 1.40311
\(848\) 31.5089 1.08202
\(849\) 46.8322 1.60728
\(850\) −31.3708 −1.07601
\(851\) −1.15864 −0.0397178
\(852\) −60.6732 −2.07863
\(853\) −3.10834 −0.106428 −0.0532138 0.998583i \(-0.516946\pi\)
−0.0532138 + 0.998583i \(0.516946\pi\)
\(854\) −3.39681 −0.116236
\(855\) −13.9578 −0.477346
\(856\) 4.69451 0.160455
\(857\) −14.0270 −0.479152 −0.239576 0.970878i \(-0.577008\pi\)
−0.239576 + 0.970878i \(0.577008\pi\)
\(858\) 5.09629 0.173985
\(859\) 38.5787 1.31629 0.658144 0.752892i \(-0.271342\pi\)
0.658144 + 0.752892i \(0.271342\pi\)
\(860\) −92.8183 −3.16508
\(861\) 31.1858 1.06281
\(862\) 6.97899 0.237705
\(863\) 21.8286 0.743053 0.371527 0.928422i \(-0.378834\pi\)
0.371527 + 0.928422i \(0.378834\pi\)
\(864\) 5.51481 0.187618
\(865\) −46.8808 −1.59400
\(866\) −45.1601 −1.53460
\(867\) −39.3137 −1.33516
\(868\) 12.4753 0.423440
\(869\) −7.19365 −0.244028
\(870\) 191.509 6.49276
\(871\) 7.99685 0.270963
\(872\) 1.66540 0.0563974
\(873\) −16.3919 −0.554780
\(874\) −6.93371 −0.234536
\(875\) 136.167 4.60328
\(876\) 64.8440 2.19088
\(877\) 21.8967 0.739400 0.369700 0.929151i \(-0.379460\pi\)
0.369700 + 0.929151i \(0.379460\pi\)
\(878\) 68.7528 2.32029
\(879\) −72.5222 −2.44611
\(880\) −9.81534 −0.330875
\(881\) 1.27404 0.0429234 0.0214617 0.999770i \(-0.493168\pi\)
0.0214617 + 0.999770i \(0.493168\pi\)
\(882\) −55.6853 −1.87502
\(883\) −38.9964 −1.31233 −0.656166 0.754616i \(-0.727823\pi\)
−0.656166 + 0.754616i \(0.727823\pi\)
\(884\) 3.63299 0.122191
\(885\) 11.8743 0.399149
\(886\) 58.2821 1.95803
\(887\) 41.6509 1.39850 0.699251 0.714877i \(-0.253517\pi\)
0.699251 + 0.714877i \(0.253517\pi\)
\(888\) 0.616977 0.0207044
\(889\) 66.1812 2.21964
\(890\) 98.9470 3.31671
\(891\) 5.82195 0.195043
\(892\) 23.6647 0.792351
\(893\) −9.35756 −0.313139
\(894\) 16.0503 0.536802
\(895\) 34.4083 1.15014
\(896\) −21.7325 −0.726031
\(897\) 11.3420 0.378700
\(898\) −7.36538 −0.245786
\(899\) −11.7807 −0.392907
\(900\) 101.026 3.36754
\(901\) −11.2185 −0.373743
\(902\) −4.78152 −0.159207
\(903\) −90.7134 −3.01875
\(904\) −3.13195 −0.104167
\(905\) 22.4837 0.747384
\(906\) −34.7448 −1.15432
\(907\) 34.8756 1.15802 0.579012 0.815319i \(-0.303438\pi\)
0.579012 + 0.815319i \(0.303438\pi\)
\(908\) −66.1767 −2.19615
\(909\) −16.1921 −0.537057
\(910\) −47.0923 −1.56109
\(911\) 6.34470 0.210209 0.105105 0.994461i \(-0.466482\pi\)
0.105105 + 0.994461i \(0.466482\pi\)
\(912\) −8.02706 −0.265802
\(913\) −0.928658 −0.0307341
\(914\) −24.8020 −0.820376
\(915\) 4.47253 0.147857
\(916\) 17.8287 0.589077
\(917\) −10.6826 −0.352772
\(918\) −1.62008 −0.0534707
\(919\) 56.4297 1.86144 0.930721 0.365729i \(-0.119180\pi\)
0.930721 + 0.365729i \(0.119180\pi\)
\(920\) 10.0478 0.331266
\(921\) −0.206137 −0.00679245
\(922\) −37.0029 −1.21863
\(923\) −14.0889 −0.463740
\(924\) 16.3840 0.538994
\(925\) −4.59364 −0.151038
\(926\) 15.0690 0.495198
\(927\) −15.3782 −0.505086
\(928\) 69.6370 2.28595
\(929\) 9.73990 0.319556 0.159778 0.987153i \(-0.448922\pi\)
0.159778 + 0.987153i \(0.448922\pi\)
\(930\) −30.4672 −0.999057
\(931\) 8.16924 0.267736
\(932\) −52.4806 −1.71906
\(933\) 39.1216 1.28078
\(934\) −34.9598 −1.14392
\(935\) 3.49468 0.114288
\(936\) −3.15083 −0.102988
\(937\) −60.6415 −1.98107 −0.990536 0.137252i \(-0.956173\pi\)
−0.990536 + 0.137252i \(0.956173\pi\)
\(938\) 47.6851 1.55697
\(939\) −34.9715 −1.14125
\(940\) 93.3929 3.04614
\(941\) 4.68933 0.152868 0.0764339 0.997075i \(-0.475647\pi\)
0.0764339 + 0.997075i \(0.475647\pi\)
\(942\) −60.8743 −1.98339
\(943\) −10.6415 −0.346535
\(944\) 3.56255 0.115951
\(945\) 11.3220 0.368306
\(946\) 13.9085 0.452205
\(947\) −51.8828 −1.68597 −0.842983 0.537941i \(-0.819202\pi\)
−0.842983 + 0.537941i \(0.819202\pi\)
\(948\) 58.7153 1.90699
\(949\) 15.0574 0.488783
\(950\) −27.4899 −0.891890
\(951\) −50.6685 −1.64304
\(952\) 3.14544 0.101944
\(953\) −6.58417 −0.213282 −0.106641 0.994298i \(-0.534010\pi\)
−0.106641 + 0.994298i \(0.534010\pi\)
\(954\) 67.0104 2.16954
\(955\) 90.7759 2.93744
\(956\) −20.3564 −0.658373
\(957\) −15.4717 −0.500129
\(958\) −6.96993 −0.225188
\(959\) 12.5781 0.406168
\(960\) 111.613 3.60231
\(961\) −29.1258 −0.939542
\(962\) 0.986721 0.0318132
\(963\) −21.7055 −0.699451
\(964\) −31.4120 −1.01171
\(965\) −92.3760 −2.97369
\(966\) 67.6324 2.17604
\(967\) −3.91548 −0.125913 −0.0629566 0.998016i \(-0.520053\pi\)
−0.0629566 + 0.998016i \(0.520053\pi\)
\(968\) 7.41994 0.238486
\(969\) 2.85798 0.0918115
\(970\) −44.5163 −1.42933
\(971\) 54.9374 1.76302 0.881512 0.472161i \(-0.156526\pi\)
0.881512 + 0.472161i \(0.156526\pi\)
\(972\) −52.3028 −1.67761
\(973\) 48.4370 1.55282
\(974\) 0.360647 0.0115559
\(975\) 44.9675 1.44011
\(976\) 1.34186 0.0429520
\(977\) −5.10472 −0.163314 −0.0816572 0.996660i \(-0.526021\pi\)
−0.0816572 + 0.996660i \(0.526021\pi\)
\(978\) 67.5515 2.16006
\(979\) −7.99377 −0.255482
\(980\) −81.5329 −2.60447
\(981\) −7.70012 −0.245846
\(982\) 7.07293 0.225706
\(983\) −7.36642 −0.234952 −0.117476 0.993076i \(-0.537480\pi\)
−0.117476 + 0.993076i \(0.537480\pi\)
\(984\) 5.66660 0.180645
\(985\) 19.5926 0.624273
\(986\) −20.4572 −0.651490
\(987\) 91.2749 2.90531
\(988\) 3.18356 0.101282
\(989\) 30.9540 0.984281
\(990\) −20.8744 −0.663433
\(991\) −36.8773 −1.17145 −0.585723 0.810512i \(-0.699189\pi\)
−0.585723 + 0.810512i \(0.699189\pi\)
\(992\) −11.0785 −0.351744
\(993\) 4.07033 0.129168
\(994\) −84.0116 −2.66469
\(995\) −116.769 −3.70182
\(996\) 7.57981 0.240176
\(997\) 31.3387 0.992508 0.496254 0.868178i \(-0.334709\pi\)
0.496254 + 0.868178i \(0.334709\pi\)
\(998\) 22.8737 0.724055
\(999\) −0.237230 −0.00750561
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 \(a_p\))