Properties

Label 4009.2.a.c.1.17
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

Related objects

Downloads

Learn more about

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 1.17
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.89616 q^{2}\) \(+2.32800 q^{3}\) \(+1.59541 q^{4}\) \(-3.08512 q^{5}\) \(-4.41426 q^{6}\) \(+2.27635 q^{7}\) \(+0.767159 q^{8}\) \(+2.41961 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.89616 q^{2}\) \(+2.32800 q^{3}\) \(+1.59541 q^{4}\) \(-3.08512 q^{5}\) \(-4.41426 q^{6}\) \(+2.27635 q^{7}\) \(+0.767159 q^{8}\) \(+2.41961 q^{9}\) \(+5.84987 q^{10}\) \(+5.52272 q^{11}\) \(+3.71413 q^{12}\) \(-0.731648 q^{13}\) \(-4.31632 q^{14}\) \(-7.18216 q^{15}\) \(-4.64548 q^{16}\) \(-2.27098 q^{17}\) \(-4.58796 q^{18}\) \(+1.00000 q^{19}\) \(-4.92204 q^{20}\) \(+5.29936 q^{21}\) \(-10.4719 q^{22}\) \(-6.66671 q^{23}\) \(+1.78595 q^{24}\) \(+4.51794 q^{25}\) \(+1.38732 q^{26}\) \(-1.35116 q^{27}\) \(+3.63173 q^{28}\) \(-8.44492 q^{29}\) \(+13.6185 q^{30}\) \(-2.58578 q^{31}\) \(+7.27425 q^{32}\) \(+12.8569 q^{33}\) \(+4.30614 q^{34}\) \(-7.02281 q^{35}\) \(+3.86027 q^{36}\) \(-1.51001 q^{37}\) \(-1.89616 q^{38}\) \(-1.70328 q^{39}\) \(-2.36677 q^{40}\) \(+9.69034 q^{41}\) \(-10.0484 q^{42}\) \(-4.59537 q^{43}\) \(+8.81102 q^{44}\) \(-7.46477 q^{45}\) \(+12.6411 q^{46}\) \(-6.50404 q^{47}\) \(-10.8147 q^{48}\) \(-1.81822 q^{49}\) \(-8.56672 q^{50}\) \(-5.28686 q^{51}\) \(-1.16728 q^{52}\) \(-5.13502 q^{53}\) \(+2.56201 q^{54}\) \(-17.0382 q^{55}\) \(+1.74632 q^{56}\) \(+2.32800 q^{57}\) \(+16.0129 q^{58}\) \(-10.8330 q^{59}\) \(-11.4585 q^{60}\) \(-4.96951 q^{61}\) \(+4.90305 q^{62}\) \(+5.50788 q^{63}\) \(-4.50216 q^{64}\) \(+2.25722 q^{65}\) \(-24.3787 q^{66}\) \(+7.19918 q^{67}\) \(-3.62316 q^{68}\) \(-15.5201 q^{69}\) \(+13.3164 q^{70}\) \(+0.258044 q^{71}\) \(+1.85622 q^{72}\) \(+12.2945 q^{73}\) \(+2.86322 q^{74}\) \(+10.5178 q^{75}\) \(+1.59541 q^{76}\) \(+12.5717 q^{77}\) \(+3.22969 q^{78}\) \(-4.96840 q^{79}\) \(+14.3319 q^{80}\) \(-10.4043 q^{81}\) \(-18.3744 q^{82}\) \(-3.29391 q^{83}\) \(+8.45467 q^{84}\) \(+7.00625 q^{85}\) \(+8.71355 q^{86}\) \(-19.6598 q^{87}\) \(+4.23680 q^{88}\) \(-10.6118 q^{89}\) \(+14.1544 q^{90}\) \(-1.66549 q^{91}\) \(-10.6362 q^{92}\) \(-6.01971 q^{93}\) \(+12.3327 q^{94}\) \(-3.08512 q^{95}\) \(+16.9345 q^{96}\) \(+10.2851 q^{97}\) \(+3.44763 q^{98}\) \(+13.3628 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.89616 −1.34079 −0.670393 0.742006i \(-0.733874\pi\)
−0.670393 + 0.742006i \(0.733874\pi\)
\(3\) 2.32800 1.34407 0.672037 0.740517i \(-0.265420\pi\)
0.672037 + 0.740517i \(0.265420\pi\)
\(4\) 1.59541 0.797707
\(5\) −3.08512 −1.37971 −0.689853 0.723950i \(-0.742325\pi\)
−0.689853 + 0.723950i \(0.742325\pi\)
\(6\) −4.41426 −1.80212
\(7\) 2.27635 0.860381 0.430190 0.902738i \(-0.358446\pi\)
0.430190 + 0.902738i \(0.358446\pi\)
\(8\) 0.767159 0.271232
\(9\) 2.41961 0.806535
\(10\) 5.84987 1.84989
\(11\) 5.52272 1.66516 0.832581 0.553904i \(-0.186862\pi\)
0.832581 + 0.553904i \(0.186862\pi\)
\(12\) 3.71413 1.07218
\(13\) −0.731648 −0.202923 −0.101461 0.994839i \(-0.532352\pi\)
−0.101461 + 0.994839i \(0.532352\pi\)
\(14\) −4.31632 −1.15359
\(15\) −7.18216 −1.85443
\(16\) −4.64548 −1.16137
\(17\) −2.27098 −0.550794 −0.275397 0.961331i \(-0.588809\pi\)
−0.275397 + 0.961331i \(0.588809\pi\)
\(18\) −4.58796 −1.08139
\(19\) 1.00000 0.229416
\(20\) −4.92204 −1.10060
\(21\) 5.29936 1.15642
\(22\) −10.4719 −2.23263
\(23\) −6.66671 −1.39010 −0.695052 0.718959i \(-0.744619\pi\)
−0.695052 + 0.718959i \(0.744619\pi\)
\(24\) 1.78595 0.364555
\(25\) 4.51794 0.903588
\(26\) 1.38732 0.272076
\(27\) −1.35116 −0.260031
\(28\) 3.63173 0.686332
\(29\) −8.44492 −1.56818 −0.784091 0.620646i \(-0.786871\pi\)
−0.784091 + 0.620646i \(0.786871\pi\)
\(30\) 13.6185 2.48639
\(31\) −2.58578 −0.464420 −0.232210 0.972666i \(-0.574596\pi\)
−0.232210 + 0.972666i \(0.574596\pi\)
\(32\) 7.27425 1.28592
\(33\) 12.8569 2.23810
\(34\) 4.30614 0.738497
\(35\) −7.02281 −1.18707
\(36\) 3.86027 0.643379
\(37\) −1.51001 −0.248244 −0.124122 0.992267i \(-0.539611\pi\)
−0.124122 + 0.992267i \(0.539611\pi\)
\(38\) −1.89616 −0.307597
\(39\) −1.70328 −0.272743
\(40\) −2.36677 −0.374220
\(41\) 9.69034 1.51338 0.756688 0.653776i \(-0.226816\pi\)
0.756688 + 0.653776i \(0.226816\pi\)
\(42\) −10.0484 −1.55051
\(43\) −4.59537 −0.700787 −0.350394 0.936603i \(-0.613952\pi\)
−0.350394 + 0.936603i \(0.613952\pi\)
\(44\) 8.81102 1.32831
\(45\) −7.46477 −1.11278
\(46\) 12.6411 1.86383
\(47\) −6.50404 −0.948711 −0.474356 0.880333i \(-0.657319\pi\)
−0.474356 + 0.880333i \(0.657319\pi\)
\(48\) −10.8147 −1.56097
\(49\) −1.81822 −0.259745
\(50\) −8.56672 −1.21152
\(51\) −5.28686 −0.740309
\(52\) −1.16728 −0.161873
\(53\) −5.13502 −0.705350 −0.352675 0.935746i \(-0.614728\pi\)
−0.352675 + 0.935746i \(0.614728\pi\)
\(54\) 2.56201 0.348646
\(55\) −17.0382 −2.29743
\(56\) 1.74632 0.233362
\(57\) 2.32800 0.308352
\(58\) 16.0129 2.10260
\(59\) −10.8330 −1.41034 −0.705171 0.709037i \(-0.749130\pi\)
−0.705171 + 0.709037i \(0.749130\pi\)
\(60\) −11.4585 −1.47929
\(61\) −4.96951 −0.636281 −0.318140 0.948044i \(-0.603058\pi\)
−0.318140 + 0.948044i \(0.603058\pi\)
\(62\) 4.90305 0.622688
\(63\) 5.50788 0.693927
\(64\) −4.50216 −0.562770
\(65\) 2.25722 0.279973
\(66\) −24.3787 −3.00081
\(67\) 7.19918 0.879520 0.439760 0.898115i \(-0.355063\pi\)
0.439760 + 0.898115i \(0.355063\pi\)
\(68\) −3.62316 −0.439373
\(69\) −15.5201 −1.86840
\(70\) 13.3164 1.59161
\(71\) 0.258044 0.0306242 0.0153121 0.999883i \(-0.495126\pi\)
0.0153121 + 0.999883i \(0.495126\pi\)
\(72\) 1.85622 0.218758
\(73\) 12.2945 1.43897 0.719483 0.694510i \(-0.244379\pi\)
0.719483 + 0.694510i \(0.244379\pi\)
\(74\) 2.86322 0.332843
\(75\) 10.5178 1.21449
\(76\) 1.59541 0.183007
\(77\) 12.5717 1.43267
\(78\) 3.22969 0.365690
\(79\) −4.96840 −0.558989 −0.279494 0.960147i \(-0.590167\pi\)
−0.279494 + 0.960147i \(0.590167\pi\)
\(80\) 14.3319 1.60235
\(81\) −10.4043 −1.15604
\(82\) −18.3744 −2.02911
\(83\) −3.29391 −0.361553 −0.180777 0.983524i \(-0.557861\pi\)
−0.180777 + 0.983524i \(0.557861\pi\)
\(84\) 8.45467 0.922481
\(85\) 7.00625 0.759934
\(86\) 8.71355 0.939606
\(87\) −19.6598 −2.10775
\(88\) 4.23680 0.451644
\(89\) −10.6118 −1.12485 −0.562426 0.826848i \(-0.690132\pi\)
−0.562426 + 0.826848i \(0.690132\pi\)
\(90\) 14.1544 1.49200
\(91\) −1.66549 −0.174591
\(92\) −10.6362 −1.10890
\(93\) −6.01971 −0.624215
\(94\) 12.3327 1.27202
\(95\) −3.08512 −0.316526
\(96\) 16.9345 1.72837
\(97\) 10.2851 1.04430 0.522149 0.852854i \(-0.325130\pi\)
0.522149 + 0.852854i \(0.325130\pi\)
\(98\) 3.44763 0.348263
\(99\) 13.3628 1.34301
\(100\) 7.20798 0.720798
\(101\) 5.98023 0.595055 0.297527 0.954713i \(-0.403838\pi\)
0.297527 + 0.954713i \(0.403838\pi\)
\(102\) 10.0247 0.992595
\(103\) −11.8444 −1.16707 −0.583534 0.812089i \(-0.698331\pi\)
−0.583534 + 0.812089i \(0.698331\pi\)
\(104\) −0.561290 −0.0550390
\(105\) −16.3491 −1.59551
\(106\) 9.73682 0.945723
\(107\) 3.41724 0.330357 0.165178 0.986264i \(-0.447180\pi\)
0.165178 + 0.986264i \(0.447180\pi\)
\(108\) −2.15566 −0.207428
\(109\) 18.8570 1.80617 0.903087 0.429459i \(-0.141296\pi\)
0.903087 + 0.429459i \(0.141296\pi\)
\(110\) 32.3071 3.08037
\(111\) −3.51532 −0.333659
\(112\) −10.5748 −0.999221
\(113\) 0.294066 0.0276634 0.0138317 0.999904i \(-0.495597\pi\)
0.0138317 + 0.999904i \(0.495597\pi\)
\(114\) −4.41426 −0.413434
\(115\) 20.5676 1.91793
\(116\) −13.4731 −1.25095
\(117\) −1.77030 −0.163664
\(118\) 20.5412 1.89097
\(119\) −5.16956 −0.473893
\(120\) −5.50986 −0.502979
\(121\) 19.5004 1.77276
\(122\) 9.42297 0.853116
\(123\) 22.5591 2.03409
\(124\) −4.12539 −0.370471
\(125\) 1.48721 0.133021
\(126\) −10.4438 −0.930408
\(127\) −1.84767 −0.163955 −0.0819773 0.996634i \(-0.526124\pi\)
−0.0819773 + 0.996634i \(0.526124\pi\)
\(128\) −6.01170 −0.531364
\(129\) −10.6980 −0.941910
\(130\) −4.28004 −0.375385
\(131\) −8.77881 −0.767008 −0.383504 0.923539i \(-0.625283\pi\)
−0.383504 + 0.923539i \(0.625283\pi\)
\(132\) 20.5121 1.78535
\(133\) 2.27635 0.197385
\(134\) −13.6508 −1.17925
\(135\) 4.16848 0.358766
\(136\) −1.74221 −0.149393
\(137\) 10.6955 0.913776 0.456888 0.889524i \(-0.348964\pi\)
0.456888 + 0.889524i \(0.348964\pi\)
\(138\) 29.4286 2.50513
\(139\) 3.39576 0.288025 0.144012 0.989576i \(-0.454000\pi\)
0.144012 + 0.989576i \(0.454000\pi\)
\(140\) −11.2043 −0.946936
\(141\) −15.1414 −1.27514
\(142\) −0.489292 −0.0410604
\(143\) −4.04068 −0.337899
\(144\) −11.2402 −0.936687
\(145\) 26.0536 2.16363
\(146\) −23.3124 −1.92935
\(147\) −4.23282 −0.349117
\(148\) −2.40909 −0.198026
\(149\) −8.52775 −0.698621 −0.349310 0.937007i \(-0.613584\pi\)
−0.349310 + 0.937007i \(0.613584\pi\)
\(150\) −19.9434 −1.62837
\(151\) 15.9320 1.29652 0.648262 0.761417i \(-0.275496\pi\)
0.648262 + 0.761417i \(0.275496\pi\)
\(152\) 0.767159 0.0622248
\(153\) −5.49489 −0.444235
\(154\) −23.8378 −1.92091
\(155\) 7.97743 0.640763
\(156\) −2.71744 −0.217569
\(157\) 6.28085 0.501267 0.250633 0.968082i \(-0.419361\pi\)
0.250633 + 0.968082i \(0.419361\pi\)
\(158\) 9.42087 0.749484
\(159\) −11.9544 −0.948042
\(160\) −22.4419 −1.77419
\(161\) −15.1758 −1.19602
\(162\) 19.7282 1.55000
\(163\) −17.3633 −1.36000 −0.680001 0.733211i \(-0.738021\pi\)
−0.680001 + 0.733211i \(0.738021\pi\)
\(164\) 15.4601 1.20723
\(165\) −39.6651 −3.08792
\(166\) 6.24576 0.484765
\(167\) −19.0969 −1.47776 −0.738881 0.673836i \(-0.764645\pi\)
−0.738881 + 0.673836i \(0.764645\pi\)
\(168\) 4.06545 0.313656
\(169\) −12.4647 −0.958822
\(170\) −13.2849 −1.01891
\(171\) 2.41961 0.185032
\(172\) −7.33152 −0.559023
\(173\) −11.2595 −0.856046 −0.428023 0.903768i \(-0.640790\pi\)
−0.428023 + 0.903768i \(0.640790\pi\)
\(174\) 37.2781 2.82605
\(175\) 10.2844 0.777429
\(176\) −25.6557 −1.93387
\(177\) −25.2194 −1.89560
\(178\) 20.1217 1.50819
\(179\) −23.7984 −1.77878 −0.889390 0.457150i \(-0.848870\pi\)
−0.889390 + 0.457150i \(0.848870\pi\)
\(180\) −11.9094 −0.887674
\(181\) −11.4578 −0.851650 −0.425825 0.904806i \(-0.640016\pi\)
−0.425825 + 0.904806i \(0.640016\pi\)
\(182\) 3.15803 0.234089
\(183\) −11.5690 −0.855208
\(184\) −5.11442 −0.377040
\(185\) 4.65856 0.342504
\(186\) 11.4143 0.836939
\(187\) −12.5420 −0.917162
\(188\) −10.3766 −0.756793
\(189\) −3.07572 −0.223725
\(190\) 5.84987 0.424394
\(191\) −20.3988 −1.47601 −0.738003 0.674798i \(-0.764231\pi\)
−0.738003 + 0.674798i \(0.764231\pi\)
\(192\) −10.4810 −0.756404
\(193\) 1.58604 0.114166 0.0570828 0.998369i \(-0.481820\pi\)
0.0570828 + 0.998369i \(0.481820\pi\)
\(194\) −19.5023 −1.40018
\(195\) 5.25482 0.376305
\(196\) −2.90081 −0.207201
\(197\) −6.09897 −0.434533 −0.217267 0.976112i \(-0.569714\pi\)
−0.217267 + 0.976112i \(0.569714\pi\)
\(198\) −25.3380 −1.80069
\(199\) 0.998849 0.0708065 0.0354032 0.999373i \(-0.488728\pi\)
0.0354032 + 0.999373i \(0.488728\pi\)
\(200\) 3.46598 0.245082
\(201\) 16.7597 1.18214
\(202\) −11.3395 −0.797841
\(203\) −19.2236 −1.34923
\(204\) −8.43473 −0.590549
\(205\) −29.8958 −2.08801
\(206\) 22.4589 1.56479
\(207\) −16.1308 −1.12117
\(208\) 3.39886 0.235668
\(209\) 5.52272 0.382014
\(210\) 31.0005 2.13924
\(211\) 1.00000 0.0688428
\(212\) −8.19249 −0.562662
\(213\) 0.600727 0.0411611
\(214\) −6.47962 −0.442938
\(215\) 14.1772 0.966880
\(216\) −1.03655 −0.0705286
\(217\) −5.88615 −0.399578
\(218\) −35.7558 −2.42169
\(219\) 28.6217 1.93408
\(220\) −27.1830 −1.83268
\(221\) 1.66156 0.111769
\(222\) 6.66559 0.447365
\(223\) −20.1905 −1.35206 −0.676029 0.736875i \(-0.736301\pi\)
−0.676029 + 0.736875i \(0.736301\pi\)
\(224\) 16.5588 1.10638
\(225\) 10.9316 0.728776
\(226\) −0.557596 −0.0370907
\(227\) 20.4304 1.35602 0.678008 0.735055i \(-0.262844\pi\)
0.678008 + 0.735055i \(0.262844\pi\)
\(228\) 3.71413 0.245974
\(229\) −1.42438 −0.0941255 −0.0470627 0.998892i \(-0.514986\pi\)
−0.0470627 + 0.998892i \(0.514986\pi\)
\(230\) −38.9993 −2.57154
\(231\) 29.2669 1.92562
\(232\) −6.47860 −0.425341
\(233\) 9.24377 0.605580 0.302790 0.953057i \(-0.402082\pi\)
0.302790 + 0.953057i \(0.402082\pi\)
\(234\) 3.35677 0.219439
\(235\) 20.0657 1.30894
\(236\) −17.2832 −1.12504
\(237\) −11.5665 −0.751323
\(238\) 9.80230 0.635389
\(239\) 14.8743 0.962140 0.481070 0.876682i \(-0.340248\pi\)
0.481070 + 0.876682i \(0.340248\pi\)
\(240\) 33.3646 2.15368
\(241\) −2.06142 −0.132788 −0.0663938 0.997793i \(-0.521149\pi\)
−0.0663938 + 0.997793i \(0.521149\pi\)
\(242\) −36.9758 −2.37690
\(243\) −20.1678 −1.29377
\(244\) −7.92843 −0.507565
\(245\) 5.60941 0.358372
\(246\) −42.7757 −2.72728
\(247\) −0.731648 −0.0465536
\(248\) −1.98371 −0.125965
\(249\) −7.66823 −0.485954
\(250\) −2.81999 −0.178352
\(251\) −15.9637 −1.00762 −0.503810 0.863814i \(-0.668069\pi\)
−0.503810 + 0.863814i \(0.668069\pi\)
\(252\) 8.78735 0.553551
\(253\) −36.8183 −2.31475
\(254\) 3.50348 0.219828
\(255\) 16.3106 1.02141
\(256\) 20.4034 1.27521
\(257\) 29.3119 1.82843 0.914214 0.405231i \(-0.132809\pi\)
0.914214 + 0.405231i \(0.132809\pi\)
\(258\) 20.2852 1.26290
\(259\) −3.43732 −0.213585
\(260\) 3.60120 0.223337
\(261\) −20.4334 −1.26479
\(262\) 16.6460 1.02839
\(263\) 2.97145 0.183227 0.0916137 0.995795i \(-0.470798\pi\)
0.0916137 + 0.995795i \(0.470798\pi\)
\(264\) 9.86329 0.607044
\(265\) 15.8421 0.973175
\(266\) −4.31632 −0.264651
\(267\) −24.7044 −1.51188
\(268\) 11.4857 0.701600
\(269\) −7.69974 −0.469461 −0.234731 0.972060i \(-0.575421\pi\)
−0.234731 + 0.972060i \(0.575421\pi\)
\(270\) −7.90410 −0.481028
\(271\) 1.13246 0.0687923 0.0343962 0.999408i \(-0.489049\pi\)
0.0343962 + 0.999408i \(0.489049\pi\)
\(272\) 10.5498 0.639676
\(273\) −3.87727 −0.234663
\(274\) −20.2803 −1.22518
\(275\) 24.9513 1.50462
\(276\) −24.7610 −1.49044
\(277\) 29.3481 1.76336 0.881679 0.471849i \(-0.156413\pi\)
0.881679 + 0.471849i \(0.156413\pi\)
\(278\) −6.43890 −0.386179
\(279\) −6.25657 −0.374571
\(280\) −5.38761 −0.321971
\(281\) −30.1794 −1.80035 −0.900177 0.435524i \(-0.856563\pi\)
−0.900177 + 0.435524i \(0.856563\pi\)
\(282\) 28.7105 1.70969
\(283\) 13.3662 0.794537 0.397269 0.917702i \(-0.369958\pi\)
0.397269 + 0.917702i \(0.369958\pi\)
\(284\) 0.411687 0.0244291
\(285\) −7.18216 −0.425435
\(286\) 7.66177 0.453050
\(287\) 22.0586 1.30208
\(288\) 17.6008 1.03714
\(289\) −11.8426 −0.696626
\(290\) −49.4016 −2.90096
\(291\) 23.9439 1.40361
\(292\) 19.6149 1.14787
\(293\) 23.7817 1.38934 0.694671 0.719328i \(-0.255550\pi\)
0.694671 + 0.719328i \(0.255550\pi\)
\(294\) 8.02609 0.468091
\(295\) 33.4212 1.94586
\(296\) −1.15842 −0.0673318
\(297\) −7.46207 −0.432993
\(298\) 16.1700 0.936701
\(299\) 4.87768 0.282084
\(300\) 16.7802 0.968806
\(301\) −10.4607 −0.602944
\(302\) −30.2095 −1.73836
\(303\) 13.9220 0.799798
\(304\) −4.64548 −0.266437
\(305\) 15.3315 0.877880
\(306\) 10.4192 0.595624
\(307\) 14.8643 0.848352 0.424176 0.905580i \(-0.360564\pi\)
0.424176 + 0.905580i \(0.360564\pi\)
\(308\) 20.0570 1.14285
\(309\) −27.5739 −1.56863
\(310\) −15.1265 −0.859126
\(311\) −8.91498 −0.505522 −0.252761 0.967529i \(-0.581339\pi\)
−0.252761 + 0.967529i \(0.581339\pi\)
\(312\) −1.30669 −0.0739766
\(313\) 2.31418 0.130805 0.0654027 0.997859i \(-0.479167\pi\)
0.0654027 + 0.997859i \(0.479167\pi\)
\(314\) −11.9095 −0.672091
\(315\) −16.9924 −0.957416
\(316\) −7.92666 −0.445909
\(317\) 13.4888 0.757608 0.378804 0.925477i \(-0.376335\pi\)
0.378804 + 0.925477i \(0.376335\pi\)
\(318\) 22.6674 1.27112
\(319\) −46.6389 −2.61128
\(320\) 13.8897 0.776457
\(321\) 7.95535 0.444024
\(322\) 28.7757 1.60361
\(323\) −2.27098 −0.126361
\(324\) −16.5992 −0.922178
\(325\) −3.30554 −0.183358
\(326\) 32.9236 1.82347
\(327\) 43.8992 2.42763
\(328\) 7.43403 0.410476
\(329\) −14.8055 −0.816253
\(330\) 75.2112 4.14024
\(331\) 14.1487 0.777682 0.388841 0.921305i \(-0.372876\pi\)
0.388841 + 0.921305i \(0.372876\pi\)
\(332\) −5.25514 −0.288413
\(333\) −3.65363 −0.200218
\(334\) 36.2107 1.98136
\(335\) −22.2103 −1.21348
\(336\) −24.6181 −1.34303
\(337\) −33.2704 −1.81235 −0.906177 0.422899i \(-0.861013\pi\)
−0.906177 + 0.422899i \(0.861013\pi\)
\(338\) 23.6350 1.28558
\(339\) 0.684588 0.0371817
\(340\) 11.1779 0.606205
\(341\) −14.2805 −0.773334
\(342\) −4.58796 −0.248088
\(343\) −20.0734 −1.08386
\(344\) −3.52538 −0.190076
\(345\) 47.8814 2.57785
\(346\) 21.3498 1.14777
\(347\) −2.57656 −0.138317 −0.0691584 0.997606i \(-0.522031\pi\)
−0.0691584 + 0.997606i \(0.522031\pi\)
\(348\) −31.3655 −1.68137
\(349\) 17.3529 0.928881 0.464440 0.885604i \(-0.346256\pi\)
0.464440 + 0.885604i \(0.346256\pi\)
\(350\) −19.5009 −1.04237
\(351\) 0.988573 0.0527661
\(352\) 40.1736 2.14126
\(353\) −4.67870 −0.249022 −0.124511 0.992218i \(-0.539736\pi\)
−0.124511 + 0.992218i \(0.539736\pi\)
\(354\) 47.8199 2.54160
\(355\) −0.796095 −0.0422523
\(356\) −16.9303 −0.897302
\(357\) −12.0348 −0.636947
\(358\) 45.1256 2.38496
\(359\) −26.0903 −1.37699 −0.688497 0.725239i \(-0.741729\pi\)
−0.688497 + 0.725239i \(0.741729\pi\)
\(360\) −5.72666 −0.301822
\(361\) 1.00000 0.0526316
\(362\) 21.7257 1.14188
\(363\) 45.3970 2.38272
\(364\) −2.65714 −0.139272
\(365\) −37.9301 −1.98535
\(366\) 21.9367 1.14665
\(367\) −16.6648 −0.869897 −0.434948 0.900455i \(-0.643233\pi\)
−0.434948 + 0.900455i \(0.643233\pi\)
\(368\) 30.9701 1.61443
\(369\) 23.4468 1.22059
\(370\) −8.83337 −0.459225
\(371\) −11.6891 −0.606869
\(372\) −9.60393 −0.497941
\(373\) −13.9629 −0.722971 −0.361486 0.932378i \(-0.617730\pi\)
−0.361486 + 0.932378i \(0.617730\pi\)
\(374\) 23.7816 1.22972
\(375\) 3.46224 0.178789
\(376\) −4.98963 −0.257320
\(377\) 6.17871 0.318220
\(378\) 5.83204 0.299968
\(379\) 12.2721 0.630377 0.315188 0.949029i \(-0.397932\pi\)
0.315188 + 0.949029i \(0.397932\pi\)
\(380\) −4.92204 −0.252495
\(381\) −4.30140 −0.220367
\(382\) 38.6793 1.97901
\(383\) −23.6871 −1.21035 −0.605177 0.796091i \(-0.706898\pi\)
−0.605177 + 0.796091i \(0.706898\pi\)
\(384\) −13.9953 −0.714192
\(385\) −38.7850 −1.97667
\(386\) −3.00738 −0.153072
\(387\) −11.1190 −0.565210
\(388\) 16.4091 0.833044
\(389\) −25.6988 −1.30298 −0.651492 0.758656i \(-0.725856\pi\)
−0.651492 + 0.758656i \(0.725856\pi\)
\(390\) −9.96396 −0.504545
\(391\) 15.1400 0.765662
\(392\) −1.39486 −0.0704511
\(393\) −20.4371 −1.03092
\(394\) 11.5646 0.582616
\(395\) 15.3281 0.771240
\(396\) 21.3192 1.07133
\(397\) −35.5477 −1.78409 −0.892045 0.451947i \(-0.850729\pi\)
−0.892045 + 0.451947i \(0.850729\pi\)
\(398\) −1.89397 −0.0949364
\(399\) 5.29936 0.265300
\(400\) −20.9880 −1.04940
\(401\) −25.8084 −1.28881 −0.644404 0.764685i \(-0.722895\pi\)
−0.644404 + 0.764685i \(0.722895\pi\)
\(402\) −31.7791 −1.58500
\(403\) 1.89188 0.0942413
\(404\) 9.54094 0.474680
\(405\) 32.0985 1.59499
\(406\) 36.4510 1.80903
\(407\) −8.33937 −0.413367
\(408\) −4.05586 −0.200795
\(409\) −6.41379 −0.317141 −0.158571 0.987348i \(-0.550689\pi\)
−0.158571 + 0.987348i \(0.550689\pi\)
\(410\) 56.6872 2.79958
\(411\) 24.8991 1.22818
\(412\) −18.8968 −0.930978
\(413\) −24.6598 −1.21343
\(414\) 30.5865 1.50325
\(415\) 10.1621 0.498837
\(416\) −5.32219 −0.260942
\(417\) 7.90535 0.387126
\(418\) −10.4719 −0.512199
\(419\) 6.68004 0.326341 0.163171 0.986598i \(-0.447828\pi\)
0.163171 + 0.986598i \(0.447828\pi\)
\(420\) −26.0836 −1.27275
\(421\) 33.9308 1.65369 0.826843 0.562433i \(-0.190135\pi\)
0.826843 + 0.562433i \(0.190135\pi\)
\(422\) −1.89616 −0.0923035
\(423\) −15.7372 −0.765169
\(424\) −3.93938 −0.191313
\(425\) −10.2602 −0.497691
\(426\) −1.13907 −0.0551883
\(427\) −11.3124 −0.547443
\(428\) 5.45191 0.263528
\(429\) −9.40673 −0.454161
\(430\) −26.8823 −1.29638
\(431\) −25.9332 −1.24916 −0.624578 0.780962i \(-0.714729\pi\)
−0.624578 + 0.780962i \(0.714729\pi\)
\(432\) 6.27679 0.301992
\(433\) −27.0827 −1.30151 −0.650756 0.759287i \(-0.725548\pi\)
−0.650756 + 0.759287i \(0.725548\pi\)
\(434\) 11.1611 0.535748
\(435\) 60.6528 2.90808
\(436\) 30.0847 1.44080
\(437\) −6.66671 −0.318912
\(438\) −54.2713 −2.59318
\(439\) 34.5516 1.64906 0.824530 0.565818i \(-0.191440\pi\)
0.824530 + 0.565818i \(0.191440\pi\)
\(440\) −13.0710 −0.623136
\(441\) −4.39937 −0.209494
\(442\) −3.15058 −0.149858
\(443\) −23.4107 −1.11228 −0.556139 0.831089i \(-0.687718\pi\)
−0.556139 + 0.831089i \(0.687718\pi\)
\(444\) −5.60838 −0.266162
\(445\) 32.7387 1.55196
\(446\) 38.2844 1.81282
\(447\) −19.8526 −0.938998
\(448\) −10.2485 −0.484196
\(449\) −12.8034 −0.604229 −0.302114 0.953272i \(-0.597692\pi\)
−0.302114 + 0.953272i \(0.597692\pi\)
\(450\) −20.7281 −0.977132
\(451\) 53.5170 2.52002
\(452\) 0.469157 0.0220673
\(453\) 37.0897 1.74262
\(454\) −38.7393 −1.81813
\(455\) 5.13823 0.240884
\(456\) 1.78595 0.0836348
\(457\) 24.8653 1.16315 0.581575 0.813493i \(-0.302437\pi\)
0.581575 + 0.813493i \(0.302437\pi\)
\(458\) 2.70084 0.126202
\(459\) 3.06846 0.143223
\(460\) 32.8138 1.52995
\(461\) 1.47167 0.0685423 0.0342712 0.999413i \(-0.489089\pi\)
0.0342712 + 0.999413i \(0.489089\pi\)
\(462\) −55.4946 −2.58184
\(463\) 21.9905 1.02198 0.510992 0.859585i \(-0.329278\pi\)
0.510992 + 0.859585i \(0.329278\pi\)
\(464\) 39.2307 1.82124
\(465\) 18.5715 0.861233
\(466\) −17.5277 −0.811953
\(467\) 18.0761 0.836462 0.418231 0.908341i \(-0.362650\pi\)
0.418231 + 0.908341i \(0.362650\pi\)
\(468\) −2.82436 −0.130556
\(469\) 16.3879 0.756722
\(470\) −38.0477 −1.75501
\(471\) 14.6219 0.673740
\(472\) −8.31067 −0.382529
\(473\) −25.3789 −1.16692
\(474\) 21.9318 1.00736
\(475\) 4.51794 0.207297
\(476\) −8.24759 −0.378028
\(477\) −12.4247 −0.568890
\(478\) −28.2041 −1.29002
\(479\) 38.0603 1.73902 0.869511 0.493914i \(-0.164434\pi\)
0.869511 + 0.493914i \(0.164434\pi\)
\(480\) −52.2448 −2.38464
\(481\) 1.10480 0.0503744
\(482\) 3.90878 0.178040
\(483\) −35.3293 −1.60754
\(484\) 31.1112 1.41415
\(485\) −31.7309 −1.44082
\(486\) 38.2414 1.73467
\(487\) −13.3572 −0.605270 −0.302635 0.953106i \(-0.597866\pi\)
−0.302635 + 0.953106i \(0.597866\pi\)
\(488\) −3.81240 −0.172579
\(489\) −40.4220 −1.82794
\(490\) −10.6363 −0.480500
\(491\) 4.18672 0.188944 0.0944720 0.995528i \(-0.469884\pi\)
0.0944720 + 0.995528i \(0.469884\pi\)
\(492\) 35.9912 1.62261
\(493\) 19.1783 0.863746
\(494\) 1.38732 0.0624185
\(495\) −41.2258 −1.85296
\(496\) 12.0122 0.539364
\(497\) 0.587399 0.0263484
\(498\) 14.5402 0.651561
\(499\) 4.46601 0.199926 0.0999630 0.994991i \(-0.468128\pi\)
0.0999630 + 0.994991i \(0.468128\pi\)
\(500\) 2.37272 0.106111
\(501\) −44.4577 −1.98622
\(502\) 30.2697 1.35100
\(503\) −34.7751 −1.55055 −0.775273 0.631626i \(-0.782388\pi\)
−0.775273 + 0.631626i \(0.782388\pi\)
\(504\) 4.22542 0.188215
\(505\) −18.4497 −0.821001
\(506\) 69.8133 3.10358
\(507\) −29.0179 −1.28873
\(508\) −2.94781 −0.130788
\(509\) 24.4115 1.08202 0.541011 0.841015i \(-0.318042\pi\)
0.541011 + 0.841015i \(0.318042\pi\)
\(510\) −30.9274 −1.36949
\(511\) 27.9867 1.23806
\(512\) −26.6647 −1.17843
\(513\) −1.35116 −0.0596551
\(514\) −55.5801 −2.45153
\(515\) 36.5415 1.61021
\(516\) −17.0678 −0.751368
\(517\) −35.9199 −1.57976
\(518\) 6.51770 0.286371
\(519\) −26.2122 −1.15059
\(520\) 1.73165 0.0759377
\(521\) −11.7435 −0.514492 −0.257246 0.966346i \(-0.582815\pi\)
−0.257246 + 0.966346i \(0.582815\pi\)
\(522\) 38.7449 1.69582
\(523\) −19.2320 −0.840957 −0.420479 0.907302i \(-0.638138\pi\)
−0.420479 + 0.907302i \(0.638138\pi\)
\(524\) −14.0058 −0.611847
\(525\) 23.9422 1.04492
\(526\) −5.63433 −0.245669
\(527\) 5.87227 0.255800
\(528\) −59.7265 −2.59926
\(529\) 21.4450 0.932390
\(530\) −30.0392 −1.30482
\(531\) −26.2117 −1.13749
\(532\) 3.63173 0.157455
\(533\) −7.08991 −0.307098
\(534\) 46.8434 2.02711
\(535\) −10.5426 −0.455795
\(536\) 5.52292 0.238554
\(537\) −55.4029 −2.39081
\(538\) 14.5999 0.629447
\(539\) −10.0415 −0.432518
\(540\) 6.65046 0.286190
\(541\) 37.3126 1.60419 0.802096 0.597195i \(-0.203718\pi\)
0.802096 + 0.597195i \(0.203718\pi\)
\(542\) −2.14733 −0.0922358
\(543\) −26.6738 −1.14468
\(544\) −16.5197 −0.708276
\(545\) −58.1760 −2.49199
\(546\) 7.35191 0.314633
\(547\) 20.9268 0.894767 0.447383 0.894342i \(-0.352356\pi\)
0.447383 + 0.894342i \(0.352356\pi\)
\(548\) 17.0637 0.728925
\(549\) −12.0243 −0.513183
\(550\) −47.3116 −2.01737
\(551\) −8.44492 −0.359766
\(552\) −11.9064 −0.506770
\(553\) −11.3098 −0.480943
\(554\) −55.6487 −2.36429
\(555\) 10.8452 0.460351
\(556\) 5.41764 0.229759
\(557\) −0.778116 −0.0329698 −0.0164849 0.999864i \(-0.505248\pi\)
−0.0164849 + 0.999864i \(0.505248\pi\)
\(558\) 11.8634 0.502220
\(559\) 3.36219 0.142206
\(560\) 32.6244 1.37863
\(561\) −29.1978 −1.23273
\(562\) 57.2250 2.41389
\(563\) 29.7582 1.25416 0.627080 0.778955i \(-0.284250\pi\)
0.627080 + 0.778955i \(0.284250\pi\)
\(564\) −24.1568 −1.01719
\(565\) −0.907228 −0.0381674
\(566\) −25.3444 −1.06530
\(567\) −23.6839 −0.994631
\(568\) 0.197961 0.00830624
\(569\) 28.7080 1.20350 0.601751 0.798684i \(-0.294470\pi\)
0.601751 + 0.798684i \(0.294470\pi\)
\(570\) 13.6185 0.570417
\(571\) −30.4712 −1.27518 −0.637590 0.770376i \(-0.720069\pi\)
−0.637590 + 0.770376i \(0.720069\pi\)
\(572\) −6.44656 −0.269544
\(573\) −47.4885 −1.98386
\(574\) −41.8266 −1.74581
\(575\) −30.1198 −1.25608
\(576\) −10.8935 −0.453894
\(577\) 39.0238 1.62458 0.812291 0.583252i \(-0.198220\pi\)
0.812291 + 0.583252i \(0.198220\pi\)
\(578\) 22.4555 0.934026
\(579\) 3.69231 0.153447
\(580\) 41.5662 1.72594
\(581\) −7.49809 −0.311073
\(582\) −45.4013 −1.88195
\(583\) −28.3593 −1.17452
\(584\) 9.43187 0.390293
\(585\) 5.46158 0.225809
\(586\) −45.0939 −1.86281
\(587\) −23.4240 −0.966811 −0.483406 0.875396i \(-0.660600\pi\)
−0.483406 + 0.875396i \(0.660600\pi\)
\(588\) −6.75310 −0.278493
\(589\) −2.58578 −0.106545
\(590\) −63.3718 −2.60898
\(591\) −14.1984 −0.584045
\(592\) 7.01473 0.288304
\(593\) −18.9687 −0.778952 −0.389476 0.921037i \(-0.627344\pi\)
−0.389476 + 0.921037i \(0.627344\pi\)
\(594\) 14.1493 0.580551
\(595\) 15.9487 0.653833
\(596\) −13.6053 −0.557295
\(597\) 2.32532 0.0951692
\(598\) −9.24885 −0.378214
\(599\) 15.0986 0.616910 0.308455 0.951239i \(-0.400188\pi\)
0.308455 + 0.951239i \(0.400188\pi\)
\(600\) 8.06881 0.329408
\(601\) 10.5525 0.430447 0.215224 0.976565i \(-0.430952\pi\)
0.215224 + 0.976565i \(0.430952\pi\)
\(602\) 19.8351 0.808419
\(603\) 17.4192 0.709364
\(604\) 25.4181 1.03425
\(605\) −60.1610 −2.44589
\(606\) −26.3983 −1.07236
\(607\) 18.8087 0.763423 0.381712 0.924281i \(-0.375335\pi\)
0.381712 + 0.924281i \(0.375335\pi\)
\(608\) 7.27425 0.295010
\(609\) −44.7527 −1.81347
\(610\) −29.0710 −1.17705
\(611\) 4.75866 0.192515
\(612\) −8.76662 −0.354370
\(613\) −40.1821 −1.62294 −0.811469 0.584395i \(-0.801332\pi\)
−0.811469 + 0.584395i \(0.801332\pi\)
\(614\) −28.1851 −1.13746
\(615\) −69.5976 −2.80645
\(616\) 9.64445 0.388586
\(617\) 16.6726 0.671212 0.335606 0.942002i \(-0.391059\pi\)
0.335606 + 0.942002i \(0.391059\pi\)
\(618\) 52.2845 2.10319
\(619\) 1.28075 0.0514776 0.0257388 0.999669i \(-0.491806\pi\)
0.0257388 + 0.999669i \(0.491806\pi\)
\(620\) 12.7273 0.511141
\(621\) 9.00778 0.361470
\(622\) 16.9042 0.677797
\(623\) −24.1563 −0.967801
\(624\) 7.91256 0.316756
\(625\) −27.1779 −1.08712
\(626\) −4.38806 −0.175382
\(627\) 12.8569 0.513455
\(628\) 10.0206 0.399864
\(629\) 3.42921 0.136732
\(630\) 32.2203 1.28369
\(631\) 16.5735 0.659781 0.329890 0.944019i \(-0.392988\pi\)
0.329890 + 0.944019i \(0.392988\pi\)
\(632\) −3.81155 −0.151615
\(633\) 2.32800 0.0925299
\(634\) −25.5769 −1.01579
\(635\) 5.70029 0.226209
\(636\) −19.0722 −0.756260
\(637\) 1.33029 0.0527082
\(638\) 88.4347 3.50116
\(639\) 0.624364 0.0246995
\(640\) 18.5468 0.733126
\(641\) 46.4913 1.83629 0.918147 0.396239i \(-0.129685\pi\)
0.918147 + 0.396239i \(0.129685\pi\)
\(642\) −15.0846 −0.595341
\(643\) 10.2482 0.404148 0.202074 0.979370i \(-0.435232\pi\)
0.202074 + 0.979370i \(0.435232\pi\)
\(644\) −24.2116 −0.954072
\(645\) 33.0047 1.29956
\(646\) 4.30614 0.169423
\(647\) −14.8252 −0.582838 −0.291419 0.956596i \(-0.594127\pi\)
−0.291419 + 0.956596i \(0.594127\pi\)
\(648\) −7.98177 −0.313554
\(649\) −59.8278 −2.34845
\(650\) 6.26783 0.245844
\(651\) −13.7030 −0.537062
\(652\) −27.7017 −1.08488
\(653\) −8.67967 −0.339662 −0.169831 0.985473i \(-0.554322\pi\)
−0.169831 + 0.985473i \(0.554322\pi\)
\(654\) −83.2398 −3.25493
\(655\) 27.0836 1.05825
\(656\) −45.0163 −1.75759
\(657\) 29.7479 1.16058
\(658\) 28.0735 1.09442
\(659\) 31.8841 1.24203 0.621015 0.783799i \(-0.286721\pi\)
0.621015 + 0.783799i \(0.286721\pi\)
\(660\) −63.2822 −2.46326
\(661\) −37.1039 −1.44318 −0.721588 0.692323i \(-0.756587\pi\)
−0.721588 + 0.692323i \(0.756587\pi\)
\(662\) −26.8281 −1.04271
\(663\) 3.86812 0.150225
\(664\) −2.52695 −0.0980646
\(665\) −7.02281 −0.272333
\(666\) 6.92787 0.268449
\(667\) 56.2998 2.17994
\(668\) −30.4674 −1.17882
\(669\) −47.0036 −1.81727
\(670\) 42.1143 1.62702
\(671\) −27.4452 −1.05951
\(672\) 38.5489 1.48705
\(673\) −22.7946 −0.878667 −0.439334 0.898324i \(-0.644785\pi\)
−0.439334 + 0.898324i \(0.644785\pi\)
\(674\) 63.0859 2.42998
\(675\) −6.10445 −0.234961
\(676\) −19.8863 −0.764859
\(677\) 19.6061 0.753523 0.376761 0.926310i \(-0.377038\pi\)
0.376761 + 0.926310i \(0.377038\pi\)
\(678\) −1.29809 −0.0498527
\(679\) 23.4126 0.898494
\(680\) 5.37491 0.206118
\(681\) 47.5621 1.82259
\(682\) 27.0781 1.03688
\(683\) −49.7870 −1.90505 −0.952523 0.304465i \(-0.901522\pi\)
−0.952523 + 0.304465i \(0.901522\pi\)
\(684\) 3.86027 0.147601
\(685\) −32.9968 −1.26074
\(686\) 38.0623 1.45322
\(687\) −3.31596 −0.126512
\(688\) 21.3477 0.813874
\(689\) 3.75703 0.143131
\(690\) −90.7906 −3.45634
\(691\) 18.0653 0.687235 0.343617 0.939110i \(-0.388348\pi\)
0.343617 + 0.939110i \(0.388348\pi\)
\(692\) −17.9636 −0.682874
\(693\) 30.4184 1.15550
\(694\) 4.88556 0.185453
\(695\) −10.4763 −0.397389
\(696\) −15.0822 −0.571689
\(697\) −22.0066 −0.833559
\(698\) −32.9039 −1.24543
\(699\) 21.5195 0.813944
\(700\) 16.4079 0.620161
\(701\) −9.62100 −0.363380 −0.181690 0.983356i \(-0.558157\pi\)
−0.181690 + 0.983356i \(0.558157\pi\)
\(702\) −1.87449 −0.0707481
\(703\) −1.51001 −0.0569512
\(704\) −24.8641 −0.937103
\(705\) 46.7131 1.75932
\(706\) 8.87156 0.333886
\(707\) 13.6131 0.511974
\(708\) −40.2353 −1.51214
\(709\) −1.77327 −0.0665967 −0.0332984 0.999445i \(-0.510601\pi\)
−0.0332984 + 0.999445i \(0.510601\pi\)
\(710\) 1.50952 0.0566513
\(711\) −12.0216 −0.450844
\(712\) −8.14096 −0.305095
\(713\) 17.2386 0.645592
\(714\) 22.8198 0.854010
\(715\) 12.4660 0.466201
\(716\) −37.9684 −1.41894
\(717\) 34.6275 1.29319
\(718\) 49.4713 1.84625
\(719\) −14.8079 −0.552241 −0.276120 0.961123i \(-0.589049\pi\)
−0.276120 + 0.961123i \(0.589049\pi\)
\(720\) 34.6774 1.29235
\(721\) −26.9621 −1.00412
\(722\) −1.89616 −0.0705677
\(723\) −4.79899 −0.178477
\(724\) −18.2799 −0.679367
\(725\) −38.1536 −1.41699
\(726\) −86.0799 −3.19472
\(727\) 21.6140 0.801618 0.400809 0.916162i \(-0.368729\pi\)
0.400809 + 0.916162i \(0.368729\pi\)
\(728\) −1.27769 −0.0473545
\(729\) −15.7379 −0.582883
\(730\) 71.9214 2.66193
\(731\) 10.4360 0.385990
\(732\) −18.4574 −0.682206
\(733\) −28.3996 −1.04896 −0.524482 0.851421i \(-0.675741\pi\)
−0.524482 + 0.851421i \(0.675741\pi\)
\(734\) 31.5991 1.16635
\(735\) 13.0587 0.481679
\(736\) −48.4953 −1.78756
\(737\) 39.7590 1.46454
\(738\) −44.4588 −1.63655
\(739\) −46.2660 −1.70192 −0.850962 0.525227i \(-0.823980\pi\)
−0.850962 + 0.525227i \(0.823980\pi\)
\(740\) 7.43233 0.273218
\(741\) −1.70328 −0.0625715
\(742\) 22.1644 0.813682
\(743\) 22.0359 0.808417 0.404209 0.914667i \(-0.367547\pi\)
0.404209 + 0.914667i \(0.367547\pi\)
\(744\) −4.61808 −0.169307
\(745\) 26.3091 0.963891
\(746\) 26.4758 0.969350
\(747\) −7.96995 −0.291605
\(748\) −20.0097 −0.731626
\(749\) 7.77884 0.284233
\(750\) −6.56496 −0.239718
\(751\) 40.5381 1.47926 0.739629 0.673015i \(-0.235001\pi\)
0.739629 + 0.673015i \(0.235001\pi\)
\(752\) 30.2144 1.10181
\(753\) −37.1636 −1.35432
\(754\) −11.7158 −0.426664
\(755\) −49.1519 −1.78882
\(756\) −4.90704 −0.178467
\(757\) 15.0943 0.548612 0.274306 0.961642i \(-0.411552\pi\)
0.274306 + 0.961642i \(0.411552\pi\)
\(758\) −23.2699 −0.845200
\(759\) −85.7132 −3.11119
\(760\) −2.36677 −0.0858519
\(761\) 10.3171 0.373995 0.186997 0.982360i \(-0.440124\pi\)
0.186997 + 0.982360i \(0.440124\pi\)
\(762\) 8.15612 0.295465
\(763\) 42.9252 1.55400
\(764\) −32.5445 −1.17742
\(765\) 16.9524 0.612914
\(766\) 44.9145 1.62283
\(767\) 7.92597 0.286190
\(768\) 47.4993 1.71398
\(769\) 4.10952 0.148193 0.0740966 0.997251i \(-0.476393\pi\)
0.0740966 + 0.997251i \(0.476393\pi\)
\(770\) 73.5425 2.65029
\(771\) 68.2383 2.45754
\(772\) 2.53039 0.0910707
\(773\) −9.62766 −0.346283 −0.173141 0.984897i \(-0.555392\pi\)
−0.173141 + 0.984897i \(0.555392\pi\)
\(774\) 21.0833 0.757825
\(775\) −11.6824 −0.419644
\(776\) 7.89034 0.283247
\(777\) −8.00210 −0.287074
\(778\) 48.7291 1.74702
\(779\) 9.69034 0.347192
\(780\) 8.38361 0.300181
\(781\) 1.42510 0.0509942
\(782\) −28.7078 −1.02659
\(783\) 11.4104 0.407776
\(784\) 8.44649 0.301661
\(785\) −19.3772 −0.691601
\(786\) 38.7520 1.38224
\(787\) −23.1976 −0.826907 −0.413453 0.910525i \(-0.635678\pi\)
−0.413453 + 0.910525i \(0.635678\pi\)
\(788\) −9.73038 −0.346630
\(789\) 6.91755 0.246271
\(790\) −29.0645 −1.03407
\(791\) 0.669399 0.0238011
\(792\) 10.2514 0.364267
\(793\) 3.63593 0.129116
\(794\) 67.4041 2.39208
\(795\) 36.8806 1.30802
\(796\) 1.59358 0.0564828
\(797\) −6.62765 −0.234764 −0.117382 0.993087i \(-0.537450\pi\)
−0.117382 + 0.993087i \(0.537450\pi\)
\(798\) −10.0484 −0.355710
\(799\) 14.7706 0.522545
\(800\) 32.8646 1.16194
\(801\) −25.6765 −0.907233
\(802\) 48.9367 1.72802
\(803\) 67.8992 2.39611
\(804\) 26.7387 0.943002
\(805\) 46.8190 1.65015
\(806\) −3.58731 −0.126357
\(807\) −17.9250 −0.630991
\(808\) 4.58779 0.161398
\(809\) −36.6407 −1.28822 −0.644109 0.764934i \(-0.722772\pi\)
−0.644109 + 0.764934i \(0.722772\pi\)
\(810\) −60.8639 −2.13854
\(811\) −30.7968 −1.08142 −0.540711 0.841209i \(-0.681845\pi\)
−0.540711 + 0.841209i \(0.681845\pi\)
\(812\) −30.6696 −1.07629
\(813\) 2.63638 0.0924620
\(814\) 15.8128 0.554237
\(815\) 53.5679 1.87640
\(816\) 24.5600 0.859773
\(817\) −4.59537 −0.160772
\(818\) 12.1616 0.425219
\(819\) −4.02983 −0.140814
\(820\) −47.6962 −1.66562
\(821\) 17.2180 0.600912 0.300456 0.953796i \(-0.402861\pi\)
0.300456 + 0.953796i \(0.402861\pi\)
\(822\) −47.2126 −1.64673
\(823\) 0.201869 0.00703672 0.00351836 0.999994i \(-0.498880\pi\)
0.00351836 + 0.999994i \(0.498880\pi\)
\(824\) −9.08657 −0.316546
\(825\) 58.0867 2.02232
\(826\) 46.7589 1.62695
\(827\) 47.6328 1.65636 0.828178 0.560465i \(-0.189378\pi\)
0.828178 + 0.560465i \(0.189378\pi\)
\(828\) −25.7353 −0.894364
\(829\) −17.2267 −0.598306 −0.299153 0.954205i \(-0.596704\pi\)
−0.299153 + 0.954205i \(0.596704\pi\)
\(830\) −19.2689 −0.668833
\(831\) 68.3226 2.37008
\(832\) 3.29399 0.114199
\(833\) 4.12914 0.143066
\(834\) −14.9898 −0.519054
\(835\) 58.9161 2.03888
\(836\) 8.81102 0.304735
\(837\) 3.49380 0.120763
\(838\) −12.6664 −0.437554
\(839\) 23.0985 0.797450 0.398725 0.917070i \(-0.369453\pi\)
0.398725 + 0.917070i \(0.369453\pi\)
\(840\) −12.5424 −0.432754
\(841\) 42.3167 1.45920
\(842\) −64.3381 −2.21724
\(843\) −70.2579 −2.41981
\(844\) 1.59541 0.0549164
\(845\) 38.4550 1.32289
\(846\) 29.8402 1.02593
\(847\) 44.3898 1.52525
\(848\) 23.8547 0.819172
\(849\) 31.1166 1.06792
\(850\) 19.4549 0.667297
\(851\) 10.0668 0.345086
\(852\) 0.958409 0.0328345
\(853\) 33.0192 1.13056 0.565279 0.824900i \(-0.308769\pi\)
0.565279 + 0.824900i \(0.308769\pi\)
\(854\) 21.4500 0.734004
\(855\) −7.46477 −0.255290
\(856\) 2.62156 0.0896032
\(857\) 51.0797 1.74485 0.872425 0.488748i \(-0.162546\pi\)
0.872425 + 0.488748i \(0.162546\pi\)
\(858\) 17.8366 0.608933
\(859\) −42.8117 −1.46072 −0.730358 0.683065i \(-0.760647\pi\)
−0.730358 + 0.683065i \(0.760647\pi\)
\(860\) 22.6186 0.771287
\(861\) 51.3526 1.75009
\(862\) 49.1734 1.67485
\(863\) 45.0771 1.53444 0.767221 0.641383i \(-0.221639\pi\)
0.767221 + 0.641383i \(0.221639\pi\)
\(864\) −9.82867 −0.334378
\(865\) 34.7369 1.18109
\(866\) 51.3531 1.74505
\(867\) −27.5697 −0.936316
\(868\) −9.39085 −0.318746
\(869\) −27.4391 −0.930807
\(870\) −115.007 −3.89911
\(871\) −5.26727 −0.178475
\(872\) 14.4663 0.489891
\(873\) 24.8860 0.842263
\(874\) 12.6411 0.427592
\(875\) 3.38543 0.114448
\(876\) 45.6635 1.54283
\(877\) 5.97682 0.201823 0.100912 0.994895i \(-0.467824\pi\)
0.100912 + 0.994895i \(0.467824\pi\)
\(878\) −65.5154 −2.21104
\(879\) 55.3639 1.86738
\(880\) 79.1507 2.66817
\(881\) −0.750727 −0.0252926 −0.0126463 0.999920i \(-0.504026\pi\)
−0.0126463 + 0.999920i \(0.504026\pi\)
\(882\) 8.34190 0.280886
\(883\) −34.1174 −1.14814 −0.574071 0.818806i \(-0.694636\pi\)
−0.574071 + 0.818806i \(0.694636\pi\)
\(884\) 2.65088 0.0891586
\(885\) 77.8047 2.61538
\(886\) 44.3905 1.49133
\(887\) −27.8845 −0.936271 −0.468136 0.883657i \(-0.655074\pi\)
−0.468136 + 0.883657i \(0.655074\pi\)
\(888\) −2.69681 −0.0904989
\(889\) −4.20596 −0.141063
\(890\) −62.0778 −2.08085
\(891\) −57.4601 −1.92499
\(892\) −32.2122 −1.07855
\(893\) −6.50404 −0.217649
\(894\) 37.6438 1.25900
\(895\) 73.4210 2.45419
\(896\) −13.6847 −0.457175
\(897\) 11.3553 0.379141
\(898\) 24.2772 0.810141
\(899\) 21.8367 0.728295
\(900\) 17.4405 0.581349
\(901\) 11.6616 0.388503
\(902\) −101.477 −3.37880
\(903\) −24.3525 −0.810401
\(904\) 0.225596 0.00750320
\(905\) 35.3486 1.17503
\(906\) −70.3279 −2.33649
\(907\) −38.1114 −1.26547 −0.632734 0.774369i \(-0.718067\pi\)
−0.632734 + 0.774369i \(0.718067\pi\)
\(908\) 32.5950 1.08170
\(909\) 14.4698 0.479933
\(910\) −9.74289 −0.322974
\(911\) −52.7748 −1.74851 −0.874253 0.485470i \(-0.838648\pi\)
−0.874253 + 0.485470i \(0.838648\pi\)
\(912\) −10.8147 −0.358111
\(913\) −18.1913 −0.602044
\(914\) −47.1486 −1.55954
\(915\) 35.6918 1.17994
\(916\) −2.27247 −0.0750846
\(917\) −19.9837 −0.659919
\(918\) −5.81828 −0.192032
\(919\) 5.34251 0.176233 0.0881165 0.996110i \(-0.471915\pi\)
0.0881165 + 0.996110i \(0.471915\pi\)
\(920\) 15.7786 0.520205
\(921\) 34.6042 1.14025
\(922\) −2.79051 −0.0919006
\(923\) −0.188797 −0.00621434
\(924\) 46.6928 1.53608
\(925\) −6.82214 −0.224311
\(926\) −41.6974 −1.37026
\(927\) −28.6589 −0.941282
\(928\) −61.4304 −2.01655
\(929\) −10.0406 −0.329421 −0.164711 0.986342i \(-0.552669\pi\)
−0.164711 + 0.986342i \(0.552669\pi\)
\(930\) −35.2145 −1.15473
\(931\) −1.81822 −0.0595897
\(932\) 14.7476 0.483075
\(933\) −20.7541 −0.679460
\(934\) −34.2751 −1.12152
\(935\) 38.6935 1.26541
\(936\) −1.35810 −0.0443909
\(937\) 8.03962 0.262643 0.131321 0.991340i \(-0.458078\pi\)
0.131321 + 0.991340i \(0.458078\pi\)
\(938\) −31.0740 −1.01460
\(939\) 5.38743 0.175812
\(940\) 32.0131 1.04415
\(941\) −3.92527 −0.127960 −0.0639801 0.997951i \(-0.520379\pi\)
−0.0639801 + 0.997951i \(0.520379\pi\)
\(942\) −27.7253 −0.903341
\(943\) −64.6026 −2.10375
\(944\) 50.3247 1.63793
\(945\) 9.48894 0.308675
\(946\) 48.1224 1.56460
\(947\) −35.5607 −1.15557 −0.577783 0.816190i \(-0.696082\pi\)
−0.577783 + 0.816190i \(0.696082\pi\)
\(948\) −18.4533 −0.599335
\(949\) −8.99527 −0.291999
\(950\) −8.56672 −0.277941
\(951\) 31.4021 1.01828
\(952\) −3.96587 −0.128535
\(953\) −26.5941 −0.861467 −0.430733 0.902479i \(-0.641745\pi\)
−0.430733 + 0.902479i \(0.641745\pi\)
\(954\) 23.5593 0.762759
\(955\) 62.9326 2.03645
\(956\) 23.7307 0.767505
\(957\) −108.576 −3.50975
\(958\) −72.1684 −2.33166
\(959\) 24.3467 0.786195
\(960\) 32.3352 1.04362
\(961\) −24.3137 −0.784314
\(962\) −2.09487 −0.0675413
\(963\) 8.26837 0.266444
\(964\) −3.28882 −0.105926
\(965\) −4.89312 −0.157515
\(966\) 66.9899 2.15536
\(967\) 11.7958 0.379328 0.189664 0.981849i \(-0.439260\pi\)
0.189664 + 0.981849i \(0.439260\pi\)
\(968\) 14.9599 0.480829
\(969\) −5.28686 −0.169838
\(970\) 60.1667 1.93184
\(971\) −22.8663 −0.733814 −0.366907 0.930258i \(-0.619583\pi\)
−0.366907 + 0.930258i \(0.619583\pi\)
\(972\) −32.1761 −1.03205
\(973\) 7.72995 0.247811
\(974\) 25.3273 0.811538
\(975\) −7.69531 −0.246447
\(976\) 23.0858 0.738957
\(977\) 30.5176 0.976346 0.488173 0.872747i \(-0.337664\pi\)
0.488173 + 0.872747i \(0.337664\pi\)
\(978\) 76.6464 2.45088
\(979\) −58.6061 −1.87306
\(980\) 8.94933 0.285876
\(981\) 45.6265 1.45674
\(982\) −7.93868 −0.253333
\(983\) 15.6256 0.498379 0.249190 0.968455i \(-0.419836\pi\)
0.249190 + 0.968455i \(0.419836\pi\)
\(984\) 17.3065 0.551710
\(985\) 18.8160 0.599528
\(986\) −36.3650 −1.15810
\(987\) −34.4672 −1.09710
\(988\) −1.16728 −0.0371362
\(989\) 30.6360 0.974167
\(990\) 78.1706 2.48442
\(991\) −14.1388 −0.449132 −0.224566 0.974459i \(-0.572097\pi\)
−0.224566 + 0.974459i \(0.572097\pi\)
\(992\) −18.8096 −0.597206
\(993\) 32.9382 1.04526
\(994\) −1.11380 −0.0353276
\(995\) −3.08156 −0.0976921
\(996\) −12.2340 −0.387649
\(997\) 10.2771 0.325479 0.162739 0.986669i \(-0.447967\pi\)
0.162739 + 0.986669i \(0.447967\pi\)
\(998\) −8.46826 −0.268058
\(999\) 2.04027 0.0645512
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 \(a_p\))