Properties

Label 4009.2.a.c.1.5
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 1.5
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.66661 q^{2}\) \(-1.96401 q^{3}\) \(+5.11081 q^{4}\) \(-2.76483 q^{5}\) \(+5.23725 q^{6}\) \(+2.50280 q^{7}\) \(-8.29531 q^{8}\) \(+0.857341 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.66661 q^{2}\) \(-1.96401 q^{3}\) \(+5.11081 q^{4}\) \(-2.76483 q^{5}\) \(+5.23725 q^{6}\) \(+2.50280 q^{7}\) \(-8.29531 q^{8}\) \(+0.857341 q^{9}\) \(+7.37272 q^{10}\) \(-4.45765 q^{11}\) \(-10.0377 q^{12}\) \(-2.71084 q^{13}\) \(-6.67400 q^{14}\) \(+5.43016 q^{15}\) \(+11.8987 q^{16}\) \(-6.37246 q^{17}\) \(-2.28619 q^{18}\) \(+1.00000 q^{19}\) \(-14.1305 q^{20}\) \(-4.91554 q^{21}\) \(+11.8868 q^{22}\) \(+4.98973 q^{23}\) \(+16.2921 q^{24}\) \(+2.64428 q^{25}\) \(+7.22875 q^{26}\) \(+4.20821 q^{27}\) \(+12.7914 q^{28}\) \(+6.14099 q^{29}\) \(-14.4801 q^{30}\) \(-4.08470 q^{31}\) \(-15.1387 q^{32}\) \(+8.75488 q^{33}\) \(+16.9929 q^{34}\) \(-6.91983 q^{35}\) \(+4.38170 q^{36}\) \(-0.469337 q^{37}\) \(-2.66661 q^{38}\) \(+5.32412 q^{39}\) \(+22.9351 q^{40}\) \(-6.42681 q^{41}\) \(+13.1078 q^{42}\) \(+9.76238 q^{43}\) \(-22.7822 q^{44}\) \(-2.37040 q^{45}\) \(-13.3057 q^{46}\) \(+13.1628 q^{47}\) \(-23.3693 q^{48}\) \(-0.735969 q^{49}\) \(-7.05126 q^{50}\) \(+12.5156 q^{51}\) \(-13.8546 q^{52}\) \(-12.3526 q^{53}\) \(-11.2216 q^{54}\) \(+12.3246 q^{55}\) \(-20.7615 q^{56}\) \(-1.96401 q^{57}\) \(-16.3756 q^{58}\) \(+8.81616 q^{59}\) \(+27.7525 q^{60}\) \(-10.6230 q^{61}\) \(+10.8923 q^{62}\) \(+2.14576 q^{63}\) \(+16.5715 q^{64}\) \(+7.49501 q^{65}\) \(-23.3458 q^{66}\) \(+5.32202 q^{67}\) \(-32.5684 q^{68}\) \(-9.79988 q^{69}\) \(+18.4525 q^{70}\) \(-14.9279 q^{71}\) \(-7.11191 q^{72}\) \(+2.77902 q^{73}\) \(+1.25154 q^{74}\) \(-5.19339 q^{75}\) \(+5.11081 q^{76}\) \(-11.1566 q^{77}\) \(-14.1973 q^{78}\) \(+4.85685 q^{79}\) \(-32.8980 q^{80}\) \(-10.8370 q^{81}\) \(+17.1378 q^{82}\) \(+14.7162 q^{83}\) \(-25.1224 q^{84}\) \(+17.6188 q^{85}\) \(-26.0325 q^{86}\) \(-12.0610 q^{87}\) \(+36.9776 q^{88}\) \(+6.53154 q^{89}\) \(+6.32093 q^{90}\) \(-6.78470 q^{91}\) \(+25.5015 q^{92}\) \(+8.02240 q^{93}\) \(-35.1001 q^{94}\) \(-2.76483 q^{95}\) \(+29.7325 q^{96}\) \(+8.97717 q^{97}\) \(+1.96254 q^{98}\) \(-3.82173 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66661 −1.88558 −0.942789 0.333390i \(-0.891807\pi\)
−0.942789 + 0.333390i \(0.891807\pi\)
\(3\) −1.96401 −1.13392 −0.566961 0.823744i \(-0.691881\pi\)
−0.566961 + 0.823744i \(0.691881\pi\)
\(4\) 5.11081 2.55540
\(5\) −2.76483 −1.23647 −0.618234 0.785994i \(-0.712152\pi\)
−0.618234 + 0.785994i \(0.712152\pi\)
\(6\) 5.23725 2.13810
\(7\) 2.50280 0.945971 0.472986 0.881070i \(-0.343176\pi\)
0.472986 + 0.881070i \(0.343176\pi\)
\(8\) −8.29531 −2.93283
\(9\) 0.857341 0.285780
\(10\) 7.37272 2.33146
\(11\) −4.45765 −1.34403 −0.672016 0.740537i \(-0.734571\pi\)
−0.672016 + 0.740537i \(0.734571\pi\)
\(12\) −10.0377 −2.89763
\(13\) −2.71084 −0.751851 −0.375926 0.926650i \(-0.622675\pi\)
−0.375926 + 0.926650i \(0.622675\pi\)
\(14\) −6.67400 −1.78370
\(15\) 5.43016 1.40206
\(16\) 11.8987 2.97468
\(17\) −6.37246 −1.54555 −0.772774 0.634681i \(-0.781132\pi\)
−0.772774 + 0.634681i \(0.781132\pi\)
\(18\) −2.28619 −0.538861
\(19\) 1.00000 0.229416
\(20\) −14.1305 −3.15968
\(21\) −4.91554 −1.07266
\(22\) 11.8868 2.53428
\(23\) 4.98973 1.04043 0.520215 0.854035i \(-0.325852\pi\)
0.520215 + 0.854035i \(0.325852\pi\)
\(24\) 16.2921 3.32561
\(25\) 2.64428 0.528856
\(26\) 7.22875 1.41767
\(27\) 4.20821 0.809870
\(28\) 12.7914 2.41734
\(29\) 6.14099 1.14035 0.570177 0.821522i \(-0.306875\pi\)
0.570177 + 0.821522i \(0.306875\pi\)
\(30\) −14.4801 −2.64369
\(31\) −4.08470 −0.733634 −0.366817 0.930293i \(-0.619552\pi\)
−0.366817 + 0.930293i \(0.619552\pi\)
\(32\) −15.1387 −2.67616
\(33\) 8.75488 1.52403
\(34\) 16.9929 2.91425
\(35\) −6.91983 −1.16966
\(36\) 4.38170 0.730284
\(37\) −0.469337 −0.0771585 −0.0385793 0.999256i \(-0.512283\pi\)
−0.0385793 + 0.999256i \(0.512283\pi\)
\(38\) −2.66661 −0.432581
\(39\) 5.32412 0.852541
\(40\) 22.9351 3.62636
\(41\) −6.42681 −1.00370 −0.501849 0.864955i \(-0.667347\pi\)
−0.501849 + 0.864955i \(0.667347\pi\)
\(42\) 13.1078 2.02258
\(43\) 9.76238 1.48875 0.744375 0.667762i \(-0.232748\pi\)
0.744375 + 0.667762i \(0.232748\pi\)
\(44\) −22.7822 −3.43454
\(45\) −2.37040 −0.353358
\(46\) −13.3057 −1.96181
\(47\) 13.1628 1.92000 0.959998 0.280006i \(-0.0903366\pi\)
0.959998 + 0.280006i \(0.0903366\pi\)
\(48\) −23.3693 −3.37306
\(49\) −0.735969 −0.105138
\(50\) −7.05126 −0.997198
\(51\) 12.5156 1.75253
\(52\) −13.8546 −1.92128
\(53\) −12.3526 −1.69676 −0.848379 0.529389i \(-0.822421\pi\)
−0.848379 + 0.529389i \(0.822421\pi\)
\(54\) −11.2216 −1.52707
\(55\) 12.3246 1.66185
\(56\) −20.7615 −2.77438
\(57\) −1.96401 −0.260140
\(58\) −16.3756 −2.15023
\(59\) 8.81616 1.14777 0.573883 0.818937i \(-0.305436\pi\)
0.573883 + 0.818937i \(0.305436\pi\)
\(60\) 27.7525 3.58283
\(61\) −10.6230 −1.36013 −0.680065 0.733152i \(-0.738048\pi\)
−0.680065 + 0.733152i \(0.738048\pi\)
\(62\) 10.8923 1.38332
\(63\) 2.14576 0.270340
\(64\) 16.5715 2.07143
\(65\) 7.49501 0.929641
\(66\) −23.3458 −2.87367
\(67\) 5.32202 0.650188 0.325094 0.945682i \(-0.394604\pi\)
0.325094 + 0.945682i \(0.394604\pi\)
\(68\) −32.5684 −3.94950
\(69\) −9.79988 −1.17977
\(70\) 18.4525 2.20549
\(71\) −14.9279 −1.77161 −0.885806 0.464055i \(-0.846394\pi\)
−0.885806 + 0.464055i \(0.846394\pi\)
\(72\) −7.11191 −0.838146
\(73\) 2.77902 0.325259 0.162630 0.986687i \(-0.448002\pi\)
0.162630 + 0.986687i \(0.448002\pi\)
\(74\) 1.25154 0.145488
\(75\) −5.19339 −0.599681
\(76\) 5.11081 0.586250
\(77\) −11.1566 −1.27142
\(78\) −14.1973 −1.60753
\(79\) 4.85685 0.546438 0.273219 0.961952i \(-0.411912\pi\)
0.273219 + 0.961952i \(0.411912\pi\)
\(80\) −32.8980 −3.67811
\(81\) −10.8370 −1.20411
\(82\) 17.1378 1.89255
\(83\) 14.7162 1.61532 0.807658 0.589652i \(-0.200735\pi\)
0.807658 + 0.589652i \(0.200735\pi\)
\(84\) −25.1224 −2.74107
\(85\) 17.6188 1.91102
\(86\) −26.0325 −2.80715
\(87\) −12.0610 −1.29307
\(88\) 36.9776 3.94182
\(89\) 6.53154 0.692342 0.346171 0.938171i \(-0.387482\pi\)
0.346171 + 0.938171i \(0.387482\pi\)
\(90\) 6.32093 0.666285
\(91\) −6.78470 −0.711230
\(92\) 25.5015 2.65872
\(93\) 8.02240 0.831884
\(94\) −35.1001 −3.62030
\(95\) −2.76483 −0.283665
\(96\) 29.7325 3.03456
\(97\) 8.97717 0.911494 0.455747 0.890109i \(-0.349372\pi\)
0.455747 + 0.890109i \(0.349372\pi\)
\(98\) 1.96254 0.198247
\(99\) −3.82173 −0.384098
\(100\) 13.5144 1.35144
\(101\) 11.0461 1.09913 0.549565 0.835451i \(-0.314793\pi\)
0.549565 + 0.835451i \(0.314793\pi\)
\(102\) −33.3742 −3.30454
\(103\) −12.7577 −1.25705 −0.628526 0.777788i \(-0.716342\pi\)
−0.628526 + 0.777788i \(0.716342\pi\)
\(104\) 22.4872 2.20506
\(105\) 13.5906 1.32631
\(106\) 32.9395 3.19937
\(107\) 5.30078 0.512446 0.256223 0.966618i \(-0.417522\pi\)
0.256223 + 0.966618i \(0.417522\pi\)
\(108\) 21.5073 2.06954
\(109\) 0.362031 0.0346763 0.0173381 0.999850i \(-0.494481\pi\)
0.0173381 + 0.999850i \(0.494481\pi\)
\(110\) −32.8650 −3.13355
\(111\) 0.921783 0.0874918
\(112\) 29.7802 2.81397
\(113\) −17.6390 −1.65934 −0.829670 0.558254i \(-0.811471\pi\)
−0.829670 + 0.558254i \(0.811471\pi\)
\(114\) 5.23725 0.490514
\(115\) −13.7957 −1.28646
\(116\) 31.3854 2.91406
\(117\) −2.32411 −0.214864
\(118\) −23.5092 −2.16420
\(119\) −15.9490 −1.46204
\(120\) −45.0448 −4.11201
\(121\) 8.87064 0.806422
\(122\) 28.3273 2.56463
\(123\) 12.6223 1.13812
\(124\) −20.8761 −1.87473
\(125\) 6.51317 0.582556
\(126\) −5.72190 −0.509747
\(127\) 19.9917 1.77397 0.886986 0.461796i \(-0.152795\pi\)
0.886986 + 0.461796i \(0.152795\pi\)
\(128\) −13.9123 −1.22968
\(129\) −19.1734 −1.68813
\(130\) −19.9863 −1.75291
\(131\) −1.66459 −0.145436 −0.0727181 0.997353i \(-0.523167\pi\)
−0.0727181 + 0.997353i \(0.523167\pi\)
\(132\) 44.7445 3.89451
\(133\) 2.50280 0.217021
\(134\) −14.1917 −1.22598
\(135\) −11.6350 −1.00138
\(136\) 52.8615 4.53284
\(137\) 11.7208 1.00138 0.500690 0.865627i \(-0.333080\pi\)
0.500690 + 0.865627i \(0.333080\pi\)
\(138\) 26.1325 2.22454
\(139\) 9.15570 0.776577 0.388288 0.921538i \(-0.373066\pi\)
0.388288 + 0.921538i \(0.373066\pi\)
\(140\) −35.3659 −2.98896
\(141\) −25.8520 −2.17713
\(142\) 39.8068 3.34051
\(143\) 12.0840 1.01051
\(144\) 10.2013 0.850106
\(145\) −16.9788 −1.41001
\(146\) −7.41055 −0.613302
\(147\) 1.44545 0.119219
\(148\) −2.39869 −0.197171
\(149\) 11.0107 0.902031 0.451015 0.892516i \(-0.351062\pi\)
0.451015 + 0.892516i \(0.351062\pi\)
\(150\) 13.8487 1.13075
\(151\) −3.53329 −0.287535 −0.143768 0.989611i \(-0.545922\pi\)
−0.143768 + 0.989611i \(0.545922\pi\)
\(152\) −8.29531 −0.672838
\(153\) −5.46337 −0.441687
\(154\) 29.7504 2.39735
\(155\) 11.2935 0.907115
\(156\) 27.2105 2.17859
\(157\) 23.2044 1.85191 0.925957 0.377630i \(-0.123261\pi\)
0.925957 + 0.377630i \(0.123261\pi\)
\(158\) −12.9513 −1.03035
\(159\) 24.2606 1.92399
\(160\) 41.8558 3.30899
\(161\) 12.4883 0.984217
\(162\) 28.8980 2.27044
\(163\) 11.5374 0.903682 0.451841 0.892099i \(-0.350767\pi\)
0.451841 + 0.892099i \(0.350767\pi\)
\(164\) −32.8462 −2.56486
\(165\) −24.2057 −1.88441
\(166\) −39.2424 −3.04580
\(167\) −13.6959 −1.05982 −0.529912 0.848053i \(-0.677775\pi\)
−0.529912 + 0.848053i \(0.677775\pi\)
\(168\) 40.7759 3.14593
\(169\) −5.65135 −0.434719
\(170\) −46.9824 −3.60338
\(171\) 0.857341 0.0655625
\(172\) 49.8936 3.80435
\(173\) −3.42622 −0.260491 −0.130245 0.991482i \(-0.541577\pi\)
−0.130245 + 0.991482i \(0.541577\pi\)
\(174\) 32.1619 2.43819
\(175\) 6.61811 0.500282
\(176\) −53.0404 −3.99807
\(177\) −17.3150 −1.30148
\(178\) −17.4171 −1.30546
\(179\) 5.32355 0.397901 0.198950 0.980010i \(-0.436247\pi\)
0.198950 + 0.980010i \(0.436247\pi\)
\(180\) −12.1147 −0.902974
\(181\) −14.2684 −1.06056 −0.530280 0.847823i \(-0.677913\pi\)
−0.530280 + 0.847823i \(0.677913\pi\)
\(182\) 18.0921 1.34108
\(183\) 20.8636 1.54228
\(184\) −41.3913 −3.05141
\(185\) 1.29764 0.0954041
\(186\) −21.3926 −1.56858
\(187\) 28.4062 2.07727
\(188\) 67.2727 4.90637
\(189\) 10.5323 0.766114
\(190\) 7.37272 0.534873
\(191\) −16.2012 −1.17227 −0.586137 0.810212i \(-0.699352\pi\)
−0.586137 + 0.810212i \(0.699352\pi\)
\(192\) −32.5465 −2.34884
\(193\) −24.6621 −1.77522 −0.887610 0.460596i \(-0.847636\pi\)
−0.887610 + 0.460596i \(0.847636\pi\)
\(194\) −23.9386 −1.71869
\(195\) −14.7203 −1.05414
\(196\) −3.76140 −0.268671
\(197\) −16.5289 −1.17763 −0.588816 0.808267i \(-0.700406\pi\)
−0.588816 + 0.808267i \(0.700406\pi\)
\(198\) 10.1911 0.724246
\(199\) −5.01692 −0.355640 −0.177820 0.984063i \(-0.556904\pi\)
−0.177820 + 0.984063i \(0.556904\pi\)
\(200\) −21.9351 −1.55105
\(201\) −10.4525 −0.737263
\(202\) −29.4557 −2.07250
\(203\) 15.3697 1.07874
\(204\) 63.9647 4.47843
\(205\) 17.7690 1.24104
\(206\) 34.0198 2.37027
\(207\) 4.27790 0.297334
\(208\) −32.2556 −2.23652
\(209\) −4.45765 −0.308342
\(210\) −36.2409 −2.50086
\(211\) 1.00000 0.0688428
\(212\) −63.1317 −4.33590
\(213\) 29.3185 2.00887
\(214\) −14.1351 −0.966256
\(215\) −26.9913 −1.84079
\(216\) −34.9084 −2.37521
\(217\) −10.2232 −0.693996
\(218\) −0.965396 −0.0653848
\(219\) −5.45802 −0.368819
\(220\) 62.9889 4.24671
\(221\) 17.2747 1.16202
\(222\) −2.45804 −0.164973
\(223\) 16.1972 1.08464 0.542322 0.840171i \(-0.317545\pi\)
0.542322 + 0.840171i \(0.317545\pi\)
\(224\) −37.8891 −2.53157
\(225\) 2.26705 0.151136
\(226\) 47.0364 3.12881
\(227\) 20.2399 1.34337 0.671684 0.740838i \(-0.265571\pi\)
0.671684 + 0.740838i \(0.265571\pi\)
\(228\) −10.0377 −0.664762
\(229\) 11.7308 0.775192 0.387596 0.921829i \(-0.373305\pi\)
0.387596 + 0.921829i \(0.373305\pi\)
\(230\) 36.7879 2.42572
\(231\) 21.9117 1.44169
\(232\) −50.9414 −3.34447
\(233\) 14.8441 0.972472 0.486236 0.873828i \(-0.338370\pi\)
0.486236 + 0.873828i \(0.338370\pi\)
\(234\) 6.19750 0.405143
\(235\) −36.3930 −2.37402
\(236\) 45.0577 2.93300
\(237\) −9.53890 −0.619618
\(238\) 42.5298 2.75680
\(239\) −1.39599 −0.0902988 −0.0451494 0.998980i \(-0.514376\pi\)
−0.0451494 + 0.998980i \(0.514376\pi\)
\(240\) 64.6120 4.17069
\(241\) −8.97454 −0.578101 −0.289051 0.957314i \(-0.593340\pi\)
−0.289051 + 0.957314i \(0.593340\pi\)
\(242\) −23.6545 −1.52057
\(243\) 8.65935 0.555498
\(244\) −54.2919 −3.47568
\(245\) 2.03483 0.130000
\(246\) −33.6588 −2.14601
\(247\) −2.71084 −0.172487
\(248\) 33.8838 2.15163
\(249\) −28.9028 −1.83164
\(250\) −17.3681 −1.09845
\(251\) 19.5062 1.23122 0.615609 0.788052i \(-0.288910\pi\)
0.615609 + 0.788052i \(0.288910\pi\)
\(252\) 10.9665 0.690828
\(253\) −22.2425 −1.39837
\(254\) −53.3099 −3.34496
\(255\) −34.6034 −2.16695
\(256\) 3.95565 0.247228
\(257\) 16.4529 1.02630 0.513152 0.858298i \(-0.328478\pi\)
0.513152 + 0.858298i \(0.328478\pi\)
\(258\) 51.1280 3.18309
\(259\) −1.17466 −0.0729898
\(260\) 38.3055 2.37561
\(261\) 5.26493 0.325891
\(262\) 4.43882 0.274231
\(263\) −3.75134 −0.231317 −0.115659 0.993289i \(-0.536898\pi\)
−0.115659 + 0.993289i \(0.536898\pi\)
\(264\) −72.6244 −4.46972
\(265\) 34.1528 2.09799
\(266\) −6.67400 −0.409209
\(267\) −12.8280 −0.785062
\(268\) 27.1998 1.66149
\(269\) 14.5866 0.889361 0.444681 0.895689i \(-0.353317\pi\)
0.444681 + 0.895689i \(0.353317\pi\)
\(270\) 31.0259 1.88818
\(271\) −11.1714 −0.678612 −0.339306 0.940676i \(-0.610192\pi\)
−0.339306 + 0.940676i \(0.610192\pi\)
\(272\) −75.8242 −4.59752
\(273\) 13.3252 0.806480
\(274\) −31.2549 −1.88818
\(275\) −11.7873 −0.710799
\(276\) −50.0853 −3.01478
\(277\) 16.8162 1.01039 0.505195 0.863005i \(-0.331421\pi\)
0.505195 + 0.863005i \(0.331421\pi\)
\(278\) −24.4147 −1.46430
\(279\) −3.50198 −0.209658
\(280\) 57.4021 3.43043
\(281\) −9.10242 −0.543005 −0.271502 0.962438i \(-0.587520\pi\)
−0.271502 + 0.962438i \(0.587520\pi\)
\(282\) 68.9371 4.10514
\(283\) −15.5475 −0.924203 −0.462102 0.886827i \(-0.652904\pi\)
−0.462102 + 0.886827i \(0.652904\pi\)
\(284\) −76.2935 −4.52718
\(285\) 5.43016 0.321655
\(286\) −32.2232 −1.90540
\(287\) −16.0850 −0.949470
\(288\) −12.9790 −0.764795
\(289\) 23.6083 1.38872
\(290\) 45.2758 2.65869
\(291\) −17.6313 −1.03356
\(292\) 14.2030 0.831169
\(293\) −23.7740 −1.38889 −0.694447 0.719544i \(-0.744351\pi\)
−0.694447 + 0.719544i \(0.744351\pi\)
\(294\) −3.85446 −0.224796
\(295\) −24.3752 −1.41918
\(296\) 3.89330 0.226293
\(297\) −18.7587 −1.08849
\(298\) −29.3612 −1.70085
\(299\) −13.5263 −0.782249
\(300\) −26.5424 −1.53243
\(301\) 24.4333 1.40831
\(302\) 9.42191 0.542170
\(303\) −21.6947 −1.24633
\(304\) 11.8987 0.682439
\(305\) 29.3707 1.68176
\(306\) 14.5687 0.832836
\(307\) 21.0146 1.19937 0.599684 0.800237i \(-0.295293\pi\)
0.599684 + 0.800237i \(0.295293\pi\)
\(308\) −57.0194 −3.24898
\(309\) 25.0563 1.42540
\(310\) −30.1153 −1.71044
\(311\) 22.2164 1.25977 0.629887 0.776687i \(-0.283101\pi\)
0.629887 + 0.776687i \(0.283101\pi\)
\(312\) −44.1652 −2.50036
\(313\) 6.69435 0.378387 0.189194 0.981940i \(-0.439413\pi\)
0.189194 + 0.981940i \(0.439413\pi\)
\(314\) −61.8771 −3.49193
\(315\) −5.93265 −0.334267
\(316\) 24.8224 1.39637
\(317\) −25.1536 −1.41277 −0.706384 0.707829i \(-0.749675\pi\)
−0.706384 + 0.707829i \(0.749675\pi\)
\(318\) −64.6936 −3.62784
\(319\) −27.3744 −1.53267
\(320\) −45.8172 −2.56126
\(321\) −10.4108 −0.581074
\(322\) −33.3015 −1.85582
\(323\) −6.37246 −0.354573
\(324\) −55.3858 −3.07699
\(325\) −7.16821 −0.397621
\(326\) −30.7658 −1.70396
\(327\) −0.711033 −0.0393202
\(328\) 53.3124 2.94368
\(329\) 32.9440 1.81626
\(330\) 64.5472 3.55321
\(331\) 12.2936 0.675716 0.337858 0.941197i \(-0.390298\pi\)
0.337858 + 0.941197i \(0.390298\pi\)
\(332\) 75.2118 4.12778
\(333\) −0.402382 −0.0220504
\(334\) 36.5217 1.99838
\(335\) −14.7145 −0.803937
\(336\) −58.4887 −3.19082
\(337\) −21.4655 −1.16930 −0.584649 0.811286i \(-0.698768\pi\)
−0.584649 + 0.811286i \(0.698768\pi\)
\(338\) 15.0700 0.819697
\(339\) 34.6432 1.88156
\(340\) 90.0461 4.88344
\(341\) 18.2082 0.986027
\(342\) −2.28619 −0.123623
\(343\) −19.3616 −1.04543
\(344\) −80.9820 −4.36625
\(345\) 27.0950 1.45875
\(346\) 9.13639 0.491176
\(347\) −18.4761 −0.991848 −0.495924 0.868366i \(-0.665170\pi\)
−0.495924 + 0.868366i \(0.665170\pi\)
\(348\) −61.6414 −3.30432
\(349\) 7.13363 0.381854 0.190927 0.981604i \(-0.438851\pi\)
0.190927 + 0.981604i \(0.438851\pi\)
\(350\) −17.6479 −0.943321
\(351\) −11.4078 −0.608902
\(352\) 67.4829 3.59685
\(353\) −32.9457 −1.75352 −0.876760 0.480927i \(-0.840300\pi\)
−0.876760 + 0.480927i \(0.840300\pi\)
\(354\) 46.1724 2.45404
\(355\) 41.2730 2.19054
\(356\) 33.3814 1.76921
\(357\) 31.3241 1.65785
\(358\) −14.1958 −0.750273
\(359\) 21.9548 1.15873 0.579365 0.815068i \(-0.303301\pi\)
0.579365 + 0.815068i \(0.303301\pi\)
\(360\) 19.6632 1.03634
\(361\) 1.00000 0.0526316
\(362\) 38.0482 1.99977
\(363\) −17.4220 −0.914420
\(364\) −34.6753 −1.81748
\(365\) −7.68350 −0.402173
\(366\) −55.6351 −2.90809
\(367\) −11.3445 −0.592176 −0.296088 0.955161i \(-0.595682\pi\)
−0.296088 + 0.955161i \(0.595682\pi\)
\(368\) 59.3715 3.09495
\(369\) −5.50996 −0.286837
\(370\) −3.46029 −0.179892
\(371\) −30.9161 −1.60508
\(372\) 41.0009 2.12580
\(373\) 14.9759 0.775420 0.387710 0.921781i \(-0.373266\pi\)
0.387710 + 0.921781i \(0.373266\pi\)
\(374\) −75.7482 −3.91685
\(375\) −12.7919 −0.660573
\(376\) −109.190 −5.63103
\(377\) −16.6472 −0.857377
\(378\) −28.0856 −1.44457
\(379\) −37.3644 −1.91928 −0.959641 0.281227i \(-0.909259\pi\)
−0.959641 + 0.281227i \(0.909259\pi\)
\(380\) −14.1305 −0.724880
\(381\) −39.2638 −2.01155
\(382\) 43.2022 2.21041
\(383\) 35.5848 1.81830 0.909149 0.416471i \(-0.136733\pi\)
0.909149 + 0.416471i \(0.136733\pi\)
\(384\) 27.3238 1.39436
\(385\) 30.8462 1.57207
\(386\) 65.7643 3.34731
\(387\) 8.36969 0.425455
\(388\) 45.8806 2.32923
\(389\) 25.4532 1.29053 0.645264 0.763960i \(-0.276747\pi\)
0.645264 + 0.763960i \(0.276747\pi\)
\(390\) 39.2532 1.98766
\(391\) −31.7968 −1.60804
\(392\) 6.10509 0.308354
\(393\) 3.26928 0.164913
\(394\) 44.0760 2.22052
\(395\) −13.4283 −0.675653
\(396\) −19.5321 −0.981525
\(397\) −10.3768 −0.520796 −0.260398 0.965501i \(-0.583854\pi\)
−0.260398 + 0.965501i \(0.583854\pi\)
\(398\) 13.3782 0.670587
\(399\) −4.91554 −0.246085
\(400\) 31.4636 1.57318
\(401\) −18.2985 −0.913784 −0.456892 0.889522i \(-0.651037\pi\)
−0.456892 + 0.889522i \(0.651037\pi\)
\(402\) 27.8728 1.39017
\(403\) 11.0730 0.551583
\(404\) 56.4546 2.80872
\(405\) 29.9624 1.48884
\(406\) −40.9850 −2.03405
\(407\) 2.09214 0.103704
\(408\) −103.821 −5.13989
\(409\) −29.8158 −1.47429 −0.737147 0.675732i \(-0.763828\pi\)
−0.737147 + 0.675732i \(0.763828\pi\)
\(410\) −47.3830 −2.34008
\(411\) −23.0199 −1.13549
\(412\) −65.2021 −3.21228
\(413\) 22.0651 1.08575
\(414\) −11.4075 −0.560647
\(415\) −40.6878 −1.99729
\(416\) 41.0385 2.01208
\(417\) −17.9819 −0.880578
\(418\) 11.8868 0.581403
\(419\) 22.0042 1.07497 0.537487 0.843272i \(-0.319374\pi\)
0.537487 + 0.843272i \(0.319374\pi\)
\(420\) 69.4590 3.38925
\(421\) −22.6175 −1.10231 −0.551155 0.834403i \(-0.685813\pi\)
−0.551155 + 0.834403i \(0.685813\pi\)
\(422\) −2.66661 −0.129809
\(423\) 11.2850 0.548697
\(424\) 102.469 4.97631
\(425\) −16.8506 −0.817372
\(426\) −78.1810 −3.78788
\(427\) −26.5872 −1.28664
\(428\) 27.0913 1.30951
\(429\) −23.7331 −1.14584
\(430\) 71.9753 3.47096
\(431\) −34.6128 −1.66724 −0.833619 0.552340i \(-0.813735\pi\)
−0.833619 + 0.552340i \(0.813735\pi\)
\(432\) 50.0724 2.40911
\(433\) −1.38682 −0.0666465 −0.0333233 0.999445i \(-0.510609\pi\)
−0.0333233 + 0.999445i \(0.510609\pi\)
\(434\) 27.2613 1.30858
\(435\) 33.3465 1.59884
\(436\) 1.85027 0.0886119
\(437\) 4.98973 0.238691
\(438\) 14.5544 0.695437
\(439\) 10.9221 0.521284 0.260642 0.965435i \(-0.416066\pi\)
0.260642 + 0.965435i \(0.416066\pi\)
\(440\) −102.237 −4.87394
\(441\) −0.630976 −0.0300465
\(442\) −46.0649 −2.19108
\(443\) −7.67323 −0.364566 −0.182283 0.983246i \(-0.558349\pi\)
−0.182283 + 0.983246i \(0.558349\pi\)
\(444\) 4.71106 0.223577
\(445\) −18.0586 −0.856059
\(446\) −43.1916 −2.04518
\(447\) −21.6251 −1.02283
\(448\) 41.4751 1.95951
\(449\) 11.4850 0.542008 0.271004 0.962578i \(-0.412644\pi\)
0.271004 + 0.962578i \(0.412644\pi\)
\(450\) −6.04533 −0.284980
\(451\) 28.6485 1.34900
\(452\) −90.1497 −4.24028
\(453\) 6.93942 0.326043
\(454\) −53.9719 −2.53303
\(455\) 18.7585 0.879414
\(456\) 16.2921 0.762947
\(457\) −19.2851 −0.902117 −0.451059 0.892494i \(-0.648953\pi\)
−0.451059 + 0.892494i \(0.648953\pi\)
\(458\) −31.2814 −1.46169
\(459\) −26.8166 −1.25169
\(460\) −70.5074 −3.28742
\(461\) 21.5088 1.00176 0.500882 0.865516i \(-0.333009\pi\)
0.500882 + 0.865516i \(0.333009\pi\)
\(462\) −58.4301 −2.71841
\(463\) −19.9383 −0.926613 −0.463307 0.886198i \(-0.653337\pi\)
−0.463307 + 0.886198i \(0.653337\pi\)
\(464\) 73.0701 3.39219
\(465\) −22.1805 −1.02860
\(466\) −39.5835 −1.83367
\(467\) 9.98586 0.462091 0.231045 0.972943i \(-0.425785\pi\)
0.231045 + 0.972943i \(0.425785\pi\)
\(468\) −11.8781 −0.549065
\(469\) 13.3200 0.615059
\(470\) 97.0459 4.47639
\(471\) −45.5737 −2.09993
\(472\) −73.1327 −3.36621
\(473\) −43.5173 −2.00093
\(474\) 25.4365 1.16834
\(475\) 2.64428 0.121328
\(476\) −81.5124 −3.73611
\(477\) −10.5904 −0.484900
\(478\) 3.72255 0.170265
\(479\) −8.11650 −0.370852 −0.185426 0.982658i \(-0.559367\pi\)
−0.185426 + 0.982658i \(0.559367\pi\)
\(480\) −82.2053 −3.75214
\(481\) 1.27230 0.0580118
\(482\) 23.9316 1.09005
\(483\) −24.5272 −1.11603
\(484\) 45.3361 2.06073
\(485\) −24.8203 −1.12703
\(486\) −23.0911 −1.04743
\(487\) 2.92797 0.132679 0.0663394 0.997797i \(-0.478868\pi\)
0.0663394 + 0.997797i \(0.478868\pi\)
\(488\) 88.1207 3.98904
\(489\) −22.6597 −1.02471
\(490\) −5.42609 −0.245126
\(491\) −29.3198 −1.32318 −0.661591 0.749865i \(-0.730119\pi\)
−0.661591 + 0.749865i \(0.730119\pi\)
\(492\) 64.5103 2.90835
\(493\) −39.1332 −1.76247
\(494\) 7.22875 0.325237
\(495\) 10.5664 0.474925
\(496\) −48.6028 −2.18233
\(497\) −37.3615 −1.67589
\(498\) 77.0726 3.45370
\(499\) −38.6208 −1.72890 −0.864452 0.502716i \(-0.832334\pi\)
−0.864452 + 0.502716i \(0.832334\pi\)
\(500\) 33.2876 1.48866
\(501\) 26.8990 1.20176
\(502\) −52.0153 −2.32156
\(503\) −29.4445 −1.31287 −0.656434 0.754384i \(-0.727936\pi\)
−0.656434 + 0.754384i \(0.727936\pi\)
\(504\) −17.7997 −0.792862
\(505\) −30.5406 −1.35904
\(506\) 59.3120 2.63674
\(507\) 11.0993 0.492938
\(508\) 102.173 4.53321
\(509\) −24.6909 −1.09441 −0.547203 0.837000i \(-0.684307\pi\)
−0.547203 + 0.837000i \(0.684307\pi\)
\(510\) 92.2739 4.08596
\(511\) 6.95533 0.307686
\(512\) 17.2763 0.763514
\(513\) 4.20821 0.185797
\(514\) −43.8735 −1.93518
\(515\) 35.2728 1.55431
\(516\) −97.9917 −4.31384
\(517\) −58.6753 −2.58054
\(518\) 3.13236 0.137628
\(519\) 6.72914 0.295376
\(520\) −62.1734 −2.72648
\(521\) −38.6480 −1.69320 −0.846600 0.532230i \(-0.821354\pi\)
−0.846600 + 0.532230i \(0.821354\pi\)
\(522\) −14.0395 −0.614492
\(523\) 17.7956 0.778147 0.389074 0.921207i \(-0.372795\pi\)
0.389074 + 0.921207i \(0.372795\pi\)
\(524\) −8.50742 −0.371648
\(525\) −12.9980 −0.567281
\(526\) 10.0033 0.436167
\(527\) 26.0296 1.13387
\(528\) 104.172 4.53350
\(529\) 1.89738 0.0824948
\(530\) −91.0721 −3.95592
\(531\) 7.55845 0.328009
\(532\) 12.7914 0.554575
\(533\) 17.4220 0.754632
\(534\) 34.2073 1.48030
\(535\) −14.6557 −0.633623
\(536\) −44.1478 −1.90689
\(537\) −10.4555 −0.451189
\(538\) −38.8968 −1.67696
\(539\) 3.28069 0.141309
\(540\) −59.4641 −2.55893
\(541\) −27.1497 −1.16726 −0.583628 0.812021i \(-0.698367\pi\)
−0.583628 + 0.812021i \(0.698367\pi\)
\(542\) 29.7896 1.27957
\(543\) 28.0233 1.20259
\(544\) 96.4706 4.13614
\(545\) −1.00095 −0.0428762
\(546\) −35.5332 −1.52068
\(547\) 18.5459 0.792964 0.396482 0.918043i \(-0.370231\pi\)
0.396482 + 0.918043i \(0.370231\pi\)
\(548\) 59.9030 2.55893
\(549\) −9.10749 −0.388698
\(550\) 31.4320 1.34027
\(551\) 6.14099 0.261615
\(552\) 81.2931 3.46006
\(553\) 12.1557 0.516914
\(554\) −44.8423 −1.90517
\(555\) −2.54857 −0.108181
\(556\) 46.7930 1.98447
\(557\) −10.0251 −0.424777 −0.212389 0.977185i \(-0.568124\pi\)
−0.212389 + 0.977185i \(0.568124\pi\)
\(558\) 9.33841 0.395327
\(559\) −26.4642 −1.11932
\(560\) −82.3372 −3.47938
\(561\) −55.7901 −2.35546
\(562\) 24.2726 1.02388
\(563\) 14.3200 0.603518 0.301759 0.953384i \(-0.402426\pi\)
0.301759 + 0.953384i \(0.402426\pi\)
\(564\) −132.124 −5.56344
\(565\) 48.7689 2.05172
\(566\) 41.4591 1.74266
\(567\) −27.1229 −1.13905
\(568\) 123.831 5.19585
\(569\) −1.68496 −0.0706374 −0.0353187 0.999376i \(-0.511245\pi\)
−0.0353187 + 0.999376i \(0.511245\pi\)
\(570\) −14.4801 −0.606505
\(571\) −11.7480 −0.491640 −0.245820 0.969316i \(-0.579057\pi\)
−0.245820 + 0.969316i \(0.579057\pi\)
\(572\) 61.7588 2.58227
\(573\) 31.8193 1.32927
\(574\) 42.8925 1.79030
\(575\) 13.1942 0.550237
\(576\) 14.2074 0.591974
\(577\) −1.85353 −0.0771635 −0.0385818 0.999255i \(-0.512284\pi\)
−0.0385818 + 0.999255i \(0.512284\pi\)
\(578\) −62.9540 −2.61854
\(579\) 48.4367 2.01296
\(580\) −86.7754 −3.60315
\(581\) 36.8318 1.52804
\(582\) 47.0157 1.94886
\(583\) 55.0635 2.28050
\(584\) −23.0528 −0.953932
\(585\) 6.42577 0.265673
\(586\) 63.3960 2.61887
\(587\) 18.8302 0.777207 0.388603 0.921405i \(-0.372958\pi\)
0.388603 + 0.921405i \(0.372958\pi\)
\(588\) 7.38743 0.304652
\(589\) −4.08470 −0.168307
\(590\) 64.9990 2.67597
\(591\) 32.4629 1.33534
\(592\) −5.58452 −0.229522
\(593\) 5.19699 0.213415 0.106707 0.994290i \(-0.465969\pi\)
0.106707 + 0.994290i \(0.465969\pi\)
\(594\) 50.0222 2.05243
\(595\) 44.0963 1.80777
\(596\) 56.2735 2.30505
\(597\) 9.85328 0.403268
\(598\) 36.0695 1.47499
\(599\) 7.90423 0.322958 0.161479 0.986876i \(-0.448374\pi\)
0.161479 + 0.986876i \(0.448374\pi\)
\(600\) 43.0808 1.75877
\(601\) −36.0806 −1.47176 −0.735879 0.677114i \(-0.763231\pi\)
−0.735879 + 0.677114i \(0.763231\pi\)
\(602\) −65.1542 −2.65549
\(603\) 4.56278 0.185811
\(604\) −18.0580 −0.734768
\(605\) −24.5258 −0.997116
\(606\) 57.8513 2.35005
\(607\) 18.0646 0.733218 0.366609 0.930375i \(-0.380519\pi\)
0.366609 + 0.930375i \(0.380519\pi\)
\(608\) −15.1387 −0.613954
\(609\) −30.1863 −1.22321
\(610\) −78.3201 −3.17109
\(611\) −35.6823 −1.44355
\(612\) −27.9222 −1.12869
\(613\) −22.8101 −0.921290 −0.460645 0.887584i \(-0.652382\pi\)
−0.460645 + 0.887584i \(0.652382\pi\)
\(614\) −56.0378 −2.26150
\(615\) −34.8986 −1.40725
\(616\) 92.5477 3.72885
\(617\) 13.0552 0.525581 0.262791 0.964853i \(-0.415357\pi\)
0.262791 + 0.964853i \(0.415357\pi\)
\(618\) −66.8152 −2.68770
\(619\) 16.9702 0.682091 0.341045 0.940047i \(-0.389219\pi\)
0.341045 + 0.940047i \(0.389219\pi\)
\(620\) 57.7189 2.31805
\(621\) 20.9978 0.842613
\(622\) −59.2424 −2.37540
\(623\) 16.3472 0.654935
\(624\) 63.3503 2.53604
\(625\) −31.2292 −1.24917
\(626\) −17.8512 −0.713478
\(627\) 8.75488 0.349636
\(628\) 118.593 4.73239
\(629\) 2.99083 0.119252
\(630\) 15.8201 0.630286
\(631\) 31.4802 1.25321 0.626604 0.779338i \(-0.284444\pi\)
0.626604 + 0.779338i \(0.284444\pi\)
\(632\) −40.2890 −1.60261
\(633\) −1.96401 −0.0780624
\(634\) 67.0749 2.66388
\(635\) −55.2735 −2.19346
\(636\) 123.991 4.91658
\(637\) 1.99509 0.0790485
\(638\) 72.9968 2.88997
\(639\) −12.7983 −0.506292
\(640\) 38.4650 1.52046
\(641\) −13.3209 −0.526143 −0.263072 0.964776i \(-0.584736\pi\)
−0.263072 + 0.964776i \(0.584736\pi\)
\(642\) 27.7615 1.09566
\(643\) −10.8218 −0.426770 −0.213385 0.976968i \(-0.568449\pi\)
−0.213385 + 0.976968i \(0.568449\pi\)
\(644\) 63.8254 2.51507
\(645\) 53.0112 2.08732
\(646\) 16.9929 0.668575
\(647\) −31.2529 −1.22868 −0.614340 0.789042i \(-0.710578\pi\)
−0.614340 + 0.789042i \(0.710578\pi\)
\(648\) 89.8962 3.53146
\(649\) −39.2993 −1.54263
\(650\) 19.1148 0.749745
\(651\) 20.0785 0.786938
\(652\) 58.9656 2.30927
\(653\) 31.7739 1.24341 0.621704 0.783253i \(-0.286441\pi\)
0.621704 + 0.783253i \(0.286441\pi\)
\(654\) 1.89605 0.0741413
\(655\) 4.60232 0.179827
\(656\) −76.4709 −2.98569
\(657\) 2.38256 0.0929527
\(658\) −87.8488 −3.42470
\(659\) 3.28492 0.127962 0.0639811 0.997951i \(-0.479620\pi\)
0.0639811 + 0.997951i \(0.479620\pi\)
\(660\) −123.711 −4.81544
\(661\) 6.07036 0.236110 0.118055 0.993007i \(-0.462334\pi\)
0.118055 + 0.993007i \(0.462334\pi\)
\(662\) −32.7822 −1.27412
\(663\) −33.9277 −1.31764
\(664\) −122.076 −4.73745
\(665\) −6.91983 −0.268339
\(666\) 1.07300 0.0415777
\(667\) 30.6419 1.18646
\(668\) −69.9973 −2.70828
\(669\) −31.8114 −1.22990
\(670\) 39.2378 1.51589
\(671\) 47.3534 1.82806
\(672\) 74.4147 2.87061
\(673\) 26.0860 1.00554 0.502771 0.864420i \(-0.332314\pi\)
0.502771 + 0.864420i \(0.332314\pi\)
\(674\) 57.2400 2.20480
\(675\) 11.1277 0.428304
\(676\) −28.8830 −1.11088
\(677\) 33.8848 1.30230 0.651149 0.758950i \(-0.274287\pi\)
0.651149 + 0.758950i \(0.274287\pi\)
\(678\) −92.3800 −3.54783
\(679\) 22.4681 0.862247
\(680\) −146.153 −5.60471
\(681\) −39.7514 −1.52328
\(682\) −48.5540 −1.85923
\(683\) −25.7275 −0.984437 −0.492219 0.870472i \(-0.663814\pi\)
−0.492219 + 0.870472i \(0.663814\pi\)
\(684\) 4.38170 0.167539
\(685\) −32.4061 −1.23817
\(686\) 51.6299 1.97124
\(687\) −23.0394 −0.879008
\(688\) 116.160 4.42856
\(689\) 33.4859 1.27571
\(690\) −72.2518 −2.75058
\(691\) −39.1024 −1.48753 −0.743763 0.668443i \(-0.766961\pi\)
−0.743763 + 0.668443i \(0.766961\pi\)
\(692\) −17.5108 −0.665659
\(693\) −9.56503 −0.363346
\(694\) 49.2685 1.87021
\(695\) −25.3140 −0.960213
\(696\) 100.050 3.79237
\(697\) 40.9546 1.55127
\(698\) −19.0226 −0.720016
\(699\) −29.1541 −1.10271
\(700\) 33.8239 1.27842
\(701\) −0.268417 −0.0101380 −0.00506898 0.999987i \(-0.501614\pi\)
−0.00506898 + 0.999987i \(0.501614\pi\)
\(702\) 30.4201 1.14813
\(703\) −0.469337 −0.0177014
\(704\) −73.8697 −2.78407
\(705\) 71.4762 2.69195
\(706\) 87.8532 3.30640
\(707\) 27.6463 1.03975
\(708\) −88.4938 −3.32580
\(709\) −38.8234 −1.45804 −0.729022 0.684490i \(-0.760025\pi\)
−0.729022 + 0.684490i \(0.760025\pi\)
\(710\) −110.059 −4.13044
\(711\) 4.16397 0.156161
\(712\) −54.1811 −2.03052
\(713\) −20.3815 −0.763294
\(714\) −83.5291 −3.12600
\(715\) −33.4101 −1.24947
\(716\) 27.2076 1.01680
\(717\) 2.74173 0.102392
\(718\) −58.5449 −2.18488
\(719\) 38.1679 1.42342 0.711711 0.702472i \(-0.247920\pi\)
0.711711 + 0.702472i \(0.247920\pi\)
\(720\) −28.2048 −1.05113
\(721\) −31.9300 −1.18914
\(722\) −2.66661 −0.0992409
\(723\) 17.6261 0.655522
\(724\) −72.9229 −2.71016
\(725\) 16.2385 0.603082
\(726\) 46.4578 1.72421
\(727\) 18.3995 0.682400 0.341200 0.939991i \(-0.389167\pi\)
0.341200 + 0.939991i \(0.389167\pi\)
\(728\) 56.2812 2.08592
\(729\) 15.5039 0.574219
\(730\) 20.4889 0.758328
\(731\) −62.2104 −2.30093
\(732\) 106.630 3.94115
\(733\) 26.0551 0.962365 0.481183 0.876620i \(-0.340207\pi\)
0.481183 + 0.876620i \(0.340207\pi\)
\(734\) 30.2512 1.11659
\(735\) −3.99643 −0.147410
\(736\) −75.5378 −2.78436
\(737\) −23.7237 −0.873874
\(738\) 14.6929 0.540854
\(739\) −27.1452 −0.998552 −0.499276 0.866443i \(-0.666401\pi\)
−0.499276 + 0.866443i \(0.666401\pi\)
\(740\) 6.63197 0.243796
\(741\) 5.32412 0.195586
\(742\) 82.4412 3.02651
\(743\) 23.5174 0.862771 0.431385 0.902168i \(-0.358025\pi\)
0.431385 + 0.902168i \(0.358025\pi\)
\(744\) −66.5483 −2.43978
\(745\) −30.4427 −1.11533
\(746\) −39.9348 −1.46212
\(747\) 12.6168 0.461625
\(748\) 145.179 5.30826
\(749\) 13.2668 0.484759
\(750\) 34.1111 1.24556
\(751\) 14.5246 0.530011 0.265005 0.964247i \(-0.414626\pi\)
0.265005 + 0.964247i \(0.414626\pi\)
\(752\) 156.621 5.71138
\(753\) −38.3103 −1.39611
\(754\) 44.3917 1.61665
\(755\) 9.76894 0.355528
\(756\) 53.8287 1.95773
\(757\) −0.249201 −0.00905735 −0.00452867 0.999990i \(-0.501442\pi\)
−0.00452867 + 0.999990i \(0.501442\pi\)
\(758\) 99.6364 3.61896
\(759\) 43.6844 1.58564
\(760\) 22.9351 0.831944
\(761\) −6.35173 −0.230250 −0.115125 0.993351i \(-0.536727\pi\)
−0.115125 + 0.993351i \(0.536727\pi\)
\(762\) 104.701 3.79293
\(763\) 0.906093 0.0328028
\(764\) −82.8010 −2.99563
\(765\) 15.1053 0.546133
\(766\) −94.8908 −3.42854
\(767\) −23.8992 −0.862949
\(768\) −7.76893 −0.280337
\(769\) 34.3504 1.23871 0.619353 0.785112i \(-0.287395\pi\)
0.619353 + 0.785112i \(0.287395\pi\)
\(770\) −82.2547 −2.96425
\(771\) −32.3137 −1.16375
\(772\) −126.043 −4.53640
\(773\) −51.6954 −1.85935 −0.929677 0.368375i \(-0.879914\pi\)
−0.929677 + 0.368375i \(0.879914\pi\)
\(774\) −22.3187 −0.802229
\(775\) −10.8011 −0.387986
\(776\) −74.4684 −2.67326
\(777\) 2.30704 0.0827647
\(778\) −67.8737 −2.43339
\(779\) −6.42681 −0.230264
\(780\) −75.2325 −2.69376
\(781\) 66.5432 2.38110
\(782\) 84.7898 3.03208
\(783\) 25.8426 0.923538
\(784\) −8.75710 −0.312754
\(785\) −64.1562 −2.28983
\(786\) −8.71790 −0.310957
\(787\) −24.5017 −0.873392 −0.436696 0.899609i \(-0.643851\pi\)
−0.436696 + 0.899609i \(0.643851\pi\)
\(788\) −84.4758 −3.00933
\(789\) 7.36767 0.262296
\(790\) 35.8082 1.27400
\(791\) −44.1470 −1.56969
\(792\) 31.7024 1.12650
\(793\) 28.7971 1.02262
\(794\) 27.6708 0.982001
\(795\) −67.0764 −2.37896
\(796\) −25.6405 −0.908803
\(797\) −1.86395 −0.0660244 −0.0330122 0.999455i \(-0.510510\pi\)
−0.0330122 + 0.999455i \(0.510510\pi\)
\(798\) 13.1078 0.464012
\(799\) −83.8796 −2.96745
\(800\) −40.0308 −1.41530
\(801\) 5.59976 0.197858
\(802\) 48.7950 1.72301
\(803\) −12.3879 −0.437159
\(804\) −53.4207 −1.88400
\(805\) −34.5280 −1.21695
\(806\) −29.5273 −1.04005
\(807\) −28.6483 −1.00847
\(808\) −91.6310 −3.22357
\(809\) −12.5263 −0.440403 −0.220201 0.975454i \(-0.570671\pi\)
−0.220201 + 0.975454i \(0.570671\pi\)
\(810\) −79.8981 −2.80733
\(811\) −32.0391 −1.12505 −0.562523 0.826782i \(-0.690169\pi\)
−0.562523 + 0.826782i \(0.690169\pi\)
\(812\) 78.5516 2.75662
\(813\) 21.9407 0.769493
\(814\) −5.57892 −0.195541
\(815\) −31.8990 −1.11737
\(816\) 148.920 5.21323
\(817\) 9.76238 0.341542
\(818\) 79.5070 2.77990
\(819\) −5.81680 −0.203255
\(820\) 90.8140 3.17136
\(821\) 31.4612 1.09800 0.549001 0.835822i \(-0.315008\pi\)
0.549001 + 0.835822i \(0.315008\pi\)
\(822\) 61.3850 2.14105
\(823\) 33.4667 1.16658 0.583288 0.812265i \(-0.301766\pi\)
0.583288 + 0.812265i \(0.301766\pi\)
\(824\) 105.829 3.68673
\(825\) 23.1503 0.805991
\(826\) −58.8391 −2.04727
\(827\) 1.92766 0.0670314 0.0335157 0.999438i \(-0.489330\pi\)
0.0335157 + 0.999438i \(0.489330\pi\)
\(828\) 21.8635 0.759810
\(829\) −34.9913 −1.21530 −0.607649 0.794206i \(-0.707887\pi\)
−0.607649 + 0.794206i \(0.707887\pi\)
\(830\) 108.499 3.76604
\(831\) −33.0273 −1.14570
\(832\) −44.9225 −1.55741
\(833\) 4.68993 0.162497
\(834\) 47.9507 1.66040
\(835\) 37.8669 1.31044
\(836\) −22.7822 −0.787939
\(837\) −17.1893 −0.594148
\(838\) −58.6765 −2.02695
\(839\) 6.36356 0.219694 0.109847 0.993948i \(-0.464964\pi\)
0.109847 + 0.993948i \(0.464964\pi\)
\(840\) −112.738 −3.88984
\(841\) 8.71181 0.300407
\(842\) 60.3121 2.07849
\(843\) 17.8773 0.615725
\(844\) 5.11081 0.175921
\(845\) 15.6250 0.537517
\(846\) −30.0928 −1.03461
\(847\) 22.2015 0.762852
\(848\) −146.980 −5.04732
\(849\) 30.5355 1.04797
\(850\) 44.9339 1.54122
\(851\) −2.34186 −0.0802781
\(852\) 149.841 5.13348
\(853\) −11.9539 −0.409292 −0.204646 0.978836i \(-0.565604\pi\)
−0.204646 + 0.978836i \(0.565604\pi\)
\(854\) 70.8976 2.42607
\(855\) −2.37040 −0.0810660
\(856\) −43.9716 −1.50292
\(857\) −11.8226 −0.403854 −0.201927 0.979401i \(-0.564720\pi\)
−0.201927 + 0.979401i \(0.564720\pi\)
\(858\) 63.2868 2.16058
\(859\) 17.6982 0.603855 0.301928 0.953331i \(-0.402370\pi\)
0.301928 + 0.953331i \(0.402370\pi\)
\(860\) −137.947 −4.70397
\(861\) 31.5912 1.07663
\(862\) 92.2987 3.14371
\(863\) −12.6011 −0.428945 −0.214472 0.976730i \(-0.568803\pi\)
−0.214472 + 0.976730i \(0.568803\pi\)
\(864\) −63.7067 −2.16734
\(865\) 9.47291 0.322089
\(866\) 3.69812 0.125667
\(867\) −46.3669 −1.57470
\(868\) −52.2488 −1.77344
\(869\) −21.6501 −0.734430
\(870\) −88.9222 −3.01475
\(871\) −14.4271 −0.488845
\(872\) −3.00316 −0.101700
\(873\) 7.69650 0.260487
\(874\) −13.3057 −0.450071
\(875\) 16.3012 0.551081
\(876\) −27.8949 −0.942481
\(877\) −18.1793 −0.613871 −0.306935 0.951730i \(-0.599304\pi\)
−0.306935 + 0.951730i \(0.599304\pi\)
\(878\) −29.1250 −0.982922
\(879\) 46.6924 1.57490
\(880\) 146.648 4.94349
\(881\) −12.2132 −0.411472 −0.205736 0.978608i \(-0.565959\pi\)
−0.205736 + 0.978608i \(0.565959\pi\)
\(882\) 1.68257 0.0566550
\(883\) −11.7768 −0.396322 −0.198161 0.980169i \(-0.563497\pi\)
−0.198161 + 0.980169i \(0.563497\pi\)
\(884\) 88.2877 2.96944
\(885\) 47.8731 1.60924
\(886\) 20.4615 0.687418
\(887\) 48.1650 1.61722 0.808611 0.588343i \(-0.200219\pi\)
0.808611 + 0.588343i \(0.200219\pi\)
\(888\) −7.64648 −0.256599
\(889\) 50.0352 1.67813
\(890\) 48.1552 1.61417
\(891\) 48.3075 1.61836
\(892\) 82.7807 2.77170
\(893\) 13.1628 0.440477
\(894\) 57.6657 1.92863
\(895\) −14.7187 −0.491992
\(896\) −34.8197 −1.16324
\(897\) 26.5659 0.887010
\(898\) −30.6259 −1.02200
\(899\) −25.0841 −0.836602
\(900\) 11.5864 0.386215
\(901\) 78.7164 2.62242
\(902\) −76.3943 −2.54365
\(903\) −47.9873 −1.59692
\(904\) 146.321 4.86657
\(905\) 39.4496 1.31135
\(906\) −18.5047 −0.614779
\(907\) 4.70486 0.156222 0.0781112 0.996945i \(-0.475111\pi\)
0.0781112 + 0.996945i \(0.475111\pi\)
\(908\) 103.442 3.43285
\(909\) 9.47030 0.314110
\(910\) −50.0217 −1.65820
\(911\) −9.79420 −0.324496 −0.162248 0.986750i \(-0.551874\pi\)
−0.162248 + 0.986750i \(0.551874\pi\)
\(912\) −23.3693 −0.773833
\(913\) −65.5998 −2.17104
\(914\) 51.4257 1.70101
\(915\) −57.6843 −1.90698
\(916\) 59.9538 1.98093
\(917\) −4.16615 −0.137579
\(918\) 71.5095 2.36016
\(919\) 13.5870 0.448195 0.224097 0.974567i \(-0.428057\pi\)
0.224097 + 0.974567i \(0.428057\pi\)
\(920\) 114.440 3.77297
\(921\) −41.2729 −1.35999
\(922\) −57.3555 −1.88890
\(923\) 40.4671 1.33199
\(924\) 111.987 3.68409
\(925\) −1.24106 −0.0408057
\(926\) 53.1678 1.74720
\(927\) −10.9377 −0.359241
\(928\) −92.9665 −3.05177
\(929\) 26.2198 0.860245 0.430122 0.902771i \(-0.358470\pi\)
0.430122 + 0.902771i \(0.358470\pi\)
\(930\) 59.1469 1.93950
\(931\) −0.735969 −0.0241204
\(932\) 75.8655 2.48506
\(933\) −43.6332 −1.42849
\(934\) −26.6284 −0.871308
\(935\) −78.5383 −2.56848
\(936\) 19.2792 0.630162
\(937\) −42.6930 −1.39472 −0.697361 0.716721i \(-0.745642\pi\)
−0.697361 + 0.716721i \(0.745642\pi\)
\(938\) −35.5192 −1.15974
\(939\) −13.1478 −0.429062
\(940\) −185.997 −6.06657
\(941\) −13.6886 −0.446235 −0.223118 0.974792i \(-0.571623\pi\)
−0.223118 + 0.974792i \(0.571623\pi\)
\(942\) 121.527 3.95957
\(943\) −32.0680 −1.04428
\(944\) 104.901 3.41424
\(945\) −29.1201 −0.947276
\(946\) 116.044 3.77290
\(947\) −55.3072 −1.79724 −0.898622 0.438724i \(-0.855430\pi\)
−0.898622 + 0.438724i \(0.855430\pi\)
\(948\) −48.7515 −1.58337
\(949\) −7.53347 −0.244547
\(950\) −7.05126 −0.228773
\(951\) 49.4020 1.60197
\(952\) 132.302 4.28794
\(953\) 0.319776 0.0103586 0.00517928 0.999987i \(-0.498351\pi\)
0.00517928 + 0.999987i \(0.498351\pi\)
\(954\) 28.2404 0.914317
\(955\) 44.7934 1.44948
\(956\) −7.13461 −0.230750
\(957\) 53.7636 1.73793
\(958\) 21.6435 0.699271
\(959\) 29.3350 0.947276
\(960\) 89.9856 2.90427
\(961\) −14.3152 −0.461782
\(962\) −3.39272 −0.109386
\(963\) 4.54458 0.146447
\(964\) −45.8672 −1.47728
\(965\) 68.1866 2.19500
\(966\) 65.4044 2.10435
\(967\) −50.8609 −1.63558 −0.817788 0.575519i \(-0.804800\pi\)
−0.817788 + 0.575519i \(0.804800\pi\)
\(968\) −73.5847 −2.36510
\(969\) 12.5156 0.402059
\(970\) 66.1862 2.12511
\(971\) 17.9892 0.577300 0.288650 0.957435i \(-0.406794\pi\)
0.288650 + 0.957435i \(0.406794\pi\)
\(972\) 44.2563 1.41952
\(973\) 22.9149 0.734619
\(974\) −7.80775 −0.250176
\(975\) 14.0784 0.450871
\(976\) −126.400 −4.04596
\(977\) 47.0123 1.50406 0.752028 0.659131i \(-0.229076\pi\)
0.752028 + 0.659131i \(0.229076\pi\)
\(978\) 60.4245 1.93216
\(979\) −29.1153 −0.930529
\(980\) 10.3996 0.332204
\(981\) 0.310384 0.00990980
\(982\) 78.1844 2.49496
\(983\) −26.6548 −0.850155 −0.425077 0.905157i \(-0.639753\pi\)
−0.425077 + 0.905157i \(0.639753\pi\)
\(984\) −104.706 −3.33791
\(985\) 45.6995 1.45611
\(986\) 104.353 3.32328
\(987\) −64.7024 −2.05950
\(988\) −13.8546 −0.440773
\(989\) 48.7116 1.54894
\(990\) −28.1765 −0.895508
\(991\) 3.41726 0.108553 0.0542765 0.998526i \(-0.482715\pi\)
0.0542765 + 0.998526i \(0.482715\pi\)
\(992\) 61.8369 1.96332
\(993\) −24.1447 −0.766210
\(994\) 99.6287 3.16003
\(995\) 13.8709 0.439738
\(996\) −147.717 −4.68059
\(997\) 15.0759 0.477459 0.238730 0.971086i \(-0.423269\pi\)
0.238730 + 0.971086i \(0.423269\pi\)
\(998\) 102.987 3.25998
\(999\) −1.97507 −0.0624884
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 \(a_p\))