Properties

Label 8023.2.a.c.1.9
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.67852 q^{2}\) \(+0.688962 q^{3}\) \(+5.17445 q^{4}\) \(-3.33373 q^{5}\) \(-1.84540 q^{6}\) \(+3.78681 q^{7}\) \(-8.50280 q^{8}\) \(-2.52533 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.67852 q^{2}\) \(+0.688962 q^{3}\) \(+5.17445 q^{4}\) \(-3.33373 q^{5}\) \(-1.84540 q^{6}\) \(+3.78681 q^{7}\) \(-8.50280 q^{8}\) \(-2.52533 q^{9}\) \(+8.92945 q^{10}\) \(+1.45005 q^{11}\) \(+3.56500 q^{12}\) \(+3.73900 q^{13}\) \(-10.1430 q^{14}\) \(-2.29681 q^{15}\) \(+12.4260 q^{16}\) \(-0.457265 q^{17}\) \(+6.76414 q^{18}\) \(-4.11903 q^{19}\) \(-17.2502 q^{20}\) \(+2.60897 q^{21}\) \(-3.88399 q^{22}\) \(-6.37891 q^{23}\) \(-5.85811 q^{24}\) \(+6.11376 q^{25}\) \(-10.0150 q^{26}\) \(-3.80674 q^{27}\) \(+19.5947 q^{28}\) \(-7.35059 q^{29}\) \(+6.15205 q^{30}\) \(+5.96142 q^{31}\) \(-16.2776 q^{32}\) \(+0.999033 q^{33}\) \(+1.22479 q^{34}\) \(-12.6242 q^{35}\) \(-13.0672 q^{36}\) \(+11.4442 q^{37}\) \(+11.0329 q^{38}\) \(+2.57603 q^{39}\) \(+28.3461 q^{40}\) \(+7.78118 q^{41}\) \(-6.98817 q^{42}\) \(-9.44692 q^{43}\) \(+7.50323 q^{44}\) \(+8.41877 q^{45}\) \(+17.0860 q^{46}\) \(+11.7459 q^{47}\) \(+8.56104 q^{48}\) \(+7.33996 q^{49}\) \(-16.3758 q^{50}\) \(-0.315038 q^{51}\) \(+19.3472 q^{52}\) \(-2.37933 q^{53}\) \(+10.1964 q^{54}\) \(-4.83409 q^{55}\) \(-32.1985 q^{56}\) \(-2.83785 q^{57}\) \(+19.6887 q^{58}\) \(+8.26952 q^{59}\) \(-11.8847 q^{60}\) \(-6.75010 q^{61}\) \(-15.9678 q^{62}\) \(-9.56296 q^{63}\) \(+18.7479 q^{64}\) \(-12.4648 q^{65}\) \(-2.67592 q^{66}\) \(-4.48494 q^{67}\) \(-2.36609 q^{68}\) \(-4.39483 q^{69}\) \(+33.8142 q^{70}\) \(-1.00000 q^{71}\) \(+21.4724 q^{72}\) \(-7.70485 q^{73}\) \(-30.6534 q^{74}\) \(+4.21215 q^{75}\) \(-21.3137 q^{76}\) \(+5.49109 q^{77}\) \(-6.89993 q^{78}\) \(-11.2483 q^{79}\) \(-41.4249 q^{80}\) \(+4.95329 q^{81}\) \(-20.8420 q^{82}\) \(-4.14568 q^{83}\) \(+13.5000 q^{84}\) \(+1.52440 q^{85}\) \(+25.3037 q^{86}\) \(-5.06428 q^{87}\) \(-12.3295 q^{88}\) \(+10.3144 q^{89}\) \(-22.5498 q^{90}\) \(+14.1589 q^{91}\) \(-33.0073 q^{92}\) \(+4.10719 q^{93}\) \(-31.4615 q^{94}\) \(+13.7317 q^{95}\) \(-11.2147 q^{96}\) \(-9.49652 q^{97}\) \(-19.6602 q^{98}\) \(-3.66187 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67852 −1.89400 −0.946998 0.321239i \(-0.895901\pi\)
−0.946998 + 0.321239i \(0.895901\pi\)
\(3\) 0.688962 0.397772 0.198886 0.980023i \(-0.436268\pi\)
0.198886 + 0.980023i \(0.436268\pi\)
\(4\) 5.17445 2.58722
\(5\) −3.33373 −1.49089 −0.745445 0.666567i \(-0.767763\pi\)
−0.745445 + 0.666567i \(0.767763\pi\)
\(6\) −1.84540 −0.753380
\(7\) 3.78681 1.43128 0.715641 0.698469i \(-0.246135\pi\)
0.715641 + 0.698469i \(0.246135\pi\)
\(8\) −8.50280 −3.00619
\(9\) −2.52533 −0.841777
\(10\) 8.92945 2.82374
\(11\) 1.45005 0.437208 0.218604 0.975814i \(-0.429850\pi\)
0.218604 + 0.975814i \(0.429850\pi\)
\(12\) 3.56500 1.02913
\(13\) 3.73900 1.03701 0.518506 0.855074i \(-0.326488\pi\)
0.518506 + 0.855074i \(0.326488\pi\)
\(14\) −10.1430 −2.71084
\(15\) −2.29681 −0.593035
\(16\) 12.4260 3.10650
\(17\) −0.457265 −0.110903 −0.0554515 0.998461i \(-0.517660\pi\)
−0.0554515 + 0.998461i \(0.517660\pi\)
\(18\) 6.76414 1.59432
\(19\) −4.11903 −0.944969 −0.472485 0.881339i \(-0.656643\pi\)
−0.472485 + 0.881339i \(0.656643\pi\)
\(20\) −17.2502 −3.85726
\(21\) 2.60897 0.569324
\(22\) −3.88399 −0.828070
\(23\) −6.37891 −1.33010 −0.665048 0.746801i \(-0.731589\pi\)
−0.665048 + 0.746801i \(0.731589\pi\)
\(24\) −5.85811 −1.19578
\(25\) 6.11376 1.22275
\(26\) −10.0150 −1.96410
\(27\) −3.80674 −0.732608
\(28\) 19.5947 3.70304
\(29\) −7.35059 −1.36497 −0.682485 0.730900i \(-0.739101\pi\)
−0.682485 + 0.730900i \(0.739101\pi\)
\(30\) 6.15205 1.12321
\(31\) 5.96142 1.07070 0.535351 0.844629i \(-0.320179\pi\)
0.535351 + 0.844629i \(0.320179\pi\)
\(32\) −16.2776 −2.87750
\(33\) 0.999033 0.173909
\(34\) 1.22479 0.210050
\(35\) −12.6242 −2.13388
\(36\) −13.0672 −2.17786
\(37\) 11.4442 1.88141 0.940706 0.339222i \(-0.110164\pi\)
0.940706 + 0.339222i \(0.110164\pi\)
\(38\) 11.0329 1.78977
\(39\) 2.57603 0.412495
\(40\) 28.3461 4.48191
\(41\) 7.78118 1.21522 0.607608 0.794237i \(-0.292129\pi\)
0.607608 + 0.794237i \(0.292129\pi\)
\(42\) −6.98817 −1.07830
\(43\) −9.44692 −1.44064 −0.720321 0.693641i \(-0.756006\pi\)
−0.720321 + 0.693641i \(0.756006\pi\)
\(44\) 7.50323 1.13115
\(45\) 8.41877 1.25500
\(46\) 17.0860 2.51920
\(47\) 11.7459 1.71331 0.856655 0.515889i \(-0.172538\pi\)
0.856655 + 0.515889i \(0.172538\pi\)
\(48\) 8.56104 1.23568
\(49\) 7.33996 1.04857
\(50\) −16.3758 −2.31589
\(51\) −0.315038 −0.0441141
\(52\) 19.3472 2.68298
\(53\) −2.37933 −0.326826 −0.163413 0.986558i \(-0.552250\pi\)
−0.163413 + 0.986558i \(0.552250\pi\)
\(54\) 10.1964 1.38756
\(55\) −4.83409 −0.651829
\(56\) −32.1985 −4.30271
\(57\) −2.83785 −0.375883
\(58\) 19.6887 2.58525
\(59\) 8.26952 1.07660 0.538300 0.842753i \(-0.319067\pi\)
0.538300 + 0.842753i \(0.319067\pi\)
\(60\) −11.8847 −1.53431
\(61\) −6.75010 −0.864261 −0.432131 0.901811i \(-0.642238\pi\)
−0.432131 + 0.901811i \(0.642238\pi\)
\(62\) −15.9678 −2.02791
\(63\) −9.56296 −1.20482
\(64\) 18.7479 2.34348
\(65\) −12.4648 −1.54607
\(66\) −2.67592 −0.329384
\(67\) −4.48494 −0.547922 −0.273961 0.961741i \(-0.588334\pi\)
−0.273961 + 0.961741i \(0.588334\pi\)
\(68\) −2.36609 −0.286931
\(69\) −4.39483 −0.529075
\(70\) 33.8142 4.04157
\(71\) −1.00000 −0.118678
\(72\) 21.4724 2.53055
\(73\) −7.70485 −0.901785 −0.450892 0.892578i \(-0.648894\pi\)
−0.450892 + 0.892578i \(0.648894\pi\)
\(74\) −30.6534 −3.56339
\(75\) 4.21215 0.486377
\(76\) −21.3137 −2.44485
\(77\) 5.49109 0.625767
\(78\) −6.89993 −0.781263
\(79\) −11.2483 −1.26554 −0.632768 0.774341i \(-0.718082\pi\)
−0.632768 + 0.774341i \(0.718082\pi\)
\(80\) −41.4249 −4.63145
\(81\) 4.95329 0.550366
\(82\) −20.8420 −2.30162
\(83\) −4.14568 −0.455047 −0.227524 0.973773i \(-0.573063\pi\)
−0.227524 + 0.973773i \(0.573063\pi\)
\(84\) 13.5000 1.47297
\(85\) 1.52440 0.165344
\(86\) 25.3037 2.72857
\(87\) −5.06428 −0.542947
\(88\) −12.3295 −1.31433
\(89\) 10.3144 1.09333 0.546663 0.837353i \(-0.315898\pi\)
0.546663 + 0.837353i \(0.315898\pi\)
\(90\) −22.5498 −2.37696
\(91\) 14.1589 1.48426
\(92\) −33.0073 −3.44125
\(93\) 4.10719 0.425896
\(94\) −31.4615 −3.24500
\(95\) 13.7317 1.40885
\(96\) −11.2147 −1.14459
\(97\) −9.49652 −0.964226 −0.482113 0.876109i \(-0.660131\pi\)
−0.482113 + 0.876109i \(0.660131\pi\)
\(98\) −19.6602 −1.98598
\(99\) −3.66187 −0.368032
\(100\) 31.6353 3.16353
\(101\) −15.4740 −1.53972 −0.769860 0.638213i \(-0.779674\pi\)
−0.769860 + 0.638213i \(0.779674\pi\)
\(102\) 0.843834 0.0835520
\(103\) 13.4795 1.32817 0.664085 0.747657i \(-0.268821\pi\)
0.664085 + 0.747657i \(0.268821\pi\)
\(104\) −31.7920 −3.11746
\(105\) −8.69761 −0.848800
\(106\) 6.37306 0.619007
\(107\) 17.8700 1.72756 0.863779 0.503870i \(-0.168091\pi\)
0.863779 + 0.503870i \(0.168091\pi\)
\(108\) −19.6978 −1.89542
\(109\) 5.37901 0.515216 0.257608 0.966250i \(-0.417066\pi\)
0.257608 + 0.966250i \(0.417066\pi\)
\(110\) 12.9482 1.23456
\(111\) 7.88461 0.748374
\(112\) 47.0549 4.44627
\(113\) −1.00000 −0.0940721
\(114\) 7.60123 0.711921
\(115\) 21.2656 1.98303
\(116\) −38.0352 −3.53148
\(117\) −9.44221 −0.872932
\(118\) −22.1500 −2.03908
\(119\) −1.73158 −0.158733
\(120\) 19.5294 1.78278
\(121\) −8.89734 −0.808849
\(122\) 18.0802 1.63691
\(123\) 5.36094 0.483380
\(124\) 30.8471 2.77015
\(125\) −3.71298 −0.332099
\(126\) 25.6145 2.28192
\(127\) −9.21300 −0.817522 −0.408761 0.912642i \(-0.634039\pi\)
−0.408761 + 0.912642i \(0.634039\pi\)
\(128\) −17.6612 −1.56105
\(129\) −6.50857 −0.573048
\(130\) 33.3872 2.92825
\(131\) −17.4164 −1.52168 −0.760841 0.648938i \(-0.775213\pi\)
−0.760841 + 0.648938i \(0.775213\pi\)
\(132\) 5.16944 0.449942
\(133\) −15.5980 −1.35252
\(134\) 12.0130 1.03776
\(135\) 12.6907 1.09224
\(136\) 3.88803 0.333396
\(137\) −8.09267 −0.691404 −0.345702 0.938344i \(-0.612359\pi\)
−0.345702 + 0.938344i \(0.612359\pi\)
\(138\) 11.7716 1.00207
\(139\) 11.1930 0.949381 0.474691 0.880153i \(-0.342560\pi\)
0.474691 + 0.880153i \(0.342560\pi\)
\(140\) −65.3233 −5.52083
\(141\) 8.09246 0.681508
\(142\) 2.67852 0.224776
\(143\) 5.42175 0.453390
\(144\) −31.3798 −2.61498
\(145\) 24.5049 2.03502
\(146\) 20.6376 1.70798
\(147\) 5.05696 0.417091
\(148\) 59.2173 4.86763
\(149\) −17.9349 −1.46928 −0.734640 0.678457i \(-0.762649\pi\)
−0.734640 + 0.678457i \(0.762649\pi\)
\(150\) −11.2823 −0.921197
\(151\) −17.6506 −1.43639 −0.718194 0.695843i \(-0.755031\pi\)
−0.718194 + 0.695843i \(0.755031\pi\)
\(152\) 35.0233 2.84076
\(153\) 1.15474 0.0933556
\(154\) −14.7080 −1.18520
\(155\) −19.8738 −1.59630
\(156\) 13.3295 1.06722
\(157\) 11.7147 0.934933 0.467466 0.884011i \(-0.345167\pi\)
0.467466 + 0.884011i \(0.345167\pi\)
\(158\) 30.1289 2.39692
\(159\) −1.63927 −0.130002
\(160\) 54.2652 4.29004
\(161\) −24.1558 −1.90374
\(162\) −13.2675 −1.04239
\(163\) 17.8070 1.39475 0.697377 0.716704i \(-0.254350\pi\)
0.697377 + 0.716704i \(0.254350\pi\)
\(164\) 40.2633 3.14404
\(165\) −3.33051 −0.259280
\(166\) 11.1043 0.861858
\(167\) 3.69353 0.285814 0.142907 0.989736i \(-0.454355\pi\)
0.142907 + 0.989736i \(0.454355\pi\)
\(168\) −22.1836 −1.71150
\(169\) 0.980105 0.0753927
\(170\) −4.08312 −0.313161
\(171\) 10.4019 0.795454
\(172\) −48.8826 −3.72726
\(173\) 15.8196 1.20274 0.601370 0.798971i \(-0.294622\pi\)
0.601370 + 0.798971i \(0.294622\pi\)
\(174\) 13.5647 1.02834
\(175\) 23.1517 1.75010
\(176\) 18.0184 1.35819
\(177\) 5.69739 0.428242
\(178\) −27.6273 −2.07076
\(179\) −4.59611 −0.343529 −0.171765 0.985138i \(-0.554947\pi\)
−0.171765 + 0.985138i \(0.554947\pi\)
\(180\) 43.5625 3.24696
\(181\) 3.24026 0.240847 0.120423 0.992723i \(-0.461575\pi\)
0.120423 + 0.992723i \(0.461575\pi\)
\(182\) −37.9248 −2.81117
\(183\) −4.65056 −0.343779
\(184\) 54.2386 3.99852
\(185\) −38.1518 −2.80498
\(186\) −11.0012 −0.806646
\(187\) −0.663059 −0.0484876
\(188\) 60.7783 4.43272
\(189\) −14.4154 −1.04857
\(190\) −36.7806 −2.66835
\(191\) 3.41034 0.246764 0.123382 0.992359i \(-0.460626\pi\)
0.123382 + 0.992359i \(0.460626\pi\)
\(192\) 12.9166 0.932174
\(193\) −21.8959 −1.57610 −0.788051 0.615610i \(-0.788910\pi\)
−0.788051 + 0.615610i \(0.788910\pi\)
\(194\) 25.4366 1.82624
\(195\) −8.58778 −0.614984
\(196\) 37.9802 2.71287
\(197\) 7.48921 0.533584 0.266792 0.963754i \(-0.414036\pi\)
0.266792 + 0.963754i \(0.414036\pi\)
\(198\) 9.80837 0.697051
\(199\) −18.3820 −1.30306 −0.651531 0.758622i \(-0.725873\pi\)
−0.651531 + 0.758622i \(0.725873\pi\)
\(200\) −51.9841 −3.67583
\(201\) −3.08995 −0.217948
\(202\) 41.4473 2.91622
\(203\) −27.8353 −1.95366
\(204\) −1.63015 −0.114133
\(205\) −25.9404 −1.81175
\(206\) −36.1049 −2.51555
\(207\) 16.1089 1.11964
\(208\) 46.4608 3.22148
\(209\) −5.97281 −0.413148
\(210\) 23.2967 1.60762
\(211\) 14.3897 0.990626 0.495313 0.868714i \(-0.335053\pi\)
0.495313 + 0.868714i \(0.335053\pi\)
\(212\) −12.3117 −0.845571
\(213\) −0.688962 −0.0472069
\(214\) −47.8651 −3.27199
\(215\) 31.4935 2.14784
\(216\) 32.3680 2.20236
\(217\) 22.5748 1.53248
\(218\) −14.4078 −0.975817
\(219\) −5.30835 −0.358705
\(220\) −25.0137 −1.68643
\(221\) −1.70971 −0.115008
\(222\) −21.1191 −1.41742
\(223\) −5.90794 −0.395625 −0.197812 0.980240i \(-0.563384\pi\)
−0.197812 + 0.980240i \(0.563384\pi\)
\(224\) −61.6403 −4.11852
\(225\) −15.4393 −1.02928
\(226\) 2.67852 0.178172
\(227\) 11.7556 0.780249 0.390124 0.920762i \(-0.372432\pi\)
0.390124 + 0.920762i \(0.372432\pi\)
\(228\) −14.6843 −0.972493
\(229\) 3.52788 0.233129 0.116565 0.993183i \(-0.462812\pi\)
0.116565 + 0.993183i \(0.462812\pi\)
\(230\) −56.9602 −3.75584
\(231\) 3.78315 0.248913
\(232\) 62.5006 4.10337
\(233\) −17.6528 −1.15648 −0.578238 0.815868i \(-0.696259\pi\)
−0.578238 + 0.815868i \(0.696259\pi\)
\(234\) 25.2911 1.65333
\(235\) −39.1576 −2.55436
\(236\) 42.7902 2.78540
\(237\) −7.74968 −0.503396
\(238\) 4.63805 0.300640
\(239\) −9.53899 −0.617026 −0.308513 0.951220i \(-0.599831\pi\)
−0.308513 + 0.951220i \(0.599831\pi\)
\(240\) −28.5402 −1.84226
\(241\) 11.4891 0.740079 0.370040 0.929016i \(-0.379344\pi\)
0.370040 + 0.929016i \(0.379344\pi\)
\(242\) 23.8317 1.53196
\(243\) 14.8329 0.951529
\(244\) −34.9280 −2.23604
\(245\) −24.4695 −1.56330
\(246\) −14.3594 −0.915519
\(247\) −15.4010 −0.979944
\(248\) −50.6888 −3.21874
\(249\) −2.85621 −0.181005
\(250\) 9.94529 0.628995
\(251\) 21.4538 1.35415 0.677075 0.735914i \(-0.263247\pi\)
0.677075 + 0.735914i \(0.263247\pi\)
\(252\) −49.4830 −3.11714
\(253\) −9.24977 −0.581528
\(254\) 24.6772 1.54838
\(255\) 1.05025 0.0657693
\(256\) 9.81012 0.613133
\(257\) 20.2895 1.26563 0.632813 0.774304i \(-0.281900\pi\)
0.632813 + 0.774304i \(0.281900\pi\)
\(258\) 17.4333 1.08535
\(259\) 43.3370 2.69283
\(260\) −64.4985 −4.00003
\(261\) 18.5627 1.14900
\(262\) 46.6502 2.88206
\(263\) −23.9610 −1.47750 −0.738748 0.673982i \(-0.764583\pi\)
−0.738748 + 0.673982i \(0.764583\pi\)
\(264\) −8.49458 −0.522805
\(265\) 7.93204 0.487261
\(266\) 41.7794 2.56166
\(267\) 7.10624 0.434895
\(268\) −23.2071 −1.41760
\(269\) 18.4345 1.12397 0.561986 0.827147i \(-0.310037\pi\)
0.561986 + 0.827147i \(0.310037\pi\)
\(270\) −33.9921 −2.06870
\(271\) −4.33208 −0.263155 −0.131578 0.991306i \(-0.542004\pi\)
−0.131578 + 0.991306i \(0.542004\pi\)
\(272\) −5.68197 −0.344520
\(273\) 9.75494 0.590396
\(274\) 21.6764 1.30952
\(275\) 8.86529 0.534597
\(276\) −22.7408 −1.36884
\(277\) −31.2168 −1.87564 −0.937819 0.347126i \(-0.887158\pi\)
−0.937819 + 0.347126i \(0.887158\pi\)
\(278\) −29.9807 −1.79812
\(279\) −15.0546 −0.901293
\(280\) 107.341 6.41487
\(281\) 15.9306 0.950338 0.475169 0.879895i \(-0.342387\pi\)
0.475169 + 0.879895i \(0.342387\pi\)
\(282\) −21.6758 −1.29077
\(283\) 7.44917 0.442807 0.221404 0.975182i \(-0.428936\pi\)
0.221404 + 0.975182i \(0.428936\pi\)
\(284\) −5.17445 −0.307047
\(285\) 9.46064 0.560400
\(286\) −14.5222 −0.858718
\(287\) 29.4659 1.73932
\(288\) 41.1064 2.42222
\(289\) −16.7909 −0.987701
\(290\) −65.6367 −3.85432
\(291\) −6.54275 −0.383543
\(292\) −39.8683 −2.33312
\(293\) −12.5486 −0.733097 −0.366548 0.930399i \(-0.619461\pi\)
−0.366548 + 0.930399i \(0.619461\pi\)
\(294\) −13.5451 −0.789968
\(295\) −27.5684 −1.60509
\(296\) −97.3077 −5.65589
\(297\) −5.51999 −0.320302
\(298\) 48.0388 2.78281
\(299\) −23.8507 −1.37932
\(300\) 21.7955 1.25837
\(301\) −35.7737 −2.06196
\(302\) 47.2775 2.72051
\(303\) −10.6610 −0.612458
\(304\) −51.1830 −2.93555
\(305\) 22.5030 1.28852
\(306\) −3.09300 −0.176815
\(307\) −5.83419 −0.332975 −0.166487 0.986044i \(-0.553243\pi\)
−0.166487 + 0.986044i \(0.553243\pi\)
\(308\) 28.4133 1.61900
\(309\) 9.28684 0.528310
\(310\) 53.2322 3.02339
\(311\) 17.3662 0.984747 0.492373 0.870384i \(-0.336129\pi\)
0.492373 + 0.870384i \(0.336129\pi\)
\(312\) −21.9035 −1.24004
\(313\) −32.5151 −1.83786 −0.918931 0.394419i \(-0.870946\pi\)
−0.918931 + 0.394419i \(0.870946\pi\)
\(314\) −31.3779 −1.77076
\(315\) 31.8803 1.79625
\(316\) −58.2039 −3.27423
\(317\) −10.7018 −0.601075 −0.300537 0.953770i \(-0.597166\pi\)
−0.300537 + 0.953770i \(0.597166\pi\)
\(318\) 4.39080 0.246224
\(319\) −10.6588 −0.596776
\(320\) −62.5004 −3.49388
\(321\) 12.3118 0.687175
\(322\) 64.7016 3.60568
\(323\) 1.88348 0.104800
\(324\) 25.6305 1.42392
\(325\) 22.8593 1.26801
\(326\) −47.6964 −2.64166
\(327\) 3.70594 0.204939
\(328\) −66.1618 −3.65318
\(329\) 44.4794 2.45223
\(330\) 8.92081 0.491075
\(331\) 11.2927 0.620700 0.310350 0.950622i \(-0.399554\pi\)
0.310350 + 0.950622i \(0.399554\pi\)
\(332\) −21.4516 −1.17731
\(333\) −28.9004 −1.58373
\(334\) −9.89317 −0.541330
\(335\) 14.9516 0.816892
\(336\) 32.4191 1.76861
\(337\) 20.1870 1.09965 0.549827 0.835279i \(-0.314694\pi\)
0.549827 + 0.835279i \(0.314694\pi\)
\(338\) −2.62523 −0.142794
\(339\) −0.688962 −0.0374193
\(340\) 7.88791 0.427782
\(341\) 8.64439 0.468120
\(342\) −27.8617 −1.50659
\(343\) 1.28738 0.0695118
\(344\) 80.3253 4.33085
\(345\) 14.6512 0.788793
\(346\) −42.3730 −2.27798
\(347\) −24.3693 −1.30821 −0.654107 0.756402i \(-0.726955\pi\)
−0.654107 + 0.756402i \(0.726955\pi\)
\(348\) −26.2048 −1.40473
\(349\) 2.48012 0.132758 0.0663788 0.997794i \(-0.478855\pi\)
0.0663788 + 0.997794i \(0.478855\pi\)
\(350\) −62.0121 −3.31469
\(351\) −14.2334 −0.759723
\(352\) −23.6034 −1.25807
\(353\) −5.10893 −0.271921 −0.135961 0.990714i \(-0.543412\pi\)
−0.135961 + 0.990714i \(0.543412\pi\)
\(354\) −15.2605 −0.811088
\(355\) 3.33373 0.176936
\(356\) 53.3714 2.82868
\(357\) −1.19299 −0.0631397
\(358\) 12.3107 0.650643
\(359\) −9.80284 −0.517374 −0.258687 0.965961i \(-0.583290\pi\)
−0.258687 + 0.965961i \(0.583290\pi\)
\(360\) −71.5832 −3.77276
\(361\) −2.03363 −0.107033
\(362\) −8.67910 −0.456163
\(363\) −6.12993 −0.321738
\(364\) 73.2644 3.84010
\(365\) 25.6859 1.34446
\(366\) 12.4566 0.651117
\(367\) 20.5968 1.07515 0.537573 0.843217i \(-0.319341\pi\)
0.537573 + 0.843217i \(0.319341\pi\)
\(368\) −79.2644 −4.13194
\(369\) −19.6501 −1.02294
\(370\) 102.190 5.31262
\(371\) −9.01007 −0.467779
\(372\) 21.2525 1.10189
\(373\) 15.8345 0.819880 0.409940 0.912112i \(-0.365550\pi\)
0.409940 + 0.912112i \(0.365550\pi\)
\(374\) 1.77601 0.0918354
\(375\) −2.55811 −0.132100
\(376\) −99.8728 −5.15055
\(377\) −27.4838 −1.41549
\(378\) 38.6120 1.98599
\(379\) −9.23204 −0.474218 −0.237109 0.971483i \(-0.576200\pi\)
−0.237109 + 0.971483i \(0.576200\pi\)
\(380\) 71.0541 3.64500
\(381\) −6.34741 −0.325188
\(382\) −9.13465 −0.467369
\(383\) −21.1520 −1.08082 −0.540409 0.841403i \(-0.681730\pi\)
−0.540409 + 0.841403i \(0.681730\pi\)
\(384\) −12.1679 −0.620941
\(385\) −18.3058 −0.932950
\(386\) 58.6485 2.98513
\(387\) 23.8566 1.21270
\(388\) −49.1392 −2.49467
\(389\) −3.13204 −0.158801 −0.0794003 0.996843i \(-0.525301\pi\)
−0.0794003 + 0.996843i \(0.525301\pi\)
\(390\) 23.0025 1.16478
\(391\) 2.91685 0.147511
\(392\) −62.4103 −3.15219
\(393\) −11.9993 −0.605283
\(394\) −20.0600 −1.01061
\(395\) 37.4989 1.88678
\(396\) −18.9481 −0.952180
\(397\) 18.4583 0.926394 0.463197 0.886255i \(-0.346702\pi\)
0.463197 + 0.886255i \(0.346702\pi\)
\(398\) 49.2364 2.46800
\(399\) −10.7464 −0.537994
\(400\) 75.9696 3.79848
\(401\) 36.3460 1.81503 0.907516 0.420018i \(-0.137976\pi\)
0.907516 + 0.420018i \(0.137976\pi\)
\(402\) 8.27649 0.412794
\(403\) 22.2897 1.11033
\(404\) −80.0693 −3.98360
\(405\) −16.5129 −0.820535
\(406\) 74.5573 3.70022
\(407\) 16.5947 0.822568
\(408\) 2.67871 0.132616
\(409\) −19.6794 −0.973083 −0.486542 0.873657i \(-0.661742\pi\)
−0.486542 + 0.873657i \(0.661742\pi\)
\(410\) 69.4817 3.43146
\(411\) −5.57555 −0.275021
\(412\) 69.7487 3.43627
\(413\) 31.3151 1.54092
\(414\) −43.1478 −2.12060
\(415\) 13.8206 0.678425
\(416\) −60.8620 −2.98401
\(417\) 7.71158 0.377638
\(418\) 15.9983 0.782501
\(419\) −6.27320 −0.306466 −0.153233 0.988190i \(-0.548968\pi\)
−0.153233 + 0.988190i \(0.548968\pi\)
\(420\) −45.0053 −2.19603
\(421\) −16.1872 −0.788915 −0.394458 0.918914i \(-0.629068\pi\)
−0.394458 + 0.918914i \(0.629068\pi\)
\(422\) −38.5430 −1.87624
\(423\) −29.6622 −1.44223
\(424\) 20.2309 0.982502
\(425\) −2.79561 −0.135607
\(426\) 1.84540 0.0894097
\(427\) −25.5614 −1.23700
\(428\) 92.4674 4.46958
\(429\) 3.73538 0.180346
\(430\) −84.3558 −4.06800
\(431\) 7.19713 0.346674 0.173337 0.984863i \(-0.444545\pi\)
0.173337 + 0.984863i \(0.444545\pi\)
\(432\) −47.3026 −2.27585
\(433\) 25.2844 1.21509 0.607544 0.794286i \(-0.292155\pi\)
0.607544 + 0.794286i \(0.292155\pi\)
\(434\) −60.4669 −2.90251
\(435\) 16.8829 0.809475
\(436\) 27.8334 1.33298
\(437\) 26.2749 1.25690
\(438\) 14.2185 0.679386
\(439\) 30.5362 1.45741 0.728706 0.684827i \(-0.240122\pi\)
0.728706 + 0.684827i \(0.240122\pi\)
\(440\) 41.1033 1.95952
\(441\) −18.5358 −0.882659
\(442\) 4.57949 0.217824
\(443\) 31.3445 1.48922 0.744611 0.667499i \(-0.232635\pi\)
0.744611 + 0.667499i \(0.232635\pi\)
\(444\) 40.7985 1.93621
\(445\) −34.3855 −1.63003
\(446\) 15.8245 0.749312
\(447\) −12.3564 −0.584439
\(448\) 70.9947 3.35419
\(449\) −1.33785 −0.0631372 −0.0315686 0.999502i \(-0.510050\pi\)
−0.0315686 + 0.999502i \(0.510050\pi\)
\(450\) 41.3543 1.94946
\(451\) 11.2831 0.531302
\(452\) −5.17445 −0.243385
\(453\) −12.1606 −0.571356
\(454\) −31.4876 −1.47779
\(455\) −47.2019 −2.21286
\(456\) 24.1297 1.12998
\(457\) −14.3544 −0.671469 −0.335735 0.941957i \(-0.608985\pi\)
−0.335735 + 0.941957i \(0.608985\pi\)
\(458\) −9.44949 −0.441546
\(459\) 1.74069 0.0812484
\(460\) 110.038 5.13053
\(461\) −5.97884 −0.278462 −0.139231 0.990260i \(-0.544463\pi\)
−0.139231 + 0.990260i \(0.544463\pi\)
\(462\) −10.1332 −0.471441
\(463\) −13.6196 −0.632959 −0.316479 0.948599i \(-0.602501\pi\)
−0.316479 + 0.948599i \(0.602501\pi\)
\(464\) −91.3384 −4.24028
\(465\) −13.6923 −0.634964
\(466\) 47.2834 2.19036
\(467\) −14.1078 −0.652832 −0.326416 0.945226i \(-0.605841\pi\)
−0.326416 + 0.945226i \(0.605841\pi\)
\(468\) −48.8582 −2.25847
\(469\) −16.9836 −0.784231
\(470\) 104.884 4.83794
\(471\) 8.07097 0.371891
\(472\) −70.3141 −3.23647
\(473\) −13.6986 −0.629860
\(474\) 20.7576 0.953430
\(475\) −25.1827 −1.15546
\(476\) −8.95995 −0.410678
\(477\) 6.00859 0.275114
\(478\) 25.5503 1.16864
\(479\) −14.8749 −0.679653 −0.339826 0.940488i \(-0.610368\pi\)
−0.339826 + 0.940488i \(0.610368\pi\)
\(480\) 37.3867 1.70646
\(481\) 42.7898 1.95105
\(482\) −30.7738 −1.40171
\(483\) −16.6424 −0.757255
\(484\) −46.0388 −2.09267
\(485\) 31.6589 1.43755
\(486\) −39.7301 −1.80219
\(487\) −32.2608 −1.46188 −0.730938 0.682443i \(-0.760917\pi\)
−0.730938 + 0.682443i \(0.760917\pi\)
\(488\) 57.3947 2.59814
\(489\) 12.2684 0.554795
\(490\) 65.5418 2.96088
\(491\) 7.19456 0.324686 0.162343 0.986734i \(-0.448095\pi\)
0.162343 + 0.986734i \(0.448095\pi\)
\(492\) 27.7399 1.25061
\(493\) 3.36116 0.151379
\(494\) 41.2519 1.85601
\(495\) 12.2077 0.548695
\(496\) 74.0766 3.32614
\(497\) −3.78681 −0.169862
\(498\) 7.65042 0.342823
\(499\) −34.5718 −1.54765 −0.773823 0.633402i \(-0.781658\pi\)
−0.773823 + 0.633402i \(0.781658\pi\)
\(500\) −19.2126 −0.859215
\(501\) 2.54470 0.113689
\(502\) −57.4642 −2.56475
\(503\) −34.8596 −1.55431 −0.777156 0.629308i \(-0.783338\pi\)
−0.777156 + 0.629308i \(0.783338\pi\)
\(504\) 81.3120 3.62192
\(505\) 51.5861 2.29555
\(506\) 24.7757 1.10141
\(507\) 0.675255 0.0299891
\(508\) −47.6722 −2.11511
\(509\) −8.94075 −0.396292 −0.198146 0.980173i \(-0.563492\pi\)
−0.198146 + 0.980173i \(0.563492\pi\)
\(510\) −2.81312 −0.124567
\(511\) −29.1768 −1.29071
\(512\) 9.04589 0.399775
\(513\) 15.6801 0.692292
\(514\) −54.3459 −2.39709
\(515\) −44.9369 −1.98016
\(516\) −33.6783 −1.48260
\(517\) 17.0321 0.749073
\(518\) −116.079 −5.10021
\(519\) 10.8991 0.478417
\(520\) 105.986 4.64779
\(521\) −31.6200 −1.38530 −0.692648 0.721276i \(-0.743556\pi\)
−0.692648 + 0.721276i \(0.743556\pi\)
\(522\) −49.7204 −2.17620
\(523\) −1.19072 −0.0520667 −0.0260333 0.999661i \(-0.508288\pi\)
−0.0260333 + 0.999661i \(0.508288\pi\)
\(524\) −90.1205 −3.93693
\(525\) 15.9506 0.696143
\(526\) 64.1798 2.79837
\(527\) −2.72595 −0.118744
\(528\) 12.4140 0.540249
\(529\) 17.6905 0.769153
\(530\) −21.2461 −0.922871
\(531\) −20.8833 −0.906257
\(532\) −80.7109 −3.49926
\(533\) 29.0938 1.26019
\(534\) −19.0342 −0.823690
\(535\) −59.5738 −2.57560
\(536\) 38.1345 1.64716
\(537\) −3.16654 −0.136646
\(538\) −49.3771 −2.12880
\(539\) 10.6433 0.458441
\(540\) 65.6671 2.82586
\(541\) −16.8249 −0.723359 −0.361680 0.932302i \(-0.617797\pi\)
−0.361680 + 0.932302i \(0.617797\pi\)
\(542\) 11.6036 0.498415
\(543\) 2.23242 0.0958023
\(544\) 7.44318 0.319124
\(545\) −17.9322 −0.768130
\(546\) −26.1288 −1.11821
\(547\) −37.0439 −1.58388 −0.791941 0.610598i \(-0.790929\pi\)
−0.791941 + 0.610598i \(0.790929\pi\)
\(548\) −41.8751 −1.78882
\(549\) 17.0462 0.727515
\(550\) −23.7458 −1.01252
\(551\) 30.2773 1.28985
\(552\) 37.3684 1.59050
\(553\) −42.5954 −1.81134
\(554\) 83.6147 3.55245
\(555\) −26.2852 −1.11574
\(556\) 57.9178 2.45626
\(557\) 37.2863 1.57987 0.789935 0.613190i \(-0.210114\pi\)
0.789935 + 0.613190i \(0.210114\pi\)
\(558\) 40.3239 1.70705
\(559\) −35.3220 −1.49396
\(560\) −156.869 −6.62891
\(561\) −0.456822 −0.0192871
\(562\) −42.6703 −1.79994
\(563\) 41.0502 1.73006 0.865031 0.501719i \(-0.167299\pi\)
0.865031 + 0.501719i \(0.167299\pi\)
\(564\) 41.8740 1.76321
\(565\) 3.33373 0.140251
\(566\) −19.9527 −0.838676
\(567\) 18.7572 0.787728
\(568\) 8.50280 0.356770
\(569\) −27.6922 −1.16092 −0.580459 0.814289i \(-0.697127\pi\)
−0.580459 + 0.814289i \(0.697127\pi\)
\(570\) −25.3405 −1.06140
\(571\) −29.6663 −1.24149 −0.620747 0.784011i \(-0.713171\pi\)
−0.620747 + 0.784011i \(0.713171\pi\)
\(572\) 28.0546 1.17302
\(573\) 2.34960 0.0981558
\(574\) −78.9248 −3.29426
\(575\) −38.9992 −1.62638
\(576\) −47.3446 −1.97269
\(577\) 27.8718 1.16032 0.580159 0.814503i \(-0.302990\pi\)
0.580159 + 0.814503i \(0.302990\pi\)
\(578\) 44.9747 1.87070
\(579\) −15.0855 −0.626930
\(580\) 126.799 5.26505
\(581\) −15.6989 −0.651300
\(582\) 17.5248 0.726428
\(583\) −3.45015 −0.142891
\(584\) 65.5129 2.71094
\(585\) 31.4778 1.30145
\(586\) 33.6116 1.38848
\(587\) −6.95666 −0.287132 −0.143566 0.989641i \(-0.545857\pi\)
−0.143566 + 0.989641i \(0.545857\pi\)
\(588\) 26.1669 1.07911
\(589\) −24.5553 −1.01178
\(590\) 73.8423 3.04004
\(591\) 5.15978 0.212245
\(592\) 142.205 5.84461
\(593\) −18.3748 −0.754561 −0.377280 0.926099i \(-0.623141\pi\)
−0.377280 + 0.926099i \(0.623141\pi\)
\(594\) 14.7854 0.606651
\(595\) 5.77261 0.236654
\(596\) −92.8029 −3.80136
\(597\) −12.6645 −0.518323
\(598\) 63.8846 2.61243
\(599\) 34.7708 1.42070 0.710348 0.703851i \(-0.248538\pi\)
0.710348 + 0.703851i \(0.248538\pi\)
\(600\) −35.8151 −1.46214
\(601\) 12.8285 0.523286 0.261643 0.965165i \(-0.415736\pi\)
0.261643 + 0.965165i \(0.415736\pi\)
\(602\) 95.8205 3.90535
\(603\) 11.3260 0.461228
\(604\) −91.3322 −3.71626
\(605\) 29.6613 1.20591
\(606\) 28.5556 1.15999
\(607\) −46.6434 −1.89320 −0.946598 0.322417i \(-0.895505\pi\)
−0.946598 + 0.322417i \(0.895505\pi\)
\(608\) 67.0480 2.71915
\(609\) −19.1775 −0.777111
\(610\) −60.2746 −2.44045
\(611\) 43.9178 1.77672
\(612\) 5.97516 0.241532
\(613\) −2.38315 −0.0962547 −0.0481274 0.998841i \(-0.515325\pi\)
−0.0481274 + 0.998841i \(0.515325\pi\)
\(614\) 15.6270 0.630653
\(615\) −17.8719 −0.720666
\(616\) −46.6896 −1.88118
\(617\) −12.9686 −0.522096 −0.261048 0.965326i \(-0.584068\pi\)
−0.261048 + 0.965326i \(0.584068\pi\)
\(618\) −24.8749 −1.00062
\(619\) −5.51505 −0.221669 −0.110834 0.993839i \(-0.535352\pi\)
−0.110834 + 0.993839i \(0.535352\pi\)
\(620\) −102.836 −4.12998
\(621\) 24.2829 0.974439
\(622\) −46.5156 −1.86511
\(623\) 39.0588 1.56486
\(624\) 32.0097 1.28141
\(625\) −18.1907 −0.727629
\(626\) 87.0922 3.48090
\(627\) −4.11504 −0.164339
\(628\) 60.6170 2.41888
\(629\) −5.23302 −0.208654
\(630\) −85.3920 −3.40210
\(631\) −5.46855 −0.217699 −0.108850 0.994058i \(-0.534717\pi\)
−0.108850 + 0.994058i \(0.534717\pi\)
\(632\) 95.6424 3.80445
\(633\) 9.91394 0.394044
\(634\) 28.6650 1.13843
\(635\) 30.7137 1.21884
\(636\) −8.48229 −0.336345
\(637\) 27.4441 1.08738
\(638\) 28.5496 1.13029
\(639\) 2.52533 0.0999006
\(640\) 58.8778 2.32735
\(641\) −3.08693 −0.121927 −0.0609633 0.998140i \(-0.519417\pi\)
−0.0609633 + 0.998140i \(0.519417\pi\)
\(642\) −32.9772 −1.30151
\(643\) −29.0813 −1.14685 −0.573427 0.819257i \(-0.694386\pi\)
−0.573427 + 0.819257i \(0.694386\pi\)
\(644\) −124.993 −4.92540
\(645\) 21.6978 0.854351
\(646\) −5.04494 −0.198491
\(647\) 6.81408 0.267889 0.133944 0.990989i \(-0.457236\pi\)
0.133944 + 0.990989i \(0.457236\pi\)
\(648\) −42.1169 −1.65451
\(649\) 11.9913 0.470698
\(650\) −61.2291 −2.40160
\(651\) 15.5532 0.609577
\(652\) 92.1415 3.60854
\(653\) −27.2333 −1.06572 −0.532860 0.846203i \(-0.678883\pi\)
−0.532860 + 0.846203i \(0.678883\pi\)
\(654\) −9.92641 −0.388153
\(655\) 58.0618 2.26866
\(656\) 96.6889 3.77507
\(657\) 19.4573 0.759102
\(658\) −119.139 −4.64451
\(659\) −28.3944 −1.10609 −0.553045 0.833151i \(-0.686534\pi\)
−0.553045 + 0.833151i \(0.686534\pi\)
\(660\) −17.2335 −0.670814
\(661\) 0.134294 0.00522343 0.00261172 0.999997i \(-0.499169\pi\)
0.00261172 + 0.999997i \(0.499169\pi\)
\(662\) −30.2475 −1.17560
\(663\) −1.17793 −0.0457469
\(664\) 35.2499 1.36796
\(665\) 51.9995 2.01645
\(666\) 77.4101 2.99958
\(667\) 46.8888 1.81554
\(668\) 19.1120 0.739464
\(669\) −4.07035 −0.157369
\(670\) −40.0480 −1.54719
\(671\) −9.78801 −0.377862
\(672\) −42.4679 −1.63823
\(673\) 26.6102 1.02575 0.512874 0.858464i \(-0.328581\pi\)
0.512874 + 0.858464i \(0.328581\pi\)
\(674\) −54.0711 −2.08274
\(675\) −23.2735 −0.895799
\(676\) 5.07150 0.195058
\(677\) 10.4269 0.400737 0.200368 0.979721i \(-0.435786\pi\)
0.200368 + 0.979721i \(0.435786\pi\)
\(678\) 1.84540 0.0708720
\(679\) −35.9616 −1.38008
\(680\) −12.9616 −0.497056
\(681\) 8.09919 0.310362
\(682\) −23.1541 −0.886617
\(683\) −31.9126 −1.22110 −0.610551 0.791977i \(-0.709052\pi\)
−0.610551 + 0.791977i \(0.709052\pi\)
\(684\) 53.8241 2.05802
\(685\) 26.9788 1.03081
\(686\) −3.44826 −0.131655
\(687\) 2.43058 0.0927323
\(688\) −117.387 −4.47535
\(689\) −8.89630 −0.338922
\(690\) −39.2434 −1.49397
\(691\) 37.3120 1.41942 0.709708 0.704496i \(-0.248827\pi\)
0.709708 + 0.704496i \(0.248827\pi\)
\(692\) 81.8575 3.11175
\(693\) −13.8668 −0.526757
\(694\) 65.2736 2.47775
\(695\) −37.3146 −1.41542
\(696\) 43.0605 1.63221
\(697\) −3.55806 −0.134771
\(698\) −6.64303 −0.251442
\(699\) −12.1621 −0.460014
\(700\) 119.797 4.52791
\(701\) −21.1421 −0.798524 −0.399262 0.916837i \(-0.630734\pi\)
−0.399262 + 0.916837i \(0.630734\pi\)
\(702\) 38.1244 1.43891
\(703\) −47.1389 −1.77788
\(704\) 27.1854 1.02459
\(705\) −26.9781 −1.01605
\(706\) 13.6844 0.515017
\(707\) −58.5971 −2.20377
\(708\) 29.4808 1.10796
\(709\) 18.2110 0.683929 0.341965 0.939713i \(-0.388908\pi\)
0.341965 + 0.939713i \(0.388908\pi\)
\(710\) −8.92945 −0.335116
\(711\) 28.4058 1.06530
\(712\) −87.7015 −3.28675
\(713\) −38.0274 −1.42414
\(714\) 3.19544 0.119586
\(715\) −18.0747 −0.675954
\(716\) −23.7823 −0.888787
\(717\) −6.57200 −0.245436
\(718\) 26.2571 0.979905
\(719\) 12.7240 0.474526 0.237263 0.971445i \(-0.423750\pi\)
0.237263 + 0.971445i \(0.423750\pi\)
\(720\) 104.612 3.89865
\(721\) 51.0442 1.90099
\(722\) 5.44710 0.202720
\(723\) 7.91557 0.294383
\(724\) 16.7666 0.623125
\(725\) −44.9397 −1.66902
\(726\) 16.4191 0.609371
\(727\) −25.9533 −0.962554 −0.481277 0.876568i \(-0.659827\pi\)
−0.481277 + 0.876568i \(0.659827\pi\)
\(728\) −120.390 −4.46196
\(729\) −4.64059 −0.171874
\(730\) −68.8001 −2.54641
\(731\) 4.31974 0.159771
\(732\) −24.0641 −0.889434
\(733\) 29.1624 1.07714 0.538569 0.842581i \(-0.318965\pi\)
0.538569 + 0.842581i \(0.318965\pi\)
\(734\) −55.1689 −2.03632
\(735\) −16.8585 −0.621836
\(736\) 103.834 3.82736
\(737\) −6.50340 −0.239556
\(738\) 52.6330 1.93745
\(739\) −33.0764 −1.21674 −0.608368 0.793655i \(-0.708176\pi\)
−0.608368 + 0.793655i \(0.708176\pi\)
\(740\) −197.415 −7.25711
\(741\) −10.6107 −0.389795
\(742\) 24.1336 0.885973
\(743\) −16.7457 −0.614340 −0.307170 0.951655i \(-0.599382\pi\)
−0.307170 + 0.951655i \(0.599382\pi\)
\(744\) −34.9227 −1.28033
\(745\) 59.7900 2.19054
\(746\) −42.4130 −1.55285
\(747\) 10.4692 0.383048
\(748\) −3.43096 −0.125448
\(749\) 67.6704 2.47262
\(750\) 6.85193 0.250197
\(751\) 31.7810 1.15971 0.579853 0.814721i \(-0.303110\pi\)
0.579853 + 0.814721i \(0.303110\pi\)
\(752\) 145.954 5.32240
\(753\) 14.7808 0.538643
\(754\) 73.6159 2.68093
\(755\) 58.8425 2.14150
\(756\) −74.5919 −2.71288
\(757\) −27.1125 −0.985422 −0.492711 0.870193i \(-0.663994\pi\)
−0.492711 + 0.870193i \(0.663994\pi\)
\(758\) 24.7282 0.898167
\(759\) −6.37274 −0.231316
\(760\) −116.758 −4.23526
\(761\) 8.76202 0.317623 0.158812 0.987309i \(-0.449234\pi\)
0.158812 + 0.987309i \(0.449234\pi\)
\(762\) 17.0016 0.615904
\(763\) 20.3693 0.737419
\(764\) 17.6466 0.638432
\(765\) −3.84961 −0.139183
\(766\) 56.6560 2.04707
\(767\) 30.9197 1.11645
\(768\) 6.75880 0.243887
\(769\) 50.1723 1.80926 0.904630 0.426199i \(-0.140148\pi\)
0.904630 + 0.426199i \(0.140148\pi\)
\(770\) 49.0324 1.76700
\(771\) 13.9787 0.503432
\(772\) −113.299 −4.07773
\(773\) −42.9464 −1.54467 −0.772337 0.635213i \(-0.780912\pi\)
−0.772337 + 0.635213i \(0.780912\pi\)
\(774\) −63.9003 −2.29685
\(775\) 36.4467 1.30920
\(776\) 80.7471 2.89865
\(777\) 29.8576 1.07113
\(778\) 8.38921 0.300768
\(779\) −32.0509 −1.14834
\(780\) −44.4370 −1.59110
\(781\) −1.45005 −0.0518870
\(782\) −7.81283 −0.279386
\(783\) 27.9818 0.999988
\(784\) 91.2064 3.25737
\(785\) −39.0536 −1.39388
\(786\) 32.1402 1.14640
\(787\) 22.8026 0.812826 0.406413 0.913689i \(-0.366779\pi\)
0.406413 + 0.913689i \(0.366779\pi\)
\(788\) 38.7525 1.38050
\(789\) −16.5082 −0.587707
\(790\) −100.441 −3.57355
\(791\) −3.78681 −0.134644
\(792\) 31.1361 1.10637
\(793\) −25.2386 −0.896249
\(794\) −49.4408 −1.75459
\(795\) 5.46487 0.193819
\(796\) −95.1165 −3.37131
\(797\) −47.0794 −1.66764 −0.833818 0.552039i \(-0.813850\pi\)
−0.833818 + 0.552039i \(0.813850\pi\)
\(798\) 28.7845 1.01896
\(799\) −5.37097 −0.190011
\(800\) −99.5175 −3.51848
\(801\) −26.0473 −0.920337
\(802\) −97.3533 −3.43766
\(803\) −11.1725 −0.394267
\(804\) −15.9888 −0.563881
\(805\) 80.5288 2.83827
\(806\) −59.7034 −2.10296
\(807\) 12.7007 0.447085
\(808\) 131.572 4.62870
\(809\) 2.36449 0.0831309 0.0415655 0.999136i \(-0.486765\pi\)
0.0415655 + 0.999136i \(0.486765\pi\)
\(810\) 44.2302 1.55409
\(811\) 0.354600 0.0124517 0.00622585 0.999981i \(-0.498018\pi\)
0.00622585 + 0.999981i \(0.498018\pi\)
\(812\) −144.032 −5.05454
\(813\) −2.98464 −0.104676
\(814\) −44.4491 −1.55794
\(815\) −59.3638 −2.07942
\(816\) −3.91466 −0.137041
\(817\) 38.9121 1.36136
\(818\) 52.7116 1.84302
\(819\) −35.7559 −1.24941
\(820\) −134.227 −4.68741
\(821\) 47.9186 1.67237 0.836186 0.548447i \(-0.184781\pi\)
0.836186 + 0.548447i \(0.184781\pi\)
\(822\) 14.9342 0.520890
\(823\) −39.1141 −1.36343 −0.681716 0.731617i \(-0.738766\pi\)
−0.681716 + 0.731617i \(0.738766\pi\)
\(824\) −114.613 −3.99274
\(825\) 6.10785 0.212648
\(826\) −83.8781 −2.91849
\(827\) −26.7323 −0.929574 −0.464787 0.885422i \(-0.653869\pi\)
−0.464787 + 0.885422i \(0.653869\pi\)
\(828\) 83.3545 2.89677
\(829\) −36.6354 −1.27240 −0.636200 0.771524i \(-0.719495\pi\)
−0.636200 + 0.771524i \(0.719495\pi\)
\(830\) −37.0186 −1.28493
\(831\) −21.5072 −0.746077
\(832\) 70.0983 2.43022
\(833\) −3.35630 −0.116289
\(834\) −20.6556 −0.715244
\(835\) −12.3132 −0.426117
\(836\) −30.9060 −1.06891
\(837\) −22.6936 −0.784406
\(838\) 16.8029 0.580445
\(839\) 9.12535 0.315042 0.157521 0.987516i \(-0.449650\pi\)
0.157521 + 0.987516i \(0.449650\pi\)
\(840\) 73.9541 2.55166
\(841\) 25.0311 0.863143
\(842\) 43.3576 1.49420
\(843\) 10.9756 0.378018
\(844\) 74.4586 2.56297
\(845\) −3.26741 −0.112402
\(846\) 79.4507 2.73157
\(847\) −33.6926 −1.15769
\(848\) −29.5655 −1.01528
\(849\) 5.13220 0.176137
\(850\) 7.48808 0.256839
\(851\) −73.0015 −2.50246
\(852\) −3.56500 −0.122135
\(853\) 33.9057 1.16091 0.580455 0.814292i \(-0.302875\pi\)
0.580455 + 0.814292i \(0.302875\pi\)
\(854\) 68.4665 2.34288
\(855\) −34.6772 −1.18593
\(856\) −151.945 −5.19338
\(857\) 22.6440 0.773505 0.386752 0.922184i \(-0.373597\pi\)
0.386752 + 0.922184i \(0.373597\pi\)
\(858\) −10.0053 −0.341575
\(859\) 46.2344 1.57750 0.788748 0.614717i \(-0.210730\pi\)
0.788748 + 0.614717i \(0.210730\pi\)
\(860\) 162.961 5.55694
\(861\) 20.3009 0.691852
\(862\) −19.2776 −0.656599
\(863\) 9.03043 0.307399 0.153700 0.988118i \(-0.450881\pi\)
0.153700 + 0.988118i \(0.450881\pi\)
\(864\) 61.9648 2.10808
\(865\) −52.7382 −1.79315
\(866\) −67.7245 −2.30137
\(867\) −11.5683 −0.392880
\(868\) 116.812 3.96486
\(869\) −16.3107 −0.553303
\(870\) −45.2212 −1.53314
\(871\) −16.7692 −0.568202
\(872\) −45.7367 −1.54884
\(873\) 23.9819 0.811663
\(874\) −70.3777 −2.38056
\(875\) −14.0604 −0.475328
\(876\) −27.4678 −0.928050
\(877\) 1.89433 0.0639671 0.0319836 0.999488i \(-0.489818\pi\)
0.0319836 + 0.999488i \(0.489818\pi\)
\(878\) −81.7916 −2.76033
\(879\) −8.64551 −0.291606
\(880\) −60.0684 −2.02491
\(881\) −42.2893 −1.42476 −0.712381 0.701793i \(-0.752383\pi\)
−0.712381 + 0.701793i \(0.752383\pi\)
\(882\) 49.6485 1.67175
\(883\) −12.4612 −0.419354 −0.209677 0.977771i \(-0.567241\pi\)
−0.209677 + 0.977771i \(0.567241\pi\)
\(884\) −8.84681 −0.297550
\(885\) −18.9936 −0.638461
\(886\) −83.9567 −2.82058
\(887\) −20.4076 −0.685219 −0.342609 0.939478i \(-0.611311\pi\)
−0.342609 + 0.939478i \(0.611311\pi\)
\(888\) −67.0413 −2.24976
\(889\) −34.8879 −1.17010
\(890\) 92.1021 3.08727
\(891\) 7.18254 0.240624
\(892\) −30.5703 −1.02357
\(893\) −48.3815 −1.61903
\(894\) 33.0969 1.10693
\(895\) 15.3222 0.512164
\(896\) −66.8798 −2.23430
\(897\) −16.4323 −0.548657
\(898\) 3.58346 0.119582
\(899\) −43.8200 −1.46148
\(900\) −79.8897 −2.66299
\(901\) 1.08798 0.0362459
\(902\) −30.2221 −1.00628
\(903\) −24.6468 −0.820193
\(904\) 8.50280 0.282799
\(905\) −10.8022 −0.359076
\(906\) 32.5724 1.08215
\(907\) 13.8214 0.458931 0.229465 0.973317i \(-0.426302\pi\)
0.229465 + 0.973317i \(0.426302\pi\)
\(908\) 60.8289 2.01868
\(909\) 39.0769 1.29610
\(910\) 126.431 4.19115
\(911\) −42.3017 −1.40152 −0.700759 0.713398i \(-0.747155\pi\)
−0.700759 + 0.713398i \(0.747155\pi\)
\(912\) −35.2632 −1.16768
\(913\) −6.01146 −0.198950
\(914\) 38.4484 1.27176
\(915\) 15.5037 0.512537
\(916\) 18.2548 0.603157
\(917\) −65.9529 −2.17796
\(918\) −4.66246 −0.153884
\(919\) −47.5567 −1.56875 −0.784376 0.620286i \(-0.787016\pi\)
−0.784376 + 0.620286i \(0.787016\pi\)
\(920\) −180.817 −5.96136
\(921\) −4.01954 −0.132448
\(922\) 16.0144 0.527406
\(923\) −3.73900 −0.123071
\(924\) 19.5757 0.643994
\(925\) 69.9670 2.30050
\(926\) 36.4804 1.19882
\(927\) −34.0401 −1.11802
\(928\) 119.650 3.92771
\(929\) −40.6423 −1.33343 −0.666716 0.745312i \(-0.732301\pi\)
−0.666716 + 0.745312i \(0.732301\pi\)
\(930\) 36.6750 1.20262
\(931\) −30.2335 −0.990863
\(932\) −91.3436 −2.99206
\(933\) 11.9647 0.391705
\(934\) 37.7880 1.23646
\(935\) 2.21046 0.0722897
\(936\) 80.2852 2.62420
\(937\) −36.6631 −1.19773 −0.598866 0.800849i \(-0.704382\pi\)
−0.598866 + 0.800849i \(0.704382\pi\)
\(938\) 45.4909 1.48533
\(939\) −22.4017 −0.731051
\(940\) −202.619 −6.60869
\(941\) −40.8944 −1.33312 −0.666560 0.745452i \(-0.732234\pi\)
−0.666560 + 0.745452i \(0.732234\pi\)
\(942\) −21.6182 −0.704359
\(943\) −49.6355 −1.61635
\(944\) 102.757 3.34446
\(945\) 48.0572 1.56330
\(946\) 36.6918 1.19295
\(947\) 6.80385 0.221095 0.110548 0.993871i \(-0.464740\pi\)
0.110548 + 0.993871i \(0.464740\pi\)
\(948\) −40.1003 −1.30240
\(949\) −28.8084 −0.935161
\(950\) 67.4524 2.18844
\(951\) −7.37316 −0.239091
\(952\) 14.7232 0.477183
\(953\) −5.91109 −0.191479 −0.0957395 0.995406i \(-0.530522\pi\)
−0.0957395 + 0.995406i \(0.530522\pi\)
\(954\) −16.0941 −0.521066
\(955\) −11.3692 −0.367897
\(956\) −49.3590 −1.59638
\(957\) −7.34348 −0.237381
\(958\) 39.8427 1.28726
\(959\) −30.6454 −0.989593
\(960\) −43.0604 −1.38977
\(961\) 4.53855 0.146405
\(962\) −114.613 −3.69528
\(963\) −45.1277 −1.45422
\(964\) 59.4498 1.91475
\(965\) 72.9951 2.34979
\(966\) 44.5769 1.43424
\(967\) −55.9694 −1.79986 −0.899928 0.436038i \(-0.856381\pi\)
−0.899928 + 0.436038i \(0.856381\pi\)
\(968\) 75.6523 2.43156
\(969\) 1.29765 0.0416865
\(970\) −84.7987 −2.72272
\(971\) −30.9489 −0.993197 −0.496599 0.867980i \(-0.665418\pi\)
−0.496599 + 0.867980i \(0.665418\pi\)
\(972\) 76.7518 2.46182
\(973\) 42.3860 1.35883
\(974\) 86.4111 2.76879
\(975\) 15.7492 0.504379
\(976\) −83.8767 −2.68483
\(977\) −41.9756 −1.34292 −0.671460 0.741041i \(-0.734332\pi\)
−0.671460 + 0.741041i \(0.734332\pi\)
\(978\) −32.8610 −1.05078
\(979\) 14.9565 0.478011
\(980\) −126.616 −4.04460
\(981\) −13.5838 −0.433697
\(982\) −19.2707 −0.614954
\(983\) −24.4535 −0.779944 −0.389972 0.920827i \(-0.627515\pi\)
−0.389972 + 0.920827i \(0.627515\pi\)
\(984\) −45.5830 −1.45313
\(985\) −24.9670 −0.795515
\(986\) −9.00293 −0.286712
\(987\) 30.6446 0.975429
\(988\) −79.6918 −2.53533
\(989\) 60.2611 1.91619
\(990\) −32.6985 −1.03923
\(991\) −13.3971 −0.425574 −0.212787 0.977099i \(-0.568254\pi\)
−0.212787 + 0.977099i \(0.568254\pi\)
\(992\) −97.0378 −3.08095
\(993\) 7.78021 0.246898
\(994\) 10.1430 0.321718
\(995\) 61.2805 1.94272
\(996\) −14.7793 −0.468301
\(997\) −31.6661 −1.00287 −0.501437 0.865194i \(-0.667195\pi\)
−0.501437 + 0.865194i \(0.667195\pi\)
\(998\) 92.6011 2.93124
\(999\) −43.5651 −1.37834
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 \(a_p\))