Properties

Label 8042.2.a.c.1.6
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.75315 q^{3}\) \(+1.00000 q^{4}\) \(+3.02853 q^{5}\) \(+2.75315 q^{6}\) \(+4.50146 q^{7}\) \(-1.00000 q^{8}\) \(+4.57981 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.75315 q^{3}\) \(+1.00000 q^{4}\) \(+3.02853 q^{5}\) \(+2.75315 q^{6}\) \(+4.50146 q^{7}\) \(-1.00000 q^{8}\) \(+4.57981 q^{9}\) \(-3.02853 q^{10}\) \(+2.88661 q^{11}\) \(-2.75315 q^{12}\) \(+5.83952 q^{13}\) \(-4.50146 q^{14}\) \(-8.33799 q^{15}\) \(+1.00000 q^{16}\) \(-2.94349 q^{17}\) \(-4.57981 q^{18}\) \(+3.68725 q^{19}\) \(+3.02853 q^{20}\) \(-12.3932 q^{21}\) \(-2.88661 q^{22}\) \(+4.87572 q^{23}\) \(+2.75315 q^{24}\) \(+4.17200 q^{25}\) \(-5.83952 q^{26}\) \(-4.34944 q^{27}\) \(+4.50146 q^{28}\) \(+1.69578 q^{29}\) \(+8.33799 q^{30}\) \(-9.89201 q^{31}\) \(-1.00000 q^{32}\) \(-7.94726 q^{33}\) \(+2.94349 q^{34}\) \(+13.6328 q^{35}\) \(+4.57981 q^{36}\) \(+1.79643 q^{37}\) \(-3.68725 q^{38}\) \(-16.0771 q^{39}\) \(-3.02853 q^{40}\) \(-0.569520 q^{41}\) \(+12.3932 q^{42}\) \(-11.7069 q^{43}\) \(+2.88661 q^{44}\) \(+13.8701 q^{45}\) \(-4.87572 q^{46}\) \(+6.29159 q^{47}\) \(-2.75315 q^{48}\) \(+13.2632 q^{49}\) \(-4.17200 q^{50}\) \(+8.10386 q^{51}\) \(+5.83952 q^{52}\) \(-1.91731 q^{53}\) \(+4.34944 q^{54}\) \(+8.74219 q^{55}\) \(-4.50146 q^{56}\) \(-10.1515 q^{57}\) \(-1.69578 q^{58}\) \(+13.2185 q^{59}\) \(-8.33799 q^{60}\) \(-11.8907 q^{61}\) \(+9.89201 q^{62}\) \(+20.6158 q^{63}\) \(+1.00000 q^{64}\) \(+17.6852 q^{65}\) \(+7.94726 q^{66}\) \(+11.6665 q^{67}\) \(-2.94349 q^{68}\) \(-13.4236 q^{69}\) \(-13.6328 q^{70}\) \(+5.38045 q^{71}\) \(-4.57981 q^{72}\) \(-1.65252 q^{73}\) \(-1.79643 q^{74}\) \(-11.4861 q^{75}\) \(+3.68725 q^{76}\) \(+12.9940 q^{77}\) \(+16.0771 q^{78}\) \(+13.5744 q^{79}\) \(+3.02853 q^{80}\) \(-1.76478 q^{81}\) \(+0.569520 q^{82}\) \(-7.47975 q^{83}\) \(-12.3932 q^{84}\) \(-8.91446 q^{85}\) \(+11.7069 q^{86}\) \(-4.66873 q^{87}\) \(-2.88661 q^{88}\) \(-2.44770 q^{89}\) \(-13.8701 q^{90}\) \(+26.2864 q^{91}\) \(+4.87572 q^{92}\) \(+27.2341 q^{93}\) \(-6.29159 q^{94}\) \(+11.1669 q^{95}\) \(+2.75315 q^{96}\) \(+13.7912 q^{97}\) \(-13.2632 q^{98}\) \(+13.2201 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.75315 −1.58953 −0.794765 0.606918i \(-0.792406\pi\)
−0.794765 + 0.606918i \(0.792406\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.02853 1.35440 0.677200 0.735799i \(-0.263193\pi\)
0.677200 + 0.735799i \(0.263193\pi\)
\(6\) 2.75315 1.12397
\(7\) 4.50146 1.70139 0.850697 0.525657i \(-0.176180\pi\)
0.850697 + 0.525657i \(0.176180\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.57981 1.52660
\(10\) −3.02853 −0.957706
\(11\) 2.88661 0.870346 0.435173 0.900347i \(-0.356687\pi\)
0.435173 + 0.900347i \(0.356687\pi\)
\(12\) −2.75315 −0.794765
\(13\) 5.83952 1.61959 0.809796 0.586711i \(-0.199578\pi\)
0.809796 + 0.586711i \(0.199578\pi\)
\(14\) −4.50146 −1.20307
\(15\) −8.33799 −2.15286
\(16\) 1.00000 0.250000
\(17\) −2.94349 −0.713902 −0.356951 0.934123i \(-0.616184\pi\)
−0.356951 + 0.934123i \(0.616184\pi\)
\(18\) −4.57981 −1.07947
\(19\) 3.68725 0.845912 0.422956 0.906150i \(-0.360992\pi\)
0.422956 + 0.906150i \(0.360992\pi\)
\(20\) 3.02853 0.677200
\(21\) −12.3932 −2.70441
\(22\) −2.88661 −0.615427
\(23\) 4.87572 1.01666 0.508328 0.861163i \(-0.330264\pi\)
0.508328 + 0.861163i \(0.330264\pi\)
\(24\) 2.75315 0.561983
\(25\) 4.17200 0.834400
\(26\) −5.83952 −1.14522
\(27\) −4.34944 −0.837051
\(28\) 4.50146 0.850697
\(29\) 1.69578 0.314898 0.157449 0.987527i \(-0.449673\pi\)
0.157449 + 0.987527i \(0.449673\pi\)
\(30\) 8.33799 1.52230
\(31\) −9.89201 −1.77666 −0.888329 0.459208i \(-0.848133\pi\)
−0.888329 + 0.459208i \(0.848133\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.94726 −1.38344
\(34\) 2.94349 0.504805
\(35\) 13.6328 2.30437
\(36\) 4.57981 0.763301
\(37\) 1.79643 0.295331 0.147665 0.989037i \(-0.452824\pi\)
0.147665 + 0.989037i \(0.452824\pi\)
\(38\) −3.68725 −0.598150
\(39\) −16.0771 −2.57439
\(40\) −3.02853 −0.478853
\(41\) −0.569520 −0.0889440 −0.0444720 0.999011i \(-0.514161\pi\)
−0.0444720 + 0.999011i \(0.514161\pi\)
\(42\) 12.3932 1.91231
\(43\) −11.7069 −1.78529 −0.892646 0.450758i \(-0.851154\pi\)
−0.892646 + 0.450758i \(0.851154\pi\)
\(44\) 2.88661 0.435173
\(45\) 13.8701 2.06763
\(46\) −4.87572 −0.718885
\(47\) 6.29159 0.917723 0.458862 0.888508i \(-0.348257\pi\)
0.458862 + 0.888508i \(0.348257\pi\)
\(48\) −2.75315 −0.397382
\(49\) 13.2632 1.89474
\(50\) −4.17200 −0.590010
\(51\) 8.10386 1.13477
\(52\) 5.83952 0.809796
\(53\) −1.91731 −0.263363 −0.131682 0.991292i \(-0.542038\pi\)
−0.131682 + 0.991292i \(0.542038\pi\)
\(54\) 4.34944 0.591884
\(55\) 8.74219 1.17880
\(56\) −4.50146 −0.601533
\(57\) −10.1515 −1.34460
\(58\) −1.69578 −0.222667
\(59\) 13.2185 1.72090 0.860451 0.509533i \(-0.170182\pi\)
0.860451 + 0.509533i \(0.170182\pi\)
\(60\) −8.33799 −1.07643
\(61\) −11.8907 −1.52245 −0.761227 0.648486i \(-0.775403\pi\)
−0.761227 + 0.648486i \(0.775403\pi\)
\(62\) 9.89201 1.25629
\(63\) 20.6158 2.59735
\(64\) 1.00000 0.125000
\(65\) 17.6852 2.19358
\(66\) 7.94726 0.978240
\(67\) 11.6665 1.42529 0.712644 0.701526i \(-0.247498\pi\)
0.712644 + 0.701526i \(0.247498\pi\)
\(68\) −2.94349 −0.356951
\(69\) −13.4236 −1.61601
\(70\) −13.6328 −1.62943
\(71\) 5.38045 0.638543 0.319271 0.947663i \(-0.396562\pi\)
0.319271 + 0.947663i \(0.396562\pi\)
\(72\) −4.57981 −0.539736
\(73\) −1.65252 −0.193413 −0.0967064 0.995313i \(-0.530831\pi\)
−0.0967064 + 0.995313i \(0.530831\pi\)
\(74\) −1.79643 −0.208830
\(75\) −11.4861 −1.32630
\(76\) 3.68725 0.422956
\(77\) 12.9940 1.48080
\(78\) 16.0771 1.82037
\(79\) 13.5744 1.52724 0.763621 0.645665i \(-0.223420\pi\)
0.763621 + 0.645665i \(0.223420\pi\)
\(80\) 3.02853 0.338600
\(81\) −1.76478 −0.196086
\(82\) 0.569520 0.0628929
\(83\) −7.47975 −0.821010 −0.410505 0.911858i \(-0.634648\pi\)
−0.410505 + 0.911858i \(0.634648\pi\)
\(84\) −12.3932 −1.35221
\(85\) −8.91446 −0.966909
\(86\) 11.7069 1.26239
\(87\) −4.66873 −0.500540
\(88\) −2.88661 −0.307714
\(89\) −2.44770 −0.259456 −0.129728 0.991550i \(-0.541410\pi\)
−0.129728 + 0.991550i \(0.541410\pi\)
\(90\) −13.8701 −1.46204
\(91\) 26.2864 2.75556
\(92\) 4.87572 0.508328
\(93\) 27.2341 2.82405
\(94\) −6.29159 −0.648928
\(95\) 11.1669 1.14570
\(96\) 2.75315 0.280992
\(97\) 13.7912 1.40028 0.700141 0.714005i \(-0.253121\pi\)
0.700141 + 0.714005i \(0.253121\pi\)
\(98\) −13.2632 −1.33978
\(99\) 13.2201 1.32867
\(100\) 4.17200 0.417200
\(101\) 17.4062 1.73198 0.865990 0.500061i \(-0.166689\pi\)
0.865990 + 0.500061i \(0.166689\pi\)
\(102\) −8.10386 −0.802402
\(103\) −12.2794 −1.20993 −0.604963 0.796254i \(-0.706812\pi\)
−0.604963 + 0.796254i \(0.706812\pi\)
\(104\) −5.83952 −0.572612
\(105\) −37.5331 −3.66286
\(106\) 1.91731 0.186226
\(107\) −16.3499 −1.58060 −0.790300 0.612719i \(-0.790076\pi\)
−0.790300 + 0.612719i \(0.790076\pi\)
\(108\) −4.34944 −0.418525
\(109\) 1.13884 0.109081 0.0545406 0.998512i \(-0.482631\pi\)
0.0545406 + 0.998512i \(0.482631\pi\)
\(110\) −8.74219 −0.833535
\(111\) −4.94582 −0.469437
\(112\) 4.50146 0.425348
\(113\) 2.68101 0.252208 0.126104 0.992017i \(-0.459753\pi\)
0.126104 + 0.992017i \(0.459753\pi\)
\(114\) 10.1515 0.950777
\(115\) 14.7663 1.37696
\(116\) 1.69578 0.157449
\(117\) 26.7439 2.47248
\(118\) −13.2185 −1.21686
\(119\) −13.2500 −1.21463
\(120\) 8.33799 0.761150
\(121\) −2.66748 −0.242499
\(122\) 11.8907 1.07654
\(123\) 1.56797 0.141379
\(124\) −9.89201 −0.888329
\(125\) −2.50763 −0.224289
\(126\) −20.6158 −1.83661
\(127\) 14.8970 1.32189 0.660946 0.750433i \(-0.270155\pi\)
0.660946 + 0.750433i \(0.270155\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 32.2309 2.83778
\(130\) −17.6852 −1.55109
\(131\) −4.79256 −0.418728 −0.209364 0.977838i \(-0.567139\pi\)
−0.209364 + 0.977838i \(0.567139\pi\)
\(132\) −7.94726 −0.691720
\(133\) 16.5980 1.43923
\(134\) −11.6665 −1.00783
\(135\) −13.1724 −1.13370
\(136\) 2.94349 0.252402
\(137\) −1.80655 −0.154344 −0.0771718 0.997018i \(-0.524589\pi\)
−0.0771718 + 0.997018i \(0.524589\pi\)
\(138\) 13.4236 1.14269
\(139\) −0.222556 −0.0188769 −0.00943846 0.999955i \(-0.503004\pi\)
−0.00943846 + 0.999955i \(0.503004\pi\)
\(140\) 13.6328 1.15218
\(141\) −17.3217 −1.45875
\(142\) −5.38045 −0.451518
\(143\) 16.8564 1.40961
\(144\) 4.57981 0.381651
\(145\) 5.13572 0.426498
\(146\) 1.65252 0.136764
\(147\) −36.5155 −3.01174
\(148\) 1.79643 0.147665
\(149\) −12.5431 −1.02757 −0.513787 0.857918i \(-0.671758\pi\)
−0.513787 + 0.857918i \(0.671758\pi\)
\(150\) 11.4861 0.937838
\(151\) 12.6082 1.02604 0.513019 0.858377i \(-0.328527\pi\)
0.513019 + 0.858377i \(0.328527\pi\)
\(152\) −3.68725 −0.299075
\(153\) −13.4806 −1.08984
\(154\) −12.9940 −1.04708
\(155\) −29.9583 −2.40631
\(156\) −16.0771 −1.28719
\(157\) −21.0653 −1.68119 −0.840596 0.541662i \(-0.817795\pi\)
−0.840596 + 0.541662i \(0.817795\pi\)
\(158\) −13.5744 −1.07992
\(159\) 5.27864 0.418623
\(160\) −3.02853 −0.239426
\(161\) 21.9479 1.72973
\(162\) 1.76478 0.138654
\(163\) 15.6421 1.22518 0.612592 0.790399i \(-0.290127\pi\)
0.612592 + 0.790399i \(0.290127\pi\)
\(164\) −0.569520 −0.0444720
\(165\) −24.0685 −1.87373
\(166\) 7.47975 0.580542
\(167\) 13.6967 1.05989 0.529943 0.848033i \(-0.322213\pi\)
0.529943 + 0.848033i \(0.322213\pi\)
\(168\) 12.3932 0.956155
\(169\) 21.1000 1.62308
\(170\) 8.91446 0.683708
\(171\) 16.8869 1.29137
\(172\) −11.7069 −0.892646
\(173\) −8.42146 −0.640272 −0.320136 0.947372i \(-0.603729\pi\)
−0.320136 + 0.947372i \(0.603729\pi\)
\(174\) 4.66873 0.353935
\(175\) 18.7801 1.41964
\(176\) 2.88661 0.217586
\(177\) −36.3924 −2.73542
\(178\) 2.44770 0.183463
\(179\) 4.45864 0.333255 0.166627 0.986020i \(-0.446712\pi\)
0.166627 + 0.986020i \(0.446712\pi\)
\(180\) 13.8701 1.03382
\(181\) 6.08728 0.452464 0.226232 0.974073i \(-0.427359\pi\)
0.226232 + 0.974073i \(0.427359\pi\)
\(182\) −26.2864 −1.94848
\(183\) 32.7369 2.41998
\(184\) −4.87572 −0.359442
\(185\) 5.44053 0.399996
\(186\) −27.2341 −1.99690
\(187\) −8.49671 −0.621341
\(188\) 6.29159 0.458862
\(189\) −19.5789 −1.42415
\(190\) −11.1669 −0.810135
\(191\) −21.5935 −1.56245 −0.781226 0.624248i \(-0.785406\pi\)
−0.781226 + 0.624248i \(0.785406\pi\)
\(192\) −2.75315 −0.198691
\(193\) 19.9811 1.43827 0.719136 0.694869i \(-0.244538\pi\)
0.719136 + 0.694869i \(0.244538\pi\)
\(194\) −13.7912 −0.990149
\(195\) −48.6899 −3.48675
\(196\) 13.2632 0.947370
\(197\) 1.61771 0.115257 0.0576287 0.998338i \(-0.481646\pi\)
0.0576287 + 0.998338i \(0.481646\pi\)
\(198\) −13.2201 −0.939513
\(199\) 7.52184 0.533209 0.266605 0.963806i \(-0.414098\pi\)
0.266605 + 0.963806i \(0.414098\pi\)
\(200\) −4.17200 −0.295005
\(201\) −32.1195 −2.26554
\(202\) −17.4062 −1.22470
\(203\) 7.63349 0.535766
\(204\) 8.10386 0.567384
\(205\) −1.72481 −0.120466
\(206\) 12.2794 0.855547
\(207\) 22.3298 1.55203
\(208\) 5.83952 0.404898
\(209\) 10.6436 0.736236
\(210\) 37.5331 2.59003
\(211\) 18.7559 1.29121 0.645606 0.763671i \(-0.276605\pi\)
0.645606 + 0.763671i \(0.276605\pi\)
\(212\) −1.91731 −0.131682
\(213\) −14.8132 −1.01498
\(214\) 16.3499 1.11765
\(215\) −35.4549 −2.41800
\(216\) 4.34944 0.295942
\(217\) −44.5285 −3.02279
\(218\) −1.13884 −0.0771320
\(219\) 4.54963 0.307435
\(220\) 8.74219 0.589398
\(221\) −17.1886 −1.15623
\(222\) 4.94582 0.331942
\(223\) −9.69629 −0.649312 −0.324656 0.945832i \(-0.605248\pi\)
−0.324656 + 0.945832i \(0.605248\pi\)
\(224\) −4.50146 −0.300767
\(225\) 19.1070 1.27380
\(226\) −2.68101 −0.178338
\(227\) −8.71525 −0.578452 −0.289226 0.957261i \(-0.593398\pi\)
−0.289226 + 0.957261i \(0.593398\pi\)
\(228\) −10.1515 −0.672301
\(229\) −27.9523 −1.84714 −0.923570 0.383430i \(-0.874743\pi\)
−0.923570 + 0.383430i \(0.874743\pi\)
\(230\) −14.7663 −0.973658
\(231\) −35.7743 −2.35378
\(232\) −1.69578 −0.111333
\(233\) −7.51877 −0.492571 −0.246286 0.969197i \(-0.579210\pi\)
−0.246286 + 0.969197i \(0.579210\pi\)
\(234\) −26.7439 −1.74830
\(235\) 19.0543 1.24296
\(236\) 13.2185 0.860451
\(237\) −37.3723 −2.42759
\(238\) 13.2500 0.858871
\(239\) 16.0126 1.03577 0.517885 0.855450i \(-0.326720\pi\)
0.517885 + 0.855450i \(0.326720\pi\)
\(240\) −8.33799 −0.538215
\(241\) −1.18272 −0.0761859 −0.0380930 0.999274i \(-0.512128\pi\)
−0.0380930 + 0.999274i \(0.512128\pi\)
\(242\) 2.66748 0.171472
\(243\) 17.9070 1.14874
\(244\) −11.8907 −0.761227
\(245\) 40.1679 2.56624
\(246\) −1.56797 −0.0999701
\(247\) 21.5318 1.37003
\(248\) 9.89201 0.628143
\(249\) 20.5929 1.30502
\(250\) 2.50763 0.158596
\(251\) −12.0311 −0.759394 −0.379697 0.925111i \(-0.623972\pi\)
−0.379697 + 0.925111i \(0.623972\pi\)
\(252\) 20.6158 1.29868
\(253\) 14.0743 0.884843
\(254\) −14.8970 −0.934719
\(255\) 24.5428 1.53693
\(256\) 1.00000 0.0625000
\(257\) −2.04290 −0.127433 −0.0637164 0.997968i \(-0.520295\pi\)
−0.0637164 + 0.997968i \(0.520295\pi\)
\(258\) −32.2309 −2.00661
\(259\) 8.08655 0.502474
\(260\) 17.6852 1.09679
\(261\) 7.76635 0.480725
\(262\) 4.79256 0.296085
\(263\) −29.8758 −1.84222 −0.921109 0.389305i \(-0.872715\pi\)
−0.921109 + 0.389305i \(0.872715\pi\)
\(264\) 7.94726 0.489120
\(265\) −5.80664 −0.356699
\(266\) −16.5980 −1.01769
\(267\) 6.73887 0.412412
\(268\) 11.6665 0.712644
\(269\) −15.8029 −0.963523 −0.481761 0.876302i \(-0.660003\pi\)
−0.481761 + 0.876302i \(0.660003\pi\)
\(270\) 13.1724 0.801648
\(271\) −14.3858 −0.873876 −0.436938 0.899492i \(-0.643937\pi\)
−0.436938 + 0.899492i \(0.643937\pi\)
\(272\) −2.94349 −0.178475
\(273\) −72.3703 −4.38005
\(274\) 1.80655 0.109137
\(275\) 12.0429 0.726216
\(276\) −13.4236 −0.808003
\(277\) 4.98762 0.299677 0.149839 0.988710i \(-0.452125\pi\)
0.149839 + 0.988710i \(0.452125\pi\)
\(278\) 0.222556 0.0133480
\(279\) −45.3035 −2.71225
\(280\) −13.6328 −0.814717
\(281\) −12.7563 −0.760974 −0.380487 0.924786i \(-0.624244\pi\)
−0.380487 + 0.924786i \(0.624244\pi\)
\(282\) 17.3217 1.03149
\(283\) 4.67345 0.277808 0.138904 0.990306i \(-0.455642\pi\)
0.138904 + 0.990306i \(0.455642\pi\)
\(284\) 5.38045 0.319271
\(285\) −30.7442 −1.82113
\(286\) −16.8564 −0.996741
\(287\) −2.56367 −0.151329
\(288\) −4.57981 −0.269868
\(289\) −8.33586 −0.490344
\(290\) −5.13572 −0.301580
\(291\) −37.9691 −2.22579
\(292\) −1.65252 −0.0967064
\(293\) −27.0645 −1.58113 −0.790563 0.612380i \(-0.790212\pi\)
−0.790563 + 0.612380i \(0.790212\pi\)
\(294\) 36.5155 2.12962
\(295\) 40.0326 2.33079
\(296\) −1.79643 −0.104415
\(297\) −12.5551 −0.728523
\(298\) 12.5431 0.726604
\(299\) 28.4719 1.64657
\(300\) −11.4861 −0.663151
\(301\) −52.6984 −3.03749
\(302\) −12.6082 −0.725518
\(303\) −47.9218 −2.75303
\(304\) 3.68725 0.211478
\(305\) −36.0115 −2.06201
\(306\) 13.4806 0.770636
\(307\) 3.03475 0.173202 0.0866012 0.996243i \(-0.472399\pi\)
0.0866012 + 0.996243i \(0.472399\pi\)
\(308\) 12.9940 0.740400
\(309\) 33.8070 1.92321
\(310\) 29.9583 1.70152
\(311\) −33.4222 −1.89520 −0.947599 0.319462i \(-0.896498\pi\)
−0.947599 + 0.319462i \(0.896498\pi\)
\(312\) 16.0771 0.910184
\(313\) 10.0688 0.569123 0.284561 0.958658i \(-0.408152\pi\)
0.284561 + 0.958658i \(0.408152\pi\)
\(314\) 21.0653 1.18878
\(315\) 62.4357 3.51785
\(316\) 13.5744 0.763621
\(317\) −17.1552 −0.963533 −0.481766 0.876300i \(-0.660005\pi\)
−0.481766 + 0.876300i \(0.660005\pi\)
\(318\) −5.27864 −0.296011
\(319\) 4.89505 0.274070
\(320\) 3.02853 0.169300
\(321\) 45.0136 2.51241
\(322\) −21.9479 −1.22311
\(323\) −10.8534 −0.603898
\(324\) −1.76478 −0.0980432
\(325\) 24.3625 1.35139
\(326\) −15.6421 −0.866336
\(327\) −3.13539 −0.173388
\(328\) 0.569520 0.0314465
\(329\) 28.3214 1.56141
\(330\) 24.0685 1.32493
\(331\) −17.8047 −0.978634 −0.489317 0.872106i \(-0.662754\pi\)
−0.489317 + 0.872106i \(0.662754\pi\)
\(332\) −7.47975 −0.410505
\(333\) 8.22729 0.450853
\(334\) −13.6967 −0.749452
\(335\) 35.3323 1.93041
\(336\) −12.3932 −0.676104
\(337\) −0.0559972 −0.00305036 −0.00152518 0.999999i \(-0.500485\pi\)
−0.00152518 + 0.999999i \(0.500485\pi\)
\(338\) −21.1000 −1.14769
\(339\) −7.38121 −0.400892
\(340\) −8.91446 −0.483454
\(341\) −28.5544 −1.54631
\(342\) −16.8869 −0.913138
\(343\) 28.1935 1.52230
\(344\) 11.7069 0.631196
\(345\) −40.6536 −2.18872
\(346\) 8.42146 0.452740
\(347\) 14.5712 0.782221 0.391111 0.920344i \(-0.372091\pi\)
0.391111 + 0.920344i \(0.372091\pi\)
\(348\) −4.66873 −0.250270
\(349\) −15.0940 −0.807964 −0.403982 0.914767i \(-0.632374\pi\)
−0.403982 + 0.914767i \(0.632374\pi\)
\(350\) −18.7801 −1.00384
\(351\) −25.3987 −1.35568
\(352\) −2.88661 −0.153857
\(353\) −14.0657 −0.748640 −0.374320 0.927300i \(-0.622124\pi\)
−0.374320 + 0.927300i \(0.622124\pi\)
\(354\) 36.3924 1.93424
\(355\) 16.2949 0.864842
\(356\) −2.44770 −0.129728
\(357\) 36.4792 1.93069
\(358\) −4.45864 −0.235647
\(359\) −36.0333 −1.90177 −0.950883 0.309552i \(-0.899821\pi\)
−0.950883 + 0.309552i \(0.899821\pi\)
\(360\) −13.8701 −0.731018
\(361\) −5.40422 −0.284432
\(362\) −6.08728 −0.319940
\(363\) 7.34397 0.385459
\(364\) 26.2864 1.37778
\(365\) −5.00471 −0.261958
\(366\) −32.7369 −1.71119
\(367\) 29.0243 1.51506 0.757528 0.652802i \(-0.226407\pi\)
0.757528 + 0.652802i \(0.226407\pi\)
\(368\) 4.87572 0.254164
\(369\) −2.60829 −0.135782
\(370\) −5.44053 −0.282840
\(371\) −8.63071 −0.448084
\(372\) 27.2341 1.41202
\(373\) −5.48833 −0.284175 −0.142088 0.989854i \(-0.545381\pi\)
−0.142088 + 0.989854i \(0.545381\pi\)
\(374\) 8.49671 0.439355
\(375\) 6.90386 0.356514
\(376\) −6.29159 −0.324464
\(377\) 9.90254 0.510007
\(378\) 19.5789 1.00703
\(379\) 23.4621 1.20517 0.602583 0.798056i \(-0.294138\pi\)
0.602583 + 0.798056i \(0.294138\pi\)
\(380\) 11.1669 0.572852
\(381\) −41.0135 −2.10119
\(382\) 21.5935 1.10482
\(383\) 3.74050 0.191131 0.0955654 0.995423i \(-0.469534\pi\)
0.0955654 + 0.995423i \(0.469534\pi\)
\(384\) 2.75315 0.140496
\(385\) 39.3526 2.00560
\(386\) −19.9811 −1.01701
\(387\) −53.6156 −2.72543
\(388\) 13.7912 0.700141
\(389\) −21.2083 −1.07530 −0.537652 0.843167i \(-0.680689\pi\)
−0.537652 + 0.843167i \(0.680689\pi\)
\(390\) 48.6899 2.46551
\(391\) −14.3516 −0.725793
\(392\) −13.2632 −0.669892
\(393\) 13.1946 0.665580
\(394\) −1.61771 −0.0814993
\(395\) 41.1105 2.06850
\(396\) 13.2201 0.664336
\(397\) 24.8701 1.24819 0.624096 0.781347i \(-0.285467\pi\)
0.624096 + 0.781347i \(0.285467\pi\)
\(398\) −7.52184 −0.377036
\(399\) −45.6967 −2.28770
\(400\) 4.17200 0.208600
\(401\) −1.88000 −0.0938826 −0.0469413 0.998898i \(-0.514947\pi\)
−0.0469413 + 0.998898i \(0.514947\pi\)
\(402\) 32.1195 1.60198
\(403\) −57.7647 −2.87746
\(404\) 17.4062 0.865990
\(405\) −5.34468 −0.265579
\(406\) −7.63349 −0.378844
\(407\) 5.18558 0.257040
\(408\) −8.10386 −0.401201
\(409\) 24.9765 1.23501 0.617504 0.786567i \(-0.288144\pi\)
0.617504 + 0.786567i \(0.288144\pi\)
\(410\) 1.72481 0.0851822
\(411\) 4.97368 0.245334
\(412\) −12.2794 −0.604963
\(413\) 59.5026 2.92793
\(414\) −22.3298 −1.09745
\(415\) −22.6527 −1.11198
\(416\) −5.83952 −0.286306
\(417\) 0.612728 0.0300054
\(418\) −10.6436 −0.520597
\(419\) 34.5174 1.68629 0.843143 0.537689i \(-0.180703\pi\)
0.843143 + 0.537689i \(0.180703\pi\)
\(420\) −37.5331 −1.83143
\(421\) 11.5232 0.561605 0.280803 0.959766i \(-0.409399\pi\)
0.280803 + 0.959766i \(0.409399\pi\)
\(422\) −18.7559 −0.913024
\(423\) 28.8143 1.40100
\(424\) 1.91731 0.0931129
\(425\) −12.2802 −0.595679
\(426\) 14.8132 0.717701
\(427\) −53.5258 −2.59029
\(428\) −16.3499 −0.790300
\(429\) −46.4082 −2.24061
\(430\) 35.4549 1.70978
\(431\) −21.4825 −1.03478 −0.517388 0.855751i \(-0.673095\pi\)
−0.517388 + 0.855751i \(0.673095\pi\)
\(432\) −4.34944 −0.209263
\(433\) 18.0303 0.866483 0.433242 0.901278i \(-0.357370\pi\)
0.433242 + 0.901278i \(0.357370\pi\)
\(434\) 44.5285 2.13744
\(435\) −14.1394 −0.677932
\(436\) 1.13884 0.0545406
\(437\) 17.9780 0.860003
\(438\) −4.54963 −0.217390
\(439\) 30.4571 1.45364 0.726820 0.686828i \(-0.240998\pi\)
0.726820 + 0.686828i \(0.240998\pi\)
\(440\) −8.74219 −0.416767
\(441\) 60.7428 2.89252
\(442\) 17.1886 0.817578
\(443\) 7.20870 0.342496 0.171248 0.985228i \(-0.445220\pi\)
0.171248 + 0.985228i \(0.445220\pi\)
\(444\) −4.94582 −0.234718
\(445\) −7.41294 −0.351407
\(446\) 9.69629 0.459133
\(447\) 34.5331 1.63336
\(448\) 4.50146 0.212674
\(449\) 2.96673 0.140009 0.0700043 0.997547i \(-0.477699\pi\)
0.0700043 + 0.997547i \(0.477699\pi\)
\(450\) −19.1070 −0.900711
\(451\) −1.64398 −0.0774120
\(452\) 2.68101 0.126104
\(453\) −34.7121 −1.63092
\(454\) 8.71525 0.409027
\(455\) 79.6092 3.73214
\(456\) 10.1515 0.475389
\(457\) −9.33857 −0.436840 −0.218420 0.975855i \(-0.570090\pi\)
−0.218420 + 0.975855i \(0.570090\pi\)
\(458\) 27.9523 1.30612
\(459\) 12.8026 0.597572
\(460\) 14.7663 0.688480
\(461\) 26.5834 1.23811 0.619056 0.785347i \(-0.287515\pi\)
0.619056 + 0.785347i \(0.287515\pi\)
\(462\) 35.7743 1.66437
\(463\) 23.1414 1.07547 0.537736 0.843113i \(-0.319280\pi\)
0.537736 + 0.843113i \(0.319280\pi\)
\(464\) 1.69578 0.0787246
\(465\) 82.4795 3.82489
\(466\) 7.51877 0.348301
\(467\) 17.5178 0.810625 0.405312 0.914178i \(-0.367163\pi\)
0.405312 + 0.914178i \(0.367163\pi\)
\(468\) 26.7439 1.23624
\(469\) 52.5162 2.42497
\(470\) −19.0543 −0.878909
\(471\) 57.9958 2.67230
\(472\) −13.2185 −0.608431
\(473\) −33.7934 −1.55382
\(474\) 37.3723 1.71657
\(475\) 15.3832 0.705829
\(476\) −13.2500 −0.607314
\(477\) −8.78092 −0.402051
\(478\) −16.0126 −0.732400
\(479\) −2.05590 −0.0939363 −0.0469681 0.998896i \(-0.514956\pi\)
−0.0469681 + 0.998896i \(0.514956\pi\)
\(480\) 8.33799 0.380575
\(481\) 10.4903 0.478315
\(482\) 1.18272 0.0538716
\(483\) −60.4256 −2.74946
\(484\) −2.66748 −0.121249
\(485\) 41.7670 1.89654
\(486\) −17.9070 −0.812279
\(487\) 14.8889 0.674679 0.337339 0.941383i \(-0.390473\pi\)
0.337339 + 0.941383i \(0.390473\pi\)
\(488\) 11.8907 0.538269
\(489\) −43.0650 −1.94747
\(490\) −40.1679 −1.81460
\(491\) 31.5368 1.42324 0.711618 0.702567i \(-0.247963\pi\)
0.711618 + 0.702567i \(0.247963\pi\)
\(492\) 1.56797 0.0706896
\(493\) −4.99151 −0.224806
\(494\) −21.5318 −0.968760
\(495\) 40.0375 1.79955
\(496\) −9.89201 −0.444164
\(497\) 24.2199 1.08641
\(498\) −20.5929 −0.922788
\(499\) −0.563085 −0.0252071 −0.0126036 0.999921i \(-0.504012\pi\)
−0.0126036 + 0.999921i \(0.504012\pi\)
\(500\) −2.50763 −0.112144
\(501\) −37.7091 −1.68472
\(502\) 12.0311 0.536973
\(503\) 9.26697 0.413194 0.206597 0.978426i \(-0.433761\pi\)
0.206597 + 0.978426i \(0.433761\pi\)
\(504\) −20.6158 −0.918303
\(505\) 52.7152 2.34579
\(506\) −14.0743 −0.625678
\(507\) −58.0915 −2.57993
\(508\) 14.8970 0.660946
\(509\) −37.4251 −1.65884 −0.829419 0.558627i \(-0.811328\pi\)
−0.829419 + 0.558627i \(0.811328\pi\)
\(510\) −24.5428 −1.08677
\(511\) −7.43876 −0.329071
\(512\) −1.00000 −0.0441942
\(513\) −16.0375 −0.708072
\(514\) 2.04290 0.0901085
\(515\) −37.1886 −1.63872
\(516\) 32.2309 1.41889
\(517\) 18.1614 0.798736
\(518\) −8.08655 −0.355303
\(519\) 23.1855 1.01773
\(520\) −17.6852 −0.775546
\(521\) −8.73957 −0.382887 −0.191444 0.981504i \(-0.561317\pi\)
−0.191444 + 0.981504i \(0.561317\pi\)
\(522\) −7.76635 −0.339924
\(523\) 5.73842 0.250924 0.125462 0.992098i \(-0.459959\pi\)
0.125462 + 0.992098i \(0.459959\pi\)
\(524\) −4.79256 −0.209364
\(525\) −51.7044 −2.25656
\(526\) 29.8758 1.30264
\(527\) 29.1171 1.26836
\(528\) −7.94726 −0.345860
\(529\) 0.772598 0.0335912
\(530\) 5.80664 0.252224
\(531\) 60.5382 2.62713
\(532\) 16.5980 0.719615
\(533\) −3.32572 −0.144053
\(534\) −6.73887 −0.291620
\(535\) −49.5161 −2.14077
\(536\) −11.6665 −0.503915
\(537\) −12.2753 −0.529718
\(538\) 15.8029 0.681314
\(539\) 38.2856 1.64908
\(540\) −13.1724 −0.566851
\(541\) −27.5898 −1.18618 −0.593089 0.805137i \(-0.702092\pi\)
−0.593089 + 0.805137i \(0.702092\pi\)
\(542\) 14.3858 0.617924
\(543\) −16.7592 −0.719204
\(544\) 2.94349 0.126201
\(545\) 3.44901 0.147740
\(546\) 72.3703 3.09716
\(547\) 27.7334 1.18580 0.592898 0.805278i \(-0.297984\pi\)
0.592898 + 0.805278i \(0.297984\pi\)
\(548\) −1.80655 −0.0771718
\(549\) −54.4573 −2.32418
\(550\) −12.0429 −0.513512
\(551\) 6.25276 0.266376
\(552\) 13.4236 0.571344
\(553\) 61.1048 2.59844
\(554\) −4.98762 −0.211904
\(555\) −14.9786 −0.635805
\(556\) −0.222556 −0.00943846
\(557\) −33.4358 −1.41672 −0.708359 0.705852i \(-0.750564\pi\)
−0.708359 + 0.705852i \(0.750564\pi\)
\(558\) 45.3035 1.91785
\(559\) −68.3630 −2.89145
\(560\) 13.6328 0.576092
\(561\) 23.3927 0.987640
\(562\) 12.7563 0.538090
\(563\) 15.0999 0.636384 0.318192 0.948026i \(-0.396924\pi\)
0.318192 + 0.948026i \(0.396924\pi\)
\(564\) −17.3217 −0.729374
\(565\) 8.11952 0.341591
\(566\) −4.67345 −0.196440
\(567\) −7.94408 −0.333620
\(568\) −5.38045 −0.225759
\(569\) 14.3409 0.601203 0.300601 0.953750i \(-0.402813\pi\)
0.300601 + 0.953750i \(0.402813\pi\)
\(570\) 30.7442 1.28773
\(571\) 13.8772 0.580743 0.290371 0.956914i \(-0.406221\pi\)
0.290371 + 0.956914i \(0.406221\pi\)
\(572\) 16.8564 0.704803
\(573\) 59.4501 2.48356
\(574\) 2.56367 0.107006
\(575\) 20.3415 0.848298
\(576\) 4.57981 0.190825
\(577\) 42.9945 1.78988 0.894942 0.446182i \(-0.147217\pi\)
0.894942 + 0.446182i \(0.147217\pi\)
\(578\) 8.33586 0.346726
\(579\) −55.0109 −2.28618
\(580\) 5.13572 0.213249
\(581\) −33.6698 −1.39686
\(582\) 37.9691 1.57387
\(583\) −5.53453 −0.229217
\(584\) 1.65252 0.0683818
\(585\) 80.9947 3.34872
\(586\) 27.0645 1.11803
\(587\) 22.5720 0.931648 0.465824 0.884877i \(-0.345758\pi\)
0.465824 + 0.884877i \(0.345758\pi\)
\(588\) −36.5155 −1.50587
\(589\) −36.4743 −1.50290
\(590\) −40.0326 −1.64812
\(591\) −4.45380 −0.183205
\(592\) 1.79643 0.0738327
\(593\) −0.103248 −0.00423988 −0.00211994 0.999998i \(-0.500675\pi\)
−0.00211994 + 0.999998i \(0.500675\pi\)
\(594\) 12.5551 0.515144
\(595\) −40.1281 −1.64509
\(596\) −12.5431 −0.513787
\(597\) −20.7087 −0.847552
\(598\) −28.4719 −1.16430
\(599\) −35.9175 −1.46755 −0.733775 0.679392i \(-0.762244\pi\)
−0.733775 + 0.679392i \(0.762244\pi\)
\(600\) 11.4861 0.468919
\(601\) −20.7879 −0.847955 −0.423978 0.905673i \(-0.639366\pi\)
−0.423978 + 0.905673i \(0.639366\pi\)
\(602\) 52.6984 2.14783
\(603\) 53.4302 2.17585
\(604\) 12.6082 0.513019
\(605\) −8.07856 −0.328440
\(606\) 47.9218 1.94669
\(607\) −42.6480 −1.73103 −0.865514 0.500885i \(-0.833008\pi\)
−0.865514 + 0.500885i \(0.833008\pi\)
\(608\) −3.68725 −0.149538
\(609\) −21.0161 −0.851616
\(610\) 36.0115 1.45806
\(611\) 36.7399 1.48634
\(612\) −13.4806 −0.544922
\(613\) 25.3915 1.02555 0.512777 0.858522i \(-0.328617\pi\)
0.512777 + 0.858522i \(0.328617\pi\)
\(614\) −3.03475 −0.122473
\(615\) 4.74865 0.191484
\(616\) −12.9940 −0.523542
\(617\) 45.0410 1.81328 0.906640 0.421905i \(-0.138638\pi\)
0.906640 + 0.421905i \(0.138638\pi\)
\(618\) −33.8070 −1.35992
\(619\) −16.4953 −0.663002 −0.331501 0.943455i \(-0.607555\pi\)
−0.331501 + 0.943455i \(0.607555\pi\)
\(620\) −29.9583 −1.20315
\(621\) −21.2066 −0.850993
\(622\) 33.4222 1.34011
\(623\) −11.0182 −0.441436
\(624\) −16.0771 −0.643597
\(625\) −28.4544 −1.13818
\(626\) −10.0688 −0.402430
\(627\) −29.3035 −1.17027
\(628\) −21.0653 −0.840596
\(629\) −5.28777 −0.210837
\(630\) −62.4357 −2.48750
\(631\) −42.7056 −1.70008 −0.850042 0.526714i \(-0.823424\pi\)
−0.850042 + 0.526714i \(0.823424\pi\)
\(632\) −13.5744 −0.539961
\(633\) −51.6378 −2.05242
\(634\) 17.1552 0.681320
\(635\) 45.1160 1.79037
\(636\) 5.27864 0.209312
\(637\) 77.4506 3.06871
\(638\) −4.89505 −0.193797
\(639\) 24.6415 0.974801
\(640\) −3.02853 −0.119713
\(641\) −29.8596 −1.17938 −0.589691 0.807629i \(-0.700751\pi\)
−0.589691 + 0.807629i \(0.700751\pi\)
\(642\) −45.0136 −1.77654
\(643\) −26.0198 −1.02612 −0.513060 0.858353i \(-0.671488\pi\)
−0.513060 + 0.858353i \(0.671488\pi\)
\(644\) 21.9479 0.864867
\(645\) 97.6124 3.84348
\(646\) 10.8534 0.427020
\(647\) −0.802335 −0.0315431 −0.0157715 0.999876i \(-0.505020\pi\)
−0.0157715 + 0.999876i \(0.505020\pi\)
\(648\) 1.76478 0.0693270
\(649\) 38.1566 1.49778
\(650\) −24.3625 −0.955576
\(651\) 122.594 4.80482
\(652\) 15.6421 0.612592
\(653\) −9.13808 −0.357601 −0.178800 0.983885i \(-0.557222\pi\)
−0.178800 + 0.983885i \(0.557222\pi\)
\(654\) 3.13539 0.122604
\(655\) −14.5144 −0.567125
\(656\) −0.569520 −0.0222360
\(657\) −7.56823 −0.295265
\(658\) −28.3214 −1.10408
\(659\) 3.08599 0.120213 0.0601065 0.998192i \(-0.480856\pi\)
0.0601065 + 0.998192i \(0.480856\pi\)
\(660\) −24.0685 −0.936865
\(661\) 32.0236 1.24557 0.622786 0.782392i \(-0.286001\pi\)
0.622786 + 0.782392i \(0.286001\pi\)
\(662\) 17.8047 0.691999
\(663\) 47.3227 1.83786
\(664\) 7.47975 0.290271
\(665\) 50.2676 1.94929
\(666\) −8.22729 −0.318801
\(667\) 8.26814 0.320144
\(668\) 13.6967 0.529943
\(669\) 26.6953 1.03210
\(670\) −35.3323 −1.36501
\(671\) −34.3239 −1.32506
\(672\) 12.3932 0.478077
\(673\) −35.9097 −1.38422 −0.692109 0.721793i \(-0.743318\pi\)
−0.692109 + 0.721793i \(0.743318\pi\)
\(674\) 0.0559972 0.00215693
\(675\) −18.1459 −0.698435
\(676\) 21.1000 0.811540
\(677\) −10.0309 −0.385518 −0.192759 0.981246i \(-0.561744\pi\)
−0.192759 + 0.981246i \(0.561744\pi\)
\(678\) 7.38121 0.283474
\(679\) 62.0805 2.38243
\(680\) 8.91446 0.341854
\(681\) 23.9944 0.919466
\(682\) 28.5544 1.09340
\(683\) 25.8459 0.988964 0.494482 0.869188i \(-0.335358\pi\)
0.494482 + 0.869188i \(0.335358\pi\)
\(684\) 16.8869 0.645686
\(685\) −5.47118 −0.209043
\(686\) −28.1935 −1.07643
\(687\) 76.9567 2.93608
\(688\) −11.7069 −0.446323
\(689\) −11.1962 −0.426541
\(690\) 40.6536 1.54766
\(691\) −18.6799 −0.710618 −0.355309 0.934749i \(-0.615624\pi\)
−0.355309 + 0.934749i \(0.615624\pi\)
\(692\) −8.42146 −0.320136
\(693\) 59.5099 2.26059
\(694\) −14.5712 −0.553114
\(695\) −0.674016 −0.0255669
\(696\) 4.66873 0.176968
\(697\) 1.67638 0.0634973
\(698\) 15.0940 0.571317
\(699\) 20.7003 0.782956
\(700\) 18.7801 0.709821
\(701\) 4.13248 0.156082 0.0780408 0.996950i \(-0.475134\pi\)
0.0780408 + 0.996950i \(0.475134\pi\)
\(702\) 25.3987 0.958611
\(703\) 6.62387 0.249824
\(704\) 2.88661 0.108793
\(705\) −52.4592 −1.97573
\(706\) 14.0657 0.529369
\(707\) 78.3533 2.94678
\(708\) −36.3924 −1.36771
\(709\) −32.3351 −1.21437 −0.607184 0.794561i \(-0.707701\pi\)
−0.607184 + 0.794561i \(0.707701\pi\)
\(710\) −16.2949 −0.611536
\(711\) 62.1682 2.33149
\(712\) 2.44770 0.0917314
\(713\) −48.2306 −1.80625
\(714\) −36.4792 −1.36520
\(715\) 51.0502 1.90917
\(716\) 4.45864 0.166627
\(717\) −44.0850 −1.64639
\(718\) 36.0333 1.34475
\(719\) −21.0380 −0.784587 −0.392293 0.919840i \(-0.628318\pi\)
−0.392293 + 0.919840i \(0.628318\pi\)
\(720\) 13.8701 0.516908
\(721\) −55.2753 −2.05856
\(722\) 5.40422 0.201124
\(723\) 3.25621 0.121100
\(724\) 6.08728 0.226232
\(725\) 7.07479 0.262751
\(726\) −7.34397 −0.272560
\(727\) 21.2766 0.789104 0.394552 0.918874i \(-0.370900\pi\)
0.394552 + 0.918874i \(0.370900\pi\)
\(728\) −26.2864 −0.974239
\(729\) −44.0063 −1.62986
\(730\) 5.00471 0.185233
\(731\) 34.4593 1.27452
\(732\) 32.7369 1.20999
\(733\) 53.9883 1.99410 0.997052 0.0767243i \(-0.0244461\pi\)
0.997052 + 0.0767243i \(0.0244461\pi\)
\(734\) −29.0243 −1.07131
\(735\) −110.588 −4.07911
\(736\) −4.87572 −0.179721
\(737\) 33.6766 1.24049
\(738\) 2.60829 0.0960125
\(739\) 8.64828 0.318132 0.159066 0.987268i \(-0.449152\pi\)
0.159066 + 0.987268i \(0.449152\pi\)
\(740\) 5.44053 0.199998
\(741\) −59.2801 −2.17771
\(742\) 8.63071 0.316843
\(743\) −21.0477 −0.772164 −0.386082 0.922464i \(-0.626172\pi\)
−0.386082 + 0.922464i \(0.626172\pi\)
\(744\) −27.2341 −0.998452
\(745\) −37.9873 −1.39175
\(746\) 5.48833 0.200942
\(747\) −34.2558 −1.25336
\(748\) −8.49671 −0.310671
\(749\) −73.5983 −2.68922
\(750\) −6.90386 −0.252093
\(751\) −25.7582 −0.939931 −0.469966 0.882685i \(-0.655734\pi\)
−0.469966 + 0.882685i \(0.655734\pi\)
\(752\) 6.29159 0.229431
\(753\) 33.1233 1.20708
\(754\) −9.90254 −0.360629
\(755\) 38.1842 1.38967
\(756\) −19.5789 −0.712076
\(757\) −29.3746 −1.06764 −0.533819 0.845599i \(-0.679244\pi\)
−0.533819 + 0.845599i \(0.679244\pi\)
\(758\) −23.4621 −0.852181
\(759\) −38.7486 −1.40648
\(760\) −11.1669 −0.405067
\(761\) −32.4995 −1.17811 −0.589053 0.808095i \(-0.700499\pi\)
−0.589053 + 0.808095i \(0.700499\pi\)
\(762\) 41.0135 1.48576
\(763\) 5.12645 0.185590
\(764\) −21.5935 −0.781226
\(765\) −40.8265 −1.47609
\(766\) −3.74050 −0.135150
\(767\) 77.1897 2.78716
\(768\) −2.75315 −0.0993456
\(769\) 12.5825 0.453736 0.226868 0.973926i \(-0.427151\pi\)
0.226868 + 0.973926i \(0.427151\pi\)
\(770\) −39.3526 −1.41817
\(771\) 5.62441 0.202558
\(772\) 19.9811 0.719136
\(773\) 26.2665 0.944739 0.472370 0.881401i \(-0.343399\pi\)
0.472370 + 0.881401i \(0.343399\pi\)
\(774\) 53.6156 1.92717
\(775\) −41.2695 −1.48244
\(776\) −13.7912 −0.495074
\(777\) −22.2634 −0.798697
\(778\) 21.2083 0.760355
\(779\) −2.09996 −0.0752388
\(780\) −48.6899 −1.74338
\(781\) 15.5313 0.555753
\(782\) 14.3516 0.513213
\(783\) −7.37570 −0.263586
\(784\) 13.2632 0.473685
\(785\) −63.7968 −2.27701
\(786\) −13.1946 −0.470636
\(787\) 10.7556 0.383395 0.191697 0.981454i \(-0.438601\pi\)
0.191697 + 0.981454i \(0.438601\pi\)
\(788\) 1.61771 0.0576287
\(789\) 82.2523 2.92826
\(790\) −41.1105 −1.46265
\(791\) 12.0685 0.429105
\(792\) −13.2201 −0.469757
\(793\) −69.4363 −2.46575
\(794\) −24.8701 −0.882606
\(795\) 15.9865 0.566984
\(796\) 7.52184 0.266605
\(797\) −49.3824 −1.74922 −0.874608 0.484832i \(-0.838881\pi\)
−0.874608 + 0.484832i \(0.838881\pi\)
\(798\) 45.6967 1.61765
\(799\) −18.5193 −0.655164
\(800\) −4.17200 −0.147502
\(801\) −11.2100 −0.396086
\(802\) 1.88000 0.0663850
\(803\) −4.77018 −0.168336
\(804\) −32.1195 −1.13277
\(805\) 66.4698 2.34275
\(806\) 57.7647 2.03467
\(807\) 43.5078 1.53155
\(808\) −17.4062 −0.612348
\(809\) 44.2939 1.55729 0.778646 0.627464i \(-0.215907\pi\)
0.778646 + 0.627464i \(0.215907\pi\)
\(810\) 5.34468 0.187793
\(811\) 3.30124 0.115922 0.0579610 0.998319i \(-0.481540\pi\)
0.0579610 + 0.998319i \(0.481540\pi\)
\(812\) 7.63349 0.267883
\(813\) 39.6063 1.38905
\(814\) −5.18558 −0.181755
\(815\) 47.3726 1.65939
\(816\) 8.10386 0.283692
\(817\) −43.1664 −1.51020
\(818\) −24.9765 −0.873283
\(819\) 120.387 4.20665
\(820\) −1.72481 −0.0602329
\(821\) 30.5554 1.06639 0.533195 0.845992i \(-0.320991\pi\)
0.533195 + 0.845992i \(0.320991\pi\)
\(822\) −4.97368 −0.173477
\(823\) −16.6829 −0.581529 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(824\) 12.2794 0.427773
\(825\) −33.1559 −1.15434
\(826\) −59.5026 −2.07036
\(827\) 15.7524 0.547766 0.273883 0.961763i \(-0.411692\pi\)
0.273883 + 0.961763i \(0.411692\pi\)
\(828\) 22.3298 0.776016
\(829\) −12.0254 −0.417660 −0.208830 0.977952i \(-0.566966\pi\)
−0.208830 + 0.977952i \(0.566966\pi\)
\(830\) 22.6527 0.786286
\(831\) −13.7317 −0.476346
\(832\) 5.83952 0.202449
\(833\) −39.0401 −1.35266
\(834\) −0.612728 −0.0212170
\(835\) 41.4810 1.43551
\(836\) 10.6436 0.368118
\(837\) 43.0247 1.48715
\(838\) −34.5174 −1.19238
\(839\) 10.8478 0.374507 0.187254 0.982312i \(-0.440041\pi\)
0.187254 + 0.982312i \(0.440041\pi\)
\(840\) 37.5331 1.29502
\(841\) −26.1243 −0.900839
\(842\) −11.5232 −0.397115
\(843\) 35.1198 1.20959
\(844\) 18.7559 0.645606
\(845\) 63.9021 2.19830
\(846\) −28.8143 −0.990656
\(847\) −12.0076 −0.412585
\(848\) −1.91731 −0.0658408
\(849\) −12.8667 −0.441584
\(850\) 12.2802 0.421209
\(851\) 8.75886 0.300250
\(852\) −14.8132 −0.507491
\(853\) −6.49724 −0.222461 −0.111231 0.993795i \(-0.535479\pi\)
−0.111231 + 0.993795i \(0.535479\pi\)
\(854\) 53.5258 1.83161
\(855\) 51.1424 1.74903
\(856\) 16.3499 0.558827
\(857\) −19.2722 −0.658327 −0.329163 0.944273i \(-0.606767\pi\)
−0.329163 + 0.944273i \(0.606767\pi\)
\(858\) 46.4082 1.58435
\(859\) 6.56139 0.223872 0.111936 0.993715i \(-0.464295\pi\)
0.111936 + 0.993715i \(0.464295\pi\)
\(860\) −35.4549 −1.20900
\(861\) 7.05816 0.240541
\(862\) 21.4825 0.731697
\(863\) 32.1228 1.09347 0.546736 0.837305i \(-0.315870\pi\)
0.546736 + 0.837305i \(0.315870\pi\)
\(864\) 4.34944 0.147971
\(865\) −25.5046 −0.867184
\(866\) −18.0303 −0.612696
\(867\) 22.9498 0.779417
\(868\) −44.5285 −1.51140
\(869\) 39.1840 1.32923
\(870\) 14.1394 0.479370
\(871\) 68.1267 2.30838
\(872\) −1.13884 −0.0385660
\(873\) 63.1610 2.13767
\(874\) −17.9780 −0.608114
\(875\) −11.2880 −0.381604
\(876\) 4.54963 0.153718
\(877\) 35.6946 1.20532 0.602661 0.797998i \(-0.294107\pi\)
0.602661 + 0.797998i \(0.294107\pi\)
\(878\) −30.4571 −1.02788
\(879\) 74.5126 2.51325
\(880\) 8.74219 0.294699
\(881\) −43.9777 −1.48165 −0.740823 0.671701i \(-0.765564\pi\)
−0.740823 + 0.671701i \(0.765564\pi\)
\(882\) −60.7428 −2.04532
\(883\) 40.4382 1.36085 0.680427 0.732816i \(-0.261794\pi\)
0.680427 + 0.732816i \(0.261794\pi\)
\(884\) −17.1886 −0.578115
\(885\) −110.216 −3.70486
\(886\) −7.20870 −0.242181
\(887\) 4.36711 0.146633 0.0733166 0.997309i \(-0.476642\pi\)
0.0733166 + 0.997309i \(0.476642\pi\)
\(888\) 4.94582 0.165971
\(889\) 67.0582 2.24906
\(890\) 7.41294 0.248482
\(891\) −5.09422 −0.170663
\(892\) −9.69629 −0.324656
\(893\) 23.1987 0.776313
\(894\) −34.5331 −1.15496
\(895\) 13.5031 0.451360
\(896\) −4.50146 −0.150383
\(897\) −78.3872 −2.61727
\(898\) −2.96673 −0.0990010
\(899\) −16.7747 −0.559467
\(900\) 19.1070 0.636899
\(901\) 5.64359 0.188015
\(902\) 1.64398 0.0547386
\(903\) 145.086 4.82817
\(904\) −2.68101 −0.0891691
\(905\) 18.4355 0.612817
\(906\) 34.7121 1.15323
\(907\) −26.5048 −0.880078 −0.440039 0.897979i \(-0.645035\pi\)
−0.440039 + 0.897979i \(0.645035\pi\)
\(908\) −8.71525 −0.289226
\(909\) 79.7170 2.64405
\(910\) −79.6092 −2.63902
\(911\) −1.17086 −0.0387923 −0.0193962 0.999812i \(-0.506174\pi\)
−0.0193962 + 0.999812i \(0.506174\pi\)
\(912\) −10.1515 −0.336151
\(913\) −21.5911 −0.714562
\(914\) 9.33857 0.308892
\(915\) 99.1449 3.27763
\(916\) −27.9523 −0.923570
\(917\) −21.5735 −0.712421
\(918\) −12.8026 −0.422547
\(919\) −0.580580 −0.0191516 −0.00957578 0.999954i \(-0.503048\pi\)
−0.00957578 + 0.999954i \(0.503048\pi\)
\(920\) −14.7663 −0.486829
\(921\) −8.35511 −0.275310
\(922\) −26.5834 −0.875478
\(923\) 31.4193 1.03418
\(924\) −35.7743 −1.17689
\(925\) 7.49469 0.246424
\(926\) −23.1414 −0.760473
\(927\) −56.2373 −1.84708
\(928\) −1.69578 −0.0556667
\(929\) 18.0140 0.591020 0.295510 0.955340i \(-0.404510\pi\)
0.295510 + 0.955340i \(0.404510\pi\)
\(930\) −82.4795 −2.70461
\(931\) 48.9046 1.60278
\(932\) −7.51877 −0.246286
\(933\) 92.0161 3.01247
\(934\) −17.5178 −0.573198
\(935\) −25.7326 −0.841545
\(936\) −26.7439 −0.874152
\(937\) 5.46987 0.178693 0.0893465 0.996001i \(-0.471522\pi\)
0.0893465 + 0.996001i \(0.471522\pi\)
\(938\) −52.5162 −1.71472
\(939\) −27.7209 −0.904637
\(940\) 19.0543 0.621482
\(941\) 2.06806 0.0674169 0.0337084 0.999432i \(-0.489268\pi\)
0.0337084 + 0.999432i \(0.489268\pi\)
\(942\) −57.9958 −1.88960
\(943\) −2.77682 −0.0904256
\(944\) 13.2185 0.430225
\(945\) −59.2952 −1.92887
\(946\) 33.7934 1.09872
\(947\) −28.9353 −0.940270 −0.470135 0.882595i \(-0.655795\pi\)
−0.470135 + 0.882595i \(0.655795\pi\)
\(948\) −37.3723 −1.21380
\(949\) −9.64993 −0.313250
\(950\) −15.3832 −0.499097
\(951\) 47.2308 1.53156
\(952\) 13.2500 0.429436
\(953\) −34.2447 −1.10930 −0.554648 0.832085i \(-0.687147\pi\)
−0.554648 + 0.832085i \(0.687147\pi\)
\(954\) 8.78092 0.284293
\(955\) −65.3967 −2.11619
\(956\) 16.0126 0.517885
\(957\) −13.4768 −0.435643
\(958\) 2.05590 0.0664230
\(959\) −8.13210 −0.262599
\(960\) −8.33799 −0.269107
\(961\) 66.8519 2.15651
\(962\) −10.4903 −0.338220
\(963\) −74.8793 −2.41295
\(964\) −1.18272 −0.0380930
\(965\) 60.5135 1.94800
\(966\) 60.4256 1.94416
\(967\) 7.27910 0.234080 0.117040 0.993127i \(-0.462659\pi\)
0.117040 + 0.993127i \(0.462659\pi\)
\(968\) 2.66748 0.0857362
\(969\) 29.8809 0.959914
\(970\) −41.7670 −1.34106
\(971\) −40.4881 −1.29932 −0.649662 0.760223i \(-0.725090\pi\)
−0.649662 + 0.760223i \(0.725090\pi\)
\(972\) 17.9070 0.574368
\(973\) −1.00183 −0.0321171
\(974\) −14.8889 −0.477070
\(975\) −67.0735 −2.14807
\(976\) −11.8907 −0.380613
\(977\) −17.2136 −0.550713 −0.275356 0.961342i \(-0.588796\pi\)
−0.275356 + 0.961342i \(0.588796\pi\)
\(978\) 43.0650 1.37707
\(979\) −7.06556 −0.225816
\(980\) 40.1679 1.28312
\(981\) 5.21567 0.166524
\(982\) −31.5368 −1.00638
\(983\) 30.2200 0.963870 0.481935 0.876207i \(-0.339934\pi\)
0.481935 + 0.876207i \(0.339934\pi\)
\(984\) −1.56797 −0.0499851
\(985\) 4.89930 0.156105
\(986\) 4.99151 0.158962
\(987\) −77.9729 −2.48190
\(988\) 21.5318 0.685017
\(989\) −57.0797 −1.81503
\(990\) −40.0375 −1.27248
\(991\) −45.3347 −1.44010 −0.720052 0.693920i \(-0.755882\pi\)
−0.720052 + 0.693920i \(0.755882\pi\)
\(992\) 9.89201 0.314072
\(993\) 49.0189 1.55557
\(994\) −24.2199 −0.768209
\(995\) 22.7801 0.722179
\(996\) 20.5929 0.652509
\(997\) −34.6550 −1.09754 −0.548768 0.835975i \(-0.684903\pi\)
−0.548768 + 0.835975i \(0.684903\pi\)
\(998\) 0.563085 0.0178241
\(999\) −7.81346 −0.247207
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 \(a_p\))