Properties

Label 8003.2.a.c.1.6
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.68137 q^{2}\) \(+1.21893 q^{3}\) \(+5.18975 q^{4}\) \(+2.92126 q^{5}\) \(-3.26842 q^{6}\) \(+4.69101 q^{7}\) \(-8.55290 q^{8}\) \(-1.51420 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.68137 q^{2}\) \(+1.21893 q^{3}\) \(+5.18975 q^{4}\) \(+2.92126 q^{5}\) \(-3.26842 q^{6}\) \(+4.69101 q^{7}\) \(-8.55290 q^{8}\) \(-1.51420 q^{9}\) \(-7.83297 q^{10}\) \(-1.10078 q^{11}\) \(+6.32596 q^{12}\) \(+3.44785 q^{13}\) \(-12.5783 q^{14}\) \(+3.56082 q^{15}\) \(+12.5540 q^{16}\) \(-4.01060 q^{17}\) \(+4.06013 q^{18}\) \(-2.14032 q^{19}\) \(+15.1606 q^{20}\) \(+5.71803 q^{21}\) \(+2.95159 q^{22}\) \(+2.58440 q^{23}\) \(-10.4254 q^{24}\) \(+3.53374 q^{25}\) \(-9.24496 q^{26}\) \(-5.50251 q^{27}\) \(+24.3452 q^{28}\) \(-6.97941 q^{29}\) \(-9.54788 q^{30}\) \(+6.93849 q^{31}\) \(-16.5561 q^{32}\) \(-1.34178 q^{33}\) \(+10.7539 q^{34}\) \(+13.7036 q^{35}\) \(-7.85831 q^{36}\) \(+10.6920 q^{37}\) \(+5.73900 q^{38}\) \(+4.20270 q^{39}\) \(-24.9852 q^{40}\) \(-4.96455 q^{41}\) \(-15.3322 q^{42}\) \(-4.73081 q^{43}\) \(-5.71276 q^{44}\) \(-4.42336 q^{45}\) \(-6.92974 q^{46}\) \(+10.5871 q^{47}\) \(+15.3025 q^{48}\) \(+15.0056 q^{49}\) \(-9.47527 q^{50}\) \(-4.88866 q^{51}\) \(+17.8935 q^{52}\) \(-1.00000 q^{53}\) \(+14.7543 q^{54}\) \(-3.21565 q^{55}\) \(-40.1217 q^{56}\) \(-2.60891 q^{57}\) \(+18.7144 q^{58}\) \(+10.0989 q^{59}\) \(+18.4798 q^{60}\) \(+9.99290 q^{61}\) \(-18.6047 q^{62}\) \(-7.10312 q^{63}\) \(+19.2851 q^{64}\) \(+10.0720 q^{65}\) \(+3.59780 q^{66}\) \(+0.502039 q^{67}\) \(-20.8140 q^{68}\) \(+3.15022 q^{69}\) \(-36.7445 q^{70}\) \(+2.73221 q^{71}\) \(+12.9508 q^{72}\) \(-8.16872 q^{73}\) \(-28.6693 q^{74}\) \(+4.30740 q^{75}\) \(-11.1077 q^{76}\) \(-5.16375 q^{77}\) \(-11.2690 q^{78}\) \(-10.5454 q^{79}\) \(+36.6734 q^{80}\) \(-2.16460 q^{81}\) \(+13.3118 q^{82}\) \(-14.2677 q^{83}\) \(+29.6751 q^{84}\) \(-11.7160 q^{85}\) \(+12.6851 q^{86}\) \(-8.50744 q^{87}\) \(+9.41484 q^{88}\) \(+11.6919 q^{89}\) \(+11.8607 q^{90}\) \(+16.1739 q^{91}\) \(+13.4124 q^{92}\) \(+8.45756 q^{93}\) \(-28.3878 q^{94}\) \(-6.25243 q^{95}\) \(-20.1808 q^{96}\) \(-3.98600 q^{97}\) \(-40.2355 q^{98}\) \(+1.66680 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68137 −1.89602 −0.948008 0.318247i \(-0.896906\pi\)
−0.948008 + 0.318247i \(0.896906\pi\)
\(3\) 1.21893 0.703752 0.351876 0.936047i \(-0.385544\pi\)
0.351876 + 0.936047i \(0.385544\pi\)
\(4\) 5.18975 2.59487
\(5\) 2.92126 1.30643 0.653213 0.757174i \(-0.273421\pi\)
0.653213 + 0.757174i \(0.273421\pi\)
\(6\) −3.26842 −1.33432
\(7\) 4.69101 1.77303 0.886517 0.462696i \(-0.153118\pi\)
0.886517 + 0.462696i \(0.153118\pi\)
\(8\) −8.55290 −3.02391
\(9\) −1.51420 −0.504733
\(10\) −7.83297 −2.47700
\(11\) −1.10078 −0.331897 −0.165948 0.986134i \(-0.553069\pi\)
−0.165948 + 0.986134i \(0.553069\pi\)
\(12\) 6.32596 1.82615
\(13\) 3.44785 0.956261 0.478130 0.878289i \(-0.341315\pi\)
0.478130 + 0.878289i \(0.341315\pi\)
\(14\) −12.5783 −3.36170
\(15\) 3.56082 0.919400
\(16\) 12.5540 3.13850
\(17\) −4.01060 −0.972715 −0.486357 0.873760i \(-0.661675\pi\)
−0.486357 + 0.873760i \(0.661675\pi\)
\(18\) 4.06013 0.956981
\(19\) −2.14032 −0.491024 −0.245512 0.969394i \(-0.578956\pi\)
−0.245512 + 0.969394i \(0.578956\pi\)
\(20\) 15.1606 3.39001
\(21\) 5.71803 1.24778
\(22\) 2.95159 0.629281
\(23\) 2.58440 0.538885 0.269443 0.963016i \(-0.413161\pi\)
0.269443 + 0.963016i \(0.413161\pi\)
\(24\) −10.4254 −2.12808
\(25\) 3.53374 0.706748
\(26\) −9.24496 −1.81309
\(27\) −5.50251 −1.05896
\(28\) 24.3452 4.60080
\(29\) −6.97941 −1.29604 −0.648022 0.761622i \(-0.724404\pi\)
−0.648022 + 0.761622i \(0.724404\pi\)
\(30\) −9.54788 −1.74320
\(31\) 6.93849 1.24619 0.623095 0.782147i \(-0.285875\pi\)
0.623095 + 0.782147i \(0.285875\pi\)
\(32\) −16.5561 −2.92674
\(33\) −1.34178 −0.233573
\(34\) 10.7539 1.84428
\(35\) 13.7036 2.31634
\(36\) −7.85831 −1.30972
\(37\) 10.6920 1.75776 0.878878 0.477046i \(-0.158292\pi\)
0.878878 + 0.477046i \(0.158292\pi\)
\(38\) 5.73900 0.930988
\(39\) 4.20270 0.672971
\(40\) −24.9852 −3.95051
\(41\) −4.96455 −0.775333 −0.387666 0.921800i \(-0.626719\pi\)
−0.387666 + 0.921800i \(0.626719\pi\)
\(42\) −15.3322 −2.36580
\(43\) −4.73081 −0.721442 −0.360721 0.932674i \(-0.617469\pi\)
−0.360721 + 0.932674i \(0.617469\pi\)
\(44\) −5.71276 −0.861231
\(45\) −4.42336 −0.659396
\(46\) −6.92974 −1.02173
\(47\) 10.5871 1.54428 0.772140 0.635452i \(-0.219186\pi\)
0.772140 + 0.635452i \(0.219186\pi\)
\(48\) 15.3025 2.20873
\(49\) 15.0056 2.14365
\(50\) −9.47527 −1.34001
\(51\) −4.88866 −0.684550
\(52\) 17.8935 2.48138
\(53\) −1.00000 −0.137361
\(54\) 14.7543 2.00780
\(55\) −3.21565 −0.433599
\(56\) −40.1217 −5.36149
\(57\) −2.60891 −0.345559
\(58\) 18.7144 2.45732
\(59\) 10.0989 1.31476 0.657381 0.753558i \(-0.271664\pi\)
0.657381 + 0.753558i \(0.271664\pi\)
\(60\) 18.4798 2.38573
\(61\) 9.99290 1.27946 0.639730 0.768600i \(-0.279046\pi\)
0.639730 + 0.768600i \(0.279046\pi\)
\(62\) −18.6047 −2.36279
\(63\) −7.10312 −0.894909
\(64\) 19.2851 2.41064
\(65\) 10.0720 1.24928
\(66\) 3.59780 0.442858
\(67\) 0.502039 0.0613338 0.0306669 0.999530i \(-0.490237\pi\)
0.0306669 + 0.999530i \(0.490237\pi\)
\(68\) −20.8140 −2.52407
\(69\) 3.15022 0.379242
\(70\) −36.7445 −4.39181
\(71\) 2.73221 0.324254 0.162127 0.986770i \(-0.448165\pi\)
0.162127 + 0.986770i \(0.448165\pi\)
\(72\) 12.9508 1.52627
\(73\) −8.16872 −0.956076 −0.478038 0.878339i \(-0.658652\pi\)
−0.478038 + 0.878339i \(0.658652\pi\)
\(74\) −28.6693 −3.33273
\(75\) 4.30740 0.497376
\(76\) −11.1077 −1.27414
\(77\) −5.16375 −0.588464
\(78\) −11.2690 −1.27596
\(79\) −10.5454 −1.18645 −0.593223 0.805038i \(-0.702145\pi\)
−0.593223 + 0.805038i \(0.702145\pi\)
\(80\) 36.6734 4.10022
\(81\) −2.16460 −0.240512
\(82\) 13.3118 1.47004
\(83\) −14.2677 −1.56609 −0.783044 0.621966i \(-0.786334\pi\)
−0.783044 + 0.621966i \(0.786334\pi\)
\(84\) 29.6751 3.23782
\(85\) −11.7160 −1.27078
\(86\) 12.6851 1.36786
\(87\) −8.50744 −0.912094
\(88\) 9.41484 1.00362
\(89\) 11.6919 1.23934 0.619671 0.784862i \(-0.287266\pi\)
0.619671 + 0.784862i \(0.287266\pi\)
\(90\) 11.8607 1.25023
\(91\) 16.1739 1.69548
\(92\) 13.4124 1.39834
\(93\) 8.45756 0.877008
\(94\) −28.3878 −2.92798
\(95\) −6.25243 −0.641486
\(96\) −20.1808 −2.05970
\(97\) −3.98600 −0.404717 −0.202358 0.979312i \(-0.564861\pi\)
−0.202358 + 0.979312i \(0.564861\pi\)
\(98\) −40.2355 −4.06440
\(99\) 1.66680 0.167519
\(100\) 18.3392 1.83392
\(101\) 14.4279 1.43563 0.717813 0.696236i \(-0.245143\pi\)
0.717813 + 0.696236i \(0.245143\pi\)
\(102\) 13.1083 1.29792
\(103\) 20.1616 1.98658 0.993292 0.115634i \(-0.0368899\pi\)
0.993292 + 0.115634i \(0.0368899\pi\)
\(104\) −29.4891 −2.89164
\(105\) 16.7038 1.63013
\(106\) 2.68137 0.260438
\(107\) −8.95035 −0.865263 −0.432632 0.901571i \(-0.642415\pi\)
−0.432632 + 0.901571i \(0.642415\pi\)
\(108\) −28.5567 −2.74787
\(109\) −1.93614 −0.185449 −0.0927244 0.995692i \(-0.529558\pi\)
−0.0927244 + 0.995692i \(0.529558\pi\)
\(110\) 8.62236 0.822109
\(111\) 13.0329 1.23703
\(112\) 58.8909 5.56467
\(113\) −13.8443 −1.30237 −0.651183 0.758920i \(-0.725727\pi\)
−0.651183 + 0.758920i \(0.725727\pi\)
\(114\) 6.99546 0.655185
\(115\) 7.54970 0.704013
\(116\) −36.2214 −3.36307
\(117\) −5.22073 −0.482656
\(118\) −27.0789 −2.49281
\(119\) −18.8138 −1.72466
\(120\) −30.4553 −2.78018
\(121\) −9.78829 −0.889845
\(122\) −26.7947 −2.42587
\(123\) −6.05146 −0.545642
\(124\) 36.0090 3.23370
\(125\) −4.28332 −0.383112
\(126\) 19.0461 1.69676
\(127\) 18.3916 1.63199 0.815994 0.578060i \(-0.196190\pi\)
0.815994 + 0.578060i \(0.196190\pi\)
\(128\) −18.5983 −1.64387
\(129\) −5.76655 −0.507716
\(130\) −27.0069 −2.36866
\(131\) 3.95117 0.345215 0.172607 0.984991i \(-0.444781\pi\)
0.172607 + 0.984991i \(0.444781\pi\)
\(132\) −6.96348 −0.606093
\(133\) −10.0403 −0.870602
\(134\) −1.34615 −0.116290
\(135\) −16.0743 −1.38345
\(136\) 34.3023 2.94140
\(137\) −6.80345 −0.581258 −0.290629 0.956836i \(-0.593865\pi\)
−0.290629 + 0.956836i \(0.593865\pi\)
\(138\) −8.44690 −0.719048
\(139\) 12.4855 1.05900 0.529502 0.848309i \(-0.322379\pi\)
0.529502 + 0.848309i \(0.322379\pi\)
\(140\) 71.1184 6.01061
\(141\) 12.9049 1.08679
\(142\) −7.32608 −0.614791
\(143\) −3.79531 −0.317380
\(144\) −19.0092 −1.58410
\(145\) −20.3886 −1.69319
\(146\) 21.9034 1.81273
\(147\) 18.2908 1.50860
\(148\) 55.4889 4.56116
\(149\) 22.6396 1.85471 0.927353 0.374187i \(-0.122078\pi\)
0.927353 + 0.374187i \(0.122078\pi\)
\(150\) −11.5497 −0.943032
\(151\) 1.00000 0.0813788
\(152\) 18.3060 1.48481
\(153\) 6.07285 0.490961
\(154\) 13.8459 1.11574
\(155\) 20.2691 1.62805
\(156\) 21.8110 1.74627
\(157\) 6.35976 0.507564 0.253782 0.967261i \(-0.418325\pi\)
0.253782 + 0.967261i \(0.418325\pi\)
\(158\) 28.2760 2.24952
\(159\) −1.21893 −0.0966678
\(160\) −48.3647 −3.82356
\(161\) 12.1235 0.955462
\(162\) 5.80411 0.456014
\(163\) −11.9469 −0.935757 −0.467879 0.883793i \(-0.654982\pi\)
−0.467879 + 0.883793i \(0.654982\pi\)
\(164\) −25.7648 −2.01189
\(165\) −3.91967 −0.305146
\(166\) 38.2571 2.96933
\(167\) −3.56868 −0.276153 −0.138076 0.990422i \(-0.544092\pi\)
−0.138076 + 0.990422i \(0.544092\pi\)
\(168\) −48.9057 −3.77316
\(169\) −1.11235 −0.0855651
\(170\) 31.4150 2.40942
\(171\) 3.24087 0.247836
\(172\) −24.5517 −1.87205
\(173\) 22.3688 1.70067 0.850336 0.526240i \(-0.176399\pi\)
0.850336 + 0.526240i \(0.176399\pi\)
\(174\) 22.8116 1.72934
\(175\) 16.5768 1.25309
\(176\) −13.8192 −1.04166
\(177\) 12.3099 0.925267
\(178\) −31.3504 −2.34981
\(179\) 16.6744 1.24630 0.623151 0.782102i \(-0.285852\pi\)
0.623151 + 0.782102i \(0.285852\pi\)
\(180\) −22.9561 −1.71105
\(181\) 1.81418 0.134847 0.0674235 0.997724i \(-0.478522\pi\)
0.0674235 + 0.997724i \(0.478522\pi\)
\(182\) −43.3682 −3.21466
\(183\) 12.1807 0.900422
\(184\) −22.1041 −1.62954
\(185\) 31.2341 2.29638
\(186\) −22.6779 −1.66282
\(187\) 4.41478 0.322841
\(188\) 54.9442 4.00721
\(189\) −25.8123 −1.87757
\(190\) 16.7651 1.21627
\(191\) 1.51412 0.109558 0.0547788 0.998499i \(-0.482555\pi\)
0.0547788 + 0.998499i \(0.482555\pi\)
\(192\) 23.5073 1.69649
\(193\) 19.2116 1.38288 0.691441 0.722433i \(-0.256976\pi\)
0.691441 + 0.722433i \(0.256976\pi\)
\(194\) 10.6879 0.767349
\(195\) 12.2772 0.879186
\(196\) 77.8751 5.56251
\(197\) −9.90637 −0.705800 −0.352900 0.935661i \(-0.614804\pi\)
−0.352900 + 0.935661i \(0.614804\pi\)
\(198\) −4.46930 −0.317619
\(199\) 21.5854 1.53015 0.765074 0.643942i \(-0.222702\pi\)
0.765074 + 0.643942i \(0.222702\pi\)
\(200\) −30.2237 −2.13714
\(201\) 0.611952 0.0431638
\(202\) −38.6864 −2.72197
\(203\) −32.7405 −2.29793
\(204\) −25.3709 −1.77632
\(205\) −14.5027 −1.01291
\(206\) −54.0608 −3.76659
\(207\) −3.91330 −0.271993
\(208\) 43.2843 3.00122
\(209\) 2.35602 0.162969
\(210\) −44.7892 −3.09075
\(211\) −17.6455 −1.21476 −0.607382 0.794410i \(-0.707780\pi\)
−0.607382 + 0.794410i \(0.707780\pi\)
\(212\) −5.18975 −0.356433
\(213\) 3.33039 0.228194
\(214\) 23.9992 1.64055
\(215\) −13.8199 −0.942510
\(216\) 47.0624 3.20219
\(217\) 32.5485 2.20954
\(218\) 5.19151 0.351614
\(219\) −9.95713 −0.672840
\(220\) −16.6884 −1.12513
\(221\) −13.8280 −0.930169
\(222\) −34.9459 −2.34542
\(223\) 19.6702 1.31721 0.658606 0.752488i \(-0.271146\pi\)
0.658606 + 0.752488i \(0.271146\pi\)
\(224\) −77.6649 −5.18920
\(225\) −5.35079 −0.356719
\(226\) 37.1218 2.46931
\(227\) −12.2203 −0.811092 −0.405546 0.914075i \(-0.632919\pi\)
−0.405546 + 0.914075i \(0.632919\pi\)
\(228\) −13.5396 −0.896682
\(229\) 10.4380 0.689763 0.344882 0.938646i \(-0.387919\pi\)
0.344882 + 0.938646i \(0.387919\pi\)
\(230\) −20.2435 −1.33482
\(231\) −6.29428 −0.414133
\(232\) 59.6942 3.91912
\(233\) 27.0294 1.77076 0.885378 0.464872i \(-0.153900\pi\)
0.885378 + 0.464872i \(0.153900\pi\)
\(234\) 13.9987 0.915124
\(235\) 30.9275 2.01749
\(236\) 52.4107 3.41164
\(237\) −12.8541 −0.834963
\(238\) 50.4467 3.26998
\(239\) 26.8055 1.73390 0.866951 0.498393i \(-0.166076\pi\)
0.866951 + 0.498393i \(0.166076\pi\)
\(240\) 44.7025 2.88554
\(241\) −7.27693 −0.468748 −0.234374 0.972146i \(-0.575304\pi\)
−0.234374 + 0.972146i \(0.575304\pi\)
\(242\) 26.2460 1.68716
\(243\) 13.8690 0.889698
\(244\) 51.8606 3.32004
\(245\) 43.8351 2.80052
\(246\) 16.2262 1.03455
\(247\) −7.37950 −0.469547
\(248\) −59.3442 −3.76836
\(249\) −17.3914 −1.10214
\(250\) 11.4852 0.726386
\(251\) 4.84985 0.306120 0.153060 0.988217i \(-0.451087\pi\)
0.153060 + 0.988217i \(0.451087\pi\)
\(252\) −36.8634 −2.32218
\(253\) −2.84485 −0.178854
\(254\) −49.3146 −3.09427
\(255\) −14.2810 −0.894314
\(256\) 11.2986 0.706164
\(257\) −10.6034 −0.661423 −0.330711 0.943732i \(-0.607289\pi\)
−0.330711 + 0.943732i \(0.607289\pi\)
\(258\) 15.4623 0.962638
\(259\) 50.1563 3.11656
\(260\) 52.2714 3.24173
\(261\) 10.5682 0.654156
\(262\) −10.5945 −0.654533
\(263\) 17.7058 1.09179 0.545893 0.837855i \(-0.316190\pi\)
0.545893 + 0.837855i \(0.316190\pi\)
\(264\) 11.4761 0.706303
\(265\) −2.92126 −0.179451
\(266\) 26.9217 1.65067
\(267\) 14.2517 0.872190
\(268\) 2.60545 0.159153
\(269\) −9.75188 −0.594583 −0.297291 0.954787i \(-0.596083\pi\)
−0.297291 + 0.954787i \(0.596083\pi\)
\(270\) 43.1010 2.62304
\(271\) −30.1988 −1.83445 −0.917223 0.398375i \(-0.869574\pi\)
−0.917223 + 0.398375i \(0.869574\pi\)
\(272\) −50.3491 −3.05286
\(273\) 19.7149 1.19320
\(274\) 18.2426 1.10207
\(275\) −3.88986 −0.234567
\(276\) 16.3488 0.984084
\(277\) 3.77798 0.226997 0.113499 0.993538i \(-0.463794\pi\)
0.113499 + 0.993538i \(0.463794\pi\)
\(278\) −33.4782 −2.00789
\(279\) −10.5062 −0.628993
\(280\) −117.206 −7.00439
\(281\) −11.4653 −0.683960 −0.341980 0.939707i \(-0.611098\pi\)
−0.341980 + 0.939707i \(0.611098\pi\)
\(282\) −34.6029 −2.06057
\(283\) 9.27547 0.551370 0.275685 0.961248i \(-0.411095\pi\)
0.275685 + 0.961248i \(0.411095\pi\)
\(284\) 14.1795 0.841398
\(285\) −7.62130 −0.451447
\(286\) 10.1766 0.601757
\(287\) −23.2888 −1.37469
\(288\) 25.0693 1.47722
\(289\) −0.915049 −0.0538264
\(290\) 54.6695 3.21031
\(291\) −4.85867 −0.284820
\(292\) −42.3936 −2.48090
\(293\) −1.38509 −0.0809179 −0.0404589 0.999181i \(-0.512882\pi\)
−0.0404589 + 0.999181i \(0.512882\pi\)
\(294\) −49.0444 −2.86033
\(295\) 29.5014 1.71764
\(296\) −91.4477 −5.31529
\(297\) 6.05704 0.351465
\(298\) −60.7051 −3.51655
\(299\) 8.91062 0.515315
\(300\) 22.3543 1.29063
\(301\) −22.1923 −1.27914
\(302\) −2.68137 −0.154296
\(303\) 17.5866 1.01032
\(304\) −26.8696 −1.54108
\(305\) 29.1918 1.67152
\(306\) −16.2836 −0.930870
\(307\) −23.3056 −1.33012 −0.665059 0.746791i \(-0.731594\pi\)
−0.665059 + 0.746791i \(0.731594\pi\)
\(308\) −26.7986 −1.52699
\(309\) 24.5757 1.39806
\(310\) −54.3490 −3.08681
\(311\) 32.3049 1.83184 0.915922 0.401356i \(-0.131461\pi\)
0.915922 + 0.401356i \(0.131461\pi\)
\(312\) −35.9453 −2.03500
\(313\) −19.2743 −1.08945 −0.544724 0.838616i \(-0.683365\pi\)
−0.544724 + 0.838616i \(0.683365\pi\)
\(314\) −17.0529 −0.962349
\(315\) −20.7500 −1.16913
\(316\) −54.7278 −3.07868
\(317\) 4.17938 0.234737 0.117369 0.993088i \(-0.462554\pi\)
0.117369 + 0.993088i \(0.462554\pi\)
\(318\) 3.26842 0.183284
\(319\) 7.68278 0.430153
\(320\) 56.3367 3.14932
\(321\) −10.9099 −0.608931
\(322\) −32.5075 −1.81157
\(323\) 8.58399 0.477626
\(324\) −11.2338 −0.624098
\(325\) 12.1838 0.675836
\(326\) 32.0342 1.77421
\(327\) −2.36003 −0.130510
\(328\) 42.4613 2.34453
\(329\) 49.6640 2.73806
\(330\) 10.5101 0.578561
\(331\) 8.60300 0.472864 0.236432 0.971648i \(-0.424022\pi\)
0.236432 + 0.971648i \(0.424022\pi\)
\(332\) −74.0460 −4.06380
\(333\) −16.1898 −0.887198
\(334\) 9.56896 0.523590
\(335\) 1.46658 0.0801280
\(336\) 71.7841 3.91615
\(337\) −18.7729 −1.02262 −0.511312 0.859395i \(-0.670840\pi\)
−0.511312 + 0.859395i \(0.670840\pi\)
\(338\) 2.98261 0.162233
\(339\) −16.8754 −0.916543
\(340\) −60.8031 −3.29751
\(341\) −7.63773 −0.413606
\(342\) −8.68998 −0.469900
\(343\) 37.5541 2.02773
\(344\) 40.4621 2.18157
\(345\) 9.20259 0.495451
\(346\) −59.9792 −3.22450
\(347\) 6.54416 0.351309 0.175654 0.984452i \(-0.443796\pi\)
0.175654 + 0.984452i \(0.443796\pi\)
\(348\) −44.1515 −2.36677
\(349\) −8.26401 −0.442362 −0.221181 0.975233i \(-0.570991\pi\)
−0.221181 + 0.975233i \(0.570991\pi\)
\(350\) −44.4486 −2.37588
\(351\) −18.9718 −1.01264
\(352\) 18.2246 0.971374
\(353\) −14.8491 −0.790338 −0.395169 0.918608i \(-0.629314\pi\)
−0.395169 + 0.918608i \(0.629314\pi\)
\(354\) −33.0073 −1.75432
\(355\) 7.98150 0.423614
\(356\) 60.6782 3.21594
\(357\) −22.9328 −1.21373
\(358\) −44.7102 −2.36301
\(359\) −28.2270 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(360\) 37.8326 1.99395
\(361\) −14.4190 −0.758896
\(362\) −4.86449 −0.255672
\(363\) −11.9313 −0.626230
\(364\) 83.9384 4.39957
\(365\) −23.8629 −1.24904
\(366\) −32.6609 −1.70721
\(367\) 2.86588 0.149598 0.0747989 0.997199i \(-0.476169\pi\)
0.0747989 + 0.997199i \(0.476169\pi\)
\(368\) 32.4446 1.69129
\(369\) 7.51732 0.391336
\(370\) −83.7503 −4.35397
\(371\) −4.69101 −0.243545
\(372\) 43.8926 2.27573
\(373\) −13.8612 −0.717706 −0.358853 0.933394i \(-0.616832\pi\)
−0.358853 + 0.933394i \(0.616832\pi\)
\(374\) −11.8377 −0.612111
\(375\) −5.22108 −0.269616
\(376\) −90.5500 −4.66976
\(377\) −24.0639 −1.23936
\(378\) 69.2124 3.55990
\(379\) 13.2846 0.682383 0.341192 0.939994i \(-0.389169\pi\)
0.341192 + 0.939994i \(0.389169\pi\)
\(380\) −32.4485 −1.66458
\(381\) 22.4181 1.14852
\(382\) −4.05991 −0.207723
\(383\) 20.4233 1.04358 0.521792 0.853073i \(-0.325264\pi\)
0.521792 + 0.853073i \(0.325264\pi\)
\(384\) −22.6701 −1.15688
\(385\) −15.0847 −0.768785
\(386\) −51.5134 −2.62196
\(387\) 7.16339 0.364135
\(388\) −20.6863 −1.05019
\(389\) 2.83500 0.143740 0.0718701 0.997414i \(-0.477103\pi\)
0.0718701 + 0.997414i \(0.477103\pi\)
\(390\) −32.9196 −1.66695
\(391\) −10.3650 −0.524181
\(392\) −128.341 −6.48220
\(393\) 4.81621 0.242946
\(394\) 26.5627 1.33821
\(395\) −30.8057 −1.55000
\(396\) 8.65025 0.434691
\(397\) −32.0599 −1.60904 −0.804519 0.593926i \(-0.797577\pi\)
−0.804519 + 0.593926i \(0.797577\pi\)
\(398\) −57.8785 −2.90118
\(399\) −12.2384 −0.612688
\(400\) 44.3626 2.21813
\(401\) 18.2701 0.912367 0.456183 0.889886i \(-0.349216\pi\)
0.456183 + 0.889886i \(0.349216\pi\)
\(402\) −1.64087 −0.0818392
\(403\) 23.9228 1.19168
\(404\) 74.8770 3.72527
\(405\) −6.32337 −0.314211
\(406\) 87.7893 4.35691
\(407\) −11.7695 −0.583394
\(408\) 41.8123 2.07001
\(409\) −7.24990 −0.358484 −0.179242 0.983805i \(-0.557365\pi\)
−0.179242 + 0.983805i \(0.557365\pi\)
\(410\) 38.8872 1.92050
\(411\) −8.29296 −0.409061
\(412\) 104.634 5.15494
\(413\) 47.3740 2.33112
\(414\) 10.4930 0.515703
\(415\) −41.6797 −2.04598
\(416\) −57.0830 −2.79872
\(417\) 15.2190 0.745276
\(418\) −6.31736 −0.308992
\(419\) −28.7534 −1.40470 −0.702349 0.711833i \(-0.747865\pi\)
−0.702349 + 0.711833i \(0.747865\pi\)
\(420\) 86.6887 4.22998
\(421\) −18.2925 −0.891523 −0.445762 0.895152i \(-0.647067\pi\)
−0.445762 + 0.895152i \(0.647067\pi\)
\(422\) 47.3141 2.30321
\(423\) −16.0309 −0.779449
\(424\) 8.55290 0.415365
\(425\) −14.1724 −0.687464
\(426\) −8.93001 −0.432660
\(427\) 46.8768 2.26853
\(428\) −46.4501 −2.24525
\(429\) −4.62624 −0.223357
\(430\) 37.0563 1.78701
\(431\) −19.6897 −0.948420 −0.474210 0.880412i \(-0.657266\pi\)
−0.474210 + 0.880412i \(0.657266\pi\)
\(432\) −69.0785 −3.32354
\(433\) 6.68017 0.321028 0.160514 0.987034i \(-0.448685\pi\)
0.160514 + 0.987034i \(0.448685\pi\)
\(434\) −87.2746 −4.18931
\(435\) −24.8524 −1.19158
\(436\) −10.0481 −0.481216
\(437\) −5.53145 −0.264605
\(438\) 26.6988 1.27572
\(439\) 40.9152 1.95277 0.976387 0.216029i \(-0.0693105\pi\)
0.976387 + 0.216029i \(0.0693105\pi\)
\(440\) 27.5032 1.31116
\(441\) −22.7214 −1.08197
\(442\) 37.0779 1.76361
\(443\) 15.2464 0.724376 0.362188 0.932105i \(-0.382030\pi\)
0.362188 + 0.932105i \(0.382030\pi\)
\(444\) 67.6373 3.20992
\(445\) 34.1551 1.61911
\(446\) −52.7430 −2.49745
\(447\) 27.5962 1.30525
\(448\) 90.4665 4.27414
\(449\) 22.5313 1.06332 0.531658 0.846959i \(-0.321569\pi\)
0.531658 + 0.846959i \(0.321569\pi\)
\(450\) 14.3474 0.676345
\(451\) 5.46487 0.257330
\(452\) −71.8487 −3.37948
\(453\) 1.21893 0.0572705
\(454\) 32.7672 1.53784
\(455\) 47.2481 2.21502
\(456\) 22.3138 1.04494
\(457\) −4.16085 −0.194636 −0.0973181 0.995253i \(-0.531026\pi\)
−0.0973181 + 0.995253i \(0.531026\pi\)
\(458\) −27.9882 −1.30780
\(459\) 22.0684 1.03006
\(460\) 39.1811 1.82683
\(461\) −9.73043 −0.453191 −0.226596 0.973989i \(-0.572760\pi\)
−0.226596 + 0.973989i \(0.572760\pi\)
\(462\) 16.8773 0.785203
\(463\) −29.0575 −1.35042 −0.675209 0.737627i \(-0.735946\pi\)
−0.675209 + 0.737627i \(0.735946\pi\)
\(464\) −87.6195 −4.06763
\(465\) 24.7067 1.14575
\(466\) −72.4759 −3.35738
\(467\) 6.80629 0.314958 0.157479 0.987522i \(-0.449663\pi\)
0.157479 + 0.987522i \(0.449663\pi\)
\(468\) −27.0943 −1.25243
\(469\) 2.35507 0.108747
\(470\) −82.9281 −3.82519
\(471\) 7.75213 0.357199
\(472\) −86.3747 −3.97572
\(473\) 5.20757 0.239444
\(474\) 34.4666 1.58310
\(475\) −7.56334 −0.347030
\(476\) −97.6388 −4.47527
\(477\) 1.51420 0.0693304
\(478\) −71.8754 −3.28751
\(479\) −29.4706 −1.34654 −0.673272 0.739395i \(-0.735112\pi\)
−0.673272 + 0.739395i \(0.735112\pi\)
\(480\) −58.9534 −2.69084
\(481\) 36.8644 1.68087
\(482\) 19.5122 0.888754
\(483\) 14.7777 0.672408
\(484\) −50.7988 −2.30903
\(485\) −11.6441 −0.528732
\(486\) −37.1880 −1.68688
\(487\) 27.8026 1.25986 0.629929 0.776653i \(-0.283084\pi\)
0.629929 + 0.776653i \(0.283084\pi\)
\(488\) −85.4682 −3.86897
\(489\) −14.5625 −0.658541
\(490\) −117.538 −5.30983
\(491\) −10.5619 −0.476652 −0.238326 0.971185i \(-0.576599\pi\)
−0.238326 + 0.971185i \(0.576599\pi\)
\(492\) −31.4056 −1.41587
\(493\) 27.9917 1.26068
\(494\) 19.7872 0.890268
\(495\) 4.86914 0.218851
\(496\) 87.1057 3.91116
\(497\) 12.8168 0.574914
\(498\) 46.6329 2.08967
\(499\) −18.7488 −0.839312 −0.419656 0.907683i \(-0.637849\pi\)
−0.419656 + 0.907683i \(0.637849\pi\)
\(500\) −22.2293 −0.994127
\(501\) −4.34999 −0.194343
\(502\) −13.0042 −0.580408
\(503\) 16.6885 0.744102 0.372051 0.928212i \(-0.378655\pi\)
0.372051 + 0.928212i \(0.378655\pi\)
\(504\) 60.7523 2.70612
\(505\) 42.1475 1.87554
\(506\) 7.62810 0.339110
\(507\) −1.35588 −0.0602166
\(508\) 95.4476 4.23480
\(509\) 15.7604 0.698566 0.349283 0.937017i \(-0.386425\pi\)
0.349283 + 0.937017i \(0.386425\pi\)
\(510\) 38.2928 1.69563
\(511\) −38.3195 −1.69516
\(512\) 6.90070 0.304971
\(513\) 11.7771 0.519974
\(514\) 28.4317 1.25407
\(515\) 58.8973 2.59532
\(516\) −29.9269 −1.31746
\(517\) −11.6540 −0.512542
\(518\) −134.488 −5.90905
\(519\) 27.2662 1.19685
\(520\) −86.1452 −3.77772
\(521\) −38.9094 −1.70465 −0.852325 0.523012i \(-0.824808\pi\)
−0.852325 + 0.523012i \(0.824808\pi\)
\(522\) −28.3373 −1.24029
\(523\) 19.2629 0.842309 0.421155 0.906989i \(-0.361625\pi\)
0.421155 + 0.906989i \(0.361625\pi\)
\(524\) 20.5056 0.895789
\(525\) 20.2060 0.881864
\(526\) −47.4758 −2.07004
\(527\) −27.8275 −1.21219
\(528\) −16.8446 −0.733069
\(529\) −16.3209 −0.709603
\(530\) 7.83297 0.340243
\(531\) −15.2917 −0.663604
\(532\) −52.1065 −2.25910
\(533\) −17.1170 −0.741420
\(534\) −38.2141 −1.65368
\(535\) −26.1463 −1.13040
\(536\) −4.29389 −0.185468
\(537\) 20.3250 0.877087
\(538\) 26.1484 1.12734
\(539\) −16.5178 −0.711471
\(540\) −83.4213 −3.58988
\(541\) 30.3990 1.30696 0.653478 0.756946i \(-0.273309\pi\)
0.653478 + 0.756946i \(0.273309\pi\)
\(542\) 80.9741 3.47814
\(543\) 2.21137 0.0948989
\(544\) 66.4000 2.84688
\(545\) −5.65597 −0.242275
\(546\) −52.8630 −2.26233
\(547\) −20.8135 −0.889919 −0.444959 0.895551i \(-0.646782\pi\)
−0.444959 + 0.895551i \(0.646782\pi\)
\(548\) −35.3082 −1.50829
\(549\) −15.1312 −0.645785
\(550\) 10.4302 0.444744
\(551\) 14.9382 0.636388
\(552\) −26.9435 −1.14679
\(553\) −49.4684 −2.10361
\(554\) −10.1302 −0.430390
\(555\) 38.0724 1.61608
\(556\) 64.7964 2.74798
\(557\) 5.09123 0.215722 0.107861 0.994166i \(-0.465600\pi\)
0.107861 + 0.994166i \(0.465600\pi\)
\(558\) 28.1711 1.19258
\(559\) −16.3111 −0.689887
\(560\) 172.035 7.26982
\(561\) 5.38133 0.227200
\(562\) 30.7426 1.29680
\(563\) −31.5721 −1.33060 −0.665302 0.746574i \(-0.731697\pi\)
−0.665302 + 0.746574i \(0.731697\pi\)
\(564\) 66.9733 2.82009
\(565\) −40.4429 −1.70145
\(566\) −24.8710 −1.04541
\(567\) −10.1542 −0.426435
\(568\) −23.3683 −0.980514
\(569\) −10.8687 −0.455639 −0.227819 0.973703i \(-0.573160\pi\)
−0.227819 + 0.973703i \(0.573160\pi\)
\(570\) 20.4355 0.855950
\(571\) 35.3517 1.47942 0.739711 0.672925i \(-0.234962\pi\)
0.739711 + 0.672925i \(0.234962\pi\)
\(572\) −19.6967 −0.823561
\(573\) 1.84561 0.0771014
\(574\) 62.4458 2.60644
\(575\) 9.13261 0.380856
\(576\) −29.2015 −1.21673
\(577\) −26.1284 −1.08774 −0.543871 0.839169i \(-0.683042\pi\)
−0.543871 + 0.839169i \(0.683042\pi\)
\(578\) 2.45358 0.102056
\(579\) 23.4177 0.973206
\(580\) −105.812 −4.39360
\(581\) −66.9301 −2.77673
\(582\) 13.0279 0.540023
\(583\) 1.10078 0.0455895
\(584\) 69.8662 2.89108
\(585\) −15.2511 −0.630555
\(586\) 3.71394 0.153422
\(587\) −35.6428 −1.47114 −0.735569 0.677450i \(-0.763085\pi\)
−0.735569 + 0.677450i \(0.763085\pi\)
\(588\) 94.9246 3.91463
\(589\) −14.8506 −0.611908
\(590\) −79.1043 −3.25667
\(591\) −12.0752 −0.496708
\(592\) 134.228 5.51672
\(593\) 33.8848 1.39148 0.695741 0.718292i \(-0.255076\pi\)
0.695741 + 0.718292i \(0.255076\pi\)
\(594\) −16.2412 −0.666383
\(595\) −54.9599 −2.25314
\(596\) 117.494 4.81273
\(597\) 26.3112 1.07685
\(598\) −23.8927 −0.977045
\(599\) −20.7880 −0.849373 −0.424687 0.905340i \(-0.639616\pi\)
−0.424687 + 0.905340i \(0.639616\pi\)
\(600\) −36.8407 −1.50402
\(601\) 29.5459 1.20520 0.602601 0.798042i \(-0.294131\pi\)
0.602601 + 0.798042i \(0.294131\pi\)
\(602\) 59.5057 2.42527
\(603\) −0.760186 −0.0309572
\(604\) 5.18975 0.211168
\(605\) −28.5941 −1.16252
\(606\) −47.1562 −1.91559
\(607\) 8.18796 0.332339 0.166170 0.986097i \(-0.446860\pi\)
0.166170 + 0.986097i \(0.446860\pi\)
\(608\) 35.4354 1.43710
\(609\) −39.9085 −1.61717
\(610\) −78.2741 −3.16922
\(611\) 36.5026 1.47674
\(612\) 31.5166 1.27398
\(613\) −1.10208 −0.0445125 −0.0222563 0.999752i \(-0.507085\pi\)
−0.0222563 + 0.999752i \(0.507085\pi\)
\(614\) 62.4908 2.52192
\(615\) −17.6779 −0.712841
\(616\) 44.1651 1.77946
\(617\) −12.7845 −0.514683 −0.257341 0.966321i \(-0.582847\pi\)
−0.257341 + 0.966321i \(0.582847\pi\)
\(618\) −65.8966 −2.65075
\(619\) 8.89493 0.357517 0.178759 0.983893i \(-0.442792\pi\)
0.178759 + 0.983893i \(0.442792\pi\)
\(620\) 105.192 4.22459
\(621\) −14.2207 −0.570657
\(622\) −86.6215 −3.47320
\(623\) 54.8469 2.19740
\(624\) 52.7607 2.11212
\(625\) −30.1814 −1.20726
\(626\) 51.6815 2.06561
\(627\) 2.87183 0.114690
\(628\) 33.0055 1.31706
\(629\) −42.8815 −1.70980
\(630\) 55.6385 2.21669
\(631\) −22.3469 −0.889618 −0.444809 0.895625i \(-0.646728\pi\)
−0.444809 + 0.895625i \(0.646728\pi\)
\(632\) 90.1934 3.58770
\(633\) −21.5087 −0.854893
\(634\) −11.2065 −0.445066
\(635\) 53.7265 2.13207
\(636\) −6.32596 −0.250841
\(637\) 51.7369 2.04989
\(638\) −20.6004 −0.815576
\(639\) −4.13711 −0.163662
\(640\) −54.3303 −2.14759
\(641\) −17.7971 −0.702942 −0.351471 0.936199i \(-0.614318\pi\)
−0.351471 + 0.936199i \(0.614318\pi\)
\(642\) 29.2535 1.15454
\(643\) −31.3236 −1.23528 −0.617642 0.786459i \(-0.711912\pi\)
−0.617642 + 0.786459i \(0.711912\pi\)
\(644\) 62.9177 2.47930
\(645\) −16.8456 −0.663293
\(646\) −23.0168 −0.905586
\(647\) −27.8477 −1.09481 −0.547403 0.836869i \(-0.684384\pi\)
−0.547403 + 0.836869i \(0.684384\pi\)
\(648\) 18.5136 0.727285
\(649\) −11.1166 −0.436366
\(650\) −32.6693 −1.28139
\(651\) 39.6745 1.55497
\(652\) −62.0017 −2.42817
\(653\) 6.73217 0.263450 0.131725 0.991286i \(-0.457948\pi\)
0.131725 + 0.991286i \(0.457948\pi\)
\(654\) 6.32811 0.247449
\(655\) 11.5424 0.450998
\(656\) −62.3250 −2.43338
\(657\) 12.3691 0.482563
\(658\) −133.167 −5.19141
\(659\) −9.10358 −0.354625 −0.177313 0.984155i \(-0.556740\pi\)
−0.177313 + 0.984155i \(0.556740\pi\)
\(660\) −20.3421 −0.791815
\(661\) −5.01809 −0.195181 −0.0975906 0.995227i \(-0.531114\pi\)
−0.0975906 + 0.995227i \(0.531114\pi\)
\(662\) −23.0678 −0.896557
\(663\) −16.8554 −0.654608
\(664\) 122.031 4.73571
\(665\) −29.3302 −1.13738
\(666\) 43.4110 1.68214
\(667\) −18.0376 −0.698419
\(668\) −18.5206 −0.716582
\(669\) 23.9766 0.926991
\(670\) −3.93245 −0.151924
\(671\) −11.0000 −0.424648
\(672\) −94.6684 −3.65191
\(673\) 37.8902 1.46056 0.730279 0.683149i \(-0.239390\pi\)
0.730279 + 0.683149i \(0.239390\pi\)
\(674\) 50.3371 1.93891
\(675\) −19.4445 −0.748417
\(676\) −5.77280 −0.222031
\(677\) 2.85575 0.109755 0.0548777 0.998493i \(-0.482523\pi\)
0.0548777 + 0.998493i \(0.482523\pi\)
\(678\) 45.2491 1.73778
\(679\) −18.6983 −0.717576
\(680\) 100.206 3.84272
\(681\) −14.8958 −0.570808
\(682\) 20.4796 0.784204
\(683\) 15.4324 0.590502 0.295251 0.955420i \(-0.404597\pi\)
0.295251 + 0.955420i \(0.404597\pi\)
\(684\) 16.8193 0.643103
\(685\) −19.8746 −0.759370
\(686\) −100.697 −3.84461
\(687\) 12.7233 0.485422
\(688\) −59.3906 −2.26424
\(689\) −3.44785 −0.131353
\(690\) −24.6756 −0.939382
\(691\) 28.5099 1.08457 0.542284 0.840195i \(-0.317560\pi\)
0.542284 + 0.840195i \(0.317560\pi\)
\(692\) 116.089 4.41303
\(693\) 7.81895 0.297017
\(694\) −17.5473 −0.666087
\(695\) 36.4733 1.38351
\(696\) 72.7633 2.75809
\(697\) 19.9109 0.754177
\(698\) 22.1589 0.838726
\(699\) 32.9471 1.24617
\(700\) 86.0295 3.25161
\(701\) −20.5586 −0.776489 −0.388245 0.921556i \(-0.626918\pi\)
−0.388245 + 0.921556i \(0.626918\pi\)
\(702\) 50.8705 1.91998
\(703\) −22.8844 −0.863100
\(704\) −21.2286 −0.800083
\(705\) 37.6986 1.41981
\(706\) 39.8160 1.49849
\(707\) 67.6812 2.54541
\(708\) 63.8852 2.40095
\(709\) 0.0249458 0.000936859 0 0.000468429 1.00000i \(-0.499851\pi\)
0.000468429 1.00000i \(0.499851\pi\)
\(710\) −21.4013 −0.803178
\(711\) 15.9678 0.598838
\(712\) −99.9999 −3.74765
\(713\) 17.9318 0.671553
\(714\) 61.4912 2.30125
\(715\) −11.0871 −0.414633
\(716\) 86.5358 3.23400
\(717\) 32.6741 1.22024
\(718\) 75.6871 2.82462
\(719\) −47.1130 −1.75702 −0.878510 0.477724i \(-0.841462\pi\)
−0.878510 + 0.477724i \(0.841462\pi\)
\(720\) −55.5309 −2.06951
\(721\) 94.5783 3.52228
\(722\) 38.6627 1.43888
\(723\) −8.87010 −0.329883
\(724\) 9.41514 0.349911
\(725\) −24.6634 −0.915977
\(726\) 31.9922 1.18734
\(727\) −34.9187 −1.29506 −0.647532 0.762039i \(-0.724199\pi\)
−0.647532 + 0.762039i \(0.724199\pi\)
\(728\) −138.334 −5.12698
\(729\) 23.3992 0.866639
\(730\) 63.9853 2.36820
\(731\) 18.9734 0.701757
\(732\) 63.2147 2.33648
\(733\) −1.93232 −0.0713717 −0.0356859 0.999363i \(-0.511362\pi\)
−0.0356859 + 0.999363i \(0.511362\pi\)
\(734\) −7.68449 −0.283640
\(735\) 53.4321 1.97087
\(736\) −42.7877 −1.57717
\(737\) −0.552633 −0.0203565
\(738\) −20.1567 −0.741979
\(739\) −23.1214 −0.850535 −0.425267 0.905068i \(-0.639820\pi\)
−0.425267 + 0.905068i \(0.639820\pi\)
\(740\) 162.097 5.95881
\(741\) −8.99513 −0.330444
\(742\) 12.5783 0.461765
\(743\) −42.0929 −1.54424 −0.772118 0.635479i \(-0.780803\pi\)
−0.772118 + 0.635479i \(0.780803\pi\)
\(744\) −72.3367 −2.65199
\(745\) 66.1360 2.42304
\(746\) 37.1670 1.36078
\(747\) 21.6042 0.790457
\(748\) 22.9116 0.837731
\(749\) −41.9862 −1.53414
\(750\) 13.9997 0.511195
\(751\) −47.0328 −1.71625 −0.858125 0.513441i \(-0.828371\pi\)
−0.858125 + 0.513441i \(0.828371\pi\)
\(752\) 132.910 4.84672
\(753\) 5.91165 0.215432
\(754\) 64.5244 2.34984
\(755\) 2.92126 0.106315
\(756\) −133.960 −4.87206
\(757\) −47.2332 −1.71672 −0.858360 0.513048i \(-0.828516\pi\)
−0.858360 + 0.513048i \(0.828516\pi\)
\(758\) −35.6209 −1.29381
\(759\) −3.46769 −0.125869
\(760\) 53.4764 1.93979
\(761\) 18.2535 0.661690 0.330845 0.943685i \(-0.392666\pi\)
0.330845 + 0.943685i \(0.392666\pi\)
\(762\) −60.1113 −2.17760
\(763\) −9.08246 −0.328807
\(764\) 7.85788 0.284288
\(765\) 17.7404 0.641404
\(766\) −54.7625 −1.97865
\(767\) 34.8194 1.25726
\(768\) 13.7723 0.496965
\(769\) −50.0820 −1.80600 −0.903001 0.429638i \(-0.858641\pi\)
−0.903001 + 0.429638i \(0.858641\pi\)
\(770\) 40.4475 1.45763
\(771\) −12.9249 −0.465477
\(772\) 99.7034 3.58840
\(773\) 37.5683 1.35124 0.675618 0.737252i \(-0.263877\pi\)
0.675618 + 0.737252i \(0.263877\pi\)
\(774\) −19.2077 −0.690406
\(775\) 24.5188 0.880742
\(776\) 34.0918 1.22383
\(777\) 61.1373 2.19329
\(778\) −7.60168 −0.272533
\(779\) 10.6257 0.380707
\(780\) 63.7154 2.28138
\(781\) −3.00756 −0.107619
\(782\) 27.7924 0.993856
\(783\) 38.4043 1.37246
\(784\) 188.380 6.72785
\(785\) 18.5785 0.663095
\(786\) −12.9140 −0.460629
\(787\) −36.2914 −1.29365 −0.646824 0.762640i \(-0.723903\pi\)
−0.646824 + 0.762640i \(0.723903\pi\)
\(788\) −51.4116 −1.83146
\(789\) 21.5822 0.768347
\(790\) 82.6015 2.93883
\(791\) −64.9440 −2.30914
\(792\) −14.2559 −0.506563
\(793\) 34.4540 1.22350
\(794\) 85.9644 3.05076
\(795\) −3.56082 −0.126289
\(796\) 112.023 3.97054
\(797\) 26.1605 0.926652 0.463326 0.886188i \(-0.346656\pi\)
0.463326 + 0.886188i \(0.346656\pi\)
\(798\) 32.8158 1.16167
\(799\) −42.4605 −1.50214
\(800\) −58.5050 −2.06847
\(801\) −17.7039 −0.625537
\(802\) −48.9890 −1.72986
\(803\) 8.99194 0.317319
\(804\) 3.17588 0.112005
\(805\) 35.4157 1.24824
\(806\) −64.1460 −2.25945
\(807\) −11.8869 −0.418439
\(808\) −123.400 −4.34120
\(809\) 12.6907 0.446181 0.223090 0.974798i \(-0.428385\pi\)
0.223090 + 0.974798i \(0.428385\pi\)
\(810\) 16.9553 0.595748
\(811\) 39.4502 1.38528 0.692642 0.721282i \(-0.256447\pi\)
0.692642 + 0.721282i \(0.256447\pi\)
\(812\) −169.915 −5.96284
\(813\) −36.8103 −1.29099
\(814\) 31.5585 1.10612
\(815\) −34.9001 −1.22250
\(816\) −61.3723 −2.14846
\(817\) 10.1255 0.354245
\(818\) 19.4397 0.679692
\(819\) −24.4905 −0.855766
\(820\) −75.2655 −2.62839
\(821\) 17.1237 0.597620 0.298810 0.954313i \(-0.403410\pi\)
0.298810 + 0.954313i \(0.403410\pi\)
\(822\) 22.2365 0.775587
\(823\) 6.04490 0.210712 0.105356 0.994435i \(-0.466402\pi\)
0.105356 + 0.994435i \(0.466402\pi\)
\(824\) −172.440 −6.00724
\(825\) −4.74149 −0.165077
\(826\) −127.027 −4.41984
\(827\) −1.80795 −0.0628685 −0.0314343 0.999506i \(-0.510007\pi\)
−0.0314343 + 0.999506i \(0.510007\pi\)
\(828\) −20.3090 −0.705788
\(829\) −14.8789 −0.516766 −0.258383 0.966043i \(-0.583190\pi\)
−0.258383 + 0.966043i \(0.583190\pi\)
\(830\) 111.759 3.87921
\(831\) 4.60512 0.159750
\(832\) 66.4921 2.30520
\(833\) −60.1814 −2.08516
\(834\) −40.8077 −1.41305
\(835\) −10.4250 −0.360773
\(836\) 12.2271 0.422884
\(837\) −38.1791 −1.31966
\(838\) 77.0986 2.66333
\(839\) 15.1223 0.522079 0.261039 0.965328i \(-0.415935\pi\)
0.261039 + 0.965328i \(0.415935\pi\)
\(840\) −142.866 −4.92935
\(841\) 19.7122 0.679730
\(842\) 49.0490 1.69034
\(843\) −13.9754 −0.481339
\(844\) −91.5756 −3.15216
\(845\) −3.24945 −0.111784
\(846\) 42.9848 1.47785
\(847\) −45.9169 −1.57773
\(848\) −12.5540 −0.431106
\(849\) 11.3062 0.388028
\(850\) 38.0016 1.30344
\(851\) 27.6325 0.947229
\(852\) 17.2839 0.592136
\(853\) −11.0372 −0.377907 −0.188954 0.981986i \(-0.560510\pi\)
−0.188954 + 0.981986i \(0.560510\pi\)
\(854\) −125.694 −4.30116
\(855\) 9.46742 0.323779
\(856\) 76.5515 2.61647
\(857\) −38.3279 −1.30926 −0.654628 0.755951i \(-0.727175\pi\)
−0.654628 + 0.755951i \(0.727175\pi\)
\(858\) 12.4047 0.423488
\(859\) −36.1308 −1.23277 −0.616384 0.787446i \(-0.711403\pi\)
−0.616384 + 0.787446i \(0.711403\pi\)
\(860\) −71.7219 −2.44570
\(861\) −28.3875 −0.967442
\(862\) 52.7954 1.79822
\(863\) −2.15671 −0.0734153 −0.0367076 0.999326i \(-0.511687\pi\)
−0.0367076 + 0.999326i \(0.511687\pi\)
\(864\) 91.1002 3.09929
\(865\) 65.3451 2.22180
\(866\) −17.9120 −0.608674
\(867\) −1.11538 −0.0378804
\(868\) 168.919 5.73347
\(869\) 11.6081 0.393777
\(870\) 66.6386 2.25926
\(871\) 1.73095 0.0586511
\(872\) 16.5596 0.560780
\(873\) 6.03559 0.204274
\(874\) 14.8319 0.501696
\(875\) −20.0931 −0.679270
\(876\) −51.6750 −1.74594
\(877\) 51.9149 1.75304 0.876521 0.481363i \(-0.159858\pi\)
0.876521 + 0.481363i \(0.159858\pi\)
\(878\) −109.709 −3.70249
\(879\) −1.68834 −0.0569461
\(880\) −40.3693 −1.36085
\(881\) −38.8556 −1.30908 −0.654539 0.756028i \(-0.727137\pi\)
−0.654539 + 0.756028i \(0.727137\pi\)
\(882\) 60.9245 2.05143
\(883\) −11.5119 −0.387405 −0.193702 0.981060i \(-0.562050\pi\)
−0.193702 + 0.981060i \(0.562050\pi\)
\(884\) −71.7636 −2.41367
\(885\) 35.9603 1.20879
\(886\) −40.8811 −1.37343
\(887\) 43.7525 1.46906 0.734532 0.678574i \(-0.237402\pi\)
0.734532 + 0.678574i \(0.237402\pi\)
\(888\) −111.469 −3.74065
\(889\) 86.2750 2.89357
\(890\) −91.5826 −3.06985
\(891\) 2.38275 0.0798251
\(892\) 102.083 3.41800
\(893\) −22.6597 −0.758278
\(894\) −73.9955 −2.47478
\(895\) 48.7101 1.62820
\(896\) −87.2446 −2.91464
\(897\) 10.8615 0.362654
\(898\) −60.4147 −2.01606
\(899\) −48.4265 −1.61512
\(900\) −27.7692 −0.925641
\(901\) 4.01060 0.133613
\(902\) −14.6533 −0.487903
\(903\) −27.0509 −0.900198
\(904\) 118.409 3.93824
\(905\) 5.29969 0.176168
\(906\) −3.26842 −0.108586
\(907\) 48.1400 1.59846 0.799231 0.601024i \(-0.205241\pi\)
0.799231 + 0.601024i \(0.205241\pi\)
\(908\) −63.4205 −2.10468
\(909\) −21.8467 −0.724608
\(910\) −126.690 −4.19972
\(911\) 45.2253 1.49838 0.749190 0.662355i \(-0.230443\pi\)
0.749190 + 0.662355i \(0.230443\pi\)
\(912\) −32.7523 −1.08454
\(913\) 15.7056 0.519780
\(914\) 11.1568 0.369033
\(915\) 35.5829 1.17633
\(916\) 54.1707 1.78985
\(917\) 18.5350 0.612078
\(918\) −59.1736 −1.95302
\(919\) 16.6422 0.548975 0.274487 0.961591i \(-0.411492\pi\)
0.274487 + 0.961591i \(0.411492\pi\)
\(920\) −64.5718 −2.12887
\(921\) −28.4079 −0.936073
\(922\) 26.0909 0.859258
\(923\) 9.42025 0.310071
\(924\) −32.6657 −1.07462
\(925\) 37.7828 1.24229
\(926\) 77.9140 2.56041
\(927\) −30.5287 −1.00269
\(928\) 115.552 3.79318
\(929\) −14.6934 −0.482075 −0.241038 0.970516i \(-0.577488\pi\)
−0.241038 + 0.970516i \(0.577488\pi\)
\(930\) −66.2478 −2.17235
\(931\) −32.1167 −1.05258
\(932\) 140.276 4.59489
\(933\) 39.3776 1.28916
\(934\) −18.2502 −0.597165
\(935\) 12.8967 0.421768
\(936\) 44.6524 1.45951
\(937\) 12.8862 0.420973 0.210486 0.977597i \(-0.432495\pi\)
0.210486 + 0.977597i \(0.432495\pi\)
\(938\) −6.31481 −0.206186
\(939\) −23.4941 −0.766701
\(940\) 160.506 5.23513
\(941\) −23.4391 −0.764092 −0.382046 0.924143i \(-0.624780\pi\)
−0.382046 + 0.924143i \(0.624780\pi\)
\(942\) −20.7863 −0.677255
\(943\) −12.8304 −0.417815
\(944\) 126.781 4.12638
\(945\) −75.4044 −2.45291
\(946\) −13.9634 −0.453990
\(947\) −23.3185 −0.757750 −0.378875 0.925448i \(-0.623689\pi\)
−0.378875 + 0.925448i \(0.623689\pi\)
\(948\) −66.7095 −2.16663
\(949\) −28.1645 −0.914258
\(950\) 20.2801 0.657974
\(951\) 5.09439 0.165197
\(952\) 160.912 5.21520
\(953\) 26.3452 0.853405 0.426702 0.904392i \(-0.359675\pi\)
0.426702 + 0.904392i \(0.359675\pi\)
\(954\) −4.06013 −0.131452
\(955\) 4.42312 0.143129
\(956\) 139.114 4.49926
\(957\) 9.36480 0.302721
\(958\) 79.0215 2.55307
\(959\) −31.9150 −1.03059
\(960\) 68.6708 2.21634
\(961\) 17.1426 0.552987
\(962\) −98.8472 −3.18696
\(963\) 13.5526 0.436727
\(964\) −37.7654 −1.21634
\(965\) 56.1220 1.80663
\(966\) −39.6245 −1.27490
\(967\) 49.2476 1.58369 0.791847 0.610719i \(-0.209120\pi\)
0.791847 + 0.610719i \(0.209120\pi\)
\(968\) 83.7183 2.69081
\(969\) 10.4633 0.336130
\(970\) 31.2222 1.00248
\(971\) −0.471001 −0.0151151 −0.00755757 0.999971i \(-0.502406\pi\)
−0.00755757 + 0.999971i \(0.502406\pi\)
\(972\) 71.9768 2.30866
\(973\) 58.5694 1.87765
\(974\) −74.5491 −2.38871
\(975\) 14.8513 0.475621
\(976\) 125.451 4.01558
\(977\) −22.2681 −0.712418 −0.356209 0.934406i \(-0.615931\pi\)
−0.356209 + 0.934406i \(0.615931\pi\)
\(978\) 39.0476 1.24860
\(979\) −12.8702 −0.411334
\(980\) 227.493 7.26700
\(981\) 2.93170 0.0936021
\(982\) 28.3204 0.903739
\(983\) 35.3584 1.12776 0.563879 0.825857i \(-0.309308\pi\)
0.563879 + 0.825857i \(0.309308\pi\)
\(984\) 51.7576 1.64997
\(985\) −28.9391 −0.922075
\(986\) −75.0560 −2.39027
\(987\) 60.5371 1.92692
\(988\) −38.2978 −1.21841
\(989\) −12.2263 −0.388774
\(990\) −13.0560 −0.414946
\(991\) −49.8362 −1.58310 −0.791550 0.611105i \(-0.790725\pi\)
−0.791550 + 0.611105i \(0.790725\pi\)
\(992\) −114.874 −3.64727
\(993\) 10.4865 0.332779
\(994\) −34.3667 −1.09004
\(995\) 63.0565 1.99903
\(996\) −90.2572 −2.85991
\(997\) −24.2646 −0.768468 −0.384234 0.923236i \(-0.625534\pi\)
−0.384234 + 0.923236i \(0.625534\pi\)
\(998\) 50.2725 1.59135
\(999\) −58.8330 −1.86139
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 \(a_p\))