Properties

Label 8015.2.a.l.1.13
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.87703 q^{2}\) \(-2.63781 q^{3}\) \(+1.52324 q^{4}\) \(-1.00000 q^{5}\) \(+4.95125 q^{6}\) \(-1.00000 q^{7}\) \(+0.894900 q^{8}\) \(+3.95806 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.87703 q^{2}\) \(-2.63781 q^{3}\) \(+1.52324 q^{4}\) \(-1.00000 q^{5}\) \(+4.95125 q^{6}\) \(-1.00000 q^{7}\) \(+0.894900 q^{8}\) \(+3.95806 q^{9}\) \(+1.87703 q^{10}\) \(-0.835767 q^{11}\) \(-4.01801 q^{12}\) \(-2.57449 q^{13}\) \(+1.87703 q^{14}\) \(+2.63781 q^{15}\) \(-4.72622 q^{16}\) \(+5.00673 q^{17}\) \(-7.42939 q^{18}\) \(+1.69114 q^{19}\) \(-1.52324 q^{20}\) \(+2.63781 q^{21}\) \(+1.56876 q^{22}\) \(+7.52045 q^{23}\) \(-2.36058 q^{24}\) \(+1.00000 q^{25}\) \(+4.83238 q^{26}\) \(-2.52718 q^{27}\) \(-1.52324 q^{28}\) \(-0.896200 q^{29}\) \(-4.95125 q^{30}\) \(+0.661756 q^{31}\) \(+7.08146 q^{32}\) \(+2.20460 q^{33}\) \(-9.39777 q^{34}\) \(+1.00000 q^{35}\) \(+6.02906 q^{36}\) \(-6.42100 q^{37}\) \(-3.17432 q^{38}\) \(+6.79101 q^{39}\) \(-0.894900 q^{40}\) \(+6.40349 q^{41}\) \(-4.95125 q^{42}\) \(+4.66509 q^{43}\) \(-1.27307 q^{44}\) \(-3.95806 q^{45}\) \(-14.1161 q^{46}\) \(+9.46667 q^{47}\) \(+12.4669 q^{48}\) \(+1.00000 q^{49}\) \(-1.87703 q^{50}\) \(-13.2068 q^{51}\) \(-3.92155 q^{52}\) \(+7.01772 q^{53}\) \(+4.74358 q^{54}\) \(+0.835767 q^{55}\) \(-0.894900 q^{56}\) \(-4.46092 q^{57}\) \(+1.68219 q^{58}\) \(-5.07702 q^{59}\) \(+4.01801 q^{60}\) \(+4.74747 q^{61}\) \(-1.24213 q^{62}\) \(-3.95806 q^{63}\) \(-3.83965 q^{64}\) \(+2.57449 q^{65}\) \(-4.13809 q^{66}\) \(+10.3551 q^{67}\) \(+7.62643 q^{68}\) \(-19.8376 q^{69}\) \(-1.87703 q^{70}\) \(-5.55683 q^{71}\) \(+3.54206 q^{72}\) \(+15.0713 q^{73}\) \(+12.0524 q^{74}\) \(-2.63781 q^{75}\) \(+2.57601 q^{76}\) \(+0.835767 q^{77}\) \(-12.7469 q^{78}\) \(+3.09837 q^{79}\) \(+4.72622 q^{80}\) \(-5.20795 q^{81}\) \(-12.0195 q^{82}\) \(+3.78224 q^{83}\) \(+4.01801 q^{84}\) \(-5.00673 q^{85}\) \(-8.75650 q^{86}\) \(+2.36401 q^{87}\) \(-0.747928 q^{88}\) \(+4.77527 q^{89}\) \(+7.42939 q^{90}\) \(+2.57449 q^{91}\) \(+11.4554 q^{92}\) \(-1.74559 q^{93}\) \(-17.7692 q^{94}\) \(-1.69114 q^{95}\) \(-18.6796 q^{96}\) \(+4.44039 q^{97}\) \(-1.87703 q^{98}\) \(-3.30801 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.87703 −1.32726 −0.663630 0.748061i \(-0.730985\pi\)
−0.663630 + 0.748061i \(0.730985\pi\)
\(3\) −2.63781 −1.52294 −0.761471 0.648199i \(-0.775523\pi\)
−0.761471 + 0.648199i \(0.775523\pi\)
\(4\) 1.52324 0.761618
\(5\) −1.00000 −0.447214
\(6\) 4.95125 2.02134
\(7\) −1.00000 −0.377964
\(8\) 0.894900 0.316395
\(9\) 3.95806 1.31935
\(10\) 1.87703 0.593569
\(11\) −0.835767 −0.251993 −0.125997 0.992031i \(-0.540213\pi\)
−0.125997 + 0.992031i \(0.540213\pi\)
\(12\) −4.01801 −1.15990
\(13\) −2.57449 −0.714034 −0.357017 0.934098i \(-0.616206\pi\)
−0.357017 + 0.934098i \(0.616206\pi\)
\(14\) 1.87703 0.501657
\(15\) 2.63781 0.681080
\(16\) −4.72622 −1.18156
\(17\) 5.00673 1.21431 0.607155 0.794583i \(-0.292311\pi\)
0.607155 + 0.794583i \(0.292311\pi\)
\(18\) −7.42939 −1.75112
\(19\) 1.69114 0.387975 0.193987 0.981004i \(-0.437858\pi\)
0.193987 + 0.981004i \(0.437858\pi\)
\(20\) −1.52324 −0.340606
\(21\) 2.63781 0.575618
\(22\) 1.56876 0.334460
\(23\) 7.52045 1.56812 0.784061 0.620683i \(-0.213145\pi\)
0.784061 + 0.620683i \(0.213145\pi\)
\(24\) −2.36058 −0.481851
\(25\) 1.00000 0.200000
\(26\) 4.83238 0.947708
\(27\) −2.52718 −0.486355
\(28\) −1.52324 −0.287865
\(29\) −0.896200 −0.166420 −0.0832101 0.996532i \(-0.526517\pi\)
−0.0832101 + 0.996532i \(0.526517\pi\)
\(30\) −4.95125 −0.903970
\(31\) 0.661756 0.118855 0.0594274 0.998233i \(-0.481073\pi\)
0.0594274 + 0.998233i \(0.481073\pi\)
\(32\) 7.08146 1.25184
\(33\) 2.20460 0.383771
\(34\) −9.39777 −1.61170
\(35\) 1.00000 0.169031
\(36\) 6.02906 1.00484
\(37\) −6.42100 −1.05561 −0.527803 0.849367i \(-0.676984\pi\)
−0.527803 + 0.849367i \(0.676984\pi\)
\(38\) −3.17432 −0.514943
\(39\) 6.79101 1.08743
\(40\) −0.894900 −0.141496
\(41\) 6.40349 1.00006 0.500029 0.866009i \(-0.333323\pi\)
0.500029 + 0.866009i \(0.333323\pi\)
\(42\) −4.95125 −0.763994
\(43\) 4.66509 0.711419 0.355710 0.934597i \(-0.384239\pi\)
0.355710 + 0.934597i \(0.384239\pi\)
\(44\) −1.27307 −0.191923
\(45\) −3.95806 −0.590032
\(46\) −14.1161 −2.08131
\(47\) 9.46667 1.38086 0.690428 0.723401i \(-0.257422\pi\)
0.690428 + 0.723401i \(0.257422\pi\)
\(48\) 12.4669 1.79944
\(49\) 1.00000 0.142857
\(50\) −1.87703 −0.265452
\(51\) −13.2068 −1.84932
\(52\) −3.92155 −0.543821
\(53\) 7.01772 0.963958 0.481979 0.876183i \(-0.339918\pi\)
0.481979 + 0.876183i \(0.339918\pi\)
\(54\) 4.74358 0.645520
\(55\) 0.835767 0.112695
\(56\) −0.894900 −0.119586
\(57\) −4.46092 −0.590863
\(58\) 1.68219 0.220883
\(59\) −5.07702 −0.660972 −0.330486 0.943811i \(-0.607213\pi\)
−0.330486 + 0.943811i \(0.607213\pi\)
\(60\) 4.01801 0.518723
\(61\) 4.74747 0.607851 0.303925 0.952696i \(-0.401703\pi\)
0.303925 + 0.952696i \(0.401703\pi\)
\(62\) −1.24213 −0.157751
\(63\) −3.95806 −0.498668
\(64\) −3.83965 −0.479956
\(65\) 2.57449 0.319326
\(66\) −4.13809 −0.509364
\(67\) 10.3551 1.26508 0.632539 0.774528i \(-0.282013\pi\)
0.632539 + 0.774528i \(0.282013\pi\)
\(68\) 7.62643 0.924840
\(69\) −19.8376 −2.38816
\(70\) −1.87703 −0.224348
\(71\) −5.55683 −0.659474 −0.329737 0.944073i \(-0.606960\pi\)
−0.329737 + 0.944073i \(0.606960\pi\)
\(72\) 3.54206 0.417436
\(73\) 15.0713 1.76396 0.881980 0.471287i \(-0.156210\pi\)
0.881980 + 0.471287i \(0.156210\pi\)
\(74\) 12.0524 1.40106
\(75\) −2.63781 −0.304588
\(76\) 2.57601 0.295488
\(77\) 0.835767 0.0952445
\(78\) −12.7469 −1.44330
\(79\) 3.09837 0.348594 0.174297 0.984693i \(-0.444235\pi\)
0.174297 + 0.984693i \(0.444235\pi\)
\(80\) 4.72622 0.528408
\(81\) −5.20795 −0.578661
\(82\) −12.0195 −1.32734
\(83\) 3.78224 0.415155 0.207577 0.978219i \(-0.433442\pi\)
0.207577 + 0.978219i \(0.433442\pi\)
\(84\) 4.01801 0.438401
\(85\) −5.00673 −0.543056
\(86\) −8.75650 −0.944238
\(87\) 2.36401 0.253448
\(88\) −0.747928 −0.0797294
\(89\) 4.77527 0.506177 0.253089 0.967443i \(-0.418554\pi\)
0.253089 + 0.967443i \(0.418554\pi\)
\(90\) 7.42939 0.783126
\(91\) 2.57449 0.269879
\(92\) 11.4554 1.19431
\(93\) −1.74559 −0.181009
\(94\) −17.7692 −1.83275
\(95\) −1.69114 −0.173508
\(96\) −18.6796 −1.90647
\(97\) 4.44039 0.450853 0.225427 0.974260i \(-0.427622\pi\)
0.225427 + 0.974260i \(0.427622\pi\)
\(98\) −1.87703 −0.189609
\(99\) −3.30801 −0.332468
\(100\) 1.52324 0.152324
\(101\) 11.6798 1.16218 0.581091 0.813839i \(-0.302626\pi\)
0.581091 + 0.813839i \(0.302626\pi\)
\(102\) 24.7896 2.45453
\(103\) −15.0595 −1.48386 −0.741929 0.670479i \(-0.766089\pi\)
−0.741929 + 0.670479i \(0.766089\pi\)
\(104\) −2.30391 −0.225917
\(105\) −2.63781 −0.257424
\(106\) −13.1725 −1.27942
\(107\) 0.413285 0.0399538 0.0199769 0.999800i \(-0.493641\pi\)
0.0199769 + 0.999800i \(0.493641\pi\)
\(108\) −3.84949 −0.370417
\(109\) −4.50672 −0.431666 −0.215833 0.976430i \(-0.569247\pi\)
−0.215833 + 0.976430i \(0.569247\pi\)
\(110\) −1.56876 −0.149575
\(111\) 16.9374 1.60763
\(112\) 4.72622 0.446586
\(113\) 19.1810 1.80439 0.902197 0.431324i \(-0.141953\pi\)
0.902197 + 0.431324i \(0.141953\pi\)
\(114\) 8.37327 0.784229
\(115\) −7.52045 −0.701286
\(116\) −1.36512 −0.126749
\(117\) −10.1900 −0.942062
\(118\) 9.52971 0.877281
\(119\) −5.00673 −0.458966
\(120\) 2.36058 0.215490
\(121\) −10.3015 −0.936499
\(122\) −8.91113 −0.806776
\(123\) −16.8912 −1.52303
\(124\) 1.00801 0.0905220
\(125\) −1.00000 −0.0894427
\(126\) 7.42939 0.661862
\(127\) 17.4795 1.55105 0.775526 0.631316i \(-0.217485\pi\)
0.775526 + 0.631316i \(0.217485\pi\)
\(128\) −6.95578 −0.614810
\(129\) −12.3056 −1.08345
\(130\) −4.83238 −0.423828
\(131\) −17.1515 −1.49853 −0.749267 0.662268i \(-0.769594\pi\)
−0.749267 + 0.662268i \(0.769594\pi\)
\(132\) 3.35812 0.292287
\(133\) −1.69114 −0.146641
\(134\) −19.4369 −1.67909
\(135\) 2.52718 0.217505
\(136\) 4.48052 0.384201
\(137\) 14.2336 1.21606 0.608029 0.793915i \(-0.291960\pi\)
0.608029 + 0.793915i \(0.291960\pi\)
\(138\) 37.2356 3.16971
\(139\) 17.6851 1.50003 0.750014 0.661422i \(-0.230047\pi\)
0.750014 + 0.661422i \(0.230047\pi\)
\(140\) 1.52324 0.128737
\(141\) −24.9713 −2.10296
\(142\) 10.4303 0.875293
\(143\) 2.15167 0.179932
\(144\) −18.7067 −1.55889
\(145\) 0.896200 0.0744254
\(146\) −28.2892 −2.34123
\(147\) −2.63781 −0.217563
\(148\) −9.78070 −0.803969
\(149\) 8.37621 0.686206 0.343103 0.939298i \(-0.388522\pi\)
0.343103 + 0.939298i \(0.388522\pi\)
\(150\) 4.95125 0.404268
\(151\) 23.9202 1.94660 0.973298 0.229546i \(-0.0737240\pi\)
0.973298 + 0.229546i \(0.0737240\pi\)
\(152\) 1.51340 0.122753
\(153\) 19.8169 1.60210
\(154\) −1.56876 −0.126414
\(155\) −0.661756 −0.0531535
\(156\) 10.3443 0.828208
\(157\) −20.8928 −1.66743 −0.833715 0.552194i \(-0.813791\pi\)
−0.833715 + 0.552194i \(0.813791\pi\)
\(158\) −5.81573 −0.462675
\(159\) −18.5114 −1.46805
\(160\) −7.08146 −0.559838
\(161\) −7.52045 −0.592695
\(162\) 9.77548 0.768034
\(163\) −15.8991 −1.24531 −0.622655 0.782496i \(-0.713946\pi\)
−0.622655 + 0.782496i \(0.713946\pi\)
\(164\) 9.75403 0.761662
\(165\) −2.20460 −0.171628
\(166\) −7.09937 −0.551018
\(167\) 9.50740 0.735704 0.367852 0.929884i \(-0.380093\pi\)
0.367852 + 0.929884i \(0.380093\pi\)
\(168\) 2.36058 0.182123
\(169\) −6.37202 −0.490156
\(170\) 9.39777 0.720776
\(171\) 6.69364 0.511875
\(172\) 7.10603 0.541830
\(173\) 3.57021 0.271438 0.135719 0.990747i \(-0.456666\pi\)
0.135719 + 0.990747i \(0.456666\pi\)
\(174\) −4.43731 −0.336392
\(175\) −1.00000 −0.0755929
\(176\) 3.95002 0.297744
\(177\) 13.3922 1.00662
\(178\) −8.96332 −0.671829
\(179\) −25.4025 −1.89867 −0.949336 0.314262i \(-0.898243\pi\)
−0.949336 + 0.314262i \(0.898243\pi\)
\(180\) −6.02906 −0.449379
\(181\) 4.20561 0.312601 0.156300 0.987710i \(-0.450043\pi\)
0.156300 + 0.987710i \(0.450043\pi\)
\(182\) −4.83238 −0.358200
\(183\) −12.5229 −0.925721
\(184\) 6.73005 0.496146
\(185\) 6.42100 0.472081
\(186\) 3.27652 0.240246
\(187\) −4.18446 −0.305998
\(188\) 14.4200 1.05168
\(189\) 2.52718 0.183825
\(190\) 3.17432 0.230290
\(191\) −17.8923 −1.29464 −0.647322 0.762217i \(-0.724111\pi\)
−0.647322 + 0.762217i \(0.724111\pi\)
\(192\) 10.1283 0.730945
\(193\) −25.4087 −1.82896 −0.914481 0.404629i \(-0.867401\pi\)
−0.914481 + 0.404629i \(0.867401\pi\)
\(194\) −8.33474 −0.598399
\(195\) −6.79101 −0.486314
\(196\) 1.52324 0.108803
\(197\) 8.66587 0.617417 0.308709 0.951157i \(-0.400103\pi\)
0.308709 + 0.951157i \(0.400103\pi\)
\(198\) 6.20924 0.441271
\(199\) 13.2680 0.940541 0.470271 0.882522i \(-0.344156\pi\)
0.470271 + 0.882522i \(0.344156\pi\)
\(200\) 0.894900 0.0632790
\(201\) −27.3149 −1.92664
\(202\) −21.9233 −1.54252
\(203\) 0.896200 0.0629009
\(204\) −20.1171 −1.40848
\(205\) −6.40349 −0.447239
\(206\) 28.2671 1.96946
\(207\) 29.7664 2.06891
\(208\) 12.1676 0.843671
\(209\) −1.41340 −0.0977670
\(210\) 4.95125 0.341669
\(211\) 20.9869 1.44480 0.722398 0.691478i \(-0.243040\pi\)
0.722398 + 0.691478i \(0.243040\pi\)
\(212\) 10.6896 0.734168
\(213\) 14.6579 1.00434
\(214\) −0.775748 −0.0530291
\(215\) −4.66509 −0.318156
\(216\) −2.26157 −0.153880
\(217\) −0.661756 −0.0449229
\(218\) 8.45924 0.572932
\(219\) −39.7552 −2.68641
\(220\) 1.27307 0.0858304
\(221\) −12.8897 −0.867058
\(222\) −31.7920 −2.13374
\(223\) −23.2213 −1.55501 −0.777505 0.628876i \(-0.783515\pi\)
−0.777505 + 0.628876i \(0.783515\pi\)
\(224\) −7.08146 −0.473150
\(225\) 3.95806 0.263871
\(226\) −36.0032 −2.39490
\(227\) 5.61757 0.372852 0.186426 0.982469i \(-0.440310\pi\)
0.186426 + 0.982469i \(0.440310\pi\)
\(228\) −6.79503 −0.450012
\(229\) 1.00000 0.0660819
\(230\) 14.1161 0.930788
\(231\) −2.20460 −0.145052
\(232\) −0.802010 −0.0526545
\(233\) −3.64771 −0.238970 −0.119485 0.992836i \(-0.538124\pi\)
−0.119485 + 0.992836i \(0.538124\pi\)
\(234\) 19.1268 1.25036
\(235\) −9.46667 −0.617538
\(236\) −7.73350 −0.503408
\(237\) −8.17292 −0.530888
\(238\) 9.39777 0.609167
\(239\) −11.7715 −0.761435 −0.380717 0.924691i \(-0.624323\pi\)
−0.380717 + 0.924691i \(0.624323\pi\)
\(240\) −12.4669 −0.804735
\(241\) 4.85143 0.312508 0.156254 0.987717i \(-0.450058\pi\)
0.156254 + 0.987717i \(0.450058\pi\)
\(242\) 19.3362 1.24298
\(243\) 21.3191 1.36762
\(244\) 7.23151 0.462950
\(245\) −1.00000 −0.0638877
\(246\) 31.7053 2.02146
\(247\) −4.35382 −0.277027
\(248\) 0.592205 0.0376051
\(249\) −9.97684 −0.632256
\(250\) 1.87703 0.118714
\(251\) −23.7678 −1.50021 −0.750107 0.661317i \(-0.769998\pi\)
−0.750107 + 0.661317i \(0.769998\pi\)
\(252\) −6.02906 −0.379795
\(253\) −6.28535 −0.395156
\(254\) −32.8095 −2.05865
\(255\) 13.2068 0.827043
\(256\) 20.7355 1.29597
\(257\) 1.50627 0.0939583 0.0469791 0.998896i \(-0.485041\pi\)
0.0469791 + 0.998896i \(0.485041\pi\)
\(258\) 23.0980 1.43802
\(259\) 6.42100 0.398982
\(260\) 3.92155 0.243204
\(261\) −3.54721 −0.219567
\(262\) 32.1939 1.98894
\(263\) −7.88263 −0.486064 −0.243032 0.970018i \(-0.578142\pi\)
−0.243032 + 0.970018i \(0.578142\pi\)
\(264\) 1.97289 0.121423
\(265\) −7.01772 −0.431095
\(266\) 3.17432 0.194630
\(267\) −12.5963 −0.770879
\(268\) 15.7733 0.963507
\(269\) −1.23044 −0.0750215 −0.0375108 0.999296i \(-0.511943\pi\)
−0.0375108 + 0.999296i \(0.511943\pi\)
\(270\) −4.74358 −0.288685
\(271\) −21.3318 −1.29581 −0.647906 0.761720i \(-0.724355\pi\)
−0.647906 + 0.761720i \(0.724355\pi\)
\(272\) −23.6629 −1.43478
\(273\) −6.79101 −0.411011
\(274\) −26.7169 −1.61402
\(275\) −0.835767 −0.0503986
\(276\) −30.2173 −1.81887
\(277\) −26.5974 −1.59808 −0.799042 0.601275i \(-0.794660\pi\)
−0.799042 + 0.601275i \(0.794660\pi\)
\(278\) −33.1954 −1.99093
\(279\) 2.61927 0.156811
\(280\) 0.894900 0.0534805
\(281\) −1.56037 −0.0930838 −0.0465419 0.998916i \(-0.514820\pi\)
−0.0465419 + 0.998916i \(0.514820\pi\)
\(282\) 46.8719 2.79118
\(283\) 13.7741 0.818784 0.409392 0.912359i \(-0.365741\pi\)
0.409392 + 0.912359i \(0.365741\pi\)
\(284\) −8.46436 −0.502267
\(285\) 4.46092 0.264242
\(286\) −4.03875 −0.238816
\(287\) −6.40349 −0.377986
\(288\) 28.0288 1.65161
\(289\) 8.06732 0.474548
\(290\) −1.68219 −0.0987818
\(291\) −11.7129 −0.686623
\(292\) 22.9571 1.34346
\(293\) 0.651516 0.0380619 0.0190310 0.999819i \(-0.493942\pi\)
0.0190310 + 0.999819i \(0.493942\pi\)
\(294\) 4.95125 0.288763
\(295\) 5.07702 0.295596
\(296\) −5.74615 −0.333988
\(297\) 2.11213 0.122558
\(298\) −15.7224 −0.910774
\(299\) −19.3613 −1.11969
\(300\) −4.01801 −0.231980
\(301\) −4.66509 −0.268891
\(302\) −44.8988 −2.58364
\(303\) −30.8091 −1.76994
\(304\) −7.99272 −0.458414
\(305\) −4.74747 −0.271839
\(306\) −37.1969 −2.12641
\(307\) 12.8516 0.733480 0.366740 0.930324i \(-0.380474\pi\)
0.366740 + 0.930324i \(0.380474\pi\)
\(308\) 1.27307 0.0725399
\(309\) 39.7242 2.25983
\(310\) 1.24213 0.0705485
\(311\) −4.36812 −0.247694 −0.123847 0.992301i \(-0.539523\pi\)
−0.123847 + 0.992301i \(0.539523\pi\)
\(312\) 6.07728 0.344058
\(313\) 29.3585 1.65944 0.829721 0.558178i \(-0.188499\pi\)
0.829721 + 0.558178i \(0.188499\pi\)
\(314\) 39.2165 2.21311
\(315\) 3.95806 0.223011
\(316\) 4.71955 0.265495
\(317\) −9.39855 −0.527875 −0.263938 0.964540i \(-0.585021\pi\)
−0.263938 + 0.964540i \(0.585021\pi\)
\(318\) 34.7465 1.94849
\(319\) 0.749015 0.0419368
\(320\) 3.83965 0.214643
\(321\) −1.09017 −0.0608473
\(322\) 14.1161 0.786660
\(323\) 8.46709 0.471121
\(324\) −7.93294 −0.440719
\(325\) −2.57449 −0.142807
\(326\) 29.8430 1.65285
\(327\) 11.8879 0.657402
\(328\) 5.73048 0.316413
\(329\) −9.46667 −0.521915
\(330\) 4.13809 0.227794
\(331\) −4.70679 −0.258709 −0.129354 0.991598i \(-0.541290\pi\)
−0.129354 + 0.991598i \(0.541290\pi\)
\(332\) 5.76124 0.316189
\(333\) −25.4147 −1.39272
\(334\) −17.8457 −0.976471
\(335\) −10.3551 −0.565760
\(336\) −12.4669 −0.680125
\(337\) −10.8898 −0.593207 −0.296604 0.955001i \(-0.595854\pi\)
−0.296604 + 0.955001i \(0.595854\pi\)
\(338\) 11.9605 0.650564
\(339\) −50.5958 −2.74799
\(340\) −7.62643 −0.413601
\(341\) −0.553074 −0.0299506
\(342\) −12.5642 −0.679391
\(343\) −1.00000 −0.0539949
\(344\) 4.17479 0.225089
\(345\) 19.8376 1.06802
\(346\) −6.70139 −0.360269
\(347\) −8.97483 −0.481794 −0.240897 0.970551i \(-0.577442\pi\)
−0.240897 + 0.970551i \(0.577442\pi\)
\(348\) 3.60094 0.193031
\(349\) 20.8846 1.11793 0.558963 0.829192i \(-0.311199\pi\)
0.558963 + 0.829192i \(0.311199\pi\)
\(350\) 1.87703 0.100331
\(351\) 6.50618 0.347274
\(352\) −5.91845 −0.315454
\(353\) −21.6208 −1.15076 −0.575380 0.817886i \(-0.695146\pi\)
−0.575380 + 0.817886i \(0.695146\pi\)
\(354\) −25.1376 −1.33605
\(355\) 5.55683 0.294926
\(356\) 7.27386 0.385514
\(357\) 13.2068 0.698979
\(358\) 47.6812 2.52003
\(359\) −15.0577 −0.794714 −0.397357 0.917664i \(-0.630073\pi\)
−0.397357 + 0.917664i \(0.630073\pi\)
\(360\) −3.54206 −0.186683
\(361\) −16.1400 −0.849476
\(362\) −7.89405 −0.414902
\(363\) 27.1734 1.42623
\(364\) 3.92155 0.205545
\(365\) −15.0713 −0.788867
\(366\) 23.5059 1.22867
\(367\) −14.0132 −0.731482 −0.365741 0.930717i \(-0.619184\pi\)
−0.365741 + 0.930717i \(0.619184\pi\)
\(368\) −35.5433 −1.85283
\(369\) 25.3454 1.31943
\(370\) −12.0524 −0.626575
\(371\) −7.01772 −0.364342
\(372\) −2.65894 −0.137860
\(373\) 19.3993 1.00446 0.502229 0.864735i \(-0.332514\pi\)
0.502229 + 0.864735i \(0.332514\pi\)
\(374\) 7.85435 0.406139
\(375\) 2.63781 0.136216
\(376\) 8.47172 0.436896
\(377\) 2.30726 0.118830
\(378\) −4.74358 −0.243984
\(379\) −0.956797 −0.0491474 −0.0245737 0.999698i \(-0.507823\pi\)
−0.0245737 + 0.999698i \(0.507823\pi\)
\(380\) −2.57601 −0.132146
\(381\) −46.1076 −2.36216
\(382\) 33.5844 1.71833
\(383\) −6.00556 −0.306870 −0.153435 0.988159i \(-0.549034\pi\)
−0.153435 + 0.988159i \(0.549034\pi\)
\(384\) 18.3481 0.936320
\(385\) −0.835767 −0.0425946
\(386\) 47.6929 2.42751
\(387\) 18.4647 0.938613
\(388\) 6.76376 0.343378
\(389\) 0.329573 0.0167100 0.00835501 0.999965i \(-0.497340\pi\)
0.00835501 + 0.999965i \(0.497340\pi\)
\(390\) 12.7469 0.645466
\(391\) 37.6529 1.90419
\(392\) 0.894900 0.0451993
\(393\) 45.2425 2.28218
\(394\) −16.2661 −0.819473
\(395\) −3.09837 −0.155896
\(396\) −5.03889 −0.253214
\(397\) −25.1035 −1.25991 −0.629954 0.776632i \(-0.716926\pi\)
−0.629954 + 0.776632i \(0.716926\pi\)
\(398\) −24.9043 −1.24834
\(399\) 4.46092 0.223325
\(400\) −4.72622 −0.236311
\(401\) −28.0654 −1.40152 −0.700759 0.713398i \(-0.747155\pi\)
−0.700759 + 0.713398i \(0.747155\pi\)
\(402\) 51.2708 2.55715
\(403\) −1.70368 −0.0848664
\(404\) 17.7911 0.885138
\(405\) 5.20795 0.258785
\(406\) −1.68219 −0.0834859
\(407\) 5.36646 0.266006
\(408\) −11.8188 −0.585116
\(409\) 8.41613 0.416151 0.208075 0.978113i \(-0.433280\pi\)
0.208075 + 0.978113i \(0.433280\pi\)
\(410\) 12.0195 0.593603
\(411\) −37.5456 −1.85199
\(412\) −22.9392 −1.13013
\(413\) 5.07702 0.249824
\(414\) −55.8724 −2.74598
\(415\) −3.78224 −0.185663
\(416\) −18.2311 −0.893854
\(417\) −46.6499 −2.28446
\(418\) 2.65299 0.129762
\(419\) 18.8440 0.920590 0.460295 0.887766i \(-0.347744\pi\)
0.460295 + 0.887766i \(0.347744\pi\)
\(420\) −4.01801 −0.196059
\(421\) 2.72399 0.132759 0.0663796 0.997794i \(-0.478855\pi\)
0.0663796 + 0.997794i \(0.478855\pi\)
\(422\) −39.3929 −1.91762
\(423\) 37.4696 1.82184
\(424\) 6.28016 0.304991
\(425\) 5.00673 0.242862
\(426\) −27.5132 −1.33302
\(427\) −4.74747 −0.229746
\(428\) 0.629531 0.0304295
\(429\) −5.67570 −0.274026
\(430\) 8.75650 0.422276
\(431\) −0.502546 −0.0242068 −0.0121034 0.999927i \(-0.503853\pi\)
−0.0121034 + 0.999927i \(0.503853\pi\)
\(432\) 11.9440 0.574656
\(433\) 38.5521 1.85269 0.926347 0.376671i \(-0.122931\pi\)
0.926347 + 0.376671i \(0.122931\pi\)
\(434\) 1.24213 0.0596244
\(435\) −2.36401 −0.113346
\(436\) −6.86480 −0.328764
\(437\) 12.7182 0.608392
\(438\) 74.6217 3.56556
\(439\) 35.5405 1.69625 0.848127 0.529793i \(-0.177730\pi\)
0.848127 + 0.529793i \(0.177730\pi\)
\(440\) 0.747928 0.0356561
\(441\) 3.95806 0.188479
\(442\) 24.1944 1.15081
\(443\) −9.88780 −0.469783 −0.234892 0.972022i \(-0.575474\pi\)
−0.234892 + 0.972022i \(0.575474\pi\)
\(444\) 25.7997 1.22440
\(445\) −4.77527 −0.226369
\(446\) 43.5870 2.06390
\(447\) −22.0949 −1.04505
\(448\) 3.83965 0.181406
\(449\) 40.5318 1.91281 0.956406 0.292040i \(-0.0943341\pi\)
0.956406 + 0.292040i \(0.0943341\pi\)
\(450\) −7.42939 −0.350225
\(451\) −5.35183 −0.252008
\(452\) 29.2172 1.37426
\(453\) −63.0969 −2.96455
\(454\) −10.5443 −0.494871
\(455\) −2.57449 −0.120694
\(456\) −3.99207 −0.186946
\(457\) 10.7056 0.500786 0.250393 0.968144i \(-0.419440\pi\)
0.250393 + 0.968144i \(0.419440\pi\)
\(458\) −1.87703 −0.0877078
\(459\) −12.6529 −0.590586
\(460\) −11.4554 −0.534112
\(461\) 11.4693 0.534180 0.267090 0.963672i \(-0.413938\pi\)
0.267090 + 0.963672i \(0.413938\pi\)
\(462\) 4.13809 0.192521
\(463\) 23.9804 1.11447 0.557233 0.830356i \(-0.311863\pi\)
0.557233 + 0.830356i \(0.311863\pi\)
\(464\) 4.23564 0.196635
\(465\) 1.74559 0.0809497
\(466\) 6.84686 0.317175
\(467\) −35.3534 −1.63596 −0.817981 0.575246i \(-0.804906\pi\)
−0.817981 + 0.575246i \(0.804906\pi\)
\(468\) −15.5217 −0.717492
\(469\) −10.3551 −0.478155
\(470\) 17.7692 0.819633
\(471\) 55.1114 2.53940
\(472\) −4.54343 −0.209128
\(473\) −3.89893 −0.179273
\(474\) 15.3408 0.704627
\(475\) 1.69114 0.0775949
\(476\) −7.62643 −0.349557
\(477\) 27.7766 1.27180
\(478\) 22.0954 1.01062
\(479\) 1.30632 0.0596872 0.0298436 0.999555i \(-0.490499\pi\)
0.0298436 + 0.999555i \(0.490499\pi\)
\(480\) 18.6796 0.852601
\(481\) 16.5308 0.753739
\(482\) −9.10627 −0.414779
\(483\) 19.8376 0.902640
\(484\) −15.6916 −0.713255
\(485\) −4.44039 −0.201628
\(486\) −40.0166 −1.81519
\(487\) 23.2701 1.05447 0.527234 0.849720i \(-0.323229\pi\)
0.527234 + 0.849720i \(0.323229\pi\)
\(488\) 4.24851 0.192321
\(489\) 41.9387 1.89653
\(490\) 1.87703 0.0847955
\(491\) −41.2192 −1.86020 −0.930099 0.367310i \(-0.880279\pi\)
−0.930099 + 0.367310i \(0.880279\pi\)
\(492\) −25.7293 −1.15997
\(493\) −4.48703 −0.202086
\(494\) 8.17225 0.367687
\(495\) 3.30801 0.148684
\(496\) −3.12761 −0.140434
\(497\) 5.55683 0.249258
\(498\) 18.7268 0.839168
\(499\) −21.3853 −0.957336 −0.478668 0.877996i \(-0.658880\pi\)
−0.478668 + 0.877996i \(0.658880\pi\)
\(500\) −1.52324 −0.0681212
\(501\) −25.0787 −1.12044
\(502\) 44.6129 1.99117
\(503\) −3.84614 −0.171491 −0.0857455 0.996317i \(-0.527327\pi\)
−0.0857455 + 0.996317i \(0.527327\pi\)
\(504\) −3.54206 −0.157776
\(505\) −11.6798 −0.519743
\(506\) 11.7978 0.524475
\(507\) 16.8082 0.746479
\(508\) 26.6254 1.18131
\(509\) −1.96040 −0.0868931 −0.0434466 0.999056i \(-0.513834\pi\)
−0.0434466 + 0.999056i \(0.513834\pi\)
\(510\) −24.7896 −1.09770
\(511\) −15.0713 −0.666714
\(512\) −25.0096 −1.10528
\(513\) −4.27382 −0.188694
\(514\) −2.82730 −0.124707
\(515\) 15.0595 0.663601
\(516\) −18.7444 −0.825175
\(517\) −7.91193 −0.347966
\(518\) −12.0524 −0.529552
\(519\) −9.41755 −0.413385
\(520\) 2.30391 0.101033
\(521\) 44.9547 1.96950 0.984751 0.173972i \(-0.0556604\pi\)
0.984751 + 0.173972i \(0.0556604\pi\)
\(522\) 6.65822 0.291422
\(523\) 40.1380 1.75511 0.877557 0.479473i \(-0.159172\pi\)
0.877557 + 0.479473i \(0.159172\pi\)
\(524\) −26.1258 −1.14131
\(525\) 2.63781 0.115124
\(526\) 14.7959 0.645133
\(527\) 3.31323 0.144327
\(528\) −10.4194 −0.453447
\(529\) 33.5572 1.45901
\(530\) 13.1725 0.572175
\(531\) −20.0951 −0.872055
\(532\) −2.57601 −0.111684
\(533\) −16.4857 −0.714075
\(534\) 23.6436 1.02316
\(535\) −0.413285 −0.0178679
\(536\) 9.26679 0.400264
\(537\) 67.0071 2.89157
\(538\) 2.30958 0.0995730
\(539\) −0.835767 −0.0359990
\(540\) 3.84949 0.165656
\(541\) −44.6724 −1.92062 −0.960309 0.278938i \(-0.910018\pi\)
−0.960309 + 0.278938i \(0.910018\pi\)
\(542\) 40.0403 1.71988
\(543\) −11.0936 −0.476073
\(544\) 35.4549 1.52012
\(545\) 4.50672 0.193047
\(546\) 12.7469 0.545518
\(547\) 24.6582 1.05431 0.527153 0.849770i \(-0.323259\pi\)
0.527153 + 0.849770i \(0.323259\pi\)
\(548\) 21.6811 0.926171
\(549\) 18.7907 0.801969
\(550\) 1.56876 0.0668921
\(551\) −1.51560 −0.0645668
\(552\) −17.7526 −0.755602
\(553\) −3.09837 −0.131756
\(554\) 49.9241 2.12107
\(555\) −16.9374 −0.718953
\(556\) 26.9385 1.14245
\(557\) 38.6938 1.63951 0.819755 0.572714i \(-0.194110\pi\)
0.819755 + 0.572714i \(0.194110\pi\)
\(558\) −4.91644 −0.208129
\(559\) −12.0102 −0.507977
\(560\) −4.72622 −0.199719
\(561\) 11.0378 0.466017
\(562\) 2.92886 0.123546
\(563\) 26.6125 1.12158 0.560792 0.827957i \(-0.310497\pi\)
0.560792 + 0.827957i \(0.310497\pi\)
\(564\) −38.0372 −1.60165
\(565\) −19.1810 −0.806950
\(566\) −25.8543 −1.08674
\(567\) 5.20795 0.218713
\(568\) −4.97280 −0.208654
\(569\) 20.5636 0.862072 0.431036 0.902335i \(-0.358148\pi\)
0.431036 + 0.902335i \(0.358148\pi\)
\(570\) −8.37327 −0.350718
\(571\) 7.16049 0.299657 0.149829 0.988712i \(-0.452128\pi\)
0.149829 + 0.988712i \(0.452128\pi\)
\(572\) 3.27750 0.137039
\(573\) 47.1966 1.97167
\(574\) 12.0195 0.501686
\(575\) 7.52045 0.313625
\(576\) −15.1976 −0.633231
\(577\) 43.7448 1.82112 0.910560 0.413377i \(-0.135651\pi\)
0.910560 + 0.413377i \(0.135651\pi\)
\(578\) −15.1426 −0.629849
\(579\) 67.0235 2.78540
\(580\) 1.36512 0.0566837
\(581\) −3.78224 −0.156914
\(582\) 21.9855 0.911327
\(583\) −5.86518 −0.242911
\(584\) 13.4873 0.558108
\(585\) 10.1900 0.421303
\(586\) −1.22291 −0.0505181
\(587\) −43.7484 −1.80569 −0.902846 0.429965i \(-0.858526\pi\)
−0.902846 + 0.429965i \(0.858526\pi\)
\(588\) −4.01801 −0.165700
\(589\) 1.11912 0.0461127
\(590\) −9.52971 −0.392332
\(591\) −22.8589 −0.940291
\(592\) 30.3471 1.24726
\(593\) 25.7238 1.05635 0.528175 0.849135i \(-0.322876\pi\)
0.528175 + 0.849135i \(0.322876\pi\)
\(594\) −3.96453 −0.162667
\(595\) 5.00673 0.205256
\(596\) 12.7589 0.522627
\(597\) −34.9984 −1.43239
\(598\) 36.3417 1.48612
\(599\) −0.342812 −0.0140069 −0.00700345 0.999975i \(-0.502229\pi\)
−0.00700345 + 0.999975i \(0.502229\pi\)
\(600\) −2.36058 −0.0963702
\(601\) 3.49654 0.142627 0.0713134 0.997454i \(-0.477281\pi\)
0.0713134 + 0.997454i \(0.477281\pi\)
\(602\) 8.75650 0.356888
\(603\) 40.9862 1.66909
\(604\) 36.4361 1.48256
\(605\) 10.3015 0.418815
\(606\) 57.8295 2.34916
\(607\) −2.89038 −0.117317 −0.0586586 0.998278i \(-0.518682\pi\)
−0.0586586 + 0.998278i \(0.518682\pi\)
\(608\) 11.9758 0.485681
\(609\) −2.36401 −0.0957945
\(610\) 8.91113 0.360801
\(611\) −24.3718 −0.985978
\(612\) 30.1858 1.22019
\(613\) 30.7954 1.24381 0.621907 0.783091i \(-0.286358\pi\)
0.621907 + 0.783091i \(0.286358\pi\)
\(614\) −24.1228 −0.973518
\(615\) 16.8912 0.681120
\(616\) 0.747928 0.0301349
\(617\) 42.6220 1.71590 0.857949 0.513734i \(-0.171738\pi\)
0.857949 + 0.513734i \(0.171738\pi\)
\(618\) −74.5634 −2.99938
\(619\) −37.2296 −1.49638 −0.748191 0.663483i \(-0.769078\pi\)
−0.748191 + 0.663483i \(0.769078\pi\)
\(620\) −1.00801 −0.0404827
\(621\) −19.0055 −0.762665
\(622\) 8.19909 0.328754
\(623\) −4.77527 −0.191317
\(624\) −32.0958 −1.28486
\(625\) 1.00000 0.0400000
\(626\) −55.1068 −2.20251
\(627\) 3.72829 0.148893
\(628\) −31.8247 −1.26995
\(629\) −32.1482 −1.28183
\(630\) −7.42939 −0.295994
\(631\) 17.9955 0.716390 0.358195 0.933647i \(-0.383392\pi\)
0.358195 + 0.933647i \(0.383392\pi\)
\(632\) 2.77273 0.110293
\(633\) −55.3594 −2.20034
\(634\) 17.6413 0.700627
\(635\) −17.4795 −0.693652
\(636\) −28.1973 −1.11810
\(637\) −2.57449 −0.102005
\(638\) −1.40592 −0.0556610
\(639\) −21.9942 −0.870079
\(640\) 6.95578 0.274952
\(641\) −10.7140 −0.423177 −0.211588 0.977359i \(-0.567864\pi\)
−0.211588 + 0.977359i \(0.567864\pi\)
\(642\) 2.04628 0.0807602
\(643\) −32.5029 −1.28179 −0.640894 0.767629i \(-0.721436\pi\)
−0.640894 + 0.767629i \(0.721436\pi\)
\(644\) −11.4554 −0.451407
\(645\) 12.3056 0.484534
\(646\) −15.8930 −0.625300
\(647\) 31.2258 1.22761 0.613806 0.789457i \(-0.289638\pi\)
0.613806 + 0.789457i \(0.289638\pi\)
\(648\) −4.66060 −0.183086
\(649\) 4.24321 0.166560
\(650\) 4.83238 0.189542
\(651\) 1.74559 0.0684150
\(652\) −24.2180 −0.948450
\(653\) −50.7514 −1.98606 −0.993028 0.117883i \(-0.962389\pi\)
−0.993028 + 0.117883i \(0.962389\pi\)
\(654\) −22.3139 −0.872543
\(655\) 17.1515 0.670165
\(656\) −30.2643 −1.18162
\(657\) 59.6530 2.32728
\(658\) 17.7692 0.692716
\(659\) −10.9571 −0.426827 −0.213413 0.976962i \(-0.568458\pi\)
−0.213413 + 0.976962i \(0.568458\pi\)
\(660\) −3.35812 −0.130715
\(661\) −9.25264 −0.359886 −0.179943 0.983677i \(-0.557591\pi\)
−0.179943 + 0.983677i \(0.557591\pi\)
\(662\) 8.83478 0.343374
\(663\) 34.0007 1.32048
\(664\) 3.38472 0.131353
\(665\) 1.69114 0.0655797
\(666\) 47.7041 1.84850
\(667\) −6.73983 −0.260967
\(668\) 14.4820 0.560326
\(669\) 61.2533 2.36819
\(670\) 19.4369 0.750911
\(671\) −3.96778 −0.153174
\(672\) 18.6796 0.720580
\(673\) 19.5396 0.753197 0.376599 0.926377i \(-0.377094\pi\)
0.376599 + 0.926377i \(0.377094\pi\)
\(674\) 20.4405 0.787340
\(675\) −2.52718 −0.0972711
\(676\) −9.70609 −0.373311
\(677\) 23.7477 0.912700 0.456350 0.889800i \(-0.349156\pi\)
0.456350 + 0.889800i \(0.349156\pi\)
\(678\) 94.9698 3.64729
\(679\) −4.44039 −0.170407
\(680\) −4.48052 −0.171820
\(681\) −14.8181 −0.567831
\(682\) 1.03813 0.0397522
\(683\) 4.43123 0.169556 0.0847782 0.996400i \(-0.472982\pi\)
0.0847782 + 0.996400i \(0.472982\pi\)
\(684\) 10.1960 0.389853
\(685\) −14.2336 −0.543838
\(686\) 1.87703 0.0716653
\(687\) −2.63781 −0.100639
\(688\) −22.0483 −0.840582
\(689\) −18.0670 −0.688299
\(690\) −37.2356 −1.41754
\(691\) 23.8436 0.907053 0.453526 0.891243i \(-0.350166\pi\)
0.453526 + 0.891243i \(0.350166\pi\)
\(692\) 5.43827 0.206732
\(693\) 3.30801 0.125661
\(694\) 16.8460 0.639466
\(695\) −17.6851 −0.670833
\(696\) 2.11555 0.0801898
\(697\) 32.0605 1.21438
\(698\) −39.2010 −1.48378
\(699\) 9.62198 0.363937
\(700\) −1.52324 −0.0575729
\(701\) −32.1321 −1.21361 −0.606806 0.794850i \(-0.707549\pi\)
−0.606806 + 0.794850i \(0.707549\pi\)
\(702\) −12.2123 −0.460923
\(703\) −10.8588 −0.409549
\(704\) 3.20905 0.120946
\(705\) 24.9713 0.940474
\(706\) 40.5829 1.52736
\(707\) −11.6798 −0.439263
\(708\) 20.3995 0.766661
\(709\) 18.0898 0.679378 0.339689 0.940538i \(-0.389678\pi\)
0.339689 + 0.940538i \(0.389678\pi\)
\(710\) −10.4303 −0.391443
\(711\) 12.2635 0.459918
\(712\) 4.27339 0.160152
\(713\) 4.97670 0.186379
\(714\) −24.7896 −0.927726
\(715\) −2.15167 −0.0804679
\(716\) −38.6940 −1.44606
\(717\) 31.0510 1.15962
\(718\) 28.2637 1.05479
\(719\) 6.27395 0.233979 0.116989 0.993133i \(-0.462676\pi\)
0.116989 + 0.993133i \(0.462676\pi\)
\(720\) 18.7067 0.697156
\(721\) 15.0595 0.560845
\(722\) 30.2953 1.12747
\(723\) −12.7972 −0.475932
\(724\) 6.40614 0.238082
\(725\) −0.896200 −0.0332840
\(726\) −51.0053 −1.89298
\(727\) −50.2441 −1.86345 −0.931725 0.363165i \(-0.881696\pi\)
−0.931725 + 0.363165i \(0.881696\pi\)
\(728\) 2.30391 0.0853885
\(729\) −40.6120 −1.50415
\(730\) 28.2892 1.04703
\(731\) 23.3568 0.863883
\(732\) −19.0754 −0.705046
\(733\) 43.4030 1.60313 0.801564 0.597909i \(-0.204002\pi\)
0.801564 + 0.597909i \(0.204002\pi\)
\(734\) 26.3031 0.970867
\(735\) 2.63781 0.0972972
\(736\) 53.2558 1.96303
\(737\) −8.65447 −0.318791
\(738\) −47.5740 −1.75122
\(739\) 39.2057 1.44221 0.721103 0.692828i \(-0.243635\pi\)
0.721103 + 0.692828i \(0.243635\pi\)
\(740\) 9.78070 0.359546
\(741\) 11.4846 0.421896
\(742\) 13.1725 0.483576
\(743\) −44.6657 −1.63863 −0.819313 0.573347i \(-0.805645\pi\)
−0.819313 + 0.573347i \(0.805645\pi\)
\(744\) −1.56213 −0.0572703
\(745\) −8.37621 −0.306881
\(746\) −36.4130 −1.33318
\(747\) 14.9703 0.547735
\(748\) −6.37392 −0.233053
\(749\) −0.413285 −0.0151011
\(750\) −4.95125 −0.180794
\(751\) −52.1124 −1.90161 −0.950804 0.309793i \(-0.899740\pi\)
−0.950804 + 0.309793i \(0.899740\pi\)
\(752\) −44.7416 −1.63156
\(753\) 62.6951 2.28474
\(754\) −4.33078 −0.157718
\(755\) −23.9202 −0.870544
\(756\) 3.84949 0.140004
\(757\) 40.5574 1.47409 0.737043 0.675846i \(-0.236222\pi\)
0.737043 + 0.675846i \(0.236222\pi\)
\(758\) 1.79593 0.0652313
\(759\) 16.5796 0.601800
\(760\) −1.51340 −0.0548969
\(761\) −11.6861 −0.423621 −0.211811 0.977311i \(-0.567936\pi\)
−0.211811 + 0.977311i \(0.567936\pi\)
\(762\) 86.5452 3.13520
\(763\) 4.50672 0.163154
\(764\) −27.2542 −0.986024
\(765\) −19.8169 −0.716482
\(766\) 11.2726 0.407296
\(767\) 13.0707 0.471956
\(768\) −54.6964 −1.97369
\(769\) −11.9369 −0.430456 −0.215228 0.976564i \(-0.569049\pi\)
−0.215228 + 0.976564i \(0.569049\pi\)
\(770\) 1.56876 0.0565341
\(771\) −3.97325 −0.143093
\(772\) −38.7035 −1.39297
\(773\) −6.52893 −0.234829 −0.117415 0.993083i \(-0.537461\pi\)
−0.117415 + 0.993083i \(0.537461\pi\)
\(774\) −34.6587 −1.24578
\(775\) 0.661756 0.0237710
\(776\) 3.97370 0.142648
\(777\) −16.9374 −0.607626
\(778\) −0.618618 −0.0221785
\(779\) 10.8292 0.387997
\(780\) −10.3443 −0.370386
\(781\) 4.64421 0.166183
\(782\) −70.6755 −2.52735
\(783\) 2.26486 0.0809394
\(784\) −4.72622 −0.168794
\(785\) 20.8928 0.745698
\(786\) −84.9214 −3.02905
\(787\) −42.1405 −1.50215 −0.751073 0.660219i \(-0.770463\pi\)
−0.751073 + 0.660219i \(0.770463\pi\)
\(788\) 13.2002 0.470236
\(789\) 20.7929 0.740247
\(790\) 5.81573 0.206914
\(791\) −19.1810 −0.681997
\(792\) −2.96034 −0.105191
\(793\) −12.2223 −0.434026
\(794\) 47.1200 1.67223
\(795\) 18.5114 0.656533
\(796\) 20.2102 0.716333
\(797\) 25.5112 0.903651 0.451826 0.892106i \(-0.350773\pi\)
0.451826 + 0.892106i \(0.350773\pi\)
\(798\) −8.37327 −0.296411
\(799\) 47.3970 1.67679
\(800\) 7.08146 0.250367
\(801\) 18.9008 0.667827
\(802\) 52.6795 1.86018
\(803\) −12.5961 −0.444506
\(804\) −41.6070 −1.46737
\(805\) 7.52045 0.265061
\(806\) 3.19786 0.112640
\(807\) 3.24568 0.114253
\(808\) 10.4522 0.367708
\(809\) −41.7146 −1.46661 −0.733304 0.679901i \(-0.762023\pi\)
−0.733304 + 0.679901i \(0.762023\pi\)
\(810\) −9.77548 −0.343475
\(811\) 41.0939 1.44300 0.721501 0.692413i \(-0.243452\pi\)
0.721501 + 0.692413i \(0.243452\pi\)
\(812\) 1.36512 0.0479065
\(813\) 56.2692 1.97345
\(814\) −10.0730 −0.353059
\(815\) 15.8991 0.556920
\(816\) 62.4184 2.18508
\(817\) 7.88933 0.276013
\(818\) −15.7973 −0.552340
\(819\) 10.1900 0.356066
\(820\) −9.75403 −0.340626
\(821\) −44.2387 −1.54394 −0.771970 0.635658i \(-0.780729\pi\)
−0.771970 + 0.635658i \(0.780729\pi\)
\(822\) 70.4741 2.45807
\(823\) −45.6664 −1.59183 −0.795915 0.605408i \(-0.793010\pi\)
−0.795915 + 0.605408i \(0.793010\pi\)
\(824\) −13.4768 −0.469485
\(825\) 2.20460 0.0767542
\(826\) −9.52971 −0.331581
\(827\) −36.4509 −1.26752 −0.633760 0.773530i \(-0.718489\pi\)
−0.633760 + 0.773530i \(0.718489\pi\)
\(828\) 45.3412 1.57572
\(829\) 47.4883 1.64934 0.824668 0.565616i \(-0.191362\pi\)
0.824668 + 0.565616i \(0.191362\pi\)
\(830\) 7.09937 0.246423
\(831\) 70.1590 2.43379
\(832\) 9.88512 0.342705
\(833\) 5.00673 0.173473
\(834\) 87.5632 3.03206
\(835\) −9.50740 −0.329017
\(836\) −2.15294 −0.0744611
\(837\) −1.67237 −0.0578057
\(838\) −35.3707 −1.22186
\(839\) 22.3479 0.771536 0.385768 0.922596i \(-0.373936\pi\)
0.385768 + 0.922596i \(0.373936\pi\)
\(840\) −2.36058 −0.0814477
\(841\) −28.1968 −0.972304
\(842\) −5.11301 −0.176206
\(843\) 4.11596 0.141761
\(844\) 31.9680 1.10038
\(845\) 6.37202 0.219204
\(846\) −70.3316 −2.41805
\(847\) 10.3015 0.353964
\(848\) −33.1673 −1.13897
\(849\) −36.3335 −1.24696
\(850\) −9.39777 −0.322341
\(851\) −48.2889 −1.65532
\(852\) 22.3274 0.764924
\(853\) 8.02611 0.274809 0.137404 0.990515i \(-0.456124\pi\)
0.137404 + 0.990515i \(0.456124\pi\)
\(854\) 8.91113 0.304933
\(855\) −6.69364 −0.228918
\(856\) 0.369849 0.0126412
\(857\) 14.3073 0.488728 0.244364 0.969684i \(-0.421421\pi\)
0.244364 + 0.969684i \(0.421421\pi\)
\(858\) 10.6535 0.363703
\(859\) 19.7835 0.675003 0.337501 0.941325i \(-0.390418\pi\)
0.337501 + 0.941325i \(0.390418\pi\)
\(860\) −7.10603 −0.242314
\(861\) 16.8912 0.575651
\(862\) 0.943293 0.0321287
\(863\) 31.2974 1.06538 0.532688 0.846311i \(-0.321182\pi\)
0.532688 + 0.846311i \(0.321182\pi\)
\(864\) −17.8961 −0.608837
\(865\) −3.57021 −0.121391
\(866\) −72.3633 −2.45901
\(867\) −21.2801 −0.722710
\(868\) −1.00801 −0.0342141
\(869\) −2.58952 −0.0878433
\(870\) 4.43731 0.150439
\(871\) −26.6591 −0.903309
\(872\) −4.03306 −0.136577
\(873\) 17.5753 0.594834
\(874\) −23.8723 −0.807494
\(875\) 1.00000 0.0338062
\(876\) −60.5566 −2.04602
\(877\) −20.3738 −0.687975 −0.343987 0.938974i \(-0.611778\pi\)
−0.343987 + 0.938974i \(0.611778\pi\)
\(878\) −66.7105 −2.25137
\(879\) −1.71858 −0.0579661
\(880\) −3.95002 −0.133155
\(881\) −3.08834 −0.104049 −0.0520243 0.998646i \(-0.516567\pi\)
−0.0520243 + 0.998646i \(0.516567\pi\)
\(882\) −7.42939 −0.250160
\(883\) −39.3746 −1.32506 −0.662530 0.749035i \(-0.730517\pi\)
−0.662530 + 0.749035i \(0.730517\pi\)
\(884\) −19.6341 −0.660367
\(885\) −13.3922 −0.450175
\(886\) 18.5597 0.623525
\(887\) −16.1720 −0.543004 −0.271502 0.962438i \(-0.587520\pi\)
−0.271502 + 0.962438i \(0.587520\pi\)
\(888\) 15.1573 0.508645
\(889\) −17.4795 −0.586243
\(890\) 8.96332 0.300451
\(891\) 4.35264 0.145819
\(892\) −35.3715 −1.18432
\(893\) 16.0095 0.535737
\(894\) 41.4727 1.38706
\(895\) 25.4025 0.849112
\(896\) 6.95578 0.232376
\(897\) 51.0715 1.70523
\(898\) −76.0793 −2.53880
\(899\) −0.593066 −0.0197799
\(900\) 6.02906 0.200969
\(901\) 35.1358 1.17054
\(902\) 10.0455 0.334480
\(903\) 12.3056 0.409506
\(904\) 17.1651 0.570901
\(905\) −4.20561 −0.139799
\(906\) 118.435 3.93473
\(907\) −15.9244 −0.528762 −0.264381 0.964418i \(-0.585168\pi\)
−0.264381 + 0.964418i \(0.585168\pi\)
\(908\) 8.55689 0.283970
\(909\) 46.2292 1.53333
\(910\) 4.83238 0.160192
\(911\) 44.8109 1.48465 0.742326 0.670038i \(-0.233722\pi\)
0.742326 + 0.670038i \(0.233722\pi\)
\(912\) 21.0833 0.698138
\(913\) −3.16107 −0.104616
\(914\) −20.0947 −0.664673
\(915\) 12.5229 0.413995
\(916\) 1.52324 0.0503291
\(917\) 17.1515 0.566393
\(918\) 23.7498 0.783861
\(919\) −4.48235 −0.147859 −0.0739296 0.997263i \(-0.523554\pi\)
−0.0739296 + 0.997263i \(0.523554\pi\)
\(920\) −6.73005 −0.221883
\(921\) −33.9001 −1.11705
\(922\) −21.5283 −0.708996
\(923\) 14.3060 0.470887
\(924\) −3.35812 −0.110474
\(925\) −6.42100 −0.211121
\(926\) −45.0120 −1.47918
\(927\) −59.6064 −1.95773
\(928\) −6.34641 −0.208331
\(929\) 33.5100 1.09943 0.549714 0.835353i \(-0.314737\pi\)
0.549714 + 0.835353i \(0.314737\pi\)
\(930\) −3.27652 −0.107441
\(931\) 1.69114 0.0554250
\(932\) −5.55632 −0.182003
\(933\) 11.5223 0.377223
\(934\) 66.3594 2.17135
\(935\) 4.18446 0.136846
\(936\) −9.11900 −0.298064
\(937\) −8.38107 −0.273798 −0.136899 0.990585i \(-0.543714\pi\)
−0.136899 + 0.990585i \(0.543714\pi\)
\(938\) 19.4369 0.634636
\(939\) −77.4423 −2.52723
\(940\) −14.4200 −0.470328
\(941\) 13.8655 0.452003 0.226002 0.974127i \(-0.427435\pi\)
0.226002 + 0.974127i \(0.427435\pi\)
\(942\) −103.446 −3.37044
\(943\) 48.1572 1.56821
\(944\) 23.9951 0.780975
\(945\) −2.52718 −0.0822091
\(946\) 7.31840 0.237942
\(947\) 30.2186 0.981973 0.490986 0.871167i \(-0.336636\pi\)
0.490986 + 0.871167i \(0.336636\pi\)
\(948\) −12.4493 −0.404334
\(949\) −38.8008 −1.25953
\(950\) −3.17432 −0.102989
\(951\) 24.7916 0.803923
\(952\) −4.48052 −0.145214
\(953\) 28.2354 0.914633 0.457316 0.889304i \(-0.348811\pi\)
0.457316 + 0.889304i \(0.348811\pi\)
\(954\) −52.1374 −1.68801
\(955\) 17.8923 0.578982
\(956\) −17.9308 −0.579922
\(957\) −1.97576 −0.0638673
\(958\) −2.45200 −0.0792205
\(959\) −14.2336 −0.459627
\(960\) −10.1283 −0.326889
\(961\) −30.5621 −0.985874
\(962\) −31.0287 −1.00041
\(963\) 1.63581 0.0527131
\(964\) 7.38987 0.238012
\(965\) 25.4087 0.817937
\(966\) −37.2356 −1.19804
\(967\) 11.5248 0.370612 0.185306 0.982681i \(-0.440672\pi\)
0.185306 + 0.982681i \(0.440672\pi\)
\(968\) −9.21880 −0.296304
\(969\) −22.3346 −0.717491
\(970\) 8.33474 0.267612
\(971\) 22.7562 0.730282 0.365141 0.930952i \(-0.381021\pi\)
0.365141 + 0.930952i \(0.381021\pi\)
\(972\) 32.4741 1.04161
\(973\) −17.6851 −0.566957
\(974\) −43.6786 −1.39955
\(975\) 6.79101 0.217486
\(976\) −22.4376 −0.718210
\(977\) −53.5666 −1.71375 −0.856874 0.515525i \(-0.827597\pi\)
−0.856874 + 0.515525i \(0.827597\pi\)
\(978\) −78.7202 −2.51719
\(979\) −3.99101 −0.127553
\(980\) −1.52324 −0.0486580
\(981\) −17.8379 −0.569519
\(982\) 77.3696 2.46896
\(983\) 25.2092 0.804050 0.402025 0.915629i \(-0.368306\pi\)
0.402025 + 0.915629i \(0.368306\pi\)
\(984\) −15.1159 −0.481879
\(985\) −8.66587 −0.276117
\(986\) 8.42229 0.268220
\(987\) 24.9713 0.794846
\(988\) −6.63190 −0.210989
\(989\) 35.0836 1.11559
\(990\) −6.20924 −0.197342
\(991\) 10.9941 0.349241 0.174620 0.984636i \(-0.444130\pi\)
0.174620 + 0.984636i \(0.444130\pi\)
\(992\) 4.68620 0.148787
\(993\) 12.4156 0.393998
\(994\) −10.4303 −0.330830
\(995\) −13.2680 −0.420623
\(996\) −15.1971 −0.481538
\(997\) −12.2800 −0.388912 −0.194456 0.980911i \(-0.562294\pi\)
−0.194456 + 0.980911i \(0.562294\pi\)
\(998\) 40.1408 1.27063
\(999\) 16.2270 0.513400
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 \(a_p\))