Properties

Label 6025.2.a.h.1.5
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.54879\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.54879 q^{2}\) \(-2.81087 q^{3}\) \(+0.398765 q^{4}\) \(+4.35346 q^{6}\) \(+4.24623 q^{7}\) \(+2.47998 q^{8}\) \(+4.90098 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.54879 q^{2}\) \(-2.81087 q^{3}\) \(+0.398765 q^{4}\) \(+4.35346 q^{6}\) \(+4.24623 q^{7}\) \(+2.47998 q^{8}\) \(+4.90098 q^{9}\) \(+0.915418 q^{11}\) \(-1.12088 q^{12}\) \(-4.81392 q^{13}\) \(-6.57654 q^{14}\) \(-4.63852 q^{16}\) \(+5.38915 q^{17}\) \(-7.59061 q^{18}\) \(-4.34799 q^{19}\) \(-11.9356 q^{21}\) \(-1.41779 q^{22}\) \(-8.10534 q^{23}\) \(-6.97091 q^{24}\) \(+7.45578 q^{26}\) \(-5.34340 q^{27}\) \(+1.69325 q^{28}\) \(-6.45221 q^{29}\) \(+10.7804 q^{31}\) \(+2.22414 q^{32}\) \(-2.57312 q^{33}\) \(-8.34668 q^{34}\) \(+1.95434 q^{36}\) \(-5.16908 q^{37}\) \(+6.73415 q^{38}\) \(+13.5313 q^{39}\) \(-0.612344 q^{41}\) \(+18.4858 q^{42}\) \(+1.85213 q^{43}\) \(+0.365036 q^{44}\) \(+12.5535 q^{46}\) \(+2.21116 q^{47}\) \(+13.0383 q^{48}\) \(+11.0305 q^{49}\) \(-15.1482 q^{51}\) \(-1.91962 q^{52}\) \(-0.00846193 q^{53}\) \(+8.27584 q^{54}\) \(+10.5306 q^{56}\) \(+12.2216 q^{57}\) \(+9.99315 q^{58}\) \(+8.85799 q^{59}\) \(+3.78644 q^{61}\) \(-16.6967 q^{62}\) \(+20.8107 q^{63}\) \(+5.83230 q^{64}\) \(+3.98523 q^{66}\) \(-4.67684 q^{67}\) \(+2.14900 q^{68}\) \(+22.7830 q^{69}\) \(+1.48694 q^{71}\) \(+12.1544 q^{72}\) \(+10.3630 q^{73}\) \(+8.00585 q^{74}\) \(-1.73383 q^{76}\) \(+3.88708 q^{77}\) \(-20.9572 q^{78}\) \(-17.6786 q^{79}\) \(+0.316666 q^{81}\) \(+0.948396 q^{82}\) \(-7.45731 q^{83}\) \(-4.75950 q^{84}\) \(-2.86857 q^{86}\) \(+18.1363 q^{87}\) \(+2.27022 q^{88}\) \(-0.520713 q^{89}\) \(-20.4410 q^{91}\) \(-3.23212 q^{92}\) \(-30.3024 q^{93}\) \(-3.42463 q^{94}\) \(-6.25177 q^{96}\) \(+6.33494 q^{97}\) \(-17.0840 q^{98}\) \(+4.48644 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54879 −1.09516 −0.547582 0.836752i \(-0.684451\pi\)
−0.547582 + 0.836752i \(0.684451\pi\)
\(3\) −2.81087 −1.62286 −0.811428 0.584453i \(-0.801309\pi\)
−0.811428 + 0.584453i \(0.801309\pi\)
\(4\) 0.398765 0.199382
\(5\) 0 0
\(6\) 4.35346 1.77729
\(7\) 4.24623 1.60493 0.802463 0.596702i \(-0.203523\pi\)
0.802463 + 0.596702i \(0.203523\pi\)
\(8\) 2.47998 0.876807
\(9\) 4.90098 1.63366
\(10\) 0 0
\(11\) 0.915418 0.276009 0.138004 0.990432i \(-0.455931\pi\)
0.138004 + 0.990432i \(0.455931\pi\)
\(12\) −1.12088 −0.323569
\(13\) −4.81392 −1.33514 −0.667571 0.744546i \(-0.732666\pi\)
−0.667571 + 0.744546i \(0.732666\pi\)
\(14\) −6.57654 −1.75766
\(15\) 0 0
\(16\) −4.63852 −1.15963
\(17\) 5.38915 1.30706 0.653530 0.756901i \(-0.273287\pi\)
0.653530 + 0.756901i \(0.273287\pi\)
\(18\) −7.59061 −1.78912
\(19\) −4.34799 −0.997498 −0.498749 0.866747i \(-0.666207\pi\)
−0.498749 + 0.866747i \(0.666207\pi\)
\(20\) 0 0
\(21\) −11.9356 −2.60456
\(22\) −1.41779 −0.302275
\(23\) −8.10534 −1.69008 −0.845040 0.534703i \(-0.820423\pi\)
−0.845040 + 0.534703i \(0.820423\pi\)
\(24\) −6.97091 −1.42293
\(25\) 0 0
\(26\) 7.45578 1.46220
\(27\) −5.34340 −1.02834
\(28\) 1.69325 0.319994
\(29\) −6.45221 −1.19815 −0.599073 0.800695i \(-0.704464\pi\)
−0.599073 + 0.800695i \(0.704464\pi\)
\(30\) 0 0
\(31\) 10.7804 1.93623 0.968113 0.250515i \(-0.0806000\pi\)
0.968113 + 0.250515i \(0.0806000\pi\)
\(32\) 2.22414 0.393176
\(33\) −2.57312 −0.447922
\(34\) −8.34668 −1.43144
\(35\) 0 0
\(36\) 1.95434 0.325723
\(37\) −5.16908 −0.849792 −0.424896 0.905242i \(-0.639689\pi\)
−0.424896 + 0.905242i \(0.639689\pi\)
\(38\) 6.73415 1.09242
\(39\) 13.5313 2.16674
\(40\) 0 0
\(41\) −0.612344 −0.0956321 −0.0478161 0.998856i \(-0.515226\pi\)
−0.0478161 + 0.998856i \(0.515226\pi\)
\(42\) 18.4858 2.85242
\(43\) 1.85213 0.282447 0.141223 0.989978i \(-0.454896\pi\)
0.141223 + 0.989978i \(0.454896\pi\)
\(44\) 0.365036 0.0550313
\(45\) 0 0
\(46\) 12.5535 1.85091
\(47\) 2.21116 0.322531 0.161265 0.986911i \(-0.448443\pi\)
0.161265 + 0.986911i \(0.448443\pi\)
\(48\) 13.0383 1.88191
\(49\) 11.0305 1.57579
\(50\) 0 0
\(51\) −15.1482 −2.12117
\(52\) −1.91962 −0.266204
\(53\) −0.00846193 −0.00116234 −0.000581168 1.00000i \(-0.500185\pi\)
−0.000581168 1.00000i \(0.500185\pi\)
\(54\) 8.27584 1.12620
\(55\) 0 0
\(56\) 10.5306 1.40721
\(57\) 12.2216 1.61879
\(58\) 9.99315 1.31216
\(59\) 8.85799 1.15321 0.576606 0.817022i \(-0.304377\pi\)
0.576606 + 0.817022i \(0.304377\pi\)
\(60\) 0 0
\(61\) 3.78644 0.484805 0.242402 0.970176i \(-0.422065\pi\)
0.242402 + 0.970176i \(0.422065\pi\)
\(62\) −16.6967 −2.12048
\(63\) 20.8107 2.62190
\(64\) 5.83230 0.729037
\(65\) 0 0
\(66\) 3.98523 0.490548
\(67\) −4.67684 −0.571367 −0.285683 0.958324i \(-0.592221\pi\)
−0.285683 + 0.958324i \(0.592221\pi\)
\(68\) 2.14900 0.260605
\(69\) 22.7830 2.74276
\(70\) 0 0
\(71\) 1.48694 0.176467 0.0882334 0.996100i \(-0.471878\pi\)
0.0882334 + 0.996100i \(0.471878\pi\)
\(72\) 12.1544 1.43240
\(73\) 10.3630 1.21290 0.606449 0.795122i \(-0.292593\pi\)
0.606449 + 0.795122i \(0.292593\pi\)
\(74\) 8.00585 0.930661
\(75\) 0 0
\(76\) −1.73383 −0.198884
\(77\) 3.88708 0.442974
\(78\) −20.9572 −2.37294
\(79\) −17.6786 −1.98900 −0.994499 0.104743i \(-0.966598\pi\)
−0.994499 + 0.104743i \(0.966598\pi\)
\(80\) 0 0
\(81\) 0.316666 0.0351851
\(82\) 0.948396 0.104733
\(83\) −7.45731 −0.818546 −0.409273 0.912412i \(-0.634218\pi\)
−0.409273 + 0.912412i \(0.634218\pi\)
\(84\) −4.75950 −0.519304
\(85\) 0 0
\(86\) −2.86857 −0.309325
\(87\) 18.1363 1.94442
\(88\) 2.27022 0.242006
\(89\) −0.520713 −0.0551955 −0.0275978 0.999619i \(-0.508786\pi\)
−0.0275978 + 0.999619i \(0.508786\pi\)
\(90\) 0 0
\(91\) −20.4410 −2.14280
\(92\) −3.23212 −0.336972
\(93\) −30.3024 −3.14221
\(94\) −3.42463 −0.353224
\(95\) 0 0
\(96\) −6.25177 −0.638068
\(97\) 6.33494 0.643216 0.321608 0.946873i \(-0.395777\pi\)
0.321608 + 0.946873i \(0.395777\pi\)
\(98\) −17.0840 −1.72574
\(99\) 4.48644 0.450904
\(100\) 0 0
\(101\) 7.20652 0.717076 0.358538 0.933515i \(-0.383275\pi\)
0.358538 + 0.933515i \(0.383275\pi\)
\(102\) 23.4614 2.32303
\(103\) −7.82738 −0.771255 −0.385627 0.922655i \(-0.626015\pi\)
−0.385627 + 0.922655i \(0.626015\pi\)
\(104\) −11.9385 −1.17066
\(105\) 0 0
\(106\) 0.0131058 0.00127295
\(107\) −3.28176 −0.317260 −0.158630 0.987338i \(-0.550708\pi\)
−0.158630 + 0.987338i \(0.550708\pi\)
\(108\) −2.13076 −0.205033
\(109\) 6.89529 0.660449 0.330224 0.943902i \(-0.392876\pi\)
0.330224 + 0.943902i \(0.392876\pi\)
\(110\) 0 0
\(111\) 14.5296 1.37909
\(112\) −19.6962 −1.86112
\(113\) 14.4737 1.36157 0.680787 0.732481i \(-0.261638\pi\)
0.680787 + 0.732481i \(0.261638\pi\)
\(114\) −18.9288 −1.77284
\(115\) 0 0
\(116\) −2.57292 −0.238889
\(117\) −23.5929 −2.18117
\(118\) −13.7192 −1.26296
\(119\) 22.8836 2.09773
\(120\) 0 0
\(121\) −10.1620 −0.923819
\(122\) −5.86443 −0.530940
\(123\) 1.72122 0.155197
\(124\) 4.29886 0.386049
\(125\) 0 0
\(126\) −32.2315 −2.87141
\(127\) −6.96745 −0.618261 −0.309130 0.951020i \(-0.600038\pi\)
−0.309130 + 0.951020i \(0.600038\pi\)
\(128\) −13.4813 −1.19159
\(129\) −5.20609 −0.458370
\(130\) 0 0
\(131\) 7.02108 0.613434 0.306717 0.951801i \(-0.400769\pi\)
0.306717 + 0.951801i \(0.400769\pi\)
\(132\) −1.02607 −0.0893079
\(133\) −18.4626 −1.60091
\(134\) 7.24346 0.625740
\(135\) 0 0
\(136\) 13.3650 1.14604
\(137\) −5.78101 −0.493905 −0.246953 0.969028i \(-0.579429\pi\)
−0.246953 + 0.969028i \(0.579429\pi\)
\(138\) −35.2862 −3.00376
\(139\) 2.34939 0.199272 0.0996362 0.995024i \(-0.468232\pi\)
0.0996362 + 0.995024i \(0.468232\pi\)
\(140\) 0 0
\(141\) −6.21527 −0.523421
\(142\) −2.30296 −0.193260
\(143\) −4.40675 −0.368511
\(144\) −22.7333 −1.89444
\(145\) 0 0
\(146\) −16.0502 −1.32832
\(147\) −31.0053 −2.55727
\(148\) −2.06125 −0.169434
\(149\) 4.44128 0.363844 0.181922 0.983313i \(-0.441768\pi\)
0.181922 + 0.983313i \(0.441768\pi\)
\(150\) 0 0
\(151\) −5.33629 −0.434261 −0.217130 0.976143i \(-0.569670\pi\)
−0.217130 + 0.976143i \(0.569670\pi\)
\(152\) −10.7830 −0.874613
\(153\) 26.4121 2.13529
\(154\) −6.02028 −0.485128
\(155\) 0 0
\(156\) 5.39581 0.432010
\(157\) 21.6127 1.72488 0.862442 0.506157i \(-0.168934\pi\)
0.862442 + 0.506157i \(0.168934\pi\)
\(158\) 27.3805 2.17828
\(159\) 0.0237854 0.00188630
\(160\) 0 0
\(161\) −34.4172 −2.71245
\(162\) −0.490451 −0.0385334
\(163\) 22.0999 1.73100 0.865500 0.500909i \(-0.167001\pi\)
0.865500 + 0.500909i \(0.167001\pi\)
\(164\) −0.244181 −0.0190674
\(165\) 0 0
\(166\) 11.5498 0.896442
\(167\) 2.58299 0.199877 0.0999387 0.994994i \(-0.468135\pi\)
0.0999387 + 0.994994i \(0.468135\pi\)
\(168\) −29.6001 −2.28370
\(169\) 10.1739 0.782604
\(170\) 0 0
\(171\) −21.3094 −1.62957
\(172\) 0.738564 0.0563149
\(173\) −9.53817 −0.725174 −0.362587 0.931950i \(-0.618106\pi\)
−0.362587 + 0.931950i \(0.618106\pi\)
\(174\) −28.0894 −2.12945
\(175\) 0 0
\(176\) −4.24618 −0.320068
\(177\) −24.8986 −1.87150
\(178\) 0.806478 0.0604481
\(179\) 11.6661 0.871963 0.435981 0.899956i \(-0.356401\pi\)
0.435981 + 0.899956i \(0.356401\pi\)
\(180\) 0 0
\(181\) −6.78106 −0.504032 −0.252016 0.967723i \(-0.581094\pi\)
−0.252016 + 0.967723i \(0.581094\pi\)
\(182\) 31.6590 2.34672
\(183\) −10.6432 −0.786768
\(184\) −20.1011 −1.48187
\(185\) 0 0
\(186\) 46.9322 3.44124
\(187\) 4.93332 0.360760
\(188\) 0.881732 0.0643069
\(189\) −22.6893 −1.65041
\(190\) 0 0
\(191\) 9.30072 0.672976 0.336488 0.941688i \(-0.390761\pi\)
0.336488 + 0.941688i \(0.390761\pi\)
\(192\) −16.3938 −1.18312
\(193\) 1.27177 0.0915440 0.0457720 0.998952i \(-0.485425\pi\)
0.0457720 + 0.998952i \(0.485425\pi\)
\(194\) −9.81153 −0.704427
\(195\) 0 0
\(196\) 4.39858 0.314184
\(197\) −9.51222 −0.677718 −0.338859 0.940837i \(-0.610041\pi\)
−0.338859 + 0.940837i \(0.610041\pi\)
\(198\) −6.94858 −0.493814
\(199\) −18.4776 −1.30984 −0.654922 0.755696i \(-0.727299\pi\)
−0.654922 + 0.755696i \(0.727299\pi\)
\(200\) 0 0
\(201\) 13.1460 0.927246
\(202\) −11.1614 −0.785315
\(203\) −27.3976 −1.92293
\(204\) −6.04056 −0.422924
\(205\) 0 0
\(206\) 12.1230 0.844650
\(207\) −39.7241 −2.76102
\(208\) 22.3295 1.54827
\(209\) −3.98023 −0.275318
\(210\) 0 0
\(211\) 5.54459 0.381705 0.190853 0.981619i \(-0.438875\pi\)
0.190853 + 0.981619i \(0.438875\pi\)
\(212\) −0.00337432 −0.000231749 0
\(213\) −4.17958 −0.286380
\(214\) 5.08278 0.347451
\(215\) 0 0
\(216\) −13.2516 −0.901654
\(217\) 45.7763 3.10750
\(218\) −10.6794 −0.723299
\(219\) −29.1290 −1.96836
\(220\) 0 0
\(221\) −25.9429 −1.74511
\(222\) −22.5034 −1.51033
\(223\) 12.8984 0.863744 0.431872 0.901935i \(-0.357853\pi\)
0.431872 + 0.901935i \(0.357853\pi\)
\(224\) 9.44422 0.631019
\(225\) 0 0
\(226\) −22.4169 −1.49115
\(227\) −2.85469 −0.189473 −0.0947364 0.995502i \(-0.530201\pi\)
−0.0947364 + 0.995502i \(0.530201\pi\)
\(228\) 4.87356 0.322759
\(229\) −16.1705 −1.06857 −0.534287 0.845303i \(-0.679420\pi\)
−0.534287 + 0.845303i \(0.679420\pi\)
\(230\) 0 0
\(231\) −10.9261 −0.718882
\(232\) −16.0014 −1.05054
\(233\) −11.3792 −0.745476 −0.372738 0.927937i \(-0.621581\pi\)
−0.372738 + 0.927937i \(0.621581\pi\)
\(234\) 36.5406 2.38874
\(235\) 0 0
\(236\) 3.53226 0.229930
\(237\) 49.6922 3.22786
\(238\) −35.4420 −2.29736
\(239\) 27.0358 1.74880 0.874400 0.485206i \(-0.161255\pi\)
0.874400 + 0.485206i \(0.161255\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 15.7389 1.01173
\(243\) 15.1401 0.971238
\(244\) 1.50990 0.0966615
\(245\) 0 0
\(246\) −2.66582 −0.169966
\(247\) 20.9309 1.33180
\(248\) 26.7353 1.69770
\(249\) 20.9615 1.32838
\(250\) 0 0
\(251\) −16.5147 −1.04240 −0.521199 0.853435i \(-0.674515\pi\)
−0.521199 + 0.853435i \(0.674515\pi\)
\(252\) 8.29858 0.522761
\(253\) −7.41977 −0.466477
\(254\) 10.7911 0.677097
\(255\) 0 0
\(256\) 9.21519 0.575949
\(257\) 9.88138 0.616383 0.308192 0.951324i \(-0.400276\pi\)
0.308192 + 0.951324i \(0.400276\pi\)
\(258\) 8.06316 0.501990
\(259\) −21.9491 −1.36385
\(260\) 0 0
\(261\) −31.6222 −1.95736
\(262\) −10.8742 −0.671811
\(263\) 31.5776 1.94716 0.973579 0.228351i \(-0.0733335\pi\)
0.973579 + 0.228351i \(0.0733335\pi\)
\(264\) −6.38129 −0.392741
\(265\) 0 0
\(266\) 28.5948 1.75326
\(267\) 1.46366 0.0895744
\(268\) −1.86496 −0.113921
\(269\) 4.21527 0.257010 0.128505 0.991709i \(-0.458982\pi\)
0.128505 + 0.991709i \(0.458982\pi\)
\(270\) 0 0
\(271\) 11.8060 0.717162 0.358581 0.933499i \(-0.383261\pi\)
0.358581 + 0.933499i \(0.383261\pi\)
\(272\) −24.9976 −1.51570
\(273\) 57.4571 3.47746
\(274\) 8.95360 0.540907
\(275\) 0 0
\(276\) 9.08508 0.546857
\(277\) −8.01314 −0.481463 −0.240731 0.970592i \(-0.577387\pi\)
−0.240731 + 0.970592i \(0.577387\pi\)
\(278\) −3.63872 −0.218236
\(279\) 52.8348 3.16313
\(280\) 0 0
\(281\) −21.6719 −1.29284 −0.646419 0.762982i \(-0.723734\pi\)
−0.646419 + 0.762982i \(0.723734\pi\)
\(282\) 9.62618 0.573231
\(283\) −2.15646 −0.128188 −0.0640941 0.997944i \(-0.520416\pi\)
−0.0640941 + 0.997944i \(0.520416\pi\)
\(284\) 0.592938 0.0351844
\(285\) 0 0
\(286\) 6.82515 0.403580
\(287\) −2.60016 −0.153482
\(288\) 10.9005 0.642316
\(289\) 12.0429 0.708406
\(290\) 0 0
\(291\) −17.8067 −1.04385
\(292\) 4.13240 0.241831
\(293\) −26.9520 −1.57455 −0.787276 0.616601i \(-0.788509\pi\)
−0.787276 + 0.616601i \(0.788509\pi\)
\(294\) 48.0208 2.80063
\(295\) 0 0
\(296\) −12.8192 −0.745103
\(297\) −4.89145 −0.283830
\(298\) −6.87863 −0.398469
\(299\) 39.0185 2.25650
\(300\) 0 0
\(301\) 7.86457 0.453306
\(302\) 8.26481 0.475586
\(303\) −20.2566 −1.16371
\(304\) 20.1682 1.15673
\(305\) 0 0
\(306\) −40.9069 −2.33849
\(307\) −16.6282 −0.949020 −0.474510 0.880250i \(-0.657375\pi\)
−0.474510 + 0.880250i \(0.657375\pi\)
\(308\) 1.55003 0.0883211
\(309\) 22.0017 1.25163
\(310\) 0 0
\(311\) −10.1432 −0.575167 −0.287584 0.957756i \(-0.592852\pi\)
−0.287584 + 0.957756i \(0.592852\pi\)
\(312\) 33.5574 1.89981
\(313\) 26.7382 1.51133 0.755667 0.654956i \(-0.227313\pi\)
0.755667 + 0.654956i \(0.227313\pi\)
\(314\) −33.4737 −1.88903
\(315\) 0 0
\(316\) −7.04961 −0.396571
\(317\) 25.6438 1.44030 0.720151 0.693817i \(-0.244072\pi\)
0.720151 + 0.693817i \(0.244072\pi\)
\(318\) −0.0368387 −0.00206581
\(319\) −5.90647 −0.330699
\(320\) 0 0
\(321\) 9.22460 0.514867
\(322\) 53.3051 2.97058
\(323\) −23.4320 −1.30379
\(324\) 0.126275 0.00701529
\(325\) 0 0
\(326\) −34.2282 −1.89573
\(327\) −19.3817 −1.07181
\(328\) −1.51860 −0.0838509
\(329\) 9.38910 0.517638
\(330\) 0 0
\(331\) 21.9178 1.20471 0.602356 0.798228i \(-0.294229\pi\)
0.602356 + 0.798228i \(0.294229\pi\)
\(332\) −2.97371 −0.163204
\(333\) −25.3336 −1.38827
\(334\) −4.00052 −0.218898
\(335\) 0 0
\(336\) 55.3635 3.02033
\(337\) −5.64948 −0.307747 −0.153873 0.988091i \(-0.549175\pi\)
−0.153873 + 0.988091i \(0.549175\pi\)
\(338\) −15.7572 −0.857079
\(339\) −40.6838 −2.20964
\(340\) 0 0
\(341\) 9.86861 0.534415
\(342\) 33.0039 1.78465
\(343\) 17.1144 0.924093
\(344\) 4.59325 0.247651
\(345\) 0 0
\(346\) 14.7727 0.794184
\(347\) −19.7057 −1.05786 −0.528928 0.848667i \(-0.677406\pi\)
−0.528928 + 0.848667i \(0.677406\pi\)
\(348\) 7.23213 0.387683
\(349\) −31.5930 −1.69113 −0.845567 0.533869i \(-0.820738\pi\)
−0.845567 + 0.533869i \(0.820738\pi\)
\(350\) 0 0
\(351\) 25.7227 1.37298
\(352\) 2.03602 0.108520
\(353\) −12.7948 −0.680999 −0.340499 0.940245i \(-0.610596\pi\)
−0.340499 + 0.940245i \(0.610596\pi\)
\(354\) 38.5629 2.04959
\(355\) 0 0
\(356\) −0.207642 −0.0110050
\(357\) −64.3227 −3.40432
\(358\) −18.0683 −0.954942
\(359\) 27.2866 1.44013 0.720066 0.693906i \(-0.244112\pi\)
0.720066 + 0.693906i \(0.244112\pi\)
\(360\) 0 0
\(361\) −0.0949647 −0.00499814
\(362\) 10.5025 0.551998
\(363\) 28.5641 1.49923
\(364\) −8.15117 −0.427237
\(365\) 0 0
\(366\) 16.4841 0.861639
\(367\) −25.9541 −1.35479 −0.677396 0.735619i \(-0.736891\pi\)
−0.677396 + 0.735619i \(0.736891\pi\)
\(368\) 37.5967 1.95987
\(369\) −3.00109 −0.156230
\(370\) 0 0
\(371\) −0.0359313 −0.00186546
\(372\) −12.0835 −0.626502
\(373\) −1.94963 −0.100948 −0.0504740 0.998725i \(-0.516073\pi\)
−0.0504740 + 0.998725i \(0.516073\pi\)
\(374\) −7.64070 −0.395091
\(375\) 0 0
\(376\) 5.48364 0.282797
\(377\) 31.0604 1.59969
\(378\) 35.1411 1.80747
\(379\) 22.0885 1.13461 0.567305 0.823508i \(-0.307986\pi\)
0.567305 + 0.823508i \(0.307986\pi\)
\(380\) 0 0
\(381\) 19.5846 1.00335
\(382\) −14.4049 −0.737019
\(383\) 32.6589 1.66879 0.834396 0.551166i \(-0.185817\pi\)
0.834396 + 0.551166i \(0.185817\pi\)
\(384\) 37.8942 1.93378
\(385\) 0 0
\(386\) −1.96971 −0.100256
\(387\) 9.07724 0.461422
\(388\) 2.52615 0.128246
\(389\) −1.59569 −0.0809045 −0.0404522 0.999181i \(-0.512880\pi\)
−0.0404522 + 0.999181i \(0.512880\pi\)
\(390\) 0 0
\(391\) −43.6809 −2.20904
\(392\) 27.3555 1.38166
\(393\) −19.7353 −0.995515
\(394\) 14.7325 0.742212
\(395\) 0 0
\(396\) 1.78904 0.0899024
\(397\) 20.5064 1.02919 0.514593 0.857434i \(-0.327943\pi\)
0.514593 + 0.857434i \(0.327943\pi\)
\(398\) 28.6181 1.43449
\(399\) 51.8959 2.59805
\(400\) 0 0
\(401\) 2.51432 0.125559 0.0627795 0.998027i \(-0.480004\pi\)
0.0627795 + 0.998027i \(0.480004\pi\)
\(402\) −20.3604 −1.01549
\(403\) −51.8962 −2.58514
\(404\) 2.87371 0.142972
\(405\) 0 0
\(406\) 42.4333 2.10593
\(407\) −4.73187 −0.234550
\(408\) −37.5672 −1.85986
\(409\) −3.99904 −0.197740 −0.0988698 0.995100i \(-0.531523\pi\)
−0.0988698 + 0.995100i \(0.531523\pi\)
\(410\) 0 0
\(411\) 16.2497 0.801537
\(412\) −3.12128 −0.153775
\(413\) 37.6131 1.85082
\(414\) 61.5245 3.02376
\(415\) 0 0
\(416\) −10.7068 −0.524946
\(417\) −6.60382 −0.323390
\(418\) 6.16456 0.301518
\(419\) 19.3567 0.945635 0.472818 0.881160i \(-0.343237\pi\)
0.472818 + 0.881160i \(0.343237\pi\)
\(420\) 0 0
\(421\) −4.81504 −0.234671 −0.117335 0.993092i \(-0.537435\pi\)
−0.117335 + 0.993092i \(0.537435\pi\)
\(422\) −8.58743 −0.418029
\(423\) 10.8368 0.526905
\(424\) −0.0209855 −0.00101914
\(425\) 0 0
\(426\) 6.47331 0.313633
\(427\) 16.0781 0.778075
\(428\) −1.30865 −0.0632561
\(429\) 12.3868 0.598040
\(430\) 0 0
\(431\) 26.8254 1.29213 0.646067 0.763281i \(-0.276413\pi\)
0.646067 + 0.763281i \(0.276413\pi\)
\(432\) 24.7855 1.19249
\(433\) −1.59224 −0.0765181 −0.0382591 0.999268i \(-0.512181\pi\)
−0.0382591 + 0.999268i \(0.512181\pi\)
\(434\) −70.8981 −3.40322
\(435\) 0 0
\(436\) 2.74960 0.131682
\(437\) 35.2419 1.68585
\(438\) 45.1149 2.15567
\(439\) −36.5165 −1.74284 −0.871418 0.490541i \(-0.836799\pi\)
−0.871418 + 0.490541i \(0.836799\pi\)
\(440\) 0 0
\(441\) 54.0603 2.57430
\(442\) 40.1803 1.91118
\(443\) 1.27451 0.0605540 0.0302770 0.999542i \(-0.490361\pi\)
0.0302770 + 0.999542i \(0.490361\pi\)
\(444\) 5.79390 0.274966
\(445\) 0 0
\(446\) −19.9770 −0.945940
\(447\) −12.4839 −0.590466
\(448\) 24.7653 1.17005
\(449\) 31.9473 1.50768 0.753842 0.657055i \(-0.228198\pi\)
0.753842 + 0.657055i \(0.228198\pi\)
\(450\) 0 0
\(451\) −0.560551 −0.0263953
\(452\) 5.77162 0.271474
\(453\) 14.9996 0.704742
\(454\) 4.42133 0.207504
\(455\) 0 0
\(456\) 30.3095 1.41937
\(457\) −12.8561 −0.601384 −0.300692 0.953721i \(-0.597218\pi\)
−0.300692 + 0.953721i \(0.597218\pi\)
\(458\) 25.0447 1.17026
\(459\) −28.7964 −1.34410
\(460\) 0 0
\(461\) 35.6691 1.66127 0.830637 0.556814i \(-0.187976\pi\)
0.830637 + 0.556814i \(0.187976\pi\)
\(462\) 16.9222 0.787293
\(463\) −2.74466 −0.127555 −0.0637776 0.997964i \(-0.520315\pi\)
−0.0637776 + 0.997964i \(0.520315\pi\)
\(464\) 29.9287 1.38940
\(465\) 0 0
\(466\) 17.6240 0.816418
\(467\) 25.5934 1.18432 0.592160 0.805821i \(-0.298275\pi\)
0.592160 + 0.805821i \(0.298275\pi\)
\(468\) −9.40804 −0.434887
\(469\) −19.8590 −0.917001
\(470\) 0 0
\(471\) −60.7505 −2.79924
\(472\) 21.9677 1.01114
\(473\) 1.69547 0.0779578
\(474\) −76.9631 −3.53503
\(475\) 0 0
\(476\) 9.12517 0.418251
\(477\) −0.0414718 −0.00189886
\(478\) −41.8729 −1.91522
\(479\) −0.610882 −0.0279119 −0.0139560 0.999903i \(-0.504442\pi\)
−0.0139560 + 0.999903i \(0.504442\pi\)
\(480\) 0 0
\(481\) 24.8836 1.13459
\(482\) −1.54879 −0.0705457
\(483\) 96.7421 4.40192
\(484\) −4.05225 −0.184193
\(485\) 0 0
\(486\) −23.4489 −1.06366
\(487\) −26.6270 −1.20658 −0.603291 0.797521i \(-0.706144\pi\)
−0.603291 + 0.797521i \(0.706144\pi\)
\(488\) 9.39032 0.425080
\(489\) −62.1200 −2.80916
\(490\) 0 0
\(491\) −31.7856 −1.43447 −0.717233 0.696833i \(-0.754592\pi\)
−0.717233 + 0.696833i \(0.754592\pi\)
\(492\) 0.686362 0.0309436
\(493\) −34.7719 −1.56605
\(494\) −32.4177 −1.45854
\(495\) 0 0
\(496\) −50.0053 −2.24530
\(497\) 6.31387 0.283216
\(498\) −32.4651 −1.45480
\(499\) −17.2468 −0.772074 −0.386037 0.922483i \(-0.626156\pi\)
−0.386037 + 0.922483i \(0.626156\pi\)
\(500\) 0 0
\(501\) −7.26043 −0.324372
\(502\) 25.5779 1.14160
\(503\) 23.6924 1.05639 0.528196 0.849122i \(-0.322868\pi\)
0.528196 + 0.849122i \(0.322868\pi\)
\(504\) 51.6102 2.29890
\(505\) 0 0
\(506\) 11.4917 0.510868
\(507\) −28.5974 −1.27005
\(508\) −2.77837 −0.123270
\(509\) 20.3227 0.900787 0.450394 0.892830i \(-0.351284\pi\)
0.450394 + 0.892830i \(0.351284\pi\)
\(510\) 0 0
\(511\) 44.0037 1.94661
\(512\) 12.6902 0.560832
\(513\) 23.2331 1.02577
\(514\) −15.3042 −0.675040
\(515\) 0 0
\(516\) −2.07600 −0.0913910
\(517\) 2.02413 0.0890213
\(518\) 33.9947 1.49364
\(519\) 26.8106 1.17685
\(520\) 0 0
\(521\) 16.3912 0.718112 0.359056 0.933316i \(-0.383099\pi\)
0.359056 + 0.933316i \(0.383099\pi\)
\(522\) 48.9762 2.14363
\(523\) −0.258754 −0.0113145 −0.00565727 0.999984i \(-0.501801\pi\)
−0.00565727 + 0.999984i \(0.501801\pi\)
\(524\) 2.79976 0.122308
\(525\) 0 0
\(526\) −48.9072 −2.13246
\(527\) 58.0974 2.53076
\(528\) 11.9354 0.519424
\(529\) 42.6965 1.85637
\(530\) 0 0
\(531\) 43.4128 1.88396
\(532\) −7.36223 −0.319193
\(533\) 2.94778 0.127682
\(534\) −2.26690 −0.0980985
\(535\) 0 0
\(536\) −11.5985 −0.500978
\(537\) −32.7918 −1.41507
\(538\) −6.52859 −0.281468
\(539\) 10.0975 0.434931
\(540\) 0 0
\(541\) −17.9084 −0.769941 −0.384970 0.922929i \(-0.625788\pi\)
−0.384970 + 0.922929i \(0.625788\pi\)
\(542\) −18.2850 −0.785410
\(543\) 19.0607 0.817971
\(544\) 11.9862 0.513905
\(545\) 0 0
\(546\) −88.9892 −3.80839
\(547\) −12.2295 −0.522897 −0.261448 0.965217i \(-0.584200\pi\)
−0.261448 + 0.965217i \(0.584200\pi\)
\(548\) −2.30526 −0.0984760
\(549\) 18.5573 0.792006
\(550\) 0 0
\(551\) 28.0542 1.19515
\(552\) 56.5016 2.40487
\(553\) −75.0675 −3.19219
\(554\) 12.4107 0.527280
\(555\) 0 0
\(556\) 0.936853 0.0397314
\(557\) −25.2541 −1.07005 −0.535024 0.844837i \(-0.679698\pi\)
−0.535024 + 0.844837i \(0.679698\pi\)
\(558\) −81.8302 −3.46415
\(559\) −8.91600 −0.377107
\(560\) 0 0
\(561\) −13.8669 −0.585461
\(562\) 33.5654 1.41587
\(563\) 10.4115 0.438794 0.219397 0.975636i \(-0.429591\pi\)
0.219397 + 0.975636i \(0.429591\pi\)
\(564\) −2.47843 −0.104361
\(565\) 0 0
\(566\) 3.33991 0.140387
\(567\) 1.34464 0.0564695
\(568\) 3.68758 0.154727
\(569\) −28.5127 −1.19532 −0.597658 0.801751i \(-0.703902\pi\)
−0.597658 + 0.801751i \(0.703902\pi\)
\(570\) 0 0
\(571\) 35.8278 1.49935 0.749674 0.661807i \(-0.230210\pi\)
0.749674 + 0.661807i \(0.230210\pi\)
\(572\) −1.75726 −0.0734746
\(573\) −26.1431 −1.09214
\(574\) 4.02711 0.168088
\(575\) 0 0
\(576\) 28.5840 1.19100
\(577\) −1.00615 −0.0418864 −0.0209432 0.999781i \(-0.506667\pi\)
−0.0209432 + 0.999781i \(0.506667\pi\)
\(578\) −18.6520 −0.775820
\(579\) −3.57478 −0.148563
\(580\) 0 0
\(581\) −31.6655 −1.31371
\(582\) 27.5789 1.14318
\(583\) −0.00774620 −0.000320815 0
\(584\) 25.7001 1.06348
\(585\) 0 0
\(586\) 41.7431 1.72439
\(587\) 7.69459 0.317590 0.158795 0.987312i \(-0.449239\pi\)
0.158795 + 0.987312i \(0.449239\pi\)
\(588\) −12.3638 −0.509875
\(589\) −46.8733 −1.93138
\(590\) 0 0
\(591\) 26.7376 1.09984
\(592\) 23.9769 0.985443
\(593\) 27.9165 1.14639 0.573197 0.819418i \(-0.305703\pi\)
0.573197 + 0.819418i \(0.305703\pi\)
\(594\) 7.57585 0.310841
\(595\) 0 0
\(596\) 1.77103 0.0725441
\(597\) 51.9382 2.12569
\(598\) −60.4316 −2.47123
\(599\) 43.2997 1.76918 0.884588 0.466372i \(-0.154439\pi\)
0.884588 + 0.466372i \(0.154439\pi\)
\(600\) 0 0
\(601\) −25.4104 −1.03651 −0.518255 0.855226i \(-0.673418\pi\)
−0.518255 + 0.855226i \(0.673418\pi\)
\(602\) −12.1806 −0.496444
\(603\) −22.9211 −0.933419
\(604\) −2.12792 −0.0865840
\(605\) 0 0
\(606\) 31.3733 1.27445
\(607\) 2.58042 0.104736 0.0523679 0.998628i \(-0.483323\pi\)
0.0523679 + 0.998628i \(0.483323\pi\)
\(608\) −9.67055 −0.392192
\(609\) 77.0110 3.12064
\(610\) 0 0
\(611\) −10.6443 −0.430624
\(612\) 10.5322 0.425740
\(613\) −24.6593 −0.995980 −0.497990 0.867183i \(-0.665928\pi\)
−0.497990 + 0.867183i \(0.665928\pi\)
\(614\) 25.7536 1.03933
\(615\) 0 0
\(616\) 9.63989 0.388402
\(617\) 17.2509 0.694497 0.347248 0.937773i \(-0.387116\pi\)
0.347248 + 0.937773i \(0.387116\pi\)
\(618\) −34.0762 −1.37074
\(619\) −0.0379403 −0.00152495 −0.000762475 1.00000i \(-0.500243\pi\)
−0.000762475 1.00000i \(0.500243\pi\)
\(620\) 0 0
\(621\) 43.3101 1.73797
\(622\) 15.7097 0.629902
\(623\) −2.21107 −0.0885847
\(624\) −62.7652 −2.51262
\(625\) 0 0
\(626\) −41.4120 −1.65516
\(627\) 11.1879 0.446802
\(628\) 8.61840 0.343911
\(629\) −27.8569 −1.11073
\(630\) 0 0
\(631\) 39.8274 1.58551 0.792753 0.609544i \(-0.208647\pi\)
0.792753 + 0.609544i \(0.208647\pi\)
\(632\) −43.8427 −1.74397
\(633\) −15.5851 −0.619452
\(634\) −39.7171 −1.57737
\(635\) 0 0
\(636\) 0.00948477 0.000376096 0
\(637\) −53.1000 −2.10390
\(638\) 9.14790 0.362169
\(639\) 7.28744 0.288287
\(640\) 0 0
\(641\) 17.4965 0.691071 0.345536 0.938406i \(-0.387697\pi\)
0.345536 + 0.938406i \(0.387697\pi\)
\(642\) −14.2870 −0.563863
\(643\) −19.8884 −0.784323 −0.392162 0.919896i \(-0.628273\pi\)
−0.392162 + 0.919896i \(0.628273\pi\)
\(644\) −13.7244 −0.540815
\(645\) 0 0
\(646\) 36.2913 1.42786
\(647\) 39.9620 1.57107 0.785535 0.618817i \(-0.212388\pi\)
0.785535 + 0.618817i \(0.212388\pi\)
\(648\) 0.785327 0.0308506
\(649\) 8.10876 0.318297
\(650\) 0 0
\(651\) −128.671 −5.04302
\(652\) 8.81267 0.345131
\(653\) 45.0393 1.76252 0.881262 0.472629i \(-0.156695\pi\)
0.881262 + 0.472629i \(0.156695\pi\)
\(654\) 30.0183 1.17381
\(655\) 0 0
\(656\) 2.84037 0.110898
\(657\) 50.7889 1.98146
\(658\) −14.5418 −0.566898
\(659\) −28.6163 −1.11473 −0.557367 0.830266i \(-0.688188\pi\)
−0.557367 + 0.830266i \(0.688188\pi\)
\(660\) 0 0
\(661\) −21.0849 −0.820106 −0.410053 0.912062i \(-0.634490\pi\)
−0.410053 + 0.912062i \(0.634490\pi\)
\(662\) −33.9462 −1.31936
\(663\) 72.9222 2.83206
\(664\) −18.4940 −0.717707
\(665\) 0 0
\(666\) 39.2365 1.52038
\(667\) 52.2974 2.02496
\(668\) 1.03000 0.0398521
\(669\) −36.2558 −1.40173
\(670\) 0 0
\(671\) 3.46618 0.133810
\(672\) −26.5465 −1.02405
\(673\) −11.9180 −0.459406 −0.229703 0.973261i \(-0.573776\pi\)
−0.229703 + 0.973261i \(0.573776\pi\)
\(674\) 8.74988 0.337033
\(675\) 0 0
\(676\) 4.05698 0.156038
\(677\) −46.0077 −1.76822 −0.884111 0.467278i \(-0.845235\pi\)
−0.884111 + 0.467278i \(0.845235\pi\)
\(678\) 63.0108 2.41992
\(679\) 26.8997 1.03231
\(680\) 0 0
\(681\) 8.02417 0.307487
\(682\) −15.2844 −0.585272
\(683\) −41.5189 −1.58868 −0.794338 0.607477i \(-0.792182\pi\)
−0.794338 + 0.607477i \(0.792182\pi\)
\(684\) −8.49745 −0.324908
\(685\) 0 0
\(686\) −26.5068 −1.01203
\(687\) 45.4531 1.73414
\(688\) −8.59113 −0.327534
\(689\) 0.0407351 0.00155188
\(690\) 0 0
\(691\) 28.5903 1.08763 0.543814 0.839206i \(-0.316980\pi\)
0.543814 + 0.839206i \(0.316980\pi\)
\(692\) −3.80349 −0.144587
\(693\) 19.0505 0.723668
\(694\) 30.5200 1.15852
\(695\) 0 0
\(696\) 44.9778 1.70488
\(697\) −3.30001 −0.124997
\(698\) 48.9311 1.85207
\(699\) 31.9854 1.20980
\(700\) 0 0
\(701\) 19.2033 0.725298 0.362649 0.931926i \(-0.381872\pi\)
0.362649 + 0.931926i \(0.381872\pi\)
\(702\) −39.8392 −1.50364
\(703\) 22.4751 0.847665
\(704\) 5.33899 0.201221
\(705\) 0 0
\(706\) 19.8165 0.745805
\(707\) 30.6006 1.15085
\(708\) −9.92870 −0.373144
\(709\) 4.05386 0.152246 0.0761229 0.997098i \(-0.475746\pi\)
0.0761229 + 0.997098i \(0.475746\pi\)
\(710\) 0 0
\(711\) −86.6425 −3.24935
\(712\) −1.29136 −0.0483958
\(713\) −87.3792 −3.27238
\(714\) 99.6227 3.72828
\(715\) 0 0
\(716\) 4.65202 0.173854
\(717\) −75.9940 −2.83805
\(718\) −42.2613 −1.57718
\(719\) 13.0438 0.486452 0.243226 0.969970i \(-0.421794\pi\)
0.243226 + 0.969970i \(0.421794\pi\)
\(720\) 0 0
\(721\) −33.2369 −1.23781
\(722\) 0.147081 0.00547378
\(723\) −2.81087 −0.104537
\(724\) −2.70405 −0.100495
\(725\) 0 0
\(726\) −44.2399 −1.64190
\(727\) 43.3367 1.60727 0.803635 0.595123i \(-0.202897\pi\)
0.803635 + 0.595123i \(0.202897\pi\)
\(728\) −50.6935 −1.87882
\(729\) −43.5068 −1.61136
\(730\) 0 0
\(731\) 9.98139 0.369175
\(732\) −4.24413 −0.156868
\(733\) 6.99674 0.258431 0.129215 0.991617i \(-0.458754\pi\)
0.129215 + 0.991617i \(0.458754\pi\)
\(734\) 40.1975 1.48372
\(735\) 0 0
\(736\) −18.0274 −0.664499
\(737\) −4.28126 −0.157702
\(738\) 4.64807 0.171098
\(739\) −1.44307 −0.0530842 −0.0265421 0.999648i \(-0.508450\pi\)
−0.0265421 + 0.999648i \(0.508450\pi\)
\(740\) 0 0
\(741\) −58.8340 −2.16132
\(742\) 0.0556503 0.00204299
\(743\) 4.24266 0.155648 0.0778240 0.996967i \(-0.475203\pi\)
0.0778240 + 0.996967i \(0.475203\pi\)
\(744\) −75.1495 −2.75511
\(745\) 0 0
\(746\) 3.01958 0.110555
\(747\) −36.5481 −1.33723
\(748\) 1.96723 0.0719292
\(749\) −13.9351 −0.509179
\(750\) 0 0
\(751\) 19.0193 0.694024 0.347012 0.937861i \(-0.387196\pi\)
0.347012 + 0.937861i \(0.387196\pi\)
\(752\) −10.2565 −0.374016
\(753\) 46.4206 1.69166
\(754\) −48.1063 −1.75193
\(755\) 0 0
\(756\) −9.04771 −0.329062
\(757\) −0.151878 −0.00552010 −0.00276005 0.999996i \(-0.500879\pi\)
−0.00276005 + 0.999996i \(0.500879\pi\)
\(758\) −34.2105 −1.24258
\(759\) 20.8560 0.757025
\(760\) 0 0
\(761\) −16.2184 −0.587916 −0.293958 0.955818i \(-0.594973\pi\)
−0.293958 + 0.955818i \(0.594973\pi\)
\(762\) −30.3325 −1.09883
\(763\) 29.2790 1.05997
\(764\) 3.70880 0.134180
\(765\) 0 0
\(766\) −50.5819 −1.82760
\(767\) −42.6417 −1.53970
\(768\) −25.9027 −0.934682
\(769\) 5.32816 0.192138 0.0960691 0.995375i \(-0.469373\pi\)
0.0960691 + 0.995375i \(0.469373\pi\)
\(770\) 0 0
\(771\) −27.7752 −1.00030
\(772\) 0.507137 0.0182523
\(773\) 6.19612 0.222859 0.111430 0.993772i \(-0.464457\pi\)
0.111430 + 0.993772i \(0.464457\pi\)
\(774\) −14.0588 −0.505333
\(775\) 0 0
\(776\) 15.7106 0.563976
\(777\) 61.6961 2.21334
\(778\) 2.47139 0.0886036
\(779\) 2.66247 0.0953929
\(780\) 0 0
\(781\) 1.36117 0.0487064
\(782\) 67.6527 2.41925
\(783\) 34.4768 1.23210
\(784\) −51.1652 −1.82733
\(785\) 0 0
\(786\) 30.5660 1.09025
\(787\) −26.4924 −0.944351 −0.472176 0.881504i \(-0.656531\pi\)
−0.472176 + 0.881504i \(0.656531\pi\)
\(788\) −3.79314 −0.135125
\(789\) −88.7604 −3.15996
\(790\) 0 0
\(791\) 61.4589 2.18523
\(792\) 11.1263 0.395356
\(793\) −18.2277 −0.647283
\(794\) −31.7602 −1.12713
\(795\) 0 0
\(796\) −7.36823 −0.261160
\(797\) −41.8090 −1.48095 −0.740476 0.672083i \(-0.765400\pi\)
−0.740476 + 0.672083i \(0.765400\pi\)
\(798\) −80.3761 −2.84528
\(799\) 11.9163 0.421567
\(800\) 0 0
\(801\) −2.55201 −0.0901707
\(802\) −3.89416 −0.137508
\(803\) 9.48648 0.334770
\(804\) 5.24215 0.184877
\(805\) 0 0
\(806\) 80.3766 2.83115
\(807\) −11.8486 −0.417090
\(808\) 17.8721 0.628737
\(809\) 1.66235 0.0584451 0.0292226 0.999573i \(-0.490697\pi\)
0.0292226 + 0.999573i \(0.490697\pi\)
\(810\) 0 0
\(811\) −13.4156 −0.471085 −0.235542 0.971864i \(-0.575687\pi\)
−0.235542 + 0.971864i \(0.575687\pi\)
\(812\) −10.9252 −0.383399
\(813\) −33.1851 −1.16385
\(814\) 7.32869 0.256870
\(815\) 0 0
\(816\) 70.2651 2.45977
\(817\) −8.05304 −0.281740
\(818\) 6.19369 0.216557
\(819\) −100.181 −3.50061
\(820\) 0 0
\(821\) 23.1210 0.806930 0.403465 0.914995i \(-0.367806\pi\)
0.403465 + 0.914995i \(0.367806\pi\)
\(822\) −25.1674 −0.877814
\(823\) −20.7084 −0.721849 −0.360924 0.932595i \(-0.617539\pi\)
−0.360924 + 0.932595i \(0.617539\pi\)
\(824\) −19.4118 −0.676241
\(825\) 0 0
\(826\) −58.2550 −2.02695
\(827\) 1.22288 0.0425235 0.0212618 0.999774i \(-0.493232\pi\)
0.0212618 + 0.999774i \(0.493232\pi\)
\(828\) −15.8406 −0.550498
\(829\) 26.5008 0.920411 0.460205 0.887813i \(-0.347776\pi\)
0.460205 + 0.887813i \(0.347776\pi\)
\(830\) 0 0
\(831\) 22.5239 0.781344
\(832\) −28.0762 −0.973368
\(833\) 59.4450 2.05965
\(834\) 10.2280 0.354165
\(835\) 0 0
\(836\) −1.58718 −0.0548936
\(837\) −57.6043 −1.99110
\(838\) −29.9795 −1.03562
\(839\) 27.5572 0.951380 0.475690 0.879613i \(-0.342198\pi\)
0.475690 + 0.879613i \(0.342198\pi\)
\(840\) 0 0
\(841\) 12.6310 0.435553
\(842\) 7.45750 0.257003
\(843\) 60.9169 2.09809
\(844\) 2.21099 0.0761053
\(845\) 0 0
\(846\) −16.7840 −0.577047
\(847\) −43.1503 −1.48266
\(848\) 0.0392508 0.00134788
\(849\) 6.06152 0.208031
\(850\) 0 0
\(851\) 41.8972 1.43622
\(852\) −1.66667 −0.0570992
\(853\) −14.3366 −0.490875 −0.245437 0.969412i \(-0.578932\pi\)
−0.245437 + 0.969412i \(0.578932\pi\)
\(854\) −24.9017 −0.852119
\(855\) 0 0
\(856\) −8.13872 −0.278176
\(857\) −33.5953 −1.14759 −0.573796 0.818998i \(-0.694530\pi\)
−0.573796 + 0.818998i \(0.694530\pi\)
\(858\) −19.1846 −0.654951
\(859\) −31.1946 −1.06435 −0.532173 0.846635i \(-0.678625\pi\)
−0.532173 + 0.846635i \(0.678625\pi\)
\(860\) 0 0
\(861\) 7.30870 0.249080
\(862\) −41.5470 −1.41510
\(863\) −23.3830 −0.795965 −0.397983 0.917393i \(-0.630290\pi\)
−0.397983 + 0.917393i \(0.630290\pi\)
\(864\) −11.8845 −0.404318
\(865\) 0 0
\(866\) 2.46605 0.0837999
\(867\) −33.8510 −1.14964
\(868\) 18.2540 0.619580
\(869\) −16.1833 −0.548981
\(870\) 0 0
\(871\) 22.5139 0.762856
\(872\) 17.1002 0.579086
\(873\) 31.0474 1.05080
\(874\) −54.5825 −1.84628
\(875\) 0 0
\(876\) −11.6156 −0.392456
\(877\) 35.6526 1.20390 0.601951 0.798533i \(-0.294390\pi\)
0.601951 + 0.798533i \(0.294390\pi\)
\(878\) 56.5565 1.90869
\(879\) 75.7585 2.55527
\(880\) 0 0
\(881\) 29.7222 1.00137 0.500683 0.865631i \(-0.333082\pi\)
0.500683 + 0.865631i \(0.333082\pi\)
\(882\) −83.7283 −2.81928
\(883\) 41.7428 1.40476 0.702379 0.711803i \(-0.252121\pi\)
0.702379 + 0.711803i \(0.252121\pi\)
\(884\) −10.3451 −0.347944
\(885\) 0 0
\(886\) −1.97396 −0.0663165
\(887\) 2.72462 0.0914838 0.0457419 0.998953i \(-0.485435\pi\)
0.0457419 + 0.998953i \(0.485435\pi\)
\(888\) 36.0332 1.20919
\(889\) −29.5854 −0.992263
\(890\) 0 0
\(891\) 0.289882 0.00971140
\(892\) 5.14345 0.172215
\(893\) −9.61410 −0.321724
\(894\) 19.3349 0.646657
\(895\) 0 0
\(896\) −57.2448 −1.91241
\(897\) −109.676 −3.66197
\(898\) −49.4797 −1.65116
\(899\) −69.5577 −2.31988
\(900\) 0 0
\(901\) −0.0456026 −0.00151924
\(902\) 0.868178 0.0289072
\(903\) −22.1063 −0.735650
\(904\) 35.8946 1.19384
\(905\) 0 0
\(906\) −23.2313 −0.771808
\(907\) 19.4428 0.645587 0.322794 0.946469i \(-0.395378\pi\)
0.322794 + 0.946469i \(0.395378\pi\)
\(908\) −1.13835 −0.0377775
\(909\) 35.3190 1.17146
\(910\) 0 0
\(911\) 35.4707 1.17520 0.587598 0.809153i \(-0.300074\pi\)
0.587598 + 0.809153i \(0.300074\pi\)
\(912\) −56.6902 −1.87720
\(913\) −6.82655 −0.225926
\(914\) 19.9115 0.658614
\(915\) 0 0
\(916\) −6.44821 −0.213055
\(917\) 29.8131 0.984516
\(918\) 44.5997 1.47201
\(919\) 30.5669 1.00831 0.504154 0.863614i \(-0.331804\pi\)
0.504154 + 0.863614i \(0.331804\pi\)
\(920\) 0 0
\(921\) 46.7396 1.54012
\(922\) −55.2441 −1.81937
\(923\) −7.15799 −0.235608
\(924\) −4.35693 −0.143332
\(925\) 0 0
\(926\) 4.25092 0.139694
\(927\) −38.3618 −1.25997
\(928\) −14.3506 −0.471082
\(929\) −59.7630 −1.96076 −0.980380 0.197116i \(-0.936842\pi\)
−0.980380 + 0.197116i \(0.936842\pi\)
\(930\) 0 0
\(931\) −47.9605 −1.57184
\(932\) −4.53762 −0.148635
\(933\) 28.5111 0.933413
\(934\) −39.6389 −1.29702
\(935\) 0 0
\(936\) −58.5101 −1.91246
\(937\) −29.4112 −0.960824 −0.480412 0.877043i \(-0.659513\pi\)
−0.480412 + 0.877043i \(0.659513\pi\)
\(938\) 30.7574 1.00427
\(939\) −75.1577 −2.45268
\(940\) 0 0
\(941\) 45.0066 1.46717 0.733587 0.679595i \(-0.237845\pi\)
0.733587 + 0.679595i \(0.237845\pi\)
\(942\) 94.0901 3.06562
\(943\) 4.96326 0.161626
\(944\) −41.0879 −1.33730
\(945\) 0 0
\(946\) −2.62594 −0.0853765
\(947\) 10.4456 0.339437 0.169719 0.985493i \(-0.445714\pi\)
0.169719 + 0.985493i \(0.445714\pi\)
\(948\) 19.8155 0.643578
\(949\) −49.8867 −1.61939
\(950\) 0 0
\(951\) −72.0815 −2.33740
\(952\) 56.7509 1.83931
\(953\) 48.6114 1.57468 0.787339 0.616521i \(-0.211458\pi\)
0.787339 + 0.616521i \(0.211458\pi\)
\(954\) 0.0642313 0.00207956
\(955\) 0 0
\(956\) 10.7809 0.348680
\(957\) 16.6023 0.536676
\(958\) 0.946131 0.0305681
\(959\) −24.5475 −0.792681
\(960\) 0 0
\(961\) 85.2180 2.74897
\(962\) −38.5395 −1.24256
\(963\) −16.0839 −0.518295
\(964\) 0.398765 0.0128434
\(965\) 0 0
\(966\) −149.834 −4.82082
\(967\) 28.8087 0.926426 0.463213 0.886247i \(-0.346697\pi\)
0.463213 + 0.886247i \(0.346697\pi\)
\(968\) −25.2016 −0.810011
\(969\) 65.8642 2.11586
\(970\) 0 0
\(971\) −4.01498 −0.128847 −0.0644234 0.997923i \(-0.520521\pi\)
−0.0644234 + 0.997923i \(0.520521\pi\)
\(972\) 6.03734 0.193648
\(973\) 9.97605 0.319817
\(974\) 41.2397 1.32140
\(975\) 0 0
\(976\) −17.5635 −0.562193
\(977\) −4.44163 −0.142100 −0.0710501 0.997473i \(-0.522635\pi\)
−0.0710501 + 0.997473i \(0.522635\pi\)
\(978\) 96.2111 3.07649
\(979\) −0.476670 −0.0152344
\(980\) 0 0
\(981\) 33.7937 1.07895
\(982\) 49.2294 1.57097
\(983\) 16.5283 0.527172 0.263586 0.964636i \(-0.415095\pi\)
0.263586 + 0.964636i \(0.415095\pi\)
\(984\) 4.26860 0.136078
\(985\) 0 0
\(986\) 53.8545 1.71508
\(987\) −26.3915 −0.840051
\(988\) 8.34651 0.265538
\(989\) −15.0121 −0.477358
\(990\) 0 0
\(991\) 34.8094 1.10576 0.552878 0.833262i \(-0.313530\pi\)
0.552878 + 0.833262i \(0.313530\pi\)
\(992\) 23.9772 0.761278
\(993\) −61.6081 −1.95507
\(994\) −9.77890 −0.310168
\(995\) 0 0
\(996\) 8.35872 0.264856
\(997\) 14.7239 0.466312 0.233156 0.972439i \(-0.425095\pi\)
0.233156 + 0.972439i \(0.425095\pi\)
\(998\) 26.7118 0.845547
\(999\) 27.6205 0.873874
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 \(a_p\))