Properties

Label 6018.2.a.p.1.1
Level 6018
Weight 2
Character 6018.1
Self dual Yes
Analytic conductor 48.054
Analytic rank 0
Dimension 5
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1668357.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.117900\)
Character \(\chi\) = 6018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.56570 q^{5}\) \(-1.00000 q^{6}\) \(-0.117900 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-3.56570 q^{5}\) \(-1.00000 q^{6}\) \(-0.117900 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.56570 q^{10}\) \(+6.11159 q^{11}\) \(+1.00000 q^{12}\) \(+3.74796 q^{13}\) \(+0.117900 q^{14}\) \(-3.56570 q^{15}\) \(+1.00000 q^{16}\) \(-1.00000 q^{17}\) \(-1.00000 q^{18}\) \(-0.663784 q^{19}\) \(-3.56570 q^{20}\) \(-0.117900 q^{21}\) \(-6.11159 q^{22}\) \(+8.53198 q^{23}\) \(-1.00000 q^{24}\) \(+7.71424 q^{25}\) \(-3.74796 q^{26}\) \(+1.00000 q^{27}\) \(-0.117900 q^{28}\) \(+7.62248 q^{29}\) \(+3.56570 q^{30}\) \(-7.73406 q^{31}\) \(-1.00000 q^{32}\) \(+6.11159 q^{33}\) \(+1.00000 q^{34}\) \(+0.420396 q^{35}\) \(+1.00000 q^{36}\) \(-2.71732 q^{37}\) \(+0.663784 q^{38}\) \(+3.74796 q^{39}\) \(+3.56570 q^{40}\) \(-4.76778 q^{41}\) \(+0.117900 q^{42}\) \(+0.835224 q^{43}\) \(+6.11159 q^{44}\) \(-3.56570 q^{45}\) \(-8.53198 q^{46}\) \(+2.98777 q^{47}\) \(+1.00000 q^{48}\) \(-6.98610 q^{49}\) \(-7.71424 q^{50}\) \(-1.00000 q^{51}\) \(+3.74796 q^{52}\) \(+5.50134 q^{53}\) \(-1.00000 q^{54}\) \(-21.7921 q^{55}\) \(+0.117900 q^{56}\) \(-0.663784 q^{57}\) \(-7.62248 q^{58}\) \(-1.00000 q^{59}\) \(-3.56570 q^{60}\) \(+5.26321 q^{61}\) \(+7.73406 q^{62}\) \(-0.117900 q^{63}\) \(+1.00000 q^{64}\) \(-13.3641 q^{65}\) \(-6.11159 q^{66}\) \(+13.6706 q^{67}\) \(-1.00000 q^{68}\) \(+8.53198 q^{69}\) \(-0.420396 q^{70}\) \(+3.38434 q^{71}\) \(-1.00000 q^{72}\) \(-16.0203 q^{73}\) \(+2.71732 q^{74}\) \(+7.71424 q^{75}\) \(-0.663784 q^{76}\) \(-0.720555 q^{77}\) \(-3.74796 q^{78}\) \(+0.152544 q^{79}\) \(-3.56570 q^{80}\) \(+1.00000 q^{81}\) \(+4.76778 q^{82}\) \(+6.37444 q^{83}\) \(-0.117900 q^{84}\) \(+3.56570 q^{85}\) \(-0.835224 q^{86}\) \(+7.62248 q^{87}\) \(-6.11159 q^{88}\) \(-3.96986 q^{89}\) \(+3.56570 q^{90}\) \(-0.441884 q^{91}\) \(+8.53198 q^{92}\) \(-7.73406 q^{93}\) \(-2.98777 q^{94}\) \(+2.36686 q^{95}\) \(-1.00000 q^{96}\) \(+2.65620 q^{97}\) \(+6.98610 q^{98}\) \(+6.11159 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(5q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 5q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 5q^{24} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 19q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 5q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 5q^{36} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut -\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut -\mathstrut 36q^{55} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 19q^{58} \) \(\mathstrut -\mathstrut 5q^{59} \) \(\mathstrut -\mathstrut q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 5q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 5q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 5q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut +\mathstrut 19q^{83} \) \(\mathstrut -\mathstrut q^{84} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut +\mathstrut 19q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 22q^{94} \) \(\mathstrut +\mathstrut q^{95} \) \(\mathstrut -\mathstrut 5q^{96} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 12q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −3.56570 −1.59463 −0.797316 0.603563i \(-0.793747\pi\)
−0.797316 + 0.603563i \(0.793747\pi\)
\(6\) −1.00000 −0.408248
\(7\) −0.117900 −0.0445620 −0.0222810 0.999752i \(-0.507093\pi\)
−0.0222810 + 0.999752i \(0.507093\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.56570 1.12757
\(11\) 6.11159 1.84271 0.921356 0.388719i \(-0.127082\pi\)
0.921356 + 0.388719i \(0.127082\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.74796 1.03950 0.519749 0.854319i \(-0.326025\pi\)
0.519749 + 0.854319i \(0.326025\pi\)
\(14\) 0.117900 0.0315101
\(15\) −3.56570 −0.920661
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) −0.663784 −0.152282 −0.0761412 0.997097i \(-0.524260\pi\)
−0.0761412 + 0.997097i \(0.524260\pi\)
\(20\) −3.56570 −0.797316
\(21\) −0.117900 −0.0257279
\(22\) −6.11159 −1.30299
\(23\) 8.53198 1.77904 0.889521 0.456895i \(-0.151038\pi\)
0.889521 + 0.456895i \(0.151038\pi\)
\(24\) −1.00000 −0.204124
\(25\) 7.71424 1.54285
\(26\) −3.74796 −0.735036
\(27\) 1.00000 0.192450
\(28\) −0.117900 −0.0222810
\(29\) 7.62248 1.41546 0.707729 0.706484i \(-0.249720\pi\)
0.707729 + 0.706484i \(0.249720\pi\)
\(30\) 3.56570 0.651005
\(31\) −7.73406 −1.38908 −0.694539 0.719455i \(-0.744392\pi\)
−0.694539 + 0.719455i \(0.744392\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.11159 1.06389
\(34\) 1.00000 0.171499
\(35\) 0.420396 0.0710599
\(36\) 1.00000 0.166667
\(37\) −2.71732 −0.446725 −0.223363 0.974735i \(-0.571703\pi\)
−0.223363 + 0.974735i \(0.571703\pi\)
\(38\) 0.663784 0.107680
\(39\) 3.74796 0.600154
\(40\) 3.56570 0.563787
\(41\) −4.76778 −0.744603 −0.372301 0.928112i \(-0.621431\pi\)
−0.372301 + 0.928112i \(0.621431\pi\)
\(42\) 0.117900 0.0181923
\(43\) 0.835224 0.127370 0.0636852 0.997970i \(-0.479715\pi\)
0.0636852 + 0.997970i \(0.479715\pi\)
\(44\) 6.11159 0.921356
\(45\) −3.56570 −0.531544
\(46\) −8.53198 −1.25797
\(47\) 2.98777 0.435811 0.217905 0.975970i \(-0.430078\pi\)
0.217905 + 0.975970i \(0.430078\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.98610 −0.998014
\(50\) −7.71424 −1.09096
\(51\) −1.00000 −0.140028
\(52\) 3.74796 0.519749
\(53\) 5.50134 0.755668 0.377834 0.925873i \(-0.376669\pi\)
0.377834 + 0.925873i \(0.376669\pi\)
\(54\) −1.00000 −0.136083
\(55\) −21.7921 −2.93845
\(56\) 0.117900 0.0157550
\(57\) −0.663784 −0.0879203
\(58\) −7.62248 −1.00088
\(59\) −1.00000 −0.130189
\(60\) −3.56570 −0.460330
\(61\) 5.26321 0.673885 0.336942 0.941525i \(-0.390607\pi\)
0.336942 + 0.941525i \(0.390607\pi\)
\(62\) 7.73406 0.982227
\(63\) −0.117900 −0.0148540
\(64\) 1.00000 0.125000
\(65\) −13.3641 −1.65762
\(66\) −6.11159 −0.752284
\(67\) 13.6706 1.67013 0.835065 0.550152i \(-0.185430\pi\)
0.835065 + 0.550152i \(0.185430\pi\)
\(68\) −1.00000 −0.121268
\(69\) 8.53198 1.02713
\(70\) −0.420396 −0.0502469
\(71\) 3.38434 0.401647 0.200824 0.979627i \(-0.435638\pi\)
0.200824 + 0.979627i \(0.435638\pi\)
\(72\) −1.00000 −0.117851
\(73\) −16.0203 −1.87504 −0.937518 0.347936i \(-0.886883\pi\)
−0.937518 + 0.347936i \(0.886883\pi\)
\(74\) 2.71732 0.315882
\(75\) 7.71424 0.890764
\(76\) −0.663784 −0.0761412
\(77\) −0.720555 −0.0821149
\(78\) −3.74796 −0.424373
\(79\) 0.152544 0.0171626 0.00858129 0.999963i \(-0.497268\pi\)
0.00858129 + 0.999963i \(0.497268\pi\)
\(80\) −3.56570 −0.398658
\(81\) 1.00000 0.111111
\(82\) 4.76778 0.526514
\(83\) 6.37444 0.699686 0.349843 0.936808i \(-0.386235\pi\)
0.349843 + 0.936808i \(0.386235\pi\)
\(84\) −0.117900 −0.0128639
\(85\) 3.56570 0.386755
\(86\) −0.835224 −0.0900645
\(87\) 7.62248 0.817215
\(88\) −6.11159 −0.651497
\(89\) −3.96986 −0.420805 −0.210402 0.977615i \(-0.567477\pi\)
−0.210402 + 0.977615i \(0.567477\pi\)
\(90\) 3.56570 0.375858
\(91\) −0.441884 −0.0463221
\(92\) 8.53198 0.889521
\(93\) −7.73406 −0.801985
\(94\) −2.98777 −0.308165
\(95\) 2.36686 0.242834
\(96\) −1.00000 −0.102062
\(97\) 2.65620 0.269696 0.134848 0.990866i \(-0.456945\pi\)
0.134848 + 0.990866i \(0.456945\pi\)
\(98\) 6.98610 0.705703
\(99\) 6.11159 0.614238
\(100\) 7.71424 0.771424
\(101\) 12.3259 1.22647 0.613236 0.789899i \(-0.289867\pi\)
0.613236 + 0.789899i \(0.289867\pi\)
\(102\) 1.00000 0.0990148
\(103\) −17.3019 −1.70481 −0.852405 0.522882i \(-0.824857\pi\)
−0.852405 + 0.522882i \(0.824857\pi\)
\(104\) −3.74796 −0.367518
\(105\) 0.420396 0.0410264
\(106\) −5.50134 −0.534338
\(107\) −7.61744 −0.736406 −0.368203 0.929746i \(-0.620027\pi\)
−0.368203 + 0.929746i \(0.620027\pi\)
\(108\) 1.00000 0.0962250
\(109\) −4.84838 −0.464391 −0.232195 0.972669i \(-0.574591\pi\)
−0.232195 + 0.972669i \(0.574591\pi\)
\(110\) 21.7921 2.07780
\(111\) −2.71732 −0.257917
\(112\) −0.117900 −0.0111405
\(113\) 9.80909 0.922762 0.461381 0.887202i \(-0.347354\pi\)
0.461381 + 0.887202i \(0.347354\pi\)
\(114\) 0.663784 0.0621690
\(115\) −30.4225 −2.83692
\(116\) 7.62248 0.707729
\(117\) 3.74796 0.346499
\(118\) 1.00000 0.0920575
\(119\) 0.117900 0.0108079
\(120\) 3.56570 0.325503
\(121\) 26.3515 2.39559
\(122\) −5.26321 −0.476508
\(123\) −4.76778 −0.429897
\(124\) −7.73406 −0.694539
\(125\) −9.67819 −0.865643
\(126\) 0.117900 0.0105034
\(127\) −8.67239 −0.769550 −0.384775 0.923010i \(-0.625721\pi\)
−0.384775 + 0.923010i \(0.625721\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.835224 0.0735373
\(130\) 13.3641 1.17211
\(131\) 12.2080 1.06662 0.533309 0.845921i \(-0.320948\pi\)
0.533309 + 0.845921i \(0.320948\pi\)
\(132\) 6.11159 0.531945
\(133\) 0.0782600 0.00678600
\(134\) −13.6706 −1.18096
\(135\) −3.56570 −0.306887
\(136\) 1.00000 0.0857493
\(137\) −22.0193 −1.88123 −0.940616 0.339472i \(-0.889752\pi\)
−0.940616 + 0.339472i \(0.889752\pi\)
\(138\) −8.53198 −0.726291
\(139\) −5.98287 −0.507460 −0.253730 0.967275i \(-0.581658\pi\)
−0.253730 + 0.967275i \(0.581658\pi\)
\(140\) 0.420396 0.0355299
\(141\) 2.98777 0.251615
\(142\) −3.38434 −0.284007
\(143\) 22.9060 1.91550
\(144\) 1.00000 0.0833333
\(145\) −27.1795 −2.25713
\(146\) 16.0203 1.32585
\(147\) −6.98610 −0.576204
\(148\) −2.71732 −0.223363
\(149\) −0.239031 −0.0195822 −0.00979109 0.999952i \(-0.503117\pi\)
−0.00979109 + 0.999952i \(0.503117\pi\)
\(150\) −7.71424 −0.629865
\(151\) −4.91184 −0.399720 −0.199860 0.979824i \(-0.564049\pi\)
−0.199860 + 0.979824i \(0.564049\pi\)
\(152\) 0.663784 0.0538400
\(153\) −1.00000 −0.0808452
\(154\) 0.720555 0.0580640
\(155\) 27.5774 2.21507
\(156\) 3.74796 0.300077
\(157\) 2.51989 0.201109 0.100554 0.994932i \(-0.467938\pi\)
0.100554 + 0.994932i \(0.467938\pi\)
\(158\) −0.152544 −0.0121358
\(159\) 5.50134 0.436285
\(160\) 3.56570 0.281894
\(161\) −1.00592 −0.0792776
\(162\) −1.00000 −0.0785674
\(163\) 6.47521 0.507178 0.253589 0.967312i \(-0.418389\pi\)
0.253589 + 0.967312i \(0.418389\pi\)
\(164\) −4.76778 −0.372301
\(165\) −21.7921 −1.69651
\(166\) −6.37444 −0.494753
\(167\) −21.3686 −1.65355 −0.826777 0.562529i \(-0.809828\pi\)
−0.826777 + 0.562529i \(0.809828\pi\)
\(168\) 0.117900 0.00909617
\(169\) 1.04723 0.0805560
\(170\) −3.56570 −0.273477
\(171\) −0.663784 −0.0507608
\(172\) 0.835224 0.0636852
\(173\) 4.59815 0.349591 0.174795 0.984605i \(-0.444074\pi\)
0.174795 + 0.984605i \(0.444074\pi\)
\(174\) −7.62248 −0.577858
\(175\) −0.909508 −0.0687523
\(176\) 6.11159 0.460678
\(177\) −1.00000 −0.0751646
\(178\) 3.96986 0.297554
\(179\) −13.2291 −0.988789 −0.494394 0.869238i \(-0.664610\pi\)
−0.494394 + 0.869238i \(0.664610\pi\)
\(180\) −3.56570 −0.265772
\(181\) −3.72222 −0.276671 −0.138335 0.990385i \(-0.544175\pi\)
−0.138335 + 0.990385i \(0.544175\pi\)
\(182\) 0.441884 0.0327546
\(183\) 5.26321 0.389068
\(184\) −8.53198 −0.628986
\(185\) 9.68917 0.712362
\(186\) 7.73406 0.567089
\(187\) −6.11159 −0.446924
\(188\) 2.98777 0.217905
\(189\) −0.117900 −0.00857595
\(190\) −2.36686 −0.171710
\(191\) 19.3258 1.39836 0.699182 0.714944i \(-0.253548\pi\)
0.699182 + 0.714944i \(0.253548\pi\)
\(192\) 1.00000 0.0721688
\(193\) −3.37044 −0.242609 −0.121305 0.992615i \(-0.538708\pi\)
−0.121305 + 0.992615i \(0.538708\pi\)
\(194\) −2.65620 −0.190704
\(195\) −13.3641 −0.957025
\(196\) −6.98610 −0.499007
\(197\) 14.7678 1.05216 0.526080 0.850435i \(-0.323661\pi\)
0.526080 + 0.850435i \(0.323661\pi\)
\(198\) −6.11159 −0.434332
\(199\) 9.14722 0.648429 0.324215 0.945984i \(-0.394900\pi\)
0.324215 + 0.945984i \(0.394900\pi\)
\(200\) −7.71424 −0.545479
\(201\) 13.6706 0.964250
\(202\) −12.3259 −0.867247
\(203\) −0.898689 −0.0630756
\(204\) −1.00000 −0.0700140
\(205\) 17.0005 1.18737
\(206\) 17.3019 1.20548
\(207\) 8.53198 0.593014
\(208\) 3.74796 0.259874
\(209\) −4.05677 −0.280613
\(210\) −0.420396 −0.0290101
\(211\) 25.5797 1.76098 0.880490 0.474065i \(-0.157214\pi\)
0.880490 + 0.474065i \(0.157214\pi\)
\(212\) 5.50134 0.377834
\(213\) 3.38434 0.231891
\(214\) 7.61744 0.520717
\(215\) −2.97816 −0.203109
\(216\) −1.00000 −0.0680414
\(217\) 0.911845 0.0619001
\(218\) 4.84838 0.328374
\(219\) −16.0203 −1.08255
\(220\) −21.7921 −1.46922
\(221\) −3.74796 −0.252115
\(222\) 2.71732 0.182375
\(223\) 23.7681 1.59163 0.795816 0.605539i \(-0.207042\pi\)
0.795816 + 0.605539i \(0.207042\pi\)
\(224\) 0.117900 0.00787752
\(225\) 7.71424 0.514283
\(226\) −9.80909 −0.652491
\(227\) 14.6124 0.969860 0.484930 0.874553i \(-0.338845\pi\)
0.484930 + 0.874553i \(0.338845\pi\)
\(228\) −0.663784 −0.0439601
\(229\) 22.3800 1.47891 0.739455 0.673206i \(-0.235083\pi\)
0.739455 + 0.673206i \(0.235083\pi\)
\(230\) 30.4225 2.00600
\(231\) −0.720555 −0.0474091
\(232\) −7.62248 −0.500440
\(233\) 16.9609 1.11114 0.555572 0.831469i \(-0.312500\pi\)
0.555572 + 0.831469i \(0.312500\pi\)
\(234\) −3.74796 −0.245012
\(235\) −10.6535 −0.694957
\(236\) −1.00000 −0.0650945
\(237\) 0.152544 0.00990882
\(238\) −0.117900 −0.00764231
\(239\) −9.32948 −0.603474 −0.301737 0.953391i \(-0.597566\pi\)
−0.301737 + 0.953391i \(0.597566\pi\)
\(240\) −3.56570 −0.230165
\(241\) 6.64255 0.427884 0.213942 0.976846i \(-0.431370\pi\)
0.213942 + 0.976846i \(0.431370\pi\)
\(242\) −26.3515 −1.69394
\(243\) 1.00000 0.0641500
\(244\) 5.26321 0.336942
\(245\) 24.9104 1.59146
\(246\) 4.76778 0.303983
\(247\) −2.48784 −0.158297
\(248\) 7.73406 0.491113
\(249\) 6.37444 0.403964
\(250\) 9.67819 0.612102
\(251\) 4.91450 0.310201 0.155100 0.987899i \(-0.450430\pi\)
0.155100 + 0.987899i \(0.450430\pi\)
\(252\) −0.117900 −0.00742699
\(253\) 52.1440 3.27826
\(254\) 8.67239 0.544154
\(255\) 3.56570 0.223293
\(256\) 1.00000 0.0625000
\(257\) −24.6585 −1.53815 −0.769077 0.639156i \(-0.779284\pi\)
−0.769077 + 0.639156i \(0.779284\pi\)
\(258\) −0.835224 −0.0519988
\(259\) 0.320372 0.0199070
\(260\) −13.3641 −0.828808
\(261\) 7.62248 0.471819
\(262\) −12.2080 −0.754213
\(263\) −6.42580 −0.396232 −0.198116 0.980179i \(-0.563482\pi\)
−0.198116 + 0.980179i \(0.563482\pi\)
\(264\) −6.11159 −0.376142
\(265\) −19.6162 −1.20501
\(266\) −0.0782600 −0.00479843
\(267\) −3.96986 −0.242952
\(268\) 13.6706 0.835065
\(269\) 0.159710 0.00973769 0.00486884 0.999988i \(-0.498450\pi\)
0.00486884 + 0.999988i \(0.498450\pi\)
\(270\) 3.56570 0.217002
\(271\) 1.81105 0.110013 0.0550066 0.998486i \(-0.482482\pi\)
0.0550066 + 0.998486i \(0.482482\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −0.441884 −0.0267441
\(274\) 22.0193 1.33023
\(275\) 47.1463 2.84303
\(276\) 8.53198 0.513565
\(277\) 27.4820 1.65123 0.825617 0.564230i \(-0.190827\pi\)
0.825617 + 0.564230i \(0.190827\pi\)
\(278\) 5.98287 0.358829
\(279\) −7.73406 −0.463026
\(280\) −0.420396 −0.0251235
\(281\) 31.2878 1.86647 0.933236 0.359263i \(-0.116972\pi\)
0.933236 + 0.359263i \(0.116972\pi\)
\(282\) −2.98777 −0.177919
\(283\) −16.0077 −0.951561 −0.475781 0.879564i \(-0.657834\pi\)
−0.475781 + 0.879564i \(0.657834\pi\)
\(284\) 3.38434 0.200824
\(285\) 2.36686 0.140200
\(286\) −22.9060 −1.35446
\(287\) 0.562121 0.0331809
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 27.1795 1.59603
\(291\) 2.65620 0.155709
\(292\) −16.0203 −0.937518
\(293\) 19.2486 1.12451 0.562257 0.826963i \(-0.309933\pi\)
0.562257 + 0.826963i \(0.309933\pi\)
\(294\) 6.98610 0.407438
\(295\) 3.56570 0.207603
\(296\) 2.71732 0.157941
\(297\) 6.11159 0.354630
\(298\) 0.239031 0.0138467
\(299\) 31.9776 1.84931
\(300\) 7.71424 0.445382
\(301\) −0.0984727 −0.00567587
\(302\) 4.91184 0.282645
\(303\) 12.3259 0.708104
\(304\) −0.663784 −0.0380706
\(305\) −18.7670 −1.07460
\(306\) 1.00000 0.0571662
\(307\) −6.54982 −0.373818 −0.186909 0.982377i \(-0.559847\pi\)
−0.186909 + 0.982377i \(0.559847\pi\)
\(308\) −0.720555 −0.0410574
\(309\) −17.3019 −0.984273
\(310\) −27.5774 −1.56629
\(311\) 27.1871 1.54164 0.770820 0.637053i \(-0.219847\pi\)
0.770820 + 0.637053i \(0.219847\pi\)
\(312\) −3.74796 −0.212187
\(313\) 21.1346 1.19460 0.597299 0.802019i \(-0.296241\pi\)
0.597299 + 0.802019i \(0.296241\pi\)
\(314\) −2.51989 −0.142206
\(315\) 0.420396 0.0236866
\(316\) 0.152544 0.00858129
\(317\) −17.5500 −0.985706 −0.492853 0.870113i \(-0.664046\pi\)
−0.492853 + 0.870113i \(0.664046\pi\)
\(318\) −5.50134 −0.308500
\(319\) 46.5854 2.60828
\(320\) −3.56570 −0.199329
\(321\) −7.61744 −0.425164
\(322\) 1.00592 0.0560577
\(323\) 0.663784 0.0369339
\(324\) 1.00000 0.0555556
\(325\) 28.9127 1.60379
\(326\) −6.47521 −0.358629
\(327\) −4.84838 −0.268116
\(328\) 4.76778 0.263257
\(329\) −0.352257 −0.0194206
\(330\) 21.7921 1.19962
\(331\) −31.1646 −1.71296 −0.856480 0.516181i \(-0.827353\pi\)
−0.856480 + 0.516181i \(0.827353\pi\)
\(332\) 6.37444 0.349843
\(333\) −2.71732 −0.148908
\(334\) 21.3686 1.16924
\(335\) −48.7453 −2.66324
\(336\) −0.117900 −0.00643196
\(337\) 3.30735 0.180163 0.0900815 0.995934i \(-0.471287\pi\)
0.0900815 + 0.995934i \(0.471287\pi\)
\(338\) −1.04723 −0.0569617
\(339\) 9.80909 0.532757
\(340\) 3.56570 0.193377
\(341\) −47.2674 −2.55967
\(342\) 0.663784 0.0358933
\(343\) 1.64896 0.0890354
\(344\) −0.835224 −0.0450322
\(345\) −30.4225 −1.63789
\(346\) −4.59815 −0.247198
\(347\) 20.2791 1.08864 0.544318 0.838879i \(-0.316788\pi\)
0.544318 + 0.838879i \(0.316788\pi\)
\(348\) 7.62248 0.408608
\(349\) −9.39605 −0.502959 −0.251480 0.967863i \(-0.580917\pi\)
−0.251480 + 0.967863i \(0.580917\pi\)
\(350\) 0.909508 0.0486153
\(351\) 3.74796 0.200051
\(352\) −6.11159 −0.325749
\(353\) 28.4262 1.51297 0.756486 0.654009i \(-0.226914\pi\)
0.756486 + 0.654009i \(0.226914\pi\)
\(354\) 1.00000 0.0531494
\(355\) −12.0675 −0.640479
\(356\) −3.96986 −0.210402
\(357\) 0.117900 0.00623992
\(358\) 13.2291 0.699179
\(359\) 1.57637 0.0831978 0.0415989 0.999134i \(-0.486755\pi\)
0.0415989 + 0.999134i \(0.486755\pi\)
\(360\) 3.56570 0.187929
\(361\) −18.5594 −0.976810
\(362\) 3.72222 0.195636
\(363\) 26.3515 1.38310
\(364\) −0.441884 −0.0231610
\(365\) 57.1237 2.98999
\(366\) −5.26321 −0.275112
\(367\) −14.0577 −0.733804 −0.366902 0.930260i \(-0.619582\pi\)
−0.366902 + 0.930260i \(0.619582\pi\)
\(368\) 8.53198 0.444760
\(369\) −4.76778 −0.248201
\(370\) −9.68917 −0.503716
\(371\) −0.648608 −0.0336740
\(372\) −7.73406 −0.400992
\(373\) 3.23349 0.167424 0.0837119 0.996490i \(-0.473322\pi\)
0.0837119 + 0.996490i \(0.473322\pi\)
\(374\) 6.11159 0.316023
\(375\) −9.67819 −0.499779
\(376\) −2.98777 −0.154082
\(377\) 28.5688 1.47137
\(378\) 0.117900 0.00606411
\(379\) −24.4567 −1.25626 −0.628129 0.778109i \(-0.716179\pi\)
−0.628129 + 0.778109i \(0.716179\pi\)
\(380\) 2.36686 0.121417
\(381\) −8.67239 −0.444300
\(382\) −19.3258 −0.988792
\(383\) −20.6255 −1.05392 −0.526958 0.849892i \(-0.676667\pi\)
−0.526958 + 0.849892i \(0.676667\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 2.56929 0.130943
\(386\) 3.37044 0.171551
\(387\) 0.835224 0.0424568
\(388\) 2.65620 0.134848
\(389\) 21.8541 1.10805 0.554024 0.832501i \(-0.313091\pi\)
0.554024 + 0.832501i \(0.313091\pi\)
\(390\) 13.3641 0.676719
\(391\) −8.53198 −0.431481
\(392\) 6.98610 0.352851
\(393\) 12.2080 0.615812
\(394\) −14.7678 −0.743990
\(395\) −0.543928 −0.0273680
\(396\) 6.11159 0.307119
\(397\) 6.27040 0.314702 0.157351 0.987543i \(-0.449705\pi\)
0.157351 + 0.987543i \(0.449705\pi\)
\(398\) −9.14722 −0.458509
\(399\) 0.0782600 0.00391790
\(400\) 7.71424 0.385712
\(401\) 26.2543 1.31108 0.655539 0.755161i \(-0.272441\pi\)
0.655539 + 0.755161i \(0.272441\pi\)
\(402\) −13.6706 −0.681827
\(403\) −28.9870 −1.44394
\(404\) 12.3259 0.613236
\(405\) −3.56570 −0.177181
\(406\) 0.898689 0.0446012
\(407\) −16.6072 −0.823186
\(408\) 1.00000 0.0495074
\(409\) 13.2838 0.656841 0.328420 0.944532i \(-0.393484\pi\)
0.328420 + 0.944532i \(0.393484\pi\)
\(410\) −17.0005 −0.839595
\(411\) −22.0193 −1.08613
\(412\) −17.3019 −0.852405
\(413\) 0.117900 0.00580147
\(414\) −8.53198 −0.419324
\(415\) −22.7294 −1.11574
\(416\) −3.74796 −0.183759
\(417\) −5.98287 −0.292982
\(418\) 4.05677 0.198423
\(419\) 28.0142 1.36858 0.684292 0.729208i \(-0.260111\pi\)
0.684292 + 0.729208i \(0.260111\pi\)
\(420\) 0.420396 0.0205132
\(421\) 40.2124 1.95983 0.979917 0.199404i \(-0.0639005\pi\)
0.979917 + 0.199404i \(0.0639005\pi\)
\(422\) −25.5797 −1.24520
\(423\) 2.98777 0.145270
\(424\) −5.50134 −0.267169
\(425\) −7.71424 −0.374196
\(426\) −3.38434 −0.163972
\(427\) −0.620531 −0.0300296
\(428\) −7.61744 −0.368203
\(429\) 22.9060 1.10591
\(430\) 2.97816 0.143620
\(431\) −14.1361 −0.680912 −0.340456 0.940260i \(-0.610581\pi\)
−0.340456 + 0.940260i \(0.610581\pi\)
\(432\) 1.00000 0.0481125
\(433\) 14.1754 0.681225 0.340613 0.940204i \(-0.389366\pi\)
0.340613 + 0.940204i \(0.389366\pi\)
\(434\) −0.911845 −0.0437700
\(435\) −27.1795 −1.30316
\(436\) −4.84838 −0.232195
\(437\) −5.66339 −0.270917
\(438\) 16.0203 0.765481
\(439\) 9.57975 0.457217 0.228608 0.973518i \(-0.426582\pi\)
0.228608 + 0.973518i \(0.426582\pi\)
\(440\) 21.7921 1.03890
\(441\) −6.98610 −0.332671
\(442\) 3.74796 0.178272
\(443\) 6.70989 0.318796 0.159398 0.987214i \(-0.449045\pi\)
0.159398 + 0.987214i \(0.449045\pi\)
\(444\) −2.71732 −0.128958
\(445\) 14.1554 0.671028
\(446\) −23.7681 −1.12545
\(447\) −0.239031 −0.0113058
\(448\) −0.117900 −0.00557024
\(449\) −12.7988 −0.604011 −0.302006 0.953306i \(-0.597656\pi\)
−0.302006 + 0.953306i \(0.597656\pi\)
\(450\) −7.71424 −0.363653
\(451\) −29.1387 −1.37209
\(452\) 9.80909 0.461381
\(453\) −4.91184 −0.230779
\(454\) −14.6124 −0.685795
\(455\) 1.57563 0.0738666
\(456\) 0.663784 0.0310845
\(457\) 24.8047 1.16032 0.580158 0.814504i \(-0.302991\pi\)
0.580158 + 0.814504i \(0.302991\pi\)
\(458\) −22.3800 −1.04575
\(459\) −1.00000 −0.0466760
\(460\) −30.4225 −1.41846
\(461\) −10.1639 −0.473378 −0.236689 0.971585i \(-0.576062\pi\)
−0.236689 + 0.971585i \(0.576062\pi\)
\(462\) 0.720555 0.0335233
\(463\) 2.29746 0.106772 0.0533860 0.998574i \(-0.482999\pi\)
0.0533860 + 0.998574i \(0.482999\pi\)
\(464\) 7.62248 0.353865
\(465\) 27.5774 1.27887
\(466\) −16.9609 −0.785697
\(467\) −28.7497 −1.33038 −0.665189 0.746675i \(-0.731649\pi\)
−0.665189 + 0.746675i \(0.731649\pi\)
\(468\) 3.74796 0.173250
\(469\) −1.61176 −0.0744242
\(470\) 10.6535 0.491409
\(471\) 2.51989 0.116110
\(472\) 1.00000 0.0460287
\(473\) 5.10454 0.234707
\(474\) −0.152544 −0.00700659
\(475\) −5.12059 −0.234949
\(476\) 0.117900 0.00540393
\(477\) 5.50134 0.251889
\(478\) 9.32948 0.426721
\(479\) −27.2878 −1.24681 −0.623405 0.781899i \(-0.714251\pi\)
−0.623405 + 0.781899i \(0.714251\pi\)
\(480\) 3.56570 0.162751
\(481\) −10.1844 −0.464370
\(482\) −6.64255 −0.302560
\(483\) −1.00592 −0.0457709
\(484\) 26.3515 1.19780
\(485\) −9.47121 −0.430065
\(486\) −1.00000 −0.0453609
\(487\) 5.51322 0.249828 0.124914 0.992168i \(-0.460134\pi\)
0.124914 + 0.992168i \(0.460134\pi\)
\(488\) −5.26321 −0.238254
\(489\) 6.47521 0.292819
\(490\) −24.9104 −1.12534
\(491\) −32.8749 −1.48362 −0.741811 0.670609i \(-0.766033\pi\)
−0.741811 + 0.670609i \(0.766033\pi\)
\(492\) −4.76778 −0.214948
\(493\) −7.62248 −0.343299
\(494\) 2.48784 0.111933
\(495\) −21.7921 −0.979483
\(496\) −7.73406 −0.347270
\(497\) −0.399013 −0.0178982
\(498\) −6.37444 −0.285646
\(499\) −14.9760 −0.670420 −0.335210 0.942144i \(-0.608807\pi\)
−0.335210 + 0.942144i \(0.608807\pi\)
\(500\) −9.67819 −0.432822
\(501\) −21.3686 −0.954680
\(502\) −4.91450 −0.219345
\(503\) 34.6732 1.54600 0.773001 0.634404i \(-0.218755\pi\)
0.773001 + 0.634404i \(0.218755\pi\)
\(504\) 0.117900 0.00525168
\(505\) −43.9505 −1.95577
\(506\) −52.1440 −2.31808
\(507\) 1.04723 0.0465090
\(508\) −8.67239 −0.384775
\(509\) −36.4780 −1.61686 −0.808430 0.588592i \(-0.799682\pi\)
−0.808430 + 0.588592i \(0.799682\pi\)
\(510\) −3.56570 −0.157892
\(511\) 1.88879 0.0835553
\(512\) −1.00000 −0.0441942
\(513\) −0.663784 −0.0293068
\(514\) 24.6585 1.08764
\(515\) 61.6936 2.71854
\(516\) 0.835224 0.0367687
\(517\) 18.2600 0.803074
\(518\) −0.320372 −0.0140763
\(519\) 4.59815 0.201836
\(520\) 13.3641 0.586056
\(521\) −15.8453 −0.694196 −0.347098 0.937829i \(-0.612833\pi\)
−0.347098 + 0.937829i \(0.612833\pi\)
\(522\) −7.62248 −0.333627
\(523\) −5.05585 −0.221077 −0.110538 0.993872i \(-0.535258\pi\)
−0.110538 + 0.993872i \(0.535258\pi\)
\(524\) 12.2080 0.533309
\(525\) −0.909508 −0.0396942
\(526\) 6.42580 0.280178
\(527\) 7.73406 0.336901
\(528\) 6.11159 0.265973
\(529\) 49.7947 2.16499
\(530\) 19.6162 0.852072
\(531\) −1.00000 −0.0433963
\(532\) 0.0782600 0.00339300
\(533\) −17.8695 −0.774013
\(534\) 3.96986 0.171793
\(535\) 27.1615 1.17430
\(536\) −13.6706 −0.590480
\(537\) −13.2291 −0.570878
\(538\) −0.159710 −0.00688558
\(539\) −42.6962 −1.83905
\(540\) −3.56570 −0.153443
\(541\) −17.6490 −0.758790 −0.379395 0.925235i \(-0.623868\pi\)
−0.379395 + 0.925235i \(0.623868\pi\)
\(542\) −1.81105 −0.0777911
\(543\) −3.72222 −0.159736
\(544\) 1.00000 0.0428746
\(545\) 17.2879 0.740532
\(546\) 0.441884 0.0189109
\(547\) −10.0749 −0.430773 −0.215386 0.976529i \(-0.569101\pi\)
−0.215386 + 0.976529i \(0.569101\pi\)
\(548\) −22.0193 −0.940616
\(549\) 5.26321 0.224628
\(550\) −47.1463 −2.01032
\(551\) −5.05967 −0.215549
\(552\) −8.53198 −0.363145
\(553\) −0.0179850 −0.000764798 0
\(554\) −27.4820 −1.16760
\(555\) 9.68917 0.411282
\(556\) −5.98287 −0.253730
\(557\) −3.90423 −0.165427 −0.0827137 0.996573i \(-0.526359\pi\)
−0.0827137 + 0.996573i \(0.526359\pi\)
\(558\) 7.73406 0.327409
\(559\) 3.13039 0.132401
\(560\) 0.420396 0.0177650
\(561\) −6.11159 −0.258031
\(562\) −31.2878 −1.31980
\(563\) −8.95057 −0.377222 −0.188611 0.982052i \(-0.560398\pi\)
−0.188611 + 0.982052i \(0.560398\pi\)
\(564\) 2.98777 0.125808
\(565\) −34.9763 −1.47146
\(566\) 16.0077 0.672855
\(567\) −0.117900 −0.00495133
\(568\) −3.38434 −0.142004
\(569\) −14.8522 −0.622635 −0.311318 0.950306i \(-0.600770\pi\)
−0.311318 + 0.950306i \(0.600770\pi\)
\(570\) −2.36686 −0.0991367
\(571\) −37.2762 −1.55996 −0.779979 0.625805i \(-0.784770\pi\)
−0.779979 + 0.625805i \(0.784770\pi\)
\(572\) 22.9060 0.957748
\(573\) 19.3258 0.807345
\(574\) −0.562121 −0.0234625
\(575\) 65.8178 2.74479
\(576\) 1.00000 0.0416667
\(577\) −12.3110 −0.512513 −0.256256 0.966609i \(-0.582489\pi\)
−0.256256 + 0.966609i \(0.582489\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −3.37044 −0.140071
\(580\) −27.1795 −1.12857
\(581\) −0.751546 −0.0311794
\(582\) −2.65620 −0.110103
\(583\) 33.6219 1.39248
\(584\) 16.0203 0.662926
\(585\) −13.3641 −0.552539
\(586\) −19.2486 −0.795151
\(587\) −17.4677 −0.720967 −0.360484 0.932766i \(-0.617388\pi\)
−0.360484 + 0.932766i \(0.617388\pi\)
\(588\) −6.98610 −0.288102
\(589\) 5.13374 0.211532
\(590\) −3.56570 −0.146798
\(591\) 14.7678 0.607465
\(592\) −2.71732 −0.111681
\(593\) −0.890571 −0.0365714 −0.0182857 0.999833i \(-0.505821\pi\)
−0.0182857 + 0.999833i \(0.505821\pi\)
\(594\) −6.11159 −0.250761
\(595\) −0.420396 −0.0172346
\(596\) −0.239031 −0.00979109
\(597\) 9.14722 0.374371
\(598\) −31.9776 −1.30766
\(599\) 4.93280 0.201549 0.100774 0.994909i \(-0.467868\pi\)
0.100774 + 0.994909i \(0.467868\pi\)
\(600\) −7.71424 −0.314933
\(601\) 7.69602 0.313927 0.156964 0.987604i \(-0.449829\pi\)
0.156964 + 0.987604i \(0.449829\pi\)
\(602\) 0.0984727 0.00401345
\(603\) 13.6706 0.556710
\(604\) −4.91184 −0.199860
\(605\) −93.9616 −3.82008
\(606\) −12.3259 −0.500705
\(607\) 15.6840 0.636593 0.318297 0.947991i \(-0.396889\pi\)
0.318297 + 0.947991i \(0.396889\pi\)
\(608\) 0.663784 0.0269200
\(609\) −0.898689 −0.0364167
\(610\) 18.7670 0.759855
\(611\) 11.1980 0.453024
\(612\) −1.00000 −0.0404226
\(613\) 25.5268 1.03102 0.515508 0.856885i \(-0.327603\pi\)
0.515508 + 0.856885i \(0.327603\pi\)
\(614\) 6.54982 0.264329
\(615\) 17.0005 0.685526
\(616\) 0.720555 0.0290320
\(617\) 5.49917 0.221388 0.110694 0.993855i \(-0.464693\pi\)
0.110694 + 0.993855i \(0.464693\pi\)
\(618\) 17.3019 0.695986
\(619\) −24.4214 −0.981580 −0.490790 0.871278i \(-0.663292\pi\)
−0.490790 + 0.871278i \(0.663292\pi\)
\(620\) 27.5774 1.10753
\(621\) 8.53198 0.342377
\(622\) −27.1871 −1.09010
\(623\) 0.468046 0.0187519
\(624\) 3.74796 0.150039
\(625\) −4.06167 −0.162467
\(626\) −21.1346 −0.844708
\(627\) −4.05677 −0.162012
\(628\) 2.51989 0.100554
\(629\) 2.71732 0.108347
\(630\) −0.420396 −0.0167490
\(631\) 41.7809 1.66327 0.831635 0.555323i \(-0.187405\pi\)
0.831635 + 0.555323i \(0.187405\pi\)
\(632\) −0.152544 −0.00606789
\(633\) 25.5797 1.01670
\(634\) 17.5500 0.696999
\(635\) 30.9232 1.22715
\(636\) 5.50134 0.218142
\(637\) −26.1836 −1.03743
\(638\) −46.5854 −1.84433
\(639\) 3.38434 0.133882
\(640\) 3.56570 0.140947
\(641\) −40.3832 −1.59504 −0.797521 0.603291i \(-0.793856\pi\)
−0.797521 + 0.603291i \(0.793856\pi\)
\(642\) 7.61744 0.300636
\(643\) −12.6028 −0.497007 −0.248503 0.968631i \(-0.579939\pi\)
−0.248503 + 0.968631i \(0.579939\pi\)
\(644\) −1.00592 −0.0396388
\(645\) −2.97816 −0.117265
\(646\) −0.663784 −0.0261162
\(647\) 40.8528 1.60609 0.803044 0.595919i \(-0.203212\pi\)
0.803044 + 0.595919i \(0.203212\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.11159 −0.239901
\(650\) −28.9127 −1.13405
\(651\) 0.911845 0.0357380
\(652\) 6.47521 0.253589
\(653\) 3.94004 0.154186 0.0770928 0.997024i \(-0.475436\pi\)
0.0770928 + 0.997024i \(0.475436\pi\)
\(654\) 4.84838 0.189587
\(655\) −43.5301 −1.70086
\(656\) −4.76778 −0.186151
\(657\) −16.0203 −0.625012
\(658\) 0.352257 0.0137324
\(659\) 11.3329 0.441469 0.220734 0.975334i \(-0.429155\pi\)
0.220734 + 0.975334i \(0.429155\pi\)
\(660\) −21.7921 −0.848257
\(661\) −35.6357 −1.38607 −0.693035 0.720904i \(-0.743727\pi\)
−0.693035 + 0.720904i \(0.743727\pi\)
\(662\) 31.1646 1.21125
\(663\) −3.74796 −0.145559
\(664\) −6.37444 −0.247376
\(665\) −0.279052 −0.0108212
\(666\) 2.71732 0.105294
\(667\) 65.0348 2.51816
\(668\) −21.3686 −0.826777
\(669\) 23.7681 0.918929
\(670\) 48.7453 1.88320
\(671\) 32.1666 1.24178
\(672\) 0.117900 0.00454809
\(673\) 36.0148 1.38827 0.694133 0.719846i \(-0.255788\pi\)
0.694133 + 0.719846i \(0.255788\pi\)
\(674\) −3.30735 −0.127395
\(675\) 7.71424 0.296921
\(676\) 1.04723 0.0402780
\(677\) −25.3463 −0.974138 −0.487069 0.873363i \(-0.661934\pi\)
−0.487069 + 0.873363i \(0.661934\pi\)
\(678\) −9.80909 −0.376716
\(679\) −0.313165 −0.0120182
\(680\) −3.56570 −0.136738
\(681\) 14.6124 0.559949
\(682\) 47.2674 1.80996
\(683\) 48.3320 1.84937 0.924686 0.380732i \(-0.124328\pi\)
0.924686 + 0.380732i \(0.124328\pi\)
\(684\) −0.663784 −0.0253804
\(685\) 78.5142 2.99987
\(686\) −1.64896 −0.0629575
\(687\) 22.3800 0.853849
\(688\) 0.835224 0.0318426
\(689\) 20.6188 0.785515
\(690\) 30.4225 1.15817
\(691\) 7.97994 0.303571 0.151786 0.988413i \(-0.451498\pi\)
0.151786 + 0.988413i \(0.451498\pi\)
\(692\) 4.59815 0.174795
\(693\) −0.720555 −0.0273716
\(694\) −20.2791 −0.769782
\(695\) 21.3331 0.809212
\(696\) −7.62248 −0.288929
\(697\) 4.76778 0.180593
\(698\) 9.39605 0.355646
\(699\) 16.9609 0.641519
\(700\) −0.909508 −0.0343762
\(701\) 21.9629 0.829526 0.414763 0.909929i \(-0.363864\pi\)
0.414763 + 0.909929i \(0.363864\pi\)
\(702\) −3.74796 −0.141458
\(703\) 1.80372 0.0680284
\(704\) 6.11159 0.230339
\(705\) −10.6535 −0.401234
\(706\) −28.4262 −1.06983
\(707\) −1.45322 −0.0546540
\(708\) −1.00000 −0.0375823
\(709\) −17.8180 −0.669171 −0.334585 0.942365i \(-0.608596\pi\)
−0.334585 + 0.942365i \(0.608596\pi\)
\(710\) 12.0675 0.452887
\(711\) 0.152544 0.00572086
\(712\) 3.96986 0.148777
\(713\) −65.9869 −2.47123
\(714\) −0.117900 −0.00441229
\(715\) −81.6760 −3.05451
\(716\) −13.2291 −0.494394
\(717\) −9.32948 −0.348416
\(718\) −1.57637 −0.0588297
\(719\) −2.83486 −0.105722 −0.0528612 0.998602i \(-0.516834\pi\)
−0.0528612 + 0.998602i \(0.516834\pi\)
\(720\) −3.56570 −0.132886
\(721\) 2.03990 0.0759697
\(722\) 18.5594 0.690709
\(723\) 6.64255 0.247039
\(724\) −3.72222 −0.138335
\(725\) 58.8016 2.18384
\(726\) −26.3515 −0.977996
\(727\) 2.41297 0.0894923 0.0447461 0.998998i \(-0.485752\pi\)
0.0447461 + 0.998998i \(0.485752\pi\)
\(728\) 0.441884 0.0163773
\(729\) 1.00000 0.0370370
\(730\) −57.1237 −2.11424
\(731\) −0.835224 −0.0308919
\(732\) 5.26321 0.194534
\(733\) 28.3155 1.04586 0.522929 0.852376i \(-0.324839\pi\)
0.522929 + 0.852376i \(0.324839\pi\)
\(734\) 14.0577 0.518878
\(735\) 24.9104 0.918833
\(736\) −8.53198 −0.314493
\(737\) 83.5491 3.07757
\(738\) 4.76778 0.175505
\(739\) −18.2325 −0.670694 −0.335347 0.942095i \(-0.608854\pi\)
−0.335347 + 0.942095i \(0.608854\pi\)
\(740\) 9.68917 0.356181
\(741\) −2.48784 −0.0913930
\(742\) 0.648608 0.0238111
\(743\) 38.2654 1.40382 0.701911 0.712264i \(-0.252330\pi\)
0.701911 + 0.712264i \(0.252330\pi\)
\(744\) 7.73406 0.283544
\(745\) 0.852314 0.0312264
\(746\) −3.23349 −0.118387
\(747\) 6.37444 0.233229
\(748\) −6.11159 −0.223462
\(749\) 0.898095 0.0328157
\(750\) 9.67819 0.353397
\(751\) −8.02423 −0.292808 −0.146404 0.989225i \(-0.546770\pi\)
−0.146404 + 0.989225i \(0.546770\pi\)
\(752\) 2.98777 0.108953
\(753\) 4.91450 0.179094
\(754\) −28.5688 −1.04041
\(755\) 17.5142 0.637406
\(756\) −0.117900 −0.00428798
\(757\) 37.1116 1.34884 0.674422 0.738346i \(-0.264393\pi\)
0.674422 + 0.738346i \(0.264393\pi\)
\(758\) 24.4567 0.888309
\(759\) 52.1440 1.89271
\(760\) −2.36686 −0.0858549
\(761\) −39.6545 −1.43747 −0.718737 0.695282i \(-0.755279\pi\)
−0.718737 + 0.695282i \(0.755279\pi\)
\(762\) 8.67239 0.314168
\(763\) 0.571623 0.0206942
\(764\) 19.3258 0.699182
\(765\) 3.56570 0.128918
\(766\) 20.6255 0.745231
\(767\) −3.74796 −0.135331
\(768\) 1.00000 0.0360844
\(769\) −15.3864 −0.554846 −0.277423 0.960748i \(-0.589480\pi\)
−0.277423 + 0.960748i \(0.589480\pi\)
\(770\) −2.56929 −0.0925907
\(771\) −24.6585 −0.888053
\(772\) −3.37044 −0.121305
\(773\) 29.1421 1.04817 0.524084 0.851667i \(-0.324408\pi\)
0.524084 + 0.851667i \(0.324408\pi\)
\(774\) −0.835224 −0.0300215
\(775\) −59.6624 −2.14314
\(776\) −2.65620 −0.0953519
\(777\) 0.320372 0.0114933
\(778\) −21.8541 −0.783509
\(779\) 3.16478 0.113390
\(780\) −13.3641 −0.478512
\(781\) 20.6837 0.740120
\(782\) 8.53198 0.305103
\(783\) 7.62248 0.272405
\(784\) −6.98610 −0.249504
\(785\) −8.98518 −0.320695
\(786\) −12.2080 −0.435445
\(787\) −42.2725 −1.50685 −0.753425 0.657533i \(-0.771600\pi\)
−0.753425 + 0.657533i \(0.771600\pi\)
\(788\) 14.7678 0.526080
\(789\) −6.42580 −0.228764
\(790\) 0.543928 0.0193521
\(791\) −1.15649 −0.0411201
\(792\) −6.11159 −0.217166
\(793\) 19.7263 0.700502
\(794\) −6.27040 −0.222528
\(795\) −19.6162 −0.695714
\(796\) 9.14722 0.324215
\(797\) 37.4616 1.32696 0.663478 0.748196i \(-0.269080\pi\)
0.663478 + 0.748196i \(0.269080\pi\)
\(798\) −0.0782600 −0.00277037
\(799\) −2.98777 −0.105700
\(800\) −7.71424 −0.272740
\(801\) −3.96986 −0.140268
\(802\) −26.2543 −0.927072
\(803\) −97.9096 −3.45515
\(804\) 13.6706 0.482125
\(805\) 3.58681 0.126418
\(806\) 28.9870 1.02102
\(807\) 0.159710 0.00562206
\(808\) −12.3259 −0.433624
\(809\) −37.3291 −1.31242 −0.656210 0.754578i \(-0.727841\pi\)
−0.656210 + 0.754578i \(0.727841\pi\)
\(810\) 3.56570 0.125286
\(811\) 52.5876 1.84660 0.923301 0.384078i \(-0.125480\pi\)
0.923301 + 0.384078i \(0.125480\pi\)
\(812\) −0.898689 −0.0315378
\(813\) 1.81105 0.0635162
\(814\) 16.6072 0.582081
\(815\) −23.0887 −0.808761
\(816\) −1.00000 −0.0350070
\(817\) −0.554408 −0.0193963
\(818\) −13.2838 −0.464457
\(819\) −0.441884 −0.0154407
\(820\) 17.0005 0.593683
\(821\) −41.0047 −1.43107 −0.715537 0.698575i \(-0.753818\pi\)
−0.715537 + 0.698575i \(0.753818\pi\)
\(822\) 22.0193 0.768010
\(823\) 11.4903 0.400526 0.200263 0.979742i \(-0.435820\pi\)
0.200263 + 0.979742i \(0.435820\pi\)
\(824\) 17.3019 0.602742
\(825\) 47.1463 1.64142
\(826\) −0.117900 −0.00410226
\(827\) −0.973551 −0.0338537 −0.0169268 0.999857i \(-0.505388\pi\)
−0.0169268 + 0.999857i \(0.505388\pi\)
\(828\) 8.53198 0.296507
\(829\) 1.33152 0.0462455 0.0231228 0.999733i \(-0.492639\pi\)
0.0231228 + 0.999733i \(0.492639\pi\)
\(830\) 22.7294 0.788948
\(831\) 27.4820 0.953341
\(832\) 3.74796 0.129937
\(833\) 6.98610 0.242054
\(834\) 5.98287 0.207170
\(835\) 76.1942 2.63681
\(836\) −4.05677 −0.140306
\(837\) −7.73406 −0.267328
\(838\) −28.0142 −0.967735
\(839\) 18.8915 0.652206 0.326103 0.945334i \(-0.394264\pi\)
0.326103 + 0.945334i \(0.394264\pi\)
\(840\) −0.420396 −0.0145050
\(841\) 29.1021 1.00352
\(842\) −40.2124 −1.38581
\(843\) 31.2878 1.07761
\(844\) 25.5797 0.880490
\(845\) −3.73410 −0.128457
\(846\) −2.98777 −0.102722
\(847\) −3.10684 −0.106752
\(848\) 5.50134 0.188917
\(849\) −16.0077 −0.549384
\(850\) 7.71424 0.264596
\(851\) −23.1842 −0.794743
\(852\) 3.38434 0.115946
\(853\) 15.8034 0.541099 0.270549 0.962706i \(-0.412795\pi\)
0.270549 + 0.962706i \(0.412795\pi\)
\(854\) 0.620531 0.0212341
\(855\) 2.36686 0.0809448
\(856\) 7.61744 0.260359
\(857\) −45.4881 −1.55385 −0.776923 0.629596i \(-0.783220\pi\)
−0.776923 + 0.629596i \(0.783220\pi\)
\(858\) −22.9060 −0.781998
\(859\) 26.4544 0.902613 0.451306 0.892369i \(-0.350958\pi\)
0.451306 + 0.892369i \(0.350958\pi\)
\(860\) −2.97816 −0.101554
\(861\) 0.562121 0.0191570
\(862\) 14.1361 0.481477
\(863\) 8.00293 0.272423 0.136212 0.990680i \(-0.456507\pi\)
0.136212 + 0.990680i \(0.456507\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −16.3956 −0.557468
\(866\) −14.1754 −0.481699
\(867\) 1.00000 0.0339618
\(868\) 0.911845 0.0309500
\(869\) 0.932288 0.0316257
\(870\) 27.1795 0.921471
\(871\) 51.2369 1.73610
\(872\) 4.84838 0.164187
\(873\) 2.65620 0.0898986
\(874\) 5.66339 0.191567
\(875\) 1.14106 0.0385748
\(876\) −16.0203 −0.541277
\(877\) −24.1230 −0.814577 −0.407289 0.913299i \(-0.633526\pi\)
−0.407289 + 0.913299i \(0.633526\pi\)
\(878\) −9.57975 −0.323301
\(879\) 19.2486 0.649238
\(880\) −21.7921 −0.734612
\(881\) −2.82944 −0.0953263 −0.0476632 0.998863i \(-0.515177\pi\)
−0.0476632 + 0.998863i \(0.515177\pi\)
\(882\) 6.98610 0.235234
\(883\) −55.7913 −1.87753 −0.938764 0.344561i \(-0.888028\pi\)
−0.938764 + 0.344561i \(0.888028\pi\)
\(884\) −3.74796 −0.126058
\(885\) 3.56570 0.119860
\(886\) −6.70989 −0.225423
\(887\) −16.8000 −0.564089 −0.282044 0.959401i \(-0.591013\pi\)
−0.282044 + 0.959401i \(0.591013\pi\)
\(888\) 2.71732 0.0911874
\(889\) 1.02247 0.0342927
\(890\) −14.1554 −0.474489
\(891\) 6.11159 0.204746
\(892\) 23.7681 0.795816
\(893\) −1.98323 −0.0663663
\(894\) 0.239031 0.00799440
\(895\) 47.1710 1.57675
\(896\) 0.117900 0.00393876
\(897\) 31.9776 1.06770
\(898\) 12.7988 0.427101
\(899\) −58.9527 −1.96618
\(900\) 7.71424 0.257141
\(901\) −5.50134 −0.183276
\(902\) 29.1387 0.970213
\(903\) −0.0984727 −0.00327697
\(904\) −9.80909 −0.326246
\(905\) 13.2723 0.441188
\(906\) 4.91184 0.163185
\(907\) 16.6671 0.553422 0.276711 0.960953i \(-0.410756\pi\)
0.276711 + 0.960953i \(0.410756\pi\)
\(908\) 14.6124 0.484930
\(909\) 12.3259 0.408824
\(910\) −1.57563 −0.0522316
\(911\) −57.3455 −1.89994 −0.949971 0.312339i \(-0.898888\pi\)
−0.949971 + 0.312339i \(0.898888\pi\)
\(912\) −0.663784 −0.0219801
\(913\) 38.9580 1.28932
\(914\) −24.8047 −0.820467
\(915\) −18.7670 −0.620419
\(916\) 22.3800 0.739455
\(917\) −1.43932 −0.0475306
\(918\) 1.00000 0.0330049
\(919\) −8.93042 −0.294587 −0.147294 0.989093i \(-0.547056\pi\)
−0.147294 + 0.989093i \(0.547056\pi\)
\(920\) 30.4225 1.00300
\(921\) −6.54982 −0.215824
\(922\) 10.1639 0.334729
\(923\) 12.6844 0.417511
\(924\) −0.720555 −0.0237045
\(925\) −20.9621 −0.689229
\(926\) −2.29746 −0.0754992
\(927\) −17.3019 −0.568270
\(928\) −7.62248 −0.250220
\(929\) −16.6158 −0.545148 −0.272574 0.962135i \(-0.587875\pi\)
−0.272574 + 0.962135i \(0.587875\pi\)
\(930\) −27.5774 −0.904298
\(931\) 4.63726 0.151980
\(932\) 16.9609 0.555572
\(933\) 27.1871 0.890066
\(934\) 28.7497 0.940719
\(935\) 21.7921 0.712678
\(936\) −3.74796 −0.122506
\(937\) −4.59473 −0.150103 −0.0750517 0.997180i \(-0.523912\pi\)
−0.0750517 + 0.997180i \(0.523912\pi\)
\(938\) 1.61176 0.0526259
\(939\) 21.1346 0.689702
\(940\) −10.6535 −0.347479
\(941\) −37.9517 −1.23719 −0.618595 0.785710i \(-0.712298\pi\)
−0.618595 + 0.785710i \(0.712298\pi\)
\(942\) −2.51989 −0.0821024
\(943\) −40.6786 −1.32468
\(944\) −1.00000 −0.0325472
\(945\) 0.420396 0.0136755
\(946\) −5.10454 −0.165963
\(947\) 32.5996 1.05935 0.529673 0.848202i \(-0.322315\pi\)
0.529673 + 0.848202i \(0.322315\pi\)
\(948\) 0.152544 0.00495441
\(949\) −60.0436 −1.94910
\(950\) 5.12059 0.166134
\(951\) −17.5500 −0.569098
\(952\) −0.117900 −0.00382116
\(953\) 10.4092 0.337186 0.168593 0.985686i \(-0.446078\pi\)
0.168593 + 0.985686i \(0.446078\pi\)
\(954\) −5.50134 −0.178113
\(955\) −68.9099 −2.22987
\(956\) −9.32948 −0.301737
\(957\) 46.5854 1.50589
\(958\) 27.2878 0.881628
\(959\) 2.59607 0.0838314
\(960\) −3.56570 −0.115083
\(961\) 28.8157 0.929540
\(962\) 10.1844 0.328359
\(963\) −7.61744 −0.245469
\(964\) 6.64255 0.213942
\(965\) 12.0180 0.386873
\(966\) 1.00592 0.0323649
\(967\) −13.4260 −0.431750 −0.215875 0.976421i \(-0.569260\pi\)
−0.215875 + 0.976421i \(0.569260\pi\)
\(968\) −26.3515 −0.846969
\(969\) 0.663784 0.0213238
\(970\) 9.47121 0.304102
\(971\) −27.0066 −0.866682 −0.433341 0.901230i \(-0.642665\pi\)
−0.433341 + 0.901230i \(0.642665\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0.705379 0.0226134
\(974\) −5.51322 −0.176655
\(975\) 28.9127 0.925947
\(976\) 5.26321 0.168471
\(977\) 28.9880 0.927408 0.463704 0.885990i \(-0.346520\pi\)
0.463704 + 0.885990i \(0.346520\pi\)
\(978\) −6.47521 −0.207054
\(979\) −24.2622 −0.775422
\(980\) 24.9104 0.795732
\(981\) −4.84838 −0.154797
\(982\) 32.8749 1.04908
\(983\) 34.0619 1.08641 0.543203 0.839602i \(-0.317212\pi\)
0.543203 + 0.839602i \(0.317212\pi\)
\(984\) 4.76778 0.151991
\(985\) −52.6575 −1.67781
\(986\) 7.62248 0.242749
\(987\) −0.352257 −0.0112125
\(988\) −2.48784 −0.0791486
\(989\) 7.12611 0.226597
\(990\) 21.7921 0.692599
\(991\) −45.5896 −1.44820 −0.724100 0.689695i \(-0.757745\pi\)
−0.724100 + 0.689695i \(0.757745\pi\)
\(992\) 7.73406 0.245557
\(993\) −31.1646 −0.988978
\(994\) 0.399013 0.0126559
\(995\) −32.6163 −1.03401
\(996\) 6.37444 0.201982
\(997\) 39.0015 1.23519 0.617595 0.786497i \(-0.288107\pi\)
0.617595 + 0.786497i \(0.288107\pi\)
\(998\) 14.9760 0.474058
\(999\) −2.71732 −0.0859723
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 \(a_p\))