Properties

Label 8042.2.a.c.1.14
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.17249 q^{3}\) \(+1.00000 q^{4}\) \(-0.488966 q^{5}\) \(+2.17249 q^{6}\) \(-0.203617 q^{7}\) \(-1.00000 q^{8}\) \(+1.71971 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.17249 q^{3}\) \(+1.00000 q^{4}\) \(-0.488966 q^{5}\) \(+2.17249 q^{6}\) \(-0.203617 q^{7}\) \(-1.00000 q^{8}\) \(+1.71971 q^{9}\) \(+0.488966 q^{10}\) \(-2.88551 q^{11}\) \(-2.17249 q^{12}\) \(+1.03871 q^{13}\) \(+0.203617 q^{14}\) \(+1.06227 q^{15}\) \(+1.00000 q^{16}\) \(-1.76208 q^{17}\) \(-1.71971 q^{18}\) \(+3.22380 q^{19}\) \(-0.488966 q^{20}\) \(+0.442356 q^{21}\) \(+2.88551 q^{22}\) \(-9.36265 q^{23}\) \(+2.17249 q^{24}\) \(-4.76091 q^{25}\) \(-1.03871 q^{26}\) \(+2.78142 q^{27}\) \(-0.203617 q^{28}\) \(-5.34763 q^{29}\) \(-1.06227 q^{30}\) \(-0.0460050 q^{31}\) \(-1.00000 q^{32}\) \(+6.26874 q^{33}\) \(+1.76208 q^{34}\) \(+0.0995620 q^{35}\) \(+1.71971 q^{36}\) \(-5.50737 q^{37}\) \(-3.22380 q^{38}\) \(-2.25660 q^{39}\) \(+0.488966 q^{40}\) \(-6.91171 q^{41}\) \(-0.442356 q^{42}\) \(+2.67630 q^{43}\) \(-2.88551 q^{44}\) \(-0.840880 q^{45}\) \(+9.36265 q^{46}\) \(+12.3295 q^{47}\) \(-2.17249 q^{48}\) \(-6.95854 q^{49}\) \(+4.76091 q^{50}\) \(+3.82809 q^{51}\) \(+1.03871 q^{52}\) \(+11.3286 q^{53}\) \(-2.78142 q^{54}\) \(+1.41092 q^{55}\) \(+0.203617 q^{56}\) \(-7.00367 q^{57}\) \(+5.34763 q^{58}\) \(-14.6626 q^{59}\) \(+1.06227 q^{60}\) \(+1.54765 q^{61}\) \(+0.0460050 q^{62}\) \(-0.350163 q^{63}\) \(+1.00000 q^{64}\) \(-0.507897 q^{65}\) \(-6.26874 q^{66}\) \(-10.4059 q^{67}\) \(-1.76208 q^{68}\) \(+20.3403 q^{69}\) \(-0.0995620 q^{70}\) \(+0.421760 q^{71}\) \(-1.71971 q^{72}\) \(+7.89700 q^{73}\) \(+5.50737 q^{74}\) \(+10.3430 q^{75}\) \(+3.22380 q^{76}\) \(+0.587540 q^{77}\) \(+2.25660 q^{78}\) \(+7.66659 q^{79}\) \(-0.488966 q^{80}\) \(-11.2017 q^{81}\) \(+6.91171 q^{82}\) \(-14.2667 q^{83}\) \(+0.442356 q^{84}\) \(+0.861596 q^{85}\) \(-2.67630 q^{86}\) \(+11.6177 q^{87}\) \(+2.88551 q^{88}\) \(+13.3220 q^{89}\) \(+0.840880 q^{90}\) \(-0.211500 q^{91}\) \(-9.36265 q^{92}\) \(+0.0999453 q^{93}\) \(-12.3295 q^{94}\) \(-1.57633 q^{95}\) \(+2.17249 q^{96}\) \(-12.4930 q^{97}\) \(+6.95854 q^{98}\) \(-4.96223 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.17249 −1.25429 −0.627144 0.778904i \(-0.715776\pi\)
−0.627144 + 0.778904i \(0.715776\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.488966 −0.218672 −0.109336 0.994005i \(-0.534873\pi\)
−0.109336 + 0.994005i \(0.534873\pi\)
\(6\) 2.17249 0.886915
\(7\) −0.203617 −0.0769601 −0.0384801 0.999259i \(-0.512252\pi\)
−0.0384801 + 0.999259i \(0.512252\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.71971 0.573236
\(10\) 0.488966 0.154625
\(11\) −2.88551 −0.870014 −0.435007 0.900427i \(-0.643254\pi\)
−0.435007 + 0.900427i \(0.643254\pi\)
\(12\) −2.17249 −0.627144
\(13\) 1.03871 0.288088 0.144044 0.989571i \(-0.453989\pi\)
0.144044 + 0.989571i \(0.453989\pi\)
\(14\) 0.203617 0.0544190
\(15\) 1.06227 0.274278
\(16\) 1.00000 0.250000
\(17\) −1.76208 −0.427366 −0.213683 0.976903i \(-0.568546\pi\)
−0.213683 + 0.976903i \(0.568546\pi\)
\(18\) −1.71971 −0.405339
\(19\) 3.22380 0.739590 0.369795 0.929113i \(-0.379428\pi\)
0.369795 + 0.929113i \(0.379428\pi\)
\(20\) −0.488966 −0.109336
\(21\) 0.442356 0.0965301
\(22\) 2.88551 0.615193
\(23\) −9.36265 −1.95225 −0.976124 0.217215i \(-0.930303\pi\)
−0.976124 + 0.217215i \(0.930303\pi\)
\(24\) 2.17249 0.443457
\(25\) −4.76091 −0.952182
\(26\) −1.03871 −0.203709
\(27\) 2.78142 0.535284
\(28\) −0.203617 −0.0384801
\(29\) −5.34763 −0.993030 −0.496515 0.868028i \(-0.665387\pi\)
−0.496515 + 0.868028i \(0.665387\pi\)
\(30\) −1.06227 −0.193944
\(31\) −0.0460050 −0.00826274 −0.00413137 0.999991i \(-0.501315\pi\)
−0.00413137 + 0.999991i \(0.501315\pi\)
\(32\) −1.00000 −0.176777
\(33\) 6.26874 1.09125
\(34\) 1.76208 0.302194
\(35\) 0.0995620 0.0168291
\(36\) 1.71971 0.286618
\(37\) −5.50737 −0.905406 −0.452703 0.891661i \(-0.649540\pi\)
−0.452703 + 0.891661i \(0.649540\pi\)
\(38\) −3.22380 −0.522969
\(39\) −2.25660 −0.361345
\(40\) 0.488966 0.0773124
\(41\) −6.91171 −1.07943 −0.539714 0.841849i \(-0.681467\pi\)
−0.539714 + 0.841849i \(0.681467\pi\)
\(42\) −0.442356 −0.0682571
\(43\) 2.67630 0.408132 0.204066 0.978957i \(-0.434584\pi\)
0.204066 + 0.978957i \(0.434584\pi\)
\(44\) −2.88551 −0.435007
\(45\) −0.840880 −0.125351
\(46\) 9.36265 1.38045
\(47\) 12.3295 1.79844 0.899220 0.437497i \(-0.144135\pi\)
0.899220 + 0.437497i \(0.144135\pi\)
\(48\) −2.17249 −0.313572
\(49\) −6.95854 −0.994077
\(50\) 4.76091 0.673295
\(51\) 3.82809 0.536040
\(52\) 1.03871 0.144044
\(53\) 11.3286 1.55610 0.778052 0.628200i \(-0.216208\pi\)
0.778052 + 0.628200i \(0.216208\pi\)
\(54\) −2.78142 −0.378503
\(55\) 1.41092 0.190248
\(56\) 0.203617 0.0272095
\(57\) −7.00367 −0.927658
\(58\) 5.34763 0.702178
\(59\) −14.6626 −1.90891 −0.954455 0.298355i \(-0.903562\pi\)
−0.954455 + 0.298355i \(0.903562\pi\)
\(60\) 1.06227 0.137139
\(61\) 1.54765 0.198157 0.0990783 0.995080i \(-0.468411\pi\)
0.0990783 + 0.995080i \(0.468411\pi\)
\(62\) 0.0460050 0.00584264
\(63\) −0.350163 −0.0441163
\(64\) 1.00000 0.125000
\(65\) −0.507897 −0.0629968
\(66\) −6.26874 −0.771628
\(67\) −10.4059 −1.27128 −0.635641 0.771985i \(-0.719264\pi\)
−0.635641 + 0.771985i \(0.719264\pi\)
\(68\) −1.76208 −0.213683
\(69\) 20.3403 2.44868
\(70\) −0.0995620 −0.0118999
\(71\) 0.421760 0.0500537 0.0250268 0.999687i \(-0.492033\pi\)
0.0250268 + 0.999687i \(0.492033\pi\)
\(72\) −1.71971 −0.202670
\(73\) 7.89700 0.924274 0.462137 0.886809i \(-0.347083\pi\)
0.462137 + 0.886809i \(0.347083\pi\)
\(74\) 5.50737 0.640219
\(75\) 10.3430 1.19431
\(76\) 3.22380 0.369795
\(77\) 0.587540 0.0669564
\(78\) 2.25660 0.255509
\(79\) 7.66659 0.862559 0.431280 0.902218i \(-0.358062\pi\)
0.431280 + 0.902218i \(0.358062\pi\)
\(80\) −0.488966 −0.0546681
\(81\) −11.2017 −1.24464
\(82\) 6.91171 0.763270
\(83\) −14.2667 −1.56597 −0.782986 0.622039i \(-0.786304\pi\)
−0.782986 + 0.622039i \(0.786304\pi\)
\(84\) 0.442356 0.0482650
\(85\) 0.861596 0.0934532
\(86\) −2.67630 −0.288593
\(87\) 11.6177 1.24555
\(88\) 2.88551 0.307596
\(89\) 13.3220 1.41213 0.706063 0.708149i \(-0.250470\pi\)
0.706063 + 0.708149i \(0.250470\pi\)
\(90\) 0.840880 0.0886365
\(91\) −0.211500 −0.0221713
\(92\) −9.36265 −0.976124
\(93\) 0.0999453 0.0103638
\(94\) −12.3295 −1.27169
\(95\) −1.57633 −0.161728
\(96\) 2.17249 0.221729
\(97\) −12.4930 −1.26847 −0.634234 0.773141i \(-0.718685\pi\)
−0.634234 + 0.773141i \(0.718685\pi\)
\(98\) 6.95854 0.702919
\(99\) −4.96223 −0.498723
\(100\) −4.76091 −0.476091
\(101\) 3.05855 0.304337 0.152169 0.988355i \(-0.451374\pi\)
0.152169 + 0.988355i \(0.451374\pi\)
\(102\) −3.82809 −0.379038
\(103\) −10.4018 −1.02492 −0.512458 0.858712i \(-0.671265\pi\)
−0.512458 + 0.858712i \(0.671265\pi\)
\(104\) −1.03871 −0.101854
\(105\) −0.216297 −0.0211085
\(106\) −11.3286 −1.10033
\(107\) −19.5104 −1.88614 −0.943069 0.332597i \(-0.892075\pi\)
−0.943069 + 0.332597i \(0.892075\pi\)
\(108\) 2.78142 0.267642
\(109\) −0.995382 −0.0953403 −0.0476702 0.998863i \(-0.515180\pi\)
−0.0476702 + 0.998863i \(0.515180\pi\)
\(110\) −1.41092 −0.134526
\(111\) 11.9647 1.13564
\(112\) −0.203617 −0.0192400
\(113\) −7.34669 −0.691118 −0.345559 0.938397i \(-0.612311\pi\)
−0.345559 + 0.938397i \(0.612311\pi\)
\(114\) 7.00367 0.655954
\(115\) 4.57802 0.426903
\(116\) −5.34763 −0.496515
\(117\) 1.78629 0.165142
\(118\) 14.6626 1.34980
\(119\) 0.358789 0.0328902
\(120\) −1.06227 −0.0969719
\(121\) −2.67384 −0.243076
\(122\) −1.54765 −0.140118
\(123\) 15.0156 1.35391
\(124\) −0.0460050 −0.00413137
\(125\) 4.77276 0.426888
\(126\) 0.350163 0.0311950
\(127\) 10.5809 0.938899 0.469450 0.882959i \(-0.344452\pi\)
0.469450 + 0.882959i \(0.344452\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.81424 −0.511915
\(130\) 0.507897 0.0445455
\(131\) −4.80680 −0.419972 −0.209986 0.977704i \(-0.567342\pi\)
−0.209986 + 0.977704i \(0.567342\pi\)
\(132\) 6.26874 0.545623
\(133\) −0.656421 −0.0569189
\(134\) 10.4059 0.898932
\(135\) −1.36002 −0.117052
\(136\) 1.76208 0.151097
\(137\) −7.66777 −0.655101 −0.327551 0.944834i \(-0.606223\pi\)
−0.327551 + 0.944834i \(0.606223\pi\)
\(138\) −20.3403 −1.73148
\(139\) 15.1655 1.28632 0.643161 0.765731i \(-0.277623\pi\)
0.643161 + 0.765731i \(0.277623\pi\)
\(140\) 0.0995620 0.00841453
\(141\) −26.7857 −2.25576
\(142\) −0.421760 −0.0353933
\(143\) −2.99722 −0.250640
\(144\) 1.71971 0.143309
\(145\) 2.61481 0.217148
\(146\) −7.89700 −0.653560
\(147\) 15.1174 1.24686
\(148\) −5.50737 −0.452703
\(149\) −19.4470 −1.59316 −0.796580 0.604533i \(-0.793360\pi\)
−0.796580 + 0.604533i \(0.793360\pi\)
\(150\) −10.3430 −0.844505
\(151\) 20.6951 1.68414 0.842070 0.539369i \(-0.181337\pi\)
0.842070 + 0.539369i \(0.181337\pi\)
\(152\) −3.22380 −0.261485
\(153\) −3.03026 −0.244982
\(154\) −0.587540 −0.0473453
\(155\) 0.0224949 0.00180683
\(156\) −2.25660 −0.180672
\(157\) 14.0367 1.12025 0.560127 0.828407i \(-0.310752\pi\)
0.560127 + 0.828407i \(0.310752\pi\)
\(158\) −7.66659 −0.609921
\(159\) −24.6113 −1.95180
\(160\) 0.488966 0.0386562
\(161\) 1.90640 0.150245
\(162\) 11.2017 0.880091
\(163\) −10.7706 −0.843615 −0.421808 0.906685i \(-0.638604\pi\)
−0.421808 + 0.906685i \(0.638604\pi\)
\(164\) −6.91171 −0.539714
\(165\) −3.06520 −0.238626
\(166\) 14.2667 1.10731
\(167\) 18.9859 1.46917 0.734586 0.678516i \(-0.237377\pi\)
0.734586 + 0.678516i \(0.237377\pi\)
\(168\) −0.442356 −0.0341285
\(169\) −11.9211 −0.917006
\(170\) −0.861596 −0.0660814
\(171\) 5.54400 0.423960
\(172\) 2.67630 0.204066
\(173\) 6.10393 0.464073 0.232037 0.972707i \(-0.425461\pi\)
0.232037 + 0.972707i \(0.425461\pi\)
\(174\) −11.6177 −0.880733
\(175\) 0.969404 0.0732801
\(176\) −2.88551 −0.217503
\(177\) 31.8544 2.39432
\(178\) −13.3220 −0.998524
\(179\) −13.2117 −0.987486 −0.493743 0.869608i \(-0.664372\pi\)
−0.493743 + 0.869608i \(0.664372\pi\)
\(180\) −0.840880 −0.0626755
\(181\) −10.2089 −0.758825 −0.379413 0.925228i \(-0.623874\pi\)
−0.379413 + 0.925228i \(0.623874\pi\)
\(182\) 0.211500 0.0156774
\(183\) −3.36226 −0.248545
\(184\) 9.36265 0.690224
\(185\) 2.69292 0.197987
\(186\) −0.0999453 −0.00732835
\(187\) 5.08449 0.371815
\(188\) 12.3295 0.899220
\(189\) −0.566345 −0.0411955
\(190\) 1.57633 0.114359
\(191\) −26.4907 −1.91680 −0.958398 0.285435i \(-0.907862\pi\)
−0.958398 + 0.285435i \(0.907862\pi\)
\(192\) −2.17249 −0.156786
\(193\) −0.470343 −0.0338560 −0.0169280 0.999857i \(-0.505389\pi\)
−0.0169280 + 0.999857i \(0.505389\pi\)
\(194\) 12.4930 0.896943
\(195\) 1.10340 0.0790161
\(196\) −6.95854 −0.497039
\(197\) 3.51558 0.250475 0.125238 0.992127i \(-0.460031\pi\)
0.125238 + 0.992127i \(0.460031\pi\)
\(198\) 4.96223 0.352651
\(199\) 13.1428 0.931671 0.465835 0.884871i \(-0.345754\pi\)
0.465835 + 0.884871i \(0.345754\pi\)
\(200\) 4.76091 0.336647
\(201\) 22.6067 1.59455
\(202\) −3.05855 −0.215199
\(203\) 1.08887 0.0764237
\(204\) 3.82809 0.268020
\(205\) 3.37959 0.236041
\(206\) 10.4018 0.724725
\(207\) −16.1010 −1.11910
\(208\) 1.03871 0.0720219
\(209\) −9.30230 −0.643453
\(210\) 0.216297 0.0149259
\(211\) 3.40461 0.234383 0.117192 0.993109i \(-0.462611\pi\)
0.117192 + 0.993109i \(0.462611\pi\)
\(212\) 11.3286 0.778052
\(213\) −0.916269 −0.0627817
\(214\) 19.5104 1.33370
\(215\) −1.30862 −0.0892472
\(216\) −2.78142 −0.189252
\(217\) 0.00936741 0.000635901 0
\(218\) 0.995382 0.0674158
\(219\) −17.1561 −1.15930
\(220\) 1.41092 0.0951240
\(221\) −1.83030 −0.123119
\(222\) −11.9647 −0.803018
\(223\) 20.3123 1.36021 0.680106 0.733114i \(-0.261934\pi\)
0.680106 + 0.733114i \(0.261934\pi\)
\(224\) 0.203617 0.0136048
\(225\) −8.18738 −0.545825
\(226\) 7.34669 0.488694
\(227\) −24.7343 −1.64168 −0.820838 0.571161i \(-0.806493\pi\)
−0.820838 + 0.571161i \(0.806493\pi\)
\(228\) −7.00367 −0.463829
\(229\) 8.57570 0.566698 0.283349 0.959017i \(-0.408555\pi\)
0.283349 + 0.959017i \(0.408555\pi\)
\(230\) −4.57802 −0.301866
\(231\) −1.27642 −0.0839825
\(232\) 5.34763 0.351089
\(233\) −26.9900 −1.76817 −0.884087 0.467322i \(-0.845219\pi\)
−0.884087 + 0.467322i \(0.845219\pi\)
\(234\) −1.78629 −0.116773
\(235\) −6.02870 −0.393269
\(236\) −14.6626 −0.954455
\(237\) −16.6556 −1.08190
\(238\) −0.358789 −0.0232569
\(239\) −2.11151 −0.136583 −0.0682913 0.997665i \(-0.521755\pi\)
−0.0682913 + 0.997665i \(0.521755\pi\)
\(240\) 1.06227 0.0685695
\(241\) −25.8562 −1.66555 −0.832773 0.553614i \(-0.813248\pi\)
−0.832773 + 0.553614i \(0.813248\pi\)
\(242\) 2.67384 0.171881
\(243\) 15.9914 1.02585
\(244\) 1.54765 0.0990783
\(245\) 3.40249 0.217377
\(246\) −15.0156 −0.957360
\(247\) 3.34861 0.213067
\(248\) 0.0460050 0.00292132
\(249\) 30.9942 1.96418
\(250\) −4.77276 −0.301856
\(251\) 5.48143 0.345985 0.172993 0.984923i \(-0.444656\pi\)
0.172993 + 0.984923i \(0.444656\pi\)
\(252\) −0.350163 −0.0220582
\(253\) 27.0160 1.69848
\(254\) −10.5809 −0.663902
\(255\) −1.87181 −0.117217
\(256\) 1.00000 0.0625000
\(257\) 15.4009 0.960681 0.480341 0.877082i \(-0.340513\pi\)
0.480341 + 0.877082i \(0.340513\pi\)
\(258\) 5.81424 0.361979
\(259\) 1.12140 0.0696802
\(260\) −0.507897 −0.0314984
\(261\) −9.19637 −0.569241
\(262\) 4.80680 0.296965
\(263\) −3.22332 −0.198758 −0.0993791 0.995050i \(-0.531686\pi\)
−0.0993791 + 0.995050i \(0.531686\pi\)
\(264\) −6.26874 −0.385814
\(265\) −5.53931 −0.340277
\(266\) 0.656421 0.0402478
\(267\) −28.9418 −1.77121
\(268\) −10.4059 −0.635641
\(269\) 6.47628 0.394866 0.197433 0.980316i \(-0.436740\pi\)
0.197433 + 0.980316i \(0.436740\pi\)
\(270\) 1.36002 0.0827682
\(271\) −1.08767 −0.0660711 −0.0330355 0.999454i \(-0.510517\pi\)
−0.0330355 + 0.999454i \(0.510517\pi\)
\(272\) −1.76208 −0.106842
\(273\) 0.459482 0.0278091
\(274\) 7.66777 0.463227
\(275\) 13.7377 0.828412
\(276\) 20.3403 1.22434
\(277\) −4.48401 −0.269418 −0.134709 0.990885i \(-0.543010\pi\)
−0.134709 + 0.990885i \(0.543010\pi\)
\(278\) −15.1655 −0.909567
\(279\) −0.0791152 −0.00473650
\(280\) −0.0995620 −0.00594997
\(281\) −10.8553 −0.647571 −0.323785 0.946131i \(-0.604956\pi\)
−0.323785 + 0.946131i \(0.604956\pi\)
\(282\) 26.7857 1.59506
\(283\) 6.81521 0.405122 0.202561 0.979270i \(-0.435074\pi\)
0.202561 + 0.979270i \(0.435074\pi\)
\(284\) 0.421760 0.0250268
\(285\) 3.42456 0.202853
\(286\) 2.99722 0.177229
\(287\) 1.40734 0.0830728
\(288\) −1.71971 −0.101335
\(289\) −13.8951 −0.817358
\(290\) −2.61481 −0.153547
\(291\) 27.1408 1.59102
\(292\) 7.89700 0.462137
\(293\) −1.98542 −0.115989 −0.0579947 0.998317i \(-0.518471\pi\)
−0.0579947 + 0.998317i \(0.518471\pi\)
\(294\) −15.1174 −0.881662
\(295\) 7.16952 0.417426
\(296\) 5.50737 0.320109
\(297\) −8.02581 −0.465705
\(298\) 19.4470 1.12653
\(299\) −9.72512 −0.562418
\(300\) 10.3430 0.597155
\(301\) −0.544941 −0.0314099
\(302\) −20.6951 −1.19087
\(303\) −6.64467 −0.381727
\(304\) 3.22380 0.184898
\(305\) −0.756750 −0.0433314
\(306\) 3.03026 0.173228
\(307\) 17.8245 1.01730 0.508648 0.860975i \(-0.330145\pi\)
0.508648 + 0.860975i \(0.330145\pi\)
\(308\) 0.587540 0.0334782
\(309\) 22.5977 1.28554
\(310\) −0.0224949 −0.00127762
\(311\) 28.4071 1.61082 0.805409 0.592719i \(-0.201946\pi\)
0.805409 + 0.592719i \(0.201946\pi\)
\(312\) 2.25660 0.127755
\(313\) −10.3805 −0.586742 −0.293371 0.955999i \(-0.594777\pi\)
−0.293371 + 0.955999i \(0.594777\pi\)
\(314\) −14.0367 −0.792139
\(315\) 0.171218 0.00964702
\(316\) 7.66659 0.431280
\(317\) 18.5391 1.04126 0.520629 0.853783i \(-0.325698\pi\)
0.520629 + 0.853783i \(0.325698\pi\)
\(318\) 24.6113 1.38013
\(319\) 15.4306 0.863950
\(320\) −0.488966 −0.0273340
\(321\) 42.3860 2.36576
\(322\) −1.90640 −0.106239
\(323\) −5.68058 −0.316076
\(324\) −11.2017 −0.622318
\(325\) −4.94523 −0.274312
\(326\) 10.7706 0.596526
\(327\) 2.16246 0.119584
\(328\) 6.91171 0.381635
\(329\) −2.51050 −0.138408
\(330\) 3.06520 0.168734
\(331\) −18.6176 −1.02331 −0.511657 0.859190i \(-0.670968\pi\)
−0.511657 + 0.859190i \(0.670968\pi\)
\(332\) −14.2667 −0.782986
\(333\) −9.47108 −0.519012
\(334\) −18.9859 −1.03886
\(335\) 5.08813 0.277994
\(336\) 0.442356 0.0241325
\(337\) −12.2109 −0.665168 −0.332584 0.943074i \(-0.607920\pi\)
−0.332584 + 0.943074i \(0.607920\pi\)
\(338\) 11.9211 0.648421
\(339\) 15.9606 0.866861
\(340\) 0.861596 0.0467266
\(341\) 0.132748 0.00718869
\(342\) −5.54400 −0.299785
\(343\) 2.84220 0.153464
\(344\) −2.67630 −0.144297
\(345\) −9.94570 −0.535459
\(346\) −6.10393 −0.328149
\(347\) 4.14405 0.222464 0.111232 0.993794i \(-0.464520\pi\)
0.111232 + 0.993794i \(0.464520\pi\)
\(348\) 11.6177 0.622773
\(349\) −24.4945 −1.31116 −0.655580 0.755126i \(-0.727576\pi\)
−0.655580 + 0.755126i \(0.727576\pi\)
\(350\) −0.969404 −0.0518168
\(351\) 2.88910 0.154209
\(352\) 2.88551 0.153798
\(353\) −9.39438 −0.500012 −0.250006 0.968244i \(-0.580433\pi\)
−0.250006 + 0.968244i \(0.580433\pi\)
\(354\) −31.8544 −1.69304
\(355\) −0.206226 −0.0109454
\(356\) 13.3220 0.706063
\(357\) −0.779466 −0.0412537
\(358\) 13.2117 0.698258
\(359\) −18.2266 −0.961965 −0.480983 0.876730i \(-0.659720\pi\)
−0.480983 + 0.876730i \(0.659720\pi\)
\(360\) 0.840880 0.0443183
\(361\) −8.60712 −0.453006
\(362\) 10.2089 0.536570
\(363\) 5.80889 0.304888
\(364\) −0.211500 −0.0110856
\(365\) −3.86137 −0.202113
\(366\) 3.36226 0.175748
\(367\) 9.46509 0.494074 0.247037 0.969006i \(-0.420543\pi\)
0.247037 + 0.969006i \(0.420543\pi\)
\(368\) −9.36265 −0.488062
\(369\) −11.8861 −0.618767
\(370\) −2.69292 −0.139998
\(371\) −2.30670 −0.119758
\(372\) 0.0999453 0.00518192
\(373\) 8.81810 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(374\) −5.08449 −0.262913
\(375\) −10.3688 −0.535441
\(376\) −12.3295 −0.635845
\(377\) −5.55466 −0.286080
\(378\) 0.566345 0.0291296
\(379\) 8.70651 0.447224 0.223612 0.974678i \(-0.428215\pi\)
0.223612 + 0.974678i \(0.428215\pi\)
\(380\) −1.57633 −0.0808640
\(381\) −22.9868 −1.17765
\(382\) 26.4907 1.35538
\(383\) 18.7321 0.957166 0.478583 0.878042i \(-0.341151\pi\)
0.478583 + 0.878042i \(0.341151\pi\)
\(384\) 2.17249 0.110864
\(385\) −0.287287 −0.0146415
\(386\) 0.470343 0.0239398
\(387\) 4.60246 0.233956
\(388\) −12.4930 −0.634234
\(389\) −38.9238 −1.97351 −0.986757 0.162208i \(-0.948138\pi\)
−0.986757 + 0.162208i \(0.948138\pi\)
\(390\) −1.10340 −0.0558728
\(391\) 16.4977 0.834325
\(392\) 6.95854 0.351459
\(393\) 10.4427 0.526766
\(394\) −3.51558 −0.177113
\(395\) −3.74871 −0.188618
\(396\) −4.96223 −0.249362
\(397\) −0.502089 −0.0251991 −0.0125996 0.999921i \(-0.504011\pi\)
−0.0125996 + 0.999921i \(0.504011\pi\)
\(398\) −13.1428 −0.658791
\(399\) 1.42607 0.0713927
\(400\) −4.76091 −0.238046
\(401\) −22.2487 −1.11105 −0.555523 0.831501i \(-0.687482\pi\)
−0.555523 + 0.831501i \(0.687482\pi\)
\(402\) −22.6067 −1.12752
\(403\) −0.0477860 −0.00238039
\(404\) 3.05855 0.152169
\(405\) 5.47727 0.272168
\(406\) −1.08887 −0.0540397
\(407\) 15.8916 0.787716
\(408\) −3.82809 −0.189519
\(409\) −22.2002 −1.09773 −0.548863 0.835912i \(-0.684939\pi\)
−0.548863 + 0.835912i \(0.684939\pi\)
\(410\) −3.37959 −0.166906
\(411\) 16.6581 0.821685
\(412\) −10.4018 −0.512458
\(413\) 2.98556 0.146910
\(414\) 16.1010 0.791323
\(415\) 6.97593 0.342435
\(416\) −1.03871 −0.0509272
\(417\) −32.9469 −1.61342
\(418\) 9.30230 0.454990
\(419\) 7.90202 0.386039 0.193020 0.981195i \(-0.438172\pi\)
0.193020 + 0.981195i \(0.438172\pi\)
\(420\) −0.216297 −0.0105542
\(421\) −15.7001 −0.765174 −0.382587 0.923919i \(-0.624967\pi\)
−0.382587 + 0.923919i \(0.624967\pi\)
\(422\) −3.40461 −0.165734
\(423\) 21.2031 1.03093
\(424\) −11.3286 −0.550166
\(425\) 8.38909 0.406931
\(426\) 0.916269 0.0443934
\(427\) −0.315129 −0.0152502
\(428\) −19.5104 −0.943069
\(429\) 6.51143 0.314375
\(430\) 1.30862 0.0631073
\(431\) −3.49340 −0.168271 −0.0841356 0.996454i \(-0.526813\pi\)
−0.0841356 + 0.996454i \(0.526813\pi\)
\(432\) 2.78142 0.133821
\(433\) 34.6022 1.66288 0.831439 0.555616i \(-0.187518\pi\)
0.831439 + 0.555616i \(0.187518\pi\)
\(434\) −0.00936741 −0.000449650 0
\(435\) −5.68065 −0.272366
\(436\) −0.995382 −0.0476702
\(437\) −30.1833 −1.44386
\(438\) 17.1561 0.819752
\(439\) −39.1443 −1.86826 −0.934129 0.356937i \(-0.883821\pi\)
−0.934129 + 0.356937i \(0.883821\pi\)
\(440\) −1.41092 −0.0672628
\(441\) −11.9667 −0.569841
\(442\) 1.83030 0.0870583
\(443\) 27.6015 1.31139 0.655693 0.755028i \(-0.272377\pi\)
0.655693 + 0.755028i \(0.272377\pi\)
\(444\) 11.9647 0.567820
\(445\) −6.51399 −0.308793
\(446\) −20.3123 −0.961816
\(447\) 42.2484 1.99828
\(448\) −0.203617 −0.00962002
\(449\) 39.9154 1.88372 0.941862 0.336000i \(-0.109074\pi\)
0.941862 + 0.336000i \(0.109074\pi\)
\(450\) 8.18738 0.385957
\(451\) 19.9438 0.939116
\(452\) −7.34669 −0.345559
\(453\) −44.9598 −2.11239
\(454\) 24.7343 1.16084
\(455\) 0.103417 0.00484824
\(456\) 7.00367 0.327977
\(457\) −14.9312 −0.698452 −0.349226 0.937039i \(-0.613555\pi\)
−0.349226 + 0.937039i \(0.613555\pi\)
\(458\) −8.57570 −0.400716
\(459\) −4.90107 −0.228763
\(460\) 4.57802 0.213451
\(461\) 39.2288 1.82707 0.913534 0.406762i \(-0.133342\pi\)
0.913534 + 0.406762i \(0.133342\pi\)
\(462\) 1.27642 0.0593846
\(463\) 42.9339 1.99531 0.997653 0.0684661i \(-0.0218105\pi\)
0.997653 + 0.0684661i \(0.0218105\pi\)
\(464\) −5.34763 −0.248258
\(465\) −0.0488699 −0.00226629
\(466\) 26.9900 1.25029
\(467\) 16.0978 0.744918 0.372459 0.928049i \(-0.378515\pi\)
0.372459 + 0.928049i \(0.378515\pi\)
\(468\) 1.78629 0.0825711
\(469\) 2.11882 0.0978380
\(470\) 6.02870 0.278083
\(471\) −30.4947 −1.40512
\(472\) 14.6626 0.674902
\(473\) −7.72249 −0.355081
\(474\) 16.6556 0.765017
\(475\) −15.3482 −0.704225
\(476\) 0.358789 0.0164451
\(477\) 19.4819 0.892015
\(478\) 2.11151 0.0965784
\(479\) 4.32721 0.197715 0.0988576 0.995102i \(-0.468481\pi\)
0.0988576 + 0.995102i \(0.468481\pi\)
\(480\) −1.06227 −0.0484860
\(481\) −5.72059 −0.260836
\(482\) 25.8562 1.17772
\(483\) −4.14163 −0.188451
\(484\) −2.67384 −0.121538
\(485\) 6.10864 0.277379
\(486\) −15.9914 −0.725384
\(487\) 30.5083 1.38246 0.691231 0.722634i \(-0.257069\pi\)
0.691231 + 0.722634i \(0.257069\pi\)
\(488\) −1.54765 −0.0700590
\(489\) 23.3989 1.05814
\(490\) −3.40249 −0.153709
\(491\) 25.7415 1.16170 0.580848 0.814012i \(-0.302721\pi\)
0.580848 + 0.814012i \(0.302721\pi\)
\(492\) 15.0156 0.676956
\(493\) 9.42294 0.424388
\(494\) −3.34861 −0.150661
\(495\) 2.42637 0.109057
\(496\) −0.0460050 −0.00206568
\(497\) −0.0858776 −0.00385214
\(498\) −30.9942 −1.38888
\(499\) 27.5830 1.23478 0.617392 0.786655i \(-0.288189\pi\)
0.617392 + 0.786655i \(0.288189\pi\)
\(500\) 4.77276 0.213444
\(501\) −41.2466 −1.84276
\(502\) −5.48143 −0.244648
\(503\) 28.3287 1.26312 0.631558 0.775328i \(-0.282416\pi\)
0.631558 + 0.775328i \(0.282416\pi\)
\(504\) 0.350163 0.0155975
\(505\) −1.49553 −0.0665502
\(506\) −27.0160 −1.20101
\(507\) 25.8984 1.15019
\(508\) 10.5809 0.469450
\(509\) 17.7260 0.785692 0.392846 0.919604i \(-0.371491\pi\)
0.392846 + 0.919604i \(0.371491\pi\)
\(510\) 1.87181 0.0828851
\(511\) −1.60797 −0.0711322
\(512\) −1.00000 −0.0441942
\(513\) 8.96673 0.395891
\(514\) −15.4009 −0.679304
\(515\) 5.08611 0.224121
\(516\) −5.81424 −0.255957
\(517\) −35.5768 −1.56467
\(518\) −1.12140 −0.0492713
\(519\) −13.2607 −0.582081
\(520\) 0.507897 0.0222727
\(521\) −20.7207 −0.907789 −0.453894 0.891056i \(-0.649966\pi\)
−0.453894 + 0.891056i \(0.649966\pi\)
\(522\) 9.19637 0.402514
\(523\) 9.25301 0.404606 0.202303 0.979323i \(-0.435157\pi\)
0.202303 + 0.979323i \(0.435157\pi\)
\(524\) −4.80680 −0.209986
\(525\) −2.10602 −0.0919143
\(526\) 3.22332 0.140543
\(527\) 0.0810643 0.00353122
\(528\) 6.26874 0.272812
\(529\) 64.6592 2.81127
\(530\) 5.53931 0.240612
\(531\) −25.2154 −1.09426
\(532\) −0.656421 −0.0284595
\(533\) −7.17929 −0.310970
\(534\) 28.9418 1.25244
\(535\) 9.53991 0.412446
\(536\) 10.4059 0.449466
\(537\) 28.7022 1.23859
\(538\) −6.47628 −0.279212
\(539\) 20.0789 0.864861
\(540\) −1.36002 −0.0585259
\(541\) 18.9714 0.815643 0.407821 0.913062i \(-0.366289\pi\)
0.407821 + 0.913062i \(0.366289\pi\)
\(542\) 1.08767 0.0467193
\(543\) 22.1788 0.951785
\(544\) 1.76208 0.0755484
\(545\) 0.486708 0.0208483
\(546\) −0.459482 −0.0196640
\(547\) 12.2319 0.522999 0.261500 0.965204i \(-0.415783\pi\)
0.261500 + 0.965204i \(0.415783\pi\)
\(548\) −7.66777 −0.327551
\(549\) 2.66151 0.113591
\(550\) −13.7377 −0.585775
\(551\) −17.2397 −0.734435
\(552\) −20.3403 −0.865739
\(553\) −1.56105 −0.0663827
\(554\) 4.48401 0.190507
\(555\) −5.85034 −0.248333
\(556\) 15.1655 0.643161
\(557\) −14.4338 −0.611578 −0.305789 0.952099i \(-0.598920\pi\)
−0.305789 + 0.952099i \(0.598920\pi\)
\(558\) 0.0791152 0.00334921
\(559\) 2.77991 0.117578
\(560\) 0.0995620 0.00420726
\(561\) −11.0460 −0.466362
\(562\) 10.8553 0.457902
\(563\) 9.26653 0.390538 0.195269 0.980750i \(-0.437442\pi\)
0.195269 + 0.980750i \(0.437442\pi\)
\(564\) −26.7857 −1.12788
\(565\) 3.59228 0.151128
\(566\) −6.81521 −0.286465
\(567\) 2.28087 0.0957874
\(568\) −0.421760 −0.0176966
\(569\) 23.7731 0.996622 0.498311 0.866998i \(-0.333954\pi\)
0.498311 + 0.866998i \(0.333954\pi\)
\(570\) −3.42456 −0.143439
\(571\) −9.49436 −0.397327 −0.198663 0.980068i \(-0.563660\pi\)
−0.198663 + 0.980068i \(0.563660\pi\)
\(572\) −2.99722 −0.125320
\(573\) 57.5507 2.40421
\(574\) −1.40734 −0.0587414
\(575\) 44.5748 1.85890
\(576\) 1.71971 0.0716545
\(577\) −42.0049 −1.74869 −0.874343 0.485308i \(-0.838707\pi\)
−0.874343 + 0.485308i \(0.838707\pi\)
\(578\) 13.8951 0.577959
\(579\) 1.02181 0.0424652
\(580\) 2.61481 0.108574
\(581\) 2.90494 0.120517
\(582\) −27.1408 −1.12502
\(583\) −32.6888 −1.35383
\(584\) −7.89700 −0.326780
\(585\) −0.873434 −0.0361121
\(586\) 1.98542 0.0820169
\(587\) 2.38132 0.0982877 0.0491438 0.998792i \(-0.484351\pi\)
0.0491438 + 0.998792i \(0.484351\pi\)
\(588\) 15.1174 0.623429
\(589\) −0.148311 −0.00611104
\(590\) −7.16952 −0.295165
\(591\) −7.63757 −0.314168
\(592\) −5.50737 −0.226352
\(593\) 43.6316 1.79173 0.895867 0.444323i \(-0.146556\pi\)
0.895867 + 0.444323i \(0.146556\pi\)
\(594\) 8.02581 0.329303
\(595\) −0.175436 −0.00719217
\(596\) −19.4470 −0.796580
\(597\) −28.5527 −1.16858
\(598\) 9.72512 0.397690
\(599\) 2.90427 0.118665 0.0593327 0.998238i \(-0.481103\pi\)
0.0593327 + 0.998238i \(0.481103\pi\)
\(600\) −10.3430 −0.422252
\(601\) −22.1328 −0.902817 −0.451409 0.892317i \(-0.649078\pi\)
−0.451409 + 0.892317i \(0.649078\pi\)
\(602\) 0.544941 0.0222102
\(603\) −17.8951 −0.728745
\(604\) 20.6951 0.842070
\(605\) 1.30742 0.0531541
\(606\) 6.64467 0.269921
\(607\) 9.56319 0.388158 0.194079 0.980986i \(-0.437828\pi\)
0.194079 + 0.980986i \(0.437828\pi\)
\(608\) −3.22380 −0.130742
\(609\) −2.36556 −0.0958573
\(610\) 0.756750 0.0306399
\(611\) 12.8068 0.518108
\(612\) −3.03026 −0.122491
\(613\) −32.0874 −1.29600 −0.647999 0.761641i \(-0.724394\pi\)
−0.647999 + 0.761641i \(0.724394\pi\)
\(614\) −17.8245 −0.719337
\(615\) −7.34213 −0.296063
\(616\) −0.587540 −0.0236726
\(617\) −18.6881 −0.752355 −0.376177 0.926548i \(-0.622762\pi\)
−0.376177 + 0.926548i \(0.622762\pi\)
\(618\) −22.5977 −0.909013
\(619\) −3.67169 −0.147578 −0.0737888 0.997274i \(-0.523509\pi\)
−0.0737888 + 0.997274i \(0.523509\pi\)
\(620\) 0.0224949 0.000903416 0
\(621\) −26.0415 −1.04501
\(622\) −28.4071 −1.13902
\(623\) −2.71258 −0.108677
\(624\) −2.25660 −0.0903362
\(625\) 21.4708 0.858834
\(626\) 10.3805 0.414889
\(627\) 20.2091 0.807075
\(628\) 14.0367 0.560127
\(629\) 9.70441 0.386940
\(630\) −0.171218 −0.00682148
\(631\) 8.42177 0.335266 0.167633 0.985850i \(-0.446388\pi\)
0.167633 + 0.985850i \(0.446388\pi\)
\(632\) −7.66659 −0.304961
\(633\) −7.39649 −0.293984
\(634\) −18.5391 −0.736280
\(635\) −5.17368 −0.205311
\(636\) −24.6113 −0.975901
\(637\) −7.22794 −0.286381
\(638\) −15.4306 −0.610905
\(639\) 0.725304 0.0286926
\(640\) 0.488966 0.0193281
\(641\) −9.44964 −0.373238 −0.186619 0.982432i \(-0.559753\pi\)
−0.186619 + 0.982432i \(0.559753\pi\)
\(642\) −42.3860 −1.67284
\(643\) 41.9318 1.65363 0.826815 0.562474i \(-0.190150\pi\)
0.826815 + 0.562474i \(0.190150\pi\)
\(644\) 1.90640 0.0751226
\(645\) 2.84297 0.111942
\(646\) 5.68058 0.223499
\(647\) −1.64765 −0.0647759 −0.0323880 0.999475i \(-0.510311\pi\)
−0.0323880 + 0.999475i \(0.510311\pi\)
\(648\) 11.2017 0.440045
\(649\) 42.3091 1.66078
\(650\) 4.94523 0.193968
\(651\) −0.0203506 −0.000797603 0
\(652\) −10.7706 −0.421808
\(653\) 16.6303 0.650793 0.325396 0.945578i \(-0.394502\pi\)
0.325396 + 0.945578i \(0.394502\pi\)
\(654\) −2.16246 −0.0845588
\(655\) 2.35036 0.0918363
\(656\) −6.91171 −0.269857
\(657\) 13.5805 0.529827
\(658\) 2.51050 0.0978694
\(659\) 5.97780 0.232862 0.116431 0.993199i \(-0.462855\pi\)
0.116431 + 0.993199i \(0.462855\pi\)
\(660\) −3.06520 −0.119313
\(661\) 42.6240 1.65788 0.828940 0.559337i \(-0.188944\pi\)
0.828940 + 0.559337i \(0.188944\pi\)
\(662\) 18.6176 0.723593
\(663\) 3.97630 0.154427
\(664\) 14.2667 0.553655
\(665\) 0.320968 0.0124466
\(666\) 9.47108 0.366997
\(667\) 50.0680 1.93864
\(668\) 18.9859 0.734586
\(669\) −44.1283 −1.70610
\(670\) −5.08813 −0.196572
\(671\) −4.46577 −0.172399
\(672\) −0.442356 −0.0170643
\(673\) −11.7469 −0.452811 −0.226406 0.974033i \(-0.572697\pi\)
−0.226406 + 0.974033i \(0.572697\pi\)
\(674\) 12.2109 0.470345
\(675\) −13.2421 −0.509688
\(676\) −11.9211 −0.458503
\(677\) 30.6925 1.17961 0.589803 0.807547i \(-0.299205\pi\)
0.589803 + 0.807547i \(0.299205\pi\)
\(678\) −15.9606 −0.612963
\(679\) 2.54379 0.0976215
\(680\) −0.861596 −0.0330407
\(681\) 53.7351 2.05913
\(682\) −0.132748 −0.00508317
\(683\) 34.3476 1.31428 0.657138 0.753770i \(-0.271767\pi\)
0.657138 + 0.753770i \(0.271767\pi\)
\(684\) 5.54400 0.211980
\(685\) 3.74928 0.143253
\(686\) −2.84220 −0.108516
\(687\) −18.6306 −0.710802
\(688\) 2.67630 0.102033
\(689\) 11.7672 0.448294
\(690\) 9.94570 0.378626
\(691\) −9.71358 −0.369522 −0.184761 0.982783i \(-0.559151\pi\)
−0.184761 + 0.982783i \(0.559151\pi\)
\(692\) 6.10393 0.232037
\(693\) 1.01040 0.0383818
\(694\) −4.14405 −0.157306
\(695\) −7.41542 −0.281283
\(696\) −11.6177 −0.440367
\(697\) 12.1790 0.461311
\(698\) 24.4945 0.927130
\(699\) 58.6355 2.21780
\(700\) 0.969404 0.0366400
\(701\) −0.375372 −0.0141776 −0.00708879 0.999975i \(-0.502256\pi\)
−0.00708879 + 0.999975i \(0.502256\pi\)
\(702\) −2.88910 −0.109042
\(703\) −17.7547 −0.669630
\(704\) −2.88551 −0.108752
\(705\) 13.0973 0.493272
\(706\) 9.39438 0.353562
\(707\) −0.622775 −0.0234218
\(708\) 31.8544 1.19716
\(709\) 12.4631 0.468062 0.234031 0.972229i \(-0.424808\pi\)
0.234031 + 0.972229i \(0.424808\pi\)
\(710\) 0.206226 0.00773954
\(711\) 13.1843 0.494450
\(712\) −13.3220 −0.499262
\(713\) 0.430729 0.0161309
\(714\) 0.779466 0.0291708
\(715\) 1.46554 0.0548081
\(716\) −13.2117 −0.493743
\(717\) 4.58724 0.171314
\(718\) 18.2266 0.680212
\(719\) 8.56040 0.319249 0.159625 0.987178i \(-0.448972\pi\)
0.159625 + 0.987178i \(0.448972\pi\)
\(720\) −0.840880 −0.0313377
\(721\) 2.11798 0.0788777
\(722\) 8.60712 0.320324
\(723\) 56.1724 2.08907
\(724\) −10.2089 −0.379413
\(725\) 25.4596 0.945546
\(726\) −5.80889 −0.215588
\(727\) −25.9133 −0.961069 −0.480535 0.876976i \(-0.659557\pi\)
−0.480535 + 0.876976i \(0.659557\pi\)
\(728\) 0.211500 0.00783872
\(729\) −1.13591 −0.0420706
\(730\) 3.86137 0.142916
\(731\) −4.71585 −0.174422
\(732\) −3.36226 −0.124273
\(733\) 49.2678 1.81975 0.909873 0.414887i \(-0.136179\pi\)
0.909873 + 0.414887i \(0.136179\pi\)
\(734\) −9.46509 −0.349363
\(735\) −7.39188 −0.272653
\(736\) 9.36265 0.345112
\(737\) 30.0263 1.10603
\(738\) 11.8861 0.437534
\(739\) −11.3619 −0.417953 −0.208977 0.977921i \(-0.567013\pi\)
−0.208977 + 0.977921i \(0.567013\pi\)
\(740\) 2.69292 0.0989937
\(741\) −7.27481 −0.267247
\(742\) 2.30670 0.0846817
\(743\) −16.9122 −0.620450 −0.310225 0.950663i \(-0.600404\pi\)
−0.310225 + 0.950663i \(0.600404\pi\)
\(744\) −0.0999453 −0.00366417
\(745\) 9.50893 0.348380
\(746\) −8.81810 −0.322854
\(747\) −24.5345 −0.897672
\(748\) 5.08449 0.185907
\(749\) 3.97265 0.145157
\(750\) 10.3688 0.378614
\(751\) 5.03224 0.183629 0.0918145 0.995776i \(-0.470733\pi\)
0.0918145 + 0.995776i \(0.470733\pi\)
\(752\) 12.3295 0.449610
\(753\) −11.9084 −0.433965
\(754\) 5.55466 0.202289
\(755\) −10.1192 −0.368275
\(756\) −0.566345 −0.0205978
\(757\) 25.4817 0.926148 0.463074 0.886320i \(-0.346746\pi\)
0.463074 + 0.886320i \(0.346746\pi\)
\(758\) −8.70651 −0.316235
\(759\) −58.6920 −2.13038
\(760\) 1.57633 0.0571795
\(761\) 47.4129 1.71872 0.859359 0.511373i \(-0.170863\pi\)
0.859359 + 0.511373i \(0.170863\pi\)
\(762\) 22.9868 0.832724
\(763\) 0.202677 0.00733740
\(764\) −26.4907 −0.958398
\(765\) 1.48169 0.0535708
\(766\) −18.7321 −0.676819
\(767\) −15.2303 −0.549933
\(768\) −2.17249 −0.0783929
\(769\) 41.9112 1.51136 0.755678 0.654944i \(-0.227308\pi\)
0.755678 + 0.654944i \(0.227308\pi\)
\(770\) 0.287287 0.0103531
\(771\) −33.4583 −1.20497
\(772\) −0.470343 −0.0169280
\(773\) −16.7872 −0.603793 −0.301897 0.953341i \(-0.597620\pi\)
−0.301897 + 0.953341i \(0.597620\pi\)
\(774\) −4.60246 −0.165432
\(775\) 0.219026 0.00786763
\(776\) 12.4930 0.448471
\(777\) −2.43622 −0.0873990
\(778\) 38.9238 1.39548
\(779\) −22.2819 −0.798334
\(780\) 1.10340 0.0395080
\(781\) −1.21699 −0.0435474
\(782\) −16.4977 −0.589957
\(783\) −14.8740 −0.531553
\(784\) −6.95854 −0.248519
\(785\) −6.86349 −0.244969
\(786\) −10.4427 −0.372480
\(787\) 26.5389 0.946010 0.473005 0.881060i \(-0.343169\pi\)
0.473005 + 0.881060i \(0.343169\pi\)
\(788\) 3.51558 0.125238
\(789\) 7.00262 0.249300
\(790\) 3.74871 0.133373
\(791\) 1.49591 0.0531885
\(792\) 4.96223 0.176325
\(793\) 1.60757 0.0570865
\(794\) 0.502089 0.0178185
\(795\) 12.0341 0.426805
\(796\) 13.1428 0.465835
\(797\) −28.9689 −1.02613 −0.513066 0.858349i \(-0.671490\pi\)
−0.513066 + 0.858349i \(0.671490\pi\)
\(798\) −1.42607 −0.0504823
\(799\) −21.7255 −0.768593
\(800\) 4.76091 0.168324
\(801\) 22.9099 0.809482
\(802\) 22.2487 0.785628
\(803\) −22.7869 −0.804131
\(804\) 22.6067 0.797276
\(805\) −0.932165 −0.0328545
\(806\) 0.0477860 0.00168319
\(807\) −14.0697 −0.495275
\(808\) −3.05855 −0.107600
\(809\) 1.07223 0.0376976 0.0188488 0.999822i \(-0.494000\pi\)
0.0188488 + 0.999822i \(0.494000\pi\)
\(810\) −5.47727 −0.192452
\(811\) 18.8385 0.661508 0.330754 0.943717i \(-0.392697\pi\)
0.330754 + 0.943717i \(0.392697\pi\)
\(812\) 1.08887 0.0382119
\(813\) 2.36294 0.0828721
\(814\) −15.8916 −0.556999
\(815\) 5.26644 0.184475
\(816\) 3.82809 0.134010
\(817\) 8.62786 0.301851
\(818\) 22.2002 0.776210
\(819\) −0.363719 −0.0127094
\(820\) 3.37959 0.118020
\(821\) 26.4016 0.921421 0.460710 0.887551i \(-0.347595\pi\)
0.460710 + 0.887551i \(0.347595\pi\)
\(822\) −16.6581 −0.581019
\(823\) 12.6884 0.442290 0.221145 0.975241i \(-0.429021\pi\)
0.221145 + 0.975241i \(0.429021\pi\)
\(824\) 10.4018 0.362363
\(825\) −29.8449 −1.03907
\(826\) −2.98556 −0.103881
\(827\) 21.8703 0.760503 0.380252 0.924883i \(-0.375837\pi\)
0.380252 + 0.924883i \(0.375837\pi\)
\(828\) −16.1010 −0.559550
\(829\) 1.79540 0.0623570 0.0311785 0.999514i \(-0.490074\pi\)
0.0311785 + 0.999514i \(0.490074\pi\)
\(830\) −6.97593 −0.242138
\(831\) 9.74145 0.337927
\(832\) 1.03871 0.0360110
\(833\) 12.2615 0.424835
\(834\) 32.9469 1.14086
\(835\) −9.28345 −0.321267
\(836\) −9.30230 −0.321727
\(837\) −0.127959 −0.00442291
\(838\) −7.90202 −0.272971
\(839\) 16.8864 0.582983 0.291491 0.956573i \(-0.405849\pi\)
0.291491 + 0.956573i \(0.405849\pi\)
\(840\) 0.216297 0.00746297
\(841\) −0.402835 −0.0138909
\(842\) 15.7001 0.541060
\(843\) 23.5829 0.812240
\(844\) 3.40461 0.117192
\(845\) 5.82900 0.200524
\(846\) −21.2031 −0.728978
\(847\) 0.544440 0.0187072
\(848\) 11.3286 0.389026
\(849\) −14.8060 −0.508139
\(850\) −8.38909 −0.287744
\(851\) 51.5636 1.76758
\(852\) −0.916269 −0.0313908
\(853\) 12.2733 0.420231 0.210116 0.977677i \(-0.432616\pi\)
0.210116 + 0.977677i \(0.432616\pi\)
\(854\) 0.315129 0.0107835
\(855\) −2.71083 −0.0927083
\(856\) 19.5104 0.666850
\(857\) 2.66241 0.0909461 0.0454731 0.998966i \(-0.485520\pi\)
0.0454731 + 0.998966i \(0.485520\pi\)
\(858\) −6.51143 −0.222297
\(859\) 17.3821 0.593068 0.296534 0.955022i \(-0.404169\pi\)
0.296534 + 0.955022i \(0.404169\pi\)
\(860\) −1.30862 −0.0446236
\(861\) −3.05744 −0.104197
\(862\) 3.49340 0.118986
\(863\) 31.0369 1.05651 0.528254 0.849086i \(-0.322847\pi\)
0.528254 + 0.849086i \(0.322847\pi\)
\(864\) −2.78142 −0.0946258
\(865\) −2.98462 −0.101480
\(866\) −34.6022 −1.17583
\(867\) 30.1869 1.02520
\(868\) 0.00936741 0.000317951 0
\(869\) −22.1220 −0.750438
\(870\) 5.68065 0.192592
\(871\) −10.8087 −0.366240
\(872\) 0.995382 0.0337079
\(873\) −21.4843 −0.727132
\(874\) 30.1833 1.02097
\(875\) −0.971816 −0.0328534
\(876\) −17.1561 −0.579652
\(877\) 1.99987 0.0675308 0.0337654 0.999430i \(-0.489250\pi\)
0.0337654 + 0.999430i \(0.489250\pi\)
\(878\) 39.1443 1.32106
\(879\) 4.31330 0.145484
\(880\) 1.41092 0.0475620
\(881\) −39.7793 −1.34020 −0.670100 0.742271i \(-0.733749\pi\)
−0.670100 + 0.742271i \(0.733749\pi\)
\(882\) 11.9667 0.402938
\(883\) −5.18990 −0.174654 −0.0873271 0.996180i \(-0.527833\pi\)
−0.0873271 + 0.996180i \(0.527833\pi\)
\(884\) −1.83030 −0.0615595
\(885\) −15.5757 −0.523572
\(886\) −27.6015 −0.927290
\(887\) −32.8075 −1.10157 −0.550784 0.834648i \(-0.685671\pi\)
−0.550784 + 0.834648i \(0.685671\pi\)
\(888\) −11.9647 −0.401509
\(889\) −2.15445 −0.0722578
\(890\) 6.51399 0.218350
\(891\) 32.3227 1.08285
\(892\) 20.3123 0.680106
\(893\) 39.7478 1.33011
\(894\) −42.2484 −1.41300
\(895\) 6.46006 0.215936
\(896\) 0.203617 0.00680238
\(897\) 21.1277 0.705434
\(898\) −39.9154 −1.33199
\(899\) 0.246018 0.00820515
\(900\) −8.18738 −0.272913
\(901\) −19.9619 −0.665027
\(902\) −19.9438 −0.664055
\(903\) 1.18388 0.0393970
\(904\) 7.34669 0.244347
\(905\) 4.99183 0.165934
\(906\) 44.9598 1.49369
\(907\) 32.2211 1.06988 0.534942 0.844889i \(-0.320334\pi\)
0.534942 + 0.844889i \(0.320334\pi\)
\(908\) −24.7343 −0.820838
\(909\) 5.25982 0.174457
\(910\) −0.103417 −0.00342823
\(911\) 46.4288 1.53826 0.769128 0.639095i \(-0.220691\pi\)
0.769128 + 0.639095i \(0.220691\pi\)
\(912\) −7.00367 −0.231915
\(913\) 41.1666 1.36242
\(914\) 14.9312 0.493880
\(915\) 1.64403 0.0543500
\(916\) 8.57570 0.283349
\(917\) 0.978748 0.0323211
\(918\) 4.90107 0.161760
\(919\) −25.4097 −0.838190 −0.419095 0.907942i \(-0.637653\pi\)
−0.419095 + 0.907942i \(0.637653\pi\)
\(920\) −4.57802 −0.150933
\(921\) −38.7235 −1.27598
\(922\) −39.2288 −1.29193
\(923\) 0.438088 0.0144198
\(924\) −1.27642 −0.0419912
\(925\) 26.2201 0.862112
\(926\) −42.9339 −1.41090
\(927\) −17.8880 −0.587519
\(928\) 5.34763 0.175545
\(929\) −7.04364 −0.231094 −0.115547 0.993302i \(-0.536862\pi\)
−0.115547 + 0.993302i \(0.536862\pi\)
\(930\) 0.0488699 0.00160251
\(931\) −22.4329 −0.735210
\(932\) −26.9900 −0.884087
\(933\) −61.7141 −2.02043
\(934\) −16.0978 −0.526737
\(935\) −2.48614 −0.0813056
\(936\) −1.78629 −0.0583866
\(937\) −2.67022 −0.0872322 −0.0436161 0.999048i \(-0.513888\pi\)
−0.0436161 + 0.999048i \(0.513888\pi\)
\(938\) −2.11882 −0.0691819
\(939\) 22.5516 0.735943
\(940\) −6.02870 −0.196635
\(941\) −34.6547 −1.12971 −0.564856 0.825190i \(-0.691068\pi\)
−0.564856 + 0.825190i \(0.691068\pi\)
\(942\) 30.4947 0.993570
\(943\) 64.7119 2.10731
\(944\) −14.6626 −0.477227
\(945\) 0.276924 0.00900833
\(946\) 7.72249 0.251080
\(947\) −28.2273 −0.917263 −0.458632 0.888626i \(-0.651660\pi\)
−0.458632 + 0.888626i \(0.651660\pi\)
\(948\) −16.6556 −0.540948
\(949\) 8.20273 0.266272
\(950\) 15.3482 0.497962
\(951\) −40.2759 −1.30604
\(952\) −0.358789 −0.0116284
\(953\) 18.3980 0.595970 0.297985 0.954571i \(-0.403685\pi\)
0.297985 + 0.954571i \(0.403685\pi\)
\(954\) −19.4819 −0.630750
\(955\) 12.9530 0.419150
\(956\) −2.11151 −0.0682913
\(957\) −33.5229 −1.08364
\(958\) −4.32721 −0.139806
\(959\) 1.56129 0.0504167
\(960\) 1.06227 0.0342847
\(961\) −30.9979 −0.999932
\(962\) 5.72059 0.184439
\(963\) −33.5521 −1.08120
\(964\) −25.8562 −0.832773
\(965\) 0.229982 0.00740337
\(966\) 4.14163 0.133255
\(967\) −27.8954 −0.897056 −0.448528 0.893769i \(-0.648052\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(968\) 2.67384 0.0859405
\(969\) 12.3410 0.396450
\(970\) −6.10864 −0.196137
\(971\) 17.5049 0.561760 0.280880 0.959743i \(-0.409374\pi\)
0.280880 + 0.959743i \(0.409374\pi\)
\(972\) 15.9914 0.512924
\(973\) −3.08796 −0.0989955
\(974\) −30.5083 −0.977548
\(975\) 10.7435 0.344066
\(976\) 1.54765 0.0495392
\(977\) 11.8848 0.380229 0.190114 0.981762i \(-0.439114\pi\)
0.190114 + 0.981762i \(0.439114\pi\)
\(978\) −23.3989 −0.748215
\(979\) −38.4407 −1.22857
\(980\) 3.40249 0.108689
\(981\) −1.71177 −0.0546525
\(982\) −25.7415 −0.821443
\(983\) −41.4259 −1.32128 −0.660640 0.750703i \(-0.729715\pi\)
−0.660640 + 0.750703i \(0.729715\pi\)
\(984\) −15.0156 −0.478680
\(985\) −1.71900 −0.0547720
\(986\) −9.42294 −0.300087
\(987\) 5.45403 0.173604
\(988\) 3.34861 0.106533
\(989\) −25.0573 −0.796775
\(990\) −2.42637 −0.0771150
\(991\) −15.3591 −0.487899 −0.243949 0.969788i \(-0.578443\pi\)
−0.243949 + 0.969788i \(0.578443\pi\)
\(992\) 0.0460050 0.00146066
\(993\) 40.4465 1.28353
\(994\) 0.0858776 0.00272387
\(995\) −6.42640 −0.203731
\(996\) 30.9942 0.982089
\(997\) 24.7752 0.784638 0.392319 0.919829i \(-0.371673\pi\)
0.392319 + 0.919829i \(0.371673\pi\)
\(998\) −27.5830 −0.873125
\(999\) −15.3183 −0.484650
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 \(a_p\))