Properties

Label 8015.2.a.l.1.2
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.65622 q^{2}\) \(-1.51381 q^{3}\) \(+5.05553 q^{4}\) \(-1.00000 q^{5}\) \(+4.02102 q^{6}\) \(-1.00000 q^{7}\) \(-8.11618 q^{8}\) \(-0.708384 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.65622 q^{2}\) \(-1.51381 q^{3}\) \(+5.05553 q^{4}\) \(-1.00000 q^{5}\) \(+4.02102 q^{6}\) \(-1.00000 q^{7}\) \(-8.11618 q^{8}\) \(-0.708384 q^{9}\) \(+2.65622 q^{10}\) \(-5.61743 q^{11}\) \(-7.65310 q^{12}\) \(+6.70734 q^{13}\) \(+2.65622 q^{14}\) \(+1.51381 q^{15}\) \(+11.4473 q^{16}\) \(-3.50154 q^{17}\) \(+1.88163 q^{18}\) \(+2.65152 q^{19}\) \(-5.05553 q^{20}\) \(+1.51381 q^{21}\) \(+14.9212 q^{22}\) \(+2.95131 q^{23}\) \(+12.2863 q^{24}\) \(+1.00000 q^{25}\) \(-17.8162 q^{26}\) \(+5.61378 q^{27}\) \(-5.05553 q^{28}\) \(+5.39028 q^{29}\) \(-4.02102 q^{30}\) \(-0.273942 q^{31}\) \(-14.1743 q^{32}\) \(+8.50372 q^{33}\) \(+9.30089 q^{34}\) \(+1.00000 q^{35}\) \(-3.58126 q^{36}\) \(+12.0812 q^{37}\) \(-7.04304 q^{38}\) \(-10.1536 q^{39}\) \(+8.11618 q^{40}\) \(+11.6828 q^{41}\) \(-4.02102 q^{42}\) \(-2.58198 q^{43}\) \(-28.3991 q^{44}\) \(+0.708384 q^{45}\) \(-7.83933 q^{46}\) \(-1.30017 q^{47}\) \(-17.3291 q^{48}\) \(+1.00000 q^{49}\) \(-2.65622 q^{50}\) \(+5.30067 q^{51}\) \(+33.9092 q^{52}\) \(+7.69853 q^{53}\) \(-14.9115 q^{54}\) \(+5.61743 q^{55}\) \(+8.11618 q^{56}\) \(-4.01390 q^{57}\) \(-14.3178 q^{58}\) \(-6.89816 q^{59}\) \(+7.65310 q^{60}\) \(+2.54520 q^{61}\) \(+0.727653 q^{62}\) \(+0.708384 q^{63}\) \(+14.7555 q^{64}\) \(-6.70734 q^{65}\) \(-22.5878 q^{66}\) \(+11.2045 q^{67}\) \(-17.7022 q^{68}\) \(-4.46771 q^{69}\) \(-2.65622 q^{70}\) \(-15.2309 q^{71}\) \(+5.74937 q^{72}\) \(+2.48419 q^{73}\) \(-32.0904 q^{74}\) \(-1.51381 q^{75}\) \(+13.4048 q^{76}\) \(+5.61743 q^{77}\) \(+26.9703 q^{78}\) \(-14.8242 q^{79}\) \(-11.4473 q^{80}\) \(-6.37304 q^{81}\) \(-31.0322 q^{82}\) \(-2.64228 q^{83}\) \(+7.65310 q^{84}\) \(+3.50154 q^{85}\) \(+6.85832 q^{86}\) \(-8.15985 q^{87}\) \(+45.5921 q^{88}\) \(-8.52428 q^{89}\) \(-1.88163 q^{90}\) \(-6.70734 q^{91}\) \(+14.9204 q^{92}\) \(+0.414696 q^{93}\) \(+3.45355 q^{94}\) \(-2.65152 q^{95}\) \(+21.4572 q^{96}\) \(-9.89389 q^{97}\) \(-2.65622 q^{98}\) \(+3.97930 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65622 −1.87823 −0.939117 0.343597i \(-0.888355\pi\)
−0.939117 + 0.343597i \(0.888355\pi\)
\(3\) −1.51381 −0.873998 −0.436999 0.899462i \(-0.643959\pi\)
−0.436999 + 0.899462i \(0.643959\pi\)
\(4\) 5.05553 2.52777
\(5\) −1.00000 −0.447214
\(6\) 4.02102 1.64157
\(7\) −1.00000 −0.377964
\(8\) −8.11618 −2.86950
\(9\) −0.708384 −0.236128
\(10\) 2.65622 0.839972
\(11\) −5.61743 −1.69372 −0.846860 0.531816i \(-0.821510\pi\)
−0.846860 + 0.531816i \(0.821510\pi\)
\(12\) −7.65310 −2.20926
\(13\) 6.70734 1.86028 0.930141 0.367202i \(-0.119684\pi\)
0.930141 + 0.367202i \(0.119684\pi\)
\(14\) 2.65622 0.709906
\(15\) 1.51381 0.390864
\(16\) 11.4473 2.86183
\(17\) −3.50154 −0.849249 −0.424625 0.905370i \(-0.639594\pi\)
−0.424625 + 0.905370i \(0.639594\pi\)
\(18\) 1.88163 0.443504
\(19\) 2.65152 0.608301 0.304150 0.952624i \(-0.401627\pi\)
0.304150 + 0.952624i \(0.401627\pi\)
\(20\) −5.05553 −1.13045
\(21\) 1.51381 0.330340
\(22\) 14.9212 3.18120
\(23\) 2.95131 0.615390 0.307695 0.951485i \(-0.400442\pi\)
0.307695 + 0.951485i \(0.400442\pi\)
\(24\) 12.2863 2.50794
\(25\) 1.00000 0.200000
\(26\) −17.8162 −3.49405
\(27\) 5.61378 1.08037
\(28\) −5.05553 −0.955405
\(29\) 5.39028 1.00095 0.500475 0.865751i \(-0.333159\pi\)
0.500475 + 0.865751i \(0.333159\pi\)
\(30\) −4.02102 −0.734134
\(31\) −0.273942 −0.0492015 −0.0246008 0.999697i \(-0.507831\pi\)
−0.0246008 + 0.999697i \(0.507831\pi\)
\(32\) −14.1743 −2.50569
\(33\) 8.50372 1.48031
\(34\) 9.30089 1.59509
\(35\) 1.00000 0.169031
\(36\) −3.58126 −0.596876
\(37\) 12.0812 1.98614 0.993069 0.117537i \(-0.0374999\pi\)
0.993069 + 0.117537i \(0.0374999\pi\)
\(38\) −7.04304 −1.14253
\(39\) −10.1536 −1.62588
\(40\) 8.11618 1.28328
\(41\) 11.6828 1.82455 0.912275 0.409577i \(-0.134324\pi\)
0.912275 + 0.409577i \(0.134324\pi\)
\(42\) −4.02102 −0.620456
\(43\) −2.58198 −0.393748 −0.196874 0.980429i \(-0.563079\pi\)
−0.196874 + 0.980429i \(0.563079\pi\)
\(44\) −28.3991 −4.28133
\(45\) 0.708384 0.105600
\(46\) −7.83933 −1.15585
\(47\) −1.30017 −0.189650 −0.0948249 0.995494i \(-0.530229\pi\)
−0.0948249 + 0.995494i \(0.530229\pi\)
\(48\) −17.3291 −2.50123
\(49\) 1.00000 0.142857
\(50\) −2.65622 −0.375647
\(51\) 5.30067 0.742242
\(52\) 33.9092 4.70236
\(53\) 7.69853 1.05747 0.528737 0.848786i \(-0.322666\pi\)
0.528737 + 0.848786i \(0.322666\pi\)
\(54\) −14.9115 −2.02919
\(55\) 5.61743 0.757454
\(56\) 8.11618 1.08457
\(57\) −4.01390 −0.531654
\(58\) −14.3178 −1.88002
\(59\) −6.89816 −0.898063 −0.449032 0.893516i \(-0.648231\pi\)
−0.449032 + 0.893516i \(0.648231\pi\)
\(60\) 7.65310 0.988012
\(61\) 2.54520 0.325879 0.162940 0.986636i \(-0.447902\pi\)
0.162940 + 0.986636i \(0.447902\pi\)
\(62\) 0.727653 0.0924120
\(63\) 0.708384 0.0892480
\(64\) 14.7555 1.84444
\(65\) −6.70734 −0.831944
\(66\) −22.5878 −2.78036
\(67\) 11.2045 1.36885 0.684426 0.729082i \(-0.260053\pi\)
0.684426 + 0.729082i \(0.260053\pi\)
\(68\) −17.7022 −2.14670
\(69\) −4.46771 −0.537849
\(70\) −2.65622 −0.317480
\(71\) −15.2309 −1.80757 −0.903787 0.427982i \(-0.859225\pi\)
−0.903787 + 0.427982i \(0.859225\pi\)
\(72\) 5.74937 0.677570
\(73\) 2.48419 0.290753 0.145376 0.989376i \(-0.453561\pi\)
0.145376 + 0.989376i \(0.453561\pi\)
\(74\) −32.0904 −3.73043
\(75\) −1.51381 −0.174800
\(76\) 13.4048 1.53764
\(77\) 5.61743 0.640166
\(78\) 26.9703 3.05379
\(79\) −14.8242 −1.66785 −0.833924 0.551879i \(-0.813911\pi\)
−0.833924 + 0.551879i \(0.813911\pi\)
\(80\) −11.4473 −1.27985
\(81\) −6.37304 −0.708116
\(82\) −31.0322 −3.42693
\(83\) −2.64228 −0.290027 −0.145014 0.989430i \(-0.546323\pi\)
−0.145014 + 0.989430i \(0.546323\pi\)
\(84\) 7.65310 0.835022
\(85\) 3.50154 0.379796
\(86\) 6.85832 0.739552
\(87\) −8.15985 −0.874828
\(88\) 45.5921 4.86013
\(89\) −8.52428 −0.903572 −0.451786 0.892126i \(-0.649213\pi\)
−0.451786 + 0.892126i \(0.649213\pi\)
\(90\) −1.88163 −0.198341
\(91\) −6.70734 −0.703121
\(92\) 14.9204 1.55556
\(93\) 0.414696 0.0430020
\(94\) 3.45355 0.356207
\(95\) −2.65152 −0.272040
\(96\) 21.4572 2.18997
\(97\) −9.89389 −1.00457 −0.502286 0.864701i \(-0.667508\pi\)
−0.502286 + 0.864701i \(0.667508\pi\)
\(98\) −2.65622 −0.268319
\(99\) 3.97930 0.399935
\(100\) 5.05553 0.505553
\(101\) 16.1935 1.61132 0.805658 0.592381i \(-0.201812\pi\)
0.805658 + 0.592381i \(0.201812\pi\)
\(102\) −14.0798 −1.39410
\(103\) 1.16218 0.114513 0.0572563 0.998360i \(-0.481765\pi\)
0.0572563 + 0.998360i \(0.481765\pi\)
\(104\) −54.4380 −5.33808
\(105\) −1.51381 −0.147733
\(106\) −20.4490 −1.98618
\(107\) 0.652067 0.0630377 0.0315188 0.999503i \(-0.489966\pi\)
0.0315188 + 0.999503i \(0.489966\pi\)
\(108\) 28.3807 2.73093
\(109\) −16.5406 −1.58430 −0.792150 0.610327i \(-0.791038\pi\)
−0.792150 + 0.610327i \(0.791038\pi\)
\(110\) −14.9212 −1.42268
\(111\) −18.2886 −1.73588
\(112\) −11.4473 −1.08167
\(113\) 11.0415 1.03870 0.519348 0.854563i \(-0.326175\pi\)
0.519348 + 0.854563i \(0.326175\pi\)
\(114\) 10.6618 0.998570
\(115\) −2.95131 −0.275211
\(116\) 27.2507 2.53017
\(117\) −4.75137 −0.439265
\(118\) 18.3231 1.68677
\(119\) 3.50154 0.320986
\(120\) −12.2863 −1.12158
\(121\) 20.5556 1.86869
\(122\) −6.76062 −0.612078
\(123\) −17.6856 −1.59465
\(124\) −1.38492 −0.124370
\(125\) −1.00000 −0.0894427
\(126\) −1.88163 −0.167629
\(127\) −12.7009 −1.12702 −0.563510 0.826109i \(-0.690549\pi\)
−0.563510 + 0.826109i \(0.690549\pi\)
\(128\) −10.8454 −0.958604
\(129\) 3.90862 0.344135
\(130\) 17.8162 1.56259
\(131\) −13.9205 −1.21624 −0.608118 0.793847i \(-0.708075\pi\)
−0.608118 + 0.793847i \(0.708075\pi\)
\(132\) 42.9908 3.74187
\(133\) −2.65152 −0.229916
\(134\) −29.7618 −2.57103
\(135\) −5.61378 −0.483158
\(136\) 28.4191 2.43692
\(137\) −12.7622 −1.09035 −0.545174 0.838323i \(-0.683536\pi\)
−0.545174 + 0.838323i \(0.683536\pi\)
\(138\) 11.8672 1.01021
\(139\) −10.9329 −0.927318 −0.463659 0.886014i \(-0.653464\pi\)
−0.463659 + 0.886014i \(0.653464\pi\)
\(140\) 5.05553 0.427270
\(141\) 1.96821 0.165754
\(142\) 40.4567 3.39505
\(143\) −37.6781 −3.15080
\(144\) −8.10910 −0.675758
\(145\) −5.39028 −0.447638
\(146\) −6.59858 −0.546102
\(147\) −1.51381 −0.124857
\(148\) 61.0769 5.02049
\(149\) 5.79702 0.474910 0.237455 0.971398i \(-0.423687\pi\)
0.237455 + 0.971398i \(0.423687\pi\)
\(150\) 4.02102 0.328315
\(151\) 13.8990 1.13108 0.565542 0.824719i \(-0.308667\pi\)
0.565542 + 0.824719i \(0.308667\pi\)
\(152\) −21.5202 −1.74552
\(153\) 2.48044 0.200531
\(154\) −14.9212 −1.20238
\(155\) 0.273942 0.0220036
\(156\) −51.3320 −4.10985
\(157\) 4.56085 0.363995 0.181998 0.983299i \(-0.441744\pi\)
0.181998 + 0.983299i \(0.441744\pi\)
\(158\) 39.3763 3.13261
\(159\) −11.6541 −0.924230
\(160\) 14.1743 1.12058
\(161\) −2.95131 −0.232595
\(162\) 16.9282 1.33001
\(163\) 18.2918 1.43273 0.716363 0.697728i \(-0.245805\pi\)
0.716363 + 0.697728i \(0.245805\pi\)
\(164\) 59.0629 4.61204
\(165\) −8.50372 −0.662014
\(166\) 7.01848 0.544740
\(167\) 9.54782 0.738833 0.369416 0.929264i \(-0.379558\pi\)
0.369416 + 0.929264i \(0.379558\pi\)
\(168\) −12.2863 −0.947911
\(169\) 31.9885 2.46065
\(170\) −9.30089 −0.713345
\(171\) −1.87830 −0.143637
\(172\) −13.0533 −0.995304
\(173\) −9.67300 −0.735424 −0.367712 0.929940i \(-0.619859\pi\)
−0.367712 + 0.929940i \(0.619859\pi\)
\(174\) 21.6744 1.64313
\(175\) −1.00000 −0.0755929
\(176\) −64.3046 −4.84714
\(177\) 10.4425 0.784905
\(178\) 22.6424 1.69712
\(179\) −9.80524 −0.732878 −0.366439 0.930442i \(-0.619423\pi\)
−0.366439 + 0.930442i \(0.619423\pi\)
\(180\) 3.58126 0.266931
\(181\) −6.60093 −0.490643 −0.245321 0.969442i \(-0.578894\pi\)
−0.245321 + 0.969442i \(0.578894\pi\)
\(182\) 17.8162 1.32063
\(183\) −3.85295 −0.284818
\(184\) −23.9533 −1.76586
\(185\) −12.0812 −0.888227
\(186\) −1.10153 −0.0807679
\(187\) 19.6697 1.43839
\(188\) −6.57307 −0.479390
\(189\) −5.61378 −0.408343
\(190\) 7.04304 0.510956
\(191\) 1.62418 0.117522 0.0587609 0.998272i \(-0.481285\pi\)
0.0587609 + 0.998272i \(0.481285\pi\)
\(192\) −22.3370 −1.61204
\(193\) 14.2891 1.02855 0.514276 0.857625i \(-0.328061\pi\)
0.514276 + 0.857625i \(0.328061\pi\)
\(194\) 26.2804 1.88682
\(195\) 10.1536 0.727117
\(196\) 5.05553 0.361109
\(197\) 15.2389 1.08573 0.542863 0.839821i \(-0.317340\pi\)
0.542863 + 0.839821i \(0.317340\pi\)
\(198\) −10.5699 −0.751171
\(199\) −23.6243 −1.67468 −0.837342 0.546679i \(-0.815892\pi\)
−0.837342 + 0.546679i \(0.815892\pi\)
\(200\) −8.11618 −0.573900
\(201\) −16.9615 −1.19637
\(202\) −43.0136 −3.02643
\(203\) −5.39028 −0.378323
\(204\) 26.7977 1.87621
\(205\) −11.6828 −0.815964
\(206\) −3.08700 −0.215081
\(207\) −2.09066 −0.145311
\(208\) 76.7812 5.32382
\(209\) −14.8947 −1.03029
\(210\) 4.02102 0.277476
\(211\) 15.4647 1.06464 0.532318 0.846545i \(-0.321321\pi\)
0.532318 + 0.846545i \(0.321321\pi\)
\(212\) 38.9201 2.67305
\(213\) 23.0567 1.57982
\(214\) −1.73204 −0.118400
\(215\) 2.58198 0.176090
\(216\) −45.5624 −3.10013
\(217\) 0.273942 0.0185964
\(218\) 43.9355 2.97569
\(219\) −3.76059 −0.254117
\(220\) 28.3991 1.91467
\(221\) −23.4861 −1.57984
\(222\) 48.5787 3.26039
\(223\) 5.23323 0.350443 0.175222 0.984529i \(-0.443936\pi\)
0.175222 + 0.984529i \(0.443936\pi\)
\(224\) 14.1743 0.947062
\(225\) −0.708384 −0.0472256
\(226\) −29.3287 −1.95092
\(227\) −3.44904 −0.228921 −0.114460 0.993428i \(-0.536514\pi\)
−0.114460 + 0.993428i \(0.536514\pi\)
\(228\) −20.2924 −1.34390
\(229\) 1.00000 0.0660819
\(230\) 7.83933 0.516910
\(231\) −8.50372 −0.559504
\(232\) −43.7484 −2.87223
\(233\) 8.49670 0.556637 0.278319 0.960489i \(-0.410223\pi\)
0.278319 + 0.960489i \(0.410223\pi\)
\(234\) 12.6207 0.825042
\(235\) 1.30017 0.0848140
\(236\) −34.8738 −2.27009
\(237\) 22.4409 1.45770
\(238\) −9.30089 −0.602887
\(239\) 27.0687 1.75093 0.875464 0.483283i \(-0.160556\pi\)
0.875464 + 0.483283i \(0.160556\pi\)
\(240\) 17.3291 1.11859
\(241\) −30.1325 −1.94100 −0.970502 0.241094i \(-0.922494\pi\)
−0.970502 + 0.241094i \(0.922494\pi\)
\(242\) −54.6002 −3.50983
\(243\) −7.19379 −0.461482
\(244\) 12.8673 0.823747
\(245\) −1.00000 −0.0638877
\(246\) 46.9768 2.99513
\(247\) 17.7847 1.13161
\(248\) 2.22336 0.141184
\(249\) 3.99990 0.253483
\(250\) 2.65622 0.167994
\(251\) 29.6848 1.87369 0.936844 0.349748i \(-0.113733\pi\)
0.936844 + 0.349748i \(0.113733\pi\)
\(252\) 3.58126 0.225598
\(253\) −16.5788 −1.04230
\(254\) 33.7364 2.11681
\(255\) −5.30067 −0.331941
\(256\) −0.703329 −0.0439581
\(257\) 16.5021 1.02938 0.514688 0.857378i \(-0.327908\pi\)
0.514688 + 0.857378i \(0.327908\pi\)
\(258\) −10.3822 −0.646367
\(259\) −12.0812 −0.750689
\(260\) −33.9092 −2.10296
\(261\) −3.81839 −0.236352
\(262\) 36.9759 2.28438
\(263\) −12.9787 −0.800299 −0.400150 0.916450i \(-0.631042\pi\)
−0.400150 + 0.916450i \(0.631042\pi\)
\(264\) −69.0177 −4.24774
\(265\) −7.69853 −0.472917
\(266\) 7.04304 0.431836
\(267\) 12.9041 0.789720
\(268\) 56.6449 3.46014
\(269\) −9.95346 −0.606873 −0.303436 0.952852i \(-0.598134\pi\)
−0.303436 + 0.952852i \(0.598134\pi\)
\(270\) 14.9115 0.907483
\(271\) 19.9720 1.21321 0.606606 0.795002i \(-0.292530\pi\)
0.606606 + 0.795002i \(0.292530\pi\)
\(272\) −40.0833 −2.43041
\(273\) 10.1536 0.614526
\(274\) 33.8992 2.04793
\(275\) −5.61743 −0.338744
\(276\) −22.5866 −1.35956
\(277\) −20.6401 −1.24014 −0.620071 0.784545i \(-0.712896\pi\)
−0.620071 + 0.784545i \(0.712896\pi\)
\(278\) 29.0403 1.74172
\(279\) 0.194056 0.0116179
\(280\) −8.11618 −0.485034
\(281\) 20.2289 1.20676 0.603379 0.797455i \(-0.293821\pi\)
0.603379 + 0.797455i \(0.293821\pi\)
\(282\) −5.22802 −0.311324
\(283\) 11.1824 0.664724 0.332362 0.943152i \(-0.392154\pi\)
0.332362 + 0.943152i \(0.392154\pi\)
\(284\) −77.0003 −4.56912
\(285\) 4.01390 0.237763
\(286\) 100.081 5.91794
\(287\) −11.6828 −0.689615
\(288\) 10.0409 0.591663
\(289\) −4.73919 −0.278776
\(290\) 14.3178 0.840770
\(291\) 14.9775 0.877994
\(292\) 12.5589 0.734955
\(293\) 17.2005 1.00486 0.502431 0.864617i \(-0.332439\pi\)
0.502431 + 0.864617i \(0.332439\pi\)
\(294\) 4.02102 0.234510
\(295\) 6.89816 0.401626
\(296\) −98.0531 −5.69922
\(297\) −31.5350 −1.82985
\(298\) −15.3982 −0.891993
\(299\) 19.7954 1.14480
\(300\) −7.65310 −0.441852
\(301\) 2.58198 0.148823
\(302\) −36.9189 −2.12444
\(303\) −24.5139 −1.40829
\(304\) 30.3528 1.74085
\(305\) −2.54520 −0.145738
\(306\) −6.58860 −0.376645
\(307\) −4.55690 −0.260076 −0.130038 0.991509i \(-0.541510\pi\)
−0.130038 + 0.991509i \(0.541510\pi\)
\(308\) 28.3991 1.61819
\(309\) −1.75931 −0.100084
\(310\) −0.727653 −0.0413279
\(311\) 9.73597 0.552076 0.276038 0.961147i \(-0.410978\pi\)
0.276038 + 0.961147i \(0.410978\pi\)
\(312\) 82.4087 4.66547
\(313\) −27.0676 −1.52995 −0.764975 0.644059i \(-0.777249\pi\)
−0.764975 + 0.644059i \(0.777249\pi\)
\(314\) −12.1146 −0.683668
\(315\) −0.708384 −0.0399129
\(316\) −74.9440 −4.21593
\(317\) −2.06045 −0.115727 −0.0578633 0.998325i \(-0.518429\pi\)
−0.0578633 + 0.998325i \(0.518429\pi\)
\(318\) 30.9559 1.73592
\(319\) −30.2795 −1.69533
\(320\) −14.7555 −0.824859
\(321\) −0.987104 −0.0550948
\(322\) 7.83933 0.436869
\(323\) −9.28442 −0.516599
\(324\) −32.2191 −1.78995
\(325\) 6.70734 0.372057
\(326\) −48.5872 −2.69100
\(327\) 25.0393 1.38467
\(328\) −94.8199 −5.23555
\(329\) 1.30017 0.0716809
\(330\) 22.5878 1.24342
\(331\) 25.6871 1.41189 0.705946 0.708266i \(-0.250522\pi\)
0.705946 + 0.708266i \(0.250522\pi\)
\(332\) −13.3581 −0.733121
\(333\) −8.55813 −0.468983
\(334\) −25.3612 −1.38770
\(335\) −11.2045 −0.612170
\(336\) 17.3291 0.945378
\(337\) −36.4109 −1.98343 −0.991715 0.128459i \(-0.958997\pi\)
−0.991715 + 0.128459i \(0.958997\pi\)
\(338\) −84.9686 −4.62168
\(339\) −16.7147 −0.907818
\(340\) 17.7022 0.960034
\(341\) 1.53885 0.0833336
\(342\) 4.98918 0.269784
\(343\) −1.00000 −0.0539949
\(344\) 20.9558 1.12986
\(345\) 4.46771 0.240533
\(346\) 25.6937 1.38130
\(347\) −23.3057 −1.25111 −0.625557 0.780179i \(-0.715128\pi\)
−0.625557 + 0.780179i \(0.715128\pi\)
\(348\) −41.2524 −2.21136
\(349\) 9.01582 0.482606 0.241303 0.970450i \(-0.422425\pi\)
0.241303 + 0.970450i \(0.422425\pi\)
\(350\) 2.65622 0.141981
\(351\) 37.6536 2.00980
\(352\) 79.6233 4.24394
\(353\) −13.3093 −0.708384 −0.354192 0.935173i \(-0.615244\pi\)
−0.354192 + 0.935173i \(0.615244\pi\)
\(354\) −27.7376 −1.47424
\(355\) 15.2309 0.808372
\(356\) −43.0948 −2.28402
\(357\) −5.30067 −0.280541
\(358\) 26.0449 1.37652
\(359\) −26.6487 −1.40646 −0.703232 0.710960i \(-0.748261\pi\)
−0.703232 + 0.710960i \(0.748261\pi\)
\(360\) −5.74937 −0.303018
\(361\) −11.9694 −0.629970
\(362\) 17.5335 0.921543
\(363\) −31.1172 −1.63323
\(364\) −33.9092 −1.77732
\(365\) −2.48419 −0.130029
\(366\) 10.2343 0.534955
\(367\) −3.89802 −0.203475 −0.101738 0.994811i \(-0.532440\pi\)
−0.101738 + 0.994811i \(0.532440\pi\)
\(368\) 33.7846 1.76114
\(369\) −8.27593 −0.430827
\(370\) 32.0904 1.66830
\(371\) −7.69853 −0.399688
\(372\) 2.09651 0.108699
\(373\) −7.23732 −0.374734 −0.187367 0.982290i \(-0.559995\pi\)
−0.187367 + 0.982290i \(0.559995\pi\)
\(374\) −52.2471 −2.70163
\(375\) 1.51381 0.0781727
\(376\) 10.5524 0.544201
\(377\) 36.1544 1.86205
\(378\) 14.9115 0.766963
\(379\) −25.4219 −1.30583 −0.652916 0.757430i \(-0.726455\pi\)
−0.652916 + 0.757430i \(0.726455\pi\)
\(380\) −13.4048 −0.687654
\(381\) 19.2267 0.985013
\(382\) −4.31420 −0.220734
\(383\) −14.8565 −0.759130 −0.379565 0.925165i \(-0.623926\pi\)
−0.379565 + 0.925165i \(0.623926\pi\)
\(384\) 16.4178 0.837818
\(385\) −5.61743 −0.286291
\(386\) −37.9550 −1.93186
\(387\) 1.82903 0.0929750
\(388\) −50.0189 −2.53932
\(389\) 38.7818 1.96632 0.983158 0.182759i \(-0.0585029\pi\)
0.983158 + 0.182759i \(0.0585029\pi\)
\(390\) −26.9703 −1.36570
\(391\) −10.3341 −0.522619
\(392\) −8.11618 −0.409929
\(393\) 21.0729 1.06299
\(394\) −40.4779 −2.03925
\(395\) 14.8242 0.745885
\(396\) 20.1175 1.01094
\(397\) 38.4140 1.92794 0.963972 0.266003i \(-0.0857033\pi\)
0.963972 + 0.266003i \(0.0857033\pi\)
\(398\) 62.7515 3.14545
\(399\) 4.01390 0.200946
\(400\) 11.4473 0.572366
\(401\) −28.4830 −1.42238 −0.711188 0.703002i \(-0.751842\pi\)
−0.711188 + 0.703002i \(0.751842\pi\)
\(402\) 45.0536 2.24707
\(403\) −1.83743 −0.0915287
\(404\) 81.8669 4.07303
\(405\) 6.37304 0.316679
\(406\) 14.3178 0.710580
\(407\) −67.8653 −3.36396
\(408\) −43.0211 −2.12986
\(409\) −1.98230 −0.0980186 −0.0490093 0.998798i \(-0.515606\pi\)
−0.0490093 + 0.998798i \(0.515606\pi\)
\(410\) 31.0322 1.53257
\(411\) 19.3195 0.952961
\(412\) 5.87541 0.289461
\(413\) 6.89816 0.339436
\(414\) 5.55326 0.272928
\(415\) 2.64228 0.129704
\(416\) −95.0721 −4.66129
\(417\) 16.5503 0.810474
\(418\) 39.5638 1.93513
\(419\) 5.48057 0.267743 0.133872 0.990999i \(-0.457259\pi\)
0.133872 + 0.990999i \(0.457259\pi\)
\(420\) −7.65310 −0.373433
\(421\) 10.4433 0.508977 0.254489 0.967076i \(-0.418093\pi\)
0.254489 + 0.967076i \(0.418093\pi\)
\(422\) −41.0778 −1.99964
\(423\) 0.921022 0.0447816
\(424\) −62.4826 −3.03442
\(425\) −3.50154 −0.169850
\(426\) −61.2437 −2.96727
\(427\) −2.54520 −0.123171
\(428\) 3.29654 0.159344
\(429\) 57.0374 2.75379
\(430\) −6.85832 −0.330738
\(431\) 31.3523 1.51019 0.755094 0.655617i \(-0.227591\pi\)
0.755094 + 0.655617i \(0.227591\pi\)
\(432\) 64.2628 3.09185
\(433\) −5.66794 −0.272384 −0.136192 0.990682i \(-0.543486\pi\)
−0.136192 + 0.990682i \(0.543486\pi\)
\(434\) −0.727653 −0.0349284
\(435\) 8.15985 0.391235
\(436\) −83.6214 −4.00474
\(437\) 7.82545 0.374342
\(438\) 9.98898 0.477292
\(439\) 13.7505 0.656277 0.328138 0.944630i \(-0.393579\pi\)
0.328138 + 0.944630i \(0.393579\pi\)
\(440\) −45.5921 −2.17352
\(441\) −0.708384 −0.0337326
\(442\) 62.3842 2.96732
\(443\) −5.84652 −0.277777 −0.138888 0.990308i \(-0.544353\pi\)
−0.138888 + 0.990308i \(0.544353\pi\)
\(444\) −92.4587 −4.38790
\(445\) 8.52428 0.404090
\(446\) −13.9006 −0.658215
\(447\) −8.77558 −0.415071
\(448\) −14.7555 −0.697133
\(449\) 32.0260 1.51140 0.755700 0.654918i \(-0.227297\pi\)
0.755700 + 0.654918i \(0.227297\pi\)
\(450\) 1.88163 0.0887007
\(451\) −65.6275 −3.09028
\(452\) 55.8206 2.62558
\(453\) −21.0404 −0.988565
\(454\) 9.16143 0.429967
\(455\) 6.70734 0.314445
\(456\) 32.5775 1.52558
\(457\) −6.31353 −0.295335 −0.147667 0.989037i \(-0.547176\pi\)
−0.147667 + 0.989037i \(0.547176\pi\)
\(458\) −2.65622 −0.124117
\(459\) −19.6569 −0.917506
\(460\) −14.9204 −0.695668
\(461\) −19.4989 −0.908155 −0.454078 0.890962i \(-0.650031\pi\)
−0.454078 + 0.890962i \(0.650031\pi\)
\(462\) 22.5878 1.05088
\(463\) −10.8987 −0.506504 −0.253252 0.967400i \(-0.581500\pi\)
−0.253252 + 0.967400i \(0.581500\pi\)
\(464\) 61.7043 2.86455
\(465\) −0.414696 −0.0192311
\(466\) −22.5691 −1.04549
\(467\) 11.1970 0.518137 0.259069 0.965859i \(-0.416584\pi\)
0.259069 + 0.965859i \(0.416584\pi\)
\(468\) −24.0207 −1.11036
\(469\) −11.2045 −0.517378
\(470\) −3.45355 −0.159301
\(471\) −6.90425 −0.318131
\(472\) 55.9867 2.57699
\(473\) 14.5041 0.666899
\(474\) −59.6082 −2.73789
\(475\) 2.65152 0.121660
\(476\) 17.7022 0.811377
\(477\) −5.45351 −0.249699
\(478\) −71.9005 −3.28865
\(479\) −2.34399 −0.107100 −0.0535499 0.998565i \(-0.517054\pi\)
−0.0535499 + 0.998565i \(0.517054\pi\)
\(480\) −21.4572 −0.979383
\(481\) 81.0328 3.69478
\(482\) 80.0386 3.64566
\(483\) 4.46771 0.203288
\(484\) 103.919 4.72360
\(485\) 9.89389 0.449258
\(486\) 19.1083 0.866771
\(487\) 25.0498 1.13512 0.567558 0.823334i \(-0.307888\pi\)
0.567558 + 0.823334i \(0.307888\pi\)
\(488\) −20.6573 −0.935112
\(489\) −27.6903 −1.25220
\(490\) 2.65622 0.119996
\(491\) 35.7735 1.61444 0.807218 0.590253i \(-0.200972\pi\)
0.807218 + 0.590253i \(0.200972\pi\)
\(492\) −89.4099 −4.03091
\(493\) −18.8743 −0.850055
\(494\) −47.2401 −2.12543
\(495\) −3.97930 −0.178856
\(496\) −3.13591 −0.140806
\(497\) 15.2309 0.683199
\(498\) −10.6246 −0.476101
\(499\) 10.2451 0.458632 0.229316 0.973352i \(-0.426351\pi\)
0.229316 + 0.973352i \(0.426351\pi\)
\(500\) −5.05553 −0.226090
\(501\) −14.4536 −0.645738
\(502\) −78.8495 −3.51923
\(503\) 2.11048 0.0941015 0.0470508 0.998892i \(-0.485018\pi\)
0.0470508 + 0.998892i \(0.485018\pi\)
\(504\) −5.74937 −0.256097
\(505\) −16.1935 −0.720602
\(506\) 44.0369 1.95768
\(507\) −48.4244 −2.15060
\(508\) −64.2096 −2.84884
\(509\) −12.4030 −0.549754 −0.274877 0.961479i \(-0.588637\pi\)
−0.274877 + 0.961479i \(0.588637\pi\)
\(510\) 14.0798 0.623462
\(511\) −2.48419 −0.109894
\(512\) 23.5589 1.04117
\(513\) 14.8851 0.657192
\(514\) −43.8334 −1.93341
\(515\) −1.16218 −0.0512116
\(516\) 19.7602 0.869893
\(517\) 7.30364 0.321214
\(518\) 32.0904 1.40997
\(519\) 14.6431 0.642759
\(520\) 54.4380 2.38726
\(521\) −43.2220 −1.89359 −0.946795 0.321838i \(-0.895699\pi\)
−0.946795 + 0.321838i \(0.895699\pi\)
\(522\) 10.1425 0.443925
\(523\) −10.6599 −0.466126 −0.233063 0.972462i \(-0.574875\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(524\) −70.3753 −3.07436
\(525\) 1.51381 0.0660680
\(526\) 34.4743 1.50315
\(527\) 0.959221 0.0417843
\(528\) 97.3448 4.23639
\(529\) −14.2898 −0.621296
\(530\) 20.4490 0.888249
\(531\) 4.88654 0.212058
\(532\) −13.4048 −0.581174
\(533\) 78.3607 3.39418
\(534\) −34.2763 −1.48328
\(535\) −0.652067 −0.0281913
\(536\) −90.9380 −3.92792
\(537\) 14.8433 0.640534
\(538\) 26.4386 1.13985
\(539\) −5.61743 −0.241960
\(540\) −28.3807 −1.22131
\(541\) −23.7434 −1.02081 −0.510405 0.859934i \(-0.670504\pi\)
−0.510405 + 0.859934i \(0.670504\pi\)
\(542\) −53.0501 −2.27870
\(543\) 9.99254 0.428821
\(544\) 49.6320 2.12795
\(545\) 16.5406 0.708520
\(546\) −26.9703 −1.15422
\(547\) −4.77270 −0.204066 −0.102033 0.994781i \(-0.532535\pi\)
−0.102033 + 0.994781i \(0.532535\pi\)
\(548\) −64.5196 −2.75614
\(549\) −1.80298 −0.0769493
\(550\) 14.9212 0.636241
\(551\) 14.2924 0.608878
\(552\) 36.2607 1.54336
\(553\) 14.8242 0.630387
\(554\) 54.8247 2.32928
\(555\) 18.2886 0.776309
\(556\) −55.2717 −2.34404
\(557\) 15.0751 0.638754 0.319377 0.947628i \(-0.396526\pi\)
0.319377 + 0.947628i \(0.396526\pi\)
\(558\) −0.515457 −0.0218211
\(559\) −17.3182 −0.732483
\(560\) 11.4473 0.483738
\(561\) −29.7761 −1.25715
\(562\) −53.7326 −2.26657
\(563\) 40.7045 1.71549 0.857744 0.514076i \(-0.171865\pi\)
0.857744 + 0.514076i \(0.171865\pi\)
\(564\) 9.95037 0.418986
\(565\) −11.0415 −0.464519
\(566\) −29.7029 −1.24851
\(567\) 6.37304 0.267643
\(568\) 123.617 5.18684
\(569\) −15.6312 −0.655294 −0.327647 0.944800i \(-0.606256\pi\)
−0.327647 + 0.944800i \(0.606256\pi\)
\(570\) −10.6618 −0.446574
\(571\) −32.6103 −1.36470 −0.682350 0.731026i \(-0.739042\pi\)
−0.682350 + 0.731026i \(0.739042\pi\)
\(572\) −190.483 −7.96448
\(573\) −2.45870 −0.102714
\(574\) 31.0322 1.29526
\(575\) 2.95131 0.123078
\(576\) −10.4526 −0.435524
\(577\) 38.0912 1.58576 0.792878 0.609380i \(-0.208582\pi\)
0.792878 + 0.609380i \(0.208582\pi\)
\(578\) 12.5884 0.523607
\(579\) −21.6309 −0.898951
\(580\) −27.2507 −1.13152
\(581\) 2.64228 0.109620
\(582\) −39.7835 −1.64908
\(583\) −43.2460 −1.79106
\(584\) −20.1622 −0.834316
\(585\) 4.75137 0.196445
\(586\) −45.6883 −1.88737
\(587\) −10.2691 −0.423852 −0.211926 0.977286i \(-0.567974\pi\)
−0.211926 + 0.977286i \(0.567974\pi\)
\(588\) −7.65310 −0.315609
\(589\) −0.726364 −0.0299293
\(590\) −18.3231 −0.754348
\(591\) −23.0688 −0.948922
\(592\) 138.297 5.68399
\(593\) −21.1890 −0.870130 −0.435065 0.900399i \(-0.643275\pi\)
−0.435065 + 0.900399i \(0.643275\pi\)
\(594\) 83.7642 3.43689
\(595\) −3.50154 −0.143549
\(596\) 29.3070 1.20046
\(597\) 35.7627 1.46367
\(598\) −52.5811 −2.15020
\(599\) 20.8047 0.850057 0.425029 0.905180i \(-0.360264\pi\)
0.425029 + 0.905180i \(0.360264\pi\)
\(600\) 12.2863 0.501588
\(601\) 3.30127 0.134662 0.0673308 0.997731i \(-0.478552\pi\)
0.0673308 + 0.997731i \(0.478552\pi\)
\(602\) −6.85832 −0.279524
\(603\) −7.93712 −0.323224
\(604\) 70.2668 2.85912
\(605\) −20.5556 −0.835702
\(606\) 65.1144 2.64509
\(607\) 22.6403 0.918940 0.459470 0.888193i \(-0.348039\pi\)
0.459470 + 0.888193i \(0.348039\pi\)
\(608\) −37.5835 −1.52421
\(609\) 8.15985 0.330654
\(610\) 6.76062 0.273730
\(611\) −8.72071 −0.352802
\(612\) 12.5399 0.506896
\(613\) −3.14411 −0.126990 −0.0634948 0.997982i \(-0.520225\pi\)
−0.0634948 + 0.997982i \(0.520225\pi\)
\(614\) 12.1042 0.488484
\(615\) 17.6856 0.713151
\(616\) −45.5921 −1.83696
\(617\) −0.941897 −0.0379193 −0.0189597 0.999820i \(-0.506035\pi\)
−0.0189597 + 0.999820i \(0.506035\pi\)
\(618\) 4.67312 0.187981
\(619\) −23.1470 −0.930358 −0.465179 0.885217i \(-0.654010\pi\)
−0.465179 + 0.885217i \(0.654010\pi\)
\(620\) 1.38492 0.0556199
\(621\) 16.5680 0.664850
\(622\) −25.8609 −1.03693
\(623\) 8.52428 0.341518
\(624\) −116.232 −4.65300
\(625\) 1.00000 0.0400000
\(626\) 71.8976 2.87361
\(627\) 22.5478 0.900472
\(628\) 23.0575 0.920094
\(629\) −42.3028 −1.68672
\(630\) 1.88163 0.0749658
\(631\) 36.7727 1.46390 0.731950 0.681358i \(-0.238610\pi\)
0.731950 + 0.681358i \(0.238610\pi\)
\(632\) 120.315 4.78589
\(633\) −23.4106 −0.930489
\(634\) 5.47303 0.217362
\(635\) 12.7009 0.504019
\(636\) −58.9176 −2.33624
\(637\) 6.70734 0.265755
\(638\) 80.4292 3.18422
\(639\) 10.7893 0.426819
\(640\) 10.8454 0.428701
\(641\) −42.2603 −1.66918 −0.834590 0.550872i \(-0.814295\pi\)
−0.834590 + 0.550872i \(0.814295\pi\)
\(642\) 2.62197 0.103481
\(643\) 7.65256 0.301788 0.150894 0.988550i \(-0.451785\pi\)
0.150894 + 0.988550i \(0.451785\pi\)
\(644\) −14.9204 −0.587947
\(645\) −3.90862 −0.153902
\(646\) 24.6615 0.970294
\(647\) −22.2364 −0.874204 −0.437102 0.899412i \(-0.643995\pi\)
−0.437102 + 0.899412i \(0.643995\pi\)
\(648\) 51.7247 2.03194
\(649\) 38.7499 1.52107
\(650\) −17.8162 −0.698809
\(651\) −0.414696 −0.0162532
\(652\) 92.4749 3.62160
\(653\) 44.7336 1.75056 0.875281 0.483614i \(-0.160676\pi\)
0.875281 + 0.483614i \(0.160676\pi\)
\(654\) −66.5099 −2.60074
\(655\) 13.9205 0.543917
\(656\) 133.737 5.22156
\(657\) −1.75976 −0.0686549
\(658\) −3.45355 −0.134634
\(659\) −1.41094 −0.0549625 −0.0274812 0.999622i \(-0.508749\pi\)
−0.0274812 + 0.999622i \(0.508749\pi\)
\(660\) −42.9908 −1.67341
\(661\) 20.0899 0.781407 0.390704 0.920516i \(-0.372232\pi\)
0.390704 + 0.920516i \(0.372232\pi\)
\(662\) −68.2307 −2.65186
\(663\) 35.5534 1.38078
\(664\) 21.4452 0.832234
\(665\) 2.65152 0.102822
\(666\) 22.7323 0.880859
\(667\) 15.9084 0.615974
\(668\) 48.2693 1.86760
\(669\) −7.92211 −0.306287
\(670\) 29.7618 1.14980
\(671\) −14.2975 −0.551948
\(672\) −21.4572 −0.827730
\(673\) 15.3919 0.593315 0.296658 0.954984i \(-0.404128\pi\)
0.296658 + 0.954984i \(0.404128\pi\)
\(674\) 96.7156 3.72535
\(675\) 5.61378 0.216075
\(676\) 161.719 6.21995
\(677\) 45.5583 1.75095 0.875475 0.483264i \(-0.160549\pi\)
0.875475 + 0.483264i \(0.160549\pi\)
\(678\) 44.3980 1.70510
\(679\) 9.89389 0.379693
\(680\) −28.4191 −1.08982
\(681\) 5.22119 0.200076
\(682\) −4.08754 −0.156520
\(683\) 11.6283 0.444943 0.222472 0.974939i \(-0.428587\pi\)
0.222472 + 0.974939i \(0.428587\pi\)
\(684\) −9.49578 −0.363080
\(685\) 12.7622 0.487618
\(686\) 2.65622 0.101415
\(687\) −1.51381 −0.0577554
\(688\) −29.5568 −1.12684
\(689\) 51.6367 1.96720
\(690\) −11.8672 −0.451778
\(691\) 41.4396 1.57644 0.788219 0.615395i \(-0.211003\pi\)
0.788219 + 0.615395i \(0.211003\pi\)
\(692\) −48.9021 −1.85898
\(693\) −3.97930 −0.151161
\(694\) 61.9051 2.34988
\(695\) 10.9329 0.414709
\(696\) 66.2268 2.51032
\(697\) −40.9079 −1.54950
\(698\) −23.9480 −0.906447
\(699\) −12.8624 −0.486500
\(700\) −5.05553 −0.191081
\(701\) −42.4078 −1.60172 −0.800860 0.598851i \(-0.795624\pi\)
−0.800860 + 0.598851i \(0.795624\pi\)
\(702\) −100.016 −3.77487
\(703\) 32.0336 1.20817
\(704\) −82.8882 −3.12397
\(705\) −1.96821 −0.0741272
\(706\) 35.3525 1.33051
\(707\) −16.1935 −0.609020
\(708\) 52.7923 1.98406
\(709\) 21.1732 0.795176 0.397588 0.917564i \(-0.369847\pi\)
0.397588 + 0.917564i \(0.369847\pi\)
\(710\) −40.4567 −1.51831
\(711\) 10.5012 0.393826
\(712\) 69.1846 2.59280
\(713\) −0.808488 −0.0302781
\(714\) 14.0798 0.526922
\(715\) 37.6781 1.40908
\(716\) −49.5707 −1.85254
\(717\) −40.9768 −1.53031
\(718\) 70.7850 2.64167
\(719\) 10.6007 0.395341 0.197670 0.980269i \(-0.436662\pi\)
0.197670 + 0.980269i \(0.436662\pi\)
\(720\) 8.10910 0.302208
\(721\) −1.16218 −0.0432817
\(722\) 31.7935 1.18323
\(723\) 45.6148 1.69643
\(724\) −33.3712 −1.24023
\(725\) 5.39028 0.200190
\(726\) 82.6542 3.06758
\(727\) 3.04442 0.112911 0.0564556 0.998405i \(-0.482020\pi\)
0.0564556 + 0.998405i \(0.482020\pi\)
\(728\) 54.4380 2.01761
\(729\) 30.0091 1.11145
\(730\) 6.59858 0.244224
\(731\) 9.04092 0.334390
\(732\) −19.4787 −0.719953
\(733\) 43.1521 1.59386 0.796929 0.604073i \(-0.206457\pi\)
0.796929 + 0.604073i \(0.206457\pi\)
\(734\) 10.3540 0.382174
\(735\) 1.51381 0.0558377
\(736\) −41.8327 −1.54198
\(737\) −62.9408 −2.31845
\(738\) 21.9827 0.809195
\(739\) −3.66420 −0.134790 −0.0673948 0.997726i \(-0.521469\pi\)
−0.0673948 + 0.997726i \(0.521469\pi\)
\(740\) −61.0769 −2.24523
\(741\) −26.9226 −0.989026
\(742\) 20.4490 0.750707
\(743\) 11.6927 0.428963 0.214482 0.976728i \(-0.431194\pi\)
0.214482 + 0.976728i \(0.431194\pi\)
\(744\) −3.36575 −0.123394
\(745\) −5.79702 −0.212386
\(746\) 19.2239 0.703838
\(747\) 1.87175 0.0684836
\(748\) 99.4407 3.63591
\(749\) −0.652067 −0.0238260
\(750\) −4.02102 −0.146827
\(751\) −48.2460 −1.76052 −0.880260 0.474492i \(-0.842632\pi\)
−0.880260 + 0.474492i \(0.842632\pi\)
\(752\) −14.8835 −0.542746
\(753\) −44.9371 −1.63760
\(754\) −96.0343 −3.49736
\(755\) −13.8990 −0.505836
\(756\) −28.3807 −1.03219
\(757\) −42.0645 −1.52886 −0.764430 0.644706i \(-0.776980\pi\)
−0.764430 + 0.644706i \(0.776980\pi\)
\(758\) 67.5262 2.45266
\(759\) 25.0971 0.910966
\(760\) 21.5202 0.780620
\(761\) −9.95970 −0.361039 −0.180519 0.983571i \(-0.557778\pi\)
−0.180519 + 0.983571i \(0.557778\pi\)
\(762\) −51.0704 −1.85009
\(763\) 16.5406 0.598809
\(764\) 8.21111 0.297068
\(765\) −2.48044 −0.0896804
\(766\) 39.4621 1.42582
\(767\) −46.2683 −1.67065
\(768\) 1.06471 0.0384193
\(769\) −17.4058 −0.627670 −0.313835 0.949478i \(-0.601614\pi\)
−0.313835 + 0.949478i \(0.601614\pi\)
\(770\) 14.9212 0.537721
\(771\) −24.9811 −0.899672
\(772\) 72.2389 2.59994
\(773\) 10.5363 0.378965 0.189483 0.981884i \(-0.439319\pi\)
0.189483 + 0.981884i \(0.439319\pi\)
\(774\) −4.85833 −0.174629
\(775\) −0.273942 −0.00984030
\(776\) 80.3005 2.88262
\(777\) 18.2886 0.656101
\(778\) −103.013 −3.69320
\(779\) 30.9773 1.10988
\(780\) 51.3320 1.83798
\(781\) 85.5585 3.06153
\(782\) 27.4498 0.981601
\(783\) 30.2598 1.08140
\(784\) 11.4473 0.408833
\(785\) −4.56085 −0.162784
\(786\) −55.9744 −1.99654
\(787\) −18.7895 −0.669773 −0.334887 0.942258i \(-0.608698\pi\)
−0.334887 + 0.942258i \(0.608698\pi\)
\(788\) 77.0407 2.74446
\(789\) 19.6472 0.699460
\(790\) −39.3763 −1.40095
\(791\) −11.0415 −0.392590
\(792\) −32.2967 −1.14761
\(793\) 17.0715 0.606228
\(794\) −102.036 −3.62113
\(795\) 11.6541 0.413328
\(796\) −119.434 −4.23321
\(797\) 12.9079 0.457220 0.228610 0.973518i \(-0.426582\pi\)
0.228610 + 0.973518i \(0.426582\pi\)
\(798\) −10.6618 −0.377424
\(799\) 4.55262 0.161060
\(800\) −14.1743 −0.501138
\(801\) 6.03846 0.213359
\(802\) 75.6574 2.67155
\(803\) −13.9548 −0.492454
\(804\) −85.7495 −3.02415
\(805\) 2.95131 0.104020
\(806\) 4.88062 0.171912
\(807\) 15.0676 0.530406
\(808\) −131.430 −4.62367
\(809\) 0.308333 0.0108404 0.00542021 0.999985i \(-0.498275\pi\)
0.00542021 + 0.999985i \(0.498275\pi\)
\(810\) −16.9282 −0.594797
\(811\) −0.768081 −0.0269710 −0.0134855 0.999909i \(-0.504293\pi\)
−0.0134855 + 0.999909i \(0.504293\pi\)
\(812\) −27.2507 −0.956313
\(813\) −30.2338 −1.06035
\(814\) 180.266 6.31830
\(815\) −18.2918 −0.640735
\(816\) 60.6785 2.12417
\(817\) −6.84618 −0.239517
\(818\) 5.26545 0.184102
\(819\) 4.75137 0.166026
\(820\) −59.0629 −2.06257
\(821\) 55.2580 1.92852 0.964258 0.264965i \(-0.0853603\pi\)
0.964258 + 0.264965i \(0.0853603\pi\)
\(822\) −51.3169 −1.78988
\(823\) −4.39604 −0.153236 −0.0766182 0.997061i \(-0.524412\pi\)
−0.0766182 + 0.997061i \(0.524412\pi\)
\(824\) −9.43242 −0.328594
\(825\) 8.50372 0.296061
\(826\) −18.3231 −0.637541
\(827\) 15.2604 0.530658 0.265329 0.964158i \(-0.414519\pi\)
0.265329 + 0.964158i \(0.414519\pi\)
\(828\) −10.5694 −0.367311
\(829\) 10.4854 0.364174 0.182087 0.983282i \(-0.441715\pi\)
0.182087 + 0.983282i \(0.441715\pi\)
\(830\) −7.01848 −0.243615
\(831\) 31.2451 1.08388
\(832\) 98.9704 3.43118
\(833\) −3.50154 −0.121321
\(834\) −43.9614 −1.52226
\(835\) −9.54782 −0.330416
\(836\) −75.3008 −2.60433
\(837\) −1.53785 −0.0531560
\(838\) −14.5576 −0.502885
\(839\) −20.3896 −0.703926 −0.351963 0.936014i \(-0.614486\pi\)
−0.351963 + 0.936014i \(0.614486\pi\)
\(840\) 12.2863 0.423919
\(841\) 0.0550947 0.00189982
\(842\) −27.7399 −0.955978
\(843\) −30.6227 −1.05470
\(844\) 78.1824 2.69115
\(845\) −31.9885 −1.10044
\(846\) −2.44644 −0.0841104
\(847\) −20.5556 −0.706297
\(848\) 88.1276 3.02631
\(849\) −16.9280 −0.580967
\(850\) 9.30089 0.319018
\(851\) 35.6553 1.22225
\(852\) 116.564 3.99340
\(853\) 40.9355 1.40161 0.700803 0.713355i \(-0.252825\pi\)
0.700803 + 0.713355i \(0.252825\pi\)
\(854\) 6.76062 0.231344
\(855\) 1.87830 0.0642364
\(856\) −5.29229 −0.180887
\(857\) −41.6726 −1.42351 −0.711754 0.702429i \(-0.752099\pi\)
−0.711754 + 0.702429i \(0.752099\pi\)
\(858\) −151.504 −5.17226
\(859\) −4.02910 −0.137471 −0.0687355 0.997635i \(-0.521896\pi\)
−0.0687355 + 0.997635i \(0.521896\pi\)
\(860\) 13.0533 0.445113
\(861\) 17.6856 0.602722
\(862\) −83.2788 −2.83649
\(863\) 10.7325 0.365340 0.182670 0.983174i \(-0.441526\pi\)
0.182670 + 0.983174i \(0.441526\pi\)
\(864\) −79.5716 −2.70708
\(865\) 9.67300 0.328892
\(866\) 15.0553 0.511601
\(867\) 7.17423 0.243650
\(868\) 1.38492 0.0470074
\(869\) 83.2737 2.82487
\(870\) −21.6744 −0.734831
\(871\) 75.1527 2.54645
\(872\) 134.246 4.54615
\(873\) 7.00867 0.237208
\(874\) −20.7862 −0.703102
\(875\) 1.00000 0.0338062
\(876\) −19.0118 −0.642349
\(877\) 33.2601 1.12311 0.561557 0.827438i \(-0.310203\pi\)
0.561557 + 0.827438i \(0.310203\pi\)
\(878\) −36.5245 −1.23264
\(879\) −26.0382 −0.878248
\(880\) 64.3046 2.16771
\(881\) −1.76688 −0.0595276 −0.0297638 0.999557i \(-0.509476\pi\)
−0.0297638 + 0.999557i \(0.509476\pi\)
\(882\) 1.88163 0.0633577
\(883\) 6.54931 0.220402 0.110201 0.993909i \(-0.464851\pi\)
0.110201 + 0.993909i \(0.464851\pi\)
\(884\) −118.734 −3.99347
\(885\) −10.4425 −0.351020
\(886\) 15.5297 0.521730
\(887\) 51.1135 1.71622 0.858112 0.513462i \(-0.171637\pi\)
0.858112 + 0.513462i \(0.171637\pi\)
\(888\) 148.434 4.98111
\(889\) 12.7009 0.425974
\(890\) −22.6424 −0.758975
\(891\) 35.8001 1.19935
\(892\) 26.4568 0.885838
\(893\) −3.44744 −0.115364
\(894\) 23.3099 0.779600
\(895\) 9.80524 0.327753
\(896\) 10.8454 0.362318
\(897\) −29.9665 −1.00055
\(898\) −85.0682 −2.83876
\(899\) −1.47663 −0.0492482
\(900\) −3.58126 −0.119375
\(901\) −26.9567 −0.898059
\(902\) 174.321 5.80427
\(903\) −3.90862 −0.130071
\(904\) −89.6147 −2.98054
\(905\) 6.60093 0.219422
\(906\) 55.8881 1.85676
\(907\) 37.1475 1.23346 0.616731 0.787174i \(-0.288457\pi\)
0.616731 + 0.787174i \(0.288457\pi\)
\(908\) −17.4367 −0.578658
\(909\) −11.4712 −0.380477
\(910\) −17.8162 −0.590602
\(911\) −3.48687 −0.115525 −0.0577625 0.998330i \(-0.518397\pi\)
−0.0577625 + 0.998330i \(0.518397\pi\)
\(912\) −45.9484 −1.52150
\(913\) 14.8428 0.491225
\(914\) 16.7702 0.554708
\(915\) 3.85295 0.127374
\(916\) 5.05553 0.167039
\(917\) 13.9205 0.459694
\(918\) 52.2132 1.72329
\(919\) 4.78324 0.157785 0.0788923 0.996883i \(-0.474862\pi\)
0.0788923 + 0.996883i \(0.474862\pi\)
\(920\) 23.9533 0.789717
\(921\) 6.89828 0.227306
\(922\) 51.7935 1.70573
\(923\) −102.159 −3.36260
\(924\) −42.9908 −1.41429
\(925\) 12.0812 0.397227
\(926\) 28.9493 0.951334
\(927\) −0.823266 −0.0270396
\(928\) −76.4035 −2.50807
\(929\) 21.3587 0.700756 0.350378 0.936608i \(-0.386053\pi\)
0.350378 + 0.936608i \(0.386053\pi\)
\(930\) 1.10153 0.0361205
\(931\) 2.65152 0.0869001
\(932\) 42.9553 1.40705
\(933\) −14.7384 −0.482514
\(934\) −29.7419 −0.973183
\(935\) −19.6697 −0.643267
\(936\) 38.5630 1.26047
\(937\) −34.6083 −1.13061 −0.565303 0.824884i \(-0.691241\pi\)
−0.565303 + 0.824884i \(0.691241\pi\)
\(938\) 29.7618 0.971757
\(939\) 40.9752 1.33717
\(940\) 6.57307 0.214390
\(941\) −18.5399 −0.604384 −0.302192 0.953247i \(-0.597718\pi\)
−0.302192 + 0.953247i \(0.597718\pi\)
\(942\) 18.3392 0.597524
\(943\) 34.4796 1.12281
\(944\) −78.9655 −2.57011
\(945\) 5.61378 0.182616
\(946\) −38.5262 −1.25259
\(947\) −18.2536 −0.593161 −0.296580 0.955008i \(-0.595846\pi\)
−0.296580 + 0.955008i \(0.595846\pi\)
\(948\) 113.451 3.68471
\(949\) 16.6623 0.540883
\(950\) −7.04304 −0.228506
\(951\) 3.11913 0.101145
\(952\) −28.4191 −0.921070
\(953\) −9.62462 −0.311772 −0.155886 0.987775i \(-0.549823\pi\)
−0.155886 + 0.987775i \(0.549823\pi\)
\(954\) 14.4858 0.468994
\(955\) −1.62418 −0.0525573
\(956\) 136.847 4.42594
\(957\) 45.8374 1.48171
\(958\) 6.22617 0.201158
\(959\) 12.7622 0.412112
\(960\) 22.3370 0.720925
\(961\) −30.9250 −0.997579
\(962\) −215.241 −6.93966
\(963\) −0.461914 −0.0148850
\(964\) −152.336 −4.90640
\(965\) −14.2891 −0.459982
\(966\) −11.8672 −0.381822
\(967\) −6.76836 −0.217656 −0.108828 0.994061i \(-0.534710\pi\)
−0.108828 + 0.994061i \(0.534710\pi\)
\(968\) −166.832 −5.36220
\(969\) 14.0548 0.451506
\(970\) −26.2804 −0.843813
\(971\) −20.6510 −0.662723 −0.331362 0.943504i \(-0.607508\pi\)
−0.331362 + 0.943504i \(0.607508\pi\)
\(972\) −36.3684 −1.16652
\(973\) 10.9329 0.350493
\(974\) −66.5380 −2.13201
\(975\) −10.1536 −0.325177
\(976\) 29.1357 0.932612
\(977\) 2.60314 0.0832819 0.0416410 0.999133i \(-0.486741\pi\)
0.0416410 + 0.999133i \(0.486741\pi\)
\(978\) 73.5517 2.35192
\(979\) 47.8846 1.53040
\(980\) −5.05553 −0.161493
\(981\) 11.7171 0.374097
\(982\) −95.0225 −3.03229
\(983\) 0.259340 0.00827165 0.00413582 0.999991i \(-0.498684\pi\)
0.00413582 + 0.999991i \(0.498684\pi\)
\(984\) 143.539 4.57586
\(985\) −15.2389 −0.485551
\(986\) 50.1344 1.59660
\(987\) −1.96821 −0.0626490
\(988\) 89.9109 2.86045
\(989\) −7.62021 −0.242309
\(990\) 10.5699 0.335934
\(991\) −57.0784 −1.81315 −0.906577 0.422040i \(-0.861314\pi\)
−0.906577 + 0.422040i \(0.861314\pi\)
\(992\) 3.88295 0.123284
\(993\) −38.8854 −1.23399
\(994\) −40.4567 −1.28321
\(995\) 23.6243 0.748942
\(996\) 20.2216 0.640746
\(997\) 55.0691 1.74405 0.872027 0.489457i \(-0.162805\pi\)
0.872027 + 0.489457i \(0.162805\pi\)
\(998\) −27.2132 −0.861418
\(999\) 67.8212 2.14577
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 \(a_p\))