Properties

Label 6041.2.a.b.1.1
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 1
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\)
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.381966 q^{3}\) \(-1.00000 q^{4}\) \(+1.61803 q^{5}\) \(-0.381966 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(-2.85410 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.381966 q^{3}\) \(-1.00000 q^{4}\) \(+1.61803 q^{5}\) \(-0.381966 q^{6}\) \(-1.00000 q^{7}\) \(+3.00000 q^{8}\) \(-2.85410 q^{9}\) \(-1.61803 q^{10}\) \(-0.381966 q^{11}\) \(-0.381966 q^{12}\) \(+3.38197 q^{13}\) \(+1.00000 q^{14}\) \(+0.618034 q^{15}\) \(-1.00000 q^{16}\) \(+1.23607 q^{17}\) \(+2.85410 q^{18}\) \(+7.09017 q^{19}\) \(-1.61803 q^{20}\) \(-0.381966 q^{21}\) \(+0.381966 q^{22}\) \(-6.09017 q^{23}\) \(+1.14590 q^{24}\) \(-2.38197 q^{25}\) \(-3.38197 q^{26}\) \(-2.23607 q^{27}\) \(+1.00000 q^{28}\) \(+4.47214 q^{29}\) \(-0.618034 q^{30}\) \(-6.47214 q^{31}\) \(-5.00000 q^{32}\) \(-0.145898 q^{33}\) \(-1.23607 q^{34}\) \(-1.61803 q^{35}\) \(+2.85410 q^{36}\) \(-8.85410 q^{37}\) \(-7.09017 q^{38}\) \(+1.29180 q^{39}\) \(+4.85410 q^{40}\) \(-8.94427 q^{41}\) \(+0.381966 q^{42}\) \(+7.70820 q^{43}\) \(+0.381966 q^{44}\) \(-4.61803 q^{45}\) \(+6.09017 q^{46}\) \(-3.23607 q^{47}\) \(-0.381966 q^{48}\) \(+1.00000 q^{49}\) \(+2.38197 q^{50}\) \(+0.472136 q^{51}\) \(-3.38197 q^{52}\) \(+11.3262 q^{53}\) \(+2.23607 q^{54}\) \(-0.618034 q^{55}\) \(-3.00000 q^{56}\) \(+2.70820 q^{57}\) \(-4.47214 q^{58}\) \(-8.38197 q^{59}\) \(-0.618034 q^{60}\) \(+0.291796 q^{61}\) \(+6.47214 q^{62}\) \(+2.85410 q^{63}\) \(+7.00000 q^{64}\) \(+5.47214 q^{65}\) \(+0.145898 q^{66}\) \(-13.8541 q^{67}\) \(-1.23607 q^{68}\) \(-2.32624 q^{69}\) \(+1.61803 q^{70}\) \(+6.47214 q^{71}\) \(-8.56231 q^{72}\) \(+4.85410 q^{73}\) \(+8.85410 q^{74}\) \(-0.909830 q^{75}\) \(-7.09017 q^{76}\) \(+0.381966 q^{77}\) \(-1.29180 q^{78}\) \(-11.3820 q^{79}\) \(-1.61803 q^{80}\) \(+7.70820 q^{81}\) \(+8.94427 q^{82}\) \(+13.2361 q^{83}\) \(+0.381966 q^{84}\) \(+2.00000 q^{85}\) \(-7.70820 q^{86}\) \(+1.70820 q^{87}\) \(-1.14590 q^{88}\) \(+10.9443 q^{89}\) \(+4.61803 q^{90}\) \(-3.38197 q^{91}\) \(+6.09017 q^{92}\) \(-2.47214 q^{93}\) \(+3.23607 q^{94}\) \(+11.4721 q^{95}\) \(-1.90983 q^{96}\) \(+1.85410 q^{97}\) \(-1.00000 q^{98}\) \(+1.09017 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut +\mathstrut 3q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut -\mathstrut 7q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 10q^{32} \) \(\mathstrut -\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut q^{35} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 3q^{40} \) \(\mathstrut +\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 9q^{52} \) \(\mathstrut +\mathstrut 7q^{53} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 19q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 14q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 11q^{69} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 3q^{72} \) \(\mathstrut +\mathstrut 3q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 13q^{75} \) \(\mathstrut -\mathstrut 3q^{76} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 25q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 22q^{83} \) \(\mathstrut +\mathstrut 3q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 7q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 2q^{94} \) \(\mathstrut +\mathstrut 14q^{95} \) \(\mathstrut -\mathstrut 15q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0.381966 0.220528 0.110264 0.993902i \(-0.464830\pi\)
0.110264 + 0.993902i \(0.464830\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.61803 0.723607 0.361803 0.932254i \(-0.382161\pi\)
0.361803 + 0.932254i \(0.382161\pi\)
\(6\) −0.381966 −0.155937
\(7\) −1.00000 −0.377964
\(8\) 3.00000 1.06066
\(9\) −2.85410 −0.951367
\(10\) −1.61803 −0.511667
\(11\) −0.381966 −0.115167 −0.0575835 0.998341i \(-0.518340\pi\)
−0.0575835 + 0.998341i \(0.518340\pi\)
\(12\) −0.381966 −0.110264
\(13\) 3.38197 0.937989 0.468994 0.883201i \(-0.344616\pi\)
0.468994 + 0.883201i \(0.344616\pi\)
\(14\) 1.00000 0.267261
\(15\) 0.618034 0.159576
\(16\) −1.00000 −0.250000
\(17\) 1.23607 0.299791 0.149895 0.988702i \(-0.452106\pi\)
0.149895 + 0.988702i \(0.452106\pi\)
\(18\) 2.85410 0.672718
\(19\) 7.09017 1.62660 0.813298 0.581847i \(-0.197670\pi\)
0.813298 + 0.581847i \(0.197670\pi\)
\(20\) −1.61803 −0.361803
\(21\) −0.381966 −0.0833518
\(22\) 0.381966 0.0814354
\(23\) −6.09017 −1.26989 −0.634944 0.772558i \(-0.718977\pi\)
−0.634944 + 0.772558i \(0.718977\pi\)
\(24\) 1.14590 0.233905
\(25\) −2.38197 −0.476393
\(26\) −3.38197 −0.663258
\(27\) −2.23607 −0.430331
\(28\) 1.00000 0.188982
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) −0.618034 −0.112837
\(31\) −6.47214 −1.16243 −0.581215 0.813750i \(-0.697422\pi\)
−0.581215 + 0.813750i \(0.697422\pi\)
\(32\) −5.00000 −0.883883
\(33\) −0.145898 −0.0253976
\(34\) −1.23607 −0.211984
\(35\) −1.61803 −0.273498
\(36\) 2.85410 0.475684
\(37\) −8.85410 −1.45561 −0.727803 0.685787i \(-0.759458\pi\)
−0.727803 + 0.685787i \(0.759458\pi\)
\(38\) −7.09017 −1.15018
\(39\) 1.29180 0.206853
\(40\) 4.85410 0.767501
\(41\) −8.94427 −1.39686 −0.698430 0.715678i \(-0.746118\pi\)
−0.698430 + 0.715678i \(0.746118\pi\)
\(42\) 0.381966 0.0589386
\(43\) 7.70820 1.17549 0.587745 0.809046i \(-0.300016\pi\)
0.587745 + 0.809046i \(0.300016\pi\)
\(44\) 0.381966 0.0575835
\(45\) −4.61803 −0.688416
\(46\) 6.09017 0.897947
\(47\) −3.23607 −0.472029 −0.236015 0.971750i \(-0.575841\pi\)
−0.236015 + 0.971750i \(0.575841\pi\)
\(48\) −0.381966 −0.0551320
\(49\) 1.00000 0.142857
\(50\) 2.38197 0.336861
\(51\) 0.472136 0.0661123
\(52\) −3.38197 −0.468994
\(53\) 11.3262 1.55578 0.777889 0.628401i \(-0.216290\pi\)
0.777889 + 0.628401i \(0.216290\pi\)
\(54\) 2.23607 0.304290
\(55\) −0.618034 −0.0833357
\(56\) −3.00000 −0.400892
\(57\) 2.70820 0.358710
\(58\) −4.47214 −0.587220
\(59\) −8.38197 −1.09124 −0.545620 0.838033i \(-0.683706\pi\)
−0.545620 + 0.838033i \(0.683706\pi\)
\(60\) −0.618034 −0.0797878
\(61\) 0.291796 0.0373607 0.0186803 0.999826i \(-0.494054\pi\)
0.0186803 + 0.999826i \(0.494054\pi\)
\(62\) 6.47214 0.821962
\(63\) 2.85410 0.359583
\(64\) 7.00000 0.875000
\(65\) 5.47214 0.678735
\(66\) 0.145898 0.0179588
\(67\) −13.8541 −1.69255 −0.846274 0.532748i \(-0.821159\pi\)
−0.846274 + 0.532748i \(0.821159\pi\)
\(68\) −1.23607 −0.149895
\(69\) −2.32624 −0.280046
\(70\) 1.61803 0.193392
\(71\) 6.47214 0.768101 0.384051 0.923312i \(-0.374529\pi\)
0.384051 + 0.923312i \(0.374529\pi\)
\(72\) −8.56231 −1.00908
\(73\) 4.85410 0.568130 0.284065 0.958805i \(-0.408317\pi\)
0.284065 + 0.958805i \(0.408317\pi\)
\(74\) 8.85410 1.02927
\(75\) −0.909830 −0.105058
\(76\) −7.09017 −0.813298
\(77\) 0.381966 0.0435291
\(78\) −1.29180 −0.146267
\(79\) −11.3820 −1.28057 −0.640286 0.768137i \(-0.721184\pi\)
−0.640286 + 0.768137i \(0.721184\pi\)
\(80\) −1.61803 −0.180902
\(81\) 7.70820 0.856467
\(82\) 8.94427 0.987730
\(83\) 13.2361 1.45285 0.726424 0.687247i \(-0.241181\pi\)
0.726424 + 0.687247i \(0.241181\pi\)
\(84\) 0.381966 0.0416759
\(85\) 2.00000 0.216930
\(86\) −7.70820 −0.831197
\(87\) 1.70820 0.183139
\(88\) −1.14590 −0.122153
\(89\) 10.9443 1.16009 0.580045 0.814584i \(-0.303035\pi\)
0.580045 + 0.814584i \(0.303035\pi\)
\(90\) 4.61803 0.486784
\(91\) −3.38197 −0.354526
\(92\) 6.09017 0.634944
\(93\) −2.47214 −0.256349
\(94\) 3.23607 0.333775
\(95\) 11.4721 1.17702
\(96\) −1.90983 −0.194921
\(97\) 1.85410 0.188256 0.0941278 0.995560i \(-0.469994\pi\)
0.0941278 + 0.995560i \(0.469994\pi\)
\(98\) −1.00000 −0.101015
\(99\) 1.09017 0.109566
\(100\) 2.38197 0.238197
\(101\) 4.47214 0.444994 0.222497 0.974933i \(-0.428579\pi\)
0.222497 + 0.974933i \(0.428579\pi\)
\(102\) −0.472136 −0.0467484
\(103\) 5.90983 0.582313 0.291156 0.956675i \(-0.405960\pi\)
0.291156 + 0.956675i \(0.405960\pi\)
\(104\) 10.1459 0.994887
\(105\) −0.618034 −0.0603139
\(106\) −11.3262 −1.10010
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 2.23607 0.215166
\(109\) −3.14590 −0.301322 −0.150661 0.988585i \(-0.548140\pi\)
−0.150661 + 0.988585i \(0.548140\pi\)
\(110\) 0.618034 0.0589272
\(111\) −3.38197 −0.321002
\(112\) 1.00000 0.0944911
\(113\) −16.6180 −1.56329 −0.781647 0.623722i \(-0.785620\pi\)
−0.781647 + 0.623722i \(0.785620\pi\)
\(114\) −2.70820 −0.253647
\(115\) −9.85410 −0.918900
\(116\) −4.47214 −0.415227
\(117\) −9.65248 −0.892372
\(118\) 8.38197 0.771623
\(119\) −1.23607 −0.113310
\(120\) 1.85410 0.169256
\(121\) −10.8541 −0.986737
\(122\) −0.291796 −0.0264180
\(123\) −3.41641 −0.308047
\(124\) 6.47214 0.581215
\(125\) −11.9443 −1.06833
\(126\) −2.85410 −0.254264
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 3.00000 0.265165
\(129\) 2.94427 0.259229
\(130\) −5.47214 −0.479938
\(131\) −19.7082 −1.72191 −0.860957 0.508678i \(-0.830134\pi\)
−0.860957 + 0.508678i \(0.830134\pi\)
\(132\) 0.145898 0.0126988
\(133\) −7.09017 −0.614796
\(134\) 13.8541 1.19681
\(135\) −3.61803 −0.311391
\(136\) 3.70820 0.317976
\(137\) 3.52786 0.301406 0.150703 0.988579i \(-0.451846\pi\)
0.150703 + 0.988579i \(0.451846\pi\)
\(138\) 2.32624 0.198023
\(139\) 15.4164 1.30760 0.653801 0.756666i \(-0.273173\pi\)
0.653801 + 0.756666i \(0.273173\pi\)
\(140\) 1.61803 0.136749
\(141\) −1.23607 −0.104096
\(142\) −6.47214 −0.543130
\(143\) −1.29180 −0.108025
\(144\) 2.85410 0.237842
\(145\) 7.23607 0.600923
\(146\) −4.85410 −0.401728
\(147\) 0.381966 0.0315040
\(148\) 8.85410 0.727803
\(149\) 21.4164 1.75450 0.877250 0.480033i \(-0.159375\pi\)
0.877250 + 0.480033i \(0.159375\pi\)
\(150\) 0.909830 0.0742873
\(151\) −11.2361 −0.914378 −0.457189 0.889369i \(-0.651144\pi\)
−0.457189 + 0.889369i \(0.651144\pi\)
\(152\) 21.2705 1.72527
\(153\) −3.52786 −0.285211
\(154\) −0.381966 −0.0307797
\(155\) −10.4721 −0.841142
\(156\) −1.29180 −0.103426
\(157\) 9.85410 0.786443 0.393221 0.919444i \(-0.371361\pi\)
0.393221 + 0.919444i \(0.371361\pi\)
\(158\) 11.3820 0.905501
\(159\) 4.32624 0.343093
\(160\) −8.09017 −0.639584
\(161\) 6.09017 0.479973
\(162\) −7.70820 −0.605614
\(163\) 2.47214 0.193633 0.0968163 0.995302i \(-0.469134\pi\)
0.0968163 + 0.995302i \(0.469134\pi\)
\(164\) 8.94427 0.698430
\(165\) −0.236068 −0.0183779
\(166\) −13.2361 −1.02732
\(167\) −10.1803 −0.787778 −0.393889 0.919158i \(-0.628871\pi\)
−0.393889 + 0.919158i \(0.628871\pi\)
\(168\) −1.14590 −0.0884080
\(169\) −1.56231 −0.120177
\(170\) −2.00000 −0.153393
\(171\) −20.2361 −1.54749
\(172\) −7.70820 −0.587745
\(173\) −18.5623 −1.41127 −0.705633 0.708578i \(-0.749337\pi\)
−0.705633 + 0.708578i \(0.749337\pi\)
\(174\) −1.70820 −0.129499
\(175\) 2.38197 0.180060
\(176\) 0.381966 0.0287918
\(177\) −3.20163 −0.240649
\(178\) −10.9443 −0.820308
\(179\) −12.3262 −0.921306 −0.460653 0.887580i \(-0.652385\pi\)
−0.460653 + 0.887580i \(0.652385\pi\)
\(180\) 4.61803 0.344208
\(181\) 14.9443 1.11080 0.555399 0.831584i \(-0.312565\pi\)
0.555399 + 0.831584i \(0.312565\pi\)
\(182\) 3.38197 0.250688
\(183\) 0.111456 0.00823908
\(184\) −18.2705 −1.34692
\(185\) −14.3262 −1.05329
\(186\) 2.47214 0.181266
\(187\) −0.472136 −0.0345260
\(188\) 3.23607 0.236015
\(189\) 2.23607 0.162650
\(190\) −11.4721 −0.832276
\(191\) −17.8885 −1.29437 −0.647185 0.762333i \(-0.724054\pi\)
−0.647185 + 0.762333i \(0.724054\pi\)
\(192\) 2.67376 0.192962
\(193\) −23.2361 −1.67257 −0.836284 0.548296i \(-0.815277\pi\)
−0.836284 + 0.548296i \(0.815277\pi\)
\(194\) −1.85410 −0.133117
\(195\) 2.09017 0.149680
\(196\) −1.00000 −0.0714286
\(197\) −20.9443 −1.49222 −0.746109 0.665824i \(-0.768080\pi\)
−0.746109 + 0.665824i \(0.768080\pi\)
\(198\) −1.09017 −0.0774750
\(199\) −5.85410 −0.414986 −0.207493 0.978236i \(-0.566530\pi\)
−0.207493 + 0.978236i \(0.566530\pi\)
\(200\) −7.14590 −0.505291
\(201\) −5.29180 −0.373255
\(202\) −4.47214 −0.314658
\(203\) −4.47214 −0.313882
\(204\) −0.472136 −0.0330561
\(205\) −14.4721 −1.01078
\(206\) −5.90983 −0.411757
\(207\) 17.3820 1.20813
\(208\) −3.38197 −0.234497
\(209\) −2.70820 −0.187330
\(210\) 0.618034 0.0426484
\(211\) −6.43769 −0.443189 −0.221595 0.975139i \(-0.571126\pi\)
−0.221595 + 0.975139i \(0.571126\pi\)
\(212\) −11.3262 −0.777889
\(213\) 2.47214 0.169388
\(214\) −6.00000 −0.410152
\(215\) 12.4721 0.850593
\(216\) −6.70820 −0.456435
\(217\) 6.47214 0.439357
\(218\) 3.14590 0.213067
\(219\) 1.85410 0.125289
\(220\) 0.618034 0.0416678
\(221\) 4.18034 0.281200
\(222\) 3.38197 0.226983
\(223\) 20.5623 1.37695 0.688477 0.725258i \(-0.258280\pi\)
0.688477 + 0.725258i \(0.258280\pi\)
\(224\) 5.00000 0.334077
\(225\) 6.79837 0.453225
\(226\) 16.6180 1.10542
\(227\) 1.05573 0.0700711 0.0350356 0.999386i \(-0.488846\pi\)
0.0350356 + 0.999386i \(0.488846\pi\)
\(228\) −2.70820 −0.179355
\(229\) −0.180340 −0.0119172 −0.00595860 0.999982i \(-0.501897\pi\)
−0.00595860 + 0.999982i \(0.501897\pi\)
\(230\) 9.85410 0.649760
\(231\) 0.145898 0.00959939
\(232\) 13.4164 0.880830
\(233\) −24.1803 −1.58411 −0.792053 0.610452i \(-0.790988\pi\)
−0.792053 + 0.610452i \(0.790988\pi\)
\(234\) 9.65248 0.631002
\(235\) −5.23607 −0.341563
\(236\) 8.38197 0.545620
\(237\) −4.34752 −0.282402
\(238\) 1.23607 0.0801224
\(239\) −29.2361 −1.89112 −0.945562 0.325442i \(-0.894487\pi\)
−0.945562 + 0.325442i \(0.894487\pi\)
\(240\) −0.618034 −0.0398939
\(241\) 12.6180 0.812799 0.406400 0.913695i \(-0.366784\pi\)
0.406400 + 0.913695i \(0.366784\pi\)
\(242\) 10.8541 0.697728
\(243\) 9.65248 0.619207
\(244\) −0.291796 −0.0186803
\(245\) 1.61803 0.103372
\(246\) 3.41641 0.217822
\(247\) 23.9787 1.52573
\(248\) −19.4164 −1.23294
\(249\) 5.05573 0.320394
\(250\) 11.9443 0.755422
\(251\) 20.6525 1.30357 0.651786 0.758403i \(-0.274020\pi\)
0.651786 + 0.758403i \(0.274020\pi\)
\(252\) −2.85410 −0.179792
\(253\) 2.32624 0.146249
\(254\) 4.00000 0.250982
\(255\) 0.763932 0.0478393
\(256\) −17.0000 −1.06250
\(257\) 0.944272 0.0589021 0.0294510 0.999566i \(-0.490624\pi\)
0.0294510 + 0.999566i \(0.490624\pi\)
\(258\) −2.94427 −0.183302
\(259\) 8.85410 0.550167
\(260\) −5.47214 −0.339367
\(261\) −12.7639 −0.790068
\(262\) 19.7082 1.21758
\(263\) −19.7426 −1.21738 −0.608692 0.793407i \(-0.708305\pi\)
−0.608692 + 0.793407i \(0.708305\pi\)
\(264\) −0.437694 −0.0269382
\(265\) 18.3262 1.12577
\(266\) 7.09017 0.434726
\(267\) 4.18034 0.255833
\(268\) 13.8541 0.846274
\(269\) 5.70820 0.348035 0.174018 0.984743i \(-0.444325\pi\)
0.174018 + 0.984743i \(0.444325\pi\)
\(270\) 3.61803 0.220187
\(271\) 15.1246 0.918755 0.459377 0.888241i \(-0.348073\pi\)
0.459377 + 0.888241i \(0.348073\pi\)
\(272\) −1.23607 −0.0749476
\(273\) −1.29180 −0.0781831
\(274\) −3.52786 −0.213126
\(275\) 0.909830 0.0548648
\(276\) 2.32624 0.140023
\(277\) −14.4721 −0.869546 −0.434773 0.900540i \(-0.643171\pi\)
−0.434773 + 0.900540i \(0.643171\pi\)
\(278\) −15.4164 −0.924615
\(279\) 18.4721 1.10590
\(280\) −4.85410 −0.290088
\(281\) 8.27051 0.493377 0.246689 0.969095i \(-0.420658\pi\)
0.246689 + 0.969095i \(0.420658\pi\)
\(282\) 1.23607 0.0736068
\(283\) 16.3262 0.970494 0.485247 0.874377i \(-0.338730\pi\)
0.485247 + 0.874377i \(0.338730\pi\)
\(284\) −6.47214 −0.384051
\(285\) 4.38197 0.259565
\(286\) 1.29180 0.0763855
\(287\) 8.94427 0.527964
\(288\) 14.2705 0.840898
\(289\) −15.4721 −0.910126
\(290\) −7.23607 −0.424917
\(291\) 0.708204 0.0415156
\(292\) −4.85410 −0.284065
\(293\) −7.52786 −0.439783 −0.219891 0.975524i \(-0.570570\pi\)
−0.219891 + 0.975524i \(0.570570\pi\)
\(294\) −0.381966 −0.0222767
\(295\) −13.5623 −0.789628
\(296\) −26.5623 −1.54390
\(297\) 0.854102 0.0495600
\(298\) −21.4164 −1.24062
\(299\) −20.5967 −1.19114
\(300\) 0.909830 0.0525291
\(301\) −7.70820 −0.444293
\(302\) 11.2361 0.646563
\(303\) 1.70820 0.0981338
\(304\) −7.09017 −0.406649
\(305\) 0.472136 0.0270344
\(306\) 3.52786 0.201675
\(307\) −5.20163 −0.296872 −0.148436 0.988922i \(-0.547424\pi\)
−0.148436 + 0.988922i \(0.547424\pi\)
\(308\) −0.381966 −0.0217645
\(309\) 2.25735 0.128416
\(310\) 10.4721 0.594777
\(311\) −8.94427 −0.507183 −0.253592 0.967311i \(-0.581612\pi\)
−0.253592 + 0.967311i \(0.581612\pi\)
\(312\) 3.87539 0.219401
\(313\) −0.180340 −0.0101934 −0.00509671 0.999987i \(-0.501622\pi\)
−0.00509671 + 0.999987i \(0.501622\pi\)
\(314\) −9.85410 −0.556099
\(315\) 4.61803 0.260197
\(316\) 11.3820 0.640286
\(317\) 2.65248 0.148978 0.0744889 0.997222i \(-0.476267\pi\)
0.0744889 + 0.997222i \(0.476267\pi\)
\(318\) −4.32624 −0.242603
\(319\) −1.70820 −0.0956411
\(320\) 11.3262 0.633156
\(321\) 2.29180 0.127916
\(322\) −6.09017 −0.339392
\(323\) 8.76393 0.487638
\(324\) −7.70820 −0.428234
\(325\) −8.05573 −0.446851
\(326\) −2.47214 −0.136919
\(327\) −1.20163 −0.0664501
\(328\) −26.8328 −1.48159
\(329\) 3.23607 0.178410
\(330\) 0.236068 0.0129951
\(331\) −13.5279 −0.743559 −0.371779 0.928321i \(-0.621252\pi\)
−0.371779 + 0.928321i \(0.621252\pi\)
\(332\) −13.2361 −0.726424
\(333\) 25.2705 1.38482
\(334\) 10.1803 0.557043
\(335\) −22.4164 −1.22474
\(336\) 0.381966 0.0208380
\(337\) 4.90983 0.267455 0.133728 0.991018i \(-0.457305\pi\)
0.133728 + 0.991018i \(0.457305\pi\)
\(338\) 1.56231 0.0849782
\(339\) −6.34752 −0.344750
\(340\) −2.00000 −0.108465
\(341\) 2.47214 0.133874
\(342\) 20.2361 1.09424
\(343\) −1.00000 −0.0539949
\(344\) 23.1246 1.24680
\(345\) −3.76393 −0.202643
\(346\) 18.5623 0.997916
\(347\) 23.4508 1.25891 0.629454 0.777038i \(-0.283279\pi\)
0.629454 + 0.777038i \(0.283279\pi\)
\(348\) −1.70820 −0.0915693
\(349\) −3.88854 −0.208149 −0.104074 0.994570i \(-0.533188\pi\)
−0.104074 + 0.994570i \(0.533188\pi\)
\(350\) −2.38197 −0.127321
\(351\) −7.56231 −0.403646
\(352\) 1.90983 0.101794
\(353\) −0.291796 −0.0155307 −0.00776537 0.999970i \(-0.502472\pi\)
−0.00776537 + 0.999970i \(0.502472\pi\)
\(354\) 3.20163 0.170165
\(355\) 10.4721 0.555803
\(356\) −10.9443 −0.580045
\(357\) −0.472136 −0.0249881
\(358\) 12.3262 0.651462
\(359\) 9.81966 0.518262 0.259131 0.965842i \(-0.416564\pi\)
0.259131 + 0.965842i \(0.416564\pi\)
\(360\) −13.8541 −0.730175
\(361\) 31.2705 1.64582
\(362\) −14.9443 −0.785453
\(363\) −4.14590 −0.217603
\(364\) 3.38197 0.177263
\(365\) 7.85410 0.411102
\(366\) −0.111456 −0.00582591
\(367\) −30.0000 −1.56599 −0.782994 0.622030i \(-0.786308\pi\)
−0.782994 + 0.622030i \(0.786308\pi\)
\(368\) 6.09017 0.317472
\(369\) 25.5279 1.32893
\(370\) 14.3262 0.744786
\(371\) −11.3262 −0.588029
\(372\) 2.47214 0.128174
\(373\) −3.67376 −0.190220 −0.0951101 0.995467i \(-0.530320\pi\)
−0.0951101 + 0.995467i \(0.530320\pi\)
\(374\) 0.472136 0.0244136
\(375\) −4.56231 −0.235596
\(376\) −9.70820 −0.500662
\(377\) 15.1246 0.778957
\(378\) −2.23607 −0.115011
\(379\) −16.0344 −0.823634 −0.411817 0.911267i \(-0.635106\pi\)
−0.411817 + 0.911267i \(0.635106\pi\)
\(380\) −11.4721 −0.588508
\(381\) −1.52786 −0.0782748
\(382\) 17.8885 0.915258
\(383\) −6.14590 −0.314041 −0.157020 0.987595i \(-0.550189\pi\)
−0.157020 + 0.987595i \(0.550189\pi\)
\(384\) 1.14590 0.0584764
\(385\) 0.618034 0.0314979
\(386\) 23.2361 1.18268
\(387\) −22.0000 −1.11832
\(388\) −1.85410 −0.0941278
\(389\) −24.9787 −1.26647 −0.633236 0.773959i \(-0.718274\pi\)
−0.633236 + 0.773959i \(0.718274\pi\)
\(390\) −2.09017 −0.105840
\(391\) −7.52786 −0.380700
\(392\) 3.00000 0.151523
\(393\) −7.52786 −0.379731
\(394\) 20.9443 1.05516
\(395\) −18.4164 −0.926630
\(396\) −1.09017 −0.0547831
\(397\) −27.8885 −1.39969 −0.699843 0.714297i \(-0.746747\pi\)
−0.699843 + 0.714297i \(0.746747\pi\)
\(398\) 5.85410 0.293440
\(399\) −2.70820 −0.135580
\(400\) 2.38197 0.119098
\(401\) −18.9443 −0.946032 −0.473016 0.881054i \(-0.656835\pi\)
−0.473016 + 0.881054i \(0.656835\pi\)
\(402\) 5.29180 0.263931
\(403\) −21.8885 −1.09035
\(404\) −4.47214 −0.222497
\(405\) 12.4721 0.619745
\(406\) 4.47214 0.221948
\(407\) 3.38197 0.167638
\(408\) 1.41641 0.0701226
\(409\) 10.6525 0.526731 0.263366 0.964696i \(-0.415167\pi\)
0.263366 + 0.964696i \(0.415167\pi\)
\(410\) 14.4721 0.714728
\(411\) 1.34752 0.0664685
\(412\) −5.90983 −0.291156
\(413\) 8.38197 0.412450
\(414\) −17.3820 −0.854277
\(415\) 21.4164 1.05129
\(416\) −16.9098 −0.829073
\(417\) 5.88854 0.288363
\(418\) 2.70820 0.132463
\(419\) −20.0000 −0.977064 −0.488532 0.872546i \(-0.662467\pi\)
−0.488532 + 0.872546i \(0.662467\pi\)
\(420\) 0.618034 0.0301570
\(421\) 26.7984 1.30607 0.653036 0.757327i \(-0.273495\pi\)
0.653036 + 0.757327i \(0.273495\pi\)
\(422\) 6.43769 0.313382
\(423\) 9.23607 0.449073
\(424\) 33.9787 1.65015
\(425\) −2.94427 −0.142818
\(426\) −2.47214 −0.119775
\(427\) −0.291796 −0.0141210
\(428\) −6.00000 −0.290021
\(429\) −0.493422 −0.0238226
\(430\) −12.4721 −0.601460
\(431\) −19.0557 −0.917882 −0.458941 0.888467i \(-0.651771\pi\)
−0.458941 + 0.888467i \(0.651771\pi\)
\(432\) 2.23607 0.107583
\(433\) 26.3607 1.26681 0.633407 0.773819i \(-0.281656\pi\)
0.633407 + 0.773819i \(0.281656\pi\)
\(434\) −6.47214 −0.310672
\(435\) 2.76393 0.132520
\(436\) 3.14590 0.150661
\(437\) −43.1803 −2.06560
\(438\) −1.85410 −0.0885924
\(439\) −23.1246 −1.10368 −0.551839 0.833951i \(-0.686074\pi\)
−0.551839 + 0.833951i \(0.686074\pi\)
\(440\) −1.85410 −0.0883908
\(441\) −2.85410 −0.135910
\(442\) −4.18034 −0.198838
\(443\) 10.7984 0.513046 0.256523 0.966538i \(-0.417423\pi\)
0.256523 + 0.966538i \(0.417423\pi\)
\(444\) 3.38197 0.160501
\(445\) 17.7082 0.839449
\(446\) −20.5623 −0.973653
\(447\) 8.18034 0.386917
\(448\) −7.00000 −0.330719
\(449\) −20.6869 −0.976276 −0.488138 0.872766i \(-0.662324\pi\)
−0.488138 + 0.872766i \(0.662324\pi\)
\(450\) −6.79837 −0.320478
\(451\) 3.41641 0.160872
\(452\) 16.6180 0.781647
\(453\) −4.29180 −0.201646
\(454\) −1.05573 −0.0495478
\(455\) −5.47214 −0.256538
\(456\) 8.12461 0.380470
\(457\) −39.6869 −1.85648 −0.928238 0.371987i \(-0.878677\pi\)
−0.928238 + 0.371987i \(0.878677\pi\)
\(458\) 0.180340 0.00842673
\(459\) −2.76393 −0.129009
\(460\) 9.85410 0.459450
\(461\) −21.5967 −1.00586 −0.502930 0.864327i \(-0.667745\pi\)
−0.502930 + 0.864327i \(0.667745\pi\)
\(462\) −0.145898 −0.00678779
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −4.47214 −0.207614
\(465\) −4.00000 −0.185496
\(466\) 24.1803 1.12013
\(467\) 8.03444 0.371790 0.185895 0.982570i \(-0.440482\pi\)
0.185895 + 0.982570i \(0.440482\pi\)
\(468\) 9.65248 0.446186
\(469\) 13.8541 0.639723
\(470\) 5.23607 0.241522
\(471\) 3.76393 0.173433
\(472\) −25.1459 −1.15743
\(473\) −2.94427 −0.135378
\(474\) 4.34752 0.199688
\(475\) −16.8885 −0.774900
\(476\) 1.23607 0.0566551
\(477\) −32.3262 −1.48012
\(478\) 29.2361 1.33723
\(479\) 24.6525 1.12640 0.563200 0.826320i \(-0.309570\pi\)
0.563200 + 0.826320i \(0.309570\pi\)
\(480\) −3.09017 −0.141046
\(481\) −29.9443 −1.36534
\(482\) −12.6180 −0.574736
\(483\) 2.32624 0.105847
\(484\) 10.8541 0.493368
\(485\) 3.00000 0.136223
\(486\) −9.65248 −0.437845
\(487\) 1.41641 0.0641836 0.0320918 0.999485i \(-0.489783\pi\)
0.0320918 + 0.999485i \(0.489783\pi\)
\(488\) 0.875388 0.0396270
\(489\) 0.944272 0.0427015
\(490\) −1.61803 −0.0730953
\(491\) −20.7426 −0.936102 −0.468051 0.883701i \(-0.655044\pi\)
−0.468051 + 0.883701i \(0.655044\pi\)
\(492\) 3.41641 0.154024
\(493\) 5.52786 0.248962
\(494\) −23.9787 −1.07885
\(495\) 1.76393 0.0792828
\(496\) 6.47214 0.290607
\(497\) −6.47214 −0.290315
\(498\) −5.05573 −0.226553
\(499\) −13.8885 −0.621737 −0.310868 0.950453i \(-0.600620\pi\)
−0.310868 + 0.950453i \(0.600620\pi\)
\(500\) 11.9443 0.534164
\(501\) −3.88854 −0.173727
\(502\) −20.6525 −0.921765
\(503\) −16.9098 −0.753972 −0.376986 0.926219i \(-0.623040\pi\)
−0.376986 + 0.926219i \(0.623040\pi\)
\(504\) 8.56231 0.381395
\(505\) 7.23607 0.322001
\(506\) −2.32624 −0.103414
\(507\) −0.596748 −0.0265025
\(508\) 4.00000 0.177471
\(509\) 26.1459 1.15890 0.579448 0.815009i \(-0.303268\pi\)
0.579448 + 0.815009i \(0.303268\pi\)
\(510\) −0.763932 −0.0338275
\(511\) −4.85410 −0.214733
\(512\) 11.0000 0.486136
\(513\) −15.8541 −0.699976
\(514\) −0.944272 −0.0416500
\(515\) 9.56231 0.421366
\(516\) −2.94427 −0.129614
\(517\) 1.23607 0.0543622
\(518\) −8.85410 −0.389027
\(519\) −7.09017 −0.311224
\(520\) 16.4164 0.719907
\(521\) 16.0902 0.704923 0.352462 0.935826i \(-0.385345\pi\)
0.352462 + 0.935826i \(0.385345\pi\)
\(522\) 12.7639 0.558662
\(523\) −11.7426 −0.513470 −0.256735 0.966482i \(-0.582647\pi\)
−0.256735 + 0.966482i \(0.582647\pi\)
\(524\) 19.7082 0.860957
\(525\) 0.909830 0.0397082
\(526\) 19.7426 0.860820
\(527\) −8.00000 −0.348485
\(528\) 0.145898 0.00634940
\(529\) 14.0902 0.612616
\(530\) −18.3262 −0.796041
\(531\) 23.9230 1.03817
\(532\) 7.09017 0.307398
\(533\) −30.2492 −1.31024
\(534\) −4.18034 −0.180901
\(535\) 9.70820 0.419722
\(536\) −41.5623 −1.79522
\(537\) −4.70820 −0.203174
\(538\) −5.70820 −0.246098
\(539\) −0.381966 −0.0164524
\(540\) 3.61803 0.155695
\(541\) −28.5410 −1.22707 −0.613537 0.789666i \(-0.710254\pi\)
−0.613537 + 0.789666i \(0.710254\pi\)
\(542\) −15.1246 −0.649658
\(543\) 5.70820 0.244962
\(544\) −6.18034 −0.264980
\(545\) −5.09017 −0.218039
\(546\) 1.29180 0.0552838
\(547\) 14.0689 0.601542 0.300771 0.953696i \(-0.402756\pi\)
0.300771 + 0.953696i \(0.402756\pi\)
\(548\) −3.52786 −0.150703
\(549\) −0.832816 −0.0355437
\(550\) −0.909830 −0.0387953
\(551\) 31.7082 1.35081
\(552\) −6.97871 −0.297034
\(553\) 11.3820 0.484010
\(554\) 14.4721 0.614862
\(555\) −5.47214 −0.232279
\(556\) −15.4164 −0.653801
\(557\) 33.1246 1.40353 0.701767 0.712406i \(-0.252395\pi\)
0.701767 + 0.712406i \(0.252395\pi\)
\(558\) −18.4721 −0.781988
\(559\) 26.0689 1.10260
\(560\) 1.61803 0.0683744
\(561\) −0.180340 −0.00761396
\(562\) −8.27051 −0.348870
\(563\) −28.0689 −1.18296 −0.591481 0.806319i \(-0.701457\pi\)
−0.591481 + 0.806319i \(0.701457\pi\)
\(564\) 1.23607 0.0520479
\(565\) −26.8885 −1.13121
\(566\) −16.3262 −0.686243
\(567\) −7.70820 −0.323714
\(568\) 19.4164 0.814694
\(569\) 26.0000 1.08998 0.544988 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) −4.38197 −0.183540
\(571\) −36.0689 −1.50944 −0.754718 0.656049i \(-0.772226\pi\)
−0.754718 + 0.656049i \(0.772226\pi\)
\(572\) 1.29180 0.0540127
\(573\) −6.83282 −0.285445
\(574\) −8.94427 −0.373327
\(575\) 14.5066 0.604966
\(576\) −19.9787 −0.832446
\(577\) −37.5623 −1.56374 −0.781870 0.623442i \(-0.785734\pi\)
−0.781870 + 0.623442i \(0.785734\pi\)
\(578\) 15.4721 0.643556
\(579\) −8.87539 −0.368849
\(580\) −7.23607 −0.300461
\(581\) −13.2361 −0.549125
\(582\) −0.708204 −0.0293560
\(583\) −4.32624 −0.179174
\(584\) 14.5623 0.602593
\(585\) −15.6180 −0.645726
\(586\) 7.52786 0.310973
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) −0.381966 −0.0157520
\(589\) −45.8885 −1.89080
\(590\) 13.5623 0.558351
\(591\) −8.00000 −0.329076
\(592\) 8.85410 0.363901
\(593\) 37.7082 1.54849 0.774245 0.632886i \(-0.218130\pi\)
0.774245 + 0.632886i \(0.218130\pi\)
\(594\) −0.854102 −0.0350442
\(595\) −2.00000 −0.0819920
\(596\) −21.4164 −0.877250
\(597\) −2.23607 −0.0915162
\(598\) 20.5967 0.842264
\(599\) −18.6525 −0.762120 −0.381060 0.924550i \(-0.624441\pi\)
−0.381060 + 0.924550i \(0.624441\pi\)
\(600\) −2.72949 −0.111431
\(601\) −32.6525 −1.33192 −0.665961 0.745986i \(-0.731978\pi\)
−0.665961 + 0.745986i \(0.731978\pi\)
\(602\) 7.70820 0.314163
\(603\) 39.5410 1.61023
\(604\) 11.2361 0.457189
\(605\) −17.5623 −0.714009
\(606\) −1.70820 −0.0693910
\(607\) 15.0557 0.611093 0.305547 0.952177i \(-0.401161\pi\)
0.305547 + 0.952177i \(0.401161\pi\)
\(608\) −35.4508 −1.43772
\(609\) −1.70820 −0.0692199
\(610\) −0.472136 −0.0191162
\(611\) −10.9443 −0.442758
\(612\) 3.52786 0.142605
\(613\) −32.4508 −1.31068 −0.655339 0.755335i \(-0.727474\pi\)
−0.655339 + 0.755335i \(0.727474\pi\)
\(614\) 5.20163 0.209921
\(615\) −5.52786 −0.222905
\(616\) 1.14590 0.0461695
\(617\) 34.3607 1.38331 0.691654 0.722229i \(-0.256882\pi\)
0.691654 + 0.722229i \(0.256882\pi\)
\(618\) −2.25735 −0.0908041
\(619\) −7.70820 −0.309819 −0.154909 0.987929i \(-0.549509\pi\)
−0.154909 + 0.987929i \(0.549509\pi\)
\(620\) 10.4721 0.420571
\(621\) 13.6180 0.546473
\(622\) 8.94427 0.358633
\(623\) −10.9443 −0.438473
\(624\) −1.29180 −0.0517132
\(625\) −7.41641 −0.296656
\(626\) 0.180340 0.00720783
\(627\) −1.03444 −0.0413116
\(628\) −9.85410 −0.393221
\(629\) −10.9443 −0.436377
\(630\) −4.61803 −0.183987
\(631\) 4.74265 0.188802 0.0944009 0.995534i \(-0.469906\pi\)
0.0944009 + 0.995534i \(0.469906\pi\)
\(632\) −34.1459 −1.35825
\(633\) −2.45898 −0.0977357
\(634\) −2.65248 −0.105343
\(635\) −6.47214 −0.256839
\(636\) −4.32624 −0.171546
\(637\) 3.38197 0.133998
\(638\) 1.70820 0.0676284
\(639\) −18.4721 −0.730746
\(640\) 4.85410 0.191875
\(641\) 41.0132 1.61992 0.809961 0.586484i \(-0.199488\pi\)
0.809961 + 0.586484i \(0.199488\pi\)
\(642\) −2.29180 −0.0904500
\(643\) 1.63932 0.0646485 0.0323242 0.999477i \(-0.489709\pi\)
0.0323242 + 0.999477i \(0.489709\pi\)
\(644\) −6.09017 −0.239986
\(645\) 4.76393 0.187580
\(646\) −8.76393 −0.344812
\(647\) 9.70820 0.381669 0.190834 0.981622i \(-0.438881\pi\)
0.190834 + 0.981622i \(0.438881\pi\)
\(648\) 23.1246 0.908421
\(649\) 3.20163 0.125675
\(650\) 8.05573 0.315972
\(651\) 2.47214 0.0968906
\(652\) −2.47214 −0.0968163
\(653\) 32.9443 1.28921 0.644604 0.764516i \(-0.277022\pi\)
0.644604 + 0.764516i \(0.277022\pi\)
\(654\) 1.20163 0.0469873
\(655\) −31.8885 −1.24599
\(656\) 8.94427 0.349215
\(657\) −13.8541 −0.540500
\(658\) −3.23607 −0.126155
\(659\) −20.0344 −0.780431 −0.390216 0.920724i \(-0.627600\pi\)
−0.390216 + 0.920724i \(0.627600\pi\)
\(660\) 0.236068 0.00918893
\(661\) −12.7639 −0.496459 −0.248230 0.968701i \(-0.579849\pi\)
−0.248230 + 0.968701i \(0.579849\pi\)
\(662\) 13.5279 0.525775
\(663\) 1.59675 0.0620125
\(664\) 39.7082 1.54098
\(665\) −11.4721 −0.444870
\(666\) −25.2705 −0.979212
\(667\) −27.2361 −1.05458
\(668\) 10.1803 0.393889
\(669\) 7.85410 0.303657
\(670\) 22.4164 0.866021
\(671\) −0.111456 −0.00430272
\(672\) 1.90983 0.0736733
\(673\) −5.49342 −0.211756 −0.105878 0.994379i \(-0.533765\pi\)
−0.105878 + 0.994379i \(0.533765\pi\)
\(674\) −4.90983 −0.189120
\(675\) 5.32624 0.205007
\(676\) 1.56231 0.0600887
\(677\) −28.8541 −1.10895 −0.554477 0.832199i \(-0.687082\pi\)
−0.554477 + 0.832199i \(0.687082\pi\)
\(678\) 6.34752 0.243775
\(679\) −1.85410 −0.0711539
\(680\) 6.00000 0.230089
\(681\) 0.403252 0.0154527
\(682\) −2.47214 −0.0946630
\(683\) −20.4721 −0.783345 −0.391672 0.920105i \(-0.628103\pi\)
−0.391672 + 0.920105i \(0.628103\pi\)
\(684\) 20.2361 0.773745
\(685\) 5.70820 0.218099
\(686\) 1.00000 0.0381802
\(687\) −0.0688837 −0.00262808
\(688\) −7.70820 −0.293873
\(689\) 38.3050 1.45930
\(690\) 3.76393 0.143290
\(691\) 20.2918 0.771936 0.385968 0.922512i \(-0.373867\pi\)
0.385968 + 0.922512i \(0.373867\pi\)
\(692\) 18.5623 0.705633
\(693\) −1.09017 −0.0414121
\(694\) −23.4508 −0.890182
\(695\) 24.9443 0.946190
\(696\) 5.12461 0.194248
\(697\) −11.0557 −0.418766
\(698\) 3.88854 0.147184
\(699\) −9.23607 −0.349340
\(700\) −2.38197 −0.0900299
\(701\) 37.8885 1.43103 0.715515 0.698597i \(-0.246192\pi\)
0.715515 + 0.698597i \(0.246192\pi\)
\(702\) 7.56231 0.285421
\(703\) −62.7771 −2.36768
\(704\) −2.67376 −0.100771
\(705\) −2.00000 −0.0753244
\(706\) 0.291796 0.0109819
\(707\) −4.47214 −0.168192
\(708\) 3.20163 0.120324
\(709\) −18.0000 −0.676004 −0.338002 0.941145i \(-0.609751\pi\)
−0.338002 + 0.941145i \(0.609751\pi\)
\(710\) −10.4721 −0.393012
\(711\) 32.4853 1.21829
\(712\) 32.8328 1.23046
\(713\) 39.4164 1.47616
\(714\) 0.472136 0.0176692
\(715\) −2.09017 −0.0781679
\(716\) 12.3262 0.460653
\(717\) −11.1672 −0.417046
\(718\) −9.81966 −0.366466
\(719\) 34.3607 1.28144 0.640719 0.767776i \(-0.278637\pi\)
0.640719 + 0.767776i \(0.278637\pi\)
\(720\) 4.61803 0.172104
\(721\) −5.90983 −0.220094
\(722\) −31.2705 −1.16377
\(723\) 4.81966 0.179245
\(724\) −14.9443 −0.555399
\(725\) −10.6525 −0.395623
\(726\) 4.14590 0.153869
\(727\) −36.5410 −1.35523 −0.677616 0.735416i \(-0.736987\pi\)
−0.677616 + 0.735416i \(0.736987\pi\)
\(728\) −10.1459 −0.376032
\(729\) −19.4377 −0.719915
\(730\) −7.85410 −0.290693
\(731\) 9.52786 0.352401
\(732\) −0.111456 −0.00411954
\(733\) −40.3262 −1.48948 −0.744742 0.667353i \(-0.767427\pi\)
−0.744742 + 0.667353i \(0.767427\pi\)
\(734\) 30.0000 1.10732
\(735\) 0.618034 0.0227965
\(736\) 30.4508 1.12243
\(737\) 5.29180 0.194926
\(738\) −25.5279 −0.939694
\(739\) 13.5279 0.497631 0.248815 0.968551i \(-0.419959\pi\)
0.248815 + 0.968551i \(0.419959\pi\)
\(740\) 14.3262 0.526643
\(741\) 9.15905 0.336466
\(742\) 11.3262 0.415799
\(743\) −2.29180 −0.0840778 −0.0420389 0.999116i \(-0.513385\pi\)
−0.0420389 + 0.999116i \(0.513385\pi\)
\(744\) −7.41641 −0.271899
\(745\) 34.6525 1.26957
\(746\) 3.67376 0.134506
\(747\) −37.7771 −1.38219
\(748\) 0.472136 0.0172630
\(749\) −6.00000 −0.219235
\(750\) 4.56231 0.166592
\(751\) −31.7082 −1.15705 −0.578524 0.815665i \(-0.696371\pi\)
−0.578524 + 0.815665i \(0.696371\pi\)
\(752\) 3.23607 0.118007
\(753\) 7.88854 0.287475
\(754\) −15.1246 −0.550806
\(755\) −18.1803 −0.661650
\(756\) −2.23607 −0.0813250
\(757\) −31.7082 −1.15245 −0.576227 0.817290i \(-0.695476\pi\)
−0.576227 + 0.817290i \(0.695476\pi\)
\(758\) 16.0344 0.582397
\(759\) 0.888544 0.0322521
\(760\) 34.4164 1.24841
\(761\) 8.67376 0.314424 0.157212 0.987565i \(-0.449749\pi\)
0.157212 + 0.987565i \(0.449749\pi\)
\(762\) 1.52786 0.0553487
\(763\) 3.14590 0.113889
\(764\) 17.8885 0.647185
\(765\) −5.70820 −0.206381
\(766\) 6.14590 0.222060
\(767\) −28.3475 −1.02357
\(768\) −6.49342 −0.234311
\(769\) 48.3607 1.74393 0.871965 0.489568i \(-0.162845\pi\)
0.871965 + 0.489568i \(0.162845\pi\)
\(770\) −0.618034 −0.0222724
\(771\) 0.360680 0.0129896
\(772\) 23.2361 0.836284
\(773\) −33.8885 −1.21889 −0.609443 0.792830i \(-0.708607\pi\)
−0.609443 + 0.792830i \(0.708607\pi\)
\(774\) 22.0000 0.790774
\(775\) 15.4164 0.553774
\(776\) 5.56231 0.199675
\(777\) 3.38197 0.121327
\(778\) 24.9787 0.895530
\(779\) −63.4164 −2.27213
\(780\) −2.09017 −0.0748401
\(781\) −2.47214 −0.0884600
\(782\) 7.52786 0.269196
\(783\) −10.0000 −0.357371
\(784\) −1.00000 −0.0357143
\(785\) 15.9443 0.569075
\(786\) 7.52786 0.268510
\(787\) −14.2918 −0.509448 −0.254724 0.967014i \(-0.581985\pi\)
−0.254724 + 0.967014i \(0.581985\pi\)
\(788\) 20.9443 0.746109
\(789\) −7.54102 −0.268467
\(790\) 18.4164 0.655226
\(791\) 16.6180 0.590869
\(792\) 3.27051 0.116213
\(793\) 0.986844 0.0350439
\(794\) 27.8885 0.989727
\(795\) 7.00000 0.248264
\(796\) 5.85410 0.207493
\(797\) 26.5836 0.941639 0.470820 0.882230i \(-0.343958\pi\)
0.470820 + 0.882230i \(0.343958\pi\)
\(798\) 2.70820 0.0958694
\(799\) −4.00000 −0.141510
\(800\) 11.9098 0.421076
\(801\) −31.2361 −1.10367
\(802\) 18.9443 0.668945
\(803\) −1.85410 −0.0654298
\(804\) 5.29180 0.186627
\(805\) 9.85410 0.347311
\(806\) 21.8885 0.770991
\(807\) 2.18034 0.0767516
\(808\) 13.4164 0.471988
\(809\) −11.8885 −0.417979 −0.208989 0.977918i \(-0.567017\pi\)
−0.208989 + 0.977918i \(0.567017\pi\)
\(810\) −12.4721 −0.438226
\(811\) 42.8541 1.50481 0.752406 0.658700i \(-0.228893\pi\)
0.752406 + 0.658700i \(0.228893\pi\)
\(812\) 4.47214 0.156941
\(813\) 5.77709 0.202611
\(814\) −3.38197 −0.118538
\(815\) 4.00000 0.140114
\(816\) −0.472136 −0.0165281
\(817\) 54.6525 1.91205
\(818\) −10.6525 −0.372455
\(819\) 9.65248 0.337285
\(820\) 14.4721 0.505389
\(821\) 35.3262 1.23289 0.616447 0.787396i \(-0.288571\pi\)
0.616447 + 0.787396i \(0.288571\pi\)
\(822\) −1.34752 −0.0470003
\(823\) −14.1115 −0.491894 −0.245947 0.969283i \(-0.579099\pi\)
−0.245947 + 0.969283i \(0.579099\pi\)
\(824\) 17.7295 0.617636
\(825\) 0.347524 0.0120992
\(826\) −8.38197 −0.291646
\(827\) −44.6869 −1.55392 −0.776958 0.629552i \(-0.783238\pi\)
−0.776958 + 0.629552i \(0.783238\pi\)
\(828\) −17.3820 −0.604065
\(829\) 42.1459 1.46379 0.731894 0.681419i \(-0.238637\pi\)
0.731894 + 0.681419i \(0.238637\pi\)
\(830\) −21.4164 −0.743374
\(831\) −5.52786 −0.191759
\(832\) 23.6738 0.820740
\(833\) 1.23607 0.0428272
\(834\) −5.88854 −0.203904
\(835\) −16.4721 −0.570042
\(836\) 2.70820 0.0936652
\(837\) 14.4721 0.500230
\(838\) 20.0000 0.690889
\(839\) −31.2361 −1.07839 −0.539194 0.842181i \(-0.681271\pi\)
−0.539194 + 0.842181i \(0.681271\pi\)
\(840\) −1.85410 −0.0639726
\(841\) −9.00000 −0.310345
\(842\) −26.7984 −0.923533
\(843\) 3.15905 0.108804
\(844\) 6.43769 0.221595
\(845\) −2.52786 −0.0869612
\(846\) −9.23607 −0.317543
\(847\) 10.8541 0.372951
\(848\) −11.3262 −0.388945
\(849\) 6.23607 0.214021
\(850\) 2.94427 0.100988
\(851\) 53.9230 1.84846
\(852\) −2.47214 −0.0846940
\(853\) 18.1803 0.622483 0.311241 0.950331i \(-0.399255\pi\)
0.311241 + 0.950331i \(0.399255\pi\)
\(854\) 0.291796 0.00998506
\(855\) −32.7426 −1.11977
\(856\) 18.0000 0.615227
\(857\) 16.4721 0.562677 0.281339 0.959609i \(-0.409222\pi\)
0.281339 + 0.959609i \(0.409222\pi\)
\(858\) 0.493422 0.0168452
\(859\) −17.5279 −0.598043 −0.299022 0.954246i \(-0.596660\pi\)
−0.299022 + 0.954246i \(0.596660\pi\)
\(860\) −12.4721 −0.425296
\(861\) 3.41641 0.116431
\(862\) 19.0557 0.649041
\(863\) −1.00000 −0.0340404
\(864\) 11.1803 0.380363
\(865\) −30.0344 −1.02120
\(866\) −26.3607 −0.895772
\(867\) −5.90983 −0.200708
\(868\) −6.47214 −0.219679
\(869\) 4.34752 0.147480
\(870\) −2.76393 −0.0937061
\(871\) −46.8541 −1.58759
\(872\) −9.43769 −0.319601
\(873\) −5.29180 −0.179100
\(874\) 43.1803 1.46060
\(875\) 11.9443 0.403790
\(876\) −1.85410 −0.0626443
\(877\) −5.05573 −0.170720 −0.0853599 0.996350i \(-0.527204\pi\)
−0.0853599 + 0.996350i \(0.527204\pi\)
\(878\) 23.1246 0.780418
\(879\) −2.87539 −0.0969844
\(880\) 0.618034 0.0208339
\(881\) 15.2361 0.513316 0.256658 0.966502i \(-0.417379\pi\)
0.256658 + 0.966502i \(0.417379\pi\)
\(882\) 2.85410 0.0961026
\(883\) −52.9443 −1.78172 −0.890858 0.454281i \(-0.849896\pi\)
−0.890858 + 0.454281i \(0.849896\pi\)
\(884\) −4.18034 −0.140600
\(885\) −5.18034 −0.174135
\(886\) −10.7984 −0.362778
\(887\) 51.1935 1.71891 0.859455 0.511212i \(-0.170803\pi\)
0.859455 + 0.511212i \(0.170803\pi\)
\(888\) −10.1459 −0.340474
\(889\) 4.00000 0.134156
\(890\) −17.7082 −0.593580
\(891\) −2.94427 −0.0986368
\(892\) −20.5623 −0.688477
\(893\) −22.9443 −0.767801
\(894\) −8.18034 −0.273591
\(895\) −19.9443 −0.666663
\(896\) −3.00000 −0.100223
\(897\) −7.86726 −0.262680
\(898\) 20.6869 0.690331
\(899\) −28.9443 −0.965346
\(900\) −6.79837 −0.226612
\(901\) 14.0000 0.466408
\(902\) −3.41641 −0.113754
\(903\) −2.94427 −0.0979792
\(904\) −49.8541 −1.65812
\(905\) 24.1803 0.803782
\(906\) 4.29180 0.142585
\(907\) 35.7426 1.18682 0.593408 0.804902i \(-0.297782\pi\)
0.593408 + 0.804902i \(0.297782\pi\)
\(908\) −1.05573 −0.0350356
\(909\) −12.7639 −0.423353
\(910\) 5.47214 0.181400
\(911\) 38.8328 1.28659 0.643294 0.765619i \(-0.277567\pi\)
0.643294 + 0.765619i \(0.277567\pi\)
\(912\) −2.70820 −0.0896776
\(913\) −5.05573 −0.167320
\(914\) 39.6869 1.31273
\(915\) 0.180340 0.00596185
\(916\) 0.180340 0.00595860
\(917\) 19.7082 0.650822
\(918\) 2.76393 0.0912234
\(919\) −27.3820 −0.903248 −0.451624 0.892208i \(-0.649155\pi\)
−0.451624 + 0.892208i \(0.649155\pi\)
\(920\) −29.5623 −0.974640
\(921\) −1.98684 −0.0654687
\(922\) 21.5967 0.711251
\(923\) 21.8885 0.720470
\(924\) −0.145898 −0.00479969
\(925\) 21.0902 0.693441
\(926\) 8.00000 0.262896
\(927\) −16.8673 −0.553993
\(928\) −22.3607 −0.734025
\(929\) 48.4508 1.58962 0.794810 0.606858i \(-0.207570\pi\)
0.794810 + 0.606858i \(0.207570\pi\)
\(930\) 4.00000 0.131165
\(931\) 7.09017 0.232371
\(932\) 24.1803 0.792053
\(933\) −3.41641 −0.111848
\(934\) −8.03444 −0.262895
\(935\) −0.763932 −0.0249832
\(936\) −28.9574 −0.946503
\(937\) −8.65248 −0.282664 −0.141332 0.989962i \(-0.545139\pi\)
−0.141332 + 0.989962i \(0.545139\pi\)
\(938\) −13.8541 −0.452352
\(939\) −0.0688837 −0.00224793
\(940\) 5.23607 0.170782
\(941\) −6.94427 −0.226377 −0.113188 0.993574i \(-0.536106\pi\)
−0.113188 + 0.993574i \(0.536106\pi\)
\(942\) −3.76393 −0.122636
\(943\) 54.4721 1.77386
\(944\) 8.38197 0.272810
\(945\) 3.61803 0.117695
\(946\) 2.94427 0.0957265
\(947\) −3.97871 −0.129291 −0.0646454 0.997908i \(-0.520592\pi\)
−0.0646454 + 0.997908i \(0.520592\pi\)
\(948\) 4.34752 0.141201
\(949\) 16.4164 0.532899
\(950\) 16.8885 0.547937
\(951\) 1.01316 0.0328538
\(952\) −3.70820 −0.120184
\(953\) −17.8885 −0.579467 −0.289733 0.957107i \(-0.593567\pi\)
−0.289733 + 0.957107i \(0.593567\pi\)
\(954\) 32.3262 1.04660
\(955\) −28.9443 −0.936615
\(956\) 29.2361 0.945562
\(957\) −0.652476 −0.0210915
\(958\) −24.6525 −0.796485
\(959\) −3.52786 −0.113921
\(960\) 4.32624 0.139629
\(961\) 10.8885 0.351243
\(962\) 29.9443 0.965442
\(963\) −17.1246 −0.551833
\(964\) −12.6180 −0.406400
\(965\) −37.5967 −1.21028
\(966\) −2.32624 −0.0748455
\(967\) 60.9787 1.96094 0.980472 0.196661i \(-0.0630097\pi\)
0.980472 + 0.196661i \(0.0630097\pi\)
\(968\) −32.5623 −1.04659
\(969\) 3.34752 0.107538
\(970\) −3.00000 −0.0963242
\(971\) −48.7214 −1.56354 −0.781771 0.623565i \(-0.785684\pi\)
−0.781771 + 0.623565i \(0.785684\pi\)
\(972\) −9.65248 −0.309603
\(973\) −15.4164 −0.494227
\(974\) −1.41641 −0.0453846
\(975\) −3.07701 −0.0985433
\(976\) −0.291796 −0.00934016
\(977\) 25.4164 0.813143 0.406571 0.913619i \(-0.366724\pi\)
0.406571 + 0.913619i \(0.366724\pi\)
\(978\) −0.944272 −0.0301945
\(979\) −4.18034 −0.133604
\(980\) −1.61803 −0.0516862
\(981\) 8.97871 0.286668
\(982\) 20.7426 0.661924
\(983\) 16.0000 0.510321 0.255160 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) −10.2492 −0.326733
\(985\) −33.8885 −1.07978
\(986\) −5.52786 −0.176043
\(987\) 1.23607 0.0393445
\(988\) −23.9787 −0.762865
\(989\) −46.9443 −1.49274
\(990\) −1.76393 −0.0560614
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) 32.3607 1.02745
\(993\) −5.16718 −0.163976
\(994\) 6.47214 0.205284
\(995\) −9.47214 −0.300287
\(996\) −5.05573 −0.160197
\(997\) −16.9787 −0.537721 −0.268861 0.963179i \(-0.586647\pi\)
−0.268861 + 0.963179i \(0.586647\pi\)
\(998\) 13.8885 0.439634
\(999\) 19.7984 0.626393
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 \(a_p\))