Properties

Label 6034.2.a.n.1.2
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.67063 q^{3}\) \(+1.00000 q^{4}\) \(+3.15601 q^{5}\) \(+2.67063 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+4.13228 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.67063 q^{3}\) \(+1.00000 q^{4}\) \(+3.15601 q^{5}\) \(+2.67063 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+4.13228 q^{9}\) \(-3.15601 q^{10}\) \(+3.01631 q^{11}\) \(-2.67063 q^{12}\) \(-4.63033 q^{13}\) \(+1.00000 q^{14}\) \(-8.42854 q^{15}\) \(+1.00000 q^{16}\) \(-6.60020 q^{17}\) \(-4.13228 q^{18}\) \(-4.22204 q^{19}\) \(+3.15601 q^{20}\) \(+2.67063 q^{21}\) \(-3.01631 q^{22}\) \(-0.524979 q^{23}\) \(+2.67063 q^{24}\) \(+4.96038 q^{25}\) \(+4.63033 q^{26}\) \(-3.02392 q^{27}\) \(-1.00000 q^{28}\) \(-9.21317 q^{29}\) \(+8.42854 q^{30}\) \(+1.00489 q^{31}\) \(-1.00000 q^{32}\) \(-8.05546 q^{33}\) \(+6.60020 q^{34}\) \(-3.15601 q^{35}\) \(+4.13228 q^{36}\) \(-8.56493 q^{37}\) \(+4.22204 q^{38}\) \(+12.3659 q^{39}\) \(-3.15601 q^{40}\) \(+6.31163 q^{41}\) \(-2.67063 q^{42}\) \(-11.7000 q^{43}\) \(+3.01631 q^{44}\) \(+13.0415 q^{45}\) \(+0.524979 q^{46}\) \(-7.89697 q^{47}\) \(-2.67063 q^{48}\) \(+1.00000 q^{49}\) \(-4.96038 q^{50}\) \(+17.6267 q^{51}\) \(-4.63033 q^{52}\) \(+0.831758 q^{53}\) \(+3.02392 q^{54}\) \(+9.51949 q^{55}\) \(+1.00000 q^{56}\) \(+11.2755 q^{57}\) \(+9.21317 q^{58}\) \(-2.18079 q^{59}\) \(-8.42854 q^{60}\) \(-1.29727 q^{61}\) \(-1.00489 q^{62}\) \(-4.13228 q^{63}\) \(+1.00000 q^{64}\) \(-14.6134 q^{65}\) \(+8.05546 q^{66}\) \(+8.28511 q^{67}\) \(-6.60020 q^{68}\) \(+1.40203 q^{69}\) \(+3.15601 q^{70}\) \(+14.0501 q^{71}\) \(-4.13228 q^{72}\) \(+16.6288 q^{73}\) \(+8.56493 q^{74}\) \(-13.2474 q^{75}\) \(-4.22204 q^{76}\) \(-3.01631 q^{77}\) \(-12.3659 q^{78}\) \(+16.4102 q^{79}\) \(+3.15601 q^{80}\) \(-4.32108 q^{81}\) \(-6.31163 q^{82}\) \(+7.07919 q^{83}\) \(+2.67063 q^{84}\) \(-20.8303 q^{85}\) \(+11.7000 q^{86}\) \(+24.6050 q^{87}\) \(-3.01631 q^{88}\) \(+14.0832 q^{89}\) \(-13.0415 q^{90}\) \(+4.63033 q^{91}\) \(-0.524979 q^{92}\) \(-2.68370 q^{93}\) \(+7.89697 q^{94}\) \(-13.3248 q^{95}\) \(+2.67063 q^{96}\) \(+14.9874 q^{97}\) \(-1.00000 q^{98}\) \(+12.4642 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.67063 −1.54189 −0.770946 0.636901i \(-0.780216\pi\)
−0.770946 + 0.636901i \(0.780216\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.15601 1.41141 0.705705 0.708506i \(-0.250631\pi\)
0.705705 + 0.708506i \(0.250631\pi\)
\(6\) 2.67063 1.09028
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 4.13228 1.37743
\(10\) −3.15601 −0.998017
\(11\) 3.01631 0.909452 0.454726 0.890632i \(-0.349737\pi\)
0.454726 + 0.890632i \(0.349737\pi\)
\(12\) −2.67063 −0.770946
\(13\) −4.63033 −1.28422 −0.642112 0.766611i \(-0.721941\pi\)
−0.642112 + 0.766611i \(0.721941\pi\)
\(14\) 1.00000 0.267261
\(15\) −8.42854 −2.17624
\(16\) 1.00000 0.250000
\(17\) −6.60020 −1.60078 −0.800392 0.599477i \(-0.795375\pi\)
−0.800392 + 0.599477i \(0.795375\pi\)
\(18\) −4.13228 −0.973989
\(19\) −4.22204 −0.968603 −0.484302 0.874901i \(-0.660926\pi\)
−0.484302 + 0.874901i \(0.660926\pi\)
\(20\) 3.15601 0.705705
\(21\) 2.67063 0.582780
\(22\) −3.01631 −0.643079
\(23\) −0.524979 −0.109466 −0.0547328 0.998501i \(-0.517431\pi\)
−0.0547328 + 0.998501i \(0.517431\pi\)
\(24\) 2.67063 0.545141
\(25\) 4.96038 0.992076
\(26\) 4.63033 0.908083
\(27\) −3.02392 −0.581953
\(28\) −1.00000 −0.188982
\(29\) −9.21317 −1.71084 −0.855421 0.517933i \(-0.826702\pi\)
−0.855421 + 0.517933i \(0.826702\pi\)
\(30\) 8.42854 1.53883
\(31\) 1.00489 0.180484 0.0902419 0.995920i \(-0.471236\pi\)
0.0902419 + 0.995920i \(0.471236\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.05546 −1.40228
\(34\) 6.60020 1.13192
\(35\) −3.15601 −0.533463
\(36\) 4.13228 0.688714
\(37\) −8.56493 −1.40807 −0.704033 0.710168i \(-0.748619\pi\)
−0.704033 + 0.710168i \(0.748619\pi\)
\(38\) 4.22204 0.684906
\(39\) 12.3659 1.98013
\(40\) −3.15601 −0.499009
\(41\) 6.31163 0.985711 0.492855 0.870111i \(-0.335953\pi\)
0.492855 + 0.870111i \(0.335953\pi\)
\(42\) −2.67063 −0.412088
\(43\) −11.7000 −1.78423 −0.892116 0.451807i \(-0.850780\pi\)
−0.892116 + 0.451807i \(0.850780\pi\)
\(44\) 3.01631 0.454726
\(45\) 13.0415 1.94411
\(46\) 0.524979 0.0774039
\(47\) −7.89697 −1.15189 −0.575946 0.817488i \(-0.695366\pi\)
−0.575946 + 0.817488i \(0.695366\pi\)
\(48\) −2.67063 −0.385473
\(49\) 1.00000 0.142857
\(50\) −4.96038 −0.701504
\(51\) 17.6267 2.46823
\(52\) −4.63033 −0.642112
\(53\) 0.831758 0.114251 0.0571254 0.998367i \(-0.481807\pi\)
0.0571254 + 0.998367i \(0.481807\pi\)
\(54\) 3.02392 0.411503
\(55\) 9.51949 1.28361
\(56\) 1.00000 0.133631
\(57\) 11.2755 1.49348
\(58\) 9.21317 1.20975
\(59\) −2.18079 −0.283914 −0.141957 0.989873i \(-0.545340\pi\)
−0.141957 + 0.989873i \(0.545340\pi\)
\(60\) −8.42854 −1.08812
\(61\) −1.29727 −0.166098 −0.0830490 0.996545i \(-0.526466\pi\)
−0.0830490 + 0.996545i \(0.526466\pi\)
\(62\) −1.00489 −0.127621
\(63\) −4.13228 −0.520619
\(64\) 1.00000 0.125000
\(65\) −14.6134 −1.81256
\(66\) 8.05546 0.991558
\(67\) 8.28511 1.01219 0.506093 0.862479i \(-0.331089\pi\)
0.506093 + 0.862479i \(0.331089\pi\)
\(68\) −6.60020 −0.800392
\(69\) 1.40203 0.168784
\(70\) 3.15601 0.377215
\(71\) 14.0501 1.66744 0.833720 0.552188i \(-0.186207\pi\)
0.833720 + 0.552188i \(0.186207\pi\)
\(72\) −4.13228 −0.486994
\(73\) 16.6288 1.94625 0.973127 0.230270i \(-0.0739610\pi\)
0.973127 + 0.230270i \(0.0739610\pi\)
\(74\) 8.56493 0.995652
\(75\) −13.2474 −1.52967
\(76\) −4.22204 −0.484302
\(77\) −3.01631 −0.343740
\(78\) −12.3659 −1.40017
\(79\) 16.4102 1.84629 0.923145 0.384453i \(-0.125610\pi\)
0.923145 + 0.384453i \(0.125610\pi\)
\(80\) 3.15601 0.352852
\(81\) −4.32108 −0.480120
\(82\) −6.31163 −0.697003
\(83\) 7.07919 0.777042 0.388521 0.921440i \(-0.372986\pi\)
0.388521 + 0.921440i \(0.372986\pi\)
\(84\) 2.67063 0.291390
\(85\) −20.8303 −2.25936
\(86\) 11.7000 1.26164
\(87\) 24.6050 2.63793
\(88\) −3.01631 −0.321540
\(89\) 14.0832 1.49282 0.746408 0.665489i \(-0.231777\pi\)
0.746408 + 0.665489i \(0.231777\pi\)
\(90\) −13.0415 −1.37470
\(91\) 4.63033 0.485391
\(92\) −0.524979 −0.0547328
\(93\) −2.68370 −0.278286
\(94\) 7.89697 0.814511
\(95\) −13.3248 −1.36710
\(96\) 2.67063 0.272570
\(97\) 14.9874 1.52174 0.760868 0.648907i \(-0.224773\pi\)
0.760868 + 0.648907i \(0.224773\pi\)
\(98\) −1.00000 −0.101015
\(99\) 12.4642 1.25270
\(100\) 4.96038 0.496038
\(101\) −0.171171 −0.0170322 −0.00851608 0.999964i \(-0.502711\pi\)
−0.00851608 + 0.999964i \(0.502711\pi\)
\(102\) −17.6267 −1.74530
\(103\) 11.0002 1.08388 0.541941 0.840417i \(-0.317690\pi\)
0.541941 + 0.840417i \(0.317690\pi\)
\(104\) 4.63033 0.454042
\(105\) 8.42854 0.822541
\(106\) −0.831758 −0.0807875
\(107\) −16.3738 −1.58292 −0.791458 0.611223i \(-0.790678\pi\)
−0.791458 + 0.611223i \(0.790678\pi\)
\(108\) −3.02392 −0.290977
\(109\) −10.6488 −1.01997 −0.509984 0.860184i \(-0.670349\pi\)
−0.509984 + 0.860184i \(0.670349\pi\)
\(110\) −9.51949 −0.907648
\(111\) 22.8738 2.17108
\(112\) −1.00000 −0.0944911
\(113\) −17.2274 −1.62062 −0.810308 0.586005i \(-0.800700\pi\)
−0.810308 + 0.586005i \(0.800700\pi\)
\(114\) −11.2755 −1.05605
\(115\) −1.65684 −0.154501
\(116\) −9.21317 −0.855421
\(117\) −19.1339 −1.76893
\(118\) 2.18079 0.200758
\(119\) 6.60020 0.605039
\(120\) 8.42854 0.769417
\(121\) −1.90188 −0.172898
\(122\) 1.29727 0.117449
\(123\) −16.8561 −1.51986
\(124\) 1.00489 0.0902419
\(125\) −0.125039 −0.0111839
\(126\) 4.13228 0.368133
\(127\) 12.3826 1.09878 0.549389 0.835567i \(-0.314861\pi\)
0.549389 + 0.835567i \(0.314861\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 31.2464 2.75109
\(130\) 14.6134 1.28168
\(131\) 11.2346 0.981574 0.490787 0.871280i \(-0.336709\pi\)
0.490787 + 0.871280i \(0.336709\pi\)
\(132\) −8.05546 −0.701138
\(133\) 4.22204 0.366098
\(134\) −8.28511 −0.715724
\(135\) −9.54350 −0.821374
\(136\) 6.60020 0.565962
\(137\) 7.05090 0.602399 0.301200 0.953561i \(-0.402613\pi\)
0.301200 + 0.953561i \(0.402613\pi\)
\(138\) −1.40203 −0.119348
\(139\) 19.2723 1.63465 0.817325 0.576176i \(-0.195456\pi\)
0.817325 + 0.576176i \(0.195456\pi\)
\(140\) −3.15601 −0.266731
\(141\) 21.0899 1.77609
\(142\) −14.0501 −1.17906
\(143\) −13.9665 −1.16794
\(144\) 4.13228 0.344357
\(145\) −29.0768 −2.41470
\(146\) −16.6288 −1.37621
\(147\) −2.67063 −0.220270
\(148\) −8.56493 −0.704033
\(149\) −16.3469 −1.33919 −0.669595 0.742726i \(-0.733532\pi\)
−0.669595 + 0.742726i \(0.733532\pi\)
\(150\) 13.2474 1.08164
\(151\) −4.57648 −0.372429 −0.186214 0.982509i \(-0.559622\pi\)
−0.186214 + 0.982509i \(0.559622\pi\)
\(152\) 4.22204 0.342453
\(153\) −27.2739 −2.20496
\(154\) 3.01631 0.243061
\(155\) 3.17144 0.254736
\(156\) 12.3659 0.990066
\(157\) −7.67641 −0.612644 −0.306322 0.951928i \(-0.599099\pi\)
−0.306322 + 0.951928i \(0.599099\pi\)
\(158\) −16.4102 −1.30552
\(159\) −2.22132 −0.176162
\(160\) −3.15601 −0.249504
\(161\) 0.524979 0.0413741
\(162\) 4.32108 0.339496
\(163\) 1.14467 0.0896571 0.0448286 0.998995i \(-0.485726\pi\)
0.0448286 + 0.998995i \(0.485726\pi\)
\(164\) 6.31163 0.492855
\(165\) −25.4231 −1.97918
\(166\) −7.07919 −0.549452
\(167\) 20.8699 1.61496 0.807482 0.589892i \(-0.200830\pi\)
0.807482 + 0.589892i \(0.200830\pi\)
\(168\) −2.67063 −0.206044
\(169\) 8.43999 0.649230
\(170\) 20.8303 1.59761
\(171\) −17.4467 −1.33418
\(172\) −11.7000 −0.892116
\(173\) 9.07022 0.689596 0.344798 0.938677i \(-0.387947\pi\)
0.344798 + 0.938677i \(0.387947\pi\)
\(174\) −24.6050 −1.86530
\(175\) −4.96038 −0.374970
\(176\) 3.01631 0.227363
\(177\) 5.82409 0.437765
\(178\) −14.0832 −1.05558
\(179\) 4.01486 0.300085 0.150042 0.988680i \(-0.452059\pi\)
0.150042 + 0.988680i \(0.452059\pi\)
\(180\) 13.0415 0.972057
\(181\) 5.69222 0.423100 0.211550 0.977367i \(-0.432149\pi\)
0.211550 + 0.977367i \(0.432149\pi\)
\(182\) −4.63033 −0.343223
\(183\) 3.46452 0.256105
\(184\) 0.524979 0.0387020
\(185\) −27.0310 −1.98736
\(186\) 2.68370 0.196778
\(187\) −19.9082 −1.45583
\(188\) −7.89697 −0.575946
\(189\) 3.02392 0.219958
\(190\) 13.3248 0.966683
\(191\) −7.41957 −0.536861 −0.268431 0.963299i \(-0.586505\pi\)
−0.268431 + 0.963299i \(0.586505\pi\)
\(192\) −2.67063 −0.192736
\(193\) −2.64434 −0.190344 −0.0951720 0.995461i \(-0.530340\pi\)
−0.0951720 + 0.995461i \(0.530340\pi\)
\(194\) −14.9874 −1.07603
\(195\) 39.0269 2.79478
\(196\) 1.00000 0.0714286
\(197\) 2.48654 0.177158 0.0885792 0.996069i \(-0.471767\pi\)
0.0885792 + 0.996069i \(0.471767\pi\)
\(198\) −12.4642 −0.885796
\(199\) 7.21010 0.511111 0.255555 0.966794i \(-0.417742\pi\)
0.255555 + 0.966794i \(0.417742\pi\)
\(200\) −4.96038 −0.350752
\(201\) −22.1265 −1.56068
\(202\) 0.171171 0.0120436
\(203\) 9.21317 0.646638
\(204\) 17.6267 1.23412
\(205\) 19.9195 1.39124
\(206\) −11.0002 −0.766420
\(207\) −2.16936 −0.150781
\(208\) −4.63033 −0.321056
\(209\) −12.7350 −0.880898
\(210\) −8.42854 −0.581624
\(211\) −14.2028 −0.977760 −0.488880 0.872351i \(-0.662594\pi\)
−0.488880 + 0.872351i \(0.662594\pi\)
\(212\) 0.831758 0.0571254
\(213\) −37.5226 −2.57101
\(214\) 16.3738 1.11929
\(215\) −36.9252 −2.51828
\(216\) 3.02392 0.205751
\(217\) −1.00489 −0.0682164
\(218\) 10.6488 0.721226
\(219\) −44.4094 −3.00091
\(220\) 9.51949 0.641804
\(221\) 30.5611 2.05576
\(222\) −22.8738 −1.53519
\(223\) −6.07525 −0.406829 −0.203414 0.979093i \(-0.565204\pi\)
−0.203414 + 0.979093i \(0.565204\pi\)
\(224\) 1.00000 0.0668153
\(225\) 20.4977 1.36651
\(226\) 17.2274 1.14595
\(227\) 26.8622 1.78291 0.891455 0.453109i \(-0.149685\pi\)
0.891455 + 0.453109i \(0.149685\pi\)
\(228\) 11.2755 0.746740
\(229\) 15.0402 0.993886 0.496943 0.867783i \(-0.334456\pi\)
0.496943 + 0.867783i \(0.334456\pi\)
\(230\) 1.65684 0.109249
\(231\) 8.05546 0.530010
\(232\) 9.21317 0.604874
\(233\) −24.5638 −1.60923 −0.804613 0.593800i \(-0.797627\pi\)
−0.804613 + 0.593800i \(0.797627\pi\)
\(234\) 19.1339 1.25082
\(235\) −24.9229 −1.62579
\(236\) −2.18079 −0.141957
\(237\) −43.8256 −2.84678
\(238\) −6.60020 −0.427827
\(239\) −6.35840 −0.411291 −0.205645 0.978627i \(-0.565929\pi\)
−0.205645 + 0.978627i \(0.565929\pi\)
\(240\) −8.42854 −0.544060
\(241\) −5.51971 −0.355556 −0.177778 0.984071i \(-0.556891\pi\)
−0.177778 + 0.984071i \(0.556891\pi\)
\(242\) 1.90188 0.122257
\(243\) 20.6118 1.32225
\(244\) −1.29727 −0.0830490
\(245\) 3.15601 0.201630
\(246\) 16.8561 1.07470
\(247\) 19.5495 1.24390
\(248\) −1.00489 −0.0638106
\(249\) −18.9059 −1.19811
\(250\) 0.125039 0.00790819
\(251\) 5.28603 0.333652 0.166826 0.985986i \(-0.446648\pi\)
0.166826 + 0.985986i \(0.446648\pi\)
\(252\) −4.13228 −0.260309
\(253\) −1.58350 −0.0995537
\(254\) −12.3826 −0.776953
\(255\) 55.6300 3.48369
\(256\) 1.00000 0.0625000
\(257\) −6.39010 −0.398603 −0.199302 0.979938i \(-0.563867\pi\)
−0.199302 + 0.979938i \(0.563867\pi\)
\(258\) −31.2464 −1.94531
\(259\) 8.56493 0.532199
\(260\) −14.6134 −0.906282
\(261\) −38.0714 −2.35656
\(262\) −11.2346 −0.694077
\(263\) −2.48872 −0.153461 −0.0767304 0.997052i \(-0.524448\pi\)
−0.0767304 + 0.997052i \(0.524448\pi\)
\(264\) 8.05546 0.495779
\(265\) 2.62504 0.161255
\(266\) −4.22204 −0.258870
\(267\) −37.6111 −2.30176
\(268\) 8.28511 0.506093
\(269\) −1.04689 −0.0638299 −0.0319150 0.999491i \(-0.510161\pi\)
−0.0319150 + 0.999491i \(0.510161\pi\)
\(270\) 9.54350 0.580799
\(271\) −6.47317 −0.393217 −0.196609 0.980482i \(-0.562993\pi\)
−0.196609 + 0.980482i \(0.562993\pi\)
\(272\) −6.60020 −0.400196
\(273\) −12.3659 −0.748420
\(274\) −7.05090 −0.425961
\(275\) 14.9620 0.902245
\(276\) 1.40203 0.0843921
\(277\) 5.18131 0.311315 0.155657 0.987811i \(-0.450250\pi\)
0.155657 + 0.987811i \(0.450250\pi\)
\(278\) −19.2723 −1.15587
\(279\) 4.15250 0.248603
\(280\) 3.15601 0.188607
\(281\) 0.340066 0.0202867 0.0101433 0.999949i \(-0.496771\pi\)
0.0101433 + 0.999949i \(0.496771\pi\)
\(282\) −21.0899 −1.25589
\(283\) −20.1181 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(284\) 14.0501 0.833720
\(285\) 35.5857 2.10791
\(286\) 13.9665 0.825857
\(287\) −6.31163 −0.372564
\(288\) −4.13228 −0.243497
\(289\) 26.5626 1.56251
\(290\) 29.0768 1.70745
\(291\) −40.0257 −2.34635
\(292\) 16.6288 0.973127
\(293\) 13.9830 0.816893 0.408447 0.912782i \(-0.366071\pi\)
0.408447 + 0.912782i \(0.366071\pi\)
\(294\) 2.67063 0.155755
\(295\) −6.88258 −0.400720
\(296\) 8.56493 0.497826
\(297\) −9.12107 −0.529258
\(298\) 16.3469 0.946950
\(299\) 2.43083 0.140578
\(300\) −13.2474 −0.764837
\(301\) 11.7000 0.674376
\(302\) 4.57648 0.263347
\(303\) 0.457135 0.0262617
\(304\) −4.22204 −0.242151
\(305\) −4.09418 −0.234432
\(306\) 27.2739 1.55915
\(307\) 28.6630 1.63588 0.817941 0.575302i \(-0.195115\pi\)
0.817941 + 0.575302i \(0.195115\pi\)
\(308\) −3.01631 −0.171870
\(309\) −29.3775 −1.67123
\(310\) −3.17144 −0.180126
\(311\) 10.8244 0.613793 0.306897 0.951743i \(-0.400709\pi\)
0.306897 + 0.951743i \(0.400709\pi\)
\(312\) −12.3659 −0.700083
\(313\) −13.5622 −0.766579 −0.383289 0.923628i \(-0.625209\pi\)
−0.383289 + 0.923628i \(0.625209\pi\)
\(314\) 7.67641 0.433205
\(315\) −13.0415 −0.734806
\(316\) 16.4102 0.923145
\(317\) 12.4644 0.700070 0.350035 0.936737i \(-0.386170\pi\)
0.350035 + 0.936737i \(0.386170\pi\)
\(318\) 2.22132 0.124566
\(319\) −27.7898 −1.55593
\(320\) 3.15601 0.176426
\(321\) 43.7285 2.44069
\(322\) −0.524979 −0.0292559
\(323\) 27.8663 1.55052
\(324\) −4.32108 −0.240060
\(325\) −22.9682 −1.27405
\(326\) −1.14467 −0.0633972
\(327\) 28.4390 1.57268
\(328\) −6.31163 −0.348501
\(329\) 7.89697 0.435374
\(330\) 25.4231 1.39949
\(331\) 7.39253 0.406330 0.203165 0.979144i \(-0.434877\pi\)
0.203165 + 0.979144i \(0.434877\pi\)
\(332\) 7.07919 0.388521
\(333\) −35.3927 −1.93951
\(334\) −20.8699 −1.14195
\(335\) 26.1479 1.42861
\(336\) 2.67063 0.145695
\(337\) 30.2671 1.64876 0.824378 0.566040i \(-0.191525\pi\)
0.824378 + 0.566040i \(0.191525\pi\)
\(338\) −8.43999 −0.459075
\(339\) 46.0080 2.49881
\(340\) −20.8303 −1.12968
\(341\) 3.03106 0.164141
\(342\) 17.4467 0.943409
\(343\) −1.00000 −0.0539949
\(344\) 11.7000 0.630821
\(345\) 4.42480 0.238223
\(346\) −9.07022 −0.487618
\(347\) 22.4200 1.20357 0.601786 0.798658i \(-0.294456\pi\)
0.601786 + 0.798658i \(0.294456\pi\)
\(348\) 24.6050 1.31897
\(349\) −14.1699 −0.758500 −0.379250 0.925294i \(-0.623818\pi\)
−0.379250 + 0.925294i \(0.623818\pi\)
\(350\) 4.96038 0.265143
\(351\) 14.0017 0.747358
\(352\) −3.01631 −0.160770
\(353\) −9.44344 −0.502624 −0.251312 0.967906i \(-0.580862\pi\)
−0.251312 + 0.967906i \(0.580862\pi\)
\(354\) −5.82409 −0.309547
\(355\) 44.3422 2.35344
\(356\) 14.0832 0.746408
\(357\) −17.6267 −0.932905
\(358\) −4.01486 −0.212192
\(359\) 2.00815 0.105986 0.0529929 0.998595i \(-0.483124\pi\)
0.0529929 + 0.998595i \(0.483124\pi\)
\(360\) −13.0415 −0.687348
\(361\) −1.17434 −0.0618076
\(362\) −5.69222 −0.299177
\(363\) 5.07922 0.266590
\(364\) 4.63033 0.242695
\(365\) 52.4806 2.74696
\(366\) −3.46452 −0.181094
\(367\) 14.7871 0.771881 0.385940 0.922524i \(-0.373877\pi\)
0.385940 + 0.922524i \(0.373877\pi\)
\(368\) −0.524979 −0.0273664
\(369\) 26.0814 1.35775
\(370\) 27.0310 1.40527
\(371\) −0.831758 −0.0431827
\(372\) −2.68370 −0.139143
\(373\) 30.6145 1.58516 0.792579 0.609769i \(-0.208738\pi\)
0.792579 + 0.609769i \(0.208738\pi\)
\(374\) 19.9082 1.02943
\(375\) 0.333934 0.0172443
\(376\) 7.89697 0.407255
\(377\) 42.6600 2.19710
\(378\) −3.02392 −0.155534
\(379\) 10.7563 0.552512 0.276256 0.961084i \(-0.410906\pi\)
0.276256 + 0.961084i \(0.410906\pi\)
\(380\) −13.3248 −0.683548
\(381\) −33.0694 −1.69420
\(382\) 7.41957 0.379618
\(383\) −1.45941 −0.0745723 −0.0372862 0.999305i \(-0.511871\pi\)
−0.0372862 + 0.999305i \(0.511871\pi\)
\(384\) 2.67063 0.136285
\(385\) −9.51949 −0.485158
\(386\) 2.64434 0.134594
\(387\) −48.3477 −2.45765
\(388\) 14.9874 0.760868
\(389\) 4.73759 0.240205 0.120103 0.992761i \(-0.461678\pi\)
0.120103 + 0.992761i \(0.461678\pi\)
\(390\) −39.0269 −1.97621
\(391\) 3.46496 0.175231
\(392\) −1.00000 −0.0505076
\(393\) −30.0036 −1.51348
\(394\) −2.48654 −0.125270
\(395\) 51.7906 2.60587
\(396\) 12.4642 0.626352
\(397\) −16.7995 −0.843143 −0.421572 0.906795i \(-0.638521\pi\)
−0.421572 + 0.906795i \(0.638521\pi\)
\(398\) −7.21010 −0.361410
\(399\) −11.2755 −0.564483
\(400\) 4.96038 0.248019
\(401\) −2.31347 −0.115529 −0.0577647 0.998330i \(-0.518397\pi\)
−0.0577647 + 0.998330i \(0.518397\pi\)
\(402\) 22.1265 1.10357
\(403\) −4.65298 −0.231781
\(404\) −0.171171 −0.00851608
\(405\) −13.6374 −0.677646
\(406\) −9.21317 −0.457242
\(407\) −25.8345 −1.28057
\(408\) −17.6267 −0.872652
\(409\) −11.6520 −0.576152 −0.288076 0.957608i \(-0.593016\pi\)
−0.288076 + 0.957608i \(0.593016\pi\)
\(410\) −19.9195 −0.983756
\(411\) −18.8304 −0.928834
\(412\) 11.0002 0.541941
\(413\) 2.18079 0.107310
\(414\) 2.16936 0.106618
\(415\) 22.3420 1.09672
\(416\) 4.63033 0.227021
\(417\) −51.4691 −2.52045
\(418\) 12.7350 0.622889
\(419\) −31.2631 −1.52730 −0.763652 0.645628i \(-0.776596\pi\)
−0.763652 + 0.645628i \(0.776596\pi\)
\(420\) 8.42854 0.411271
\(421\) 24.4387 1.19107 0.595534 0.803330i \(-0.296941\pi\)
0.595534 + 0.803330i \(0.296941\pi\)
\(422\) 14.2028 0.691381
\(423\) −32.6325 −1.58665
\(424\) −0.831758 −0.0403938
\(425\) −32.7395 −1.58810
\(426\) 37.5226 1.81798
\(427\) 1.29727 0.0627791
\(428\) −16.3738 −0.791458
\(429\) 37.2995 1.80083
\(430\) 36.9252 1.78069
\(431\) 1.00000 0.0481683
\(432\) −3.02392 −0.145488
\(433\) −25.2393 −1.21292 −0.606462 0.795112i \(-0.707412\pi\)
−0.606462 + 0.795112i \(0.707412\pi\)
\(434\) 1.00489 0.0482363
\(435\) 77.6535 3.72320
\(436\) −10.6488 −0.509984
\(437\) 2.21648 0.106029
\(438\) 44.4094 2.12196
\(439\) 12.9214 0.616706 0.308353 0.951272i \(-0.400222\pi\)
0.308353 + 0.951272i \(0.400222\pi\)
\(440\) −9.51949 −0.453824
\(441\) 4.13228 0.196775
\(442\) −30.5611 −1.45364
\(443\) 3.93412 0.186916 0.0934578 0.995623i \(-0.470208\pi\)
0.0934578 + 0.995623i \(0.470208\pi\)
\(444\) 22.8738 1.08554
\(445\) 44.4467 2.10697
\(446\) 6.07525 0.287671
\(447\) 43.6566 2.06488
\(448\) −1.00000 −0.0472456
\(449\) 31.8219 1.50177 0.750883 0.660435i \(-0.229628\pi\)
0.750883 + 0.660435i \(0.229628\pi\)
\(450\) −20.4977 −0.966271
\(451\) 19.0378 0.896456
\(452\) −17.2274 −0.810308
\(453\) 12.2221 0.574245
\(454\) −26.8622 −1.26071
\(455\) 14.6134 0.685085
\(456\) −11.2755 −0.528025
\(457\) −15.1960 −0.710838 −0.355419 0.934707i \(-0.615662\pi\)
−0.355419 + 0.934707i \(0.615662\pi\)
\(458\) −15.0402 −0.702784
\(459\) 19.9585 0.931581
\(460\) −1.65684 −0.0772504
\(461\) −5.80779 −0.270496 −0.135248 0.990812i \(-0.543183\pi\)
−0.135248 + 0.990812i \(0.543183\pi\)
\(462\) −8.05546 −0.374774
\(463\) 21.0429 0.977948 0.488974 0.872298i \(-0.337371\pi\)
0.488974 + 0.872298i \(0.337371\pi\)
\(464\) −9.21317 −0.427711
\(465\) −8.46976 −0.392776
\(466\) 24.5638 1.13789
\(467\) 25.8605 1.19668 0.598341 0.801241i \(-0.295827\pi\)
0.598341 + 0.801241i \(0.295827\pi\)
\(468\) −19.1339 −0.884463
\(469\) −8.28511 −0.382571
\(470\) 24.9229 1.14961
\(471\) 20.5009 0.944631
\(472\) 2.18079 0.100379
\(473\) −35.2908 −1.62267
\(474\) 43.8256 2.01298
\(475\) −20.9429 −0.960928
\(476\) 6.60020 0.302520
\(477\) 3.43706 0.157372
\(478\) 6.35840 0.290826
\(479\) −21.8365 −0.997733 −0.498866 0.866679i \(-0.666250\pi\)
−0.498866 + 0.866679i \(0.666250\pi\)
\(480\) 8.42854 0.384708
\(481\) 39.6585 1.80827
\(482\) 5.51971 0.251416
\(483\) −1.40203 −0.0637944
\(484\) −1.90188 −0.0864490
\(485\) 47.3002 2.14779
\(486\) −20.6118 −0.934969
\(487\) −31.9434 −1.44749 −0.723746 0.690066i \(-0.757581\pi\)
−0.723746 + 0.690066i \(0.757581\pi\)
\(488\) 1.29727 0.0587245
\(489\) −3.05698 −0.138242
\(490\) −3.15601 −0.142574
\(491\) 4.08024 0.184139 0.0920694 0.995753i \(-0.470652\pi\)
0.0920694 + 0.995753i \(0.470652\pi\)
\(492\) −16.8561 −0.759929
\(493\) 60.8087 2.73869
\(494\) −19.5495 −0.879572
\(495\) 39.3373 1.76808
\(496\) 1.00489 0.0451209
\(497\) −14.0501 −0.630233
\(498\) 18.9059 0.847195
\(499\) 43.4544 1.94529 0.972644 0.232302i \(-0.0746257\pi\)
0.972644 + 0.232302i \(0.0746257\pi\)
\(500\) −0.125039 −0.00559193
\(501\) −55.7360 −2.49010
\(502\) −5.28603 −0.235927
\(503\) −1.47723 −0.0658665 −0.0329333 0.999458i \(-0.510485\pi\)
−0.0329333 + 0.999458i \(0.510485\pi\)
\(504\) 4.13228 0.184067
\(505\) −0.540217 −0.0240393
\(506\) 1.58350 0.0703951
\(507\) −22.5401 −1.00104
\(508\) 12.3826 0.549389
\(509\) −12.5665 −0.557000 −0.278500 0.960436i \(-0.589837\pi\)
−0.278500 + 0.960436i \(0.589837\pi\)
\(510\) −55.6300 −2.46334
\(511\) −16.6288 −0.735615
\(512\) −1.00000 −0.0441942
\(513\) 12.7671 0.563682
\(514\) 6.39010 0.281855
\(515\) 34.7167 1.52980
\(516\) 31.2464 1.37555
\(517\) −23.8197 −1.04759
\(518\) −8.56493 −0.376321
\(519\) −24.2232 −1.06328
\(520\) 14.6134 0.640838
\(521\) −0.365819 −0.0160268 −0.00801340 0.999968i \(-0.502551\pi\)
−0.00801340 + 0.999968i \(0.502551\pi\)
\(522\) 38.0714 1.66634
\(523\) −24.9640 −1.09160 −0.545800 0.837915i \(-0.683774\pi\)
−0.545800 + 0.837915i \(0.683774\pi\)
\(524\) 11.2346 0.490787
\(525\) 13.2474 0.578162
\(526\) 2.48872 0.108513
\(527\) −6.63248 −0.288915
\(528\) −8.05546 −0.350569
\(529\) −22.7244 −0.988017
\(530\) −2.62504 −0.114024
\(531\) −9.01164 −0.391072
\(532\) 4.22204 0.183049
\(533\) −29.2249 −1.26587
\(534\) 37.6111 1.62759
\(535\) −51.6759 −2.23414
\(536\) −8.28511 −0.357862
\(537\) −10.7222 −0.462698
\(538\) 1.04689 0.0451346
\(539\) 3.01631 0.129922
\(540\) −9.54350 −0.410687
\(541\) −40.6148 −1.74617 −0.873083 0.487571i \(-0.837883\pi\)
−0.873083 + 0.487571i \(0.837883\pi\)
\(542\) 6.47317 0.278046
\(543\) −15.2018 −0.652374
\(544\) 6.60020 0.282981
\(545\) −33.6076 −1.43959
\(546\) 12.3659 0.529213
\(547\) −13.5048 −0.577422 −0.288711 0.957416i \(-0.593227\pi\)
−0.288711 + 0.957416i \(0.593227\pi\)
\(548\) 7.05090 0.301200
\(549\) −5.36068 −0.228788
\(550\) −14.9620 −0.637984
\(551\) 38.8984 1.65713
\(552\) −1.40203 −0.0596742
\(553\) −16.4102 −0.697832
\(554\) −5.18131 −0.220133
\(555\) 72.1898 3.06429
\(556\) 19.2723 0.817325
\(557\) 9.82915 0.416474 0.208237 0.978078i \(-0.433227\pi\)
0.208237 + 0.978078i \(0.433227\pi\)
\(558\) −4.15250 −0.175789
\(559\) 54.1748 2.29135
\(560\) −3.15601 −0.133366
\(561\) 53.1676 2.24474
\(562\) −0.340066 −0.0143448
\(563\) 1.12295 0.0473267 0.0236634 0.999720i \(-0.492467\pi\)
0.0236634 + 0.999720i \(0.492467\pi\)
\(564\) 21.0899 0.888046
\(565\) −54.3697 −2.28735
\(566\) 20.1181 0.845626
\(567\) 4.32108 0.181468
\(568\) −14.0501 −0.589529
\(569\) −30.7579 −1.28944 −0.644719 0.764420i \(-0.723026\pi\)
−0.644719 + 0.764420i \(0.723026\pi\)
\(570\) −35.5857 −1.49052
\(571\) 3.90203 0.163295 0.0816474 0.996661i \(-0.473982\pi\)
0.0816474 + 0.996661i \(0.473982\pi\)
\(572\) −13.9665 −0.583969
\(573\) 19.8150 0.827782
\(574\) 6.31163 0.263442
\(575\) −2.60409 −0.108598
\(576\) 4.13228 0.172179
\(577\) 4.41862 0.183949 0.0919747 0.995761i \(-0.470682\pi\)
0.0919747 + 0.995761i \(0.470682\pi\)
\(578\) −26.5626 −1.10486
\(579\) 7.06207 0.293490
\(580\) −29.0768 −1.20735
\(581\) −7.07919 −0.293694
\(582\) 40.0257 1.65912
\(583\) 2.50884 0.103906
\(584\) −16.6288 −0.688105
\(585\) −60.3866 −2.49668
\(586\) −13.9830 −0.577631
\(587\) −22.3402 −0.922080 −0.461040 0.887379i \(-0.652524\pi\)
−0.461040 + 0.887379i \(0.652524\pi\)
\(588\) −2.67063 −0.110135
\(589\) −4.24269 −0.174817
\(590\) 6.88258 0.283352
\(591\) −6.64063 −0.273159
\(592\) −8.56493 −0.352016
\(593\) 22.0369 0.904948 0.452474 0.891778i \(-0.350542\pi\)
0.452474 + 0.891778i \(0.350542\pi\)
\(594\) 9.12107 0.374242
\(595\) 20.8303 0.853958
\(596\) −16.3469 −0.669595
\(597\) −19.2555 −0.788077
\(598\) −2.43083 −0.0994039
\(599\) −20.8130 −0.850397 −0.425199 0.905100i \(-0.639796\pi\)
−0.425199 + 0.905100i \(0.639796\pi\)
\(600\) 13.2474 0.540821
\(601\) 36.2110 1.47708 0.738540 0.674210i \(-0.235516\pi\)
0.738540 + 0.674210i \(0.235516\pi\)
\(602\) −11.7000 −0.476856
\(603\) 34.2364 1.39421
\(604\) −4.57648 −0.186214
\(605\) −6.00234 −0.244030
\(606\) −0.457135 −0.0185698
\(607\) 30.2052 1.22599 0.612995 0.790087i \(-0.289965\pi\)
0.612995 + 0.790087i \(0.289965\pi\)
\(608\) 4.22204 0.171226
\(609\) −24.6050 −0.997045
\(610\) 4.09418 0.165769
\(611\) 36.5656 1.47929
\(612\) −27.2739 −1.10248
\(613\) −43.0840 −1.74014 −0.870072 0.492924i \(-0.835928\pi\)
−0.870072 + 0.492924i \(0.835928\pi\)
\(614\) −28.6630 −1.15674
\(615\) −53.1978 −2.14514
\(616\) 3.01631 0.121531
\(617\) 13.6269 0.548597 0.274298 0.961645i \(-0.411554\pi\)
0.274298 + 0.961645i \(0.411554\pi\)
\(618\) 29.3775 1.18174
\(619\) 6.17501 0.248195 0.124097 0.992270i \(-0.460396\pi\)
0.124097 + 0.992270i \(0.460396\pi\)
\(620\) 3.17144 0.127368
\(621\) 1.58749 0.0637039
\(622\) −10.8244 −0.434017
\(623\) −14.0832 −0.564231
\(624\) 12.3659 0.495033
\(625\) −25.1965 −1.00786
\(626\) 13.5622 0.542053
\(627\) 34.0105 1.35825
\(628\) −7.67641 −0.306322
\(629\) 56.5302 2.25401
\(630\) 13.0415 0.519587
\(631\) 23.9546 0.953619 0.476809 0.879007i \(-0.341793\pi\)
0.476809 + 0.879007i \(0.341793\pi\)
\(632\) −16.4102 −0.652762
\(633\) 37.9305 1.50760
\(634\) −12.4644 −0.495024
\(635\) 39.0796 1.55083
\(636\) −2.22132 −0.0880812
\(637\) −4.63033 −0.183460
\(638\) 27.7898 1.10021
\(639\) 58.0590 2.29678
\(640\) −3.15601 −0.124752
\(641\) 11.3253 0.447321 0.223661 0.974667i \(-0.428199\pi\)
0.223661 + 0.974667i \(0.428199\pi\)
\(642\) −43.7285 −1.72583
\(643\) −37.7847 −1.49008 −0.745042 0.667018i \(-0.767571\pi\)
−0.745042 + 0.667018i \(0.767571\pi\)
\(644\) 0.524979 0.0206871
\(645\) 98.6138 3.88291
\(646\) −27.8663 −1.09639
\(647\) 23.2338 0.913415 0.456707 0.889617i \(-0.349029\pi\)
0.456707 + 0.889617i \(0.349029\pi\)
\(648\) 4.32108 0.169748
\(649\) −6.57793 −0.258206
\(650\) 22.9682 0.900887
\(651\) 2.68370 0.105182
\(652\) 1.14467 0.0448286
\(653\) 43.7520 1.71215 0.856074 0.516853i \(-0.172897\pi\)
0.856074 + 0.516853i \(0.172897\pi\)
\(654\) −28.4390 −1.11205
\(655\) 35.4565 1.38540
\(656\) 6.31163 0.246428
\(657\) 68.7149 2.68082
\(658\) −7.89697 −0.307856
\(659\) −41.2372 −1.60637 −0.803186 0.595728i \(-0.796864\pi\)
−0.803186 + 0.595728i \(0.796864\pi\)
\(660\) −25.4231 −0.989592
\(661\) −13.4403 −0.522766 −0.261383 0.965235i \(-0.584179\pi\)
−0.261383 + 0.965235i \(0.584179\pi\)
\(662\) −7.39253 −0.287319
\(663\) −81.6176 −3.16976
\(664\) −7.07919 −0.274726
\(665\) 13.3248 0.516714
\(666\) 35.3927 1.37144
\(667\) 4.83672 0.187278
\(668\) 20.8699 0.807482
\(669\) 16.2248 0.627286
\(670\) −26.1479 −1.01018
\(671\) −3.91296 −0.151058
\(672\) −2.67063 −0.103022
\(673\) 27.4599 1.05850 0.529251 0.848465i \(-0.322473\pi\)
0.529251 + 0.848465i \(0.322473\pi\)
\(674\) −30.2671 −1.16585
\(675\) −14.9998 −0.577342
\(676\) 8.43999 0.324615
\(677\) 39.3655 1.51294 0.756469 0.654030i \(-0.226923\pi\)
0.756469 + 0.654030i \(0.226923\pi\)
\(678\) −46.0080 −1.76693
\(679\) −14.9874 −0.575162
\(680\) 20.8303 0.798805
\(681\) −71.7392 −2.74905
\(682\) −3.03106 −0.116065
\(683\) −32.4141 −1.24029 −0.620146 0.784487i \(-0.712927\pi\)
−0.620146 + 0.784487i \(0.712927\pi\)
\(684\) −17.4467 −0.667091
\(685\) 22.2527 0.850232
\(686\) 1.00000 0.0381802
\(687\) −40.1669 −1.53246
\(688\) −11.7000 −0.446058
\(689\) −3.85132 −0.146724
\(690\) −4.42480 −0.168449
\(691\) −15.0473 −0.572427 −0.286213 0.958166i \(-0.592397\pi\)
−0.286213 + 0.958166i \(0.592397\pi\)
\(692\) 9.07022 0.344798
\(693\) −12.4642 −0.473478
\(694\) −22.4200 −0.851053
\(695\) 60.8234 2.30716
\(696\) −24.6050 −0.932650
\(697\) −41.6580 −1.57791
\(698\) 14.1699 0.536340
\(699\) 65.6008 2.48125
\(700\) −4.96038 −0.187485
\(701\) 17.8235 0.673186 0.336593 0.941650i \(-0.390725\pi\)
0.336593 + 0.941650i \(0.390725\pi\)
\(702\) −14.0017 −0.528462
\(703\) 36.1615 1.36386
\(704\) 3.01631 0.113681
\(705\) 66.5600 2.50679
\(706\) 9.44344 0.355409
\(707\) 0.171171 0.00643755
\(708\) 5.82409 0.218883
\(709\) 42.6540 1.60190 0.800952 0.598728i \(-0.204327\pi\)
0.800952 + 0.598728i \(0.204327\pi\)
\(710\) −44.3422 −1.66413
\(711\) 67.8115 2.54313
\(712\) −14.0832 −0.527790
\(713\) −0.527547 −0.0197568
\(714\) 17.6267 0.659663
\(715\) −44.0784 −1.64844
\(716\) 4.01486 0.150042
\(717\) 16.9809 0.634165
\(718\) −2.00815 −0.0749433
\(719\) −16.0627 −0.599038 −0.299519 0.954090i \(-0.596826\pi\)
−0.299519 + 0.954090i \(0.596826\pi\)
\(720\) 13.0415 0.486029
\(721\) −11.0002 −0.409669
\(722\) 1.17434 0.0437046
\(723\) 14.7411 0.548229
\(724\) 5.69222 0.211550
\(725\) −45.7008 −1.69729
\(726\) −5.07922 −0.188507
\(727\) −9.33177 −0.346096 −0.173048 0.984913i \(-0.555362\pi\)
−0.173048 + 0.984913i \(0.555362\pi\)
\(728\) −4.63033 −0.171612
\(729\) −42.0833 −1.55864
\(730\) −52.4806 −1.94239
\(731\) 77.2222 2.85617
\(732\) 3.46452 0.128053
\(733\) 44.0899 1.62850 0.814248 0.580517i \(-0.197149\pi\)
0.814248 + 0.580517i \(0.197149\pi\)
\(734\) −14.7871 −0.545802
\(735\) −8.42854 −0.310891
\(736\) 0.524979 0.0193510
\(737\) 24.9904 0.920535
\(738\) −26.0814 −0.960071
\(739\) 37.6307 1.38427 0.692134 0.721769i \(-0.256670\pi\)
0.692134 + 0.721769i \(0.256670\pi\)
\(740\) −27.0310 −0.993678
\(741\) −52.2095 −1.91796
\(742\) 0.831758 0.0305348
\(743\) 16.9980 0.623597 0.311799 0.950148i \(-0.399069\pi\)
0.311799 + 0.950148i \(0.399069\pi\)
\(744\) 2.68370 0.0983891
\(745\) −51.5909 −1.89015
\(746\) −30.6145 −1.12088
\(747\) 29.2532 1.07032
\(748\) −19.9082 −0.727917
\(749\) 16.3738 0.598286
\(750\) −0.333934 −0.0121936
\(751\) 24.0331 0.876981 0.438491 0.898736i \(-0.355513\pi\)
0.438491 + 0.898736i \(0.355513\pi\)
\(752\) −7.89697 −0.287973
\(753\) −14.1171 −0.514454
\(754\) −42.6600 −1.55359
\(755\) −14.4434 −0.525650
\(756\) 3.02392 0.109979
\(757\) 9.02734 0.328104 0.164052 0.986452i \(-0.447543\pi\)
0.164052 + 0.986452i \(0.447543\pi\)
\(758\) −10.7563 −0.390685
\(759\) 4.22894 0.153501
\(760\) 13.3248 0.483341
\(761\) −42.4388 −1.53841 −0.769203 0.639005i \(-0.779346\pi\)
−0.769203 + 0.639005i \(0.779346\pi\)
\(762\) 33.0694 1.19798
\(763\) 10.6488 0.385512
\(764\) −7.41957 −0.268431
\(765\) −86.0766 −3.11211
\(766\) 1.45941 0.0527306
\(767\) 10.0978 0.364610
\(768\) −2.67063 −0.0963682
\(769\) −39.2468 −1.41528 −0.707639 0.706575i \(-0.750239\pi\)
−0.707639 + 0.706575i \(0.750239\pi\)
\(770\) 9.51949 0.343059
\(771\) 17.0656 0.614603
\(772\) −2.64434 −0.0951720
\(773\) 13.2797 0.477638 0.238819 0.971064i \(-0.423240\pi\)
0.238819 + 0.971064i \(0.423240\pi\)
\(774\) 48.3477 1.73782
\(775\) 4.98464 0.179054
\(776\) −14.9874 −0.538015
\(777\) −22.8738 −0.820592
\(778\) −4.73759 −0.169851
\(779\) −26.6480 −0.954763
\(780\) 39.0269 1.39739
\(781\) 42.3794 1.51645
\(782\) −3.46496 −0.123907
\(783\) 27.8599 0.995630
\(784\) 1.00000 0.0357143
\(785\) −24.2268 −0.864692
\(786\) 30.0036 1.07019
\(787\) −30.6190 −1.09145 −0.545725 0.837964i \(-0.683746\pi\)
−0.545725 + 0.837964i \(0.683746\pi\)
\(788\) 2.48654 0.0885792
\(789\) 6.64645 0.236620
\(790\) −51.7906 −1.84263
\(791\) 17.2274 0.612535
\(792\) −12.4642 −0.442898
\(793\) 6.00678 0.213307
\(794\) 16.7995 0.596192
\(795\) −7.01051 −0.248637
\(796\) 7.21010 0.255555
\(797\) 2.40628 0.0852348 0.0426174 0.999091i \(-0.486430\pi\)
0.0426174 + 0.999091i \(0.486430\pi\)
\(798\) 11.2755 0.399150
\(799\) 52.1216 1.84393
\(800\) −4.96038 −0.175376
\(801\) 58.1958 2.05625
\(802\) 2.31347 0.0816916
\(803\) 50.1576 1.77002
\(804\) −22.1265 −0.780341
\(805\) 1.65684 0.0583958
\(806\) 4.65298 0.163894
\(807\) 2.79586 0.0984188
\(808\) 0.171171 0.00602178
\(809\) 20.3487 0.715421 0.357711 0.933833i \(-0.383557\pi\)
0.357711 + 0.933833i \(0.383557\pi\)
\(810\) 13.6374 0.479168
\(811\) −13.6894 −0.480700 −0.240350 0.970686i \(-0.577262\pi\)
−0.240350 + 0.970686i \(0.577262\pi\)
\(812\) 9.21317 0.323319
\(813\) 17.2875 0.606298
\(814\) 25.8345 0.905498
\(815\) 3.61257 0.126543
\(816\) 17.6267 0.617058
\(817\) 49.3979 1.72821
\(818\) 11.6520 0.407401
\(819\) 19.1339 0.668591
\(820\) 19.9195 0.695621
\(821\) 27.8882 0.973306 0.486653 0.873595i \(-0.338218\pi\)
0.486653 + 0.873595i \(0.338218\pi\)
\(822\) 18.8304 0.656785
\(823\) 36.9433 1.28776 0.643881 0.765126i \(-0.277323\pi\)
0.643881 + 0.765126i \(0.277323\pi\)
\(824\) −11.0002 −0.383210
\(825\) −39.9581 −1.39116
\(826\) −2.18079 −0.0758793
\(827\) −47.4353 −1.64949 −0.824743 0.565507i \(-0.808681\pi\)
−0.824743 + 0.565507i \(0.808681\pi\)
\(828\) −2.16936 −0.0753905
\(829\) −42.0991 −1.46216 −0.731081 0.682291i \(-0.760984\pi\)
−0.731081 + 0.682291i \(0.760984\pi\)
\(830\) −22.3420 −0.775502
\(831\) −13.8374 −0.480013
\(832\) −4.63033 −0.160528
\(833\) −6.60020 −0.228683
\(834\) 51.4691 1.78223
\(835\) 65.8657 2.27938
\(836\) −12.7350 −0.440449
\(837\) −3.03871 −0.105033
\(838\) 31.2631 1.07997
\(839\) 48.2754 1.66665 0.833326 0.552782i \(-0.186434\pi\)
0.833326 + 0.552782i \(0.186434\pi\)
\(840\) −8.42854 −0.290812
\(841\) 55.8824 1.92698
\(842\) −24.4387 −0.842212
\(843\) −0.908192 −0.0312798
\(844\) −14.2028 −0.488880
\(845\) 26.6367 0.916329
\(846\) 32.6325 1.12193
\(847\) 1.90188 0.0653493
\(848\) 0.831758 0.0285627
\(849\) 53.7280 1.84394
\(850\) 32.7395 1.12296
\(851\) 4.49640 0.154135
\(852\) −37.5226 −1.28550
\(853\) −11.2223 −0.384246 −0.192123 0.981371i \(-0.561537\pi\)
−0.192123 + 0.981371i \(0.561537\pi\)
\(854\) −1.29727 −0.0443916
\(855\) −55.0619 −1.88308
\(856\) 16.3738 0.559646
\(857\) 39.1309 1.33669 0.668343 0.743853i \(-0.267004\pi\)
0.668343 + 0.743853i \(0.267004\pi\)
\(858\) −37.2995 −1.27338
\(859\) 2.68444 0.0915917 0.0457959 0.998951i \(-0.485418\pi\)
0.0457959 + 0.998951i \(0.485418\pi\)
\(860\) −36.9252 −1.25914
\(861\) 16.8561 0.574453
\(862\) −1.00000 −0.0340601
\(863\) −50.4232 −1.71643 −0.858213 0.513294i \(-0.828425\pi\)
−0.858213 + 0.513294i \(0.828425\pi\)
\(864\) 3.02392 0.102876
\(865\) 28.6257 0.973302
\(866\) 25.2393 0.857667
\(867\) −70.9390 −2.40922
\(868\) −1.00489 −0.0341082
\(869\) 49.4982 1.67911
\(870\) −77.6535 −2.63270
\(871\) −38.3628 −1.29987
\(872\) 10.6488 0.360613
\(873\) 61.9320 2.09608
\(874\) −2.21648 −0.0749737
\(875\) 0.125039 0.00422710
\(876\) −44.4094 −1.50046
\(877\) −41.8989 −1.41483 −0.707413 0.706800i \(-0.750138\pi\)
−0.707413 + 0.706800i \(0.750138\pi\)
\(878\) −12.9214 −0.436077
\(879\) −37.3434 −1.25956
\(880\) 9.51949 0.320902
\(881\) −28.5652 −0.962385 −0.481192 0.876615i \(-0.659796\pi\)
−0.481192 + 0.876615i \(0.659796\pi\)
\(882\) −4.13228 −0.139141
\(883\) −46.3681 −1.56041 −0.780206 0.625523i \(-0.784886\pi\)
−0.780206 + 0.625523i \(0.784886\pi\)
\(884\) 30.5611 1.02788
\(885\) 18.3809 0.617866
\(886\) −3.93412 −0.132169
\(887\) 41.9775 1.40947 0.704733 0.709472i \(-0.251067\pi\)
0.704733 + 0.709472i \(0.251067\pi\)
\(888\) −22.8738 −0.767594
\(889\) −12.3826 −0.415299
\(890\) −44.4467 −1.48986
\(891\) −13.0337 −0.436646
\(892\) −6.07525 −0.203414
\(893\) 33.3414 1.11573
\(894\) −43.6566 −1.46009
\(895\) 12.6709 0.423542
\(896\) 1.00000 0.0334077
\(897\) −6.49185 −0.216757
\(898\) −31.8219 −1.06191
\(899\) −9.25823 −0.308779
\(900\) 20.4977 0.683257
\(901\) −5.48977 −0.182891
\(902\) −19.0378 −0.633890
\(903\) −31.2464 −1.03981
\(904\) 17.2274 0.572974
\(905\) 17.9647 0.597167
\(906\) −12.2221 −0.406052
\(907\) −34.6891 −1.15183 −0.575917 0.817508i \(-0.695355\pi\)
−0.575917 + 0.817508i \(0.695355\pi\)
\(908\) 26.8622 0.891455
\(909\) −0.707327 −0.0234606
\(910\) −14.6134 −0.484428
\(911\) 59.0097 1.95508 0.977540 0.210750i \(-0.0675906\pi\)
0.977540 + 0.210750i \(0.0675906\pi\)
\(912\) 11.2755 0.373370
\(913\) 21.3530 0.706682
\(914\) 15.1960 0.502638
\(915\) 10.9341 0.361469
\(916\) 15.0402 0.496943
\(917\) −11.2346 −0.371000
\(918\) −19.9585 −0.658727
\(919\) 3.70958 0.122368 0.0611839 0.998127i \(-0.480512\pi\)
0.0611839 + 0.998127i \(0.480512\pi\)
\(920\) 1.65684 0.0546243
\(921\) −76.5483 −2.52235
\(922\) 5.80779 0.191270
\(923\) −65.0566 −2.14136
\(924\) 8.05546 0.265005
\(925\) −42.4853 −1.39691
\(926\) −21.0429 −0.691514
\(927\) 45.4559 1.49297
\(928\) 9.21317 0.302437
\(929\) 35.6276 1.16891 0.584453 0.811428i \(-0.301309\pi\)
0.584453 + 0.811428i \(0.301309\pi\)
\(930\) 8.46976 0.277734
\(931\) −4.22204 −0.138372
\(932\) −24.5638 −0.804613
\(933\) −28.9079 −0.946402
\(934\) −25.8605 −0.846182
\(935\) −62.8306 −2.05478
\(936\) 19.1339 0.625410
\(937\) −22.5160 −0.735567 −0.367783 0.929911i \(-0.619883\pi\)
−0.367783 + 0.929911i \(0.619883\pi\)
\(938\) 8.28511 0.270518
\(939\) 36.2196 1.18198
\(940\) −24.9229 −0.812896
\(941\) −36.3844 −1.18610 −0.593049 0.805166i \(-0.702076\pi\)
−0.593049 + 0.805166i \(0.702076\pi\)
\(942\) −20.5009 −0.667955
\(943\) −3.31347 −0.107901
\(944\) −2.18079 −0.0709786
\(945\) 9.54350 0.310450
\(946\) 35.2908 1.14740
\(947\) −44.9617 −1.46106 −0.730530 0.682881i \(-0.760727\pi\)
−0.730530 + 0.682881i \(0.760727\pi\)
\(948\) −43.8256 −1.42339
\(949\) −76.9969 −2.49942
\(950\) 20.9429 0.679479
\(951\) −33.2878 −1.07943
\(952\) −6.60020 −0.213914
\(953\) 6.43848 0.208563 0.104281 0.994548i \(-0.466746\pi\)
0.104281 + 0.994548i \(0.466746\pi\)
\(954\) −3.43706 −0.111279
\(955\) −23.4162 −0.757731
\(956\) −6.35840 −0.205645
\(957\) 74.2163 2.39907
\(958\) 21.8365 0.705504
\(959\) −7.05090 −0.227685
\(960\) −8.42854 −0.272030
\(961\) −29.9902 −0.967426
\(962\) −39.6585 −1.27864
\(963\) −67.6613 −2.18035
\(964\) −5.51971 −0.177778
\(965\) −8.34557 −0.268653
\(966\) 1.40203 0.0451095
\(967\) 58.5436 1.88263 0.941317 0.337523i \(-0.109589\pi\)
0.941317 + 0.337523i \(0.109589\pi\)
\(968\) 1.90188 0.0611287
\(969\) −74.4208 −2.39074
\(970\) −47.3002 −1.51872
\(971\) −11.2801 −0.361995 −0.180998 0.983484i \(-0.557933\pi\)
−0.180998 + 0.983484i \(0.557933\pi\)
\(972\) 20.6118 0.661123
\(973\) −19.2723 −0.617840
\(974\) 31.9434 1.02353
\(975\) 61.3397 1.96444
\(976\) −1.29727 −0.0415245
\(977\) 33.9580 1.08641 0.543206 0.839599i \(-0.317210\pi\)
0.543206 + 0.839599i \(0.317210\pi\)
\(978\) 3.05698 0.0977515
\(979\) 42.4793 1.35764
\(980\) 3.15601 0.100815
\(981\) −44.0038 −1.40493
\(982\) −4.08024 −0.130206
\(983\) 44.3483 1.41449 0.707246 0.706967i \(-0.249937\pi\)
0.707246 + 0.706967i \(0.249937\pi\)
\(984\) 16.8561 0.537351
\(985\) 7.84753 0.250043
\(986\) −60.8087 −1.93654
\(987\) −21.0899 −0.671300
\(988\) 19.5495 0.621952
\(989\) 6.14225 0.195312
\(990\) −39.3373 −1.25022
\(991\) −11.4795 −0.364657 −0.182329 0.983238i \(-0.558363\pi\)
−0.182329 + 0.983238i \(0.558363\pi\)
\(992\) −1.00489 −0.0319053
\(993\) −19.7427 −0.626517
\(994\) 14.0501 0.445642
\(995\) 22.7551 0.721386
\(996\) −18.9059 −0.599057
\(997\) −18.1121 −0.573615 −0.286808 0.957988i \(-0.592594\pi\)
−0.286808 + 0.957988i \(0.592594\pi\)
\(998\) −43.4544 −1.37553
\(999\) 25.8996 0.819428
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 \(a_p\))