Properties

Label 8013.2.a.d.1.10
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.52474 q^{2}\) \(+1.00000 q^{3}\) \(+4.37429 q^{4}\) \(-3.85140 q^{5}\) \(-2.52474 q^{6}\) \(-2.38848 q^{7}\) \(-5.99445 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.52474 q^{2}\) \(+1.00000 q^{3}\) \(+4.37429 q^{4}\) \(-3.85140 q^{5}\) \(-2.52474 q^{6}\) \(-2.38848 q^{7}\) \(-5.99445 q^{8}\) \(+1.00000 q^{9}\) \(+9.72375 q^{10}\) \(+2.74060 q^{11}\) \(+4.37429 q^{12}\) \(-3.61293 q^{13}\) \(+6.03028 q^{14}\) \(-3.85140 q^{15}\) \(+6.38582 q^{16}\) \(+3.21123 q^{17}\) \(-2.52474 q^{18}\) \(+2.80535 q^{19}\) \(-16.8471 q^{20}\) \(-2.38848 q^{21}\) \(-6.91929 q^{22}\) \(+6.49753 q^{23}\) \(-5.99445 q^{24}\) \(+9.83324 q^{25}\) \(+9.12168 q^{26}\) \(+1.00000 q^{27}\) \(-10.4479 q^{28}\) \(-8.36138 q^{29}\) \(+9.72375 q^{30}\) \(+8.59267 q^{31}\) \(-4.13361 q^{32}\) \(+2.74060 q^{33}\) \(-8.10750 q^{34}\) \(+9.19898 q^{35}\) \(+4.37429 q^{36}\) \(+7.52532 q^{37}\) \(-7.08278 q^{38}\) \(-3.61293 q^{39}\) \(+23.0870 q^{40}\) \(-8.06601 q^{41}\) \(+6.03028 q^{42}\) \(+7.98588 q^{43}\) \(+11.9882 q^{44}\) \(-3.85140 q^{45}\) \(-16.4045 q^{46}\) \(+0.880568 q^{47}\) \(+6.38582 q^{48}\) \(-1.29516 q^{49}\) \(-24.8263 q^{50}\) \(+3.21123 q^{51}\) \(-15.8040 q^{52}\) \(-12.0805 q^{53}\) \(-2.52474 q^{54}\) \(-10.5551 q^{55}\) \(+14.3176 q^{56}\) \(+2.80535 q^{57}\) \(+21.1103 q^{58}\) \(+2.81822 q^{59}\) \(-16.8471 q^{60}\) \(-0.790749 q^{61}\) \(-21.6942 q^{62}\) \(-2.38848 q^{63}\) \(-2.33537 q^{64}\) \(+13.9148 q^{65}\) \(-6.91929 q^{66}\) \(+1.16645 q^{67}\) \(+14.0468 q^{68}\) \(+6.49753 q^{69}\) \(-23.2250 q^{70}\) \(-13.1614 q^{71}\) \(-5.99445 q^{72}\) \(+9.47889 q^{73}\) \(-18.9994 q^{74}\) \(+9.83324 q^{75}\) \(+12.2714 q^{76}\) \(-6.54587 q^{77}\) \(+9.12168 q^{78}\) \(-3.34001 q^{79}\) \(-24.5943 q^{80}\) \(+1.00000 q^{81}\) \(+20.3645 q^{82}\) \(+6.64805 q^{83}\) \(-10.4479 q^{84}\) \(-12.3677 q^{85}\) \(-20.1622 q^{86}\) \(-8.36138 q^{87}\) \(-16.4284 q^{88}\) \(-6.56077 q^{89}\) \(+9.72375 q^{90}\) \(+8.62940 q^{91}\) \(+28.4220 q^{92}\) \(+8.59267 q^{93}\) \(-2.22320 q^{94}\) \(-10.8045 q^{95}\) \(-4.13361 q^{96}\) \(+3.51600 q^{97}\) \(+3.26994 q^{98}\) \(+2.74060 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52474 −1.78526 −0.892629 0.450793i \(-0.851141\pi\)
−0.892629 + 0.450793i \(0.851141\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.37429 2.18714
\(5\) −3.85140 −1.72240 −0.861198 0.508269i \(-0.830285\pi\)
−0.861198 + 0.508269i \(0.830285\pi\)
\(6\) −2.52474 −1.03072
\(7\) −2.38848 −0.902761 −0.451380 0.892332i \(-0.649068\pi\)
−0.451380 + 0.892332i \(0.649068\pi\)
\(8\) −5.99445 −2.11936
\(9\) 1.00000 0.333333
\(10\) 9.72375 3.07492
\(11\) 2.74060 0.826322 0.413161 0.910658i \(-0.364425\pi\)
0.413161 + 0.910658i \(0.364425\pi\)
\(12\) 4.37429 1.26275
\(13\) −3.61293 −1.00205 −0.501023 0.865434i \(-0.667043\pi\)
−0.501023 + 0.865434i \(0.667043\pi\)
\(14\) 6.03028 1.61166
\(15\) −3.85140 −0.994426
\(16\) 6.38582 1.59646
\(17\) 3.21123 0.778838 0.389419 0.921061i \(-0.372676\pi\)
0.389419 + 0.921061i \(0.372676\pi\)
\(18\) −2.52474 −0.595086
\(19\) 2.80535 0.643592 0.321796 0.946809i \(-0.395713\pi\)
0.321796 + 0.946809i \(0.395713\pi\)
\(20\) −16.8471 −3.76713
\(21\) −2.38848 −0.521209
\(22\) −6.91929 −1.47520
\(23\) 6.49753 1.35483 0.677414 0.735602i \(-0.263101\pi\)
0.677414 + 0.735602i \(0.263101\pi\)
\(24\) −5.99445 −1.22361
\(25\) 9.83324 1.96665
\(26\) 9.12168 1.78891
\(27\) 1.00000 0.192450
\(28\) −10.4479 −1.97447
\(29\) −8.36138 −1.55267 −0.776335 0.630320i \(-0.782924\pi\)
−0.776335 + 0.630320i \(0.782924\pi\)
\(30\) 9.72375 1.77531
\(31\) 8.59267 1.54329 0.771645 0.636054i \(-0.219434\pi\)
0.771645 + 0.636054i \(0.219434\pi\)
\(32\) −4.13361 −0.730726
\(33\) 2.74060 0.477077
\(34\) −8.10750 −1.39043
\(35\) 9.19898 1.55491
\(36\) 4.37429 0.729048
\(37\) 7.52532 1.23715 0.618577 0.785724i \(-0.287709\pi\)
0.618577 + 0.785724i \(0.287709\pi\)
\(38\) −7.08278 −1.14898
\(39\) −3.61293 −0.578531
\(40\) 23.0870 3.65037
\(41\) −8.06601 −1.25970 −0.629850 0.776717i \(-0.716884\pi\)
−0.629850 + 0.776717i \(0.716884\pi\)
\(42\) 6.03028 0.930493
\(43\) 7.98588 1.21783 0.608917 0.793234i \(-0.291604\pi\)
0.608917 + 0.793234i \(0.291604\pi\)
\(44\) 11.9882 1.80729
\(45\) −3.85140 −0.574132
\(46\) −16.4045 −2.41872
\(47\) 0.880568 0.128444 0.0642220 0.997936i \(-0.479543\pi\)
0.0642220 + 0.997936i \(0.479543\pi\)
\(48\) 6.38582 0.921714
\(49\) −1.29516 −0.185023
\(50\) −24.8263 −3.51097
\(51\) 3.21123 0.449662
\(52\) −15.8040 −2.19162
\(53\) −12.0805 −1.65938 −0.829691 0.558222i \(-0.811484\pi\)
−0.829691 + 0.558222i \(0.811484\pi\)
\(54\) −2.52474 −0.343573
\(55\) −10.5551 −1.42325
\(56\) 14.3176 1.91327
\(57\) 2.80535 0.371578
\(58\) 21.1103 2.77192
\(59\) 2.81822 0.366901 0.183451 0.983029i \(-0.441273\pi\)
0.183451 + 0.983029i \(0.441273\pi\)
\(60\) −16.8471 −2.17495
\(61\) −0.790749 −0.101245 −0.0506225 0.998718i \(-0.516121\pi\)
−0.0506225 + 0.998718i \(0.516121\pi\)
\(62\) −21.6942 −2.75517
\(63\) −2.38848 −0.300920
\(64\) −2.33537 −0.291922
\(65\) 13.9148 1.72592
\(66\) −6.91929 −0.851706
\(67\) 1.16645 0.142504 0.0712521 0.997458i \(-0.477301\pi\)
0.0712521 + 0.997458i \(0.477301\pi\)
\(68\) 14.0468 1.70343
\(69\) 6.49753 0.782210
\(70\) −23.2250 −2.77592
\(71\) −13.1614 −1.56197 −0.780987 0.624548i \(-0.785283\pi\)
−0.780987 + 0.624548i \(0.785283\pi\)
\(72\) −5.99445 −0.706453
\(73\) 9.47889 1.10942 0.554710 0.832044i \(-0.312829\pi\)
0.554710 + 0.832044i \(0.312829\pi\)
\(74\) −18.9994 −2.20864
\(75\) 9.83324 1.13545
\(76\) 12.2714 1.40763
\(77\) −6.54587 −0.745971
\(78\) 9.12168 1.03283
\(79\) −3.34001 −0.375781 −0.187890 0.982190i \(-0.560165\pi\)
−0.187890 + 0.982190i \(0.560165\pi\)
\(80\) −24.5943 −2.74973
\(81\) 1.00000 0.111111
\(82\) 20.3645 2.24889
\(83\) 6.64805 0.729718 0.364859 0.931063i \(-0.381117\pi\)
0.364859 + 0.931063i \(0.381117\pi\)
\(84\) −10.4479 −1.13996
\(85\) −12.3677 −1.34147
\(86\) −20.1622 −2.17415
\(87\) −8.36138 −0.896435
\(88\) −16.4284 −1.75127
\(89\) −6.56077 −0.695440 −0.347720 0.937598i \(-0.613044\pi\)
−0.347720 + 0.937598i \(0.613044\pi\)
\(90\) 9.72375 1.02497
\(91\) 8.62940 0.904607
\(92\) 28.4220 2.96320
\(93\) 8.59267 0.891018
\(94\) −2.22320 −0.229306
\(95\) −10.8045 −1.10852
\(96\) −4.13361 −0.421885
\(97\) 3.51600 0.356996 0.178498 0.983940i \(-0.442876\pi\)
0.178498 + 0.983940i \(0.442876\pi\)
\(98\) 3.26994 0.330314
\(99\) 2.74060 0.275441
\(100\) 43.0134 4.30134
\(101\) −6.21900 −0.618814 −0.309407 0.950930i \(-0.600131\pi\)
−0.309407 + 0.950930i \(0.600131\pi\)
\(102\) −8.10750 −0.802763
\(103\) 0.411627 0.0405588 0.0202794 0.999794i \(-0.493544\pi\)
0.0202794 + 0.999794i \(0.493544\pi\)
\(104\) 21.6575 2.12369
\(105\) 9.19898 0.897729
\(106\) 30.5000 2.96243
\(107\) −9.11005 −0.880701 −0.440351 0.897826i \(-0.645146\pi\)
−0.440351 + 0.897826i \(0.645146\pi\)
\(108\) 4.37429 0.420916
\(109\) 17.9366 1.71802 0.859008 0.511962i \(-0.171081\pi\)
0.859008 + 0.511962i \(0.171081\pi\)
\(110\) 26.6489 2.54087
\(111\) 7.52532 0.714272
\(112\) −15.2524 −1.44122
\(113\) −4.60725 −0.433414 −0.216707 0.976237i \(-0.569532\pi\)
−0.216707 + 0.976237i \(0.569532\pi\)
\(114\) −7.08278 −0.663363
\(115\) −25.0245 −2.33355
\(116\) −36.5751 −3.39591
\(117\) −3.61293 −0.334015
\(118\) −7.11526 −0.655013
\(119\) −7.66996 −0.703104
\(120\) 23.0870 2.10754
\(121\) −3.48911 −0.317192
\(122\) 1.99643 0.180749
\(123\) −8.06601 −0.727288
\(124\) 37.5868 3.37540
\(125\) −18.6147 −1.66495
\(126\) 6.03028 0.537220
\(127\) −21.6363 −1.91991 −0.959956 0.280152i \(-0.909615\pi\)
−0.959956 + 0.280152i \(0.909615\pi\)
\(128\) 14.1634 1.25188
\(129\) 7.98588 0.703117
\(130\) −35.1312 −3.08121
\(131\) 2.96309 0.258886 0.129443 0.991587i \(-0.458681\pi\)
0.129443 + 0.991587i \(0.458681\pi\)
\(132\) 11.9882 1.04344
\(133\) −6.70053 −0.581010
\(134\) −2.94497 −0.254407
\(135\) −3.85140 −0.331475
\(136\) −19.2496 −1.65064
\(137\) 8.00789 0.684160 0.342080 0.939671i \(-0.388869\pi\)
0.342080 + 0.939671i \(0.388869\pi\)
\(138\) −16.4045 −1.39645
\(139\) −0.524472 −0.0444851 −0.0222425 0.999753i \(-0.507081\pi\)
−0.0222425 + 0.999753i \(0.507081\pi\)
\(140\) 40.2390 3.40082
\(141\) 0.880568 0.0741572
\(142\) 33.2291 2.78852
\(143\) −9.90159 −0.828012
\(144\) 6.38582 0.532152
\(145\) 32.2030 2.67431
\(146\) −23.9317 −1.98060
\(147\) −1.29516 −0.106823
\(148\) 32.9179 2.70584
\(149\) 2.60479 0.213393 0.106696 0.994292i \(-0.465973\pi\)
0.106696 + 0.994292i \(0.465973\pi\)
\(150\) −24.8263 −2.02706
\(151\) 7.29110 0.593342 0.296671 0.954980i \(-0.404124\pi\)
0.296671 + 0.954980i \(0.404124\pi\)
\(152\) −16.8165 −1.36400
\(153\) 3.21123 0.259613
\(154\) 16.5266 1.33175
\(155\) −33.0938 −2.65816
\(156\) −15.8040 −1.26533
\(157\) −21.9592 −1.75254 −0.876269 0.481823i \(-0.839975\pi\)
−0.876269 + 0.481823i \(0.839975\pi\)
\(158\) 8.43265 0.670866
\(159\) −12.0805 −0.958045
\(160\) 15.9202 1.25860
\(161\) −15.5192 −1.22309
\(162\) −2.52474 −0.198362
\(163\) −20.0097 −1.56728 −0.783639 0.621217i \(-0.786639\pi\)
−0.783639 + 0.621217i \(0.786639\pi\)
\(164\) −35.2831 −2.75514
\(165\) −10.5551 −0.821716
\(166\) −16.7846 −1.30273
\(167\) −18.6278 −1.44146 −0.720732 0.693214i \(-0.756194\pi\)
−0.720732 + 0.693214i \(0.756194\pi\)
\(168\) 14.3176 1.10463
\(169\) 0.0532379 0.00409522
\(170\) 31.2252 2.39486
\(171\) 2.80535 0.214531
\(172\) 34.9325 2.66358
\(173\) 5.91824 0.449955 0.224978 0.974364i \(-0.427769\pi\)
0.224978 + 0.974364i \(0.427769\pi\)
\(174\) 21.1103 1.60037
\(175\) −23.4865 −1.77541
\(176\) 17.5010 1.31919
\(177\) 2.81822 0.211830
\(178\) 16.5642 1.24154
\(179\) 5.05634 0.377928 0.188964 0.981984i \(-0.439487\pi\)
0.188964 + 0.981984i \(0.439487\pi\)
\(180\) −16.8471 −1.25571
\(181\) −5.51490 −0.409919 −0.204960 0.978770i \(-0.565706\pi\)
−0.204960 + 0.978770i \(0.565706\pi\)
\(182\) −21.7870 −1.61496
\(183\) −0.790749 −0.0584539
\(184\) −38.9491 −2.87136
\(185\) −28.9830 −2.13087
\(186\) −21.6942 −1.59070
\(187\) 8.80070 0.643571
\(188\) 3.85186 0.280926
\(189\) −2.38848 −0.173736
\(190\) 27.2786 1.97900
\(191\) 13.0717 0.945832 0.472916 0.881107i \(-0.343201\pi\)
0.472916 + 0.881107i \(0.343201\pi\)
\(192\) −2.33537 −0.168541
\(193\) 14.0284 1.00979 0.504893 0.863182i \(-0.331532\pi\)
0.504893 + 0.863182i \(0.331532\pi\)
\(194\) −8.87698 −0.637330
\(195\) 13.9148 0.996460
\(196\) −5.66540 −0.404672
\(197\) 7.84621 0.559020 0.279510 0.960143i \(-0.409828\pi\)
0.279510 + 0.960143i \(0.409828\pi\)
\(198\) −6.91929 −0.491733
\(199\) −14.8347 −1.05160 −0.525800 0.850608i \(-0.676234\pi\)
−0.525800 + 0.850608i \(0.676234\pi\)
\(200\) −58.9449 −4.16803
\(201\) 1.16645 0.0822748
\(202\) 15.7013 1.10474
\(203\) 19.9710 1.40169
\(204\) 14.0468 0.983476
\(205\) 31.0654 2.16970
\(206\) −1.03925 −0.0724078
\(207\) 6.49753 0.451609
\(208\) −23.0715 −1.59972
\(209\) 7.68835 0.531815
\(210\) −23.2250 −1.60268
\(211\) 25.2903 1.74105 0.870527 0.492121i \(-0.163778\pi\)
0.870527 + 0.492121i \(0.163778\pi\)
\(212\) −52.8435 −3.62931
\(213\) −13.1614 −0.901806
\(214\) 23.0005 1.57228
\(215\) −30.7568 −2.09759
\(216\) −5.99445 −0.407871
\(217\) −20.5234 −1.39322
\(218\) −45.2852 −3.06710
\(219\) 9.47889 0.640524
\(220\) −46.1712 −3.11286
\(221\) −11.6019 −0.780431
\(222\) −18.9994 −1.27516
\(223\) 7.46384 0.499816 0.249908 0.968270i \(-0.419600\pi\)
0.249908 + 0.968270i \(0.419600\pi\)
\(224\) 9.87304 0.659670
\(225\) 9.83324 0.655550
\(226\) 11.6321 0.773755
\(227\) 18.5341 1.23015 0.615075 0.788468i \(-0.289126\pi\)
0.615075 + 0.788468i \(0.289126\pi\)
\(228\) 12.2714 0.812695
\(229\) 1.24767 0.0824483 0.0412241 0.999150i \(-0.486874\pi\)
0.0412241 + 0.999150i \(0.486874\pi\)
\(230\) 63.1803 4.16599
\(231\) −6.54587 −0.430687
\(232\) 50.1219 3.29066
\(233\) 24.2907 1.59134 0.795668 0.605733i \(-0.207120\pi\)
0.795668 + 0.605733i \(0.207120\pi\)
\(234\) 9.12168 0.596303
\(235\) −3.39142 −0.221232
\(236\) 12.3277 0.802466
\(237\) −3.34001 −0.216957
\(238\) 19.3646 1.25522
\(239\) −1.69618 −0.109716 −0.0548582 0.998494i \(-0.517471\pi\)
−0.0548582 + 0.998494i \(0.517471\pi\)
\(240\) −24.5943 −1.58756
\(241\) 27.2484 1.75522 0.877612 0.479371i \(-0.159135\pi\)
0.877612 + 0.479371i \(0.159135\pi\)
\(242\) 8.80908 0.566269
\(243\) 1.00000 0.0641500
\(244\) −3.45897 −0.221438
\(245\) 4.98817 0.318683
\(246\) 20.3645 1.29840
\(247\) −10.1355 −0.644909
\(248\) −51.5083 −3.27078
\(249\) 6.64805 0.421303
\(250\) 46.9973 2.97237
\(251\) −19.8275 −1.25150 −0.625749 0.780024i \(-0.715207\pi\)
−0.625749 + 0.780024i \(0.715207\pi\)
\(252\) −10.4479 −0.658156
\(253\) 17.8071 1.11952
\(254\) 54.6259 3.42754
\(255\) −12.3677 −0.774496
\(256\) −31.0881 −1.94301
\(257\) 10.5451 0.657786 0.328893 0.944367i \(-0.393324\pi\)
0.328893 + 0.944367i \(0.393324\pi\)
\(258\) −20.1622 −1.25525
\(259\) −17.9741 −1.11685
\(260\) 60.8674 3.77483
\(261\) −8.36138 −0.517557
\(262\) −7.48101 −0.462178
\(263\) 0.231840 0.0142959 0.00714793 0.999974i \(-0.497725\pi\)
0.00714793 + 0.999974i \(0.497725\pi\)
\(264\) −16.4284 −1.01110
\(265\) 46.5267 2.85811
\(266\) 16.9171 1.03725
\(267\) −6.56077 −0.401513
\(268\) 5.10237 0.311677
\(269\) −7.83423 −0.477662 −0.238831 0.971061i \(-0.576764\pi\)
−0.238831 + 0.971061i \(0.576764\pi\)
\(270\) 9.72375 0.591769
\(271\) 5.91309 0.359195 0.179597 0.983740i \(-0.442521\pi\)
0.179597 + 0.983740i \(0.442521\pi\)
\(272\) 20.5063 1.24338
\(273\) 8.62940 0.522275
\(274\) −20.2178 −1.22140
\(275\) 26.9490 1.62509
\(276\) 28.4220 1.71081
\(277\) 24.5162 1.47304 0.736518 0.676418i \(-0.236469\pi\)
0.736518 + 0.676418i \(0.236469\pi\)
\(278\) 1.32415 0.0794174
\(279\) 8.59267 0.514430
\(280\) −55.1428 −3.29541
\(281\) 12.0700 0.720034 0.360017 0.932946i \(-0.382771\pi\)
0.360017 + 0.932946i \(0.382771\pi\)
\(282\) −2.22320 −0.132390
\(283\) −24.9156 −1.48108 −0.740539 0.672013i \(-0.765430\pi\)
−0.740539 + 0.672013i \(0.765430\pi\)
\(284\) −57.5718 −3.41626
\(285\) −10.8045 −0.640005
\(286\) 24.9989 1.47822
\(287\) 19.2655 1.13721
\(288\) −4.13361 −0.243575
\(289\) −6.68801 −0.393412
\(290\) −81.3040 −4.77434
\(291\) 3.51600 0.206112
\(292\) 41.4634 2.42646
\(293\) 3.10159 0.181197 0.0905986 0.995887i \(-0.471122\pi\)
0.0905986 + 0.995887i \(0.471122\pi\)
\(294\) 3.26994 0.190707
\(295\) −10.8541 −0.631949
\(296\) −45.1101 −2.62197
\(297\) 2.74060 0.159026
\(298\) −6.57641 −0.380961
\(299\) −23.4751 −1.35760
\(300\) 43.0134 2.48338
\(301\) −19.0741 −1.09941
\(302\) −18.4081 −1.05927
\(303\) −6.21900 −0.357272
\(304\) 17.9145 1.02747
\(305\) 3.04549 0.174384
\(306\) −8.10750 −0.463475
\(307\) −0.768827 −0.0438793 −0.0219396 0.999759i \(-0.506984\pi\)
−0.0219396 + 0.999759i \(0.506984\pi\)
\(308\) −28.6335 −1.63155
\(309\) 0.411627 0.0234166
\(310\) 83.5530 4.74549
\(311\) −33.1149 −1.87778 −0.938888 0.344222i \(-0.888143\pi\)
−0.938888 + 0.344222i \(0.888143\pi\)
\(312\) 21.6575 1.22611
\(313\) 10.3270 0.583714 0.291857 0.956462i \(-0.405727\pi\)
0.291857 + 0.956462i \(0.405727\pi\)
\(314\) 55.4412 3.12873
\(315\) 9.19898 0.518304
\(316\) −14.6102 −0.821887
\(317\) 22.8529 1.28355 0.641773 0.766894i \(-0.278199\pi\)
0.641773 + 0.766894i \(0.278199\pi\)
\(318\) 30.5000 1.71036
\(319\) −22.9152 −1.28301
\(320\) 8.99445 0.502805
\(321\) −9.11005 −0.508473
\(322\) 39.1819 2.18352
\(323\) 9.00863 0.501254
\(324\) 4.37429 0.243016
\(325\) −35.5268 −1.97067
\(326\) 50.5191 2.79799
\(327\) 17.9366 0.991897
\(328\) 48.3513 2.66975
\(329\) −2.10322 −0.115954
\(330\) 26.6489 1.46697
\(331\) 24.8871 1.36792 0.683961 0.729519i \(-0.260256\pi\)
0.683961 + 0.729519i \(0.260256\pi\)
\(332\) 29.0805 1.59600
\(333\) 7.52532 0.412385
\(334\) 47.0303 2.57338
\(335\) −4.49245 −0.245449
\(336\) −15.2524 −0.832087
\(337\) 15.1339 0.824397 0.412199 0.911094i \(-0.364761\pi\)
0.412199 + 0.911094i \(0.364761\pi\)
\(338\) −0.134412 −0.00731103
\(339\) −4.60725 −0.250232
\(340\) −54.0999 −2.93398
\(341\) 23.5491 1.27525
\(342\) −7.08278 −0.382993
\(343\) 19.8128 1.06979
\(344\) −47.8709 −2.58103
\(345\) −25.0245 −1.34728
\(346\) −14.9420 −0.803286
\(347\) 34.4242 1.84799 0.923995 0.382405i \(-0.124904\pi\)
0.923995 + 0.382405i \(0.124904\pi\)
\(348\) −36.5751 −1.96063
\(349\) 15.8342 0.847585 0.423792 0.905759i \(-0.360699\pi\)
0.423792 + 0.905759i \(0.360699\pi\)
\(350\) 59.2972 3.16957
\(351\) −3.61293 −0.192844
\(352\) −11.3286 −0.603815
\(353\) −32.5921 −1.73470 −0.867351 0.497697i \(-0.834179\pi\)
−0.867351 + 0.497697i \(0.834179\pi\)
\(354\) −7.11526 −0.378172
\(355\) 50.6898 2.69034
\(356\) −28.6987 −1.52103
\(357\) −7.66996 −0.405937
\(358\) −12.7659 −0.674699
\(359\) 16.6471 0.878601 0.439300 0.898340i \(-0.355226\pi\)
0.439300 + 0.898340i \(0.355226\pi\)
\(360\) 23.0870 1.21679
\(361\) −11.1300 −0.585789
\(362\) 13.9237 0.731811
\(363\) −3.48911 −0.183131
\(364\) 37.7475 1.97851
\(365\) −36.5069 −1.91086
\(366\) 1.99643 0.104355
\(367\) 12.7814 0.667181 0.333591 0.942718i \(-0.391740\pi\)
0.333591 + 0.942718i \(0.391740\pi\)
\(368\) 41.4920 2.16292
\(369\) −8.06601 −0.419900
\(370\) 73.1743 3.80415
\(371\) 28.8540 1.49803
\(372\) 37.5868 1.94879
\(373\) −3.54559 −0.183584 −0.0917918 0.995778i \(-0.529259\pi\)
−0.0917918 + 0.995778i \(0.529259\pi\)
\(374\) −22.2194 −1.14894
\(375\) −18.6147 −0.961261
\(376\) −5.27852 −0.272219
\(377\) 30.2091 1.55585
\(378\) 6.03028 0.310164
\(379\) −13.3756 −0.687059 −0.343529 0.939142i \(-0.611622\pi\)
−0.343529 + 0.939142i \(0.611622\pi\)
\(380\) −47.2621 −2.42449
\(381\) −21.6363 −1.10846
\(382\) −33.0025 −1.68855
\(383\) 3.25206 0.166172 0.0830862 0.996542i \(-0.473522\pi\)
0.0830862 + 0.996542i \(0.473522\pi\)
\(384\) 14.1634 0.722774
\(385\) 25.2107 1.28486
\(386\) −35.4180 −1.80273
\(387\) 7.98588 0.405945
\(388\) 15.3800 0.780802
\(389\) 4.81363 0.244061 0.122030 0.992526i \(-0.461059\pi\)
0.122030 + 0.992526i \(0.461059\pi\)
\(390\) −35.1312 −1.77894
\(391\) 20.8650 1.05519
\(392\) 7.76377 0.392130
\(393\) 2.96309 0.149468
\(394\) −19.8096 −0.997994
\(395\) 12.8637 0.647244
\(396\) 11.9882 0.602428
\(397\) 39.3519 1.97501 0.987507 0.157578i \(-0.0503684\pi\)
0.987507 + 0.157578i \(0.0503684\pi\)
\(398\) 37.4536 1.87738
\(399\) −6.70053 −0.335446
\(400\) 62.7933 3.13967
\(401\) −17.1791 −0.857882 −0.428941 0.903333i \(-0.641113\pi\)
−0.428941 + 0.903333i \(0.641113\pi\)
\(402\) −2.94497 −0.146882
\(403\) −31.0447 −1.54645
\(404\) −27.2037 −1.35343
\(405\) −3.85140 −0.191377
\(406\) −50.4215 −2.50238
\(407\) 20.6239 1.02229
\(408\) −19.2496 −0.952995
\(409\) 10.3295 0.510761 0.255380 0.966841i \(-0.417799\pi\)
0.255380 + 0.966841i \(0.417799\pi\)
\(410\) −78.4319 −3.87348
\(411\) 8.00789 0.395000
\(412\) 1.80057 0.0887079
\(413\) −6.73127 −0.331224
\(414\) −16.4045 −0.806239
\(415\) −25.6042 −1.25686
\(416\) 14.9344 0.732220
\(417\) −0.524472 −0.0256835
\(418\) −19.4111 −0.949426
\(419\) −19.8726 −0.970842 −0.485421 0.874280i \(-0.661334\pi\)
−0.485421 + 0.874280i \(0.661334\pi\)
\(420\) 40.2390 1.96346
\(421\) −3.97384 −0.193673 −0.0968365 0.995300i \(-0.530872\pi\)
−0.0968365 + 0.995300i \(0.530872\pi\)
\(422\) −63.8512 −3.10823
\(423\) 0.880568 0.0428147
\(424\) 72.4159 3.51683
\(425\) 31.5768 1.53170
\(426\) 33.2291 1.60996
\(427\) 1.88869 0.0914001
\(428\) −39.8500 −1.92622
\(429\) −9.90159 −0.478053
\(430\) 77.6527 3.74475
\(431\) −25.5888 −1.23257 −0.616284 0.787524i \(-0.711363\pi\)
−0.616284 + 0.787524i \(0.711363\pi\)
\(432\) 6.38582 0.307238
\(433\) −9.55417 −0.459144 −0.229572 0.973292i \(-0.573733\pi\)
−0.229572 + 0.973292i \(0.573733\pi\)
\(434\) 51.8162 2.48726
\(435\) 32.2030 1.54402
\(436\) 78.4599 3.75755
\(437\) 18.2279 0.871957
\(438\) −23.9317 −1.14350
\(439\) −0.00249176 −0.000118925 0 −5.94627e−5 1.00000i \(-0.500019\pi\)
−5.94627e−5 1.00000i \(0.500019\pi\)
\(440\) 63.2722 3.01638
\(441\) −1.29516 −0.0616743
\(442\) 29.2918 1.39327
\(443\) 29.2953 1.39186 0.695932 0.718108i \(-0.254992\pi\)
0.695932 + 0.718108i \(0.254992\pi\)
\(444\) 32.9179 1.56222
\(445\) 25.2681 1.19782
\(446\) −18.8442 −0.892299
\(447\) 2.60479 0.123202
\(448\) 5.57800 0.263536
\(449\) −5.95252 −0.280917 −0.140458 0.990087i \(-0.544858\pi\)
−0.140458 + 0.990087i \(0.544858\pi\)
\(450\) −24.8263 −1.17032
\(451\) −22.1057 −1.04092
\(452\) −20.1535 −0.947939
\(453\) 7.29110 0.342566
\(454\) −46.7937 −2.19613
\(455\) −33.2352 −1.55809
\(456\) −16.8165 −0.787507
\(457\) −12.5805 −0.588492 −0.294246 0.955730i \(-0.595068\pi\)
−0.294246 + 0.955730i \(0.595068\pi\)
\(458\) −3.15003 −0.147191
\(459\) 3.21123 0.149887
\(460\) −109.465 −5.10381
\(461\) 28.7592 1.33945 0.669725 0.742610i \(-0.266412\pi\)
0.669725 + 0.742610i \(0.266412\pi\)
\(462\) 16.5266 0.768887
\(463\) −6.23576 −0.289800 −0.144900 0.989446i \(-0.546286\pi\)
−0.144900 + 0.989446i \(0.546286\pi\)
\(464\) −53.3943 −2.47877
\(465\) −33.0938 −1.53469
\(466\) −61.3276 −2.84094
\(467\) −24.1476 −1.11742 −0.558709 0.829364i \(-0.688703\pi\)
−0.558709 + 0.829364i \(0.688703\pi\)
\(468\) −15.8040 −0.730539
\(469\) −2.78603 −0.128647
\(470\) 8.56243 0.394955
\(471\) −21.9592 −1.01183
\(472\) −16.8937 −0.777595
\(473\) 21.8861 1.00632
\(474\) 8.43265 0.387324
\(475\) 27.5857 1.26572
\(476\) −33.5506 −1.53779
\(477\) −12.0805 −0.553128
\(478\) 4.28239 0.195872
\(479\) −19.1698 −0.875893 −0.437946 0.899001i \(-0.644294\pi\)
−0.437946 + 0.899001i \(0.644294\pi\)
\(480\) 15.9202 0.726653
\(481\) −27.1884 −1.23969
\(482\) −68.7950 −3.13353
\(483\) −15.5192 −0.706149
\(484\) −15.2624 −0.693744
\(485\) −13.5415 −0.614889
\(486\) −2.52474 −0.114524
\(487\) −22.1688 −1.00456 −0.502281 0.864704i \(-0.667506\pi\)
−0.502281 + 0.864704i \(0.667506\pi\)
\(488\) 4.74011 0.214575
\(489\) −20.0097 −0.904868
\(490\) −12.5938 −0.568931
\(491\) 7.63490 0.344558 0.172279 0.985048i \(-0.444887\pi\)
0.172279 + 0.985048i \(0.444887\pi\)
\(492\) −35.2831 −1.59068
\(493\) −26.8503 −1.20928
\(494\) 25.5895 1.15133
\(495\) −10.5551 −0.474418
\(496\) 54.8712 2.46379
\(497\) 31.4358 1.41009
\(498\) −16.7846 −0.752134
\(499\) −14.9648 −0.669918 −0.334959 0.942233i \(-0.608722\pi\)
−0.334959 + 0.942233i \(0.608722\pi\)
\(500\) −81.4262 −3.64149
\(501\) −18.6278 −0.832229
\(502\) 50.0591 2.23425
\(503\) 33.3017 1.48485 0.742425 0.669929i \(-0.233676\pi\)
0.742425 + 0.669929i \(0.233676\pi\)
\(504\) 14.3176 0.637758
\(505\) 23.9518 1.06584
\(506\) −44.9583 −1.99864
\(507\) 0.0532379 0.00236438
\(508\) −94.6434 −4.19912
\(509\) −8.99566 −0.398725 −0.199363 0.979926i \(-0.563887\pi\)
−0.199363 + 0.979926i \(0.563887\pi\)
\(510\) 31.2252 1.38268
\(511\) −22.6401 −1.00154
\(512\) 50.1625 2.21689
\(513\) 2.80535 0.123859
\(514\) −26.6236 −1.17432
\(515\) −1.58534 −0.0698583
\(516\) 34.9325 1.53782
\(517\) 2.41329 0.106136
\(518\) 45.3798 1.99387
\(519\) 5.91824 0.259782
\(520\) −83.4116 −3.65784
\(521\) 13.4879 0.590914 0.295457 0.955356i \(-0.404528\pi\)
0.295457 + 0.955356i \(0.404528\pi\)
\(522\) 21.1103 0.923972
\(523\) −4.89434 −0.214015 −0.107007 0.994258i \(-0.534127\pi\)
−0.107007 + 0.994258i \(0.534127\pi\)
\(524\) 12.9614 0.566221
\(525\) −23.4865 −1.02504
\(526\) −0.585334 −0.0255218
\(527\) 27.5930 1.20197
\(528\) 17.5010 0.761632
\(529\) 19.2178 0.835558
\(530\) −117.468 −5.10247
\(531\) 2.81822 0.122300
\(532\) −29.3101 −1.27075
\(533\) 29.1419 1.26228
\(534\) 16.5642 0.716803
\(535\) 35.0864 1.51692
\(536\) −6.99220 −0.302017
\(537\) 5.05634 0.218197
\(538\) 19.7794 0.852749
\(539\) −3.54952 −0.152889
\(540\) −16.8471 −0.724984
\(541\) −21.5110 −0.924830 −0.462415 0.886663i \(-0.653017\pi\)
−0.462415 + 0.886663i \(0.653017\pi\)
\(542\) −14.9290 −0.641255
\(543\) −5.51490 −0.236667
\(544\) −13.2740 −0.569117
\(545\) −69.0810 −2.95910
\(546\) −21.7870 −0.932396
\(547\) 31.1215 1.33066 0.665330 0.746549i \(-0.268291\pi\)
0.665330 + 0.746549i \(0.268291\pi\)
\(548\) 35.0288 1.49636
\(549\) −0.790749 −0.0337484
\(550\) −68.0391 −2.90120
\(551\) −23.4566 −0.999287
\(552\) −38.9491 −1.65778
\(553\) 7.97756 0.339240
\(554\) −61.8969 −2.62975
\(555\) −28.9830 −1.23026
\(556\) −2.29419 −0.0972953
\(557\) 23.4618 0.994110 0.497055 0.867719i \(-0.334415\pi\)
0.497055 + 0.867719i \(0.334415\pi\)
\(558\) −21.6942 −0.918389
\(559\) −28.8524 −1.22033
\(560\) 58.7431 2.48235
\(561\) 8.80070 0.371566
\(562\) −30.4735 −1.28545
\(563\) 14.2867 0.602112 0.301056 0.953607i \(-0.402661\pi\)
0.301056 + 0.953607i \(0.402661\pi\)
\(564\) 3.85186 0.162192
\(565\) 17.7444 0.746510
\(566\) 62.9053 2.64411
\(567\) −2.38848 −0.100307
\(568\) 78.8955 3.31038
\(569\) −21.2898 −0.892517 −0.446258 0.894904i \(-0.647244\pi\)
−0.446258 + 0.894904i \(0.647244\pi\)
\(570\) 27.2786 1.14257
\(571\) 26.9396 1.12739 0.563694 0.825984i \(-0.309380\pi\)
0.563694 + 0.825984i \(0.309380\pi\)
\(572\) −43.3124 −1.81098
\(573\) 13.0717 0.546077
\(574\) −48.6403 −2.03021
\(575\) 63.8918 2.66447
\(576\) −2.33537 −0.0973073
\(577\) 27.4739 1.14375 0.571877 0.820340i \(-0.306216\pi\)
0.571877 + 0.820340i \(0.306216\pi\)
\(578\) 16.8854 0.702342
\(579\) 14.0284 0.583000
\(580\) 140.865 5.84911
\(581\) −15.8787 −0.658761
\(582\) −8.87698 −0.367963
\(583\) −33.1078 −1.37118
\(584\) −56.8207 −2.35126
\(585\) 13.9148 0.575306
\(586\) −7.83071 −0.323483
\(587\) −1.34629 −0.0555672 −0.0277836 0.999614i \(-0.508845\pi\)
−0.0277836 + 0.999614i \(0.508845\pi\)
\(588\) −5.66540 −0.233637
\(589\) 24.1055 0.993249
\(590\) 27.4037 1.12819
\(591\) 7.84621 0.322750
\(592\) 48.0553 1.97506
\(593\) 31.7009 1.30180 0.650901 0.759163i \(-0.274391\pi\)
0.650901 + 0.759163i \(0.274391\pi\)
\(594\) −6.91929 −0.283902
\(595\) 29.5400 1.21102
\(596\) 11.3941 0.466721
\(597\) −14.8347 −0.607142
\(598\) 59.2684 2.42366
\(599\) 24.0642 0.983237 0.491618 0.870811i \(-0.336405\pi\)
0.491618 + 0.870811i \(0.336405\pi\)
\(600\) −58.9449 −2.40641
\(601\) −44.7671 −1.82609 −0.913045 0.407859i \(-0.866275\pi\)
−0.913045 + 0.407859i \(0.866275\pi\)
\(602\) 48.1571 1.96274
\(603\) 1.16645 0.0475014
\(604\) 31.8934 1.29772
\(605\) 13.4379 0.546330
\(606\) 15.7013 0.637823
\(607\) −37.6117 −1.52661 −0.763305 0.646038i \(-0.776425\pi\)
−0.763305 + 0.646038i \(0.776425\pi\)
\(608\) −11.5962 −0.470289
\(609\) 19.9710 0.809266
\(610\) −7.68905 −0.311321
\(611\) −3.18143 −0.128707
\(612\) 14.0468 0.567810
\(613\) −14.6798 −0.592912 −0.296456 0.955047i \(-0.595805\pi\)
−0.296456 + 0.955047i \(0.595805\pi\)
\(614\) 1.94108 0.0783358
\(615\) 31.0654 1.25268
\(616\) 39.2389 1.58098
\(617\) 9.57983 0.385670 0.192835 0.981231i \(-0.438232\pi\)
0.192835 + 0.981231i \(0.438232\pi\)
\(618\) −1.03925 −0.0418047
\(619\) −40.1024 −1.61185 −0.805926 0.592016i \(-0.798332\pi\)
−0.805926 + 0.592016i \(0.798332\pi\)
\(620\) −144.762 −5.81377
\(621\) 6.49753 0.260737
\(622\) 83.6065 3.35231
\(623\) 15.6703 0.627816
\(624\) −23.0715 −0.923599
\(625\) 22.5265 0.901059
\(626\) −26.0728 −1.04208
\(627\) 7.68835 0.307043
\(628\) −96.0560 −3.83305
\(629\) 24.1655 0.963543
\(630\) −23.2250 −0.925306
\(631\) 36.7149 1.46160 0.730799 0.682593i \(-0.239148\pi\)
0.730799 + 0.682593i \(0.239148\pi\)
\(632\) 20.0215 0.796414
\(633\) 25.2903 1.00520
\(634\) −57.6975 −2.29146
\(635\) 83.3300 3.30685
\(636\) −52.8435 −2.09538
\(637\) 4.67932 0.185401
\(638\) 57.8548 2.29050
\(639\) −13.1614 −0.520658
\(640\) −54.5489 −2.15624
\(641\) −41.6282 −1.64422 −0.822108 0.569331i \(-0.807202\pi\)
−0.822108 + 0.569331i \(0.807202\pi\)
\(642\) 23.0005 0.907755
\(643\) 7.73847 0.305176 0.152588 0.988290i \(-0.451239\pi\)
0.152588 + 0.988290i \(0.451239\pi\)
\(644\) −67.8855 −2.67506
\(645\) −30.7568 −1.21105
\(646\) −22.7444 −0.894867
\(647\) 42.9923 1.69020 0.845101 0.534607i \(-0.179540\pi\)
0.845101 + 0.534607i \(0.179540\pi\)
\(648\) −5.99445 −0.235484
\(649\) 7.72362 0.303179
\(650\) 89.6957 3.51816
\(651\) −20.5234 −0.804376
\(652\) −87.5280 −3.42786
\(653\) −43.7821 −1.71333 −0.856663 0.515876i \(-0.827467\pi\)
−0.856663 + 0.515876i \(0.827467\pi\)
\(654\) −45.2852 −1.77079
\(655\) −11.4120 −0.445904
\(656\) −51.5081 −2.01105
\(657\) 9.47889 0.369807
\(658\) 5.31007 0.207008
\(659\) 35.6241 1.38772 0.693858 0.720111i \(-0.255909\pi\)
0.693858 + 0.720111i \(0.255909\pi\)
\(660\) −46.1712 −1.79721
\(661\) −10.9606 −0.426319 −0.213160 0.977017i \(-0.568375\pi\)
−0.213160 + 0.977017i \(0.568375\pi\)
\(662\) −62.8334 −2.44209
\(663\) −11.6019 −0.450582
\(664\) −39.8514 −1.54653
\(665\) 25.8064 1.00073
\(666\) −18.9994 −0.736213
\(667\) −54.3283 −2.10360
\(668\) −81.4834 −3.15269
\(669\) 7.46384 0.288569
\(670\) 11.3422 0.438189
\(671\) −2.16713 −0.0836610
\(672\) 9.87304 0.380861
\(673\) 11.8586 0.457114 0.228557 0.973531i \(-0.426599\pi\)
0.228557 + 0.973531i \(0.426599\pi\)
\(674\) −38.2091 −1.47176
\(675\) 9.83324 0.378482
\(676\) 0.232878 0.00895685
\(677\) 32.5221 1.24993 0.624964 0.780654i \(-0.285114\pi\)
0.624964 + 0.780654i \(0.285114\pi\)
\(678\) 11.6321 0.446728
\(679\) −8.39791 −0.322282
\(680\) 74.1376 2.84305
\(681\) 18.5341 0.710228
\(682\) −59.4552 −2.27666
\(683\) 19.1058 0.731065 0.365532 0.930799i \(-0.380887\pi\)
0.365532 + 0.930799i \(0.380887\pi\)
\(684\) 12.2714 0.469210
\(685\) −30.8415 −1.17839
\(686\) −50.0221 −1.90985
\(687\) 1.24767 0.0476015
\(688\) 50.9964 1.94422
\(689\) 43.6459 1.66278
\(690\) 63.1803 2.40523
\(691\) −29.4203 −1.11920 −0.559601 0.828762i \(-0.689045\pi\)
−0.559601 + 0.828762i \(0.689045\pi\)
\(692\) 25.8881 0.984117
\(693\) −6.54587 −0.248657
\(694\) −86.9121 −3.29914
\(695\) 2.01995 0.0766210
\(696\) 50.1219 1.89987
\(697\) −25.9018 −0.981101
\(698\) −39.9771 −1.51316
\(699\) 24.2907 0.918758
\(700\) −102.737 −3.88309
\(701\) −23.5389 −0.889053 −0.444526 0.895766i \(-0.646628\pi\)
−0.444526 + 0.895766i \(0.646628\pi\)
\(702\) 9.12168 0.344276
\(703\) 21.1112 0.796223
\(704\) −6.40033 −0.241221
\(705\) −3.39142 −0.127728
\(706\) 82.2864 3.09689
\(707\) 14.8540 0.558641
\(708\) 12.3277 0.463304
\(709\) −32.4617 −1.21912 −0.609562 0.792738i \(-0.708655\pi\)
−0.609562 + 0.792738i \(0.708655\pi\)
\(710\) −127.978 −4.80294
\(711\) −3.34001 −0.125260
\(712\) 39.3282 1.47389
\(713\) 55.8311 2.09089
\(714\) 19.3646 0.724703
\(715\) 38.1349 1.42617
\(716\) 22.1179 0.826584
\(717\) −1.69618 −0.0633448
\(718\) −42.0295 −1.56853
\(719\) 18.2122 0.679200 0.339600 0.940570i \(-0.389708\pi\)
0.339600 + 0.940570i \(0.389708\pi\)
\(720\) −24.5943 −0.916576
\(721\) −0.983162 −0.0366149
\(722\) 28.1003 1.04578
\(723\) 27.2484 1.01338
\(724\) −24.1238 −0.896552
\(725\) −82.2195 −3.05356
\(726\) 8.80908 0.326936
\(727\) −34.5138 −1.28005 −0.640024 0.768355i \(-0.721075\pi\)
−0.640024 + 0.768355i \(0.721075\pi\)
\(728\) −51.7285 −1.91719
\(729\) 1.00000 0.0370370
\(730\) 92.1703 3.41138
\(731\) 25.6445 0.948495
\(732\) −3.45897 −0.127847
\(733\) 20.3054 0.749998 0.374999 0.927025i \(-0.377643\pi\)
0.374999 + 0.927025i \(0.377643\pi\)
\(734\) −32.2695 −1.19109
\(735\) 4.98817 0.183992
\(736\) −26.8582 −0.990007
\(737\) 3.19676 0.117754
\(738\) 20.3645 0.749629
\(739\) 44.9274 1.65268 0.826341 0.563171i \(-0.190419\pi\)
0.826341 + 0.563171i \(0.190419\pi\)
\(740\) −126.780 −4.66052
\(741\) −10.1355 −0.372338
\(742\) −72.8487 −2.67436
\(743\) −43.1160 −1.58177 −0.790886 0.611964i \(-0.790380\pi\)
−0.790886 + 0.611964i \(0.790380\pi\)
\(744\) −51.5083 −1.88839
\(745\) −10.0321 −0.367547
\(746\) 8.95167 0.327744
\(747\) 6.64805 0.243239
\(748\) 38.4968 1.40758
\(749\) 21.7592 0.795063
\(750\) 46.9973 1.71610
\(751\) 22.4440 0.818994 0.409497 0.912311i \(-0.365704\pi\)
0.409497 + 0.912311i \(0.365704\pi\)
\(752\) 5.62315 0.205055
\(753\) −19.8275 −0.722553
\(754\) −76.2699 −2.77759
\(755\) −28.0809 −1.02197
\(756\) −10.4479 −0.379987
\(757\) 18.2227 0.662317 0.331158 0.943575i \(-0.392561\pi\)
0.331158 + 0.943575i \(0.392561\pi\)
\(758\) 33.7699 1.22658
\(759\) 17.8071 0.646358
\(760\) 64.7672 2.34935
\(761\) 14.4150 0.522545 0.261272 0.965265i \(-0.415858\pi\)
0.261272 + 0.965265i \(0.415858\pi\)
\(762\) 54.6259 1.97889
\(763\) −42.8412 −1.55096
\(764\) 57.1792 2.06867
\(765\) −12.3677 −0.447156
\(766\) −8.21059 −0.296661
\(767\) −10.1820 −0.367652
\(768\) −31.0881 −1.12180
\(769\) −32.4294 −1.16943 −0.584717 0.811237i \(-0.698794\pi\)
−0.584717 + 0.811237i \(0.698794\pi\)
\(770\) −63.6504 −2.29380
\(771\) 10.5451 0.379773
\(772\) 61.3642 2.20855
\(773\) −37.2204 −1.33873 −0.669363 0.742936i \(-0.733433\pi\)
−0.669363 + 0.742936i \(0.733433\pi\)
\(774\) −20.1622 −0.724716
\(775\) 84.4938 3.03511
\(776\) −21.0765 −0.756603
\(777\) −17.9741 −0.644817
\(778\) −12.1531 −0.435711
\(779\) −22.6280 −0.810733
\(780\) 60.8674 2.17940
\(781\) −36.0702 −1.29069
\(782\) −52.6787 −1.88379
\(783\) −8.36138 −0.298812
\(784\) −8.27066 −0.295381
\(785\) 84.5737 3.01856
\(786\) −7.48101 −0.266839
\(787\) 6.68368 0.238247 0.119124 0.992879i \(-0.461992\pi\)
0.119124 + 0.992879i \(0.461992\pi\)
\(788\) 34.3216 1.22266
\(789\) 0.231840 0.00825372
\(790\) −32.4775 −1.15550
\(791\) 11.0043 0.391269
\(792\) −16.4284 −0.583757
\(793\) 2.85692 0.101452
\(794\) −99.3530 −3.52591
\(795\) 46.5267 1.65013
\(796\) −64.8910 −2.30000
\(797\) 47.6171 1.68669 0.843343 0.537376i \(-0.180584\pi\)
0.843343 + 0.537376i \(0.180584\pi\)
\(798\) 16.9171 0.598858
\(799\) 2.82771 0.100037
\(800\) −40.6468 −1.43708
\(801\) −6.56077 −0.231813
\(802\) 43.3726 1.53154
\(803\) 25.9778 0.916738
\(804\) 5.10237 0.179947
\(805\) 59.7706 2.10664
\(806\) 78.3796 2.76080
\(807\) −7.83423 −0.275778
\(808\) 37.2795 1.31149
\(809\) −0.798495 −0.0280736 −0.0140368 0.999901i \(-0.504468\pi\)
−0.0140368 + 0.999901i \(0.504468\pi\)
\(810\) 9.72375 0.341658
\(811\) −3.19469 −0.112181 −0.0560904 0.998426i \(-0.517863\pi\)
−0.0560904 + 0.998426i \(0.517863\pi\)
\(812\) 87.3589 3.06570
\(813\) 5.91309 0.207381
\(814\) −52.0699 −1.82505
\(815\) 77.0651 2.69947
\(816\) 20.5063 0.717865
\(817\) 22.4032 0.783789
\(818\) −26.0792 −0.911839
\(819\) 8.62940 0.301536
\(820\) 135.889 4.74545
\(821\) 30.3215 1.05823 0.529114 0.848550i \(-0.322524\pi\)
0.529114 + 0.848550i \(0.322524\pi\)
\(822\) −20.2178 −0.705177
\(823\) 23.5609 0.821280 0.410640 0.911798i \(-0.365305\pi\)
0.410640 + 0.911798i \(0.365305\pi\)
\(824\) −2.46747 −0.0859585
\(825\) 26.9490 0.938243
\(826\) 16.9947 0.591320
\(827\) −44.2385 −1.53832 −0.769162 0.639053i \(-0.779326\pi\)
−0.769162 + 0.639053i \(0.779326\pi\)
\(828\) 28.4220 0.987734
\(829\) 13.0384 0.452841 0.226421 0.974030i \(-0.427298\pi\)
0.226421 + 0.974030i \(0.427298\pi\)
\(830\) 64.6440 2.24382
\(831\) 24.5162 0.850457
\(832\) 8.43754 0.292519
\(833\) −4.15906 −0.144103
\(834\) 1.32415 0.0458516
\(835\) 71.7431 2.48277
\(836\) 33.6311 1.16315
\(837\) 8.59267 0.297006
\(838\) 50.1732 1.73320
\(839\) 0.0618721 0.00213606 0.00106803 0.999999i \(-0.499660\pi\)
0.00106803 + 0.999999i \(0.499660\pi\)
\(840\) −55.1428 −1.90261
\(841\) 40.9128 1.41078
\(842\) 10.0329 0.345756
\(843\) 12.0700 0.415712
\(844\) 110.627 3.80793
\(845\) −0.205040 −0.00705360
\(846\) −2.22320 −0.0764352
\(847\) 8.33367 0.286348
\(848\) −77.1438 −2.64913
\(849\) −24.9156 −0.855101
\(850\) −79.7231 −2.73448
\(851\) 48.8960 1.67613
\(852\) −57.5718 −1.97238
\(853\) 19.2790 0.660100 0.330050 0.943963i \(-0.392934\pi\)
0.330050 + 0.943963i \(0.392934\pi\)
\(854\) −4.76844 −0.163173
\(855\) −10.8045 −0.369507
\(856\) 54.6097 1.86652
\(857\) −10.9193 −0.372998 −0.186499 0.982455i \(-0.559714\pi\)
−0.186499 + 0.982455i \(0.559714\pi\)
\(858\) 24.9989 0.853448
\(859\) −45.3113 −1.54600 −0.773001 0.634404i \(-0.781245\pi\)
−0.773001 + 0.634404i \(0.781245\pi\)
\(860\) −134.539 −4.58774
\(861\) 19.2655 0.656567
\(862\) 64.6049 2.20045
\(863\) 46.3825 1.57888 0.789439 0.613829i \(-0.210372\pi\)
0.789439 + 0.613829i \(0.210372\pi\)
\(864\) −4.13361 −0.140628
\(865\) −22.7935 −0.775001
\(866\) 24.1218 0.819690
\(867\) −6.68801 −0.227137
\(868\) −89.7754 −3.04717
\(869\) −9.15364 −0.310516
\(870\) −81.3040 −2.75647
\(871\) −4.21428 −0.142796
\(872\) −107.520 −3.64109
\(873\) 3.51600 0.118999
\(874\) −46.0205 −1.55667
\(875\) 44.4609 1.50305
\(876\) 41.4634 1.40092
\(877\) 25.4440 0.859182 0.429591 0.903024i \(-0.358658\pi\)
0.429591 + 0.903024i \(0.358658\pi\)
\(878\) 0.00629104 0.000212312 0
\(879\) 3.10159 0.104614
\(880\) −67.4032 −2.27216
\(881\) 24.5084 0.825708 0.412854 0.910797i \(-0.364532\pi\)
0.412854 + 0.910797i \(0.364532\pi\)
\(882\) 3.26994 0.110105
\(883\) −22.4176 −0.754411 −0.377206 0.926130i \(-0.623115\pi\)
−0.377206 + 0.926130i \(0.623115\pi\)
\(884\) −50.7502 −1.70691
\(885\) −10.8541 −0.364856
\(886\) −73.9630 −2.48483
\(887\) −1.72541 −0.0579337 −0.0289669 0.999580i \(-0.509222\pi\)
−0.0289669 + 0.999580i \(0.509222\pi\)
\(888\) −45.1101 −1.51380
\(889\) 51.6779 1.73322
\(890\) −63.7953 −2.13842
\(891\) 2.74060 0.0918136
\(892\) 32.6490 1.09317
\(893\) 2.47030 0.0826656
\(894\) −6.57641 −0.219948
\(895\) −19.4739 −0.650942
\(896\) −33.8291 −1.13015
\(897\) −23.4751 −0.783810
\(898\) 15.0285 0.501509
\(899\) −71.8466 −2.39622
\(900\) 43.0134 1.43378
\(901\) −38.7932 −1.29239
\(902\) 55.8111 1.85831
\(903\) −19.0741 −0.634747
\(904\) 27.6179 0.918559
\(905\) 21.2401 0.706043
\(906\) −18.4081 −0.611568
\(907\) −41.9545 −1.39308 −0.696538 0.717520i \(-0.745277\pi\)
−0.696538 + 0.717520i \(0.745277\pi\)
\(908\) 81.0734 2.69052
\(909\) −6.21900 −0.206271
\(910\) 83.9102 2.78160
\(911\) −11.2720 −0.373458 −0.186729 0.982412i \(-0.559789\pi\)
−0.186729 + 0.982412i \(0.559789\pi\)
\(912\) 17.9145 0.593208
\(913\) 18.2196 0.602982
\(914\) 31.7625 1.05061
\(915\) 3.04549 0.100681
\(916\) 5.45766 0.180326
\(917\) −7.07727 −0.233712
\(918\) −8.10750 −0.267588
\(919\) 31.4022 1.03586 0.517931 0.855422i \(-0.326702\pi\)
0.517931 + 0.855422i \(0.326702\pi\)
\(920\) 150.008 4.94563
\(921\) −0.768827 −0.0253337
\(922\) −72.6093 −2.39126
\(923\) 47.5512 1.56517
\(924\) −28.6335 −0.941974
\(925\) 73.9983 2.43305
\(926\) 15.7436 0.517368
\(927\) 0.411627 0.0135196
\(928\) 34.5627 1.13458
\(929\) −36.6322 −1.20186 −0.600931 0.799301i \(-0.705203\pi\)
−0.600931 + 0.799301i \(0.705203\pi\)
\(930\) 83.5530 2.73981
\(931\) −3.63338 −0.119079
\(932\) 106.254 3.48048
\(933\) −33.1149 −1.08413
\(934\) 60.9663 1.99488
\(935\) −33.8950 −1.10848
\(936\) 21.6575 0.707898
\(937\) −22.0208 −0.719387 −0.359694 0.933070i \(-0.617119\pi\)
−0.359694 + 0.933070i \(0.617119\pi\)
\(938\) 7.03400 0.229668
\(939\) 10.3270 0.337008
\(940\) −14.8350 −0.483865
\(941\) 42.9991 1.40173 0.700866 0.713293i \(-0.252797\pi\)
0.700866 + 0.713293i \(0.252797\pi\)
\(942\) 55.4412 1.80637
\(943\) −52.4091 −1.70668
\(944\) 17.9967 0.585741
\(945\) 9.19898 0.299243
\(946\) −55.2566 −1.79655
\(947\) 34.8175 1.13142 0.565708 0.824606i \(-0.308603\pi\)
0.565708 + 0.824606i \(0.308603\pi\)
\(948\) −14.6102 −0.474517
\(949\) −34.2465 −1.11169
\(950\) −69.6467 −2.25964
\(951\) 22.8529 0.741056
\(952\) 45.9772 1.49013
\(953\) −26.7827 −0.867575 −0.433788 0.901015i \(-0.642823\pi\)
−0.433788 + 0.901015i \(0.642823\pi\)
\(954\) 30.5000 0.987475
\(955\) −50.3441 −1.62910
\(956\) −7.41956 −0.239966
\(957\) −22.9152 −0.740744
\(958\) 48.3988 1.56369
\(959\) −19.1267 −0.617633
\(960\) 8.99445 0.290295
\(961\) 42.8340 1.38174
\(962\) 68.6436 2.21316
\(963\) −9.11005 −0.293567
\(964\) 119.192 3.83893
\(965\) −54.0289 −1.73925
\(966\) 39.1819 1.26066
\(967\) −24.0113 −0.772153 −0.386076 0.922467i \(-0.626170\pi\)
−0.386076 + 0.922467i \(0.626170\pi\)
\(968\) 20.9153 0.672243
\(969\) 9.00863 0.289399
\(970\) 34.1888 1.09773
\(971\) 41.3098 1.32570 0.662848 0.748754i \(-0.269348\pi\)
0.662848 + 0.748754i \(0.269348\pi\)
\(972\) 4.37429 0.140305
\(973\) 1.25269 0.0401594
\(974\) 55.9702 1.79340
\(975\) −35.5268 −1.13777
\(976\) −5.04958 −0.161633
\(977\) 18.2498 0.583863 0.291932 0.956439i \(-0.405702\pi\)
0.291932 + 0.956439i \(0.405702\pi\)
\(978\) 50.5191 1.61542
\(979\) −17.9804 −0.574658
\(980\) 21.8197 0.697005
\(981\) 17.9366 0.572672
\(982\) −19.2761 −0.615125
\(983\) 38.8201 1.23817 0.619085 0.785324i \(-0.287504\pi\)
0.619085 + 0.785324i \(0.287504\pi\)
\(984\) 48.3513 1.54138
\(985\) −30.2189 −0.962853
\(986\) 67.7900 2.15887
\(987\) −2.10322 −0.0669462
\(988\) −44.3358 −1.41051
\(989\) 51.8884 1.64996
\(990\) 26.6489 0.846958
\(991\) 0.0226372 0.000719095 0 0.000359548 1.00000i \(-0.499886\pi\)
0.000359548 1.00000i \(0.499886\pi\)
\(992\) −35.5187 −1.12772
\(993\) 24.8871 0.789770
\(994\) −79.3671 −2.51737
\(995\) 57.1341 1.81127
\(996\) 29.0805 0.921450
\(997\) 46.0751 1.45921 0.729607 0.683867i \(-0.239703\pi\)
0.729607 + 0.683867i \(0.239703\pi\)
\(998\) 37.7822 1.19598
\(999\) 7.52532 0.238091
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 \(a_p\))