Properties

Label 8001.2.a.v.1.15
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(-1.48888\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.48888 q^{2}\) \(+0.216778 q^{4}\) \(+2.91159 q^{5}\) \(+1.00000 q^{7}\) \(-2.65501 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.48888 q^{2}\) \(+0.216778 q^{4}\) \(+2.91159 q^{5}\) \(+1.00000 q^{7}\) \(-2.65501 q^{8}\) \(+4.33502 q^{10}\) \(-4.14635 q^{11}\) \(+3.36668 q^{13}\) \(+1.48888 q^{14}\) \(-4.38656 q^{16}\) \(-4.79573 q^{17}\) \(+0.147823 q^{19}\) \(+0.631168 q^{20}\) \(-6.17343 q^{22}\) \(+5.23645 q^{23}\) \(+3.47735 q^{25}\) \(+5.01260 q^{26}\) \(+0.216778 q^{28}\) \(+1.23094 q^{29}\) \(+6.14440 q^{31}\) \(-1.22106 q^{32}\) \(-7.14029 q^{34}\) \(+2.91159 q^{35}\) \(+7.83605 q^{37}\) \(+0.220092 q^{38}\) \(-7.73031 q^{40}\) \(-0.0490986 q^{41}\) \(-8.18235 q^{43}\) \(-0.898836 q^{44}\) \(+7.79646 q^{46}\) \(+3.35398 q^{47}\) \(+1.00000 q^{49}\) \(+5.17738 q^{50}\) \(+0.729822 q^{52}\) \(-4.90402 q^{53}\) \(-12.0725 q^{55}\) \(-2.65501 q^{56}\) \(+1.83273 q^{58}\) \(+12.0362 q^{59}\) \(+10.8592 q^{61}\) \(+9.14831 q^{62}\) \(+6.95510 q^{64}\) \(+9.80239 q^{65}\) \(-1.83840 q^{67}\) \(-1.03961 q^{68}\) \(+4.33502 q^{70}\) \(+9.72828 q^{71}\) \(+7.33222 q^{73}\) \(+11.6670 q^{74}\) \(+0.0320448 q^{76}\) \(-4.14635 q^{77}\) \(+6.96474 q^{79}\) \(-12.7719 q^{80}\) \(-0.0731022 q^{82}\) \(+13.2685 q^{83}\) \(-13.9632 q^{85}\) \(-12.1826 q^{86}\) \(+11.0086 q^{88}\) \(+11.1337 q^{89}\) \(+3.36668 q^{91}\) \(+1.13515 q^{92}\) \(+4.99369 q^{94}\) \(+0.430400 q^{95}\) \(-0.471210 q^{97}\) \(+1.48888 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48888 1.05280 0.526400 0.850237i \(-0.323541\pi\)
0.526400 + 0.850237i \(0.323541\pi\)
\(3\) 0 0
\(4\) 0.216778 0.108389
\(5\) 2.91159 1.30210 0.651051 0.759034i \(-0.274328\pi\)
0.651051 + 0.759034i \(0.274328\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.65501 −0.938689
\(9\) 0 0
\(10\) 4.33502 1.37085
\(11\) −4.14635 −1.25017 −0.625085 0.780556i \(-0.714936\pi\)
−0.625085 + 0.780556i \(0.714936\pi\)
\(12\) 0 0
\(13\) 3.36668 0.933749 0.466874 0.884324i \(-0.345380\pi\)
0.466874 + 0.884324i \(0.345380\pi\)
\(14\) 1.48888 0.397921
\(15\) 0 0
\(16\) −4.38656 −1.09664
\(17\) −4.79573 −1.16314 −0.581568 0.813498i \(-0.697560\pi\)
−0.581568 + 0.813498i \(0.697560\pi\)
\(18\) 0 0
\(19\) 0.147823 0.0339130 0.0169565 0.999856i \(-0.494602\pi\)
0.0169565 + 0.999856i \(0.494602\pi\)
\(20\) 0.631168 0.141134
\(21\) 0 0
\(22\) −6.17343 −1.31618
\(23\) 5.23645 1.09187 0.545937 0.837826i \(-0.316174\pi\)
0.545937 + 0.837826i \(0.316174\pi\)
\(24\) 0 0
\(25\) 3.47735 0.695471
\(26\) 5.01260 0.983051
\(27\) 0 0
\(28\) 0.216778 0.0409672
\(29\) 1.23094 0.228580 0.114290 0.993447i \(-0.463541\pi\)
0.114290 + 0.993447i \(0.463541\pi\)
\(30\) 0 0
\(31\) 6.14440 1.10357 0.551784 0.833987i \(-0.313947\pi\)
0.551784 + 0.833987i \(0.313947\pi\)
\(32\) −1.22106 −0.215855
\(33\) 0 0
\(34\) −7.14029 −1.22455
\(35\) 2.91159 0.492148
\(36\) 0 0
\(37\) 7.83605 1.28824 0.644120 0.764925i \(-0.277224\pi\)
0.644120 + 0.764925i \(0.277224\pi\)
\(38\) 0.220092 0.0357036
\(39\) 0 0
\(40\) −7.73031 −1.22227
\(41\) −0.0490986 −0.00766792 −0.00383396 0.999993i \(-0.501220\pi\)
−0.00383396 + 0.999993i \(0.501220\pi\)
\(42\) 0 0
\(43\) −8.18235 −1.24780 −0.623899 0.781505i \(-0.714452\pi\)
−0.623899 + 0.781505i \(0.714452\pi\)
\(44\) −0.898836 −0.135505
\(45\) 0 0
\(46\) 7.79646 1.14953
\(47\) 3.35398 0.489229 0.244614 0.969620i \(-0.421339\pi\)
0.244614 + 0.969620i \(0.421339\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 5.17738 0.732192
\(51\) 0 0
\(52\) 0.729822 0.101208
\(53\) −4.90402 −0.673619 −0.336809 0.941573i \(-0.609348\pi\)
−0.336809 + 0.941573i \(0.609348\pi\)
\(54\) 0 0
\(55\) −12.0725 −1.62785
\(56\) −2.65501 −0.354791
\(57\) 0 0
\(58\) 1.83273 0.240649
\(59\) 12.0362 1.56698 0.783492 0.621402i \(-0.213436\pi\)
0.783492 + 0.621402i \(0.213436\pi\)
\(60\) 0 0
\(61\) 10.8592 1.39037 0.695186 0.718830i \(-0.255322\pi\)
0.695186 + 0.718830i \(0.255322\pi\)
\(62\) 9.14831 1.16184
\(63\) 0 0
\(64\) 6.95510 0.869388
\(65\) 9.80239 1.21584
\(66\) 0 0
\(67\) −1.83840 −0.224596 −0.112298 0.993675i \(-0.535821\pi\)
−0.112298 + 0.993675i \(0.535821\pi\)
\(68\) −1.03961 −0.126071
\(69\) 0 0
\(70\) 4.33502 0.518134
\(71\) 9.72828 1.15453 0.577267 0.816555i \(-0.304119\pi\)
0.577267 + 0.816555i \(0.304119\pi\)
\(72\) 0 0
\(73\) 7.33222 0.858171 0.429086 0.903264i \(-0.358836\pi\)
0.429086 + 0.903264i \(0.358836\pi\)
\(74\) 11.6670 1.35626
\(75\) 0 0
\(76\) 0.0320448 0.00367579
\(77\) −4.14635 −0.472520
\(78\) 0 0
\(79\) 6.96474 0.783595 0.391797 0.920052i \(-0.371853\pi\)
0.391797 + 0.920052i \(0.371853\pi\)
\(80\) −12.7719 −1.42794
\(81\) 0 0
\(82\) −0.0731022 −0.00807279
\(83\) 13.2685 1.45641 0.728204 0.685360i \(-0.240355\pi\)
0.728204 + 0.685360i \(0.240355\pi\)
\(84\) 0 0
\(85\) −13.9632 −1.51452
\(86\) −12.1826 −1.31368
\(87\) 0 0
\(88\) 11.0086 1.17352
\(89\) 11.1337 1.18017 0.590086 0.807340i \(-0.299094\pi\)
0.590086 + 0.807340i \(0.299094\pi\)
\(90\) 0 0
\(91\) 3.36668 0.352924
\(92\) 1.13515 0.118347
\(93\) 0 0
\(94\) 4.99369 0.515060
\(95\) 0.430400 0.0441581
\(96\) 0 0
\(97\) −0.471210 −0.0478441 −0.0239220 0.999714i \(-0.507615\pi\)
−0.0239220 + 0.999714i \(0.507615\pi\)
\(98\) 1.48888 0.150400
\(99\) 0 0
\(100\) 0.753813 0.0753813
\(101\) 5.16598 0.514034 0.257017 0.966407i \(-0.417260\pi\)
0.257017 + 0.966407i \(0.417260\pi\)
\(102\) 0 0
\(103\) −2.38399 −0.234901 −0.117451 0.993079i \(-0.537472\pi\)
−0.117451 + 0.993079i \(0.537472\pi\)
\(104\) −8.93857 −0.876499
\(105\) 0 0
\(106\) −7.30152 −0.709186
\(107\) −16.9004 −1.63382 −0.816909 0.576766i \(-0.804314\pi\)
−0.816909 + 0.576766i \(0.804314\pi\)
\(108\) 0 0
\(109\) 11.0708 1.06039 0.530193 0.847877i \(-0.322119\pi\)
0.530193 + 0.847877i \(0.322119\pi\)
\(110\) −17.9745 −1.71380
\(111\) 0 0
\(112\) −4.38656 −0.414491
\(113\) −14.9881 −1.40996 −0.704982 0.709225i \(-0.749045\pi\)
−0.704982 + 0.709225i \(0.749045\pi\)
\(114\) 0 0
\(115\) 15.2464 1.42173
\(116\) 0.266840 0.0247755
\(117\) 0 0
\(118\) 17.9206 1.64972
\(119\) −4.79573 −0.439624
\(120\) 0 0
\(121\) 6.19220 0.562927
\(122\) 16.1680 1.46378
\(123\) 0 0
\(124\) 1.33197 0.119615
\(125\) −4.43332 −0.396528
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 12.7975 1.13115
\(129\) 0 0
\(130\) 14.5946 1.28003
\(131\) 5.79631 0.506426 0.253213 0.967411i \(-0.418513\pi\)
0.253213 + 0.967411i \(0.418513\pi\)
\(132\) 0 0
\(133\) 0.147823 0.0128179
\(134\) −2.73716 −0.236455
\(135\) 0 0
\(136\) 12.7327 1.09182
\(137\) −22.1491 −1.89233 −0.946164 0.323688i \(-0.895077\pi\)
−0.946164 + 0.323688i \(0.895077\pi\)
\(138\) 0 0
\(139\) 16.1472 1.36959 0.684794 0.728737i \(-0.259892\pi\)
0.684794 + 0.728737i \(0.259892\pi\)
\(140\) 0.631168 0.0533434
\(141\) 0 0
\(142\) 14.4843 1.21549
\(143\) −13.9594 −1.16735
\(144\) 0 0
\(145\) 3.58399 0.297634
\(146\) 10.9168 0.903483
\(147\) 0 0
\(148\) 1.69868 0.139631
\(149\) −11.4146 −0.935123 −0.467562 0.883961i \(-0.654867\pi\)
−0.467562 + 0.883961i \(0.654867\pi\)
\(150\) 0 0
\(151\) 21.7197 1.76752 0.883761 0.467939i \(-0.155003\pi\)
0.883761 + 0.467939i \(0.155003\pi\)
\(152\) −0.392472 −0.0318337
\(153\) 0 0
\(154\) −6.17343 −0.497469
\(155\) 17.8900 1.43696
\(156\) 0 0
\(157\) −13.6447 −1.08897 −0.544484 0.838771i \(-0.683275\pi\)
−0.544484 + 0.838771i \(0.683275\pi\)
\(158\) 10.3697 0.824969
\(159\) 0 0
\(160\) −3.55523 −0.281066
\(161\) 5.23645 0.412690
\(162\) 0 0
\(163\) −0.934160 −0.0731690 −0.0365845 0.999331i \(-0.511648\pi\)
−0.0365845 + 0.999331i \(0.511648\pi\)
\(164\) −0.0106435 −0.000831118 0
\(165\) 0 0
\(166\) 19.7553 1.53331
\(167\) −14.1430 −1.09442 −0.547209 0.836996i \(-0.684310\pi\)
−0.547209 + 0.836996i \(0.684310\pi\)
\(168\) 0 0
\(169\) −1.66547 −0.128113
\(170\) −20.7896 −1.59449
\(171\) 0 0
\(172\) −1.77375 −0.135247
\(173\) 4.53586 0.344855 0.172428 0.985022i \(-0.444839\pi\)
0.172428 + 0.985022i \(0.444839\pi\)
\(174\) 0 0
\(175\) 3.47735 0.262863
\(176\) 18.1882 1.37099
\(177\) 0 0
\(178\) 16.5768 1.24249
\(179\) 0.416214 0.0311093 0.0155546 0.999879i \(-0.495049\pi\)
0.0155546 + 0.999879i \(0.495049\pi\)
\(180\) 0 0
\(181\) 24.2415 1.80186 0.900928 0.433969i \(-0.142887\pi\)
0.900928 + 0.433969i \(0.142887\pi\)
\(182\) 5.01260 0.371558
\(183\) 0 0
\(184\) −13.9028 −1.02493
\(185\) 22.8154 1.67742
\(186\) 0 0
\(187\) 19.8848 1.45412
\(188\) 0.727069 0.0530270
\(189\) 0 0
\(190\) 0.640816 0.0464897
\(191\) 26.6373 1.92741 0.963704 0.266975i \(-0.0860240\pi\)
0.963704 + 0.266975i \(0.0860240\pi\)
\(192\) 0 0
\(193\) −19.0498 −1.37123 −0.685616 0.727964i \(-0.740467\pi\)
−0.685616 + 0.727964i \(0.740467\pi\)
\(194\) −0.701577 −0.0503703
\(195\) 0 0
\(196\) 0.216778 0.0154841
\(197\) 5.83599 0.415797 0.207898 0.978150i \(-0.433338\pi\)
0.207898 + 0.978150i \(0.433338\pi\)
\(198\) 0 0
\(199\) 22.8300 1.61837 0.809187 0.587551i \(-0.199908\pi\)
0.809187 + 0.587551i \(0.199908\pi\)
\(200\) −9.23241 −0.652830
\(201\) 0 0
\(202\) 7.69154 0.541175
\(203\) 1.23094 0.0863950
\(204\) 0 0
\(205\) −0.142955 −0.00998442
\(206\) −3.54948 −0.247304
\(207\) 0 0
\(208\) −14.7681 −1.02399
\(209\) −0.612926 −0.0423970
\(210\) 0 0
\(211\) −25.8008 −1.77620 −0.888099 0.459652i \(-0.847974\pi\)
−0.888099 + 0.459652i \(0.847974\pi\)
\(212\) −1.06308 −0.0730128
\(213\) 0 0
\(214\) −25.1627 −1.72009
\(215\) −23.8237 −1.62476
\(216\) 0 0
\(217\) 6.14440 0.417109
\(218\) 16.4831 1.11638
\(219\) 0 0
\(220\) −2.61704 −0.176441
\(221\) −16.1457 −1.08608
\(222\) 0 0
\(223\) −8.47086 −0.567251 −0.283625 0.958935i \(-0.591537\pi\)
−0.283625 + 0.958935i \(0.591537\pi\)
\(224\) −1.22106 −0.0815857
\(225\) 0 0
\(226\) −22.3156 −1.48441
\(227\) 8.01720 0.532120 0.266060 0.963956i \(-0.414278\pi\)
0.266060 + 0.963956i \(0.414278\pi\)
\(228\) 0 0
\(229\) 20.2786 1.34005 0.670023 0.742340i \(-0.266284\pi\)
0.670023 + 0.742340i \(0.266284\pi\)
\(230\) 22.7001 1.49680
\(231\) 0 0
\(232\) −3.26816 −0.214565
\(233\) 6.73232 0.441049 0.220524 0.975381i \(-0.429223\pi\)
0.220524 + 0.975381i \(0.429223\pi\)
\(234\) 0 0
\(235\) 9.76542 0.637026
\(236\) 2.60919 0.169844
\(237\) 0 0
\(238\) −7.14029 −0.462836
\(239\) −13.7010 −0.886247 −0.443123 0.896461i \(-0.646130\pi\)
−0.443123 + 0.896461i \(0.646130\pi\)
\(240\) 0 0
\(241\) 6.48260 0.417581 0.208791 0.977960i \(-0.433047\pi\)
0.208791 + 0.977960i \(0.433047\pi\)
\(242\) 9.21947 0.592650
\(243\) 0 0
\(244\) 2.35402 0.150701
\(245\) 2.91159 0.186015
\(246\) 0 0
\(247\) 0.497673 0.0316662
\(248\) −16.3135 −1.03591
\(249\) 0 0
\(250\) −6.60071 −0.417465
\(251\) −21.9241 −1.38384 −0.691920 0.721975i \(-0.743235\pi\)
−0.691920 + 0.721975i \(0.743235\pi\)
\(252\) 0 0
\(253\) −21.7121 −1.36503
\(254\) 1.48888 0.0934209
\(255\) 0 0
\(256\) 5.14376 0.321485
\(257\) −25.1781 −1.57056 −0.785282 0.619138i \(-0.787482\pi\)
−0.785282 + 0.619138i \(0.787482\pi\)
\(258\) 0 0
\(259\) 7.83605 0.486909
\(260\) 2.12494 0.131783
\(261\) 0 0
\(262\) 8.63004 0.533166
\(263\) −2.57791 −0.158961 −0.0794804 0.996836i \(-0.525326\pi\)
−0.0794804 + 0.996836i \(0.525326\pi\)
\(264\) 0 0
\(265\) −14.2785 −0.877121
\(266\) 0.220092 0.0134947
\(267\) 0 0
\(268\) −0.398523 −0.0243437
\(269\) −15.9217 −0.970760 −0.485380 0.874303i \(-0.661319\pi\)
−0.485380 + 0.874303i \(0.661319\pi\)
\(270\) 0 0
\(271\) 2.87200 0.174462 0.0872308 0.996188i \(-0.472198\pi\)
0.0872308 + 0.996188i \(0.472198\pi\)
\(272\) 21.0368 1.27554
\(273\) 0 0
\(274\) −32.9775 −1.99224
\(275\) −14.4183 −0.869457
\(276\) 0 0
\(277\) −5.15941 −0.309999 −0.154999 0.987915i \(-0.549538\pi\)
−0.154999 + 0.987915i \(0.549538\pi\)
\(278\) 24.0413 1.44190
\(279\) 0 0
\(280\) −7.73031 −0.461974
\(281\) −8.81624 −0.525933 −0.262966 0.964805i \(-0.584701\pi\)
−0.262966 + 0.964805i \(0.584701\pi\)
\(282\) 0 0
\(283\) −8.37512 −0.497849 −0.248925 0.968523i \(-0.580077\pi\)
−0.248925 + 0.968523i \(0.580077\pi\)
\(284\) 2.10888 0.125139
\(285\) 0 0
\(286\) −20.7840 −1.22898
\(287\) −0.0490986 −0.00289820
\(288\) 0 0
\(289\) 5.99902 0.352884
\(290\) 5.33615 0.313349
\(291\) 0 0
\(292\) 1.58946 0.0930163
\(293\) 14.4763 0.845717 0.422858 0.906196i \(-0.361027\pi\)
0.422858 + 0.906196i \(0.361027\pi\)
\(294\) 0 0
\(295\) 35.0446 2.04037
\(296\) −20.8048 −1.20926
\(297\) 0 0
\(298\) −16.9951 −0.984498
\(299\) 17.6294 1.01954
\(300\) 0 0
\(301\) −8.18235 −0.471623
\(302\) 32.3381 1.86085
\(303\) 0 0
\(304\) −0.648436 −0.0371903
\(305\) 31.6174 1.81041
\(306\) 0 0
\(307\) 3.23887 0.184852 0.0924260 0.995720i \(-0.470538\pi\)
0.0924260 + 0.995720i \(0.470538\pi\)
\(308\) −0.898836 −0.0512160
\(309\) 0 0
\(310\) 26.6361 1.51283
\(311\) 16.0805 0.911840 0.455920 0.890021i \(-0.349310\pi\)
0.455920 + 0.890021i \(0.349310\pi\)
\(312\) 0 0
\(313\) −21.3203 −1.20510 −0.602548 0.798083i \(-0.705848\pi\)
−0.602548 + 0.798083i \(0.705848\pi\)
\(314\) −20.3154 −1.14647
\(315\) 0 0
\(316\) 1.50980 0.0849330
\(317\) −4.98067 −0.279742 −0.139871 0.990170i \(-0.544669\pi\)
−0.139871 + 0.990170i \(0.544669\pi\)
\(318\) 0 0
\(319\) −5.10390 −0.285764
\(320\) 20.2504 1.13203
\(321\) 0 0
\(322\) 7.79646 0.434480
\(323\) −0.708920 −0.0394454
\(324\) 0 0
\(325\) 11.7071 0.649395
\(326\) −1.39086 −0.0770324
\(327\) 0 0
\(328\) 0.130357 0.00719779
\(329\) 3.35398 0.184911
\(330\) 0 0
\(331\) −4.19417 −0.230532 −0.115266 0.993335i \(-0.536772\pi\)
−0.115266 + 0.993335i \(0.536772\pi\)
\(332\) 2.87632 0.157859
\(333\) 0 0
\(334\) −21.0573 −1.15220
\(335\) −5.35265 −0.292447
\(336\) 0 0
\(337\) 10.8184 0.589314 0.294657 0.955603i \(-0.404795\pi\)
0.294657 + 0.955603i \(0.404795\pi\)
\(338\) −2.47970 −0.134878
\(339\) 0 0
\(340\) −3.02691 −0.164157
\(341\) −25.4768 −1.37965
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 21.7243 1.17129
\(345\) 0 0
\(346\) 6.75338 0.363064
\(347\) −17.1092 −0.918471 −0.459236 0.888315i \(-0.651877\pi\)
−0.459236 + 0.888315i \(0.651877\pi\)
\(348\) 0 0
\(349\) 9.72106 0.520356 0.260178 0.965561i \(-0.416219\pi\)
0.260178 + 0.965561i \(0.416219\pi\)
\(350\) 5.17738 0.276742
\(351\) 0 0
\(352\) 5.06295 0.269856
\(353\) −12.6247 −0.671946 −0.335973 0.941872i \(-0.609065\pi\)
−0.335973 + 0.941872i \(0.609065\pi\)
\(354\) 0 0
\(355\) 28.3247 1.50332
\(356\) 2.41354 0.127918
\(357\) 0 0
\(358\) 0.619694 0.0327519
\(359\) 9.48768 0.500741 0.250370 0.968150i \(-0.419448\pi\)
0.250370 + 0.968150i \(0.419448\pi\)
\(360\) 0 0
\(361\) −18.9781 −0.998850
\(362\) 36.0928 1.89699
\(363\) 0 0
\(364\) 0.729822 0.0382530
\(365\) 21.3484 1.11743
\(366\) 0 0
\(367\) 9.78894 0.510978 0.255489 0.966812i \(-0.417763\pi\)
0.255489 + 0.966812i \(0.417763\pi\)
\(368\) −22.9700 −1.19739
\(369\) 0 0
\(370\) 33.9695 1.76599
\(371\) −4.90402 −0.254604
\(372\) 0 0
\(373\) −29.8399 −1.54505 −0.772525 0.634984i \(-0.781006\pi\)
−0.772525 + 0.634984i \(0.781006\pi\)
\(374\) 29.6061 1.53090
\(375\) 0 0
\(376\) −8.90486 −0.459233
\(377\) 4.14418 0.213436
\(378\) 0 0
\(379\) −19.1294 −0.982610 −0.491305 0.870988i \(-0.663480\pi\)
−0.491305 + 0.870988i \(0.663480\pi\)
\(380\) 0.0933013 0.00478625
\(381\) 0 0
\(382\) 39.6599 2.02918
\(383\) −9.49745 −0.485297 −0.242648 0.970114i \(-0.578016\pi\)
−0.242648 + 0.970114i \(0.578016\pi\)
\(384\) 0 0
\(385\) −12.0725 −0.615270
\(386\) −28.3629 −1.44363
\(387\) 0 0
\(388\) −0.102148 −0.00518577
\(389\) −27.4189 −1.39020 −0.695098 0.718915i \(-0.744639\pi\)
−0.695098 + 0.718915i \(0.744639\pi\)
\(390\) 0 0
\(391\) −25.1126 −1.27000
\(392\) −2.65501 −0.134098
\(393\) 0 0
\(394\) 8.68911 0.437751
\(395\) 20.2785 1.02032
\(396\) 0 0
\(397\) 13.5805 0.681585 0.340792 0.940139i \(-0.389305\pi\)
0.340792 + 0.940139i \(0.389305\pi\)
\(398\) 33.9912 1.70383
\(399\) 0 0
\(400\) −15.2536 −0.762681
\(401\) −12.6146 −0.629941 −0.314970 0.949101i \(-0.601995\pi\)
−0.314970 + 0.949101i \(0.601995\pi\)
\(402\) 0 0
\(403\) 20.6862 1.03045
\(404\) 1.11987 0.0557156
\(405\) 0 0
\(406\) 1.83273 0.0909567
\(407\) −32.4910 −1.61052
\(408\) 0 0
\(409\) −0.129840 −0.00642020 −0.00321010 0.999995i \(-0.501022\pi\)
−0.00321010 + 0.999995i \(0.501022\pi\)
\(410\) −0.212844 −0.0105116
\(411\) 0 0
\(412\) −0.516795 −0.0254607
\(413\) 12.0362 0.592264
\(414\) 0 0
\(415\) 38.6324 1.89639
\(416\) −4.11093 −0.201555
\(417\) 0 0
\(418\) −0.912576 −0.0446356
\(419\) −14.5425 −0.710449 −0.355224 0.934781i \(-0.615596\pi\)
−0.355224 + 0.934781i \(0.615596\pi\)
\(420\) 0 0
\(421\) 12.9591 0.631586 0.315793 0.948828i \(-0.397730\pi\)
0.315793 + 0.948828i \(0.397730\pi\)
\(422\) −38.4144 −1.86998
\(423\) 0 0
\(424\) 13.0202 0.632318
\(425\) −16.6764 −0.808926
\(426\) 0 0
\(427\) 10.8592 0.525511
\(428\) −3.66362 −0.177088
\(429\) 0 0
\(430\) −35.4707 −1.71055
\(431\) 26.1264 1.25846 0.629232 0.777218i \(-0.283370\pi\)
0.629232 + 0.777218i \(0.283370\pi\)
\(432\) 0 0
\(433\) 27.6129 1.32699 0.663496 0.748180i \(-0.269072\pi\)
0.663496 + 0.748180i \(0.269072\pi\)
\(434\) 9.14831 0.439133
\(435\) 0 0
\(436\) 2.39990 0.114934
\(437\) 0.774068 0.0370287
\(438\) 0 0
\(439\) 4.55135 0.217224 0.108612 0.994084i \(-0.465359\pi\)
0.108612 + 0.994084i \(0.465359\pi\)
\(440\) 32.0525 1.52804
\(441\) 0 0
\(442\) −24.0391 −1.14342
\(443\) −2.30191 −0.109367 −0.0546836 0.998504i \(-0.517415\pi\)
−0.0546836 + 0.998504i \(0.517415\pi\)
\(444\) 0 0
\(445\) 32.4168 1.53670
\(446\) −12.6121 −0.597202
\(447\) 0 0
\(448\) 6.95510 0.328598
\(449\) 25.9591 1.22509 0.612544 0.790437i \(-0.290146\pi\)
0.612544 + 0.790437i \(0.290146\pi\)
\(450\) 0 0
\(451\) 0.203580 0.00958621
\(452\) −3.24910 −0.152825
\(453\) 0 0
\(454\) 11.9367 0.560216
\(455\) 9.80239 0.459543
\(456\) 0 0
\(457\) −11.9556 −0.559258 −0.279629 0.960108i \(-0.590211\pi\)
−0.279629 + 0.960108i \(0.590211\pi\)
\(458\) 30.1925 1.41080
\(459\) 0 0
\(460\) 3.30508 0.154100
\(461\) 7.55639 0.351936 0.175968 0.984396i \(-0.443694\pi\)
0.175968 + 0.984396i \(0.443694\pi\)
\(462\) 0 0
\(463\) −1.92100 −0.0892762 −0.0446381 0.999003i \(-0.514213\pi\)
−0.0446381 + 0.999003i \(0.514213\pi\)
\(464\) −5.39959 −0.250670
\(465\) 0 0
\(466\) 10.0236 0.464336
\(467\) 1.55517 0.0719648 0.0359824 0.999352i \(-0.488544\pi\)
0.0359824 + 0.999352i \(0.488544\pi\)
\(468\) 0 0
\(469\) −1.83840 −0.0848892
\(470\) 14.5396 0.670661
\(471\) 0 0
\(472\) −31.9564 −1.47091
\(473\) 33.9269 1.55996
\(474\) 0 0
\(475\) 0.514033 0.0235855
\(476\) −1.03961 −0.0476504
\(477\) 0 0
\(478\) −20.3993 −0.933041
\(479\) −3.79672 −0.173477 −0.0867384 0.996231i \(-0.527644\pi\)
−0.0867384 + 0.996231i \(0.527644\pi\)
\(480\) 0 0
\(481\) 26.3815 1.20289
\(482\) 9.65185 0.439630
\(483\) 0 0
\(484\) 1.34233 0.0610151
\(485\) −1.37197 −0.0622979
\(486\) 0 0
\(487\) 42.8719 1.94271 0.971357 0.237626i \(-0.0763694\pi\)
0.971357 + 0.237626i \(0.0763694\pi\)
\(488\) −28.8312 −1.30513
\(489\) 0 0
\(490\) 4.33502 0.195836
\(491\) 22.3751 1.00977 0.504887 0.863185i \(-0.331534\pi\)
0.504887 + 0.863185i \(0.331534\pi\)
\(492\) 0 0
\(493\) −5.90325 −0.265869
\(494\) 0.740978 0.0333382
\(495\) 0 0
\(496\) −26.9528 −1.21022
\(497\) 9.72828 0.436373
\(498\) 0 0
\(499\) −5.93137 −0.265525 −0.132762 0.991148i \(-0.542385\pi\)
−0.132762 + 0.991148i \(0.542385\pi\)
\(500\) −0.961046 −0.0429793
\(501\) 0 0
\(502\) −32.6425 −1.45691
\(503\) −7.56282 −0.337210 −0.168605 0.985684i \(-0.553926\pi\)
−0.168605 + 0.985684i \(0.553926\pi\)
\(504\) 0 0
\(505\) 15.0412 0.669325
\(506\) −32.3268 −1.43710
\(507\) 0 0
\(508\) 0.216778 0.00961796
\(509\) 3.13987 0.139172 0.0695861 0.997576i \(-0.477832\pi\)
0.0695861 + 0.997576i \(0.477832\pi\)
\(510\) 0 0
\(511\) 7.33222 0.324358
\(512\) −17.9365 −0.792688
\(513\) 0 0
\(514\) −37.4872 −1.65349
\(515\) −6.94119 −0.305865
\(516\) 0 0
\(517\) −13.9068 −0.611619
\(518\) 11.6670 0.512618
\(519\) 0 0
\(520\) −26.0255 −1.14129
\(521\) −17.8111 −0.780321 −0.390160 0.920747i \(-0.627580\pi\)
−0.390160 + 0.920747i \(0.627580\pi\)
\(522\) 0 0
\(523\) 33.8549 1.48037 0.740185 0.672403i \(-0.234738\pi\)
0.740185 + 0.672403i \(0.234738\pi\)
\(524\) 1.25651 0.0548910
\(525\) 0 0
\(526\) −3.83821 −0.167354
\(527\) −29.4669 −1.28360
\(528\) 0 0
\(529\) 4.42036 0.192189
\(530\) −21.2590 −0.923433
\(531\) 0 0
\(532\) 0.0320448 0.00138932
\(533\) −0.165299 −0.00715991
\(534\) 0 0
\(535\) −49.2069 −2.12740
\(536\) 4.88096 0.210825
\(537\) 0 0
\(538\) −23.7055 −1.02202
\(539\) −4.14635 −0.178596
\(540\) 0 0
\(541\) 3.35902 0.144415 0.0722077 0.997390i \(-0.476996\pi\)
0.0722077 + 0.997390i \(0.476996\pi\)
\(542\) 4.27608 0.183673
\(543\) 0 0
\(544\) 5.85589 0.251069
\(545\) 32.2335 1.38073
\(546\) 0 0
\(547\) −10.8941 −0.465798 −0.232899 0.972501i \(-0.574821\pi\)
−0.232899 + 0.972501i \(0.574821\pi\)
\(548\) −4.80144 −0.205107
\(549\) 0 0
\(550\) −21.4672 −0.915365
\(551\) 0.181961 0.00775181
\(552\) 0 0
\(553\) 6.96474 0.296171
\(554\) −7.68177 −0.326367
\(555\) 0 0
\(556\) 3.50035 0.148448
\(557\) 24.0627 1.01957 0.509784 0.860302i \(-0.329725\pi\)
0.509784 + 0.860302i \(0.329725\pi\)
\(558\) 0 0
\(559\) −27.5474 −1.16513
\(560\) −12.7719 −0.539710
\(561\) 0 0
\(562\) −13.1264 −0.553702
\(563\) 27.1050 1.14234 0.571169 0.820832i \(-0.306490\pi\)
0.571169 + 0.820832i \(0.306490\pi\)
\(564\) 0 0
\(565\) −43.6393 −1.83592
\(566\) −12.4696 −0.524136
\(567\) 0 0
\(568\) −25.8287 −1.08375
\(569\) 42.7501 1.79218 0.896089 0.443875i \(-0.146397\pi\)
0.896089 + 0.443875i \(0.146397\pi\)
\(570\) 0 0
\(571\) 18.7978 0.786665 0.393333 0.919396i \(-0.371322\pi\)
0.393333 + 0.919396i \(0.371322\pi\)
\(572\) −3.02609 −0.126527
\(573\) 0 0
\(574\) −0.0731022 −0.00305123
\(575\) 18.2090 0.759366
\(576\) 0 0
\(577\) −1.84444 −0.0767849 −0.0383925 0.999263i \(-0.512224\pi\)
−0.0383925 + 0.999263i \(0.512224\pi\)
\(578\) 8.93185 0.371516
\(579\) 0 0
\(580\) 0.776930 0.0322603
\(581\) 13.2685 0.550470
\(582\) 0 0
\(583\) 20.3338 0.842139
\(584\) −19.4671 −0.805556
\(585\) 0 0
\(586\) 21.5536 0.890371
\(587\) −0.0278962 −0.00115140 −0.000575700 1.00000i \(-0.500183\pi\)
−0.000575700 1.00000i \(0.500183\pi\)
\(588\) 0 0
\(589\) 0.908285 0.0374252
\(590\) 52.1773 2.14811
\(591\) 0 0
\(592\) −34.3733 −1.41274
\(593\) 4.26821 0.175274 0.0876371 0.996152i \(-0.472068\pi\)
0.0876371 + 0.996152i \(0.472068\pi\)
\(594\) 0 0
\(595\) −13.9632 −0.572435
\(596\) −2.47444 −0.101357
\(597\) 0 0
\(598\) 26.2482 1.07337
\(599\) 28.3223 1.15722 0.578610 0.815605i \(-0.303596\pi\)
0.578610 + 0.815605i \(0.303596\pi\)
\(600\) 0 0
\(601\) −5.52773 −0.225481 −0.112740 0.993624i \(-0.535963\pi\)
−0.112740 + 0.993624i \(0.535963\pi\)
\(602\) −12.1826 −0.496525
\(603\) 0 0
\(604\) 4.70834 0.191580
\(605\) 18.0291 0.732989
\(606\) 0 0
\(607\) −0.370522 −0.0150390 −0.00751951 0.999972i \(-0.502394\pi\)
−0.00751951 + 0.999972i \(0.502394\pi\)
\(608\) −0.180501 −0.00732029
\(609\) 0 0
\(610\) 47.0747 1.90600
\(611\) 11.2918 0.456817
\(612\) 0 0
\(613\) 15.5785 0.629211 0.314605 0.949223i \(-0.398128\pi\)
0.314605 + 0.949223i \(0.398128\pi\)
\(614\) 4.82230 0.194612
\(615\) 0 0
\(616\) 11.0086 0.443549
\(617\) 3.80748 0.153283 0.0766417 0.997059i \(-0.475580\pi\)
0.0766417 + 0.997059i \(0.475580\pi\)
\(618\) 0 0
\(619\) −2.32509 −0.0934531 −0.0467265 0.998908i \(-0.514879\pi\)
−0.0467265 + 0.998908i \(0.514879\pi\)
\(620\) 3.87815 0.155750
\(621\) 0 0
\(622\) 23.9420 0.959986
\(623\) 11.1337 0.446063
\(624\) 0 0
\(625\) −30.2948 −1.21179
\(626\) −31.7435 −1.26872
\(627\) 0 0
\(628\) −2.95788 −0.118032
\(629\) −37.5796 −1.49840
\(630\) 0 0
\(631\) −36.8091 −1.46535 −0.732673 0.680581i \(-0.761728\pi\)
−0.732673 + 0.680581i \(0.761728\pi\)
\(632\) −18.4915 −0.735551
\(633\) 0 0
\(634\) −7.41564 −0.294513
\(635\) 2.91159 0.115543
\(636\) 0 0
\(637\) 3.36668 0.133393
\(638\) −7.59912 −0.300852
\(639\) 0 0
\(640\) 37.2610 1.47287
\(641\) 44.7785 1.76864 0.884322 0.466878i \(-0.154621\pi\)
0.884322 + 0.466878i \(0.154621\pi\)
\(642\) 0 0
\(643\) −13.7232 −0.541191 −0.270595 0.962693i \(-0.587221\pi\)
−0.270595 + 0.962693i \(0.587221\pi\)
\(644\) 1.13515 0.0447310
\(645\) 0 0
\(646\) −1.05550 −0.0415281
\(647\) −38.4468 −1.51150 −0.755750 0.654861i \(-0.772727\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(648\) 0 0
\(649\) −49.9064 −1.95900
\(650\) 17.4306 0.683683
\(651\) 0 0
\(652\) −0.202505 −0.00793072
\(653\) 8.68324 0.339801 0.169901 0.985461i \(-0.445655\pi\)
0.169901 + 0.985461i \(0.445655\pi\)
\(654\) 0 0
\(655\) 16.8765 0.659419
\(656\) 0.215374 0.00840895
\(657\) 0 0
\(658\) 4.99369 0.194674
\(659\) 19.4390 0.757237 0.378619 0.925553i \(-0.376399\pi\)
0.378619 + 0.925553i \(0.376399\pi\)
\(660\) 0 0
\(661\) 15.8557 0.616715 0.308358 0.951270i \(-0.400221\pi\)
0.308358 + 0.951270i \(0.400221\pi\)
\(662\) −6.24464 −0.242705
\(663\) 0 0
\(664\) −35.2281 −1.36711
\(665\) 0.430400 0.0166902
\(666\) 0 0
\(667\) 6.44575 0.249580
\(668\) −3.06589 −0.118623
\(669\) 0 0
\(670\) −7.96948 −0.307888
\(671\) −45.0258 −1.73820
\(672\) 0 0
\(673\) −46.4164 −1.78922 −0.894611 0.446846i \(-0.852547\pi\)
−0.894611 + 0.446846i \(0.852547\pi\)
\(674\) 16.1073 0.620430
\(675\) 0 0
\(676\) −0.361038 −0.0138861
\(677\) −29.2402 −1.12379 −0.561896 0.827208i \(-0.689928\pi\)
−0.561896 + 0.827208i \(0.689928\pi\)
\(678\) 0 0
\(679\) −0.471210 −0.0180834
\(680\) 37.0725 1.42166
\(681\) 0 0
\(682\) −37.9321 −1.45249
\(683\) −47.5983 −1.82130 −0.910649 0.413182i \(-0.864417\pi\)
−0.910649 + 0.413182i \(0.864417\pi\)
\(684\) 0 0
\(685\) −64.4892 −2.46400
\(686\) 1.48888 0.0568459
\(687\) 0 0
\(688\) 35.8924 1.36839
\(689\) −16.5103 −0.628991
\(690\) 0 0
\(691\) 42.7666 1.62692 0.813459 0.581622i \(-0.197582\pi\)
0.813459 + 0.581622i \(0.197582\pi\)
\(692\) 0.983274 0.0373785
\(693\) 0 0
\(694\) −25.4737 −0.966967
\(695\) 47.0140 1.78334
\(696\) 0 0
\(697\) 0.235464 0.00891883
\(698\) 14.4735 0.547831
\(699\) 0 0
\(700\) 0.753813 0.0284915
\(701\) −35.1099 −1.32608 −0.663042 0.748582i \(-0.730735\pi\)
−0.663042 + 0.748582i \(0.730735\pi\)
\(702\) 0 0
\(703\) 1.15835 0.0436880
\(704\) −28.8383 −1.08688
\(705\) 0 0
\(706\) −18.7967 −0.707425
\(707\) 5.16598 0.194287
\(708\) 0 0
\(709\) 12.5880 0.472754 0.236377 0.971661i \(-0.424040\pi\)
0.236377 + 0.971661i \(0.424040\pi\)
\(710\) 42.1723 1.58270
\(711\) 0 0
\(712\) −29.5602 −1.10781
\(713\) 32.1748 1.20496
\(714\) 0 0
\(715\) −40.6441 −1.52000
\(716\) 0.0902259 0.00337190
\(717\) 0 0
\(718\) 14.1261 0.527180
\(719\) 0.862145 0.0321526 0.0160763 0.999871i \(-0.494883\pi\)
0.0160763 + 0.999871i \(0.494883\pi\)
\(720\) 0 0
\(721\) −2.38399 −0.0887843
\(722\) −28.2563 −1.05159
\(723\) 0 0
\(724\) 5.25502 0.195301
\(725\) 4.28041 0.158970
\(726\) 0 0
\(727\) 33.1990 1.23128 0.615641 0.788027i \(-0.288897\pi\)
0.615641 + 0.788027i \(0.288897\pi\)
\(728\) −8.93857 −0.331286
\(729\) 0 0
\(730\) 31.7853 1.17643
\(731\) 39.2404 1.45136
\(732\) 0 0
\(733\) −40.4452 −1.49388 −0.746939 0.664893i \(-0.768477\pi\)
−0.746939 + 0.664893i \(0.768477\pi\)
\(734\) 14.5746 0.537958
\(735\) 0 0
\(736\) −6.39403 −0.235687
\(737\) 7.62263 0.280783
\(738\) 0 0
\(739\) 5.49746 0.202227 0.101114 0.994875i \(-0.467759\pi\)
0.101114 + 0.994875i \(0.467759\pi\)
\(740\) 4.94587 0.181814
\(741\) 0 0
\(742\) −7.30152 −0.268047
\(743\) −40.3053 −1.47866 −0.739329 0.673345i \(-0.764857\pi\)
−0.739329 + 0.673345i \(0.764857\pi\)
\(744\) 0 0
\(745\) −33.2347 −1.21763
\(746\) −44.4281 −1.62663
\(747\) 0 0
\(748\) 4.31058 0.157610
\(749\) −16.9004 −0.617525
\(750\) 0 0
\(751\) 5.92678 0.216271 0.108136 0.994136i \(-0.465512\pi\)
0.108136 + 0.994136i \(0.465512\pi\)
\(752\) −14.7125 −0.536508
\(753\) 0 0
\(754\) 6.17020 0.224706
\(755\) 63.2388 2.30149
\(756\) 0 0
\(757\) 12.4772 0.453493 0.226747 0.973954i \(-0.427191\pi\)
0.226747 + 0.973954i \(0.427191\pi\)
\(758\) −28.4814 −1.03449
\(759\) 0 0
\(760\) −1.14272 −0.0414507
\(761\) 31.7213 1.14989 0.574947 0.818190i \(-0.305022\pi\)
0.574947 + 0.818190i \(0.305022\pi\)
\(762\) 0 0
\(763\) 11.0708 0.400789
\(764\) 5.77438 0.208910
\(765\) 0 0
\(766\) −14.1406 −0.510921
\(767\) 40.5221 1.46317
\(768\) 0 0
\(769\) 22.6399 0.816415 0.408207 0.912889i \(-0.366154\pi\)
0.408207 + 0.912889i \(0.366154\pi\)
\(770\) −17.9745 −0.647756
\(771\) 0 0
\(772\) −4.12957 −0.148626
\(773\) 35.4318 1.27439 0.637197 0.770701i \(-0.280094\pi\)
0.637197 + 0.770701i \(0.280094\pi\)
\(774\) 0 0
\(775\) 21.3663 0.767499
\(776\) 1.25107 0.0449107
\(777\) 0 0
\(778\) −40.8236 −1.46360
\(779\) −0.00725792 −0.000260042 0
\(780\) 0 0
\(781\) −40.3368 −1.44336
\(782\) −37.3897 −1.33705
\(783\) 0 0
\(784\) −4.38656 −0.156663
\(785\) −39.7279 −1.41795
\(786\) 0 0
\(787\) −29.1953 −1.04070 −0.520349 0.853954i \(-0.674198\pi\)
−0.520349 + 0.853954i \(0.674198\pi\)
\(788\) 1.26511 0.0450678
\(789\) 0 0
\(790\) 30.1923 1.07419
\(791\) −14.9881 −0.532917
\(792\) 0 0
\(793\) 36.5593 1.29826
\(794\) 20.2198 0.717573
\(795\) 0 0
\(796\) 4.94904 0.175414
\(797\) −23.7870 −0.842579 −0.421290 0.906926i \(-0.638422\pi\)
−0.421290 + 0.906926i \(0.638422\pi\)
\(798\) 0 0
\(799\) −16.0848 −0.569039
\(800\) −4.24607 −0.150121
\(801\) 0 0
\(802\) −18.7816 −0.663202
\(803\) −30.4019 −1.07286
\(804\) 0 0
\(805\) 15.2464 0.537364
\(806\) 30.7994 1.08486
\(807\) 0 0
\(808\) −13.7157 −0.482518
\(809\) 41.1655 1.44730 0.723652 0.690165i \(-0.242462\pi\)
0.723652 + 0.690165i \(0.242462\pi\)
\(810\) 0 0
\(811\) −16.1626 −0.567544 −0.283772 0.958892i \(-0.591586\pi\)
−0.283772 + 0.958892i \(0.591586\pi\)
\(812\) 0.266840 0.00936427
\(813\) 0 0
\(814\) −48.3754 −1.69556
\(815\) −2.71989 −0.0952736
\(816\) 0 0
\(817\) −1.20954 −0.0423165
\(818\) −0.193318 −0.00675919
\(819\) 0 0
\(820\) −0.0309895 −0.00108220
\(821\) −18.2548 −0.637097 −0.318548 0.947907i \(-0.603195\pi\)
−0.318548 + 0.947907i \(0.603195\pi\)
\(822\) 0 0
\(823\) 42.2479 1.47267 0.736334 0.676618i \(-0.236555\pi\)
0.736334 + 0.676618i \(0.236555\pi\)
\(824\) 6.32951 0.220499
\(825\) 0 0
\(826\) 17.9206 0.623536
\(827\) 46.8151 1.62792 0.813961 0.580920i \(-0.197307\pi\)
0.813961 + 0.580920i \(0.197307\pi\)
\(828\) 0 0
\(829\) −47.1289 −1.63685 −0.818426 0.574611i \(-0.805153\pi\)
−0.818426 + 0.574611i \(0.805153\pi\)
\(830\) 57.5193 1.99652
\(831\) 0 0
\(832\) 23.4156 0.811790
\(833\) −4.79573 −0.166162
\(834\) 0 0
\(835\) −41.1786 −1.42504
\(836\) −0.132869 −0.00459536
\(837\) 0 0
\(838\) −21.6521 −0.747961
\(839\) −42.7882 −1.47721 −0.738606 0.674137i \(-0.764516\pi\)
−0.738606 + 0.674137i \(0.764516\pi\)
\(840\) 0 0
\(841\) −27.4848 −0.947751
\(842\) 19.2945 0.664934
\(843\) 0 0
\(844\) −5.59304 −0.192520
\(845\) −4.84917 −0.166817
\(846\) 0 0
\(847\) 6.19220 0.212766
\(848\) 21.5118 0.738718
\(849\) 0 0
\(850\) −24.8293 −0.851638
\(851\) 41.0331 1.40660
\(852\) 0 0
\(853\) −26.0928 −0.893402 −0.446701 0.894683i \(-0.647401\pi\)
−0.446701 + 0.894683i \(0.647401\pi\)
\(854\) 16.1680 0.553259
\(855\) 0 0
\(856\) 44.8706 1.53365
\(857\) 34.3896 1.17473 0.587363 0.809324i \(-0.300166\pi\)
0.587363 + 0.809324i \(0.300166\pi\)
\(858\) 0 0
\(859\) 1.52930 0.0521790 0.0260895 0.999660i \(-0.491695\pi\)
0.0260895 + 0.999660i \(0.491695\pi\)
\(860\) −5.16444 −0.176106
\(861\) 0 0
\(862\) 38.8992 1.32491
\(863\) 37.4603 1.27516 0.637582 0.770383i \(-0.279935\pi\)
0.637582 + 0.770383i \(0.279935\pi\)
\(864\) 0 0
\(865\) 13.2066 0.449037
\(866\) 41.1125 1.39706
\(867\) 0 0
\(868\) 1.33197 0.0452100
\(869\) −28.8782 −0.979627
\(870\) 0 0
\(871\) −6.18929 −0.209716
\(872\) −29.3930 −0.995373
\(873\) 0 0
\(874\) 1.15250 0.0389838
\(875\) −4.43332 −0.149874
\(876\) 0 0
\(877\) −16.6275 −0.561470 −0.280735 0.959785i \(-0.590578\pi\)
−0.280735 + 0.959785i \(0.590578\pi\)
\(878\) 6.77643 0.228694
\(879\) 0 0
\(880\) 52.9566 1.78517
\(881\) −27.3896 −0.922780 −0.461390 0.887197i \(-0.652649\pi\)
−0.461390 + 0.887197i \(0.652649\pi\)
\(882\) 0 0
\(883\) −10.6137 −0.357179 −0.178589 0.983924i \(-0.557153\pi\)
−0.178589 + 0.983924i \(0.557153\pi\)
\(884\) −3.50003 −0.117719
\(885\) 0 0
\(886\) −3.42728 −0.115142
\(887\) −21.4033 −0.718652 −0.359326 0.933212i \(-0.616993\pi\)
−0.359326 + 0.933212i \(0.616993\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 48.2649 1.61784
\(891\) 0 0
\(892\) −1.83629 −0.0614837
\(893\) 0.495796 0.0165912
\(894\) 0 0
\(895\) 1.21184 0.0405075
\(896\) 12.7975 0.427534
\(897\) 0 0
\(898\) 38.6502 1.28977
\(899\) 7.56339 0.252253
\(900\) 0 0
\(901\) 23.5183 0.783510
\(902\) 0.303107 0.0100924
\(903\) 0 0
\(904\) 39.7937 1.32352
\(905\) 70.5812 2.34620
\(906\) 0 0
\(907\) 49.9246 1.65772 0.828859 0.559458i \(-0.188991\pi\)
0.828859 + 0.559458i \(0.188991\pi\)
\(908\) 1.73795 0.0576759
\(909\) 0 0
\(910\) 14.5946 0.483807
\(911\) 32.6343 1.08122 0.540611 0.841273i \(-0.318193\pi\)
0.540611 + 0.841273i \(0.318193\pi\)
\(912\) 0 0
\(913\) −55.0158 −1.82076
\(914\) −17.8005 −0.588787
\(915\) 0 0
\(916\) 4.39595 0.145246
\(917\) 5.79631 0.191411
\(918\) 0 0
\(919\) −38.9648 −1.28533 −0.642666 0.766147i \(-0.722172\pi\)
−0.642666 + 0.766147i \(0.722172\pi\)
\(920\) −40.4793 −1.33456
\(921\) 0 0
\(922\) 11.2506 0.370519
\(923\) 32.7520 1.07804
\(924\) 0 0
\(925\) 27.2487 0.895933
\(926\) −2.86014 −0.0939901
\(927\) 0 0
\(928\) −1.50305 −0.0493402
\(929\) −33.5112 −1.09947 −0.549734 0.835340i \(-0.685271\pi\)
−0.549734 + 0.835340i \(0.685271\pi\)
\(930\) 0 0
\(931\) 0.147823 0.00484471
\(932\) 1.45942 0.0478048
\(933\) 0 0
\(934\) 2.31547 0.0757646
\(935\) 57.8963 1.89341
\(936\) 0 0
\(937\) 33.7304 1.10193 0.550963 0.834530i \(-0.314261\pi\)
0.550963 + 0.834530i \(0.314261\pi\)
\(938\) −2.73716 −0.0893714
\(939\) 0 0
\(940\) 2.11693 0.0690465
\(941\) −25.1685 −0.820469 −0.410235 0.911980i \(-0.634553\pi\)
−0.410235 + 0.911980i \(0.634553\pi\)
\(942\) 0 0
\(943\) −0.257102 −0.00837240
\(944\) −52.7977 −1.71842
\(945\) 0 0
\(946\) 50.5132 1.64233
\(947\) 3.93697 0.127934 0.0639672 0.997952i \(-0.479625\pi\)
0.0639672 + 0.997952i \(0.479625\pi\)
\(948\) 0 0
\(949\) 24.6852 0.801316
\(950\) 0.765336 0.0248308
\(951\) 0 0
\(952\) 12.7327 0.412670
\(953\) −53.3391 −1.72782 −0.863911 0.503645i \(-0.831992\pi\)
−0.863911 + 0.503645i \(0.831992\pi\)
\(954\) 0 0
\(955\) 77.5569 2.50968
\(956\) −2.97008 −0.0960593
\(957\) 0 0
\(958\) −5.65288 −0.182636
\(959\) −22.1491 −0.715233
\(960\) 0 0
\(961\) 6.75371 0.217862
\(962\) 39.2790 1.26641
\(963\) 0 0
\(964\) 1.40529 0.0452612
\(965\) −55.4651 −1.78548
\(966\) 0 0
\(967\) −34.1465 −1.09808 −0.549038 0.835797i \(-0.685006\pi\)
−0.549038 + 0.835797i \(0.685006\pi\)
\(968\) −16.4404 −0.528413
\(969\) 0 0
\(970\) −2.04270 −0.0655873
\(971\) 30.5079 0.979045 0.489522 0.871991i \(-0.337171\pi\)
0.489522 + 0.871991i \(0.337171\pi\)
\(972\) 0 0
\(973\) 16.1472 0.517655
\(974\) 63.8314 2.04529
\(975\) 0 0
\(976\) −47.6344 −1.52474
\(977\) 16.3516 0.523135 0.261568 0.965185i \(-0.415761\pi\)
0.261568 + 0.965185i \(0.415761\pi\)
\(978\) 0 0
\(979\) −46.1643 −1.47542
\(980\) 0.631168 0.0201619
\(981\) 0 0
\(982\) 33.3140 1.06309
\(983\) −41.7219 −1.33072 −0.665360 0.746522i \(-0.731722\pi\)
−0.665360 + 0.746522i \(0.731722\pi\)
\(984\) 0 0
\(985\) 16.9920 0.541410
\(986\) −8.78926 −0.279907
\(987\) 0 0
\(988\) 0.107885 0.00343226
\(989\) −42.8464 −1.36244
\(990\) 0 0
\(991\) −46.3370 −1.47194 −0.735972 0.677012i \(-0.763275\pi\)
−0.735972 + 0.677012i \(0.763275\pi\)
\(992\) −7.50270 −0.238211
\(993\) 0 0
\(994\) 14.4843 0.459414
\(995\) 66.4715 2.10729
\(996\) 0 0
\(997\) 45.1748 1.43070 0.715350 0.698766i \(-0.246267\pi\)
0.715350 + 0.698766i \(0.246267\pi\)
\(998\) −8.83113 −0.279545
\(999\) 0 0
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 \(a_p\))