Properties

Label 3549.2.a.bf.1.2
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.60159\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.60159 q^{2} -1.00000 q^{3} +0.565099 q^{4} -2.27787 q^{5} +1.60159 q^{6} -1.00000 q^{7} +2.29813 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.60159 q^{2} -1.00000 q^{3} +0.565099 q^{4} -2.27787 q^{5} +1.60159 q^{6} -1.00000 q^{7} +2.29813 q^{8} +1.00000 q^{9} +3.64823 q^{10} -2.53947 q^{11} -0.565099 q^{12} +1.60159 q^{14} +2.27787 q^{15} -4.81086 q^{16} -4.05395 q^{17} -1.60159 q^{18} -7.93457 q^{19} -1.28722 q^{20} +1.00000 q^{21} +4.06719 q^{22} +0.458029 q^{23} -2.29813 q^{24} +0.188713 q^{25} -1.00000 q^{27} -0.565099 q^{28} +6.01106 q^{29} -3.64823 q^{30} +0.340678 q^{31} +3.10879 q^{32} +2.53947 q^{33} +6.49278 q^{34} +2.27787 q^{35} +0.565099 q^{36} -4.74702 q^{37} +12.7080 q^{38} -5.23485 q^{40} -8.88028 q^{41} -1.60159 q^{42} -2.14282 q^{43} -1.43505 q^{44} -2.27787 q^{45} -0.733576 q^{46} +7.16883 q^{47} +4.81086 q^{48} +1.00000 q^{49} -0.302241 q^{50} +4.05395 q^{51} +3.30421 q^{53} +1.60159 q^{54} +5.78459 q^{55} -2.29813 q^{56} +7.93457 q^{57} -9.62727 q^{58} -4.30373 q^{59} +1.28722 q^{60} -11.4865 q^{61} -0.545627 q^{62} -1.00000 q^{63} +4.64271 q^{64} -4.06719 q^{66} -10.4979 q^{67} -2.29088 q^{68} -0.458029 q^{69} -3.64823 q^{70} -4.25291 q^{71} +2.29813 q^{72} -1.59136 q^{73} +7.60279 q^{74} -0.188713 q^{75} -4.48382 q^{76} +2.53947 q^{77} -9.42077 q^{79} +10.9585 q^{80} +1.00000 q^{81} +14.2226 q^{82} -1.87743 q^{83} +0.565099 q^{84} +9.23439 q^{85} +3.43193 q^{86} -6.01106 q^{87} -5.83602 q^{88} -17.9934 q^{89} +3.64823 q^{90} +0.258832 q^{92} -0.340678 q^{93} -11.4815 q^{94} +18.0740 q^{95} -3.10879 q^{96} -18.9563 q^{97} -1.60159 q^{98} -2.53947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60159 −1.13250 −0.566248 0.824235i \(-0.691606\pi\)
−0.566248 + 0.824235i \(0.691606\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.565099 0.282549
\(5\) −2.27787 −1.01870 −0.509348 0.860560i \(-0.670113\pi\)
−0.509348 + 0.860560i \(0.670113\pi\)
\(6\) 1.60159 0.653847
\(7\) −1.00000 −0.377964
\(8\) 2.29813 0.812511
\(9\) 1.00000 0.333333
\(10\) 3.64823 1.15367
\(11\) −2.53947 −0.765678 −0.382839 0.923815i \(-0.625054\pi\)
−0.382839 + 0.923815i \(0.625054\pi\)
\(12\) −0.565099 −0.163130
\(13\) 0 0
\(14\) 1.60159 0.428044
\(15\) 2.27787 0.588145
\(16\) −4.81086 −1.20272
\(17\) −4.05395 −0.983228 −0.491614 0.870813i \(-0.663593\pi\)
−0.491614 + 0.870813i \(0.663593\pi\)
\(18\) −1.60159 −0.377499
\(19\) −7.93457 −1.82032 −0.910158 0.414261i \(-0.864040\pi\)
−0.910158 + 0.414261i \(0.864040\pi\)
\(20\) −1.28722 −0.287832
\(21\) 1.00000 0.218218
\(22\) 4.06719 0.867128
\(23\) 0.458029 0.0955057 0.0477529 0.998859i \(-0.484794\pi\)
0.0477529 + 0.998859i \(0.484794\pi\)
\(24\) −2.29813 −0.469103
\(25\) 0.188713 0.0377425
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −0.565099 −0.106794
\(29\) 6.01106 1.11623 0.558113 0.829765i \(-0.311526\pi\)
0.558113 + 0.829765i \(0.311526\pi\)
\(30\) −3.64823 −0.666072
\(31\) 0.340678 0.0611875 0.0305938 0.999532i \(-0.490260\pi\)
0.0305938 + 0.999532i \(0.490260\pi\)
\(32\) 3.10879 0.549561
\(33\) 2.53947 0.442064
\(34\) 6.49278 1.11350
\(35\) 2.27787 0.385031
\(36\) 0.565099 0.0941831
\(37\) −4.74702 −0.780405 −0.390202 0.920729i \(-0.627595\pi\)
−0.390202 + 0.920729i \(0.627595\pi\)
\(38\) 12.7080 2.06150
\(39\) 0 0
\(40\) −5.23485 −0.827702
\(41\) −8.88028 −1.38687 −0.693433 0.720521i \(-0.743903\pi\)
−0.693433 + 0.720521i \(0.743903\pi\)
\(42\) −1.60159 −0.247131
\(43\) −2.14282 −0.326777 −0.163389 0.986562i \(-0.552242\pi\)
−0.163389 + 0.986562i \(0.552242\pi\)
\(44\) −1.43505 −0.216342
\(45\) −2.27787 −0.339565
\(46\) −0.733576 −0.108160
\(47\) 7.16883 1.04568 0.522841 0.852430i \(-0.324872\pi\)
0.522841 + 0.852430i \(0.324872\pi\)
\(48\) 4.81086 0.694388
\(49\) 1.00000 0.142857
\(50\) −0.302241 −0.0427433
\(51\) 4.05395 0.567667
\(52\) 0 0
\(53\) 3.30421 0.453868 0.226934 0.973910i \(-0.427130\pi\)
0.226934 + 0.973910i \(0.427130\pi\)
\(54\) 1.60159 0.217949
\(55\) 5.78459 0.779993
\(56\) −2.29813 −0.307100
\(57\) 7.93457 1.05096
\(58\) −9.62727 −1.26412
\(59\) −4.30373 −0.560298 −0.280149 0.959957i \(-0.590384\pi\)
−0.280149 + 0.959957i \(0.590384\pi\)
\(60\) 1.28722 0.166180
\(61\) −11.4865 −1.47069 −0.735347 0.677691i \(-0.762981\pi\)
−0.735347 + 0.677691i \(0.762981\pi\)
\(62\) −0.545627 −0.0692947
\(63\) −1.00000 −0.125988
\(64\) 4.64271 0.580339
\(65\) 0 0
\(66\) −4.06719 −0.500637
\(67\) −10.4979 −1.28252 −0.641258 0.767325i \(-0.721587\pi\)
−0.641258 + 0.767325i \(0.721587\pi\)
\(68\) −2.29088 −0.277810
\(69\) −0.458029 −0.0551402
\(70\) −3.64823 −0.436047
\(71\) −4.25291 −0.504727 −0.252364 0.967633i \(-0.581208\pi\)
−0.252364 + 0.967633i \(0.581208\pi\)
\(72\) 2.29813 0.270837
\(73\) −1.59136 −0.186255 −0.0931273 0.995654i \(-0.529686\pi\)
−0.0931273 + 0.995654i \(0.529686\pi\)
\(74\) 7.60279 0.883806
\(75\) −0.188713 −0.0217907
\(76\) −4.48382 −0.514329
\(77\) 2.53947 0.289399
\(78\) 0 0
\(79\) −9.42077 −1.05992 −0.529960 0.848023i \(-0.677793\pi\)
−0.529960 + 0.848023i \(0.677793\pi\)
\(80\) 10.9585 1.22520
\(81\) 1.00000 0.111111
\(82\) 14.2226 1.57062
\(83\) −1.87743 −0.206074 −0.103037 0.994678i \(-0.532856\pi\)
−0.103037 + 0.994678i \(0.532856\pi\)
\(84\) 0.565099 0.0616573
\(85\) 9.23439 1.00161
\(86\) 3.43193 0.370074
\(87\) −6.01106 −0.644453
\(88\) −5.83602 −0.622121
\(89\) −17.9934 −1.90730 −0.953648 0.300923i \(-0.902705\pi\)
−0.953648 + 0.300923i \(0.902705\pi\)
\(90\) 3.64823 0.384557
\(91\) 0 0
\(92\) 0.258832 0.0269851
\(93\) −0.340678 −0.0353266
\(94\) −11.4815 −1.18423
\(95\) 18.0740 1.85435
\(96\) −3.10879 −0.317289
\(97\) −18.9563 −1.92472 −0.962359 0.271780i \(-0.912388\pi\)
−0.962359 + 0.271780i \(0.912388\pi\)
\(98\) −1.60159 −0.161785
\(99\) −2.53947 −0.255226
\(100\) 0.106641 0.0106641
\(101\) −4.02671 −0.400672 −0.200336 0.979727i \(-0.564203\pi\)
−0.200336 + 0.979727i \(0.564203\pi\)
\(102\) −6.49278 −0.642881
\(103\) −11.3431 −1.11767 −0.558835 0.829279i \(-0.688751\pi\)
−0.558835 + 0.829279i \(0.688751\pi\)
\(104\) 0 0
\(105\) −2.27787 −0.222298
\(106\) −5.29200 −0.514004
\(107\) −15.8563 −1.53289 −0.766444 0.642311i \(-0.777976\pi\)
−0.766444 + 0.642311i \(0.777976\pi\)
\(108\) −0.565099 −0.0543767
\(109\) −13.1406 −1.25864 −0.629320 0.777146i \(-0.716666\pi\)
−0.629320 + 0.777146i \(0.716666\pi\)
\(110\) −9.26455 −0.883340
\(111\) 4.74702 0.450567
\(112\) 4.81086 0.454584
\(113\) 0.392747 0.0369465 0.0184733 0.999829i \(-0.494119\pi\)
0.0184733 + 0.999829i \(0.494119\pi\)
\(114\) −12.7080 −1.19021
\(115\) −1.04333 −0.0972913
\(116\) 3.39684 0.315389
\(117\) 0 0
\(118\) 6.89282 0.634535
\(119\) 4.05395 0.371625
\(120\) 5.23485 0.477874
\(121\) −4.55111 −0.413737
\(122\) 18.3967 1.66556
\(123\) 8.88028 0.800708
\(124\) 0.192517 0.0172885
\(125\) 10.9595 0.980248
\(126\) 1.60159 0.142681
\(127\) 15.9958 1.41940 0.709701 0.704503i \(-0.248830\pi\)
0.709701 + 0.704503i \(0.248830\pi\)
\(128\) −13.6533 −1.20679
\(129\) 2.14282 0.188665
\(130\) 0 0
\(131\) 16.6090 1.45113 0.725567 0.688151i \(-0.241577\pi\)
0.725567 + 0.688151i \(0.241577\pi\)
\(132\) 1.43505 0.124905
\(133\) 7.93457 0.688015
\(134\) 16.8133 1.45245
\(135\) 2.27787 0.196048
\(136\) −9.31650 −0.798883
\(137\) 1.57748 0.134773 0.0673865 0.997727i \(-0.478534\pi\)
0.0673865 + 0.997727i \(0.478534\pi\)
\(138\) 0.733576 0.0624462
\(139\) 12.0257 1.02000 0.510001 0.860174i \(-0.329645\pi\)
0.510001 + 0.860174i \(0.329645\pi\)
\(140\) 1.28722 0.108790
\(141\) −7.16883 −0.603724
\(142\) 6.81142 0.571602
\(143\) 0 0
\(144\) −4.81086 −0.400905
\(145\) −13.6924 −1.13710
\(146\) 2.54871 0.210933
\(147\) −1.00000 −0.0824786
\(148\) −2.68253 −0.220503
\(149\) 24.1801 1.98091 0.990456 0.137827i \(-0.0440120\pi\)
0.990456 + 0.137827i \(0.0440120\pi\)
\(150\) 0.302241 0.0246779
\(151\) 8.98472 0.731167 0.365583 0.930779i \(-0.380870\pi\)
0.365583 + 0.930779i \(0.380870\pi\)
\(152\) −18.2347 −1.47903
\(153\) −4.05395 −0.327743
\(154\) −4.06719 −0.327744
\(155\) −0.776021 −0.0623315
\(156\) 0 0
\(157\) −2.71212 −0.216451 −0.108225 0.994126i \(-0.534517\pi\)
−0.108225 + 0.994126i \(0.534517\pi\)
\(158\) 15.0882 1.20036
\(159\) −3.30421 −0.262041
\(160\) −7.08142 −0.559836
\(161\) −0.458029 −0.0360978
\(162\) −1.60159 −0.125833
\(163\) 17.3562 1.35944 0.679722 0.733470i \(-0.262101\pi\)
0.679722 + 0.733470i \(0.262101\pi\)
\(164\) −5.01823 −0.391858
\(165\) −5.78459 −0.450329
\(166\) 3.00687 0.233379
\(167\) −12.7077 −0.983349 −0.491674 0.870779i \(-0.663615\pi\)
−0.491674 + 0.870779i \(0.663615\pi\)
\(168\) 2.29813 0.177304
\(169\) 0 0
\(170\) −14.7897 −1.13432
\(171\) −7.93457 −0.606772
\(172\) −1.21091 −0.0923307
\(173\) 1.35443 0.102975 0.0514876 0.998674i \(-0.483604\pi\)
0.0514876 + 0.998674i \(0.483604\pi\)
\(174\) 9.62727 0.729842
\(175\) −0.188713 −0.0142653
\(176\) 12.2170 0.920892
\(177\) 4.30373 0.323488
\(178\) 28.8181 2.16001
\(179\) 21.0691 1.57478 0.787390 0.616456i \(-0.211432\pi\)
0.787390 + 0.616456i \(0.211432\pi\)
\(180\) −1.28722 −0.0959440
\(181\) −0.269780 −0.0200526 −0.0100263 0.999950i \(-0.503192\pi\)
−0.0100263 + 0.999950i \(0.503192\pi\)
\(182\) 0 0
\(183\) 11.4865 0.849106
\(184\) 1.05261 0.0775994
\(185\) 10.8131 0.794995
\(186\) 0.545627 0.0400073
\(187\) 10.2949 0.752836
\(188\) 4.05110 0.295457
\(189\) 1.00000 0.0727393
\(190\) −28.9471 −2.10005
\(191\) −6.28281 −0.454608 −0.227304 0.973824i \(-0.572991\pi\)
−0.227304 + 0.973824i \(0.572991\pi\)
\(192\) −4.64271 −0.335059
\(193\) −19.3154 −1.39035 −0.695177 0.718839i \(-0.744674\pi\)
−0.695177 + 0.718839i \(0.744674\pi\)
\(194\) 30.3602 2.17974
\(195\) 0 0
\(196\) 0.565099 0.0403642
\(197\) 21.0050 1.49654 0.748272 0.663392i \(-0.230884\pi\)
0.748272 + 0.663392i \(0.230884\pi\)
\(198\) 4.06719 0.289043
\(199\) 17.0312 1.20731 0.603653 0.797247i \(-0.293711\pi\)
0.603653 + 0.797247i \(0.293711\pi\)
\(200\) 0.433686 0.0306662
\(201\) 10.4979 0.740461
\(202\) 6.44914 0.453760
\(203\) −6.01106 −0.421894
\(204\) 2.29088 0.160394
\(205\) 20.2282 1.41280
\(206\) 18.1670 1.26576
\(207\) 0.458029 0.0318352
\(208\) 0 0
\(209\) 20.1496 1.39378
\(210\) 3.64823 0.251752
\(211\) −10.0436 −0.691428 −0.345714 0.938340i \(-0.612363\pi\)
−0.345714 + 0.938340i \(0.612363\pi\)
\(212\) 1.86721 0.128240
\(213\) 4.25291 0.291404
\(214\) 25.3954 1.73599
\(215\) 4.88108 0.332887
\(216\) −2.29813 −0.156368
\(217\) −0.340678 −0.0231267
\(218\) 21.0459 1.42541
\(219\) 1.59136 0.107534
\(220\) 3.26886 0.220387
\(221\) 0 0
\(222\) −7.60279 −0.510266
\(223\) −1.30689 −0.0875156 −0.0437578 0.999042i \(-0.513933\pi\)
−0.0437578 + 0.999042i \(0.513933\pi\)
\(224\) −3.10879 −0.207714
\(225\) 0.188713 0.0125808
\(226\) −0.629020 −0.0418418
\(227\) −7.31823 −0.485728 −0.242864 0.970060i \(-0.578087\pi\)
−0.242864 + 0.970060i \(0.578087\pi\)
\(228\) 4.48382 0.296948
\(229\) 16.5282 1.09221 0.546107 0.837715i \(-0.316109\pi\)
0.546107 + 0.837715i \(0.316109\pi\)
\(230\) 1.67099 0.110182
\(231\) −2.53947 −0.167085
\(232\) 13.8142 0.906946
\(233\) 5.48450 0.359302 0.179651 0.983730i \(-0.442503\pi\)
0.179651 + 0.983730i \(0.442503\pi\)
\(234\) 0 0
\(235\) −16.3297 −1.06523
\(236\) −2.43203 −0.158312
\(237\) 9.42077 0.611945
\(238\) −6.49278 −0.420864
\(239\) −17.8572 −1.15509 −0.577543 0.816360i \(-0.695988\pi\)
−0.577543 + 0.816360i \(0.695988\pi\)
\(240\) −10.9585 −0.707371
\(241\) −23.1081 −1.48852 −0.744262 0.667887i \(-0.767199\pi\)
−0.744262 + 0.667887i \(0.767199\pi\)
\(242\) 7.28903 0.468556
\(243\) −1.00000 −0.0641500
\(244\) −6.49100 −0.415544
\(245\) −2.27787 −0.145528
\(246\) −14.2226 −0.906799
\(247\) 0 0
\(248\) 0.782921 0.0497155
\(249\) 1.87743 0.118977
\(250\) −17.5527 −1.11013
\(251\) 11.7442 0.741290 0.370645 0.928775i \(-0.379137\pi\)
0.370645 + 0.928775i \(0.379137\pi\)
\(252\) −0.565099 −0.0355979
\(253\) −1.16315 −0.0731266
\(254\) −25.6188 −1.60747
\(255\) −9.23439 −0.578280
\(256\) 12.5816 0.786350
\(257\) −9.53811 −0.594971 −0.297486 0.954726i \(-0.596148\pi\)
−0.297486 + 0.954726i \(0.596148\pi\)
\(258\) −3.43193 −0.213662
\(259\) 4.74702 0.294965
\(260\) 0 0
\(261\) 6.01106 0.372075
\(262\) −26.6008 −1.64341
\(263\) −5.26624 −0.324730 −0.162365 0.986731i \(-0.551912\pi\)
−0.162365 + 0.986731i \(0.551912\pi\)
\(264\) 5.83602 0.359182
\(265\) −7.52658 −0.462354
\(266\) −12.7080 −0.779175
\(267\) 17.9934 1.10118
\(268\) −5.93232 −0.362374
\(269\) 0.602644 0.0367438 0.0183719 0.999831i \(-0.494152\pi\)
0.0183719 + 0.999831i \(0.494152\pi\)
\(270\) −3.64823 −0.222024
\(271\) 5.69585 0.345998 0.172999 0.984922i \(-0.444654\pi\)
0.172999 + 0.984922i \(0.444654\pi\)
\(272\) 19.5030 1.18254
\(273\) 0 0
\(274\) −2.52648 −0.152630
\(275\) −0.479229 −0.0288986
\(276\) −0.258832 −0.0155798
\(277\) −8.00692 −0.481089 −0.240545 0.970638i \(-0.577326\pi\)
−0.240545 + 0.970638i \(0.577326\pi\)
\(278\) −19.2602 −1.15515
\(279\) 0.340678 0.0203958
\(280\) 5.23485 0.312842
\(281\) 3.01814 0.180047 0.0900236 0.995940i \(-0.471306\pi\)
0.0900236 + 0.995940i \(0.471306\pi\)
\(282\) 11.4815 0.683716
\(283\) 8.91703 0.530062 0.265031 0.964240i \(-0.414618\pi\)
0.265031 + 0.964240i \(0.414618\pi\)
\(284\) −2.40331 −0.142610
\(285\) −18.0740 −1.07061
\(286\) 0 0
\(287\) 8.88028 0.524186
\(288\) 3.10879 0.183187
\(289\) −0.565477 −0.0332633
\(290\) 21.9297 1.28776
\(291\) 18.9563 1.11124
\(292\) −0.899276 −0.0526261
\(293\) 5.32016 0.310807 0.155403 0.987851i \(-0.450332\pi\)
0.155403 + 0.987851i \(0.450332\pi\)
\(294\) 1.60159 0.0934068
\(295\) 9.80335 0.570773
\(296\) −10.9092 −0.634087
\(297\) 2.53947 0.147355
\(298\) −38.7267 −2.24338
\(299\) 0 0
\(300\) −0.106641 −0.00615694
\(301\) 2.14282 0.123510
\(302\) −14.3899 −0.828044
\(303\) 4.02671 0.231328
\(304\) 38.1721 2.18932
\(305\) 26.1648 1.49819
\(306\) 6.49278 0.371167
\(307\) 3.65245 0.208457 0.104228 0.994553i \(-0.466763\pi\)
0.104228 + 0.994553i \(0.466763\pi\)
\(308\) 1.43505 0.0817695
\(309\) 11.3431 0.645287
\(310\) 1.24287 0.0705903
\(311\) 4.97775 0.282262 0.141131 0.989991i \(-0.454926\pi\)
0.141131 + 0.989991i \(0.454926\pi\)
\(312\) 0 0
\(313\) −30.8020 −1.74103 −0.870516 0.492140i \(-0.836215\pi\)
−0.870516 + 0.492140i \(0.836215\pi\)
\(314\) 4.34371 0.245130
\(315\) 2.27787 0.128344
\(316\) −5.32367 −0.299480
\(317\) 22.5252 1.26514 0.632570 0.774503i \(-0.282000\pi\)
0.632570 + 0.774503i \(0.282000\pi\)
\(318\) 5.29200 0.296761
\(319\) −15.2649 −0.854670
\(320\) −10.5755 −0.591190
\(321\) 15.8563 0.885013
\(322\) 0.733576 0.0408806
\(323\) 32.1664 1.78979
\(324\) 0.565099 0.0313944
\(325\) 0 0
\(326\) −27.7976 −1.53957
\(327\) 13.1406 0.726676
\(328\) −20.4080 −1.12684
\(329\) −7.16883 −0.395230
\(330\) 9.26455 0.509997
\(331\) −4.73222 −0.260106 −0.130053 0.991507i \(-0.541515\pi\)
−0.130053 + 0.991507i \(0.541515\pi\)
\(332\) −1.06093 −0.0582262
\(333\) −4.74702 −0.260135
\(334\) 20.3525 1.11364
\(335\) 23.9128 1.30650
\(336\) −4.81086 −0.262454
\(337\) −27.2574 −1.48480 −0.742402 0.669955i \(-0.766313\pi\)
−0.742402 + 0.669955i \(0.766313\pi\)
\(338\) 0 0
\(339\) −0.392747 −0.0213311
\(340\) 5.21834 0.283004
\(341\) −0.865140 −0.0468499
\(342\) 12.7080 0.687168
\(343\) −1.00000 −0.0539949
\(344\) −4.92447 −0.265510
\(345\) 1.04333 0.0561712
\(346\) −2.16924 −0.116619
\(347\) −34.5372 −1.85406 −0.927028 0.374993i \(-0.877645\pi\)
−0.927028 + 0.374993i \(0.877645\pi\)
\(348\) −3.39684 −0.182090
\(349\) 25.5552 1.36794 0.683969 0.729511i \(-0.260252\pi\)
0.683969 + 0.729511i \(0.260252\pi\)
\(350\) 0.302241 0.0161554
\(351\) 0 0
\(352\) −7.89465 −0.420787
\(353\) 26.8466 1.42890 0.714450 0.699686i \(-0.246677\pi\)
0.714450 + 0.699686i \(0.246677\pi\)
\(354\) −6.89282 −0.366349
\(355\) 9.68759 0.514164
\(356\) −10.1680 −0.538906
\(357\) −4.05395 −0.214558
\(358\) −33.7441 −1.78343
\(359\) 23.6724 1.24938 0.624690 0.780873i \(-0.285225\pi\)
0.624690 + 0.780873i \(0.285225\pi\)
\(360\) −5.23485 −0.275901
\(361\) 43.9575 2.31355
\(362\) 0.432077 0.0227095
\(363\) 4.55111 0.238871
\(364\) 0 0
\(365\) 3.62492 0.189737
\(366\) −18.3967 −0.961610
\(367\) 11.5392 0.602341 0.301171 0.953570i \(-0.402623\pi\)
0.301171 + 0.953570i \(0.402623\pi\)
\(368\) −2.20352 −0.114866
\(369\) −8.88028 −0.462289
\(370\) −17.3182 −0.900330
\(371\) −3.30421 −0.171546
\(372\) −0.192517 −0.00998152
\(373\) 1.52172 0.0787916 0.0393958 0.999224i \(-0.487457\pi\)
0.0393958 + 0.999224i \(0.487457\pi\)
\(374\) −16.4882 −0.852584
\(375\) −10.9595 −0.565947
\(376\) 16.4749 0.849627
\(377\) 0 0
\(378\) −1.60159 −0.0823770
\(379\) 34.4586 1.77002 0.885010 0.465571i \(-0.154151\pi\)
0.885010 + 0.465571i \(0.154151\pi\)
\(380\) 10.2136 0.523945
\(381\) −15.9958 −0.819492
\(382\) 10.0625 0.514842
\(383\) 3.91678 0.200138 0.100069 0.994980i \(-0.468094\pi\)
0.100069 + 0.994980i \(0.468094\pi\)
\(384\) 13.6533 0.696742
\(385\) −5.78459 −0.294810
\(386\) 30.9354 1.57457
\(387\) −2.14282 −0.108926
\(388\) −10.7122 −0.543828
\(389\) −31.0836 −1.57600 −0.788002 0.615673i \(-0.788884\pi\)
−0.788002 + 0.615673i \(0.788884\pi\)
\(390\) 0 0
\(391\) −1.85683 −0.0939039
\(392\) 2.29813 0.116073
\(393\) −16.6090 −0.837813
\(394\) −33.6414 −1.69483
\(395\) 21.4593 1.07974
\(396\) −1.43505 −0.0721139
\(397\) 9.75019 0.489348 0.244674 0.969605i \(-0.421319\pi\)
0.244674 + 0.969605i \(0.421319\pi\)
\(398\) −27.2770 −1.36727
\(399\) −7.93457 −0.397226
\(400\) −0.907870 −0.0453935
\(401\) 2.38904 0.119303 0.0596515 0.998219i \(-0.481001\pi\)
0.0596515 + 0.998219i \(0.481001\pi\)
\(402\) −16.8133 −0.838570
\(403\) 0 0
\(404\) −2.27549 −0.113210
\(405\) −2.27787 −0.113188
\(406\) 9.62727 0.477793
\(407\) 12.0549 0.597539
\(408\) 9.31650 0.461235
\(409\) −19.0527 −0.942094 −0.471047 0.882108i \(-0.656124\pi\)
−0.471047 + 0.882108i \(0.656124\pi\)
\(410\) −32.3973 −1.59999
\(411\) −1.57748 −0.0778113
\(412\) −6.40997 −0.315797
\(413\) 4.30373 0.211773
\(414\) −0.733576 −0.0360533
\(415\) 4.27654 0.209927
\(416\) 0 0
\(417\) −12.0257 −0.588899
\(418\) −32.2714 −1.57845
\(419\) 19.6916 0.961998 0.480999 0.876721i \(-0.340274\pi\)
0.480999 + 0.876721i \(0.340274\pi\)
\(420\) −1.28722 −0.0628101
\(421\) 25.2278 1.22953 0.614765 0.788711i \(-0.289251\pi\)
0.614765 + 0.788711i \(0.289251\pi\)
\(422\) 16.0857 0.783040
\(423\) 7.16883 0.348560
\(424\) 7.59350 0.368773
\(425\) −0.765032 −0.0371095
\(426\) −6.81142 −0.330014
\(427\) 11.4865 0.555870
\(428\) −8.96038 −0.433117
\(429\) 0 0
\(430\) −7.81750 −0.376993
\(431\) −7.87972 −0.379553 −0.189776 0.981827i \(-0.560776\pi\)
−0.189776 + 0.981827i \(0.560776\pi\)
\(432\) 4.81086 0.231463
\(433\) −24.8346 −1.19348 −0.596738 0.802436i \(-0.703537\pi\)
−0.596738 + 0.802436i \(0.703537\pi\)
\(434\) 0.545627 0.0261909
\(435\) 13.6924 0.656502
\(436\) −7.42573 −0.355628
\(437\) −3.63427 −0.173851
\(438\) −2.54871 −0.121782
\(439\) −19.0971 −0.911457 −0.455728 0.890119i \(-0.650621\pi\)
−0.455728 + 0.890119i \(0.650621\pi\)
\(440\) 13.2937 0.633753
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 39.1199 1.85864 0.929320 0.369275i \(-0.120394\pi\)
0.929320 + 0.369275i \(0.120394\pi\)
\(444\) 2.68253 0.127307
\(445\) 40.9867 1.94296
\(446\) 2.09310 0.0991112
\(447\) −24.1801 −1.14368
\(448\) −4.64271 −0.219348
\(449\) −2.38383 −0.112500 −0.0562500 0.998417i \(-0.517914\pi\)
−0.0562500 + 0.998417i \(0.517914\pi\)
\(450\) −0.302241 −0.0142478
\(451\) 22.5512 1.06189
\(452\) 0.221941 0.0104392
\(453\) −8.98472 −0.422139
\(454\) 11.7208 0.550085
\(455\) 0 0
\(456\) 18.2347 0.853916
\(457\) 14.9656 0.700061 0.350031 0.936738i \(-0.386171\pi\)
0.350031 + 0.936738i \(0.386171\pi\)
\(458\) −26.4714 −1.23693
\(459\) 4.05395 0.189222
\(460\) −0.589586 −0.0274896
\(461\) −33.0078 −1.53733 −0.768664 0.639653i \(-0.779078\pi\)
−0.768664 + 0.639653i \(0.779078\pi\)
\(462\) 4.06719 0.189223
\(463\) −34.2144 −1.59008 −0.795039 0.606559i \(-0.792550\pi\)
−0.795039 + 0.606559i \(0.792550\pi\)
\(464\) −28.9184 −1.34250
\(465\) 0.776021 0.0359871
\(466\) −8.78393 −0.406908
\(467\) −25.2750 −1.16959 −0.584795 0.811181i \(-0.698825\pi\)
−0.584795 + 0.811181i \(0.698825\pi\)
\(468\) 0 0
\(469\) 10.4979 0.484746
\(470\) 26.1535 1.20637
\(471\) 2.71212 0.124968
\(472\) −9.89051 −0.455248
\(473\) 5.44162 0.250206
\(474\) −15.0882 −0.693026
\(475\) −1.49735 −0.0687033
\(476\) 2.29088 0.105002
\(477\) 3.30421 0.151289
\(478\) 28.5999 1.30813
\(479\) 37.4251 1.70999 0.854997 0.518633i \(-0.173559\pi\)
0.854997 + 0.518633i \(0.173559\pi\)
\(480\) 7.08142 0.323221
\(481\) 0 0
\(482\) 37.0098 1.68575
\(483\) 0.458029 0.0208411
\(484\) −2.57183 −0.116901
\(485\) 43.1800 1.96070
\(486\) 1.60159 0.0726497
\(487\) 30.3596 1.37572 0.687862 0.725842i \(-0.258549\pi\)
0.687862 + 0.725842i \(0.258549\pi\)
\(488\) −26.3974 −1.19495
\(489\) −17.3562 −0.784875
\(490\) 3.64823 0.164810
\(491\) −5.62758 −0.253969 −0.126984 0.991905i \(-0.540530\pi\)
−0.126984 + 0.991905i \(0.540530\pi\)
\(492\) 5.01823 0.226239
\(493\) −24.3686 −1.09750
\(494\) 0 0
\(495\) 5.78459 0.259998
\(496\) −1.63895 −0.0735912
\(497\) 4.25291 0.190769
\(498\) −3.00687 −0.134741
\(499\) −34.1534 −1.52892 −0.764459 0.644673i \(-0.776994\pi\)
−0.764459 + 0.644673i \(0.776994\pi\)
\(500\) 6.19321 0.276969
\(501\) 12.7077 0.567737
\(502\) −18.8095 −0.839509
\(503\) 10.4426 0.465612 0.232806 0.972523i \(-0.425209\pi\)
0.232806 + 0.972523i \(0.425209\pi\)
\(504\) −2.29813 −0.102367
\(505\) 9.17233 0.408163
\(506\) 1.86289 0.0828157
\(507\) 0 0
\(508\) 9.03923 0.401051
\(509\) −18.2623 −0.809463 −0.404732 0.914436i \(-0.632635\pi\)
−0.404732 + 0.914436i \(0.632635\pi\)
\(510\) 14.7897 0.654901
\(511\) 1.59136 0.0703976
\(512\) 7.15601 0.316254
\(513\) 7.93457 0.350320
\(514\) 15.2762 0.673803
\(515\) 25.8382 1.13857
\(516\) 1.21091 0.0533071
\(517\) −18.2050 −0.800655
\(518\) −7.60279 −0.334047
\(519\) −1.35443 −0.0594527
\(520\) 0 0
\(521\) 34.9086 1.52937 0.764687 0.644401i \(-0.222893\pi\)
0.764687 + 0.644401i \(0.222893\pi\)
\(522\) −9.62727 −0.421374
\(523\) −4.61292 −0.201709 −0.100854 0.994901i \(-0.532158\pi\)
−0.100854 + 0.994901i \(0.532158\pi\)
\(524\) 9.38572 0.410017
\(525\) 0.188713 0.00823609
\(526\) 8.43437 0.367756
\(527\) −1.38109 −0.0601613
\(528\) −12.2170 −0.531677
\(529\) −22.7902 −0.990879
\(530\) 12.0545 0.523614
\(531\) −4.30373 −0.186766
\(532\) 4.48382 0.194398
\(533\) 0 0
\(534\) −28.8181 −1.24708
\(535\) 36.1187 1.56155
\(536\) −24.1254 −1.04206
\(537\) −21.0691 −0.909199
\(538\) −0.965190 −0.0416123
\(539\) −2.53947 −0.109383
\(540\) 1.28722 0.0553933
\(541\) 31.6729 1.36172 0.680862 0.732412i \(-0.261605\pi\)
0.680862 + 0.732412i \(0.261605\pi\)
\(542\) −9.12243 −0.391842
\(543\) 0.269780 0.0115774
\(544\) −12.6029 −0.540343
\(545\) 29.9326 1.28217
\(546\) 0 0
\(547\) 21.6899 0.927393 0.463697 0.885994i \(-0.346523\pi\)
0.463697 + 0.885994i \(0.346523\pi\)
\(548\) 0.891431 0.0380800
\(549\) −11.4865 −0.490231
\(550\) 0.767530 0.0327276
\(551\) −47.6952 −2.03188
\(552\) −1.05261 −0.0448020
\(553\) 9.42077 0.400612
\(554\) 12.8238 0.544832
\(555\) −10.8131 −0.458991
\(556\) 6.79568 0.288201
\(557\) 32.4871 1.37652 0.688262 0.725462i \(-0.258374\pi\)
0.688262 + 0.725462i \(0.258374\pi\)
\(558\) −0.545627 −0.0230982
\(559\) 0 0
\(560\) −10.9585 −0.463083
\(561\) −10.2949 −0.434650
\(562\) −4.83383 −0.203903
\(563\) −13.0529 −0.550115 −0.275058 0.961428i \(-0.588697\pi\)
−0.275058 + 0.961428i \(0.588697\pi\)
\(564\) −4.05110 −0.170582
\(565\) −0.894628 −0.0376373
\(566\) −14.2814 −0.600294
\(567\) −1.00000 −0.0419961
\(568\) −9.77372 −0.410096
\(569\) −15.3184 −0.642182 −0.321091 0.947048i \(-0.604049\pi\)
−0.321091 + 0.947048i \(0.604049\pi\)
\(570\) 28.9471 1.21246
\(571\) −44.0404 −1.84303 −0.921517 0.388337i \(-0.873050\pi\)
−0.921517 + 0.388337i \(0.873050\pi\)
\(572\) 0 0
\(573\) 6.28281 0.262468
\(574\) −14.2226 −0.593639
\(575\) 0.0864359 0.00360463
\(576\) 4.64271 0.193446
\(577\) −13.7961 −0.574338 −0.287169 0.957880i \(-0.592714\pi\)
−0.287169 + 0.957880i \(0.592714\pi\)
\(578\) 0.905663 0.0376706
\(579\) 19.3154 0.802721
\(580\) −7.73758 −0.321286
\(581\) 1.87743 0.0778888
\(582\) −30.3602 −1.25847
\(583\) −8.39093 −0.347517
\(584\) −3.65715 −0.151334
\(585\) 0 0
\(586\) −8.52072 −0.351988
\(587\) −29.7424 −1.22760 −0.613801 0.789461i \(-0.710360\pi\)
−0.613801 + 0.789461i \(0.710360\pi\)
\(588\) −0.565099 −0.0233043
\(589\) −2.70313 −0.111381
\(590\) −15.7010 −0.646399
\(591\) −21.0050 −0.864030
\(592\) 22.8372 0.938605
\(593\) −26.2248 −1.07692 −0.538461 0.842650i \(-0.680994\pi\)
−0.538461 + 0.842650i \(0.680994\pi\)
\(594\) −4.06719 −0.166879
\(595\) −9.23439 −0.378573
\(596\) 13.6642 0.559706
\(597\) −17.0312 −0.697039
\(598\) 0 0
\(599\) −7.80961 −0.319092 −0.159546 0.987191i \(-0.551003\pi\)
−0.159546 + 0.987191i \(0.551003\pi\)
\(600\) −0.433686 −0.0177051
\(601\) 13.4938 0.550422 0.275211 0.961384i \(-0.411252\pi\)
0.275211 + 0.961384i \(0.411252\pi\)
\(602\) −3.43193 −0.139875
\(603\) −10.4979 −0.427506
\(604\) 5.07726 0.206591
\(605\) 10.3669 0.421473
\(606\) −6.44914 −0.261978
\(607\) −18.5539 −0.753078 −0.376539 0.926401i \(-0.622886\pi\)
−0.376539 + 0.926401i \(0.622886\pi\)
\(608\) −24.6669 −1.00037
\(609\) 6.01106 0.243580
\(610\) −41.9053 −1.69670
\(611\) 0 0
\(612\) −2.29088 −0.0926035
\(613\) 12.9374 0.522536 0.261268 0.965266i \(-0.415859\pi\)
0.261268 + 0.965266i \(0.415859\pi\)
\(614\) −5.84974 −0.236076
\(615\) −20.2282 −0.815678
\(616\) 5.83602 0.235140
\(617\) 33.2636 1.33914 0.669571 0.742748i \(-0.266478\pi\)
0.669571 + 0.742748i \(0.266478\pi\)
\(618\) −18.1670 −0.730785
\(619\) 18.8470 0.757523 0.378762 0.925494i \(-0.376350\pi\)
0.378762 + 0.925494i \(0.376350\pi\)
\(620\) −0.438529 −0.0176117
\(621\) −0.458029 −0.0183801
\(622\) −7.97233 −0.319661
\(623\) 17.9934 0.720890
\(624\) 0 0
\(625\) −25.9080 −1.03632
\(626\) 49.3323 1.97171
\(627\) −20.1496 −0.804697
\(628\) −1.53262 −0.0611581
\(629\) 19.2442 0.767315
\(630\) −3.64823 −0.145349
\(631\) 25.5434 1.01687 0.508433 0.861101i \(-0.330225\pi\)
0.508433 + 0.861101i \(0.330225\pi\)
\(632\) −21.6501 −0.861196
\(633\) 10.0436 0.399196
\(634\) −36.0762 −1.43277
\(635\) −36.4365 −1.44594
\(636\) −1.86721 −0.0740395
\(637\) 0 0
\(638\) 24.4481 0.967911
\(639\) −4.25291 −0.168242
\(640\) 31.1005 1.22936
\(641\) 14.6984 0.580552 0.290276 0.956943i \(-0.406253\pi\)
0.290276 + 0.956943i \(0.406253\pi\)
\(642\) −25.3954 −1.00227
\(643\) 8.13670 0.320880 0.160440 0.987046i \(-0.448709\pi\)
0.160440 + 0.987046i \(0.448709\pi\)
\(644\) −0.258832 −0.0101994
\(645\) −4.88108 −0.192192
\(646\) −51.5174 −2.02693
\(647\) −17.9914 −0.707315 −0.353658 0.935375i \(-0.615062\pi\)
−0.353658 + 0.935375i \(0.615062\pi\)
\(648\) 2.29813 0.0902790
\(649\) 10.9292 0.429008
\(650\) 0 0
\(651\) 0.340678 0.0133522
\(652\) 9.80798 0.384110
\(653\) −9.74392 −0.381309 −0.190654 0.981657i \(-0.561061\pi\)
−0.190654 + 0.981657i \(0.561061\pi\)
\(654\) −21.0459 −0.822958
\(655\) −37.8332 −1.47827
\(656\) 42.7218 1.66801
\(657\) −1.59136 −0.0620849
\(658\) 11.4815 0.447597
\(659\) 39.8534 1.55247 0.776234 0.630445i \(-0.217128\pi\)
0.776234 + 0.630445i \(0.217128\pi\)
\(660\) −3.26886 −0.127240
\(661\) 4.70505 0.183005 0.0915025 0.995805i \(-0.470833\pi\)
0.0915025 + 0.995805i \(0.470833\pi\)
\(662\) 7.57908 0.294570
\(663\) 0 0
\(664\) −4.31457 −0.167438
\(665\) −18.0740 −0.700878
\(666\) 7.60279 0.294602
\(667\) 2.75324 0.106606
\(668\) −7.18109 −0.277845
\(669\) 1.30689 0.0505272
\(670\) −38.2985 −1.47960
\(671\) 29.1696 1.12608
\(672\) 3.10879 0.119924
\(673\) −51.1974 −1.97351 −0.986757 0.162205i \(-0.948139\pi\)
−0.986757 + 0.162205i \(0.948139\pi\)
\(674\) 43.6552 1.68154
\(675\) −0.188713 −0.00726355
\(676\) 0 0
\(677\) −6.98340 −0.268394 −0.134197 0.990955i \(-0.542845\pi\)
−0.134197 + 0.990955i \(0.542845\pi\)
\(678\) 0.629020 0.0241574
\(679\) 18.9563 0.727475
\(680\) 21.2218 0.813819
\(681\) 7.31823 0.280435
\(682\) 1.38560 0.0530574
\(683\) −14.7082 −0.562793 −0.281396 0.959592i \(-0.590798\pi\)
−0.281396 + 0.959592i \(0.590798\pi\)
\(684\) −4.48382 −0.171443
\(685\) −3.59330 −0.137293
\(686\) 1.60159 0.0611491
\(687\) −16.5282 −0.630590
\(688\) 10.3088 0.393020
\(689\) 0 0
\(690\) −1.67099 −0.0636137
\(691\) −45.3789 −1.72629 −0.863147 0.504953i \(-0.831510\pi\)
−0.863147 + 0.504953i \(0.831510\pi\)
\(692\) 0.765385 0.0290956
\(693\) 2.53947 0.0964663
\(694\) 55.3146 2.09971
\(695\) −27.3929 −1.03907
\(696\) −13.8142 −0.523625
\(697\) 36.0002 1.36361
\(698\) −40.9290 −1.54918
\(699\) −5.48450 −0.207443
\(700\) −0.106641 −0.00403066
\(701\) −16.8794 −0.637525 −0.318763 0.947835i \(-0.603267\pi\)
−0.318763 + 0.947835i \(0.603267\pi\)
\(702\) 0 0
\(703\) 37.6656 1.42058
\(704\) −11.7900 −0.444353
\(705\) 16.3297 0.615012
\(706\) −42.9973 −1.61823
\(707\) 4.02671 0.151440
\(708\) 2.43203 0.0914014
\(709\) 41.2478 1.54909 0.774547 0.632516i \(-0.217978\pi\)
0.774547 + 0.632516i \(0.217978\pi\)
\(710\) −15.5156 −0.582289
\(711\) −9.42077 −0.353307
\(712\) −41.3511 −1.54970
\(713\) 0.156040 0.00584376
\(714\) 6.49278 0.242986
\(715\) 0 0
\(716\) 11.9061 0.444953
\(717\) 17.8572 0.666889
\(718\) −37.9135 −1.41492
\(719\) 14.8928 0.555409 0.277704 0.960667i \(-0.410426\pi\)
0.277704 + 0.960667i \(0.410426\pi\)
\(720\) 10.9585 0.408401
\(721\) 11.3431 0.422439
\(722\) −70.4020 −2.62009
\(723\) 23.1081 0.859400
\(724\) −0.152452 −0.00566584
\(725\) 1.13436 0.0421292
\(726\) −7.28903 −0.270521
\(727\) 31.4330 1.16578 0.582892 0.812550i \(-0.301921\pi\)
0.582892 + 0.812550i \(0.301921\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −5.80564 −0.214876
\(731\) 8.68689 0.321296
\(732\) 6.49100 0.239914
\(733\) 5.22860 0.193123 0.0965613 0.995327i \(-0.469216\pi\)
0.0965613 + 0.995327i \(0.469216\pi\)
\(734\) −18.4811 −0.682150
\(735\) 2.27787 0.0840207
\(736\) 1.42391 0.0524862
\(737\) 26.6589 0.981995
\(738\) 14.2226 0.523541
\(739\) 23.0653 0.848469 0.424235 0.905552i \(-0.360543\pi\)
0.424235 + 0.905552i \(0.360543\pi\)
\(740\) 6.11047 0.224626
\(741\) 0 0
\(742\) 5.29200 0.194275
\(743\) 0.991530 0.0363757 0.0181878 0.999835i \(-0.494210\pi\)
0.0181878 + 0.999835i \(0.494210\pi\)
\(744\) −0.782921 −0.0287033
\(745\) −55.0793 −2.01795
\(746\) −2.43717 −0.0892312
\(747\) −1.87743 −0.0686915
\(748\) 5.81762 0.212713
\(749\) 15.8563 0.579377
\(750\) 17.5527 0.640933
\(751\) 29.7806 1.08671 0.543356 0.839503i \(-0.317154\pi\)
0.543356 + 0.839503i \(0.317154\pi\)
\(752\) −34.4882 −1.25766
\(753\) −11.7442 −0.427984
\(754\) 0 0
\(755\) −20.4661 −0.744837
\(756\) 0.565099 0.0205524
\(757\) −9.12624 −0.331699 −0.165849 0.986151i \(-0.553037\pi\)
−0.165849 + 0.986151i \(0.553037\pi\)
\(758\) −55.1887 −2.00454
\(759\) 1.16315 0.0422197
\(760\) 41.5363 1.50668
\(761\) 14.2507 0.516586 0.258293 0.966067i \(-0.416840\pi\)
0.258293 + 0.966067i \(0.416840\pi\)
\(762\) 25.6188 0.928072
\(763\) 13.1406 0.475721
\(764\) −3.55041 −0.128449
\(765\) 9.23439 0.333870
\(766\) −6.27309 −0.226656
\(767\) 0 0
\(768\) −12.5816 −0.454000
\(769\) 43.0440 1.55221 0.776103 0.630606i \(-0.217193\pi\)
0.776103 + 0.630606i \(0.217193\pi\)
\(770\) 9.26455 0.333871
\(771\) 9.53811 0.343507
\(772\) −10.9151 −0.392844
\(773\) 30.5971 1.10050 0.550251 0.834999i \(-0.314532\pi\)
0.550251 + 0.834999i \(0.314532\pi\)
\(774\) 3.43193 0.123358
\(775\) 0.0642902 0.00230937
\(776\) −43.5639 −1.56385
\(777\) −4.74702 −0.170298
\(778\) 49.7833 1.78482
\(779\) 70.4612 2.52453
\(780\) 0 0
\(781\) 10.8001 0.386458
\(782\) 2.97388 0.106346
\(783\) −6.01106 −0.214818
\(784\) −4.81086 −0.171816
\(785\) 6.17787 0.220498
\(786\) 26.6008 0.948820
\(787\) 23.2516 0.828830 0.414415 0.910088i \(-0.363986\pi\)
0.414415 + 0.910088i \(0.363986\pi\)
\(788\) 11.8699 0.422848
\(789\) 5.26624 0.187483
\(790\) −34.3691 −1.22280
\(791\) −0.392747 −0.0139645
\(792\) −5.83602 −0.207374
\(793\) 0 0
\(794\) −15.6158 −0.554185
\(795\) 7.52658 0.266940
\(796\) 9.62428 0.341124
\(797\) −48.7696 −1.72751 −0.863754 0.503914i \(-0.831893\pi\)
−0.863754 + 0.503914i \(0.831893\pi\)
\(798\) 12.7080 0.449857
\(799\) −29.0621 −1.02814
\(800\) 0.586667 0.0207418
\(801\) −17.9934 −0.635766
\(802\) −3.82627 −0.135110
\(803\) 4.04120 0.142611
\(804\) 5.93232 0.209217
\(805\) 1.04333 0.0367727
\(806\) 0 0
\(807\) −0.602644 −0.0212141
\(808\) −9.25388 −0.325550
\(809\) −4.26862 −0.150077 −0.0750383 0.997181i \(-0.523908\pi\)
−0.0750383 + 0.997181i \(0.523908\pi\)
\(810\) 3.64823 0.128186
\(811\) −16.1267 −0.566287 −0.283143 0.959078i \(-0.591377\pi\)
−0.283143 + 0.959078i \(0.591377\pi\)
\(812\) −3.39684 −0.119206
\(813\) −5.69585 −0.199762
\(814\) −19.3070 −0.676711
\(815\) −39.5353 −1.38486
\(816\) −19.5030 −0.682741
\(817\) 17.0024 0.594838
\(818\) 30.5146 1.06692
\(819\) 0 0
\(820\) 11.4309 0.399185
\(821\) −42.1403 −1.47071 −0.735354 0.677684i \(-0.762984\pi\)
−0.735354 + 0.677684i \(0.762984\pi\)
\(822\) 2.52648 0.0881210
\(823\) 34.5376 1.20391 0.601953 0.798531i \(-0.294389\pi\)
0.601953 + 0.798531i \(0.294389\pi\)
\(824\) −26.0679 −0.908118
\(825\) 0.479229 0.0166846
\(826\) −6.89282 −0.239832
\(827\) −43.7311 −1.52068 −0.760340 0.649525i \(-0.774968\pi\)
−0.760340 + 0.649525i \(0.774968\pi\)
\(828\) 0.258832 0.00899503
\(829\) −0.927355 −0.0322084 −0.0161042 0.999870i \(-0.505126\pi\)
−0.0161042 + 0.999870i \(0.505126\pi\)
\(830\) −6.84928 −0.237742
\(831\) 8.00692 0.277757
\(832\) 0 0
\(833\) −4.05395 −0.140461
\(834\) 19.2602 0.666926
\(835\) 28.9465 1.00173
\(836\) 11.3865 0.393811
\(837\) −0.340678 −0.0117755
\(838\) −31.5379 −1.08946
\(839\) −24.1448 −0.833571 −0.416785 0.909005i \(-0.636843\pi\)
−0.416785 + 0.909005i \(0.636843\pi\)
\(840\) −5.23485 −0.180619
\(841\) 7.13286 0.245961
\(842\) −40.4047 −1.39244
\(843\) −3.01814 −0.103950
\(844\) −5.67561 −0.195363
\(845\) 0 0
\(846\) −11.4815 −0.394744
\(847\) 4.55111 0.156378
\(848\) −15.8961 −0.545874
\(849\) −8.91703 −0.306032
\(850\) 1.22527 0.0420264
\(851\) −2.17427 −0.0745331
\(852\) 2.40331 0.0823361
\(853\) −54.7857 −1.87583 −0.937914 0.346868i \(-0.887245\pi\)
−0.937914 + 0.346868i \(0.887245\pi\)
\(854\) −18.3967 −0.629521
\(855\) 18.0740 0.618117
\(856\) −36.4398 −1.24549
\(857\) 2.79688 0.0955396 0.0477698 0.998858i \(-0.484789\pi\)
0.0477698 + 0.998858i \(0.484789\pi\)
\(858\) 0 0
\(859\) −37.7430 −1.28778 −0.643888 0.765120i \(-0.722680\pi\)
−0.643888 + 0.765120i \(0.722680\pi\)
\(860\) 2.75829 0.0940569
\(861\) −8.88028 −0.302639
\(862\) 12.6201 0.429843
\(863\) −25.0401 −0.852376 −0.426188 0.904635i \(-0.640144\pi\)
−0.426188 + 0.904635i \(0.640144\pi\)
\(864\) −3.10879 −0.105763
\(865\) −3.08521 −0.104900
\(866\) 39.7749 1.35161
\(867\) 0.565477 0.0192046
\(868\) −0.192517 −0.00653444
\(869\) 23.9237 0.811557
\(870\) −21.9297 −0.743487
\(871\) 0 0
\(872\) −30.1987 −1.02266
\(873\) −18.9563 −0.641573
\(874\) 5.82062 0.196885
\(875\) −10.9595 −0.370499
\(876\) 0.899276 0.0303837
\(877\) 32.5220 1.09819 0.549095 0.835760i \(-0.314973\pi\)
0.549095 + 0.835760i \(0.314973\pi\)
\(878\) 30.5858 1.03222
\(879\) −5.32016 −0.179444
\(880\) −27.8288 −0.938110
\(881\) 27.6515 0.931604 0.465802 0.884889i \(-0.345766\pi\)
0.465802 + 0.884889i \(0.345766\pi\)
\(882\) −1.60159 −0.0539284
\(883\) 18.0601 0.607771 0.303885 0.952709i \(-0.401716\pi\)
0.303885 + 0.952709i \(0.401716\pi\)
\(884\) 0 0
\(885\) −9.80335 −0.329536
\(886\) −62.6541 −2.10490
\(887\) 44.6426 1.49895 0.749476 0.662032i \(-0.230306\pi\)
0.749476 + 0.662032i \(0.230306\pi\)
\(888\) 10.9092 0.366090
\(889\) −15.9958 −0.536483
\(890\) −65.6440 −2.20039
\(891\) −2.53947 −0.0850753
\(892\) −0.738520 −0.0247275
\(893\) −56.8816 −1.90347
\(894\) 38.7267 1.29521
\(895\) −47.9928 −1.60422
\(896\) 13.6533 0.456125
\(897\) 0 0
\(898\) 3.81793 0.127406
\(899\) 2.04783 0.0682991
\(900\) 0.106641 0.00355471
\(901\) −13.3951 −0.446256
\(902\) −36.1178 −1.20259
\(903\) −2.14282 −0.0713086
\(904\) 0.902582 0.0300194
\(905\) 0.614524 0.0204275
\(906\) 14.3899 0.478071
\(907\) −26.3976 −0.876517 −0.438259 0.898849i \(-0.644405\pi\)
−0.438259 + 0.898849i \(0.644405\pi\)
\(908\) −4.13552 −0.137242
\(909\) −4.02671 −0.133557
\(910\) 0 0
\(911\) 4.45669 0.147657 0.0738283 0.997271i \(-0.476478\pi\)
0.0738283 + 0.997271i \(0.476478\pi\)
\(912\) −38.1721 −1.26401
\(913\) 4.76766 0.157787
\(914\) −23.9688 −0.792817
\(915\) −26.1648 −0.864981
\(916\) 9.34006 0.308604
\(917\) −16.6090 −0.548477
\(918\) −6.49278 −0.214294
\(919\) −6.71089 −0.221372 −0.110686 0.993855i \(-0.535305\pi\)
−0.110686 + 0.993855i \(0.535305\pi\)
\(920\) −2.39771 −0.0790502
\(921\) −3.65245 −0.120352
\(922\) 52.8651 1.74102
\(923\) 0 0
\(924\) −1.43505 −0.0472097
\(925\) −0.895822 −0.0294544
\(926\) 54.7975 1.80076
\(927\) −11.3431 −0.372556
\(928\) 18.6871 0.613434
\(929\) 28.2471 0.926759 0.463379 0.886160i \(-0.346637\pi\)
0.463379 + 0.886160i \(0.346637\pi\)
\(930\) −1.24287 −0.0407553
\(931\) −7.93457 −0.260045
\(932\) 3.09928 0.101520
\(933\) −4.97775 −0.162964
\(934\) 40.4803 1.32456
\(935\) −23.4504 −0.766911
\(936\) 0 0
\(937\) −33.0728 −1.08044 −0.540220 0.841524i \(-0.681659\pi\)
−0.540220 + 0.841524i \(0.681659\pi\)
\(938\) −16.8133 −0.548973
\(939\) 30.8020 1.00519
\(940\) −9.22789 −0.300981
\(941\) −40.0527 −1.30568 −0.652840 0.757495i \(-0.726423\pi\)
−0.652840 + 0.757495i \(0.726423\pi\)
\(942\) −4.34371 −0.141526
\(943\) −4.06743 −0.132454
\(944\) 20.7046 0.673879
\(945\) −2.27787 −0.0740993
\(946\) −8.71526 −0.283358
\(947\) −52.8629 −1.71781 −0.858907 0.512132i \(-0.828856\pi\)
−0.858907 + 0.512132i \(0.828856\pi\)
\(948\) 5.32367 0.172905
\(949\) 0 0
\(950\) 2.39815 0.0778063
\(951\) −22.5252 −0.730429
\(952\) 9.31650 0.301949
\(953\) −47.6352 −1.54306 −0.771528 0.636196i \(-0.780507\pi\)
−0.771528 + 0.636196i \(0.780507\pi\)
\(954\) −5.29200 −0.171335
\(955\) 14.3114 0.463108
\(956\) −10.0911 −0.326369
\(957\) 15.2649 0.493444
\(958\) −59.9397 −1.93656
\(959\) −1.57748 −0.0509394
\(960\) 10.5755 0.341324
\(961\) −30.8839 −0.996256
\(962\) 0 0
\(963\) −15.8563 −0.510963
\(964\) −13.0584 −0.420582
\(965\) 43.9981 1.41635
\(966\) −0.733576 −0.0236024
\(967\) 34.0050 1.09353 0.546764 0.837287i \(-0.315860\pi\)
0.546764 + 0.837287i \(0.315860\pi\)
\(968\) −10.4590 −0.336166
\(969\) −32.1664 −1.03333
\(970\) −69.1568 −2.22049
\(971\) −1.28177 −0.0411338 −0.0205669 0.999788i \(-0.506547\pi\)
−0.0205669 + 0.999788i \(0.506547\pi\)
\(972\) −0.565099 −0.0181256
\(973\) −12.0257 −0.385525
\(974\) −48.6237 −1.55800
\(975\) 0 0
\(976\) 55.2599 1.76883
\(977\) −53.5945 −1.71464 −0.857320 0.514783i \(-0.827872\pi\)
−0.857320 + 0.514783i \(0.827872\pi\)
\(978\) 27.7976 0.888869
\(979\) 45.6936 1.46037
\(980\) −1.28722 −0.0411189
\(981\) −13.1406 −0.419547
\(982\) 9.01309 0.287619
\(983\) −12.2091 −0.389410 −0.194705 0.980862i \(-0.562375\pi\)
−0.194705 + 0.980862i \(0.562375\pi\)
\(984\) 20.4080 0.650583
\(985\) −47.8468 −1.52452
\(986\) 39.0285 1.24292
\(987\) 7.16883 0.228186
\(988\) 0 0
\(989\) −0.981475 −0.0312091
\(990\) −9.26455 −0.294447
\(991\) −7.83719 −0.248957 −0.124478 0.992222i \(-0.539726\pi\)
−0.124478 + 0.992222i \(0.539726\pi\)
\(992\) 1.05909 0.0336263
\(993\) 4.73222 0.150172
\(994\) −6.81142 −0.216045
\(995\) −38.7948 −1.22988
\(996\) 1.06093 0.0336169
\(997\) 57.3019 1.81477 0.907385 0.420302i \(-0.138076\pi\)
0.907385 + 0.420302i \(0.138076\pi\)
\(998\) 54.6999 1.73149
\(999\) 4.74702 0.150189
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3549.2.a.bf.1.2 yes 9
13.12 even 2 3549.2.a.be.1.8 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.8 9 13.12 even 2
3549.2.a.bf.1.2 yes 9 1.1 even 1 trivial