Properties

Label 3549.2.a.bf.1.6
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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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 1.6
Root \(0.494186\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.494186 q^{2} -1.00000 q^{3} -1.75578 q^{4} +1.64627 q^{5} -0.494186 q^{6} -1.00000 q^{7} -1.85605 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.494186 q^{2} -1.00000 q^{3} -1.75578 q^{4} +1.64627 q^{5} -0.494186 q^{6} -1.00000 q^{7} -1.85605 q^{8} +1.00000 q^{9} +0.813565 q^{10} +1.00650 q^{11} +1.75578 q^{12} -0.494186 q^{14} -1.64627 q^{15} +2.59432 q^{16} -4.38900 q^{17} +0.494186 q^{18} +1.17541 q^{19} -2.89049 q^{20} +1.00000 q^{21} +0.497400 q^{22} +2.62816 q^{23} +1.85605 q^{24} -2.28979 q^{25} -1.00000 q^{27} +1.75578 q^{28} +5.13954 q^{29} -0.813565 q^{30} -0.705141 q^{31} +4.99419 q^{32} -1.00650 q^{33} -2.16898 q^{34} -1.64627 q^{35} -1.75578 q^{36} +2.72506 q^{37} +0.580871 q^{38} -3.05557 q^{40} -3.05611 q^{41} +0.494186 q^{42} -10.5077 q^{43} -1.76720 q^{44} +1.64627 q^{45} +1.29880 q^{46} -2.16111 q^{47} -2.59432 q^{48} +1.00000 q^{49} -1.13158 q^{50} +4.38900 q^{51} -1.96782 q^{53} -0.494186 q^{54} +1.65698 q^{55} +1.85605 q^{56} -1.17541 q^{57} +2.53989 q^{58} -4.90995 q^{59} +2.89049 q^{60} +0.563211 q^{61} -0.348471 q^{62} -1.00000 q^{63} -2.72059 q^{64} -0.497400 q^{66} +13.1061 q^{67} +7.70611 q^{68} -2.62816 q^{69} -0.813565 q^{70} +15.3807 q^{71} -1.85605 q^{72} +13.5942 q^{73} +1.34669 q^{74} +2.28979 q^{75} -2.06376 q^{76} -1.00650 q^{77} +7.63275 q^{79} +4.27096 q^{80} +1.00000 q^{81} -1.51029 q^{82} +0.0542580 q^{83} -1.75578 q^{84} -7.22548 q^{85} -5.19278 q^{86} -5.13954 q^{87} -1.86813 q^{88} -0.601205 q^{89} +0.813565 q^{90} -4.61447 q^{92} +0.705141 q^{93} -1.06799 q^{94} +1.93504 q^{95} -4.99419 q^{96} +1.74080 q^{97} +0.494186 q^{98} +1.00650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.494186 0.349442 0.174721 0.984618i \(-0.444098\pi\)
0.174721 + 0.984618i \(0.444098\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.75578 −0.877890
\(5\) 1.64627 0.736236 0.368118 0.929779i \(-0.380002\pi\)
0.368118 + 0.929779i \(0.380002\pi\)
\(6\) −0.494186 −0.201751
\(7\) −1.00000 −0.377964
\(8\) −1.85605 −0.656214
\(9\) 1.00000 0.333333
\(10\) 0.813565 0.257272
\(11\) 1.00650 0.303472 0.151736 0.988421i \(-0.451514\pi\)
0.151736 + 0.988421i \(0.451514\pi\)
\(12\) 1.75578 0.506850
\(13\) 0 0
\(14\) −0.494186 −0.132077
\(15\) −1.64627 −0.425066
\(16\) 2.59432 0.648581
\(17\) −4.38900 −1.06449 −0.532244 0.846591i \(-0.678651\pi\)
−0.532244 + 0.846591i \(0.678651\pi\)
\(18\) 0.494186 0.116481
\(19\) 1.17541 0.269657 0.134829 0.990869i \(-0.456952\pi\)
0.134829 + 0.990869i \(0.456952\pi\)
\(20\) −2.89049 −0.646334
\(21\) 1.00000 0.218218
\(22\) 0.497400 0.106046
\(23\) 2.62816 0.548010 0.274005 0.961728i \(-0.411652\pi\)
0.274005 + 0.961728i \(0.411652\pi\)
\(24\) 1.85605 0.378866
\(25\) −2.28979 −0.457957
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.75578 0.331811
\(29\) 5.13954 0.954388 0.477194 0.878798i \(-0.341654\pi\)
0.477194 + 0.878798i \(0.341654\pi\)
\(30\) −0.813565 −0.148536
\(31\) −0.705141 −0.126647 −0.0633235 0.997993i \(-0.520170\pi\)
−0.0633235 + 0.997993i \(0.520170\pi\)
\(32\) 4.99419 0.882856
\(33\) −1.00650 −0.175210
\(34\) −2.16898 −0.371977
\(35\) −1.64627 −0.278271
\(36\) −1.75578 −0.292630
\(37\) 2.72506 0.447997 0.223999 0.974589i \(-0.428089\pi\)
0.223999 + 0.974589i \(0.428089\pi\)
\(38\) 0.580871 0.0942297
\(39\) 0 0
\(40\) −3.05557 −0.483128
\(41\) −3.05611 −0.477284 −0.238642 0.971108i \(-0.576702\pi\)
−0.238642 + 0.971108i \(0.576702\pi\)
\(42\) 0.494186 0.0762546
\(43\) −10.5077 −1.60242 −0.801208 0.598386i \(-0.795809\pi\)
−0.801208 + 0.598386i \(0.795809\pi\)
\(44\) −1.76720 −0.266415
\(45\) 1.64627 0.245412
\(46\) 1.29880 0.191498
\(47\) −2.16111 −0.315231 −0.157615 0.987501i \(-0.550381\pi\)
−0.157615 + 0.987501i \(0.550381\pi\)
\(48\) −2.59432 −0.374458
\(49\) 1.00000 0.142857
\(50\) −1.13158 −0.160030
\(51\) 4.38900 0.614582
\(52\) 0 0
\(53\) −1.96782 −0.270301 −0.135150 0.990825i \(-0.543152\pi\)
−0.135150 + 0.990825i \(0.543152\pi\)
\(54\) −0.494186 −0.0672502
\(55\) 1.65698 0.223427
\(56\) 1.85605 0.248026
\(57\) −1.17541 −0.155687
\(58\) 2.53989 0.333504
\(59\) −4.90995 −0.639221 −0.319611 0.947549i \(-0.603552\pi\)
−0.319611 + 0.947549i \(0.603552\pi\)
\(60\) 2.89049 0.373161
\(61\) 0.563211 0.0721117 0.0360559 0.999350i \(-0.488521\pi\)
0.0360559 + 0.999350i \(0.488521\pi\)
\(62\) −0.348471 −0.0442558
\(63\) −1.00000 −0.125988
\(64\) −2.72059 −0.340073
\(65\) 0 0
\(66\) −0.497400 −0.0612258
\(67\) 13.1061 1.60116 0.800580 0.599225i \(-0.204525\pi\)
0.800580 + 0.599225i \(0.204525\pi\)
\(68\) 7.70611 0.934503
\(69\) −2.62816 −0.316394
\(70\) −0.813565 −0.0972397
\(71\) 15.3807 1.82536 0.912678 0.408678i \(-0.134010\pi\)
0.912678 + 0.408678i \(0.134010\pi\)
\(72\) −1.85605 −0.218738
\(73\) 13.5942 1.59108 0.795541 0.605900i \(-0.207187\pi\)
0.795541 + 0.605900i \(0.207187\pi\)
\(74\) 1.34669 0.156549
\(75\) 2.28979 0.264402
\(76\) −2.06376 −0.236729
\(77\) −1.00650 −0.114702
\(78\) 0 0
\(79\) 7.63275 0.858751 0.429376 0.903126i \(-0.358734\pi\)
0.429376 + 0.903126i \(0.358734\pi\)
\(80\) 4.27096 0.477508
\(81\) 1.00000 0.111111
\(82\) −1.51029 −0.166783
\(83\) 0.0542580 0.00595559 0.00297779 0.999996i \(-0.499052\pi\)
0.00297779 + 0.999996i \(0.499052\pi\)
\(84\) −1.75578 −0.191571
\(85\) −7.22548 −0.783714
\(86\) −5.19278 −0.559952
\(87\) −5.13954 −0.551016
\(88\) −1.86813 −0.199143
\(89\) −0.601205 −0.0637276 −0.0318638 0.999492i \(-0.510144\pi\)
−0.0318638 + 0.999492i \(0.510144\pi\)
\(90\) 0.813565 0.0857573
\(91\) 0 0
\(92\) −4.61447 −0.481092
\(93\) 0.705141 0.0731197
\(94\) −1.06799 −0.110155
\(95\) 1.93504 0.198531
\(96\) −4.99419 −0.509717
\(97\) 1.74080 0.176751 0.0883757 0.996087i \(-0.471832\pi\)
0.0883757 + 0.996087i \(0.471832\pi\)
\(98\) 0.494186 0.0499203
\(99\) 1.00650 0.101157
\(100\) 4.02036 0.402036
\(101\) 12.8587 1.27949 0.639746 0.768586i \(-0.279039\pi\)
0.639746 + 0.768586i \(0.279039\pi\)
\(102\) 2.16898 0.214761
\(103\) 14.6917 1.44761 0.723806 0.690004i \(-0.242391\pi\)
0.723806 + 0.690004i \(0.242391\pi\)
\(104\) 0 0
\(105\) 1.64627 0.160660
\(106\) −0.972469 −0.0944546
\(107\) 3.37556 0.326328 0.163164 0.986599i \(-0.447830\pi\)
0.163164 + 0.986599i \(0.447830\pi\)
\(108\) 1.75578 0.168950
\(109\) −9.90520 −0.948746 −0.474373 0.880324i \(-0.657325\pi\)
−0.474373 + 0.880324i \(0.657325\pi\)
\(110\) 0.818857 0.0780749
\(111\) −2.72506 −0.258651
\(112\) −2.59432 −0.245141
\(113\) −13.5673 −1.27631 −0.638154 0.769909i \(-0.720302\pi\)
−0.638154 + 0.769909i \(0.720302\pi\)
\(114\) −0.580871 −0.0544035
\(115\) 4.32667 0.403464
\(116\) −9.02390 −0.837848
\(117\) 0 0
\(118\) −2.42643 −0.223371
\(119\) 4.38900 0.402339
\(120\) 3.05557 0.278934
\(121\) −9.98695 −0.907905
\(122\) 0.278331 0.0251989
\(123\) 3.05611 0.275560
\(124\) 1.23807 0.111182
\(125\) −12.0010 −1.07340
\(126\) −0.494186 −0.0440256
\(127\) 7.65651 0.679405 0.339703 0.940533i \(-0.389674\pi\)
0.339703 + 0.940533i \(0.389674\pi\)
\(128\) −11.3329 −1.00169
\(129\) 10.5077 0.925155
\(130\) 0 0
\(131\) 1.25502 0.109652 0.0548258 0.998496i \(-0.482540\pi\)
0.0548258 + 0.998496i \(0.482540\pi\)
\(132\) 1.76720 0.153815
\(133\) −1.17541 −0.101921
\(134\) 6.47684 0.559514
\(135\) −1.64627 −0.141689
\(136\) 8.14622 0.698532
\(137\) 2.55836 0.218576 0.109288 0.994010i \(-0.465143\pi\)
0.109288 + 0.994010i \(0.465143\pi\)
\(138\) −1.29880 −0.110561
\(139\) 5.63993 0.478373 0.239186 0.970974i \(-0.423119\pi\)
0.239186 + 0.970974i \(0.423119\pi\)
\(140\) 2.89049 0.244291
\(141\) 2.16111 0.181999
\(142\) 7.60094 0.637857
\(143\) 0 0
\(144\) 2.59432 0.216194
\(145\) 8.46108 0.702655
\(146\) 6.71807 0.555992
\(147\) −1.00000 −0.0824786
\(148\) −4.78461 −0.393292
\(149\) 5.49922 0.450514 0.225257 0.974299i \(-0.427678\pi\)
0.225257 + 0.974299i \(0.427678\pi\)
\(150\) 1.13158 0.0923932
\(151\) 8.31087 0.676329 0.338165 0.941087i \(-0.390194\pi\)
0.338165 + 0.941087i \(0.390194\pi\)
\(152\) −2.18162 −0.176953
\(153\) −4.38900 −0.354829
\(154\) −0.497400 −0.0400817
\(155\) −1.16085 −0.0932420
\(156\) 0 0
\(157\) 12.8123 1.02253 0.511265 0.859423i \(-0.329177\pi\)
0.511265 + 0.859423i \(0.329177\pi\)
\(158\) 3.77200 0.300084
\(159\) 1.96782 0.156058
\(160\) 8.22180 0.649990
\(161\) −2.62816 −0.207128
\(162\) 0.494186 0.0388269
\(163\) 10.7587 0.842684 0.421342 0.906902i \(-0.361559\pi\)
0.421342 + 0.906902i \(0.361559\pi\)
\(164\) 5.36585 0.419003
\(165\) −1.65698 −0.128996
\(166\) 0.0268135 0.00208113
\(167\) −25.0059 −1.93502 −0.967509 0.252838i \(-0.918636\pi\)
−0.967509 + 0.252838i \(0.918636\pi\)
\(168\) −1.85605 −0.143198
\(169\) 0 0
\(170\) −3.57073 −0.273863
\(171\) 1.17541 0.0898857
\(172\) 18.4493 1.40675
\(173\) 16.7347 1.27232 0.636159 0.771558i \(-0.280522\pi\)
0.636159 + 0.771558i \(0.280522\pi\)
\(174\) −2.53989 −0.192549
\(175\) 2.28979 0.173092
\(176\) 2.61120 0.196826
\(177\) 4.90995 0.369055
\(178\) −0.297107 −0.0222691
\(179\) 12.2780 0.917699 0.458849 0.888514i \(-0.348262\pi\)
0.458849 + 0.888514i \(0.348262\pi\)
\(180\) −2.89049 −0.215445
\(181\) 22.8077 1.69528 0.847640 0.530572i \(-0.178023\pi\)
0.847640 + 0.530572i \(0.178023\pi\)
\(182\) 0 0
\(183\) −0.563211 −0.0416337
\(184\) −4.87801 −0.359612
\(185\) 4.48619 0.329831
\(186\) 0.348471 0.0255511
\(187\) −4.41754 −0.323043
\(188\) 3.79444 0.276738
\(189\) 1.00000 0.0727393
\(190\) 0.956271 0.0693752
\(191\) 27.4058 1.98302 0.991508 0.130047i \(-0.0415128\pi\)
0.991508 + 0.130047i \(0.0415128\pi\)
\(192\) 2.72059 0.196342
\(193\) −6.41304 −0.461621 −0.230810 0.972999i \(-0.574138\pi\)
−0.230810 + 0.972999i \(0.574138\pi\)
\(194\) 0.860279 0.0617644
\(195\) 0 0
\(196\) −1.75578 −0.125413
\(197\) −17.2081 −1.22603 −0.613014 0.790072i \(-0.710043\pi\)
−0.613014 + 0.790072i \(0.710043\pi\)
\(198\) 0.497400 0.0353487
\(199\) −3.01028 −0.213393 −0.106696 0.994292i \(-0.534027\pi\)
−0.106696 + 0.994292i \(0.534027\pi\)
\(200\) 4.24997 0.300518
\(201\) −13.1061 −0.924431
\(202\) 6.35461 0.447109
\(203\) −5.13954 −0.360725
\(204\) −7.70611 −0.539536
\(205\) −5.03119 −0.351393
\(206\) 7.26041 0.505857
\(207\) 2.62816 0.182670
\(208\) 0 0
\(209\) 1.18305 0.0818335
\(210\) 0.813565 0.0561413
\(211\) 26.6548 1.83499 0.917497 0.397743i \(-0.130207\pi\)
0.917497 + 0.397743i \(0.130207\pi\)
\(212\) 3.45506 0.237294
\(213\) −15.3807 −1.05387
\(214\) 1.66815 0.114033
\(215\) −17.2986 −1.17976
\(216\) 1.85605 0.126289
\(217\) 0.705141 0.0478681
\(218\) −4.89501 −0.331532
\(219\) −13.5942 −0.918612
\(220\) −2.90929 −0.196144
\(221\) 0 0
\(222\) −1.34669 −0.0903837
\(223\) 13.8795 0.929443 0.464722 0.885457i \(-0.346154\pi\)
0.464722 + 0.885457i \(0.346154\pi\)
\(224\) −4.99419 −0.333688
\(225\) −2.28979 −0.152652
\(226\) −6.70479 −0.445996
\(227\) 13.7180 0.910496 0.455248 0.890365i \(-0.349551\pi\)
0.455248 + 0.890365i \(0.349551\pi\)
\(228\) 2.06376 0.136676
\(229\) 9.93225 0.656342 0.328171 0.944618i \(-0.393568\pi\)
0.328171 + 0.944618i \(0.393568\pi\)
\(230\) 2.13818 0.140988
\(231\) 1.00650 0.0662231
\(232\) −9.53927 −0.626283
\(233\) 19.4424 1.27371 0.636857 0.770982i \(-0.280234\pi\)
0.636857 + 0.770982i \(0.280234\pi\)
\(234\) 0 0
\(235\) −3.55778 −0.232084
\(236\) 8.62080 0.561166
\(237\) −7.63275 −0.495800
\(238\) 2.16898 0.140594
\(239\) 16.3885 1.06009 0.530043 0.847971i \(-0.322176\pi\)
0.530043 + 0.847971i \(0.322176\pi\)
\(240\) −4.27096 −0.275690
\(241\) −16.0048 −1.03096 −0.515479 0.856902i \(-0.672386\pi\)
−0.515479 + 0.856902i \(0.672386\pi\)
\(242\) −4.93541 −0.317260
\(243\) −1.00000 −0.0641500
\(244\) −0.988874 −0.0633062
\(245\) 1.64627 0.105177
\(246\) 1.51029 0.0962923
\(247\) 0 0
\(248\) 1.30878 0.0831076
\(249\) −0.0542580 −0.00343846
\(250\) −5.93072 −0.375091
\(251\) −13.7389 −0.867193 −0.433597 0.901107i \(-0.642756\pi\)
−0.433597 + 0.901107i \(0.642756\pi\)
\(252\) 1.75578 0.110604
\(253\) 2.64526 0.166306
\(254\) 3.78374 0.237413
\(255\) 7.22548 0.452477
\(256\) −0.159364 −0.00996028
\(257\) 25.1001 1.56570 0.782851 0.622210i \(-0.213765\pi\)
0.782851 + 0.622210i \(0.213765\pi\)
\(258\) 5.19278 0.323289
\(259\) −2.72506 −0.169327
\(260\) 0 0
\(261\) 5.13954 0.318129
\(262\) 0.620214 0.0383169
\(263\) 6.86224 0.423144 0.211572 0.977362i \(-0.432142\pi\)
0.211572 + 0.977362i \(0.432142\pi\)
\(264\) 1.86813 0.114975
\(265\) −3.23957 −0.199005
\(266\) −0.580871 −0.0356155
\(267\) 0.601205 0.0367931
\(268\) −23.0114 −1.40564
\(269\) 18.2175 1.11074 0.555369 0.831604i \(-0.312577\pi\)
0.555369 + 0.831604i \(0.312577\pi\)
\(270\) −0.813565 −0.0495120
\(271\) 15.0414 0.913697 0.456849 0.889544i \(-0.348978\pi\)
0.456849 + 0.889544i \(0.348978\pi\)
\(272\) −11.3865 −0.690406
\(273\) 0 0
\(274\) 1.26431 0.0763797
\(275\) −2.30468 −0.138977
\(276\) 4.61447 0.277759
\(277\) 1.39436 0.0837787 0.0418894 0.999122i \(-0.486662\pi\)
0.0418894 + 0.999122i \(0.486662\pi\)
\(278\) 2.78718 0.167164
\(279\) −0.705141 −0.0422157
\(280\) 3.05557 0.182605
\(281\) 11.2011 0.668200 0.334100 0.942538i \(-0.391568\pi\)
0.334100 + 0.942538i \(0.391568\pi\)
\(282\) 1.06799 0.0635981
\(283\) −14.8446 −0.882422 −0.441211 0.897403i \(-0.645451\pi\)
−0.441211 + 0.897403i \(0.645451\pi\)
\(284\) −27.0052 −1.60246
\(285\) −1.93504 −0.114622
\(286\) 0 0
\(287\) 3.05611 0.180396
\(288\) 4.99419 0.294285
\(289\) 2.26328 0.133134
\(290\) 4.18135 0.245537
\(291\) −1.74080 −0.102047
\(292\) −23.8684 −1.39680
\(293\) −17.8257 −1.04139 −0.520695 0.853743i \(-0.674327\pi\)
−0.520695 + 0.853743i \(0.674327\pi\)
\(294\) −0.494186 −0.0288215
\(295\) −8.08312 −0.470618
\(296\) −5.05786 −0.293982
\(297\) −1.00650 −0.0584033
\(298\) 2.71764 0.157429
\(299\) 0 0
\(300\) −4.02036 −0.232116
\(301\) 10.5077 0.605656
\(302\) 4.10712 0.236338
\(303\) −12.8587 −0.738716
\(304\) 3.04939 0.174894
\(305\) 0.927198 0.0530912
\(306\) −2.16898 −0.123992
\(307\) −30.6385 −1.74863 −0.874317 0.485356i \(-0.838690\pi\)
−0.874317 + 0.485356i \(0.838690\pi\)
\(308\) 1.76720 0.100696
\(309\) −14.6917 −0.835779
\(310\) −0.573678 −0.0325827
\(311\) 9.27236 0.525788 0.262894 0.964825i \(-0.415323\pi\)
0.262894 + 0.964825i \(0.415323\pi\)
\(312\) 0 0
\(313\) −25.7441 −1.45514 −0.727572 0.686031i \(-0.759351\pi\)
−0.727572 + 0.686031i \(0.759351\pi\)
\(314\) 6.33164 0.357315
\(315\) −1.64627 −0.0927570
\(316\) −13.4014 −0.753889
\(317\) 5.98521 0.336163 0.168082 0.985773i \(-0.446243\pi\)
0.168082 + 0.985773i \(0.446243\pi\)
\(318\) 0.972469 0.0545334
\(319\) 5.17297 0.289631
\(320\) −4.47883 −0.250374
\(321\) −3.37556 −0.188405
\(322\) −1.29880 −0.0723794
\(323\) −5.15886 −0.287047
\(324\) −1.75578 −0.0975433
\(325\) 0 0
\(326\) 5.31679 0.294470
\(327\) 9.90520 0.547759
\(328\) 5.67230 0.313200
\(329\) 2.16111 0.119146
\(330\) −0.818857 −0.0450766
\(331\) −24.7010 −1.35769 −0.678846 0.734281i \(-0.737520\pi\)
−0.678846 + 0.734281i \(0.737520\pi\)
\(332\) −0.0952651 −0.00522835
\(333\) 2.72506 0.149332
\(334\) −12.3576 −0.676177
\(335\) 21.5762 1.17883
\(336\) 2.59432 0.141532
\(337\) −6.44446 −0.351052 −0.175526 0.984475i \(-0.556163\pi\)
−0.175526 + 0.984475i \(0.556163\pi\)
\(338\) 0 0
\(339\) 13.5673 0.736877
\(340\) 12.6864 0.688014
\(341\) −0.709727 −0.0384339
\(342\) 0.580871 0.0314099
\(343\) −1.00000 −0.0539949
\(344\) 19.5029 1.05153
\(345\) −4.32667 −0.232940
\(346\) 8.27008 0.444602
\(347\) 15.7956 0.847955 0.423977 0.905673i \(-0.360634\pi\)
0.423977 + 0.905673i \(0.360634\pi\)
\(348\) 9.02390 0.483732
\(349\) 21.2652 1.13830 0.569150 0.822234i \(-0.307273\pi\)
0.569150 + 0.822234i \(0.307273\pi\)
\(350\) 1.13158 0.0604855
\(351\) 0 0
\(352\) 5.02667 0.267922
\(353\) 10.0764 0.536311 0.268156 0.963376i \(-0.413586\pi\)
0.268156 + 0.963376i \(0.413586\pi\)
\(354\) 2.42643 0.128963
\(355\) 25.3209 1.34389
\(356\) 1.05558 0.0559458
\(357\) −4.38900 −0.232290
\(358\) 6.06761 0.320683
\(359\) −22.7145 −1.19883 −0.599413 0.800440i \(-0.704599\pi\)
−0.599413 + 0.800440i \(0.704599\pi\)
\(360\) −3.05557 −0.161043
\(361\) −17.6184 −0.927285
\(362\) 11.2712 0.592403
\(363\) 9.98695 0.524179
\(364\) 0 0
\(365\) 22.3798 1.17141
\(366\) −0.278331 −0.0145486
\(367\) −19.7830 −1.03267 −0.516333 0.856388i \(-0.672703\pi\)
−0.516333 + 0.856388i \(0.672703\pi\)
\(368\) 6.81830 0.355429
\(369\) −3.05611 −0.159095
\(370\) 2.21701 0.115257
\(371\) 1.96782 0.102164
\(372\) −1.23807 −0.0641910
\(373\) −4.21238 −0.218109 −0.109054 0.994036i \(-0.534782\pi\)
−0.109054 + 0.994036i \(0.534782\pi\)
\(374\) −2.18309 −0.112885
\(375\) 12.0010 0.619728
\(376\) 4.01115 0.206859
\(377\) 0 0
\(378\) 0.494186 0.0254182
\(379\) 1.62828 0.0836393 0.0418197 0.999125i \(-0.486685\pi\)
0.0418197 + 0.999125i \(0.486685\pi\)
\(380\) −3.39751 −0.174289
\(381\) −7.65651 −0.392255
\(382\) 13.5436 0.692950
\(383\) 3.21481 0.164269 0.0821346 0.996621i \(-0.473826\pi\)
0.0821346 + 0.996621i \(0.473826\pi\)
\(384\) 11.3329 0.578327
\(385\) −1.65698 −0.0844475
\(386\) −3.16924 −0.161310
\(387\) −10.5077 −0.534139
\(388\) −3.05646 −0.155168
\(389\) −4.30323 −0.218183 −0.109091 0.994032i \(-0.534794\pi\)
−0.109091 + 0.994032i \(0.534794\pi\)
\(390\) 0 0
\(391\) −11.5350 −0.583350
\(392\) −1.85605 −0.0937449
\(393\) −1.25502 −0.0633074
\(394\) −8.50402 −0.428426
\(395\) 12.5656 0.632243
\(396\) −1.76720 −0.0888051
\(397\) −31.5480 −1.58335 −0.791673 0.610945i \(-0.790790\pi\)
−0.791673 + 0.610945i \(0.790790\pi\)
\(398\) −1.48764 −0.0745685
\(399\) 1.17541 0.0588440
\(400\) −5.94045 −0.297022
\(401\) 21.7130 1.08429 0.542147 0.840284i \(-0.317612\pi\)
0.542147 + 0.840284i \(0.317612\pi\)
\(402\) −6.47684 −0.323035
\(403\) 0 0
\(404\) −22.5771 −1.12325
\(405\) 1.64627 0.0818040
\(406\) −2.53989 −0.126053
\(407\) 2.74278 0.135955
\(408\) −8.14622 −0.403298
\(409\) −9.98412 −0.493683 −0.246842 0.969056i \(-0.579393\pi\)
−0.246842 + 0.969056i \(0.579393\pi\)
\(410\) −2.48634 −0.122792
\(411\) −2.55836 −0.126195
\(412\) −25.7953 −1.27084
\(413\) 4.90995 0.241603
\(414\) 1.29880 0.0638326
\(415\) 0.0893234 0.00438472
\(416\) 0 0
\(417\) −5.63993 −0.276189
\(418\) 0.584649 0.0285961
\(419\) −25.9114 −1.26586 −0.632928 0.774211i \(-0.718147\pi\)
−0.632928 + 0.774211i \(0.718147\pi\)
\(420\) −2.89049 −0.141042
\(421\) 22.8898 1.11558 0.557791 0.829981i \(-0.311649\pi\)
0.557791 + 0.829981i \(0.311649\pi\)
\(422\) 13.1724 0.641225
\(423\) −2.16111 −0.105077
\(424\) 3.65238 0.177375
\(425\) 10.0499 0.487490
\(426\) −7.60094 −0.368267
\(427\) −0.563211 −0.0272557
\(428\) −5.92674 −0.286480
\(429\) 0 0
\(430\) −8.54874 −0.412257
\(431\) −18.1818 −0.875787 −0.437893 0.899027i \(-0.644275\pi\)
−0.437893 + 0.899027i \(0.644275\pi\)
\(432\) −2.59432 −0.124819
\(433\) −22.5154 −1.08202 −0.541010 0.841016i \(-0.681958\pi\)
−0.541010 + 0.841016i \(0.681958\pi\)
\(434\) 0.348471 0.0167271
\(435\) −8.46108 −0.405678
\(436\) 17.3913 0.832894
\(437\) 3.08916 0.147775
\(438\) −6.71807 −0.321002
\(439\) 7.31288 0.349025 0.174512 0.984655i \(-0.444165\pi\)
0.174512 + 0.984655i \(0.444165\pi\)
\(440\) −3.07545 −0.146616
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −7.00281 −0.332714 −0.166357 0.986066i \(-0.553200\pi\)
−0.166357 + 0.986066i \(0.553200\pi\)
\(444\) 4.78461 0.227067
\(445\) −0.989747 −0.0469185
\(446\) 6.85908 0.324787
\(447\) −5.49922 −0.260104
\(448\) 2.72059 0.128536
\(449\) 1.74630 0.0824132 0.0412066 0.999151i \(-0.486880\pi\)
0.0412066 + 0.999151i \(0.486880\pi\)
\(450\) −1.13158 −0.0533432
\(451\) −3.07598 −0.144842
\(452\) 23.8213 1.12046
\(453\) −8.31087 −0.390479
\(454\) 6.77925 0.318166
\(455\) 0 0
\(456\) 2.18162 0.102164
\(457\) −18.2001 −0.851367 −0.425683 0.904872i \(-0.639966\pi\)
−0.425683 + 0.904872i \(0.639966\pi\)
\(458\) 4.90838 0.229354
\(459\) 4.38900 0.204861
\(460\) −7.59668 −0.354197
\(461\) −36.4349 −1.69694 −0.848471 0.529242i \(-0.822477\pi\)
−0.848471 + 0.529242i \(0.822477\pi\)
\(462\) 0.497400 0.0231412
\(463\) 33.5410 1.55878 0.779391 0.626538i \(-0.215529\pi\)
0.779391 + 0.626538i \(0.215529\pi\)
\(464\) 13.3336 0.618998
\(465\) 1.16085 0.0538333
\(466\) 9.60817 0.445090
\(467\) 3.86589 0.178892 0.0894461 0.995992i \(-0.471490\pi\)
0.0894461 + 0.995992i \(0.471490\pi\)
\(468\) 0 0
\(469\) −13.1061 −0.605182
\(470\) −1.75821 −0.0811001
\(471\) −12.8123 −0.590358
\(472\) 9.11314 0.419466
\(473\) −10.5761 −0.486289
\(474\) −3.77200 −0.173254
\(475\) −2.69143 −0.123491
\(476\) −7.70611 −0.353209
\(477\) −1.96782 −0.0901003
\(478\) 8.09899 0.370439
\(479\) 37.2104 1.70019 0.850094 0.526631i \(-0.176545\pi\)
0.850094 + 0.526631i \(0.176545\pi\)
\(480\) −8.22180 −0.375272
\(481\) 0 0
\(482\) −7.90934 −0.360261
\(483\) 2.62816 0.119586
\(484\) 17.5349 0.797040
\(485\) 2.86583 0.130131
\(486\) −0.494186 −0.0224167
\(487\) 19.0179 0.861783 0.430892 0.902404i \(-0.358199\pi\)
0.430892 + 0.902404i \(0.358199\pi\)
\(488\) −1.04535 −0.0473208
\(489\) −10.7587 −0.486524
\(490\) 0.813565 0.0367531
\(491\) 14.7990 0.667868 0.333934 0.942596i \(-0.391624\pi\)
0.333934 + 0.942596i \(0.391624\pi\)
\(492\) −5.36585 −0.241911
\(493\) −22.5574 −1.01593
\(494\) 0 0
\(495\) 1.65698 0.0744757
\(496\) −1.82936 −0.0821408
\(497\) −15.3807 −0.689920
\(498\) −0.0268135 −0.00120154
\(499\) −27.5937 −1.23526 −0.617632 0.786467i \(-0.711908\pi\)
−0.617632 + 0.786467i \(0.711908\pi\)
\(500\) 21.0711 0.942327
\(501\) 25.0059 1.11718
\(502\) −6.78959 −0.303034
\(503\) 42.9458 1.91486 0.957428 0.288671i \(-0.0932135\pi\)
0.957428 + 0.288671i \(0.0932135\pi\)
\(504\) 1.85605 0.0826752
\(505\) 21.1690 0.942008
\(506\) 1.30725 0.0581143
\(507\) 0 0
\(508\) −13.4431 −0.596443
\(509\) −25.7321 −1.14056 −0.570278 0.821452i \(-0.693165\pi\)
−0.570278 + 0.821452i \(0.693165\pi\)
\(510\) 3.57073 0.158115
\(511\) −13.5942 −0.601373
\(512\) 22.5870 0.998212
\(513\) −1.17541 −0.0518955
\(514\) 12.4041 0.547122
\(515\) 24.1865 1.06578
\(516\) −18.4493 −0.812185
\(517\) −2.17517 −0.0956639
\(518\) −1.34669 −0.0591700
\(519\) −16.7347 −0.734573
\(520\) 0 0
\(521\) 33.4269 1.46446 0.732229 0.681059i \(-0.238480\pi\)
0.732229 + 0.681059i \(0.238480\pi\)
\(522\) 2.53989 0.111168
\(523\) −23.8931 −1.04477 −0.522386 0.852709i \(-0.674958\pi\)
−0.522386 + 0.852709i \(0.674958\pi\)
\(524\) −2.20354 −0.0962621
\(525\) −2.28979 −0.0999345
\(526\) 3.39123 0.147864
\(527\) 3.09486 0.134814
\(528\) −2.61120 −0.113638
\(529\) −16.0928 −0.699685
\(530\) −1.60095 −0.0695408
\(531\) −4.90995 −0.213074
\(532\) 2.06376 0.0894753
\(533\) 0 0
\(534\) 0.297107 0.0128571
\(535\) 5.55709 0.240254
\(536\) −24.3256 −1.05070
\(537\) −12.2780 −0.529834
\(538\) 9.00282 0.388139
\(539\) 1.00650 0.0433532
\(540\) 2.89049 0.124387
\(541\) 5.29873 0.227810 0.113905 0.993492i \(-0.463664\pi\)
0.113905 + 0.993492i \(0.463664\pi\)
\(542\) 7.43323 0.319285
\(543\) −22.8077 −0.978770
\(544\) −21.9195 −0.939789
\(545\) −16.3067 −0.698500
\(546\) 0 0
\(547\) 37.2193 1.59138 0.795691 0.605703i \(-0.207108\pi\)
0.795691 + 0.605703i \(0.207108\pi\)
\(548\) −4.49192 −0.191886
\(549\) 0.563211 0.0240372
\(550\) −1.13894 −0.0485646
\(551\) 6.04106 0.257358
\(552\) 4.87801 0.207622
\(553\) −7.63275 −0.324577
\(554\) 0.689072 0.0292758
\(555\) −4.48619 −0.190428
\(556\) −9.90248 −0.419959
\(557\) 5.40182 0.228883 0.114441 0.993430i \(-0.463492\pi\)
0.114441 + 0.993430i \(0.463492\pi\)
\(558\) −0.348471 −0.0147519
\(559\) 0 0
\(560\) −4.27096 −0.180481
\(561\) 4.41754 0.186509
\(562\) 5.53541 0.233497
\(563\) −10.9360 −0.460898 −0.230449 0.973084i \(-0.574019\pi\)
−0.230449 + 0.973084i \(0.574019\pi\)
\(564\) −3.79444 −0.159775
\(565\) −22.3355 −0.939663
\(566\) −7.33602 −0.308356
\(567\) −1.00000 −0.0419961
\(568\) −28.5475 −1.19783
\(569\) −30.5762 −1.28182 −0.640911 0.767615i \(-0.721443\pi\)
−0.640911 + 0.767615i \(0.721443\pi\)
\(570\) −0.956271 −0.0400538
\(571\) 6.37732 0.266882 0.133441 0.991057i \(-0.457397\pi\)
0.133441 + 0.991057i \(0.457397\pi\)
\(572\) 0 0
\(573\) −27.4058 −1.14489
\(574\) 1.51029 0.0630381
\(575\) −6.01793 −0.250965
\(576\) −2.72059 −0.113358
\(577\) 0.900721 0.0374975 0.0187487 0.999824i \(-0.494032\pi\)
0.0187487 + 0.999824i \(0.494032\pi\)
\(578\) 1.11848 0.0465227
\(579\) 6.41304 0.266517
\(580\) −14.8558 −0.616854
\(581\) −0.0542580 −0.00225100
\(582\) −0.860279 −0.0356597
\(583\) −1.98062 −0.0820288
\(584\) −25.2316 −1.04409
\(585\) 0 0
\(586\) −8.80923 −0.363906
\(587\) −43.8262 −1.80890 −0.904451 0.426577i \(-0.859719\pi\)
−0.904451 + 0.426577i \(0.859719\pi\)
\(588\) 1.75578 0.0724071
\(589\) −0.828828 −0.0341513
\(590\) −3.99457 −0.164454
\(591\) 17.2081 0.707848
\(592\) 7.06969 0.290562
\(593\) −30.8733 −1.26781 −0.633907 0.773409i \(-0.718550\pi\)
−0.633907 + 0.773409i \(0.718550\pi\)
\(594\) −0.497400 −0.0204086
\(595\) 7.22548 0.296216
\(596\) −9.65543 −0.395502
\(597\) 3.01028 0.123202
\(598\) 0 0
\(599\) 33.0466 1.35025 0.675123 0.737705i \(-0.264091\pi\)
0.675123 + 0.737705i \(0.264091\pi\)
\(600\) −4.24997 −0.173504
\(601\) −23.2566 −0.948658 −0.474329 0.880348i \(-0.657309\pi\)
−0.474329 + 0.880348i \(0.657309\pi\)
\(602\) 5.19278 0.211642
\(603\) 13.1061 0.533720
\(604\) −14.5921 −0.593743
\(605\) −16.4412 −0.668432
\(606\) −6.35461 −0.258139
\(607\) 36.9583 1.50009 0.750045 0.661386i \(-0.230032\pi\)
0.750045 + 0.661386i \(0.230032\pi\)
\(608\) 5.87021 0.238068
\(609\) 5.13954 0.208265
\(610\) 0.458209 0.0185523
\(611\) 0 0
\(612\) 7.70611 0.311501
\(613\) −6.74925 −0.272600 −0.136300 0.990668i \(-0.543521\pi\)
−0.136300 + 0.990668i \(0.543521\pi\)
\(614\) −15.1411 −0.611047
\(615\) 5.03119 0.202877
\(616\) 1.86813 0.0752690
\(617\) 34.7076 1.39727 0.698637 0.715476i \(-0.253790\pi\)
0.698637 + 0.715476i \(0.253790\pi\)
\(618\) −7.26041 −0.292057
\(619\) 7.42759 0.298540 0.149270 0.988796i \(-0.452308\pi\)
0.149270 + 0.988796i \(0.452308\pi\)
\(620\) 2.03820 0.0818562
\(621\) −2.62816 −0.105465
\(622\) 4.58227 0.183732
\(623\) 0.601205 0.0240868
\(624\) 0 0
\(625\) −8.30795 −0.332318
\(626\) −12.7224 −0.508489
\(627\) −1.18305 −0.0472466
\(628\) −22.4955 −0.897668
\(629\) −11.9603 −0.476887
\(630\) −0.813565 −0.0324132
\(631\) −30.4787 −1.21334 −0.606669 0.794954i \(-0.707495\pi\)
−0.606669 + 0.794954i \(0.707495\pi\)
\(632\) −14.1668 −0.563525
\(633\) −26.6548 −1.05943
\(634\) 2.95781 0.117470
\(635\) 12.6047 0.500202
\(636\) −3.45506 −0.137002
\(637\) 0 0
\(638\) 2.55641 0.101209
\(639\) 15.3807 0.608452
\(640\) −18.6570 −0.737481
\(641\) 27.6795 1.09328 0.546638 0.837369i \(-0.315907\pi\)
0.546638 + 0.837369i \(0.315907\pi\)
\(642\) −1.66815 −0.0658368
\(643\) −29.0749 −1.14660 −0.573302 0.819344i \(-0.694338\pi\)
−0.573302 + 0.819344i \(0.694338\pi\)
\(644\) 4.61447 0.181836
\(645\) 17.2986 0.681132
\(646\) −2.54944 −0.100306
\(647\) 8.93804 0.351391 0.175695 0.984445i \(-0.443783\pi\)
0.175695 + 0.984445i \(0.443783\pi\)
\(648\) −1.85605 −0.0729127
\(649\) −4.94189 −0.193986
\(650\) 0 0
\(651\) −0.705141 −0.0276366
\(652\) −18.8899 −0.739784
\(653\) −27.1525 −1.06256 −0.531280 0.847196i \(-0.678289\pi\)
−0.531280 + 0.847196i \(0.678289\pi\)
\(654\) 4.89501 0.191410
\(655\) 2.06611 0.0807295
\(656\) −7.92853 −0.309557
\(657\) 13.5942 0.530361
\(658\) 1.06799 0.0416347
\(659\) −5.63077 −0.219344 −0.109672 0.993968i \(-0.534980\pi\)
−0.109672 + 0.993968i \(0.534980\pi\)
\(660\) 2.90929 0.113244
\(661\) −12.6352 −0.491453 −0.245727 0.969339i \(-0.579027\pi\)
−0.245727 + 0.969339i \(0.579027\pi\)
\(662\) −12.2069 −0.474435
\(663\) 0 0
\(664\) −0.100706 −0.00390814
\(665\) −1.93504 −0.0750377
\(666\) 1.34669 0.0521831
\(667\) 13.5075 0.523014
\(668\) 43.9049 1.69873
\(669\) −13.8795 −0.536614
\(670\) 10.6626 0.411934
\(671\) 0.566874 0.0218839
\(672\) 4.99419 0.192655
\(673\) −45.5652 −1.75641 −0.878204 0.478286i \(-0.841258\pi\)
−0.878204 + 0.478286i \(0.841258\pi\)
\(674\) −3.18476 −0.122673
\(675\) 2.28979 0.0881339
\(676\) 0 0
\(677\) −26.6074 −1.02261 −0.511303 0.859400i \(-0.670837\pi\)
−0.511303 + 0.859400i \(0.670837\pi\)
\(678\) 6.70479 0.257496
\(679\) −1.74080 −0.0668057
\(680\) 13.4109 0.514284
\(681\) −13.7180 −0.525675
\(682\) −0.350737 −0.0134304
\(683\) 21.5696 0.825338 0.412669 0.910881i \(-0.364597\pi\)
0.412669 + 0.910881i \(0.364597\pi\)
\(684\) −2.06376 −0.0789098
\(685\) 4.21177 0.160923
\(686\) −0.494186 −0.0188681
\(687\) −9.93225 −0.378939
\(688\) −27.2605 −1.03930
\(689\) 0 0
\(690\) −2.13818 −0.0813992
\(691\) −36.2297 −1.37824 −0.689121 0.724646i \(-0.742003\pi\)
−0.689121 + 0.724646i \(0.742003\pi\)
\(692\) −29.3825 −1.11696
\(693\) −1.00650 −0.0382339
\(694\) 7.80599 0.296311
\(695\) 9.28487 0.352195
\(696\) 9.53927 0.361585
\(697\) 13.4132 0.508063
\(698\) 10.5090 0.397770
\(699\) −19.4424 −0.735379
\(700\) −4.02036 −0.151955
\(701\) 4.73093 0.178685 0.0893424 0.996001i \(-0.471523\pi\)
0.0893424 + 0.996001i \(0.471523\pi\)
\(702\) 0 0
\(703\) 3.20306 0.120806
\(704\) −2.73828 −0.103203
\(705\) 3.55778 0.133994
\(706\) 4.97961 0.187410
\(707\) −12.8587 −0.483603
\(708\) −8.62080 −0.323989
\(709\) 23.5959 0.886163 0.443082 0.896481i \(-0.353885\pi\)
0.443082 + 0.896481i \(0.353885\pi\)
\(710\) 12.5132 0.469613
\(711\) 7.63275 0.286250
\(712\) 1.11587 0.0418190
\(713\) −1.85322 −0.0694038
\(714\) −2.16898 −0.0811721
\(715\) 0 0
\(716\) −21.5574 −0.805639
\(717\) −16.3885 −0.612041
\(718\) −11.2252 −0.418921
\(719\) 16.1744 0.603203 0.301601 0.953434i \(-0.402479\pi\)
0.301601 + 0.953434i \(0.402479\pi\)
\(720\) 4.27096 0.159169
\(721\) −14.6917 −0.547146
\(722\) −8.70678 −0.324033
\(723\) 16.0048 0.595224
\(724\) −40.0452 −1.48827
\(725\) −11.7684 −0.437069
\(726\) 4.93541 0.183170
\(727\) −12.1774 −0.451633 −0.225817 0.974170i \(-0.572505\pi\)
−0.225817 + 0.974170i \(0.572505\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 11.0598 0.409341
\(731\) 46.1184 1.70575
\(732\) 0.988874 0.0365498
\(733\) −35.6552 −1.31695 −0.658477 0.752601i \(-0.728799\pi\)
−0.658477 + 0.752601i \(0.728799\pi\)
\(734\) −9.77650 −0.360857
\(735\) −1.64627 −0.0607237
\(736\) 13.1255 0.483814
\(737\) 13.1913 0.485908
\(738\) −1.51029 −0.0555944
\(739\) −18.0473 −0.663880 −0.331940 0.943300i \(-0.607703\pi\)
−0.331940 + 0.943300i \(0.607703\pi\)
\(740\) −7.87677 −0.289556
\(741\) 0 0
\(742\) 0.972469 0.0357005
\(743\) −52.9988 −1.94434 −0.972168 0.234285i \(-0.924725\pi\)
−0.972168 + 0.234285i \(0.924725\pi\)
\(744\) −1.30878 −0.0479822
\(745\) 9.05322 0.331684
\(746\) −2.08170 −0.0762165
\(747\) 0.0542580 0.00198520
\(748\) 7.75623 0.283596
\(749\) −3.37556 −0.123340
\(750\) 5.93072 0.216559
\(751\) 38.3089 1.39791 0.698956 0.715165i \(-0.253648\pi\)
0.698956 + 0.715165i \(0.253648\pi\)
\(752\) −5.60663 −0.204453
\(753\) 13.7389 0.500674
\(754\) 0 0
\(755\) 13.6820 0.497938
\(756\) −1.75578 −0.0638571
\(757\) 26.3033 0.956010 0.478005 0.878357i \(-0.341360\pi\)
0.478005 + 0.878357i \(0.341360\pi\)
\(758\) 0.804675 0.0292271
\(759\) −2.64526 −0.0960167
\(760\) −3.59155 −0.130279
\(761\) 41.3290 1.49818 0.749088 0.662470i \(-0.230492\pi\)
0.749088 + 0.662470i \(0.230492\pi\)
\(762\) −3.78374 −0.137071
\(763\) 9.90520 0.358592
\(764\) −48.1186 −1.74087
\(765\) −7.22548 −0.261238
\(766\) 1.58872 0.0574026
\(767\) 0 0
\(768\) 0.159364 0.00575057
\(769\) −19.8950 −0.717431 −0.358715 0.933447i \(-0.616785\pi\)
−0.358715 + 0.933447i \(0.616785\pi\)
\(770\) −0.818857 −0.0295095
\(771\) −25.1001 −0.903958
\(772\) 11.2599 0.405252
\(773\) −37.3499 −1.34338 −0.671692 0.740831i \(-0.734432\pi\)
−0.671692 + 0.740831i \(0.734432\pi\)
\(774\) −5.19278 −0.186651
\(775\) 1.61462 0.0579989
\(776\) −3.23102 −0.115987
\(777\) 2.72506 0.0977610
\(778\) −2.12660 −0.0762422
\(779\) −3.59217 −0.128703
\(780\) 0 0
\(781\) 15.4808 0.553945
\(782\) −5.70043 −0.203847
\(783\) −5.13954 −0.183672
\(784\) 2.59432 0.0926544
\(785\) 21.0925 0.752822
\(786\) −0.620214 −0.0221223
\(787\) 15.9051 0.566955 0.283478 0.958979i \(-0.408512\pi\)
0.283478 + 0.958979i \(0.408512\pi\)
\(788\) 30.2137 1.07632
\(789\) −6.86224 −0.244302
\(790\) 6.20974 0.220933
\(791\) 13.5673 0.482399
\(792\) −1.86813 −0.0663810
\(793\) 0 0
\(794\) −15.5906 −0.553288
\(795\) 3.23957 0.114896
\(796\) 5.28538 0.187335
\(797\) 13.5259 0.479111 0.239555 0.970883i \(-0.422998\pi\)
0.239555 + 0.970883i \(0.422998\pi\)
\(798\) 0.580871 0.0205626
\(799\) 9.48512 0.335560
\(800\) −11.4356 −0.404310
\(801\) −0.601205 −0.0212425
\(802\) 10.7302 0.378898
\(803\) 13.6826 0.482849
\(804\) 23.0114 0.811548
\(805\) −4.32667 −0.152495
\(806\) 0 0
\(807\) −18.2175 −0.641285
\(808\) −23.8665 −0.839622
\(809\) 7.60313 0.267312 0.133656 0.991028i \(-0.457328\pi\)
0.133656 + 0.991028i \(0.457328\pi\)
\(810\) 0.813565 0.0285858
\(811\) −23.9460 −0.840859 −0.420429 0.907325i \(-0.638121\pi\)
−0.420429 + 0.907325i \(0.638121\pi\)
\(812\) 9.02390 0.316677
\(813\) −15.0414 −0.527523
\(814\) 1.35545 0.0475084
\(815\) 17.7117 0.620414
\(816\) 11.3865 0.398606
\(817\) −12.3509 −0.432103
\(818\) −4.93402 −0.172514
\(819\) 0 0
\(820\) 8.83366 0.308485
\(821\) 13.5062 0.471370 0.235685 0.971829i \(-0.424267\pi\)
0.235685 + 0.971829i \(0.424267\pi\)
\(822\) −1.26431 −0.0440978
\(823\) 26.6348 0.928430 0.464215 0.885723i \(-0.346336\pi\)
0.464215 + 0.885723i \(0.346336\pi\)
\(824\) −27.2685 −0.949944
\(825\) 2.30468 0.0802386
\(826\) 2.42643 0.0844263
\(827\) 32.3365 1.12445 0.562225 0.826984i \(-0.309945\pi\)
0.562225 + 0.826984i \(0.309945\pi\)
\(828\) −4.61447 −0.160364
\(829\) −38.3742 −1.33279 −0.666395 0.745598i \(-0.732164\pi\)
−0.666395 + 0.745598i \(0.732164\pi\)
\(830\) 0.0441424 0.00153221
\(831\) −1.39436 −0.0483697
\(832\) 0 0
\(833\) −4.38900 −0.152070
\(834\) −2.78718 −0.0965120
\(835\) −41.1666 −1.42463
\(836\) −2.07718 −0.0718408
\(837\) 0.705141 0.0243732
\(838\) −12.8051 −0.442344
\(839\) −15.9684 −0.551290 −0.275645 0.961260i \(-0.588891\pi\)
−0.275645 + 0.961260i \(0.588891\pi\)
\(840\) −3.05557 −0.105427
\(841\) −2.58514 −0.0891427
\(842\) 11.3118 0.389832
\(843\) −11.2011 −0.385785
\(844\) −46.8000 −1.61092
\(845\) 0 0
\(846\) −1.06799 −0.0367184
\(847\) 9.98695 0.343156
\(848\) −5.10516 −0.175312
\(849\) 14.8446 0.509467
\(850\) 4.96650 0.170350
\(851\) 7.16190 0.245507
\(852\) 27.0052 0.925182
\(853\) 17.3245 0.593181 0.296590 0.955005i \(-0.404150\pi\)
0.296590 + 0.955005i \(0.404150\pi\)
\(854\) −0.278331 −0.00952429
\(855\) 1.93504 0.0661771
\(856\) −6.26522 −0.214141
\(857\) −42.8681 −1.46435 −0.732174 0.681118i \(-0.761494\pi\)
−0.732174 + 0.681118i \(0.761494\pi\)
\(858\) 0 0
\(859\) −5.98645 −0.204255 −0.102128 0.994771i \(-0.532565\pi\)
−0.102128 + 0.994771i \(0.532565\pi\)
\(860\) 30.3726 1.03570
\(861\) −3.05611 −0.104152
\(862\) −8.98520 −0.306037
\(863\) 9.24121 0.314575 0.157287 0.987553i \(-0.449725\pi\)
0.157287 + 0.987553i \(0.449725\pi\)
\(864\) −4.99419 −0.169906
\(865\) 27.5499 0.936726
\(866\) −11.1268 −0.378104
\(867\) −2.26328 −0.0768650
\(868\) −1.23807 −0.0420229
\(869\) 7.68239 0.260607
\(870\) −4.18135 −0.141761
\(871\) 0 0
\(872\) 18.3846 0.622581
\(873\) 1.74080 0.0589171
\(874\) 1.52662 0.0516388
\(875\) 12.0010 0.405707
\(876\) 23.8684 0.806440
\(877\) −36.2804 −1.22510 −0.612551 0.790431i \(-0.709856\pi\)
−0.612551 + 0.790431i \(0.709856\pi\)
\(878\) 3.61392 0.121964
\(879\) 17.8257 0.601247
\(880\) 4.29874 0.144911
\(881\) 35.8216 1.20686 0.603431 0.797416i \(-0.293800\pi\)
0.603431 + 0.797416i \(0.293800\pi\)
\(882\) 0.494186 0.0166401
\(883\) 2.07802 0.0699311 0.0349655 0.999389i \(-0.488868\pi\)
0.0349655 + 0.999389i \(0.488868\pi\)
\(884\) 0 0
\(885\) 8.08312 0.271711
\(886\) −3.46069 −0.116264
\(887\) 5.39229 0.181055 0.0905277 0.995894i \(-0.471145\pi\)
0.0905277 + 0.995894i \(0.471145\pi\)
\(888\) 5.05786 0.169731
\(889\) −7.65651 −0.256791
\(890\) −0.489119 −0.0163953
\(891\) 1.00650 0.0337191
\(892\) −24.3694 −0.815949
\(893\) −2.54019 −0.0850043
\(894\) −2.71764 −0.0908915
\(895\) 20.2129 0.675642
\(896\) 11.3329 0.378604
\(897\) 0 0
\(898\) 0.862999 0.0287987
\(899\) −3.62410 −0.120870
\(900\) 4.02036 0.134012
\(901\) 8.63675 0.287732
\(902\) −1.52011 −0.0506141
\(903\) −10.5077 −0.349676
\(904\) 25.1817 0.837532
\(905\) 37.5476 1.24813
\(906\) −4.10712 −0.136450
\(907\) −22.5753 −0.749601 −0.374801 0.927105i \(-0.622289\pi\)
−0.374801 + 0.927105i \(0.622289\pi\)
\(908\) −24.0858 −0.799315
\(909\) 12.8587 0.426498
\(910\) 0 0
\(911\) 55.3163 1.83271 0.916355 0.400367i \(-0.131117\pi\)
0.916355 + 0.400367i \(0.131117\pi\)
\(912\) −3.04939 −0.100975
\(913\) 0.0546109 0.00180736
\(914\) −8.99426 −0.297504
\(915\) −0.927198 −0.0306522
\(916\) −17.4388 −0.576196
\(917\) −1.25502 −0.0414444
\(918\) 2.16898 0.0715870
\(919\) −13.0981 −0.432067 −0.216034 0.976386i \(-0.569312\pi\)
−0.216034 + 0.976386i \(0.569312\pi\)
\(920\) −8.03054 −0.264759
\(921\) 30.6385 1.00957
\(922\) −18.0056 −0.592984
\(923\) 0 0
\(924\) −1.76720 −0.0581366
\(925\) −6.23980 −0.205164
\(926\) 16.5755 0.544704
\(927\) 14.6917 0.482537
\(928\) 25.6678 0.842588
\(929\) −35.5476 −1.16628 −0.583139 0.812372i \(-0.698176\pi\)
−0.583139 + 0.812372i \(0.698176\pi\)
\(930\) 0.573678 0.0188116
\(931\) 1.17541 0.0385225
\(932\) −34.1366 −1.11818
\(933\) −9.27236 −0.303564
\(934\) 1.91047 0.0625125
\(935\) −7.27248 −0.237835
\(936\) 0 0
\(937\) −2.01075 −0.0656884 −0.0328442 0.999460i \(-0.510457\pi\)
−0.0328442 + 0.999460i \(0.510457\pi\)
\(938\) −6.47684 −0.211476
\(939\) 25.7441 0.840128
\(940\) 6.24669 0.203744
\(941\) 47.7893 1.55789 0.778943 0.627095i \(-0.215756\pi\)
0.778943 + 0.627095i \(0.215756\pi\)
\(942\) −6.33164 −0.206296
\(943\) −8.03194 −0.261556
\(944\) −12.7380 −0.414587
\(945\) 1.64627 0.0535533
\(946\) −5.22656 −0.169930
\(947\) 40.3924 1.31258 0.656288 0.754510i \(-0.272126\pi\)
0.656288 + 0.754510i \(0.272126\pi\)
\(948\) 13.4014 0.435258
\(949\) 0 0
\(950\) −1.33007 −0.0431531
\(951\) −5.98521 −0.194084
\(952\) −8.14622 −0.264020
\(953\) 27.0429 0.876007 0.438003 0.898973i \(-0.355686\pi\)
0.438003 + 0.898973i \(0.355686\pi\)
\(954\) −0.972469 −0.0314849
\(955\) 45.1175 1.45997
\(956\) −28.7747 −0.930639
\(957\) −5.17297 −0.167218
\(958\) 18.3889 0.594118
\(959\) −2.55836 −0.0826139
\(960\) 4.47883 0.144554
\(961\) −30.5028 −0.983961
\(962\) 0 0
\(963\) 3.37556 0.108776
\(964\) 28.1009 0.905069
\(965\) −10.5576 −0.339862
\(966\) 1.29880 0.0417882
\(967\) 33.5839 1.07998 0.539992 0.841670i \(-0.318427\pi\)
0.539992 + 0.841670i \(0.318427\pi\)
\(968\) 18.5363 0.595780
\(969\) 5.15886 0.165727
\(970\) 1.41625 0.0454732
\(971\) 37.0838 1.19008 0.595038 0.803698i \(-0.297137\pi\)
0.595038 + 0.803698i \(0.297137\pi\)
\(972\) 1.75578 0.0563167
\(973\) −5.63993 −0.180808
\(974\) 9.39838 0.301144
\(975\) 0 0
\(976\) 1.46115 0.0467703
\(977\) −44.9088 −1.43676 −0.718379 0.695652i \(-0.755116\pi\)
−0.718379 + 0.695652i \(0.755116\pi\)
\(978\) −5.31679 −0.170012
\(979\) −0.605115 −0.0193396
\(980\) −2.89049 −0.0923334
\(981\) −9.90520 −0.316249
\(982\) 7.31344 0.233381
\(983\) 6.22613 0.198583 0.0992914 0.995058i \(-0.468342\pi\)
0.0992914 + 0.995058i \(0.468342\pi\)
\(984\) −5.67230 −0.180826
\(985\) −28.3293 −0.902646
\(986\) −11.1476 −0.355011
\(987\) −2.16111 −0.0687890
\(988\) 0 0
\(989\) −27.6161 −0.878139
\(990\) 0.818857 0.0260250
\(991\) 23.7212 0.753529 0.376765 0.926309i \(-0.377037\pi\)
0.376765 + 0.926309i \(0.377037\pi\)
\(992\) −3.52160 −0.111811
\(993\) 24.7010 0.783864
\(994\) −7.60094 −0.241087
\(995\) −4.95573 −0.157107
\(996\) 0.0952651 0.00301859
\(997\) −55.6549 −1.76261 −0.881303 0.472551i \(-0.843333\pi\)
−0.881303 + 0.472551i \(0.843333\pi\)
\(998\) −13.6364 −0.431654
\(999\) −2.72506 −0.0862171
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.1.6 yes 9
13.12 even 2 3549.2.a.be.1.4 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.4 9 13.12 even 2
3549.2.a.bf.1.6 yes 9 1.1 even 1 trivial