Properties

Label 5577.2.a.x.1.7
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.5325692073\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 21 x^{4} + 13 x^{3} - 33 x^{2} - 7 x + 7\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.15754\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.15754 q^{2} +1.00000 q^{3} +2.65498 q^{4} -0.710210 q^{5} +2.15754 q^{6} -2.30964 q^{7} +1.41315 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.15754 q^{2} +1.00000 q^{3} +2.65498 q^{4} -0.710210 q^{5} +2.15754 q^{6} -2.30964 q^{7} +1.41315 q^{8} +1.00000 q^{9} -1.53231 q^{10} -1.00000 q^{11} +2.65498 q^{12} -4.98315 q^{14} -0.710210 q^{15} -2.26104 q^{16} -6.68027 q^{17} +2.15754 q^{18} +0.242517 q^{19} -1.88559 q^{20} -2.30964 q^{21} -2.15754 q^{22} +9.53531 q^{23} +1.41315 q^{24} -4.49560 q^{25} +1.00000 q^{27} -6.13206 q^{28} -2.95273 q^{29} -1.53231 q^{30} +4.02017 q^{31} -7.70458 q^{32} -1.00000 q^{33} -14.4130 q^{34} +1.64033 q^{35} +2.65498 q^{36} -3.42304 q^{37} +0.523240 q^{38} -1.00363 q^{40} -9.46022 q^{41} -4.98315 q^{42} -11.8791 q^{43} -2.65498 q^{44} -0.710210 q^{45} +20.5728 q^{46} +12.9178 q^{47} -2.26104 q^{48} -1.66555 q^{49} -9.69944 q^{50} -6.68027 q^{51} +6.78954 q^{53} +2.15754 q^{54} +0.710210 q^{55} -3.26386 q^{56} +0.242517 q^{57} -6.37063 q^{58} -7.81320 q^{59} -1.88559 q^{60} +0.910585 q^{61} +8.67368 q^{62} -2.30964 q^{63} -12.1009 q^{64} -2.15754 q^{66} -9.32216 q^{67} -17.7360 q^{68} +9.53531 q^{69} +3.53908 q^{70} -12.9704 q^{71} +1.41315 q^{72} -8.51665 q^{73} -7.38534 q^{74} -4.49560 q^{75} +0.643877 q^{76} +2.30964 q^{77} +1.82360 q^{79} +1.60581 q^{80} +1.00000 q^{81} -20.4108 q^{82} -4.64671 q^{83} -6.13206 q^{84} +4.74440 q^{85} -25.6297 q^{86} -2.95273 q^{87} -1.41315 q^{88} -14.7714 q^{89} -1.53231 q^{90} +25.3161 q^{92} +4.02017 q^{93} +27.8707 q^{94} -0.172238 q^{95} -7.70458 q^{96} -1.86542 q^{97} -3.59349 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{2} + 7q^{3} + 9q^{4} - 6q^{5} - 3q^{6} - 6q^{7} - 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 3q^{2} + 7q^{3} + 9q^{4} - 6q^{5} - 3q^{6} - 6q^{7} - 15q^{8} + 7q^{9} - 7q^{11} + 9q^{12} + 8q^{14} - 6q^{15} + 17q^{16} - 2q^{17} - 3q^{18} - 8q^{19} + 2q^{20} - 6q^{21} + 3q^{22} + 4q^{23} - 15q^{24} + 13q^{25} + 7q^{27} - 12q^{28} - 12q^{29} + 10q^{31} - 33q^{32} - 7q^{33} - 28q^{34} - 4q^{35} + 9q^{36} - 6q^{37} + 16q^{38} - 10q^{40} - 2q^{41} + 8q^{42} - 16q^{43} - 9q^{44} - 6q^{45} + 26q^{46} - 18q^{47} + 17q^{48} + 23q^{49} - 39q^{50} - 2q^{51} + 10q^{53} - 3q^{54} + 6q^{55} + 16q^{56} - 8q^{57} - 10q^{58} - 2q^{59} + 2q^{60} - 10q^{61} - 36q^{62} - 6q^{63} + 29q^{64} + 3q^{66} - 8q^{67} - 10q^{68} + 4q^{69} + 20q^{70} - 36q^{71} - 15q^{72} - 20q^{73} + 13q^{75} - 10q^{76} + 6q^{77} + 6q^{79} + 20q^{80} + 7q^{81} - 10q^{82} - 30q^{83} - 12q^{84} + 40q^{85} - 6q^{86} - 12q^{87} + 15q^{88} - 34q^{89} - 12q^{92} + 10q^{93} + 32q^{94} + 18q^{95} - 33q^{96} - 16q^{97} - q^{98} - 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.15754 1.52561 0.762806 0.646628i \(-0.223821\pi\)
0.762806 + 0.646628i \(0.223821\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.65498 1.32749
\(5\) −0.710210 −0.317616 −0.158808 0.987310i \(-0.550765\pi\)
−0.158808 + 0.987310i \(0.550765\pi\)
\(6\) 2.15754 0.880812
\(7\) −2.30964 −0.872963 −0.436482 0.899713i \(-0.643776\pi\)
−0.436482 + 0.899713i \(0.643776\pi\)
\(8\) 1.41315 0.499622
\(9\) 1.00000 0.333333
\(10\) −1.53231 −0.484558
\(11\) −1.00000 −0.301511
\(12\) 2.65498 0.766427
\(13\) 0 0
\(14\) −4.98315 −1.33180
\(15\) −0.710210 −0.183375
\(16\) −2.26104 −0.565261
\(17\) −6.68027 −1.62020 −0.810102 0.586289i \(-0.800588\pi\)
−0.810102 + 0.586289i \(0.800588\pi\)
\(18\) 2.15754 0.508537
\(19\) 0.242517 0.0556372 0.0278186 0.999613i \(-0.491144\pi\)
0.0278186 + 0.999613i \(0.491144\pi\)
\(20\) −1.88559 −0.421631
\(21\) −2.30964 −0.504005
\(22\) −2.15754 −0.459989
\(23\) 9.53531 1.98825 0.994125 0.108242i \(-0.0345220\pi\)
0.994125 + 0.108242i \(0.0345220\pi\)
\(24\) 1.41315 0.288457
\(25\) −4.49560 −0.899120
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −6.13206 −1.15885
\(29\) −2.95273 −0.548308 −0.274154 0.961686i \(-0.588398\pi\)
−0.274154 + 0.961686i \(0.588398\pi\)
\(30\) −1.53231 −0.279760
\(31\) 4.02017 0.722044 0.361022 0.932557i \(-0.382428\pi\)
0.361022 + 0.932557i \(0.382428\pi\)
\(32\) −7.70458 −1.36199
\(33\) −1.00000 −0.174078
\(34\) −14.4130 −2.47180
\(35\) 1.64033 0.277267
\(36\) 2.65498 0.442497
\(37\) −3.42304 −0.562744 −0.281372 0.959599i \(-0.590789\pi\)
−0.281372 + 0.959599i \(0.590789\pi\)
\(38\) 0.523240 0.0848807
\(39\) 0 0
\(40\) −1.00363 −0.158688
\(41\) −9.46022 −1.47744 −0.738719 0.674013i \(-0.764569\pi\)
−0.738719 + 0.674013i \(0.764569\pi\)
\(42\) −4.98315 −0.768916
\(43\) −11.8791 −1.81155 −0.905776 0.423757i \(-0.860711\pi\)
−0.905776 + 0.423757i \(0.860711\pi\)
\(44\) −2.65498 −0.400253
\(45\) −0.710210 −0.105872
\(46\) 20.5728 3.03330
\(47\) 12.9178 1.88426 0.942130 0.335249i \(-0.108820\pi\)
0.942130 + 0.335249i \(0.108820\pi\)
\(48\) −2.26104 −0.326353
\(49\) −1.66555 −0.237935
\(50\) −9.69944 −1.37171
\(51\) −6.68027 −0.935425
\(52\) 0 0
\(53\) 6.78954 0.932615 0.466307 0.884623i \(-0.345584\pi\)
0.466307 + 0.884623i \(0.345584\pi\)
\(54\) 2.15754 0.293604
\(55\) 0.710210 0.0957647
\(56\) −3.26386 −0.436152
\(57\) 0.242517 0.0321221
\(58\) −6.37063 −0.836504
\(59\) −7.81320 −1.01719 −0.508596 0.861005i \(-0.669835\pi\)
−0.508596 + 0.861005i \(0.669835\pi\)
\(60\) −1.88559 −0.243429
\(61\) 0.910585 0.116588 0.0582942 0.998299i \(-0.481434\pi\)
0.0582942 + 0.998299i \(0.481434\pi\)
\(62\) 8.67368 1.10156
\(63\) −2.30964 −0.290988
\(64\) −12.1009 −1.51261
\(65\) 0 0
\(66\) −2.15754 −0.265575
\(67\) −9.32216 −1.13888 −0.569442 0.822032i \(-0.692841\pi\)
−0.569442 + 0.822032i \(0.692841\pi\)
\(68\) −17.7360 −2.15080
\(69\) 9.53531 1.14792
\(70\) 3.53908 0.423001
\(71\) −12.9704 −1.53930 −0.769650 0.638466i \(-0.779569\pi\)
−0.769650 + 0.638466i \(0.779569\pi\)
\(72\) 1.41315 0.166541
\(73\) −8.51665 −0.996798 −0.498399 0.866948i \(-0.666079\pi\)
−0.498399 + 0.866948i \(0.666079\pi\)
\(74\) −7.38534 −0.858529
\(75\) −4.49560 −0.519107
\(76\) 0.643877 0.0738578
\(77\) 2.30964 0.263208
\(78\) 0 0
\(79\) 1.82360 0.205172 0.102586 0.994724i \(-0.467288\pi\)
0.102586 + 0.994724i \(0.467288\pi\)
\(80\) 1.60581 0.179536
\(81\) 1.00000 0.111111
\(82\) −20.4108 −2.25400
\(83\) −4.64671 −0.510042 −0.255021 0.966935i \(-0.582082\pi\)
−0.255021 + 0.966935i \(0.582082\pi\)
\(84\) −6.13206 −0.669062
\(85\) 4.74440 0.514602
\(86\) −25.6297 −2.76372
\(87\) −2.95273 −0.316566
\(88\) −1.41315 −0.150642
\(89\) −14.7714 −1.56576 −0.782881 0.622171i \(-0.786251\pi\)
−0.782881 + 0.622171i \(0.786251\pi\)
\(90\) −1.53231 −0.161519
\(91\) 0 0
\(92\) 25.3161 2.63938
\(93\) 4.02017 0.416872
\(94\) 27.8707 2.87465
\(95\) −0.172238 −0.0176712
\(96\) −7.70458 −0.786345
\(97\) −1.86542 −0.189405 −0.0947025 0.995506i \(-0.530190\pi\)
−0.0947025 + 0.995506i \(0.530190\pi\)
\(98\) −3.59349 −0.362997
\(99\) −1.00000 −0.100504
\(100\) −11.9357 −1.19357
\(101\) −2.45086 −0.243870 −0.121935 0.992538i \(-0.538910\pi\)
−0.121935 + 0.992538i \(0.538910\pi\)
\(102\) −14.4130 −1.42709
\(103\) 10.2811 1.01302 0.506512 0.862233i \(-0.330934\pi\)
0.506512 + 0.862233i \(0.330934\pi\)
\(104\) 0 0
\(105\) 1.64033 0.160080
\(106\) 14.6487 1.42281
\(107\) 19.6690 1.90148 0.950739 0.309993i \(-0.100327\pi\)
0.950739 + 0.309993i \(0.100327\pi\)
\(108\) 2.65498 0.255476
\(109\) −1.27506 −0.122128 −0.0610642 0.998134i \(-0.519449\pi\)
−0.0610642 + 0.998134i \(0.519449\pi\)
\(110\) 1.53231 0.146100
\(111\) −3.42304 −0.324900
\(112\) 5.22220 0.493452
\(113\) −0.638739 −0.0600875 −0.0300438 0.999549i \(-0.509565\pi\)
−0.0300438 + 0.999549i \(0.509565\pi\)
\(114\) 0.523240 0.0490059
\(115\) −6.77207 −0.631499
\(116\) −7.83943 −0.727873
\(117\) 0 0
\(118\) −16.8573 −1.55184
\(119\) 15.4290 1.41438
\(120\) −1.00363 −0.0916185
\(121\) 1.00000 0.0909091
\(122\) 1.96462 0.177869
\(123\) −9.46022 −0.853000
\(124\) 10.6735 0.958506
\(125\) 6.74387 0.603190
\(126\) −4.98315 −0.443934
\(127\) 10.3681 0.920021 0.460010 0.887914i \(-0.347846\pi\)
0.460010 + 0.887914i \(0.347846\pi\)
\(128\) −10.6989 −0.945660
\(129\) −11.8791 −1.04590
\(130\) 0 0
\(131\) −5.68692 −0.496868 −0.248434 0.968649i \(-0.579916\pi\)
−0.248434 + 0.968649i \(0.579916\pi\)
\(132\) −2.65498 −0.231086
\(133\) −0.560127 −0.0485692
\(134\) −20.1129 −1.73749
\(135\) −0.710210 −0.0611251
\(136\) −9.44019 −0.809490
\(137\) −4.86363 −0.415528 −0.207764 0.978179i \(-0.566619\pi\)
−0.207764 + 0.978179i \(0.566619\pi\)
\(138\) 20.5728 1.75127
\(139\) −4.41515 −0.374488 −0.187244 0.982313i \(-0.559956\pi\)
−0.187244 + 0.982313i \(0.559956\pi\)
\(140\) 4.35505 0.368069
\(141\) 12.9178 1.08788
\(142\) −27.9841 −2.34837
\(143\) 0 0
\(144\) −2.26104 −0.188420
\(145\) 2.09706 0.174151
\(146\) −18.3750 −1.52073
\(147\) −1.66555 −0.137372
\(148\) −9.08810 −0.747037
\(149\) −9.50356 −0.778562 −0.389281 0.921119i \(-0.627276\pi\)
−0.389281 + 0.921119i \(0.627276\pi\)
\(150\) −9.69944 −0.791956
\(151\) −15.2126 −1.23798 −0.618991 0.785398i \(-0.712458\pi\)
−0.618991 + 0.785398i \(0.712458\pi\)
\(152\) 0.342711 0.0277976
\(153\) −6.68027 −0.540068
\(154\) 4.98315 0.401554
\(155\) −2.85516 −0.229332
\(156\) 0 0
\(157\) 20.1949 1.61173 0.805866 0.592098i \(-0.201700\pi\)
0.805866 + 0.592098i \(0.201700\pi\)
\(158\) 3.93450 0.313012
\(159\) 6.78954 0.538445
\(160\) 5.47187 0.432589
\(161\) −22.0232 −1.73567
\(162\) 2.15754 0.169512
\(163\) 16.4974 1.29217 0.646087 0.763264i \(-0.276404\pi\)
0.646087 + 0.763264i \(0.276404\pi\)
\(164\) −25.1167 −1.96129
\(165\) 0.710210 0.0552898
\(166\) −10.0255 −0.778126
\(167\) 5.50507 0.425995 0.212998 0.977053i \(-0.431677\pi\)
0.212998 + 0.977053i \(0.431677\pi\)
\(168\) −3.26386 −0.251812
\(169\) 0 0
\(170\) 10.2362 0.785082
\(171\) 0.242517 0.0185457
\(172\) −31.5389 −2.40482
\(173\) −12.7126 −0.966524 −0.483262 0.875476i \(-0.660548\pi\)
−0.483262 + 0.875476i \(0.660548\pi\)
\(174\) −6.37063 −0.482956
\(175\) 10.3832 0.784899
\(176\) 2.26104 0.170432
\(177\) −7.81320 −0.587276
\(178\) −31.8698 −2.38875
\(179\) 24.4279 1.82583 0.912913 0.408154i \(-0.133828\pi\)
0.912913 + 0.408154i \(0.133828\pi\)
\(180\) −1.88559 −0.140544
\(181\) 0.931324 0.0692248 0.0346124 0.999401i \(-0.488980\pi\)
0.0346124 + 0.999401i \(0.488980\pi\)
\(182\) 0 0
\(183\) 0.910585 0.0673124
\(184\) 13.4748 0.993374
\(185\) 2.43108 0.178736
\(186\) 8.67368 0.635985
\(187\) 6.68027 0.488510
\(188\) 34.2966 2.50134
\(189\) −2.30964 −0.168002
\(190\) −0.371610 −0.0269594
\(191\) 4.68209 0.338784 0.169392 0.985549i \(-0.445820\pi\)
0.169392 + 0.985549i \(0.445820\pi\)
\(192\) −12.1009 −0.873304
\(193\) 10.2671 0.739039 0.369520 0.929223i \(-0.379522\pi\)
0.369520 + 0.929223i \(0.379522\pi\)
\(194\) −4.02473 −0.288959
\(195\) 0 0
\(196\) −4.42200 −0.315857
\(197\) −11.5842 −0.825341 −0.412671 0.910880i \(-0.635404\pi\)
−0.412671 + 0.910880i \(0.635404\pi\)
\(198\) −2.15754 −0.153330
\(199\) 17.2330 1.22162 0.610808 0.791779i \(-0.290845\pi\)
0.610808 + 0.791779i \(0.290845\pi\)
\(200\) −6.35294 −0.449221
\(201\) −9.32216 −0.657535
\(202\) −5.28783 −0.372050
\(203\) 6.81975 0.478652
\(204\) −17.7360 −1.24177
\(205\) 6.71875 0.469258
\(206\) 22.1818 1.54548
\(207\) 9.53531 0.662750
\(208\) 0 0
\(209\) −0.242517 −0.0167752
\(210\) 3.53908 0.244220
\(211\) −10.6905 −0.735967 −0.367983 0.929832i \(-0.619952\pi\)
−0.367983 + 0.929832i \(0.619952\pi\)
\(212\) 18.0261 1.23804
\(213\) −12.9704 −0.888716
\(214\) 42.4367 2.90092
\(215\) 8.43668 0.575377
\(216\) 1.41315 0.0961523
\(217\) −9.28516 −0.630318
\(218\) −2.75099 −0.186320
\(219\) −8.51665 −0.575502
\(220\) 1.88559 0.127127
\(221\) 0 0
\(222\) −7.38534 −0.495672
\(223\) 5.33992 0.357587 0.178794 0.983887i \(-0.442781\pi\)
0.178794 + 0.983887i \(0.442781\pi\)
\(224\) 17.7948 1.18897
\(225\) −4.49560 −0.299707
\(226\) −1.37811 −0.0916702
\(227\) 7.82431 0.519318 0.259659 0.965700i \(-0.416390\pi\)
0.259659 + 0.965700i \(0.416390\pi\)
\(228\) 0.643877 0.0426418
\(229\) 10.6805 0.705784 0.352892 0.935664i \(-0.385198\pi\)
0.352892 + 0.935664i \(0.385198\pi\)
\(230\) −14.6110 −0.963422
\(231\) 2.30964 0.151963
\(232\) −4.17263 −0.273947
\(233\) 15.4509 1.01222 0.506112 0.862468i \(-0.331082\pi\)
0.506112 + 0.862468i \(0.331082\pi\)
\(234\) 0 0
\(235\) −9.17437 −0.598470
\(236\) −20.7439 −1.35031
\(237\) 1.82360 0.118456
\(238\) 33.2888 2.15779
\(239\) 16.9365 1.09553 0.547765 0.836632i \(-0.315479\pi\)
0.547765 + 0.836632i \(0.315479\pi\)
\(240\) 1.60581 0.103655
\(241\) 0.0799646 0.00515098 0.00257549 0.999997i \(-0.499180\pi\)
0.00257549 + 0.999997i \(0.499180\pi\)
\(242\) 2.15754 0.138692
\(243\) 1.00000 0.0641500
\(244\) 2.41758 0.154770
\(245\) 1.18289 0.0755720
\(246\) −20.4108 −1.30135
\(247\) 0 0
\(248\) 5.68108 0.360749
\(249\) −4.64671 −0.294473
\(250\) 14.5502 0.920234
\(251\) −7.57174 −0.477924 −0.238962 0.971029i \(-0.576807\pi\)
−0.238962 + 0.971029i \(0.576807\pi\)
\(252\) −6.13206 −0.386283
\(253\) −9.53531 −0.599480
\(254\) 22.3696 1.40359
\(255\) 4.74440 0.297106
\(256\) 1.11835 0.0698970
\(257\) 23.0242 1.43621 0.718105 0.695935i \(-0.245010\pi\)
0.718105 + 0.695935i \(0.245010\pi\)
\(258\) −25.6297 −1.59564
\(259\) 7.90600 0.491255
\(260\) 0 0
\(261\) −2.95273 −0.182769
\(262\) −12.2698 −0.758028
\(263\) −5.95047 −0.366922 −0.183461 0.983027i \(-0.558730\pi\)
−0.183461 + 0.983027i \(0.558730\pi\)
\(264\) −1.41315 −0.0869731
\(265\) −4.82200 −0.296213
\(266\) −1.20850 −0.0740977
\(267\) −14.7714 −0.903994
\(268\) −24.7502 −1.51186
\(269\) −1.17571 −0.0716841 −0.0358420 0.999357i \(-0.511411\pi\)
−0.0358420 + 0.999357i \(0.511411\pi\)
\(270\) −1.53231 −0.0932532
\(271\) 7.12706 0.432938 0.216469 0.976290i \(-0.430546\pi\)
0.216469 + 0.976290i \(0.430546\pi\)
\(272\) 15.1044 0.915837
\(273\) 0 0
\(274\) −10.4935 −0.633934
\(275\) 4.49560 0.271095
\(276\) 25.3161 1.52385
\(277\) −11.9736 −0.719426 −0.359713 0.933063i \(-0.617125\pi\)
−0.359713 + 0.933063i \(0.617125\pi\)
\(278\) −9.52586 −0.571323
\(279\) 4.02017 0.240681
\(280\) 2.31803 0.138529
\(281\) −18.7901 −1.12092 −0.560461 0.828181i \(-0.689376\pi\)
−0.560461 + 0.828181i \(0.689376\pi\)
\(282\) 27.8707 1.65968
\(283\) 10.5237 0.625568 0.312784 0.949824i \(-0.398738\pi\)
0.312784 + 0.949824i \(0.398738\pi\)
\(284\) −34.4361 −2.04341
\(285\) −0.172238 −0.0102025
\(286\) 0 0
\(287\) 21.8497 1.28975
\(288\) −7.70458 −0.453997
\(289\) 27.6260 1.62506
\(290\) 4.52448 0.265687
\(291\) −1.86542 −0.109353
\(292\) −22.6115 −1.32324
\(293\) 14.0111 0.818540 0.409270 0.912413i \(-0.365783\pi\)
0.409270 + 0.912413i \(0.365783\pi\)
\(294\) −3.59349 −0.209576
\(295\) 5.54901 0.323076
\(296\) −4.83725 −0.281159
\(297\) −1.00000 −0.0580259
\(298\) −20.5043 −1.18778
\(299\) 0 0
\(300\) −11.9357 −0.689110
\(301\) 27.4366 1.58142
\(302\) −32.8217 −1.88868
\(303\) −2.45086 −0.140798
\(304\) −0.548341 −0.0314495
\(305\) −0.646706 −0.0370303
\(306\) −14.4130 −0.823934
\(307\) −2.52126 −0.143896 −0.0719481 0.997408i \(-0.522922\pi\)
−0.0719481 + 0.997408i \(0.522922\pi\)
\(308\) 6.13206 0.349406
\(309\) 10.2811 0.584870
\(310\) −6.16013 −0.349872
\(311\) −22.9380 −1.30069 −0.650347 0.759638i \(-0.725376\pi\)
−0.650347 + 0.759638i \(0.725376\pi\)
\(312\) 0 0
\(313\) −21.6566 −1.22410 −0.612051 0.790818i \(-0.709655\pi\)
−0.612051 + 0.790818i \(0.709655\pi\)
\(314\) 43.5714 2.45888
\(315\) 1.64033 0.0924222
\(316\) 4.84163 0.272363
\(317\) −26.6050 −1.49429 −0.747143 0.664664i \(-0.768575\pi\)
−0.747143 + 0.664664i \(0.768575\pi\)
\(318\) 14.6487 0.821458
\(319\) 2.95273 0.165321
\(320\) 8.59415 0.480428
\(321\) 19.6690 1.09782
\(322\) −47.5159 −2.64796
\(323\) −1.62008 −0.0901435
\(324\) 2.65498 0.147499
\(325\) 0 0
\(326\) 35.5937 1.97135
\(327\) −1.27506 −0.0705108
\(328\) −13.3687 −0.738161
\(329\) −29.8356 −1.64489
\(330\) 1.53231 0.0843507
\(331\) 24.7670 1.36132 0.680659 0.732600i \(-0.261693\pi\)
0.680659 + 0.732600i \(0.261693\pi\)
\(332\) −12.3369 −0.677076
\(333\) −3.42304 −0.187581
\(334\) 11.8774 0.649903
\(335\) 6.62069 0.361727
\(336\) 5.22220 0.284894
\(337\) −28.2890 −1.54100 −0.770499 0.637441i \(-0.779993\pi\)
−0.770499 + 0.637441i \(0.779993\pi\)
\(338\) 0 0
\(339\) −0.638739 −0.0346916
\(340\) 12.5963 0.683129
\(341\) −4.02017 −0.217704
\(342\) 0.523240 0.0282936
\(343\) 20.0143 1.08067
\(344\) −16.7869 −0.905091
\(345\) −6.77207 −0.364596
\(346\) −27.4280 −1.47454
\(347\) −18.0814 −0.970661 −0.485331 0.874331i \(-0.661301\pi\)
−0.485331 + 0.874331i \(0.661301\pi\)
\(348\) −7.83943 −0.420238
\(349\) −21.0326 −1.12585 −0.562924 0.826508i \(-0.690324\pi\)
−0.562924 + 0.826508i \(0.690324\pi\)
\(350\) 22.4022 1.19745
\(351\) 0 0
\(352\) 7.70458 0.410655
\(353\) −2.20127 −0.117162 −0.0585810 0.998283i \(-0.518658\pi\)
−0.0585810 + 0.998283i \(0.518658\pi\)
\(354\) −16.8573 −0.895955
\(355\) 9.21169 0.488906
\(356\) −39.2177 −2.07853
\(357\) 15.4290 0.816591
\(358\) 52.7041 2.78550
\(359\) 7.76540 0.409842 0.204921 0.978778i \(-0.434306\pi\)
0.204921 + 0.978778i \(0.434306\pi\)
\(360\) −1.00363 −0.0528959
\(361\) −18.9412 −0.996905
\(362\) 2.00937 0.105610
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 6.04861 0.316599
\(366\) 1.96462 0.102692
\(367\) −11.9604 −0.624326 −0.312163 0.950028i \(-0.601054\pi\)
−0.312163 + 0.950028i \(0.601054\pi\)
\(368\) −21.5597 −1.12388
\(369\) −9.46022 −0.492480
\(370\) 5.24514 0.272682
\(371\) −15.6814 −0.814138
\(372\) 10.6735 0.553394
\(373\) 14.1243 0.731330 0.365665 0.930747i \(-0.380842\pi\)
0.365665 + 0.930747i \(0.380842\pi\)
\(374\) 14.4130 0.745276
\(375\) 6.74387 0.348252
\(376\) 18.2548 0.941418
\(377\) 0 0
\(378\) −4.98315 −0.256305
\(379\) 3.34432 0.171786 0.0858931 0.996304i \(-0.472626\pi\)
0.0858931 + 0.996304i \(0.472626\pi\)
\(380\) −0.457288 −0.0234584
\(381\) 10.3681 0.531174
\(382\) 10.1018 0.516853
\(383\) 5.63621 0.287997 0.143998 0.989578i \(-0.454004\pi\)
0.143998 + 0.989578i \(0.454004\pi\)
\(384\) −10.6989 −0.545977
\(385\) −1.64033 −0.0835991
\(386\) 22.1516 1.12749
\(387\) −11.8791 −0.603850
\(388\) −4.95266 −0.251433
\(389\) 14.3490 0.727523 0.363761 0.931492i \(-0.381492\pi\)
0.363761 + 0.931492i \(0.381492\pi\)
\(390\) 0 0
\(391\) −63.6984 −3.22137
\(392\) −2.35366 −0.118878
\(393\) −5.68692 −0.286867
\(394\) −24.9934 −1.25915
\(395\) −1.29514 −0.0651657
\(396\) −2.65498 −0.133418
\(397\) 14.8769 0.746648 0.373324 0.927701i \(-0.378218\pi\)
0.373324 + 0.927701i \(0.378218\pi\)
\(398\) 37.1809 1.86371
\(399\) −0.560127 −0.0280414
\(400\) 10.1647 0.508237
\(401\) −19.6380 −0.980675 −0.490337 0.871533i \(-0.663126\pi\)
−0.490337 + 0.871533i \(0.663126\pi\)
\(402\) −20.1129 −1.00314
\(403\) 0 0
\(404\) −6.50698 −0.323734
\(405\) −0.710210 −0.0352906
\(406\) 14.7139 0.730237
\(407\) 3.42304 0.169674
\(408\) −9.44019 −0.467359
\(409\) −23.1731 −1.14584 −0.572918 0.819613i \(-0.694189\pi\)
−0.572918 + 0.819613i \(0.694189\pi\)
\(410\) 14.4960 0.715905
\(411\) −4.86363 −0.239905
\(412\) 27.2961 1.34478
\(413\) 18.0457 0.887971
\(414\) 20.5728 1.01110
\(415\) 3.30014 0.161997
\(416\) 0 0
\(417\) −4.41515 −0.216211
\(418\) −0.523240 −0.0255925
\(419\) −3.70294 −0.180900 −0.0904502 0.995901i \(-0.528831\pi\)
−0.0904502 + 0.995901i \(0.528831\pi\)
\(420\) 4.35505 0.212505
\(421\) −23.7239 −1.15623 −0.578116 0.815955i \(-0.696212\pi\)
−0.578116 + 0.815955i \(0.696212\pi\)
\(422\) −23.0653 −1.12280
\(423\) 12.9178 0.628086
\(424\) 9.59460 0.465955
\(425\) 30.0318 1.45676
\(426\) −27.9841 −1.35583
\(427\) −2.10313 −0.101777
\(428\) 52.2209 2.52419
\(429\) 0 0
\(430\) 18.2025 0.877802
\(431\) 31.0695 1.49656 0.748282 0.663381i \(-0.230879\pi\)
0.748282 + 0.663381i \(0.230879\pi\)
\(432\) −2.26104 −0.108784
\(433\) 23.0541 1.10791 0.553954 0.832547i \(-0.313118\pi\)
0.553954 + 0.832547i \(0.313118\pi\)
\(434\) −20.0331 −0.961620
\(435\) 2.09706 0.100546
\(436\) −3.38525 −0.162124
\(437\) 2.31247 0.110621
\(438\) −18.3750 −0.877992
\(439\) 2.39273 0.114199 0.0570994 0.998368i \(-0.481815\pi\)
0.0570994 + 0.998368i \(0.481815\pi\)
\(440\) 1.00363 0.0478462
\(441\) −1.66555 −0.0793118
\(442\) 0 0
\(443\) −17.1624 −0.815411 −0.407705 0.913113i \(-0.633671\pi\)
−0.407705 + 0.913113i \(0.633671\pi\)
\(444\) −9.08810 −0.431302
\(445\) 10.4908 0.497311
\(446\) 11.5211 0.545539
\(447\) −9.50356 −0.449503
\(448\) 27.9487 1.32045
\(449\) −29.0646 −1.37164 −0.685822 0.727769i \(-0.740557\pi\)
−0.685822 + 0.727769i \(0.740557\pi\)
\(450\) −9.69944 −0.457236
\(451\) 9.46022 0.445465
\(452\) −1.69584 −0.0797656
\(453\) −15.2126 −0.714749
\(454\) 16.8813 0.792277
\(455\) 0 0
\(456\) 0.342711 0.0160489
\(457\) 31.9111 1.49274 0.746369 0.665532i \(-0.231795\pi\)
0.746369 + 0.665532i \(0.231795\pi\)
\(458\) 23.0435 1.07675
\(459\) −6.68027 −0.311808
\(460\) −17.9797 −0.838308
\(461\) 0.706685 0.0329136 0.0164568 0.999865i \(-0.494761\pi\)
0.0164568 + 0.999865i \(0.494761\pi\)
\(462\) 4.98315 0.231837
\(463\) −25.7813 −1.19816 −0.599079 0.800690i \(-0.704467\pi\)
−0.599079 + 0.800690i \(0.704467\pi\)
\(464\) 6.67624 0.309937
\(465\) −2.85516 −0.132405
\(466\) 33.3360 1.54426
\(467\) 37.3541 1.72854 0.864270 0.503028i \(-0.167781\pi\)
0.864270 + 0.503028i \(0.167781\pi\)
\(468\) 0 0
\(469\) 21.5309 0.994203
\(470\) −19.7941 −0.913033
\(471\) 20.1949 0.930533
\(472\) −11.0412 −0.508212
\(473\) 11.8791 0.546203
\(474\) 3.93450 0.180718
\(475\) −1.09026 −0.0500245
\(476\) 40.9638 1.87757
\(477\) 6.78954 0.310872
\(478\) 36.5411 1.67135
\(479\) −1.74064 −0.0795318 −0.0397659 0.999209i \(-0.512661\pi\)
−0.0397659 + 0.999209i \(0.512661\pi\)
\(480\) 5.47187 0.249756
\(481\) 0 0
\(482\) 0.172527 0.00785839
\(483\) −22.0232 −1.00209
\(484\) 2.65498 0.120681
\(485\) 1.32484 0.0601580
\(486\) 2.15754 0.0978680
\(487\) −5.69783 −0.258193 −0.129097 0.991632i \(-0.541208\pi\)
−0.129097 + 0.991632i \(0.541208\pi\)
\(488\) 1.28679 0.0582502
\(489\) 16.4974 0.746037
\(490\) 2.55213 0.115293
\(491\) −27.7388 −1.25183 −0.625917 0.779890i \(-0.715275\pi\)
−0.625917 + 0.779890i \(0.715275\pi\)
\(492\) −25.1167 −1.13235
\(493\) 19.7250 0.888370
\(494\) 0 0
\(495\) 0.710210 0.0319216
\(496\) −9.08977 −0.408143
\(497\) 29.9569 1.34375
\(498\) −10.0255 −0.449251
\(499\) −8.27073 −0.370249 −0.185124 0.982715i \(-0.559269\pi\)
−0.185124 + 0.982715i \(0.559269\pi\)
\(500\) 17.9048 0.800729
\(501\) 5.50507 0.245948
\(502\) −16.3363 −0.729126
\(503\) −12.7099 −0.566706 −0.283353 0.959016i \(-0.591447\pi\)
−0.283353 + 0.959016i \(0.591447\pi\)
\(504\) −3.26386 −0.145384
\(505\) 1.74062 0.0774568
\(506\) −20.5728 −0.914573
\(507\) 0 0
\(508\) 27.5271 1.22132
\(509\) −5.55978 −0.246433 −0.123216 0.992380i \(-0.539321\pi\)
−0.123216 + 0.992380i \(0.539321\pi\)
\(510\) 10.2362 0.453268
\(511\) 19.6704 0.870168
\(512\) 23.8107 1.05230
\(513\) 0.242517 0.0107074
\(514\) 49.6756 2.19110
\(515\) −7.30172 −0.321752
\(516\) −31.5389 −1.38842
\(517\) −12.9178 −0.568126
\(518\) 17.0575 0.749464
\(519\) −12.7126 −0.558023
\(520\) 0 0
\(521\) −4.41425 −0.193392 −0.0966958 0.995314i \(-0.530827\pi\)
−0.0966958 + 0.995314i \(0.530827\pi\)
\(522\) −6.37063 −0.278835
\(523\) 15.5162 0.678474 0.339237 0.940701i \(-0.389831\pi\)
0.339237 + 0.940701i \(0.389831\pi\)
\(524\) −15.0986 −0.659587
\(525\) 10.3832 0.453162
\(526\) −12.8384 −0.559780
\(527\) −26.8558 −1.16986
\(528\) 2.26104 0.0983992
\(529\) 67.9221 2.95314
\(530\) −10.4037 −0.451906
\(531\) −7.81320 −0.339064
\(532\) −1.48713 −0.0644751
\(533\) 0 0
\(534\) −31.8698 −1.37914
\(535\) −13.9691 −0.603939
\(536\) −13.1736 −0.569011
\(537\) 24.4279 1.05414
\(538\) −2.53663 −0.109362
\(539\) 1.66555 0.0717402
\(540\) −1.88559 −0.0811430
\(541\) 27.9827 1.20307 0.601536 0.798846i \(-0.294556\pi\)
0.601536 + 0.798846i \(0.294556\pi\)
\(542\) 15.3769 0.660495
\(543\) 0.931324 0.0399669
\(544\) 51.4687 2.20670
\(545\) 0.905559 0.0387899
\(546\) 0 0
\(547\) −24.1470 −1.03245 −0.516226 0.856453i \(-0.672663\pi\)
−0.516226 + 0.856453i \(0.672663\pi\)
\(548\) −12.9128 −0.551609
\(549\) 0.910585 0.0388628
\(550\) 9.69944 0.413586
\(551\) −0.716086 −0.0305063
\(552\) 13.4748 0.573524
\(553\) −4.21188 −0.179107
\(554\) −25.8336 −1.09756
\(555\) 2.43108 0.103193
\(556\) −11.7221 −0.497129
\(557\) −19.1326 −0.810675 −0.405337 0.914167i \(-0.632846\pi\)
−0.405337 + 0.914167i \(0.632846\pi\)
\(558\) 8.67368 0.367186
\(559\) 0 0
\(560\) −3.70886 −0.156728
\(561\) 6.68027 0.282041
\(562\) −40.5404 −1.71009
\(563\) −3.91199 −0.164871 −0.0824353 0.996596i \(-0.526270\pi\)
−0.0824353 + 0.996596i \(0.526270\pi\)
\(564\) 34.2966 1.44415
\(565\) 0.453639 0.0190847
\(566\) 22.7053 0.954373
\(567\) −2.30964 −0.0969959
\(568\) −18.3290 −0.769069
\(569\) −15.8002 −0.662377 −0.331189 0.943565i \(-0.607450\pi\)
−0.331189 + 0.943565i \(0.607450\pi\)
\(570\) −0.371610 −0.0155650
\(571\) 20.2458 0.847262 0.423631 0.905835i \(-0.360755\pi\)
0.423631 + 0.905835i \(0.360755\pi\)
\(572\) 0 0
\(573\) 4.68209 0.195597
\(574\) 47.1417 1.96766
\(575\) −42.8669 −1.78768
\(576\) −12.1009 −0.504202
\(577\) 7.07073 0.294358 0.147179 0.989110i \(-0.452981\pi\)
0.147179 + 0.989110i \(0.452981\pi\)
\(578\) 59.6042 2.47921
\(579\) 10.2671 0.426685
\(580\) 5.56764 0.231184
\(581\) 10.7322 0.445248
\(582\) −4.02473 −0.166830
\(583\) −6.78954 −0.281194
\(584\) −12.0353 −0.498023
\(585\) 0 0
\(586\) 30.2296 1.24877
\(587\) −27.1767 −1.12170 −0.560851 0.827917i \(-0.689526\pi\)
−0.560851 + 0.827917i \(0.689526\pi\)
\(588\) −4.42200 −0.182360
\(589\) 0.974959 0.0401725
\(590\) 11.9722 0.492889
\(591\) −11.5842 −0.476511
\(592\) 7.73963 0.318097
\(593\) −20.0431 −0.823070 −0.411535 0.911394i \(-0.635007\pi\)
−0.411535 + 0.911394i \(0.635007\pi\)
\(594\) −2.15754 −0.0885249
\(595\) −10.9579 −0.449228
\(596\) −25.2318 −1.03353
\(597\) 17.2330 0.705300
\(598\) 0 0
\(599\) −24.5855 −1.00454 −0.502268 0.864712i \(-0.667501\pi\)
−0.502268 + 0.864712i \(0.667501\pi\)
\(600\) −6.35294 −0.259358
\(601\) −34.1098 −1.39137 −0.695683 0.718349i \(-0.744898\pi\)
−0.695683 + 0.718349i \(0.744898\pi\)
\(602\) 59.1955 2.41263
\(603\) −9.32216 −0.379628
\(604\) −40.3891 −1.64341
\(605\) −0.710210 −0.0288741
\(606\) −5.28783 −0.214803
\(607\) 20.9453 0.850143 0.425071 0.905160i \(-0.360249\pi\)
0.425071 + 0.905160i \(0.360249\pi\)
\(608\) −1.86849 −0.0757773
\(609\) 6.81975 0.276350
\(610\) −1.39530 −0.0564938
\(611\) 0 0
\(612\) −17.7360 −0.716935
\(613\) 22.2792 0.899848 0.449924 0.893067i \(-0.351451\pi\)
0.449924 + 0.893067i \(0.351451\pi\)
\(614\) −5.43973 −0.219530
\(615\) 6.71875 0.270926
\(616\) 3.26386 0.131505
\(617\) −27.4366 −1.10456 −0.552279 0.833660i \(-0.686242\pi\)
−0.552279 + 0.833660i \(0.686242\pi\)
\(618\) 22.1818 0.892284
\(619\) 47.9288 1.92642 0.963211 0.268747i \(-0.0866096\pi\)
0.963211 + 0.268747i \(0.0866096\pi\)
\(620\) −7.58040 −0.304436
\(621\) 9.53531 0.382639
\(622\) −49.4896 −1.98435
\(623\) 34.1166 1.36685
\(624\) 0 0
\(625\) 17.6884 0.707538
\(626\) −46.7250 −1.86751
\(627\) −0.242517 −0.00968519
\(628\) 53.6171 2.13956
\(629\) 22.8668 0.911760
\(630\) 3.53908 0.141000
\(631\) −23.8277 −0.948567 −0.474284 0.880372i \(-0.657293\pi\)
−0.474284 + 0.880372i \(0.657293\pi\)
\(632\) 2.57702 0.102508
\(633\) −10.6905 −0.424911
\(634\) −57.4013 −2.27970
\(635\) −7.36353 −0.292213
\(636\) 18.0261 0.714781
\(637\) 0 0
\(638\) 6.37063 0.252216
\(639\) −12.9704 −0.513100
\(640\) 7.59848 0.300356
\(641\) −8.30355 −0.327970 −0.163985 0.986463i \(-0.552435\pi\)
−0.163985 + 0.986463i \(0.552435\pi\)
\(642\) 42.4367 1.67484
\(643\) −29.9185 −1.17987 −0.589934 0.807451i \(-0.700846\pi\)
−0.589934 + 0.807451i \(0.700846\pi\)
\(644\) −58.4710 −2.30408
\(645\) 8.43668 0.332194
\(646\) −3.49538 −0.137524
\(647\) 5.87308 0.230895 0.115447 0.993314i \(-0.463170\pi\)
0.115447 + 0.993314i \(0.463170\pi\)
\(648\) 1.41315 0.0555136
\(649\) 7.81320 0.306695
\(650\) 0 0
\(651\) −9.28516 −0.363914
\(652\) 43.8002 1.71535
\(653\) −5.43262 −0.212595 −0.106297 0.994334i \(-0.533900\pi\)
−0.106297 + 0.994334i \(0.533900\pi\)
\(654\) −2.75099 −0.107572
\(655\) 4.03891 0.157813
\(656\) 21.3900 0.835138
\(657\) −8.51665 −0.332266
\(658\) −64.3715 −2.50946
\(659\) 26.5954 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(660\) 1.88559 0.0733966
\(661\) 27.7763 1.08037 0.540187 0.841545i \(-0.318354\pi\)
0.540187 + 0.841545i \(0.318354\pi\)
\(662\) 53.4359 2.07684
\(663\) 0 0
\(664\) −6.56647 −0.254828
\(665\) 0.397808 0.0154263
\(666\) −7.38534 −0.286176
\(667\) −28.1552 −1.09017
\(668\) 14.6158 0.565504
\(669\) 5.33992 0.206453
\(670\) 14.2844 0.551855
\(671\) −0.910585 −0.0351527
\(672\) 17.7948 0.686450
\(673\) 3.00054 0.115663 0.0578313 0.998326i \(-0.481581\pi\)
0.0578313 + 0.998326i \(0.481581\pi\)
\(674\) −61.0346 −2.35096
\(675\) −4.49560 −0.173036
\(676\) 0 0
\(677\) −25.1724 −0.967452 −0.483726 0.875219i \(-0.660717\pi\)
−0.483726 + 0.875219i \(0.660717\pi\)
\(678\) −1.37811 −0.0529258
\(679\) 4.30846 0.165344
\(680\) 6.70452 0.257107
\(681\) 7.82431 0.299828
\(682\) −8.67368 −0.332132
\(683\) −39.1652 −1.49861 −0.749307 0.662223i \(-0.769613\pi\)
−0.749307 + 0.662223i \(0.769613\pi\)
\(684\) 0.643877 0.0246193
\(685\) 3.45420 0.131978
\(686\) 43.1817 1.64869
\(687\) 10.6805 0.407485
\(688\) 26.8592 1.02400
\(689\) 0 0
\(690\) −14.6110 −0.556232
\(691\) −33.3472 −1.26859 −0.634294 0.773092i \(-0.718709\pi\)
−0.634294 + 0.773092i \(0.718709\pi\)
\(692\) −33.7518 −1.28305
\(693\) 2.30964 0.0877361
\(694\) −39.0114 −1.48085
\(695\) 3.13568 0.118943
\(696\) −4.17263 −0.158163
\(697\) 63.1969 2.39375
\(698\) −45.3787 −1.71761
\(699\) 15.4509 0.584408
\(700\) 27.5673 1.04195
\(701\) 8.45704 0.319418 0.159709 0.987164i \(-0.448944\pi\)
0.159709 + 0.987164i \(0.448944\pi\)
\(702\) 0 0
\(703\) −0.830144 −0.0313095
\(704\) 12.1009 0.456068
\(705\) −9.17437 −0.345527
\(706\) −4.74934 −0.178744
\(707\) 5.66061 0.212889
\(708\) −20.7439 −0.779603
\(709\) 7.03783 0.264311 0.132156 0.991229i \(-0.457810\pi\)
0.132156 + 0.991229i \(0.457810\pi\)
\(710\) 19.8746 0.745880
\(711\) 1.82360 0.0683905
\(712\) −20.8741 −0.782290
\(713\) 38.3336 1.43560
\(714\) 33.2888 1.24580
\(715\) 0 0
\(716\) 64.8555 2.42377
\(717\) 16.9365 0.632504
\(718\) 16.7542 0.625260
\(719\) −5.52947 −0.206215 −0.103107 0.994670i \(-0.532879\pi\)
−0.103107 + 0.994670i \(0.532879\pi\)
\(720\) 1.60581 0.0598452
\(721\) −23.7456 −0.884333
\(722\) −40.8664 −1.52089
\(723\) 0.0799646 0.00297392
\(724\) 2.47265 0.0918952
\(725\) 13.2743 0.492995
\(726\) 2.15754 0.0800738
\(727\) −38.7533 −1.43728 −0.718640 0.695383i \(-0.755235\pi\)
−0.718640 + 0.695383i \(0.755235\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 13.0501 0.483006
\(731\) 79.3558 2.93508
\(732\) 2.41758 0.0893565
\(733\) −9.60595 −0.354804 −0.177402 0.984138i \(-0.556769\pi\)
−0.177402 + 0.984138i \(0.556769\pi\)
\(734\) −25.8050 −0.952480
\(735\) 1.18289 0.0436315
\(736\) −73.4655 −2.70798
\(737\) 9.32216 0.343386
\(738\) −20.4108 −0.751332
\(739\) −21.6659 −0.796995 −0.398497 0.917169i \(-0.630468\pi\)
−0.398497 + 0.917169i \(0.630468\pi\)
\(740\) 6.45446 0.237271
\(741\) 0 0
\(742\) −33.8333 −1.24206
\(743\) −12.3149 −0.451790 −0.225895 0.974152i \(-0.572531\pi\)
−0.225895 + 0.974152i \(0.572531\pi\)
\(744\) 5.68108 0.208279
\(745\) 6.74952 0.247283
\(746\) 30.4738 1.11572
\(747\) −4.64671 −0.170014
\(748\) 17.7360 0.648492
\(749\) −45.4285 −1.65992
\(750\) 14.5502 0.531297
\(751\) 2.50813 0.0915231 0.0457616 0.998952i \(-0.485429\pi\)
0.0457616 + 0.998952i \(0.485429\pi\)
\(752\) −29.2078 −1.06510
\(753\) −7.57174 −0.275930
\(754\) 0 0
\(755\) 10.8041 0.393202
\(756\) −6.13206 −0.223021
\(757\) 2.89889 0.105362 0.0526809 0.998611i \(-0.483223\pi\)
0.0526809 + 0.998611i \(0.483223\pi\)
\(758\) 7.21551 0.262079
\(759\) −9.53531 −0.346110
\(760\) −0.243397 −0.00882894
\(761\) 33.6764 1.22077 0.610384 0.792105i \(-0.291015\pi\)
0.610384 + 0.792105i \(0.291015\pi\)
\(762\) 22.3696 0.810365
\(763\) 2.94493 0.106614
\(764\) 12.4309 0.449733
\(765\) 4.74440 0.171534
\(766\) 12.1604 0.439371
\(767\) 0 0
\(768\) 1.11835 0.0403551
\(769\) −25.1224 −0.905935 −0.452968 0.891527i \(-0.649635\pi\)
−0.452968 + 0.891527i \(0.649635\pi\)
\(770\) −3.53908 −0.127540
\(771\) 23.0242 0.829196
\(772\) 27.2588 0.981067
\(773\) −31.6336 −1.13778 −0.568891 0.822413i \(-0.692627\pi\)
−0.568891 + 0.822413i \(0.692627\pi\)
\(774\) −25.6297 −0.921241
\(775\) −18.0731 −0.649204
\(776\) −2.63611 −0.0946310
\(777\) 7.90600 0.283626
\(778\) 30.9585 1.10992
\(779\) −2.29426 −0.0822005
\(780\) 0 0
\(781\) 12.9704 0.464117
\(782\) −137.432 −4.91456
\(783\) −2.95273 −0.105522
\(784\) 3.76587 0.134495
\(785\) −14.3426 −0.511911
\(786\) −12.2698 −0.437648
\(787\) −23.2041 −0.827137 −0.413569 0.910473i \(-0.635718\pi\)
−0.413569 + 0.910473i \(0.635718\pi\)
\(788\) −30.7559 −1.09563
\(789\) −5.95047 −0.211842
\(790\) −2.79432 −0.0994175
\(791\) 1.47526 0.0524542
\(792\) −1.41315 −0.0502139
\(793\) 0 0
\(794\) 32.0974 1.13909
\(795\) −4.82200 −0.171019
\(796\) 45.7533 1.62168
\(797\) 16.5706 0.586960 0.293480 0.955965i \(-0.405187\pi\)
0.293480 + 0.955965i \(0.405187\pi\)
\(798\) −1.20850 −0.0427803
\(799\) −86.2946 −3.05288
\(800\) 34.6367 1.22459
\(801\) −14.7714 −0.521921
\(802\) −42.3698 −1.49613
\(803\) 8.51665 0.300546
\(804\) −24.7502 −0.872871
\(805\) 15.6411 0.551275
\(806\) 0 0
\(807\) −1.17571 −0.0413868
\(808\) −3.46342 −0.121843
\(809\) 8.97637 0.315592 0.157796 0.987472i \(-0.449561\pi\)
0.157796 + 0.987472i \(0.449561\pi\)
\(810\) −1.53231 −0.0538398
\(811\) −2.09499 −0.0735651 −0.0367826 0.999323i \(-0.511711\pi\)
−0.0367826 + 0.999323i \(0.511711\pi\)
\(812\) 18.1063 0.635406
\(813\) 7.12706 0.249957
\(814\) 7.38534 0.258856
\(815\) −11.7166 −0.410414
\(816\) 15.1044 0.528759
\(817\) −2.88089 −0.100790
\(818\) −49.9969 −1.74810
\(819\) 0 0
\(820\) 17.8381 0.622935
\(821\) 32.8066 1.14496 0.572480 0.819919i \(-0.305982\pi\)
0.572480 + 0.819919i \(0.305982\pi\)
\(822\) −10.4935 −0.366002
\(823\) −6.37447 −0.222200 −0.111100 0.993809i \(-0.535437\pi\)
−0.111100 + 0.993809i \(0.535437\pi\)
\(824\) 14.5287 0.506130
\(825\) 4.49560 0.156517
\(826\) 38.9343 1.35470
\(827\) 14.7476 0.512825 0.256413 0.966567i \(-0.417459\pi\)
0.256413 + 0.966567i \(0.417459\pi\)
\(828\) 25.3161 0.879794
\(829\) −25.4837 −0.885085 −0.442542 0.896748i \(-0.645923\pi\)
−0.442542 + 0.896748i \(0.645923\pi\)
\(830\) 7.12018 0.247145
\(831\) −11.9736 −0.415361
\(832\) 0 0
\(833\) 11.1263 0.385504
\(834\) −9.52586 −0.329854
\(835\) −3.90976 −0.135303
\(836\) −0.643877 −0.0222690
\(837\) 4.02017 0.138957
\(838\) −7.98924 −0.275984
\(839\) 41.7953 1.44293 0.721467 0.692449i \(-0.243468\pi\)
0.721467 + 0.692449i \(0.243468\pi\)
\(840\) 2.31803 0.0799795
\(841\) −20.2814 −0.699359
\(842\) −51.1852 −1.76396
\(843\) −18.7901 −0.647165
\(844\) −28.3831 −0.976988
\(845\) 0 0
\(846\) 27.8707 0.958216
\(847\) −2.30964 −0.0793603
\(848\) −15.3514 −0.527170
\(849\) 10.5237 0.361172
\(850\) 64.7949 2.22245
\(851\) −32.6397 −1.11888
\(852\) −34.4361 −1.17976
\(853\) 25.2825 0.865655 0.432827 0.901477i \(-0.357516\pi\)
0.432827 + 0.901477i \(0.357516\pi\)
\(854\) −4.53758 −0.155273
\(855\) −0.172238 −0.00589041
\(856\) 27.7952 0.950021
\(857\) −26.8626 −0.917609 −0.458804 0.888537i \(-0.651722\pi\)
−0.458804 + 0.888537i \(0.651722\pi\)
\(858\) 0 0
\(859\) 6.11713 0.208714 0.104357 0.994540i \(-0.466722\pi\)
0.104357 + 0.994540i \(0.466722\pi\)
\(860\) 22.3992 0.763807
\(861\) 21.8497 0.744637
\(862\) 67.0336 2.28318
\(863\) −32.1517 −1.09446 −0.547228 0.836984i \(-0.684317\pi\)
−0.547228 + 0.836984i \(0.684317\pi\)
\(864\) −7.70458 −0.262115
\(865\) 9.02865 0.306983
\(866\) 49.7401 1.69024
\(867\) 27.6260 0.938228
\(868\) −24.6519 −0.836740
\(869\) −1.82360 −0.0618616
\(870\) 4.52448 0.153394
\(871\) 0 0
\(872\) −1.80184 −0.0610180
\(873\) −1.86542 −0.0631350
\(874\) 4.98925 0.168764
\(875\) −15.5759 −0.526563
\(876\) −22.6115 −0.763973
\(877\) 17.9062 0.604648 0.302324 0.953205i \(-0.402237\pi\)
0.302324 + 0.953205i \(0.402237\pi\)
\(878\) 5.16241 0.174223
\(879\) 14.0111 0.472584
\(880\) −1.60581 −0.0541320
\(881\) 40.5751 1.36701 0.683504 0.729947i \(-0.260455\pi\)
0.683504 + 0.729947i \(0.260455\pi\)
\(882\) −3.59349 −0.120999
\(883\) −24.6601 −0.829879 −0.414940 0.909849i \(-0.636197\pi\)
−0.414940 + 0.909849i \(0.636197\pi\)
\(884\) 0 0
\(885\) 5.54901 0.186528
\(886\) −37.0286 −1.24400
\(887\) 27.2662 0.915510 0.457755 0.889078i \(-0.348654\pi\)
0.457755 + 0.889078i \(0.348654\pi\)
\(888\) −4.83725 −0.162327
\(889\) −23.9466 −0.803144
\(890\) 22.6343 0.758703
\(891\) −1.00000 −0.0335013
\(892\) 14.1774 0.474693
\(893\) 3.13279 0.104835
\(894\) −20.5043 −0.685767
\(895\) −17.3489 −0.579911
\(896\) 24.7107 0.825526
\(897\) 0 0
\(898\) −62.7081 −2.09260
\(899\) −11.8705 −0.395902
\(900\) −11.9357 −0.397858
\(901\) −45.3560 −1.51103
\(902\) 20.4108 0.679606
\(903\) 27.4366 0.913032
\(904\) −0.902631 −0.0300211
\(905\) −0.661436 −0.0219869
\(906\) −32.8217 −1.09043
\(907\) 0.121526 0.00403521 0.00201760 0.999998i \(-0.499358\pi\)
0.00201760 + 0.999998i \(0.499358\pi\)
\(908\) 20.7734 0.689389
\(909\) −2.45086 −0.0812898
\(910\) 0 0
\(911\) −40.6736 −1.34758 −0.673788 0.738925i \(-0.735334\pi\)
−0.673788 + 0.738925i \(0.735334\pi\)
\(912\) −0.548341 −0.0181574
\(913\) 4.64671 0.153784
\(914\) 68.8495 2.27734
\(915\) −0.646706 −0.0213795
\(916\) 28.3564 0.936921
\(917\) 13.1347 0.433748
\(918\) −14.4130 −0.475698
\(919\) −26.0713 −0.860012 −0.430006 0.902826i \(-0.641489\pi\)
−0.430006 + 0.902826i \(0.641489\pi\)
\(920\) −9.56992 −0.315511
\(921\) −2.52126 −0.0830785
\(922\) 1.52470 0.0502134
\(923\) 0 0
\(924\) 6.13206 0.201730
\(925\) 15.3886 0.505975
\(926\) −55.6242 −1.82792
\(927\) 10.2811 0.337675
\(928\) 22.7495 0.746790
\(929\) 26.9849 0.885346 0.442673 0.896683i \(-0.354030\pi\)
0.442673 + 0.896683i \(0.354030\pi\)
\(930\) −6.16013 −0.201999
\(931\) −0.403923 −0.0132381
\(932\) 41.0219 1.34372
\(933\) −22.9380 −0.750956
\(934\) 80.5929 2.63708
\(935\) −4.74440 −0.155158
\(936\) 0 0
\(937\) 31.9915 1.04512 0.522559 0.852603i \(-0.324977\pi\)
0.522559 + 0.852603i \(0.324977\pi\)
\(938\) 46.4537 1.51677
\(939\) −21.6566 −0.706736
\(940\) −24.3578 −0.794463
\(941\) 31.7257 1.03423 0.517115 0.855916i \(-0.327006\pi\)
0.517115 + 0.855916i \(0.327006\pi\)
\(942\) 43.5714 1.41963
\(943\) −90.2062 −2.93752
\(944\) 17.6660 0.574979
\(945\) 1.64033 0.0533600
\(946\) 25.6297 0.833294
\(947\) 46.5444 1.51249 0.756245 0.654289i \(-0.227032\pi\)
0.756245 + 0.654289i \(0.227032\pi\)
\(948\) 4.84163 0.157249
\(949\) 0 0
\(950\) −2.35228 −0.0763180
\(951\) −26.6050 −0.862726
\(952\) 21.8035 0.706655
\(953\) 37.1054 1.20196 0.600981 0.799263i \(-0.294777\pi\)
0.600981 + 0.799263i \(0.294777\pi\)
\(954\) 14.6487 0.474269
\(955\) −3.32527 −0.107603
\(956\) 44.9660 1.45430
\(957\) 2.95273 0.0954481
\(958\) −3.75550 −0.121335
\(959\) 11.2332 0.362740
\(960\) 8.59415 0.277375
\(961\) −14.8382 −0.478653
\(962\) 0 0
\(963\) 19.6690 0.633826
\(964\) 0.212305 0.00683787
\(965\) −7.29177 −0.234730
\(966\) −47.5159 −1.52880
\(967\) −33.1854 −1.06717 −0.533586 0.845746i \(-0.679156\pi\)
−0.533586 + 0.845746i \(0.679156\pi\)
\(968\) 1.41315 0.0454202
\(969\) −1.62008 −0.0520444
\(970\) 2.85840 0.0917777
\(971\) 23.0990 0.741283 0.370642 0.928776i \(-0.379138\pi\)
0.370642 + 0.928776i \(0.379138\pi\)
\(972\) 2.65498 0.0851585
\(973\) 10.1974 0.326914
\(974\) −12.2933 −0.393903
\(975\) 0 0
\(976\) −2.05887 −0.0659028
\(977\) −32.4063 −1.03677 −0.518385 0.855147i \(-0.673467\pi\)
−0.518385 + 0.855147i \(0.673467\pi\)
\(978\) 35.5937 1.13816
\(979\) 14.7714 0.472095
\(980\) 3.14055 0.100321
\(981\) −1.27506 −0.0407095
\(982\) −59.8475 −1.90981
\(983\) 1.17252 0.0373976 0.0186988 0.999825i \(-0.494048\pi\)
0.0186988 + 0.999825i \(0.494048\pi\)
\(984\) −13.3687 −0.426178
\(985\) 8.22723 0.262141
\(986\) 42.5575 1.35531
\(987\) −29.8356 −0.949677
\(988\) 0 0
\(989\) −113.271 −3.60182
\(990\) 1.53231 0.0486999
\(991\) −4.78159 −0.151892 −0.0759462 0.997112i \(-0.524198\pi\)
−0.0759462 + 0.997112i \(0.524198\pi\)
\(992\) −30.9737 −0.983416
\(993\) 24.7670 0.785958
\(994\) 64.6333 2.05004
\(995\) −12.2391 −0.388004
\(996\) −12.3369 −0.390910
\(997\) 55.7577 1.76586 0.882932 0.469502i \(-0.155566\pi\)
0.882932 + 0.469502i \(0.155566\pi\)
\(998\) −17.8444 −0.564856
\(999\) −3.42304 −0.108300
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 5577.2.a.x.1.7 7
13.5 odd 4 429.2.b.b.298.3 14
13.8 odd 4 429.2.b.b.298.12 yes 14
13.12 even 2 5577.2.a.y.1.1 7
39.5 even 4 1287.2.b.c.298.12 14
39.8 even 4 1287.2.b.c.298.3 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.3 14 13.5 odd 4
429.2.b.b.298.12 yes 14 13.8 odd 4
1287.2.b.c.298.3 14 39.8 even 4
1287.2.b.c.298.12 14 39.5 even 4
5577.2.a.x.1.7 7 1.1 even 1 trivial
5577.2.a.y.1.1 7 13.12 even 2