Properties

Label 5577.2.a.y.1.1
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $0$
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: \(0\)
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 1.1
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 \(-0.776179\pi\)
−0.762806 + 0.646628i \(0.776179\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.65498 1.32749
\(5\) 0.710210 0.317616 0.158808 0.987310i \(-0.449235\pi\)
0.158808 + 0.987310i \(0.449235\pi\)
\(6\) −2.15754 −0.880812
\(7\) 2.30964 0.872963 0.436482 0.899713i \(-0.356224\pi\)
0.436482 + 0.899713i \(0.356224\pi\)
\(8\) −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 \(-0.508856\pi\)
−0.0278186 + 0.999613i \(0.508856\pi\)
\(20\) 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 \(-0.617572\pi\)
−0.361022 + 0.932557i \(0.617572\pi\)
\(32\) 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 \(-0.409211\pi\)
0.281372 + 0.959599i \(0.409211\pi\)
\(38\) 0.523240 0.0848807
\(39\) 0 0
\(40\) −1.00363 −0.158688
\(41\) 9.46022 1.47744 0.738719 0.674013i \(-0.235431\pi\)
0.738719 + 0.674013i \(0.235431\pi\)
\(42\) −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 \(-0.891180\pi\)
−0.942130 + 0.335249i \(0.891180\pi\)
\(48\) −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 \(-0.330165\pi\)
0.508596 + 0.861005i \(0.330165\pi\)
\(60\) 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 \(-0.307159\pi\)
0.569442 + 0.822032i \(0.307159\pi\)
\(68\) −17.7360 −2.15080
\(69\) 9.53531 1.14792
\(70\) −3.53908 −0.423001
\(71\) 12.9704 1.53930 0.769650 0.638466i \(-0.220431\pi\)
0.769650 + 0.638466i \(0.220431\pi\)
\(72\) −1.41315 −0.166541
\(73\) 8.51665 0.996798 0.498399 0.866948i \(-0.333921\pi\)
0.498399 + 0.866948i \(0.333921\pi\)
\(74\) −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 \(-0.417918\pi\)
0.255021 + 0.966935i \(0.417918\pi\)
\(84\) 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 \(-0.213749\pi\)
0.782881 + 0.622171i \(0.213749\pi\)
\(90\) −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 \(-0.469810\pi\)
0.0947025 + 0.995506i \(0.469810\pi\)
\(98\) 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 \(-0.480551\pi\)
0.0610642 + 0.998134i \(0.480551\pi\)
\(110\) −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 \(-0.433381\pi\)
0.207764 + 0.978179i \(0.433381\pi\)
\(138\) −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 \(-0.372724\pi\)
0.389281 + 0.921119i \(0.372724\pi\)
\(150\) 9.69944 0.791956
\(151\) 15.2126 1.23798 0.618991 0.785398i \(-0.287542\pi\)
0.618991 + 0.785398i \(0.287542\pi\)
\(152\) 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 \(-0.723596\pi\)
−0.646087 + 0.763264i \(0.723596\pi\)
\(164\) 25.1167 1.96129
\(165\) 0.710210 0.0552898
\(166\) −10.0255 −0.778126
\(167\) −5.50507 −0.425995 −0.212998 0.977053i \(-0.568323\pi\)
−0.212998 + 0.977053i \(0.568323\pi\)
\(168\) −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 \(-0.620478\pi\)
−0.369520 + 0.929223i \(0.620478\pi\)
\(194\) −4.02473 −0.288959
\(195\) 0 0
\(196\) −4.42200 −0.315857
\(197\) 11.5842 0.825341 0.412671 0.910880i \(-0.364596\pi\)
0.412671 + 0.910880i \(0.364596\pi\)
\(198\) −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 \(-0.557219\pi\)
−0.178794 + 0.983887i \(0.557219\pi\)
\(224\) 17.7948 1.18897
\(225\) −4.49560 −0.299707
\(226\) 1.37811 0.0916702
\(227\) −7.82431 −0.519318 −0.259659 0.965700i \(-0.583610\pi\)
−0.259659 + 0.965700i \(0.583610\pi\)
\(228\) −0.643877 −0.0426418
\(229\) −10.6805 −0.705784 −0.352892 0.935664i \(-0.614802\pi\)
−0.352892 + 0.935664i \(0.614802\pi\)
\(230\) −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 \(-0.684521\pi\)
−0.547765 + 0.836632i \(0.684521\pi\)
\(240\) −1.60581 −0.103655
\(241\) −0.0799646 −0.00515098 −0.00257549 0.999997i \(-0.500820\pi\)
−0.00257549 + 0.999997i \(0.500820\pi\)
\(242\) −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 \(-0.569454\pi\)
−0.216469 + 0.976290i \(0.569454\pi\)
\(272\) 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 \(-0.310624\pi\)
0.560461 + 0.828181i \(0.310624\pi\)
\(282\) 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 \(-0.634217\pi\)
−0.409270 + 0.912413i \(0.634217\pi\)
\(294\) 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 \(-0.477078\pi\)
0.0719481 + 0.997408i \(0.477078\pi\)
\(308\) 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 \(-0.231425\pi\)
0.747143 + 0.664664i \(0.231425\pi\)
\(318\) −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 \(-0.738307\pi\)
−0.680659 + 0.732600i \(0.738307\pi\)
\(332\) 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 \(-0.309676\pi\)
0.562924 + 0.826508i \(0.309676\pi\)
\(350\) 22.4022 1.19745
\(351\) 0 0
\(352\) 7.70458 0.410655
\(353\) 2.20127 0.117162 0.0585810 0.998283i \(-0.481342\pi\)
0.0585810 + 0.998283i \(0.481342\pi\)
\(354\) −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 \(-0.565694\pi\)
−0.204921 + 0.978778i \(0.565694\pi\)
\(360\) −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 \(-0.527374\pi\)
−0.0858931 + 0.996304i \(0.527374\pi\)
\(380\) −0.457288 −0.0234584
\(381\) 10.3681 0.531174
\(382\) −10.1018 −0.516853
\(383\) −5.63621 −0.287997 −0.143998 0.989578i \(-0.545996\pi\)
−0.143998 + 0.989578i \(0.545996\pi\)
\(384\) 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 \(-0.621782\pi\)
−0.373324 + 0.927701i \(0.621782\pi\)
\(398\) −37.1809 −1.86371
\(399\) −0.560127 −0.0280414
\(400\) 10.1647 0.508237
\(401\) 19.6380 0.980675 0.490337 0.871533i \(-0.336874\pi\)
0.490337 + 0.871533i \(0.336874\pi\)
\(402\) −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 \(-0.305811\pi\)
0.572918 + 0.819613i \(0.305811\pi\)
\(410\) −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 \(-0.303788\pi\)
0.578116 + 0.815955i \(0.303788\pi\)
\(422\) 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 \(-0.769121\pi\)
−0.748282 + 0.663381i \(0.769121\pi\)
\(432\) −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 \(-0.259443\pi\)
0.685822 + 0.727769i \(0.259443\pi\)
\(450\) 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 \(-0.768205\pi\)
−0.746369 + 0.665532i \(0.768205\pi\)
\(458\) 23.0435 1.07675
\(459\) −6.68027 −0.311808
\(460\) 17.9797 0.838308
\(461\) −0.706685 −0.0329136 −0.0164568 0.999865i \(-0.505239\pi\)
−0.0164568 + 0.999865i \(0.505239\pi\)
\(462\) −4.98315 −0.231837
\(463\) 25.7813 1.19816 0.599079 0.800690i \(-0.295533\pi\)
0.599079 + 0.800690i \(0.295533\pi\)
\(464\) 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 \(-0.487339\pi\)
0.0397659 + 0.999209i \(0.487339\pi\)
\(480\) 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 \(-0.458792\pi\)
0.129097 + 0.991632i \(0.458792\pi\)
\(488\) −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 \(-0.440731\pi\)
0.185124 + 0.982715i \(0.440731\pi\)
\(500\) −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 \(-0.460679\pi\)
0.123216 + 0.992380i \(0.460679\pi\)
\(510\) 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 \(-0.705444\pi\)
−0.601536 + 0.798846i \(0.705444\pi\)
\(542\) 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 \(-0.367154\pi\)
0.405337 + 0.914167i \(0.367154\pi\)
\(558\) 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 \(-0.547019\pi\)
−0.147179 + 0.989110i \(0.547019\pi\)
\(578\) −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 \(-0.310474\pi\)
0.560851 + 0.827917i \(0.310474\pi\)
\(588\) −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 \(-0.364993\pi\)
0.411535 + 0.911394i \(0.364993\pi\)
\(594\) −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 \(-0.648549\pi\)
−0.449924 + 0.893067i \(0.648549\pi\)
\(614\) −5.43973 −0.219530
\(615\) 6.71875 0.270926
\(616\) −3.26386 −0.131505
\(617\) 27.4366 1.10456 0.552279 0.833660i \(-0.313758\pi\)
0.552279 + 0.833660i \(0.313758\pi\)
\(618\) −22.1818 −0.892284
\(619\) −47.9288 −1.92642 −0.963211 0.268747i \(-0.913390\pi\)
−0.963211 + 0.268747i \(0.913390\pi\)
\(620\) −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 \(-0.342707\pi\)
0.474284 + 0.880372i \(0.342707\pi\)
\(632\) −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 \(-0.299154\pi\)
0.589934 + 0.807451i \(0.299154\pi\)
\(644\) 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 \(-0.681646\pi\)
−0.540187 + 0.841545i \(0.681646\pi\)
\(662\) 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 \(-0.230387\pi\)
0.749307 + 0.662223i \(0.230387\pi\)
\(684\) −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 \(-0.281291\pi\)
0.634294 + 0.773092i \(0.281291\pi\)
\(692\) −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 \(-0.542190\pi\)
−0.132156 + 0.991229i \(0.542190\pi\)
\(710\) −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 \(-0.443231\pi\)
0.177402 + 0.984138i \(0.443231\pi\)
\(734\) 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 \(-0.369532\pi\)
0.398497 + 0.917169i \(0.369532\pi\)
\(740\) 6.45446 0.237271
\(741\) 0 0
\(742\) −33.8333 −1.24206
\(743\) 12.3149 0.451790 0.225895 0.974152i \(-0.427469\pi\)
0.225895 + 0.974152i \(0.427469\pi\)
\(744\) 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 \(-0.708985\pi\)
−0.610384 + 0.792105i \(0.708985\pi\)
\(762\) −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 \(-0.350365\pi\)
0.452968 + 0.891527i \(0.350365\pi\)
\(770\) −3.53908 −0.127540
\(771\) 23.0242 0.829196
\(772\) −27.2588 −0.981067
\(773\) 31.6336 1.13778 0.568891 0.822413i \(-0.307373\pi\)
0.568891 + 0.822413i \(0.307373\pi\)
\(774\) 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 \(-0.364282\pi\)
0.413569 + 0.910473i \(0.364282\pi\)
\(788\) 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 \(-0.488289\pi\)
0.0367826 + 0.999323i \(0.488289\pi\)
\(812\) −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 \(-0.694018\pi\)
−0.572480 + 0.819919i \(0.694018\pi\)
\(822\) −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 \(-0.582541\pi\)
−0.256413 + 0.966567i \(0.582541\pi\)
\(828\) 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 \(-0.756532\pi\)
−0.721467 + 0.692449i \(0.756532\pi\)
\(840\) −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 \(-0.642484\pi\)
−0.432827 + 0.901477i \(0.642484\pi\)
\(854\) −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 \(-0.315683\pi\)
0.547228 + 0.836984i \(0.315683\pi\)
\(864\) 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 \(-0.597763\pi\)
−0.302324 + 0.953205i \(0.597763\pi\)
\(878\) −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 \(-0.645970\pi\)
−0.442673 + 0.896683i \(0.645970\pi\)
\(930\) 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 \(-0.672994\pi\)
−0.517115 + 0.855916i \(0.672994\pi\)
\(942\) −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 \(-0.772968\pi\)
−0.756245 + 0.654289i \(0.772968\pi\)
\(948\) 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 \(-0.320844\pi\)
0.533586 + 0.845746i \(0.320844\pi\)
\(968\) −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 \(-0.326533\pi\)
0.518385 + 0.855147i \(0.326533\pi\)
\(978\) 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 \(-0.505952\pi\)
−0.0186988 + 0.999825i \(0.505952\pi\)
\(984\) −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.y.1.1 7
13.5 odd 4 429.2.b.b.298.12 yes 14
13.8 odd 4 429.2.b.b.298.3 14
13.12 even 2 5577.2.a.x.1.7 7
39.5 even 4 1287.2.b.c.298.3 14
39.8 even 4 1287.2.b.c.298.12 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.3 14 13.8 odd 4
429.2.b.b.298.12 yes 14 13.5 odd 4
1287.2.b.c.298.3 14 39.5 even 4
1287.2.b.c.298.12 14 39.8 even 4
5577.2.a.x.1.7 7 13.12 even 2
5577.2.a.y.1.1 7 1.1 even 1 trivial