Properties

Label 177.12.a.d.1.16
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+23.0914 q^{2} +243.000 q^{3} -1514.79 q^{4} +32.6758 q^{5} +5611.21 q^{6} -80813.9 q^{7} -82269.7 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+23.0914 q^{2} +243.000 q^{3} -1514.79 q^{4} +32.6758 q^{5} +5611.21 q^{6} -80813.9 q^{7} -82269.7 q^{8} +59049.0 q^{9} +754.528 q^{10} -196616. q^{11} -368093. q^{12} -2.11622e6 q^{13} -1.86611e6 q^{14} +7940.21 q^{15} +1.20256e6 q^{16} -4.62145e6 q^{17} +1.36352e6 q^{18} +4.04501e6 q^{19} -49496.8 q^{20} -1.96378e7 q^{21} -4.54013e6 q^{22} -2.90999e7 q^{23} -1.99915e7 q^{24} -4.88271e7 q^{25} -4.88664e7 q^{26} +1.43489e7 q^{27} +1.22416e8 q^{28} +1.75499e8 q^{29} +183350. q^{30} -2.81038e8 q^{31} +1.96257e8 q^{32} -4.77776e7 q^{33} -1.06716e8 q^{34} -2.64066e6 q^{35} -8.94467e7 q^{36} -3.05876e8 q^{37} +9.34049e7 q^{38} -5.14241e8 q^{39} -2.68822e6 q^{40} -1.04911e9 q^{41} -4.53464e8 q^{42} +8.82678e8 q^{43} +2.97831e8 q^{44} +1.92947e6 q^{45} -6.71957e8 q^{46} +2.35478e9 q^{47} +2.92223e8 q^{48} +4.55357e9 q^{49} -1.12748e9 q^{50} -1.12301e9 q^{51} +3.20562e9 q^{52} -2.72305e9 q^{53} +3.31336e8 q^{54} -6.42457e6 q^{55} +6.64854e9 q^{56} +9.82937e8 q^{57} +4.05252e9 q^{58} +7.14924e8 q^{59} -1.20277e7 q^{60} -7.46101e9 q^{61} -6.48956e9 q^{62} -4.77198e9 q^{63} +2.06900e9 q^{64} -6.91491e7 q^{65} -1.10325e9 q^{66} -1.03666e9 q^{67} +7.00052e9 q^{68} -7.07128e9 q^{69} -6.09764e7 q^{70} +2.41936e9 q^{71} -4.85794e9 q^{72} +2.86219e10 q^{73} -7.06309e9 q^{74} -1.18650e10 q^{75} -6.12733e9 q^{76} +1.58893e10 q^{77} -1.18745e10 q^{78} +6.54301e9 q^{79} +3.92947e7 q^{80} +3.48678e9 q^{81} -2.42255e10 q^{82} -5.44336e10 q^{83} +2.97471e10 q^{84} -1.51009e8 q^{85} +2.03823e10 q^{86} +4.26463e10 q^{87} +1.61755e10 q^{88} +4.77033e10 q^{89} +4.45542e7 q^{90} +1.71020e11 q^{91} +4.40802e10 q^{92} -6.82922e10 q^{93} +5.43751e10 q^{94} +1.32174e8 q^{95} +4.76905e10 q^{96} +6.19173e10 q^{97} +1.05148e11 q^{98} -1.16100e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.0914 0.510252 0.255126 0.966908i \(-0.417883\pi\)
0.255126 + 0.966908i \(0.417883\pi\)
\(3\) 243.000 0.577350
\(4\) −1514.79 −0.739643
\(5\) 32.6758 0.00467617 0.00233809 0.999997i \(-0.499256\pi\)
0.00233809 + 0.999997i \(0.499256\pi\)
\(6\) 5611.21 0.294594
\(7\) −80813.9 −1.81739 −0.908693 0.417466i \(-0.862918\pi\)
−0.908693 + 0.417466i \(0.862918\pi\)
\(8\) −82269.7 −0.887657
\(9\) 59049.0 0.333333
\(10\) 754.528 0.00238603
\(11\) −196616. −0.368094 −0.184047 0.982917i \(-0.558920\pi\)
−0.184047 + 0.982917i \(0.558920\pi\)
\(12\) −368093. −0.427033
\(13\) −2.11622e6 −1.58078 −0.790392 0.612602i \(-0.790123\pi\)
−0.790392 + 0.612602i \(0.790123\pi\)
\(14\) −1.86611e6 −0.927325
\(15\) 7940.21 0.00269979
\(16\) 1.20256e6 0.286714
\(17\) −4.62145e6 −0.789422 −0.394711 0.918805i \(-0.629155\pi\)
−0.394711 + 0.918805i \(0.629155\pi\)
\(18\) 1.36352e6 0.170084
\(19\) 4.04501e6 0.374779 0.187389 0.982286i \(-0.439997\pi\)
0.187389 + 0.982286i \(0.439997\pi\)
\(20\) −49496.8 −0.00345870
\(21\) −1.96378e7 −1.04927
\(22\) −4.54013e6 −0.187821
\(23\) −2.90999e7 −0.942732 −0.471366 0.881938i \(-0.656239\pi\)
−0.471366 + 0.881938i \(0.656239\pi\)
\(24\) −1.99915e7 −0.512489
\(25\) −4.88271e7 −0.999978
\(26\) −4.88664e7 −0.806598
\(27\) 1.43489e7 0.192450
\(28\) 1.22416e8 1.34422
\(29\) 1.75499e8 1.58886 0.794432 0.607353i \(-0.207769\pi\)
0.794432 + 0.607353i \(0.207769\pi\)
\(30\) 183350. 0.00137757
\(31\) −2.81038e8 −1.76309 −0.881547 0.472095i \(-0.843498\pi\)
−0.881547 + 0.472095i \(0.843498\pi\)
\(32\) 1.96257e8 1.03395
\(33\) −4.77776e7 −0.212519
\(34\) −1.06716e8 −0.402804
\(35\) −2.64066e6 −0.00849841
\(36\) −8.94467e7 −0.246548
\(37\) −3.05876e8 −0.725163 −0.362581 0.931952i \(-0.618105\pi\)
−0.362581 + 0.931952i \(0.618105\pi\)
\(38\) 9.34049e7 0.191232
\(39\) −5.14241e8 −0.912666
\(40\) −2.68822e6 −0.00415084
\(41\) −1.04911e9 −1.41420 −0.707100 0.707113i \(-0.749997\pi\)
−0.707100 + 0.707113i \(0.749997\pi\)
\(42\) −4.53464e8 −0.535391
\(43\) 8.82678e8 0.915642 0.457821 0.889044i \(-0.348630\pi\)
0.457821 + 0.889044i \(0.348630\pi\)
\(44\) 2.97831e8 0.272258
\(45\) 1.92947e6 0.00155872
\(46\) −6.71957e8 −0.481031
\(47\) 2.35478e9 1.49766 0.748828 0.662764i \(-0.230617\pi\)
0.748828 + 0.662764i \(0.230617\pi\)
\(48\) 2.92223e8 0.165534
\(49\) 4.55357e9 2.30289
\(50\) −1.12748e9 −0.510241
\(51\) −1.12301e9 −0.455773
\(52\) 3.20562e9 1.16921
\(53\) −2.72305e9 −0.894413 −0.447206 0.894431i \(-0.647581\pi\)
−0.447206 + 0.894431i \(0.647581\pi\)
\(54\) 3.31336e8 0.0981981
\(55\) −6.42457e6 −0.00172127
\(56\) 6.64854e9 1.61321
\(57\) 9.82937e8 0.216378
\(58\) 4.05252e9 0.810721
\(59\) 7.14924e8 0.130189
\(60\) −1.20277e7 −0.00199688
\(61\) −7.46101e9 −1.13106 −0.565528 0.824729i \(-0.691327\pi\)
−0.565528 + 0.824729i \(0.691327\pi\)
\(62\) −6.48956e9 −0.899623
\(63\) −4.77198e9 −0.605795
\(64\) 2.06900e9 0.240863
\(65\) −6.91491e7 −0.00739202
\(66\) −1.10325e9 −0.108438
\(67\) −1.03666e9 −0.0938051 −0.0469025 0.998899i \(-0.514935\pi\)
−0.0469025 + 0.998899i \(0.514935\pi\)
\(68\) 7.00052e9 0.583890
\(69\) −7.07128e9 −0.544287
\(70\) −6.09764e7 −0.00433633
\(71\) 2.41936e9 0.159140 0.0795702 0.996829i \(-0.474645\pi\)
0.0795702 + 0.996829i \(0.474645\pi\)
\(72\) −4.85794e9 −0.295886
\(73\) 2.86219e10 1.61593 0.807966 0.589229i \(-0.200569\pi\)
0.807966 + 0.589229i \(0.200569\pi\)
\(74\) −7.06309e9 −0.370016
\(75\) −1.18650e10 −0.577338
\(76\) −6.12733e9 −0.277202
\(77\) 1.58893e10 0.668968
\(78\) −1.18745e10 −0.465690
\(79\) 6.54301e9 0.239237 0.119619 0.992820i \(-0.461833\pi\)
0.119619 + 0.992820i \(0.461833\pi\)
\(80\) 3.92947e7 0.00134072
\(81\) 3.48678e9 0.111111
\(82\) −2.42255e10 −0.721599
\(83\) −5.44336e10 −1.51683 −0.758416 0.651770i \(-0.774027\pi\)
−0.758416 + 0.651770i \(0.774027\pi\)
\(84\) 2.97471e10 0.776083
\(85\) −1.51009e8 −0.00369147
\(86\) 2.03823e10 0.467209
\(87\) 4.26463e10 0.917331
\(88\) 1.61755e10 0.326741
\(89\) 4.77033e10 0.905531 0.452765 0.891630i \(-0.350438\pi\)
0.452765 + 0.891630i \(0.350438\pi\)
\(90\) 4.45542e7 0.000795343 0
\(91\) 1.71020e11 2.87289
\(92\) 4.40802e10 0.697285
\(93\) −6.82922e10 −1.01792
\(94\) 5.43751e10 0.764183
\(95\) 1.32174e8 0.00175253
\(96\) 4.76905e10 0.596953
\(97\) 6.19173e10 0.732095 0.366048 0.930596i \(-0.380711\pi\)
0.366048 + 0.930596i \(0.380711\pi\)
\(98\) 1.05148e11 1.17505
\(99\) −1.16100e10 −0.122698
\(100\) 7.39626e10 0.739626
\(101\) −1.48326e11 −1.40427 −0.702133 0.712046i \(-0.747769\pi\)
−0.702133 + 0.712046i \(0.747769\pi\)
\(102\) −2.59319e10 −0.232559
\(103\) −1.07904e11 −0.917136 −0.458568 0.888659i \(-0.651638\pi\)
−0.458568 + 0.888659i \(0.651638\pi\)
\(104\) 1.74101e11 1.40319
\(105\) −6.41680e8 −0.00490656
\(106\) −6.28789e10 −0.456376
\(107\) −1.79873e9 −0.0123981 −0.00619906 0.999981i \(-0.501973\pi\)
−0.00619906 + 0.999981i \(0.501973\pi\)
\(108\) −2.17356e10 −0.142344
\(109\) 2.47694e11 1.54195 0.770975 0.636865i \(-0.219769\pi\)
0.770975 + 0.636865i \(0.219769\pi\)
\(110\) −1.48352e8 −0.000878282 0
\(111\) −7.43278e10 −0.418673
\(112\) −9.71839e10 −0.521069
\(113\) −1.33748e10 −0.0682899 −0.0341450 0.999417i \(-0.510871\pi\)
−0.0341450 + 0.999417i \(0.510871\pi\)
\(114\) 2.26974e10 0.110408
\(115\) −9.50861e8 −0.00440838
\(116\) −2.65844e11 −1.17519
\(117\) −1.24961e11 −0.526928
\(118\) 1.65086e10 0.0664292
\(119\) 3.73478e11 1.43468
\(120\) −6.53239e8 −0.00239649
\(121\) −2.46654e11 −0.864507
\(122\) −1.72285e11 −0.577124
\(123\) −2.54934e11 −0.816489
\(124\) 4.25713e11 1.30406
\(125\) −3.19096e9 −0.00935224
\(126\) −1.10192e11 −0.309108
\(127\) 7.43211e11 1.99614 0.998072 0.0620676i \(-0.0197694\pi\)
0.998072 + 0.0620676i \(0.0197694\pi\)
\(128\) −3.54159e11 −0.911052
\(129\) 2.14491e11 0.528646
\(130\) −1.59675e9 −0.00377179
\(131\) −7.58634e11 −1.71807 −0.859034 0.511919i \(-0.828935\pi\)
−0.859034 + 0.511919i \(0.828935\pi\)
\(132\) 7.23729e10 0.157188
\(133\) −3.26893e11 −0.681117
\(134\) −2.39380e10 −0.0478643
\(135\) 4.68861e8 0.000899930 0
\(136\) 3.80205e11 0.700736
\(137\) −6.77878e11 −1.20002 −0.600010 0.799993i \(-0.704837\pi\)
−0.600010 + 0.799993i \(0.704837\pi\)
\(138\) −1.63286e11 −0.277724
\(139\) −8.19489e11 −1.33956 −0.669779 0.742560i \(-0.733611\pi\)
−0.669779 + 0.742560i \(0.733611\pi\)
\(140\) 4.00003e9 0.00628579
\(141\) 5.72212e11 0.864672
\(142\) 5.58665e10 0.0812017
\(143\) 4.16082e11 0.581876
\(144\) 7.10102e10 0.0955712
\(145\) 5.73457e9 0.00742980
\(146\) 6.60920e11 0.824533
\(147\) 1.10652e12 1.32957
\(148\) 4.63337e11 0.536361
\(149\) 7.79795e11 0.869873 0.434937 0.900461i \(-0.356771\pi\)
0.434937 + 0.900461i \(0.356771\pi\)
\(150\) −2.73979e11 −0.294588
\(151\) −2.00521e11 −0.207867 −0.103934 0.994584i \(-0.533143\pi\)
−0.103934 + 0.994584i \(0.533143\pi\)
\(152\) −3.32782e11 −0.332675
\(153\) −2.72892e11 −0.263141
\(154\) 3.66906e11 0.341343
\(155\) −9.18313e9 −0.00824454
\(156\) 7.78967e11 0.675046
\(157\) 1.61750e11 0.135330 0.0676652 0.997708i \(-0.478445\pi\)
0.0676652 + 0.997708i \(0.478445\pi\)
\(158\) 1.51087e11 0.122071
\(159\) −6.61700e11 −0.516389
\(160\) 6.41285e9 0.00483494
\(161\) 2.35168e12 1.71331
\(162\) 8.05147e10 0.0566947
\(163\) −1.89658e12 −1.29104 −0.645519 0.763744i \(-0.723359\pi\)
−0.645519 + 0.763744i \(0.723359\pi\)
\(164\) 1.58918e12 1.04600
\(165\) −1.56117e9 −0.000993776 0
\(166\) −1.25695e12 −0.773968
\(167\) −7.97901e11 −0.475344 −0.237672 0.971345i \(-0.576384\pi\)
−0.237672 + 0.971345i \(0.576384\pi\)
\(168\) 1.61559e12 0.931390
\(169\) 2.68623e12 1.49888
\(170\) −3.48702e9 −0.00188358
\(171\) 2.38854e11 0.124926
\(172\) −1.33707e12 −0.677248
\(173\) 3.52739e12 1.73061 0.865307 0.501242i \(-0.167123\pi\)
0.865307 + 0.501242i \(0.167123\pi\)
\(174\) 9.84763e11 0.468070
\(175\) 3.94591e12 1.81735
\(176\) −2.36443e11 −0.105537
\(177\) 1.73727e11 0.0751646
\(178\) 1.10153e12 0.462049
\(179\) −2.73949e12 −1.11424 −0.557120 0.830432i \(-0.688094\pi\)
−0.557120 + 0.830432i \(0.688094\pi\)
\(180\) −2.92274e9 −0.00115290
\(181\) 1.78794e12 0.684101 0.342050 0.939682i \(-0.388879\pi\)
0.342050 + 0.939682i \(0.388879\pi\)
\(182\) 3.94909e12 1.46590
\(183\) −1.81303e12 −0.653015
\(184\) 2.39404e12 0.836823
\(185\) −9.99472e9 −0.00339099
\(186\) −1.57696e12 −0.519398
\(187\) 9.08650e11 0.290581
\(188\) −3.56699e12 −1.10773
\(189\) −1.15959e12 −0.349756
\(190\) 3.05207e9 0.000894232 0
\(191\) 3.55645e12 1.01236 0.506178 0.862429i \(-0.331058\pi\)
0.506178 + 0.862429i \(0.331058\pi\)
\(192\) 5.02767e11 0.139062
\(193\) −1.22933e12 −0.330447 −0.165224 0.986256i \(-0.552835\pi\)
−0.165224 + 0.986256i \(0.552835\pi\)
\(194\) 1.42976e12 0.373553
\(195\) −1.68032e10 −0.00426778
\(196\) −6.89769e12 −1.70332
\(197\) 1.01555e12 0.243859 0.121930 0.992539i \(-0.461092\pi\)
0.121930 + 0.992539i \(0.461092\pi\)
\(198\) −2.68090e11 −0.0626069
\(199\) 6.19152e12 1.40639 0.703194 0.710998i \(-0.251756\pi\)
0.703194 + 0.710998i \(0.251756\pi\)
\(200\) 4.01699e12 0.887637
\(201\) −2.51909e11 −0.0541584
\(202\) −3.42505e12 −0.716530
\(203\) −1.41828e13 −2.88758
\(204\) 1.70113e12 0.337109
\(205\) −3.42806e10 −0.00661305
\(206\) −2.49166e12 −0.467971
\(207\) −1.71832e12 −0.314244
\(208\) −2.54489e12 −0.453232
\(209\) −7.95312e11 −0.137954
\(210\) −1.48173e10 −0.00250358
\(211\) 2.52523e12 0.415668 0.207834 0.978164i \(-0.433359\pi\)
0.207834 + 0.978164i \(0.433359\pi\)
\(212\) 4.12484e12 0.661546
\(213\) 5.87905e11 0.0918797
\(214\) −4.15352e10 −0.00632617
\(215\) 2.88422e10 0.00428170
\(216\) −1.18048e12 −0.170830
\(217\) 2.27118e13 3.20422
\(218\) 5.71960e12 0.786784
\(219\) 6.95513e12 0.932959
\(220\) 9.73185e9 0.00127312
\(221\) 9.78000e12 1.24791
\(222\) −1.71633e12 −0.213629
\(223\) 1.21374e13 1.47384 0.736918 0.675983i \(-0.236281\pi\)
0.736918 + 0.675983i \(0.236281\pi\)
\(224\) −1.58603e13 −1.87909
\(225\) −2.88319e12 −0.333326
\(226\) −3.08843e11 −0.0348451
\(227\) 4.34287e12 0.478227 0.239114 0.970992i \(-0.423143\pi\)
0.239114 + 0.970992i \(0.423143\pi\)
\(228\) −1.48894e12 −0.160043
\(229\) 1.10467e13 1.15914 0.579572 0.814921i \(-0.303220\pi\)
0.579572 + 0.814921i \(0.303220\pi\)
\(230\) −2.19567e10 −0.00224939
\(231\) 3.86110e12 0.386229
\(232\) −1.44383e13 −1.41037
\(233\) 1.16025e13 1.10687 0.553433 0.832894i \(-0.313318\pi\)
0.553433 + 0.832894i \(0.313318\pi\)
\(234\) −2.88551e12 −0.268866
\(235\) 7.69442e10 0.00700330
\(236\) −1.08296e12 −0.0962933
\(237\) 1.58995e12 0.138124
\(238\) 8.62412e12 0.732051
\(239\) −1.88821e13 −1.56625 −0.783127 0.621862i \(-0.786377\pi\)
−0.783127 + 0.621862i \(0.786377\pi\)
\(240\) 9.54861e9 0.000774067 0
\(241\) −1.27106e13 −1.00710 −0.503548 0.863967i \(-0.667972\pi\)
−0.503548 + 0.863967i \(0.667972\pi\)
\(242\) −5.69558e12 −0.441117
\(243\) 8.47289e11 0.0641500
\(244\) 1.13019e13 0.836576
\(245\) 1.48791e11 0.0107687
\(246\) −5.88679e12 −0.416615
\(247\) −8.56013e12 −0.592444
\(248\) 2.31209e13 1.56502
\(249\) −1.32274e13 −0.875744
\(250\) −7.36836e10 −0.00477200
\(251\) −7.60243e12 −0.481667 −0.240833 0.970566i \(-0.577421\pi\)
−0.240833 + 0.970566i \(0.577421\pi\)
\(252\) 7.22854e12 0.448072
\(253\) 5.72150e12 0.347014
\(254\) 1.71618e13 1.01854
\(255\) −3.66953e10 −0.00213127
\(256\) −1.24153e13 −0.705730
\(257\) −8.58575e10 −0.00477690 −0.00238845 0.999997i \(-0.500760\pi\)
−0.00238845 + 0.999997i \(0.500760\pi\)
\(258\) 4.95289e12 0.269743
\(259\) 2.47190e13 1.31790
\(260\) 1.04746e11 0.00546745
\(261\) 1.03631e13 0.529621
\(262\) −1.75179e13 −0.876648
\(263\) 8.70407e12 0.426546 0.213273 0.976993i \(-0.431588\pi\)
0.213273 + 0.976993i \(0.431588\pi\)
\(264\) 3.93065e12 0.188644
\(265\) −8.89776e10 −0.00418243
\(266\) −7.54841e12 −0.347542
\(267\) 1.15919e13 0.522808
\(268\) 1.57033e12 0.0693822
\(269\) −3.50062e13 −1.51533 −0.757664 0.652644i \(-0.773660\pi\)
−0.757664 + 0.652644i \(0.773660\pi\)
\(270\) 1.08267e10 0.000459191 0
\(271\) 1.26831e13 0.527100 0.263550 0.964646i \(-0.415107\pi\)
0.263550 + 0.964646i \(0.415107\pi\)
\(272\) −5.55759e12 −0.226338
\(273\) 4.15579e13 1.65867
\(274\) −1.56531e13 −0.612313
\(275\) 9.60016e12 0.368086
\(276\) 1.07115e13 0.402578
\(277\) −1.18944e13 −0.438230 −0.219115 0.975699i \(-0.570317\pi\)
−0.219115 + 0.975699i \(0.570317\pi\)
\(278\) −1.89231e13 −0.683513
\(279\) −1.65950e13 −0.587698
\(280\) 2.17246e11 0.00754367
\(281\) −4.97437e13 −1.69376 −0.846882 0.531781i \(-0.821523\pi\)
−0.846882 + 0.531781i \(0.821523\pi\)
\(282\) 1.32132e13 0.441201
\(283\) 7.59641e11 0.0248762 0.0124381 0.999923i \(-0.496041\pi\)
0.0124381 + 0.999923i \(0.496041\pi\)
\(284\) −3.66482e12 −0.117707
\(285\) 3.21182e10 0.00101182
\(286\) 9.60791e12 0.296904
\(287\) 8.47829e13 2.57015
\(288\) 1.15888e13 0.344651
\(289\) −1.29141e13 −0.376813
\(290\) 1.32419e11 0.00379107
\(291\) 1.50459e13 0.422675
\(292\) −4.33561e13 −1.19521
\(293\) 8.39756e12 0.227186 0.113593 0.993527i \(-0.463764\pi\)
0.113593 + 0.993527i \(0.463764\pi\)
\(294\) 2.55510e13 0.678418
\(295\) 2.33607e10 0.000608786 0
\(296\) 2.51643e13 0.643696
\(297\) −2.82122e12 −0.0708397
\(298\) 1.80065e13 0.443855
\(299\) 6.15818e13 1.49026
\(300\) 1.79729e13 0.427023
\(301\) −7.13327e13 −1.66407
\(302\) −4.63030e12 −0.106065
\(303\) −3.60432e13 −0.810753
\(304\) 4.86438e12 0.107454
\(305\) −2.43794e11 −0.00528901
\(306\) −6.30146e12 −0.134268
\(307\) −3.01401e13 −0.630787 −0.315394 0.948961i \(-0.602137\pi\)
−0.315394 + 0.948961i \(0.602137\pi\)
\(308\) −2.40689e13 −0.494797
\(309\) −2.62207e13 −0.529509
\(310\) −2.12051e11 −0.00420679
\(311\) 5.01933e13 0.978281 0.489140 0.872205i \(-0.337311\pi\)
0.489140 + 0.872205i \(0.337311\pi\)
\(312\) 4.23065e13 0.810134
\(313\) −4.47804e13 −0.842547 −0.421274 0.906934i \(-0.638417\pi\)
−0.421274 + 0.906934i \(0.638417\pi\)
\(314\) 3.73503e12 0.0690527
\(315\) −1.55928e11 −0.00283280
\(316\) −9.91127e12 −0.176950
\(317\) −7.52336e13 −1.32004 −0.660018 0.751250i \(-0.729451\pi\)
−0.660018 + 0.751250i \(0.729451\pi\)
\(318\) −1.52796e13 −0.263489
\(319\) −3.45059e13 −0.584851
\(320\) 6.76061e10 0.00112632
\(321\) −4.37092e11 −0.00715805
\(322\) 5.43035e13 0.874220
\(323\) −1.86938e13 −0.295858
\(324\) −5.28174e12 −0.0821825
\(325\) 1.03329e14 1.58075
\(326\) −4.37946e13 −0.658755
\(327\) 6.01897e13 0.890245
\(328\) 8.63102e13 1.25532
\(329\) −1.90299e14 −2.72182
\(330\) −3.60496e10 −0.000507076 0
\(331\) 3.77022e13 0.521571 0.260785 0.965397i \(-0.416019\pi\)
0.260785 + 0.965397i \(0.416019\pi\)
\(332\) 8.24554e13 1.12191
\(333\) −1.80617e13 −0.241721
\(334\) −1.84246e13 −0.242546
\(335\) −3.38738e10 −0.000438649 0
\(336\) −2.36157e13 −0.300839
\(337\) −7.70482e13 −0.965602 −0.482801 0.875730i \(-0.660381\pi\)
−0.482801 + 0.875730i \(0.660381\pi\)
\(338\) 6.20287e13 0.764805
\(339\) −3.25008e12 −0.0394272
\(340\) 2.28747e11 0.00273037
\(341\) 5.52565e13 0.648984
\(342\) 5.51546e12 0.0637439
\(343\) −2.08196e14 −2.36785
\(344\) −7.26177e13 −0.812776
\(345\) −2.31059e11 −0.00254518
\(346\) 8.14524e13 0.883050
\(347\) −1.50757e14 −1.60867 −0.804334 0.594177i \(-0.797478\pi\)
−0.804334 + 0.594177i \(0.797478\pi\)
\(348\) −6.46002e13 −0.678497
\(349\) 8.88573e13 0.918657 0.459329 0.888266i \(-0.348090\pi\)
0.459329 + 0.888266i \(0.348090\pi\)
\(350\) 9.11165e13 0.927305
\(351\) −3.03654e13 −0.304222
\(352\) −3.85872e13 −0.380592
\(353\) 1.96988e13 0.191284 0.0956420 0.995416i \(-0.469510\pi\)
0.0956420 + 0.995416i \(0.469510\pi\)
\(354\) 4.01159e12 0.0383529
\(355\) 7.90545e10 0.000744168 0
\(356\) −7.22603e13 −0.669769
\(357\) 9.07551e13 0.828315
\(358\) −6.32587e13 −0.568543
\(359\) −1.26180e14 −1.11679 −0.558393 0.829577i \(-0.688582\pi\)
−0.558393 + 0.829577i \(0.688582\pi\)
\(360\) −1.58737e11 −0.00138361
\(361\) −1.00128e14 −0.859541
\(362\) 4.12859e13 0.349064
\(363\) −5.99369e13 −0.499123
\(364\) −2.59059e14 −2.12491
\(365\) 9.35243e11 0.00755638
\(366\) −4.18653e13 −0.333202
\(367\) −2.20870e14 −1.73170 −0.865851 0.500301i \(-0.833223\pi\)
−0.865851 + 0.500301i \(0.833223\pi\)
\(368\) −3.49945e13 −0.270294
\(369\) −6.19491e13 −0.471400
\(370\) −2.30792e11 −0.00173026
\(371\) 2.20060e14 1.62549
\(372\) 1.03448e14 0.752899
\(373\) 9.05981e13 0.649711 0.324856 0.945764i \(-0.394684\pi\)
0.324856 + 0.945764i \(0.394684\pi\)
\(374\) 2.09820e13 0.148270
\(375\) −7.75403e11 −0.00539952
\(376\) −1.93727e14 −1.32940
\(377\) −3.71395e14 −2.51165
\(378\) −2.67766e13 −0.178464
\(379\) −1.24245e14 −0.816135 −0.408067 0.912952i \(-0.633797\pi\)
−0.408067 + 0.912952i \(0.633797\pi\)
\(380\) −2.00215e11 −0.00129625
\(381\) 1.80600e14 1.15247
\(382\) 8.21233e13 0.516557
\(383\) 1.28435e14 0.796326 0.398163 0.917315i \(-0.369648\pi\)
0.398163 + 0.917315i \(0.369648\pi\)
\(384\) −8.60606e13 −0.525996
\(385\) 5.19194e11 0.00312821
\(386\) −2.83869e13 −0.168611
\(387\) 5.21212e13 0.305214
\(388\) −9.37916e13 −0.541489
\(389\) −2.45451e14 −1.39714 −0.698572 0.715539i \(-0.746181\pi\)
−0.698572 + 0.715539i \(0.746181\pi\)
\(390\) −3.88010e11 −0.00217765
\(391\) 1.34484e14 0.744214
\(392\) −3.74621e14 −2.04418
\(393\) −1.84348e14 −0.991927
\(394\) 2.34506e13 0.124430
\(395\) 2.13798e11 0.00111871
\(396\) 1.75866e13 0.0907526
\(397\) 2.08288e14 1.06003 0.530013 0.847989i \(-0.322187\pi\)
0.530013 + 0.847989i \(0.322187\pi\)
\(398\) 1.42971e14 0.717613
\(399\) −7.94350e13 −0.393243
\(400\) −5.87177e13 −0.286707
\(401\) −1.25727e14 −0.605528 −0.302764 0.953066i \(-0.597909\pi\)
−0.302764 + 0.953066i \(0.597909\pi\)
\(402\) −5.81693e12 −0.0276344
\(403\) 5.94738e14 2.78707
\(404\) 2.24682e14 1.03865
\(405\) 1.13933e11 0.000519575 0
\(406\) −3.27500e14 −1.47339
\(407\) 6.01399e13 0.266928
\(408\) 9.23899e13 0.404570
\(409\) −1.28206e14 −0.553899 −0.276950 0.960884i \(-0.589323\pi\)
−0.276950 + 0.960884i \(0.589323\pi\)
\(410\) −7.91585e11 −0.00337432
\(411\) −1.64724e14 −0.692831
\(412\) 1.63452e14 0.678353
\(413\) −5.77758e13 −0.236603
\(414\) −3.96784e13 −0.160344
\(415\) −1.77866e12 −0.00709297
\(416\) −4.15323e14 −1.63446
\(417\) −1.99136e14 −0.773394
\(418\) −1.83649e13 −0.0703911
\(419\) −2.42222e14 −0.916296 −0.458148 0.888876i \(-0.651487\pi\)
−0.458148 + 0.888876i \(0.651487\pi\)
\(420\) 9.72008e11 0.00362910
\(421\) −4.87087e14 −1.79496 −0.897481 0.441053i \(-0.854605\pi\)
−0.897481 + 0.441053i \(0.854605\pi\)
\(422\) 5.83110e13 0.212096
\(423\) 1.39047e14 0.499219
\(424\) 2.24024e14 0.793931
\(425\) 2.25652e14 0.789405
\(426\) 1.35756e13 0.0468818
\(427\) 6.02954e14 2.05556
\(428\) 2.72470e12 0.00917017
\(429\) 1.01108e14 0.335946
\(430\) 6.66006e11 0.00218475
\(431\) 5.99881e13 0.194286 0.0971428 0.995270i \(-0.469030\pi\)
0.0971428 + 0.995270i \(0.469030\pi\)
\(432\) 1.72555e13 0.0551781
\(433\) 3.38430e14 1.06853 0.534264 0.845318i \(-0.320589\pi\)
0.534264 + 0.845318i \(0.320589\pi\)
\(434\) 5.24447e14 1.63496
\(435\) 1.39350e12 0.00428960
\(436\) −3.75204e14 −1.14049
\(437\) −1.17709e14 −0.353316
\(438\) 1.60604e14 0.476044
\(439\) −8.87244e13 −0.259710 −0.129855 0.991533i \(-0.541451\pi\)
−0.129855 + 0.991533i \(0.541451\pi\)
\(440\) 5.28547e11 0.00152790
\(441\) 2.68883e14 0.767630
\(442\) 2.25834e14 0.636747
\(443\) 4.91192e14 1.36782 0.683912 0.729564i \(-0.260277\pi\)
0.683912 + 0.729564i \(0.260277\pi\)
\(444\) 1.12591e14 0.309668
\(445\) 1.55874e12 0.00423442
\(446\) 2.80269e14 0.752028
\(447\) 1.89490e14 0.502221
\(448\) −1.67204e14 −0.437741
\(449\) 8.30943e13 0.214890 0.107445 0.994211i \(-0.465733\pi\)
0.107445 + 0.994211i \(0.465733\pi\)
\(450\) −6.65768e13 −0.170080
\(451\) 2.06272e14 0.520558
\(452\) 2.02600e13 0.0505101
\(453\) −4.87265e13 −0.120012
\(454\) 1.00283e14 0.244017
\(455\) 5.58821e12 0.0134341
\(456\) −8.08660e13 −0.192070
\(457\) −6.65893e14 −1.56266 −0.781332 0.624116i \(-0.785459\pi\)
−0.781332 + 0.624116i \(0.785459\pi\)
\(458\) 2.55084e14 0.591456
\(459\) −6.63128e13 −0.151924
\(460\) 1.44035e12 0.00326063
\(461\) 1.15391e14 0.258116 0.129058 0.991637i \(-0.458805\pi\)
0.129058 + 0.991637i \(0.458805\pi\)
\(462\) 8.91581e13 0.197074
\(463\) −6.74287e14 −1.47282 −0.736409 0.676536i \(-0.763480\pi\)
−0.736409 + 0.676536i \(0.763480\pi\)
\(464\) 2.11049e14 0.455549
\(465\) −2.23150e12 −0.00475999
\(466\) 2.67918e14 0.564780
\(467\) 2.62842e14 0.547586 0.273793 0.961789i \(-0.411722\pi\)
0.273793 + 0.961789i \(0.411722\pi\)
\(468\) 1.89289e14 0.389738
\(469\) 8.37769e13 0.170480
\(470\) 1.77675e12 0.00357345
\(471\) 3.93052e13 0.0781331
\(472\) −5.88166e13 −0.115563
\(473\) −1.73548e14 −0.337042
\(474\) 3.67142e13 0.0704779
\(475\) −1.97506e14 −0.374770
\(476\) −5.65739e14 −1.06115
\(477\) −1.60793e14 −0.298138
\(478\) −4.36014e14 −0.799185
\(479\) 1.35085e14 0.244772 0.122386 0.992483i \(-0.460945\pi\)
0.122386 + 0.992483i \(0.460945\pi\)
\(480\) 1.55832e12 0.00279146
\(481\) 6.47300e14 1.14633
\(482\) −2.93504e14 −0.513873
\(483\) 5.71458e14 0.989179
\(484\) 3.73628e14 0.639426
\(485\) 2.02319e12 0.00342340
\(486\) 1.95651e13 0.0327327
\(487\) 2.99730e14 0.495817 0.247908 0.968783i \(-0.420257\pi\)
0.247908 + 0.968783i \(0.420257\pi\)
\(488\) 6.13815e14 1.00399
\(489\) −4.60869e14 −0.745381
\(490\) 3.43579e12 0.00549476
\(491\) 9.64896e14 1.52592 0.762961 0.646445i \(-0.223745\pi\)
0.762961 + 0.646445i \(0.223745\pi\)
\(492\) 3.86172e14 0.603910
\(493\) −8.11062e14 −1.25428
\(494\) −1.97665e14 −0.302296
\(495\) −3.79364e11 −0.000573757 0
\(496\) −3.37966e14 −0.505503
\(497\) −1.95518e14 −0.289219
\(498\) −3.05438e14 −0.446850
\(499\) 8.18754e14 1.18468 0.592339 0.805689i \(-0.298204\pi\)
0.592339 + 0.805689i \(0.298204\pi\)
\(500\) 4.83362e12 0.00691732
\(501\) −1.93890e14 −0.274440
\(502\) −1.75551e14 −0.245772
\(503\) 7.25668e14 1.00488 0.502440 0.864612i \(-0.332436\pi\)
0.502440 + 0.864612i \(0.332436\pi\)
\(504\) 3.92590e14 0.537738
\(505\) −4.84666e12 −0.00656659
\(506\) 1.32117e14 0.177065
\(507\) 6.52753e14 0.865376
\(508\) −1.12581e15 −1.47643
\(509\) −1.69377e14 −0.219739 −0.109870 0.993946i \(-0.535043\pi\)
−0.109870 + 0.993946i \(0.535043\pi\)
\(510\) −8.47345e11 −0.00108749
\(511\) −2.31305e15 −2.93677
\(512\) 4.38630e14 0.550952
\(513\) 5.80415e13 0.0721262
\(514\) −1.98257e12 −0.00243742
\(515\) −3.52585e12 −0.00428869
\(516\) −3.24908e14 −0.391009
\(517\) −4.62987e14 −0.551278
\(518\) 5.70796e14 0.672462
\(519\) 8.57157e14 0.999171
\(520\) 5.68887e12 0.00656157
\(521\) −7.53695e14 −0.860178 −0.430089 0.902787i \(-0.641518\pi\)
−0.430089 + 0.902787i \(0.641518\pi\)
\(522\) 2.39297e14 0.270240
\(523\) −1.10013e15 −1.22938 −0.614689 0.788770i \(-0.710718\pi\)
−0.614689 + 0.788770i \(0.710718\pi\)
\(524\) 1.14917e15 1.27076
\(525\) 9.58855e14 1.04925
\(526\) 2.00989e14 0.217646
\(527\) 1.29880e15 1.39183
\(528\) −5.74556e13 −0.0609321
\(529\) −1.06005e14 −0.111255
\(530\) −2.05462e12 −0.00213409
\(531\) 4.22156e13 0.0433963
\(532\) 4.95174e14 0.503783
\(533\) 2.22015e15 2.23554
\(534\) 2.67673e14 0.266764
\(535\) −5.87749e10 −5.79757e−5 0
\(536\) 8.52860e13 0.0832667
\(537\) −6.65697e14 −0.643306
\(538\) −8.08341e14 −0.773200
\(539\) −8.95302e14 −0.847679
\(540\) −7.10226e11 −0.000665627 0
\(541\) −2.13492e14 −0.198060 −0.0990298 0.995084i \(-0.531574\pi\)
−0.0990298 + 0.995084i \(0.531574\pi\)
\(542\) 2.92869e14 0.268954
\(543\) 4.34469e14 0.394966
\(544\) −9.06993e14 −0.816225
\(545\) 8.09360e12 0.00721043
\(546\) 9.59629e14 0.846338
\(547\) 9.40079e14 0.820793 0.410397 0.911907i \(-0.365390\pi\)
0.410397 + 0.911907i \(0.365390\pi\)
\(548\) 1.02684e15 0.887585
\(549\) −4.40565e14 −0.377018
\(550\) 2.21681e14 0.187817
\(551\) 7.09897e14 0.595472
\(552\) 5.81752e14 0.483140
\(553\) −5.28766e14 −0.434786
\(554\) −2.74657e14 −0.223608
\(555\) −2.42872e12 −0.00195779
\(556\) 1.24135e15 0.990794
\(557\) 1.26663e15 1.00103 0.500513 0.865729i \(-0.333145\pi\)
0.500513 + 0.865729i \(0.333145\pi\)
\(558\) −3.83202e14 −0.299874
\(559\) −1.86794e15 −1.44743
\(560\) −3.17556e12 −0.00243661
\(561\) 2.20802e14 0.167767
\(562\) −1.14865e15 −0.864247
\(563\) 6.71361e14 0.500219 0.250109 0.968218i \(-0.419533\pi\)
0.250109 + 0.968218i \(0.419533\pi\)
\(564\) −8.66779e14 −0.639548
\(565\) −4.37033e11 −0.000319336 0
\(566\) 1.75412e13 0.0126931
\(567\) −2.81781e14 −0.201932
\(568\) −1.99040e14 −0.141262
\(569\) 7.24889e14 0.509512 0.254756 0.967005i \(-0.418005\pi\)
0.254756 + 0.967005i \(0.418005\pi\)
\(570\) 7.41654e11 0.000516285 0
\(571\) −2.62128e15 −1.80724 −0.903619 0.428338i \(-0.859099\pi\)
−0.903619 + 0.428338i \(0.859099\pi\)
\(572\) −6.30276e14 −0.430380
\(573\) 8.64217e14 0.584484
\(574\) 1.95776e15 1.31142
\(575\) 1.42086e15 0.942712
\(576\) 1.22172e14 0.0802878
\(577\) −5.30497e14 −0.345315 −0.172658 0.984982i \(-0.555235\pi\)
−0.172658 + 0.984982i \(0.555235\pi\)
\(578\) −2.98204e14 −0.192270
\(579\) −2.98726e14 −0.190784
\(580\) −8.68666e12 −0.00549540
\(581\) 4.39900e15 2.75667
\(582\) 3.47431e14 0.215671
\(583\) 5.35394e14 0.329228
\(584\) −2.35472e15 −1.43439
\(585\) −4.08318e12 −0.00246401
\(586\) 1.93911e14 0.115922
\(587\) 1.76214e15 1.04359 0.521795 0.853071i \(-0.325262\pi\)
0.521795 + 0.853071i \(0.325262\pi\)
\(588\) −1.67614e15 −0.983409
\(589\) −1.13680e15 −0.660770
\(590\) 5.39431e11 0.000310634 0
\(591\) 2.46780e14 0.140792
\(592\) −3.67835e14 −0.207914
\(593\) −2.25566e15 −1.26320 −0.631600 0.775294i \(-0.717601\pi\)
−0.631600 + 0.775294i \(0.717601\pi\)
\(594\) −6.51459e13 −0.0361461
\(595\) 1.22037e13 0.00670883
\(596\) −1.18122e15 −0.643395
\(597\) 1.50454e15 0.811979
\(598\) 1.42201e15 0.760406
\(599\) 3.85161e14 0.204078 0.102039 0.994780i \(-0.467463\pi\)
0.102039 + 0.994780i \(0.467463\pi\)
\(600\) 9.76128e14 0.512478
\(601\) 3.23146e14 0.168109 0.0840543 0.996461i \(-0.473213\pi\)
0.0840543 + 0.996461i \(0.473213\pi\)
\(602\) −1.64717e15 −0.849098
\(603\) −6.12139e13 −0.0312684
\(604\) 3.03746e14 0.153747
\(605\) −8.05960e12 −0.00404259
\(606\) −8.32287e14 −0.413689
\(607\) 2.70154e15 1.33068 0.665339 0.746541i \(-0.268287\pi\)
0.665339 + 0.746541i \(0.268287\pi\)
\(608\) 7.93862e14 0.387503
\(609\) −3.44642e15 −1.66714
\(610\) −5.62955e12 −0.00269873
\(611\) −4.98323e15 −2.36747
\(612\) 4.13374e14 0.194630
\(613\) 2.58621e15 1.20679 0.603394 0.797443i \(-0.293815\pi\)
0.603394 + 0.797443i \(0.293815\pi\)
\(614\) −6.95976e14 −0.321861
\(615\) −8.33017e12 −0.00381804
\(616\) −1.30721e15 −0.593814
\(617\) 4.09511e15 1.84373 0.921864 0.387514i \(-0.126666\pi\)
0.921864 + 0.387514i \(0.126666\pi\)
\(618\) −6.05473e14 −0.270183
\(619\) −1.43141e15 −0.633092 −0.316546 0.948577i \(-0.602523\pi\)
−0.316546 + 0.948577i \(0.602523\pi\)
\(620\) 1.39105e13 0.00609801
\(621\) −4.17552e14 −0.181429
\(622\) 1.15903e15 0.499170
\(623\) −3.85509e15 −1.64570
\(624\) −6.18408e14 −0.261674
\(625\) 2.38403e15 0.999934
\(626\) −1.03404e15 −0.429912
\(627\) −1.93261e14 −0.0796475
\(628\) −2.45017e14 −0.100096
\(629\) 1.41359e15 0.572459
\(630\) −3.60060e12 −0.00144544
\(631\) 2.98660e15 1.18854 0.594272 0.804264i \(-0.297440\pi\)
0.594272 + 0.804264i \(0.297440\pi\)
\(632\) −5.38291e14 −0.212360
\(633\) 6.13630e14 0.239986
\(634\) −1.73725e15 −0.673552
\(635\) 2.42850e13 0.00933432
\(636\) 1.00234e15 0.381943
\(637\) −9.63635e15 −3.64037
\(638\) −7.96790e14 −0.298421
\(639\) 1.42861e14 0.0530468
\(640\) −1.15724e13 −0.00426024
\(641\) −3.24322e15 −1.18374 −0.591871 0.806032i \(-0.701611\pi\)
−0.591871 + 0.806032i \(0.701611\pi\)
\(642\) −1.00931e13 −0.00365241
\(643\) −7.11517e14 −0.255285 −0.127642 0.991820i \(-0.540741\pi\)
−0.127642 + 0.991820i \(0.540741\pi\)
\(644\) −3.56229e15 −1.26724
\(645\) 7.00865e12 0.00247204
\(646\) −4.31666e14 −0.150962
\(647\) 2.83929e15 0.984546 0.492273 0.870441i \(-0.336166\pi\)
0.492273 + 0.870441i \(0.336166\pi\)
\(648\) −2.86857e14 −0.0986285
\(649\) −1.40565e14 −0.0479217
\(650\) 2.38600e15 0.806581
\(651\) 5.51896e15 1.84996
\(652\) 2.87292e15 0.954907
\(653\) 2.12909e15 0.701733 0.350866 0.936425i \(-0.385887\pi\)
0.350866 + 0.936425i \(0.385887\pi\)
\(654\) 1.38986e15 0.454250
\(655\) −2.47889e13 −0.00803398
\(656\) −1.26163e15 −0.405471
\(657\) 1.69010e15 0.538644
\(658\) −4.39427e15 −1.38881
\(659\) −3.01446e15 −0.944799 −0.472399 0.881385i \(-0.656612\pi\)
−0.472399 + 0.881385i \(0.656612\pi\)
\(660\) 2.36484e12 0.000735039 0
\(661\) −6.64300e14 −0.204765 −0.102383 0.994745i \(-0.532647\pi\)
−0.102383 + 0.994745i \(0.532647\pi\)
\(662\) 8.70597e14 0.266133
\(663\) 2.37654e15 0.720478
\(664\) 4.47824e15 1.34643
\(665\) −1.06815e13 −0.00318502
\(666\) −4.17069e14 −0.123339
\(667\) −5.10702e15 −1.49787
\(668\) 1.20865e15 0.351585
\(669\) 2.94939e15 0.850919
\(670\) −7.82192e11 −0.000223822 0
\(671\) 1.46695e15 0.416334
\(672\) −3.85406e15 −1.08489
\(673\) 3.38199e15 0.944257 0.472128 0.881530i \(-0.343486\pi\)
0.472128 + 0.881530i \(0.343486\pi\)
\(674\) −1.77915e15 −0.492701
\(675\) −7.00615e14 −0.192446
\(676\) −4.06906e15 −1.10863
\(677\) 3.81617e15 1.03131 0.515656 0.856796i \(-0.327548\pi\)
0.515656 + 0.856796i \(0.327548\pi\)
\(678\) −7.50489e13 −0.0201178
\(679\) −5.00378e15 −1.33050
\(680\) 1.24235e13 0.00327676
\(681\) 1.05532e15 0.276105
\(682\) 1.27595e15 0.331146
\(683\) −2.73376e14 −0.0703796 −0.0351898 0.999381i \(-0.511204\pi\)
−0.0351898 + 0.999381i \(0.511204\pi\)
\(684\) −3.61813e14 −0.0924007
\(685\) −2.21502e13 −0.00561150
\(686\) −4.80753e15 −1.20820
\(687\) 2.68435e15 0.669232
\(688\) 1.06148e15 0.262527
\(689\) 5.76257e15 1.41387
\(690\) −5.33548e12 −0.00129868
\(691\) 7.82046e14 0.188844 0.0944219 0.995532i \(-0.469900\pi\)
0.0944219 + 0.995532i \(0.469900\pi\)
\(692\) −5.34325e15 −1.28004
\(693\) 9.38246e14 0.222989
\(694\) −3.48120e15 −0.820827
\(695\) −2.67774e13 −0.00626401
\(696\) −3.50850e15 −0.814275
\(697\) 4.84842e15 1.11640
\(698\) 2.05184e15 0.468747
\(699\) 2.81941e15 0.639049
\(700\) −5.97721e15 −1.34419
\(701\) 4.73443e15 1.05638 0.528189 0.849127i \(-0.322871\pi\)
0.528189 + 0.849127i \(0.322871\pi\)
\(702\) −7.01180e14 −0.155230
\(703\) −1.23727e15 −0.271775
\(704\) −4.06798e14 −0.0886603
\(705\) 1.86974e13 0.00404336
\(706\) 4.54872e14 0.0976031
\(707\) 1.19868e16 2.55209
\(708\) −2.63159e14 −0.0555949
\(709\) −3.55437e15 −0.745089 −0.372544 0.928014i \(-0.621515\pi\)
−0.372544 + 0.928014i \(0.621515\pi\)
\(710\) 1.82548e12 0.000379713 0
\(711\) 3.86358e14 0.0797457
\(712\) −3.92453e15 −0.803800
\(713\) 8.17818e15 1.66213
\(714\) 2.09566e15 0.422650
\(715\) 1.35958e13 0.00272095
\(716\) 4.14975e15 0.824139
\(717\) −4.58835e15 −0.904277
\(718\) −2.91366e15 −0.569842
\(719\) 4.65529e15 0.903520 0.451760 0.892140i \(-0.350796\pi\)
0.451760 + 0.892140i \(0.350796\pi\)
\(720\) 2.32031e12 0.000446908 0
\(721\) 8.72017e15 1.66679
\(722\) −2.31210e15 −0.438583
\(723\) −3.08867e15 −0.581447
\(724\) −2.70834e15 −0.505990
\(725\) −8.56912e15 −1.58883
\(726\) −1.38403e15 −0.254679
\(727\) 1.70435e15 0.311257 0.155628 0.987816i \(-0.450260\pi\)
0.155628 + 0.987816i \(0.450260\pi\)
\(728\) −1.40698e16 −2.55014
\(729\) 2.05891e14 0.0370370
\(730\) 2.15961e13 0.00385566
\(731\) −4.07925e15 −0.722828
\(732\) 2.74635e15 0.482998
\(733\) 2.90878e15 0.507737 0.253869 0.967239i \(-0.418297\pi\)
0.253869 + 0.967239i \(0.418297\pi\)
\(734\) −5.10019e15 −0.883605
\(735\) 3.61563e13 0.00621732
\(736\) −5.71107e15 −0.974741
\(737\) 2.03824e14 0.0345291
\(738\) −1.43049e15 −0.240533
\(739\) −8.19566e15 −1.36785 −0.683926 0.729551i \(-0.739729\pi\)
−0.683926 + 0.729551i \(0.739729\pi\)
\(740\) 1.51399e13 0.00250812
\(741\) −2.08011e15 −0.342047
\(742\) 5.08149e15 0.829411
\(743\) 5.72916e15 0.928223 0.464111 0.885777i \(-0.346374\pi\)
0.464111 + 0.885777i \(0.346374\pi\)
\(744\) 5.61838e15 0.903566
\(745\) 2.54804e13 0.00406768
\(746\) 2.09204e15 0.331517
\(747\) −3.21425e15 −0.505611
\(748\) −1.37641e15 −0.214926
\(749\) 1.45363e14 0.0225322
\(750\) −1.79051e13 −0.00275512
\(751\) −1.03765e16 −1.58501 −0.792504 0.609866i \(-0.791223\pi\)
−0.792504 + 0.609866i \(0.791223\pi\)
\(752\) 2.83177e15 0.429398
\(753\) −1.84739e15 −0.278090
\(754\) −8.57603e15 −1.28157
\(755\) −6.55217e12 −0.000972024 0
\(756\) 1.75654e15 0.258694
\(757\) −4.55421e15 −0.665864 −0.332932 0.942951i \(-0.608038\pi\)
−0.332932 + 0.942951i \(0.608038\pi\)
\(758\) −2.86898e15 −0.416435
\(759\) 1.39032e15 0.200349
\(760\) −1.08739e13 −0.00155564
\(761\) −6.12924e15 −0.870544 −0.435272 0.900299i \(-0.643348\pi\)
−0.435272 + 0.900299i \(0.643348\pi\)
\(762\) 4.17031e15 0.588053
\(763\) −2.00172e16 −2.80232
\(764\) −5.38727e15 −0.748781
\(765\) −8.91695e12 −0.00123049
\(766\) 2.96575e15 0.406327
\(767\) −1.51294e15 −0.205800
\(768\) −3.01692e15 −0.407453
\(769\) −5.25841e14 −0.0705115 −0.0352557 0.999378i \(-0.511225\pi\)
−0.0352557 + 0.999378i \(0.511225\pi\)
\(770\) 1.19889e13 0.00159618
\(771\) −2.08634e13 −0.00275794
\(772\) 1.86217e15 0.244413
\(773\) −4.59777e14 −0.0599184 −0.0299592 0.999551i \(-0.509538\pi\)
−0.0299592 + 0.999551i \(0.509538\pi\)
\(774\) 1.20355e15 0.155736
\(775\) 1.37223e16 1.76306
\(776\) −5.09392e15 −0.649849
\(777\) 6.00672e15 0.760890
\(778\) −5.66780e15 −0.712896
\(779\) −4.24367e15 −0.530012
\(780\) 2.54533e13 0.00315663
\(781\) −4.75685e14 −0.0585785
\(782\) 3.10542e15 0.379737
\(783\) 2.51822e15 0.305777
\(784\) 5.47595e15 0.660270
\(785\) 5.28530e12 0.000632829 0
\(786\) −4.25685e15 −0.506133
\(787\) 1.58443e16 1.87074 0.935369 0.353674i \(-0.115068\pi\)
0.935369 + 0.353674i \(0.115068\pi\)
\(788\) −1.53835e15 −0.180369
\(789\) 2.11509e15 0.246267
\(790\) 4.93689e12 0.000570827 0
\(791\) 1.08087e15 0.124109
\(792\) 9.55148e14 0.108914
\(793\) 1.57891e16 1.78795
\(794\) 4.80966e15 0.540881
\(795\) −2.16216e13 −0.00241473
\(796\) −9.37884e15 −1.04022
\(797\) 1.10469e16 1.21680 0.608400 0.793631i \(-0.291812\pi\)
0.608400 + 0.793631i \(0.291812\pi\)
\(798\) −1.83426e15 −0.200653
\(799\) −1.08825e16 −1.18228
\(800\) −9.58266e15 −1.03393
\(801\) 2.81683e15 0.301844
\(802\) −2.90321e15 −0.308972
\(803\) −5.62752e15 −0.594814
\(804\) 3.81589e14 0.0400578
\(805\) 7.68429e13 0.00801173
\(806\) 1.37333e16 1.42211
\(807\) −8.50650e15 −0.874876
\(808\) 1.22027e16 1.24651
\(809\) −1.65576e16 −1.67989 −0.839947 0.542669i \(-0.817414\pi\)
−0.839947 + 0.542669i \(0.817414\pi\)
\(810\) 2.63088e12 0.000265114 0
\(811\) −4.97584e15 −0.498025 −0.249013 0.968500i \(-0.580106\pi\)
−0.249013 + 0.968500i \(0.580106\pi\)
\(812\) 2.14839e16 2.13578
\(813\) 3.08198e15 0.304321
\(814\) 1.38871e15 0.136201
\(815\) −6.19722e13 −0.00603712
\(816\) −1.35049e15 −0.130676
\(817\) 3.57044e15 0.343163
\(818\) −2.96046e15 −0.282628
\(819\) 1.00986e16 0.957631
\(820\) 5.19278e13 0.00489129
\(821\) −1.06268e16 −0.994295 −0.497147 0.867666i \(-0.665619\pi\)
−0.497147 + 0.867666i \(0.665619\pi\)
\(822\) −3.80371e15 −0.353519
\(823\) 4.84440e15 0.447240 0.223620 0.974676i \(-0.428213\pi\)
0.223620 + 0.974676i \(0.428213\pi\)
\(824\) 8.87725e15 0.814102
\(825\) 2.33284e15 0.212514
\(826\) −1.33412e15 −0.120727
\(827\) −1.28296e16 −1.15327 −0.576636 0.817001i \(-0.695635\pi\)
−0.576636 + 0.817001i \(0.695635\pi\)
\(828\) 2.60289e15 0.232428
\(829\) −4.09240e15 −0.363018 −0.181509 0.983389i \(-0.558098\pi\)
−0.181509 + 0.983389i \(0.558098\pi\)
\(830\) −4.10717e13 −0.00361921
\(831\) −2.89033e15 −0.253012
\(832\) −4.37846e15 −0.380753
\(833\) −2.10441e16 −1.81795
\(834\) −4.59832e15 −0.394626
\(835\) −2.60720e13 −0.00222279
\(836\) 1.20473e15 0.102036
\(837\) −4.03259e15 −0.339308
\(838\) −5.59323e15 −0.467542
\(839\) −2.34497e13 −0.00194736 −0.000973681 1.00000i \(-0.500310\pi\)
−0.000973681 1.00000i \(0.500310\pi\)
\(840\) 5.27908e13 0.00435534
\(841\) 1.85995e16 1.52449
\(842\) −1.12475e16 −0.915883
\(843\) −1.20877e16 −0.977895
\(844\) −3.82518e15 −0.307446
\(845\) 8.77745e13 0.00700900
\(846\) 3.21080e15 0.254728
\(847\) 1.99331e16 1.57114
\(848\) −3.27464e15 −0.256440
\(849\) 1.84593e14 0.0143623
\(850\) 5.21061e15 0.402796
\(851\) 8.90095e15 0.683634
\(852\) −8.90552e14 −0.0679581
\(853\) 1.55756e16 1.18094 0.590468 0.807061i \(-0.298943\pi\)
0.590468 + 0.807061i \(0.298943\pi\)
\(854\) 1.39230e16 1.04886
\(855\) 7.80473e12 0.000584176 0
\(856\) 1.47981e14 0.0110053
\(857\) −5.14979e15 −0.380535 −0.190268 0.981732i \(-0.560936\pi\)
−0.190268 + 0.981732i \(0.560936\pi\)
\(858\) 2.33472e15 0.171417
\(859\) 1.33478e16 0.973748 0.486874 0.873472i \(-0.338137\pi\)
0.486874 + 0.873472i \(0.338137\pi\)
\(860\) −4.36898e13 −0.00316693
\(861\) 2.06023e16 1.48388
\(862\) 1.38521e15 0.0991347
\(863\) −1.56635e16 −1.11386 −0.556929 0.830560i \(-0.688020\pi\)
−0.556929 + 0.830560i \(0.688020\pi\)
\(864\) 2.81608e15 0.198984
\(865\) 1.15260e14 0.00809265
\(866\) 7.81482e15 0.545219
\(867\) −3.13812e15 −0.217553
\(868\) −3.44035e16 −2.36998
\(869\) −1.28646e15 −0.0880617
\(870\) 3.21779e13 0.00218878
\(871\) 2.19381e15 0.148285
\(872\) −2.03777e16 −1.36872
\(873\) 3.65615e15 0.244032
\(874\) −2.71807e15 −0.180280
\(875\) 2.57874e14 0.0169966
\(876\) −1.05355e16 −0.690056
\(877\) 2.79689e15 0.182045 0.0910223 0.995849i \(-0.470987\pi\)
0.0910223 + 0.995849i \(0.470987\pi\)
\(878\) −2.04877e15 −0.132518
\(879\) 2.04061e15 0.131166
\(880\) −7.72595e12 −0.000493512 0
\(881\) 2.21053e16 1.40323 0.701615 0.712556i \(-0.252462\pi\)
0.701615 + 0.712556i \(0.252462\pi\)
\(882\) 6.20889e15 0.391685
\(883\) 1.88831e16 1.18383 0.591916 0.805999i \(-0.298372\pi\)
0.591916 + 0.805999i \(0.298372\pi\)
\(884\) −1.48146e16 −0.923004
\(885\) 5.67665e12 0.000351483 0
\(886\) 1.13423e16 0.697936
\(887\) −6.82286e15 −0.417240 −0.208620 0.977997i \(-0.566897\pi\)
−0.208620 + 0.977997i \(0.566897\pi\)
\(888\) 6.11493e15 0.371638
\(889\) −6.00618e16 −3.62776
\(890\) 3.59935e13 0.00216062
\(891\) −6.85556e14 −0.0408993
\(892\) −1.83856e16 −1.09011
\(893\) 9.52511e15 0.561289
\(894\) 4.37559e15 0.256260
\(895\) −8.95150e13 −0.00521038
\(896\) 2.86210e16 1.65573
\(897\) 1.49644e16 0.860400
\(898\) 1.91876e15 0.109648
\(899\) −4.93220e16 −2.80132
\(900\) 4.36742e15 0.246542
\(901\) 1.25844e16 0.706069
\(902\) 4.76311e15 0.265616
\(903\) −1.73338e16 −0.960754
\(904\) 1.10034e15 0.0606180
\(905\) 5.84222e13 0.00319897
\(906\) −1.12516e15 −0.0612365
\(907\) 3.32482e16 1.79857 0.899285 0.437362i \(-0.144087\pi\)
0.899285 + 0.437362i \(0.144087\pi\)
\(908\) −6.57852e15 −0.353717
\(909\) −8.75849e15 −0.468088
\(910\) 1.29039e14 0.00685480
\(911\) 3.33817e16 1.76261 0.881307 0.472544i \(-0.156664\pi\)
0.881307 + 0.472544i \(0.156664\pi\)
\(912\) 1.18205e15 0.0620387
\(913\) 1.07025e16 0.558337
\(914\) −1.53764e16 −0.797353
\(915\) −5.92420e13 −0.00305361
\(916\) −1.67334e16 −0.857353
\(917\) 6.13082e16 3.12239
\(918\) −1.53125e15 −0.0775198
\(919\) −3.87899e15 −0.195201 −0.0976007 0.995226i \(-0.531117\pi\)
−0.0976007 + 0.995226i \(0.531117\pi\)
\(920\) 7.82271e13 0.00391313
\(921\) −7.32403e15 −0.364185
\(922\) 2.66453e15 0.131705
\(923\) −5.11991e15 −0.251566
\(924\) −5.84874e15 −0.285671
\(925\) 1.49350e16 0.725147
\(926\) −1.55702e16 −0.751509
\(927\) −6.37164e15 −0.305712
\(928\) 3.44430e16 1.64281
\(929\) 2.71315e16 1.28643 0.643217 0.765684i \(-0.277599\pi\)
0.643217 + 0.765684i \(0.277599\pi\)
\(930\) −5.15284e13 −0.00242879
\(931\) 1.84192e16 0.863074
\(932\) −1.75754e16 −0.818684
\(933\) 1.21970e16 0.564811
\(934\) 6.06940e15 0.279407
\(935\) 2.96908e13 0.00135881
\(936\) 1.02805e16 0.467731
\(937\) −1.07760e15 −0.0487404 −0.0243702 0.999703i \(-0.507758\pi\)
−0.0243702 + 0.999703i \(0.507758\pi\)
\(938\) 1.93452e15 0.0869878
\(939\) −1.08816e16 −0.486445
\(940\) −1.16554e14 −0.00517994
\(941\) 3.70173e16 1.63554 0.817771 0.575544i \(-0.195210\pi\)
0.817771 + 0.575544i \(0.195210\pi\)
\(942\) 9.07611e14 0.0398676
\(943\) 3.05291e16 1.33321
\(944\) 8.59742e14 0.0373269
\(945\) −3.78905e13 −0.00163552
\(946\) −4.00747e15 −0.171977
\(947\) −1.04889e16 −0.447513 −0.223756 0.974645i \(-0.571832\pi\)
−0.223756 + 0.974645i \(0.571832\pi\)
\(948\) −2.40844e15 −0.102162
\(949\) −6.05703e16 −2.55444
\(950\) −4.56068e15 −0.191227
\(951\) −1.82818e16 −0.762123
\(952\) −3.07259e16 −1.27351
\(953\) 3.94046e15 0.162381 0.0811906 0.996699i \(-0.474128\pi\)
0.0811906 + 0.996699i \(0.474128\pi\)
\(954\) −3.71294e15 −0.152125
\(955\) 1.16210e14 0.00473395
\(956\) 2.86024e16 1.15847
\(957\) −8.38494e15 −0.337664
\(958\) 3.11930e15 0.124896
\(959\) 5.47820e16 2.18090
\(960\) 1.64283e13 0.000650280 0
\(961\) 5.35739e16 2.10850
\(962\) 1.49471e16 0.584915
\(963\) −1.06213e14 −0.00413270
\(964\) 1.92538e16 0.744891
\(965\) −4.01692e13 −0.00154523
\(966\) 1.31958e16 0.504731
\(967\) −1.48756e16 −0.565756 −0.282878 0.959156i \(-0.591289\pi\)
−0.282878 + 0.959156i \(0.591289\pi\)
\(968\) 2.02921e16 0.767385
\(969\) −4.54260e15 −0.170814
\(970\) 4.67184e13 0.00174680
\(971\) 1.88583e16 0.701126 0.350563 0.936539i \(-0.385990\pi\)
0.350563 + 0.936539i \(0.385990\pi\)
\(972\) −1.28346e15 −0.0474481
\(973\) 6.62261e16 2.43449
\(974\) 6.92119e15 0.252992
\(975\) 2.51089e16 0.912646
\(976\) −8.97235e15 −0.324289
\(977\) −1.93781e16 −0.696450 −0.348225 0.937411i \(-0.613216\pi\)
−0.348225 + 0.937411i \(0.613216\pi\)
\(978\) −1.06421e16 −0.380333
\(979\) −9.37921e15 −0.333320
\(980\) −2.25387e14 −0.00796500
\(981\) 1.46261e16 0.513983
\(982\) 2.22808e16 0.778605
\(983\) 4.98162e16 1.73112 0.865558 0.500809i \(-0.166964\pi\)
0.865558 + 0.500809i \(0.166964\pi\)
\(984\) 2.09734e16 0.724762
\(985\) 3.31840e13 0.00114033
\(986\) −1.87285e16 −0.640001
\(987\) −4.62427e16 −1.57144
\(988\) 1.29668e16 0.438197
\(989\) −2.56858e16 −0.863206
\(990\) −8.76004e12 −0.000292761 0
\(991\) −9.60040e15 −0.319069 −0.159534 0.987192i \(-0.550999\pi\)
−0.159534 + 0.987192i \(0.550999\pi\)
\(992\) −5.51557e16 −1.82296
\(993\) 9.16164e15 0.301129
\(994\) −4.51479e15 −0.147575
\(995\) 2.02313e14 0.00657652
\(996\) 2.00367e16 0.647737
\(997\) 2.54447e16 0.818039 0.409020 0.912526i \(-0.365871\pi\)
0.409020 + 0.912526i \(0.365871\pi\)
\(998\) 1.89062e16 0.604485
\(999\) −4.38898e15 −0.139558
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 177.12.a.d.1.16 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.16 28 1.1 even 1 trivial