Properties

Label 3.14.a.b.1.1
Level $3$
Weight $14$
Character 3.1
Self dual yes
Analytic conductor $3.217$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,14,Mod(1,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 3.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(3.21692786856\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{1969}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 492 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(22.6867\) of defining polynomial
Character \(\chi\) \(=\) 3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-160.120 q^{2} +729.000 q^{3} +17446.5 q^{4} +3318.61 q^{5} -116728. q^{6} +449560. q^{7} -1.48183e6 q^{8} +531441. q^{9} +O(q^{10})\) \(q-160.120 q^{2} +729.000 q^{3} +17446.5 q^{4} +3318.61 q^{5} -116728. q^{6} +449560. q^{7} -1.48183e6 q^{8} +531441. q^{9} -531376. q^{10} +5.20947e6 q^{11} +1.27185e7 q^{12} -3.19535e6 q^{13} -7.19836e7 q^{14} +2.41927e6 q^{15} +9.43496e7 q^{16} +3.22068e7 q^{17} -8.50945e7 q^{18} +2.60127e7 q^{19} +5.78981e7 q^{20} +3.27729e8 q^{21} -8.34142e8 q^{22} +9.21991e8 q^{23} -1.08026e9 q^{24} -1.20969e9 q^{25} +5.11640e8 q^{26} +3.87420e8 q^{27} +7.84324e9 q^{28} -3.17741e9 q^{29} -3.87373e8 q^{30} -7.65586e9 q^{31} -2.96811e9 q^{32} +3.79770e9 q^{33} -5.15697e9 q^{34} +1.49191e9 q^{35} +9.27178e9 q^{36} +1.60133e10 q^{37} -4.16515e9 q^{38} -2.32941e9 q^{39} -4.91762e9 q^{40} -5.42402e9 q^{41} -5.24760e10 q^{42} +3.58248e10 q^{43} +9.08870e10 q^{44} +1.76364e9 q^{45} -1.47629e11 q^{46} -1.26460e11 q^{47} +6.87809e10 q^{48} +1.05215e11 q^{49} +1.93696e11 q^{50} +2.34788e10 q^{51} -5.57477e10 q^{52} +6.08596e10 q^{53} -6.20339e10 q^{54} +1.72882e10 q^{55} -6.66172e11 q^{56} +1.89632e10 q^{57} +5.08767e11 q^{58} -4.10975e11 q^{59} +4.22077e10 q^{60} -1.17141e11 q^{61} +1.22586e12 q^{62} +2.38914e11 q^{63} -2.97657e11 q^{64} -1.06041e10 q^{65} -6.08089e11 q^{66} -1.16014e12 q^{67} +5.61896e11 q^{68} +6.72131e11 q^{69} -2.38885e11 q^{70} +2.58837e11 q^{71} -7.87506e11 q^{72} +1.87421e12 q^{73} -2.56405e12 q^{74} -8.81864e11 q^{75} +4.53830e11 q^{76} +2.34197e12 q^{77} +3.72986e11 q^{78} -2.22847e11 q^{79} +3.13109e11 q^{80} +2.82430e11 q^{81} +8.68495e11 q^{82} -2.08940e12 q^{83} +5.71772e12 q^{84} +1.06882e11 q^{85} -5.73628e12 q^{86} -2.31633e12 q^{87} -7.71956e12 q^{88} -1.34175e12 q^{89} -2.82395e11 q^{90} -1.43650e12 q^{91} +1.60855e13 q^{92} -5.58112e12 q^{93} +2.02488e13 q^{94} +8.63258e10 q^{95} -2.16376e12 q^{96} -3.12485e9 q^{97} -1.68470e13 q^{98} +2.76853e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 54 q^{2} + 1458 q^{3} + 20516 q^{4} + 40716 q^{5} - 39366 q^{6} - 21008 q^{7} - 2025432 q^{8} + 1062882 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 54 q^{2} + 1458 q^{3} + 20516 q^{4} + 40716 q^{5} - 39366 q^{6} - 21008 q^{7} - 2025432 q^{8} + 1062882 q^{9} + 3437244 q^{10} + 672408 q^{11} + 14956164 q^{12} + 17532604 q^{13} - 121920336 q^{14} + 29681964 q^{15} + 11517200 q^{16} + 83838564 q^{17} - 28697814 q^{18} + 256293544 q^{19} + 172689624 q^{20} - 15314832 q^{21} - 1315615752 q^{22} + 859581936 q^{23} - 1476539928 q^{24} - 1031828194 q^{25} + 2711296044 q^{26} + 774840978 q^{27} + 6398827744 q^{28} - 4728475332 q^{29} + 2505750876 q^{30} - 5982551648 q^{31} - 7305134688 q^{32} + 490185432 q^{33} + 322207092 q^{34} - 16106087520 q^{35} + 10903043556 q^{36} + 27411194092 q^{37} + 20272310856 q^{38} + 12781268316 q^{39} - 25246850832 q^{40} + 15258974292 q^{41} - 88879924944 q^{42} - 11314499240 q^{43} + 76960441008 q^{44} + 21638151756 q^{45} - 154252246608 q^{46} - 69035142240 q^{47} + 8396038800 q^{48} + 229759626930 q^{49} + 212570589654 q^{50} + 61118313156 q^{51} + 7876928824 q^{52} - 226336894164 q^{53} - 20920706406 q^{54} - 152386092144 q^{55} - 410370995520 q^{56} + 186837993576 q^{57} + 344167850412 q^{58} - 927820824264 q^{59} + 125890735896 q^{60} + 179395461340 q^{61} + 1403430184224 q^{62} - 11164512528 q^{63} - 79339420096 q^{64} + 764567325288 q^{65} - 959083883208 q^{66} - 698315061176 q^{67} + 720380180232 q^{68} + 626635231344 q^{69} - 2106389414880 q^{70} - 784458549936 q^{71} - 1076397607512 q^{72} + 1857400245076 q^{73} - 1354499801316 q^{74} - 752202753426 q^{75} + 1160678400976 q^{76} + 4476961329984 q^{77} + 1976534816076 q^{78} - 714025470080 q^{79} - 2784606024096 q^{80} + 564859072962 q^{81} + 3063378763044 q^{82} - 4574293917912 q^{83} + 4664745425376 q^{84} + 2037774070872 q^{85} - 10738721134152 q^{86} - 3447058517028 q^{87} - 5253209973792 q^{88} + 3270178701684 q^{89} + 1826692388604 q^{90} - 11190403944928 q^{91} + 15893942353632 q^{92} - 4361280151392 q^{93} + 26342795766816 q^{94} + 8698230246384 q^{95} - 5325443187552 q^{96} - 9874926156476 q^{97} - 3630291434694 q^{98} + 357345179928 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −160.120 −1.76910 −0.884548 0.466450i \(-0.845533\pi\)
−0.884548 + 0.466450i \(0.845533\pi\)
\(3\) 729.000 0.577350
\(4\) 17446.5 2.12970
\(5\) 3318.61 0.0949841 0.0474921 0.998872i \(-0.484877\pi\)
0.0474921 + 0.998872i \(0.484877\pi\)
\(6\) −116728. −1.02139
\(7\) 449560. 1.44428 0.722138 0.691749i \(-0.243160\pi\)
0.722138 + 0.691749i \(0.243160\pi\)
\(8\) −1.48183e6 −1.99855
\(9\) 531441. 0.333333
\(10\) −531376. −0.168036
\(11\) 5.20947e6 0.886627 0.443314 0.896367i \(-0.353803\pi\)
0.443314 + 0.896367i \(0.353803\pi\)
\(12\) 1.27185e7 1.22958
\(13\) −3.19535e6 −0.183606 −0.0918030 0.995777i \(-0.529263\pi\)
−0.0918030 + 0.995777i \(0.529263\pi\)
\(14\) −7.19836e7 −2.55506
\(15\) 2.41927e6 0.0548391
\(16\) 9.43496e7 1.40592
\(17\) 3.22068e7 0.323616 0.161808 0.986822i \(-0.448267\pi\)
0.161808 + 0.986822i \(0.448267\pi\)
\(18\) −8.50945e7 −0.589699
\(19\) 2.60127e7 0.126849 0.0634244 0.997987i \(-0.479798\pi\)
0.0634244 + 0.997987i \(0.479798\pi\)
\(20\) 5.78981e7 0.202288
\(21\) 3.27729e8 0.833853
\(22\) −8.34142e8 −1.56853
\(23\) 9.21991e8 1.29866 0.649330 0.760507i \(-0.275049\pi\)
0.649330 + 0.760507i \(0.275049\pi\)
\(24\) −1.08026e9 −1.15386
\(25\) −1.20969e9 −0.990978
\(26\) 5.11640e8 0.324816
\(27\) 3.87420e8 0.192450
\(28\) 7.84324e9 3.07587
\(29\) −3.17741e9 −0.991942 −0.495971 0.868339i \(-0.665188\pi\)
−0.495971 + 0.868339i \(0.665188\pi\)
\(30\) −3.87373e8 −0.0970156
\(31\) −7.65586e9 −1.54933 −0.774663 0.632374i \(-0.782081\pi\)
−0.774663 + 0.632374i \(0.782081\pi\)
\(32\) −2.96811e9 −0.488659
\(33\) 3.79770e9 0.511894
\(34\) −5.15697e9 −0.572508
\(35\) 1.49191e9 0.137183
\(36\) 9.27178e9 0.709900
\(37\) 1.60133e10 1.02605 0.513026 0.858373i \(-0.328525\pi\)
0.513026 + 0.858373i \(0.328525\pi\)
\(38\) −4.16515e9 −0.224408
\(39\) −2.32941e9 −0.106005
\(40\) −4.91762e9 −0.189830
\(41\) −5.42402e9 −0.178331 −0.0891653 0.996017i \(-0.528420\pi\)
−0.0891653 + 0.996017i \(0.528420\pi\)
\(42\) −5.24760e10 −1.47517
\(43\) 3.58248e10 0.864250 0.432125 0.901814i \(-0.357764\pi\)
0.432125 + 0.901814i \(0.357764\pi\)
\(44\) 9.08870e10 1.88825
\(45\) 1.76364e9 0.0316614
\(46\) −1.47629e11 −2.29745
\(47\) −1.26460e11 −1.71127 −0.855633 0.517582i \(-0.826832\pi\)
−0.855633 + 0.517582i \(0.826832\pi\)
\(48\) 6.87809e10 0.811707
\(49\) 1.05215e11 1.08593
\(50\) 1.93696e11 1.75313
\(51\) 2.34788e10 0.186840
\(52\) −5.57477e10 −0.391025
\(53\) 6.08596e10 0.377169 0.188585 0.982057i \(-0.439610\pi\)
0.188585 + 0.982057i \(0.439610\pi\)
\(54\) −6.20339e10 −0.340463
\(55\) 1.72882e10 0.0842155
\(56\) −6.66172e11 −2.88645
\(57\) 1.89632e10 0.0732362
\(58\) 5.08767e11 1.75484
\(59\) −4.10975e11 −1.26846 −0.634230 0.773144i \(-0.718683\pi\)
−0.634230 + 0.773144i \(0.718683\pi\)
\(60\) 4.22077e10 0.116791
\(61\) −1.17141e11 −0.291116 −0.145558 0.989350i \(-0.546498\pi\)
−0.145558 + 0.989350i \(0.546498\pi\)
\(62\) 1.22586e12 2.74091
\(63\) 2.38914e11 0.481425
\(64\) −2.97657e11 −0.541434
\(65\) −1.06041e10 −0.0174396
\(66\) −6.08089e11 −0.905590
\(67\) −1.16014e12 −1.56684 −0.783419 0.621494i \(-0.786526\pi\)
−0.783419 + 0.621494i \(0.786526\pi\)
\(68\) 5.61896e11 0.689205
\(69\) 6.72131e11 0.749782
\(70\) −2.38885e11 −0.242690
\(71\) 2.58837e11 0.239799 0.119899 0.992786i \(-0.461743\pi\)
0.119899 + 0.992786i \(0.461743\pi\)
\(72\) −7.87506e11 −0.666182
\(73\) 1.87421e12 1.44950 0.724752 0.689010i \(-0.241954\pi\)
0.724752 + 0.689010i \(0.241954\pi\)
\(74\) −2.56405e12 −1.81518
\(75\) −8.81864e11 −0.572141
\(76\) 4.53830e11 0.270150
\(77\) 2.34197e12 1.28053
\(78\) 3.72986e11 0.187533
\(79\) −2.22847e11 −0.103141 −0.0515704 0.998669i \(-0.516423\pi\)
−0.0515704 + 0.998669i \(0.516423\pi\)
\(80\) 3.13109e11 0.133540
\(81\) 2.82430e11 0.111111
\(82\) 8.68495e11 0.315484
\(83\) −2.08940e12 −0.701477 −0.350739 0.936473i \(-0.614069\pi\)
−0.350739 + 0.936473i \(0.614069\pi\)
\(84\) 5.71772e12 1.77586
\(85\) 1.06882e11 0.0307384
\(86\) −5.73628e12 −1.52894
\(87\) −2.31633e12 −0.572698
\(88\) −7.71956e12 −1.77196
\(89\) −1.34175e12 −0.286177 −0.143089 0.989710i \(-0.545703\pi\)
−0.143089 + 0.989710i \(0.545703\pi\)
\(90\) −2.82395e11 −0.0560120
\(91\) −1.43650e12 −0.265178
\(92\) 1.60855e13 2.76576
\(93\) −5.58112e12 −0.894504
\(94\) 2.02488e13 3.02739
\(95\) 8.63258e10 0.0120486
\(96\) −2.16376e12 −0.282127
\(97\) −3.12485e9 −0.000380902 0 −0.000190451 1.00000i \(-0.500061\pi\)
−0.000190451 1.00000i \(0.500061\pi\)
\(98\) −1.68470e13 −1.92112
\(99\) 2.76853e12 0.295542
\(100\) −2.11048e13 −2.11048
\(101\) 1.35294e13 1.26820 0.634102 0.773249i \(-0.281370\pi\)
0.634102 + 0.773249i \(0.281370\pi\)
\(102\) −3.75943e12 −0.330537
\(103\) 3.69605e12 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(104\) 4.73497e12 0.366945
\(105\) 1.08760e12 0.0792028
\(106\) −9.74486e12 −0.667248
\(107\) 7.56519e12 0.487332 0.243666 0.969859i \(-0.421650\pi\)
0.243666 + 0.969859i \(0.421650\pi\)
\(108\) 6.75913e12 0.409861
\(109\) −2.05699e13 −1.17479 −0.587394 0.809301i \(-0.699846\pi\)
−0.587394 + 0.809301i \(0.699846\pi\)
\(110\) −2.76819e12 −0.148985
\(111\) 1.16737e13 0.592391
\(112\) 4.24158e13 2.03053
\(113\) −1.50599e13 −0.680475 −0.340238 0.940340i \(-0.610507\pi\)
−0.340238 + 0.940340i \(0.610507\pi\)
\(114\) −3.03640e12 −0.129562
\(115\) 3.05973e12 0.123352
\(116\) −5.54346e13 −2.11254
\(117\) −1.69814e12 −0.0612020
\(118\) 6.58054e13 2.24403
\(119\) 1.44789e13 0.467391
\(120\) −3.58494e12 −0.109598
\(121\) −7.38413e12 −0.213892
\(122\) 1.87567e13 0.515012
\(123\) −3.95411e12 −0.102959
\(124\) −1.33568e14 −3.29960
\(125\) −8.06552e12 −0.189111
\(126\) −3.82550e13 −0.851687
\(127\) 3.25187e13 0.687717 0.343858 0.939022i \(-0.388266\pi\)
0.343858 + 0.939022i \(0.388266\pi\)
\(128\) 7.19757e13 1.44651
\(129\) 2.61163e13 0.498975
\(130\) 1.69793e12 0.0308524
\(131\) −4.24335e13 −0.733577 −0.366788 0.930304i \(-0.619543\pi\)
−0.366788 + 0.930304i \(0.619543\pi\)
\(132\) 6.62566e13 1.09018
\(133\) 1.16942e13 0.183205
\(134\) 1.85762e14 2.77188
\(135\) 1.28570e12 0.0182797
\(136\) −4.77251e13 −0.646761
\(137\) −1.38138e14 −1.78496 −0.892481 0.451085i \(-0.851037\pi\)
−0.892481 + 0.451085i \(0.851037\pi\)
\(138\) −1.07622e14 −1.32644
\(139\) 6.55318e13 0.770648 0.385324 0.922781i \(-0.374090\pi\)
0.385324 + 0.922781i \(0.374090\pi\)
\(140\) 2.60286e13 0.292159
\(141\) −9.21895e13 −0.988000
\(142\) −4.14450e13 −0.424227
\(143\) −1.66461e13 −0.162790
\(144\) 5.01412e13 0.468639
\(145\) −1.05446e13 −0.0942187
\(146\) −3.00099e14 −2.56431
\(147\) 7.67016e13 0.626963
\(148\) 2.79376e14 2.18518
\(149\) 1.62826e14 1.21902 0.609512 0.792777i \(-0.291365\pi\)
0.609512 + 0.792777i \(0.291365\pi\)
\(150\) 1.41204e14 1.01217
\(151\) 7.18136e13 0.493011 0.246505 0.969141i \(-0.420718\pi\)
0.246505 + 0.969141i \(0.420718\pi\)
\(152\) −3.85464e13 −0.253513
\(153\) 1.71160e13 0.107872
\(154\) −3.74996e14 −2.26539
\(155\) −2.54068e13 −0.147161
\(156\) −4.06400e13 −0.225759
\(157\) −4.46499e13 −0.237943 −0.118971 0.992898i \(-0.537960\pi\)
−0.118971 + 0.992898i \(0.537960\pi\)
\(158\) 3.56823e13 0.182466
\(159\) 4.43667e13 0.217759
\(160\) −9.85001e12 −0.0464148
\(161\) 4.14490e14 1.87562
\(162\) −4.52227e13 −0.196566
\(163\) −7.29720e13 −0.304745 −0.152373 0.988323i \(-0.548691\pi\)
−0.152373 + 0.988323i \(0.548691\pi\)
\(164\) −9.46301e13 −0.379790
\(165\) 1.26031e13 0.0486218
\(166\) 3.34555e14 1.24098
\(167\) −5.24603e14 −1.87143 −0.935715 0.352757i \(-0.885244\pi\)
−0.935715 + 0.352757i \(0.885244\pi\)
\(168\) −4.85639e14 −1.66649
\(169\) −2.92665e14 −0.966289
\(170\) −1.71139e13 −0.0543791
\(171\) 1.38242e13 0.0422829
\(172\) 6.25018e14 1.84059
\(173\) 3.74739e14 1.06275 0.531373 0.847138i \(-0.321676\pi\)
0.531373 + 0.847138i \(0.321676\pi\)
\(174\) 3.70891e14 1.01316
\(175\) −5.43828e14 −1.43125
\(176\) 4.91511e14 1.24653
\(177\) −2.99601e14 −0.732346
\(178\) 2.14841e14 0.506275
\(179\) 1.41559e14 0.321657 0.160828 0.986982i \(-0.448583\pi\)
0.160828 + 0.986982i \(0.448583\pi\)
\(180\) 3.07694e13 0.0674292
\(181\) 2.66316e14 0.562973 0.281486 0.959565i \(-0.409173\pi\)
0.281486 + 0.959565i \(0.409173\pi\)
\(182\) 2.30013e14 0.469124
\(183\) −8.53960e13 −0.168076
\(184\) −1.36624e15 −2.59543
\(185\) 5.31418e13 0.0974586
\(186\) 8.93651e14 1.58246
\(187\) 1.67781e14 0.286927
\(188\) −2.20629e15 −3.64448
\(189\) 1.74169e14 0.277951
\(190\) −1.38225e13 −0.0213152
\(191\) −1.59059e14 −0.237051 −0.118526 0.992951i \(-0.537817\pi\)
−0.118526 + 0.992951i \(0.537817\pi\)
\(192\) −2.16992e14 −0.312597
\(193\) 5.78312e14 0.805452 0.402726 0.915320i \(-0.368063\pi\)
0.402726 + 0.915320i \(0.368063\pi\)
\(194\) 5.00352e11 0.000673852 0
\(195\) −7.73040e12 −0.0100688
\(196\) 1.83563e15 2.31271
\(197\) 7.45344e14 0.908503 0.454252 0.890873i \(-0.349907\pi\)
0.454252 + 0.890873i \(0.349907\pi\)
\(198\) −4.43297e14 −0.522843
\(199\) 9.14435e14 1.04378 0.521889 0.853014i \(-0.325228\pi\)
0.521889 + 0.853014i \(0.325228\pi\)
\(200\) 1.79256e15 1.98051
\(201\) −8.45741e14 −0.904614
\(202\) −2.16633e15 −2.24358
\(203\) −1.42843e15 −1.43264
\(204\) 4.09622e14 0.397912
\(205\) −1.80002e13 −0.0169386
\(206\) −5.91812e14 −0.539569
\(207\) 4.89984e14 0.432887
\(208\) −3.01480e14 −0.258135
\(209\) 1.35512e14 0.112468
\(210\) −1.74147e14 −0.140117
\(211\) 4.28835e14 0.334545 0.167272 0.985911i \(-0.446504\pi\)
0.167272 + 0.985911i \(0.446504\pi\)
\(212\) 1.06179e15 0.803257
\(213\) 1.88692e14 0.138448
\(214\) −1.21134e15 −0.862137
\(215\) 1.18889e14 0.0820900
\(216\) −5.74092e14 −0.384620
\(217\) −3.44177e15 −2.23765
\(218\) 3.29365e15 2.07831
\(219\) 1.36630e15 0.836871
\(220\) 3.01618e14 0.179354
\(221\) −1.02912e14 −0.0594178
\(222\) −1.86919e15 −1.04800
\(223\) 2.03442e15 1.10779 0.553897 0.832585i \(-0.313140\pi\)
0.553897 + 0.832585i \(0.313140\pi\)
\(224\) −1.33434e15 −0.705758
\(225\) −6.42879e14 −0.330326
\(226\) 2.41139e15 1.20383
\(227\) −2.60190e15 −1.26218 −0.631091 0.775708i \(-0.717393\pi\)
−0.631091 + 0.775708i \(0.717393\pi\)
\(228\) 3.30842e14 0.155971
\(229\) 7.15955e14 0.328061 0.164031 0.986455i \(-0.447550\pi\)
0.164031 + 0.986455i \(0.447550\pi\)
\(230\) −4.89924e14 −0.218222
\(231\) 1.70729e15 0.739317
\(232\) 4.70838e15 1.98244
\(233\) 2.42556e15 0.993112 0.496556 0.868005i \(-0.334598\pi\)
0.496556 + 0.868005i \(0.334598\pi\)
\(234\) 2.71907e14 0.108272
\(235\) −4.19672e14 −0.162543
\(236\) −7.17007e15 −2.70144
\(237\) −1.62455e14 −0.0595483
\(238\) −2.31836e15 −0.826859
\(239\) −2.17202e15 −0.753836 −0.376918 0.926247i \(-0.623016\pi\)
−0.376918 + 0.926247i \(0.623016\pi\)
\(240\) 2.28257e14 0.0770993
\(241\) −4.62659e15 −1.52108 −0.760538 0.649294i \(-0.775065\pi\)
−0.760538 + 0.649294i \(0.775065\pi\)
\(242\) 1.18235e15 0.378396
\(243\) 2.05891e14 0.0641500
\(244\) −2.04371e15 −0.619990
\(245\) 3.49167e14 0.103146
\(246\) 6.33133e14 0.182145
\(247\) −8.31196e13 −0.0232902
\(248\) 1.13447e16 3.09640
\(249\) −1.52317e15 −0.404998
\(250\) 1.29145e15 0.334556
\(251\) 5.16492e15 1.30372 0.651860 0.758339i \(-0.273989\pi\)
0.651860 + 0.758339i \(0.273989\pi\)
\(252\) 4.16822e15 1.02529
\(253\) 4.80308e15 1.15143
\(254\) −5.20691e15 −1.21664
\(255\) 7.79169e13 0.0177468
\(256\) −9.08636e15 −2.01758
\(257\) −6.62253e15 −1.43370 −0.716851 0.697227i \(-0.754417\pi\)
−0.716851 + 0.697227i \(0.754417\pi\)
\(258\) −4.18175e15 −0.882734
\(259\) 7.19892e15 1.48190
\(260\) −1.85005e14 −0.0371412
\(261\) −1.68861e15 −0.330647
\(262\) 6.79447e15 1.29777
\(263\) 8.43203e14 0.157116 0.0785579 0.996910i \(-0.474968\pi\)
0.0785579 + 0.996910i \(0.474968\pi\)
\(264\) −5.62756e15 −1.02304
\(265\) 2.01969e14 0.0358251
\(266\) −1.87248e15 −0.324106
\(267\) −9.78133e14 −0.165225
\(268\) −2.02404e16 −3.33689
\(269\) 1.22523e16 1.97164 0.985821 0.167803i \(-0.0536672\pi\)
0.985821 + 0.167803i \(0.0536672\pi\)
\(270\) −2.05866e14 −0.0323385
\(271\) −2.29585e14 −0.0352082 −0.0176041 0.999845i \(-0.505604\pi\)
−0.0176041 + 0.999845i \(0.505604\pi\)
\(272\) 3.03870e15 0.454978
\(273\) −1.04721e15 −0.153100
\(274\) 2.21187e16 3.15777
\(275\) −6.30184e15 −0.878628
\(276\) 1.17263e16 1.59681
\(277\) −2.21417e15 −0.294505 −0.147252 0.989099i \(-0.547043\pi\)
−0.147252 + 0.989099i \(0.547043\pi\)
\(278\) −1.04930e16 −1.36335
\(279\) −4.06864e15 −0.516442
\(280\) −2.21076e15 −0.274167
\(281\) −3.89035e15 −0.471409 −0.235704 0.971825i \(-0.575740\pi\)
−0.235704 + 0.971825i \(0.575740\pi\)
\(282\) 1.47614e16 1.74787
\(283\) −1.39198e16 −1.61072 −0.805362 0.592783i \(-0.798029\pi\)
−0.805362 + 0.592783i \(0.798029\pi\)
\(284\) 4.51580e15 0.510699
\(285\) 6.29315e13 0.00695627
\(286\) 2.66538e15 0.287991
\(287\) −2.43842e15 −0.257558
\(288\) −1.57738e15 −0.162886
\(289\) −8.86730e15 −0.895273
\(290\) 1.68840e15 0.166682
\(291\) −2.27802e12 −0.000219914 0
\(292\) 3.26984e16 3.08701
\(293\) 1.52234e16 1.40563 0.702817 0.711371i \(-0.251925\pi\)
0.702817 + 0.711371i \(0.251925\pi\)
\(294\) −1.22815e16 −1.10916
\(295\) −1.36386e15 −0.120484
\(296\) −2.37290e16 −2.05061
\(297\) 2.01826e15 0.170631
\(298\) −2.60717e16 −2.15657
\(299\) −2.94608e15 −0.238442
\(300\) −1.53854e16 −1.21849
\(301\) 1.61054e16 1.24821
\(302\) −1.14988e16 −0.872183
\(303\) 9.86293e15 0.732198
\(304\) 2.45428e15 0.178339
\(305\) −3.88746e14 −0.0276514
\(306\) −2.74062e15 −0.190836
\(307\) −8.48697e14 −0.0578566 −0.0289283 0.999581i \(-0.509209\pi\)
−0.0289283 + 0.999581i \(0.509209\pi\)
\(308\) 4.08591e16 2.72715
\(309\) 2.69442e15 0.176090
\(310\) 4.06814e15 0.260343
\(311\) −2.48376e15 −0.155657 −0.0778283 0.996967i \(-0.524799\pi\)
−0.0778283 + 0.996967i \(0.524799\pi\)
\(312\) 3.45179e15 0.211856
\(313\) 4.39913e15 0.264441 0.132220 0.991220i \(-0.457789\pi\)
0.132220 + 0.991220i \(0.457789\pi\)
\(314\) 7.14935e15 0.420944
\(315\) 7.92863e14 0.0457277
\(316\) −3.88789e15 −0.219659
\(317\) 2.19567e16 1.21530 0.607648 0.794206i \(-0.292113\pi\)
0.607648 + 0.794206i \(0.292113\pi\)
\(318\) −7.10400e15 −0.385236
\(319\) −1.65526e16 −0.879482
\(320\) −9.87806e14 −0.0514277
\(321\) 5.51502e15 0.281361
\(322\) −6.63682e16 −3.31816
\(323\) 8.37785e14 0.0410503
\(324\) 4.92741e15 0.236633
\(325\) 3.86538e15 0.181949
\(326\) 1.16843e16 0.539124
\(327\) −1.49954e16 −0.678264
\(328\) 8.03748e15 0.356402
\(329\) −5.68514e16 −2.47154
\(330\) −2.01801e15 −0.0860167
\(331\) 2.65474e16 1.10953 0.554767 0.832006i \(-0.312808\pi\)
0.554767 + 0.832006i \(0.312808\pi\)
\(332\) −3.64527e16 −1.49394
\(333\) 8.51011e15 0.342017
\(334\) 8.39995e16 3.31074
\(335\) −3.85005e15 −0.148825
\(336\) 3.09211e16 1.17233
\(337\) 1.40823e16 0.523697 0.261848 0.965109i \(-0.415668\pi\)
0.261848 + 0.965109i \(0.415668\pi\)
\(338\) 4.68616e16 1.70946
\(339\) −1.09787e16 −0.392872
\(340\) 1.86471e15 0.0654635
\(341\) −3.98830e16 −1.37368
\(342\) −2.21353e15 −0.0748025
\(343\) 3.74294e15 0.124108
\(344\) −5.30864e16 −1.72724
\(345\) 2.23054e15 0.0712174
\(346\) −6.00033e16 −1.88010
\(347\) 4.85833e16 1.49398 0.746992 0.664834i \(-0.231498\pi\)
0.746992 + 0.664834i \(0.231498\pi\)
\(348\) −4.04119e16 −1.21967
\(349\) 1.20256e16 0.356239 0.178119 0.984009i \(-0.442999\pi\)
0.178119 + 0.984009i \(0.442999\pi\)
\(350\) 8.70778e16 2.53201
\(351\) −1.23794e15 −0.0353350
\(352\) −1.54623e16 −0.433258
\(353\) −3.68917e16 −1.01483 −0.507415 0.861702i \(-0.669399\pi\)
−0.507415 + 0.861702i \(0.669399\pi\)
\(354\) 4.79721e16 1.29559
\(355\) 8.58978e14 0.0227771
\(356\) −2.34088e16 −0.609472
\(357\) 1.05551e16 0.269848
\(358\) −2.26664e16 −0.569041
\(359\) 2.30169e16 0.567456 0.283728 0.958905i \(-0.408429\pi\)
0.283728 + 0.958905i \(0.408429\pi\)
\(360\) −2.61342e15 −0.0632767
\(361\) −4.13763e16 −0.983909
\(362\) −4.26427e16 −0.995952
\(363\) −5.38303e15 −0.123491
\(364\) −2.50619e16 −0.564748
\(365\) 6.21976e15 0.137680
\(366\) 1.36736e16 0.297342
\(367\) 6.59133e15 0.140813 0.0704066 0.997518i \(-0.477570\pi\)
0.0704066 + 0.997518i \(0.477570\pi\)
\(368\) 8.69895e16 1.82581
\(369\) −2.88254e15 −0.0594435
\(370\) −8.50908e15 −0.172413
\(371\) 2.73600e16 0.544736
\(372\) −9.73710e16 −1.90502
\(373\) 9.60592e15 0.184685 0.0923425 0.995727i \(-0.470565\pi\)
0.0923425 + 0.995727i \(0.470565\pi\)
\(374\) −2.68651e16 −0.507601
\(375\) −5.87977e15 −0.109183
\(376\) 1.87393e17 3.42004
\(377\) 1.01529e16 0.182126
\(378\) −2.78879e16 −0.491722
\(379\) −8.91020e16 −1.54430 −0.772151 0.635439i \(-0.780819\pi\)
−0.772151 + 0.635439i \(0.780819\pi\)
\(380\) 1.50608e15 0.0256599
\(381\) 2.37062e16 0.397053
\(382\) 2.54686e16 0.419366
\(383\) 7.32809e16 1.18631 0.593156 0.805088i \(-0.297882\pi\)
0.593156 + 0.805088i \(0.297882\pi\)
\(384\) 5.24703e16 0.835142
\(385\) 7.77207e15 0.121630
\(386\) −9.25995e16 −1.42492
\(387\) 1.90388e16 0.288083
\(388\) −5.45177e13 −0.000811206 0
\(389\) −4.08834e16 −0.598239 −0.299119 0.954216i \(-0.596693\pi\)
−0.299119 + 0.954216i \(0.596693\pi\)
\(390\) 1.23779e15 0.0178126
\(391\) 2.96944e16 0.420267
\(392\) −1.55911e17 −2.17028
\(393\) −3.09340e16 −0.423531
\(394\) −1.19345e17 −1.60723
\(395\) −7.39541e14 −0.00979673
\(396\) 4.83011e16 0.629416
\(397\) −1.12376e16 −0.144058 −0.0720289 0.997403i \(-0.522947\pi\)
−0.0720289 + 0.997403i \(0.522947\pi\)
\(398\) −1.46420e17 −1.84654
\(399\) 8.52510e15 0.105773
\(400\) −1.14134e17 −1.39323
\(401\) 1.32254e17 1.58844 0.794219 0.607632i \(-0.207880\pi\)
0.794219 + 0.607632i \(0.207880\pi\)
\(402\) 1.35420e17 1.60035
\(403\) 2.44632e16 0.284466
\(404\) 2.36040e17 2.70089
\(405\) 9.37273e14 0.0105538
\(406\) 2.28721e17 2.53447
\(407\) 8.34207e16 0.909725
\(408\) −3.47916e16 −0.373408
\(409\) −1.13059e17 −1.19428 −0.597139 0.802138i \(-0.703696\pi\)
−0.597139 + 0.802138i \(0.703696\pi\)
\(410\) 2.88219e15 0.0299660
\(411\) −1.00703e17 −1.03055
\(412\) 6.44831e16 0.649552
\(413\) −1.84758e17 −1.83201
\(414\) −7.84563e16 −0.765818
\(415\) −6.93389e15 −0.0666292
\(416\) 9.48417e15 0.0897207
\(417\) 4.77727e16 0.444934
\(418\) −2.16982e16 −0.198966
\(419\) −6.14346e16 −0.554654 −0.277327 0.960776i \(-0.589448\pi\)
−0.277327 + 0.960776i \(0.589448\pi\)
\(420\) 1.89749e16 0.168678
\(421\) 1.62906e17 1.42595 0.712974 0.701190i \(-0.247348\pi\)
0.712974 + 0.701190i \(0.247348\pi\)
\(422\) −6.86651e16 −0.591841
\(423\) −6.72061e16 −0.570422
\(424\) −9.01838e16 −0.753790
\(425\) −3.89603e16 −0.320696
\(426\) −3.02134e16 −0.244927
\(427\) −5.26620e16 −0.420452
\(428\) 1.31986e17 1.03787
\(429\) −1.21350e16 −0.0939869
\(430\) −1.90365e16 −0.145225
\(431\) −2.03574e17 −1.52975 −0.764875 0.644179i \(-0.777199\pi\)
−0.764875 + 0.644179i \(0.777199\pi\)
\(432\) 3.65530e16 0.270569
\(433\) 1.73408e17 1.26444 0.632218 0.774791i \(-0.282145\pi\)
0.632218 + 0.774791i \(0.282145\pi\)
\(434\) 5.51096e17 3.95862
\(435\) −7.68700e15 −0.0543972
\(436\) −3.58872e17 −2.50195
\(437\) 2.39834e16 0.164734
\(438\) −2.18772e17 −1.48050
\(439\) −7.14926e16 −0.476696 −0.238348 0.971180i \(-0.576606\pi\)
−0.238348 + 0.971180i \(0.576606\pi\)
\(440\) −2.56182e16 −0.168309
\(441\) 5.59155e16 0.361977
\(442\) 1.64783e16 0.105116
\(443\) 2.09427e17 1.31646 0.658231 0.752816i \(-0.271305\pi\)
0.658231 + 0.752816i \(0.271305\pi\)
\(444\) 2.03665e17 1.26161
\(445\) −4.45273e15 −0.0271823
\(446\) −3.25752e17 −1.95979
\(447\) 1.18700e17 0.703804
\(448\) −1.33814e17 −0.781980
\(449\) 4.62356e16 0.266302 0.133151 0.991096i \(-0.457490\pi\)
0.133151 + 0.991096i \(0.457490\pi\)
\(450\) 1.02938e17 0.584378
\(451\) −2.82562e16 −0.158113
\(452\) −2.62742e17 −1.44921
\(453\) 5.23521e16 0.284640
\(454\) 4.16617e17 2.23292
\(455\) −4.76718e15 −0.0251877
\(456\) −2.81003e16 −0.146366
\(457\) 3.28135e17 1.68499 0.842494 0.538706i \(-0.181087\pi\)
0.842494 + 0.538706i \(0.181087\pi\)
\(458\) −1.14639e17 −0.580371
\(459\) 1.24776e16 0.0622799
\(460\) 5.33815e16 0.262703
\(461\) 7.87892e16 0.382306 0.191153 0.981560i \(-0.438777\pi\)
0.191153 + 0.981560i \(0.438777\pi\)
\(462\) −2.73372e17 −1.30792
\(463\) 6.33656e16 0.298935 0.149468 0.988767i \(-0.452244\pi\)
0.149468 + 0.988767i \(0.452244\pi\)
\(464\) −2.99787e17 −1.39459
\(465\) −1.85216e16 −0.0849637
\(466\) −3.88381e17 −1.75691
\(467\) −2.32240e17 −1.03604 −0.518020 0.855368i \(-0.673331\pi\)
−0.518020 + 0.855368i \(0.673331\pi\)
\(468\) −2.96266e16 −0.130342
\(469\) −5.21552e17 −2.26294
\(470\) 6.71980e16 0.287554
\(471\) −3.25498e16 −0.137376
\(472\) 6.08995e17 2.53508
\(473\) 1.86628e17 0.766268
\(474\) 2.60124e16 0.105347
\(475\) −3.14673e16 −0.125704
\(476\) 2.52606e17 0.995401
\(477\) 3.23433e16 0.125723
\(478\) 3.47784e17 1.33361
\(479\) −4.79339e17 −1.81327 −0.906634 0.421919i \(-0.861357\pi\)
−0.906634 + 0.421919i \(0.861357\pi\)
\(480\) −7.18066e15 −0.0267976
\(481\) −5.11680e16 −0.188389
\(482\) 7.40811e17 2.69093
\(483\) 3.02163e17 1.08289
\(484\) −1.28827e17 −0.455526
\(485\) −1.03702e13 −3.61796e−5 0
\(486\) −3.29673e16 −0.113488
\(487\) −2.92692e17 −0.994197 −0.497098 0.867694i \(-0.665601\pi\)
−0.497098 + 0.867694i \(0.665601\pi\)
\(488\) 1.73584e17 0.581809
\(489\) −5.31966e16 −0.175945
\(490\) −5.59087e16 −0.182476
\(491\) 6.92352e16 0.222996 0.111498 0.993765i \(-0.464435\pi\)
0.111498 + 0.993765i \(0.464435\pi\)
\(492\) −6.89853e16 −0.219272
\(493\) −1.02334e17 −0.321008
\(494\) 1.33091e16 0.0412026
\(495\) 9.18765e15 0.0280718
\(496\) −7.22327e17 −2.17823
\(497\) 1.16363e17 0.346335
\(498\) 2.43891e17 0.716480
\(499\) 4.50229e17 1.30551 0.652755 0.757569i \(-0.273613\pi\)
0.652755 + 0.757569i \(0.273613\pi\)
\(500\) −1.40715e17 −0.402750
\(501\) −3.82435e17 −1.08047
\(502\) −8.27008e17 −2.30641
\(503\) 3.62365e17 0.997596 0.498798 0.866718i \(-0.333775\pi\)
0.498798 + 0.866718i \(0.333775\pi\)
\(504\) −3.54031e17 −0.962150
\(505\) 4.48988e16 0.120459
\(506\) −7.69071e17 −2.03699
\(507\) −2.13353e17 −0.557887
\(508\) 5.67338e17 1.46463
\(509\) −4.92663e16 −0.125569 −0.0627847 0.998027i \(-0.519998\pi\)
−0.0627847 + 0.998027i \(0.519998\pi\)
\(510\) −1.24761e16 −0.0313958
\(511\) 8.42568e17 2.09348
\(512\) 8.65285e17 2.12278
\(513\) 1.00778e16 0.0244121
\(514\) 1.06040e18 2.53636
\(515\) 1.22657e16 0.0289699
\(516\) 4.55638e17 1.06267
\(517\) −6.58791e17 −1.51726
\(518\) −1.15269e18 −2.62162
\(519\) 2.73185e17 0.613576
\(520\) 1.57135e16 0.0348539
\(521\) 8.86374e16 0.194165 0.0970826 0.995276i \(-0.469049\pi\)
0.0970826 + 0.995276i \(0.469049\pi\)
\(522\) 2.70380e17 0.584946
\(523\) −8.32000e16 −0.177772 −0.0888858 0.996042i \(-0.528331\pi\)
−0.0888858 + 0.996042i \(0.528331\pi\)
\(524\) −7.40316e17 −1.56230
\(525\) −3.96450e17 −0.826330
\(526\) −1.35014e17 −0.277953
\(527\) −2.46571e17 −0.501387
\(528\) 3.58312e17 0.719682
\(529\) 3.46031e17 0.686519
\(530\) −3.23394e16 −0.0633780
\(531\) −2.18409e17 −0.422820
\(532\) 2.04023e17 0.390171
\(533\) 1.73316e16 0.0327426
\(534\) 1.56619e17 0.292298
\(535\) 2.51059e16 0.0462888
\(536\) 1.71913e18 3.13140
\(537\) 1.03196e17 0.185709
\(538\) −1.96184e18 −3.48802
\(539\) 5.48113e17 0.962816
\(540\) 2.24309e16 0.0389303
\(541\) −4.36899e16 −0.0749201 −0.0374601 0.999298i \(-0.511927\pi\)
−0.0374601 + 0.999298i \(0.511927\pi\)
\(542\) 3.67612e16 0.0622866
\(543\) 1.94145e17 0.325032
\(544\) −9.55935e16 −0.158138
\(545\) −6.82634e16 −0.111586
\(546\) 1.67679e17 0.270849
\(547\) −3.78763e17 −0.604575 −0.302287 0.953217i \(-0.597750\pi\)
−0.302287 + 0.953217i \(0.597750\pi\)
\(548\) −2.41002e18 −3.80143
\(549\) −6.22537e16 −0.0970387
\(550\) 1.00905e18 1.55438
\(551\) −8.26528e16 −0.125827
\(552\) −9.95986e17 −1.49847
\(553\) −1.00183e17 −0.148964
\(554\) 3.54534e17 0.521007
\(555\) 3.87404e16 0.0562677
\(556\) 1.14330e18 1.64125
\(557\) 6.88487e17 0.976871 0.488435 0.872600i \(-0.337568\pi\)
0.488435 + 0.872600i \(0.337568\pi\)
\(558\) 6.51471e17 0.913636
\(559\) −1.14473e17 −0.158681
\(560\) 1.40761e17 0.192868
\(561\) 1.22312e17 0.165657
\(562\) 6.22924e17 0.833967
\(563\) −2.26569e17 −0.299844 −0.149922 0.988698i \(-0.547902\pi\)
−0.149922 + 0.988698i \(0.547902\pi\)
\(564\) −1.60838e18 −2.10414
\(565\) −4.99779e16 −0.0646343
\(566\) 2.22884e18 2.84953
\(567\) 1.26969e17 0.160475
\(568\) −3.83553e17 −0.479249
\(569\) 7.35304e17 0.908316 0.454158 0.890921i \(-0.349940\pi\)
0.454158 + 0.890921i \(0.349940\pi\)
\(570\) −1.00766e16 −0.0123063
\(571\) 4.30093e16 0.0519311 0.0259655 0.999663i \(-0.491734\pi\)
0.0259655 + 0.999663i \(0.491734\pi\)
\(572\) −2.90416e17 −0.346694
\(573\) −1.15954e17 −0.136862
\(574\) 3.90440e17 0.455646
\(575\) −1.11532e18 −1.28694
\(576\) −1.58187e17 −0.180478
\(577\) −1.37324e18 −1.54919 −0.774594 0.632458i \(-0.782046\pi\)
−0.774594 + 0.632458i \(0.782046\pi\)
\(578\) 1.41983e18 1.58382
\(579\) 4.21590e17 0.465028
\(580\) −1.83966e17 −0.200657
\(581\) −9.39309e17 −1.01313
\(582\) 3.64757e14 0.000389049 0
\(583\) 3.17047e17 0.334409
\(584\) −2.77726e18 −2.89690
\(585\) −5.63546e15 −0.00581322
\(586\) −2.43758e18 −2.48670
\(587\) −6.95010e17 −0.701203 −0.350601 0.936525i \(-0.614023\pi\)
−0.350601 + 0.936525i \(0.614023\pi\)
\(588\) 1.33817e18 1.33524
\(589\) −1.99149e17 −0.196530
\(590\) 2.18382e17 0.213147
\(591\) 5.43356e17 0.524525
\(592\) 1.51085e18 1.44254
\(593\) 1.10257e18 1.04124 0.520620 0.853789i \(-0.325701\pi\)
0.520620 + 0.853789i \(0.325701\pi\)
\(594\) −3.23164e17 −0.301863
\(595\) 4.80498e16 0.0443947
\(596\) 2.84074e18 2.59616
\(597\) 6.66623e17 0.602625
\(598\) 4.71728e17 0.421826
\(599\) −9.09357e17 −0.804377 −0.402189 0.915557i \(-0.631750\pi\)
−0.402189 + 0.915557i \(0.631750\pi\)
\(600\) 1.30677e18 1.14345
\(601\) 1.26383e18 1.09397 0.546984 0.837143i \(-0.315776\pi\)
0.546984 + 0.837143i \(0.315776\pi\)
\(602\) −2.57880e18 −2.20821
\(603\) −6.16546e17 −0.522279
\(604\) 1.25290e18 1.04996
\(605\) −2.45051e16 −0.0203164
\(606\) −1.57925e18 −1.29533
\(607\) −2.53124e17 −0.205403 −0.102701 0.994712i \(-0.532749\pi\)
−0.102701 + 0.994712i \(0.532749\pi\)
\(608\) −7.72085e16 −0.0619858
\(609\) −1.04133e18 −0.827133
\(610\) 6.22461e16 0.0489180
\(611\) 4.04085e17 0.314199
\(612\) 2.98615e17 0.229735
\(613\) 2.18461e18 1.66295 0.831476 0.555560i \(-0.187496\pi\)
0.831476 + 0.555560i \(0.187496\pi\)
\(614\) 1.35894e17 0.102354
\(615\) −1.31221e16 −0.00977949
\(616\) −3.47040e18 −2.55920
\(617\) 1.93526e17 0.141217 0.0706083 0.997504i \(-0.477506\pi\)
0.0706083 + 0.997504i \(0.477506\pi\)
\(618\) −4.31431e17 −0.311520
\(619\) 1.78009e17 0.127190 0.0635948 0.997976i \(-0.479743\pi\)
0.0635948 + 0.997976i \(0.479743\pi\)
\(620\) −4.43260e17 −0.313410
\(621\) 3.57198e17 0.249927
\(622\) 3.97701e17 0.275371
\(623\) −6.03195e17 −0.413319
\(624\) −2.19779e17 −0.149034
\(625\) 1.44991e18 0.973015
\(626\) −7.04389e17 −0.467821
\(627\) 9.87884e16 0.0649332
\(628\) −7.78984e17 −0.506747
\(629\) 5.15737e17 0.332047
\(630\) −1.26953e17 −0.0808967
\(631\) 1.13174e18 0.713769 0.356884 0.934149i \(-0.383839\pi\)
0.356884 + 0.934149i \(0.383839\pi\)
\(632\) 3.30221e17 0.206131
\(633\) 3.12621e17 0.193149
\(634\) −3.51571e18 −2.14998
\(635\) 1.07917e17 0.0653222
\(636\) 7.74043e17 0.463761
\(637\) −3.36198e17 −0.199383
\(638\) 2.65041e18 1.55589
\(639\) 1.37557e17 0.0799329
\(640\) 2.38859e17 0.137395
\(641\) −2.32314e18 −1.32281 −0.661406 0.750028i \(-0.730040\pi\)
−0.661406 + 0.750028i \(0.730040\pi\)
\(642\) −8.83067e17 −0.497755
\(643\) −2.63934e18 −1.47273 −0.736366 0.676583i \(-0.763460\pi\)
−0.736366 + 0.676583i \(0.763460\pi\)
\(644\) 7.23139e18 3.99451
\(645\) 8.66698e16 0.0473947
\(646\) −1.34146e17 −0.0726219
\(647\) 1.32570e18 0.710503 0.355251 0.934771i \(-0.384395\pi\)
0.355251 + 0.934771i \(0.384395\pi\)
\(648\) −4.18513e17 −0.222061
\(649\) −2.14096e18 −1.12465
\(650\) −6.18926e17 −0.321886
\(651\) −2.50905e18 −1.29191
\(652\) −1.27311e18 −0.649016
\(653\) −2.10774e18 −1.06385 −0.531926 0.846791i \(-0.678532\pi\)
−0.531926 + 0.846791i \(0.678532\pi\)
\(654\) 2.40107e18 1.19991
\(655\) −1.40820e17 −0.0696781
\(656\) −5.11754e17 −0.250718
\(657\) 9.96031e17 0.483168
\(658\) 9.10306e18 4.37239
\(659\) 2.06081e18 0.980126 0.490063 0.871687i \(-0.336974\pi\)
0.490063 + 0.871687i \(0.336974\pi\)
\(660\) 2.19880e17 0.103550
\(661\) 2.22419e18 1.03720 0.518600 0.855017i \(-0.326453\pi\)
0.518600 + 0.855017i \(0.326453\pi\)
\(662\) −4.25078e18 −1.96287
\(663\) −7.50229e16 −0.0343049
\(664\) 3.09614e18 1.40193
\(665\) 3.88086e16 0.0174015
\(666\) −1.36264e18 −0.605061
\(667\) −2.92954e18 −1.28820
\(668\) −9.15248e18 −3.98558
\(669\) 1.48309e18 0.639585
\(670\) 6.16471e17 0.263285
\(671\) −6.10244e17 −0.258111
\(672\) −9.72737e17 −0.407469
\(673\) −3.24859e18 −1.34771 −0.673856 0.738863i \(-0.735363\pi\)
−0.673856 + 0.738863i \(0.735363\pi\)
\(674\) −2.25486e18 −0.926470
\(675\) −4.68659e17 −0.190714
\(676\) −5.10598e18 −2.05790
\(677\) 3.36868e18 1.34472 0.672362 0.740222i \(-0.265280\pi\)
0.672362 + 0.740222i \(0.265280\pi\)
\(678\) 1.75791e18 0.695029
\(679\) −1.40481e15 −0.000550127 0
\(680\) −1.58381e17 −0.0614320
\(681\) −1.89678e18 −0.728722
\(682\) 6.38607e18 2.43016
\(683\) 5.02495e18 1.89408 0.947038 0.321122i \(-0.104060\pi\)
0.947038 + 0.321122i \(0.104060\pi\)
\(684\) 2.41184e17 0.0900499
\(685\) −4.58425e17 −0.169543
\(686\) −5.99320e17 −0.219559
\(687\) 5.21931e17 0.189406
\(688\) 3.38006e18 1.21506
\(689\) −1.94468e17 −0.0692505
\(690\) −3.57155e17 −0.125990
\(691\) 3.84714e18 1.34441 0.672204 0.740366i \(-0.265348\pi\)
0.672204 + 0.740366i \(0.265348\pi\)
\(692\) 6.53788e18 2.26333
\(693\) 1.24462e18 0.426845
\(694\) −7.77917e18 −2.64300
\(695\) 2.17474e17 0.0731993
\(696\) 3.43241e18 1.14456
\(697\) −1.74690e17 −0.0577106
\(698\) −1.92554e18 −0.630220
\(699\) 1.76823e18 0.573373
\(700\) −9.48789e18 −3.04812
\(701\) −3.06033e18 −0.974095 −0.487048 0.873375i \(-0.661926\pi\)
−0.487048 + 0.873375i \(0.661926\pi\)
\(702\) 1.98220e17 0.0625110
\(703\) 4.16548e17 0.130153
\(704\) −1.55063e18 −0.480050
\(705\) −3.05941e17 −0.0938443
\(706\) 5.90711e18 1.79533
\(707\) 6.08227e18 1.83164
\(708\) −5.22698e18 −1.55968
\(709\) −2.08211e18 −0.615605 −0.307803 0.951450i \(-0.599594\pi\)
−0.307803 + 0.951450i \(0.599594\pi\)
\(710\) −1.37540e17 −0.0402948
\(711\) −1.18430e17 −0.0343802
\(712\) 1.98824e18 0.571938
\(713\) −7.05863e18 −2.01205
\(714\) −1.69009e18 −0.477387
\(715\) −5.52418e16 −0.0154625
\(716\) 2.46971e18 0.685032
\(717\) −1.58340e18 −0.435227
\(718\) −3.68547e18 −1.00388
\(719\) −3.53851e18 −0.955175 −0.477588 0.878584i \(-0.658489\pi\)
−0.477588 + 0.878584i \(0.658489\pi\)
\(720\) 1.66399e17 0.0445133
\(721\) 1.66159e18 0.440500
\(722\) 6.62519e18 1.74063
\(723\) −3.37279e18 −0.878193
\(724\) 4.64629e18 1.19896
\(725\) 3.84368e18 0.982992
\(726\) 8.61933e17 0.218467
\(727\) 1.72239e17 0.0432671 0.0216335 0.999766i \(-0.493113\pi\)
0.0216335 + 0.999766i \(0.493113\pi\)
\(728\) 2.12865e18 0.529969
\(729\) 1.50095e17 0.0370370
\(730\) −9.95910e17 −0.243569
\(731\) 1.15380e18 0.279685
\(732\) −1.48986e18 −0.357951
\(733\) 4.07961e18 0.971501 0.485751 0.874097i \(-0.338546\pi\)
0.485751 + 0.874097i \(0.338546\pi\)
\(734\) −1.05541e18 −0.249112
\(735\) 2.54543e17 0.0595515
\(736\) −2.73657e18 −0.634602
\(737\) −6.04371e18 −1.38920
\(738\) 4.61554e17 0.105161
\(739\) 2.80600e18 0.633722 0.316861 0.948472i \(-0.397371\pi\)
0.316861 + 0.948472i \(0.397371\pi\)
\(740\) 9.27138e17 0.207557
\(741\) −6.05942e16 −0.0134466
\(742\) −4.38090e18 −0.963690
\(743\) −3.51196e18 −0.765813 −0.382907 0.923787i \(-0.625077\pi\)
−0.382907 + 0.923787i \(0.625077\pi\)
\(744\) 8.27028e18 1.78771
\(745\) 5.40355e17 0.115788
\(746\) −1.53810e18 −0.326725
\(747\) −1.11039e18 −0.233826
\(748\) 2.92718e18 0.611068
\(749\) 3.40100e18 0.703842
\(750\) 9.41470e17 0.193156
\(751\) −1.57963e18 −0.321289 −0.160644 0.987012i \(-0.551357\pi\)
−0.160644 + 0.987012i \(0.551357\pi\)
\(752\) −1.19315e19 −2.40590
\(753\) 3.76523e18 0.752703
\(754\) −1.62569e18 −0.322199
\(755\) 2.38321e17 0.0468282
\(756\) 3.03863e18 0.591952
\(757\) 4.57886e18 0.884371 0.442185 0.896924i \(-0.354203\pi\)
0.442185 + 0.896924i \(0.354203\pi\)
\(758\) 1.42670e19 2.73202
\(759\) 3.50145e18 0.664777
\(760\) −1.27920e17 −0.0240797
\(761\) −3.19192e18 −0.595733 −0.297867 0.954608i \(-0.596275\pi\)
−0.297867 + 0.954608i \(0.596275\pi\)
\(762\) −3.79584e18 −0.702425
\(763\) −9.24739e18 −1.69672
\(764\) −2.77503e18 −0.504848
\(765\) 5.68014e16 0.0102461
\(766\) −1.17338e19 −2.09870
\(767\) 1.31321e18 0.232897
\(768\) −6.62395e18 −1.16485
\(769\) −2.98686e18 −0.520827 −0.260414 0.965497i \(-0.583859\pi\)
−0.260414 + 0.965497i \(0.583859\pi\)
\(770\) −1.24447e18 −0.215176
\(771\) −4.82783e18 −0.827748
\(772\) 1.00895e19 1.71537
\(773\) −6.01573e18 −1.01420 −0.507098 0.861888i \(-0.669282\pi\)
−0.507098 + 0.861888i \(0.669282\pi\)
\(774\) −3.04850e18 −0.509647
\(775\) 9.26122e18 1.53535
\(776\) 4.63050e15 0.000761250 0
\(777\) 5.24801e18 0.855576
\(778\) 6.54626e18 1.05834
\(779\) −1.41093e17 −0.0226210
\(780\) −1.34868e17 −0.0214435
\(781\) 1.34840e18 0.212612
\(782\) −4.75467e18 −0.743493
\(783\) −1.23099e18 −0.190899
\(784\) 9.92697e18 1.52673
\(785\) −1.48175e17 −0.0226008
\(786\) 4.95317e18 0.749266
\(787\) −8.17242e18 −1.22607 −0.613034 0.790056i \(-0.710051\pi\)
−0.613034 + 0.790056i \(0.710051\pi\)
\(788\) 1.30036e19 1.93484
\(789\) 6.14695e17 0.0907108
\(790\) 1.18415e17 0.0173313
\(791\) −6.77032e18 −0.982793
\(792\) −4.10249e18 −0.590655
\(793\) 3.74308e17 0.0534506
\(794\) 1.79937e18 0.254852
\(795\) 1.47236e17 0.0206836
\(796\) 1.59537e19 2.22293
\(797\) 1.06035e19 1.46545 0.732726 0.680523i \(-0.238248\pi\)
0.732726 + 0.680523i \(0.238248\pi\)
\(798\) −1.36504e18 −0.187123
\(799\) −4.07288e18 −0.553793
\(800\) 3.59050e18 0.484250
\(801\) −7.13059e17 −0.0953925
\(802\) −2.11765e19 −2.81010
\(803\) 9.76363e18 1.28517
\(804\) −1.47552e19 −1.92656
\(805\) 1.37553e18 0.178154
\(806\) −3.91705e18 −0.503247
\(807\) 8.93193e18 1.13833
\(808\) −2.00483e19 −2.53456
\(809\) 9.68399e18 1.21448 0.607238 0.794520i \(-0.292278\pi\)
0.607238 + 0.794520i \(0.292278\pi\)
\(810\) −1.50076e17 −0.0186707
\(811\) −5.91477e18 −0.729966 −0.364983 0.931014i \(-0.618925\pi\)
−0.364983 + 0.931014i \(0.618925\pi\)
\(812\) −2.49212e19 −3.05108
\(813\) −1.67368e17 −0.0203275
\(814\) −1.33573e19 −1.60939
\(815\) −2.42166e17 −0.0289460
\(816\) 2.21521e18 0.262681
\(817\) 9.31899e17 0.109629
\(818\) 1.81031e19 2.11279
\(819\) −7.63415e17 −0.0883925
\(820\) −3.14040e17 −0.0360741
\(821\) 7.57709e17 0.0863519 0.0431759 0.999067i \(-0.486252\pi\)
0.0431759 + 0.999067i \(0.486252\pi\)
\(822\) 1.61245e19 1.82314
\(823\) 1.14913e19 1.28905 0.644523 0.764585i \(-0.277056\pi\)
0.644523 + 0.764585i \(0.277056\pi\)
\(824\) −5.47692e18 −0.609551
\(825\) −4.59404e18 −0.507276
\(826\) 2.95834e19 3.24099
\(827\) −1.01647e19 −1.10486 −0.552430 0.833559i \(-0.686299\pi\)
−0.552430 + 0.833559i \(0.686299\pi\)
\(828\) 8.54850e18 0.921919
\(829\) 2.72808e18 0.291913 0.145956 0.989291i \(-0.453374\pi\)
0.145956 + 0.989291i \(0.453374\pi\)
\(830\) 1.11026e18 0.117873
\(831\) −1.61413e18 −0.170033
\(832\) 9.51118e17 0.0994106
\(833\) 3.38863e18 0.351425
\(834\) −7.64938e18 −0.787130
\(835\) −1.74095e18 −0.177756
\(836\) 2.36421e18 0.239522
\(837\) −2.96604e18 −0.298168
\(838\) 9.83692e18 0.981235
\(839\) −1.69983e19 −1.68249 −0.841245 0.540655i \(-0.818177\pi\)
−0.841245 + 0.540655i \(0.818177\pi\)
\(840\) −1.61165e18 −0.158290
\(841\) −1.64704e17 −0.0160520
\(842\) −2.60846e19 −2.52264
\(843\) −2.83606e18 −0.272168
\(844\) 7.48166e18 0.712479
\(845\) −9.71240e17 −0.0917821
\(846\) 1.07611e19 1.00913
\(847\) −3.31961e18 −0.308919
\(848\) 5.74208e18 0.530269
\(849\) −1.01475e19 −0.929952
\(850\) 6.23833e18 0.567342
\(851\) 1.47641e19 1.33249
\(852\) 3.29201e18 0.294852
\(853\) −2.07516e19 −1.84452 −0.922261 0.386568i \(-0.873660\pi\)
−0.922261 + 0.386568i \(0.873660\pi\)
\(854\) 8.43225e18 0.743819
\(855\) 4.58771e16 0.00401621
\(856\) −1.12103e19 −0.973956
\(857\) 8.07408e18 0.696174 0.348087 0.937462i \(-0.386831\pi\)
0.348087 + 0.937462i \(0.386831\pi\)
\(858\) 1.94306e18 0.166272
\(859\) 1.35586e19 1.15149 0.575743 0.817631i \(-0.304713\pi\)
0.575743 + 0.817631i \(0.304713\pi\)
\(860\) 2.07419e18 0.174827
\(861\) −1.77761e18 −0.148701
\(862\) 3.25964e19 2.70627
\(863\) −1.19838e19 −0.987469 −0.493735 0.869613i \(-0.664369\pi\)
−0.493735 + 0.869613i \(0.664369\pi\)
\(864\) −1.14991e18 −0.0940424
\(865\) 1.24361e18 0.100944
\(866\) −2.77661e19 −2.23691
\(867\) −6.46426e18 −0.516886
\(868\) −6.00467e19 −4.76553
\(869\) −1.16091e18 −0.0914474
\(870\) 1.23084e18 0.0962338
\(871\) 3.70705e18 0.287681
\(872\) 3.04811e19 2.34787
\(873\) −1.66067e15 −0.000126967 0
\(874\) −3.84023e18 −0.291429
\(875\) −3.62593e18 −0.273129
\(876\) 2.38371e19 1.78228
\(877\) −6.80753e18 −0.505234 −0.252617 0.967566i \(-0.581291\pi\)
−0.252617 + 0.967566i \(0.581291\pi\)
\(878\) 1.14474e19 0.843322
\(879\) 1.10979e19 0.811543
\(880\) 1.63113e18 0.118400
\(881\) 1.23865e19 0.892492 0.446246 0.894910i \(-0.352761\pi\)
0.446246 + 0.894910i \(0.352761\pi\)
\(882\) −8.95320e18 −0.640372
\(883\) 1.00764e19 0.715421 0.357711 0.933832i \(-0.383557\pi\)
0.357711 + 0.933832i \(0.383557\pi\)
\(884\) −1.79546e18 −0.126542
\(885\) −9.94257e17 −0.0695613
\(886\) −3.35335e19 −2.32895
\(887\) 1.28943e17 0.00888981 0.00444491 0.999990i \(-0.498585\pi\)
0.00444491 + 0.999990i \(0.498585\pi\)
\(888\) −1.72984e19 −1.18392
\(889\) 1.46191e19 0.993252
\(890\) 7.12972e17 0.0480881
\(891\) 1.47131e18 0.0985141
\(892\) 3.54935e19 2.35927
\(893\) −3.28957e18 −0.217072
\(894\) −1.90063e19 −1.24510
\(895\) 4.69779e17 0.0305523
\(896\) 3.23573e19 2.08916
\(897\) −2.14770e18 −0.137664
\(898\) −7.40325e18 −0.471114
\(899\) 2.43258e19 1.53684
\(900\) −1.12160e19 −0.703495
\(901\) 1.96010e18 0.122058
\(902\) 4.52440e18 0.279717
\(903\) 1.17408e19 0.720657
\(904\) 2.23162e19 1.35996
\(905\) 8.83800e17 0.0534735
\(906\) −8.38263e18 −0.503555
\(907\) −1.98412e19 −1.18337 −0.591685 0.806169i \(-0.701537\pi\)
−0.591685 + 0.806169i \(0.701537\pi\)
\(908\) −4.53940e19 −2.68807
\(909\) 7.19007e18 0.422735
\(910\) 7.63323e17 0.0445594
\(911\) −9.94765e18 −0.576568 −0.288284 0.957545i \(-0.593085\pi\)
−0.288284 + 0.957545i \(0.593085\pi\)
\(912\) 1.78917e18 0.102964
\(913\) −1.08847e19 −0.621949
\(914\) −5.25410e19 −2.98090
\(915\) −2.83396e17 −0.0159645
\(916\) 1.24909e19 0.698671
\(917\) −1.90764e19 −1.05949
\(918\) −1.99791e18 −0.110179
\(919\) 2.38402e19 1.30544 0.652722 0.757598i \(-0.273627\pi\)
0.652722 + 0.757598i \(0.273627\pi\)
\(920\) −4.53400e18 −0.246525
\(921\) −6.18700e17 −0.0334035
\(922\) −1.26157e19 −0.676335
\(923\) −8.27075e17 −0.0440285
\(924\) 2.97863e19 1.57452
\(925\) −1.93711e19 −1.01679
\(926\) −1.01461e19 −0.528845
\(927\) 1.96423e18 0.101666
\(928\) 9.43091e18 0.484721
\(929\) 1.47875e19 0.754731 0.377366 0.926064i \(-0.376830\pi\)
0.377366 + 0.926064i \(0.376830\pi\)
\(930\) 2.96568e18 0.150309
\(931\) 2.73692e18 0.137749
\(932\) 4.23175e19 2.11503
\(933\) −1.81066e18 −0.0898684
\(934\) 3.71863e19 1.83285
\(935\) 5.56798e17 0.0272535
\(936\) 2.51636e18 0.122315
\(937\) −2.68119e19 −1.29425 −0.647127 0.762382i \(-0.724030\pi\)
−0.647127 + 0.762382i \(0.724030\pi\)
\(938\) 8.35110e19 4.00336
\(939\) 3.20696e18 0.152675
\(940\) −7.32180e18 −0.346168
\(941\) −3.43324e19 −1.61202 −0.806011 0.591900i \(-0.798378\pi\)
−0.806011 + 0.591900i \(0.798378\pi\)
\(942\) 5.21188e18 0.243032
\(943\) −5.00089e18 −0.231591
\(944\) −3.87753e19 −1.78335
\(945\) 5.77997e17 0.0264009
\(946\) −2.98830e19 −1.35560
\(947\) 1.84464e19 0.831067 0.415534 0.909578i \(-0.363595\pi\)
0.415534 + 0.909578i \(0.363595\pi\)
\(948\) −2.83427e18 −0.126820
\(949\) −5.98875e18 −0.266137
\(950\) 5.03854e18 0.222383
\(951\) 1.60064e19 0.701652
\(952\) −2.14553e19 −0.934101
\(953\) 1.31082e19 0.566814 0.283407 0.959000i \(-0.408535\pi\)
0.283407 + 0.959000i \(0.408535\pi\)
\(954\) −5.17882e18 −0.222416
\(955\) −5.27856e17 −0.0225161
\(956\) −3.78941e19 −1.60544
\(957\) −1.20669e19 −0.507769
\(958\) 7.67519e19 3.20784
\(959\) −6.21012e19 −2.57798
\(960\) −7.20111e17 −0.0296918
\(961\) 3.41947e19 1.40041
\(962\) 8.19304e18 0.333278
\(963\) 4.02045e18 0.162444
\(964\) −8.07179e19 −3.23943
\(965\) 1.91919e18 0.0765052
\(966\) −4.83824e19 −1.91574
\(967\) 2.99771e19 1.17901 0.589505 0.807765i \(-0.299323\pi\)
0.589505 + 0.807765i \(0.299323\pi\)
\(968\) 1.09420e19 0.427473
\(969\) 6.10745e17 0.0237004
\(970\) 1.66047e15 6.40052e−5 0
\(971\) −7.97793e18 −0.305468 −0.152734 0.988267i \(-0.548808\pi\)
−0.152734 + 0.988267i \(0.548808\pi\)
\(972\) 3.59208e18 0.136620
\(973\) 2.94605e19 1.11303
\(974\) 4.68659e19 1.75883
\(975\) 2.81786e18 0.105049
\(976\) −1.10522e19 −0.409286
\(977\) 2.51869e19 0.926530 0.463265 0.886220i \(-0.346678\pi\)
0.463265 + 0.886220i \(0.346678\pi\)
\(978\) 8.51786e18 0.311263
\(979\) −6.98979e18 −0.253733
\(980\) 6.09173e18 0.219670
\(981\) −1.09317e19 −0.391596
\(982\) −1.10860e19 −0.394501
\(983\) −2.17925e19 −0.770387 −0.385193 0.922836i \(-0.625865\pi\)
−0.385193 + 0.922836i \(0.625865\pi\)
\(984\) 5.85932e18 0.205769
\(985\) 2.47351e18 0.0862934
\(986\) 1.63858e19 0.567894
\(987\) −4.14447e19 −1.42694
\(988\) −1.45015e18 −0.0496011
\(989\) 3.30302e19 1.12237
\(990\) −1.47113e18 −0.0496618
\(991\) −1.55987e18 −0.0523132 −0.0261566 0.999658i \(-0.508327\pi\)
−0.0261566 + 0.999658i \(0.508327\pi\)
\(992\) 2.27235e19 0.757092
\(993\) 1.93531e19 0.640589
\(994\) −1.86320e19 −0.612700
\(995\) 3.03465e18 0.0991422
\(996\) −2.65740e19 −0.862524
\(997\) −1.80157e19 −0.580942 −0.290471 0.956884i \(-0.593812\pi\)
−0.290471 + 0.956884i \(0.593812\pi\)
\(998\) −7.20908e19 −2.30957
\(999\) 6.20387e18 0.197464
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 3.14.a.b.1.1 2
3.2 odd 2 9.14.a.c.1.2 2
4.3 odd 2 48.14.a.g.1.1 2
5.2 odd 4 75.14.b.c.49.1 4
5.3 odd 4 75.14.b.c.49.4 4
5.4 even 2 75.14.a.e.1.2 2
7.6 odd 2 147.14.a.b.1.1 2
8.3 odd 2 192.14.a.o.1.2 2
8.5 even 2 192.14.a.k.1.2 2
12.11 even 2 144.14.a.m.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.14.a.b.1.1 2 1.1 even 1 trivial
9.14.a.c.1.2 2 3.2 odd 2
48.14.a.g.1.1 2 4.3 odd 2
75.14.a.e.1.2 2 5.4 even 2
75.14.b.c.49.1 4 5.2 odd 4
75.14.b.c.49.4 4 5.3 odd 4
144.14.a.m.1.2 2 12.11 even 2
147.14.a.b.1.1 2 7.6 odd 2
192.14.a.k.1.2 2 8.5 even 2
192.14.a.o.1.2 2 8.3 odd 2