Properties

Label 197.14.a.a.1.15
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $1$
Dimension $104$
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] = [197,14,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, 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("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.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: \(211.244930035\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-140.225 q^{2} -1671.46 q^{3} +11470.9 q^{4} +31759.0 q^{5} +234379. q^{6} -135007. q^{7} -459789. q^{8} +1.19945e6 q^{9} +O(q^{10})\) \(q-140.225 q^{2} -1671.46 q^{3} +11470.9 q^{4} +31759.0 q^{5} +234379. q^{6} -135007. q^{7} -459789. q^{8} +1.19945e6 q^{9} -4.45339e6 q^{10} +6.61641e6 q^{11} -1.91732e7 q^{12} +4.45473e6 q^{13} +1.89313e7 q^{14} -5.30838e7 q^{15} -2.94963e7 q^{16} +1.10551e8 q^{17} -1.68192e8 q^{18} +2.92939e8 q^{19} +3.64306e8 q^{20} +2.25658e8 q^{21} -9.27784e8 q^{22} +5.09095e8 q^{23} +7.68517e8 q^{24} -2.12070e8 q^{25} -6.24663e8 q^{26} +6.60019e8 q^{27} -1.54866e9 q^{28} -1.71152e9 q^{29} +7.44365e9 q^{30} +3.16666e9 q^{31} +7.90269e9 q^{32} -1.10591e10 q^{33} -1.55019e10 q^{34} -4.28768e9 q^{35} +1.37588e10 q^{36} +8.61199e9 q^{37} -4.10773e10 q^{38} -7.44590e9 q^{39} -1.46024e10 q^{40} -3.93198e10 q^{41} -3.16428e10 q^{42} -2.13346e10 q^{43} +7.58965e10 q^{44} +3.80932e10 q^{45} -7.13876e10 q^{46} -3.20059e10 q^{47} +4.93018e10 q^{48} -7.86621e10 q^{49} +2.97374e10 q^{50} -1.84780e11 q^{51} +5.11000e10 q^{52} -1.62511e11 q^{53} -9.25510e10 q^{54} +2.10131e11 q^{55} +6.20746e10 q^{56} -4.89636e11 q^{57} +2.39998e11 q^{58} -3.08362e11 q^{59} -6.08921e11 q^{60} -1.33000e11 q^{61} -4.44043e11 q^{62} -1.61934e11 q^{63} -8.66519e11 q^{64} +1.41478e11 q^{65} +1.55075e12 q^{66} -5.24160e11 q^{67} +1.26812e12 q^{68} -8.50930e11 q^{69} +6.01239e11 q^{70} -2.72013e11 q^{71} -5.51492e11 q^{72} -1.27492e12 q^{73} -1.20761e12 q^{74} +3.54466e11 q^{75} +3.36029e12 q^{76} -8.93261e11 q^{77} +1.04410e12 q^{78} +1.40738e12 q^{79} -9.36772e11 q^{80} -3.01550e12 q^{81} +5.51361e12 q^{82} -1.20424e12 q^{83} +2.58851e12 q^{84} +3.51097e12 q^{85} +2.99163e12 q^{86} +2.86074e12 q^{87} -3.04215e12 q^{88} +3.94850e12 q^{89} -5.34160e12 q^{90} -6.01420e11 q^{91} +5.83980e12 q^{92} -5.29293e12 q^{93} +4.48801e12 q^{94} +9.30346e12 q^{95} -1.32090e13 q^{96} +1.10967e13 q^{97} +1.10304e13 q^{98} +7.93603e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14} - 186128761 q^{15} + 1543503872 q^{16} - 109572251 q^{17} - 449658263 q^{18} - 1495268031 q^{19} - 1194030741 q^{20} - 832275538 q^{21} - 2695120703 q^{22} - 2632554532 q^{23} - 190649667 q^{24} + 22696779124 q^{25} - 2460454754 q^{26} - 16267542277 q^{27} - 18137835250 q^{28} + 47556769 q^{29} - 9613748117 q^{30} - 24774628288 q^{31} - 29246249180 q^{32} - 42367036666 q^{33} - 39395206606 q^{34} - 26216433864 q^{35} + 190013501626 q^{36} - 82419664050 q^{37} - 34593622142 q^{38} - 39498281801 q^{39} - 150303128514 q^{40} - 25862853768 q^{41} - 138889965149 q^{42} - 258164897781 q^{43} - 197365738094 q^{44} - 240782892021 q^{45} - 218441397971 q^{46} - 208905762731 q^{47} - 664063830814 q^{48} + 1113758315863 q^{49} - 1516068087607 q^{50} - 1019253294393 q^{51} - 1162941441840 q^{52} + 161684855900 q^{53} + 1679137315823 q^{54} - 557952233701 q^{55} + 2842561845328 q^{56} + 801593765429 q^{57} - 7249760433 q^{58} - 775487110641 q^{59} - 57598844627 q^{60} - 36786715662 q^{61} + 681529132643 q^{62} - 4349115033663 q^{63} + 4600420238797 q^{64} - 2531819073161 q^{65} - 3958922748734 q^{66} - 7314072405766 q^{67} - 10297353950393 q^{68} - 2089200206275 q^{69} - 14268943913713 q^{70} - 6055724651085 q^{71} - 26860198563805 q^{72} - 7572811533391 q^{73} - 11175265675817 q^{74} - 24431657592434 q^{75} - 26425925198106 q^{76} - 9735327037686 q^{77} - 35310017230907 q^{78} - 8981210762721 q^{79} - 25913753436330 q^{80} + 15437375349812 q^{81} - 19721330628227 q^{82} - 22209909714532 q^{83} - 18837805278768 q^{84} - 5905005171430 q^{85} - 8913876797772 q^{86} - 7341562344401 q^{87} - 35154329886441 q^{88} - 4646484034146 q^{89} + 9564902968095 q^{90} - 22752431457047 q^{91} - 13601121953458 q^{92} - 9615114240293 q^{93} + 15352521272967 q^{94} + 5258551767043 q^{95} + 87277848810881 q^{96} - 42298840804040 q^{97} + 27000102375354 q^{98} - 8666459567773 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −140.225 −1.54928 −0.774639 0.632404i \(-0.782068\pi\)
−0.774639 + 0.632404i \(0.782068\pi\)
\(3\) −1671.46 −1.32375 −0.661877 0.749613i \(-0.730240\pi\)
−0.661877 + 0.749613i \(0.730240\pi\)
\(4\) 11470.9 1.40026
\(5\) 31759.0 0.908995 0.454498 0.890748i \(-0.349819\pi\)
0.454498 + 0.890748i \(0.349819\pi\)
\(6\) 234379. 2.05086
\(7\) −135007. −0.433729 −0.216865 0.976202i \(-0.569583\pi\)
−0.216865 + 0.976202i \(0.569583\pi\)
\(8\) −459789. −0.620117
\(9\) 1.19945e6 0.752323
\(10\) −4.45339e6 −1.40829
\(11\) 6.61641e6 1.12608 0.563041 0.826429i \(-0.309631\pi\)
0.563041 + 0.826429i \(0.309631\pi\)
\(12\) −1.91732e7 −1.85360
\(13\) 4.45473e6 0.255971 0.127985 0.991776i \(-0.459149\pi\)
0.127985 + 0.991776i \(0.459149\pi\)
\(14\) 1.89313e7 0.671967
\(15\) −5.30838e7 −1.20329
\(16\) −2.94963e7 −0.439529
\(17\) 1.10551e8 1.11082 0.555409 0.831577i \(-0.312562\pi\)
0.555409 + 0.831577i \(0.312562\pi\)
\(18\) −1.68192e8 −1.16556
\(19\) 2.92939e8 1.42850 0.714249 0.699892i \(-0.246769\pi\)
0.714249 + 0.699892i \(0.246769\pi\)
\(20\) 3.64306e8 1.27283
\(21\) 2.25658e8 0.574151
\(22\) −9.27784e8 −1.74461
\(23\) 5.09095e8 0.717080 0.358540 0.933514i \(-0.383275\pi\)
0.358540 + 0.933514i \(0.383275\pi\)
\(24\) 7.68517e8 0.820881
\(25\) −2.12070e8 −0.173728
\(26\) −6.24663e8 −0.396570
\(27\) 6.60019e8 0.327863
\(28\) −1.54866e9 −0.607334
\(29\) −1.71152e9 −0.534314 −0.267157 0.963653i \(-0.586084\pi\)
−0.267157 + 0.963653i \(0.586084\pi\)
\(30\) 7.44365e9 1.86422
\(31\) 3.16666e9 0.640840 0.320420 0.947276i \(-0.396176\pi\)
0.320420 + 0.947276i \(0.396176\pi\)
\(32\) 7.90269e9 1.30107
\(33\) −1.10591e10 −1.49066
\(34\) −1.55019e10 −1.72097
\(35\) −4.28768e9 −0.394258
\(36\) 1.37588e10 1.05345
\(37\) 8.61199e9 0.551814 0.275907 0.961184i \(-0.411022\pi\)
0.275907 + 0.961184i \(0.411022\pi\)
\(38\) −4.10773e10 −2.21314
\(39\) −7.44590e9 −0.338842
\(40\) −1.46024e10 −0.563683
\(41\) −3.93198e10 −1.29276 −0.646378 0.763017i \(-0.723717\pi\)
−0.646378 + 0.763017i \(0.723717\pi\)
\(42\) −3.16428e10 −0.889519
\(43\) −2.13346e10 −0.514682 −0.257341 0.966321i \(-0.582846\pi\)
−0.257341 + 0.966321i \(0.582846\pi\)
\(44\) 7.58965e10 1.57681
\(45\) 3.80932e10 0.683858
\(46\) −7.13876e10 −1.11096
\(47\) −3.20059e10 −0.433106 −0.216553 0.976271i \(-0.569481\pi\)
−0.216553 + 0.976271i \(0.569481\pi\)
\(48\) 4.93018e10 0.581828
\(49\) −7.86621e10 −0.811879
\(50\) 2.97374e10 0.269152
\(51\) −1.84780e11 −1.47045
\(52\) 5.11000e10 0.358426
\(53\) −1.62511e11 −1.00714 −0.503570 0.863955i \(-0.667980\pi\)
−0.503570 + 0.863955i \(0.667980\pi\)
\(54\) −9.25510e10 −0.507951
\(55\) 2.10131e11 1.02360
\(56\) 6.20746e10 0.268963
\(57\) −4.89636e11 −1.89098
\(58\) 2.39998e11 0.827800
\(59\) −3.08362e11 −0.951749 −0.475875 0.879513i \(-0.657868\pi\)
−0.475875 + 0.879513i \(0.657868\pi\)
\(60\) −6.08921e11 −1.68491
\(61\) −1.33000e11 −0.330528 −0.165264 0.986249i \(-0.552848\pi\)
−0.165264 + 0.986249i \(0.552848\pi\)
\(62\) −4.44043e11 −0.992840
\(63\) −1.61934e11 −0.326305
\(64\) −8.66519e11 −1.57619
\(65\) 1.41478e11 0.232676
\(66\) 1.55075e12 2.30944
\(67\) −5.24160e11 −0.707909 −0.353955 0.935263i \(-0.615163\pi\)
−0.353955 + 0.935263i \(0.615163\pi\)
\(68\) 1.26812e12 1.55544
\(69\) −8.50930e11 −0.949237
\(70\) 6.01239e11 0.610815
\(71\) −2.72013e11 −0.252005 −0.126003 0.992030i \(-0.540215\pi\)
−0.126003 + 0.992030i \(0.540215\pi\)
\(72\) −5.51492e11 −0.466528
\(73\) −1.27492e12 −0.986020 −0.493010 0.870024i \(-0.664103\pi\)
−0.493010 + 0.870024i \(0.664103\pi\)
\(74\) −1.20761e12 −0.854913
\(75\) 3.54466e11 0.229973
\(76\) 3.36029e12 2.00027
\(77\) −8.93261e11 −0.488415
\(78\) 1.04410e12 0.524960
\(79\) 1.40738e12 0.651383 0.325692 0.945476i \(-0.394403\pi\)
0.325692 + 0.945476i \(0.394403\pi\)
\(80\) −9.36772e11 −0.399530
\(81\) −3.01550e12 −1.18633
\(82\) 5.51361e12 2.00284
\(83\) −1.20424e12 −0.404303 −0.202151 0.979354i \(-0.564793\pi\)
−0.202151 + 0.979354i \(0.564793\pi\)
\(84\) 2.58851e12 0.803961
\(85\) 3.51097e12 1.00973
\(86\) 2.99163e12 0.797386
\(87\) 2.86074e12 0.707300
\(88\) −3.04215e12 −0.698302
\(89\) 3.94850e12 0.842165 0.421082 0.907022i \(-0.361650\pi\)
0.421082 + 0.907022i \(0.361650\pi\)
\(90\) −5.34160e12 −1.05949
\(91\) −6.01420e11 −0.111022
\(92\) 5.83980e12 1.00410
\(93\) −5.29293e12 −0.848314
\(94\) 4.48801e12 0.671001
\(95\) 9.30346e12 1.29850
\(96\) −1.32090e13 −1.72229
\(97\) 1.10967e13 1.35262 0.676311 0.736616i \(-0.263578\pi\)
0.676311 + 0.736616i \(0.263578\pi\)
\(98\) 1.10304e13 1.25783
\(99\) 7.93603e12 0.847178
\(100\) −2.43264e12 −0.243264
\(101\) 6.50973e12 0.610202 0.305101 0.952320i \(-0.401310\pi\)
0.305101 + 0.952320i \(0.401310\pi\)
\(102\) 2.59108e13 2.27813
\(103\) −3.57787e12 −0.295245 −0.147623 0.989044i \(-0.547162\pi\)
−0.147623 + 0.989044i \(0.547162\pi\)
\(104\) −2.04824e12 −0.158732
\(105\) 7.16668e12 0.521900
\(106\) 2.27880e13 1.56034
\(107\) 3.88532e12 0.250284 0.125142 0.992139i \(-0.460061\pi\)
0.125142 + 0.992139i \(0.460061\pi\)
\(108\) 7.57105e12 0.459094
\(109\) 1.78459e13 1.01922 0.509609 0.860406i \(-0.329790\pi\)
0.509609 + 0.860406i \(0.329790\pi\)
\(110\) −2.94655e13 −1.58585
\(111\) −1.43946e13 −0.730465
\(112\) 3.98220e12 0.190637
\(113\) −3.60185e13 −1.62748 −0.813740 0.581228i \(-0.802572\pi\)
−0.813740 + 0.581228i \(0.802572\pi\)
\(114\) 6.86590e13 2.92965
\(115\) 1.61683e13 0.651822
\(116\) −1.96328e13 −0.748179
\(117\) 5.34322e12 0.192573
\(118\) 4.32399e13 1.47452
\(119\) −1.49251e13 −0.481794
\(120\) 2.44073e13 0.746177
\(121\) 9.25421e12 0.268061
\(122\) 1.86499e13 0.512079
\(123\) 6.57214e13 1.71129
\(124\) 3.63245e13 0.897344
\(125\) −4.55034e13 −1.06691
\(126\) 2.27071e13 0.505537
\(127\) −4.42550e13 −0.935919 −0.467959 0.883750i \(-0.655011\pi\)
−0.467959 + 0.883750i \(0.655011\pi\)
\(128\) 5.67684e13 1.14088
\(129\) 3.56599e13 0.681313
\(130\) −1.98387e13 −0.360480
\(131\) −7.50175e13 −1.29688 −0.648439 0.761267i \(-0.724578\pi\)
−0.648439 + 0.761267i \(0.724578\pi\)
\(132\) −1.26858e14 −2.08731
\(133\) −3.95489e13 −0.619581
\(134\) 7.35001e13 1.09675
\(135\) 2.09615e13 0.298026
\(136\) −5.08299e13 −0.688836
\(137\) −1.03816e14 −1.34147 −0.670737 0.741695i \(-0.734022\pi\)
−0.670737 + 0.741695i \(0.734022\pi\)
\(138\) 1.19321e14 1.47063
\(139\) −1.04040e13 −0.122351 −0.0611753 0.998127i \(-0.519485\pi\)
−0.0611753 + 0.998127i \(0.519485\pi\)
\(140\) −4.91838e13 −0.552064
\(141\) 5.34965e13 0.573325
\(142\) 3.81429e13 0.390426
\(143\) 2.94744e13 0.288244
\(144\) −3.53792e13 −0.330668
\(145\) −5.43563e13 −0.485689
\(146\) 1.78776e14 1.52762
\(147\) 1.31480e14 1.07473
\(148\) 9.87877e13 0.772684
\(149\) 1.12802e14 0.844513 0.422257 0.906476i \(-0.361238\pi\)
0.422257 + 0.906476i \(0.361238\pi\)
\(150\) −4.97048e13 −0.356292
\(151\) 1.03365e14 0.709619 0.354809 0.934939i \(-0.384546\pi\)
0.354809 + 0.934939i \(0.384546\pi\)
\(152\) −1.34690e14 −0.885835
\(153\) 1.32599e14 0.835694
\(154\) 1.25257e14 0.756690
\(155\) 1.00570e14 0.582521
\(156\) −8.54115e13 −0.474467
\(157\) 1.87835e14 1.00099 0.500493 0.865740i \(-0.333152\pi\)
0.500493 + 0.865740i \(0.333152\pi\)
\(158\) −1.97350e14 −1.00917
\(159\) 2.71630e14 1.33320
\(160\) 2.50982e14 1.18267
\(161\) −6.87313e13 −0.311019
\(162\) 4.22847e14 1.83796
\(163\) −3.78993e13 −0.158275 −0.0791375 0.996864i \(-0.525217\pi\)
−0.0791375 + 0.996864i \(0.525217\pi\)
\(164\) −4.51036e14 −1.81020
\(165\) −3.51224e14 −1.35500
\(166\) 1.68865e14 0.626377
\(167\) −1.24321e14 −0.443493 −0.221746 0.975104i \(-0.571176\pi\)
−0.221746 + 0.975104i \(0.571176\pi\)
\(168\) −1.03755e14 −0.356040
\(169\) −2.83030e14 −0.934479
\(170\) −4.92325e14 −1.56435
\(171\) 3.51365e14 1.07469
\(172\) −2.44728e14 −0.720690
\(173\) −1.99199e14 −0.564920 −0.282460 0.959279i \(-0.591150\pi\)
−0.282460 + 0.959279i \(0.591150\pi\)
\(174\) −4.01146e14 −1.09580
\(175\) 2.86309e13 0.0753508
\(176\) −1.95160e14 −0.494946
\(177\) 5.15414e14 1.25988
\(178\) −5.53677e14 −1.30475
\(179\) −2.31982e14 −0.527119 −0.263560 0.964643i \(-0.584897\pi\)
−0.263560 + 0.964643i \(0.584897\pi\)
\(180\) 4.36965e14 0.957581
\(181\) 6.65129e14 1.40603 0.703016 0.711174i \(-0.251836\pi\)
0.703016 + 0.711174i \(0.251836\pi\)
\(182\) 8.43339e13 0.172004
\(183\) 2.22304e14 0.437537
\(184\) −2.34076e14 −0.444673
\(185\) 2.73508e14 0.501596
\(186\) 7.42199e14 1.31427
\(187\) 7.31448e14 1.25087
\(188\) −3.67138e14 −0.606461
\(189\) −8.91072e13 −0.142204
\(190\) −1.30457e15 −2.01173
\(191\) 5.58080e14 0.831725 0.415862 0.909428i \(-0.363480\pi\)
0.415862 + 0.909428i \(0.363480\pi\)
\(192\) 1.44835e15 2.08648
\(193\) −1.11274e15 −1.54979 −0.774893 0.632092i \(-0.782196\pi\)
−0.774893 + 0.632092i \(0.782196\pi\)
\(194\) −1.55603e15 −2.09559
\(195\) −2.36474e14 −0.308006
\(196\) −9.02329e14 −1.13684
\(197\) −5.84517e13 −0.0712470
\(198\) −1.11283e15 −1.31251
\(199\) −3.09044e14 −0.352757 −0.176378 0.984322i \(-0.556438\pi\)
−0.176378 + 0.984322i \(0.556438\pi\)
\(200\) 9.75074e13 0.107731
\(201\) 8.76111e14 0.937097
\(202\) −9.12824e14 −0.945373
\(203\) 2.31068e14 0.231747
\(204\) −2.11961e15 −2.05901
\(205\) −1.24876e15 −1.17511
\(206\) 5.01706e14 0.457417
\(207\) 6.10632e14 0.539476
\(208\) −1.31398e14 −0.112506
\(209\) 1.93821e15 1.60861
\(210\) −1.00494e15 −0.808568
\(211\) −1.10742e15 −0.863929 −0.431965 0.901891i \(-0.642179\pi\)
−0.431965 + 0.901891i \(0.642179\pi\)
\(212\) −1.86415e15 −1.41026
\(213\) 4.54657e14 0.333593
\(214\) −5.44818e14 −0.387759
\(215\) −6.77565e14 −0.467844
\(216\) −3.03469e14 −0.203313
\(217\) −4.27520e14 −0.277951
\(218\) −2.50244e15 −1.57905
\(219\) 2.13098e15 1.30525
\(220\) 2.41040e15 1.43331
\(221\) 4.92473e14 0.284337
\(222\) 2.01847e15 1.13169
\(223\) −3.14593e14 −0.171304 −0.0856520 0.996325i \(-0.527297\pi\)
−0.0856520 + 0.996325i \(0.527297\pi\)
\(224\) −1.06692e15 −0.564312
\(225\) −2.54367e14 −0.130699
\(226\) 5.05068e15 2.52142
\(227\) 3.77257e14 0.183007 0.0915037 0.995805i \(-0.470833\pi\)
0.0915037 + 0.995805i \(0.470833\pi\)
\(228\) −5.61658e15 −2.64786
\(229\) 1.98983e15 0.911770 0.455885 0.890039i \(-0.349323\pi\)
0.455885 + 0.890039i \(0.349323\pi\)
\(230\) −2.26720e15 −1.00985
\(231\) 1.49305e15 0.646541
\(232\) 7.86940e14 0.331337
\(233\) −6.03475e14 −0.247085 −0.123542 0.992339i \(-0.539425\pi\)
−0.123542 + 0.992339i \(0.539425\pi\)
\(234\) −7.49250e14 −0.298348
\(235\) −1.01647e15 −0.393691
\(236\) −3.53720e15 −1.33270
\(237\) −2.35238e15 −0.862271
\(238\) 2.09286e15 0.746433
\(239\) 2.10461e14 0.0730441 0.0365220 0.999333i \(-0.488372\pi\)
0.0365220 + 0.999333i \(0.488372\pi\)
\(240\) 1.56577e15 0.528879
\(241\) 1.78464e15 0.586731 0.293365 0.956000i \(-0.405225\pi\)
0.293365 + 0.956000i \(0.405225\pi\)
\(242\) −1.29767e15 −0.415302
\(243\) 3.98799e15 1.24255
\(244\) −1.52564e15 −0.462826
\(245\) −2.49823e15 −0.737994
\(246\) −9.21576e15 −2.65126
\(247\) 1.30497e15 0.365653
\(248\) −1.45599e15 −0.397396
\(249\) 2.01284e15 0.535197
\(250\) 6.38070e15 1.65294
\(251\) −5.13746e14 −0.129679 −0.0648395 0.997896i \(-0.520654\pi\)
−0.0648395 + 0.997896i \(0.520654\pi\)
\(252\) −1.85753e15 −0.456912
\(253\) 3.36838e15 0.807491
\(254\) 6.20564e15 1.45000
\(255\) −5.86844e15 −1.33663
\(256\) −8.61804e14 −0.191359
\(257\) 6.08202e15 1.31669 0.658343 0.752718i \(-0.271257\pi\)
0.658343 + 0.752718i \(0.271257\pi\)
\(258\) −5.00039e15 −1.05554
\(259\) −1.16268e15 −0.239338
\(260\) 1.62288e15 0.325807
\(261\) −2.05288e15 −0.401977
\(262\) 1.05193e16 2.00922
\(263\) −9.29108e15 −1.73123 −0.865613 0.500714i \(-0.833071\pi\)
−0.865613 + 0.500714i \(0.833071\pi\)
\(264\) 5.08483e15 0.924380
\(265\) −5.16118e15 −0.915485
\(266\) 5.54572e15 0.959903
\(267\) −6.59975e15 −1.11482
\(268\) −6.01261e15 −0.991258
\(269\) −1.46786e15 −0.236208 −0.118104 0.993001i \(-0.537682\pi\)
−0.118104 + 0.993001i \(0.537682\pi\)
\(270\) −2.93932e15 −0.461725
\(271\) −5.57160e15 −0.854436 −0.427218 0.904149i \(-0.640506\pi\)
−0.427218 + 0.904149i \(0.640506\pi\)
\(272\) −3.26083e15 −0.488237
\(273\) 1.00525e15 0.146966
\(274\) 1.45576e16 2.07832
\(275\) −1.40314e15 −0.195632
\(276\) −9.76097e15 −1.32918
\(277\) −1.02135e16 −1.35849 −0.679243 0.733913i \(-0.737692\pi\)
−0.679243 + 0.733913i \(0.737692\pi\)
\(278\) 1.45890e15 0.189555
\(279\) 3.79823e15 0.482119
\(280\) 1.97143e15 0.244486
\(281\) 1.25359e16 1.51903 0.759513 0.650492i \(-0.225437\pi\)
0.759513 + 0.650492i \(0.225437\pi\)
\(282\) −7.50152e15 −0.888240
\(283\) −1.06728e16 −1.23500 −0.617502 0.786569i \(-0.711855\pi\)
−0.617502 + 0.786569i \(0.711855\pi\)
\(284\) −3.12024e15 −0.352873
\(285\) −1.55503e16 −1.71889
\(286\) −4.13303e15 −0.446570
\(287\) 5.30845e15 0.560706
\(288\) 9.47886e15 0.978824
\(289\) 2.31684e15 0.233916
\(290\) 7.62209e15 0.752466
\(291\) −1.85476e16 −1.79054
\(292\) −1.46246e16 −1.38069
\(293\) −1.20060e16 −1.10856 −0.554279 0.832331i \(-0.687006\pi\)
−0.554279 + 0.832331i \(0.687006\pi\)
\(294\) −1.84368e16 −1.66505
\(295\) −9.79326e15 −0.865136
\(296\) −3.95970e15 −0.342189
\(297\) 4.36696e15 0.369201
\(298\) −1.58176e16 −1.30839
\(299\) 2.26788e15 0.183551
\(300\) 4.06606e15 0.322022
\(301\) 2.88032e15 0.223233
\(302\) −1.44944e16 −1.09940
\(303\) −1.08807e16 −0.807757
\(304\) −8.64063e15 −0.627866
\(305\) −4.22395e15 −0.300448
\(306\) −1.85937e16 −1.29472
\(307\) −1.38748e16 −0.945862 −0.472931 0.881100i \(-0.656804\pi\)
−0.472931 + 0.881100i \(0.656804\pi\)
\(308\) −1.02466e16 −0.683909
\(309\) 5.98026e15 0.390832
\(310\) −1.41024e16 −0.902486
\(311\) −2.02532e16 −1.26926 −0.634630 0.772816i \(-0.718848\pi\)
−0.634630 + 0.772816i \(0.718848\pi\)
\(312\) 3.42354e15 0.210121
\(313\) 2.26452e16 1.36125 0.680626 0.732631i \(-0.261708\pi\)
0.680626 + 0.732631i \(0.261708\pi\)
\(314\) −2.63391e16 −1.55081
\(315\) −5.14285e15 −0.296609
\(316\) 1.61440e16 0.912107
\(317\) −1.44965e16 −0.802378 −0.401189 0.915995i \(-0.631403\pi\)
−0.401189 + 0.915995i \(0.631403\pi\)
\(318\) −3.80892e16 −2.06550
\(319\) −1.13242e16 −0.601681
\(320\) −2.75198e16 −1.43275
\(321\) −6.49415e15 −0.331314
\(322\) 9.63782e15 0.481854
\(323\) 3.23846e16 1.58680
\(324\) −3.45906e16 −1.66118
\(325\) −9.44715e14 −0.0444692
\(326\) 5.31442e15 0.245212
\(327\) −2.98287e16 −1.34919
\(328\) 1.80788e16 0.801660
\(329\) 4.32102e15 0.187851
\(330\) 4.92503e16 2.09927
\(331\) 2.35879e16 0.985844 0.492922 0.870074i \(-0.335929\pi\)
0.492922 + 0.870074i \(0.335929\pi\)
\(332\) −1.38138e16 −0.566130
\(333\) 1.03296e16 0.415142
\(334\) 1.74328e16 0.687093
\(335\) −1.66468e16 −0.643486
\(336\) −6.65608e15 −0.252356
\(337\) 1.40141e16 0.521158 0.260579 0.965452i \(-0.416086\pi\)
0.260579 + 0.965452i \(0.416086\pi\)
\(338\) 3.96878e16 1.44777
\(339\) 6.02034e16 2.15438
\(340\) 4.02742e16 1.41388
\(341\) 2.09519e16 0.721639
\(342\) −4.92701e16 −1.66500
\(343\) 2.37006e16 0.785865
\(344\) 9.80940e15 0.319163
\(345\) −2.70247e16 −0.862852
\(346\) 2.79326e16 0.875218
\(347\) 4.89592e16 1.50554 0.752771 0.658283i \(-0.228717\pi\)
0.752771 + 0.658283i \(0.228717\pi\)
\(348\) 3.28154e16 0.990404
\(349\) 1.69796e16 0.502993 0.251497 0.967858i \(-0.419077\pi\)
0.251497 + 0.967858i \(0.419077\pi\)
\(350\) −4.01476e15 −0.116739
\(351\) 2.94021e15 0.0839232
\(352\) 5.22875e16 1.46511
\(353\) 6.34394e15 0.174511 0.0872556 0.996186i \(-0.472190\pi\)
0.0872556 + 0.996186i \(0.472190\pi\)
\(354\) −7.22737e16 −1.95191
\(355\) −8.63884e15 −0.229072
\(356\) 4.52930e16 1.17925
\(357\) 2.49466e16 0.637777
\(358\) 3.25295e16 0.816654
\(359\) 6.16263e16 1.51933 0.759665 0.650314i \(-0.225363\pi\)
0.759665 + 0.650314i \(0.225363\pi\)
\(360\) −1.75148e16 −0.424072
\(361\) 4.37606e16 1.04061
\(362\) −9.32675e16 −2.17834
\(363\) −1.54680e16 −0.354847
\(364\) −6.89885e15 −0.155460
\(365\) −4.04903e16 −0.896287
\(366\) −3.11725e16 −0.677867
\(367\) −9.13912e16 −1.95243 −0.976214 0.216808i \(-0.930435\pi\)
−0.976214 + 0.216808i \(0.930435\pi\)
\(368\) −1.50164e16 −0.315177
\(369\) −4.71620e16 −0.972571
\(370\) −3.83526e16 −0.777111
\(371\) 2.19401e16 0.436826
\(372\) −6.07149e16 −1.18786
\(373\) −4.21386e16 −0.810163 −0.405082 0.914280i \(-0.632757\pi\)
−0.405082 + 0.914280i \(0.632757\pi\)
\(374\) −1.02567e17 −1.93795
\(375\) 7.60570e16 1.41233
\(376\) 1.47159e16 0.268576
\(377\) −7.62439e15 −0.136769
\(378\) 1.24950e16 0.220313
\(379\) −4.93938e16 −0.856087 −0.428043 0.903758i \(-0.640797\pi\)
−0.428043 + 0.903758i \(0.640797\pi\)
\(380\) 1.06719e17 1.81824
\(381\) 7.39703e16 1.23893
\(382\) −7.82566e16 −1.28857
\(383\) −9.22544e16 −1.49347 −0.746733 0.665124i \(-0.768379\pi\)
−0.746733 + 0.665124i \(0.768379\pi\)
\(384\) −9.48859e16 −1.51025
\(385\) −2.83691e16 −0.443967
\(386\) 1.56034e17 2.40105
\(387\) −2.55897e16 −0.387208
\(388\) 1.27289e17 1.89402
\(389\) 9.87570e16 1.44509 0.722546 0.691323i \(-0.242972\pi\)
0.722546 + 0.691323i \(0.242972\pi\)
\(390\) 3.31595e16 0.477186
\(391\) 5.62807e16 0.796545
\(392\) 3.61680e16 0.503460
\(393\) 1.25389e17 1.71675
\(394\) 8.19637e15 0.110381
\(395\) 4.46971e16 0.592104
\(396\) 9.10338e16 1.18627
\(397\) −3.96288e16 −0.508011 −0.254005 0.967203i \(-0.581748\pi\)
−0.254005 + 0.967203i \(0.581748\pi\)
\(398\) 4.33356e16 0.546519
\(399\) 6.61042e16 0.820173
\(400\) 6.25528e15 0.0763584
\(401\) −2.02446e14 −0.00243148 −0.00121574 0.999999i \(-0.500387\pi\)
−0.00121574 + 0.999999i \(0.500387\pi\)
\(402\) −1.22852e17 −1.45182
\(403\) 1.41066e16 0.164036
\(404\) 7.46727e16 0.854443
\(405\) −9.57692e16 −1.07837
\(406\) −3.24014e16 −0.359041
\(407\) 5.69805e16 0.621388
\(408\) 8.49600e16 0.911850
\(409\) 8.76083e16 0.925430 0.462715 0.886507i \(-0.346875\pi\)
0.462715 + 0.886507i \(0.346875\pi\)
\(410\) 1.75107e17 1.82057
\(411\) 1.73525e17 1.77578
\(412\) −4.10416e16 −0.413421
\(413\) 4.16310e16 0.412802
\(414\) −8.56256e16 −0.835798
\(415\) −3.82456e16 −0.367509
\(416\) 3.52044e16 0.333035
\(417\) 1.73899e16 0.161962
\(418\) −2.71785e17 −2.49218
\(419\) −3.36606e16 −0.303900 −0.151950 0.988388i \(-0.548555\pi\)
−0.151950 + 0.988388i \(0.548555\pi\)
\(420\) 8.22086e16 0.730797
\(421\) −1.23424e17 −1.08036 −0.540178 0.841551i \(-0.681643\pi\)
−0.540178 + 0.841551i \(0.681643\pi\)
\(422\) 1.55288e17 1.33847
\(423\) −3.83893e16 −0.325835
\(424\) 7.47207e16 0.624544
\(425\) −2.34444e16 −0.192980
\(426\) −6.37542e16 −0.516828
\(427\) 1.79559e16 0.143360
\(428\) 4.45683e16 0.350463
\(429\) −4.92651e16 −0.381564
\(430\) 9.50113e16 0.724820
\(431\) −9.22113e16 −0.692918 −0.346459 0.938065i \(-0.612616\pi\)
−0.346459 + 0.938065i \(0.612616\pi\)
\(432\) −1.94681e16 −0.144105
\(433\) 1.75215e17 1.27762 0.638808 0.769366i \(-0.279428\pi\)
0.638808 + 0.769366i \(0.279428\pi\)
\(434\) 5.99489e16 0.430624
\(435\) 9.08542e16 0.642932
\(436\) 2.04710e17 1.42717
\(437\) 1.49134e17 1.02435
\(438\) −2.98816e17 −2.02219
\(439\) 7.21607e15 0.0481151 0.0240576 0.999711i \(-0.492342\pi\)
0.0240576 + 0.999711i \(0.492342\pi\)
\(440\) −9.66156e16 −0.634753
\(441\) −9.43510e16 −0.610795
\(442\) −6.90569e16 −0.440516
\(443\) 5.08150e16 0.319424 0.159712 0.987164i \(-0.448943\pi\)
0.159712 + 0.987164i \(0.448943\pi\)
\(444\) −1.65119e17 −1.02284
\(445\) 1.25400e17 0.765524
\(446\) 4.41137e16 0.265397
\(447\) −1.88544e17 −1.11793
\(448\) 1.16986e17 0.683639
\(449\) −5.14420e15 −0.0296290 −0.0148145 0.999890i \(-0.504716\pi\)
−0.0148145 + 0.999890i \(0.504716\pi\)
\(450\) 3.56685e16 0.202490
\(451\) −2.60156e17 −1.45575
\(452\) −4.13166e17 −2.27890
\(453\) −1.72771e17 −0.939360
\(454\) −5.29007e16 −0.283529
\(455\) −1.91005e16 −0.100918
\(456\) 2.25129e17 1.17263
\(457\) −1.83536e17 −0.942465 −0.471232 0.882009i \(-0.656191\pi\)
−0.471232 + 0.882009i \(0.656191\pi\)
\(458\) −2.79023e17 −1.41259
\(459\) 7.29655e16 0.364196
\(460\) 1.85466e17 0.912722
\(461\) 1.48249e17 0.719341 0.359670 0.933079i \(-0.382889\pi\)
0.359670 + 0.933079i \(0.382889\pi\)
\(462\) −2.09362e17 −1.00167
\(463\) −3.08487e17 −1.45533 −0.727664 0.685933i \(-0.759394\pi\)
−0.727664 + 0.685933i \(0.759394\pi\)
\(464\) 5.04836e16 0.234846
\(465\) −1.68098e17 −0.771114
\(466\) 8.46221e16 0.382803
\(467\) −9.63205e16 −0.429694 −0.214847 0.976648i \(-0.568925\pi\)
−0.214847 + 0.976648i \(0.568925\pi\)
\(468\) 6.12917e16 0.269652
\(469\) 7.07652e16 0.307041
\(470\) 1.42535e17 0.609937
\(471\) −3.13958e17 −1.32506
\(472\) 1.41781e17 0.590196
\(473\) −1.41158e17 −0.579575
\(474\) 3.29862e17 1.33590
\(475\) −6.21237e16 −0.248170
\(476\) −1.71205e17 −0.674638
\(477\) −1.94923e17 −0.757695
\(478\) −2.95118e16 −0.113166
\(479\) 1.71642e17 0.649297 0.324649 0.945835i \(-0.394754\pi\)
0.324649 + 0.945835i \(0.394754\pi\)
\(480\) −4.19505e17 −1.56556
\(481\) 3.83641e16 0.141248
\(482\) −2.50250e17 −0.909009
\(483\) 1.14881e17 0.411712
\(484\) 1.06154e17 0.375356
\(485\) 3.52419e17 1.22953
\(486\) −5.59215e17 −1.92505
\(487\) −2.36270e17 −0.802548 −0.401274 0.915958i \(-0.631432\pi\)
−0.401274 + 0.915958i \(0.631432\pi\)
\(488\) 6.11519e16 0.204966
\(489\) 6.33471e16 0.209517
\(490\) 3.50313e17 1.14336
\(491\) 4.32643e17 1.39348 0.696738 0.717325i \(-0.254634\pi\)
0.696738 + 0.717325i \(0.254634\pi\)
\(492\) 7.53887e17 2.39625
\(493\) −1.89210e17 −0.593525
\(494\) −1.82989e17 −0.566499
\(495\) 2.52040e17 0.770081
\(496\) −9.34046e16 −0.281668
\(497\) 3.67236e16 0.109302
\(498\) −2.82250e17 −0.829169
\(499\) 2.78328e17 0.807056 0.403528 0.914967i \(-0.367784\pi\)
0.403528 + 0.914967i \(0.367784\pi\)
\(500\) −5.21967e17 −1.49396
\(501\) 2.07797e17 0.587075
\(502\) 7.20399e16 0.200909
\(503\) −1.59643e17 −0.439499 −0.219749 0.975556i \(-0.570524\pi\)
−0.219749 + 0.975556i \(0.570524\pi\)
\(504\) 7.44552e16 0.202347
\(505\) 2.06742e17 0.554671
\(506\) −4.72330e17 −1.25103
\(507\) 4.73073e17 1.23702
\(508\) −5.07646e17 −1.31053
\(509\) −3.21473e17 −0.819369 −0.409684 0.912227i \(-0.634361\pi\)
−0.409684 + 0.912227i \(0.634361\pi\)
\(510\) 8.22900e17 2.07081
\(511\) 1.72124e17 0.427666
\(512\) −3.44200e17 −0.844417
\(513\) 1.93346e17 0.468351
\(514\) −8.52849e17 −2.03991
\(515\) −1.13630e17 −0.268377
\(516\) 4.09052e17 0.954016
\(517\) −2.11764e17 −0.487713
\(518\) 1.63036e17 0.370801
\(519\) 3.32952e17 0.747815
\(520\) −6.50499e16 −0.144286
\(521\) −1.35189e17 −0.296140 −0.148070 0.988977i \(-0.547306\pi\)
−0.148070 + 0.988977i \(0.547306\pi\)
\(522\) 2.87865e17 0.622773
\(523\) 3.80866e17 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(524\) −8.60522e17 −1.81597
\(525\) −4.78553e16 −0.0997459
\(526\) 1.30284e18 2.68215
\(527\) 3.50075e17 0.711857
\(528\) 3.26201e17 0.655186
\(529\) −2.44859e17 −0.485796
\(530\) 7.23725e17 1.41834
\(531\) −3.69864e17 −0.716023
\(532\) −4.53663e17 −0.867576
\(533\) −1.75159e17 −0.330908
\(534\) 9.25447e17 1.72716
\(535\) 1.23394e17 0.227507
\(536\) 2.41003e17 0.438986
\(537\) 3.87748e17 0.697776
\(538\) 2.05830e17 0.365953
\(539\) −5.20461e17 −0.914242
\(540\) 2.40449e17 0.417314
\(541\) −5.22071e17 −0.895256 −0.447628 0.894220i \(-0.647731\pi\)
−0.447628 + 0.894220i \(0.647731\pi\)
\(542\) 7.81276e17 1.32376
\(543\) −1.11174e18 −1.86124
\(544\) 8.73647e17 1.44525
\(545\) 5.66769e17 0.926464
\(546\) −1.40960e17 −0.227691
\(547\) −1.46225e17 −0.233401 −0.116701 0.993167i \(-0.537232\pi\)
−0.116701 + 0.993167i \(0.537232\pi\)
\(548\) −1.19087e18 −1.87841
\(549\) −1.59527e17 −0.248664
\(550\) 1.96755e17 0.303088
\(551\) −5.01373e17 −0.763266
\(552\) 3.91248e17 0.588638
\(553\) −1.90007e17 −0.282524
\(554\) 1.43218e18 2.10467
\(555\) −4.57157e17 −0.663989
\(556\) −1.19344e17 −0.171323
\(557\) −4.99226e17 −0.708334 −0.354167 0.935182i \(-0.615236\pi\)
−0.354167 + 0.935182i \(0.615236\pi\)
\(558\) −5.32606e17 −0.746936
\(559\) −9.50399e16 −0.131744
\(560\) 1.26471e17 0.173288
\(561\) −1.22258e18 −1.65585
\(562\) −1.75785e18 −2.35339
\(563\) −2.77688e17 −0.367496 −0.183748 0.982973i \(-0.558823\pi\)
−0.183748 + 0.982973i \(0.558823\pi\)
\(564\) 6.13655e17 0.802805
\(565\) −1.14391e18 −1.47937
\(566\) 1.49660e18 1.91336
\(567\) 4.07113e17 0.514547
\(568\) 1.25068e17 0.156273
\(569\) −6.91353e17 −0.854024 −0.427012 0.904246i \(-0.640434\pi\)
−0.427012 + 0.904246i \(0.640434\pi\)
\(570\) 2.18054e18 2.66304
\(571\) 1.30435e16 0.0157492 0.00787461 0.999969i \(-0.497493\pi\)
0.00787461 + 0.999969i \(0.497493\pi\)
\(572\) 3.38099e17 0.403617
\(573\) −9.32807e17 −1.10100
\(574\) −7.44375e17 −0.868690
\(575\) −1.07964e17 −0.124577
\(576\) −1.03934e18 −1.18580
\(577\) 1.28416e18 1.44869 0.724345 0.689438i \(-0.242142\pi\)
0.724345 + 0.689438i \(0.242142\pi\)
\(578\) −3.24878e17 −0.362401
\(579\) 1.85990e18 2.05154
\(580\) −6.23518e17 −0.680091
\(581\) 1.62581e17 0.175358
\(582\) 2.60083e18 2.77404
\(583\) −1.07524e18 −1.13412
\(584\) 5.86195e17 0.611447
\(585\) 1.69695e17 0.175048
\(586\) 1.68354e18 1.71747
\(587\) 1.70835e17 0.172357 0.0861786 0.996280i \(-0.472534\pi\)
0.0861786 + 0.996280i \(0.472534\pi\)
\(588\) 1.50820e18 1.50490
\(589\) 9.27638e17 0.915439
\(590\) 1.37326e18 1.34034
\(591\) 9.76996e16 0.0943135
\(592\) −2.54022e17 −0.242538
\(593\) 5.64393e17 0.532999 0.266499 0.963835i \(-0.414133\pi\)
0.266499 + 0.963835i \(0.414133\pi\)
\(594\) −6.12355e17 −0.571994
\(595\) −4.74006e17 −0.437949
\(596\) 1.29395e18 1.18254
\(597\) 5.16554e17 0.466963
\(598\) −3.18013e17 −0.284372
\(599\) −9.10814e17 −0.805667 −0.402833 0.915273i \(-0.631975\pi\)
−0.402833 + 0.915273i \(0.631975\pi\)
\(600\) −1.62979e17 −0.142610
\(601\) −1.48131e18 −1.28222 −0.641109 0.767450i \(-0.721525\pi\)
−0.641109 + 0.767450i \(0.721525\pi\)
\(602\) −4.03891e17 −0.345850
\(603\) −6.28702e17 −0.532577
\(604\) 1.18570e18 0.993652
\(605\) 2.93904e17 0.243667
\(606\) 1.52575e18 1.25144
\(607\) −1.87906e18 −1.52481 −0.762403 0.647102i \(-0.775981\pi\)
−0.762403 + 0.647102i \(0.775981\pi\)
\(608\) 2.31501e18 1.85857
\(609\) −3.86220e17 −0.306777
\(610\) 5.92302e17 0.465478
\(611\) −1.42578e17 −0.110862
\(612\) 1.52104e18 1.17019
\(613\) 7.24602e17 0.551578 0.275789 0.961218i \(-0.411061\pi\)
0.275789 + 0.961218i \(0.411061\pi\)
\(614\) 1.94559e18 1.46540
\(615\) 2.08725e18 1.55555
\(616\) 4.10711e17 0.302874
\(617\) 2.58867e17 0.188896 0.0944481 0.995530i \(-0.469891\pi\)
0.0944481 + 0.995530i \(0.469891\pi\)
\(618\) −8.38580e17 −0.605507
\(619\) −7.66455e17 −0.547643 −0.273822 0.961781i \(-0.588288\pi\)
−0.273822 + 0.961781i \(0.588288\pi\)
\(620\) 1.15363e18 0.815681
\(621\) 3.36012e17 0.235104
\(622\) 2.83999e18 1.96644
\(623\) −5.33075e17 −0.365271
\(624\) 2.19626e17 0.148931
\(625\) −1.18627e18 −0.796091
\(626\) −3.17542e18 −2.10896
\(627\) −3.23963e18 −2.12940
\(628\) 2.15464e18 1.40164
\(629\) 9.52060e17 0.612964
\(630\) 7.21154e17 0.459530
\(631\) −3.29066e17 −0.207536 −0.103768 0.994602i \(-0.533090\pi\)
−0.103768 + 0.994602i \(0.533090\pi\)
\(632\) −6.47099e17 −0.403933
\(633\) 1.85101e18 1.14363
\(634\) 2.03277e18 1.24311
\(635\) −1.40549e18 −0.850745
\(636\) 3.11585e18 1.86684
\(637\) −3.50419e17 −0.207817
\(638\) 1.58793e18 0.932171
\(639\) −3.26264e17 −0.189589
\(640\) 1.80291e18 1.03706
\(641\) −1.29971e18 −0.740063 −0.370032 0.929019i \(-0.620653\pi\)
−0.370032 + 0.929019i \(0.620653\pi\)
\(642\) 9.10639e17 0.513297
\(643\) 2.63085e18 1.46800 0.733998 0.679152i \(-0.237652\pi\)
0.733998 + 0.679152i \(0.237652\pi\)
\(644\) −7.88413e17 −0.435508
\(645\) 1.13252e18 0.619310
\(646\) −4.54112e18 −2.45839
\(647\) −5.10620e17 −0.273666 −0.136833 0.990594i \(-0.543692\pi\)
−0.136833 + 0.990594i \(0.543692\pi\)
\(648\) 1.38649e18 0.735665
\(649\) −2.04025e18 −1.07175
\(650\) 1.32472e17 0.0688951
\(651\) 7.14582e17 0.367939
\(652\) −4.34741e17 −0.221626
\(653\) 3.87962e18 1.95818 0.979091 0.203422i \(-0.0652063\pi\)
0.979091 + 0.203422i \(0.0652063\pi\)
\(654\) 4.18272e18 2.09027
\(655\) −2.38248e18 −1.17886
\(656\) 1.15979e18 0.568204
\(657\) −1.52920e18 −0.741806
\(658\) −6.05913e17 −0.291033
\(659\) −3.20815e18 −1.52581 −0.762903 0.646513i \(-0.776227\pi\)
−0.762903 + 0.646513i \(0.776227\pi\)
\(660\) −4.02887e18 −1.89735
\(661\) 4.53145e17 0.211314 0.105657 0.994403i \(-0.466306\pi\)
0.105657 + 0.994403i \(0.466306\pi\)
\(662\) −3.30761e18 −1.52735
\(663\) −8.23148e17 −0.376392
\(664\) 5.53698e17 0.250715
\(665\) −1.25603e18 −0.563196
\(666\) −1.44847e18 −0.643171
\(667\) −8.71328e17 −0.383146
\(668\) −1.42608e18 −0.621006
\(669\) 5.25829e17 0.226764
\(670\) 2.33429e18 0.996939
\(671\) −8.79984e17 −0.372202
\(672\) 1.78331e18 0.747010
\(673\) −9.76762e17 −0.405220 −0.202610 0.979260i \(-0.564942\pi\)
−0.202610 + 0.979260i \(0.564942\pi\)
\(674\) −1.96512e18 −0.807419
\(675\) −1.39970e17 −0.0569589
\(676\) −3.24663e18 −1.30852
\(677\) −2.03337e18 −0.811692 −0.405846 0.913942i \(-0.633023\pi\)
−0.405846 + 0.913942i \(0.633023\pi\)
\(678\) −8.44200e18 −3.33774
\(679\) −1.49813e18 −0.586672
\(680\) −1.61431e18 −0.626149
\(681\) −6.30568e17 −0.242257
\(682\) −2.93797e18 −1.11802
\(683\) −4.56778e18 −1.72175 −0.860876 0.508816i \(-0.830084\pi\)
−0.860876 + 0.508816i \(0.830084\pi\)
\(684\) 4.03049e18 1.50485
\(685\) −3.29710e18 −1.21939
\(686\) −3.32341e18 −1.21752
\(687\) −3.32592e18 −1.20696
\(688\) 6.29291e17 0.226218
\(689\) −7.23943e17 −0.257798
\(690\) 3.78953e18 1.33680
\(691\) 5.08266e18 1.77617 0.888083 0.459683i \(-0.152037\pi\)
0.888083 + 0.459683i \(0.152037\pi\)
\(692\) −2.28500e18 −0.791036
\(693\) −1.07142e18 −0.367446
\(694\) −6.86528e18 −2.33250
\(695\) −3.30422e17 −0.111216
\(696\) −1.31534e18 −0.438608
\(697\) −4.34683e18 −1.43602
\(698\) −2.38096e18 −0.779277
\(699\) 1.00868e18 0.327079
\(700\) 3.28424e17 0.105511
\(701\) 1.72071e18 0.547697 0.273848 0.961773i \(-0.411703\pi\)
0.273848 + 0.961773i \(0.411703\pi\)
\(702\) −4.12290e17 −0.130020
\(703\) 2.52279e18 0.788264
\(704\) −5.73325e18 −1.77492
\(705\) 1.69899e18 0.521150
\(706\) −8.89576e17 −0.270366
\(707\) −8.78858e17 −0.264663
\(708\) 5.91228e18 1.76416
\(709\) 1.83559e18 0.542720 0.271360 0.962478i \(-0.412527\pi\)
0.271360 + 0.962478i \(0.412527\pi\)
\(710\) 1.21138e18 0.354896
\(711\) 1.68808e18 0.490051
\(712\) −1.81547e18 −0.522240
\(713\) 1.61213e18 0.459534
\(714\) −3.49813e18 −0.988093
\(715\) 9.36076e17 0.262012
\(716\) −2.66105e18 −0.738105
\(717\) −3.51776e17 −0.0966924
\(718\) −8.64153e18 −2.35387
\(719\) 6.61710e18 1.78620 0.893099 0.449859i \(-0.148526\pi\)
0.893099 + 0.449859i \(0.148526\pi\)
\(720\) −1.12361e18 −0.300575
\(721\) 4.83038e17 0.128057
\(722\) −6.13631e18 −1.61219
\(723\) −2.98294e18 −0.776687
\(724\) 7.62966e18 1.96881
\(725\) 3.62963e17 0.0928251
\(726\) 2.16900e18 0.549757
\(727\) −7.10273e18 −1.78423 −0.892116 0.451806i \(-0.850780\pi\)
−0.892116 + 0.451806i \(0.850780\pi\)
\(728\) 2.76526e17 0.0688465
\(729\) −1.85808e18 −0.458496
\(730\) 5.67774e18 1.38860
\(731\) −2.35855e18 −0.571718
\(732\) 2.55004e18 0.612667
\(733\) −1.94777e18 −0.463832 −0.231916 0.972736i \(-0.574499\pi\)
−0.231916 + 0.972736i \(0.574499\pi\)
\(734\) 1.28153e19 3.02485
\(735\) 4.17568e18 0.976922
\(736\) 4.02322e18 0.932971
\(737\) −3.46806e18 −0.797164
\(738\) 6.61328e18 1.50678
\(739\) −6.56867e18 −1.48350 −0.741752 0.670674i \(-0.766005\pi\)
−0.741752 + 0.670674i \(0.766005\pi\)
\(740\) 3.13740e18 0.702366
\(741\) −2.18120e18 −0.484035
\(742\) −3.07654e18 −0.676765
\(743\) −3.26392e18 −0.711726 −0.355863 0.934538i \(-0.615813\pi\)
−0.355863 + 0.934538i \(0.615813\pi\)
\(744\) 2.43363e18 0.526054
\(745\) 3.58248e18 0.767658
\(746\) 5.90887e18 1.25517
\(747\) −1.44443e18 −0.304166
\(748\) 8.39040e18 1.75155
\(749\) −5.24545e17 −0.108555
\(750\) −1.06651e19 −2.18809
\(751\) −8.54318e18 −1.73764 −0.868821 0.495127i \(-0.835122\pi\)
−0.868821 + 0.495127i \(0.835122\pi\)
\(752\) 9.44055e17 0.190362
\(753\) 8.58705e17 0.171663
\(754\) 1.06913e18 0.211892
\(755\) 3.28278e18 0.645040
\(756\) −1.02214e18 −0.199122
\(757\) −3.28203e18 −0.633898 −0.316949 0.948443i \(-0.602658\pi\)
−0.316949 + 0.948443i \(0.602658\pi\)
\(758\) 6.92623e18 1.32632
\(759\) −5.63011e18 −1.06892
\(760\) −4.27763e18 −0.805220
\(761\) 7.20733e18 1.34516 0.672580 0.740024i \(-0.265186\pi\)
0.672580 + 0.740024i \(0.265186\pi\)
\(762\) −1.03725e19 −1.91944
\(763\) −2.40932e18 −0.442065
\(764\) 6.40171e18 1.16463
\(765\) 4.21122e18 0.759642
\(766\) 1.29363e19 2.31379
\(767\) −1.37367e18 −0.243620
\(768\) 1.44047e18 0.253312
\(769\) 2.30431e18 0.401809 0.200904 0.979611i \(-0.435612\pi\)
0.200904 + 0.979611i \(0.435612\pi\)
\(770\) 3.97804e18 0.687828
\(771\) −1.01658e19 −1.74297
\(772\) −1.27642e19 −2.17011
\(773\) −7.52594e17 −0.126880 −0.0634401 0.997986i \(-0.520207\pi\)
−0.0634401 + 0.997986i \(0.520207\pi\)
\(774\) 3.58831e18 0.599892
\(775\) −6.71552e17 −0.111332
\(776\) −5.10212e18 −0.838783
\(777\) 1.94337e18 0.316824
\(778\) −1.38482e19 −2.23885
\(779\) −1.15183e19 −1.84670
\(780\) −2.71258e18 −0.431289
\(781\) −1.79975e18 −0.283779
\(782\) −7.89194e18 −1.23407
\(783\) −1.12964e18 −0.175182
\(784\) 2.32024e18 0.356844
\(785\) 5.96544e18 0.909892
\(786\) −1.75826e19 −2.65972
\(787\) −6.55210e18 −0.982980 −0.491490 0.870883i \(-0.663548\pi\)
−0.491490 + 0.870883i \(0.663548\pi\)
\(788\) −6.70496e17 −0.0997645
\(789\) 1.55296e19 2.29172
\(790\) −6.26763e18 −0.917334
\(791\) 4.86275e18 0.705886
\(792\) −3.64890e18 −0.525349
\(793\) −5.92480e17 −0.0846054
\(794\) 5.55694e18 0.787050
\(795\) 8.62670e18 1.21188
\(796\) −3.54503e18 −0.493952
\(797\) 7.85344e18 1.08538 0.542689 0.839934i \(-0.317406\pi\)
0.542689 + 0.839934i \(0.317406\pi\)
\(798\) −9.26944e18 −1.27068
\(799\) −3.53827e18 −0.481101
\(800\) −1.67592e18 −0.226032
\(801\) 4.73601e18 0.633580
\(802\) 2.83879e16 0.00376704
\(803\) −8.43542e18 −1.11034
\(804\) 1.00498e19 1.31218
\(805\) −2.18284e18 −0.282714
\(806\) −1.97809e18 −0.254138
\(807\) 2.45347e18 0.312682
\(808\) −2.99310e18 −0.378397
\(809\) −1.88785e18 −0.236757 −0.118378 0.992969i \(-0.537770\pi\)
−0.118378 + 0.992969i \(0.537770\pi\)
\(810\) 1.34292e19 1.67070
\(811\) −6.01258e18 −0.742037 −0.371018 0.928625i \(-0.620991\pi\)
−0.371018 + 0.928625i \(0.620991\pi\)
\(812\) 2.65056e18 0.324507
\(813\) 9.31270e18 1.13106
\(814\) −7.99007e18 −0.962702
\(815\) −1.20364e18 −0.143871
\(816\) 5.45034e18 0.646305
\(817\) −6.24974e18 −0.735223
\(818\) −1.22848e19 −1.43375
\(819\) −7.21371e17 −0.0835244
\(820\) −1.43244e19 −1.64546
\(821\) −3.43222e18 −0.391151 −0.195575 0.980689i \(-0.562657\pi\)
−0.195575 + 0.980689i \(0.562657\pi\)
\(822\) −2.43324e19 −2.75118
\(823\) −1.57612e19 −1.76803 −0.884014 0.467461i \(-0.845169\pi\)
−0.884014 + 0.467461i \(0.845169\pi\)
\(824\) 1.64507e18 0.183086
\(825\) 2.34529e18 0.258968
\(826\) −5.83769e18 −0.639544
\(827\) 1.12764e19 1.22570 0.612851 0.790198i \(-0.290023\pi\)
0.612851 + 0.790198i \(0.290023\pi\)
\(828\) 7.00452e18 0.755408
\(829\) 7.10256e18 0.759994 0.379997 0.924988i \(-0.375925\pi\)
0.379997 + 0.924988i \(0.375925\pi\)
\(830\) 5.36297e18 0.569374
\(831\) 1.70714e19 1.79830
\(832\) −3.86011e18 −0.403458
\(833\) −8.69614e18 −0.901849
\(834\) −2.43849e18 −0.250924
\(835\) −3.94830e18 −0.403133
\(836\) 2.22331e19 2.25247
\(837\) 2.09005e18 0.210108
\(838\) 4.72005e18 0.470826
\(839\) 4.43372e18 0.438850 0.219425 0.975629i \(-0.429582\pi\)
0.219425 + 0.975629i \(0.429582\pi\)
\(840\) −3.29516e18 −0.323639
\(841\) −7.33131e18 −0.714509
\(842\) 1.73071e19 1.67377
\(843\) −2.09533e19 −2.01082
\(844\) −1.27032e19 −1.20973
\(845\) −8.98876e18 −0.849437
\(846\) 5.38313e18 0.504810
\(847\) −1.24938e18 −0.116266
\(848\) 4.79347e18 0.442667
\(849\) 1.78392e19 1.63484
\(850\) 3.28749e18 0.298979
\(851\) 4.38432e18 0.395695
\(852\) 5.21535e18 0.467117
\(853\) 9.43072e18 0.838255 0.419127 0.907927i \(-0.362336\pi\)
0.419127 + 0.907927i \(0.362336\pi\)
\(854\) −2.51786e18 −0.222104
\(855\) 1.11590e19 0.976890
\(856\) −1.78643e18 −0.155205
\(857\) 1.19757e19 1.03258 0.516292 0.856413i \(-0.327312\pi\)
0.516292 + 0.856413i \(0.327312\pi\)
\(858\) 6.90819e18 0.591148
\(859\) 1.78274e19 1.51403 0.757013 0.653400i \(-0.226658\pi\)
0.757013 + 0.653400i \(0.226658\pi\)
\(860\) −7.77231e18 −0.655104
\(861\) −8.87285e18 −0.742237
\(862\) 1.29303e19 1.07352
\(863\) −5.36874e17 −0.0442387 −0.0221193 0.999755i \(-0.507041\pi\)
−0.0221193 + 0.999755i \(0.507041\pi\)
\(864\) 5.21593e18 0.426572
\(865\) −6.32635e18 −0.513510
\(866\) −2.45695e19 −1.97938
\(867\) −3.87250e18 −0.309647
\(868\) −4.90406e18 −0.389204
\(869\) 9.31183e18 0.733511
\(870\) −1.27400e19 −0.996080
\(871\) −2.33499e18 −0.181204
\(872\) −8.20536e18 −0.632034
\(873\) 1.33099e19 1.01761
\(874\) −2.09123e19 −1.58700
\(875\) 6.14328e18 0.462751
\(876\) 2.44444e19 1.82769
\(877\) −2.07348e19 −1.53887 −0.769435 0.638725i \(-0.779462\pi\)
−0.769435 + 0.638725i \(0.779462\pi\)
\(878\) −1.01187e18 −0.0745437
\(879\) 2.00675e19 1.46746
\(880\) −6.19807e18 −0.449903
\(881\) 1.03039e19 0.742435 0.371217 0.928546i \(-0.378940\pi\)
0.371217 + 0.928546i \(0.378940\pi\)
\(882\) 1.32303e19 0.946292
\(883\) 1.57010e19 1.11476 0.557381 0.830257i \(-0.311806\pi\)
0.557381 + 0.830257i \(0.311806\pi\)
\(884\) 5.64913e18 0.398146
\(885\) 1.63690e19 1.14523
\(886\) −7.12551e18 −0.494877
\(887\) −7.12346e18 −0.491120 −0.245560 0.969381i \(-0.578972\pi\)
−0.245560 + 0.969381i \(0.578972\pi\)
\(888\) 6.61846e18 0.452974
\(889\) 5.97473e18 0.405935
\(890\) −1.75842e19 −1.18601
\(891\) −1.99518e19 −1.33591
\(892\) −3.60868e18 −0.239870
\(893\) −9.37579e18 −0.618690
\(894\) 2.64385e19 1.73198
\(895\) −7.36750e18 −0.479149
\(896\) −7.66412e18 −0.494835
\(897\) −3.79067e18 −0.242977
\(898\) 7.21344e17 0.0459036
\(899\) −5.41981e18 −0.342410
\(900\) −2.91782e18 −0.183013
\(901\) −1.79657e19 −1.11875
\(902\) 3.64803e19 2.25536
\(903\) −4.81433e18 −0.295505
\(904\) 1.65609e19 1.00923
\(905\) 2.11238e19 1.27808
\(906\) 2.42267e19 1.45533
\(907\) 1.29043e19 0.769641 0.384820 0.922991i \(-0.374263\pi\)
0.384820 + 0.922991i \(0.374263\pi\)
\(908\) 4.32749e18 0.256258
\(909\) 7.80807e18 0.459069
\(910\) 2.67836e18 0.156351
\(911\) 5.82587e18 0.337669 0.168834 0.985644i \(-0.446000\pi\)
0.168834 + 0.985644i \(0.446000\pi\)
\(912\) 1.44424e19 0.831140
\(913\) −7.96777e18 −0.455278
\(914\) 2.57362e19 1.46014
\(915\) 7.06015e18 0.397719
\(916\) 2.28252e19 1.27672
\(917\) 1.01279e19 0.562494
\(918\) −1.02316e19 −0.564241
\(919\) 2.39241e19 1.31004 0.655020 0.755612i \(-0.272660\pi\)
0.655020 + 0.755612i \(0.272660\pi\)
\(920\) −7.43402e18 −0.404206
\(921\) 2.31912e19 1.25209
\(922\) −2.07881e19 −1.11446
\(923\) −1.21174e18 −0.0645059
\(924\) 1.71267e19 0.905326
\(925\) −1.82634e18 −0.0958653
\(926\) 4.32575e19 2.25471
\(927\) −4.29147e18 −0.222120
\(928\) −1.35257e19 −0.695179
\(929\) −2.55828e19 −1.30571 −0.652853 0.757484i \(-0.726428\pi\)
−0.652853 + 0.757484i \(0.726428\pi\)
\(930\) 2.35715e19 1.19467
\(931\) −2.30432e19 −1.15977
\(932\) −6.92243e18 −0.345983
\(933\) 3.38523e19 1.68019
\(934\) 1.35065e19 0.665715
\(935\) 2.32300e19 1.13704
\(936\) −2.45675e18 −0.119417
\(937\) −2.52399e18 −0.121837 −0.0609187 0.998143i \(-0.519403\pi\)
−0.0609187 + 0.998143i \(0.519403\pi\)
\(938\) −9.92302e18 −0.475692
\(939\) −3.78505e19 −1.80196
\(940\) −1.16599e19 −0.551270
\(941\) −4.79789e18 −0.225278 −0.112639 0.993636i \(-0.535930\pi\)
−0.112639 + 0.993636i \(0.535930\pi\)
\(942\) 4.40246e19 2.05289
\(943\) −2.00175e19 −0.927010
\(944\) 9.09553e18 0.418321
\(945\) −2.82995e18 −0.129263
\(946\) 1.97939e19 0.897922
\(947\) 3.39201e19 1.52821 0.764103 0.645094i \(-0.223182\pi\)
0.764103 + 0.645094i \(0.223182\pi\)
\(948\) −2.69840e19 −1.20740
\(949\) −5.67945e18 −0.252392
\(950\) 8.71127e18 0.384484
\(951\) 2.42303e19 1.06215
\(952\) 6.86238e18 0.298769
\(953\) −2.25875e19 −0.976709 −0.488354 0.872645i \(-0.662403\pi\)
−0.488354 + 0.872645i \(0.662403\pi\)
\(954\) 2.73330e19 1.17388
\(955\) 1.77241e19 0.756034
\(956\) 2.41419e18 0.102281
\(957\) 1.89278e19 0.796477
\(958\) −2.40685e19 −1.00594
\(959\) 1.40159e19 0.581836
\(960\) 4.59981e19 1.89660
\(961\) −1.43898e19 −0.589324
\(962\) −5.37960e18 −0.218832
\(963\) 4.66023e18 0.188294
\(964\) 2.04714e19 0.821576
\(965\) −3.53395e19 −1.40875
\(966\) −1.61092e19 −0.637856
\(967\) 2.54682e19 1.00167 0.500837 0.865542i \(-0.333026\pi\)
0.500837 + 0.865542i \(0.333026\pi\)
\(968\) −4.25498e18 −0.166229
\(969\) −5.41295e19 −2.10053
\(970\) −4.94178e19 −1.90488
\(971\) 2.13048e19 0.815740 0.407870 0.913040i \(-0.366272\pi\)
0.407870 + 0.913040i \(0.366272\pi\)
\(972\) 4.57461e19 1.73989
\(973\) 1.40462e18 0.0530670
\(974\) 3.31309e19 1.24337
\(975\) 1.57905e18 0.0588662
\(976\) 3.92301e18 0.145277
\(977\) 1.69605e19 0.623912 0.311956 0.950097i \(-0.399016\pi\)
0.311956 + 0.950097i \(0.399016\pi\)
\(978\) −8.88283e18 −0.324600
\(979\) 2.61249e19 0.948347
\(980\) −2.86571e19 −1.03338
\(981\) 2.14052e19 0.766781
\(982\) −6.06672e19 −2.15888
\(983\) −4.25684e18 −0.150484 −0.0752419 0.997165i \(-0.523973\pi\)
−0.0752419 + 0.997165i \(0.523973\pi\)
\(984\) −3.02180e19 −1.06120
\(985\) −1.85637e18 −0.0647632
\(986\) 2.65319e19 0.919535
\(987\) −7.22239e18 −0.248668
\(988\) 1.49692e19 0.512010
\(989\) −1.08613e19 −0.369069
\(990\) −3.53423e19 −1.19307
\(991\) 4.55047e18 0.152608 0.0763041 0.997085i \(-0.475688\pi\)
0.0763041 + 0.997085i \(0.475688\pi\)
\(992\) 2.50251e19 0.833777
\(993\) −3.94262e19 −1.30501
\(994\) −5.14955e18 −0.169339
\(995\) −9.81493e18 −0.320654
\(996\) 2.30892e19 0.749416
\(997\) 4.92378e19 1.58774 0.793872 0.608085i \(-0.208062\pi\)
0.793872 + 0.608085i \(0.208062\pi\)
\(998\) −3.90285e19 −1.25035
\(999\) 5.68408e18 0.180919
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 197.14.a.a.1.15 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.15 104 1.1 even 1 trivial