Properties

Label 177.14.a.c.1.4
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-126.798 q^{2} +729.000 q^{3} +7885.84 q^{4} +57088.2 q^{5} -92436.0 q^{6} +543807. q^{7} +38821.0 q^{8} +531441. q^{9} +O(q^{10})\) \(q-126.798 q^{2} +729.000 q^{3} +7885.84 q^{4} +57088.2 q^{5} -92436.0 q^{6} +543807. q^{7} +38821.0 q^{8} +531441. q^{9} -7.23869e6 q^{10} +4.27310e6 q^{11} +5.74878e6 q^{12} +1.89254e7 q^{13} -6.89538e7 q^{14} +4.16173e7 q^{15} -6.95232e7 q^{16} +6.68663e7 q^{17} -6.73859e7 q^{18} -1.27598e8 q^{19} +4.50188e8 q^{20} +3.96435e8 q^{21} -5.41822e8 q^{22} -1.18294e9 q^{23} +2.83005e7 q^{24} +2.03836e9 q^{25} -2.39971e9 q^{26} +3.87420e8 q^{27} +4.28837e9 q^{28} -4.39611e8 q^{29} -5.27701e9 q^{30} -4.50096e8 q^{31} +8.49741e9 q^{32} +3.11509e9 q^{33} -8.47854e9 q^{34} +3.10449e10 q^{35} +4.19086e9 q^{36} -1.47236e10 q^{37} +1.61793e10 q^{38} +1.37966e10 q^{39} +2.21622e9 q^{40} -1.44432e10 q^{41} -5.02673e10 q^{42} -6.17662e9 q^{43} +3.36969e10 q^{44} +3.03390e10 q^{45} +1.49995e11 q^{46} +1.00774e11 q^{47} -5.06824e10 q^{48} +1.98837e11 q^{49} -2.58461e11 q^{50} +4.87455e10 q^{51} +1.49243e11 q^{52} +3.49052e10 q^{53} -4.91243e10 q^{54} +2.43943e11 q^{55} +2.11111e10 q^{56} -9.30192e10 q^{57} +5.57419e10 q^{58} -4.21805e10 q^{59} +3.28187e11 q^{60} +4.06898e11 q^{61} +5.70714e10 q^{62} +2.89001e11 q^{63} -5.07924e11 q^{64} +1.08042e12 q^{65} -3.94988e11 q^{66} +1.91805e11 q^{67} +5.27297e11 q^{68} -8.62366e11 q^{69} -3.93645e12 q^{70} -1.26723e12 q^{71} +2.06310e10 q^{72} +7.26492e11 q^{73} +1.86693e12 q^{74} +1.48596e12 q^{75} -1.00622e12 q^{76} +2.32374e12 q^{77} -1.74939e12 q^{78} +1.13147e12 q^{79} -3.96896e12 q^{80} +2.82430e11 q^{81} +1.83137e12 q^{82} +4.87459e12 q^{83} +3.12622e12 q^{84} +3.81728e12 q^{85} +7.83185e11 q^{86} -3.20476e11 q^{87} +1.65886e11 q^{88} +3.48139e12 q^{89} -3.84694e12 q^{90} +1.02918e13 q^{91} -9.32850e12 q^{92} -3.28120e11 q^{93} -1.27779e13 q^{94} -7.28436e12 q^{95} +6.19461e12 q^{96} +1.18763e13 q^{97} -2.52122e13 q^{98} +2.27090e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −126.798 −1.40094 −0.700469 0.713683i \(-0.747026\pi\)
−0.700469 + 0.713683i \(0.747026\pi\)
\(3\) 729.000 0.577350
\(4\) 7885.84 0.962627
\(5\) 57088.2 1.63396 0.816980 0.576666i \(-0.195647\pi\)
0.816980 + 0.576666i \(0.195647\pi\)
\(6\) −92436.0 −0.808832
\(7\) 543807. 1.74706 0.873529 0.486772i \(-0.161826\pi\)
0.873529 + 0.486772i \(0.161826\pi\)
\(8\) 38821.0 0.0523578
\(9\) 531441. 0.333333
\(10\) −7.23869e6 −2.28908
\(11\) 4.27310e6 0.727261 0.363630 0.931543i \(-0.381537\pi\)
0.363630 + 0.931543i \(0.381537\pi\)
\(12\) 5.74878e6 0.555773
\(13\) 1.89254e7 1.08746 0.543730 0.839260i \(-0.317012\pi\)
0.543730 + 0.839260i \(0.317012\pi\)
\(14\) −6.89538e7 −2.44752
\(15\) 4.16173e7 0.943367
\(16\) −6.95232e7 −1.03598
\(17\) 6.68663e7 0.671876 0.335938 0.941884i \(-0.390947\pi\)
0.335938 + 0.941884i \(0.390947\pi\)
\(18\) −6.73859e7 −0.466979
\(19\) −1.27598e8 −0.622224 −0.311112 0.950373i \(-0.600701\pi\)
−0.311112 + 0.950373i \(0.600701\pi\)
\(20\) 4.50188e8 1.57289
\(21\) 3.96435e8 1.00866
\(22\) −5.41822e8 −1.01885
\(23\) −1.18294e9 −1.66622 −0.833112 0.553105i \(-0.813443\pi\)
−0.833112 + 0.553105i \(0.813443\pi\)
\(24\) 2.83005e7 0.0302288
\(25\) 2.03836e9 1.66982
\(26\) −2.39971e9 −1.52346
\(27\) 3.87420e8 0.192450
\(28\) 4.28837e9 1.68176
\(29\) −4.39611e8 −0.137240 −0.0686201 0.997643i \(-0.521860\pi\)
−0.0686201 + 0.997643i \(0.521860\pi\)
\(30\) −5.27701e9 −1.32160
\(31\) −4.50096e8 −0.0910864 −0.0455432 0.998962i \(-0.514502\pi\)
−0.0455432 + 0.998962i \(0.514502\pi\)
\(32\) 8.49741e9 1.39898
\(33\) 3.11509e9 0.419884
\(34\) −8.47854e9 −0.941257
\(35\) 3.10449e10 2.85462
\(36\) 4.19086e9 0.320876
\(37\) −1.47236e10 −0.943414 −0.471707 0.881755i \(-0.656362\pi\)
−0.471707 + 0.881755i \(0.656362\pi\)
\(38\) 1.61793e10 0.871697
\(39\) 1.37966e10 0.627845
\(40\) 2.21622e9 0.0855505
\(41\) −1.44432e10 −0.474863 −0.237431 0.971404i \(-0.576305\pi\)
−0.237431 + 0.971404i \(0.576305\pi\)
\(42\) −5.02673e10 −1.41308
\(43\) −6.17662e9 −0.149007 −0.0745033 0.997221i \(-0.523737\pi\)
−0.0745033 + 0.997221i \(0.523737\pi\)
\(44\) 3.36969e10 0.700080
\(45\) 3.03390e10 0.544653
\(46\) 1.49995e11 2.33427
\(47\) 1.00774e11 1.36367 0.681837 0.731504i \(-0.261181\pi\)
0.681837 + 0.731504i \(0.261181\pi\)
\(48\) −5.06824e10 −0.598121
\(49\) 1.98837e11 2.05221
\(50\) −2.58461e11 −2.33932
\(51\) 4.87455e10 0.387908
\(52\) 1.49243e11 1.04682
\(53\) 3.49052e10 0.216320 0.108160 0.994133i \(-0.465504\pi\)
0.108160 + 0.994133i \(0.465504\pi\)
\(54\) −4.91243e10 −0.269611
\(55\) 2.43943e11 1.18831
\(56\) 2.11111e10 0.0914721
\(57\) −9.30192e10 −0.359241
\(58\) 5.57419e10 0.192265
\(59\) −4.21805e10 −0.130189
\(60\) 3.28187e11 0.908110
\(61\) 4.06898e11 1.01121 0.505605 0.862765i \(-0.331269\pi\)
0.505605 + 0.862765i \(0.331269\pi\)
\(62\) 5.70714e10 0.127606
\(63\) 2.89001e11 0.582353
\(64\) −5.07924e11 −0.923909
\(65\) 1.08042e12 1.77687
\(66\) −3.94988e11 −0.588232
\(67\) 1.91805e11 0.259044 0.129522 0.991577i \(-0.458656\pi\)
0.129522 + 0.991577i \(0.458656\pi\)
\(68\) 5.27297e11 0.646766
\(69\) −8.62366e11 −0.961994
\(70\) −3.93645e12 −3.99915
\(71\) −1.26723e12 −1.17403 −0.587013 0.809578i \(-0.699696\pi\)
−0.587013 + 0.809578i \(0.699696\pi\)
\(72\) 2.06310e10 0.0174526
\(73\) 7.26492e11 0.561865 0.280933 0.959727i \(-0.409356\pi\)
0.280933 + 0.959727i \(0.409356\pi\)
\(74\) 1.86693e12 1.32166
\(75\) 1.48596e12 0.964073
\(76\) −1.00622e12 −0.598970
\(77\) 2.32374e12 1.27057
\(78\) −1.74939e12 −0.879572
\(79\) 1.13147e12 0.523679 0.261839 0.965111i \(-0.415671\pi\)
0.261839 + 0.965111i \(0.415671\pi\)
\(80\) −3.96896e12 −1.69274
\(81\) 2.82430e11 0.111111
\(82\) 1.83137e12 0.665253
\(83\) 4.87459e12 1.63655 0.818277 0.574824i \(-0.194929\pi\)
0.818277 + 0.574824i \(0.194929\pi\)
\(84\) 3.12622e12 0.970967
\(85\) 3.81728e12 1.09782
\(86\) 7.83185e11 0.208749
\(87\) −3.20476e11 −0.0792357
\(88\) 1.65886e11 0.0380778
\(89\) 3.48139e12 0.742536 0.371268 0.928526i \(-0.378923\pi\)
0.371268 + 0.928526i \(0.378923\pi\)
\(90\) −3.84694e12 −0.763025
\(91\) 1.02918e13 1.89986
\(92\) −9.32850e12 −1.60395
\(93\) −3.28120e11 −0.0525888
\(94\) −1.27779e13 −1.91042
\(95\) −7.28436e12 −1.01669
\(96\) 6.19461e12 0.807702
\(97\) 1.18763e13 1.44765 0.723826 0.689983i \(-0.242382\pi\)
0.723826 + 0.689983i \(0.242382\pi\)
\(98\) −2.52122e13 −2.87502
\(99\) 2.27090e12 0.242420
\(100\) 1.60742e13 1.60742
\(101\) −1.57426e13 −1.47567 −0.737834 0.674982i \(-0.764151\pi\)
−0.737834 + 0.674982i \(0.764151\pi\)
\(102\) −6.18086e12 −0.543435
\(103\) 1.25174e12 0.103293 0.0516466 0.998665i \(-0.483553\pi\)
0.0516466 + 0.998665i \(0.483553\pi\)
\(104\) 7.34702e11 0.0569370
\(105\) 2.26318e13 1.64812
\(106\) −4.42593e12 −0.303051
\(107\) −1.64026e13 −1.05662 −0.528308 0.849053i \(-0.677173\pi\)
−0.528308 + 0.849053i \(0.677173\pi\)
\(108\) 3.05513e12 0.185258
\(109\) −2.54712e13 −1.45471 −0.727356 0.686261i \(-0.759251\pi\)
−0.727356 + 0.686261i \(0.759251\pi\)
\(110\) −3.09316e13 −1.66475
\(111\) −1.07335e13 −0.544680
\(112\) −3.78072e13 −1.80991
\(113\) 7.02449e11 0.0317398 0.0158699 0.999874i \(-0.494948\pi\)
0.0158699 + 0.999874i \(0.494948\pi\)
\(114\) 1.17947e13 0.503275
\(115\) −6.75321e13 −2.72254
\(116\) −3.46670e12 −0.132111
\(117\) 1.00577e13 0.362487
\(118\) 5.34842e12 0.182387
\(119\) 3.63623e13 1.17381
\(120\) 1.61562e12 0.0493926
\(121\) −1.62634e13 −0.471092
\(122\) −5.15940e13 −1.41664
\(123\) −1.05291e13 −0.274162
\(124\) −3.54938e12 −0.0876822
\(125\) 4.66785e13 1.09447
\(126\) −3.66449e13 −0.815840
\(127\) −2.17612e13 −0.460213 −0.230107 0.973165i \(-0.573907\pi\)
−0.230107 + 0.973165i \(0.573907\pi\)
\(128\) −5.20682e12 −0.104642
\(129\) −4.50275e12 −0.0860290
\(130\) −1.36995e14 −2.48928
\(131\) 5.05864e13 0.874520 0.437260 0.899335i \(-0.355949\pi\)
0.437260 + 0.899335i \(0.355949\pi\)
\(132\) 2.45651e13 0.404192
\(133\) −6.93889e13 −1.08706
\(134\) −2.43205e13 −0.362904
\(135\) 2.21171e13 0.314456
\(136\) 2.59581e12 0.0351780
\(137\) 9.19406e13 1.18802 0.594010 0.804458i \(-0.297544\pi\)
0.594010 + 0.804458i \(0.297544\pi\)
\(138\) 1.09347e14 1.34769
\(139\) −8.25654e13 −0.970961 −0.485480 0.874248i \(-0.661355\pi\)
−0.485480 + 0.874248i \(0.661355\pi\)
\(140\) 2.44815e14 2.74793
\(141\) 7.34639e13 0.787317
\(142\) 1.60683e14 1.64474
\(143\) 8.08700e13 0.790867
\(144\) −3.69475e13 −0.345326
\(145\) −2.50966e13 −0.224245
\(146\) −9.21180e13 −0.787138
\(147\) 1.44952e14 1.18484
\(148\) −1.16108e14 −0.908156
\(149\) −1.15044e14 −0.861301 −0.430650 0.902519i \(-0.641716\pi\)
−0.430650 + 0.902519i \(0.641716\pi\)
\(150\) −1.88418e14 −1.35061
\(151\) 2.30382e14 1.58161 0.790805 0.612069i \(-0.209662\pi\)
0.790805 + 0.612069i \(0.209662\pi\)
\(152\) −4.95349e12 −0.0325783
\(153\) 3.55355e13 0.223959
\(154\) −2.94646e14 −1.77998
\(155\) −2.56951e13 −0.148832
\(156\) 1.08798e14 0.604381
\(157\) −2.00111e14 −1.06641 −0.533204 0.845987i \(-0.679012\pi\)
−0.533204 + 0.845987i \(0.679012\pi\)
\(158\) −1.43468e14 −0.733642
\(159\) 2.54459e13 0.124893
\(160\) 4.85102e14 2.28588
\(161\) −6.43293e14 −2.91099
\(162\) −3.58116e13 −0.155660
\(163\) −2.91103e14 −1.21570 −0.607852 0.794050i \(-0.707969\pi\)
−0.607852 + 0.794050i \(0.707969\pi\)
\(164\) −1.13897e14 −0.457115
\(165\) 1.77835e14 0.686074
\(166\) −6.18090e14 −2.29271
\(167\) 1.80557e14 0.644106 0.322053 0.946722i \(-0.395627\pi\)
0.322053 + 0.946722i \(0.395627\pi\)
\(168\) 1.53900e13 0.0528114
\(169\) 5.52956e13 0.182569
\(170\) −4.84025e14 −1.53798
\(171\) −6.78110e13 −0.207408
\(172\) −4.87078e13 −0.143438
\(173\) 4.92993e14 1.39811 0.699054 0.715069i \(-0.253605\pi\)
0.699054 + 0.715069i \(0.253605\pi\)
\(174\) 4.06359e13 0.111004
\(175\) 1.10847e15 2.91728
\(176\) −2.97079e14 −0.753425
\(177\) −3.07496e13 −0.0751646
\(178\) −4.41435e14 −1.04025
\(179\) 4.21410e14 0.957548 0.478774 0.877938i \(-0.341081\pi\)
0.478774 + 0.877938i \(0.341081\pi\)
\(180\) 2.39248e14 0.524298
\(181\) 4.22654e14 0.893459 0.446729 0.894669i \(-0.352589\pi\)
0.446729 + 0.894669i \(0.352589\pi\)
\(182\) −1.30498e15 −2.66158
\(183\) 2.96628e14 0.583822
\(184\) −4.59230e13 −0.0872398
\(185\) −8.40543e14 −1.54150
\(186\) 4.16051e13 0.0736736
\(187\) 2.85726e14 0.488629
\(188\) 7.94684e14 1.31271
\(189\) 2.10682e14 0.336221
\(190\) 9.23646e14 1.42432
\(191\) 1.04831e15 1.56233 0.781163 0.624327i \(-0.214627\pi\)
0.781163 + 0.624327i \(0.214627\pi\)
\(192\) −3.70277e14 −0.533419
\(193\) −2.77452e14 −0.386425 −0.193213 0.981157i \(-0.561891\pi\)
−0.193213 + 0.981157i \(0.561891\pi\)
\(194\) −1.50589e15 −2.02807
\(195\) 7.87624e14 1.02587
\(196\) 1.56799e15 1.97551
\(197\) 1.09387e14 0.133333 0.0666664 0.997775i \(-0.478764\pi\)
0.0666664 + 0.997775i \(0.478764\pi\)
\(198\) −2.87946e14 −0.339616
\(199\) 9.79714e14 1.11829 0.559145 0.829070i \(-0.311129\pi\)
0.559145 + 0.829070i \(0.311129\pi\)
\(200\) 7.91311e13 0.0874283
\(201\) 1.39826e14 0.149559
\(202\) 1.99614e15 2.06732
\(203\) −2.39063e14 −0.239767
\(204\) 3.84399e14 0.373411
\(205\) −8.24536e14 −0.775906
\(206\) −1.58718e14 −0.144707
\(207\) −6.28665e14 −0.555408
\(208\) −1.31575e15 −1.12658
\(209\) −5.45240e14 −0.452519
\(210\) −2.86967e15 −2.30891
\(211\) 2.38723e14 0.186234 0.0931168 0.995655i \(-0.470317\pi\)
0.0931168 + 0.995655i \(0.470317\pi\)
\(212\) 2.75257e14 0.208236
\(213\) −9.23813e14 −0.677824
\(214\) 2.07982e15 1.48025
\(215\) −3.52612e14 −0.243471
\(216\) 1.50400e13 0.0100763
\(217\) −2.44765e14 −0.159133
\(218\) 3.22971e15 2.03796
\(219\) 5.29613e14 0.324393
\(220\) 1.92370e15 1.14390
\(221\) 1.26547e15 0.730639
\(222\) 1.36099e15 0.763063
\(223\) 1.03581e15 0.564024 0.282012 0.959411i \(-0.408998\pi\)
0.282012 + 0.959411i \(0.408998\pi\)
\(224\) 4.62095e15 2.44410
\(225\) 1.08327e15 0.556608
\(226\) −8.90694e13 −0.0444655
\(227\) 2.68518e15 1.30258 0.651290 0.758829i \(-0.274228\pi\)
0.651290 + 0.758829i \(0.274228\pi\)
\(228\) −7.33535e14 −0.345815
\(229\) −1.19812e15 −0.548995 −0.274497 0.961588i \(-0.588512\pi\)
−0.274497 + 0.961588i \(0.588512\pi\)
\(230\) 8.56297e15 3.81411
\(231\) 1.69400e15 0.733562
\(232\) −1.70661e13 −0.00718559
\(233\) −3.97777e15 −1.62865 −0.814323 0.580412i \(-0.802892\pi\)
−0.814323 + 0.580412i \(0.802892\pi\)
\(234\) −1.27530e15 −0.507821
\(235\) 5.75298e15 2.22819
\(236\) −3.32629e14 −0.125323
\(237\) 8.24838e14 0.302346
\(238\) −4.61069e15 −1.64443
\(239\) 4.96261e15 1.72236 0.861179 0.508302i \(-0.169727\pi\)
0.861179 + 0.508302i \(0.169727\pi\)
\(240\) −2.89337e15 −0.977306
\(241\) 1.37022e15 0.450484 0.225242 0.974303i \(-0.427683\pi\)
0.225242 + 0.974303i \(0.427683\pi\)
\(242\) 2.06217e15 0.659970
\(243\) 2.05891e14 0.0641500
\(244\) 3.20873e15 0.973417
\(245\) 1.13512e16 3.35323
\(246\) 1.33507e15 0.384084
\(247\) −2.41485e15 −0.676644
\(248\) −1.74731e13 −0.00476908
\(249\) 3.55358e15 0.944865
\(250\) −5.91876e15 −1.53328
\(251\) −2.25218e15 −0.568491 −0.284246 0.958752i \(-0.591743\pi\)
−0.284246 + 0.958752i \(0.591743\pi\)
\(252\) 2.27902e15 0.560588
\(253\) −5.05483e15 −1.21178
\(254\) 2.75929e15 0.644730
\(255\) 2.78280e15 0.633826
\(256\) 4.82113e15 1.07051
\(257\) −6.59299e15 −1.42731 −0.713653 0.700499i \(-0.752961\pi\)
−0.713653 + 0.700499i \(0.752961\pi\)
\(258\) 5.70942e14 0.120521
\(259\) −8.00678e15 −1.64820
\(260\) 8.51999e15 1.71046
\(261\) −2.33627e14 −0.0457467
\(262\) −6.41427e15 −1.22515
\(263\) −5.78677e15 −1.07826 −0.539131 0.842222i \(-0.681247\pi\)
−0.539131 + 0.842222i \(0.681247\pi\)
\(264\) 1.20931e14 0.0219842
\(265\) 1.99268e15 0.353459
\(266\) 8.79840e15 1.52291
\(267\) 2.53793e15 0.428703
\(268\) 1.51254e15 0.249362
\(269\) 1.19272e16 1.91933 0.959664 0.281148i \(-0.0907153\pi\)
0.959664 + 0.281148i \(0.0907153\pi\)
\(270\) −2.80442e15 −0.440533
\(271\) 5.02154e15 0.770081 0.385040 0.922900i \(-0.374187\pi\)
0.385040 + 0.922900i \(0.374187\pi\)
\(272\) −4.64876e15 −0.696048
\(273\) 7.50269e15 1.09688
\(274\) −1.16579e16 −1.66434
\(275\) 8.71010e15 1.21440
\(276\) −6.80048e15 −0.926041
\(277\) −1.26988e16 −1.68906 −0.844530 0.535508i \(-0.820120\pi\)
−0.844530 + 0.535508i \(0.820120\pi\)
\(278\) 1.04692e16 1.36026
\(279\) −2.39199e14 −0.0303621
\(280\) 1.20519e15 0.149462
\(281\) 1.22023e16 1.47860 0.739302 0.673374i \(-0.235156\pi\)
0.739302 + 0.673374i \(0.235156\pi\)
\(282\) −9.31510e15 −1.10298
\(283\) −6.35053e15 −0.734849 −0.367424 0.930053i \(-0.619760\pi\)
−0.367424 + 0.930053i \(0.619760\pi\)
\(284\) −9.99320e15 −1.13015
\(285\) −5.31030e15 −0.586986
\(286\) −1.02542e16 −1.10796
\(287\) −7.85430e15 −0.829612
\(288\) 4.51587e15 0.466327
\(289\) −5.43347e15 −0.548582
\(290\) 3.18221e15 0.314153
\(291\) 8.65781e15 0.835802
\(292\) 5.72900e15 0.540867
\(293\) 4.85848e15 0.448601 0.224301 0.974520i \(-0.427990\pi\)
0.224301 + 0.974520i \(0.427990\pi\)
\(294\) −1.83797e16 −1.65989
\(295\) −2.40801e15 −0.212723
\(296\) −5.71584e14 −0.0493951
\(297\) 1.65548e15 0.139961
\(298\) 1.45874e16 1.20663
\(299\) −2.23877e16 −1.81195
\(300\) 1.17181e16 0.928043
\(301\) −3.35888e15 −0.260323
\(302\) −2.92121e16 −2.21574
\(303\) −1.14764e16 −0.851977
\(304\) 8.87105e15 0.644610
\(305\) 2.32290e16 1.65228
\(306\) −4.50584e15 −0.313752
\(307\) −1.26430e16 −0.861888 −0.430944 0.902379i \(-0.641819\pi\)
−0.430944 + 0.902379i \(0.641819\pi\)
\(308\) 1.83246e16 1.22308
\(309\) 9.12517e14 0.0596363
\(310\) 3.25810e15 0.208504
\(311\) −2.08567e16 −1.30708 −0.653541 0.756891i \(-0.726717\pi\)
−0.653541 + 0.756891i \(0.726717\pi\)
\(312\) 5.35598e14 0.0328726
\(313\) 2.10378e16 1.26463 0.632314 0.774712i \(-0.282105\pi\)
0.632314 + 0.774712i \(0.282105\pi\)
\(314\) 2.53738e16 1.49397
\(315\) 1.64986e16 0.951541
\(316\) 8.92255e15 0.504107
\(317\) 1.96726e15 0.108887 0.0544437 0.998517i \(-0.482661\pi\)
0.0544437 + 0.998517i \(0.482661\pi\)
\(318\) −3.22650e15 −0.174967
\(319\) −1.87850e15 −0.0998094
\(320\) −2.89965e16 −1.50963
\(321\) −1.19575e16 −0.610037
\(322\) 8.15685e16 4.07811
\(323\) −8.53204e15 −0.418058
\(324\) 2.22719e15 0.106959
\(325\) 3.85768e16 1.81587
\(326\) 3.69115e16 1.70313
\(327\) −1.85685e16 −0.839878
\(328\) −5.60698e14 −0.0248628
\(329\) 5.48013e16 2.38242
\(330\) −2.25492e16 −0.961147
\(331\) −1.13113e16 −0.472748 −0.236374 0.971662i \(-0.575959\pi\)
−0.236374 + 0.971662i \(0.575959\pi\)
\(332\) 3.84402e16 1.57539
\(333\) −7.82472e15 −0.314471
\(334\) −2.28943e16 −0.902352
\(335\) 1.09498e16 0.423267
\(336\) −2.75614e16 −1.04495
\(337\) −3.98649e16 −1.48251 −0.741253 0.671225i \(-0.765768\pi\)
−0.741253 + 0.671225i \(0.765768\pi\)
\(338\) −7.01139e15 −0.255768
\(339\) 5.12085e14 0.0183250
\(340\) 3.01024e16 1.05679
\(341\) −1.92330e15 −0.0662436
\(342\) 8.59833e15 0.290566
\(343\) 5.54398e16 1.83827
\(344\) −2.39782e14 −0.00780166
\(345\) −4.92309e16 −1.57186
\(346\) −6.25107e16 −1.95866
\(347\) −2.60771e16 −0.801894 −0.400947 0.916101i \(-0.631319\pi\)
−0.400947 + 0.916101i \(0.631319\pi\)
\(348\) −2.52722e15 −0.0762743
\(349\) −5.55368e16 −1.64519 −0.822594 0.568629i \(-0.807474\pi\)
−0.822594 + 0.568629i \(0.807474\pi\)
\(350\) −1.40553e17 −4.08693
\(351\) 7.33209e15 0.209282
\(352\) 3.63102e16 1.01742
\(353\) 3.77223e16 1.03768 0.518838 0.854872i \(-0.326365\pi\)
0.518838 + 0.854872i \(0.326365\pi\)
\(354\) 3.89900e15 0.105301
\(355\) −7.23441e16 −1.91831
\(356\) 2.74537e16 0.714785
\(357\) 2.65081e16 0.677698
\(358\) −5.34342e16 −1.34147
\(359\) 3.81306e16 0.940069 0.470035 0.882648i \(-0.344241\pi\)
0.470035 + 0.882648i \(0.344241\pi\)
\(360\) 1.17779e15 0.0285168
\(361\) −2.57716e16 −0.612837
\(362\) −5.35919e16 −1.25168
\(363\) −1.18560e16 −0.271985
\(364\) 8.11591e16 1.82885
\(365\) 4.14741e16 0.918065
\(366\) −3.76120e16 −0.817898
\(367\) 1.07064e16 0.228725 0.114363 0.993439i \(-0.463517\pi\)
0.114363 + 0.993439i \(0.463517\pi\)
\(368\) 8.22420e16 1.72617
\(369\) −7.67570e15 −0.158288
\(370\) 1.06580e17 2.15955
\(371\) 1.89817e16 0.377924
\(372\) −2.58750e15 −0.0506234
\(373\) −9.62522e16 −1.85056 −0.925280 0.379285i \(-0.876170\pi\)
−0.925280 + 0.379285i \(0.876170\pi\)
\(374\) −3.62296e16 −0.684539
\(375\) 3.40286e16 0.631890
\(376\) 3.91212e15 0.0713989
\(377\) −8.31981e15 −0.149243
\(378\) −2.67141e16 −0.471025
\(379\) −6.96076e16 −1.20643 −0.603215 0.797579i \(-0.706114\pi\)
−0.603215 + 0.797579i \(0.706114\pi\)
\(380\) −5.74433e16 −0.978692
\(381\) −1.58639e16 −0.265704
\(382\) −1.32924e17 −2.18872
\(383\) 1.73851e15 0.0281439 0.0140720 0.999901i \(-0.495521\pi\)
0.0140720 + 0.999901i \(0.495521\pi\)
\(384\) −3.79577e15 −0.0604153
\(385\) 1.32658e17 2.07605
\(386\) 3.51805e16 0.541358
\(387\) −3.28251e15 −0.0496689
\(388\) 9.36544e16 1.39355
\(389\) −8.31322e16 −1.21646 −0.608228 0.793762i \(-0.708119\pi\)
−0.608228 + 0.793762i \(0.708119\pi\)
\(390\) −9.98695e16 −1.43719
\(391\) −7.90991e16 −1.11950
\(392\) 7.71903e15 0.107449
\(393\) 3.68775e16 0.504905
\(394\) −1.38702e16 −0.186791
\(395\) 6.45933e16 0.855670
\(396\) 1.79079e16 0.233360
\(397\) −9.57949e16 −1.22802 −0.614008 0.789300i \(-0.710444\pi\)
−0.614008 + 0.789300i \(0.710444\pi\)
\(398\) −1.24226e17 −1.56665
\(399\) −5.05845e16 −0.627615
\(400\) −1.41713e17 −1.72990
\(401\) 1.00372e17 1.20552 0.602761 0.797922i \(-0.294067\pi\)
0.602761 + 0.797922i \(0.294067\pi\)
\(402\) −1.77297e16 −0.209523
\(403\) −8.51824e15 −0.0990528
\(404\) −1.24144e17 −1.42052
\(405\) 1.61234e16 0.181551
\(406\) 3.03128e16 0.335898
\(407\) −6.29153e16 −0.686108
\(408\) 1.89235e15 0.0203100
\(409\) −1.05825e17 −1.11786 −0.558928 0.829216i \(-0.688787\pi\)
−0.558928 + 0.829216i \(0.688787\pi\)
\(410\) 1.04550e17 1.08700
\(411\) 6.70247e16 0.685904
\(412\) 9.87100e15 0.0994327
\(413\) −2.29381e16 −0.227448
\(414\) 7.97137e16 0.778092
\(415\) 2.78282e17 2.67406
\(416\) 1.60817e17 1.52134
\(417\) −6.01902e16 −0.560585
\(418\) 6.91356e16 0.633951
\(419\) 2.06263e17 1.86222 0.931108 0.364745i \(-0.118844\pi\)
0.931108 + 0.364745i \(0.118844\pi\)
\(420\) 1.78470e17 1.58652
\(421\) 1.85110e17 1.62031 0.810153 0.586218i \(-0.199384\pi\)
0.810153 + 0.586218i \(0.199384\pi\)
\(422\) −3.02697e16 −0.260902
\(423\) 5.35552e16 0.454558
\(424\) 1.35505e15 0.0113261
\(425\) 1.36298e17 1.12192
\(426\) 1.17138e17 0.949589
\(427\) 2.21274e17 1.76664
\(428\) −1.29348e17 −1.01713
\(429\) 5.89542e16 0.456607
\(430\) 4.47106e16 0.341088
\(431\) 9.02699e16 0.678329 0.339165 0.940727i \(-0.389856\pi\)
0.339165 + 0.940727i \(0.389856\pi\)
\(432\) −2.69347e16 −0.199374
\(433\) 5.35452e16 0.390436 0.195218 0.980760i \(-0.437459\pi\)
0.195218 + 0.980760i \(0.437459\pi\)
\(434\) 3.10358e16 0.222936
\(435\) −1.82954e16 −0.129468
\(436\) −2.00862e17 −1.40034
\(437\) 1.50942e17 1.03676
\(438\) −6.71540e16 −0.454455
\(439\) 5.80855e16 0.387300 0.193650 0.981071i \(-0.437967\pi\)
0.193650 + 0.981071i \(0.437967\pi\)
\(440\) 9.47011e15 0.0622175
\(441\) 1.05670e17 0.684070
\(442\) −1.60460e17 −1.02358
\(443\) −4.83363e16 −0.303843 −0.151921 0.988393i \(-0.548546\pi\)
−0.151921 + 0.988393i \(0.548546\pi\)
\(444\) −8.46426e16 −0.524324
\(445\) 1.98746e17 1.21327
\(446\) −1.31339e17 −0.790163
\(447\) −8.38674e16 −0.497272
\(448\) −2.76213e17 −1.61412
\(449\) −1.25262e17 −0.721470 −0.360735 0.932668i \(-0.617474\pi\)
−0.360735 + 0.932668i \(0.617474\pi\)
\(450\) −1.37357e17 −0.779773
\(451\) −6.17171e16 −0.345349
\(452\) 5.53940e15 0.0305536
\(453\) 1.67949e17 0.913143
\(454\) −3.40476e17 −1.82483
\(455\) 5.87538e17 3.10429
\(456\) −3.61110e15 −0.0188091
\(457\) −1.02986e17 −0.528839 −0.264420 0.964408i \(-0.585180\pi\)
−0.264420 + 0.964408i \(0.585180\pi\)
\(458\) 1.51919e17 0.769108
\(459\) 2.59054e16 0.129303
\(460\) −5.32547e17 −2.62079
\(461\) 1.65942e17 0.805194 0.402597 0.915377i \(-0.368108\pi\)
0.402597 + 0.915377i \(0.368108\pi\)
\(462\) −2.14797e17 −1.02767
\(463\) −8.22815e16 −0.388173 −0.194087 0.980984i \(-0.562174\pi\)
−0.194087 + 0.980984i \(0.562174\pi\)
\(464\) 3.05631e16 0.142178
\(465\) −1.87318e16 −0.0859279
\(466\) 5.04376e17 2.28163
\(467\) −2.57308e17 −1.14787 −0.573935 0.818901i \(-0.694584\pi\)
−0.573935 + 0.818901i \(0.694584\pi\)
\(468\) 7.93136e16 0.348939
\(469\) 1.04305e17 0.452564
\(470\) −7.29469e17 −3.12155
\(471\) −1.45881e17 −0.615691
\(472\) −1.63749e15 −0.00681640
\(473\) −2.63933e16 −0.108367
\(474\) −1.04588e17 −0.423568
\(475\) −2.60091e17 −1.03900
\(476\) 2.86748e17 1.12994
\(477\) 1.85501e16 0.0721068
\(478\) −6.29251e17 −2.41292
\(479\) −3.59462e17 −1.35979 −0.679895 0.733309i \(-0.737975\pi\)
−0.679895 + 0.733309i \(0.737975\pi\)
\(480\) 3.53639e17 1.31975
\(481\) −2.78650e17 −1.02593
\(482\) −1.73742e17 −0.631100
\(483\) −4.68960e17 −1.68066
\(484\) −1.28250e17 −0.453486
\(485\) 6.77995e17 2.36540
\(486\) −2.61067e16 −0.0898702
\(487\) −2.15348e17 −0.731481 −0.365741 0.930717i \(-0.619184\pi\)
−0.365741 + 0.930717i \(0.619184\pi\)
\(488\) 1.57962e16 0.0529447
\(489\) −2.12214e17 −0.701887
\(490\) −1.43932e18 −4.69767
\(491\) 3.08298e17 0.992981 0.496491 0.868042i \(-0.334622\pi\)
0.496491 + 0.868042i \(0.334622\pi\)
\(492\) −8.30306e16 −0.263916
\(493\) −2.93951e16 −0.0922084
\(494\) 3.06199e17 0.947936
\(495\) 1.29641e17 0.396105
\(496\) 3.12921e16 0.0943634
\(497\) −6.89130e17 −2.05109
\(498\) −4.50588e17 −1.32370
\(499\) −4.63642e17 −1.34440 −0.672200 0.740369i \(-0.734651\pi\)
−0.672200 + 0.740369i \(0.734651\pi\)
\(500\) 3.68099e17 1.05356
\(501\) 1.31626e17 0.371875
\(502\) 2.85573e17 0.796421
\(503\) 2.03093e17 0.559117 0.279558 0.960129i \(-0.409812\pi\)
0.279558 + 0.960129i \(0.409812\pi\)
\(504\) 1.12193e16 0.0304907
\(505\) −8.98719e17 −2.41118
\(506\) 6.40945e17 1.69763
\(507\) 4.03105e16 0.105406
\(508\) −1.71605e17 −0.443013
\(509\) 6.29871e16 0.160541 0.0802705 0.996773i \(-0.474422\pi\)
0.0802705 + 0.996773i \(0.474422\pi\)
\(510\) −3.52854e17 −0.887951
\(511\) 3.95071e17 0.981611
\(512\) −5.68658e17 −1.39507
\(513\) −4.94342e16 −0.119747
\(514\) 8.35981e17 1.99957
\(515\) 7.14595e16 0.168777
\(516\) −3.55080e16 −0.0828138
\(517\) 4.30615e17 0.991746
\(518\) 1.01525e18 2.30902
\(519\) 3.59392e17 0.807198
\(520\) 4.19428e16 0.0930327
\(521\) 3.40065e17 0.744932 0.372466 0.928046i \(-0.378512\pi\)
0.372466 + 0.928046i \(0.378512\pi\)
\(522\) 2.96236e16 0.0640883
\(523\) −6.59434e16 −0.140900 −0.0704499 0.997515i \(-0.522443\pi\)
−0.0704499 + 0.997515i \(0.522443\pi\)
\(524\) 3.98916e17 0.841837
\(525\) 8.08077e17 1.68429
\(526\) 7.33753e17 1.51058
\(527\) −3.00962e16 −0.0611988
\(528\) −2.16571e17 −0.434990
\(529\) 8.95319e17 1.77630
\(530\) −2.52668e17 −0.495174
\(531\) −2.24165e16 −0.0433963
\(532\) −5.47189e17 −1.04643
\(533\) −2.73343e17 −0.516394
\(534\) −3.21806e17 −0.600587
\(535\) −9.36393e17 −1.72647
\(536\) 7.44604e15 0.0135629
\(537\) 3.07208e17 0.552841
\(538\) −1.51235e18 −2.68886
\(539\) 8.49648e17 1.49249
\(540\) 1.74412e17 0.302703
\(541\) −5.08956e17 −0.872767 −0.436383 0.899761i \(-0.643741\pi\)
−0.436383 + 0.899761i \(0.643741\pi\)
\(542\) −6.36723e17 −1.07884
\(543\) 3.08115e17 0.515839
\(544\) 5.68191e17 0.939942
\(545\) −1.45410e18 −2.37694
\(546\) −9.51329e17 −1.53666
\(547\) 7.78960e17 1.24336 0.621681 0.783271i \(-0.286450\pi\)
0.621681 + 0.783271i \(0.286450\pi\)
\(548\) 7.25029e17 1.14362
\(549\) 2.16242e17 0.337070
\(550\) −1.10443e18 −1.70130
\(551\) 5.60936e16 0.0853942
\(552\) −3.34779e16 −0.0503679
\(553\) 6.15298e17 0.914897
\(554\) 1.61019e18 2.36627
\(555\) −6.12756e17 −0.889986
\(556\) −6.51097e17 −0.934673
\(557\) −1.22662e18 −1.74040 −0.870201 0.492696i \(-0.836011\pi\)
−0.870201 + 0.492696i \(0.836011\pi\)
\(558\) 3.03301e16 0.0425355
\(559\) −1.16895e17 −0.162039
\(560\) −2.15834e18 −2.95732
\(561\) 2.08294e17 0.282110
\(562\) −1.54724e18 −2.07143
\(563\) −1.24151e18 −1.64303 −0.821515 0.570187i \(-0.806871\pi\)
−0.821515 + 0.570187i \(0.806871\pi\)
\(564\) 5.79324e17 0.757892
\(565\) 4.01015e16 0.0518616
\(566\) 8.05237e17 1.02948
\(567\) 1.53587e17 0.194118
\(568\) −4.91952e16 −0.0614694
\(569\) −8.02977e17 −0.991913 −0.495956 0.868347i \(-0.665182\pi\)
−0.495956 + 0.868347i \(0.665182\pi\)
\(570\) 6.73338e17 0.822331
\(571\) 1.26137e18 1.52303 0.761517 0.648145i \(-0.224455\pi\)
0.761517 + 0.648145i \(0.224455\pi\)
\(572\) 6.37728e17 0.761309
\(573\) 7.64216e17 0.902010
\(574\) 9.95913e17 1.16224
\(575\) −2.41126e18 −2.78230
\(576\) −2.69932e17 −0.307970
\(577\) −2.66138e17 −0.300237 −0.150118 0.988668i \(-0.547965\pi\)
−0.150118 + 0.988668i \(0.547965\pi\)
\(578\) 6.88956e17 0.768529
\(579\) −2.02263e17 −0.223103
\(580\) −1.97908e17 −0.215864
\(581\) 2.65083e18 2.85916
\(582\) −1.09780e18 −1.17091
\(583\) 1.49153e17 0.157321
\(584\) 2.82031e16 0.0294180
\(585\) 5.74178e17 0.592288
\(586\) −6.16047e17 −0.628462
\(587\) −5.96616e15 −0.00601932 −0.00300966 0.999995i \(-0.500958\pi\)
−0.00300966 + 0.999995i \(0.500958\pi\)
\(588\) 1.14307e18 1.14056
\(589\) 5.74315e16 0.0566762
\(590\) 3.05332e17 0.298012
\(591\) 7.97435e16 0.0769798
\(592\) 1.02363e18 0.977355
\(593\) −2.05384e17 −0.193959 −0.0969796 0.995286i \(-0.530918\pi\)
−0.0969796 + 0.995286i \(0.530918\pi\)
\(594\) −2.09913e17 −0.196077
\(595\) 2.07586e18 1.91795
\(596\) −9.07221e17 −0.829111
\(597\) 7.14212e17 0.645645
\(598\) 2.83872e18 2.53843
\(599\) 1.54318e18 1.36503 0.682514 0.730873i \(-0.260887\pi\)
0.682514 + 0.730873i \(0.260887\pi\)
\(600\) 5.76865e16 0.0504767
\(601\) −1.24282e18 −1.07578 −0.537890 0.843015i \(-0.680778\pi\)
−0.537890 + 0.843015i \(0.680778\pi\)
\(602\) 4.25901e17 0.364697
\(603\) 1.01933e17 0.0863478
\(604\) 1.81676e18 1.52250
\(605\) −9.28447e17 −0.769745
\(606\) 1.45519e18 1.19357
\(607\) −1.15880e18 −0.940331 −0.470166 0.882578i \(-0.655806\pi\)
−0.470166 + 0.882578i \(0.655806\pi\)
\(608\) −1.08426e18 −0.870480
\(609\) −1.74277e17 −0.138429
\(610\) −2.94541e18 −2.31474
\(611\) 1.90718e18 1.48294
\(612\) 2.80227e17 0.215589
\(613\) 1.10886e18 0.844083 0.422042 0.906576i \(-0.361314\pi\)
0.422042 + 0.906576i \(0.361314\pi\)
\(614\) 1.60311e18 1.20745
\(615\) −6.01086e17 −0.447970
\(616\) 9.02097e16 0.0665240
\(617\) 2.55361e18 1.86338 0.931689 0.363256i \(-0.118335\pi\)
0.931689 + 0.363256i \(0.118335\pi\)
\(618\) −1.15706e17 −0.0835468
\(619\) −2.51856e18 −1.79955 −0.899775 0.436355i \(-0.856269\pi\)
−0.899775 + 0.436355i \(0.856269\pi\)
\(620\) −2.02628e17 −0.143269
\(621\) −4.58297e17 −0.320665
\(622\) 2.64459e18 1.83114
\(623\) 1.89320e18 1.29725
\(624\) −9.59185e17 −0.650433
\(625\) 1.76561e17 0.118488
\(626\) −2.66756e18 −1.77166
\(627\) −3.97480e17 −0.261262
\(628\) −1.57804e18 −1.02655
\(629\) −9.84512e17 −0.633858
\(630\) −2.09199e18 −1.33305
\(631\) 2.66852e18 1.68298 0.841490 0.540272i \(-0.181679\pi\)
0.841490 + 0.540272i \(0.181679\pi\)
\(632\) 4.39246e16 0.0274187
\(633\) 1.74029e17 0.107522
\(634\) −2.49446e17 −0.152544
\(635\) −1.24231e18 −0.751970
\(636\) 2.00662e17 0.120225
\(637\) 3.76306e18 2.23170
\(638\) 2.38191e17 0.139827
\(639\) −6.73460e17 −0.391342
\(640\) −2.97248e17 −0.170982
\(641\) 3.06517e18 1.74533 0.872665 0.488319i \(-0.162390\pi\)
0.872665 + 0.488319i \(0.162390\pi\)
\(642\) 1.51619e18 0.854624
\(643\) −9.10555e17 −0.508083 −0.254042 0.967193i \(-0.581760\pi\)
−0.254042 + 0.967193i \(0.581760\pi\)
\(644\) −5.07290e18 −2.80219
\(645\) −2.57054e17 −0.140568
\(646\) 1.08185e18 0.585673
\(647\) −1.71798e18 −0.920749 −0.460375 0.887725i \(-0.652285\pi\)
−0.460375 + 0.887725i \(0.652285\pi\)
\(648\) 1.09642e16 0.00581753
\(649\) −1.80241e17 −0.0946813
\(650\) −4.89147e18 −2.54392
\(651\) −1.78434e17 −0.0918756
\(652\) −2.29559e18 −1.17027
\(653\) −2.37148e18 −1.19697 −0.598487 0.801133i \(-0.704231\pi\)
−0.598487 + 0.801133i \(0.704231\pi\)
\(654\) 2.35446e18 1.17662
\(655\) 2.88788e18 1.42893
\(656\) 1.00414e18 0.491947
\(657\) 3.86088e17 0.187288
\(658\) −6.94872e18 −3.33762
\(659\) −1.83481e18 −0.872639 −0.436320 0.899792i \(-0.643718\pi\)
−0.436320 + 0.899792i \(0.643718\pi\)
\(660\) 1.40238e18 0.660433
\(661\) −2.23094e18 −1.04035 −0.520174 0.854060i \(-0.674133\pi\)
−0.520174 + 0.854060i \(0.674133\pi\)
\(662\) 1.43425e18 0.662290
\(663\) 9.22529e17 0.421834
\(664\) 1.89236e17 0.0856864
\(665\) −3.96129e18 −1.77621
\(666\) 9.92162e17 0.440555
\(667\) 5.20035e17 0.228673
\(668\) 1.42384e18 0.620034
\(669\) 7.55104e17 0.325640
\(670\) −1.38841e18 −0.592970
\(671\) 1.73871e18 0.735413
\(672\) 3.36867e18 1.41110
\(673\) 2.05076e18 0.850781 0.425390 0.905010i \(-0.360137\pi\)
0.425390 + 0.905010i \(0.360137\pi\)
\(674\) 5.05481e18 2.07690
\(675\) 7.89702e17 0.321358
\(676\) 4.36052e17 0.175746
\(677\) 1.55946e18 0.622511 0.311255 0.950326i \(-0.399251\pi\)
0.311255 + 0.950326i \(0.399251\pi\)
\(678\) −6.49316e16 −0.0256722
\(679\) 6.45840e18 2.52913
\(680\) 1.48190e17 0.0574794
\(681\) 1.95749e18 0.752045
\(682\) 2.43872e17 0.0928031
\(683\) 9.55275e17 0.360076 0.180038 0.983660i \(-0.442378\pi\)
0.180038 + 0.983660i \(0.442378\pi\)
\(684\) −5.34747e17 −0.199657
\(685\) 5.24873e18 1.94118
\(686\) −7.02968e18 −2.57531
\(687\) −8.73427e17 −0.316962
\(688\) 4.29418e17 0.154367
\(689\) 6.60595e17 0.235240
\(690\) 6.24240e18 2.20208
\(691\) −3.41134e18 −1.19212 −0.596058 0.802942i \(-0.703267\pi\)
−0.596058 + 0.802942i \(0.703267\pi\)
\(692\) 3.88766e18 1.34586
\(693\) 1.23493e18 0.423522
\(694\) 3.30653e18 1.12340
\(695\) −4.71351e18 −1.58651
\(696\) −1.24412e16 −0.00414860
\(697\) −9.65763e17 −0.319049
\(698\) 7.04198e18 2.30481
\(699\) −2.89980e18 −0.940299
\(700\) 8.74124e18 2.80825
\(701\) −9.69972e17 −0.308740 −0.154370 0.988013i \(-0.549335\pi\)
−0.154370 + 0.988013i \(0.549335\pi\)
\(702\) −9.29697e17 −0.293191
\(703\) 1.87871e18 0.587015
\(704\) −2.17041e18 −0.671922
\(705\) 4.19392e18 1.28644
\(706\) −4.78312e18 −1.45372
\(707\) −8.56095e18 −2.57808
\(708\) −2.42486e17 −0.0723554
\(709\) −1.85546e18 −0.548595 −0.274297 0.961645i \(-0.588445\pi\)
−0.274297 + 0.961645i \(0.588445\pi\)
\(710\) 9.17312e18 2.68743
\(711\) 6.01307e17 0.174560
\(712\) 1.35151e17 0.0388775
\(713\) 5.32438e17 0.151770
\(714\) −3.36119e18 −0.949412
\(715\) 4.61672e18 1.29224
\(716\) 3.32317e18 0.921761
\(717\) 3.61774e18 0.994404
\(718\) −4.83490e18 −1.31698
\(719\) −5.00313e17 −0.135053 −0.0675264 0.997717i \(-0.521511\pi\)
−0.0675264 + 0.997717i \(0.521511\pi\)
\(720\) −2.10927e18 −0.564248
\(721\) 6.80703e17 0.180459
\(722\) 3.26780e18 0.858547
\(723\) 9.98891e17 0.260087
\(724\) 3.33298e18 0.860067
\(725\) −8.96085e17 −0.229167
\(726\) 1.50332e18 0.381034
\(727\) 3.88274e18 0.975359 0.487679 0.873023i \(-0.337843\pi\)
0.487679 + 0.873023i \(0.337843\pi\)
\(728\) 3.99536e17 0.0994722
\(729\) 1.50095e17 0.0370370
\(730\) −5.25885e18 −1.28615
\(731\) −4.13008e17 −0.100114
\(732\) 2.33916e18 0.562003
\(733\) 2.86795e18 0.682961 0.341480 0.939889i \(-0.389072\pi\)
0.341480 + 0.939889i \(0.389072\pi\)
\(734\) −1.35756e18 −0.320430
\(735\) 8.27504e18 1.93599
\(736\) −1.00520e19 −2.33101
\(737\) 8.19599e17 0.188392
\(738\) 9.73267e17 0.221751
\(739\) 7.23182e18 1.63327 0.816636 0.577152i \(-0.195836\pi\)
0.816636 + 0.577152i \(0.195836\pi\)
\(740\) −6.62839e18 −1.48389
\(741\) −1.76043e18 −0.390660
\(742\) −2.40685e18 −0.529448
\(743\) 2.64189e18 0.576087 0.288044 0.957617i \(-0.406995\pi\)
0.288044 + 0.957617i \(0.406995\pi\)
\(744\) −1.27379e16 −0.00275343
\(745\) −6.56768e18 −1.40733
\(746\) 1.22046e19 2.59252
\(747\) 2.59056e18 0.545518
\(748\) 2.25319e18 0.470368
\(749\) −8.91982e18 −1.84597
\(750\) −4.31478e18 −0.885238
\(751\) −7.29114e18 −1.48298 −0.741490 0.670963i \(-0.765881\pi\)
−0.741490 + 0.670963i \(0.765881\pi\)
\(752\) −7.00610e18 −1.41273
\(753\) −1.64184e18 −0.328218
\(754\) 1.05494e18 0.209080
\(755\) 1.31521e19 2.58429
\(756\) 1.66140e18 0.323656
\(757\) 4.76634e18 0.920580 0.460290 0.887769i \(-0.347745\pi\)
0.460290 + 0.887769i \(0.347745\pi\)
\(758\) 8.82614e18 1.69013
\(759\) −3.68497e18 −0.699621
\(760\) −2.82786e17 −0.0532316
\(761\) −7.10313e18 −1.32571 −0.662857 0.748746i \(-0.730656\pi\)
−0.662857 + 0.748746i \(0.730656\pi\)
\(762\) 2.01152e18 0.372235
\(763\) −1.38514e19 −2.54147
\(764\) 8.26678e18 1.50394
\(765\) 2.02866e18 0.365940
\(766\) −2.20440e17 −0.0394279
\(767\) −7.98283e17 −0.141575
\(768\) 3.51460e18 0.618057
\(769\) −1.21414e18 −0.211714 −0.105857 0.994381i \(-0.533759\pi\)
−0.105857 + 0.994381i \(0.533759\pi\)
\(770\) −1.68208e19 −2.90842
\(771\) −4.80629e18 −0.824056
\(772\) −2.18794e18 −0.371983
\(773\) 5.39991e18 0.910373 0.455187 0.890396i \(-0.349573\pi\)
0.455187 + 0.890396i \(0.349573\pi\)
\(774\) 4.16217e17 0.0695830
\(775\) −9.17457e17 −0.152098
\(776\) 4.61048e17 0.0757958
\(777\) −5.83695e18 −0.951588
\(778\) 1.05410e19 1.70418
\(779\) 1.84293e18 0.295471
\(780\) 6.21107e18 0.987533
\(781\) −5.41501e18 −0.853822
\(782\) 1.00296e19 1.56834
\(783\) −1.70314e17 −0.0264119
\(784\) −1.38238e19 −2.12604
\(785\) −1.14240e19 −1.74247
\(786\) −4.67600e18 −0.707340
\(787\) −2.01405e18 −0.302159 −0.151079 0.988522i \(-0.548275\pi\)
−0.151079 + 0.988522i \(0.548275\pi\)
\(788\) 8.62612e17 0.128350
\(789\) −4.21856e18 −0.622534
\(790\) −8.19033e18 −1.19874
\(791\) 3.81996e17 0.0554513
\(792\) 8.81584e16 0.0126926
\(793\) 7.70070e18 1.09965
\(794\) 1.21466e19 1.72037
\(795\) 1.45266e18 0.204070
\(796\) 7.72587e18 1.07650
\(797\) 5.61457e17 0.0775956 0.0387978 0.999247i \(-0.487647\pi\)
0.0387978 + 0.999247i \(0.487647\pi\)
\(798\) 6.41403e18 0.879250
\(799\) 6.73835e18 0.916220
\(800\) 1.73208e19 2.33605
\(801\) 1.85015e18 0.247512
\(802\) −1.27270e19 −1.68886
\(803\) 3.10437e18 0.408623
\(804\) 1.10264e18 0.143969
\(805\) −3.67244e19 −4.75644
\(806\) 1.08010e18 0.138767
\(807\) 8.69494e18 1.10812
\(808\) −6.11144e17 −0.0772627
\(809\) −8.15503e18 −1.02273 −0.511364 0.859364i \(-0.670860\pi\)
−0.511364 + 0.859364i \(0.670860\pi\)
\(810\) −2.04442e18 −0.254342
\(811\) −1.12812e19 −1.39226 −0.696130 0.717916i \(-0.745096\pi\)
−0.696130 + 0.717916i \(0.745096\pi\)
\(812\) −1.88521e18 −0.230806
\(813\) 3.66070e18 0.444606
\(814\) 7.97756e18 0.961195
\(815\) −1.66186e19 −1.98641
\(816\) −3.38895e18 −0.401864
\(817\) 7.88126e17 0.0927155
\(818\) 1.34184e19 1.56605
\(819\) 5.46946e18 0.633285
\(820\) −6.50215e18 −0.746908
\(821\) 1.25463e18 0.142983 0.0714916 0.997441i \(-0.477224\pi\)
0.0714916 + 0.997441i \(0.477224\pi\)
\(822\) −8.49863e18 −0.960909
\(823\) −1.27294e19 −1.42794 −0.713971 0.700175i \(-0.753105\pi\)
−0.713971 + 0.700175i \(0.753105\pi\)
\(824\) 4.85937e16 0.00540820
\(825\) 6.34967e18 0.701133
\(826\) 2.90851e18 0.318640
\(827\) 5.71850e18 0.621579 0.310790 0.950479i \(-0.399407\pi\)
0.310790 + 0.950479i \(0.399407\pi\)
\(828\) −4.95755e18 −0.534650
\(829\) 3.94703e18 0.422344 0.211172 0.977449i \(-0.432272\pi\)
0.211172 + 0.977449i \(0.432272\pi\)
\(830\) −3.52857e19 −3.74620
\(831\) −9.25745e18 −0.975179
\(832\) −9.61267e18 −1.00471
\(833\) 1.32955e19 1.37883
\(834\) 7.63202e18 0.785344
\(835\) 1.03077e19 1.05244
\(836\) −4.29968e18 −0.435607
\(837\) −1.74376e17 −0.0175296
\(838\) −2.61538e19 −2.60885
\(839\) −1.24102e19 −1.22836 −0.614180 0.789166i \(-0.710513\pi\)
−0.614180 + 0.789166i \(0.710513\pi\)
\(840\) 8.78587e17 0.0862917
\(841\) −1.00674e19 −0.981165
\(842\) −2.34717e19 −2.26995
\(843\) 8.89550e18 0.853673
\(844\) 1.88253e18 0.179273
\(845\) 3.15672e18 0.298310
\(846\) −6.79071e18 −0.636807
\(847\) −8.84413e18 −0.823025
\(848\) −2.42672e18 −0.224103
\(849\) −4.62953e18 −0.424265
\(850\) −1.72823e19 −1.57173
\(851\) 1.74172e19 1.57194
\(852\) −7.28504e18 −0.652491
\(853\) −1.51135e19 −1.34337 −0.671685 0.740837i \(-0.734429\pi\)
−0.671685 + 0.740837i \(0.734429\pi\)
\(854\) −2.80571e19 −2.47495
\(855\) −3.87121e18 −0.338896
\(856\) −6.36763e17 −0.0553221
\(857\) −7.32167e18 −0.631299 −0.315649 0.948876i \(-0.602222\pi\)
−0.315649 + 0.948876i \(0.602222\pi\)
\(858\) −7.47530e18 −0.639678
\(859\) 1.59872e19 1.35774 0.678870 0.734258i \(-0.262470\pi\)
0.678870 + 0.734258i \(0.262470\pi\)
\(860\) −2.78064e18 −0.234372
\(861\) −5.72579e18 −0.478977
\(862\) −1.14461e19 −0.950297
\(863\) 8.34284e18 0.687454 0.343727 0.939070i \(-0.388310\pi\)
0.343727 + 0.939070i \(0.388310\pi\)
\(864\) 3.29207e18 0.269234
\(865\) 2.81441e19 2.28445
\(866\) −6.78945e18 −0.546976
\(867\) −3.96100e18 −0.316724
\(868\) −1.93018e18 −0.153186
\(869\) 4.83486e18 0.380851
\(870\) 2.31983e18 0.181376
\(871\) 3.62998e18 0.281699
\(872\) −9.88816e17 −0.0761655
\(873\) 6.31154e18 0.482551
\(874\) −1.91392e19 −1.45244
\(875\) 2.53841e19 1.91209
\(876\) 4.17644e18 0.312269
\(877\) 1.23699e19 0.918057 0.459029 0.888421i \(-0.348197\pi\)
0.459029 + 0.888421i \(0.348197\pi\)
\(878\) −7.36514e18 −0.542584
\(879\) 3.54183e18 0.259000
\(880\) −1.69597e19 −1.23107
\(881\) 8.10626e17 0.0584086 0.0292043 0.999573i \(-0.490703\pi\)
0.0292043 + 0.999573i \(0.490703\pi\)
\(882\) −1.33988e19 −0.958340
\(883\) 1.06000e19 0.752593 0.376296 0.926499i \(-0.377197\pi\)
0.376296 + 0.926499i \(0.377197\pi\)
\(884\) 9.97930e18 0.703332
\(885\) −1.75544e18 −0.122816
\(886\) 6.12896e18 0.425665
\(887\) 2.00306e19 1.38099 0.690494 0.723338i \(-0.257393\pi\)
0.690494 + 0.723338i \(0.257393\pi\)
\(888\) −4.16684e17 −0.0285183
\(889\) −1.18339e19 −0.804019
\(890\) −2.52007e19 −1.69972
\(891\) 1.20685e18 0.0808067
\(892\) 8.16822e18 0.542945
\(893\) −1.28585e19 −0.848511
\(894\) 1.06342e19 0.696647
\(895\) 2.40576e19 1.56460
\(896\) −2.83150e18 −0.182816
\(897\) −1.63206e19 −1.04613
\(898\) 1.58830e19 1.01073
\(899\) 1.97867e17 0.0125007
\(900\) 8.54247e18 0.535806
\(901\) 2.33398e18 0.145341
\(902\) 7.82563e18 0.483812
\(903\) −2.44863e18 −0.150298
\(904\) 2.72697e16 0.00166183
\(905\) 2.41286e19 1.45988
\(906\) −2.12956e19 −1.27926
\(907\) −1.31339e19 −0.783332 −0.391666 0.920107i \(-0.628101\pi\)
−0.391666 + 0.920107i \(0.628101\pi\)
\(908\) 2.11749e19 1.25390
\(909\) −8.36629e18 −0.491889
\(910\) −7.44989e19 −4.34891
\(911\) −1.45501e19 −0.843326 −0.421663 0.906753i \(-0.638554\pi\)
−0.421663 + 0.906753i \(0.638554\pi\)
\(912\) 6.46700e18 0.372166
\(913\) 2.08296e19 1.19020
\(914\) 1.30585e19 0.740871
\(915\) 1.69340e19 0.953942
\(916\) −9.44815e18 −0.528477
\(917\) 2.75092e19 1.52784
\(918\) −3.28476e18 −0.181145
\(919\) 5.02915e18 0.275387 0.137693 0.990475i \(-0.456031\pi\)
0.137693 + 0.990475i \(0.456031\pi\)
\(920\) −2.62166e18 −0.142546
\(921\) −9.21675e18 −0.497611
\(922\) −2.10412e19 −1.12803
\(923\) −2.39829e19 −1.27671
\(924\) 1.33586e19 0.706146
\(925\) −3.00120e19 −1.57534
\(926\) 1.04332e19 0.543807
\(927\) 6.65225e17 0.0344310
\(928\) −3.73555e18 −0.191996
\(929\) 2.60627e19 1.33020 0.665099 0.746755i \(-0.268389\pi\)
0.665099 + 0.746755i \(0.268389\pi\)
\(930\) 2.37516e18 0.120380
\(931\) −2.53712e19 −1.27694
\(932\) −3.13681e19 −1.56778
\(933\) −1.52045e19 −0.754644
\(934\) 3.26262e19 1.60810
\(935\) 1.63116e19 0.798400
\(936\) 3.90451e17 0.0189790
\(937\) 5.36747e18 0.259097 0.129548 0.991573i \(-0.458647\pi\)
0.129548 + 0.991573i \(0.458647\pi\)
\(938\) −1.32257e19 −0.634014
\(939\) 1.53366e19 0.730133
\(940\) 4.53671e19 2.14491
\(941\) −1.16226e19 −0.545721 −0.272860 0.962054i \(-0.587970\pi\)
−0.272860 + 0.962054i \(0.587970\pi\)
\(942\) 1.84975e19 0.862545
\(943\) 1.70855e19 0.791227
\(944\) 2.93253e18 0.134873
\(945\) 1.20274e19 0.549372
\(946\) 3.34662e18 0.151815
\(947\) −1.69017e19 −0.761476 −0.380738 0.924683i \(-0.624330\pi\)
−0.380738 + 0.924683i \(0.624330\pi\)
\(948\) 6.50454e18 0.291046
\(949\) 1.37491e19 0.611006
\(950\) 3.29792e19 1.45558
\(951\) 1.43414e18 0.0628661
\(952\) 1.41162e18 0.0614579
\(953\) 1.64360e19 0.710711 0.355356 0.934731i \(-0.384360\pi\)
0.355356 + 0.934731i \(0.384360\pi\)
\(954\) −2.35212e18 −0.101017
\(955\) 5.98460e19 2.55278
\(956\) 3.91343e19 1.65799
\(957\) −1.36943e18 −0.0576250
\(958\) 4.55792e19 1.90498
\(959\) 4.99979e19 2.07554
\(960\) −2.11384e19 −0.871585
\(961\) −2.42150e19 −0.991703
\(962\) 3.53323e19 1.43726
\(963\) −8.71699e18 −0.352205
\(964\) 1.08053e19 0.433648
\(965\) −1.58392e19 −0.631404
\(966\) 5.94634e19 2.35450
\(967\) −4.36155e19 −1.71541 −0.857707 0.514139i \(-0.828111\pi\)
−0.857707 + 0.514139i \(0.828111\pi\)
\(968\) −6.31360e17 −0.0246653
\(969\) −6.21985e18 −0.241366
\(970\) −8.59687e19 −3.31378
\(971\) −4.79427e19 −1.83568 −0.917842 0.396947i \(-0.870070\pi\)
−0.917842 + 0.396947i \(0.870070\pi\)
\(972\) 1.62362e18 0.0617525
\(973\) −4.48996e19 −1.69632
\(974\) 2.73058e19 1.02476
\(975\) 2.81225e19 1.04839
\(976\) −2.82888e19 −1.04759
\(977\) −3.37789e18 −0.124260 −0.0621300 0.998068i \(-0.519789\pi\)
−0.0621300 + 0.998068i \(0.519789\pi\)
\(978\) 2.69085e19 0.983300
\(979\) 1.48763e19 0.540017
\(980\) 8.95139e19 3.22791
\(981\) −1.35364e19 −0.484904
\(982\) −3.90917e19 −1.39110
\(983\) −3.79740e19 −1.34242 −0.671210 0.741267i \(-0.734225\pi\)
−0.671210 + 0.741267i \(0.734225\pi\)
\(984\) −4.08749e17 −0.0143545
\(985\) 6.24473e18 0.217860
\(986\) 3.72726e18 0.129178
\(987\) 3.99502e19 1.37549
\(988\) −1.90431e19 −0.651355
\(989\) 7.30659e18 0.248278
\(990\) −1.64383e19 −0.554918
\(991\) 1.37136e19 0.459911 0.229956 0.973201i \(-0.426142\pi\)
0.229956 + 0.973201i \(0.426142\pi\)
\(992\) −3.82465e18 −0.127428
\(993\) −8.24592e18 −0.272941
\(994\) 8.73806e19 2.87345
\(995\) 5.59301e19 1.82724
\(996\) 2.80229e19 0.909552
\(997\) 2.06934e19 0.667288 0.333644 0.942699i \(-0.391722\pi\)
0.333644 + 0.942699i \(0.391722\pi\)
\(998\) 5.87890e19 1.88342
\(999\) −5.70422e18 −0.181560
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.14.a.c.1.4 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.4 31 1.1 even 1 trivial