Properties

Label 177.14.a.a.1.11
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $30$
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: \(1\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-49.4802 q^{2} +729.000 q^{3} -5743.71 q^{4} +45167.9 q^{5} -36071.0 q^{6} +116012. q^{7} +689542. q^{8} +531441. q^{9} +O(q^{10})\) \(q-49.4802 q^{2} +729.000 q^{3} -5743.71 q^{4} +45167.9 q^{5} -36071.0 q^{6} +116012. q^{7} +689542. q^{8} +531441. q^{9} -2.23492e6 q^{10} +2.81280e6 q^{11} -4.18717e6 q^{12} -3.96387e6 q^{13} -5.74029e6 q^{14} +3.29274e7 q^{15} +1.29339e7 q^{16} -9.19750e7 q^{17} -2.62958e7 q^{18} +2.77273e8 q^{19} -2.59432e8 q^{20} +8.45727e7 q^{21} -1.39178e8 q^{22} -6.95853e8 q^{23} +5.02676e8 q^{24} +8.19439e8 q^{25} +1.96133e8 q^{26} +3.87420e8 q^{27} -6.66339e8 q^{28} -4.72216e9 q^{29} -1.62925e9 q^{30} +1.19494e9 q^{31} -6.28869e9 q^{32} +2.05053e9 q^{33} +4.55094e9 q^{34} +5.24002e9 q^{35} -3.05244e9 q^{36} -1.10540e10 q^{37} -1.37195e10 q^{38} -2.88966e9 q^{39} +3.11452e10 q^{40} -4.13527e10 q^{41} -4.18467e9 q^{42} -4.95977e10 q^{43} -1.61559e10 q^{44} +2.40041e10 q^{45} +3.44309e10 q^{46} +1.54159e10 q^{47} +9.42878e9 q^{48} -8.34302e10 q^{49} -4.05460e10 q^{50} -6.70498e10 q^{51} +2.27673e10 q^{52} +1.00986e11 q^{53} -1.91696e10 q^{54} +1.27048e11 q^{55} +7.99950e10 q^{56} +2.02132e11 q^{57} +2.33653e11 q^{58} +4.21805e10 q^{59} -1.89126e11 q^{60} -4.41939e11 q^{61} -5.91257e10 q^{62} +6.16535e10 q^{63} +2.05212e11 q^{64} -1.79040e11 q^{65} -1.01461e11 q^{66} -1.19202e12 q^{67} +5.28278e11 q^{68} -5.07277e11 q^{69} -2.59277e11 q^{70} +2.02385e12 q^{71} +3.66451e11 q^{72} -1.19897e11 q^{73} +5.46952e11 q^{74} +5.97371e11 q^{75} -1.59258e12 q^{76} +3.26318e11 q^{77} +1.42981e11 q^{78} -1.71085e11 q^{79} +5.84195e11 q^{80} +2.82430e11 q^{81} +2.04614e12 q^{82} -5.24484e12 q^{83} -4.85761e11 q^{84} -4.15432e12 q^{85} +2.45410e12 q^{86} -3.44245e12 q^{87} +1.93954e12 q^{88} +2.52640e12 q^{89} -1.18773e12 q^{90} -4.59856e11 q^{91} +3.99678e12 q^{92} +8.71109e11 q^{93} -7.62781e11 q^{94} +1.25239e13 q^{95} -4.58446e12 q^{96} -6.11249e12 q^{97} +4.12814e12 q^{98} +1.49484e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \) \( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −49.4802 −0.546684 −0.273342 0.961917i \(-0.588129\pi\)
−0.273342 + 0.961917i \(0.588129\pi\)
\(3\) 729.000 0.577350
\(4\) −5743.71 −0.701137
\(5\) 45167.9 1.29278 0.646391 0.763007i \(-0.276278\pi\)
0.646391 + 0.763007i \(0.276278\pi\)
\(6\) −36071.0 −0.315628
\(7\) 116012. 0.372705 0.186353 0.982483i \(-0.440333\pi\)
0.186353 + 0.982483i \(0.440333\pi\)
\(8\) 689542. 0.929984
\(9\) 531441. 0.333333
\(10\) −2.23492e6 −0.706743
\(11\) 2.81280e6 0.478725 0.239362 0.970930i \(-0.423062\pi\)
0.239362 + 0.970930i \(0.423062\pi\)
\(12\) −4.18717e6 −0.404801
\(13\) −3.96387e6 −0.227765 −0.113883 0.993494i \(-0.536329\pi\)
−0.113883 + 0.993494i \(0.536329\pi\)
\(14\) −5.74029e6 −0.203752
\(15\) 3.29274e7 0.746388
\(16\) 1.29339e7 0.192729
\(17\) −9.19750e7 −0.924170 −0.462085 0.886836i \(-0.652899\pi\)
−0.462085 + 0.886836i \(0.652899\pi\)
\(18\) −2.62958e7 −0.182228
\(19\) 2.77273e8 1.35210 0.676051 0.736855i \(-0.263690\pi\)
0.676051 + 0.736855i \(0.263690\pi\)
\(20\) −2.59432e8 −0.906417
\(21\) 8.45727e7 0.215181
\(22\) −1.39178e8 −0.261711
\(23\) −6.95853e8 −0.980136 −0.490068 0.871684i \(-0.663028\pi\)
−0.490068 + 0.871684i \(0.663028\pi\)
\(24\) 5.02676e8 0.536927
\(25\) 8.19439e8 0.671284
\(26\) 1.96133e8 0.124516
\(27\) 3.87420e8 0.192450
\(28\) −6.66339e8 −0.261317
\(29\) −4.72216e9 −1.47419 −0.737095 0.675789i \(-0.763803\pi\)
−0.737095 + 0.675789i \(0.763803\pi\)
\(30\) −1.62925e9 −0.408038
\(31\) 1.19494e9 0.241821 0.120910 0.992663i \(-0.461419\pi\)
0.120910 + 0.992663i \(0.461419\pi\)
\(32\) −6.28869e9 −1.03535
\(33\) 2.05053e9 0.276392
\(34\) 4.55094e9 0.505229
\(35\) 5.24002e9 0.481826
\(36\) −3.05244e9 −0.233712
\(37\) −1.10540e10 −0.708283 −0.354142 0.935192i \(-0.615227\pi\)
−0.354142 + 0.935192i \(0.615227\pi\)
\(38\) −1.37195e10 −0.739173
\(39\) −2.88966e9 −0.131500
\(40\) 3.11452e10 1.20227
\(41\) −4.13527e10 −1.35959 −0.679796 0.733402i \(-0.737932\pi\)
−0.679796 + 0.733402i \(0.737932\pi\)
\(42\) −4.18467e9 −0.117636
\(43\) −4.95977e10 −1.19651 −0.598255 0.801306i \(-0.704139\pi\)
−0.598255 + 0.801306i \(0.704139\pi\)
\(44\) −1.61559e10 −0.335652
\(45\) 2.40041e10 0.430927
\(46\) 3.44309e10 0.535825
\(47\) 1.54159e10 0.208609 0.104304 0.994545i \(-0.466738\pi\)
0.104304 + 0.994545i \(0.466738\pi\)
\(48\) 9.42878e9 0.111272
\(49\) −8.34302e10 −0.861091
\(50\) −4.05460e10 −0.366980
\(51\) −6.70498e10 −0.533570
\(52\) 2.27673e10 0.159695
\(53\) 1.00986e11 0.625848 0.312924 0.949778i \(-0.398691\pi\)
0.312924 + 0.949778i \(0.398691\pi\)
\(54\) −1.91696e10 −0.105209
\(55\) 1.27048e11 0.618887
\(56\) 7.99950e10 0.346610
\(57\) 2.02132e11 0.780637
\(58\) 2.33653e11 0.805916
\(59\) 4.21805e10 0.130189
\(60\) −1.89126e11 −0.523320
\(61\) −4.41939e11 −1.09829 −0.549147 0.835726i \(-0.685047\pi\)
−0.549147 + 0.835726i \(0.685047\pi\)
\(62\) −5.91257e10 −0.132200
\(63\) 6.16535e10 0.124235
\(64\) 2.05212e11 0.373278
\(65\) −1.79040e11 −0.294451
\(66\) −1.01461e11 −0.151099
\(67\) −1.19202e12 −1.60990 −0.804948 0.593346i \(-0.797807\pi\)
−0.804948 + 0.593346i \(0.797807\pi\)
\(68\) 5.28278e11 0.647970
\(69\) −5.07277e11 −0.565882
\(70\) −2.59277e11 −0.263407
\(71\) 2.02385e12 1.87499 0.937493 0.348004i \(-0.113140\pi\)
0.937493 + 0.348004i \(0.113140\pi\)
\(72\) 3.66451e11 0.309995
\(73\) −1.19897e11 −0.0927278 −0.0463639 0.998925i \(-0.514763\pi\)
−0.0463639 + 0.998925i \(0.514763\pi\)
\(74\) 5.46952e11 0.387207
\(75\) 5.97371e11 0.387566
\(76\) −1.59258e12 −0.948009
\(77\) 3.26318e11 0.178423
\(78\) 1.42981e11 0.0718892
\(79\) −1.71085e11 −0.0791838 −0.0395919 0.999216i \(-0.512606\pi\)
−0.0395919 + 0.999216i \(0.512606\pi\)
\(80\) 5.84195e11 0.249157
\(81\) 2.82430e11 0.111111
\(82\) 2.04614e12 0.743267
\(83\) −5.24484e12 −1.76086 −0.880430 0.474176i \(-0.842746\pi\)
−0.880430 + 0.474176i \(0.842746\pi\)
\(84\) −4.85761e11 −0.150872
\(85\) −4.15432e12 −1.19475
\(86\) 2.45410e12 0.654113
\(87\) −3.44245e12 −0.851124
\(88\) 1.93954e12 0.445206
\(89\) 2.52640e12 0.538849 0.269425 0.963021i \(-0.413166\pi\)
0.269425 + 0.963021i \(0.413166\pi\)
\(90\) −1.18773e12 −0.235581
\(91\) −4.59856e11 −0.0848893
\(92\) 3.99678e12 0.687209
\(93\) 8.71109e11 0.139615
\(94\) −7.62781e11 −0.114043
\(95\) 1.25239e13 1.74797
\(96\) −4.58446e12 −0.597757
\(97\) −6.11249e12 −0.745078 −0.372539 0.928016i \(-0.621513\pi\)
−0.372539 + 0.928016i \(0.621513\pi\)
\(98\) 4.12814e12 0.470745
\(99\) 1.49484e12 0.159575
\(100\) −4.70662e12 −0.470662
\(101\) −1.01497e12 −0.0951407 −0.0475703 0.998868i \(-0.515148\pi\)
−0.0475703 + 0.998868i \(0.515148\pi\)
\(102\) 3.31764e12 0.291694
\(103\) 2.30285e13 1.90031 0.950153 0.311785i \(-0.100927\pi\)
0.950153 + 0.311785i \(0.100927\pi\)
\(104\) −2.73325e12 −0.211818
\(105\) 3.81997e12 0.278183
\(106\) −4.99681e12 −0.342141
\(107\) −4.93765e12 −0.318072 −0.159036 0.987273i \(-0.550839\pi\)
−0.159036 + 0.987273i \(0.550839\pi\)
\(108\) −2.22523e12 −0.134934
\(109\) 2.12524e13 1.21377 0.606883 0.794791i \(-0.292420\pi\)
0.606883 + 0.794791i \(0.292420\pi\)
\(110\) −6.28637e12 −0.338335
\(111\) −8.05834e12 −0.408927
\(112\) 1.50048e12 0.0718312
\(113\) −2.30395e13 −1.04103 −0.520514 0.853853i \(-0.674260\pi\)
−0.520514 + 0.853853i \(0.674260\pi\)
\(114\) −1.00015e13 −0.426762
\(115\) −3.14302e13 −1.26710
\(116\) 2.71227e13 1.03361
\(117\) −2.10656e12 −0.0759218
\(118\) −2.08710e12 −0.0711722
\(119\) −1.06702e13 −0.344443
\(120\) 2.27048e13 0.694129
\(121\) −2.66109e13 −0.770822
\(122\) 2.18672e13 0.600420
\(123\) −3.01461e13 −0.784960
\(124\) −6.86337e12 −0.169549
\(125\) −1.81243e13 −0.424958
\(126\) −3.05063e12 −0.0679173
\(127\) 5.96752e13 1.26203 0.631015 0.775771i \(-0.282639\pi\)
0.631015 + 0.775771i \(0.282639\pi\)
\(128\) 4.13631e13 0.831281
\(129\) −3.61567e13 −0.690806
\(130\) 8.85893e12 0.160972
\(131\) 2.82008e13 0.487527 0.243763 0.969835i \(-0.421618\pi\)
0.243763 + 0.969835i \(0.421618\pi\)
\(132\) −1.17776e13 −0.193789
\(133\) 3.21670e13 0.503935
\(134\) 5.89814e13 0.880104
\(135\) 1.74990e13 0.248796
\(136\) −6.34206e13 −0.859464
\(137\) −3.39933e13 −0.439248 −0.219624 0.975585i \(-0.570483\pi\)
−0.219624 + 0.975585i \(0.570483\pi\)
\(138\) 2.51001e13 0.309358
\(139\) −5.29965e13 −0.623234 −0.311617 0.950208i \(-0.600871\pi\)
−0.311617 + 0.950208i \(0.600871\pi\)
\(140\) −3.00972e13 −0.337826
\(141\) 1.12382e13 0.120440
\(142\) −1.00140e14 −1.02502
\(143\) −1.11496e13 −0.109037
\(144\) 6.87358e12 0.0642431
\(145\) −2.13290e14 −1.90581
\(146\) 5.93253e12 0.0506928
\(147\) −6.08207e13 −0.497151
\(148\) 6.34908e13 0.496603
\(149\) 2.05324e13 0.153720 0.0768598 0.997042i \(-0.475511\pi\)
0.0768598 + 0.997042i \(0.475511\pi\)
\(150\) −2.95580e13 −0.211876
\(151\) 1.23313e14 0.846565 0.423282 0.905998i \(-0.360878\pi\)
0.423282 + 0.905998i \(0.360878\pi\)
\(152\) 1.91191e14 1.25743
\(153\) −4.88793e13 −0.308057
\(154\) −1.61463e13 −0.0975411
\(155\) 5.39728e13 0.312622
\(156\) 1.65974e13 0.0921998
\(157\) 3.04482e14 1.62261 0.811306 0.584622i \(-0.198757\pi\)
0.811306 + 0.584622i \(0.198757\pi\)
\(158\) 8.46532e12 0.0432885
\(159\) 7.36189e13 0.361333
\(160\) −2.84047e14 −1.33848
\(161\) −8.07272e13 −0.365302
\(162\) −1.39747e13 −0.0607427
\(163\) 1.60383e14 0.669791 0.334895 0.942255i \(-0.391299\pi\)
0.334895 + 0.942255i \(0.391299\pi\)
\(164\) 2.37518e14 0.953259
\(165\) 9.26182e13 0.357314
\(166\) 2.59516e14 0.962634
\(167\) −2.25333e14 −0.803837 −0.401919 0.915675i \(-0.631657\pi\)
−0.401919 + 0.915675i \(0.631657\pi\)
\(168\) 5.83164e13 0.200115
\(169\) −2.87163e14 −0.948123
\(170\) 2.05557e14 0.653151
\(171\) 1.47354e14 0.450701
\(172\) 2.84875e14 0.838917
\(173\) 3.94268e14 1.11813 0.559064 0.829125i \(-0.311161\pi\)
0.559064 + 0.829125i \(0.311161\pi\)
\(174\) 1.70333e14 0.465296
\(175\) 9.50646e13 0.250191
\(176\) 3.63803e13 0.0922644
\(177\) 3.07496e13 0.0751646
\(178\) −1.25007e14 −0.294580
\(179\) 8.16873e14 1.85614 0.928068 0.372410i \(-0.121468\pi\)
0.928068 + 0.372410i \(0.121468\pi\)
\(180\) −1.37873e14 −0.302139
\(181\) 4.65273e14 0.983552 0.491776 0.870722i \(-0.336348\pi\)
0.491776 + 0.870722i \(0.336348\pi\)
\(182\) 2.27538e13 0.0464076
\(183\) −3.22174e14 −0.634101
\(184\) −4.79819e14 −0.911511
\(185\) −4.99285e14 −0.915655
\(186\) −4.31026e13 −0.0763255
\(187\) −2.58707e14 −0.442423
\(188\) −8.85445e13 −0.146263
\(189\) 4.49454e13 0.0717271
\(190\) −6.19683e14 −0.955589
\(191\) 1.56260e14 0.232879 0.116439 0.993198i \(-0.462852\pi\)
0.116439 + 0.993198i \(0.462852\pi\)
\(192\) 1.49599e14 0.215512
\(193\) −1.36488e15 −1.90095 −0.950475 0.310801i \(-0.899403\pi\)
−0.950475 + 0.310801i \(0.899403\pi\)
\(194\) 3.02447e14 0.407322
\(195\) −1.30520e14 −0.170001
\(196\) 4.79199e14 0.603742
\(197\) −1.12615e15 −1.37266 −0.686332 0.727288i \(-0.740780\pi\)
−0.686332 + 0.727288i \(0.740780\pi\)
\(198\) −7.39647e13 −0.0872371
\(199\) −1.46375e15 −1.67080 −0.835398 0.549646i \(-0.814763\pi\)
−0.835398 + 0.549646i \(0.814763\pi\)
\(200\) 5.65037e14 0.624284
\(201\) −8.68983e14 −0.929474
\(202\) 5.02211e13 0.0520119
\(203\) −5.47826e14 −0.549438
\(204\) 3.85115e14 0.374105
\(205\) −1.86781e15 −1.75765
\(206\) −1.13945e15 −1.03887
\(207\) −3.69805e14 −0.326712
\(208\) −5.12681e13 −0.0438971
\(209\) 7.79914e14 0.647285
\(210\) −1.89013e14 −0.152078
\(211\) −7.23736e14 −0.564605 −0.282302 0.959325i \(-0.591098\pi\)
−0.282302 + 0.959325i \(0.591098\pi\)
\(212\) −5.80036e14 −0.438805
\(213\) 1.47538e15 1.08252
\(214\) 2.44316e14 0.173885
\(215\) −2.24022e15 −1.54683
\(216\) 2.67143e14 0.178976
\(217\) 1.38627e14 0.0901279
\(218\) −1.05157e15 −0.663546
\(219\) −8.74050e13 −0.0535364
\(220\) −7.29728e14 −0.433924
\(221\) 3.64577e14 0.210494
\(222\) 3.98728e14 0.223554
\(223\) −3.59902e15 −1.95976 −0.979880 0.199586i \(-0.936040\pi\)
−0.979880 + 0.199586i \(0.936040\pi\)
\(224\) −7.29563e14 −0.385879
\(225\) 4.35483e14 0.223761
\(226\) 1.14000e15 0.569114
\(227\) −2.80159e15 −1.35905 −0.679526 0.733651i \(-0.737815\pi\)
−0.679526 + 0.733651i \(0.737815\pi\)
\(228\) −1.16099e15 −0.547333
\(229\) −1.81469e15 −0.831520 −0.415760 0.909474i \(-0.636484\pi\)
−0.415760 + 0.909474i \(0.636484\pi\)
\(230\) 1.55517e15 0.692704
\(231\) 2.37886e14 0.103013
\(232\) −3.25612e15 −1.37097
\(233\) −4.57053e15 −1.87134 −0.935672 0.352872i \(-0.885205\pi\)
−0.935672 + 0.352872i \(0.885205\pi\)
\(234\) 1.04233e14 0.0415052
\(235\) 6.96304e14 0.269686
\(236\) −2.42273e14 −0.0912802
\(237\) −1.24721e14 −0.0457168
\(238\) 5.27963e14 0.188301
\(239\) 3.93199e15 1.36466 0.682332 0.731042i \(-0.260966\pi\)
0.682332 + 0.731042i \(0.260966\pi\)
\(240\) 4.25878e14 0.143851
\(241\) −2.65595e15 −0.873190 −0.436595 0.899658i \(-0.643816\pi\)
−0.436595 + 0.899658i \(0.643816\pi\)
\(242\) 1.31671e15 0.421396
\(243\) 2.05891e14 0.0641500
\(244\) 2.53837e15 0.770055
\(245\) −3.76837e15 −1.11320
\(246\) 1.49163e15 0.429125
\(247\) −1.09908e15 −0.307962
\(248\) 8.23958e14 0.224890
\(249\) −3.82349e15 −1.01663
\(250\) 8.96793e14 0.232318
\(251\) 1.62523e14 0.0410238 0.0205119 0.999790i \(-0.493470\pi\)
0.0205119 + 0.999790i \(0.493470\pi\)
\(252\) −3.54120e14 −0.0871057
\(253\) −1.95729e15 −0.469216
\(254\) −2.95274e15 −0.689931
\(255\) −3.02850e15 −0.689789
\(256\) −3.72775e15 −0.827726
\(257\) −8.58304e15 −1.85813 −0.929064 0.369918i \(-0.879386\pi\)
−0.929064 + 0.369918i \(0.879386\pi\)
\(258\) 1.78904e15 0.377652
\(259\) −1.28239e15 −0.263981
\(260\) 1.02835e15 0.206450
\(261\) −2.50955e15 −0.491397
\(262\) −1.39538e15 −0.266523
\(263\) 9.79891e14 0.182585 0.0912926 0.995824i \(-0.470900\pi\)
0.0912926 + 0.995824i \(0.470900\pi\)
\(264\) 1.41393e15 0.257040
\(265\) 4.56134e15 0.809085
\(266\) −1.59163e15 −0.275493
\(267\) 1.84175e15 0.311105
\(268\) 6.84663e15 1.12876
\(269\) 3.73415e15 0.600900 0.300450 0.953798i \(-0.402863\pi\)
0.300450 + 0.953798i \(0.402863\pi\)
\(270\) −8.65853e14 −0.136013
\(271\) 9.60543e15 1.47305 0.736523 0.676413i \(-0.236466\pi\)
0.736523 + 0.676413i \(0.236466\pi\)
\(272\) −1.18959e15 −0.178115
\(273\) −3.35235e14 −0.0490109
\(274\) 1.68199e15 0.240130
\(275\) 2.30491e15 0.321360
\(276\) 2.91365e15 0.396761
\(277\) −2.83716e15 −0.377369 −0.188684 0.982038i \(-0.560422\pi\)
−0.188684 + 0.982038i \(0.560422\pi\)
\(278\) 2.62228e15 0.340712
\(279\) 6.35038e14 0.0806070
\(280\) 3.61321e15 0.448091
\(281\) −8.61754e15 −1.04422 −0.522110 0.852878i \(-0.674855\pi\)
−0.522110 + 0.852878i \(0.674855\pi\)
\(282\) −5.56068e14 −0.0658428
\(283\) 9.38782e15 1.08631 0.543154 0.839633i \(-0.317230\pi\)
0.543154 + 0.839633i \(0.317230\pi\)
\(284\) −1.16244e16 −1.31462
\(285\) 9.12989e15 1.00919
\(286\) 5.51683e14 0.0596088
\(287\) −4.79740e15 −0.506727
\(288\) −3.34207e15 −0.345115
\(289\) −1.44517e15 −0.145909
\(290\) 1.05536e16 1.04187
\(291\) −4.45601e15 −0.430171
\(292\) 6.88655e14 0.0650149
\(293\) −1.06056e16 −0.979258 −0.489629 0.871931i \(-0.662868\pi\)
−0.489629 + 0.871931i \(0.662868\pi\)
\(294\) 3.00942e15 0.271784
\(295\) 1.90521e15 0.168306
\(296\) −7.62217e15 −0.658692
\(297\) 1.08974e15 0.0921306
\(298\) −1.01595e15 −0.0840361
\(299\) 2.75827e15 0.223241
\(300\) −3.43113e15 −0.271737
\(301\) −5.75392e15 −0.445945
\(302\) −6.10157e15 −0.462803
\(303\) −7.39916e14 −0.0549295
\(304\) 3.58621e15 0.260590
\(305\) −1.99615e16 −1.41985
\(306\) 2.41856e15 0.168410
\(307\) −7.13186e15 −0.486187 −0.243093 0.970003i \(-0.578162\pi\)
−0.243093 + 0.970003i \(0.578162\pi\)
\(308\) −1.87428e15 −0.125099
\(309\) 1.67878e16 1.09714
\(310\) −2.67058e15 −0.170905
\(311\) 2.89266e16 1.81282 0.906409 0.422402i \(-0.138813\pi\)
0.906409 + 0.422402i \(0.138813\pi\)
\(312\) −1.99254e15 −0.122293
\(313\) −3.69552e15 −0.222145 −0.111073 0.993812i \(-0.535429\pi\)
−0.111073 + 0.993812i \(0.535429\pi\)
\(314\) −1.50658e16 −0.887055
\(315\) 2.78476e15 0.160609
\(316\) 9.82664e14 0.0555187
\(317\) −7.31483e15 −0.404873 −0.202437 0.979295i \(-0.564886\pi\)
−0.202437 + 0.979295i \(0.564886\pi\)
\(318\) −3.64268e15 −0.197535
\(319\) −1.32825e16 −0.705731
\(320\) 9.26898e15 0.482566
\(321\) −3.59955e15 −0.183639
\(322\) 3.99440e15 0.199705
\(323\) −2.55022e16 −1.24957
\(324\) −1.62219e15 −0.0779041
\(325\) −3.24815e15 −0.152895
\(326\) −7.93578e15 −0.366164
\(327\) 1.54930e16 0.700768
\(328\) −2.85144e16 −1.26440
\(329\) 1.78843e15 0.0777496
\(330\) −4.58276e15 −0.195338
\(331\) 1.60515e16 0.670862 0.335431 0.942065i \(-0.391118\pi\)
0.335431 + 0.942065i \(0.391118\pi\)
\(332\) 3.01249e16 1.23460
\(333\) −5.87453e15 −0.236094
\(334\) 1.11495e16 0.439445
\(335\) −5.38411e16 −2.08124
\(336\) 1.09385e15 0.0414718
\(337\) 5.53045e15 0.205668 0.102834 0.994699i \(-0.467209\pi\)
0.102834 + 0.994699i \(0.467209\pi\)
\(338\) 1.42089e16 0.518324
\(339\) −1.67958e16 −0.601038
\(340\) 2.38612e16 0.837683
\(341\) 3.36111e15 0.115766
\(342\) −7.29112e15 −0.246391
\(343\) −2.09192e16 −0.693638
\(344\) −3.41997e16 −1.11274
\(345\) −2.29126e16 −0.731562
\(346\) −1.95084e16 −0.611262
\(347\) −1.39023e16 −0.427507 −0.213754 0.976888i \(-0.568569\pi\)
−0.213754 + 0.976888i \(0.568569\pi\)
\(348\) 1.97725e16 0.596754
\(349\) −6.02345e15 −0.178435 −0.0892174 0.996012i \(-0.528437\pi\)
−0.0892174 + 0.996012i \(0.528437\pi\)
\(350\) −4.70382e15 −0.136775
\(351\) −1.53569e15 −0.0438335
\(352\) −1.76888e16 −0.495646
\(353\) −5.04897e16 −1.38889 −0.694444 0.719547i \(-0.744350\pi\)
−0.694444 + 0.719547i \(0.744350\pi\)
\(354\) −1.52150e15 −0.0410913
\(355\) 9.14129e16 2.42395
\(356\) −1.45109e16 −0.377807
\(357\) −7.77858e15 −0.198864
\(358\) −4.04190e16 −1.01472
\(359\) 5.12566e16 1.26368 0.631838 0.775100i \(-0.282301\pi\)
0.631838 + 0.775100i \(0.282301\pi\)
\(360\) 1.65518e16 0.400755
\(361\) 3.48275e16 0.828181
\(362\) −2.30218e16 −0.537692
\(363\) −1.93993e16 −0.445035
\(364\) 2.64128e15 0.0595190
\(365\) −5.41550e15 −0.119877
\(366\) 1.59412e16 0.346653
\(367\) 3.05992e16 0.653703 0.326851 0.945076i \(-0.394012\pi\)
0.326851 + 0.945076i \(0.394012\pi\)
\(368\) −9.00006e15 −0.188901
\(369\) −2.19765e16 −0.453197
\(370\) 2.47047e16 0.500574
\(371\) 1.17156e16 0.233257
\(372\) −5.00340e15 −0.0978894
\(373\) −3.50925e16 −0.674695 −0.337347 0.941380i \(-0.609530\pi\)
−0.337347 + 0.941380i \(0.609530\pi\)
\(374\) 1.28009e16 0.241866
\(375\) −1.32126e16 −0.245350
\(376\) 1.06299e16 0.194003
\(377\) 1.87180e16 0.335769
\(378\) −2.22391e15 −0.0392121
\(379\) −4.01424e16 −0.695742 −0.347871 0.937542i \(-0.613095\pi\)
−0.347871 + 0.937542i \(0.613095\pi\)
\(380\) −7.19334e16 −1.22557
\(381\) 4.35032e16 0.728633
\(382\) −7.73176e15 −0.127311
\(383\) 1.16199e17 1.88109 0.940543 0.339675i \(-0.110317\pi\)
0.940543 + 0.339675i \(0.110317\pi\)
\(384\) 3.01537e16 0.479940
\(385\) 1.47391e16 0.230662
\(386\) 6.75343e16 1.03922
\(387\) −2.63582e16 −0.398837
\(388\) 3.51084e16 0.522402
\(389\) 7.91494e16 1.15818 0.579089 0.815265i \(-0.303409\pi\)
0.579089 + 0.815265i \(0.303409\pi\)
\(390\) 6.45816e15 0.0929370
\(391\) 6.40011e16 0.905813
\(392\) −5.75286e16 −0.800801
\(393\) 2.05584e16 0.281474
\(394\) 5.57219e16 0.750414
\(395\) −7.72756e15 −0.102367
\(396\) −8.58591e15 −0.111884
\(397\) −3.88974e16 −0.498634 −0.249317 0.968422i \(-0.580206\pi\)
−0.249317 + 0.968422i \(0.580206\pi\)
\(398\) 7.24268e16 0.913397
\(399\) 2.34497e16 0.290947
\(400\) 1.05985e16 0.129376
\(401\) 6.84850e16 0.822540 0.411270 0.911513i \(-0.365085\pi\)
0.411270 + 0.911513i \(0.365085\pi\)
\(402\) 4.29974e16 0.508128
\(403\) −4.73657e15 −0.0550784
\(404\) 5.82972e15 0.0667066
\(405\) 1.27568e16 0.143642
\(406\) 2.71065e16 0.300369
\(407\) −3.10926e16 −0.339073
\(408\) −4.62336e16 −0.496212
\(409\) 1.49171e17 1.57573 0.787864 0.615849i \(-0.211187\pi\)
0.787864 + 0.615849i \(0.211187\pi\)
\(410\) 9.24198e16 0.960881
\(411\) −2.47811e16 −0.253600
\(412\) −1.32269e17 −1.33237
\(413\) 4.89344e15 0.0485221
\(414\) 1.82980e16 0.178608
\(415\) −2.36899e17 −2.27641
\(416\) 2.49276e16 0.235816
\(417\) −3.86344e16 −0.359824
\(418\) −3.85903e16 −0.353860
\(419\) −1.77108e17 −1.59899 −0.799496 0.600672i \(-0.794900\pi\)
−0.799496 + 0.600672i \(0.794900\pi\)
\(420\) −2.19408e16 −0.195044
\(421\) 1.06774e17 0.934610 0.467305 0.884096i \(-0.345225\pi\)
0.467305 + 0.884096i \(0.345225\pi\)
\(422\) 3.58106e16 0.308660
\(423\) 8.19264e15 0.0695363
\(424\) 6.96342e16 0.582029
\(425\) −7.53679e16 −0.620381
\(426\) −7.30022e16 −0.591798
\(427\) −5.12702e16 −0.409340
\(428\) 2.83605e16 0.223012
\(429\) −8.12804e15 −0.0629525
\(430\) 1.10847e17 0.845625
\(431\) −5.54125e16 −0.416395 −0.208198 0.978087i \(-0.566760\pi\)
−0.208198 + 0.978087i \(0.566760\pi\)
\(432\) 5.01084e15 0.0370908
\(433\) 2.63489e17 1.92128 0.960641 0.277793i \(-0.0896029\pi\)
0.960641 + 0.277793i \(0.0896029\pi\)
\(434\) −6.85928e15 −0.0492715
\(435\) −1.55488e17 −1.10032
\(436\) −1.22067e17 −0.851016
\(437\) −1.92941e17 −1.32524
\(438\) 4.32481e15 0.0292675
\(439\) −2.30044e16 −0.153388 −0.0766941 0.997055i \(-0.524436\pi\)
−0.0766941 + 0.997055i \(0.524436\pi\)
\(440\) 8.76050e16 0.575555
\(441\) −4.43383e16 −0.287030
\(442\) −1.80393e16 −0.115074
\(443\) 1.69714e17 1.06682 0.533412 0.845856i \(-0.320910\pi\)
0.533412 + 0.845856i \(0.320910\pi\)
\(444\) 4.62848e16 0.286714
\(445\) 1.14112e17 0.696614
\(446\) 1.78080e17 1.07137
\(447\) 1.49681e16 0.0887501
\(448\) 2.38070e16 0.139122
\(449\) 2.77603e16 0.159891 0.0799453 0.996799i \(-0.474525\pi\)
0.0799453 + 0.996799i \(0.474525\pi\)
\(450\) −2.15478e16 −0.122327
\(451\) −1.16317e17 −0.650870
\(452\) 1.32332e17 0.729903
\(453\) 8.98955e16 0.488764
\(454\) 1.38623e17 0.742972
\(455\) −2.07708e16 −0.109743
\(456\) 1.39379e17 0.725980
\(457\) −1.57594e17 −0.809254 −0.404627 0.914482i \(-0.632599\pi\)
−0.404627 + 0.914482i \(0.632599\pi\)
\(458\) 8.97914e16 0.454579
\(459\) −3.56330e16 −0.177857
\(460\) 1.80526e17 0.888412
\(461\) −8.30522e16 −0.402991 −0.201495 0.979489i \(-0.564580\pi\)
−0.201495 + 0.979489i \(0.564580\pi\)
\(462\) −1.17706e16 −0.0563154
\(463\) −1.07084e17 −0.505184 −0.252592 0.967573i \(-0.581283\pi\)
−0.252592 + 0.967573i \(0.581283\pi\)
\(464\) −6.10757e16 −0.284120
\(465\) 3.93462e16 0.180492
\(466\) 2.26151e17 1.02303
\(467\) 1.05563e17 0.470926 0.235463 0.971883i \(-0.424339\pi\)
0.235463 + 0.971883i \(0.424339\pi\)
\(468\) 1.20995e16 0.0532316
\(469\) −1.38289e17 −0.600016
\(470\) −3.44532e16 −0.147433
\(471\) 2.21968e17 0.936815
\(472\) 2.90852e16 0.121074
\(473\) −1.39508e17 −0.572799
\(474\) 6.17122e15 0.0249926
\(475\) 2.27208e17 0.907645
\(476\) 6.12866e16 0.241502
\(477\) 5.36682e16 0.208616
\(478\) −1.94555e17 −0.746040
\(479\) −2.85877e17 −1.08143 −0.540716 0.841205i \(-0.681846\pi\)
−0.540716 + 0.841205i \(0.681846\pi\)
\(480\) −2.07070e17 −0.772770
\(481\) 4.38165e16 0.161322
\(482\) 1.31417e17 0.477359
\(483\) −5.88501e16 −0.210907
\(484\) 1.52845e17 0.540452
\(485\) −2.76089e17 −0.963224
\(486\) −1.01875e16 −0.0350698
\(487\) −1.47491e17 −0.500989 −0.250495 0.968118i \(-0.580593\pi\)
−0.250495 + 0.968118i \(0.580593\pi\)
\(488\) −3.04736e17 −1.02140
\(489\) 1.16919e17 0.386704
\(490\) 1.86460e17 0.608570
\(491\) −4.91532e17 −1.58315 −0.791575 0.611072i \(-0.790739\pi\)
−0.791575 + 0.611072i \(0.790739\pi\)
\(492\) 1.73150e17 0.550365
\(493\) 4.34320e17 1.36240
\(494\) 5.43825e16 0.168358
\(495\) 6.75186e16 0.206296
\(496\) 1.54551e16 0.0466060
\(497\) 2.34790e17 0.698817
\(498\) 1.89187e17 0.555777
\(499\) 3.38522e17 0.981598 0.490799 0.871273i \(-0.336705\pi\)
0.490799 + 0.871273i \(0.336705\pi\)
\(500\) 1.04101e17 0.297954
\(501\) −1.64268e17 −0.464096
\(502\) −8.04166e15 −0.0224270
\(503\) −2.54609e17 −0.700942 −0.350471 0.936574i \(-0.613978\pi\)
−0.350471 + 0.936574i \(0.613978\pi\)
\(504\) 4.25126e16 0.115537
\(505\) −4.58443e16 −0.122996
\(506\) 9.68472e16 0.256513
\(507\) −2.09342e17 −0.547399
\(508\) −3.42757e17 −0.884855
\(509\) 1.95923e17 0.499366 0.249683 0.968328i \(-0.419674\pi\)
0.249683 + 0.968328i \(0.419674\pi\)
\(510\) 1.49851e17 0.377097
\(511\) −1.39095e16 −0.0345601
\(512\) −1.54397e17 −0.378777
\(513\) 1.07421e17 0.260212
\(514\) 4.24690e17 1.01581
\(515\) 1.04015e18 2.45668
\(516\) 2.07674e17 0.484349
\(517\) 4.33618e16 0.0998662
\(518\) 6.34530e16 0.144314
\(519\) 2.87421e17 0.645551
\(520\) −1.23455e17 −0.273835
\(521\) −7.64099e16 −0.167380 −0.0836902 0.996492i \(-0.526671\pi\)
−0.0836902 + 0.996492i \(0.526671\pi\)
\(522\) 1.24173e17 0.268639
\(523\) 6.49832e17 1.38848 0.694240 0.719743i \(-0.255741\pi\)
0.694240 + 0.719743i \(0.255741\pi\)
\(524\) −1.61977e17 −0.341823
\(525\) 6.93021e16 0.144448
\(526\) −4.84852e16 −0.0998163
\(527\) −1.09904e17 −0.223484
\(528\) 2.65212e16 0.0532689
\(529\) −1.98253e16 −0.0393332
\(530\) −2.25696e17 −0.442314
\(531\) 2.24165e16 0.0433963
\(532\) −1.84758e17 −0.353328
\(533\) 1.63917e17 0.309668
\(534\) −9.11299e16 −0.170076
\(535\) −2.23024e17 −0.411198
\(536\) −8.21948e17 −1.49718
\(537\) 5.95501e17 1.07164
\(538\) −1.84766e17 −0.328502
\(539\) −2.34672e17 −0.412226
\(540\) −1.00509e17 −0.174440
\(541\) −1.92053e16 −0.0329336 −0.0164668 0.999864i \(-0.505242\pi\)
−0.0164668 + 0.999864i \(0.505242\pi\)
\(542\) −4.75278e17 −0.805290
\(543\) 3.39184e17 0.567854
\(544\) 5.78403e17 0.956836
\(545\) 9.59925e17 1.56913
\(546\) 1.65875e16 0.0267935
\(547\) 4.09634e17 0.653851 0.326926 0.945050i \(-0.393987\pi\)
0.326926 + 0.945050i \(0.393987\pi\)
\(548\) 1.95248e17 0.307973
\(549\) −2.34865e17 −0.366098
\(550\) −1.14048e17 −0.175683
\(551\) −1.30933e18 −1.99326
\(552\) −3.49788e17 −0.526261
\(553\) −1.98479e16 −0.0295122
\(554\) 1.40383e17 0.206301
\(555\) −3.63979e17 −0.528654
\(556\) 3.04397e17 0.436972
\(557\) −3.51029e16 −0.0498063 −0.0249031 0.999690i \(-0.507928\pi\)
−0.0249031 + 0.999690i \(0.507928\pi\)
\(558\) −3.14218e16 −0.0440665
\(559\) 1.96599e17 0.272524
\(560\) 6.77736e16 0.0928621
\(561\) −1.88598e17 −0.255433
\(562\) 4.26397e17 0.570858
\(563\) 7.47411e17 0.989134 0.494567 0.869140i \(-0.335327\pi\)
0.494567 + 0.869140i \(0.335327\pi\)
\(564\) −6.45489e16 −0.0844452
\(565\) −1.04065e18 −1.34582
\(566\) −4.64511e17 −0.593867
\(567\) 3.27652e16 0.0414117
\(568\) 1.39553e18 1.74371
\(569\) 8.74316e17 1.08004 0.540018 0.841653i \(-0.318417\pi\)
0.540018 + 0.841653i \(0.318417\pi\)
\(570\) −4.51749e17 −0.551709
\(571\) −7.66178e17 −0.925114 −0.462557 0.886590i \(-0.653068\pi\)
−0.462557 + 0.886590i \(0.653068\pi\)
\(572\) 6.40399e16 0.0764498
\(573\) 1.13913e17 0.134453
\(574\) 2.37376e17 0.277019
\(575\) −5.70209e17 −0.657950
\(576\) 1.09058e17 0.124426
\(577\) −1.54561e17 −0.174364 −0.0871821 0.996192i \(-0.527786\pi\)
−0.0871821 + 0.996192i \(0.527786\pi\)
\(578\) 7.15073e16 0.0797663
\(579\) −9.94995e17 −1.09751
\(580\) 1.22508e18 1.33623
\(581\) −6.08464e17 −0.656282
\(582\) 2.20484e17 0.235168
\(583\) 2.84054e17 0.299609
\(584\) −8.26740e16 −0.0862354
\(585\) −9.51491e16 −0.0981503
\(586\) 5.24769e17 0.535345
\(587\) 1.29963e18 1.31121 0.655605 0.755104i \(-0.272414\pi\)
0.655605 + 0.755104i \(0.272414\pi\)
\(588\) 3.49336e17 0.348571
\(589\) 3.31324e17 0.326967
\(590\) −9.42700e16 −0.0920101
\(591\) −8.20961e17 −0.792508
\(592\) −1.42970e17 −0.136507
\(593\) −1.73461e18 −1.63812 −0.819062 0.573705i \(-0.805506\pi\)
−0.819062 + 0.573705i \(0.805506\pi\)
\(594\) −5.39203e16 −0.0503663
\(595\) −4.81951e17 −0.445289
\(596\) −1.17932e17 −0.107779
\(597\) −1.06708e18 −0.964634
\(598\) −1.36480e17 −0.122042
\(599\) −5.57315e17 −0.492976 −0.246488 0.969146i \(-0.579277\pi\)
−0.246488 + 0.969146i \(0.579277\pi\)
\(600\) 4.11912e17 0.360430
\(601\) −1.84473e18 −1.59679 −0.798395 0.602134i \(-0.794317\pi\)
−0.798395 + 0.602134i \(0.794317\pi\)
\(602\) 2.84705e17 0.243791
\(603\) −6.33489e17 −0.536632
\(604\) −7.08277e17 −0.593558
\(605\) −1.20196e18 −0.996505
\(606\) 3.66112e16 0.0300291
\(607\) 1.87633e18 1.52259 0.761295 0.648405i \(-0.224564\pi\)
0.761295 + 0.648405i \(0.224564\pi\)
\(608\) −1.74369e18 −1.39989
\(609\) −3.99365e17 −0.317218
\(610\) 9.87698e17 0.776212
\(611\) −6.11066e16 −0.0475139
\(612\) 2.80749e17 0.215990
\(613\) −1.43070e18 −1.08907 −0.544535 0.838738i \(-0.683294\pi\)
−0.544535 + 0.838738i \(0.683294\pi\)
\(614\) 3.52885e17 0.265790
\(615\) −1.36164e18 −1.01478
\(616\) 2.25010e17 0.165931
\(617\) 9.18832e17 0.670475 0.335238 0.942134i \(-0.391183\pi\)
0.335238 + 0.942134i \(0.391183\pi\)
\(618\) −8.30661e17 −0.599790
\(619\) 1.60857e18 1.14935 0.574674 0.818383i \(-0.305129\pi\)
0.574674 + 0.818383i \(0.305129\pi\)
\(620\) −3.10004e17 −0.219190
\(621\) −2.69588e17 −0.188627
\(622\) −1.43129e18 −0.991038
\(623\) 2.93093e17 0.200832
\(624\) −3.73745e16 −0.0253440
\(625\) −1.81893e18 −1.22066
\(626\) 1.82855e17 0.121443
\(627\) 5.68557e17 0.373710
\(628\) −1.74886e18 −1.13767
\(629\) 1.01669e18 0.654574
\(630\) −1.37790e17 −0.0878022
\(631\) −1.14567e18 −0.722550 −0.361275 0.932459i \(-0.617658\pi\)
−0.361275 + 0.932459i \(0.617658\pi\)
\(632\) −1.17970e17 −0.0736396
\(633\) −5.27604e17 −0.325975
\(634\) 3.61939e17 0.221338
\(635\) 2.69540e18 1.63153
\(636\) −4.22846e17 −0.253344
\(637\) 3.30707e17 0.196127
\(638\) 6.57219e17 0.385812
\(639\) 1.07555e18 0.624995
\(640\) 1.86828e18 1.07467
\(641\) 2.85339e18 1.62474 0.812371 0.583141i \(-0.198177\pi\)
0.812371 + 0.583141i \(0.198177\pi\)
\(642\) 1.78106e17 0.100393
\(643\) −2.71854e18 −1.51693 −0.758464 0.651715i \(-0.774050\pi\)
−0.758464 + 0.651715i \(0.774050\pi\)
\(644\) 4.63674e17 0.256126
\(645\) −1.63312e18 −0.893061
\(646\) 1.26185e18 0.683121
\(647\) −3.14020e18 −1.68298 −0.841491 0.540272i \(-0.818322\pi\)
−0.841491 + 0.540272i \(0.818322\pi\)
\(648\) 1.94747e17 0.103332
\(649\) 1.18645e17 0.0623247
\(650\) 1.60719e17 0.0835854
\(651\) 1.01059e17 0.0520353
\(652\) −9.21194e17 −0.469615
\(653\) 2.80797e18 1.41728 0.708642 0.705568i \(-0.249308\pi\)
0.708642 + 0.705568i \(0.249308\pi\)
\(654\) −7.66595e17 −0.383099
\(655\) 1.27377e18 0.630265
\(656\) −5.34849e17 −0.262033
\(657\) −6.37182e16 −0.0309093
\(658\) −8.84917e16 −0.0425044
\(659\) −2.36009e18 −1.12247 −0.561233 0.827658i \(-0.689673\pi\)
−0.561233 + 0.827658i \(0.689673\pi\)
\(660\) −5.31972e17 −0.250526
\(661\) 5.16477e17 0.240847 0.120424 0.992723i \(-0.461575\pi\)
0.120424 + 0.992723i \(0.461575\pi\)
\(662\) −7.94230e17 −0.366749
\(663\) 2.65777e17 0.121529
\(664\) −3.61654e18 −1.63757
\(665\) 1.45292e18 0.651478
\(666\) 2.90673e17 0.129069
\(667\) 3.28593e18 1.44491
\(668\) 1.29425e18 0.563600
\(669\) −2.62369e18 −1.13147
\(670\) 2.66407e18 1.13778
\(671\) −1.24309e18 −0.525781
\(672\) −5.31852e17 −0.222787
\(673\) 1.59299e18 0.660870 0.330435 0.943829i \(-0.392805\pi\)
0.330435 + 0.943829i \(0.392805\pi\)
\(674\) −2.73648e17 −0.112435
\(675\) 3.17467e17 0.129189
\(676\) 1.64938e18 0.664764
\(677\) −1.54364e18 −0.616198 −0.308099 0.951354i \(-0.599693\pi\)
−0.308099 + 0.951354i \(0.599693\pi\)
\(678\) 8.31058e17 0.328578
\(679\) −7.09122e17 −0.277694
\(680\) −2.86458e18 −1.11110
\(681\) −2.04236e18 −0.784650
\(682\) −1.66309e17 −0.0632872
\(683\) −5.23911e17 −0.197480 −0.0987399 0.995113i \(-0.531481\pi\)
−0.0987399 + 0.995113i \(0.531481\pi\)
\(684\) −8.46361e17 −0.316003
\(685\) −1.53541e18 −0.567851
\(686\) 1.03508e18 0.379201
\(687\) −1.32291e18 −0.480078
\(688\) −6.41489e17 −0.230603
\(689\) −4.00296e17 −0.142547
\(690\) 1.13372e18 0.399933
\(691\) 9.33605e17 0.326254 0.163127 0.986605i \(-0.447842\pi\)
0.163127 + 0.986605i \(0.447842\pi\)
\(692\) −2.26456e18 −0.783960
\(693\) 1.73419e17 0.0594744
\(694\) 6.87886e17 0.233711
\(695\) −2.39374e18 −0.805705
\(696\) −2.37371e18 −0.791532
\(697\) 3.80341e18 1.25649
\(698\) 2.98041e17 0.0975475
\(699\) −3.33192e18 −1.08042
\(700\) −5.46024e17 −0.175418
\(701\) −4.26621e17 −0.135792 −0.0678962 0.997692i \(-0.521629\pi\)
−0.0678962 + 0.997692i \(0.521629\pi\)
\(702\) 7.59860e16 0.0239631
\(703\) −3.06497e18 −0.957671
\(704\) 5.77218e17 0.178697
\(705\) 5.07606e17 0.155703
\(706\) 2.49824e18 0.759283
\(707\) −1.17749e17 −0.0354594
\(708\) −1.76617e17 −0.0527007
\(709\) −3.18574e18 −0.941910 −0.470955 0.882157i \(-0.656091\pi\)
−0.470955 + 0.882157i \(0.656091\pi\)
\(710\) −4.52313e18 −1.32513
\(711\) −9.09217e16 −0.0263946
\(712\) 1.74206e18 0.501121
\(713\) −8.31500e17 −0.237017
\(714\) 3.84885e17 0.108716
\(715\) −5.03603e17 −0.140961
\(716\) −4.69189e18 −1.30141
\(717\) 2.86642e18 0.787889
\(718\) −2.53619e18 −0.690832
\(719\) 9.40698e17 0.253929 0.126965 0.991907i \(-0.459477\pi\)
0.126965 + 0.991907i \(0.459477\pi\)
\(720\) 3.10465e17 0.0830523
\(721\) 2.67158e18 0.708253
\(722\) −1.72327e18 −0.452753
\(723\) −1.93619e18 −0.504137
\(724\) −2.67239e18 −0.689604
\(725\) −3.86952e18 −0.989600
\(726\) 9.59882e17 0.243293
\(727\) −5.82825e18 −1.46408 −0.732040 0.681262i \(-0.761432\pi\)
−0.732040 + 0.681262i \(0.761432\pi\)
\(728\) −3.17090e17 −0.0789457
\(729\) 1.50095e17 0.0370370
\(730\) 2.67960e17 0.0655347
\(731\) 4.56175e18 1.10578
\(732\) 1.85047e18 0.444591
\(733\) 3.47252e18 0.826931 0.413466 0.910520i \(-0.364318\pi\)
0.413466 + 0.910520i \(0.364318\pi\)
\(734\) −1.51405e18 −0.357369
\(735\) −2.74714e18 −0.642708
\(736\) 4.37600e18 1.01478
\(737\) −3.35291e18 −0.770697
\(738\) 1.08740e18 0.247756
\(739\) −1.68498e18 −0.380545 −0.190273 0.981731i \(-0.560937\pi\)
−0.190273 + 0.981731i \(0.560937\pi\)
\(740\) 2.86775e18 0.642000
\(741\) −8.01226e17 −0.177802
\(742\) −5.79690e17 −0.127518
\(743\) 2.87648e18 0.627241 0.313620 0.949548i \(-0.398458\pi\)
0.313620 + 0.949548i \(0.398458\pi\)
\(744\) 6.00666e17 0.129840
\(745\) 9.27407e17 0.198726
\(746\) 1.73639e18 0.368845
\(747\) −2.78732e18 −0.586953
\(748\) 1.48594e18 0.310199
\(749\) −5.72827e17 −0.118547
\(750\) 6.53762e17 0.134129
\(751\) −1.25091e18 −0.254429 −0.127215 0.991875i \(-0.540604\pi\)
−0.127215 + 0.991875i \(0.540604\pi\)
\(752\) 1.99387e17 0.0402051
\(753\) 1.18479e17 0.0236851
\(754\) −9.26171e17 −0.183560
\(755\) 5.56981e18 1.09442
\(756\) −2.58153e17 −0.0502905
\(757\) 9.78014e18 1.88896 0.944478 0.328574i \(-0.106568\pi\)
0.944478 + 0.328574i \(0.106568\pi\)
\(758\) 1.98625e18 0.380351
\(759\) −1.42687e18 −0.270902
\(760\) 8.63572e18 1.62559
\(761\) −2.61183e18 −0.487467 −0.243734 0.969842i \(-0.578372\pi\)
−0.243734 + 0.969842i \(0.578372\pi\)
\(762\) −2.15255e18 −0.398332
\(763\) 2.46553e18 0.452377
\(764\) −8.97511e17 −0.163280
\(765\) −2.20778e18 −0.398250
\(766\) −5.74952e18 −1.02836
\(767\) −1.67198e17 −0.0296525
\(768\) −2.71753e18 −0.477888
\(769\) 4.05338e18 0.706799 0.353400 0.935472i \(-0.385026\pi\)
0.353400 + 0.935472i \(0.385026\pi\)
\(770\) −7.29294e17 −0.126099
\(771\) −6.25704e18 −1.07279
\(772\) 7.83945e18 1.33283
\(773\) 1.38763e18 0.233941 0.116970 0.993135i \(-0.462682\pi\)
0.116970 + 0.993135i \(0.462682\pi\)
\(774\) 1.30421e18 0.218038
\(775\) 9.79177e17 0.162331
\(776\) −4.21482e18 −0.692911
\(777\) −9.34863e17 −0.152409
\(778\) −3.91632e18 −0.633157
\(779\) −1.14660e19 −1.83831
\(780\) 7.49670e17 0.119194
\(781\) 5.69267e18 0.897603
\(782\) −3.16678e18 −0.495193
\(783\) −1.82946e18 −0.283708
\(784\) −1.07907e18 −0.165958
\(785\) 1.37528e19 2.09768
\(786\) −1.01723e18 −0.153877
\(787\) −2.36169e18 −0.354313 −0.177157 0.984183i \(-0.556690\pi\)
−0.177157 + 0.984183i \(0.556690\pi\)
\(788\) 6.46826e18 0.962426
\(789\) 7.14340e17 0.105416
\(790\) 3.82361e17 0.0559626
\(791\) −2.67285e18 −0.387997
\(792\) 1.03075e18 0.148402
\(793\) 1.75179e18 0.250154
\(794\) 1.92465e18 0.272595
\(795\) 3.32521e18 0.467125
\(796\) 8.40739e18 1.17146
\(797\) −9.88256e18 −1.36581 −0.682905 0.730507i \(-0.739284\pi\)
−0.682905 + 0.730507i \(0.739284\pi\)
\(798\) −1.16030e18 −0.159056
\(799\) −1.41788e18 −0.192790
\(800\) −5.15320e18 −0.695011
\(801\) 1.34263e18 0.179616
\(802\) −3.38865e18 −0.449670
\(803\) −3.37246e17 −0.0443911
\(804\) 4.99119e18 0.651688
\(805\) −3.64628e18 −0.472255
\(806\) 2.34367e17 0.0301105
\(807\) 2.72220e18 0.346930
\(808\) −6.99867e17 −0.0884793
\(809\) 9.16850e18 1.14983 0.574914 0.818214i \(-0.305035\pi\)
0.574914 + 0.818214i \(0.305035\pi\)
\(810\) −6.31207e17 −0.0785270
\(811\) 1.02083e19 1.25984 0.629921 0.776659i \(-0.283087\pi\)
0.629921 + 0.776659i \(0.283087\pi\)
\(812\) 3.14656e18 0.385231
\(813\) 7.00236e18 0.850463
\(814\) 1.53847e18 0.185366
\(815\) 7.24417e18 0.865893
\(816\) −8.67212e17 −0.102835
\(817\) −1.37521e19 −1.61780
\(818\) −7.38098e18 −0.861426
\(819\) −2.44387e17 −0.0282964
\(820\) 1.07282e19 1.23236
\(821\) −7.37435e18 −0.840414 −0.420207 0.907428i \(-0.638043\pi\)
−0.420207 + 0.907428i \(0.638043\pi\)
\(822\) 1.22617e18 0.138639
\(823\) 6.15624e18 0.690584 0.345292 0.938495i \(-0.387780\pi\)
0.345292 + 0.938495i \(0.387780\pi\)
\(824\) 1.58791e19 1.76725
\(825\) 1.68028e18 0.185538
\(826\) −2.42128e17 −0.0265262
\(827\) −1.23456e19 −1.34191 −0.670957 0.741496i \(-0.734117\pi\)
−0.670957 + 0.741496i \(0.734117\pi\)
\(828\) 2.12405e18 0.229070
\(829\) 2.56859e18 0.274847 0.137423 0.990512i \(-0.456118\pi\)
0.137423 + 0.990512i \(0.456118\pi\)
\(830\) 1.17218e19 1.24448
\(831\) −2.06829e18 −0.217874
\(832\) −8.13432e17 −0.0850197
\(833\) 7.67350e18 0.795795
\(834\) 1.91164e18 0.196710
\(835\) −1.01778e19 −1.03919
\(836\) −4.47960e18 −0.453835
\(837\) 4.62943e17 0.0465384
\(838\) 8.76332e18 0.874143
\(839\) −6.60491e18 −0.653754 −0.326877 0.945067i \(-0.605996\pi\)
−0.326877 + 0.945067i \(0.605996\pi\)
\(840\) 2.63403e18 0.258705
\(841\) 1.20381e19 1.17323
\(842\) −5.28318e18 −0.510936
\(843\) −6.28219e18 −0.602881
\(844\) 4.15693e18 0.395865
\(845\) −1.29705e19 −1.22572
\(846\) −4.05373e17 −0.0380144
\(847\) −3.08718e18 −0.287289
\(848\) 1.30614e18 0.120619
\(849\) 6.84372e18 0.627180
\(850\) 3.72922e18 0.339152
\(851\) 7.69193e18 0.694214
\(852\) −8.47418e18 −0.758997
\(853\) 1.36136e18 0.121006 0.0605028 0.998168i \(-0.480730\pi\)
0.0605028 + 0.998168i \(0.480730\pi\)
\(854\) 2.53686e18 0.223780
\(855\) 6.65569e18 0.582658
\(856\) −3.40472e18 −0.295802
\(857\) −4.49699e18 −0.387745 −0.193873 0.981027i \(-0.562105\pi\)
−0.193873 + 0.981027i \(0.562105\pi\)
\(858\) 4.02177e17 0.0344151
\(859\) 3.76827e17 0.0320027 0.0160013 0.999872i \(-0.494906\pi\)
0.0160013 + 0.999872i \(0.494906\pi\)
\(860\) 1.28672e19 1.08454
\(861\) −3.49731e18 −0.292559
\(862\) 2.74182e18 0.227637
\(863\) 7.43499e18 0.612647 0.306323 0.951928i \(-0.400901\pi\)
0.306323 + 0.951928i \(0.400901\pi\)
\(864\) −2.43637e18 −0.199252
\(865\) 1.78082e19 1.44549
\(866\) −1.30375e19 −1.05033
\(867\) −1.05353e18 −0.0842408
\(868\) −7.96233e17 −0.0631920
\(869\) −4.81228e17 −0.0379072
\(870\) 7.69359e18 0.601526
\(871\) 4.72502e18 0.366679
\(872\) 1.46544e19 1.12878
\(873\) −3.24843e18 −0.248359
\(874\) 9.54677e18 0.724490
\(875\) −2.10263e18 −0.158384
\(876\) 5.02029e17 0.0375364
\(877\) −1.41996e18 −0.105385 −0.0526925 0.998611i \(-0.516780\pi\)
−0.0526925 + 0.998611i \(0.516780\pi\)
\(878\) 1.13826e18 0.0838549
\(879\) −7.73151e18 −0.565375
\(880\) 1.64322e18 0.119278
\(881\) 5.51464e17 0.0397350 0.0198675 0.999803i \(-0.493676\pi\)
0.0198675 + 0.999803i \(0.493676\pi\)
\(882\) 2.19386e18 0.156915
\(883\) 7.55926e18 0.536704 0.268352 0.963321i \(-0.413521\pi\)
0.268352 + 0.963321i \(0.413521\pi\)
\(884\) −2.09403e18 −0.147585
\(885\) 1.38890e18 0.0971714
\(886\) −8.39746e18 −0.583215
\(887\) −1.17171e19 −0.807826 −0.403913 0.914797i \(-0.632350\pi\)
−0.403913 + 0.914797i \(0.632350\pi\)
\(888\) −5.55656e18 −0.380296
\(889\) 6.92303e18 0.470365
\(890\) −5.64630e18 −0.380828
\(891\) 7.94417e17 0.0531917
\(892\) 2.06718e19 1.37406
\(893\) 4.27442e18 0.282061
\(894\) −7.40626e17 −0.0485183
\(895\) 3.68965e19 2.39958
\(896\) 4.79861e18 0.309823
\(897\) 2.01078e18 0.128888
\(898\) −1.37358e18 −0.0874096
\(899\) −5.64268e18 −0.356490
\(900\) −2.50129e18 −0.156887
\(901\) −9.28821e18 −0.578390
\(902\) 5.75537e18 0.355820
\(903\) −4.19461e18 −0.257467
\(904\) −1.58867e19 −0.968140
\(905\) 2.10154e19 1.27152
\(906\) −4.44805e18 −0.267200
\(907\) 1.34218e19 0.800502 0.400251 0.916406i \(-0.368923\pi\)
0.400251 + 0.916406i \(0.368923\pi\)
\(908\) 1.60915e19 0.952882
\(909\) −5.39399e17 −0.0317136
\(910\) 1.02774e18 0.0599949
\(911\) 2.44836e19 1.41908 0.709538 0.704667i \(-0.248904\pi\)
0.709538 + 0.704667i \(0.248904\pi\)
\(912\) 2.61435e18 0.150452
\(913\) −1.47527e19 −0.842968
\(914\) 7.79779e18 0.442406
\(915\) −1.45519e19 −0.819754
\(916\) 1.04231e19 0.583009
\(917\) 3.27163e18 0.181704
\(918\) 1.76313e18 0.0972314
\(919\) −2.13400e19 −1.16854 −0.584270 0.811559i \(-0.698619\pi\)
−0.584270 + 0.811559i \(0.698619\pi\)
\(920\) −2.16724e19 −1.17838
\(921\) −5.19912e18 −0.280700
\(922\) 4.10944e18 0.220309
\(923\) −8.02227e18 −0.427057
\(924\) −1.36635e18 −0.0722260
\(925\) −9.05805e18 −0.475459
\(926\) 5.29855e18 0.276176
\(927\) 1.22383e19 0.633435
\(928\) 2.96962e19 1.52630
\(929\) −3.42915e19 −1.75018 −0.875092 0.483956i \(-0.839199\pi\)
−0.875092 + 0.483956i \(0.839199\pi\)
\(930\) −1.94686e18 −0.0986721
\(931\) −2.31330e19 −1.16428
\(932\) 2.62518e19 1.31207
\(933\) 2.10875e19 1.04663
\(934\) −5.22329e18 −0.257448
\(935\) −1.16853e19 −0.571957
\(936\) −1.45256e18 −0.0706061
\(937\) −3.23335e18 −0.156080 −0.0780398 0.996950i \(-0.524866\pi\)
−0.0780398 + 0.996950i \(0.524866\pi\)
\(938\) 6.84255e18 0.328019
\(939\) −2.69404e18 −0.128256
\(940\) −3.99937e18 −0.189087
\(941\) 1.33516e19 0.626902 0.313451 0.949604i \(-0.398515\pi\)
0.313451 + 0.949604i \(0.398515\pi\)
\(942\) −1.09830e19 −0.512142
\(943\) 2.87754e19 1.33258
\(944\) 5.45557e17 0.0250912
\(945\) 2.03009e18 0.0927275
\(946\) 6.90289e18 0.313140
\(947\) −2.64881e19 −1.19337 −0.596686 0.802474i \(-0.703516\pi\)
−0.596686 + 0.802474i \(0.703516\pi\)
\(948\) 7.16362e17 0.0320537
\(949\) 4.75257e17 0.0211202
\(950\) −1.12423e19 −0.496195
\(951\) −5.33251e18 −0.233754
\(952\) −7.35755e18 −0.320326
\(953\) −1.90636e19 −0.824328 −0.412164 0.911110i \(-0.635227\pi\)
−0.412164 + 0.911110i \(0.635227\pi\)
\(954\) −2.65551e18 −0.114047
\(955\) 7.05793e18 0.301062
\(956\) −2.25842e19 −0.956816
\(957\) −9.68292e18 −0.407454
\(958\) 1.41453e19 0.591201
\(959\) −3.94363e18 −0.163710
\(960\) 6.75709e18 0.278610
\(961\) −2.29897e19 −0.941523
\(962\) −2.16805e18 −0.0881924
\(963\) −2.62407e18 −0.106024
\(964\) 1.52550e19 0.612226
\(965\) −6.16486e19 −2.45751
\(966\) 2.91191e18 0.115299
\(967\) 1.19401e19 0.469607 0.234803 0.972043i \(-0.424555\pi\)
0.234803 + 0.972043i \(0.424555\pi\)
\(968\) −1.83493e19 −0.716853
\(969\) −1.85911e19 −0.721441
\(970\) 1.36609e19 0.526579
\(971\) −2.27579e19 −0.871378 −0.435689 0.900097i \(-0.643495\pi\)
−0.435689 + 0.900097i \(0.643495\pi\)
\(972\) −1.18258e18 −0.0449779
\(973\) −6.14822e18 −0.232282
\(974\) 7.29790e18 0.273883
\(975\) −2.36790e18 −0.0882742
\(976\) −5.71598e18 −0.211674
\(977\) 1.73613e18 0.0638657 0.0319328 0.999490i \(-0.489834\pi\)
0.0319328 + 0.999490i \(0.489834\pi\)
\(978\) −5.78519e18 −0.211405
\(979\) 7.10625e18 0.257961
\(980\) 2.16444e19 0.780507
\(981\) 1.12944e19 0.404589
\(982\) 2.43211e19 0.865483
\(983\) 4.30016e19 1.52015 0.760075 0.649835i \(-0.225162\pi\)
0.760075 + 0.649835i \(0.225162\pi\)
\(984\) −2.07870e19 −0.730001
\(985\) −5.08657e19 −1.77456
\(986\) −2.14903e19 −0.744803
\(987\) 1.30376e18 0.0448887
\(988\) 6.31277e18 0.215924
\(989\) 3.45127e19 1.17274
\(990\) −3.34083e18 −0.112778
\(991\) 7.41012e17 0.0248512 0.0124256 0.999923i \(-0.496045\pi\)
0.0124256 + 0.999923i \(0.496045\pi\)
\(992\) −7.51459e18 −0.250368
\(993\) 1.17015e19 0.387322
\(994\) −1.16175e19 −0.382032
\(995\) −6.61148e19 −2.15997
\(996\) 2.19610e19 0.712799
\(997\) 5.06954e19 1.63474 0.817372 0.576110i \(-0.195430\pi\)
0.817372 + 0.576110i \(0.195430\pi\)
\(998\) −1.67501e19 −0.536624
\(999\) −4.28253e18 −0.136309
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.a.1.11 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.a.1.11 30 1.1 even 1 trivial