Properties

Label 177.14.a.b.1.8
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $1$
Dimension $31$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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: \(31\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-98.0136 q^{2} -729.000 q^{3} +1414.67 q^{4} +43954.8 q^{5} +71451.9 q^{6} -396678. q^{7} +664271. q^{8} +531441. q^{9} +O(q^{10})\) \(q-98.0136 q^{2} -729.000 q^{3} +1414.67 q^{4} +43954.8 q^{5} +71451.9 q^{6} -396678. q^{7} +664271. q^{8} +531441. q^{9} -4.30817e6 q^{10} -1.79804e6 q^{11} -1.03129e6 q^{12} +6.51184e6 q^{13} +3.88799e7 q^{14} -3.20431e7 q^{15} -7.66965e7 q^{16} +9.76681e7 q^{17} -5.20884e7 q^{18} -6.83663e7 q^{19} +6.21814e7 q^{20} +2.89178e8 q^{21} +1.76232e8 q^{22} +1.72252e8 q^{23} -4.84253e8 q^{24} +7.11324e8 q^{25} -6.38249e8 q^{26} -3.87420e8 q^{27} -5.61168e8 q^{28} -5.74570e8 q^{29} +3.14066e9 q^{30} +3.46020e8 q^{31} +2.07560e9 q^{32} +1.31077e9 q^{33} -9.57281e9 q^{34} -1.74359e10 q^{35} +7.51812e8 q^{36} +2.87382e10 q^{37} +6.70083e9 q^{38} -4.74713e9 q^{39} +2.91979e10 q^{40} -3.40879e10 q^{41} -2.83434e10 q^{42} -5.78702e10 q^{43} -2.54363e9 q^{44} +2.33594e10 q^{45} -1.68830e10 q^{46} -1.12577e11 q^{47} +5.59118e10 q^{48} +6.04647e10 q^{49} -6.97194e10 q^{50} -7.12001e10 q^{51} +9.21208e9 q^{52} -1.23263e11 q^{53} +3.79725e10 q^{54} -7.90325e10 q^{55} -2.63502e11 q^{56} +4.98390e10 q^{57} +5.63157e10 q^{58} -4.21805e10 q^{59} -4.53303e10 q^{60} +5.05675e11 q^{61} -3.39147e10 q^{62} -2.10811e11 q^{63} +4.24861e11 q^{64} +2.86227e11 q^{65} -1.28473e11 q^{66} +1.07434e9 q^{67} +1.38168e11 q^{68} -1.25572e11 q^{69} +1.70896e12 q^{70} +8.42822e11 q^{71} +3.53021e11 q^{72} -6.23496e11 q^{73} -2.81674e12 q^{74} -5.18555e11 q^{75} -9.67155e10 q^{76} +7.13243e11 q^{77} +4.65283e11 q^{78} -2.92796e12 q^{79} -3.37118e12 q^{80} +2.82430e11 q^{81} +3.34107e12 q^{82} +1.48483e12 q^{83} +4.09091e11 q^{84} +4.29299e12 q^{85} +5.67207e12 q^{86} +4.18862e11 q^{87} -1.19439e12 q^{88} +8.15790e12 q^{89} -2.28954e12 q^{90} -2.58311e12 q^{91} +2.43679e11 q^{92} -2.52249e11 q^{93} +1.10341e13 q^{94} -3.00503e12 q^{95} -1.51311e12 q^{96} +1.16685e13 q^{97} -5.92636e12 q^{98} -9.55552e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q - 52q^{2} - 22599q^{3} + 126886q^{4} + 33486q^{5} + 37908q^{6} - 1135539q^{7} - 1519749q^{8} + 16474671q^{9} - 3854663q^{10} + 3943968q^{11} - 92499894q^{12} - 48510022q^{13} - 51427459q^{14} - 24411294q^{15} + 370110498q^{16} + 83288419q^{17} - 27634932q^{18} - 180425297q^{19} + 753620445q^{20} + 827807931q^{21} + 2300196142q^{22} - 1305810279q^{23} + 1107897021q^{24} + 8070954867q^{25} + 464550322q^{26} - 12010035159q^{27} - 9887169562q^{28} + 6248352277q^{29} + 2810049327q^{30} - 26730150789q^{31} - 24001343230q^{32} - 2875152672q^{33} - 36571033348q^{34} + 10255900979q^{35} + 67432422726q^{36} - 43284776933q^{37} - 36293696947q^{38} + 35363806038q^{39} - 105980683856q^{40} - 9961079285q^{41} + 37490617611q^{42} - 51755851288q^{43} - 59623729442q^{44} + 17795833326q^{45} - 202287132683q^{46} - 82747063727q^{47} - 269810553042q^{48} + 535277836542q^{49} + 526974390461q^{50} - 60717257451q^{51} + 544982341446q^{52} + 561701818494q^{53} + 20145865428q^{54} - 521861534450q^{55} - 228056576664q^{56} + 131530041513q^{57} + 10555409160q^{58} - 1307596542871q^{59} - 549389304405q^{60} + 618193248201q^{61} - 1486611437386q^{62} - 603471981699q^{63} + 679062548045q^{64} - 1130583307122q^{65} - 1676842987518q^{66} - 4137387490592q^{67} - 3901389300295q^{68} + 951935693391q^{69} - 819291947844q^{70} - 3766439869810q^{71} - 807656928309q^{72} - 2386775553523q^{73} + 3060770694642q^{74} - 5883726098043q^{75} - 847741068784q^{76} + 1650423006137q^{77} - 338657184738q^{78} + 787155757766q^{79} + 13999832121779q^{80} + 8755315630911q^{81} + 10083281915577q^{82} + 8743877051639q^{83} + 7207746610698q^{84} + 15373177520565q^{85} + 18939443838984q^{86} - 4555048809933q^{87} + 39713314506713q^{88} + 11026795445259q^{89} - 2048525959383q^{90} + 23285721962531q^{91} + 40411079823254q^{92} + 19486279925181q^{93} + 35237377585624q^{94} + 13730236994039q^{95} + 17496979214670q^{96} + 10134565481560q^{97} + 70916776240976q^{98} + 2095986297888q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −98.0136 −1.08291 −0.541454 0.840731i \(-0.682126\pi\)
−0.541454 + 0.840731i \(0.682126\pi\)
\(3\) −729.000 −0.577350
\(4\) 1414.67 0.172689
\(5\) 43954.8 1.25806 0.629030 0.777381i \(-0.283452\pi\)
0.629030 + 0.777381i \(0.283452\pi\)
\(6\) 71451.9 0.625217
\(7\) −396678. −1.27439 −0.637193 0.770704i \(-0.719905\pi\)
−0.637193 + 0.770704i \(0.719905\pi\)
\(8\) 664271. 0.895902
\(9\) 531441. 0.333333
\(10\) −4.30817e6 −1.36236
\(11\) −1.79804e6 −0.306018 −0.153009 0.988225i \(-0.548896\pi\)
−0.153009 + 0.988225i \(0.548896\pi\)
\(12\) −1.03129e6 −0.0997019
\(13\) 6.51184e6 0.374172 0.187086 0.982343i \(-0.440096\pi\)
0.187086 + 0.982343i \(0.440096\pi\)
\(14\) 3.88799e7 1.38004
\(15\) −3.20431e7 −0.726342
\(16\) −7.66965e7 −1.14287
\(17\) 9.76681e7 0.981375 0.490687 0.871336i \(-0.336746\pi\)
0.490687 + 0.871336i \(0.336746\pi\)
\(18\) −5.20884e7 −0.360969
\(19\) −6.83663e7 −0.333383 −0.166692 0.986009i \(-0.553308\pi\)
−0.166692 + 0.986009i \(0.553308\pi\)
\(20\) 6.21814e7 0.217253
\(21\) 2.89178e8 0.735767
\(22\) 1.76232e8 0.331389
\(23\) 1.72252e8 0.242624 0.121312 0.992614i \(-0.461290\pi\)
0.121312 + 0.992614i \(0.461290\pi\)
\(24\) −4.84253e8 −0.517249
\(25\) 7.11324e8 0.582716
\(26\) −6.38249e8 −0.405194
\(27\) −3.87420e8 −0.192450
\(28\) −5.61168e8 −0.220072
\(29\) −5.74570e8 −0.179373 −0.0896863 0.995970i \(-0.528586\pi\)
−0.0896863 + 0.995970i \(0.528586\pi\)
\(30\) 3.14066e9 0.786561
\(31\) 3.46020e8 0.0700246 0.0350123 0.999387i \(-0.488853\pi\)
0.0350123 + 0.999387i \(0.488853\pi\)
\(32\) 2.07560e9 0.341718
\(33\) 1.31077e9 0.176680
\(34\) −9.57281e9 −1.06274
\(35\) −1.74359e10 −1.60326
\(36\) 7.51812e8 0.0575629
\(37\) 2.87382e10 1.84140 0.920701 0.390268i \(-0.127618\pi\)
0.920701 + 0.390268i \(0.127618\pi\)
\(38\) 6.70083e9 0.361023
\(39\) −4.74713e9 −0.216029
\(40\) 2.91979e10 1.12710
\(41\) −3.40879e10 −1.12074 −0.560370 0.828243i \(-0.689341\pi\)
−0.560370 + 0.828243i \(0.689341\pi\)
\(42\) −2.83434e10 −0.796768
\(43\) −5.78702e10 −1.39608 −0.698040 0.716059i \(-0.745944\pi\)
−0.698040 + 0.716059i \(0.745944\pi\)
\(44\) −2.54363e9 −0.0528459
\(45\) 2.33594e10 0.419354
\(46\) −1.68830e10 −0.262739
\(47\) −1.12577e11 −1.52339 −0.761697 0.647933i \(-0.775634\pi\)
−0.761697 + 0.647933i \(0.775634\pi\)
\(48\) 5.59118e10 0.659835
\(49\) 6.04647e10 0.624061
\(50\) −6.97194e10 −0.631028
\(51\) −7.12001e10 −0.566597
\(52\) 9.21208e9 0.0646154
\(53\) −1.23263e11 −0.763906 −0.381953 0.924182i \(-0.624748\pi\)
−0.381953 + 0.924182i \(0.624748\pi\)
\(54\) 3.79725e10 0.208406
\(55\) −7.90325e10 −0.384989
\(56\) −2.63502e11 −1.14172
\(57\) 4.98390e10 0.192479
\(58\) 5.63157e10 0.194244
\(59\) −4.21805e10 −0.130189
\(60\) −4.53303e10 −0.125431
\(61\) 5.05675e11 1.25669 0.628344 0.777936i \(-0.283733\pi\)
0.628344 + 0.777936i \(0.283733\pi\)
\(62\) −3.39147e10 −0.0758302
\(63\) −2.10811e11 −0.424796
\(64\) 4.24861e11 0.772818
\(65\) 2.86227e11 0.470732
\(66\) −1.28473e11 −0.191328
\(67\) 1.07434e9 0.00145096 0.000725482 1.00000i \(-0.499769\pi\)
0.000725482 1.00000i \(0.499769\pi\)
\(68\) 1.38168e11 0.169472
\(69\) −1.25572e11 −0.140079
\(70\) 1.70896e12 1.73618
\(71\) 8.42822e11 0.780830 0.390415 0.920639i \(-0.372332\pi\)
0.390415 + 0.920639i \(0.372332\pi\)
\(72\) 3.53021e11 0.298634
\(73\) −6.23496e11 −0.482208 −0.241104 0.970499i \(-0.577510\pi\)
−0.241104 + 0.970499i \(0.577510\pi\)
\(74\) −2.81674e12 −1.99407
\(75\) −5.18555e11 −0.336431
\(76\) −9.67155e10 −0.0575715
\(77\) 7.13243e11 0.389985
\(78\) 4.65283e11 0.233939
\(79\) −2.92796e12 −1.35515 −0.677577 0.735452i \(-0.736970\pi\)
−0.677577 + 0.735452i \(0.736970\pi\)
\(80\) −3.37118e12 −1.43780
\(81\) 2.82430e11 0.111111
\(82\) 3.34107e12 1.21366
\(83\) 1.48483e12 0.498503 0.249252 0.968439i \(-0.419815\pi\)
0.249252 + 0.968439i \(0.419815\pi\)
\(84\) 4.09091e11 0.127059
\(85\) 4.29299e12 1.23463
\(86\) 5.67207e12 1.51183
\(87\) 4.18862e11 0.103561
\(88\) −1.19439e12 −0.274162
\(89\) 8.15790e12 1.73998 0.869988 0.493073i \(-0.164126\pi\)
0.869988 + 0.493073i \(0.164126\pi\)
\(90\) −2.28954e12 −0.454121
\(91\) −2.58311e12 −0.476840
\(92\) 2.43679e11 0.0418984
\(93\) −2.52249e11 −0.0404287
\(94\) 1.10341e13 1.64970
\(95\) −3.00503e12 −0.419416
\(96\) −1.51311e12 −0.197291
\(97\) 1.16685e13 1.42233 0.711165 0.703026i \(-0.248168\pi\)
0.711165 + 0.703026i \(0.248168\pi\)
\(98\) −5.92636e12 −0.675801
\(99\) −9.55552e11 −0.102006
\(100\) 1.00629e12 0.100629
\(101\) 5.07705e12 0.475908 0.237954 0.971276i \(-0.423523\pi\)
0.237954 + 0.971276i \(0.423523\pi\)
\(102\) 6.97858e12 0.613572
\(103\) 2.23272e13 1.84243 0.921217 0.389050i \(-0.127197\pi\)
0.921217 + 0.389050i \(0.127197\pi\)
\(104\) 4.32562e12 0.335222
\(105\) 1.27108e13 0.925640
\(106\) 1.20815e13 0.827239
\(107\) −8.65420e12 −0.557484 −0.278742 0.960366i \(-0.589917\pi\)
−0.278742 + 0.960366i \(0.589917\pi\)
\(108\) −5.48071e11 −0.0332340
\(109\) 2.16117e13 1.23429 0.617145 0.786850i \(-0.288289\pi\)
0.617145 + 0.786850i \(0.288289\pi\)
\(110\) 7.74626e12 0.416908
\(111\) −2.09502e13 −1.06313
\(112\) 3.04239e13 1.45645
\(113\) −1.90976e12 −0.0862915 −0.0431457 0.999069i \(-0.513738\pi\)
−0.0431457 + 0.999069i \(0.513738\pi\)
\(114\) −4.88490e12 −0.208437
\(115\) 7.57131e12 0.305235
\(116\) −8.12825e11 −0.0309756
\(117\) 3.46066e12 0.124724
\(118\) 4.13427e12 0.140983
\(119\) −3.87428e13 −1.25065
\(120\) −2.12853e13 −0.650731
\(121\) −3.12898e13 −0.906353
\(122\) −4.95630e13 −1.36088
\(123\) 2.48501e13 0.647059
\(124\) 4.89504e11 0.0120925
\(125\) −2.23897e13 −0.524968
\(126\) 2.06624e13 0.460014
\(127\) −4.53065e13 −0.958157 −0.479079 0.877772i \(-0.659029\pi\)
−0.479079 + 0.877772i \(0.659029\pi\)
\(128\) −5.86455e13 −1.17861
\(129\) 4.21874e13 0.806027
\(130\) −2.80541e13 −0.509759
\(131\) −1.12857e13 −0.195103 −0.0975515 0.995230i \(-0.531101\pi\)
−0.0975515 + 0.995230i \(0.531101\pi\)
\(132\) 1.85430e12 0.0305106
\(133\) 2.71194e13 0.424859
\(134\) −1.05300e11 −0.00157126
\(135\) −1.70290e13 −0.242114
\(136\) 6.48781e13 0.879215
\(137\) 7.67214e13 0.991363 0.495681 0.868504i \(-0.334918\pi\)
0.495681 + 0.868504i \(0.334918\pi\)
\(138\) 1.23077e13 0.151693
\(139\) −4.18439e13 −0.492080 −0.246040 0.969260i \(-0.579129\pi\)
−0.246040 + 0.969260i \(0.579129\pi\)
\(140\) −2.46660e13 −0.276864
\(141\) 8.20684e13 0.879533
\(142\) −8.26080e13 −0.845567
\(143\) −1.17085e13 −0.114503
\(144\) −4.07597e13 −0.380956
\(145\) −2.52551e13 −0.225662
\(146\) 6.11111e13 0.522187
\(147\) −4.40788e13 −0.360302
\(148\) 4.06550e13 0.317990
\(149\) −8.40108e13 −0.628962 −0.314481 0.949264i \(-0.601830\pi\)
−0.314481 + 0.949264i \(0.601830\pi\)
\(150\) 5.08254e13 0.364324
\(151\) 2.33896e14 1.60573 0.802865 0.596161i \(-0.203308\pi\)
0.802865 + 0.596161i \(0.203308\pi\)
\(152\) −4.54138e13 −0.298679
\(153\) 5.19049e13 0.327125
\(154\) −6.99076e13 −0.422318
\(155\) 1.52093e13 0.0880952
\(156\) −6.71561e12 −0.0373057
\(157\) 1.54696e14 0.824385 0.412192 0.911097i \(-0.364763\pi\)
0.412192 + 0.911097i \(0.364763\pi\)
\(158\) 2.86980e14 1.46751
\(159\) 8.98588e13 0.441041
\(160\) 9.12325e13 0.429902
\(161\) −6.83286e13 −0.309197
\(162\) −2.76819e13 −0.120323
\(163\) 2.14513e14 0.895846 0.447923 0.894072i \(-0.352164\pi\)
0.447923 + 0.894072i \(0.352164\pi\)
\(164\) −4.82230e13 −0.193539
\(165\) 5.76147e13 0.222274
\(166\) −1.45533e14 −0.539833
\(167\) 4.60772e14 1.64372 0.821862 0.569687i \(-0.192936\pi\)
0.821862 + 0.569687i \(0.192936\pi\)
\(168\) 1.92093e14 0.659175
\(169\) −2.60471e14 −0.859995
\(170\) −4.20771e14 −1.33699
\(171\) −3.63327e13 −0.111128
\(172\) −8.18671e13 −0.241087
\(173\) −1.40439e14 −0.398280 −0.199140 0.979971i \(-0.563815\pi\)
−0.199140 + 0.979971i \(0.563815\pi\)
\(174\) −4.10541e13 −0.112147
\(175\) −2.82167e14 −0.742606
\(176\) 1.37903e14 0.349738
\(177\) 3.07496e13 0.0751646
\(178\) −7.99585e14 −1.88423
\(179\) −3.25729e14 −0.740136 −0.370068 0.929005i \(-0.620666\pi\)
−0.370068 + 0.929005i \(0.620666\pi\)
\(180\) 3.30458e13 0.0724176
\(181\) −6.48931e13 −0.137179 −0.0685896 0.997645i \(-0.521850\pi\)
−0.0685896 + 0.997645i \(0.521850\pi\)
\(182\) 2.53179e14 0.516374
\(183\) −3.68637e14 −0.725549
\(184\) 1.14422e14 0.217367
\(185\) 1.26318e15 2.31660
\(186\) 2.47238e13 0.0437806
\(187\) −1.75611e14 −0.300318
\(188\) −1.59259e14 −0.263073
\(189\) 1.53681e14 0.245256
\(190\) 2.94534e14 0.454189
\(191\) −1.25464e15 −1.86984 −0.934918 0.354865i \(-0.884527\pi\)
−0.934918 + 0.354865i \(0.884527\pi\)
\(192\) −3.09724e14 −0.446187
\(193\) −1.13796e13 −0.0158490 −0.00792452 0.999969i \(-0.502522\pi\)
−0.00792452 + 0.999969i \(0.502522\pi\)
\(194\) −1.14368e15 −1.54025
\(195\) −2.08659e14 −0.271777
\(196\) 8.55374e13 0.107768
\(197\) 3.13415e14 0.382022 0.191011 0.981588i \(-0.438823\pi\)
0.191011 + 0.981588i \(0.438823\pi\)
\(198\) 9.36571e13 0.110463
\(199\) 6.90722e14 0.788421 0.394211 0.919020i \(-0.371018\pi\)
0.394211 + 0.919020i \(0.371018\pi\)
\(200\) 4.72512e14 0.522056
\(201\) −7.83196e11 −0.000837714 0
\(202\) −4.97620e14 −0.515364
\(203\) 2.27919e14 0.228590
\(204\) −1.00724e14 −0.0978449
\(205\) −1.49833e15 −1.40996
\(206\) −2.18837e15 −1.99518
\(207\) 9.15418e13 0.0808746
\(208\) −4.99435e14 −0.427630
\(209\) 1.22925e14 0.102021
\(210\) −1.24583e15 −1.00238
\(211\) −1.09845e15 −0.856925 −0.428463 0.903560i \(-0.640945\pi\)
−0.428463 + 0.903560i \(0.640945\pi\)
\(212\) −1.74376e14 −0.131918
\(213\) −6.14417e14 −0.450812
\(214\) 8.48230e14 0.603704
\(215\) −2.54368e15 −1.75635
\(216\) −2.57352e14 −0.172416
\(217\) −1.37259e14 −0.0892384
\(218\) −2.11824e15 −1.33662
\(219\) 4.54528e14 0.278403
\(220\) −1.11805e14 −0.0664833
\(221\) 6.35999e14 0.367203
\(222\) 2.05340e15 1.15128
\(223\) −2.02103e14 −0.110050 −0.0550252 0.998485i \(-0.517524\pi\)
−0.0550252 + 0.998485i \(0.517524\pi\)
\(224\) −8.23344e14 −0.435481
\(225\) 3.78026e14 0.194239
\(226\) 1.87182e14 0.0934457
\(227\) 3.68958e15 1.78982 0.894908 0.446250i \(-0.147241\pi\)
0.894908 + 0.446250i \(0.147241\pi\)
\(228\) 7.05056e13 0.0332389
\(229\) −1.70193e15 −0.779848 −0.389924 0.920847i \(-0.627499\pi\)
−0.389924 + 0.920847i \(0.627499\pi\)
\(230\) −7.42091e14 −0.330542
\(231\) −5.19954e14 −0.225158
\(232\) −3.81670e14 −0.160700
\(233\) 1.44631e13 0.00592172 0.00296086 0.999996i \(-0.499058\pi\)
0.00296086 + 0.999996i \(0.499058\pi\)
\(234\) −3.39192e14 −0.135065
\(235\) −4.94829e15 −1.91652
\(236\) −5.96714e13 −0.0224822
\(237\) 2.13448e15 0.782398
\(238\) 3.79732e15 1.35434
\(239\) −1.24049e15 −0.430534 −0.215267 0.976555i \(-0.569062\pi\)
−0.215267 + 0.976555i \(0.569062\pi\)
\(240\) 2.45759e15 0.830112
\(241\) −5.51883e15 −1.81441 −0.907207 0.420685i \(-0.861790\pi\)
−0.907207 + 0.420685i \(0.861790\pi\)
\(242\) 3.06682e15 0.981497
\(243\) −2.05891e14 −0.0641500
\(244\) 7.15361e14 0.217016
\(245\) 2.65771e15 0.785107
\(246\) −2.43564e15 −0.700705
\(247\) −4.45190e14 −0.124743
\(248\) 2.29851e14 0.0627352
\(249\) −1.08244e15 −0.287811
\(250\) 2.19449e15 0.568492
\(251\) −4.36406e15 −1.10157 −0.550784 0.834648i \(-0.685671\pi\)
−0.550784 + 0.834648i \(0.685671\pi\)
\(252\) −2.98227e14 −0.0733574
\(253\) −3.09716e14 −0.0742472
\(254\) 4.44066e15 1.03760
\(255\) −3.12959e15 −0.712813
\(256\) 2.26759e15 0.503506
\(257\) −3.31441e15 −0.717531 −0.358766 0.933428i \(-0.616802\pi\)
−0.358766 + 0.933428i \(0.616802\pi\)
\(258\) −4.13494e15 −0.872853
\(259\) −1.13998e16 −2.34666
\(260\) 4.04915e14 0.0812901
\(261\) −3.05350e14 −0.0597909
\(262\) 1.10615e15 0.211279
\(263\) −9.91017e15 −1.84658 −0.923291 0.384101i \(-0.874511\pi\)
−0.923291 + 0.384101i \(0.874511\pi\)
\(264\) 8.70707e14 0.158287
\(265\) −5.41801e15 −0.961040
\(266\) −2.65807e15 −0.460083
\(267\) −5.94711e15 −1.00458
\(268\) 1.51984e12 0.000250565 0
\(269\) 1.08935e15 0.175299 0.0876495 0.996151i \(-0.472064\pi\)
0.0876495 + 0.996151i \(0.472064\pi\)
\(270\) 1.66907e15 0.262187
\(271\) −1.62457e13 −0.00249137 −0.00124568 0.999999i \(-0.500397\pi\)
−0.00124568 + 0.999999i \(0.500397\pi\)
\(272\) −7.49081e15 −1.12158
\(273\) 1.88308e15 0.275304
\(274\) −7.51974e15 −1.07355
\(275\) −1.27899e15 −0.178322
\(276\) −1.77642e14 −0.0241901
\(277\) −5.67135e15 −0.754341 −0.377171 0.926144i \(-0.623103\pi\)
−0.377171 + 0.926144i \(0.623103\pi\)
\(278\) 4.10127e15 0.532877
\(279\) 1.83889e14 0.0233415
\(280\) −1.15822e16 −1.43636
\(281\) 1.53869e15 0.186449 0.0932243 0.995645i \(-0.470283\pi\)
0.0932243 + 0.995645i \(0.470283\pi\)
\(282\) −8.04382e15 −0.952452
\(283\) −6.94777e15 −0.803958 −0.401979 0.915649i \(-0.631677\pi\)
−0.401979 + 0.915649i \(0.631677\pi\)
\(284\) 1.19231e15 0.134841
\(285\) 2.19067e15 0.242150
\(286\) 1.14760e15 0.123997
\(287\) 1.35219e16 1.42826
\(288\) 1.10306e15 0.113906
\(289\) −3.65514e14 −0.0369035
\(290\) 2.47535e15 0.244371
\(291\) −8.50636e15 −0.821182
\(292\) −8.82038e14 −0.0832720
\(293\) −3.05245e15 −0.281844 −0.140922 0.990021i \(-0.545007\pi\)
−0.140922 + 0.990021i \(0.545007\pi\)
\(294\) 4.32032e15 0.390174
\(295\) −1.85404e15 −0.163786
\(296\) 1.90900e16 1.64972
\(297\) 6.96597e14 0.0588932
\(298\) 8.23420e15 0.681108
\(299\) 1.12168e15 0.0907832
\(300\) −7.33582e14 −0.0580979
\(301\) 2.29559e16 1.77915
\(302\) −2.29250e16 −1.73886
\(303\) −3.70117e15 −0.274766
\(304\) 5.24346e15 0.381013
\(305\) 2.22268e16 1.58099
\(306\) −5.08738e15 −0.354246
\(307\) 5.47480e15 0.373223 0.186612 0.982434i \(-0.440249\pi\)
0.186612 + 0.982434i \(0.440249\pi\)
\(308\) 1.00900e15 0.0673461
\(309\) −1.62765e16 −1.06373
\(310\) −1.49072e15 −0.0953990
\(311\) 1.11347e16 0.697806 0.348903 0.937159i \(-0.386554\pi\)
0.348903 + 0.937159i \(0.386554\pi\)
\(312\) −3.15338e15 −0.193540
\(313\) −6.11381e15 −0.367514 −0.183757 0.982972i \(-0.558826\pi\)
−0.183757 + 0.982972i \(0.558826\pi\)
\(314\) −1.51623e16 −0.892733
\(315\) −9.26617e15 −0.534419
\(316\) −4.14208e15 −0.234020
\(317\) 2.22496e15 0.123151 0.0615753 0.998102i \(-0.480388\pi\)
0.0615753 + 0.998102i \(0.480388\pi\)
\(318\) −8.80738e15 −0.477607
\(319\) 1.03310e15 0.0548912
\(320\) 1.86747e16 0.972252
\(321\) 6.30892e15 0.321864
\(322\) 6.69714e15 0.334831
\(323\) −6.67721e15 −0.327174
\(324\) 3.99544e14 0.0191876
\(325\) 4.63202e15 0.218036
\(326\) −2.10251e16 −0.970118
\(327\) −1.57549e16 −0.712617
\(328\) −2.26436e16 −1.00407
\(329\) 4.46567e16 1.94139
\(330\) −5.64703e15 −0.240702
\(331\) 1.77998e16 0.743934 0.371967 0.928246i \(-0.378684\pi\)
0.371967 + 0.928246i \(0.378684\pi\)
\(332\) 2.10053e15 0.0860859
\(333\) 1.52727e16 0.613801
\(334\) −4.51619e16 −1.78000
\(335\) 4.72225e13 0.00182540
\(336\) −2.21790e16 −0.840885
\(337\) −8.05639e14 −0.0299603 −0.0149801 0.999888i \(-0.504769\pi\)
−0.0149801 + 0.999888i \(0.504769\pi\)
\(338\) 2.55297e16 0.931295
\(339\) 1.39221e15 0.0498204
\(340\) 6.07314e15 0.213207
\(341\) −6.22158e14 −0.0214288
\(342\) 3.56110e15 0.120341
\(343\) 1.44487e16 0.479091
\(344\) −3.84415e16 −1.25075
\(345\) −5.51948e15 −0.176228
\(346\) 1.37649e16 0.431300
\(347\) −2.01330e16 −0.619108 −0.309554 0.950882i \(-0.600180\pi\)
−0.309554 + 0.950882i \(0.600180\pi\)
\(348\) 5.92549e14 0.0178838
\(349\) −3.93224e15 −0.116486 −0.0582431 0.998302i \(-0.518550\pi\)
−0.0582431 + 0.998302i \(0.518550\pi\)
\(350\) 2.76562e16 0.804173
\(351\) −2.52282e15 −0.0720095
\(352\) −3.73200e15 −0.104572
\(353\) 2.27174e16 0.624918 0.312459 0.949931i \(-0.398847\pi\)
0.312459 + 0.949931i \(0.398847\pi\)
\(354\) −3.01388e15 −0.0813963
\(355\) 3.70461e16 0.982331
\(356\) 1.15407e16 0.300474
\(357\) 2.82435e16 0.722064
\(358\) 3.19259e16 0.801499
\(359\) 3.34599e16 0.824917 0.412458 0.910976i \(-0.364670\pi\)
0.412458 + 0.910976i \(0.364670\pi\)
\(360\) 1.55170e16 0.375699
\(361\) −3.73790e16 −0.888856
\(362\) 6.36041e15 0.148552
\(363\) 2.28102e16 0.523283
\(364\) −3.65423e15 −0.0823450
\(365\) −2.74056e16 −0.606647
\(366\) 3.61314e16 0.785702
\(367\) −2.96174e16 −0.632729 −0.316364 0.948638i \(-0.602462\pi\)
−0.316364 + 0.948638i \(0.602462\pi\)
\(368\) −1.32111e16 −0.277287
\(369\) −1.81157e16 −0.373580
\(370\) −1.23809e17 −2.50866
\(371\) 4.88958e16 0.973511
\(372\) −3.56848e14 −0.00698159
\(373\) −3.03136e15 −0.0582814 −0.0291407 0.999575i \(-0.509277\pi\)
−0.0291407 + 0.999575i \(0.509277\pi\)
\(374\) 1.72123e16 0.325217
\(375\) 1.63221e16 0.303091
\(376\) −7.47814e16 −1.36481
\(377\) −3.74151e15 −0.0671163
\(378\) −1.50629e16 −0.265589
\(379\) 1.68088e16 0.291329 0.145664 0.989334i \(-0.453468\pi\)
0.145664 + 0.989334i \(0.453468\pi\)
\(380\) −4.25111e15 −0.0724285
\(381\) 3.30285e16 0.553192
\(382\) 1.22972e17 2.02486
\(383\) 7.39427e16 1.19702 0.598512 0.801114i \(-0.295759\pi\)
0.598512 + 0.801114i \(0.295759\pi\)
\(384\) 4.27525e16 0.680470
\(385\) 3.13505e16 0.490625
\(386\) 1.11535e15 0.0171630
\(387\) −3.07546e16 −0.465360
\(388\) 1.65071e16 0.245620
\(389\) 2.70944e16 0.396467 0.198234 0.980155i \(-0.436480\pi\)
0.198234 + 0.980155i \(0.436480\pi\)
\(390\) 2.04514e16 0.294309
\(391\) 1.68235e16 0.238105
\(392\) 4.01649e16 0.559098
\(393\) 8.22726e15 0.112643
\(394\) −3.07189e16 −0.413695
\(395\) −1.28698e17 −1.70487
\(396\) −1.35179e15 −0.0176153
\(397\) −1.12309e16 −0.143971 −0.0719854 0.997406i \(-0.522934\pi\)
−0.0719854 + 0.997406i \(0.522934\pi\)
\(398\) −6.77002e16 −0.853787
\(399\) −1.97701e16 −0.245293
\(400\) −5.45560e16 −0.665967
\(401\) 2.22390e16 0.267101 0.133551 0.991042i \(-0.457362\pi\)
0.133551 + 0.991042i \(0.457362\pi\)
\(402\) 7.67638e13 0.000907167 0
\(403\) 2.25323e15 0.0262013
\(404\) 7.18234e15 0.0821840
\(405\) 1.24141e16 0.139785
\(406\) −2.23392e16 −0.247542
\(407\) −5.16725e16 −0.563502
\(408\) −4.72961e16 −0.507615
\(409\) −1.55417e17 −1.64172 −0.820858 0.571133i \(-0.806504\pi\)
−0.820858 + 0.571133i \(0.806504\pi\)
\(410\) 1.46856e17 1.52685
\(411\) −5.59299e16 −0.572364
\(412\) 3.15855e16 0.318168
\(413\) 1.67321e16 0.165911
\(414\) −8.97234e15 −0.0875797
\(415\) 6.52653e16 0.627147
\(416\) 1.35159e16 0.127862
\(417\) 3.05042e16 0.284103
\(418\) −1.20484e16 −0.110480
\(419\) 9.43507e16 0.851832 0.425916 0.904763i \(-0.359952\pi\)
0.425916 + 0.904763i \(0.359952\pi\)
\(420\) 1.79815e16 0.159848
\(421\) 2.00336e17 1.75358 0.876792 0.480870i \(-0.159679\pi\)
0.876792 + 0.480870i \(0.159679\pi\)
\(422\) 1.07663e17 0.927971
\(423\) −5.98279e16 −0.507798
\(424\) −8.18801e16 −0.684384
\(425\) 6.94736e16 0.571863
\(426\) 6.02212e16 0.488188
\(427\) −2.00590e17 −1.60151
\(428\) −1.22428e16 −0.0962713
\(429\) 8.53553e15 0.0661086
\(430\) 2.49315e17 1.90197
\(431\) 9.65868e16 0.725797 0.362899 0.931829i \(-0.381787\pi\)
0.362899 + 0.931829i \(0.381787\pi\)
\(432\) 2.97138e16 0.219945
\(433\) −6.71250e16 −0.489455 −0.244728 0.969592i \(-0.578699\pi\)
−0.244728 + 0.969592i \(0.578699\pi\)
\(434\) 1.34532e16 0.0966370
\(435\) 1.84110e16 0.130286
\(436\) 3.05734e16 0.213148
\(437\) −1.17762e16 −0.0808867
\(438\) −4.45500e16 −0.301485
\(439\) −1.19945e17 −0.799763 −0.399881 0.916567i \(-0.630949\pi\)
−0.399881 + 0.916567i \(0.630949\pi\)
\(440\) −5.24990e16 −0.344912
\(441\) 3.21334e16 0.208020
\(442\) −6.23366e16 −0.397647
\(443\) −1.11001e16 −0.0697752 −0.0348876 0.999391i \(-0.511107\pi\)
−0.0348876 + 0.999391i \(0.511107\pi\)
\(444\) −2.96375e16 −0.183591
\(445\) 3.58579e17 2.18900
\(446\) 1.98089e16 0.119174
\(447\) 6.12439e16 0.363131
\(448\) −1.68533e17 −0.984869
\(449\) −2.25580e17 −1.29927 −0.649635 0.760247i \(-0.725078\pi\)
−0.649635 + 0.760247i \(0.725078\pi\)
\(450\) −3.70517e16 −0.210343
\(451\) 6.12913e16 0.342966
\(452\) −2.70167e15 −0.0149016
\(453\) −1.70510e17 −0.927069
\(454\) −3.61629e17 −1.93821
\(455\) −1.13540e17 −0.599894
\(456\) 3.31066e16 0.172442
\(457\) −2.82152e17 −1.44886 −0.724432 0.689347i \(-0.757898\pi\)
−0.724432 + 0.689347i \(0.757898\pi\)
\(458\) 1.66812e17 0.844504
\(459\) −3.78386e16 −0.188866
\(460\) 1.07109e16 0.0527107
\(461\) −1.95029e17 −0.946333 −0.473167 0.880973i \(-0.656889\pi\)
−0.473167 + 0.880973i \(0.656889\pi\)
\(462\) 5.09626e16 0.243825
\(463\) 2.97176e17 1.40197 0.700983 0.713178i \(-0.252745\pi\)
0.700983 + 0.713178i \(0.252745\pi\)
\(464\) 4.40675e16 0.204999
\(465\) −1.10876e16 −0.0508618
\(466\) −1.41758e15 −0.00641268
\(467\) −3.64073e17 −1.62416 −0.812079 0.583548i \(-0.801664\pi\)
−0.812079 + 0.583548i \(0.801664\pi\)
\(468\) 4.89568e15 0.0215385
\(469\) −4.26168e14 −0.00184909
\(470\) 4.85000e17 2.07542
\(471\) −1.12773e17 −0.475959
\(472\) −2.80193e16 −0.116636
\(473\) 1.04053e17 0.427225
\(474\) −2.09208e17 −0.847265
\(475\) −4.86306e16 −0.194268
\(476\) −5.48082e16 −0.215973
\(477\) −6.55071e16 −0.254635
\(478\) 1.21585e17 0.466229
\(479\) −1.29900e17 −0.491392 −0.245696 0.969347i \(-0.579016\pi\)
−0.245696 + 0.969347i \(0.579016\pi\)
\(480\) −6.65085e16 −0.248204
\(481\) 1.87139e17 0.689002
\(482\) 5.40920e17 1.96484
\(483\) 4.98116e16 0.178515
\(484\) −4.42646e16 −0.156517
\(485\) 5.12889e17 1.78938
\(486\) 2.01801e16 0.0694686
\(487\) −2.01035e17 −0.682862 −0.341431 0.939907i \(-0.610912\pi\)
−0.341431 + 0.939907i \(0.610912\pi\)
\(488\) 3.35905e17 1.12587
\(489\) −1.56380e17 −0.517217
\(490\) −2.60492e17 −0.850198
\(491\) −3.03144e17 −0.976382 −0.488191 0.872737i \(-0.662343\pi\)
−0.488191 + 0.872737i \(0.662343\pi\)
\(492\) 3.51545e16 0.111740
\(493\) −5.61172e16 −0.176032
\(494\) 4.36347e16 0.135085
\(495\) −4.20011e16 −0.128330
\(496\) −2.65386e16 −0.0800289
\(497\) −3.34329e17 −0.995079
\(498\) 1.06094e17 0.311673
\(499\) −6.67583e16 −0.193576 −0.0967880 0.995305i \(-0.530857\pi\)
−0.0967880 + 0.995305i \(0.530857\pi\)
\(500\) −3.16739e16 −0.0906561
\(501\) −3.35903e17 −0.949004
\(502\) 4.27737e17 1.19290
\(503\) −4.65095e17 −1.28041 −0.640206 0.768204i \(-0.721151\pi\)
−0.640206 + 0.768204i \(0.721151\pi\)
\(504\) −1.40036e17 −0.380575
\(505\) 2.23161e17 0.598721
\(506\) 3.03564e16 0.0804029
\(507\) 1.89883e17 0.496518
\(508\) −6.40936e16 −0.165463
\(509\) 3.08399e17 0.786044 0.393022 0.919529i \(-0.371430\pi\)
0.393022 + 0.919529i \(0.371430\pi\)
\(510\) 3.06742e17 0.771911
\(511\) 2.47327e17 0.614520
\(512\) 2.58169e17 0.633358
\(513\) 2.64865e16 0.0641596
\(514\) 3.24857e17 0.777020
\(515\) 9.81387e17 2.31789
\(516\) 5.96811e16 0.139192
\(517\) 2.02417e17 0.466186
\(518\) 1.11734e18 2.54121
\(519\) 1.02380e17 0.229947
\(520\) 1.90132e17 0.421729
\(521\) −2.52706e17 −0.553567 −0.276784 0.960932i \(-0.589269\pi\)
−0.276784 + 0.960932i \(0.589269\pi\)
\(522\) 2.99285e16 0.0647480
\(523\) −7.28616e17 −1.55682 −0.778409 0.627757i \(-0.783973\pi\)
−0.778409 + 0.627757i \(0.783973\pi\)
\(524\) −1.59655e16 −0.0336921
\(525\) 2.05699e17 0.428744
\(526\) 9.71331e17 1.99968
\(527\) 3.37952e16 0.0687204
\(528\) −1.00532e17 −0.201921
\(529\) −4.74366e17 −0.941134
\(530\) 5.31038e17 1.04072
\(531\) −2.24165e16 −0.0433963
\(532\) 3.83650e16 0.0733684
\(533\) −2.21975e17 −0.419350
\(534\) 5.82898e17 1.08786
\(535\) −3.80394e17 −0.701349
\(536\) 7.13654e14 0.00129992
\(537\) 2.37456e17 0.427318
\(538\) −1.06772e17 −0.189833
\(539\) −1.08718e17 −0.190974
\(540\) −2.40904e16 −0.0418103
\(541\) 1.03306e17 0.177151 0.0885756 0.996069i \(-0.471769\pi\)
0.0885756 + 0.996069i \(0.471769\pi\)
\(542\) 1.59230e15 0.00269792
\(543\) 4.73071e16 0.0792004
\(544\) 2.02720e17 0.335354
\(545\) 9.49939e17 1.55281
\(546\) −1.84568e17 −0.298129
\(547\) −1.17000e18 −1.86753 −0.933763 0.357892i \(-0.883495\pi\)
−0.933763 + 0.357892i \(0.883495\pi\)
\(548\) 1.08535e17 0.171197
\(549\) 2.68736e17 0.418896
\(550\) 1.25358e17 0.193106
\(551\) 3.92812e16 0.0597998
\(552\) −8.34136e16 −0.125497
\(553\) 1.16146e18 1.72699
\(554\) 5.55869e17 0.816882
\(555\) −9.20861e17 −1.33749
\(556\) −5.91951e16 −0.0849767
\(557\) 7.54719e16 0.107084 0.0535422 0.998566i \(-0.482949\pi\)
0.0535422 + 0.998566i \(0.482949\pi\)
\(558\) −1.80237e16 −0.0252767
\(559\) −3.76842e17 −0.522375
\(560\) 1.33728e18 1.83231
\(561\) 1.28021e17 0.173389
\(562\) −1.50812e17 −0.201907
\(563\) 4.98148e17 0.659256 0.329628 0.944111i \(-0.393077\pi\)
0.329628 + 0.944111i \(0.393077\pi\)
\(564\) 1.16099e17 0.151885
\(565\) −8.39430e16 −0.108560
\(566\) 6.80975e17 0.870612
\(567\) −1.12034e17 −0.141599
\(568\) 5.59862e17 0.699547
\(569\) 2.49767e16 0.0308535 0.0154268 0.999881i \(-0.495089\pi\)
0.0154268 + 0.999881i \(0.495089\pi\)
\(570\) −2.14715e17 −0.262226
\(571\) −3.03773e17 −0.366787 −0.183394 0.983040i \(-0.558708\pi\)
−0.183394 + 0.983040i \(0.558708\pi\)
\(572\) −1.65637e16 −0.0197735
\(573\) 9.14635e17 1.07955
\(574\) −1.32533e18 −1.54667
\(575\) 1.22527e17 0.141381
\(576\) 2.25789e17 0.257606
\(577\) −1.35220e18 −1.52545 −0.762724 0.646724i \(-0.776139\pi\)
−0.762724 + 0.646724i \(0.776139\pi\)
\(578\) 3.58253e16 0.0399631
\(579\) 8.29570e15 0.00915045
\(580\) −3.57276e16 −0.0389692
\(581\) −5.88999e17 −0.635286
\(582\) 8.33739e17 0.889264
\(583\) 2.21632e17 0.233769
\(584\) −4.14170e17 −0.432011
\(585\) 1.52113e17 0.156911
\(586\) 2.99182e17 0.305211
\(587\) −1.28182e18 −1.29324 −0.646619 0.762813i \(-0.723818\pi\)
−0.646619 + 0.762813i \(0.723818\pi\)
\(588\) −6.23567e16 −0.0622201
\(589\) −2.36561e16 −0.0233450
\(590\) 1.81721e17 0.177365
\(591\) −2.28479e17 −0.220561
\(592\) −2.20412e18 −2.10448
\(593\) 6.39424e17 0.603856 0.301928 0.953331i \(-0.402370\pi\)
0.301928 + 0.953331i \(0.402370\pi\)
\(594\) −6.82760e16 −0.0637759
\(595\) −1.70293e18 −1.57339
\(596\) −1.18847e17 −0.108615
\(597\) −5.03536e17 −0.455195
\(598\) −1.09940e17 −0.0983098
\(599\) −7.65253e17 −0.676910 −0.338455 0.940983i \(-0.609904\pi\)
−0.338455 + 0.940983i \(0.609904\pi\)
\(600\) −3.44461e17 −0.301409
\(601\) 1.09286e18 0.945976 0.472988 0.881069i \(-0.343175\pi\)
0.472988 + 0.881069i \(0.343175\pi\)
\(602\) −2.24999e18 −1.92665
\(603\) 5.70950e14 0.000483655 0
\(604\) 3.30885e17 0.277292
\(605\) −1.37534e18 −1.14025
\(606\) 3.62765e17 0.297546
\(607\) 6.43496e17 0.522179 0.261089 0.965315i \(-0.415918\pi\)
0.261089 + 0.965315i \(0.415918\pi\)
\(608\) −1.41901e17 −0.113923
\(609\) −1.66153e17 −0.131976
\(610\) −2.17853e18 −1.71206
\(611\) −7.33081e17 −0.570013
\(612\) 7.34281e16 0.0564908
\(613\) −1.64149e18 −1.24953 −0.624763 0.780814i \(-0.714804\pi\)
−0.624763 + 0.780814i \(0.714804\pi\)
\(614\) −5.36605e17 −0.404166
\(615\) 1.09228e18 0.814040
\(616\) 4.73787e17 0.349388
\(617\) −2.19011e18 −1.59813 −0.799066 0.601244i \(-0.794672\pi\)
−0.799066 + 0.601244i \(0.794672\pi\)
\(618\) 1.59532e18 1.15192
\(619\) 2.33506e18 1.66843 0.834216 0.551438i \(-0.185921\pi\)
0.834216 + 0.551438i \(0.185921\pi\)
\(620\) 2.15160e16 0.0152131
\(621\) −6.67340e16 −0.0466930
\(622\) −1.09135e18 −0.755660
\(623\) −3.23606e18 −2.21740
\(624\) 3.64088e17 0.246892
\(625\) −1.85245e18 −1.24316
\(626\) 5.99237e17 0.397984
\(627\) −8.96126e16 −0.0589020
\(628\) 2.18843e17 0.142362
\(629\) 2.80681e18 1.80711
\(630\) 9.08210e17 0.578726
\(631\) 2.95666e17 0.186471 0.0932354 0.995644i \(-0.470279\pi\)
0.0932354 + 0.995644i \(0.470279\pi\)
\(632\) −1.94496e18 −1.21408
\(633\) 8.00767e17 0.494746
\(634\) −2.18076e17 −0.133361
\(635\) −1.99144e18 −1.20542
\(636\) 1.27120e17 0.0761629
\(637\) 3.93736e17 0.233507
\(638\) −1.01258e17 −0.0594421
\(639\) 4.47910e17 0.260277
\(640\) −2.57775e18 −1.48276
\(641\) −1.72246e18 −0.980780 −0.490390 0.871503i \(-0.663146\pi\)
−0.490390 + 0.871503i \(0.663146\pi\)
\(642\) −6.18360e17 −0.348549
\(643\) 9.63720e17 0.537749 0.268875 0.963175i \(-0.413348\pi\)
0.268875 + 0.963175i \(0.413348\pi\)
\(644\) −9.66622e16 −0.0533948
\(645\) 1.85434e18 1.01403
\(646\) 6.54457e17 0.354299
\(647\) 1.08203e18 0.579909 0.289955 0.957040i \(-0.406360\pi\)
0.289955 + 0.957040i \(0.406360\pi\)
\(648\) 1.87610e17 0.0995446
\(649\) 7.58423e16 0.0398401
\(650\) −4.54001e17 −0.236113
\(651\) 1.00062e17 0.0515218
\(652\) 3.03464e17 0.154703
\(653\) −8.01051e17 −0.404319 −0.202160 0.979353i \(-0.564796\pi\)
−0.202160 + 0.979353i \(0.564796\pi\)
\(654\) 1.54420e18 0.771699
\(655\) −4.96060e17 −0.245451
\(656\) 2.61442e18 1.28086
\(657\) −3.31351e17 −0.160736
\(658\) −4.37697e18 −2.10235
\(659\) −1.24626e18 −0.592724 −0.296362 0.955076i \(-0.595773\pi\)
−0.296362 + 0.955076i \(0.595773\pi\)
\(660\) 8.15056e16 0.0383841
\(661\) 2.34871e18 1.09527 0.547633 0.836719i \(-0.315529\pi\)
0.547633 + 0.836719i \(0.315529\pi\)
\(662\) −1.74463e18 −0.805611
\(663\) −4.63643e17 −0.212005
\(664\) 9.86327e17 0.446610
\(665\) 1.19203e18 0.534499
\(666\) −1.49693e18 −0.664690
\(667\) −9.89709e16 −0.0435201
\(668\) 6.51838e17 0.283853
\(669\) 1.47333e17 0.0635377
\(670\) −4.62845e15 −0.00197674
\(671\) −9.09223e17 −0.384569
\(672\) 6.00218e17 0.251425
\(673\) 4.08779e18 1.69586 0.847931 0.530106i \(-0.177848\pi\)
0.847931 + 0.530106i \(0.177848\pi\)
\(674\) 7.89636e16 0.0324442
\(675\) −2.75581e17 −0.112144
\(676\) −3.68480e17 −0.148511
\(677\) −3.34933e18 −1.33700 −0.668500 0.743712i \(-0.733063\pi\)
−0.668500 + 0.743712i \(0.733063\pi\)
\(678\) −1.36456e17 −0.0539509
\(679\) −4.62866e18 −1.81260
\(680\) 2.85171e18 1.10611
\(681\) −2.68970e18 −1.03335
\(682\) 6.09800e16 0.0232054
\(683\) −2.32332e18 −0.875737 −0.437868 0.899039i \(-0.644266\pi\)
−0.437868 + 0.899039i \(0.644266\pi\)
\(684\) −5.13986e16 −0.0191905
\(685\) 3.37227e18 1.24719
\(686\) −1.41617e18 −0.518812
\(687\) 1.24070e18 0.450246
\(688\) 4.43845e18 1.59553
\(689\) −8.02669e17 −0.285833
\(690\) 5.40984e17 0.190838
\(691\) 5.87579e17 0.205333 0.102666 0.994716i \(-0.467263\pi\)
0.102666 + 0.994716i \(0.467263\pi\)
\(692\) −1.98675e17 −0.0687785
\(693\) 3.79047e17 0.129995
\(694\) 1.97331e18 0.670437
\(695\) −1.83924e18 −0.619067
\(696\) 2.78238e17 0.0927803
\(697\) −3.32930e18 −1.09987
\(698\) 3.85413e17 0.126144
\(699\) −1.05436e16 −0.00341891
\(700\) −3.99172e17 −0.128240
\(701\) −3.77375e18 −1.20117 −0.600587 0.799559i \(-0.705066\pi\)
−0.600587 + 0.799559i \(0.705066\pi\)
\(702\) 2.47271e17 0.0779797
\(703\) −1.96473e18 −0.613893
\(704\) −7.63917e17 −0.236496
\(705\) 3.60730e18 1.10651
\(706\) −2.22661e18 −0.676729
\(707\) −2.01396e18 −0.606491
\(708\) 4.35004e16 0.0129801
\(709\) 5.70959e17 0.168813 0.0844063 0.996431i \(-0.473101\pi\)
0.0844063 + 0.996431i \(0.473101\pi\)
\(710\) −3.63102e18 −1.06377
\(711\) −1.55604e18 −0.451718
\(712\) 5.41905e18 1.55885
\(713\) 5.96027e16 0.0169896
\(714\) −2.76825e18 −0.781928
\(715\) −5.14647e17 −0.144052
\(716\) −4.60798e17 −0.127813
\(717\) 9.04318e17 0.248569
\(718\) −3.27952e18 −0.893309
\(719\) −4.09843e18 −1.10632 −0.553159 0.833076i \(-0.686578\pi\)
−0.553159 + 0.833076i \(0.686578\pi\)
\(720\) −1.79158e18 −0.479265
\(721\) −8.85670e18 −2.34797
\(722\) 3.66365e18 0.962548
\(723\) 4.02323e18 1.04755
\(724\) −9.18021e16 −0.0236893
\(725\) −4.08705e17 −0.104523
\(726\) −2.23571e18 −0.566667
\(727\) −6.55964e18 −1.64781 −0.823904 0.566729i \(-0.808209\pi\)
−0.823904 + 0.566729i \(0.808209\pi\)
\(728\) −1.71588e18 −0.427202
\(729\) 1.50095e17 0.0370370
\(730\) 2.68613e18 0.656943
\(731\) −5.65208e18 −1.37008
\(732\) −5.21498e17 −0.125294
\(733\) 8.63234e17 0.205567 0.102783 0.994704i \(-0.467225\pi\)
0.102783 + 0.994704i \(0.467225\pi\)
\(734\) 2.90291e18 0.685187
\(735\) −1.93747e18 −0.453282
\(736\) 3.57526e17 0.0829090
\(737\) −1.93171e15 −0.000444021 0
\(738\) 1.77558e18 0.404552
\(739\) 3.66698e18 0.828171 0.414086 0.910238i \(-0.364101\pi\)
0.414086 + 0.910238i \(0.364101\pi\)
\(740\) 1.78698e18 0.400050
\(741\) 3.24544e17 0.0720203
\(742\) −4.79245e18 −1.05422
\(743\) −3.20909e18 −0.699769 −0.349885 0.936793i \(-0.613779\pi\)
−0.349885 + 0.936793i \(0.613779\pi\)
\(744\) −1.67562e17 −0.0362202
\(745\) −3.69268e18 −0.791272
\(746\) 2.97114e17 0.0631134
\(747\) 7.89098e17 0.166168
\(748\) −2.48431e17 −0.0518616
\(749\) 3.43294e18 0.710450
\(750\) −1.59979e18 −0.328219
\(751\) −7.66711e18 −1.55945 −0.779726 0.626121i \(-0.784642\pi\)
−0.779726 + 0.626121i \(0.784642\pi\)
\(752\) 8.63424e18 1.74104
\(753\) 3.18140e18 0.635991
\(754\) 3.66719e17 0.0726807
\(755\) 1.02809e19 2.02011
\(756\) 2.17408e17 0.0423529
\(757\) 3.40955e18 0.658528 0.329264 0.944238i \(-0.393199\pi\)
0.329264 + 0.944238i \(0.393199\pi\)
\(758\) −1.64750e18 −0.315482
\(759\) 2.25783e17 0.0428667
\(760\) −1.99615e18 −0.375756
\(761\) 6.05897e18 1.13083 0.565417 0.824805i \(-0.308715\pi\)
0.565417 + 0.824805i \(0.308715\pi\)
\(762\) −3.23724e18 −0.599056
\(763\) −8.57290e18 −1.57296
\(764\) −1.77490e18 −0.322900
\(765\) 2.28147e18 0.411543
\(766\) −7.24739e18 −1.29627
\(767\) −2.74673e17 −0.0487131
\(768\) −1.65307e18 −0.290699
\(769\) 7.76829e18 1.35458 0.677289 0.735717i \(-0.263155\pi\)
0.677289 + 0.735717i \(0.263155\pi\)
\(770\) −3.07277e18 −0.531301
\(771\) 2.41620e18 0.414267
\(772\) −1.60983e16 −0.00273695
\(773\) 6.22741e18 1.04988 0.524941 0.851139i \(-0.324087\pi\)
0.524941 + 0.851139i \(0.324087\pi\)
\(774\) 3.01437e18 0.503942
\(775\) 2.46132e17 0.0408045
\(776\) 7.75107e18 1.27427
\(777\) 8.31048e18 1.35484
\(778\) −2.65562e18 −0.429337
\(779\) 2.33046e18 0.373636
\(780\) −2.95183e17 −0.0469328
\(781\) −1.51543e18 −0.238948
\(782\) −1.64894e18 −0.257846
\(783\) 2.22600e17 0.0345203
\(784\) −4.63743e18 −0.713219
\(785\) 6.79961e18 1.03713
\(786\) −8.06383e17 −0.121982
\(787\) −2.74400e17 −0.0411670 −0.0205835 0.999788i \(-0.506552\pi\)
−0.0205835 + 0.999788i \(0.506552\pi\)
\(788\) 4.43377e17 0.0659710
\(789\) 7.22451e18 1.06612
\(790\) 1.26141e19 1.84621
\(791\) 7.57559e17 0.109969
\(792\) −6.34745e17 −0.0913873
\(793\) 3.29287e18 0.470218
\(794\) 1.10078e18 0.155907
\(795\) 3.94973e18 0.554857
\(796\) 9.77141e17 0.136151
\(797\) −1.68707e18 −0.233160 −0.116580 0.993181i \(-0.537193\pi\)
−0.116580 + 0.993181i \(0.537193\pi\)
\(798\) 1.93774e18 0.265629
\(799\) −1.09952e19 −1.49502
\(800\) 1.47642e18 0.199125
\(801\) 4.33544e18 0.579992
\(802\) −2.17972e18 −0.289246
\(803\) 1.12107e18 0.147564
\(804\) −1.10796e15 −0.000144664 0
\(805\) −3.00337e18 −0.388988
\(806\) −2.20847e17 −0.0283736
\(807\) −7.94140e17 −0.101209
\(808\) 3.37254e18 0.426367
\(809\) 8.85570e18 1.11060 0.555300 0.831650i \(-0.312604\pi\)
0.555300 + 0.831650i \(0.312604\pi\)
\(810\) −1.21675e18 −0.151374
\(811\) −1.43789e18 −0.177456 −0.0887280 0.996056i \(-0.528280\pi\)
−0.0887280 + 0.996056i \(0.528280\pi\)
\(812\) 3.22430e17 0.0394749
\(813\) 1.18431e16 0.00143839
\(814\) 5.06461e18 0.610221
\(815\) 9.42886e18 1.12703
\(816\) 5.46080e18 0.647545
\(817\) 3.95637e18 0.465430
\(818\) 1.52330e19 1.77783
\(819\) −1.37277e18 −0.158947
\(820\) −2.11963e18 −0.243484
\(821\) −7.99413e18 −0.911046 −0.455523 0.890224i \(-0.650548\pi\)
−0.455523 + 0.890224i \(0.650548\pi\)
\(822\) 5.48189e18 0.619817
\(823\) 1.03119e18 0.115675 0.0578373 0.998326i \(-0.481580\pi\)
0.0578373 + 0.998326i \(0.481580\pi\)
\(824\) 1.48313e19 1.65064
\(825\) 9.32382e17 0.102954
\(826\) −1.63997e18 −0.179666
\(827\) −5.41749e17 −0.0588860 −0.0294430 0.999566i \(-0.509373\pi\)
−0.0294430 + 0.999566i \(0.509373\pi\)
\(828\) 1.29501e17 0.0139661
\(829\) 3.08642e18 0.330256 0.165128 0.986272i \(-0.447196\pi\)
0.165128 + 0.986272i \(0.447196\pi\)
\(830\) −6.39689e18 −0.679143
\(831\) 4.13441e18 0.435519
\(832\) 2.76663e18 0.289167
\(833\) 5.90547e18 0.612438
\(834\) −2.98983e18 −0.307657
\(835\) 2.02531e19 2.06790
\(836\) 1.73898e17 0.0176179
\(837\) −1.34055e17 −0.0134762
\(838\) −9.24766e18 −0.922456
\(839\) −5.52405e18 −0.546771 −0.273385 0.961905i \(-0.588143\pi\)
−0.273385 + 0.961905i \(0.588143\pi\)
\(840\) 8.44341e18 0.829282
\(841\) −9.93050e18 −0.967825
\(842\) −1.96357e19 −1.89897
\(843\) −1.12170e18 −0.107646
\(844\) −1.55394e18 −0.147981
\(845\) −1.14490e19 −1.08193
\(846\) 5.86395e18 0.549899
\(847\) 1.24120e19 1.15504
\(848\) 9.45385e18 0.873043
\(849\) 5.06492e18 0.464165
\(850\) −6.80936e18 −0.619275
\(851\) 4.95022e18 0.446768
\(852\) −8.69195e17 −0.0778502
\(853\) −1.76911e19 −1.57248 −0.786240 0.617921i \(-0.787975\pi\)
−0.786240 + 0.617921i \(0.787975\pi\)
\(854\) 1.96606e19 1.73428
\(855\) −1.59700e18 −0.139805
\(856\) −5.74874e18 −0.499451
\(857\) −2.92655e18 −0.252337 −0.126168 0.992009i \(-0.540268\pi\)
−0.126168 + 0.992009i \(0.540268\pi\)
\(858\) −8.36598e17 −0.0715895
\(859\) 1.31028e19 1.11278 0.556389 0.830922i \(-0.312186\pi\)
0.556389 + 0.830922i \(0.312186\pi\)
\(860\) −3.59845e18 −0.303302
\(861\) −9.85748e18 −0.824604
\(862\) −9.46682e18 −0.785972
\(863\) 9.80759e18 0.808150 0.404075 0.914726i \(-0.367593\pi\)
0.404075 + 0.914726i \(0.367593\pi\)
\(864\) −8.04129e17 −0.0657637
\(865\) −6.17298e18 −0.501060
\(866\) 6.57916e18 0.530035
\(867\) 2.66459e17 0.0213062
\(868\) −1.94175e17 −0.0154105
\(869\) 5.26458e18 0.414701
\(870\) −1.80453e18 −0.141087
\(871\) 6.99594e15 0.000542911 0
\(872\) 1.43560e19 1.10580
\(873\) 6.20114e18 0.474110
\(874\) 1.15423e18 0.0875928
\(875\) 8.88150e18 0.669012
\(876\) 6.43006e17 0.0480771
\(877\) −1.77473e19 −1.31715 −0.658574 0.752516i \(-0.728840\pi\)
−0.658574 + 0.752516i \(0.728840\pi\)
\(878\) 1.17562e19 0.866069
\(879\) 2.22524e18 0.162723
\(880\) 6.06152e18 0.439991
\(881\) 5.68538e17 0.0409653 0.0204826 0.999790i \(-0.493480\pi\)
0.0204826 + 0.999790i \(0.493480\pi\)
\(882\) −3.14951e18 −0.225267
\(883\) −1.31235e19 −0.931765 −0.465882 0.884847i \(-0.654263\pi\)
−0.465882 + 0.884847i \(0.654263\pi\)
\(884\) 8.99727e17 0.0634119
\(885\) 1.35159e18 0.0945616
\(886\) 1.08796e18 0.0755601
\(887\) −5.67124e18 −0.390998 −0.195499 0.980704i \(-0.562633\pi\)
−0.195499 + 0.980704i \(0.562633\pi\)
\(888\) −1.39166e19 −0.952464
\(889\) 1.79721e19 1.22106
\(890\) −3.51456e19 −2.37048
\(891\) −5.07820e17 −0.0340020
\(892\) −2.85909e17 −0.0190045
\(893\) 7.69646e18 0.507874
\(894\) −6.00273e18 −0.393238
\(895\) −1.43174e19 −0.931136
\(896\) 2.32634e19 1.50200
\(897\) −8.17703e17 −0.0524137
\(898\) 2.21099e19 1.40699
\(899\) −1.98813e17 −0.0125605
\(900\) 5.34781e17 0.0335429
\(901\) −1.20389e19 −0.749678
\(902\) −6.00738e18 −0.371401
\(903\) −1.67348e19 −1.02719
\(904\) −1.26860e18 −0.0773087
\(905\) −2.85237e18 −0.172580
\(906\) 1.67123e19 1.00393
\(907\) −2.26476e19 −1.35075 −0.675374 0.737475i \(-0.736018\pi\)
−0.675374 + 0.737475i \(0.736018\pi\)
\(908\) 5.21952e18 0.309081
\(909\) 2.69815e18 0.158636
\(910\) 1.11285e19 0.649630
\(911\) 3.19163e19 1.84988 0.924939 0.380117i \(-0.124116\pi\)
0.924939 + 0.380117i \(0.124116\pi\)
\(912\) −3.82248e18 −0.219978
\(913\) −2.66978e18 −0.152551
\(914\) 2.76547e19 1.56898
\(915\) −1.62034e19 −0.912784
\(916\) −2.40766e18 −0.134671
\(917\) 4.47678e18 0.248637
\(918\) 3.70870e18 0.204524
\(919\) 6.67933e18 0.365748 0.182874 0.983136i \(-0.441460\pi\)
0.182874 + 0.983136i \(0.441460\pi\)
\(920\) 5.02940e18 0.273461
\(921\) −3.99113e18 −0.215481
\(922\) 1.91155e19 1.02479
\(923\) 5.48832e18 0.292165
\(924\) −7.35562e17 −0.0388823
\(925\) 2.04422e19 1.07302
\(926\) −2.91273e19 −1.51820
\(927\) 1.18656e19 0.614144
\(928\) −1.19258e18 −0.0612949
\(929\) −1.94975e19 −0.995123 −0.497561 0.867429i \(-0.665771\pi\)
−0.497561 + 0.867429i \(0.665771\pi\)
\(930\) 1.08673e18 0.0550786
\(931\) −4.13375e18 −0.208052
\(932\) 2.04605e16 0.00102262
\(933\) −8.11718e18 −0.402879
\(934\) 3.56841e19 1.75881
\(935\) −7.71896e18 −0.377819
\(936\) 2.29881e18 0.111741
\(937\) −1.98727e19 −0.959289 −0.479645 0.877463i \(-0.659234\pi\)
−0.479645 + 0.877463i \(0.659234\pi\)
\(938\) 4.17703e16 0.00200239
\(939\) 4.45697e18 0.212184
\(940\) −7.00018e18 −0.330962
\(941\) −4.48542e18 −0.210606 −0.105303 0.994440i \(-0.533581\pi\)
−0.105303 + 0.994440i \(0.533581\pi\)
\(942\) 1.10533e19 0.515419
\(943\) −5.87170e18 −0.271918
\(944\) 3.23510e18 0.148789
\(945\) 6.75504e18 0.308547
\(946\) −1.01986e19 −0.462646
\(947\) −2.27860e18 −0.102658 −0.0513290 0.998682i \(-0.516346\pi\)
−0.0513290 + 0.998682i \(0.516346\pi\)
\(948\) 3.01958e18 0.135111
\(949\) −4.06010e18 −0.180429
\(950\) 4.76646e18 0.210374
\(951\) −1.62199e18 −0.0711010
\(952\) −2.57357e19 −1.12046
\(953\) 9.30159e18 0.402210 0.201105 0.979570i \(-0.435547\pi\)
0.201105 + 0.979570i \(0.435547\pi\)
\(954\) 6.42058e18 0.275746
\(955\) −5.51476e19 −2.35237
\(956\) −1.75488e18 −0.0743484
\(957\) −7.53130e17 −0.0316915
\(958\) 1.27320e19 0.532132
\(959\) −3.04337e19 −1.26338
\(960\) −1.36139e19 −0.561330
\(961\) −2.42978e19 −0.995097
\(962\) −1.83421e19 −0.746126
\(963\) −4.59920e18 −0.185828
\(964\) −7.80730e18 −0.313329
\(965\) −5.00186e17 −0.0199390
\(966\) −4.88221e18 −0.193315
\(967\) −1.83135e19 −0.720277 −0.360139 0.932899i \(-0.617271\pi\)
−0.360139 + 0.932899i \(0.617271\pi\)
\(968\) −2.07849e19 −0.812003
\(969\) 4.86769e18 0.188894
\(970\) −5.02701e19 −1.93773
\(971\) −1.03164e19 −0.395005 −0.197503 0.980302i \(-0.563283\pi\)
−0.197503 + 0.980302i \(0.563283\pi\)
\(972\) −2.91267e17 −0.0110780
\(973\) 1.65986e19 0.627100
\(974\) 1.97041e19 0.739476
\(975\) −3.37675e18 −0.125883
\(976\) −3.87835e19 −1.43623
\(977\) 4.89176e19 1.79949 0.899747 0.436413i \(-0.143751\pi\)
0.899747 + 0.436413i \(0.143751\pi\)
\(978\) 1.53273e19 0.560098
\(979\) −1.46682e19 −0.532464
\(980\) 3.75978e18 0.135579
\(981\) 1.14854e19 0.411430
\(982\) 2.97123e19 1.05733
\(983\) −1.15301e19 −0.407600 −0.203800 0.979013i \(-0.565329\pi\)
−0.203800 + 0.979013i \(0.565329\pi\)
\(984\) 1.65072e19 0.579701
\(985\) 1.37761e19 0.480607
\(986\) 5.50025e18 0.190626
\(987\) −3.25548e19 −1.12086
\(988\) −6.29796e17 −0.0215417
\(989\) −9.96826e18 −0.338722
\(990\) 4.11668e18 0.138969
\(991\) 2.90894e19 0.975565 0.487783 0.872965i \(-0.337806\pi\)
0.487783 + 0.872965i \(0.337806\pi\)
\(992\) 7.18199e17 0.0239287
\(993\) −1.29761e19 −0.429510
\(994\) 3.27688e19 1.07758
\(995\) 3.03606e19 0.991882
\(996\) −1.53129e18 −0.0497017
\(997\) 2.78215e19 0.897144 0.448572 0.893747i \(-0.351933\pi\)
0.448572 + 0.893747i \(0.351933\pi\)
\(998\) 6.54322e18 0.209625
\(999\) −1.11338e19 −0.354378
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.b.1.8 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.b.1.8 31 1.1 even 1 trivial