Properties

Label 177.10.a.d.1.2
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-39.1029 q^{2} +81.0000 q^{3} +1017.03 q^{4} +1845.13 q^{5} -3167.33 q^{6} +8719.40 q^{7} -19748.3 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-39.1029 q^{2} +81.0000 q^{3} +1017.03 q^{4} +1845.13 q^{5} -3167.33 q^{6} +8719.40 q^{7} -19748.3 q^{8} +6561.00 q^{9} -72149.9 q^{10} +11592.4 q^{11} +82379.8 q^{12} +8112.04 q^{13} -340953. q^{14} +149456. q^{15} +251493. q^{16} -258717. q^{17} -256554. q^{18} -511787. q^{19} +1.87656e6 q^{20} +706271. q^{21} -453298. q^{22} +1.50681e6 q^{23} -1.59961e6 q^{24} +1.45138e6 q^{25} -317204. q^{26} +531441. q^{27} +8.86793e6 q^{28} +3.60183e6 q^{29} -5.84414e6 q^{30} +517886. q^{31} +277024. q^{32} +938988. q^{33} +1.01166e7 q^{34} +1.60884e7 q^{35} +6.67276e6 q^{36} +5.37194e6 q^{37} +2.00123e7 q^{38} +657076. q^{39} -3.64382e7 q^{40} +1.04132e7 q^{41} -2.76172e7 q^{42} +1.15939e6 q^{43} +1.17899e7 q^{44} +1.21059e7 q^{45} -5.89207e7 q^{46} +2.05249e7 q^{47} +2.03709e7 q^{48} +3.56743e7 q^{49} -5.67531e7 q^{50} -2.09560e7 q^{51} +8.25023e6 q^{52} -6.04606e7 q^{53} -2.07809e7 q^{54} +2.13896e7 q^{55} -1.72193e8 q^{56} -4.14547e7 q^{57} -1.40842e8 q^{58} -1.21174e7 q^{59} +1.52001e8 q^{60} +1.74520e8 q^{61} -2.02508e7 q^{62} +5.72080e7 q^{63} -1.39597e8 q^{64} +1.49678e7 q^{65} -3.67171e7 q^{66} +7.95827e7 q^{67} -2.63124e8 q^{68} +1.22052e8 q^{69} -6.29103e8 q^{70} +1.53469e8 q^{71} -1.29568e8 q^{72} -3.49414e8 q^{73} -2.10058e8 q^{74} +1.17562e8 q^{75} -5.20505e8 q^{76} +1.01079e8 q^{77} -2.56935e7 q^{78} -3.98120e8 q^{79} +4.64037e8 q^{80} +4.30467e7 q^{81} -4.07186e8 q^{82} -4.09387e6 q^{83} +7.18302e8 q^{84} -4.77366e8 q^{85} -4.53354e7 q^{86} +2.91748e8 q^{87} -2.28931e8 q^{88} +2.94766e8 q^{89} -4.73375e8 q^{90} +7.07321e7 q^{91} +1.53248e9 q^{92} +4.19488e7 q^{93} -8.02581e8 q^{94} -9.44313e8 q^{95} +2.24389e7 q^{96} -4.22911e8 q^{97} -1.39497e9 q^{98} +7.60580e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −39.1029 −1.72812 −0.864059 0.503390i \(-0.832086\pi\)
−0.864059 + 0.503390i \(0.832086\pi\)
\(3\) 81.0000 0.577350
\(4\) 1017.03 1.98639
\(5\) 1845.13 1.32027 0.660134 0.751148i \(-0.270500\pi\)
0.660134 + 0.751148i \(0.270500\pi\)
\(6\) −3167.33 −0.997730
\(7\) 8719.40 1.37260 0.686302 0.727317i \(-0.259233\pi\)
0.686302 + 0.727317i \(0.259233\pi\)
\(8\) −19748.3 −1.70461
\(9\) 6561.00 0.333333
\(10\) −72149.9 −2.28158
\(11\) 11592.4 0.238731 0.119365 0.992850i \(-0.461914\pi\)
0.119365 + 0.992850i \(0.461914\pi\)
\(12\) 82379.8 1.14685
\(13\) 8112.04 0.0787744 0.0393872 0.999224i \(-0.487459\pi\)
0.0393872 + 0.999224i \(0.487459\pi\)
\(14\) −340953. −2.37202
\(15\) 149456. 0.762257
\(16\) 251493. 0.959370
\(17\) −258717. −0.751284 −0.375642 0.926765i \(-0.622578\pi\)
−0.375642 + 0.926765i \(0.622578\pi\)
\(18\) −256554. −0.576040
\(19\) −511787. −0.900944 −0.450472 0.892790i \(-0.648744\pi\)
−0.450472 + 0.892790i \(0.648744\pi\)
\(20\) 1.87656e6 2.62257
\(21\) 706271. 0.792473
\(22\) −453298. −0.412555
\(23\) 1.50681e6 1.12275 0.561376 0.827561i \(-0.310272\pi\)
0.561376 + 0.827561i \(0.310272\pi\)
\(24\) −1.59961e6 −0.984156
\(25\) 1.45138e6 0.743107
\(26\) −317204. −0.136132
\(27\) 531441. 0.192450
\(28\) 8.86793e6 2.72653
\(29\) 3.60183e6 0.945655 0.472827 0.881155i \(-0.343233\pi\)
0.472827 + 0.881155i \(0.343233\pi\)
\(30\) −5.84414e6 −1.31727
\(31\) 517886. 0.100718 0.0503590 0.998731i \(-0.483963\pi\)
0.0503590 + 0.998731i \(0.483963\pi\)
\(32\) 277024. 0.0467027
\(33\) 938988. 0.137831
\(34\) 1.01166e7 1.29831
\(35\) 1.60884e7 1.81220
\(36\) 6.67276e6 0.662132
\(37\) 5.37194e6 0.471220 0.235610 0.971848i \(-0.424291\pi\)
0.235610 + 0.971848i \(0.424291\pi\)
\(38\) 2.00123e7 1.55694
\(39\) 657076. 0.0454804
\(40\) −3.64382e7 −2.25054
\(41\) 1.04132e7 0.575515 0.287757 0.957703i \(-0.407090\pi\)
0.287757 + 0.957703i \(0.407090\pi\)
\(42\) −2.76172e7 −1.36949
\(43\) 1.15939e6 0.0517155 0.0258577 0.999666i \(-0.491768\pi\)
0.0258577 + 0.999666i \(0.491768\pi\)
\(44\) 1.17899e7 0.474213
\(45\) 1.21059e7 0.440089
\(46\) −5.89207e7 −1.94025
\(47\) 2.05249e7 0.613535 0.306768 0.951784i \(-0.400753\pi\)
0.306768 + 0.951784i \(0.400753\pi\)
\(48\) 2.03709e7 0.553892
\(49\) 3.56743e7 0.884042
\(50\) −5.67531e7 −1.28418
\(51\) −2.09560e7 −0.433754
\(52\) 8.25023e6 0.156477
\(53\) −6.04606e7 −1.05252 −0.526260 0.850323i \(-0.676406\pi\)
−0.526260 + 0.850323i \(0.676406\pi\)
\(54\) −2.07809e7 −0.332577
\(55\) 2.13896e7 0.315188
\(56\) −1.72193e8 −2.33975
\(57\) −4.14547e7 −0.520160
\(58\) −1.40842e8 −1.63420
\(59\) −1.21174e7 −0.130189
\(60\) 1.52001e8 1.51414
\(61\) 1.74520e8 1.61384 0.806920 0.590661i \(-0.201133\pi\)
0.806920 + 0.590661i \(0.201133\pi\)
\(62\) −2.02508e7 −0.174053
\(63\) 5.72080e7 0.457535
\(64\) −1.39597e8 −1.04008
\(65\) 1.49678e7 0.104003
\(66\) −3.67171e7 −0.238189
\(67\) 7.95827e7 0.482483 0.241242 0.970465i \(-0.422445\pi\)
0.241242 + 0.970465i \(0.422445\pi\)
\(68\) −2.63124e8 −1.49235
\(69\) 1.22052e8 0.648221
\(70\) −6.29103e8 −3.13171
\(71\) 1.53469e8 0.716736 0.358368 0.933580i \(-0.383333\pi\)
0.358368 + 0.933580i \(0.383333\pi\)
\(72\) −1.29568e8 −0.568203
\(73\) −3.49414e8 −1.44008 −0.720042 0.693931i \(-0.755877\pi\)
−0.720042 + 0.693931i \(0.755877\pi\)
\(74\) −2.10058e8 −0.814324
\(75\) 1.17562e8 0.429033
\(76\) −5.20505e8 −1.78963
\(77\) 1.01079e8 0.327683
\(78\) −2.56935e7 −0.0785956
\(79\) −3.98120e8 −1.14998 −0.574992 0.818159i \(-0.694995\pi\)
−0.574992 + 0.818159i \(0.694995\pi\)
\(80\) 4.64037e8 1.26662
\(81\) 4.30467e7 0.111111
\(82\) −4.07186e8 −0.994558
\(83\) −4.09387e6 −0.00946852 −0.00473426 0.999989i \(-0.501507\pi\)
−0.00473426 + 0.999989i \(0.501507\pi\)
\(84\) 7.18302e8 1.57417
\(85\) −4.77366e8 −0.991896
\(86\) −4.53354e7 −0.0893705
\(87\) 2.91748e8 0.545974
\(88\) −2.28931e8 −0.406942
\(89\) 2.94766e8 0.497992 0.248996 0.968504i \(-0.419899\pi\)
0.248996 + 0.968504i \(0.419899\pi\)
\(90\) −4.73375e8 −0.760526
\(91\) 7.07321e7 0.108126
\(92\) 1.53248e9 2.23023
\(93\) 4.19488e7 0.0581495
\(94\) −8.02581e8 −1.06026
\(95\) −9.44313e8 −1.18949
\(96\) 2.24389e7 0.0269638
\(97\) −4.22911e8 −0.485039 −0.242519 0.970147i \(-0.577974\pi\)
−0.242519 + 0.970147i \(0.577974\pi\)
\(98\) −1.39497e9 −1.52773
\(99\) 7.60580e7 0.0795768
\(100\) 1.47610e9 1.47610
\(101\) 1.76540e9 1.68809 0.844046 0.536271i \(-0.180167\pi\)
0.844046 + 0.536271i \(0.180167\pi\)
\(102\) 8.19442e8 0.749579
\(103\) −8.41804e7 −0.0736959 −0.0368480 0.999321i \(-0.511732\pi\)
−0.0368480 + 0.999321i \(0.511732\pi\)
\(104\) −1.60199e8 −0.134279
\(105\) 1.30316e9 1.04628
\(106\) 2.36418e9 1.81888
\(107\) 2.00988e9 1.48232 0.741161 0.671328i \(-0.234276\pi\)
0.741161 + 0.671328i \(0.234276\pi\)
\(108\) 5.40494e8 0.382282
\(109\) 2.50764e9 1.70155 0.850776 0.525529i \(-0.176132\pi\)
0.850776 + 0.525529i \(0.176132\pi\)
\(110\) −8.36393e8 −0.544683
\(111\) 4.35127e8 0.272059
\(112\) 2.19287e9 1.31683
\(113\) −7.59390e8 −0.438139 −0.219069 0.975709i \(-0.570302\pi\)
−0.219069 + 0.975709i \(0.570302\pi\)
\(114\) 1.62100e9 0.898899
\(115\) 2.78026e9 1.48233
\(116\) 3.66319e9 1.87844
\(117\) 5.32231e7 0.0262581
\(118\) 4.73824e8 0.224982
\(119\) −2.25585e9 −1.03122
\(120\) −2.95149e9 −1.29935
\(121\) −2.22356e9 −0.943008
\(122\) −6.82422e9 −2.78891
\(123\) 8.43468e8 0.332274
\(124\) 5.26708e8 0.200066
\(125\) −9.25785e8 −0.339168
\(126\) −2.23700e9 −0.790674
\(127\) 2.81966e9 0.961789 0.480895 0.876778i \(-0.340312\pi\)
0.480895 + 0.876778i \(0.340312\pi\)
\(128\) 5.31680e9 1.75067
\(129\) 9.39103e7 0.0298579
\(130\) −5.85283e8 −0.179730
\(131\) 3.02532e9 0.897533 0.448766 0.893649i \(-0.351864\pi\)
0.448766 + 0.893649i \(0.351864\pi\)
\(132\) 9.54983e8 0.273787
\(133\) −4.46247e9 −1.23664
\(134\) −3.11191e9 −0.833788
\(135\) 9.80578e8 0.254086
\(136\) 5.10921e9 1.28064
\(137\) 6.21211e9 1.50660 0.753298 0.657680i \(-0.228462\pi\)
0.753298 + 0.657680i \(0.228462\pi\)
\(138\) −4.77257e9 −1.12020
\(139\) −7.25432e9 −1.64828 −0.824139 0.566388i \(-0.808340\pi\)
−0.824139 + 0.566388i \(0.808340\pi\)
\(140\) 1.63625e10 3.59975
\(141\) 1.66251e9 0.354225
\(142\) −6.00109e9 −1.23860
\(143\) 9.40384e7 0.0188059
\(144\) 1.65005e9 0.319790
\(145\) 6.64585e9 1.24852
\(146\) 1.36631e10 2.48863
\(147\) 2.88962e9 0.510402
\(148\) 5.46345e9 0.936028
\(149\) 3.73612e9 0.620988 0.310494 0.950575i \(-0.399506\pi\)
0.310494 + 0.950575i \(0.399506\pi\)
\(150\) −4.59700e9 −0.741420
\(151\) 3.66181e9 0.573192 0.286596 0.958052i \(-0.407476\pi\)
0.286596 + 0.958052i \(0.407476\pi\)
\(152\) 1.01069e10 1.53576
\(153\) −1.69744e9 −0.250428
\(154\) −3.95248e9 −0.566274
\(155\) 9.55568e8 0.132975
\(156\) 6.68268e8 0.0903421
\(157\) −8.36523e9 −1.09883 −0.549414 0.835550i \(-0.685149\pi\)
−0.549414 + 0.835550i \(0.685149\pi\)
\(158\) 1.55676e10 1.98731
\(159\) −4.89730e9 −0.607673
\(160\) 5.11145e8 0.0616601
\(161\) 1.31385e10 1.54109
\(162\) −1.68325e9 −0.192013
\(163\) −8.59620e9 −0.953811 −0.476905 0.878955i \(-0.658242\pi\)
−0.476905 + 0.878955i \(0.658242\pi\)
\(164\) 1.05906e10 1.14320
\(165\) 1.73256e9 0.181974
\(166\) 1.60082e8 0.0163627
\(167\) −1.76924e10 −1.76020 −0.880102 0.474785i \(-0.842526\pi\)
−0.880102 + 0.474785i \(0.842526\pi\)
\(168\) −1.39476e10 −1.35086
\(169\) −1.05387e10 −0.993795
\(170\) 1.86664e10 1.71411
\(171\) −3.35783e9 −0.300315
\(172\) 1.17914e9 0.102727
\(173\) 1.10926e10 0.941516 0.470758 0.882262i \(-0.343981\pi\)
0.470758 + 0.882262i \(0.343981\pi\)
\(174\) −1.14082e10 −0.943508
\(175\) 1.26552e10 1.01999
\(176\) 2.91542e9 0.229031
\(177\) −9.81506e8 −0.0751646
\(178\) −1.15262e10 −0.860590
\(179\) 3.55499e9 0.258821 0.129411 0.991591i \(-0.458691\pi\)
0.129411 + 0.991591i \(0.458691\pi\)
\(180\) 1.23121e10 0.874191
\(181\) −1.27355e10 −0.881986 −0.440993 0.897511i \(-0.645374\pi\)
−0.440993 + 0.897511i \(0.645374\pi\)
\(182\) −2.76583e9 −0.186855
\(183\) 1.41361e10 0.931751
\(184\) −2.97569e10 −1.91385
\(185\) 9.91193e9 0.622136
\(186\) −1.64032e9 −0.100489
\(187\) −2.99916e9 −0.179354
\(188\) 2.08745e10 1.21872
\(189\) 4.63385e9 0.264158
\(190\) 3.69254e10 2.05558
\(191\) −1.21114e10 −0.658482 −0.329241 0.944246i \(-0.606793\pi\)
−0.329241 + 0.944246i \(0.606793\pi\)
\(192\) −1.13073e10 −0.600489
\(193\) 1.32381e10 0.686781 0.343390 0.939193i \(-0.388425\pi\)
0.343390 + 0.939193i \(0.388425\pi\)
\(194\) 1.65370e10 0.838205
\(195\) 1.21239e9 0.0600463
\(196\) 3.62820e10 1.75606
\(197\) −3.74378e9 −0.177098 −0.0885488 0.996072i \(-0.528223\pi\)
−0.0885488 + 0.996072i \(0.528223\pi\)
\(198\) −2.97409e9 −0.137518
\(199\) 1.45493e10 0.657663 0.328831 0.944389i \(-0.393345\pi\)
0.328831 + 0.944389i \(0.393345\pi\)
\(200\) −2.86623e10 −1.26671
\(201\) 6.44620e9 0.278562
\(202\) −6.90321e10 −2.91722
\(203\) 3.14058e10 1.29801
\(204\) −2.13130e10 −0.861607
\(205\) 1.92137e10 0.759833
\(206\) 3.29169e9 0.127355
\(207\) 9.88619e9 0.374251
\(208\) 2.04012e9 0.0755738
\(209\) −5.93286e9 −0.215083
\(210\) −5.09574e10 −1.80809
\(211\) −3.38777e10 −1.17664 −0.588319 0.808629i \(-0.700210\pi\)
−0.588319 + 0.808629i \(0.700210\pi\)
\(212\) −6.14904e10 −2.09072
\(213\) 1.24310e10 0.413808
\(214\) −7.85919e10 −2.56163
\(215\) 2.13922e9 0.0682782
\(216\) −1.04950e10 −0.328052
\(217\) 4.51566e9 0.138246
\(218\) −9.80557e10 −2.94048
\(219\) −2.83025e10 −0.831432
\(220\) 2.17539e10 0.626088
\(221\) −2.09872e9 −0.0591820
\(222\) −1.70147e10 −0.470150
\(223\) −4.03514e10 −1.09267 −0.546333 0.837568i \(-0.683977\pi\)
−0.546333 + 0.837568i \(0.683977\pi\)
\(224\) 2.41548e9 0.0641044
\(225\) 9.52250e9 0.247702
\(226\) 2.96943e10 0.757156
\(227\) −1.12508e10 −0.281234 −0.140617 0.990064i \(-0.544909\pi\)
−0.140617 + 0.990064i \(0.544909\pi\)
\(228\) −4.21609e10 −1.03324
\(229\) −6.60532e9 −0.158721 −0.0793605 0.996846i \(-0.525288\pi\)
−0.0793605 + 0.996846i \(0.525288\pi\)
\(230\) −1.08716e11 −2.56165
\(231\) 8.18741e9 0.189188
\(232\) −7.11300e10 −1.61197
\(233\) 1.70989e10 0.380072 0.190036 0.981777i \(-0.439139\pi\)
0.190036 + 0.981777i \(0.439139\pi\)
\(234\) −2.08118e9 −0.0453772
\(235\) 3.78710e10 0.810031
\(236\) −1.23238e10 −0.258607
\(237\) −3.22477e10 −0.663944
\(238\) 8.82103e10 1.78206
\(239\) 3.34258e10 0.662661 0.331331 0.943515i \(-0.392502\pi\)
0.331331 + 0.943515i \(0.392502\pi\)
\(240\) 3.75870e10 0.731286
\(241\) −1.19790e10 −0.228741 −0.114370 0.993438i \(-0.536485\pi\)
−0.114370 + 0.993438i \(0.536485\pi\)
\(242\) 8.69477e10 1.62963
\(243\) 3.48678e9 0.0641500
\(244\) 1.77493e11 3.20572
\(245\) 6.58237e10 1.16717
\(246\) −3.29820e10 −0.574208
\(247\) −4.15164e9 −0.0709714
\(248\) −1.02274e10 −0.171685
\(249\) −3.31603e8 −0.00546665
\(250\) 3.62008e10 0.586123
\(251\) 1.78053e10 0.283151 0.141575 0.989927i \(-0.454783\pi\)
0.141575 + 0.989927i \(0.454783\pi\)
\(252\) 5.81825e10 0.908845
\(253\) 1.74676e10 0.268035
\(254\) −1.10257e11 −1.66209
\(255\) −3.86666e10 −0.572672
\(256\) −1.36429e11 −1.98530
\(257\) 3.60577e10 0.515583 0.257792 0.966201i \(-0.417005\pi\)
0.257792 + 0.966201i \(0.417005\pi\)
\(258\) −3.67216e9 −0.0515981
\(259\) 4.68401e10 0.646798
\(260\) 1.52227e10 0.206592
\(261\) 2.36316e10 0.315218
\(262\) −1.18299e11 −1.55104
\(263\) −3.71011e9 −0.0478174 −0.0239087 0.999714i \(-0.507611\pi\)
−0.0239087 + 0.999714i \(0.507611\pi\)
\(264\) −1.85434e10 −0.234948
\(265\) −1.11558e11 −1.38961
\(266\) 1.74496e11 2.13706
\(267\) 2.38761e10 0.287516
\(268\) 8.09384e10 0.958402
\(269\) −4.27276e9 −0.0497535 −0.0248767 0.999691i \(-0.507919\pi\)
−0.0248767 + 0.999691i \(0.507919\pi\)
\(270\) −3.83434e10 −0.439090
\(271\) 7.45985e10 0.840172 0.420086 0.907484i \(-0.362000\pi\)
0.420086 + 0.907484i \(0.362000\pi\)
\(272\) −6.50654e10 −0.720759
\(273\) 5.72930e9 0.0624266
\(274\) −2.42911e11 −2.60358
\(275\) 1.68250e10 0.177402
\(276\) 1.24131e11 1.28762
\(277\) 1.38405e11 1.41252 0.706258 0.707955i \(-0.250382\pi\)
0.706258 + 0.707955i \(0.250382\pi\)
\(278\) 2.83665e11 2.84842
\(279\) 3.39785e9 0.0335726
\(280\) −3.17719e11 −3.08910
\(281\) −6.29759e10 −0.602554 −0.301277 0.953537i \(-0.597413\pi\)
−0.301277 + 0.953537i \(0.597413\pi\)
\(282\) −6.50090e10 −0.612143
\(283\) 1.42028e11 1.31624 0.658121 0.752912i \(-0.271352\pi\)
0.658121 + 0.752912i \(0.271352\pi\)
\(284\) 1.56084e11 1.42372
\(285\) −7.64894e10 −0.686751
\(286\) −3.67717e9 −0.0324988
\(287\) 9.07967e10 0.789954
\(288\) 1.81755e9 0.0155676
\(289\) −5.16536e10 −0.435572
\(290\) −2.59872e11 −2.15759
\(291\) −3.42558e10 −0.280037
\(292\) −3.55366e11 −2.86057
\(293\) 8.04654e10 0.637830 0.318915 0.947783i \(-0.396682\pi\)
0.318915 + 0.947783i \(0.396682\pi\)
\(294\) −1.12992e11 −0.882035
\(295\) −2.23581e10 −0.171884
\(296\) −1.06087e11 −0.803245
\(297\) 6.16070e9 0.0459437
\(298\) −1.46093e11 −1.07314
\(299\) 1.22233e10 0.0884441
\(300\) 1.19564e11 0.852229
\(301\) 1.01092e10 0.0709848
\(302\) −1.43187e11 −0.990544
\(303\) 1.42997e11 0.974621
\(304\) −1.28711e11 −0.864339
\(305\) 3.22012e11 2.13070
\(306\) 6.63748e10 0.432769
\(307\) 9.07324e10 0.582962 0.291481 0.956577i \(-0.405852\pi\)
0.291481 + 0.956577i \(0.405852\pi\)
\(308\) 1.02801e11 0.650907
\(309\) −6.81861e9 −0.0425483
\(310\) −3.73654e10 −0.229796
\(311\) −1.13266e11 −0.686556 −0.343278 0.939234i \(-0.611537\pi\)
−0.343278 + 0.939234i \(0.611537\pi\)
\(312\) −1.29761e10 −0.0775263
\(313\) 3.75570e10 0.221178 0.110589 0.993866i \(-0.464726\pi\)
0.110589 + 0.993866i \(0.464726\pi\)
\(314\) 3.27105e11 1.89890
\(315\) 1.05556e11 0.604068
\(316\) −4.04901e11 −2.28432
\(317\) 9.19099e10 0.511206 0.255603 0.966782i \(-0.417726\pi\)
0.255603 + 0.966782i \(0.417726\pi\)
\(318\) 1.91499e11 1.05013
\(319\) 4.17541e10 0.225757
\(320\) −2.57574e11 −1.37318
\(321\) 1.62800e11 0.855819
\(322\) −5.13753e11 −2.66319
\(323\) 1.32408e11 0.676865
\(324\) 4.37800e10 0.220711
\(325\) 1.17737e10 0.0585378
\(326\) 3.36136e11 1.64830
\(327\) 2.03118e11 0.982391
\(328\) −2.05643e11 −0.981027
\(329\) 1.78964e11 0.842141
\(330\) −6.77479e10 −0.314473
\(331\) 1.37968e11 0.631762 0.315881 0.948799i \(-0.397700\pi\)
0.315881 + 0.948799i \(0.397700\pi\)
\(332\) −4.16360e9 −0.0188082
\(333\) 3.52453e10 0.157073
\(334\) 6.91824e11 3.04184
\(335\) 1.46840e11 0.637007
\(336\) 1.77622e11 0.760275
\(337\) 5.67015e10 0.239475 0.119738 0.992806i \(-0.461795\pi\)
0.119738 + 0.992806i \(0.461795\pi\)
\(338\) 4.12093e11 1.71740
\(339\) −6.15106e10 −0.252960
\(340\) −4.85497e11 −1.97030
\(341\) 6.00357e9 0.0240444
\(342\) 1.31301e11 0.518980
\(343\) −4.08008e10 −0.159164
\(344\) −2.28959e10 −0.0881546
\(345\) 2.25201e11 0.855825
\(346\) −4.33754e11 −1.62705
\(347\) −2.48717e11 −0.920921 −0.460460 0.887680i \(-0.652316\pi\)
−0.460460 + 0.887680i \(0.652316\pi\)
\(348\) 2.96718e11 1.08452
\(349\) 4.33331e11 1.56353 0.781763 0.623576i \(-0.214321\pi\)
0.781763 + 0.623576i \(0.214321\pi\)
\(350\) −4.94853e11 −1.76267
\(351\) 4.31107e9 0.0151601
\(352\) 3.21138e9 0.0111494
\(353\) −5.43531e11 −1.86311 −0.931554 0.363604i \(-0.881546\pi\)
−0.931554 + 0.363604i \(0.881546\pi\)
\(354\) 3.83797e10 0.129893
\(355\) 2.83171e11 0.946283
\(356\) 2.99787e11 0.989209
\(357\) −1.82724e11 −0.595373
\(358\) −1.39010e11 −0.447274
\(359\) −5.45243e10 −0.173247 −0.0866234 0.996241i \(-0.527608\pi\)
−0.0866234 + 0.996241i \(0.527608\pi\)
\(360\) −2.39071e11 −0.750179
\(361\) −6.07619e10 −0.188299
\(362\) 4.97994e11 1.52418
\(363\) −1.80109e11 −0.544446
\(364\) 7.19370e10 0.214781
\(365\) −6.44714e11 −1.90130
\(366\) −5.52762e11 −1.61018
\(367\) 2.37654e10 0.0683829 0.0341914 0.999415i \(-0.489114\pi\)
0.0341914 + 0.999415i \(0.489114\pi\)
\(368\) 3.78953e11 1.07713
\(369\) 6.83209e10 0.191838
\(370\) −3.87585e11 −1.07512
\(371\) −5.27180e11 −1.44469
\(372\) 4.26634e10 0.115508
\(373\) −2.46802e11 −0.660176 −0.330088 0.943950i \(-0.607078\pi\)
−0.330088 + 0.943950i \(0.607078\pi\)
\(374\) 1.17276e11 0.309946
\(375\) −7.49886e10 −0.195819
\(376\) −4.05331e11 −1.04584
\(377\) 2.92182e10 0.0744934
\(378\) −1.81197e11 −0.456496
\(379\) 5.39891e11 1.34409 0.672047 0.740509i \(-0.265415\pi\)
0.672047 + 0.740509i \(0.265415\pi\)
\(380\) −9.60399e11 −2.36279
\(381\) 2.28392e11 0.555289
\(382\) 4.73590e11 1.13794
\(383\) −6.64007e11 −1.57681 −0.788403 0.615159i \(-0.789092\pi\)
−0.788403 + 0.615159i \(0.789092\pi\)
\(384\) 4.30661e11 1.01075
\(385\) 1.86504e11 0.432629
\(386\) −5.17648e11 −1.18684
\(387\) 7.60674e9 0.0172385
\(388\) −4.30115e11 −0.963479
\(389\) −8.92311e10 −0.197580 −0.0987900 0.995108i \(-0.531497\pi\)
−0.0987900 + 0.995108i \(0.531497\pi\)
\(390\) −4.74079e10 −0.103767
\(391\) −3.89837e11 −0.843506
\(392\) −7.04506e11 −1.50695
\(393\) 2.45051e11 0.518191
\(394\) 1.46393e11 0.306046
\(395\) −7.34583e11 −1.51829
\(396\) 7.73536e10 0.158071
\(397\) −8.34544e11 −1.68613 −0.843067 0.537808i \(-0.819252\pi\)
−0.843067 + 0.537808i \(0.819252\pi\)
\(398\) −5.68919e11 −1.13652
\(399\) −3.61460e11 −0.713974
\(400\) 3.65012e11 0.712914
\(401\) 6.21503e11 1.20031 0.600155 0.799884i \(-0.295106\pi\)
0.600155 + 0.799884i \(0.295106\pi\)
\(402\) −2.52065e11 −0.481388
\(403\) 4.20112e9 0.00793400
\(404\) 1.79547e12 3.35322
\(405\) 7.94268e10 0.146696
\(406\) −1.22806e12 −2.24311
\(407\) 6.22739e10 0.112495
\(408\) 4.13846e11 0.739381
\(409\) 5.26321e10 0.0930028 0.0465014 0.998918i \(-0.485193\pi\)
0.0465014 + 0.998918i \(0.485193\pi\)
\(410\) −7.51310e11 −1.31308
\(411\) 5.03181e11 0.869833
\(412\) −8.56143e10 −0.146389
\(413\) −1.05656e11 −0.178698
\(414\) −3.86578e11 −0.646749
\(415\) −7.55372e9 −0.0125010
\(416\) 2.24723e9 0.00367898
\(417\) −5.87600e11 −0.951633
\(418\) 2.31992e11 0.371689
\(419\) 2.70229e11 0.428321 0.214161 0.976798i \(-0.431298\pi\)
0.214161 + 0.976798i \(0.431298\pi\)
\(420\) 1.32536e12 2.07832
\(421\) 2.25697e11 0.350152 0.175076 0.984555i \(-0.443983\pi\)
0.175076 + 0.984555i \(0.443983\pi\)
\(422\) 1.32472e12 2.03337
\(423\) 1.34664e11 0.204512
\(424\) 1.19399e12 1.79413
\(425\) −3.75496e11 −0.558284
\(426\) −4.86089e11 −0.715109
\(427\) 1.52171e12 2.21516
\(428\) 2.04411e12 2.94448
\(429\) 7.61711e9 0.0108576
\(430\) −8.36496e10 −0.117993
\(431\) −1.41241e12 −1.97158 −0.985789 0.167990i \(-0.946272\pi\)
−0.985789 + 0.167990i \(0.946272\pi\)
\(432\) 1.33654e11 0.184631
\(433\) 9.00250e11 1.23074 0.615372 0.788237i \(-0.289006\pi\)
0.615372 + 0.788237i \(0.289006\pi\)
\(434\) −1.76575e11 −0.238905
\(435\) 5.38314e11 0.720832
\(436\) 2.55035e12 3.37995
\(437\) −7.71167e11 −1.01154
\(438\) 1.10671e12 1.43681
\(439\) 1.91834e11 0.246511 0.123255 0.992375i \(-0.460667\pi\)
0.123255 + 0.992375i \(0.460667\pi\)
\(440\) −4.22407e11 −0.537272
\(441\) 2.34059e11 0.294681
\(442\) 8.20660e10 0.102273
\(443\) 1.26560e12 1.56127 0.780637 0.624985i \(-0.214895\pi\)
0.780637 + 0.624985i \(0.214895\pi\)
\(444\) 4.42539e11 0.540416
\(445\) 5.43882e11 0.657483
\(446\) 1.57786e12 1.88826
\(447\) 3.02626e11 0.358527
\(448\) −1.21720e12 −1.42761
\(449\) 3.63594e11 0.422190 0.211095 0.977466i \(-0.432297\pi\)
0.211095 + 0.977466i \(0.432297\pi\)
\(450\) −3.72357e11 −0.428059
\(451\) 1.20714e11 0.137393
\(452\) −7.72325e11 −0.870317
\(453\) 2.96607e11 0.330933
\(454\) 4.39940e11 0.486007
\(455\) 1.30510e11 0.142755
\(456\) 8.18660e11 0.886669
\(457\) −4.51697e11 −0.484423 −0.242211 0.970224i \(-0.577873\pi\)
−0.242211 + 0.970224i \(0.577873\pi\)
\(458\) 2.58287e11 0.274289
\(459\) −1.37493e11 −0.144585
\(460\) 2.82762e12 2.94450
\(461\) −6.18511e11 −0.637813 −0.318906 0.947786i \(-0.603316\pi\)
−0.318906 + 0.947786i \(0.603316\pi\)
\(462\) −3.20151e11 −0.326939
\(463\) 4.03552e10 0.0408117 0.0204059 0.999792i \(-0.493504\pi\)
0.0204059 + 0.999792i \(0.493504\pi\)
\(464\) 9.05836e11 0.907232
\(465\) 7.74010e10 0.0767729
\(466\) −6.68616e11 −0.656810
\(467\) 9.59256e11 0.933273 0.466637 0.884449i \(-0.345466\pi\)
0.466637 + 0.884449i \(0.345466\pi\)
\(468\) 5.41297e10 0.0521590
\(469\) 6.93914e11 0.662259
\(470\) −1.48087e12 −1.39983
\(471\) −6.77584e11 −0.634408
\(472\) 2.39297e11 0.221921
\(473\) 1.34401e10 0.0123461
\(474\) 1.26098e12 1.14737
\(475\) −7.42797e11 −0.669498
\(476\) −2.29428e12 −2.04840
\(477\) −3.96682e11 −0.350840
\(478\) −1.30705e12 −1.14516
\(479\) 8.31520e11 0.721711 0.360855 0.932622i \(-0.382485\pi\)
0.360855 + 0.932622i \(0.382485\pi\)
\(480\) 4.14028e10 0.0355995
\(481\) 4.35774e10 0.0371201
\(482\) 4.68413e11 0.395291
\(483\) 1.06422e12 0.889751
\(484\) −2.26144e12 −1.87319
\(485\) −7.80327e11 −0.640381
\(486\) −1.36343e11 −0.110859
\(487\) 1.60466e12 1.29271 0.646356 0.763036i \(-0.276292\pi\)
0.646356 + 0.763036i \(0.276292\pi\)
\(488\) −3.44647e12 −2.75096
\(489\) −6.96292e11 −0.550683
\(490\) −2.57390e12 −2.01701
\(491\) −9.63225e11 −0.747930 −0.373965 0.927443i \(-0.622002\pi\)
−0.373965 + 0.927443i \(0.622002\pi\)
\(492\) 8.57836e11 0.660026
\(493\) −9.31854e11 −0.710455
\(494\) 1.62341e11 0.122647
\(495\) 1.40337e11 0.105063
\(496\) 1.30245e11 0.0966257
\(497\) 1.33816e12 0.983795
\(498\) 1.29666e10 0.00944703
\(499\) −2.21909e12 −1.60222 −0.801112 0.598515i \(-0.795758\pi\)
−0.801112 + 0.598515i \(0.795758\pi\)
\(500\) −9.41555e11 −0.673722
\(501\) −1.43309e12 −1.01625
\(502\) −6.96239e11 −0.489319
\(503\) 1.05270e12 0.733245 0.366622 0.930370i \(-0.380514\pi\)
0.366622 + 0.930370i \(0.380514\pi\)
\(504\) −1.12976e12 −0.779917
\(505\) 3.25739e12 2.22873
\(506\) −6.83035e11 −0.463197
\(507\) −8.53634e11 −0.573768
\(508\) 2.86769e12 1.91049
\(509\) −2.21547e11 −0.146297 −0.0731486 0.997321i \(-0.523305\pi\)
−0.0731486 + 0.997321i \(0.523305\pi\)
\(510\) 1.51198e12 0.989644
\(511\) −3.04668e12 −1.97666
\(512\) 2.61255e12 1.68015
\(513\) −2.71985e11 −0.173387
\(514\) −1.40996e12 −0.890989
\(515\) −1.55324e11 −0.0972983
\(516\) 9.55100e10 0.0593096
\(517\) 2.37933e11 0.146470
\(518\) −1.83158e12 −1.11774
\(519\) 8.98504e11 0.543584
\(520\) −2.95588e11 −0.177285
\(521\) 2.36950e12 1.40892 0.704460 0.709743i \(-0.251189\pi\)
0.704460 + 0.709743i \(0.251189\pi\)
\(522\) −9.24064e11 −0.544735
\(523\) 2.09943e12 1.22700 0.613499 0.789696i \(-0.289762\pi\)
0.613499 + 0.789696i \(0.289762\pi\)
\(524\) 3.07685e12 1.78285
\(525\) 1.02507e12 0.588892
\(526\) 1.45076e11 0.0826342
\(527\) −1.33986e11 −0.0756678
\(528\) 2.36149e11 0.132231
\(529\) 4.69329e11 0.260571
\(530\) 4.36222e12 2.40141
\(531\) −7.95020e10 −0.0433963
\(532\) −4.53849e12 −2.45646
\(533\) 8.44722e10 0.0453358
\(534\) −9.33622e11 −0.496862
\(535\) 3.70848e12 1.95706
\(536\) −1.57162e12 −0.822445
\(537\) 2.87954e11 0.149431
\(538\) 1.67077e11 0.0859799
\(539\) 4.13552e11 0.211048
\(540\) 9.97281e11 0.504714
\(541\) −2.68282e12 −1.34649 −0.673245 0.739419i \(-0.735100\pi\)
−0.673245 + 0.739419i \(0.735100\pi\)
\(542\) −2.91701e12 −1.45192
\(543\) −1.03157e12 −0.509215
\(544\) −7.16707e10 −0.0350870
\(545\) 4.62691e12 2.24650
\(546\) −2.24032e11 −0.107881
\(547\) −1.34648e12 −0.643066 −0.321533 0.946898i \(-0.604198\pi\)
−0.321533 + 0.946898i \(0.604198\pi\)
\(548\) 6.31793e12 2.99269
\(549\) 1.14502e12 0.537947
\(550\) −6.57907e11 −0.306572
\(551\) −1.84337e12 −0.851982
\(552\) −2.41031e12 −1.10496
\(553\) −3.47136e12 −1.57847
\(554\) −5.41204e12 −2.44100
\(555\) 8.02866e11 0.359190
\(556\) −7.37789e12 −3.27413
\(557\) −3.58326e12 −1.57736 −0.788678 0.614807i \(-0.789234\pi\)
−0.788678 + 0.614807i \(0.789234\pi\)
\(558\) −1.32866e11 −0.0580175
\(559\) 9.40500e9 0.00407385
\(560\) 4.04613e12 1.73857
\(561\) −2.42932e11 −0.103550
\(562\) 2.46254e12 1.04129
\(563\) −1.13265e12 −0.475125 −0.237562 0.971372i \(-0.576348\pi\)
−0.237562 + 0.971372i \(0.576348\pi\)
\(564\) 1.69083e12 0.703630
\(565\) −1.40117e12 −0.578461
\(566\) −5.55371e12 −2.27462
\(567\) 3.75341e11 0.152512
\(568\) −3.03076e12 −1.22175
\(569\) −4.59730e12 −1.83865 −0.919323 0.393504i \(-0.871263\pi\)
−0.919323 + 0.393504i \(0.871263\pi\)
\(570\) 2.99095e12 1.18679
\(571\) −2.23247e12 −0.878865 −0.439433 0.898276i \(-0.644821\pi\)
−0.439433 + 0.898276i \(0.644821\pi\)
\(572\) 9.56403e10 0.0373559
\(573\) −9.81023e11 −0.380175
\(574\) −3.55041e12 −1.36513
\(575\) 2.18696e12 0.834324
\(576\) −9.15895e11 −0.346693
\(577\) 1.72653e12 0.648461 0.324230 0.945978i \(-0.394895\pi\)
0.324230 + 0.945978i \(0.394895\pi\)
\(578\) 2.01980e12 0.752720
\(579\) 1.07229e12 0.396513
\(580\) 6.75906e12 2.48005
\(581\) −3.56960e10 −0.0129965
\(582\) 1.33950e12 0.483938
\(583\) −7.00886e11 −0.251269
\(584\) 6.90033e12 2.45478
\(585\) 9.82036e10 0.0346678
\(586\) −3.14643e12 −1.10225
\(587\) −7.42662e11 −0.258178 −0.129089 0.991633i \(-0.541205\pi\)
−0.129089 + 0.991633i \(0.541205\pi\)
\(588\) 2.93884e12 1.01386
\(589\) −2.65047e11 −0.0907412
\(590\) 8.74266e11 0.297036
\(591\) −3.03246e11 −0.102247
\(592\) 1.35101e12 0.452074
\(593\) 1.34284e10 0.00445940 0.00222970 0.999998i \(-0.499290\pi\)
0.00222970 + 0.999998i \(0.499290\pi\)
\(594\) −2.40901e11 −0.0793962
\(595\) −4.16234e12 −1.36148
\(596\) 3.79976e12 1.23353
\(597\) 1.17849e12 0.379702
\(598\) −4.77967e11 −0.152842
\(599\) 3.86405e12 1.22637 0.613186 0.789939i \(-0.289888\pi\)
0.613186 + 0.789939i \(0.289888\pi\)
\(600\) −2.32164e12 −0.731333
\(601\) 3.04249e12 0.951248 0.475624 0.879649i \(-0.342222\pi\)
0.475624 + 0.879649i \(0.342222\pi\)
\(602\) −3.95297e11 −0.122670
\(603\) 5.22142e11 0.160828
\(604\) 3.72419e12 1.13859
\(605\) −4.10276e12 −1.24502
\(606\) −5.59160e12 −1.68426
\(607\) 2.18130e12 0.652179 0.326090 0.945339i \(-0.394269\pi\)
0.326090 + 0.945339i \(0.394269\pi\)
\(608\) −1.41777e11 −0.0420766
\(609\) 2.54387e12 0.749406
\(610\) −1.25916e13 −3.68210
\(611\) 1.66498e11 0.0483309
\(612\) −1.72635e12 −0.497449
\(613\) −4.85568e12 −1.38892 −0.694460 0.719531i \(-0.744357\pi\)
−0.694460 + 0.719531i \(0.744357\pi\)
\(614\) −3.54790e12 −1.00743
\(615\) 1.55631e12 0.438690
\(616\) −1.99614e12 −0.558570
\(617\) −3.66289e12 −1.01751 −0.508757 0.860910i \(-0.669895\pi\)
−0.508757 + 0.860910i \(0.669895\pi\)
\(618\) 2.66627e11 0.0735286
\(619\) −1.50800e12 −0.412852 −0.206426 0.978462i \(-0.566183\pi\)
−0.206426 + 0.978462i \(0.566183\pi\)
\(620\) 9.71845e11 0.264140
\(621\) 8.00782e11 0.216074
\(622\) 4.42901e12 1.18645
\(623\) 2.57018e12 0.683546
\(624\) 1.65250e11 0.0436325
\(625\) −4.54292e12 −1.19090
\(626\) −1.46859e12 −0.382222
\(627\) −4.80562e11 −0.124178
\(628\) −8.50773e12 −2.18271
\(629\) −1.38981e12 −0.354020
\(630\) −4.12755e12 −1.04390
\(631\) −5.10589e12 −1.28215 −0.641076 0.767477i \(-0.721512\pi\)
−0.641076 + 0.767477i \(0.721512\pi\)
\(632\) 7.86218e12 1.96027
\(633\) −2.74410e12 −0.679333
\(634\) −3.59394e12 −0.883424
\(635\) 5.20264e12 1.26982
\(636\) −4.98073e12 −1.20708
\(637\) 2.89391e11 0.0696399
\(638\) −1.63270e12 −0.390134
\(639\) 1.00691e12 0.238912
\(640\) 9.81019e12 2.31136
\(641\) 4.14832e12 0.970536 0.485268 0.874365i \(-0.338722\pi\)
0.485268 + 0.874365i \(0.338722\pi\)
\(642\) −6.36595e12 −1.47896
\(643\) 6.70027e12 1.54576 0.772882 0.634550i \(-0.218815\pi\)
0.772882 + 0.634550i \(0.218815\pi\)
\(644\) 1.33623e13 3.06122
\(645\) 1.73277e11 0.0394205
\(646\) −5.17752e12 −1.16970
\(647\) 4.57762e12 1.02700 0.513500 0.858090i \(-0.328349\pi\)
0.513500 + 0.858090i \(0.328349\pi\)
\(648\) −8.50099e11 −0.189401
\(649\) −1.40470e11 −0.0310801
\(650\) −4.60384e11 −0.101160
\(651\) 3.65768e11 0.0798163
\(652\) −8.74263e12 −1.89464
\(653\) 6.06978e12 1.30636 0.653181 0.757201i \(-0.273434\pi\)
0.653181 + 0.757201i \(0.273434\pi\)
\(654\) −7.94251e12 −1.69769
\(655\) 5.58211e12 1.18498
\(656\) 2.61884e12 0.552131
\(657\) −2.29251e12 −0.480028
\(658\) −6.99802e12 −1.45532
\(659\) 3.83697e12 0.792510 0.396255 0.918141i \(-0.370310\pi\)
0.396255 + 0.918141i \(0.370310\pi\)
\(660\) 1.76207e12 0.361472
\(661\) 2.48540e12 0.506396 0.253198 0.967415i \(-0.418518\pi\)
0.253198 + 0.967415i \(0.418518\pi\)
\(662\) −5.39496e12 −1.09176
\(663\) −1.69996e11 −0.0341687
\(664\) 8.08468e10 0.0161401
\(665\) −8.23384e12 −1.63270
\(666\) −1.37819e12 −0.271441
\(667\) 5.42728e12 1.06174
\(668\) −1.79938e13 −3.49646
\(669\) −3.26847e12 −0.630851
\(670\) −5.74188e12 −1.10082
\(671\) 2.02311e12 0.385273
\(672\) 1.95654e11 0.0370107
\(673\) 8.77320e12 1.64851 0.824253 0.566222i \(-0.191596\pi\)
0.824253 + 0.566222i \(0.191596\pi\)
\(674\) −2.21719e12 −0.413841
\(675\) 7.71323e11 0.143011
\(676\) −1.07182e13 −1.97407
\(677\) −4.36975e12 −0.799480 −0.399740 0.916629i \(-0.630900\pi\)
−0.399740 + 0.916629i \(0.630900\pi\)
\(678\) 2.40524e12 0.437144
\(679\) −3.68753e12 −0.665766
\(680\) 9.42716e12 1.69079
\(681\) −9.11318e11 −0.162371
\(682\) −2.34757e11 −0.0415517
\(683\) −1.39296e12 −0.244931 −0.122466 0.992473i \(-0.539080\pi\)
−0.122466 + 0.992473i \(0.539080\pi\)
\(684\) −3.41503e12 −0.596544
\(685\) 1.14622e13 1.98911
\(686\) 1.59543e12 0.275055
\(687\) −5.35031e11 −0.0916376
\(688\) 2.91578e11 0.0496142
\(689\) −4.90459e11 −0.0829117
\(690\) −8.80602e12 −1.47897
\(691\) −5.40642e12 −0.902108 −0.451054 0.892497i \(-0.648952\pi\)
−0.451054 + 0.892497i \(0.648952\pi\)
\(692\) 1.12816e13 1.87022
\(693\) 6.63180e11 0.109228
\(694\) 9.72553e12 1.59146
\(695\) −1.33852e13 −2.17617
\(696\) −5.76153e12 −0.930671
\(697\) −2.69407e12 −0.432375
\(698\) −1.69445e13 −2.70196
\(699\) 1.38501e12 0.219435
\(700\) 1.28707e13 2.02611
\(701\) −4.54692e12 −0.711191 −0.355596 0.934640i \(-0.615722\pi\)
−0.355596 + 0.934640i \(0.615722\pi\)
\(702\) −1.68575e11 −0.0261985
\(703\) −2.74929e12 −0.424543
\(704\) −1.61827e12 −0.248298
\(705\) 3.06755e12 0.467672
\(706\) 2.12536e13 3.21967
\(707\) 1.53932e13 2.31708
\(708\) −9.98225e11 −0.149307
\(709\) 9.83888e12 1.46230 0.731152 0.682215i \(-0.238983\pi\)
0.731152 + 0.682215i \(0.238983\pi\)
\(710\) −1.10728e13 −1.63529
\(711\) −2.61206e12 −0.383328
\(712\) −5.82113e12 −0.848881
\(713\) 7.80357e11 0.113081
\(714\) 7.14504e12 1.02887
\(715\) 1.73513e11 0.0248288
\(716\) 3.61555e12 0.514121
\(717\) 2.70749e12 0.382588
\(718\) 2.13206e12 0.299391
\(719\) −1.30734e13 −1.82435 −0.912176 0.409799i \(-0.865599\pi\)
−0.912176 + 0.409799i \(0.865599\pi\)
\(720\) 3.04455e12 0.422208
\(721\) −7.34002e11 −0.101155
\(722\) 2.37596e12 0.325403
\(723\) −9.70299e11 −0.132064
\(724\) −1.29524e13 −1.75197
\(725\) 5.22763e12 0.702722
\(726\) 7.04276e12 0.940867
\(727\) −6.00761e12 −0.797622 −0.398811 0.917033i \(-0.630577\pi\)
−0.398811 + 0.917033i \(0.630577\pi\)
\(728\) −1.39684e12 −0.184313
\(729\) 2.82430e11 0.0370370
\(730\) 2.52102e13 3.28566
\(731\) −2.99953e11 −0.0388530
\(732\) 1.43769e13 1.85082
\(733\) 7.73276e12 0.989388 0.494694 0.869067i \(-0.335280\pi\)
0.494694 + 0.869067i \(0.335280\pi\)
\(734\) −9.29294e11 −0.118174
\(735\) 5.33172e12 0.673867
\(736\) 4.17423e11 0.0524356
\(737\) 9.22558e11 0.115183
\(738\) −2.67154e12 −0.331519
\(739\) −2.21157e12 −0.272773 −0.136386 0.990656i \(-0.543549\pi\)
−0.136386 + 0.990656i \(0.543549\pi\)
\(740\) 1.00808e13 1.23581
\(741\) −3.36283e11 −0.0409753
\(742\) 2.06142e13 2.49660
\(743\) 1.19309e12 0.143623 0.0718113 0.997418i \(-0.477122\pi\)
0.0718113 + 0.997418i \(0.477122\pi\)
\(744\) −8.28417e11 −0.0991221
\(745\) 6.89363e12 0.819870
\(746\) 9.65068e12 1.14086
\(747\) −2.68599e10 −0.00315617
\(748\) −3.05025e12 −0.356269
\(749\) 1.75249e13 2.03464
\(750\) 2.93227e12 0.338398
\(751\) 1.66285e13 1.90754 0.953771 0.300536i \(-0.0971655\pi\)
0.953771 + 0.300536i \(0.0971655\pi\)
\(752\) 5.16186e12 0.588607
\(753\) 1.44223e12 0.163477
\(754\) −1.14252e12 −0.128733
\(755\) 6.75652e12 0.756767
\(756\) 4.71278e12 0.524722
\(757\) −1.66782e13 −1.84594 −0.922971 0.384870i \(-0.874246\pi\)
−0.922971 + 0.384870i \(0.874246\pi\)
\(758\) −2.11113e13 −2.32275
\(759\) 1.41488e12 0.154750
\(760\) 1.86486e13 2.02761
\(761\) −1.15553e13 −1.24897 −0.624483 0.781039i \(-0.714690\pi\)
−0.624483 + 0.781039i \(0.714690\pi\)
\(762\) −8.93080e12 −0.959606
\(763\) 2.18651e13 2.33556
\(764\) −1.23177e13 −1.30801
\(765\) −3.13200e12 −0.330632
\(766\) 2.59646e13 2.72491
\(767\) −9.82966e10 −0.0102556
\(768\) −1.10507e13 −1.14621
\(769\) 1.38467e13 1.42784 0.713918 0.700229i \(-0.246919\pi\)
0.713918 + 0.700229i \(0.246919\pi\)
\(770\) −7.29285e12 −0.747634
\(771\) 2.92067e12 0.297672
\(772\) 1.34636e13 1.36422
\(773\) −1.65102e13 −1.66321 −0.831603 0.555371i \(-0.812576\pi\)
−0.831603 + 0.555371i \(0.812576\pi\)
\(774\) −2.97445e11 −0.0297902
\(775\) 7.51650e11 0.0748442
\(776\) 8.35177e12 0.826801
\(777\) 3.79405e12 0.373429
\(778\) 3.48919e12 0.341442
\(779\) −5.32933e12 −0.518507
\(780\) 1.23304e12 0.119276
\(781\) 1.77909e12 0.171107
\(782\) 1.52438e13 1.45768
\(783\) 1.91416e12 0.181991
\(784\) 8.97183e12 0.848123
\(785\) −1.54349e13 −1.45075
\(786\) −9.58219e12 −0.895495
\(787\) −1.32806e13 −1.23405 −0.617023 0.786945i \(-0.711662\pi\)
−0.617023 + 0.786945i \(0.711662\pi\)
\(788\) −3.80755e12 −0.351786
\(789\) −3.00519e11 −0.0276074
\(790\) 2.87243e13 2.62378
\(791\) −6.62142e12 −0.601391
\(792\) −1.50202e12 −0.135647
\(793\) 1.41571e12 0.127129
\(794\) 3.26331e13 2.91384
\(795\) −9.03616e12 −0.802291
\(796\) 1.47971e13 1.30638
\(797\) 1.31311e13 1.15276 0.576380 0.817182i \(-0.304465\pi\)
0.576380 + 0.817182i \(0.304465\pi\)
\(798\) 1.41341e13 1.23383
\(799\) −5.31012e12 −0.460939
\(800\) 4.02067e11 0.0347051
\(801\) 1.93396e12 0.165997
\(802\) −2.43025e13 −2.07428
\(803\) −4.05056e12 −0.343792
\(804\) 6.55601e12 0.553334
\(805\) 2.42422e13 2.03466
\(806\) −1.64276e11 −0.0137109
\(807\) −3.46094e11 −0.0287252
\(808\) −3.48636e13 −2.87753
\(809\) 9.61532e12 0.789215 0.394608 0.918850i \(-0.370881\pi\)
0.394608 + 0.918850i \(0.370881\pi\)
\(810\) −3.10582e12 −0.253509
\(811\) −2.41421e13 −1.95966 −0.979830 0.199831i \(-0.935961\pi\)
−0.979830 + 0.199831i \(0.935961\pi\)
\(812\) 3.19408e13 2.57836
\(813\) 6.04248e12 0.485073
\(814\) −2.43509e12 −0.194404
\(815\) −1.58611e13 −1.25929
\(816\) −5.27030e12 −0.416131
\(817\) −5.93359e11 −0.0465927
\(818\) −2.05807e12 −0.160720
\(819\) 4.64074e11 0.0360420
\(820\) 1.95410e13 1.50933
\(821\) 1.73842e13 1.33540 0.667698 0.744432i \(-0.267280\pi\)
0.667698 + 0.744432i \(0.267280\pi\)
\(822\) −1.96758e13 −1.50318
\(823\) −9.25703e12 −0.703352 −0.351676 0.936122i \(-0.614388\pi\)
−0.351676 + 0.936122i \(0.614388\pi\)
\(824\) 1.66242e12 0.125623
\(825\) 1.36283e12 0.102423
\(826\) 4.13146e12 0.308811
\(827\) −1.05186e12 −0.0781954 −0.0390977 0.999235i \(-0.512448\pi\)
−0.0390977 + 0.999235i \(0.512448\pi\)
\(828\) 1.00546e13 0.743409
\(829\) −2.12061e13 −1.55943 −0.779715 0.626135i \(-0.784636\pi\)
−0.779715 + 0.626135i \(0.784636\pi\)
\(830\) 2.95372e11 0.0216032
\(831\) 1.12108e13 0.815516
\(832\) −1.13242e12 −0.0819315
\(833\) −9.22953e12 −0.664167
\(834\) 2.29769e13 1.64454
\(835\) −3.26448e13 −2.32394
\(836\) −6.03392e12 −0.427240
\(837\) 2.75226e11 0.0193832
\(838\) −1.05667e13 −0.740190
\(839\) −1.87032e13 −1.30312 −0.651562 0.758595i \(-0.725886\pi\)
−0.651562 + 0.758595i \(0.725886\pi\)
\(840\) −2.57352e13 −1.78349
\(841\) −1.53394e12 −0.105737
\(842\) −8.82541e12 −0.605104
\(843\) −5.10105e12 −0.347885
\(844\) −3.44548e13 −2.33727
\(845\) −1.94453e13 −1.31207
\(846\) −5.26573e12 −0.353421
\(847\) −1.93881e13 −1.29438
\(848\) −1.52054e13 −1.00976
\(849\) 1.15043e13 0.759932
\(850\) 1.46830e13 0.964781
\(851\) 8.09450e12 0.529063
\(852\) 1.26428e13 0.821985
\(853\) 2.78903e13 1.80378 0.901889 0.431968i \(-0.142181\pi\)
0.901889 + 0.431968i \(0.142181\pi\)
\(854\) −5.95031e13 −3.82807
\(855\) −6.19564e12 −0.396496
\(856\) −3.96916e13 −2.52678
\(857\) 2.51339e13 1.59164 0.795821 0.605532i \(-0.207040\pi\)
0.795821 + 0.605532i \(0.207040\pi\)
\(858\) −2.97851e11 −0.0187632
\(859\) 3.78665e12 0.237293 0.118647 0.992937i \(-0.462144\pi\)
0.118647 + 0.992937i \(0.462144\pi\)
\(860\) 2.17566e12 0.135628
\(861\) 7.35454e12 0.456080
\(862\) 5.52294e13 3.40712
\(863\) 2.66996e13 1.63854 0.819268 0.573410i \(-0.194380\pi\)
0.819268 + 0.573410i \(0.194380\pi\)
\(864\) 1.47222e11 0.00898795
\(865\) 2.04674e13 1.24305
\(866\) −3.52024e13 −2.12687
\(867\) −4.18394e12 −0.251478
\(868\) 4.59258e12 0.274611
\(869\) −4.61518e12 −0.274536
\(870\) −2.10496e13 −1.24568
\(871\) 6.45579e11 0.0380073
\(872\) −4.95215e13 −2.90048
\(873\) −2.77472e12 −0.161680
\(874\) 3.01548e13 1.74806
\(875\) −8.07229e12 −0.465543
\(876\) −2.87847e13 −1.65155
\(877\) −1.78051e13 −1.01636 −0.508179 0.861252i \(-0.669681\pi\)
−0.508179 + 0.861252i \(0.669681\pi\)
\(878\) −7.50126e12 −0.425999
\(879\) 6.51770e12 0.368251
\(880\) 5.37933e12 0.302382
\(881\) −8.30442e12 −0.464427 −0.232214 0.972665i \(-0.574597\pi\)
−0.232214 + 0.972665i \(0.574597\pi\)
\(882\) −9.15238e12 −0.509243
\(883\) −1.50196e13 −0.831451 −0.415725 0.909490i \(-0.636472\pi\)
−0.415725 + 0.909490i \(0.636472\pi\)
\(884\) −2.13447e12 −0.117559
\(885\) −1.81101e12 −0.0992374
\(886\) −4.94885e13 −2.69807
\(887\) 1.96507e13 1.06591 0.532957 0.846142i \(-0.321081\pi\)
0.532957 + 0.846142i \(0.321081\pi\)
\(888\) −8.59301e12 −0.463753
\(889\) 2.45857e13 1.32016
\(890\) −2.12673e13 −1.13621
\(891\) 4.99017e11 0.0265256
\(892\) −4.10388e13 −2.17046
\(893\) −1.05044e13 −0.552761
\(894\) −1.18335e13 −0.619578
\(895\) 6.55942e12 0.341713
\(896\) 4.63593e13 2.40298
\(897\) 9.90089e11 0.0510632
\(898\) −1.42176e13 −0.729594
\(899\) 1.86534e12 0.0952444
\(900\) 9.68471e12 0.492034
\(901\) 1.56422e13 0.790742
\(902\) −4.72028e12 −0.237431
\(903\) 8.18842e11 0.0409831
\(904\) 1.49966e13 0.746855
\(905\) −2.34986e13 −1.16446
\(906\) −1.15982e13 −0.571891
\(907\) 2.74590e13 1.34726 0.673632 0.739067i \(-0.264733\pi\)
0.673632 + 0.739067i \(0.264733\pi\)
\(908\) −1.14425e13 −0.558643
\(909\) 1.15828e13 0.562697
\(910\) −5.10331e12 −0.246698
\(911\) −1.74124e13 −0.837580 −0.418790 0.908083i \(-0.637546\pi\)
−0.418790 + 0.908083i \(0.637546\pi\)
\(912\) −1.04256e13 −0.499026
\(913\) −4.74579e10 −0.00226043
\(914\) 1.76627e13 0.837140
\(915\) 2.60829e13 1.23016
\(916\) −6.71784e12 −0.315282
\(917\) 2.63790e13 1.23196
\(918\) 5.37636e12 0.249860
\(919\) −2.97047e13 −1.37374 −0.686870 0.726780i \(-0.741016\pi\)
−0.686870 + 0.726780i \(0.741016\pi\)
\(920\) −5.49054e13 −2.52680
\(921\) 7.34933e12 0.336573
\(922\) 2.41855e13 1.10222
\(923\) 1.24495e12 0.0564605
\(924\) 8.32688e12 0.375801
\(925\) 7.79673e12 0.350166
\(926\) −1.57800e12 −0.0705275
\(927\) −5.52307e11 −0.0245653
\(928\) 9.97794e11 0.0441647
\(929\) −1.80937e13 −0.796997 −0.398499 0.917169i \(-0.630469\pi\)
−0.398499 + 0.917169i \(0.630469\pi\)
\(930\) −3.02660e12 −0.132673
\(931\) −1.82576e13 −0.796473
\(932\) 1.73902e13 0.754974
\(933\) −9.17451e12 −0.396383
\(934\) −3.75097e13 −1.61281
\(935\) −5.53384e12 −0.236796
\(936\) −1.05107e12 −0.0447598
\(937\) 4.36774e13 1.85109 0.925546 0.378634i \(-0.123606\pi\)
0.925546 + 0.378634i \(0.123606\pi\)
\(938\) −2.71340e13 −1.14446
\(939\) 3.04212e12 0.127697
\(940\) 3.85161e13 1.60904
\(941\) 9.49535e12 0.394782 0.197391 0.980325i \(-0.436753\pi\)
0.197391 + 0.980325i \(0.436753\pi\)
\(942\) 2.64955e13 1.09633
\(943\) 1.56907e13 0.646160
\(944\) −3.04743e12 −0.124899
\(945\) 8.55005e12 0.348759
\(946\) −5.25548e11 −0.0213355
\(947\) −2.73029e13 −1.10315 −0.551574 0.834126i \(-0.685973\pi\)
−0.551574 + 0.834126i \(0.685973\pi\)
\(948\) −3.27970e13 −1.31885
\(949\) −2.83446e12 −0.113442
\(950\) 2.90455e13 1.15697
\(951\) 7.44470e12 0.295145
\(952\) 4.45492e13 1.75782
\(953\) −4.22883e13 −1.66074 −0.830372 0.557210i \(-0.811872\pi\)
−0.830372 + 0.557210i \(0.811872\pi\)
\(954\) 1.55114e13 0.606294
\(955\) −2.23471e13 −0.869373
\(956\) 3.39952e13 1.31631
\(957\) 3.38208e12 0.130341
\(958\) −3.25148e13 −1.24720
\(959\) 5.41659e13 2.06796
\(960\) −2.08635e13 −0.792806
\(961\) −2.61714e13 −0.989856
\(962\) −1.70400e12 −0.0641479
\(963\) 1.31868e13 0.494107
\(964\) −1.21830e13 −0.454370
\(965\) 2.44260e13 0.906734
\(966\) −4.16140e13 −1.53760
\(967\) 2.99642e13 1.10201 0.551003 0.834504i \(-0.314245\pi\)
0.551003 + 0.834504i \(0.314245\pi\)
\(968\) 4.39116e13 1.60746
\(969\) 1.07250e13 0.390788
\(970\) 3.05130e13 1.10665
\(971\) −2.93830e13 −1.06074 −0.530371 0.847766i \(-0.677947\pi\)
−0.530371 + 0.847766i \(0.677947\pi\)
\(972\) 3.54618e12 0.127427
\(973\) −6.32533e13 −2.26243
\(974\) −6.27467e13 −2.23396
\(975\) 9.53666e11 0.0337968
\(976\) 4.38905e13 1.54827
\(977\) −6.55846e12 −0.230291 −0.115145 0.993349i \(-0.536733\pi\)
−0.115145 + 0.993349i \(0.536733\pi\)
\(978\) 2.72270e13 0.951645
\(979\) 3.41706e12 0.118886
\(980\) 6.69450e13 2.31847
\(981\) 1.64526e13 0.567184
\(982\) 3.76649e13 1.29251
\(983\) −2.36158e13 −0.806698 −0.403349 0.915046i \(-0.632154\pi\)
−0.403349 + 0.915046i \(0.632154\pi\)
\(984\) −1.66571e13 −0.566396
\(985\) −6.90776e12 −0.233816
\(986\) 3.64382e13 1.22775
\(987\) 1.44961e13 0.486211
\(988\) −4.22236e12 −0.140977
\(989\) 1.74698e12 0.0580636
\(990\) −5.48758e12 −0.181561
\(991\) −2.63307e13 −0.867223 −0.433611 0.901100i \(-0.642761\pi\)
−0.433611 + 0.901100i \(0.642761\pi\)
\(992\) 1.43467e11 0.00470380
\(993\) 1.11754e13 0.364748
\(994\) −5.23259e13 −1.70011
\(995\) 2.68454e13 0.868291
\(996\) −3.37252e11 −0.0108589
\(997\) 4.34187e13 1.39171 0.695855 0.718182i \(-0.255025\pi\)
0.695855 + 0.718182i \(0.255025\pi\)
\(998\) 8.67729e13 2.76883
\(999\) 2.85487e12 0.0906863
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 177.10.a.d.1.2 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.2 22 1.1 even 1 trivial