Properties

Label 177.10.a.d.1.1
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 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-39.7571 q^{2} +81.0000 q^{3} +1068.63 q^{4} -1871.54 q^{5} -3220.33 q^{6} -43.1074 q^{7} -22129.9 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-39.7571 q^{2} +81.0000 q^{3} +1068.63 q^{4} -1871.54 q^{5} -3220.33 q^{6} -43.1074 q^{7} -22129.9 q^{8} +6561.00 q^{9} +74407.2 q^{10} +76107.0 q^{11} +86558.9 q^{12} -43732.0 q^{13} +1713.83 q^{14} -151595. q^{15} +332685. q^{16} +420385. q^{17} -260846. q^{18} -333780. q^{19} -1.99999e6 q^{20} -3491.70 q^{21} -3.02579e6 q^{22} -114536. q^{23} -1.79253e6 q^{24} +1.54955e6 q^{25} +1.73866e6 q^{26} +531441. q^{27} -46065.8 q^{28} +2.58705e6 q^{29} +6.02699e6 q^{30} -1.72886e6 q^{31} -1.89606e6 q^{32} +6.16467e6 q^{33} -1.67133e7 q^{34} +80677.4 q^{35} +7.01127e6 q^{36} +4.90694e6 q^{37} +1.32701e7 q^{38} -3.54229e6 q^{39} +4.14172e7 q^{40} +7.23989e6 q^{41} +138820. q^{42} -8.98509e6 q^{43} +8.13301e7 q^{44} -1.22792e7 q^{45} +4.55360e6 q^{46} +5.61464e7 q^{47} +2.69475e7 q^{48} -4.03517e7 q^{49} -6.16058e7 q^{50} +3.40512e7 q^{51} -4.67333e7 q^{52} -9.20424e7 q^{53} -2.11286e7 q^{54} -1.42438e8 q^{55} +953964. q^{56} -2.70362e7 q^{57} -1.02854e8 q^{58} -1.21174e7 q^{59} -1.61999e8 q^{60} -8.95394e7 q^{61} +6.87344e7 q^{62} -282828. q^{63} -9.49527e7 q^{64} +8.18464e7 q^{65} -2.45089e8 q^{66} -1.59831e8 q^{67} +4.49235e8 q^{68} -9.27738e6 q^{69} -3.20750e6 q^{70} +1.68944e8 q^{71} -1.45195e8 q^{72} -1.57076e8 q^{73} -1.95086e8 q^{74} +1.25514e8 q^{75} -3.56687e8 q^{76} -3.28077e6 q^{77} +1.40831e8 q^{78} +5.77979e8 q^{79} -6.22635e8 q^{80} +4.30467e7 q^{81} -2.87837e8 q^{82} -4.29141e8 q^{83} -3.73133e6 q^{84} -7.86769e8 q^{85} +3.57221e8 q^{86} +2.09551e8 q^{87} -1.68424e9 q^{88} -6.09435e8 q^{89} +4.88186e8 q^{90} +1.88517e6 q^{91} -1.22396e8 q^{92} -1.40037e8 q^{93} -2.23222e9 q^{94} +6.24684e8 q^{95} -1.53581e8 q^{96} +1.42423e9 q^{97} +1.60427e9 q^{98} +4.99338e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −39.7571 −1.75703 −0.878516 0.477712i \(-0.841466\pi\)
−0.878516 + 0.477712i \(0.841466\pi\)
\(3\) 81.0000 0.577350
\(4\) 1068.63 2.08716
\(5\) −1871.54 −1.33917 −0.669584 0.742736i \(-0.733528\pi\)
−0.669584 + 0.742736i \(0.733528\pi\)
\(6\) −3220.33 −1.01442
\(7\) −43.1074 −0.00678595 −0.00339298 0.999994i \(-0.501080\pi\)
−0.00339298 + 0.999994i \(0.501080\pi\)
\(8\) −22129.9 −1.91018
\(9\) 6561.00 0.333333
\(10\) 74407.2 2.35296
\(11\) 76107.0 1.56732 0.783659 0.621191i \(-0.213351\pi\)
0.783659 + 0.621191i \(0.213351\pi\)
\(12\) 86558.9 1.20503
\(13\) −43732.0 −0.424673 −0.212336 0.977197i \(-0.568107\pi\)
−0.212336 + 0.977197i \(0.568107\pi\)
\(14\) 1713.83 0.0119231
\(15\) −151595. −0.773169
\(16\) 332685. 1.26909
\(17\) 420385. 1.22075 0.610375 0.792113i \(-0.291019\pi\)
0.610375 + 0.792113i \(0.291019\pi\)
\(18\) −260846. −0.585678
\(19\) −333780. −0.587583 −0.293791 0.955870i \(-0.594917\pi\)
−0.293791 + 0.955870i \(0.594917\pi\)
\(20\) −1.99999e6 −2.79507
\(21\) −3491.70 −0.00391787
\(22\) −3.02579e6 −2.75383
\(23\) −114536. −0.0853424 −0.0426712 0.999089i \(-0.513587\pi\)
−0.0426712 + 0.999089i \(0.513587\pi\)
\(24\) −1.79253e6 −1.10285
\(25\) 1.54955e6 0.793372
\(26\) 1.73866e6 0.746164
\(27\) 531441. 0.192450
\(28\) −46065.8 −0.0141634
\(29\) 2.58705e6 0.679226 0.339613 0.940565i \(-0.389704\pi\)
0.339613 + 0.940565i \(0.389704\pi\)
\(30\) 6.02699e6 1.35848
\(31\) −1.72886e6 −0.336226 −0.168113 0.985768i \(-0.553767\pi\)
−0.168113 + 0.985768i \(0.553767\pi\)
\(32\) −1.89606e6 −0.319652
\(33\) 6.16467e6 0.904892
\(34\) −1.67133e7 −2.14490
\(35\) 80677.4 0.00908753
\(36\) 7.01127e6 0.695722
\(37\) 4.90694e6 0.430430 0.215215 0.976567i \(-0.430955\pi\)
0.215215 + 0.976567i \(0.430955\pi\)
\(38\) 1.32701e7 1.03240
\(39\) −3.54229e6 −0.245185
\(40\) 4.14172e7 2.55806
\(41\) 7.23989e6 0.400133 0.200067 0.979782i \(-0.435884\pi\)
0.200067 + 0.979782i \(0.435884\pi\)
\(42\) 138820. 0.00688383
\(43\) −8.98509e6 −0.400788 −0.200394 0.979715i \(-0.564222\pi\)
−0.200394 + 0.979715i \(0.564222\pi\)
\(44\) 8.13301e7 3.27125
\(45\) −1.22792e7 −0.446389
\(46\) 4.55360e6 0.149949
\(47\) 5.61464e7 1.67835 0.839174 0.543864i \(-0.183039\pi\)
0.839174 + 0.543864i \(0.183039\pi\)
\(48\) 2.69475e7 0.732711
\(49\) −4.03517e7 −0.999954
\(50\) −6.16058e7 −1.39398
\(51\) 3.40512e7 0.704800
\(52\) −4.67333e7 −0.886362
\(53\) −9.20424e7 −1.60231 −0.801155 0.598457i \(-0.795781\pi\)
−0.801155 + 0.598457i \(0.795781\pi\)
\(54\) −2.11286e7 −0.338141
\(55\) −1.42438e8 −2.09890
\(56\) 953964. 0.0129624
\(57\) −2.70362e7 −0.339241
\(58\) −1.02854e8 −1.19342
\(59\) −1.21174e7 −0.130189
\(60\) −1.61999e8 −1.61373
\(61\) −8.95394e7 −0.827999 −0.413999 0.910277i \(-0.635868\pi\)
−0.413999 + 0.910277i \(0.635868\pi\)
\(62\) 6.87344e7 0.590761
\(63\) −282828. −0.00226198
\(64\) −9.49527e7 −0.707453
\(65\) 8.18464e7 0.568708
\(66\) −2.45089e8 −1.58993
\(67\) −1.59831e8 −0.969004 −0.484502 0.874790i \(-0.660999\pi\)
−0.484502 + 0.874790i \(0.660999\pi\)
\(68\) 4.49235e8 2.54791
\(69\) −9.27738e6 −0.0492725
\(70\) −3.20750e6 −0.0159671
\(71\) 1.68944e8 0.789007 0.394504 0.918894i \(-0.370917\pi\)
0.394504 + 0.918894i \(0.370917\pi\)
\(72\) −1.45195e8 −0.636728
\(73\) −1.57076e8 −0.647378 −0.323689 0.946163i \(-0.604923\pi\)
−0.323689 + 0.946163i \(0.604923\pi\)
\(74\) −1.95086e8 −0.756281
\(75\) 1.25514e8 0.458054
\(76\) −3.56687e8 −1.22638
\(77\) −3.28077e6 −0.0106357
\(78\) 1.40831e8 0.430798
\(79\) 5.77979e8 1.66951 0.834757 0.550619i \(-0.185608\pi\)
0.834757 + 0.550619i \(0.185608\pi\)
\(80\) −6.22635e8 −1.69953
\(81\) 4.30467e7 0.111111
\(82\) −2.87837e8 −0.703047
\(83\) −4.29141e8 −0.992541 −0.496270 0.868168i \(-0.665297\pi\)
−0.496270 + 0.868168i \(0.665297\pi\)
\(84\) −3.73133e6 −0.00817724
\(85\) −7.86769e8 −1.63479
\(86\) 3.57221e8 0.704197
\(87\) 2.09551e8 0.392151
\(88\) −1.68424e9 −2.99387
\(89\) −6.09435e8 −1.02961 −0.514805 0.857308i \(-0.672135\pi\)
−0.514805 + 0.857308i \(0.672135\pi\)
\(90\) 4.88186e8 0.784321
\(91\) 1.88517e6 0.00288181
\(92\) −1.22396e8 −0.178124
\(93\) −1.40037e8 −0.194120
\(94\) −2.23222e9 −2.94891
\(95\) 6.24684e8 0.786872
\(96\) −1.53581e8 −0.184551
\(97\) 1.42423e9 1.63345 0.816727 0.577025i \(-0.195786\pi\)
0.816727 + 0.577025i \(0.195786\pi\)
\(98\) 1.60427e9 1.75695
\(99\) 4.99338e8 0.522440
\(100\) 1.65590e9 1.65590
\(101\) −2.28375e8 −0.218374 −0.109187 0.994021i \(-0.534825\pi\)
−0.109187 + 0.994021i \(0.534825\pi\)
\(102\) −1.35378e9 −1.23836
\(103\) 1.56336e9 1.36864 0.684321 0.729180i \(-0.260099\pi\)
0.684321 + 0.729180i \(0.260099\pi\)
\(104\) 9.67787e8 0.811203
\(105\) 6.53487e6 0.00524669
\(106\) 3.65934e9 2.81531
\(107\) −1.24104e9 −0.915288 −0.457644 0.889136i \(-0.651307\pi\)
−0.457644 + 0.889136i \(0.651307\pi\)
\(108\) 5.67913e8 0.401675
\(109\) −2.59764e9 −1.76263 −0.881314 0.472532i \(-0.843340\pi\)
−0.881314 + 0.472532i \(0.843340\pi\)
\(110\) 5.66291e9 3.68784
\(111\) 3.97462e8 0.248509
\(112\) −1.43412e7 −0.00861200
\(113\) 6.59340e7 0.0380414 0.0190207 0.999819i \(-0.493945\pi\)
0.0190207 + 0.999819i \(0.493945\pi\)
\(114\) 1.07488e9 0.596058
\(115\) 2.14358e8 0.114288
\(116\) 2.76460e9 1.41766
\(117\) −2.86926e8 −0.141558
\(118\) 4.81751e8 0.228746
\(119\) −1.81217e7 −0.00828395
\(120\) 3.35479e9 1.47690
\(121\) 3.43432e9 1.45649
\(122\) 3.55983e9 1.45482
\(123\) 5.86431e8 0.231017
\(124\) −1.84751e9 −0.701760
\(125\) 7.55300e8 0.276710
\(126\) 1.12444e7 0.00397438
\(127\) 9.03648e8 0.308235 0.154118 0.988052i \(-0.450747\pi\)
0.154118 + 0.988052i \(0.450747\pi\)
\(128\) 4.74583e9 1.56267
\(129\) −7.27792e8 −0.231395
\(130\) −3.25398e9 −0.999239
\(131\) −1.48993e9 −0.442024 −0.221012 0.975271i \(-0.570936\pi\)
−0.221012 + 0.975271i \(0.570936\pi\)
\(132\) 6.58774e9 1.88866
\(133\) 1.43884e7 0.00398731
\(134\) 6.35444e9 1.70257
\(135\) −9.94616e8 −0.257723
\(136\) −9.30309e9 −2.33186
\(137\) 3.80197e9 0.922074 0.461037 0.887381i \(-0.347478\pi\)
0.461037 + 0.887381i \(0.347478\pi\)
\(138\) 3.68842e8 0.0865734
\(139\) −3.94690e8 −0.0896788 −0.0448394 0.998994i \(-0.514278\pi\)
−0.0448394 + 0.998994i \(0.514278\pi\)
\(140\) 8.62142e7 0.0189672
\(141\) 4.54786e9 0.968994
\(142\) −6.71674e9 −1.38631
\(143\) −3.32831e9 −0.665598
\(144\) 2.18275e9 0.423031
\(145\) −4.84178e9 −0.909598
\(146\) 6.24491e9 1.13746
\(147\) −3.26849e9 −0.577324
\(148\) 5.24370e9 0.898379
\(149\) 2.09979e9 0.349009 0.174505 0.984656i \(-0.444168\pi\)
0.174505 + 0.984656i \(0.444168\pi\)
\(150\) −4.99007e9 −0.804815
\(151\) 5.15317e9 0.806638 0.403319 0.915060i \(-0.367857\pi\)
0.403319 + 0.915060i \(0.367857\pi\)
\(152\) 7.38653e9 1.12239
\(153\) 2.75814e9 0.406917
\(154\) 1.30434e8 0.0186874
\(155\) 3.23563e9 0.450264
\(156\) −3.78540e9 −0.511741
\(157\) 6.27151e9 0.823804 0.411902 0.911228i \(-0.364865\pi\)
0.411902 + 0.911228i \(0.364865\pi\)
\(158\) −2.29788e10 −2.93339
\(159\) −7.45544e9 −0.925094
\(160\) 3.54856e9 0.428068
\(161\) 4.93733e6 0.000579129 0
\(162\) −1.71141e9 −0.195226
\(163\) 2.97767e9 0.330394 0.165197 0.986261i \(-0.447174\pi\)
0.165197 + 0.986261i \(0.447174\pi\)
\(164\) 7.73675e9 0.835144
\(165\) −1.15374e10 −1.21180
\(166\) 1.70614e10 1.74393
\(167\) −1.67149e9 −0.166295 −0.0831474 0.996537i \(-0.526497\pi\)
−0.0831474 + 0.996537i \(0.526497\pi\)
\(168\) 7.72711e7 0.00748385
\(169\) −8.69201e9 −0.819653
\(170\) 3.12797e10 2.87238
\(171\) −2.18993e9 −0.195861
\(172\) −9.60172e9 −0.836510
\(173\) 1.34059e10 1.13786 0.568929 0.822387i \(-0.307358\pi\)
0.568929 + 0.822387i \(0.307358\pi\)
\(174\) −8.33115e9 −0.689023
\(175\) −6.67973e7 −0.00538378
\(176\) 2.53196e10 1.98907
\(177\) −9.81506e8 −0.0751646
\(178\) 2.42294e10 1.80906
\(179\) −1.19814e10 −0.872307 −0.436154 0.899872i \(-0.643660\pi\)
−0.436154 + 0.899872i \(0.643660\pi\)
\(180\) −1.31219e10 −0.931688
\(181\) 1.22163e10 0.846027 0.423014 0.906123i \(-0.360972\pi\)
0.423014 + 0.906123i \(0.360972\pi\)
\(182\) −7.49491e7 −0.00506343
\(183\) −7.25269e9 −0.478045
\(184\) 2.53466e9 0.163020
\(185\) −9.18356e9 −0.576419
\(186\) 5.56749e9 0.341076
\(187\) 3.19942e10 1.91330
\(188\) 5.99997e10 3.50299
\(189\) −2.29090e7 −0.00130596
\(190\) −2.48356e10 −1.38256
\(191\) 1.63472e10 0.888779 0.444390 0.895834i \(-0.353421\pi\)
0.444390 + 0.895834i \(0.353421\pi\)
\(192\) −7.69117e9 −0.408448
\(193\) 3.04342e10 1.57890 0.789448 0.613817i \(-0.210367\pi\)
0.789448 + 0.613817i \(0.210367\pi\)
\(194\) −5.66232e10 −2.87003
\(195\) 6.62956e9 0.328344
\(196\) −4.31210e10 −2.08707
\(197\) 1.94201e10 0.918656 0.459328 0.888267i \(-0.348090\pi\)
0.459328 + 0.888267i \(0.348090\pi\)
\(198\) −1.98522e10 −0.917944
\(199\) 1.94633e10 0.879786 0.439893 0.898050i \(-0.355016\pi\)
0.439893 + 0.898050i \(0.355016\pi\)
\(200\) −3.42916e10 −1.51549
\(201\) −1.29463e10 −0.559455
\(202\) 9.07952e9 0.383691
\(203\) −1.11521e8 −0.00460919
\(204\) 3.63880e10 1.47103
\(205\) −1.35498e10 −0.535846
\(206\) −6.21545e10 −2.40475
\(207\) −7.51468e8 −0.0284475
\(208\) −1.45490e10 −0.538949
\(209\) −2.54030e10 −0.920929
\(210\) −2.59808e8 −0.00921860
\(211\) −9.77363e9 −0.339457 −0.169728 0.985491i \(-0.554289\pi\)
−0.169728 + 0.985491i \(0.554289\pi\)
\(212\) −9.83591e10 −3.34429
\(213\) 1.36845e10 0.455534
\(214\) 4.93400e10 1.60819
\(215\) 1.68160e10 0.536722
\(216\) −1.17608e10 −0.367615
\(217\) 7.45266e7 0.00228161
\(218\) 1.03275e11 3.09699
\(219\) −1.27232e10 −0.373764
\(220\) −1.52213e11 −4.38076
\(221\) −1.83843e10 −0.518419
\(222\) −1.58020e10 −0.436639
\(223\) −1.07041e10 −0.289853 −0.144926 0.989442i \(-0.546295\pi\)
−0.144926 + 0.989442i \(0.546295\pi\)
\(224\) 8.17343e7 0.00216914
\(225\) 1.01666e10 0.264457
\(226\) −2.62134e9 −0.0668399
\(227\) −7.59741e9 −0.189911 −0.0949553 0.995482i \(-0.530271\pi\)
−0.0949553 + 0.995482i \(0.530271\pi\)
\(228\) −2.88916e10 −0.708052
\(229\) 3.95453e10 0.950244 0.475122 0.879920i \(-0.342404\pi\)
0.475122 + 0.879920i \(0.342404\pi\)
\(230\) −8.52227e9 −0.200808
\(231\) −2.65743e8 −0.00614055
\(232\) −5.72513e10 −1.29745
\(233\) 8.75737e10 1.94658 0.973290 0.229581i \(-0.0737355\pi\)
0.973290 + 0.229581i \(0.0737355\pi\)
\(234\) 1.14073e10 0.248721
\(235\) −1.05081e11 −2.24759
\(236\) −1.29490e10 −0.271726
\(237\) 4.68163e10 0.963894
\(238\) 7.20466e8 0.0145552
\(239\) 3.19699e10 0.633797 0.316899 0.948459i \(-0.397358\pi\)
0.316899 + 0.948459i \(0.397358\pi\)
\(240\) −5.04334e10 −0.981223
\(241\) 3.52544e10 0.673188 0.336594 0.941650i \(-0.390725\pi\)
0.336594 + 0.941650i \(0.390725\pi\)
\(242\) −1.36539e11 −2.55910
\(243\) 3.48678e9 0.0641500
\(244\) −9.56843e10 −1.72817
\(245\) 7.55201e10 1.33911
\(246\) −2.33148e10 −0.405905
\(247\) 1.45969e10 0.249530
\(248\) 3.82595e10 0.642254
\(249\) −3.47604e10 −0.573044
\(250\) −3.00285e10 −0.486188
\(251\) 1.19741e10 0.190419 0.0952093 0.995457i \(-0.469648\pi\)
0.0952093 + 0.995457i \(0.469648\pi\)
\(252\) −3.02238e8 −0.00472113
\(253\) −8.71695e9 −0.133759
\(254\) −3.59264e10 −0.541580
\(255\) −6.37283e10 −0.943846
\(256\) −1.40065e11 −2.03821
\(257\) 6.96218e10 0.995511 0.497755 0.867318i \(-0.334158\pi\)
0.497755 + 0.867318i \(0.334158\pi\)
\(258\) 2.89349e10 0.406568
\(259\) −2.11525e8 −0.00292088
\(260\) 8.74634e10 1.18699
\(261\) 1.69736e10 0.226409
\(262\) 5.92354e10 0.776650
\(263\) 8.95325e10 1.15393 0.576965 0.816769i \(-0.304237\pi\)
0.576965 + 0.816769i \(0.304237\pi\)
\(264\) −1.36424e11 −1.72851
\(265\) 1.72261e11 2.14576
\(266\) −5.72041e8 −0.00700583
\(267\) −4.93642e10 −0.594445
\(268\) −1.70800e11 −2.02247
\(269\) 1.11073e11 1.29337 0.646685 0.762758i \(-0.276155\pi\)
0.646685 + 0.762758i \(0.276155\pi\)
\(270\) 3.95431e10 0.452828
\(271\) −2.70781e10 −0.304970 −0.152485 0.988306i \(-0.548728\pi\)
−0.152485 + 0.988306i \(0.548728\pi\)
\(272\) 1.39856e11 1.54924
\(273\) 1.52699e8 0.00166381
\(274\) −1.51155e11 −1.62011
\(275\) 1.17932e11 1.24347
\(276\) −9.91407e9 −0.102840
\(277\) −4.80043e10 −0.489916 −0.244958 0.969534i \(-0.578774\pi\)
−0.244958 + 0.969534i \(0.578774\pi\)
\(278\) 1.56917e10 0.157569
\(279\) −1.13430e10 −0.112075
\(280\) −1.78539e9 −0.0173589
\(281\) −1.13338e11 −1.08442 −0.542208 0.840244i \(-0.682412\pi\)
−0.542208 + 0.840244i \(0.682412\pi\)
\(282\) −1.80810e11 −1.70255
\(283\) −6.41100e10 −0.594138 −0.297069 0.954856i \(-0.596009\pi\)
−0.297069 + 0.954856i \(0.596009\pi\)
\(284\) 1.80539e11 1.64679
\(285\) 5.05994e10 0.454301
\(286\) 1.32324e11 1.16948
\(287\) −3.12093e8 −0.00271528
\(288\) −1.24401e10 −0.106551
\(289\) 5.81354e10 0.490231
\(290\) 1.92495e11 1.59819
\(291\) 1.15362e11 0.943075
\(292\) −1.67856e11 −1.35119
\(293\) 1.30027e11 1.03069 0.515345 0.856983i \(-0.327664\pi\)
0.515345 + 0.856983i \(0.327664\pi\)
\(294\) 1.29946e11 1.01438
\(295\) 2.26782e10 0.174345
\(296\) −1.08590e11 −0.822202
\(297\) 4.04464e10 0.301631
\(298\) −8.34814e10 −0.613221
\(299\) 5.00887e9 0.0362426
\(300\) 1.34128e11 0.956033
\(301\) 3.87324e8 0.00271972
\(302\) −2.04875e11 −1.41729
\(303\) −1.84983e10 −0.126079
\(304\) −1.11044e11 −0.745696
\(305\) 1.67577e11 1.10883
\(306\) −1.09656e11 −0.714966
\(307\) 9.33203e10 0.599589 0.299794 0.954004i \(-0.403082\pi\)
0.299794 + 0.954004i \(0.403082\pi\)
\(308\) −3.50593e9 −0.0221986
\(309\) 1.26632e11 0.790186
\(310\) −1.28639e11 −0.791128
\(311\) 1.57941e11 0.957352 0.478676 0.877992i \(-0.341117\pi\)
0.478676 + 0.877992i \(0.341117\pi\)
\(312\) 7.83907e10 0.468348
\(313\) −8.35400e10 −0.491977 −0.245989 0.969273i \(-0.579113\pi\)
−0.245989 + 0.969273i \(0.579113\pi\)
\(314\) −2.49337e11 −1.44745
\(315\) 5.29325e8 0.00302918
\(316\) 6.17645e11 3.48455
\(317\) −1.98225e11 −1.10253 −0.551265 0.834330i \(-0.685855\pi\)
−0.551265 + 0.834330i \(0.685855\pi\)
\(318\) 2.96407e11 1.62542
\(319\) 1.96893e11 1.06456
\(320\) 1.77708e11 0.947398
\(321\) −1.00524e11 −0.528442
\(322\) −1.96294e8 −0.00101755
\(323\) −1.40316e11 −0.717291
\(324\) 4.60009e10 0.231907
\(325\) −6.77652e10 −0.336924
\(326\) −1.18383e11 −0.580513
\(327\) −2.10409e11 −1.01765
\(328\) −1.60218e11 −0.764328
\(329\) −2.42033e9 −0.0113892
\(330\) 4.58696e11 2.12918
\(331\) −2.61910e10 −0.119930 −0.0599648 0.998200i \(-0.519099\pi\)
−0.0599648 + 0.998200i \(0.519099\pi\)
\(332\) −4.58592e11 −2.07160
\(333\) 3.21944e10 0.143477
\(334\) 6.64535e10 0.292185
\(335\) 2.99132e11 1.29766
\(336\) −1.16164e9 −0.00497214
\(337\) 1.09795e11 0.463714 0.231857 0.972750i \(-0.425520\pi\)
0.231857 + 0.972750i \(0.425520\pi\)
\(338\) 3.45569e11 1.44016
\(339\) 5.34065e9 0.0219632
\(340\) −8.40763e11 −3.41208
\(341\) −1.31578e11 −0.526974
\(342\) 8.70653e10 0.344134
\(343\) 3.47900e9 0.0135716
\(344\) 1.98839e11 0.765578
\(345\) 1.73630e10 0.0659841
\(346\) −5.32980e11 −1.99925
\(347\) 4.82368e10 0.178606 0.0893029 0.996005i \(-0.471536\pi\)
0.0893029 + 0.996005i \(0.471536\pi\)
\(348\) 2.23932e11 0.818484
\(349\) −3.17295e11 −1.14485 −0.572425 0.819957i \(-0.693997\pi\)
−0.572425 + 0.819957i \(0.693997\pi\)
\(350\) 2.65567e9 0.00945949
\(351\) −2.32410e10 −0.0817283
\(352\) −1.44304e11 −0.500997
\(353\) 2.17995e11 0.747239 0.373620 0.927582i \(-0.378117\pi\)
0.373620 + 0.927582i \(0.378117\pi\)
\(354\) 3.90219e10 0.132067
\(355\) −3.16187e11 −1.05661
\(356\) −6.51259e11 −2.14896
\(357\) −1.46786e9 −0.00478274
\(358\) 4.76346e11 1.53267
\(359\) −4.21124e11 −1.33809 −0.669044 0.743222i \(-0.733296\pi\)
−0.669044 + 0.743222i \(0.733296\pi\)
\(360\) 2.71738e11 0.852686
\(361\) −2.11279e11 −0.654747
\(362\) −4.85683e11 −1.48650
\(363\) 2.78180e11 0.840904
\(364\) 2.01455e9 0.00601481
\(365\) 2.93976e11 0.866949
\(366\) 2.88346e11 0.839942
\(367\) −4.66968e11 −1.34366 −0.671831 0.740705i \(-0.734492\pi\)
−0.671831 + 0.740705i \(0.734492\pi\)
\(368\) −3.81042e10 −0.108307
\(369\) 4.75009e10 0.133378
\(370\) 3.65112e11 1.01279
\(371\) 3.96771e9 0.0108732
\(372\) −1.49648e11 −0.405161
\(373\) −7.06913e11 −1.89093 −0.945467 0.325719i \(-0.894394\pi\)
−0.945467 + 0.325719i \(0.894394\pi\)
\(374\) −1.27200e12 −3.36174
\(375\) 6.11793e10 0.159758
\(376\) −1.24252e12 −3.20595
\(377\) −1.13137e11 −0.288449
\(378\) 9.10797e8 0.00229461
\(379\) 4.89494e11 1.21863 0.609313 0.792930i \(-0.291445\pi\)
0.609313 + 0.792930i \(0.291445\pi\)
\(380\) 6.67555e11 1.64233
\(381\) 7.31955e10 0.177960
\(382\) −6.49918e11 −1.56161
\(383\) 1.59864e11 0.379627 0.189814 0.981820i \(-0.439212\pi\)
0.189814 + 0.981820i \(0.439212\pi\)
\(384\) 3.84412e11 0.902208
\(385\) 6.14012e9 0.0142431
\(386\) −1.20997e12 −2.77417
\(387\) −5.89512e10 −0.133596
\(388\) 1.52197e12 3.40929
\(389\) 3.92974e11 0.870143 0.435072 0.900396i \(-0.356723\pi\)
0.435072 + 0.900396i \(0.356723\pi\)
\(390\) −2.63572e11 −0.576911
\(391\) −4.81490e10 −0.104182
\(392\) 8.92982e11 1.91010
\(393\) −1.20684e11 −0.255202
\(394\) −7.72087e11 −1.61411
\(395\) −1.08171e12 −2.23576
\(396\) 5.33607e11 1.09042
\(397\) 8.13926e11 1.64448 0.822238 0.569144i \(-0.192725\pi\)
0.822238 + 0.569144i \(0.192725\pi\)
\(398\) −7.73804e11 −1.54581
\(399\) 1.16546e9 0.00230207
\(400\) 5.15513e11 1.00686
\(401\) −4.34991e11 −0.840099 −0.420050 0.907501i \(-0.637987\pi\)
−0.420050 + 0.907501i \(0.637987\pi\)
\(402\) 5.14709e11 0.982980
\(403\) 7.56064e10 0.142786
\(404\) −2.44048e11 −0.455783
\(405\) −8.05639e10 −0.148796
\(406\) 4.43376e9 0.00809850
\(407\) 3.73452e11 0.674622
\(408\) −7.53550e11 −1.34630
\(409\) −3.30766e11 −0.584475 −0.292237 0.956346i \(-0.594400\pi\)
−0.292237 + 0.956346i \(0.594400\pi\)
\(410\) 5.38700e11 0.941499
\(411\) 3.07959e11 0.532360
\(412\) 1.67065e12 2.85658
\(413\) 5.22348e8 0.000883456 0
\(414\) 2.98762e10 0.0499832
\(415\) 8.03156e11 1.32918
\(416\) 8.29186e10 0.135748
\(417\) −3.19699e10 −0.0517761
\(418\) 1.00995e12 1.61810
\(419\) 7.85962e10 0.124577 0.0622886 0.998058i \(-0.480160\pi\)
0.0622886 + 0.998058i \(0.480160\pi\)
\(420\) 6.98335e9 0.0109507
\(421\) 1.15531e12 1.79238 0.896190 0.443671i \(-0.146324\pi\)
0.896190 + 0.443671i \(0.146324\pi\)
\(422\) 3.88571e11 0.596437
\(423\) 3.68377e11 0.559449
\(424\) 2.03689e12 3.06071
\(425\) 6.51409e11 0.968509
\(426\) −5.44056e11 −0.800388
\(427\) 3.85981e9 0.00561876
\(428\) −1.32621e12 −1.91036
\(429\) −2.69593e11 −0.384283
\(430\) −6.68555e11 −0.943038
\(431\) 9.27162e11 1.29422 0.647109 0.762397i \(-0.275978\pi\)
0.647109 + 0.762397i \(0.275978\pi\)
\(432\) 1.76802e11 0.244237
\(433\) −5.34982e11 −0.731381 −0.365690 0.930737i \(-0.619167\pi\)
−0.365690 + 0.930737i \(0.619167\pi\)
\(434\) −2.96296e9 −0.00400887
\(435\) −3.92184e11 −0.525157
\(436\) −2.77592e12 −3.67889
\(437\) 3.82297e10 0.0501457
\(438\) 5.05837e11 0.656716
\(439\) −3.68635e11 −0.473703 −0.236852 0.971546i \(-0.576116\pi\)
−0.236852 + 0.971546i \(0.576116\pi\)
\(440\) 3.15214e12 4.00929
\(441\) −2.64748e11 −0.333318
\(442\) 7.30906e11 0.910880
\(443\) −1.14608e12 −1.41384 −0.706919 0.707294i \(-0.749916\pi\)
−0.706919 + 0.707294i \(0.749916\pi\)
\(444\) 4.24739e11 0.518680
\(445\) 1.14058e12 1.37882
\(446\) 4.25563e11 0.509281
\(447\) 1.70083e11 0.201501
\(448\) 4.09316e9 0.00480074
\(449\) 7.33272e11 0.851445 0.425722 0.904854i \(-0.360020\pi\)
0.425722 + 0.904854i \(0.360020\pi\)
\(450\) −4.04196e11 −0.464660
\(451\) 5.51006e11 0.627137
\(452\) 7.04589e10 0.0793986
\(453\) 4.17407e11 0.465712
\(454\) 3.02051e11 0.333679
\(455\) −3.52819e9 −0.00385923
\(456\) 5.98309e11 0.648013
\(457\) 6.95065e11 0.745422 0.372711 0.927947i \(-0.378428\pi\)
0.372711 + 0.927947i \(0.378428\pi\)
\(458\) −1.57221e12 −1.66961
\(459\) 2.23410e11 0.234933
\(460\) 2.29069e11 0.238538
\(461\) 5.56679e11 0.574052 0.287026 0.957923i \(-0.407333\pi\)
0.287026 + 0.957923i \(0.407333\pi\)
\(462\) 1.05652e10 0.0107892
\(463\) 1.58767e12 1.60563 0.802815 0.596228i \(-0.203334\pi\)
0.802815 + 0.596228i \(0.203334\pi\)
\(464\) 8.60673e11 0.862000
\(465\) 2.62086e11 0.259960
\(466\) −3.48168e12 −3.42020
\(467\) −9.73788e10 −0.0947411 −0.0473706 0.998877i \(-0.515084\pi\)
−0.0473706 + 0.998877i \(0.515084\pi\)
\(468\) −3.06617e11 −0.295454
\(469\) 6.88992e9 0.00657561
\(470\) 4.17770e12 3.94909
\(471\) 5.07993e11 0.475623
\(472\) 2.68156e11 0.248685
\(473\) −6.83828e11 −0.628162
\(474\) −1.86128e12 −1.69359
\(475\) −5.17210e11 −0.466172
\(476\) −1.93654e10 −0.0172900
\(477\) −6.03890e11 −0.534103
\(478\) −1.27103e12 −1.11360
\(479\) −4.31480e11 −0.374499 −0.187249 0.982312i \(-0.559957\pi\)
−0.187249 + 0.982312i \(0.559957\pi\)
\(480\) 2.87434e11 0.247145
\(481\) −2.14590e11 −0.182792
\(482\) −1.40161e12 −1.18281
\(483\) 3.99924e8 0.000334361 0
\(484\) 3.67002e12 3.03993
\(485\) −2.66551e12 −2.18747
\(486\) −1.38624e11 −0.112714
\(487\) −2.09753e12 −1.68977 −0.844886 0.534946i \(-0.820332\pi\)
−0.844886 + 0.534946i \(0.820332\pi\)
\(488\) 1.98150e12 1.58163
\(489\) 2.41191e11 0.190753
\(490\) −3.00246e12 −2.35285
\(491\) −1.32643e11 −0.102995 −0.0514976 0.998673i \(-0.516399\pi\)
−0.0514976 + 0.998673i \(0.516399\pi\)
\(492\) 6.26677e11 0.482171
\(493\) 1.08756e12 0.829165
\(494\) −5.80329e11 −0.438433
\(495\) −9.34533e11 −0.699635
\(496\) −5.75165e11 −0.426702
\(497\) −7.28275e9 −0.00535416
\(498\) 1.38197e12 1.00686
\(499\) −3.85614e11 −0.278420 −0.139210 0.990263i \(-0.544456\pi\)
−0.139210 + 0.990263i \(0.544456\pi\)
\(500\) 8.07135e11 0.577538
\(501\) −1.35390e11 −0.0960103
\(502\) −4.76054e11 −0.334572
\(503\) −1.68499e11 −0.117366 −0.0586829 0.998277i \(-0.518690\pi\)
−0.0586829 + 0.998277i \(0.518690\pi\)
\(504\) 6.25896e9 0.00432081
\(505\) 4.27413e11 0.292440
\(506\) 3.46561e11 0.235019
\(507\) −7.04053e11 −0.473227
\(508\) 9.65664e11 0.643338
\(509\) 4.71940e11 0.311642 0.155821 0.987785i \(-0.450198\pi\)
0.155821 + 0.987785i \(0.450198\pi\)
\(510\) 2.53365e12 1.65837
\(511\) 6.77116e9 0.00439308
\(512\) 3.13870e12 2.01853
\(513\) −1.77384e11 −0.113080
\(514\) −2.76796e12 −1.74914
\(515\) −2.92589e12 −1.83284
\(516\) −7.77739e11 −0.482959
\(517\) 4.27314e12 2.63051
\(518\) 8.40964e9 0.00513208
\(519\) 1.08588e12 0.656943
\(520\) −1.81126e12 −1.08634
\(521\) −2.64327e12 −1.57171 −0.785853 0.618414i \(-0.787776\pi\)
−0.785853 + 0.618414i \(0.787776\pi\)
\(522\) −6.74823e11 −0.397807
\(523\) −3.72234e11 −0.217549 −0.108775 0.994066i \(-0.534693\pi\)
−0.108775 + 0.994066i \(0.534693\pi\)
\(524\) −1.59218e12 −0.922576
\(525\) −5.41058e9 −0.00310833
\(526\) −3.55955e12 −2.02749
\(527\) −7.26785e11 −0.410448
\(528\) 2.05089e12 1.14839
\(529\) −1.78803e12 −0.992717
\(530\) −6.84862e12 −3.77018
\(531\) −7.95020e10 −0.0433963
\(532\) 1.53758e10 0.00832217
\(533\) −3.16615e11 −0.169926
\(534\) 1.96258e12 1.04446
\(535\) 2.32266e12 1.22572
\(536\) 3.53706e12 1.85098
\(537\) −9.70494e11 −0.503627
\(538\) −4.41593e12 −2.27249
\(539\) −3.07105e12 −1.56725
\(540\) −1.06287e12 −0.537911
\(541\) 3.80779e12 1.91111 0.955554 0.294815i \(-0.0952579\pi\)
0.955554 + 0.294815i \(0.0952579\pi\)
\(542\) 1.07655e12 0.535842
\(543\) 9.89516e11 0.488454
\(544\) −7.97075e11 −0.390215
\(545\) 4.86161e12 2.36045
\(546\) −6.07088e9 −0.00292337
\(547\) 2.49470e12 1.19145 0.595725 0.803189i \(-0.296865\pi\)
0.595725 + 0.803189i \(0.296865\pi\)
\(548\) 4.06289e12 1.92452
\(549\) −5.87468e11 −0.276000
\(550\) −4.68863e12 −2.18481
\(551\) −8.63506e11 −0.399101
\(552\) 2.05308e11 0.0941195
\(553\) −2.49152e10 −0.0113292
\(554\) 1.90851e12 0.860798
\(555\) −7.43868e11 −0.332796
\(556\) −4.21777e11 −0.187174
\(557\) 3.97099e12 1.74804 0.874019 0.485892i \(-0.161505\pi\)
0.874019 + 0.485892i \(0.161505\pi\)
\(558\) 4.50966e11 0.196920
\(559\) 3.92936e11 0.170204
\(560\) 2.68402e10 0.0115329
\(561\) 2.59153e12 1.10465
\(562\) 4.50598e12 1.90535
\(563\) 3.54645e12 1.48767 0.743833 0.668365i \(-0.233006\pi\)
0.743833 + 0.668365i \(0.233006\pi\)
\(564\) 4.85997e12 2.02245
\(565\) −1.23398e11 −0.0509438
\(566\) 2.54883e12 1.04392
\(567\) −1.85563e9 −0.000753995 0
\(568\) −3.73873e12 −1.50715
\(569\) 3.10044e12 1.23999 0.619994 0.784606i \(-0.287135\pi\)
0.619994 + 0.784606i \(0.287135\pi\)
\(570\) −2.01169e12 −0.798221
\(571\) −4.49759e12 −1.77059 −0.885294 0.465032i \(-0.846043\pi\)
−0.885294 + 0.465032i \(0.846043\pi\)
\(572\) −3.55673e12 −1.38921
\(573\) 1.32413e12 0.513137
\(574\) 1.24079e10 0.00477084
\(575\) −1.77479e11 −0.0677083
\(576\) −6.22985e11 −0.235818
\(577\) 3.67193e12 1.37912 0.689562 0.724227i \(-0.257803\pi\)
0.689562 + 0.724227i \(0.257803\pi\)
\(578\) −2.31130e12 −0.861351
\(579\) 2.46517e12 0.911576
\(580\) −5.17407e12 −1.89848
\(581\) 1.84991e10 0.00673533
\(582\) −4.58648e12 −1.65701
\(583\) −7.00507e12 −2.51133
\(584\) 3.47609e12 1.23661
\(585\) 5.36994e11 0.189569
\(586\) −5.16948e12 −1.81095
\(587\) −3.14786e12 −1.09432 −0.547159 0.837029i \(-0.684291\pi\)
−0.547159 + 0.837029i \(0.684291\pi\)
\(588\) −3.49280e12 −1.20497
\(589\) 5.77058e11 0.197561
\(590\) −9.01619e11 −0.306330
\(591\) 1.57303e12 0.530387
\(592\) 1.63246e12 0.546256
\(593\) 1.66698e12 0.553584 0.276792 0.960930i \(-0.410729\pi\)
0.276792 + 0.960930i \(0.410729\pi\)
\(594\) −1.60803e12 −0.529975
\(595\) 3.39156e10 0.0110936
\(596\) 2.24389e12 0.728440
\(597\) 1.57652e12 0.507945
\(598\) −1.99138e11 −0.0636795
\(599\) −1.17016e12 −0.371387 −0.185693 0.982608i \(-0.559453\pi\)
−0.185693 + 0.982608i \(0.559453\pi\)
\(600\) −2.77762e12 −0.874967
\(601\) −4.19866e12 −1.31273 −0.656366 0.754443i \(-0.727907\pi\)
−0.656366 + 0.754443i \(0.727907\pi\)
\(602\) −1.53989e10 −0.00477865
\(603\) −1.04865e12 −0.323001
\(604\) 5.50683e12 1.68359
\(605\) −6.42749e12 −1.95048
\(606\) 7.35441e11 0.221524
\(607\) −3.46965e12 −1.03738 −0.518689 0.854963i \(-0.673580\pi\)
−0.518689 + 0.854963i \(0.673580\pi\)
\(608\) 6.32867e11 0.187822
\(609\) −9.03321e9 −0.00266112
\(610\) −6.66238e12 −1.94825
\(611\) −2.45540e12 −0.712748
\(612\) 2.94743e12 0.849302
\(613\) −1.07824e12 −0.308420 −0.154210 0.988038i \(-0.549283\pi\)
−0.154210 + 0.988038i \(0.549283\pi\)
\(614\) −3.71015e12 −1.05350
\(615\) −1.09753e12 −0.309371
\(616\) 7.26033e10 0.0203162
\(617\) 3.25905e11 0.0905331 0.0452666 0.998975i \(-0.485586\pi\)
0.0452666 + 0.998975i \(0.485586\pi\)
\(618\) −5.03451e12 −1.38838
\(619\) −3.86487e12 −1.05810 −0.529051 0.848590i \(-0.677452\pi\)
−0.529051 + 0.848590i \(0.677452\pi\)
\(620\) 3.45769e12 0.939774
\(621\) −6.08689e10 −0.0164242
\(622\) −6.27926e12 −1.68210
\(623\) 2.62712e10 0.00698688
\(624\) −1.17847e12 −0.311162
\(625\) −4.44005e12 −1.16393
\(626\) 3.32131e12 0.864420
\(627\) −2.05764e12 −0.531699
\(628\) 6.70192e12 1.71941
\(629\) 2.06280e12 0.525448
\(630\) −2.10444e10 −0.00532236
\(631\) 5.72504e12 1.43763 0.718813 0.695203i \(-0.244686\pi\)
0.718813 + 0.695203i \(0.244686\pi\)
\(632\) −1.27906e13 −3.18908
\(633\) −7.91664e11 −0.195986
\(634\) 7.88084e12 1.93718
\(635\) −1.69122e12 −0.412779
\(636\) −7.96709e12 −1.93082
\(637\) 1.76466e12 0.424653
\(638\) −7.82789e12 −1.87047
\(639\) 1.10844e12 0.263002
\(640\) −8.88203e12 −2.09268
\(641\) 2.78162e12 0.650785 0.325392 0.945579i \(-0.394504\pi\)
0.325392 + 0.945579i \(0.394504\pi\)
\(642\) 3.99654e12 0.928489
\(643\) 5.67681e12 1.30965 0.654824 0.755781i \(-0.272743\pi\)
0.654824 + 0.755781i \(0.272743\pi\)
\(644\) 5.27617e9 0.00120874
\(645\) 1.36210e12 0.309877
\(646\) 5.57856e12 1.26030
\(647\) 6.36165e10 0.0142725 0.00713626 0.999975i \(-0.497728\pi\)
0.00713626 + 0.999975i \(0.497728\pi\)
\(648\) −9.52621e11 −0.212243
\(649\) −9.22216e11 −0.204048
\(650\) 2.69415e12 0.591986
\(651\) 6.03665e9 0.00131729
\(652\) 3.18202e12 0.689586
\(653\) 3.08169e12 0.663255 0.331627 0.943410i \(-0.392402\pi\)
0.331627 + 0.943410i \(0.392402\pi\)
\(654\) 8.36526e12 1.78805
\(655\) 2.78847e12 0.591944
\(656\) 2.40860e12 0.507806
\(657\) −1.03058e12 −0.215793
\(658\) 9.62252e10 0.0200112
\(659\) −7.50754e11 −0.155065 −0.0775324 0.996990i \(-0.524704\pi\)
−0.0775324 + 0.996990i \(0.524704\pi\)
\(660\) −1.23292e13 −2.52923
\(661\) −5.89525e12 −1.20115 −0.600573 0.799570i \(-0.705061\pi\)
−0.600573 + 0.799570i \(0.705061\pi\)
\(662\) 1.04128e12 0.210720
\(663\) −1.48913e12 −0.299310
\(664\) 9.49686e12 1.89594
\(665\) −2.69285e10 −0.00533967
\(666\) −1.27996e12 −0.252094
\(667\) −2.96309e11 −0.0579668
\(668\) −1.78620e12 −0.347085
\(669\) −8.67031e11 −0.167347
\(670\) −1.18926e13 −2.28003
\(671\) −6.81457e12 −1.29774
\(672\) 6.62048e9 0.00125236
\(673\) −1.26722e11 −0.0238113 −0.0119057 0.999929i \(-0.503790\pi\)
−0.0119057 + 0.999929i \(0.503790\pi\)
\(674\) −4.36515e12 −0.814760
\(675\) 8.23497e11 0.152685
\(676\) −9.28853e12 −1.71075
\(677\) 5.40759e12 0.989361 0.494681 0.869075i \(-0.335285\pi\)
0.494681 + 0.869075i \(0.335285\pi\)
\(678\) −2.12329e11 −0.0385901
\(679\) −6.13948e10 −0.0110845
\(680\) 1.74111e13 3.12275
\(681\) −6.15390e11 −0.109645
\(682\) 5.23117e12 0.925910
\(683\) −3.34048e12 −0.587376 −0.293688 0.955901i \(-0.594883\pi\)
−0.293688 + 0.955901i \(0.594883\pi\)
\(684\) −2.34022e12 −0.408794
\(685\) −7.11555e12 −1.23481
\(686\) −1.38315e11 −0.0238457
\(687\) 3.20317e12 0.548623
\(688\) −2.98920e12 −0.508636
\(689\) 4.02520e12 0.680458
\(690\) −6.90304e11 −0.115936
\(691\) −5.76394e12 −0.961764 −0.480882 0.876785i \(-0.659683\pi\)
−0.480882 + 0.876785i \(0.659683\pi\)
\(692\) 1.43259e13 2.37490
\(693\) −2.15252e10 −0.00354525
\(694\) −1.91776e12 −0.313816
\(695\) 7.38680e11 0.120095
\(696\) −4.63736e12 −0.749081
\(697\) 3.04354e12 0.488463
\(698\) 1.26147e13 2.01154
\(699\) 7.09347e12 1.12386
\(700\) −7.13815e10 −0.0112368
\(701\) −5.48007e12 −0.857147 −0.428573 0.903507i \(-0.640984\pi\)
−0.428573 + 0.903507i \(0.640984\pi\)
\(702\) 9.23995e11 0.143599
\(703\) −1.63784e12 −0.252913
\(704\) −7.22656e12 −1.10880
\(705\) −8.51153e12 −1.29765
\(706\) −8.66684e12 −1.31292
\(707\) 9.84464e9 0.00148188
\(708\) −1.04887e12 −0.156881
\(709\) 8.14487e12 1.21053 0.605265 0.796024i \(-0.293067\pi\)
0.605265 + 0.796024i \(0.293067\pi\)
\(710\) 1.25707e13 1.85651
\(711\) 3.79212e12 0.556505
\(712\) 1.34868e13 1.96674
\(713\) 1.98016e11 0.0286944
\(714\) 5.83578e10 0.00840343
\(715\) 6.22909e12 0.891348
\(716\) −1.28037e13 −1.82065
\(717\) 2.58956e12 0.365923
\(718\) 1.67427e13 2.35107
\(719\) 9.83293e12 1.37215 0.686077 0.727529i \(-0.259331\pi\)
0.686077 + 0.727529i \(0.259331\pi\)
\(720\) −4.08511e12 −0.566509
\(721\) −6.73922e10 −0.00928754
\(722\) 8.39983e12 1.15041
\(723\) 2.85560e12 0.388665
\(724\) 1.30546e13 1.76580
\(725\) 4.00878e12 0.538879
\(726\) −1.10596e13 −1.47750
\(727\) −3.89292e12 −0.516857 −0.258428 0.966030i \(-0.583205\pi\)
−0.258428 + 0.966030i \(0.583205\pi\)
\(728\) −4.17188e10 −0.00550479
\(729\) 2.82430e11 0.0370370
\(730\) −1.16876e13 −1.52326
\(731\) −3.77719e12 −0.489261
\(732\) −7.75043e12 −0.997760
\(733\) −8.99834e12 −1.15132 −0.575658 0.817691i \(-0.695254\pi\)
−0.575658 + 0.817691i \(0.695254\pi\)
\(734\) 1.85653e13 2.36086
\(735\) 6.11713e12 0.773134
\(736\) 2.17166e11 0.0272799
\(737\) −1.21643e13 −1.51874
\(738\) −1.88850e12 −0.234349
\(739\) 5.20306e12 0.641739 0.320870 0.947123i \(-0.396025\pi\)
0.320870 + 0.947123i \(0.396025\pi\)
\(740\) −9.81381e12 −1.20308
\(741\) 1.18235e12 0.144066
\(742\) −1.57745e11 −0.0191046
\(743\) −1.31280e12 −0.158033 −0.0790165 0.996873i \(-0.525178\pi\)
−0.0790165 + 0.996873i \(0.525178\pi\)
\(744\) 3.09902e12 0.370806
\(745\) −3.92984e12 −0.467382
\(746\) 2.81048e13 3.32243
\(747\) −2.81559e12 −0.330847
\(748\) 3.41899e13 3.99338
\(749\) 5.34979e10 0.00621110
\(750\) −2.43231e12 −0.280701
\(751\) 1.71718e13 1.96987 0.984933 0.172939i \(-0.0553262\pi\)
0.984933 + 0.172939i \(0.0553262\pi\)
\(752\) 1.86791e13 2.12998
\(753\) 9.69898e11 0.109938
\(754\) 4.49800e12 0.506814
\(755\) −9.64439e12 −1.08022
\(756\) −2.44813e10 −0.00272575
\(757\) 1.66475e13 1.84255 0.921273 0.388916i \(-0.127150\pi\)
0.921273 + 0.388916i \(0.127150\pi\)
\(758\) −1.94609e13 −2.14117
\(759\) −7.06073e11 −0.0772257
\(760\) −1.38242e13 −1.50307
\(761\) 6.16014e12 0.665825 0.332912 0.942958i \(-0.391969\pi\)
0.332912 + 0.942958i \(0.391969\pi\)
\(762\) −2.91004e12 −0.312681
\(763\) 1.11978e11 0.0119611
\(764\) 1.74691e13 1.85503
\(765\) −5.16199e12 −0.544930
\(766\) −6.35575e12 −0.667017
\(767\) 5.29917e11 0.0552877
\(768\) −1.13452e13 −1.17676
\(769\) 1.33568e13 1.37731 0.688657 0.725087i \(-0.258200\pi\)
0.688657 + 0.725087i \(0.258200\pi\)
\(770\) −2.44113e11 −0.0250255
\(771\) 5.63936e12 0.574758
\(772\) 3.25228e13 3.29542
\(773\) −3.22073e12 −0.324449 −0.162225 0.986754i \(-0.551867\pi\)
−0.162225 + 0.986754i \(0.551867\pi\)
\(774\) 2.34373e12 0.234732
\(775\) −2.67896e12 −0.266753
\(776\) −3.15181e13 −3.12020
\(777\) −1.71336e10 −0.00168637
\(778\) −1.56235e13 −1.52887
\(779\) −2.41653e12 −0.235111
\(780\) 7.08454e12 0.685308
\(781\) 1.28578e13 1.23663
\(782\) 1.91426e12 0.183051
\(783\) 1.37487e12 0.130717
\(784\) −1.34244e13 −1.26903
\(785\) −1.17374e13 −1.10321
\(786\) 4.79807e12 0.448399
\(787\) 1.14501e13 1.06395 0.531977 0.846759i \(-0.321449\pi\)
0.531977 + 0.846759i \(0.321449\pi\)
\(788\) 2.07529e13 1.91739
\(789\) 7.25213e12 0.666222
\(790\) 4.30058e13 3.92830
\(791\) −2.84224e9 −0.000258147 0
\(792\) −1.10503e13 −0.997956
\(793\) 3.91574e12 0.351629
\(794\) −3.23593e13 −2.88940
\(795\) 1.39532e13 1.23886
\(796\) 2.07990e13 1.83626
\(797\) 7.25906e12 0.637262 0.318631 0.947879i \(-0.396777\pi\)
0.318631 + 0.947879i \(0.396777\pi\)
\(798\) −4.63353e10 −0.00404482
\(799\) 2.36031e13 2.04884
\(800\) −2.93805e12 −0.253603
\(801\) −3.99850e12 −0.343203
\(802\) 1.72940e13 1.47608
\(803\) −1.19546e13 −1.01465
\(804\) −1.38348e13 −1.16767
\(805\) −9.24043e9 −0.000775552 0
\(806\) −3.00589e12 −0.250880
\(807\) 8.99690e12 0.746727
\(808\) 5.05392e12 0.417135
\(809\) −1.85851e13 −1.52544 −0.762722 0.646726i \(-0.776138\pi\)
−0.762722 + 0.646726i \(0.776138\pi\)
\(810\) 3.20299e12 0.261440
\(811\) 2.15522e13 1.74944 0.874719 0.484630i \(-0.161046\pi\)
0.874719 + 0.484630i \(0.161046\pi\)
\(812\) −1.19175e11 −0.00962014
\(813\) −2.19333e12 −0.176074
\(814\) −1.48474e13 −1.18533
\(815\) −5.57284e12 −0.442453
\(816\) 1.13283e13 0.894457
\(817\) 2.99904e12 0.235496
\(818\) 1.31503e13 1.02694
\(819\) 1.23686e10 0.000960603 0
\(820\) −1.44797e13 −1.11840
\(821\) 2.08276e13 1.59991 0.799954 0.600062i \(-0.204857\pi\)
0.799954 + 0.600062i \(0.204857\pi\)
\(822\) −1.22436e13 −0.935373
\(823\) −9.47540e12 −0.719943 −0.359972 0.932963i \(-0.617214\pi\)
−0.359972 + 0.932963i \(0.617214\pi\)
\(824\) −3.45970e13 −2.61436
\(825\) 9.55249e12 0.717916
\(826\) −2.07670e10 −0.00155226
\(827\) 3.45208e12 0.256629 0.128315 0.991734i \(-0.459043\pi\)
0.128315 + 0.991734i \(0.459043\pi\)
\(828\) −8.03040e11 −0.0593746
\(829\) −1.59708e13 −1.17444 −0.587222 0.809426i \(-0.699779\pi\)
−0.587222 + 0.809426i \(0.699779\pi\)
\(830\) −3.19312e13 −2.33541
\(831\) −3.88835e12 −0.282853
\(832\) 4.15247e12 0.300436
\(833\) −1.69633e13 −1.22069
\(834\) 1.27103e12 0.0909723
\(835\) 3.12826e12 0.222697
\(836\) −2.71463e13 −1.92213
\(837\) −9.18786e11 −0.0647068
\(838\) −3.12476e12 −0.218886
\(839\) 5.84124e12 0.406983 0.203491 0.979077i \(-0.434771\pi\)
0.203491 + 0.979077i \(0.434771\pi\)
\(840\) −1.44616e11 −0.0100221
\(841\) −7.81431e12 −0.538652
\(842\) −4.59319e13 −3.14927
\(843\) −9.18035e12 −0.626088
\(844\) −1.04444e13 −0.708503
\(845\) 1.62675e13 1.09765
\(846\) −1.46456e13 −0.982971
\(847\) −1.48045e11 −0.00988366
\(848\) −3.06211e13 −2.03348
\(849\) −5.19291e12 −0.343025
\(850\) −2.58982e13 −1.70170
\(851\) −5.62019e11 −0.0367340
\(852\) 1.46236e13 0.950774
\(853\) 2.01733e10 0.00130468 0.000652342 1.00000i \(-0.499792\pi\)
0.000652342 1.00000i \(0.499792\pi\)
\(854\) −1.53455e11 −0.00987235
\(855\) 4.09855e12 0.262291
\(856\) 2.74641e13 1.74837
\(857\) 2.71965e12 0.172226 0.0861130 0.996285i \(-0.472555\pi\)
0.0861130 + 0.996285i \(0.472555\pi\)
\(858\) 1.07183e13 0.675198
\(859\) −1.34952e13 −0.845688 −0.422844 0.906203i \(-0.638968\pi\)
−0.422844 + 0.906203i \(0.638968\pi\)
\(860\) 1.79700e13 1.12023
\(861\) −2.52795e10 −0.00156767
\(862\) −3.68613e13 −2.27399
\(863\) −1.46281e13 −0.897717 −0.448859 0.893603i \(-0.648169\pi\)
−0.448859 + 0.893603i \(0.648169\pi\)
\(864\) −1.00765e12 −0.0615171
\(865\) −2.50897e13 −1.52378
\(866\) 2.12693e13 1.28506
\(867\) 4.70897e12 0.283035
\(868\) 7.96412e10 0.00476211
\(869\) 4.39882e13 2.61666
\(870\) 1.55921e13 0.922717
\(871\) 6.98975e12 0.411510
\(872\) 5.74857e13 3.36694
\(873\) 9.34436e12 0.544484
\(874\) −1.51990e12 −0.0881077
\(875\) −3.25590e10 −0.00187774
\(876\) −1.35964e13 −0.780107
\(877\) 1.06900e13 0.610209 0.305105 0.952319i \(-0.401309\pi\)
0.305105 + 0.952319i \(0.401309\pi\)
\(878\) 1.46559e13 0.832312
\(879\) 1.05321e13 0.595069
\(880\) −4.73868e13 −2.66370
\(881\) −2.64579e13 −1.47967 −0.739833 0.672790i \(-0.765096\pi\)
−0.739833 + 0.672790i \(0.765096\pi\)
\(882\) 1.05256e13 0.585651
\(883\) −1.05016e13 −0.581342 −0.290671 0.956823i \(-0.593879\pi\)
−0.290671 + 0.956823i \(0.593879\pi\)
\(884\) −1.96460e13 −1.08203
\(885\) 1.83693e12 0.100658
\(886\) 4.55650e13 2.48416
\(887\) 1.51558e13 0.822098 0.411049 0.911613i \(-0.365162\pi\)
0.411049 + 0.911613i \(0.365162\pi\)
\(888\) −8.79581e12 −0.474698
\(889\) −3.89539e10 −0.00209167
\(890\) −4.53464e13 −2.42263
\(891\) 3.27616e12 0.174147
\(892\) −1.14387e13 −0.604971
\(893\) −1.87405e13 −0.986168
\(894\) −6.76200e12 −0.354043
\(895\) 2.24237e13 1.16817
\(896\) −2.04580e11 −0.0106042
\(897\) 4.05719e11 0.0209247
\(898\) −2.91528e13 −1.49602
\(899\) −4.47264e12 −0.228374
\(900\) 1.08643e13 0.551966
\(901\) −3.86932e13 −1.95602
\(902\) −2.19064e13 −1.10190
\(903\) 3.13732e10 0.00157023
\(904\) −1.45911e12 −0.0726660
\(905\) −2.28633e13 −1.13297
\(906\) −1.65949e13 −0.818272
\(907\) 1.91598e13 0.940067 0.470034 0.882649i \(-0.344242\pi\)
0.470034 + 0.882649i \(0.344242\pi\)
\(908\) −8.11881e12 −0.396375
\(909\) −1.49837e12 −0.0727915
\(910\) 1.40271e11 0.00678079
\(911\) 9.06518e12 0.436058 0.218029 0.975942i \(-0.430037\pi\)
0.218029 + 0.975942i \(0.430037\pi\)
\(912\) −8.99452e12 −0.430528
\(913\) −3.26606e13 −1.55563
\(914\) −2.76338e13 −1.30973
\(915\) 1.35737e13 0.640183
\(916\) 4.22592e13 1.98332
\(917\) 6.42271e10 0.00299955
\(918\) −8.88212e12 −0.412786
\(919\) 3.18663e13 1.47371 0.736854 0.676052i \(-0.236310\pi\)
0.736854 + 0.676052i \(0.236310\pi\)
\(920\) −4.74374e12 −0.218311
\(921\) 7.55894e12 0.346173
\(922\) −2.21320e13 −1.00863
\(923\) −7.38828e12 −0.335070
\(924\) −2.83980e11 −0.0128163
\(925\) 7.60357e12 0.341492
\(926\) −6.31212e13 −2.82115
\(927\) 1.02572e13 0.456214
\(928\) −4.90521e12 −0.217116
\(929\) −1.82057e13 −0.801930 −0.400965 0.916093i \(-0.631325\pi\)
−0.400965 + 0.916093i \(0.631325\pi\)
\(930\) −1.04198e13 −0.456758
\(931\) 1.34686e13 0.587556
\(932\) 9.35837e13 4.06283
\(933\) 1.27932e13 0.552728
\(934\) 3.87150e12 0.166463
\(935\) −5.98786e13 −2.56224
\(936\) 6.34965e12 0.270401
\(937\) 2.86463e13 1.21406 0.607029 0.794679i \(-0.292361\pi\)
0.607029 + 0.794679i \(0.292361\pi\)
\(938\) −2.73923e11 −0.0115536
\(939\) −6.76674e12 −0.284043
\(940\) −1.12292e14 −4.69109
\(941\) 2.02281e13 0.841012 0.420506 0.907290i \(-0.361853\pi\)
0.420506 + 0.907290i \(0.361853\pi\)
\(942\) −2.01963e13 −0.835686
\(943\) −8.29225e11 −0.0341483
\(944\) −4.03126e12 −0.165222
\(945\) 4.28753e10 0.00174890
\(946\) 2.71870e13 1.10370
\(947\) 4.65361e13 1.88025 0.940124 0.340833i \(-0.110709\pi\)
0.940124 + 0.340833i \(0.110709\pi\)
\(948\) 5.00292e13 2.01181
\(949\) 6.86927e12 0.274924
\(950\) 2.05628e13 0.819079
\(951\) −1.60562e13 −0.636546
\(952\) 4.01032e11 0.0158239
\(953\) −7.93310e11 −0.0311548 −0.0155774 0.999879i \(-0.504959\pi\)
−0.0155774 + 0.999879i \(0.504959\pi\)
\(954\) 2.40089e13 0.938437
\(955\) −3.05946e13 −1.19022
\(956\) 3.41639e13 1.32284
\(957\) 1.59483e13 0.614626
\(958\) 1.71544e13 0.658007
\(959\) −1.63893e11 −0.00625715
\(960\) 1.43944e13 0.546981
\(961\) −2.34507e13 −0.886952
\(962\) 8.53150e12 0.321172
\(963\) −8.14244e12 −0.305096
\(964\) 3.76738e13 1.40505
\(965\) −5.69589e13 −2.11441
\(966\) −1.58998e10 −0.000587483 0
\(967\) 2.13665e13 0.785805 0.392903 0.919580i \(-0.371471\pi\)
0.392903 + 0.919580i \(0.371471\pi\)
\(968\) −7.60014e13 −2.78216
\(969\) −1.13656e13 −0.414128
\(970\) 1.05973e14 3.84346
\(971\) −3.68918e13 −1.33181 −0.665906 0.746036i \(-0.731955\pi\)
−0.665906 + 0.746036i \(0.731955\pi\)
\(972\) 3.72608e12 0.133892
\(973\) 1.70141e10 0.000608556 0
\(974\) 8.33918e13 2.96899
\(975\) −5.48898e12 −0.194523
\(976\) −2.97884e13 −1.05081
\(977\) 2.31976e13 0.814550 0.407275 0.913306i \(-0.366479\pi\)
0.407275 + 0.913306i \(0.366479\pi\)
\(978\) −9.58906e12 −0.335159
\(979\) −4.63823e13 −1.61373
\(980\) 8.07029e13 2.79494
\(981\) −1.70431e13 −0.587542
\(982\) 5.27350e12 0.180966
\(983\) −3.48605e13 −1.19081 −0.595405 0.803425i \(-0.703009\pi\)
−0.595405 + 0.803425i \(0.703009\pi\)
\(984\) −1.29777e13 −0.441285
\(985\) −3.63456e13 −1.23024
\(986\) −4.32381e13 −1.45687
\(987\) −1.96046e11 −0.00657555
\(988\) 1.55986e13 0.520811
\(989\) 1.02911e12 0.0342042
\(990\) 3.71543e13 1.22928
\(991\) −5.67925e13 −1.87051 −0.935254 0.353977i \(-0.884829\pi\)
−0.935254 + 0.353977i \(0.884829\pi\)
\(992\) 3.27802e12 0.107475
\(993\) −2.12147e12 −0.0692413
\(994\) 2.89541e11 0.00940744
\(995\) −3.64264e13 −1.17818
\(996\) −3.71459e13 −1.19604
\(997\) −2.65675e13 −0.851575 −0.425787 0.904823i \(-0.640003\pi\)
−0.425787 + 0.904823i \(0.640003\pi\)
\(998\) 1.53309e13 0.489192
\(999\) 2.60775e12 0.0828364
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.1.1 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.1 22 1.1 even 1 trivial