Properties

Label 177.10.a.d.1.20
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 1.20
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+40.5682 q^{2} +81.0000 q^{3} +1133.78 q^{4} -281.912 q^{5} +3286.03 q^{6} -11944.6 q^{7} +25224.6 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+40.5682 q^{2} +81.0000 q^{3} +1133.78 q^{4} -281.912 q^{5} +3286.03 q^{6} -11944.6 q^{7} +25224.6 q^{8} +6561.00 q^{9} -11436.7 q^{10} +38053.5 q^{11} +91836.3 q^{12} +124569. q^{13} -484571. q^{14} -22834.8 q^{15} +442820. q^{16} +483647. q^{17} +266168. q^{18} +118744. q^{19} -319626. q^{20} -967511. q^{21} +1.54376e6 q^{22} +1.81149e6 q^{23} +2.04319e6 q^{24} -1.87365e6 q^{25} +5.05356e6 q^{26} +531441. q^{27} -1.35425e7 q^{28} +1.59230e6 q^{29} -926369. q^{30} +3.75720e6 q^{31} +5.04944e6 q^{32} +3.08233e6 q^{33} +1.96207e7 q^{34} +3.36732e6 q^{35} +7.43874e6 q^{36} +1.86388e7 q^{37} +4.81725e6 q^{38} +1.00901e7 q^{39} -7.11109e6 q^{40} +223048. q^{41} -3.92502e7 q^{42} +9.66466e6 q^{43} +4.31443e7 q^{44} -1.84962e6 q^{45} +7.34889e7 q^{46} -2.98480e6 q^{47} +3.58684e7 q^{48} +1.02320e8 q^{49} -7.60107e7 q^{50} +3.91754e7 q^{51} +1.41235e8 q^{52} -3.40106e7 q^{53} +2.15596e7 q^{54} -1.07277e7 q^{55} -3.01297e8 q^{56} +9.61829e6 q^{57} +6.45968e7 q^{58} -1.21174e7 q^{59} -2.58897e7 q^{60} -1.41279e8 q^{61} +1.52423e8 q^{62} -7.83684e7 q^{63} -2.18769e7 q^{64} -3.51176e7 q^{65} +1.25045e8 q^{66} +2.24453e7 q^{67} +5.48350e8 q^{68} +1.46731e8 q^{69} +1.36606e8 q^{70} -2.18355e8 q^{71} +1.65498e8 q^{72} -2.38222e8 q^{73} +7.56143e8 q^{74} -1.51766e8 q^{75} +1.34630e8 q^{76} -4.54533e8 q^{77} +4.09339e8 q^{78} -4.97164e7 q^{79} -1.24836e8 q^{80} +4.30467e7 q^{81} +9.04867e6 q^{82} -5.31042e8 q^{83} -1.09695e9 q^{84} -1.36346e8 q^{85} +3.92078e8 q^{86} +1.28976e8 q^{87} +9.59882e8 q^{88} -1.52080e6 q^{89} -7.50359e7 q^{90} -1.48793e9 q^{91} +2.05383e9 q^{92} +3.04333e8 q^{93} -1.21088e8 q^{94} -3.34754e7 q^{95} +4.09005e8 q^{96} +1.14057e9 q^{97} +4.15092e9 q^{98} +2.49669e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 40.5682 1.79288 0.896440 0.443166i \(-0.146145\pi\)
0.896440 + 0.443166i \(0.146145\pi\)
\(3\) 81.0000 0.577350
\(4\) 1133.78 2.21442
\(5\) −281.912 −0.201719 −0.100860 0.994901i \(-0.532159\pi\)
−0.100860 + 0.994901i \(0.532159\pi\)
\(6\) 3286.03 1.03512
\(7\) −11944.6 −1.88031 −0.940156 0.340744i \(-0.889321\pi\)
−0.940156 + 0.340744i \(0.889321\pi\)
\(8\) 25224.6 2.17730
\(9\) 6561.00 0.333333
\(10\) −11436.7 −0.361659
\(11\) 38053.5 0.783659 0.391829 0.920038i \(-0.371842\pi\)
0.391829 + 0.920038i \(0.371842\pi\)
\(12\) 91836.3 1.27849
\(13\) 124569. 1.20967 0.604834 0.796351i \(-0.293239\pi\)
0.604834 + 0.796351i \(0.293239\pi\)
\(14\) −484571. −3.37117
\(15\) −22834.8 −0.116463
\(16\) 442820. 1.68922
\(17\) 483647. 1.40446 0.702228 0.711952i \(-0.252189\pi\)
0.702228 + 0.711952i \(0.252189\pi\)
\(18\) 266168. 0.597626
\(19\) 118744. 0.209036 0.104518 0.994523i \(-0.466670\pi\)
0.104518 + 0.994523i \(0.466670\pi\)
\(20\) −319626. −0.446691
\(21\) −967511. −1.08560
\(22\) 1.54376e6 1.40501
\(23\) 1.81149e6 1.34977 0.674886 0.737922i \(-0.264193\pi\)
0.674886 + 0.737922i \(0.264193\pi\)
\(24\) 2.04319e6 1.25707
\(25\) −1.87365e6 −0.959309
\(26\) 5.05356e6 2.16879
\(27\) 531441. 0.192450
\(28\) −1.35425e7 −4.16379
\(29\) 1.59230e6 0.418056 0.209028 0.977910i \(-0.432970\pi\)
0.209028 + 0.977910i \(0.432970\pi\)
\(30\) −926369. −0.208804
\(31\) 3.75720e6 0.730696 0.365348 0.930871i \(-0.380950\pi\)
0.365348 + 0.930871i \(0.380950\pi\)
\(32\) 5.04944e6 0.851272
\(33\) 3.08233e6 0.452446
\(34\) 1.96207e7 2.51802
\(35\) 3.36732e6 0.379296
\(36\) 7.43874e6 0.738139
\(37\) 1.86388e7 1.63497 0.817485 0.575950i \(-0.195368\pi\)
0.817485 + 0.575950i \(0.195368\pi\)
\(38\) 4.81725e6 0.374777
\(39\) 1.00901e7 0.698403
\(40\) −7.11109e6 −0.439204
\(41\) 223048. 0.0123274 0.00616370 0.999981i \(-0.498038\pi\)
0.00616370 + 0.999981i \(0.498038\pi\)
\(42\) −3.92502e7 −1.94635
\(43\) 9.66466e6 0.431101 0.215550 0.976493i \(-0.430845\pi\)
0.215550 + 0.976493i \(0.430845\pi\)
\(44\) 4.31443e7 1.73535
\(45\) −1.84962e6 −0.0672398
\(46\) 7.34889e7 2.41998
\(47\) −2.98480e6 −0.0892227 −0.0446113 0.999004i \(-0.514205\pi\)
−0.0446113 + 0.999004i \(0.514205\pi\)
\(48\) 3.58684e7 0.975274
\(49\) 1.02320e8 2.53557
\(50\) −7.60107e7 −1.71993
\(51\) 3.91754e7 0.810863
\(52\) 1.41235e8 2.67871
\(53\) −3.40106e7 −0.592070 −0.296035 0.955177i \(-0.595664\pi\)
−0.296035 + 0.955177i \(0.595664\pi\)
\(54\) 2.15596e7 0.345040
\(55\) −1.07277e7 −0.158079
\(56\) −3.01297e8 −4.09401
\(57\) 9.61829e6 0.120687
\(58\) 6.45968e7 0.749524
\(59\) −1.21174e7 −0.130189
\(60\) −2.58897e7 −0.257897
\(61\) −1.41279e8 −1.30645 −0.653225 0.757164i \(-0.726584\pi\)
−0.653225 + 0.757164i \(0.726584\pi\)
\(62\) 1.52423e8 1.31005
\(63\) −7.83684e7 −0.626771
\(64\) −2.18769e7 −0.162996
\(65\) −3.51176e7 −0.244014
\(66\) 1.25045e8 0.811181
\(67\) 2.24453e7 0.136078 0.0680390 0.997683i \(-0.478326\pi\)
0.0680390 + 0.997683i \(0.478326\pi\)
\(68\) 5.48350e8 3.11005
\(69\) 1.46731e8 0.779291
\(70\) 1.36606e8 0.680031
\(71\) −2.18355e8 −1.01977 −0.509884 0.860243i \(-0.670312\pi\)
−0.509884 + 0.860243i \(0.670312\pi\)
\(72\) 1.65498e8 0.725767
\(73\) −2.38222e8 −0.981815 −0.490907 0.871212i \(-0.663335\pi\)
−0.490907 + 0.871212i \(0.663335\pi\)
\(74\) 7.56143e8 2.93130
\(75\) −1.51766e8 −0.553857
\(76\) 1.34630e8 0.462893
\(77\) −4.54533e8 −1.47352
\(78\) 4.09339e8 1.25215
\(79\) −4.97164e7 −0.143608 −0.0718038 0.997419i \(-0.522876\pi\)
−0.0718038 + 0.997419i \(0.522876\pi\)
\(80\) −1.24836e8 −0.340749
\(81\) 4.30467e7 0.111111
\(82\) 9.04867e6 0.0221015
\(83\) −5.31042e8 −1.22822 −0.614112 0.789219i \(-0.710486\pi\)
−0.614112 + 0.789219i \(0.710486\pi\)
\(84\) −1.09695e9 −2.40397
\(85\) −1.36346e8 −0.283306
\(86\) 3.92078e8 0.772912
\(87\) 1.28976e8 0.241365
\(88\) 9.59882e8 1.70626
\(89\) −1.52080e6 −0.00256931 −0.00128466 0.999999i \(-0.500409\pi\)
−0.00128466 + 0.999999i \(0.500409\pi\)
\(90\) −7.50359e7 −0.120553
\(91\) −1.48793e9 −2.27455
\(92\) 2.05383e9 2.98896
\(93\) 3.04333e8 0.421867
\(94\) −1.21088e8 −0.159966
\(95\) −3.34754e7 −0.0421667
\(96\) 4.09005e8 0.491482
\(97\) 1.14057e9 1.30812 0.654061 0.756442i \(-0.273064\pi\)
0.654061 + 0.756442i \(0.273064\pi\)
\(98\) 4.15092e9 4.54598
\(99\) 2.49669e8 0.261220
\(100\) −2.12431e9 −2.12431
\(101\) 4.02295e8 0.384679 0.192340 0.981328i \(-0.438392\pi\)
0.192340 + 0.981328i \(0.438392\pi\)
\(102\) 1.58928e9 1.45378
\(103\) 1.17667e9 1.03012 0.515058 0.857155i \(-0.327770\pi\)
0.515058 + 0.857155i \(0.327770\pi\)
\(104\) 3.14221e9 2.63381
\(105\) 2.72753e8 0.218986
\(106\) −1.37975e9 −1.06151
\(107\) 1.91003e8 0.140869 0.0704343 0.997516i \(-0.477561\pi\)
0.0704343 + 0.997516i \(0.477561\pi\)
\(108\) 6.02538e8 0.426165
\(109\) −1.51121e9 −1.02543 −0.512715 0.858559i \(-0.671360\pi\)
−0.512715 + 0.858559i \(0.671360\pi\)
\(110\) −4.35204e8 −0.283417
\(111\) 1.50974e9 0.943951
\(112\) −5.28930e9 −3.17627
\(113\) 2.19941e8 0.126897 0.0634487 0.997985i \(-0.479790\pi\)
0.0634487 + 0.997985i \(0.479790\pi\)
\(114\) 3.90197e8 0.216377
\(115\) −5.10679e8 −0.272275
\(116\) 1.80532e9 0.925750
\(117\) 8.17300e8 0.403223
\(118\) −4.91580e8 −0.233413
\(119\) −5.77696e9 −2.64082
\(120\) −5.75999e8 −0.253575
\(121\) −9.09882e8 −0.385879
\(122\) −5.73143e9 −2.34231
\(123\) 1.80669e7 0.00711723
\(124\) 4.25984e9 1.61807
\(125\) 1.07881e9 0.395231
\(126\) −3.17927e9 −1.12372
\(127\) 3.82328e9 1.30413 0.652063 0.758165i \(-0.273904\pi\)
0.652063 + 0.758165i \(0.273904\pi\)
\(128\) −3.47282e9 −1.14350
\(129\) 7.82838e8 0.248896
\(130\) −1.42466e9 −0.437487
\(131\) −9.03851e7 −0.0268149 −0.0134074 0.999910i \(-0.504268\pi\)
−0.0134074 + 0.999910i \(0.504268\pi\)
\(132\) 3.49469e9 1.00190
\(133\) −1.41835e9 −0.393053
\(134\) 9.10565e8 0.243972
\(135\) −1.49819e8 −0.0388209
\(136\) 1.21998e10 3.05793
\(137\) −6.57593e9 −1.59483 −0.797416 0.603430i \(-0.793800\pi\)
−0.797416 + 0.603430i \(0.793800\pi\)
\(138\) 5.95260e9 1.39717
\(139\) −4.80391e9 −1.09151 −0.545756 0.837944i \(-0.683757\pi\)
−0.545756 + 0.837944i \(0.683757\pi\)
\(140\) 3.81780e9 0.839918
\(141\) −2.41769e8 −0.0515127
\(142\) −8.85829e9 −1.82832
\(143\) 4.74030e9 0.947968
\(144\) 2.90534e9 0.563075
\(145\) −4.48888e8 −0.0843300
\(146\) −9.66426e9 −1.76028
\(147\) 8.28788e9 1.46391
\(148\) 2.11323e10 3.62051
\(149\) 3.61683e9 0.601159 0.300580 0.953757i \(-0.402820\pi\)
0.300580 + 0.953757i \(0.402820\pi\)
\(150\) −6.15687e9 −0.993000
\(151\) 1.27313e10 1.99286 0.996429 0.0844386i \(-0.0269097\pi\)
0.996429 + 0.0844386i \(0.0269097\pi\)
\(152\) 2.99527e9 0.455135
\(153\) 3.17321e9 0.468152
\(154\) −1.84396e10 −2.64185
\(155\) −1.05920e9 −0.147396
\(156\) 1.14400e10 1.54655
\(157\) −1.14915e10 −1.50948 −0.754739 0.656026i \(-0.772236\pi\)
−0.754739 + 0.656026i \(0.772236\pi\)
\(158\) −2.01690e9 −0.257471
\(159\) −2.75486e9 −0.341832
\(160\) −1.42350e9 −0.171718
\(161\) −2.16375e10 −2.53799
\(162\) 1.74633e9 0.199209
\(163\) −9.49867e9 −1.05395 −0.526973 0.849882i \(-0.676673\pi\)
−0.526973 + 0.849882i \(0.676673\pi\)
\(164\) 2.52888e8 0.0272980
\(165\) −8.68944e8 −0.0912671
\(166\) −2.15434e10 −2.20206
\(167\) −9.02614e9 −0.898004 −0.449002 0.893531i \(-0.648220\pi\)
−0.449002 + 0.893531i \(0.648220\pi\)
\(168\) −2.44051e10 −2.36368
\(169\) 4.91305e9 0.463299
\(170\) −5.53130e9 −0.507934
\(171\) 7.79081e8 0.0696787
\(172\) 1.09576e10 0.954636
\(173\) 6.93115e9 0.588299 0.294150 0.955759i \(-0.404964\pi\)
0.294150 + 0.955759i \(0.404964\pi\)
\(174\) 5.23234e9 0.432738
\(175\) 2.23800e10 1.80380
\(176\) 1.68508e10 1.32378
\(177\) −9.81506e8 −0.0751646
\(178\) −6.16962e7 −0.00460647
\(179\) 1.90308e10 1.38554 0.692769 0.721160i \(-0.256391\pi\)
0.692769 + 0.721160i \(0.256391\pi\)
\(180\) −2.09707e9 −0.148897
\(181\) 1.08861e10 0.753906 0.376953 0.926232i \(-0.376972\pi\)
0.376953 + 0.926232i \(0.376972\pi\)
\(182\) −6.03627e10 −4.07800
\(183\) −1.14436e10 −0.754279
\(184\) 4.56940e10 2.93886
\(185\) −5.25449e9 −0.329805
\(186\) 1.23463e10 0.756358
\(187\) 1.84044e10 1.10061
\(188\) −3.38411e9 −0.197576
\(189\) −6.34784e9 −0.361866
\(190\) −1.35804e9 −0.0755998
\(191\) 2.02801e10 1.10261 0.551303 0.834305i \(-0.314131\pi\)
0.551303 + 0.834305i \(0.314131\pi\)
\(192\) −1.77203e9 −0.0941056
\(193\) 3.01806e9 0.156574 0.0782869 0.996931i \(-0.475055\pi\)
0.0782869 + 0.996931i \(0.475055\pi\)
\(194\) 4.62708e10 2.34530
\(195\) −2.84452e9 −0.140881
\(196\) 1.16008e11 5.61481
\(197\) −2.02898e10 −0.959797 −0.479899 0.877324i \(-0.659327\pi\)
−0.479899 + 0.877324i \(0.659327\pi\)
\(198\) 1.01286e10 0.468335
\(199\) −1.10122e10 −0.497777 −0.248888 0.968532i \(-0.580065\pi\)
−0.248888 + 0.968532i \(0.580065\pi\)
\(200\) −4.72620e10 −2.08871
\(201\) 1.81807e9 0.0785647
\(202\) 1.63204e10 0.689684
\(203\) −1.90194e10 −0.786075
\(204\) 4.44163e10 1.79559
\(205\) −6.28799e7 −0.00248668
\(206\) 4.77353e10 1.84688
\(207\) 1.18852e10 0.449924
\(208\) 5.51618e10 2.04340
\(209\) 4.51863e9 0.163813
\(210\) 1.10651e10 0.392616
\(211\) 3.97643e10 1.38109 0.690546 0.723289i \(-0.257371\pi\)
0.690546 + 0.723289i \(0.257371\pi\)
\(212\) −3.85606e10 −1.31109
\(213\) −1.76868e10 −0.588763
\(214\) 7.74867e9 0.252560
\(215\) −2.72458e9 −0.0869614
\(216\) 1.34054e10 0.419022
\(217\) −4.48782e10 −1.37394
\(218\) −6.13072e10 −1.83847
\(219\) −1.92960e10 −0.566851
\(220\) −1.21629e10 −0.350053
\(221\) 6.02476e10 1.69893
\(222\) 6.12475e10 1.69239
\(223\) 7.26492e10 1.96725 0.983624 0.180234i \(-0.0576854\pi\)
0.983624 + 0.180234i \(0.0576854\pi\)
\(224\) −6.03135e10 −1.60066
\(225\) −1.22930e10 −0.319770
\(226\) 8.92260e9 0.227512
\(227\) 2.91674e10 0.729092 0.364546 0.931185i \(-0.381224\pi\)
0.364546 + 0.931185i \(0.381224\pi\)
\(228\) 1.09050e10 0.267252
\(229\) −7.04501e10 −1.69286 −0.846432 0.532497i \(-0.821254\pi\)
−0.846432 + 0.532497i \(0.821254\pi\)
\(230\) −2.07174e10 −0.488157
\(231\) −3.68172e10 −0.850739
\(232\) 4.01651e10 0.910234
\(233\) −2.66720e10 −0.592863 −0.296432 0.955054i \(-0.595797\pi\)
−0.296432 + 0.955054i \(0.595797\pi\)
\(234\) 3.31564e10 0.722930
\(235\) 8.41450e8 0.0179980
\(236\) −1.37384e10 −0.288292
\(237\) −4.02703e9 −0.0829119
\(238\) −2.34361e11 −4.73467
\(239\) −5.20140e10 −1.03117 −0.515584 0.856839i \(-0.672425\pi\)
−0.515584 + 0.856839i \(0.672425\pi\)
\(240\) −1.01117e10 −0.196732
\(241\) 9.31533e10 1.77878 0.889389 0.457152i \(-0.151130\pi\)
0.889389 + 0.457152i \(0.151130\pi\)
\(242\) −3.69123e10 −0.691834
\(243\) 3.48678e9 0.0641500
\(244\) −1.60179e11 −2.89302
\(245\) −2.88451e10 −0.511474
\(246\) 7.32942e8 0.0127603
\(247\) 1.47919e10 0.252865
\(248\) 9.47737e10 1.59095
\(249\) −4.30144e10 −0.709116
\(250\) 4.37655e10 0.708601
\(251\) 1.01318e10 0.161122 0.0805612 0.996750i \(-0.474329\pi\)
0.0805612 + 0.996750i \(0.474329\pi\)
\(252\) −8.88526e10 −1.38793
\(253\) 6.89334e10 1.05776
\(254\) 1.55104e11 2.33814
\(255\) −1.10440e10 −0.163567
\(256\) −1.29685e11 −1.88717
\(257\) −9.92179e10 −1.41870 −0.709351 0.704856i \(-0.751012\pi\)
−0.709351 + 0.704856i \(0.751012\pi\)
\(258\) 3.17583e10 0.446241
\(259\) −2.22633e11 −3.07425
\(260\) −3.98156e10 −0.540348
\(261\) 1.04471e10 0.139352
\(262\) −3.66676e9 −0.0480759
\(263\) −1.04898e11 −1.35197 −0.675983 0.736917i \(-0.736281\pi\)
−0.675983 + 0.736917i \(0.736281\pi\)
\(264\) 7.77504e10 0.985111
\(265\) 9.58798e9 0.119432
\(266\) −5.75400e10 −0.704697
\(267\) −1.23185e8 −0.00148339
\(268\) 2.54480e10 0.301334
\(269\) −1.39602e11 −1.62557 −0.812785 0.582563i \(-0.802050\pi\)
−0.812785 + 0.582563i \(0.802050\pi\)
\(270\) −6.07791e9 −0.0696012
\(271\) −4.91722e10 −0.553807 −0.276903 0.960898i \(-0.589308\pi\)
−0.276903 + 0.960898i \(0.589308\pi\)
\(272\) 2.14168e11 2.37244
\(273\) −1.20522e11 −1.31321
\(274\) −2.66774e11 −2.85934
\(275\) −7.12989e10 −0.751771
\(276\) 1.66360e11 1.72567
\(277\) −3.34988e10 −0.341878 −0.170939 0.985282i \(-0.554680\pi\)
−0.170939 + 0.985282i \(0.554680\pi\)
\(278\) −1.94886e11 −1.95695
\(279\) 2.46510e10 0.243565
\(280\) 8.49391e10 0.825841
\(281\) 1.83976e11 1.76028 0.880140 0.474714i \(-0.157449\pi\)
0.880140 + 0.474714i \(0.157449\pi\)
\(282\) −9.80814e9 −0.0923561
\(283\) −9.61863e10 −0.891404 −0.445702 0.895181i \(-0.647046\pi\)
−0.445702 + 0.895181i \(0.647046\pi\)
\(284\) −2.47567e11 −2.25819
\(285\) −2.71151e9 −0.0243449
\(286\) 1.92306e11 1.69959
\(287\) −2.66422e9 −0.0231794
\(288\) 3.31294e10 0.283757
\(289\) 1.15327e11 0.972498
\(290\) −1.82106e10 −0.151194
\(291\) 9.23859e10 0.755244
\(292\) −2.70092e11 −2.17415
\(293\) −2.03250e11 −1.61111 −0.805556 0.592519i \(-0.798134\pi\)
−0.805556 + 0.592519i \(0.798134\pi\)
\(294\) 3.36225e11 2.62462
\(295\) 3.41602e9 0.0262616
\(296\) 4.70155e11 3.55982
\(297\) 2.02232e10 0.150815
\(298\) 1.46728e11 1.07781
\(299\) 2.25656e11 1.63278
\(300\) −1.72069e11 −1.22647
\(301\) −1.15440e11 −0.810604
\(302\) 5.16486e11 3.57295
\(303\) 3.25859e10 0.222095
\(304\) 5.25823e10 0.353109
\(305\) 3.98281e10 0.263536
\(306\) 1.28731e11 0.839340
\(307\) 7.47524e10 0.480289 0.240144 0.970737i \(-0.422805\pi\)
0.240144 + 0.970737i \(0.422805\pi\)
\(308\) −5.15341e11 −3.26299
\(309\) 9.53101e10 0.594738
\(310\) −4.29698e10 −0.264263
\(311\) −1.42843e11 −0.865841 −0.432921 0.901432i \(-0.642517\pi\)
−0.432921 + 0.901432i \(0.642517\pi\)
\(312\) 2.54519e11 1.52063
\(313\) 3.18510e11 1.87574 0.937871 0.346984i \(-0.112794\pi\)
0.937871 + 0.346984i \(0.112794\pi\)
\(314\) −4.66188e11 −2.70631
\(315\) 2.20930e10 0.126432
\(316\) −5.63675e10 −0.318007
\(317\) −1.73974e11 −0.967647 −0.483823 0.875166i \(-0.660752\pi\)
−0.483823 + 0.875166i \(0.660752\pi\)
\(318\) −1.11760e11 −0.612863
\(319\) 6.05926e10 0.327613
\(320\) 6.16735e9 0.0328794
\(321\) 1.54713e10 0.0813305
\(322\) −8.77794e11 −4.55031
\(323\) 5.74303e10 0.293582
\(324\) 4.88056e10 0.246046
\(325\) −2.33400e11 −1.16045
\(326\) −3.85344e11 −1.88960
\(327\) −1.22408e11 −0.592032
\(328\) 5.62629e9 0.0268405
\(329\) 3.56522e10 0.167766
\(330\) −3.52515e10 −0.163631
\(331\) 1.01046e11 0.462692 0.231346 0.972872i \(-0.425687\pi\)
0.231346 + 0.972872i \(0.425687\pi\)
\(332\) −6.02086e11 −2.71980
\(333\) 1.22289e11 0.544990
\(334\) −3.66175e11 −1.61001
\(335\) −6.32758e9 −0.0274496
\(336\) −4.28433e11 −1.83382
\(337\) −2.47111e11 −1.04366 −0.521828 0.853051i \(-0.674750\pi\)
−0.521828 + 0.853051i \(0.674750\pi\)
\(338\) 1.99314e11 0.830639
\(339\) 1.78152e10 0.0732642
\(340\) −1.54586e11 −0.627358
\(341\) 1.42974e11 0.572616
\(342\) 3.16060e10 0.124926
\(343\) −7.40157e11 −2.88736
\(344\) 2.43787e11 0.938636
\(345\) −4.13650e10 −0.157198
\(346\) 2.81185e11 1.05475
\(347\) −1.26269e11 −0.467536 −0.233768 0.972292i \(-0.575106\pi\)
−0.233768 + 0.972292i \(0.575106\pi\)
\(348\) 1.46231e11 0.534482
\(349\) 4.17641e11 1.50692 0.753458 0.657496i \(-0.228384\pi\)
0.753458 + 0.657496i \(0.228384\pi\)
\(350\) 9.07916e11 3.23400
\(351\) 6.62013e10 0.232801
\(352\) 1.92149e11 0.667107
\(353\) 3.55099e10 0.121720 0.0608602 0.998146i \(-0.480616\pi\)
0.0608602 + 0.998146i \(0.480616\pi\)
\(354\) −3.98180e10 −0.134761
\(355\) 6.15569e10 0.205707
\(356\) −1.72426e9 −0.00568953
\(357\) −4.67934e11 −1.52468
\(358\) 7.72045e11 2.48410
\(359\) 3.59038e11 1.14082 0.570408 0.821362i \(-0.306785\pi\)
0.570408 + 0.821362i \(0.306785\pi\)
\(360\) −4.66559e10 −0.146401
\(361\) −3.08587e11 −0.956304
\(362\) 4.41628e11 1.35166
\(363\) −7.37004e10 −0.222787
\(364\) −1.68699e12 −5.03681
\(365\) 6.71576e10 0.198051
\(366\) −4.64246e11 −1.35233
\(367\) 1.15361e11 0.331941 0.165971 0.986131i \(-0.446924\pi\)
0.165971 + 0.986131i \(0.446924\pi\)
\(368\) 8.02163e11 2.28007
\(369\) 1.46342e9 0.00410913
\(370\) −2.13165e11 −0.591301
\(371\) 4.06242e11 1.11328
\(372\) 3.45047e11 0.934190
\(373\) −4.98354e11 −1.33306 −0.666528 0.745480i \(-0.732220\pi\)
−0.666528 + 0.745480i \(0.732220\pi\)
\(374\) 7.46636e11 1.97327
\(375\) 8.73838e10 0.228187
\(376\) −7.52904e10 −0.194265
\(377\) 1.98352e11 0.505709
\(378\) −2.57521e11 −0.648782
\(379\) 3.12014e11 0.776780 0.388390 0.921495i \(-0.373031\pi\)
0.388390 + 0.921495i \(0.373031\pi\)
\(380\) −3.79538e10 −0.0933746
\(381\) 3.09686e11 0.752937
\(382\) 8.22728e11 1.97684
\(383\) 2.71390e11 0.644466 0.322233 0.946660i \(-0.395567\pi\)
0.322233 + 0.946660i \(0.395567\pi\)
\(384\) −2.81298e11 −0.660202
\(385\) 1.28138e11 0.297238
\(386\) 1.22437e11 0.280718
\(387\) 6.34099e10 0.143700
\(388\) 1.29315e12 2.89673
\(389\) −4.06550e11 −0.900204 −0.450102 0.892977i \(-0.648612\pi\)
−0.450102 + 0.892977i \(0.648612\pi\)
\(390\) −1.15397e11 −0.252583
\(391\) 8.76121e11 1.89570
\(392\) 2.58096e12 5.52071
\(393\) −7.32119e9 −0.0154816
\(394\) −8.23121e11 −1.72080
\(395\) 1.40156e10 0.0289685
\(396\) 2.83070e11 0.578449
\(397\) −2.24286e11 −0.453153 −0.226576 0.973993i \(-0.572753\pi\)
−0.226576 + 0.973993i \(0.572753\pi\)
\(398\) −4.46745e11 −0.892454
\(399\) −1.14886e11 −0.226929
\(400\) −8.29690e11 −1.62049
\(401\) 2.88476e11 0.557135 0.278568 0.960417i \(-0.410140\pi\)
0.278568 + 0.960417i \(0.410140\pi\)
\(402\) 7.37558e10 0.140857
\(403\) 4.68032e11 0.883900
\(404\) 4.56115e11 0.851840
\(405\) −1.21354e10 −0.0224133
\(406\) −7.71583e11 −1.40934
\(407\) 7.09270e11 1.28126
\(408\) 9.88182e11 1.76549
\(409\) −7.08376e11 −1.25173 −0.625863 0.779933i \(-0.715253\pi\)
−0.625863 + 0.779933i \(0.715253\pi\)
\(410\) −2.55092e9 −0.00445831
\(411\) −5.32650e11 −0.920776
\(412\) 1.33408e12 2.28111
\(413\) 1.44737e11 0.244796
\(414\) 4.82161e11 0.806659
\(415\) 1.49707e11 0.247757
\(416\) 6.29006e11 1.02976
\(417\) −3.89117e11 −0.630184
\(418\) 1.83313e11 0.293697
\(419\) −2.04860e11 −0.324709 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(420\) 3.09242e11 0.484927
\(421\) −2.91573e11 −0.452353 −0.226176 0.974086i \(-0.572623\pi\)
−0.226176 + 0.974086i \(0.572623\pi\)
\(422\) 1.61317e12 2.47613
\(423\) −1.95833e10 −0.0297409
\(424\) −8.57902e11 −1.28911
\(425\) −9.06186e11 −1.34731
\(426\) −7.17522e11 −1.05558
\(427\) 1.68752e12 2.45653
\(428\) 2.16556e11 0.311942
\(429\) 3.83964e11 0.547309
\(430\) −1.10531e11 −0.155911
\(431\) −1.09016e12 −1.52175 −0.760874 0.648900i \(-0.775229\pi\)
−0.760874 + 0.648900i \(0.775229\pi\)
\(432\) 2.35333e11 0.325091
\(433\) −1.27445e12 −1.74232 −0.871162 0.490997i \(-0.836633\pi\)
−0.871162 + 0.490997i \(0.836633\pi\)
\(434\) −1.82063e12 −2.46330
\(435\) −3.63599e10 −0.0486879
\(436\) −1.71338e12 −2.27073
\(437\) 2.15104e11 0.282151
\(438\) −7.82805e11 −1.01630
\(439\) 3.76534e11 0.483853 0.241926 0.970295i \(-0.422221\pi\)
0.241926 + 0.970295i \(0.422221\pi\)
\(440\) −2.70602e11 −0.344186
\(441\) 6.71318e11 0.845191
\(442\) 2.44414e12 3.04597
\(443\) −9.96474e11 −1.22928 −0.614638 0.788810i \(-0.710698\pi\)
−0.614638 + 0.788810i \(0.710698\pi\)
\(444\) 1.71172e12 2.09030
\(445\) 4.28731e8 0.000518281 0
\(446\) 2.94725e12 3.52704
\(447\) 2.92963e11 0.347079
\(448\) 2.61311e11 0.306483
\(449\) 1.48027e11 0.171883 0.0859416 0.996300i \(-0.472610\pi\)
0.0859416 + 0.996300i \(0.472610\pi\)
\(450\) −4.98706e11 −0.573309
\(451\) 8.48776e9 0.00966047
\(452\) 2.49365e11 0.281004
\(453\) 1.03123e12 1.15058
\(454\) 1.18327e12 1.30717
\(455\) 4.19465e11 0.458822
\(456\) 2.42617e11 0.262772
\(457\) −8.19298e11 −0.878657 −0.439328 0.898327i \(-0.644784\pi\)
−0.439328 + 0.898327i \(0.644784\pi\)
\(458\) −2.85804e12 −3.03510
\(459\) 2.57030e11 0.270288
\(460\) −5.78999e11 −0.602931
\(461\) 1.53125e12 1.57904 0.789518 0.613727i \(-0.210331\pi\)
0.789518 + 0.613727i \(0.210331\pi\)
\(462\) −1.49361e12 −1.52527
\(463\) −5.77069e11 −0.583598 −0.291799 0.956480i \(-0.594254\pi\)
−0.291799 + 0.956480i \(0.594254\pi\)
\(464\) 7.05103e11 0.706190
\(465\) −8.57950e10 −0.0850989
\(466\) −1.08204e12 −1.06293
\(467\) −4.88015e11 −0.474796 −0.237398 0.971412i \(-0.576295\pi\)
−0.237398 + 0.971412i \(0.576295\pi\)
\(468\) 9.26640e11 0.892904
\(469\) −2.68099e11 −0.255869
\(470\) 3.41362e10 0.0322682
\(471\) −9.30808e11 −0.871497
\(472\) −3.05655e11 −0.283461
\(473\) 3.67774e11 0.337836
\(474\) −1.63369e11 −0.148651
\(475\) −2.22485e11 −0.200530
\(476\) −6.54981e12 −5.84787
\(477\) −2.23144e11 −0.197357
\(478\) −2.11011e12 −1.84876
\(479\) 2.02874e12 1.76083 0.880413 0.474207i \(-0.157265\pi\)
0.880413 + 0.474207i \(0.157265\pi\)
\(480\) −1.15303e11 −0.0991415
\(481\) 2.32182e12 1.97777
\(482\) 3.77906e12 3.18913
\(483\) −1.75264e12 −1.46531
\(484\) −1.03161e12 −0.854496
\(485\) −3.21539e11 −0.263874
\(486\) 1.41453e11 0.115013
\(487\) −3.85405e11 −0.310482 −0.155241 0.987877i \(-0.549615\pi\)
−0.155241 + 0.987877i \(0.549615\pi\)
\(488\) −3.56370e12 −2.84454
\(489\) −7.69392e11 −0.608496
\(490\) −1.17019e12 −0.917012
\(491\) −5.78610e11 −0.449282 −0.224641 0.974442i \(-0.572121\pi\)
−0.224641 + 0.974442i \(0.572121\pi\)
\(492\) 2.04839e10 0.0157605
\(493\) 7.70112e11 0.587141
\(494\) 6.00082e11 0.453356
\(495\) −7.03845e10 −0.0526931
\(496\) 1.66376e12 1.23431
\(497\) 2.60816e12 1.91748
\(498\) −1.74502e12 −1.27136
\(499\) −2.53831e12 −1.83271 −0.916353 0.400372i \(-0.868881\pi\)
−0.916353 + 0.400372i \(0.868881\pi\)
\(500\) 1.22314e12 0.875206
\(501\) −7.31118e11 −0.518463
\(502\) 4.11030e11 0.288873
\(503\) 2.31730e12 1.61409 0.807043 0.590492i \(-0.201066\pi\)
0.807043 + 0.590492i \(0.201066\pi\)
\(504\) −1.97681e12 −1.36467
\(505\) −1.13412e11 −0.0775973
\(506\) 2.79651e12 1.89644
\(507\) 3.97957e11 0.267486
\(508\) 4.33476e12 2.88788
\(509\) 1.52851e12 1.00934 0.504671 0.863312i \(-0.331614\pi\)
0.504671 + 0.863312i \(0.331614\pi\)
\(510\) −4.48035e11 −0.293256
\(511\) 2.84547e12 1.84612
\(512\) −3.48301e12 −2.23996
\(513\) 6.31056e10 0.0402290
\(514\) −4.02509e12 −2.54356
\(515\) −3.31716e11 −0.207795
\(516\) 8.87567e11 0.551160
\(517\) −1.13582e11 −0.0699202
\(518\) −9.03181e12 −5.51177
\(519\) 5.61424e11 0.339655
\(520\) −8.85825e11 −0.531292
\(521\) −5.49591e11 −0.326791 −0.163396 0.986561i \(-0.552245\pi\)
−0.163396 + 0.986561i \(0.552245\pi\)
\(522\) 4.23820e11 0.249841
\(523\) −1.21125e12 −0.707905 −0.353953 0.935263i \(-0.615163\pi\)
−0.353953 + 0.935263i \(0.615163\pi\)
\(524\) −1.02477e11 −0.0593793
\(525\) 1.81278e12 1.04142
\(526\) −4.25552e12 −2.42391
\(527\) 1.81716e12 1.02623
\(528\) 1.36492e12 0.764282
\(529\) 1.48034e12 0.821884
\(530\) 3.88967e11 0.214127
\(531\) −7.95020e10 −0.0433963
\(532\) −1.60810e12 −0.870384
\(533\) 2.77850e10 0.0149121
\(534\) −4.99739e9 −0.00265955
\(535\) −5.38461e10 −0.0284159
\(536\) 5.66172e11 0.296283
\(537\) 1.54149e12 0.799940
\(538\) −5.66340e12 −2.91445
\(539\) 3.89361e12 1.98702
\(540\) −1.69862e11 −0.0859657
\(541\) −1.18365e12 −0.594067 −0.297033 0.954867i \(-0.595997\pi\)
−0.297033 + 0.954867i \(0.595997\pi\)
\(542\) −1.99483e12 −0.992908
\(543\) 8.81771e11 0.435268
\(544\) 2.44215e12 1.19557
\(545\) 4.26028e11 0.206849
\(546\) −4.88938e12 −2.35444
\(547\) −1.81035e12 −0.864609 −0.432305 0.901728i \(-0.642300\pi\)
−0.432305 + 0.901728i \(0.642300\pi\)
\(548\) −7.45567e12 −3.53162
\(549\) −9.26930e11 −0.435483
\(550\) −2.89247e12 −1.34784
\(551\) 1.89077e11 0.0873888
\(552\) 3.70121e12 1.69675
\(553\) 5.93841e11 0.270027
\(554\) −1.35899e12 −0.612946
\(555\) −4.25614e11 −0.190413
\(556\) −5.44658e12 −2.41706
\(557\) 2.97827e12 1.31104 0.655519 0.755178i \(-0.272450\pi\)
0.655519 + 0.755178i \(0.272450\pi\)
\(558\) 1.00005e12 0.436683
\(559\) 1.20392e12 0.521489
\(560\) 1.49111e12 0.640715
\(561\) 1.49076e12 0.635440
\(562\) 7.46356e12 3.15597
\(563\) 1.21487e12 0.509616 0.254808 0.966992i \(-0.417988\pi\)
0.254808 + 0.966992i \(0.417988\pi\)
\(564\) −2.74113e11 −0.114071
\(565\) −6.20038e10 −0.0255977
\(566\) −3.90211e12 −1.59818
\(567\) −5.14175e11 −0.208924
\(568\) −5.50792e12 −2.22034
\(569\) 4.43625e12 1.77423 0.887116 0.461546i \(-0.152705\pi\)
0.887116 + 0.461546i \(0.152705\pi\)
\(570\) −1.10001e11 −0.0436476
\(571\) −7.36560e11 −0.289965 −0.144983 0.989434i \(-0.546313\pi\)
−0.144983 + 0.989434i \(0.546313\pi\)
\(572\) 5.37446e12 2.09920
\(573\) 1.64269e12 0.636590
\(574\) −1.08083e11 −0.0415578
\(575\) −3.39410e12 −1.29485
\(576\) −1.43534e11 −0.0543319
\(577\) −3.15376e12 −1.18451 −0.592253 0.805752i \(-0.701761\pi\)
−0.592253 + 0.805752i \(0.701761\pi\)
\(578\) 4.67859e12 1.74357
\(579\) 2.44462e11 0.0903980
\(580\) −5.08941e11 −0.186742
\(581\) 6.34308e12 2.30945
\(582\) 3.74793e12 1.35406
\(583\) −1.29422e12 −0.463981
\(584\) −6.00905e12 −2.13771
\(585\) −2.30406e11 −0.0813379
\(586\) −8.24549e12 −2.88853
\(587\) −5.09156e12 −1.77002 −0.885012 0.465567i \(-0.845850\pi\)
−0.885012 + 0.465567i \(0.845850\pi\)
\(588\) 9.39664e12 3.24171
\(589\) 4.46146e11 0.152742
\(590\) 1.38582e11 0.0470840
\(591\) −1.64347e12 −0.554139
\(592\) 8.25362e12 2.76183
\(593\) 3.55550e12 1.18074 0.590371 0.807132i \(-0.298982\pi\)
0.590371 + 0.807132i \(0.298982\pi\)
\(594\) 8.20418e11 0.270394
\(595\) 1.62859e12 0.532704
\(596\) 4.10069e12 1.33122
\(597\) −8.91987e11 −0.287392
\(598\) 9.15447e12 2.92737
\(599\) −2.80603e12 −0.890576 −0.445288 0.895387i \(-0.646899\pi\)
−0.445288 + 0.895387i \(0.646899\pi\)
\(600\) −3.82822e12 −1.20591
\(601\) 3.34060e12 1.04446 0.522228 0.852806i \(-0.325101\pi\)
0.522228 + 0.852806i \(0.325101\pi\)
\(602\) −4.68321e12 −1.45331
\(603\) 1.47263e11 0.0453594
\(604\) 1.44345e13 4.41302
\(605\) 2.56506e11 0.0778393
\(606\) 1.32195e12 0.398189
\(607\) 5.25103e12 1.56998 0.784992 0.619506i \(-0.212667\pi\)
0.784992 + 0.619506i \(0.212667\pi\)
\(608\) 5.99592e11 0.177947
\(609\) −1.54057e12 −0.453841
\(610\) 1.61576e12 0.472489
\(611\) −3.71815e11 −0.107930
\(612\) 3.59772e12 1.03668
\(613\) −3.05318e11 −0.0873335 −0.0436668 0.999046i \(-0.513904\pi\)
−0.0436668 + 0.999046i \(0.513904\pi\)
\(614\) 3.03257e12 0.861100
\(615\) −5.09327e9 −0.00143568
\(616\) −1.14654e13 −3.20831
\(617\) −3.46151e12 −0.961572 −0.480786 0.876838i \(-0.659649\pi\)
−0.480786 + 0.876838i \(0.659649\pi\)
\(618\) 3.86656e12 1.06629
\(619\) 4.23333e11 0.115897 0.0579487 0.998320i \(-0.481544\pi\)
0.0579487 + 0.998320i \(0.481544\pi\)
\(620\) −1.20090e12 −0.326395
\(621\) 9.62699e11 0.259764
\(622\) −5.79490e12 −1.55235
\(623\) 1.81653e10 0.00483111
\(624\) 4.46811e12 1.17976
\(625\) 3.35534e12 0.879583
\(626\) 1.29214e13 3.36298
\(627\) 3.66009e11 0.0945775
\(628\) −1.30288e13 −3.34261
\(629\) 9.01459e12 2.29624
\(630\) 8.96272e11 0.226677
\(631\) 5.83317e12 1.46478 0.732390 0.680886i \(-0.238405\pi\)
0.732390 + 0.680886i \(0.238405\pi\)
\(632\) −1.25407e12 −0.312677
\(633\) 3.22091e12 0.797373
\(634\) −7.05780e12 −1.73487
\(635\) −1.07783e12 −0.263068
\(636\) −3.12341e12 −0.756957
\(637\) 1.27459e13 3.06720
\(638\) 2.45813e12 0.587371
\(639\) −1.43263e12 −0.339923
\(640\) 9.79028e11 0.230667
\(641\) −3.63777e12 −0.851087 −0.425543 0.904938i \(-0.639917\pi\)
−0.425543 + 0.904938i \(0.639917\pi\)
\(642\) 6.27642e11 0.145816
\(643\) 4.65808e12 1.07463 0.537313 0.843383i \(-0.319439\pi\)
0.537313 + 0.843383i \(0.319439\pi\)
\(644\) −2.45322e13 −5.62017
\(645\) −2.20691e11 −0.0502072
\(646\) 2.32985e12 0.526358
\(647\) 3.10601e11 0.0696841 0.0348421 0.999393i \(-0.488907\pi\)
0.0348421 + 0.999393i \(0.488907\pi\)
\(648\) 1.08583e12 0.241922
\(649\) −4.61108e11 −0.102024
\(650\) −9.46861e12 −2.08054
\(651\) −3.63513e12 −0.793242
\(652\) −1.07694e13 −2.33388
\(653\) −3.77027e12 −0.811452 −0.405726 0.913995i \(-0.632981\pi\)
−0.405726 + 0.913995i \(0.632981\pi\)
\(654\) −4.96588e12 −1.06144
\(655\) 2.54806e10 0.00540908
\(656\) 9.87702e10 0.0208237
\(657\) −1.56298e12 −0.327272
\(658\) 1.44635e12 0.300785
\(659\) −7.34637e12 −1.51736 −0.758680 0.651463i \(-0.774155\pi\)
−0.758680 + 0.651463i \(0.774155\pi\)
\(660\) −9.85193e11 −0.202103
\(661\) −1.83465e12 −0.373806 −0.186903 0.982378i \(-0.559845\pi\)
−0.186903 + 0.982378i \(0.559845\pi\)
\(662\) 4.09924e12 0.829550
\(663\) 4.88006e12 0.980876
\(664\) −1.33953e13 −2.67422
\(665\) 3.99850e11 0.0792865
\(666\) 4.96105e12 0.977102
\(667\) 2.88444e12 0.564280
\(668\) −1.02337e13 −1.98855
\(669\) 5.88459e12 1.13579
\(670\) −2.56699e11 −0.0492138
\(671\) −5.37615e12 −1.02381
\(672\) −4.88539e12 −0.924140
\(673\) −5.91558e12 −1.11155 −0.555776 0.831332i \(-0.687579\pi\)
−0.555776 + 0.831332i \(0.687579\pi\)
\(674\) −1.00248e13 −1.87115
\(675\) −9.95735e11 −0.184619
\(676\) 5.57033e12 1.02594
\(677\) 2.97452e12 0.544212 0.272106 0.962267i \(-0.412280\pi\)
0.272106 + 0.962267i \(0.412280\pi\)
\(678\) 7.22731e11 0.131354
\(679\) −1.36236e13 −2.45968
\(680\) −3.43926e12 −0.616843
\(681\) 2.36256e12 0.420941
\(682\) 5.80022e12 1.02663
\(683\) 1.10993e13 1.95166 0.975830 0.218529i \(-0.0701259\pi\)
0.975830 + 0.218529i \(0.0701259\pi\)
\(684\) 8.83308e11 0.154298
\(685\) 1.85383e12 0.321709
\(686\) −3.00269e13 −5.17668
\(687\) −5.70646e12 −0.977375
\(688\) 4.27970e12 0.728225
\(689\) −4.23668e12 −0.716208
\(690\) −1.67811e12 −0.281837
\(691\) 1.92510e12 0.321219 0.160609 0.987018i \(-0.448654\pi\)
0.160609 + 0.987018i \(0.448654\pi\)
\(692\) 7.85841e12 1.30274
\(693\) −2.98219e12 −0.491174
\(694\) −5.12252e12 −0.838236
\(695\) 1.35428e12 0.220179
\(696\) 3.25337e12 0.525524
\(697\) 1.07877e11 0.0173133
\(698\) 1.69430e13 2.70172
\(699\) −2.16043e12 −0.342290
\(700\) 2.53740e13 3.99437
\(701\) 8.67559e12 1.35696 0.678481 0.734618i \(-0.262639\pi\)
0.678481 + 0.734618i \(0.262639\pi\)
\(702\) 2.68567e12 0.417384
\(703\) 2.21325e12 0.341768
\(704\) −8.32492e11 −0.127733
\(705\) 6.81575e10 0.0103911
\(706\) 1.44057e12 0.218230
\(707\) −4.80525e12 −0.723317
\(708\) −1.11281e12 −0.166446
\(709\) −8.64020e11 −0.128415 −0.0642075 0.997937i \(-0.520452\pi\)
−0.0642075 + 0.997937i \(0.520452\pi\)
\(710\) 2.49725e12 0.368808
\(711\) −3.26189e11 −0.0478692
\(712\) −3.83615e10 −0.00559417
\(713\) 6.80612e12 0.986273
\(714\) −1.89833e13 −2.73356
\(715\) −1.33634e12 −0.191224
\(716\) 2.15768e13 3.06816
\(717\) −4.21313e12 −0.595345
\(718\) 1.45655e13 2.04534
\(719\) −1.29472e13 −1.80674 −0.903369 0.428864i \(-0.858914\pi\)
−0.903369 + 0.428864i \(0.858914\pi\)
\(720\) −8.19049e11 −0.113583
\(721\) −1.40548e13 −1.93694
\(722\) −1.25188e13 −1.71454
\(723\) 7.54542e12 1.02698
\(724\) 1.23424e13 1.66946
\(725\) −2.98342e12 −0.401045
\(726\) −2.98990e12 −0.399431
\(727\) −8.51037e11 −0.112991 −0.0564955 0.998403i \(-0.517993\pi\)
−0.0564955 + 0.998403i \(0.517993\pi\)
\(728\) −3.75324e13 −4.95239
\(729\) 2.82430e11 0.0370370
\(730\) 2.72447e12 0.355082
\(731\) 4.67429e12 0.605462
\(732\) −1.29745e13 −1.67029
\(733\) 7.42264e12 0.949709 0.474855 0.880064i \(-0.342501\pi\)
0.474855 + 0.880064i \(0.342501\pi\)
\(734\) 4.67999e12 0.595131
\(735\) −2.33645e12 −0.295300
\(736\) 9.14700e12 1.14902
\(737\) 8.54120e11 0.106639
\(738\) 5.93683e10 0.00736718
\(739\) 5.31381e12 0.655399 0.327700 0.944782i \(-0.393727\pi\)
0.327700 + 0.944782i \(0.393727\pi\)
\(740\) −5.95744e12 −0.730326
\(741\) 1.19815e12 0.145991
\(742\) 1.64805e13 1.99597
\(743\) 1.03262e13 1.24306 0.621529 0.783391i \(-0.286512\pi\)
0.621529 + 0.783391i \(0.286512\pi\)
\(744\) 7.67667e12 0.918533
\(745\) −1.01963e12 −0.121266
\(746\) −2.02174e13 −2.39001
\(747\) −3.48417e12 −0.409408
\(748\) 2.08666e13 2.43722
\(749\) −2.28146e12 −0.264877
\(750\) 3.54501e12 0.409111
\(751\) −9.37694e12 −1.07568 −0.537838 0.843048i \(-0.680759\pi\)
−0.537838 + 0.843048i \(0.680759\pi\)
\(752\) −1.32173e12 −0.150717
\(753\) 8.20677e11 0.0930240
\(754\) 8.04679e12 0.906675
\(755\) −3.58910e12 −0.401998
\(756\) −7.19706e12 −0.801322
\(757\) −1.35880e13 −1.50392 −0.751960 0.659208i \(-0.770892\pi\)
−0.751960 + 0.659208i \(0.770892\pi\)
\(758\) 1.26579e13 1.39267
\(759\) 5.58361e12 0.610698
\(760\) −8.44402e11 −0.0918096
\(761\) 2.78203e12 0.300698 0.150349 0.988633i \(-0.451960\pi\)
0.150349 + 0.988633i \(0.451960\pi\)
\(762\) 1.25634e13 1.34993
\(763\) 1.80508e13 1.92813
\(764\) 2.29932e13 2.44163
\(765\) −8.94564e11 −0.0944354
\(766\) 1.10098e13 1.15545
\(767\) −1.50945e12 −0.157485
\(768\) −1.05045e13 −1.08956
\(769\) −1.13304e13 −1.16836 −0.584180 0.811624i \(-0.698584\pi\)
−0.584180 + 0.811624i \(0.698584\pi\)
\(770\) 5.19833e12 0.532912
\(771\) −8.03665e12 −0.819087
\(772\) 3.42181e12 0.346720
\(773\) 2.73666e12 0.275685 0.137842 0.990454i \(-0.455983\pi\)
0.137842 + 0.990454i \(0.455983\pi\)
\(774\) 2.57243e12 0.257637
\(775\) −7.03968e12 −0.700963
\(776\) 2.87703e13 2.84818
\(777\) −1.80332e13 −1.77492
\(778\) −1.64930e13 −1.61396
\(779\) 2.64857e10 0.00257687
\(780\) −3.22507e12 −0.311970
\(781\) −8.30918e12 −0.799150
\(782\) 3.55427e13 3.39875
\(783\) 8.46214e11 0.0804549
\(784\) 4.53091e13 4.28315
\(785\) 3.23957e12 0.304491
\(786\) −2.97008e11 −0.0277566
\(787\) 3.43999e12 0.319647 0.159824 0.987146i \(-0.448907\pi\)
0.159824 + 0.987146i \(0.448907\pi\)
\(788\) −2.30042e13 −2.12539
\(789\) −8.49673e12 −0.780558
\(790\) 5.68589e11 0.0519369
\(791\) −2.62710e12 −0.238607
\(792\) 6.29778e12 0.568754
\(793\) −1.75990e13 −1.58037
\(794\) −9.09888e12 −0.812448
\(795\) 7.76626e11 0.0689541
\(796\) −1.24854e13 −1.10229
\(797\) 1.68943e13 1.48313 0.741564 0.670882i \(-0.234084\pi\)
0.741564 + 0.670882i \(0.234084\pi\)
\(798\) −4.66074e12 −0.406857
\(799\) −1.44359e12 −0.125309
\(800\) −9.46089e12 −0.816633
\(801\) −9.97798e9 −0.000856438 0
\(802\) 1.17030e13 0.998876
\(803\) −9.06518e12 −0.769408
\(804\) 2.06129e12 0.173975
\(805\) 6.09985e12 0.511962
\(806\) 1.89872e13 1.58473
\(807\) −1.13077e13 −0.938524
\(808\) 1.01477e13 0.837563
\(809\) −7.90565e12 −0.648887 −0.324444 0.945905i \(-0.605177\pi\)
−0.324444 + 0.945905i \(0.605177\pi\)
\(810\) −4.92310e11 −0.0401843
\(811\) −1.91135e13 −1.55148 −0.775740 0.631053i \(-0.782623\pi\)
−0.775740 + 0.631053i \(0.782623\pi\)
\(812\) −2.15638e13 −1.74070
\(813\) −3.98295e12 −0.319740
\(814\) 2.87738e13 2.29714
\(815\) 2.67778e12 0.212601
\(816\) 1.73476e13 1.36973
\(817\) 1.14762e12 0.0901157
\(818\) −2.87376e13 −2.24419
\(819\) −9.76231e12 −0.758185
\(820\) −7.12920e10 −0.00550654
\(821\) 2.51585e10 0.00193260 0.000966298 1.00000i \(-0.499692\pi\)
0.000966298 1.00000i \(0.499692\pi\)
\(822\) −2.16087e13 −1.65084
\(823\) 6.43524e12 0.488951 0.244475 0.969655i \(-0.421384\pi\)
0.244475 + 0.969655i \(0.421384\pi\)
\(824\) 2.96809e13 2.24288
\(825\) −5.77521e12 −0.434035
\(826\) 5.87172e12 0.438889
\(827\) 1.22657e13 0.911841 0.455920 0.890021i \(-0.349310\pi\)
0.455920 + 0.890021i \(0.349310\pi\)
\(828\) 1.34752e13 0.996319
\(829\) 5.05540e12 0.371758 0.185879 0.982573i \(-0.440487\pi\)
0.185879 + 0.982573i \(0.440487\pi\)
\(830\) 6.07335e12 0.444198
\(831\) −2.71341e12 −0.197383
\(832\) −2.72519e12 −0.197171
\(833\) 4.94865e13 3.56110
\(834\) −1.57858e13 −1.12984
\(835\) 2.54457e12 0.181145
\(836\) 5.12314e12 0.362750
\(837\) 1.99673e12 0.140622
\(838\) −8.31081e12 −0.582164
\(839\) −1.26668e13 −0.882550 −0.441275 0.897372i \(-0.645474\pi\)
−0.441275 + 0.897372i \(0.645474\pi\)
\(840\) 6.88007e12 0.476800
\(841\) −1.19717e13 −0.825229
\(842\) −1.18286e13 −0.811014
\(843\) 1.49020e13 1.01630
\(844\) 4.50840e13 3.05831
\(845\) −1.38505e12 −0.0934564
\(846\) −7.94460e11 −0.0533218
\(847\) 1.08682e13 0.725572
\(848\) −1.50606e13 −1.00014
\(849\) −7.79109e12 −0.514652
\(850\) −3.67623e13 −2.41556
\(851\) 3.37639e13 2.20684
\(852\) −2.00529e13 −1.30377
\(853\) 2.09793e13 1.35681 0.678406 0.734687i \(-0.262671\pi\)
0.678406 + 0.734687i \(0.262671\pi\)
\(854\) 6.84596e13 4.40427
\(855\) −2.19632e11 −0.0140556
\(856\) 4.81798e12 0.306714
\(857\) −2.21766e13 −1.40437 −0.702186 0.711993i \(-0.747793\pi\)
−0.702186 + 0.711993i \(0.747793\pi\)
\(858\) 1.55767e13 0.981260
\(859\) −3.66631e12 −0.229753 −0.114876 0.993380i \(-0.536647\pi\)
−0.114876 + 0.993380i \(0.536647\pi\)
\(860\) −3.08908e12 −0.192569
\(861\) −2.15802e11 −0.0133826
\(862\) −4.42259e13 −2.72831
\(863\) −6.55735e12 −0.402420 −0.201210 0.979548i \(-0.564487\pi\)
−0.201210 + 0.979548i \(0.564487\pi\)
\(864\) 2.68348e12 0.163827
\(865\) −1.95397e12 −0.118671
\(866\) −5.17023e13 −3.12378
\(867\) 9.34145e12 0.561472
\(868\) −5.08821e13 −3.04247
\(869\) −1.89188e12 −0.112539
\(870\) −1.47506e12 −0.0872916
\(871\) 2.79600e12 0.164609
\(872\) −3.81196e13 −2.23267
\(873\) 7.48326e12 0.436040
\(874\) 8.72639e12 0.505863
\(875\) −1.28860e13 −0.743157
\(876\) −2.18774e13 −1.25524
\(877\) 9.97574e12 0.569438 0.284719 0.958611i \(-0.408100\pi\)
0.284719 + 0.958611i \(0.408100\pi\)
\(878\) 1.52753e13 0.867490
\(879\) −1.64632e13 −0.930177
\(880\) −4.75044e12 −0.267031
\(881\) 2.65054e12 0.148232 0.0741160 0.997250i \(-0.476386\pi\)
0.0741160 + 0.997250i \(0.476386\pi\)
\(882\) 2.72342e13 1.51533
\(883\) −2.56410e13 −1.41942 −0.709710 0.704494i \(-0.751174\pi\)
−0.709710 + 0.704494i \(0.751174\pi\)
\(884\) 6.83076e13 3.76213
\(885\) 2.76698e11 0.0151622
\(886\) −4.04252e13 −2.20394
\(887\) −2.79022e13 −1.51350 −0.756748 0.653706i \(-0.773213\pi\)
−0.756748 + 0.653706i \(0.773213\pi\)
\(888\) 3.80826e13 2.05527
\(889\) −4.56675e13 −2.45216
\(890\) 1.73929e10 0.000929215 0
\(891\) 1.63808e12 0.0870732
\(892\) 8.23683e13 4.35631
\(893\) −3.54428e11 −0.0186508
\(894\) 1.18850e13 0.622272
\(895\) −5.36500e12 −0.279490
\(896\) 4.14814e13 2.15014
\(897\) 1.82781e13 0.942684
\(898\) 6.00521e12 0.308166
\(899\) 5.98259e12 0.305472
\(900\) −1.39376e13 −0.708103
\(901\) −1.64491e13 −0.831536
\(902\) 3.44333e11 0.0173201
\(903\) −9.35067e12 −0.468002
\(904\) 5.54791e12 0.276294
\(905\) −3.06891e12 −0.152078
\(906\) 4.18354e13 2.06285
\(907\) 3.50674e12 0.172056 0.0860282 0.996293i \(-0.472582\pi\)
0.0860282 + 0.996293i \(0.472582\pi\)
\(908\) 3.30695e13 1.61451
\(909\) 2.63946e12 0.128226
\(910\) 1.70169e13 0.822612
\(911\) 2.04657e13 0.984452 0.492226 0.870467i \(-0.336183\pi\)
0.492226 + 0.870467i \(0.336183\pi\)
\(912\) 4.25917e12 0.203868
\(913\) −2.02080e13 −0.962509
\(914\) −3.32375e13 −1.57533
\(915\) 3.22608e12 0.152153
\(916\) −7.98750e13 −3.74870
\(917\) 1.07961e12 0.0504203
\(918\) 1.04272e13 0.484593
\(919\) 2.10812e13 0.974935 0.487468 0.873141i \(-0.337921\pi\)
0.487468 + 0.873141i \(0.337921\pi\)
\(920\) −1.28817e13 −0.592825
\(921\) 6.05494e12 0.277295
\(922\) 6.21201e13 2.83102
\(923\) −2.72004e13 −1.23358
\(924\) −4.17426e13 −1.88389
\(925\) −3.49226e13 −1.56844
\(926\) −2.34107e13 −1.04632
\(927\) 7.72012e12 0.343372
\(928\) 8.04023e12 0.355879
\(929\) 2.79571e13 1.23146 0.615731 0.787956i \(-0.288861\pi\)
0.615731 + 0.787956i \(0.288861\pi\)
\(930\) −3.48055e12 −0.152572
\(931\) 1.21499e13 0.530027
\(932\) −3.02402e13 −1.31285
\(933\) −1.15703e13 −0.499894
\(934\) −1.97979e13 −0.851252
\(935\) −5.18842e12 −0.222015
\(936\) 2.06160e13 0.877938
\(937\) −1.17695e13 −0.498804 −0.249402 0.968400i \(-0.580234\pi\)
−0.249402 + 0.968400i \(0.580234\pi\)
\(938\) −1.08763e13 −0.458743
\(939\) 2.57993e13 1.08296
\(940\) 9.54021e11 0.0398550
\(941\) 3.95533e13 1.64448 0.822242 0.569137i \(-0.192723\pi\)
0.822242 + 0.569137i \(0.192723\pi\)
\(942\) −3.77612e13 −1.56249
\(943\) 4.04049e11 0.0166392
\(944\) −5.36581e12 −0.219918
\(945\) 1.78953e12 0.0729955
\(946\) 1.49199e13 0.605699
\(947\) 2.61668e13 1.05724 0.528622 0.848857i \(-0.322709\pi\)
0.528622 + 0.848857i \(0.322709\pi\)
\(948\) −4.56577e12 −0.183601
\(949\) −2.96752e13 −1.18767
\(950\) −9.02584e12 −0.359527
\(951\) −1.40919e13 −0.558671
\(952\) −1.45721e14 −5.74986
\(953\) −4.58939e13 −1.80234 −0.901170 0.433466i \(-0.857290\pi\)
−0.901170 + 0.433466i \(0.857290\pi\)
\(954\) −9.05254e12 −0.353836
\(955\) −5.71720e12 −0.222417
\(956\) −5.89725e13 −2.28344
\(957\) 4.90800e12 0.189148
\(958\) 8.23024e13 3.15695
\(959\) 7.85468e13 2.99878
\(960\) 4.99556e11 0.0189829
\(961\) −1.23231e13 −0.466083
\(962\) 9.41923e13 3.54591
\(963\) 1.25317e12 0.0469562
\(964\) 1.05615e14 3.93895
\(965\) −8.50825e11 −0.0315840
\(966\) −7.11013e13 −2.62712
\(967\) −3.95626e13 −1.45501 −0.727505 0.686102i \(-0.759320\pi\)
−0.727505 + 0.686102i \(0.759320\pi\)
\(968\) −2.29514e13 −0.840175
\(969\) 4.65186e12 0.169500
\(970\) −1.30443e13 −0.473093
\(971\) −4.07858e13 −1.47239 −0.736195 0.676770i \(-0.763379\pi\)
−0.736195 + 0.676770i \(0.763379\pi\)
\(972\) 3.95325e12 0.142055
\(973\) 5.73807e13 2.05238
\(974\) −1.56352e13 −0.556657
\(975\) −1.89054e13 −0.669984
\(976\) −6.25611e13 −2.20689
\(977\) 1.36935e13 0.480828 0.240414 0.970670i \(-0.422717\pi\)
0.240414 + 0.970670i \(0.422717\pi\)
\(978\) −3.12129e13 −1.09096
\(979\) −5.78717e10 −0.00201347
\(980\) −3.27040e13 −1.13262
\(981\) −9.91506e12 −0.341810
\(982\) −2.34732e13 −0.805509
\(983\) 3.07077e13 1.04895 0.524477 0.851424i \(-0.324261\pi\)
0.524477 + 0.851424i \(0.324261\pi\)
\(984\) 4.55730e11 0.0154964
\(985\) 5.71993e12 0.193610
\(986\) 3.12421e13 1.05267
\(987\) 2.88783e12 0.0968600
\(988\) 1.67708e13 0.559948
\(989\) 1.75074e13 0.581888
\(990\) −2.85537e12 −0.0944723
\(991\) 7.26101e12 0.239147 0.119574 0.992825i \(-0.461847\pi\)
0.119574 + 0.992825i \(0.461847\pi\)
\(992\) 1.89718e13 0.622021
\(993\) 8.18470e12 0.267135
\(994\) 1.05809e14 3.43781
\(995\) 3.10446e12 0.100411
\(996\) −4.87690e13 −1.57028
\(997\) 3.20796e13 1.02826 0.514128 0.857714i \(-0.328116\pi\)
0.514128 + 0.857714i \(0.328116\pi\)
\(998\) −1.02975e14 −3.28582
\(999\) 9.90542e12 0.314650
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.1.20 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.20 22 1.1 even 1 trivial