Properties

Label 177.10.a.d.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-28.6453 q^{2} +81.0000 q^{3} +308.554 q^{4} +1354.22 q^{5} -2320.27 q^{6} +4084.12 q^{7} +5827.78 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-28.6453 q^{2} +81.0000 q^{3} +308.554 q^{4} +1354.22 q^{5} -2320.27 q^{6} +4084.12 q^{7} +5827.78 q^{8} +6561.00 q^{9} -38792.0 q^{10} -47231.4 q^{11} +24992.9 q^{12} -33052.0 q^{13} -116991. q^{14} +109692. q^{15} -324918. q^{16} +443216. q^{17} -187942. q^{18} +725628. q^{19} +417849. q^{20} +330814. q^{21} +1.35296e6 q^{22} -125298. q^{23} +472050. q^{24} -119222. q^{25} +946784. q^{26} +531441. q^{27} +1.26017e6 q^{28} -4.03480e6 q^{29} -3.14215e6 q^{30} +8.12353e6 q^{31} +6.32356e6 q^{32} -3.82574e6 q^{33} -1.26961e7 q^{34} +5.53079e6 q^{35} +2.02442e6 q^{36} +1.61698e7 q^{37} -2.07858e7 q^{38} -2.67721e6 q^{39} +7.89208e6 q^{40} +2.56190e7 q^{41} -9.47627e6 q^{42} -5.08260e6 q^{43} -1.45734e7 q^{44} +8.88501e6 q^{45} +3.58920e6 q^{46} +3.17136e6 q^{47} -2.63184e7 q^{48} -2.36736e7 q^{49} +3.41516e6 q^{50} +3.59005e7 q^{51} -1.01983e7 q^{52} +2.86075e6 q^{53} -1.52233e7 q^{54} -6.39615e7 q^{55} +2.38014e7 q^{56} +5.87759e7 q^{57} +1.15578e8 q^{58} -1.21174e7 q^{59} +3.38457e7 q^{60} -1.34012e8 q^{61} -2.32701e8 q^{62} +2.67959e7 q^{63} -1.47822e7 q^{64} -4.47595e7 q^{65} +1.09590e8 q^{66} -2.02434e8 q^{67} +1.36756e8 q^{68} -1.01491e7 q^{69} -1.58431e8 q^{70} -2.73218e8 q^{71} +3.82361e7 q^{72} -4.58780e7 q^{73} -4.63189e8 q^{74} -9.65702e6 q^{75} +2.23895e8 q^{76} -1.92899e8 q^{77} +7.66895e7 q^{78} +1.56459e7 q^{79} -4.40009e8 q^{80} +4.30467e7 q^{81} -7.33865e8 q^{82} +4.78761e8 q^{83} +1.02074e8 q^{84} +6.00210e8 q^{85} +1.45593e8 q^{86} -3.26819e8 q^{87} -2.75254e8 q^{88} +5.24028e8 q^{89} -2.54514e8 q^{90} -1.34988e8 q^{91} -3.86612e7 q^{92} +6.58006e8 q^{93} -9.08446e7 q^{94} +9.82657e8 q^{95} +5.12208e8 q^{96} +5.11682e8 q^{97} +6.78136e8 q^{98} -3.09885e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −28.6453 −1.26596 −0.632978 0.774170i \(-0.718168\pi\)
−0.632978 + 0.774170i \(0.718168\pi\)
\(3\) 81.0000 0.577350
\(4\) 308.554 0.602644
\(5\) 1354.22 0.968999 0.484499 0.874792i \(-0.339002\pi\)
0.484499 + 0.874792i \(0.339002\pi\)
\(6\) −2320.27 −0.730900
\(7\) 4084.12 0.642921 0.321460 0.946923i \(-0.395826\pi\)
0.321460 + 0.946923i \(0.395826\pi\)
\(8\) 5827.78 0.503035
\(9\) 6561.00 0.333333
\(10\) −38792.0 −1.22671
\(11\) −47231.4 −0.972666 −0.486333 0.873774i \(-0.661666\pi\)
−0.486333 + 0.873774i \(0.661666\pi\)
\(12\) 24992.9 0.347937
\(13\) −33052.0 −0.320961 −0.160481 0.987039i \(-0.551304\pi\)
−0.160481 + 0.987039i \(0.551304\pi\)
\(14\) −116991. −0.813909
\(15\) 109692. 0.559452
\(16\) −324918. −1.23946
\(17\) 443216. 1.28705 0.643524 0.765426i \(-0.277471\pi\)
0.643524 + 0.765426i \(0.277471\pi\)
\(18\) −187942. −0.421985
\(19\) 725628. 1.27739 0.638694 0.769461i \(-0.279475\pi\)
0.638694 + 0.769461i \(0.279475\pi\)
\(20\) 417849. 0.583961
\(21\) 330814. 0.371191
\(22\) 1.35296e6 1.23135
\(23\) −125298. −0.0933618 −0.0466809 0.998910i \(-0.514864\pi\)
−0.0466809 + 0.998910i \(0.514864\pi\)
\(24\) 472050. 0.290427
\(25\) −119222. −0.0610419
\(26\) 946784. 0.406323
\(27\) 531441. 0.192450
\(28\) 1.26017e6 0.387452
\(29\) −4.03480e6 −1.05933 −0.529664 0.848207i \(-0.677682\pi\)
−0.529664 + 0.848207i \(0.677682\pi\)
\(30\) −3.14215e6 −0.708241
\(31\) 8.12353e6 1.57985 0.789927 0.613201i \(-0.210118\pi\)
0.789927 + 0.613201i \(0.210118\pi\)
\(32\) 6.32356e6 1.06607
\(33\) −3.82574e6 −0.561569
\(34\) −1.26961e7 −1.62935
\(35\) 5.53079e6 0.622989
\(36\) 2.02442e6 0.200881
\(37\) 1.61698e7 1.41839 0.709197 0.705011i \(-0.249058\pi\)
0.709197 + 0.705011i \(0.249058\pi\)
\(38\) −2.07858e7 −1.61712
\(39\) −2.67721e6 −0.185307
\(40\) 7.89208e6 0.487440
\(41\) 2.56190e7 1.41591 0.707954 0.706258i \(-0.249618\pi\)
0.707954 + 0.706258i \(0.249618\pi\)
\(42\) −9.47627e6 −0.469911
\(43\) −5.08260e6 −0.226714 −0.113357 0.993554i \(-0.536160\pi\)
−0.113357 + 0.993554i \(0.536160\pi\)
\(44\) −1.45734e7 −0.586171
\(45\) 8.88501e6 0.323000
\(46\) 3.58920e6 0.118192
\(47\) 3.17136e6 0.0947993 0.0473996 0.998876i \(-0.484907\pi\)
0.0473996 + 0.998876i \(0.484907\pi\)
\(48\) −2.63184e7 −0.715605
\(49\) −2.36736e7 −0.586653
\(50\) 3.41516e6 0.0772763
\(51\) 3.59005e7 0.743078
\(52\) −1.01983e7 −0.193425
\(53\) 2.86075e6 0.0498011 0.0249005 0.999690i \(-0.492073\pi\)
0.0249005 + 0.999690i \(0.492073\pi\)
\(54\) −1.52233e7 −0.243633
\(55\) −6.39615e7 −0.942512
\(56\) 2.38014e7 0.323412
\(57\) 5.87759e7 0.737500
\(58\) 1.15578e8 1.34106
\(59\) −1.21174e7 −0.130189
\(60\) 3.38457e7 0.337150
\(61\) −1.34012e8 −1.23926 −0.619628 0.784896i \(-0.712716\pi\)
−0.619628 + 0.784896i \(0.712716\pi\)
\(62\) −2.32701e8 −2.00003
\(63\) 2.67959e7 0.214307
\(64\) −1.47822e7 −0.110136
\(65\) −4.47595e7 −0.311011
\(66\) 1.09590e8 0.710921
\(67\) −2.02434e8 −1.22729 −0.613645 0.789582i \(-0.710297\pi\)
−0.613645 + 0.789582i \(0.710297\pi\)
\(68\) 1.36756e8 0.775632
\(69\) −1.01491e7 −0.0539025
\(70\) −1.58431e8 −0.788677
\(71\) −2.73218e8 −1.27599 −0.637994 0.770041i \(-0.720235\pi\)
−0.637994 + 0.770041i \(0.720235\pi\)
\(72\) 3.82361e7 0.167678
\(73\) −4.58780e7 −0.189083 −0.0945413 0.995521i \(-0.530138\pi\)
−0.0945413 + 0.995521i \(0.530138\pi\)
\(74\) −4.63189e8 −1.79562
\(75\) −9.65702e6 −0.0352426
\(76\) 2.23895e8 0.769810
\(77\) −1.92899e8 −0.625347
\(78\) 7.66895e7 0.234590
\(79\) 1.56459e7 0.0451939 0.0225969 0.999745i \(-0.492807\pi\)
0.0225969 + 0.999745i \(0.492807\pi\)
\(80\) −4.40009e8 −1.20104
\(81\) 4.30467e7 0.111111
\(82\) −7.33865e8 −1.79248
\(83\) 4.78761e8 1.10730 0.553652 0.832748i \(-0.313234\pi\)
0.553652 + 0.832748i \(0.313234\pi\)
\(84\) 1.02074e8 0.223696
\(85\) 6.00210e8 1.24715
\(86\) 1.45593e8 0.287009
\(87\) −3.26819e8 −0.611604
\(88\) −2.75254e8 −0.489285
\(89\) 5.24028e8 0.885318 0.442659 0.896690i \(-0.354035\pi\)
0.442659 + 0.896690i \(0.354035\pi\)
\(90\) −2.54514e8 −0.408903
\(91\) −1.34988e8 −0.206353
\(92\) −3.86612e7 −0.0562640
\(93\) 6.58006e8 0.912129
\(94\) −9.08446e7 −0.120012
\(95\) 9.82657e8 1.23779
\(96\) 5.12208e8 0.615497
\(97\) 5.11682e8 0.586850 0.293425 0.955982i \(-0.405205\pi\)
0.293425 + 0.955982i \(0.405205\pi\)
\(98\) 6.78136e8 0.742676
\(99\) −3.09885e8 −0.324222
\(100\) −3.67865e7 −0.0367865
\(101\) 1.06176e9 1.01526 0.507632 0.861574i \(-0.330521\pi\)
0.507632 + 0.861574i \(0.330521\pi\)
\(102\) −1.02838e9 −0.940704
\(103\) 2.00504e9 1.75532 0.877659 0.479286i \(-0.159104\pi\)
0.877659 + 0.479286i \(0.159104\pi\)
\(104\) −1.92620e8 −0.161455
\(105\) 4.47994e8 0.359683
\(106\) −8.19472e7 −0.0630460
\(107\) −2.24978e9 −1.65926 −0.829628 0.558316i \(-0.811448\pi\)
−0.829628 + 0.558316i \(0.811448\pi\)
\(108\) 1.63978e8 0.115979
\(109\) −6.76835e8 −0.459265 −0.229633 0.973277i \(-0.573752\pi\)
−0.229633 + 0.973277i \(0.573752\pi\)
\(110\) 1.83220e9 1.19318
\(111\) 1.30975e9 0.818910
\(112\) −1.32701e9 −0.796877
\(113\) 2.76684e9 1.59636 0.798180 0.602419i \(-0.205796\pi\)
0.798180 + 0.602419i \(0.205796\pi\)
\(114\) −1.68365e9 −0.933643
\(115\) −1.69681e8 −0.0904675
\(116\) −1.24495e9 −0.638398
\(117\) −2.16854e8 −0.106987
\(118\) 3.47106e8 0.164813
\(119\) 1.81015e9 0.827471
\(120\) 6.39258e8 0.281424
\(121\) −1.27143e8 −0.0539212
\(122\) 3.83883e9 1.56884
\(123\) 2.07514e9 0.817475
\(124\) 2.50654e9 0.952090
\(125\) −2.80641e9 −1.02815
\(126\) −7.67578e8 −0.271303
\(127\) −4.06332e9 −1.38600 −0.693001 0.720937i \(-0.743712\pi\)
−0.693001 + 0.720937i \(0.743712\pi\)
\(128\) −2.81422e9 −0.926645
\(129\) −4.11690e8 −0.130893
\(130\) 1.28215e9 0.393726
\(131\) 3.39487e9 1.00717 0.503585 0.863946i \(-0.332014\pi\)
0.503585 + 0.863946i \(0.332014\pi\)
\(132\) −1.18045e9 −0.338426
\(133\) 2.96355e9 0.821259
\(134\) 5.79879e9 1.55369
\(135\) 7.19686e8 0.186484
\(136\) 2.58296e9 0.647431
\(137\) −4.94042e8 −0.119818 −0.0599089 0.998204i \(-0.519081\pi\)
−0.0599089 + 0.998204i \(0.519081\pi\)
\(138\) 2.90725e8 0.0682381
\(139\) 6.29148e9 1.42951 0.714753 0.699377i \(-0.246539\pi\)
0.714753 + 0.699377i \(0.246539\pi\)
\(140\) 1.70654e9 0.375441
\(141\) 2.56880e8 0.0547324
\(142\) 7.82641e9 1.61534
\(143\) 1.56109e9 0.312188
\(144\) −2.13179e9 −0.413155
\(145\) −5.46399e9 −1.02649
\(146\) 1.31419e9 0.239370
\(147\) −1.91756e9 −0.338704
\(148\) 4.98925e9 0.854787
\(149\) 8.26886e9 1.37438 0.687191 0.726477i \(-0.258844\pi\)
0.687191 + 0.726477i \(0.258844\pi\)
\(150\) 2.76628e8 0.0446155
\(151\) 3.56053e9 0.557337 0.278669 0.960387i \(-0.410107\pi\)
0.278669 + 0.960387i \(0.410107\pi\)
\(152\) 4.22880e9 0.642571
\(153\) 2.90794e9 0.429016
\(154\) 5.52564e9 0.791662
\(155\) 1.10010e10 1.53088
\(156\) −8.26063e8 −0.111674
\(157\) 2.52887e8 0.0332183 0.0166091 0.999862i \(-0.494713\pi\)
0.0166091 + 0.999862i \(0.494713\pi\)
\(158\) −4.48182e8 −0.0572134
\(159\) 2.31721e8 0.0287527
\(160\) 8.56347e9 1.03302
\(161\) −5.11733e8 −0.0600243
\(162\) −1.23309e9 −0.140662
\(163\) −6.06403e9 −0.672848 −0.336424 0.941711i \(-0.609218\pi\)
−0.336424 + 0.941711i \(0.609218\pi\)
\(164\) 7.90484e9 0.853289
\(165\) −5.18088e9 −0.544159
\(166\) −1.37143e10 −1.40180
\(167\) 1.12715e10 1.12139 0.560697 0.828021i \(-0.310533\pi\)
0.560697 + 0.828021i \(0.310533\pi\)
\(168\) 1.92791e9 0.186722
\(169\) −9.51207e9 −0.896984
\(170\) −1.71932e10 −1.57883
\(171\) 4.76084e9 0.425796
\(172\) −1.56825e9 −0.136628
\(173\) 3.53662e8 0.0300179 0.0150090 0.999887i \(-0.495222\pi\)
0.0150090 + 0.999887i \(0.495222\pi\)
\(174\) 9.36182e9 0.774263
\(175\) −4.86919e8 −0.0392451
\(176\) 1.53463e10 1.20558
\(177\) −9.81506e8 −0.0751646
\(178\) −1.50109e10 −1.12077
\(179\) 2.67931e10 1.95067 0.975337 0.220723i \(-0.0708417\pi\)
0.975337 + 0.220723i \(0.0708417\pi\)
\(180\) 2.74151e9 0.194654
\(181\) 8.45963e9 0.585865 0.292933 0.956133i \(-0.405369\pi\)
0.292933 + 0.956133i \(0.405369\pi\)
\(182\) 3.86678e9 0.261233
\(183\) −1.08550e10 −0.715484
\(184\) −7.30210e8 −0.0469643
\(185\) 2.18974e10 1.37442
\(186\) −1.88488e10 −1.15472
\(187\) −2.09337e10 −1.25187
\(188\) 9.78535e8 0.0571302
\(189\) 2.17047e9 0.123730
\(190\) −2.81485e10 −1.56698
\(191\) 2.08046e10 1.13112 0.565562 0.824706i \(-0.308659\pi\)
0.565562 + 0.824706i \(0.308659\pi\)
\(192\) −1.19736e9 −0.0635869
\(193\) −3.43043e10 −1.77967 −0.889837 0.456278i \(-0.849182\pi\)
−0.889837 + 0.456278i \(0.849182\pi\)
\(194\) −1.46573e10 −0.742927
\(195\) −3.62552e9 −0.179562
\(196\) −7.30457e9 −0.353543
\(197\) 1.76011e10 0.832612 0.416306 0.909225i \(-0.363325\pi\)
0.416306 + 0.909225i \(0.363325\pi\)
\(198\) 8.87676e9 0.410451
\(199\) 2.10369e10 0.950919 0.475459 0.879738i \(-0.342282\pi\)
0.475459 + 0.879738i \(0.342282\pi\)
\(200\) −6.94802e8 −0.0307062
\(201\) −1.63972e10 −0.708576
\(202\) −3.04144e10 −1.28528
\(203\) −1.64786e10 −0.681064
\(204\) 1.10772e10 0.447812
\(205\) 3.46937e10 1.37201
\(206\) −5.74350e10 −2.22215
\(207\) −8.22081e8 −0.0311206
\(208\) 1.07392e10 0.397820
\(209\) −3.42724e10 −1.24247
\(210\) −1.28329e10 −0.455343
\(211\) −2.39137e10 −0.830569 −0.415285 0.909692i \(-0.636318\pi\)
−0.415285 + 0.909692i \(0.636318\pi\)
\(212\) 8.82696e8 0.0300123
\(213\) −2.21306e10 −0.736692
\(214\) 6.44457e10 2.10055
\(215\) −6.88294e9 −0.219685
\(216\) 3.09712e9 0.0968091
\(217\) 3.31775e10 1.01572
\(218\) 1.93882e10 0.581410
\(219\) −3.71612e9 −0.109167
\(220\) −1.97356e10 −0.567999
\(221\) −1.46492e10 −0.413093
\(222\) −3.75183e10 −1.03670
\(223\) −2.05884e10 −0.557506 −0.278753 0.960363i \(-0.589921\pi\)
−0.278753 + 0.960363i \(0.589921\pi\)
\(224\) 2.58262e10 0.685400
\(225\) −7.82219e8 −0.0203473
\(226\) −7.92569e10 −2.02092
\(227\) −3.29798e10 −0.824388 −0.412194 0.911096i \(-0.635237\pi\)
−0.412194 + 0.911096i \(0.635237\pi\)
\(228\) 1.81355e10 0.444450
\(229\) −1.94734e10 −0.467931 −0.233965 0.972245i \(-0.575170\pi\)
−0.233965 + 0.972245i \(0.575170\pi\)
\(230\) 4.86056e9 0.114528
\(231\) −1.56248e10 −0.361044
\(232\) −2.35139e10 −0.532879
\(233\) 6.07481e10 1.35030 0.675152 0.737679i \(-0.264078\pi\)
0.675152 + 0.737679i \(0.264078\pi\)
\(234\) 6.21185e9 0.135441
\(235\) 4.29471e9 0.0918604
\(236\) −3.73886e9 −0.0784576
\(237\) 1.26732e9 0.0260927
\(238\) −5.18522e10 −1.04754
\(239\) −3.35535e10 −0.665193 −0.332596 0.943069i \(-0.607925\pi\)
−0.332596 + 0.943069i \(0.607925\pi\)
\(240\) −3.56408e10 −0.693420
\(241\) 3.23723e10 0.618154 0.309077 0.951037i \(-0.399980\pi\)
0.309077 + 0.951037i \(0.399980\pi\)
\(242\) 3.64206e9 0.0682619
\(243\) 3.48678e9 0.0641500
\(244\) −4.13500e10 −0.746830
\(245\) −3.20591e10 −0.568466
\(246\) −5.94430e10 −1.03489
\(247\) −2.39834e10 −0.409992
\(248\) 4.73421e10 0.794722
\(249\) 3.87796e10 0.639303
\(250\) 8.03904e10 1.30159
\(251\) 5.38436e10 0.856253 0.428127 0.903719i \(-0.359174\pi\)
0.428127 + 0.903719i \(0.359174\pi\)
\(252\) 8.26798e9 0.129151
\(253\) 5.91800e9 0.0908098
\(254\) 1.16395e11 1.75462
\(255\) 4.86170e10 0.720041
\(256\) 8.81827e10 1.28323
\(257\) 6.94605e10 0.993205 0.496602 0.867978i \(-0.334581\pi\)
0.496602 + 0.867978i \(0.334581\pi\)
\(258\) 1.17930e10 0.165705
\(259\) 6.60394e10 0.911915
\(260\) −1.38107e10 −0.187429
\(261\) −2.64723e10 −0.353109
\(262\) −9.72471e10 −1.27503
\(263\) 2.38776e10 0.307744 0.153872 0.988091i \(-0.450826\pi\)
0.153872 + 0.988091i \(0.450826\pi\)
\(264\) −2.22956e10 −0.282489
\(265\) 3.87408e9 0.0482572
\(266\) −8.48919e10 −1.03968
\(267\) 4.24462e10 0.511139
\(268\) −6.24618e10 −0.739619
\(269\) −2.93724e10 −0.342022 −0.171011 0.985269i \(-0.554703\pi\)
−0.171011 + 0.985269i \(0.554703\pi\)
\(270\) −2.06156e10 −0.236080
\(271\) −6.30264e10 −0.709841 −0.354920 0.934897i \(-0.615492\pi\)
−0.354920 + 0.934897i \(0.615492\pi\)
\(272\) −1.44009e11 −1.59525
\(273\) −1.09341e10 −0.119138
\(274\) 1.41520e10 0.151684
\(275\) 5.63104e9 0.0593734
\(276\) −3.13156e9 −0.0324840
\(277\) −1.38561e11 −1.41411 −0.707055 0.707158i \(-0.749977\pi\)
−0.707055 + 0.707158i \(0.749977\pi\)
\(278\) −1.80221e11 −1.80969
\(279\) 5.32984e10 0.526618
\(280\) 3.22322e10 0.313385
\(281\) 9.40553e10 0.899922 0.449961 0.893048i \(-0.351438\pi\)
0.449961 + 0.893048i \(0.351438\pi\)
\(282\) −7.35841e9 −0.0692888
\(283\) 2.32349e10 0.215328 0.107664 0.994187i \(-0.465663\pi\)
0.107664 + 0.994187i \(0.465663\pi\)
\(284\) −8.43024e10 −0.768967
\(285\) 7.95952e10 0.714636
\(286\) −4.47179e10 −0.395216
\(287\) 1.04631e11 0.910317
\(288\) 4.14889e10 0.355357
\(289\) 7.78523e10 0.656495
\(290\) 1.56518e11 1.29949
\(291\) 4.14463e10 0.338818
\(292\) −1.41558e10 −0.113950
\(293\) −6.03723e10 −0.478557 −0.239278 0.970951i \(-0.576911\pi\)
−0.239278 + 0.970951i \(0.576911\pi\)
\(294\) 5.49290e10 0.428784
\(295\) −1.64095e10 −0.126153
\(296\) 9.42340e10 0.713502
\(297\) −2.51007e10 −0.187190
\(298\) −2.36864e11 −1.73991
\(299\) 4.14135e9 0.0299655
\(300\) −2.97971e9 −0.0212387
\(301\) −2.07579e10 −0.145759
\(302\) −1.01992e11 −0.705564
\(303\) 8.60024e10 0.586163
\(304\) −2.35770e11 −1.58328
\(305\) −1.81482e11 −1.20084
\(306\) −8.32988e10 −0.543116
\(307\) −1.34298e11 −0.862870 −0.431435 0.902144i \(-0.641993\pi\)
−0.431435 + 0.902144i \(0.641993\pi\)
\(308\) −5.95196e10 −0.376862
\(309\) 1.62408e11 1.01343
\(310\) −3.15127e11 −1.93802
\(311\) 3.18179e11 1.92864 0.964318 0.264747i \(-0.0852883\pi\)
0.964318 + 0.264747i \(0.0852883\pi\)
\(312\) −1.56022e10 −0.0932159
\(313\) −7.68389e10 −0.452513 −0.226257 0.974068i \(-0.572649\pi\)
−0.226257 + 0.974068i \(0.572649\pi\)
\(314\) −7.24401e9 −0.0420529
\(315\) 3.62875e10 0.207663
\(316\) 4.82761e9 0.0272358
\(317\) 1.69384e11 0.942121 0.471060 0.882101i \(-0.343871\pi\)
0.471060 + 0.882101i \(0.343871\pi\)
\(318\) −6.63772e9 −0.0363996
\(319\) 1.90569e11 1.03037
\(320\) −2.00183e10 −0.106721
\(321\) −1.82232e11 −0.957972
\(322\) 1.46587e10 0.0759881
\(323\) 3.21610e11 1.64406
\(324\) 1.32822e10 0.0669605
\(325\) 3.94054e9 0.0195921
\(326\) 1.73706e11 0.851796
\(327\) −5.48236e10 −0.265157
\(328\) 1.49302e11 0.712251
\(329\) 1.29522e10 0.0609484
\(330\) 1.48408e11 0.688882
\(331\) 2.71014e11 1.24098 0.620491 0.784214i \(-0.286933\pi\)
0.620491 + 0.784214i \(0.286933\pi\)
\(332\) 1.47723e11 0.667311
\(333\) 1.06090e11 0.472798
\(334\) −3.22876e11 −1.41964
\(335\) −2.74140e11 −1.18924
\(336\) −1.07487e11 −0.460077
\(337\) 2.83802e11 1.19862 0.599310 0.800517i \(-0.295442\pi\)
0.599310 + 0.800517i \(0.295442\pi\)
\(338\) 2.72476e11 1.13554
\(339\) 2.24114e11 0.921659
\(340\) 1.85197e11 0.751587
\(341\) −3.83685e11 −1.53667
\(342\) −1.36376e11 −0.539039
\(343\) −2.61495e11 −1.02009
\(344\) −2.96203e10 −0.114045
\(345\) −1.37441e10 −0.0522314
\(346\) −1.01308e10 −0.0380014
\(347\) −4.25894e10 −0.157695 −0.0788477 0.996887i \(-0.525124\pi\)
−0.0788477 + 0.996887i \(0.525124\pi\)
\(348\) −1.00841e11 −0.368579
\(349\) 4.18211e11 1.50897 0.754485 0.656317i \(-0.227887\pi\)
0.754485 + 0.656317i \(0.227887\pi\)
\(350\) 1.39479e10 0.0496826
\(351\) −1.75652e10 −0.0617690
\(352\) −2.98670e11 −1.03693
\(353\) −3.98462e11 −1.36584 −0.682921 0.730492i \(-0.739291\pi\)
−0.682921 + 0.730492i \(0.739291\pi\)
\(354\) 2.81156e10 0.0951551
\(355\) −3.69996e11 −1.23643
\(356\) 1.61691e11 0.533532
\(357\) 1.46622e11 0.477740
\(358\) −7.67497e11 −2.46947
\(359\) 2.30556e11 0.732573 0.366287 0.930502i \(-0.380629\pi\)
0.366287 + 0.930502i \(0.380629\pi\)
\(360\) 5.17799e10 0.162480
\(361\) 2.03848e11 0.631719
\(362\) −2.42329e11 −0.741679
\(363\) −1.02986e10 −0.0311314
\(364\) −4.16512e10 −0.124357
\(365\) −6.21288e10 −0.183221
\(366\) 3.10945e11 0.905772
\(367\) 2.13955e11 0.615639 0.307819 0.951445i \(-0.400401\pi\)
0.307819 + 0.951445i \(0.400401\pi\)
\(368\) 4.07116e10 0.115719
\(369\) 1.68086e11 0.471969
\(370\) −6.27258e11 −1.73996
\(371\) 1.16837e10 0.0320182
\(372\) 2.03030e11 0.549689
\(373\) 5.62850e11 1.50558 0.752789 0.658262i \(-0.228708\pi\)
0.752789 + 0.658262i \(0.228708\pi\)
\(374\) 5.99652e11 1.58481
\(375\) −2.27319e11 −0.593602
\(376\) 1.84820e10 0.0476874
\(377\) 1.33358e11 0.340003
\(378\) −6.21738e10 −0.156637
\(379\) −6.38760e11 −1.59023 −0.795117 0.606456i \(-0.792591\pi\)
−0.795117 + 0.606456i \(0.792591\pi\)
\(380\) 3.03203e11 0.745945
\(381\) −3.29129e11 −0.800209
\(382\) −5.95955e11 −1.43195
\(383\) −3.26247e11 −0.774734 −0.387367 0.921926i \(-0.626615\pi\)
−0.387367 + 0.921926i \(0.626615\pi\)
\(384\) −2.27952e11 −0.534999
\(385\) −2.61227e11 −0.605960
\(386\) 9.82657e11 2.25299
\(387\) −3.33469e10 −0.0755712
\(388\) 1.57881e11 0.353662
\(389\) −5.60425e11 −1.24092 −0.620460 0.784238i \(-0.713054\pi\)
−0.620460 + 0.784238i \(0.713054\pi\)
\(390\) 1.03854e11 0.227318
\(391\) −5.55341e10 −0.120161
\(392\) −1.37964e11 −0.295107
\(393\) 2.74985e11 0.581489
\(394\) −5.04190e11 −1.05405
\(395\) 2.11880e10 0.0437928
\(396\) −9.56162e10 −0.195390
\(397\) 6.45371e11 1.30392 0.651962 0.758252i \(-0.273946\pi\)
0.651962 + 0.758252i \(0.273946\pi\)
\(398\) −6.02609e11 −1.20382
\(399\) 2.40048e11 0.474154
\(400\) 3.87375e10 0.0756592
\(401\) −1.70193e11 −0.328693 −0.164347 0.986403i \(-0.552552\pi\)
−0.164347 + 0.986403i \(0.552552\pi\)
\(402\) 4.69702e11 0.897026
\(403\) −2.68499e11 −0.507072
\(404\) 3.27609e11 0.611843
\(405\) 5.82946e10 0.107667
\(406\) 4.72035e11 0.862197
\(407\) −7.63722e11 −1.37962
\(408\) 2.09220e11 0.373794
\(409\) −1.19142e11 −0.210529 −0.105264 0.994444i \(-0.533569\pi\)
−0.105264 + 0.994444i \(0.533569\pi\)
\(410\) −9.93812e11 −1.73691
\(411\) −4.00174e10 −0.0691768
\(412\) 6.18663e11 1.05783
\(413\) −4.94888e10 −0.0837012
\(414\) 2.35488e10 0.0393973
\(415\) 6.48346e11 1.07298
\(416\) −2.09006e11 −0.342168
\(417\) 5.09610e11 0.825326
\(418\) 9.81744e11 1.57291
\(419\) −5.36922e10 −0.0851036 −0.0425518 0.999094i \(-0.513549\pi\)
−0.0425518 + 0.999094i \(0.513549\pi\)
\(420\) 1.38230e11 0.216761
\(421\) −7.34555e10 −0.113961 −0.0569803 0.998375i \(-0.518147\pi\)
−0.0569803 + 0.998375i \(0.518147\pi\)
\(422\) 6.85015e11 1.05146
\(423\) 2.08073e10 0.0315998
\(424\) 1.66718e10 0.0250517
\(425\) −5.28413e10 −0.0785639
\(426\) 6.33939e11 0.932619
\(427\) −5.47323e11 −0.796743
\(428\) −6.94179e11 −0.999941
\(429\) 1.26448e11 0.180242
\(430\) 1.97164e11 0.278112
\(431\) 6.88580e11 0.961184 0.480592 0.876944i \(-0.340422\pi\)
0.480592 + 0.876944i \(0.340422\pi\)
\(432\) −1.72675e11 −0.238535
\(433\) 5.38627e10 0.0736364 0.0368182 0.999322i \(-0.488278\pi\)
0.0368182 + 0.999322i \(0.488278\pi\)
\(434\) −9.50379e11 −1.28586
\(435\) −4.42583e11 −0.592643
\(436\) −2.08840e11 −0.276774
\(437\) −9.09198e10 −0.119259
\(438\) 1.06449e11 0.138201
\(439\) 1.10606e12 1.42130 0.710652 0.703544i \(-0.248400\pi\)
0.710652 + 0.703544i \(0.248400\pi\)
\(440\) −3.72754e11 −0.474116
\(441\) −1.55322e11 −0.195551
\(442\) 4.19630e11 0.522957
\(443\) −2.16781e11 −0.267427 −0.133714 0.991020i \(-0.542690\pi\)
−0.133714 + 0.991020i \(0.542690\pi\)
\(444\) 4.04129e11 0.493511
\(445\) 7.09647e11 0.857872
\(446\) 5.89760e11 0.705778
\(447\) 6.69778e11 0.793500
\(448\) −6.03722e10 −0.0708086
\(449\) 2.71054e11 0.314736 0.157368 0.987540i \(-0.449699\pi\)
0.157368 + 0.987540i \(0.449699\pi\)
\(450\) 2.24069e10 0.0257588
\(451\) −1.21002e12 −1.37721
\(452\) 8.53719e11 0.962037
\(453\) 2.88403e11 0.321779
\(454\) 9.44717e11 1.04364
\(455\) −1.82803e11 −0.199955
\(456\) 3.42533e11 0.370988
\(457\) 8.41235e11 0.902182 0.451091 0.892478i \(-0.351035\pi\)
0.451091 + 0.892478i \(0.351035\pi\)
\(458\) 5.57821e11 0.592379
\(459\) 2.35543e11 0.247693
\(460\) −5.23557e10 −0.0545197
\(461\) −2.27551e11 −0.234652 −0.117326 0.993093i \(-0.537432\pi\)
−0.117326 + 0.993093i \(0.537432\pi\)
\(462\) 4.47577e11 0.457066
\(463\) 8.72284e11 0.882152 0.441076 0.897470i \(-0.354597\pi\)
0.441076 + 0.897470i \(0.354597\pi\)
\(464\) 1.31098e12 1.31300
\(465\) 8.91082e11 0.883852
\(466\) −1.74015e12 −1.70942
\(467\) 1.10977e12 1.07971 0.539854 0.841758i \(-0.318479\pi\)
0.539854 + 0.841758i \(0.318479\pi\)
\(468\) −6.69111e10 −0.0644751
\(469\) −8.26766e11 −0.789050
\(470\) −1.23023e11 −0.116291
\(471\) 2.04838e10 0.0191786
\(472\) −7.06173e10 −0.0654896
\(473\) 2.40058e11 0.220517
\(474\) −3.63028e10 −0.0330322
\(475\) −8.65111e10 −0.0779742
\(476\) 5.58528e11 0.498670
\(477\) 1.87694e10 0.0166004
\(478\) 9.61151e11 0.842105
\(479\) 1.61589e12 1.40249 0.701247 0.712918i \(-0.252627\pi\)
0.701247 + 0.712918i \(0.252627\pi\)
\(480\) 6.93641e11 0.596416
\(481\) −5.34444e11 −0.455249
\(482\) −9.27314e11 −0.782555
\(483\) −4.14504e10 −0.0346550
\(484\) −3.92306e10 −0.0324953
\(485\) 6.92928e11 0.568657
\(486\) −9.98800e10 −0.0812111
\(487\) 3.44921e11 0.277868 0.138934 0.990302i \(-0.455632\pi\)
0.138934 + 0.990302i \(0.455632\pi\)
\(488\) −7.80995e11 −0.623389
\(489\) −4.91187e11 −0.388469
\(490\) 9.18343e11 0.719652
\(491\) −1.29529e12 −1.00578 −0.502889 0.864351i \(-0.667729\pi\)
−0.502889 + 0.864351i \(0.667729\pi\)
\(492\) 6.40292e11 0.492647
\(493\) −1.78829e12 −1.36341
\(494\) 6.87013e11 0.519031
\(495\) −4.19652e11 −0.314171
\(496\) −2.63948e12 −1.95817
\(497\) −1.11585e12 −0.820359
\(498\) −1.11085e12 −0.809329
\(499\) 2.12865e12 1.53692 0.768460 0.639898i \(-0.221023\pi\)
0.768460 + 0.639898i \(0.221023\pi\)
\(500\) −8.65928e11 −0.619607
\(501\) 9.12993e11 0.647437
\(502\) −1.54237e12 −1.08398
\(503\) 3.00207e11 0.209105 0.104552 0.994519i \(-0.466659\pi\)
0.104552 + 0.994519i \(0.466659\pi\)
\(504\) 1.56161e11 0.107804
\(505\) 1.43785e12 0.983790
\(506\) −1.69523e11 −0.114961
\(507\) −7.70477e11 −0.517874
\(508\) −1.25375e12 −0.835266
\(509\) −1.25461e12 −0.828476 −0.414238 0.910169i \(-0.635952\pi\)
−0.414238 + 0.910169i \(0.635952\pi\)
\(510\) −1.39265e12 −0.911541
\(511\) −1.87371e11 −0.121565
\(512\) −1.08514e12 −0.697864
\(513\) 3.85628e11 0.245833
\(514\) −1.98972e12 −1.25735
\(515\) 2.71526e12 1.70090
\(516\) −1.27029e11 −0.0788820
\(517\) −1.49788e11 −0.0922080
\(518\) −1.89172e12 −1.15444
\(519\) 2.86466e10 0.0173309
\(520\) −2.60849e11 −0.156449
\(521\) 9.46973e11 0.563077 0.281538 0.959550i \(-0.409155\pi\)
0.281538 + 0.959550i \(0.409155\pi\)
\(522\) 7.58307e11 0.447021
\(523\) 8.86122e11 0.517888 0.258944 0.965892i \(-0.416626\pi\)
0.258944 + 0.965892i \(0.416626\pi\)
\(524\) 1.04750e12 0.606965
\(525\) −3.94404e10 −0.0226582
\(526\) −6.83980e11 −0.389590
\(527\) 3.60047e12 2.03335
\(528\) 1.24305e12 0.696044
\(529\) −1.78545e12 −0.991284
\(530\) −1.10974e11 −0.0610915
\(531\) −7.95020e10 −0.0433963
\(532\) 9.14415e11 0.494927
\(533\) −8.46759e11 −0.454451
\(534\) −1.21589e12 −0.647079
\(535\) −3.04669e12 −1.60782
\(536\) −1.17974e12 −0.617370
\(537\) 2.17024e12 1.12622
\(538\) 8.41381e11 0.432985
\(539\) 1.11813e12 0.570617
\(540\) 2.22062e11 0.112383
\(541\) 1.98760e11 0.0997566 0.0498783 0.998755i \(-0.484117\pi\)
0.0498783 + 0.998755i \(0.484117\pi\)
\(542\) 1.80541e12 0.898627
\(543\) 6.85230e11 0.338249
\(544\) 2.80270e12 1.37209
\(545\) −9.16581e11 −0.445027
\(546\) 3.13209e11 0.150823
\(547\) −3.79463e12 −1.81228 −0.906141 0.422975i \(-0.860986\pi\)
−0.906141 + 0.422975i \(0.860986\pi\)
\(548\) −1.52438e11 −0.0722075
\(549\) −8.79255e11 −0.413085
\(550\) −1.61303e11 −0.0751641
\(551\) −2.92776e12 −1.35317
\(552\) −5.91470e10 −0.0271148
\(553\) 6.38999e10 0.0290561
\(554\) 3.96913e12 1.79020
\(555\) 1.77369e12 0.793522
\(556\) 1.94126e12 0.861484
\(557\) −3.70966e12 −1.63300 −0.816499 0.577347i \(-0.804088\pi\)
−0.816499 + 0.577347i \(0.804088\pi\)
\(558\) −1.52675e12 −0.666675
\(559\) 1.67990e11 0.0727662
\(560\) −1.79705e12 −0.772173
\(561\) −1.69563e12 −0.722767
\(562\) −2.69424e12 −1.13926
\(563\) 2.84950e12 1.19531 0.597656 0.801753i \(-0.296099\pi\)
0.597656 + 0.801753i \(0.296099\pi\)
\(564\) 7.92613e10 0.0329842
\(565\) 3.74690e12 1.54687
\(566\) −6.65570e11 −0.272596
\(567\) 1.75808e11 0.0714357
\(568\) −1.59225e12 −0.641866
\(569\) −2.26268e12 −0.904934 −0.452467 0.891781i \(-0.649456\pi\)
−0.452467 + 0.891781i \(0.649456\pi\)
\(570\) −2.28003e12 −0.904698
\(571\) −2.06202e12 −0.811763 −0.405882 0.913926i \(-0.633035\pi\)
−0.405882 + 0.913926i \(0.633035\pi\)
\(572\) 4.81681e11 0.188138
\(573\) 1.68518e12 0.653054
\(574\) −2.99719e12 −1.15242
\(575\) 1.49383e10 0.00569898
\(576\) −9.69859e10 −0.0367119
\(577\) −4.03734e12 −1.51636 −0.758182 0.652043i \(-0.773912\pi\)
−0.758182 + 0.652043i \(0.773912\pi\)
\(578\) −2.23010e12 −0.831093
\(579\) −2.77865e12 −1.02750
\(580\) −1.68593e12 −0.618607
\(581\) 1.95532e12 0.711909
\(582\) −1.18724e12 −0.428929
\(583\) −1.35117e11 −0.0484398
\(584\) −2.67367e11 −0.0951152
\(585\) −2.93667e11 −0.103670
\(586\) 1.72938e12 0.605832
\(587\) 9.45156e11 0.328573 0.164287 0.986413i \(-0.447468\pi\)
0.164287 + 0.986413i \(0.447468\pi\)
\(588\) −5.91670e11 −0.204118
\(589\) 5.89466e12 2.01809
\(590\) 4.70056e11 0.159704
\(591\) 1.42569e12 0.480709
\(592\) −5.25386e12 −1.75805
\(593\) −1.49025e12 −0.494894 −0.247447 0.968901i \(-0.579592\pi\)
−0.247447 + 0.968901i \(0.579592\pi\)
\(594\) 7.19017e11 0.236974
\(595\) 2.45133e12 0.801818
\(596\) 2.55139e12 0.828263
\(597\) 1.70399e12 0.549013
\(598\) −1.18630e11 −0.0379350
\(599\) −3.03885e12 −0.964468 −0.482234 0.876042i \(-0.660175\pi\)
−0.482234 + 0.876042i \(0.660175\pi\)
\(600\) −5.62790e10 −0.0177282
\(601\) −1.25441e12 −0.392196 −0.196098 0.980584i \(-0.562827\pi\)
−0.196098 + 0.980584i \(0.562827\pi\)
\(602\) 5.94618e11 0.184524
\(603\) −1.32817e12 −0.409097
\(604\) 1.09861e12 0.335876
\(605\) −1.72180e11 −0.0522496
\(606\) −2.46356e12 −0.742057
\(607\) −4.35236e12 −1.30130 −0.650648 0.759380i \(-0.725503\pi\)
−0.650648 + 0.759380i \(0.725503\pi\)
\(608\) 4.58855e12 1.36179
\(609\) −1.33477e12 −0.393213
\(610\) 5.19860e12 1.52021
\(611\) −1.04820e11 −0.0304269
\(612\) 8.97255e11 0.258544
\(613\) −1.38782e12 −0.396974 −0.198487 0.980104i \(-0.563603\pi\)
−0.198487 + 0.980104i \(0.563603\pi\)
\(614\) 3.84700e12 1.09236
\(615\) 2.81019e12 0.792132
\(616\) −1.12417e12 −0.314571
\(617\) 5.72130e12 1.58932 0.794660 0.607055i \(-0.207649\pi\)
0.794660 + 0.607055i \(0.207649\pi\)
\(618\) −4.65224e12 −1.28296
\(619\) −3.70038e12 −1.01307 −0.506534 0.862220i \(-0.669073\pi\)
−0.506534 + 0.862220i \(0.669073\pi\)
\(620\) 3.39440e12 0.922573
\(621\) −6.65886e10 −0.0179675
\(622\) −9.11435e12 −2.44157
\(623\) 2.14019e12 0.569189
\(624\) 8.69874e11 0.229681
\(625\) −3.56763e12 −0.935232
\(626\) 2.20107e12 0.572862
\(627\) −2.77607e12 −0.717341
\(628\) 7.80291e10 0.0200188
\(629\) 7.16671e12 1.82554
\(630\) −1.03947e12 −0.262892
\(631\) −2.31097e12 −0.580313 −0.290156 0.956979i \(-0.593707\pi\)
−0.290156 + 0.956979i \(0.593707\pi\)
\(632\) 9.11810e10 0.0227341
\(633\) −1.93701e12 −0.479529
\(634\) −4.85207e12 −1.19268
\(635\) −5.50261e12 −1.34303
\(636\) 7.14984e10 0.0173276
\(637\) 7.82458e11 0.188293
\(638\) −5.45891e12 −1.30441
\(639\) −1.79258e12 −0.425329
\(640\) −3.81106e12 −0.897918
\(641\) 4.10989e12 0.961544 0.480772 0.876846i \(-0.340357\pi\)
0.480772 + 0.876846i \(0.340357\pi\)
\(642\) 5.22010e12 1.21275
\(643\) 4.69775e12 1.08378 0.541889 0.840450i \(-0.317709\pi\)
0.541889 + 0.840450i \(0.317709\pi\)
\(644\) −1.57897e11 −0.0361733
\(645\) −5.57518e11 −0.126835
\(646\) −9.21261e12 −2.08131
\(647\) 5.84716e11 0.131183 0.0655913 0.997847i \(-0.479107\pi\)
0.0655913 + 0.997847i \(0.479107\pi\)
\(648\) 2.50867e11 0.0558928
\(649\) 5.72320e11 0.126630
\(650\) −1.12878e11 −0.0248027
\(651\) 2.68737e12 0.586427
\(652\) −1.87108e12 −0.405488
\(653\) −4.93511e12 −1.06215 −0.531077 0.847324i \(-0.678212\pi\)
−0.531077 + 0.847324i \(0.678212\pi\)
\(654\) 1.57044e12 0.335677
\(655\) 4.59739e12 0.975945
\(656\) −8.32408e12 −1.75497
\(657\) −3.01006e11 −0.0630276
\(658\) −3.71020e11 −0.0771580
\(659\) −6.38476e12 −1.31874 −0.659372 0.751817i \(-0.729178\pi\)
−0.659372 + 0.751817i \(0.729178\pi\)
\(660\) −1.59858e12 −0.327934
\(661\) −6.05954e12 −1.23462 −0.617310 0.786720i \(-0.711777\pi\)
−0.617310 + 0.786720i \(0.711777\pi\)
\(662\) −7.76327e12 −1.57103
\(663\) −1.18658e12 −0.238499
\(664\) 2.79011e12 0.557013
\(665\) 4.01329e12 0.795799
\(666\) −3.03898e12 −0.598541
\(667\) 5.05552e11 0.0989008
\(668\) 3.47787e12 0.675802
\(669\) −1.66766e12 −0.321876
\(670\) 7.85281e12 1.50553
\(671\) 6.32959e12 1.20538
\(672\) 2.09192e12 0.395716
\(673\) −3.64991e12 −0.685827 −0.342913 0.939367i \(-0.611414\pi\)
−0.342913 + 0.939367i \(0.611414\pi\)
\(674\) −8.12961e12 −1.51740
\(675\) −6.33597e10 −0.0117475
\(676\) −2.93498e12 −0.540562
\(677\) −3.48204e12 −0.637067 −0.318534 0.947912i \(-0.603190\pi\)
−0.318534 + 0.947912i \(0.603190\pi\)
\(678\) −6.41981e12 −1.16678
\(679\) 2.08977e12 0.377298
\(680\) 3.49789e12 0.627359
\(681\) −2.67136e12 −0.475961
\(682\) 1.09908e13 1.94536
\(683\) −7.32087e12 −1.28727 −0.643635 0.765332i \(-0.722575\pi\)
−0.643635 + 0.765332i \(0.722575\pi\)
\(684\) 1.46898e12 0.256603
\(685\) −6.69040e11 −0.116103
\(686\) 7.49060e12 1.29139
\(687\) −1.57734e12 −0.270160
\(688\) 1.65143e12 0.281003
\(689\) −9.45535e10 −0.0159842
\(690\) 3.93705e11 0.0661227
\(691\) 6.66621e12 1.11232 0.556158 0.831077i \(-0.312275\pi\)
0.556158 + 0.831077i \(0.312275\pi\)
\(692\) 1.09124e11 0.0180901
\(693\) −1.26561e12 −0.208449
\(694\) 1.21999e12 0.199635
\(695\) 8.52002e12 1.38519
\(696\) −1.90463e12 −0.307658
\(697\) 1.13548e13 1.82234
\(698\) −1.19798e13 −1.91029
\(699\) 4.92060e12 0.779598
\(700\) −1.50241e11 −0.0236508
\(701\) −7.34214e12 −1.14840 −0.574198 0.818717i \(-0.694686\pi\)
−0.574198 + 0.818717i \(0.694686\pi\)
\(702\) 5.03160e11 0.0781968
\(703\) 1.17333e13 1.81184
\(704\) 6.98183e11 0.107125
\(705\) 3.47871e11 0.0530356
\(706\) 1.14141e13 1.72910
\(707\) 4.33635e12 0.652735
\(708\) −3.02847e11 −0.0452975
\(709\) −1.07027e13 −1.59068 −0.795342 0.606161i \(-0.792709\pi\)
−0.795342 + 0.606161i \(0.792709\pi\)
\(710\) 1.05987e13 1.56527
\(711\) 1.02653e11 0.0150646
\(712\) 3.05392e12 0.445346
\(713\) −1.01786e12 −0.147498
\(714\) −4.20003e12 −0.604798
\(715\) 2.11406e12 0.302510
\(716\) 8.26712e12 1.17556
\(717\) −2.71784e12 −0.384049
\(718\) −6.60434e12 −0.927405
\(719\) 2.17776e12 0.303900 0.151950 0.988388i \(-0.451445\pi\)
0.151950 + 0.988388i \(0.451445\pi\)
\(720\) −2.88690e12 −0.400346
\(721\) 8.18883e12 1.12853
\(722\) −5.83929e12 −0.799729
\(723\) 2.62215e12 0.356891
\(724\) 2.61025e12 0.353068
\(725\) 4.81038e11 0.0646634
\(726\) 2.95007e11 0.0394110
\(727\) 1.12664e13 1.49583 0.747915 0.663795i \(-0.231055\pi\)
0.747915 + 0.663795i \(0.231055\pi\)
\(728\) −7.86682e11 −0.103803
\(729\) 2.82430e11 0.0370370
\(730\) 1.77970e12 0.231949
\(731\) −2.25269e12 −0.291791
\(732\) −3.34935e12 −0.431182
\(733\) 1.14706e13 1.46764 0.733818 0.679346i \(-0.237737\pi\)
0.733818 + 0.679346i \(0.237737\pi\)
\(734\) −6.12882e12 −0.779371
\(735\) −2.59679e12 −0.328204
\(736\) −7.92330e11 −0.0995304
\(737\) 9.56124e12 1.19374
\(738\) −4.81489e12 −0.597492
\(739\) 5.18921e12 0.640032 0.320016 0.947412i \(-0.396312\pi\)
0.320016 + 0.947412i \(0.396312\pi\)
\(740\) 6.75653e12 0.828287
\(741\) −1.94266e12 −0.236709
\(742\) −3.34682e11 −0.0405336
\(743\) −1.22170e13 −1.47067 −0.735335 0.677704i \(-0.762975\pi\)
−0.735335 + 0.677704i \(0.762975\pi\)
\(744\) 3.83471e12 0.458833
\(745\) 1.11978e13 1.33177
\(746\) −1.61230e13 −1.90599
\(747\) 3.14115e12 0.369102
\(748\) −6.45917e12 −0.754431
\(749\) −9.18839e12 −1.06677
\(750\) 6.51162e12 0.751473
\(751\) −1.48708e13 −1.70591 −0.852953 0.521987i \(-0.825191\pi\)
−0.852953 + 0.521987i \(0.825191\pi\)
\(752\) −1.03043e12 −0.117500
\(753\) 4.36133e12 0.494358
\(754\) −3.82008e12 −0.430429
\(755\) 4.82172e12 0.540059
\(756\) 6.69707e11 0.0745653
\(757\) 1.16388e13 1.28818 0.644088 0.764951i \(-0.277237\pi\)
0.644088 + 0.764951i \(0.277237\pi\)
\(758\) 1.82975e13 2.01317
\(759\) 4.79358e11 0.0524291
\(760\) 5.72671e12 0.622650
\(761\) 1.49171e13 1.61233 0.806163 0.591694i \(-0.201541\pi\)
0.806163 + 0.591694i \(0.201541\pi\)
\(762\) 9.42799e12 1.01303
\(763\) −2.76428e12 −0.295271
\(764\) 6.41935e12 0.681665
\(765\) 3.93798e12 0.415716
\(766\) 9.34545e12 0.980779
\(767\) 4.00503e11 0.0417856
\(768\) 7.14280e12 0.740872
\(769\) 3.29875e12 0.340158 0.170079 0.985430i \(-0.445598\pi\)
0.170079 + 0.985430i \(0.445598\pi\)
\(770\) 7.48292e12 0.767119
\(771\) 5.62630e12 0.573427
\(772\) −1.05847e13 −1.07251
\(773\) −1.33569e13 −1.34554 −0.672770 0.739851i \(-0.734896\pi\)
−0.672770 + 0.739851i \(0.734896\pi\)
\(774\) 9.55233e11 0.0956698
\(775\) −9.68507e11 −0.0964373
\(776\) 2.98197e12 0.295206
\(777\) 5.34919e12 0.526494
\(778\) 1.60535e13 1.57095
\(779\) 1.85899e13 1.80866
\(780\) −1.11867e12 −0.108212
\(781\) 1.29045e13 1.24111
\(782\) 1.59079e12 0.152119
\(783\) −2.14426e12 −0.203868
\(784\) 7.69197e12 0.727135
\(785\) 3.42463e11 0.0321885
\(786\) −7.87702e12 −0.736140
\(787\) −1.80700e13 −1.67908 −0.839542 0.543294i \(-0.817177\pi\)
−0.839542 + 0.543294i \(0.817177\pi\)
\(788\) 5.43090e12 0.501769
\(789\) 1.93408e12 0.177676
\(790\) −6.06936e11 −0.0554397
\(791\) 1.13001e13 1.02633
\(792\) −1.80594e12 −0.163095
\(793\) 4.42938e12 0.397753
\(794\) −1.84869e13 −1.65071
\(795\) 3.13800e11 0.0278613
\(796\) 6.49102e12 0.573066
\(797\) −1.44535e13 −1.26885 −0.634423 0.772986i \(-0.718762\pi\)
−0.634423 + 0.772986i \(0.718762\pi\)
\(798\) −6.87624e12 −0.600258
\(799\) 1.40560e12 0.122011
\(800\) −7.53910e11 −0.0650751
\(801\) 3.43815e12 0.295106
\(802\) 4.87522e12 0.416111
\(803\) 2.16688e12 0.183914
\(804\) −5.05941e12 −0.427019
\(805\) −6.92997e11 −0.0581634
\(806\) 7.69123e12 0.641930
\(807\) −2.37916e12 −0.197466
\(808\) 6.18769e12 0.510714
\(809\) 2.01256e13 1.65188 0.825942 0.563755i \(-0.190644\pi\)
0.825942 + 0.563755i \(0.190644\pi\)
\(810\) −1.66987e12 −0.136301
\(811\) −1.90075e13 −1.54288 −0.771439 0.636303i \(-0.780463\pi\)
−0.771439 + 0.636303i \(0.780463\pi\)
\(812\) −5.08454e12 −0.410439
\(813\) −5.10514e12 −0.409827
\(814\) 2.18771e13 1.74654
\(815\) −8.21201e12 −0.651989
\(816\) −1.16647e13 −0.921019
\(817\) −3.68807e12 −0.289601
\(818\) 3.41287e12 0.266520
\(819\) −8.85658e11 −0.0687842
\(820\) 1.07049e13 0.826836
\(821\) −5.47269e12 −0.420394 −0.210197 0.977659i \(-0.567411\pi\)
−0.210197 + 0.977659i \(0.567411\pi\)
\(822\) 1.14631e12 0.0875748
\(823\) −3.86167e12 −0.293411 −0.146705 0.989180i \(-0.546867\pi\)
−0.146705 + 0.989180i \(0.546867\pi\)
\(824\) 1.16849e13 0.882986
\(825\) 4.56114e11 0.0342792
\(826\) 1.41762e12 0.105962
\(827\) −2.06193e13 −1.53285 −0.766425 0.642333i \(-0.777966\pi\)
−0.766425 + 0.642333i \(0.777966\pi\)
\(828\) −2.53656e11 −0.0187547
\(829\) −1.10675e13 −0.813870 −0.406935 0.913457i \(-0.633402\pi\)
−0.406935 + 0.913457i \(0.633402\pi\)
\(830\) −1.85721e13 −1.35834
\(831\) −1.12235e13 −0.816437
\(832\) 4.88580e11 0.0353493
\(833\) −1.04925e13 −0.755051
\(834\) −1.45979e13 −1.04483
\(835\) 1.52641e13 1.08663
\(836\) −1.05749e13 −0.748768
\(837\) 4.31717e12 0.304043
\(838\) 1.53803e12 0.107737
\(839\) −1.11383e13 −0.776052 −0.388026 0.921649i \(-0.626843\pi\)
−0.388026 + 0.921649i \(0.626843\pi\)
\(840\) 2.61081e12 0.180933
\(841\) 1.77244e12 0.122177
\(842\) 2.10416e12 0.144269
\(843\) 7.61848e12 0.519570
\(844\) −7.37866e12 −0.500538
\(845\) −1.28814e13 −0.869176
\(846\) −5.96031e11 −0.0400039
\(847\) −5.19269e11 −0.0346671
\(848\) −9.29510e11 −0.0617267
\(849\) 1.88202e12 0.124320
\(850\) 1.51365e12 0.0994584
\(851\) −2.02604e12 −0.132424
\(852\) −6.82849e12 −0.443963
\(853\) 1.30570e12 0.0844447 0.0422224 0.999108i \(-0.486556\pi\)
0.0422224 + 0.999108i \(0.486556\pi\)
\(854\) 1.56782e13 1.00864
\(855\) 6.44721e12 0.412596
\(856\) −1.31112e13 −0.834664
\(857\) 4.94604e12 0.313216 0.156608 0.987661i \(-0.449944\pi\)
0.156608 + 0.987661i \(0.449944\pi\)
\(858\) −3.62215e12 −0.228178
\(859\) −1.36929e13 −0.858079 −0.429040 0.903286i \(-0.641148\pi\)
−0.429040 + 0.903286i \(0.641148\pi\)
\(860\) −2.12376e12 −0.132392
\(861\) 8.47513e12 0.525572
\(862\) −1.97246e13 −1.21682
\(863\) 5.25820e12 0.322692 0.161346 0.986898i \(-0.448416\pi\)
0.161346 + 0.986898i \(0.448416\pi\)
\(864\) 3.36060e12 0.205166
\(865\) 4.78935e11 0.0290873
\(866\) −1.54291e12 −0.0932204
\(867\) 6.30604e12 0.379027
\(868\) 1.02370e13 0.612118
\(869\) −7.38979e11 −0.0439585
\(870\) 1.26779e13 0.750260
\(871\) 6.69085e12 0.393912
\(872\) −3.94445e12 −0.231026
\(873\) 3.35715e12 0.195617
\(874\) 2.60443e12 0.150977
\(875\) −1.14617e13 −0.661018
\(876\) −1.14662e12 −0.0657888
\(877\) 2.98371e13 1.70317 0.851585 0.524216i \(-0.175642\pi\)
0.851585 + 0.524216i \(0.175642\pi\)
\(878\) −3.16833e13 −1.79931
\(879\) −4.89016e12 −0.276295
\(880\) 2.07823e13 1.16821
\(881\) −1.01896e13 −0.569858 −0.284929 0.958549i \(-0.591970\pi\)
−0.284929 + 0.958549i \(0.591970\pi\)
\(882\) 4.44925e12 0.247559
\(883\) −1.30284e13 −0.721220 −0.360610 0.932717i \(-0.617431\pi\)
−0.360610 + 0.932717i \(0.617431\pi\)
\(884\) −4.52005e12 −0.248948
\(885\) −1.32917e12 −0.0728344
\(886\) 6.20977e12 0.338551
\(887\) −1.76648e13 −0.958189 −0.479095 0.877763i \(-0.659035\pi\)
−0.479095 + 0.877763i \(0.659035\pi\)
\(888\) 7.63295e12 0.411940
\(889\) −1.65951e13 −0.891089
\(890\) −2.03281e13 −1.08603
\(891\) −2.03316e12 −0.108074
\(892\) −6.35262e12 −0.335978
\(893\) 2.30123e12 0.121095
\(894\) −1.91860e13 −1.00454
\(895\) 3.62837e13 1.89020
\(896\) −1.14936e13 −0.595759
\(897\) 3.35449e11 0.0173006
\(898\) −7.76442e12 −0.398442
\(899\) −3.27768e13 −1.67358
\(900\) −2.41357e11 −0.0122622
\(901\) 1.26793e12 0.0640964
\(902\) 3.46614e13 1.74348
\(903\) −1.68139e12 −0.0841539
\(904\) 1.61245e13 0.803025
\(905\) 1.14562e13 0.567702
\(906\) −8.26138e12 −0.407358
\(907\) 1.51366e13 0.742670 0.371335 0.928499i \(-0.378900\pi\)
0.371335 + 0.928499i \(0.378900\pi\)
\(908\) −1.01760e13 −0.496813
\(909\) 6.96619e12 0.338421
\(910\) 5.23646e12 0.253135
\(911\) −1.57055e13 −0.755475 −0.377737 0.925913i \(-0.623298\pi\)
−0.377737 + 0.925913i \(0.623298\pi\)
\(912\) −1.90973e13 −0.914105
\(913\) −2.26125e13 −1.07704
\(914\) −2.40974e13 −1.14212
\(915\) −1.47000e13 −0.693303
\(916\) −6.00858e12 −0.281996
\(917\) 1.38651e13 0.647530
\(918\) −6.74720e12 −0.313568
\(919\) −1.90392e13 −0.880499 −0.440249 0.897876i \(-0.645110\pi\)
−0.440249 + 0.897876i \(0.645110\pi\)
\(920\) −9.88862e11 −0.0455083
\(921\) −1.08781e13 −0.498178
\(922\) 6.51826e12 0.297059
\(923\) 9.03039e12 0.409542
\(924\) −4.82109e12 −0.217581
\(925\) −1.92780e12 −0.0865814
\(926\) −2.49868e13 −1.11677
\(927\) 1.31551e13 0.585106
\(928\) −2.55143e13 −1.12932
\(929\) −6.52504e12 −0.287417 −0.143709 0.989620i \(-0.545903\pi\)
−0.143709 + 0.989620i \(0.545903\pi\)
\(930\) −2.55253e13 −1.11892
\(931\) −1.71782e13 −0.749383
\(932\) 1.87441e13 0.813752
\(933\) 2.57725e13 1.11350
\(934\) −3.17897e13 −1.36686
\(935\) −2.83488e13 −1.21306
\(936\) −1.26378e12 −0.0538182
\(937\) 2.08263e13 0.882639 0.441320 0.897350i \(-0.354511\pi\)
0.441320 + 0.897350i \(0.354511\pi\)
\(938\) 2.36830e13 0.998903
\(939\) −6.22395e12 −0.261259
\(940\) 1.32515e12 0.0553591
\(941\) −3.04865e13 −1.26752 −0.633759 0.773531i \(-0.718489\pi\)
−0.633759 + 0.773531i \(0.718489\pi\)
\(942\) −5.86765e11 −0.0242792
\(943\) −3.21001e12 −0.132192
\(944\) 3.93715e12 0.161364
\(945\) 2.93929e12 0.119894
\(946\) −6.87654e12 −0.279164
\(947\) −2.68526e13 −1.08495 −0.542477 0.840070i \(-0.682514\pi\)
−0.542477 + 0.840070i \(0.682514\pi\)
\(948\) 3.91036e11 0.0157246
\(949\) 1.51636e12 0.0606882
\(950\) 2.47814e12 0.0987118
\(951\) 1.37201e13 0.543934
\(952\) 1.05491e13 0.416247
\(953\) 3.94794e13 1.55043 0.775215 0.631698i \(-0.217642\pi\)
0.775215 + 0.631698i \(0.217642\pi\)
\(954\) −5.37655e11 −0.0210153
\(955\) 2.81740e13 1.09606
\(956\) −1.03531e13 −0.400875
\(957\) 1.54361e13 0.594886
\(958\) −4.62876e13 −1.77550
\(959\) −2.01773e12 −0.0770333
\(960\) −1.62148e12 −0.0616156
\(961\) 3.95520e13 1.49594
\(962\) 1.53093e13 0.576325
\(963\) −1.47608e13 −0.553086
\(964\) 9.98859e12 0.372527
\(965\) −4.64554e13 −1.72450
\(966\) 1.18736e12 0.0438717
\(967\) −2.15101e13 −0.791084 −0.395542 0.918448i \(-0.629443\pi\)
−0.395542 + 0.918448i \(0.629443\pi\)
\(968\) −7.40964e11 −0.0271243
\(969\) 2.60504e13 0.949199
\(970\) −1.98492e13 −0.719895
\(971\) 3.93783e13 1.42158 0.710788 0.703407i \(-0.248339\pi\)
0.710788 + 0.703407i \(0.248339\pi\)
\(972\) 1.07586e12 0.0386596
\(973\) 2.56952e13 0.919059
\(974\) −9.88036e12 −0.351769
\(975\) 3.19184e11 0.0113115
\(976\) 4.35431e13 1.53601
\(977\) 1.28009e13 0.449486 0.224743 0.974418i \(-0.427846\pi\)
0.224743 + 0.974418i \(0.427846\pi\)
\(978\) 1.40702e13 0.491785
\(979\) −2.47506e13 −0.861118
\(980\) −9.89196e12 −0.342582
\(981\) −4.44071e12 −0.153088
\(982\) 3.71041e13 1.27327
\(983\) −1.49540e13 −0.510817 −0.255409 0.966833i \(-0.582210\pi\)
−0.255409 + 0.966833i \(0.582210\pi\)
\(984\) 1.20935e13 0.411218
\(985\) 2.38357e13 0.806800
\(986\) 5.12260e13 1.72601
\(987\) 1.04913e12 0.0351886
\(988\) −7.40018e12 −0.247079
\(989\) 6.36840e11 0.0211664
\(990\) 1.20211e13 0.397726
\(991\) −1.75648e13 −0.578510 −0.289255 0.957252i \(-0.593408\pi\)
−0.289255 + 0.957252i \(0.593408\pi\)
\(992\) 5.13696e13 1.68424
\(993\) 2.19521e13 0.716481
\(994\) 3.19640e13 1.03854
\(995\) 2.84886e13 0.921439
\(996\) 1.19656e13 0.385272
\(997\) 1.48830e13 0.477047 0.238523 0.971137i \(-0.423337\pi\)
0.238523 + 0.971137i \(0.423337\pi\)
\(998\) −6.09758e13 −1.94567
\(999\) 8.59329e12 0.272970
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.1.5 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.5 22 1.1 even 1 trivial