Properties

Label 177.10.a.d.1.7
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 1.7
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-16.3468 q^{2} +81.0000 q^{3} -244.784 q^{4} -1401.93 q^{5} -1324.09 q^{6} +3361.75 q^{7} +12371.0 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-16.3468 q^{2} +81.0000 q^{3} -244.784 q^{4} -1401.93 q^{5} -1324.09 q^{6} +3361.75 q^{7} +12371.0 q^{8} +6561.00 q^{9} +22917.0 q^{10} +31144.9 q^{11} -19827.5 q^{12} +181333. q^{13} -54953.6 q^{14} -113556. q^{15} -76895.6 q^{16} +560395. q^{17} -107251. q^{18} -392444. q^{19} +343169. q^{20} +272301. q^{21} -509118. q^{22} -2.10816e6 q^{23} +1.00205e6 q^{24} +12274.7 q^{25} -2.96421e6 q^{26} +531441. q^{27} -822901. q^{28} -1.57396e6 q^{29} +1.85627e6 q^{30} -2.88698e6 q^{31} -5.07694e6 q^{32} +2.52274e6 q^{33} -9.16064e6 q^{34} -4.71292e6 q^{35} -1.60603e6 q^{36} -2.17752e6 q^{37} +6.41518e6 q^{38} +1.46880e7 q^{39} -1.73432e7 q^{40} +1.94028e7 q^{41} -4.45124e6 q^{42} +1.36630e7 q^{43} -7.62377e6 q^{44} -9.19804e6 q^{45} +3.44615e7 q^{46} +1.56640e7 q^{47} -6.22855e6 q^{48} -2.90523e7 q^{49} -200652. q^{50} +4.53920e7 q^{51} -4.43874e7 q^{52} +7.05119e7 q^{53} -8.68733e6 q^{54} -4.36629e7 q^{55} +4.15880e7 q^{56} -3.17879e7 q^{57} +2.57291e7 q^{58} -1.21174e7 q^{59} +2.77967e7 q^{60} +1.38031e8 q^{61} +4.71928e7 q^{62} +2.20564e7 q^{63} +1.22362e8 q^{64} -2.54216e8 q^{65} -4.12386e7 q^{66} +2.09373e8 q^{67} -1.37176e8 q^{68} -1.70761e8 q^{69} +7.70410e7 q^{70} -1.48646e8 q^{71} +8.11658e7 q^{72} -2.48240e8 q^{73} +3.55954e7 q^{74} +994253. q^{75} +9.60639e7 q^{76} +1.04701e8 q^{77} -2.40101e8 q^{78} -5.22199e8 q^{79} +1.07802e8 q^{80} +4.30467e7 q^{81} -3.17173e8 q^{82} +6.25714e8 q^{83} -6.66549e7 q^{84} -7.85633e8 q^{85} -2.23346e8 q^{86} -1.27490e8 q^{87} +3.85292e8 q^{88} -6.80185e8 q^{89} +1.50358e8 q^{90} +6.09596e8 q^{91} +5.16042e8 q^{92} -2.33846e8 q^{93} -2.56056e8 q^{94} +5.50178e8 q^{95} -4.11232e8 q^{96} +9.35972e7 q^{97} +4.74910e8 q^{98} +2.04342e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.3468 −0.722431 −0.361216 0.932482i \(-0.617638\pi\)
−0.361216 + 0.932482i \(0.617638\pi\)
\(3\) 81.0000 0.577350
\(4\) −244.784 −0.478093
\(5\) −1401.93 −1.00314 −0.501569 0.865118i \(-0.667244\pi\)
−0.501569 + 0.865118i \(0.667244\pi\)
\(6\) −1324.09 −0.417096
\(7\) 3361.75 0.529205 0.264602 0.964358i \(-0.414759\pi\)
0.264602 + 0.964358i \(0.414759\pi\)
\(8\) 12371.0 1.06782
\(9\) 6561.00 0.333333
\(10\) 22917.0 0.724698
\(11\) 31144.9 0.641387 0.320693 0.947183i \(-0.396084\pi\)
0.320693 + 0.947183i \(0.396084\pi\)
\(12\) −19827.5 −0.276027
\(13\) 181333. 1.76089 0.880445 0.474148i \(-0.157244\pi\)
0.880445 + 0.474148i \(0.157244\pi\)
\(14\) −54953.6 −0.382314
\(15\) −113556. −0.579162
\(16\) −76895.6 −0.293334
\(17\) 560395. 1.62733 0.813663 0.581337i \(-0.197470\pi\)
0.813663 + 0.581337i \(0.197470\pi\)
\(18\) −107251. −0.240810
\(19\) −392444. −0.690854 −0.345427 0.938446i \(-0.612266\pi\)
−0.345427 + 0.938446i \(0.612266\pi\)
\(20\) 343169. 0.479593
\(21\) 272301. 0.305536
\(22\) −509118. −0.463358
\(23\) −2.10816e6 −1.57082 −0.785412 0.618974i \(-0.787549\pi\)
−0.785412 + 0.618974i \(0.787549\pi\)
\(24\) 1.00205e6 0.616507
\(25\) 12274.7 0.00628466
\(26\) −2.96421e6 −1.27212
\(27\) 531441. 0.192450
\(28\) −822901. −0.253009
\(29\) −1.57396e6 −0.413239 −0.206620 0.978421i \(-0.566246\pi\)
−0.206620 + 0.978421i \(0.566246\pi\)
\(30\) 1.85627e6 0.418404
\(31\) −2.88698e6 −0.561457 −0.280729 0.959787i \(-0.590576\pi\)
−0.280729 + 0.959787i \(0.590576\pi\)
\(32\) −5.07694e6 −0.855907
\(33\) 2.52274e6 0.370305
\(34\) −9.16064e6 −1.17563
\(35\) −4.71292e6 −0.530865
\(36\) −1.60603e6 −0.159364
\(37\) −2.17752e6 −0.191009 −0.0955046 0.995429i \(-0.530446\pi\)
−0.0955046 + 0.995429i \(0.530446\pi\)
\(38\) 6.41518e6 0.499094
\(39\) 1.46880e7 1.01665
\(40\) −1.73432e7 −1.07117
\(41\) 1.94028e7 1.07235 0.536177 0.844106i \(-0.319868\pi\)
0.536177 + 0.844106i \(0.319868\pi\)
\(42\) −4.45124e6 −0.220729
\(43\) 1.36630e7 0.609452 0.304726 0.952440i \(-0.401435\pi\)
0.304726 + 0.952440i \(0.401435\pi\)
\(44\) −7.62377e6 −0.306643
\(45\) −9.19804e6 −0.334379
\(46\) 3.44615e7 1.13481
\(47\) 1.56640e7 0.468234 0.234117 0.972208i \(-0.424780\pi\)
0.234117 + 0.972208i \(0.424780\pi\)
\(48\) −6.22855e6 −0.169356
\(49\) −2.90523e7 −0.719942
\(50\) −200652. −0.00454023
\(51\) 4.53920e7 0.939537
\(52\) −4.43874e7 −0.841870
\(53\) 7.05119e7 1.22750 0.613749 0.789501i \(-0.289661\pi\)
0.613749 + 0.789501i \(0.289661\pi\)
\(54\) −8.68733e6 −0.139032
\(55\) −4.36629e7 −0.643399
\(56\) 4.15880e7 0.565096
\(57\) −3.17879e7 −0.398865
\(58\) 2.57291e7 0.298537
\(59\) −1.21174e7 −0.130189
\(60\) 2.77967e7 0.276893
\(61\) 1.38031e8 1.27641 0.638207 0.769865i \(-0.279676\pi\)
0.638207 + 0.769865i \(0.279676\pi\)
\(62\) 4.71928e7 0.405614
\(63\) 2.20564e7 0.176402
\(64\) 1.22362e8 0.911668
\(65\) −2.54216e8 −1.76641
\(66\) −4.12386e7 −0.267520
\(67\) 2.09373e8 1.26936 0.634678 0.772777i \(-0.281133\pi\)
0.634678 + 0.772777i \(0.281133\pi\)
\(68\) −1.37176e8 −0.778013
\(69\) −1.70761e8 −0.906915
\(70\) 7.70410e7 0.383513
\(71\) −1.48646e8 −0.694210 −0.347105 0.937826i \(-0.612835\pi\)
−0.347105 + 0.937826i \(0.612835\pi\)
\(72\) 8.11658e7 0.355940
\(73\) −2.48240e8 −1.02310 −0.511552 0.859252i \(-0.670929\pi\)
−0.511552 + 0.859252i \(0.670929\pi\)
\(74\) 3.55954e7 0.137991
\(75\) 994253. 0.00362845
\(76\) 9.60639e7 0.330293
\(77\) 1.04701e8 0.339425
\(78\) −2.40101e8 −0.734460
\(79\) −5.22199e8 −1.50839 −0.754196 0.656650i \(-0.771973\pi\)
−0.754196 + 0.656650i \(0.771973\pi\)
\(80\) 1.07802e8 0.294254
\(81\) 4.30467e7 0.111111
\(82\) −3.17173e8 −0.774702
\(83\) 6.25714e8 1.44719 0.723593 0.690226i \(-0.242489\pi\)
0.723593 + 0.690226i \(0.242489\pi\)
\(84\) −6.66549e7 −0.146075
\(85\) −7.85633e8 −1.63243
\(86\) −2.23346e8 −0.440287
\(87\) −1.27490e8 −0.238584
\(88\) 3.85292e8 0.684886
\(89\) −6.80185e8 −1.14914 −0.574569 0.818456i \(-0.694830\pi\)
−0.574569 + 0.818456i \(0.694830\pi\)
\(90\) 1.50358e8 0.241566
\(91\) 6.09596e8 0.931871
\(92\) 5.16042e8 0.751000
\(93\) −2.33846e8 −0.324157
\(94\) −2.56056e8 −0.338267
\(95\) 5.50178e8 0.693021
\(96\) −4.11232e8 −0.494158
\(97\) 9.35972e7 0.107347 0.0536735 0.998559i \(-0.482907\pi\)
0.0536735 + 0.998559i \(0.482907\pi\)
\(98\) 4.74910e8 0.520109
\(99\) 2.04342e8 0.213796
\(100\) −3.00465e6 −0.00300465
\(101\) 1.18057e9 1.12888 0.564438 0.825475i \(-0.309093\pi\)
0.564438 + 0.825475i \(0.309093\pi\)
\(102\) −7.42012e8 −0.678751
\(103\) −1.32026e8 −0.115582 −0.0577912 0.998329i \(-0.518406\pi\)
−0.0577912 + 0.998329i \(0.518406\pi\)
\(104\) 2.24327e9 1.88031
\(105\) −3.81747e8 −0.306495
\(106\) −1.15264e9 −0.886783
\(107\) 1.39713e9 1.03041 0.515205 0.857067i \(-0.327716\pi\)
0.515205 + 0.857067i \(0.327716\pi\)
\(108\) −1.30088e8 −0.0920091
\(109\) 9.61582e8 0.652480 0.326240 0.945287i \(-0.394218\pi\)
0.326240 + 0.945287i \(0.394218\pi\)
\(110\) 7.13747e8 0.464812
\(111\) −1.76379e8 −0.110279
\(112\) −2.58504e8 −0.155233
\(113\) −3.28060e9 −1.89278 −0.946391 0.323024i \(-0.895301\pi\)
−0.946391 + 0.323024i \(0.895301\pi\)
\(114\) 5.19630e8 0.288152
\(115\) 2.95548e9 1.57575
\(116\) 3.85279e8 0.197567
\(117\) 1.18973e9 0.586963
\(118\) 1.98079e8 0.0940525
\(119\) 1.88391e9 0.861188
\(120\) −1.40480e9 −0.618441
\(121\) −1.38794e9 −0.588623
\(122\) −2.25636e9 −0.922122
\(123\) 1.57163e9 0.619124
\(124\) 7.06686e8 0.268429
\(125\) 2.72093e9 0.996833
\(126\) −3.60551e8 −0.127438
\(127\) 5.47584e9 1.86781 0.933907 0.357516i \(-0.116376\pi\)
0.933907 + 0.357516i \(0.116376\pi\)
\(128\) 5.99170e8 0.197290
\(129\) 1.10671e9 0.351867
\(130\) 4.15561e9 1.27611
\(131\) 3.05429e9 0.906128 0.453064 0.891478i \(-0.350331\pi\)
0.453064 + 0.891478i \(0.350331\pi\)
\(132\) −6.17525e8 −0.177040
\(133\) −1.31930e9 −0.365603
\(134\) −3.42256e9 −0.917023
\(135\) −7.45042e8 −0.193054
\(136\) 6.93263e9 1.73769
\(137\) −6.36427e9 −1.54350 −0.771748 0.635928i \(-0.780618\pi\)
−0.771748 + 0.635928i \(0.780618\pi\)
\(138\) 2.79138e9 0.655184
\(139\) 2.77153e9 0.629728 0.314864 0.949137i \(-0.398041\pi\)
0.314864 + 0.949137i \(0.398041\pi\)
\(140\) 1.15365e9 0.253803
\(141\) 1.26879e9 0.270335
\(142\) 2.42988e9 0.501519
\(143\) 5.64761e9 1.12941
\(144\) −5.04512e8 −0.0977779
\(145\) 2.20657e9 0.414536
\(146\) 4.05792e9 0.739122
\(147\) −2.35323e9 −0.415659
\(148\) 5.33021e8 0.0913202
\(149\) 1.14918e10 1.91008 0.955040 0.296478i \(-0.0958123\pi\)
0.955040 + 0.296478i \(0.0958123\pi\)
\(150\) −1.62528e7 −0.00262130
\(151\) −4.20609e9 −0.658388 −0.329194 0.944262i \(-0.606777\pi\)
−0.329194 + 0.944262i \(0.606777\pi\)
\(152\) −4.85490e9 −0.737708
\(153\) 3.67675e9 0.542442
\(154\) −1.71153e9 −0.245211
\(155\) 4.04734e9 0.563219
\(156\) −3.59538e9 −0.486054
\(157\) −4.77264e9 −0.626917 −0.313459 0.949602i \(-0.601488\pi\)
−0.313459 + 0.949602i \(0.601488\pi\)
\(158\) 8.53626e9 1.08971
\(159\) 5.71146e9 0.708697
\(160\) 7.11749e9 0.858593
\(161\) −7.08708e9 −0.831287
\(162\) −7.03674e8 −0.0802701
\(163\) −8.24908e9 −0.915295 −0.457648 0.889134i \(-0.651308\pi\)
−0.457648 + 0.889134i \(0.651308\pi\)
\(164\) −4.74950e9 −0.512685
\(165\) −3.53669e9 −0.371467
\(166\) −1.02284e10 −1.04549
\(167\) 4.76936e9 0.474499 0.237250 0.971449i \(-0.423754\pi\)
0.237250 + 0.971449i \(0.423754\pi\)
\(168\) 3.36863e9 0.326258
\(169\) 2.22772e10 2.10073
\(170\) 1.28426e10 1.17932
\(171\) −2.57482e9 −0.230285
\(172\) −3.34449e9 −0.291375
\(173\) −7.56434e9 −0.642042 −0.321021 0.947072i \(-0.604026\pi\)
−0.321021 + 0.947072i \(0.604026\pi\)
\(174\) 2.08405e9 0.172360
\(175\) 4.12645e7 0.00332587
\(176\) −2.39491e9 −0.188140
\(177\) −9.81506e8 −0.0751646
\(178\) 1.11188e10 0.830173
\(179\) 2.65450e10 1.93261 0.966303 0.257407i \(-0.0828682\pi\)
0.966303 + 0.257407i \(0.0828682\pi\)
\(180\) 2.25153e9 0.159864
\(181\) −5.67564e9 −0.393062 −0.196531 0.980498i \(-0.562968\pi\)
−0.196531 + 0.980498i \(0.562968\pi\)
\(182\) −9.96492e9 −0.673213
\(183\) 1.11805e10 0.736938
\(184\) −2.60799e10 −1.67736
\(185\) 3.05272e9 0.191608
\(186\) 3.82262e9 0.234181
\(187\) 1.74535e10 1.04375
\(188\) −3.83430e9 −0.223859
\(189\) 1.78657e9 0.101845
\(190\) −8.99362e9 −0.500660
\(191\) −1.78592e9 −0.0970985 −0.0485493 0.998821i \(-0.515460\pi\)
−0.0485493 + 0.998821i \(0.515460\pi\)
\(192\) 9.91132e9 0.526352
\(193\) −9.29193e9 −0.482056 −0.241028 0.970518i \(-0.577485\pi\)
−0.241028 + 0.970518i \(0.577485\pi\)
\(194\) −1.53001e9 −0.0775509
\(195\) −2.05915e10 −1.01984
\(196\) 7.11152e9 0.344200
\(197\) 2.37061e9 0.112141 0.0560703 0.998427i \(-0.482143\pi\)
0.0560703 + 0.998427i \(0.482143\pi\)
\(198\) −3.34032e9 −0.154453
\(199\) −2.86581e10 −1.29541 −0.647706 0.761890i \(-0.724271\pi\)
−0.647706 + 0.761890i \(0.724271\pi\)
\(200\) 1.51850e8 0.00671089
\(201\) 1.69592e10 0.732863
\(202\) −1.92985e10 −0.815535
\(203\) −5.29124e9 −0.218688
\(204\) −1.11112e10 −0.449186
\(205\) −2.72014e10 −1.07572
\(206\) 2.15820e9 0.0835004
\(207\) −1.38316e10 −0.523608
\(208\) −1.39437e10 −0.516528
\(209\) −1.22226e10 −0.443105
\(210\) 6.24032e9 0.221422
\(211\) −7.11025e9 −0.246953 −0.123476 0.992348i \(-0.539404\pi\)
−0.123476 + 0.992348i \(0.539404\pi\)
\(212\) −1.72602e10 −0.586859
\(213\) −1.20403e10 −0.400802
\(214\) −2.28385e10 −0.744400
\(215\) −1.91546e10 −0.611364
\(216\) 6.57443e9 0.205502
\(217\) −9.70530e9 −0.297126
\(218\) −1.57187e10 −0.471372
\(219\) −2.01075e10 −0.590689
\(220\) 1.06880e10 0.307605
\(221\) 1.01618e11 2.86554
\(222\) 2.88322e9 0.0796691
\(223\) 1.40377e10 0.380124 0.190062 0.981772i \(-0.439131\pi\)
0.190062 + 0.981772i \(0.439131\pi\)
\(224\) −1.70674e10 −0.452950
\(225\) 8.05345e7 0.00209489
\(226\) 5.36272e10 1.36740
\(227\) 6.18630e10 1.54637 0.773187 0.634178i \(-0.218661\pi\)
0.773187 + 0.634178i \(0.218661\pi\)
\(228\) 7.78117e9 0.190695
\(229\) −1.23510e9 −0.0296786 −0.0148393 0.999890i \(-0.504724\pi\)
−0.0148393 + 0.999890i \(0.504724\pi\)
\(230\) −4.83125e10 −1.13837
\(231\) 8.48080e9 0.195967
\(232\) −1.94713e10 −0.441266
\(233\) 1.31833e10 0.293036 0.146518 0.989208i \(-0.453193\pi\)
0.146518 + 0.989208i \(0.453193\pi\)
\(234\) −1.94482e10 −0.424041
\(235\) −2.19598e10 −0.469703
\(236\) 2.96613e9 0.0622424
\(237\) −4.22981e10 −0.870870
\(238\) −3.07957e10 −0.622149
\(239\) 7.31541e10 1.45027 0.725133 0.688608i \(-0.241778\pi\)
0.725133 + 0.688608i \(0.241778\pi\)
\(240\) 8.73197e9 0.169888
\(241\) 6.96186e10 1.32938 0.664689 0.747120i \(-0.268564\pi\)
0.664689 + 0.747120i \(0.268564\pi\)
\(242\) 2.26883e10 0.425240
\(243\) 3.48678e9 0.0641500
\(244\) −3.37877e10 −0.610245
\(245\) 4.07292e10 0.722201
\(246\) −2.56910e10 −0.447274
\(247\) −7.11631e10 −1.21652
\(248\) −3.57147e10 −0.599535
\(249\) 5.06829e10 0.835534
\(250\) −4.44784e10 −0.720143
\(251\) −5.79655e10 −0.921802 −0.460901 0.887452i \(-0.652474\pi\)
−0.460901 + 0.887452i \(0.652474\pi\)
\(252\) −5.39905e9 −0.0843364
\(253\) −6.56583e10 −1.00751
\(254\) −8.95121e10 −1.34937
\(255\) −6.36363e10 −0.942484
\(256\) −7.24438e10 −1.05420
\(257\) 1.10867e10 0.158527 0.0792633 0.996854i \(-0.474743\pi\)
0.0792633 + 0.996854i \(0.474743\pi\)
\(258\) −1.80910e10 −0.254200
\(259\) −7.32026e9 −0.101083
\(260\) 6.22279e10 0.844511
\(261\) −1.03267e10 −0.137746
\(262\) −4.99277e10 −0.654615
\(263\) 1.03693e11 1.33644 0.668222 0.743962i \(-0.267056\pi\)
0.668222 + 0.743962i \(0.267056\pi\)
\(264\) 3.12087e10 0.395419
\(265\) −9.88525e10 −1.23135
\(266\) 2.15662e10 0.264123
\(267\) −5.50950e10 −0.663455
\(268\) −5.12510e10 −0.606871
\(269\) 4.72847e10 0.550599 0.275299 0.961359i \(-0.411223\pi\)
0.275299 + 0.961359i \(0.411223\pi\)
\(270\) 1.21790e10 0.139468
\(271\) 1.34795e10 0.151814 0.0759070 0.997115i \(-0.475815\pi\)
0.0759070 + 0.997115i \(0.475815\pi\)
\(272\) −4.30920e10 −0.477349
\(273\) 4.93773e10 0.538016
\(274\) 1.04035e11 1.11507
\(275\) 3.82295e8 0.00403090
\(276\) 4.17994e10 0.433590
\(277\) 1.74328e11 1.77913 0.889564 0.456810i \(-0.151008\pi\)
0.889564 + 0.456810i \(0.151008\pi\)
\(278\) −4.53055e10 −0.454935
\(279\) −1.89415e10 −0.187152
\(280\) −5.83033e10 −0.566869
\(281\) 1.10032e11 1.05278 0.526392 0.850242i \(-0.323545\pi\)
0.526392 + 0.850242i \(0.323545\pi\)
\(282\) −2.07405e10 −0.195298
\(283\) −8.34242e10 −0.773131 −0.386566 0.922262i \(-0.626339\pi\)
−0.386566 + 0.922262i \(0.626339\pi\)
\(284\) 3.63862e10 0.331897
\(285\) 4.45644e10 0.400116
\(286\) −9.23200e10 −0.815922
\(287\) 6.52274e10 0.567495
\(288\) −3.33098e10 −0.285302
\(289\) 1.95455e11 1.64819
\(290\) −3.60703e10 −0.299474
\(291\) 7.58137e9 0.0619769
\(292\) 6.07652e10 0.489139
\(293\) 8.47020e10 0.671412 0.335706 0.941967i \(-0.391025\pi\)
0.335706 + 0.941967i \(0.391025\pi\)
\(294\) 3.84677e10 0.300285
\(295\) 1.69877e10 0.130597
\(296\) −2.69380e10 −0.203963
\(297\) 1.65517e10 0.123435
\(298\) −1.87854e11 −1.37990
\(299\) −3.82279e11 −2.76605
\(300\) −2.43377e8 −0.00173474
\(301\) 4.59317e10 0.322525
\(302\) 6.87558e10 0.475640
\(303\) 9.56263e10 0.651757
\(304\) 3.01772e10 0.202651
\(305\) −1.93509e11 −1.28042
\(306\) −6.01030e10 −0.391877
\(307\) −2.10679e11 −1.35363 −0.676814 0.736154i \(-0.736640\pi\)
−0.676814 + 0.736154i \(0.736640\pi\)
\(308\) −2.56292e10 −0.162277
\(309\) −1.06941e10 −0.0667316
\(310\) −6.61608e10 −0.406887
\(311\) 2.21798e11 1.34442 0.672211 0.740359i \(-0.265345\pi\)
0.672211 + 0.740359i \(0.265345\pi\)
\(312\) 1.81704e11 1.08560
\(313\) −2.84657e11 −1.67638 −0.838189 0.545380i \(-0.816385\pi\)
−0.838189 + 0.545380i \(0.816385\pi\)
\(314\) 7.80172e10 0.452905
\(315\) −3.09215e10 −0.176955
\(316\) 1.27826e11 0.721152
\(317\) 3.66864e9 0.0204051 0.0102026 0.999948i \(-0.496752\pi\)
0.0102026 + 0.999948i \(0.496752\pi\)
\(318\) −9.33639e10 −0.511985
\(319\) −4.90207e10 −0.265046
\(320\) −1.71543e11 −0.914528
\(321\) 1.13168e11 0.594907
\(322\) 1.15851e11 0.600548
\(323\) −2.19924e11 −1.12424
\(324\) −1.05371e10 −0.0531215
\(325\) 2.22582e9 0.0110666
\(326\) 1.34846e11 0.661238
\(327\) 7.78881e10 0.376709
\(328\) 2.40032e11 1.14508
\(329\) 5.26584e10 0.247791
\(330\) 5.78135e10 0.268359
\(331\) 1.19871e11 0.548895 0.274447 0.961602i \(-0.411505\pi\)
0.274447 + 0.961602i \(0.411505\pi\)
\(332\) −1.53165e11 −0.691890
\(333\) −1.42867e10 −0.0636697
\(334\) −7.79635e10 −0.342793
\(335\) −2.93525e11 −1.27334
\(336\) −2.09388e10 −0.0896241
\(337\) −2.27970e11 −0.962816 −0.481408 0.876497i \(-0.659874\pi\)
−0.481408 + 0.876497i \(0.659874\pi\)
\(338\) −3.64161e11 −1.51764
\(339\) −2.65729e11 −1.09280
\(340\) 1.92310e11 0.780454
\(341\) −8.99148e10 −0.360111
\(342\) 4.20900e10 0.166365
\(343\) −2.33325e11 −0.910201
\(344\) 1.69025e11 0.650785
\(345\) 2.39394e11 0.909761
\(346\) 1.23652e11 0.463831
\(347\) 2.82682e11 1.04668 0.523341 0.852123i \(-0.324685\pi\)
0.523341 + 0.852123i \(0.324685\pi\)
\(348\) 3.12076e10 0.114065
\(349\) −2.13705e11 −0.771082 −0.385541 0.922691i \(-0.625985\pi\)
−0.385541 + 0.922691i \(0.625985\pi\)
\(350\) −6.74540e8 −0.00240271
\(351\) 9.63679e10 0.338884
\(352\) −1.58121e11 −0.548968
\(353\) −1.01077e11 −0.346472 −0.173236 0.984880i \(-0.555422\pi\)
−0.173236 + 0.984880i \(0.555422\pi\)
\(354\) 1.60444e10 0.0543012
\(355\) 2.08391e11 0.696388
\(356\) 1.66498e11 0.549395
\(357\) 1.52596e11 0.497207
\(358\) −4.33924e11 −1.39617
\(359\) 6.52223e10 0.207239 0.103619 0.994617i \(-0.466958\pi\)
0.103619 + 0.994617i \(0.466958\pi\)
\(360\) −1.13789e11 −0.357057
\(361\) −1.68676e11 −0.522721
\(362\) 9.27782e10 0.283960
\(363\) −1.12423e11 −0.339842
\(364\) −1.49219e11 −0.445521
\(365\) 3.48015e11 1.02631
\(366\) −1.82765e11 −0.532387
\(367\) 5.97288e11 1.71865 0.859323 0.511434i \(-0.170885\pi\)
0.859323 + 0.511434i \(0.170885\pi\)
\(368\) 1.62108e11 0.460775
\(369\) 1.27302e11 0.357451
\(370\) −4.99021e10 −0.138424
\(371\) 2.37043e11 0.649598
\(372\) 5.72416e10 0.154977
\(373\) −5.35635e11 −1.43278 −0.716389 0.697701i \(-0.754206\pi\)
−0.716389 + 0.697701i \(0.754206\pi\)
\(374\) −2.85307e11 −0.754034
\(375\) 2.20395e11 0.575522
\(376\) 1.93779e11 0.499990
\(377\) −2.85411e11 −0.727669
\(378\) −2.92046e10 −0.0735763
\(379\) 3.00653e11 0.748496 0.374248 0.927329i \(-0.377901\pi\)
0.374248 + 0.927329i \(0.377901\pi\)
\(380\) −1.34675e11 −0.331329
\(381\) 4.43543e11 1.07838
\(382\) 2.91940e10 0.0701470
\(383\) 1.30463e11 0.309809 0.154905 0.987929i \(-0.450493\pi\)
0.154905 + 0.987929i \(0.450493\pi\)
\(384\) 4.85328e10 0.113906
\(385\) −1.46784e11 −0.340490
\(386\) 1.51893e11 0.348253
\(387\) 8.96432e10 0.203151
\(388\) −2.29111e10 −0.0513219
\(389\) 7.22330e11 1.59942 0.799710 0.600386i \(-0.204986\pi\)
0.799710 + 0.600386i \(0.204986\pi\)
\(390\) 3.36604e11 0.736764
\(391\) −1.18140e12 −2.55624
\(392\) −3.59404e11 −0.768769
\(393\) 2.47397e11 0.523153
\(394\) −3.87518e10 −0.0810139
\(395\) 7.32085e11 1.51312
\(396\) −5.00195e10 −0.102214
\(397\) 6.36817e11 1.28664 0.643321 0.765597i \(-0.277556\pi\)
0.643321 + 0.765597i \(0.277556\pi\)
\(398\) 4.68466e11 0.935846
\(399\) −1.06863e11 −0.211081
\(400\) −9.43873e8 −0.00184350
\(401\) 3.75683e11 0.725557 0.362778 0.931875i \(-0.381828\pi\)
0.362778 + 0.931875i \(0.381828\pi\)
\(402\) −2.77228e11 −0.529443
\(403\) −5.23506e11 −0.988664
\(404\) −2.88985e11 −0.539708
\(405\) −6.03484e10 −0.111460
\(406\) 8.64946e10 0.157987
\(407\) −6.78186e10 −0.122511
\(408\) 5.61543e11 1.00326
\(409\) −4.30578e11 −0.760847 −0.380424 0.924812i \(-0.624222\pi\)
−0.380424 + 0.924812i \(0.624222\pi\)
\(410\) 4.44654e11 0.777132
\(411\) −5.15506e11 −0.891138
\(412\) 3.23178e10 0.0552592
\(413\) −4.07355e10 −0.0688966
\(414\) 2.26102e11 0.378271
\(415\) −8.77206e11 −1.45173
\(416\) −9.20617e11 −1.50716
\(417\) 2.24494e11 0.363574
\(418\) 1.99800e11 0.320113
\(419\) −4.21627e11 −0.668291 −0.334146 0.942521i \(-0.608448\pi\)
−0.334146 + 0.942521i \(0.608448\pi\)
\(420\) 9.34454e10 0.146533
\(421\) 5.44686e11 0.845039 0.422519 0.906354i \(-0.361146\pi\)
0.422519 + 0.906354i \(0.361146\pi\)
\(422\) 1.16230e11 0.178406
\(423\) 1.02772e11 0.156078
\(424\) 8.72300e11 1.31075
\(425\) 6.87870e9 0.0102272
\(426\) 1.96820e11 0.289552
\(427\) 4.64024e11 0.675485
\(428\) −3.41995e11 −0.492632
\(429\) 4.57456e11 0.652066
\(430\) 3.13115e11 0.441668
\(431\) 1.30392e11 0.182013 0.0910067 0.995850i \(-0.470992\pi\)
0.0910067 + 0.995850i \(0.470992\pi\)
\(432\) −4.08655e10 −0.0564521
\(433\) 1.21450e12 1.66035 0.830177 0.557501i \(-0.188240\pi\)
0.830177 + 0.557501i \(0.188240\pi\)
\(434\) 1.58650e11 0.214653
\(435\) 1.78732e11 0.239332
\(436\) −2.35380e11 −0.311946
\(437\) 8.27333e11 1.08521
\(438\) 3.28692e11 0.426732
\(439\) −2.42493e11 −0.311608 −0.155804 0.987788i \(-0.549797\pi\)
−0.155804 + 0.987788i \(0.549797\pi\)
\(440\) −5.40152e11 −0.687035
\(441\) −1.90612e11 −0.239981
\(442\) −1.66113e12 −2.07016
\(443\) 7.51319e11 0.926846 0.463423 0.886137i \(-0.346621\pi\)
0.463423 + 0.886137i \(0.346621\pi\)
\(444\) 4.31747e10 0.0527237
\(445\) 9.53570e11 1.15274
\(446\) −2.29471e11 −0.274613
\(447\) 9.30839e11 1.10278
\(448\) 4.11350e11 0.482459
\(449\) 4.50564e11 0.523176 0.261588 0.965180i \(-0.415754\pi\)
0.261588 + 0.965180i \(0.415754\pi\)
\(450\) −1.31648e9 −0.00151341
\(451\) 6.04300e11 0.687794
\(452\) 8.03038e11 0.904926
\(453\) −3.40693e11 −0.380120
\(454\) −1.01126e12 −1.11715
\(455\) −8.54609e11 −0.934795
\(456\) −3.93247e11 −0.425916
\(457\) −8.20512e11 −0.879958 −0.439979 0.898008i \(-0.645014\pi\)
−0.439979 + 0.898008i \(0.645014\pi\)
\(458\) 2.01899e10 0.0214407
\(459\) 2.97817e11 0.313179
\(460\) −7.23454e11 −0.753356
\(461\) −3.57199e11 −0.368346 −0.184173 0.982894i \(-0.558961\pi\)
−0.184173 + 0.982894i \(0.558961\pi\)
\(462\) −1.38634e11 −0.141573
\(463\) 8.01850e11 0.810922 0.405461 0.914112i \(-0.367111\pi\)
0.405461 + 0.914112i \(0.367111\pi\)
\(464\) 1.21030e11 0.121217
\(465\) 3.27834e11 0.325174
\(466\) −2.15504e11 −0.211699
\(467\) −9.38973e10 −0.0913540 −0.0456770 0.998956i \(-0.514544\pi\)
−0.0456770 + 0.998956i \(0.514544\pi\)
\(468\) −2.91226e11 −0.280623
\(469\) 7.03858e11 0.671749
\(470\) 3.58972e11 0.339328
\(471\) −3.86584e11 −0.361951
\(472\) −1.49903e11 −0.139018
\(473\) 4.25534e11 0.390894
\(474\) 6.91437e11 0.629144
\(475\) −4.81714e9 −0.00434178
\(476\) −4.61150e11 −0.411728
\(477\) 4.62629e11 0.409166
\(478\) −1.19583e12 −1.04772
\(479\) 1.82709e11 0.158580 0.0792902 0.996852i \(-0.474735\pi\)
0.0792902 + 0.996852i \(0.474735\pi\)
\(480\) 5.76517e11 0.495709
\(481\) −3.94856e11 −0.336346
\(482\) −1.13804e12 −0.960384
\(483\) −5.74054e11 −0.479944
\(484\) 3.39746e11 0.281417
\(485\) −1.31216e11 −0.107684
\(486\) −5.69976e10 −0.0463440
\(487\) 7.57497e10 0.0610240 0.0305120 0.999534i \(-0.490286\pi\)
0.0305120 + 0.999534i \(0.490286\pi\)
\(488\) 1.70757e12 1.36298
\(489\) −6.68175e11 −0.528446
\(490\) −6.65790e11 −0.521741
\(491\) 2.98778e11 0.231997 0.115998 0.993249i \(-0.462993\pi\)
0.115998 + 0.993249i \(0.462993\pi\)
\(492\) −3.84710e11 −0.295999
\(493\) −8.82038e11 −0.672475
\(494\) 1.16329e12 0.878851
\(495\) −2.86472e11 −0.214466
\(496\) 2.21996e11 0.164694
\(497\) −4.99710e11 −0.367379
\(498\) −8.28500e11 −0.603616
\(499\) 1.82082e12 1.31466 0.657331 0.753602i \(-0.271685\pi\)
0.657331 + 0.753602i \(0.271685\pi\)
\(500\) −6.66040e11 −0.476579
\(501\) 3.86318e11 0.273952
\(502\) 9.47547e11 0.665938
\(503\) 1.20304e12 0.837964 0.418982 0.907994i \(-0.362387\pi\)
0.418982 + 0.907994i \(0.362387\pi\)
\(504\) 2.72859e11 0.188365
\(505\) −1.65508e12 −1.13242
\(506\) 1.07330e12 0.727853
\(507\) 1.80446e12 1.21286
\(508\) −1.34040e12 −0.892989
\(509\) −2.85545e12 −1.88558 −0.942788 0.333391i \(-0.891807\pi\)
−0.942788 + 0.333391i \(0.891807\pi\)
\(510\) 1.04025e12 0.680880
\(511\) −8.34521e11 −0.541431
\(512\) 8.77446e11 0.564294
\(513\) −2.08561e11 −0.132955
\(514\) −1.81231e11 −0.114525
\(515\) 1.85091e11 0.115945
\(516\) −2.70904e11 −0.168225
\(517\) 4.87854e11 0.300319
\(518\) 1.19662e11 0.0730254
\(519\) −6.12712e11 −0.370683
\(520\) −3.14489e12 −1.88621
\(521\) 2.69409e12 1.60193 0.800963 0.598713i \(-0.204321\pi\)
0.800963 + 0.598713i \(0.204321\pi\)
\(522\) 1.68808e11 0.0995123
\(523\) 7.79450e11 0.455544 0.227772 0.973714i \(-0.426856\pi\)
0.227772 + 0.973714i \(0.426856\pi\)
\(524\) −7.47640e11 −0.433214
\(525\) 3.34242e9 0.00192019
\(526\) −1.69505e12 −0.965488
\(527\) −1.61785e12 −0.913673
\(528\) −1.93988e11 −0.108623
\(529\) 2.64317e12 1.46749
\(530\) 1.61592e12 0.889565
\(531\) −7.95020e10 −0.0433963
\(532\) 3.22942e11 0.174792
\(533\) 3.51838e12 1.88830
\(534\) 9.00624e11 0.479301
\(535\) −1.95868e12 −1.03364
\(536\) 2.59014e12 1.35544
\(537\) 2.15014e12 1.11579
\(538\) −7.72951e11 −0.397770
\(539\) −9.04831e11 −0.461762
\(540\) 1.82374e11 0.0922978
\(541\) −1.13636e12 −0.570335 −0.285167 0.958478i \(-0.592049\pi\)
−0.285167 + 0.958478i \(0.592049\pi\)
\(542\) −2.20346e11 −0.109675
\(543\) −4.59727e11 −0.226934
\(544\) −2.84509e12 −1.39284
\(545\) −1.34807e12 −0.654527
\(546\) −8.07158e11 −0.388680
\(547\) 1.13181e12 0.540542 0.270271 0.962784i \(-0.412887\pi\)
0.270271 + 0.962784i \(0.412887\pi\)
\(548\) 1.55787e12 0.737935
\(549\) 9.05620e11 0.425472
\(550\) −6.24928e9 −0.00291205
\(551\) 6.17689e11 0.285488
\(552\) −2.11247e12 −0.968423
\(553\) −1.75550e12 −0.798248
\(554\) −2.84969e12 −1.28530
\(555\) 2.47270e11 0.110625
\(556\) −6.78426e11 −0.301069
\(557\) 2.12002e11 0.0933238 0.0466619 0.998911i \(-0.485142\pi\)
0.0466619 + 0.998911i \(0.485142\pi\)
\(558\) 3.09632e11 0.135205
\(559\) 2.47756e12 1.07318
\(560\) 3.62403e11 0.155721
\(561\) 1.41373e12 0.602606
\(562\) −1.79866e12 −0.760563
\(563\) −3.99743e12 −1.67684 −0.838422 0.545022i \(-0.816521\pi\)
−0.838422 + 0.545022i \(0.816521\pi\)
\(564\) −3.10578e11 −0.129245
\(565\) 4.59916e12 1.89872
\(566\) 1.36372e12 0.558534
\(567\) 1.44712e11 0.0588005
\(568\) −1.83889e12 −0.741292
\(569\) 2.47154e12 0.988469 0.494235 0.869329i \(-0.335448\pi\)
0.494235 + 0.869329i \(0.335448\pi\)
\(570\) −7.28483e11 −0.289056
\(571\) −3.38809e12 −1.33381 −0.666903 0.745145i \(-0.732380\pi\)
−0.666903 + 0.745145i \(0.732380\pi\)
\(572\) −1.38244e12 −0.539964
\(573\) −1.44660e11 −0.0560599
\(574\) −1.06626e12 −0.409976
\(575\) −2.58770e10 −0.00987209
\(576\) 8.02817e11 0.303889
\(577\) −2.44916e12 −0.919869 −0.459934 0.887953i \(-0.652127\pi\)
−0.459934 + 0.887953i \(0.652127\pi\)
\(578\) −3.19506e12 −1.19070
\(579\) −7.52646e11 −0.278315
\(580\) −5.40133e11 −0.198187
\(581\) 2.10349e12 0.765858
\(582\) −1.23931e11 −0.0447740
\(583\) 2.19609e12 0.787301
\(584\) −3.07097e12 −1.09249
\(585\) −1.66791e12 −0.588805
\(586\) −1.38460e12 −0.485049
\(587\) −4.46433e12 −1.55197 −0.775987 0.630749i \(-0.782748\pi\)
−0.775987 + 0.630749i \(0.782748\pi\)
\(588\) 5.76034e11 0.198724
\(589\) 1.13298e12 0.387885
\(590\) −2.77693e11 −0.0943476
\(591\) 1.92020e11 0.0647444
\(592\) 1.67442e11 0.0560294
\(593\) −3.99401e12 −1.32637 −0.663183 0.748457i \(-0.730795\pi\)
−0.663183 + 0.748457i \(0.730795\pi\)
\(594\) −2.70566e11 −0.0891733
\(595\) −2.64110e12 −0.863890
\(596\) −2.81302e12 −0.913196
\(597\) −2.32130e12 −0.747906
\(598\) 6.24901e12 1.99828
\(599\) 9.60826e11 0.304947 0.152473 0.988308i \(-0.451276\pi\)
0.152473 + 0.988308i \(0.451276\pi\)
\(600\) 1.22999e10 0.00387453
\(601\) 8.37458e11 0.261835 0.130918 0.991393i \(-0.458208\pi\)
0.130918 + 0.991393i \(0.458208\pi\)
\(602\) −7.50833e11 −0.233002
\(603\) 1.37369e12 0.423119
\(604\) 1.02958e12 0.314771
\(605\) 1.94579e12 0.590470
\(606\) −1.56318e12 −0.470850
\(607\) 2.20940e11 0.0660578 0.0330289 0.999454i \(-0.489485\pi\)
0.0330289 + 0.999454i \(0.489485\pi\)
\(608\) 1.99241e12 0.591307
\(609\) −4.28590e11 −0.126260
\(610\) 3.16325e12 0.925015
\(611\) 2.84041e12 0.824508
\(612\) −9.00010e11 −0.259338
\(613\) −5.34560e12 −1.52906 −0.764530 0.644588i \(-0.777029\pi\)
−0.764530 + 0.644588i \(0.777029\pi\)
\(614\) 3.44392e12 0.977903
\(615\) −2.20331e12 −0.621066
\(616\) 1.29525e12 0.362445
\(617\) 1.02111e12 0.283656 0.141828 0.989891i \(-0.454702\pi\)
0.141828 + 0.989891i \(0.454702\pi\)
\(618\) 1.74814e11 0.0482090
\(619\) 6.46932e12 1.77113 0.885566 0.464514i \(-0.153771\pi\)
0.885566 + 0.464514i \(0.153771\pi\)
\(620\) −9.90723e11 −0.269271
\(621\) −1.12036e12 −0.302305
\(622\) −3.62568e12 −0.971253
\(623\) −2.28661e12 −0.608129
\(624\) −1.12944e12 −0.298218
\(625\) −3.83852e12 −1.00625
\(626\) 4.65321e12 1.21107
\(627\) −9.90033e11 −0.255827
\(628\) 1.16826e12 0.299725
\(629\) −1.22027e12 −0.310834
\(630\) 5.05466e11 0.127838
\(631\) 2.92249e12 0.733873 0.366936 0.930246i \(-0.380407\pi\)
0.366936 + 0.930246i \(0.380407\pi\)
\(632\) −6.46010e12 −1.61069
\(633\) −5.75931e11 −0.142578
\(634\) −5.99704e10 −0.0147413
\(635\) −7.67672e12 −1.87367
\(636\) −1.39807e12 −0.338823
\(637\) −5.26814e12 −1.26774
\(638\) 8.01330e11 0.191478
\(639\) −9.75267e11 −0.231403
\(640\) −8.39993e11 −0.197909
\(641\) 9.07867e11 0.212403 0.106202 0.994345i \(-0.466131\pi\)
0.106202 + 0.994345i \(0.466131\pi\)
\(642\) −1.84992e12 −0.429780
\(643\) −7.71700e12 −1.78033 −0.890163 0.455643i \(-0.849409\pi\)
−0.890163 + 0.455643i \(0.849409\pi\)
\(644\) 1.73480e12 0.397433
\(645\) −1.55152e12 −0.352971
\(646\) 3.59504e12 0.812189
\(647\) −6.56641e12 −1.47319 −0.736595 0.676334i \(-0.763568\pi\)
−0.736595 + 0.676334i \(0.763568\pi\)
\(648\) 5.32529e11 0.118647
\(649\) −3.77394e11 −0.0835015
\(650\) −3.63848e10 −0.00799485
\(651\) −7.86129e11 −0.171546
\(652\) 2.01924e12 0.437597
\(653\) −6.60194e12 −1.42090 −0.710448 0.703750i \(-0.751508\pi\)
−0.710448 + 0.703750i \(0.751508\pi\)
\(654\) −1.27322e12 −0.272146
\(655\) −4.28189e12 −0.908971
\(656\) −1.49199e12 −0.314557
\(657\) −1.62871e12 −0.341034
\(658\) −8.60794e11 −0.179012
\(659\) −3.09082e12 −0.638394 −0.319197 0.947688i \(-0.603413\pi\)
−0.319197 + 0.947688i \(0.603413\pi\)
\(660\) 8.65725e11 0.177596
\(661\) −4.17896e12 −0.851456 −0.425728 0.904851i \(-0.639982\pi\)
−0.425728 + 0.904851i \(0.639982\pi\)
\(662\) −1.95951e12 −0.396539
\(663\) 8.23108e12 1.65442
\(664\) 7.74068e12 1.54534
\(665\) 1.84956e12 0.366750
\(666\) 2.33541e11 0.0459970
\(667\) 3.31814e12 0.649126
\(668\) −1.16746e12 −0.226855
\(669\) 1.13706e12 0.219465
\(670\) 4.79819e12 0.919900
\(671\) 4.29896e12 0.818676
\(672\) −1.38246e12 −0.261511
\(673\) −4.82850e12 −0.907287 −0.453644 0.891183i \(-0.649876\pi\)
−0.453644 + 0.891183i \(0.649876\pi\)
\(674\) 3.72657e12 0.695568
\(675\) 6.52329e9 0.00120948
\(676\) −5.45311e12 −1.00435
\(677\) 8.64207e12 1.58114 0.790568 0.612375i \(-0.209786\pi\)
0.790568 + 0.612375i \(0.209786\pi\)
\(678\) 4.34380e12 0.789471
\(679\) 3.14650e11 0.0568086
\(680\) −9.71904e12 −1.74314
\(681\) 5.01090e12 0.892799
\(682\) 1.46982e12 0.260156
\(683\) 2.80206e12 0.492703 0.246351 0.969181i \(-0.420768\pi\)
0.246351 + 0.969181i \(0.420768\pi\)
\(684\) 6.30275e11 0.110098
\(685\) 8.92224e12 1.54834
\(686\) 3.81410e12 0.657558
\(687\) −1.00043e11 −0.0171349
\(688\) −1.05063e12 −0.178773
\(689\) 1.27862e13 2.16149
\(690\) −3.91331e12 −0.657239
\(691\) 5.96570e12 0.995429 0.497714 0.867341i \(-0.334173\pi\)
0.497714 + 0.867341i \(0.334173\pi\)
\(692\) 1.85163e12 0.306956
\(693\) 6.86945e11 0.113142
\(694\) −4.62093e12 −0.756156
\(695\) −3.88548e12 −0.631704
\(696\) −1.57718e12 −0.254765
\(697\) 1.08733e13 1.74507
\(698\) 3.49338e12 0.557053
\(699\) 1.06785e12 0.169185
\(700\) −1.01009e10 −0.00159008
\(701\) 6.02618e12 0.942565 0.471283 0.881982i \(-0.343791\pi\)
0.471283 + 0.881982i \(0.343791\pi\)
\(702\) −1.57530e12 −0.244820
\(703\) 8.54554e11 0.131959
\(704\) 3.81095e12 0.584732
\(705\) −1.77874e12 −0.271183
\(706\) 1.65229e12 0.250302
\(707\) 3.96878e12 0.597406
\(708\) 2.40257e11 0.0359357
\(709\) 9.37965e12 1.39405 0.697025 0.717047i \(-0.254507\pi\)
0.697025 + 0.717047i \(0.254507\pi\)
\(710\) −3.40652e12 −0.503093
\(711\) −3.42615e12 −0.502797
\(712\) −8.41454e12 −1.22707
\(713\) 6.08621e12 0.881950
\(714\) −2.49446e12 −0.359198
\(715\) −7.91753e12 −1.13296
\(716\) −6.49777e12 −0.923966
\(717\) 5.92548e12 0.837312
\(718\) −1.06617e12 −0.149716
\(719\) 2.94327e12 0.410724 0.205362 0.978686i \(-0.434163\pi\)
0.205362 + 0.978686i \(0.434163\pi\)
\(720\) 7.07289e11 0.0980846
\(721\) −4.43838e11 −0.0611668
\(722\) 2.75730e12 0.377630
\(723\) 5.63911e12 0.767517
\(724\) 1.38930e12 0.187920
\(725\) −1.93199e10 −0.00259707
\(726\) 1.83776e12 0.245512
\(727\) 4.80339e12 0.637739 0.318870 0.947799i \(-0.396697\pi\)
0.318870 + 0.947799i \(0.396697\pi\)
\(728\) 7.54129e12 0.995071
\(729\) 2.82430e11 0.0370370
\(730\) −5.68891e12 −0.741441
\(731\) 7.65670e12 0.991776
\(732\) −2.73680e12 −0.352325
\(733\) −3.39490e12 −0.434370 −0.217185 0.976130i \(-0.569687\pi\)
−0.217185 + 0.976130i \(0.569687\pi\)
\(734\) −9.76371e12 −1.24160
\(735\) 3.29906e12 0.416963
\(736\) 1.07030e13 1.34448
\(737\) 6.52090e12 0.814148
\(738\) −2.08098e12 −0.258234
\(739\) 2.13168e12 0.262919 0.131460 0.991322i \(-0.458034\pi\)
0.131460 + 0.991322i \(0.458034\pi\)
\(740\) −7.47257e11 −0.0916067
\(741\) −5.76421e12 −0.702357
\(742\) −3.87488e12 −0.469290
\(743\) 2.82447e12 0.340006 0.170003 0.985444i \(-0.445622\pi\)
0.170003 + 0.985444i \(0.445622\pi\)
\(744\) −2.89289e12 −0.346142
\(745\) −1.61107e13 −1.91607
\(746\) 8.75588e12 1.03508
\(747\) 4.10531e12 0.482396
\(748\) −4.27232e12 −0.499007
\(749\) 4.69680e12 0.545298
\(750\) −3.60275e12 −0.415775
\(751\) −2.42385e12 −0.278052 −0.139026 0.990289i \(-0.544397\pi\)
−0.139026 + 0.990289i \(0.544397\pi\)
\(752\) −1.20449e12 −0.137349
\(753\) −4.69520e12 −0.532203
\(754\) 4.66554e12 0.525691
\(755\) 5.89663e12 0.660454
\(756\) −4.37323e11 −0.0486916
\(757\) 3.90640e12 0.432359 0.216180 0.976354i \(-0.430640\pi\)
0.216180 + 0.976354i \(0.430640\pi\)
\(758\) −4.91470e12 −0.540737
\(759\) −5.31832e12 −0.581684
\(760\) 6.80622e12 0.740023
\(761\) 6.76565e12 0.731272 0.365636 0.930758i \(-0.380852\pi\)
0.365636 + 0.930758i \(0.380852\pi\)
\(762\) −7.25048e12 −0.779057
\(763\) 3.23259e12 0.345295
\(764\) 4.37165e11 0.0464222
\(765\) −5.15454e12 −0.544144
\(766\) −2.13265e12 −0.223816
\(767\) −2.19728e12 −0.229248
\(768\) −5.86795e12 −0.608640
\(769\) 1.08276e13 1.11651 0.558255 0.829669i \(-0.311471\pi\)
0.558255 + 0.829669i \(0.311471\pi\)
\(770\) 2.39943e12 0.245980
\(771\) 8.98021e11 0.0915254
\(772\) 2.27451e12 0.230468
\(773\) −1.93513e13 −1.94941 −0.974704 0.223500i \(-0.928252\pi\)
−0.974704 + 0.223500i \(0.928252\pi\)
\(774\) −1.46537e12 −0.146762
\(775\) −3.54369e10 −0.00352857
\(776\) 1.15789e12 0.114627
\(777\) −5.92941e11 −0.0583602
\(778\) −1.18078e13 −1.15547
\(779\) −7.61453e12 −0.740840
\(780\) 5.04046e12 0.487579
\(781\) −4.62957e12 −0.445257
\(782\) 1.93121e13 1.84671
\(783\) −8.36465e11 −0.0795280
\(784\) 2.23399e12 0.211183
\(785\) 6.69090e12 0.628884
\(786\) −4.04414e12 −0.377942
\(787\) 1.80989e13 1.68177 0.840885 0.541214i \(-0.182035\pi\)
0.840885 + 0.541214i \(0.182035\pi\)
\(788\) −5.80288e11 −0.0536137
\(789\) 8.39917e12 0.771596
\(790\) −1.19672e13 −1.09313
\(791\) −1.10285e13 −1.00167
\(792\) 2.52790e12 0.228295
\(793\) 2.50296e13 2.24763
\(794\) −1.04099e13 −0.929510
\(795\) −8.00706e12 −0.710920
\(796\) 7.01503e12 0.619328
\(797\) 5.88413e12 0.516559 0.258279 0.966070i \(-0.416844\pi\)
0.258279 + 0.966070i \(0.416844\pi\)
\(798\) 1.74686e12 0.152492
\(799\) 8.77804e12 0.761969
\(800\) −6.23180e10 −0.00537909
\(801\) −4.46270e12 −0.383046
\(802\) −6.14119e12 −0.524165
\(803\) −7.73142e12 −0.656205
\(804\) −4.15133e12 −0.350377
\(805\) 9.93557e12 0.833895
\(806\) 8.55762e12 0.714242
\(807\) 3.83006e12 0.317888
\(808\) 1.46048e13 1.20544
\(809\) −8.22827e12 −0.675368 −0.337684 0.941260i \(-0.609643\pi\)
−0.337684 + 0.941260i \(0.609643\pi\)
\(810\) 9.86500e11 0.0805220
\(811\) 1.36302e13 1.10639 0.553196 0.833051i \(-0.313408\pi\)
0.553196 + 0.833051i \(0.313408\pi\)
\(812\) 1.29521e12 0.104553
\(813\) 1.09184e12 0.0876498
\(814\) 1.10861e12 0.0885056
\(815\) 1.15646e13 0.918167
\(816\) −3.49045e12 −0.275598
\(817\) −5.36197e12 −0.421042
\(818\) 7.03856e12 0.549660
\(819\) 3.99956e12 0.310624
\(820\) 6.65845e12 0.514294
\(821\) −2.06555e13 −1.58668 −0.793342 0.608776i \(-0.791661\pi\)
−0.793342 + 0.608776i \(0.791661\pi\)
\(822\) 8.42684e12 0.643786
\(823\) 2.84174e12 0.215916 0.107958 0.994155i \(-0.465569\pi\)
0.107958 + 0.994155i \(0.465569\pi\)
\(824\) −1.63329e12 −0.123421
\(825\) 3.09659e10 0.00232724
\(826\) 6.65893e11 0.0497730
\(827\) −4.68952e12 −0.348621 −0.174311 0.984691i \(-0.555770\pi\)
−0.174311 + 0.984691i \(0.555770\pi\)
\(828\) 3.38575e12 0.250333
\(829\) 2.39047e13 1.75788 0.878939 0.476935i \(-0.158252\pi\)
0.878939 + 0.476935i \(0.158252\pi\)
\(830\) 1.43395e13 1.04877
\(831\) 1.41205e13 1.02718
\(832\) 2.21883e13 1.60535
\(833\) −1.62808e13 −1.17158
\(834\) −3.66975e12 −0.262657
\(835\) −6.68629e12 −0.475988
\(836\) 2.99190e12 0.211845
\(837\) −1.53426e12 −0.108052
\(838\) 6.89224e12 0.482794
\(839\) −2.47263e13 −1.72278 −0.861392 0.507940i \(-0.830407\pi\)
−0.861392 + 0.507940i \(0.830407\pi\)
\(840\) −4.72257e12 −0.327282
\(841\) −1.20298e13 −0.829233
\(842\) −8.90384e12 −0.610482
\(843\) 8.91256e12 0.607825
\(844\) 1.74047e12 0.118066
\(845\) −3.12311e13 −2.10733
\(846\) −1.67998e12 −0.112756
\(847\) −4.66591e12 −0.311502
\(848\) −5.42206e12 −0.360067
\(849\) −6.75736e12 −0.446368
\(850\) −1.12444e11 −0.00738844
\(851\) 4.59055e12 0.300042
\(852\) 2.94728e12 0.191621
\(853\) −1.17423e13 −0.759420 −0.379710 0.925106i \(-0.623976\pi\)
−0.379710 + 0.925106i \(0.623976\pi\)
\(854\) −7.58529e12 −0.487991
\(855\) 3.60972e12 0.231007
\(856\) 1.72838e13 1.10029
\(857\) 2.65634e11 0.0168217 0.00841084 0.999965i \(-0.497323\pi\)
0.00841084 + 0.999965i \(0.497323\pi\)
\(858\) −7.47792e12 −0.471073
\(859\) 4.27853e12 0.268117 0.134059 0.990973i \(-0.457199\pi\)
0.134059 + 0.990973i \(0.457199\pi\)
\(860\) 4.68873e12 0.292289
\(861\) 5.28342e12 0.327643
\(862\) −2.13149e12 −0.131492
\(863\) 1.26461e13 0.776081 0.388041 0.921642i \(-0.373152\pi\)
0.388041 + 0.921642i \(0.373152\pi\)
\(864\) −2.69809e12 −0.164719
\(865\) 1.06047e13 0.644057
\(866\) −1.98531e13 −1.19949
\(867\) 1.58319e13 0.951582
\(868\) 2.37570e12 0.142054
\(869\) −1.62638e13 −0.967463
\(870\) −2.92169e12 −0.172901
\(871\) 3.79662e13 2.23520
\(872\) 1.18957e13 0.696731
\(873\) 6.14091e11 0.0357824
\(874\) −1.35242e13 −0.783989
\(875\) 9.14708e12 0.527529
\(876\) 4.92198e12 0.282404
\(877\) −1.31246e13 −0.749185 −0.374593 0.927189i \(-0.622217\pi\)
−0.374593 + 0.927189i \(0.622217\pi\)
\(878\) 3.96397e12 0.225115
\(879\) 6.86086e12 0.387640
\(880\) 3.35749e12 0.188731
\(881\) −9.07975e12 −0.507788 −0.253894 0.967232i \(-0.581711\pi\)
−0.253894 + 0.967232i \(0.581711\pi\)
\(882\) 3.11589e12 0.173370
\(883\) −1.54949e12 −0.0857757 −0.0428879 0.999080i \(-0.513656\pi\)
−0.0428879 + 0.999080i \(0.513656\pi\)
\(884\) −2.48745e13 −1.37000
\(885\) 1.37600e12 0.0754004
\(886\) −1.22816e13 −0.669582
\(887\) −5.54485e12 −0.300769 −0.150385 0.988628i \(-0.548051\pi\)
−0.150385 + 0.988628i \(0.548051\pi\)
\(888\) −2.18198e12 −0.117758
\(889\) 1.84084e13 0.988456
\(890\) −1.55878e13 −0.832778
\(891\) 1.34069e12 0.0712652
\(892\) −3.43621e12 −0.181735
\(893\) −6.14725e12 −0.323481
\(894\) −1.52162e13 −0.796686
\(895\) −3.72141e13 −1.93867
\(896\) 2.01426e12 0.104407
\(897\) −3.09646e13 −1.59698
\(898\) −7.36525e12 −0.377958
\(899\) 4.54398e12 0.232016
\(900\) −1.97135e10 −0.00100155
\(901\) 3.95145e13 1.99754
\(902\) −9.87834e12 −0.496883
\(903\) 3.72046e12 0.186210
\(904\) −4.05842e13 −2.02115
\(905\) 7.95683e12 0.394295
\(906\) 5.56922e12 0.274611
\(907\) −8.14492e12 −0.399627 −0.199813 0.979834i \(-0.564034\pi\)
−0.199813 + 0.979834i \(0.564034\pi\)
\(908\) −1.51431e13 −0.739311
\(909\) 7.74573e12 0.376292
\(910\) 1.39701e13 0.675325
\(911\) −1.57553e13 −0.757867 −0.378934 0.925424i \(-0.623709\pi\)
−0.378934 + 0.925424i \(0.623709\pi\)
\(912\) 2.44435e12 0.117000
\(913\) 1.94878e13 0.928207
\(914\) 1.34127e13 0.635709
\(915\) −1.56742e13 −0.739250
\(916\) 3.02333e11 0.0141891
\(917\) 1.02677e13 0.479527
\(918\) −4.86834e12 −0.226250
\(919\) 1.43731e12 0.0664708 0.0332354 0.999448i \(-0.489419\pi\)
0.0332354 + 0.999448i \(0.489419\pi\)
\(920\) 3.65621e13 1.68262
\(921\) −1.70650e13 −0.781518
\(922\) 5.83904e12 0.266104
\(923\) −2.69545e13 −1.22243
\(924\) −2.07596e12 −0.0936905
\(925\) −2.67284e10 −0.00120043
\(926\) −1.31076e13 −0.585835
\(927\) −8.66223e11 −0.0385275
\(928\) 7.99087e12 0.353695
\(929\) −2.20360e13 −0.970651 −0.485325 0.874334i \(-0.661299\pi\)
−0.485325 + 0.874334i \(0.661299\pi\)
\(930\) −5.35903e12 −0.234916
\(931\) 1.14014e13 0.497375
\(932\) −3.22705e12 −0.140099
\(933\) 1.79656e13 0.776203
\(934\) 1.53492e12 0.0659969
\(935\) −2.44685e13 −1.04702
\(936\) 1.47181e13 0.626772
\(937\) −9.91396e12 −0.420164 −0.210082 0.977684i \(-0.567373\pi\)
−0.210082 + 0.977684i \(0.567373\pi\)
\(938\) −1.15058e13 −0.485293
\(939\) −2.30572e13 −0.967857
\(940\) 5.37540e12 0.224562
\(941\) 1.18619e11 0.00493175 0.00246587 0.999997i \(-0.499215\pi\)
0.00246587 + 0.999997i \(0.499215\pi\)
\(942\) 6.31939e12 0.261485
\(943\) −4.09042e13 −1.68448
\(944\) 9.31772e11 0.0381888
\(945\) −2.50464e12 −0.102165
\(946\) −6.95610e12 −0.282394
\(947\) 3.13848e13 1.26807 0.634037 0.773302i \(-0.281397\pi\)
0.634037 + 0.773302i \(0.281397\pi\)
\(948\) 1.03539e13 0.416357
\(949\) −4.50142e13 −1.80157
\(950\) 7.87446e10 0.00313664
\(951\) 2.97160e11 0.0117809
\(952\) 2.33057e13 0.919594
\(953\) −3.04762e13 −1.19686 −0.598430 0.801175i \(-0.704209\pi\)
−0.598430 + 0.801175i \(0.704209\pi\)
\(954\) −7.56247e12 −0.295594
\(955\) 2.50373e12 0.0974032
\(956\) −1.79069e13 −0.693363
\(957\) −3.97068e12 −0.153025
\(958\) −2.98669e12 −0.114563
\(959\) −2.13950e13 −0.816826
\(960\) −1.38949e13 −0.528003
\(961\) −1.81050e13 −0.684766
\(962\) 6.45462e12 0.242987
\(963\) 9.16657e12 0.343470
\(964\) −1.70415e13 −0.635567
\(965\) 1.30266e13 0.483569
\(966\) 9.38391e12 0.346726
\(967\) 1.60103e13 0.588815 0.294408 0.955680i \(-0.404878\pi\)
0.294408 + 0.955680i \(0.404878\pi\)
\(968\) −1.71702e13 −0.628544
\(969\) −1.78138e13 −0.649083
\(970\) 2.14496e12 0.0777942
\(971\) −1.63968e13 −0.591932 −0.295966 0.955198i \(-0.595642\pi\)
−0.295966 + 0.955198i \(0.595642\pi\)
\(972\) −8.53508e11 −0.0306697
\(973\) 9.31718e12 0.333255
\(974\) −1.23826e12 −0.0440856
\(975\) 1.80291e11 0.00638930
\(976\) −1.06140e13 −0.374415
\(977\) −1.57320e13 −0.552407 −0.276204 0.961099i \(-0.589076\pi\)
−0.276204 + 0.961099i \(0.589076\pi\)
\(978\) 1.09225e13 0.381766
\(979\) −2.11843e13 −0.737042
\(980\) −9.96984e12 −0.345280
\(981\) 6.30894e12 0.217493
\(982\) −4.88405e12 −0.167602
\(983\) 1.51445e13 0.517326 0.258663 0.965968i \(-0.416718\pi\)
0.258663 + 0.965968i \(0.416718\pi\)
\(984\) 1.94426e13 0.661113
\(985\) −3.32343e12 −0.112492
\(986\) 1.44185e13 0.485817
\(987\) 4.26533e12 0.143062
\(988\) 1.74196e13 0.581609
\(989\) −2.88038e13 −0.957341
\(990\) 4.68289e12 0.154937
\(991\) 3.91091e13 1.28809 0.644046 0.764987i \(-0.277255\pi\)
0.644046 + 0.764987i \(0.277255\pi\)
\(992\) 1.46570e13 0.480555
\(993\) 9.70957e12 0.316905
\(994\) 8.16864e12 0.265406
\(995\) 4.01765e13 1.29948
\(996\) −1.24063e13 −0.399463
\(997\) 3.21837e12 0.103159 0.0515796 0.998669i \(-0.483574\pi\)
0.0515796 + 0.998669i \(0.483574\pi\)
\(998\) −2.97645e13 −0.949753
\(999\) −1.15722e12 −0.0367597
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.1.7 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.7 22 1.1 even 1 trivial