Properties

Label 177.10.a.d.1.13
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 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.2821 q^{2} +81.0000 q^{3} -406.278 q^{4} +1021.11 q^{5} +832.853 q^{6} -5408.24 q^{7} -9441.86 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+10.2821 q^{2} +81.0000 q^{3} -406.278 q^{4} +1021.11 q^{5} +832.853 q^{6} -5408.24 q^{7} -9441.86 q^{8} +6561.00 q^{9} +10499.2 q^{10} +83087.8 q^{11} -32908.5 q^{12} +79756.4 q^{13} -55608.3 q^{14} +82710.3 q^{15} +110932. q^{16} -3716.65 q^{17} +67461.1 q^{18} -920691. q^{19} -414856. q^{20} -438067. q^{21} +854320. q^{22} -802158. q^{23} -764791. q^{24} -910449. q^{25} +820066. q^{26} +531441. q^{27} +2.19725e6 q^{28} +1.05704e6 q^{29} +850439. q^{30} -4.68310e6 q^{31} +5.97485e6 q^{32} +6.73011e6 q^{33} -38215.1 q^{34} -5.52244e6 q^{35} -2.66559e6 q^{36} +1.75608e7 q^{37} -9.46667e6 q^{38} +6.46027e6 q^{39} -9.64122e6 q^{40} +2.26645e7 q^{41} -4.50427e6 q^{42} +3.56651e7 q^{43} -3.37567e7 q^{44} +6.69954e6 q^{45} -8.24790e6 q^{46} +1.91417e7 q^{47} +8.98546e6 q^{48} -1.11045e7 q^{49} -9.36137e6 q^{50} -301048. q^{51} -3.24032e7 q^{52} -4.74993e7 q^{53} +5.46435e6 q^{54} +8.48422e7 q^{55} +5.10638e7 q^{56} -7.45759e7 q^{57} +1.08686e7 q^{58} -1.21174e7 q^{59} -3.36033e7 q^{60} -1.71221e7 q^{61} -4.81523e7 q^{62} -3.54835e7 q^{63} +4.63722e6 q^{64} +8.14404e7 q^{65} +6.91999e7 q^{66} +2.36658e8 q^{67} +1.50999e6 q^{68} -6.49748e7 q^{69} -5.67825e7 q^{70} +3.46163e8 q^{71} -6.19480e7 q^{72} +4.22598e8 q^{73} +1.80563e8 q^{74} -7.37464e7 q^{75} +3.74056e8 q^{76} -4.49359e8 q^{77} +6.64254e7 q^{78} +5.45210e8 q^{79} +1.13274e8 q^{80} +4.30467e7 q^{81} +2.33040e8 q^{82} -5.05775e7 q^{83} +1.77977e8 q^{84} -3.79512e6 q^{85} +3.66714e8 q^{86} +8.56200e7 q^{87} -7.84503e8 q^{88} -1.50176e8 q^{89} +6.88856e7 q^{90} -4.31342e8 q^{91} +3.25899e8 q^{92} -3.79331e8 q^{93} +1.96817e8 q^{94} -9.40131e8 q^{95} +4.83963e8 q^{96} -1.06697e9 q^{97} -1.14178e8 q^{98} +5.45139e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.2821 0.454411 0.227205 0.973847i \(-0.427041\pi\)
0.227205 + 0.973847i \(0.427041\pi\)
\(3\) 81.0000 0.577350
\(4\) −406.278 −0.793511
\(5\) 1021.11 0.730650 0.365325 0.930880i \(-0.380958\pi\)
0.365325 + 0.930880i \(0.380958\pi\)
\(6\) 832.853 0.262354
\(7\) −5408.24 −0.851363 −0.425682 0.904873i \(-0.639966\pi\)
−0.425682 + 0.904873i \(0.639966\pi\)
\(8\) −9441.86 −0.814991
\(9\) 6561.00 0.333333
\(10\) 10499.2 0.332015
\(11\) 83087.8 1.71108 0.855540 0.517737i \(-0.173226\pi\)
0.855540 + 0.517737i \(0.173226\pi\)
\(12\) −32908.5 −0.458134
\(13\) 79756.4 0.774498 0.387249 0.921975i \(-0.373425\pi\)
0.387249 + 0.921975i \(0.373425\pi\)
\(14\) −55608.3 −0.386868
\(15\) 82710.3 0.421841
\(16\) 110932. 0.423171
\(17\) −3716.65 −0.0107927 −0.00539636 0.999985i \(-0.501718\pi\)
−0.00539636 + 0.999985i \(0.501718\pi\)
\(18\) 67461.1 0.151470
\(19\) −920691. −1.62077 −0.810387 0.585895i \(-0.800743\pi\)
−0.810387 + 0.585895i \(0.800743\pi\)
\(20\) −414856. −0.579779
\(21\) −438067. −0.491535
\(22\) 854320. 0.777533
\(23\) −802158. −0.597702 −0.298851 0.954300i \(-0.596603\pi\)
−0.298851 + 0.954300i \(0.596603\pi\)
\(24\) −764791. −0.470535
\(25\) −910449. −0.466150
\(26\) 820066. 0.351940
\(27\) 531441. 0.192450
\(28\) 2.19725e6 0.675566
\(29\) 1.05704e6 0.277523 0.138762 0.990326i \(-0.455688\pi\)
0.138762 + 0.990326i \(0.455688\pi\)
\(30\) 850439. 0.191689
\(31\) −4.68310e6 −0.910763 −0.455382 0.890296i \(-0.650497\pi\)
−0.455382 + 0.890296i \(0.650497\pi\)
\(32\) 5.97485e6 1.00728
\(33\) 6.73011e6 0.987892
\(34\) −38215.1 −0.00490433
\(35\) −5.52244e6 −0.622049
\(36\) −2.66559e6 −0.264504
\(37\) 1.75608e7 1.54041 0.770206 0.637795i \(-0.220153\pi\)
0.770206 + 0.637795i \(0.220153\pi\)
\(38\) −9.46667e6 −0.736497
\(39\) 6.46027e6 0.447157
\(40\) −9.64122e6 −0.595473
\(41\) 2.26645e7 1.25262 0.626309 0.779575i \(-0.284565\pi\)
0.626309 + 0.779575i \(0.284565\pi\)
\(42\) −4.50427e6 −0.223359
\(43\) 3.56651e7 1.59087 0.795436 0.606037i \(-0.207242\pi\)
0.795436 + 0.606037i \(0.207242\pi\)
\(44\) −3.37567e7 −1.35776
\(45\) 6.69954e6 0.243550
\(46\) −8.24790e6 −0.271602
\(47\) 1.91417e7 0.572189 0.286094 0.958201i \(-0.407643\pi\)
0.286094 + 0.958201i \(0.407643\pi\)
\(48\) 8.98546e6 0.244318
\(49\) −1.11045e7 −0.275181
\(50\) −9.36137e6 −0.211824
\(51\) −301048. −0.00623118
\(52\) −3.24032e7 −0.614573
\(53\) −4.74993e7 −0.826886 −0.413443 0.910530i \(-0.635674\pi\)
−0.413443 + 0.910530i \(0.635674\pi\)
\(54\) 5.46435e6 0.0874514
\(55\) 8.48422e7 1.25020
\(56\) 5.10638e7 0.693853
\(57\) −7.45759e7 −0.935754
\(58\) 1.08686e7 0.126109
\(59\) −1.21174e7 −0.130189
\(60\) −3.36033e7 −0.334736
\(61\) −1.71221e7 −0.158334 −0.0791669 0.996861i \(-0.525226\pi\)
−0.0791669 + 0.996861i \(0.525226\pi\)
\(62\) −4.81523e7 −0.413861
\(63\) −3.54835e7 −0.283788
\(64\) 4.63722e6 0.0345500
\(65\) 8.14404e7 0.565887
\(66\) 6.91999e7 0.448909
\(67\) 2.36658e8 1.43477 0.717387 0.696674i \(-0.245338\pi\)
0.717387 + 0.696674i \(0.245338\pi\)
\(68\) 1.50999e6 0.00856415
\(69\) −6.49748e7 −0.345083
\(70\) −5.67825e7 −0.282666
\(71\) 3.46163e8 1.61666 0.808329 0.588731i \(-0.200372\pi\)
0.808329 + 0.588731i \(0.200372\pi\)
\(72\) −6.19480e7 −0.271664
\(73\) 4.22598e8 1.74170 0.870852 0.491544i \(-0.163567\pi\)
0.870852 + 0.491544i \(0.163567\pi\)
\(74\) 1.80563e8 0.699980
\(75\) −7.37464e7 −0.269132
\(76\) 3.74056e8 1.28610
\(77\) −4.49359e8 −1.45675
\(78\) 6.64254e7 0.203193
\(79\) 5.45210e8 1.57486 0.787429 0.616405i \(-0.211412\pi\)
0.787429 + 0.616405i \(0.211412\pi\)
\(80\) 1.13274e8 0.309190
\(81\) 4.30467e7 0.111111
\(82\) 2.33040e8 0.569203
\(83\) −5.05775e7 −0.116978 −0.0584892 0.998288i \(-0.518628\pi\)
−0.0584892 + 0.998288i \(0.518628\pi\)
\(84\) 1.77977e8 0.390038
\(85\) −3.79512e6 −0.00788571
\(86\) 3.66714e8 0.722909
\(87\) 8.56200e7 0.160228
\(88\) −7.84503e8 −1.39451
\(89\) −1.50176e8 −0.253715 −0.126857 0.991921i \(-0.540489\pi\)
−0.126857 + 0.991921i \(0.540489\pi\)
\(90\) 6.88856e7 0.110672
\(91\) −4.31342e8 −0.659379
\(92\) 3.25899e8 0.474283
\(93\) −3.79331e8 −0.525829
\(94\) 1.96817e8 0.260009
\(95\) −9.40131e8 −1.18422
\(96\) 4.83963e8 0.581556
\(97\) −1.06697e9 −1.22371 −0.611854 0.790970i \(-0.709576\pi\)
−0.611854 + 0.790970i \(0.709576\pi\)
\(98\) −1.14178e8 −0.125045
\(99\) 5.45139e8 0.570360
\(100\) 3.69895e8 0.369895
\(101\) −3.63643e8 −0.347720 −0.173860 0.984770i \(-0.555624\pi\)
−0.173860 + 0.984770i \(0.555624\pi\)
\(102\) −3.09542e6 −0.00283152
\(103\) 1.28954e9 1.12893 0.564467 0.825456i \(-0.309082\pi\)
0.564467 + 0.825456i \(0.309082\pi\)
\(104\) −7.53049e8 −0.631209
\(105\) −4.47317e8 −0.359140
\(106\) −4.88395e8 −0.375746
\(107\) −8.78243e8 −0.647720 −0.323860 0.946105i \(-0.604981\pi\)
−0.323860 + 0.946105i \(0.604981\pi\)
\(108\) −2.15913e8 −0.152711
\(109\) 2.59822e9 1.76302 0.881508 0.472169i \(-0.156529\pi\)
0.881508 + 0.472169i \(0.156529\pi\)
\(110\) 8.72359e8 0.568105
\(111\) 1.42243e9 0.889357
\(112\) −5.99945e8 −0.360272
\(113\) −2.19142e7 −0.0126437 −0.00632183 0.999980i \(-0.502012\pi\)
−0.00632183 + 0.999980i \(0.502012\pi\)
\(114\) −7.66800e8 −0.425217
\(115\) −8.19096e8 −0.436711
\(116\) −4.29450e8 −0.220218
\(117\) 5.23282e8 0.258166
\(118\) −1.24592e8 −0.0591592
\(119\) 2.01005e7 0.00918853
\(120\) −7.80939e8 −0.343797
\(121\) 4.54563e9 1.92779
\(122\) −1.76052e8 −0.0719485
\(123\) 1.83582e9 0.723200
\(124\) 1.90264e9 0.722701
\(125\) −2.92404e9 −1.07124
\(126\) −3.64846e8 −0.128956
\(127\) −3.69422e9 −1.26010 −0.630052 0.776553i \(-0.716967\pi\)
−0.630052 + 0.776553i \(0.716967\pi\)
\(128\) −3.01144e9 −0.991584
\(129\) 2.88887e9 0.918491
\(130\) 8.37382e8 0.257145
\(131\) 3.85636e8 0.114408 0.0572040 0.998363i \(-0.481781\pi\)
0.0572040 + 0.998363i \(0.481781\pi\)
\(132\) −2.73429e9 −0.783903
\(133\) 4.97932e9 1.37987
\(134\) 2.43335e9 0.651977
\(135\) 5.42662e8 0.140614
\(136\) 3.50921e7 0.00879597
\(137\) 6.21695e9 1.50777 0.753885 0.657007i \(-0.228178\pi\)
0.753885 + 0.657007i \(0.228178\pi\)
\(138\) −6.68080e8 −0.156810
\(139\) 3.62783e9 0.824290 0.412145 0.911118i \(-0.364780\pi\)
0.412145 + 0.911118i \(0.364780\pi\)
\(140\) 2.24364e9 0.493603
\(141\) 1.55047e9 0.330353
\(142\) 3.55930e9 0.734627
\(143\) 6.62678e9 1.32523
\(144\) 7.27822e8 0.141057
\(145\) 1.07936e9 0.202772
\(146\) 4.34521e9 0.791449
\(147\) −8.99468e8 −0.158876
\(148\) −7.13457e9 −1.22233
\(149\) 8.69055e8 0.144447 0.0722236 0.997388i \(-0.476990\pi\)
0.0722236 + 0.997388i \(0.476990\pi\)
\(150\) −7.58271e8 −0.122296
\(151\) 4.90512e9 0.767809 0.383904 0.923373i \(-0.374579\pi\)
0.383904 + 0.923373i \(0.374579\pi\)
\(152\) 8.69303e9 1.32092
\(153\) −2.43849e7 −0.00359758
\(154\) −4.62037e9 −0.661963
\(155\) −4.78198e9 −0.665450
\(156\) −2.62466e9 −0.354824
\(157\) −9.75892e9 −1.28190 −0.640949 0.767583i \(-0.721459\pi\)
−0.640949 + 0.767583i \(0.721459\pi\)
\(158\) 5.60592e9 0.715632
\(159\) −3.84744e9 −0.477403
\(160\) 6.10100e9 0.735972
\(161\) 4.33826e9 0.508861
\(162\) 4.42612e8 0.0504901
\(163\) 9.82042e9 1.08965 0.544823 0.838551i \(-0.316597\pi\)
0.544823 + 0.838551i \(0.316597\pi\)
\(164\) −9.20808e9 −0.993966
\(165\) 6.87222e9 0.721804
\(166\) −5.20045e8 −0.0531563
\(167\) 1.77473e10 1.76566 0.882831 0.469690i \(-0.155634\pi\)
0.882831 + 0.469690i \(0.155634\pi\)
\(168\) 4.13617e9 0.400596
\(169\) −4.24342e9 −0.400152
\(170\) −3.90220e7 −0.00358335
\(171\) −6.04065e9 −0.540258
\(172\) −1.44899e10 −1.26237
\(173\) −2.02008e9 −0.171460 −0.0857298 0.996318i \(-0.527322\pi\)
−0.0857298 + 0.996318i \(0.527322\pi\)
\(174\) 8.80357e8 0.0728093
\(175\) 4.92393e9 0.396863
\(176\) 9.21706e9 0.724078
\(177\) −9.81506e8 −0.0751646
\(178\) −1.54413e9 −0.115291
\(179\) −5.99197e9 −0.436245 −0.218123 0.975921i \(-0.569993\pi\)
−0.218123 + 0.975921i \(0.569993\pi\)
\(180\) −2.72187e9 −0.193260
\(181\) 1.86075e10 1.28865 0.644324 0.764753i \(-0.277139\pi\)
0.644324 + 0.764753i \(0.277139\pi\)
\(182\) −4.43512e9 −0.299629
\(183\) −1.38689e9 −0.0914140
\(184\) 7.57386e9 0.487122
\(185\) 1.79316e10 1.12550
\(186\) −3.90033e9 −0.238943
\(187\) −3.08808e8 −0.0184672
\(188\) −7.77683e9 −0.454038
\(189\) −2.87416e9 −0.163845
\(190\) −9.66656e9 −0.538122
\(191\) −1.08703e10 −0.591004 −0.295502 0.955342i \(-0.595487\pi\)
−0.295502 + 0.955342i \(0.595487\pi\)
\(192\) 3.75615e8 0.0199474
\(193\) −3.52554e10 −1.82902 −0.914510 0.404564i \(-0.867423\pi\)
−0.914510 + 0.404564i \(0.867423\pi\)
\(194\) −1.09707e10 −0.556066
\(195\) 6.59668e9 0.326715
\(196\) 4.51153e9 0.218359
\(197\) −3.49511e10 −1.65334 −0.826670 0.562687i \(-0.809768\pi\)
−0.826670 + 0.562687i \(0.809768\pi\)
\(198\) 5.60520e9 0.259178
\(199\) 8.09055e9 0.365712 0.182856 0.983140i \(-0.441466\pi\)
0.182856 + 0.983140i \(0.441466\pi\)
\(200\) 8.59633e9 0.379908
\(201\) 1.91693e10 0.828368
\(202\) −3.73903e9 −0.158007
\(203\) −5.71671e9 −0.236273
\(204\) 1.22309e8 0.00494451
\(205\) 2.31431e10 0.915226
\(206\) 1.32593e10 0.513000
\(207\) −5.26296e9 −0.199234
\(208\) 8.84751e9 0.327745
\(209\) −7.64981e10 −2.77327
\(210\) −4.59938e9 −0.163197
\(211\) 1.92887e9 0.0669934 0.0334967 0.999439i \(-0.489336\pi\)
0.0334967 + 0.999439i \(0.489336\pi\)
\(212\) 1.92979e10 0.656143
\(213\) 2.80392e10 0.933378
\(214\) −9.03021e9 −0.294331
\(215\) 3.64182e10 1.16237
\(216\) −5.01779e9 −0.156845
\(217\) 2.53273e10 0.775390
\(218\) 2.67152e10 0.801133
\(219\) 3.42304e10 1.00557
\(220\) −3.44695e10 −0.992048
\(221\) −2.96426e8 −0.00835895
\(222\) 1.46256e10 0.404133
\(223\) −2.36958e9 −0.0641653 −0.0320827 0.999485i \(-0.510214\pi\)
−0.0320827 + 0.999485i \(0.510214\pi\)
\(224\) −3.23134e10 −0.857564
\(225\) −5.97346e9 −0.155383
\(226\) −2.25325e8 −0.00574542
\(227\) −5.19431e10 −1.29841 −0.649205 0.760614i \(-0.724898\pi\)
−0.649205 + 0.760614i \(0.724898\pi\)
\(228\) 3.02985e10 0.742531
\(229\) 3.55924e9 0.0855260 0.0427630 0.999085i \(-0.486384\pi\)
0.0427630 + 0.999085i \(0.486384\pi\)
\(230\) −8.42206e9 −0.198446
\(231\) −3.63981e10 −0.841055
\(232\) −9.98039e9 −0.226179
\(233\) 1.10887e10 0.246478 0.123239 0.992377i \(-0.460672\pi\)
0.123239 + 0.992377i \(0.460672\pi\)
\(234\) 5.38046e9 0.117313
\(235\) 1.95458e10 0.418070
\(236\) 4.92301e9 0.103306
\(237\) 4.41620e10 0.909245
\(238\) 2.06676e8 0.00417537
\(239\) −8.65942e10 −1.71671 −0.858357 0.513052i \(-0.828515\pi\)
−0.858357 + 0.513052i \(0.828515\pi\)
\(240\) 9.17519e9 0.178511
\(241\) −1.31367e10 −0.250848 −0.125424 0.992103i \(-0.540029\pi\)
−0.125424 + 0.992103i \(0.540029\pi\)
\(242\) 4.67388e10 0.876009
\(243\) 3.48678e9 0.0641500
\(244\) 6.95634e9 0.125640
\(245\) −1.13390e10 −0.201061
\(246\) 1.88762e10 0.328630
\(247\) −7.34310e10 −1.25529
\(248\) 4.42171e10 0.742263
\(249\) −4.09678e9 −0.0675376
\(250\) −3.00654e10 −0.486784
\(251\) 1.25306e11 1.99268 0.996342 0.0854528i \(-0.0272337\pi\)
0.996342 + 0.0854528i \(0.0272337\pi\)
\(252\) 1.44161e10 0.225189
\(253\) −6.66495e10 −1.02272
\(254\) −3.79845e10 −0.572605
\(255\) −3.07405e8 −0.00455282
\(256\) −3.33383e10 −0.485136
\(257\) 9.80273e10 1.40168 0.700838 0.713320i \(-0.252809\pi\)
0.700838 + 0.713320i \(0.252809\pi\)
\(258\) 2.97038e10 0.417372
\(259\) −9.49731e10 −1.31145
\(260\) −3.30874e10 −0.449038
\(261\) 6.93522e9 0.0925077
\(262\) 3.96516e9 0.0519882
\(263\) −1.02117e11 −1.31613 −0.658065 0.752961i \(-0.728625\pi\)
−0.658065 + 0.752961i \(0.728625\pi\)
\(264\) −6.35448e10 −0.805123
\(265\) −4.85023e10 −0.604165
\(266\) 5.11980e10 0.627026
\(267\) −1.21643e10 −0.146482
\(268\) −9.61487e10 −1.13851
\(269\) 6.03682e10 0.702948 0.351474 0.936198i \(-0.385681\pi\)
0.351474 + 0.936198i \(0.385681\pi\)
\(270\) 5.57973e9 0.0638964
\(271\) 8.51802e10 0.959350 0.479675 0.877446i \(-0.340755\pi\)
0.479675 + 0.877446i \(0.340755\pi\)
\(272\) −4.12294e8 −0.00456716
\(273\) −3.49387e10 −0.380693
\(274\) 6.39236e10 0.685147
\(275\) −7.56472e10 −0.797620
\(276\) 2.63978e10 0.273827
\(277\) 1.02318e10 0.104422 0.0522112 0.998636i \(-0.483373\pi\)
0.0522112 + 0.998636i \(0.483373\pi\)
\(278\) 3.73018e10 0.374566
\(279\) −3.07258e10 −0.303588
\(280\) 5.21421e10 0.506964
\(281\) 3.22800e10 0.308855 0.154428 0.988004i \(-0.450647\pi\)
0.154428 + 0.988004i \(0.450647\pi\)
\(282\) 1.59422e10 0.150116
\(283\) 1.78367e11 1.65301 0.826507 0.562926i \(-0.190324\pi\)
0.826507 + 0.562926i \(0.190324\pi\)
\(284\) −1.40638e11 −1.28284
\(285\) −7.61506e10 −0.683709
\(286\) 6.81375e10 0.602198
\(287\) −1.22575e11 −1.06643
\(288\) 3.92010e10 0.335761
\(289\) −1.18574e11 −0.999884
\(290\) 1.10981e10 0.0921419
\(291\) −8.64243e10 −0.706509
\(292\) −1.71692e11 −1.38206
\(293\) −1.22710e11 −0.972689 −0.486345 0.873767i \(-0.661670\pi\)
−0.486345 + 0.873767i \(0.661670\pi\)
\(294\) −9.24845e9 −0.0721948
\(295\) −1.23732e10 −0.0951226
\(296\) −1.65807e11 −1.25542
\(297\) 4.41563e10 0.329297
\(298\) 8.93575e9 0.0656383
\(299\) −6.39772e10 −0.462919
\(300\) 2.99615e10 0.213559
\(301\) −1.92885e11 −1.35441
\(302\) 5.04351e10 0.348900
\(303\) −2.94551e10 −0.200756
\(304\) −1.02134e11 −0.685864
\(305\) −1.74837e10 −0.115687
\(306\) −2.50729e8 −0.00163478
\(307\) 4.87069e10 0.312945 0.156473 0.987682i \(-0.449988\pi\)
0.156473 + 0.987682i \(0.449988\pi\)
\(308\) 1.82564e11 1.15595
\(309\) 1.04453e11 0.651791
\(310\) −4.91690e10 −0.302387
\(311\) 2.92063e10 0.177033 0.0885165 0.996075i \(-0.471787\pi\)
0.0885165 + 0.996075i \(0.471787\pi\)
\(312\) −6.09969e10 −0.364429
\(313\) −2.12156e11 −1.24941 −0.624706 0.780860i \(-0.714781\pi\)
−0.624706 + 0.780860i \(0.714781\pi\)
\(314\) −1.00343e11 −0.582508
\(315\) −3.62327e10 −0.207350
\(316\) −2.21506e11 −1.24967
\(317\) 9.39993e9 0.0522827 0.0261413 0.999658i \(-0.491678\pi\)
0.0261413 + 0.999658i \(0.491678\pi\)
\(318\) −3.95600e10 −0.216937
\(319\) 8.78269e10 0.474864
\(320\) 4.73513e9 0.0252440
\(321\) −7.11376e10 −0.373961
\(322\) 4.46066e10 0.231232
\(323\) 3.42188e9 0.0174926
\(324\) −1.74889e10 −0.0881679
\(325\) −7.26141e10 −0.361032
\(326\) 1.00975e11 0.495147
\(327\) 2.10456e11 1.01788
\(328\) −2.13995e11 −1.02087
\(329\) −1.03523e11 −0.487140
\(330\) 7.06611e10 0.327995
\(331\) −2.23051e11 −1.02136 −0.510680 0.859771i \(-0.670606\pi\)
−0.510680 + 0.859771i \(0.670606\pi\)
\(332\) 2.05485e10 0.0928237
\(333\) 1.15217e11 0.513471
\(334\) 1.82480e11 0.802336
\(335\) 2.41655e11 1.04832
\(336\) −4.85955e10 −0.208003
\(337\) −2.53877e11 −1.07223 −0.536117 0.844144i \(-0.680109\pi\)
−0.536117 + 0.844144i \(0.680109\pi\)
\(338\) −4.36314e10 −0.181834
\(339\) −1.77505e9 −0.00729982
\(340\) 1.54187e9 0.00625740
\(341\) −3.89108e11 −1.55839
\(342\) −6.21108e10 −0.245499
\(343\) 2.78298e11 1.08564
\(344\) −3.36745e11 −1.29655
\(345\) −6.63468e10 −0.252135
\(346\) −2.07708e10 −0.0779131
\(347\) 2.33811e11 0.865729 0.432864 0.901459i \(-0.357503\pi\)
0.432864 + 0.901459i \(0.357503\pi\)
\(348\) −3.47855e10 −0.127143
\(349\) −4.83086e10 −0.174305 −0.0871525 0.996195i \(-0.527777\pi\)
−0.0871525 + 0.996195i \(0.527777\pi\)
\(350\) 5.06285e10 0.180339
\(351\) 4.23858e10 0.149052
\(352\) 4.96437e11 1.72354
\(353\) 1.95997e11 0.671834 0.335917 0.941892i \(-0.390954\pi\)
0.335917 + 0.941892i \(0.390954\pi\)
\(354\) −1.00920e10 −0.0341556
\(355\) 3.53472e11 1.18121
\(356\) 6.10132e10 0.201325
\(357\) 1.62814e9 0.00530500
\(358\) −6.16103e10 −0.198235
\(359\) 1.10952e10 0.0352543 0.0176271 0.999845i \(-0.494389\pi\)
0.0176271 + 0.999845i \(0.494389\pi\)
\(360\) −6.32561e10 −0.198491
\(361\) 5.24983e11 1.62691
\(362\) 1.91325e11 0.585575
\(363\) 3.68196e11 1.11301
\(364\) 1.75244e11 0.523225
\(365\) 4.31521e11 1.27258
\(366\) −1.42602e10 −0.0415395
\(367\) 1.41329e11 0.406663 0.203331 0.979110i \(-0.434823\pi\)
0.203331 + 0.979110i \(0.434823\pi\)
\(368\) −8.89847e10 −0.252930
\(369\) 1.48702e11 0.417539
\(370\) 1.84375e11 0.511440
\(371\) 2.56888e11 0.703981
\(372\) 1.54114e11 0.417251
\(373\) −2.00258e11 −0.535673 −0.267836 0.963464i \(-0.586309\pi\)
−0.267836 + 0.963464i \(0.586309\pi\)
\(374\) −3.17521e9 −0.00839170
\(375\) −2.36847e11 −0.618482
\(376\) −1.80733e11 −0.466328
\(377\) 8.43055e10 0.214941
\(378\) −2.95525e10 −0.0744529
\(379\) −7.47339e11 −1.86055 −0.930274 0.366865i \(-0.880431\pi\)
−0.930274 + 0.366865i \(0.880431\pi\)
\(380\) 3.81954e11 0.939691
\(381\) −2.99232e11 −0.727522
\(382\) −1.11770e11 −0.268558
\(383\) 5.64880e11 1.34141 0.670705 0.741724i \(-0.265992\pi\)
0.670705 + 0.741724i \(0.265992\pi\)
\(384\) −2.43927e11 −0.572491
\(385\) −4.58847e11 −1.06437
\(386\) −3.62501e11 −0.831126
\(387\) 2.33999e11 0.530291
\(388\) 4.33485e11 0.971026
\(389\) 3.37311e11 0.746890 0.373445 0.927652i \(-0.378176\pi\)
0.373445 + 0.927652i \(0.378176\pi\)
\(390\) 6.78280e10 0.148463
\(391\) 2.98134e9 0.00645084
\(392\) 1.04848e11 0.224270
\(393\) 3.12365e10 0.0660535
\(394\) −3.59372e11 −0.751296
\(395\) 5.56722e11 1.15067
\(396\) −2.21478e11 −0.452587
\(397\) −3.78094e11 −0.763911 −0.381956 0.924181i \(-0.624749\pi\)
−0.381956 + 0.924181i \(0.624749\pi\)
\(398\) 8.31882e10 0.166183
\(399\) 4.03325e11 0.796667
\(400\) −1.00998e11 −0.197261
\(401\) 2.23371e11 0.431397 0.215698 0.976460i \(-0.430797\pi\)
0.215698 + 0.976460i \(0.430797\pi\)
\(402\) 1.97101e11 0.376419
\(403\) −3.73507e11 −0.705385
\(404\) 1.47740e11 0.275919
\(405\) 4.39557e10 0.0811834
\(406\) −5.87800e10 −0.107365
\(407\) 1.45909e12 2.63577
\(408\) 2.84246e9 0.00507836
\(409\) −7.63055e11 −1.34834 −0.674172 0.738574i \(-0.735500\pi\)
−0.674172 + 0.738574i \(0.735500\pi\)
\(410\) 2.37960e11 0.415889
\(411\) 5.03573e11 0.870511
\(412\) −5.23913e11 −0.895822
\(413\) 6.55336e10 0.110838
\(414\) −5.41145e10 −0.0905341
\(415\) −5.16455e10 −0.0854704
\(416\) 4.76532e11 0.780139
\(417\) 2.93854e11 0.475904
\(418\) −7.86565e11 −1.26020
\(419\) −8.80094e11 −1.39497 −0.697487 0.716598i \(-0.745698\pi\)
−0.697487 + 0.716598i \(0.745698\pi\)
\(420\) 1.81735e11 0.284982
\(421\) 2.56266e11 0.397577 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(422\) 1.98329e10 0.0304425
\(423\) 1.25588e11 0.190730
\(424\) 4.48482e11 0.673905
\(425\) 3.38382e9 0.00503103
\(426\) 2.88303e11 0.424137
\(427\) 9.26006e10 0.134799
\(428\) 3.56810e11 0.513973
\(429\) 5.36769e11 0.765121
\(430\) 3.74457e11 0.528194
\(431\) −3.10399e11 −0.433284 −0.216642 0.976251i \(-0.569510\pi\)
−0.216642 + 0.976251i \(0.569510\pi\)
\(432\) 5.89536e10 0.0814392
\(433\) −8.40602e10 −0.114920 −0.0574599 0.998348i \(-0.518300\pi\)
−0.0574599 + 0.998348i \(0.518300\pi\)
\(434\) 2.60419e11 0.352346
\(435\) 8.74279e10 0.117071
\(436\) −1.05560e12 −1.39897
\(437\) 7.38539e11 0.968740
\(438\) 3.51962e11 0.456943
\(439\) 3.22184e11 0.414012 0.207006 0.978340i \(-0.433628\pi\)
0.207006 + 0.978340i \(0.433628\pi\)
\(440\) −8.01068e11 −1.01890
\(441\) −7.28569e10 −0.0917270
\(442\) −3.04790e9 −0.00379840
\(443\) 9.07439e11 1.11944 0.559720 0.828682i \(-0.310909\pi\)
0.559720 + 0.828682i \(0.310909\pi\)
\(444\) −5.77900e11 −0.705715
\(445\) −1.53347e11 −0.185377
\(446\) −2.43644e10 −0.0291574
\(447\) 7.03935e10 0.0833966
\(448\) −2.50792e10 −0.0294146
\(449\) 1.17081e12 1.35950 0.679750 0.733444i \(-0.262088\pi\)
0.679750 + 0.733444i \(0.262088\pi\)
\(450\) −6.14199e10 −0.0706078
\(451\) 1.88314e12 2.14333
\(452\) 8.90326e9 0.0100329
\(453\) 3.97314e11 0.443295
\(454\) −5.34087e11 −0.590011
\(455\) −4.40450e11 −0.481776
\(456\) 7.04135e11 0.762631
\(457\) −1.29882e12 −1.39292 −0.696458 0.717597i \(-0.745242\pi\)
−0.696458 + 0.717597i \(0.745242\pi\)
\(458\) 3.65966e10 0.0388639
\(459\) −1.97518e9 −0.00207706
\(460\) 3.32780e11 0.346535
\(461\) −9.50693e11 −0.980362 −0.490181 0.871621i \(-0.663069\pi\)
−0.490181 + 0.871621i \(0.663069\pi\)
\(462\) −3.74250e11 −0.382184
\(463\) −1.14359e12 −1.15652 −0.578261 0.815852i \(-0.696269\pi\)
−0.578261 + 0.815852i \(0.696269\pi\)
\(464\) 1.17259e11 0.117440
\(465\) −3.87340e11 −0.384198
\(466\) 1.14015e11 0.112002
\(467\) −1.38510e12 −1.34758 −0.673792 0.738921i \(-0.735336\pi\)
−0.673792 + 0.738921i \(0.735336\pi\)
\(468\) −2.12598e11 −0.204858
\(469\) −1.27990e12 −1.22151
\(470\) 2.00973e11 0.189975
\(471\) −7.90473e11 −0.740104
\(472\) 1.14410e11 0.106103
\(473\) 2.96333e12 2.72211
\(474\) 4.54080e11 0.413171
\(475\) 8.38242e11 0.755524
\(476\) −8.16639e9 −0.00729120
\(477\) −3.11643e11 −0.275629
\(478\) −8.90373e11 −0.780093
\(479\) −1.68282e12 −1.46059 −0.730295 0.683132i \(-0.760617\pi\)
−0.730295 + 0.683132i \(0.760617\pi\)
\(480\) 4.94181e11 0.424914
\(481\) 1.40059e12 1.19305
\(482\) −1.35073e11 −0.113988
\(483\) 3.51399e11 0.293791
\(484\) −1.84679e12 −1.52972
\(485\) −1.08950e12 −0.894103
\(486\) 3.58516e10 0.0291505
\(487\) −3.61535e11 −0.291253 −0.145626 0.989340i \(-0.546520\pi\)
−0.145626 + 0.989340i \(0.546520\pi\)
\(488\) 1.61665e11 0.129040
\(489\) 7.95454e11 0.629108
\(490\) −1.16589e11 −0.0913643
\(491\) −1.88832e12 −1.46625 −0.733127 0.680092i \(-0.761940\pi\)
−0.733127 + 0.680092i \(0.761940\pi\)
\(492\) −7.45854e11 −0.573867
\(493\) −3.92863e9 −0.00299523
\(494\) −7.55027e11 −0.570416
\(495\) 5.56650e11 0.416734
\(496\) −5.19504e11 −0.385408
\(497\) −1.87213e12 −1.37636
\(498\) −4.21236e10 −0.0306898
\(499\) 2.16118e12 1.56041 0.780205 0.625524i \(-0.215115\pi\)
0.780205 + 0.625524i \(0.215115\pi\)
\(500\) 1.18797e12 0.850043
\(501\) 1.43753e12 1.01941
\(502\) 1.28841e12 0.905497
\(503\) 1.35300e12 0.942416 0.471208 0.882022i \(-0.343818\pi\)
0.471208 + 0.882022i \(0.343818\pi\)
\(504\) 3.35030e11 0.231284
\(505\) −3.71321e11 −0.254061
\(506\) −6.85300e11 −0.464733
\(507\) −3.43717e11 −0.231028
\(508\) 1.50088e12 0.999907
\(509\) 1.28269e12 0.847019 0.423509 0.905892i \(-0.360798\pi\)
0.423509 + 0.905892i \(0.360798\pi\)
\(510\) −3.16078e9 −0.00206885
\(511\) −2.28551e12 −1.48282
\(512\) 1.19907e12 0.771133
\(513\) −4.89293e11 −0.311918
\(514\) 1.00793e12 0.636937
\(515\) 1.31677e12 0.824856
\(516\) −1.17368e12 −0.728832
\(517\) 1.59044e12 0.979060
\(518\) −9.76527e11 −0.595937
\(519\) −1.63627e11 −0.0989923
\(520\) −7.68949e11 −0.461193
\(521\) 2.70756e12 1.60993 0.804967 0.593320i \(-0.202183\pi\)
0.804967 + 0.593320i \(0.202183\pi\)
\(522\) 7.13089e10 0.0420365
\(523\) 1.55055e12 0.906208 0.453104 0.891458i \(-0.350317\pi\)
0.453104 + 0.891458i \(0.350317\pi\)
\(524\) −1.56675e11 −0.0907840
\(525\) 3.98838e11 0.229129
\(526\) −1.04998e12 −0.598063
\(527\) 1.74054e10 0.00982962
\(528\) 7.46582e11 0.418047
\(529\) −1.15769e12 −0.642752
\(530\) −4.98707e11 −0.274539
\(531\) −7.95020e10 −0.0433963
\(532\) −2.02298e12 −1.09494
\(533\) 1.80764e12 0.970151
\(534\) −1.25075e11 −0.0665631
\(535\) −8.96787e11 −0.473257
\(536\) −2.23449e12 −1.16933
\(537\) −4.85350e11 −0.251866
\(538\) 6.20715e11 0.319427
\(539\) −9.22652e11 −0.470856
\(540\) −2.20472e11 −0.111579
\(541\) −3.07338e12 −1.54251 −0.771257 0.636524i \(-0.780372\pi\)
−0.771257 + 0.636524i \(0.780372\pi\)
\(542\) 8.75835e11 0.435939
\(543\) 1.50721e12 0.744001
\(544\) −2.22064e10 −0.0108713
\(545\) 2.65308e12 1.28815
\(546\) −3.59244e11 −0.172991
\(547\) −2.55306e12 −1.21932 −0.609661 0.792663i \(-0.708694\pi\)
−0.609661 + 0.792663i \(0.708694\pi\)
\(548\) −2.52581e12 −1.19643
\(549\) −1.12338e11 −0.0527779
\(550\) −7.77815e11 −0.362447
\(551\) −9.73204e11 −0.449802
\(552\) 6.13483e11 0.281240
\(553\) −2.94862e12 −1.34078
\(554\) 1.05205e11 0.0474506
\(555\) 1.45246e12 0.649809
\(556\) −1.47391e12 −0.654083
\(557\) −2.18123e12 −0.960182 −0.480091 0.877219i \(-0.659396\pi\)
−0.480091 + 0.877219i \(0.659396\pi\)
\(558\) −3.15927e11 −0.137954
\(559\) 2.84452e12 1.23213
\(560\) −6.12613e11 −0.263233
\(561\) −2.50134e10 −0.0106620
\(562\) 3.31907e11 0.140347
\(563\) −2.74986e12 −1.15351 −0.576756 0.816916i \(-0.695682\pi\)
−0.576756 + 0.816916i \(0.695682\pi\)
\(564\) −6.29923e11 −0.262139
\(565\) −2.23769e10 −0.00923810
\(566\) 1.83400e12 0.751147
\(567\) −2.32807e11 −0.0945959
\(568\) −3.26842e12 −1.31756
\(569\) −1.19313e12 −0.477179 −0.238590 0.971120i \(-0.576685\pi\)
−0.238590 + 0.971120i \(0.576685\pi\)
\(570\) −7.82991e11 −0.310685
\(571\) 4.05845e12 1.59771 0.798854 0.601525i \(-0.205440\pi\)
0.798854 + 0.601525i \(0.205440\pi\)
\(572\) −2.69231e12 −1.05158
\(573\) −8.80492e11 −0.341216
\(574\) −1.26033e12 −0.484599
\(575\) 7.30324e11 0.278619
\(576\) 3.04248e10 0.0115167
\(577\) 1.91055e12 0.717573 0.358787 0.933420i \(-0.383191\pi\)
0.358787 + 0.933420i \(0.383191\pi\)
\(578\) −1.21920e12 −0.454358
\(579\) −2.85569e12 −1.05598
\(580\) −4.38518e11 −0.160902
\(581\) 2.73535e11 0.0995912
\(582\) −8.88627e11 −0.321045
\(583\) −3.94661e12 −1.41487
\(584\) −3.99011e12 −1.41947
\(585\) 5.34331e11 0.188629
\(586\) −1.26172e12 −0.442000
\(587\) 3.64868e12 1.26842 0.634212 0.773159i \(-0.281324\pi\)
0.634212 + 0.773159i \(0.281324\pi\)
\(588\) 3.65434e11 0.126070
\(589\) 4.31168e12 1.47614
\(590\) −1.27223e11 −0.0432247
\(591\) −2.83104e12 −0.954557
\(592\) 1.94805e12 0.651857
\(593\) −6.85524e11 −0.227655 −0.113827 0.993501i \(-0.536311\pi\)
−0.113827 + 0.993501i \(0.536311\pi\)
\(594\) 4.54021e11 0.149636
\(595\) 2.05249e10 0.00671360
\(596\) −3.53078e11 −0.114620
\(597\) 6.55335e11 0.211144
\(598\) −6.57823e11 −0.210355
\(599\) 5.21431e12 1.65492 0.827459 0.561526i \(-0.189786\pi\)
0.827459 + 0.561526i \(0.189786\pi\)
\(600\) 6.96303e11 0.219340
\(601\) 2.91650e12 0.911857 0.455928 0.890016i \(-0.349307\pi\)
0.455928 + 0.890016i \(0.349307\pi\)
\(602\) −1.98327e12 −0.615458
\(603\) 1.55271e12 0.478258
\(604\) −1.99284e12 −0.609265
\(605\) 4.64161e12 1.40854
\(606\) −3.02861e11 −0.0912257
\(607\) 3.45121e12 1.03186 0.515932 0.856630i \(-0.327446\pi\)
0.515932 + 0.856630i \(0.327446\pi\)
\(608\) −5.50098e12 −1.63258
\(609\) −4.63053e11 −0.136412
\(610\) −1.79769e11 −0.0525692
\(611\) 1.52667e12 0.443159
\(612\) 9.90705e9 0.00285472
\(613\) 3.13362e11 0.0896343 0.0448171 0.998995i \(-0.485729\pi\)
0.0448171 + 0.998995i \(0.485729\pi\)
\(614\) 5.00812e11 0.142206
\(615\) 1.87459e12 0.528406
\(616\) 4.24278e12 1.18724
\(617\) 3.57799e12 0.993930 0.496965 0.867770i \(-0.334448\pi\)
0.496965 + 0.867770i \(0.334448\pi\)
\(618\) 1.07400e12 0.296181
\(619\) −6.72065e11 −0.183994 −0.0919969 0.995759i \(-0.529325\pi\)
−0.0919969 + 0.995759i \(0.529325\pi\)
\(620\) 1.94281e12 0.528042
\(621\) −4.26300e11 −0.115028
\(622\) 3.00303e11 0.0804457
\(623\) 8.12188e11 0.216003
\(624\) 7.16648e11 0.189224
\(625\) −1.20756e12 −0.316554
\(626\) −2.18142e12 −0.567746
\(627\) −6.19635e12 −1.60115
\(628\) 3.96483e12 1.01720
\(629\) −6.52674e10 −0.0166252
\(630\) −3.72550e11 −0.0942219
\(631\) −5.53679e11 −0.139035 −0.0695177 0.997581i \(-0.522146\pi\)
−0.0695177 + 0.997581i \(0.522146\pi\)
\(632\) −5.14779e12 −1.28349
\(633\) 1.56239e11 0.0386787
\(634\) 9.66514e10 0.0237578
\(635\) −3.77223e12 −0.920696
\(636\) 1.56313e12 0.378825
\(637\) −8.85658e11 −0.213127
\(638\) 9.03048e11 0.215783
\(639\) 2.27118e12 0.538886
\(640\) −3.07503e12 −0.724501
\(641\) 2.23104e12 0.521970 0.260985 0.965343i \(-0.415953\pi\)
0.260985 + 0.965343i \(0.415953\pi\)
\(642\) −7.31447e11 −0.169932
\(643\) −1.66757e12 −0.384711 −0.192355 0.981325i \(-0.561613\pi\)
−0.192355 + 0.981325i \(0.561613\pi\)
\(644\) −1.76254e12 −0.403787
\(645\) 2.94987e12 0.671096
\(646\) 3.51843e10 0.00794881
\(647\) −2.62265e12 −0.588397 −0.294199 0.955744i \(-0.595053\pi\)
−0.294199 + 0.955744i \(0.595053\pi\)
\(648\) −4.06441e11 −0.0905545
\(649\) −1.00680e12 −0.222764
\(650\) −7.46629e11 −0.164057
\(651\) 2.05151e12 0.447672
\(652\) −3.98982e12 −0.864647
\(653\) 4.14476e12 0.892052 0.446026 0.895020i \(-0.352839\pi\)
0.446026 + 0.895020i \(0.352839\pi\)
\(654\) 2.16393e12 0.462535
\(655\) 3.93778e11 0.0835923
\(656\) 2.51421e12 0.530071
\(657\) 2.77267e12 0.580568
\(658\) −1.06443e12 −0.221362
\(659\) −3.06194e12 −0.632429 −0.316215 0.948688i \(-0.602412\pi\)
−0.316215 + 0.948688i \(0.602412\pi\)
\(660\) −2.79203e12 −0.572759
\(661\) 2.31516e11 0.0471710 0.0235855 0.999722i \(-0.492492\pi\)
0.0235855 + 0.999722i \(0.492492\pi\)
\(662\) −2.29345e12 −0.464117
\(663\) −2.40105e10 −0.00482604
\(664\) 4.77546e11 0.0953364
\(665\) 5.08445e12 1.00820
\(666\) 1.18467e12 0.233327
\(667\) −8.47911e11 −0.165876
\(668\) −7.21032e12 −1.40107
\(669\) −1.91936e11 −0.0370459
\(670\) 2.48473e12 0.476367
\(671\) −1.42264e12 −0.270921
\(672\) −2.61739e12 −0.495115
\(673\) −4.40918e12 −0.828495 −0.414248 0.910164i \(-0.635955\pi\)
−0.414248 + 0.910164i \(0.635955\pi\)
\(674\) −2.61040e12 −0.487234
\(675\) −4.83850e11 −0.0897106
\(676\) 1.72401e12 0.317525
\(677\) −3.29730e12 −0.603266 −0.301633 0.953424i \(-0.597532\pi\)
−0.301633 + 0.953424i \(0.597532\pi\)
\(678\) −1.82513e10 −0.00331712
\(679\) 5.77041e12 1.04182
\(680\) 3.58330e10 0.00642678
\(681\) −4.20739e12 −0.749637
\(682\) −4.00086e12 −0.708148
\(683\) −8.57985e12 −1.50864 −0.754322 0.656505i \(-0.772034\pi\)
−0.754322 + 0.656505i \(0.772034\pi\)
\(684\) 2.45418e12 0.428701
\(685\) 6.34822e12 1.10165
\(686\) 2.86150e12 0.493327
\(687\) 2.88299e11 0.0493784
\(688\) 3.95639e12 0.673210
\(689\) −3.78837e12 −0.640422
\(690\) −6.82187e11 −0.114573
\(691\) 3.91597e12 0.653414 0.326707 0.945126i \(-0.394061\pi\)
0.326707 + 0.945126i \(0.394061\pi\)
\(692\) 8.20715e11 0.136055
\(693\) −2.94824e12 −0.485583
\(694\) 2.40407e12 0.393396
\(695\) 3.70443e12 0.602268
\(696\) −8.08412e11 −0.130584
\(697\) −8.42360e10 −0.0135192
\(698\) −4.96716e11 −0.0792061
\(699\) 8.98182e11 0.142304
\(700\) −2.00048e12 −0.314915
\(701\) 5.83452e12 0.912587 0.456293 0.889829i \(-0.349177\pi\)
0.456293 + 0.889829i \(0.349177\pi\)
\(702\) 4.35817e11 0.0677309
\(703\) −1.61681e13 −2.49666
\(704\) 3.85296e11 0.0591177
\(705\) 1.58321e12 0.241373
\(706\) 2.01526e12 0.305289
\(707\) 1.96667e12 0.296036
\(708\) 3.98764e11 0.0596439
\(709\) −5.16653e12 −0.767875 −0.383938 0.923359i \(-0.625432\pi\)
−0.383938 + 0.923359i \(0.625432\pi\)
\(710\) 3.63445e12 0.536755
\(711\) 3.57712e12 0.524953
\(712\) 1.41794e12 0.206775
\(713\) 3.75658e12 0.544365
\(714\) 1.67408e10 0.00241065
\(715\) 6.76671e12 0.968278
\(716\) 2.43440e12 0.346166
\(717\) −7.01413e12 −0.991146
\(718\) 1.14083e11 0.0160199
\(719\) −1.32221e13 −1.84510 −0.922548 0.385882i \(-0.873897\pi\)
−0.922548 + 0.385882i \(0.873897\pi\)
\(720\) 7.43190e11 0.103063
\(721\) −6.97416e12 −0.961133
\(722\) 5.39795e12 0.739285
\(723\) −1.06407e12 −0.144827
\(724\) −7.55981e12 −1.02256
\(725\) −9.62378e11 −0.129367
\(726\) 3.78585e12 0.505764
\(727\) 4.22774e12 0.561311 0.280656 0.959809i \(-0.409448\pi\)
0.280656 + 0.959809i \(0.409448\pi\)
\(728\) 4.07267e12 0.537388
\(729\) 2.82430e11 0.0370370
\(730\) 4.43696e12 0.578273
\(731\) −1.32555e11 −0.0171699
\(732\) 5.63463e11 0.0725380
\(733\) 9.98133e12 1.27709 0.638544 0.769586i \(-0.279537\pi\)
0.638544 + 0.769586i \(0.279537\pi\)
\(734\) 1.45317e12 0.184792
\(735\) −9.18460e11 −0.116083
\(736\) −4.79277e12 −0.602056
\(737\) 1.96634e13 2.45501
\(738\) 1.52897e12 0.189734
\(739\) 5.83082e12 0.719166 0.359583 0.933113i \(-0.382919\pi\)
0.359583 + 0.933113i \(0.382919\pi\)
\(740\) −7.28521e12 −0.893099
\(741\) −5.94791e12 −0.724740
\(742\) 2.64136e12 0.319896
\(743\) −1.00539e13 −1.21028 −0.605142 0.796118i \(-0.706884\pi\)
−0.605142 + 0.796118i \(0.706884\pi\)
\(744\) 3.58159e12 0.428546
\(745\) 8.87405e11 0.105540
\(746\) −2.05908e12 −0.243415
\(747\) −3.31839e11 −0.0389928
\(748\) 1.25462e11 0.0146539
\(749\) 4.74975e12 0.551445
\(750\) −2.43530e12 −0.281045
\(751\) 1.25152e12 0.143568 0.0717842 0.997420i \(-0.477131\pi\)
0.0717842 + 0.997420i \(0.477131\pi\)
\(752\) 2.12342e12 0.242133
\(753\) 1.01497e13 1.15048
\(754\) 8.66840e11 0.0976716
\(755\) 5.00869e12 0.561000
\(756\) 1.16771e12 0.130013
\(757\) 1.29325e13 1.43136 0.715681 0.698427i \(-0.246116\pi\)
0.715681 + 0.698427i \(0.246116\pi\)
\(758\) −7.68424e12 −0.845453
\(759\) −5.39861e12 −0.590465
\(760\) 8.87658e12 0.965127
\(761\) −1.02245e13 −1.10513 −0.552563 0.833471i \(-0.686350\pi\)
−0.552563 + 0.833471i \(0.686350\pi\)
\(762\) −3.07675e12 −0.330594
\(763\) −1.40518e13 −1.50097
\(764\) 4.41635e12 0.468968
\(765\) −2.48998e10 −0.00262857
\(766\) 5.80817e12 0.609551
\(767\) −9.66437e11 −0.100831
\(768\) −2.70040e12 −0.280094
\(769\) 1.09064e12 0.112464 0.0562319 0.998418i \(-0.482091\pi\)
0.0562319 + 0.998418i \(0.482091\pi\)
\(770\) −4.71793e12 −0.483663
\(771\) 7.94021e12 0.809258
\(772\) 1.43235e13 1.45135
\(773\) −9.93713e12 −1.00104 −0.500522 0.865724i \(-0.666859\pi\)
−0.500522 + 0.865724i \(0.666859\pi\)
\(774\) 2.40601e12 0.240970
\(775\) 4.26372e12 0.424552
\(776\) 1.00741e13 0.997311
\(777\) −7.69282e12 −0.757166
\(778\) 3.46828e12 0.339395
\(779\) −2.08670e13 −2.03021
\(780\) −2.68008e12 −0.259252
\(781\) 2.87619e13 2.76623
\(782\) 3.06545e10 0.00293133
\(783\) 5.61753e11 0.0534093
\(784\) −1.23184e12 −0.116448
\(785\) −9.96498e12 −0.936619
\(786\) 3.21178e11 0.0300154
\(787\) 6.66953e12 0.619739 0.309870 0.950779i \(-0.399715\pi\)
0.309870 + 0.950779i \(0.399715\pi\)
\(788\) 1.41998e13 1.31194
\(789\) −8.27151e12 −0.759868
\(790\) 5.72429e12 0.522877
\(791\) 1.18517e11 0.0107643
\(792\) −5.14713e12 −0.464838
\(793\) −1.36560e12 −0.122629
\(794\) −3.88762e12 −0.347130
\(795\) −3.92868e12 −0.348815
\(796\) −3.28701e12 −0.290196
\(797\) 1.12543e12 0.0987997 0.0493998 0.998779i \(-0.484269\pi\)
0.0493998 + 0.998779i \(0.484269\pi\)
\(798\) 4.14704e12 0.362014
\(799\) −7.11428e10 −0.00617548
\(800\) −5.43979e12 −0.469545
\(801\) −9.85305e11 −0.0845716
\(802\) 2.29673e12 0.196031
\(803\) 3.51127e13 2.98020
\(804\) −7.78804e12 −0.657319
\(805\) 4.42987e12 0.371800
\(806\) −3.84045e12 −0.320534
\(807\) 4.88983e12 0.405847
\(808\) 3.43347e12 0.283388
\(809\) −8.12047e12 −0.666520 −0.333260 0.942835i \(-0.608149\pi\)
−0.333260 + 0.942835i \(0.608149\pi\)
\(810\) 4.51958e11 0.0368906
\(811\) −3.12578e12 −0.253726 −0.126863 0.991920i \(-0.540491\pi\)
−0.126863 + 0.991920i \(0.540491\pi\)
\(812\) 2.32257e12 0.187485
\(813\) 6.89960e12 0.553881
\(814\) 1.50026e13 1.19772
\(815\) 1.00278e13 0.796151
\(816\) −3.33958e10 −0.00263685
\(817\) −3.28365e13 −2.57844
\(818\) −7.84584e12 −0.612702
\(819\) −2.83003e12 −0.219793
\(820\) −9.40251e12 −0.726242
\(821\) 1.34118e13 1.03025 0.515126 0.857114i \(-0.327745\pi\)
0.515126 + 0.857114i \(0.327745\pi\)
\(822\) 5.17781e12 0.395570
\(823\) 1.27209e13 0.966538 0.483269 0.875472i \(-0.339449\pi\)
0.483269 + 0.875472i \(0.339449\pi\)
\(824\) −1.21757e13 −0.920071
\(825\) −6.12742e12 −0.460506
\(826\) 6.73826e11 0.0503660
\(827\) 1.44497e13 1.07420 0.537100 0.843519i \(-0.319520\pi\)
0.537100 + 0.843519i \(0.319520\pi\)
\(828\) 2.13822e12 0.158094
\(829\) 2.04951e13 1.50714 0.753571 0.657366i \(-0.228330\pi\)
0.753571 + 0.657366i \(0.228330\pi\)
\(830\) −5.31026e11 −0.0388387
\(831\) 8.28776e11 0.0602883
\(832\) 3.69848e11 0.0267589
\(833\) 4.12717e10 0.00296995
\(834\) 3.02145e12 0.216256
\(835\) 1.81220e13 1.29008
\(836\) 3.10795e13 2.20062
\(837\) −2.48879e12 −0.175276
\(838\) −9.04925e12 −0.633891
\(839\) 3.36903e11 0.0234734 0.0117367 0.999931i \(-0.496264\pi\)
0.0117367 + 0.999931i \(0.496264\pi\)
\(840\) 4.22351e12 0.292696
\(841\) −1.33898e13 −0.922981
\(842\) 2.63496e12 0.180663
\(843\) 2.61468e12 0.178318
\(844\) −7.83657e11 −0.0531600
\(845\) −4.33302e12 −0.292372
\(846\) 1.29132e12 0.0866696
\(847\) −2.45839e13 −1.64125
\(848\) −5.26917e12 −0.349914
\(849\) 1.44478e13 0.954368
\(850\) 3.47929e10 0.00228615
\(851\) −1.40866e13 −0.920707
\(852\) −1.13917e13 −0.740646
\(853\) 2.53831e13 1.64162 0.820812 0.571199i \(-0.193521\pi\)
0.820812 + 0.571199i \(0.193521\pi\)
\(854\) 9.52132e11 0.0612543
\(855\) −6.16820e12 −0.394740
\(856\) 8.29224e12 0.527886
\(857\) −7.76188e12 −0.491534 −0.245767 0.969329i \(-0.579040\pi\)
−0.245767 + 0.969329i \(0.579040\pi\)
\(858\) 5.51914e12 0.347679
\(859\) −1.33642e13 −0.837477 −0.418739 0.908107i \(-0.637528\pi\)
−0.418739 + 0.908107i \(0.637528\pi\)
\(860\) −1.47959e13 −0.922355
\(861\) −9.92858e12 −0.615705
\(862\) −3.19157e12 −0.196889
\(863\) −3.15557e13 −1.93655 −0.968275 0.249886i \(-0.919607\pi\)
−0.968275 + 0.249886i \(0.919607\pi\)
\(864\) 3.17528e12 0.193852
\(865\) −2.06274e12 −0.125277
\(866\) −8.64319e11 −0.0522208
\(867\) −9.60450e12 −0.577283
\(868\) −1.02899e13 −0.615281
\(869\) 4.53003e13 2.69471
\(870\) 8.98945e11 0.0531982
\(871\) 1.88750e13 1.11123
\(872\) −2.45320e13 −1.43684
\(873\) −7.00037e12 −0.407903
\(874\) 7.59377e12 0.440206
\(875\) 1.58139e13 0.912017
\(876\) −1.39071e13 −0.797934
\(877\) −1.90311e13 −1.08634 −0.543171 0.839622i \(-0.682776\pi\)
−0.543171 + 0.839622i \(0.682776\pi\)
\(878\) 3.31274e12 0.188131
\(879\) −9.93947e12 −0.561582
\(880\) 9.41168e12 0.529048
\(881\) −2.06010e13 −1.15211 −0.576057 0.817409i \(-0.695410\pi\)
−0.576057 + 0.817409i \(0.695410\pi\)
\(882\) −7.49125e11 −0.0416817
\(883\) −4.21821e12 −0.233510 −0.116755 0.993161i \(-0.537249\pi\)
−0.116755 + 0.993161i \(0.537249\pi\)
\(884\) 1.20431e11 0.00663292
\(885\) −1.00223e12 −0.0549190
\(886\) 9.33041e12 0.508685
\(887\) 2.06824e12 0.112188 0.0560939 0.998426i \(-0.482135\pi\)
0.0560939 + 0.998426i \(0.482135\pi\)
\(888\) −1.34303e13 −0.724818
\(889\) 1.99793e13 1.07281
\(890\) −1.57674e12 −0.0842372
\(891\) 3.57666e12 0.190120
\(892\) 9.62709e11 0.0509159
\(893\) −1.76235e13 −0.927389
\(894\) 7.23795e11 0.0378963
\(895\) −6.11849e12 −0.318743
\(896\) 1.62866e13 0.844198
\(897\) −5.18216e12 −0.267267
\(898\) 1.20385e13 0.617771
\(899\) −4.95021e12 −0.252758
\(900\) 2.42688e12 0.123298
\(901\) 1.76538e11 0.00892436
\(902\) 1.93627e13 0.973952
\(903\) −1.56237e13 −0.781969
\(904\) 2.06911e11 0.0103045
\(905\) 1.90004e13 0.941551
\(906\) 4.08524e12 0.201438
\(907\) −1.79596e13 −0.881176 −0.440588 0.897709i \(-0.645230\pi\)
−0.440588 + 0.897709i \(0.645230\pi\)
\(908\) 2.11033e13 1.03030
\(909\) −2.38586e12 −0.115907
\(910\) −4.52876e12 −0.218924
\(911\) 3.19918e13 1.53888 0.769442 0.638717i \(-0.220535\pi\)
0.769442 + 0.638717i \(0.220535\pi\)
\(912\) −8.27283e12 −0.395984
\(913\) −4.20237e12 −0.200159
\(914\) −1.33546e13 −0.632956
\(915\) −1.41618e12 −0.0667917
\(916\) −1.44604e12 −0.0678658
\(917\) −2.08561e12 −0.0974027
\(918\) −2.03091e10 −0.000943839 0
\(919\) 1.61849e13 0.748496 0.374248 0.927329i \(-0.377901\pi\)
0.374248 + 0.927329i \(0.377901\pi\)
\(920\) 7.73379e12 0.355916
\(921\) 3.94526e12 0.180679
\(922\) −9.77516e12 −0.445487
\(923\) 2.76087e13 1.25210
\(924\) 1.47877e13 0.667386
\(925\) −1.59882e13 −0.718063
\(926\) −1.17585e13 −0.525536
\(927\) 8.46070e12 0.376311
\(928\) 6.31563e12 0.279545
\(929\) 3.56724e12 0.157131 0.0785654 0.996909i \(-0.474966\pi\)
0.0785654 + 0.996909i \(0.474966\pi\)
\(930\) −3.98269e12 −0.174583
\(931\) 1.02238e13 0.446006
\(932\) −4.50508e12 −0.195583
\(933\) 2.36571e12 0.102210
\(934\) −1.42418e13 −0.612356
\(935\) −3.15328e11 −0.0134931
\(936\) −4.94075e12 −0.210403
\(937\) −4.09993e12 −0.173759 −0.0868797 0.996219i \(-0.527690\pi\)
−0.0868797 + 0.996219i \(0.527690\pi\)
\(938\) −1.31601e13 −0.555069
\(939\) −1.71846e13 −0.721349
\(940\) −7.94104e12 −0.331743
\(941\) −8.94587e12 −0.371937 −0.185968 0.982556i \(-0.559542\pi\)
−0.185968 + 0.982556i \(0.559542\pi\)
\(942\) −8.12775e12 −0.336311
\(943\) −1.81805e13 −0.748693
\(944\) −1.34420e12 −0.0550921
\(945\) −2.93485e12 −0.119713
\(946\) 3.04694e13 1.23696
\(947\) −5.04823e12 −0.203969 −0.101984 0.994786i \(-0.532519\pi\)
−0.101984 + 0.994786i \(0.532519\pi\)
\(948\) −1.79420e13 −0.721496
\(949\) 3.37049e13 1.34895
\(950\) 8.61892e12 0.343318
\(951\) 7.61394e11 0.0301854
\(952\) −1.89786e11 −0.00748856
\(953\) −3.63509e13 −1.42757 −0.713784 0.700366i \(-0.753020\pi\)
−0.713784 + 0.700366i \(0.753020\pi\)
\(954\) −3.20436e12 −0.125249
\(955\) −1.10998e13 −0.431817
\(956\) 3.51813e13 1.36223
\(957\) 7.11398e12 0.274163
\(958\) −1.73030e13 −0.663708
\(959\) −3.36228e13 −1.28366
\(960\) 3.83546e11 0.0145746
\(961\) −4.50822e12 −0.170510
\(962\) 1.44010e13 0.542133
\(963\) −5.76215e12 −0.215907
\(964\) 5.33715e12 0.199050
\(965\) −3.59999e13 −1.33637
\(966\) 3.61314e12 0.133502
\(967\) 2.21272e13 0.813779 0.406889 0.913477i \(-0.366613\pi\)
0.406889 + 0.913477i \(0.366613\pi\)
\(968\) −4.29192e13 −1.57113
\(969\) 2.77172e11 0.0100993
\(970\) −1.12023e13 −0.406290
\(971\) 1.48279e13 0.535296 0.267648 0.963517i \(-0.413754\pi\)
0.267648 + 0.963517i \(0.413754\pi\)
\(972\) −1.41660e12 −0.0509037
\(973\) −1.96202e13 −0.701770
\(974\) −3.71735e12 −0.132348
\(975\) −5.88175e12 −0.208442
\(976\) −1.89938e12 −0.0670022
\(977\) −4.50100e13 −1.58046 −0.790231 0.612810i \(-0.790039\pi\)
−0.790231 + 0.612810i \(0.790039\pi\)
\(978\) 8.17897e12 0.285873
\(979\) −1.24778e13 −0.434126
\(980\) 4.60679e12 0.159544
\(981\) 1.70469e13 0.587672
\(982\) −1.94160e13 −0.666281
\(983\) −3.84240e13 −1.31254 −0.656269 0.754527i \(-0.727866\pi\)
−0.656269 + 0.754527i \(0.727866\pi\)
\(984\) −1.73336e13 −0.589401
\(985\) −3.56891e13 −1.20801
\(986\) −4.03948e10 −0.00136107
\(987\) −8.38534e12 −0.281251
\(988\) 2.98334e13 0.996084
\(989\) −2.86090e13 −0.950868
\(990\) 5.72355e12 0.189368
\(991\) −2.04665e13 −0.674081 −0.337040 0.941490i \(-0.609426\pi\)
−0.337040 + 0.941490i \(0.609426\pi\)
\(992\) −2.79808e13 −0.917397
\(993\) −1.80672e13 −0.589683
\(994\) −1.92495e13 −0.625434
\(995\) 8.26138e12 0.267208
\(996\) 1.66443e12 0.0535918
\(997\) −2.11028e13 −0.676413 −0.338206 0.941072i \(-0.609820\pi\)
−0.338206 + 0.941072i \(0.609820\pi\)
\(998\) 2.22216e13 0.709067
\(999\) 9.33254e12 0.296452
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.1.13 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.13 22 1.1 even 1 trivial