Properties

Label 177.10.a.d.1.10
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 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.00717 q^{2} +81.0000 q^{3} -475.914 q^{4} +2084.99 q^{5} -486.580 q^{6} -6970.40 q^{7} +5934.56 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-6.00717 q^{2} +81.0000 q^{3} -475.914 q^{4} +2084.99 q^{5} -486.580 q^{6} -6970.40 q^{7} +5934.56 q^{8} +6561.00 q^{9} -12524.9 q^{10} -39367.9 q^{11} -38549.0 q^{12} -185559. q^{13} +41872.3 q^{14} +168884. q^{15} +208018. q^{16} +311978. q^{17} -39413.0 q^{18} -320095. q^{19} -992274. q^{20} -564602. q^{21} +236490. q^{22} +573097. q^{23} +480700. q^{24} +2.39404e6 q^{25} +1.11468e6 q^{26} +531441. q^{27} +3.31731e6 q^{28} +896559. q^{29} -1.01451e6 q^{30} +7.63959e6 q^{31} -4.28809e6 q^{32} -3.18880e6 q^{33} -1.87410e6 q^{34} -1.45332e7 q^{35} -3.12247e6 q^{36} -1.40613e7 q^{37} +1.92287e6 q^{38} -1.50303e7 q^{39} +1.23735e7 q^{40} +7.43518e6 q^{41} +3.39166e6 q^{42} +3.38470e7 q^{43} +1.87357e7 q^{44} +1.36796e7 q^{45} -3.44269e6 q^{46} -3.46557e7 q^{47} +1.68495e7 q^{48} +8.23280e6 q^{49} -1.43814e7 q^{50} +2.52702e7 q^{51} +8.83102e7 q^{52} +2.21693e7 q^{53} -3.19245e6 q^{54} -8.20816e7 q^{55} -4.13662e7 q^{56} -2.59277e7 q^{57} -5.38578e6 q^{58} -1.21174e7 q^{59} -8.03742e7 q^{60} +1.30661e7 q^{61} -4.58923e7 q^{62} -4.57328e7 q^{63} -8.07460e7 q^{64} -3.86888e8 q^{65} +1.91557e7 q^{66} +2.44148e8 q^{67} -1.48475e8 q^{68} +4.64208e7 q^{69} +8.73032e7 q^{70} +3.04234e8 q^{71} +3.89367e7 q^{72} +2.17807e8 q^{73} +8.44685e7 q^{74} +1.93918e8 q^{75} +1.52338e8 q^{76} +2.74410e8 q^{77} +9.02894e7 q^{78} -4.29738e7 q^{79} +4.33715e8 q^{80} +4.30467e7 q^{81} -4.46644e7 q^{82} -8.56942e8 q^{83} +2.68702e8 q^{84} +6.50470e8 q^{85} -2.03325e8 q^{86} +7.26213e7 q^{87} -2.33631e8 q^{88} -6.49239e8 q^{89} -8.21756e7 q^{90} +1.29342e9 q^{91} -2.72745e8 q^{92} +6.18807e8 q^{93} +2.08182e8 q^{94} -6.67394e8 q^{95} -3.47336e8 q^{96} +1.14836e9 q^{97} -4.94558e7 q^{98} -2.58293e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.00717 −0.265482 −0.132741 0.991151i \(-0.542378\pi\)
−0.132741 + 0.991151i \(0.542378\pi\)
\(3\) 81.0000 0.577350
\(4\) −475.914 −0.929519
\(5\) 2084.99 1.49189 0.745947 0.666005i \(-0.231997\pi\)
0.745947 + 0.666005i \(0.231997\pi\)
\(6\) −486.580 −0.153276
\(7\) −6970.40 −1.09728 −0.548638 0.836060i \(-0.684854\pi\)
−0.548638 + 0.836060i \(0.684854\pi\)
\(8\) 5934.56 0.512252
\(9\) 6561.00 0.333333
\(10\) −12524.9 −0.396071
\(11\) −39367.9 −0.810728 −0.405364 0.914155i \(-0.632855\pi\)
−0.405364 + 0.914155i \(0.632855\pi\)
\(12\) −38549.0 −0.536658
\(13\) −185559. −1.80193 −0.900964 0.433895i \(-0.857139\pi\)
−0.900964 + 0.433895i \(0.857139\pi\)
\(14\) 41872.3 0.291307
\(15\) 168884. 0.861346
\(16\) 208018. 0.793526
\(17\) 311978. 0.905949 0.452974 0.891524i \(-0.350363\pi\)
0.452974 + 0.891524i \(0.350363\pi\)
\(18\) −39413.0 −0.0884939
\(19\) −320095. −0.563492 −0.281746 0.959489i \(-0.590914\pi\)
−0.281746 + 0.959489i \(0.590914\pi\)
\(20\) −992274. −1.38675
\(21\) −564602. −0.633513
\(22\) 236490. 0.215233
\(23\) 573097. 0.427024 0.213512 0.976940i \(-0.431510\pi\)
0.213512 + 0.976940i \(0.431510\pi\)
\(24\) 480700. 0.295749
\(25\) 2.39404e6 1.22575
\(26\) 1.11468e6 0.478379
\(27\) 531441. 0.192450
\(28\) 3.31731e6 1.01994
\(29\) 896559. 0.235390 0.117695 0.993050i \(-0.462449\pi\)
0.117695 + 0.993050i \(0.462449\pi\)
\(30\) −1.01451e6 −0.228672
\(31\) 7.63959e6 1.48574 0.742869 0.669436i \(-0.233464\pi\)
0.742869 + 0.669436i \(0.233464\pi\)
\(32\) −4.28809e6 −0.722919
\(33\) −3.18880e6 −0.468074
\(34\) −1.87410e6 −0.240513
\(35\) −1.45332e7 −1.63702
\(36\) −3.12247e6 −0.309840
\(37\) −1.40613e7 −1.23344 −0.616719 0.787183i \(-0.711538\pi\)
−0.616719 + 0.787183i \(0.711538\pi\)
\(38\) 1.92287e6 0.149597
\(39\) −1.50303e7 −1.04034
\(40\) 1.23735e7 0.764226
\(41\) 7.43518e6 0.410927 0.205463 0.978665i \(-0.434130\pi\)
0.205463 + 0.978665i \(0.434130\pi\)
\(42\) 3.39166e6 0.168186
\(43\) 3.38470e7 1.50978 0.754888 0.655853i \(-0.227691\pi\)
0.754888 + 0.655853i \(0.227691\pi\)
\(44\) 1.87357e7 0.753588
\(45\) 1.36796e7 0.497298
\(46\) −3.44269e6 −0.113367
\(47\) −3.46557e7 −1.03594 −0.517969 0.855399i \(-0.673312\pi\)
−0.517969 + 0.855399i \(0.673312\pi\)
\(48\) 1.68495e7 0.458142
\(49\) 8.23280e6 0.204017
\(50\) −1.43814e7 −0.325414
\(51\) 2.52702e7 0.523050
\(52\) 8.83102e7 1.67493
\(53\) 2.21693e7 0.385932 0.192966 0.981205i \(-0.438189\pi\)
0.192966 + 0.981205i \(0.438189\pi\)
\(54\) −3.19245e6 −0.0510920
\(55\) −8.20816e7 −1.20952
\(56\) −4.13662e7 −0.562082
\(57\) −2.59277e7 −0.325332
\(58\) −5.38578e6 −0.0624917
\(59\) −1.21174e7 −0.130189
\(60\) −8.03742e7 −0.800638
\(61\) 1.30661e7 0.120827 0.0604133 0.998173i \(-0.480758\pi\)
0.0604133 + 0.998173i \(0.480758\pi\)
\(62\) −4.58923e7 −0.394436
\(63\) −4.57328e7 −0.365759
\(64\) −8.07460e7 −0.601604
\(65\) −3.86888e8 −2.68829
\(66\) 1.91557e7 0.124265
\(67\) 2.44148e8 1.48018 0.740092 0.672505i \(-0.234782\pi\)
0.740092 + 0.672505i \(0.234782\pi\)
\(68\) −1.48475e8 −0.842097
\(69\) 4.64208e7 0.246543
\(70\) 8.73032e7 0.434599
\(71\) 3.04234e8 1.42084 0.710420 0.703778i \(-0.248505\pi\)
0.710420 + 0.703778i \(0.248505\pi\)
\(72\) 3.89367e7 0.170751
\(73\) 2.17807e8 0.897673 0.448837 0.893614i \(-0.351839\pi\)
0.448837 + 0.893614i \(0.351839\pi\)
\(74\) 8.44685e7 0.327455
\(75\) 1.93918e8 0.707687
\(76\) 1.52338e8 0.523777
\(77\) 2.74410e8 0.889593
\(78\) 9.02894e7 0.276192
\(79\) −4.29738e7 −0.124132 −0.0620658 0.998072i \(-0.519769\pi\)
−0.0620658 + 0.998072i \(0.519769\pi\)
\(80\) 4.33715e8 1.18386
\(81\) 4.30467e7 0.111111
\(82\) −4.46644e7 −0.109094
\(83\) −8.56942e8 −1.98198 −0.990991 0.133925i \(-0.957242\pi\)
−0.990991 + 0.133925i \(0.957242\pi\)
\(84\) 2.68702e8 0.588863
\(85\) 6.50470e8 1.35158
\(86\) −2.03325e8 −0.400818
\(87\) 7.26213e7 0.135902
\(88\) −2.33631e8 −0.415297
\(89\) −6.49239e8 −1.09686 −0.548428 0.836198i \(-0.684774\pi\)
−0.548428 + 0.836198i \(0.684774\pi\)
\(90\) −8.21756e7 −0.132024
\(91\) 1.29342e9 1.97721
\(92\) −2.72745e8 −0.396927
\(93\) 6.18807e8 0.857792
\(94\) 2.08182e8 0.275023
\(95\) −6.67394e8 −0.840671
\(96\) −3.47336e8 −0.417377
\(97\) 1.14836e9 1.31706 0.658528 0.752556i \(-0.271179\pi\)
0.658528 + 0.752556i \(0.271179\pi\)
\(98\) −4.94558e7 −0.0541627
\(99\) −2.58293e8 −0.270243
\(100\) −1.13936e9 −1.13936
\(101\) 8.98191e8 0.858860 0.429430 0.903100i \(-0.358714\pi\)
0.429430 + 0.903100i \(0.358714\pi\)
\(102\) −1.51802e8 −0.138860
\(103\) −6.04439e8 −0.529157 −0.264579 0.964364i \(-0.585233\pi\)
−0.264579 + 0.964364i \(0.585233\pi\)
\(104\) −1.10121e9 −0.923041
\(105\) −1.17719e9 −0.945135
\(106\) −1.33175e8 −0.102458
\(107\) 2.30250e9 1.69814 0.849068 0.528283i \(-0.177164\pi\)
0.849068 + 0.528283i \(0.177164\pi\)
\(108\) −2.52920e8 −0.178886
\(109\) 1.44302e9 0.979159 0.489580 0.871959i \(-0.337150\pi\)
0.489580 + 0.871959i \(0.337150\pi\)
\(110\) 4.93077e8 0.321106
\(111\) −1.13896e9 −0.712126
\(112\) −1.44997e9 −0.870718
\(113\) 4.83813e8 0.279141 0.139571 0.990212i \(-0.455428\pi\)
0.139571 + 0.990212i \(0.455428\pi\)
\(114\) 1.55752e8 0.0863698
\(115\) 1.19490e9 0.637075
\(116\) −4.26685e8 −0.218799
\(117\) −1.21745e9 −0.600642
\(118\) 7.27910e7 0.0345628
\(119\) −2.17461e9 −0.994077
\(120\) 1.00225e9 0.441226
\(121\) −8.08116e8 −0.342720
\(122\) −7.84903e7 −0.0320772
\(123\) 6.02250e8 0.237249
\(124\) −3.63579e9 −1.38102
\(125\) 9.19310e8 0.336796
\(126\) 2.74724e8 0.0971023
\(127\) 1.35220e9 0.461237 0.230619 0.973044i \(-0.425925\pi\)
0.230619 + 0.973044i \(0.425925\pi\)
\(128\) 2.68056e9 0.882634
\(129\) 2.74161e9 0.871670
\(130\) 2.32410e9 0.713691
\(131\) 4.03325e9 1.19656 0.598280 0.801287i \(-0.295851\pi\)
0.598280 + 0.801287i \(0.295851\pi\)
\(132\) 1.51759e9 0.435084
\(133\) 2.23119e9 0.618307
\(134\) −1.46664e9 −0.392962
\(135\) 1.10805e9 0.287115
\(136\) 1.85145e9 0.464074
\(137\) 4.79550e8 0.116303 0.0581515 0.998308i \(-0.481479\pi\)
0.0581515 + 0.998308i \(0.481479\pi\)
\(138\) −2.78858e8 −0.0654526
\(139\) 2.01524e9 0.457890 0.228945 0.973439i \(-0.426472\pi\)
0.228945 + 0.973439i \(0.426472\pi\)
\(140\) 6.91654e9 1.52164
\(141\) −2.80711e9 −0.598099
\(142\) −1.82758e9 −0.377207
\(143\) 7.30507e9 1.46087
\(144\) 1.36481e9 0.264509
\(145\) 1.86931e9 0.351177
\(146\) −1.30840e9 −0.238316
\(147\) 6.66857e8 0.117789
\(148\) 6.69196e9 1.14650
\(149\) 6.27978e9 1.04377 0.521887 0.853015i \(-0.325228\pi\)
0.521887 + 0.853015i \(0.325228\pi\)
\(150\) −1.16489e9 −0.187878
\(151\) 9.86636e9 1.54440 0.772201 0.635378i \(-0.219156\pi\)
0.772201 + 0.635378i \(0.219156\pi\)
\(152\) −1.89963e9 −0.288650
\(153\) 2.04689e9 0.301983
\(154\) −1.64843e9 −0.236171
\(155\) 1.59284e10 2.21657
\(156\) 7.15312e9 0.967019
\(157\) 1.21615e10 1.59750 0.798748 0.601666i \(-0.205496\pi\)
0.798748 + 0.601666i \(0.205496\pi\)
\(158\) 2.58151e8 0.0329547
\(159\) 1.79571e9 0.222818
\(160\) −8.94062e9 −1.07852
\(161\) −3.99471e9 −0.468564
\(162\) −2.58589e8 −0.0294980
\(163\) −1.18179e10 −1.31128 −0.655642 0.755072i \(-0.727602\pi\)
−0.655642 + 0.755072i \(0.727602\pi\)
\(164\) −3.53851e9 −0.381964
\(165\) −6.64861e9 −0.698317
\(166\) 5.14779e9 0.526180
\(167\) 5.66807e9 0.563911 0.281956 0.959427i \(-0.409017\pi\)
0.281956 + 0.959427i \(0.409017\pi\)
\(168\) −3.35067e9 −0.324518
\(169\) 2.38277e10 2.24694
\(170\) −3.90748e9 −0.358820
\(171\) −2.10015e9 −0.187831
\(172\) −1.61083e10 −1.40337
\(173\) 1.76972e10 1.50210 0.751049 0.660246i \(-0.229548\pi\)
0.751049 + 0.660246i \(0.229548\pi\)
\(174\) −4.36248e8 −0.0360796
\(175\) −1.66874e10 −1.34499
\(176\) −8.18924e9 −0.643334
\(177\) −9.81506e8 −0.0751646
\(178\) 3.90009e9 0.291195
\(179\) 1.59584e10 1.16186 0.580928 0.813955i \(-0.302690\pi\)
0.580928 + 0.813955i \(0.302690\pi\)
\(180\) −6.51031e9 −0.462248
\(181\) −9.26360e9 −0.641543 −0.320772 0.947157i \(-0.603942\pi\)
−0.320772 + 0.947157i \(0.603942\pi\)
\(182\) −7.76979e9 −0.524914
\(183\) 1.05836e9 0.0697592
\(184\) 3.40108e9 0.218744
\(185\) −2.93176e10 −1.84016
\(186\) −3.71727e9 −0.227728
\(187\) −1.22819e10 −0.734478
\(188\) 1.64931e10 0.962925
\(189\) −3.70435e9 −0.211171
\(190\) 4.00915e9 0.223183
\(191\) −1.65202e10 −0.898182 −0.449091 0.893486i \(-0.648252\pi\)
−0.449091 + 0.893486i \(0.648252\pi\)
\(192\) −6.54042e9 −0.347336
\(193\) 1.33694e8 0.00693591 0.00346796 0.999994i \(-0.498896\pi\)
0.00346796 + 0.999994i \(0.498896\pi\)
\(194\) −6.89837e9 −0.349654
\(195\) −3.13380e10 −1.55208
\(196\) −3.91811e9 −0.189637
\(197\) 6.83918e9 0.323524 0.161762 0.986830i \(-0.448282\pi\)
0.161762 + 0.986830i \(0.448282\pi\)
\(198\) 1.55161e9 0.0717445
\(199\) −1.06544e9 −0.0481605 −0.0240803 0.999710i \(-0.507666\pi\)
−0.0240803 + 0.999710i \(0.507666\pi\)
\(200\) 1.42076e10 0.627893
\(201\) 1.97760e10 0.854585
\(202\) −5.39558e9 −0.228012
\(203\) −6.24937e9 −0.258288
\(204\) −1.20264e10 −0.486185
\(205\) 1.55023e10 0.613059
\(206\) 3.63096e9 0.140482
\(207\) 3.76009e9 0.142341
\(208\) −3.85996e10 −1.42988
\(209\) 1.26015e10 0.456839
\(210\) 7.07156e9 0.250916
\(211\) −1.58072e10 −0.549013 −0.274507 0.961585i \(-0.588515\pi\)
−0.274507 + 0.961585i \(0.588515\pi\)
\(212\) −1.05507e10 −0.358731
\(213\) 2.46430e10 0.820323
\(214\) −1.38315e10 −0.450824
\(215\) 7.05706e10 2.25243
\(216\) 3.15387e9 0.0985830
\(217\) −5.32510e10 −1.63027
\(218\) −8.66846e9 −0.259949
\(219\) 1.76423e10 0.518272
\(220\) 3.90638e10 1.12427
\(221\) −5.78903e10 −1.63245
\(222\) 6.84195e9 0.189056
\(223\) −2.32521e10 −0.629636 −0.314818 0.949152i \(-0.601943\pi\)
−0.314818 + 0.949152i \(0.601943\pi\)
\(224\) 2.98897e10 0.793242
\(225\) 1.57073e10 0.408583
\(226\) −2.90634e9 −0.0741069
\(227\) 2.67471e10 0.668591 0.334296 0.942468i \(-0.391502\pi\)
0.334296 + 0.942468i \(0.391502\pi\)
\(228\) 1.23394e10 0.302403
\(229\) −5.20429e10 −1.25055 −0.625276 0.780404i \(-0.715014\pi\)
−0.625276 + 0.780404i \(0.715014\pi\)
\(230\) −7.17795e9 −0.169132
\(231\) 2.22272e10 0.513607
\(232\) 5.32068e9 0.120579
\(233\) −3.89449e10 −0.865663 −0.432832 0.901475i \(-0.642486\pi\)
−0.432832 + 0.901475i \(0.642486\pi\)
\(234\) 7.31344e9 0.159460
\(235\) −7.22566e10 −1.54551
\(236\) 5.76682e9 0.121013
\(237\) −3.48088e9 −0.0716674
\(238\) 1.30632e10 0.263909
\(239\) 1.34283e10 0.266214 0.133107 0.991102i \(-0.457505\pi\)
0.133107 + 0.991102i \(0.457505\pi\)
\(240\) 3.51309e10 0.683500
\(241\) −1.42708e10 −0.272504 −0.136252 0.990674i \(-0.543506\pi\)
−0.136252 + 0.990674i \(0.543506\pi\)
\(242\) 4.85448e9 0.0909859
\(243\) 3.48678e9 0.0641500
\(244\) −6.21835e9 −0.112311
\(245\) 1.71653e10 0.304371
\(246\) −3.61781e9 −0.0629852
\(247\) 5.93966e10 1.01537
\(248\) 4.53376e10 0.761073
\(249\) −6.94123e10 −1.14430
\(250\) −5.52245e9 −0.0894132
\(251\) −9.85654e10 −1.56745 −0.783724 0.621110i \(-0.786682\pi\)
−0.783724 + 0.621110i \(0.786682\pi\)
\(252\) 2.17649e10 0.339980
\(253\) −2.25616e10 −0.346201
\(254\) −8.12289e9 −0.122450
\(255\) 5.26880e10 0.780335
\(256\) 2.52394e10 0.367281
\(257\) −9.44707e10 −1.35082 −0.675411 0.737442i \(-0.736034\pi\)
−0.675411 + 0.737442i \(0.736034\pi\)
\(258\) −1.64693e10 −0.231412
\(259\) 9.80127e10 1.35342
\(260\) 1.84126e11 2.49881
\(261\) 5.88232e9 0.0784633
\(262\) −2.42284e10 −0.317665
\(263\) 3.07403e10 0.396194 0.198097 0.980182i \(-0.436524\pi\)
0.198097 + 0.980182i \(0.436524\pi\)
\(264\) −1.89241e10 −0.239772
\(265\) 4.62227e10 0.575770
\(266\) −1.34031e10 −0.164149
\(267\) −5.25884e10 −0.633270
\(268\) −1.16193e11 −1.37586
\(269\) −6.19302e10 −0.721137 −0.360568 0.932733i \(-0.617417\pi\)
−0.360568 + 0.932733i \(0.617417\pi\)
\(270\) −6.65622e9 −0.0762239
\(271\) −5.29125e10 −0.595931 −0.297966 0.954577i \(-0.596308\pi\)
−0.297966 + 0.954577i \(0.596308\pi\)
\(272\) 6.48970e10 0.718894
\(273\) 1.04767e11 1.14154
\(274\) −2.88073e9 −0.0308763
\(275\) −9.42485e10 −0.993750
\(276\) −2.20923e10 −0.229166
\(277\) 4.92700e10 0.502833 0.251416 0.967879i \(-0.419104\pi\)
0.251416 + 0.967879i \(0.419104\pi\)
\(278\) −1.21059e10 −0.121561
\(279\) 5.01234e10 0.495246
\(280\) −8.62481e10 −0.838568
\(281\) −1.04213e11 −0.997111 −0.498556 0.866858i \(-0.666136\pi\)
−0.498556 + 0.866858i \(0.666136\pi\)
\(282\) 1.68628e10 0.158784
\(283\) 1.29363e11 1.19887 0.599435 0.800423i \(-0.295392\pi\)
0.599435 + 0.800423i \(0.295392\pi\)
\(284\) −1.44789e11 −1.32070
\(285\) −5.40589e10 −0.485362
\(286\) −4.38828e10 −0.387835
\(287\) −5.18262e10 −0.450900
\(288\) −2.81342e10 −0.240973
\(289\) −2.12577e10 −0.179257
\(290\) −1.12293e10 −0.0932311
\(291\) 9.30169e10 0.760403
\(292\) −1.03657e11 −0.834405
\(293\) 1.85348e10 0.146921 0.0734604 0.997298i \(-0.476596\pi\)
0.0734604 + 0.997298i \(0.476596\pi\)
\(294\) −4.00592e9 −0.0312708
\(295\) −2.52645e10 −0.194228
\(296\) −8.34476e10 −0.631831
\(297\) −2.09217e10 −0.156025
\(298\) −3.77237e10 −0.277103
\(299\) −1.06343e11 −0.769467
\(300\) −9.22881e10 −0.657809
\(301\) −2.35927e11 −1.65664
\(302\) −5.92688e10 −0.410011
\(303\) 7.27534e10 0.495863
\(304\) −6.65856e10 −0.447146
\(305\) 2.72427e10 0.180260
\(306\) −1.22960e10 −0.0801709
\(307\) 2.80374e11 1.80142 0.900709 0.434424i \(-0.143048\pi\)
0.900709 + 0.434424i \(0.143048\pi\)
\(308\) −1.30595e11 −0.826894
\(309\) −4.89595e10 −0.305509
\(310\) −9.56848e10 −0.588458
\(311\) 2.75615e11 1.67063 0.835315 0.549771i \(-0.185285\pi\)
0.835315 + 0.549771i \(0.185285\pi\)
\(312\) −8.91982e10 −0.532918
\(313\) 1.54872e11 0.912060 0.456030 0.889964i \(-0.349271\pi\)
0.456030 + 0.889964i \(0.349271\pi\)
\(314\) −7.30563e10 −0.424106
\(315\) −9.53522e10 −0.545674
\(316\) 2.04518e10 0.115383
\(317\) −1.30019e11 −0.723168 −0.361584 0.932340i \(-0.617764\pi\)
−0.361584 + 0.932340i \(0.617764\pi\)
\(318\) −1.07872e10 −0.0591541
\(319\) −3.52956e10 −0.190837
\(320\) −1.68354e11 −0.897530
\(321\) 1.86502e11 0.980419
\(322\) 2.39969e10 0.124395
\(323\) −9.98626e10 −0.510495
\(324\) −2.04865e10 −0.103280
\(325\) −4.44237e11 −2.20871
\(326\) 7.09922e10 0.348122
\(327\) 1.16885e11 0.565318
\(328\) 4.41246e10 0.210498
\(329\) 2.41564e11 1.13671
\(330\) 3.99393e10 0.185390
\(331\) −1.78508e11 −0.817396 −0.408698 0.912670i \(-0.634017\pi\)
−0.408698 + 0.912670i \(0.634017\pi\)
\(332\) 4.07831e11 1.84229
\(333\) −9.22561e10 −0.411146
\(334\) −3.40490e10 −0.149708
\(335\) 5.09044e11 2.20828
\(336\) −1.17447e11 −0.502709
\(337\) 3.18272e10 0.134420 0.0672100 0.997739i \(-0.478590\pi\)
0.0672100 + 0.997739i \(0.478590\pi\)
\(338\) −1.43137e11 −0.596522
\(339\) 3.91888e10 0.161162
\(340\) −3.09568e11 −1.25632
\(341\) −3.00755e11 −1.20453
\(342\) 1.26159e10 0.0498656
\(343\) 2.23895e11 0.873414
\(344\) 2.00867e11 0.773386
\(345\) 9.67868e10 0.367816
\(346\) −1.06310e11 −0.398780
\(347\) −9.04488e10 −0.334904 −0.167452 0.985880i \(-0.553554\pi\)
−0.167452 + 0.985880i \(0.553554\pi\)
\(348\) −3.45615e10 −0.126324
\(349\) −5.17329e11 −1.86660 −0.933302 0.359092i \(-0.883086\pi\)
−0.933302 + 0.359092i \(0.883086\pi\)
\(350\) 1.00244e11 0.357070
\(351\) −9.86137e10 −0.346781
\(352\) 1.68813e11 0.586091
\(353\) 3.58289e11 1.22814 0.614068 0.789253i \(-0.289532\pi\)
0.614068 + 0.789253i \(0.289532\pi\)
\(354\) 5.89607e9 0.0199548
\(355\) 6.34324e11 2.11975
\(356\) 3.08982e11 1.01955
\(357\) −1.76143e11 −0.573930
\(358\) −9.58650e10 −0.308451
\(359\) 1.13310e11 0.360033 0.180016 0.983664i \(-0.442385\pi\)
0.180016 + 0.983664i \(0.442385\pi\)
\(360\) 8.11824e10 0.254742
\(361\) −2.20227e11 −0.682476
\(362\) 5.56480e10 0.170318
\(363\) −6.54574e10 −0.197869
\(364\) −6.15557e11 −1.83786
\(365\) 4.54124e11 1.33923
\(366\) −6.35772e9 −0.0185198
\(367\) 5.94459e11 1.71050 0.855252 0.518212i \(-0.173402\pi\)
0.855252 + 0.518212i \(0.173402\pi\)
\(368\) 1.19214e11 0.338855
\(369\) 4.87822e10 0.136976
\(370\) 1.76116e11 0.488529
\(371\) −1.54529e11 −0.423474
\(372\) −2.94499e11 −0.797334
\(373\) −5.26553e11 −1.40849 −0.704243 0.709959i \(-0.748713\pi\)
−0.704243 + 0.709959i \(0.748713\pi\)
\(374\) 7.37795e10 0.194991
\(375\) 7.44641e10 0.194449
\(376\) −2.05666e11 −0.530662
\(377\) −1.66365e11 −0.424155
\(378\) 2.22527e10 0.0560620
\(379\) 7.85785e11 1.95626 0.978131 0.207989i \(-0.0666920\pi\)
0.978131 + 0.207989i \(0.0666920\pi\)
\(380\) 3.17622e11 0.781420
\(381\) 1.09528e11 0.266295
\(382\) 9.92394e10 0.238451
\(383\) 4.44736e11 1.05611 0.528053 0.849211i \(-0.322922\pi\)
0.528053 + 0.849211i \(0.322922\pi\)
\(384\) 2.17125e11 0.509589
\(385\) 5.72141e11 1.32718
\(386\) −8.03121e8 −0.00184136
\(387\) 2.22070e11 0.503259
\(388\) −5.46519e11 −1.22423
\(389\) −5.50601e11 −1.21917 −0.609584 0.792722i \(-0.708663\pi\)
−0.609584 + 0.792722i \(0.708663\pi\)
\(390\) 1.88252e11 0.412050
\(391\) 1.78793e11 0.386862
\(392\) 4.88581e10 0.104508
\(393\) 3.26694e11 0.690835
\(394\) −4.10841e10 −0.0858896
\(395\) −8.95999e10 −0.185191
\(396\) 1.22925e11 0.251196
\(397\) 3.53364e11 0.713946 0.356973 0.934115i \(-0.383809\pi\)
0.356973 + 0.934115i \(0.383809\pi\)
\(398\) 6.40029e9 0.0127857
\(399\) 1.80726e11 0.356980
\(400\) 4.98004e11 0.972665
\(401\) −5.64703e11 −1.09061 −0.545306 0.838237i \(-0.683587\pi\)
−0.545306 + 0.838237i \(0.683587\pi\)
\(402\) −1.18797e11 −0.226877
\(403\) −1.41760e12 −2.67719
\(404\) −4.27462e11 −0.798327
\(405\) 8.97518e10 0.165766
\(406\) 3.75410e10 0.0685707
\(407\) 5.53563e11 0.999983
\(408\) 1.49968e11 0.267933
\(409\) 5.11455e11 0.903759 0.451880 0.892079i \(-0.350754\pi\)
0.451880 + 0.892079i \(0.350754\pi\)
\(410\) −9.31246e10 −0.162756
\(411\) 3.88435e10 0.0671476
\(412\) 2.87661e11 0.491862
\(413\) 8.44628e10 0.142853
\(414\) −2.25875e10 −0.0377890
\(415\) −1.78671e12 −2.95691
\(416\) 7.95695e11 1.30265
\(417\) 1.63235e11 0.264363
\(418\) −7.56992e10 −0.121282
\(419\) 3.01888e11 0.478500 0.239250 0.970958i \(-0.423098\pi\)
0.239250 + 0.970958i \(0.423098\pi\)
\(420\) 5.60240e11 0.878521
\(421\) 6.20585e11 0.962790 0.481395 0.876504i \(-0.340130\pi\)
0.481395 + 0.876504i \(0.340130\pi\)
\(422\) 9.49562e10 0.145753
\(423\) −2.27376e11 −0.345313
\(424\) 1.31565e11 0.197694
\(425\) 7.46889e11 1.11047
\(426\) −1.48034e11 −0.217781
\(427\) −9.10760e10 −0.132580
\(428\) −1.09579e12 −1.57845
\(429\) 5.91711e11 0.843435
\(430\) −4.23929e11 −0.597978
\(431\) −4.33998e10 −0.0605814 −0.0302907 0.999541i \(-0.509643\pi\)
−0.0302907 + 0.999541i \(0.509643\pi\)
\(432\) 1.10549e11 0.152714
\(433\) −9.53516e11 −1.30356 −0.651782 0.758406i \(-0.725978\pi\)
−0.651782 + 0.758406i \(0.725978\pi\)
\(434\) 3.19887e11 0.432806
\(435\) 1.51414e11 0.202752
\(436\) −6.86754e11 −0.910148
\(437\) −1.83446e11 −0.240625
\(438\) −1.05980e11 −0.137592
\(439\) −2.66042e11 −0.341869 −0.170934 0.985282i \(-0.554679\pi\)
−0.170934 + 0.985282i \(0.554679\pi\)
\(440\) −4.87118e11 −0.619580
\(441\) 5.40154e10 0.0680055
\(442\) 3.47757e11 0.433387
\(443\) −8.41868e11 −1.03855 −0.519275 0.854607i \(-0.673798\pi\)
−0.519275 + 0.854607i \(0.673798\pi\)
\(444\) 5.42049e11 0.661935
\(445\) −1.35366e12 −1.63639
\(446\) 1.39679e11 0.167157
\(447\) 5.08662e11 0.602623
\(448\) 5.62831e11 0.660126
\(449\) −1.19292e12 −1.38517 −0.692583 0.721338i \(-0.743527\pi\)
−0.692583 + 0.721338i \(0.743527\pi\)
\(450\) −9.43565e10 −0.108471
\(451\) −2.92708e11 −0.333150
\(452\) −2.30253e11 −0.259467
\(453\) 7.99175e11 0.891661
\(454\) −1.60674e11 −0.177499
\(455\) 2.69676e12 2.94979
\(456\) −1.53870e11 −0.166652
\(457\) 4.51300e11 0.483997 0.241998 0.970277i \(-0.422197\pi\)
0.241998 + 0.970277i \(0.422197\pi\)
\(458\) 3.12630e11 0.331999
\(459\) 1.65798e11 0.174350
\(460\) −5.68669e11 −0.592174
\(461\) 3.74613e11 0.386304 0.193152 0.981169i \(-0.438129\pi\)
0.193152 + 0.981169i \(0.438129\pi\)
\(462\) −1.33522e11 −0.136353
\(463\) −1.27942e11 −0.129390 −0.0646948 0.997905i \(-0.520607\pi\)
−0.0646948 + 0.997905i \(0.520607\pi\)
\(464\) 1.86500e11 0.186788
\(465\) 1.29020e12 1.27974
\(466\) 2.33948e11 0.229818
\(467\) 1.24686e12 1.21309 0.606544 0.795050i \(-0.292555\pi\)
0.606544 + 0.795050i \(0.292555\pi\)
\(468\) 5.79403e11 0.558309
\(469\) −1.70181e12 −1.62417
\(470\) 4.34057e11 0.410305
\(471\) 9.85083e11 0.922314
\(472\) −7.19112e10 −0.0666895
\(473\) −1.33249e12 −1.22402
\(474\) 2.09102e10 0.0190264
\(475\) −7.66322e11 −0.690701
\(476\) 1.03493e12 0.924014
\(477\) 1.45453e11 0.128644
\(478\) −8.06661e10 −0.0706750
\(479\) 1.89190e12 1.64206 0.821031 0.570884i \(-0.193399\pi\)
0.821031 + 0.570884i \(0.193399\pi\)
\(480\) −7.24190e11 −0.622683
\(481\) 2.60920e12 2.22257
\(482\) 8.57273e10 0.0723449
\(483\) −3.23572e11 −0.270526
\(484\) 3.84593e11 0.318565
\(485\) 2.39431e12 1.96491
\(486\) −2.09457e10 −0.0170307
\(487\) −8.53099e11 −0.687256 −0.343628 0.939106i \(-0.611656\pi\)
−0.343628 + 0.939106i \(0.611656\pi\)
\(488\) 7.75417e10 0.0618936
\(489\) −9.57252e11 −0.757071
\(490\) −1.03115e11 −0.0808050
\(491\) 3.54150e11 0.274993 0.137496 0.990502i \(-0.456094\pi\)
0.137496 + 0.990502i \(0.456094\pi\)
\(492\) −2.86619e11 −0.220527
\(493\) 2.79707e11 0.213251
\(494\) −3.56805e11 −0.269563
\(495\) −5.38537e11 −0.403174
\(496\) 1.58917e12 1.17897
\(497\) −2.12063e12 −1.55906
\(498\) 4.16971e11 0.303790
\(499\) 1.13264e12 0.817787 0.408893 0.912582i \(-0.365915\pi\)
0.408893 + 0.912582i \(0.365915\pi\)
\(500\) −4.37512e11 −0.313058
\(501\) 4.59113e11 0.325574
\(502\) 5.92099e11 0.416129
\(503\) −2.19217e12 −1.52692 −0.763462 0.645852i \(-0.776502\pi\)
−0.763462 + 0.645852i \(0.776502\pi\)
\(504\) −2.71404e11 −0.187361
\(505\) 1.87272e12 1.28133
\(506\) 1.35531e11 0.0919099
\(507\) 1.93004e12 1.29727
\(508\) −6.43531e11 −0.428729
\(509\) 8.24907e11 0.544722 0.272361 0.962195i \(-0.412196\pi\)
0.272361 + 0.962195i \(0.412196\pi\)
\(510\) −3.16506e11 −0.207165
\(511\) −1.51820e12 −0.984996
\(512\) −1.52406e12 −0.980140
\(513\) −1.70112e11 −0.108444
\(514\) 5.67501e11 0.358618
\(515\) −1.26025e12 −0.789447
\(516\) −1.30477e12 −0.810234
\(517\) 1.36432e12 0.839864
\(518\) −5.88779e11 −0.359309
\(519\) 1.43348e12 0.867237
\(520\) −2.29601e12 −1.37708
\(521\) −2.63163e12 −1.56479 −0.782395 0.622783i \(-0.786002\pi\)
−0.782395 + 0.622783i \(0.786002\pi\)
\(522\) −3.53361e10 −0.0208306
\(523\) −2.33142e12 −1.36258 −0.681292 0.732011i \(-0.738582\pi\)
−0.681292 + 0.732011i \(0.738582\pi\)
\(524\) −1.91948e12 −1.11223
\(525\) −1.35168e12 −0.776529
\(526\) −1.84662e11 −0.105182
\(527\) 2.38338e12 1.34600
\(528\) −6.63328e11 −0.371429
\(529\) −1.47271e12 −0.817650
\(530\) −2.77667e11 −0.152856
\(531\) −7.95020e10 −0.0433963
\(532\) −1.06185e12 −0.574729
\(533\) −1.37967e12 −0.740460
\(534\) 3.15907e11 0.168122
\(535\) 4.80068e12 2.53344
\(536\) 1.44891e12 0.758228
\(537\) 1.29263e12 0.670797
\(538\) 3.72025e11 0.191449
\(539\) −3.24108e11 −0.165402
\(540\) −5.27335e11 −0.266879
\(541\) 1.55823e12 0.782069 0.391035 0.920376i \(-0.372117\pi\)
0.391035 + 0.920376i \(0.372117\pi\)
\(542\) 3.17854e11 0.158209
\(543\) −7.50351e11 −0.370395
\(544\) −1.33779e12 −0.654927
\(545\) 3.00868e12 1.46080
\(546\) −6.29353e11 −0.303059
\(547\) −2.18819e12 −1.04506 −0.522530 0.852621i \(-0.675012\pi\)
−0.522530 + 0.852621i \(0.675012\pi\)
\(548\) −2.28224e11 −0.108106
\(549\) 8.57268e10 0.0402755
\(550\) 5.66166e11 0.263823
\(551\) −2.86984e11 −0.132640
\(552\) 2.75487e11 0.126292
\(553\) 2.99545e11 0.136207
\(554\) −2.95973e11 −0.133493
\(555\) −2.37472e12 −1.06242
\(556\) −9.59083e11 −0.425618
\(557\) −2.09021e12 −0.920115 −0.460058 0.887889i \(-0.652171\pi\)
−0.460058 + 0.887889i \(0.652171\pi\)
\(558\) −3.01099e11 −0.131479
\(559\) −6.28063e12 −2.72051
\(560\) −3.02316e12 −1.29902
\(561\) −9.94835e11 −0.424051
\(562\) 6.26025e11 0.264715
\(563\) −2.00077e12 −0.839287 −0.419643 0.907689i \(-0.637845\pi\)
−0.419643 + 0.907689i \(0.637845\pi\)
\(564\) 1.33594e12 0.555945
\(565\) 1.00874e12 0.416450
\(566\) −7.77107e11 −0.318278
\(567\) −3.00053e11 −0.121920
\(568\) 1.80550e12 0.727829
\(569\) 4.13455e12 1.65357 0.826786 0.562517i \(-0.190167\pi\)
0.826786 + 0.562517i \(0.190167\pi\)
\(570\) 3.24741e11 0.128855
\(571\) −4.71661e11 −0.185681 −0.0928404 0.995681i \(-0.529595\pi\)
−0.0928404 + 0.995681i \(0.529595\pi\)
\(572\) −3.47659e12 −1.35791
\(573\) −1.33813e12 −0.518566
\(574\) 3.11328e11 0.119706
\(575\) 1.37202e12 0.523425
\(576\) −5.29774e11 −0.200535
\(577\) −6.67106e11 −0.250555 −0.125278 0.992122i \(-0.539982\pi\)
−0.125278 + 0.992122i \(0.539982\pi\)
\(578\) 1.27698e11 0.0475894
\(579\) 1.08292e10 0.00400445
\(580\) −8.89632e11 −0.326426
\(581\) 5.97322e12 2.17478
\(582\) −5.58768e11 −0.201873
\(583\) −8.72759e11 −0.312886
\(584\) 1.29259e12 0.459835
\(585\) −2.53837e12 −0.896095
\(586\) −1.11342e11 −0.0390048
\(587\) 8.89904e11 0.309365 0.154683 0.987964i \(-0.450564\pi\)
0.154683 + 0.987964i \(0.450564\pi\)
\(588\) −3.17367e11 −0.109487
\(589\) −2.44540e12 −0.837203
\(590\) 1.51768e11 0.0515640
\(591\) 5.53973e11 0.186786
\(592\) −2.92500e12 −0.978765
\(593\) 3.07082e12 1.01979 0.509893 0.860238i \(-0.329685\pi\)
0.509893 + 0.860238i \(0.329685\pi\)
\(594\) 1.25680e11 0.0414217
\(595\) −4.53403e12 −1.48306
\(596\) −2.98864e12 −0.970208
\(597\) −8.63009e10 −0.0278055
\(598\) 6.38822e11 0.204279
\(599\) 4.06896e12 1.29141 0.645703 0.763589i \(-0.276564\pi\)
0.645703 + 0.763589i \(0.276564\pi\)
\(600\) 1.15082e12 0.362514
\(601\) 4.36201e12 1.36380 0.681902 0.731444i \(-0.261153\pi\)
0.681902 + 0.731444i \(0.261153\pi\)
\(602\) 1.41725e12 0.439808
\(603\) 1.60185e12 0.493395
\(604\) −4.69554e12 −1.43555
\(605\) −1.68491e12 −0.511302
\(606\) −4.37042e11 −0.131643
\(607\) 1.66672e11 0.0498326 0.0249163 0.999690i \(-0.492068\pi\)
0.0249163 + 0.999690i \(0.492068\pi\)
\(608\) 1.37260e12 0.407359
\(609\) −5.06199e11 −0.149123
\(610\) −1.63651e11 −0.0478559
\(611\) 6.43068e12 1.86669
\(612\) −9.74142e11 −0.280699
\(613\) 6.34195e12 1.81406 0.907028 0.421071i \(-0.138346\pi\)
0.907028 + 0.421071i \(0.138346\pi\)
\(614\) −1.68425e12 −0.478243
\(615\) 1.25568e12 0.353950
\(616\) 1.62850e12 0.455696
\(617\) −1.22926e12 −0.341476 −0.170738 0.985317i \(-0.554615\pi\)
−0.170738 + 0.985317i \(0.554615\pi\)
\(618\) 2.94108e11 0.0811071
\(619\) −6.37479e12 −1.74525 −0.872625 0.488390i \(-0.837584\pi\)
−0.872625 + 0.488390i \(0.837584\pi\)
\(620\) −7.58057e12 −2.06034
\(621\) 3.04567e11 0.0821809
\(622\) −1.65566e12 −0.443522
\(623\) 4.52546e12 1.20356
\(624\) −3.12657e12 −0.825539
\(625\) −2.75912e12 −0.723286
\(626\) −9.30342e11 −0.242135
\(627\) 1.02072e12 0.263756
\(628\) −5.78784e12 −1.48490
\(629\) −4.38681e12 −1.11743
\(630\) 5.72796e11 0.144866
\(631\) 6.92899e12 1.73995 0.869977 0.493092i \(-0.164133\pi\)
0.869977 + 0.493092i \(0.164133\pi\)
\(632\) −2.55031e11 −0.0635867
\(633\) −1.28038e12 −0.316973
\(634\) 7.81044e11 0.191988
\(635\) 2.81932e12 0.688117
\(636\) −8.54605e11 −0.207114
\(637\) −1.52767e12 −0.367623
\(638\) 2.12027e11 0.0506638
\(639\) 1.99608e12 0.473614
\(640\) 5.58893e12 1.31680
\(641\) −2.35358e12 −0.550641 −0.275321 0.961352i \(-0.588784\pi\)
−0.275321 + 0.961352i \(0.588784\pi\)
\(642\) −1.12035e12 −0.260283
\(643\) −4.24079e12 −0.978357 −0.489178 0.872184i \(-0.662703\pi\)
−0.489178 + 0.872184i \(0.662703\pi\)
\(644\) 1.90114e12 0.435539
\(645\) 5.71622e12 1.30044
\(646\) 5.99891e11 0.135527
\(647\) −2.88401e12 −0.647035 −0.323517 0.946222i \(-0.604865\pi\)
−0.323517 + 0.946222i \(0.604865\pi\)
\(648\) 2.55463e11 0.0569169
\(649\) 4.77035e11 0.105548
\(650\) 2.66860e12 0.586373
\(651\) −4.31333e12 −0.941235
\(652\) 5.62432e12 1.21886
\(653\) −3.51257e12 −0.755990 −0.377995 0.925808i \(-0.623386\pi\)
−0.377995 + 0.925808i \(0.623386\pi\)
\(654\) −7.02146e11 −0.150082
\(655\) 8.40928e12 1.78514
\(656\) 1.54665e12 0.326081
\(657\) 1.42903e12 0.299224
\(658\) −1.45111e12 −0.301776
\(659\) −3.31529e12 −0.684758 −0.342379 0.939562i \(-0.611233\pi\)
−0.342379 + 0.939562i \(0.611233\pi\)
\(660\) 3.16416e12 0.649100
\(661\) −2.28687e12 −0.465945 −0.232972 0.972483i \(-0.574845\pi\)
−0.232972 + 0.972483i \(0.574845\pi\)
\(662\) 1.07233e12 0.217004
\(663\) −4.68912e12 −0.942498
\(664\) −5.08557e12 −1.01527
\(665\) 4.65200e12 0.922449
\(666\) 5.54198e11 0.109152
\(667\) 5.13815e11 0.100517
\(668\) −2.69751e12 −0.524166
\(669\) −1.88342e12 −0.363520
\(670\) −3.05791e12 −0.586258
\(671\) −5.14386e11 −0.0979575
\(672\) 2.42107e12 0.457978
\(673\) −2.07786e12 −0.390435 −0.195217 0.980760i \(-0.562541\pi\)
−0.195217 + 0.980760i \(0.562541\pi\)
\(674\) −1.91191e11 −0.0356860
\(675\) 1.27229e12 0.235896
\(676\) −1.13399e13 −2.08858
\(677\) 2.27593e12 0.416400 0.208200 0.978086i \(-0.433240\pi\)
0.208200 + 0.978086i \(0.433240\pi\)
\(678\) −2.35414e11 −0.0427857
\(679\) −8.00450e12 −1.44517
\(680\) 3.86025e12 0.692350
\(681\) 2.16652e12 0.386011
\(682\) 1.80668e12 0.319781
\(683\) −9.62632e12 −1.69265 −0.846325 0.532667i \(-0.821190\pi\)
−0.846325 + 0.532667i \(0.821190\pi\)
\(684\) 9.99488e11 0.174592
\(685\) 9.99855e11 0.173512
\(686\) −1.34497e12 −0.231876
\(687\) −4.21547e12 −0.722006
\(688\) 7.04080e12 1.19805
\(689\) −4.11372e12 −0.695421
\(690\) −5.81414e11 −0.0976483
\(691\) 3.42976e12 0.572286 0.286143 0.958187i \(-0.407627\pi\)
0.286143 + 0.958187i \(0.407627\pi\)
\(692\) −8.42237e12 −1.39623
\(693\) 1.80040e12 0.296531
\(694\) 5.43341e11 0.0889108
\(695\) 4.20176e12 0.683124
\(696\) 4.30975e11 0.0696163
\(697\) 2.31961e12 0.372279
\(698\) 3.10768e12 0.495549
\(699\) −3.15454e12 −0.499791
\(700\) 7.94178e12 1.25019
\(701\) −7.51204e12 −1.17497 −0.587485 0.809235i \(-0.699882\pi\)
−0.587485 + 0.809235i \(0.699882\pi\)
\(702\) 5.92389e11 0.0920640
\(703\) 4.50095e12 0.695033
\(704\) 3.17880e12 0.487737
\(705\) −5.85279e12 −0.892301
\(706\) −2.15230e12 −0.326048
\(707\) −6.26074e12 −0.942407
\(708\) 4.67113e11 0.0698670
\(709\) 1.66785e12 0.247885 0.123942 0.992289i \(-0.460446\pi\)
0.123942 + 0.992289i \(0.460446\pi\)
\(710\) −3.81049e12 −0.562754
\(711\) −2.81951e11 −0.0413772
\(712\) −3.85295e12 −0.561867
\(713\) 4.37822e12 0.634447
\(714\) 1.05812e12 0.152368
\(715\) 1.52310e13 2.17947
\(716\) −7.59485e12 −1.07997
\(717\) 1.08769e12 0.153699
\(718\) −6.80670e11 −0.0955821
\(719\) −4.70556e11 −0.0656646 −0.0328323 0.999461i \(-0.510453\pi\)
−0.0328323 + 0.999461i \(0.510453\pi\)
\(720\) 2.84560e12 0.394619
\(721\) 4.21318e12 0.580632
\(722\) 1.32294e12 0.181185
\(723\) −1.15594e12 −0.157330
\(724\) 4.40867e12 0.596327
\(725\) 2.14640e12 0.288529
\(726\) 3.93213e11 0.0525307
\(727\) 3.60837e12 0.479078 0.239539 0.970887i \(-0.423004\pi\)
0.239539 + 0.970887i \(0.423004\pi\)
\(728\) 7.67588e12 1.01283
\(729\) 2.82430e11 0.0370370
\(730\) −2.72800e12 −0.355542
\(731\) 1.05595e13 1.36778
\(732\) −5.03686e11 −0.0648426
\(733\) 7.63962e12 0.977470 0.488735 0.872432i \(-0.337458\pi\)
0.488735 + 0.872432i \(0.337458\pi\)
\(734\) −3.57101e12 −0.454108
\(735\) 1.39039e12 0.175729
\(736\) −2.45749e12 −0.308704
\(737\) −9.61158e12 −1.20003
\(738\) −2.93043e11 −0.0363645
\(739\) −1.87258e11 −0.0230962 −0.0115481 0.999933i \(-0.503676\pi\)
−0.0115481 + 0.999933i \(0.503676\pi\)
\(740\) 1.39527e13 1.71046
\(741\) 4.81112e12 0.586225
\(742\) 9.28280e11 0.112425
\(743\) −9.93138e11 −0.119553 −0.0597764 0.998212i \(-0.519039\pi\)
−0.0597764 + 0.998212i \(0.519039\pi\)
\(744\) 3.67235e12 0.439406
\(745\) 1.30933e13 1.55720
\(746\) 3.16309e12 0.373927
\(747\) −5.62240e12 −0.660661
\(748\) 5.84514e12 0.682712
\(749\) −1.60493e13 −1.86333
\(750\) −4.47318e11 −0.0516227
\(751\) 1.41702e13 1.62553 0.812766 0.582590i \(-0.197961\pi\)
0.812766 + 0.582590i \(0.197961\pi\)
\(752\) −7.20901e12 −0.822044
\(753\) −7.98380e12 −0.904966
\(754\) 9.99380e11 0.112606
\(755\) 2.05712e13 2.30409
\(756\) 1.76295e12 0.196288
\(757\) −2.14614e12 −0.237535 −0.118767 0.992922i \(-0.537894\pi\)
−0.118767 + 0.992922i \(0.537894\pi\)
\(758\) −4.72034e12 −0.519352
\(759\) −1.82749e12 −0.199879
\(760\) −3.96069e12 −0.430636
\(761\) 5.13455e11 0.0554972 0.0277486 0.999615i \(-0.491166\pi\)
0.0277486 + 0.999615i \(0.491166\pi\)
\(762\) −6.57954e11 −0.0706965
\(763\) −1.00584e13 −1.07441
\(764\) 7.86218e12 0.834878
\(765\) 4.26773e12 0.450527
\(766\) −2.67160e12 −0.280377
\(767\) 2.24849e12 0.234591
\(768\) 2.04439e12 0.212050
\(769\) 1.32023e13 1.36138 0.680692 0.732570i \(-0.261679\pi\)
0.680692 + 0.732570i \(0.261679\pi\)
\(770\) −3.43694e12 −0.352342
\(771\) −7.65213e12 −0.779897
\(772\) −6.36268e10 −0.00644707
\(773\) −1.99216e12 −0.200686 −0.100343 0.994953i \(-0.531994\pi\)
−0.100343 + 0.994953i \(0.531994\pi\)
\(774\) −1.33401e12 −0.133606
\(775\) 1.82895e13 1.82115
\(776\) 6.81500e12 0.674665
\(777\) 7.93903e12 0.781399
\(778\) 3.30755e12 0.323667
\(779\) −2.37997e12 −0.231554
\(780\) 1.49142e13 1.44269
\(781\) −1.19771e13 −1.15192
\(782\) −1.07404e12 −0.102705
\(783\) 4.76468e11 0.0453008
\(784\) 1.71257e12 0.161892
\(785\) 2.53566e13 2.38329
\(786\) −1.96250e12 −0.183404
\(787\) 1.14986e13 1.06846 0.534229 0.845340i \(-0.320602\pi\)
0.534229 + 0.845340i \(0.320602\pi\)
\(788\) −3.25486e12 −0.300721
\(789\) 2.48997e12 0.228742
\(790\) 5.38241e11 0.0491649
\(791\) −3.37237e12 −0.306295
\(792\) −1.53285e12 −0.138432
\(793\) −2.42454e12 −0.217721
\(794\) −2.12272e12 −0.189540
\(795\) 3.74404e12 0.332421
\(796\) 5.07059e11 0.0447661
\(797\) −8.15663e12 −0.716058 −0.358029 0.933710i \(-0.616551\pi\)
−0.358029 + 0.933710i \(0.616551\pi\)
\(798\) −1.08565e12 −0.0947716
\(799\) −1.08118e13 −0.938507
\(800\) −1.02659e13 −0.886118
\(801\) −4.25966e12 −0.365619
\(802\) 3.39226e12 0.289538
\(803\) −8.57459e12 −0.727769
\(804\) −9.41165e12 −0.794353
\(805\) −8.32892e12 −0.699048
\(806\) 8.51573e12 0.710746
\(807\) −5.01635e12 −0.416348
\(808\) 5.33037e12 0.439953
\(809\) 1.29744e13 1.06493 0.532464 0.846453i \(-0.321266\pi\)
0.532464 + 0.846453i \(0.321266\pi\)
\(810\) −5.39154e11 −0.0440079
\(811\) 1.26001e13 1.02278 0.511389 0.859349i \(-0.329131\pi\)
0.511389 + 0.859349i \(0.329131\pi\)
\(812\) 2.97416e12 0.240084
\(813\) −4.28591e12 −0.344061
\(814\) −3.32535e12 −0.265477
\(815\) −2.46402e13 −1.95630
\(816\) 5.25666e12 0.415054
\(817\) −1.08343e13 −0.850748
\(818\) −3.07240e12 −0.239931
\(819\) 8.48613e12 0.659071
\(820\) −7.37774e12 −0.569851
\(821\) 1.56350e13 1.20103 0.600516 0.799613i \(-0.294962\pi\)
0.600516 + 0.799613i \(0.294962\pi\)
\(822\) −2.33339e11 −0.0178265
\(823\) −5.24256e12 −0.398331 −0.199166 0.979966i \(-0.563823\pi\)
−0.199166 + 0.979966i \(0.563823\pi\)
\(824\) −3.58708e12 −0.271062
\(825\) −7.63413e12 −0.573742
\(826\) −5.07382e11 −0.0379249
\(827\) −2.12406e13 −1.57903 −0.789517 0.613729i \(-0.789669\pi\)
−0.789517 + 0.613729i \(0.789669\pi\)
\(828\) −1.78948e12 −0.132309
\(829\) −5.92257e12 −0.435527 −0.217763 0.976002i \(-0.569876\pi\)
−0.217763 + 0.976002i \(0.569876\pi\)
\(830\) 1.07331e13 0.785006
\(831\) 3.99087e12 0.290311
\(832\) 1.49831e13 1.08405
\(833\) 2.56845e12 0.184829
\(834\) −9.80579e11 −0.0701835
\(835\) 1.18178e13 0.841296
\(836\) −5.99722e12 −0.424641
\(837\) 4.05999e12 0.285931
\(838\) −1.81349e12 −0.127033
\(839\) −8.63296e12 −0.601493 −0.300747 0.953704i \(-0.597236\pi\)
−0.300747 + 0.953704i \(0.597236\pi\)
\(840\) −6.98609e12 −0.484147
\(841\) −1.37033e13 −0.944592
\(842\) −3.72795e12 −0.255603
\(843\) −8.44126e12 −0.575682
\(844\) 7.52285e12 0.510319
\(845\) 4.96804e13 3.35220
\(846\) 1.36588e12 0.0916742
\(847\) 5.63288e12 0.376059
\(848\) 4.61162e12 0.306247
\(849\) 1.04784e13 0.692168
\(850\) −4.48668e12 −0.294809
\(851\) −8.05848e12 −0.526708
\(852\) −1.17279e13 −0.762506
\(853\) 6.69552e12 0.433026 0.216513 0.976280i \(-0.430532\pi\)
0.216513 + 0.976280i \(0.430532\pi\)
\(854\) 5.47109e11 0.0351976
\(855\) −4.37877e12 −0.280224
\(856\) 1.36643e13 0.869874
\(857\) −6.92268e12 −0.438390 −0.219195 0.975681i \(-0.570343\pi\)
−0.219195 + 0.975681i \(0.570343\pi\)
\(858\) −3.55451e12 −0.223917
\(859\) −7.38422e12 −0.462738 −0.231369 0.972866i \(-0.574321\pi\)
−0.231369 + 0.972866i \(0.574321\pi\)
\(860\) −3.35855e13 −2.09368
\(861\) −4.19792e12 −0.260327
\(862\) 2.60709e11 0.0160833
\(863\) 2.45681e13 1.50773 0.753865 0.657029i \(-0.228187\pi\)
0.753865 + 0.657029i \(0.228187\pi\)
\(864\) −2.27887e12 −0.139126
\(865\) 3.68985e13 2.24097
\(866\) 5.72793e12 0.346072
\(867\) −1.72187e12 −0.103494
\(868\) 2.53429e13 1.51536
\(869\) 1.69179e12 0.100637
\(870\) −9.09571e11 −0.0538270
\(871\) −4.53038e13 −2.66718
\(872\) 8.56370e12 0.501576
\(873\) 7.53437e12 0.439019
\(874\) 1.10199e12 0.0638815
\(875\) −6.40795e12 −0.369558
\(876\) −8.39623e12 −0.481744
\(877\) 7.18173e12 0.409950 0.204975 0.978767i \(-0.434289\pi\)
0.204975 + 0.978767i \(0.434289\pi\)
\(878\) 1.59816e12 0.0907599
\(879\) 1.50132e12 0.0848248
\(880\) −1.70744e13 −0.959786
\(881\) 1.52735e12 0.0854177 0.0427088 0.999088i \(-0.486401\pi\)
0.0427088 + 0.999088i \(0.486401\pi\)
\(882\) −3.24480e11 −0.0180542
\(883\) −8.48668e12 −0.469802 −0.234901 0.972019i \(-0.575477\pi\)
−0.234901 + 0.972019i \(0.575477\pi\)
\(884\) 2.75508e13 1.51740
\(885\) −2.04643e12 −0.112138
\(886\) 5.05724e12 0.275716
\(887\) −2.03638e13 −1.10459 −0.552297 0.833648i \(-0.686248\pi\)
−0.552297 + 0.833648i \(0.686248\pi\)
\(888\) −6.75925e12 −0.364788
\(889\) −9.42537e12 −0.506105
\(890\) 8.13163e12 0.434433
\(891\) −1.69466e12 −0.0900809
\(892\) 1.10660e13 0.585259
\(893\) 1.10931e13 0.583743
\(894\) −3.05562e12 −0.159985
\(895\) 3.32731e13 1.73337
\(896\) −1.86846e13 −0.968493
\(897\) −8.61381e12 −0.444252
\(898\) 7.16605e12 0.367736
\(899\) 6.84934e12 0.349728
\(900\) −7.47533e12 −0.379786
\(901\) 6.91633e12 0.349635
\(902\) 1.75834e12 0.0884452
\(903\) −1.91101e13 −0.956463
\(904\) 2.87122e12 0.142991
\(905\) −1.93145e13 −0.957115
\(906\) −4.80078e12 −0.236720
\(907\) −2.75665e13 −1.35254 −0.676269 0.736655i \(-0.736404\pi\)
−0.676269 + 0.736655i \(0.736404\pi\)
\(908\) −1.27293e13 −0.621469
\(909\) 5.89303e12 0.286287
\(910\) −1.61999e13 −0.783116
\(911\) −2.40644e13 −1.15755 −0.578777 0.815486i \(-0.696470\pi\)
−0.578777 + 0.815486i \(0.696470\pi\)
\(912\) −5.39343e12 −0.258160
\(913\) 3.37360e13 1.60685
\(914\) −2.71103e12 −0.128492
\(915\) 2.20666e12 0.104073
\(916\) 2.47679e13 1.16241
\(917\) −2.81134e13 −1.31296
\(918\) −9.95975e11 −0.0462867
\(919\) −2.04595e12 −0.0946185 −0.0473092 0.998880i \(-0.515065\pi\)
−0.0473092 + 0.998880i \(0.515065\pi\)
\(920\) 7.09120e12 0.326343
\(921\) 2.27103e13 1.04005
\(922\) −2.25036e12 −0.102557
\(923\) −5.64534e13 −2.56025
\(924\) −1.05782e13 −0.477408
\(925\) −3.36633e13 −1.51189
\(926\) 7.68570e11 0.0343506
\(927\) −3.96572e12 −0.176386
\(928\) −3.84453e12 −0.170168
\(929\) 1.09000e13 0.480128 0.240064 0.970757i \(-0.422832\pi\)
0.240064 + 0.970757i \(0.422832\pi\)
\(930\) −7.75047e12 −0.339746
\(931\) −2.63528e12 −0.114962
\(932\) 1.85344e13 0.804651
\(933\) 2.23248e13 0.964539
\(934\) −7.49011e12 −0.322053
\(935\) −2.56076e13 −1.09576
\(936\) −7.22505e12 −0.307680
\(937\) 2.11912e13 0.898105 0.449053 0.893505i \(-0.351762\pi\)
0.449053 + 0.893505i \(0.351762\pi\)
\(938\) 1.02230e13 0.431188
\(939\) 1.25446e13 0.526578
\(940\) 3.43879e13 1.43658
\(941\) 6.28519e11 0.0261315 0.0130658 0.999915i \(-0.495841\pi\)
0.0130658 + 0.999915i \(0.495841\pi\)
\(942\) −5.91756e12 −0.244858
\(943\) 4.26108e12 0.175476
\(944\) −2.52063e12 −0.103308
\(945\) −7.72353e12 −0.315045
\(946\) 8.00447e12 0.324954
\(947\) −1.19856e13 −0.484269 −0.242134 0.970243i \(-0.577848\pi\)
−0.242134 + 0.970243i \(0.577848\pi\)
\(948\) 1.65660e12 0.0666162
\(949\) −4.04160e13 −1.61754
\(950\) 4.60342e12 0.183368
\(951\) −1.05315e13 −0.417521
\(952\) −1.29054e13 −0.509218
\(953\) −2.35282e13 −0.923995 −0.461998 0.886881i \(-0.652867\pi\)
−0.461998 + 0.886881i \(0.652867\pi\)
\(954\) −8.73759e11 −0.0341526
\(955\) −3.44443e13 −1.33999
\(956\) −6.39072e12 −0.247451
\(957\) −2.85895e12 −0.110180
\(958\) −1.13650e13 −0.435937
\(959\) −3.34265e12 −0.127617
\(960\) −1.36367e13 −0.518189
\(961\) 3.19237e13 1.20742
\(962\) −1.56739e13 −0.590050
\(963\) 1.51067e13 0.566045
\(964\) 6.79170e12 0.253298
\(965\) 2.78750e11 0.0103477
\(966\) 1.94375e12 0.0718196
\(967\) 3.66589e13 1.34822 0.674109 0.738632i \(-0.264528\pi\)
0.674109 + 0.738632i \(0.264528\pi\)
\(968\) −4.79581e12 −0.175559
\(969\) −8.08887e12 −0.294735
\(970\) −1.43830e13 −0.521647
\(971\) 2.79106e13 1.00759 0.503793 0.863824i \(-0.331937\pi\)
0.503793 + 0.863824i \(0.331937\pi\)
\(972\) −1.65941e12 −0.0596287
\(973\) −1.40471e13 −0.502432
\(974\) 5.12470e12 0.182454
\(975\) −3.59832e13 −1.27520
\(976\) 2.71799e12 0.0958790
\(977\) 2.08276e13 0.731331 0.365665 0.930746i \(-0.380841\pi\)
0.365665 + 0.930746i \(0.380841\pi\)
\(978\) 5.75037e12 0.200988
\(979\) 2.55592e13 0.889253
\(980\) −8.16920e12 −0.282919
\(981\) 9.46766e12 0.326386
\(982\) −2.12744e12 −0.0730055
\(983\) −5.69777e11 −0.0194632 −0.00973160 0.999953i \(-0.503098\pi\)
−0.00973160 + 0.999953i \(0.503098\pi\)
\(984\) 3.57409e12 0.121531
\(985\) 1.42596e13 0.482663
\(986\) −1.68024e12 −0.0566143
\(987\) 1.95667e13 0.656281
\(988\) −2.82677e13 −0.943808
\(989\) 1.93976e13 0.644711
\(990\) 3.23508e12 0.107035
\(991\) −1.93568e13 −0.637532 −0.318766 0.947833i \(-0.603268\pi\)
−0.318766 + 0.947833i \(0.603268\pi\)
\(992\) −3.27593e13 −1.07407
\(993\) −1.44592e13 −0.471924
\(994\) 1.27390e13 0.413901
\(995\) −2.22143e12 −0.0718504
\(996\) 3.30343e13 1.06365
\(997\) −1.00007e11 −0.00320555 −0.00160277 0.999999i \(-0.500510\pi\)
−0.00160277 + 0.999999i \(0.500510\pi\)
\(998\) −6.80396e12 −0.217107
\(999\) −7.47274e12 −0.237375
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.1.10 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.10 22 1.1 even 1 trivial