Properties

Label 177.10.a.b.1.10
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
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: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.11702 q^{2} -81.0000 q^{3} -495.050 q^{4} -2185.60 q^{5} +333.479 q^{6} -4537.74 q^{7} +4146.05 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-4.11702 q^{2} -81.0000 q^{3} -495.050 q^{4} -2185.60 q^{5} +333.479 q^{6} -4537.74 q^{7} +4146.05 q^{8} +6561.00 q^{9} +8998.14 q^{10} -28540.1 q^{11} +40099.1 q^{12} -102441. q^{13} +18681.9 q^{14} +177033. q^{15} +236396. q^{16} +121059. q^{17} -27011.8 q^{18} -212496. q^{19} +1.08198e6 q^{20} +367557. q^{21} +117500. q^{22} -1.13375e6 q^{23} -335830. q^{24} +2.82370e6 q^{25} +421753. q^{26} -531441. q^{27} +2.24641e6 q^{28} +4.92713e6 q^{29} -728849. q^{30} +8.24073e6 q^{31} -3.09602e6 q^{32} +2.31174e6 q^{33} -498400. q^{34} +9.91765e6 q^{35} -3.24802e6 q^{36} +2.14954e7 q^{37} +874852. q^{38} +8.29775e6 q^{39} -9.06158e6 q^{40} +1.27066e7 q^{41} -1.51324e6 q^{42} -4.07034e7 q^{43} +1.41288e7 q^{44} -1.43397e7 q^{45} +4.66765e6 q^{46} +1.82085e7 q^{47} -1.91481e7 q^{48} -1.97626e7 q^{49} -1.16252e7 q^{50} -9.80574e6 q^{51} +5.07136e7 q^{52} -6.37339e7 q^{53} +2.18795e6 q^{54} +6.23770e7 q^{55} -1.88137e7 q^{56} +1.72122e7 q^{57} -2.02851e7 q^{58} -1.21174e7 q^{59} -8.76403e7 q^{60} +2.27505e7 q^{61} -3.39272e7 q^{62} -2.97721e7 q^{63} -1.08289e8 q^{64} +2.23895e8 q^{65} -9.51750e6 q^{66} -3.95243e7 q^{67} -5.99301e7 q^{68} +9.18334e7 q^{69} -4.08312e7 q^{70} -1.08585e7 q^{71} +2.72022e7 q^{72} +1.10383e8 q^{73} -8.84968e7 q^{74} -2.28720e8 q^{75} +1.05196e8 q^{76} +1.29507e8 q^{77} -3.41620e7 q^{78} -2.80040e7 q^{79} -5.16667e8 q^{80} +4.30467e7 q^{81} -5.23132e7 q^{82} -2.16977e8 q^{83} -1.81959e8 q^{84} -2.64585e8 q^{85} +1.67577e8 q^{86} -3.99098e8 q^{87} -1.18328e8 q^{88} +4.03240e8 q^{89} +5.90368e7 q^{90} +4.64852e8 q^{91} +5.61261e8 q^{92} -6.67499e8 q^{93} -7.49647e7 q^{94} +4.64431e8 q^{95} +2.50778e8 q^{96} +7.17322e8 q^{97} +8.13629e7 q^{98} -1.87251e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.11702 −0.181948 −0.0909741 0.995853i \(-0.528998\pi\)
−0.0909741 + 0.995853i \(0.528998\pi\)
\(3\) −81.0000 −0.577350
\(4\) −495.050 −0.966895
\(5\) −2185.60 −1.56388 −0.781942 0.623351i \(-0.785771\pi\)
−0.781942 + 0.623351i \(0.785771\pi\)
\(6\) 333.479 0.105048
\(7\) −4537.74 −0.714329 −0.357164 0.934042i \(-0.616256\pi\)
−0.357164 + 0.934042i \(0.616256\pi\)
\(8\) 4146.05 0.357873
\(9\) 6561.00 0.333333
\(10\) 8998.14 0.284546
\(11\) −28540.1 −0.587743 −0.293872 0.955845i \(-0.594944\pi\)
−0.293872 + 0.955845i \(0.594944\pi\)
\(12\) 40099.1 0.558237
\(13\) −102441. −0.994787 −0.497394 0.867525i \(-0.665709\pi\)
−0.497394 + 0.867525i \(0.665709\pi\)
\(14\) 18681.9 0.129971
\(15\) 177033. 0.902909
\(16\) 236396. 0.901780
\(17\) 121059. 0.351540 0.175770 0.984431i \(-0.443758\pi\)
0.175770 + 0.984431i \(0.443758\pi\)
\(18\) −27011.8 −0.0606494
\(19\) −212496. −0.374076 −0.187038 0.982353i \(-0.559889\pi\)
−0.187038 + 0.982353i \(0.559889\pi\)
\(20\) 1.08198e6 1.51211
\(21\) 367557. 0.412418
\(22\) 117500. 0.106939
\(23\) −1.13375e6 −0.844773 −0.422387 0.906416i \(-0.638808\pi\)
−0.422387 + 0.906416i \(0.638808\pi\)
\(24\) −335830. −0.206618
\(25\) 2.82370e6 1.44573
\(26\) 421753. 0.181000
\(27\) −531441. −0.192450
\(28\) 2.24641e6 0.690681
\(29\) 4.92713e6 1.29361 0.646805 0.762656i \(-0.276105\pi\)
0.646805 + 0.762656i \(0.276105\pi\)
\(30\) −728849. −0.164283
\(31\) 8.24073e6 1.60265 0.801324 0.598231i \(-0.204130\pi\)
0.801324 + 0.598231i \(0.204130\pi\)
\(32\) −3.09602e6 −0.521951
\(33\) 2.31174e6 0.339334
\(34\) −498400. −0.0639622
\(35\) 9.91765e6 1.11713
\(36\) −3.24802e6 −0.322298
\(37\) 2.14954e7 1.88555 0.942773 0.333436i \(-0.108208\pi\)
0.942773 + 0.333436i \(0.108208\pi\)
\(38\) 874852. 0.0680626
\(39\) 8.29775e6 0.574341
\(40\) −9.06158e6 −0.559672
\(41\) 1.27066e7 0.702265 0.351132 0.936326i \(-0.385797\pi\)
0.351132 + 0.936326i \(0.385797\pi\)
\(42\) −1.51324e6 −0.0750387
\(43\) −4.07034e7 −1.81561 −0.907806 0.419391i \(-0.862244\pi\)
−0.907806 + 0.419391i \(0.862244\pi\)
\(44\) 1.41288e7 0.568286
\(45\) −1.43397e7 −0.521295
\(46\) 4.66765e6 0.153705
\(47\) 1.82085e7 0.544294 0.272147 0.962256i \(-0.412266\pi\)
0.272147 + 0.962256i \(0.412266\pi\)
\(48\) −1.91481e7 −0.520643
\(49\) −1.97626e7 −0.489735
\(50\) −1.16252e7 −0.263049
\(51\) −9.80574e6 −0.202962
\(52\) 5.07136e7 0.961854
\(53\) −6.37339e7 −1.10950 −0.554752 0.832016i \(-0.687187\pi\)
−0.554752 + 0.832016i \(0.687187\pi\)
\(54\) 2.18795e6 0.0350160
\(55\) 6.23770e7 0.919163
\(56\) −1.88137e7 −0.255639
\(57\) 1.72122e7 0.215973
\(58\) −2.02851e7 −0.235370
\(59\) −1.21174e7 −0.130189
\(60\) −8.76403e7 −0.873018
\(61\) 2.27505e7 0.210382 0.105191 0.994452i \(-0.466455\pi\)
0.105191 + 0.994452i \(0.466455\pi\)
\(62\) −3.39272e7 −0.291599
\(63\) −2.97721e7 −0.238110
\(64\) −1.08289e8 −0.806812
\(65\) 2.23895e8 1.55573
\(66\) −9.51750e6 −0.0617412
\(67\) −3.95243e7 −0.239623 −0.119811 0.992797i \(-0.538229\pi\)
−0.119811 + 0.992797i \(0.538229\pi\)
\(68\) −5.99301e7 −0.339903
\(69\) 9.18334e7 0.487730
\(70\) −4.08312e7 −0.203259
\(71\) −1.08585e7 −0.0507114 −0.0253557 0.999678i \(-0.508072\pi\)
−0.0253557 + 0.999678i \(0.508072\pi\)
\(72\) 2.72022e7 0.119291
\(73\) 1.10383e8 0.454935 0.227467 0.973786i \(-0.426955\pi\)
0.227467 + 0.973786i \(0.426955\pi\)
\(74\) −8.84968e7 −0.343072
\(75\) −2.28720e8 −0.834695
\(76\) 1.05196e8 0.361693
\(77\) 1.29507e8 0.419842
\(78\) −3.41620e7 −0.104500
\(79\) −2.80040e7 −0.0808906 −0.0404453 0.999182i \(-0.512878\pi\)
−0.0404453 + 0.999182i \(0.512878\pi\)
\(80\) −5.16667e8 −1.41028
\(81\) 4.30467e7 0.111111
\(82\) −5.23132e7 −0.127776
\(83\) −2.16977e8 −0.501836 −0.250918 0.968008i \(-0.580732\pi\)
−0.250918 + 0.968008i \(0.580732\pi\)
\(84\) −1.81959e8 −0.398765
\(85\) −2.64585e8 −0.549769
\(86\) 1.67577e8 0.330347
\(87\) −3.99098e8 −0.746866
\(88\) −1.18328e8 −0.210338
\(89\) 4.03240e8 0.681253 0.340627 0.940199i \(-0.389361\pi\)
0.340627 + 0.940199i \(0.389361\pi\)
\(90\) 5.90368e7 0.0948487
\(91\) 4.64852e8 0.710605
\(92\) 5.61261e8 0.816807
\(93\) −6.67499e8 −0.925289
\(94\) −7.49647e7 −0.0990334
\(95\) 4.64431e8 0.585012
\(96\) 2.50778e8 0.301348
\(97\) 7.17322e8 0.822699 0.411350 0.911478i \(-0.365058\pi\)
0.411350 + 0.911478i \(0.365058\pi\)
\(98\) 8.13629e7 0.0891064
\(99\) −1.87251e8 −0.195914
\(100\) −1.39787e9 −1.39787
\(101\) 1.28611e9 1.22980 0.614898 0.788607i \(-0.289197\pi\)
0.614898 + 0.788607i \(0.289197\pi\)
\(102\) 4.03704e7 0.0369286
\(103\) −1.87942e9 −1.64534 −0.822672 0.568517i \(-0.807517\pi\)
−0.822672 + 0.568517i \(0.807517\pi\)
\(104\) −4.24726e8 −0.356008
\(105\) −8.03330e8 −0.644974
\(106\) 2.62394e8 0.201872
\(107\) −5.07856e6 −0.00374553 −0.00187277 0.999998i \(-0.500596\pi\)
−0.00187277 + 0.999998i \(0.500596\pi\)
\(108\) 2.63090e8 0.186079
\(109\) 2.03800e9 1.38288 0.691442 0.722432i \(-0.256976\pi\)
0.691442 + 0.722432i \(0.256976\pi\)
\(110\) −2.56807e8 −0.167240
\(111\) −1.74112e9 −1.08862
\(112\) −1.07270e9 −0.644168
\(113\) −2.04814e9 −1.18170 −0.590848 0.806783i \(-0.701207\pi\)
−0.590848 + 0.806783i \(0.701207\pi\)
\(114\) −7.08630e7 −0.0392959
\(115\) 2.47791e9 1.32113
\(116\) −2.43918e9 −1.25078
\(117\) −6.72118e8 −0.331596
\(118\) 4.98874e7 0.0236876
\(119\) −5.49332e8 −0.251115
\(120\) 7.33988e8 0.323127
\(121\) −1.54341e9 −0.654558
\(122\) −9.36645e7 −0.0382786
\(123\) −1.02923e9 −0.405453
\(124\) −4.07957e9 −1.54959
\(125\) −1.90273e9 −0.697078
\(126\) 1.22572e8 0.0433236
\(127\) −1.67854e9 −0.572553 −0.286276 0.958147i \(-0.592418\pi\)
−0.286276 + 0.958147i \(0.592418\pi\)
\(128\) 2.03099e9 0.668749
\(129\) 3.29698e9 1.04824
\(130\) −9.21781e8 −0.283063
\(131\) 1.04403e9 0.309736 0.154868 0.987935i \(-0.450505\pi\)
0.154868 + 0.987935i \(0.450505\pi\)
\(132\) −1.14443e9 −0.328100
\(133\) 9.64253e8 0.267214
\(134\) 1.62722e8 0.0435989
\(135\) 1.16151e9 0.300970
\(136\) 5.01914e8 0.125807
\(137\) −5.73514e9 −1.39092 −0.695458 0.718566i \(-0.744799\pi\)
−0.695458 + 0.718566i \(0.744799\pi\)
\(138\) −3.78080e8 −0.0887417
\(139\) 3.09481e9 0.703182 0.351591 0.936154i \(-0.385641\pi\)
0.351591 + 0.936154i \(0.385641\pi\)
\(140\) −4.90974e9 −1.08014
\(141\) −1.47489e9 −0.314248
\(142\) 4.47045e7 0.00922686
\(143\) 2.92368e9 0.584680
\(144\) 1.55100e9 0.300593
\(145\) −1.07687e10 −2.02306
\(146\) −4.54449e8 −0.0827746
\(147\) 1.60077e9 0.282748
\(148\) −1.06413e10 −1.82312
\(149\) 4.59376e9 0.763538 0.381769 0.924258i \(-0.375315\pi\)
0.381769 + 0.924258i \(0.375315\pi\)
\(150\) 9.41644e8 0.151871
\(151\) −1.25131e9 −0.195871 −0.0979356 0.995193i \(-0.531224\pi\)
−0.0979356 + 0.995193i \(0.531224\pi\)
\(152\) −8.81020e8 −0.133872
\(153\) 7.94265e8 0.117180
\(154\) −5.33184e8 −0.0763895
\(155\) −1.80109e10 −2.50636
\(156\) −4.10780e9 −0.555327
\(157\) −5.24043e8 −0.0688364 −0.0344182 0.999408i \(-0.510958\pi\)
−0.0344182 + 0.999408i \(0.510958\pi\)
\(158\) 1.15293e8 0.0147179
\(159\) 5.16245e9 0.640573
\(160\) 6.76665e9 0.816270
\(161\) 5.14464e9 0.603446
\(162\) −1.77224e8 −0.0202165
\(163\) 1.58599e10 1.75978 0.879888 0.475182i \(-0.157618\pi\)
0.879888 + 0.475182i \(0.157618\pi\)
\(164\) −6.29039e9 −0.679016
\(165\) −5.05254e9 −0.530679
\(166\) 8.93298e8 0.0913082
\(167\) −2.20185e9 −0.219060 −0.109530 0.993983i \(-0.534935\pi\)
−0.109530 + 0.993983i \(0.534935\pi\)
\(168\) 1.52391e9 0.147593
\(169\) −1.10273e8 −0.0103987
\(170\) 1.08930e9 0.100029
\(171\) −1.39419e9 −0.124692
\(172\) 2.01502e10 1.75551
\(173\) 1.23180e10 1.04552 0.522759 0.852481i \(-0.324903\pi\)
0.522759 + 0.852481i \(0.324903\pi\)
\(174\) 1.64309e9 0.135891
\(175\) −1.28132e10 −1.03273
\(176\) −6.74677e9 −0.530016
\(177\) 9.81506e8 0.0751646
\(178\) −1.66015e9 −0.123953
\(179\) 3.98351e9 0.290020 0.145010 0.989430i \(-0.453679\pi\)
0.145010 + 0.989430i \(0.453679\pi\)
\(180\) 7.09887e9 0.504037
\(181\) 1.22416e10 0.847781 0.423890 0.905713i \(-0.360664\pi\)
0.423890 + 0.905713i \(0.360664\pi\)
\(182\) −1.91380e9 −0.129293
\(183\) −1.84279e9 −0.121464
\(184\) −4.70056e9 −0.302322
\(185\) −4.69802e10 −2.94878
\(186\) 2.74811e9 0.168355
\(187\) −3.45502e9 −0.206616
\(188\) −9.01412e9 −0.526275
\(189\) 2.41154e9 0.137473
\(190\) −1.91207e9 −0.106442
\(191\) −1.74290e10 −0.947592 −0.473796 0.880635i \(-0.657117\pi\)
−0.473796 + 0.880635i \(0.657117\pi\)
\(192\) 8.77137e9 0.465813
\(193\) −3.72667e10 −1.93336 −0.966682 0.255982i \(-0.917601\pi\)
−0.966682 + 0.255982i \(0.917601\pi\)
\(194\) −2.95323e9 −0.149689
\(195\) −1.81355e10 −0.898202
\(196\) 9.78346e9 0.473522
\(197\) 2.23776e10 1.05856 0.529280 0.848447i \(-0.322462\pi\)
0.529280 + 0.848447i \(0.322462\pi\)
\(198\) 7.70917e8 0.0356463
\(199\) −4.17052e8 −0.0188517 −0.00942587 0.999956i \(-0.503000\pi\)
−0.00942587 + 0.999956i \(0.503000\pi\)
\(200\) 1.17072e10 0.517390
\(201\) 3.20147e9 0.138346
\(202\) −5.29495e9 −0.223759
\(203\) −2.23580e10 −0.924062
\(204\) 4.85433e9 0.196243
\(205\) −2.77714e10 −1.09826
\(206\) 7.73761e9 0.299367
\(207\) −7.43850e9 −0.281591
\(208\) −2.42168e10 −0.897079
\(209\) 6.06466e9 0.219861
\(210\) 3.30733e9 0.117352
\(211\) 4.42985e10 1.53857 0.769286 0.638904i \(-0.220612\pi\)
0.769286 + 0.638904i \(0.220612\pi\)
\(212\) 3.15515e10 1.07277
\(213\) 8.79536e8 0.0292783
\(214\) 2.09085e7 0.000681493 0
\(215\) 8.89612e10 2.83941
\(216\) −2.20338e9 −0.0688727
\(217\) −3.73942e10 −1.14482
\(218\) −8.39050e9 −0.251613
\(219\) −8.94102e9 −0.262657
\(220\) −3.08798e10 −0.888734
\(221\) −1.24014e10 −0.349708
\(222\) 7.16824e9 0.198073
\(223\) −4.23952e10 −1.14801 −0.574004 0.818852i \(-0.694611\pi\)
−0.574004 + 0.818852i \(0.694611\pi\)
\(224\) 1.40489e10 0.372844
\(225\) 1.85263e10 0.481912
\(226\) 8.43221e9 0.215008
\(227\) 6.90422e10 1.72583 0.862916 0.505347i \(-0.168636\pi\)
0.862916 + 0.505347i \(0.168636\pi\)
\(228\) −8.52091e9 −0.208823
\(229\) −3.84678e10 −0.924352 −0.462176 0.886788i \(-0.652931\pi\)
−0.462176 + 0.886788i \(0.652931\pi\)
\(230\) −1.02016e10 −0.240377
\(231\) −1.04901e10 −0.242396
\(232\) 2.04281e10 0.462948
\(233\) 4.93231e10 1.09635 0.548174 0.836364i \(-0.315323\pi\)
0.548174 + 0.836364i \(0.315323\pi\)
\(234\) 2.76712e9 0.0603333
\(235\) −3.97964e10 −0.851213
\(236\) 5.99870e9 0.125879
\(237\) 2.26832e9 0.0467022
\(238\) 2.26161e9 0.0456900
\(239\) 6.71458e10 1.33115 0.665577 0.746329i \(-0.268185\pi\)
0.665577 + 0.746329i \(0.268185\pi\)
\(240\) 4.18500e10 0.814226
\(241\) 4.26510e8 0.00814428 0.00407214 0.999992i \(-0.498704\pi\)
0.00407214 + 0.999992i \(0.498704\pi\)
\(242\) 6.35426e9 0.119096
\(243\) −3.48678e9 −0.0641500
\(244\) −1.12627e10 −0.203417
\(245\) 4.31930e10 0.765888
\(246\) 4.23737e9 0.0737714
\(247\) 2.17684e10 0.372126
\(248\) 3.41664e10 0.573544
\(249\) 1.75751e10 0.289735
\(250\) 7.83356e9 0.126832
\(251\) 2.84787e10 0.452886 0.226443 0.974024i \(-0.427290\pi\)
0.226443 + 0.974024i \(0.427290\pi\)
\(252\) 1.47387e10 0.230227
\(253\) 3.23572e10 0.496510
\(254\) 6.91059e9 0.104175
\(255\) 2.14314e10 0.317409
\(256\) 4.70821e10 0.685135
\(257\) 8.11981e9 0.116104 0.0580520 0.998314i \(-0.481511\pi\)
0.0580520 + 0.998314i \(0.481511\pi\)
\(258\) −1.35737e10 −0.190726
\(259\) −9.75403e10 −1.34690
\(260\) −1.10839e11 −1.50423
\(261\) 3.23269e10 0.431203
\(262\) −4.29829e9 −0.0563560
\(263\) 8.00335e10 1.03150 0.515752 0.856738i \(-0.327513\pi\)
0.515752 + 0.856738i \(0.327513\pi\)
\(264\) 9.58460e9 0.121438
\(265\) 1.39296e11 1.73514
\(266\) −3.96985e9 −0.0486190
\(267\) −3.26624e10 −0.393322
\(268\) 1.95665e10 0.231690
\(269\) −5.89366e10 −0.686277 −0.343139 0.939285i \(-0.611490\pi\)
−0.343139 + 0.939285i \(0.611490\pi\)
\(270\) −4.78198e9 −0.0547609
\(271\) −4.77297e10 −0.537560 −0.268780 0.963202i \(-0.586620\pi\)
−0.268780 + 0.963202i \(0.586620\pi\)
\(272\) 2.86178e10 0.317012
\(273\) −3.76530e10 −0.410268
\(274\) 2.36117e10 0.253075
\(275\) −8.05886e10 −0.849721
\(276\) −4.54621e10 −0.471584
\(277\) 1.52146e11 1.55275 0.776374 0.630273i \(-0.217057\pi\)
0.776374 + 0.630273i \(0.217057\pi\)
\(278\) −1.27414e10 −0.127943
\(279\) 5.40674e10 0.534216
\(280\) 4.11190e10 0.399790
\(281\) 1.46537e11 1.40207 0.701036 0.713126i \(-0.252721\pi\)
0.701036 + 0.713126i \(0.252721\pi\)
\(282\) 6.07214e9 0.0571769
\(283\) −8.94439e10 −0.828918 −0.414459 0.910068i \(-0.636029\pi\)
−0.414459 + 0.910068i \(0.636029\pi\)
\(284\) 5.37548e9 0.0490326
\(285\) −3.76189e10 −0.337757
\(286\) −1.20369e10 −0.106381
\(287\) −5.76590e10 −0.501648
\(288\) −2.03130e10 −0.173984
\(289\) −1.03933e11 −0.876419
\(290\) 4.43350e10 0.368092
\(291\) −5.81031e10 −0.474986
\(292\) −5.46451e10 −0.439874
\(293\) 1.36928e11 1.08540 0.542699 0.839928i \(-0.317403\pi\)
0.542699 + 0.839928i \(0.317403\pi\)
\(294\) −6.59039e9 −0.0514456
\(295\) 2.64836e10 0.203600
\(296\) 8.91208e10 0.674786
\(297\) 1.51674e10 0.113111
\(298\) −1.89126e10 −0.138924
\(299\) 1.16142e11 0.840370
\(300\) 1.13228e11 0.807063
\(301\) 1.84701e11 1.29694
\(302\) 5.15169e9 0.0356384
\(303\) −1.04175e11 −0.710023
\(304\) −5.02334e10 −0.337335
\(305\) −4.97235e10 −0.329012
\(306\) −3.27001e9 −0.0213207
\(307\) −1.57622e11 −1.01273 −0.506364 0.862320i \(-0.669011\pi\)
−0.506364 + 0.862320i \(0.669011\pi\)
\(308\) −6.41126e10 −0.405943
\(309\) 1.52233e11 0.949939
\(310\) 7.41512e10 0.456027
\(311\) −2.48195e11 −1.50443 −0.752214 0.658919i \(-0.771014\pi\)
−0.752214 + 0.658919i \(0.771014\pi\)
\(312\) 3.44028e10 0.205541
\(313\) 3.42026e10 0.201423 0.100712 0.994916i \(-0.467888\pi\)
0.100712 + 0.994916i \(0.467888\pi\)
\(314\) 2.15749e9 0.0125247
\(315\) 6.50697e10 0.372376
\(316\) 1.38634e10 0.0782127
\(317\) −8.90724e10 −0.495423 −0.247712 0.968834i \(-0.579679\pi\)
−0.247712 + 0.968834i \(0.579679\pi\)
\(318\) −2.12539e10 −0.116551
\(319\) −1.40621e11 −0.760310
\(320\) 2.36675e11 1.26176
\(321\) 4.11363e8 0.00216248
\(322\) −2.11806e10 −0.109796
\(323\) −2.57245e10 −0.131503
\(324\) −2.13103e10 −0.107433
\(325\) −2.89264e11 −1.43820
\(326\) −6.52957e10 −0.320188
\(327\) −1.65078e11 −0.798409
\(328\) 5.26820e10 0.251322
\(329\) −8.26253e10 −0.388805
\(330\) 2.08014e10 0.0965561
\(331\) 2.22269e11 1.01778 0.508889 0.860832i \(-0.330056\pi\)
0.508889 + 0.860832i \(0.330056\pi\)
\(332\) 1.07414e11 0.485223
\(333\) 1.41031e11 0.628515
\(334\) 9.06507e9 0.0398577
\(335\) 8.63842e10 0.374742
\(336\) 8.68890e10 0.371910
\(337\) 5.95001e10 0.251295 0.125647 0.992075i \(-0.459899\pi\)
0.125647 + 0.992075i \(0.459899\pi\)
\(338\) 4.53998e8 0.00189203
\(339\) 1.65899e11 0.682252
\(340\) 1.30983e11 0.531568
\(341\) −2.35191e11 −0.941945
\(342\) 5.73990e9 0.0226875
\(343\) 2.72791e11 1.06416
\(344\) −1.68758e11 −0.649759
\(345\) −2.00711e11 −0.762754
\(346\) −5.07133e10 −0.190230
\(347\) 7.30117e10 0.270340 0.135170 0.990822i \(-0.456842\pi\)
0.135170 + 0.990822i \(0.456842\pi\)
\(348\) 1.97573e11 0.722141
\(349\) 2.73470e11 0.986722 0.493361 0.869825i \(-0.335768\pi\)
0.493361 + 0.869825i \(0.335768\pi\)
\(350\) 5.27522e10 0.187903
\(351\) 5.44415e10 0.191447
\(352\) 8.83607e10 0.306773
\(353\) 3.47728e11 1.19194 0.595969 0.803008i \(-0.296768\pi\)
0.595969 + 0.803008i \(0.296768\pi\)
\(354\) −4.04088e9 −0.0136761
\(355\) 2.37322e10 0.0793068
\(356\) −1.99624e11 −0.658700
\(357\) 4.44959e10 0.144982
\(358\) −1.64002e10 −0.0527686
\(359\) 1.13271e11 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(360\) −5.94530e10 −0.186557
\(361\) −2.77533e11 −0.860067
\(362\) −5.03988e10 −0.154252
\(363\) 1.25016e11 0.377909
\(364\) −2.30125e11 −0.687080
\(365\) −2.41252e11 −0.711465
\(366\) 7.58682e9 0.0221001
\(367\) −6.24382e11 −1.79661 −0.898303 0.439376i \(-0.855200\pi\)
−0.898303 + 0.439376i \(0.855200\pi\)
\(368\) −2.68013e11 −0.761800
\(369\) 8.33678e10 0.234088
\(370\) 1.93418e11 0.536525
\(371\) 2.89208e11 0.792551
\(372\) 3.30445e11 0.894657
\(373\) −4.41064e11 −1.17981 −0.589905 0.807473i \(-0.700835\pi\)
−0.589905 + 0.807473i \(0.700835\pi\)
\(374\) 1.42244e10 0.0375934
\(375\) 1.54121e11 0.402458
\(376\) 7.54932e10 0.194788
\(377\) −5.04742e11 −1.28687
\(378\) −9.92835e9 −0.0250129
\(379\) −4.38615e11 −1.09196 −0.545981 0.837798i \(-0.683843\pi\)
−0.545981 + 0.837798i \(0.683843\pi\)
\(380\) −2.29917e11 −0.565645
\(381\) 1.35962e11 0.330564
\(382\) 7.17554e10 0.172413
\(383\) 6.07210e11 1.44193 0.720965 0.692971i \(-0.243699\pi\)
0.720965 + 0.692971i \(0.243699\pi\)
\(384\) −1.64510e11 −0.386102
\(385\) −2.83050e11 −0.656584
\(386\) 1.53428e11 0.351772
\(387\) −2.67055e11 −0.605204
\(388\) −3.55110e11 −0.795464
\(389\) −8.77368e10 −0.194271 −0.0971356 0.995271i \(-0.530968\pi\)
−0.0971356 + 0.995271i \(0.530968\pi\)
\(390\) 7.46643e10 0.163426
\(391\) −1.37250e11 −0.296972
\(392\) −8.19365e10 −0.175263
\(393\) −8.45664e10 −0.178826
\(394\) −9.21291e10 −0.192603
\(395\) 6.12054e10 0.126504
\(396\) 9.26988e10 0.189429
\(397\) −9.23550e11 −1.86596 −0.932982 0.359923i \(-0.882803\pi\)
−0.932982 + 0.359923i \(0.882803\pi\)
\(398\) 1.71701e9 0.00343004
\(399\) −7.81045e10 −0.154276
\(400\) 6.67512e11 1.30374
\(401\) −6.29706e11 −1.21615 −0.608076 0.793879i \(-0.708059\pi\)
−0.608076 + 0.793879i \(0.708059\pi\)
\(402\) −1.31805e10 −0.0251719
\(403\) −8.44191e11 −1.59429
\(404\) −6.36690e11 −1.18908
\(405\) −9.40827e10 −0.173765
\(406\) 9.20484e10 0.168132
\(407\) −6.13479e11 −1.10822
\(408\) −4.06551e10 −0.0726346
\(409\) −2.55790e11 −0.451990 −0.225995 0.974129i \(-0.572563\pi\)
−0.225995 + 0.974129i \(0.572563\pi\)
\(410\) 1.14335e11 0.199827
\(411\) 4.64546e11 0.803046
\(412\) 9.30407e11 1.59087
\(413\) 5.49854e10 0.0929977
\(414\) 3.06245e10 0.0512350
\(415\) 4.74223e11 0.784814
\(416\) 3.17161e11 0.519230
\(417\) −2.50680e11 −0.405982
\(418\) −2.49683e10 −0.0400033
\(419\) 3.00606e11 0.476468 0.238234 0.971208i \(-0.423431\pi\)
0.238234 + 0.971208i \(0.423431\pi\)
\(420\) 3.97689e11 0.623622
\(421\) −5.34648e11 −0.829465 −0.414733 0.909943i \(-0.636125\pi\)
−0.414733 + 0.909943i \(0.636125\pi\)
\(422\) −1.82378e11 −0.279941
\(423\) 1.19466e11 0.181431
\(424\) −2.64244e11 −0.397062
\(425\) 3.41833e11 0.508234
\(426\) −3.62107e9 −0.00532713
\(427\) −1.03236e11 −0.150282
\(428\) 2.51414e9 0.00362153
\(429\) −2.36818e11 −0.337565
\(430\) −3.66255e11 −0.516625
\(431\) 1.04001e12 1.45174 0.725872 0.687830i \(-0.241436\pi\)
0.725872 + 0.687830i \(0.241436\pi\)
\(432\) −1.25631e11 −0.173548
\(433\) −6.20670e11 −0.848526 −0.424263 0.905539i \(-0.639467\pi\)
−0.424263 + 0.905539i \(0.639467\pi\)
\(434\) 1.53953e11 0.208297
\(435\) 8.72266e11 1.16801
\(436\) −1.00891e12 −1.33710
\(437\) 2.40917e11 0.316010
\(438\) 3.68104e10 0.0477899
\(439\) −1.54852e10 −0.0198987 −0.00994937 0.999951i \(-0.503167\pi\)
−0.00994937 + 0.999951i \(0.503167\pi\)
\(440\) 2.58618e11 0.328944
\(441\) −1.29662e11 −0.163245
\(442\) 5.10568e10 0.0636288
\(443\) 1.29678e12 1.59974 0.799870 0.600174i \(-0.204902\pi\)
0.799870 + 0.600174i \(0.204902\pi\)
\(444\) 8.61944e11 1.05258
\(445\) −8.81319e11 −1.06540
\(446\) 1.74542e11 0.208878
\(447\) −3.72095e11 −0.440829
\(448\) 4.91385e11 0.576329
\(449\) 1.20779e12 1.40244 0.701220 0.712945i \(-0.252639\pi\)
0.701220 + 0.712945i \(0.252639\pi\)
\(450\) −7.62731e10 −0.0876830
\(451\) −3.62646e11 −0.412751
\(452\) 1.01393e12 1.14258
\(453\) 1.01357e11 0.113086
\(454\) −2.84248e11 −0.314012
\(455\) −1.01598e12 −1.11130
\(456\) 7.13626e10 0.0772910
\(457\) −4.64846e11 −0.498524 −0.249262 0.968436i \(-0.580188\pi\)
−0.249262 + 0.968436i \(0.580188\pi\)
\(458\) 1.58373e11 0.168184
\(459\) −6.43355e10 −0.0676540
\(460\) −1.22669e12 −1.27739
\(461\) −6.03462e11 −0.622294 −0.311147 0.950362i \(-0.600713\pi\)
−0.311147 + 0.950362i \(0.600713\pi\)
\(462\) 4.31879e10 0.0441035
\(463\) −1.84771e12 −1.86861 −0.934306 0.356473i \(-0.883979\pi\)
−0.934306 + 0.356473i \(0.883979\pi\)
\(464\) 1.16476e12 1.16655
\(465\) 1.45888e12 1.44704
\(466\) −2.03064e11 −0.199479
\(467\) −1.07799e12 −1.04879 −0.524394 0.851475i \(-0.675708\pi\)
−0.524394 + 0.851475i \(0.675708\pi\)
\(468\) 3.32732e11 0.320618
\(469\) 1.79351e11 0.171169
\(470\) 1.63843e11 0.154877
\(471\) 4.24475e10 0.0397427
\(472\) −5.02391e10 −0.0465911
\(473\) 1.16168e12 1.06711
\(474\) −9.33874e9 −0.00849739
\(475\) −6.00026e11 −0.540815
\(476\) 2.71947e11 0.242802
\(477\) −4.18158e11 −0.369835
\(478\) −2.76441e11 −0.242201
\(479\) −2.02790e12 −1.76010 −0.880050 0.474881i \(-0.842491\pi\)
−0.880050 + 0.474881i \(0.842491\pi\)
\(480\) −5.48099e11 −0.471274
\(481\) −2.20201e12 −1.87572
\(482\) −1.75595e9 −0.00148184
\(483\) −4.16716e11 −0.348400
\(484\) 7.64067e11 0.632888
\(485\) −1.56777e12 −1.28661
\(486\) 1.43552e10 0.0116720
\(487\) 1.07277e12 0.864226 0.432113 0.901820i \(-0.357768\pi\)
0.432113 + 0.901820i \(0.357768\pi\)
\(488\) 9.43248e10 0.0752899
\(489\) −1.28465e12 −1.01601
\(490\) −1.77826e11 −0.139352
\(491\) 3.65166e11 0.283546 0.141773 0.989899i \(-0.454720\pi\)
0.141773 + 0.989899i \(0.454720\pi\)
\(492\) 5.09521e11 0.392030
\(493\) 5.96471e11 0.454756
\(494\) −8.96210e10 −0.0677078
\(495\) 4.09256e11 0.306388
\(496\) 1.94808e12 1.44524
\(497\) 4.92728e10 0.0362246
\(498\) −7.23571e10 −0.0527168
\(499\) 3.12250e11 0.225450 0.112725 0.993626i \(-0.464042\pi\)
0.112725 + 0.993626i \(0.464042\pi\)
\(500\) 9.41945e11 0.674001
\(501\) 1.78350e11 0.126475
\(502\) −1.17247e11 −0.0824018
\(503\) −8.92839e11 −0.621895 −0.310948 0.950427i \(-0.600646\pi\)
−0.310948 + 0.950427i \(0.600646\pi\)
\(504\) −1.23436e11 −0.0852130
\(505\) −2.81092e12 −1.92326
\(506\) −1.33215e11 −0.0903392
\(507\) 8.93214e9 0.00600371
\(508\) 8.30963e11 0.553598
\(509\) 3.33406e11 0.220162 0.110081 0.993923i \(-0.464889\pi\)
0.110081 + 0.993923i \(0.464889\pi\)
\(510\) −8.82334e10 −0.0577520
\(511\) −5.00889e11 −0.324973
\(512\) −1.23370e12 −0.793408
\(513\) 1.12929e11 0.0719911
\(514\) −3.34294e10 −0.0211249
\(515\) 4.10765e12 2.57313
\(516\) −1.63217e12 −1.01354
\(517\) −5.19671e11 −0.319905
\(518\) 4.01575e11 0.245066
\(519\) −9.97755e11 −0.603630
\(520\) 9.28280e11 0.556755
\(521\) 5.42475e10 0.0322559 0.0161280 0.999870i \(-0.494866\pi\)
0.0161280 + 0.999870i \(0.494866\pi\)
\(522\) −1.33091e11 −0.0784567
\(523\) −1.01037e12 −0.590502 −0.295251 0.955420i \(-0.595403\pi\)
−0.295251 + 0.955420i \(0.595403\pi\)
\(524\) −5.16847e11 −0.299482
\(525\) 1.03787e12 0.596247
\(526\) −3.29499e11 −0.187680
\(527\) 9.97610e11 0.563395
\(528\) 5.46488e11 0.306005
\(529\) −5.15774e11 −0.286358
\(530\) −5.73486e11 −0.315705
\(531\) −7.95020e10 −0.0433963
\(532\) −4.77353e11 −0.258367
\(533\) −1.30168e12 −0.698604
\(534\) 1.34472e11 0.0715642
\(535\) 1.10997e10 0.00585758
\(536\) −1.63870e11 −0.0857545
\(537\) −3.22664e11 −0.167443
\(538\) 2.42643e11 0.124867
\(539\) 5.64025e11 0.287838
\(540\) −5.75008e11 −0.291006
\(541\) 5.44947e11 0.273506 0.136753 0.990605i \(-0.456333\pi\)
0.136753 + 0.990605i \(0.456333\pi\)
\(542\) 1.96504e11 0.0978081
\(543\) −9.91567e11 −0.489467
\(544\) −3.74800e11 −0.183487
\(545\) −4.45425e12 −2.16267
\(546\) 1.55018e11 0.0746475
\(547\) 2.16389e12 1.03346 0.516728 0.856150i \(-0.327150\pi\)
0.516728 + 0.856150i \(0.327150\pi\)
\(548\) 2.83918e12 1.34487
\(549\) 1.49266e11 0.0701272
\(550\) 3.31785e11 0.154605
\(551\) −1.04700e12 −0.483909
\(552\) 3.80745e11 0.174546
\(553\) 1.27075e11 0.0577825
\(554\) −6.26387e11 −0.282520
\(555\) 3.80539e12 1.70248
\(556\) −1.53209e12 −0.679903
\(557\) −1.07781e12 −0.474455 −0.237227 0.971454i \(-0.576239\pi\)
−0.237227 + 0.971454i \(0.576239\pi\)
\(558\) −2.22597e11 −0.0971996
\(559\) 4.16971e12 1.80615
\(560\) 2.34450e12 1.00740
\(561\) 2.79856e11 0.119290
\(562\) −6.03298e11 −0.255105
\(563\) 2.44892e12 1.02727 0.513637 0.858008i \(-0.328298\pi\)
0.513637 + 0.858008i \(0.328298\pi\)
\(564\) 7.30143e11 0.303845
\(565\) 4.47639e12 1.84804
\(566\) 3.68242e11 0.150820
\(567\) −1.95335e11 −0.0793698
\(568\) −4.50197e10 −0.0181483
\(569\) 1.30612e12 0.522368 0.261184 0.965289i \(-0.415887\pi\)
0.261184 + 0.965289i \(0.415887\pi\)
\(570\) 1.54878e11 0.0614543
\(571\) −3.54701e12 −1.39637 −0.698185 0.715918i \(-0.746009\pi\)
−0.698185 + 0.715918i \(0.746009\pi\)
\(572\) −1.44737e12 −0.565324
\(573\) 1.41175e12 0.547092
\(574\) 2.37383e11 0.0912739
\(575\) −3.20136e12 −1.22132
\(576\) −7.10481e11 −0.268937
\(577\) −3.18837e11 −0.119751 −0.0598753 0.998206i \(-0.519070\pi\)
−0.0598753 + 0.998206i \(0.519070\pi\)
\(578\) 4.27893e11 0.159463
\(579\) 3.01861e12 1.11623
\(580\) 5.33105e12 1.95608
\(581\) 9.84583e11 0.358476
\(582\) 2.39211e11 0.0864228
\(583\) 1.81897e12 0.652104
\(584\) 4.57653e11 0.162809
\(585\) 1.46898e12 0.518577
\(586\) −5.63736e11 −0.197486
\(587\) −4.42811e11 −0.153938 −0.0769692 0.997033i \(-0.524524\pi\)
−0.0769692 + 0.997033i \(0.524524\pi\)
\(588\) −7.92460e11 −0.273388
\(589\) −1.75112e12 −0.599513
\(590\) −1.09034e11 −0.0370447
\(591\) −1.81259e12 −0.611160
\(592\) 5.08143e12 1.70035
\(593\) −3.09210e12 −1.02685 −0.513426 0.858134i \(-0.671624\pi\)
−0.513426 + 0.858134i \(0.671624\pi\)
\(594\) −6.24443e10 −0.0205804
\(595\) 1.20062e12 0.392715
\(596\) −2.27414e12 −0.738261
\(597\) 3.37812e10 0.0108841
\(598\) −4.78160e11 −0.152904
\(599\) 3.17880e12 1.00889 0.504444 0.863445i \(-0.331698\pi\)
0.504444 + 0.863445i \(0.331698\pi\)
\(600\) −9.48283e11 −0.298715
\(601\) 1.03443e12 0.323420 0.161710 0.986838i \(-0.448299\pi\)
0.161710 + 0.986838i \(0.448299\pi\)
\(602\) −7.60419e11 −0.235977
\(603\) −2.59319e11 −0.0798742
\(604\) 6.19464e11 0.189387
\(605\) 3.37328e12 1.02365
\(606\) 4.28891e11 0.129187
\(607\) −1.05095e10 −0.00314220 −0.00157110 0.999999i \(-0.500500\pi\)
−0.00157110 + 0.999999i \(0.500500\pi\)
\(608\) 6.57894e11 0.195249
\(609\) 1.81100e12 0.533508
\(610\) 2.04713e11 0.0598632
\(611\) −1.86530e12 −0.541457
\(612\) −3.93201e11 −0.113301
\(613\) 6.62484e12 1.89498 0.947488 0.319792i \(-0.103613\pi\)
0.947488 + 0.319792i \(0.103613\pi\)
\(614\) 6.48931e11 0.184264
\(615\) 2.24948e12 0.634081
\(616\) 5.36943e11 0.150250
\(617\) 6.32056e12 1.75579 0.877895 0.478854i \(-0.158948\pi\)
0.877895 + 0.478854i \(0.158948\pi\)
\(618\) −6.26747e11 −0.172840
\(619\) 9.68111e10 0.0265044 0.0132522 0.999912i \(-0.495782\pi\)
0.0132522 + 0.999912i \(0.495782\pi\)
\(620\) 8.91630e12 2.42338
\(621\) 6.02519e11 0.162577
\(622\) 1.02182e12 0.273728
\(623\) −1.82980e12 −0.486639
\(624\) 1.96156e12 0.517929
\(625\) −1.35645e12 −0.355586
\(626\) −1.40813e11 −0.0366486
\(627\) −4.91237e11 −0.126937
\(628\) 2.59427e11 0.0665576
\(629\) 2.60220e12 0.662846
\(630\) −2.67893e11 −0.0677531
\(631\) 1.23445e12 0.309986 0.154993 0.987916i \(-0.450464\pi\)
0.154993 + 0.987916i \(0.450464\pi\)
\(632\) −1.16106e11 −0.0289486
\(633\) −3.58818e12 −0.888295
\(634\) 3.66713e11 0.0901415
\(635\) 3.66861e12 0.895407
\(636\) −2.55567e12 −0.619366
\(637\) 2.02450e12 0.487182
\(638\) 5.78938e11 0.138337
\(639\) −7.12424e10 −0.0169038
\(640\) −4.43892e12 −1.04585
\(641\) −6.56416e11 −0.153574 −0.0767870 0.997048i \(-0.524466\pi\)
−0.0767870 + 0.997048i \(0.524466\pi\)
\(642\) −1.69359e9 −0.000393460 0
\(643\) 1.17626e12 0.271366 0.135683 0.990752i \(-0.456677\pi\)
0.135683 + 0.990752i \(0.456677\pi\)
\(644\) −2.54685e12 −0.583469
\(645\) −7.20586e12 −1.63933
\(646\) 1.05908e11 0.0239267
\(647\) −4.97075e12 −1.11520 −0.557599 0.830110i \(-0.688277\pi\)
−0.557599 + 0.830110i \(0.688277\pi\)
\(648\) 1.78474e11 0.0397637
\(649\) 3.45830e11 0.0765177
\(650\) 1.19090e12 0.261678
\(651\) 3.02893e12 0.660960
\(652\) −7.85146e12 −1.70152
\(653\) −7.55691e12 −1.62643 −0.813214 0.581964i \(-0.802284\pi\)
−0.813214 + 0.581964i \(0.802284\pi\)
\(654\) 6.79631e11 0.145269
\(655\) −2.28183e12 −0.484392
\(656\) 3.00379e12 0.633289
\(657\) 7.24223e11 0.151645
\(658\) 3.40170e11 0.0707424
\(659\) 1.16657e12 0.240949 0.120475 0.992716i \(-0.461558\pi\)
0.120475 + 0.992716i \(0.461558\pi\)
\(660\) 2.50126e12 0.513111
\(661\) −4.45159e12 −0.907003 −0.453502 0.891255i \(-0.649825\pi\)
−0.453502 + 0.891255i \(0.649825\pi\)
\(662\) −9.15086e11 −0.185183
\(663\) 1.00451e12 0.201904
\(664\) −8.99596e11 −0.179594
\(665\) −2.10747e12 −0.417891
\(666\) −5.80628e11 −0.114357
\(667\) −5.58611e12 −1.09281
\(668\) 1.09003e12 0.211808
\(669\) 3.43401e12 0.662803
\(670\) −3.55645e11 −0.0681837
\(671\) −6.49302e11 −0.123650
\(672\) −1.13796e12 −0.215262
\(673\) −8.24006e11 −0.154833 −0.0774163 0.996999i \(-0.524667\pi\)
−0.0774163 + 0.996999i \(0.524667\pi\)
\(674\) −2.44963e11 −0.0457226
\(675\) −1.50063e12 −0.278232
\(676\) 5.45908e10 0.0100545
\(677\) −8.90116e12 −1.62854 −0.814268 0.580489i \(-0.802862\pi\)
−0.814268 + 0.580489i \(0.802862\pi\)
\(678\) −6.83009e11 −0.124135
\(679\) −3.25502e12 −0.587678
\(680\) −1.09698e12 −0.196747
\(681\) −5.59242e12 −0.996409
\(682\) 9.68285e11 0.171385
\(683\) 1.83731e12 0.323065 0.161533 0.986867i \(-0.448356\pi\)
0.161533 + 0.986867i \(0.448356\pi\)
\(684\) 6.90193e11 0.120564
\(685\) 1.25347e13 2.17523
\(686\) −1.12309e12 −0.193622
\(687\) 3.11589e12 0.533675
\(688\) −9.62214e12 −1.63728
\(689\) 6.52899e12 1.10372
\(690\) 8.26329e11 0.138782
\(691\) −1.19065e12 −0.198670 −0.0993351 0.995054i \(-0.531672\pi\)
−0.0993351 + 0.995054i \(0.531672\pi\)
\(692\) −6.09801e12 −1.01091
\(693\) 8.49697e11 0.139947
\(694\) −3.00591e11 −0.0491878
\(695\) −6.76401e12 −1.09970
\(696\) −1.65468e12 −0.267283
\(697\) 1.53824e12 0.246874
\(698\) −1.12588e12 −0.179532
\(699\) −3.99517e12 −0.632977
\(700\) 6.34318e12 0.998541
\(701\) 1.69029e12 0.264381 0.132191 0.991224i \(-0.457799\pi\)
0.132191 + 0.991224i \(0.457799\pi\)
\(702\) −2.24137e11 −0.0348334
\(703\) −4.56769e12 −0.705338
\(704\) 3.09056e12 0.474199
\(705\) 3.22351e12 0.491448
\(706\) −1.43160e12 −0.216871
\(707\) −5.83604e12 −0.878478
\(708\) −4.85895e11 −0.0726763
\(709\) 8.69883e12 1.29286 0.646432 0.762971i \(-0.276260\pi\)
0.646432 + 0.762971i \(0.276260\pi\)
\(710\) −9.77060e10 −0.0144297
\(711\) −1.83734e11 −0.0269635
\(712\) 1.67185e12 0.243802
\(713\) −9.34289e12 −1.35387
\(714\) −1.83190e11 −0.0263791
\(715\) −6.38998e12 −0.914371
\(716\) −1.97204e12 −0.280418
\(717\) −5.43881e12 −0.768543
\(718\) −4.66337e11 −0.0654847
\(719\) −2.71206e12 −0.378460 −0.189230 0.981933i \(-0.560599\pi\)
−0.189230 + 0.981933i \(0.560599\pi\)
\(720\) −3.38985e12 −0.470093
\(721\) 8.52831e12 1.17532
\(722\) 1.14261e12 0.156488
\(723\) −3.45473e10 −0.00470210
\(724\) −6.06019e12 −0.819715
\(725\) 1.39127e13 1.87022
\(726\) −5.14695e11 −0.0687599
\(727\) 1.96997e11 0.0261550 0.0130775 0.999914i \(-0.495837\pi\)
0.0130775 + 0.999914i \(0.495837\pi\)
\(728\) 1.92730e12 0.254306
\(729\) 2.82430e11 0.0370370
\(730\) 9.93241e11 0.129450
\(731\) −4.92750e12 −0.638261
\(732\) 9.12276e11 0.117443
\(733\) 4.11357e12 0.526321 0.263161 0.964752i \(-0.415235\pi\)
0.263161 + 0.964752i \(0.415235\pi\)
\(734\) 2.57059e12 0.326889
\(735\) −3.49863e12 −0.442186
\(736\) 3.51010e12 0.440930
\(737\) 1.12803e12 0.140837
\(738\) −3.43227e11 −0.0425920
\(739\) −1.45772e13 −1.79794 −0.898968 0.438015i \(-0.855682\pi\)
−0.898968 + 0.438015i \(0.855682\pi\)
\(740\) 2.32575e13 2.85116
\(741\) −1.76324e12 −0.214847
\(742\) −1.19067e12 −0.144203
\(743\) −1.04103e13 −1.25318 −0.626591 0.779349i \(-0.715550\pi\)
−0.626591 + 0.779349i \(0.715550\pi\)
\(744\) −2.76748e12 −0.331136
\(745\) −1.00401e13 −1.19408
\(746\) 1.81587e12 0.214664
\(747\) −1.42358e12 −0.167279
\(748\) 1.71041e12 0.199776
\(749\) 2.30451e10 0.00267554
\(750\) −6.34518e11 −0.0732265
\(751\) −9.98578e12 −1.14552 −0.572760 0.819723i \(-0.694127\pi\)
−0.572760 + 0.819723i \(0.694127\pi\)
\(752\) 4.30442e12 0.490834
\(753\) −2.30678e12 −0.261474
\(754\) 2.07803e12 0.234143
\(755\) 2.73487e12 0.306320
\(756\) −1.19383e12 −0.132922
\(757\) −5.63871e12 −0.624091 −0.312046 0.950067i \(-0.601014\pi\)
−0.312046 + 0.950067i \(0.601014\pi\)
\(758\) 1.80579e12 0.198681
\(759\) −2.62093e12 −0.286660
\(760\) 1.92555e12 0.209360
\(761\) −1.70348e13 −1.84122 −0.920611 0.390481i \(-0.872309\pi\)
−0.920611 + 0.390481i \(0.872309\pi\)
\(762\) −5.59758e11 −0.0601455
\(763\) −9.24793e12 −0.987834
\(764\) 8.62821e12 0.916222
\(765\) −1.73594e12 −0.183256
\(766\) −2.49989e12 −0.262357
\(767\) 1.24132e12 0.129510
\(768\) −3.81365e12 −0.395563
\(769\) 3.87246e12 0.399317 0.199659 0.979866i \(-0.436017\pi\)
0.199659 + 0.979866i \(0.436017\pi\)
\(770\) 1.16532e12 0.119464
\(771\) −6.57705e11 −0.0670326
\(772\) 1.84489e13 1.86936
\(773\) −4.36357e12 −0.439576 −0.219788 0.975548i \(-0.570537\pi\)
−0.219788 + 0.975548i \(0.570537\pi\)
\(774\) 1.09947e12 0.110116
\(775\) 2.32693e13 2.31700
\(776\) 2.97405e12 0.294422
\(777\) 7.90076e12 0.777633
\(778\) 3.61214e11 0.0353473
\(779\) −2.70010e12 −0.262701
\(780\) 8.97799e12 0.868467
\(781\) 3.09901e11 0.0298053
\(782\) 5.65059e11 0.0540336
\(783\) −2.61848e12 −0.248955
\(784\) −4.67180e12 −0.441633
\(785\) 1.14535e12 0.107652
\(786\) 3.48161e11 0.0325371
\(787\) 1.26301e13 1.17360 0.586800 0.809732i \(-0.300388\pi\)
0.586800 + 0.809732i \(0.300388\pi\)
\(788\) −1.10780e13 −1.02352
\(789\) −6.48271e12 −0.595539
\(790\) −2.51984e11 −0.0230171
\(791\) 9.29390e12 0.844119
\(792\) −7.76353e11 −0.0701125
\(793\) −2.33060e12 −0.209285
\(794\) 3.80227e12 0.339509
\(795\) −1.12830e13 −1.00178
\(796\) 2.06462e11 0.0182276
\(797\) 1.04796e13 0.919988 0.459994 0.887922i \(-0.347852\pi\)
0.459994 + 0.887922i \(0.347852\pi\)
\(798\) 3.21558e11 0.0280702
\(799\) 2.20429e12 0.191341
\(800\) −8.74224e12 −0.754602
\(801\) 2.64566e12 0.227084
\(802\) 2.59251e12 0.221277
\(803\) −3.15034e12 −0.267385
\(804\) −1.58489e12 −0.133766
\(805\) −1.12441e13 −0.943720
\(806\) 3.47555e12 0.290079
\(807\) 4.77386e12 0.396222
\(808\) 5.33228e12 0.440111
\(809\) −5.80061e12 −0.476108 −0.238054 0.971252i \(-0.576509\pi\)
−0.238054 + 0.971252i \(0.576509\pi\)
\(810\) 3.87340e11 0.0316162
\(811\) −3.93373e11 −0.0319309 −0.0159654 0.999873i \(-0.505082\pi\)
−0.0159654 + 0.999873i \(0.505082\pi\)
\(812\) 1.10683e13 0.893471
\(813\) 3.86610e12 0.310360
\(814\) 2.52571e12 0.201638
\(815\) −3.46634e13 −2.75209
\(816\) −2.31804e12 −0.183027
\(817\) 8.64933e12 0.679178
\(818\) 1.05309e12 0.0822387
\(819\) 3.04989e12 0.236868
\(820\) 1.37482e13 1.06190
\(821\) 2.02203e13 1.55326 0.776629 0.629958i \(-0.216928\pi\)
0.776629 + 0.629958i \(0.216928\pi\)
\(822\) −1.91255e12 −0.146113
\(823\) 1.11306e13 0.845704 0.422852 0.906199i \(-0.361029\pi\)
0.422852 + 0.906199i \(0.361029\pi\)
\(824\) −7.79216e12 −0.588824
\(825\) 6.52768e12 0.490587
\(826\) −2.26376e11 −0.0169208
\(827\) −5.16551e12 −0.384007 −0.192003 0.981394i \(-0.561498\pi\)
−0.192003 + 0.981394i \(0.561498\pi\)
\(828\) 3.68243e12 0.272269
\(829\) −2.28015e13 −1.67675 −0.838373 0.545097i \(-0.816493\pi\)
−0.838373 + 0.545097i \(0.816493\pi\)
\(830\) −1.95239e12 −0.142795
\(831\) −1.23238e13 −0.896479
\(832\) 1.10932e13 0.802607
\(833\) −2.39243e12 −0.172162
\(834\) 1.03205e12 0.0738678
\(835\) 4.81236e12 0.342585
\(836\) −3.00231e12 −0.212582
\(837\) −4.37946e12 −0.308430
\(838\) −1.23760e12 −0.0866926
\(839\) −2.67338e13 −1.86265 −0.931326 0.364187i \(-0.881347\pi\)
−0.931326 + 0.364187i \(0.881347\pi\)
\(840\) −3.33064e12 −0.230819
\(841\) 9.76948e12 0.673425
\(842\) 2.20115e12 0.150920
\(843\) −1.18695e13 −0.809486
\(844\) −2.19300e13 −1.48764
\(845\) 2.41013e11 0.0162624
\(846\) −4.91844e11 −0.0330111
\(847\) 7.00360e12 0.467569
\(848\) −1.50665e13 −1.00053
\(849\) 7.24495e12 0.478576
\(850\) −1.40733e12 −0.0924724
\(851\) −2.43703e13 −1.59286
\(852\) −4.35414e11 −0.0283090
\(853\) −4.21472e11 −0.0272583 −0.0136291 0.999907i \(-0.504338\pi\)
−0.0136291 + 0.999907i \(0.504338\pi\)
\(854\) 4.25025e11 0.0273435
\(855\) 3.04713e12 0.195004
\(856\) −2.10559e10 −0.00134042
\(857\) 1.66883e13 1.05682 0.528408 0.848991i \(-0.322789\pi\)
0.528408 + 0.848991i \(0.322789\pi\)
\(858\) 9.74985e11 0.0614194
\(859\) −6.34553e12 −0.397648 −0.198824 0.980035i \(-0.563712\pi\)
−0.198824 + 0.980035i \(0.563712\pi\)
\(860\) −4.40403e13 −2.74541
\(861\) 4.67038e12 0.289626
\(862\) −4.28175e12 −0.264142
\(863\) −1.35407e13 −0.830982 −0.415491 0.909597i \(-0.636390\pi\)
−0.415491 + 0.909597i \(0.636390\pi\)
\(864\) 1.64535e12 0.100449
\(865\) −2.69221e13 −1.63507
\(866\) 2.55531e12 0.154388
\(867\) 8.41855e12 0.506001
\(868\) 1.85120e13 1.10692
\(869\) 7.99236e11 0.0475429
\(870\) −3.59114e12 −0.212518
\(871\) 4.04893e12 0.238374
\(872\) 8.44966e12 0.494897
\(873\) 4.70635e12 0.274233
\(874\) −9.91859e11 −0.0574975
\(875\) 8.63407e12 0.497943
\(876\) 4.42625e12 0.253961
\(877\) −1.99340e13 −1.13788 −0.568940 0.822379i \(-0.692646\pi\)
−0.568940 + 0.822379i \(0.692646\pi\)
\(878\) 6.37528e10 0.00362054
\(879\) −1.10912e13 −0.626654
\(880\) 1.47457e13 0.828883
\(881\) −1.87654e13 −1.04946 −0.524731 0.851268i \(-0.675834\pi\)
−0.524731 + 0.851268i \(0.675834\pi\)
\(882\) 5.33822e11 0.0297021
\(883\) 2.61652e13 1.44844 0.724222 0.689567i \(-0.242199\pi\)
0.724222 + 0.689567i \(0.242199\pi\)
\(884\) 6.13931e12 0.338131
\(885\) −2.14518e12 −0.117549
\(886\) −5.33886e12 −0.291070
\(887\) −2.15861e13 −1.17089 −0.585446 0.810711i \(-0.699081\pi\)
−0.585446 + 0.810711i \(0.699081\pi\)
\(888\) −7.21878e12 −0.389588
\(889\) 7.61678e12 0.408991
\(890\) 3.62841e12 0.193848
\(891\) −1.22856e12 −0.0653048
\(892\) 2.09878e13 1.11000
\(893\) −3.86924e12 −0.203608
\(894\) 1.53192e12 0.0802080
\(895\) −8.70634e12 −0.453557
\(896\) −9.21610e12 −0.477706
\(897\) −9.40753e12 −0.485188
\(898\) −4.97251e12 −0.255172
\(899\) 4.06031e13 2.07320
\(900\) −9.17145e12 −0.465958
\(901\) −7.71553e12 −0.390036
\(902\) 1.49302e12 0.0750994
\(903\) −1.49608e13 −0.748791
\(904\) −8.49166e12 −0.422897
\(905\) −2.67551e13 −1.32583
\(906\) −4.17287e11 −0.0205758
\(907\) 3.13055e13 1.53599 0.767993 0.640458i \(-0.221255\pi\)
0.767993 + 0.640458i \(0.221255\pi\)
\(908\) −3.41794e13 −1.66870
\(909\) 8.43818e12 0.409932
\(910\) 4.18280e12 0.202200
\(911\) −2.87721e12 −0.138401 −0.0692003 0.997603i \(-0.522045\pi\)
−0.0692003 + 0.997603i \(0.522045\pi\)
\(912\) 4.06890e12 0.194760
\(913\) 6.19253e12 0.294951
\(914\) 1.91378e12 0.0907056
\(915\) 4.02760e12 0.189955
\(916\) 1.90435e13 0.893751
\(917\) −4.73753e12 −0.221253
\(918\) 2.64870e11 0.0123095
\(919\) 2.26769e12 0.104873 0.0524365 0.998624i \(-0.483301\pi\)
0.0524365 + 0.998624i \(0.483301\pi\)
\(920\) 1.02735e13 0.472796
\(921\) 1.27673e13 0.584699
\(922\) 2.48446e12 0.113225
\(923\) 1.11236e12 0.0504471
\(924\) 5.19312e12 0.234371
\(925\) 6.06965e13 2.72600
\(926\) 7.60705e12 0.339991
\(927\) −1.23309e13 −0.548448
\(928\) −1.52545e13 −0.675200
\(929\) 2.30174e13 1.01388 0.506939 0.861982i \(-0.330777\pi\)
0.506939 + 0.861982i \(0.330777\pi\)
\(930\) −6.00625e12 −0.263287
\(931\) 4.19947e12 0.183198
\(932\) −2.44174e13 −1.06005
\(933\) 2.01038e13 0.868582
\(934\) 4.43810e12 0.190825
\(935\) 7.55127e12 0.323123
\(936\) −2.78663e12 −0.118669
\(937\) 4.32512e13 1.83303 0.916515 0.399999i \(-0.130990\pi\)
0.916515 + 0.399999i \(0.130990\pi\)
\(938\) −7.38392e11 −0.0311440
\(939\) −2.77041e12 −0.116292
\(940\) 1.97012e13 0.823033
\(941\) −3.10490e12 −0.129091 −0.0645453 0.997915i \(-0.520560\pi\)
−0.0645453 + 0.997915i \(0.520560\pi\)
\(942\) −1.74757e11 −0.00723112
\(943\) −1.44060e13 −0.593255
\(944\) −2.86450e12 −0.117402
\(945\) −5.27065e12 −0.214991
\(946\) −4.78265e12 −0.194160
\(947\) 3.07748e13 1.24343 0.621713 0.783245i \(-0.286437\pi\)
0.621713 + 0.783245i \(0.286437\pi\)
\(948\) −1.12293e12 −0.0451561
\(949\) −1.13078e13 −0.452563
\(950\) 2.47032e12 0.0984004
\(951\) 7.21487e12 0.286033
\(952\) −2.27755e12 −0.0898675
\(953\) 3.98634e13 1.56551 0.782756 0.622328i \(-0.213813\pi\)
0.782756 + 0.622328i \(0.213813\pi\)
\(954\) 1.72157e12 0.0672908
\(955\) 3.80926e13 1.48192
\(956\) −3.32406e13 −1.28709
\(957\) 1.13903e13 0.438965
\(958\) 8.34892e12 0.320247
\(959\) 2.60245e13 0.993572
\(960\) −1.91707e13 −0.728478
\(961\) 4.14700e13 1.56848
\(962\) 9.06573e12 0.341283
\(963\) −3.33204e10 −0.00124851
\(964\) −2.11144e11 −0.00787466
\(965\) 8.14500e13 3.02356
\(966\) 1.71563e12 0.0633907
\(967\) 1.25763e13 0.462522 0.231261 0.972892i \(-0.425715\pi\)
0.231261 + 0.972892i \(0.425715\pi\)
\(968\) −6.39906e12 −0.234249
\(969\) 2.08369e12 0.0759233
\(970\) 6.45456e12 0.234096
\(971\) −2.35665e13 −0.850763 −0.425381 0.905014i \(-0.639860\pi\)
−0.425381 + 0.905014i \(0.639860\pi\)
\(972\) 1.72613e12 0.0620263
\(973\) −1.40434e13 −0.502303
\(974\) −4.41662e12 −0.157244
\(975\) 2.34304e13 0.830344
\(976\) 5.37815e12 0.189718
\(977\) 3.13588e13 1.10112 0.550559 0.834796i \(-0.314415\pi\)
0.550559 + 0.834796i \(0.314415\pi\)
\(978\) 5.28895e12 0.184861
\(979\) −1.15085e13 −0.400402
\(980\) −2.13827e13 −0.740534
\(981\) 1.33713e13 0.460961
\(982\) −1.50340e12 −0.0515908
\(983\) 7.07864e12 0.241802 0.120901 0.992665i \(-0.461422\pi\)
0.120901 + 0.992665i \(0.461422\pi\)
\(984\) −4.26724e12 −0.145101
\(985\) −4.89084e13 −1.65547
\(986\) −2.45568e12 −0.0827421
\(987\) 6.69265e12 0.224477
\(988\) −1.07765e13 −0.359807
\(989\) 4.61473e13 1.53378
\(990\) −1.68491e12 −0.0557467
\(991\) −1.23331e13 −0.406201 −0.203100 0.979158i \(-0.565102\pi\)
−0.203100 + 0.979158i \(0.565102\pi\)
\(992\) −2.55135e13 −0.836503
\(993\) −1.80038e13 −0.587614
\(994\) −2.02857e11 −0.00659101
\(995\) 9.11507e11 0.0294819
\(996\) −8.70056e12 −0.280143
\(997\) 8.76998e12 0.281106 0.140553 0.990073i \(-0.455112\pi\)
0.140553 + 0.990073i \(0.455112\pi\)
\(998\) −1.28554e12 −0.0410202
\(999\) −1.14235e13 −0.362873
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.b.1.10 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.10 21 1.1 even 1 trivial