Properties

Label 177.12.a.d.1.15
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.5323 q^{2} +243.000 q^{3} -1937.07 q^{4} +8300.31 q^{5} +2559.34 q^{6} +46494.5 q^{7} -41971.8 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+10.5323 q^{2} +243.000 q^{3} -1937.07 q^{4} +8300.31 q^{5} +2559.34 q^{6} +46494.5 q^{7} -41971.8 q^{8} +59049.0 q^{9} +87421.0 q^{10} +529548. q^{11} -470708. q^{12} +1.93215e6 q^{13} +489692. q^{14} +2.01697e6 q^{15} +3.52506e6 q^{16} +5.64515e6 q^{17} +621920. q^{18} +2.69993e6 q^{19} -1.60783e7 q^{20} +1.12982e7 q^{21} +5.57734e6 q^{22} -1.76053e7 q^{23} -1.01992e7 q^{24} +2.00670e7 q^{25} +2.03499e7 q^{26} +1.43489e7 q^{27} -9.00631e7 q^{28} +1.24255e8 q^{29} +2.12433e7 q^{30} -1.09207e8 q^{31} +1.23085e8 q^{32} +1.28680e8 q^{33} +5.94562e7 q^{34} +3.85918e8 q^{35} -1.14382e8 q^{36} -1.90182e8 q^{37} +2.84363e7 q^{38} +4.69513e8 q^{39} -3.48379e8 q^{40} +2.79770e8 q^{41} +1.18995e8 q^{42} +5.67211e8 q^{43} -1.02577e9 q^{44} +4.90125e8 q^{45} -1.85424e8 q^{46} -1.78256e9 q^{47} +8.56591e8 q^{48} +1.84409e8 q^{49} +2.11351e8 q^{50} +1.37177e9 q^{51} -3.74272e9 q^{52} -5.80925e8 q^{53} +1.51126e8 q^{54} +4.39541e9 q^{55} -1.95146e9 q^{56} +6.56082e8 q^{57} +1.30869e9 q^{58} +7.14924e8 q^{59} -3.90702e9 q^{60} -2.90286e9 q^{61} -1.15019e9 q^{62} +2.74545e9 q^{63} -5.92297e9 q^{64} +1.60375e10 q^{65} +1.35529e9 q^{66} -5.69045e9 q^{67} -1.09351e10 q^{68} -4.27809e9 q^{69} +4.06459e9 q^{70} -4.85266e9 q^{71} -2.47839e9 q^{72} -5.37633e9 q^{73} -2.00304e9 q^{74} +4.87627e9 q^{75} -5.22995e9 q^{76} +2.46211e10 q^{77} +4.94504e9 q^{78} +1.77678e10 q^{79} +2.92591e10 q^{80} +3.48678e9 q^{81} +2.94661e9 q^{82} -1.09364e10 q^{83} -2.18853e10 q^{84} +4.68565e10 q^{85} +5.97402e9 q^{86} +3.01941e10 q^{87} -2.22261e10 q^{88} -1.49816e10 q^{89} +5.16212e9 q^{90} +8.98344e10 q^{91} +3.41028e10 q^{92} -2.65373e10 q^{93} -1.87744e10 q^{94} +2.24102e10 q^{95} +2.99097e10 q^{96} +7.14115e10 q^{97} +1.94225e9 q^{98} +3.12693e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + O(q^{10}) \) \( 28q + 96q^{2} + 6804q^{3} + 29214q^{4} + 26562q^{5} + 23328q^{6} + 142333q^{7} + 332331q^{8} + 1653372q^{9} + 616281q^{10} + 1082362q^{11} + 7099002q^{12} + 503712q^{13} + 1321669q^{14} + 6454566q^{15} + 34870338q^{16} + 13513579q^{17} + 5668704q^{18} + 35971687q^{19} + 96105997q^{20} + 34586919q^{21} - 47598882q^{22} + 61380539q^{23} + 80756433q^{24} + 294744746q^{25} + 62820734q^{26} + 401769396q^{27} + 148068294q^{28} + 322339307q^{29} + 149756283q^{30} + 151247077q^{31} + 466383494q^{32} + 263013966q^{33} + 684479860q^{34} + 960297361q^{35} + 1725057486q^{36} + 863508437q^{37} + 992640509q^{38} + 122402016q^{39} + 3067680252q^{40} + 3081170377q^{41} + 321165567q^{42} + 2554238300q^{43} + 4350123570q^{44} + 1568459538q^{45} - 1987059155q^{46} + 6203398333q^{47} + 8473492134q^{48} + 10327857997q^{49} + 17577682253q^{50} + 3283799697q^{51} + 32137181618q^{52} + 14571770754q^{53} + 1377495072q^{54} + 18251419334q^{55} + 33498842836q^{56} + 8741119941q^{57} + 11860778276q^{58} + 20017880372q^{59} + 23353757271q^{60} + 2761613771q^{61} + 13785829526q^{62} + 8404621317q^{63} + 86547545293q^{64} + 32034985256q^{65} - 11566528326q^{66} + 39381333296q^{67} + 38995496621q^{68} + 14915470977q^{69} + 8551800364q^{70} + 26130020296q^{71} + 19623813219q^{72} + 41382402799q^{73} + 23815315058q^{74} + 71622973278q^{75} + 10611720128q^{76} - 8426124313q^{77} + 15265438362q^{78} + 59825111206q^{79} + 4009687655q^{80} + 97629963228q^{81} - 39592715115q^{82} + 35433122727q^{83} + 35980595442q^{84} - 8950496085q^{85} - 182032360688q^{86} + 78328451601q^{87} - 220003602335q^{88} + 102303043039q^{89} + 36390776769q^{90} - 111146323655q^{91} - 163000203526q^{92} + 36753039711q^{93} - 81314346008q^{94} + 208102168887q^{95} + 113331189042q^{96} - 171891031490q^{97} + 72304707792q^{98} + 63912393738q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.5323 0.232732 0.116366 0.993206i \(-0.462875\pi\)
0.116366 + 0.993206i \(0.462875\pi\)
\(3\) 243.000 0.577350
\(4\) −1937.07 −0.945836
\(5\) 8300.31 1.18784 0.593922 0.804523i \(-0.297579\pi\)
0.593922 + 0.804523i \(0.297579\pi\)
\(6\) 2559.34 0.134368
\(7\) 46494.5 1.04559 0.522796 0.852458i \(-0.324889\pi\)
0.522796 + 0.852458i \(0.324889\pi\)
\(8\) −41971.8 −0.452859
\(9\) 59049.0 0.333333
\(10\) 87421.0 0.276450
\(11\) 529548. 0.991393 0.495696 0.868496i \(-0.334913\pi\)
0.495696 + 0.868496i \(0.334913\pi\)
\(12\) −470708. −0.546078
\(13\) 1.93215e6 1.44329 0.721644 0.692264i \(-0.243387\pi\)
0.721644 + 0.692264i \(0.243387\pi\)
\(14\) 489692. 0.243343
\(15\) 2.01697e6 0.685802
\(16\) 3.52506e6 0.840441
\(17\) 5.64515e6 0.964287 0.482144 0.876092i \(-0.339858\pi\)
0.482144 + 0.876092i \(0.339858\pi\)
\(18\) 621920. 0.0775774
\(19\) 2.69993e6 0.250154 0.125077 0.992147i \(-0.460082\pi\)
0.125077 + 0.992147i \(0.460082\pi\)
\(20\) −1.60783e7 −1.12350
\(21\) 1.12982e7 0.603673
\(22\) 5.57734e6 0.230729
\(23\) −1.76053e7 −0.570349 −0.285175 0.958476i \(-0.592052\pi\)
−0.285175 + 0.958476i \(0.592052\pi\)
\(24\) −1.01992e7 −0.261458
\(25\) 2.00670e7 0.410971
\(26\) 2.03499e7 0.335900
\(27\) 1.43489e7 0.192450
\(28\) −9.00631e7 −0.988958
\(29\) 1.24255e8 1.12493 0.562466 0.826820i \(-0.309853\pi\)
0.562466 + 0.826820i \(0.309853\pi\)
\(30\) 2.12433e7 0.159608
\(31\) −1.09207e8 −0.685110 −0.342555 0.939498i \(-0.611292\pi\)
−0.342555 + 0.939498i \(0.611292\pi\)
\(32\) 1.23085e8 0.648457
\(33\) 1.28680e8 0.572381
\(34\) 5.94562e7 0.224421
\(35\) 3.85918e8 1.24200
\(36\) −1.14382e8 −0.315279
\(37\) −1.90182e8 −0.450878 −0.225439 0.974257i \(-0.572382\pi\)
−0.225439 + 0.974257i \(0.572382\pi\)
\(38\) 2.84363e7 0.0582189
\(39\) 4.69513e8 0.833283
\(40\) −3.48379e8 −0.537925
\(41\) 2.79770e8 0.377128 0.188564 0.982061i \(-0.439617\pi\)
0.188564 + 0.982061i \(0.439617\pi\)
\(42\) 1.18995e8 0.140494
\(43\) 5.67211e8 0.588394 0.294197 0.955745i \(-0.404948\pi\)
0.294197 + 0.955745i \(0.404948\pi\)
\(44\) −1.02577e9 −0.937695
\(45\) 4.90125e8 0.395948
\(46\) −1.85424e8 −0.132739
\(47\) −1.78256e9 −1.13372 −0.566860 0.823814i \(-0.691842\pi\)
−0.566860 + 0.823814i \(0.691842\pi\)
\(48\) 8.56591e8 0.485229
\(49\) 1.84409e8 0.0932620
\(50\) 2.11351e8 0.0956463
\(51\) 1.37177e9 0.556731
\(52\) −3.74272e9 −1.36511
\(53\) −5.80925e8 −0.190811 −0.0954054 0.995438i \(-0.530415\pi\)
−0.0954054 + 0.995438i \(0.530415\pi\)
\(54\) 1.51126e8 0.0447894
\(55\) 4.39541e9 1.17762
\(56\) −1.95146e9 −0.473506
\(57\) 6.56082e8 0.144426
\(58\) 1.30869e9 0.261808
\(59\) 7.14924e8 0.130189
\(60\) −3.90702e9 −0.648656
\(61\) −2.90286e9 −0.440060 −0.220030 0.975493i \(-0.570615\pi\)
−0.220030 + 0.975493i \(0.570615\pi\)
\(62\) −1.15019e9 −0.159447
\(63\) 2.74545e9 0.348531
\(64\) −5.92297e9 −0.689524
\(65\) 1.60375e10 1.71440
\(66\) 1.35529e9 0.133212
\(67\) −5.69045e9 −0.514915 −0.257457 0.966290i \(-0.582885\pi\)
−0.257457 + 0.966290i \(0.582885\pi\)
\(68\) −1.09351e10 −0.912057
\(69\) −4.27809e9 −0.329291
\(70\) 4.06459e9 0.289053
\(71\) −4.85266e9 −0.319197 −0.159599 0.987182i \(-0.551020\pi\)
−0.159599 + 0.987182i \(0.551020\pi\)
\(72\) −2.47839e9 −0.150953
\(73\) −5.37633e9 −0.303536 −0.151768 0.988416i \(-0.548497\pi\)
−0.151768 + 0.988416i \(0.548497\pi\)
\(74\) −2.00304e9 −0.104934
\(75\) 4.87627e9 0.237274
\(76\) −5.22995e9 −0.236604
\(77\) 2.46211e10 1.03659
\(78\) 4.94504e9 0.193932
\(79\) 1.77678e10 0.649658 0.324829 0.945773i \(-0.394693\pi\)
0.324829 + 0.945773i \(0.394693\pi\)
\(80\) 2.92591e10 0.998312
\(81\) 3.48678e9 0.111111
\(82\) 2.94661e9 0.0877700
\(83\) −1.09364e10 −0.304751 −0.152375 0.988323i \(-0.548692\pi\)
−0.152375 + 0.988323i \(0.548692\pi\)
\(84\) −2.18853e10 −0.570975
\(85\) 4.68565e10 1.14542
\(86\) 5.97402e9 0.136938
\(87\) 3.01941e10 0.649480
\(88\) −2.22261e10 −0.448961
\(89\) −1.49816e10 −0.284390 −0.142195 0.989839i \(-0.545416\pi\)
−0.142195 + 0.989839i \(0.545416\pi\)
\(90\) 5.16212e9 0.0921498
\(91\) 8.98344e10 1.50909
\(92\) 3.41028e10 0.539457
\(93\) −2.65373e10 −0.395548
\(94\) −1.87744e10 −0.263853
\(95\) 2.24102e10 0.297143
\(96\) 2.99097e10 0.374387
\(97\) 7.14115e10 0.844352 0.422176 0.906514i \(-0.361266\pi\)
0.422176 + 0.906514i \(0.361266\pi\)
\(98\) 1.94225e9 0.0217051
\(99\) 3.12693e10 0.330464
\(100\) −3.88711e10 −0.388711
\(101\) −6.72698e10 −0.636873 −0.318436 0.947944i \(-0.603158\pi\)
−0.318436 + 0.947944i \(0.603158\pi\)
\(102\) 1.44479e10 0.129569
\(103\) 6.47555e10 0.550391 0.275196 0.961388i \(-0.411257\pi\)
0.275196 + 0.961388i \(0.411257\pi\)
\(104\) −8.10960e10 −0.653606
\(105\) 9.37782e10 0.717068
\(106\) −6.11846e9 −0.0444079
\(107\) 8.20962e10 0.565864 0.282932 0.959140i \(-0.408693\pi\)
0.282932 + 0.959140i \(0.408693\pi\)
\(108\) −2.77949e10 −0.182026
\(109\) −3.78461e10 −0.235600 −0.117800 0.993037i \(-0.537584\pi\)
−0.117800 + 0.993037i \(0.537584\pi\)
\(110\) 4.62937e10 0.274070
\(111\) −4.62142e10 −0.260315
\(112\) 1.63896e11 0.878758
\(113\) −1.51677e11 −0.774440 −0.387220 0.921987i \(-0.626565\pi\)
−0.387220 + 0.921987i \(0.626565\pi\)
\(114\) 6.91003e9 0.0336127
\(115\) −1.46130e11 −0.677486
\(116\) −2.40692e11 −1.06400
\(117\) 1.14092e11 0.481096
\(118\) 7.52977e9 0.0302992
\(119\) 2.62468e11 1.00825
\(120\) −8.46561e10 −0.310571
\(121\) −4.89026e9 −0.0171400
\(122\) −3.05737e10 −0.102416
\(123\) 6.79840e10 0.217735
\(124\) 2.11541e11 0.648002
\(125\) −2.38726e11 −0.699674
\(126\) 2.89158e10 0.0811143
\(127\) 1.24742e11 0.335037 0.167519 0.985869i \(-0.446425\pi\)
0.167519 + 0.985869i \(0.446425\pi\)
\(128\) −3.14461e11 −0.808931
\(129\) 1.37832e11 0.339710
\(130\) 1.68911e11 0.398996
\(131\) 4.89647e11 1.10890 0.554448 0.832219i \(-0.312930\pi\)
0.554448 + 0.832219i \(0.312930\pi\)
\(132\) −2.49263e11 −0.541378
\(133\) 1.25532e11 0.261559
\(134\) −5.99333e10 −0.119837
\(135\) 1.19100e11 0.228601
\(136\) −2.36937e11 −0.436686
\(137\) −7.97179e11 −1.41121 −0.705607 0.708603i \(-0.749326\pi\)
−0.705607 + 0.708603i \(0.749326\pi\)
\(138\) −4.50580e10 −0.0766368
\(139\) −2.50206e10 −0.0408993 −0.0204497 0.999791i \(-0.506510\pi\)
−0.0204497 + 0.999791i \(0.506510\pi\)
\(140\) −7.47551e11 −1.17473
\(141\) −4.33162e11 −0.654554
\(142\) −5.11095e10 −0.0742875
\(143\) 1.02317e12 1.43087
\(144\) 2.08152e11 0.280147
\(145\) 1.03136e12 1.33624
\(146\) −5.66249e10 −0.0706427
\(147\) 4.48115e10 0.0538448
\(148\) 3.68396e11 0.426457
\(149\) −1.00979e12 −1.12644 −0.563219 0.826308i \(-0.690437\pi\)
−0.563219 + 0.826308i \(0.690437\pi\)
\(150\) 5.13582e10 0.0552214
\(151\) 1.40479e12 1.45626 0.728130 0.685439i \(-0.240390\pi\)
0.728130 + 0.685439i \(0.240390\pi\)
\(152\) −1.13321e11 −0.113284
\(153\) 3.33340e11 0.321429
\(154\) 2.59316e11 0.241249
\(155\) −9.06450e11 −0.813803
\(156\) −9.09481e11 −0.788149
\(157\) 1.91187e12 1.59960 0.799799 0.600268i \(-0.204939\pi\)
0.799799 + 0.600268i \(0.204939\pi\)
\(158\) 1.87135e11 0.151196
\(159\) −1.41165e11 −0.110165
\(160\) 1.02164e12 0.770265
\(161\) −8.18550e11 −0.596353
\(162\) 3.67237e10 0.0258591
\(163\) 4.34423e11 0.295720 0.147860 0.989008i \(-0.452761\pi\)
0.147860 + 0.989008i \(0.452761\pi\)
\(164\) −5.41934e11 −0.356702
\(165\) 1.06809e12 0.679899
\(166\) −1.15185e11 −0.0709254
\(167\) −1.63621e12 −0.974764 −0.487382 0.873189i \(-0.662048\pi\)
−0.487382 + 0.873189i \(0.662048\pi\)
\(168\) −4.74204e11 −0.273379
\(169\) 1.94106e12 1.08308
\(170\) 4.93505e11 0.266577
\(171\) 1.59428e11 0.0833846
\(172\) −1.09873e12 −0.556524
\(173\) 2.15869e12 1.05910 0.529551 0.848278i \(-0.322361\pi\)
0.529551 + 0.848278i \(0.322361\pi\)
\(174\) 3.18012e11 0.151155
\(175\) 9.33003e11 0.429708
\(176\) 1.86669e12 0.833207
\(177\) 1.73727e11 0.0751646
\(178\) −1.57790e11 −0.0661867
\(179\) 4.43277e12 1.80295 0.901476 0.432830i \(-0.142485\pi\)
0.901476 + 0.432830i \(0.142485\pi\)
\(180\) −9.49407e11 −0.374501
\(181\) −2.27330e12 −0.869812 −0.434906 0.900476i \(-0.643218\pi\)
−0.434906 + 0.900476i \(0.643218\pi\)
\(182\) 9.46160e11 0.351214
\(183\) −7.05394e11 −0.254069
\(184\) 7.38928e11 0.258288
\(185\) −1.57857e12 −0.535573
\(186\) −2.79497e11 −0.0920569
\(187\) 2.98938e12 0.955987
\(188\) 3.45295e12 1.07231
\(189\) 6.67145e11 0.201224
\(190\) 2.36030e11 0.0691549
\(191\) 2.74464e12 0.781272 0.390636 0.920545i \(-0.372255\pi\)
0.390636 + 0.920545i \(0.372255\pi\)
\(192\) −1.43928e12 −0.398097
\(193\) 4.05528e12 1.09007 0.545036 0.838412i \(-0.316516\pi\)
0.545036 + 0.838412i \(0.316516\pi\)
\(194\) 7.52124e11 0.196508
\(195\) 3.89710e12 0.989809
\(196\) −3.57214e11 −0.0882105
\(197\) 5.80542e12 1.39402 0.697010 0.717061i \(-0.254513\pi\)
0.697010 + 0.717061i \(0.254513\pi\)
\(198\) 3.29336e11 0.0769097
\(199\) 6.61352e12 1.50224 0.751122 0.660163i \(-0.229513\pi\)
0.751122 + 0.660163i \(0.229513\pi\)
\(200\) −8.42247e11 −0.186112
\(201\) −1.38278e12 −0.297286
\(202\) −7.08503e11 −0.148221
\(203\) 5.77719e12 1.17622
\(204\) −2.65722e12 −0.526576
\(205\) 2.32217e12 0.447969
\(206\) 6.82022e11 0.128094
\(207\) −1.03958e12 −0.190116
\(208\) 6.81096e12 1.21300
\(209\) 1.42974e12 0.248001
\(210\) 9.87696e11 0.166885
\(211\) −1.14902e13 −1.89136 −0.945678 0.325104i \(-0.894601\pi\)
−0.945678 + 0.325104i \(0.894601\pi\)
\(212\) 1.12529e12 0.180476
\(213\) −1.17920e12 −0.184288
\(214\) 8.64659e11 0.131695
\(215\) 4.70803e12 0.698920
\(216\) −6.02250e11 −0.0871527
\(217\) −5.07751e12 −0.716345
\(218\) −3.98605e11 −0.0548317
\(219\) −1.30645e12 −0.175247
\(220\) −8.51423e12 −1.11383
\(221\) 1.09073e13 1.39174
\(222\) −4.86740e11 −0.0605837
\(223\) −4.24076e12 −0.514953 −0.257476 0.966285i \(-0.582891\pi\)
−0.257476 + 0.966285i \(0.582891\pi\)
\(224\) 5.72278e12 0.678021
\(225\) 1.18493e12 0.136990
\(226\) −1.59750e12 −0.180237
\(227\) −1.07805e13 −1.18712 −0.593561 0.804789i \(-0.702278\pi\)
−0.593561 + 0.804789i \(0.702278\pi\)
\(228\) −1.27088e12 −0.136604
\(229\) −1.39610e13 −1.46495 −0.732474 0.680795i \(-0.761635\pi\)
−0.732474 + 0.680795i \(0.761635\pi\)
\(230\) −1.53908e12 −0.157673
\(231\) 5.98292e12 0.598477
\(232\) −5.21523e12 −0.509436
\(233\) −4.11516e12 −0.392581 −0.196291 0.980546i \(-0.562890\pi\)
−0.196291 + 0.980546i \(0.562890\pi\)
\(234\) 1.20164e12 0.111967
\(235\) −1.47958e13 −1.34668
\(236\) −1.38486e12 −0.123137
\(237\) 4.31758e12 0.375080
\(238\) 2.76438e12 0.234653
\(239\) −1.46015e13 −1.21118 −0.605591 0.795776i \(-0.707063\pi\)
−0.605591 + 0.795776i \(0.707063\pi\)
\(240\) 7.10996e12 0.576376
\(241\) 1.53414e13 1.21554 0.607771 0.794112i \(-0.292064\pi\)
0.607771 + 0.794112i \(0.292064\pi\)
\(242\) −5.15055e10 −0.00398904
\(243\) 8.47289e11 0.0641500
\(244\) 5.62304e12 0.416224
\(245\) 1.53065e12 0.110781
\(246\) 7.16025e11 0.0506740
\(247\) 5.21667e12 0.361044
\(248\) 4.58361e12 0.310258
\(249\) −2.65754e12 −0.175948
\(250\) −2.51433e12 −0.162837
\(251\) 4.24783e12 0.269129 0.134565 0.990905i \(-0.457036\pi\)
0.134565 + 0.990905i \(0.457036\pi\)
\(252\) −5.31814e12 −0.329653
\(253\) −9.32287e12 −0.565440
\(254\) 1.31382e12 0.0779740
\(255\) 1.13861e13 0.661310
\(256\) 8.81825e12 0.501259
\(257\) 1.06801e13 0.594214 0.297107 0.954844i \(-0.403978\pi\)
0.297107 + 0.954844i \(0.403978\pi\)
\(258\) 1.45169e12 0.0790614
\(259\) −8.84240e12 −0.471435
\(260\) −3.10657e13 −1.62154
\(261\) 7.33716e12 0.374978
\(262\) 5.15709e12 0.258076
\(263\) 1.08111e13 0.529800 0.264900 0.964276i \(-0.414661\pi\)
0.264900 + 0.964276i \(0.414661\pi\)
\(264\) −5.40094e12 −0.259208
\(265\) −4.82186e12 −0.226653
\(266\) 1.32213e12 0.0608732
\(267\) −3.64054e12 −0.164193
\(268\) 1.10228e13 0.487025
\(269\) −1.75753e13 −0.760789 −0.380395 0.924824i \(-0.624212\pi\)
−0.380395 + 0.924824i \(0.624212\pi\)
\(270\) 1.25440e12 0.0532027
\(271\) −7.88672e12 −0.327767 −0.163884 0.986480i \(-0.552402\pi\)
−0.163884 + 0.986480i \(0.552402\pi\)
\(272\) 1.98995e13 0.810426
\(273\) 2.18298e13 0.871274
\(274\) −8.39610e12 −0.328435
\(275\) 1.06264e13 0.407434
\(276\) 8.28697e12 0.311456
\(277\) 3.03489e13 1.11816 0.559081 0.829113i \(-0.311154\pi\)
0.559081 + 0.829113i \(0.311154\pi\)
\(278\) −2.63524e11 −0.00951860
\(279\) −6.44855e12 −0.228370
\(280\) −1.61977e13 −0.562450
\(281\) −1.52497e12 −0.0519252 −0.0259626 0.999663i \(-0.508265\pi\)
−0.0259626 + 0.999663i \(0.508265\pi\)
\(282\) −4.56218e12 −0.152336
\(283\) 5.83294e13 1.91013 0.955064 0.296401i \(-0.0957865\pi\)
0.955064 + 0.296401i \(0.0957865\pi\)
\(284\) 9.39995e12 0.301908
\(285\) 5.44568e12 0.171556
\(286\) 1.07763e13 0.333009
\(287\) 1.30077e13 0.394322
\(288\) 7.26806e12 0.216152
\(289\) −2.40419e12 −0.0701504
\(290\) 1.08625e13 0.310987
\(291\) 1.73530e13 0.487487
\(292\) 1.04143e13 0.287095
\(293\) 2.59127e13 0.701037 0.350519 0.936556i \(-0.386005\pi\)
0.350519 + 0.936556i \(0.386005\pi\)
\(294\) 4.71966e11 0.0125314
\(295\) 5.93409e12 0.154644
\(296\) 7.98228e12 0.204184
\(297\) 7.59844e12 0.190794
\(298\) −1.06354e13 −0.262159
\(299\) −3.40162e13 −0.823179
\(300\) −9.44569e12 −0.224423
\(301\) 2.63722e13 0.615220
\(302\) 1.47956e13 0.338919
\(303\) −1.63466e13 −0.367699
\(304\) 9.51741e12 0.210239
\(305\) −2.40946e13 −0.522722
\(306\) 3.51083e12 0.0748069
\(307\) −3.59083e13 −0.751508 −0.375754 0.926719i \(-0.622616\pi\)
−0.375754 + 0.926719i \(0.622616\pi\)
\(308\) −4.76928e13 −0.980446
\(309\) 1.57356e13 0.317769
\(310\) −9.54697e12 −0.189398
\(311\) 3.43753e13 0.669985 0.334992 0.942221i \(-0.391266\pi\)
0.334992 + 0.942221i \(0.391266\pi\)
\(312\) −1.97063e13 −0.377360
\(313\) −9.06372e13 −1.70535 −0.852673 0.522445i \(-0.825020\pi\)
−0.852673 + 0.522445i \(0.825020\pi\)
\(314\) 2.01363e13 0.372278
\(315\) 2.27881e13 0.414000
\(316\) −3.44175e13 −0.614470
\(317\) 1.24565e13 0.218559 0.109279 0.994011i \(-0.465146\pi\)
0.109279 + 0.994011i \(0.465146\pi\)
\(318\) −1.48679e12 −0.0256389
\(319\) 6.57993e13 1.11525
\(320\) −4.91624e13 −0.819046
\(321\) 1.99494e13 0.326702
\(322\) −8.62119e12 −0.138791
\(323\) 1.52415e13 0.241220
\(324\) −6.75415e12 −0.105093
\(325\) 3.87724e13 0.593150
\(326\) 4.57546e12 0.0688237
\(327\) −9.19660e12 −0.136024
\(328\) −1.17424e13 −0.170786
\(329\) −8.28792e13 −1.18541
\(330\) 1.12494e13 0.158234
\(331\) 3.65138e12 0.0505130 0.0252565 0.999681i \(-0.491960\pi\)
0.0252565 + 0.999681i \(0.491960\pi\)
\(332\) 2.11846e13 0.288244
\(333\) −1.12300e13 −0.150293
\(334\) −1.72330e13 −0.226859
\(335\) −4.72325e13 −0.611638
\(336\) 3.98267e13 0.507351
\(337\) −1.32289e14 −1.65791 −0.828954 0.559317i \(-0.811064\pi\)
−0.828954 + 0.559317i \(0.811064\pi\)
\(338\) 2.04437e13 0.252068
\(339\) −3.68575e13 −0.447123
\(340\) −9.07643e13 −1.08338
\(341\) −5.78303e13 −0.679213
\(342\) 1.67914e12 0.0194063
\(343\) −8.33607e13 −0.948078
\(344\) −2.38069e13 −0.266460
\(345\) −3.55095e13 −0.391146
\(346\) 2.27359e13 0.246487
\(347\) −1.68357e14 −1.79646 −0.898232 0.439522i \(-0.855148\pi\)
−0.898232 + 0.439522i \(0.855148\pi\)
\(348\) −5.84881e13 −0.614302
\(349\) 1.68121e13 0.173813 0.0869067 0.996216i \(-0.472302\pi\)
0.0869067 + 0.996216i \(0.472302\pi\)
\(350\) 9.82663e12 0.100007
\(351\) 2.77243e13 0.277761
\(352\) 6.51796e13 0.642875
\(353\) −1.80494e14 −1.75268 −0.876339 0.481695i \(-0.840021\pi\)
−0.876339 + 0.481695i \(0.840021\pi\)
\(354\) 1.82973e12 0.0174932
\(355\) −4.02786e13 −0.379156
\(356\) 2.90205e13 0.268986
\(357\) 6.37798e13 0.582114
\(358\) 4.66871e13 0.419605
\(359\) −1.62816e14 −1.44105 −0.720523 0.693431i \(-0.756098\pi\)
−0.720523 + 0.693431i \(0.756098\pi\)
\(360\) −2.05714e13 −0.179308
\(361\) −1.09201e14 −0.937423
\(362\) −2.39430e13 −0.202433
\(363\) −1.18833e12 −0.00989581
\(364\) −1.74016e14 −1.42735
\(365\) −4.46252e13 −0.360553
\(366\) −7.42940e12 −0.0591300
\(367\) −8.46944e13 −0.664035 −0.332018 0.943273i \(-0.607729\pi\)
−0.332018 + 0.943273i \(0.607729\pi\)
\(368\) −6.20599e13 −0.479345
\(369\) 1.65201e13 0.125709
\(370\) −1.66259e13 −0.124645
\(371\) −2.70098e13 −0.199510
\(372\) 5.14046e13 0.374124
\(373\) 3.14593e13 0.225606 0.112803 0.993617i \(-0.464017\pi\)
0.112803 + 0.993617i \(0.464017\pi\)
\(374\) 3.14849e13 0.222489
\(375\) −5.80105e13 −0.403957
\(376\) 7.48173e13 0.513415
\(377\) 2.40081e14 1.62360
\(378\) 7.02655e12 0.0468314
\(379\) 5.94402e13 0.390449 0.195225 0.980759i \(-0.437456\pi\)
0.195225 + 0.980759i \(0.437456\pi\)
\(380\) −4.34102e13 −0.281049
\(381\) 3.03124e13 0.193434
\(382\) 2.89073e13 0.181827
\(383\) 8.25725e13 0.511967 0.255984 0.966681i \(-0.417601\pi\)
0.255984 + 0.966681i \(0.417601\pi\)
\(384\) −7.64140e13 −0.467037
\(385\) 2.04362e14 1.23131
\(386\) 4.27113e13 0.253695
\(387\) 3.34933e13 0.196131
\(388\) −1.38329e14 −0.798618
\(389\) −1.16261e13 −0.0661777 −0.0330888 0.999452i \(-0.510534\pi\)
−0.0330888 + 0.999452i \(0.510534\pi\)
\(390\) 4.10453e13 0.230361
\(391\) −9.93847e13 −0.549981
\(392\) −7.74000e12 −0.0422345
\(393\) 1.18984e14 0.640221
\(394\) 6.11442e13 0.324434
\(395\) 1.47478e14 0.771692
\(396\) −6.05709e13 −0.312565
\(397\) 1.29965e14 0.661419 0.330710 0.943733i \(-0.392712\pi\)
0.330710 + 0.943733i \(0.392712\pi\)
\(398\) 6.96553e13 0.349621
\(399\) 3.05042e13 0.151011
\(400\) 7.07373e13 0.345397
\(401\) −9.22351e13 −0.444224 −0.222112 0.975021i \(-0.571295\pi\)
−0.222112 + 0.975021i \(0.571295\pi\)
\(402\) −1.45638e13 −0.0691881
\(403\) −2.11004e14 −0.988811
\(404\) 1.30306e14 0.602377
\(405\) 2.89414e13 0.131983
\(406\) 6.08469e13 0.273745
\(407\) −1.00710e14 −0.446998
\(408\) −5.75757e13 −0.252121
\(409\) −2.17087e14 −0.937897 −0.468949 0.883225i \(-0.655367\pi\)
−0.468949 + 0.883225i \(0.655367\pi\)
\(410\) 2.44577e13 0.104257
\(411\) −1.93715e14 −0.814765
\(412\) −1.25436e14 −0.520580
\(413\) 3.32400e13 0.136124
\(414\) −1.09491e13 −0.0442462
\(415\) −9.07755e13 −0.361996
\(416\) 2.37819e14 0.935910
\(417\) −6.08001e12 −0.0236132
\(418\) 1.50584e13 0.0577178
\(419\) 2.46901e14 0.933998 0.466999 0.884258i \(-0.345335\pi\)
0.466999 + 0.884258i \(0.345335\pi\)
\(420\) −1.81655e14 −0.678229
\(421\) −3.49559e14 −1.28816 −0.644080 0.764958i \(-0.722759\pi\)
−0.644080 + 0.764958i \(0.722759\pi\)
\(422\) −1.21018e14 −0.440180
\(423\) −1.05258e14 −0.377907
\(424\) 2.43825e13 0.0864104
\(425\) 1.13281e14 0.396294
\(426\) −1.24196e13 −0.0428899
\(427\) −1.34967e14 −0.460123
\(428\) −1.59026e14 −0.535214
\(429\) 2.48630e14 0.826111
\(430\) 4.95862e13 0.162661
\(431\) −2.31486e14 −0.749720 −0.374860 0.927081i \(-0.622309\pi\)
−0.374860 + 0.927081i \(0.622309\pi\)
\(432\) 5.05808e13 0.161743
\(433\) 2.11942e14 0.669166 0.334583 0.942366i \(-0.391405\pi\)
0.334583 + 0.942366i \(0.391405\pi\)
\(434\) −5.34777e13 −0.166717
\(435\) 2.50620e14 0.771481
\(436\) 7.33106e13 0.222839
\(437\) −4.75331e13 −0.142675
\(438\) −1.37599e13 −0.0407856
\(439\) −4.37167e14 −1.27965 −0.639826 0.768520i \(-0.720994\pi\)
−0.639826 + 0.768520i \(0.720994\pi\)
\(440\) −1.84484e14 −0.533295
\(441\) 1.08892e13 0.0310873
\(442\) 1.14878e14 0.323904
\(443\) −2.32859e14 −0.648443 −0.324222 0.945981i \(-0.605102\pi\)
−0.324222 + 0.945981i \(0.605102\pi\)
\(444\) 8.95202e13 0.246215
\(445\) −1.24352e14 −0.337810
\(446\) −4.46648e13 −0.119846
\(447\) −2.45379e14 −0.650350
\(448\) −2.75385e14 −0.720960
\(449\) −3.20003e12 −0.00827560 −0.00413780 0.999991i \(-0.501317\pi\)
−0.00413780 + 0.999991i \(0.501317\pi\)
\(450\) 1.24800e13 0.0318821
\(451\) 1.48152e14 0.373882
\(452\) 2.93809e14 0.732493
\(453\) 3.41364e14 0.840772
\(454\) −1.13543e14 −0.276282
\(455\) 7.45653e14 1.79256
\(456\) −2.75370e13 −0.0654047
\(457\) −5.70523e13 −0.133886 −0.0669429 0.997757i \(-0.521325\pi\)
−0.0669429 + 0.997757i \(0.521325\pi\)
\(458\) −1.47041e14 −0.340941
\(459\) 8.10017e13 0.185577
\(460\) 2.83063e14 0.640790
\(461\) 5.13155e14 1.14787 0.573936 0.818900i \(-0.305416\pi\)
0.573936 + 0.818900i \(0.305416\pi\)
\(462\) 6.30137e13 0.139285
\(463\) 1.18238e14 0.258262 0.129131 0.991628i \(-0.458781\pi\)
0.129131 + 0.991628i \(0.458781\pi\)
\(464\) 4.38009e14 0.945439
\(465\) −2.20267e14 −0.469850
\(466\) −4.33420e13 −0.0913663
\(467\) 5.89495e14 1.22811 0.614055 0.789263i \(-0.289537\pi\)
0.614055 + 0.789263i \(0.289537\pi\)
\(468\) −2.21004e14 −0.455038
\(469\) −2.64574e14 −0.538390
\(470\) −1.55833e14 −0.313417
\(471\) 4.64585e14 0.923528
\(472\) −3.00067e13 −0.0589572
\(473\) 3.00366e14 0.583330
\(474\) 4.54739e13 0.0872933
\(475\) 5.41793e13 0.102806
\(476\) −5.08420e14 −0.953639
\(477\) −3.43031e13 −0.0636036
\(478\) −1.53787e14 −0.281881
\(479\) −2.41097e14 −0.436863 −0.218432 0.975852i \(-0.570094\pi\)
−0.218432 + 0.975852i \(0.570094\pi\)
\(480\) 2.48260e14 0.444713
\(481\) −3.67460e14 −0.650748
\(482\) 1.61579e14 0.282896
\(483\) −1.98908e14 −0.344304
\(484\) 9.47277e12 0.0162117
\(485\) 5.92737e14 1.00296
\(486\) 8.92387e12 0.0149298
\(487\) 7.11458e14 1.17690 0.588450 0.808533i \(-0.299738\pi\)
0.588450 + 0.808533i \(0.299738\pi\)
\(488\) 1.21838e14 0.199285
\(489\) 1.05565e14 0.170734
\(490\) 1.61213e13 0.0257822
\(491\) 7.98098e14 1.26214 0.631070 0.775726i \(-0.282616\pi\)
0.631070 + 0.775726i \(0.282616\pi\)
\(492\) −1.31690e14 −0.205942
\(493\) 7.01441e14 1.08476
\(494\) 5.49433e13 0.0840266
\(495\) 2.59545e14 0.392540
\(496\) −3.84961e14 −0.575794
\(497\) −2.25622e14 −0.333750
\(498\) −2.79900e13 −0.0409488
\(499\) −3.06692e14 −0.443762 −0.221881 0.975074i \(-0.571220\pi\)
−0.221881 + 0.975074i \(0.571220\pi\)
\(500\) 4.62430e14 0.661776
\(501\) −3.97600e14 −0.562780
\(502\) 4.47392e13 0.0626351
\(503\) 3.90342e14 0.540532 0.270266 0.962786i \(-0.412888\pi\)
0.270266 + 0.962786i \(0.412888\pi\)
\(504\) −1.15232e14 −0.157835
\(505\) −5.58360e14 −0.756505
\(506\) −9.81909e13 −0.131596
\(507\) 4.71677e14 0.625317
\(508\) −2.41635e14 −0.316890
\(509\) −9.21181e14 −1.19508 −0.597540 0.801839i \(-0.703855\pi\)
−0.597540 + 0.801839i \(0.703855\pi\)
\(510\) 1.19922e14 0.153908
\(511\) −2.49970e14 −0.317375
\(512\) 7.36892e14 0.925590
\(513\) 3.87410e13 0.0481421
\(514\) 1.12486e14 0.138293
\(515\) 5.37490e14 0.653779
\(516\) −2.66991e14 −0.321309
\(517\) −9.43952e14 −1.12396
\(518\) −9.31305e13 −0.109718
\(519\) 5.24563e14 0.611473
\(520\) −6.73122e14 −0.776381
\(521\) 1.79069e14 0.204368 0.102184 0.994765i \(-0.467417\pi\)
0.102184 + 0.994765i \(0.467417\pi\)
\(522\) 7.72769e13 0.0872694
\(523\) 7.02264e14 0.784768 0.392384 0.919802i \(-0.371650\pi\)
0.392384 + 0.919802i \(0.371650\pi\)
\(524\) −9.48480e14 −1.04883
\(525\) 2.26720e14 0.248092
\(526\) 1.13865e14 0.123302
\(527\) −6.16489e14 −0.660643
\(528\) 4.53606e14 0.481052
\(529\) −6.42862e14 −0.674702
\(530\) −5.07851e13 −0.0527496
\(531\) 4.22156e13 0.0433963
\(532\) −2.43164e14 −0.247391
\(533\) 5.40558e14 0.544305
\(534\) −3.83431e13 −0.0382129
\(535\) 6.81423e14 0.672158
\(536\) 2.38839e14 0.233184
\(537\) 1.07716e15 1.04093
\(538\) −1.85107e14 −0.177060
\(539\) 9.76537e13 0.0924593
\(540\) −2.30706e14 −0.216219
\(541\) 1.68340e15 1.56172 0.780859 0.624708i \(-0.214782\pi\)
0.780859 + 0.624708i \(0.214782\pi\)
\(542\) −8.30651e13 −0.0762820
\(543\) −5.52413e14 −0.502186
\(544\) 6.94834e14 0.625298
\(545\) −3.14134e14 −0.279856
\(546\) 2.29917e14 0.202774
\(547\) −2.20542e15 −1.92558 −0.962788 0.270257i \(-0.912891\pi\)
−0.962788 + 0.270257i \(0.912891\pi\)
\(548\) 1.54419e15 1.33478
\(549\) −1.71411e14 −0.146687
\(550\) 1.11920e14 0.0948231
\(551\) 3.35481e14 0.281406
\(552\) 1.79559e14 0.149123
\(553\) 8.26105e14 0.679277
\(554\) 3.19643e14 0.260232
\(555\) −3.83592e14 −0.309213
\(556\) 4.84667e13 0.0386841
\(557\) −1.48311e14 −0.117211 −0.0586057 0.998281i \(-0.518665\pi\)
−0.0586057 + 0.998281i \(0.518665\pi\)
\(558\) −6.79179e13 −0.0531491
\(559\) 1.09594e15 0.849222
\(560\) 1.36039e15 1.04383
\(561\) 7.26419e14 0.551940
\(562\) −1.60614e13 −0.0120847
\(563\) 9.70328e14 0.722973 0.361487 0.932377i \(-0.382269\pi\)
0.361487 + 0.932377i \(0.382269\pi\)
\(564\) 8.39066e14 0.619100
\(565\) −1.25896e15 −0.919914
\(566\) 6.14341e14 0.444548
\(567\) 1.62116e14 0.116177
\(568\) 2.03675e14 0.144551
\(569\) −1.56308e15 −1.09866 −0.549330 0.835606i \(-0.685117\pi\)
−0.549330 + 0.835606i \(0.685117\pi\)
\(570\) 5.73553e13 0.0399266
\(571\) −1.28059e15 −0.882899 −0.441450 0.897286i \(-0.645536\pi\)
−0.441450 + 0.897286i \(0.645536\pi\)
\(572\) −1.98195e15 −1.35336
\(573\) 6.66948e14 0.451068
\(574\) 1.37001e14 0.0917716
\(575\) −3.53285e14 −0.234397
\(576\) −3.49745e14 −0.229841
\(577\) 2.00667e15 1.30620 0.653100 0.757272i \(-0.273468\pi\)
0.653100 + 0.757272i \(0.273468\pi\)
\(578\) −2.53215e13 −0.0163263
\(579\) 9.85433e14 0.629354
\(580\) −1.99782e15 −1.26387
\(581\) −5.08482e14 −0.318645
\(582\) 1.82766e14 0.113454
\(583\) −3.07628e14 −0.189169
\(584\) 2.25654e14 0.137459
\(585\) 9.46996e14 0.571467
\(586\) 2.72920e14 0.163154
\(587\) 1.66363e13 0.00985251 0.00492625 0.999988i \(-0.498432\pi\)
0.00492625 + 0.999988i \(0.498432\pi\)
\(588\) −8.68031e13 −0.0509284
\(589\) −2.94850e14 −0.171383
\(590\) 6.24994e13 0.0359907
\(591\) 1.41072e15 0.804838
\(592\) −6.70403e14 −0.378937
\(593\) 3.20402e15 1.79430 0.897148 0.441730i \(-0.145635\pi\)
0.897148 + 0.441730i \(0.145635\pi\)
\(594\) 8.00288e13 0.0444039
\(595\) 2.17857e15 1.19764
\(596\) 1.95604e15 1.06543
\(597\) 1.60708e15 0.867321
\(598\) −3.58267e14 −0.191580
\(599\) 1.72077e15 0.911752 0.455876 0.890043i \(-0.349326\pi\)
0.455876 + 0.890043i \(0.349326\pi\)
\(600\) −2.04666e14 −0.107452
\(601\) −2.39539e15 −1.24614 −0.623069 0.782167i \(-0.714114\pi\)
−0.623069 + 0.782167i \(0.714114\pi\)
\(602\) 2.77759e14 0.143182
\(603\) −3.36015e14 −0.171638
\(604\) −2.72118e15 −1.37738
\(605\) −4.05906e13 −0.0203597
\(606\) −1.72166e14 −0.0855754
\(607\) −3.86178e15 −1.90217 −0.951085 0.308929i \(-0.900029\pi\)
−0.951085 + 0.308929i \(0.900029\pi\)
\(608\) 3.32321e14 0.162214
\(609\) 1.40386e15 0.679091
\(610\) −2.53771e14 −0.121654
\(611\) −3.44418e15 −1.63629
\(612\) −6.45704e14 −0.304019
\(613\) −1.45374e15 −0.678350 −0.339175 0.940723i \(-0.610148\pi\)
−0.339175 + 0.940723i \(0.610148\pi\)
\(614\) −3.78195e14 −0.174900
\(615\) 5.64288e14 0.258635
\(616\) −1.03339e15 −0.469430
\(617\) −7.93563e14 −0.357284 −0.178642 0.983914i \(-0.557170\pi\)
−0.178642 + 0.983914i \(0.557170\pi\)
\(618\) 1.65731e14 0.0739550
\(619\) −1.29098e15 −0.570981 −0.285491 0.958382i \(-0.592157\pi\)
−0.285491 + 0.958382i \(0.592157\pi\)
\(620\) 1.75586e15 0.769724
\(621\) −2.52617e14 −0.109764
\(622\) 3.62050e14 0.155927
\(623\) −6.96563e14 −0.297356
\(624\) 1.65506e15 0.700325
\(625\) −2.96133e15 −1.24207
\(626\) −9.54615e14 −0.396889
\(627\) 3.47427e14 0.143183
\(628\) −3.70343e15 −1.51296
\(629\) −1.07360e15 −0.434776
\(630\) 2.40010e14 0.0963511
\(631\) 6.53217e14 0.259954 0.129977 0.991517i \(-0.458510\pi\)
0.129977 + 0.991517i \(0.458510\pi\)
\(632\) −7.45747e14 −0.294203
\(633\) −2.79211e15 −1.09198
\(634\) 1.31195e14 0.0508657
\(635\) 1.03540e15 0.397972
\(636\) 2.73446e14 0.104198
\(637\) 3.56307e14 0.134604
\(638\) 6.93015e14 0.259555
\(639\) −2.86545e14 −0.106399
\(640\) −2.61012e15 −0.960883
\(641\) 2.04218e15 0.745374 0.372687 0.927957i \(-0.378436\pi\)
0.372687 + 0.927957i \(0.378436\pi\)
\(642\) 2.10112e14 0.0760341
\(643\) 2.99974e15 1.07628 0.538138 0.842857i \(-0.319128\pi\)
0.538138 + 0.842857i \(0.319128\pi\)
\(644\) 1.58559e15 0.564052
\(645\) 1.14405e15 0.403522
\(646\) 1.60527e14 0.0561397
\(647\) −1.39460e14 −0.0483589 −0.0241795 0.999708i \(-0.507697\pi\)
−0.0241795 + 0.999708i \(0.507697\pi\)
\(648\) −1.46347e14 −0.0503177
\(649\) 3.78587e14 0.129068
\(650\) 4.08362e14 0.138045
\(651\) −1.23384e15 −0.413582
\(652\) −8.41509e14 −0.279703
\(653\) 5.44858e14 0.179581 0.0897906 0.995961i \(-0.471380\pi\)
0.0897906 + 0.995961i \(0.471380\pi\)
\(654\) −9.68610e13 −0.0316571
\(655\) 4.06422e15 1.31719
\(656\) 9.86206e14 0.316954
\(657\) −3.17467e14 −0.101179
\(658\) −8.72906e14 −0.275883
\(659\) 5.06140e15 1.58636 0.793179 0.608989i \(-0.208425\pi\)
0.793179 + 0.608989i \(0.208425\pi\)
\(660\) −2.06896e15 −0.643073
\(661\) 1.64713e15 0.507713 0.253857 0.967242i \(-0.418301\pi\)
0.253857 + 0.967242i \(0.418301\pi\)
\(662\) 3.84573e13 0.0117560
\(663\) 2.65047e15 0.803524
\(664\) 4.59021e14 0.138009
\(665\) 1.04195e15 0.310691
\(666\) −1.18278e14 −0.0349780
\(667\) −2.18756e15 −0.641605
\(668\) 3.16946e15 0.921967
\(669\) −1.03051e15 −0.297308
\(670\) −4.97465e14 −0.142348
\(671\) −1.53720e15 −0.436272
\(672\) 1.39064e15 0.391456
\(673\) −1.65542e15 −0.462194 −0.231097 0.972931i \(-0.574232\pi\)
−0.231097 + 0.972931i \(0.574232\pi\)
\(674\) −1.39331e15 −0.385849
\(675\) 2.87939e14 0.0790915
\(676\) −3.75996e15 −1.02442
\(677\) −2.03395e15 −0.549671 −0.274835 0.961491i \(-0.588623\pi\)
−0.274835 + 0.961491i \(0.588623\pi\)
\(678\) −3.88193e14 −0.104060
\(679\) 3.32024e15 0.882847
\(680\) −1.96665e15 −0.518714
\(681\) −2.61965e15 −0.685385
\(682\) −6.09084e14 −0.158075
\(683\) 4.24192e15 1.09207 0.546033 0.837764i \(-0.316137\pi\)
0.546033 + 0.837764i \(0.316137\pi\)
\(684\) −3.08823e14 −0.0788681
\(685\) −6.61683e15 −1.67630
\(686\) −8.77977e14 −0.220648
\(687\) −3.39253e15 −0.845788
\(688\) 1.99946e15 0.494510
\(689\) −1.12244e15 −0.275395
\(690\) −3.73995e14 −0.0910324
\(691\) 1.35658e15 0.327579 0.163789 0.986495i \(-0.447628\pi\)
0.163789 + 0.986495i \(0.447628\pi\)
\(692\) −4.18155e15 −1.00174
\(693\) 1.45385e15 0.345531
\(694\) −1.77318e15 −0.418095
\(695\) −2.07679e14 −0.0485820
\(696\) −1.26730e15 −0.294123
\(697\) 1.57934e15 0.363660
\(698\) 1.77070e14 0.0404520
\(699\) −9.99984e14 −0.226657
\(700\) −1.80729e15 −0.406433
\(701\) 1.74735e15 0.389881 0.194940 0.980815i \(-0.437549\pi\)
0.194940 + 0.980815i \(0.437549\pi\)
\(702\) 2.91999e14 0.0646440
\(703\) −5.13477e14 −0.112789
\(704\) −3.13650e15 −0.683589
\(705\) −3.59538e15 −0.777507
\(706\) −1.90101e15 −0.407905
\(707\) −3.12767e15 −0.665909
\(708\) −3.36521e14 −0.0710934
\(709\) 2.11534e15 0.443430 0.221715 0.975112i \(-0.428835\pi\)
0.221715 + 0.975112i \(0.428835\pi\)
\(710\) −4.24224e14 −0.0882419
\(711\) 1.04917e15 0.216553
\(712\) 6.28806e14 0.128788
\(713\) 1.92262e15 0.390752
\(714\) 6.71746e14 0.135477
\(715\) 8.49261e15 1.69964
\(716\) −8.58660e15 −1.70530
\(717\) −3.54817e15 −0.699276
\(718\) −1.71482e15 −0.335378
\(719\) −6.69755e14 −0.129989 −0.0649945 0.997886i \(-0.520703\pi\)
−0.0649945 + 0.997886i \(0.520703\pi\)
\(720\) 1.72772e15 0.332771
\(721\) 3.01077e15 0.575485
\(722\) −1.15013e15 −0.218169
\(723\) 3.72795e15 0.701794
\(724\) 4.40355e15 0.822699
\(725\) 2.49343e15 0.462315
\(726\) −1.25158e13 −0.00230308
\(727\) 4.65915e15 0.850879 0.425439 0.904987i \(-0.360120\pi\)
0.425439 + 0.904987i \(0.360120\pi\)
\(728\) −3.77052e15 −0.683405
\(729\) 2.05891e14 0.0370370
\(730\) −4.70004e14 −0.0839124
\(731\) 3.20199e15 0.567381
\(732\) 1.36640e15 0.240307
\(733\) 6.21756e15 1.08530 0.542648 0.839961i \(-0.317422\pi\)
0.542648 + 0.839961i \(0.317422\pi\)
\(734\) −8.92023e14 −0.154542
\(735\) 3.71949e14 0.0639592
\(736\) −2.16695e15 −0.369847
\(737\) −3.01337e15 −0.510483
\(738\) 1.73994e14 0.0292567
\(739\) 7.78238e14 0.129888 0.0649439 0.997889i \(-0.479313\pi\)
0.0649439 + 0.997889i \(0.479313\pi\)
\(740\) 3.05780e15 0.506564
\(741\) 1.26765e15 0.208449
\(742\) −2.84475e14 −0.0464325
\(743\) −1.05630e16 −1.71139 −0.855696 0.517479i \(-0.826871\pi\)
−0.855696 + 0.517479i \(0.826871\pi\)
\(744\) 1.11382e15 0.179128
\(745\) −8.38158e15 −1.33803
\(746\) 3.31337e14 0.0525058
\(747\) −6.45783e14 −0.101584
\(748\) −5.79064e15 −0.904207
\(749\) 3.81702e15 0.591663
\(750\) −6.10982e14 −0.0940138
\(751\) −9.17216e14 −0.140105 −0.0700523 0.997543i \(-0.522317\pi\)
−0.0700523 + 0.997543i \(0.522317\pi\)
\(752\) −6.28364e15 −0.952825
\(753\) 1.03222e15 0.155382
\(754\) 2.52859e15 0.377865
\(755\) 1.16602e16 1.72981
\(756\) −1.29231e15 −0.190325
\(757\) −7.57673e15 −1.10778 −0.553891 0.832589i \(-0.686858\pi\)
−0.553891 + 0.832589i \(0.686858\pi\)
\(758\) 6.26039e14 0.0908701
\(759\) −2.26546e15 −0.326457
\(760\) −9.40597e14 −0.134564
\(761\) 4.74339e15 0.673711 0.336855 0.941556i \(-0.390637\pi\)
0.336855 + 0.941556i \(0.390637\pi\)
\(762\) 3.19258e14 0.0450183
\(763\) −1.75963e15 −0.246341
\(764\) −5.31657e15 −0.738955
\(765\) 2.76683e15 0.381807
\(766\) 8.69676e14 0.119151
\(767\) 1.38134e15 0.187900
\(768\) 2.14283e15 0.289402
\(769\) −3.00905e15 −0.403492 −0.201746 0.979438i \(-0.564662\pi\)
−0.201746 + 0.979438i \(0.564662\pi\)
\(770\) 2.15240e15 0.286565
\(771\) 2.59526e15 0.343070
\(772\) −7.85536e15 −1.03103
\(773\) 6.36741e15 0.829805 0.414902 0.909866i \(-0.363816\pi\)
0.414902 + 0.909866i \(0.363816\pi\)
\(774\) 3.52760e14 0.0456461
\(775\) −2.19145e15 −0.281561
\(776\) −2.99727e15 −0.382372
\(777\) −2.14870e15 −0.272183
\(778\) −1.22449e14 −0.0154017
\(779\) 7.55357e14 0.0943401
\(780\) −7.54897e15 −0.936197
\(781\) −2.56972e15 −0.316450
\(782\) −1.04675e15 −0.127998
\(783\) 1.78293e15 0.216493
\(784\) 6.50055e14 0.0783812
\(785\) 1.58691e16 1.90007
\(786\) 1.25317e15 0.149000
\(787\) −6.42132e15 −0.758164 −0.379082 0.925363i \(-0.623760\pi\)
−0.379082 + 0.925363i \(0.623760\pi\)
\(788\) −1.12455e16 −1.31851
\(789\) 2.62709e15 0.305880
\(790\) 1.55328e15 0.179598
\(791\) −7.05214e15 −0.809749
\(792\) −1.31243e15 −0.149654
\(793\) −5.60876e15 −0.635133
\(794\) 1.36882e15 0.153934
\(795\) −1.17171e15 −0.130858
\(796\) −1.28109e16 −1.42088
\(797\) −1.29411e16 −1.42544 −0.712721 0.701448i \(-0.752537\pi\)
−0.712721 + 0.701448i \(0.752537\pi\)
\(798\) 3.21278e14 0.0351451
\(799\) −1.00628e16 −1.09323
\(800\) 2.46995e15 0.266497
\(801\) −8.84650e14 −0.0947966
\(802\) −9.71445e14 −0.103385
\(803\) −2.84703e15 −0.300923
\(804\) 2.67854e15 0.281184
\(805\) −6.79422e15 −0.708373
\(806\) −2.22235e15 −0.230128
\(807\) −4.27079e15 −0.439242
\(808\) 2.82344e15 0.288413
\(809\) 2.18983e15 0.222174 0.111087 0.993811i \(-0.464567\pi\)
0.111087 + 0.993811i \(0.464567\pi\)
\(810\) 3.04818e14 0.0307166
\(811\) 7.41175e15 0.741833 0.370917 0.928666i \(-0.379044\pi\)
0.370917 + 0.928666i \(0.379044\pi\)
\(812\) −1.11908e16 −1.11251
\(813\) −1.91647e15 −0.189236
\(814\) −1.06071e15 −0.104031
\(815\) 3.60585e15 0.351270
\(816\) 4.83558e15 0.467900
\(817\) 1.53143e15 0.147189
\(818\) −2.28642e15 −0.218279
\(819\) 5.30463e15 0.503030
\(820\) −4.49822e15 −0.423705
\(821\) 6.34847e15 0.593994 0.296997 0.954878i \(-0.404015\pi\)
0.296997 + 0.954878i \(0.404015\pi\)
\(822\) −2.04025e15 −0.189622
\(823\) 1.90319e16 1.75704 0.878521 0.477704i \(-0.158531\pi\)
0.878521 + 0.477704i \(0.158531\pi\)
\(824\) −2.71790e15 −0.249250
\(825\) 2.58222e15 0.235232
\(826\) 3.50093e14 0.0316806
\(827\) 9.51689e15 0.855489 0.427745 0.903900i \(-0.359308\pi\)
0.427745 + 0.903900i \(0.359308\pi\)
\(828\) 2.01373e15 0.179819
\(829\) −4.20099e15 −0.372650 −0.186325 0.982488i \(-0.559658\pi\)
−0.186325 + 0.982488i \(0.559658\pi\)
\(830\) −9.56071e14 −0.0842482
\(831\) 7.37479e15 0.645571
\(832\) −1.14441e16 −0.995182
\(833\) 1.04102e15 0.0899313
\(834\) −6.40362e13 −0.00549557
\(835\) −1.35811e16 −1.15787
\(836\) −2.76951e15 −0.234568
\(837\) −1.56700e15 −0.131849
\(838\) 2.60043e15 0.217371
\(839\) 3.02779e15 0.251440 0.125720 0.992066i \(-0.459876\pi\)
0.125720 + 0.992066i \(0.459876\pi\)
\(840\) −3.93604e15 −0.324731
\(841\) 3.23892e15 0.265474
\(842\) −3.68165e15 −0.299796
\(843\) −3.70569e14 −0.0299790
\(844\) 2.22573e16 1.78891
\(845\) 1.61114e16 1.28653
\(846\) −1.10861e15 −0.0879512
\(847\) −2.27370e14 −0.0179215
\(848\) −2.04780e15 −0.160365
\(849\) 1.41740e16 1.10281
\(850\) 1.19311e15 0.0922305
\(851\) 3.34821e15 0.257158
\(852\) 2.28419e15 0.174307
\(853\) −2.17603e16 −1.64985 −0.824926 0.565241i \(-0.808783\pi\)
−0.824926 + 0.565241i \(0.808783\pi\)
\(854\) −1.42151e15 −0.107085
\(855\) 1.32330e15 0.0990478
\(856\) −3.44573e15 −0.256257
\(857\) 1.58468e15 0.117097 0.0585485 0.998285i \(-0.481353\pi\)
0.0585485 + 0.998285i \(0.481353\pi\)
\(858\) 2.61864e15 0.192263
\(859\) 2.23915e16 1.63351 0.816754 0.576986i \(-0.195771\pi\)
0.816754 + 0.576986i \(0.195771\pi\)
\(860\) −9.11979e15 −0.661063
\(861\) 3.16088e15 0.227662
\(862\) −2.43807e15 −0.174484
\(863\) 1.84795e16 1.31411 0.657055 0.753843i \(-0.271802\pi\)
0.657055 + 0.753843i \(0.271802\pi\)
\(864\) 1.76614e15 0.124796
\(865\) 1.79178e16 1.25805
\(866\) 2.23223e15 0.155737
\(867\) −5.84217e14 −0.0405013
\(868\) 9.83550e15 0.677545
\(869\) 9.40891e15 0.644066
\(870\) 2.63960e15 0.179549
\(871\) −1.09948e16 −0.743170
\(872\) 1.58847e15 0.106694
\(873\) 4.21678e15 0.281451
\(874\) −5.00631e14 −0.0332051
\(875\) −1.10995e16 −0.731573
\(876\) 2.53068e15 0.165754
\(877\) 2.40887e16 1.56789 0.783945 0.620830i \(-0.213204\pi\)
0.783945 + 0.620830i \(0.213204\pi\)
\(878\) −4.60435e15 −0.297817
\(879\) 6.29679e15 0.404744
\(880\) 1.54941e16 0.989719
\(881\) 1.85528e16 1.17772 0.588860 0.808235i \(-0.299577\pi\)
0.588860 + 0.808235i \(0.299577\pi\)
\(882\) 1.14688e14 0.00723503
\(883\) −2.24230e16 −1.40575 −0.702877 0.711311i \(-0.748102\pi\)
−0.702877 + 0.711311i \(0.748102\pi\)
\(884\) −2.11282e16 −1.31636
\(885\) 1.44198e15 0.0892838
\(886\) −2.45253e15 −0.150914
\(887\) −1.76236e16 −1.07774 −0.538870 0.842389i \(-0.681149\pi\)
−0.538870 + 0.842389i \(0.681149\pi\)
\(888\) 1.93969e15 0.117886
\(889\) 5.79983e15 0.350312
\(890\) −1.30971e15 −0.0786194
\(891\) 1.84642e15 0.110155
\(892\) 8.21466e15 0.487061
\(893\) −4.81278e15 −0.283604
\(894\) −2.58440e15 −0.151357
\(895\) 3.67934e16 2.14162
\(896\) −1.46207e16 −0.845812
\(897\) −8.26593e15 −0.475262
\(898\) −3.37036e13 −0.00192600
\(899\) −1.35695e16 −0.770703
\(900\) −2.29530e15 −0.129570
\(901\) −3.27941e15 −0.183996
\(902\) 1.56037e15 0.0870145
\(903\) 6.40844e15 0.355197
\(904\) 6.36616e15 0.350712
\(905\) −1.88691e16 −1.03320
\(906\) 3.59534e15 0.195675
\(907\) −2.58341e16 −1.39750 −0.698752 0.715364i \(-0.746261\pi\)
−0.698752 + 0.715364i \(0.746261\pi\)
\(908\) 2.08825e16 1.12282
\(909\) −3.97222e15 −0.212291
\(910\) 7.85342e15 0.417187
\(911\) −7.39276e14 −0.0390351 −0.0195176 0.999810i \(-0.506213\pi\)
−0.0195176 + 0.999810i \(0.506213\pi\)
\(912\) 2.31273e15 0.121382
\(913\) −5.79135e15 −0.302128
\(914\) −6.00890e14 −0.0311595
\(915\) −5.85499e15 −0.301794
\(916\) 2.70435e16 1.38560
\(917\) 2.27659e16 1.15945
\(918\) 8.53131e14 0.0431898
\(919\) 6.32240e15 0.318161 0.159080 0.987266i \(-0.449147\pi\)
0.159080 + 0.987266i \(0.449147\pi\)
\(920\) 6.13333e15 0.306805
\(921\) −8.72571e15 −0.433883
\(922\) 5.40469e15 0.267147
\(923\) −9.37608e15 −0.460693
\(924\) −1.15893e16 −0.566061
\(925\) −3.81637e15 −0.185298
\(926\) 1.24531e15 0.0601059
\(927\) 3.82375e15 0.183464
\(928\) 1.52940e16 0.729470
\(929\) 1.11302e15 0.0527735 0.0263868 0.999652i \(-0.491600\pi\)
0.0263868 + 0.999652i \(0.491600\pi\)
\(930\) −2.31991e15 −0.109349
\(931\) 4.97892e14 0.0233298
\(932\) 7.97136e15 0.371317
\(933\) 8.35321e15 0.386816
\(934\) 6.20872e15 0.285821
\(935\) 2.48128e16 1.13556
\(936\) −4.78864e15 −0.217869
\(937\) −2.97929e15 −0.134755 −0.0673774 0.997728i \(-0.521463\pi\)
−0.0673774 + 0.997728i \(0.521463\pi\)
\(938\) −2.78657e15 −0.125301
\(939\) −2.20248e16 −0.984582
\(940\) 2.86605e16 1.27374
\(941\) −7.29885e15 −0.322487 −0.161243 0.986915i \(-0.551550\pi\)
−0.161243 + 0.986915i \(0.551550\pi\)
\(942\) 4.89313e15 0.214935
\(943\) −4.92543e15 −0.215095
\(944\) 2.52015e15 0.109416
\(945\) 5.53751e15 0.239023
\(946\) 3.16353e15 0.135760
\(947\) −1.47142e16 −0.627784 −0.313892 0.949459i \(-0.601633\pi\)
−0.313892 + 0.949459i \(0.601633\pi\)
\(948\) −8.36345e15 −0.354764
\(949\) −1.03879e16 −0.438090
\(950\) 5.70631e14 0.0239263
\(951\) 3.02692e15 0.126185
\(952\) −1.10163e16 −0.456595
\(953\) −2.56522e16 −1.05709 −0.528547 0.848904i \(-0.677263\pi\)
−0.528547 + 0.848904i \(0.677263\pi\)
\(954\) −3.61289e14 −0.0148026
\(955\) 2.27814e16 0.928028
\(956\) 2.82842e16 1.14558
\(957\) 1.59892e16 0.643890
\(958\) −2.53929e15 −0.101672
\(959\) −3.70644e16 −1.47555
\(960\) −1.19465e16 −0.472877
\(961\) −1.34824e16 −0.530624
\(962\) −3.87019e15 −0.151450
\(963\) 4.84770e15 0.188621
\(964\) −2.97173e16 −1.14970
\(965\) 3.36601e16 1.29484
\(966\) −2.09495e15 −0.0801308
\(967\) −2.49894e16 −0.950409 −0.475205 0.879875i \(-0.657626\pi\)
−0.475205 + 0.879875i \(0.657626\pi\)
\(968\) 2.05253e14 0.00776202
\(969\) 3.70368e15 0.139268
\(970\) 6.24286e15 0.233421
\(971\) 5.05666e16 1.88000 0.940000 0.341174i \(-0.110825\pi\)
0.940000 + 0.341174i \(0.110825\pi\)
\(972\) −1.64126e15 −0.0606754
\(973\) −1.16332e15 −0.0427640
\(974\) 7.49326e15 0.273903
\(975\) 9.42170e15 0.342455
\(976\) −1.02328e16 −0.369844
\(977\) 6.57844e15 0.236430 0.118215 0.992988i \(-0.462283\pi\)
0.118215 + 0.992988i \(0.462283\pi\)
\(978\) 1.11184e15 0.0397354
\(979\) −7.93350e15 −0.281942
\(980\) −2.96499e15 −0.104780
\(981\) −2.23477e15 −0.0785333
\(982\) 8.40577e15 0.293741
\(983\) 9.91690e15 0.344613 0.172306 0.985043i \(-0.444878\pi\)
0.172306 + 0.985043i \(0.444878\pi\)
\(984\) −2.85341e15 −0.0986033
\(985\) 4.81867e16 1.65588
\(986\) 7.38776e15 0.252458
\(987\) −2.01396e16 −0.684396
\(988\) −1.01051e16 −0.341488
\(989\) −9.98594e15 −0.335590
\(990\) 2.73359e15 0.0913567
\(991\) −2.18032e15 −0.0724630 −0.0362315 0.999343i \(-0.511535\pi\)
−0.0362315 + 0.999343i \(0.511535\pi\)
\(992\) −1.34417e16 −0.444264
\(993\) 8.87286e14 0.0291637
\(994\) −2.37631e15 −0.0776744
\(995\) 5.48942e16 1.78443
\(996\) 5.14785e15 0.166418
\(997\) 1.94934e16 0.626707 0.313354 0.949636i \(-0.398547\pi\)
0.313354 + 0.949636i \(0.398547\pi\)
\(998\) −3.23017e15 −0.103278
\(999\) −2.72890e15 −0.0867716
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 177.12.a.d.1.15 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.d.1.15 28 1.1 even 1 trivial