Properties

Label 177.10.a.a.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-29.8118 q^{2} +81.0000 q^{3} +376.741 q^{4} +1198.15 q^{5} -2414.75 q^{6} +3753.28 q^{7} +4032.31 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-29.8118 q^{2} +81.0000 q^{3} +376.741 q^{4} +1198.15 q^{5} -2414.75 q^{6} +3753.28 q^{7} +4032.31 q^{8} +6561.00 q^{9} -35719.0 q^{10} +57581.4 q^{11} +30516.0 q^{12} -96612.2 q^{13} -111892. q^{14} +97050.2 q^{15} -313102. q^{16} +199617. q^{17} -195595. q^{18} -341838. q^{19} +451392. q^{20} +304015. q^{21} -1.71660e6 q^{22} -730028. q^{23} +326617. q^{24} -517560. q^{25} +2.88018e6 q^{26} +531441. q^{27} +1.41401e6 q^{28} -6.39864e6 q^{29} -2.89324e6 q^{30} -5.53055e6 q^{31} +7.26957e6 q^{32} +4.66410e6 q^{33} -5.95092e6 q^{34} +4.49699e6 q^{35} +2.47180e6 q^{36} -1.72095e7 q^{37} +1.01908e7 q^{38} -7.82559e6 q^{39} +4.83131e6 q^{40} -3.16553e7 q^{41} -9.06323e6 q^{42} +1.31337e7 q^{43} +2.16933e7 q^{44} +7.86107e6 q^{45} +2.17634e7 q^{46} -1.21817e7 q^{47} -2.53612e7 q^{48} -2.62665e7 q^{49} +1.54294e7 q^{50} +1.61689e7 q^{51} -3.63978e7 q^{52} +3.91644e7 q^{53} -1.58432e7 q^{54} +6.89912e7 q^{55} +1.51344e7 q^{56} -2.76889e7 q^{57} +1.90755e8 q^{58} +1.21174e7 q^{59} +3.65628e7 q^{60} -4.88904e7 q^{61} +1.64875e8 q^{62} +2.46252e7 q^{63} -5.64106e7 q^{64} -1.15756e8 q^{65} -1.39045e8 q^{66} +4.81274e7 q^{67} +7.52037e7 q^{68} -5.91322e7 q^{69} -1.34063e8 q^{70} -1.07918e7 q^{71} +2.64560e7 q^{72} +3.67275e8 q^{73} +5.13046e8 q^{74} -4.19224e7 q^{75} -1.28784e8 q^{76} +2.16119e8 q^{77} +2.33295e8 q^{78} +3.81830e8 q^{79} -3.75143e8 q^{80} +4.30467e7 q^{81} +9.43701e8 q^{82} -3.92397e8 q^{83} +1.14535e8 q^{84} +2.39171e8 q^{85} -3.91537e8 q^{86} -5.18290e8 q^{87} +2.32186e8 q^{88} -2.06771e8 q^{89} -2.34352e8 q^{90} -3.62612e8 q^{91} -2.75031e8 q^{92} -4.47974e8 q^{93} +3.63159e8 q^{94} -4.09573e8 q^{95} +5.88835e8 q^{96} -1.55606e9 q^{97} +7.83051e8 q^{98} +3.77792e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −29.8118 −1.31751 −0.658753 0.752359i \(-0.728916\pi\)
−0.658753 + 0.752359i \(0.728916\pi\)
\(3\) 81.0000 0.577350
\(4\) 376.741 0.735822
\(5\) 1198.15 0.857327 0.428663 0.903464i \(-0.358985\pi\)
0.428663 + 0.903464i \(0.358985\pi\)
\(6\) −2414.75 −0.760662
\(7\) 3753.28 0.590839 0.295420 0.955368i \(-0.404541\pi\)
0.295420 + 0.955368i \(0.404541\pi\)
\(8\) 4032.31 0.348056
\(9\) 6561.00 0.333333
\(10\) −35719.0 −1.12953
\(11\) 57581.4 1.18581 0.592905 0.805272i \(-0.297981\pi\)
0.592905 + 0.805272i \(0.297981\pi\)
\(12\) 30516.0 0.424827
\(13\) −96612.2 −0.938182 −0.469091 0.883150i \(-0.655418\pi\)
−0.469091 + 0.883150i \(0.655418\pi\)
\(14\) −111892. −0.778434
\(15\) 97050.2 0.494978
\(16\) −313102. −1.19439
\(17\) 199617. 0.579664 0.289832 0.957078i \(-0.406401\pi\)
0.289832 + 0.957078i \(0.406401\pi\)
\(18\) −195595. −0.439169
\(19\) −341838. −0.601768 −0.300884 0.953661i \(-0.597282\pi\)
−0.300884 + 0.953661i \(0.597282\pi\)
\(20\) 451392. 0.630840
\(21\) 304015. 0.341121
\(22\) −1.71660e6 −1.56231
\(23\) −730028. −0.543956 −0.271978 0.962303i \(-0.587678\pi\)
−0.271978 + 0.962303i \(0.587678\pi\)
\(24\) 326617. 0.200950
\(25\) −517560. −0.264991
\(26\) 2.88018e6 1.23606
\(27\) 531441. 0.192450
\(28\) 1.41401e6 0.434753
\(29\) −6.39864e6 −1.67995 −0.839976 0.542623i \(-0.817431\pi\)
−0.839976 + 0.542623i \(0.817431\pi\)
\(30\) −2.89324e6 −0.652136
\(31\) −5.53055e6 −1.07557 −0.537787 0.843081i \(-0.680740\pi\)
−0.537787 + 0.843081i \(0.680740\pi\)
\(32\) 7.26957e6 1.22556
\(33\) 4.66410e6 0.684628
\(34\) −5.95092e6 −0.763711
\(35\) 4.49699e6 0.506542
\(36\) 2.47180e6 0.245274
\(37\) −1.72095e7 −1.50960 −0.754798 0.655958i \(-0.772265\pi\)
−0.754798 + 0.655958i \(0.772265\pi\)
\(38\) 1.01908e7 0.792832
\(39\) −7.82559e6 −0.541660
\(40\) 4.83131e6 0.298398
\(41\) −3.16553e7 −1.74952 −0.874761 0.484555i \(-0.838982\pi\)
−0.874761 + 0.484555i \(0.838982\pi\)
\(42\) −9.06323e6 −0.449429
\(43\) 1.31337e7 0.585838 0.292919 0.956137i \(-0.405373\pi\)
0.292919 + 0.956137i \(0.405373\pi\)
\(44\) 2.16933e7 0.872546
\(45\) 7.86107e6 0.285776
\(46\) 2.17634e7 0.716666
\(47\) −1.21817e7 −0.364140 −0.182070 0.983286i \(-0.558280\pi\)
−0.182070 + 0.983286i \(0.558280\pi\)
\(48\) −2.53612e7 −0.689580
\(49\) −2.62665e7 −0.650909
\(50\) 1.54294e7 0.349127
\(51\) 1.61689e7 0.334669
\(52\) −3.63978e7 −0.690335
\(53\) 3.91644e7 0.681789 0.340894 0.940102i \(-0.389270\pi\)
0.340894 + 0.940102i \(0.389270\pi\)
\(54\) −1.58432e7 −0.253554
\(55\) 6.89912e7 1.01663
\(56\) 1.51344e7 0.205645
\(57\) −2.76889e7 −0.347431
\(58\) 1.90755e8 2.21335
\(59\) 1.21174e7 0.130189
\(60\) 3.65628e7 0.364216
\(61\) −4.88904e7 −0.452105 −0.226052 0.974115i \(-0.572582\pi\)
−0.226052 + 0.974115i \(0.572582\pi\)
\(62\) 1.64875e8 1.41708
\(63\) 2.46252e7 0.196946
\(64\) −5.64106e7 −0.420291
\(65\) −1.15756e8 −0.804329
\(66\) −1.39045e8 −0.902002
\(67\) 4.81274e7 0.291780 0.145890 0.989301i \(-0.453395\pi\)
0.145890 + 0.989301i \(0.453395\pi\)
\(68\) 7.52037e7 0.426530
\(69\) −5.91322e7 −0.314053
\(70\) −1.34063e8 −0.667373
\(71\) −1.07918e7 −0.0504001 −0.0252000 0.999682i \(-0.508022\pi\)
−0.0252000 + 0.999682i \(0.508022\pi\)
\(72\) 2.64560e7 0.116019
\(73\) 3.67275e8 1.51369 0.756847 0.653592i \(-0.226739\pi\)
0.756847 + 0.653592i \(0.226739\pi\)
\(74\) 5.13046e8 1.98890
\(75\) −4.19224e7 −0.152992
\(76\) −1.28784e8 −0.442794
\(77\) 2.16119e8 0.700624
\(78\) 2.33295e8 0.713640
\(79\) 3.81830e8 1.10293 0.551466 0.834198i \(-0.314069\pi\)
0.551466 + 0.834198i \(0.314069\pi\)
\(80\) −3.75143e8 −1.02398
\(81\) 4.30467e7 0.111111
\(82\) 9.43701e8 2.30501
\(83\) −3.92397e8 −0.907557 −0.453778 0.891115i \(-0.649924\pi\)
−0.453778 + 0.891115i \(0.649924\pi\)
\(84\) 1.14535e8 0.251005
\(85\) 2.39171e8 0.496961
\(86\) −3.91537e8 −0.771845
\(87\) −5.18290e8 −0.969921
\(88\) 2.32186e8 0.412728
\(89\) −2.06771e8 −0.349329 −0.174665 0.984628i \(-0.555884\pi\)
−0.174665 + 0.984628i \(0.555884\pi\)
\(90\) −2.34352e8 −0.376511
\(91\) −3.62612e8 −0.554315
\(92\) −2.75031e8 −0.400255
\(93\) −4.47974e8 −0.620983
\(94\) 3.63159e8 0.479757
\(95\) −4.09573e8 −0.515911
\(96\) 5.88835e8 0.707576
\(97\) −1.55606e9 −1.78465 −0.892324 0.451396i \(-0.850926\pi\)
−0.892324 + 0.451396i \(0.850926\pi\)
\(98\) 7.83051e8 0.857576
\(99\) 3.77792e8 0.395270
\(100\) −1.94986e8 −0.194986
\(101\) 3.34551e8 0.319901 0.159951 0.987125i \(-0.448867\pi\)
0.159951 + 0.987125i \(0.448867\pi\)
\(102\) −4.82024e8 −0.440929
\(103\) −5.05827e8 −0.442827 −0.221414 0.975180i \(-0.571067\pi\)
−0.221414 + 0.975180i \(0.571067\pi\)
\(104\) −3.89570e8 −0.326540
\(105\) 3.64256e8 0.292452
\(106\) −1.16756e9 −0.898261
\(107\) 1.20865e8 0.0891399 0.0445699 0.999006i \(-0.485808\pi\)
0.0445699 + 0.999006i \(0.485808\pi\)
\(108\) 2.00216e8 0.141609
\(109\) −4.83140e8 −0.327834 −0.163917 0.986474i \(-0.552413\pi\)
−0.163917 + 0.986474i \(0.552413\pi\)
\(110\) −2.05675e9 −1.33941
\(111\) −1.39397e9 −0.871565
\(112\) −1.17516e9 −0.705691
\(113\) 2.71907e8 0.156880 0.0784399 0.996919i \(-0.475006\pi\)
0.0784399 + 0.996919i \(0.475006\pi\)
\(114\) 8.25453e8 0.457742
\(115\) −8.74683e8 −0.466348
\(116\) −2.41063e9 −1.23615
\(117\) −6.33873e8 −0.312727
\(118\) −3.61240e8 −0.171525
\(119\) 7.49216e8 0.342488
\(120\) 3.91336e8 0.172280
\(121\) 9.57675e8 0.406148
\(122\) 1.45751e9 0.595651
\(123\) −2.56408e9 −1.01009
\(124\) −2.08358e9 −0.791432
\(125\) −2.96025e9 −1.08451
\(126\) −7.34122e8 −0.259478
\(127\) 3.84542e9 1.31168 0.655839 0.754901i \(-0.272315\pi\)
0.655839 + 0.754901i \(0.272315\pi\)
\(128\) −2.04032e9 −0.671821
\(129\) 1.06383e9 0.338234
\(130\) 3.45089e9 1.05971
\(131\) 1.21601e9 0.360759 0.180379 0.983597i \(-0.442267\pi\)
0.180379 + 0.983597i \(0.442267\pi\)
\(132\) 1.75716e9 0.503765
\(133\) −1.28301e9 −0.355548
\(134\) −1.43476e9 −0.384422
\(135\) 6.36746e8 0.164993
\(136\) 8.04916e8 0.201755
\(137\) −1.94951e9 −0.472805 −0.236403 0.971655i \(-0.575968\pi\)
−0.236403 + 0.971655i \(0.575968\pi\)
\(138\) 1.76284e9 0.413767
\(139\) −5.65775e9 −1.28552 −0.642758 0.766070i \(-0.722210\pi\)
−0.642758 + 0.766070i \(0.722210\pi\)
\(140\) 1.69420e9 0.372725
\(141\) −9.86721e8 −0.210237
\(142\) 3.21722e8 0.0664024
\(143\) −5.56307e9 −1.11251
\(144\) −2.05426e9 −0.398129
\(145\) −7.66654e9 −1.44027
\(146\) −1.09491e10 −1.99430
\(147\) −2.12759e9 −0.375802
\(148\) −6.48352e9 −1.11079
\(149\) −4.00709e9 −0.666025 −0.333013 0.942922i \(-0.608065\pi\)
−0.333013 + 0.942922i \(0.608065\pi\)
\(150\) 1.24978e9 0.201569
\(151\) −5.01208e9 −0.784552 −0.392276 0.919848i \(-0.628312\pi\)
−0.392276 + 0.919848i \(0.628312\pi\)
\(152\) −1.37840e9 −0.209449
\(153\) 1.30968e9 0.193221
\(154\) −6.44289e9 −0.923076
\(155\) −6.62643e9 −0.922119
\(156\) −2.94822e9 −0.398565
\(157\) −2.10960e9 −0.277109 −0.138555 0.990355i \(-0.544246\pi\)
−0.138555 + 0.990355i \(0.544246\pi\)
\(158\) −1.13830e10 −1.45312
\(159\) 3.17231e9 0.393631
\(160\) 8.71004e9 1.05070
\(161\) −2.74000e9 −0.321391
\(162\) −1.28330e9 −0.146390
\(163\) 9.54943e9 1.05958 0.529789 0.848129i \(-0.322271\pi\)
0.529789 + 0.848129i \(0.322271\pi\)
\(164\) −1.19259e10 −1.28734
\(165\) 5.58829e9 0.586950
\(166\) 1.16980e10 1.19571
\(167\) 2.24868e9 0.223720 0.111860 0.993724i \(-0.464319\pi\)
0.111860 + 0.993724i \(0.464319\pi\)
\(168\) 1.22588e9 0.118729
\(169\) −1.27057e9 −0.119815
\(170\) −7.13010e9 −0.654750
\(171\) −2.24280e9 −0.200589
\(172\) 4.94799e9 0.431073
\(173\) −1.94978e10 −1.65492 −0.827461 0.561523i \(-0.810216\pi\)
−0.827461 + 0.561523i \(0.810216\pi\)
\(174\) 1.54511e10 1.27788
\(175\) −1.94255e9 −0.156567
\(176\) −1.80288e10 −1.41632
\(177\) 9.81506e8 0.0751646
\(178\) 6.16421e9 0.460244
\(179\) 8.88715e9 0.647029 0.323515 0.946223i \(-0.395136\pi\)
0.323515 + 0.946223i \(0.395136\pi\)
\(180\) 2.96159e9 0.210280
\(181\) −2.18779e9 −0.151514 −0.0757569 0.997126i \(-0.524137\pi\)
−0.0757569 + 0.997126i \(0.524137\pi\)
\(182\) 1.08101e10 0.730313
\(183\) −3.96012e9 −0.261023
\(184\) −2.94370e9 −0.189327
\(185\) −2.06196e10 −1.29422
\(186\) 1.33549e10 0.818149
\(187\) 1.14942e10 0.687372
\(188\) −4.58936e9 −0.267943
\(189\) 1.99465e9 0.113707
\(190\) 1.22101e10 0.679716
\(191\) 1.59262e10 0.865889 0.432945 0.901420i \(-0.357475\pi\)
0.432945 + 0.901420i \(0.357475\pi\)
\(192\) −4.56926e9 −0.242655
\(193\) 2.85154e10 1.47935 0.739676 0.672963i \(-0.234979\pi\)
0.739676 + 0.672963i \(0.234979\pi\)
\(194\) 4.63888e10 2.35128
\(195\) −9.37624e9 −0.464379
\(196\) −9.89568e9 −0.478953
\(197\) −1.07158e10 −0.506904 −0.253452 0.967348i \(-0.581566\pi\)
−0.253452 + 0.967348i \(0.581566\pi\)
\(198\) −1.12626e10 −0.520771
\(199\) 1.84571e10 0.834306 0.417153 0.908836i \(-0.363028\pi\)
0.417153 + 0.908836i \(0.363028\pi\)
\(200\) −2.08696e9 −0.0922316
\(201\) 3.89832e9 0.168459
\(202\) −9.97355e9 −0.421472
\(203\) −2.40159e10 −0.992582
\(204\) 6.09150e9 0.246257
\(205\) −3.79278e10 −1.49991
\(206\) 1.50796e10 0.583428
\(207\) −4.78971e9 −0.181319
\(208\) 3.02494e10 1.12055
\(209\) −1.96835e10 −0.713583
\(210\) −1.08591e10 −0.385308
\(211\) 5.31574e10 1.84626 0.923129 0.384491i \(-0.125623\pi\)
0.923129 + 0.384491i \(0.125623\pi\)
\(212\) 1.47548e10 0.501675
\(213\) −8.74135e8 −0.0290985
\(214\) −3.60319e9 −0.117442
\(215\) 1.57361e10 0.502255
\(216\) 2.14293e9 0.0669834
\(217\) −2.07577e10 −0.635492
\(218\) 1.44032e10 0.431923
\(219\) 2.97492e10 0.873932
\(220\) 2.59918e10 0.748057
\(221\) −1.92854e10 −0.543830
\(222\) 4.15567e10 1.14829
\(223\) −3.56353e10 −0.964958 −0.482479 0.875908i \(-0.660263\pi\)
−0.482479 + 0.875908i \(0.660263\pi\)
\(224\) 2.72847e10 0.724108
\(225\) −3.39571e9 −0.0883302
\(226\) −8.10602e9 −0.206690
\(227\) 3.84790e10 0.961851 0.480925 0.876762i \(-0.340301\pi\)
0.480925 + 0.876762i \(0.340301\pi\)
\(228\) −1.04315e10 −0.255647
\(229\) 3.71856e10 0.893543 0.446772 0.894648i \(-0.352574\pi\)
0.446772 + 0.894648i \(0.352574\pi\)
\(230\) 2.60758e10 0.614417
\(231\) 1.75056e10 0.404505
\(232\) −2.58013e10 −0.584717
\(233\) −1.16087e10 −0.258037 −0.129019 0.991642i \(-0.541183\pi\)
−0.129019 + 0.991642i \(0.541183\pi\)
\(234\) 1.88969e10 0.412020
\(235\) −1.45956e10 −0.312187
\(236\) 4.56511e9 0.0957959
\(237\) 3.09283e10 0.636778
\(238\) −2.23354e10 −0.451230
\(239\) −4.35010e10 −0.862401 −0.431200 0.902256i \(-0.641910\pi\)
−0.431200 + 0.902256i \(0.641910\pi\)
\(240\) −3.03866e10 −0.591196
\(241\) 9.88603e10 1.88775 0.943876 0.330300i \(-0.107150\pi\)
0.943876 + 0.330300i \(0.107150\pi\)
\(242\) −2.85500e10 −0.535102
\(243\) 3.48678e9 0.0641500
\(244\) −1.84190e10 −0.332669
\(245\) −3.14712e10 −0.558042
\(246\) 7.64398e10 1.33080
\(247\) 3.30257e10 0.564567
\(248\) −2.23009e10 −0.374360
\(249\) −3.17841e10 −0.523978
\(250\) 8.82503e10 1.42885
\(251\) −2.80288e10 −0.445731 −0.222866 0.974849i \(-0.571541\pi\)
−0.222866 + 0.974849i \(0.571541\pi\)
\(252\) 9.27734e9 0.144918
\(253\) −4.20361e10 −0.645030
\(254\) −1.14639e11 −1.72814
\(255\) 1.93728e10 0.286921
\(256\) 8.97077e10 1.30542
\(257\) 1.25678e11 1.79705 0.898525 0.438921i \(-0.144639\pi\)
0.898525 + 0.438921i \(0.144639\pi\)
\(258\) −3.17145e10 −0.445625
\(259\) −6.45920e10 −0.891928
\(260\) −4.36100e10 −0.591843
\(261\) −4.19815e10 −0.559984
\(262\) −3.62514e10 −0.475302
\(263\) 4.88379e10 0.629443 0.314721 0.949184i \(-0.398089\pi\)
0.314721 + 0.949184i \(0.398089\pi\)
\(264\) 1.88071e10 0.238289
\(265\) 4.69248e10 0.584516
\(266\) 3.82488e10 0.468437
\(267\) −1.67485e10 −0.201685
\(268\) 1.81315e10 0.214698
\(269\) −1.30250e11 −1.51668 −0.758338 0.651862i \(-0.773988\pi\)
−0.758338 + 0.651862i \(0.773988\pi\)
\(270\) −1.89825e10 −0.217379
\(271\) −1.48630e11 −1.67396 −0.836981 0.547232i \(-0.815682\pi\)
−0.836981 + 0.547232i \(0.815682\pi\)
\(272\) −6.25003e10 −0.692344
\(273\) −2.93716e10 −0.320034
\(274\) 5.81183e10 0.622924
\(275\) −2.98019e10 −0.314229
\(276\) −2.22775e10 −0.231087
\(277\) −7.44131e10 −0.759435 −0.379717 0.925103i \(-0.623979\pi\)
−0.379717 + 0.925103i \(0.623979\pi\)
\(278\) 1.68668e11 1.69367
\(279\) −3.62859e10 −0.358525
\(280\) 1.81333e10 0.176305
\(281\) −7.52263e10 −0.719766 −0.359883 0.932997i \(-0.617183\pi\)
−0.359883 + 0.932997i \(0.617183\pi\)
\(282\) 2.94159e10 0.276988
\(283\) 1.70354e11 1.57875 0.789376 0.613910i \(-0.210404\pi\)
0.789376 + 0.613910i \(0.210404\pi\)
\(284\) −4.06571e9 −0.0370855
\(285\) −3.31754e10 −0.297862
\(286\) 1.65845e11 1.46573
\(287\) −1.18811e11 −1.03369
\(288\) 4.76956e10 0.408519
\(289\) −7.87411e10 −0.663990
\(290\) 2.28553e11 1.89756
\(291\) −1.26041e11 −1.03037
\(292\) 1.38367e11 1.11381
\(293\) −2.21986e11 −1.75963 −0.879817 0.475313i \(-0.842335\pi\)
−0.879817 + 0.475313i \(0.842335\pi\)
\(294\) 6.34271e10 0.495122
\(295\) 1.45184e10 0.111614
\(296\) −6.93940e10 −0.525423
\(297\) 3.06011e10 0.228209
\(298\) 1.19458e11 0.877493
\(299\) 7.05296e10 0.510330
\(300\) −1.57939e10 −0.112575
\(301\) 4.92942e10 0.346136
\(302\) 1.49419e11 1.03365
\(303\) 2.70986e10 0.184695
\(304\) 1.07030e11 0.718744
\(305\) −5.85781e10 −0.387602
\(306\) −3.90440e10 −0.254570
\(307\) 9.40822e10 0.604484 0.302242 0.953231i \(-0.402265\pi\)
0.302242 + 0.953231i \(0.402265\pi\)
\(308\) 8.14209e10 0.515535
\(309\) −4.09720e10 −0.255667
\(310\) 1.97545e11 1.21490
\(311\) −1.49871e11 −0.908442 −0.454221 0.890889i \(-0.650082\pi\)
−0.454221 + 0.890889i \(0.650082\pi\)
\(312\) −3.15552e10 −0.188528
\(313\) 2.84656e9 0.0167637 0.00838187 0.999965i \(-0.497332\pi\)
0.00838187 + 0.999965i \(0.497332\pi\)
\(314\) 6.28908e10 0.365093
\(315\) 2.95048e10 0.168847
\(316\) 1.43851e11 0.811562
\(317\) 2.45570e11 1.36587 0.682935 0.730479i \(-0.260703\pi\)
0.682935 + 0.730479i \(0.260703\pi\)
\(318\) −9.45723e10 −0.518611
\(319\) −3.68443e11 −1.99211
\(320\) −6.75884e10 −0.360327
\(321\) 9.79003e9 0.0514649
\(322\) 8.16841e10 0.423434
\(323\) −6.82365e10 −0.348823
\(324\) 1.62175e10 0.0817580
\(325\) 5.00026e10 0.248610
\(326\) −2.84685e11 −1.39600
\(327\) −3.91343e10 −0.189275
\(328\) −1.27644e11 −0.608931
\(329\) −4.57214e10 −0.215148
\(330\) −1.66597e11 −0.773310
\(331\) −2.49653e11 −1.14317 −0.571585 0.820543i \(-0.693671\pi\)
−0.571585 + 0.820543i \(0.693671\pi\)
\(332\) −1.47832e11 −0.667800
\(333\) −1.12912e11 −0.503198
\(334\) −6.70372e10 −0.294752
\(335\) 5.76638e10 0.250151
\(336\) −9.51877e10 −0.407431
\(337\) 6.41280e10 0.270840 0.135420 0.990788i \(-0.456762\pi\)
0.135420 + 0.990788i \(0.456762\pi\)
\(338\) 3.78781e10 0.157857
\(339\) 2.20245e10 0.0905746
\(340\) 9.01054e10 0.365675
\(341\) −3.18457e11 −1.27543
\(342\) 6.68617e10 0.264277
\(343\) −2.50044e11 −0.975422
\(344\) 5.29590e10 0.203904
\(345\) −7.08493e10 −0.269246
\(346\) 5.81263e11 2.18037
\(347\) −3.30945e11 −1.22539 −0.612693 0.790321i \(-0.709914\pi\)
−0.612693 + 0.790321i \(0.709914\pi\)
\(348\) −1.95261e11 −0.713689
\(349\) 2.96053e11 1.06821 0.534103 0.845419i \(-0.320649\pi\)
0.534103 + 0.845419i \(0.320649\pi\)
\(350\) 5.79107e10 0.206278
\(351\) −5.13437e10 −0.180553
\(352\) 4.18592e11 1.45328
\(353\) 4.89924e11 1.67936 0.839678 0.543084i \(-0.182744\pi\)
0.839678 + 0.543084i \(0.182744\pi\)
\(354\) −2.92604e10 −0.0990298
\(355\) −1.29302e10 −0.0432093
\(356\) −7.78992e10 −0.257044
\(357\) 6.06865e10 0.197736
\(358\) −2.64942e11 −0.852465
\(359\) 3.30923e10 0.105148 0.0525742 0.998617i \(-0.483257\pi\)
0.0525742 + 0.998617i \(0.483257\pi\)
\(360\) 3.16983e10 0.0994659
\(361\) −2.05835e11 −0.637876
\(362\) 6.52219e10 0.199620
\(363\) 7.75717e10 0.234489
\(364\) −1.36611e11 −0.407877
\(365\) 4.40050e11 1.29773
\(366\) 1.18058e11 0.343899
\(367\) 3.55123e11 1.02184 0.510918 0.859629i \(-0.329305\pi\)
0.510918 + 0.859629i \(0.329305\pi\)
\(368\) 2.28573e11 0.649695
\(369\) −2.07691e11 −0.583174
\(370\) 6.14706e11 1.70514
\(371\) 1.46995e11 0.402828
\(372\) −1.68770e11 −0.456933
\(373\) −1.46968e11 −0.393128 −0.196564 0.980491i \(-0.562978\pi\)
−0.196564 + 0.980491i \(0.562978\pi\)
\(374\) −3.42663e11 −0.905617
\(375\) −2.39780e11 −0.626142
\(376\) −4.91205e10 −0.126741
\(377\) 6.18187e11 1.57610
\(378\) −5.94639e10 −0.149810
\(379\) 5.48957e11 1.36666 0.683332 0.730108i \(-0.260530\pi\)
0.683332 + 0.730108i \(0.260530\pi\)
\(380\) −1.54303e11 −0.379619
\(381\) 3.11479e11 0.757298
\(382\) −4.74788e11 −1.14081
\(383\) −5.30270e11 −1.25922 −0.629611 0.776910i \(-0.716786\pi\)
−0.629611 + 0.776910i \(0.716786\pi\)
\(384\) −1.65266e11 −0.387876
\(385\) 2.58943e11 0.600664
\(386\) −8.50094e11 −1.94906
\(387\) 8.61699e10 0.195279
\(388\) −5.86230e11 −1.31318
\(389\) 4.66846e11 1.03371 0.516857 0.856072i \(-0.327102\pi\)
0.516857 + 0.856072i \(0.327102\pi\)
\(390\) 2.79522e11 0.611823
\(391\) −1.45726e11 −0.315312
\(392\) −1.05915e11 −0.226553
\(393\) 9.84969e10 0.208284
\(394\) 3.19456e11 0.667849
\(395\) 4.57490e11 0.945573
\(396\) 1.42330e11 0.290849
\(397\) 1.89910e11 0.383699 0.191850 0.981424i \(-0.438551\pi\)
0.191850 + 0.981424i \(0.438551\pi\)
\(398\) −5.50240e11 −1.09920
\(399\) −1.03924e11 −0.205276
\(400\) 1.62049e11 0.316502
\(401\) 6.94730e11 1.34173 0.670867 0.741578i \(-0.265922\pi\)
0.670867 + 0.741578i \(0.265922\pi\)
\(402\) −1.16216e11 −0.221946
\(403\) 5.34318e11 1.00908
\(404\) 1.26039e11 0.235390
\(405\) 5.15765e10 0.0952585
\(406\) 7.15956e11 1.30773
\(407\) −9.90948e11 −1.79009
\(408\) 6.51982e10 0.116484
\(409\) −1.08026e12 −1.90885 −0.954424 0.298454i \(-0.903529\pi\)
−0.954424 + 0.298454i \(0.903529\pi\)
\(410\) 1.13070e12 1.97614
\(411\) −1.57910e11 −0.272974
\(412\) −1.90566e11 −0.325842
\(413\) 4.54798e10 0.0769207
\(414\) 1.42790e11 0.238889
\(415\) −4.70150e11 −0.778073
\(416\) −7.02329e11 −1.14980
\(417\) −4.58278e11 −0.742193
\(418\) 5.86800e11 0.940149
\(419\) 4.74824e11 0.752609 0.376304 0.926496i \(-0.377195\pi\)
0.376304 + 0.926496i \(0.377195\pi\)
\(420\) 1.37230e11 0.215193
\(421\) 4.95917e11 0.769378 0.384689 0.923046i \(-0.374309\pi\)
0.384689 + 0.923046i \(0.374309\pi\)
\(422\) −1.58471e12 −2.43246
\(423\) −7.99244e10 −0.121380
\(424\) 1.57923e11 0.237301
\(425\) −1.03314e11 −0.153606
\(426\) 2.60595e10 0.0383374
\(427\) −1.83499e11 −0.267121
\(428\) 4.55346e10 0.0655911
\(429\) −4.50609e11 −0.642306
\(430\) −4.69121e11 −0.661724
\(431\) 1.94411e11 0.271378 0.135689 0.990752i \(-0.456675\pi\)
0.135689 + 0.990752i \(0.456675\pi\)
\(432\) −1.66395e11 −0.229860
\(433\) −1.31522e12 −1.79805 −0.899027 0.437893i \(-0.855725\pi\)
−0.899027 + 0.437893i \(0.855725\pi\)
\(434\) 6.18823e11 0.837264
\(435\) −6.20990e11 −0.831539
\(436\) −1.82019e11 −0.241227
\(437\) 2.49551e11 0.327335
\(438\) −8.86877e11 −1.15141
\(439\) −6.36451e11 −0.817851 −0.408926 0.912568i \(-0.634096\pi\)
−0.408926 + 0.912568i \(0.634096\pi\)
\(440\) 2.78194e11 0.353843
\(441\) −1.72335e11 −0.216970
\(442\) 5.74932e11 0.716500
\(443\) 4.80061e11 0.592215 0.296108 0.955155i \(-0.404311\pi\)
0.296108 + 0.955155i \(0.404311\pi\)
\(444\) −5.25166e11 −0.641317
\(445\) −2.47743e11 −0.299489
\(446\) 1.06235e12 1.27134
\(447\) −3.24574e11 −0.384530
\(448\) −2.11724e11 −0.248325
\(449\) 2.16718e11 0.251644 0.125822 0.992053i \(-0.459843\pi\)
0.125822 + 0.992053i \(0.459843\pi\)
\(450\) 1.01232e11 0.116376
\(451\) −1.82276e12 −2.07460
\(452\) 1.02438e11 0.115436
\(453\) −4.05978e11 −0.452961
\(454\) −1.14713e12 −1.26724
\(455\) −4.34464e11 −0.475229
\(456\) −1.11650e11 −0.120925
\(457\) −1.74336e12 −1.86966 −0.934832 0.355090i \(-0.884450\pi\)
−0.934832 + 0.355090i \(0.884450\pi\)
\(458\) −1.10857e12 −1.17725
\(459\) 1.06084e11 0.111556
\(460\) −3.29529e11 −0.343150
\(461\) −1.17476e12 −1.21142 −0.605712 0.795684i \(-0.707112\pi\)
−0.605712 + 0.795684i \(0.707112\pi\)
\(462\) −5.21874e11 −0.532938
\(463\) 5.26497e11 0.532453 0.266227 0.963910i \(-0.414223\pi\)
0.266227 + 0.963910i \(0.414223\pi\)
\(464\) 2.00343e12 2.00651
\(465\) −5.36741e11 −0.532386
\(466\) 3.46076e11 0.339966
\(467\) 1.16256e11 0.113107 0.0565533 0.998400i \(-0.481989\pi\)
0.0565533 + 0.998400i \(0.481989\pi\)
\(468\) −2.38806e11 −0.230112
\(469\) 1.80635e11 0.172395
\(470\) 4.35119e11 0.411309
\(471\) −1.70877e11 −0.159989
\(472\) 4.88609e10 0.0453130
\(473\) 7.56255e11 0.694693
\(474\) −9.22026e11 −0.838959
\(475\) 1.76922e11 0.159463
\(476\) 2.82260e11 0.252010
\(477\) 2.56957e11 0.227263
\(478\) 1.29684e12 1.13622
\(479\) 1.21539e12 1.05489 0.527443 0.849591i \(-0.323151\pi\)
0.527443 + 0.849591i \(0.323151\pi\)
\(480\) 7.05513e11 0.606624
\(481\) 1.66265e12 1.41628
\(482\) −2.94720e12 −2.48713
\(483\) −2.21940e11 −0.185555
\(484\) 3.60795e11 0.298853
\(485\) −1.86439e12 −1.53003
\(486\) −1.03947e11 −0.0845181
\(487\) 1.78960e12 1.44170 0.720852 0.693089i \(-0.243751\pi\)
0.720852 + 0.693089i \(0.243751\pi\)
\(488\) −1.97141e11 −0.157358
\(489\) 7.73504e11 0.611748
\(490\) 9.38213e11 0.735223
\(491\) −7.13125e11 −0.553731 −0.276866 0.960909i \(-0.589296\pi\)
−0.276866 + 0.960909i \(0.589296\pi\)
\(492\) −9.65994e11 −0.743244
\(493\) −1.27728e12 −0.973808
\(494\) −9.84554e11 −0.743821
\(495\) 4.52652e11 0.338876
\(496\) 1.73162e12 1.28465
\(497\) −4.05046e10 −0.0297783
\(498\) 9.47541e11 0.690344
\(499\) 6.38235e11 0.460817 0.230408 0.973094i \(-0.425994\pi\)
0.230408 + 0.973094i \(0.425994\pi\)
\(500\) −1.11525e12 −0.798007
\(501\) 1.82143e11 0.129165
\(502\) 8.35588e11 0.587254
\(503\) 2.65519e12 1.84944 0.924719 0.380651i \(-0.124300\pi\)
0.924719 + 0.380651i \(0.124300\pi\)
\(504\) 9.92966e10 0.0685484
\(505\) 4.00842e11 0.274260
\(506\) 1.25317e12 0.849830
\(507\) −1.02917e11 −0.0691750
\(508\) 1.44873e12 0.965162
\(509\) −1.39225e12 −0.919365 −0.459682 0.888083i \(-0.652037\pi\)
−0.459682 + 0.888083i \(0.652037\pi\)
\(510\) −5.77538e11 −0.378020
\(511\) 1.37848e12 0.894350
\(512\) −1.62970e12 −1.04808
\(513\) −1.81667e11 −0.115810
\(514\) −3.74668e12 −2.36763
\(515\) −6.06057e11 −0.379648
\(516\) 4.00787e11 0.248880
\(517\) −7.01442e11 −0.431802
\(518\) 1.92560e12 1.17512
\(519\) −1.57932e12 −0.955470
\(520\) −4.66764e11 −0.279951
\(521\) −1.60344e12 −0.953418 −0.476709 0.879061i \(-0.658170\pi\)
−0.476709 + 0.879061i \(0.658170\pi\)
\(522\) 1.25154e12 0.737782
\(523\) −1.88675e11 −0.110270 −0.0551350 0.998479i \(-0.517559\pi\)
−0.0551350 + 0.998479i \(0.517559\pi\)
\(524\) 4.58121e11 0.265454
\(525\) −1.57346e11 −0.0903940
\(526\) −1.45594e12 −0.829294
\(527\) −1.10399e12 −0.623472
\(528\) −1.46034e12 −0.817712
\(529\) −1.26821e12 −0.704111
\(530\) −1.39891e12 −0.770103
\(531\) 7.95020e10 0.0433963
\(532\) −4.83363e11 −0.261620
\(533\) 3.05829e12 1.64137
\(534\) 4.99301e11 0.265722
\(535\) 1.44814e11 0.0764220
\(536\) 1.94064e11 0.101556
\(537\) 7.19859e11 0.373562
\(538\) 3.88298e12 1.99823
\(539\) −1.51246e12 −0.771855
\(540\) 2.39888e11 0.121405
\(541\) 2.56290e12 1.28631 0.643153 0.765738i \(-0.277626\pi\)
0.643153 + 0.765738i \(0.277626\pi\)
\(542\) 4.43093e12 2.20546
\(543\) −1.77211e11 −0.0874765
\(544\) 1.45113e12 0.710412
\(545\) −5.78874e11 −0.281061
\(546\) 8.75619e11 0.421646
\(547\) −7.77077e11 −0.371126 −0.185563 0.982632i \(-0.559411\pi\)
−0.185563 + 0.982632i \(0.559411\pi\)
\(548\) −7.34460e11 −0.347901
\(549\) −3.20770e11 −0.150702
\(550\) 8.88446e11 0.413999
\(551\) 2.18730e12 1.01094
\(552\) −2.38440e11 −0.109308
\(553\) 1.43311e12 0.651655
\(554\) 2.21839e12 1.00056
\(555\) −1.67019e12 −0.747216
\(556\) −2.13151e12 −0.945911
\(557\) 1.02712e12 0.452139 0.226069 0.974111i \(-0.427412\pi\)
0.226069 + 0.974111i \(0.427412\pi\)
\(558\) 1.08175e12 0.472359
\(559\) −1.26887e12 −0.549623
\(560\) −1.40802e12 −0.605008
\(561\) 9.31031e11 0.396854
\(562\) 2.24263e12 0.948296
\(563\) −5.35963e11 −0.224826 −0.112413 0.993662i \(-0.535858\pi\)
−0.112413 + 0.993662i \(0.535858\pi\)
\(564\) −3.71738e11 −0.154697
\(565\) 3.25785e11 0.134497
\(566\) −5.07856e12 −2.08002
\(567\) 1.61566e11 0.0656488
\(568\) −4.35159e10 −0.0175420
\(569\) −2.75925e12 −1.10353 −0.551766 0.833999i \(-0.686046\pi\)
−0.551766 + 0.833999i \(0.686046\pi\)
\(570\) 9.89018e11 0.392435
\(571\) 1.39378e12 0.548694 0.274347 0.961631i \(-0.411538\pi\)
0.274347 + 0.961631i \(0.411538\pi\)
\(572\) −2.09584e12 −0.818607
\(573\) 1.29002e12 0.499921
\(574\) 3.54197e12 1.36189
\(575\) 3.77833e11 0.144143
\(576\) −3.70110e11 −0.140097
\(577\) −2.12754e12 −0.799073 −0.399536 0.916717i \(-0.630829\pi\)
−0.399536 + 0.916717i \(0.630829\pi\)
\(578\) 2.34741e12 0.874810
\(579\) 2.30975e12 0.854105
\(580\) −2.88830e12 −1.05978
\(581\) −1.47277e12 −0.536220
\(582\) 3.75749e12 1.35751
\(583\) 2.25514e12 0.808472
\(584\) 1.48096e12 0.526850
\(585\) −7.59475e11 −0.268110
\(586\) 6.61781e12 2.31833
\(587\) −3.82897e12 −1.33110 −0.665550 0.746353i \(-0.731803\pi\)
−0.665550 + 0.746353i \(0.731803\pi\)
\(588\) −8.01550e11 −0.276524
\(589\) 1.89055e12 0.647246
\(590\) −4.32820e11 −0.147053
\(591\) −8.67977e11 −0.292661
\(592\) 5.38832e12 1.80304
\(593\) 4.08560e11 0.135678 0.0678390 0.997696i \(-0.478390\pi\)
0.0678390 + 0.997696i \(0.478390\pi\)
\(594\) −9.12274e11 −0.300667
\(595\) 8.97674e11 0.293624
\(596\) −1.50963e12 −0.490076
\(597\) 1.49503e12 0.481687
\(598\) −2.10261e12 −0.672363
\(599\) −8.44290e11 −0.267961 −0.133980 0.990984i \(-0.542776\pi\)
−0.133980 + 0.990984i \(0.542776\pi\)
\(600\) −1.69044e11 −0.0532499
\(601\) 2.53159e12 0.791513 0.395756 0.918356i \(-0.370482\pi\)
0.395756 + 0.918356i \(0.370482\pi\)
\(602\) −1.46955e12 −0.456036
\(603\) 3.15764e11 0.0972600
\(604\) −1.88826e12 −0.577291
\(605\) 1.14744e12 0.348201
\(606\) −8.07857e11 −0.243337
\(607\) −5.34035e11 −0.159669 −0.0798345 0.996808i \(-0.525439\pi\)
−0.0798345 + 0.996808i \(0.525439\pi\)
\(608\) −2.48501e12 −0.737501
\(609\) −1.94529e12 −0.573067
\(610\) 1.74631e12 0.510668
\(611\) 1.17691e12 0.341630
\(612\) 4.93412e11 0.142177
\(613\) 3.77745e12 1.08050 0.540252 0.841504i \(-0.318329\pi\)
0.540252 + 0.841504i \(0.318329\pi\)
\(614\) −2.80476e12 −0.796411
\(615\) −3.07215e12 −0.865974
\(616\) 8.71459e11 0.243856
\(617\) −2.81469e12 −0.781894 −0.390947 0.920413i \(-0.627852\pi\)
−0.390947 + 0.920413i \(0.627852\pi\)
\(618\) 1.22145e12 0.336842
\(619\) 2.92964e12 0.802059 0.401030 0.916065i \(-0.368652\pi\)
0.401030 + 0.916065i \(0.368652\pi\)
\(620\) −2.49645e12 −0.678515
\(621\) −3.87967e11 −0.104684
\(622\) 4.46793e12 1.19688
\(623\) −7.76070e11 −0.206398
\(624\) 2.45021e12 0.646952
\(625\) −2.53597e12 −0.664789
\(626\) −8.48610e10 −0.0220863
\(627\) −1.59436e12 −0.411987
\(628\) −7.94772e11 −0.203903
\(629\) −3.43530e12 −0.875058
\(630\) −8.79589e11 −0.222458
\(631\) −2.11792e12 −0.531834 −0.265917 0.963996i \(-0.585675\pi\)
−0.265917 + 0.963996i \(0.585675\pi\)
\(632\) 1.53966e12 0.383882
\(633\) 4.30575e12 1.06594
\(634\) −7.32089e12 −1.79954
\(635\) 4.60739e12 1.12454
\(636\) 1.19514e12 0.289642
\(637\) 2.53767e12 0.610671
\(638\) 1.09839e13 2.62461
\(639\) −7.08050e10 −0.0168000
\(640\) −2.44461e12 −0.575970
\(641\) 2.89567e12 0.677466 0.338733 0.940882i \(-0.390002\pi\)
0.338733 + 0.940882i \(0.390002\pi\)
\(642\) −2.91858e11 −0.0678054
\(643\) 3.13182e11 0.0722517 0.0361258 0.999347i \(-0.488498\pi\)
0.0361258 + 0.999347i \(0.488498\pi\)
\(644\) −1.03227e12 −0.236487
\(645\) 1.27462e12 0.289977
\(646\) 2.03425e12 0.459576
\(647\) 5.41387e12 1.21461 0.607307 0.794467i \(-0.292250\pi\)
0.607307 + 0.794467i \(0.292250\pi\)
\(648\) 1.73578e11 0.0386729
\(649\) 6.97735e11 0.154379
\(650\) −1.49067e12 −0.327545
\(651\) −1.68137e12 −0.366901
\(652\) 3.59766e12 0.779661
\(653\) −3.57083e12 −0.768528 −0.384264 0.923223i \(-0.625545\pi\)
−0.384264 + 0.923223i \(0.625545\pi\)
\(654\) 1.16666e12 0.249371
\(655\) 1.45696e12 0.309288
\(656\) 9.91133e12 2.08961
\(657\) 2.40969e12 0.504565
\(658\) 1.36304e12 0.283459
\(659\) −4.34664e12 −0.897778 −0.448889 0.893588i \(-0.648180\pi\)
−0.448889 + 0.893588i \(0.648180\pi\)
\(660\) 2.10534e12 0.431891
\(661\) −8.51008e11 −0.173391 −0.0866956 0.996235i \(-0.527631\pi\)
−0.0866956 + 0.996235i \(0.527631\pi\)
\(662\) 7.44260e12 1.50613
\(663\) −1.56212e12 −0.313981
\(664\) −1.58226e12 −0.315880
\(665\) −1.53724e12 −0.304821
\(666\) 3.36609e12 0.662967
\(667\) 4.67119e12 0.913821
\(668\) 8.47171e11 0.164618
\(669\) −2.88646e12 −0.557119
\(670\) −1.71906e12 −0.329575
\(671\) −2.81518e12 −0.536111
\(672\) 2.21006e12 0.418064
\(673\) 2.27797e12 0.428036 0.214018 0.976830i \(-0.431345\pi\)
0.214018 + 0.976830i \(0.431345\pi\)
\(674\) −1.91177e12 −0.356834
\(675\) −2.75053e11 −0.0509975
\(676\) −4.78678e11 −0.0881623
\(677\) −1.92066e12 −0.351400 −0.175700 0.984444i \(-0.556219\pi\)
−0.175700 + 0.984444i \(0.556219\pi\)
\(678\) −6.56588e11 −0.119333
\(679\) −5.84031e12 −1.05444
\(680\) 9.64410e11 0.172970
\(681\) 3.11680e12 0.555325
\(682\) 9.49376e12 1.68038
\(683\) 4.73681e12 0.832900 0.416450 0.909159i \(-0.363274\pi\)
0.416450 + 0.909159i \(0.363274\pi\)
\(684\) −8.44954e11 −0.147598
\(685\) −2.33580e12 −0.405349
\(686\) 7.45424e12 1.28512
\(687\) 3.01204e12 0.515887
\(688\) −4.11217e12 −0.699718
\(689\) −3.78376e12 −0.639642
\(690\) 2.11214e12 0.354734
\(691\) −5.76580e12 −0.962074 −0.481037 0.876700i \(-0.659740\pi\)
−0.481037 + 0.876700i \(0.659740\pi\)
\(692\) −7.34561e12 −1.21773
\(693\) 1.41796e12 0.233541
\(694\) 9.86604e12 1.61445
\(695\) −6.77884e12 −1.10211
\(696\) −2.08991e12 −0.337587
\(697\) −6.31892e12 −1.01413
\(698\) −8.82586e12 −1.40737
\(699\) −9.40306e11 −0.148978
\(700\) −7.31837e11 −0.115205
\(701\) −4.93783e11 −0.0772334 −0.0386167 0.999254i \(-0.512295\pi\)
−0.0386167 + 0.999254i \(0.512295\pi\)
\(702\) 1.53065e12 0.237880
\(703\) 5.88286e12 0.908426
\(704\) −3.24820e12 −0.498386
\(705\) −1.18224e12 −0.180241
\(706\) −1.46055e13 −2.21256
\(707\) 1.25566e12 0.189010
\(708\) 3.69774e11 0.0553078
\(709\) −1.04931e13 −1.55953 −0.779766 0.626071i \(-0.784662\pi\)
−0.779766 + 0.626071i \(0.784662\pi\)
\(710\) 3.85472e11 0.0569285
\(711\) 2.50519e12 0.367644
\(712\) −8.33766e11 −0.121586
\(713\) 4.03745e12 0.585066
\(714\) −1.80917e12 −0.260518
\(715\) −6.66540e12 −0.953782
\(716\) 3.34815e12 0.476098
\(717\) −3.52358e12 −0.497907
\(718\) −9.86541e11 −0.138534
\(719\) −3.92845e12 −0.548203 −0.274101 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(720\) −2.46131e12 −0.341327
\(721\) −1.89851e12 −0.261640
\(722\) 6.13629e12 0.840405
\(723\) 8.00768e12 1.08989
\(724\) −8.24230e11 −0.111487
\(725\) 3.31168e12 0.445172
\(726\) −2.31255e12 −0.308941
\(727\) −1.31532e13 −1.74633 −0.873167 0.487420i \(-0.837938\pi\)
−0.873167 + 0.487420i \(0.837938\pi\)
\(728\) −1.46217e12 −0.192932
\(729\) 2.82430e11 0.0370370
\(730\) −1.31187e13 −1.70977
\(731\) 2.62169e12 0.339589
\(732\) −1.49194e12 −0.192066
\(733\) −8.49071e12 −1.08637 −0.543183 0.839614i \(-0.682781\pi\)
−0.543183 + 0.839614i \(0.682781\pi\)
\(734\) −1.05868e13 −1.34628
\(735\) −2.54917e12 −0.322185
\(736\) −5.30699e12 −0.666650
\(737\) 2.77124e12 0.345996
\(738\) 6.19162e12 0.768335
\(739\) 1.44722e13 1.78499 0.892496 0.451056i \(-0.148953\pi\)
0.892496 + 0.451056i \(0.148953\pi\)
\(740\) −7.76824e12 −0.952313
\(741\) 2.67508e12 0.325953
\(742\) −4.38217e12 −0.530728
\(743\) −2.79119e11 −0.0336000 −0.0168000 0.999859i \(-0.505348\pi\)
−0.0168000 + 0.999859i \(0.505348\pi\)
\(744\) −1.80637e12 −0.216137
\(745\) −4.80110e12 −0.571001
\(746\) 4.38139e12 0.517949
\(747\) −2.57451e12 −0.302519
\(748\) 4.33034e12 0.505784
\(749\) 4.53638e11 0.0526673
\(750\) 7.14828e12 0.824946
\(751\) −9.34249e12 −1.07172 −0.535862 0.844305i \(-0.680013\pi\)
−0.535862 + 0.844305i \(0.680013\pi\)
\(752\) 3.81412e12 0.434925
\(753\) −2.27033e12 −0.257343
\(754\) −1.84293e13 −2.07652
\(755\) −6.00522e12 −0.672617
\(756\) 7.51465e11 0.0836682
\(757\) −1.07230e13 −1.18682 −0.593410 0.804900i \(-0.702219\pi\)
−0.593410 + 0.804900i \(0.702219\pi\)
\(758\) −1.63654e13 −1.80059
\(759\) −3.40492e12 −0.372408
\(760\) −1.65153e12 −0.179566
\(761\) 2.42453e12 0.262058 0.131029 0.991379i \(-0.458172\pi\)
0.131029 + 0.991379i \(0.458172\pi\)
\(762\) −9.28574e12 −0.997744
\(763\) −1.81336e12 −0.193697
\(764\) 6.00006e12 0.637141
\(765\) 1.56920e12 0.165654
\(766\) 1.58083e13 1.65903
\(767\) −1.17069e12 −0.122141
\(768\) 7.26633e12 0.753684
\(769\) −2.80810e12 −0.289564 −0.144782 0.989464i \(-0.546248\pi\)
−0.144782 + 0.989464i \(0.546248\pi\)
\(770\) −7.71955e12 −0.791378
\(771\) 1.01799e13 1.03753
\(772\) 1.07429e13 1.08854
\(773\) −4.43601e12 −0.446874 −0.223437 0.974718i \(-0.571728\pi\)
−0.223437 + 0.974718i \(0.571728\pi\)
\(774\) −2.56888e12 −0.257282
\(775\) 2.86239e12 0.285017
\(776\) −6.27450e12 −0.621157
\(777\) −5.23195e12 −0.514955
\(778\) −1.39175e13 −1.36193
\(779\) 1.08210e13 1.05281
\(780\) −3.53241e12 −0.341701
\(781\) −6.21407e11 −0.0597649
\(782\) 4.34434e12 0.415425
\(783\) −3.40050e12 −0.323307
\(784\) 8.22409e12 0.777438
\(785\) −2.52761e12 −0.237573
\(786\) −2.93637e12 −0.274416
\(787\) −1.29011e13 −1.19878 −0.599390 0.800457i \(-0.704590\pi\)
−0.599390 + 0.800457i \(0.704590\pi\)
\(788\) −4.03707e12 −0.372991
\(789\) 3.95587e12 0.363409
\(790\) −1.36386e13 −1.24580
\(791\) 1.02054e12 0.0926908
\(792\) 1.52337e12 0.137576
\(793\) 4.72341e12 0.424157
\(794\) −5.66156e12 −0.505526
\(795\) 3.80091e12 0.337470
\(796\) 6.95356e12 0.613901
\(797\) −1.60038e13 −1.40495 −0.702475 0.711708i \(-0.747922\pi\)
−0.702475 + 0.711708i \(0.747922\pi\)
\(798\) 3.09816e12 0.270452
\(799\) −2.43168e12 −0.211079
\(800\) −3.76244e12 −0.324761
\(801\) −1.35663e12 −0.116443
\(802\) −2.07111e13 −1.76774
\(803\) 2.11482e13 1.79495
\(804\) 1.46866e12 0.123956
\(805\) −3.28293e12 −0.275537
\(806\) −1.59290e13 −1.32947
\(807\) −1.05503e13 −0.875653
\(808\) 1.34901e12 0.111343
\(809\) 1.71444e13 1.40719 0.703595 0.710601i \(-0.251577\pi\)
0.703595 + 0.710601i \(0.251577\pi\)
\(810\) −1.53758e12 −0.125504
\(811\) −1.90092e13 −1.54302 −0.771509 0.636218i \(-0.780498\pi\)
−0.771509 + 0.636218i \(0.780498\pi\)
\(812\) −9.04777e12 −0.730364
\(813\) −1.20391e13 −0.966463
\(814\) 2.95419e13 2.35846
\(815\) 1.14417e13 0.908405
\(816\) −5.06252e12 −0.399725
\(817\) −4.48958e12 −0.352538
\(818\) 3.22043e13 2.51492
\(819\) −2.37910e12 −0.184772
\(820\) −1.42890e13 −1.10367
\(821\) 2.37312e13 1.82295 0.911477 0.411351i \(-0.134943\pi\)
0.911477 + 0.411351i \(0.134943\pi\)
\(822\) 4.70758e12 0.359645
\(823\) 8.15915e12 0.619934 0.309967 0.950747i \(-0.399682\pi\)
0.309967 + 0.950747i \(0.399682\pi\)
\(824\) −2.03965e12 −0.154129
\(825\) −2.41395e12 −0.181420
\(826\) −1.35583e12 −0.101344
\(827\) −8.76548e12 −0.651630 −0.325815 0.945434i \(-0.605639\pi\)
−0.325815 + 0.945434i \(0.605639\pi\)
\(828\) −1.80448e12 −0.133418
\(829\) 1.34289e13 0.987521 0.493760 0.869598i \(-0.335622\pi\)
0.493760 + 0.869598i \(0.335622\pi\)
\(830\) 1.40160e13 1.02512
\(831\) −6.02746e12 −0.438460
\(832\) 5.44995e12 0.394310
\(833\) −5.24323e12 −0.377308
\(834\) 1.36621e13 0.977843
\(835\) 2.69426e12 0.191801
\(836\) −7.41558e12 −0.525070
\(837\) −2.93916e12 −0.206994
\(838\) −1.41553e13 −0.991566
\(839\) −9.77049e12 −0.680750 −0.340375 0.940290i \(-0.610554\pi\)
−0.340375 + 0.940290i \(0.610554\pi\)
\(840\) 1.46879e12 0.101790
\(841\) 2.64355e13 1.82224
\(842\) −1.47842e13 −1.01366
\(843\) −6.09333e12 −0.415557
\(844\) 2.00266e13 1.35852
\(845\) −1.52234e12 −0.102720
\(846\) 2.38269e12 0.159919
\(847\) 3.59442e12 0.239968
\(848\) −1.22624e13 −0.814320
\(849\) 1.37987e13 0.911493
\(850\) 3.07996e12 0.202376
\(851\) 1.25634e13 0.821154
\(852\) −3.29323e11 −0.0214113
\(853\) −1.40208e13 −0.906778 −0.453389 0.891313i \(-0.649785\pi\)
−0.453389 + 0.891313i \(0.649785\pi\)
\(854\) 5.47043e12 0.351934
\(855\) −2.68721e12 −0.171970
\(856\) 4.87363e11 0.0310257
\(857\) 1.86132e12 0.117871 0.0589356 0.998262i \(-0.481229\pi\)
0.0589356 + 0.998262i \(0.481229\pi\)
\(858\) 1.34334e13 0.846242
\(859\) −1.13968e12 −0.0714189 −0.0357095 0.999362i \(-0.511369\pi\)
−0.0357095 + 0.999362i \(0.511369\pi\)
\(860\) 5.92843e12 0.369570
\(861\) −9.62370e12 −0.596799
\(862\) −5.79575e12 −0.357542
\(863\) 8.56652e12 0.525721 0.262861 0.964834i \(-0.415334\pi\)
0.262861 + 0.964834i \(0.415334\pi\)
\(864\) 3.86335e12 0.235859
\(865\) −2.33613e13 −1.41881
\(866\) 3.92090e13 2.36895
\(867\) −6.37803e12 −0.383355
\(868\) −7.82027e12 −0.467609
\(869\) 2.19863e13 1.30787
\(870\) 1.85128e13 1.09556
\(871\) −4.64969e12 −0.273743
\(872\) −1.94817e12 −0.114104
\(873\) −1.02093e13 −0.594882
\(874\) −7.43956e12 −0.431266
\(875\) −1.11106e13 −0.640771
\(876\) 1.12078e13 0.643058
\(877\) −1.85029e13 −1.05619 −0.528096 0.849185i \(-0.677094\pi\)
−0.528096 + 0.849185i \(0.677094\pi\)
\(878\) 1.89737e13 1.07752
\(879\) −1.79809e13 −1.01592
\(880\) −2.16013e13 −1.21425
\(881\) 2.73534e12 0.152974 0.0764872 0.997071i \(-0.475630\pi\)
0.0764872 + 0.997071i \(0.475630\pi\)
\(882\) 5.13760e12 0.285859
\(883\) 1.11575e13 0.617652 0.308826 0.951118i \(-0.400064\pi\)
0.308826 + 0.951118i \(0.400064\pi\)
\(884\) −7.26560e12 −0.400162
\(885\) 1.17599e12 0.0644406
\(886\) −1.43115e13 −0.780247
\(887\) 2.87342e12 0.155863 0.0779316 0.996959i \(-0.475168\pi\)
0.0779316 + 0.996959i \(0.475168\pi\)
\(888\) −5.62092e12 −0.303353
\(889\) 1.44329e13 0.774991
\(890\) 7.38566e12 0.394579
\(891\) 2.47869e12 0.131757
\(892\) −1.34253e13 −0.710037
\(893\) 4.16418e12 0.219128
\(894\) 9.67613e12 0.506621
\(895\) 1.06481e13 0.554715
\(896\) −7.65789e12 −0.396938
\(897\) 5.71290e12 0.294639
\(898\) −6.46076e12 −0.331543
\(899\) 3.53880e13 1.80691
\(900\) −1.27930e12 −0.0649954
\(901\) 7.81786e12 0.395208
\(902\) 5.43396e13 2.73330
\(903\) 3.99283e12 0.199842
\(904\) 1.09641e12 0.0546029
\(905\) −2.62130e12 −0.129897
\(906\) 1.21029e13 0.596779
\(907\) 3.71918e13 1.82480 0.912398 0.409303i \(-0.134228\pi\)
0.912398 + 0.409303i \(0.134228\pi\)
\(908\) 1.44966e13 0.707751
\(909\) 2.19499e12 0.106634
\(910\) 1.29521e13 0.626117
\(911\) −1.53745e13 −0.739552 −0.369776 0.929121i \(-0.620566\pi\)
−0.369776 + 0.929121i \(0.620566\pi\)
\(912\) 8.66943e12 0.414967
\(913\) −2.25948e13 −1.07619
\(914\) 5.19726e13 2.46329
\(915\) −4.74482e12 −0.223782
\(916\) 1.40094e13 0.657489
\(917\) 4.56403e12 0.213150
\(918\) −3.16256e12 −0.146976
\(919\) −1.64189e13 −0.759317 −0.379659 0.925127i \(-0.623959\pi\)
−0.379659 + 0.925127i \(0.623959\pi\)
\(920\) −3.52699e12 −0.162315
\(921\) 7.62066e12 0.348999
\(922\) 3.50217e13 1.59606
\(923\) 1.04262e12 0.0472844
\(924\) 6.59509e12 0.297644
\(925\) 8.90695e12 0.400029
\(926\) −1.56958e13 −0.701511
\(927\) −3.31873e12 −0.147609
\(928\) −4.65154e13 −2.05888
\(929\) 6.63995e12 0.292479 0.146239 0.989249i \(-0.453283\pi\)
0.146239 + 0.989249i \(0.453283\pi\)
\(930\) 1.60012e13 0.701421
\(931\) 8.97889e12 0.391696
\(932\) −4.37348e12 −0.189870
\(933\) −1.21396e13 −0.524489
\(934\) −3.46578e12 −0.149019
\(935\) 1.37718e13 0.589302
\(936\) −2.55597e12 −0.108847
\(937\) −4.04370e12 −0.171376 −0.0856881 0.996322i \(-0.527309\pi\)
−0.0856881 + 0.996322i \(0.527309\pi\)
\(938\) −5.38506e12 −0.227132
\(939\) 2.30571e11 0.00967855
\(940\) −5.49874e12 −0.229714
\(941\) −9.70117e12 −0.403340 −0.201670 0.979454i \(-0.564637\pi\)
−0.201670 + 0.979454i \(0.564637\pi\)
\(942\) 5.09415e12 0.210787
\(943\) 2.31093e13 0.951664
\(944\) −3.79397e12 −0.155496
\(945\) 2.38989e12 0.0974841
\(946\) −2.25453e13 −0.915262
\(947\) 2.70375e11 0.0109243 0.00546213 0.999985i \(-0.498261\pi\)
0.00546213 + 0.999985i \(0.498261\pi\)
\(948\) 1.16519e13 0.468555
\(949\) −3.54832e13 −1.42012
\(950\) −5.27434e12 −0.210093
\(951\) 1.98912e13 0.788586
\(952\) 3.02107e12 0.119205
\(953\) −1.46064e13 −0.573622 −0.286811 0.957987i \(-0.592595\pi\)
−0.286811 + 0.957987i \(0.592595\pi\)
\(954\) −7.66035e12 −0.299420
\(955\) 1.90820e13 0.742350
\(956\) −1.63886e13 −0.634573
\(957\) −2.98439e13 −1.15014
\(958\) −3.62329e13 −1.38982
\(959\) −7.31704e12 −0.279352
\(960\) −5.47466e12 −0.208035
\(961\) 4.14733e12 0.156860
\(962\) −4.95665e13 −1.86595
\(963\) 7.92992e11 0.0297133
\(964\) 3.72447e13 1.38905
\(965\) 3.41658e13 1.26829
\(966\) 6.61641e12 0.244470
\(967\) −1.63067e13 −0.599717 −0.299859 0.953984i \(-0.596940\pi\)
−0.299859 + 0.953984i \(0.596940\pi\)
\(968\) 3.86164e12 0.141362
\(969\) −5.52715e12 −0.201393
\(970\) 5.55807e13 2.01582
\(971\) 7.03233e12 0.253871 0.126935 0.991911i \(-0.459486\pi\)
0.126935 + 0.991911i \(0.459486\pi\)
\(972\) 1.31361e12 0.0472030
\(973\) −2.12351e13 −0.759533
\(974\) −5.33512e13 −1.89945
\(975\) 4.05021e12 0.143535
\(976\) 1.53077e13 0.539989
\(977\) −5.02095e13 −1.76303 −0.881516 0.472155i \(-0.843476\pi\)
−0.881516 + 0.472155i \(0.843476\pi\)
\(978\) −2.30595e13 −0.805982
\(979\) −1.19062e13 −0.414239
\(980\) −1.18565e13 −0.410619
\(981\) −3.16988e12 −0.109278
\(982\) 2.12595e13 0.729544
\(983\) 3.28721e13 1.12289 0.561443 0.827515i \(-0.310246\pi\)
0.561443 + 0.827515i \(0.310246\pi\)
\(984\) −1.03392e13 −0.351567
\(985\) −1.28391e13 −0.434582
\(986\) 3.80778e13 1.28300
\(987\) −3.70344e12 −0.124216
\(988\) 1.24421e13 0.415421
\(989\) −9.58793e12 −0.318670
\(990\) −1.34943e13 −0.446471
\(991\) 4.22004e13 1.38990 0.694952 0.719056i \(-0.255425\pi\)
0.694952 + 0.719056i \(0.255425\pi\)
\(992\) −4.02047e13 −1.31818
\(993\) −2.02219e13 −0.660010
\(994\) 1.20751e12 0.0392331
\(995\) 2.21144e13 0.715273
\(996\) −1.19744e13 −0.385555
\(997\) 1.38251e13 0.443138 0.221569 0.975145i \(-0.428882\pi\)
0.221569 + 0.975145i \(0.428882\pi\)
\(998\) −1.90269e13 −0.607129
\(999\) −9.14584e12 −0.290522
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.a.1.5 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.5 21 1.1 even 1 trivial