Properties

Label 177.10.a.a.1.10
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q-12.7580 q^{2} +81.0000 q^{3} -349.234 q^{4} +1739.29 q^{5} -1033.40 q^{6} +7509.10 q^{7} +10987.6 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-12.7580 q^{2} +81.0000 q^{3} -349.234 q^{4} +1739.29 q^{5} -1033.40 q^{6} +7509.10 q^{7} +10987.6 q^{8} +6561.00 q^{9} -22189.8 q^{10} -73867.0 q^{11} -28288.0 q^{12} +162700. q^{13} -95800.9 q^{14} +140883. q^{15} +38628.6 q^{16} -663069. q^{17} -83705.0 q^{18} -716119. q^{19} -607420. q^{20} +608237. q^{21} +942393. q^{22} -1.59218e6 q^{23} +889995. q^{24} +1.07201e6 q^{25} -2.07572e6 q^{26} +531441. q^{27} -2.62244e6 q^{28} -2.50545e6 q^{29} -1.79738e6 q^{30} +2.91112e6 q^{31} -6.11847e6 q^{32} -5.98323e6 q^{33} +8.45942e6 q^{34} +1.30605e7 q^{35} -2.29133e6 q^{36} -1.43874e7 q^{37} +9.13622e6 q^{38} +1.31787e7 q^{39} +1.91106e7 q^{40} +1.18070e7 q^{41} -7.75987e6 q^{42} +1.63694e7 q^{43} +2.57969e7 q^{44} +1.14115e7 q^{45} +2.03130e7 q^{46} -5.19546e7 q^{47} +3.12891e6 q^{48} +1.60330e7 q^{49} -1.36767e7 q^{50} -5.37086e7 q^{51} -5.68204e7 q^{52} -1.54905e7 q^{53} -6.78011e6 q^{54} -1.28476e8 q^{55} +8.25070e7 q^{56} -5.80056e7 q^{57} +3.19645e7 q^{58} +1.21174e7 q^{59} -4.92010e7 q^{60} -1.00668e8 q^{61} -3.71399e7 q^{62} +4.92672e7 q^{63} +5.82814e7 q^{64} +2.82982e8 q^{65} +7.63338e7 q^{66} -2.65492e7 q^{67} +2.31567e8 q^{68} -1.28967e8 q^{69} -1.66626e8 q^{70} +1.72825e7 q^{71} +7.20896e7 q^{72} +5.63024e7 q^{73} +1.83554e8 q^{74} +8.68328e7 q^{75} +2.50093e8 q^{76} -5.54675e8 q^{77} -1.68133e8 q^{78} +5.55414e8 q^{79} +6.71863e7 q^{80} +4.30467e7 q^{81} -1.50634e8 q^{82} +6.01877e8 q^{83} -2.12417e8 q^{84} -1.15327e9 q^{85} -2.08841e8 q^{86} -2.02942e8 q^{87} -8.11621e8 q^{88} -4.74335e8 q^{89} -1.45587e8 q^{90} +1.22173e9 q^{91} +5.56044e8 q^{92} +2.35800e8 q^{93} +6.62835e8 q^{94} -1.24554e9 q^{95} -4.95596e8 q^{96} -5.39952e8 q^{97} -2.04549e8 q^{98} -4.84642e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.7580 −0.563828 −0.281914 0.959440i \(-0.590969\pi\)
−0.281914 + 0.959440i \(0.590969\pi\)
\(3\) 81.0000 0.577350
\(4\) −349.234 −0.682098
\(5\) 1739.29 1.24454 0.622268 0.782804i \(-0.286211\pi\)
0.622268 + 0.782804i \(0.286211\pi\)
\(6\) −1033.40 −0.325526
\(7\) 7509.10 1.18208 0.591040 0.806642i \(-0.298718\pi\)
0.591040 + 0.806642i \(0.298718\pi\)
\(8\) 10987.6 0.948414
\(9\) 6561.00 0.333333
\(10\) −22189.8 −0.701704
\(11\) −73867.0 −1.52119 −0.760595 0.649227i \(-0.775093\pi\)
−0.760595 + 0.649227i \(0.775093\pi\)
\(12\) −28288.0 −0.393810
\(13\) 162700. 1.57995 0.789973 0.613142i \(-0.210095\pi\)
0.789973 + 0.613142i \(0.210095\pi\)
\(14\) −95800.9 −0.666490
\(15\) 140883. 0.718533
\(16\) 38628.6 0.147356
\(17\) −663069. −1.92548 −0.962740 0.270430i \(-0.912834\pi\)
−0.962740 + 0.270430i \(0.912834\pi\)
\(18\) −83705.0 −0.187943
\(19\) −716119. −1.26065 −0.630324 0.776332i \(-0.717078\pi\)
−0.630324 + 0.776332i \(0.717078\pi\)
\(20\) −607420. −0.848896
\(21\) 608237. 0.682474
\(22\) 942393. 0.857689
\(23\) −1.59218e6 −1.18636 −0.593181 0.805069i \(-0.702128\pi\)
−0.593181 + 0.805069i \(0.702128\pi\)
\(24\) 889995. 0.547567
\(25\) 1.07201e6 0.548869
\(26\) −2.07572e6 −0.890817
\(27\) 531441. 0.192450
\(28\) −2.62244e6 −0.806295
\(29\) −2.50545e6 −0.657802 −0.328901 0.944364i \(-0.606678\pi\)
−0.328901 + 0.944364i \(0.606678\pi\)
\(30\) −1.79738e6 −0.405129
\(31\) 2.91112e6 0.566150 0.283075 0.959098i \(-0.408645\pi\)
0.283075 + 0.959098i \(0.408645\pi\)
\(32\) −6.11847e6 −1.03150
\(33\) −5.98323e6 −0.878260
\(34\) 8.45942e6 1.08564
\(35\) 1.30605e7 1.47114
\(36\) −2.29133e6 −0.227366
\(37\) −1.43874e7 −1.26204 −0.631021 0.775766i \(-0.717364\pi\)
−0.631021 + 0.775766i \(0.717364\pi\)
\(38\) 9.13622e6 0.710788
\(39\) 1.31787e7 0.912182
\(40\) 1.91106e7 1.18033
\(41\) 1.18070e7 0.652550 0.326275 0.945275i \(-0.394206\pi\)
0.326275 + 0.945275i \(0.394206\pi\)
\(42\) −7.75987e6 −0.384798
\(43\) 1.63694e7 0.730173 0.365086 0.930974i \(-0.381039\pi\)
0.365086 + 0.930974i \(0.381039\pi\)
\(44\) 2.57969e7 1.03760
\(45\) 1.14115e7 0.414845
\(46\) 2.03130e7 0.668904
\(47\) −5.19546e7 −1.55304 −0.776521 0.630091i \(-0.783018\pi\)
−0.776521 + 0.630091i \(0.783018\pi\)
\(48\) 3.12891e6 0.0850762
\(49\) 1.60330e7 0.397313
\(50\) −1.36767e7 −0.309468
\(51\) −5.37086e7 −1.11168
\(52\) −5.68204e7 −1.07768
\(53\) −1.54905e7 −0.269664 −0.134832 0.990868i \(-0.543049\pi\)
−0.134832 + 0.990868i \(0.543049\pi\)
\(54\) −6.78011e6 −0.108509
\(55\) −1.28476e8 −1.89318
\(56\) 8.25070e7 1.12110
\(57\) −5.80056e7 −0.727835
\(58\) 3.19645e7 0.370887
\(59\) 1.21174e7 0.130189
\(60\) −4.92010e7 −0.490110
\(61\) −1.00668e8 −0.930908 −0.465454 0.885072i \(-0.654109\pi\)
−0.465454 + 0.885072i \(0.654109\pi\)
\(62\) −3.71399e7 −0.319211
\(63\) 4.92672e7 0.394027
\(64\) 5.82814e7 0.434231
\(65\) 2.82982e8 1.96630
\(66\) 7.63338e7 0.495187
\(67\) −2.65492e7 −0.160959 −0.0804793 0.996756i \(-0.525645\pi\)
−0.0804793 + 0.996756i \(0.525645\pi\)
\(68\) 2.31567e8 1.31337
\(69\) −1.28967e8 −0.684947
\(70\) −1.66626e8 −0.829470
\(71\) 1.72825e7 0.0807130 0.0403565 0.999185i \(-0.487151\pi\)
0.0403565 + 0.999185i \(0.487151\pi\)
\(72\) 7.20896e7 0.316138
\(73\) 5.63024e7 0.232046 0.116023 0.993247i \(-0.462985\pi\)
0.116023 + 0.993247i \(0.462985\pi\)
\(74\) 1.83554e8 0.711574
\(75\) 8.68328e7 0.316890
\(76\) 2.50093e8 0.859886
\(77\) −5.54675e8 −1.79817
\(78\) −1.68133e8 −0.514313
\(79\) 5.55414e8 1.60433 0.802167 0.597099i \(-0.203680\pi\)
0.802167 + 0.597099i \(0.203680\pi\)
\(80\) 6.71863e7 0.183390
\(81\) 4.30467e7 0.111111
\(82\) −1.50634e8 −0.367926
\(83\) 6.01877e8 1.39206 0.696028 0.718015i \(-0.254949\pi\)
0.696028 + 0.718015i \(0.254949\pi\)
\(84\) −2.12417e8 −0.465514
\(85\) −1.15327e9 −2.39633
\(86\) −2.08841e8 −0.411692
\(87\) −2.02942e8 −0.379782
\(88\) −8.11621e8 −1.44272
\(89\) −4.74335e8 −0.801365 −0.400682 0.916217i \(-0.631227\pi\)
−0.400682 + 0.916217i \(0.631227\pi\)
\(90\) −1.45587e8 −0.233901
\(91\) 1.22173e9 1.86762
\(92\) 5.56044e8 0.809216
\(93\) 2.35800e8 0.326867
\(94\) 6.62835e8 0.875648
\(95\) −1.24554e9 −1.56892
\(96\) −4.95596e8 −0.595535
\(97\) −5.39952e8 −0.619273 −0.309636 0.950855i \(-0.600207\pi\)
−0.309636 + 0.950855i \(0.600207\pi\)
\(98\) −2.04549e8 −0.224016
\(99\) −4.84642e8 −0.507063
\(100\) −3.74383e8 −0.374383
\(101\) 8.61496e8 0.823772 0.411886 0.911235i \(-0.364870\pi\)
0.411886 + 0.911235i \(0.364870\pi\)
\(102\) 6.85213e8 0.626794
\(103\) −1.81166e9 −1.58602 −0.793010 0.609209i \(-0.791487\pi\)
−0.793010 + 0.609209i \(0.791487\pi\)
\(104\) 1.78768e9 1.49844
\(105\) 1.05790e9 0.849364
\(106\) 1.97627e8 0.152044
\(107\) −2.64093e9 −1.94774 −0.973868 0.227117i \(-0.927070\pi\)
−0.973868 + 0.227117i \(0.927070\pi\)
\(108\) −1.85597e8 −0.131270
\(109\) 1.63965e9 1.11258 0.556291 0.830988i \(-0.312224\pi\)
0.556291 + 0.830988i \(0.312224\pi\)
\(110\) 1.63910e9 1.06742
\(111\) −1.16538e9 −0.728640
\(112\) 2.90066e8 0.174187
\(113\) −8.07127e8 −0.465682 −0.232841 0.972515i \(-0.574802\pi\)
−0.232841 + 0.972515i \(0.574802\pi\)
\(114\) 7.40034e8 0.410374
\(115\) −2.76927e9 −1.47647
\(116\) 8.74990e8 0.448686
\(117\) 1.06747e9 0.526648
\(118\) −1.54593e8 −0.0734041
\(119\) −4.97906e9 −2.27607
\(120\) 1.54796e9 0.681467
\(121\) 3.09839e9 1.31402
\(122\) 1.28432e9 0.524872
\(123\) 9.56370e8 0.376750
\(124\) −1.01666e9 −0.386170
\(125\) −1.53252e9 −0.561449
\(126\) −6.28550e8 −0.222163
\(127\) −4.54461e9 −1.55017 −0.775086 0.631856i \(-0.782293\pi\)
−0.775086 + 0.631856i \(0.782293\pi\)
\(128\) 2.38911e9 0.786666
\(129\) 1.32592e9 0.421565
\(130\) −3.61028e9 −1.10865
\(131\) 1.30881e9 0.388289 0.194145 0.980973i \(-0.437807\pi\)
0.194145 + 0.980973i \(0.437807\pi\)
\(132\) 2.08955e9 0.599059
\(133\) −5.37741e9 −1.49019
\(134\) 3.38713e8 0.0907529
\(135\) 9.24331e8 0.239511
\(136\) −7.28554e9 −1.82615
\(137\) 2.61531e9 0.634278 0.317139 0.948379i \(-0.397278\pi\)
0.317139 + 0.948379i \(0.397278\pi\)
\(138\) 1.64535e9 0.386192
\(139\) −4.93205e9 −1.12063 −0.560314 0.828281i \(-0.689319\pi\)
−0.560314 + 0.828281i \(0.689319\pi\)
\(140\) −4.56118e9 −1.00346
\(141\) −4.20832e9 −0.896649
\(142\) −2.20489e8 −0.0455082
\(143\) −1.20182e10 −2.40340
\(144\) 2.53442e8 0.0491188
\(145\) −4.35771e9 −0.818658
\(146\) −7.18304e8 −0.130834
\(147\) 1.29867e9 0.229389
\(148\) 5.02456e9 0.860837
\(149\) −7.57899e9 −1.25972 −0.629858 0.776710i \(-0.716887\pi\)
−0.629858 + 0.776710i \(0.716887\pi\)
\(150\) −1.10781e9 −0.178671
\(151\) 1.47211e9 0.230432 0.115216 0.993340i \(-0.463244\pi\)
0.115216 + 0.993340i \(0.463244\pi\)
\(152\) −7.86843e9 −1.19562
\(153\) −4.35040e9 −0.641826
\(154\) 7.07653e9 1.01386
\(155\) 5.06328e9 0.704594
\(156\) −4.60245e9 −0.622198
\(157\) 1.05021e10 1.37952 0.689762 0.724037i \(-0.257715\pi\)
0.689762 + 0.724037i \(0.257715\pi\)
\(158\) −7.08596e9 −0.904569
\(159\) −1.25473e9 −0.155691
\(160\) −1.06418e10 −1.28374
\(161\) −1.19559e10 −1.40238
\(162\) −5.49189e8 −0.0626475
\(163\) −1.68860e9 −0.187362 −0.0936811 0.995602i \(-0.529863\pi\)
−0.0936811 + 0.995602i \(0.529863\pi\)
\(164\) −4.12342e9 −0.445103
\(165\) −1.04066e10 −1.09303
\(166\) −7.67873e9 −0.784879
\(167\) −6.84704e8 −0.0681207 −0.0340603 0.999420i \(-0.510844\pi\)
−0.0340603 + 0.999420i \(0.510844\pi\)
\(168\) 6.68307e9 0.647268
\(169\) 1.58667e10 1.49623
\(170\) 1.47134e10 1.35112
\(171\) −4.69846e9 −0.420216
\(172\) −5.71677e9 −0.498050
\(173\) 1.08407e10 0.920133 0.460067 0.887884i \(-0.347826\pi\)
0.460067 + 0.887884i \(0.347826\pi\)
\(174\) 2.58912e9 0.214132
\(175\) 8.04983e9 0.648807
\(176\) −2.85338e9 −0.224157
\(177\) 9.81506e8 0.0751646
\(178\) 6.05155e9 0.451832
\(179\) −2.45631e10 −1.78832 −0.894160 0.447747i \(-0.852226\pi\)
−0.894160 + 0.447747i \(0.852226\pi\)
\(180\) −3.98528e9 −0.282965
\(181\) 6.62375e9 0.458723 0.229361 0.973341i \(-0.426336\pi\)
0.229361 + 0.973341i \(0.426336\pi\)
\(182\) −1.55868e10 −1.05302
\(183\) −8.15410e9 −0.537460
\(184\) −1.74943e10 −1.12516
\(185\) −2.50238e10 −1.57066
\(186\) −3.00833e9 −0.184297
\(187\) 4.89790e10 2.92902
\(188\) 1.81443e10 1.05933
\(189\) 3.99065e9 0.227491
\(190\) 1.58905e10 0.884601
\(191\) 2.27509e9 0.123694 0.0618469 0.998086i \(-0.480301\pi\)
0.0618469 + 0.998086i \(0.480301\pi\)
\(192\) 4.72080e9 0.250703
\(193\) 4.96866e9 0.257769 0.128885 0.991660i \(-0.458860\pi\)
0.128885 + 0.991660i \(0.458860\pi\)
\(194\) 6.88869e9 0.349163
\(195\) 2.29216e10 1.13524
\(196\) −5.59928e9 −0.271007
\(197\) −1.44778e10 −0.684865 −0.342432 0.939543i \(-0.611251\pi\)
−0.342432 + 0.939543i \(0.611251\pi\)
\(198\) 6.18304e9 0.285896
\(199\) −8.12208e9 −0.367137 −0.183569 0.983007i \(-0.558765\pi\)
−0.183569 + 0.983007i \(0.558765\pi\)
\(200\) 1.17788e10 0.520555
\(201\) −2.15048e9 −0.0929295
\(202\) −1.09909e10 −0.464466
\(203\) −1.88137e10 −0.777574
\(204\) 1.87569e10 0.758272
\(205\) 2.05359e10 0.812122
\(206\) 2.31131e10 0.894242
\(207\) −1.04463e10 −0.395454
\(208\) 6.28486e9 0.232815
\(209\) 5.28976e10 1.91769
\(210\) −1.34967e10 −0.478895
\(211\) 4.43430e10 1.54012 0.770060 0.637972i \(-0.220226\pi\)
0.770060 + 0.637972i \(0.220226\pi\)
\(212\) 5.40980e9 0.183937
\(213\) 1.39988e9 0.0465997
\(214\) 3.36929e10 1.09819
\(215\) 2.84712e10 0.908726
\(216\) 5.83926e9 0.182522
\(217\) 2.18599e10 0.669235
\(218\) −2.09186e10 −0.627305
\(219\) 4.56049e9 0.133972
\(220\) 4.48683e10 1.29133
\(221\) −1.07881e11 −3.04215
\(222\) 1.48678e10 0.410828
\(223\) 4.53861e10 1.22900 0.614499 0.788918i \(-0.289358\pi\)
0.614499 + 0.788918i \(0.289358\pi\)
\(224\) −4.59442e10 −1.21931
\(225\) 7.03346e9 0.182956
\(226\) 1.02973e10 0.262564
\(227\) −4.69791e10 −1.17433 −0.587163 0.809469i \(-0.699755\pi\)
−0.587163 + 0.809469i \(0.699755\pi\)
\(228\) 2.02576e10 0.496455
\(229\) −6.10936e10 −1.46803 −0.734017 0.679131i \(-0.762357\pi\)
−0.734017 + 0.679131i \(0.762357\pi\)
\(230\) 3.53302e10 0.832475
\(231\) −4.49287e10 −1.03817
\(232\) −2.75289e10 −0.623868
\(233\) 1.32852e10 0.295302 0.147651 0.989040i \(-0.452829\pi\)
0.147651 + 0.989040i \(0.452829\pi\)
\(234\) −1.36188e10 −0.296939
\(235\) −9.03641e10 −1.93282
\(236\) −4.23180e9 −0.0888016
\(237\) 4.49885e10 0.926263
\(238\) 6.35226e10 1.28331
\(239\) 4.18144e10 0.828963 0.414481 0.910058i \(-0.363963\pi\)
0.414481 + 0.910058i \(0.363963\pi\)
\(240\) 5.44209e9 0.105880
\(241\) −8.05400e10 −1.53792 −0.768962 0.639295i \(-0.779226\pi\)
−0.768962 + 0.639295i \(0.779226\pi\)
\(242\) −3.95291e10 −0.740881
\(243\) 3.48678e9 0.0641500
\(244\) 3.51567e10 0.634971
\(245\) 2.78861e10 0.494471
\(246\) −1.22013e10 −0.212422
\(247\) −1.16512e11 −1.99176
\(248\) 3.19862e10 0.536945
\(249\) 4.87520e10 0.803703
\(250\) 1.95518e10 0.316560
\(251\) −9.22880e9 −0.146762 −0.0733810 0.997304i \(-0.523379\pi\)
−0.0733810 + 0.997304i \(0.523379\pi\)
\(252\) −1.72058e10 −0.268765
\(253\) 1.17610e11 1.80468
\(254\) 5.79800e10 0.874030
\(255\) −9.34149e10 −1.38352
\(256\) −6.03202e10 −0.877775
\(257\) −1.68553e10 −0.241011 −0.120505 0.992713i \(-0.538451\pi\)
−0.120505 + 0.992713i \(0.538451\pi\)
\(258\) −1.69161e10 −0.237690
\(259\) −1.08036e11 −1.49183
\(260\) −9.88272e10 −1.34121
\(261\) −1.64383e10 −0.219267
\(262\) −1.66977e10 −0.218928
\(263\) 1.22903e11 1.58403 0.792014 0.610503i \(-0.209033\pi\)
0.792014 + 0.610503i \(0.209033\pi\)
\(264\) −6.57413e10 −0.832953
\(265\) −2.69424e10 −0.335606
\(266\) 6.86048e10 0.840209
\(267\) −3.84211e10 −0.462668
\(268\) 9.27188e9 0.109790
\(269\) 1.34363e11 1.56457 0.782286 0.622920i \(-0.214054\pi\)
0.782286 + 0.622920i \(0.214054\pi\)
\(270\) −1.17926e10 −0.135043
\(271\) 1.88205e9 0.0211967 0.0105984 0.999944i \(-0.496626\pi\)
0.0105984 + 0.999944i \(0.496626\pi\)
\(272\) −2.56134e10 −0.283731
\(273\) 9.89601e10 1.07827
\(274\) −3.33660e10 −0.357624
\(275\) −7.91862e10 −0.834934
\(276\) 4.50396e10 0.467201
\(277\) 3.67108e10 0.374658 0.187329 0.982297i \(-0.440017\pi\)
0.187329 + 0.982297i \(0.440017\pi\)
\(278\) 6.29230e10 0.631841
\(279\) 1.90998e10 0.188717
\(280\) 1.43504e11 1.39525
\(281\) 1.92591e11 1.84271 0.921356 0.388720i \(-0.127083\pi\)
0.921356 + 0.388720i \(0.127083\pi\)
\(282\) 5.36896e10 0.505556
\(283\) 8.03371e10 0.744521 0.372261 0.928128i \(-0.378583\pi\)
0.372261 + 0.928128i \(0.378583\pi\)
\(284\) −6.03564e9 −0.0550542
\(285\) −1.00889e11 −0.905817
\(286\) 1.53327e11 1.35510
\(287\) 8.86603e10 0.771366
\(288\) −4.01433e10 −0.343832
\(289\) 3.21073e11 2.70747
\(290\) 5.55955e10 0.461582
\(291\) −4.37361e10 −0.357537
\(292\) −1.96627e10 −0.158278
\(293\) −1.17861e9 −0.00934253 −0.00467127 0.999989i \(-0.501487\pi\)
−0.00467127 + 0.999989i \(0.501487\pi\)
\(294\) −1.65685e10 −0.129336
\(295\) 2.10756e10 0.162025
\(296\) −1.58083e11 −1.19694
\(297\) −3.92560e10 −0.292753
\(298\) 9.66924e10 0.710263
\(299\) −2.59048e11 −1.87439
\(300\) −3.03250e10 −0.216150
\(301\) 1.22920e11 0.863123
\(302\) −1.87811e10 −0.129924
\(303\) 6.97812e10 0.475605
\(304\) −2.76626e10 −0.185764
\(305\) −1.75091e11 −1.15855
\(306\) 5.55022e10 0.361880
\(307\) −1.56337e11 −1.00447 −0.502237 0.864730i \(-0.667490\pi\)
−0.502237 + 0.864730i \(0.667490\pi\)
\(308\) 1.93712e11 1.22653
\(309\) −1.46744e11 −0.915689
\(310\) −6.45971e10 −0.397270
\(311\) 2.63103e9 0.0159479 0.00797396 0.999968i \(-0.497462\pi\)
0.00797396 + 0.999968i \(0.497462\pi\)
\(312\) 1.44802e11 0.865126
\(313\) −1.30025e10 −0.0765730 −0.0382865 0.999267i \(-0.512190\pi\)
−0.0382865 + 0.999267i \(0.512190\pi\)
\(314\) −1.33986e11 −0.777813
\(315\) 8.56901e10 0.490380
\(316\) −1.93970e11 −1.09431
\(317\) 1.49671e10 0.0832472 0.0416236 0.999133i \(-0.486747\pi\)
0.0416236 + 0.999133i \(0.486747\pi\)
\(318\) 1.60078e10 0.0877826
\(319\) 1.85070e11 1.00064
\(320\) 1.01368e11 0.540415
\(321\) −2.13915e11 −1.12453
\(322\) 1.52532e11 0.790698
\(323\) 4.74836e11 2.42735
\(324\) −1.50334e10 −0.0757887
\(325\) 1.74416e11 0.867183
\(326\) 2.15431e10 0.105640
\(327\) 1.32812e11 0.642349
\(328\) 1.29731e11 0.618887
\(329\) −3.90132e11 −1.83582
\(330\) 1.32767e11 0.616278
\(331\) −1.15965e11 −0.531009 −0.265504 0.964110i \(-0.585538\pi\)
−0.265504 + 0.964110i \(0.585538\pi\)
\(332\) −2.10196e11 −0.949518
\(333\) −9.43956e10 −0.420681
\(334\) 8.73543e9 0.0384083
\(335\) −4.61767e10 −0.200319
\(336\) 2.34953e10 0.100567
\(337\) 4.01252e10 0.169466 0.0847329 0.996404i \(-0.472996\pi\)
0.0847329 + 0.996404i \(0.472996\pi\)
\(338\) −2.02427e11 −0.843614
\(339\) −6.53773e10 −0.268861
\(340\) 4.02762e11 1.63453
\(341\) −2.15035e11 −0.861222
\(342\) 5.99427e10 0.236929
\(343\) −1.82626e11 −0.712424
\(344\) 1.79861e11 0.692506
\(345\) −2.24311e11 −0.852441
\(346\) −1.38306e11 −0.518797
\(347\) 2.83797e11 1.05081 0.525406 0.850852i \(-0.323914\pi\)
0.525406 + 0.850852i \(0.323914\pi\)
\(348\) 7.08742e10 0.259049
\(349\) −9.89684e10 −0.357094 −0.178547 0.983931i \(-0.557140\pi\)
−0.178547 + 0.983931i \(0.557140\pi\)
\(350\) −1.02699e11 −0.365816
\(351\) 8.64654e10 0.304061
\(352\) 4.51953e11 1.56910
\(353\) −4.13864e11 −1.41864 −0.709319 0.704888i \(-0.750997\pi\)
−0.709319 + 0.704888i \(0.750997\pi\)
\(354\) −1.25220e10 −0.0423799
\(355\) 3.00593e10 0.100450
\(356\) 1.65654e11 0.546610
\(357\) −4.03304e11 −1.31409
\(358\) 3.13376e11 1.00830
\(359\) −5.20511e11 −1.65388 −0.826941 0.562288i \(-0.809921\pi\)
−0.826941 + 0.562288i \(0.809921\pi\)
\(360\) 1.25385e11 0.393445
\(361\) 1.90138e11 0.589233
\(362\) −8.45056e10 −0.258641
\(363\) 2.50970e11 0.758649
\(364\) −4.26670e11 −1.27390
\(365\) 9.79262e10 0.288789
\(366\) 1.04030e11 0.303035
\(367\) −6.58062e11 −1.89352 −0.946759 0.321943i \(-0.895664\pi\)
−0.946759 + 0.321943i \(0.895664\pi\)
\(368\) −6.15037e10 −0.174818
\(369\) 7.74660e10 0.217517
\(370\) 3.19253e11 0.885579
\(371\) −1.16319e11 −0.318764
\(372\) −8.23496e10 −0.222955
\(373\) 4.46324e10 0.119388 0.0596940 0.998217i \(-0.480988\pi\)
0.0596940 + 0.998217i \(0.480988\pi\)
\(374\) −6.24872e11 −1.65146
\(375\) −1.24134e11 −0.324152
\(376\) −5.70856e11 −1.47293
\(377\) −4.07637e11 −1.03929
\(378\) −5.09125e10 −0.128266
\(379\) −1.03766e11 −0.258332 −0.129166 0.991623i \(-0.541230\pi\)
−0.129166 + 0.991623i \(0.541230\pi\)
\(380\) 4.34985e11 1.07016
\(381\) −3.68113e11 −0.894992
\(382\) −2.90255e10 −0.0697419
\(383\) −2.71556e11 −0.644860 −0.322430 0.946593i \(-0.604500\pi\)
−0.322430 + 0.946593i \(0.604500\pi\)
\(384\) 1.93518e11 0.454182
\(385\) −9.64742e11 −2.23788
\(386\) −6.33900e10 −0.145338
\(387\) 1.07400e11 0.243391
\(388\) 1.88570e11 0.422405
\(389\) 9.45844e10 0.209434 0.104717 0.994502i \(-0.466606\pi\)
0.104717 + 0.994502i \(0.466606\pi\)
\(390\) −2.92433e11 −0.640081
\(391\) 1.05573e12 2.28432
\(392\) 1.76164e11 0.376817
\(393\) 1.06014e11 0.224179
\(394\) 1.84707e11 0.386146
\(395\) 9.66027e11 1.99665
\(396\) 1.69253e11 0.345867
\(397\) 5.98081e11 1.20838 0.604189 0.796841i \(-0.293497\pi\)
0.604189 + 0.796841i \(0.293497\pi\)
\(398\) 1.03621e11 0.207002
\(399\) −4.35570e11 −0.860360
\(400\) 4.14102e10 0.0808793
\(401\) 7.44476e11 1.43781 0.718904 0.695109i \(-0.244644\pi\)
0.718904 + 0.695109i \(0.244644\pi\)
\(402\) 2.74358e10 0.0523962
\(403\) 4.73638e11 0.894487
\(404\) −3.00864e11 −0.561894
\(405\) 7.48708e10 0.138282
\(406\) 2.40025e11 0.438418
\(407\) 1.06275e12 1.91981
\(408\) −5.90129e11 −1.05433
\(409\) 1.01980e11 0.180202 0.0901010 0.995933i \(-0.471281\pi\)
0.0901010 + 0.995933i \(0.471281\pi\)
\(410\) −2.61996e11 −0.457897
\(411\) 2.11840e11 0.366201
\(412\) 6.32693e11 1.08182
\(413\) 9.09905e10 0.153894
\(414\) 1.33274e11 0.222968
\(415\) 1.04684e12 1.73246
\(416\) −9.95474e11 −1.62971
\(417\) −3.99496e11 −0.646994
\(418\) −6.74865e11 −1.08124
\(419\) −1.11843e12 −1.77275 −0.886375 0.462968i \(-0.846784\pi\)
−0.886375 + 0.462968i \(0.846784\pi\)
\(420\) −3.69456e11 −0.579349
\(421\) 3.12652e11 0.485056 0.242528 0.970144i \(-0.422023\pi\)
0.242528 + 0.970144i \(0.422023\pi\)
\(422\) −5.65727e11 −0.868362
\(423\) −3.40874e11 −0.517681
\(424\) −1.70203e11 −0.255753
\(425\) −7.10817e11 −1.05684
\(426\) −1.78596e10 −0.0262742
\(427\) −7.55926e11 −1.10041
\(428\) 9.22303e11 1.32855
\(429\) −9.73470e11 −1.38760
\(430\) −3.63235e11 −0.512365
\(431\) 6.75381e11 0.942760 0.471380 0.881930i \(-0.343756\pi\)
0.471380 + 0.881930i \(0.343756\pi\)
\(432\) 2.05288e10 0.0283587
\(433\) −5.25804e10 −0.0718833 −0.0359417 0.999354i \(-0.511443\pi\)
−0.0359417 + 0.999354i \(0.511443\pi\)
\(434\) −2.78887e11 −0.377333
\(435\) −3.52975e11 −0.472652
\(436\) −5.72622e11 −0.758890
\(437\) 1.14019e12 1.49559
\(438\) −5.81826e10 −0.0755370
\(439\) −8.88917e11 −1.14228 −0.571138 0.820854i \(-0.693498\pi\)
−0.571138 + 0.820854i \(0.693498\pi\)
\(440\) −1.41165e12 −1.79551
\(441\) 1.05193e11 0.132438
\(442\) 1.37635e12 1.71525
\(443\) −1.05658e12 −1.30342 −0.651712 0.758467i \(-0.725949\pi\)
−0.651712 + 0.758467i \(0.725949\pi\)
\(444\) 4.06990e11 0.497004
\(445\) −8.25007e11 −0.997327
\(446\) −5.79034e11 −0.692943
\(447\) −6.13898e11 −0.727298
\(448\) 4.37641e11 0.513295
\(449\) −1.35032e12 −1.56793 −0.783966 0.620803i \(-0.786806\pi\)
−0.783966 + 0.620803i \(0.786806\pi\)
\(450\) −8.97326e10 −0.103156
\(451\) −8.72151e11 −0.992652
\(452\) 2.81877e11 0.317641
\(453\) 1.19241e11 0.133040
\(454\) 5.99358e11 0.662117
\(455\) 2.12494e12 2.32432
\(456\) −6.37342e11 −0.690289
\(457\) −5.30062e11 −0.568465 −0.284233 0.958755i \(-0.591739\pi\)
−0.284233 + 0.958755i \(0.591739\pi\)
\(458\) 7.79431e11 0.827719
\(459\) −3.52382e11 −0.370559
\(460\) 9.67123e11 1.00710
\(461\) 2.63945e11 0.272181 0.136091 0.990696i \(-0.456546\pi\)
0.136091 + 0.990696i \(0.456546\pi\)
\(462\) 5.73199e11 0.585351
\(463\) 7.13021e11 0.721088 0.360544 0.932742i \(-0.382591\pi\)
0.360544 + 0.932742i \(0.382591\pi\)
\(464\) −9.67820e10 −0.0969312
\(465\) 4.10126e11 0.406798
\(466\) −1.69492e11 −0.166499
\(467\) −1.27483e12 −1.24030 −0.620149 0.784484i \(-0.712928\pi\)
−0.620149 + 0.784484i \(0.712928\pi\)
\(468\) −3.72798e11 −0.359226
\(469\) −1.99360e11 −0.190266
\(470\) 1.15286e12 1.08978
\(471\) 8.50673e11 0.796468
\(472\) 1.33141e11 0.123473
\(473\) −1.20916e12 −1.11073
\(474\) −5.73962e11 −0.522253
\(475\) −7.67686e11 −0.691931
\(476\) 1.73886e12 1.55250
\(477\) −1.01633e11 −0.0898880
\(478\) −5.33466e11 −0.467392
\(479\) 1.10751e12 0.961254 0.480627 0.876925i \(-0.340409\pi\)
0.480627 + 0.876925i \(0.340409\pi\)
\(480\) −8.61986e11 −0.741165
\(481\) −2.34082e12 −1.99396
\(482\) 1.02753e12 0.867124
\(483\) −9.68424e11 −0.809662
\(484\) −1.08206e12 −0.896290
\(485\) −9.39133e11 −0.770707
\(486\) −4.44843e10 −0.0361696
\(487\) 1.73479e12 1.39755 0.698775 0.715341i \(-0.253729\pi\)
0.698775 + 0.715341i \(0.253729\pi\)
\(488\) −1.10610e12 −0.882886
\(489\) −1.36776e11 −0.108174
\(490\) −3.55770e11 −0.278796
\(491\) −2.79615e11 −0.217117 −0.108559 0.994090i \(-0.534624\pi\)
−0.108559 + 0.994090i \(0.534624\pi\)
\(492\) −3.33997e11 −0.256980
\(493\) 1.66129e12 1.26658
\(494\) 1.48646e12 1.12301
\(495\) −8.42933e11 −0.631058
\(496\) 1.12452e11 0.0834258
\(497\) 1.29776e11 0.0954092
\(498\) −6.21977e11 −0.453150
\(499\) −1.73268e12 −1.25103 −0.625513 0.780214i \(-0.715110\pi\)
−0.625513 + 0.780214i \(0.715110\pi\)
\(500\) 5.35207e11 0.382963
\(501\) −5.54610e10 −0.0393295
\(502\) 1.17741e11 0.0827485
\(503\) −1.53274e12 −1.06761 −0.533805 0.845607i \(-0.679239\pi\)
−0.533805 + 0.845607i \(0.679239\pi\)
\(504\) 5.41328e11 0.373700
\(505\) 1.49839e12 1.02521
\(506\) −1.50046e12 −1.01753
\(507\) 1.28521e12 0.863847
\(508\) 1.58713e12 1.05737
\(509\) −1.22778e12 −0.810760 −0.405380 0.914148i \(-0.632861\pi\)
−0.405380 + 0.914148i \(0.632861\pi\)
\(510\) 1.19178e12 0.780067
\(511\) 4.22780e11 0.274297
\(512\) −4.53659e11 −0.291752
\(513\) −3.80575e11 −0.242612
\(514\) 2.15039e11 0.135889
\(515\) −3.15100e12 −1.97386
\(516\) −4.63058e11 −0.287549
\(517\) 3.83773e12 2.36247
\(518\) 1.37832e12 0.841138
\(519\) 8.78099e11 0.531239
\(520\) 3.10930e12 1.86486
\(521\) 8.56707e11 0.509404 0.254702 0.967020i \(-0.418023\pi\)
0.254702 + 0.967020i \(0.418023\pi\)
\(522\) 2.09719e11 0.123629
\(523\) −1.42937e12 −0.835385 −0.417692 0.908589i \(-0.637161\pi\)
−0.417692 + 0.908589i \(0.637161\pi\)
\(524\) −4.57081e11 −0.264851
\(525\) 6.52036e11 0.374589
\(526\) −1.56800e12 −0.893119
\(527\) −1.93027e12 −1.09011
\(528\) −2.31124e11 −0.129417
\(529\) 7.33890e11 0.407456
\(530\) 3.43731e11 0.189224
\(531\) 7.95020e10 0.0433963
\(532\) 1.87798e12 1.01645
\(533\) 1.92100e12 1.03099
\(534\) 4.90176e11 0.260865
\(535\) −4.59335e12 −2.42403
\(536\) −2.91712e11 −0.152655
\(537\) −1.98961e12 −1.03249
\(538\) −1.71420e12 −0.882149
\(539\) −1.18431e12 −0.604389
\(540\) −3.22808e11 −0.163370
\(541\) 9.13135e11 0.458297 0.229149 0.973391i \(-0.426406\pi\)
0.229149 + 0.973391i \(0.426406\pi\)
\(542\) −2.40111e10 −0.0119513
\(543\) 5.36524e11 0.264844
\(544\) 4.05697e12 1.98613
\(545\) 2.85183e12 1.38465
\(546\) −1.26253e12 −0.607960
\(547\) 1.79117e12 0.855448 0.427724 0.903909i \(-0.359316\pi\)
0.427724 + 0.903909i \(0.359316\pi\)
\(548\) −9.13354e11 −0.432640
\(549\) −6.60482e11 −0.310303
\(550\) 1.01025e12 0.470759
\(551\) 1.79420e12 0.829257
\(552\) −1.41703e12 −0.649613
\(553\) 4.17066e12 1.89645
\(554\) −4.68355e11 −0.211242
\(555\) −2.02693e12 −0.906819
\(556\) 1.72244e12 0.764378
\(557\) −2.69969e12 −1.18841 −0.594203 0.804315i \(-0.702533\pi\)
−0.594203 + 0.804315i \(0.702533\pi\)
\(558\) −2.43675e11 −0.106404
\(559\) 2.66330e12 1.15363
\(560\) 5.04509e11 0.216782
\(561\) 3.96730e12 1.69107
\(562\) −2.45707e12 −1.03897
\(563\) −2.13576e12 −0.895910 −0.447955 0.894056i \(-0.647847\pi\)
−0.447955 + 0.894056i \(0.647847\pi\)
\(564\) 1.46969e12 0.611603
\(565\) −1.40383e12 −0.579557
\(566\) −1.02494e12 −0.419782
\(567\) 3.23242e11 0.131342
\(568\) 1.89893e11 0.0765493
\(569\) 2.14904e12 0.859489 0.429744 0.902951i \(-0.358604\pi\)
0.429744 + 0.902951i \(0.358604\pi\)
\(570\) 1.28713e12 0.510725
\(571\) 2.27870e12 0.897067 0.448533 0.893766i \(-0.351947\pi\)
0.448533 + 0.893766i \(0.351947\pi\)
\(572\) 4.19715e12 1.63935
\(573\) 1.84282e11 0.0714146
\(574\) −1.13112e12 −0.434918
\(575\) −1.70683e12 −0.651158
\(576\) 3.82384e11 0.144744
\(577\) −1.61675e12 −0.607228 −0.303614 0.952795i \(-0.598193\pi\)
−0.303614 + 0.952795i \(0.598193\pi\)
\(578\) −4.09624e12 −1.52655
\(579\) 4.02461e11 0.148823
\(580\) 1.52186e12 0.558405
\(581\) 4.51956e12 1.64552
\(582\) 5.57984e11 0.201590
\(583\) 1.14423e12 0.410210
\(584\) 6.18628e11 0.220075
\(585\) 1.85665e12 0.655433
\(586\) 1.50366e10 0.00526758
\(587\) −2.42203e12 −0.841993 −0.420996 0.907062i \(-0.638320\pi\)
−0.420996 + 0.907062i \(0.638320\pi\)
\(588\) −4.53542e11 −0.156466
\(589\) −2.08470e12 −0.713716
\(590\) −2.68882e11 −0.0913541
\(591\) −1.17270e12 −0.395407
\(592\) −5.55764e11 −0.185970
\(593\) −4.67893e12 −1.55382 −0.776910 0.629611i \(-0.783214\pi\)
−0.776910 + 0.629611i \(0.783214\pi\)
\(594\) 5.00826e11 0.165062
\(595\) −8.66003e12 −2.83265
\(596\) 2.64684e12 0.859250
\(597\) −6.57888e11 −0.211967
\(598\) 3.30492e12 1.05683
\(599\) 4.42395e12 1.40407 0.702036 0.712141i \(-0.252274\pi\)
0.702036 + 0.712141i \(0.252274\pi\)
\(600\) 9.54084e11 0.300543
\(601\) 1.93036e12 0.603536 0.301768 0.953381i \(-0.402423\pi\)
0.301768 + 0.953381i \(0.402423\pi\)
\(602\) −1.56821e12 −0.486652
\(603\) −1.74189e11 −0.0536529
\(604\) −5.14110e11 −0.157177
\(605\) 5.38900e12 1.63534
\(606\) −8.90266e11 −0.268159
\(607\) 2.14021e12 0.639893 0.319947 0.947436i \(-0.396335\pi\)
0.319947 + 0.947436i \(0.396335\pi\)
\(608\) 4.38155e12 1.30036
\(609\) −1.52391e12 −0.448933
\(610\) 2.23380e12 0.653222
\(611\) −8.45300e12 −2.45372
\(612\) 1.51931e12 0.437789
\(613\) 3.34392e12 0.956499 0.478249 0.878224i \(-0.341272\pi\)
0.478249 + 0.878224i \(0.341272\pi\)
\(614\) 1.99454e12 0.566351
\(615\) 1.66341e12 0.468879
\(616\) −6.09455e12 −1.70541
\(617\) 1.60127e12 0.444817 0.222408 0.974954i \(-0.428608\pi\)
0.222408 + 0.974954i \(0.428608\pi\)
\(618\) 1.87216e12 0.516291
\(619\) 3.69026e12 1.01030 0.505148 0.863033i \(-0.331438\pi\)
0.505148 + 0.863033i \(0.331438\pi\)
\(620\) −1.76827e12 −0.480603
\(621\) −8.46151e11 −0.228316
\(622\) −3.35666e10 −0.00899188
\(623\) −3.56183e12 −0.947277
\(624\) 5.09074e11 0.134416
\(625\) −4.75926e12 −1.24761
\(626\) 1.65885e11 0.0431740
\(627\) 4.28470e12 1.10718
\(628\) −3.66770e12 −0.940970
\(629\) 9.53983e12 2.43004
\(630\) −1.09323e12 −0.276490
\(631\) −4.36858e12 −1.09700 −0.548502 0.836149i \(-0.684802\pi\)
−0.548502 + 0.836149i \(0.684802\pi\)
\(632\) 6.10267e12 1.52157
\(633\) 3.59179e12 0.889188
\(634\) −1.90949e11 −0.0469371
\(635\) −7.90440e12 −1.92924
\(636\) 4.38194e11 0.106196
\(637\) 2.60857e12 0.627733
\(638\) −2.36112e12 −0.564190
\(639\) 1.13390e11 0.0269043
\(640\) 4.15535e12 0.979034
\(641\) −4.25253e12 −0.994916 −0.497458 0.867488i \(-0.665733\pi\)
−0.497458 + 0.867488i \(0.665733\pi\)
\(642\) 2.72912e12 0.634039
\(643\) 5.18438e12 1.19604 0.598022 0.801479i \(-0.295953\pi\)
0.598022 + 0.801479i \(0.295953\pi\)
\(644\) 4.17540e12 0.956558
\(645\) 2.30617e12 0.524653
\(646\) −6.05795e12 −1.36861
\(647\) 6.51180e12 1.46094 0.730468 0.682946i \(-0.239302\pi\)
0.730468 + 0.682946i \(0.239302\pi\)
\(648\) 4.72980e11 0.105379
\(649\) −8.95073e11 −0.198042
\(650\) −2.22519e12 −0.488942
\(651\) 1.77065e12 0.386383
\(652\) 5.89716e11 0.127799
\(653\) 7.98599e11 0.171878 0.0859388 0.996300i \(-0.472611\pi\)
0.0859388 + 0.996300i \(0.472611\pi\)
\(654\) −1.69441e12 −0.362174
\(655\) 2.27640e12 0.483240
\(656\) 4.56089e11 0.0961573
\(657\) 3.69400e11 0.0773486
\(658\) 4.97729e12 1.03509
\(659\) −2.53693e12 −0.523992 −0.261996 0.965069i \(-0.584381\pi\)
−0.261996 + 0.965069i \(0.584381\pi\)
\(660\) 3.63433e12 0.745551
\(661\) −4.69117e12 −0.955817 −0.477909 0.878410i \(-0.658605\pi\)
−0.477909 + 0.878410i \(0.658605\pi\)
\(662\) 1.47948e12 0.299397
\(663\) −8.73838e12 −1.75639
\(664\) 6.61318e12 1.32024
\(665\) −9.35288e12 −1.85459
\(666\) 1.20430e12 0.237191
\(667\) 3.98913e12 0.780391
\(668\) 2.39122e11 0.0464650
\(669\) 3.67627e12 0.709562
\(670\) 5.89121e11 0.112945
\(671\) 7.43604e12 1.41609
\(672\) −3.72148e12 −0.703970
\(673\) −2.88094e12 −0.541336 −0.270668 0.962673i \(-0.587244\pi\)
−0.270668 + 0.962673i \(0.587244\pi\)
\(674\) −5.11915e11 −0.0955495
\(675\) 5.69710e11 0.105630
\(676\) −5.54121e12 −1.02057
\(677\) −2.82495e12 −0.516847 −0.258424 0.966032i \(-0.583203\pi\)
−0.258424 + 0.966032i \(0.583203\pi\)
\(678\) 8.34082e11 0.151592
\(679\) −4.05455e12 −0.732030
\(680\) −1.26717e13 −2.27271
\(681\) −3.80531e12 −0.677997
\(682\) 2.74341e12 0.485581
\(683\) 8.92345e12 1.56906 0.784530 0.620091i \(-0.212904\pi\)
0.784530 + 0.620091i \(0.212904\pi\)
\(684\) 1.64086e12 0.286629
\(685\) 4.54878e12 0.789382
\(686\) 2.32993e12 0.401684
\(687\) −4.94858e12 −0.847570
\(688\) 6.32328e11 0.107596
\(689\) −2.52030e12 −0.426054
\(690\) 2.86175e12 0.480630
\(691\) 5.24694e12 0.875498 0.437749 0.899097i \(-0.355776\pi\)
0.437749 + 0.899097i \(0.355776\pi\)
\(692\) −3.78595e12 −0.627621
\(693\) −3.63922e12 −0.599390
\(694\) −3.62067e12 −0.592476
\(695\) −8.57828e12 −1.39466
\(696\) −2.22984e12 −0.360191
\(697\) −7.82889e12 −1.25647
\(698\) 1.26263e12 0.201339
\(699\) 1.07610e12 0.170493
\(700\) −2.81128e12 −0.442550
\(701\) 8.82988e12 1.38110 0.690548 0.723287i \(-0.257370\pi\)
0.690548 + 0.723287i \(0.257370\pi\)
\(702\) −1.10312e12 −0.171438
\(703\) 1.03031e13 1.59099
\(704\) −4.30508e12 −0.660547
\(705\) −7.31949e12 −1.11591
\(706\) 5.28006e12 0.799867
\(707\) 6.46907e12 0.973765
\(708\) −3.42776e11 −0.0512696
\(709\) 5.84677e12 0.868977 0.434488 0.900677i \(-0.356929\pi\)
0.434488 + 0.900677i \(0.356929\pi\)
\(710\) −3.83495e11 −0.0566366
\(711\) 3.64407e12 0.534778
\(712\) −5.21180e12 −0.760025
\(713\) −4.63502e12 −0.671660
\(714\) 5.14533e12 0.740920
\(715\) −2.09031e13 −2.99111
\(716\) 8.57829e12 1.21981
\(717\) 3.38696e12 0.478602
\(718\) 6.64066e12 0.932505
\(719\) −1.95656e12 −0.273032 −0.136516 0.990638i \(-0.543590\pi\)
−0.136516 + 0.990638i \(0.543590\pi\)
\(720\) 4.40810e11 0.0611300
\(721\) −1.36039e13 −1.87480
\(722\) −2.42578e12 −0.332226
\(723\) −6.52374e12 −0.887920
\(724\) −2.31324e12 −0.312894
\(725\) −2.68587e12 −0.361047
\(726\) −3.20186e12 −0.427748
\(727\) −3.82900e12 −0.508370 −0.254185 0.967156i \(-0.581807\pi\)
−0.254185 + 0.967156i \(0.581807\pi\)
\(728\) 1.34239e13 1.77128
\(729\) 2.82430e11 0.0370370
\(730\) −1.24934e12 −0.162827
\(731\) −1.08541e13 −1.40593
\(732\) 2.84769e12 0.366601
\(733\) 6.07535e12 0.777327 0.388663 0.921380i \(-0.372937\pi\)
0.388663 + 0.921380i \(0.372937\pi\)
\(734\) 8.39553e12 1.06762
\(735\) 2.25877e12 0.285483
\(736\) 9.74172e12 1.22373
\(737\) 1.96111e12 0.244849
\(738\) −9.88308e11 −0.122642
\(739\) −1.29264e13 −1.59433 −0.797167 0.603759i \(-0.793669\pi\)
−0.797167 + 0.603759i \(0.793669\pi\)
\(740\) 8.73918e12 1.07134
\(741\) −9.43751e12 −1.14994
\(742\) 1.48400e12 0.179728
\(743\) 6.22278e12 0.749091 0.374546 0.927209i \(-0.377799\pi\)
0.374546 + 0.927209i \(0.377799\pi\)
\(744\) 2.59088e12 0.310005
\(745\) −1.31821e13 −1.56776
\(746\) −5.69419e11 −0.0673142
\(747\) 3.94892e12 0.464018
\(748\) −1.71051e13 −1.99788
\(749\) −1.98310e13 −2.30238
\(750\) 1.58369e12 0.182766
\(751\) 1.46813e12 0.168416 0.0842082 0.996448i \(-0.473164\pi\)
0.0842082 + 0.996448i \(0.473164\pi\)
\(752\) −2.00693e12 −0.228851
\(753\) −7.47533e11 −0.0847331
\(754\) 5.20061e12 0.585981
\(755\) 2.56042e12 0.286781
\(756\) −1.39367e12 −0.155171
\(757\) −3.31049e11 −0.0366405 −0.0183202 0.999832i \(-0.505832\pi\)
−0.0183202 + 0.999832i \(0.505832\pi\)
\(758\) 1.32384e12 0.145655
\(759\) 9.52639e12 1.04193
\(760\) −1.36855e13 −1.48799
\(761\) −2.90517e10 −0.00314008 −0.00157004 0.999999i \(-0.500500\pi\)
−0.00157004 + 0.999999i \(0.500500\pi\)
\(762\) 4.69638e12 0.504621
\(763\) 1.23123e13 1.31516
\(764\) −7.94538e11 −0.0843713
\(765\) −7.56661e12 −0.798776
\(766\) 3.46450e12 0.363590
\(767\) 1.97149e12 0.205691
\(768\) −4.88594e12 −0.506783
\(769\) −9.36673e12 −0.965872 −0.482936 0.875656i \(-0.660430\pi\)
−0.482936 + 0.875656i \(0.660430\pi\)
\(770\) 1.23081e13 1.26178
\(771\) −1.36528e12 −0.139148
\(772\) −1.73523e12 −0.175824
\(773\) −5.92112e12 −0.596480 −0.298240 0.954491i \(-0.596400\pi\)
−0.298240 + 0.954491i \(0.596400\pi\)
\(774\) −1.37020e12 −0.137231
\(775\) 3.12074e12 0.310742
\(776\) −5.93277e12 −0.587327
\(777\) −8.75094e12 −0.861311
\(778\) −1.20670e12 −0.118084
\(779\) −8.45524e12 −0.822636
\(780\) −8.00500e12 −0.774347
\(781\) −1.27661e12 −0.122780
\(782\) −1.34689e13 −1.28796
\(783\) −1.33150e12 −0.126594
\(784\) 6.19333e11 0.0585466
\(785\) 1.82663e13 1.71687
\(786\) −1.35252e12 −0.126398
\(787\) 1.09623e13 1.01863 0.509315 0.860580i \(-0.329899\pi\)
0.509315 + 0.860580i \(0.329899\pi\)
\(788\) 5.05615e12 0.467145
\(789\) 9.95517e12 0.914539
\(790\) −1.23245e13 −1.12577
\(791\) −6.06080e12 −0.550473
\(792\) −5.32505e12 −0.480906
\(793\) −1.63787e13 −1.47078
\(794\) −7.63030e12 −0.681317
\(795\) −2.18234e12 −0.193762
\(796\) 2.83651e12 0.250424
\(797\) 1.23075e13 1.08046 0.540229 0.841518i \(-0.318338\pi\)
0.540229 + 0.841518i \(0.318338\pi\)
\(798\) 5.55699e12 0.485095
\(799\) 3.44495e13 2.99035
\(800\) −6.55906e12 −0.566157
\(801\) −3.11211e12 −0.267122
\(802\) −9.49800e12 −0.810676
\(803\) −4.15889e12 −0.352986
\(804\) 7.51022e11 0.0633871
\(805\) −2.07947e13 −1.74531
\(806\) −6.04266e12 −0.504336
\(807\) 1.08834e13 0.903306
\(808\) 9.46578e12 0.781277
\(809\) 6.04381e12 0.496069 0.248035 0.968751i \(-0.420215\pi\)
0.248035 + 0.968751i \(0.420215\pi\)
\(810\) −9.55199e11 −0.0779671
\(811\) −4.73277e12 −0.384169 −0.192084 0.981378i \(-0.561525\pi\)
−0.192084 + 0.981378i \(0.561525\pi\)
\(812\) 6.57039e12 0.530382
\(813\) 1.52446e11 0.0122379
\(814\) −1.35586e13 −1.08244
\(815\) −2.93696e12 −0.233179
\(816\) −2.07469e12 −0.163812
\(817\) −1.17225e13 −0.920491
\(818\) −1.30106e12 −0.101603
\(819\) 8.01577e12 0.622541
\(820\) −7.17184e12 −0.553947
\(821\) 9.83876e12 0.755781 0.377891 0.925850i \(-0.376650\pi\)
0.377891 + 0.925850i \(0.376650\pi\)
\(822\) −2.70264e12 −0.206474
\(823\) −1.89616e12 −0.144071 −0.0720355 0.997402i \(-0.522949\pi\)
−0.0720355 + 0.997402i \(0.522949\pi\)
\(824\) −1.99058e13 −1.50420
\(825\) −6.41408e12 −0.482049
\(826\) −1.16085e12 −0.0867695
\(827\) −1.24758e13 −0.927460 −0.463730 0.885977i \(-0.653489\pi\)
−0.463730 + 0.885977i \(0.653489\pi\)
\(828\) 3.64821e12 0.269739
\(829\) −2.54424e13 −1.87095 −0.935475 0.353393i \(-0.885028\pi\)
−0.935475 + 0.353393i \(0.885028\pi\)
\(830\) −1.33555e13 −0.976810
\(831\) 2.97357e12 0.216309
\(832\) 9.48238e12 0.686060
\(833\) −1.06310e13 −0.765018
\(834\) 5.09676e12 0.364793
\(835\) −1.19090e12 −0.0847786
\(836\) −1.84736e13 −1.30805
\(837\) 1.54709e12 0.108956
\(838\) 1.42689e13 0.999526
\(839\) 6.98126e12 0.486413 0.243207 0.969975i \(-0.421801\pi\)
0.243207 + 0.969975i \(0.421801\pi\)
\(840\) 1.16238e13 0.805548
\(841\) −8.22986e12 −0.567297
\(842\) −3.98880e12 −0.273488
\(843\) 1.55999e13 1.06389
\(844\) −1.54861e13 −1.05051
\(845\) 2.75969e13 1.86211
\(846\) 4.34886e12 0.291883
\(847\) 2.32661e13 1.55328
\(848\) −5.98374e11 −0.0397367
\(849\) 6.50731e12 0.429850
\(850\) 9.06858e12 0.595873
\(851\) 2.29073e13 1.49724
\(852\) −4.88886e11 −0.0317856
\(853\) −1.84886e12 −0.119573 −0.0597866 0.998211i \(-0.519042\pi\)
−0.0597866 + 0.998211i \(0.519042\pi\)
\(854\) 9.64408e12 0.620441
\(855\) −8.17198e12 −0.522974
\(856\) −2.90175e13 −1.84726
\(857\) 1.45086e13 0.918782 0.459391 0.888234i \(-0.348068\pi\)
0.459391 + 0.888234i \(0.348068\pi\)
\(858\) 1.24195e13 0.782369
\(859\) 2.74113e13 1.71775 0.858875 0.512186i \(-0.171164\pi\)
0.858875 + 0.512186i \(0.171164\pi\)
\(860\) −9.94313e12 −0.619840
\(861\) 7.18148e12 0.445348
\(862\) −8.61649e12 −0.531554
\(863\) −1.70047e13 −1.04357 −0.521783 0.853078i \(-0.674733\pi\)
−0.521783 + 0.853078i \(0.674733\pi\)
\(864\) −3.25161e12 −0.198512
\(865\) 1.88552e13 1.14514
\(866\) 6.70819e11 0.0405298
\(867\) 2.60069e13 1.56316
\(868\) −7.63422e12 −0.456484
\(869\) −4.10268e13 −2.44050
\(870\) 4.50324e12 0.266495
\(871\) −4.31955e12 −0.254306
\(872\) 1.80158e13 1.05519
\(873\) −3.54262e12 −0.206424
\(874\) −1.45465e13 −0.843253
\(875\) −1.15078e13 −0.663677
\(876\) −1.59268e12 −0.0913819
\(877\) 1.26828e13 0.723965 0.361983 0.932185i \(-0.382100\pi\)
0.361983 + 0.932185i \(0.382100\pi\)
\(878\) 1.13408e13 0.644047
\(879\) −9.54672e10 −0.00539391
\(880\) −4.96285e12 −0.278971
\(881\) 3.27635e13 1.83231 0.916155 0.400825i \(-0.131276\pi\)
0.916155 + 0.400825i \(0.131276\pi\)
\(882\) −1.34204e12 −0.0746721
\(883\) 3.49858e13 1.93673 0.968364 0.249542i \(-0.0802802\pi\)
0.968364 + 0.249542i \(0.0802802\pi\)
\(884\) 3.76758e13 2.07505
\(885\) 1.70713e12 0.0935450
\(886\) 1.34798e13 0.734907
\(887\) −1.92767e13 −1.04562 −0.522812 0.852448i \(-0.675117\pi\)
−0.522812 + 0.852448i \(0.675117\pi\)
\(888\) −1.28047e13 −0.691052
\(889\) −3.41259e13 −1.83243
\(890\) 1.05254e13 0.562321
\(891\) −3.17973e12 −0.169021
\(892\) −1.58504e13 −0.838297
\(893\) 3.72056e13 1.95784
\(894\) 7.83209e12 0.410071
\(895\) −4.27225e13 −2.22563
\(896\) 1.79400e13 0.929902
\(897\) −2.09829e13 −1.08218
\(898\) 1.72273e13 0.884044
\(899\) −7.29366e12 −0.372415
\(900\) −2.45632e12 −0.124794
\(901\) 1.02712e13 0.519232
\(902\) 1.11269e13 0.559685
\(903\) 9.95650e12 0.498324
\(904\) −8.86839e12 −0.441659
\(905\) 1.15206e13 0.570897
\(906\) −1.52127e12 −0.0750116
\(907\) 1.51666e13 0.744141 0.372070 0.928204i \(-0.378648\pi\)
0.372070 + 0.928204i \(0.378648\pi\)
\(908\) 1.64067e13 0.801005
\(909\) 5.65228e12 0.274591
\(910\) −2.71100e13 −1.31052
\(911\) −8.07083e12 −0.388227 −0.194113 0.980979i \(-0.562183\pi\)
−0.194113 + 0.980979i \(0.562183\pi\)
\(912\) −2.24067e12 −0.107251
\(913\) −4.44589e13 −2.11758
\(914\) 6.76251e12 0.320516
\(915\) −1.41824e13 −0.668888
\(916\) 2.13360e13 1.00134
\(917\) 9.82798e12 0.458989
\(918\) 4.49568e12 0.208931
\(919\) −5.04236e12 −0.233192 −0.116596 0.993179i \(-0.537198\pi\)
−0.116596 + 0.993179i \(0.537198\pi\)
\(920\) −3.04276e13 −1.40030
\(921\) −1.26633e13 −0.579934
\(922\) −3.36740e12 −0.153463
\(923\) 2.81186e12 0.127522
\(924\) 1.56906e13 0.708136
\(925\) −1.54234e13 −0.692696
\(926\) −9.09670e12 −0.406569
\(927\) −1.18863e13 −0.528673
\(928\) 1.53295e13 0.678521
\(929\) 3.27657e13 1.44328 0.721638 0.692271i \(-0.243390\pi\)
0.721638 + 0.692271i \(0.243390\pi\)
\(930\) −5.23237e12 −0.229364
\(931\) −1.14815e13 −0.500872
\(932\) −4.63965e12 −0.201425
\(933\) 2.13114e11 0.00920754
\(934\) 1.62642e13 0.699314
\(935\) 8.51887e13 3.64527
\(936\) 1.17290e13 0.499481
\(937\) 2.31762e13 0.982230 0.491115 0.871095i \(-0.336589\pi\)
0.491115 + 0.871095i \(0.336589\pi\)
\(938\) 2.54343e12 0.107277
\(939\) −1.05320e12 −0.0442095
\(940\) 3.15583e13 1.31837
\(941\) −1.95362e12 −0.0812244 −0.0406122 0.999175i \(-0.512931\pi\)
−0.0406122 + 0.999175i \(0.512931\pi\)
\(942\) −1.08529e13 −0.449071
\(943\) −1.87990e13 −0.774161
\(944\) 4.68076e11 0.0191842
\(945\) 6.94090e12 0.283121
\(946\) 1.54264e13 0.626261
\(947\) −4.55372e13 −1.83989 −0.919945 0.392048i \(-0.871767\pi\)
−0.919945 + 0.392048i \(0.871767\pi\)
\(948\) −1.57115e13 −0.631803
\(949\) 9.16039e12 0.366620
\(950\) 9.79412e12 0.390130
\(951\) 1.21233e12 0.0480628
\(952\) −5.47079e13 −2.15866
\(953\) −1.87415e11 −0.00736015 −0.00368007 0.999993i \(-0.501171\pi\)
−0.00368007 + 0.999993i \(0.501171\pi\)
\(954\) 1.29663e12 0.0506813
\(955\) 3.95704e12 0.153941
\(956\) −1.46030e13 −0.565434
\(957\) 1.49907e13 0.577721
\(958\) −1.41296e13 −0.541982
\(959\) 1.96386e13 0.749768
\(960\) 8.21084e12 0.312009
\(961\) −1.79650e13 −0.679474
\(962\) 2.98641e13 1.12425
\(963\) −1.73271e13 −0.649245
\(964\) 2.81273e13 1.04901
\(965\) 8.64195e12 0.320803
\(966\) 1.23551e13 0.456510
\(967\) 8.34513e12 0.306912 0.153456 0.988155i \(-0.450960\pi\)
0.153456 + 0.988155i \(0.450960\pi\)
\(968\) 3.40439e13 1.24623
\(969\) 3.84617e13 1.40143
\(970\) 1.19814e13 0.434546
\(971\) 8.89056e11 0.0320954 0.0160477 0.999871i \(-0.494892\pi\)
0.0160477 + 0.999871i \(0.494892\pi\)
\(972\) −1.21770e12 −0.0437566
\(973\) −3.70353e13 −1.32467
\(974\) −2.21324e13 −0.787978
\(975\) 1.41277e13 0.500668
\(976\) −3.88866e12 −0.137175
\(977\) 3.98018e13 1.39758 0.698791 0.715326i \(-0.253722\pi\)
0.698791 + 0.715326i \(0.253722\pi\)
\(978\) 1.74499e12 0.0609913
\(979\) 3.50377e13 1.21903
\(980\) −9.73878e12 −0.337277
\(981\) 1.07577e13 0.370861
\(982\) 3.56732e12 0.122417
\(983\) 6.88619e12 0.235228 0.117614 0.993059i \(-0.462476\pi\)
0.117614 + 0.993059i \(0.462476\pi\)
\(984\) 1.05082e13 0.357315
\(985\) −2.51811e13 −0.852338
\(986\) −2.11947e13 −0.714135
\(987\) −3.16007e13 −1.05991
\(988\) 4.06901e13 1.35857
\(989\) −2.60631e13 −0.866249
\(990\) 1.07541e13 0.355808
\(991\) 1.66826e13 0.549455 0.274728 0.961522i \(-0.411412\pi\)
0.274728 + 0.961522i \(0.411412\pi\)
\(992\) −1.78116e13 −0.583983
\(993\) −9.39318e12 −0.306578
\(994\) −1.65568e12 −0.0537944
\(995\) −1.41267e13 −0.456915
\(996\) −1.70259e13 −0.548205
\(997\) −5.55920e13 −1.78190 −0.890952 0.454097i \(-0.849962\pi\)
−0.890952 + 0.454097i \(0.849962\pi\)
\(998\) 2.21055e13 0.705363
\(999\) −7.64604e12 −0.242880
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.1.10 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.10 21 1.1 even 1 trivial