Properties

Label 177.10.a.a.1.16
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 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+24.3661 q^{2} +81.0000 q^{3} +81.7051 q^{4} +1969.67 q^{5} +1973.65 q^{6} -11418.4 q^{7} -10484.6 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+24.3661 q^{2} +81.0000 q^{3} +81.7051 q^{4} +1969.67 q^{5} +1973.65 q^{6} -11418.4 q^{7} -10484.6 q^{8} +6561.00 q^{9} +47993.2 q^{10} -163.508 q^{11} +6618.11 q^{12} +34660.3 q^{13} -278221. q^{14} +159544. q^{15} -297301. q^{16} +170589. q^{17} +159866. q^{18} +527238. q^{19} +160932. q^{20} -924887. q^{21} -3984.04 q^{22} -1.60409e6 q^{23} -849252. q^{24} +1.92649e6 q^{25} +844534. q^{26} +531441. q^{27} -932938. q^{28} -3.05218e6 q^{29} +3.88745e6 q^{30} -7.55415e6 q^{31} -1.87595e6 q^{32} -13244.1 q^{33} +4.15659e6 q^{34} -2.24905e7 q^{35} +536067. q^{36} -1.02157e7 q^{37} +1.28467e7 q^{38} +2.80748e6 q^{39} -2.06512e7 q^{40} -3.13265e7 q^{41} -2.25359e7 q^{42} -4.71324e6 q^{43} -13359.4 q^{44} +1.29230e7 q^{45} -3.90854e7 q^{46} -6.57834e7 q^{47} -2.40814e7 q^{48} +9.00253e7 q^{49} +4.69411e7 q^{50} +1.38177e7 q^{51} +2.83192e6 q^{52} +9.26249e7 q^{53} +1.29491e7 q^{54} -322057. q^{55} +1.19717e8 q^{56} +4.27063e7 q^{57} -7.43696e7 q^{58} +1.21174e7 q^{59} +1.30355e7 q^{60} +1.91690e7 q^{61} -1.84065e8 q^{62} -7.49159e7 q^{63} +1.06509e8 q^{64} +6.82695e7 q^{65} -322708. q^{66} -2.95657e8 q^{67} +1.39380e7 q^{68} -1.29931e8 q^{69} -5.48004e8 q^{70} +3.68585e8 q^{71} -6.87894e7 q^{72} -4.08014e8 q^{73} -2.48917e8 q^{74} +1.56046e8 q^{75} +4.30780e7 q^{76} +1.86699e6 q^{77} +6.84073e7 q^{78} -3.77605e8 q^{79} -5.85587e8 q^{80} +4.30467e7 q^{81} -7.63305e8 q^{82} +5.62309e8 q^{83} -7.55680e7 q^{84} +3.36005e8 q^{85} -1.14843e8 q^{86} -2.47227e8 q^{87} +1.71431e6 q^{88} -9.87922e8 q^{89} +3.14884e8 q^{90} -3.95763e8 q^{91} -1.31062e8 q^{92} -6.11886e8 q^{93} -1.60288e9 q^{94} +1.03849e9 q^{95} -1.51952e8 q^{96} +5.29357e8 q^{97} +2.19356e9 q^{98} -1.07278e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.3661 1.07684 0.538419 0.842677i \(-0.319022\pi\)
0.538419 + 0.842677i \(0.319022\pi\)
\(3\) 81.0000 0.577350
\(4\) 81.7051 0.159580
\(5\) 1969.67 1.40938 0.704692 0.709513i \(-0.251085\pi\)
0.704692 + 0.709513i \(0.251085\pi\)
\(6\) 1973.65 0.621713
\(7\) −11418.4 −1.79747 −0.898737 0.438488i \(-0.855514\pi\)
−0.898737 + 0.438488i \(0.855514\pi\)
\(8\) −10484.6 −0.904996
\(9\) 6561.00 0.333333
\(10\) 47993.2 1.51768
\(11\) −163.508 −0.00336722 −0.00168361 0.999999i \(-0.500536\pi\)
−0.00168361 + 0.999999i \(0.500536\pi\)
\(12\) 6618.11 0.0921337
\(13\) 34660.3 0.336579 0.168289 0.985738i \(-0.446176\pi\)
0.168289 + 0.985738i \(0.446176\pi\)
\(14\) −278221. −1.93559
\(15\) 159544. 0.813709
\(16\) −297301. −1.13411
\(17\) 170589. 0.495372 0.247686 0.968840i \(-0.420330\pi\)
0.247686 + 0.968840i \(0.420330\pi\)
\(18\) 159866. 0.358946
\(19\) 527238. 0.928144 0.464072 0.885798i \(-0.346388\pi\)
0.464072 + 0.885798i \(0.346388\pi\)
\(20\) 160932. 0.224910
\(21\) −924887. −1.03777
\(22\) −3984.04 −0.00362595
\(23\) −1.60409e6 −1.19524 −0.597618 0.801781i \(-0.703886\pi\)
−0.597618 + 0.801781i \(0.703886\pi\)
\(24\) −849252. −0.522500
\(25\) 1.92649e6 0.986365
\(26\) 844534. 0.362441
\(27\) 531441. 0.192450
\(28\) −932938. −0.286841
\(29\) −3.05218e6 −0.801344 −0.400672 0.916222i \(-0.631223\pi\)
−0.400672 + 0.916222i \(0.631223\pi\)
\(30\) 3.88745e6 0.876232
\(31\) −7.55415e6 −1.46912 −0.734561 0.678542i \(-0.762612\pi\)
−0.734561 + 0.678542i \(0.762612\pi\)
\(32\) −1.87595e6 −0.316262
\(33\) −13244.1 −0.00194407
\(34\) 4.15659e6 0.533436
\(35\) −2.24905e7 −2.53333
\(36\) 536067. 0.0531934
\(37\) −1.02157e7 −0.896110 −0.448055 0.894006i \(-0.647883\pi\)
−0.448055 + 0.894006i \(0.647883\pi\)
\(38\) 1.28467e7 0.999461
\(39\) 2.80748e6 0.194324
\(40\) −2.06512e7 −1.27549
\(41\) −3.13265e7 −1.73135 −0.865676 0.500605i \(-0.833111\pi\)
−0.865676 + 0.500605i \(0.833111\pi\)
\(42\) −2.25359e7 −1.11751
\(43\) −4.71324e6 −0.210238 −0.105119 0.994460i \(-0.533522\pi\)
−0.105119 + 0.994460i \(0.533522\pi\)
\(44\) −13359.4 −0.000537342 0
\(45\) 1.29230e7 0.469795
\(46\) −3.90854e7 −1.28708
\(47\) −6.57834e7 −1.96642 −0.983209 0.182484i \(-0.941586\pi\)
−0.983209 + 0.182484i \(0.941586\pi\)
\(48\) −2.40814e7 −0.654781
\(49\) 9.00253e7 2.23091
\(50\) 4.69411e7 1.06216
\(51\) 1.38177e7 0.286003
\(52\) 2.83192e6 0.0537113
\(53\) 9.26249e7 1.61245 0.806226 0.591608i \(-0.201507\pi\)
0.806226 + 0.591608i \(0.201507\pi\)
\(54\) 1.29491e7 0.207238
\(55\) −322057. −0.00474571
\(56\) 1.19717e8 1.62671
\(57\) 4.27063e7 0.535864
\(58\) −7.43696e7 −0.862918
\(59\) 1.21174e7 0.130189
\(60\) 1.30355e7 0.129852
\(61\) 1.91690e7 0.177262 0.0886308 0.996065i \(-0.471751\pi\)
0.0886308 + 0.996065i \(0.471751\pi\)
\(62\) −1.84065e8 −1.58201
\(63\) −7.49159e7 −0.599158
\(64\) 1.06509e8 0.793552
\(65\) 6.82695e7 0.474369
\(66\) −322708. −0.00209344
\(67\) −2.95657e8 −1.79247 −0.896234 0.443582i \(-0.853707\pi\)
−0.896234 + 0.443582i \(0.853707\pi\)
\(68\) 1.39380e7 0.0790516
\(69\) −1.29931e8 −0.690070
\(70\) −5.48004e8 −2.72799
\(71\) 3.68585e8 1.72137 0.860687 0.509134i \(-0.170034\pi\)
0.860687 + 0.509134i \(0.170034\pi\)
\(72\) −6.87894e7 −0.301665
\(73\) −4.08014e8 −1.68160 −0.840799 0.541347i \(-0.817915\pi\)
−0.840799 + 0.541347i \(0.817915\pi\)
\(74\) −2.48917e8 −0.964966
\(75\) 1.56046e8 0.569478
\(76\) 4.30780e7 0.148113
\(77\) 1.86699e6 0.00605249
\(78\) 6.84073e7 0.209255
\(79\) −3.77605e8 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(80\) −5.85587e8 −1.59840
\(81\) 4.30467e7 0.111111
\(82\) −7.63305e8 −1.86438
\(83\) 5.62309e8 1.30054 0.650270 0.759703i \(-0.274656\pi\)
0.650270 + 0.759703i \(0.274656\pi\)
\(84\) −7.55680e7 −0.165608
\(85\) 3.36005e8 0.698170
\(86\) −1.14843e8 −0.226392
\(87\) −2.47227e8 −0.462656
\(88\) 1.71431e6 0.00304732
\(89\) −9.87922e8 −1.66904 −0.834522 0.550975i \(-0.814256\pi\)
−0.834522 + 0.550975i \(0.814256\pi\)
\(90\) 3.14884e8 0.505893
\(91\) −3.95763e8 −0.604992
\(92\) −1.31062e8 −0.190736
\(93\) −6.11886e8 −0.848199
\(94\) −1.60288e9 −2.11751
\(95\) 1.03849e9 1.30811
\(96\) −1.51952e8 −0.182594
\(97\) 5.29357e8 0.607122 0.303561 0.952812i \(-0.401824\pi\)
0.303561 + 0.952812i \(0.401824\pi\)
\(98\) 2.19356e9 2.40233
\(99\) −1.07278e6 −0.00112241
\(100\) 1.57404e8 0.157404
\(101\) −3.84396e8 −0.367564 −0.183782 0.982967i \(-0.558834\pi\)
−0.183782 + 0.982967i \(0.558834\pi\)
\(102\) 3.36684e8 0.307979
\(103\) 1.13707e9 0.995454 0.497727 0.867334i \(-0.334168\pi\)
0.497727 + 0.867334i \(0.334168\pi\)
\(104\) −3.63399e8 −0.304602
\(105\) −1.82173e9 −1.46262
\(106\) 2.25691e9 1.73635
\(107\) −1.98918e9 −1.46705 −0.733527 0.679660i \(-0.762127\pi\)
−0.733527 + 0.679660i \(0.762127\pi\)
\(108\) 4.34214e7 0.0307112
\(109\) 2.22816e9 1.51192 0.755958 0.654621i \(-0.227172\pi\)
0.755958 + 0.654621i \(0.227172\pi\)
\(110\) −7.84727e6 −0.00511036
\(111\) −8.27474e8 −0.517370
\(112\) 3.39469e9 2.03854
\(113\) 1.95600e9 1.12854 0.564270 0.825590i \(-0.309158\pi\)
0.564270 + 0.825590i \(0.309158\pi\)
\(114\) 1.04058e9 0.577039
\(115\) −3.15954e9 −1.68455
\(116\) −2.49379e8 −0.127879
\(117\) 2.27406e8 0.112193
\(118\) 2.95252e8 0.140192
\(119\) −1.94785e9 −0.890418
\(120\) −1.67275e9 −0.736403
\(121\) −2.35792e9 −0.999989
\(122\) 4.67072e8 0.190882
\(123\) −2.53745e9 −0.999596
\(124\) −6.17213e8 −0.234443
\(125\) −5.24550e7 −0.0192173
\(126\) −1.82540e9 −0.645196
\(127\) −2.18815e9 −0.746381 −0.373190 0.927755i \(-0.621736\pi\)
−0.373190 + 0.927755i \(0.621736\pi\)
\(128\) 3.55569e9 1.17079
\(129\) −3.81772e8 −0.121381
\(130\) 1.66346e9 0.510819
\(131\) 3.64627e9 1.08175 0.540877 0.841102i \(-0.318093\pi\)
0.540877 + 0.841102i \(0.318093\pi\)
\(132\) −1.08211e6 −0.000310235 0
\(133\) −6.02019e9 −1.66831
\(134\) −7.20399e9 −1.93020
\(135\) 1.04677e9 0.271236
\(136\) −1.78856e9 −0.448310
\(137\) 4.11830e9 0.998794 0.499397 0.866373i \(-0.333555\pi\)
0.499397 + 0.866373i \(0.333555\pi\)
\(138\) −3.16592e9 −0.743094
\(139\) 4.19549e9 0.953269 0.476635 0.879101i \(-0.341856\pi\)
0.476635 + 0.879101i \(0.341856\pi\)
\(140\) −1.83758e9 −0.404270
\(141\) −5.32845e9 −1.13531
\(142\) 8.98097e9 1.85364
\(143\) −5.66723e6 −0.00113334
\(144\) −1.95059e9 −0.378038
\(145\) −6.01180e9 −1.12940
\(146\) −9.94170e9 −1.81081
\(147\) 7.29205e9 1.28802
\(148\) −8.34677e8 −0.143002
\(149\) 3.08558e8 0.0512860 0.0256430 0.999671i \(-0.491837\pi\)
0.0256430 + 0.999671i \(0.491837\pi\)
\(150\) 3.80223e9 0.613236
\(151\) −2.95545e8 −0.0462623 −0.0231311 0.999732i \(-0.507364\pi\)
−0.0231311 + 0.999732i \(0.507364\pi\)
\(152\) −5.52787e9 −0.839966
\(153\) 1.11924e9 0.165124
\(154\) 4.54913e7 0.00651755
\(155\) −1.48792e10 −2.07056
\(156\) 2.29386e8 0.0310103
\(157\) −2.30398e9 −0.302643 −0.151321 0.988485i \(-0.548353\pi\)
−0.151321 + 0.988485i \(0.548353\pi\)
\(158\) −9.20074e9 −1.17453
\(159\) 7.50262e9 0.930949
\(160\) −3.69501e9 −0.445734
\(161\) 1.83161e10 2.14841
\(162\) 1.04888e9 0.119649
\(163\) −5.74955e9 −0.637954 −0.318977 0.947762i \(-0.603339\pi\)
−0.318977 + 0.947762i \(0.603339\pi\)
\(164\) −2.55954e9 −0.276289
\(165\) −2.60867e7 −0.00273994
\(166\) 1.37013e10 1.40047
\(167\) 3.18576e9 0.316949 0.158475 0.987363i \(-0.449342\pi\)
0.158475 + 0.987363i \(0.449342\pi\)
\(168\) 9.69707e9 0.939179
\(169\) −9.40317e9 −0.886715
\(170\) 8.18713e9 0.751816
\(171\) 3.45921e9 0.309381
\(172\) −3.85095e8 −0.0335498
\(173\) 3.91550e9 0.332338 0.166169 0.986097i \(-0.446860\pi\)
0.166169 + 0.986097i \(0.446860\pi\)
\(174\) −6.02394e9 −0.498206
\(175\) −2.19974e10 −1.77296
\(176\) 4.86111e7 0.00381881
\(177\) 9.81506e8 0.0751646
\(178\) −2.40718e10 −1.79729
\(179\) 1.42299e10 1.03601 0.518003 0.855379i \(-0.326676\pi\)
0.518003 + 0.855379i \(0.326676\pi\)
\(180\) 1.05588e9 0.0749700
\(181\) −3.86710e9 −0.267813 −0.133907 0.990994i \(-0.542752\pi\)
−0.133907 + 0.990994i \(0.542752\pi\)
\(182\) −9.64320e9 −0.651478
\(183\) 1.55269e9 0.102342
\(184\) 1.68182e10 1.08168
\(185\) −2.01217e10 −1.26296
\(186\) −1.49093e10 −0.913372
\(187\) −2.78927e7 −0.00166803
\(188\) −5.37484e9 −0.313801
\(189\) −6.06818e9 −0.345924
\(190\) 2.53038e10 1.40862
\(191\) −1.00043e10 −0.543922 −0.271961 0.962308i \(-0.587672\pi\)
−0.271961 + 0.962308i \(0.587672\pi\)
\(192\) 8.62721e9 0.458157
\(193\) 6.84308e9 0.355013 0.177506 0.984120i \(-0.443197\pi\)
0.177506 + 0.984120i \(0.443197\pi\)
\(194\) 1.28983e10 0.653772
\(195\) 5.52983e9 0.273877
\(196\) 7.35553e9 0.356010
\(197\) 2.71105e10 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −2.61393e7 −0.00120865
\(199\) −2.79531e10 −1.26354 −0.631772 0.775154i \(-0.717672\pi\)
−0.631772 + 0.775154i \(0.717672\pi\)
\(200\) −2.01985e10 −0.892656
\(201\) −2.39482e10 −1.03488
\(202\) −9.36622e9 −0.395807
\(203\) 3.48509e10 1.44039
\(204\) 1.12898e9 0.0456405
\(205\) −6.17031e10 −2.44014
\(206\) 2.77060e10 1.07194
\(207\) −1.05244e10 −0.398412
\(208\) −1.03045e10 −0.381719
\(209\) −8.62075e7 −0.00312527
\(210\) −4.43883e10 −1.57500
\(211\) −6.30108e8 −0.0218849 −0.0109424 0.999940i \(-0.503483\pi\)
−0.0109424 + 0.999940i \(0.503483\pi\)
\(212\) 7.56793e9 0.257315
\(213\) 2.98554e10 0.993836
\(214\) −4.84684e10 −1.57978
\(215\) −9.28354e9 −0.296306
\(216\) −5.57194e9 −0.174167
\(217\) 8.62560e10 2.64071
\(218\) 5.42915e10 1.62809
\(219\) −3.30491e10 −0.970871
\(220\) −2.63137e7 −0.000757322 0
\(221\) 5.91267e9 0.166732
\(222\) −2.01623e10 −0.557123
\(223\) −1.14373e10 −0.309708 −0.154854 0.987937i \(-0.549491\pi\)
−0.154854 + 0.987937i \(0.549491\pi\)
\(224\) 2.14203e10 0.568472
\(225\) 1.26397e10 0.328788
\(226\) 4.76601e10 1.21525
\(227\) −1.22875e10 −0.307148 −0.153574 0.988137i \(-0.549078\pi\)
−0.153574 + 0.988137i \(0.549078\pi\)
\(228\) 3.48932e9 0.0855133
\(229\) 5.01198e10 1.20434 0.602170 0.798368i \(-0.294303\pi\)
0.602170 + 0.798368i \(0.294303\pi\)
\(230\) −7.69855e10 −1.81398
\(231\) 1.51226e8 0.00349441
\(232\) 3.20009e10 0.725213
\(233\) 7.31676e10 1.62636 0.813181 0.582011i \(-0.197734\pi\)
0.813181 + 0.582011i \(0.197734\pi\)
\(234\) 5.54099e9 0.120814
\(235\) −1.29572e11 −2.77144
\(236\) 9.90050e8 0.0207756
\(237\) −3.05860e10 −0.629730
\(238\) −4.74614e10 −0.958836
\(239\) −6.54718e10 −1.29797 −0.648983 0.760802i \(-0.724806\pi\)
−0.648983 + 0.760802i \(0.724806\pi\)
\(240\) −4.74325e10 −0.922839
\(241\) −3.98263e9 −0.0760490 −0.0380245 0.999277i \(-0.512106\pi\)
−0.0380245 + 0.999277i \(0.512106\pi\)
\(242\) −5.74533e10 −1.07683
\(243\) 3.48678e9 0.0641500
\(244\) 1.56620e9 0.0282875
\(245\) 1.77321e11 3.14421
\(246\) −6.18277e10 −1.07640
\(247\) 1.82742e10 0.312394
\(248\) 7.92022e10 1.32955
\(249\) 4.55470e10 0.750867
\(250\) −1.27812e9 −0.0206939
\(251\) 7.55610e10 1.20162 0.600809 0.799393i \(-0.294845\pi\)
0.600809 + 0.799393i \(0.294845\pi\)
\(252\) −6.12101e9 −0.0956138
\(253\) 2.62282e8 0.00402463
\(254\) −5.33166e10 −0.803731
\(255\) 2.72164e10 0.403089
\(256\) 3.21056e10 0.467198
\(257\) −8.18538e10 −1.17041 −0.585207 0.810884i \(-0.698987\pi\)
−0.585207 + 0.810884i \(0.698987\pi\)
\(258\) −9.30228e9 −0.130708
\(259\) 1.16647e11 1.61073
\(260\) 5.57796e9 0.0756999
\(261\) −2.00253e10 −0.267115
\(262\) 8.88453e10 1.16487
\(263\) −3.20908e10 −0.413600 −0.206800 0.978383i \(-0.566305\pi\)
−0.206800 + 0.978383i \(0.566305\pi\)
\(264\) 1.38859e8 0.00175937
\(265\) 1.82441e11 2.27256
\(266\) −1.46688e11 −1.79650
\(267\) −8.00217e10 −0.963623
\(268\) −2.41567e10 −0.286042
\(269\) 5.88850e10 0.685677 0.342839 0.939394i \(-0.388612\pi\)
0.342839 + 0.939394i \(0.388612\pi\)
\(270\) 2.55056e10 0.292077
\(271\) −7.85759e10 −0.884968 −0.442484 0.896776i \(-0.645903\pi\)
−0.442484 + 0.896776i \(0.645903\pi\)
\(272\) −5.07164e10 −0.561809
\(273\) −3.20568e10 −0.349292
\(274\) 1.00347e11 1.07554
\(275\) −3.14997e8 −0.00332131
\(276\) −1.06161e10 −0.110122
\(277\) 7.50991e9 0.0766436 0.0383218 0.999265i \(-0.487799\pi\)
0.0383218 + 0.999265i \(0.487799\pi\)
\(278\) 1.02227e11 1.02652
\(279\) −4.95628e10 −0.489708
\(280\) 2.35803e11 2.29266
\(281\) 1.47535e11 1.41161 0.705806 0.708405i \(-0.250585\pi\)
0.705806 + 0.708405i \(0.250585\pi\)
\(282\) −1.29833e11 −1.22255
\(283\) 1.74018e11 1.61270 0.806351 0.591437i \(-0.201439\pi\)
0.806351 + 0.591437i \(0.201439\pi\)
\(284\) 3.01153e10 0.274697
\(285\) 8.41174e10 0.755239
\(286\) −1.38088e8 −0.00122042
\(287\) 3.57698e11 3.11206
\(288\) −1.23081e10 −0.105421
\(289\) −8.94872e10 −0.754606
\(290\) −1.46484e11 −1.21618
\(291\) 4.28779e10 0.350522
\(292\) −3.33368e10 −0.268350
\(293\) −3.36852e10 −0.267015 −0.133507 0.991048i \(-0.542624\pi\)
−0.133507 + 0.991048i \(0.542624\pi\)
\(294\) 1.77679e11 1.38699
\(295\) 2.38673e10 0.183486
\(296\) 1.07108e11 0.810976
\(297\) −8.68948e7 −0.000648022 0
\(298\) 7.51835e9 0.0552267
\(299\) −5.55982e10 −0.402291
\(300\) 1.27498e10 0.0908774
\(301\) 5.38174e10 0.377897
\(302\) −7.20126e9 −0.0498170
\(303\) −3.11361e10 −0.212213
\(304\) −1.56748e11 −1.05262
\(305\) 3.77566e10 0.249830
\(306\) 2.72714e10 0.177812
\(307\) −1.20229e11 −0.772479 −0.386239 0.922399i \(-0.626226\pi\)
−0.386239 + 0.922399i \(0.626226\pi\)
\(308\) 1.52543e8 0.000965858 0
\(309\) 9.21029e10 0.574725
\(310\) −3.62548e11 −2.22966
\(311\) −1.28346e11 −0.777963 −0.388982 0.921246i \(-0.627173\pi\)
−0.388982 + 0.921246i \(0.627173\pi\)
\(312\) −2.94353e10 −0.175862
\(313\) 8.18729e10 0.482159 0.241080 0.970505i \(-0.422499\pi\)
0.241080 + 0.970505i \(0.422499\pi\)
\(314\) −5.61389e10 −0.325897
\(315\) −1.47560e11 −0.844444
\(316\) −3.08522e10 −0.174058
\(317\) −5.60769e10 −0.311901 −0.155951 0.987765i \(-0.549844\pi\)
−0.155951 + 0.987765i \(0.549844\pi\)
\(318\) 1.82809e11 1.00248
\(319\) 4.99055e8 0.00269830
\(320\) 2.09788e11 1.11842
\(321\) −1.61123e11 −0.847004
\(322\) 4.46291e11 2.31349
\(323\) 8.99411e10 0.459777
\(324\) 3.51714e9 0.0177311
\(325\) 6.67728e10 0.331990
\(326\) −1.40094e11 −0.686974
\(327\) 1.80481e11 0.872905
\(328\) 3.28446e11 1.56687
\(329\) 7.51138e11 3.53458
\(330\) −6.35629e8 −0.00295047
\(331\) −2.57967e10 −0.118124 −0.0590621 0.998254i \(-0.518811\pi\)
−0.0590621 + 0.998254i \(0.518811\pi\)
\(332\) 4.59435e10 0.207540
\(333\) −6.70254e10 −0.298703
\(334\) 7.76245e10 0.341303
\(335\) −5.82348e11 −2.52628
\(336\) 2.74970e11 1.17695
\(337\) −1.97795e9 −0.00835372 −0.00417686 0.999991i \(-0.501330\pi\)
−0.00417686 + 0.999991i \(0.501330\pi\)
\(338\) −2.29118e11 −0.954848
\(339\) 1.58436e11 0.651563
\(340\) 2.74534e10 0.111414
\(341\) 1.23516e9 0.00494686
\(342\) 8.42872e10 0.333154
\(343\) −5.67170e11 −2.21253
\(344\) 4.94164e10 0.190264
\(345\) −2.55923e11 −0.972574
\(346\) 9.54053e10 0.357874
\(347\) 2.23107e11 0.826098 0.413049 0.910709i \(-0.364464\pi\)
0.413049 + 0.910709i \(0.364464\pi\)
\(348\) −2.01997e10 −0.0738308
\(349\) 4.57962e11 1.65240 0.826200 0.563377i \(-0.190498\pi\)
0.826200 + 0.563377i \(0.190498\pi\)
\(350\) −5.35990e11 −1.90920
\(351\) 1.84199e10 0.0647746
\(352\) 3.06733e8 0.00106492
\(353\) −7.16061e10 −0.245450 −0.122725 0.992441i \(-0.539163\pi\)
−0.122725 + 0.992441i \(0.539163\pi\)
\(354\) 2.39154e10 0.0809401
\(355\) 7.25993e11 2.42608
\(356\) −8.07183e10 −0.266346
\(357\) −1.57776e11 −0.514083
\(358\) 3.46726e11 1.11561
\(359\) −2.45488e11 −0.780019 −0.390009 0.920811i \(-0.627528\pi\)
−0.390009 + 0.920811i \(0.627528\pi\)
\(360\) −1.35493e11 −0.425162
\(361\) −4.47081e10 −0.138549
\(362\) −9.42261e10 −0.288392
\(363\) −1.90992e11 −0.577344
\(364\) −3.23359e10 −0.0965447
\(365\) −8.03655e11 −2.37002
\(366\) 3.78329e10 0.110206
\(367\) −3.46509e11 −0.997050 −0.498525 0.866875i \(-0.666125\pi\)
−0.498525 + 0.866875i \(0.666125\pi\)
\(368\) 4.76898e11 1.35553
\(369\) −2.05533e11 −0.577117
\(370\) −4.90286e11 −1.36001
\(371\) −1.05763e12 −2.89834
\(372\) −4.99942e10 −0.135356
\(373\) −4.06613e11 −1.08765 −0.543827 0.839197i \(-0.683025\pi\)
−0.543827 + 0.839197i \(0.683025\pi\)
\(374\) −6.79635e8 −0.00179620
\(375\) −4.24885e9 −0.0110951
\(376\) 6.89712e11 1.77960
\(377\) −1.05789e11 −0.269715
\(378\) −1.47858e11 −0.372504
\(379\) 5.44078e10 0.135452 0.0677259 0.997704i \(-0.478426\pi\)
0.0677259 + 0.997704i \(0.478426\pi\)
\(380\) 8.48497e10 0.208749
\(381\) −1.77240e11 −0.430923
\(382\) −2.43765e11 −0.585715
\(383\) −6.75496e11 −1.60409 −0.802044 0.597265i \(-0.796254\pi\)
−0.802044 + 0.597265i \(0.796254\pi\)
\(384\) 2.88011e11 0.675955
\(385\) 3.67737e9 0.00853029
\(386\) 1.66739e11 0.382291
\(387\) −3.09235e10 −0.0700793
\(388\) 4.32512e10 0.0968847
\(389\) −8.38031e10 −0.185561 −0.0927805 0.995687i \(-0.529575\pi\)
−0.0927805 + 0.995687i \(0.529575\pi\)
\(390\) 1.34740e11 0.294921
\(391\) −2.73641e11 −0.592087
\(392\) −9.43879e11 −2.01897
\(393\) 2.95348e11 0.624551
\(394\) 6.60576e11 1.38099
\(395\) −7.43758e11 −1.53725
\(396\) −8.76512e7 −0.000179114 0
\(397\) 6.35581e11 1.28414 0.642072 0.766645i \(-0.278075\pi\)
0.642072 + 0.766645i \(0.278075\pi\)
\(398\) −6.81106e11 −1.36063
\(399\) −4.87635e11 −0.963202
\(400\) −5.72749e11 −1.11865
\(401\) 1.97151e11 0.380759 0.190379 0.981711i \(-0.439028\pi\)
0.190379 + 0.981711i \(0.439028\pi\)
\(402\) −5.83523e11 −1.11440
\(403\) −2.61829e11 −0.494476
\(404\) −3.14071e10 −0.0586559
\(405\) 8.47880e10 0.156598
\(406\) 8.49179e11 1.55107
\(407\) 1.67035e9 0.00301740
\(408\) −1.44873e11 −0.258832
\(409\) 1.56475e11 0.276497 0.138248 0.990398i \(-0.455853\pi\)
0.138248 + 0.990398i \(0.455853\pi\)
\(410\) −1.50346e12 −2.62764
\(411\) 3.33583e11 0.576654
\(412\) 9.29047e10 0.158855
\(413\) −1.38360e11 −0.234011
\(414\) −2.56439e11 −0.429025
\(415\) 1.10757e12 1.83296
\(416\) −6.50209e10 −0.106447
\(417\) 3.39834e11 0.550370
\(418\) −2.10054e9 −0.00336541
\(419\) 7.43475e11 1.17843 0.589214 0.807977i \(-0.299437\pi\)
0.589214 + 0.807977i \(0.299437\pi\)
\(420\) −1.48844e11 −0.233405
\(421\) 7.93062e11 1.23038 0.615188 0.788380i \(-0.289080\pi\)
0.615188 + 0.788380i \(0.289080\pi\)
\(422\) −1.53533e10 −0.0235665
\(423\) −4.31605e11 −0.655473
\(424\) −9.71135e11 −1.45926
\(425\) 3.28639e11 0.488618
\(426\) 7.27459e11 1.07020
\(427\) −2.18878e11 −0.318623
\(428\) −1.62526e11 −0.234113
\(429\) −4.59045e8 −0.000654332 0
\(430\) −2.26203e11 −0.319074
\(431\) −2.78691e11 −0.389023 −0.194511 0.980900i \(-0.562312\pi\)
−0.194511 + 0.980900i \(0.562312\pi\)
\(432\) −1.57998e11 −0.218260
\(433\) 1.02963e12 1.40762 0.703808 0.710391i \(-0.251482\pi\)
0.703808 + 0.710391i \(0.251482\pi\)
\(434\) 2.10172e12 2.84362
\(435\) −4.86956e11 −0.652060
\(436\) 1.82052e11 0.241272
\(437\) −8.45737e11 −1.10935
\(438\) −8.05278e11 −1.04547
\(439\) −4.58042e11 −0.588592 −0.294296 0.955714i \(-0.595085\pi\)
−0.294296 + 0.955714i \(0.595085\pi\)
\(440\) 3.37664e9 0.00429485
\(441\) 5.90656e11 0.743637
\(442\) 1.44068e11 0.179543
\(443\) 3.01320e11 0.371716 0.185858 0.982577i \(-0.440494\pi\)
0.185858 + 0.982577i \(0.440494\pi\)
\(444\) −6.76088e10 −0.0825620
\(445\) −1.94589e12 −2.35232
\(446\) −2.78683e11 −0.333506
\(447\) 2.49932e10 0.0296100
\(448\) −1.21616e12 −1.42639
\(449\) 8.03886e11 0.933439 0.466720 0.884405i \(-0.345436\pi\)
0.466720 + 0.884405i \(0.345436\pi\)
\(450\) 3.07980e11 0.354052
\(451\) 5.12214e9 0.00582984
\(452\) 1.59816e11 0.180093
\(453\) −2.39391e10 −0.0267095
\(454\) −2.99399e11 −0.330749
\(455\) −7.79525e11 −0.852666
\(456\) −4.47758e11 −0.484955
\(457\) −1.23947e12 −1.32927 −0.664635 0.747168i \(-0.731413\pi\)
−0.664635 + 0.747168i \(0.731413\pi\)
\(458\) 1.22122e12 1.29688
\(459\) 9.06581e10 0.0953344
\(460\) −2.58150e11 −0.268821
\(461\) −4.79141e11 −0.494094 −0.247047 0.969004i \(-0.579460\pi\)
−0.247047 + 0.969004i \(0.579460\pi\)
\(462\) 3.68479e9 0.00376291
\(463\) −2.70417e11 −0.273477 −0.136738 0.990607i \(-0.543662\pi\)
−0.136738 + 0.990607i \(0.543662\pi\)
\(464\) 9.07417e11 0.908816
\(465\) −1.20522e12 −1.19544
\(466\) 1.78281e12 1.75133
\(467\) −3.00544e10 −0.0292403 −0.0146202 0.999893i \(-0.504654\pi\)
−0.0146202 + 0.999893i \(0.504654\pi\)
\(468\) 1.85802e10 0.0179038
\(469\) 3.37592e12 3.22191
\(470\) −3.15716e12 −2.98439
\(471\) −1.86622e11 −0.174731
\(472\) −1.27046e11 −0.117820
\(473\) 7.70651e8 0.000707918 0
\(474\) −7.45260e11 −0.678118
\(475\) 1.01572e12 0.915488
\(476\) −1.59149e11 −0.142093
\(477\) 6.07712e11 0.537484
\(478\) −1.59529e12 −1.39770
\(479\) 7.18997e11 0.624047 0.312024 0.950074i \(-0.398993\pi\)
0.312024 + 0.950074i \(0.398993\pi\)
\(480\) −2.99296e11 −0.257345
\(481\) −3.54080e11 −0.301612
\(482\) −9.70411e10 −0.0818924
\(483\) 1.48360e12 1.24038
\(484\) −1.92654e11 −0.159578
\(485\) 1.04266e12 0.855668
\(486\) 8.49592e10 0.0690792
\(487\) −4.97045e11 −0.400419 −0.200210 0.979753i \(-0.564162\pi\)
−0.200210 + 0.979753i \(0.564162\pi\)
\(488\) −2.00979e11 −0.160421
\(489\) −4.65714e11 −0.368323
\(490\) 4.32061e12 3.38581
\(491\) −7.29851e11 −0.566718 −0.283359 0.959014i \(-0.591449\pi\)
−0.283359 + 0.959014i \(0.591449\pi\)
\(492\) −2.07323e11 −0.159516
\(493\) −5.20669e11 −0.396963
\(494\) 4.45270e11 0.336397
\(495\) −2.11302e9 −0.00158190
\(496\) 2.24586e12 1.66615
\(497\) −4.20864e12 −3.09412
\(498\) 1.10980e12 0.808562
\(499\) −4.58759e11 −0.331232 −0.165616 0.986190i \(-0.552961\pi\)
−0.165616 + 0.986190i \(0.552961\pi\)
\(500\) −4.28584e9 −0.00306670
\(501\) 2.58047e11 0.182991
\(502\) 1.84112e12 1.29395
\(503\) −1.74649e12 −1.21649 −0.608246 0.793748i \(-0.708127\pi\)
−0.608246 + 0.793748i \(0.708127\pi\)
\(504\) 7.85462e11 0.542236
\(505\) −7.57135e11 −0.518039
\(506\) 6.39077e9 0.00433387
\(507\) −7.61656e11 −0.511945
\(508\) −1.78783e11 −0.119108
\(509\) −1.27325e12 −0.840783 −0.420392 0.907343i \(-0.638107\pi\)
−0.420392 + 0.907343i \(0.638107\pi\)
\(510\) 6.63157e11 0.434061
\(511\) 4.65885e12 3.02263
\(512\) −1.03822e12 −0.667692
\(513\) 2.80196e11 0.178621
\(514\) −1.99446e12 −1.26035
\(515\) 2.23966e12 1.40298
\(516\) −3.11927e10 −0.0193700
\(517\) 1.07561e10 0.00662136
\(518\) 2.84222e12 1.73450
\(519\) 3.17155e11 0.191875
\(520\) −7.15777e11 −0.429302
\(521\) 2.27744e12 1.35418 0.677092 0.735898i \(-0.263240\pi\)
0.677092 + 0.735898i \(0.263240\pi\)
\(522\) −4.87939e11 −0.287639
\(523\) 2.42794e11 0.141899 0.0709497 0.997480i \(-0.477397\pi\)
0.0709497 + 0.997480i \(0.477397\pi\)
\(524\) 2.97919e11 0.172626
\(525\) −1.78179e12 −1.02362
\(526\) −7.81928e11 −0.445380
\(527\) −1.28866e12 −0.727763
\(528\) 3.93750e9 0.00220479
\(529\) 7.71956e11 0.428590
\(530\) 4.44537e12 2.44718
\(531\) 7.95020e10 0.0433963
\(532\) −4.91880e11 −0.266230
\(533\) −1.08579e12 −0.582736
\(534\) −1.94981e12 −1.03767
\(535\) −3.91803e12 −2.06764
\(536\) 3.09984e12 1.62218
\(537\) 1.15262e12 0.598138
\(538\) 1.43480e12 0.738363
\(539\) −1.47199e10 −0.00751198
\(540\) 8.55261e10 0.0432839
\(541\) −3.46493e12 −1.73903 −0.869514 0.493909i \(-0.835568\pi\)
−0.869514 + 0.493909i \(0.835568\pi\)
\(542\) −1.91459e12 −0.952967
\(543\) −3.13235e11 −0.154622
\(544\) −3.20017e11 −0.156667
\(545\) 4.38875e12 2.13087
\(546\) −7.81099e11 −0.376131
\(547\) −1.18857e11 −0.0567653 −0.0283827 0.999597i \(-0.509036\pi\)
−0.0283827 + 0.999597i \(0.509036\pi\)
\(548\) 3.36486e11 0.159388
\(549\) 1.25768e11 0.0590872
\(550\) −7.67524e9 −0.00357651
\(551\) −1.60922e12 −0.743762
\(552\) 1.36228e12 0.624511
\(553\) 4.31162e12 1.96055
\(554\) 1.82987e11 0.0825328
\(555\) −1.62985e12 −0.729173
\(556\) 3.42793e11 0.152123
\(557\) −1.55559e12 −0.684774 −0.342387 0.939559i \(-0.611235\pi\)
−0.342387 + 0.939559i \(0.611235\pi\)
\(558\) −1.20765e12 −0.527336
\(559\) −1.63362e11 −0.0707616
\(560\) 6.68644e12 2.87309
\(561\) −2.25931e9 −0.000963036 0
\(562\) 3.59484e12 1.52008
\(563\) −1.59042e12 −0.667151 −0.333576 0.942723i \(-0.608255\pi\)
−0.333576 + 0.942723i \(0.608255\pi\)
\(564\) −4.35362e11 −0.181173
\(565\) 3.85269e12 1.59055
\(566\) 4.24013e12 1.73662
\(567\) −4.91523e11 −0.199719
\(568\) −3.86447e12 −1.55784
\(569\) 2.68982e12 1.07577 0.537883 0.843020i \(-0.319224\pi\)
0.537883 + 0.843020i \(0.319224\pi\)
\(570\) 2.04961e12 0.813270
\(571\) 3.24238e11 0.127644 0.0638222 0.997961i \(-0.479671\pi\)
0.0638222 + 0.997961i \(0.479671\pi\)
\(572\) −4.63041e8 −0.000180858 0
\(573\) −8.10348e11 −0.314033
\(574\) 8.71569e12 3.35118
\(575\) −3.09027e12 −1.17894
\(576\) 6.98804e11 0.264517
\(577\) −3.19975e12 −1.20178 −0.600890 0.799332i \(-0.705187\pi\)
−0.600890 + 0.799332i \(0.705187\pi\)
\(578\) −2.18045e12 −0.812589
\(579\) 5.54290e11 0.204967
\(580\) −4.91195e11 −0.180230
\(581\) −6.42065e12 −2.33769
\(582\) 1.04477e12 0.377455
\(583\) −1.51449e10 −0.00542948
\(584\) 4.27786e12 1.52184
\(585\) 4.47916e11 0.158123
\(586\) −8.20777e11 −0.287532
\(587\) −3.86904e12 −1.34503 −0.672515 0.740084i \(-0.734786\pi\)
−0.672515 + 0.740084i \(0.734786\pi\)
\(588\) 5.95798e11 0.205542
\(589\) −3.98283e12 −1.36356
\(590\) 5.81551e11 0.197585
\(591\) 2.19595e12 0.740421
\(592\) 3.03715e12 1.01629
\(593\) 1.92789e12 0.640231 0.320116 0.947378i \(-0.396278\pi\)
0.320116 + 0.947378i \(0.396278\pi\)
\(594\) −2.11728e9 −0.000697815 0
\(595\) −3.83663e12 −1.25494
\(596\) 2.52108e10 0.00818423
\(597\) −2.26420e12 −0.729508
\(598\) −1.35471e12 −0.433203
\(599\) −3.87247e12 −1.22904 −0.614522 0.788899i \(-0.710651\pi\)
−0.614522 + 0.788899i \(0.710651\pi\)
\(600\) −1.63608e12 −0.515375
\(601\) −9.66512e11 −0.302185 −0.151092 0.988520i \(-0.548279\pi\)
−0.151092 + 0.988520i \(0.548279\pi\)
\(602\) 1.31132e12 0.406934
\(603\) −1.93980e12 −0.597489
\(604\) −2.41475e10 −0.00738255
\(605\) −4.64434e12 −1.40937
\(606\) −7.58664e11 −0.228519
\(607\) −2.95510e12 −0.883532 −0.441766 0.897130i \(-0.645648\pi\)
−0.441766 + 0.897130i \(0.645648\pi\)
\(608\) −9.89072e11 −0.293536
\(609\) 2.82292e12 0.831612
\(610\) 9.19981e11 0.269026
\(611\) −2.28007e12 −0.661855
\(612\) 9.14473e10 0.0263505
\(613\) −5.24886e11 −0.150139 −0.0750694 0.997178i \(-0.523918\pi\)
−0.0750694 + 0.997178i \(0.523918\pi\)
\(614\) −2.92951e12 −0.831835
\(615\) −4.99795e12 −1.40882
\(616\) −1.95747e10 −0.00547748
\(617\) −5.21786e12 −1.44947 −0.724735 0.689028i \(-0.758038\pi\)
−0.724735 + 0.689028i \(0.758038\pi\)
\(618\) 2.24419e12 0.618886
\(619\) −3.81456e12 −1.04433 −0.522164 0.852845i \(-0.674875\pi\)
−0.522164 + 0.852845i \(0.674875\pi\)
\(620\) −1.21571e12 −0.330420
\(621\) −8.52480e11 −0.230023
\(622\) −3.12728e12 −0.837740
\(623\) 1.12805e13 3.00006
\(624\) −8.34668e11 −0.220386
\(625\) −3.86600e12 −1.01345
\(626\) 1.99492e12 0.519207
\(627\) −6.98281e9 −0.00180437
\(628\) −1.88247e11 −0.0482958
\(629\) −1.74269e12 −0.443908
\(630\) −3.59545e12 −0.909329
\(631\) 4.02719e12 1.01128 0.505639 0.862745i \(-0.331257\pi\)
0.505639 + 0.862745i \(0.331257\pi\)
\(632\) 3.95903e12 0.987102
\(633\) −5.10388e10 −0.0126352
\(634\) −1.36637e12 −0.335867
\(635\) −4.30994e12 −1.05194
\(636\) 6.13002e11 0.148561
\(637\) 3.12030e12 0.750878
\(638\) 1.21600e10 0.00290564
\(639\) 2.41829e12 0.573791
\(640\) 7.00354e12 1.65009
\(641\) −6.19672e12 −1.44978 −0.724888 0.688867i \(-0.758108\pi\)
−0.724888 + 0.688867i \(0.758108\pi\)
\(642\) −3.92594e12 −0.912087
\(643\) −4.06286e12 −0.937307 −0.468654 0.883382i \(-0.655261\pi\)
−0.468654 + 0.883382i \(0.655261\pi\)
\(644\) 1.49652e12 0.342843
\(645\) −7.51967e11 −0.171072
\(646\) 2.19151e12 0.495105
\(647\) 8.21017e12 1.84197 0.920986 0.389595i \(-0.127385\pi\)
0.920986 + 0.389595i \(0.127385\pi\)
\(648\) −4.51327e11 −0.100555
\(649\) −1.98128e9 −0.000438375 0
\(650\) 1.62699e12 0.357499
\(651\) 6.98674e12 1.52461
\(652\) −4.69768e11 −0.101805
\(653\) −4.34797e12 −0.935788 −0.467894 0.883785i \(-0.654987\pi\)
−0.467894 + 0.883785i \(0.654987\pi\)
\(654\) 4.39761e12 0.939977
\(655\) 7.18197e12 1.52461
\(656\) 9.31342e12 1.96355
\(657\) −2.67698e12 −0.560533
\(658\) 1.83023e13 3.80617
\(659\) 4.78548e12 0.988419 0.494209 0.869343i \(-0.335458\pi\)
0.494209 + 0.869343i \(0.335458\pi\)
\(660\) −2.13141e9 −0.000437240 0
\(661\) 4.13765e12 0.843037 0.421519 0.906820i \(-0.361497\pi\)
0.421519 + 0.906820i \(0.361497\pi\)
\(662\) −6.28565e11 −0.127201
\(663\) 4.78926e11 0.0962626
\(664\) −5.89558e12 −1.17698
\(665\) −1.18578e13 −2.35130
\(666\) −1.63314e12 −0.321655
\(667\) 4.89597e12 0.957795
\(668\) 2.60293e11 0.0505788
\(669\) −9.26424e11 −0.178810
\(670\) −1.41895e13 −2.72039
\(671\) −3.13428e9 −0.000596879 0
\(672\) 1.73504e12 0.328207
\(673\) −1.01419e13 −1.90568 −0.952842 0.303468i \(-0.901855\pi\)
−0.952842 + 0.303468i \(0.901855\pi\)
\(674\) −4.81948e10 −0.00899560
\(675\) 1.02382e12 0.189826
\(676\) −7.68287e11 −0.141502
\(677\) 2.71619e12 0.496948 0.248474 0.968639i \(-0.420071\pi\)
0.248474 + 0.968639i \(0.420071\pi\)
\(678\) 3.86047e12 0.701628
\(679\) −6.04439e12 −1.09129
\(680\) −3.52288e12 −0.631841
\(681\) −9.95289e11 −0.177332
\(682\) 3.00961e10 0.00532697
\(683\) 6.20232e12 1.09059 0.545295 0.838244i \(-0.316418\pi\)
0.545295 + 0.838244i \(0.316418\pi\)
\(684\) 2.82635e11 0.0493711
\(685\) 8.11172e12 1.40768
\(686\) −1.38197e13 −2.38254
\(687\) 4.05970e12 0.695326
\(688\) 1.40125e12 0.238434
\(689\) 3.21041e12 0.542717
\(690\) −6.23583e12 −1.04730
\(691\) 1.09681e12 0.183012 0.0915059 0.995805i \(-0.470832\pi\)
0.0915059 + 0.995805i \(0.470832\pi\)
\(692\) 3.19916e11 0.0530346
\(693\) 1.22493e10 0.00201750
\(694\) 5.43625e12 0.889573
\(695\) 8.26374e12 1.34352
\(696\) 2.59207e12 0.418702
\(697\) −5.34397e12 −0.857663
\(698\) 1.11587e13 1.77937
\(699\) 5.92657e12 0.938980
\(700\) −1.79730e12 −0.282930
\(701\) 3.96407e12 0.620026 0.310013 0.950732i \(-0.399667\pi\)
0.310013 + 0.950732i \(0.399667\pi\)
\(702\) 4.48820e11 0.0697518
\(703\) −5.38612e12 −0.831719
\(704\) −1.74150e10 −0.00267207
\(705\) −1.04953e13 −1.60009
\(706\) −1.74476e12 −0.264310
\(707\) 4.38917e12 0.660686
\(708\) 8.01941e10 0.0119948
\(709\) 9.53447e12 1.41706 0.708531 0.705680i \(-0.249358\pi\)
0.708531 + 0.705680i \(0.249358\pi\)
\(710\) 1.76896e13 2.61249
\(711\) −2.47746e12 −0.363575
\(712\) 1.03580e13 1.51048
\(713\) 1.21175e13 1.75595
\(714\) −3.84438e12 −0.553584
\(715\) −1.11626e10 −0.00159731
\(716\) 1.16265e12 0.165326
\(717\) −5.30321e12 −0.749382
\(718\) −5.98157e12 −0.839954
\(719\) 7.92743e12 1.10625 0.553124 0.833099i \(-0.313436\pi\)
0.553124 + 0.833099i \(0.313436\pi\)
\(720\) −3.84204e12 −0.532801
\(721\) −1.29835e13 −1.78930
\(722\) −1.08936e12 −0.149195
\(723\) −3.22593e11 −0.0439069
\(724\) −3.15962e11 −0.0427377
\(725\) −5.88000e12 −0.790418
\(726\) −4.65371e12 −0.621706
\(727\) 6.85823e12 0.910557 0.455279 0.890349i \(-0.349540\pi\)
0.455279 + 0.890349i \(0.349540\pi\)
\(728\) 4.14942e12 0.547515
\(729\) 2.82430e11 0.0370370
\(730\) −1.95819e13 −2.55213
\(731\) −8.04027e11 −0.104146
\(732\) 1.26862e11 0.0163318
\(733\) 5.44537e11 0.0696722 0.0348361 0.999393i \(-0.488909\pi\)
0.0348361 + 0.999393i \(0.488909\pi\)
\(734\) −8.44305e12 −1.07366
\(735\) 1.43630e13 1.81531
\(736\) 3.00920e12 0.378007
\(737\) 4.83422e10 0.00603564
\(738\) −5.00804e12 −0.621462
\(739\) 3.53532e12 0.436043 0.218021 0.975944i \(-0.430040\pi\)
0.218021 + 0.975944i \(0.430040\pi\)
\(740\) −1.64404e12 −0.201544
\(741\) 1.48021e12 0.180361
\(742\) −2.57702e13 −3.12104
\(743\) −2.30154e12 −0.277057 −0.138528 0.990358i \(-0.544237\pi\)
−0.138528 + 0.990358i \(0.544237\pi\)
\(744\) 6.41538e12 0.767616
\(745\) 6.07759e11 0.0722817
\(746\) −9.90755e12 −1.17123
\(747\) 3.68931e12 0.433513
\(748\) −2.27898e9 −0.000266184 0
\(749\) 2.27131e13 2.63699
\(750\) −1.03528e11 −0.0119476
\(751\) 7.25611e12 0.832385 0.416192 0.909277i \(-0.363364\pi\)
0.416192 + 0.909277i \(0.363364\pi\)
\(752\) 1.95575e13 2.23014
\(753\) 6.12044e12 0.693754
\(754\) −2.57767e12 −0.290440
\(755\) −5.82127e11 −0.0652013
\(756\) −4.95802e11 −0.0552026
\(757\) 5.18581e12 0.573965 0.286983 0.957936i \(-0.407348\pi\)
0.286983 + 0.957936i \(0.407348\pi\)
\(758\) 1.32571e12 0.145860
\(759\) 2.12448e10 0.00232362
\(760\) −1.08881e13 −1.18384
\(761\) −1.54747e13 −1.67260 −0.836298 0.548276i \(-0.815284\pi\)
−0.836298 + 0.548276i \(0.815284\pi\)
\(762\) −4.31864e12 −0.464034
\(763\) −2.54420e13 −2.71763
\(764\) −8.17402e11 −0.0867991
\(765\) 2.20453e12 0.232723
\(766\) −1.64592e13 −1.72734
\(767\) 4.19991e11 0.0438188
\(768\) 2.60055e12 0.269737
\(769\) 3.71081e12 0.382649 0.191324 0.981527i \(-0.438722\pi\)
0.191324 + 0.981527i \(0.438722\pi\)
\(770\) 8.96030e10 0.00918574
\(771\) −6.63016e12 −0.675739
\(772\) 5.59115e11 0.0566530
\(773\) −9.85132e12 −0.992400 −0.496200 0.868208i \(-0.665272\pi\)
−0.496200 + 0.868208i \(0.665272\pi\)
\(774\) −7.53485e11 −0.0754641
\(775\) −1.45530e13 −1.44909
\(776\) −5.55009e12 −0.549443
\(777\) 9.44839e12 0.929958
\(778\) −2.04195e12 −0.199819
\(779\) −1.65165e13 −1.60694
\(780\) 4.51815e11 0.0437054
\(781\) −6.02666e10 −0.00579625
\(782\) −6.66755e12 −0.637582
\(783\) −1.62205e12 −0.154219
\(784\) −2.67647e13 −2.53011
\(785\) −4.53809e12 −0.426540
\(786\) 7.19647e12 0.672540
\(787\) −2.69862e12 −0.250758 −0.125379 0.992109i \(-0.540015\pi\)
−0.125379 + 0.992109i \(0.540015\pi\)
\(788\) 2.21506e12 0.204653
\(789\) −2.59936e12 −0.238792
\(790\) −1.81225e13 −1.65537
\(791\) −2.23344e13 −2.02852
\(792\) 1.12476e10 0.00101577
\(793\) 6.64402e11 0.0596625
\(794\) 1.54866e13 1.38281
\(795\) 1.47777e13 1.31207
\(796\) −2.28391e12 −0.201637
\(797\) 1.29260e13 1.13475 0.567375 0.823459i \(-0.307959\pi\)
0.567375 + 0.823459i \(0.307959\pi\)
\(798\) −1.18818e13 −1.03721
\(799\) −1.12219e13 −0.974109
\(800\) −3.61401e12 −0.311949
\(801\) −6.48176e12 −0.556348
\(802\) 4.80380e12 0.410015
\(803\) 6.67135e10 0.00566232
\(804\) −1.95669e12 −0.165147
\(805\) 3.60767e13 3.02793
\(806\) −6.37974e12 −0.532470
\(807\) 4.76969e12 0.395876
\(808\) 4.03024e12 0.332644
\(809\) −1.00097e13 −0.821588 −0.410794 0.911728i \(-0.634749\pi\)
−0.410794 + 0.911728i \(0.634749\pi\)
\(810\) 2.06595e12 0.168631
\(811\) −1.58905e13 −1.28987 −0.644933 0.764240i \(-0.723115\pi\)
−0.644933 + 0.764240i \(0.723115\pi\)
\(812\) 2.84749e12 0.229859
\(813\) −6.36465e12 −0.510937
\(814\) 4.06999e10 0.00324925
\(815\) −1.13247e13 −0.899123
\(816\) −4.10803e12 −0.324360
\(817\) −2.48500e12 −0.195131
\(818\) 3.81268e12 0.297742
\(819\) −2.59660e12 −0.201664
\(820\) −5.04146e12 −0.389398
\(821\) −2.38099e13 −1.82900 −0.914499 0.404589i \(-0.867415\pi\)
−0.914499 + 0.404589i \(0.867415\pi\)
\(822\) 8.12810e12 0.620963
\(823\) 1.23990e13 0.942083 0.471041 0.882111i \(-0.343878\pi\)
0.471041 + 0.882111i \(0.343878\pi\)
\(824\) −1.19218e13 −0.900881
\(825\) −2.55148e10 −0.00191756
\(826\) −3.37130e12 −0.251992
\(827\) 1.47095e13 1.09351 0.546757 0.837291i \(-0.315862\pi\)
0.546757 + 0.837291i \(0.315862\pi\)
\(828\) −8.59901e11 −0.0635787
\(829\) 1.53622e13 1.12969 0.564843 0.825199i \(-0.308937\pi\)
0.564843 + 0.825199i \(0.308937\pi\)
\(830\) 2.69870e13 1.97380
\(831\) 6.08303e11 0.0442502
\(832\) 3.69162e12 0.267093
\(833\) 1.53574e13 1.10513
\(834\) 8.28043e12 0.592660
\(835\) 6.27492e12 0.446703
\(836\) −7.04360e9 −0.000498731 0
\(837\) −4.01459e12 −0.282733
\(838\) 1.81156e13 1.26898
\(839\) 2.05818e12 0.143402 0.0717008 0.997426i \(-0.477157\pi\)
0.0717008 + 0.997426i \(0.477157\pi\)
\(840\) 1.91001e13 1.32366
\(841\) −5.19135e12 −0.357848
\(842\) 1.93238e13 1.32492
\(843\) 1.19503e13 0.814994
\(844\) −5.14831e10 −0.00349240
\(845\) −1.85212e13 −1.24972
\(846\) −1.05165e13 −0.705838
\(847\) 2.69236e13 1.79745
\(848\) −2.75375e13 −1.82870
\(849\) 1.40954e13 0.931094
\(850\) 8.00764e12 0.526162
\(851\) 1.63870e13 1.07106
\(852\) 2.43934e12 0.158597
\(853\) −2.08559e13 −1.34883 −0.674416 0.738351i \(-0.735605\pi\)
−0.674416 + 0.738351i \(0.735605\pi\)
\(854\) −5.33320e12 −0.343105
\(855\) 6.81351e12 0.436037
\(856\) 2.08557e13 1.32768
\(857\) −1.45661e13 −0.922424 −0.461212 0.887290i \(-0.652585\pi\)
−0.461212 + 0.887290i \(0.652585\pi\)
\(858\) −1.11851e10 −0.000704609 0
\(859\) 9.60347e11 0.0601810 0.0300905 0.999547i \(-0.490420\pi\)
0.0300905 + 0.999547i \(0.490420\pi\)
\(860\) −7.58513e11 −0.0472846
\(861\) 2.89735e13 1.79675
\(862\) −6.79060e12 −0.418914
\(863\) −9.73567e12 −0.597472 −0.298736 0.954336i \(-0.596565\pi\)
−0.298736 + 0.954336i \(0.596565\pi\)
\(864\) −9.96957e11 −0.0608646
\(865\) 7.71226e12 0.468392
\(866\) 2.50879e13 1.51577
\(867\) −7.24846e12 −0.435672
\(868\) 7.04756e12 0.421405
\(869\) 6.17413e10 0.00367271
\(870\) −1.18652e13 −0.702164
\(871\) −1.02475e13 −0.603307
\(872\) −2.33614e13 −1.36828
\(873\) 3.47311e12 0.202374
\(874\) −2.06073e13 −1.19459
\(875\) 5.98950e11 0.0345425
\(876\) −2.70028e12 −0.154932
\(877\) −2.93628e13 −1.67610 −0.838050 0.545594i \(-0.816304\pi\)
−0.838050 + 0.545594i \(0.816304\pi\)
\(878\) −1.11607e13 −0.633819
\(879\) −2.72850e12 −0.154161
\(880\) 9.57481e10 0.00538218
\(881\) 8.09642e12 0.452795 0.226397 0.974035i \(-0.427305\pi\)
0.226397 + 0.974035i \(0.427305\pi\)
\(882\) 1.43920e13 0.800777
\(883\) −2.10323e13 −1.16429 −0.582147 0.813083i \(-0.697787\pi\)
−0.582147 + 0.813083i \(0.697787\pi\)
\(884\) 4.83095e11 0.0266071
\(885\) 1.93325e12 0.105936
\(886\) 7.34198e12 0.400278
\(887\) −5.84746e12 −0.317184 −0.158592 0.987344i \(-0.550695\pi\)
−0.158592 + 0.987344i \(0.550695\pi\)
\(888\) 8.67573e12 0.468217
\(889\) 2.49851e13 1.34160
\(890\) −4.74136e13 −2.53307
\(891\) −7.03848e9 −0.000374136 0
\(892\) −9.34489e11 −0.0494234
\(893\) −3.46835e13 −1.82512
\(894\) 6.08986e11 0.0318852
\(895\) 2.80282e13 1.46013
\(896\) −4.06001e13 −2.10446
\(897\) −4.50346e12 −0.232263
\(898\) 1.95875e13 1.00516
\(899\) 2.30566e13 1.17727
\(900\) 1.03273e12 0.0524681
\(901\) 1.58008e13 0.798763
\(902\) 1.24806e11 0.00627780
\(903\) 4.35921e12 0.218179
\(904\) −2.05079e13 −1.02132
\(905\) −7.61694e12 −0.377452
\(906\) −5.83302e11 −0.0287618
\(907\) −1.72857e13 −0.848116 −0.424058 0.905635i \(-0.639395\pi\)
−0.424058 + 0.905635i \(0.639395\pi\)
\(908\) −1.00395e12 −0.0490148
\(909\) −2.52202e12 −0.122521
\(910\) −1.89940e13 −0.918183
\(911\) −7.01792e12 −0.337579 −0.168790 0.985652i \(-0.553986\pi\)
−0.168790 + 0.985652i \(0.553986\pi\)
\(912\) −1.26966e13 −0.607731
\(913\) −9.19420e10 −0.00437920
\(914\) −3.02010e13 −1.43141
\(915\) 3.05829e12 0.144239
\(916\) 4.09504e12 0.192189
\(917\) −4.16344e13 −1.94442
\(918\) 2.20898e12 0.102660
\(919\) 7.88658e12 0.364728 0.182364 0.983231i \(-0.441625\pi\)
0.182364 + 0.983231i \(0.441625\pi\)
\(920\) 3.31265e13 1.52451
\(921\) −9.73855e12 −0.445991
\(922\) −1.16748e13 −0.532059
\(923\) 1.27753e13 0.579378
\(924\) 1.23560e10 0.000557639 0
\(925\) −1.96805e13 −0.883892
\(926\) −6.58901e12 −0.294490
\(927\) 7.46034e12 0.331818
\(928\) 5.72574e12 0.253434
\(929\) −6.34384e12 −0.279436 −0.139718 0.990191i \(-0.544620\pi\)
−0.139718 + 0.990191i \(0.544620\pi\)
\(930\) −2.93664e13 −1.28729
\(931\) 4.74648e13 2.07061
\(932\) 5.97816e12 0.259535
\(933\) −1.03960e13 −0.449157
\(934\) −7.32307e11 −0.0314871
\(935\) −5.49395e10 −0.00235089
\(936\) −2.38426e12 −0.101534
\(937\) 1.92500e13 0.815835 0.407917 0.913019i \(-0.366255\pi\)
0.407917 + 0.913019i \(0.366255\pi\)
\(938\) 8.22578e13 3.46948
\(939\) 6.63170e12 0.278375
\(940\) −1.05867e13 −0.442267
\(941\) 2.38250e13 0.990557 0.495278 0.868734i \(-0.335066\pi\)
0.495278 + 0.868734i \(0.335066\pi\)
\(942\) −4.54725e12 −0.188157
\(943\) 5.02506e13 2.06937
\(944\) −3.60251e12 −0.147649
\(945\) −1.19524e13 −0.487540
\(946\) 1.87777e10 0.000762313 0
\(947\) −1.21392e13 −0.490473 −0.245236 0.969463i \(-0.578866\pi\)
−0.245236 + 0.969463i \(0.578866\pi\)
\(948\) −2.49903e12 −0.100493
\(949\) −1.41419e13 −0.565990
\(950\) 2.47491e13 0.985833
\(951\) −4.54223e12 −0.180076
\(952\) 2.04224e13 0.805825
\(953\) 3.61714e13 1.42052 0.710259 0.703940i \(-0.248578\pi\)
0.710259 + 0.703940i \(0.248578\pi\)
\(954\) 1.48076e13 0.578783
\(955\) −1.97052e13 −0.766595
\(956\) −5.34938e12 −0.207130
\(957\) 4.04235e10 0.00155787
\(958\) 1.75191e13 0.671998
\(959\) −4.70243e13 −1.79531
\(960\) 1.69928e13 0.645720
\(961\) 3.06256e13 1.15832
\(962\) −8.62753e12 −0.324787
\(963\) −1.30510e13 −0.489018
\(964\) −3.25401e11 −0.0121359
\(965\) 1.34786e13 0.500349
\(966\) 3.61496e13 1.33569
\(967\) −3.77071e13 −1.38677 −0.693385 0.720568i \(-0.743881\pi\)
−0.693385 + 0.720568i \(0.743881\pi\)
\(968\) 2.47218e13 0.904986
\(969\) 7.28523e12 0.265452
\(970\) 2.54056e13 0.921416
\(971\) 2.75982e13 0.996309 0.498154 0.867088i \(-0.334011\pi\)
0.498154 + 0.867088i \(0.334011\pi\)
\(972\) 2.84888e11 0.0102371
\(973\) −4.79056e13 −1.71348
\(974\) −1.21110e13 −0.431187
\(975\) 5.40860e12 0.191674
\(976\) −5.69896e12 −0.201035
\(977\) 5.47035e13 1.92083 0.960416 0.278570i \(-0.0898604\pi\)
0.960416 + 0.278570i \(0.0898604\pi\)
\(978\) −1.13476e13 −0.396624
\(979\) 1.61533e11 0.00562004
\(980\) 1.44880e13 0.501754
\(981\) 1.46190e13 0.503972
\(982\) −1.77836e13 −0.610264
\(983\) 3.91993e12 0.133902 0.0669510 0.997756i \(-0.478673\pi\)
0.0669510 + 0.997756i \(0.478673\pi\)
\(984\) 2.66041e13 0.904630
\(985\) 5.33988e13 1.80746
\(986\) −1.26867e13 −0.427465
\(987\) 6.08422e13 2.04069
\(988\) 1.49310e12 0.0498518
\(989\) 7.56046e12 0.251284
\(990\) −5.14860e10 −0.00170345
\(991\) 2.45813e13 0.809607 0.404803 0.914404i \(-0.367340\pi\)
0.404803 + 0.914404i \(0.367340\pi\)
\(992\) 1.41712e13 0.464627
\(993\) −2.08954e12 −0.0681990
\(994\) −1.02548e14 −3.33187
\(995\) −5.50584e13 −1.78082
\(996\) 3.72142e12 0.119824
\(997\) 3.15608e13 1.01163 0.505813 0.862643i \(-0.331192\pi\)
0.505813 + 0.862643i \(0.331192\pi\)
\(998\) −1.11781e13 −0.356683
\(999\) −5.42906e12 −0.172457
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.1.16 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.16 21 1.1 even 1 trivial