Properties

Label 177.14.a.c.1.11
Level $177$
Weight $14$
Character 177.1
Self dual yes
Analytic conductor $189.799$
Analytic rank $0$
Dimension $31$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(189.798744245\)
Analytic rank: \(0\)
Dimension: \(31\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-59.5570 q^{2} +729.000 q^{3} -4644.96 q^{4} -45189.8 q^{5} -43417.1 q^{6} -134821. q^{7} +764531. q^{8} +531441. q^{9} +O(q^{10})\) \(q-59.5570 q^{2} +729.000 q^{3} -4644.96 q^{4} -45189.8 q^{5} -43417.1 q^{6} -134821. q^{7} +764531. q^{8} +531441. q^{9} +2.69137e6 q^{10} +9.07000e6 q^{11} -3.38617e6 q^{12} -1.72380e6 q^{13} +8.02957e6 q^{14} -3.29434e7 q^{15} -7.48174e6 q^{16} +5.25990e7 q^{17} -3.16511e7 q^{18} +1.91390e8 q^{19} +2.09905e8 q^{20} -9.82849e7 q^{21} -5.40183e8 q^{22} +6.96259e8 q^{23} +5.57343e8 q^{24} +8.21418e8 q^{25} +1.02665e8 q^{26} +3.87420e8 q^{27} +6.26240e8 q^{28} -5.96170e8 q^{29} +1.96201e9 q^{30} +4.04822e9 q^{31} -5.81745e9 q^{32} +6.61203e9 q^{33} -3.13264e9 q^{34} +6.09256e9 q^{35} -2.46852e9 q^{36} +5.23136e9 q^{37} -1.13986e10 q^{38} -1.25665e9 q^{39} -3.45490e10 q^{40} -5.61271e10 q^{41} +5.85356e9 q^{42} +3.71000e10 q^{43} -4.21298e10 q^{44} -2.40157e10 q^{45} -4.14671e10 q^{46} -7.30879e10 q^{47} -5.45419e9 q^{48} -7.87122e10 q^{49} -4.89213e10 q^{50} +3.83447e10 q^{51} +8.00699e9 q^{52} -6.59362e10 q^{53} -2.30736e10 q^{54} -4.09872e11 q^{55} -1.03075e11 q^{56} +1.39523e11 q^{57} +3.55061e10 q^{58} -4.21805e10 q^{59} +1.53021e11 q^{60} +5.17079e11 q^{61} -2.41100e11 q^{62} -7.16497e10 q^{63} +4.07761e11 q^{64} +7.78983e10 q^{65} -3.93793e11 q^{66} +1.40765e11 q^{67} -2.44320e11 q^{68} +5.07573e11 q^{69} -3.62855e11 q^{70} +7.79097e11 q^{71} +4.06303e11 q^{72} -1.35323e12 q^{73} -3.11564e11 q^{74} +5.98814e11 q^{75} -8.88999e11 q^{76} -1.22283e12 q^{77} +7.48425e10 q^{78} +1.33603e12 q^{79} +3.38098e11 q^{80} +2.82430e11 q^{81} +3.34277e12 q^{82} -9.97241e11 q^{83} +4.56529e11 q^{84} -2.37694e12 q^{85} -2.20957e12 q^{86} -4.34608e11 q^{87} +6.93430e12 q^{88} +6.23630e12 q^{89} +1.43031e12 q^{90} +2.32406e11 q^{91} -3.23409e12 q^{92} +2.95115e12 q^{93} +4.35290e12 q^{94} -8.64889e12 q^{95} -4.24092e12 q^{96} +8.66937e12 q^{97} +4.68786e12 q^{98} +4.82017e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \) \( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −59.5570 −0.658019 −0.329009 0.944327i \(-0.606715\pi\)
−0.329009 + 0.944327i \(0.606715\pi\)
\(3\) 729.000 0.577350
\(4\) −4644.96 −0.567011
\(5\) −45189.8 −1.29341 −0.646704 0.762741i \(-0.723853\pi\)
−0.646704 + 0.762741i \(0.723853\pi\)
\(6\) −43417.1 −0.379907
\(7\) −134821. −0.433134 −0.216567 0.976268i \(-0.569486\pi\)
−0.216567 + 0.976268i \(0.569486\pi\)
\(8\) 764531. 1.03112
\(9\) 531441. 0.333333
\(10\) 2.69137e6 0.851087
\(11\) 9.07000e6 1.54367 0.771836 0.635822i \(-0.219339\pi\)
0.771836 + 0.635822i \(0.219339\pi\)
\(12\) −3.38617e6 −0.327364
\(13\) −1.72380e6 −0.0990503 −0.0495251 0.998773i \(-0.515771\pi\)
−0.0495251 + 0.998773i \(0.515771\pi\)
\(14\) 8.02957e6 0.285010
\(15\) −3.29434e7 −0.746750
\(16\) −7.48174e6 −0.111487
\(17\) 5.25990e7 0.528518 0.264259 0.964452i \(-0.414873\pi\)
0.264259 + 0.964452i \(0.414873\pi\)
\(18\) −3.16511e7 −0.219340
\(19\) 1.91390e8 0.933299 0.466650 0.884442i \(-0.345461\pi\)
0.466650 + 0.884442i \(0.345461\pi\)
\(20\) 2.09905e8 0.733378
\(21\) −9.82849e7 −0.250070
\(22\) −5.40183e8 −1.01576
\(23\) 6.96259e8 0.980708 0.490354 0.871523i \(-0.336867\pi\)
0.490354 + 0.871523i \(0.336867\pi\)
\(24\) 5.57343e8 0.595319
\(25\) 8.21418e8 0.672906
\(26\) 1.02665e8 0.0651769
\(27\) 3.87420e8 0.192450
\(28\) 6.26240e8 0.245592
\(29\) −5.96170e8 −0.186116 −0.0930579 0.995661i \(-0.529664\pi\)
−0.0930579 + 0.995661i \(0.529664\pi\)
\(30\) 1.96201e9 0.491375
\(31\) 4.04822e9 0.819243 0.409622 0.912255i \(-0.365661\pi\)
0.409622 + 0.912255i \(0.365661\pi\)
\(32\) −5.81745e9 −0.957763
\(33\) 6.61203e9 0.891239
\(34\) −3.13264e9 −0.347775
\(35\) 6.09256e9 0.560219
\(36\) −2.46852e9 −0.189004
\(37\) 5.23136e9 0.335199 0.167600 0.985855i \(-0.446398\pi\)
0.167600 + 0.985855i \(0.446398\pi\)
\(38\) −1.13986e10 −0.614128
\(39\) −1.25665e9 −0.0571867
\(40\) −3.45490e10 −1.33366
\(41\) −5.61271e10 −1.84535 −0.922673 0.385584i \(-0.874000\pi\)
−0.922673 + 0.385584i \(0.874000\pi\)
\(42\) 5.85356e9 0.164551
\(43\) 3.71000e10 0.895012 0.447506 0.894281i \(-0.352312\pi\)
0.447506 + 0.894281i \(0.352312\pi\)
\(44\) −4.21298e10 −0.875279
\(45\) −2.40157e10 −0.431136
\(46\) −4.14671e10 −0.645324
\(47\) −7.30879e10 −0.989030 −0.494515 0.869169i \(-0.664654\pi\)
−0.494515 + 0.869169i \(0.664654\pi\)
\(48\) −5.45419e9 −0.0643668
\(49\) −7.87122e10 −0.812395
\(50\) −4.89213e10 −0.442785
\(51\) 3.83447e10 0.305140
\(52\) 8.00699e9 0.0561626
\(53\) −6.59362e10 −0.408630 −0.204315 0.978905i \(-0.565497\pi\)
−0.204315 + 0.978905i \(0.565497\pi\)
\(54\) −2.30736e10 −0.126636
\(55\) −4.09872e11 −1.99660
\(56\) −1.03075e11 −0.446614
\(57\) 1.39523e11 0.538841
\(58\) 3.55061e10 0.122468
\(59\) −4.21805e10 −0.130189
\(60\) 1.53021e11 0.423416
\(61\) 5.17079e11 1.28503 0.642515 0.766273i \(-0.277891\pi\)
0.642515 + 0.766273i \(0.277891\pi\)
\(62\) −2.41100e11 −0.539077
\(63\) −7.16497e10 −0.144378
\(64\) 4.07761e11 0.741712
\(65\) 7.78983e10 0.128112
\(66\) −3.93793e11 −0.586452
\(67\) 1.40765e11 0.190112 0.0950558 0.995472i \(-0.469697\pi\)
0.0950558 + 0.995472i \(0.469697\pi\)
\(68\) −2.44320e11 −0.299676
\(69\) 5.07573e11 0.566212
\(70\) −3.62855e11 −0.368634
\(71\) 7.79097e11 0.721792 0.360896 0.932606i \(-0.382471\pi\)
0.360896 + 0.932606i \(0.382471\pi\)
\(72\) 4.06303e11 0.343708
\(73\) −1.35323e12 −1.04658 −0.523289 0.852155i \(-0.675295\pi\)
−0.523289 + 0.852155i \(0.675295\pi\)
\(74\) −3.11564e11 −0.220567
\(75\) 5.98814e11 0.388502
\(76\) −8.88999e11 −0.529191
\(77\) −1.22283e12 −0.668616
\(78\) 7.48425e10 0.0376299
\(79\) 1.33603e12 0.618356 0.309178 0.951004i \(-0.399946\pi\)
0.309178 + 0.951004i \(0.399946\pi\)
\(80\) 3.38098e11 0.144198
\(81\) 2.82430e11 0.111111
\(82\) 3.34277e12 1.21427
\(83\) −9.97241e11 −0.334805 −0.167403 0.985889i \(-0.553538\pi\)
−0.167403 + 0.985889i \(0.553538\pi\)
\(84\) 4.56529e11 0.141792
\(85\) −2.37694e12 −0.683590
\(86\) −2.20957e12 −0.588935
\(87\) −4.34608e11 −0.107454
\(88\) 6.93430e12 1.59171
\(89\) 6.23630e12 1.33012 0.665062 0.746788i \(-0.268405\pi\)
0.665062 + 0.746788i \(0.268405\pi\)
\(90\) 1.43031e12 0.283696
\(91\) 2.32406e11 0.0429020
\(92\) −3.23409e12 −0.556073
\(93\) 2.95115e12 0.472990
\(94\) 4.35290e12 0.650800
\(95\) −8.64889e12 −1.20714
\(96\) −4.24092e12 −0.552964
\(97\) 8.66937e12 1.05675 0.528374 0.849012i \(-0.322802\pi\)
0.528374 + 0.849012i \(0.322802\pi\)
\(98\) 4.68786e12 0.534571
\(99\) 4.82017e12 0.514557
\(100\) −3.81545e12 −0.381545
\(101\) −7.77831e12 −0.729115 −0.364558 0.931181i \(-0.618780\pi\)
−0.364558 + 0.931181i \(0.618780\pi\)
\(102\) −2.28370e12 −0.200788
\(103\) −7.94006e12 −0.655212 −0.327606 0.944814i \(-0.606242\pi\)
−0.327606 + 0.944814i \(0.606242\pi\)
\(104\) −1.31790e12 −0.102133
\(105\) 4.44148e12 0.323442
\(106\) 3.92696e12 0.268886
\(107\) 1.15110e13 0.741515 0.370757 0.928730i \(-0.379098\pi\)
0.370757 + 0.928730i \(0.379098\pi\)
\(108\) −1.79955e12 −0.109121
\(109\) −2.40502e13 −1.37355 −0.686777 0.726868i \(-0.740975\pi\)
−0.686777 + 0.726868i \(0.740975\pi\)
\(110\) 2.44108e13 1.31380
\(111\) 3.81366e12 0.193527
\(112\) 1.00870e12 0.0482886
\(113\) 1.17525e13 0.531033 0.265516 0.964106i \(-0.414458\pi\)
0.265516 + 0.964106i \(0.414458\pi\)
\(114\) −8.30960e12 −0.354567
\(115\) −3.14638e13 −1.26846
\(116\) 2.76919e12 0.105530
\(117\) −9.16099e11 −0.0330168
\(118\) 2.51215e12 0.0856667
\(119\) −7.09148e12 −0.228919
\(120\) −2.51863e13 −0.769991
\(121\) 4.77422e13 1.38292
\(122\) −3.07957e13 −0.845574
\(123\) −4.09167e13 −1.06541
\(124\) −1.88038e13 −0.464520
\(125\) 1.80436e13 0.423066
\(126\) 4.26724e12 0.0950033
\(127\) 3.63379e13 0.768486 0.384243 0.923232i \(-0.374463\pi\)
0.384243 + 0.923232i \(0.374463\pi\)
\(128\) 2.33715e13 0.469702
\(129\) 2.70459e13 0.516736
\(130\) −4.63940e12 −0.0843004
\(131\) −2.87549e13 −0.497106 −0.248553 0.968618i \(-0.579955\pi\)
−0.248553 + 0.968618i \(0.579955\pi\)
\(132\) −3.07126e13 −0.505343
\(133\) −2.58035e13 −0.404243
\(134\) −8.38355e12 −0.125097
\(135\) −1.75075e13 −0.248917
\(136\) 4.02136e13 0.544967
\(137\) −8.80067e13 −1.13719 −0.568594 0.822618i \(-0.692512\pi\)
−0.568594 + 0.822618i \(0.692512\pi\)
\(138\) −3.02295e13 −0.372578
\(139\) −1.49388e14 −1.75679 −0.878395 0.477935i \(-0.841385\pi\)
−0.878395 + 0.477935i \(0.841385\pi\)
\(140\) −2.82997e13 −0.317650
\(141\) −5.32811e13 −0.571017
\(142\) −4.64007e13 −0.474953
\(143\) −1.56349e13 −0.152901
\(144\) −3.97610e12 −0.0371622
\(145\) 2.69408e13 0.240724
\(146\) 8.05941e13 0.688668
\(147\) −5.73812e13 −0.469037
\(148\) −2.42994e13 −0.190062
\(149\) 1.77691e14 1.33032 0.665158 0.746703i \(-0.268364\pi\)
0.665158 + 0.746703i \(0.268364\pi\)
\(150\) −3.56636e13 −0.255642
\(151\) 1.90855e14 1.31025 0.655124 0.755521i \(-0.272616\pi\)
0.655124 + 0.755521i \(0.272616\pi\)
\(152\) 1.46324e14 0.962346
\(153\) 2.79533e13 0.176173
\(154\) 7.28282e13 0.439962
\(155\) −1.82938e14 −1.05962
\(156\) 5.83710e12 0.0324255
\(157\) −1.22982e13 −0.0655378 −0.0327689 0.999463i \(-0.510433\pi\)
−0.0327689 + 0.999463i \(0.510433\pi\)
\(158\) −7.95698e13 −0.406890
\(159\) −4.80675e13 −0.235923
\(160\) 2.62890e14 1.23878
\(161\) −9.38707e13 −0.424778
\(162\) −1.68207e13 −0.0731132
\(163\) −4.25701e14 −1.77781 −0.888906 0.458090i \(-0.848534\pi\)
−0.888906 + 0.458090i \(0.848534\pi\)
\(164\) 2.60708e14 1.04633
\(165\) −2.98797e14 −1.15274
\(166\) 5.93927e13 0.220308
\(167\) 1.67407e14 0.597197 0.298598 0.954379i \(-0.403481\pi\)
0.298598 + 0.954379i \(0.403481\pi\)
\(168\) −7.51419e13 −0.257853
\(169\) −2.99904e14 −0.990189
\(170\) 1.41564e14 0.449815
\(171\) 1.01713e14 0.311100
\(172\) −1.72328e14 −0.507482
\(173\) −7.92408e13 −0.224724 −0.112362 0.993667i \(-0.535842\pi\)
−0.112362 + 0.993667i \(0.535842\pi\)
\(174\) 2.58840e13 0.0707067
\(175\) −1.10745e14 −0.291458
\(176\) −6.78594e13 −0.172099
\(177\) −3.07496e13 −0.0751646
\(178\) −3.71416e14 −0.875247
\(179\) 4.77119e14 1.08413 0.542065 0.840336i \(-0.317643\pi\)
0.542065 + 0.840336i \(0.317643\pi\)
\(180\) 1.11552e14 0.244459
\(181\) −8.76045e12 −0.0185189 −0.00925946 0.999957i \(-0.502947\pi\)
−0.00925946 + 0.999957i \(0.502947\pi\)
\(182\) −1.38414e13 −0.0282303
\(183\) 3.76951e14 0.741912
\(184\) 5.32312e14 1.01123
\(185\) −2.36404e14 −0.433550
\(186\) −1.75762e14 −0.311237
\(187\) 4.77073e14 0.815858
\(188\) 3.39490e14 0.560791
\(189\) −5.22326e13 −0.0833566
\(190\) 5.15102e14 0.794319
\(191\) 4.85886e14 0.724132 0.362066 0.932153i \(-0.382072\pi\)
0.362066 + 0.932153i \(0.382072\pi\)
\(192\) 2.97257e14 0.428228
\(193\) −1.31300e15 −1.82870 −0.914349 0.404926i \(-0.867297\pi\)
−0.914349 + 0.404926i \(0.867297\pi\)
\(194\) −5.16322e14 −0.695360
\(195\) 5.67879e13 0.0739658
\(196\) 3.65615e14 0.460637
\(197\) 1.08128e15 1.31798 0.658991 0.752151i \(-0.270983\pi\)
0.658991 + 0.752151i \(0.270983\pi\)
\(198\) −2.87075e14 −0.338588
\(199\) 1.77636e14 0.202762 0.101381 0.994848i \(-0.467674\pi\)
0.101381 + 0.994848i \(0.467674\pi\)
\(200\) 6.28000e14 0.693849
\(201\) 1.02618e14 0.109761
\(202\) 4.63253e14 0.479771
\(203\) 8.03766e13 0.0806130
\(204\) −1.78110e14 −0.173018
\(205\) 2.53638e15 2.38679
\(206\) 4.72887e14 0.431142
\(207\) 3.70021e14 0.326903
\(208\) 1.28970e13 0.0110428
\(209\) 1.73591e15 1.44071
\(210\) −2.64521e14 −0.212831
\(211\) −4.09611e14 −0.319548 −0.159774 0.987154i \(-0.551077\pi\)
−0.159774 + 0.987154i \(0.551077\pi\)
\(212\) 3.06271e14 0.231698
\(213\) 5.67961e14 0.416727
\(214\) −6.85563e14 −0.487931
\(215\) −1.67654e15 −1.15762
\(216\) 2.96195e14 0.198440
\(217\) −5.45787e14 −0.354842
\(218\) 1.43236e15 0.903824
\(219\) −9.86501e14 −0.604242
\(220\) 1.90384e15 1.13209
\(221\) −9.06703e13 −0.0523499
\(222\) −2.27130e14 −0.127345
\(223\) 2.39484e15 1.30405 0.652025 0.758197i \(-0.273920\pi\)
0.652025 + 0.758197i \(0.273920\pi\)
\(224\) 7.84317e14 0.414839
\(225\) 4.36535e14 0.224302
\(226\) −6.99946e14 −0.349429
\(227\) 2.73801e15 1.32821 0.664105 0.747639i \(-0.268813\pi\)
0.664105 + 0.747639i \(0.268813\pi\)
\(228\) −6.48080e14 −0.305529
\(229\) 1.06226e15 0.486742 0.243371 0.969933i \(-0.421747\pi\)
0.243371 + 0.969933i \(0.421747\pi\)
\(230\) 1.87389e15 0.834668
\(231\) −8.91444e14 −0.386026
\(232\) −4.55791e14 −0.191908
\(233\) −2.15492e15 −0.882303 −0.441151 0.897433i \(-0.645430\pi\)
−0.441151 + 0.897433i \(0.645430\pi\)
\(234\) 5.45602e13 0.0217256
\(235\) 3.30283e15 1.27922
\(236\) 1.95927e14 0.0738186
\(237\) 9.73963e14 0.357008
\(238\) 4.22348e14 0.150633
\(239\) −4.00486e15 −1.38995 −0.694977 0.719031i \(-0.744586\pi\)
−0.694977 + 0.719031i \(0.744586\pi\)
\(240\) 2.46474e14 0.0832526
\(241\) 4.38531e15 1.44175 0.720874 0.693066i \(-0.243741\pi\)
0.720874 + 0.693066i \(0.243741\pi\)
\(242\) −2.84339e15 −0.909988
\(243\) 2.05891e14 0.0641500
\(244\) −2.40181e15 −0.728627
\(245\) 3.55699e15 1.05076
\(246\) 2.43688e15 0.701060
\(247\) −3.29919e14 −0.0924436
\(248\) 3.09499e15 0.844741
\(249\) −7.26988e14 −0.193300
\(250\) −1.07462e15 −0.278386
\(251\) −4.46785e15 −1.12777 −0.563884 0.825854i \(-0.690693\pi\)
−0.563884 + 0.825854i \(0.690693\pi\)
\(252\) 3.32810e14 0.0818639
\(253\) 6.31507e15 1.51389
\(254\) −2.16418e15 −0.505678
\(255\) −1.73279e15 −0.394671
\(256\) −4.73231e15 −1.05078
\(257\) 8.62081e15 1.86631 0.933153 0.359479i \(-0.117046\pi\)
0.933153 + 0.359479i \(0.117046\pi\)
\(258\) −1.61077e15 −0.340022
\(259\) −7.05300e14 −0.145186
\(260\) −3.61835e14 −0.0726412
\(261\) −3.16829e14 −0.0620386
\(262\) 1.71256e15 0.327105
\(263\) −4.99556e15 −0.930832 −0.465416 0.885092i \(-0.654095\pi\)
−0.465416 + 0.885092i \(0.654095\pi\)
\(264\) 5.05510e15 0.918977
\(265\) 2.97964e15 0.528526
\(266\) 1.53678e15 0.266000
\(267\) 4.54627e15 0.767948
\(268\) −6.53848e14 −0.107795
\(269\) 3.62083e15 0.582664 0.291332 0.956622i \(-0.405902\pi\)
0.291332 + 0.956622i \(0.405902\pi\)
\(270\) 1.04269e15 0.163792
\(271\) 8.66129e15 1.32826 0.664129 0.747618i \(-0.268803\pi\)
0.664129 + 0.747618i \(0.268803\pi\)
\(272\) −3.93532e14 −0.0589227
\(273\) 1.69424e14 0.0247695
\(274\) 5.24142e15 0.748291
\(275\) 7.45027e15 1.03875
\(276\) −2.35765e15 −0.321049
\(277\) −1.49263e15 −0.198533 −0.0992665 0.995061i \(-0.531650\pi\)
−0.0992665 + 0.995061i \(0.531650\pi\)
\(278\) 8.89712e15 1.15600
\(279\) 2.15139e15 0.273081
\(280\) 4.65795e15 0.577654
\(281\) −4.11381e15 −0.498487 −0.249243 0.968441i \(-0.580182\pi\)
−0.249243 + 0.968441i \(0.580182\pi\)
\(282\) 3.17326e15 0.375740
\(283\) 1.32900e16 1.53784 0.768921 0.639343i \(-0.220794\pi\)
0.768921 + 0.639343i \(0.220794\pi\)
\(284\) −3.61887e15 −0.409264
\(285\) −6.30504e15 −0.696941
\(286\) 9.31168e14 0.100612
\(287\) 7.56714e15 0.799281
\(288\) −3.09163e15 −0.319254
\(289\) −7.13792e15 −0.720669
\(290\) −1.60452e15 −0.158401
\(291\) 6.31997e15 0.610114
\(292\) 6.28567e15 0.593421
\(293\) −8.91714e15 −0.823353 −0.411676 0.911330i \(-0.635057\pi\)
−0.411676 + 0.911330i \(0.635057\pi\)
\(294\) 3.41745e15 0.308635
\(295\) 1.90613e15 0.168387
\(296\) 3.99954e15 0.345632
\(297\) 3.51390e15 0.297080
\(298\) −1.05827e16 −0.875372
\(299\) −1.20021e15 −0.0971394
\(300\) −2.78147e15 −0.220285
\(301\) −5.00188e15 −0.387660
\(302\) −1.13668e16 −0.862168
\(303\) −5.67039e15 −0.420955
\(304\) −1.43193e15 −0.104050
\(305\) −2.33667e16 −1.66207
\(306\) −1.66482e15 −0.115925
\(307\) 9.61918e15 0.655750 0.327875 0.944721i \(-0.393667\pi\)
0.327875 + 0.944721i \(0.393667\pi\)
\(308\) 5.68000e15 0.379113
\(309\) −5.78831e15 −0.378287
\(310\) 1.08953e16 0.697247
\(311\) −1.90887e16 −1.19628 −0.598141 0.801391i \(-0.704094\pi\)
−0.598141 + 0.801391i \(0.704094\pi\)
\(312\) −9.60750e14 −0.0589665
\(313\) −1.53859e16 −0.924881 −0.462440 0.886650i \(-0.653026\pi\)
−0.462440 + 0.886650i \(0.653026\pi\)
\(314\) 7.32442e14 0.0431251
\(315\) 3.23784e15 0.186740
\(316\) −6.20579e15 −0.350615
\(317\) 1.66660e16 0.922456 0.461228 0.887282i \(-0.347409\pi\)
0.461228 + 0.887282i \(0.347409\pi\)
\(318\) 2.86276e15 0.155242
\(319\) −5.40726e15 −0.287302
\(320\) −1.84266e16 −0.959337
\(321\) 8.39154e15 0.428114
\(322\) 5.59066e15 0.279512
\(323\) 1.00669e16 0.493266
\(324\) −1.31187e15 −0.0630013
\(325\) −1.41596e15 −0.0666515
\(326\) 2.53535e16 1.16983
\(327\) −1.75326e16 −0.793022
\(328\) −4.29109e16 −1.90278
\(329\) 9.85382e15 0.428382
\(330\) 1.77954e16 0.758522
\(331\) −4.11778e16 −1.72100 −0.860500 0.509450i \(-0.829849\pi\)
−0.860500 + 0.509450i \(0.829849\pi\)
\(332\) 4.63214e15 0.189838
\(333\) 2.78016e15 0.111733
\(334\) −9.97029e15 −0.392967
\(335\) −6.36115e15 −0.245892
\(336\) 7.35341e14 0.0278794
\(337\) 2.75920e16 1.02610 0.513049 0.858359i \(-0.328516\pi\)
0.513049 + 0.858359i \(0.328516\pi\)
\(338\) 1.78614e16 0.651563
\(339\) 8.56759e15 0.306592
\(340\) 1.10408e16 0.387603
\(341\) 3.67174e16 1.26464
\(342\) −6.05770e15 −0.204709
\(343\) 2.36748e16 0.785009
\(344\) 2.83641e16 0.922868
\(345\) −2.29371e16 −0.732344
\(346\) 4.71935e15 0.147872
\(347\) 6.36051e16 1.95592 0.977959 0.208799i \(-0.0669554\pi\)
0.977959 + 0.208799i \(0.0669554\pi\)
\(348\) 2.01874e15 0.0609277
\(349\) 1.43799e16 0.425982 0.212991 0.977054i \(-0.431679\pi\)
0.212991 + 0.977054i \(0.431679\pi\)
\(350\) 6.59564e15 0.191785
\(351\) −6.67836e14 −0.0190622
\(352\) −5.27643e16 −1.47847
\(353\) 1.93706e16 0.532853 0.266426 0.963855i \(-0.414157\pi\)
0.266426 + 0.963855i \(0.414157\pi\)
\(354\) 1.83136e15 0.0494597
\(355\) −3.52073e16 −0.933572
\(356\) −2.89674e16 −0.754196
\(357\) −5.16969e15 −0.132166
\(358\) −2.84158e16 −0.713378
\(359\) 2.49972e16 0.616280 0.308140 0.951341i \(-0.400293\pi\)
0.308140 + 0.951341i \(0.400293\pi\)
\(360\) −1.83608e16 −0.444554
\(361\) −5.42282e15 −0.128952
\(362\) 5.21746e14 0.0121858
\(363\) 3.48041e16 0.798430
\(364\) −1.07951e15 −0.0243259
\(365\) 6.11520e16 1.35365
\(366\) −2.24501e16 −0.488192
\(367\) −4.85759e16 −1.03775 −0.518874 0.854851i \(-0.673648\pi\)
−0.518874 + 0.854851i \(0.673648\pi\)
\(368\) −5.20923e15 −0.109336
\(369\) −2.98283e16 −0.615115
\(370\) 1.40795e16 0.285284
\(371\) 8.88961e15 0.176991
\(372\) −1.37080e16 −0.268191
\(373\) −1.31338e15 −0.0252513 −0.0126256 0.999920i \(-0.504019\pi\)
−0.0126256 + 0.999920i \(0.504019\pi\)
\(374\) −2.84131e16 −0.536850
\(375\) 1.31538e16 0.244257
\(376\) −5.58780e16 −1.01981
\(377\) 1.02768e15 0.0184348
\(378\) 3.11082e15 0.0548502
\(379\) 1.05317e16 0.182534 0.0912669 0.995826i \(-0.470908\pi\)
0.0912669 + 0.995826i \(0.470908\pi\)
\(380\) 4.01737e16 0.684461
\(381\) 2.64903e16 0.443686
\(382\) −2.89379e16 −0.476492
\(383\) 6.55176e16 1.06063 0.530317 0.847799i \(-0.322073\pi\)
0.530317 + 0.847799i \(0.322073\pi\)
\(384\) 1.70379e16 0.271183
\(385\) 5.52595e16 0.864794
\(386\) 7.81984e16 1.20332
\(387\) 1.97165e16 0.298337
\(388\) −4.02689e16 −0.599188
\(389\) 1.20482e17 1.76299 0.881496 0.472191i \(-0.156537\pi\)
0.881496 + 0.472191i \(0.156537\pi\)
\(390\) −3.38212e15 −0.0486709
\(391\) 3.66226e16 0.518322
\(392\) −6.01779e16 −0.837679
\(393\) −2.09623e16 −0.287004
\(394\) −6.43981e16 −0.867257
\(395\) −6.03748e16 −0.799788
\(396\) −2.23895e16 −0.291760
\(397\) 1.15995e17 1.48697 0.743483 0.668754i \(-0.233172\pi\)
0.743483 + 0.668754i \(0.233172\pi\)
\(398\) −1.05795e16 −0.133421
\(399\) −1.88107e16 −0.233390
\(400\) −6.14564e15 −0.0750200
\(401\) −1.24610e17 −1.49663 −0.748315 0.663344i \(-0.769137\pi\)
−0.748315 + 0.663344i \(0.769137\pi\)
\(402\) −6.11161e15 −0.0722248
\(403\) −6.97833e15 −0.0811463
\(404\) 3.61299e16 0.413417
\(405\) −1.27629e16 −0.143712
\(406\) −4.78699e15 −0.0530449
\(407\) 4.74484e16 0.517438
\(408\) 2.93157e16 0.314637
\(409\) 2.38763e16 0.252212 0.126106 0.992017i \(-0.459752\pi\)
0.126106 + 0.992017i \(0.459752\pi\)
\(410\) −1.51059e17 −1.57055
\(411\) −6.41569e16 −0.656556
\(412\) 3.68813e16 0.371513
\(413\) 5.68684e15 0.0563892
\(414\) −2.20373e16 −0.215108
\(415\) 4.50651e16 0.433040
\(416\) 1.00281e16 0.0948666
\(417\) −1.08904e17 −1.01428
\(418\) −1.03386e17 −0.948013
\(419\) 3.35191e16 0.302623 0.151311 0.988486i \(-0.451650\pi\)
0.151311 + 0.988486i \(0.451650\pi\)
\(420\) −2.06305e16 −0.183396
\(421\) −2.88845e16 −0.252831 −0.126416 0.991977i \(-0.540347\pi\)
−0.126416 + 0.991977i \(0.540347\pi\)
\(422\) 2.43952e16 0.210268
\(423\) −3.88419e16 −0.329677
\(424\) −5.04103e16 −0.421348
\(425\) 4.32058e16 0.355643
\(426\) −3.38261e16 −0.274214
\(427\) −6.97134e16 −0.556590
\(428\) −5.34683e16 −0.420447
\(429\) −1.13978e16 −0.0882775
\(430\) 9.98500e16 0.761733
\(431\) −1.21328e17 −0.911716 −0.455858 0.890053i \(-0.650667\pi\)
−0.455858 + 0.890053i \(0.650667\pi\)
\(432\) −2.89858e15 −0.0214556
\(433\) 1.90552e16 0.138945 0.0694723 0.997584i \(-0.477868\pi\)
0.0694723 + 0.997584i \(0.477868\pi\)
\(434\) 3.25055e16 0.233493
\(435\) 1.96399e16 0.138982
\(436\) 1.11712e17 0.778821
\(437\) 1.33257e17 0.915295
\(438\) 5.87531e16 0.397602
\(439\) −8.69195e15 −0.0579559 −0.0289780 0.999580i \(-0.509225\pi\)
−0.0289780 + 0.999580i \(0.509225\pi\)
\(440\) −3.13360e17 −2.05874
\(441\) −4.18309e16 −0.270798
\(442\) 5.40006e15 0.0344472
\(443\) −1.09768e16 −0.0690002 −0.0345001 0.999405i \(-0.510984\pi\)
−0.0345001 + 0.999405i \(0.510984\pi\)
\(444\) −1.77143e16 −0.109732
\(445\) −2.81818e17 −1.72039
\(446\) −1.42629e17 −0.858089
\(447\) 1.29537e17 0.768058
\(448\) −5.49749e16 −0.321260
\(449\) 1.62989e17 0.938764 0.469382 0.882995i \(-0.344477\pi\)
0.469382 + 0.882995i \(0.344477\pi\)
\(450\) −2.59988e16 −0.147595
\(451\) −5.09073e17 −2.84861
\(452\) −5.45900e16 −0.301102
\(453\) 1.39133e17 0.756472
\(454\) −1.63068e17 −0.873987
\(455\) −1.05024e16 −0.0554898
\(456\) 1.06670e17 0.555611
\(457\) −1.14683e17 −0.588904 −0.294452 0.955666i \(-0.595137\pi\)
−0.294452 + 0.955666i \(0.595137\pi\)
\(458\) −6.32648e16 −0.320285
\(459\) 2.03779e16 0.101713
\(460\) 1.46148e17 0.719230
\(461\) 4.02933e17 1.95514 0.977568 0.210620i \(-0.0675482\pi\)
0.977568 + 0.210620i \(0.0675482\pi\)
\(462\) 5.30918e16 0.254012
\(463\) −1.40505e17 −0.662851 −0.331425 0.943481i \(-0.607530\pi\)
−0.331425 + 0.943481i \(0.607530\pi\)
\(464\) 4.46039e15 0.0207494
\(465\) −1.33362e17 −0.611770
\(466\) 1.28341e17 0.580572
\(467\) −1.70827e17 −0.762075 −0.381038 0.924560i \(-0.624433\pi\)
−0.381038 + 0.924560i \(0.624433\pi\)
\(468\) 4.25524e15 0.0187209
\(469\) −1.89782e16 −0.0823437
\(470\) −1.96707e17 −0.841751
\(471\) −8.96535e15 −0.0378383
\(472\) −3.22483e16 −0.134241
\(473\) 3.36497e17 1.38161
\(474\) −5.80064e16 −0.234918
\(475\) 1.57211e17 0.628023
\(476\) 3.29396e16 0.129800
\(477\) −3.50412e16 −0.136210
\(478\) 2.38518e17 0.914616
\(479\) −3.06124e17 −1.15802 −0.579011 0.815320i \(-0.696561\pi\)
−0.579011 + 0.815320i \(0.696561\pi\)
\(480\) 1.91647e17 0.715209
\(481\) −9.01783e15 −0.0332016
\(482\) −2.61176e17 −0.948697
\(483\) −6.84317e16 −0.245246
\(484\) −2.21761e17 −0.784133
\(485\) −3.91768e17 −1.36681
\(486\) −1.22623e16 −0.0422119
\(487\) 1.69965e17 0.577325 0.288662 0.957431i \(-0.406789\pi\)
0.288662 + 0.957431i \(0.406789\pi\)
\(488\) 3.95323e17 1.32502
\(489\) −3.10336e17 −1.02642
\(490\) −2.11844e17 −0.691419
\(491\) 2.78093e17 0.895696 0.447848 0.894110i \(-0.352191\pi\)
0.447848 + 0.894110i \(0.352191\pi\)
\(492\) 1.90056e17 0.604100
\(493\) −3.13580e16 −0.0983656
\(494\) 1.96490e16 0.0608296
\(495\) −2.17823e17 −0.665533
\(496\) −3.02877e16 −0.0913346
\(497\) −1.05039e17 −0.312632
\(498\) 4.32973e16 0.127195
\(499\) 3.02691e17 0.877699 0.438849 0.898561i \(-0.355386\pi\)
0.438849 + 0.898561i \(0.355386\pi\)
\(500\) −8.38118e16 −0.239883
\(501\) 1.22040e17 0.344792
\(502\) 2.66092e17 0.742092
\(503\) 1.29667e17 0.356975 0.178488 0.983942i \(-0.442880\pi\)
0.178488 + 0.983942i \(0.442880\pi\)
\(504\) −5.47784e16 −0.148871
\(505\) 3.51500e17 0.943044
\(506\) −3.76107e17 −0.996169
\(507\) −2.18630e17 −0.571686
\(508\) −1.68788e17 −0.435740
\(509\) −2.39374e17 −0.610114 −0.305057 0.952334i \(-0.598675\pi\)
−0.305057 + 0.952334i \(0.598675\pi\)
\(510\) 1.03200e17 0.259701
\(511\) 1.82444e17 0.453308
\(512\) 9.03830e16 0.221734
\(513\) 7.41484e16 0.179614
\(514\) −5.13430e17 −1.22806
\(515\) 3.58810e17 0.847457
\(516\) −1.25627e17 −0.292995
\(517\) −6.62908e17 −1.52674
\(518\) 4.20056e16 0.0955352
\(519\) −5.77665e16 −0.129744
\(520\) 5.95557e16 0.132100
\(521\) 3.97041e17 0.869742 0.434871 0.900493i \(-0.356794\pi\)
0.434871 + 0.900493i \(0.356794\pi\)
\(522\) 1.88694e16 0.0408226
\(523\) −6.11723e16 −0.130706 −0.0653528 0.997862i \(-0.520817\pi\)
−0.0653528 + 0.997862i \(0.520817\pi\)
\(524\) 1.33565e17 0.281865
\(525\) −8.07330e16 −0.168273
\(526\) 2.97521e17 0.612505
\(527\) 2.12932e17 0.432985
\(528\) −4.94695e16 −0.0993612
\(529\) −1.92597e16 −0.0382109
\(530\) −1.77459e17 −0.347780
\(531\) −2.24165e16 −0.0433963
\(532\) 1.19856e17 0.229211
\(533\) 9.67521e16 0.182782
\(534\) −2.70762e17 −0.505324
\(535\) −5.20182e17 −0.959082
\(536\) 1.07619e17 0.196028
\(537\) 3.47819e17 0.625923
\(538\) −2.15646e17 −0.383404
\(539\) −7.13920e17 −1.25407
\(540\) 8.13215e16 0.141139
\(541\) −2.03828e17 −0.349527 −0.174764 0.984610i \(-0.555916\pi\)
−0.174764 + 0.984610i \(0.555916\pi\)
\(542\) −5.15841e17 −0.874018
\(543\) −6.38637e15 −0.0106919
\(544\) −3.05992e17 −0.506195
\(545\) 1.08682e18 1.77657
\(546\) −1.00904e16 −0.0162988
\(547\) −1.15064e17 −0.183663 −0.0918317 0.995775i \(-0.529272\pi\)
−0.0918317 + 0.995775i \(0.529272\pi\)
\(548\) 4.08788e17 0.644799
\(549\) 2.74797e17 0.428343
\(550\) −4.43716e17 −0.683514
\(551\) −1.14101e17 −0.173702
\(552\) 3.88055e17 0.583834
\(553\) −1.80125e17 −0.267831
\(554\) 8.88964e16 0.130638
\(555\) −1.72339e17 −0.250310
\(556\) 6.93902e17 0.996120
\(557\) −7.47413e17 −1.06048 −0.530239 0.847848i \(-0.677898\pi\)
−0.530239 + 0.847848i \(0.677898\pi\)
\(558\) −1.28130e17 −0.179692
\(559\) −6.39531e16 −0.0886512
\(560\) −4.55829e16 −0.0624569
\(561\) 3.47786e17 0.471036
\(562\) 2.45007e17 0.328013
\(563\) −2.82012e16 −0.0373218 −0.0186609 0.999826i \(-0.505940\pi\)
−0.0186609 + 0.999826i \(0.505940\pi\)
\(564\) 2.47488e17 0.323773
\(565\) −5.31095e17 −0.686842
\(566\) −7.91511e17 −1.01193
\(567\) −3.80776e16 −0.0481260
\(568\) 5.95644e17 0.744256
\(569\) −5.71155e17 −0.705544 −0.352772 0.935709i \(-0.614761\pi\)
−0.352772 + 0.935709i \(0.614761\pi\)
\(570\) 3.75509e17 0.458600
\(571\) −2.15094e17 −0.259712 −0.129856 0.991533i \(-0.541452\pi\)
−0.129856 + 0.991533i \(0.541452\pi\)
\(572\) 7.26234e16 0.0866967
\(573\) 3.54211e17 0.418078
\(574\) −4.50677e17 −0.525942
\(575\) 5.71920e17 0.659925
\(576\) 2.16701e17 0.247237
\(577\) −2.62228e17 −0.295826 −0.147913 0.989000i \(-0.547256\pi\)
−0.147913 + 0.989000i \(0.547256\pi\)
\(578\) 4.25113e17 0.474213
\(579\) −9.57177e17 −1.05580
\(580\) −1.25139e17 −0.136493
\(581\) 1.34449e17 0.145015
\(582\) −3.76399e17 −0.401466
\(583\) −5.98041e17 −0.630791
\(584\) −1.03458e18 −1.07915
\(585\) 4.13984e16 0.0427042
\(586\) 5.31079e17 0.541782
\(587\) 1.05272e18 1.06210 0.531052 0.847339i \(-0.321797\pi\)
0.531052 + 0.847339i \(0.321797\pi\)
\(588\) 2.66533e17 0.265949
\(589\) 7.74789e17 0.764599
\(590\) −1.13524e17 −0.110802
\(591\) 7.88256e17 0.760937
\(592\) −3.91396e16 −0.0373702
\(593\) 4.55448e17 0.430114 0.215057 0.976602i \(-0.431006\pi\)
0.215057 + 0.976602i \(0.431006\pi\)
\(594\) −2.09278e17 −0.195484
\(595\) 3.20463e17 0.296086
\(596\) −8.25367e17 −0.754304
\(597\) 1.29497e17 0.117065
\(598\) 7.14811e16 0.0639196
\(599\) 8.24583e17 0.729391 0.364695 0.931127i \(-0.381173\pi\)
0.364695 + 0.931127i \(0.381173\pi\)
\(600\) 4.57812e17 0.400594
\(601\) −1.28978e17 −0.111643 −0.0558215 0.998441i \(-0.517778\pi\)
−0.0558215 + 0.998441i \(0.517778\pi\)
\(602\) 2.97897e17 0.255087
\(603\) 7.48083e16 0.0633705
\(604\) −8.86514e17 −0.742926
\(605\) −2.15746e18 −1.78868
\(606\) 3.37711e17 0.276996
\(607\) −3.83628e17 −0.311303 −0.155652 0.987812i \(-0.549748\pi\)
−0.155652 + 0.987812i \(0.549748\pi\)
\(608\) −1.11340e18 −0.893879
\(609\) 5.85945e16 0.0465419
\(610\) 1.39165e18 1.09367
\(611\) 1.25989e17 0.0979637
\(612\) −1.29842e17 −0.0998919
\(613\) 1.02087e16 0.00777104 0.00388552 0.999992i \(-0.498763\pi\)
0.00388552 + 0.999992i \(0.498763\pi\)
\(614\) −5.72890e17 −0.431496
\(615\) 1.84902e18 1.37801
\(616\) −9.34893e17 −0.689425
\(617\) 1.89669e18 1.38402 0.692010 0.721888i \(-0.256726\pi\)
0.692010 + 0.721888i \(0.256726\pi\)
\(618\) 3.44734e17 0.248920
\(619\) 3.10704e17 0.222003 0.111001 0.993820i \(-0.464594\pi\)
0.111001 + 0.993820i \(0.464594\pi\)
\(620\) 8.49741e17 0.600815
\(621\) 2.69745e17 0.188737
\(622\) 1.13687e18 0.787175
\(623\) −8.40788e17 −0.576122
\(624\) 9.40194e15 0.00637555
\(625\) −1.81810e18 −1.22010
\(626\) 9.16341e17 0.608589
\(627\) 1.26548e18 0.831793
\(628\) 5.71244e16 0.0371607
\(629\) 2.75164e17 0.177159
\(630\) −1.92836e17 −0.122878
\(631\) 5.18274e17 0.326865 0.163433 0.986555i \(-0.447743\pi\)
0.163433 + 0.986555i \(0.447743\pi\)
\(632\) 1.02143e18 0.637601
\(633\) −2.98607e17 −0.184491
\(634\) −9.92576e17 −0.606993
\(635\) −1.64210e18 −0.993966
\(636\) 2.23271e17 0.133771
\(637\) 1.35684e17 0.0804680
\(638\) 3.22041e17 0.189050
\(639\) 4.14044e17 0.240597
\(640\) −1.05616e18 −0.607517
\(641\) 1.84752e18 1.05199 0.525995 0.850488i \(-0.323693\pi\)
0.525995 + 0.850488i \(0.323693\pi\)
\(642\) −4.99776e17 −0.281707
\(643\) −1.43063e18 −0.798279 −0.399140 0.916890i \(-0.630691\pi\)
−0.399140 + 0.916890i \(0.630691\pi\)
\(644\) 4.36025e17 0.240854
\(645\) −1.22220e18 −0.668350
\(646\) −5.99557e17 −0.324578
\(647\) 3.09734e17 0.166001 0.0830004 0.996550i \(-0.473550\pi\)
0.0830004 + 0.996550i \(0.473550\pi\)
\(648\) 2.15926e17 0.114569
\(649\) −3.82578e17 −0.200969
\(650\) 8.43306e16 0.0438579
\(651\) −3.97879e17 −0.204868
\(652\) 1.97736e18 1.00804
\(653\) −1.28762e18 −0.649907 −0.324953 0.945730i \(-0.605349\pi\)
−0.324953 + 0.945730i \(0.605349\pi\)
\(654\) 1.04419e18 0.521823
\(655\) 1.29943e18 0.642961
\(656\) 4.19928e17 0.205731
\(657\) −7.19159e17 −0.348859
\(658\) −5.86865e17 −0.281883
\(659\) 3.11431e18 1.48118 0.740589 0.671959i \(-0.234547\pi\)
0.740589 + 0.671959i \(0.234547\pi\)
\(660\) 1.38790e18 0.653615
\(661\) 1.19424e18 0.556908 0.278454 0.960450i \(-0.410178\pi\)
0.278454 + 0.960450i \(0.410178\pi\)
\(662\) 2.45243e18 1.13245
\(663\) −6.60987e16 −0.0302242
\(664\) −7.62422e17 −0.345225
\(665\) 1.16606e18 0.522852
\(666\) −1.65578e17 −0.0735225
\(667\) −4.15089e17 −0.182525
\(668\) −7.77600e17 −0.338617
\(669\) 1.74584e18 0.752894
\(670\) 3.78851e17 0.161802
\(671\) 4.68991e18 1.98366
\(672\) 5.71767e17 0.239507
\(673\) 1.38397e18 0.574156 0.287078 0.957907i \(-0.407316\pi\)
0.287078 + 0.957907i \(0.407316\pi\)
\(674\) −1.64330e18 −0.675192
\(675\) 3.18234e17 0.129501
\(676\) 1.39304e18 0.561449
\(677\) 1.01189e18 0.403929 0.201965 0.979393i \(-0.435267\pi\)
0.201965 + 0.979393i \(0.435267\pi\)
\(678\) −5.10260e17 −0.201743
\(679\) −1.16882e18 −0.457713
\(680\) −1.81725e18 −0.704865
\(681\) 1.99601e18 0.766843
\(682\) −2.18678e18 −0.832159
\(683\) 9.89456e17 0.372960 0.186480 0.982459i \(-0.440292\pi\)
0.186480 + 0.982459i \(0.440292\pi\)
\(684\) −4.72450e17 −0.176397
\(685\) 3.97701e18 1.47085
\(686\) −1.41000e18 −0.516551
\(687\) 7.74385e17 0.281020
\(688\) −2.77572e17 −0.0997818
\(689\) 1.13661e17 0.0404749
\(690\) 1.36607e18 0.481896
\(691\) −5.17046e17 −0.180685 −0.0903425 0.995911i \(-0.528796\pi\)
−0.0903425 + 0.995911i \(0.528796\pi\)
\(692\) 3.68070e17 0.127421
\(693\) −6.49863e17 −0.222872
\(694\) −3.78813e18 −1.28703
\(695\) 6.75083e18 2.27225
\(696\) −3.32271e17 −0.110798
\(697\) −2.95223e18 −0.975298
\(698\) −8.56426e17 −0.280304
\(699\) −1.57094e18 −0.509398
\(700\) 5.14405e17 0.165260
\(701\) 1.68136e18 0.535174 0.267587 0.963534i \(-0.413774\pi\)
0.267587 + 0.963534i \(0.413774\pi\)
\(702\) 3.97744e16 0.0125433
\(703\) 1.00123e18 0.312841
\(704\) 3.69839e18 1.14496
\(705\) 2.40776e18 0.738558
\(706\) −1.15366e18 −0.350627
\(707\) 1.04868e18 0.315804
\(708\) 1.42831e17 0.0426192
\(709\) −6.90252e17 −0.204083 −0.102042 0.994780i \(-0.532537\pi\)
−0.102042 + 0.994780i \(0.532537\pi\)
\(710\) 2.09684e18 0.614308
\(711\) 7.10019e17 0.206119
\(712\) 4.76785e18 1.37152
\(713\) 2.81861e18 0.803439
\(714\) 3.07891e17 0.0869680
\(715\) 7.06538e17 0.197764
\(716\) −2.21620e18 −0.614714
\(717\) −2.91954e18 −0.802491
\(718\) −1.48876e18 −0.405524
\(719\) 5.40242e18 1.45831 0.729156 0.684347i \(-0.239913\pi\)
0.729156 + 0.684347i \(0.239913\pi\)
\(720\) 1.79679e17 0.0480659
\(721\) 1.07049e18 0.283794
\(722\) 3.22967e17 0.0848529
\(723\) 3.19689e18 0.832394
\(724\) 4.06919e16 0.0105004
\(725\) −4.89705e17 −0.125238
\(726\) −2.07283e18 −0.525382
\(727\) −1.24875e18 −0.313690 −0.156845 0.987623i \(-0.550132\pi\)
−0.156845 + 0.987623i \(0.550132\pi\)
\(728\) 1.77681e17 0.0442372
\(729\) 1.50095e17 0.0370370
\(730\) −3.64203e18 −0.890729
\(731\) 1.95142e18 0.473030
\(732\) −1.75092e18 −0.420673
\(733\) 4.46147e18 1.06243 0.531217 0.847236i \(-0.321735\pi\)
0.531217 + 0.847236i \(0.321735\pi\)
\(734\) 2.89304e18 0.682857
\(735\) 2.59305e18 0.606656
\(736\) −4.05045e18 −0.939286
\(737\) 1.27674e18 0.293470
\(738\) 1.77648e18 0.404757
\(739\) −5.61390e17 −0.126787 −0.0633936 0.997989i \(-0.520192\pi\)
−0.0633936 + 0.997989i \(0.520192\pi\)
\(740\) 1.09809e18 0.245828
\(741\) −2.40511e17 −0.0533723
\(742\) −5.29439e17 −0.116464
\(743\) −8.20357e18 −1.78886 −0.894429 0.447210i \(-0.852418\pi\)
−0.894429 + 0.447210i \(0.852418\pi\)
\(744\) 2.25625e18 0.487711
\(745\) −8.02982e18 −1.72064
\(746\) 7.82211e16 0.0166158
\(747\) −5.29974e17 −0.111602
\(748\) −2.21599e18 −0.462601
\(749\) −1.55194e18 −0.321175
\(750\) −7.83401e17 −0.160726
\(751\) −8.99630e18 −1.82980 −0.914901 0.403677i \(-0.867732\pi\)
−0.914901 + 0.403677i \(0.867732\pi\)
\(752\) 5.46825e17 0.110264
\(753\) −3.25706e18 −0.651117
\(754\) −6.12056e16 −0.0121305
\(755\) −8.62471e18 −1.69469
\(756\) 2.42618e17 0.0472641
\(757\) 2.59715e18 0.501619 0.250809 0.968037i \(-0.419303\pi\)
0.250809 + 0.968037i \(0.419303\pi\)
\(758\) −6.27237e17 −0.120111
\(759\) 4.60369e18 0.874046
\(760\) −6.61234e18 −1.24471
\(761\) −5.82680e18 −1.08750 −0.543751 0.839247i \(-0.682996\pi\)
−0.543751 + 0.839247i \(0.682996\pi\)
\(762\) −1.57769e18 −0.291953
\(763\) 3.24248e18 0.594932
\(764\) −2.25692e18 −0.410591
\(765\) −1.26320e18 −0.227863
\(766\) −3.90203e18 −0.697917
\(767\) 7.27109e16 0.0128952
\(768\) −3.44986e18 −0.606671
\(769\) −2.94972e18 −0.514352 −0.257176 0.966365i \(-0.582792\pi\)
−0.257176 + 0.966365i \(0.582792\pi\)
\(770\) −3.29110e18 −0.569050
\(771\) 6.28457e18 1.07751
\(772\) 6.09883e18 1.03689
\(773\) 5.71839e18 0.964066 0.482033 0.876153i \(-0.339899\pi\)
0.482033 + 0.876153i \(0.339899\pi\)
\(774\) −1.17425e18 −0.196312
\(775\) 3.32528e18 0.551274
\(776\) 6.62801e18 1.08964
\(777\) −5.14163e17 −0.0838233
\(778\) −7.17557e18 −1.16008
\(779\) −1.07422e19 −1.72226
\(780\) −2.63777e17 −0.0419394
\(781\) 7.06641e18 1.11421
\(782\) −2.18113e18 −0.341066
\(783\) −2.30969e17 −0.0358180
\(784\) 5.88904e17 0.0905712
\(785\) 5.55751e17 0.0847672
\(786\) 1.24846e18 0.188854
\(787\) 6.57880e18 0.986985 0.493493 0.869750i \(-0.335720\pi\)
0.493493 + 0.869750i \(0.335720\pi\)
\(788\) −5.02252e18 −0.747311
\(789\) −3.64176e18 −0.537416
\(790\) 3.59575e18 0.526275
\(791\) −1.58449e18 −0.230008
\(792\) 3.68517e18 0.530572
\(793\) −8.91342e17 −0.127283
\(794\) −6.90832e18 −0.978452
\(795\) 2.17216e18 0.305145
\(796\) −8.25112e17 −0.114968
\(797\) −1.87746e18 −0.259473 −0.129736 0.991549i \(-0.541413\pi\)
−0.129736 + 0.991549i \(0.541413\pi\)
\(798\) 1.12031e18 0.153575
\(799\) −3.84435e18 −0.522720
\(800\) −4.77856e18 −0.644484
\(801\) 3.31423e18 0.443375
\(802\) 7.42140e18 0.984810
\(803\) −1.22738e19 −1.61557
\(804\) −4.76655e17 −0.0622357
\(805\) 4.24200e18 0.549411
\(806\) 4.15609e17 0.0533958
\(807\) 2.63959e18 0.336401
\(808\) −5.94676e18 −0.751807
\(809\) −3.09582e17 −0.0388249 −0.0194124 0.999812i \(-0.506180\pi\)
−0.0194124 + 0.999812i \(0.506180\pi\)
\(810\) 7.60123e17 0.0945652
\(811\) −6.98595e18 −0.862164 −0.431082 0.902313i \(-0.641868\pi\)
−0.431082 + 0.902313i \(0.641868\pi\)
\(812\) −3.73346e17 −0.0457085
\(813\) 6.31408e18 0.766870
\(814\) −2.82589e18 −0.340484
\(815\) 1.92374e19 2.29944
\(816\) −2.86885e17 −0.0340190
\(817\) 7.10057e18 0.835315
\(818\) −1.42200e18 −0.165960
\(819\) 1.23510e17 0.0143007
\(820\) −1.17814e19 −1.35333
\(821\) 9.33305e18 1.06364 0.531818 0.846859i \(-0.321509\pi\)
0.531818 + 0.846859i \(0.321509\pi\)
\(822\) 3.82100e18 0.432026
\(823\) 5.87090e18 0.658576 0.329288 0.944230i \(-0.393191\pi\)
0.329288 + 0.944230i \(0.393191\pi\)
\(824\) −6.07043e18 −0.675604
\(825\) 5.43124e18 0.599720
\(826\) −3.38692e17 −0.0371051
\(827\) −1.37779e19 −1.49761 −0.748803 0.662793i \(-0.769371\pi\)
−0.748803 + 0.662793i \(0.769371\pi\)
\(828\) −1.71873e18 −0.185358
\(829\) −2.95388e18 −0.316074 −0.158037 0.987433i \(-0.550516\pi\)
−0.158037 + 0.987433i \(0.550516\pi\)
\(830\) −2.68395e18 −0.284948
\(831\) −1.08812e18 −0.114623
\(832\) −7.02899e17 −0.0734668
\(833\) −4.14018e18 −0.429366
\(834\) 6.48600e18 0.667417
\(835\) −7.56511e18 −0.772420
\(836\) −8.06322e18 −0.816898
\(837\) 1.56836e18 0.157663
\(838\) −1.99630e18 −0.199132
\(839\) −9.73635e18 −0.963704 −0.481852 0.876253i \(-0.660036\pi\)
−0.481852 + 0.876253i \(0.660036\pi\)
\(840\) 3.39565e18 0.333509
\(841\) −9.90521e18 −0.965361
\(842\) 1.72027e18 0.166368
\(843\) −2.99897e18 −0.287801
\(844\) 1.90263e18 0.181187
\(845\) 1.35526e19 1.28072
\(846\) 2.31331e18 0.216933
\(847\) −6.43668e18 −0.598990
\(848\) 4.93317e17 0.0455568
\(849\) 9.68838e18 0.887874
\(850\) −2.57321e18 −0.234020
\(851\) 3.64238e18 0.328733
\(852\) −2.63816e18 −0.236289
\(853\) 7.50937e18 0.667475 0.333737 0.942666i \(-0.391690\pi\)
0.333737 + 0.942666i \(0.391690\pi\)
\(854\) 4.15192e18 0.366246
\(855\) −4.59637e18 −0.402379
\(856\) 8.80055e18 0.764593
\(857\) 1.31637e19 1.13502 0.567511 0.823366i \(-0.307907\pi\)
0.567511 + 0.823366i \(0.307907\pi\)
\(858\) 6.78821e17 0.0580882
\(859\) −1.51845e19 −1.28957 −0.644783 0.764365i \(-0.723052\pi\)
−0.644783 + 0.764365i \(0.723052\pi\)
\(860\) 7.78747e18 0.656382
\(861\) 5.51645e18 0.461465
\(862\) 7.22595e18 0.599926
\(863\) −1.82119e19 −1.50067 −0.750333 0.661060i \(-0.770107\pi\)
−0.750333 + 0.661060i \(0.770107\pi\)
\(864\) −2.25380e18 −0.184321
\(865\) 3.58088e18 0.290660
\(866\) −1.13487e18 −0.0914281
\(867\) −5.20354e18 −0.416078
\(868\) 2.53516e18 0.201199
\(869\) 1.21178e19 0.954539
\(870\) −1.16969e18 −0.0914527
\(871\) −2.42651e17 −0.0188306
\(872\) −1.83871e19 −1.41630
\(873\) 4.60726e18 0.352249
\(874\) −7.93640e18 −0.602281
\(875\) −2.43267e18 −0.183244
\(876\) 4.58226e18 0.342612
\(877\) −1.82543e19 −1.35478 −0.677388 0.735626i \(-0.736888\pi\)
−0.677388 + 0.735626i \(0.736888\pi\)
\(878\) 5.17667e17 0.0381361
\(879\) −6.50059e18 −0.475363
\(880\) 3.06655e18 0.222594
\(881\) −1.73508e19 −1.25019 −0.625096 0.780548i \(-0.714940\pi\)
−0.625096 + 0.780548i \(0.714940\pi\)
\(882\) 2.49132e18 0.178190
\(883\) −2.73186e19 −1.93960 −0.969802 0.243892i \(-0.921576\pi\)
−0.969802 + 0.243892i \(0.921576\pi\)
\(884\) 4.21160e17 0.0296830
\(885\) 1.38957e18 0.0972185
\(886\) 6.53744e17 0.0454034
\(887\) −2.81597e17 −0.0194144 −0.00970721 0.999953i \(-0.503090\pi\)
−0.00970721 + 0.999953i \(0.503090\pi\)
\(888\) 2.91566e18 0.199551
\(889\) −4.89913e18 −0.332857
\(890\) 1.67842e19 1.13205
\(891\) 2.56164e18 0.171519
\(892\) −1.11239e19 −0.739411
\(893\) −1.39883e19 −0.923061
\(894\) −7.71482e18 −0.505396
\(895\) −2.15609e19 −1.40222
\(896\) −3.15099e18 −0.203444
\(897\) −8.74955e17 −0.0560835
\(898\) −9.70713e18 −0.617724
\(899\) −2.41343e18 −0.152474
\(900\) −2.02769e18 −0.127182
\(901\) −3.46818e18 −0.215968
\(902\) 3.03189e19 1.87444
\(903\) −3.64637e18 −0.223816
\(904\) 8.98517e18 0.547560
\(905\) 3.95883e17 0.0239525
\(906\) −8.28637e18 −0.497773
\(907\) 8.76691e17 0.0522877 0.0261438 0.999658i \(-0.491677\pi\)
0.0261438 + 0.999658i \(0.491677\pi\)
\(908\) −1.27179e19 −0.753110
\(909\) −4.13371e18 −0.243038
\(910\) 6.25490e17 0.0365133
\(911\) 7.44433e18 0.431475 0.215738 0.976451i \(-0.430784\pi\)
0.215738 + 0.976451i \(0.430784\pi\)
\(912\) −1.04388e18 −0.0600735
\(913\) −9.04497e18 −0.516829
\(914\) 6.83019e18 0.387510
\(915\) −1.70343e19 −0.959596
\(916\) −4.93413e18 −0.275988
\(917\) 3.87678e18 0.215313
\(918\) −1.21365e18 −0.0669293
\(919\) −2.98040e18 −0.163202 −0.0816008 0.996665i \(-0.526003\pi\)
−0.0816008 + 0.996665i \(0.526003\pi\)
\(920\) −2.40551e19 −1.30793
\(921\) 7.01238e18 0.378598
\(922\) −2.39975e19 −1.28652
\(923\) −1.34301e18 −0.0714937
\(924\) 4.14072e18 0.218881
\(925\) 4.29713e18 0.225558
\(926\) 8.36807e18 0.436168
\(927\) −4.21968e18 −0.218404
\(928\) 3.46819e18 0.178255
\(929\) 3.31642e19 1.69265 0.846324 0.532668i \(-0.178810\pi\)
0.846324 + 0.532668i \(0.178810\pi\)
\(930\) 7.94265e18 0.402556
\(931\) −1.50647e19 −0.758208
\(932\) 1.00095e19 0.500276
\(933\) −1.39156e19 −0.690673
\(934\) 1.01740e19 0.501460
\(935\) −2.15589e19 −1.05524
\(936\) −7.00387e17 −0.0340443
\(937\) 5.45377e18 0.263263 0.131631 0.991299i \(-0.457978\pi\)
0.131631 + 0.991299i \(0.457978\pi\)
\(938\) 1.13028e18 0.0541837
\(939\) −1.12163e19 −0.533980
\(940\) −1.53415e19 −0.725332
\(941\) 1.56407e19 0.734383 0.367192 0.930145i \(-0.380319\pi\)
0.367192 + 0.930145i \(0.380319\pi\)
\(942\) 5.33950e17 0.0248983
\(943\) −3.90790e19 −1.80975
\(944\) 3.15584e17 0.0145143
\(945\) 2.36038e18 0.107814
\(946\) −2.00408e19 −0.909122
\(947\) 2.79136e19 1.25760 0.628798 0.777569i \(-0.283547\pi\)
0.628798 + 0.777569i \(0.283547\pi\)
\(948\) −4.52402e18 −0.202428
\(949\) 2.33269e18 0.103664
\(950\) −9.36304e18 −0.413251
\(951\) 1.21495e19 0.532580
\(952\) −5.42166e18 −0.236044
\(953\) 4.06069e19 1.75588 0.877942 0.478767i \(-0.158916\pi\)
0.877942 + 0.478767i \(0.158916\pi\)
\(954\) 2.08695e18 0.0896288
\(955\) −2.19571e19 −0.936598
\(956\) 1.86024e19 0.788120
\(957\) −3.94190e18 −0.165874
\(958\) 1.82318e19 0.762000
\(959\) 1.18652e19 0.492554
\(960\) −1.34330e19 −0.553873
\(961\) −8.02947e18 −0.328840
\(962\) 5.37075e17 0.0218473
\(963\) 6.11744e18 0.247172
\(964\) −2.03696e19 −0.817488
\(965\) 5.93343e19 2.36525
\(966\) 4.07559e18 0.161376
\(967\) 5.39868e18 0.212332 0.106166 0.994348i \(-0.466143\pi\)
0.106166 + 0.994348i \(0.466143\pi\)
\(968\) 3.65004e19 1.42596
\(969\) 7.33880e18 0.284787
\(970\) 2.33325e19 0.899385
\(971\) 1.69667e19 0.649639 0.324819 0.945776i \(-0.394696\pi\)
0.324819 + 0.945776i \(0.394696\pi\)
\(972\) −9.56356e17 −0.0363738
\(973\) 2.01407e19 0.760925
\(974\) −1.01226e19 −0.379891
\(975\) −1.03224e18 −0.0384813
\(976\) −3.86865e18 −0.143264
\(977\) −2.06032e19 −0.757914 −0.378957 0.925414i \(-0.623717\pi\)
−0.378957 + 0.925414i \(0.623717\pi\)
\(978\) 1.84827e19 0.675403
\(979\) 5.65633e19 2.05328
\(980\) −1.65221e19 −0.595792
\(981\) −1.27812e19 −0.457851
\(982\) −1.65624e19 −0.589385
\(983\) −2.09589e19 −0.740918 −0.370459 0.928849i \(-0.620800\pi\)
−0.370459 + 0.928849i \(0.620800\pi\)
\(984\) −3.12821e19 −1.09857
\(985\) −4.88631e19 −1.70469
\(986\) 1.86759e18 0.0647264
\(987\) 7.18344e18 0.247327
\(988\) 1.53246e18 0.0524166
\(989\) 2.58312e19 0.877746
\(990\) 1.29729e19 0.437933
\(991\) −1.89520e19 −0.635588 −0.317794 0.948160i \(-0.602942\pi\)
−0.317794 + 0.948160i \(0.602942\pi\)
\(992\) −2.35503e19 −0.784641
\(993\) −3.00186e19 −0.993620
\(994\) 6.25581e18 0.205718
\(995\) −8.02734e18 −0.262254
\(996\) 3.37683e18 0.109603
\(997\) 4.77772e19 1.54064 0.770322 0.637655i \(-0.220095\pi\)
0.770322 + 0.637655i \(0.220095\pi\)
\(998\) −1.80274e19 −0.577542
\(999\) 2.02674e18 0.0645092
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 177.14.a.c.1.11 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.14.a.c.1.11 31 1.1 even 1 trivial