Properties

Label 177.12.a.b.1.16
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $1$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(1\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+10.6976 q^{2} +243.000 q^{3} -1933.56 q^{4} +12608.0 q^{5} +2599.53 q^{6} -75685.5 q^{7} -42593.3 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+10.6976 q^{2} +243.000 q^{3} -1933.56 q^{4} +12608.0 q^{5} +2599.53 q^{6} -75685.5 q^{7} -42593.3 q^{8} +59049.0 q^{9} +134876. q^{10} +77504.2 q^{11} -469855. q^{12} +1.47974e6 q^{13} -809655. q^{14} +3.06375e6 q^{15} +3.50428e6 q^{16} -9.88109e6 q^{17} +631685. q^{18} -5.07206e6 q^{19} -2.43784e7 q^{20} -1.83916e7 q^{21} +829112. q^{22} +4.46983e7 q^{23} -1.03502e7 q^{24} +1.10134e8 q^{25} +1.58297e7 q^{26} +1.43489e7 q^{27} +1.46342e8 q^{28} -8.95326e7 q^{29} +3.27749e7 q^{30} +4.40237e7 q^{31} +1.24719e8 q^{32} +1.88335e7 q^{33} -1.05704e8 q^{34} -9.54244e8 q^{35} -1.14175e8 q^{36} -3.52130e7 q^{37} -5.42590e7 q^{38} +3.59577e8 q^{39} -5.37017e8 q^{40} +5.31218e8 q^{41} -1.96746e8 q^{42} -1.39647e9 q^{43} -1.49859e8 q^{44} +7.44491e8 q^{45} +4.78166e8 q^{46} -2.26305e9 q^{47} +8.51541e8 q^{48} +3.75096e9 q^{49} +1.17817e9 q^{50} -2.40111e9 q^{51} -2.86117e9 q^{52} -5.83333e9 q^{53} +1.53499e8 q^{54} +9.77174e8 q^{55} +3.22369e9 q^{56} -1.23251e9 q^{57} -9.57786e8 q^{58} -7.14924e8 q^{59} -5.92394e9 q^{60} +1.97255e9 q^{61} +4.70950e8 q^{62} -4.46915e9 q^{63} -5.84258e9 q^{64} +1.86566e10 q^{65} +2.01474e8 q^{66} -1.49525e10 q^{67} +1.91057e10 q^{68} +1.08617e10 q^{69} -1.02081e10 q^{70} +1.84247e10 q^{71} -2.51509e9 q^{72} +1.03519e10 q^{73} -3.76695e8 q^{74} +2.67626e10 q^{75} +9.80714e9 q^{76} -5.86594e9 q^{77} +3.84663e9 q^{78} -4.76733e9 q^{79} +4.41821e10 q^{80} +3.48678e9 q^{81} +5.68277e9 q^{82} -6.60401e10 q^{83} +3.55612e10 q^{84} -1.24581e11 q^{85} -1.49389e10 q^{86} -2.17564e10 q^{87} -3.30116e9 q^{88} +6.92452e10 q^{89} +7.96429e9 q^{90} -1.11995e11 q^{91} -8.64268e10 q^{92} +1.06978e10 q^{93} -2.42093e10 q^{94} -6.39486e10 q^{95} +3.03066e10 q^{96} +1.01541e11 q^{97} +4.01264e10 q^{98} +4.57655e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 128q^{2} + 6561q^{3} + 26142q^{4} - 17188q^{5} - 31104q^{6} - 126579q^{7} - 355797q^{8} + 1594323q^{9} - 383719q^{10} - 1816556q^{11} + 6352506q^{12} - 3951804q^{13} - 6207867q^{14} - 4176684q^{15} + 28295194q^{16} - 17723275q^{17} - 7558272q^{18} - 19573013q^{19} - 48468099q^{20} - 30758697q^{21} - 1729910q^{22} - 88593797q^{23} - 86458671q^{24} + 345714963q^{25} - 6676346q^{26} + 387420489q^{27} + 126954286q^{28} - 276632427q^{29} - 93243717q^{30} - 357680917q^{31} - 859842334q^{32} - 441423108q^{33} + 232730000q^{34} - 510315139q^{35} + 1543658958q^{36} - 660238257q^{37} - 2067286961q^{38} - 960288372q^{39} - 3388951110q^{40} - 1671147569q^{41} - 1508511681q^{42} - 1883107790q^{43} - 3895687630q^{44} - 1014934212q^{45} - 1720344243q^{46} - 5818572501q^{47} + 6875732142q^{48} - 18858180q^{49} - 21474519647q^{50} - 4306755825q^{51} - 42214560062q^{52} - 11444513368q^{53} - 1836660096q^{54} - 24401486484q^{55} - 50583585764q^{56} - 4756242159q^{57} - 45017395090q^{58} - 19302956073q^{59} - 11777748057q^{60} + 408637955q^{61} - 28543084070q^{62} - 7474363371q^{63} + 33067284293q^{64} - 21656714730q^{65} - 420368130q^{66} - 49803132690q^{67} - 16500749319q^{68} - 21528292671q^{69} - 45808890782q^{70} - 34127492216q^{71} - 21009457053q^{72} - 55734362153q^{73} - 40367816298q^{74} + 84008736009q^{75} - 14840406404q^{76} - 99723443615q^{77} - 1622352078q^{78} - 76484916442q^{79} + 93882788915q^{80} + 94143178827q^{81} + 52951239205q^{82} - 140433865655q^{83} + 30849891498q^{84} + 34329063335q^{85} + 175223869508q^{86} - 67221679761q^{87} + 268823645069q^{88} - 1191878597q^{89} - 22658223231q^{90} + 201632581559q^{91} - 206501888812q^{92} - 86916462831q^{93} + 319770144384q^{94} - 81387074885q^{95} - 208941687162q^{96} - 144896178730q^{97} + 135739195260q^{98} - 107265815244q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.6976 0.236387 0.118193 0.992991i \(-0.462290\pi\)
0.118193 + 0.992991i \(0.462290\pi\)
\(3\) 243.000 0.577350
\(4\) −1933.56 −0.944121
\(5\) 12608.0 1.80431 0.902156 0.431409i \(-0.141984\pi\)
0.902156 + 0.431409i \(0.141984\pi\)
\(6\) 2599.53 0.136478
\(7\) −75685.5 −1.70205 −0.851027 0.525122i \(-0.824020\pi\)
−0.851027 + 0.525122i \(0.824020\pi\)
\(8\) −42593.3 −0.459564
\(9\) 59049.0 0.333333
\(10\) 134876. 0.426515
\(11\) 77504.2 0.145099 0.0725497 0.997365i \(-0.476886\pi\)
0.0725497 + 0.997365i \(0.476886\pi\)
\(12\) −469855. −0.545089
\(13\) 1.47974e6 1.10534 0.552672 0.833399i \(-0.313608\pi\)
0.552672 + 0.833399i \(0.313608\pi\)
\(14\) −809655. −0.402343
\(15\) 3.06375e6 1.04172
\(16\) 3.50428e6 0.835487
\(17\) −9.88109e6 −1.68786 −0.843929 0.536455i \(-0.819763\pi\)
−0.843929 + 0.536455i \(0.819763\pi\)
\(18\) 631685. 0.0787955
\(19\) −5.07206e6 −0.469937 −0.234968 0.972003i \(-0.575499\pi\)
−0.234968 + 0.972003i \(0.575499\pi\)
\(20\) −2.43784e7 −1.70349
\(21\) −1.83916e7 −0.982681
\(22\) 829112. 0.0342995
\(23\) 4.46983e7 1.44806 0.724032 0.689767i \(-0.242287\pi\)
0.724032 + 0.689767i \(0.242287\pi\)
\(24\) −1.03502e7 −0.265329
\(25\) 1.10134e8 2.25554
\(26\) 1.58297e7 0.261288
\(27\) 1.43489e7 0.192450
\(28\) 1.46342e8 1.60695
\(29\) −8.95326e7 −0.810573 −0.405286 0.914190i \(-0.632828\pi\)
−0.405286 + 0.914190i \(0.632828\pi\)
\(30\) 3.27749e7 0.246249
\(31\) 4.40237e7 0.276183 0.138092 0.990419i \(-0.455903\pi\)
0.138092 + 0.990419i \(0.455903\pi\)
\(32\) 1.24719e8 0.657062
\(33\) 1.88335e7 0.0837731
\(34\) −1.05704e8 −0.398987
\(35\) −9.54244e8 −3.07104
\(36\) −1.14175e8 −0.314707
\(37\) −3.52130e7 −0.0834821 −0.0417410 0.999128i \(-0.513290\pi\)
−0.0417410 + 0.999128i \(0.513290\pi\)
\(38\) −5.42590e7 −0.111087
\(39\) 3.59577e8 0.638171
\(40\) −5.37017e8 −0.829197
\(41\) 5.31218e8 0.716079 0.358040 0.933706i \(-0.383445\pi\)
0.358040 + 0.933706i \(0.383445\pi\)
\(42\) −1.96746e8 −0.232293
\(43\) −1.39647e9 −1.44862 −0.724311 0.689473i \(-0.757842\pi\)
−0.724311 + 0.689473i \(0.757842\pi\)
\(44\) −1.49859e8 −0.136991
\(45\) 7.44491e8 0.601438
\(46\) 4.78166e8 0.342303
\(47\) −2.26305e9 −1.43932 −0.719659 0.694328i \(-0.755702\pi\)
−0.719659 + 0.694328i \(0.755702\pi\)
\(48\) 8.51541e8 0.482368
\(49\) 3.75096e9 1.89699
\(50\) 1.17817e9 0.533180
\(51\) −2.40111e9 −0.974485
\(52\) −2.86117e9 −1.04358
\(53\) −5.83333e9 −1.91602 −0.958008 0.286742i \(-0.907428\pi\)
−0.958008 + 0.286742i \(0.907428\pi\)
\(54\) 1.53499e8 0.0454926
\(55\) 9.77174e8 0.261805
\(56\) 3.22369e9 0.782203
\(57\) −1.23251e9 −0.271318
\(58\) −9.57786e8 −0.191608
\(59\) −7.14924e8 −0.130189
\(60\) −5.92394e9 −0.983510
\(61\) 1.97255e9 0.299030 0.149515 0.988759i \(-0.452229\pi\)
0.149515 + 0.988759i \(0.452229\pi\)
\(62\) 4.70950e8 0.0652860
\(63\) −4.46915e9 −0.567351
\(64\) −5.84258e9 −0.680166
\(65\) 1.86566e10 1.99439
\(66\) 2.01474e8 0.0198028
\(67\) −1.49525e10 −1.35302 −0.676509 0.736435i \(-0.736508\pi\)
−0.676509 + 0.736435i \(0.736508\pi\)
\(68\) 1.91057e10 1.59354
\(69\) 1.08617e10 0.836040
\(70\) −1.02081e10 −0.725952
\(71\) 1.84247e10 1.21193 0.605966 0.795490i \(-0.292787\pi\)
0.605966 + 0.795490i \(0.292787\pi\)
\(72\) −2.51509e9 −0.153188
\(73\) 1.03519e10 0.584447 0.292224 0.956350i \(-0.405605\pi\)
0.292224 + 0.956350i \(0.405605\pi\)
\(74\) −3.76695e8 −0.0197340
\(75\) 2.67626e10 1.30224
\(76\) 9.80714e9 0.443678
\(77\) −5.86594e9 −0.246967
\(78\) 3.84663e9 0.150855
\(79\) −4.76733e9 −0.174312 −0.0871559 0.996195i \(-0.527778\pi\)
−0.0871559 + 0.996195i \(0.527778\pi\)
\(80\) 4.41821e10 1.50748
\(81\) 3.48678e9 0.111111
\(82\) 5.68277e9 0.169272
\(83\) −6.60401e10 −1.84025 −0.920127 0.391619i \(-0.871915\pi\)
−0.920127 + 0.391619i \(0.871915\pi\)
\(84\) 3.55612e10 0.927770
\(85\) −1.24581e11 −3.04542
\(86\) −1.49389e10 −0.342435
\(87\) −2.17564e10 −0.467984
\(88\) −3.30116e9 −0.0666825
\(89\) 6.92452e10 1.31445 0.657226 0.753694i \(-0.271730\pi\)
0.657226 + 0.753694i \(0.271730\pi\)
\(90\) 7.96429e9 0.142172
\(91\) −1.11995e11 −1.88136
\(92\) −8.64268e10 −1.36715
\(93\) 1.06978e10 0.159455
\(94\) −2.42093e10 −0.340235
\(95\) −6.39486e10 −0.847913
\(96\) 3.03066e10 0.379355
\(97\) 1.01541e11 1.20059 0.600295 0.799778i \(-0.295050\pi\)
0.600295 + 0.799778i \(0.295050\pi\)
\(98\) 4.01264e10 0.448422
\(99\) 4.57655e9 0.0483664
\(100\) −2.12951e11 −2.12951
\(101\) 1.23150e11 1.16592 0.582958 0.812502i \(-0.301895\pi\)
0.582958 + 0.812502i \(0.301895\pi\)
\(102\) −2.56861e10 −0.230355
\(103\) −1.08902e11 −0.925618 −0.462809 0.886458i \(-0.653158\pi\)
−0.462809 + 0.886458i \(0.653158\pi\)
\(104\) −6.30271e10 −0.507977
\(105\) −2.31881e11 −1.77306
\(106\) −6.24028e10 −0.452920
\(107\) −7.98634e10 −0.550474 −0.275237 0.961376i \(-0.588756\pi\)
−0.275237 + 0.961376i \(0.588756\pi\)
\(108\) −2.77445e10 −0.181696
\(109\) −2.02795e11 −1.26244 −0.631222 0.775602i \(-0.717446\pi\)
−0.631222 + 0.775602i \(0.717446\pi\)
\(110\) 1.04535e10 0.0618871
\(111\) −8.55675e9 −0.0481984
\(112\) −2.65223e11 −1.42204
\(113\) −1.71570e11 −0.876012 −0.438006 0.898972i \(-0.644315\pi\)
−0.438006 + 0.898972i \(0.644315\pi\)
\(114\) −1.31849e10 −0.0641360
\(115\) 5.63556e11 2.61276
\(116\) 1.73117e11 0.765279
\(117\) 8.73773e10 0.368448
\(118\) −7.64800e9 −0.0307749
\(119\) 7.47855e11 2.87283
\(120\) −1.30495e11 −0.478737
\(121\) −2.79305e11 −0.978946
\(122\) 2.11017e10 0.0706866
\(123\) 1.29086e11 0.413429
\(124\) −8.51226e10 −0.260751
\(125\) 7.72945e11 2.26539
\(126\) −4.78093e10 −0.134114
\(127\) −2.24500e11 −0.602971 −0.301485 0.953471i \(-0.597482\pi\)
−0.301485 + 0.953471i \(0.597482\pi\)
\(128\) −3.17925e11 −0.817844
\(129\) −3.39342e11 −0.836363
\(130\) 1.99582e11 0.471446
\(131\) 1.94886e11 0.441354 0.220677 0.975347i \(-0.429173\pi\)
0.220677 + 0.975347i \(0.429173\pi\)
\(132\) −3.64158e10 −0.0790920
\(133\) 3.83881e11 0.799858
\(134\) −1.59957e11 −0.319835
\(135\) 1.80911e11 0.347240
\(136\) 4.20868e11 0.775679
\(137\) −2.31749e11 −0.410256 −0.205128 0.978735i \(-0.565761\pi\)
−0.205128 + 0.978735i \(0.565761\pi\)
\(138\) 1.16194e11 0.197629
\(139\) −7.66906e11 −1.25361 −0.626803 0.779178i \(-0.715637\pi\)
−0.626803 + 0.779178i \(0.715637\pi\)
\(140\) 1.84509e12 2.89943
\(141\) −5.49922e11 −0.830990
\(142\) 1.97100e11 0.286485
\(143\) 1.14686e11 0.160385
\(144\) 2.06925e11 0.278496
\(145\) −1.12883e12 −1.46253
\(146\) 1.10741e11 0.138155
\(147\) 9.11484e11 1.09523
\(148\) 6.80864e10 0.0788172
\(149\) −4.09977e11 −0.457335 −0.228668 0.973505i \(-0.573437\pi\)
−0.228668 + 0.973505i \(0.573437\pi\)
\(150\) 2.86296e11 0.307832
\(151\) −1.09706e12 −1.13726 −0.568628 0.822595i \(-0.692525\pi\)
−0.568628 + 0.822595i \(0.692525\pi\)
\(152\) 2.16036e11 0.215966
\(153\) −5.83469e11 −0.562619
\(154\) −6.27517e10 −0.0583797
\(155\) 5.55052e11 0.498321
\(156\) −6.95264e11 −0.602511
\(157\) −4.85099e11 −0.405865 −0.202933 0.979193i \(-0.565047\pi\)
−0.202933 + 0.979193i \(0.565047\pi\)
\(158\) −5.09992e10 −0.0412049
\(159\) −1.41750e12 −1.10621
\(160\) 1.57245e12 1.18555
\(161\) −3.38301e12 −2.46468
\(162\) 3.73003e10 0.0262652
\(163\) 2.00016e12 1.36155 0.680774 0.732494i \(-0.261644\pi\)
0.680774 + 0.732494i \(0.261644\pi\)
\(164\) −1.02714e12 −0.676066
\(165\) 2.37453e11 0.151153
\(166\) −7.06472e11 −0.435011
\(167\) −2.88974e12 −1.72154 −0.860772 0.508991i \(-0.830018\pi\)
−0.860772 + 0.508991i \(0.830018\pi\)
\(168\) 7.83357e11 0.451605
\(169\) 3.97475e11 0.221786
\(170\) −1.33272e12 −0.719897
\(171\) −2.99500e11 −0.156646
\(172\) 2.70016e12 1.36768
\(173\) −1.64101e12 −0.805114 −0.402557 0.915395i \(-0.631878\pi\)
−0.402557 + 0.915395i \(0.631878\pi\)
\(174\) −2.32742e11 −0.110625
\(175\) −8.33554e12 −3.83906
\(176\) 2.71597e11 0.121229
\(177\) −1.73727e11 −0.0751646
\(178\) 7.40760e11 0.310719
\(179\) 1.52449e12 0.620058 0.310029 0.950727i \(-0.399661\pi\)
0.310029 + 0.950727i \(0.399661\pi\)
\(180\) −1.43952e12 −0.567830
\(181\) −3.25654e12 −1.24602 −0.623010 0.782214i \(-0.714090\pi\)
−0.623010 + 0.782214i \(0.714090\pi\)
\(182\) −1.19808e12 −0.444727
\(183\) 4.79330e11 0.172645
\(184\) −1.90385e12 −0.665478
\(185\) −4.43966e11 −0.150628
\(186\) 1.14441e11 0.0376929
\(187\) −7.65826e11 −0.244907
\(188\) 4.37575e12 1.35889
\(189\) −1.08600e12 −0.327560
\(190\) −6.84099e11 −0.200435
\(191\) −4.50654e12 −1.28280 −0.641402 0.767205i \(-0.721647\pi\)
−0.641402 + 0.767205i \(0.721647\pi\)
\(192\) −1.41975e12 −0.392694
\(193\) −4.73174e12 −1.27191 −0.635954 0.771727i \(-0.719393\pi\)
−0.635954 + 0.771727i \(0.719393\pi\)
\(194\) 1.08624e12 0.283804
\(195\) 4.53356e12 1.15146
\(196\) −7.25272e12 −1.79099
\(197\) −6.75309e12 −1.62158 −0.810790 0.585338i \(-0.800962\pi\)
−0.810790 + 0.585338i \(0.800962\pi\)
\(198\) 4.89582e10 0.0114332
\(199\) 2.26182e12 0.513767 0.256884 0.966442i \(-0.417304\pi\)
0.256884 + 0.966442i \(0.417304\pi\)
\(200\) −4.69097e12 −1.03657
\(201\) −3.63347e12 −0.781165
\(202\) 1.31742e12 0.275607
\(203\) 6.77631e12 1.37964
\(204\) 4.64268e12 0.920032
\(205\) 6.69760e12 1.29203
\(206\) −1.16500e12 −0.218804
\(207\) 2.63939e12 0.482688
\(208\) 5.18544e12 0.923500
\(209\) −3.93106e11 −0.0681875
\(210\) −2.48058e12 −0.419129
\(211\) 2.16403e12 0.356213 0.178106 0.984011i \(-0.443003\pi\)
0.178106 + 0.984011i \(0.443003\pi\)
\(212\) 1.12791e13 1.80895
\(213\) 4.47719e12 0.699710
\(214\) −8.54349e11 −0.130125
\(215\) −1.76067e13 −2.61377
\(216\) −6.11167e11 −0.0884432
\(217\) −3.33196e12 −0.470079
\(218\) −2.16943e12 −0.298425
\(219\) 2.51552e12 0.337431
\(220\) −1.88943e12 −0.247175
\(221\) −1.46215e13 −1.86566
\(222\) −9.15370e10 −0.0113935
\(223\) 1.44094e12 0.174972 0.0874861 0.996166i \(-0.472117\pi\)
0.0874861 + 0.996166i \(0.472117\pi\)
\(224\) −9.43939e12 −1.11835
\(225\) 6.50330e12 0.751848
\(226\) −1.83539e12 −0.207077
\(227\) −8.12350e12 −0.894542 −0.447271 0.894398i \(-0.647604\pi\)
−0.447271 + 0.894398i \(0.647604\pi\)
\(228\) 2.38313e12 0.256157
\(229\) 1.36595e13 1.43331 0.716653 0.697430i \(-0.245673\pi\)
0.716653 + 0.697430i \(0.245673\pi\)
\(230\) 6.02872e12 0.617621
\(231\) −1.42542e12 −0.142586
\(232\) 3.81348e12 0.372510
\(233\) 6.34784e12 0.605576 0.302788 0.953058i \(-0.402083\pi\)
0.302788 + 0.953058i \(0.402083\pi\)
\(234\) 9.34730e11 0.0870962
\(235\) −2.85326e13 −2.59698
\(236\) 1.38235e12 0.122914
\(237\) −1.15846e12 −0.100639
\(238\) 8.00028e12 0.679097
\(239\) 9.27269e12 0.769161 0.384580 0.923091i \(-0.374346\pi\)
0.384580 + 0.923091i \(0.374346\pi\)
\(240\) 1.07362e13 0.870343
\(241\) 1.00141e13 0.793446 0.396723 0.917938i \(-0.370147\pi\)
0.396723 + 0.917938i \(0.370147\pi\)
\(242\) −2.98790e12 −0.231410
\(243\) 8.47289e11 0.0641500
\(244\) −3.81405e12 −0.282321
\(245\) 4.72922e13 3.42276
\(246\) 1.38091e12 0.0977290
\(247\) −7.50534e12 −0.519442
\(248\) −1.87512e12 −0.126924
\(249\) −1.60477e13 −1.06247
\(250\) 8.26868e12 0.535508
\(251\) −4.68629e12 −0.296909 −0.148455 0.988919i \(-0.547430\pi\)
−0.148455 + 0.988919i \(0.547430\pi\)
\(252\) 8.64138e12 0.535648
\(253\) 3.46430e12 0.210113
\(254\) −2.40162e12 −0.142534
\(255\) −3.02732e13 −1.75828
\(256\) 8.56456e12 0.486839
\(257\) −1.62432e13 −0.903730 −0.451865 0.892086i \(-0.649241\pi\)
−0.451865 + 0.892086i \(0.649241\pi\)
\(258\) −3.63016e12 −0.197705
\(259\) 2.66511e12 0.142091
\(260\) −3.60737e13 −1.88294
\(261\) −5.28681e12 −0.270191
\(262\) 2.08481e12 0.104330
\(263\) 1.75074e13 0.857955 0.428978 0.903315i \(-0.358874\pi\)
0.428978 + 0.903315i \(0.358874\pi\)
\(264\) −8.02181e11 −0.0384991
\(265\) −7.35467e13 −3.45709
\(266\) 4.10662e12 0.189076
\(267\) 1.68266e13 0.758899
\(268\) 2.89116e13 1.27741
\(269\) 2.83159e13 1.22573 0.612863 0.790189i \(-0.290018\pi\)
0.612863 + 0.790189i \(0.290018\pi\)
\(270\) 1.93532e12 0.0820829
\(271\) 3.16183e13 1.31404 0.657019 0.753874i \(-0.271817\pi\)
0.657019 + 0.753874i \(0.271817\pi\)
\(272\) −3.46262e13 −1.41018
\(273\) −2.72148e13 −1.08620
\(274\) −2.47917e12 −0.0969790
\(275\) 8.53584e12 0.327278
\(276\) −2.10017e13 −0.789323
\(277\) −4.49678e13 −1.65677 −0.828387 0.560156i \(-0.810741\pi\)
−0.828387 + 0.560156i \(0.810741\pi\)
\(278\) −8.20408e12 −0.296336
\(279\) 2.59956e12 0.0920611
\(280\) 4.06444e13 1.41134
\(281\) −2.03149e11 −0.00691718 −0.00345859 0.999994i \(-0.501101\pi\)
−0.00345859 + 0.999994i \(0.501101\pi\)
\(282\) −5.88286e12 −0.196435
\(283\) −3.83681e13 −1.25645 −0.628225 0.778031i \(-0.716218\pi\)
−0.628225 + 0.778031i \(0.716218\pi\)
\(284\) −3.56252e13 −1.14421
\(285\) −1.55395e13 −0.489543
\(286\) 1.22687e12 0.0379128
\(287\) −4.02055e13 −1.21881
\(288\) 7.36451e12 0.219021
\(289\) 6.33641e13 1.84886
\(290\) −1.20758e13 −0.345722
\(291\) 2.46744e13 0.693162
\(292\) −2.00161e13 −0.551789
\(293\) 4.18480e12 0.113215 0.0566073 0.998397i \(-0.481972\pi\)
0.0566073 + 0.998397i \(0.481972\pi\)
\(294\) 9.75072e12 0.258897
\(295\) −9.01378e12 −0.234901
\(296\) 1.49984e12 0.0383654
\(297\) 1.11210e12 0.0279244
\(298\) −4.38578e12 −0.108108
\(299\) 6.61419e13 1.60061
\(300\) −5.17470e13 −1.22947
\(301\) 1.05693e14 2.46563
\(302\) −1.17360e13 −0.268832
\(303\) 2.99255e13 0.673142
\(304\) −1.77739e13 −0.392626
\(305\) 2.48700e13 0.539543
\(306\) −6.24173e12 −0.132996
\(307\) −3.13464e13 −0.656033 −0.328017 0.944672i \(-0.606380\pi\)
−0.328017 + 0.944672i \(0.606380\pi\)
\(308\) 1.13422e13 0.233167
\(309\) −2.64632e13 −0.534406
\(310\) 5.93774e12 0.117796
\(311\) −2.08261e13 −0.405907 −0.202954 0.979188i \(-0.565054\pi\)
−0.202954 + 0.979188i \(0.565054\pi\)
\(312\) −1.53156e13 −0.293280
\(313\) 2.40315e13 0.452154 0.226077 0.974109i \(-0.427410\pi\)
0.226077 + 0.974109i \(0.427410\pi\)
\(314\) −5.18941e12 −0.0959411
\(315\) −5.63471e13 −1.02368
\(316\) 9.21793e12 0.164571
\(317\) 4.91354e13 0.862122 0.431061 0.902323i \(-0.358139\pi\)
0.431061 + 0.902323i \(0.358139\pi\)
\(318\) −1.51639e13 −0.261494
\(319\) −6.93915e12 −0.117614
\(320\) −7.36634e13 −1.22723
\(321\) −1.94068e13 −0.317816
\(322\) −3.61902e13 −0.582618
\(323\) 5.01175e13 0.793187
\(324\) −6.74191e12 −0.104902
\(325\) 1.62970e14 2.49315
\(326\) 2.13970e13 0.321852
\(327\) −4.92793e13 −0.728872
\(328\) −2.26263e13 −0.329084
\(329\) 1.71280e14 2.44980
\(330\) 2.54019e12 0.0357305
\(331\) −9.52583e13 −1.31780 −0.658899 0.752231i \(-0.728978\pi\)
−0.658899 + 0.752231i \(0.728978\pi\)
\(332\) 1.27692e14 1.73742
\(333\) −2.07929e12 −0.0278274
\(334\) −3.09134e13 −0.406950
\(335\) −1.88522e14 −2.44127
\(336\) −6.44493e13 −0.821017
\(337\) −8.43699e13 −1.05736 −0.528680 0.848821i \(-0.677313\pi\)
−0.528680 + 0.848821i \(0.677313\pi\)
\(338\) 4.25205e12 0.0524271
\(339\) −4.16915e13 −0.505766
\(340\) 2.40885e14 2.87525
\(341\) 3.41202e12 0.0400740
\(342\) −3.20394e12 −0.0370289
\(343\) −1.34239e14 −1.52672
\(344\) 5.94803e13 0.665735
\(345\) 1.36944e14 1.50848
\(346\) −1.75549e13 −0.190318
\(347\) 4.12347e12 0.0439998 0.0219999 0.999758i \(-0.492997\pi\)
0.0219999 + 0.999758i \(0.492997\pi\)
\(348\) 4.20673e13 0.441834
\(349\) 1.74296e14 1.80197 0.900987 0.433847i \(-0.142844\pi\)
0.900987 + 0.433847i \(0.142844\pi\)
\(350\) −8.91706e13 −0.907501
\(351\) 2.12327e13 0.212724
\(352\) 9.66621e12 0.0953393
\(353\) 1.48365e14 1.44069 0.720345 0.693616i \(-0.243983\pi\)
0.720345 + 0.693616i \(0.243983\pi\)
\(354\) −1.85846e12 −0.0177679
\(355\) 2.32298e14 2.18671
\(356\) −1.33890e14 −1.24100
\(357\) 1.81729e14 1.65863
\(358\) 1.63084e13 0.146573
\(359\) 2.14138e14 1.89528 0.947640 0.319341i \(-0.103462\pi\)
0.947640 + 0.319341i \(0.103462\pi\)
\(360\) −3.17103e13 −0.276399
\(361\) −9.07645e13 −0.779159
\(362\) −3.48373e13 −0.294542
\(363\) −6.78711e13 −0.565195
\(364\) 2.16549e14 1.77623
\(365\) 1.30517e14 1.05453
\(366\) 5.12770e12 0.0408110
\(367\) 7.54506e13 0.591560 0.295780 0.955256i \(-0.404420\pi\)
0.295780 + 0.955256i \(0.404420\pi\)
\(368\) 1.56635e14 1.20984
\(369\) 3.13679e13 0.238693
\(370\) −4.74938e12 −0.0356064
\(371\) 4.41498e14 3.26116
\(372\) −2.06848e13 −0.150544
\(373\) 4.45810e13 0.319706 0.159853 0.987141i \(-0.448898\pi\)
0.159853 + 0.987141i \(0.448898\pi\)
\(374\) −8.19253e12 −0.0578927
\(375\) 1.87826e14 1.30793
\(376\) 9.63909e13 0.661459
\(377\) −1.32485e14 −0.895962
\(378\) −1.16177e13 −0.0774309
\(379\) −2.12277e14 −1.39440 −0.697200 0.716877i \(-0.745571\pi\)
−0.697200 + 0.716877i \(0.745571\pi\)
\(380\) 1.23649e14 0.800533
\(381\) −5.45536e13 −0.348125
\(382\) −4.82094e13 −0.303237
\(383\) −2.00563e14 −1.24354 −0.621768 0.783202i \(-0.713585\pi\)
−0.621768 + 0.783202i \(0.713585\pi\)
\(384\) −7.72559e13 −0.472182
\(385\) −7.39579e13 −0.445605
\(386\) −5.06184e13 −0.300662
\(387\) −8.24602e13 −0.482874
\(388\) −1.96335e14 −1.13350
\(389\) −1.28882e14 −0.733615 −0.366808 0.930297i \(-0.619549\pi\)
−0.366808 + 0.930297i \(0.619549\pi\)
\(390\) 4.84983e13 0.272190
\(391\) −4.41668e14 −2.44413
\(392\) −1.59766e14 −0.871787
\(393\) 4.73572e13 0.254816
\(394\) −7.22421e13 −0.383320
\(395\) −6.01066e13 −0.314513
\(396\) −8.84903e12 −0.0456638
\(397\) 2.77310e14 1.41129 0.705647 0.708563i \(-0.250656\pi\)
0.705647 + 0.708563i \(0.250656\pi\)
\(398\) 2.41961e13 0.121448
\(399\) 9.32832e13 0.461798
\(400\) 3.85941e14 1.88448
\(401\) −3.34964e13 −0.161326 −0.0806631 0.996741i \(-0.525704\pi\)
−0.0806631 + 0.996741i \(0.525704\pi\)
\(402\) −3.88695e13 −0.184657
\(403\) 6.51438e13 0.305278
\(404\) −2.38118e14 −1.10077
\(405\) 4.39614e13 0.200479
\(406\) 7.24905e13 0.326128
\(407\) −2.72915e12 −0.0121132
\(408\) 1.02271e14 0.447839
\(409\) −8.55004e13 −0.369394 −0.184697 0.982795i \(-0.559130\pi\)
−0.184697 + 0.982795i \(0.559130\pi\)
\(410\) 7.16485e13 0.305419
\(411\) −5.63150e13 −0.236861
\(412\) 2.10569e14 0.873896
\(413\) 5.41094e13 0.221589
\(414\) 2.82352e13 0.114101
\(415\) −8.32634e14 −3.32039
\(416\) 1.84551e14 0.726280
\(417\) −1.86358e14 −0.723770
\(418\) −4.20530e12 −0.0161186
\(419\) 3.83763e14 1.45173 0.725865 0.687837i \(-0.241439\pi\)
0.725865 + 0.687837i \(0.241439\pi\)
\(420\) 4.48356e14 1.67399
\(421\) 6.87047e13 0.253183 0.126592 0.991955i \(-0.459596\pi\)
0.126592 + 0.991955i \(0.459596\pi\)
\(422\) 2.31500e13 0.0842039
\(423\) −1.33631e14 −0.479772
\(424\) 2.48460e14 0.880532
\(425\) −1.08824e15 −3.80704
\(426\) 4.78954e13 0.165402
\(427\) −1.49294e14 −0.508965
\(428\) 1.54421e14 0.519714
\(429\) 2.78687e13 0.0925982
\(430\) −1.88350e14 −0.617860
\(431\) 3.82711e14 1.23950 0.619749 0.784800i \(-0.287234\pi\)
0.619749 + 0.784800i \(0.287234\pi\)
\(432\) 5.02827e13 0.160789
\(433\) −2.01869e14 −0.637364 −0.318682 0.947862i \(-0.603240\pi\)
−0.318682 + 0.947862i \(0.603240\pi\)
\(434\) −3.56441e13 −0.111120
\(435\) −2.74305e14 −0.844390
\(436\) 3.92117e14 1.19190
\(437\) −2.26712e14 −0.680498
\(438\) 2.69101e13 0.0797641
\(439\) −6.71377e13 −0.196522 −0.0982611 0.995161i \(-0.531328\pi\)
−0.0982611 + 0.995161i \(0.531328\pi\)
\(440\) −4.16211e13 −0.120316
\(441\) 2.21491e14 0.632329
\(442\) −1.56415e14 −0.441018
\(443\) −1.02274e14 −0.284803 −0.142401 0.989809i \(-0.545482\pi\)
−0.142401 + 0.989809i \(0.545482\pi\)
\(444\) 1.65450e13 0.0455051
\(445\) 8.73044e14 2.37168
\(446\) 1.54146e13 0.0413611
\(447\) −9.96243e13 −0.264043
\(448\) 4.42199e14 1.15768
\(449\) 3.03892e13 0.0785894 0.0392947 0.999228i \(-0.487489\pi\)
0.0392947 + 0.999228i \(0.487489\pi\)
\(450\) 6.95699e13 0.177727
\(451\) 4.11716e13 0.103903
\(452\) 3.31741e14 0.827061
\(453\) −2.66586e14 −0.656595
\(454\) −8.69022e13 −0.211458
\(455\) −1.41203e15 −3.39455
\(456\) 5.24967e13 0.124688
\(457\) 3.10511e14 0.728681 0.364340 0.931266i \(-0.381295\pi\)
0.364340 + 0.931266i \(0.381295\pi\)
\(458\) 1.46124e14 0.338814
\(459\) −1.41783e14 −0.324828
\(460\) −1.08967e15 −2.46676
\(461\) −1.47681e14 −0.330347 −0.165173 0.986265i \(-0.552818\pi\)
−0.165173 + 0.986265i \(0.552818\pi\)
\(462\) −1.52487e13 −0.0337055
\(463\) 5.29520e14 1.15661 0.578305 0.815821i \(-0.303715\pi\)
0.578305 + 0.815821i \(0.303715\pi\)
\(464\) −3.13748e14 −0.677223
\(465\) 1.34878e14 0.287706
\(466\) 6.79069e13 0.143150
\(467\) 2.82042e14 0.587585 0.293792 0.955869i \(-0.405083\pi\)
0.293792 + 0.955869i \(0.405083\pi\)
\(468\) −1.68949e14 −0.347860
\(469\) 1.13169e15 2.30291
\(470\) −3.05231e14 −0.613891
\(471\) −1.17879e14 −0.234326
\(472\) 3.04510e13 0.0598302
\(473\) −1.08232e14 −0.210194
\(474\) −1.23928e13 −0.0237897
\(475\) −5.58606e14 −1.05996
\(476\) −1.44602e15 −2.71230
\(477\) −3.44452e14 −0.638672
\(478\) 9.91958e13 0.181819
\(479\) 7.44418e14 1.34888 0.674438 0.738332i \(-0.264386\pi\)
0.674438 + 0.738332i \(0.264386\pi\)
\(480\) 3.82106e14 0.684475
\(481\) −5.21061e13 −0.0922764
\(482\) 1.07127e14 0.187560
\(483\) −8.22071e14 −1.42298
\(484\) 5.40053e14 0.924244
\(485\) 1.28023e15 2.16624
\(486\) 9.06398e12 0.0151642
\(487\) 2.90278e14 0.480181 0.240090 0.970751i \(-0.422823\pi\)
0.240090 + 0.970751i \(0.422823\pi\)
\(488\) −8.40175e13 −0.137423
\(489\) 4.86039e14 0.786090
\(490\) 5.05915e14 0.809094
\(491\) 4.36016e13 0.0689532 0.0344766 0.999406i \(-0.489024\pi\)
0.0344766 + 0.999406i \(0.489024\pi\)
\(492\) −2.49595e14 −0.390327
\(493\) 8.84680e14 1.36813
\(494\) −8.02894e13 −0.122789
\(495\) 5.77012e13 0.0872682
\(496\) 1.54272e14 0.230748
\(497\) −1.39448e15 −2.06277
\(498\) −1.71673e14 −0.251154
\(499\) −3.22220e14 −0.466229 −0.233115 0.972449i \(-0.574892\pi\)
−0.233115 + 0.972449i \(0.574892\pi\)
\(500\) −1.49454e15 −2.13881
\(501\) −7.02206e14 −0.993933
\(502\) −5.01322e13 −0.0701853
\(503\) 9.03185e14 1.25070 0.625350 0.780345i \(-0.284956\pi\)
0.625350 + 0.780345i \(0.284956\pi\)
\(504\) 1.90356e14 0.260734
\(505\) 1.55268e15 2.10368
\(506\) 3.70598e13 0.0496679
\(507\) 9.65865e13 0.128048
\(508\) 4.34085e14 0.569278
\(509\) −4.38071e14 −0.568325 −0.284162 0.958776i \(-0.591715\pi\)
−0.284162 + 0.958776i \(0.591715\pi\)
\(510\) −3.23851e14 −0.415633
\(511\) −7.83490e14 −0.994760
\(512\) 7.42732e14 0.932926
\(513\) −7.27785e13 −0.0904394
\(514\) −1.73764e14 −0.213630
\(515\) −1.37304e15 −1.67010
\(516\) 6.56139e14 0.789628
\(517\) −1.75396e14 −0.208844
\(518\) 2.85104e13 0.0335884
\(519\) −3.98765e14 −0.464833
\(520\) −7.94646e14 −0.916548
\(521\) −1.19830e14 −0.136759 −0.0683797 0.997659i \(-0.521783\pi\)
−0.0683797 + 0.997659i \(0.521783\pi\)
\(522\) −5.65563e13 −0.0638695
\(523\) 1.22735e15 1.37154 0.685771 0.727818i \(-0.259465\pi\)
0.685771 + 0.727818i \(0.259465\pi\)
\(524\) −3.76823e14 −0.416692
\(525\) −2.02554e15 −2.21648
\(526\) 1.87288e14 0.202809
\(527\) −4.35003e14 −0.466158
\(528\) 6.59980e13 0.0699913
\(529\) 1.04512e15 1.09689
\(530\) −7.86775e14 −0.817210
\(531\) −4.22156e13 −0.0433963
\(532\) −7.42258e14 −0.755163
\(533\) 7.86065e14 0.791514
\(534\) 1.80005e14 0.179393
\(535\) −1.00692e15 −0.993227
\(536\) 6.36877e14 0.621798
\(537\) 3.70450e14 0.357990
\(538\) 3.02914e14 0.289745
\(539\) 2.90715e14 0.275252
\(540\) −3.49803e14 −0.327837
\(541\) 9.04575e14 0.839188 0.419594 0.907712i \(-0.362172\pi\)
0.419594 + 0.907712i \(0.362172\pi\)
\(542\) 3.38241e14 0.310621
\(543\) −7.91340e14 −0.719390
\(544\) −1.23236e15 −1.10903
\(545\) −2.55685e15 −2.27784
\(546\) −2.91134e14 −0.256763
\(547\) −1.57116e15 −1.37180 −0.685900 0.727696i \(-0.740591\pi\)
−0.685900 + 0.727696i \(0.740591\pi\)
\(548\) 4.48101e14 0.387331
\(549\) 1.16477e14 0.0996766
\(550\) 9.13133e13 0.0773641
\(551\) 4.54115e14 0.380918
\(552\) −4.62634e14 −0.384214
\(553\) 3.60818e14 0.296688
\(554\) −4.81050e14 −0.391639
\(555\) −1.07884e14 −0.0869650
\(556\) 1.48286e15 1.18356
\(557\) −1.14870e15 −0.907830 −0.453915 0.891045i \(-0.649973\pi\)
−0.453915 + 0.891045i \(0.649973\pi\)
\(558\) 2.78091e13 0.0217620
\(559\) −2.06642e15 −1.60123
\(560\) −3.34394e15 −2.56581
\(561\) −1.86096e14 −0.141397
\(562\) −2.17321e12 −0.00163513
\(563\) −3.34715e14 −0.249390 −0.124695 0.992195i \(-0.539795\pi\)
−0.124695 + 0.992195i \(0.539795\pi\)
\(564\) 1.06331e15 0.784556
\(565\) −2.16316e15 −1.58060
\(566\) −4.10448e14 −0.297008
\(567\) −2.63899e14 −0.189117
\(568\) −7.84766e14 −0.556961
\(569\) 8.92451e14 0.627288 0.313644 0.949541i \(-0.398450\pi\)
0.313644 + 0.949541i \(0.398450\pi\)
\(570\) −1.66236e14 −0.115721
\(571\) −1.26374e15 −0.871283 −0.435642 0.900120i \(-0.643478\pi\)
−0.435642 + 0.900120i \(0.643478\pi\)
\(572\) −2.21753e14 −0.151423
\(573\) −1.09509e15 −0.740627
\(574\) −4.30103e14 −0.288109
\(575\) 4.92280e15 3.26617
\(576\) −3.44999e14 −0.226722
\(577\) −1.00358e15 −0.653261 −0.326631 0.945152i \(-0.605913\pi\)
−0.326631 + 0.945152i \(0.605913\pi\)
\(578\) 6.77846e14 0.437047
\(579\) −1.14981e15 −0.734336
\(580\) 2.18266e15 1.38080
\(581\) 4.99827e15 3.13221
\(582\) 2.63957e14 0.163854
\(583\) −4.52107e14 −0.278013
\(584\) −4.40922e14 −0.268591
\(585\) 1.10165e15 0.664795
\(586\) 4.47674e13 0.0267624
\(587\) 2.44010e15 1.44510 0.722549 0.691320i \(-0.242970\pi\)
0.722549 + 0.691320i \(0.242970\pi\)
\(588\) −1.76241e15 −1.03403
\(589\) −2.23291e14 −0.129789
\(590\) −9.64261e13 −0.0555275
\(591\) −1.64100e15 −0.936219
\(592\) −1.23396e14 −0.0697482
\(593\) −6.01651e14 −0.336933 −0.168467 0.985707i \(-0.553882\pi\)
−0.168467 + 0.985707i \(0.553882\pi\)
\(594\) 1.18968e13 0.00660095
\(595\) 9.42897e15 5.18347
\(596\) 7.92715e14 0.431780
\(597\) 5.49623e14 0.296624
\(598\) 7.07562e14 0.378362
\(599\) −1.52053e15 −0.805650 −0.402825 0.915277i \(-0.631972\pi\)
−0.402825 + 0.915277i \(0.631972\pi\)
\(600\) −1.13990e15 −0.598462
\(601\) 9.06559e14 0.471614 0.235807 0.971800i \(-0.424227\pi\)
0.235807 + 0.971800i \(0.424227\pi\)
\(602\) 1.13066e15 0.582843
\(603\) −8.82932e14 −0.451006
\(604\) 2.12124e15 1.07371
\(605\) −3.52148e15 −1.76632
\(606\) 3.20132e14 0.159122
\(607\) −3.24469e14 −0.159822 −0.0799108 0.996802i \(-0.525464\pi\)
−0.0799108 + 0.996802i \(0.525464\pi\)
\(608\) −6.32580e14 −0.308778
\(609\) 1.64664e15 0.796535
\(610\) 2.66050e14 0.127541
\(611\) −3.34873e15 −1.59094
\(612\) 1.12817e15 0.531181
\(613\) 1.86652e15 0.870963 0.435482 0.900198i \(-0.356578\pi\)
0.435482 + 0.900198i \(0.356578\pi\)
\(614\) −3.35332e14 −0.155077
\(615\) 1.62752e15 0.745955
\(616\) 2.49850e14 0.113497
\(617\) 1.21806e15 0.548406 0.274203 0.961672i \(-0.411586\pi\)
0.274203 + 0.961672i \(0.411586\pi\)
\(618\) −2.83094e14 −0.126326
\(619\) −2.04250e15 −0.903367 −0.451684 0.892178i \(-0.649176\pi\)
−0.451684 + 0.892178i \(0.649176\pi\)
\(620\) −1.07323e15 −0.470476
\(621\) 6.41371e14 0.278680
\(622\) −2.22790e14 −0.0959510
\(623\) −5.24085e15 −2.23727
\(624\) 1.26006e15 0.533183
\(625\) 4.36767e15 1.83193
\(626\) 2.57080e14 0.106883
\(627\) −9.55248e13 −0.0393681
\(628\) 9.37967e14 0.383186
\(629\) 3.47943e14 0.140906
\(630\) −6.02781e14 −0.241984
\(631\) −7.92447e14 −0.315361 −0.157681 0.987490i \(-0.550402\pi\)
−0.157681 + 0.987490i \(0.550402\pi\)
\(632\) 2.03056e14 0.0801074
\(633\) 5.25859e14 0.205660
\(634\) 5.25633e14 0.203794
\(635\) −2.83050e15 −1.08795
\(636\) 2.74082e15 1.04440
\(637\) 5.55046e15 2.09682
\(638\) −7.42325e13 −0.0278023
\(639\) 1.08796e15 0.403978
\(640\) −4.00841e15 −1.47565
\(641\) −1.96917e15 −0.718725 −0.359363 0.933198i \(-0.617006\pi\)
−0.359363 + 0.933198i \(0.617006\pi\)
\(642\) −2.07607e14 −0.0751275
\(643\) −2.86477e15 −1.02785 −0.513924 0.857836i \(-0.671809\pi\)
−0.513924 + 0.857836i \(0.671809\pi\)
\(644\) 6.54125e15 2.32696
\(645\) −4.27843e15 −1.50906
\(646\) 5.36139e14 0.187499
\(647\) −4.81632e15 −1.67010 −0.835048 0.550177i \(-0.814560\pi\)
−0.835048 + 0.550177i \(0.814560\pi\)
\(648\) −1.48514e14 −0.0510627
\(649\) −5.54096e13 −0.0188903
\(650\) 1.74339e15 0.589348
\(651\) −8.09666e14 −0.271400
\(652\) −3.86743e15 −1.28547
\(653\) 1.26231e15 0.416049 0.208024 0.978124i \(-0.433297\pi\)
0.208024 + 0.978124i \(0.433297\pi\)
\(654\) −5.27171e14 −0.172296
\(655\) 2.45712e15 0.796341
\(656\) 1.86154e15 0.598275
\(657\) 6.11270e14 0.194816
\(658\) 1.83229e15 0.579099
\(659\) −3.64839e15 −1.14349 −0.571744 0.820432i \(-0.693733\pi\)
−0.571744 + 0.820432i \(0.693733\pi\)
\(660\) −4.59130e14 −0.142707
\(661\) 4.10991e15 1.26685 0.633424 0.773805i \(-0.281649\pi\)
0.633424 + 0.773805i \(0.281649\pi\)
\(662\) −1.01904e15 −0.311510
\(663\) −3.55302e15 −1.07714
\(664\) 2.81286e15 0.845715
\(665\) 4.83998e15 1.44319
\(666\) −2.22435e13 −0.00657801
\(667\) −4.00195e15 −1.17376
\(668\) 5.58748e15 1.62535
\(669\) 3.50148e14 0.101020
\(670\) −2.01674e15 −0.577082
\(671\) 1.52881e14 0.0433890
\(672\) −2.29377e15 −0.645682
\(673\) 4.16376e14 0.116253 0.0581264 0.998309i \(-0.481487\pi\)
0.0581264 + 0.998309i \(0.481487\pi\)
\(674\) −9.02558e14 −0.249946
\(675\) 1.58030e15 0.434080
\(676\) −7.68543e14 −0.209393
\(677\) −8.56154e14 −0.231374 −0.115687 0.993286i \(-0.536907\pi\)
−0.115687 + 0.993286i \(0.536907\pi\)
\(678\) −4.46000e14 −0.119556
\(679\) −7.68515e15 −2.04347
\(680\) 5.30631e15 1.39957
\(681\) −1.97401e15 −0.516464
\(682\) 3.65006e13 0.00947296
\(683\) 2.03764e15 0.524583 0.262291 0.964989i \(-0.415522\pi\)
0.262291 + 0.964989i \(0.415522\pi\)
\(684\) 5.79102e14 0.147893
\(685\) −2.92190e15 −0.740230
\(686\) −1.43604e15 −0.360896
\(687\) 3.31925e15 0.827519
\(688\) −4.89363e15 −1.21030
\(689\) −8.63182e15 −2.11786
\(690\) 1.46498e15 0.356584
\(691\) −4.83876e15 −1.16844 −0.584218 0.811597i \(-0.698599\pi\)
−0.584218 + 0.811597i \(0.698599\pi\)
\(692\) 3.17299e15 0.760125
\(693\) −3.46378e14 −0.0823223
\(694\) 4.41114e13 0.0104010
\(695\) −9.66917e15 −2.26190
\(696\) 9.26677e14 0.215069
\(697\) −5.24901e15 −1.20864
\(698\) 1.86456e15 0.425962
\(699\) 1.54253e15 0.349629
\(700\) 1.61173e16 3.62454
\(701\) 4.38418e15 0.978226 0.489113 0.872221i \(-0.337321\pi\)
0.489113 + 0.872221i \(0.337321\pi\)
\(702\) 2.27139e14 0.0502850
\(703\) 1.78602e14 0.0392313
\(704\) −4.52825e14 −0.0986916
\(705\) −6.93343e15 −1.49937
\(706\) 1.58716e15 0.340560
\(707\) −9.32068e15 −1.98445
\(708\) 3.35911e14 0.0709645
\(709\) 3.57448e15 0.749305 0.374653 0.927165i \(-0.377762\pi\)
0.374653 + 0.927165i \(0.377762\pi\)
\(710\) 2.48504e15 0.516908
\(711\) −2.81506e14 −0.0581039
\(712\) −2.94938e15 −0.604075
\(713\) 1.96778e15 0.399931
\(714\) 1.94407e15 0.392077
\(715\) 1.44597e15 0.289384
\(716\) −2.94769e15 −0.585410
\(717\) 2.25326e15 0.444075
\(718\) 2.29076e15 0.448019
\(719\) 1.68219e15 0.326488 0.163244 0.986586i \(-0.447804\pi\)
0.163244 + 0.986586i \(0.447804\pi\)
\(720\) 2.60891e15 0.502493
\(721\) 8.24231e15 1.57545
\(722\) −9.70965e14 −0.184183
\(723\) 2.43342e15 0.458096
\(724\) 6.29673e15 1.17639
\(725\) −9.86058e15 −1.82828
\(726\) −7.26060e14 −0.133604
\(727\) 7.58110e15 1.38450 0.692250 0.721658i \(-0.256620\pi\)
0.692250 + 0.721658i \(0.256620\pi\)
\(728\) 4.77023e15 0.864603
\(729\) 2.05891e14 0.0370370
\(730\) 1.39622e15 0.249276
\(731\) 1.37987e16 2.44507
\(732\) −9.26814e14 −0.162998
\(733\) −8.07548e13 −0.0140960 −0.00704801 0.999975i \(-0.502243\pi\)
−0.00704801 + 0.999975i \(0.502243\pi\)
\(734\) 8.07142e14 0.139837
\(735\) 1.14920e16 1.97613
\(736\) 5.57470e15 0.951467
\(737\) −1.15888e15 −0.196322
\(738\) 3.35562e14 0.0564239
\(739\) 8.64960e15 1.44362 0.721808 0.692094i \(-0.243311\pi\)
0.721808 + 0.692094i \(0.243311\pi\)
\(740\) 8.58435e14 0.142211
\(741\) −1.82380e15 −0.299900
\(742\) 4.72298e15 0.770895
\(743\) −9.43377e15 −1.52843 −0.764217 0.644959i \(-0.776875\pi\)
−0.764217 + 0.644959i \(0.776875\pi\)
\(744\) −4.55653e14 −0.0732796
\(745\) −5.16899e15 −0.825175
\(746\) 4.76911e14 0.0755742
\(747\) −3.89960e15 −0.613418
\(748\) 1.48077e15 0.231222
\(749\) 6.04450e15 0.936936
\(750\) 2.00929e15 0.309176
\(751\) 1.86122e14 0.0284301 0.0142150 0.999899i \(-0.495475\pi\)
0.0142150 + 0.999899i \(0.495475\pi\)
\(752\) −7.93038e15 −1.20253
\(753\) −1.13877e15 −0.171421
\(754\) −1.41728e15 −0.211793
\(755\) −1.38318e16 −2.05196
\(756\) 2.09985e15 0.309257
\(757\) −8.94198e15 −1.30739 −0.653696 0.756757i \(-0.726783\pi\)
−0.653696 + 0.756757i \(0.726783\pi\)
\(758\) −2.27086e15 −0.329617
\(759\) 8.41826e14 0.121309
\(760\) 2.72378e15 0.389670
\(761\) −6.68066e14 −0.0948864 −0.0474432 0.998874i \(-0.515107\pi\)
−0.0474432 + 0.998874i \(0.515107\pi\)
\(762\) −5.83594e14 −0.0822922
\(763\) 1.53487e16 2.14875
\(764\) 8.71367e15 1.21112
\(765\) −7.35638e15 −1.01514
\(766\) −2.14555e15 −0.293955
\(767\) −1.05790e15 −0.143904
\(768\) 2.08119e15 0.281076
\(769\) 3.76569e13 0.00504951 0.00252476 0.999997i \(-0.499196\pi\)
0.00252476 + 0.999997i \(0.499196\pi\)
\(770\) −7.91174e14 −0.105335
\(771\) −3.94709e15 −0.521769
\(772\) 9.14910e15 1.20084
\(773\) 1.24856e15 0.162713 0.0813564 0.996685i \(-0.474075\pi\)
0.0813564 + 0.996685i \(0.474075\pi\)
\(774\) −8.82129e14 −0.114145
\(775\) 4.84851e15 0.622944
\(776\) −4.32495e15 −0.551749
\(777\) 6.47622e14 0.0820363
\(778\) −1.37873e15 −0.173417
\(779\) −2.69437e15 −0.336512
\(780\) −8.76591e15 −1.08712
\(781\) 1.42799e15 0.175851
\(782\) −4.72480e15 −0.577758
\(783\) −1.28469e15 −0.155995
\(784\) 1.31444e16 1.58491
\(785\) −6.11613e15 −0.732308
\(786\) 5.06610e14 0.0602351
\(787\) 1.12544e16 1.32881 0.664405 0.747373i \(-0.268685\pi\)
0.664405 + 0.747373i \(0.268685\pi\)
\(788\) 1.30575e16 1.53097
\(789\) 4.25429e15 0.495341
\(790\) −6.42999e14 −0.0743466
\(791\) 1.29854e16 1.49102
\(792\) −1.94930e14 −0.0222275
\(793\) 2.91887e15 0.330531
\(794\) 2.96656e15 0.333611
\(795\) −1.78718e16 −1.99595
\(796\) −4.37337e15 −0.485059
\(797\) 7.79466e15 0.858571 0.429286 0.903169i \(-0.358765\pi\)
0.429286 + 0.903169i \(0.358765\pi\)
\(798\) 9.97909e14 0.109163
\(799\) 2.23614e16 2.42936
\(800\) 1.37358e16 1.48203
\(801\) 4.08886e15 0.438150
\(802\) −3.58333e14 −0.0381353
\(803\) 8.02317e14 0.0848029
\(804\) 7.02553e15 0.737515
\(805\) −4.26530e16 −4.44706
\(806\) 6.96884e14 0.0721635
\(807\) 6.88077e15 0.707673
\(808\) −5.24537e15 −0.535813
\(809\) 1.09980e16 1.11583 0.557914 0.829899i \(-0.311602\pi\)
0.557914 + 0.829899i \(0.311602\pi\)
\(810\) 4.70283e14 0.0473906
\(811\) −1.55405e16 −1.55543 −0.777713 0.628620i \(-0.783620\pi\)
−0.777713 + 0.628620i \(0.783620\pi\)
\(812\) −1.31024e16 −1.30255
\(813\) 7.68325e15 0.758660
\(814\) −2.91955e13 −0.00286340
\(815\) 2.52180e16 2.45666
\(816\) −8.41416e15 −0.814169
\(817\) 7.08298e15 0.680761
\(818\) −9.14652e14 −0.0873198
\(819\) −6.61319e15 −0.627118
\(820\) −1.29502e16 −1.21983
\(821\) 7.17636e15 0.671455 0.335727 0.941959i \(-0.391018\pi\)
0.335727 + 0.941959i \(0.391018\pi\)
\(822\) −6.02437e14 −0.0559908
\(823\) −1.15146e16 −1.06304 −0.531521 0.847045i \(-0.678379\pi\)
−0.531521 + 0.847045i \(0.678379\pi\)
\(824\) 4.63850e15 0.425381
\(825\) 2.07421e15 0.188954
\(826\) 5.78842e14 0.0523805
\(827\) 4.41263e15 0.396659 0.198330 0.980135i \(-0.436448\pi\)
0.198330 + 0.980135i \(0.436448\pi\)
\(828\) −5.10342e15 −0.455716
\(829\) 3.94618e15 0.350047 0.175024 0.984564i \(-0.444000\pi\)
0.175024 + 0.984564i \(0.444000\pi\)
\(830\) −8.90722e15 −0.784897
\(831\) −1.09272e16 −0.956539
\(832\) −8.64551e15 −0.751818
\(833\) −3.70636e16 −3.20185
\(834\) −1.99359e15 −0.171089
\(835\) −3.64339e16 −3.10620
\(836\) 7.60094e14 0.0643773
\(837\) 6.31692e14 0.0531515
\(838\) 4.10536e15 0.343170
\(839\) 1.83103e16 1.52056 0.760280 0.649595i \(-0.225062\pi\)
0.760280 + 0.649595i \(0.225062\pi\)
\(840\) 9.87658e15 0.814837
\(841\) −4.18443e15 −0.342972
\(842\) 7.34978e14 0.0598491
\(843\) −4.93651e13 −0.00399364
\(844\) −4.18428e15 −0.336308
\(845\) 5.01138e15 0.400171
\(846\) −1.42954e15 −0.113412
\(847\) 2.11393e16 1.66622
\(848\) −2.04416e16 −1.60081
\(849\) −9.32346e15 −0.725412
\(850\) −1.16416e16 −0.899932
\(851\) −1.57396e15 −0.120887
\(852\) −8.65692e15 −0.660611
\(853\) 8.39617e15 0.636593 0.318296 0.947991i \(-0.396889\pi\)
0.318296 + 0.947991i \(0.396889\pi\)
\(854\) −1.59709e15 −0.120312
\(855\) −3.77610e15 −0.282638
\(856\) 3.40164e15 0.252978
\(857\) 1.97835e16 1.46187 0.730933 0.682449i \(-0.239085\pi\)
0.730933 + 0.682449i \(0.239085\pi\)
\(858\) 2.98130e14 0.0218890
\(859\) 3.67738e15 0.268273 0.134136 0.990963i \(-0.457174\pi\)
0.134136 + 0.990963i \(0.457174\pi\)
\(860\) 3.40437e16 2.46771
\(861\) −9.76993e15 −0.703678
\(862\) 4.09410e15 0.293001
\(863\) 9.74477e15 0.692967 0.346483 0.938056i \(-0.387376\pi\)
0.346483 + 0.938056i \(0.387376\pi\)
\(864\) 1.78958e15 0.126452
\(865\) −2.06899e16 −1.45268
\(866\) −2.15953e15 −0.150664
\(867\) 1.53975e16 1.06744
\(868\) 6.44254e15 0.443812
\(869\) −3.69488e14 −0.0252925
\(870\) −2.93442e15 −0.199602
\(871\) −2.21259e16 −1.49555
\(872\) 8.63772e15 0.580174
\(873\) 5.99587e15 0.400197
\(874\) −2.42528e15 −0.160861
\(875\) −5.85007e16 −3.85582
\(876\) −4.86390e15 −0.318575
\(877\) −2.29169e16 −1.49162 −0.745808 0.666161i \(-0.767937\pi\)
−0.745808 + 0.666161i \(0.767937\pi\)
\(878\) −7.18214e14 −0.0464552
\(879\) 1.01691e15 0.0653645
\(880\) 3.42430e15 0.218734
\(881\) −9.38155e15 −0.595535 −0.297767 0.954638i \(-0.596242\pi\)
−0.297767 + 0.954638i \(0.596242\pi\)
\(882\) 2.36943e15 0.149474
\(883\) −2.38795e16 −1.49707 −0.748533 0.663097i \(-0.769242\pi\)
−0.748533 + 0.663097i \(0.769242\pi\)
\(884\) 2.82715e16 1.76141
\(885\) −2.19035e15 −0.135620
\(886\) −1.09409e15 −0.0673235
\(887\) −1.22475e16 −0.748976 −0.374488 0.927232i \(-0.622182\pi\)
−0.374488 + 0.927232i \(0.622182\pi\)
\(888\) 3.64460e14 0.0221503
\(889\) 1.69914e16 1.02629
\(890\) 9.33951e15 0.560633
\(891\) 2.70240e14 0.0161221
\(892\) −2.78614e15 −0.165195
\(893\) 1.14783e16 0.676388
\(894\) −1.06574e15 −0.0624161
\(895\) 1.92208e16 1.11878
\(896\) 2.40623e16 1.39201
\(897\) 1.60725e16 0.924112
\(898\) 3.25092e14 0.0185775
\(899\) −3.94156e15 −0.223867
\(900\) −1.25745e16 −0.709836
\(901\) 5.76396e16 3.23396
\(902\) 4.40439e14 0.0245612
\(903\) 2.56833e16 1.42353
\(904\) 7.30773e15 0.402583
\(905\) −4.10586e16 −2.24821
\(906\) −2.85184e15 −0.155210
\(907\) −6.19815e15 −0.335291 −0.167645 0.985847i \(-0.553616\pi\)
−0.167645 + 0.985847i \(0.553616\pi\)
\(908\) 1.57073e16 0.844557
\(909\) 7.27189e15 0.388639
\(910\) −1.51054e16 −0.802427
\(911\) 6.49524e15 0.342961 0.171480 0.985188i \(-0.445145\pi\)
0.171480 + 0.985188i \(0.445145\pi\)
\(912\) −4.31907e15 −0.226683
\(913\) −5.11838e15 −0.267020
\(914\) 3.32173e15 0.172250
\(915\) 6.04341e15 0.311506
\(916\) −2.64114e16 −1.35321
\(917\) −1.47500e16 −0.751209
\(918\) −1.51674e15 −0.0767851
\(919\) −5.32116e15 −0.267775 −0.133888 0.990997i \(-0.542746\pi\)
−0.133888 + 0.990997i \(0.542746\pi\)
\(920\) −2.40037e16 −1.20073
\(921\) −7.61716e15 −0.378761
\(922\) −1.57984e15 −0.0780896
\(923\) 2.72637e16 1.33960
\(924\) 2.75614e15 0.134619
\(925\) −3.87814e15 −0.188297
\(926\) 5.66461e15 0.273407
\(927\) −6.43056e15 −0.308539
\(928\) −1.11664e16 −0.532596
\(929\) −2.10013e16 −0.995772 −0.497886 0.867242i \(-0.665890\pi\)
−0.497886 + 0.867242i \(0.665890\pi\)
\(930\) 1.44287e15 0.0680098
\(931\) −1.90251e16 −0.891465
\(932\) −1.22739e16 −0.571737
\(933\) −5.06075e15 −0.234351
\(934\) 3.01718e15 0.138897
\(935\) −9.65555e15 −0.441889
\(936\) −3.72168e15 −0.169326
\(937\) −7.65855e15 −0.346401 −0.173200 0.984887i \(-0.555411\pi\)
−0.173200 + 0.984887i \(0.555411\pi\)
\(938\) 1.21064e16 0.544377
\(939\) 5.83965e15 0.261051
\(940\) 5.51695e16 2.45186
\(941\) −1.63583e16 −0.722760 −0.361380 0.932419i \(-0.617694\pi\)
−0.361380 + 0.932419i \(0.617694\pi\)
\(942\) −1.26103e15 −0.0553916
\(943\) 2.37445e16 1.03693
\(944\) −2.50530e15 −0.108771
\(945\) −1.36924e16 −0.591021
\(946\) −1.15783e15 −0.0496871
\(947\) 1.74846e16 0.745988 0.372994 0.927834i \(-0.378331\pi\)
0.372994 + 0.927834i \(0.378331\pi\)
\(948\) 2.23996e15 0.0950154
\(949\) 1.53182e16 0.646015
\(950\) −5.97576e15 −0.250561
\(951\) 1.19399e16 0.497746
\(952\) −3.18536e16 −1.32025
\(953\) 4.34637e15 0.179108 0.0895542 0.995982i \(-0.471456\pi\)
0.0895542 + 0.995982i \(0.471456\pi\)
\(954\) −3.68482e15 −0.150973
\(955\) −5.68186e16 −2.31458
\(956\) −1.79293e16 −0.726181
\(957\) −1.68621e15 −0.0679042
\(958\) 7.96352e15 0.318856
\(959\) 1.75400e16 0.698278
\(960\) −1.79002e16 −0.708543
\(961\) −2.34704e16 −0.923723
\(962\) −5.57412e14 −0.0218129
\(963\) −4.71585e15 −0.183491
\(964\) −1.93628e16 −0.749110
\(965\) −5.96578e16 −2.29492
\(966\) −8.79422e15 −0.336374
\(967\) −3.47539e16 −1.32177 −0.660887 0.750485i \(-0.729820\pi\)
−0.660887 + 0.750485i \(0.729820\pi\)
\(968\) 1.18965e16 0.449889
\(969\) 1.21786e16 0.457947
\(970\) 1.36954e16 0.512070
\(971\) 1.18674e15 0.0441214 0.0220607 0.999757i \(-0.492977\pi\)
0.0220607 + 0.999757i \(0.492977\pi\)
\(972\) −1.63828e15 −0.0605654
\(973\) 5.80437e16 2.13370
\(974\) 3.10529e15 0.113508
\(975\) 3.96017e16 1.43942
\(976\) 6.91239e15 0.249835
\(977\) −1.83386e16 −0.659092 −0.329546 0.944139i \(-0.606896\pi\)
−0.329546 + 0.944139i \(0.606896\pi\)
\(978\) 5.19947e15 0.185821
\(979\) 5.36679e15 0.190726
\(980\) −9.14424e16 −3.23150
\(981\) −1.19749e16 −0.420815
\(982\) 4.66434e14 0.0162996
\(983\) 5.64873e15 0.196294 0.0981468 0.995172i \(-0.468709\pi\)
0.0981468 + 0.995172i \(0.468709\pi\)
\(984\) −5.49819e15 −0.189997
\(985\) −8.51431e16 −2.92584
\(986\) 9.46398e15 0.323408
\(987\) 4.16211e16 1.41439
\(988\) 1.45120e16 0.490416
\(989\) −6.24198e16 −2.09770
\(990\) 6.17266e14 0.0206290
\(991\) −3.41359e16 −1.13450 −0.567252 0.823544i \(-0.691993\pi\)
−0.567252 + 0.823544i \(0.691993\pi\)
\(992\) 5.49058e15 0.181470
\(993\) −2.31478e16 −0.760831
\(994\) −1.49176e16 −0.487612
\(995\) 2.85171e16 0.926997
\(996\) 3.10293e16 1.00310
\(997\) 5.30851e16 1.70667 0.853335 0.521364i \(-0.174577\pi\)
0.853335 + 0.521364i \(0.174577\pi\)
\(998\) −3.44699e15 −0.110210
\(999\) −5.05268e14 −0.0160661
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.b.1.16 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.b.1.16 27 1.1 even 1 trivial