Properties

Label 273.12.a.c.1.15
Level $273$
Weight $12$
Character 273.1
Self dual yes
Analytic conductor $209.758$
Analytic rank $1$
Dimension $16$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,12,Mod(1,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.1");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 273.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(209.757688293\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 26640 x^{14} - 38138 x^{13} + 279954048 x^{12} + 940095168 x^{11} - 1473489774048 x^{10} - 6951601887328 x^{9} + \cdots + 45\!\cdots\!68 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{12}\cdot 5\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(78.0478\) of defining polynomial
Character \(\chi\) \(=\) 273.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+74.0478 q^{2} -243.000 q^{3} +3435.08 q^{4} -7551.16 q^{5} -17993.6 q^{6} +16807.0 q^{7} +102710. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+74.0478 q^{2} -243.000 q^{3} +3435.08 q^{4} -7551.16 q^{5} -17993.6 q^{6} +16807.0 q^{7} +102710. q^{8} +59049.0 q^{9} -559147. q^{10} +26767.7 q^{11} -834724. q^{12} -371293. q^{13} +1.24452e6 q^{14} +1.83493e6 q^{15} +570411. q^{16} +4.90051e6 q^{17} +4.37245e6 q^{18} +7.70090e6 q^{19} -2.59388e7 q^{20} -4.08410e6 q^{21} +1.98209e6 q^{22} -4.21892e6 q^{23} -2.49585e7 q^{24} +8.19188e6 q^{25} -2.74934e7 q^{26} -1.43489e7 q^{27} +5.77333e7 q^{28} +3.93732e7 q^{29} +1.35873e8 q^{30} +1.64135e8 q^{31} -1.68112e8 q^{32} -6.50454e6 q^{33} +3.62872e8 q^{34} -1.26912e8 q^{35} +2.02838e8 q^{36} -5.78538e7 q^{37} +5.70235e8 q^{38} +9.02242e7 q^{39} -7.75579e8 q^{40} +8.05799e7 q^{41} -3.02419e8 q^{42} +4.19612e8 q^{43} +9.19489e7 q^{44} -4.45888e8 q^{45} -3.12402e8 q^{46} -2.32137e9 q^{47} -1.38610e8 q^{48} +2.82475e8 q^{49} +6.06590e8 q^{50} -1.19082e9 q^{51} -1.27542e9 q^{52} -5.68055e9 q^{53} -1.06250e9 q^{54} -2.02127e8 q^{55} +1.72625e9 q^{56} -1.87132e9 q^{57} +2.91550e9 q^{58} +7.14205e9 q^{59} +6.30313e9 q^{60} -5.20435e9 q^{61} +1.21539e10 q^{62} +9.92437e8 q^{63} -1.36166e10 q^{64} +2.80369e9 q^{65} -4.81647e8 q^{66} +9.22856e8 q^{67} +1.68336e10 q^{68} +1.02520e9 q^{69} -9.39758e9 q^{70} +9.37905e9 q^{71} +6.06492e9 q^{72} -6.60345e8 q^{73} -4.28395e9 q^{74} -1.99063e9 q^{75} +2.64532e10 q^{76} +4.49884e8 q^{77} +6.68090e9 q^{78} -2.52311e10 q^{79} -4.30726e9 q^{80} +3.48678e9 q^{81} +5.96676e9 q^{82} -4.44273e10 q^{83} -1.40292e10 q^{84} -3.70045e10 q^{85} +3.10713e10 q^{86} -9.56768e9 q^{87} +2.74931e9 q^{88} -3.34083e10 q^{89} -3.30171e10 q^{90} -6.24032e9 q^{91} -1.44923e10 q^{92} -3.98849e10 q^{93} -1.71893e11 q^{94} -5.81507e10 q^{95} +4.08513e10 q^{96} -7.25700e10 q^{97} +2.09167e10 q^{98} +1.58060e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 63 q^{2} - 3888 q^{3} + 20761 q^{4} - 3168 q^{5} + 15309 q^{6} + 268912 q^{7} - 187965 q^{8} + 944784 q^{9} + 1056711 q^{10} - 466884 q^{11} - 5044923 q^{12} - 5940688 q^{13} - 1058841 q^{14} + 769824 q^{15} + 40058265 q^{16} + 1753452 q^{17} - 3720087 q^{18} + 4237800 q^{19} - 20710503 q^{20} - 65345616 q^{21} - 37479661 q^{22} - 150481440 q^{23} + 45675495 q^{24} + 150983176 q^{25} + 23391459 q^{26} - 229582512 q^{27} + 348930127 q^{28} - 111411432 q^{29} - 256780773 q^{30} - 90536236 q^{31} - 609941313 q^{32} + 113452812 q^{33} + 443745577 q^{34} - 53244576 q^{35} + 1225916289 q^{36} - 1756337900 q^{37} - 4378868973 q^{38} + 1443587184 q^{39} + 57535383 q^{40} + 649575720 q^{41} + 257298363 q^{42} - 1889554520 q^{43} - 4979587689 q^{44} - 187067232 q^{45} - 3204000867 q^{46} - 4036082940 q^{47} - 9734158395 q^{48} + 4519603984 q^{49} - 15928886862 q^{50} - 426088836 q^{51} - 7708413973 q^{52} + 511144020 q^{53} + 903981141 q^{54} - 8519365572 q^{55} - 3159127755 q^{56} - 1029785400 q^{57} - 7851149577 q^{58} + 3728287296 q^{59} + 5032652229 q^{60} + 26227205052 q^{61} + 2996618490 q^{62} + 15878984688 q^{63} + 51104408465 q^{64} + 1176256224 q^{65} + 9107557623 q^{66} - 5295680024 q^{67} + 7919540325 q^{68} + 36566989920 q^{69} + 17760141777 q^{70} + 17082800928 q^{71} - 11099145285 q^{72} + 21076301488 q^{73} + 52794333675 q^{74} - 36688911768 q^{75} + 81459179177 q^{76} - 7846919388 q^{77} - 5684124537 q^{78} - 83677977852 q^{79} - 163988465427 q^{80} + 55788550416 q^{81} - 61543728760 q^{82} - 72857072340 q^{83} - 84790020861 q^{84} - 12608565060 q^{85} - 20177818011 q^{86} + 27072977976 q^{87} - 202213679643 q^{88} + 32238476676 q^{89} + 62397727839 q^{90} - 99845143216 q^{91} - 487057197033 q^{92} + 22000305348 q^{93} + 183904776602 q^{94} - 143022915504 q^{95} + 148215739059 q^{96} + 6973535140 q^{97} - 17795940687 q^{98} - 27569033316 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 74.0478 1.63624 0.818120 0.575047i \(-0.195016\pi\)
0.818120 + 0.575047i \(0.195016\pi\)
\(3\) −243.000 −0.577350
\(4\) 3435.08 1.67728
\(5\) −7551.16 −1.08063 −0.540317 0.841462i \(-0.681696\pi\)
−0.540317 + 0.841462i \(0.681696\pi\)
\(6\) −17993.6 −0.944684
\(7\) 16807.0 0.377964
\(8\) 102710. 1.10820
\(9\) 59049.0 0.333333
\(10\) −559147. −1.76818
\(11\) 26767.7 0.0501130 0.0250565 0.999686i \(-0.492023\pi\)
0.0250565 + 0.999686i \(0.492023\pi\)
\(12\) −834724. −0.968380
\(13\) −371293. −0.277350
\(14\) 1.24452e6 0.618441
\(15\) 1.83493e6 0.623904
\(16\) 570411. 0.135997
\(17\) 4.90051e6 0.837091 0.418545 0.908196i \(-0.362540\pi\)
0.418545 + 0.908196i \(0.362540\pi\)
\(18\) 4.37245e6 0.545414
\(19\) 7.70090e6 0.713505 0.356752 0.934199i \(-0.383884\pi\)
0.356752 + 0.934199i \(0.383884\pi\)
\(20\) −2.59388e7 −1.81253
\(21\) −4.08410e6 −0.218218
\(22\) 1.98209e6 0.0819970
\(23\) −4.21892e6 −0.136678 −0.0683390 0.997662i \(-0.521770\pi\)
−0.0683390 + 0.997662i \(0.521770\pi\)
\(24\) −2.49585e7 −0.639819
\(25\) 8.19188e6 0.167770
\(26\) −2.74934e7 −0.453812
\(27\) −1.43489e7 −0.192450
\(28\) 5.77333e7 0.633954
\(29\) 3.93732e7 0.356461 0.178230 0.983989i \(-0.442963\pi\)
0.178230 + 0.983989i \(0.442963\pi\)
\(30\) 1.35873e8 1.02086
\(31\) 1.64135e8 1.02970 0.514852 0.857279i \(-0.327847\pi\)
0.514852 + 0.857279i \(0.327847\pi\)
\(32\) −1.68112e8 −0.885676
\(33\) −6.50454e6 −0.0289328
\(34\) 3.62872e8 1.36968
\(35\) −1.26912e8 −0.408441
\(36\) 2.02838e8 0.559095
\(37\) −5.78538e7 −0.137158 −0.0685792 0.997646i \(-0.521847\pi\)
−0.0685792 + 0.997646i \(0.521847\pi\)
\(38\) 5.70235e8 1.16747
\(39\) 9.02242e7 0.160128
\(40\) −7.75579e8 −1.19756
\(41\) 8.05799e7 0.108621 0.0543107 0.998524i \(-0.482704\pi\)
0.0543107 + 0.998524i \(0.482704\pi\)
\(42\) −3.02419e8 −0.357057
\(43\) 4.19612e8 0.435283 0.217641 0.976029i \(-0.430164\pi\)
0.217641 + 0.976029i \(0.430164\pi\)
\(44\) 9.19489e7 0.0840537
\(45\) −4.45888e8 −0.360211
\(46\) −3.12402e8 −0.223638
\(47\) −2.32137e9 −1.47641 −0.738205 0.674576i \(-0.764326\pi\)
−0.738205 + 0.674576i \(0.764326\pi\)
\(48\) −1.38610e8 −0.0785177
\(49\) 2.82475e8 0.142857
\(50\) 6.06590e8 0.274511
\(51\) −1.19082e9 −0.483294
\(52\) −1.27542e9 −0.465195
\(53\) −5.68055e9 −1.86584 −0.932918 0.360090i \(-0.882746\pi\)
−0.932918 + 0.360090i \(0.882746\pi\)
\(54\) −1.06250e9 −0.314895
\(55\) −2.02127e8 −0.0541538
\(56\) 1.72625e9 0.418860
\(57\) −1.87132e9 −0.411942
\(58\) 2.91550e9 0.583255
\(59\) 7.14205e9 1.30058 0.650290 0.759686i \(-0.274648\pi\)
0.650290 + 0.759686i \(0.274648\pi\)
\(60\) 6.30313e9 1.04646
\(61\) −5.20435e9 −0.788955 −0.394477 0.918906i \(-0.629074\pi\)
−0.394477 + 0.918906i \(0.629074\pi\)
\(62\) 1.21539e10 1.68484
\(63\) 9.92437e8 0.125988
\(64\) −1.36166e10 −1.58518
\(65\) 2.80369e9 0.299714
\(66\) −4.81647e8 −0.0473410
\(67\) 9.22856e8 0.0835069 0.0417535 0.999128i \(-0.486706\pi\)
0.0417535 + 0.999128i \(0.486706\pi\)
\(68\) 1.68336e10 1.40404
\(69\) 1.02520e9 0.0789110
\(70\) −9.39758e9 −0.668308
\(71\) 9.37905e9 0.616933 0.308467 0.951235i \(-0.400184\pi\)
0.308467 + 0.951235i \(0.400184\pi\)
\(72\) 6.06492e9 0.369400
\(73\) −6.60345e8 −0.0372817 −0.0186408 0.999826i \(-0.505934\pi\)
−0.0186408 + 0.999826i \(0.505934\pi\)
\(74\) −4.28395e9 −0.224424
\(75\) −1.99063e9 −0.0968618
\(76\) 2.64532e10 1.19675
\(77\) 4.49884e8 0.0189409
\(78\) 6.68090e9 0.262008
\(79\) −2.52311e10 −0.922543 −0.461272 0.887259i \(-0.652607\pi\)
−0.461272 + 0.887259i \(0.652607\pi\)
\(80\) −4.30726e9 −0.146962
\(81\) 3.48678e9 0.111111
\(82\) 5.96676e9 0.177731
\(83\) −4.44273e10 −1.23800 −0.618999 0.785392i \(-0.712462\pi\)
−0.618999 + 0.785392i \(0.712462\pi\)
\(84\) −1.40292e10 −0.366013
\(85\) −3.70045e10 −0.904588
\(86\) 3.10713e10 0.712227
\(87\) −9.56768e9 −0.205803
\(88\) 2.74931e9 0.0555352
\(89\) −3.34083e10 −0.634175 −0.317087 0.948396i \(-0.602705\pi\)
−0.317087 + 0.948396i \(0.602705\pi\)
\(90\) −3.30171e10 −0.589392
\(91\) −6.24032e9 −0.104828
\(92\) −1.44923e10 −0.229248
\(93\) −3.98849e10 −0.594500
\(94\) −1.71893e11 −2.41576
\(95\) −5.81507e10 −0.771037
\(96\) 4.08513e10 0.511345
\(97\) −7.25700e10 −0.858050 −0.429025 0.903293i \(-0.641143\pi\)
−0.429025 + 0.903293i \(0.641143\pi\)
\(98\) 2.09167e10 0.233749
\(99\) 1.58060e9 0.0167043
\(100\) 2.81397e10 0.281397
\(101\) 9.43401e10 0.893159 0.446580 0.894744i \(-0.352642\pi\)
0.446580 + 0.894744i \(0.352642\pi\)
\(102\) −8.81779e10 −0.790786
\(103\) 6.03518e10 0.512963 0.256481 0.966549i \(-0.417437\pi\)
0.256481 + 0.966549i \(0.417437\pi\)
\(104\) −3.81355e10 −0.307359
\(105\) 3.08397e10 0.235814
\(106\) −4.20632e11 −3.05296
\(107\) −6.07139e9 −0.0418483 −0.0209241 0.999781i \(-0.506661\pi\)
−0.0209241 + 0.999781i \(0.506661\pi\)
\(108\) −4.92896e10 −0.322793
\(109\) −1.82295e11 −1.13482 −0.567412 0.823434i \(-0.692055\pi\)
−0.567412 + 0.823434i \(0.692055\pi\)
\(110\) −1.49670e10 −0.0886087
\(111\) 1.40585e10 0.0791885
\(112\) 9.58690e9 0.0514019
\(113\) −3.05548e11 −1.56008 −0.780042 0.625727i \(-0.784802\pi\)
−0.780042 + 0.625727i \(0.784802\pi\)
\(114\) −1.38567e11 −0.674037
\(115\) 3.18578e10 0.147699
\(116\) 1.35250e11 0.597885
\(117\) −2.19245e10 −0.0924500
\(118\) 5.28853e11 2.12806
\(119\) 8.23629e10 0.316390
\(120\) 1.88466e11 0.691410
\(121\) −2.84595e11 −0.997489
\(122\) −3.85370e11 −1.29092
\(123\) −1.95809e10 −0.0627126
\(124\) 5.63817e11 1.72711
\(125\) 3.06851e11 0.899336
\(126\) 7.34877e10 0.206147
\(127\) −8.29857e10 −0.222886 −0.111443 0.993771i \(-0.535547\pi\)
−0.111443 + 0.993771i \(0.535547\pi\)
\(128\) −6.63982e11 −1.70805
\(129\) −1.01966e11 −0.251310
\(130\) 2.07607e11 0.490404
\(131\) −3.54952e11 −0.803854 −0.401927 0.915672i \(-0.631659\pi\)
−0.401927 + 0.915672i \(0.631659\pi\)
\(132\) −2.23436e10 −0.0485284
\(133\) 1.29429e11 0.269679
\(134\) 6.83354e10 0.136637
\(135\) 1.08351e11 0.207968
\(136\) 5.03332e11 0.927663
\(137\) −1.81410e11 −0.321142 −0.160571 0.987024i \(-0.551334\pi\)
−0.160571 + 0.987024i \(0.551334\pi\)
\(138\) 7.59137e10 0.129117
\(139\) −1.56877e11 −0.256436 −0.128218 0.991746i \(-0.540926\pi\)
−0.128218 + 0.991746i \(0.540926\pi\)
\(140\) −4.35954e11 −0.685072
\(141\) 5.64094e11 0.852406
\(142\) 6.94498e11 1.00945
\(143\) −9.93864e9 −0.0138988
\(144\) 3.36822e10 0.0453322
\(145\) −2.97313e11 −0.385203
\(146\) −4.88971e10 −0.0610018
\(147\) −6.86415e10 −0.0824786
\(148\) −1.98732e11 −0.230054
\(149\) 8.00500e11 0.892970 0.446485 0.894791i \(-0.352676\pi\)
0.446485 + 0.894791i \(0.352676\pi\)
\(150\) −1.47401e11 −0.158489
\(151\) 1.03859e11 0.107664 0.0538319 0.998550i \(-0.482856\pi\)
0.0538319 + 0.998550i \(0.482856\pi\)
\(152\) 7.90960e11 0.790705
\(153\) 2.89370e11 0.279030
\(154\) 3.33129e10 0.0309919
\(155\) −1.23941e12 −1.11273
\(156\) 3.09927e11 0.268580
\(157\) 5.90129e11 0.493741 0.246870 0.969049i \(-0.420598\pi\)
0.246870 + 0.969049i \(0.420598\pi\)
\(158\) −1.86831e12 −1.50950
\(159\) 1.38037e12 1.07724
\(160\) 1.26944e12 0.957091
\(161\) −7.09074e10 −0.0516594
\(162\) 2.58189e11 0.181805
\(163\) −2.44174e12 −1.66214 −0.831069 0.556169i \(-0.812271\pi\)
−0.831069 + 0.556169i \(0.812271\pi\)
\(164\) 2.76798e11 0.182189
\(165\) 4.91168e10 0.0312657
\(166\) −3.28974e12 −2.02566
\(167\) −1.06031e12 −0.631675 −0.315838 0.948813i \(-0.602285\pi\)
−0.315838 + 0.948813i \(0.602285\pi\)
\(168\) −4.19478e11 −0.241829
\(169\) 1.37858e11 0.0769231
\(170\) −2.74011e12 −1.48012
\(171\) 4.54731e11 0.237835
\(172\) 1.44140e12 0.730092
\(173\) −2.75822e12 −1.35324 −0.676620 0.736332i \(-0.736556\pi\)
−0.676620 + 0.736332i \(0.736556\pi\)
\(174\) −7.08466e11 −0.336743
\(175\) 1.37681e11 0.0634110
\(176\) 1.52686e10 0.00681520
\(177\) −1.73552e12 −0.750890
\(178\) −2.47381e12 −1.03766
\(179\) −3.22952e12 −1.31355 −0.656774 0.754088i \(-0.728079\pi\)
−0.656774 + 0.754088i \(0.728079\pi\)
\(180\) −1.53166e12 −0.604176
\(181\) −3.90867e10 −0.0149554 −0.00747768 0.999972i \(-0.502380\pi\)
−0.00747768 + 0.999972i \(0.502380\pi\)
\(182\) −4.62082e11 −0.171525
\(183\) 1.26466e12 0.455503
\(184\) −4.33325e11 −0.151466
\(185\) 4.36864e11 0.148218
\(186\) −2.95339e12 −0.972746
\(187\) 1.31175e11 0.0419491
\(188\) −7.97410e12 −2.47636
\(189\) −2.41162e11 −0.0727393
\(190\) −4.30593e12 −1.26160
\(191\) −2.64705e12 −0.753493 −0.376747 0.926316i \(-0.622957\pi\)
−0.376747 + 0.926316i \(0.622957\pi\)
\(192\) 3.30882e12 0.915201
\(193\) −1.33531e12 −0.358935 −0.179467 0.983764i \(-0.557437\pi\)
−0.179467 + 0.983764i \(0.557437\pi\)
\(194\) −5.37365e12 −1.40398
\(195\) −6.81297e11 −0.173040
\(196\) 9.70324e11 0.239612
\(197\) −7.91698e12 −1.90106 −0.950529 0.310636i \(-0.899458\pi\)
−0.950529 + 0.310636i \(0.899458\pi\)
\(198\) 1.17040e11 0.0273323
\(199\) 4.02527e12 0.914331 0.457165 0.889382i \(-0.348865\pi\)
0.457165 + 0.889382i \(0.348865\pi\)
\(200\) 8.41387e11 0.185922
\(201\) −2.24254e11 −0.0482127
\(202\) 6.98568e12 1.46142
\(203\) 6.61745e11 0.134729
\(204\) −4.09057e12 −0.810622
\(205\) −6.08471e11 −0.117380
\(206\) 4.46892e12 0.839330
\(207\) −2.49123e11 −0.0455593
\(208\) −2.11790e11 −0.0377187
\(209\) 2.06135e11 0.0357559
\(210\) 2.28361e12 0.385848
\(211\) 6.06937e12 0.999056 0.499528 0.866298i \(-0.333507\pi\)
0.499528 + 0.866298i \(0.333507\pi\)
\(212\) −1.95131e13 −3.12953
\(213\) −2.27911e12 −0.356186
\(214\) −4.49573e11 −0.0684739
\(215\) −3.16856e12 −0.470381
\(216\) −1.47378e12 −0.213273
\(217\) 2.75862e12 0.389192
\(218\) −1.34985e13 −1.85685
\(219\) 1.60464e11 0.0215246
\(220\) −6.94321e11 −0.0908313
\(221\) −1.81953e12 −0.232167
\(222\) 1.04100e12 0.129571
\(223\) −3.68640e12 −0.447636 −0.223818 0.974631i \(-0.571852\pi\)
−0.223818 + 0.974631i \(0.571852\pi\)
\(224\) −2.82546e12 −0.334754
\(225\) 4.83722e11 0.0559232
\(226\) −2.26252e13 −2.55267
\(227\) 8.41053e12 0.926149 0.463075 0.886319i \(-0.346746\pi\)
0.463075 + 0.886319i \(0.346746\pi\)
\(228\) −6.42813e12 −0.690944
\(229\) 2.57053e12 0.269729 0.134865 0.990864i \(-0.456940\pi\)
0.134865 + 0.990864i \(0.456940\pi\)
\(230\) 2.35900e12 0.241671
\(231\) −1.09322e11 −0.0109356
\(232\) 4.04402e12 0.395029
\(233\) −1.07349e12 −0.102409 −0.0512047 0.998688i \(-0.516306\pi\)
−0.0512047 + 0.998688i \(0.516306\pi\)
\(234\) −1.62346e12 −0.151271
\(235\) 1.75291e13 1.59546
\(236\) 2.45335e13 2.18144
\(237\) 6.13115e12 0.532631
\(238\) 6.09879e12 0.517691
\(239\) −1.27872e12 −0.106069 −0.0530343 0.998593i \(-0.516889\pi\)
−0.0530343 + 0.998593i \(0.516889\pi\)
\(240\) 1.04667e12 0.0848488
\(241\) 7.22056e12 0.572107 0.286053 0.958214i \(-0.407657\pi\)
0.286053 + 0.958214i \(0.407657\pi\)
\(242\) −2.10736e13 −1.63213
\(243\) −8.47289e11 −0.0641500
\(244\) −1.78773e13 −1.32330
\(245\) −2.13302e12 −0.154376
\(246\) −1.44992e12 −0.102613
\(247\) −2.85929e12 −0.197891
\(248\) 1.68583e13 1.14112
\(249\) 1.07958e13 0.714759
\(250\) 2.27216e13 1.47153
\(251\) 2.42498e13 1.53639 0.768197 0.640214i \(-0.221154\pi\)
0.768197 + 0.640214i \(0.221154\pi\)
\(252\) 3.40910e12 0.211318
\(253\) −1.12931e11 −0.00684934
\(254\) −6.14491e12 −0.364695
\(255\) 8.99211e12 0.522264
\(256\) −2.12797e13 −1.20961
\(257\) 4.89674e12 0.272442 0.136221 0.990678i \(-0.456504\pi\)
0.136221 + 0.990678i \(0.456504\pi\)
\(258\) −7.55033e12 −0.411204
\(259\) −9.72349e11 −0.0518410
\(260\) 9.63090e12 0.502705
\(261\) 2.32495e12 0.118820
\(262\) −2.62834e13 −1.31530
\(263\) −8.13628e12 −0.398721 −0.199361 0.979926i \(-0.563886\pi\)
−0.199361 + 0.979926i \(0.563886\pi\)
\(264\) −6.68081e11 −0.0320633
\(265\) 4.28948e13 2.01628
\(266\) 9.58394e12 0.441260
\(267\) 8.11821e12 0.366141
\(268\) 3.17008e12 0.140065
\(269\) 4.93951e11 0.0213819 0.0106910 0.999943i \(-0.496597\pi\)
0.0106910 + 0.999943i \(0.496597\pi\)
\(270\) 8.02314e12 0.340286
\(271\) 8.89977e12 0.369869 0.184934 0.982751i \(-0.440793\pi\)
0.184934 + 0.982751i \(0.440793\pi\)
\(272\) 2.79531e12 0.113841
\(273\) 1.51640e12 0.0605228
\(274\) −1.34330e13 −0.525466
\(275\) 2.19277e11 0.00840744
\(276\) 3.52163e12 0.132356
\(277\) −1.30989e11 −0.00482608 −0.00241304 0.999997i \(-0.500768\pi\)
−0.00241304 + 0.999997i \(0.500768\pi\)
\(278\) −1.16164e13 −0.419591
\(279\) 9.69203e12 0.343235
\(280\) −1.30352e13 −0.452634
\(281\) −7.91457e12 −0.269490 −0.134745 0.990880i \(-0.543022\pi\)
−0.134745 + 0.990880i \(0.543022\pi\)
\(282\) 4.17699e13 1.39474
\(283\) −4.12306e12 −0.135019 −0.0675094 0.997719i \(-0.521505\pi\)
−0.0675094 + 0.997719i \(0.521505\pi\)
\(284\) 3.22178e13 1.03477
\(285\) 1.41306e13 0.445159
\(286\) −7.35935e11 −0.0227419
\(287\) 1.35431e12 0.0410550
\(288\) −9.92687e12 −0.295225
\(289\) −1.02569e13 −0.299279
\(290\) −2.20154e13 −0.630285
\(291\) 1.76345e13 0.495395
\(292\) −2.26834e12 −0.0625319
\(293\) 7.85049e11 0.0212385 0.0106193 0.999944i \(-0.496620\pi\)
0.0106193 + 0.999944i \(0.496620\pi\)
\(294\) −5.08275e12 −0.134955
\(295\) −5.39307e13 −1.40545
\(296\) −5.94217e12 −0.151999
\(297\) −3.84087e11 −0.00964425
\(298\) 5.92753e13 1.46111
\(299\) 1.56646e12 0.0379076
\(300\) −6.83795e12 −0.162465
\(301\) 7.05242e12 0.164521
\(302\) 7.69051e12 0.176164
\(303\) −2.29246e13 −0.515666
\(304\) 4.39268e12 0.0970342
\(305\) 3.92989e13 0.852571
\(306\) 2.14272e13 0.456561
\(307\) 3.69209e13 0.772700 0.386350 0.922352i \(-0.373736\pi\)
0.386350 + 0.922352i \(0.373736\pi\)
\(308\) 1.54539e12 0.0317693
\(309\) −1.46655e13 −0.296159
\(310\) −9.17757e13 −1.82070
\(311\) −8.09125e12 −0.157701 −0.0788503 0.996886i \(-0.525125\pi\)
−0.0788503 + 0.996886i \(0.525125\pi\)
\(312\) 9.26693e12 0.177454
\(313\) −3.29887e13 −0.620686 −0.310343 0.950625i \(-0.600444\pi\)
−0.310343 + 0.950625i \(0.600444\pi\)
\(314\) 4.36978e13 0.807879
\(315\) −7.49405e12 −0.136147
\(316\) −8.66707e13 −1.54737
\(317\) 9.24380e13 1.62190 0.810951 0.585114i \(-0.198950\pi\)
0.810951 + 0.585114i \(0.198950\pi\)
\(318\) 1.02214e14 1.76262
\(319\) 1.05393e12 0.0178633
\(320\) 1.02821e14 1.71299
\(321\) 1.47535e12 0.0241611
\(322\) −5.25054e12 −0.0845272
\(323\) 3.77384e13 0.597268
\(324\) 1.19774e13 0.186365
\(325\) −3.04159e12 −0.0465309
\(326\) −1.80805e14 −2.71966
\(327\) 4.42976e13 0.655191
\(328\) 8.27636e12 0.120374
\(329\) −3.90153e13 −0.558031
\(330\) 3.63699e12 0.0511582
\(331\) 8.77559e13 1.21401 0.607005 0.794698i \(-0.292371\pi\)
0.607005 + 0.794698i \(0.292371\pi\)
\(332\) −1.52611e14 −2.07647
\(333\) −3.41621e12 −0.0457195
\(334\) −7.85139e13 −1.03357
\(335\) −6.96863e12 −0.0902404
\(336\) −2.32962e12 −0.0296769
\(337\) 1.55668e13 0.195090 0.0975448 0.995231i \(-0.468901\pi\)
0.0975448 + 0.995231i \(0.468901\pi\)
\(338\) 1.02081e13 0.125865
\(339\) 7.42482e13 0.900715
\(340\) −1.27113e14 −1.51725
\(341\) 4.39352e12 0.0516016
\(342\) 3.36718e13 0.389155
\(343\) 4.74756e12 0.0539949
\(344\) 4.30983e13 0.482380
\(345\) −7.74143e12 −0.0852739
\(346\) −2.04240e14 −2.21423
\(347\) −1.33313e14 −1.42253 −0.711264 0.702925i \(-0.751877\pi\)
−0.711264 + 0.702925i \(0.751877\pi\)
\(348\) −3.28657e13 −0.345189
\(349\) −8.67103e12 −0.0896459 −0.0448230 0.998995i \(-0.514272\pi\)
−0.0448230 + 0.998995i \(0.514272\pi\)
\(350\) 1.01950e13 0.103756
\(351\) 5.32765e12 0.0533761
\(352\) −4.49997e12 −0.0443839
\(353\) −8.26111e13 −0.802190 −0.401095 0.916036i \(-0.631370\pi\)
−0.401095 + 0.916036i \(0.631370\pi\)
\(354\) −1.28511e14 −1.22864
\(355\) −7.08227e13 −0.666679
\(356\) −1.14760e14 −1.06369
\(357\) −2.00142e13 −0.182668
\(358\) −2.39139e14 −2.14928
\(359\) −1.08444e14 −0.959810 −0.479905 0.877321i \(-0.659329\pi\)
−0.479905 + 0.877321i \(0.659329\pi\)
\(360\) −4.57972e13 −0.399186
\(361\) −5.71863e13 −0.490911
\(362\) −2.89428e12 −0.0244706
\(363\) 6.91566e13 0.575900
\(364\) −2.14360e13 −0.175827
\(365\) 4.98637e12 0.0402878
\(366\) 9.36450e13 0.745313
\(367\) −6.54309e13 −0.513003 −0.256501 0.966544i \(-0.582570\pi\)
−0.256501 + 0.966544i \(0.582570\pi\)
\(368\) −2.40652e12 −0.0185877
\(369\) 4.75816e12 0.0362071
\(370\) 3.23488e13 0.242520
\(371\) −9.54730e13 −0.705219
\(372\) −1.37008e14 −0.997146
\(373\) −1.56255e14 −1.12056 −0.560279 0.828304i \(-0.689306\pi\)
−0.560279 + 0.828304i \(0.689306\pi\)
\(374\) 9.71324e12 0.0686389
\(375\) −7.45647e13 −0.519232
\(376\) −2.38428e14 −1.63616
\(377\) −1.46190e13 −0.0988644
\(378\) −1.78575e13 −0.119019
\(379\) 1.97868e14 1.29975 0.649875 0.760041i \(-0.274821\pi\)
0.649875 + 0.760041i \(0.274821\pi\)
\(380\) −1.99752e14 −1.29325
\(381\) 2.01655e13 0.128683
\(382\) −1.96009e14 −1.23290
\(383\) 1.37771e14 0.854207 0.427103 0.904203i \(-0.359534\pi\)
0.427103 + 0.904203i \(0.359534\pi\)
\(384\) 1.61348e14 0.986145
\(385\) −3.39715e12 −0.0204682
\(386\) −9.88765e13 −0.587304
\(387\) 2.47777e13 0.145094
\(388\) −2.49283e14 −1.43919
\(389\) −1.98544e14 −1.13014 −0.565072 0.825042i \(-0.691152\pi\)
−0.565072 + 0.825042i \(0.691152\pi\)
\(390\) −5.04486e13 −0.283135
\(391\) −2.06749e13 −0.114412
\(392\) 2.90130e13 0.158314
\(393\) 8.62533e13 0.464105
\(394\) −5.86235e14 −3.11059
\(395\) 1.90524e14 0.996932
\(396\) 5.42949e12 0.0280179
\(397\) −3.35455e14 −1.70721 −0.853605 0.520922i \(-0.825588\pi\)
−0.853605 + 0.520922i \(0.825588\pi\)
\(398\) 2.98062e14 1.49606
\(399\) −3.14513e13 −0.155700
\(400\) 4.67274e12 0.0228161
\(401\) 3.09515e14 1.49069 0.745346 0.666678i \(-0.232284\pi\)
0.745346 + 0.666678i \(0.232284\pi\)
\(402\) −1.66055e13 −0.0788877
\(403\) −6.09423e13 −0.285589
\(404\) 3.24066e14 1.49808
\(405\) −2.63293e13 −0.120070
\(406\) 4.90008e13 0.220450
\(407\) −1.54861e12 −0.00687343
\(408\) −1.22310e14 −0.535586
\(409\) 6.06851e12 0.0262183 0.0131091 0.999914i \(-0.495827\pi\)
0.0131091 + 0.999914i \(0.495827\pi\)
\(410\) −4.50560e13 −0.192062
\(411\) 4.40826e13 0.185412
\(412\) 2.07313e14 0.860384
\(413\) 1.20036e14 0.491573
\(414\) −1.84470e13 −0.0745460
\(415\) 3.35477e14 1.33782
\(416\) 6.24189e13 0.245642
\(417\) 3.81212e13 0.148053
\(418\) 1.52639e13 0.0585052
\(419\) −2.80816e13 −0.106229 −0.0531147 0.998588i \(-0.516915\pi\)
−0.0531147 + 0.998588i \(0.516915\pi\)
\(420\) 1.05937e14 0.395526
\(421\) 2.30457e14 0.849254 0.424627 0.905368i \(-0.360405\pi\)
0.424627 + 0.905368i \(0.360405\pi\)
\(422\) 4.49423e14 1.63470
\(423\) −1.37075e14 −0.492137
\(424\) −5.83449e14 −2.06772
\(425\) 4.01444e13 0.140438
\(426\) −1.68763e14 −0.582807
\(427\) −8.74695e13 −0.298197
\(428\) −2.08557e13 −0.0701914
\(429\) 2.41509e12 0.00802450
\(430\) −2.34625e14 −0.769657
\(431\) 2.21137e14 0.716202 0.358101 0.933683i \(-0.383424\pi\)
0.358101 + 0.933683i \(0.383424\pi\)
\(432\) −8.18477e12 −0.0261726
\(433\) −2.61484e14 −0.825586 −0.412793 0.910825i \(-0.635447\pi\)
−0.412793 + 0.910825i \(0.635447\pi\)
\(434\) 2.04270e14 0.636812
\(435\) 7.22471e13 0.222397
\(436\) −6.26197e14 −1.90342
\(437\) −3.24895e13 −0.0975204
\(438\) 1.18820e13 0.0352194
\(439\) 5.90911e14 1.72969 0.864843 0.502042i \(-0.167418\pi\)
0.864843 + 0.502042i \(0.167418\pi\)
\(440\) −2.07604e13 −0.0600132
\(441\) 1.66799e13 0.0476190
\(442\) −1.34732e14 −0.379881
\(443\) −2.36657e14 −0.659021 −0.329511 0.944152i \(-0.606884\pi\)
−0.329511 + 0.944152i \(0.606884\pi\)
\(444\) 4.82920e13 0.132822
\(445\) 2.52271e14 0.685311
\(446\) −2.72969e14 −0.732440
\(447\) −1.94521e14 −0.515556
\(448\) −2.28853e14 −0.599140
\(449\) 6.05587e14 1.56611 0.783054 0.621954i \(-0.213661\pi\)
0.783054 + 0.621954i \(0.213661\pi\)
\(450\) 3.58186e13 0.0915038
\(451\) 2.15693e12 0.00544334
\(452\) −1.04958e15 −2.61670
\(453\) −2.52377e13 −0.0621597
\(454\) 6.22781e14 1.51540
\(455\) 4.71217e13 0.113281
\(456\) −1.92203e14 −0.456514
\(457\) −2.20199e14 −0.516746 −0.258373 0.966045i \(-0.583186\pi\)
−0.258373 + 0.966045i \(0.583186\pi\)
\(458\) 1.90342e14 0.441342
\(459\) −7.03170e13 −0.161098
\(460\) 1.09434e14 0.247733
\(461\) 1.02556e14 0.229406 0.114703 0.993400i \(-0.463408\pi\)
0.114703 + 0.993400i \(0.463408\pi\)
\(462\) −8.09504e12 −0.0178932
\(463\) 4.97674e14 1.08705 0.543525 0.839393i \(-0.317089\pi\)
0.543525 + 0.839393i \(0.317089\pi\)
\(464\) 2.24589e13 0.0484774
\(465\) 3.01177e14 0.642437
\(466\) −7.94894e13 −0.167566
\(467\) 8.45430e14 1.76131 0.880653 0.473763i \(-0.157105\pi\)
0.880653 + 0.473763i \(0.157105\pi\)
\(468\) −7.53123e13 −0.155065
\(469\) 1.55104e13 0.0315626
\(470\) 1.29799e15 2.61055
\(471\) −1.43401e14 −0.285061
\(472\) 7.33560e14 1.44130
\(473\) 1.12320e13 0.0218133
\(474\) 4.53998e14 0.871512
\(475\) 6.30848e13 0.119704
\(476\) 2.82923e14 0.530677
\(477\) −3.35431e14 −0.621945
\(478\) −9.46864e13 −0.173554
\(479\) −7.91708e14 −1.43456 −0.717281 0.696784i \(-0.754614\pi\)
−0.717281 + 0.696784i \(0.754614\pi\)
\(480\) −3.08475e14 −0.552577
\(481\) 2.14807e13 0.0380409
\(482\) 5.34667e14 0.936105
\(483\) 1.72305e13 0.0298256
\(484\) −9.77606e14 −1.67307
\(485\) 5.47987e14 0.927238
\(486\) −6.27399e13 −0.104965
\(487\) −7.26034e14 −1.20101 −0.600506 0.799620i \(-0.705034\pi\)
−0.600506 + 0.799620i \(0.705034\pi\)
\(488\) −5.34538e14 −0.874319
\(489\) 5.93342e14 0.959636
\(490\) −1.57945e14 −0.252597
\(491\) 2.64224e14 0.417853 0.208926 0.977931i \(-0.433003\pi\)
0.208926 + 0.977931i \(0.433003\pi\)
\(492\) −6.72619e13 −0.105187
\(493\) 1.92949e14 0.298390
\(494\) −2.11724e14 −0.323797
\(495\) −1.19354e13 −0.0180513
\(496\) 9.36246e13 0.140036
\(497\) 1.57634e14 0.233179
\(498\) 7.99407e14 1.16952
\(499\) −3.62474e14 −0.524474 −0.262237 0.965003i \(-0.584460\pi\)
−0.262237 + 0.965003i \(0.584460\pi\)
\(500\) 1.05406e15 1.50844
\(501\) 2.57656e14 0.364698
\(502\) 1.79564e15 2.51391
\(503\) −1.20660e15 −1.67086 −0.835431 0.549595i \(-0.814782\pi\)
−0.835431 + 0.549595i \(0.814782\pi\)
\(504\) 1.01933e14 0.139620
\(505\) −7.12377e14 −0.965178
\(506\) −8.36227e12 −0.0112072
\(507\) −3.34996e13 −0.0444116
\(508\) −2.85062e14 −0.373843
\(509\) 3.83919e14 0.498072 0.249036 0.968494i \(-0.419886\pi\)
0.249036 + 0.968494i \(0.419886\pi\)
\(510\) 6.65846e14 0.854550
\(511\) −1.10984e13 −0.0140912
\(512\) −2.15879e14 −0.271160
\(513\) −1.10500e14 −0.137314
\(514\) 3.62593e14 0.445781
\(515\) −4.55726e14 −0.554325
\(516\) −3.50260e14 −0.421519
\(517\) −6.21378e13 −0.0739874
\(518\) −7.20003e13 −0.0848244
\(519\) 6.70247e14 0.781294
\(520\) 2.87967e14 0.332143
\(521\) −2.07500e14 −0.236815 −0.118408 0.992965i \(-0.537779\pi\)
−0.118408 + 0.992965i \(0.537779\pi\)
\(522\) 1.72157e14 0.194418
\(523\) 7.56464e14 0.845335 0.422668 0.906285i \(-0.361094\pi\)
0.422668 + 0.906285i \(0.361094\pi\)
\(524\) −1.21929e15 −1.34829
\(525\) −3.34564e13 −0.0366103
\(526\) −6.02473e14 −0.652404
\(527\) 8.04347e14 0.861956
\(528\) −3.71026e12 −0.00393476
\(529\) −9.35010e14 −0.981319
\(530\) 3.17626e15 3.29913
\(531\) 4.21731e14 0.433526
\(532\) 4.44599e14 0.452329
\(533\) −2.99187e13 −0.0301262
\(534\) 6.01136e14 0.599095
\(535\) 4.58461e13 0.0452227
\(536\) 9.47865e13 0.0925423
\(537\) 7.84772e14 0.758377
\(538\) 3.65760e13 0.0349859
\(539\) 7.56120e12 0.00715900
\(540\) 3.72194e14 0.348821
\(541\) 3.73843e14 0.346820 0.173410 0.984850i \(-0.444521\pi\)
0.173410 + 0.984850i \(0.444521\pi\)
\(542\) 6.59008e14 0.605194
\(543\) 9.49807e12 0.00863448
\(544\) −8.23837e14 −0.741391
\(545\) 1.37654e15 1.22633
\(546\) 1.12286e14 0.0990298
\(547\) 1.25122e14 0.109246 0.0546229 0.998507i \(-0.482604\pi\)
0.0546229 + 0.998507i \(0.482604\pi\)
\(548\) −6.23157e14 −0.538647
\(549\) −3.07312e14 −0.262985
\(550\) 1.62370e13 0.0137566
\(551\) 3.03209e14 0.254336
\(552\) 1.05298e14 0.0874491
\(553\) −4.24059e14 −0.348689
\(554\) −9.69941e12 −0.00789663
\(555\) −1.06158e14 −0.0855738
\(556\) −5.38886e14 −0.430116
\(557\) −1.67532e15 −1.32402 −0.662009 0.749496i \(-0.730296\pi\)
−0.662009 + 0.749496i \(0.730296\pi\)
\(558\) 7.17673e14 0.561615
\(559\) −1.55799e14 −0.120726
\(560\) −7.23922e13 −0.0555466
\(561\) −3.18756e13 −0.0242193
\(562\) −5.86056e14 −0.440950
\(563\) 3.81298e14 0.284098 0.142049 0.989860i \(-0.454631\pi\)
0.142049 + 0.989860i \(0.454631\pi\)
\(564\) 1.93771e15 1.42973
\(565\) 2.30724e15 1.68588
\(566\) −3.05304e14 −0.220923
\(567\) 5.86024e13 0.0419961
\(568\) 9.63322e14 0.683684
\(569\) −2.07246e15 −1.45669 −0.728346 0.685210i \(-0.759711\pi\)
−0.728346 + 0.685210i \(0.759711\pi\)
\(570\) 1.04634e15 0.728387
\(571\) 5.18865e14 0.357730 0.178865 0.983874i \(-0.442757\pi\)
0.178865 + 0.983874i \(0.442757\pi\)
\(572\) −3.41400e13 −0.0233123
\(573\) 6.43234e14 0.435029
\(574\) 1.00283e14 0.0671759
\(575\) −3.45609e13 −0.0229304
\(576\) −8.04044e14 −0.528392
\(577\) −3.40748e14 −0.221802 −0.110901 0.993831i \(-0.535374\pi\)
−0.110901 + 0.993831i \(0.535374\pi\)
\(578\) −7.59499e14 −0.489693
\(579\) 3.24479e14 0.207231
\(580\) −1.02129e15 −0.646095
\(581\) −7.46689e14 −0.467919
\(582\) 1.30580e15 0.810586
\(583\) −1.52055e14 −0.0935026
\(584\) −6.78241e13 −0.0413155
\(585\) 1.65555e14 0.0999046
\(586\) 5.81311e13 0.0347514
\(587\) −1.68276e15 −0.996579 −0.498289 0.867011i \(-0.666038\pi\)
−0.498289 + 0.867011i \(0.666038\pi\)
\(588\) −2.35789e14 −0.138340
\(589\) 1.26399e15 0.734699
\(590\) −3.99345e15 −2.29965
\(591\) 1.92383e15 1.09758
\(592\) −3.30005e13 −0.0186531
\(593\) −1.14269e15 −0.639924 −0.319962 0.947430i \(-0.603670\pi\)
−0.319962 + 0.947430i \(0.603670\pi\)
\(594\) −2.84408e13 −0.0157803
\(595\) −6.21935e14 −0.341902
\(596\) 2.74978e15 1.49776
\(597\) −9.78141e14 −0.527889
\(598\) 1.15993e14 0.0620260
\(599\) 6.29717e14 0.333655 0.166828 0.985986i \(-0.446648\pi\)
0.166828 + 0.985986i \(0.446648\pi\)
\(600\) −2.04457e14 −0.107342
\(601\) 1.27665e14 0.0664142 0.0332071 0.999448i \(-0.489428\pi\)
0.0332071 + 0.999448i \(0.489428\pi\)
\(602\) 5.22216e14 0.269197
\(603\) 5.44937e13 0.0278356
\(604\) 3.56763e14 0.180583
\(605\) 2.14902e15 1.07792
\(606\) −1.69752e15 −0.843753
\(607\) 2.44083e15 1.20226 0.601131 0.799150i \(-0.294717\pi\)
0.601131 + 0.799150i \(0.294717\pi\)
\(608\) −1.29462e15 −0.631934
\(609\) −1.60804e14 −0.0777861
\(610\) 2.90999e15 1.39501
\(611\) 8.61910e14 0.409483
\(612\) 9.94009e14 0.468013
\(613\) −4.98053e14 −0.232404 −0.116202 0.993226i \(-0.537072\pi\)
−0.116202 + 0.993226i \(0.537072\pi\)
\(614\) 2.73391e15 1.26432
\(615\) 1.47859e14 0.0677693
\(616\) 4.62076e13 0.0209903
\(617\) 3.55669e15 1.60132 0.800660 0.599119i \(-0.204482\pi\)
0.800660 + 0.599119i \(0.204482\pi\)
\(618\) −1.08595e15 −0.484587
\(619\) 3.46294e15 1.53161 0.765803 0.643076i \(-0.222342\pi\)
0.765803 + 0.643076i \(0.222342\pi\)
\(620\) −4.25748e15 −1.86637
\(621\) 6.05369e13 0.0263037
\(622\) −5.99139e14 −0.258036
\(623\) −5.61493e14 −0.239696
\(624\) 5.14649e13 0.0217769
\(625\) −2.71707e15 −1.13962
\(626\) −2.44274e15 −1.01559
\(627\) −5.00908e13 −0.0206437
\(628\) 2.02714e15 0.828143
\(629\) −2.83513e14 −0.114814
\(630\) −5.54918e14 −0.222769
\(631\) −9.75899e14 −0.388368 −0.194184 0.980965i \(-0.562206\pi\)
−0.194184 + 0.980965i \(0.562206\pi\)
\(632\) −2.59148e15 −1.02236
\(633\) −1.47486e15 −0.576806
\(634\) 6.84483e15 2.65382
\(635\) 6.26638e14 0.240858
\(636\) 4.74169e15 1.80684
\(637\) −1.04881e14 −0.0396214
\(638\) 7.80410e13 0.0292287
\(639\) 5.53824e14 0.205644
\(640\) 5.01383e15 1.84578
\(641\) 8.49728e14 0.310142 0.155071 0.987903i \(-0.450439\pi\)
0.155071 + 0.987903i \(0.450439\pi\)
\(642\) 1.09246e14 0.0395334
\(643\) −2.73146e15 −0.980019 −0.490009 0.871717i \(-0.663007\pi\)
−0.490009 + 0.871717i \(0.663007\pi\)
\(644\) −2.43572e14 −0.0866475
\(645\) 7.69959e14 0.271575
\(646\) 2.79444e15 0.977274
\(647\) 3.19400e15 1.10755 0.553773 0.832668i \(-0.313188\pi\)
0.553773 + 0.832668i \(0.313188\pi\)
\(648\) 3.58128e14 0.123133
\(649\) 1.91176e14 0.0651759
\(650\) −2.25223e14 −0.0761358
\(651\) −6.70345e14 −0.224700
\(652\) −8.38755e15 −2.78788
\(653\) 6.96891e14 0.229690 0.114845 0.993383i \(-0.463363\pi\)
0.114845 + 0.993383i \(0.463363\pi\)
\(654\) 3.28014e15 1.07205
\(655\) 2.68030e15 0.868672
\(656\) 4.59636e13 0.0147721
\(657\) −3.89927e13 −0.0124272
\(658\) −2.88900e15 −0.913072
\(659\) 1.50402e15 0.471393 0.235697 0.971827i \(-0.424263\pi\)
0.235697 + 0.971827i \(0.424263\pi\)
\(660\) 1.68720e14 0.0524415
\(661\) 4.38530e15 1.35173 0.675867 0.737024i \(-0.263770\pi\)
0.675867 + 0.737024i \(0.263770\pi\)
\(662\) 6.49813e15 1.98641
\(663\) 4.42145e14 0.134042
\(664\) −4.56312e15 −1.37195
\(665\) −9.77340e14 −0.291425
\(666\) −2.52963e14 −0.0748081
\(667\) −1.66112e14 −0.0487203
\(668\) −3.64226e15 −1.05950
\(669\) 8.95794e14 0.258443
\(670\) −5.16012e14 −0.147655
\(671\) −1.39308e14 −0.0395369
\(672\) 6.86588e14 0.193270
\(673\) 6.14083e15 1.71453 0.857263 0.514879i \(-0.172163\pi\)
0.857263 + 0.514879i \(0.172163\pi\)
\(674\) 1.15268e15 0.319213
\(675\) −1.17544e14 −0.0322873
\(676\) 4.73554e14 0.129022
\(677\) −1.92471e15 −0.520149 −0.260074 0.965589i \(-0.583747\pi\)
−0.260074 + 0.965589i \(0.583747\pi\)
\(678\) 5.49791e15 1.47379
\(679\) −1.21968e15 −0.324312
\(680\) −3.80074e15 −1.00246
\(681\) −2.04376e15 −0.534713
\(682\) 3.25330e14 0.0844327
\(683\) −2.11279e15 −0.543930 −0.271965 0.962307i \(-0.587673\pi\)
−0.271965 + 0.962307i \(0.587673\pi\)
\(684\) 1.56203e15 0.398917
\(685\) 1.36985e15 0.347037
\(686\) 3.51546e14 0.0883487
\(687\) −6.24639e14 −0.155728
\(688\) 2.39351e14 0.0591969
\(689\) 2.10915e15 0.517490
\(690\) −5.73236e14 −0.139529
\(691\) 3.89904e15 0.941518 0.470759 0.882262i \(-0.343980\pi\)
0.470759 + 0.882262i \(0.343980\pi\)
\(692\) −9.47469e15 −2.26977
\(693\) 2.65652e13 0.00631365
\(694\) −9.87155e15 −2.32760
\(695\) 1.18461e15 0.277114
\(696\) −9.82696e14 −0.228070
\(697\) 3.94883e14 0.0909259
\(698\) −6.42070e14 −0.146682
\(699\) 2.60858e14 0.0591261
\(700\) 4.72944e14 0.106358
\(701\) 1.40144e15 0.312699 0.156349 0.987702i \(-0.450027\pi\)
0.156349 + 0.987702i \(0.450027\pi\)
\(702\) 3.94501e14 0.0873361
\(703\) −4.45527e14 −0.0978632
\(704\) −3.64483e14 −0.0794379
\(705\) −4.25956e15 −0.921139
\(706\) −6.11717e15 −1.31258
\(707\) 1.58557e15 0.337582
\(708\) −5.96164e15 −1.25945
\(709\) −1.28974e15 −0.270364 −0.135182 0.990821i \(-0.543162\pi\)
−0.135182 + 0.990821i \(0.543162\pi\)
\(710\) −5.24427e15 −1.09085
\(711\) −1.48987e15 −0.307514
\(712\) −3.43136e15 −0.702792
\(713\) −6.92474e14 −0.140738
\(714\) −1.48201e15 −0.298889
\(715\) 7.50483e13 0.0150196
\(716\) −1.10936e16 −2.20319
\(717\) 3.10729e14 0.0612388
\(718\) −8.03002e15 −1.57048
\(719\) −8.30132e14 −0.161116 −0.0805579 0.996750i \(-0.525670\pi\)
−0.0805579 + 0.996750i \(0.525670\pi\)
\(720\) −2.54340e14 −0.0489875
\(721\) 1.01433e15 0.193882
\(722\) −4.23452e15 −0.803248
\(723\) −1.75460e15 −0.330306
\(724\) −1.34266e14 −0.0250844
\(725\) 3.22540e14 0.0598033
\(726\) 5.12090e15 0.942312
\(727\) 7.61457e15 1.39061 0.695306 0.718714i \(-0.255269\pi\)
0.695306 + 0.718714i \(0.255269\pi\)
\(728\) −6.40943e14 −0.116171
\(729\) 2.05891e14 0.0370370
\(730\) 3.69230e14 0.0659206
\(731\) 2.05631e15 0.364371
\(732\) 4.34419e15 0.764008
\(733\) −6.17483e15 −1.07784 −0.538918 0.842358i \(-0.681167\pi\)
−0.538918 + 0.842358i \(0.681167\pi\)
\(734\) −4.84501e15 −0.839396
\(735\) 5.18323e14 0.0891292
\(736\) 7.09253e14 0.121052
\(737\) 2.47027e13 0.00418478
\(738\) 3.52331e14 0.0592436
\(739\) 1.02585e16 1.71214 0.856071 0.516859i \(-0.172899\pi\)
0.856071 + 0.516859i \(0.172899\pi\)
\(740\) 1.50066e15 0.248604
\(741\) 6.94808e14 0.114252
\(742\) −7.06957e15 −1.15391
\(743\) −6.76264e15 −1.09567 −0.547833 0.836588i \(-0.684547\pi\)
−0.547833 + 0.836588i \(0.684547\pi\)
\(744\) −4.09658e15 −0.658825
\(745\) −6.04470e15 −0.964974
\(746\) −1.15703e16 −1.83350
\(747\) −2.62339e15 −0.412666
\(748\) 4.50597e14 0.0703606
\(749\) −1.02042e14 −0.0158172
\(750\) −5.52135e15 −0.849589
\(751\) 5.71122e15 0.872387 0.436193 0.899853i \(-0.356326\pi\)
0.436193 + 0.899853i \(0.356326\pi\)
\(752\) −1.32414e15 −0.200787
\(753\) −5.89270e15 −0.887037
\(754\) −1.08250e15 −0.161766
\(755\) −7.84254e14 −0.116345
\(756\) −8.28410e14 −0.122004
\(757\) 9.93012e15 1.45187 0.725934 0.687765i \(-0.241408\pi\)
0.725934 + 0.687765i \(0.241408\pi\)
\(758\) 1.46517e16 2.12671
\(759\) 2.74421e13 0.00395447
\(760\) −5.97266e15 −0.854463
\(761\) −9.02345e15 −1.28161 −0.640807 0.767702i \(-0.721400\pi\)
−0.640807 + 0.767702i \(0.721400\pi\)
\(762\) 1.49321e15 0.210557
\(763\) −3.06383e15 −0.428923
\(764\) −9.09283e15 −1.26382
\(765\) −2.18508e15 −0.301529
\(766\) 1.02016e16 1.39769
\(767\) −2.65179e15 −0.360716
\(768\) 5.17096e15 0.698369
\(769\) −2.66286e15 −0.357070 −0.178535 0.983934i \(-0.557136\pi\)
−0.178535 + 0.983934i \(0.557136\pi\)
\(770\) −2.51551e14 −0.0334909
\(771\) −1.18991e15 −0.157295
\(772\) −4.58688e15 −0.602035
\(773\) 5.60938e15 0.731018 0.365509 0.930808i \(-0.380895\pi\)
0.365509 + 0.930808i \(0.380895\pi\)
\(774\) 1.83473e15 0.237409
\(775\) 1.34458e15 0.172753
\(776\) −7.45366e15 −0.950890
\(777\) 2.36281e14 0.0299304
\(778\) −1.47017e16 −1.84919
\(779\) 6.20538e14 0.0775019
\(780\) −2.34031e15 −0.290237
\(781\) 2.51055e14 0.0309164
\(782\) −1.53093e15 −0.187205
\(783\) −5.64962e14 −0.0686009
\(784\) 1.61127e14 0.0194281
\(785\) −4.45616e15 −0.533553
\(786\) 6.38687e15 0.759388
\(787\) −9.15425e15 −1.08084 −0.540420 0.841395i \(-0.681735\pi\)
−0.540420 + 0.841395i \(0.681735\pi\)
\(788\) −2.71954e16 −3.18861
\(789\) 1.97712e15 0.230202
\(790\) 1.41079e16 1.63122
\(791\) −5.13535e15 −0.589657
\(792\) 1.62344e14 0.0185117
\(793\) 1.93234e15 0.218817
\(794\) −2.48397e16 −2.79340
\(795\) −1.04234e16 −1.16410
\(796\) 1.38271e16 1.53359
\(797\) 3.59302e14 0.0395767 0.0197883 0.999804i \(-0.493701\pi\)
0.0197883 + 0.999804i \(0.493701\pi\)
\(798\) −2.32890e15 −0.254762
\(799\) −1.13759e16 −1.23589
\(800\) −1.37716e15 −0.148589
\(801\) −1.97272e15 −0.211392
\(802\) 2.29189e16 2.43913
\(803\) −1.76759e13 −0.00186830
\(804\) −7.70330e14 −0.0808664
\(805\) 5.35433e14 0.0558249
\(806\) −4.51264e15 −0.467292
\(807\) −1.20030e14 −0.0123448
\(808\) 9.68967e15 0.989798
\(809\) 2.58777e14 0.0262548 0.0131274 0.999914i \(-0.495821\pi\)
0.0131274 + 0.999914i \(0.495821\pi\)
\(810\) −1.94962e15 −0.196464
\(811\) 2.69714e15 0.269953 0.134977 0.990849i \(-0.456904\pi\)
0.134977 + 0.990849i \(0.456904\pi\)
\(812\) 2.27314e15 0.225979
\(813\) −2.16264e15 −0.213544
\(814\) −1.14671e14 −0.0112466
\(815\) 1.84379e16 1.79616
\(816\) −6.79259e14 −0.0657264
\(817\) 3.23139e15 0.310576
\(818\) 4.49360e14 0.0428994
\(819\) −3.68485e14 −0.0349428
\(820\) −2.09015e15 −0.196879
\(821\) −8.55122e15 −0.800093 −0.400047 0.916495i \(-0.631006\pi\)
−0.400047 + 0.916495i \(0.631006\pi\)
\(822\) 3.26422e15 0.303378
\(823\) 3.60803e15 0.333097 0.166549 0.986033i \(-0.446738\pi\)
0.166549 + 0.986033i \(0.446738\pi\)
\(824\) 6.19873e15 0.568464
\(825\) −5.32844e13 −0.00485404
\(826\) 8.88843e15 0.804331
\(827\) −5.08928e14 −0.0457484 −0.0228742 0.999738i \(-0.507282\pi\)
−0.0228742 + 0.999738i \(0.507282\pi\)
\(828\) −8.55757e14 −0.0764159
\(829\) −5.41270e15 −0.480136 −0.240068 0.970756i \(-0.577170\pi\)
−0.240068 + 0.970756i \(0.577170\pi\)
\(830\) 2.48414e16 2.18900
\(831\) 3.18302e13 0.00278634
\(832\) 5.05573e15 0.439649
\(833\) 1.38427e15 0.119584
\(834\) 2.82279e15 0.242251
\(835\) 8.00660e15 0.682610
\(836\) 7.08090e14 0.0599727
\(837\) −2.35516e15 −0.198167
\(838\) −2.07938e15 −0.173817
\(839\) −2.07436e16 −1.72263 −0.861316 0.508069i \(-0.830359\pi\)
−0.861316 + 0.508069i \(0.830359\pi\)
\(840\) 3.16754e15 0.261328
\(841\) −1.06503e16 −0.872936
\(842\) 1.70648e16 1.38958
\(843\) 1.92324e15 0.155590
\(844\) 2.08487e16 1.67570
\(845\) −1.04099e15 −0.0831257
\(846\) −1.01501e16 −0.805254
\(847\) −4.78319e15 −0.377015
\(848\) −3.24025e15 −0.253747
\(849\) 1.00190e15 0.0779532
\(850\) 2.97260e15 0.229791
\(851\) 2.44081e14 0.0187465
\(852\) −7.82892e15 −0.597426
\(853\) −2.46016e16 −1.86528 −0.932639 0.360810i \(-0.882500\pi\)
−0.932639 + 0.360810i \(0.882500\pi\)
\(854\) −6.47692e15 −0.487922
\(855\) −3.43374e15 −0.257012
\(856\) −6.23593e14 −0.0463762
\(857\) 1.68045e16 1.24174 0.620871 0.783913i \(-0.286779\pi\)
0.620871 + 0.783913i \(0.286779\pi\)
\(858\) 1.78832e14 0.0131300
\(859\) 6.85287e15 0.499931 0.249966 0.968255i \(-0.419581\pi\)
0.249966 + 0.968255i \(0.419581\pi\)
\(860\) −1.08842e16 −0.788962
\(861\) −3.29096e14 −0.0237031
\(862\) 1.63747e16 1.17188
\(863\) −6.49574e15 −0.461922 −0.230961 0.972963i \(-0.574187\pi\)
−0.230961 + 0.972963i \(0.574187\pi\)
\(864\) 2.41223e15 0.170448
\(865\) 2.08277e16 1.46236
\(866\) −1.93623e16 −1.35086
\(867\) 2.49242e15 0.172789
\(868\) 9.47608e15 0.652785
\(869\) −6.75377e14 −0.0462314
\(870\) 5.34974e15 0.363895
\(871\) −3.42650e14 −0.0231607
\(872\) −1.87235e16 −1.25761
\(873\) −4.28518e15 −0.286017
\(874\) −2.40578e15 −0.159567
\(875\) 5.15724e15 0.339917
\(876\) 5.51206e14 0.0361028
\(877\) 2.71964e15 0.177017 0.0885084 0.996075i \(-0.471790\pi\)
0.0885084 + 0.996075i \(0.471790\pi\)
\(878\) 4.37557e16 2.83018
\(879\) −1.90767e14 −0.0122621
\(880\) −1.15295e14 −0.00736473
\(881\) −2.82071e16 −1.79057 −0.895283 0.445498i \(-0.853027\pi\)
−0.895283 + 0.445498i \(0.853027\pi\)
\(882\) 1.23511e15 0.0779162
\(883\) 8.56937e15 0.537236 0.268618 0.963247i \(-0.413433\pi\)
0.268618 + 0.963247i \(0.413433\pi\)
\(884\) −6.25021e15 −0.389410
\(885\) 1.31052e16 0.811437
\(886\) −1.75239e16 −1.07832
\(887\) 1.03919e16 0.635501 0.317750 0.948174i \(-0.397073\pi\)
0.317750 + 0.948174i \(0.397073\pi\)
\(888\) 1.44395e15 0.0877566
\(889\) −1.39474e15 −0.0842430
\(890\) 1.86801e16 1.12133
\(891\) 9.33330e13 0.00556811
\(892\) −1.26631e16 −0.750813
\(893\) −1.78767e16 −1.05343
\(894\) −1.44039e16 −0.843574
\(895\) 2.43866e16 1.41946
\(896\) −1.11595e16 −0.645583
\(897\) −3.80649e14 −0.0218860
\(898\) 4.48424e16 2.56253
\(899\) 6.46253e15 0.367049
\(900\) 1.66162e15 0.0937991
\(901\) −2.78376e16 −1.56187
\(902\) 1.59716e14 0.00890662
\(903\) −1.71374e15 −0.0949864
\(904\) −3.13828e16 −1.72888
\(905\) 2.95150e14 0.0161613
\(906\) −1.86879e15 −0.101708
\(907\) 1.59311e16 0.861801 0.430900 0.902399i \(-0.358196\pi\)
0.430900 + 0.902399i \(0.358196\pi\)
\(908\) 2.88908e16 1.55342
\(909\) 5.57069e15 0.297720
\(910\) 3.48926e15 0.185355
\(911\) 1.39159e16 0.734783 0.367391 0.930066i \(-0.380251\pi\)
0.367391 + 0.930066i \(0.380251\pi\)
\(912\) −1.06742e15 −0.0560227
\(913\) −1.18921e15 −0.0620398
\(914\) −1.63053e16 −0.845521
\(915\) −9.54962e15 −0.492232
\(916\) 8.82997e15 0.452412
\(917\) −5.96567e15 −0.303828
\(918\) −5.20682e15 −0.263595
\(919\) −1.78142e16 −0.896461 −0.448231 0.893918i \(-0.647946\pi\)
−0.448231 + 0.893918i \(0.647946\pi\)
\(920\) 3.27211e15 0.163680
\(921\) −8.97177e15 −0.446119
\(922\) 7.59402e15 0.375363
\(923\) −3.48238e15 −0.171106
\(924\) −3.75529e14 −0.0183420
\(925\) −4.73931e14 −0.0230110
\(926\) 3.68517e16 1.77868
\(927\) 3.56371e15 0.170988
\(928\) −6.61912e15 −0.315708
\(929\) −1.85742e15 −0.0880689 −0.0440344 0.999030i \(-0.514021\pi\)
−0.0440344 + 0.999030i \(0.514021\pi\)
\(930\) 2.23015e16 1.05118
\(931\) 2.17531e15 0.101929
\(932\) −3.68751e15 −0.171770
\(933\) 1.96617e15 0.0910485
\(934\) 6.26022e16 2.88192
\(935\) −9.90525e14 −0.0453317
\(936\) −2.25186e15 −0.102453
\(937\) 5.68991e15 0.257358 0.128679 0.991686i \(-0.458926\pi\)
0.128679 + 0.991686i \(0.458926\pi\)
\(938\) 1.14851e15 0.0516441
\(939\) 8.01626e15 0.358353
\(940\) 6.02137e16 2.67604
\(941\) 5.60191e15 0.247510 0.123755 0.992313i \(-0.460506\pi\)
0.123755 + 0.992313i \(0.460506\pi\)
\(942\) −1.06186e16 −0.466429
\(943\) −3.39960e14 −0.0148461
\(944\) 4.07390e15 0.176874
\(945\) 1.82105e15 0.0786045
\(946\) 8.31707e14 0.0356918
\(947\) 4.81691e15 0.205515 0.102758 0.994706i \(-0.467233\pi\)
0.102758 + 0.994706i \(0.467233\pi\)
\(948\) 2.10610e16 0.893373
\(949\) 2.45182e14 0.0103401
\(950\) 4.67129e15 0.195865
\(951\) −2.24624e16 −0.936405
\(952\) 8.45949e15 0.350624
\(953\) −3.95501e16 −1.62981 −0.814905 0.579594i \(-0.803211\pi\)
−0.814905 + 0.579594i \(0.803211\pi\)
\(954\) −2.48379e16 −1.01765
\(955\) 1.99883e16 0.814250
\(956\) −4.39250e15 −0.177907
\(957\) −2.56104e14 −0.0103134
\(958\) −5.86242e16 −2.34729
\(959\) −3.04895e15 −0.121380
\(960\) −2.49854e16 −0.988998
\(961\) 1.53193e15 0.0602920
\(962\) 1.59060e15 0.0622441
\(963\) −3.58510e14 −0.0139494
\(964\) 2.48032e16 0.959585
\(965\) 1.00831e16 0.387877
\(966\) 1.27588e15 0.0488018
\(967\) −1.96372e16 −0.746851 −0.373425 0.927660i \(-0.621817\pi\)
−0.373425 + 0.927660i \(0.621817\pi\)
\(968\) −2.92308e16 −1.10542
\(969\) −9.17043e15 −0.344833
\(970\) 4.05773e16 1.51718
\(971\) −4.13717e16 −1.53814 −0.769072 0.639162i \(-0.779281\pi\)
−0.769072 + 0.639162i \(0.779281\pi\)
\(972\) −2.91050e15 −0.107598
\(973\) −2.63664e15 −0.0969237
\(974\) −5.37612e16 −1.96515
\(975\) 7.39105e14 0.0268646
\(976\) −2.96862e15 −0.107295
\(977\) 6.47244e15 0.232620 0.116310 0.993213i \(-0.462893\pi\)
0.116310 + 0.993213i \(0.462893\pi\)
\(978\) 4.39357e16 1.57020
\(979\) −8.94261e14 −0.0317804
\(980\) −7.32707e15 −0.258933
\(981\) −1.07643e16 −0.378275
\(982\) 1.95652e16 0.683708
\(983\) −2.03123e16 −0.705852 −0.352926 0.935651i \(-0.614813\pi\)
−0.352926 + 0.935651i \(0.614813\pi\)
\(984\) −2.01115e15 −0.0694980
\(985\) 5.97824e16 2.05435
\(986\) 1.42874e16 0.488237
\(987\) 9.48073e15 0.322179
\(988\) −9.82189e15 −0.331919
\(989\) −1.77031e15 −0.0594935
\(990\) −8.83789e14 −0.0295362
\(991\) 1.53995e16 0.511801 0.255901 0.966703i \(-0.417628\pi\)
0.255901 + 0.966703i \(0.417628\pi\)
\(992\) −2.75932e16 −0.911985
\(993\) −2.13247e16 −0.700909
\(994\) 1.16724e16 0.381537
\(995\) −3.03955e16 −0.988057
\(996\) 3.70845e16 1.19885
\(997\) −1.44352e15 −0.0464088 −0.0232044 0.999731i \(-0.507387\pi\)
−0.0232044 + 0.999731i \(0.507387\pi\)
\(998\) −2.68404e16 −0.858166
\(999\) 8.30139e14 0.0263962
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 273.12.a.c.1.15 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.12.a.c.1.15 16 1.1 even 1 trivial