Properties

Label 10.26.a.d.1.2
Level $10$
Weight $26$
Character 10.1
Self dual yes
Analytic conductor $39.600$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [10,26,Mod(1,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 26, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.1");
 
S:= CuspForms(chi, 26);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 10.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: \(39.5996779952\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{95351}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 95351 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3}\cdot 5 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(308.790\) of defining polynomial
Character \(\chi\) \(=\) 10.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4096.00 q^{2} +618439. q^{3} +1.67772e7 q^{4} -2.44141e8 q^{5} +2.53313e9 q^{6} +4.78762e10 q^{7} +6.87195e10 q^{8} -4.64821e11 q^{9} -1.00000e12 q^{10} +3.58198e11 q^{11} +1.03757e13 q^{12} +7.76408e13 q^{13} +1.96101e14 q^{14} -1.50986e14 q^{15} +2.81475e14 q^{16} +1.50624e15 q^{17} -1.90391e15 q^{18} +4.83611e15 q^{19} -4.09600e15 q^{20} +2.96085e16 q^{21} +1.46718e15 q^{22} +2.59330e16 q^{23} +4.24988e16 q^{24} +5.96046e16 q^{25} +3.18017e17 q^{26} -8.11461e17 q^{27} +8.03229e17 q^{28} +9.30223e17 q^{29} -6.18439e17 q^{30} +3.10982e18 q^{31} +1.15292e18 q^{32} +2.21524e17 q^{33} +6.16957e18 q^{34} -1.16885e19 q^{35} -7.79841e18 q^{36} -4.54619e19 q^{37} +1.98087e19 q^{38} +4.80162e19 q^{39} -1.67772e19 q^{40} +1.02459e20 q^{41} +1.21276e20 q^{42} +4.58049e20 q^{43} +6.00957e18 q^{44} +1.13482e20 q^{45} +1.06222e20 q^{46} +1.51063e21 q^{47} +1.74075e20 q^{48} +9.51058e20 q^{49} +2.44141e20 q^{50} +9.31520e20 q^{51} +1.30260e21 q^{52} -2.00272e21 q^{53} -3.32374e21 q^{54} -8.74507e19 q^{55} +3.29002e21 q^{56} +2.99084e21 q^{57} +3.81019e21 q^{58} +2.00362e22 q^{59} -2.53313e21 q^{60} -2.40289e22 q^{61} +1.27378e22 q^{62} -2.22539e22 q^{63} +4.72237e21 q^{64} -1.89553e22 q^{65} +9.07362e20 q^{66} -5.68406e22 q^{67} +2.52706e22 q^{68} +1.60380e22 q^{69} -4.78762e22 q^{70} +2.06619e22 q^{71} -3.19423e22 q^{72} -3.20846e23 q^{73} -1.86212e23 q^{74} +3.68619e22 q^{75} +8.11365e22 q^{76} +1.71492e22 q^{77} +1.96674e23 q^{78} -4.28561e23 q^{79} -6.87195e22 q^{80} -1.08001e23 q^{81} +4.19671e23 q^{82} -1.11807e24 q^{83} +4.96748e23 q^{84} -3.67735e23 q^{85} +1.87617e24 q^{86} +5.75287e23 q^{87} +2.46152e22 q^{88} +1.75157e24 q^{89} +4.64821e23 q^{90} +3.71714e24 q^{91} +4.35084e23 q^{92} +1.92323e24 q^{93} +6.18754e24 q^{94} -1.18069e24 q^{95} +7.13012e23 q^{96} -1.28690e25 q^{97} +3.89553e24 q^{98} -1.66498e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 8192 q^{2} - 97092 q^{3} + 33554432 q^{4} - 488281250 q^{5} - 397688832 q^{6} - 16137160124 q^{7} + 137438953472 q^{8} - 800124539454 q^{9} - 2000000000000 q^{10} + 14416600801344 q^{11} - 1628933455872 q^{12}+ \cdots - 48\!\cdots\!88 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4096.00 0.707107
\(3\) 618439. 0.671864 0.335932 0.941886i \(-0.390949\pi\)
0.335932 + 0.941886i \(0.390949\pi\)
\(4\) 1.67772e7 0.500000
\(5\) −2.44141e8 −0.447214
\(6\) 2.53313e9 0.475080
\(7\) 4.78762e10 1.30736 0.653678 0.756773i \(-0.273225\pi\)
0.653678 + 0.756773i \(0.273225\pi\)
\(8\) 6.87195e10 0.353553
\(9\) −4.64821e11 −0.548598
\(10\) −1.00000e12 −0.316228
\(11\) 3.58198e11 0.0344124 0.0172062 0.999852i \(-0.494523\pi\)
0.0172062 + 0.999852i \(0.494523\pi\)
\(12\) 1.03757e13 0.335932
\(13\) 7.76408e13 0.924269 0.462134 0.886810i \(-0.347084\pi\)
0.462134 + 0.886810i \(0.347084\pi\)
\(14\) 1.96101e14 0.924440
\(15\) −1.50986e14 −0.300467
\(16\) 2.81475e14 0.250000
\(17\) 1.50624e15 0.627023 0.313511 0.949584i \(-0.398495\pi\)
0.313511 + 0.949584i \(0.398495\pi\)
\(18\) −1.90391e15 −0.387918
\(19\) 4.83611e15 0.501276 0.250638 0.968081i \(-0.419360\pi\)
0.250638 + 0.968081i \(0.419360\pi\)
\(20\) −4.09600e15 −0.223607
\(21\) 2.96085e16 0.878366
\(22\) 1.46718e15 0.0243332
\(23\) 2.59330e16 0.246749 0.123374 0.992360i \(-0.460628\pi\)
0.123374 + 0.992360i \(0.460628\pi\)
\(24\) 4.24988e16 0.237540
\(25\) 5.96046e16 0.200000
\(26\) 3.18017e17 0.653557
\(27\) −8.11461e17 −1.04045
\(28\) 8.03229e17 0.653678
\(29\) 9.30223e17 0.488216 0.244108 0.969748i \(-0.421505\pi\)
0.244108 + 0.969748i \(0.421505\pi\)
\(30\) −6.18439e17 −0.212462
\(31\) 3.10982e18 0.709110 0.354555 0.935035i \(-0.384632\pi\)
0.354555 + 0.935035i \(0.384632\pi\)
\(32\) 1.15292e18 0.176777
\(33\) 2.21524e17 0.0231205
\(34\) 6.16957e18 0.443372
\(35\) −1.16885e19 −0.584667
\(36\) −7.79841e18 −0.274299
\(37\) −4.54619e19 −1.13534 −0.567670 0.823256i \(-0.692155\pi\)
−0.567670 + 0.823256i \(0.692155\pi\)
\(38\) 1.98087e19 0.354455
\(39\) 4.80162e19 0.620983
\(40\) −1.67772e19 −0.158114
\(41\) 1.02459e20 0.709172 0.354586 0.935023i \(-0.384622\pi\)
0.354586 + 0.935023i \(0.384622\pi\)
\(42\) 1.21276e20 0.621098
\(43\) 4.58049e20 1.74806 0.874029 0.485874i \(-0.161498\pi\)
0.874029 + 0.485874i \(0.161498\pi\)
\(44\) 6.00957e18 0.0172062
\(45\) 1.13482e20 0.245341
\(46\) 1.06222e20 0.174478
\(47\) 1.51063e21 1.89642 0.948210 0.317644i \(-0.102892\pi\)
0.948210 + 0.317644i \(0.102892\pi\)
\(48\) 1.74075e20 0.167966
\(49\) 9.51058e20 0.709179
\(50\) 2.44141e20 0.141421
\(51\) 9.31520e20 0.421274
\(52\) 1.30260e21 0.462134
\(53\) −2.00272e21 −0.559980 −0.279990 0.960003i \(-0.590331\pi\)
−0.279990 + 0.960003i \(0.590331\pi\)
\(54\) −3.32374e21 −0.735708
\(55\) −8.74507e19 −0.0153897
\(56\) 3.29002e21 0.462220
\(57\) 2.99084e21 0.336789
\(58\) 3.81019e21 0.345221
\(59\) 2.00362e22 1.46611 0.733053 0.680171i \(-0.238095\pi\)
0.733053 + 0.680171i \(0.238095\pi\)
\(60\) −2.53313e21 −0.150233
\(61\) −2.40289e22 −1.15908 −0.579538 0.814945i \(-0.696767\pi\)
−0.579538 + 0.814945i \(0.696767\pi\)
\(62\) 1.27378e22 0.501417
\(63\) −2.22539e22 −0.717213
\(64\) 4.72237e21 0.125000
\(65\) −1.89553e22 −0.413346
\(66\) 9.07362e20 0.0163486
\(67\) −5.68406e22 −0.848640 −0.424320 0.905512i \(-0.639487\pi\)
−0.424320 + 0.905512i \(0.639487\pi\)
\(68\) 2.52706e22 0.313511
\(69\) 1.60380e22 0.165782
\(70\) −4.78762e22 −0.413422
\(71\) 2.06619e22 0.149431 0.0747156 0.997205i \(-0.476195\pi\)
0.0747156 + 0.997205i \(0.476195\pi\)
\(72\) −3.19423e22 −0.193959
\(73\) −3.20846e23 −1.63969 −0.819843 0.572588i \(-0.805939\pi\)
−0.819843 + 0.572588i \(0.805939\pi\)
\(74\) −1.86212e23 −0.802806
\(75\) 3.68619e22 0.134373
\(76\) 8.11365e22 0.250638
\(77\) 1.71492e22 0.0449892
\(78\) 1.96674e23 0.439101
\(79\) −4.28561e23 −0.815969 −0.407985 0.912989i \(-0.633768\pi\)
−0.407985 + 0.912989i \(0.633768\pi\)
\(80\) −6.87195e22 −0.111803
\(81\) −1.08001e23 −0.150441
\(82\) 4.19671e23 0.501460
\(83\) −1.11807e24 −1.14814 −0.574069 0.818807i \(-0.694636\pi\)
−0.574069 + 0.818807i \(0.694636\pi\)
\(84\) 4.96748e23 0.439183
\(85\) −3.67735e23 −0.280413
\(86\) 1.87617e24 1.23606
\(87\) 5.75287e23 0.328015
\(88\) 2.46152e22 0.0121666
\(89\) 1.75157e24 0.751712 0.375856 0.926678i \(-0.377349\pi\)
0.375856 + 0.926678i \(0.377349\pi\)
\(90\) 4.64821e23 0.173482
\(91\) 3.71714e24 1.20835
\(92\) 4.35084e23 0.123374
\(93\) 1.92323e24 0.476426
\(94\) 6.18754e24 1.34097
\(95\) −1.18069e24 −0.224177
\(96\) 7.13012e23 0.118770
\(97\) −1.28690e25 −1.88320 −0.941601 0.336729i \(-0.890679\pi\)
−0.941601 + 0.336729i \(0.890679\pi\)
\(98\) 3.89553e24 0.501466
\(99\) −1.66498e23 −0.0188786
\(100\) 1.00000e24 0.100000
\(101\) −3.20176e24 −0.282730 −0.141365 0.989958i \(-0.545149\pi\)
−0.141365 + 0.989958i \(0.545149\pi\)
\(102\) 3.81551e24 0.297886
\(103\) −5.43797e23 −0.0375813 −0.0187906 0.999823i \(-0.505982\pi\)
−0.0187906 + 0.999823i \(0.505982\pi\)
\(104\) 5.33544e24 0.326778
\(105\) −7.22864e24 −0.392817
\(106\) −8.20316e24 −0.395966
\(107\) −1.45562e25 −0.624816 −0.312408 0.949948i \(-0.601136\pi\)
−0.312408 + 0.949948i \(0.601136\pi\)
\(108\) −1.36140e25 −0.520224
\(109\) −3.33253e25 −1.13486 −0.567431 0.823421i \(-0.692063\pi\)
−0.567431 + 0.823421i \(0.692063\pi\)
\(110\) −3.58198e23 −0.0108822
\(111\) −2.81154e25 −0.762794
\(112\) 1.34759e25 0.326839
\(113\) 1.71253e25 0.371670 0.185835 0.982581i \(-0.440501\pi\)
0.185835 + 0.982581i \(0.440501\pi\)
\(114\) 1.22505e25 0.238146
\(115\) −6.33130e24 −0.110349
\(116\) 1.56066e25 0.244108
\(117\) −3.60891e25 −0.507052
\(118\) 8.20683e25 1.03669
\(119\) 7.21131e25 0.819742
\(120\) −1.03757e25 −0.106231
\(121\) −1.08219e26 −0.998816
\(122\) −9.84225e25 −0.819590
\(123\) 6.33646e25 0.476467
\(124\) 5.21741e25 0.354555
\(125\) −1.45519e25 −0.0894427
\(126\) −9.11518e25 −0.507146
\(127\) −2.80916e26 −1.41589 −0.707947 0.706266i \(-0.750378\pi\)
−0.707947 + 0.706266i \(0.750378\pi\)
\(128\) 1.93428e25 0.0883883
\(129\) 2.83275e26 1.17446
\(130\) −7.76408e25 −0.292279
\(131\) 3.91683e26 1.33981 0.669906 0.742446i \(-0.266334\pi\)
0.669906 + 0.742446i \(0.266334\pi\)
\(132\) 3.71655e24 0.0115602
\(133\) 2.31535e26 0.655346
\(134\) −2.32819e26 −0.600079
\(135\) 1.98110e26 0.465302
\(136\) 1.03508e26 0.221686
\(137\) 7.30593e24 0.0142780 0.00713902 0.999975i \(-0.497728\pi\)
0.00713902 + 0.999975i \(0.497728\pi\)
\(138\) 6.56916e25 0.117225
\(139\) 9.32000e26 1.51961 0.759803 0.650154i \(-0.225295\pi\)
0.759803 + 0.650154i \(0.225295\pi\)
\(140\) −1.96101e26 −0.292334
\(141\) 9.34233e26 1.27414
\(142\) 8.46313e25 0.105664
\(143\) 2.78108e25 0.0318063
\(144\) −1.30836e26 −0.137150
\(145\) −2.27105e26 −0.218337
\(146\) −1.31419e27 −1.15943
\(147\) 5.88172e26 0.476472
\(148\) −7.62723e26 −0.567670
\(149\) −2.86893e27 −1.96287 −0.981434 0.191800i \(-0.938567\pi\)
−0.981434 + 0.191800i \(0.938567\pi\)
\(150\) 1.50986e26 0.0950160
\(151\) 6.35122e26 0.367828 0.183914 0.982942i \(-0.441123\pi\)
0.183914 + 0.982942i \(0.441123\pi\)
\(152\) 3.32335e26 0.177228
\(153\) −7.00134e26 −0.343984
\(154\) 7.02429e25 0.0318122
\(155\) −7.59233e26 −0.317124
\(156\) 8.05577e26 0.310492
\(157\) −2.51786e27 −0.895954 −0.447977 0.894045i \(-0.647855\pi\)
−0.447977 + 0.894045i \(0.647855\pi\)
\(158\) −1.75538e27 −0.576977
\(159\) −1.23856e27 −0.376231
\(160\) −2.81475e26 −0.0790569
\(161\) 1.24157e27 0.322588
\(162\) −4.42374e26 −0.106378
\(163\) −4.89494e26 −0.108994 −0.0544970 0.998514i \(-0.517356\pi\)
−0.0544970 + 0.998514i \(0.517356\pi\)
\(164\) 1.71897e27 0.354586
\(165\) −5.40830e25 −0.0103398
\(166\) −4.57963e27 −0.811856
\(167\) 2.73255e27 0.449378 0.224689 0.974430i \(-0.427863\pi\)
0.224689 + 0.974430i \(0.427863\pi\)
\(168\) 2.03468e27 0.310549
\(169\) −1.02831e27 −0.145727
\(170\) −1.50624e27 −0.198282
\(171\) −2.24793e27 −0.274999
\(172\) 7.68478e27 0.874029
\(173\) 8.64082e27 0.914069 0.457034 0.889449i \(-0.348912\pi\)
0.457034 + 0.889449i \(0.348912\pi\)
\(174\) 2.35637e27 0.231942
\(175\) 2.85364e27 0.261471
\(176\) 1.00824e26 0.00860310
\(177\) 1.23912e28 0.985025
\(178\) 7.17441e27 0.531540
\(179\) −2.03598e28 −1.40640 −0.703201 0.710991i \(-0.748247\pi\)
−0.703201 + 0.710991i \(0.748247\pi\)
\(180\) 1.90391e27 0.122670
\(181\) 1.34351e28 0.807718 0.403859 0.914821i \(-0.367669\pi\)
0.403859 + 0.914821i \(0.367669\pi\)
\(182\) 1.52254e28 0.854431
\(183\) −1.48604e28 −0.778741
\(184\) 1.78210e27 0.0872388
\(185\) 1.10991e28 0.507739
\(186\) 7.87757e27 0.336884
\(187\) 5.39533e26 0.0215774
\(188\) 2.53441e28 0.948210
\(189\) −3.88496e28 −1.36024
\(190\) −4.83611e27 −0.158517
\(191\) −1.46283e28 −0.449030 −0.224515 0.974471i \(-0.572080\pi\)
−0.224515 + 0.974471i \(0.572080\pi\)
\(192\) 2.92050e27 0.0839830
\(193\) 3.37927e28 0.910659 0.455330 0.890323i \(-0.349521\pi\)
0.455330 + 0.890323i \(0.349521\pi\)
\(194\) −5.27113e28 −1.33163
\(195\) −1.17227e28 −0.277712
\(196\) 1.59561e28 0.354590
\(197\) −5.93119e28 −1.23684 −0.618420 0.785847i \(-0.712227\pi\)
−0.618420 + 0.785847i \(0.712227\pi\)
\(198\) −6.81976e26 −0.0133492
\(199\) −1.85919e28 −0.341712 −0.170856 0.985296i \(-0.554653\pi\)
−0.170856 + 0.985296i \(0.554653\pi\)
\(200\) 4.09600e27 0.0707107
\(201\) −3.51525e28 −0.570171
\(202\) −1.31144e28 −0.199920
\(203\) 4.45355e28 0.638272
\(204\) 1.56283e28 0.210637
\(205\) −2.50144e28 −0.317151
\(206\) −2.22739e27 −0.0265740
\(207\) −1.20542e28 −0.135366
\(208\) 2.18540e28 0.231067
\(209\) 1.73229e27 0.0172501
\(210\) −2.96085e28 −0.277764
\(211\) 1.59544e29 1.41042 0.705212 0.708996i \(-0.250852\pi\)
0.705212 + 0.708996i \(0.250852\pi\)
\(212\) −3.36001e28 −0.279990
\(213\) 1.27782e28 0.100398
\(214\) −5.96224e28 −0.441812
\(215\) −1.11828e29 −0.781755
\(216\) −5.57631e28 −0.367854
\(217\) 1.48886e29 0.927060
\(218\) −1.36501e29 −0.802469
\(219\) −1.98424e29 −1.10165
\(220\) −1.46718e27 −0.00769484
\(221\) 1.16946e29 0.579538
\(222\) −1.15161e29 −0.539377
\(223\) 2.93272e29 1.29855 0.649277 0.760552i \(-0.275072\pi\)
0.649277 + 0.760552i \(0.275072\pi\)
\(224\) 5.51975e28 0.231110
\(225\) −2.77055e28 −0.109720
\(226\) 7.01452e28 0.262810
\(227\) 2.86033e29 1.01413 0.507065 0.861908i \(-0.330730\pi\)
0.507065 + 0.861908i \(0.330730\pi\)
\(228\) 5.01780e28 0.168395
\(229\) −2.27815e29 −0.723833 −0.361916 0.932211i \(-0.617877\pi\)
−0.361916 + 0.932211i \(0.617877\pi\)
\(230\) −2.59330e28 −0.0780288
\(231\) 1.06057e28 0.0302267
\(232\) 6.39244e28 0.172610
\(233\) 6.95835e29 1.78056 0.890281 0.455411i \(-0.150508\pi\)
0.890281 + 0.455411i \(0.150508\pi\)
\(234\) −1.47821e29 −0.358540
\(235\) −3.68806e29 −0.848105
\(236\) 3.36152e29 0.733053
\(237\) −2.65039e29 −0.548220
\(238\) 2.95375e29 0.579645
\(239\) 1.46812e29 0.273393 0.136696 0.990613i \(-0.456352\pi\)
0.136696 + 0.990613i \(0.456352\pi\)
\(240\) −4.24988e28 −0.0751167
\(241\) 7.86832e29 1.32029 0.660144 0.751139i \(-0.270495\pi\)
0.660144 + 0.751139i \(0.270495\pi\)
\(242\) −4.43264e29 −0.706269
\(243\) 6.20749e29 0.939372
\(244\) −4.03139e29 −0.579538
\(245\) −2.32192e29 −0.317155
\(246\) 2.59541e29 0.336913
\(247\) 3.75480e29 0.463313
\(248\) 2.13705e29 0.250708
\(249\) −6.91461e29 −0.771393
\(250\) −5.96046e28 −0.0632456
\(251\) −1.30352e30 −1.31582 −0.657910 0.753097i \(-0.728559\pi\)
−0.657910 + 0.753097i \(0.728559\pi\)
\(252\) −3.73358e29 −0.358607
\(253\) 9.28916e27 0.00849121
\(254\) −1.15063e30 −1.00119
\(255\) −2.27422e29 −0.188400
\(256\) 7.92282e28 0.0625000
\(257\) −2.21600e30 −1.66496 −0.832482 0.554052i \(-0.813081\pi\)
−0.832482 + 0.554052i \(0.813081\pi\)
\(258\) 1.16030e30 0.830467
\(259\) −2.17654e30 −1.48429
\(260\) −3.18017e29 −0.206673
\(261\) −4.32387e29 −0.267835
\(262\) 1.60433e30 0.947390
\(263\) 3.37258e29 0.189896 0.0949479 0.995482i \(-0.469732\pi\)
0.0949479 + 0.995482i \(0.469732\pi\)
\(264\) 1.52230e28 0.00817431
\(265\) 4.88946e29 0.250431
\(266\) 9.48366e29 0.463399
\(267\) 1.08324e30 0.505048
\(268\) −9.53627e29 −0.424320
\(269\) −4.13865e30 −1.75774 −0.878871 0.477059i \(-0.841703\pi\)
−0.878871 + 0.477059i \(0.841703\pi\)
\(270\) 8.11461e29 0.329019
\(271\) 2.28080e29 0.0883021 0.0441511 0.999025i \(-0.485942\pi\)
0.0441511 + 0.999025i \(0.485942\pi\)
\(272\) 4.23970e29 0.156756
\(273\) 2.29883e30 0.811846
\(274\) 2.99251e28 0.0100961
\(275\) 2.13503e28 0.00688248
\(276\) 2.69073e29 0.0828908
\(277\) 3.78637e30 1.11487 0.557437 0.830219i \(-0.311785\pi\)
0.557437 + 0.830219i \(0.311785\pi\)
\(278\) 3.81747e30 1.07452
\(279\) −1.44551e30 −0.389017
\(280\) −8.03229e29 −0.206711
\(281\) 4.87412e30 1.19969 0.599843 0.800118i \(-0.295230\pi\)
0.599843 + 0.800118i \(0.295230\pi\)
\(282\) 3.82662e30 0.900951
\(283\) −7.79414e29 −0.175565 −0.0877825 0.996140i \(-0.527978\pi\)
−0.0877825 + 0.996140i \(0.527978\pi\)
\(284\) 3.46650e29 0.0747156
\(285\) −7.30186e29 −0.150617
\(286\) 1.13913e29 0.0224904
\(287\) 4.90534e30 0.927140
\(288\) −5.35902e29 −0.0969794
\(289\) −3.50186e30 −0.606842
\(290\) −9.30223e29 −0.154387
\(291\) −7.95868e30 −1.26526
\(292\) −5.38290e30 −0.819843
\(293\) 8.97738e30 1.31010 0.655050 0.755586i \(-0.272648\pi\)
0.655050 + 0.755586i \(0.272648\pi\)
\(294\) 2.40915e30 0.336917
\(295\) −4.89165e30 −0.655663
\(296\) −3.12412e30 −0.401403
\(297\) −2.90664e29 −0.0358043
\(298\) −1.17511e31 −1.38796
\(299\) 2.01346e30 0.228062
\(300\) 6.18439e29 0.0671864
\(301\) 2.19296e31 2.28533
\(302\) 2.60146e30 0.260094
\(303\) −1.98009e30 −0.189956
\(304\) 1.36125e30 0.125319
\(305\) 5.86644e30 0.518354
\(306\) −2.86775e30 −0.243233
\(307\) −1.03718e31 −0.844547 −0.422274 0.906468i \(-0.638768\pi\)
−0.422274 + 0.906468i \(0.638768\pi\)
\(308\) 2.87715e29 0.0224946
\(309\) −3.36306e29 −0.0252495
\(310\) −3.10982e30 −0.224240
\(311\) −3.85228e30 −0.266817 −0.133408 0.991061i \(-0.542592\pi\)
−0.133408 + 0.991061i \(0.542592\pi\)
\(312\) 3.29965e30 0.219551
\(313\) −2.63756e31 −1.68616 −0.843079 0.537789i \(-0.819260\pi\)
−0.843079 + 0.537789i \(0.819260\pi\)
\(314\) −1.03132e31 −0.633535
\(315\) 5.43307e30 0.320748
\(316\) −7.19006e30 −0.407985
\(317\) −3.65330e30 −0.199271 −0.0996355 0.995024i \(-0.531768\pi\)
−0.0996355 + 0.995024i \(0.531768\pi\)
\(318\) −5.07316e30 −0.266035
\(319\) 3.33204e29 0.0168007
\(320\) −1.15292e30 −0.0559017
\(321\) −9.00216e30 −0.419792
\(322\) 5.08548e30 0.228104
\(323\) 7.28436e30 0.314311
\(324\) −1.81196e30 −0.0752206
\(325\) 4.62775e30 0.184854
\(326\) −2.00497e30 −0.0770703
\(327\) −2.06097e31 −0.762474
\(328\) 7.04092e30 0.250730
\(329\) 7.23231e31 2.47930
\(330\) −2.21524e29 −0.00731133
\(331\) −2.52293e31 −0.801781 −0.400890 0.916126i \(-0.631299\pi\)
−0.400890 + 0.916126i \(0.631299\pi\)
\(332\) −1.87582e31 −0.574069
\(333\) 2.11316e31 0.622845
\(334\) 1.11925e31 0.317759
\(335\) 1.38771e31 0.379523
\(336\) 8.33405e30 0.219591
\(337\) −2.57479e31 −0.653684 −0.326842 0.945079i \(-0.605985\pi\)
−0.326842 + 0.945079i \(0.605985\pi\)
\(338\) −4.21196e30 −0.103045
\(339\) 1.05910e31 0.249712
\(340\) −6.16957e30 −0.140207
\(341\) 1.11393e30 0.0244022
\(342\) −9.20751e30 −0.194454
\(343\) −1.86722e31 −0.380206
\(344\) 3.14769e31 0.618032
\(345\) −3.91553e30 −0.0741398
\(346\) 3.53928e31 0.646344
\(347\) −1.71059e31 −0.301319 −0.150660 0.988586i \(-0.548140\pi\)
−0.150660 + 0.988586i \(0.548140\pi\)
\(348\) 9.65171e30 0.164007
\(349\) 6.93560e31 1.13702 0.568508 0.822678i \(-0.307521\pi\)
0.568508 + 0.822678i \(0.307521\pi\)
\(350\) 1.16885e31 0.184888
\(351\) −6.30025e31 −0.961653
\(352\) 4.12974e29 0.00608331
\(353\) 1.22234e31 0.173783 0.0868914 0.996218i \(-0.472307\pi\)
0.0868914 + 0.996218i \(0.472307\pi\)
\(354\) 5.07543e31 0.696518
\(355\) −5.04442e30 −0.0668277
\(356\) 2.93864e31 0.375856
\(357\) 4.45976e31 0.550755
\(358\) −8.33936e31 −0.994477
\(359\) 5.26279e31 0.606087 0.303044 0.952977i \(-0.401997\pi\)
0.303044 + 0.952977i \(0.401997\pi\)
\(360\) 7.79841e30 0.0867410
\(361\) −6.96885e31 −0.748723
\(362\) 5.50303e31 0.571143
\(363\) −6.69267e31 −0.671069
\(364\) 6.23633e31 0.604174
\(365\) 7.83315e31 0.733290
\(366\) −6.08684e31 −0.550653
\(367\) −1.04735e31 −0.0915729 −0.0457864 0.998951i \(-0.514579\pi\)
−0.0457864 + 0.998951i \(0.514579\pi\)
\(368\) 7.29949e30 0.0616872
\(369\) −4.76250e31 −0.389050
\(370\) 4.54619e31 0.359026
\(371\) −9.58828e31 −0.732094
\(372\) 3.22665e31 0.238213
\(373\) −1.24978e32 −0.892221 −0.446111 0.894978i \(-0.647191\pi\)
−0.446111 + 0.894978i \(0.647191\pi\)
\(374\) 2.20993e30 0.0152575
\(375\) −8.99948e30 −0.0600934
\(376\) 1.03810e32 0.670486
\(377\) 7.22233e31 0.451243
\(378\) −1.59128e32 −0.961832
\(379\) −1.71176e32 −1.00104 −0.500522 0.865724i \(-0.666859\pi\)
−0.500522 + 0.865724i \(0.666859\pi\)
\(380\) −1.98087e31 −0.112089
\(381\) −1.73730e32 −0.951288
\(382\) −5.99173e31 −0.317512
\(383\) −2.63626e32 −1.35209 −0.676043 0.736862i \(-0.736307\pi\)
−0.676043 + 0.736862i \(0.736307\pi\)
\(384\) 1.19624e31 0.0593850
\(385\) −4.18680e30 −0.0201198
\(386\) 1.38415e32 0.643933
\(387\) −2.12911e32 −0.958982
\(388\) −2.15905e32 −0.941601
\(389\) 3.01567e32 1.27354 0.636772 0.771052i \(-0.280269\pi\)
0.636772 + 0.771052i \(0.280269\pi\)
\(390\) −4.80162e31 −0.196372
\(391\) 3.90614e31 0.154717
\(392\) 6.53562e31 0.250733
\(393\) 2.42232e32 0.900172
\(394\) −2.42941e32 −0.874578
\(395\) 1.04629e32 0.364912
\(396\) −2.79337e30 −0.00943929
\(397\) 3.60886e32 1.18165 0.590824 0.806800i \(-0.298803\pi\)
0.590824 + 0.806800i \(0.298803\pi\)
\(398\) −7.61523e31 −0.241627
\(399\) 1.43190e32 0.440303
\(400\) 1.67772e31 0.0500000
\(401\) 3.40848e32 0.984591 0.492295 0.870428i \(-0.336158\pi\)
0.492295 + 0.870428i \(0.336158\pi\)
\(402\) −1.43985e32 −0.403172
\(403\) 2.41449e32 0.655409
\(404\) −5.37166e31 −0.141365
\(405\) 2.63676e31 0.0672794
\(406\) 1.82417e32 0.451327
\(407\) −1.62844e31 −0.0390697
\(408\) 6.40136e31 0.148943
\(409\) 1.88820e32 0.426095 0.213048 0.977042i \(-0.431661\pi\)
0.213048 + 0.977042i \(0.431661\pi\)
\(410\) −1.02459e32 −0.224260
\(411\) 4.51827e30 0.00959290
\(412\) −9.12340e30 −0.0187906
\(413\) 9.59257e32 1.91672
\(414\) −4.93741e31 −0.0957182
\(415\) 2.72967e32 0.513463
\(416\) 8.95138e31 0.163389
\(417\) 5.76386e32 1.02097
\(418\) 7.09545e30 0.0121977
\(419\) −6.53498e32 −1.09036 −0.545179 0.838320i \(-0.683538\pi\)
−0.545179 + 0.838320i \(0.683538\pi\)
\(420\) −1.21276e32 −0.196409
\(421\) −8.06557e32 −1.26797 −0.633985 0.773345i \(-0.718582\pi\)
−0.633985 + 0.773345i \(0.718582\pi\)
\(422\) 6.53492e32 0.997321
\(423\) −7.02172e32 −1.04037
\(424\) −1.37626e32 −0.197983
\(425\) 8.97791e31 0.125405
\(426\) 5.23393e31 0.0709918
\(427\) −1.15041e33 −1.51532
\(428\) −2.44213e32 −0.312408
\(429\) 1.71993e31 0.0213695
\(430\) −4.58049e32 −0.552785
\(431\) −1.89617e32 −0.222285 −0.111143 0.993804i \(-0.535451\pi\)
−0.111143 + 0.993804i \(0.535451\pi\)
\(432\) −2.28406e32 −0.260112
\(433\) 1.55976e33 1.72567 0.862835 0.505485i \(-0.168687\pi\)
0.862835 + 0.505485i \(0.168687\pi\)
\(434\) 6.09838e32 0.655530
\(435\) −1.40451e32 −0.146693
\(436\) −5.59106e32 −0.567431
\(437\) 1.25415e32 0.123689
\(438\) −8.12744e32 −0.778982
\(439\) −1.73749e33 −1.61851 −0.809254 0.587460i \(-0.800128\pi\)
−0.809254 + 0.587460i \(0.800128\pi\)
\(440\) −6.00957e30 −0.00544108
\(441\) −4.42072e32 −0.389055
\(442\) 4.79011e32 0.409795
\(443\) 2.09110e33 1.73912 0.869559 0.493830i \(-0.164403\pi\)
0.869559 + 0.493830i \(0.164403\pi\)
\(444\) −4.71698e32 −0.381397
\(445\) −4.27628e32 −0.336176
\(446\) 1.20124e33 0.918216
\(447\) −1.77426e33 −1.31878
\(448\) 2.26089e32 0.163419
\(449\) −2.57391e32 −0.180932 −0.0904659 0.995900i \(-0.528836\pi\)
−0.0904659 + 0.995900i \(0.528836\pi\)
\(450\) −1.13482e32 −0.0775835
\(451\) 3.67006e31 0.0244043
\(452\) 2.87315e32 0.185835
\(453\) 3.92785e32 0.247131
\(454\) 1.17159e33 0.717098
\(455\) −9.07506e32 −0.540390
\(456\) 2.05529e32 0.119073
\(457\) −3.29162e33 −1.85548 −0.927742 0.373222i \(-0.878253\pi\)
−0.927742 + 0.373222i \(0.878253\pi\)
\(458\) −9.33129e32 −0.511827
\(459\) −1.22226e33 −0.652385
\(460\) −1.06222e32 −0.0551747
\(461\) 2.82594e33 1.42857 0.714286 0.699854i \(-0.246752\pi\)
0.714286 + 0.699854i \(0.246752\pi\)
\(462\) 4.34410e31 0.0213735
\(463\) 3.15530e33 1.51105 0.755523 0.655122i \(-0.227383\pi\)
0.755523 + 0.655122i \(0.227383\pi\)
\(464\) 2.61834e32 0.122054
\(465\) −4.69540e32 −0.213064
\(466\) 2.85014e33 1.25905
\(467\) 1.46352e33 0.629417 0.314709 0.949188i \(-0.398093\pi\)
0.314709 + 0.949188i \(0.398093\pi\)
\(468\) −6.05475e32 −0.253526
\(469\) −2.72131e33 −1.10947
\(470\) −1.51063e33 −0.599701
\(471\) −1.55714e33 −0.601960
\(472\) 1.37688e33 0.518347
\(473\) 1.64072e32 0.0601549
\(474\) −1.08560e33 −0.387650
\(475\) 2.88255e32 0.100255
\(476\) 1.20986e33 0.409871
\(477\) 9.30909e32 0.307204
\(478\) 6.01341e32 0.193318
\(479\) −9.44658e31 −0.0295856 −0.0147928 0.999891i \(-0.504709\pi\)
−0.0147928 + 0.999891i \(0.504709\pi\)
\(480\) −1.74075e32 −0.0531155
\(481\) −3.52970e33 −1.04936
\(482\) 3.22286e33 0.933585
\(483\) 7.67838e32 0.216736
\(484\) −1.81561e33 −0.499408
\(485\) 3.14184e33 0.842194
\(486\) 2.54259e33 0.664236
\(487\) 2.95578e33 0.752593 0.376296 0.926499i \(-0.377197\pi\)
0.376296 + 0.926499i \(0.377197\pi\)
\(488\) −1.65126e33 −0.409795
\(489\) −3.02722e32 −0.0732291
\(490\) −9.51058e32 −0.224262
\(491\) 3.19357e33 0.734103 0.367052 0.930201i \(-0.380367\pi\)
0.367052 + 0.930201i \(0.380367\pi\)
\(492\) 1.06308e33 0.238233
\(493\) 1.40114e33 0.306123
\(494\) 1.53797e33 0.327612
\(495\) 4.06490e31 0.00844276
\(496\) 8.75336e32 0.177278
\(497\) 9.89214e32 0.195360
\(498\) −2.83222e33 −0.545457
\(499\) −3.38640e33 −0.636036 −0.318018 0.948085i \(-0.603017\pi\)
−0.318018 + 0.948085i \(0.603017\pi\)
\(500\) −2.44141e32 −0.0447214
\(501\) 1.68992e33 0.301921
\(502\) −5.33922e33 −0.930425
\(503\) 6.76442e33 1.14982 0.574911 0.818216i \(-0.305037\pi\)
0.574911 + 0.818216i \(0.305037\pi\)
\(504\) −1.52927e33 −0.253573
\(505\) 7.81679e32 0.126441
\(506\) 3.80484e31 0.00600419
\(507\) −6.35948e32 −0.0979089
\(508\) −4.71299e33 −0.707947
\(509\) 6.69189e33 0.980791 0.490395 0.871500i \(-0.336852\pi\)
0.490395 + 0.871500i \(0.336852\pi\)
\(510\) −9.31520e32 −0.133219
\(511\) −1.53609e34 −2.14365
\(512\) 3.24519e32 0.0441942
\(513\) −3.92432e33 −0.521551
\(514\) −9.07672e33 −1.17731
\(515\) 1.32763e32 0.0168069
\(516\) 4.75257e33 0.587229
\(517\) 5.41105e32 0.0652603
\(518\) −8.91511e33 −1.04955
\(519\) 5.34383e33 0.614130
\(520\) −1.30260e33 −0.146140
\(521\) −1.12229e34 −1.22923 −0.614616 0.788826i \(-0.710689\pi\)
−0.614616 + 0.788826i \(0.710689\pi\)
\(522\) −1.77106e33 −0.189388
\(523\) 7.35349e33 0.767754 0.383877 0.923384i \(-0.374589\pi\)
0.383877 + 0.923384i \(0.374589\pi\)
\(524\) 6.57136e33 0.669906
\(525\) 1.76480e33 0.175673
\(526\) 1.38141e33 0.134277
\(527\) 4.68414e33 0.444628
\(528\) 6.23534e31 0.00578011
\(529\) −1.03732e34 −0.939115
\(530\) 2.00272e33 0.177081
\(531\) −9.31326e33 −0.804304
\(532\) 3.88451e33 0.327673
\(533\) 7.95499e33 0.655465
\(534\) 4.43694e33 0.357123
\(535\) 3.55377e33 0.279426
\(536\) −3.90606e33 −0.300040
\(537\) −1.25913e34 −0.944912
\(538\) −1.69519e34 −1.24291
\(539\) 3.40667e32 0.0244046
\(540\) 3.32374e33 0.232651
\(541\) 6.91384e32 0.0472883 0.0236441 0.999720i \(-0.492473\pi\)
0.0236441 + 0.999720i \(0.492473\pi\)
\(542\) 9.34216e32 0.0624390
\(543\) 8.30881e33 0.542677
\(544\) 1.73658e33 0.110843
\(545\) 8.13607e33 0.507526
\(546\) 9.41600e33 0.574062
\(547\) 1.40577e34 0.837672 0.418836 0.908062i \(-0.362438\pi\)
0.418836 + 0.908062i \(0.362438\pi\)
\(548\) 1.22573e32 0.00713902
\(549\) 1.11692e34 0.635867
\(550\) 8.74507e31 0.00486665
\(551\) 4.49866e33 0.244731
\(552\) 1.10212e33 0.0586127
\(553\) −2.05178e34 −1.06676
\(554\) 1.55090e34 0.788335
\(555\) 6.86411e33 0.341132
\(556\) 1.56364e34 0.759803
\(557\) −2.49292e34 −1.18445 −0.592227 0.805771i \(-0.701751\pi\)
−0.592227 + 0.805771i \(0.701751\pi\)
\(558\) −5.92081e33 −0.275076
\(559\) 3.55633e34 1.61568
\(560\) −3.29002e33 −0.146167
\(561\) 3.33669e32 0.0144971
\(562\) 1.99644e34 0.848306
\(563\) −1.70240e34 −0.707466 −0.353733 0.935346i \(-0.615088\pi\)
−0.353733 + 0.935346i \(0.615088\pi\)
\(564\) 1.56738e34 0.637068
\(565\) −4.18098e33 −0.166216
\(566\) −3.19248e33 −0.124143
\(567\) −5.17070e33 −0.196680
\(568\) 1.41988e33 0.0528319
\(569\) 1.90307e34 0.692709 0.346355 0.938104i \(-0.387419\pi\)
0.346355 + 0.938104i \(0.387419\pi\)
\(570\) −2.99084e33 −0.106502
\(571\) 2.13655e34 0.744323 0.372162 0.928168i \(-0.378617\pi\)
0.372162 + 0.928168i \(0.378617\pi\)
\(572\) 4.66588e32 0.0159031
\(573\) −9.04669e33 −0.301687
\(574\) 2.00923e34 0.655587
\(575\) 1.54573e33 0.0493497
\(576\) −2.19506e33 −0.0685748
\(577\) −2.06745e34 −0.632030 −0.316015 0.948754i \(-0.602345\pi\)
−0.316015 + 0.948754i \(0.602345\pi\)
\(578\) −1.43436e34 −0.429102
\(579\) 2.08987e34 0.611839
\(580\) −3.81019e33 −0.109168
\(581\) −5.35291e34 −1.50103
\(582\) −3.25988e34 −0.894672
\(583\) −7.17372e32 −0.0192703
\(584\) −2.20484e34 −0.579717
\(585\) 8.81082e33 0.226761
\(586\) 3.67713e34 0.926380
\(587\) −5.55725e34 −1.37052 −0.685258 0.728301i \(-0.740310\pi\)
−0.685258 + 0.728301i \(0.740310\pi\)
\(588\) 9.86789e33 0.238236
\(589\) 1.50394e34 0.355460
\(590\) −2.00362e34 −0.463624
\(591\) −3.66808e34 −0.830989
\(592\) −1.27964e34 −0.283835
\(593\) −6.93628e34 −1.50641 −0.753204 0.657787i \(-0.771493\pi\)
−0.753204 + 0.657787i \(0.771493\pi\)
\(594\) −1.19056e33 −0.0253175
\(595\) −1.76057e34 −0.366600
\(596\) −4.81326e34 −0.981434
\(597\) −1.14979e34 −0.229584
\(598\) 8.24713e33 0.161264
\(599\) −3.28492e34 −0.629056 −0.314528 0.949248i \(-0.601846\pi\)
−0.314528 + 0.949248i \(0.601846\pi\)
\(600\) 2.53313e33 0.0475080
\(601\) −2.89648e34 −0.532034 −0.266017 0.963968i \(-0.585708\pi\)
−0.266017 + 0.963968i \(0.585708\pi\)
\(602\) 8.98237e34 1.61598
\(603\) 2.64207e34 0.465563
\(604\) 1.06556e34 0.183914
\(605\) 2.64206e34 0.446684
\(606\) −8.11046e33 −0.134319
\(607\) 8.42327e34 1.36654 0.683270 0.730166i \(-0.260557\pi\)
0.683270 + 0.730166i \(0.260557\pi\)
\(608\) 5.57566e33 0.0886138
\(609\) 2.75425e34 0.428832
\(610\) 2.40289e34 0.366532
\(611\) 1.17286e35 1.75280
\(612\) −1.17463e34 −0.171992
\(613\) 1.08389e34 0.155499 0.0777496 0.996973i \(-0.475227\pi\)
0.0777496 + 0.996973i \(0.475227\pi\)
\(614\) −4.24829e34 −0.597185
\(615\) −1.54699e34 −0.213083
\(616\) 1.17848e33 0.0159061
\(617\) 7.99721e33 0.105773 0.0528864 0.998601i \(-0.483158\pi\)
0.0528864 + 0.998601i \(0.483158\pi\)
\(618\) −1.37751e33 −0.0178541
\(619\) −6.34272e34 −0.805643 −0.402822 0.915279i \(-0.631970\pi\)
−0.402822 + 0.915279i \(0.631970\pi\)
\(620\) −1.27378e34 −0.158562
\(621\) −2.10436e34 −0.256729
\(622\) −1.57789e34 −0.188668
\(623\) 8.38582e34 0.982755
\(624\) 1.35153e34 0.155246
\(625\) 3.55271e33 0.0400000
\(626\) −1.08035e35 −1.19229
\(627\) 1.07131e33 0.0115897
\(628\) −4.22427e34 −0.447977
\(629\) −6.84766e34 −0.711884
\(630\) 2.22539e34 0.226803
\(631\) 1.41569e35 1.41449 0.707245 0.706968i \(-0.249938\pi\)
0.707245 + 0.706968i \(0.249938\pi\)
\(632\) −2.94505e34 −0.288489
\(633\) 9.86683e34 0.947614
\(634\) −1.49639e34 −0.140906
\(635\) 6.85831e34 0.633207
\(636\) −2.07797e34 −0.188115
\(637\) 7.38409e34 0.655472
\(638\) 1.36480e33 0.0118799
\(639\) −9.60410e33 −0.0819778
\(640\) −4.72237e33 −0.0395285
\(641\) −4.50631e34 −0.369910 −0.184955 0.982747i \(-0.559214\pi\)
−0.184955 + 0.982747i \(0.559214\pi\)
\(642\) −3.68728e34 −0.296837
\(643\) 1.18877e35 0.938561 0.469280 0.883049i \(-0.344513\pi\)
0.469280 + 0.883049i \(0.344513\pi\)
\(644\) 2.08301e34 0.161294
\(645\) −6.91590e34 −0.525233
\(646\) 2.98367e34 0.222252
\(647\) 1.85298e34 0.135384 0.0676921 0.997706i \(-0.478436\pi\)
0.0676921 + 0.997706i \(0.478436\pi\)
\(648\) −7.42181e33 −0.0531890
\(649\) 7.17694e33 0.0504522
\(650\) 1.89553e34 0.130711
\(651\) 9.20771e34 0.622858
\(652\) −8.21234e33 −0.0544970
\(653\) −1.84607e35 −1.20180 −0.600902 0.799323i \(-0.705192\pi\)
−0.600902 + 0.799323i \(0.705192\pi\)
\(654\) −8.44173e34 −0.539150
\(655\) −9.56258e34 −0.599182
\(656\) 2.88396e34 0.177293
\(657\) 1.49136e35 0.899530
\(658\) 2.96235e35 1.75313
\(659\) −3.04390e35 −1.76752 −0.883758 0.467944i \(-0.844995\pi\)
−0.883758 + 0.467944i \(0.844995\pi\)
\(660\) −9.07362e32 −0.00516989
\(661\) 2.88465e34 0.161278 0.0806389 0.996743i \(-0.474304\pi\)
0.0806389 + 0.996743i \(0.474304\pi\)
\(662\) −1.03339e35 −0.566945
\(663\) 7.23240e34 0.389371
\(664\) −7.68334e34 −0.405928
\(665\) −5.65270e34 −0.293079
\(666\) 8.65552e34 0.440418
\(667\) 2.41235e34 0.120467
\(668\) 4.58446e34 0.224689
\(669\) 1.81371e35 0.872452
\(670\) 5.68406e34 0.268364
\(671\) −8.60712e33 −0.0398865
\(672\) 3.41363e34 0.155275
\(673\) −6.39436e34 −0.285502 −0.142751 0.989759i \(-0.545595\pi\)
−0.142751 + 0.989759i \(0.545595\pi\)
\(674\) −1.05463e35 −0.462225
\(675\) −4.83668e34 −0.208090
\(676\) −1.72522e34 −0.0728636
\(677\) 6.00220e34 0.248858 0.124429 0.992229i \(-0.460290\pi\)
0.124429 + 0.992229i \(0.460290\pi\)
\(678\) 4.33806e34 0.176573
\(679\) −6.16117e35 −2.46202
\(680\) −2.52706e34 −0.0991410
\(681\) 1.76894e35 0.681358
\(682\) 4.56266e33 0.0172549
\(683\) −3.76829e35 −1.39922 −0.699610 0.714525i \(-0.746643\pi\)
−0.699610 + 0.714525i \(0.746643\pi\)
\(684\) −3.77140e34 −0.137499
\(685\) −1.78367e33 −0.00638533
\(686\) −7.64813e34 −0.268846
\(687\) −1.40890e35 −0.486317
\(688\) 1.28929e35 0.437015
\(689\) −1.55493e35 −0.517572
\(690\) −1.60380e34 −0.0524248
\(691\) −3.26709e35 −1.04878 −0.524392 0.851477i \(-0.675707\pi\)
−0.524392 + 0.851477i \(0.675707\pi\)
\(692\) 1.44969e35 0.457034
\(693\) −7.97129e33 −0.0246810
\(694\) −7.00657e34 −0.213065
\(695\) −2.27539e35 −0.679588
\(696\) 3.95334e34 0.115971
\(697\) 1.54328e35 0.444667
\(698\) 2.84082e35 0.803991
\(699\) 4.30332e35 1.19630
\(700\) 4.78762e34 0.130736
\(701\) 3.88741e35 1.04276 0.521381 0.853324i \(-0.325417\pi\)
0.521381 + 0.853324i \(0.325417\pi\)
\(702\) −2.58058e35 −0.679992
\(703\) −2.19859e35 −0.569118
\(704\) 1.69154e33 0.00430155
\(705\) −2.28084e35 −0.569811
\(706\) 5.00669e34 0.122883
\(707\) −1.53288e35 −0.369628
\(708\) 2.07890e35 0.492512
\(709\) 4.23533e35 0.985848 0.492924 0.870072i \(-0.335928\pi\)
0.492924 + 0.870072i \(0.335928\pi\)
\(710\) −2.06619e34 −0.0472543
\(711\) 1.99204e35 0.447639
\(712\) 1.20367e35 0.265770
\(713\) 8.06469e34 0.174972
\(714\) 1.82672e35 0.389443
\(715\) −6.78975e33 −0.0142242
\(716\) −3.41580e35 −0.703201
\(717\) 9.07941e34 0.183683
\(718\) 2.15564e35 0.428568
\(719\) 6.21554e35 1.21442 0.607208 0.794543i \(-0.292289\pi\)
0.607208 + 0.794543i \(0.292289\pi\)
\(720\) 3.19423e34 0.0613352
\(721\) −2.60349e34 −0.0491321
\(722\) −2.85444e35 −0.529427
\(723\) 4.86608e35 0.887055
\(724\) 2.25404e35 0.403859
\(725\) 5.54456e34 0.0976432
\(726\) −2.74132e35 −0.474517
\(727\) −4.24475e35 −0.722225 −0.361112 0.932522i \(-0.617603\pi\)
−0.361112 + 0.932522i \(0.617603\pi\)
\(728\) 2.55440e35 0.427216
\(729\) 4.75404e35 0.781572
\(730\) 3.20846e35 0.518514
\(731\) 6.89932e35 1.09607
\(732\) −2.49317e35 −0.389371
\(733\) 7.04925e34 0.108229 0.0541145 0.998535i \(-0.482766\pi\)
0.0541145 + 0.998535i \(0.482766\pi\)
\(734\) −4.28995e34 −0.0647518
\(735\) −1.43597e35 −0.213085
\(736\) 2.98987e34 0.0436194
\(737\) −2.03602e34 −0.0292037
\(738\) −1.95072e35 −0.275100
\(739\) −9.55082e35 −1.32430 −0.662148 0.749373i \(-0.730355\pi\)
−0.662148 + 0.749373i \(0.730355\pi\)
\(740\) 1.86212e35 0.253870
\(741\) 2.32212e35 0.311284
\(742\) −3.92736e35 −0.517668
\(743\) −1.29129e35 −0.167364 −0.0836820 0.996493i \(-0.526668\pi\)
−0.0836820 + 0.996493i \(0.526668\pi\)
\(744\) 1.32164e35 0.168442
\(745\) 7.00422e35 0.877821
\(746\) −5.11909e35 −0.630896
\(747\) 5.19704e35 0.629867
\(748\) 9.05187e33 0.0107887
\(749\) −6.96897e35 −0.816857
\(750\) −3.68619e34 −0.0424924
\(751\) −1.00002e36 −1.13373 −0.566864 0.823812i \(-0.691843\pi\)
−0.566864 + 0.823812i \(0.691843\pi\)
\(752\) 4.25204e35 0.474105
\(753\) −8.06149e35 −0.884052
\(754\) 2.95827e35 0.319077
\(755\) −1.55059e35 −0.164498
\(756\) −6.51788e35 −0.680118
\(757\) −4.62323e35 −0.474511 −0.237256 0.971447i \(-0.576248\pi\)
−0.237256 + 0.971447i \(0.576248\pi\)
\(758\) −7.01138e35 −0.707846
\(759\) 5.74478e33 0.00570494
\(760\) −8.11365e34 −0.0792586
\(761\) 1.71968e36 1.65249 0.826247 0.563308i \(-0.190471\pi\)
0.826247 + 0.563308i \(0.190471\pi\)
\(762\) −7.11597e35 −0.672662
\(763\) −1.59549e36 −1.48367
\(764\) −2.45421e35 −0.224515
\(765\) 1.70931e35 0.153834
\(766\) −1.07981e36 −0.956069
\(767\) 1.55563e36 1.35508
\(768\) 4.89978e34 0.0419915
\(769\) 1.91462e36 1.61437 0.807184 0.590299i \(-0.200990\pi\)
0.807184 + 0.590299i \(0.200990\pi\)
\(770\) −1.71492e34 −0.0142268
\(771\) −1.37046e36 −1.11863
\(772\) 5.66947e35 0.455330
\(773\) −9.08398e35 −0.717848 −0.358924 0.933367i \(-0.616856\pi\)
−0.358924 + 0.933367i \(0.616856\pi\)
\(774\) −8.72082e35 −0.678103
\(775\) 1.85360e35 0.141822
\(776\) −8.84349e35 −0.665813
\(777\) −1.34606e36 −0.997243
\(778\) 1.23522e36 0.900532
\(779\) 4.95503e35 0.355490
\(780\) −1.96674e35 −0.138856
\(781\) 7.40106e33 0.00514229
\(782\) 1.59995e35 0.109402
\(783\) −7.54839e35 −0.507963
\(784\) 2.67699e35 0.177295
\(785\) 6.14712e35 0.400683
\(786\) 9.92184e35 0.636518
\(787\) 5.77613e35 0.364714 0.182357 0.983232i \(-0.441627\pi\)
0.182357 + 0.983232i \(0.441627\pi\)
\(788\) −9.95088e35 −0.618420
\(789\) 2.08574e35 0.127584
\(790\) 4.28561e35 0.258032
\(791\) 8.19893e35 0.485905
\(792\) −1.14417e34 −0.00667459
\(793\) −1.86563e36 −1.07130
\(794\) 1.47819e36 0.835552
\(795\) 3.02384e35 0.168256
\(796\) −3.11920e35 −0.170856
\(797\) 1.37116e36 0.739364 0.369682 0.929158i \(-0.379467\pi\)
0.369682 + 0.929158i \(0.379467\pi\)
\(798\) 5.86507e35 0.311341
\(799\) 2.27537e36 1.18910
\(800\) 6.87195e34 0.0353553
\(801\) −8.14165e35 −0.412388
\(802\) 1.39611e36 0.696211
\(803\) −1.14926e35 −0.0564255
\(804\) −5.89761e35 −0.285085
\(805\) −3.03118e35 −0.144266
\(806\) 9.88975e35 0.463444
\(807\) −2.55951e36 −1.18096
\(808\) −2.20023e35 −0.0999600
\(809\) 3.58962e36 1.60580 0.802902 0.596111i \(-0.203288\pi\)
0.802902 + 0.596111i \(0.203288\pi\)
\(810\) 1.08001e35 0.0475737
\(811\) 1.03429e35 0.0448624 0.0224312 0.999748i \(-0.492859\pi\)
0.0224312 + 0.999748i \(0.492859\pi\)
\(812\) 7.47182e35 0.319136
\(813\) 1.41054e35 0.0593270
\(814\) −6.67007e34 −0.0276265
\(815\) 1.19505e35 0.0487436
\(816\) 2.62200e35 0.105319
\(817\) 2.21518e36 0.876259
\(818\) 7.73407e35 0.301295
\(819\) −1.72781e36 −0.662898
\(820\) −4.19671e35 −0.158576
\(821\) −2.70025e36 −1.00488 −0.502439 0.864612i \(-0.667564\pi\)
−0.502439 + 0.864612i \(0.667564\pi\)
\(822\) 1.85069e34 0.00678320
\(823\) −2.53917e36 −0.916630 −0.458315 0.888790i \(-0.651547\pi\)
−0.458315 + 0.888790i \(0.651547\pi\)
\(824\) −3.73695e34 −0.0132870
\(825\) 1.32039e34 0.00462409
\(826\) 3.92912e36 1.35533
\(827\) 2.67322e36 0.908270 0.454135 0.890933i \(-0.349948\pi\)
0.454135 + 0.890933i \(0.349948\pi\)
\(828\) −2.02236e35 −0.0676830
\(829\) −5.79155e36 −1.90925 −0.954626 0.297806i \(-0.903745\pi\)
−0.954626 + 0.297806i \(0.903745\pi\)
\(830\) 1.11807e36 0.363073
\(831\) 2.34164e36 0.749044
\(832\) 3.66648e35 0.115534
\(833\) 1.43252e36 0.444672
\(834\) 2.36088e36 0.721934
\(835\) −6.67126e35 −0.200968
\(836\) 2.90630e34 0.00862504
\(837\) −2.52349e36 −0.737792
\(838\) −2.67673e36 −0.770999
\(839\) −2.27845e36 −0.646568 −0.323284 0.946302i \(-0.604787\pi\)
−0.323284 + 0.946302i \(0.604787\pi\)
\(840\) −4.96748e35 −0.138882
\(841\) −2.76505e36 −0.761645
\(842\) −3.30366e36 −0.896590
\(843\) 3.01435e36 0.806026
\(844\) 2.67671e36 0.705212
\(845\) 2.51053e35 0.0651712
\(846\) −2.87610e36 −0.735655
\(847\) −5.18110e36 −1.30581
\(848\) −5.63717e35 −0.139995
\(849\) −4.82020e35 −0.117956
\(850\) 3.67735e35 0.0886744
\(851\) −1.17896e36 −0.280144
\(852\) 2.14382e35 0.0501988
\(853\) 3.72321e36 0.859122 0.429561 0.903038i \(-0.358668\pi\)
0.429561 + 0.903038i \(0.358668\pi\)
\(854\) −4.71209e36 −1.07150
\(855\) 5.48811e35 0.122983
\(856\) −1.00030e36 −0.220906
\(857\) 1.02353e36 0.222761 0.111381 0.993778i \(-0.464473\pi\)
0.111381 + 0.993778i \(0.464473\pi\)
\(858\) 7.04483e34 0.0151105
\(859\) 1.85947e36 0.393074 0.196537 0.980496i \(-0.437030\pi\)
0.196537 + 0.980496i \(0.437030\pi\)
\(860\) −1.87617e36 −0.390878
\(861\) 3.03365e36 0.622912
\(862\) −7.76670e35 −0.157180
\(863\) 8.67106e36 1.72957 0.864783 0.502146i \(-0.167456\pi\)
0.864783 + 0.502146i \(0.167456\pi\)
\(864\) −9.35550e35 −0.183927
\(865\) −2.10958e36 −0.408784
\(866\) 6.38876e36 1.22023
\(867\) −2.16569e36 −0.407716
\(868\) 2.49790e36 0.463530
\(869\) −1.53510e35 −0.0280794
\(870\) −5.75287e35 −0.103727
\(871\) −4.41315e36 −0.784372
\(872\) −2.29010e36 −0.401235
\(873\) 5.98177e36 1.03312
\(874\) 5.13700e35 0.0874614
\(875\) −6.96690e35 −0.116933
\(876\) −3.32900e36 −0.550823
\(877\) −7.14177e36 −1.16496 −0.582480 0.812845i \(-0.697918\pi\)
−0.582480 + 0.812845i \(0.697918\pi\)
\(878\) −7.11674e36 −1.14446
\(879\) 5.55196e36 0.880209
\(880\) −2.46152e34 −0.00384742
\(881\) −3.00182e36 −0.462579 −0.231290 0.972885i \(-0.574294\pi\)
−0.231290 + 0.972885i \(0.574294\pi\)
\(882\) −1.81073e36 −0.275103
\(883\) −2.65767e36 −0.398100 −0.199050 0.979989i \(-0.563786\pi\)
−0.199050 + 0.979989i \(0.563786\pi\)
\(884\) 1.96203e36 0.289769
\(885\) −3.02519e36 −0.440516
\(886\) 8.56516e36 1.22974
\(887\) 2.39194e36 0.338613 0.169307 0.985563i \(-0.445847\pi\)
0.169307 + 0.985563i \(0.445847\pi\)
\(888\) −1.93208e36 −0.269688
\(889\) −1.34492e37 −1.85108
\(890\) −1.75157e36 −0.237712
\(891\) −3.86859e34 −0.00517704
\(892\) 4.92029e36 0.649277
\(893\) 7.30557e36 0.950629
\(894\) −7.26736e36 −0.932519
\(895\) 4.97064e36 0.628962
\(896\) 9.26060e35 0.115555
\(897\) 1.24520e36 0.153227
\(898\) −1.05428e36 −0.127938
\(899\) 2.89282e36 0.346199
\(900\) −4.64821e35 −0.0548598
\(901\) −3.01659e36 −0.351121
\(902\) 1.50326e35 0.0172564
\(903\) 1.35621e37 1.53543
\(904\) 1.17684e36 0.131405
\(905\) −3.28006e36 −0.361222
\(906\) 1.60885e36 0.174748
\(907\) 1.27834e37 1.36948 0.684741 0.728787i \(-0.259915\pi\)
0.684741 + 0.728787i \(0.259915\pi\)
\(908\) 4.79885e36 0.507065
\(909\) 1.48824e36 0.155105
\(910\) −3.71714e36 −0.382113
\(911\) 1.51675e37 1.53792 0.768961 0.639296i \(-0.220774\pi\)
0.768961 + 0.639296i \(0.220774\pi\)
\(912\) 8.41848e35 0.0841973
\(913\) −4.00492e35 −0.0395102
\(914\) −1.34825e37 −1.31203
\(915\) 3.62804e36 0.348264
\(916\) −3.82210e36 −0.361916
\(917\) 1.87523e37 1.75161
\(918\) −5.00636e36 −0.461306
\(919\) −1.63543e36 −0.148658 −0.0743292 0.997234i \(-0.523682\pi\)
−0.0743292 + 0.997234i \(0.523682\pi\)
\(920\) −4.35084e35 −0.0390144
\(921\) −6.41432e36 −0.567421
\(922\) 1.15751e37 1.01015
\(923\) 1.60421e36 0.138115
\(924\) 1.77934e35 0.0151133
\(925\) −2.70974e36 −0.227068
\(926\) 1.29241e37 1.06847
\(927\) 2.52769e35 0.0206170
\(928\) 1.07247e36 0.0863052
\(929\) −7.47115e36 −0.593186 −0.296593 0.955004i \(-0.595850\pi\)
−0.296593 + 0.955004i \(0.595850\pi\)
\(930\) −1.92323e36 −0.150659
\(931\) 4.59943e36 0.355494
\(932\) 1.16742e37 0.890281
\(933\) −2.38240e36 −0.179265
\(934\) 5.99459e36 0.445065
\(935\) −1.31722e35 −0.00964969
\(936\) −2.48002e36 −0.179270
\(937\) −2.45447e37 −1.75070 −0.875351 0.483488i \(-0.839370\pi\)
−0.875351 + 0.483488i \(0.839370\pi\)
\(938\) −1.11465e37 −0.784517
\(939\) −1.63117e37 −1.13287
\(940\) −6.18754e36 −0.424052
\(941\) −1.35589e36 −0.0916968 −0.0458484 0.998948i \(-0.514599\pi\)
−0.0458484 + 0.998948i \(0.514599\pi\)
\(942\) −6.37806e36 −0.425650
\(943\) 2.65707e36 0.174987
\(944\) 5.63969e36 0.366527
\(945\) 9.48477e36 0.608316
\(946\) 6.72040e35 0.0425359
\(947\) −2.07354e37 −1.29520 −0.647601 0.761980i \(-0.724227\pi\)
−0.647601 + 0.761980i \(0.724227\pi\)
\(948\) −4.44661e36 −0.274110
\(949\) −2.49107e37 −1.51551
\(950\) 1.18069e36 0.0708911
\(951\) −2.25934e36 −0.133883
\(952\) 4.95558e36 0.289823
\(953\) −2.04124e37 −1.17823 −0.589117 0.808048i \(-0.700524\pi\)
−0.589117 + 0.808048i \(0.700524\pi\)
\(954\) 3.81300e36 0.217226
\(955\) 3.57135e36 0.200812
\(956\) 2.46309e36 0.136696
\(957\) 2.06067e35 0.0112878
\(958\) −3.86932e35 −0.0209202
\(959\) 3.49780e35 0.0186665
\(960\) −7.13012e35 −0.0375584
\(961\) −9.56182e36 −0.497163
\(962\) −1.44576e37 −0.742009
\(963\) 6.76605e36 0.342773
\(964\) 1.32008e37 0.660144
\(965\) −8.25016e36 −0.407259
\(966\) 3.14506e36 0.153255
\(967\) −1.88209e37 −0.905333 −0.452666 0.891680i \(-0.649527\pi\)
−0.452666 + 0.891680i \(0.649527\pi\)
\(968\) −7.43674e36 −0.353135
\(969\) 4.50494e36 0.211174
\(970\) 1.28690e37 0.595521
\(971\) −2.62810e37 −1.20061 −0.600305 0.799771i \(-0.704954\pi\)
−0.600305 + 0.799771i \(0.704954\pi\)
\(972\) 1.04144e37 0.469686
\(973\) 4.46206e37 1.98667
\(974\) 1.21069e37 0.532163
\(975\) 2.86199e36 0.124197
\(976\) −6.76354e36 −0.289769
\(977\) 6.14194e36 0.259791 0.129895 0.991528i \(-0.458536\pi\)
0.129895 + 0.991528i \(0.458536\pi\)
\(978\) −1.23995e36 −0.0517808
\(979\) 6.27407e35 0.0258682
\(980\) −3.89553e36 −0.158577
\(981\) 1.54903e37 0.622584
\(982\) 1.30808e37 0.519089
\(983\) −5.02851e37 −1.97025 −0.985123 0.171849i \(-0.945026\pi\)
−0.985123 + 0.171849i \(0.945026\pi\)
\(984\) 4.35438e36 0.168457
\(985\) 1.44804e37 0.553132
\(986\) 5.73908e36 0.216461
\(987\) 4.47275e37 1.66575
\(988\) 6.29951e36 0.231657
\(989\) 1.18786e37 0.431331
\(990\) 1.66498e35 0.00596993
\(991\) −2.22624e37 −0.788226 −0.394113 0.919062i \(-0.628948\pi\)
−0.394113 + 0.919062i \(0.628948\pi\)
\(992\) 3.58538e36 0.125354
\(993\) −1.56028e37 −0.538688
\(994\) 4.05182e36 0.138140
\(995\) 4.53903e36 0.152818
\(996\) −1.16008e37 −0.385697
\(997\) −7.44693e36 −0.244505 −0.122253 0.992499i \(-0.539012\pi\)
−0.122253 + 0.992499i \(0.539012\pi\)
\(998\) −1.38707e37 −0.449745
\(999\) 3.68905e37 1.18126
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 10.26.a.d.1.2 2
5.2 odd 4 50.26.b.d.49.3 4
5.3 odd 4 50.26.b.d.49.2 4
5.4 even 2 50.26.a.d.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.26.a.d.1.2 2 1.1 even 1 trivial
50.26.a.d.1.1 2 5.4 even 2
50.26.b.d.49.2 4 5.3 odd 4
50.26.b.d.49.3 4 5.2 odd 4