Properties

Label 14.14.a.c.1.1
Level $14$
Weight $14$
Character 14.1
Self dual yes
Analytic conductor $15.012$
Analytic rank $0$
Dimension $2$
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] = [14,14,Mod(1,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 14.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: \(15.0123300533\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{100129}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 25032 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(158.716\) of defining polynomial
Character \(\chi\) \(=\) 14.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-64.0000 q^{2} -156.863 q^{3} +4096.00 q^{4} -23868.4 q^{5} +10039.3 q^{6} +117649. q^{7} -262144. q^{8} -1.56972e6 q^{9} +O(q^{10})\) \(q-64.0000 q^{2} -156.863 q^{3} +4096.00 q^{4} -23868.4 q^{5} +10039.3 q^{6} +117649. q^{7} -262144. q^{8} -1.56972e6 q^{9} +1.52758e6 q^{10} -7.69356e6 q^{11} -642512. q^{12} +3.39648e7 q^{13} -7.52954e6 q^{14} +3.74408e6 q^{15} +1.67772e7 q^{16} +2.76685e7 q^{17} +1.00462e8 q^{18} +3.67896e8 q^{19} -9.77649e7 q^{20} -1.84548e7 q^{21} +4.92388e8 q^{22} +1.11611e9 q^{23} +4.11208e7 q^{24} -6.51003e8 q^{25} -2.17375e9 q^{26} +4.96322e8 q^{27} +4.81890e8 q^{28} +1.26815e9 q^{29} -2.39621e8 q^{30} -1.12245e9 q^{31} -1.07374e9 q^{32} +1.20684e9 q^{33} -1.77078e9 q^{34} -2.80809e9 q^{35} -6.42956e9 q^{36} +6.44073e9 q^{37} -2.35453e10 q^{38} -5.32783e9 q^{39} +6.25696e9 q^{40} -2.85618e10 q^{41} +1.18111e9 q^{42} +3.62003e10 q^{43} -3.15128e10 q^{44} +3.74666e10 q^{45} -7.14308e10 q^{46} +6.27841e10 q^{47} -2.63173e9 q^{48} +1.38413e10 q^{49} +4.16642e10 q^{50} -4.34017e9 q^{51} +1.39120e11 q^{52} +2.48076e11 q^{53} -3.17646e10 q^{54} +1.83633e11 q^{55} -3.08410e10 q^{56} -5.77094e10 q^{57} -8.11618e10 q^{58} -3.81015e11 q^{59} +1.53357e10 q^{60} +3.52805e11 q^{61} +7.18371e10 q^{62} -1.84676e11 q^{63} +6.87195e10 q^{64} -8.10684e11 q^{65} -7.72376e10 q^{66} -1.39117e12 q^{67} +1.13330e11 q^{68} -1.75076e11 q^{69} +1.79718e11 q^{70} +8.06319e11 q^{71} +4.11492e11 q^{72} -1.13789e12 q^{73} -4.12207e11 q^{74} +1.02119e11 q^{75} +1.50690e12 q^{76} -9.05139e11 q^{77} +3.40981e11 q^{78} +3.95957e11 q^{79} -4.00445e11 q^{80} +2.42478e12 q^{81} +1.82795e12 q^{82} +1.41067e11 q^{83} -7.55909e10 q^{84} -6.60402e11 q^{85} -2.31682e12 q^{86} -1.98927e11 q^{87} +2.01682e12 q^{88} +3.02962e12 q^{89} -2.39786e12 q^{90} +3.99592e12 q^{91} +4.57157e12 q^{92} +1.76072e11 q^{93} -4.01818e12 q^{94} -8.78108e12 q^{95} +1.68431e11 q^{96} +6.73995e12 q^{97} -8.85842e11 q^{98} +1.20767e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 128 q^{2} + 952 q^{3} + 8192 q^{4} + 32004 q^{5} - 60928 q^{6} + 235298 q^{7} - 524288 q^{8} - 1934462 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 128 q^{2} + 952 q^{3} + 8192 q^{4} + 32004 q^{5} - 60928 q^{6} + 235298 q^{7} - 524288 q^{8} - 1934462 q^{9} - 2048256 q^{10} - 1352736 q^{11} + 3899392 q^{12} + 3510388 q^{13} - 15059072 q^{14} + 65698920 q^{15} + 33554432 q^{16} + 217711956 q^{17} + 123805568 q^{18} + 591335752 q^{19} + 131088384 q^{20} + 112001848 q^{21} + 86575104 q^{22} + 840735000 q^{23} - 249561088 q^{24} + 1250017766 q^{25} - 224664832 q^{26} - 1676016944 q^{27} + 963780608 q^{28} - 487623540 q^{29} - 4204730880 q^{30} + 2193076144 q^{31} - 2147483648 q^{32} + 8237940480 q^{33} - 13933565184 q^{34} + 3765238596 q^{35} - 7923556352 q^{36} + 405060268 q^{37} - 37845488128 q^{38} - 39097578952 q^{39} - 8389656576 q^{40} + 8518172628 q^{41} - 7168118272 q^{42} + 26225045296 q^{43} - 5540806656 q^{44} + 17087434308 q^{45} - 53807040000 q^{46} + 155048849760 q^{47} + 15971909632 q^{48} + 27682574402 q^{49} - 80001137024 q^{50} + 206392082208 q^{51} + 14378549248 q^{52} + 66007050492 q^{53} + 107265084416 q^{54} + 537909615936 q^{55} - 61681958912 q^{56} + 190054836824 q^{57} + 31207906560 q^{58} - 476362296984 q^{59} + 269102776320 q^{60} + 197378850004 q^{61} - 140356873216 q^{62} - 227587519838 q^{63} + 137438953472 q^{64} - 2512243760544 q^{65} - 527228190720 q^{66} - 1718732859488 q^{67} + 891748171776 q^{68} - 480424669200 q^{69} - 240975270144 q^{70} - 695543478336 q^{71} + 507107606528 q^{72} - 466085239340 q^{73} - 25923857152 q^{74} + 2210090828680 q^{75} + 2422111240192 q^{76} - 159148037664 q^{77} + 2502245052928 q^{78} - 2432016575840 q^{79} + 536938020864 q^{80} + 597475723018 q^{81} - 545163048192 q^{82} - 1743984494616 q^{83} + 458759569408 q^{84} + 9957781762488 q^{85} - 1678402898944 q^{86} - 2145843141792 q^{87} + 354611625984 q^{88} + 3022580240484 q^{89} - 1093595795712 q^{90} + 412993637812 q^{91} + 3443650560000 q^{92} + 3852541919312 q^{93} - 9923126384640 q^{94} + 3703032892440 q^{95} - 1022202216448 q^{96} + 7760062661092 q^{97} - 1771684761728 q^{98} + 9763922554848 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −64.0000 −0.707107
\(3\) −156.863 −0.124232 −0.0621160 0.998069i \(-0.519785\pi\)
−0.0621160 + 0.998069i \(0.519785\pi\)
\(4\) 4096.00 0.500000
\(5\) −23868.4 −0.683153 −0.341577 0.939854i \(-0.610961\pi\)
−0.341577 + 0.939854i \(0.610961\pi\)
\(6\) 10039.3 0.0878453
\(7\) 117649. 0.377964
\(8\) −262144. −0.353553
\(9\) −1.56972e6 −0.984566
\(10\) 1.52758e6 0.483062
\(11\) −7.69356e6 −1.30941 −0.654704 0.755886i \(-0.727207\pi\)
−0.654704 + 0.755886i \(0.727207\pi\)
\(12\) −642512. −0.0621160
\(13\) 3.39648e7 1.95163 0.975814 0.218604i \(-0.0701501\pi\)
0.975814 + 0.218604i \(0.0701501\pi\)
\(14\) −7.52954e6 −0.267261
\(15\) 3.74408e6 0.0848694
\(16\) 1.67772e7 0.250000
\(17\) 2.76685e7 0.278014 0.139007 0.990291i \(-0.455609\pi\)
0.139007 + 0.990291i \(0.455609\pi\)
\(18\) 1.00462e8 0.696194
\(19\) 3.67896e8 1.79402 0.897009 0.442013i \(-0.145736\pi\)
0.897009 + 0.442013i \(0.145736\pi\)
\(20\) −9.77649e7 −0.341577
\(21\) −1.84548e7 −0.0469553
\(22\) 4.92388e8 0.925891
\(23\) 1.11611e9 1.57208 0.786040 0.618176i \(-0.212128\pi\)
0.786040 + 0.618176i \(0.212128\pi\)
\(24\) 4.11208e7 0.0439226
\(25\) −6.51003e8 −0.533302
\(26\) −2.17375e9 −1.38001
\(27\) 4.96322e8 0.246547
\(28\) 4.81890e8 0.188982
\(29\) 1.26815e9 0.395899 0.197950 0.980212i \(-0.436572\pi\)
0.197950 + 0.980212i \(0.436572\pi\)
\(30\) −2.39621e8 −0.0600118
\(31\) −1.12245e9 −0.227153 −0.113576 0.993529i \(-0.536231\pi\)
−0.113576 + 0.993529i \(0.536231\pi\)
\(32\) −1.07374e9 −0.176777
\(33\) 1.20684e9 0.162670
\(34\) −1.77078e9 −0.196586
\(35\) −2.80809e9 −0.258208
\(36\) −6.42956e9 −0.492283
\(37\) 6.44073e9 0.412690 0.206345 0.978479i \(-0.433843\pi\)
0.206345 + 0.978479i \(0.433843\pi\)
\(38\) −2.35453e10 −1.26856
\(39\) −5.32783e9 −0.242454
\(40\) 6.25696e9 0.241531
\(41\) −2.85618e10 −0.939052 −0.469526 0.882919i \(-0.655575\pi\)
−0.469526 + 0.882919i \(0.655575\pi\)
\(42\) 1.18111e9 0.0332024
\(43\) 3.62003e10 0.873309 0.436654 0.899629i \(-0.356163\pi\)
0.436654 + 0.899629i \(0.356163\pi\)
\(44\) −3.15128e10 −0.654704
\(45\) 3.74666e10 0.672610
\(46\) −7.14308e10 −1.11163
\(47\) 6.27841e10 0.849599 0.424799 0.905288i \(-0.360345\pi\)
0.424799 + 0.905288i \(0.360345\pi\)
\(48\) −2.63173e9 −0.0310580
\(49\) 1.38413e10 0.142857
\(50\) 4.16642e10 0.377101
\(51\) −4.34017e9 −0.0345383
\(52\) 1.39120e11 0.975814
\(53\) 2.48076e11 1.53742 0.768708 0.639600i \(-0.220900\pi\)
0.768708 + 0.639600i \(0.220900\pi\)
\(54\) −3.17646e10 −0.174335
\(55\) 1.83633e11 0.894526
\(56\) −3.08410e10 −0.133631
\(57\) −5.77094e10 −0.222874
\(58\) −8.11618e10 −0.279943
\(59\) −3.81015e11 −1.17599 −0.587995 0.808865i \(-0.700082\pi\)
−0.587995 + 0.808865i \(0.700082\pi\)
\(60\) 1.53357e10 0.0424347
\(61\) 3.52805e11 0.876780 0.438390 0.898785i \(-0.355549\pi\)
0.438390 + 0.898785i \(0.355549\pi\)
\(62\) 7.18371e10 0.160621
\(63\) −1.84676e11 −0.372131
\(64\) 6.87195e10 0.125000
\(65\) −8.10684e11 −1.33326
\(66\) −7.72376e10 −0.115025
\(67\) −1.39117e12 −1.87886 −0.939429 0.342744i \(-0.888644\pi\)
−0.939429 + 0.342744i \(0.888644\pi\)
\(68\) 1.13330e11 0.139007
\(69\) −1.75076e11 −0.195302
\(70\) 1.79718e11 0.182580
\(71\) 8.06319e11 0.747012 0.373506 0.927628i \(-0.378155\pi\)
0.373506 + 0.927628i \(0.378155\pi\)
\(72\) 4.11492e11 0.348097
\(73\) −1.13789e12 −0.880035 −0.440018 0.897989i \(-0.645028\pi\)
−0.440018 + 0.897989i \(0.645028\pi\)
\(74\) −4.12207e11 −0.291816
\(75\) 1.02119e11 0.0662531
\(76\) 1.50690e12 0.897009
\(77\) −9.05139e11 −0.494909
\(78\) 3.40981e11 0.171441
\(79\) 3.95957e11 0.183262 0.0916308 0.995793i \(-0.470792\pi\)
0.0916308 + 0.995793i \(0.470792\pi\)
\(80\) −4.00445e11 −0.170788
\(81\) 2.42478e12 0.953937
\(82\) 1.82795e12 0.664010
\(83\) 1.41067e11 0.0473608 0.0236804 0.999720i \(-0.492462\pi\)
0.0236804 + 0.999720i \(0.492462\pi\)
\(84\) −7.55909e10 −0.0234776
\(85\) −6.60402e11 −0.189926
\(86\) −2.31682e12 −0.617523
\(87\) −1.98927e11 −0.0491833
\(88\) 2.01682e12 0.462945
\(89\) 3.02962e12 0.646180 0.323090 0.946368i \(-0.395278\pi\)
0.323090 + 0.946368i \(0.395278\pi\)
\(90\) −2.39786e12 −0.475607
\(91\) 3.99592e12 0.737646
\(92\) 4.57157e12 0.786040
\(93\) 1.76072e11 0.0282196
\(94\) −4.01818e12 −0.600757
\(95\) −8.78108e12 −1.22559
\(96\) 1.68431e11 0.0219613
\(97\) 6.73995e12 0.821562 0.410781 0.911734i \(-0.365256\pi\)
0.410781 + 0.911734i \(0.365256\pi\)
\(98\) −8.85842e11 −0.101015
\(99\) 1.20767e13 1.28920
\(100\) −2.66651e12 −0.266651
\(101\) −9.08439e12 −0.851543 −0.425772 0.904831i \(-0.639997\pi\)
−0.425772 + 0.904831i \(0.639997\pi\)
\(102\) 2.77771e11 0.0244222
\(103\) 1.26254e12 0.104185 0.0520924 0.998642i \(-0.483411\pi\)
0.0520924 + 0.998642i \(0.483411\pi\)
\(104\) −8.90366e12 −0.690005
\(105\) 4.40487e11 0.0320776
\(106\) −1.58768e13 −1.08712
\(107\) −1.91740e13 −1.23515 −0.617573 0.786514i \(-0.711884\pi\)
−0.617573 + 0.786514i \(0.711884\pi\)
\(108\) 2.03293e12 0.123273
\(109\) 3.17798e13 1.81501 0.907505 0.420040i \(-0.137984\pi\)
0.907505 + 0.420040i \(0.137984\pi\)
\(110\) −1.17525e13 −0.632525
\(111\) −1.01031e12 −0.0512693
\(112\) 1.97382e12 0.0944911
\(113\) 7.26494e12 0.328263 0.164132 0.986438i \(-0.447518\pi\)
0.164132 + 0.986438i \(0.447518\pi\)
\(114\) 3.69340e12 0.157596
\(115\) −2.66396e13 −1.07397
\(116\) 5.19436e12 0.197950
\(117\) −5.33151e13 −1.92151
\(118\) 2.43849e13 0.831550
\(119\) 3.25517e12 0.105080
\(120\) −9.81487e11 −0.0300059
\(121\) 2.46681e13 0.714547
\(122\) −2.25795e13 −0.619977
\(123\) 4.48029e12 0.116660
\(124\) −4.59757e12 −0.113576
\(125\) 4.46746e13 1.04748
\(126\) 1.18192e13 0.263136
\(127\) 2.95105e13 0.624098 0.312049 0.950066i \(-0.398985\pi\)
0.312049 + 0.950066i \(0.398985\pi\)
\(128\) −4.39805e12 −0.0883883
\(129\) −5.67851e12 −0.108493
\(130\) 5.18838e13 0.942758
\(131\) −1.77852e13 −0.307465 −0.153732 0.988113i \(-0.549129\pi\)
−0.153732 + 0.988113i \(0.549129\pi\)
\(132\) 4.94320e12 0.0813351
\(133\) 4.32826e13 0.678075
\(134\) 8.90349e13 1.32855
\(135\) −1.18464e13 −0.168429
\(136\) −7.25312e12 −0.0982929
\(137\) 1.05369e14 1.36153 0.680767 0.732500i \(-0.261647\pi\)
0.680767 + 0.732500i \(0.261647\pi\)
\(138\) 1.12049e13 0.138100
\(139\) −5.89997e13 −0.693831 −0.346915 0.937896i \(-0.612771\pi\)
−0.346915 + 0.937896i \(0.612771\pi\)
\(140\) −1.15019e13 −0.129104
\(141\) −9.84853e12 −0.105547
\(142\) −5.16044e13 −0.528217
\(143\) −2.61310e14 −2.55547
\(144\) −2.63355e13 −0.246142
\(145\) −3.02688e13 −0.270460
\(146\) 7.28247e13 0.622279
\(147\) −2.17119e12 −0.0177474
\(148\) 2.63812e13 0.206345
\(149\) −1.56999e14 −1.17540 −0.587700 0.809079i \(-0.699967\pi\)
−0.587700 + 0.809079i \(0.699967\pi\)
\(150\) −6.53558e12 −0.0468480
\(151\) 6.48245e13 0.445030 0.222515 0.974929i \(-0.428573\pi\)
0.222515 + 0.974929i \(0.428573\pi\)
\(152\) −9.64417e13 −0.634281
\(153\) −4.34317e13 −0.273724
\(154\) 5.79289e13 0.349954
\(155\) 2.67912e13 0.155180
\(156\) −2.18228e13 −0.121227
\(157\) −4.47531e12 −0.0238493 −0.0119246 0.999929i \(-0.503796\pi\)
−0.0119246 + 0.999929i \(0.503796\pi\)
\(158\) −2.53412e13 −0.129586
\(159\) −3.89140e13 −0.190996
\(160\) 2.56285e13 0.120766
\(161\) 1.31309e14 0.594190
\(162\) −1.55186e14 −0.674536
\(163\) −7.19194e13 −0.300349 −0.150175 0.988659i \(-0.547984\pi\)
−0.150175 + 0.988659i \(0.547984\pi\)
\(164\) −1.16989e14 −0.469526
\(165\) −2.88053e13 −0.111129
\(166\) −9.02831e12 −0.0334891
\(167\) 1.24252e14 0.443246 0.221623 0.975132i \(-0.428864\pi\)
0.221623 + 0.975132i \(0.428864\pi\)
\(168\) 4.83782e12 0.0166012
\(169\) 8.50731e14 2.80885
\(170\) 4.22657e13 0.134298
\(171\) −5.77492e14 −1.76633
\(172\) 1.48277e14 0.436654
\(173\) 4.99887e14 1.41766 0.708830 0.705380i \(-0.249224\pi\)
0.708830 + 0.705380i \(0.249224\pi\)
\(174\) 1.27313e13 0.0347779
\(175\) −7.65899e13 −0.201569
\(176\) −1.29076e14 −0.327352
\(177\) 5.97672e13 0.146095
\(178\) −1.93896e14 −0.456919
\(179\) 2.16915e14 0.492883 0.246442 0.969158i \(-0.420739\pi\)
0.246442 + 0.969158i \(0.420739\pi\)
\(180\) 1.53463e14 0.336305
\(181\) 5.44744e14 1.15155 0.575774 0.817609i \(-0.304701\pi\)
0.575774 + 0.817609i \(0.304701\pi\)
\(182\) −2.55739e14 −0.521594
\(183\) −5.53421e13 −0.108924
\(184\) −2.92580e14 −0.555814
\(185\) −1.53730e14 −0.281930
\(186\) −1.12686e13 −0.0199543
\(187\) −2.12869e14 −0.364034
\(188\) 2.57164e14 0.424799
\(189\) 5.83918e13 0.0931858
\(190\) 5.61989e14 0.866622
\(191\) −4.16278e14 −0.620393 −0.310197 0.950672i \(-0.600395\pi\)
−0.310197 + 0.950672i \(0.600395\pi\)
\(192\) −1.07796e13 −0.0155290
\(193\) −2.53824e14 −0.353517 −0.176759 0.984254i \(-0.556561\pi\)
−0.176759 + 0.984254i \(0.556561\pi\)
\(194\) −4.31357e14 −0.580932
\(195\) 1.27167e14 0.165634
\(196\) 5.66939e13 0.0714286
\(197\) −4.45065e14 −0.542491 −0.271246 0.962510i \(-0.587436\pi\)
−0.271246 + 0.962510i \(0.587436\pi\)
\(198\) −7.72909e14 −0.911601
\(199\) 6.21823e14 0.709777 0.354888 0.934909i \(-0.384519\pi\)
0.354888 + 0.934909i \(0.384519\pi\)
\(200\) 1.70657e14 0.188551
\(201\) 2.18224e14 0.233414
\(202\) 5.81401e14 0.602132
\(203\) 1.49197e14 0.149636
\(204\) −1.77773e13 −0.0172691
\(205\) 6.81723e14 0.641517
\(206\) −8.08028e13 −0.0736698
\(207\) −1.75197e15 −1.54782
\(208\) 5.69834e14 0.487907
\(209\) −2.83043e15 −2.34910
\(210\) −2.81911e13 −0.0226823
\(211\) −1.76477e14 −0.137674 −0.0688370 0.997628i \(-0.521929\pi\)
−0.0688370 + 0.997628i \(0.521929\pi\)
\(212\) 1.01612e15 0.768708
\(213\) −1.26482e14 −0.0928028
\(214\) 1.22714e15 0.873380
\(215\) −8.64044e14 −0.596604
\(216\) −1.30108e14 −0.0871674
\(217\) −1.32056e14 −0.0858556
\(218\) −2.03391e15 −1.28341
\(219\) 1.78493e14 0.109328
\(220\) 7.52160e14 0.447263
\(221\) 9.39753e14 0.542580
\(222\) 6.46601e13 0.0362529
\(223\) −9.89687e14 −0.538910 −0.269455 0.963013i \(-0.586844\pi\)
−0.269455 + 0.963013i \(0.586844\pi\)
\(224\) −1.26325e14 −0.0668153
\(225\) 1.02189e15 0.525071
\(226\) −4.64956e14 −0.232117
\(227\) 1.13962e15 0.552832 0.276416 0.961038i \(-0.410853\pi\)
0.276416 + 0.961038i \(0.410853\pi\)
\(228\) −2.36378e14 −0.111437
\(229\) 2.34581e15 1.07489 0.537443 0.843300i \(-0.319390\pi\)
0.537443 + 0.843300i \(0.319390\pi\)
\(230\) 1.70494e15 0.759412
\(231\) 1.41983e14 0.0614836
\(232\) −3.32439e14 −0.139972
\(233\) 2.61893e14 0.107229 0.0536143 0.998562i \(-0.482926\pi\)
0.0536143 + 0.998562i \(0.482926\pi\)
\(234\) 3.41217e15 1.35871
\(235\) −1.49856e15 −0.580406
\(236\) −1.56064e15 −0.587995
\(237\) −6.21111e13 −0.0227669
\(238\) −2.08331e14 −0.0743025
\(239\) 4.55614e14 0.158129 0.0790644 0.996870i \(-0.474807\pi\)
0.0790644 + 0.996870i \(0.474807\pi\)
\(240\) 6.28152e13 0.0212174
\(241\) 2.83710e15 0.932746 0.466373 0.884588i \(-0.345561\pi\)
0.466373 + 0.884588i \(0.345561\pi\)
\(242\) −1.57876e15 −0.505261
\(243\) −1.17166e15 −0.365056
\(244\) 1.44509e15 0.438390
\(245\) −3.30369e14 −0.0975933
\(246\) −2.86739e14 −0.0824913
\(247\) 1.24955e16 3.50125
\(248\) 2.94245e14 0.0803106
\(249\) −2.21283e13 −0.00588372
\(250\) −2.85918e15 −0.740680
\(251\) −5.04809e15 −1.27423 −0.637115 0.770769i \(-0.719873\pi\)
−0.637115 + 0.770769i \(0.719873\pi\)
\(252\) −7.56431e14 −0.186066
\(253\) −8.58682e15 −2.05849
\(254\) −1.88867e15 −0.441304
\(255\) 1.03593e14 0.0235949
\(256\) 2.81475e14 0.0625000
\(257\) 1.58419e15 0.342959 0.171480 0.985188i \(-0.445145\pi\)
0.171480 + 0.985188i \(0.445145\pi\)
\(258\) 3.63424e14 0.0767160
\(259\) 7.57746e14 0.155982
\(260\) −3.32056e15 −0.666630
\(261\) −1.99064e15 −0.389789
\(262\) 1.13825e15 0.217411
\(263\) −6.88068e14 −0.128209 −0.0641046 0.997943i \(-0.520419\pi\)
−0.0641046 + 0.997943i \(0.520419\pi\)
\(264\) −3.16365e14 −0.0575126
\(265\) −5.92117e15 −1.05029
\(266\) −2.77009e15 −0.479471
\(267\) −4.75237e14 −0.0802762
\(268\) −5.69823e15 −0.939429
\(269\) 7.45199e15 1.19917 0.599587 0.800310i \(-0.295331\pi\)
0.599587 + 0.800310i \(0.295331\pi\)
\(270\) 7.58170e14 0.119097
\(271\) −8.43521e14 −0.129359 −0.0646793 0.997906i \(-0.520602\pi\)
−0.0646793 + 0.997906i \(0.520602\pi\)
\(272\) 4.64200e14 0.0695036
\(273\) −6.26814e14 −0.0916392
\(274\) −6.74361e15 −0.962750
\(275\) 5.00853e15 0.698309
\(276\) −7.17112e14 −0.0976512
\(277\) −1.28498e16 −1.70914 −0.854572 0.519334i \(-0.826180\pi\)
−0.854572 + 0.519334i \(0.826180\pi\)
\(278\) 3.77598e15 0.490612
\(279\) 1.76194e15 0.223647
\(280\) 7.36125e14 0.0912902
\(281\) 8.51626e15 1.03195 0.515974 0.856604i \(-0.327430\pi\)
0.515974 + 0.856604i \(0.327430\pi\)
\(282\) 6.30306e14 0.0746332
\(283\) 8.22266e15 0.951482 0.475741 0.879585i \(-0.342180\pi\)
0.475741 + 0.879585i \(0.342180\pi\)
\(284\) 3.30268e15 0.373506
\(285\) 1.37743e15 0.152257
\(286\) 1.67238e16 1.80699
\(287\) −3.36026e15 −0.354928
\(288\) 1.68547e15 0.174048
\(289\) −9.13903e15 −0.922708
\(290\) 1.93720e15 0.191244
\(291\) −1.05725e15 −0.102064
\(292\) −4.66078e15 −0.440018
\(293\) −8.61473e15 −0.795430 −0.397715 0.917509i \(-0.630197\pi\)
−0.397715 + 0.917509i \(0.630197\pi\)
\(294\) 1.38956e14 0.0125493
\(295\) 9.09420e15 0.803381
\(296\) −1.68840e15 −0.145908
\(297\) −3.81848e15 −0.322830
\(298\) 1.00479e16 0.831134
\(299\) 3.79083e16 3.06811
\(300\) 4.18277e14 0.0331266
\(301\) 4.25893e15 0.330080
\(302\) −4.14877e15 −0.314684
\(303\) 1.42501e15 0.105789
\(304\) 6.17227e15 0.448504
\(305\) −8.42088e15 −0.598975
\(306\) 2.77963e15 0.193552
\(307\) −2.20767e16 −1.50499 −0.752496 0.658597i \(-0.771150\pi\)
−0.752496 + 0.658597i \(0.771150\pi\)
\(308\) −3.70745e15 −0.247455
\(309\) −1.98047e14 −0.0129431
\(310\) −1.71464e15 −0.109729
\(311\) −2.38285e16 −1.49333 −0.746663 0.665203i \(-0.768345\pi\)
−0.746663 + 0.665203i \(0.768345\pi\)
\(312\) 1.39666e15 0.0857206
\(313\) −2.62444e16 −1.57760 −0.788802 0.614648i \(-0.789298\pi\)
−0.788802 + 0.614648i \(0.789298\pi\)
\(314\) 2.86420e14 0.0168640
\(315\) 4.40791e15 0.254223
\(316\) 1.62184e15 0.0916308
\(317\) 2.62984e16 1.45561 0.727805 0.685785i \(-0.240541\pi\)
0.727805 + 0.685785i \(0.240541\pi\)
\(318\) 2.49050e15 0.135055
\(319\) −9.75661e15 −0.518393
\(320\) −1.64022e15 −0.0853941
\(321\) 3.00770e15 0.153445
\(322\) −8.40376e15 −0.420156
\(323\) 1.01791e16 0.498762
\(324\) 9.93190e15 0.476969
\(325\) −2.21112e16 −1.04081
\(326\) 4.60284e15 0.212379
\(327\) −4.98509e15 −0.225482
\(328\) 7.48729e15 0.332005
\(329\) 7.38649e15 0.321118
\(330\) 1.84354e15 0.0785798
\(331\) −3.32594e16 −1.39005 −0.695027 0.718983i \(-0.744608\pi\)
−0.695027 + 0.718983i \(0.744608\pi\)
\(332\) 5.77812e14 0.0236804
\(333\) −1.01101e16 −0.406321
\(334\) −7.95211e15 −0.313423
\(335\) 3.32050e16 1.28355
\(336\) −3.09620e14 −0.0117388
\(337\) 1.94532e16 0.723429 0.361715 0.932289i \(-0.382191\pi\)
0.361715 + 0.932289i \(0.382191\pi\)
\(338\) −5.44468e16 −1.98616
\(339\) −1.13960e15 −0.0407808
\(340\) −2.70501e15 −0.0949632
\(341\) 8.63566e15 0.297435
\(342\) 3.69595e16 1.24898
\(343\) 1.62841e15 0.0539949
\(344\) −9.48970e15 −0.308761
\(345\) 4.17878e15 0.133421
\(346\) −3.19927e16 −1.00244
\(347\) 3.23704e16 0.995421 0.497711 0.867343i \(-0.334174\pi\)
0.497711 + 0.867343i \(0.334174\pi\)
\(348\) −8.14804e14 −0.0245917
\(349\) −5.23174e16 −1.54982 −0.774909 0.632073i \(-0.782204\pi\)
−0.774909 + 0.632073i \(0.782204\pi\)
\(350\) 4.90175e15 0.142531
\(351\) 1.68575e16 0.481167
\(352\) 8.26089e15 0.231473
\(353\) −2.57219e16 −0.707565 −0.353783 0.935328i \(-0.615105\pi\)
−0.353783 + 0.935328i \(0.615105\pi\)
\(354\) −3.82510e15 −0.103305
\(355\) −1.92455e16 −0.510324
\(356\) 1.24093e16 0.323090
\(357\) −5.10617e14 −0.0130542
\(358\) −1.38825e16 −0.348521
\(359\) 3.04674e16 0.751141 0.375571 0.926794i \(-0.377447\pi\)
0.375571 + 0.926794i \(0.377447\pi\)
\(360\) −9.82165e15 −0.237803
\(361\) 9.32944e16 2.21850
\(362\) −3.48636e16 −0.814267
\(363\) −3.86952e15 −0.0887696
\(364\) 1.63673e16 0.368823
\(365\) 2.71595e16 0.601199
\(366\) 3.54190e15 0.0770210
\(367\) −1.73795e16 −0.371285 −0.185643 0.982617i \(-0.559437\pi\)
−0.185643 + 0.982617i \(0.559437\pi\)
\(368\) 1.87251e16 0.393020
\(369\) 4.48339e16 0.924559
\(370\) 9.83871e15 0.199355
\(371\) 2.91859e16 0.581088
\(372\) 7.21191e14 0.0141098
\(373\) −4.63979e15 −0.0892053 −0.0446026 0.999005i \(-0.514202\pi\)
−0.0446026 + 0.999005i \(0.514202\pi\)
\(374\) 1.36236e16 0.257411
\(375\) −7.00781e15 −0.130130
\(376\) −1.64585e16 −0.300378
\(377\) 4.30725e16 0.772648
\(378\) −3.73707e15 −0.0658923
\(379\) −8.74316e15 −0.151535 −0.0757676 0.997126i \(-0.524141\pi\)
−0.0757676 + 0.997126i \(0.524141\pi\)
\(380\) −3.59673e16 −0.612794
\(381\) −4.62912e15 −0.0775329
\(382\) 2.66418e16 0.438684
\(383\) −7.53155e16 −1.21925 −0.609625 0.792690i \(-0.708680\pi\)
−0.609625 + 0.792690i \(0.708680\pi\)
\(384\) 6.89892e14 0.0109807
\(385\) 2.16042e16 0.338099
\(386\) 1.62447e16 0.249974
\(387\) −5.68243e16 −0.859830
\(388\) 2.76068e16 0.410781
\(389\) −2.25509e16 −0.329983 −0.164991 0.986295i \(-0.552760\pi\)
−0.164991 + 0.986295i \(0.552760\pi\)
\(390\) −8.13867e15 −0.117121
\(391\) 3.08809e16 0.437061
\(392\) −3.62841e15 −0.0505076
\(393\) 2.78985e15 0.0381970
\(394\) 2.84842e16 0.383599
\(395\) −9.45084e15 −0.125196
\(396\) 4.94662e16 0.644599
\(397\) −3.26995e16 −0.419182 −0.209591 0.977789i \(-0.567213\pi\)
−0.209591 + 0.977789i \(0.567213\pi\)
\(398\) −3.97967e16 −0.501888
\(399\) −6.78945e15 −0.0842385
\(400\) −1.09220e16 −0.133325
\(401\) 3.07711e16 0.369577 0.184789 0.982778i \(-0.440840\pi\)
0.184789 + 0.982778i \(0.440840\pi\)
\(402\) −1.39663e16 −0.165049
\(403\) −3.81239e16 −0.443317
\(404\) −3.72097e16 −0.425772
\(405\) −5.78756e16 −0.651685
\(406\) −9.54860e15 −0.105809
\(407\) −4.95521e16 −0.540379
\(408\) 1.13775e15 0.0122111
\(409\) −1.56215e17 −1.65014 −0.825071 0.565029i \(-0.808865\pi\)
−0.825071 + 0.565029i \(0.808865\pi\)
\(410\) −4.36303e16 −0.453621
\(411\) −1.65285e16 −0.169146
\(412\) 5.17138e15 0.0520924
\(413\) −4.48260e16 −0.444482
\(414\) 1.12126e17 1.09447
\(415\) −3.36705e15 −0.0323547
\(416\) −3.64694e16 −0.345002
\(417\) 9.25489e15 0.0861959
\(418\) 1.81147e17 1.66106
\(419\) −1.46057e17 −1.31865 −0.659327 0.751856i \(-0.729159\pi\)
−0.659327 + 0.751856i \(0.729159\pi\)
\(420\) 1.80423e15 0.0160388
\(421\) 9.63368e16 0.843255 0.421627 0.906769i \(-0.361459\pi\)
0.421627 + 0.906769i \(0.361459\pi\)
\(422\) 1.12945e16 0.0973503
\(423\) −9.85533e16 −0.836486
\(424\) −6.50316e16 −0.543558
\(425\) −1.80123e16 −0.148266
\(426\) 8.09484e15 0.0656215
\(427\) 4.15071e16 0.331392
\(428\) −7.85367e16 −0.617573
\(429\) 4.09899e16 0.317472
\(430\) 5.52988e16 0.421862
\(431\) −1.43677e16 −0.107965 −0.0539826 0.998542i \(-0.517192\pi\)
−0.0539826 + 0.998542i \(0.517192\pi\)
\(432\) 8.32690e15 0.0616366
\(433\) 2.68630e17 1.95877 0.979385 0.202002i \(-0.0647446\pi\)
0.979385 + 0.202002i \(0.0647446\pi\)
\(434\) 8.45156e15 0.0607091
\(435\) 4.74806e15 0.0335998
\(436\) 1.30170e17 0.907505
\(437\) 4.10611e17 2.82034
\(438\) −1.14235e16 −0.0773069
\(439\) 5.75567e16 0.383775 0.191887 0.981417i \(-0.438539\pi\)
0.191887 + 0.981417i \(0.438539\pi\)
\(440\) −4.81382e16 −0.316263
\(441\) −2.17269e16 −0.140652
\(442\) −6.01442e16 −0.383662
\(443\) −1.08881e17 −0.684428 −0.342214 0.939622i \(-0.611177\pi\)
−0.342214 + 0.939622i \(0.611177\pi\)
\(444\) −4.13825e15 −0.0256346
\(445\) −7.23123e16 −0.441440
\(446\) 6.33400e16 0.381067
\(447\) 2.46274e16 0.146022
\(448\) 8.08478e15 0.0472456
\(449\) −1.23522e16 −0.0711449 −0.0355725 0.999367i \(-0.511325\pi\)
−0.0355725 + 0.999367i \(0.511325\pi\)
\(450\) −6.54010e16 −0.371281
\(451\) 2.19741e17 1.22960
\(452\) 2.97572e16 0.164132
\(453\) −1.01686e16 −0.0552869
\(454\) −7.29359e16 −0.390911
\(455\) −9.53762e16 −0.503925
\(456\) 1.51282e16 0.0787979
\(457\) −2.23133e16 −0.114580 −0.0572901 0.998358i \(-0.518246\pi\)
−0.0572901 + 0.998358i \(0.518246\pi\)
\(458\) −1.50132e17 −0.760059
\(459\) 1.37325e16 0.0685435
\(460\) −1.09116e17 −0.536985
\(461\) 2.25114e17 1.09231 0.546156 0.837683i \(-0.316091\pi\)
0.546156 + 0.837683i \(0.316091\pi\)
\(462\) −9.08692e15 −0.0434754
\(463\) −2.32113e17 −1.09502 −0.547511 0.836798i \(-0.684425\pi\)
−0.547511 + 0.836798i \(0.684425\pi\)
\(464\) 2.12761e16 0.0989748
\(465\) −4.20255e15 −0.0192783
\(466\) −1.67612e16 −0.0758221
\(467\) 4.08601e17 1.82280 0.911402 0.411518i \(-0.135001\pi\)
0.911402 + 0.411518i \(0.135001\pi\)
\(468\) −2.18379e17 −0.960753
\(469\) −1.63670e17 −0.710142
\(470\) 9.59076e16 0.410409
\(471\) 7.02011e14 0.00296284
\(472\) 9.98807e16 0.415775
\(473\) −2.78509e17 −1.14352
\(474\) 3.97511e15 0.0160987
\(475\) −2.39501e17 −0.956752
\(476\) 1.33332e16 0.0525398
\(477\) −3.89409e17 −1.51369
\(478\) −2.91593e16 −0.111814
\(479\) 2.05872e17 0.778783 0.389391 0.921072i \(-0.372685\pi\)
0.389391 + 0.921072i \(0.372685\pi\)
\(480\) −4.02017e15 −0.0150029
\(481\) 2.18758e17 0.805417
\(482\) −1.81574e17 −0.659551
\(483\) −2.05975e16 −0.0738174
\(484\) 1.01041e17 0.357274
\(485\) −1.60872e17 −0.561252
\(486\) 7.49860e16 0.258134
\(487\) 2.42234e17 0.822806 0.411403 0.911454i \(-0.365039\pi\)
0.411403 + 0.911454i \(0.365039\pi\)
\(488\) −9.24857e16 −0.309989
\(489\) 1.12815e16 0.0373130
\(490\) 2.11436e16 0.0690089
\(491\) −2.00232e17 −0.644916 −0.322458 0.946584i \(-0.604509\pi\)
−0.322458 + 0.946584i \(0.604509\pi\)
\(492\) 1.83513e16 0.0583301
\(493\) 3.50879e16 0.110066
\(494\) −7.99712e17 −2.47576
\(495\) −2.88252e17 −0.880720
\(496\) −1.88317e16 −0.0567881
\(497\) 9.48626e16 0.282344
\(498\) 1.41621e15 0.00416042
\(499\) 3.10865e17 0.901402 0.450701 0.892675i \(-0.351174\pi\)
0.450701 + 0.892675i \(0.351174\pi\)
\(500\) 1.82987e17 0.523740
\(501\) −1.94905e16 −0.0550654
\(502\) 3.23078e17 0.901017
\(503\) 3.90092e17 1.07393 0.536964 0.843605i \(-0.319571\pi\)
0.536964 + 0.843605i \(0.319571\pi\)
\(504\) 4.84116e16 0.131568
\(505\) 2.16830e17 0.581735
\(506\) 5.49557e17 1.45557
\(507\) −1.33448e17 −0.348949
\(508\) 1.20875e17 0.312049
\(509\) −4.02933e17 −1.02699 −0.513497 0.858092i \(-0.671650\pi\)
−0.513497 + 0.858092i \(0.671650\pi\)
\(510\) −6.62994e15 −0.0166841
\(511\) −1.33871e17 −0.332622
\(512\) −1.80144e16 −0.0441942
\(513\) 1.82595e17 0.442309
\(514\) −1.01388e17 −0.242509
\(515\) −3.01349e16 −0.0711742
\(516\) −2.32592e16 −0.0542464
\(517\) −4.83033e17 −1.11247
\(518\) −4.84957e16 −0.110296
\(519\) −7.84139e16 −0.176119
\(520\) 2.12516e17 0.471379
\(521\) 6.24074e17 1.36707 0.683536 0.729917i \(-0.260441\pi\)
0.683536 + 0.729917i \(0.260441\pi\)
\(522\) 1.27401e17 0.275623
\(523\) −6.81767e17 −1.45672 −0.728358 0.685196i \(-0.759716\pi\)
−0.728358 + 0.685196i \(0.759716\pi\)
\(524\) −7.28482e16 −0.153732
\(525\) 1.20141e16 0.0250413
\(526\) 4.40363e16 0.0906575
\(527\) −3.10566e16 −0.0631517
\(528\) 2.02474e16 0.0406675
\(529\) 7.41656e17 1.47143
\(530\) 3.78955e17 0.742667
\(531\) 5.98085e17 1.15784
\(532\) 1.77285e17 0.339037
\(533\) −9.70093e17 −1.83268
\(534\) 3.04152e16 0.0567639
\(535\) 4.57653e17 0.843794
\(536\) 3.64687e17 0.664277
\(537\) −3.40260e16 −0.0612319
\(538\) −4.76927e17 −0.847944
\(539\) −1.06489e17 −0.187058
\(540\) −4.85229e16 −0.0842145
\(541\) −4.36270e17 −0.748122 −0.374061 0.927404i \(-0.622035\pi\)
−0.374061 + 0.927404i \(0.622035\pi\)
\(542\) 5.39854e16 0.0914704
\(543\) −8.54504e16 −0.143059
\(544\) −2.97088e16 −0.0491465
\(545\) −7.58533e17 −1.23993
\(546\) 4.01161e16 0.0647987
\(547\) 8.65775e17 1.38193 0.690967 0.722886i \(-0.257185\pi\)
0.690967 + 0.722886i \(0.257185\pi\)
\(548\) 4.31591e17 0.680767
\(549\) −5.53804e17 −0.863248
\(550\) −3.20546e17 −0.493779
\(551\) 4.66548e17 0.710250
\(552\) 4.58951e16 0.0690498
\(553\) 4.65839e16 0.0692664
\(554\) 8.22388e17 1.20855
\(555\) 2.41146e16 0.0350248
\(556\) −2.41663e17 −0.346915
\(557\) −2.37958e17 −0.337630 −0.168815 0.985648i \(-0.553994\pi\)
−0.168815 + 0.985648i \(0.553994\pi\)
\(558\) −1.12764e17 −0.158142
\(559\) 1.22954e18 1.70437
\(560\) −4.71120e16 −0.0645519
\(561\) 3.33913e16 0.0452246
\(562\) −5.45040e17 −0.729697
\(563\) −4.98751e17 −0.660054 −0.330027 0.943971i \(-0.607058\pi\)
−0.330027 + 0.943971i \(0.607058\pi\)
\(564\) −4.03396e16 −0.0527736
\(565\) −1.73403e17 −0.224254
\(566\) −5.26250e17 −0.672799
\(567\) 2.85273e17 0.360554
\(568\) −2.11372e17 −0.264109
\(569\) −1.27035e17 −0.156926 −0.0784629 0.996917i \(-0.525001\pi\)
−0.0784629 + 0.996917i \(0.525001\pi\)
\(570\) −8.81555e16 −0.107662
\(571\) −6.42693e17 −0.776013 −0.388006 0.921657i \(-0.626836\pi\)
−0.388006 + 0.921657i \(0.626836\pi\)
\(572\) −1.07033e18 −1.27774
\(573\) 6.52988e16 0.0770727
\(574\) 2.15057e17 0.250972
\(575\) −7.26588e17 −0.838393
\(576\) −1.07870e17 −0.123071
\(577\) −3.21707e17 −0.362926 −0.181463 0.983398i \(-0.558083\pi\)
−0.181463 + 0.983398i \(0.558083\pi\)
\(578\) 5.84898e17 0.652453
\(579\) 3.98157e16 0.0439181
\(580\) −1.23981e17 −0.135230
\(581\) 1.65964e16 0.0179007
\(582\) 6.76640e16 0.0721703
\(583\) −1.90858e18 −2.01310
\(584\) 2.98290e17 0.311139
\(585\) 1.27255e18 1.31268
\(586\) 5.51343e17 0.562454
\(587\) 5.64618e17 0.569649 0.284825 0.958580i \(-0.408065\pi\)
0.284825 + 0.958580i \(0.408065\pi\)
\(588\) −8.89320e15 −0.00887371
\(589\) −4.12946e17 −0.407516
\(590\) −5.82029e17 −0.568076
\(591\) 6.98144e16 0.0673948
\(592\) 1.08058e17 0.103173
\(593\) −7.34438e17 −0.693585 −0.346792 0.937942i \(-0.612729\pi\)
−0.346792 + 0.937942i \(0.612729\pi\)
\(594\) 2.44383e17 0.228275
\(595\) −7.76956e16 −0.0717854
\(596\) −6.43067e17 −0.587700
\(597\) −9.75412e16 −0.0881769
\(598\) −2.42613e18 −2.16948
\(599\) 1.62460e18 1.43705 0.718526 0.695500i \(-0.244817\pi\)
0.718526 + 0.695500i \(0.244817\pi\)
\(600\) −2.67698e16 −0.0234240
\(601\) 1.35612e18 1.17385 0.586927 0.809640i \(-0.300338\pi\)
0.586927 + 0.809640i \(0.300338\pi\)
\(602\) −2.72572e17 −0.233402
\(603\) 2.18374e18 1.84986
\(604\) 2.65521e17 0.222515
\(605\) −5.88788e17 −0.488145
\(606\) −9.12005e16 −0.0748040
\(607\) 2.18499e17 0.177306 0.0886528 0.996063i \(-0.471744\pi\)
0.0886528 + 0.996063i \(0.471744\pi\)
\(608\) −3.95025e17 −0.317140
\(609\) −2.34035e16 −0.0185896
\(610\) 5.38937e17 0.423539
\(611\) 2.13245e18 1.65810
\(612\) −1.77896e17 −0.136862
\(613\) −1.30291e18 −0.991797 −0.495898 0.868380i \(-0.665161\pi\)
−0.495898 + 0.868380i \(0.665161\pi\)
\(614\) 1.41291e18 1.06419
\(615\) −1.06937e17 −0.0796968
\(616\) 2.37277e17 0.174977
\(617\) 2.22565e18 1.62406 0.812031 0.583614i \(-0.198362\pi\)
0.812031 + 0.583614i \(0.198362\pi\)
\(618\) 1.26750e16 0.00915215
\(619\) −1.86509e18 −1.33263 −0.666317 0.745668i \(-0.732130\pi\)
−0.666317 + 0.745668i \(0.732130\pi\)
\(620\) 1.09737e17 0.0775900
\(621\) 5.53948e17 0.387591
\(622\) 1.52503e18 1.05594
\(623\) 3.56432e17 0.244233
\(624\) −8.93861e16 −0.0606136
\(625\) −2.71630e17 −0.182288
\(626\) 1.67964e18 1.11553
\(627\) 4.43990e17 0.291833
\(628\) −1.83309e16 −0.0119246
\(629\) 1.78205e17 0.114734
\(630\) −2.82106e17 −0.179763
\(631\) 1.09793e18 0.692445 0.346222 0.938152i \(-0.387464\pi\)
0.346222 + 0.938152i \(0.387464\pi\)
\(632\) −1.03798e17 −0.0647928
\(633\) 2.76828e16 0.0171035
\(634\) −1.68310e18 −1.02927
\(635\) −7.04369e17 −0.426354
\(636\) −1.59392e17 −0.0954980
\(637\) 4.70116e17 0.278804
\(638\) 6.24423e17 0.366559
\(639\) −1.26569e18 −0.735483
\(640\) 1.04974e17 0.0603828
\(641\) −1.03316e18 −0.588290 −0.294145 0.955761i \(-0.595035\pi\)
−0.294145 + 0.955761i \(0.595035\pi\)
\(642\) −1.92493e17 −0.108502
\(643\) −2.84730e18 −1.58877 −0.794386 0.607413i \(-0.792207\pi\)
−0.794386 + 0.607413i \(0.792207\pi\)
\(644\) 5.37841e17 0.297095
\(645\) 1.35537e17 0.0741172
\(646\) −6.51464e17 −0.352678
\(647\) −2.96154e18 −1.58723 −0.793616 0.608419i \(-0.791804\pi\)
−0.793616 + 0.608419i \(0.791804\pi\)
\(648\) −6.35642e17 −0.337268
\(649\) 2.93136e18 1.53985
\(650\) 1.41512e18 0.735961
\(651\) 2.07147e16 0.0106660
\(652\) −2.94582e17 −0.150175
\(653\) −1.76423e18 −0.890471 −0.445236 0.895413i \(-0.646880\pi\)
−0.445236 + 0.895413i \(0.646880\pi\)
\(654\) 3.19046e17 0.159440
\(655\) 4.24504e17 0.210046
\(656\) −4.79187e17 −0.234763
\(657\) 1.78616e18 0.866453
\(658\) −4.72735e17 −0.227065
\(659\) −2.97544e18 −1.41513 −0.707565 0.706648i \(-0.750207\pi\)
−0.707565 + 0.706648i \(0.750207\pi\)
\(660\) −1.17986e17 −0.0555643
\(661\) −2.68609e18 −1.25260 −0.626298 0.779584i \(-0.715431\pi\)
−0.626298 + 0.779584i \(0.715431\pi\)
\(662\) 2.12860e18 0.982917
\(663\) −1.47413e17 −0.0674058
\(664\) −3.69800e16 −0.0167446
\(665\) −1.03309e18 −0.463229
\(666\) 6.47048e17 0.287312
\(667\) 1.41539e18 0.622385
\(668\) 5.08935e17 0.221623
\(669\) 1.55246e17 0.0669498
\(670\) −2.12512e18 −0.907605
\(671\) −2.71432e18 −1.14806
\(672\) 1.98157e16 0.00830060
\(673\) −4.74026e17 −0.196655 −0.0983273 0.995154i \(-0.531349\pi\)
−0.0983273 + 0.995154i \(0.531349\pi\)
\(674\) −1.24500e18 −0.511542
\(675\) −3.23107e17 −0.131484
\(676\) 3.48459e18 1.40442
\(677\) 3.87922e16 0.0154853 0.00774263 0.999970i \(-0.497535\pi\)
0.00774263 + 0.999970i \(0.497535\pi\)
\(678\) 7.29346e16 0.0288364
\(679\) 7.92948e17 0.310521
\(680\) 1.73120e17 0.0671491
\(681\) −1.78765e17 −0.0686794
\(682\) −5.52683e17 −0.210318
\(683\) −9.31461e17 −0.351099 −0.175550 0.984471i \(-0.556170\pi\)
−0.175550 + 0.984471i \(0.556170\pi\)
\(684\) −2.36541e18 −0.883165
\(685\) −2.51499e18 −0.930137
\(686\) −1.04218e17 −0.0381802
\(687\) −3.67972e17 −0.133535
\(688\) 6.07341e17 0.218327
\(689\) 8.42584e18 3.00046
\(690\) −2.67442e17 −0.0943432
\(691\) −2.86951e18 −1.00277 −0.501384 0.865225i \(-0.667176\pi\)
−0.501384 + 0.865225i \(0.667176\pi\)
\(692\) 2.04754e18 0.708830
\(693\) 1.42081e18 0.487271
\(694\) −2.07171e18 −0.703869
\(695\) 1.40823e18 0.473993
\(696\) 5.21474e16 0.0173889
\(697\) −7.90260e17 −0.261070
\(698\) 3.34831e18 1.09589
\(699\) −4.10815e16 −0.0133212
\(700\) −3.13712e17 −0.100785
\(701\) 1.12523e17 0.0358158 0.0179079 0.999840i \(-0.494299\pi\)
0.0179079 + 0.999840i \(0.494299\pi\)
\(702\) −1.07888e18 −0.340236
\(703\) 2.36952e18 0.740373
\(704\) −5.28697e17 −0.163676
\(705\) 2.35068e17 0.0721050
\(706\) 1.64620e18 0.500324
\(707\) −1.06877e18 −0.321853
\(708\) 2.44806e17 0.0730477
\(709\) 3.66046e18 1.08227 0.541134 0.840937i \(-0.317995\pi\)
0.541134 + 0.840937i \(0.317995\pi\)
\(710\) 1.23171e18 0.360853
\(711\) −6.21540e17 −0.180433
\(712\) −7.94198e17 −0.228459
\(713\) −1.25278e18 −0.357102
\(714\) 3.26795e16 0.00923074
\(715\) 6.23705e18 1.74578
\(716\) 8.88482e17 0.246442
\(717\) −7.14691e16 −0.0196446
\(718\) −1.94991e18 −0.531137
\(719\) 1.97154e18 0.532190 0.266095 0.963947i \(-0.414266\pi\)
0.266095 + 0.963947i \(0.414266\pi\)
\(720\) 6.28585e17 0.168152
\(721\) 1.48537e17 0.0393782
\(722\) −5.97084e18 −1.56871
\(723\) −4.45036e17 −0.115877
\(724\) 2.23127e18 0.575774
\(725\) −8.25572e17 −0.211134
\(726\) 2.47649e17 0.0627696
\(727\) −7.34060e17 −0.184399 −0.0921994 0.995741i \(-0.529390\pi\)
−0.0921994 + 0.995741i \(0.529390\pi\)
\(728\) −1.04751e18 −0.260797
\(729\) −3.68209e18 −0.908586
\(730\) −1.73821e18 −0.425112
\(731\) 1.00161e18 0.242792
\(732\) −2.26681e17 −0.0544620
\(733\) −1.48745e18 −0.354215 −0.177108 0.984192i \(-0.556674\pi\)
−0.177108 + 0.984192i \(0.556674\pi\)
\(734\) 1.11229e18 0.262538
\(735\) 5.18228e16 0.0121242
\(736\) −1.19841e18 −0.277907
\(737\) 1.07030e19 2.46019
\(738\) −2.86937e18 −0.653762
\(739\) 1.88091e18 0.424796 0.212398 0.977183i \(-0.431873\pi\)
0.212398 + 0.977183i \(0.431873\pi\)
\(740\) −6.29678e17 −0.140965
\(741\) −1.96009e18 −0.434967
\(742\) −1.86790e18 −0.410891
\(743\) −5.79526e18 −1.26371 −0.631853 0.775088i \(-0.717705\pi\)
−0.631853 + 0.775088i \(0.717705\pi\)
\(744\) −4.61562e16 −0.00997714
\(745\) 3.74731e18 0.802979
\(746\) 2.96946e17 0.0630777
\(747\) −2.21436e17 −0.0466298
\(748\) −8.71911e17 −0.182017
\(749\) −2.25580e18 −0.466841
\(750\) 4.48500e17 0.0920161
\(751\) −4.05166e15 −0.000824087 0 −0.000412043 1.00000i \(-0.500131\pi\)
−0.000412043 1.00000i \(0.500131\pi\)
\(752\) 1.05334e18 0.212400
\(753\) 7.91860e17 0.158300
\(754\) −2.75664e18 −0.546345
\(755\) −1.54726e18 −0.304023
\(756\) 2.39173e17 0.0465929
\(757\) 6.86221e17 0.132538 0.0662691 0.997802i \(-0.478890\pi\)
0.0662691 + 0.997802i \(0.478890\pi\)
\(758\) 5.59562e17 0.107152
\(759\) 1.34696e18 0.255730
\(760\) 2.30191e18 0.433311
\(761\) 2.75544e18 0.514269 0.257135 0.966376i \(-0.417222\pi\)
0.257135 + 0.966376i \(0.417222\pi\)
\(762\) 2.96264e17 0.0548240
\(763\) 3.73886e18 0.686010
\(764\) −1.70508e18 −0.310197
\(765\) 1.03664e18 0.186995
\(766\) 4.82019e18 0.862139
\(767\) −1.29411e19 −2.29509
\(768\) −4.41531e16 −0.00776450
\(769\) −4.07852e18 −0.711183 −0.355592 0.934641i \(-0.615721\pi\)
−0.355592 + 0.934641i \(0.615721\pi\)
\(770\) −1.38267e18 −0.239072
\(771\) −2.48502e17 −0.0426065
\(772\) −1.03966e18 −0.176759
\(773\) −8.60493e17 −0.145071 −0.0725355 0.997366i \(-0.523109\pi\)
−0.0725355 + 0.997366i \(0.523109\pi\)
\(774\) 3.63676e18 0.607992
\(775\) 7.30721e17 0.121141
\(776\) −1.76684e18 −0.290466
\(777\) −1.18862e17 −0.0193780
\(778\) 1.44326e18 0.233333
\(779\) −1.05078e19 −1.68468
\(780\) 5.20875e17 0.0828168
\(781\) −6.20346e18 −0.978143
\(782\) −1.97638e18 −0.309048
\(783\) 6.29412e17 0.0976076
\(784\) 2.32218e17 0.0357143
\(785\) 1.06818e17 0.0162927
\(786\) −1.78550e17 −0.0270093
\(787\) 2.29610e18 0.344473 0.172236 0.985056i \(-0.444901\pi\)
0.172236 + 0.985056i \(0.444901\pi\)
\(788\) −1.82299e18 −0.271246
\(789\) 1.07933e17 0.0159277
\(790\) 6.04854e17 0.0885267
\(791\) 8.54713e17 0.124072
\(792\) −3.16584e18 −0.455800
\(793\) 1.19829e19 1.71115
\(794\) 2.09277e18 0.296406
\(795\) 9.28814e17 0.130480
\(796\) 2.54699e18 0.354888
\(797\) −1.04185e19 −1.43988 −0.719938 0.694039i \(-0.755830\pi\)
−0.719938 + 0.694039i \(0.755830\pi\)
\(798\) 4.34525e17 0.0595656
\(799\) 1.73714e18 0.236201
\(800\) 6.99009e17 0.0942753
\(801\) −4.75565e18 −0.636207
\(802\) −1.96935e18 −0.261331
\(803\) 8.75439e18 1.15232
\(804\) 8.93844e17 0.116707
\(805\) −3.13413e18 −0.405923
\(806\) 2.43993e18 0.313473
\(807\) −1.16894e18 −0.148976
\(808\) 2.38142e18 0.301066
\(809\) −5.32128e18 −0.667345 −0.333673 0.942689i \(-0.608288\pi\)
−0.333673 + 0.942689i \(0.608288\pi\)
\(810\) 3.70404e18 0.460811
\(811\) 1.29734e18 0.160110 0.0800550 0.996790i \(-0.474490\pi\)
0.0800550 + 0.996790i \(0.474490\pi\)
\(812\) 6.11111e17 0.0748179
\(813\) 1.32318e17 0.0160705
\(814\) 3.17134e18 0.382106
\(815\) 1.71660e18 0.205185
\(816\) −7.28159e16 −0.00863457
\(817\) 1.33180e19 1.56673
\(818\) 9.99776e18 1.16683
\(819\) −6.27247e18 −0.726261
\(820\) 2.79234e18 0.320758
\(821\) −9.96562e18 −1.13573 −0.567863 0.823123i \(-0.692230\pi\)
−0.567863 + 0.823123i \(0.692230\pi\)
\(822\) 1.05782e18 0.119604
\(823\) 1.59169e19 1.78549 0.892747 0.450558i \(-0.148775\pi\)
0.892747 + 0.450558i \(0.148775\pi\)
\(824\) −3.30968e17 −0.0368349
\(825\) −7.85655e17 −0.0867523
\(826\) 2.86886e18 0.314296
\(827\) 3.63722e18 0.395352 0.197676 0.980267i \(-0.436661\pi\)
0.197676 + 0.980267i \(0.436661\pi\)
\(828\) −7.17607e18 −0.773908
\(829\) 1.00664e18 0.107713 0.0538567 0.998549i \(-0.482849\pi\)
0.0538567 + 0.998549i \(0.482849\pi\)
\(830\) 2.15491e17 0.0228782
\(831\) 2.01567e18 0.212330
\(832\) 2.33404e18 0.243953
\(833\) 3.82967e17 0.0397163
\(834\) −5.92313e17 −0.0609497
\(835\) −2.96569e18 −0.302805
\(836\) −1.15934e19 −1.17455
\(837\) −5.57099e17 −0.0560037
\(838\) 9.34764e18 0.932429
\(839\) 1.17697e19 1.16496 0.582481 0.812844i \(-0.302082\pi\)
0.582481 + 0.812844i \(0.302082\pi\)
\(840\) −1.15471e17 −0.0113412
\(841\) −8.65242e18 −0.843264
\(842\) −6.16556e18 −0.596271
\(843\) −1.33589e18 −0.128201
\(844\) −7.22850e17 −0.0688370
\(845\) −2.03056e19 −1.91887
\(846\) 6.30741e18 0.591485
\(847\) 2.90218e18 0.270073
\(848\) 4.16202e18 0.384354
\(849\) −1.28983e18 −0.118204
\(850\) 1.15278e18 0.104840
\(851\) 7.18854e18 0.648781
\(852\) −5.18070e17 −0.0464014
\(853\) 6.77053e18 0.601803 0.300901 0.953655i \(-0.402713\pi\)
0.300901 + 0.953655i \(0.402713\pi\)
\(854\) −2.65646e18 −0.234329
\(855\) 1.37838e19 1.20667
\(856\) 5.02635e18 0.436690
\(857\) 1.30576e19 1.12587 0.562933 0.826503i \(-0.309673\pi\)
0.562933 + 0.826503i \(0.309673\pi\)
\(858\) −2.62336e18 −0.224486
\(859\) −1.06213e19 −0.902034 −0.451017 0.892515i \(-0.648939\pi\)
−0.451017 + 0.892515i \(0.648939\pi\)
\(860\) −3.53912e18 −0.298302
\(861\) 5.27102e17 0.0440934
\(862\) 9.19530e17 0.0763429
\(863\) 1.70375e19 1.40390 0.701949 0.712227i \(-0.252314\pi\)
0.701949 + 0.712227i \(0.252314\pi\)
\(864\) −5.32922e17 −0.0435837
\(865\) −1.19315e19 −0.968478
\(866\) −1.71923e19 −1.38506
\(867\) 1.43358e18 0.114630
\(868\) −5.40900e17 −0.0429278
\(869\) −3.04631e18 −0.239964
\(870\) −3.03876e17 −0.0237586
\(871\) −4.72508e19 −3.66683
\(872\) −8.33089e18 −0.641703
\(873\) −1.05798e19 −0.808882
\(874\) −2.62791e19 −1.99428
\(875\) 5.25592e18 0.395910
\(876\) 7.31105e17 0.0546642
\(877\) −1.26202e19 −0.936633 −0.468316 0.883561i \(-0.655139\pi\)
−0.468316 + 0.883561i \(0.655139\pi\)
\(878\) −3.68363e18 −0.271370
\(879\) 1.35134e18 0.0988179
\(880\) 3.08085e18 0.223631
\(881\) 8.97828e18 0.646919 0.323459 0.946242i \(-0.395154\pi\)
0.323459 + 0.946242i \(0.395154\pi\)
\(882\) 1.39052e18 0.0994562
\(883\) 1.09184e19 0.775201 0.387601 0.921827i \(-0.373304\pi\)
0.387601 + 0.921827i \(0.373304\pi\)
\(884\) 3.84923e18 0.271290
\(885\) −1.42655e18 −0.0998056
\(886\) 6.96838e18 0.483964
\(887\) 9.88099e18 0.681235 0.340618 0.940202i \(-0.389364\pi\)
0.340618 + 0.940202i \(0.389364\pi\)
\(888\) 2.64848e17 0.0181264
\(889\) 3.47188e18 0.235887
\(890\) 4.62798e18 0.312145
\(891\) −1.86552e19 −1.24909
\(892\) −4.05376e18 −0.269455
\(893\) 2.30980e19 1.52419
\(894\) −1.57615e18 −0.103253
\(895\) −5.17740e18 −0.336715
\(896\) −5.17426e17 −0.0334077
\(897\) −5.94642e18 −0.381158
\(898\) 7.90542e17 0.0503071
\(899\) −1.42344e18 −0.0899295
\(900\) 4.18566e18 0.262535
\(901\) 6.86388e18 0.427423
\(902\) −1.40635e19 −0.869460
\(903\) −6.68071e17 −0.0410064
\(904\) −1.90446e18 −0.116059
\(905\) −1.30022e19 −0.786683
\(906\) 6.50790e17 0.0390938
\(907\) 2.22017e19 1.32416 0.662078 0.749435i \(-0.269675\pi\)
0.662078 + 0.749435i \(0.269675\pi\)
\(908\) 4.66790e18 0.276416
\(909\) 1.42599e19 0.838401
\(910\) 6.10408e18 0.356329
\(911\) 4.58123e18 0.265530 0.132765 0.991148i \(-0.457615\pi\)
0.132765 + 0.991148i \(0.457615\pi\)
\(912\) −9.68203e17 −0.0557186
\(913\) −1.08531e18 −0.0620146
\(914\) 1.42805e18 0.0810204
\(915\) 1.32093e18 0.0744118
\(916\) 9.60844e18 0.537443
\(917\) −2.09241e18 −0.116211
\(918\) −8.78878e17 −0.0484676
\(919\) 2.38248e19 1.30460 0.652302 0.757959i \(-0.273803\pi\)
0.652302 + 0.757959i \(0.273803\pi\)
\(920\) 6.98342e18 0.379706
\(921\) 3.46302e18 0.186968
\(922\) −1.44073e19 −0.772381
\(923\) 2.73864e19 1.45789
\(924\) 5.81563e17 0.0307418
\(925\) −4.19294e18 −0.220088
\(926\) 1.48552e19 0.774298
\(927\) −1.98184e18 −0.102577
\(928\) −1.36167e18 −0.0699858
\(929\) −6.20632e18 −0.316761 −0.158381 0.987378i \(-0.550627\pi\)
−0.158381 + 0.987378i \(0.550627\pi\)
\(930\) 2.68963e17 0.0136318
\(931\) 5.09215e18 0.256288
\(932\) 1.07272e18 0.0536143
\(933\) 3.73782e18 0.185519
\(934\) −2.61505e19 −1.28892
\(935\) 5.08084e18 0.248691
\(936\) 1.39762e19 0.679355
\(937\) −6.23647e18 −0.301045 −0.150523 0.988607i \(-0.548096\pi\)
−0.150523 + 0.988607i \(0.548096\pi\)
\(938\) 1.04749e19 0.502146
\(939\) 4.11678e18 0.195989
\(940\) −6.13809e18 −0.290203
\(941\) 2.44374e19 1.14742 0.573710 0.819059i \(-0.305504\pi\)
0.573710 + 0.819059i \(0.305504\pi\)
\(942\) −4.49287e16 −0.00209504
\(943\) −3.18779e19 −1.47626
\(944\) −6.39236e18 −0.293997
\(945\) −1.39372e18 −0.0636602
\(946\) 1.78246e19 0.808588
\(947\) −3.75329e19 −1.69097 −0.845487 0.533996i \(-0.820690\pi\)
−0.845487 + 0.533996i \(0.820690\pi\)
\(948\) −2.54407e17 −0.0113835
\(949\) −3.86480e19 −1.71750
\(950\) 1.53281e19 0.676526
\(951\) −4.12526e18 −0.180833
\(952\) −8.53323e17 −0.0371512
\(953\) 2.13125e19 0.921573 0.460786 0.887511i \(-0.347567\pi\)
0.460786 + 0.887511i \(0.347567\pi\)
\(954\) 2.49222e19 1.07034
\(955\) 9.93590e18 0.423824
\(956\) 1.86619e18 0.0790644
\(957\) 1.53045e18 0.0644010
\(958\) −1.31758e19 −0.550683
\(959\) 1.23965e19 0.514612
\(960\) 2.57291e17 0.0106087
\(961\) −2.31576e19 −0.948402
\(962\) −1.40005e19 −0.569516
\(963\) 3.00978e19 1.21608
\(964\) 1.16207e19 0.466373
\(965\) 6.05837e18 0.241506
\(966\) 1.31824e18 0.0521968
\(967\) −1.72188e19 −0.677222 −0.338611 0.940926i \(-0.609957\pi\)
−0.338611 + 0.940926i \(0.609957\pi\)
\(968\) −6.46659e18 −0.252631
\(969\) −1.59673e18 −0.0619622
\(970\) 1.02958e19 0.396865
\(971\) −4.71671e19 −1.80598 −0.902992 0.429656i \(-0.858635\pi\)
−0.902992 + 0.429656i \(0.858635\pi\)
\(972\) −4.79911e18 −0.182528
\(973\) −6.94125e18 −0.262243
\(974\) −1.55030e19 −0.581812
\(975\) 3.46843e18 0.129301
\(976\) 5.91908e18 0.219195
\(977\) 3.68129e19 1.35421 0.677105 0.735887i \(-0.263234\pi\)
0.677105 + 0.735887i \(0.263234\pi\)
\(978\) −7.22017e17 −0.0263843
\(979\) −2.33086e19 −0.846113
\(980\) −1.35319e18 −0.0487967
\(981\) −4.98853e19 −1.78700
\(982\) 1.28148e19 0.456024
\(983\) −5.24638e19 −1.85465 −0.927325 0.374258i \(-0.877898\pi\)
−0.927325 + 0.374258i \(0.877898\pi\)
\(984\) −1.17448e18 −0.0412456
\(985\) 1.06230e19 0.370605
\(986\) −2.24562e18 −0.0778282
\(987\) −1.15867e18 −0.0398931
\(988\) 5.11816e19 1.75063
\(989\) 4.04034e19 1.37291
\(990\) 1.84481e19 0.622763
\(991\) −2.94165e19 −0.986535 −0.493268 0.869878i \(-0.664198\pi\)
−0.493268 + 0.869878i \(0.664198\pi\)
\(992\) 1.20523e18 0.0401553
\(993\) 5.21717e18 0.172689
\(994\) −6.07121e18 −0.199647
\(995\) −1.48419e19 −0.484886
\(996\) −9.06375e16 −0.00294186
\(997\) 2.42460e19 0.781847 0.390924 0.920423i \(-0.372156\pi\)
0.390924 + 0.920423i \(0.372156\pi\)
\(998\) −1.98954e19 −0.637387
\(999\) 3.19668e18 0.101747
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 14.14.a.c.1.1 2
3.2 odd 2 126.14.a.l.1.2 2
4.3 odd 2 112.14.a.d.1.2 2
7.2 even 3 98.14.c.l.67.2 4
7.3 odd 6 98.14.c.m.79.1 4
7.4 even 3 98.14.c.l.79.2 4
7.5 odd 6 98.14.c.m.67.1 4
7.6 odd 2 98.14.a.e.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.14.a.c.1.1 2 1.1 even 1 trivial
98.14.a.e.1.2 2 7.6 odd 2
98.14.c.l.67.2 4 7.2 even 3
98.14.c.l.79.2 4 7.4 even 3
98.14.c.m.67.1 4 7.5 odd 6
98.14.c.m.79.1 4 7.3 odd 6
112.14.a.d.1.2 2 4.3 odd 2
126.14.a.l.1.2 2 3.2 odd 2