Properties

Label 23.12.a.b.1.7
Level $23$
Weight $12$
Character 23.1
Self dual yes
Analytic conductor $17.672$
Analytic rank $0$
Dimension $11$
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] = [23,12,Mod(1,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.1");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 23.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: \(17.6718931529\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - x^{10} - 16849 x^{9} - 2148 x^{8} + 97176782 x^{7} + 169360278 x^{6} - 226650696110 x^{5} - 940430954112 x^{4} + 180101325169073 x^{3} + \cdots - 51\!\cdots\!56 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-13.8911\) of defining polynomial
Character \(\chi\) \(=\) 23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+16.8911 q^{2} -378.630 q^{3} -1762.69 q^{4} -6541.27 q^{5} -6395.47 q^{6} -3800.70 q^{7} -64366.7 q^{8} -33786.5 q^{9} +O(q^{10})\) \(q+16.8911 q^{2} -378.630 q^{3} -1762.69 q^{4} -6541.27 q^{5} -6395.47 q^{6} -3800.70 q^{7} -64366.7 q^{8} -33786.5 q^{9} -110489. q^{10} +1.02487e6 q^{11} +667407. q^{12} -1.69626e6 q^{13} -64198.0 q^{14} +2.47672e6 q^{15} +2.52277e6 q^{16} +8.27076e6 q^{17} -570691. q^{18} -1.14578e7 q^{19} +1.15302e7 q^{20} +1.43906e6 q^{21} +1.73113e7 q^{22} -6.43634e6 q^{23} +2.43712e7 q^{24} -6.03993e6 q^{25} -2.86518e7 q^{26} +7.98657e7 q^{27} +6.69946e6 q^{28} +4.47832e7 q^{29} +4.18345e7 q^{30} +2.61664e8 q^{31} +1.74435e8 q^{32} -3.88048e8 q^{33} +1.39702e8 q^{34} +2.48614e7 q^{35} +5.95552e7 q^{36} -1.68474e8 q^{37} -1.93535e8 q^{38} +6.42256e8 q^{39} +4.21040e8 q^{40} -1.43869e9 q^{41} +2.43073e7 q^{42} -1.05453e9 q^{43} -1.80654e9 q^{44} +2.21007e8 q^{45} -1.08717e8 q^{46} +2.31808e9 q^{47} -9.55195e8 q^{48} -1.96288e9 q^{49} -1.02021e8 q^{50} -3.13156e9 q^{51} +2.98999e9 q^{52} +1.59647e9 q^{53} +1.34902e9 q^{54} -6.70398e9 q^{55} +2.44639e8 q^{56} +4.33827e9 q^{57} +7.56438e8 q^{58} +4.93268e9 q^{59} -4.36569e9 q^{60} -3.28664e8 q^{61} +4.41978e9 q^{62} +1.28413e8 q^{63} -2.22023e9 q^{64} +1.10957e10 q^{65} -6.55455e9 q^{66} +5.77514e9 q^{67} -1.45788e10 q^{68} +2.43699e9 q^{69} +4.19936e8 q^{70} +1.37955e10 q^{71} +2.17473e9 q^{72} +2.90528e10 q^{73} -2.84571e9 q^{74} +2.28690e9 q^{75} +2.01966e10 q^{76} -3.89524e9 q^{77} +1.08484e10 q^{78} -3.11198e8 q^{79} -1.65021e10 q^{80} -2.42543e10 q^{81} -2.43010e10 q^{82} +4.34819e10 q^{83} -2.53662e9 q^{84} -5.41013e10 q^{85} -1.78121e10 q^{86} -1.69563e10 q^{87} -6.59678e10 q^{88} +6.88021e9 q^{89} +3.73305e9 q^{90} +6.44699e9 q^{91} +1.13453e10 q^{92} -9.90736e10 q^{93} +3.91549e10 q^{94} +7.49486e10 q^{95} -6.60464e10 q^{96} +8.92894e10 q^{97} -3.31552e10 q^{98} -3.46270e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9} - 627650 q^{10} - 771396 q^{11} - 1720771 q^{12} + 3433434 q^{13} + 4585896 q^{14} + 5551840 q^{15} + 18802384 q^{16} + 29035398 q^{17} + 26169127 q^{18} + 21398428 q^{19} + 72466260 q^{20} + 61896432 q^{21} + 100463524 q^{22} - 70799773 q^{23} + 161844076 q^{24} + 233562509 q^{25} + 328796191 q^{26} + 356379712 q^{27} + 499445210 q^{28} + 226699042 q^{29} + 510413234 q^{30} + 251932328 q^{31} + 806116648 q^{32} + 221442992 q^{33} + 325378622 q^{34} - 355232072 q^{35} - 1034240009 q^{36} + 573876170 q^{37} - 770782036 q^{38} - 1199522184 q^{39} - 1009699226 q^{40} - 1733596378 q^{41} - 6499506824 q^{42} + 647370308 q^{43} - 4662321170 q^{44} - 5023123422 q^{45} - 205962976 q^{46} - 5436527248 q^{47} - 4050950401 q^{48} + 4356386219 q^{49} - 10296502416 q^{50} - 1050918064 q^{51} - 5616607137 q^{52} - 3387203910 q^{53} - 21748294807 q^{54} - 10571441512 q^{55} + 635842210 q^{56} - 4678697728 q^{57} + 1991171353 q^{58} + 15113662084 q^{59} + 19934836476 q^{60} + 23895772578 q^{61} + 7557529251 q^{62} + 56666471160 q^{63} + 32993181147 q^{64} + 3660035708 q^{65} + 33342886858 q^{66} + 46806014468 q^{67} + 40754169364 q^{68} + 128726860 q^{69} - 12274756860 q^{70} + 45541532768 q^{71} + 12763980783 q^{72} + 63786612542 q^{73} - 41720765910 q^{74} + 88573702476 q^{75} + 5581739704 q^{76} + 19147126968 q^{77} - 111443125499 q^{78} + 21847812496 q^{79} - 67715736674 q^{80} + 122793712411 q^{81} - 30216129401 q^{82} + 40153340788 q^{83} - 221098994762 q^{84} + 116854272412 q^{85} - 47307463306 q^{86} - 5595049008 q^{87} - 263050721364 q^{88} + 37300228382 q^{89} - 419483354956 q^{90} + 109416811256 q^{91} - 72498967552 q^{92} - 224700035960 q^{93} - 378035850441 q^{94} - 255722421456 q^{95} - 96864379937 q^{96} - 243602730 q^{97} - 514347061348 q^{98} + 97029276404 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.8911 0.373244 0.186622 0.982432i \(-0.440246\pi\)
0.186622 + 0.982432i \(0.440246\pi\)
\(3\) −378.630 −0.899597 −0.449798 0.893130i \(-0.648504\pi\)
−0.449798 + 0.893130i \(0.648504\pi\)
\(4\) −1762.69 −0.860689
\(5\) −6541.27 −0.936110 −0.468055 0.883699i \(-0.655045\pi\)
−0.468055 + 0.883699i \(0.655045\pi\)
\(6\) −6395.47 −0.335769
\(7\) −3800.70 −0.0854721 −0.0427361 0.999086i \(-0.513607\pi\)
−0.0427361 + 0.999086i \(0.513607\pi\)
\(8\) −64366.7 −0.694491
\(9\) −33786.5 −0.190726
\(10\) −110489. −0.349397
\(11\) 1.02487e6 1.91872 0.959359 0.282189i \(-0.0910605\pi\)
0.959359 + 0.282189i \(0.0910605\pi\)
\(12\) 667407. 0.774273
\(13\) −1.69626e6 −1.26708 −0.633542 0.773709i \(-0.718399\pi\)
−0.633542 + 0.773709i \(0.718399\pi\)
\(14\) −64198.0 −0.0319019
\(15\) 2.47672e6 0.842122
\(16\) 2.52277e6 0.601475
\(17\) 8.27076e6 1.41279 0.706393 0.707820i \(-0.250321\pi\)
0.706393 + 0.707820i \(0.250321\pi\)
\(18\) −570691. −0.0711873
\(19\) −1.14578e7 −1.06159 −0.530795 0.847500i \(-0.678107\pi\)
−0.530795 + 0.847500i \(0.678107\pi\)
\(20\) 1.15302e7 0.805700
\(21\) 1.43906e6 0.0768904
\(22\) 1.73113e7 0.716150
\(23\) −6.43634e6 −0.208514
\(24\) 2.43712e7 0.624761
\(25\) −6.03993e6 −0.123698
\(26\) −2.86518e7 −0.472931
\(27\) 7.98657e7 1.07117
\(28\) 6.69946e6 0.0735649
\(29\) 4.47832e7 0.405440 0.202720 0.979237i \(-0.435022\pi\)
0.202720 + 0.979237i \(0.435022\pi\)
\(30\) 4.18345e7 0.314317
\(31\) 2.61664e8 1.64155 0.820775 0.571252i \(-0.193542\pi\)
0.820775 + 0.571252i \(0.193542\pi\)
\(32\) 1.74435e8 0.918987
\(33\) −3.88048e8 −1.72607
\(34\) 1.39702e8 0.527314
\(35\) 2.48614e7 0.0800113
\(36\) 5.95552e7 0.164156
\(37\) −1.68474e8 −0.399414 −0.199707 0.979856i \(-0.563999\pi\)
−0.199707 + 0.979856i \(0.563999\pi\)
\(38\) −1.93535e8 −0.396232
\(39\) 6.42256e8 1.13986
\(40\) 4.21040e8 0.650120
\(41\) −1.43869e9 −1.93935 −0.969673 0.244408i \(-0.921406\pi\)
−0.969673 + 0.244408i \(0.921406\pi\)
\(42\) 2.43073e7 0.0286989
\(43\) −1.05453e9 −1.09391 −0.546955 0.837162i \(-0.684213\pi\)
−0.546955 + 0.837162i \(0.684213\pi\)
\(44\) −1.80654e9 −1.65142
\(45\) 2.21007e8 0.178541
\(46\) −1.08717e8 −0.0778267
\(47\) 2.31808e9 1.47432 0.737158 0.675721i \(-0.236167\pi\)
0.737158 + 0.675721i \(0.236167\pi\)
\(48\) −9.55195e8 −0.541085
\(49\) −1.96288e9 −0.992695
\(50\) −1.02021e8 −0.0461694
\(51\) −3.13156e9 −1.27094
\(52\) 2.98999e9 1.09056
\(53\) 1.59647e9 0.524378 0.262189 0.965017i \(-0.415556\pi\)
0.262189 + 0.965017i \(0.415556\pi\)
\(54\) 1.34902e9 0.399809
\(55\) −6.70398e9 −1.79613
\(56\) 2.44639e8 0.0593596
\(57\) 4.33827e9 0.955003
\(58\) 7.56438e8 0.151328
\(59\) 4.93268e9 0.898250 0.449125 0.893469i \(-0.351736\pi\)
0.449125 + 0.893469i \(0.351736\pi\)
\(60\) −4.36569e9 −0.724805
\(61\) −3.28664e8 −0.0498239 −0.0249119 0.999690i \(-0.507931\pi\)
−0.0249119 + 0.999690i \(0.507931\pi\)
\(62\) 4.41978e9 0.612698
\(63\) 1.28413e8 0.0163018
\(64\) −2.22023e9 −0.258468
\(65\) 1.10957e10 1.18613
\(66\) −6.55455e9 −0.644246
\(67\) 5.77514e9 0.522578 0.261289 0.965261i \(-0.415853\pi\)
0.261289 + 0.965261i \(0.415853\pi\)
\(68\) −1.45788e10 −1.21597
\(69\) 2.43699e9 0.187579
\(70\) 4.19936e8 0.0298637
\(71\) 1.37955e10 0.907438 0.453719 0.891145i \(-0.350097\pi\)
0.453719 + 0.891145i \(0.350097\pi\)
\(72\) 2.17473e9 0.132457
\(73\) 2.90528e10 1.64026 0.820128 0.572180i \(-0.193902\pi\)
0.820128 + 0.572180i \(0.193902\pi\)
\(74\) −2.84571e9 −0.149079
\(75\) 2.28690e9 0.111278
\(76\) 2.01966e10 0.913699
\(77\) −3.89524e9 −0.163997
\(78\) 1.08484e10 0.425447
\(79\) −3.11198e8 −0.0113786 −0.00568929 0.999984i \(-0.501811\pi\)
−0.00568929 + 0.999984i \(0.501811\pi\)
\(80\) −1.65021e10 −0.563047
\(81\) −2.42543e10 −0.772898
\(82\) −2.43010e10 −0.723849
\(83\) 4.34819e10 1.21165 0.605827 0.795596i \(-0.292842\pi\)
0.605827 + 0.795596i \(0.292842\pi\)
\(84\) −2.53662e9 −0.0661787
\(85\) −5.41013e10 −1.32252
\(86\) −1.78121e10 −0.408295
\(87\) −1.69563e10 −0.364732
\(88\) −6.59678e10 −1.33253
\(89\) 6.88021e9 0.130604 0.0653020 0.997866i \(-0.479199\pi\)
0.0653020 + 0.997866i \(0.479199\pi\)
\(90\) 3.73305e9 0.0666392
\(91\) 6.44699e9 0.108300
\(92\) 1.13453e10 0.179466
\(93\) −9.90736e10 −1.47673
\(94\) 3.91549e10 0.550279
\(95\) 7.49486e10 0.993765
\(96\) −6.60464e10 −0.826718
\(97\) 8.92894e10 1.05574 0.527868 0.849326i \(-0.322992\pi\)
0.527868 + 0.849326i \(0.322992\pi\)
\(98\) −3.31552e10 −0.370517
\(99\) −3.46270e10 −0.365949
\(100\) 1.06465e10 0.106465
\(101\) 1.19965e11 1.13576 0.567882 0.823110i \(-0.307763\pi\)
0.567882 + 0.823110i \(0.307763\pi\)
\(102\) −5.28954e10 −0.474370
\(103\) 6.01002e10 0.510824 0.255412 0.966832i \(-0.417789\pi\)
0.255412 + 0.966832i \(0.417789\pi\)
\(104\) 1.09183e11 0.879977
\(105\) −9.41327e9 −0.0719779
\(106\) 2.69662e10 0.195721
\(107\) −2.39646e11 −1.65181 −0.825903 0.563812i \(-0.809334\pi\)
−0.825903 + 0.563812i \(0.809334\pi\)
\(108\) −1.40779e11 −0.921947
\(109\) −1.12756e11 −0.701928 −0.350964 0.936389i \(-0.614146\pi\)
−0.350964 + 0.936389i \(0.614146\pi\)
\(110\) −1.13238e11 −0.670395
\(111\) 6.37893e10 0.359312
\(112\) −9.58828e9 −0.0514093
\(113\) 9.05850e10 0.462514 0.231257 0.972893i \(-0.425716\pi\)
0.231257 + 0.972893i \(0.425716\pi\)
\(114\) 7.32781e10 0.356449
\(115\) 4.21018e10 0.195192
\(116\) −7.89390e10 −0.348958
\(117\) 5.73109e10 0.241666
\(118\) 8.33184e10 0.335266
\(119\) −3.14347e10 −0.120754
\(120\) −1.59418e11 −0.584846
\(121\) 7.65057e11 2.68148
\(122\) −5.55149e9 −0.0185965
\(123\) 5.44730e11 1.74463
\(124\) −4.61232e11 −1.41286
\(125\) 3.58907e11 1.05190
\(126\) 2.16903e9 0.00608453
\(127\) 4.75970e10 0.127838 0.0639189 0.997955i \(-0.479640\pi\)
0.0639189 + 0.997955i \(0.479640\pi\)
\(128\) −3.94746e11 −1.01546
\(129\) 3.99275e11 0.984077
\(130\) 1.87419e11 0.442715
\(131\) −4.22725e10 −0.0957340 −0.0478670 0.998854i \(-0.515242\pi\)
−0.0478670 + 0.998854i \(0.515242\pi\)
\(132\) 6.84009e11 1.48561
\(133\) 4.35477e10 0.0907363
\(134\) 9.75483e10 0.195049
\(135\) −5.22423e11 −1.00274
\(136\) −5.32362e11 −0.981167
\(137\) −2.26639e11 −0.401209 −0.200605 0.979672i \(-0.564291\pi\)
−0.200605 + 0.979672i \(0.564291\pi\)
\(138\) 4.11634e10 0.0700127
\(139\) 1.60580e9 0.00262489 0.00131244 0.999999i \(-0.499582\pi\)
0.00131244 + 0.999999i \(0.499582\pi\)
\(140\) −4.38230e10 −0.0688649
\(141\) −8.77695e11 −1.32629
\(142\) 2.33021e11 0.338696
\(143\) −1.73846e12 −2.43117
\(144\) −8.52356e10 −0.114717
\(145\) −2.92939e11 −0.379537
\(146\) 4.90733e11 0.612215
\(147\) 7.43205e11 0.893025
\(148\) 2.96968e11 0.343772
\(149\) 9.73616e11 1.08608 0.543042 0.839706i \(-0.317273\pi\)
0.543042 + 0.839706i \(0.317273\pi\)
\(150\) 3.86282e10 0.0415339
\(151\) −8.00653e11 −0.829987 −0.414993 0.909824i \(-0.636216\pi\)
−0.414993 + 0.909824i \(0.636216\pi\)
\(152\) 7.37502e11 0.737264
\(153\) −2.79440e11 −0.269455
\(154\) −6.57949e10 −0.0612108
\(155\) −1.71161e12 −1.53667
\(156\) −1.13210e12 −0.981068
\(157\) −7.49867e11 −0.627388 −0.313694 0.949524i \(-0.601567\pi\)
−0.313694 + 0.949524i \(0.601567\pi\)
\(158\) −5.25647e9 −0.00424698
\(159\) −6.04472e11 −0.471729
\(160\) −1.14103e12 −0.860273
\(161\) 2.44626e10 0.0178222
\(162\) −4.09682e11 −0.288479
\(163\) −4.12146e11 −0.280556 −0.140278 0.990112i \(-0.544800\pi\)
−0.140278 + 0.990112i \(0.544800\pi\)
\(164\) 2.53596e12 1.66917
\(165\) 2.53833e12 1.61579
\(166\) 7.34456e11 0.452242
\(167\) −4.65535e11 −0.277340 −0.138670 0.990339i \(-0.544283\pi\)
−0.138670 + 0.990339i \(0.544283\pi\)
\(168\) −9.26275e10 −0.0533997
\(169\) 1.08515e12 0.605500
\(170\) −9.13830e11 −0.493624
\(171\) 3.87120e11 0.202473
\(172\) 1.85881e12 0.941516
\(173\) −3.73536e11 −0.183264 −0.0916322 0.995793i \(-0.529208\pi\)
−0.0916322 + 0.995793i \(0.529208\pi\)
\(174\) −2.86410e11 −0.136134
\(175\) 2.29560e10 0.0105727
\(176\) 2.58552e12 1.15406
\(177\) −1.86766e12 −0.808063
\(178\) 1.16214e11 0.0487471
\(179\) 1.15011e12 0.467788 0.233894 0.972262i \(-0.424853\pi\)
0.233894 + 0.972262i \(0.424853\pi\)
\(180\) −3.89567e11 −0.153668
\(181\) −9.40884e11 −0.360001 −0.180001 0.983666i \(-0.557610\pi\)
−0.180001 + 0.983666i \(0.557610\pi\)
\(182\) 1.08897e11 0.0404224
\(183\) 1.24442e11 0.0448214
\(184\) 4.14286e11 0.144811
\(185\) 1.10203e12 0.373896
\(186\) −1.67346e12 −0.551181
\(187\) 8.47650e12 2.71074
\(188\) −4.08606e12 −1.26893
\(189\) −3.03546e11 −0.0915554
\(190\) 1.26596e12 0.370917
\(191\) −4.32339e12 −1.23067 −0.615334 0.788266i \(-0.710979\pi\)
−0.615334 + 0.788266i \(0.710979\pi\)
\(192\) 8.40643e11 0.232517
\(193\) 3.56015e12 0.956980 0.478490 0.878093i \(-0.341184\pi\)
0.478490 + 0.878093i \(0.341184\pi\)
\(194\) 1.50820e12 0.394047
\(195\) −4.20117e12 −1.06704
\(196\) 3.45995e12 0.854401
\(197\) −2.01248e12 −0.483246 −0.241623 0.970370i \(-0.577680\pi\)
−0.241623 + 0.970370i \(0.577680\pi\)
\(198\) −5.84887e11 −0.136588
\(199\) −6.26753e12 −1.42365 −0.711827 0.702355i \(-0.752132\pi\)
−0.711827 + 0.702355i \(0.752132\pi\)
\(200\) 3.88770e11 0.0859070
\(201\) −2.18664e12 −0.470109
\(202\) 2.02634e12 0.423917
\(203\) −1.70208e11 −0.0346538
\(204\) 5.51997e12 1.09388
\(205\) 9.41084e12 1.81544
\(206\) 1.01516e12 0.190662
\(207\) 2.17462e11 0.0397691
\(208\) −4.27928e12 −0.762118
\(209\) −1.17428e13 −2.03689
\(210\) −1.59000e11 −0.0268653
\(211\) 9.34110e12 1.53760 0.768802 0.639487i \(-0.220853\pi\)
0.768802 + 0.639487i \(0.220853\pi\)
\(212\) −2.81409e12 −0.451326
\(213\) −5.22339e12 −0.816329
\(214\) −4.04788e12 −0.616526
\(215\) 6.89795e12 1.02402
\(216\) −5.14069e12 −0.743920
\(217\) −9.94505e11 −0.140307
\(218\) −1.90457e12 −0.261990
\(219\) −1.10002e13 −1.47557
\(220\) 1.18170e13 1.54591
\(221\) −1.40294e13 −1.79012
\(222\) 1.07747e12 0.134111
\(223\) 4.61925e12 0.560912 0.280456 0.959867i \(-0.409514\pi\)
0.280456 + 0.959867i \(0.409514\pi\)
\(224\) −6.62977e11 −0.0785478
\(225\) 2.04068e11 0.0235924
\(226\) 1.53008e12 0.172630
\(227\) −1.58752e12 −0.174814 −0.0874071 0.996173i \(-0.527858\pi\)
−0.0874071 + 0.996173i \(0.527858\pi\)
\(228\) −7.64702e12 −0.821960
\(229\) 4.60351e12 0.483052 0.241526 0.970394i \(-0.422352\pi\)
0.241526 + 0.970394i \(0.422352\pi\)
\(230\) 7.11146e11 0.0728544
\(231\) 1.47485e12 0.147531
\(232\) −2.88255e12 −0.281574
\(233\) 5.72926e11 0.0546564 0.0273282 0.999627i \(-0.491300\pi\)
0.0273282 + 0.999627i \(0.491300\pi\)
\(234\) 9.68043e11 0.0902002
\(235\) −1.51632e13 −1.38012
\(236\) −8.69480e12 −0.773114
\(237\) 1.17829e11 0.0102361
\(238\) −5.30966e11 −0.0450706
\(239\) −4.64149e12 −0.385007 −0.192504 0.981296i \(-0.561661\pi\)
−0.192504 + 0.981296i \(0.561661\pi\)
\(240\) 6.24819e12 0.506515
\(241\) 2.10084e13 1.66456 0.832279 0.554358i \(-0.187036\pi\)
0.832279 + 0.554358i \(0.187036\pi\)
\(242\) 1.29226e13 1.00085
\(243\) −4.96455e12 −0.375877
\(244\) 5.79333e11 0.0428829
\(245\) 1.28397e13 0.929271
\(246\) 9.20108e12 0.651172
\(247\) 1.94355e13 1.34512
\(248\) −1.68424e13 −1.14004
\(249\) −1.64635e13 −1.09000
\(250\) 6.06232e12 0.392617
\(251\) −5.75426e12 −0.364573 −0.182286 0.983245i \(-0.558350\pi\)
−0.182286 + 0.983245i \(0.558350\pi\)
\(252\) −2.26352e11 −0.0140307
\(253\) −6.59645e12 −0.400080
\(254\) 8.03965e11 0.0477147
\(255\) 2.04844e13 1.18974
\(256\) −2.12066e12 −0.120546
\(257\) 1.72946e13 0.962226 0.481113 0.876658i \(-0.340233\pi\)
0.481113 + 0.876658i \(0.340233\pi\)
\(258\) 6.74420e12 0.367301
\(259\) 6.40320e11 0.0341388
\(260\) −1.95583e13 −1.02089
\(261\) −1.51307e12 −0.0773279
\(262\) −7.14029e11 −0.0357321
\(263\) 1.92961e13 0.945611 0.472805 0.881167i \(-0.343241\pi\)
0.472805 + 0.881167i \(0.343241\pi\)
\(264\) 2.49774e13 1.19874
\(265\) −1.04430e13 −0.490876
\(266\) 7.35568e11 0.0338668
\(267\) −2.60505e12 −0.117491
\(268\) −1.01798e13 −0.449777
\(269\) −2.10306e13 −0.910363 −0.455182 0.890399i \(-0.650426\pi\)
−0.455182 + 0.890399i \(0.650426\pi\)
\(270\) −8.82429e12 −0.374265
\(271\) 2.44065e13 1.01432 0.507160 0.861852i \(-0.330695\pi\)
0.507160 + 0.861852i \(0.330695\pi\)
\(272\) 2.08652e13 0.849755
\(273\) −2.44102e12 −0.0974266
\(274\) −3.82817e12 −0.149749
\(275\) −6.19017e12 −0.237341
\(276\) −4.29566e12 −0.161447
\(277\) 1.68895e13 0.622269 0.311134 0.950366i \(-0.399291\pi\)
0.311134 + 0.950366i \(0.399291\pi\)
\(278\) 2.71238e10 0.000979724 0
\(279\) −8.84071e12 −0.313086
\(280\) −1.60025e12 −0.0555671
\(281\) 1.46711e13 0.499549 0.249774 0.968304i \(-0.419644\pi\)
0.249774 + 0.968304i \(0.419644\pi\)
\(282\) −1.48252e13 −0.495029
\(283\) 2.33741e13 0.765436 0.382718 0.923865i \(-0.374988\pi\)
0.382718 + 0.923865i \(0.374988\pi\)
\(284\) −2.43172e13 −0.781022
\(285\) −2.83778e13 −0.893988
\(286\) −2.93645e13 −0.907421
\(287\) 5.46802e12 0.165760
\(288\) −5.89357e12 −0.175275
\(289\) 3.41336e13 0.995966
\(290\) −4.94806e12 −0.141660
\(291\) −3.38076e13 −0.949737
\(292\) −5.12110e13 −1.41175
\(293\) 3.92652e13 1.06227 0.531137 0.847286i \(-0.321765\pi\)
0.531137 + 0.847286i \(0.321765\pi\)
\(294\) 1.25535e13 0.333316
\(295\) −3.22660e13 −0.840861
\(296\) 1.08441e13 0.277390
\(297\) 8.18524e13 2.05528
\(298\) 1.64454e13 0.405374
\(299\) 1.09177e13 0.264205
\(300\) −4.03109e12 −0.0957758
\(301\) 4.00794e12 0.0934988
\(302\) −1.35239e13 −0.309787
\(303\) −4.54224e13 −1.02173
\(304\) −2.89054e13 −0.638519
\(305\) 2.14988e12 0.0466407
\(306\) −4.72005e12 −0.100572
\(307\) −4.58221e13 −0.958989 −0.479495 0.877545i \(-0.659180\pi\)
−0.479495 + 0.877545i \(0.659180\pi\)
\(308\) 6.86611e12 0.141150
\(309\) −2.27557e13 −0.459535
\(310\) −2.89110e13 −0.573553
\(311\) −5.88235e13 −1.14649 −0.573243 0.819386i \(-0.694315\pi\)
−0.573243 + 0.819386i \(0.694315\pi\)
\(312\) −4.13399e13 −0.791625
\(313\) 3.23539e13 0.608741 0.304371 0.952554i \(-0.401554\pi\)
0.304371 + 0.952554i \(0.401554\pi\)
\(314\) −1.26661e13 −0.234169
\(315\) −8.39981e11 −0.0152602
\(316\) 5.48546e11 0.00979342
\(317\) −7.31260e13 −1.28306 −0.641528 0.767100i \(-0.721699\pi\)
−0.641528 + 0.767100i \(0.721699\pi\)
\(318\) −1.02102e13 −0.176070
\(319\) 4.58972e13 0.777925
\(320\) 1.45231e13 0.241955
\(321\) 9.07370e13 1.48596
\(322\) 4.13200e11 0.00665201
\(323\) −9.47648e13 −1.49980
\(324\) 4.27529e13 0.665224
\(325\) 1.02453e13 0.156735
\(326\) −6.96159e12 −0.104716
\(327\) 4.26927e13 0.631452
\(328\) 9.26036e13 1.34686
\(329\) −8.81033e12 −0.126013
\(330\) 4.28751e13 0.603085
\(331\) 2.93876e13 0.406547 0.203273 0.979122i \(-0.434842\pi\)
0.203273 + 0.979122i \(0.434842\pi\)
\(332\) −7.66451e13 −1.04286
\(333\) 5.69216e12 0.0761787
\(334\) −7.86339e12 −0.103515
\(335\) −3.77767e13 −0.489190
\(336\) 3.63041e12 0.0462476
\(337\) 1.02524e13 0.128487 0.0642435 0.997934i \(-0.479537\pi\)
0.0642435 + 0.997934i \(0.479537\pi\)
\(338\) 1.83294e13 0.225999
\(339\) −3.42982e13 −0.416076
\(340\) 9.53639e13 1.13828
\(341\) 2.68173e14 3.14967
\(342\) 6.53887e12 0.0755717
\(343\) 1.49756e13 0.170320
\(344\) 6.78765e13 0.759710
\(345\) −1.59410e13 −0.175594
\(346\) −6.30942e12 −0.0684023
\(347\) 1.20191e14 1.28251 0.641256 0.767327i \(-0.278414\pi\)
0.641256 + 0.767327i \(0.278414\pi\)
\(348\) 2.98887e13 0.313921
\(349\) −1.24212e14 −1.28417 −0.642085 0.766634i \(-0.721930\pi\)
−0.642085 + 0.766634i \(0.721930\pi\)
\(350\) 3.87751e11 0.00394620
\(351\) −1.35473e14 −1.35727
\(352\) 1.78774e14 1.76328
\(353\) 6.01003e13 0.583601 0.291800 0.956479i \(-0.405746\pi\)
0.291800 + 0.956479i \(0.405746\pi\)
\(354\) −3.15468e13 −0.301604
\(355\) −9.02402e13 −0.849462
\(356\) −1.21277e13 −0.112409
\(357\) 1.19021e13 0.108630
\(358\) 1.94267e13 0.174599
\(359\) 8.94457e13 0.791662 0.395831 0.918323i \(-0.370457\pi\)
0.395831 + 0.918323i \(0.370457\pi\)
\(360\) −1.42255e13 −0.123995
\(361\) 1.47911e13 0.126973
\(362\) −1.58926e13 −0.134368
\(363\) −2.89673e14 −2.41225
\(364\) −1.13641e13 −0.0932129
\(365\) −1.90042e14 −1.53546
\(366\) 2.10196e12 0.0167293
\(367\) −1.97416e14 −1.54782 −0.773909 0.633297i \(-0.781701\pi\)
−0.773909 + 0.633297i \(0.781701\pi\)
\(368\) −1.62374e13 −0.125416
\(369\) 4.86082e13 0.369884
\(370\) 1.86146e13 0.139554
\(371\) −6.06772e12 −0.0448197
\(372\) 1.74636e14 1.27101
\(373\) −2.10543e13 −0.150988 −0.0754941 0.997146i \(-0.524053\pi\)
−0.0754941 + 0.997146i \(0.524053\pi\)
\(374\) 1.43177e14 1.01177
\(375\) −1.35893e14 −0.946290
\(376\) −1.49207e14 −1.02390
\(377\) −7.59642e13 −0.513726
\(378\) −5.12722e12 −0.0341725
\(379\) 9.20106e13 0.604397 0.302198 0.953245i \(-0.402279\pi\)
0.302198 + 0.953245i \(0.402279\pi\)
\(380\) −1.32111e14 −0.855323
\(381\) −1.80216e13 −0.115002
\(382\) −7.30268e13 −0.459339
\(383\) 2.78887e14 1.72916 0.864580 0.502495i \(-0.167585\pi\)
0.864580 + 0.502495i \(0.167585\pi\)
\(384\) 1.49462e14 0.913504
\(385\) 2.54798e13 0.153519
\(386\) 6.01348e13 0.357187
\(387\) 3.56288e13 0.208637
\(388\) −1.57390e14 −0.908660
\(389\) −7.22226e13 −0.411103 −0.205551 0.978646i \(-0.565899\pi\)
−0.205551 + 0.978646i \(0.565899\pi\)
\(390\) −7.09623e13 −0.398265
\(391\) −5.32335e13 −0.294586
\(392\) 1.26344e14 0.689417
\(393\) 1.60056e13 0.0861220
\(394\) −3.39930e13 −0.180369
\(395\) 2.03563e12 0.0106516
\(396\) 6.10367e13 0.314969
\(397\) 2.26699e14 1.15372 0.576862 0.816842i \(-0.304277\pi\)
0.576862 + 0.816842i \(0.304277\pi\)
\(398\) −1.05865e14 −0.531370
\(399\) −1.64885e13 −0.0816261
\(400\) −1.52373e13 −0.0744011
\(401\) 8.00200e12 0.0385394 0.0192697 0.999814i \(-0.493866\pi\)
0.0192697 + 0.999814i \(0.493866\pi\)
\(402\) −3.69347e13 −0.175465
\(403\) −4.43851e14 −2.07998
\(404\) −2.11462e14 −0.977540
\(405\) 1.58654e14 0.723517
\(406\) −2.87499e12 −0.0129343
\(407\) −1.72665e14 −0.766364
\(408\) 2.01568e14 0.882655
\(409\) 2.38273e14 1.02943 0.514714 0.857362i \(-0.327898\pi\)
0.514714 + 0.857362i \(0.327898\pi\)
\(410\) 1.58959e14 0.677602
\(411\) 8.58121e13 0.360926
\(412\) −1.05938e14 −0.439660
\(413\) −1.87477e13 −0.0767753
\(414\) 3.67317e12 0.0148436
\(415\) −2.84427e14 −1.13424
\(416\) −2.95888e14 −1.16443
\(417\) −6.08005e11 −0.00236134
\(418\) −1.98349e14 −0.760257
\(419\) 2.34045e14 0.885366 0.442683 0.896678i \(-0.354027\pi\)
0.442683 + 0.896678i \(0.354027\pi\)
\(420\) 1.65927e13 0.0619506
\(421\) −4.46364e14 −1.64489 −0.822447 0.568842i \(-0.807392\pi\)
−0.822447 + 0.568842i \(0.807392\pi\)
\(422\) 1.57781e14 0.573901
\(423\) −7.83199e13 −0.281190
\(424\) −1.02760e14 −0.364176
\(425\) −4.99548e13 −0.174759
\(426\) −8.82288e13 −0.304690
\(427\) 1.24915e12 0.00425855
\(428\) 4.22421e14 1.42169
\(429\) 6.58232e14 2.18708
\(430\) 1.16514e14 0.382209
\(431\) −2.21713e14 −0.718070 −0.359035 0.933324i \(-0.616894\pi\)
−0.359035 + 0.933324i \(0.616894\pi\)
\(432\) 2.01483e14 0.644283
\(433\) 2.98167e14 0.941404 0.470702 0.882292i \(-0.344001\pi\)
0.470702 + 0.882292i \(0.344001\pi\)
\(434\) −1.67983e13 −0.0523686
\(435\) 1.10916e14 0.341430
\(436\) 1.98753e14 0.604142
\(437\) 7.37464e13 0.221357
\(438\) −1.85806e14 −0.550747
\(439\) 4.49628e14 1.31613 0.658064 0.752962i \(-0.271375\pi\)
0.658064 + 0.752962i \(0.271375\pi\)
\(440\) 4.31513e14 1.24740
\(441\) 6.63190e13 0.189333
\(442\) −2.36972e14 −0.668151
\(443\) 3.08225e14 0.858316 0.429158 0.903230i \(-0.358810\pi\)
0.429158 + 0.903230i \(0.358810\pi\)
\(444\) −1.12441e14 −0.309256
\(445\) −4.50053e13 −0.122260
\(446\) 7.80242e13 0.209357
\(447\) −3.68640e14 −0.977037
\(448\) 8.43841e12 0.0220918
\(449\) 1.43170e14 0.370253 0.185127 0.982715i \(-0.440731\pi\)
0.185127 + 0.982715i \(0.440731\pi\)
\(450\) 3.44694e12 0.00880571
\(451\) −1.47447e15 −3.72106
\(452\) −1.59673e14 −0.398081
\(453\) 3.03151e14 0.746653
\(454\) −2.68149e13 −0.0652483
\(455\) −4.21715e13 −0.101381
\(456\) −2.79240e14 −0.663240
\(457\) 5.44489e14 1.27776 0.638881 0.769305i \(-0.279398\pi\)
0.638881 + 0.769305i \(0.279398\pi\)
\(458\) 7.77583e13 0.180296
\(459\) 6.60550e14 1.51334
\(460\) −7.42126e13 −0.168000
\(461\) 8.11079e12 0.0181430 0.00907148 0.999959i \(-0.497112\pi\)
0.00907148 + 0.999959i \(0.497112\pi\)
\(462\) 2.49119e13 0.0550650
\(463\) 5.42140e14 1.18418 0.592088 0.805873i \(-0.298304\pi\)
0.592088 + 0.805873i \(0.298304\pi\)
\(464\) 1.12978e14 0.243862
\(465\) 6.48067e14 1.38238
\(466\) 9.67734e12 0.0204002
\(467\) −2.62493e14 −0.546859 −0.273430 0.961892i \(-0.588158\pi\)
−0.273430 + 0.961892i \(0.588158\pi\)
\(468\) −1.01021e14 −0.207999
\(469\) −2.19496e13 −0.0446658
\(470\) −2.56123e14 −0.515122
\(471\) 2.83922e14 0.564396
\(472\) −3.17501e14 −0.623826
\(473\) −1.08076e15 −2.09890
\(474\) 1.99026e12 0.00382057
\(475\) 6.92044e13 0.131316
\(476\) 5.54097e13 0.103932
\(477\) −5.39393e13 −0.100013
\(478\) −7.83998e13 −0.143702
\(479\) −2.72054e14 −0.492958 −0.246479 0.969148i \(-0.579274\pi\)
−0.246479 + 0.969148i \(0.579274\pi\)
\(480\) 4.32027e14 0.773899
\(481\) 2.85777e14 0.506091
\(482\) 3.54854e14 0.621286
\(483\) −9.26227e12 −0.0160328
\(484\) −1.34856e15 −2.30792
\(485\) −5.84066e14 −0.988285
\(486\) −8.38567e13 −0.140294
\(487\) 1.73949e14 0.287748 0.143874 0.989596i \(-0.454044\pi\)
0.143874 + 0.989596i \(0.454044\pi\)
\(488\) 2.11550e13 0.0346022
\(489\) 1.56051e14 0.252387
\(490\) 2.16877e14 0.346845
\(491\) 2.26324e14 0.357916 0.178958 0.983857i \(-0.442727\pi\)
0.178958 + 0.983857i \(0.442727\pi\)
\(492\) −9.60190e14 −1.50158
\(493\) 3.70392e14 0.572800
\(494\) 3.28286e14 0.502059
\(495\) 2.26504e14 0.342569
\(496\) 6.60117e14 0.987351
\(497\) −5.24327e13 −0.0775607
\(498\) −2.78087e14 −0.406836
\(499\) −3.66205e14 −0.529873 −0.264936 0.964266i \(-0.585351\pi\)
−0.264936 + 0.964266i \(0.585351\pi\)
\(500\) −6.32642e14 −0.905363
\(501\) 1.76265e14 0.249494
\(502\) −9.71958e13 −0.136075
\(503\) −6.01196e14 −0.832515 −0.416257 0.909247i \(-0.636659\pi\)
−0.416257 + 0.909247i \(0.636659\pi\)
\(504\) −8.26549e12 −0.0113214
\(505\) −7.84725e14 −1.06320
\(506\) −1.11421e14 −0.149328
\(507\) −4.10871e14 −0.544705
\(508\) −8.38988e13 −0.110029
\(509\) −8.42096e14 −1.09248 −0.546241 0.837628i \(-0.683942\pi\)
−0.546241 + 0.837628i \(0.683942\pi\)
\(510\) 3.46003e14 0.444062
\(511\) −1.10421e14 −0.140196
\(512\) 7.72619e14 0.970466
\(513\) −9.15086e14 −1.13715
\(514\) 2.92124e14 0.359145
\(515\) −3.93131e14 −0.478187
\(516\) −7.03799e14 −0.846985
\(517\) 2.37574e15 2.82880
\(518\) 1.08157e13 0.0127421
\(519\) 1.41432e14 0.164864
\(520\) −7.14195e14 −0.823756
\(521\) 6.79230e14 0.775192 0.387596 0.921829i \(-0.373306\pi\)
0.387596 + 0.921829i \(0.373306\pi\)
\(522\) −2.55574e13 −0.0288622
\(523\) −3.67670e14 −0.410864 −0.205432 0.978671i \(-0.565860\pi\)
−0.205432 + 0.978671i \(0.565860\pi\)
\(524\) 7.45134e13 0.0823972
\(525\) −8.69181e12 −0.00951117
\(526\) 3.25932e14 0.352943
\(527\) 2.16416e15 2.31916
\(528\) −9.78955e14 −1.03819
\(529\) 4.14265e13 0.0434783
\(530\) −1.76393e14 −0.183216
\(531\) −1.66658e14 −0.171320
\(532\) −7.67612e13 −0.0780958
\(533\) 2.44039e15 2.45731
\(534\) −4.40022e13 −0.0438528
\(535\) 1.56759e15 1.54627
\(536\) −3.71727e14 −0.362925
\(537\) −4.35468e14 −0.420821
\(538\) −3.55230e14 −0.339788
\(539\) −2.01171e15 −1.90470
\(540\) 9.20870e14 0.863044
\(541\) −1.69417e15 −1.57171 −0.785855 0.618411i \(-0.787777\pi\)
−0.785855 + 0.618411i \(0.787777\pi\)
\(542\) 4.12253e14 0.378589
\(543\) 3.56247e14 0.323856
\(544\) 1.44271e15 1.29833
\(545\) 7.37565e14 0.657082
\(546\) −4.12315e13 −0.0363639
\(547\) −5.60422e14 −0.489311 −0.244655 0.969610i \(-0.578675\pi\)
−0.244655 + 0.969610i \(0.578675\pi\)
\(548\) 3.99494e14 0.345316
\(549\) 1.11044e13 0.00950271
\(550\) −1.04559e14 −0.0885861
\(551\) −5.13118e14 −0.430411
\(552\) −1.56861e14 −0.130272
\(553\) 1.18277e12 0.000972551 0
\(554\) 2.85282e14 0.232258
\(555\) −4.17263e14 −0.336355
\(556\) −2.83054e12 −0.00225921
\(557\) 6.65773e13 0.0526166 0.0263083 0.999654i \(-0.491625\pi\)
0.0263083 + 0.999654i \(0.491625\pi\)
\(558\) −1.49329e14 −0.116858
\(559\) 1.78876e15 1.38607
\(560\) 6.27195e13 0.0481248
\(561\) −3.20945e15 −2.43857
\(562\) 2.47811e14 0.186453
\(563\) 2.54438e15 1.89577 0.947887 0.318607i \(-0.103215\pi\)
0.947887 + 0.318607i \(0.103215\pi\)
\(564\) 1.54710e15 1.14152
\(565\) −5.92541e14 −0.432964
\(566\) 3.94813e14 0.285694
\(567\) 9.21835e13 0.0660612
\(568\) −8.87972e14 −0.630208
\(569\) −5.21696e13 −0.0366691 −0.0183346 0.999832i \(-0.505836\pi\)
−0.0183346 + 0.999832i \(0.505836\pi\)
\(570\) −4.79331e14 −0.333675
\(571\) −2.79494e15 −1.92696 −0.963482 0.267773i \(-0.913712\pi\)
−0.963482 + 0.267773i \(0.913712\pi\)
\(572\) 3.06437e15 2.09249
\(573\) 1.63696e15 1.10711
\(574\) 9.23608e13 0.0618689
\(575\) 3.88751e13 0.0257928
\(576\) 7.50137e13 0.0492966
\(577\) 1.97977e15 1.28869 0.644344 0.764736i \(-0.277130\pi\)
0.644344 + 0.764736i \(0.277130\pi\)
\(578\) 5.76554e14 0.371738
\(579\) −1.34798e15 −0.860896
\(580\) 5.16361e14 0.326663
\(581\) −1.65262e14 −0.103563
\(582\) −5.71048e14 −0.354483
\(583\) 1.63619e15 1.00613
\(584\) −1.87003e15 −1.13914
\(585\) −3.74886e14 −0.226226
\(586\) 6.63233e14 0.396487
\(587\) −1.11113e15 −0.658047 −0.329024 0.944322i \(-0.606720\pi\)
−0.329024 + 0.944322i \(0.606720\pi\)
\(588\) −1.31004e15 −0.768616
\(589\) −2.99809e15 −1.74265
\(590\) −5.45008e14 −0.313846
\(591\) 7.61986e14 0.434726
\(592\) −4.25021e14 −0.240238
\(593\) 1.47414e15 0.825537 0.412768 0.910836i \(-0.364562\pi\)
0.412768 + 0.910836i \(0.364562\pi\)
\(594\) 1.38258e15 0.767120
\(595\) 2.05623e14 0.113039
\(596\) −1.71618e15 −0.934780
\(597\) 2.37307e15 1.28071
\(598\) 1.84413e14 0.0986129
\(599\) −3.73330e15 −1.97809 −0.989044 0.147624i \(-0.952837\pi\)
−0.989044 + 0.147624i \(0.952837\pi\)
\(600\) −1.47200e14 −0.0772816
\(601\) −7.03077e13 −0.0365757 −0.0182879 0.999833i \(-0.505822\pi\)
−0.0182879 + 0.999833i \(0.505822\pi\)
\(602\) 6.76985e13 0.0348978
\(603\) −1.95122e14 −0.0996691
\(604\) 1.41130e15 0.714360
\(605\) −5.00444e15 −2.51016
\(606\) −7.67234e14 −0.381354
\(607\) 2.40417e15 1.18420 0.592102 0.805863i \(-0.298298\pi\)
0.592102 + 0.805863i \(0.298298\pi\)
\(608\) −1.99865e15 −0.975588
\(609\) 6.44457e13 0.0311745
\(610\) 3.63138e13 0.0174083
\(611\) −3.93208e15 −1.86808
\(612\) 4.92567e14 0.231917
\(613\) 9.54801e14 0.445533 0.222767 0.974872i \(-0.428491\pi\)
0.222767 + 0.974872i \(0.428491\pi\)
\(614\) −7.73985e14 −0.357937
\(615\) −3.56322e15 −1.63316
\(616\) 2.50724e14 0.113894
\(617\) −8.16920e14 −0.367800 −0.183900 0.982945i \(-0.558872\pi\)
−0.183900 + 0.982945i \(0.558872\pi\)
\(618\) −3.84369e14 −0.171519
\(619\) 3.03728e15 1.34334 0.671672 0.740849i \(-0.265577\pi\)
0.671672 + 0.740849i \(0.265577\pi\)
\(620\) 3.01704e15 1.32260
\(621\) −5.14043e14 −0.223355
\(622\) −9.93592e14 −0.427919
\(623\) −2.61496e13 −0.0111630
\(624\) 1.62026e15 0.685599
\(625\) −2.05279e15 −0.861001
\(626\) 5.46493e14 0.227209
\(627\) 4.44618e15 1.83238
\(628\) 1.32178e15 0.539986
\(629\) −1.39341e15 −0.564287
\(630\) −1.41882e13 −0.00569579
\(631\) −2.90418e15 −1.15575 −0.577873 0.816127i \(-0.696117\pi\)
−0.577873 + 0.816127i \(0.696117\pi\)
\(632\) 2.00308e13 0.00790232
\(633\) −3.53682e15 −1.38322
\(634\) −1.23518e15 −0.478893
\(635\) −3.11345e14 −0.119670
\(636\) 1.06550e15 0.406012
\(637\) 3.32957e15 1.25783
\(638\) 7.75254e14 0.290356
\(639\) −4.66103e14 −0.173072
\(640\) 2.58214e15 0.950582
\(641\) 1.07107e15 0.390931 0.195466 0.980711i \(-0.437378\pi\)
0.195466 + 0.980711i \(0.437378\pi\)
\(642\) 1.53265e15 0.554625
\(643\) −3.09817e14 −0.111159 −0.0555795 0.998454i \(-0.517701\pi\)
−0.0555795 + 0.998454i \(0.517701\pi\)
\(644\) −4.31200e13 −0.0153393
\(645\) −2.61177e15 −0.921205
\(646\) −1.60068e15 −0.559791
\(647\) 1.64231e15 0.569485 0.284743 0.958604i \(-0.408092\pi\)
0.284743 + 0.958604i \(0.408092\pi\)
\(648\) 1.56117e15 0.536770
\(649\) 5.05538e15 1.72349
\(650\) 1.73055e14 0.0585005
\(651\) 3.76549e14 0.126219
\(652\) 7.26486e14 0.241471
\(653\) −2.52493e14 −0.0832198 −0.0416099 0.999134i \(-0.513249\pi\)
−0.0416099 + 0.999134i \(0.513249\pi\)
\(654\) 7.21125e14 0.235686
\(655\) 2.76516e14 0.0896176
\(656\) −3.62947e15 −1.16647
\(657\) −9.81592e14 −0.312839
\(658\) −1.48816e14 −0.0470335
\(659\) 3.85339e15 1.20774 0.603869 0.797084i \(-0.293625\pi\)
0.603869 + 0.797084i \(0.293625\pi\)
\(660\) −4.47429e15 −1.39070
\(661\) 5.10081e15 1.57228 0.786142 0.618045i \(-0.212075\pi\)
0.786142 + 0.618045i \(0.212075\pi\)
\(662\) 4.96389e14 0.151741
\(663\) 5.31195e15 1.61038
\(664\) −2.79879e15 −0.841483
\(665\) −2.84857e14 −0.0849392
\(666\) 9.61467e13 0.0284332
\(667\) −2.88240e14 −0.0845401
\(668\) 8.20594e14 0.238703
\(669\) −1.74899e15 −0.504595
\(670\) −6.38090e14 −0.182587
\(671\) −3.36839e14 −0.0955980
\(672\) 2.51023e14 0.0706613
\(673\) 2.75725e15 0.769827 0.384914 0.922953i \(-0.374231\pi\)
0.384914 + 0.922953i \(0.374231\pi\)
\(674\) 1.73174e14 0.0479570
\(675\) −4.82383e14 −0.132502
\(676\) −1.91279e15 −0.521147
\(677\) −1.16755e15 −0.315528 −0.157764 0.987477i \(-0.550428\pi\)
−0.157764 + 0.987477i \(0.550428\pi\)
\(678\) −5.79333e14 −0.155298
\(679\) −3.39362e14 −0.0902360
\(680\) 3.48232e15 0.918481
\(681\) 6.01082e14 0.157262
\(682\) 4.52973e15 1.17560
\(683\) 1.19784e15 0.308380 0.154190 0.988041i \(-0.450723\pi\)
0.154190 + 0.988041i \(0.450723\pi\)
\(684\) −6.82372e14 −0.174266
\(685\) 1.48250e15 0.375576
\(686\) 2.52953e14 0.0635708
\(687\) −1.74303e15 −0.434552
\(688\) −2.66033e15 −0.657959
\(689\) −2.70804e15 −0.664431
\(690\) −2.69261e14 −0.0655396
\(691\) −4.05987e15 −0.980354 −0.490177 0.871623i \(-0.663068\pi\)
−0.490177 + 0.871623i \(0.663068\pi\)
\(692\) 6.58428e14 0.157734
\(693\) 1.31607e14 0.0312785
\(694\) 2.03016e15 0.478690
\(695\) −1.05040e13 −0.00245719
\(696\) 1.09142e15 0.253303
\(697\) −1.18990e16 −2.73988
\(698\) −2.09807e15 −0.479308
\(699\) −2.16927e14 −0.0491687
\(700\) −4.04643e13 −0.00909982
\(701\) −2.71723e14 −0.0606285 −0.0303142 0.999540i \(-0.509651\pi\)
−0.0303142 + 0.999540i \(0.509651\pi\)
\(702\) −2.28829e15 −0.506591
\(703\) 1.93034e15 0.424014
\(704\) −2.27545e15 −0.495928
\(705\) 5.74124e15 1.24155
\(706\) 1.01516e15 0.217825
\(707\) −4.55952e14 −0.0970761
\(708\) 3.29211e15 0.695491
\(709\) 7.65619e15 1.60494 0.802469 0.596694i \(-0.203519\pi\)
0.802469 + 0.596694i \(0.203519\pi\)
\(710\) −1.52426e15 −0.317057
\(711\) 1.05143e13 0.00217019
\(712\) −4.42856e14 −0.0907033
\(713\) −1.68416e15 −0.342287
\(714\) 2.01040e14 0.0405454
\(715\) 1.13717e16 2.27585
\(716\) −2.02730e15 −0.402620
\(717\) 1.75741e15 0.346351
\(718\) 1.51084e15 0.295483
\(719\) −7.64440e14 −0.148366 −0.0741830 0.997245i \(-0.523635\pi\)
−0.0741830 + 0.997245i \(0.523635\pi\)
\(720\) 5.57549e14 0.107388
\(721\) −2.28423e14 −0.0436612
\(722\) 2.49838e14 0.0473919
\(723\) −7.95439e15 −1.49743
\(724\) 1.65849e15 0.309849
\(725\) −2.70488e14 −0.0501520
\(726\) −4.89290e15 −0.900357
\(727\) 5.88535e15 1.07481 0.537406 0.843324i \(-0.319404\pi\)
0.537406 + 0.843324i \(0.319404\pi\)
\(728\) −4.14972e14 −0.0752135
\(729\) 6.17631e15 1.11104
\(730\) −3.21001e15 −0.573101
\(731\) −8.72175e15 −1.54546
\(732\) −2.19353e14 −0.0385773
\(733\) −8.92879e15 −1.55855 −0.779275 0.626682i \(-0.784413\pi\)
−0.779275 + 0.626682i \(0.784413\pi\)
\(734\) −3.33458e15 −0.577714
\(735\) −4.86151e15 −0.835969
\(736\) −1.12273e15 −0.191622
\(737\) 5.91879e15 1.00268
\(738\) 8.21046e14 0.138057
\(739\) 8.63680e15 1.44148 0.720739 0.693206i \(-0.243802\pi\)
0.720739 + 0.693206i \(0.243802\pi\)
\(740\) −1.94255e15 −0.321808
\(741\) −7.35885e15 −1.21007
\(742\) −1.02490e14 −0.0167287
\(743\) 6.31103e15 1.02250 0.511248 0.859433i \(-0.329183\pi\)
0.511248 + 0.859433i \(0.329183\pi\)
\(744\) 6.37705e15 1.02558
\(745\) −6.36868e15 −1.01669
\(746\) −3.55631e14 −0.0563554
\(747\) −1.46910e15 −0.231094
\(748\) −1.49414e16 −2.33310
\(749\) 9.10822e14 0.141183
\(750\) −2.29538e15 −0.353197
\(751\) −6.31269e15 −0.964261 −0.482131 0.876099i \(-0.660137\pi\)
−0.482131 + 0.876099i \(0.660137\pi\)
\(752\) 5.84798e15 0.886763
\(753\) 2.17874e15 0.327968
\(754\) −1.28312e15 −0.191745
\(755\) 5.23729e15 0.776959
\(756\) 5.35057e14 0.0788008
\(757\) −8.86188e15 −1.29568 −0.647841 0.761775i \(-0.724328\pi\)
−0.647841 + 0.761775i \(0.724328\pi\)
\(758\) 1.55416e15 0.225587
\(759\) 2.49761e15 0.359911
\(760\) −4.82420e15 −0.690161
\(761\) 1.22632e15 0.174176 0.0870879 0.996201i \(-0.472244\pi\)
0.0870879 + 0.996201i \(0.472244\pi\)
\(762\) −3.04405e14 −0.0429239
\(763\) 4.28551e14 0.0599953
\(764\) 7.62081e15 1.05922
\(765\) 1.82790e15 0.252240
\(766\) 4.71071e15 0.645398
\(767\) −8.36714e15 −1.13816
\(768\) 8.02946e14 0.108442
\(769\) −8.27966e15 −1.11024 −0.555121 0.831770i \(-0.687328\pi\)
−0.555121 + 0.831770i \(0.687328\pi\)
\(770\) 4.30382e14 0.0573001
\(771\) −6.54823e15 −0.865616
\(772\) −6.27544e15 −0.823663
\(773\) −6.44373e15 −0.839750 −0.419875 0.907582i \(-0.637926\pi\)
−0.419875 + 0.907582i \(0.637926\pi\)
\(774\) 6.01810e14 0.0778725
\(775\) −1.58043e15 −0.203056
\(776\) −5.74727e15 −0.733199
\(777\) −2.42444e14 −0.0307111
\(778\) −1.21992e15 −0.153442
\(779\) 1.64842e16 2.05879
\(780\) 7.40536e15 0.918388
\(781\) 1.41387e16 1.74112
\(782\) −8.99171e14 −0.109953
\(783\) 3.57665e15 0.434296
\(784\) −4.95189e15 −0.597081
\(785\) 4.90508e15 0.587304
\(786\) 2.70353e14 0.0321445
\(787\) 2.25581e15 0.266343 0.133171 0.991093i \(-0.457484\pi\)
0.133171 + 0.991093i \(0.457484\pi\)
\(788\) 3.54739e15 0.415924
\(789\) −7.30607e15 −0.850668
\(790\) 3.43840e13 0.00397564
\(791\) −3.44286e14 −0.0395320
\(792\) 2.22882e15 0.254148
\(793\) 5.57501e14 0.0631310
\(794\) 3.82919e15 0.430620
\(795\) 3.95402e15 0.441590
\(796\) 1.10477e16 1.22532
\(797\) 6.89086e15 0.759019 0.379509 0.925188i \(-0.376093\pi\)
0.379509 + 0.925188i \(0.376093\pi\)
\(798\) −2.78508e14 −0.0304664
\(799\) 1.91723e16 2.08289
\(800\) −1.05358e15 −0.113677
\(801\) −2.32458e14 −0.0249096
\(802\) 1.35163e14 0.0143846
\(803\) 2.97754e16 3.14719
\(804\) 3.85437e15 0.404618
\(805\) −1.60017e14 −0.0166835
\(806\) −7.49712e15 −0.776340
\(807\) 7.96282e15 0.818960
\(808\) −7.72177e15 −0.788778
\(809\) −1.48659e16 −1.50825 −0.754127 0.656729i \(-0.771940\pi\)
−0.754127 + 0.656729i \(0.771940\pi\)
\(810\) 2.67984e15 0.270048
\(811\) −1.88038e15 −0.188205 −0.0941026 0.995563i \(-0.529998\pi\)
−0.0941026 + 0.995563i \(0.529998\pi\)
\(812\) 3.00024e14 0.0298262
\(813\) −9.24104e15 −0.912479
\(814\) −2.91650e15 −0.286040
\(815\) 2.69596e15 0.262631
\(816\) −7.90019e15 −0.764437
\(817\) 1.20826e16 1.16128
\(818\) 4.02468e15 0.384228
\(819\) −2.17822e14 −0.0206557
\(820\) −1.65884e16 −1.56253
\(821\) −1.83324e16 −1.71526 −0.857632 0.514263i \(-0.828065\pi\)
−0.857632 + 0.514263i \(0.828065\pi\)
\(822\) 1.44946e15 0.134714
\(823\) 6.27295e15 0.579126 0.289563 0.957159i \(-0.406490\pi\)
0.289563 + 0.957159i \(0.406490\pi\)
\(824\) −3.86845e15 −0.354762
\(825\) 2.34378e15 0.213511
\(826\) −3.16668e14 −0.0286559
\(827\) 1.64096e14 0.0147509 0.00737545 0.999973i \(-0.497652\pi\)
0.00737545 + 0.999973i \(0.497652\pi\)
\(828\) −3.83318e14 −0.0342288
\(829\) −7.03744e15 −0.624259 −0.312130 0.950040i \(-0.601042\pi\)
−0.312130 + 0.950040i \(0.601042\pi\)
\(830\) −4.80427e15 −0.423349
\(831\) −6.39487e15 −0.559791
\(832\) 3.76609e15 0.327501
\(833\) −1.62345e16 −1.40247
\(834\) −1.02699e13 −0.000881356 0
\(835\) 3.04519e15 0.259620
\(836\) 2.06990e16 1.75313
\(837\) 2.08980e16 1.75838
\(838\) 3.95328e15 0.330457
\(839\) 2.24738e16 1.86632 0.933160 0.359461i \(-0.117039\pi\)
0.933160 + 0.359461i \(0.117039\pi\)
\(840\) 6.05901e14 0.0499880
\(841\) −1.01950e16 −0.835618
\(842\) −7.53958e15 −0.613947
\(843\) −5.55491e15 −0.449392
\(844\) −1.64655e16 −1.32340
\(845\) −7.09827e15 −0.566814
\(846\) −1.32291e15 −0.104953
\(847\) −2.90775e15 −0.229192
\(848\) 4.02753e15 0.315400
\(849\) −8.85012e15 −0.688584
\(850\) −8.43792e14 −0.0652276
\(851\) 1.08436e15 0.0832837
\(852\) 9.20723e15 0.702605
\(853\) −2.39348e16 −1.81472 −0.907360 0.420355i \(-0.861906\pi\)
−0.907360 + 0.420355i \(0.861906\pi\)
\(854\) 2.10995e13 0.00158948
\(855\) −2.53225e15 −0.189537
\(856\) 1.54252e16 1.14716
\(857\) −8.96955e15 −0.662790 −0.331395 0.943492i \(-0.607519\pi\)
−0.331395 + 0.943492i \(0.607519\pi\)
\(858\) 1.11183e16 0.816313
\(859\) −1.70389e16 −1.24303 −0.621513 0.783404i \(-0.713482\pi\)
−0.621513 + 0.783404i \(0.713482\pi\)
\(860\) −1.21590e16 −0.881363
\(861\) −2.07035e15 −0.149117
\(862\) −3.74498e15 −0.268015
\(863\) 1.39607e16 0.992767 0.496383 0.868103i \(-0.334661\pi\)
0.496383 + 0.868103i \(0.334661\pi\)
\(864\) 1.39314e16 0.984395
\(865\) 2.44340e15 0.171556
\(866\) 5.03637e15 0.351373
\(867\) −1.29240e16 −0.895968
\(868\) 1.75301e15 0.120760
\(869\) −3.18939e14 −0.0218323
\(870\) 1.87348e15 0.127437
\(871\) −9.79616e15 −0.662149
\(872\) 7.25771e15 0.487483
\(873\) −3.01678e15 −0.201356
\(874\) 1.24566e15 0.0826201
\(875\) −1.36410e15 −0.0899085
\(876\) 1.93900e16 1.27001
\(877\) 2.17535e15 0.141589 0.0707947 0.997491i \(-0.477446\pi\)
0.0707947 + 0.997491i \(0.477446\pi\)
\(878\) 7.59471e15 0.491237
\(879\) −1.48670e16 −0.955618
\(880\) −1.69126e16 −1.08033
\(881\) −1.14121e15 −0.0724431 −0.0362215 0.999344i \(-0.511532\pi\)
−0.0362215 + 0.999344i \(0.511532\pi\)
\(882\) 1.12020e15 0.0706672
\(883\) −2.62009e16 −1.64260 −0.821302 0.570494i \(-0.806752\pi\)
−0.821302 + 0.570494i \(0.806752\pi\)
\(884\) 2.47295e16 1.54073
\(885\) 1.22169e16 0.756436
\(886\) 5.20625e15 0.320361
\(887\) −4.67640e15 −0.285977 −0.142989 0.989724i \(-0.545671\pi\)
−0.142989 + 0.989724i \(0.545671\pi\)
\(888\) −4.10591e15 −0.249539
\(889\) −1.80902e14 −0.0109266
\(890\) −7.60188e14 −0.0456327
\(891\) −2.48577e16 −1.48297
\(892\) −8.14232e15 −0.482771
\(893\) −2.65601e16 −1.56512
\(894\) −6.22673e15 −0.364673
\(895\) −7.52321e15 −0.437901
\(896\) 1.50031e15 0.0867934
\(897\) −4.13378e15 −0.237678
\(898\) 2.41831e15 0.138195
\(899\) 1.17181e16 0.665550
\(900\) −3.59709e14 −0.0203057
\(901\) 1.32041e16 0.740834
\(902\) −2.49055e16 −1.38886
\(903\) −1.51753e15 −0.0841112
\(904\) −5.83066e15 −0.321212
\(905\) 6.15458e15 0.337001
\(906\) 5.12055e15 0.278684
\(907\) −9.99364e15 −0.540610 −0.270305 0.962775i \(-0.587124\pi\)
−0.270305 + 0.962775i \(0.587124\pi\)
\(908\) 2.79831e15 0.150461
\(909\) −4.05321e15 −0.216620
\(910\) −7.12323e14 −0.0378398
\(911\) 1.46086e16 0.771363 0.385682 0.922632i \(-0.373966\pi\)
0.385682 + 0.922632i \(0.373966\pi\)
\(912\) 1.09444e16 0.574410
\(913\) 4.45635e16 2.32482
\(914\) 9.19701e15 0.476917
\(915\) −8.14008e14 −0.0419578
\(916\) −8.11456e15 −0.415758
\(917\) 1.60665e14 0.00818259
\(918\) 1.11574e16 0.564844
\(919\) −9.65126e15 −0.485678 −0.242839 0.970067i \(-0.578079\pi\)
−0.242839 + 0.970067i \(0.578079\pi\)
\(920\) −2.70996e15 −0.135559
\(921\) 1.73496e16 0.862704
\(922\) 1.37000e14 0.00677175
\(923\) −2.34009e16 −1.14980
\(924\) −2.59971e15 −0.126978
\(925\) 1.01757e15 0.0494067
\(926\) 9.15734e15 0.441986
\(927\) −2.03058e15 −0.0974274
\(928\) 7.81178e15 0.372594
\(929\) 3.11901e16 1.47887 0.739437 0.673226i \(-0.235092\pi\)
0.739437 + 0.673226i \(0.235092\pi\)
\(930\) 1.09466e16 0.515966
\(931\) 2.24903e16 1.05383
\(932\) −1.00989e15 −0.0470422
\(933\) 2.22723e16 1.03137
\(934\) −4.43380e15 −0.204112
\(935\) −5.54471e16 −2.53755
\(936\) −3.68891e15 −0.167835
\(937\) 1.81848e16 0.822509 0.411255 0.911521i \(-0.365091\pi\)
0.411255 + 0.911521i \(0.365091\pi\)
\(938\) −3.70752e14 −0.0166712
\(939\) −1.22502e16 −0.547622
\(940\) 2.67280e16 1.18786
\(941\) −2.76588e16 −1.22205 −0.611027 0.791610i \(-0.709243\pi\)
−0.611027 + 0.791610i \(0.709243\pi\)
\(942\) 4.79575e15 0.210657
\(943\) 9.25988e15 0.404381
\(944\) 1.24440e16 0.540275
\(945\) 1.98557e15 0.0857060
\(946\) −1.82552e16 −0.783403
\(947\) 3.44283e16 1.46890 0.734448 0.678665i \(-0.237441\pi\)
0.734448 + 0.678665i \(0.237441\pi\)
\(948\) −2.07696e14 −0.00881012
\(949\) −4.92812e16 −2.07834
\(950\) 1.16894e15 0.0490130
\(951\) 2.76877e16 1.15423
\(952\) 2.02335e15 0.0838624
\(953\) 3.73682e16 1.53990 0.769948 0.638106i \(-0.220282\pi\)
0.769948 + 0.638106i \(0.220282\pi\)
\(954\) −9.11094e14 −0.0373291
\(955\) 2.82805e16 1.15204
\(956\) 8.18152e15 0.331372
\(957\) −1.73781e16 −0.699819
\(958\) −4.59529e15 −0.183993
\(959\) 8.61386e14 0.0342922
\(960\) −5.49887e15 −0.217662
\(961\) 4.30594e16 1.69469
\(962\) 4.82708e15 0.188895
\(963\) 8.09680e15 0.315042
\(964\) −3.70313e16 −1.43267
\(965\) −2.32879e16 −0.895839
\(966\) −1.56450e14 −0.00598413
\(967\) 1.55579e16 0.591706 0.295853 0.955233i \(-0.404396\pi\)
0.295853 + 0.955233i \(0.404396\pi\)
\(968\) −4.92442e16 −1.86226
\(969\) 3.58808e16 1.34921
\(970\) −9.86551e15 −0.368871
\(971\) −1.02839e16 −0.382342 −0.191171 0.981557i \(-0.561229\pi\)
−0.191171 + 0.981557i \(0.561229\pi\)
\(972\) 8.75098e15 0.323513
\(973\) −6.10318e12 −0.000224355 0
\(974\) 2.93819e15 0.107400
\(975\) −3.87918e15 −0.140999
\(976\) −8.29142e14 −0.0299678
\(977\) −5.16632e16 −1.85678 −0.928391 0.371604i \(-0.878808\pi\)
−0.928391 + 0.371604i \(0.878808\pi\)
\(978\) 2.63587e15 0.0942019
\(979\) 7.05135e15 0.250592
\(980\) −2.26325e16 −0.799814
\(981\) 3.80962e15 0.133876
\(982\) 3.82285e15 0.133590
\(983\) 1.75164e16 0.608694 0.304347 0.952561i \(-0.401562\pi\)
0.304347 + 0.952561i \(0.401562\pi\)
\(984\) −3.50625e16 −1.21163
\(985\) 1.31642e16 0.452371
\(986\) 6.25632e15 0.213794
\(987\) 3.33585e15 0.113361
\(988\) −3.42587e16 −1.15773
\(989\) 6.78730e15 0.228096
\(990\) 3.82590e15 0.127862
\(991\) −3.86595e16 −1.28485 −0.642423 0.766350i \(-0.722071\pi\)
−0.642423 + 0.766350i \(0.722071\pi\)
\(992\) 4.56434e16 1.50856
\(993\) −1.11270e16 −0.365728
\(994\) −8.85645e14 −0.0289491
\(995\) 4.09976e16 1.33270
\(996\) 2.90201e16 0.938151
\(997\) −3.63590e15 −0.116893 −0.0584465 0.998291i \(-0.518615\pi\)
−0.0584465 + 0.998291i \(0.518615\pi\)
\(998\) −6.18561e15 −0.197772
\(999\) −1.34553e16 −0.427842
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 23.12.a.b.1.7 11
3.2 odd 2 207.12.a.d.1.5 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.12.a.b.1.7 11 1.1 even 1 trivial
207.12.a.d.1.5 11 3.2 odd 2