Properties

Label 23.16.a.a.1.5
Level $23$
Weight $16$
Character 23.1
Self dual yes
Analytic conductor $32.820$
Analytic rank $1$
Dimension $12$
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] = [23,16,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, 16, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.1");
 
S:= CuspForms(chi, 16);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 16 \)
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: \(32.8195061730\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 4 x^{11} - 68942 x^{10} - 977032 x^{9} + 1644150380 x^{8} + 50352376602 x^{7} - 15614385123802 x^{6} - 702635376772966 x^{5} + \cdots + 34\!\cdots\!76 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{22}\cdot 3^{6}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-61.7354\) 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)
 
\(f(q)\) \(=\) \(q-145.471 q^{2} +254.987 q^{3} -11606.2 q^{4} -233086. q^{5} -37093.1 q^{6} +2.20456e6 q^{7} +6.45516e6 q^{8} -1.42839e7 q^{9} +O(q^{10})\) \(q-145.471 q^{2} +254.987 q^{3} -11606.2 q^{4} -233086. q^{5} -37093.1 q^{6} +2.20456e6 q^{7} +6.45516e6 q^{8} -1.42839e7 q^{9} +3.39071e7 q^{10} +9.38765e7 q^{11} -2.95944e6 q^{12} -1.18996e8 q^{13} -3.20700e8 q^{14} -5.94337e7 q^{15} -5.58724e8 q^{16} -1.65607e8 q^{17} +2.07789e9 q^{18} +7.03866e9 q^{19} +2.70524e9 q^{20} +5.62134e8 q^{21} -1.36563e10 q^{22} +3.40483e9 q^{23} +1.64598e9 q^{24} +2.38113e10 q^{25} +1.73105e10 q^{26} -7.30098e9 q^{27} -2.55867e10 q^{28} -2.60002e10 q^{29} +8.64587e9 q^{30} -1.38242e11 q^{31} -1.30245e11 q^{32} +2.39373e10 q^{33} +2.40910e10 q^{34} -5.13852e11 q^{35} +1.65782e11 q^{36} +1.31561e11 q^{37} -1.02392e12 q^{38} -3.03425e10 q^{39} -1.50460e12 q^{40} -4.64703e11 q^{41} -8.17741e10 q^{42} -2.76285e12 q^{43} -1.08955e12 q^{44} +3.32937e12 q^{45} -4.95303e11 q^{46} +8.88872e11 q^{47} -1.42467e11 q^{48} +1.12534e11 q^{49} -3.46385e12 q^{50} -4.22277e10 q^{51} +1.38110e12 q^{52} -3.03201e12 q^{53} +1.06208e12 q^{54} -2.18813e13 q^{55} +1.42308e13 q^{56} +1.79477e12 q^{57} +3.78227e12 q^{58} +3.46464e11 q^{59} +6.89801e11 q^{60} -1.69272e13 q^{61} +2.01102e13 q^{62} -3.14897e13 q^{63} +3.72551e13 q^{64} +2.77363e13 q^{65} -3.48217e12 q^{66} -3.26635e13 q^{67} +1.92208e12 q^{68} +8.68185e11 q^{69} +7.47504e13 q^{70} +4.12553e13 q^{71} -9.22047e13 q^{72} +1.12820e14 q^{73} -1.91383e13 q^{74} +6.07156e12 q^{75} -8.16924e13 q^{76} +2.06957e14 q^{77} +4.41395e12 q^{78} -2.27725e14 q^{79} +1.30231e14 q^{80} +2.03097e14 q^{81} +6.76007e13 q^{82} +8.49695e13 q^{83} -6.52426e12 q^{84} +3.86007e13 q^{85} +4.01914e14 q^{86} -6.62970e12 q^{87} +6.05988e14 q^{88} +2.27743e13 q^{89} -4.84326e14 q^{90} -2.62335e14 q^{91} -3.95172e13 q^{92} -3.52498e13 q^{93} -1.29305e14 q^{94} -1.64061e15 q^{95} -3.32106e13 q^{96} -1.34059e15 q^{97} -1.63704e13 q^{98} -1.34092e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 256 q^{2} - 1745 q^{3} + 163840 q^{4} - 204476 q^{5} - 199430 q^{6} - 5717328 q^{7} + 10323168 q^{8} + 32660341 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 256 q^{2} - 1745 q^{3} + 163840 q^{4} - 204476 q^{5} - 199430 q^{6} - 5717328 q^{7} + 10323168 q^{8} + 32660341 q^{9} - 137846540 q^{10} - 87636002 q^{11} - 398208076 q^{12} - 292496079 q^{13} + 415954912 q^{14} + 548079030 q^{15} + 4273503168 q^{16} - 2462528162 q^{17} + 7261215718 q^{18} + 175321758 q^{19} + 2660811480 q^{20} + 205665472 q^{21} - 21718153768 q^{22} + 40857905364 q^{23} - 63413289624 q^{24} + 20443225284 q^{25} - 137268652810 q^{26} - 151915208903 q^{27} - 325638721712 q^{28} - 164667697193 q^{29} - 356944003956 q^{30} + 20222384151 q^{31} - 369109524032 q^{32} + 132365097022 q^{33} - 582887018988 q^{34} - 1578083373112 q^{35} - 1903913944516 q^{36} - 869669414912 q^{37} - 5525312078376 q^{38} - 5762413466499 q^{39} - 4733269274576 q^{40} - 7510147709883 q^{41} - 7436463221624 q^{42} - 5682603487020 q^{43} - 11849381658176 q^{44} - 10780493432442 q^{45} - 871635314432 q^{46} - 5828073094301 q^{47} - 29418911592496 q^{48} - 6518780198860 q^{49} - 16781003942456 q^{50} - 771327642584 q^{51} - 3841511618340 q^{52} + 1452974784324 q^{53} - 32167598069522 q^{54} - 14882020037092 q^{55} + 416192984288 q^{56} - 12135794354818 q^{57} - 60065613521022 q^{58} - 11503084624084 q^{59} - 6378557828664 q^{60} - 23587566667200 q^{61} + 49359974806402 q^{62} + 87886039196104 q^{63} + 80321007324160 q^{64} + 54548135308138 q^{65} + 316922278045948 q^{66} + 61525019345122 q^{67} + 45114528974104 q^{68} - 5941420405015 q^{69} + 374016699556320 q^{70} + 197895887067063 q^{71} + 439014895837656 q^{72} - 22888563242709 q^{73} + 694696716227036 q^{74} + 612085940395201 q^{75} + 301381886149904 q^{76} + 209007839834200 q^{77} + 350406148895766 q^{78} + 229938065096294 q^{79} + 555529032250016 q^{80} + 37596523177660 q^{81} - 414508112727306 q^{82} + 369402590629184 q^{83} + 559863541234208 q^{84} - 343366303925348 q^{85} + 12\!\cdots\!08 q^{86}+ \cdots - 32\!\cdots\!24 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −145.471 −0.803621 −0.401810 0.915723i \(-0.631619\pi\)
−0.401810 + 0.915723i \(0.631619\pi\)
\(3\) 254.987 0.0673144 0.0336572 0.999433i \(-0.489285\pi\)
0.0336572 + 0.999433i \(0.489285\pi\)
\(4\) −11606.2 −0.354194
\(5\) −233086. −1.33426 −0.667130 0.744942i \(-0.732477\pi\)
−0.667130 + 0.744942i \(0.732477\pi\)
\(6\) −37093.1 −0.0540953
\(7\) 2.20456e6 1.01178 0.505891 0.862597i \(-0.331164\pi\)
0.505891 + 0.862597i \(0.331164\pi\)
\(8\) 6.45516e6 1.08826
\(9\) −1.42839e7 −0.995469
\(10\) 3.39071e7 1.07224
\(11\) 9.38765e7 1.45249 0.726243 0.687438i \(-0.241265\pi\)
0.726243 + 0.687438i \(0.241265\pi\)
\(12\) −2.95944e6 −0.0238424
\(13\) −1.18996e8 −0.525967 −0.262983 0.964800i \(-0.584706\pi\)
−0.262983 + 0.964800i \(0.584706\pi\)
\(14\) −3.20700e8 −0.813089
\(15\) −5.94337e7 −0.0898149
\(16\) −5.58724e8 −0.520352
\(17\) −1.65607e8 −0.0978842 −0.0489421 0.998802i \(-0.515585\pi\)
−0.0489421 + 0.998802i \(0.515585\pi\)
\(18\) 2.07789e9 0.799979
\(19\) 7.03866e9 1.80650 0.903251 0.429113i \(-0.141174\pi\)
0.903251 + 0.429113i \(0.141174\pi\)
\(20\) 2.70524e9 0.472587
\(21\) 5.62134e8 0.0681076
\(22\) −1.36563e10 −1.16725
\(23\) 3.40483e9 0.208514
\(24\) 1.64598e9 0.0732555
\(25\) 2.38113e10 0.780248
\(26\) 1.73105e10 0.422678
\(27\) −7.30098e9 −0.134324
\(28\) −2.55867e10 −0.358367
\(29\) −2.60002e10 −0.279892 −0.139946 0.990159i \(-0.544693\pi\)
−0.139946 + 0.990159i \(0.544693\pi\)
\(30\) 8.64587e9 0.0721771
\(31\) −1.38242e11 −0.902457 −0.451229 0.892408i \(-0.649014\pi\)
−0.451229 + 0.892408i \(0.649014\pi\)
\(32\) −1.30245e11 −0.670092
\(33\) 2.39373e10 0.0977732
\(34\) 2.40910e10 0.0786618
\(35\) −5.13852e11 −1.34998
\(36\) 1.65782e11 0.352589
\(37\) 1.31561e11 0.227832 0.113916 0.993490i \(-0.463661\pi\)
0.113916 + 0.993490i \(0.463661\pi\)
\(38\) −1.02392e12 −1.45174
\(39\) −3.03425e10 −0.0354052
\(40\) −1.50460e12 −1.45202
\(41\) −4.64703e11 −0.372646 −0.186323 0.982489i \(-0.559657\pi\)
−0.186323 + 0.982489i \(0.559657\pi\)
\(42\) −8.17741e10 −0.0547326
\(43\) −2.76285e12 −1.55004 −0.775021 0.631936i \(-0.782261\pi\)
−0.775021 + 0.631936i \(0.782261\pi\)
\(44\) −1.08955e12 −0.514462
\(45\) 3.32937e12 1.32821
\(46\) −4.95303e11 −0.167566
\(47\) 8.88872e11 0.255921 0.127960 0.991779i \(-0.459157\pi\)
0.127960 + 0.991779i \(0.459157\pi\)
\(48\) −1.42467e11 −0.0350272
\(49\) 1.12534e11 0.0237036
\(50\) −3.46385e12 −0.627023
\(51\) −4.22277e10 −0.00658902
\(52\) 1.38110e12 0.186294
\(53\) −3.03201e12 −0.354537 −0.177269 0.984163i \(-0.556726\pi\)
−0.177269 + 0.984163i \(0.556726\pi\)
\(54\) 1.06208e12 0.107945
\(55\) −2.18813e13 −1.93799
\(56\) 1.42308e13 1.10108
\(57\) 1.79477e12 0.121604
\(58\) 3.78227e12 0.224927
\(59\) 3.46464e11 0.0181246 0.00906230 0.999959i \(-0.497115\pi\)
0.00906230 + 0.999959i \(0.497115\pi\)
\(60\) 6.89801e11 0.0318119
\(61\) −1.69272e13 −0.689624 −0.344812 0.938672i \(-0.612057\pi\)
−0.344812 + 0.938672i \(0.612057\pi\)
\(62\) 2.01102e13 0.725233
\(63\) −3.14897e13 −1.00720
\(64\) 3.72551e13 1.05885
\(65\) 2.77363e13 0.701776
\(66\) −3.48217e12 −0.0785726
\(67\) −3.26635e13 −0.658417 −0.329209 0.944257i \(-0.606782\pi\)
−0.329209 + 0.944257i \(0.606782\pi\)
\(68\) 1.92208e12 0.0346700
\(69\) 8.68185e11 0.0140360
\(70\) 7.47504e13 1.08487
\(71\) 4.12553e13 0.538323 0.269161 0.963095i \(-0.413254\pi\)
0.269161 + 0.963095i \(0.413254\pi\)
\(72\) −9.22047e13 −1.08333
\(73\) 1.12820e14 1.19527 0.597635 0.801768i \(-0.296107\pi\)
0.597635 + 0.801768i \(0.296107\pi\)
\(74\) −1.91383e13 −0.183091
\(75\) 6.07156e12 0.0525220
\(76\) −8.16924e13 −0.639852
\(77\) 2.06957e14 1.46960
\(78\) 4.41395e12 0.0284523
\(79\) −2.27725e14 −1.33416 −0.667080 0.744986i \(-0.732456\pi\)
−0.667080 + 0.744986i \(0.732456\pi\)
\(80\) 1.30231e14 0.694285
\(81\) 2.03097e14 0.986427
\(82\) 6.76007e13 0.299466
\(83\) 8.49695e13 0.343698 0.171849 0.985123i \(-0.445026\pi\)
0.171849 + 0.985123i \(0.445026\pi\)
\(84\) −6.52426e12 −0.0241233
\(85\) 3.86007e13 0.130603
\(86\) 4.01914e14 1.24565
\(87\) −6.62970e12 −0.0188408
\(88\) 6.05988e14 1.58068
\(89\) 2.27743e13 0.0545783 0.0272892 0.999628i \(-0.491313\pi\)
0.0272892 + 0.999628i \(0.491313\pi\)
\(90\) −4.84326e14 −1.06738
\(91\) −2.62335e14 −0.532164
\(92\) −3.95172e13 −0.0738546
\(93\) −3.52498e13 −0.0607484
\(94\) −1.29305e14 −0.205663
\(95\) −1.64061e15 −2.41034
\(96\) −3.32106e13 −0.0451069
\(97\) −1.34059e15 −1.68464 −0.842319 0.538979i \(-0.818810\pi\)
−0.842319 + 0.538979i \(0.818810\pi\)
\(98\) −1.63704e13 −0.0190487
\(99\) −1.34092e15 −1.44590
\(100\) −2.76359e14 −0.276359
\(101\) 1.33589e15 1.23982 0.619912 0.784671i \(-0.287168\pi\)
0.619912 + 0.784671i \(0.287168\pi\)
\(102\) 6.14290e12 0.00529507
\(103\) 2.10271e15 1.68461 0.842306 0.538999i \(-0.181197\pi\)
0.842306 + 0.538999i \(0.181197\pi\)
\(104\) −7.68140e14 −0.572388
\(105\) −1.31025e14 −0.0908731
\(106\) 4.41069e14 0.284913
\(107\) −1.80074e15 −1.08411 −0.542054 0.840344i \(-0.682353\pi\)
−0.542054 + 0.840344i \(0.682353\pi\)
\(108\) 8.47369e13 0.0475767
\(109\) −2.37799e15 −1.24598 −0.622991 0.782229i \(-0.714083\pi\)
−0.622991 + 0.782229i \(0.714083\pi\)
\(110\) 3.18308e15 1.55741
\(111\) 3.35464e13 0.0153364
\(112\) −1.23174e15 −0.526483
\(113\) −3.29653e15 −1.31816 −0.659080 0.752073i \(-0.729054\pi\)
−0.659080 + 0.752073i \(0.729054\pi\)
\(114\) −2.61086e14 −0.0977232
\(115\) −7.93615e14 −0.278212
\(116\) 3.01764e14 0.0991362
\(117\) 1.69973e15 0.523583
\(118\) −5.04004e13 −0.0145653
\(119\) −3.65092e14 −0.0990375
\(120\) −3.83654e14 −0.0977418
\(121\) 4.63555e15 1.10971
\(122\) 2.46242e15 0.554196
\(123\) −1.18493e14 −0.0250845
\(124\) 1.60447e15 0.319645
\(125\) 1.56314e15 0.293206
\(126\) 4.58084e15 0.809405
\(127\) 1.03840e16 1.72917 0.864586 0.502485i \(-0.167581\pi\)
0.864586 + 0.502485i \(0.167581\pi\)
\(128\) −1.15167e15 −0.180823
\(129\) −7.04489e14 −0.104340
\(130\) −4.03482e15 −0.563962
\(131\) −1.22834e16 −1.62100 −0.810502 0.585735i \(-0.800806\pi\)
−0.810502 + 0.585735i \(0.800806\pi\)
\(132\) −2.77821e14 −0.0346307
\(133\) 1.55172e16 1.82779
\(134\) 4.75158e15 0.529118
\(135\) 1.70175e15 0.179223
\(136\) −1.06902e15 −0.106523
\(137\) 1.00516e16 0.948047 0.474024 0.880512i \(-0.342801\pi\)
0.474024 + 0.880512i \(0.342801\pi\)
\(138\) −1.26296e14 −0.0112796
\(139\) −1.28795e16 −1.08965 −0.544825 0.838550i \(-0.683404\pi\)
−0.544825 + 0.838550i \(0.683404\pi\)
\(140\) 5.96388e15 0.478155
\(141\) 2.26651e14 0.0172272
\(142\) −6.00145e15 −0.432607
\(143\) −1.11710e16 −0.763959
\(144\) 7.98075e15 0.517995
\(145\) 6.06026e15 0.373449
\(146\) −1.64121e16 −0.960544
\(147\) 2.86947e13 0.00159559
\(148\) −1.52693e15 −0.0806968
\(149\) −1.30886e16 −0.657651 −0.328826 0.944391i \(-0.606653\pi\)
−0.328826 + 0.944391i \(0.606653\pi\)
\(150\) −8.83235e14 −0.0422077
\(151\) −3.07794e16 −1.39937 −0.699686 0.714450i \(-0.746677\pi\)
−0.699686 + 0.714450i \(0.746677\pi\)
\(152\) 4.54357e16 1.96594
\(153\) 2.36552e15 0.0974407
\(154\) −3.01062e16 −1.18100
\(155\) 3.22222e16 1.20411
\(156\) 3.52162e14 0.0125403
\(157\) −3.69229e16 −1.25328 −0.626641 0.779308i \(-0.715571\pi\)
−0.626641 + 0.779308i \(0.715571\pi\)
\(158\) 3.31274e16 1.07216
\(159\) −7.73123e14 −0.0238655
\(160\) 3.03581e16 0.894077
\(161\) 7.50615e15 0.210971
\(162\) −2.95446e16 −0.792713
\(163\) −5.23541e15 −0.134135 −0.0670677 0.997748i \(-0.521364\pi\)
−0.0670677 + 0.997748i \(0.521364\pi\)
\(164\) 5.39345e15 0.131989
\(165\) −5.57943e15 −0.130455
\(166\) −1.23606e16 −0.276203
\(167\) −8.53288e14 −0.0182273 −0.00911364 0.999958i \(-0.502901\pi\)
−0.00911364 + 0.999958i \(0.502901\pi\)
\(168\) 3.62866e15 0.0741186
\(169\) −3.70258e16 −0.723359
\(170\) −5.61527e15 −0.104955
\(171\) −1.00540e17 −1.79832
\(172\) 3.20662e16 0.549016
\(173\) 4.95062e16 0.811546 0.405773 0.913974i \(-0.367002\pi\)
0.405773 + 0.913974i \(0.367002\pi\)
\(174\) 9.64428e14 0.0151409
\(175\) 5.24935e16 0.789441
\(176\) −5.24511e16 −0.755804
\(177\) 8.83438e13 0.00122005
\(178\) −3.31300e15 −0.0438603
\(179\) −1.22568e17 −1.55589 −0.777946 0.628331i \(-0.783738\pi\)
−0.777946 + 0.628331i \(0.783738\pi\)
\(180\) −3.86414e16 −0.470445
\(181\) −6.08764e16 −0.710984 −0.355492 0.934679i \(-0.615687\pi\)
−0.355492 + 0.934679i \(0.615687\pi\)
\(182\) 3.81621e16 0.427658
\(183\) −4.31622e15 −0.0464216
\(184\) 2.19787e16 0.226918
\(185\) −3.06650e16 −0.303987
\(186\) 5.12782e15 0.0488187
\(187\) −1.55466e16 −0.142175
\(188\) −1.03165e16 −0.0906456
\(189\) −1.60955e16 −0.135907
\(190\) 2.38661e17 1.93700
\(191\) 2.28398e17 1.78214 0.891072 0.453861i \(-0.149954\pi\)
0.891072 + 0.453861i \(0.149954\pi\)
\(192\) 9.49955e15 0.0712760
\(193\) −2.06335e17 −1.48899 −0.744497 0.667626i \(-0.767311\pi\)
−0.744497 + 0.667626i \(0.767311\pi\)
\(194\) 1.95016e17 1.35381
\(195\) 7.07239e15 0.0472397
\(196\) −1.30610e15 −0.00839567
\(197\) −8.71433e16 −0.539185 −0.269592 0.962975i \(-0.586889\pi\)
−0.269592 + 0.962975i \(0.586889\pi\)
\(198\) 1.95065e17 1.16196
\(199\) −2.12118e17 −1.21669 −0.608345 0.793673i \(-0.708166\pi\)
−0.608345 + 0.793673i \(0.708166\pi\)
\(200\) 1.53706e17 0.849111
\(201\) −8.32875e15 −0.0443210
\(202\) −1.94333e17 −0.996348
\(203\) −5.73190e16 −0.283190
\(204\) 4.90104e14 0.00233379
\(205\) 1.08316e17 0.497206
\(206\) −3.05883e17 −1.35379
\(207\) −4.86341e16 −0.207570
\(208\) 6.64861e16 0.273688
\(209\) 6.60765e17 2.62392
\(210\) 1.90604e16 0.0730275
\(211\) 4.65805e16 0.172221 0.0861105 0.996286i \(-0.472556\pi\)
0.0861105 + 0.996286i \(0.472556\pi\)
\(212\) 3.51902e16 0.125575
\(213\) 1.05196e16 0.0362369
\(214\) 2.61955e17 0.871212
\(215\) 6.43980e17 2.06816
\(216\) −4.71290e16 −0.146179
\(217\) −3.04763e17 −0.913091
\(218\) 3.45928e17 1.00130
\(219\) 2.87677e16 0.0804589
\(220\) 2.53959e17 0.686425
\(221\) 1.97067e16 0.0514838
\(222\) −4.88002e15 −0.0123246
\(223\) −6.90479e17 −1.68603 −0.843013 0.537894i \(-0.819220\pi\)
−0.843013 + 0.537894i \(0.819220\pi\)
\(224\) −2.87132e17 −0.677987
\(225\) −3.40118e17 −0.776712
\(226\) 4.79548e17 1.05930
\(227\) −3.86349e17 −0.825631 −0.412816 0.910815i \(-0.635455\pi\)
−0.412816 + 0.910815i \(0.635455\pi\)
\(228\) −2.08305e16 −0.0430713
\(229\) −6.43885e17 −1.28837 −0.644187 0.764868i \(-0.722804\pi\)
−0.644187 + 0.764868i \(0.722804\pi\)
\(230\) 1.15448e17 0.223577
\(231\) 5.27712e16 0.0989252
\(232\) −1.67835e17 −0.304595
\(233\) −7.96458e17 −1.39957 −0.699783 0.714355i \(-0.746720\pi\)
−0.699783 + 0.714355i \(0.746720\pi\)
\(234\) −2.47261e17 −0.420762
\(235\) −2.07183e17 −0.341464
\(236\) −4.02114e15 −0.00641962
\(237\) −5.80669e16 −0.0898083
\(238\) 5.31102e16 0.0795886
\(239\) 4.05410e17 0.588722 0.294361 0.955694i \(-0.404893\pi\)
0.294361 + 0.955694i \(0.404893\pi\)
\(240\) 3.32071e16 0.0467354
\(241\) −3.42909e16 −0.0467791 −0.0233895 0.999726i \(-0.507446\pi\)
−0.0233895 + 0.999726i \(0.507446\pi\)
\(242\) −6.74337e17 −0.891789
\(243\) 1.56548e17 0.200725
\(244\) 1.96461e17 0.244261
\(245\) −2.62301e16 −0.0316267
\(246\) 1.72373e16 0.0201584
\(247\) −8.37575e17 −0.950160
\(248\) −8.92373e17 −0.982107
\(249\) 2.16661e16 0.0231359
\(250\) −2.27391e17 −0.235626
\(251\) 1.21742e18 1.22430 0.612150 0.790742i \(-0.290305\pi\)
0.612150 + 0.790742i \(0.290305\pi\)
\(252\) 3.65477e17 0.356743
\(253\) 3.19633e17 0.302864
\(254\) −1.51057e18 −1.38960
\(255\) 9.84266e15 0.00879146
\(256\) −1.05324e18 −0.913539
\(257\) 9.87898e17 0.832174 0.416087 0.909325i \(-0.363401\pi\)
0.416087 + 0.909325i \(0.363401\pi\)
\(258\) 1.02483e17 0.0838499
\(259\) 2.90035e17 0.230516
\(260\) −3.21914e17 −0.248565
\(261\) 3.71383e17 0.278624
\(262\) 1.78688e18 1.30267
\(263\) 3.94844e16 0.0279742 0.0139871 0.999902i \(-0.495548\pi\)
0.0139871 + 0.999902i \(0.495548\pi\)
\(264\) 1.54519e17 0.106403
\(265\) 7.06718e17 0.473044
\(266\) −2.25730e18 −1.46885
\(267\) 5.80715e15 0.00367391
\(268\) 3.79100e17 0.233207
\(269\) −7.87854e17 −0.471306 −0.235653 0.971837i \(-0.575723\pi\)
−0.235653 + 0.971837i \(0.575723\pi\)
\(270\) −2.47556e17 −0.144027
\(271\) 2.78972e18 1.57867 0.789334 0.613964i \(-0.210426\pi\)
0.789334 + 0.613964i \(0.210426\pi\)
\(272\) 9.25289e16 0.0509343
\(273\) −6.68919e16 −0.0358223
\(274\) −1.46221e18 −0.761870
\(275\) 2.23532e18 1.13330
\(276\) −1.00764e16 −0.00497148
\(277\) 3.07769e18 1.47784 0.738918 0.673795i \(-0.235337\pi\)
0.738918 + 0.673795i \(0.235337\pi\)
\(278\) 1.87359e18 0.875665
\(279\) 1.97463e18 0.898368
\(280\) −3.31699e18 −1.46913
\(281\) 4.14344e18 1.78675 0.893375 0.449313i \(-0.148331\pi\)
0.893375 + 0.449313i \(0.148331\pi\)
\(282\) −3.29710e16 −0.0138441
\(283\) −1.46638e18 −0.599581 −0.299790 0.954005i \(-0.596917\pi\)
−0.299790 + 0.954005i \(0.596917\pi\)
\(284\) −4.78819e17 −0.190671
\(285\) −4.18334e17 −0.162251
\(286\) 1.62505e18 0.613933
\(287\) −1.02447e18 −0.377037
\(288\) 1.86040e18 0.667056
\(289\) −2.83500e18 −0.990419
\(290\) −8.81591e17 −0.300111
\(291\) −3.41832e17 −0.113400
\(292\) −1.30942e18 −0.423358
\(293\) 1.19799e18 0.377526 0.188763 0.982023i \(-0.439552\pi\)
0.188763 + 0.982023i \(0.439552\pi\)
\(294\) −4.17425e15 −0.00128225
\(295\) −8.07558e16 −0.0241829
\(296\) 8.49248e17 0.247940
\(297\) −6.85391e17 −0.195103
\(298\) 1.90401e18 0.528502
\(299\) −4.05162e17 −0.109672
\(300\) −7.04679e16 −0.0186030
\(301\) −6.09087e18 −1.56831
\(302\) 4.47751e18 1.12456
\(303\) 3.40634e17 0.0834581
\(304\) −3.93267e18 −0.940017
\(305\) 3.94549e18 0.920137
\(306\) −3.44114e17 −0.0783053
\(307\) −3.53107e18 −0.784094 −0.392047 0.919945i \(-0.628233\pi\)
−0.392047 + 0.919945i \(0.628233\pi\)
\(308\) −2.40199e18 −0.520523
\(309\) 5.36163e17 0.113399
\(310\) −4.68739e18 −0.967649
\(311\) −2.60736e18 −0.525410 −0.262705 0.964876i \(-0.584615\pi\)
−0.262705 + 0.964876i \(0.584615\pi\)
\(312\) −1.95865e17 −0.0385299
\(313\) −2.42498e18 −0.465722 −0.232861 0.972510i \(-0.574809\pi\)
−0.232861 + 0.972510i \(0.574809\pi\)
\(314\) 5.37121e18 1.00716
\(315\) 7.33980e18 1.34386
\(316\) 2.64303e18 0.472552
\(317\) 5.66141e18 0.988508 0.494254 0.869318i \(-0.335441\pi\)
0.494254 + 0.869318i \(0.335441\pi\)
\(318\) 1.12467e17 0.0191788
\(319\) −2.44080e18 −0.406540
\(320\) −8.68361e18 −1.41278
\(321\) −4.59165e17 −0.0729761
\(322\) −1.09193e18 −0.169541
\(323\) −1.16565e18 −0.176828
\(324\) −2.35719e18 −0.349387
\(325\) −2.83345e18 −0.410384
\(326\) 7.61599e17 0.107794
\(327\) −6.06356e17 −0.0838725
\(328\) −2.99973e18 −0.405535
\(329\) 1.95957e18 0.258936
\(330\) 8.11644e17 0.104836
\(331\) −7.23418e16 −0.00913438 −0.00456719 0.999990i \(-0.501454\pi\)
−0.00456719 + 0.999990i \(0.501454\pi\)
\(332\) −9.86175e17 −0.121736
\(333\) −1.87921e18 −0.226800
\(334\) 1.24128e17 0.0146478
\(335\) 7.61338e18 0.878499
\(336\) −3.14078e17 −0.0354399
\(337\) 9.42326e18 1.03987 0.519933 0.854207i \(-0.325957\pi\)
0.519933 + 0.854207i \(0.325957\pi\)
\(338\) 5.38617e18 0.581306
\(339\) −8.40570e17 −0.0887312
\(340\) −4.48008e17 −0.0462588
\(341\) −1.29777e19 −1.31081
\(342\) 1.46256e19 1.44516
\(343\) −1.02182e19 −0.987800
\(344\) −1.78346e19 −1.68685
\(345\) −2.02361e17 −0.0187277
\(346\) −7.20170e18 −0.652175
\(347\) −9.59185e18 −0.850024 −0.425012 0.905188i \(-0.639730\pi\)
−0.425012 + 0.905188i \(0.639730\pi\)
\(348\) 7.69458e16 0.00667330
\(349\) 6.56731e18 0.557438 0.278719 0.960373i \(-0.410090\pi\)
0.278719 + 0.960373i \(0.410090\pi\)
\(350\) −7.63627e18 −0.634411
\(351\) 8.68790e17 0.0706499
\(352\) −1.22269e19 −0.973299
\(353\) −8.79452e18 −0.685334 −0.342667 0.939457i \(-0.611330\pi\)
−0.342667 + 0.939457i \(0.611330\pi\)
\(354\) −1.28514e16 −0.000980455 0
\(355\) −9.61602e18 −0.718262
\(356\) −2.64324e17 −0.0193313
\(357\) −9.30936e16 −0.00666666
\(358\) 1.78301e19 1.25035
\(359\) 1.67070e19 1.14733 0.573667 0.819089i \(-0.305520\pi\)
0.573667 + 0.819089i \(0.305520\pi\)
\(360\) 2.14916e19 1.44544
\(361\) 3.43617e19 2.26345
\(362\) 8.85575e18 0.571361
\(363\) 1.18200e18 0.0746998
\(364\) 3.04472e18 0.188489
\(365\) −2.62968e19 −1.59480
\(366\) 6.27884e17 0.0373054
\(367\) −5.31239e18 −0.309239 −0.154620 0.987974i \(-0.549415\pi\)
−0.154620 + 0.987974i \(0.549415\pi\)
\(368\) −1.90236e18 −0.108501
\(369\) 6.63777e18 0.370958
\(370\) 4.46087e18 0.244290
\(371\) −6.68426e18 −0.358714
\(372\) 4.09118e17 0.0215167
\(373\) 2.34477e19 1.20860 0.604302 0.796756i \(-0.293452\pi\)
0.604302 + 0.796756i \(0.293452\pi\)
\(374\) 2.26158e18 0.114255
\(375\) 3.98580e17 0.0197370
\(376\) 5.73781e18 0.278508
\(377\) 3.09392e18 0.147214
\(378\) 2.34142e18 0.109217
\(379\) −1.60533e19 −0.734125 −0.367063 0.930196i \(-0.619637\pi\)
−0.367063 + 0.930196i \(0.619637\pi\)
\(380\) 1.90413e19 0.853729
\(381\) 2.64779e18 0.116398
\(382\) −3.32253e19 −1.43217
\(383\) −4.40510e19 −1.86194 −0.930969 0.365099i \(-0.881035\pi\)
−0.930969 + 0.365099i \(0.881035\pi\)
\(384\) −2.93661e17 −0.0121720
\(385\) −4.82386e19 −1.96083
\(386\) 3.00157e19 1.19659
\(387\) 3.94642e19 1.54302
\(388\) 1.55591e19 0.596689
\(389\) 3.79555e19 1.42775 0.713876 0.700273i \(-0.246938\pi\)
0.713876 + 0.700273i \(0.246938\pi\)
\(390\) −1.02883e18 −0.0379628
\(391\) −5.63864e17 −0.0204103
\(392\) 7.26426e17 0.0257956
\(393\) −3.13211e18 −0.109117
\(394\) 1.26768e19 0.433300
\(395\) 5.30795e19 1.78012
\(396\) 1.55630e19 0.512131
\(397\) −1.75731e19 −0.567439 −0.283719 0.958907i \(-0.591568\pi\)
−0.283719 + 0.958907i \(0.591568\pi\)
\(398\) 3.08570e19 0.977757
\(399\) 3.95667e18 0.123036
\(400\) −1.33039e19 −0.406004
\(401\) −1.14532e19 −0.343040 −0.171520 0.985181i \(-0.554868\pi\)
−0.171520 + 0.985181i \(0.554868\pi\)
\(402\) 1.21159e18 0.0356172
\(403\) 1.64503e19 0.474663
\(404\) −1.55046e19 −0.439138
\(405\) −4.73389e19 −1.31615
\(406\) 8.33824e18 0.227577
\(407\) 1.23505e19 0.330923
\(408\) −2.72586e17 −0.00717056
\(409\) −3.70597e19 −0.957143 −0.478572 0.878049i \(-0.658845\pi\)
−0.478572 + 0.878049i \(0.658845\pi\)
\(410\) −1.57568e19 −0.399565
\(411\) 2.56302e18 0.0638173
\(412\) −2.44045e19 −0.596680
\(413\) 7.63802e17 0.0183381
\(414\) 7.07485e18 0.166807
\(415\) −1.98052e19 −0.458583
\(416\) 1.54986e19 0.352446
\(417\) −3.28410e18 −0.0733492
\(418\) −9.61221e19 −2.10863
\(419\) 8.68391e19 1.87116 0.935578 0.353120i \(-0.114879\pi\)
0.935578 + 0.353120i \(0.114879\pi\)
\(420\) 1.52071e18 0.0321867
\(421\) −3.76050e18 −0.0781861 −0.0390931 0.999236i \(-0.512447\pi\)
−0.0390931 + 0.999236i \(0.512447\pi\)
\(422\) −6.77611e18 −0.138400
\(423\) −1.26965e19 −0.254761
\(424\) −1.95721e19 −0.385828
\(425\) −3.94332e18 −0.0763740
\(426\) −1.53029e18 −0.0291207
\(427\) −3.73171e19 −0.697749
\(428\) 2.08998e19 0.383985
\(429\) −2.84845e18 −0.0514255
\(430\) −9.36803e19 −1.66201
\(431\) −1.04399e20 −1.82019 −0.910095 0.414400i \(-0.863992\pi\)
−0.910095 + 0.414400i \(0.863992\pi\)
\(432\) 4.07924e18 0.0698958
\(433\) −1.06713e20 −1.79705 −0.898525 0.438923i \(-0.855360\pi\)
−0.898525 + 0.438923i \(0.855360\pi\)
\(434\) 4.43341e19 0.733778
\(435\) 1.54529e18 0.0251385
\(436\) 2.75995e19 0.441319
\(437\) 2.39654e19 0.376682
\(438\) −4.18486e18 −0.0646584
\(439\) −2.63377e19 −0.400031 −0.200016 0.979793i \(-0.564099\pi\)
−0.200016 + 0.979793i \(0.564099\pi\)
\(440\) −1.41247e20 −2.10904
\(441\) −1.60743e18 −0.0235962
\(442\) −2.86674e18 −0.0413735
\(443\) 1.05962e20 1.50357 0.751785 0.659408i \(-0.229193\pi\)
0.751785 + 0.659408i \(0.229193\pi\)
\(444\) −3.89347e17 −0.00543206
\(445\) −5.30836e18 −0.0728217
\(446\) 1.00445e20 1.35492
\(447\) −3.33742e18 −0.0442694
\(448\) 8.21311e19 1.07133
\(449\) −4.12026e18 −0.0528539 −0.0264269 0.999651i \(-0.508413\pi\)
−0.0264269 + 0.999651i \(0.508413\pi\)
\(450\) 4.94772e19 0.624182
\(451\) −4.36247e19 −0.541263
\(452\) 3.82602e19 0.466884
\(453\) −7.84835e18 −0.0941980
\(454\) 5.62026e19 0.663494
\(455\) 6.11464e19 0.710045
\(456\) 1.15855e19 0.132336
\(457\) 1.76790e19 0.198649 0.0993246 0.995055i \(-0.468332\pi\)
0.0993246 + 0.995055i \(0.468332\pi\)
\(458\) 9.36664e19 1.03536
\(459\) 1.20910e18 0.0131482
\(460\) 9.21088e18 0.0985411
\(461\) 3.96193e19 0.417013 0.208507 0.978021i \(-0.433140\pi\)
0.208507 + 0.978021i \(0.433140\pi\)
\(462\) −7.67667e18 −0.0794983
\(463\) −1.46144e20 −1.48910 −0.744551 0.667566i \(-0.767336\pi\)
−0.744551 + 0.667566i \(0.767336\pi\)
\(464\) 1.45269e19 0.145643
\(465\) 8.21623e18 0.0810541
\(466\) 1.15861e20 1.12472
\(467\) 1.89194e20 1.80730 0.903651 0.428269i \(-0.140877\pi\)
0.903651 + 0.428269i \(0.140877\pi\)
\(468\) −1.97275e19 −0.185450
\(469\) −7.20086e19 −0.666175
\(470\) 3.01391e19 0.274408
\(471\) −9.41486e18 −0.0843640
\(472\) 2.23648e18 0.0197242
\(473\) −2.59366e20 −2.25141
\(474\) 8.44705e18 0.0721718
\(475\) 1.67600e20 1.40952
\(476\) 4.23734e18 0.0350785
\(477\) 4.33089e19 0.352931
\(478\) −5.89754e19 −0.473109
\(479\) −1.42619e20 −1.12632 −0.563158 0.826349i \(-0.690414\pi\)
−0.563158 + 0.826349i \(0.690414\pi\)
\(480\) 7.74092e18 0.0601843
\(481\) −1.56553e19 −0.119832
\(482\) 4.98833e18 0.0375926
\(483\) 1.91397e18 0.0142014
\(484\) −5.38013e19 −0.393054
\(485\) 3.12471e20 2.24774
\(486\) −2.27732e19 −0.161306
\(487\) −4.00797e19 −0.279548 −0.139774 0.990183i \(-0.544638\pi\)
−0.139774 + 0.990183i \(0.544638\pi\)
\(488\) −1.09268e20 −0.750489
\(489\) −1.33496e18 −0.00902925
\(490\) 3.81571e18 0.0254159
\(491\) 9.80799e19 0.643382 0.321691 0.946845i \(-0.395749\pi\)
0.321691 + 0.946845i \(0.395749\pi\)
\(492\) 1.37526e18 0.00888477
\(493\) 4.30582e18 0.0273971
\(494\) 1.21843e20 0.763568
\(495\) 3.12549e20 1.92921
\(496\) 7.72391e19 0.469596
\(497\) 9.09500e19 0.544665
\(498\) −3.15178e18 −0.0185924
\(499\) 1.53727e20 0.893297 0.446648 0.894710i \(-0.352618\pi\)
0.446648 + 0.894710i \(0.352618\pi\)
\(500\) −1.81422e19 −0.103852
\(501\) −2.17577e17 −0.00122696
\(502\) −1.77099e20 −0.983873
\(503\) −8.89831e19 −0.487021 −0.243510 0.969898i \(-0.578299\pi\)
−0.243510 + 0.969898i \(0.578299\pi\)
\(504\) −2.03271e20 −1.09609
\(505\) −3.11376e20 −1.65425
\(506\) −4.64973e19 −0.243388
\(507\) −9.44108e18 −0.0486925
\(508\) −1.20519e20 −0.612462
\(509\) −8.52937e19 −0.427104 −0.213552 0.976932i \(-0.568503\pi\)
−0.213552 + 0.976932i \(0.568503\pi\)
\(510\) −1.43182e18 −0.00706500
\(511\) 2.48720e20 1.20935
\(512\) 1.90954e20 0.914962
\(513\) −5.13892e19 −0.242656
\(514\) −1.43710e20 −0.668752
\(515\) −4.90111e20 −2.24771
\(516\) 8.17647e18 0.0369567
\(517\) 8.34442e19 0.371721
\(518\) −4.21916e19 −0.185248
\(519\) 1.26234e19 0.0546288
\(520\) 1.79042e20 0.763713
\(521\) −1.91291e20 −0.804287 −0.402143 0.915577i \(-0.631735\pi\)
−0.402143 + 0.915577i \(0.631735\pi\)
\(522\) −5.40255e19 −0.223908
\(523\) −3.26310e20 −1.33312 −0.666558 0.745453i \(-0.732233\pi\)
−0.666558 + 0.745453i \(0.732233\pi\)
\(524\) 1.42564e20 0.574150
\(525\) 1.33851e19 0.0531408
\(526\) −5.74383e18 −0.0224806
\(527\) 2.28939e19 0.0883364
\(528\) −1.33743e19 −0.0508765
\(529\) 1.15928e19 0.0434783
\(530\) −1.02807e20 −0.380148
\(531\) −4.94886e18 −0.0180425
\(532\) −1.80096e20 −0.647391
\(533\) 5.52979e19 0.195999
\(534\) −8.44771e17 −0.00295243
\(535\) 4.19726e20 1.44648
\(536\) −2.10848e20 −0.716528
\(537\) −3.12532e19 −0.104734
\(538\) 1.14610e20 0.378752
\(539\) 1.05643e19 0.0344291
\(540\) −1.97509e19 −0.0634797
\(541\) 3.49946e20 1.10923 0.554615 0.832107i \(-0.312866\pi\)
0.554615 + 0.832107i \(0.312866\pi\)
\(542\) −4.05823e20 −1.26865
\(543\) −1.55227e19 −0.0478595
\(544\) 2.15695e19 0.0655915
\(545\) 5.54275e20 1.66246
\(546\) 9.73082e18 0.0287875
\(547\) 7.11736e19 0.207689 0.103845 0.994594i \(-0.466886\pi\)
0.103845 + 0.994594i \(0.466886\pi\)
\(548\) −1.16661e20 −0.335793
\(549\) 2.41787e20 0.686499
\(550\) −3.25174e20 −0.910742
\(551\) −1.83006e20 −0.505626
\(552\) 5.60427e18 0.0152748
\(553\) −5.02035e20 −1.34988
\(554\) −4.47714e20 −1.18762
\(555\) −7.81917e18 −0.0204627
\(556\) 1.49482e20 0.385948
\(557\) 4.00940e20 1.02133 0.510664 0.859780i \(-0.329400\pi\)
0.510664 + 0.859780i \(0.329400\pi\)
\(558\) −2.87251e20 −0.721947
\(559\) 3.28769e20 0.815270
\(560\) 2.87101e20 0.702465
\(561\) −3.96419e18 −0.00957046
\(562\) −6.02750e20 −1.43587
\(563\) −5.48584e20 −1.28953 −0.644763 0.764383i \(-0.723044\pi\)
−0.644763 + 0.764383i \(0.723044\pi\)
\(564\) −2.63056e18 −0.00610175
\(565\) 7.68372e20 1.75877
\(566\) 2.13315e20 0.481836
\(567\) 4.47739e20 0.998049
\(568\) 2.66310e20 0.585834
\(569\) −6.89130e20 −1.49609 −0.748047 0.663645i \(-0.769008\pi\)
−0.748047 + 0.663645i \(0.769008\pi\)
\(570\) 6.08554e19 0.130388
\(571\) 6.10610e20 1.29120 0.645599 0.763676i \(-0.276608\pi\)
0.645599 + 0.763676i \(0.276608\pi\)
\(572\) 1.29653e20 0.270590
\(573\) 5.82386e19 0.119964
\(574\) 1.49030e20 0.302994
\(575\) 8.10732e19 0.162693
\(576\) −5.32147e20 −1.05405
\(577\) −4.96230e20 −0.970206 −0.485103 0.874457i \(-0.661218\pi\)
−0.485103 + 0.874457i \(0.661218\pi\)
\(578\) 4.12409e20 0.795921
\(579\) −5.26127e19 −0.100231
\(580\) −7.03368e19 −0.132273
\(581\) 1.87321e20 0.347748
\(582\) 4.97265e19 0.0911309
\(583\) −2.84635e20 −0.514960
\(584\) 7.28273e20 1.30076
\(585\) −3.96182e20 −0.698596
\(586\) −1.74273e20 −0.303388
\(587\) −1.19460e20 −0.205322 −0.102661 0.994716i \(-0.532736\pi\)
−0.102661 + 0.994716i \(0.532736\pi\)
\(588\) −3.33038e17 −0.000565150 0
\(589\) −9.73038e20 −1.63029
\(590\) 1.17476e19 0.0194339
\(591\) −2.22204e19 −0.0362949
\(592\) −7.35064e19 −0.118553
\(593\) 3.03034e20 0.482593 0.241297 0.970451i \(-0.422427\pi\)
0.241297 + 0.970451i \(0.422427\pi\)
\(594\) 9.97044e19 0.156789
\(595\) 8.50976e19 0.132142
\(596\) 1.51909e20 0.232936
\(597\) −5.40873e19 −0.0819008
\(598\) 5.89392e19 0.0881344
\(599\) 4.74013e20 0.699986 0.349993 0.936752i \(-0.386184\pi\)
0.349993 + 0.936752i \(0.386184\pi\)
\(600\) 3.91929e19 0.0571574
\(601\) 9.70281e20 1.39746 0.698729 0.715386i \(-0.253749\pi\)
0.698729 + 0.715386i \(0.253749\pi\)
\(602\) 8.86044e20 1.26032
\(603\) 4.66561e20 0.655434
\(604\) 3.57233e20 0.495650
\(605\) −1.08048e21 −1.48065
\(606\) −4.95523e19 −0.0670686
\(607\) 7.84690e20 1.04902 0.524509 0.851405i \(-0.324249\pi\)
0.524509 + 0.851405i \(0.324249\pi\)
\(608\) −9.16747e20 −1.21052
\(609\) −1.46156e19 −0.0190628
\(610\) −5.73954e20 −0.739441
\(611\) −1.05772e20 −0.134606
\(612\) −2.74547e19 −0.0345129
\(613\) 1.18575e21 1.47244 0.736222 0.676740i \(-0.236608\pi\)
0.736222 + 0.676740i \(0.236608\pi\)
\(614\) 5.13667e20 0.630114
\(615\) 2.76190e19 0.0334692
\(616\) 1.33594e21 1.59930
\(617\) −7.47579e20 −0.884134 −0.442067 0.896982i \(-0.645755\pi\)
−0.442067 + 0.896982i \(0.645755\pi\)
\(618\) −7.79961e19 −0.0911296
\(619\) 6.53384e20 0.754204 0.377102 0.926172i \(-0.376921\pi\)
0.377102 + 0.926172i \(0.376921\pi\)
\(620\) −3.73978e20 −0.426489
\(621\) −2.48586e19 −0.0280085
\(622\) 3.79295e20 0.422230
\(623\) 5.02074e19 0.0552214
\(624\) 1.69531e19 0.0184232
\(625\) −1.09101e21 −1.17146
\(626\) 3.52765e20 0.374263
\(627\) 1.68486e20 0.176627
\(628\) 4.28536e20 0.443905
\(629\) −2.17875e19 −0.0223012
\(630\) −1.06773e21 −1.07996
\(631\) 1.54960e21 1.54882 0.774408 0.632686i \(-0.218048\pi\)
0.774408 + 0.632686i \(0.218048\pi\)
\(632\) −1.47000e21 −1.45191
\(633\) 1.18774e19 0.0115930
\(634\) −8.23570e20 −0.794385
\(635\) −2.42037e21 −2.30716
\(636\) 8.97304e18 0.00845301
\(637\) −1.33912e19 −0.0124673
\(638\) 3.55066e20 0.326704
\(639\) −5.89287e20 −0.535883
\(640\) 2.68438e20 0.241265
\(641\) −1.46173e21 −1.29847 −0.649235 0.760588i \(-0.724911\pi\)
−0.649235 + 0.760588i \(0.724911\pi\)
\(642\) 6.67951e19 0.0586451
\(643\) 2.22399e20 0.192997 0.0964986 0.995333i \(-0.469236\pi\)
0.0964986 + 0.995333i \(0.469236\pi\)
\(644\) −8.71181e19 −0.0747248
\(645\) 1.64206e20 0.139217
\(646\) 1.69569e20 0.142103
\(647\) 3.95771e20 0.327840 0.163920 0.986474i \(-0.447586\pi\)
0.163920 + 0.986474i \(0.447586\pi\)
\(648\) 1.31102e21 1.07349
\(649\) 3.25248e19 0.0263257
\(650\) 4.12185e20 0.329793
\(651\) −7.77105e19 −0.0614642
\(652\) 6.07633e19 0.0475100
\(653\) −1.35609e21 −1.04819 −0.524096 0.851659i \(-0.675597\pi\)
−0.524096 + 0.851659i \(0.675597\pi\)
\(654\) 8.82072e19 0.0674017
\(655\) 2.86309e21 2.16284
\(656\) 2.59641e20 0.193907
\(657\) −1.61151e21 −1.18985
\(658\) −2.85061e20 −0.208086
\(659\) 1.52648e21 1.10167 0.550834 0.834615i \(-0.314310\pi\)
0.550834 + 0.834615i \(0.314310\pi\)
\(660\) 6.47562e19 0.0462063
\(661\) −2.55018e21 −1.79912 −0.899558 0.436802i \(-0.856111\pi\)
−0.899558 + 0.436802i \(0.856111\pi\)
\(662\) 1.05236e19 0.00734058
\(663\) 5.02494e18 0.00346561
\(664\) 5.48491e20 0.374032
\(665\) −3.61683e21 −2.43874
\(666\) 2.73370e20 0.182261
\(667\) −8.85260e19 −0.0583616
\(668\) 9.90345e18 0.00645599
\(669\) −1.76063e20 −0.113494
\(670\) −1.10752e21 −0.705980
\(671\) −1.58907e21 −1.00167
\(672\) −7.32149e19 −0.0456383
\(673\) −1.57816e20 −0.0972832 −0.0486416 0.998816i \(-0.515489\pi\)
−0.0486416 + 0.998816i \(0.515489\pi\)
\(674\) −1.37081e21 −0.835657
\(675\) −1.73846e20 −0.104806
\(676\) 4.29730e20 0.256209
\(677\) 6.80625e20 0.401322 0.200661 0.979661i \(-0.435691\pi\)
0.200661 + 0.979661i \(0.435691\pi\)
\(678\) 1.22278e20 0.0713062
\(679\) −2.95541e21 −1.70449
\(680\) 2.49173e20 0.142130
\(681\) −9.85140e19 −0.0555769
\(682\) 1.88787e21 1.05339
\(683\) −1.57669e20 −0.0870145 −0.0435073 0.999053i \(-0.513853\pi\)
−0.0435073 + 0.999053i \(0.513853\pi\)
\(684\) 1.16688e21 0.636953
\(685\) −2.34288e21 −1.26494
\(686\) 1.48645e21 0.793816
\(687\) −1.64182e20 −0.0867262
\(688\) 1.54367e21 0.806568
\(689\) 3.60798e20 0.186475
\(690\) 2.94377e19 0.0150500
\(691\) 5.50128e20 0.278214 0.139107 0.990277i \(-0.455577\pi\)
0.139107 + 0.990277i \(0.455577\pi\)
\(692\) −5.74580e20 −0.287445
\(693\) −2.95615e21 −1.46294
\(694\) 1.39533e21 0.683097
\(695\) 3.00202e21 1.45388
\(696\) −4.27957e19 −0.0205037
\(697\) 7.69582e19 0.0364762
\(698\) −9.55351e20 −0.447969
\(699\) −2.03086e20 −0.0942110
\(700\) −6.09251e20 −0.279615
\(701\) 2.68019e21 1.21697 0.608487 0.793564i \(-0.291777\pi\)
0.608487 + 0.793564i \(0.291777\pi\)
\(702\) −1.26384e20 −0.0567757
\(703\) 9.26015e20 0.411579
\(704\) 3.49737e21 1.53797
\(705\) −5.28290e19 −0.0229855
\(706\) 1.27935e21 0.550748
\(707\) 2.94505e21 1.25443
\(708\) −1.02534e18 −0.000432133 0
\(709\) −2.48670e21 −1.03700 −0.518498 0.855079i \(-0.673509\pi\)
−0.518498 + 0.855079i \(0.673509\pi\)
\(710\) 1.39885e21 0.577210
\(711\) 3.25280e21 1.32811
\(712\) 1.47012e20 0.0593953
\(713\) −4.70689e20 −0.188175
\(714\) 1.35424e19 0.00535746
\(715\) 2.60379e21 1.01932
\(716\) 1.42255e21 0.551088
\(717\) 1.03374e20 0.0396295
\(718\) −2.43038e21 −0.922021
\(719\) 2.06378e21 0.774811 0.387406 0.921909i \(-0.373371\pi\)
0.387406 + 0.921909i \(0.373371\pi\)
\(720\) −1.86020e21 −0.691139
\(721\) 4.63555e21 1.70446
\(722\) −4.99862e21 −1.81895
\(723\) −8.74374e18 −0.00314891
\(724\) 7.06546e20 0.251826
\(725\) −6.19097e20 −0.218385
\(726\) −1.71947e20 −0.0600303
\(727\) 2.34336e21 0.809714 0.404857 0.914380i \(-0.367321\pi\)
0.404857 + 0.914380i \(0.367321\pi\)
\(728\) −1.69341e21 −0.579132
\(729\) −2.87430e21 −0.972915
\(730\) 3.82542e21 1.28161
\(731\) 4.57548e20 0.151725
\(732\) 5.00950e19 0.0164423
\(733\) 3.54047e21 1.15022 0.575111 0.818076i \(-0.304959\pi\)
0.575111 + 0.818076i \(0.304959\pi\)
\(734\) 7.72798e20 0.248511
\(735\) −6.68833e18 −0.00212894
\(736\) −4.43460e20 −0.139724
\(737\) −3.06633e21 −0.956341
\(738\) −9.65601e20 −0.298109
\(739\) −2.35180e21 −0.718733 −0.359366 0.933197i \(-0.617007\pi\)
−0.359366 + 0.933197i \(0.617007\pi\)
\(740\) 3.55905e20 0.107670
\(741\) −2.13571e20 −0.0639595
\(742\) 9.72365e20 0.288270
\(743\) −4.10274e21 −1.20409 −0.602044 0.798463i \(-0.705647\pi\)
−0.602044 + 0.798463i \(0.705647\pi\)
\(744\) −2.27543e20 −0.0661100
\(745\) 3.05076e21 0.877477
\(746\) −3.41096e21 −0.971258
\(747\) −1.21369e21 −0.342141
\(748\) 1.80438e20 0.0503577
\(749\) −3.96984e21 −1.09688
\(750\) −5.79818e19 −0.0158611
\(751\) −1.93322e21 −0.523579 −0.261790 0.965125i \(-0.584313\pi\)
−0.261790 + 0.965125i \(0.584313\pi\)
\(752\) −4.96634e20 −0.133169
\(753\) 3.10426e20 0.0824131
\(754\) −4.50076e20 −0.118304
\(755\) 7.17424e21 1.86713
\(756\) 1.86808e20 0.0481373
\(757\) 6.12942e21 1.56387 0.781935 0.623360i \(-0.214233\pi\)
0.781935 + 0.623360i \(0.214233\pi\)
\(758\) 2.33529e21 0.589958
\(759\) 8.15022e19 0.0203871
\(760\) −1.05904e22 −2.62307
\(761\) 8.03720e21 1.97115 0.985575 0.169238i \(-0.0541306\pi\)
0.985575 + 0.169238i \(0.0541306\pi\)
\(762\) −3.85176e20 −0.0935400
\(763\) −5.24243e21 −1.26066
\(764\) −2.65085e21 −0.631225
\(765\) −5.51368e20 −0.130011
\(766\) 6.40814e21 1.49629
\(767\) −4.12279e19 −0.00953293
\(768\) −2.68562e20 −0.0614944
\(769\) −3.38739e21 −0.768100 −0.384050 0.923312i \(-0.625471\pi\)
−0.384050 + 0.923312i \(0.625471\pi\)
\(770\) 7.01731e21 1.57576
\(771\) 2.51901e20 0.0560173
\(772\) 2.39477e21 0.527393
\(773\) −4.69410e21 −1.02378 −0.511889 0.859051i \(-0.671054\pi\)
−0.511889 + 0.859051i \(0.671054\pi\)
\(774\) −5.74089e21 −1.24000
\(775\) −3.29171e21 −0.704141
\(776\) −8.65369e21 −1.83332
\(777\) 7.39551e19 0.0155171
\(778\) −5.52142e21 −1.14737
\(779\) −3.27089e21 −0.673186
\(780\) −8.20838e19 −0.0167320
\(781\) 3.87291e21 0.781906
\(782\) 8.20258e19 0.0164021
\(783\) 1.89827e20 0.0375962
\(784\) −6.28756e19 −0.0123342
\(785\) 8.60620e21 1.67220
\(786\) 4.55630e20 0.0876887
\(787\) −5.09190e21 −0.970665 −0.485332 0.874330i \(-0.661301\pi\)
−0.485332 + 0.874330i \(0.661301\pi\)
\(788\) 1.01141e21 0.190976
\(789\) 1.00680e19 0.00188307
\(790\) −7.72151e21 −1.43054
\(791\) −7.26740e21 −1.33369
\(792\) −8.65586e21 −1.57352
\(793\) 2.01428e21 0.362719
\(794\) 2.55637e21 0.456005
\(795\) 1.80204e20 0.0318427
\(796\) 2.46189e21 0.430944
\(797\) −1.04193e21 −0.180676 −0.0903380 0.995911i \(-0.528795\pi\)
−0.0903380 + 0.995911i \(0.528795\pi\)
\(798\) −5.75581e20 −0.0988746
\(799\) −1.47204e20 −0.0250506
\(800\) −3.10129e21 −0.522838
\(801\) −3.25306e20 −0.0543310
\(802\) 1.66611e21 0.275674
\(803\) 1.05912e22 1.73611
\(804\) 9.66654e19 0.0156982
\(805\) −1.74957e21 −0.281490
\(806\) −2.39303e21 −0.381449
\(807\) −2.00892e20 −0.0317257
\(808\) 8.62337e21 1.34925
\(809\) 4.47787e21 0.694157 0.347079 0.937836i \(-0.387174\pi\)
0.347079 + 0.937836i \(0.387174\pi\)
\(810\) 6.88642e21 1.05768
\(811\) 7.25868e21 1.10459 0.552295 0.833649i \(-0.313752\pi\)
0.552295 + 0.833649i \(0.313752\pi\)
\(812\) 6.65257e20 0.100304
\(813\) 7.11341e20 0.106267
\(814\) −1.79664e21 −0.265936
\(815\) 1.22030e21 0.178971
\(816\) 2.35936e19 0.00342861
\(817\) −1.94468e22 −2.80015
\(818\) 5.39110e21 0.769180
\(819\) 3.74716e21 0.529752
\(820\) −1.25714e21 −0.176108
\(821\) −7.54628e21 −1.04751 −0.523756 0.851868i \(-0.675470\pi\)
−0.523756 + 0.851868i \(0.675470\pi\)
\(822\) −3.72844e20 −0.0512849
\(823\) 3.66981e21 0.500201 0.250101 0.968220i \(-0.419536\pi\)
0.250101 + 0.968220i \(0.419536\pi\)
\(824\) 1.35733e22 1.83329
\(825\) 5.69977e20 0.0762874
\(826\) −1.11111e20 −0.0147369
\(827\) 8.69685e20 0.114306 0.0571532 0.998365i \(-0.481798\pi\)
0.0571532 + 0.998365i \(0.481798\pi\)
\(828\) 5.64459e20 0.0735199
\(829\) 3.01196e20 0.0388768 0.0194384 0.999811i \(-0.493812\pi\)
0.0194384 + 0.999811i \(0.493812\pi\)
\(830\) 2.88107e21 0.368526
\(831\) 7.84770e20 0.0994797
\(832\) −4.43321e21 −0.556921
\(833\) −1.86365e19 −0.00232021
\(834\) 4.77740e20 0.0589449
\(835\) 1.98889e20 0.0243199
\(836\) −7.66899e21 −0.929376
\(837\) 1.00930e21 0.121222
\(838\) −1.26326e22 −1.50370
\(839\) 1.09299e22 1.28945 0.644723 0.764416i \(-0.276973\pi\)
0.644723 + 0.764416i \(0.276973\pi\)
\(840\) −8.45789e20 −0.0988934
\(841\) −7.95318e21 −0.921660
\(842\) 5.47043e20 0.0628320
\(843\) 1.05652e21 0.120274
\(844\) −5.40624e20 −0.0609996
\(845\) 8.63017e21 0.965149
\(846\) 1.84698e21 0.204731
\(847\) 1.02194e22 1.12279
\(848\) 1.69406e21 0.184484
\(849\) −3.73907e20 −0.0403605
\(850\) 5.73639e20 0.0613757
\(851\) 4.47943e20 0.0475063
\(852\) −1.22093e20 −0.0128349
\(853\) −3.43543e21 −0.357984 −0.178992 0.983851i \(-0.557284\pi\)
−0.178992 + 0.983851i \(0.557284\pi\)
\(854\) 5.42856e21 0.560725
\(855\) 2.34343e22 2.39942
\(856\) −1.16241e22 −1.17979
\(857\) −1.39531e22 −1.40383 −0.701913 0.712263i \(-0.747670\pi\)
−0.701913 + 0.712263i \(0.747670\pi\)
\(858\) 4.14366e20 0.0413266
\(859\) 4.49229e21 0.444139 0.222069 0.975031i \(-0.428719\pi\)
0.222069 + 0.975031i \(0.428719\pi\)
\(860\) −7.47418e21 −0.732529
\(861\) −2.61225e20 −0.0253800
\(862\) 1.51870e22 1.46274
\(863\) −1.06612e22 −1.01795 −0.508975 0.860781i \(-0.669976\pi\)
−0.508975 + 0.860781i \(0.669976\pi\)
\(864\) 9.50913e20 0.0900094
\(865\) −1.15392e22 −1.08281
\(866\) 1.55237e22 1.44415
\(867\) −7.22887e20 −0.0666695
\(868\) 3.53715e21 0.323411
\(869\) −2.13781e22 −1.93785
\(870\) −2.24794e20 −0.0202018
\(871\) 3.88683e21 0.346305
\(872\) −1.53503e22 −1.35595
\(873\) 1.91488e22 1.67700
\(874\) −3.48627e21 −0.302709
\(875\) 3.44604e21 0.296661
\(876\) −3.33885e20 −0.0284981
\(877\) −2.71530e21 −0.229785 −0.114892 0.993378i \(-0.536652\pi\)
−0.114892 + 0.993378i \(0.536652\pi\)
\(878\) 3.83137e21 0.321473
\(879\) 3.05473e20 0.0254130
\(880\) 1.22256e22 1.00844
\(881\) −1.49011e22 −1.21871 −0.609355 0.792898i \(-0.708572\pi\)
−0.609355 + 0.792898i \(0.708572\pi\)
\(882\) 2.33834e20 0.0189624
\(883\) −5.10279e21 −0.410301 −0.205150 0.978730i \(-0.565768\pi\)
−0.205150 + 0.978730i \(0.565768\pi\)
\(884\) −2.28720e20 −0.0182353
\(885\) −2.05917e19 −0.00162786
\(886\) −1.54144e22 −1.20830
\(887\) −1.22436e22 −0.951658 −0.475829 0.879538i \(-0.657852\pi\)
−0.475829 + 0.879538i \(0.657852\pi\)
\(888\) 2.16547e20 0.0166900
\(889\) 2.28922e22 1.74955
\(890\) 7.72212e20 0.0585210
\(891\) 1.90660e22 1.43277
\(892\) 8.01386e21 0.597180
\(893\) 6.25647e21 0.462321
\(894\) 4.85497e20 0.0355758
\(895\) 2.85688e22 2.07596
\(896\) −2.53893e21 −0.182954
\(897\) −1.03311e20 −0.00738248
\(898\) 5.99377e20 0.0424744
\(899\) 3.59431e21 0.252591
\(900\) 3.94748e21 0.275107
\(901\) 5.02123e20 0.0347036
\(902\) 6.34612e21 0.434970
\(903\) −1.55309e21 −0.105570
\(904\) −2.12796e22 −1.43450
\(905\) 1.41894e22 0.948637
\(906\) 1.14171e21 0.0756994
\(907\) −8.29904e21 −0.545724 −0.272862 0.962053i \(-0.587970\pi\)
−0.272862 + 0.962053i \(0.587970\pi\)
\(908\) 4.48406e21 0.292434
\(909\) −1.90817e22 −1.23421
\(910\) −8.89502e21 −0.570606
\(911\) −4.57221e21 −0.290896 −0.145448 0.989366i \(-0.546462\pi\)
−0.145448 + 0.989366i \(0.546462\pi\)
\(912\) −1.00278e21 −0.0632767
\(913\) 7.97664e21 0.499217
\(914\) −2.57178e21 −0.159639
\(915\) 1.00605e21 0.0619385
\(916\) 7.47307e21 0.456334
\(917\) −2.70796e22 −1.64010
\(918\) −1.75888e20 −0.0105662
\(919\) −1.91276e22 −1.13971 −0.569856 0.821745i \(-0.693001\pi\)
−0.569856 + 0.821745i \(0.693001\pi\)
\(920\) −5.12291e21 −0.302767
\(921\) −9.00375e20 −0.0527809
\(922\) −5.76345e21 −0.335120
\(923\) −4.90923e21 −0.283140
\(924\) −6.12475e20 −0.0350387
\(925\) 3.13264e21 0.177766
\(926\) 2.12597e22 1.19667
\(927\) −3.00349e22 −1.67698
\(928\) 3.38638e21 0.187554
\(929\) −2.52638e22 −1.38797 −0.693987 0.719987i \(-0.744148\pi\)
−0.693987 + 0.719987i \(0.744148\pi\)
\(930\) −1.19522e21 −0.0651368
\(931\) 7.92091e20 0.0428206
\(932\) 9.24388e21 0.495718
\(933\) −6.64842e20 −0.0353677
\(934\) −2.75222e22 −1.45239
\(935\) 3.62370e21 0.189699
\(936\) 1.09720e22 0.569794
\(937\) −7.57750e21 −0.390372 −0.195186 0.980766i \(-0.562531\pi\)
−0.195186 + 0.980766i \(0.562531\pi\)
\(938\) 1.04752e22 0.535352
\(939\) −6.18339e20 −0.0313498
\(940\) 2.40462e21 0.120945
\(941\) 2.62206e21 0.130834 0.0654169 0.997858i \(-0.479162\pi\)
0.0654169 + 0.997858i \(0.479162\pi\)
\(942\) 1.36959e21 0.0677966
\(943\) −1.58223e21 −0.0777021
\(944\) −1.93578e20 −0.00943118
\(945\) 3.75162e21 0.181335
\(946\) 3.77303e22 1.80928
\(947\) −1.96405e22 −0.934387 −0.467193 0.884155i \(-0.654735\pi\)
−0.467193 + 0.884155i \(0.654735\pi\)
\(948\) 6.73938e20 0.0318095
\(949\) −1.34252e22 −0.628672
\(950\) −2.43809e22 −1.13272
\(951\) 1.44358e21 0.0665409
\(952\) −2.35673e21 −0.107778
\(953\) 1.28475e22 0.582935 0.291468 0.956581i \(-0.405856\pi\)
0.291468 + 0.956581i \(0.405856\pi\)
\(954\) −6.30018e21 −0.283622
\(955\) −5.32364e22 −2.37784
\(956\) −4.70529e21 −0.208522
\(957\) −6.22373e20 −0.0273660
\(958\) 2.07469e22 0.905130
\(959\) 2.21593e22 0.959217
\(960\) −2.21421e21 −0.0951007
\(961\) −4.35446e21 −0.185571
\(962\) 2.27739e21 0.0962995
\(963\) 2.57216e22 1.07920
\(964\) 3.97989e20 0.0165689
\(965\) 4.80937e22 1.98670
\(966\) −2.78427e20 −0.0114125
\(967\) −4.78106e22 −1.94458 −0.972289 0.233780i \(-0.924890\pi\)
−0.972289 + 0.233780i \(0.924890\pi\)
\(968\) 2.99232e22 1.20766
\(969\) −2.97227e20 −0.0119031
\(970\) −4.54554e22 −1.80633
\(971\) 2.76633e22 1.09084 0.545418 0.838164i \(-0.316371\pi\)
0.545418 + 0.838164i \(0.316371\pi\)
\(972\) −1.81693e21 −0.0710955
\(973\) −2.83936e22 −1.10249
\(974\) 5.83042e21 0.224651
\(975\) −7.22493e20 −0.0276248
\(976\) 9.45765e21 0.358847
\(977\) 2.80871e22 1.05754 0.528771 0.848764i \(-0.322653\pi\)
0.528771 + 0.848764i \(0.322653\pi\)
\(978\) 1.94198e20 0.00725609
\(979\) 2.13797e21 0.0792742
\(980\) 3.04433e20 0.0112020
\(981\) 3.39670e22 1.24034
\(982\) −1.42678e22 −0.517035
\(983\) −2.12935e22 −0.765767 −0.382883 0.923797i \(-0.625069\pi\)
−0.382883 + 0.923797i \(0.625069\pi\)
\(984\) −7.64892e20 −0.0272984
\(985\) 2.03119e22 0.719412
\(986\) −6.26371e20 −0.0220168
\(987\) 4.99665e20 0.0174301
\(988\) 9.72109e21 0.336541
\(989\) −9.40701e21 −0.323206
\(990\) −4.54668e22 −1.55035
\(991\) −2.88007e22 −0.974655 −0.487327 0.873219i \(-0.662028\pi\)
−0.487327 + 0.873219i \(0.662028\pi\)
\(992\) 1.80052e22 0.604730
\(993\) −1.84462e19 −0.000614876 0
\(994\) −1.32306e22 −0.437704
\(995\) 4.94417e22 1.62338
\(996\) −2.51462e20 −0.00819458
\(997\) 2.14781e22 0.694676 0.347338 0.937740i \(-0.387086\pi\)
0.347338 + 0.937740i \(0.387086\pi\)
\(998\) −2.23628e22 −0.717871
\(999\) −9.60526e20 −0.0306033
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 23.16.a.a.1.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.16.a.a.1.5 12 1.1 even 1 trivial