Properties

Label 3.27.b.a.2.4
Level $3$
Weight $27$
Character 3.2
Analytic conductor $12.849$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,27,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 27, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 27);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 27 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(12.8487876219\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 2728193x^{6} + 2071419806976x^{4} + 503906274711956480x^{2} + 26754716118873014272000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{33}\cdot 3^{38}\cdot 5^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.4
Root \(-269.997i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.27.b.a.2.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3239.96i q^{2} +(-1.06686e6 - 1.18477e6i) q^{3} +5.66115e7 q^{4} +1.50979e9i q^{5} +(-3.83861e9 + 3.45659e9i) q^{6} +7.23448e10 q^{7} -4.00850e11i q^{8} +(-2.65486e11 + 2.52796e12i) q^{9} +O(q^{10})\) \(q-3239.96i q^{2} +(-1.06686e6 - 1.18477e6i) q^{3} +5.66115e7 q^{4} +1.50979e9i q^{5} +(-3.83861e9 + 3.45659e9i) q^{6} +7.23448e10 q^{7} -4.00850e11i q^{8} +(-2.65486e11 + 2.52796e12i) q^{9} +4.89166e12 q^{10} -2.86233e13i q^{11} +(-6.03965e13 - 6.70715e13i) q^{12} +4.12039e14 q^{13} -2.34394e14i q^{14} +(1.78875e15 - 1.61073e15i) q^{15} +2.50039e15 q^{16} -1.55296e16i q^{17} +(8.19051e15 + 8.60165e14i) q^{18} +2.79629e15 q^{19} +8.54713e16i q^{20} +(-7.71817e16 - 8.57118e16i) q^{21} -9.27386e16 q^{22} +6.09267e17i q^{23} +(-4.74914e17 + 4.27650e17i) q^{24} -7.89340e17 q^{25} -1.33499e18i q^{26} +(3.27829e18 - 2.38244e18i) q^{27} +4.09554e18 q^{28} +1.18881e18i q^{29} +(-5.21871e18 - 5.79548e18i) q^{30} +2.23543e19 q^{31} -3.50017e19i q^{32} +(-3.39120e19 + 3.05371e19i) q^{33} -5.03153e19 q^{34} +1.09225e20i q^{35} +(-1.50296e19 + 1.43112e20i) q^{36} +4.09546e19 q^{37} -9.05987e18i q^{38} +(-4.39588e20 - 4.88171e20i) q^{39} +6.05197e20 q^{40} -2.65906e20i q^{41} +(-2.77703e20 + 2.50066e20i) q^{42} +2.85094e21 q^{43} -1.62041e21i q^{44} +(-3.81669e21 - 4.00827e20i) q^{45} +1.97400e21 q^{46} +6.83375e21i q^{47} +(-2.66757e21 - 2.96239e21i) q^{48} -4.15372e21 q^{49} +2.55743e21i q^{50} +(-1.83990e22 + 1.65679e22i) q^{51} +2.33261e22 q^{52} -2.17521e22i q^{53} +(-7.71903e21 - 1.06215e22i) q^{54} +4.32151e22 q^{55} -2.89994e22i q^{56} +(-2.98325e21 - 3.31295e21i) q^{57} +3.85171e21 q^{58} +6.38240e22i q^{59} +(1.01264e23 - 9.11859e22i) q^{60} -2.23066e23 q^{61} -7.24272e22i q^{62} +(-1.92065e22 + 1.82885e23i) q^{63} +5.43943e22 q^{64} +6.22091e23i q^{65} +(9.89391e22 + 1.09874e23i) q^{66} -7.65550e23 q^{67} -8.79154e23i q^{68} +(7.21840e23 - 6.50003e23i) q^{69} +3.53886e23 q^{70} -4.93143e22i q^{71} +(1.01333e24 + 1.06420e23i) q^{72} -7.06916e23 q^{73} -1.32691e23i q^{74} +(8.42115e23 + 9.35185e23i) q^{75} +1.58302e23 q^{76} -2.07075e24i q^{77} +(-1.58166e24 + 1.42425e24i) q^{78} -1.47639e24 q^{79} +3.77506e24i q^{80} +(-6.32012e24 - 1.34228e24i) q^{81} -8.61527e23 q^{82} +1.16553e25i q^{83} +(-4.36937e24 - 4.85227e24i) q^{84} +2.34464e25 q^{85} -9.23693e24i q^{86} +(1.40847e24 - 1.26829e24i) q^{87} -1.14737e25 q^{88} -3.65050e25i q^{89} +(-1.29867e24 + 1.23659e25i) q^{90} +2.98089e25 q^{91} +3.44915e25i q^{92} +(-2.38489e25 - 2.64847e25i) q^{93} +2.21411e25 q^{94} +4.22180e24i q^{95} +(-4.14690e25 + 3.73420e25i) q^{96} -6.39313e25 q^{97} +1.34579e25i q^{98} +(7.23588e25 + 7.59909e24i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9} - 19160376580800 q^{10} + 361652147111520 q^{12} - 397915354631600 q^{13} - 719893807027200 q^{15} + 14\!\cdots\!24 q^{16}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3239.96i 0.395503i −0.980252 0.197752i \(-0.936636\pi\)
0.980252 0.197752i \(-0.0633640\pi\)
\(3\) −1.06686e6 1.18477e6i −0.669162 0.743117i
\(4\) 5.66115e7 0.843577
\(5\) 1.50979e9i 1.23682i 0.785857 + 0.618409i \(0.212222\pi\)
−0.785857 + 0.618409i \(0.787778\pi\)
\(6\) −3.83861e9 + 3.45659e9i −0.293905 + 0.264656i
\(7\) 7.23448e10 0.746677 0.373338 0.927695i \(-0.378213\pi\)
0.373338 + 0.927695i \(0.378213\pi\)
\(8\) 4.00850e11i 0.729141i
\(9\) −2.65486e11 + 2.52796e12i −0.104445 + 0.994531i
\(10\) 4.89166e12 0.489166
\(11\) 2.86233e13i 0.829116i −0.910023 0.414558i \(-0.863936\pi\)
0.910023 0.414558i \(-0.136064\pi\)
\(12\) −6.03965e13 6.70715e13i −0.564489 0.626876i
\(13\) 4.12039e14 1.36043 0.680213 0.733015i \(-0.261887\pi\)
0.680213 + 0.733015i \(0.261887\pi\)
\(14\) 2.34394e14i 0.295313i
\(15\) 1.78875e15 1.61073e15i 0.919100 0.827631i
\(16\) 2.50039e15 0.555199
\(17\) 1.55296e16i 1.56792i −0.620811 0.783960i \(-0.713196\pi\)
0.620811 0.783960i \(-0.286804\pi\)
\(18\) 8.19051e15 + 8.60165e14i 0.393340 + 0.0413085i
\(19\) 2.79629e15 0.0664944 0.0332472 0.999447i \(-0.489415\pi\)
0.0332472 + 0.999447i \(0.489415\pi\)
\(20\) 8.54713e16i 1.04335i
\(21\) −7.71817e16 8.57118e16i −0.499647 0.554868i
\(22\) −9.27386e16 −0.327918
\(23\) 6.09267e17i 1.20878i 0.796690 + 0.604388i \(0.206582\pi\)
−0.796690 + 0.604388i \(0.793418\pi\)
\(24\) −4.74914e17 + 4.27650e17i −0.541837 + 0.487913i
\(25\) −7.89340e17 −0.529717
\(26\) 1.33499e18i 0.538053i
\(27\) 3.27829e18 2.38244e18i 0.808943 0.587887i
\(28\) 4.09554e18 0.629879
\(29\) 1.18881e18i 0.115861i 0.998321 + 0.0579307i \(0.0184502\pi\)
−0.998321 + 0.0579307i \(0.981550\pi\)
\(30\) −5.21871e18 5.79548e18i −0.327331 0.363507i
\(31\) 2.23543e19 0.915502 0.457751 0.889080i \(-0.348655\pi\)
0.457751 + 0.889080i \(0.348655\pi\)
\(32\) 3.50017e19i 0.948724i
\(33\) −3.39120e19 + 3.05371e19i −0.616130 + 0.554813i
\(34\) −5.03153e19 −0.620118
\(35\) 1.09225e20i 0.923503i
\(36\) −1.50296e19 + 1.43112e20i −0.0881076 + 0.838963i
\(37\) 4.09546e19 0.168144 0.0840718 0.996460i \(-0.473207\pi\)
0.0840718 + 0.996460i \(0.473207\pi\)
\(38\) 9.05987e18i 0.0262988i
\(39\) −4.39588e20 4.88171e20i −0.910345 1.01096i
\(40\) 6.05197e20 0.901814
\(41\) 2.65906e20i 0.287434i −0.989619 0.143717i \(-0.954094\pi\)
0.989619 0.143717i \(-0.0459055\pi\)
\(42\) −2.77703e20 + 2.50066e20i −0.219452 + 0.197612i
\(43\) 2.85094e21 1.65920 0.829598 0.558361i \(-0.188570\pi\)
0.829598 + 0.558361i \(0.188570\pi\)
\(44\) 1.62041e21i 0.699423i
\(45\) −3.81669e21 4.00827e20i −1.23005 0.129180i
\(46\) 1.97400e21 0.478075
\(47\) 6.83375e21i 1.25137i 0.780075 + 0.625687i \(0.215181\pi\)
−0.780075 + 0.625687i \(0.784819\pi\)
\(48\) −2.66757e21 2.96239e21i −0.371518 0.412578i
\(49\) −4.15372e21 −0.442474
\(50\) 2.55743e21i 0.209505i
\(51\) −1.83990e22 + 1.65679e22i −1.16515 + 1.04919i
\(52\) 2.33261e22 1.14762
\(53\) 2.17521e22i 0.835441i −0.908576 0.417720i \(-0.862829\pi\)
0.908576 0.417720i \(-0.137171\pi\)
\(54\) −7.71903e21 1.06215e22i −0.232511 0.319940i
\(55\) 4.32151e22 1.02547
\(56\) 2.89994e22i 0.544433i
\(57\) −2.98325e21 3.31295e21i −0.0444955 0.0494131i
\(58\) 3.85171e21 0.0458236
\(59\) 6.38240e22i 0.608006i 0.952671 + 0.304003i \(0.0983233\pi\)
−0.952671 + 0.304003i \(0.901677\pi\)
\(60\) 1.01264e23 9.11859e22i 0.775331 0.698170i
\(61\) −2.23066e23 −1.37767 −0.688837 0.724916i \(-0.741878\pi\)
−0.688837 + 0.724916i \(0.741878\pi\)
\(62\) 7.24272e22i 0.362084i
\(63\) −1.92065e22 + 1.82885e23i −0.0779869 + 0.742593i
\(64\) 5.43943e22 0.179975
\(65\) 6.22091e23i 1.68260i
\(66\) 9.89391e22 + 1.09874e23i 0.219430 + 0.243682i
\(67\) −7.65550e23 −1.39637 −0.698186 0.715917i \(-0.746009\pi\)
−0.698186 + 0.715917i \(0.746009\pi\)
\(68\) 8.79154e23i 1.32266i
\(69\) 7.21840e23 6.50003e23i 0.898262 0.808867i
\(70\) 3.53886e23 0.365248
\(71\) 4.93143e22i 0.0423267i −0.999776 0.0211633i \(-0.993263\pi\)
0.999776 0.0211633i \(-0.00673700\pi\)
\(72\) 1.01333e24 + 1.06420e23i 0.725153 + 0.0761553i
\(73\) −7.06916e23 −0.422835 −0.211417 0.977396i \(-0.567808\pi\)
−0.211417 + 0.977396i \(0.567808\pi\)
\(74\) 1.32691e23i 0.0665014i
\(75\) 8.42115e23 + 9.35185e23i 0.354466 + 0.393642i
\(76\) 1.58302e23 0.0560931
\(77\) 2.07075e24i 0.619082i
\(78\) −1.58166e24 + 1.42425e24i −0.399836 + 0.360044i
\(79\) −1.47639e24 −0.316263 −0.158132 0.987418i \(-0.550547\pi\)
−0.158132 + 0.987418i \(0.550547\pi\)
\(80\) 3.77506e24i 0.686680i
\(81\) −6.32012e24 1.34228e24i −0.978182 0.207748i
\(82\) −8.61527e23 −0.113681
\(83\) 1.16553e25i 1.31374i 0.754006 + 0.656868i \(0.228119\pi\)
−0.754006 + 0.656868i \(0.771881\pi\)
\(84\) −4.36937e24 4.85227e24i −0.421491 0.468074i
\(85\) 2.34464e25 1.93923
\(86\) 9.23693e24i 0.656218i
\(87\) 1.40847e24 1.26829e24i 0.0860986 0.0775300i
\(88\) −1.14737e25 −0.604543
\(89\) 3.65050e25i 1.66067i −0.557266 0.830334i \(-0.688150\pi\)
0.557266 0.830334i \(-0.311850\pi\)
\(90\) −1.29867e24 + 1.23659e25i −0.0510910 + 0.486490i
\(91\) 2.98089e25 1.01580
\(92\) 3.44915e25i 1.01970i
\(93\) −2.38489e25 2.64847e25i −0.612619 0.680325i
\(94\) 2.21411e25 0.494922
\(95\) 4.22180e24i 0.0822414i
\(96\) −4.14690e25 + 3.73420e25i −0.705013 + 0.634850i
\(97\) −6.39313e25 −0.949907 −0.474953 0.880011i \(-0.657535\pi\)
−0.474953 + 0.880011i \(0.657535\pi\)
\(98\) 1.34579e25i 0.175000i
\(99\) 7.23588e25 + 7.59909e24i 0.824582 + 0.0865973i
\(100\) −4.46857e25 −0.446857
\(101\) 5.16061e25i 0.453444i 0.973960 + 0.226722i \(0.0728009\pi\)
−0.973960 + 0.226722i \(0.927199\pi\)
\(102\) 5.36794e25 + 5.96120e25i 0.414959 + 0.460820i
\(103\) −7.98999e25 −0.544080 −0.272040 0.962286i \(-0.587698\pi\)
−0.272040 + 0.962286i \(0.587698\pi\)
\(104\) 1.65166e26i 0.991942i
\(105\) 1.29406e26 1.16528e26i 0.686270 0.617973i
\(106\) −7.04761e25 −0.330420
\(107\) 4.87315e25i 0.202218i 0.994875 + 0.101109i \(0.0322392\pi\)
−0.994875 + 0.101109i \(0.967761\pi\)
\(108\) 1.85589e26 1.34874e26i 0.682406 0.495928i
\(109\) 9.21751e25 0.300655 0.150328 0.988636i \(-0.451967\pi\)
0.150328 + 0.988636i \(0.451967\pi\)
\(110\) 1.40016e26i 0.405575i
\(111\) −4.36928e25 4.85217e25i −0.112515 0.124950i
\(112\) 1.80890e26 0.414554
\(113\) 5.50376e26i 1.12367i 0.827249 + 0.561836i \(0.189905\pi\)
−0.827249 + 0.561836i \(0.810095\pi\)
\(114\) −1.07338e25 + 9.66561e24i −0.0195430 + 0.0175981i
\(115\) −9.19864e26 −1.49504
\(116\) 6.73004e25i 0.0977380i
\(117\) −1.09391e26 + 1.04162e27i −0.142090 + 1.35298i
\(118\) 2.06788e26 0.240469
\(119\) 1.12348e27i 1.17073i
\(120\) −6.45661e26 7.17019e26i −0.603460 0.670153i
\(121\) 3.72522e26 0.312566
\(122\) 7.22727e26i 0.544875i
\(123\) −3.15037e26 + 2.83685e26i −0.213597 + 0.192340i
\(124\) 1.26551e27 0.772296
\(125\) 1.05802e27i 0.581654i
\(126\) 5.92541e26 + 6.22284e25i 0.293698 + 0.0308441i
\(127\) 2.20531e27 0.986326 0.493163 0.869937i \(-0.335841\pi\)
0.493163 + 0.869937i \(0.335841\pi\)
\(128\) 2.52516e27i 1.01991i
\(129\) −3.04155e27 3.37770e27i −1.11027 1.23298i
\(130\) 2.01555e27 0.665473
\(131\) 1.52198e27i 0.454865i −0.973794 0.227432i \(-0.926967\pi\)
0.973794 0.227432i \(-0.0730331\pi\)
\(132\) −1.91981e27 + 1.72875e27i −0.519753 + 0.468027i
\(133\) 2.02297e26 0.0496498
\(134\) 2.48035e27i 0.552270i
\(135\) 3.59698e27 + 4.94951e27i 0.727108 + 1.00051i
\(136\) −6.22503e27 −1.14324
\(137\) 4.94120e27i 0.825021i 0.910953 + 0.412510i \(0.135348\pi\)
−0.910953 + 0.412510i \(0.864652\pi\)
\(138\) −2.10599e27 2.33874e27i −0.319910 0.355266i
\(139\) −4.32039e27 −0.597490 −0.298745 0.954333i \(-0.596568\pi\)
−0.298745 + 0.954333i \(0.596568\pi\)
\(140\) 6.18340e27i 0.779046i
\(141\) 8.09641e27 7.29065e27i 0.929917 0.837371i
\(142\) −1.59776e26 −0.0167403
\(143\) 1.17939e28i 1.12795i
\(144\) −6.63820e26 + 6.32091e27i −0.0579879 + 0.552163i
\(145\) −1.79485e27 −0.143299
\(146\) 2.29038e27i 0.167233i
\(147\) 4.43143e27 + 4.92119e27i 0.296087 + 0.328810i
\(148\) 2.31850e27 0.141842
\(149\) 2.51496e28i 1.40965i −0.709383 0.704824i \(-0.751026\pi\)
0.709383 0.704824i \(-0.248974\pi\)
\(150\) 3.02997e27 2.72842e27i 0.155687 0.140193i
\(151\) 2.08256e26 0.00981514 0.00490757 0.999988i \(-0.498438\pi\)
0.00490757 + 0.999988i \(0.498438\pi\)
\(152\) 1.12089e27i 0.0484838i
\(153\) 3.92582e28 + 4.12289e27i 1.55935 + 0.163762i
\(154\) −6.70915e27 −0.244849
\(155\) 3.37502e28i 1.13231i
\(156\) −2.48857e28 2.76361e28i −0.767946 0.852818i
\(157\) −5.10679e28 −1.45028 −0.725141 0.688600i \(-0.758226\pi\)
−0.725141 + 0.688600i \(0.758226\pi\)
\(158\) 4.78345e27i 0.125083i
\(159\) −2.57712e28 + 2.32065e28i −0.620830 + 0.559045i
\(160\) 5.28452e28 1.17340
\(161\) 4.40773e28i 0.902565i
\(162\) −4.34893e27 + 2.04770e28i −0.0821651 + 0.386875i
\(163\) −1.22193e28 −0.213112 −0.106556 0.994307i \(-0.533982\pi\)
−0.106556 + 0.994307i \(0.533982\pi\)
\(164\) 1.50534e28i 0.242473i
\(165\) −4.61045e28 5.11999e28i −0.686202 0.762041i
\(166\) 3.77627e28 0.519587
\(167\) 5.19846e28i 0.661547i −0.943710 0.330774i \(-0.892690\pi\)
0.943710 0.330774i \(-0.107310\pi\)
\(168\) −3.43575e28 + 3.09383e28i −0.404577 + 0.364313i
\(169\) 7.80428e28 0.850757
\(170\) 7.59654e28i 0.766973i
\(171\) −7.42375e26 + 7.06891e27i −0.00694502 + 0.0661307i
\(172\) 1.61396e29 1.39966
\(173\) 6.26303e28i 0.503716i 0.967764 + 0.251858i \(0.0810415\pi\)
−0.967764 + 0.251858i \(0.918958\pi\)
\(174\) −4.10923e27 4.56338e27i −0.0306634 0.0340523i
\(175\) −5.71046e28 −0.395527
\(176\) 7.15697e28i 0.460325i
\(177\) 7.56167e28 6.80913e28i 0.451820 0.406854i
\(178\) −1.18275e29 −0.656800
\(179\) 1.39021e29i 0.717778i 0.933380 + 0.358889i \(0.116844\pi\)
−0.933380 + 0.358889i \(0.883156\pi\)
\(180\) −2.16068e29 2.26914e28i −1.03764 0.108973i
\(181\) −2.06516e29 −0.922854 −0.461427 0.887178i \(-0.652662\pi\)
−0.461427 + 0.887178i \(0.652662\pi\)
\(182\) 9.65796e28i 0.401752i
\(183\) 2.37981e29 + 2.64282e29i 0.921887 + 1.02377i
\(184\) 2.44224e29 0.881368
\(185\) 6.18327e28i 0.207963i
\(186\) −8.58094e28 + 7.72696e28i −0.269071 + 0.242293i
\(187\) −4.44509e29 −1.29999
\(188\) 3.86869e29i 1.05563i
\(189\) 2.37167e29 1.72357e29i 0.604019 0.438961i
\(190\) 1.36785e28 0.0325268
\(191\) 3.87887e29i 0.861533i −0.902463 0.430766i \(-0.858243\pi\)
0.902463 0.430766i \(-0.141757\pi\)
\(192\) −5.80310e28 6.44446e28i −0.120433 0.133743i
\(193\) 1.73735e29 0.337010 0.168505 0.985701i \(-0.446106\pi\)
0.168505 + 0.985701i \(0.446106\pi\)
\(194\) 2.07135e29i 0.375691i
\(195\) 7.37034e29 6.63684e29i 1.25037 1.12593i
\(196\) −2.35148e29 −0.373261
\(197\) 7.64816e29i 1.13631i −0.822922 0.568154i \(-0.807658\pi\)
0.822922 0.568154i \(-0.192342\pi\)
\(198\) 2.46208e28 2.34440e29i 0.0342495 0.326125i
\(199\) −5.16667e29 −0.673164 −0.336582 0.941654i \(-0.609271\pi\)
−0.336582 + 0.941654i \(0.609271\pi\)
\(200\) 3.16407e29i 0.386238i
\(201\) 8.16734e29 + 9.06999e29i 0.934398 + 1.03767i
\(202\) 1.67202e29 0.179339
\(203\) 8.60043e28i 0.0865110i
\(204\) −1.04159e30 + 9.37934e29i −0.982892 + 0.885075i
\(205\) 4.01462e29 0.355504
\(206\) 2.58873e29i 0.215185i
\(207\) −1.54021e30 1.61752e29i −1.20217 0.126251i
\(208\) 1.03026e30 0.755307
\(209\) 8.00391e28i 0.0551316i
\(210\) −3.77546e29 4.19272e29i −0.244410 0.271422i
\(211\) −1.03117e30 −0.627564 −0.313782 0.949495i \(-0.601596\pi\)
−0.313782 + 0.949495i \(0.601596\pi\)
\(212\) 1.23142e30i 0.704759i
\(213\) −5.84260e28 + 5.26114e28i −0.0314537 + 0.0283234i
\(214\) 1.57888e29 0.0799781
\(215\) 4.30431e30i 2.05212i
\(216\) −9.55001e29 1.31410e30i −0.428652 0.589834i
\(217\) 1.61722e30 0.683584
\(218\) 2.98644e29i 0.118910i
\(219\) 7.54181e29 + 8.37532e29i 0.282945 + 0.314216i
\(220\) 2.44647e30 0.865059
\(221\) 6.39880e30i 2.13304i
\(222\) −1.57209e29 + 1.41563e29i −0.0494183 + 0.0445002i
\(223\) 4.34086e29 0.128710 0.0643550 0.997927i \(-0.479501\pi\)
0.0643550 + 0.997927i \(0.479501\pi\)
\(224\) 2.53219e30i 0.708390i
\(225\) 2.09559e29 1.99542e30i 0.0553264 0.526820i
\(226\) 1.78320e30 0.444416
\(227\) 6.97813e30i 1.64211i 0.570848 + 0.821056i \(0.306615\pi\)
−0.570848 + 0.821056i \(0.693385\pi\)
\(228\) −1.68886e29 1.87551e29i −0.0375354 0.0416838i
\(229\) −3.64200e30 −0.764678 −0.382339 0.924022i \(-0.624881\pi\)
−0.382339 + 0.924022i \(0.624881\pi\)
\(230\) 2.98033e30i 0.591292i
\(231\) −2.45336e30 + 2.20920e30i −0.460050 + 0.414266i
\(232\) 4.76534e29 0.0844793
\(233\) 3.66681e30i 0.614698i −0.951597 0.307349i \(-0.900558\pi\)
0.951597 0.307349i \(-0.0994419\pi\)
\(234\) 3.37481e30 + 3.54421e29i 0.535110 + 0.0561971i
\(235\) −1.03175e31 −1.54772
\(236\) 3.61317e30i 0.512900i
\(237\) 1.57510e30 + 1.74918e30i 0.211631 + 0.235020i
\(238\) −3.64005e30 −0.463028
\(239\) 5.55263e29i 0.0668846i 0.999441 + 0.0334423i \(0.0106470\pi\)
−0.999441 + 0.0334423i \(0.989353\pi\)
\(240\) 4.47258e30 4.02746e30i 0.510283 0.459500i
\(241\) 7.73779e30 0.836364 0.418182 0.908363i \(-0.362667\pi\)
0.418182 + 0.908363i \(0.362667\pi\)
\(242\) 1.20696e30i 0.123621i
\(243\) 5.15239e30 + 8.91990e30i 0.500181 + 0.865921i
\(244\) −1.26281e31 −1.16217
\(245\) 6.27123e30i 0.547260i
\(246\) 9.19129e29 + 1.02071e30i 0.0760711 + 0.0844784i
\(247\) 1.15218e30 0.0904607
\(248\) 8.96071e30i 0.667530i
\(249\) 1.38088e31 1.24346e31i 0.976259 0.879102i
\(250\) 3.42796e30 0.230046
\(251\) 2.05034e30i 0.130638i 0.997864 + 0.0653188i \(0.0208064\pi\)
−0.997864 + 0.0653188i \(0.979194\pi\)
\(252\) −1.08731e30 + 1.03534e31i −0.0657879 + 0.626434i
\(253\) 1.74393e31 1.00222
\(254\) 7.14511e30i 0.390095i
\(255\) −2.50140e31 2.77785e31i −1.29766 1.44108i
\(256\) −4.53110e30 −0.223401
\(257\) 1.47948e31i 0.693390i 0.937978 + 0.346695i \(0.112696\pi\)
−0.937978 + 0.346695i \(0.887304\pi\)
\(258\) −1.09436e31 + 9.85452e30i −0.487647 + 0.439116i
\(259\) 2.96285e30 0.125549
\(260\) 3.52175e31i 1.41940i
\(261\) −3.00527e30 3.15613e29i −0.115228 0.0121012i
\(262\) −4.93116e30 −0.179901
\(263\) 4.00479e30i 0.139045i −0.997580 0.0695225i \(-0.977852\pi\)
0.997580 0.0695225i \(-0.0221476\pi\)
\(264\) 1.22408e31 + 1.35936e31i 0.404537 + 0.449246i
\(265\) 3.28411e31 1.03329
\(266\) 6.55434e29i 0.0196367i
\(267\) −4.32500e31 + 3.89458e31i −1.23407 + 1.11126i
\(268\) −4.33389e31 −1.17795
\(269\) 2.96267e31i 0.767190i −0.923501 0.383595i \(-0.874686\pi\)
0.923501 0.383595i \(-0.125314\pi\)
\(270\) 1.60362e31 1.16541e31i 0.395707 0.287574i
\(271\) 1.36862e31 0.321871 0.160936 0.986965i \(-0.448549\pi\)
0.160936 + 0.986965i \(0.448549\pi\)
\(272\) 3.88301e31i 0.870508i
\(273\) −3.18019e31 3.53166e31i −0.679733 0.754857i
\(274\) 1.60093e31 0.326298
\(275\) 2.25935e31i 0.439197i
\(276\) 4.08645e31 3.67976e31i 0.757753 0.682341i
\(277\) 7.51885e31 1.33019 0.665096 0.746758i \(-0.268391\pi\)
0.665096 + 0.746758i \(0.268391\pi\)
\(278\) 1.39979e31i 0.236309i
\(279\) −5.93475e30 + 5.65109e31i −0.0956198 + 0.910495i
\(280\) 4.37829e31 0.673364
\(281\) 1.65770e31i 0.243402i −0.992567 0.121701i \(-0.961165\pi\)
0.992567 0.121701i \(-0.0388350\pi\)
\(282\) −2.36215e31 2.62321e31i −0.331183 0.367785i
\(283\) −5.53803e31 −0.741535 −0.370768 0.928726i \(-0.620905\pi\)
−0.370768 + 0.928726i \(0.620905\pi\)
\(284\) 2.79175e30i 0.0357058i
\(285\) 5.00185e30 4.50407e30i 0.0611150 0.0550328i
\(286\) −3.82119e31 −0.446108
\(287\) 1.92369e31i 0.214620i
\(288\) 8.84831e31 + 9.29247e30i 0.943535 + 0.0990898i
\(289\) −1.43068e32 −1.45838
\(290\) 5.81525e30i 0.0566754i
\(291\) 6.82057e31 + 7.57438e31i 0.635641 + 0.705892i
\(292\) −4.00196e31 −0.356694
\(293\) 7.12735e31i 0.607644i 0.952729 + 0.303822i \(0.0982628\pi\)
−0.952729 + 0.303822i \(0.901737\pi\)
\(294\) 1.59445e31 1.43577e31i 0.130045 0.117103i
\(295\) −9.63607e31 −0.751993
\(296\) 1.64166e31i 0.122600i
\(297\) −6.81935e31 9.38355e31i −0.487426 0.670708i
\(298\) −8.14840e31 −0.557520
\(299\) 2.51042e32i 1.64445i
\(300\) 4.76734e31 + 5.29422e31i 0.299020 + 0.332067i
\(301\) 2.06250e32 1.23888
\(302\) 6.74741e29i 0.00388192i
\(303\) 6.11413e31 5.50565e31i 0.336962 0.303427i
\(304\) 6.99182e30 0.0369176
\(305\) 3.36783e32i 1.70393i
\(306\) 1.33580e31 1.27195e32i 0.0647684 0.616726i
\(307\) 3.23426e31 0.150306 0.0751529 0.997172i \(-0.476056\pi\)
0.0751529 + 0.997172i \(0.476056\pi\)
\(308\) 1.17228e32i 0.522243i
\(309\) 8.52420e31 + 9.46629e31i 0.364077 + 0.404315i
\(310\) 1.09350e32 0.447832
\(311\) 2.14585e32i 0.842782i −0.906879 0.421391i \(-0.861542\pi\)
0.906879 0.421391i \(-0.138458\pi\)
\(312\) −1.95683e32 + 1.76209e32i −0.737129 + 0.663770i
\(313\) 1.69832e32 0.613680 0.306840 0.951761i \(-0.400728\pi\)
0.306840 + 0.951761i \(0.400728\pi\)
\(314\) 1.65458e32i 0.573592i
\(315\) −2.76117e32 2.89977e31i −0.918452 0.0964555i
\(316\) −8.35806e31 −0.266792
\(317\) 1.88890e32i 0.578681i 0.957226 + 0.289341i \(0.0934360\pi\)
−0.957226 + 0.289341i \(0.906564\pi\)
\(318\) 7.51882e31 + 8.34979e31i 0.221104 + 0.245540i
\(319\) 3.40277e31 0.0960626
\(320\) 8.21237e31i 0.222597i
\(321\) 5.77356e31 5.19897e31i 0.150272 0.135317i
\(322\) 1.42809e32 0.356968
\(323\) 4.34252e31i 0.104258i
\(324\) −3.57791e32 7.59883e31i −0.825172 0.175251i
\(325\) −3.25239e32 −0.720641
\(326\) 3.95901e31i 0.0842865i
\(327\) −9.83379e31 1.09206e32i −0.201187 0.223422i
\(328\) −1.06588e32 −0.209580
\(329\) 4.94386e32i 0.934371i
\(330\) −1.65886e32 + 1.49377e32i −0.301390 + 0.271395i
\(331\) 9.85527e32 1.72149 0.860745 0.509036i \(-0.169998\pi\)
0.860745 + 0.509036i \(0.169998\pi\)
\(332\) 6.59824e32i 1.10824i
\(333\) −1.08729e31 + 1.03532e32i −0.0175618 + 0.167224i
\(334\) −1.68428e32 −0.261644
\(335\) 1.15582e33i 1.72706i
\(336\) −1.92985e32 2.14313e32i −0.277404 0.308062i
\(337\) −6.35654e32 −0.879087 −0.439543 0.898221i \(-0.644860\pi\)
−0.439543 + 0.898221i \(0.644860\pi\)
\(338\) 2.52856e32i 0.336478i
\(339\) 6.52067e32 5.87174e32i 0.835019 0.751918i
\(340\) 1.32733e33 1.63589
\(341\) 6.39855e32i 0.759057i
\(342\) 2.29030e31 + 2.40527e30i 0.0261549 + 0.00274678i
\(343\) −9.79635e32 −1.07706
\(344\) 1.14280e33i 1.20979i
\(345\) 9.81366e32 + 1.08983e33i 1.00042 + 1.11099i
\(346\) 2.02920e32 0.199221
\(347\) 2.07743e33i 1.96446i 0.187676 + 0.982231i \(0.439904\pi\)
−0.187676 + 0.982231i \(0.560096\pi\)
\(348\) 7.97353e31 7.18001e31i 0.0726308 0.0654026i
\(349\) −1.70165e33 −1.49327 −0.746637 0.665232i \(-0.768333\pi\)
−0.746637 + 0.665232i \(0.768333\pi\)
\(350\) 1.85017e32i 0.156432i
\(351\) 1.35078e33 9.81660e32i 1.10051 0.799776i
\(352\) −1.00187e33 −0.786603
\(353\) 1.98122e33i 1.49921i 0.661885 + 0.749605i \(0.269757\pi\)
−0.661885 + 0.749605i \(0.730243\pi\)
\(354\) −2.20613e32 2.44995e32i −0.160912 0.178696i
\(355\) 7.44540e31 0.0523503
\(356\) 2.06660e33i 1.40090i
\(357\) −1.33107e33 + 1.19860e33i −0.869989 + 0.783408i
\(358\) 4.50422e32 0.283884
\(359\) 7.03773e32i 0.427764i −0.976859 0.213882i \(-0.931389\pi\)
0.976859 0.213882i \(-0.0686109\pi\)
\(360\) −1.60671e32 + 1.52992e33i −0.0941902 + 0.896882i
\(361\) −1.76063e33 −0.995578
\(362\) 6.69106e32i 0.364992i
\(363\) −3.97429e32 4.41352e32i −0.209157 0.232273i
\(364\) 1.68752e33 0.856904
\(365\) 1.06729e33i 0.522969i
\(366\) 8.56264e32 7.71049e32i 0.404906 0.364609i
\(367\) 2.59950e32 0.118640 0.0593200 0.998239i \(-0.481107\pi\)
0.0593200 + 0.998239i \(0.481107\pi\)
\(368\) 1.52341e33i 0.671112i
\(369\) 6.72201e32 + 7.05944e31i 0.285862 + 0.0300212i
\(370\) 2.00336e32 0.0822500
\(371\) 1.57365e33i 0.623804i
\(372\) −1.35012e33 1.49934e33i −0.516791 0.573906i
\(373\) 2.97352e33 1.09915 0.549573 0.835446i \(-0.314790\pi\)
0.549573 + 0.835446i \(0.314790\pi\)
\(374\) 1.44019e33i 0.514150i
\(375\) 1.25351e33 1.12876e33i 0.432237 0.389221i
\(376\) 2.73931e33 0.912428
\(377\) 4.89837e32i 0.157621i
\(378\) −5.58431e32 7.68412e32i −0.173611 0.238892i
\(379\) −2.17945e33 −0.654692 −0.327346 0.944905i \(-0.606154\pi\)
−0.327346 + 0.944905i \(0.606154\pi\)
\(380\) 2.39002e32i 0.0693770i
\(381\) −2.35275e33 2.61278e33i −0.660011 0.732955i
\(382\) −1.25674e33 −0.340739
\(383\) 4.63588e33i 1.21492i −0.794350 0.607460i \(-0.792188\pi\)
0.794350 0.607460i \(-0.207812\pi\)
\(384\) −2.99173e33 + 2.69400e33i −0.757909 + 0.682481i
\(385\) 3.12639e33 0.765691
\(386\) 5.62896e32i 0.133289i
\(387\) −7.56884e32 + 7.20707e33i −0.173295 + 1.65012i
\(388\) −3.61925e33 −0.801320
\(389\) 6.97643e33i 1.49379i 0.664944 + 0.746893i \(0.268455\pi\)
−0.664944 + 0.746893i \(0.731545\pi\)
\(390\) −2.15031e33 2.38796e33i −0.445309 0.494524i
\(391\) 9.46167e33 1.89527
\(392\) 1.66502e33i 0.322626i
\(393\) −1.80319e33 + 1.62374e33i −0.338018 + 0.304378i
\(394\) −2.47798e33 −0.449414
\(395\) 2.22903e33i 0.391160i
\(396\) 4.09634e33 + 4.30196e32i 0.695598 + 0.0730515i
\(397\) −1.07984e34 −1.77453 −0.887267 0.461257i \(-0.847399\pi\)
−0.887267 + 0.461257i \(0.847399\pi\)
\(398\) 1.67398e33i 0.266239i
\(399\) −2.15822e32 2.39675e32i −0.0332237 0.0368956i
\(400\) −1.97366e33 −0.294098
\(401\) 8.32622e33i 1.20108i −0.799596 0.600538i \(-0.794953\pi\)
0.799596 0.600538i \(-0.205047\pi\)
\(402\) 2.93864e33 2.64619e33i 0.410401 0.369558i
\(403\) 9.21085e33 1.24547
\(404\) 2.92150e33i 0.382515i
\(405\) 2.02655e33 9.54203e33i 0.256946 1.20983i
\(406\) 2.78651e32 0.0342154
\(407\) 1.17226e33i 0.139411i
\(408\) 6.64124e33 + 7.37522e33i 0.765009 + 0.849558i
\(409\) −1.60150e33 −0.178700 −0.0893501 0.996000i \(-0.528479\pi\)
−0.0893501 + 0.996000i \(0.528479\pi\)
\(410\) 1.30072e33i 0.140603i
\(411\) 5.85417e33 5.27156e33i 0.613087 0.552072i
\(412\) −4.52325e33 −0.458973
\(413\) 4.61733e33i 0.453984i
\(414\) −5.24070e32 + 4.99021e33i −0.0499327 + 0.475460i
\(415\) −1.75970e34 −1.62485
\(416\) 1.44221e34i 1.29067i
\(417\) 4.60925e33 + 5.11866e33i 0.399817 + 0.444005i
\(418\) −2.59324e32 −0.0218047
\(419\) 9.70810e33i 0.791320i 0.918397 + 0.395660i \(0.129484\pi\)
−0.918397 + 0.395660i \(0.870516\pi\)
\(420\) 7.32590e33 6.59682e33i 0.578922 0.521307i
\(421\) 2.25116e34 1.72480 0.862400 0.506227i \(-0.168960\pi\)
0.862400 + 0.506227i \(0.168960\pi\)
\(422\) 3.34095e33i 0.248204i
\(423\) −1.72755e34 1.81426e33i −1.24453 0.130700i
\(424\) −8.71933e33 −0.609154
\(425\) 1.22581e34i 0.830554i
\(426\) 1.70459e32 + 1.89298e32i 0.0112020 + 0.0124400i
\(427\) −1.61377e34 −1.02868
\(428\) 2.75876e33i 0.170587i
\(429\) −1.39731e34 + 1.25825e34i −0.838199 + 0.754782i
\(430\) 1.39458e34 0.811622
\(431\) 4.70060e33i 0.265429i 0.991154 + 0.132715i \(0.0423694\pi\)
−0.991154 + 0.132715i \(0.957631\pi\)
\(432\) 8.19701e33 5.95705e33i 0.449125 0.326394i
\(433\) −2.36737e34 −1.25871 −0.629353 0.777120i \(-0.716680\pi\)
−0.629353 + 0.777120i \(0.716680\pi\)
\(434\) 5.23973e33i 0.270360i
\(435\) 1.91485e33 + 2.12648e33i 0.0958905 + 0.106488i
\(436\) 5.21817e33 0.253626
\(437\) 1.70369e33i 0.0803768i
\(438\) 2.71357e33 2.44352e33i 0.124273 0.111906i
\(439\) 3.98133e34 1.77006 0.885032 0.465530i \(-0.154136\pi\)
0.885032 + 0.465530i \(0.154136\pi\)
\(440\) 1.73228e34i 0.747709i
\(441\) 1.10275e33 1.05004e34i 0.0462143 0.440054i
\(442\) −2.07319e34 −0.843624
\(443\) 3.14794e34i 1.24388i −0.783065 0.621940i \(-0.786345\pi\)
0.783065 0.621940i \(-0.213655\pi\)
\(444\) −2.47352e33 2.74689e33i −0.0949153 0.105405i
\(445\) 5.51148e34 2.05394
\(446\) 1.40642e33i 0.0509053i
\(447\) −2.97965e34 + 2.68312e34i −1.04753 + 0.943282i
\(448\) 3.93514e33 0.134383
\(449\) 1.99275e34i 0.661073i −0.943793 0.330536i \(-0.892770\pi\)
0.943793 0.330536i \(-0.107230\pi\)
\(450\) −6.46510e33 6.78962e32i −0.208359 0.0218818i
\(451\) −7.61113e33 −0.238316
\(452\) 3.11576e34i 0.947903i
\(453\) −2.22180e32 2.46735e32i −0.00656791 0.00729379i
\(454\) 2.26089e34 0.649461
\(455\) 4.50050e34i 1.25636i
\(456\) −1.32800e33 + 1.19583e33i −0.0360291 + 0.0324435i
\(457\) 1.23188e34 0.324831 0.162415 0.986722i \(-0.448072\pi\)
0.162415 + 0.986722i \(0.448072\pi\)
\(458\) 1.18000e34i 0.302433i
\(459\) −3.69984e34 5.09105e34i −0.921760 1.26836i
\(460\) −5.20749e34 −1.26118
\(461\) 3.82432e34i 0.900413i −0.892924 0.450207i \(-0.851350\pi\)
0.892924 0.450207i \(-0.148650\pi\)
\(462\) 7.15772e33 + 7.94879e33i 0.163844 + 0.181951i
\(463\) −2.50099e34 −0.556619 −0.278310 0.960491i \(-0.589774\pi\)
−0.278310 + 0.960491i \(0.589774\pi\)
\(464\) 2.97250e33i 0.0643262i
\(465\) 3.99862e34 3.60068e34i 0.841437 0.757697i
\(466\) −1.18803e34 −0.243115
\(467\) 7.58886e34i 1.51028i 0.655564 + 0.755140i \(0.272431\pi\)
−0.655564 + 0.755140i \(0.727569\pi\)
\(468\) −6.19276e33 + 5.89676e34i −0.119864 + 1.14135i
\(469\) −5.53835e34 −1.04264
\(470\) 3.34283e34i 0.612129i
\(471\) 5.44823e34 + 6.05037e34i 0.970474 + 1.07773i
\(472\) 2.55838e34 0.443322
\(473\) 8.16034e34i 1.37567i
\(474\) 5.66727e33 5.10327e33i 0.0929514 0.0837008i
\(475\) −2.20722e33 −0.0352232
\(476\) 6.36022e34i 0.987601i
\(477\) 5.49886e34 + 5.77489e33i 0.830871 + 0.0872578i
\(478\) 1.79903e33 0.0264531
\(479\) 1.96148e34i 0.280686i 0.990103 + 0.140343i \(0.0448206\pi\)
−0.990103 + 0.140343i \(0.955179\pi\)
\(480\) −5.63784e34 6.26093e34i −0.785193 0.871972i
\(481\) 1.68749e34 0.228747
\(482\) 2.50702e34i 0.330785i
\(483\) 5.22214e34 4.70243e34i 0.670711 0.603962i
\(484\) 2.10890e34 0.263674
\(485\) 9.65226e34i 1.17486i
\(486\) 2.89001e34 1.66936e34i 0.342475 0.197823i
\(487\) −6.39772e34 −0.738157 −0.369079 0.929398i \(-0.620327\pi\)
−0.369079 + 0.929398i \(0.620327\pi\)
\(488\) 8.94161e34i 1.00452i
\(489\) 1.30363e34 + 1.44770e34i 0.142606 + 0.158367i
\(490\) −2.03185e34 −0.216443
\(491\) 3.95052e34i 0.409822i 0.978781 + 0.204911i \(0.0656905\pi\)
−0.978781 + 0.204911i \(0.934309\pi\)
\(492\) −1.78347e34 + 1.60598e34i −0.180186 + 0.162254i
\(493\) 1.84618e34 0.181662
\(494\) 3.73302e33i 0.0357775i
\(495\) −1.14730e34 + 1.09246e35i −0.107105 + 1.01986i
\(496\) 5.58946e34 0.508286
\(497\) 3.56763e33i 0.0316043i
\(498\) −4.02875e34 4.47401e34i −0.347688 0.386114i
\(499\) −6.99361e34 −0.588023 −0.294011 0.955802i \(-0.594990\pi\)
−0.294011 + 0.955802i \(0.594990\pi\)
\(500\) 5.98962e34i 0.490670i
\(501\) −6.15897e34 + 5.54603e34i −0.491607 + 0.442682i
\(502\) 6.64304e33 0.0516676
\(503\) 2.74354e34i 0.207935i 0.994581 + 0.103967i \(0.0331538\pi\)
−0.994581 + 0.103967i \(0.966846\pi\)
\(504\) 7.33093e34 + 7.69892e33i 0.541455 + 0.0568634i
\(505\) −7.79143e34 −0.560827
\(506\) 5.65026e34i 0.396380i
\(507\) −8.32607e34 9.24627e34i −0.569294 0.632212i
\(508\) 1.24846e35 0.832042
\(509\) 1.87923e35i 1.22081i 0.792089 + 0.610406i \(0.208994\pi\)
−0.792089 + 0.610406i \(0.791006\pi\)
\(510\) −9.00014e34 + 8.10445e34i −0.569950 + 0.513229i
\(511\) −5.11417e34 −0.315721
\(512\) 1.54780e35i 0.931550i
\(513\) 9.16703e33 6.66200e33i 0.0537902 0.0390912i
\(514\) 4.79345e34 0.274238
\(515\) 1.20632e35i 0.672927i
\(516\) −1.72187e35 1.91217e35i −0.936599 1.04011i
\(517\) 1.95605e35 1.03753
\(518\) 9.59953e33i 0.0496550i
\(519\) 7.42024e34 6.68178e34i 0.374320 0.337067i
\(520\) 2.49365e35 1.22685
\(521\) 3.32580e35i 1.59590i 0.602725 + 0.797949i \(0.294082\pi\)
−0.602725 + 0.797949i \(0.705918\pi\)
\(522\) −1.02257e33 + 9.73697e33i −0.00478606 + 0.0455730i
\(523\) 9.57976e34 0.437354 0.218677 0.975797i \(-0.429826\pi\)
0.218677 + 0.975797i \(0.429826\pi\)
\(524\) 8.61616e34i 0.383713i
\(525\) 6.09226e34 + 6.76557e34i 0.264672 + 0.293923i
\(526\) −1.29754e34 −0.0549927
\(527\) 3.47153e35i 1.43543i
\(528\) −8.47935e34 + 7.63548e34i −0.342075 + 0.308032i
\(529\) −1.17154e35 −0.461140
\(530\) 1.06404e35i 0.408669i
\(531\) −1.61345e35 1.69444e34i −0.604681 0.0635034i
\(532\) 1.14523e34 0.0418834
\(533\) 1.09564e35i 0.391033i
\(534\) 1.26183e35 + 1.40128e35i 0.439505 + 0.488079i
\(535\) −7.35742e34 −0.250107
\(536\) 3.06870e35i 1.01815i
\(537\) 1.64707e35 1.48316e35i 0.533393 0.480310i
\(538\) −9.59893e34 −0.303426
\(539\) 1.18893e35i 0.366862i
\(540\) 2.03631e35 + 2.80199e35i 0.613372 + 0.844011i
\(541\) −6.65949e35 −1.95829 −0.979144 0.203168i \(-0.934876\pi\)
−0.979144 + 0.203168i \(0.934876\pi\)
\(542\) 4.43428e34i 0.127301i
\(543\) 2.20324e35 + 2.44674e35i 0.617538 + 0.685788i
\(544\) −5.43563e35 −1.48752
\(545\) 1.39165e35i 0.371856i
\(546\) −1.14425e35 + 1.03037e35i −0.298548 + 0.268837i
\(547\) 4.84906e35 1.23544 0.617720 0.786398i \(-0.288056\pi\)
0.617720 + 0.786398i \(0.288056\pi\)
\(548\) 2.79729e35i 0.695968i
\(549\) 5.92210e34 5.63904e35i 0.143892 1.37014i
\(550\) 7.32023e34 0.173704
\(551\) 3.32426e33i 0.00770413i
\(552\) −2.60553e35 2.89349e35i −0.589778 0.654960i
\(553\) −1.06809e35 −0.236146
\(554\) 2.43608e35i 0.526095i
\(555\) 7.32574e34 6.59668e34i 0.154541 0.139161i
\(556\) −2.44584e35 −0.504029
\(557\) 1.95574e35i 0.393726i −0.980431 0.196863i \(-0.936925\pi\)
0.980431 0.196863i \(-0.0630754\pi\)
\(558\) 1.83093e35 + 1.92284e34i 0.360104 + 0.0378180i
\(559\) 1.17470e36 2.25721
\(560\) 2.73106e35i 0.512728i
\(561\) 4.74229e35 + 5.26640e35i 0.869903 + 0.966043i
\(562\) −5.37090e34 −0.0962665
\(563\) 6.33217e35i 1.10903i −0.832173 0.554515i \(-0.812904\pi\)
0.832173 0.554515i \(-0.187096\pi\)
\(564\) 4.58350e35 4.12735e35i 0.784456 0.706387i
\(565\) −8.30950e35 −1.38978
\(566\) 1.79430e35i 0.293280i
\(567\) −4.57227e35 9.71067e34i −0.730386 0.155121i
\(568\) −1.97676e34 −0.0308621
\(569\) 3.30032e35i 0.503612i 0.967778 + 0.251806i \(0.0810245\pi\)
−0.967778 + 0.251806i \(0.918976\pi\)
\(570\) −1.45930e34 1.62058e34i −0.0217657 0.0241712i
\(571\) −1.69115e35 −0.246554 −0.123277 0.992372i \(-0.539340\pi\)
−0.123277 + 0.992372i \(0.539340\pi\)
\(572\) 6.67672e35i 0.951513i
\(573\) −4.59557e35 + 4.13821e35i −0.640220 + 0.576505i
\(574\) −6.23270e34 −0.0848831
\(575\) 4.80919e35i 0.640309i
\(576\) −1.44409e34 + 1.37507e35i −0.0187976 + 0.178991i
\(577\) 1.26120e36 1.60509 0.802544 0.596592i \(-0.203479\pi\)
0.802544 + 0.596592i \(0.203479\pi\)
\(578\) 4.63534e35i 0.576793i
\(579\) −1.85351e35 2.05836e35i −0.225514 0.250438i
\(580\) −1.01609e35 −0.120884
\(581\) 8.43199e35i 0.980936i
\(582\) 2.45407e35 2.20984e35i 0.279183 0.251398i
\(583\) −6.22619e35 −0.692677
\(584\) 2.83367e35i 0.308306i
\(585\) −1.57262e36 1.65156e35i −1.67340 0.175739i
\(586\) 2.30924e35 0.240325
\(587\) 1.21848e36i 1.24029i 0.784487 + 0.620146i \(0.212927\pi\)
−0.784487 + 0.620146i \(0.787073\pi\)
\(588\) 2.50870e35 + 2.78596e35i 0.249772 + 0.277376i
\(589\) 6.25091e34 0.0608757
\(590\) 3.12205e35i 0.297416i
\(591\) −9.06130e35 + 8.15952e35i −0.844410 + 0.760374i
\(592\) 1.02403e35 0.0933532
\(593\) 1.08175e36i 0.964756i −0.875963 0.482378i \(-0.839773\pi\)
0.875963 0.482378i \(-0.160227\pi\)
\(594\) −3.04024e35 + 2.20944e35i −0.265267 + 0.192779i
\(595\) 1.69622e36 1.44798
\(596\) 1.42376e36i 1.18915i
\(597\) 5.51211e35 + 6.12131e35i 0.450456 + 0.500239i
\(598\) 8.13367e35 0.650386
\(599\) 1.32797e36i 1.03906i −0.854454 0.519528i \(-0.826108\pi\)
0.854454 0.519528i \(-0.173892\pi\)
\(600\) 3.74868e35 3.37561e35i 0.287020 0.258456i
\(601\) −1.28827e36 −0.965248 −0.482624 0.875828i \(-0.660316\pi\)
−0.482624 + 0.875828i \(0.660316\pi\)
\(602\) 6.68244e35i 0.489982i
\(603\) 2.03243e35 1.93528e36i 0.145844 1.38873i
\(604\) 1.17897e34 0.00827982
\(605\) 5.62429e35i 0.386587i
\(606\) −1.78381e35 1.98096e35i −0.120007 0.133270i
\(607\) 3.53784e35 0.232962 0.116481 0.993193i \(-0.462839\pi\)
0.116481 + 0.993193i \(0.462839\pi\)
\(608\) 9.78749e34i 0.0630848i
\(609\) 1.01895e35 9.17545e34i 0.0642878 0.0578899i
\(610\) −1.09116e36 −0.673911
\(611\) 2.81577e36i 1.70240i
\(612\) 2.22247e36 + 2.33403e35i 1.31543 + 0.138146i
\(613\) 1.14461e36 0.663242 0.331621 0.943413i \(-0.392405\pi\)
0.331621 + 0.943413i \(0.392405\pi\)
\(614\) 1.04789e35i 0.0594465i
\(615\) −4.28304e35 4.75639e35i −0.237889 0.264181i
\(616\) −8.30059e35 −0.451398
\(617\) 3.77998e35i 0.201271i 0.994923 + 0.100636i \(0.0320876\pi\)
−0.994923 + 0.100636i \(0.967912\pi\)
\(618\) 3.06704e35 2.76181e35i 0.159908 0.143994i
\(619\) −8.13578e35 −0.415356 −0.207678 0.978197i \(-0.566591\pi\)
−0.207678 + 0.978197i \(0.566591\pi\)
\(620\) 1.91065e36i 0.955189i
\(621\) 1.45154e36 + 1.99735e36i 0.710624 + 0.977831i
\(622\) −6.95249e35 −0.333323
\(623\) 2.64095e36i 1.23998i
\(624\) −1.09914e36 1.22062e36i −0.505423 0.561281i
\(625\) −2.77360e36 −1.24912
\(626\) 5.50248e35i 0.242713i
\(627\) −9.48278e34 + 8.53905e34i −0.0409692 + 0.0368919i
\(628\) −2.89103e36 −1.22343
\(629\) 6.36008e35i 0.263636i
\(630\) −9.39516e34 + 8.94610e35i −0.0381485 + 0.363251i
\(631\) 2.20267e36 0.876130 0.438065 0.898943i \(-0.355664\pi\)
0.438065 + 0.898943i \(0.355664\pi\)
\(632\) 5.91810e35i 0.230600i
\(633\) 1.10011e36 + 1.22170e36i 0.419942 + 0.466354i
\(634\) 6.11998e35 0.228870
\(635\) 3.32954e36i 1.21990i
\(636\) −1.45895e36 + 1.31375e36i −0.523718 + 0.471597i
\(637\) −1.71149e36 −0.601953
\(638\) 1.10249e35i 0.0379931i
\(639\) 1.24665e35 + 1.30922e34i 0.0420952 + 0.00442082i
\(640\) 3.81246e36 1.26144
\(641\) 4.59533e36i 1.48992i −0.667110 0.744959i \(-0.732469\pi\)
0.667110 0.744959i \(-0.267531\pi\)
\(642\) −1.68445e35 1.87061e35i −0.0535183 0.0594331i
\(643\) −9.02499e35 −0.280998 −0.140499 0.990081i \(-0.544871\pi\)
−0.140499 + 0.990081i \(0.544871\pi\)
\(644\) 2.49528e36i 0.761383i
\(645\) 5.09961e36 4.59209e36i 1.52497 1.37320i
\(646\) −1.40696e35 −0.0412344
\(647\) 5.93690e36i 1.70531i −0.522473 0.852656i \(-0.674990\pi\)
0.522473 0.852656i \(-0.325010\pi\)
\(648\) −5.38051e35 + 2.53342e36i −0.151478 + 0.713233i
\(649\) 1.82686e36 0.504108
\(650\) 1.05376e36i 0.285016i
\(651\) −1.72534e36 1.91603e36i −0.457428 0.507983i
\(652\) −6.91753e35 −0.179776
\(653\) 1.77971e36i 0.453396i 0.973965 + 0.226698i \(0.0727930\pi\)
−0.973965 + 0.226698i \(0.927207\pi\)
\(654\) −3.53824e35 + 3.18611e35i −0.0883642 + 0.0795702i
\(655\) 2.29787e36 0.562585
\(656\) 6.64871e35i 0.159583i
\(657\) 1.87676e35 1.78706e36i 0.0441631 0.420522i
\(658\) 1.60179e36 0.369547
\(659\) 5.05032e36i 1.14238i 0.820819 + 0.571188i \(0.193517\pi\)
−0.820819 + 0.571188i \(0.806483\pi\)
\(660\) −2.61004e36 2.89850e36i −0.578864 0.642840i
\(661\) −7.89441e35 −0.171672 −0.0858362 0.996309i \(-0.527356\pi\)
−0.0858362 + 0.996309i \(0.527356\pi\)
\(662\) 3.19307e36i 0.680855i
\(663\) −7.58109e36 + 6.82662e36i −1.58510 + 1.42735i
\(664\) 4.67202e36 0.957899
\(665\) 3.05425e35i 0.0614077i
\(666\) 3.35439e35 + 3.52277e34i 0.0661377 + 0.00694575i
\(667\) −7.24304e35 −0.140051
\(668\) 2.94293e36i 0.558066i
\(669\) −4.63109e35 5.14291e35i −0.0861279 0.0956466i
\(670\) −3.74480e36 −0.683057
\(671\) 6.38491e36i 1.14225i
\(672\) −3.00006e36 + 2.70150e36i −0.526417 + 0.474028i
\(673\) 3.68376e36 0.634008 0.317004 0.948424i \(-0.397323\pi\)
0.317004 + 0.948424i \(0.397323\pi\)
\(674\) 2.05950e36i 0.347682i
\(675\) −2.58768e36 + 1.88056e36i −0.428511 + 0.311414i
\(676\) 4.41812e36 0.717679
\(677\) 6.57244e36i 1.04731i 0.851931 + 0.523653i \(0.175431\pi\)
−0.851931 + 0.523653i \(0.824569\pi\)
\(678\) −1.90242e36 2.11268e36i −0.297386 0.330253i
\(679\) −4.62509e36 −0.709273
\(680\) 9.39847e36i 1.41397i
\(681\) 8.26747e36 7.44469e36i 1.22028 1.09884i
\(682\) −2.07311e36 −0.300210
\(683\) 1.77368e36i 0.252003i 0.992030 + 0.126001i \(0.0402144\pi\)
−0.992030 + 0.126001i \(0.959786\pi\)
\(684\) −4.20269e34 + 4.00182e35i −0.00585866 + 0.0557863i
\(685\) −7.46015e36 −1.02040
\(686\) 3.17398e36i 0.425982i
\(687\) 3.88550e36 + 4.31493e36i 0.511693 + 0.568245i
\(688\) 7.12847e36 0.921184
\(689\) 8.96273e36i 1.13655i
\(690\) 3.53099e36 3.17959e36i 0.439399 0.395670i
\(691\) −2.55446e36 −0.311949 −0.155975 0.987761i \(-0.549852\pi\)
−0.155975 + 0.987761i \(0.549852\pi\)
\(692\) 3.54560e36i 0.424923i
\(693\) 5.23478e36 + 5.49755e35i 0.615696 + 0.0646602i
\(694\) 6.73080e36 0.776951
\(695\) 6.52287e36i 0.738986i
\(696\) −5.08395e35 5.64583e35i −0.0565303 0.0627780i
\(697\) −4.12942e36 −0.450674
\(698\) 5.51328e36i 0.590595i
\(699\) −4.34432e36 + 3.91197e36i −0.456792 + 0.411332i
\(700\) −3.23278e36 −0.333658
\(701\) 1.82234e37i 1.84627i −0.384481 0.923133i \(-0.625620\pi\)
0.384481 0.923133i \(-0.374380\pi\)
\(702\) −3.18054e36 4.37649e36i −0.316314 0.435254i
\(703\) 1.14521e35 0.0111806
\(704\) 1.55695e36i 0.149221i
\(705\) 1.10073e37 + 1.22239e37i 1.03567 + 1.15014i
\(706\) 6.41910e36 0.592943
\(707\) 3.73343e36i 0.338576i
\(708\) 4.28077e36 3.85475e36i 0.381145 0.343213i
\(709\) −1.90577e37 −1.66598 −0.832990 0.553288i \(-0.813373\pi\)
−0.832990 + 0.553288i \(0.813373\pi\)
\(710\) 2.41228e35i 0.0207047i
\(711\) 3.91960e35 3.73226e36i 0.0330322 0.314533i
\(712\) −1.46330e37 −1.21086
\(713\) 1.36197e37i 1.10664i
\(714\) 3.88342e36 + 4.31262e36i 0.309840 + 0.344084i
\(715\) 1.78063e37 1.39507
\(716\) 7.87017e36i 0.605501i
\(717\) 6.57858e35 5.92388e35i 0.0497031 0.0447566i
\(718\) −2.28020e36 −0.169182
\(719\) 2.36064e37i 1.72010i 0.510207 + 0.860052i \(0.329569\pi\)
−0.510207 + 0.860052i \(0.670431\pi\)
\(720\) −9.54322e36 1.00223e36i −0.682924 0.0717205i
\(721\) −5.78034e36 −0.406252
\(722\) 5.70439e36i 0.393755i
\(723\) −8.25514e36 9.16749e36i −0.559663 0.621516i
\(724\) −1.16912e37 −0.778498
\(725\) 9.38376e35i 0.0613738i
\(726\) −1.42997e36 + 1.28765e36i −0.0918649 + 0.0827224i
\(727\) 1.46646e36 0.0925385 0.0462692 0.998929i \(-0.485267\pi\)
0.0462692 + 0.998929i \(0.485267\pi\)
\(728\) 1.19489e37i 0.740660i
\(729\) 5.07113e36 1.56207e37i 0.308778 0.951134i
\(730\) −3.45799e36 −0.206836
\(731\) 4.42739e37i 2.60149i
\(732\) 1.34724e37 + 1.49614e37i 0.777682 + 0.863631i
\(733\) 8.03765e36 0.455803 0.227901 0.973684i \(-0.426814\pi\)
0.227901 + 0.973684i \(0.426814\pi\)
\(734\) 8.42230e35i 0.0469226i
\(735\) −7.42995e36 + 6.69052e36i −0.406678 + 0.366205i
\(736\) 2.13254e37 1.14680
\(737\) 2.19126e37i 1.15775i
\(738\) 2.28723e35 2.17791e36i 0.0118735 0.113059i
\(739\) 1.99427e37 1.01720 0.508600 0.861003i \(-0.330163\pi\)
0.508600 + 0.861003i \(0.330163\pi\)
\(740\) 3.50044e36i 0.175433i
\(741\) −1.22921e36 1.36507e36i −0.0605328 0.0672228i
\(742\) −5.09858e36 −0.246717
\(743\) 1.63133e37i 0.775689i −0.921725 0.387845i \(-0.873220\pi\)
0.921725 0.387845i \(-0.126780\pi\)
\(744\) −1.06164e37 + 9.55983e36i −0.496053 + 0.446685i
\(745\) 3.79706e37 1.74348
\(746\) 9.63409e36i 0.434716i
\(747\) −2.94642e37 3.09432e36i −1.30655 0.137214i
\(748\) −2.51643e37 −1.09664
\(749\) 3.52547e36i 0.150992i
\(750\) −3.65715e36 4.06133e36i −0.153938 0.170951i
\(751\) 2.87515e37 1.18944 0.594718 0.803934i \(-0.297264\pi\)
0.594718 + 0.803934i \(0.297264\pi\)
\(752\) 1.70871e37i 0.694761i
\(753\) 2.42918e36 2.18743e36i 0.0970790 0.0874177i
\(754\) 1.58705e36 0.0623396
\(755\) 3.14421e35i 0.0121395i
\(756\) 1.34264e37 9.75740e36i 0.509537 0.370298i
\(757\) −2.47242e37 −0.922308 −0.461154 0.887320i \(-0.652564\pi\)
−0.461154 + 0.887320i \(0.652564\pi\)
\(758\) 7.06134e36i 0.258933i
\(759\) −1.86053e37 2.06615e37i −0.670645 0.744764i
\(760\) 1.69231e36 0.0599656
\(761\) 3.81096e36i 0.132750i −0.997795 0.0663749i \(-0.978857\pi\)
0.997795 0.0663749i \(-0.0211433\pi\)
\(762\) −8.46530e36 + 7.62283e36i −0.289886 + 0.261037i
\(763\) 6.66839e36 0.224492
\(764\) 2.19589e37i 0.726769i
\(765\) −6.22468e36 + 5.92716e37i −0.202544 + 1.92863i
\(766\) −1.50201e37 −0.480505
\(767\) 2.62980e37i 0.827147i
\(768\) 4.83405e36 + 5.36831e36i 0.149491 + 0.166013i
\(769\) −5.50932e37 −1.67516 −0.837579 0.546317i \(-0.816030\pi\)
−0.837579 + 0.546317i \(0.816030\pi\)
\(770\) 1.01294e37i 0.302833i
\(771\) 1.75284e37 1.57840e37i 0.515270 0.463990i
\(772\) 9.83541e36 0.284294
\(773\) 4.07752e37i 1.15895i 0.814991 + 0.579473i \(0.196742\pi\)
−0.814991 + 0.579473i \(0.803258\pi\)
\(774\) 2.33506e37 + 2.45228e36i 0.652629 + 0.0685389i
\(775\) −1.76451e37 −0.484957
\(776\) 2.56268e37i 0.692616i
\(777\) −3.16095e36 3.51029e36i −0.0840125 0.0932975i
\(778\) 2.26034e37 0.590797
\(779\) 7.43550e35i 0.0191128i
\(780\) 4.17246e37 3.75721e37i 1.05478 0.949809i
\(781\) −1.41154e36 −0.0350937
\(782\) 3.06555e37i 0.749584i
\(783\) 2.83228e36 + 3.89726e36i 0.0681134 + 0.0937253i
\(784\) −1.03859e37 −0.245661
\(785\) 7.71017e37i 1.79373i
\(786\) 5.26086e36 + 5.84228e36i 0.120383 + 0.133687i
\(787\) 7.37959e37 1.66097 0.830483 0.557044i \(-0.188065\pi\)
0.830483 + 0.557044i \(0.188065\pi\)
\(788\) 4.32974e37i 0.958564i
\(789\) −4.74475e36 + 4.27255e36i −0.103327 + 0.0930435i
\(790\) −7.22198e36 −0.154705
\(791\) 3.98168e37i 0.839019i
\(792\) 3.04609e36 2.90050e37i 0.0631416 0.601236i
\(793\) −9.19121e37 −1.87422
\(794\) 3.49865e37i 0.701834i
\(795\) −3.50368e37 3.89091e37i −0.691436 0.767853i
\(796\) −2.92493e37 −0.567866
\(797\) 1.96755e37i 0.375809i 0.982187 + 0.187905i \(0.0601696\pi\)
−0.982187 + 0.187905i \(0.939830\pi\)
\(798\) −7.76538e35 + 6.99256e35i −0.0145923 + 0.0131401i
\(799\) 1.06125e38 1.96205
\(800\) 2.76283e37i 0.502555i
\(801\) 9.22834e37 + 9.69157e36i 1.65158 + 0.173449i
\(802\) −2.69766e37 −0.475030
\(803\) 2.02343e37i 0.350579i
\(804\) 4.62365e37 + 5.13466e37i 0.788237 + 0.875352i
\(805\) −6.65473e37 −1.11631
\(806\) 2.98428e37i 0.492588i
\(807\) −3.51007e37 + 3.16075e37i −0.570112 + 0.513374i
\(808\) 2.06863e37 0.330625
\(809\) 4.85719e37i 0.763931i −0.924177 0.381966i \(-0.875247\pi\)
0.924177 0.381966i \(-0.124753\pi\)
\(810\) −3.09158e37 6.56596e36i −0.478493 0.101623i
\(811\) −8.26891e37 −1.25944 −0.629719 0.776823i \(-0.716830\pi\)
−0.629719 + 0.776823i \(0.716830\pi\)
\(812\) 4.86883e36i 0.0729787i
\(813\) −1.46013e37 1.62150e37i −0.215384 0.239188i
\(814\) −3.79807e36 −0.0551374
\(815\) 1.84485e37i 0.263581i
\(816\) −4.60047e37 + 4.14263e37i −0.646889 + 0.582511i
\(817\) 7.97204e36 0.110327
\(818\) 5.18882e36i 0.0706765i
\(819\) −7.91383e36 + 7.53557e37i −0.106095 + 1.01024i
\(820\) 2.27274e37 0.299895
\(821\) 8.74647e37i 1.13598i 0.823035 + 0.567991i \(0.192279\pi\)
−0.823035 + 0.567991i \(0.807721\pi\)
\(822\) −1.70797e37 1.89673e37i −0.218346 0.242478i
\(823\) 1.11665e38 1.40514 0.702568 0.711616i \(-0.252037\pi\)
0.702568 + 0.711616i \(0.252037\pi\)
\(824\) 3.20279e37i 0.396711i
\(825\) 2.67681e37 2.41041e37i 0.326375 0.293894i
\(826\) 1.49600e37 0.179552
\(827\) 1.30092e38i 1.53702i −0.639840 0.768508i \(-0.720999\pi\)
0.639840 0.768508i \(-0.279001\pi\)
\(828\) −8.71933e37 9.15701e36i −1.01412 0.106502i
\(829\) −3.22666e36 −0.0369440 −0.0184720 0.999829i \(-0.505880\pi\)
−0.0184720 + 0.999829i \(0.505880\pi\)
\(830\) 5.70137e37i 0.642634i
\(831\) −8.02156e37 8.90809e37i −0.890113 0.988488i
\(832\) 2.24126e37 0.244843
\(833\) 6.45055e37i 0.693764i
\(834\) 1.65843e37 1.49338e37i 0.175605 0.158129i
\(835\) 7.84857e37 0.818213
\(836\) 4.53113e36i 0.0465077i
\(837\) 7.32838e37 5.32579e37i 0.740589 0.538211i
\(838\) 3.14539e37 0.312970
\(839\) 1.31088e38i 1.28427i −0.766592 0.642135i \(-0.778049\pi\)
0.766592 0.642135i \(-0.221951\pi\)
\(840\) −4.67102e37 5.18725e37i −0.450589 0.500388i
\(841\) 1.03867e38 0.986576
\(842\) 7.29368e37i 0.682165i
\(843\) −1.96400e37 + 1.76854e37i −0.180876 + 0.162876i
\(844\) −5.83761e37 −0.529399
\(845\) 1.17828e38i 1.05223i
\(846\) −5.87815e36 + 5.59719e37i −0.0516923 + 0.492216i
\(847\) 2.69500e37 0.233386
\(848\) 5.43889e37i 0.463836i
\(849\) 5.90830e37 + 6.56129e37i 0.496207 + 0.551047i
\(850\) 3.97159e37 0.328487
\(851\) 2.49523e37i 0.203248i
\(852\) −3.30758e36 + 2.97841e36i −0.0265336 + 0.0238930i
\(853\) −8.59530e37 −0.679084 −0.339542 0.940591i \(-0.610272\pi\)
−0.339542 + 0.940591i \(0.610272\pi\)
\(854\) 5.22855e37i 0.406845i
\(855\) −1.06725e37 1.12083e36i −0.0817916 0.00858973i
\(856\) 1.95340e37 0.147446
\(857\) 1.69202e38i 1.25793i −0.777434 0.628964i \(-0.783479\pi\)
0.777434 0.628964i \(-0.216521\pi\)
\(858\) 4.07668e37 + 4.52723e37i 0.298519 + 0.331511i
\(859\) −2.10542e38 −1.51854 −0.759272 0.650773i \(-0.774445\pi\)
−0.759272 + 0.650773i \(0.774445\pi\)
\(860\) 2.43673e38i 1.73112i
\(861\) −2.27913e37 + 2.05231e37i −0.159488 + 0.143616i
\(862\) 1.52298e37 0.104978
\(863\) 3.73003e37i 0.253263i −0.991950 0.126632i \(-0.959583\pi\)
0.991950 0.126632i \(-0.0404166\pi\)
\(864\) −8.33897e37 1.14746e38i −0.557742 0.767464i
\(865\) −9.45584e37 −0.623004
\(866\) 7.67021e37i 0.497822i
\(867\) 1.52633e38 + 1.69502e38i 0.975889 + 1.08374i
\(868\) 9.15531e37 0.576656
\(869\) 4.22592e37i 0.262219i
\(870\) 6.88973e36 6.20406e36i 0.0421165 0.0379250i
\(871\) −3.15436e38 −1.89966
\(872\) 3.69483e37i 0.219220i
\(873\) 1.69729e37 1.61616e38i 0.0992133 0.944711i
\(874\) 5.51988e36 0.0317893
\(875\) 7.65424e37i 0.434308i
\(876\) 4.26953e37 + 4.74139e37i 0.238686 + 0.265065i
\(877\) −6.36707e37 −0.350708 −0.175354 0.984505i \(-0.556107\pi\)
−0.175354 + 0.984505i \(0.556107\pi\)
\(878\) 1.28994e38i 0.700066i
\(879\) 8.44426e37 7.60389e37i 0.451551 0.406612i
\(880\) 1.08055e38 0.569338
\(881\) 1.20838e37i 0.0627359i −0.999508 0.0313679i \(-0.990014\pi\)
0.999508 0.0313679i \(-0.00998636\pi\)
\(882\) −3.40211e37 3.57288e36i −0.174043 0.0182779i
\(883\) 2.84990e38 1.43662 0.718308 0.695726i \(-0.244917\pi\)
0.718308 + 0.695726i \(0.244917\pi\)
\(884\) 3.62246e38i 1.79938i
\(885\) 1.02803e38 + 1.14165e38i 0.503205 + 0.558818i
\(886\) −1.01992e38 −0.491959
\(887\) 3.48761e38i 1.65776i 0.559429 + 0.828878i \(0.311020\pi\)
−0.559429 + 0.828878i \(0.688980\pi\)
\(888\) −1.94499e37 + 1.75142e37i −0.0911064 + 0.0820395i
\(889\) 1.59542e38 0.736466
\(890\) 1.78570e38i 0.812341i
\(891\) −3.84205e37 + 1.80903e38i −0.172247 + 0.811027i
\(892\) 2.45743e37 0.108577
\(893\) 1.91091e37i 0.0832093i
\(894\) 8.69320e37 + 9.65396e37i 0.373071 + 0.414303i
\(895\) −2.09892e38 −0.887760
\(896\) 1.82682e38i 0.761539i
\(897\) 2.97426e38 2.67826e38i 1.22202 1.10040i
\(898\) −6.45642e37 −0.261457
\(899\) 2.65750e37i 0.106071i
\(900\) 1.18634e37 1.12964e38i 0.0466721 0.444413i
\(901\) −3.37802e38 −1.30990
\(902\) 2.46598e37i 0.0942550i
\(903\) −2.20040e38 2.44359e38i −0.829013 0.920635i
\(904\) 2.20618e38 0.819315
\(905\) 3.11796e38i 1.14140i
\(906\) −7.99411e35 + 7.19854e35i −0.00288472 + 0.00259763i
\(907\) −8.23661e37 −0.292991 −0.146495 0.989211i \(-0.546799\pi\)
−0.146495 + 0.989211i \(0.546799\pi\)
\(908\) 3.95042e38i 1.38525i
\(909\) −1.30458e38 1.37007e37i −0.450964 0.0473601i
\(910\) 1.45815e38 0.496893
\(911\) 5.93021e38i 1.99219i 0.0882755 + 0.996096i \(0.471864\pi\)
−0.0882755 + 0.996096i \(0.528136\pi\)
\(912\) −7.45929e36 8.28369e36i −0.0247039 0.0274341i
\(913\) 3.33613e38 1.08924
\(914\) 3.99124e37i 0.128472i
\(915\) −3.99010e38 + 3.59300e38i −1.26622 + 1.14021i
\(916\) −2.06179e38 −0.645065
\(917\) 1.10107e38i 0.339637i
\(918\) −1.64948e38 + 1.19873e38i −0.501640 + 0.364559i
\(919\) 3.88502e38 1.16491 0.582453 0.812864i \(-0.302093\pi\)
0.582453 + 0.812864i \(0.302093\pi\)
\(920\) 3.68727e38i 1.09009i
\(921\) −3.45050e37 3.83185e37i −0.100579 0.111695i
\(922\) −1.23906e38 −0.356116
\(923\) 2.03194e37i 0.0575823i
\(924\) −1.38888e38 + 1.25066e38i −0.388088 + 0.349465i
\(925\) −3.23271e37 −0.0890685
\(926\) 8.10311e37i 0.220145i
\(927\) 2.12123e37 2.01984e38i 0.0568266 0.541104i
\(928\) 4.16105e37 0.109921
\(929\) 4.97643e38i 1.29632i −0.761502 0.648162i \(-0.775538\pi\)
0.761502 0.648162i \(-0.224462\pi\)
\(930\) −1.16661e38 1.29554e38i −0.299672 0.332791i
\(931\) −1.16150e37 −0.0294220
\(932\) 2.07584e38i 0.518545i
\(933\) −2.54234e38 + 2.28933e38i −0.626285 + 0.563957i
\(934\) 2.45876e38 0.597321
\(935\) 6.71114e38i 1.60785i
\(936\) 4.17533e38 + 4.38492e37i 0.986517 + 0.103604i
\(937\) 8.43272e38 1.96496 0.982478 0.186378i \(-0.0596750\pi\)
0.982478 + 0.186378i \(0.0596750\pi\)
\(938\) 1.79441e38i 0.412367i
\(939\) −1.81187e38 2.01211e38i −0.410651 0.456036i
\(940\) −5.84089e38 −1.30562
\(941\) 8.27185e37i 0.182363i −0.995834 0.0911817i \(-0.970936\pi\)
0.995834 0.0911817i \(-0.0290644\pi\)
\(942\) 1.96030e38 1.76521e38i 0.426246 0.383826i
\(943\) 1.62008e38 0.347444
\(944\) 1.59585e38i 0.337565i
\(945\) 2.60223e38 + 3.58071e38i 0.542915 + 0.747061i
\(946\) −2.64392e38 −0.544081
\(947\) 9.84098e36i 0.0199751i 0.999950 + 0.00998754i \(0.00317919\pi\)
−0.999950 + 0.00998754i \(0.996821\pi\)
\(948\) 8.91687e37 + 9.90236e37i 0.178527 + 0.198258i
\(949\) −2.91277e38 −0.575235
\(950\) 7.15132e36i 0.0139309i
\(951\) 2.23791e38 2.01520e38i 0.430028 0.387231i
\(952\) −4.50348e38 −0.853627
\(953\) 4.90868e37i 0.0917820i 0.998946 + 0.0458910i \(0.0146127\pi\)
−0.998946 + 0.0458910i \(0.985387\pi\)
\(954\) 1.87104e37 1.78161e38i 0.0345108 0.328612i
\(955\) 5.85627e38 1.06556
\(956\) 3.14343e37i 0.0564223i
\(957\) −3.63028e37 4.03150e37i −0.0642814 0.0713857i
\(958\) 6.35511e37 0.111012
\(959\) 3.57470e38i 0.616024i
\(960\) 9.72976e37 8.76145e37i 0.165415 0.148953i
\(961\) −9.65015e37 −0.161856
\(962\) 5.46741e37i 0.0904702i
\(963\) −1.23192e38 1.29375e37i −0.201112 0.0211208i
\(964\) 4.38048e38 0.705538
\(965\) 2.62303e38i 0.416820i
\(966\) −1.52357e38 1.69195e38i −0.238869 0.265269i
\(967\) −1.06101e39 −1.64126 −0.820629 0.571462i \(-0.806377\pi\)
−0.820629 + 0.571462i \(0.806377\pi\)
\(968\) 1.49325e38i 0.227905i
\(969\) −5.14488e37 + 4.63286e37i −0.0774758 + 0.0697654i
\(970\) −3.12730e38 −0.464662
\(971\) 4.24410e38i 0.622207i 0.950376 + 0.311104i \(0.100699\pi\)
−0.950376 + 0.311104i \(0.899301\pi\)
\(972\) 2.91685e38 + 5.04969e38i 0.421941 + 0.730471i
\(973\) −3.12557e38 −0.446132
\(974\) 2.07284e38i 0.291944i
\(975\) 3.46984e38 + 3.85333e38i 0.482225 + 0.535520i
\(976\) −5.57754e38 −0.764883
\(977\) 1.44920e38i 0.196109i 0.995181 + 0.0980547i \(0.0312620\pi\)
−0.995181 + 0.0980547i \(0.968738\pi\)
\(978\) 4.69051e37 4.22371e37i 0.0626347 0.0564013i
\(979\) −1.04490e39 −1.37689
\(980\) 3.55023e38i 0.461656i
\(981\) −2.44712e37 + 2.33015e38i −0.0314020 + 0.299011i
\(982\) 1.27996e38 0.162086
\(983\) 8.89643e38i 1.11178i −0.831255 0.555891i \(-0.812377\pi\)
0.831255 0.555891i \(-0.187623\pi\)
\(984\) 1.13715e38 + 1.26283e38i 0.140243 + 0.155743i
\(985\) 1.15471e39 1.40541
\(986\) 5.98154e37i 0.0718478i
\(987\) 5.85733e38 5.27440e38i 0.694347 0.625245i
\(988\) 6.52266e37 0.0763105
\(989\) 1.73698e39i 2.00560i
\(990\) 3.53954e38 + 3.71721e37i 0.403357 + 0.0423604i
\(991\) 1.20951e39 1.36035 0.680176 0.733048i \(-0.261903\pi\)
0.680176 + 0.733048i \(0.261903\pi\)
\(992\) 7.82440e38i 0.868559i
\(993\) −1.05142e39 1.16762e39i −1.15196 1.27927i
\(994\) −1.15590e37 −0.0124996
\(995\) 7.80057e38i 0.832581i
\(996\) 7.81738e38 7.03939e38i 0.823550 0.741590i
\(997\) −1.34485e39 −1.39842 −0.699211 0.714915i \(-0.746465\pi\)
−0.699211 + 0.714915i \(0.746465\pi\)
\(998\) 2.26590e38i 0.232565i
\(999\) 1.34261e38 9.75720e37i 0.136019 0.0988494i
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 3.27.b.a.2.4 8
3.2 odd 2 inner 3.27.b.a.2.5 yes 8
4.3 odd 2 48.27.e.d.17.6 8
12.11 even 2 48.27.e.d.17.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.27.b.a.2.4 8 1.1 even 1 trivial
3.27.b.a.2.5 yes 8 3.2 odd 2 inner
48.27.e.d.17.5 8 12.11 even 2
48.27.e.d.17.6 8 4.3 odd 2