Properties

Label 43.10.e.a.4.9
Level $43$
Weight $10$
Character 43.4
Analytic conductor $22.147$
Analytic rank $0$
Dimension $192$
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] = [43,10,Mod(4,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.e (of order \(7\), degree \(6\), 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: \(22.1465409550\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 4.9
Character \(\chi\) \(=\) 43.4
Dual form 43.10.e.a.11.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-15.4630 + 19.3900i) q^{2} +(-85.3477 - 107.023i) q^{3} +(-22.9363 - 100.491i) q^{4} +(-767.251 - 369.489i) q^{5} +3394.90 q^{6} -181.232 q^{7} +(-9137.29 - 4400.29i) q^{8} +(210.268 - 921.243i) q^{9} +O(q^{10})\) \(q+(-15.4630 + 19.3900i) q^{2} +(-85.3477 - 107.023i) q^{3} +(-22.9363 - 100.491i) q^{4} +(-767.251 - 369.489i) q^{5} +3394.90 q^{6} -181.232 q^{7} +(-9137.29 - 4400.29i) q^{8} +(210.268 - 921.243i) q^{9} +(19028.4 - 9163.58i) q^{10} +(16914.7 - 74108.0i) q^{11} +(-8797.21 + 11031.4i) q^{12} +(95053.5 + 45775.3i) q^{13} +(2802.38 - 3514.08i) q^{14} +(25939.5 + 113648. i) q^{15} +(274159. - 132028. i) q^{16} +(-374184. + 180197. i) q^{17} +(14611.5 + 18322.2i) q^{18} +(114037. + 499630. i) q^{19} +(-19532.2 + 85576.3i) q^{20} +(15467.7 + 19395.9i) q^{21} +(1.17540e6 + 1.47391e6i) q^{22} +(428096. - 1.87561e6i) q^{23} +(308916. + 1.35345e6i) q^{24} +(-765601. - 960033. i) q^{25} +(-2.35739e6 + 1.13526e6i) q^{26} +(-2.54406e6 + 1.22516e6i) q^{27} +(4156.79 + 18212.1i) q^{28} +(-1.40720e6 + 1.76457e6i) q^{29} +(-2.60474e6 - 1.25438e6i) q^{30} +(-4.51421e6 + 5.66064e6i) q^{31} +(-523857. + 2.29517e6i) q^{32} +(-9.37485e6 + 4.51469e6i) q^{33} +(2.29197e6 - 1.00418e7i) q^{34} +(139050. + 66963.0i) q^{35} -97399.0 q^{36} -1.99202e6 q^{37} +(-1.14512e7 - 5.51459e6i) q^{38} +(-3.21360e6 - 1.40797e7i) q^{39} +(5.38474e6 + 6.75225e6i) q^{40} +(-1.20615e7 + 1.51246e7i) q^{41} -615262. q^{42} +(1.37755e7 + 1.76869e7i) q^{43} -7.83512e6 q^{44} +(-501717. + 629133. i) q^{45} +(2.97484e7 + 3.73033e7i) q^{46} +(7.88417e6 + 3.45428e7i) q^{47} +(-3.75289e7 - 1.80730e7i) q^{48} -4.03208e7 q^{49} +3.04535e7 q^{50} +(5.12209e7 + 2.46667e7i) q^{51} +(2.41982e6 - 1.06019e7i) q^{52} +(5.89451e7 - 2.83865e7i) q^{53} +(1.55831e7 - 6.82739e7i) q^{54} +(-4.03599e7 + 5.06097e7i) q^{55} +(1.65597e6 + 797471. i) q^{56} +(4.37389e7 - 5.48468e7i) q^{57} +(-1.24555e7 - 5.45711e7i) q^{58} +(5.08501e7 - 2.44881e7i) q^{59} +(1.08256e7 - 5.21335e6i) q^{60} +(1.07270e8 + 1.34512e8i) q^{61} +(-3.99565e7 - 1.75061e8i) q^{62} +(-38107.1 + 166958. i) q^{63} +(6.07360e7 + 7.61605e7i) q^{64} +(-5.60164e7 - 7.02424e7i) q^{65} +(5.74235e7 - 2.51589e8i) q^{66} +(-4.98143e7 - 2.18251e8i) q^{67} +(2.66905e7 + 3.34689e7i) q^{68} +(-2.37270e8 + 1.14263e8i) q^{69} +(-3.44854e6 + 1.66073e6i) q^{70} +(4.87056e7 + 2.13393e8i) q^{71} +(-5.97501e6 + 7.49242e6i) q^{72} +(-2.71786e8 - 1.30885e8i) q^{73} +(3.08026e7 - 3.86252e7i) q^{74} +(-3.74030e7 + 1.63873e8i) q^{75} +(4.75925e7 - 2.29194e7i) q^{76} +(-3.06547e6 + 1.34307e7i) q^{77} +(3.22697e8 + 1.55403e8i) q^{78} +3.35322e8 q^{79} -2.59132e8 q^{80} +(3.31492e8 + 1.59638e8i) q^{81} +(-1.06760e8 - 4.67744e8i) q^{82} +(-2.01111e8 - 2.52186e8i) q^{83} +(1.59433e6 - 1.99923e6i) q^{84} +3.53674e8 q^{85} +(-5.55960e8 - 6.38497e6i) q^{86} +3.08950e8 q^{87} +(-4.80651e8 + 6.02717e8i) q^{88} +(4.81210e8 + 6.03418e8i) q^{89} +(-4.44083e6 - 1.94566e7i) q^{90} +(-1.72267e7 - 8.29594e6i) q^{91} -1.98300e8 q^{92} +9.91094e8 q^{93} +(-7.91697e8 - 3.81261e8i) q^{94} +(9.71124e7 - 4.25477e8i) q^{95} +(2.90345e8 - 1.39823e8i) q^{96} +(-3.49269e8 + 1.53025e9i) q^{97} +(6.23479e8 - 7.81818e8i) q^{98} +(-6.47148e7 - 3.11650e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q - 23 q^{2} + 141 q^{3} - 7771 q^{4} + 677 q^{5} - 6572 q^{6} - 23872 q^{7} + 40269 q^{8} - 322935 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 192 q - 23 q^{2} + 141 q^{3} - 7771 q^{4} + 677 q^{5} - 6572 q^{6} - 23872 q^{7} + 40269 q^{8} - 322935 q^{9} + 12467 q^{10} + 26107 q^{11} - 8535 q^{12} - 124789 q^{13} + 402537 q^{14} + 536701 q^{15} + 470873 q^{16} + 157321 q^{17} - 126108 q^{18} + 1524020 q^{19} - 3731811 q^{20} - 1204984 q^{21} + 5705415 q^{22} - 1812193 q^{23} + 1656287 q^{24} - 6908369 q^{25} + 11484147 q^{26} + 4196853 q^{27} + 13689789 q^{28} + 14198685 q^{29} - 43510444 q^{30} + 2623633 q^{31} + 68431179 q^{32} + 35109256 q^{33} - 31068733 q^{34} - 25357310 q^{35} + 251714416 q^{36} - 19142308 q^{37} + 119772015 q^{38} - 31427027 q^{39} - 33090881 q^{40} - 50107991 q^{41} - 162738222 q^{42} - 73848259 q^{43} - 321658712 q^{44} + 91481051 q^{45} + 137200254 q^{46} + 17832081 q^{47} + 196320169 q^{48} + 845134600 q^{49} - 440263230 q^{50} - 49676244 q^{51} - 317591839 q^{52} - 69882873 q^{53} - 60806391 q^{54} - 120195607 q^{55} - 926966829 q^{56} + 282620123 q^{57} + 1032073799 q^{58} - 5290157 q^{59} - 1271653181 q^{60} - 217057103 q^{61} - 185133921 q^{62} + 802790658 q^{63} - 1352549483 q^{64} + 503543227 q^{65} - 234740783 q^{66} - 688857817 q^{67} + 1407702672 q^{68} - 234230557 q^{69} - 207245722 q^{70} + 315865545 q^{71} + 2050452844 q^{72} - 1188540917 q^{73} - 580770182 q^{74} - 1096370858 q^{75} - 1030976936 q^{76} + 126981666 q^{77} + 712275668 q^{78} - 355387036 q^{79} + 1135667026 q^{80} + 816824016 q^{81} - 1149421181 q^{82} + 554073368 q^{83} - 5832481562 q^{84} - 6971027678 q^{85} + 3317069529 q^{86} - 3939884094 q^{87} + 5966424645 q^{88} + 172293025 q^{89} + 11626974152 q^{90} + 852733752 q^{91} + 7930102584 q^{92} + 1786213690 q^{93} + 3419396521 q^{94} - 439143565 q^{95} - 7908382084 q^{96} - 619685773 q^{97} - 4402632007 q^{98} - 5258298740 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −15.4630 + 19.3900i −0.683374 + 0.856924i −0.995660 0.0930643i \(-0.970334\pi\)
0.312286 + 0.949988i \(0.398905\pi\)
\(3\) −85.3477 107.023i −0.608340 0.762834i 0.378312 0.925678i \(-0.376505\pi\)
−0.986652 + 0.162844i \(0.947933\pi\)
\(4\) −22.9363 100.491i −0.0447975 0.196271i
\(5\) −767.251 369.489i −0.549000 0.264385i 0.138756 0.990327i \(-0.455690\pi\)
−0.687756 + 0.725942i \(0.741404\pi\)
\(6\) 3394.90 1.06941
\(7\) −181.232 −0.0285294 −0.0142647 0.999898i \(-0.504541\pi\)
−0.0142647 + 0.999898i \(0.504541\pi\)
\(8\) −9137.29 4400.29i −0.788701 0.379819i
\(9\) 210.268 921.243i 0.0106827 0.0468040i
\(10\) 19028.4 9163.58i 0.601730 0.289778i
\(11\) 16914.7 74108.0i 0.348334 1.52615i −0.432627 0.901573i \(-0.642413\pi\)
0.780962 0.624579i \(-0.214729\pi\)
\(12\) −8797.21 + 11031.4i −0.122470 + 0.153572i
\(13\) 95053.5 + 45775.3i 0.923045 + 0.444515i 0.834157 0.551527i \(-0.185954\pi\)
0.0888878 + 0.996042i \(0.471669\pi\)
\(14\) 2802.38 3514.08i 0.0194963 0.0244475i
\(15\) 25939.5 + 113648.i 0.132297 + 0.579632i
\(16\) 274159. 132028.i 1.04583 0.503648i
\(17\) −374184. + 180197.i −1.08659 + 0.523273i −0.889417 0.457097i \(-0.848889\pi\)
−0.197170 + 0.980369i \(0.563175\pi\)
\(18\) 14611.5 + 18322.2i 0.0328072 + 0.0411389i
\(19\) 114037. + 499630.i 0.200750 + 0.879543i 0.970482 + 0.241175i \(0.0775329\pi\)
−0.769732 + 0.638368i \(0.779610\pi\)
\(20\) −19532.2 + 85576.3i −0.0272971 + 0.119597i
\(21\) 15467.7 + 19395.9i 0.0173556 + 0.0217632i
\(22\) 1.17540e6 + 1.47391e6i 1.06975 + 1.34143i
\(23\) 428096. 1.87561e6i 0.318982 1.39755i −0.520360 0.853947i \(-0.674202\pi\)
0.839342 0.543604i \(-0.182941\pi\)
\(24\) 308916. + 1.35345e6i 0.190060 + 0.832707i
\(25\) −765601. 960033.i −0.391988 0.491537i
\(26\) −2.35739e6 + 1.13526e6i −1.01170 + 0.487209i
\(27\) −2.54406e6 + 1.22516e6i −0.921279 + 0.443664i
\(28\) 4156.79 + 18212.1i 0.00127805 + 0.00559949i
\(29\) −1.40720e6 + 1.76457e6i −0.369457 + 0.463285i −0.931456 0.363853i \(-0.881461\pi\)
0.561999 + 0.827138i \(0.310032\pi\)
\(30\) −2.60474e6 1.25438e6i −0.587109 0.282737i
\(31\) −4.51421e6 + 5.66064e6i −0.877919 + 1.10088i 0.116269 + 0.993218i \(0.462906\pi\)
−0.994188 + 0.107657i \(0.965665\pi\)
\(32\) −523857. + 2.29517e6i −0.0883156 + 0.386936i
\(33\) −9.37485e6 + 4.51469e6i −1.37611 + 0.662698i
\(34\) 2.29197e6 1.00418e7i 0.294140 1.28871i
\(35\) 139050. + 66963.0i 0.0156627 + 0.00754274i
\(36\) −97399.0 −0.00966481
\(37\) −1.99202e6 −0.174738 −0.0873688 0.996176i \(-0.527846\pi\)
−0.0873688 + 0.996176i \(0.527846\pi\)
\(38\) −1.14512e7 5.51459e6i −0.890889 0.429029i
\(39\) −3.21360e6 1.40797e7i −0.222434 0.974546i
\(40\) 5.38474e6 + 6.75225e6i 0.332579 + 0.417041i
\(41\) −1.20615e7 + 1.51246e7i −0.666613 + 0.835906i −0.994045 0.108968i \(-0.965245\pi\)
0.327432 + 0.944875i \(0.393817\pi\)
\(42\) −615262. −0.0305097
\(43\) 1.37755e7 + 1.76869e7i 0.614470 + 0.788940i
\(44\) −7.83512e6 −0.315144
\(45\) −501717. + 629133.i −0.0182391 + 0.0228711i
\(46\) 2.97484e7 + 3.73033e7i 0.979611 + 1.22839i
\(47\) 7.88417e6 + 3.45428e7i 0.235676 + 1.03256i 0.944843 + 0.327524i \(0.106214\pi\)
−0.709167 + 0.705041i \(0.750929\pi\)
\(48\) −3.75289e7 1.80730e7i −1.02042 0.491409i
\(49\) −4.03208e7 −0.999186
\(50\) 3.04535e7 0.689084
\(51\) 5.12209e7 + 2.46667e7i 1.06018 + 0.510558i
\(52\) 2.41982e6 1.06019e7i 0.0458952 0.201080i
\(53\) 5.89451e7 2.83865e7i 1.02614 0.494162i 0.156410 0.987692i \(-0.450008\pi\)
0.869729 + 0.493530i \(0.164294\pi\)
\(54\) 1.55831e7 6.82739e7i 0.249391 1.09265i
\(55\) −4.03599e7 + 5.06097e7i −0.594727 + 0.745764i
\(56\) 1.65597e6 + 797471.i 0.0225012 + 0.0108360i
\(57\) 4.37389e7 5.48468e7i 0.548821 0.688200i
\(58\) −1.24555e7 5.45711e7i −0.144522 0.633193i
\(59\) 5.08501e7 2.44881e7i 0.546333 0.263100i −0.140294 0.990110i \(-0.544805\pi\)
0.686627 + 0.727010i \(0.259090\pi\)
\(60\) 1.08256e7 5.21335e6i 0.107838 0.0519321i
\(61\) 1.07270e8 + 1.34512e8i 0.991957 + 1.24387i 0.969745 + 0.244122i \(0.0784996\pi\)
0.0222126 + 0.999753i \(0.492929\pi\)
\(62\) −3.99565e7 1.75061e8i −0.343419 1.50462i
\(63\) −38107.1 + 166958.i −0.000304771 + 0.00133529i
\(64\) 6.07360e7 + 7.61605e7i 0.452518 + 0.567440i
\(65\) −5.60164e7 7.02424e7i −0.389229 0.488078i
\(66\) 5.74235e7 2.51589e8i 0.372513 1.63209i
\(67\) −4.98143e7 2.18251e8i −0.302007 1.32318i −0.867092 0.498147i \(-0.834014\pi\)
0.565085 0.825032i \(-0.308843\pi\)
\(68\) 2.66905e7 + 3.34689e7i 0.151380 + 0.189824i
\(69\) −2.37270e8 + 1.14263e8i −1.26015 + 0.606855i
\(70\) −3.44854e6 + 1.66073e6i −0.0171670 + 0.00826719i
\(71\) 4.87056e7 + 2.13393e8i 0.227466 + 0.996594i 0.951698 + 0.307037i \(0.0993375\pi\)
−0.724232 + 0.689557i \(0.757805\pi\)
\(72\) −5.97501e6 + 7.49242e6i −0.0262025 + 0.0328569i
\(73\) −2.71786e8 1.30885e8i −1.12014 0.539433i −0.220208 0.975453i \(-0.570673\pi\)
−0.899937 + 0.436020i \(0.856388\pi\)
\(74\) 3.08026e7 3.86252e7i 0.119411 0.149737i
\(75\) −3.74030e7 + 1.63873e8i −0.136499 + 0.598043i
\(76\) 4.75925e7 2.29194e7i 0.163636 0.0788027i
\(77\) −3.06547e6 + 1.34307e7i −0.00993777 + 0.0435402i
\(78\) 3.22697e8 + 1.55403e8i 0.987117 + 0.475371i
\(79\) 3.35322e8 0.968591 0.484296 0.874904i \(-0.339076\pi\)
0.484296 + 0.874904i \(0.339076\pi\)
\(80\) −2.59132e8 −0.707321
\(81\) 3.31492e8 + 1.59638e8i 0.855639 + 0.412054i
\(82\) −1.06760e8 4.67744e8i −0.260762 1.14247i
\(83\) −2.01111e8 2.52186e8i −0.465141 0.583269i 0.492833 0.870124i \(-0.335962\pi\)
−0.957974 + 0.286855i \(0.907390\pi\)
\(84\) 1.59433e6 1.99923e6i 0.00349399 0.00438133i
\(85\) 3.53674e8 0.734882
\(86\) −5.55960e8 6.38497e6i −1.09597 0.0125868i
\(87\) 3.08950e8 0.578165
\(88\) −4.80651e8 + 6.02717e8i −0.854392 + 1.07137i
\(89\) 4.81210e8 + 6.03418e8i 0.812979 + 1.01944i 0.999317 + 0.0369576i \(0.0117666\pi\)
−0.186338 + 0.982486i \(0.559662\pi\)
\(90\) −4.44083e6 1.94566e7i −0.00713466 0.0312590i
\(91\) −1.72267e7 8.29594e6i −0.0263339 0.0126818i
\(92\) −1.98300e8 −0.288588
\(93\) 9.91094e8 1.37386
\(94\) −7.91697e8 3.81261e8i −1.04588 0.503671i
\(95\) 9.71124e7 4.25477e8i 0.122326 0.535945i
\(96\) 2.90345e8 1.39823e8i 0.348894 0.168018i
\(97\) −3.49269e8 + 1.53025e9i −0.400578 + 1.75505i 0.224491 + 0.974476i \(0.427928\pi\)
−0.625068 + 0.780570i \(0.714929\pi\)
\(98\) 6.23479e8 7.81818e8i 0.682818 0.856226i
\(99\) −6.47148e7 3.11650e7i −0.0677088 0.0326068i
\(100\) −7.89143e7 + 9.89554e7i −0.0789143 + 0.0989554i
\(101\) 7.37079e7 + 3.22935e8i 0.0704803 + 0.308794i 0.997865 0.0653156i \(-0.0208054\pi\)
−0.927384 + 0.374110i \(0.877948\pi\)
\(102\) −1.27031e9 + 6.11751e8i −1.16201 + 0.559595i
\(103\) −7.79824e8 + 3.75544e8i −0.682699 + 0.328770i −0.742887 0.669417i \(-0.766544\pi\)
0.0601883 + 0.998187i \(0.480830\pi\)
\(104\) −6.67107e8 8.36525e8i −0.559172 0.701179i
\(105\) −4.70105e6 2.05967e7i −0.00377436 0.0165365i
\(106\) −3.61054e8 + 1.58188e9i −0.277777 + 1.21702i
\(107\) 1.89329e8 + 2.37412e8i 0.139634 + 0.175095i 0.846731 0.532021i \(-0.178567\pi\)
−0.707097 + 0.707116i \(0.749996\pi\)
\(108\) 1.81468e8 + 2.27554e8i 0.128349 + 0.160945i
\(109\) 3.94067e8 1.72652e9i 0.267393 1.17153i −0.645640 0.763642i \(-0.723409\pi\)
0.913033 0.407885i \(-0.133734\pi\)
\(110\) −3.57236e8 1.56515e9i −0.232642 1.01927i
\(111\) 1.70014e8 + 2.13191e8i 0.106300 + 0.133296i
\(112\) −4.96863e7 + 2.39277e7i −0.0298370 + 0.0143688i
\(113\) 2.57627e8 1.24067e8i 0.148641 0.0715818i −0.358084 0.933689i \(-0.616570\pi\)
0.506726 + 0.862107i \(0.330856\pi\)
\(114\) 3.87144e8 + 1.69619e9i 0.214685 + 0.940595i
\(115\) −1.02147e9 + 1.28089e9i −0.544612 + 0.682922i
\(116\) 2.09599e8 + 1.00937e8i 0.107480 + 0.0517597i
\(117\) 6.21569e7 7.79422e7i 0.0306657 0.0384536i
\(118\) −3.11470e8 + 1.36464e9i −0.147893 + 0.647962i
\(119\) 6.78139e7 3.26574e7i 0.0309997 0.0149287i
\(120\) 2.63069e8 1.15258e9i 0.115812 0.507405i
\(121\) −3.08145e9 1.48395e9i −1.30683 0.629338i
\(122\) −4.26689e9 −1.74378
\(123\) 2.64810e9 1.04318
\(124\) 6.72381e8 + 3.23802e8i 0.255398 + 0.122993i
\(125\) 6.02795e8 + 2.64102e9i 0.220838 + 0.967556i
\(126\) −2.64807e6 3.32057e6i −0.000935969 0.00117367i
\(127\) −1.62043e9 + 2.03196e9i −0.552731 + 0.693103i −0.977195 0.212342i \(-0.931891\pi\)
0.424464 + 0.905445i \(0.360462\pi\)
\(128\) −3.62125e9 −1.19238
\(129\) 7.17188e8 2.98383e9i 0.228023 0.948682i
\(130\) 2.22818e9 0.684235
\(131\) 1.60881e9 2.01738e9i 0.477290 0.598503i −0.483649 0.875262i \(-0.660689\pi\)
0.960939 + 0.276759i \(0.0892603\pi\)
\(132\) 6.68709e8 + 8.38535e8i 0.191714 + 0.240402i
\(133\) −2.06671e7 9.05487e7i −0.00572728 0.0250928i
\(134\) 5.00215e9 + 2.40891e9i 1.34025 + 0.645429i
\(135\) 2.40462e9 0.623080
\(136\) 4.21194e9 1.05574
\(137\) −4.50899e9 2.17142e9i −1.09355 0.526624i −0.201922 0.979402i \(-0.564719\pi\)
−0.891623 + 0.452778i \(0.850433\pi\)
\(138\) 1.45334e9 6.36751e9i 0.341124 1.49456i
\(139\) −9.14543e8 + 4.40421e8i −0.207796 + 0.100069i −0.534887 0.844923i \(-0.679646\pi\)
0.327091 + 0.944993i \(0.393932\pi\)
\(140\) 3.53986e6 1.55091e7i 0.000778771 0.00341202i
\(141\) 3.02397e9 3.79193e9i 0.644304 0.807932i
\(142\) −4.89082e9 2.35530e9i −1.00945 0.486125i
\(143\) 5.00011e9 6.26995e9i 0.999926 1.25387i
\(144\) −6.39832e7 2.80329e8i −0.0124004 0.0543295i
\(145\) 1.73166e9 8.33925e8i 0.325318 0.156665i
\(146\) 6.74048e9 3.24605e9i 1.22773 0.591244i
\(147\) 3.44128e9 + 4.31523e9i 0.607844 + 0.762213i
\(148\) 4.56897e7 + 2.00180e8i 0.00782781 + 0.0342959i
\(149\) −4.09705e8 + 1.79503e9i −0.0680978 + 0.298356i −0.997496 0.0707226i \(-0.977469\pi\)
0.929398 + 0.369078i \(0.120327\pi\)
\(150\) −2.59913e9 3.25921e9i −0.419197 0.525656i
\(151\) 5.70694e9 + 7.15628e9i 0.893320 + 1.12019i 0.992146 + 0.125083i \(0.0399199\pi\)
−0.0988259 + 0.995105i \(0.531509\pi\)
\(152\) 1.15652e9 5.06706e9i 0.175735 0.769945i
\(153\) 8.73267e7 + 3.82603e8i 0.0128836 + 0.0564465i
\(154\) −2.13020e8 2.67118e8i −0.0305194 0.0382702i
\(155\) 5.55508e9 2.67519e9i 0.773032 0.372273i
\(156\) −1.34117e9 + 6.45873e8i −0.181310 + 0.0873145i
\(157\) 5.91672e8 + 2.59228e9i 0.0777200 + 0.340513i 0.998806 0.0488448i \(-0.0155540\pi\)
−0.921086 + 0.389358i \(0.872697\pi\)
\(158\) −5.18508e9 + 6.50189e9i −0.661910 + 0.830009i
\(159\) −8.06882e9 3.88574e9i −1.00120 0.482155i
\(160\) 1.24997e9 1.56741e9i 0.150785 0.189079i
\(161\) −7.75845e7 + 3.39920e8i −0.00910036 + 0.0398713i
\(162\) −8.22124e9 + 3.95914e9i −0.937820 + 0.451630i
\(163\) −3.57627e9 + 1.56687e10i −0.396813 + 1.73855i 0.243006 + 0.970025i \(0.421867\pi\)
−0.639819 + 0.768526i \(0.720991\pi\)
\(164\) 1.79653e9 + 8.65164e8i 0.193927 + 0.0933901i
\(165\) 8.86100e9 0.930690
\(166\) 7.99965e9 0.817682
\(167\) 1.95401e9 + 9.41000e8i 0.194403 + 0.0936194i 0.528553 0.848901i \(-0.322735\pi\)
−0.334150 + 0.942520i \(0.608449\pi\)
\(168\) −5.59854e7 2.45288e8i −0.00542229 0.0237566i
\(169\) 3.27985e8 + 4.11281e8i 0.0309289 + 0.0387836i
\(170\) −5.46885e9 + 6.85772e9i −0.502199 + 0.629738i
\(171\) 4.84259e8 0.0433107
\(172\) 1.46141e9 1.78999e9i 0.127319 0.155945i
\(173\) −1.14825e10 −0.974607 −0.487304 0.873233i \(-0.662019\pi\)
−0.487304 + 0.873233i \(0.662019\pi\)
\(174\) −4.77729e9 + 5.99053e9i −0.395103 + 0.495443i
\(175\) 1.38751e8 + 1.73988e8i 0.0111832 + 0.0140233i
\(176\) −5.14703e9 2.25506e10i −0.404343 1.77154i
\(177\) −6.96072e9 3.35211e9i −0.533058 0.256707i
\(178\) −1.91412e10 −1.42915
\(179\) 8.48978e7 0.00618099 0.00309049 0.999995i \(-0.499016\pi\)
0.00309049 + 0.999995i \(0.499016\pi\)
\(180\) 7.47295e7 + 3.59879e7i 0.00530599 + 0.00255523i
\(181\) 5.71786e8 2.50516e9i 0.0395986 0.173493i −0.951262 0.308385i \(-0.900212\pi\)
0.990860 + 0.134892i \(0.0430687\pi\)
\(182\) 4.27234e8 2.05745e8i 0.0288632 0.0138998i
\(183\) 5.24060e9 2.29606e10i 0.345423 1.51340i
\(184\) −1.21649e10 + 1.52543e10i −0.782397 + 0.981095i
\(185\) 1.52838e9 + 7.36030e8i 0.0959310 + 0.0461979i
\(186\) −1.53253e10 + 1.92173e10i −0.938858 + 1.17729i
\(187\) 7.02487e9 + 3.07780e10i 0.420098 + 1.84057i
\(188\) 3.29040e9 1.58457e9i 0.192105 0.0925127i
\(189\) 4.61065e8 2.22037e8i 0.0262835 0.0126575i
\(190\) 6.74834e9 + 8.46215e9i 0.375669 + 0.471075i
\(191\) −1.01891e9 4.46412e9i −0.0553967 0.242709i 0.939647 0.342145i \(-0.111153\pi\)
−0.995044 + 0.0994359i \(0.968296\pi\)
\(192\) 2.96722e9 1.30002e10i 0.157578 0.690392i
\(193\) −8.82382e9 1.10647e10i −0.457772 0.574027i 0.498358 0.866971i \(-0.333937\pi\)
−0.956130 + 0.292944i \(0.905365\pi\)
\(194\) −2.42707e10 3.04345e10i −1.23020 1.54262i
\(195\) −2.73665e9 + 1.19901e10i −0.135539 + 0.593834i
\(196\) 9.24811e8 + 4.05186e9i 0.0447611 + 0.196111i
\(197\) 7.10689e9 + 8.91175e9i 0.336187 + 0.421566i 0.920976 0.389620i \(-0.127394\pi\)
−0.584788 + 0.811186i \(0.698822\pi\)
\(198\) 1.60497e9 7.72914e8i 0.0742120 0.0357386i
\(199\) −7.46203e9 + 3.59353e9i −0.337302 + 0.162436i −0.594865 0.803825i \(-0.702795\pi\)
0.257564 + 0.966261i \(0.417080\pi\)
\(200\) 2.77110e9 + 1.21410e10i 0.122466 + 0.536560i
\(201\) −1.91062e10 + 2.39584e10i −0.825643 + 1.03532i
\(202\) −7.40145e9 3.56435e9i −0.312778 0.150626i
\(203\) 2.55029e8 3.19796e8i 0.0105404 0.0132172i
\(204\) 1.30395e9 5.71298e9i 0.0527139 0.230955i
\(205\) 1.48426e10 7.14781e9i 0.586972 0.282671i
\(206\) 4.77663e9 2.09278e10i 0.184807 0.809694i
\(207\) −1.63788e9 7.88761e8i −0.0620033 0.0298592i
\(208\) 3.21034e10 1.18923
\(209\) 3.89554e10 1.41224
\(210\) 4.72061e8 + 2.27333e8i 0.0167499 + 0.00806631i
\(211\) 9.80007e9 + 4.29369e10i 0.340375 + 1.49128i 0.798283 + 0.602282i \(0.205742\pi\)
−0.457908 + 0.889000i \(0.651401\pi\)
\(212\) −4.20456e9 5.27235e9i −0.142958 0.179264i
\(213\) 1.86810e10 2.34252e10i 0.621859 0.779786i
\(214\) −7.53100e9 −0.245466
\(215\) −4.03419e9 1.86602e10i −0.128761 0.595585i
\(216\) 2.86369e10 0.895126
\(217\) 8.18118e8 1.02589e9i 0.0250465 0.0314073i
\(218\) 2.73837e10 + 3.43381e10i 0.821180 + 1.02973i
\(219\) 9.18862e9 + 4.02580e10i 0.269930 + 1.18264i
\(220\) 6.01151e9 + 2.89499e9i 0.173014 + 0.0833191i
\(221\) −4.38160e10 −1.23557
\(222\) −6.76270e9 −0.186867
\(223\) 1.27191e10 + 6.12519e9i 0.344417 + 0.165862i 0.598093 0.801427i \(-0.295925\pi\)
−0.253676 + 0.967289i \(0.581640\pi\)
\(224\) 9.49394e7 4.15956e8i 0.00251959 0.0110391i
\(225\) −1.04540e9 + 5.03440e8i −0.0271934 + 0.0130956i
\(226\) −1.57804e9 + 6.91383e9i −0.0402373 + 0.176291i
\(227\) −2.98266e10 + 3.74013e10i −0.745567 + 0.934912i −0.999478 0.0323160i \(-0.989712\pi\)
0.253911 + 0.967228i \(0.418283\pi\)
\(228\) −6.51480e9 3.13736e9i −0.159659 0.0768879i
\(229\) 2.82300e10 3.53993e10i 0.678345 0.850618i −0.316855 0.948474i \(-0.602627\pi\)
0.995201 + 0.0978560i \(0.0311985\pi\)
\(230\) −9.04135e9 3.96127e10i −0.213038 0.933382i
\(231\) 1.69902e9 8.18205e8i 0.0392595 0.0189064i
\(232\) 2.06226e10 9.93132e9i 0.467356 0.225067i
\(233\) −5.03251e10 6.31057e10i −1.11862 1.40271i −0.904802 0.425833i \(-0.859981\pi\)
−0.213819 0.976873i \(-0.568590\pi\)
\(234\) 5.50167e8 + 2.41044e9i 0.0119956 + 0.0525563i
\(235\) 6.71404e9 2.94161e10i 0.143608 0.629188i
\(236\) −3.62714e9 4.54829e9i −0.0761133 0.0954430i
\(237\) −2.86190e10 3.58871e10i −0.589232 0.738874i
\(238\) −4.15378e8 + 1.81989e9i −0.00839165 + 0.0367662i
\(239\) −8.62562e9 3.77913e10i −0.171001 0.749206i −0.985588 0.169164i \(-0.945893\pi\)
0.814586 0.580042i \(-0.196964\pi\)
\(240\) 2.21163e10 + 2.77330e10i 0.430291 + 0.539568i
\(241\) 6.63642e10 3.19593e10i 1.26723 0.610268i 0.325156 0.945660i \(-0.394583\pi\)
0.942079 + 0.335392i \(0.108869\pi\)
\(242\) 7.64221e10 3.68029e10i 1.43235 0.689784i
\(243\) 1.16027e9 + 5.08346e9i 0.0213466 + 0.0935257i
\(244\) 1.10568e10 1.38648e10i 0.199699 0.250415i
\(245\) 3.09362e10 + 1.48981e10i 0.548554 + 0.264169i
\(246\) −4.09475e10 + 5.13466e10i −0.712885 + 0.893930i
\(247\) −1.20311e10 + 5.27116e10i −0.205669 + 0.901094i
\(248\) 6.61561e10 3.18591e10i 1.11055 0.534812i
\(249\) −9.82517e9 + 4.30469e10i −0.161973 + 0.709651i
\(250\) −6.05303e10 2.91498e10i −0.980037 0.471961i
\(251\) −7.88661e10 −1.25418 −0.627089 0.778948i \(-0.715754\pi\)
−0.627089 + 0.778948i \(0.715754\pi\)
\(252\) 1.76518e7 0.000275731
\(253\) −1.31757e11 6.34507e10i −2.02176 0.973630i
\(254\) −1.43429e10 6.28402e10i −0.216214 0.947297i
\(255\) −3.01852e10 3.78511e10i −0.447058 0.560593i
\(256\) 2.48986e10 3.12218e10i 0.362322 0.454338i
\(257\) 2.74873e10 0.393036 0.196518 0.980500i \(-0.437037\pi\)
0.196518 + 0.980500i \(0.437037\pi\)
\(258\) 4.67665e10 + 6.00452e10i 0.657123 + 0.843703i
\(259\) 3.61017e8 0.00498516
\(260\) −5.77389e9 + 7.24023e9i −0.0783590 + 0.0982590i
\(261\) 1.32971e9 + 1.66740e9i 0.0177368 + 0.0222412i
\(262\) 1.42400e10 + 6.23894e10i 0.186704 + 0.818003i
\(263\) 2.68253e10 + 1.29184e10i 0.345736 + 0.166498i 0.598690 0.800981i \(-0.295688\pi\)
−0.252955 + 0.967478i \(0.581402\pi\)
\(264\) 1.05527e11 1.33704
\(265\) −5.57142e10 −0.694000
\(266\) 2.07531e9 + 9.99418e8i 0.0254165 + 0.0122400i
\(267\) 2.35092e10 1.03001e11i 0.283098 1.24034i
\(268\) −2.07896e10 + 1.00117e10i −0.246172 + 0.118550i
\(269\) −1.57604e10 + 6.90510e10i −0.183520 + 0.804053i 0.796418 + 0.604747i \(0.206726\pi\)
−0.979937 + 0.199306i \(0.936131\pi\)
\(270\) −3.71826e10 + 4.66255e10i −0.425797 + 0.533932i
\(271\) 5.93705e10 + 2.85913e10i 0.668665 + 0.322012i 0.737237 0.675634i \(-0.236130\pi\)
−0.0685719 + 0.997646i \(0.521844\pi\)
\(272\) −7.87948e10 + 9.88055e10i −0.872846 + 1.09451i
\(273\) 5.82405e8 + 2.55168e9i 0.00634590 + 0.0278032i
\(274\) 1.11826e11 5.38526e10i 1.19858 0.577204i
\(275\) −8.40960e10 + 4.04985e10i −0.886703 + 0.427014i
\(276\) 1.69245e10 + 2.12226e10i 0.175560 + 0.220145i
\(277\) −1.24598e10 5.45902e10i −0.127161 0.557129i −0.997864 0.0653201i \(-0.979193\pi\)
0.870703 0.491808i \(-0.163664\pi\)
\(278\) 5.60182e9 2.45432e10i 0.0562507 0.246450i
\(279\) 4.26563e9 + 5.34893e9i 0.0421468 + 0.0528504i
\(280\) −9.75886e8 1.22372e9i −0.00948829 0.0118979i
\(281\) −4.46399e9 + 1.95580e10i −0.0427115 + 0.187131i −0.991783 0.127928i \(-0.959167\pi\)
0.949072 + 0.315059i \(0.102024\pi\)
\(282\) 2.67659e10 + 1.17269e11i 0.252035 + 1.10424i
\(283\) −1.84536e10 2.31401e10i −0.171018 0.214450i 0.688935 0.724823i \(-0.258079\pi\)
−0.859953 + 0.510373i \(0.829507\pi\)
\(284\) 2.03269e10 9.78892e9i 0.185412 0.0892899i
\(285\) −5.38240e10 + 2.59203e10i −0.483252 + 0.232722i
\(286\) 4.42574e10 + 1.93904e11i 0.391146 + 1.71372i
\(287\) 2.18592e9 2.74106e9i 0.0190181 0.0238479i
\(288\) 2.00425e9 + 9.65198e8i 0.0171667 + 0.00826704i
\(289\) 3.36039e10 4.21380e10i 0.283367 0.355331i
\(290\) −1.06069e10 + 4.64719e10i −0.0880638 + 0.385833i
\(291\) 1.93580e11 9.32233e10i 1.58250 0.762090i
\(292\) −6.91897e9 + 3.03140e10i −0.0556953 + 0.244017i
\(293\) −1.32926e11 6.40136e10i −1.05367 0.507420i −0.174860 0.984593i \(-0.555947\pi\)
−0.878809 + 0.477173i \(0.841662\pi\)
\(294\) −1.36885e11 −1.06854
\(295\) −4.80629e10 −0.369497
\(296\) 1.82017e10 + 8.76547e9i 0.137816 + 0.0663686i
\(297\) 4.77619e10 + 2.09258e11i 0.356186 + 1.56055i
\(298\) −2.84704e10 3.57008e10i −0.209132 0.262243i
\(299\) 1.26549e11 1.58687e11i 0.915667 1.14821i
\(300\) 1.73256e10 0.123493
\(301\) −2.49656e9 3.20543e9i −0.0175305 0.0225080i
\(302\) −2.27006e11 −1.57039
\(303\) 2.82706e10 3.54502e10i 0.192683 0.241617i
\(304\) 9.72296e10 + 1.21922e11i 0.652931 + 0.818750i
\(305\) −3.26022e10 1.42839e11i −0.215723 0.945146i
\(306\) −8.76900e9 4.22293e9i −0.0571747 0.0275339i
\(307\) −1.82488e11 −1.17249 −0.586247 0.810132i \(-0.699395\pi\)
−0.586247 + 0.810132i \(0.699395\pi\)
\(308\) 1.41997e9 0.00899086
\(309\) 1.06748e11 + 5.14071e10i 0.666110 + 0.320782i
\(310\) −3.40264e10 + 1.49079e11i −0.209261 + 0.916831i
\(311\) −1.06027e11 + 5.10600e10i −0.642681 + 0.309499i −0.726689 0.686966i \(-0.758942\pi\)
0.0840085 + 0.996465i \(0.473228\pi\)
\(312\) −3.25911e10 + 1.42791e11i −0.194717 + 0.853110i
\(313\) 7.39750e10 9.27618e10i 0.435648 0.546285i −0.514742 0.857345i \(-0.672112\pi\)
0.950390 + 0.311060i \(0.100684\pi\)
\(314\) −5.94133e10 2.86120e10i −0.344906 0.166098i
\(315\) 9.09270e7 1.14019e8i 0.000520350 0.000652498i
\(316\) −7.69106e9 3.36968e10i −0.0433905 0.190106i
\(317\) −9.79988e10 + 4.71937e10i −0.545072 + 0.262493i −0.686093 0.727514i \(-0.740676\pi\)
0.141021 + 0.990007i \(0.454961\pi\)
\(318\) 2.00112e11 9.63690e10i 1.09737 0.528464i
\(319\) 1.06966e11 + 1.34132e11i 0.578348 + 0.725226i
\(320\) −1.84593e10 8.08755e10i −0.0984103 0.431164i
\(321\) 9.24958e9 4.05251e10i 0.0486239 0.213035i
\(322\) −5.39135e9 6.76054e9i −0.0279477 0.0350453i
\(323\) −1.32703e11 1.66404e11i −0.678373 0.850653i
\(324\) 8.43893e9 3.69734e10i 0.0425437 0.186396i
\(325\) −2.88272e10 1.26300e11i −0.143327 0.627955i
\(326\) −2.48515e11 3.11628e11i −1.21863 1.52812i
\(327\) −2.18409e11 + 1.05180e11i −1.05635 + 0.508709i
\(328\) 1.76762e11 8.51242e10i 0.843251 0.406088i
\(329\) −1.42886e9 6.26025e9i −0.00672370 0.0294585i
\(330\) −1.37017e11 + 1.71815e11i −0.636009 + 0.797530i
\(331\) −2.38548e11 1.14879e11i −1.09232 0.526035i −0.201086 0.979574i \(-0.564447\pi\)
−0.891236 + 0.453539i \(0.850161\pi\)
\(332\) −2.07295e10 + 2.59940e10i −0.0936415 + 0.117423i
\(333\) −4.18858e8 + 1.83513e9i −0.00186667 + 0.00817841i
\(334\) −4.84608e10 + 2.33375e10i −0.213074 + 0.102611i
\(335\) −4.24211e10 + 1.85859e11i −0.184026 + 0.806272i
\(336\) 6.80142e9 + 3.27539e9i 0.0291120 + 0.0140196i
\(337\) 4.28657e11 1.81040 0.905201 0.424984i \(-0.139720\pi\)
0.905201 + 0.424984i \(0.139720\pi\)
\(338\) −1.30464e10 −0.0543706
\(339\) −3.52659e10 1.69831e10i −0.145029 0.0698424i
\(340\) −8.11198e9 3.55409e10i −0.0329209 0.144236i
\(341\) 3.43142e11 + 4.30287e11i 1.37429 + 1.72331i
\(342\) −7.48808e9 + 9.38976e9i −0.0295974 + 0.0371139i
\(343\) 1.46207e10 0.0570356
\(344\) −4.80437e10 2.22227e11i −0.184979 0.855625i
\(345\) 2.24265e11 0.852265
\(346\) 1.77554e11 2.22646e11i 0.666021 0.835164i
\(347\) 9.48263e10 + 1.18908e11i 0.351112 + 0.440281i 0.925755 0.378123i \(-0.123430\pi\)
−0.574643 + 0.818404i \(0.694859\pi\)
\(348\) −7.08618e9 3.10466e10i −0.0259004 0.113477i
\(349\) 2.41687e10 + 1.16390e10i 0.0872044 + 0.0419954i 0.476978 0.878915i \(-0.341732\pi\)
−0.389773 + 0.920911i \(0.627447\pi\)
\(350\) −5.51913e9 −0.0196591
\(351\) −2.97904e11 −1.04760
\(352\) 1.61229e11 + 7.76439e10i 0.559760 + 0.269566i
\(353\) 4.74842e10 2.08042e11i 0.162766 0.713124i −0.826002 0.563667i \(-0.809390\pi\)
0.988768 0.149457i \(-0.0477525\pi\)
\(354\) 1.72631e11 8.31346e10i 0.584256 0.281363i
\(355\) 4.14770e10 1.81722e11i 0.138605 0.607269i
\(356\) 4.96007e10 6.21973e10i 0.163668 0.205233i
\(357\) −9.28284e9 4.47038e9i −0.0302464 0.0145659i
\(358\) −1.31277e9 + 1.64617e9i −0.00422392 + 0.00529663i
\(359\) −2.38254e10 1.04386e11i −0.0757034 0.331678i 0.922868 0.385117i \(-0.125839\pi\)
−0.998571 + 0.0534387i \(0.982982\pi\)
\(360\) 7.35270e9 3.54087e9i 0.0230720 0.0111109i
\(361\) 5.41061e10 2.60561e10i 0.167673 0.0807473i
\(362\) 3.97334e10 + 4.98241e10i 0.121609 + 0.152493i
\(363\) 1.04179e11 + 4.56436e11i 0.314919 + 1.37975i
\(364\) −4.38547e8 + 1.92140e9i −0.00130936 + 0.00573669i
\(365\) 1.60168e11 + 2.00844e11i 0.472342 + 0.592298i
\(366\) 3.64170e11 + 4.56654e11i 1.06081 + 1.33022i
\(367\) 4.13912e10 1.81347e11i 0.119100 0.521810i −0.879819 0.475310i \(-0.842336\pi\)
0.998918 0.0465002i \(-0.0148068\pi\)
\(368\) −1.30267e11 5.70737e11i −0.370271 1.62226i
\(369\) 1.13973e10 + 1.42918e10i 0.0320025 + 0.0401299i
\(370\) −3.79049e10 + 1.82541e10i −0.105145 + 0.0506351i
\(371\) −1.06827e10 + 5.14452e9i −0.0292751 + 0.0140982i
\(372\) −2.27321e10 9.95957e10i −0.0615454 0.269648i
\(373\) −6.93753e10 + 8.69939e10i −0.185573 + 0.232701i −0.865912 0.500196i \(-0.833261\pi\)
0.680339 + 0.732898i \(0.261833\pi\)
\(374\) −7.05409e11 3.39707e11i −1.86431 0.897806i
\(375\) 2.31201e11 2.89917e11i 0.603740 0.757066i
\(376\) 7.99583e10 3.50320e11i 0.206309 0.903899i
\(377\) −2.14533e11 + 1.03314e11i −0.546963 + 0.263403i
\(378\) −2.82414e9 + 1.23734e10i −0.00711498 + 0.0311728i
\(379\) 5.30131e11 + 2.55298e11i 1.31980 + 0.635580i 0.955304 0.295627i \(-0.0955284\pi\)
0.364492 + 0.931207i \(0.381243\pi\)
\(380\) −4.49839e10 −0.110670
\(381\) 3.55765e11 0.864971
\(382\) 1.02314e11 + 4.92720e10i 0.245840 + 0.118390i
\(383\) −8.34885e10 3.65787e11i −0.198259 0.868628i −0.971973 0.235093i \(-0.924461\pi\)
0.773714 0.633535i \(-0.218397\pi\)
\(384\) 3.09066e11 + 3.87556e11i 0.725371 + 0.909587i
\(385\) 7.31448e9 9.17207e9i 0.0169672 0.0212762i
\(386\) 3.50987e11 0.804727
\(387\) 1.91905e10 8.97164e9i 0.0434897 0.0203316i
\(388\) 1.61786e11 0.362409
\(389\) 3.58480e11 4.49520e11i 0.793765 0.995349i −0.206094 0.978532i \(-0.566075\pi\)
0.999859 0.0168172i \(-0.00535333\pi\)
\(390\) −1.90170e11 2.38466e11i −0.416247 0.521957i
\(391\) 1.77794e11 + 7.78965e11i 0.384699 + 1.68548i
\(392\) 3.68423e11 + 1.77423e11i 0.788059 + 0.379509i
\(393\) −3.53213e11 −0.746913
\(394\) −2.82692e11 −0.590991
\(395\) −2.57276e11 1.23898e11i −0.531757 0.256081i
\(396\) −1.64747e9 + 7.21804e9i −0.00336658 + 0.0147500i
\(397\) −6.63503e11 + 3.19526e11i −1.34056 + 0.645578i −0.960213 0.279267i \(-0.909909\pi\)
−0.380344 + 0.924845i \(0.624194\pi\)
\(398\) 4.57070e10 2.00255e11i 0.0913079 0.400046i
\(399\) −7.92686e9 + 9.93997e9i −0.0156575 + 0.0196339i
\(400\) −3.36648e11 1.62121e11i −0.657516 0.316643i
\(401\) 1.78091e11 2.23320e11i 0.343948 0.431298i −0.579528 0.814952i \(-0.696763\pi\)
0.923477 + 0.383655i \(0.125335\pi\)
\(402\) −1.69114e11 7.40938e11i −0.322971 1.41503i
\(403\) −6.88209e11 + 3.31424e11i −1.29971 + 0.625909i
\(404\) 3.07614e10 1.48139e10i 0.0574500 0.0276664i
\(405\) −1.95353e11 2.44965e11i −0.360805 0.452436i
\(406\) 2.25733e9 + 9.89000e9i 0.00412313 + 0.0180646i
\(407\) −3.36944e10 + 1.47625e11i −0.0608671 + 0.266676i
\(408\) −3.59480e11 4.50773e11i −0.642249 0.805355i
\(409\) −3.82059e10 4.79087e10i −0.0675111 0.0846563i 0.746929 0.664904i \(-0.231527\pi\)
−0.814440 + 0.580247i \(0.802956\pi\)
\(410\) −9.09148e10 + 3.98324e11i −0.158894 + 0.696160i
\(411\) 1.52441e11 + 6.67889e11i 0.263521 + 1.15456i
\(412\) 5.56249e10 + 6.97515e10i 0.0951113 + 0.119266i
\(413\) −9.21564e9 + 4.43802e9i −0.0155866 + 0.00750609i
\(414\) 4.06205e10 1.95618e10i 0.0679586 0.0327271i
\(415\) 6.11232e10 + 2.67798e11i 0.101155 + 0.443191i
\(416\) −1.54856e11 + 1.94184e11i −0.253518 + 0.317902i
\(417\) 1.25189e11 + 6.02879e10i 0.202747 + 0.0976378i
\(418\) −6.02368e11 + 7.55345e11i −0.965091 + 1.21019i
\(419\) −1.13597e11 + 4.97699e11i −0.180054 + 0.788867i 0.801549 + 0.597930i \(0.204010\pi\)
−0.981602 + 0.190937i \(0.938847\pi\)
\(420\) −1.96195e9 + 9.44824e8i −0.00307656 + 0.00148159i
\(421\) −2.27879e11 + 9.98404e11i −0.353537 + 1.54895i 0.415408 + 0.909635i \(0.363639\pi\)
−0.768946 + 0.639314i \(0.779218\pi\)
\(422\) −9.84084e11 4.73910e11i −1.51052 0.727428i
\(423\) 3.34801e10 0.0508458
\(424\) −6.63507e11 −0.997009
\(425\) 4.59471e11 + 2.21269e11i 0.683136 + 0.328981i
\(426\) 1.65350e11 + 7.24448e11i 0.243255 + 1.06577i
\(427\) −1.94407e10 2.43778e10i −0.0282999 0.0354870i
\(428\) 1.95151e10 2.44712e10i 0.0281109 0.0352499i
\(429\) −1.09777e12 −1.56479
\(430\) 4.24202e11 + 2.10320e11i 0.598363 + 0.296669i
\(431\) 1.18614e12 1.65573 0.827863 0.560931i \(-0.189557\pi\)
0.827863 + 0.560931i \(0.189557\pi\)
\(432\) −5.35724e11 + 6.71776e11i −0.740055 + 0.927999i
\(433\) −3.69035e11 4.62755e11i −0.504513 0.632639i 0.462728 0.886500i \(-0.346871\pi\)
−0.967241 + 0.253861i \(0.918299\pi\)
\(434\) 7.24138e9 + 3.17266e10i 0.00979755 + 0.0429259i
\(435\) −2.37042e11 1.14154e11i −0.317413 0.152858i
\(436\) −1.82538e11 −0.241915
\(437\) 9.85930e11 1.29324
\(438\) −9.22685e11 4.44342e11i −1.19790 0.576877i
\(439\) −9.67814e10 + 4.24027e11i −0.124366 + 0.544883i 0.873905 + 0.486097i \(0.161580\pi\)
−0.998271 + 0.0587854i \(0.981277\pi\)
\(440\) 5.91477e11 2.84840e11i 0.752317 0.362297i
\(441\) −8.47815e9 + 3.71452e10i −0.0106740 + 0.0467659i
\(442\) 6.77527e11 8.49592e11i 0.844357 1.05879i
\(443\) −9.05835e11 4.36227e11i −1.11746 0.538141i −0.218354 0.975870i \(-0.570069\pi\)
−0.899107 + 0.437729i \(0.855783\pi\)
\(444\) 1.75242e10 2.19747e10i 0.0214001 0.0268349i
\(445\) −1.46253e11 6.40775e11i −0.176801 0.774614i
\(446\) −3.15442e11 + 1.51909e11i −0.377497 + 0.181793i
\(447\) 2.27077e11 1.09354e11i 0.269022 0.129554i
\(448\) −1.10073e10 1.38027e10i −0.0129101 0.0161887i
\(449\) 1.58785e11 + 6.95683e11i 0.184375 + 0.807799i 0.979515 + 0.201373i \(0.0645402\pi\)
−0.795140 + 0.606426i \(0.792603\pi\)
\(450\) 6.40338e9 2.80550e10i 0.00736128 0.0322519i
\(451\) 9.16840e11 + 1.14968e12i 1.04352 + 1.30853i
\(452\) −1.83766e10 2.30435e10i −0.0207082 0.0259672i
\(453\) 2.78809e11 1.22154e12i 0.311075 1.36291i
\(454\) −2.64003e11 1.15667e12i −0.291647 1.27779i
\(455\) 1.01519e10 + 1.27301e10i 0.0111045 + 0.0139246i
\(456\) −6.40997e11 + 3.08688e11i −0.694247 + 0.334332i
\(457\) 7.97835e11 3.84217e11i 0.855638 0.412054i 0.0459708 0.998943i \(-0.485362\pi\)
0.809667 + 0.586889i \(0.199648\pi\)
\(458\) 2.49871e11 + 1.09476e12i 0.265351 + 1.16258i
\(459\) 7.31177e11 9.16867e11i 0.768892 0.964160i
\(460\) 1.52146e11 + 7.32698e10i 0.158435 + 0.0762983i
\(461\) 6.66444e11 8.35694e11i 0.687241 0.861773i −0.308757 0.951141i \(-0.599913\pi\)
0.995999 + 0.0893674i \(0.0284845\pi\)
\(462\) −1.04070e10 + 4.55958e10i −0.0106276 + 0.0465625i
\(463\) 2.20943e11 1.06400e11i 0.223442 0.107604i −0.318814 0.947817i \(-0.603284\pi\)
0.542256 + 0.840213i \(0.317570\pi\)
\(464\) −1.52823e11 + 6.69563e11i −0.153059 + 0.670596i
\(465\) −7.60418e11 3.66198e11i −0.754248 0.363227i
\(466\) 2.00179e12 1.96645
\(467\) −1.69056e12 −1.64477 −0.822383 0.568934i \(-0.807356\pi\)
−0.822383 + 0.568934i \(0.807356\pi\)
\(468\) −9.25812e9 4.45847e9i −0.00892106 0.00429616i
\(469\) 9.02792e9 + 3.95539e10i 0.00861608 + 0.0377495i
\(470\) 4.66559e11 + 5.85046e11i 0.441028 + 0.553031i
\(471\) 2.26935e11 2.84568e11i 0.212475 0.266435i
\(472\) −5.72387e11 −0.530824
\(473\) 1.54375e12 7.21710e11i 1.41808 0.662960i
\(474\) 1.13838e12 1.03582
\(475\) 3.92354e11 4.91996e11i 0.353636 0.443446i
\(476\) −4.83717e9 6.06562e9i −0.00431877 0.00541557i
\(477\) −1.37566e10 6.02715e10i −0.0121668 0.0533064i
\(478\) 8.66150e11 + 4.17116e11i 0.758871 + 0.365453i
\(479\) −1.13327e12 −0.983609 −0.491805 0.870706i \(-0.663663\pi\)
−0.491805 + 0.870706i \(0.663663\pi\)
\(480\) −2.74430e11 −0.235964
\(481\) −1.89349e11 9.11855e10i −0.161291 0.0776735i
\(482\) −4.06498e11 + 1.78099e12i −0.343042 + 1.50297i
\(483\) 4.30008e10 2.07081e10i 0.0359513 0.0173132i
\(484\) −7.84457e10 + 3.43693e11i −0.0649778 + 0.284686i
\(485\) 8.33386e11 1.04503e12i 0.683925 0.857614i
\(486\) −1.16509e11 5.61079e10i −0.0947321 0.0456206i
\(487\) −1.46649e12 + 1.83892e12i −1.18140 + 1.48143i −0.340506 + 0.940242i \(0.610598\pi\)
−0.840899 + 0.541192i \(0.817973\pi\)
\(488\) −3.88263e11 1.70109e12i −0.309911 1.35781i
\(489\) 1.98213e12 9.54542e11i 1.56762 0.754927i
\(490\) −7.67239e11 + 3.69483e11i −0.601240 + 0.289542i
\(491\) 6.50036e11 + 8.15120e11i 0.504744 + 0.632928i 0.967292 0.253666i \(-0.0816363\pi\)
−0.462548 + 0.886594i \(0.653065\pi\)
\(492\) −6.07377e10 2.66109e11i −0.0467321 0.204747i
\(493\) 2.08579e11 9.13846e11i 0.159023 0.696726i
\(494\) −8.36041e11 1.04836e12i −0.631620 0.792027i
\(495\) 3.81374e10 + 4.78228e10i 0.0285514 + 0.0358023i
\(496\) −4.90249e11 + 2.14792e12i −0.363705 + 1.59350i
\(497\) −8.82700e9 3.86736e10i −0.00648947 0.0284322i
\(498\) −6.82752e11 8.56143e11i −0.497429 0.623756i
\(499\) −1.73175e12 + 8.33965e11i −1.25035 + 0.602137i −0.937606 0.347700i \(-0.886963\pi\)
−0.312745 + 0.949837i \(0.601249\pi\)
\(500\) 2.51572e11 1.21151e11i 0.180010 0.0866883i
\(501\) −6.60617e10 2.89435e11i −0.0468468 0.205249i
\(502\) 1.21951e12 1.52921e12i 0.857072 1.07473i
\(503\) 1.92271e12 + 9.25931e11i 1.33924 + 0.644945i 0.959908 0.280315i \(-0.0904390\pi\)
0.379334 + 0.925260i \(0.376153\pi\)
\(504\) 1.08286e9 1.35786e9i 0.000747541 0.000937387i
\(505\) 6.27685e10 2.75007e11i 0.0429468 0.188162i
\(506\) 3.26766e12 1.57362e12i 2.21595 1.06714i
\(507\) 1.60235e10 7.02037e10i 0.0107702 0.0471872i
\(508\) 2.41359e11 + 1.16233e11i 0.160797 + 0.0774357i
\(509\) −2.48724e12 −1.64243 −0.821215 0.570619i \(-0.806703\pi\)
−0.821215 + 0.570619i \(0.806703\pi\)
\(510\) 1.20069e12 0.785893
\(511\) 4.92562e10 + 2.37205e10i 0.0319571 + 0.0153897i
\(512\) −1.92188e11 8.42030e11i −0.123598 0.541518i
\(513\) −9.02242e11 1.13138e12i −0.575169 0.721239i
\(514\) −4.25035e11 + 5.32978e11i −0.268591 + 0.336802i
\(515\) 7.37080e11 0.461724
\(516\) −3.16297e11 3.63254e9i −0.196413 0.00225573i
\(517\) 2.69326e12 1.65794
\(518\) −5.58240e9 + 7.00011e9i −0.00340673 + 0.00427190i
\(519\) 9.80006e11 + 1.22889e12i 0.592892 + 0.743463i
\(520\) 2.02752e11 + 8.88314e11i 0.121605 + 0.532784i
\(521\) −1.82971e12 8.81141e11i −1.08796 0.523933i −0.198105 0.980181i \(-0.563479\pi\)
−0.889853 + 0.456248i \(0.849193\pi\)
\(522\) −5.28922e10 −0.0311799
\(523\) −1.59314e12 −0.931102 −0.465551 0.885021i \(-0.654144\pi\)
−0.465551 + 0.885021i \(0.654144\pi\)
\(524\) −2.39628e11 1.15399e11i −0.138850 0.0668667i
\(525\) 6.77860e9 2.96990e10i 0.00389425 0.0170618i
\(526\) −6.65287e11 + 3.20385e11i −0.378943 + 0.182489i
\(527\) 6.69111e11 2.93157e12i 0.377877 1.65559i
\(528\) −1.97414e12 + 2.47549e12i −1.10541 + 1.38614i
\(529\) −1.71187e12 8.24393e11i −0.950430 0.457703i
\(530\) 8.61507e11 1.08030e12i 0.474261 0.594705i
\(531\) −1.18674e10 5.19943e10i −0.00647782 0.0283812i
\(532\) −8.62527e9 + 4.15371e9i −0.00466842 + 0.00224819i
\(533\) −1.83882e12 + 8.85530e11i −0.986887 + 0.475260i
\(534\) 1.63366e12 + 2.04854e12i 0.869411 + 1.09021i
\(535\) −5.75423e10 2.52110e11i −0.0303666 0.133045i
\(536\) −5.05198e11 + 2.21342e12i −0.264375 + 1.15830i
\(537\) −7.24583e9 9.08598e9i −0.00376014 0.00471506i
\(538\) −1.09519e12 1.37333e12i −0.563599 0.706731i
\(539\) −6.82012e11 + 2.98809e12i −0.348051 + 1.52491i
\(540\) −5.51531e10 2.41642e11i −0.0279125 0.122292i
\(541\) −1.76551e12 2.21388e12i −0.886102 1.11114i −0.993146 0.116882i \(-0.962710\pi\)
0.107044 0.994254i \(-0.465861\pi\)
\(542\) −1.47243e12 + 7.09085e11i −0.732888 + 0.352940i
\(543\) −3.16909e11 + 1.52615e11i −0.156436 + 0.0753354i
\(544\) −2.17564e11 9.53211e11i −0.106510 0.466653i
\(545\) −9.40278e11 + 1.17907e12i −0.456533 + 0.572474i
\(546\) −5.84828e10 2.81638e10i −0.0281619 0.0135620i
\(547\) −2.05348e10 + 2.57498e10i −0.00980725 + 0.0122979i −0.786711 0.617322i \(-0.788218\pi\)
0.776904 + 0.629619i \(0.216789\pi\)
\(548\) −1.14787e11 + 5.02916e11i −0.0543727 + 0.238222i
\(549\) 1.46474e11 7.05379e10i 0.0688151 0.0331396i
\(550\) 5.15110e11 2.25685e12i 0.240031 1.05165i
\(551\) −1.04210e12 5.01851e11i −0.481647 0.231949i
\(552\) 2.67079e12 1.22438
\(553\) −6.07710e10 −0.0276333
\(554\) 1.25117e12 + 6.02531e11i 0.564315 + 0.271760i
\(555\) −5.16720e10 2.26390e11i −0.0231173 0.101283i
\(556\) 6.52345e10 + 8.18014e10i 0.0289495 + 0.0363015i
\(557\) 8.73492e11 1.09532e12i 0.384513 0.482164i −0.551477 0.834190i \(-0.685936\pi\)
0.935990 + 0.352026i \(0.114507\pi\)
\(558\) −1.69675e11 −0.0740908
\(559\) 4.99789e11 + 2.31178e12i 0.216488 + 1.00137i
\(560\) 4.69629e10 0.0201794
\(561\) 2.69438e12 3.37865e12i 1.14849 1.44016i
\(562\) −3.10203e11 3.88982e11i −0.131169 0.164481i
\(563\) 8.34965e11 + 3.65822e12i 0.350252 + 1.53455i 0.776599 + 0.629995i \(0.216943\pi\)
−0.426347 + 0.904559i \(0.640200\pi\)
\(564\) −4.50413e11 2.16907e11i −0.187437 0.0902647i
\(565\) −2.43506e11 −0.100529
\(566\) 7.34034e11 0.300637
\(567\) −6.00768e10 2.89315e10i −0.0244109 0.0117557i
\(568\) 4.93954e11 2.16416e12i 0.199122 0.872411i
\(569\) 1.23997e12 5.97136e11i 0.495912 0.238819i −0.169173 0.985586i \(-0.554110\pi\)
0.665085 + 0.746768i \(0.268395\pi\)
\(570\) 3.29686e11 1.44445e12i 0.130817 0.573147i
\(571\) −1.78548e12 + 2.23892e12i −0.702898 + 0.881406i −0.997236 0.0742954i \(-0.976329\pi\)
0.294339 + 0.955701i \(0.404901\pi\)
\(572\) −7.44755e11 3.58655e11i −0.290892 0.140086i
\(573\) −3.90800e11 + 4.90048e11i −0.151446 + 0.189908i
\(574\) 1.93482e10 + 8.47700e10i 0.00743939 + 0.0325941i
\(575\) −2.12840e12 + 1.02498e12i −0.811985 + 0.391031i
\(576\) 8.29331e10 3.99385e10i 0.0313926 0.0151179i
\(577\) 1.53132e12 + 1.92021e12i 0.575141 + 0.721204i 0.981275 0.192610i \(-0.0616951\pi\)
−0.406135 + 0.913813i \(0.633124\pi\)
\(578\) 2.97437e11 + 1.30316e12i 0.110846 + 0.485648i
\(579\) −4.31083e11 + 1.88870e12i −0.159407 + 0.698407i
\(580\) −1.23520e11 1.54889e11i −0.0453221 0.0568322i
\(581\) 3.64477e10 + 4.57040e10i 0.0132702 + 0.0166403i
\(582\) −1.18573e12 + 5.19503e12i −0.428383 + 1.87687i
\(583\) −1.10663e12 4.84845e12i −0.396728 1.73818i
\(584\) 1.90745e12 + 2.39187e12i 0.678573 + 0.850903i
\(585\) −7.64887e10 + 3.68350e10i −0.0270020 + 0.0130035i
\(586\) 3.29665e12 1.58758e12i 1.15487 0.556156i
\(587\) 6.33690e11 + 2.77638e12i 0.220295 + 0.965177i 0.957256 + 0.289242i \(0.0934031\pi\)
−0.736961 + 0.675936i \(0.763740\pi\)
\(588\) 3.54710e11 4.44792e11i 0.122370 0.153447i
\(589\) −3.34301e12 1.60991e12i −1.14451 0.551167i
\(590\) 7.43196e11 9.31938e11i 0.252505 0.316631i
\(591\) 3.47203e11 1.52119e12i 0.117068 0.512910i
\(592\) −5.46131e11 + 2.63003e11i −0.182747 + 0.0880061i
\(593\) −9.04922e11 + 3.96472e12i −0.300514 + 1.31664i 0.568840 + 0.822448i \(0.307392\pi\)
−0.869354 + 0.494190i \(0.835465\pi\)
\(594\) −4.79606e12 2.30966e12i −1.58068 0.761218i
\(595\) −6.40968e10 −0.0209657
\(596\) 1.89781e11 0.0616092
\(597\) 1.02146e12 + 4.91907e11i 0.329106 + 0.158489i
\(598\) 1.12012e12 + 4.90756e12i 0.358186 + 1.56931i
\(599\) 2.44532e12 + 3.06634e12i 0.776096 + 0.973194i 0.999999 0.00141791i \(-0.000451335\pi\)
−0.223903 + 0.974611i \(0.571880\pi\)
\(600\) 1.06285e12 1.33277e12i 0.334805 0.419832i
\(601\) −3.73327e12 −1.16722 −0.583612 0.812032i \(-0.698361\pi\)
−0.583612 + 0.812032i \(0.698361\pi\)
\(602\) 1.00757e11 + 1.15716e9i 0.0312675 + 0.000359094i
\(603\) −2.11536e11 −0.0651563
\(604\) 5.88243e11 7.37633e11i 0.179842 0.225514i
\(605\) 1.81594e12 + 2.27712e12i 0.551065 + 0.691014i
\(606\) 2.50230e11 + 1.09633e12i 0.0753726 + 0.330229i
\(607\) −2.45516e12 1.18234e12i −0.734058 0.353504i 0.0292210 0.999573i \(-0.490697\pi\)
−0.763279 + 0.646069i \(0.776412\pi\)
\(608\) −1.20647e12 −0.358056
\(609\) −5.59915e10 −0.0164947
\(610\) 3.27378e12 + 1.57657e12i 0.957338 + 0.461030i
\(611\) −8.31791e11 + 3.64431e12i −0.241451 + 1.05787i
\(612\) 3.64451e10 1.75510e10i 0.0105017 0.00505733i
\(613\) 1.26200e12 5.52916e12i 0.360982 1.58157i −0.389725 0.920931i \(-0.627430\pi\)
0.750707 0.660635i \(-0.229713\pi\)
\(614\) 2.82180e12 3.53843e12i 0.801252 1.00474i
\(615\) −2.03176e12 9.78443e11i −0.572709 0.275802i
\(616\) 8.71091e10 1.09231e11i 0.0243753 0.0305657i
\(617\) −2.52623e11 1.10681e12i −0.0701761 0.307462i 0.927643 0.373468i \(-0.121831\pi\)
−0.997819 + 0.0660063i \(0.978974\pi\)
\(618\) −2.64742e12 + 1.27493e12i −0.730088 + 0.351592i
\(619\) −3.39841e12 + 1.63659e12i −0.930397 + 0.448055i −0.836772 0.547552i \(-0.815560\pi\)
−0.0936251 + 0.995608i \(0.529846\pi\)
\(620\) −3.96244e11 4.96875e11i −0.107696 0.135047i
\(621\) 1.20881e12 + 5.29616e12i 0.326172 + 1.42905i
\(622\) 6.49445e11 2.84540e12i 0.173974 0.762232i
\(623\) −8.72104e10 1.09358e11i −0.0231938 0.0290841i
\(624\) −2.73995e12 3.43579e12i −0.723457 0.907186i
\(625\) −2.03402e10 + 8.91163e10i −0.00533207 + 0.0233613i
\(626\) 6.54773e11 + 2.86875e12i 0.170414 + 0.746634i
\(627\) −3.32476e12 4.16911e12i −0.859124 1.07731i
\(628\) 2.46930e11 1.18915e11i 0.0633512 0.0305083i
\(629\) 7.45381e11 3.58957e11i 0.189868 0.0914354i
\(630\) 8.04819e8 + 3.52614e9i 0.000203547 + 0.000891800i
\(631\) 1.40437e12 1.76102e12i 0.352654 0.442214i −0.573588 0.819144i \(-0.694449\pi\)
0.926242 + 0.376930i \(0.123020\pi\)
\(632\) −3.06394e12 1.47551e12i −0.763929 0.367889i
\(633\) 3.75881e12 4.71340e12i 0.930537 1.16686i
\(634\) 6.00269e11 2.62995e12i 0.147552 0.646466i
\(635\) 1.99406e12 9.60290e11i 0.486695 0.234380i
\(636\) −2.05411e11 + 8.99965e11i −0.0497814 + 0.218107i
\(637\) −3.83263e12 1.84570e12i −0.922294 0.444153i
\(638\) −4.25483e12 −1.01669
\(639\) 2.06828e11 0.0490745
\(640\) 2.77841e12 + 1.33801e12i 0.654616 + 0.315247i
\(641\) −4.43099e11 1.94134e12i −0.103667 0.454194i −0.999943 0.0106970i \(-0.996595\pi\)
0.896276 0.443497i \(-0.146262\pi\)
\(642\) 6.42754e11 + 8.05988e11i 0.149327 + 0.187250i
\(643\) 5.36646e12 6.72933e12i 1.23805 1.55247i 0.525632 0.850712i \(-0.323829\pi\)
0.712419 0.701755i \(-0.247600\pi\)
\(644\) 3.59383e10 0.00823325
\(645\) −1.65276e12 + 2.02436e12i −0.376002 + 0.460541i
\(646\) 5.27855e12 1.19253
\(647\) 3.90544e11 4.89727e11i 0.0876196 0.109872i −0.736089 0.676884i \(-0.763330\pi\)
0.823709 + 0.567013i \(0.191901\pi\)
\(648\) −2.32649e12 2.91732e12i −0.518338 0.649975i
\(649\) −9.54652e11 4.18260e12i −0.211224 0.925434i
\(650\) 2.89471e12 + 1.39402e12i 0.636055 + 0.306308i
\(651\) −1.79618e11 −0.0391953
\(652\) 1.65658e12 0.359003
\(653\) −4.36365e12 2.10142e12i −0.939162 0.452277i −0.0992887 0.995059i \(-0.531657\pi\)
−0.839874 + 0.542782i \(0.817371\pi\)
\(654\) 1.33782e12 5.86135e12i 0.285954 1.25285i
\(655\) −1.97976e12 + 9.53401e11i −0.420268 + 0.202390i
\(656\) −1.30989e12 + 5.73902e12i −0.276165 + 1.20996i
\(657\) −1.77725e11 + 2.22860e11i −0.0372138 + 0.0466646i
\(658\) 1.43480e11 + 6.90966e10i 0.0298385 + 0.0143694i
\(659\) −3.27454e12 + 4.10614e12i −0.676341 + 0.848104i −0.995011 0.0997612i \(-0.968192\pi\)
0.318671 + 0.947865i \(0.396764\pi\)
\(660\) −2.03239e11 8.90448e11i −0.0416926 0.182667i
\(661\) 3.26350e12 1.57162e12i 0.664932 0.320214i −0.0707966 0.997491i \(-0.522554\pi\)
0.735729 + 0.677276i \(0.236840\pi\)
\(662\) 5.91617e12 2.84908e12i 1.19724 0.576558i
\(663\) 3.73960e12 + 4.68931e12i 0.751647 + 0.942536i
\(664\) 7.27923e11 + 3.18924e12i 0.145321 + 0.636694i
\(665\) −1.75998e10 + 7.71099e10i −0.00348988 + 0.0152902i
\(666\) −2.91064e10 3.64983e10i −0.00573264 0.00718851i
\(667\) 2.70723e12 + 3.39476e12i 0.529614 + 0.664115i
\(668\) 4.97440e10 2.17943e11i 0.00966599 0.0423495i
\(669\) −4.30011e11 1.88400e12i −0.0829969 0.363633i
\(670\) −2.94784e12 3.69648e12i −0.565155 0.708682i
\(671\) 1.17828e13 5.67432e12i 2.24387 1.08059i
\(672\) −5.26196e10 + 2.53403e10i −0.00995373 + 0.00479346i
\(673\) 3.61063e11 + 1.58192e12i 0.0678447 + 0.297247i 0.997455 0.0712966i \(-0.0227137\pi\)
−0.929610 + 0.368544i \(0.879857\pi\)
\(674\) −6.62831e12 + 8.31164e12i −1.23718 + 1.55138i
\(675\) 3.12393e12 + 1.50440e12i 0.579207 + 0.278931i
\(676\) 3.38071e10 4.23927e10i 0.00622655 0.00780785i
\(677\) 1.11083e12 4.86686e12i 0.203235 0.890430i −0.765716 0.643178i \(-0.777615\pi\)
0.968951 0.247252i \(-0.0795275\pi\)
\(678\) 8.74618e11 4.21194e11i 0.158959 0.0765506i
\(679\) 6.32985e10 2.77329e11i 0.0114282 0.0500704i
\(680\) −3.23162e12 1.55627e12i −0.579602 0.279122i
\(681\) 6.54841e12 1.16674
\(682\) −1.36493e13 −2.41590
\(683\) 2.23115e12 + 1.07446e12i 0.392315 + 0.188929i 0.619633 0.784892i \(-0.287281\pi\)
−0.227318 + 0.973821i \(0.572996\pi\)
\(684\) −1.11071e10 4.86635e10i −0.00194021 0.00850062i
\(685\) 2.65722e12 + 3.33204e12i 0.461126 + 0.578233i
\(686\) −2.26080e11 + 2.83496e11i −0.0389766 + 0.0488752i
\(687\) −6.19788e12 −1.06154
\(688\) 6.11187e12 + 3.03027e12i 1.03998 + 0.515625i
\(689\) 6.90233e12 1.16684
\(690\) −3.46780e12 + 4.34848e12i −0.582416 + 0.730326i
\(691\) 2.29980e12 + 2.88385e12i 0.383741 + 0.481196i 0.935761 0.352635i \(-0.114714\pi\)
−0.552020 + 0.833831i \(0.686143\pi\)
\(692\) 2.63367e11 + 1.15389e12i 0.0436600 + 0.191287i
\(693\) 1.17284e10 + 5.64808e9i 0.00193169 + 0.000930254i
\(694\) −3.77193e12 −0.617228
\(695\) 8.64415e11 0.140537
\(696\) −2.82297e12 1.35947e12i −0.455999 0.219598i
\(697\) 1.78779e12 7.83284e12i 0.286926 1.25711i
\(698\) −5.99400e11 + 2.88656e11i −0.0955801 + 0.0460290i
\(699\) −2.45860e12 + 1.07718e13i −0.389530 + 1.70664i
\(700\) 1.43018e10 1.79338e10i 0.00225138 0.00282314i
\(701\) 4.15360e12 + 2.00027e12i 0.649671 + 0.312865i 0.729538 0.683940i \(-0.239735\pi\)
−0.0798667 + 0.996806i \(0.525449\pi\)
\(702\) 4.60649e12 5.77635e12i 0.715901 0.897711i
\(703\) −2.27165e11 9.95273e11i −0.0350786 0.153689i
\(704\) 6.67143e12 3.21279e12i 1.02363 0.492953i
\(705\) −3.72122e12 + 1.79204e12i −0.567328 + 0.273211i
\(706\) 3.29968e12 + 4.13767e12i 0.499863 + 0.626808i
\(707\) −1.33582e10 5.85261e10i −0.00201076 0.00880972i
\(708\) −1.77202e11 + 7.76372e11i −0.0265044 + 0.116124i
\(709\) 6.06667e11 + 7.60737e11i 0.0901659 + 0.113065i 0.824868 0.565325i \(-0.191249\pi\)
−0.734702 + 0.678390i \(0.762678\pi\)
\(710\) 2.88224e12 + 3.61421e12i 0.425664 + 0.533766i
\(711\) 7.05074e10 3.08913e11i 0.0103472 0.0453339i
\(712\) −1.74174e12 7.63107e12i −0.253994 1.11282i
\(713\) 8.68465e12 + 1.08902e13i 1.25849 + 1.57810i
\(714\) 2.30221e11 1.10869e11i 0.0331515 0.0159649i
\(715\) −6.15302e12 + 2.96314e12i −0.880463 + 0.424009i
\(716\) −1.94724e9 8.53143e9i −0.000276893 0.00121315i
\(717\) −3.30835e12 + 4.14854e12i −0.467493 + 0.586218i
\(718\) 2.39245e12 + 1.15215e12i 0.335957 + 0.161788i
\(719\) 3.18355e12 3.99204e12i 0.444254 0.557077i −0.508405 0.861118i \(-0.669765\pi\)
0.952659 + 0.304041i \(0.0983361\pi\)
\(720\) −5.44871e10 + 2.38724e11i −0.00755609 + 0.0331054i
\(721\) 1.41329e11 6.80604e10i 0.0194770 0.00937963i
\(722\) −3.31415e11 + 1.45202e12i −0.0453894 + 0.198864i
\(723\) −9.08440e12 4.37482e12i −1.23644 0.595439i
\(724\) −2.64860e11 −0.0358255
\(725\) 2.77140e12 0.372544
\(726\) −1.04612e13 5.03784e12i −1.39755 0.673023i
\(727\) −5.73397e11 2.51222e12i −0.0761291 0.333544i 0.922493 0.386013i \(-0.126148\pi\)
−0.998623 + 0.0524693i \(0.983291\pi\)
\(728\) 1.20901e11 + 1.51605e11i 0.0159528 + 0.0200042i
\(729\) 4.96029e12 6.22001e12i 0.650479 0.815675i
\(730\) −6.37102e12 −0.830341
\(731\) −8.34172e12 4.13583e12i −1.08051 0.535716i
\(732\) −2.42752e12 −0.312510
\(733\) 4.12300e12 5.17008e12i 0.527528 0.661499i −0.444661 0.895699i \(-0.646676\pi\)
0.972188 + 0.234200i \(0.0752472\pi\)
\(734\) 2.87627e12 + 3.60673e12i 0.365762 + 0.458651i
\(735\) −1.04590e12 4.58238e12i −0.132189 0.579160i
\(736\) 4.08058e12 + 1.96510e12i 0.512592 + 0.246851i
\(737\) −1.70167e13 −2.12457
\(738\) −4.53354e11 −0.0562579
\(739\) −9.21123e12 4.43590e12i −1.13610 0.547119i −0.231272 0.972889i \(-0.574289\pi\)
−0.904831 + 0.425770i \(0.860003\pi\)
\(740\) 3.89086e10 1.70470e11i 0.00476983 0.0208980i
\(741\) 6.66816e12 3.21122e12i 0.812502 0.391280i
\(742\) 6.54345e10 2.86687e11i 0.00792481 0.0347209i
\(743\) −8.24534e12 + 1.03393e13i −0.992564 + 1.24464i −0.0230163 + 0.999735i \(0.507327\pi\)
−0.969548 + 0.244901i \(0.921244\pi\)
\(744\) −9.05592e12 4.36110e12i −1.08356 0.521817i
\(745\) 9.77592e11 1.22586e12i 0.116266 0.145793i
\(746\) −6.14060e11 2.69037e12i −0.0725915 0.318044i
\(747\) −2.74611e11 + 1.32246e11i −0.0322683 + 0.0155396i
\(748\) 2.93177e12 1.41187e12i 0.342431 0.164906i
\(749\) −3.43125e10 4.30265e10i −0.00398367 0.00499537i
\(750\) 2.04643e12 + 8.96598e12i 0.236168 + 1.03472i
\(751\) 1.77219e11 7.76449e11i 0.0203297 0.0890703i −0.963745 0.266824i \(-0.914026\pi\)
0.984075 + 0.177753i \(0.0568830\pi\)
\(752\) 6.72214e12 + 8.42930e12i 0.766527 + 0.961195i
\(753\) 6.73104e12 + 8.44046e12i 0.762966 + 0.956729i
\(754\) 1.31407e12 5.75732e12i 0.148063 0.648708i
\(755\) −1.73449e12 7.59932e12i −0.194273 0.851164i
\(756\) −3.28878e10 4.12400e10i −0.00366173 0.00459167i
\(757\) −1.44320e13 + 6.95006e12i −1.59733 + 0.769232i −0.999476 0.0323757i \(-0.989693\pi\)
−0.597851 + 0.801608i \(0.703978\pi\)
\(758\) −1.31476e13 + 6.33156e12i −1.44656 + 0.696625i
\(759\) 4.45447e12 + 1.95163e13i 0.487201 + 2.13457i
\(760\) −2.75957e12 + 3.46039e12i −0.300040 + 0.376239i
\(761\) −1.33600e13 6.43385e12i −1.44403 0.695408i −0.462483 0.886628i \(-0.653041\pi\)
−0.981547 + 0.191220i \(0.938755\pi\)
\(762\) −5.50120e12 + 6.89828e12i −0.591098 + 0.741214i
\(763\) −7.14174e10 + 3.12900e11i −0.00762857 + 0.0334230i
\(764\) −4.25232e11 + 2.04781e11i −0.0451550 + 0.0217455i
\(765\) 7.43661e10 3.25819e11i 0.00785052 0.0343954i
\(766\) 8.38358e12 + 4.03732e12i 0.879833 + 0.423705i
\(767\) 5.95443e12 0.621242
\(768\) −5.46648e12 −0.566999
\(769\) −8.15104e12 3.92533e12i −0.840513 0.404770i −0.0364658 0.999335i \(-0.511610\pi\)
−0.804048 + 0.594565i \(0.797324\pi\)
\(770\) 6.47424e10 + 2.83655e11i 0.00663714 + 0.0290792i
\(771\) −2.34598e12 2.94176e12i −0.239100 0.299821i
\(772\) −9.09515e11 + 1.14050e12i −0.0921578 + 0.115562i
\(773\) 6.20430e12 0.625008 0.312504 0.949917i \(-0.398832\pi\)
0.312504 + 0.949917i \(0.398832\pi\)
\(774\) −1.22782e11 + 5.10831e11i −0.0122971 + 0.0511615i
\(775\) 8.89049e12 0.885254
\(776\) 9.92490e12 1.24454e13i 0.982535 1.23206i
\(777\) −3.08120e10 3.86370e10i −0.00303267 0.00380285i
\(778\) 3.17300e12 + 1.39018e13i 0.310501 + 1.36039i
\(779\) −8.93218e12 4.30151e12i −0.869038 0.418507i
\(780\) 1.26766e12 0.122624
\(781\) 1.66380e13 1.60019
\(782\) −1.78533e13 8.59771e12i −1.70722 0.822152i
\(783\) 1.41813e12 6.21322e12i 0.134830 0.590729i
\(784\) −1.10543e13 + 5.32348e12i −1.04498 + 0.503238i
\(785\) 5.03859e11 2.20755e12i 0.0473582 0.207490i
\(786\) 5.46173e12 6.84879e12i 0.510421 0.640048i
\(787\) 1.12434e13 + 5.41454e12i 1.04475 + 0.503124i 0.875887 0.482516i \(-0.160277\pi\)
0.168861 + 0.985640i \(0.445991\pi\)
\(788\) 7.32542e11 9.18579e11i 0.0676807 0.0848689i
\(789\) −9.06919e11 3.97347e12i −0.0833148 0.365026i
\(790\) 6.38064e12 3.07275e12i 0.582830 0.280676i
\(791\) −4.66902e10 + 2.24848e10i −0.00424064 + 0.00204219i
\(792\) 4.54183e11 + 5.69528e11i 0.0410174 + 0.0514341i
\(793\) 4.03903e12 + 1.76961e13i 0.362700 + 1.58909i
\(794\) 4.06413e12 1.78061e13i 0.362890 1.58993i
\(795\) 4.75508e12 + 5.96268e12i 0.422187 + 0.529406i
\(796\) 5.32268e11 + 6.67442e11i 0.0469917 + 0.0589257i
\(797\) −3.17719e12 + 1.39202e13i −0.278921 + 1.22203i 0.620240 + 0.784412i \(0.287035\pi\)
−0.899161 + 0.437619i \(0.855822\pi\)
\(798\) −7.01628e10 3.07403e11i −0.00612483 0.0268346i
\(799\) −9.17465e12 1.15046e13i −0.796396 0.998648i
\(800\) 2.60450e12 1.25426e12i 0.224812 0.108264i
\(801\) 6.57077e11 3.16432e11i 0.0563988 0.0271602i
\(802\) 1.57633e12 + 6.90637e12i 0.134544 + 0.589475i
\(803\) −1.42968e13 + 1.79276e13i −1.21344 + 1.52161i
\(804\) 2.84583e12 + 1.37048e12i 0.240191 + 0.115670i
\(805\) 1.85123e11 2.32138e11i 0.0155375 0.0194834i
\(806\) 4.21547e12 1.84692e13i 0.351834 1.54149i
\(807\) 8.73513e12 4.20662e12i 0.725001 0.349142i
\(808\) 7.47518e11 3.27509e12i 0.0616979 0.270316i
\(809\) −6.01331e11 2.89586e11i −0.0493566 0.0237689i 0.409043 0.912515i \(-0.365863\pi\)
−0.458399 + 0.888746i \(0.651577\pi\)
\(810\) 7.77061e12 0.634268
\(811\) 5.12312e12 0.415854 0.207927 0.978144i \(-0.433328\pi\)
0.207927 + 0.978144i \(0.433328\pi\)
\(812\) −3.79859e10 1.82931e10i −0.00306634 0.00147667i
\(813\) −2.00722e12 8.79419e12i −0.161134 0.705973i
\(814\) −2.34142e12 2.93605e12i −0.186926 0.234398i
\(815\) 8.53329e12 1.07004e13i 0.677497 0.849554i
\(816\) 1.72994e13 1.36592
\(817\) −7.26598e12 + 8.89964e12i −0.570552 + 0.698833i
\(818\) 1.51972e12 0.118679
\(819\) −1.12648e10 + 1.41256e10i −0.000874874 + 0.00109706i
\(820\) −1.05872e12 1.32760e12i −0.0817749 0.102542i
\(821\) 4.66037e12 + 2.04184e13i 0.357994 + 1.56847i 0.758183 + 0.652042i \(0.226087\pi\)
−0.400189 + 0.916433i \(0.631055\pi\)
\(822\) −1.53076e13 7.37173e12i −1.16945 0.563179i
\(823\) 8.29775e12 0.630465 0.315232 0.949015i \(-0.397918\pi\)
0.315232 + 0.949015i \(0.397918\pi\)
\(824\) 8.77798e12 0.663319
\(825\) 1.15116e13 + 5.54372e12i 0.865157 + 0.416638i
\(826\) 5.64483e10 2.47316e11i 0.00421930 0.0184860i
\(827\) 1.52677e13 7.35253e12i 1.13501 0.546590i 0.230509 0.973070i \(-0.425961\pi\)
0.904497 + 0.426480i \(0.140246\pi\)
\(828\) −4.16961e10 + 1.82683e11i −0.00308290 + 0.0135071i
\(829\) −4.66198e11 + 5.84594e11i −0.0342827 + 0.0429892i −0.798677 0.601760i \(-0.794467\pi\)
0.764395 + 0.644749i \(0.223038\pi\)
\(830\) −6.13774e12 2.95578e12i −0.448908 0.216183i
\(831\) −4.77896e12 + 5.99263e12i −0.347639 + 0.435926i
\(832\) 2.28689e12 + 1.00195e13i 0.165459 + 0.724924i
\(833\) 1.50874e13 7.26569e12i 1.08570 0.522847i
\(834\) −3.10478e12 + 1.49518e12i −0.222220 + 0.107016i
\(835\) −1.15153e12 1.44397e12i −0.0819756 0.102794i
\(836\) −8.93495e11 3.91466e12i −0.0632651 0.277182i
\(837\) 4.54927e12 1.99316e13i 0.320389 1.40371i
\(838\) −7.89383e12 9.89855e12i −0.552955 0.693383i
\(839\) 4.03761e12 + 5.06301e12i 0.281317 + 0.352760i 0.902335 0.431036i \(-0.141852\pi\)
−0.621018 + 0.783797i \(0.713280\pi\)
\(840\) −4.76763e10 + 2.08884e11i −0.00330405 + 0.0144760i
\(841\) 2.09464e12 + 9.17722e12i 0.144387 + 0.632600i
\(842\) −1.58353e13 1.98569e13i −1.08573 1.36147i
\(843\) 2.47414e12 1.19148e12i 0.168733 0.0812576i
\(844\) 4.08998e12 1.96963e12i 0.277447 0.133612i
\(845\) −9.96836e10 4.36743e11i −0.00672618 0.0294693i
\(846\) −5.17702e11 + 6.49178e11i −0.0347467 + 0.0435710i
\(847\) 5.58456e11 + 2.68938e11i 0.0372832 + 0.0179546i
\(848\) 1.24125e13 1.55648e13i 0.824288 1.03362i
\(849\) −9.01540e11 + 3.94991e12i −0.0595526 + 0.260917i
\(850\) −1.13952e13 + 5.48764e12i −0.748749 + 0.360579i
\(851\) −8.52777e11 + 3.73626e12i −0.0557381 + 0.244205i
\(852\) −2.78249e12 1.33998e12i −0.180907 0.0871202i
\(853\) 1.53605e13 0.993424 0.496712 0.867915i \(-0.334540\pi\)
0.496712 + 0.867915i \(0.334540\pi\)
\(854\) 7.73296e11 0.0497491
\(855\) −3.71548e11 1.78928e11i −0.0237776 0.0114507i
\(856\) −6.85279e11 3.00240e12i −0.0436250 0.191134i
\(857\) −1.05541e13 1.32344e13i −0.668355 0.838091i 0.325869 0.945415i \(-0.394343\pi\)
−0.994224 + 0.107324i \(0.965772\pi\)
\(858\) 1.69749e13 2.12858e13i 1.06933 1.34090i
\(859\) 1.32502e13 0.830335 0.415168 0.909745i \(-0.363723\pi\)
0.415168 + 0.909745i \(0.363723\pi\)
\(860\) −1.78265e12 + 8.33396e11i −0.111128 + 0.0519527i
\(861\) −4.79919e11 −0.0297614
\(862\) −1.83413e13 + 2.29992e13i −1.13148 + 1.41883i
\(863\) −3.89006e12 4.87798e12i −0.238730 0.299358i 0.648005 0.761636i \(-0.275604\pi\)
−0.886735 + 0.462278i \(0.847032\pi\)
\(864\) −1.47921e12 6.48085e12i −0.0903064 0.395658i
\(865\) 8.80998e12 + 4.24266e12i 0.535060 + 0.257671i
\(866\) 1.46792e13 0.886894
\(867\) −7.37773e12 −0.443442
\(868\) −1.21857e11 5.86831e10i −0.00728636 0.00350893i
\(869\) 5.67186e12 2.48501e13i 0.337393 1.47822i
\(870\) 5.87882e12 2.83109e12i 0.347899 0.167539i
\(871\) 5.25548e12 2.30257e13i 0.309407 1.35560i
\(872\) −1.11979e13 + 1.40417e13i −0.655861 + 0.822424i
\(873\) 1.33629e12 + 6.43522e11i 0.0778639 + 0.0374973i
\(874\) −1.52454e13 + 1.91172e13i −0.883768 + 1.10821i
\(875\) −1.09246e11 4.78636e11i −0.00630039 0.0276038i
\(876\) 3.83480e12 1.84674e12i 0.220026 0.105959i
\(877\) −3.00797e13 + 1.44856e13i −1.71702 + 0.826873i −0.726884 + 0.686760i \(0.759032\pi\)
−0.990136 + 0.140113i \(0.955254\pi\)
\(878\) −6.72534e12 8.43331e12i −0.381934 0.478931i
\(879\) 4.49399e12 + 1.96895e13i 0.253911 + 1.11246i
\(880\) −4.38313e12 + 1.92038e13i −0.246384 + 1.07948i
\(881\) −6.63351e12 8.31815e12i −0.370981 0.465195i 0.560940 0.827856i \(-0.310440\pi\)
−0.931921 + 0.362661i \(0.881868\pi\)
\(882\) −5.89147e11 7.38767e11i −0.0327805 0.0411054i
\(883\) −3.54699e12 + 1.55404e13i −0.196353 + 0.860278i 0.776732 + 0.629831i \(0.216876\pi\)
−0.973085 + 0.230447i \(0.925981\pi\)
\(884\) 1.00498e12 + 4.40310e12i 0.0553506 + 0.242507i
\(885\) 4.10206e12 + 5.14382e12i 0.224780 + 0.281865i
\(886\) 2.24653e13 1.08187e13i 1.22479 0.589827i
\(887\) −2.35363e12 + 1.13345e12i −0.127668 + 0.0614816i −0.496627 0.867964i \(-0.665428\pi\)
0.368959 + 0.929446i \(0.379714\pi\)
\(888\) −6.15368e11 2.69610e12i −0.0332106 0.145505i
\(889\) 2.93673e11 3.68255e11i 0.0157691 0.0197738i
\(890\) 1.46861e13 + 7.07246e12i 0.784606 + 0.377846i
\(891\) 1.74375e13 2.18660e13i 0.926905 1.16230i
\(892\) 3.23795e11 1.41864e12i 0.0171249 0.0750291i
\(893\) −1.63595e13 + 7.87833e12i −0.860873 + 0.414575i
\(894\) −1.39091e12 + 6.09395e12i −0.0728247 + 0.319066i
\(895\) −6.51379e10 3.13688e10i −0.00339336 0.00163416i
\(896\) 6.56286e11 0.0340179
\(897\) −2.77838e13 −1.43293
\(898\) −1.59446e13 7.67850e12i −0.818219 0.394033i
\(899\) −3.63621e12 1.59313e13i −0.185665 0.813453i
\(900\) 7.45688e10 + 9.35063e10i 0.00378849 + 0.00475061i
\(901\) −1.69411e13 + 2.12435e13i −0.856407 + 1.07390i
\(902\) −3.64694e13 −1.83442
\(903\) −1.29977e11 + 5.40765e11i −0.00650537 + 0.0270653i
\(904\) −2.89995e12 −0.144422
\(905\) −1.36433e12 + 1.71082e12i −0.0676085 + 0.0847784i
\(906\) 1.93745e13 + 2.42948e13i 0.955329 + 1.19794i
\(907\) −3.14860e12 1.37949e13i −0.154484 0.676840i −0.991549 0.129735i \(-0.958587\pi\)
0.837064 0.547104i \(-0.184270\pi\)
\(908\) 4.44260e12 + 2.13944e12i 0.216895 + 0.104451i
\(909\) 3.13000e11 0.0152057
\(910\) −4.03817e11 −0.0195208
\(911\) −2.60382e13 1.25394e13i −1.25250 0.603174i −0.314321 0.949317i \(-0.601777\pi\)
−0.938182 + 0.346143i \(0.887491\pi\)
\(912\) 4.75010e12 2.08115e13i 0.227366 0.996156i
\(913\) −2.20907e13 + 1.06383e13i −1.05218 + 0.506704i
\(914\) −4.88695e12 + 2.14111e13i −0.231622 + 1.01480i
\(915\) −1.25045e13 + 1.56802e13i −0.589756 + 0.739531i
\(916\) −4.20479e12 2.02492e12i −0.197340 0.0950338i
\(917\) −2.91566e11 + 3.65613e11i −0.0136168 + 0.0170749i
\(918\) 6.47184e12 + 2.83550e13i 0.300771 + 1.31776i
\(919\) 5.05457e12 2.43415e12i 0.233757 0.112571i −0.313339 0.949641i \(-0.601448\pi\)
0.547096 + 0.837070i \(0.315733\pi\)
\(920\) 1.49698e13 7.20907e12i 0.688923 0.331768i
\(921\) 1.55749e13 + 1.95303e13i 0.713275 + 0.894418i
\(922\) 5.89887e12 + 2.58447e13i 0.268831 + 1.17783i
\(923\) −5.13851e12 + 2.25133e13i −0.233040 + 1.02101i
\(924\) −1.21191e11 1.51969e11i −0.00546950 0.00685853i
\(925\) 1.52509e12 + 1.91241e12i 0.0684949 + 0.0858899i
\(926\) −1.35333e12 + 5.92935e12i −0.0604861 + 0.265007i
\(927\) 1.81995e11 + 7.97372e11i 0.00809470 + 0.0354652i
\(928\) −3.31281e12 4.15413e12i −0.146633 0.183872i
\(929\) −7.79572e12 + 3.75422e12i −0.343388 + 0.165367i −0.597627 0.801774i \(-0.703890\pi\)
0.254238 + 0.967142i \(0.418175\pi\)
\(930\) 1.88589e13 9.08197e12i 0.826691 0.398114i
\(931\) −4.59807e12 2.01455e13i −0.200587 0.878827i
\(932\) −5.18726e12 + 6.50461e12i −0.225199 + 0.282390i
\(933\) 1.45137e13 + 6.98945e12i 0.627064 + 0.301978i
\(934\) 2.61411e13 3.27799e13i 1.12399 1.40944i
\(935\) 5.98227e12 2.62100e13i 0.255985 1.12154i
\(936\) −9.10914e11 + 4.38673e11i −0.0387914 + 0.0186810i
\(937\) 3.16081e12 1.38484e13i 0.133958 0.586910i −0.862735 0.505656i \(-0.831250\pi\)
0.996693 0.0812539i \(-0.0258925\pi\)
\(938\) −9.06548e11 4.36570e11i −0.0382365 0.0184137i
\(939\) −1.62412e13 −0.681747
\(940\) −3.11004e12 −0.129924
\(941\) −1.69479e13 8.16167e12i −0.704632 0.339333i 0.0470192 0.998894i \(-0.485028\pi\)
−0.751651 + 0.659561i \(0.770742\pi\)
\(942\) 2.00866e12 + 8.80053e12i 0.0831148 + 0.364150i
\(943\) 2.32045e13 + 2.90975e13i 0.955584 + 1.19826i
\(944\) 1.07079e13 1.34273e13i 0.438865 0.550319i
\(945\) −4.35793e11 −0.0177761
\(946\) −9.87705e12 + 4.10931e13i −0.400975 + 1.66824i
\(947\) −1.11517e13 −0.450573 −0.225286 0.974293i \(-0.572332\pi\)
−0.225286 + 0.974293i \(0.572332\pi\)
\(948\) −2.94990e12 + 3.69906e12i −0.118623 + 0.148749i
\(949\) −1.98429e13 2.48822e13i −0.794158 0.995843i
\(950\) 3.47283e12 + 1.52155e13i 0.138334 + 0.606079i
\(951\) 1.34148e13 + 6.46021e12i 0.531827 + 0.256115i
\(952\) −7.63337e11 −0.0301197
\(953\) 1.60819e13 0.631568 0.315784 0.948831i \(-0.397733\pi\)
0.315784 + 0.948831i \(0.397733\pi\)
\(954\) 1.38138e12 + 6.65237e11i 0.0539940 + 0.0260021i
\(955\) −8.67685e11 + 3.80158e12i −0.0337557 + 0.147893i
\(956\) −3.59983e12 + 1.73359e12i −0.139387 + 0.0671252i
\(957\) 5.22578e12 2.28957e13i 0.201395 0.882367i
\(958\) 1.75237e13 2.19740e13i 0.672173 0.842878i
\(959\) 8.17172e11 + 3.93529e11i 0.0311982 + 0.0150243i
\(960\) −7.08005e12 + 8.87810e12i −0.269039 + 0.337365i
\(961\) −5.78140e12 2.53299e13i −0.218664 0.958030i
\(962\) 4.69598e12 2.26146e12i 0.176782 0.0851338i
\(963\) 2.58524e11 1.24498e11i 0.00968683 0.00466493i
\(964\) −4.73376e12 5.93595e12i −0.176547 0.221383i
\(965\) 2.68180e12 + 1.17497e13i 0.0995527 + 0.436169i
\(966\) −2.63391e11 + 1.15399e12i −0.00973205 + 0.0426389i
\(967\) −2.28196e13 2.86149e13i −0.839246 1.05238i −0.997882 0.0650445i \(-0.979281\pi\)
0.158636 0.987337i \(-0.449290\pi\)
\(968\) 2.16263e13 + 2.71185e13i 0.791668 + 0.992720i
\(969\) −6.48312e12 + 2.84044e13i −0.236226 + 1.03497i
\(970\) 7.37652e12 + 3.23187e13i 0.267534 + 1.17214i
\(971\) −1.63809e13 2.05410e13i −0.591360 0.741543i 0.392643 0.919691i \(-0.371561\pi\)
−0.984004 + 0.178148i \(0.942989\pi\)
\(972\) 4.84228e11 2.33192e11i 0.0174001 0.00837944i
\(973\) 1.65744e11 7.98182e10i 0.00592830 0.00285492i
\(974\) −1.29803e13 5.68704e13i −0.462135 2.02475i
\(975\) −1.10566e13 + 1.38646e13i −0.391834 + 0.491344i
\(976\) 4.71684e13 + 2.27151e13i 1.66390 + 0.801291i
\(977\) −1.30759e12 + 1.63967e12i −0.0459143 + 0.0575746i −0.804258 0.594280i \(-0.797437\pi\)
0.758344 + 0.651854i \(0.226009\pi\)
\(978\) −1.21411e13 + 5.31934e13i −0.424357 + 1.85923i
\(979\) 5.28576e13 2.54549e13i 1.83901 0.885622i
\(980\) 7.87555e11 3.45050e12i 0.0272749 0.119499i
\(981\) −1.50768e12 7.26062e11i −0.0519756 0.0250301i
\(982\) −2.58566e13 −0.887300
\(983\) −4.43958e13 −1.51653 −0.758265 0.651947i \(-0.773953\pi\)
−0.758265 + 0.651947i \(0.773953\pi\)
\(984\) −2.41965e13 1.16524e13i −0.822761 0.396221i
\(985\) −2.15998e12 9.46347e12i −0.0731115 0.320322i
\(986\) 1.44942e13 + 1.81751e13i 0.488369 + 0.612395i
\(987\) −5.48038e11 + 6.87218e11i −0.0183816 + 0.0230498i
\(988\) 5.57298e12 0.186072
\(989\) 3.90710e13 1.82659e13i 1.29859 0.607096i
\(990\) −1.51700e12 −0.0501912
\(991\) −5.93833e12 + 7.44643e12i −0.195584 + 0.245254i −0.869947 0.493146i \(-0.835847\pi\)
0.674363 + 0.738400i \(0.264418\pi\)
\(992\) −1.06273e13 1.33262e13i −0.348434 0.436923i
\(993\) 8.06492e12 + 3.53347e13i 0.263226 + 1.15327i
\(994\) 8.86372e11 + 4.26854e11i 0.0287990 + 0.0138689i
\(995\) 7.05302e12 0.228124
\(996\) 4.55116e12 0.146540
\(997\) −1.12520e12 5.41870e11i −0.0360664 0.0173687i 0.415764 0.909473i \(-0.363514\pi\)
−0.451830 + 0.892104i \(0.649229\pi\)
\(998\) 1.06074e13 4.64741e13i 0.338471 1.48294i
\(999\) 5.06783e12 2.44054e12i 0.160982 0.0775248i
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 43.10.e.a.4.9 192
43.11 even 7 inner 43.10.e.a.11.9 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.e.a.4.9 192 1.1 even 1 trivial
43.10.e.a.11.9 yes 192 43.11 even 7 inner