Properties

Label 29.10.e.a.4.4
Level $29$
Weight $10$
Character 29.4
Analytic conductor $14.936$
Analytic rank $0$
Dimension $132$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [29,10,Mod(4,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 29.e (of order \(14\), 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: \(14.9360392488\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 4.4
Character \(\chi\) \(=\) 29.4
Dual form 29.10.e.a.22.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-31.7893 - 7.25570i) q^{2} +(38.8499 + 80.6726i) q^{3} +(496.618 + 239.158i) q^{4} +(230.482 - 1009.81i) q^{5} +(-649.674 - 2846.41i) q^{6} +(-5320.98 + 2562.45i) q^{7} +(-999.429 - 797.018i) q^{8} +(7273.39 - 9120.54i) q^{9} +O(q^{10})\) \(q+(-31.7893 - 7.25570i) q^{2} +(38.8499 + 80.6726i) q^{3} +(496.618 + 239.158i) q^{4} +(230.482 - 1009.81i) q^{5} +(-649.674 - 2846.41i) q^{6} +(-5320.98 + 2562.45i) q^{7} +(-999.429 - 797.018i) q^{8} +(7273.39 - 9120.54i) q^{9} +(-14653.7 + 30428.7i) q^{10} +(-69837.1 + 55693.2i) q^{11} +49354.7i q^{12} +(54680.3 + 68567.0i) q^{13} +(187742. - 42851.0i) q^{14} +(90418.0 - 20637.3i) q^{15} +(-149971. - 188058. i) q^{16} -135801. i q^{17} +(-297392. + 237162. i) q^{18} +(416661. - 865206. i) q^{19} +(355965. - 446366. i) q^{20} +(-413439. - 329707. i) q^{21} +(2.62416e6 - 1.26373e6i) q^{22} +(-101489. - 444653. i) q^{23} +(25469.8 - 111591. i) q^{24} +(793118. + 381945. i) q^{25} +(-1.24075e6 - 2.57644e6i) q^{26} +(2.73657e6 + 624605. i) q^{27} -3.25532e6 q^{28} +(1.15337e6 - 3.63000e6i) q^{29} -3.02406e6 q^{30} +(6.42736e6 + 1.46700e6i) q^{31} +(3.68695e6 + 7.65604e6i) q^{32} +(-7.20608e6 - 3.47027e6i) q^{33} +(-985331. + 4.31702e6i) q^{34} +(1.36119e6 + 5.96376e6i) q^{35} +(5.79335e6 - 2.78993e6i) q^{36} +(-6.16924e6 - 4.91981e6i) q^{37} +(-1.95230e7 + 2.44811e7i) q^{38} +(-3.40715e6 + 7.07503e6i) q^{39} +(-1.03518e6 + 825532. i) q^{40} -2.04942e7i q^{41} +(1.07507e7 + 1.34809e7i) q^{42} +(2.10519e7 - 4.80495e6i) q^{43} +(-4.80018e7 + 1.09561e7i) q^{44} +(-7.53360e6 - 9.44683e6i) q^{45} +1.48716e7i q^{46} +(3.22645e7 - 2.57300e7i) q^{47} +(9.34474e6 - 1.94046e7i) q^{48} +(-3.41339e6 + 4.28025e6i) q^{49} +(-2.24414e7 - 1.78964e7i) q^{50} +(1.09554e7 - 5.27586e6i) q^{51} +(1.07568e7 + 4.71288e7i) q^{52} +(1.19566e7 - 5.23855e7i) q^{53} +(-8.24618e7 - 3.97115e7i) q^{54} +(4.01432e7 + 8.33582e7i) q^{55} +(7.36026e6 + 1.67993e6i) q^{56} +8.59857e7 q^{57} +(-6.30030e7 + 1.07027e8i) q^{58} -1.35055e7 q^{59} +(4.98387e7 + 1.13754e7i) q^{60} +(3.80307e7 + 7.89715e7i) q^{61} +(-1.93677e8 - 9.32700e7i) q^{62} +(-1.53306e7 + 6.71679e7i) q^{63} +(-3.42515e7 - 1.50066e8i) q^{64} +(8.18422e7 - 3.94131e7i) q^{65} +(2.03897e8 + 1.62602e8i) q^{66} +(3.75293e6 - 4.70602e6i) q^{67} +(3.24780e7 - 6.74412e7i) q^{68} +(3.19285e7 - 2.54621e7i) q^{69} -1.99460e8i q^{70} +(-2.29445e8 - 2.87715e8i) q^{71} +(-1.45385e7 + 3.31831e6i) q^{72} +(-2.00211e8 + 4.56969e7i) q^{73} +(1.60419e8 + 2.01159e8i) q^{74} +7.88214e7i q^{75} +(4.13843e8 - 3.30028e8i) q^{76} +(2.28891e8 - 4.75296e8i) q^{77} +(1.59645e8 - 2.00189e8i) q^{78} +(2.12177e8 + 1.69206e8i) q^{79} +(-2.24467e8 + 1.08098e8i) q^{80} +(4.83313e6 + 2.11753e7i) q^{81} +(-1.48700e8 + 6.51496e8i) q^{82} +(4.42598e8 + 2.13144e8i) q^{83} +(-1.26469e8 - 2.62616e8i) q^{84} +(-1.37133e8 - 3.12997e7i) q^{85} -7.04087e8 q^{86} +(3.37650e8 - 4.79794e7i) q^{87} +1.14186e8 q^{88} +(-1.85049e8 - 4.22361e7i) q^{89} +(1.70944e8 + 3.54970e8i) q^{90} +(-4.66652e8 - 2.24728e8i) q^{91} +(5.59412e7 - 2.45095e8i) q^{92} +(1.31355e8 + 5.75505e8i) q^{93} +(-1.21235e9 + 5.83839e8i) q^{94} +(-7.77658e8 - 6.20161e8i) q^{95} +(-4.74395e8 + 5.94873e8i) q^{96} +(3.48171e8 - 7.22985e8i) q^{97} +(1.39565e8 - 1.11300e8i) q^{98} +1.04203e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q - 7 q^{2} - 7 q^{3} + 5797 q^{4} + 1367 q^{5} - 7607 q^{6} + 4949 q^{7} + 31766 q^{8} + 112237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 132 q - 7 q^{2} - 7 q^{3} + 5797 q^{4} + 1367 q^{5} - 7607 q^{6} + 4949 q^{7} + 31766 q^{8} + 112237 q^{9} - 7 q^{10} + 230503 q^{11} + 370719 q^{13} - 7 q^{14} - 134953 q^{15} - 942171 q^{16} + 2518152 q^{18} - 7 q^{19} + 2630005 q^{20} - 5671057 q^{21} - 1956426 q^{22} - 5580815 q^{23} + 3549677 q^{24} - 4029457 q^{25} + 9649689 q^{26} + 6835241 q^{27} - 24789228 q^{28} - 4235889 q^{29} + 34444162 q^{30} + 10383597 q^{31} + 8347164 q^{32} + 35912671 q^{33} - 11257679 q^{34} + 873325 q^{35} - 125256554 q^{36} - 32126087 q^{37} + 131520700 q^{38} + 192355527 q^{39} - 158097415 q^{40} + 127695676 q^{42} - 78365203 q^{43} - 238378098 q^{44} + 57884904 q^{45} + 6546071 q^{47} - 400523802 q^{48} - 221520647 q^{49} + 154918442 q^{50} + 278243026 q^{51} - 52352040 q^{52} + 352279862 q^{53} + 155358204 q^{54} + 143671997 q^{55} - 575895495 q^{56} - 298751838 q^{57} - 1211966547 q^{58} + 776098748 q^{59} + 112101752 q^{60} - 124049779 q^{61} + 669065875 q^{62} + 1929121403 q^{63} + 1625889382 q^{64} - 866654028 q^{65} - 852661411 q^{66} + 13275097 q^{67} - 1504278412 q^{68} - 1267751723 q^{69} + 1776837051 q^{71} + 6219206035 q^{72} - 1507755424 q^{73} - 4950184776 q^{74} + 422070887 q^{76} - 561272089 q^{77} - 1228370591 q^{78} - 973234717 q^{79} + 1423181574 q^{80} + 2306016039 q^{81} - 1386574594 q^{82} - 932915983 q^{83} + 261177525 q^{84} - 3402309596 q^{85} - 3486024644 q^{86} - 1597393079 q^{87} + 5582534 q^{88} + 2316401563 q^{89} - 4748880458 q^{90} + 659194133 q^{91} + 11318573556 q^{92} + 3911968919 q^{93} + 3703837052 q^{94} + 2797945913 q^{95} - 1910264674 q^{96} - 2438073624 q^{97} - 1034416404 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31.7893 7.25570i −1.40490 0.320660i −0.548146 0.836383i \(-0.684666\pi\)
−0.856755 + 0.515723i \(0.827523\pi\)
\(3\) 38.8499 + 80.6726i 0.276914 + 0.575017i 0.992321 0.123691i \(-0.0394731\pi\)
−0.715407 + 0.698708i \(0.753759\pi\)
\(4\) 496.618 + 239.158i 0.969956 + 0.467106i
\(5\) 230.482 1009.81i 0.164919 0.722559i −0.823058 0.567958i \(-0.807734\pi\)
0.987977 0.154601i \(-0.0494092\pi\)
\(6\) −649.674 2846.41i −0.204652 0.896637i
\(7\) −5320.98 + 2562.45i −0.837626 + 0.403380i −0.802970 0.596020i \(-0.796748\pi\)
−0.0346566 + 0.999399i \(0.511034\pi\)
\(8\) −999.429 797.018i −0.0862675 0.0687960i
\(9\) 7273.39 9120.54i 0.369526 0.463371i
\(10\) −14653.7 + 30428.7i −0.463391 + 0.962241i
\(11\) −69837.1 + 55693.2i −1.43820 + 1.14693i −0.474395 + 0.880312i \(0.657333\pi\)
−0.963804 + 0.266613i \(0.914096\pi\)
\(12\) 49354.7i 0.687089i
\(13\) 54680.3 + 68567.0i 0.530990 + 0.665840i 0.972902 0.231218i \(-0.0742712\pi\)
−0.441912 + 0.897058i \(0.645700\pi\)
\(14\) 187742. 42851.0i 1.30613 0.298116i
\(15\) 90418.0 20637.3i 0.461152 0.105255i
\(16\) −149971. 188058.i −0.572093 0.717382i
\(17\) 135801.i 0.394351i −0.980368 0.197175i \(-0.936823\pi\)
0.980368 0.197175i \(-0.0631769\pi\)
\(18\) −297392. + 237162.i −0.667733 + 0.532499i
\(19\) 416661. 865206.i 0.733486 1.52310i −0.114700 0.993400i \(-0.536591\pi\)
0.848186 0.529699i \(-0.177695\pi\)
\(20\) 355965. 446366.i 0.497476 0.623816i
\(21\) −413439. 329707.i −0.463900 0.369948i
\(22\) 2.62416e6 1.26373e6i 2.38830 1.15014i
\(23\) −101489. 444653.i −0.0756214 0.331319i 0.922940 0.384944i \(-0.125779\pi\)
−0.998561 + 0.0536256i \(0.982922\pi\)
\(24\) 25469.8 111591.i 0.0156702 0.0686558i
\(25\) 793118. + 381945.i 0.406076 + 0.195556i
\(26\) −1.24075e6 2.57644e6i −0.532480 1.10571i
\(27\) 2.73657e6 + 624605.i 0.990993 + 0.226188i
\(28\) −3.25532e6 −1.00088
\(29\) 1.15337e6 3.63000e6i 0.302816 0.953049i
\(30\) −3.02406e6 −0.681624
\(31\) 6.42736e6 + 1.46700e6i 1.24999 + 0.285301i 0.795774 0.605593i \(-0.207064\pi\)
0.454211 + 0.890894i \(0.349921\pi\)
\(32\) 3.68695e6 + 7.65604e6i 0.621574 + 1.29071i
\(33\) −7.20608e6 3.47027e6i −1.05776 0.509389i
\(34\) −985331. + 4.31702e6i −0.126452 + 0.554024i
\(35\) 1.36119e6 + 5.96376e6i 0.153325 + 0.671759i
\(36\) 5.79335e6 2.78993e6i 0.574868 0.276842i
\(37\) −6.16924e6 4.91981e6i −0.541158 0.431559i 0.314381 0.949297i \(-0.398203\pi\)
−0.855539 + 0.517738i \(0.826774\pi\)
\(38\) −1.95230e7 + 2.44811e7i −1.51887 + 1.90460i
\(39\) −3.40715e6 + 7.07503e6i −0.235831 + 0.489708i
\(40\) −1.03518e6 + 825532.i −0.0639363 + 0.0509875i
\(41\) 2.04942e7i 1.13267i −0.824175 0.566335i \(-0.808361\pi\)
0.824175 0.566335i \(-0.191639\pi\)
\(42\) 1.07507e7 + 1.34809e7i 0.533107 + 0.668495i
\(43\) 2.10519e7 4.80495e6i 0.939036 0.214329i 0.274502 0.961587i \(-0.411487\pi\)
0.664534 + 0.747258i \(0.268630\pi\)
\(44\) −4.80018e7 + 1.09561e7i −1.93073 + 0.440676i
\(45\) −7.53360e6 9.44683e6i −0.273871 0.343423i
\(46\) 1.48716e7i 0.489719i
\(47\) 3.22645e7 2.57300e7i 0.964459 0.769131i −0.00853400 0.999964i \(-0.502716\pi\)
0.972993 + 0.230833i \(0.0741451\pi\)
\(48\) 9.34474e6 1.94046e7i 0.254087 0.527616i
\(49\) −3.41339e6 + 4.28025e6i −0.0845869 + 0.106069i
\(50\) −2.24414e7 1.78964e7i −0.507790 0.404949i
\(51\) 1.09554e7 5.27586e6i 0.226758 0.109201i
\(52\) 1.07568e7 + 4.71288e7i 0.204019 + 0.893864i
\(53\) 1.19566e7 5.23855e7i 0.208146 0.911947i −0.757654 0.652657i \(-0.773654\pi\)
0.965799 0.259290i \(-0.0834886\pi\)
\(54\) −8.24618e7 3.97115e7i −1.31972 0.635542i
\(55\) 4.01432e7 + 8.33582e7i 0.591534 + 1.22833i
\(56\) 7.36026e6 + 1.67993e6i 0.100011 + 0.0228268i
\(57\) 8.59857e7 1.07892
\(58\) −6.30030e7 + 1.07027e8i −0.731031 + 1.24184i
\(59\) −1.35055e7 −0.145104 −0.0725518 0.997365i \(-0.523114\pi\)
−0.0725518 + 0.997365i \(0.523114\pi\)
\(60\) 4.98387e7 + 1.13754e7i 0.496462 + 0.113314i
\(61\) 3.80307e7 + 7.89715e7i 0.351682 + 0.730275i 0.999503 0.0315176i \(-0.0100340\pi\)
−0.647821 + 0.761792i \(0.724320\pi\)
\(62\) −1.93677e8 9.32700e7i −1.66462 0.801640i
\(63\) −1.53306e7 + 6.71679e7i −0.122610 + 0.537192i
\(64\) −3.42515e7 1.50066e8i −0.255193 1.11808i
\(65\) 8.18422e7 3.94131e7i 0.568679 0.273861i
\(66\) 2.03897e8 + 1.62602e8i 1.32271 + 1.05482i
\(67\) 3.75293e6 4.70602e6i 0.0227527 0.0285310i −0.770325 0.637652i \(-0.779906\pi\)
0.793078 + 0.609120i \(0.208477\pi\)
\(68\) 3.24780e7 6.74412e7i 0.184204 0.382503i
\(69\) 3.19285e7 2.54621e7i 0.169573 0.135230i
\(70\) 1.99460e8i 0.992921i
\(71\) −2.29445e8 2.87715e8i −1.07156 1.34369i −0.935634 0.352972i \(-0.885171\pi\)
−0.135924 0.990719i \(-0.543400\pi\)
\(72\) −1.45385e7 + 3.31831e6i −0.0637562 + 0.0145519i
\(73\) −2.00211e8 + 4.56969e7i −0.825154 + 0.188336i −0.614190 0.789158i \(-0.710517\pi\)
−0.210964 + 0.977494i \(0.567660\pi\)
\(74\) 1.60419e8 + 2.01159e8i 0.621890 + 0.779826i
\(75\) 7.88214e7i 0.287653i
\(76\) 4.13843e8 3.30028e8i 1.42290 1.13472i
\(77\) 2.28891e8 4.75296e8i 0.742027 1.54083i
\(78\) 1.59645e8 2.00189e8i 0.488349 0.612370i
\(79\) 2.12177e8 + 1.69206e8i 0.612882 + 0.488757i 0.880042 0.474895i \(-0.157514\pi\)
−0.267161 + 0.963652i \(0.586085\pi\)
\(80\) −2.24467e8 + 1.08098e8i −0.612700 + 0.295061i
\(81\) 4.83313e6 + 2.11753e7i 0.0124751 + 0.0546572i
\(82\) −1.48700e8 + 6.51496e8i −0.363201 + 1.59129i
\(83\) 4.42598e8 + 2.13144e8i 1.02366 + 0.492971i 0.868904 0.494981i \(-0.164825\pi\)
0.154761 + 0.987952i \(0.450539\pi\)
\(84\) −1.26469e8 2.62616e8i −0.277158 0.575524i
\(85\) −1.37133e8 3.12997e7i −0.284942 0.0650361i
\(86\) −7.04087e8 −1.38798
\(87\) 3.37650e8 4.79794e7i 0.631873 0.0897880i
\(88\) 1.14186e8 0.202974
\(89\) −1.85049e8 4.22361e7i −0.312630 0.0713557i 0.0633271 0.997993i \(-0.479829\pi\)
−0.375957 + 0.926637i \(0.622686\pi\)
\(90\) 1.70944e8 + 3.54970e8i 0.274640 + 0.570295i
\(91\) −4.66652e8 2.24728e8i −0.713357 0.343535i
\(92\) 5.59412e7 2.45095e8i 0.0814117 0.356688i
\(93\) 1.31355e8 + 5.75505e8i 0.182085 + 0.797767i
\(94\) −1.21235e9 + 5.83839e8i −1.60160 + 0.771290i
\(95\) −7.77658e8 6.20161e8i −0.979563 0.781175i
\(96\) −4.74395e8 + 5.94873e8i −0.570059 + 0.714831i
\(97\) 3.48171e8 7.22985e8i 0.399319 0.829194i −0.600249 0.799813i \(-0.704932\pi\)
0.999568 0.0293815i \(-0.00935376\pi\)
\(98\) 1.39565e8 1.11300e8i 0.152848 0.121892i
\(99\) 1.04203e9i 1.09024i
\(100\) 3.02531e8 + 3.79362e8i 0.302531 + 0.379362i
\(101\) 5.43093e8 1.23958e8i 0.519312 0.118530i 0.0451723 0.998979i \(-0.485616\pi\)
0.474140 + 0.880450i \(0.342759\pi\)
\(102\) −3.86545e8 + 8.82264e7i −0.353590 + 0.0807045i
\(103\) 8.76016e8 + 1.09849e9i 0.766910 + 0.961675i 0.999942 0.0107941i \(-0.00343594\pi\)
−0.233031 + 0.972469i \(0.574865\pi\)
\(104\) 1.12109e8i 0.0939703i
\(105\) −4.28230e8 + 3.41502e8i −0.343815 + 0.274184i
\(106\) −7.60187e8 + 1.57854e9i −0.584849 + 1.21445i
\(107\) −6.55813e8 + 8.22363e8i −0.483674 + 0.606508i −0.962460 0.271424i \(-0.912506\pi\)
0.478786 + 0.877932i \(0.341077\pi\)
\(108\) 1.20965e9 + 9.64665e8i 0.855566 + 0.682291i
\(109\) −4.30825e8 + 2.07474e8i −0.292335 + 0.140781i −0.574303 0.818642i \(-0.694727\pi\)
0.281968 + 0.959424i \(0.409013\pi\)
\(110\) −6.71301e8 2.94116e9i −0.437170 1.91537i
\(111\) 1.57219e8 6.88823e8i 0.0982998 0.430680i
\(112\) 1.27988e9 + 6.16358e8i 0.768578 + 0.370128i
\(113\) 1.16552e8 + 2.42023e8i 0.0672461 + 0.139638i 0.931883 0.362760i \(-0.118166\pi\)
−0.864637 + 0.502398i \(0.832451\pi\)
\(114\) −2.73342e9 6.23886e8i −1.51578 0.345966i
\(115\) −4.72405e8 −0.251869
\(116\) 1.44093e9 1.52688e9i 0.738893 0.782969i
\(117\) 1.02308e9 0.504746
\(118\) 4.29331e8 + 9.79921e7i 0.203856 + 0.0465288i
\(119\) 3.47983e8 + 7.22594e8i 0.159073 + 0.330319i
\(120\) −1.06815e8 5.14392e7i −0.0470235 0.0226453i
\(121\) 1.25079e9 5.48007e9i 0.530457 2.32408i
\(122\) −6.35975e8 2.78639e9i −0.259909 1.13873i
\(123\) 1.65332e9 7.96197e8i 0.651304 0.313652i
\(124\) 2.84109e9 + 2.26570e9i 1.07917 + 0.860606i
\(125\) 1.82981e9 2.29451e9i 0.670364 0.840610i
\(126\) 9.74700e8 2.02398e9i 0.344511 0.715385i
\(127\) 4.03612e9 3.21870e9i 1.37672 1.09790i 0.392739 0.919650i \(-0.371528\pi\)
0.983985 0.178251i \(-0.0570439\pi\)
\(128\) 6.68242e8i 0.220034i
\(129\) 1.20549e9 + 1.51164e9i 0.383275 + 0.480611i
\(130\) −2.88767e9 + 6.59093e8i −0.886754 + 0.202396i
\(131\) −4.42080e9 + 1.00902e9i −1.31154 + 0.299349i −0.820428 0.571750i \(-0.806265\pi\)
−0.491107 + 0.871099i \(0.663408\pi\)
\(132\) −2.74872e9 3.44679e9i −0.788040 0.988171i
\(133\) 5.67141e9i 1.57166i
\(134\) −1.53448e8 + 1.22371e8i −0.0411141 + 0.0327874i
\(135\) 1.26146e9 2.61945e9i 0.326868 0.678748i
\(136\) −1.08236e8 + 1.35724e8i −0.0271298 + 0.0340197i
\(137\) −2.41724e9 1.92768e9i −0.586241 0.467512i 0.284891 0.958560i \(-0.408043\pi\)
−0.871132 + 0.491048i \(0.836614\pi\)
\(138\) −1.19973e9 + 5.77760e8i −0.281597 + 0.135610i
\(139\) 5.39402e8 + 2.36328e9i 0.122559 + 0.536967i 0.998510 + 0.0545668i \(0.0173778\pi\)
−0.875951 + 0.482400i \(0.839765\pi\)
\(140\) −7.50293e8 + 3.28725e9i −0.165065 + 0.723196i
\(141\) 3.32918e9 + 1.60325e9i 0.709335 + 0.341598i
\(142\) 5.20632e9 + 1.08110e10i 1.07457 + 2.23136i
\(143\) −7.63743e9 1.74319e9i −1.52734 0.348605i
\(144\) −2.80598e9 −0.543818
\(145\) −3.39976e9 2.00133e9i −0.638694 0.375978i
\(146\) 6.69613e9 1.21965
\(147\) −4.77909e8 1.09080e8i −0.0844145 0.0192671i
\(148\) −1.88714e9 3.91869e9i −0.323316 0.671372i
\(149\) 2.32330e9 + 1.11884e9i 0.386159 + 0.185965i 0.616883 0.787055i \(-0.288395\pi\)
−0.230724 + 0.973019i \(0.574109\pi\)
\(150\) 5.71905e8 2.50568e9i 0.0922386 0.404124i
\(151\) 2.49168e9 + 1.09167e10i 0.390028 + 1.70882i 0.664552 + 0.747242i \(0.268622\pi\)
−0.274524 + 0.961580i \(0.588520\pi\)
\(152\) −1.10601e9 + 5.32625e8i −0.168059 + 0.0809330i
\(153\) −1.23858e9 9.87733e8i −0.182731 0.145723i
\(154\) −1.07249e10 + 1.34486e10i −1.53656 + 1.92678i
\(155\) 2.96278e9 6.15227e9i 0.412293 0.856136i
\(156\) −3.38410e9 + 2.69873e9i −0.457492 + 0.364837i
\(157\) 1.17167e9i 0.153906i 0.997035 + 0.0769531i \(0.0245192\pi\)
−0.997035 + 0.0769531i \(0.975481\pi\)
\(158\) −5.51725e9 6.91842e9i −0.704314 0.883181i
\(159\) 4.69059e9 1.07060e9i 0.582024 0.132843i
\(160\) 8.58089e9 1.95853e9i 1.03512 0.236260i
\(161\) 1.67942e9 + 2.10593e9i 0.196990 + 0.247017i
\(162\) 7.08216e8i 0.0807882i
\(163\) 5.17280e9 4.12517e9i 0.573959 0.457717i −0.292989 0.956116i \(-0.594650\pi\)
0.866948 + 0.498399i \(0.166078\pi\)
\(164\) 4.90136e9 1.01778e10i 0.529077 1.09864i
\(165\) −5.16517e9 + 6.47691e9i −0.542508 + 0.680284i
\(166\) −1.25234e10 9.98704e9i −1.28007 1.02082i
\(167\) −3.69605e9 + 1.77993e9i −0.367717 + 0.177083i −0.608612 0.793468i \(-0.708273\pi\)
0.240895 + 0.970551i \(0.422559\pi\)
\(168\) 1.50421e8 + 6.59037e8i 0.0145685 + 0.0638290i
\(169\) 6.48233e8 2.84010e9i 0.0611281 0.267820i
\(170\) 4.13225e9 + 1.98999e9i 0.379461 + 0.182739i
\(171\) −4.86061e9 1.00932e10i −0.434718 0.902702i
\(172\) 1.16039e10 + 2.64851e9i 1.01094 + 0.230740i
\(173\) −1.52814e10 −1.29705 −0.648524 0.761194i \(-0.724613\pi\)
−0.648524 + 0.761194i \(0.724613\pi\)
\(174\) −1.10818e10 9.24654e8i −0.916511 0.0764729i
\(175\) −5.19888e9 −0.419024
\(176\) 2.09470e10 + 4.78103e9i 1.64557 + 0.375590i
\(177\) −5.24689e8 1.08953e9i −0.0401811 0.0834370i
\(178\) 5.57611e9 + 2.68531e9i 0.416333 + 0.200496i
\(179\) −2.73408e9 + 1.19788e10i −0.199055 + 0.872117i 0.772446 + 0.635081i \(0.219033\pi\)
−0.971501 + 0.237036i \(0.923824\pi\)
\(180\) −1.48203e9 6.49319e9i −0.105228 0.461033i
\(181\) −1.04660e10 + 5.04014e9i −0.724812 + 0.349051i −0.759641 0.650342i \(-0.774625\pi\)
0.0348294 + 0.999393i \(0.488911\pi\)
\(182\) 1.32040e10 + 1.05298e10i 0.892039 + 0.711377i
\(183\) −4.89335e9 + 6.13607e9i −0.322535 + 0.404446i
\(184\) −2.52965e8 + 5.25288e8i −0.0162698 + 0.0337845i
\(185\) −6.38995e9 + 5.09582e9i −0.401074 + 0.319846i
\(186\) 1.92480e10i 1.17917i
\(187\) 7.56319e9 + 9.48394e9i 0.452291 + 0.567155i
\(188\) 2.21767e10 5.06168e9i 1.29475 0.295518i
\(189\) −1.61618e10 + 3.68882e9i −0.921321 + 0.210286i
\(190\) 2.02215e10 + 2.53569e10i 1.12570 + 1.41158i
\(191\) 4.66252e8i 0.0253496i 0.999920 + 0.0126748i \(0.00403462\pi\)
−0.999920 + 0.0126748i \(0.995965\pi\)
\(192\) 1.07755e10 8.59319e9i 0.572246 0.456351i
\(193\) 9.33632e9 1.93871e10i 0.484360 1.00578i −0.505380 0.862897i \(-0.668648\pi\)
0.989739 0.142886i \(-0.0456382\pi\)
\(194\) −1.63139e10 + 2.04569e10i −0.826893 + 1.03689i
\(195\) 6.35912e9 + 5.07123e9i 0.314950 + 0.251164i
\(196\) −2.71881e9 + 1.30931e9i −0.131591 + 0.0633708i
\(197\) −6.71233e9 2.94086e10i −0.317523 1.39116i −0.841882 0.539662i \(-0.818552\pi\)
0.524359 0.851497i \(-0.324305\pi\)
\(198\) 7.56065e9 3.31254e10i 0.349596 1.53168i
\(199\) −1.09433e10 5.27004e9i −0.494665 0.238218i 0.169882 0.985464i \(-0.445661\pi\)
−0.664547 + 0.747246i \(0.731376\pi\)
\(200\) −4.88248e8 1.01386e9i −0.0215777 0.0448066i
\(201\) 5.25448e8 + 1.19930e8i 0.0227064 + 0.00518258i
\(202\) −1.81640e10 −0.767590
\(203\) 3.16461e9 + 2.22706e10i 0.130794 + 0.920449i
\(204\) 6.70242e9 0.270954
\(205\) −2.06952e10 4.72354e9i −0.818420 0.186799i
\(206\) −1.98776e10 4.12763e10i −0.769063 1.59698i
\(207\) −4.79365e9 2.30850e9i −0.181468 0.0873903i
\(208\) 4.69408e9 2.05661e10i 0.173886 0.761845i
\(209\) 1.90877e10 + 8.36286e10i 0.691982 + 3.03177i
\(210\) 1.60910e10 7.74900e9i 0.570946 0.274953i
\(211\) 2.32753e10 + 1.85614e10i 0.808395 + 0.644674i 0.937900 0.346905i \(-0.112767\pi\)
−0.129505 + 0.991579i \(0.541339\pi\)
\(212\) 1.84663e10 2.31560e10i 0.627869 0.787323i
\(213\) 1.42968e10 2.96876e10i 0.475916 0.988251i
\(214\) 2.68146e10 2.13840e10i 0.873997 0.696989i
\(215\) 2.23658e10i 0.713856i
\(216\) −2.23719e9 2.80535e9i −0.0699296 0.0876890i
\(217\) −3.79590e10 + 8.66389e9i −1.16211 + 0.265243i
\(218\) 1.52010e10 3.46952e9i 0.455845 0.104044i
\(219\) −1.14647e10 1.43762e10i −0.336793 0.422325i
\(220\) 5.09977e10i 1.46774i
\(221\) 9.31146e9 7.42564e9i 0.262575 0.209396i
\(222\) −9.99579e9 + 2.07565e10i −0.276203 + 0.573542i
\(223\) −3.05961e10 + 3.83663e10i −0.828503 + 1.03891i 0.170066 + 0.985433i \(0.445602\pi\)
−0.998569 + 0.0534768i \(0.982970\pi\)
\(224\) −3.92364e10 3.12900e10i −1.04129 0.830404i
\(225\) 9.25220e9 4.45562e9i 0.240671 0.115901i
\(226\) −1.94906e9 8.53940e9i −0.0496979 0.217741i
\(227\) 7.35510e9 3.22248e10i 0.183854 0.805515i −0.795919 0.605403i \(-0.793012\pi\)
0.979773 0.200112i \(-0.0641307\pi\)
\(228\) 4.27020e10 + 2.05642e10i 1.04651 + 0.503970i
\(229\) −1.41674e10 2.94189e10i −0.340432 0.706914i 0.658526 0.752558i \(-0.271180\pi\)
−0.998958 + 0.0456439i \(0.985466\pi\)
\(230\) 1.50174e10 + 3.42763e9i 0.353851 + 0.0807641i
\(231\) 4.72358e10 1.09148
\(232\) −4.04589e9 + 2.70867e9i −0.0916891 + 0.0613846i
\(233\) 5.71567e10 1.27047 0.635237 0.772318i \(-0.280903\pi\)
0.635237 + 0.772318i \(0.280903\pi\)
\(234\) −3.25229e10 7.42315e9i −0.709118 0.161852i
\(235\) −1.85460e10 3.85112e10i −0.396684 0.823723i
\(236\) −6.70709e9 3.22996e9i −0.140744 0.0677788i
\(237\) −5.40720e9 + 2.36905e10i −0.111328 + 0.487761i
\(238\) −5.81921e9 2.54956e10i −0.117562 0.515074i
\(239\) −6.04577e10 + 2.91149e10i −1.19856 + 0.577197i −0.923266 0.384162i \(-0.874490\pi\)
−0.275297 + 0.961359i \(0.588776\pi\)
\(240\) −1.74411e10 1.39088e10i −0.339330 0.270607i
\(241\) −3.65064e10 + 4.57776e10i −0.697096 + 0.874131i −0.996803 0.0799001i \(-0.974540\pi\)
0.299706 + 0.954031i \(0.403111\pi\)
\(242\) −7.95234e10 + 1.65132e11i −1.49048 + 3.09501i
\(243\) 4.16751e10 3.32348e10i 0.766740 0.611455i
\(244\) 4.83140e10i 0.872607i
\(245\) 3.53550e9 + 4.43338e9i 0.0626908 + 0.0786117i
\(246\) −5.83348e10 + 1.33145e10i −1.01559 + 0.231803i
\(247\) 8.21077e10 1.87405e10i 1.40361 0.320366i
\(248\) −5.25446e9 6.58889e9i −0.0882055 0.110606i
\(249\) 4.39861e10i 0.725135i
\(250\) −7.48166e10 + 5.96642e10i −1.21135 + 0.966015i
\(251\) 3.56086e10 7.39421e10i 0.566270 1.17587i −0.399563 0.916706i \(-0.630838\pi\)
0.965833 0.259166i \(-0.0834475\pi\)
\(252\) −2.36772e10 + 2.96903e10i −0.369852 + 0.463780i
\(253\) 3.18519e10 + 2.54010e10i 0.488756 + 0.389770i
\(254\) −1.51659e11 + 7.30352e10i −2.28621 + 1.10098i
\(255\) −2.80257e9 1.22788e10i −0.0415074 0.181856i
\(256\) −1.26882e10 + 5.55906e10i −0.184638 + 0.808950i
\(257\) 1.93558e10 + 9.32127e9i 0.276766 + 0.133283i 0.567118 0.823636i \(-0.308058\pi\)
−0.290352 + 0.956920i \(0.593773\pi\)
\(258\) −2.73537e10 5.68006e10i −0.384351 0.798112i
\(259\) 4.54332e10 + 1.03698e10i 0.627371 + 0.143193i
\(260\) 5.00702e10 0.679516
\(261\) −2.47186e10 3.69218e10i −0.329717 0.492493i
\(262\) 1.47855e11 1.93857
\(263\) 1.26261e11 + 2.88183e10i 1.62731 + 0.371422i 0.936237 0.351368i \(-0.114283\pi\)
0.691068 + 0.722790i \(0.257141\pi\)
\(264\) 4.43610e9 + 9.21166e9i 0.0562062 + 0.116713i
\(265\) −5.01434e10 2.41478e10i −0.624608 0.300795i
\(266\) 4.11501e10 1.80290e11i 0.503968 2.20803i
\(267\) −3.78182e9 1.65692e10i −0.0455407 0.199527i
\(268\) 2.98925e9 1.43955e9i 0.0353962 0.0170459i
\(269\) −1.00738e11 8.03359e10i −1.17303 0.935458i −0.174240 0.984703i \(-0.555747\pi\)
−0.998787 + 0.0492455i \(0.984318\pi\)
\(270\) −5.91069e10 + 7.41177e10i −0.676864 + 0.848760i
\(271\) 1.23127e10 2.55676e10i 0.138673 0.287957i −0.820054 0.572286i \(-0.806057\pi\)
0.958727 + 0.284329i \(0.0917709\pi\)
\(272\) −2.55384e10 + 2.03662e10i −0.282900 + 0.225606i
\(273\) 4.63767e10i 0.505322i
\(274\) 6.28555e10 + 7.88183e10i 0.673699 + 0.844792i
\(275\) −7.66608e10 + 1.74973e10i −0.808306 + 0.184491i
\(276\) 2.19457e10 5.00897e9i 0.227646 0.0519586i
\(277\) −6.62879e10 8.31224e10i −0.676512 0.848319i 0.318516 0.947918i \(-0.396816\pi\)
−0.995028 + 0.0995985i \(0.968244\pi\)
\(278\) 7.90406e10i 0.793686i
\(279\) 6.01285e10 4.79509e10i 0.594103 0.473781i
\(280\) 3.39281e9 7.04524e9i 0.0329874 0.0684991i
\(281\) 5.70289e10 7.15120e10i 0.545653 0.684228i −0.430180 0.902743i \(-0.641550\pi\)
0.975833 + 0.218515i \(0.0701214\pi\)
\(282\) −9.41996e10 7.51217e10i −0.887009 0.707366i
\(283\) 1.34916e11 6.49719e10i 1.25033 0.602125i 0.312727 0.949843i \(-0.398758\pi\)
0.937599 + 0.347718i \(0.113043\pi\)
\(284\) −4.51369e10 1.97758e11i −0.411718 1.80385i
\(285\) 1.98181e10 8.68289e10i 0.177935 0.779583i
\(286\) 2.30140e11 + 1.10830e11i 2.03397 + 0.979510i
\(287\) 5.25153e10 + 1.09049e11i 0.456896 + 0.948754i
\(288\) 9.66439e10 + 2.20583e10i 0.827767 + 0.188932i
\(289\) 1.00146e11 0.844487
\(290\) 9.35550e10 + 8.82885e10i 0.776741 + 0.733016i
\(291\) 7.18515e10 0.587378
\(292\) −1.10357e11 2.51883e10i −0.888337 0.202757i
\(293\) 2.70561e10 + 5.61826e10i 0.214467 + 0.445346i 0.980252 0.197750i \(-0.0633636\pi\)
−0.765785 + 0.643097i \(0.777649\pi\)
\(294\) 1.44009e10 + 6.93512e9i 0.112416 + 0.0541366i
\(295\) −3.11278e9 + 1.36380e10i −0.0239304 + 0.104846i
\(296\) 2.24455e9 + 9.83400e9i 0.0169948 + 0.0744590i
\(297\) −2.25901e11 + 1.08788e11i −1.68466 + 0.811291i
\(298\) −6.57380e10 5.24243e10i −0.482884 0.385087i
\(299\) 2.49391e10 3.12726e10i 0.180451 0.226279i
\(300\) −1.88508e10 + 3.91441e10i −0.134364 + 0.279011i
\(301\) −9.97041e10 + 7.95113e10i −0.700106 + 0.558316i
\(302\) 3.65114e11i 2.52579i
\(303\) 3.10991e10 + 3.89970e10i 0.211961 + 0.265791i
\(304\) −2.25195e11 + 5.13994e10i −1.51227 + 0.345165i
\(305\) 8.85113e10 2.02021e10i 0.585665 0.133674i
\(306\) 3.22068e10 + 4.03861e10i 0.209991 + 0.263321i
\(307\) 1.76426e11i 1.13355i 0.823873 + 0.566775i \(0.191809\pi\)
−0.823873 + 0.566775i \(0.808191\pi\)
\(308\) 2.27342e11 1.81299e11i 1.43947 1.14794i
\(309\) −5.45849e10 + 1.13347e11i −0.340612 + 0.707287i
\(310\) −1.38824e11 + 1.74079e11i −0.853760 + 1.07058i
\(311\) −1.52385e11 1.21523e11i −0.923676 0.736607i 0.0412449 0.999149i \(-0.486868\pi\)
−0.964920 + 0.262542i \(0.915439\pi\)
\(312\) 9.04413e9 4.35542e9i 0.0540345 0.0260217i
\(313\) 1.29599e10 + 5.67810e10i 0.0763224 + 0.334390i 0.998646 0.0520292i \(-0.0165689\pi\)
−0.922323 + 0.386419i \(0.873712\pi\)
\(314\) 8.50127e9 3.72465e10i 0.0493515 0.216223i
\(315\) 6.42931e10 + 3.09619e10i 0.367932 + 0.177187i
\(316\) 6.49039e10 + 1.34774e11i 0.366167 + 0.760354i
\(317\) 2.41115e10 + 5.50330e9i 0.134109 + 0.0306095i 0.289049 0.957314i \(-0.406661\pi\)
−0.154939 + 0.987924i \(0.549518\pi\)
\(318\) −1.56878e11 −0.860283
\(319\) 1.21618e11 + 3.17743e11i 0.657567 + 1.71798i
\(320\) −1.59431e11 −0.849961
\(321\) −9.18205e10 2.09574e10i −0.482688 0.110170i
\(322\) −3.81077e10 7.91314e10i −0.197543 0.410202i
\(323\) −1.17496e11 5.65830e10i −0.600636 0.289251i
\(324\) −2.66404e9 + 1.16719e10i −0.0134304 + 0.0588423i
\(325\) 1.71791e10 + 7.52666e10i 0.0854133 + 0.374220i
\(326\) −1.94371e11 + 9.36039e10i −0.953128 + 0.459002i
\(327\) −3.34750e10 2.66954e10i −0.161903 0.129114i
\(328\) −1.63342e10 + 2.04825e10i −0.0779232 + 0.0977126i
\(329\) −1.05747e11 + 2.19585e11i −0.497605 + 1.03329i
\(330\) 2.11191e11 1.68420e11i 0.980310 0.781772i
\(331\) 3.97364e11i 1.81954i −0.415108 0.909772i \(-0.636256\pi\)
0.415108 0.909772i \(-0.363744\pi\)
\(332\) 1.68827e11 + 2.11702e11i 0.762640 + 0.956320i
\(333\) −8.97426e10 + 2.04832e10i −0.399944 + 0.0912847i
\(334\) 1.30410e11 2.97651e10i 0.573390 0.130873i
\(335\) −3.88719e9 4.87438e9i −0.0168630 0.0211455i
\(336\) 1.27197e11i 0.544439i
\(337\) 1.78487e11 1.42338e11i 0.753826 0.601156i −0.169340 0.985558i \(-0.554164\pi\)
0.923166 + 0.384401i \(0.125592\pi\)
\(338\) −4.12138e10 + 8.55812e10i −0.171758 + 0.356659i
\(339\) −1.49966e10 + 1.88051e10i −0.0616728 + 0.0773353i
\(340\) −6.06170e10 4.83404e10i −0.246002 0.196180i
\(341\) −5.30570e11 + 2.55509e11i −2.12495 + 1.02332i
\(342\) 8.12823e10 + 3.56121e11i 0.321276 + 1.40760i
\(343\) 6.02263e10 2.63869e11i 0.234943 1.02935i
\(344\) −2.48695e10 1.19765e10i −0.0957533 0.0461124i
\(345\) −1.83529e10 3.81102e10i −0.0697459 0.144829i
\(346\) 4.85785e11 + 1.10877e11i 1.82222 + 0.415911i
\(347\) 1.53016e11 0.566571 0.283286 0.959036i \(-0.408576\pi\)
0.283286 + 0.959036i \(0.408576\pi\)
\(348\) 1.79158e11 + 5.69244e10i 0.654830 + 0.208062i
\(349\) 9.12474e10 0.329235 0.164617 0.986357i \(-0.447361\pi\)
0.164617 + 0.986357i \(0.447361\pi\)
\(350\) 1.65269e11 + 3.77215e10i 0.588687 + 0.134364i
\(351\) 1.06810e11 + 2.21792e11i 0.375602 + 0.779946i
\(352\) −6.83875e11 3.29337e11i −2.37430 1.14340i
\(353\) 5.94829e10 2.60612e11i 0.203895 0.893321i −0.764643 0.644454i \(-0.777085\pi\)
0.968538 0.248867i \(-0.0800582\pi\)
\(354\) 8.77420e9 + 3.84423e10i 0.0296957 + 0.130105i
\(355\) −3.43419e11 + 1.65382e11i −1.14762 + 0.552663i
\(356\) −8.17972e10 6.52311e10i −0.269907 0.215243i
\(357\) −4.47745e10 + 5.61454e10i −0.145889 + 0.182940i
\(358\) 1.73829e11 3.60960e11i 0.559305 1.16141i
\(359\) −3.05509e11 + 2.43635e11i −0.970731 + 0.774132i −0.974159 0.225862i \(-0.927480\pi\)
0.00342839 + 0.999994i \(0.498909\pi\)
\(360\) 1.54459e10i 0.0484675i
\(361\) −3.73782e11 4.68708e11i −1.15834 1.45251i
\(362\) 3.69275e11 8.42846e10i 1.13022 0.257964i
\(363\) 4.90685e11 1.11996e11i 1.48328 0.338549i
\(364\) −1.78002e11 2.23208e11i −0.531458 0.666427i
\(365\) 2.12707e11i 0.627283i
\(366\) 2.00078e11 1.59557e11i 0.582819 0.464783i
\(367\) 1.22558e11 2.54495e11i 0.352652 0.732289i −0.646889 0.762584i \(-0.723930\pi\)
0.999541 + 0.0302951i \(0.00964471\pi\)
\(368\) −6.83999e10 + 8.57708e10i −0.194420 + 0.243795i
\(369\) −1.86918e11 1.49062e11i −0.524847 0.418551i
\(370\) 2.40106e11 1.15629e11i 0.666031 0.320744i
\(371\) 7.06141e10 + 3.09380e11i 0.193512 + 0.847833i
\(372\) −7.24036e10 + 3.17221e11i −0.196027 + 0.858852i
\(373\) 1.16764e11 + 5.62308e10i 0.312335 + 0.150413i 0.583484 0.812125i \(-0.301689\pi\)
−0.271149 + 0.962537i \(0.587404\pi\)
\(374\) −1.71616e11 3.56364e11i −0.453561 0.941828i
\(375\) 2.56192e11 + 5.84741e10i 0.668998 + 0.152694i
\(376\) −5.27534e10 −0.136115
\(377\) 3.11965e11 1.19406e11i 0.795370 0.304432i
\(378\) 5.40536e11 1.36180
\(379\) −4.90032e11 1.11847e11i −1.21997 0.278450i −0.436398 0.899754i \(-0.643746\pi\)
−0.783570 + 0.621304i \(0.786603\pi\)
\(380\) −2.37882e11 4.93966e11i −0.585241 1.21527i
\(381\) 4.16463e11 + 2.00558e11i 1.01255 + 0.487616i
\(382\) 3.38298e9 1.48218e10i 0.00812858 0.0356136i
\(383\) 1.26448e11 + 5.54005e11i 0.300274 + 1.31559i 0.869715 + 0.493554i \(0.164303\pi\)
−0.569441 + 0.822032i \(0.692840\pi\)
\(384\) −5.39089e10 + 2.59611e10i −0.126523 + 0.0609303i
\(385\) −4.27202e11 3.40682e11i −0.990969 0.790271i
\(386\) −4.37462e11 + 5.48560e11i −1.00299 + 1.25771i
\(387\) 1.09295e11 2.26953e11i 0.247685 0.514323i
\(388\) 3.45816e11 2.75779e11i 0.774644 0.617758i
\(389\) 6.53513e10i 0.144704i −0.997379 0.0723520i \(-0.976949\pi\)
0.997379 0.0723520i \(-0.0230505\pi\)
\(390\) −1.65357e11 2.07351e11i −0.361935 0.453852i
\(391\) −6.03844e10 + 1.37823e10i −0.130656 + 0.0298214i
\(392\) 6.82287e9 1.55728e9i 0.0145942 0.00333103i
\(393\) −2.53148e11 3.17437e11i −0.535313 0.671261i
\(394\) 9.83582e11i 2.05626i
\(395\) 2.19768e11 1.75259e11i 0.454231 0.362237i
\(396\) −2.49210e11 + 5.17490e11i −0.509258 + 1.05748i
\(397\) −1.10401e11 + 1.38439e11i −0.223058 + 0.279706i −0.880750 0.473581i \(-0.842961\pi\)
0.657693 + 0.753287i \(0.271533\pi\)
\(398\) 3.09643e11 + 2.46932e11i 0.618569 + 0.493292i
\(399\) −4.57528e11 + 2.20334e11i −0.903732 + 0.435214i
\(400\) −4.71168e10 2.06432e11i −0.0920251 0.403188i
\(401\) −5.03458e10 + 2.20579e11i −0.0972330 + 0.426006i −0.999991 0.00414231i \(-0.998681\pi\)
0.902758 + 0.430148i \(0.141539\pi\)
\(402\) −1.58334e10 7.62498e9i −0.0302383 0.0145620i
\(403\) 2.50862e11 + 5.20921e11i 0.473764 + 0.983782i
\(404\) 2.99355e11 + 6.83259e10i 0.559076 + 0.127605i
\(405\) 2.24969e10 0.0415504
\(406\) 6.09880e10 7.30928e11i 0.111398 1.33508i
\(407\) 7.04842e11 1.27326
\(408\) −1.51541e10 3.45883e9i −0.0270745 0.00617957i
\(409\) −1.98110e11 4.11380e11i −0.350067 0.726923i 0.649370 0.760473i \(-0.275033\pi\)
−0.999437 + 0.0335504i \(0.989319\pi\)
\(410\) 6.23612e11 + 3.00316e11i 1.08990 + 0.524869i
\(411\) 6.16018e10 2.69895e11i 0.106489 0.466559i
\(412\) 1.72332e11 + 7.55036e11i 0.294665 + 1.29101i
\(413\) 7.18627e10 3.46073e10i 0.121543 0.0585318i
\(414\) 1.35637e11 + 1.08167e11i 0.226922 + 0.180964i
\(415\) 3.17245e11 3.97812e11i 0.525022 0.658357i
\(416\) −3.23348e11 + 6.71438e11i −0.529358 + 1.09922i
\(417\) −1.69696e11 + 1.35328e11i −0.274827 + 0.219167i
\(418\) 2.79699e12i 4.48123i
\(419\) 4.77329e11 + 5.98552e11i 0.756580 + 0.948721i 0.999774 0.0212562i \(-0.00676657\pi\)
−0.243194 + 0.969978i \(0.578195\pi\)
\(420\) −2.94340e11 + 6.71811e10i −0.461559 + 0.105348i
\(421\) −4.23476e11 + 9.66556e10i −0.656991 + 0.149954i −0.538004 0.842942i \(-0.680822\pi\)
−0.118986 + 0.992896i \(0.537964\pi\)
\(422\) −6.05228e11 7.58932e11i −0.928995 1.16492i
\(423\) 4.81414e11i 0.731117i
\(424\) −5.37020e10 + 4.28259e10i −0.0806946 + 0.0643518i
\(425\) 5.18686e10 1.07706e11i 0.0771177 0.160137i
\(426\) −6.69889e11 + 8.40015e11i −0.985508 + 1.23579i
\(427\) −4.04721e11 3.22754e11i −0.589156 0.469836i
\(428\) −5.22363e11 + 2.51557e11i −0.752446 + 0.362359i
\(429\) −1.56085e11 6.83854e11i −0.222487 0.974778i
\(430\) −1.62279e11 + 7.10992e11i −0.228905 + 1.00290i
\(431\) 1.19510e11 + 5.75530e10i 0.166823 + 0.0803378i 0.515432 0.856931i \(-0.327632\pi\)
−0.348609 + 0.937268i \(0.613346\pi\)
\(432\) −2.92945e11 6.08306e11i −0.404677 0.840321i
\(433\) −3.91037e10 8.92517e9i −0.0534592 0.0122017i 0.195708 0.980662i \(-0.437300\pi\)
−0.249167 + 0.968461i \(0.580157\pi\)
\(434\) 1.26955e12 1.71770
\(435\) 2.93722e10 3.52019e11i 0.0393310 0.471373i
\(436\) −2.63574e11 −0.349312
\(437\) −4.27003e11 9.74607e10i −0.560099 0.127839i
\(438\) 2.60144e11 + 5.40194e11i 0.337738 + 0.701321i
\(439\) 6.03555e11 + 2.90657e11i 0.775580 + 0.373500i 0.779427 0.626493i \(-0.215510\pi\)
−0.00384724 + 0.999993i \(0.501225\pi\)
\(440\) 2.63177e10 1.15305e11i 0.0334743 0.146660i
\(441\) 1.42113e10 + 6.22638e10i 0.0178921 + 0.0783903i
\(442\) −3.49883e11 + 1.68495e11i −0.436036 + 0.209984i
\(443\) −1.04953e11 8.36976e10i −0.129473 0.103251i 0.556612 0.830772i \(-0.312101\pi\)
−0.686085 + 0.727521i \(0.740672\pi\)
\(444\) 2.42816e11 3.04481e11i 0.296520 0.371824i
\(445\) −8.53006e10 + 1.77129e11i −0.103117 + 0.214126i
\(446\) 1.25100e12 9.97640e11i 1.49710 1.19390i
\(447\) 2.30893e11i 0.273544i
\(448\) 5.66787e11 + 7.10728e11i 0.664766 + 0.833590i
\(449\) −1.42370e12 + 3.24950e11i −1.65314 + 0.377318i −0.944567 0.328319i \(-0.893518\pi\)
−0.708573 + 0.705637i \(0.750661\pi\)
\(450\) −3.26450e11 + 7.45100e10i −0.375284 + 0.0856561i
\(451\) 1.14139e12 + 1.43125e12i 1.29909 + 1.62900i
\(452\) 1.48067e11i 0.166854i
\(453\) −7.83881e11 + 6.25125e11i −0.874598 + 0.697469i
\(454\) −4.67627e11 + 9.71037e11i −0.516592 + 1.07271i
\(455\) −3.34486e11 + 4.19433e11i −0.365870 + 0.458787i
\(456\) −8.59366e10 6.85322e10i −0.0930757 0.0742254i
\(457\) 7.57411e11 3.64750e11i 0.812285 0.391176i 0.0188436 0.999822i \(-0.494002\pi\)
0.793441 + 0.608647i \(0.208287\pi\)
\(458\) 2.36917e11 + 1.03800e12i 0.251595 + 1.10231i
\(459\) 8.48220e10 3.71630e11i 0.0891973 0.390799i
\(460\) −2.34605e11 1.12980e11i −0.244302 0.117649i
\(461\) 4.95110e11 + 1.02811e12i 0.510561 + 1.06019i 0.983802 + 0.179258i \(0.0573698\pi\)
−0.473241 + 0.880933i \(0.656916\pi\)
\(462\) −1.50159e12 3.42729e11i −1.53343 0.349995i
\(463\) −1.47562e12 −1.49231 −0.746155 0.665772i \(-0.768102\pi\)
−0.746155 + 0.665772i \(0.768102\pi\)
\(464\) −8.55620e11 + 3.27493e11i −0.856940 + 0.327998i
\(465\) 6.11424e11 0.606463
\(466\) −1.81697e12 4.14712e11i −1.78489 0.407389i
\(467\) −8.67491e9 1.80136e10i −0.00843994 0.0175257i 0.896706 0.442626i \(-0.145953\pi\)
−0.905146 + 0.425100i \(0.860239\pi\)
\(468\) 5.08079e11 + 2.44678e11i 0.489581 + 0.235770i
\(469\) −7.91031e9 + 3.46573e10i −0.00754945 + 0.0330763i
\(470\) 3.10139e11 + 1.35881e12i 0.293167 + 1.28445i
\(471\) −9.45215e10 + 4.55192e10i −0.0884986 + 0.0426187i
\(472\) 1.34978e10 + 1.07642e10i 0.0125177 + 0.00998254i
\(473\) −1.20260e12 + 1.50801e12i −1.10470 + 1.38525i
\(474\) 3.43782e11 7.13871e11i 0.312810 0.649557i
\(475\) 6.60923e11 5.27068e11i 0.595702 0.475057i
\(476\) 4.42076e11i 0.394699i
\(477\) −3.90819e11 4.90071e11i −0.345655 0.433437i
\(478\) 2.13315e12 4.86879e11i 1.86895 0.426575i
\(479\) 5.53591e11 1.26354e11i 0.480484 0.109667i 0.0245830 0.999698i \(-0.492174\pi\)
0.455901 + 0.890030i \(0.349317\pi\)
\(480\) 4.91367e11 + 6.16155e11i 0.422494 + 0.529791i
\(481\) 6.92023e11i 0.589478i
\(482\) 1.49266e12 1.19036e12i 1.25965 1.00454i
\(483\) −1.04646e11 + 2.17299e11i −0.0874900 + 0.181675i
\(484\) 1.93177e12 2.42236e12i 1.60011 2.00648i
\(485\) −6.49828e11 5.18220e11i −0.533286 0.425282i
\(486\) −1.56596e12 + 7.54128e11i −1.27326 + 0.613171i
\(487\) −4.10717e11 1.79947e12i −0.330874 1.44965i −0.817443 0.576010i \(-0.804609\pi\)
0.486569 0.873642i \(-0.338248\pi\)
\(488\) 2.49328e10 1.09238e11i 0.0199013 0.0871932i
\(489\) 5.33751e11 + 2.57041e11i 0.422132 + 0.203288i
\(490\) −8.02238e10 1.66586e11i −0.0628667 0.130544i
\(491\) 1.92987e11 + 4.40480e10i 0.149851 + 0.0342026i 0.296789 0.954943i \(-0.404084\pi\)
−0.146937 + 0.989146i \(0.546941\pi\)
\(492\) 1.01149e12 0.778246
\(493\) −4.92957e11 1.56629e11i −0.375836 0.119416i
\(494\) −2.74612e12 −2.07467
\(495\) 1.05225e12 + 2.40169e11i 0.787762 + 0.179801i
\(496\) −6.88036e11 1.42872e12i −0.510439 1.05994i
\(497\) 1.95813e12 + 9.42984e11i 1.43958 + 0.693267i
\(498\) 3.19150e11 1.39829e12i 0.232521 1.01874i
\(499\) 1.34747e11 + 5.90366e11i 0.0972898 + 0.426254i 0.999992 0.00401151i \(-0.00127691\pi\)
−0.902702 + 0.430266i \(0.858420\pi\)
\(500\) 1.45747e12 7.01879e11i 1.04288 0.502224i
\(501\) −2.87183e11 2.29021e11i −0.203652 0.162407i
\(502\) −1.66847e12 + 2.09220e12i −1.17261 + 1.47040i
\(503\) 3.82126e11 7.93492e11i 0.266164 0.552696i −0.724459 0.689318i \(-0.757910\pi\)
0.990623 + 0.136622i \(0.0436245\pi\)
\(504\) 6.88559e10 5.49108e10i 0.0475339 0.0379071i
\(505\) 5.76989e11i 0.394781i
\(506\) −8.28246e11 1.03859e12i −0.561671 0.704313i
\(507\) 2.54302e11 5.80427e10i 0.170928 0.0390132i
\(508\) 2.77418e12 6.33190e11i 1.84820 0.421839i
\(509\) 1.22188e11 + 1.53219e11i 0.0806859 + 0.101177i 0.820536 0.571595i \(-0.193675\pi\)
−0.739850 + 0.672772i \(0.765104\pi\)
\(510\) 4.10670e11i 0.268799i
\(511\) 9.48223e11 7.56182e11i 0.615200 0.490606i
\(512\) 9.55146e11 1.98338e12i 0.614264 1.27553i
\(513\) 1.68064e12 2.10745e12i 1.07139 1.34347i
\(514\) −5.47676e11 4.36757e11i −0.346090 0.275998i
\(515\) 1.31117e12 6.31425e11i 0.821345 0.395539i
\(516\) 2.37147e11 + 1.03901e12i 0.147263 + 0.645202i
\(517\) −8.20266e11 + 3.59382e12i −0.504949 + 2.21233i
\(518\) −1.36905e12 6.59299e11i −0.835477 0.402345i
\(519\) −5.93681e11 1.23279e12i −0.359170 0.745825i
\(520\) −1.13208e11 2.58391e10i −0.0678991 0.0154975i
\(521\) −7.84084e11 −0.466222 −0.233111 0.972450i \(-0.574891\pi\)
−0.233111 + 0.972450i \(0.574891\pi\)
\(522\) 5.17894e11 + 1.35307e12i 0.305298 + 0.797631i
\(523\) −2.84758e11 −0.166425 −0.0832124 0.996532i \(-0.526518\pi\)
−0.0832124 + 0.996532i \(0.526518\pi\)
\(524\) −2.43676e12 5.56175e11i −1.41196 0.322271i
\(525\) −2.01976e11 4.19407e11i −0.116033 0.240946i
\(526\) −3.80466e12 1.83223e12i −2.16710 1.04362i
\(527\) 1.99220e11 8.72842e11i 0.112509 0.492933i
\(528\) 4.28093e11 + 1.87560e12i 0.239709 + 1.05024i
\(529\) 1.43537e12 6.91236e11i 0.796915 0.383774i
\(530\) 1.41881e12 + 1.13147e12i 0.781060 + 0.622874i
\(531\) −9.82310e10 + 1.23178e11i −0.0536196 + 0.0672368i
\(532\) −1.35637e12 + 2.81652e12i −0.734133 + 1.52444i
\(533\) 1.40522e12 1.12063e12i 0.754177 0.601436i
\(534\) 5.54164e11i 0.294919i
\(535\) 6.79275e11 + 8.51783e11i 0.358470 + 0.449508i
\(536\) −7.50157e9 + 1.71218e9i −0.00392564 + 0.000896002i
\(537\) −1.07258e12 + 2.44810e11i −0.556603 + 0.127041i
\(538\) 2.61950e12 + 3.28474e12i 1.34802 + 1.69037i
\(539\) 4.89022e11i 0.249562i
\(540\) 1.25293e12 9.99176e11i 0.634095 0.505674i
\(541\) −6.55265e11 + 1.36067e12i −0.328874 + 0.682913i −0.998195 0.0600601i \(-0.980871\pi\)
0.669321 + 0.742973i \(0.266585\pi\)
\(542\) −5.76923e11 + 7.23438e11i −0.287158 + 0.360085i
\(543\) −8.13203e11 6.48508e11i −0.401421 0.320122i
\(544\) 1.03970e12 5.00692e11i 0.508993 0.245118i
\(545\) 1.10212e11 + 4.82869e11i 0.0535110 + 0.234447i
\(546\) −3.36495e11 + 1.47428e12i −0.162036 + 0.709927i
\(547\) −1.98662e12 9.56708e11i −0.948796 0.456916i −0.105532 0.994416i \(-0.533655\pi\)
−0.843264 + 0.537500i \(0.819369\pi\)
\(548\) −7.39421e11 1.53542e12i −0.350251 0.727303i
\(549\) 9.96875e11 + 2.27530e11i 0.468344 + 0.106896i
\(550\) 2.56395e12 1.19475
\(551\) −2.66013e12 2.51038e12i −1.22948 1.16027i
\(552\) −5.22041e10 −0.0239320
\(553\) −1.56257e12 3.56646e11i −0.710520 0.162172i
\(554\) 1.50413e12 + 3.12337e12i 0.678411 + 1.40873i
\(555\) −6.59342e11 3.17522e11i −0.294980 0.142055i
\(556\) −2.97321e11 + 1.30265e12i −0.131944 + 0.578083i
\(557\) 1.46873e11 + 6.43494e11i 0.0646539 + 0.283267i 0.996912 0.0785267i \(-0.0250216\pi\)
−0.932258 + 0.361794i \(0.882164\pi\)
\(558\) −2.25936e12 + 1.08805e12i −0.986579 + 0.475111i
\(559\) 1.48058e12 + 1.18073e12i 0.641327 + 0.511441i
\(560\) 9.17391e11 1.15037e12i 0.394192 0.494302i
\(561\) −4.71266e11 + 9.78593e11i −0.200878 + 0.417128i
\(562\) −2.33178e12 + 1.85953e12i −0.985993 + 0.786303i
\(563\) 3.74411e12i 1.57058i 0.619127 + 0.785291i \(0.287487\pi\)
−0.619127 + 0.785291i \(0.712513\pi\)
\(564\) 1.26990e12 + 1.59240e12i 0.528462 + 0.662670i
\(565\) 2.71259e11 6.19132e10i 0.111987 0.0255602i
\(566\) −4.76029e12 + 1.08650e12i −1.94966 + 0.444998i
\(567\) −7.99776e10 1.00289e11i −0.0324971 0.0407501i
\(568\) 4.70422e11i 0.189636i
\(569\) 3.59935e12 2.87039e12i 1.43953 1.14798i 0.476302 0.879282i \(-0.341977\pi\)
0.963224 0.268701i \(-0.0865944\pi\)
\(570\) −1.26001e12 + 2.61643e12i −0.499962 + 1.03818i
\(571\) −4.20550e11 + 5.27353e11i −0.165560 + 0.207606i −0.857690 0.514167i \(-0.828101\pi\)
0.692130 + 0.721773i \(0.256673\pi\)
\(572\) −3.37598e12 2.69226e12i −1.31861 1.05156i
\(573\) −3.76138e10 + 1.81138e10i −0.0145764 + 0.00701964i
\(574\) −8.78196e11 3.84763e12i −0.337667 1.47941i
\(575\) 8.93403e10 3.91426e11i 0.0340834 0.149329i
\(576\) −1.61780e12 7.79093e11i −0.612385 0.294909i
\(577\) 1.93440e12 + 4.01682e12i 0.726532 + 1.50866i 0.855944 + 0.517069i \(0.172977\pi\)
−0.129412 + 0.991591i \(0.541309\pi\)
\(578\) −3.18357e12 7.26629e11i −1.18642 0.270793i
\(579\) 1.92672e12 0.712468
\(580\) −1.20975e12 1.80698e12i −0.443883 0.663021i
\(581\) −2.90122e12 −1.05630
\(582\) −2.28411e12 5.21333e11i −0.825208 0.188348i
\(583\) 2.08250e12 + 4.32435e12i 0.746580 + 1.55029i
\(584\) 2.36518e11 + 1.13901e11i 0.0841407 + 0.0405200i
\(585\) 2.35801e11 1.03311e12i 0.0832423 0.364708i
\(586\) −4.52451e11 1.98232e12i −0.158501 0.694439i
\(587\) −2.06715e12 + 9.95489e11i −0.718623 + 0.346071i −0.757198 0.653185i \(-0.773432\pi\)
0.0385750 + 0.999256i \(0.487718\pi\)
\(588\) −2.11251e11 1.68467e11i −0.0728786 0.0581187i
\(589\) 3.94729e12 4.94975e12i 1.35139 1.69459i
\(590\) 1.97906e11 4.10956e11i 0.0672396 0.139624i
\(591\) 2.11170e12 1.68402e12i 0.712014 0.567812i
\(592\) 1.89800e12i 0.635110i
\(593\) −3.15959e11 3.96200e11i −0.104926 0.131573i 0.726596 0.687065i \(-0.241101\pi\)
−0.831522 + 0.555492i \(0.812530\pi\)
\(594\) 7.97055e12 1.81923e12i 2.62694 0.599581i
\(595\) 8.09884e11 1.84851e11i 0.264909 0.0604637i
\(596\) 8.86210e11 + 1.11127e12i 0.287692 + 0.360755i
\(597\) 1.08757e12i 0.350407i
\(598\) −1.01970e12 + 8.13183e11i −0.326074 + 0.260036i
\(599\) 6.46215e11 1.34188e12i 0.205096 0.425885i −0.772895 0.634534i \(-0.781192\pi\)
0.977991 + 0.208649i \(0.0669065\pi\)
\(600\) 6.28221e10 7.87765e10i 0.0197894 0.0248151i
\(601\) 3.08173e12 + 2.45760e12i 0.963517 + 0.768379i 0.972816 0.231578i \(-0.0743888\pi\)
−0.00929961 + 0.999957i \(0.502960\pi\)
\(602\) 3.74643e12 1.80419e12i 1.16261 0.559883i
\(603\) −1.56250e10 6.84574e10i −0.00481273 0.0210859i
\(604\) −1.37342e12 + 6.01735e12i −0.419892 + 1.83967i
\(605\) −5.24552e12 2.52611e12i −1.59180 0.766573i
\(606\) −7.05668e11 1.46533e12i −0.212556 0.441377i
\(607\) −2.68479e12 6.12786e11i −0.802715 0.183215i −0.198568 0.980087i \(-0.563629\pi\)
−0.604147 + 0.796873i \(0.706486\pi\)
\(608\) 8.16026e12 2.42180
\(609\) −1.67368e12 + 1.12051e12i −0.493055 + 0.330094i
\(610\) −2.96029e12 −0.865666
\(611\) 3.52846e12 + 8.05348e11i 1.02424 + 0.233775i
\(612\) −3.78875e11 7.86742e11i −0.109173 0.226700i
\(613\) 5.85996e11 + 2.82201e11i 0.167619 + 0.0807209i 0.515812 0.856702i \(-0.327490\pi\)
−0.348193 + 0.937423i \(0.613205\pi\)
\(614\) 1.28010e12 5.60846e12i 0.363483 1.59253i
\(615\) −4.22945e11 1.85304e12i −0.119219 0.522333i
\(616\) −6.07580e11 + 2.92595e11i −0.170016 + 0.0818754i
\(617\) −2.41289e12 1.92422e12i −0.670277 0.534528i 0.228164 0.973623i \(-0.426728\pi\)
−0.898441 + 0.439094i \(0.855299\pi\)
\(618\) 2.55763e12 3.20716e12i 0.705324 0.884449i
\(619\) 6.76990e11 1.40578e12i 0.185342 0.384867i −0.787507 0.616305i \(-0.788629\pi\)
0.972850 + 0.231438i \(0.0743430\pi\)
\(620\) 2.94274e12 2.34675e12i 0.799813 0.637830i
\(621\) 1.28022e12i 0.345439i
\(622\) 3.96247e12 + 4.96878e12i 1.06147 + 1.33105i
\(623\) 1.09287e12 2.49440e11i 0.290651 0.0663391i
\(624\) 1.84149e12 4.20307e11i 0.486225 0.110978i
\(625\) −8.23290e11 1.03237e12i −0.215821 0.270630i
\(626\) 1.89906e12i 0.494259i
\(627\) −6.00499e12 + 4.78882e12i −1.55170 + 1.23744i
\(628\) −2.80214e11 + 5.81871e11i −0.0718905 + 0.149282i
\(629\) −6.68115e11 + 8.37790e11i −0.170186 + 0.213406i
\(630\) −1.81918e12 1.45075e12i −0.460091 0.366910i
\(631\) −4.68738e12 + 2.25732e12i −1.17706 + 0.566842i −0.917053 0.398765i \(-0.869439\pi\)
−0.260006 + 0.965607i \(0.583725\pi\)
\(632\) −7.71960e10 3.38218e11i −0.0192472 0.0843276i
\(633\) −5.93156e11 + 2.59879e12i −0.146843 + 0.643360i
\(634\) −7.26558e11 3.49892e11i −0.178595 0.0860067i
\(635\) −2.32001e12 4.81755e12i −0.566249 1.17583i
\(636\) 2.58547e12 + 5.90117e11i 0.626589 + 0.143015i
\(637\) −4.80129e11 −0.115539
\(638\) −1.56070e12 1.09833e13i −0.372929 2.62445i
\(639\) −4.29296e12 −1.01860
\(640\) 6.74795e11 + 1.54018e11i 0.158987 + 0.0362878i
\(641\) 3.62409e12 + 7.52549e12i 0.847886 + 1.76065i 0.615698 + 0.787982i \(0.288874\pi\)
0.232188 + 0.972671i \(0.425411\pi\)
\(642\) 2.76685e12 + 1.33244e12i 0.642802 + 0.309557i
\(643\) −9.71439e11 + 4.25615e12i −0.224113 + 0.981901i 0.730233 + 0.683198i \(0.239411\pi\)
−0.954346 + 0.298703i \(0.903446\pi\)
\(644\) 3.30380e11 + 1.44749e12i 0.0756881 + 0.331611i
\(645\) 1.80430e12 8.68907e11i 0.410479 0.197676i
\(646\) 3.32456e12 + 2.65125e12i 0.751083 + 0.598968i
\(647\) −9.68957e11 + 1.21503e12i −0.217388 + 0.272596i −0.878553 0.477644i \(-0.841491\pi\)
0.661165 + 0.750240i \(0.270062\pi\)
\(648\) 1.20467e10 2.50153e10i 0.00268400 0.00557338i
\(649\) 9.43187e11 7.52167e11i 0.208688 0.166423i
\(650\) 2.51732e12i 0.553131i
\(651\) −2.17364e12 2.72566e12i −0.474322 0.594781i
\(652\) 3.55547e12 8.11513e11i 0.770518 0.175866i
\(653\) 3.24226e12 7.40024e11i 0.697812 0.159271i 0.141123 0.989992i \(-0.454929\pi\)
0.556689 + 0.830721i \(0.312072\pi\)
\(654\) 8.70452e11 + 1.09151e12i 0.186057 + 0.233308i
\(655\) 4.69671e12i 0.997030i
\(656\) −3.85409e12 + 3.07353e12i −0.812558 + 0.647993i
\(657\) −1.03943e12 + 2.15840e12i −0.217647 + 0.451948i
\(658\) 4.95485e12 6.21319e12i 1.03042 1.29211i
\(659\) −4.13269e12 3.29571e12i −0.853589 0.680714i 0.0956007 0.995420i \(-0.469523\pi\)
−0.949189 + 0.314706i \(0.898094\pi\)
\(660\) −4.11412e12 + 1.98126e12i −0.843975 + 0.406437i
\(661\) 8.02800e11 + 3.51730e12i 0.163569 + 0.716643i 0.988476 + 0.151375i \(0.0483700\pi\)
−0.824907 + 0.565268i \(0.808773\pi\)
\(662\) −2.88315e12 + 1.26319e13i −0.583454 + 2.55628i
\(663\) 9.60796e11 + 4.62695e11i 0.193117 + 0.0930002i
\(664\) −2.72466e11 5.65780e11i −0.0543945 0.112951i
\(665\) 5.72703e12 + 1.30716e12i 1.13562 + 0.259197i
\(666\) 3.00147e12 0.591154
\(667\) −1.73114e12 1.44445e11i −0.338662 0.0282577i
\(668\) −2.26121e12 −0.439387
\(669\) −4.28376e12 9.77741e11i −0.826814 0.188715i
\(670\) 8.82039e10 + 1.83157e11i 0.0169103 + 0.0351146i
\(671\) −7.05413e12 3.39709e12i −1.34336 0.646927i
\(672\) 9.99916e11 4.38092e12i 0.189148 0.828712i
\(673\) −1.54664e12 6.77626e12i −0.290617 1.27328i −0.883669 0.468111i \(-0.844935\pi\)
0.593053 0.805164i \(-0.297923\pi\)
\(674\) −6.70673e12 + 3.22979e12i −1.25182 + 0.602844i
\(675\) 1.93186e12 + 1.54061e12i 0.358186 + 0.285644i
\(676\) 1.00116e12 1.25541e12i 0.184392 0.231220i
\(677\) 7.03588e11 1.46102e12i 0.128727 0.267304i −0.826637 0.562735i \(-0.809749\pi\)
0.955364 + 0.295431i \(0.0954633\pi\)
\(678\) 6.13175e11 4.88991e11i 0.111443 0.0888724i
\(679\) 4.73916e12i 0.855632i
\(680\) 1.12108e11 + 1.40579e11i 0.0201070 + 0.0252134i
\(681\) 2.88540e12 6.58574e11i 0.514096 0.117339i
\(682\) 1.87203e13 4.27279e12i 3.31348 0.756280i
\(683\) 2.88502e12 + 3.61770e12i 0.507289 + 0.636120i 0.967856 0.251505i \(-0.0809254\pi\)
−0.460567 + 0.887625i \(0.652354\pi\)
\(684\) 6.17489e12i 1.07864i
\(685\) −2.50371e12 + 1.99664e12i −0.434487 + 0.346492i
\(686\) −3.82910e12 + 7.95121e12i −0.660143 + 1.37080i
\(687\) 1.82290e12 2.28584e12i 0.312217 0.391508i
\(688\) −4.06077e12 3.23836e12i −0.690972 0.551032i
\(689\) 4.24571e12 2.04462e12i 0.717734 0.345643i
\(690\) 3.06909e11 + 1.34466e12i 0.0515453 + 0.225835i
\(691\) 3.85927e10 1.69086e11i 0.00643952 0.0282134i −0.971606 0.236604i \(-0.923965\pi\)
0.978046 + 0.208391i \(0.0668226\pi\)
\(692\) −7.58902e12 3.65468e12i −1.25808 0.605859i
\(693\) −2.67015e12 5.54462e12i −0.439780 0.913213i
\(694\) −4.86427e12 1.11024e12i −0.795977 0.181676i
\(695\) 2.51077e12 0.408203
\(696\) −3.75698e11 2.21161e11i −0.0606872 0.0357246i
\(697\) −2.78313e12 −0.446669
\(698\) −2.90069e12 6.62063e11i −0.462543 0.105572i
\(699\) 2.22053e12 + 4.61098e12i 0.351811 + 0.730544i
\(700\) −2.58185e12 1.24336e12i −0.406435 0.195729i
\(701\) −4.77800e11 + 2.09338e12i −0.0747334 + 0.327429i −0.998451 0.0556469i \(-0.982278\pi\)
0.923717 + 0.383075i \(0.125135\pi\)
\(702\) −1.78614e12 7.82559e12i −0.277587 1.21619i
\(703\) −6.82713e12 + 3.28777e12i −1.05424 + 0.507695i
\(704\) 1.07497e13 + 8.57256e12i 1.64937 + 1.31533i
\(705\) 2.38629e12 2.99231e12i 0.363808 0.456200i
\(706\) −3.78184e12 + 7.85307e12i −0.572904 + 1.18965i
\(707\) −2.57215e12 + 2.05122e12i −0.387177 + 0.308763i
\(708\) 6.66562e11i 0.0996991i
\(709\) −8.03098e11 1.00705e12i −0.119360 0.149673i 0.718561 0.695464i \(-0.244801\pi\)
−0.837922 + 0.545790i \(0.816230\pi\)
\(710\) 1.21170e13 2.76563e12i 1.78950 0.408443i
\(711\) 3.08649e12 7.04472e11i 0.452952 0.103383i
\(712\) 1.51280e11 + 1.89699e11i 0.0220608 + 0.0276634i
\(713\) 3.00683e12i 0.435719i
\(714\) 1.83072e12 1.45995e12i 0.263622 0.210231i
\(715\) −3.52057e12 + 7.31055e12i −0.503775 + 1.04610i
\(716\) −4.22263e12 + 5.29501e12i −0.600446 + 0.752936i
\(717\) −4.69755e12 3.74617e12i −0.663797 0.529360i
\(718\) 1.14797e13 5.52831e12i 1.61201 0.776305i
\(719\) 8.62783e11 + 3.78010e12i 0.120399 + 0.527501i 0.998773 + 0.0495272i \(0.0157715\pi\)
−0.878374 + 0.477974i \(0.841371\pi\)
\(720\) −6.46728e11 + 2.83350e12i −0.0896861 + 0.392941i
\(721\) −7.47609e12 3.60029e12i −1.03030 0.496168i
\(722\) 8.48146e12 + 1.76119e13i 1.16159 + 2.41207i
\(723\) −5.11128e12 1.16662e12i −0.695676 0.158783i
\(724\) −6.40297e12 −0.866080
\(725\) 2.30122e12 2.43849e12i 0.309341 0.327793i
\(726\) −1.64111e13 −2.19242
\(727\) −8.51840e12 1.94427e12i −1.13097 0.258138i −0.384223 0.923240i \(-0.625531\pi\)
−0.746752 + 0.665103i \(0.768388\pi\)
\(728\) 2.87274e11 + 5.96530e11i 0.0379057 + 0.0787120i
\(729\) 4.68538e12 + 2.25636e12i 0.614428 + 0.295893i
\(730\) 1.54334e12 6.76179e12i 0.201144 0.881270i
\(731\) −6.52517e11 2.85886e12i −0.0845208 0.370310i
\(732\) −3.89762e12 + 1.87699e12i −0.501764 + 0.241637i
\(733\) 1.01626e13 + 8.10442e12i 1.30028 + 1.03694i 0.996448 + 0.0842158i \(0.0268385\pi\)
0.303835 + 0.952725i \(0.401733\pi\)
\(734\) −5.74259e12 + 7.20098e12i −0.730256 + 0.915712i
\(735\) −2.20298e11 + 4.57454e11i −0.0278432 + 0.0578169i
\(736\) 3.03010e12 2.41642e12i 0.380633 0.303545i
\(737\) 5.37667e11i 0.0671289i
\(738\) 4.86044e12 + 6.09480e12i 0.603146 + 0.756321i
\(739\) 3.84410e12 8.77391e11i 0.474127 0.108216i 0.0212215 0.999775i \(-0.493244\pi\)
0.452906 + 0.891558i \(0.350387\pi\)
\(740\) −4.39207e12 + 1.00246e12i −0.538427 + 0.122892i
\(741\) 4.70173e12 + 5.89578e12i 0.572895 + 0.718388i
\(742\) 1.03473e13i 1.25317i
\(743\) 3.23163e12 2.57714e12i 0.389020 0.310233i −0.409376 0.912366i \(-0.634254\pi\)
0.798396 + 0.602133i \(0.205682\pi\)
\(744\) 3.27408e11 6.79869e11i 0.0391752 0.0813480i
\(745\) 1.66529e12 2.08821e12i 0.198055 0.248354i
\(746\) −3.30386e12 2.63474e12i −0.390569 0.311468i
\(747\) 5.16317e12 2.48645e12i 0.606700 0.292171i
\(748\) 1.48785e12 + 6.51869e12i 0.173781 + 0.761384i
\(749\) 1.38230e12 6.05626e12i 0.160485 0.703131i
\(750\) −7.71989e12 3.71770e12i −0.890913 0.429041i
\(751\) −4.47811e12 9.29890e12i −0.513707 1.06672i −0.982987 0.183674i \(-0.941201\pi\)
0.469280 0.883049i \(-0.344513\pi\)
\(752\) −9.67746e12 2.20882e12i −1.10352 0.251872i
\(753\) 7.34849e12 0.832954
\(754\) −1.07835e13 + 1.53232e12i −1.21504 + 0.172654i
\(755\) 1.15981e13 1.29905
\(756\) −8.90844e12 2.03329e12i −0.991867 0.226387i
\(757\) 2.37320e12 + 4.92799e12i 0.262665 + 0.545429i 0.990036 0.140815i \(-0.0449723\pi\)
−0.727371 + 0.686244i \(0.759258\pi\)
\(758\) 1.47663e13 + 7.11106e12i 1.62465 + 0.782389i
\(759\) −8.11725e11 + 3.55640e12i −0.0887812 + 0.388976i
\(760\) 2.82934e11 + 1.23961e12i 0.0307627 + 0.134780i
\(761\) 1.29271e13 6.22537e12i 1.39724 0.672875i 0.424640 0.905362i \(-0.360401\pi\)
0.972599 + 0.232487i \(0.0746863\pi\)
\(762\) −1.17839e13 9.39734e12i −1.26617 1.00973i
\(763\) 1.76077e12 2.20793e12i 0.188080 0.235844i
\(764\) −1.11508e11 + 2.31549e11i −0.0118409 + 0.0245880i
\(765\) −1.28289e12 + 1.02307e12i −0.135429 + 0.108001i
\(766\) 1.85289e13i 1.94455i
\(767\) −7.38487e11 9.26034e11i −0.0770484 0.0966157i
\(768\) −4.97758e12 + 1.13610e12i −0.516289 + 0.117839i
\(769\) −1.44387e13 + 3.29554e12i −1.48888 + 0.339827i −0.888123 0.459606i \(-0.847991\pi\)
−0.600756 + 0.799433i \(0.705134\pi\)
\(770\) 1.11086e13 + 1.39297e13i 1.13881 + 1.42802i
\(771\) 1.92362e12i 0.196053i
\(772\) 9.27316e12 7.39510e12i 0.939615 0.749318i
\(773\) −9.76286e11 + 2.02728e12i −0.0983489 + 0.204224i −0.944338 0.328976i \(-0.893296\pi\)
0.845989 + 0.533200i \(0.179011\pi\)
\(774\) −5.12110e12 + 6.42165e12i −0.512895 + 0.643150i
\(775\) 4.53734e12 + 3.61841e12i 0.451797 + 0.360296i
\(776\) −9.24205e11 + 4.45073e11i −0.0914935 + 0.0440610i
\(777\) 9.28513e11 + 4.06808e12i 0.0913889 + 0.400401i
\(778\) −4.74169e11 + 2.07747e12i −0.0464007 + 0.203295i
\(779\) −1.77317e13 8.53913e12i −1.72517 0.830797i
\(780\) 1.94522e12 + 4.03930e12i 0.188167 + 0.390733i
\(781\) 3.20475e13 + 7.31463e12i 3.08223 + 0.703498i
\(782\) 2.01958e12 0.193121
\(783\) 5.42360e12 9.21336e12i 0.515656 0.875971i
\(784\) 1.31684e12 0.124483
\(785\) 1.18316e12 + 2.70048e11i 0.111206 + 0.0253821i
\(786\) 5.74416e12 + 1.19279e13i 0.536816 + 1.11471i
\(787\) −1.40673e13 6.77445e12i −1.30715 0.629488i −0.354924 0.934895i \(-0.615493\pi\)
−0.952222 + 0.305407i \(0.901207\pi\)
\(788\) 3.69986e12 1.62102e13i 0.341836 1.49768i
\(789\) 2.58039e12 + 1.13054e13i 0.237049 + 1.03858i
\(790\) −8.25789e12 + 3.97679e12i −0.754305 + 0.363254i
\(791\) −1.24034e12 9.89140e11i −0.112654 0.0898387i
\(792\) 8.30517e11 1.04144e12i 0.0750041 0.0940522i
\(793\) −3.33531e12 + 6.92584e12i −0.299507 + 0.621932i
\(794\) 4.51406e12 3.59984e12i 0.403065 0.321433i
\(795\) 4.98334e12i 0.442455i
\(796\) −4.17429e12 5.23439e12i −0.368530 0.462122i
\(797\) 1.52134e13 3.47237e12i 1.33557 0.304834i 0.505657 0.862734i \(-0.331250\pi\)
0.829908 + 0.557900i \(0.188393\pi\)
\(798\) 1.61432e13 3.68457e12i 1.40921 0.321643i
\(799\) −3.49417e12 4.38155e12i −0.303307 0.380335i
\(800\) 7.48036e12i 0.645680i
\(801\) −1.73115e12 + 1.38054e12i −0.148589 + 0.118496i
\(802\) 3.20092e12 6.64677e12i 0.273206 0.567317i
\(803\) 1.14371e13 1.43417e13i 0.970728 1.21725i
\(804\) 2.32264e11 + 1.85225e11i 0.0196034 + 0.0156332i
\(805\) 2.51366e12 1.21051e12i 0.210972 0.101599i
\(806\) −4.19509e12 1.83799e13i −0.350133 1.53403i
\(807\) 2.56725e12 1.12478e13i 0.213077 0.933551i
\(808\) −6.41580e11 3.08969e11i −0.0529541 0.0255014i
\(809\) −1.87901e11 3.90181e11i −0.0154227 0.0320256i 0.893115 0.449828i \(-0.148515\pi\)
−0.908538 + 0.417802i \(0.862800\pi\)
\(810\) −7.15161e11 1.63231e11i −0.0583742 0.0133235i
\(811\) 1.41234e13 1.14642 0.573212 0.819407i \(-0.305697\pi\)
0.573212 + 0.819407i \(0.305697\pi\)
\(812\) −3.75460e12 + 1.18168e13i −0.303083 + 0.953890i
\(813\) 2.54095e12 0.203981
\(814\) −2.24064e13 5.11412e12i −1.78880 0.408283i
\(815\) −2.97339e12 6.17430e12i −0.236071 0.490206i
\(816\) −2.63516e12 1.26903e12i −0.208066 0.100199i
\(817\) 4.61422e12 2.02162e13i 0.362326 1.58745i
\(818\) 3.31293e12 + 1.45149e13i 0.258716 + 1.13351i
\(819\) −5.44378e12 + 2.62159e12i −0.422788 + 0.203604i
\(820\) −9.14791e12 7.29521e12i −0.706577 0.563476i
\(821\) −9.29982e12 + 1.16616e13i −0.714381 + 0.895806i −0.998005 0.0631297i \(-0.979892\pi\)
0.283624 + 0.958936i \(0.408463\pi\)
\(822\) −3.91655e12 + 8.13281e12i −0.299213 + 0.621323i
\(823\) −6.86846e12 + 5.47741e12i −0.521867 + 0.416175i −0.848674 0.528916i \(-0.822599\pi\)
0.326807 + 0.945091i \(0.394027\pi\)
\(824\) 1.79606e12i 0.135722i
\(825\) −4.38982e12 5.50466e12i −0.329916 0.413702i
\(826\) −2.53556e12 + 5.78726e11i −0.189524 + 0.0432576i
\(827\) −7.14672e11 + 1.63119e11i −0.0531290 + 0.0121264i −0.249003 0.968503i \(-0.580103\pi\)
0.195874 + 0.980629i \(0.437246\pi\)
\(828\) −1.82851e12 2.29288e12i −0.135195 0.169530i
\(829\) 7.92846e12i 0.583033i −0.956566 0.291517i \(-0.905840\pi\)
0.956566 0.291517i \(-0.0941599\pi\)
\(830\) −1.29714e13 + 1.03443e13i −0.948713 + 0.756573i
\(831\) 4.13043e12 8.57692e12i 0.300463 0.623917i
\(832\) 8.41665e12 1.05542e13i 0.608954 0.763604i
\(833\) 5.81262e11 + 4.63541e11i 0.0418282 + 0.0333569i
\(834\) 6.37641e12 3.07072e12i 0.456383 0.219782i
\(835\) 9.45508e11 + 4.14254e12i 0.0673094 + 0.294902i
\(836\) −1.05212e13 + 4.60964e13i −0.744968 + 3.26392i
\(837\) 1.66727e13 + 8.02913e12i 1.17419 + 0.565462i
\(838\) −1.08310e13 2.24909e13i −0.758704 1.57546i
\(839\) −2.54181e13 5.80151e12i −1.77098 0.404215i −0.792387 0.610019i \(-0.791162\pi\)
−0.978593 + 0.205804i \(0.934019\pi\)
\(840\) 7.00169e11 0.0485228
\(841\) −1.18466e13 8.37348e12i −0.816605 0.577197i
\(842\) 1.41633e13 0.971091
\(843\) 7.98463e12 + 1.82244e12i 0.544541 + 0.124288i
\(844\) 7.11979e12 + 1.47844e13i 0.482977 + 1.00291i
\(845\) −2.71854e12 1.30918e12i −0.183434 0.0883373i
\(846\) −3.49299e12 + 1.53038e13i −0.234440 + 1.02715i
\(847\) 7.38697e12 + 3.23644e13i 0.493163 + 2.16069i
\(848\) −1.16446e13 + 5.60776e12i −0.773294 + 0.372399i
\(849\) 1.04829e13 + 8.35985e12i 0.692464 + 0.552222i
\(850\) −2.43035e12 + 3.04756e12i −0.159692 + 0.200248i
\(851\) −1.56150e12 + 3.24248e12i −0.102061 + 0.211931i
\(852\) 1.42001e13 1.13242e13i 0.923236 0.736256i
\(853\) 9.85374e12i 0.637280i 0.947876 + 0.318640i \(0.103226\pi\)
−0.947876 + 0.318640i \(0.896774\pi\)
\(854\) 1.05240e13 + 1.31967e13i 0.677048 + 0.848992i
\(855\) −1.13124e13 + 2.58198e12i −0.723948 + 0.165237i
\(856\) 1.31088e12 2.99199e11i 0.0834507 0.0190471i
\(857\) −1.21420e13 1.52256e13i −0.768911 0.964184i 0.231051 0.972942i \(-0.425784\pi\)
−0.999962 + 0.00875771i \(0.997212\pi\)
\(858\) 2.28717e13i 1.44081i
\(859\) 1.70271e13 1.35787e13i 1.06702 0.850919i 0.0777426 0.996973i \(-0.475229\pi\)
0.989277 + 0.146054i \(0.0466573\pi\)
\(860\) 5.34896e12 1.11072e13i 0.333447 0.692409i
\(861\) −6.75707e12 + 8.47310e12i −0.419029 + 0.525446i
\(862\) −3.38155e12 2.69670e12i −0.208609 0.166360i
\(863\) −2.40279e13 + 1.15712e13i −1.47458 + 0.710119i −0.986664 0.162773i \(-0.947956\pi\)
−0.487914 + 0.872892i \(0.662242\pi\)
\(864\) 5.30762e12 + 2.32542e13i 0.324032 + 1.41968i
\(865\) −3.52209e12 + 1.54313e13i −0.213908 + 0.937193i
\(866\) 1.17832e12 + 5.67450e11i 0.0711923 + 0.0342844i
\(867\) 3.89066e12 + 8.07904e12i 0.233850 + 0.485595i
\(868\) −2.09231e13 4.77557e12i −1.25109 0.285553i
\(869\) −2.42414e13 −1.44201
\(870\) −3.48787e12 + 1.09773e13i −0.206406 + 0.649621i
\(871\) 5.27889e11 0.0310785
\(872\) 5.95940e11 + 1.36019e11i 0.0349042 + 0.00796666i
\(873\) −4.06163e12 8.43406e12i −0.236666 0.491442i
\(874\) 1.28670e13 + 6.19641e12i 0.745891 + 0.359202i
\(875\) −3.85682e12 + 1.68978e13i −0.222430 + 0.974528i
\(876\) −2.25536e12 9.88136e12i −0.129404 0.566955i
\(877\) −3.35293e12 + 1.61468e12i −0.191393 + 0.0921700i −0.527126 0.849787i \(-0.676730\pi\)
0.335733 + 0.941957i \(0.391016\pi\)
\(878\) −1.70777e13 1.36190e13i −0.969847 0.773427i
\(879\) −3.48127e12 + 4.36538e12i −0.196693 + 0.246645i
\(880\) 9.65582e12 2.00505e13i 0.542772 1.12708i
\(881\) 2.40368e13 1.91687e13i 1.34427 1.07202i 0.353646 0.935379i \(-0.384942\pi\)
0.990621 0.136638i \(-0.0436296\pi\)
\(882\) 2.08244e12i 0.115868i
\(883\) 1.28505e13 + 1.61141e13i 0.711375 + 0.892036i 0.997815 0.0660624i \(-0.0210436\pi\)
−0.286441 + 0.958098i \(0.592472\pi\)
\(884\) 6.40014e12 1.46079e12i 0.352496 0.0804550i
\(885\) −1.22114e12 + 2.78718e11i −0.0669148 + 0.0152729i
\(886\) 2.72911e12 + 3.42220e12i 0.148789 + 0.186575i
\(887\) 1.14268e13i 0.619824i 0.950765 + 0.309912i \(0.100300\pi\)
−0.950765 + 0.309912i \(0.899700\pi\)
\(888\) −7.06134e11 + 5.63123e11i −0.0381091 + 0.0303910i
\(889\) −1.32284e13 + 2.74690e13i −0.710310 + 1.47497i
\(890\) 3.99684e12 5.01187e12i 0.213531 0.267760i
\(891\) −1.51685e12 1.20965e12i −0.0806294 0.0642998i
\(892\) −2.43702e13 + 1.17361e13i −1.28889 + 0.620698i
\(893\) −8.81844e12 3.86361e13i −0.464045 2.03311i
\(894\) 1.67529e12 7.33994e12i 0.0877146 0.384303i
\(895\) 1.14661e13 + 5.52179e12i 0.597328 + 0.287658i
\(896\) −1.71234e12 3.55570e12i −0.0887571 0.184306i
\(897\) 3.49172e12 + 7.96963e11i 0.180083 + 0.0411029i
\(898\) 4.76161e13 2.44349
\(899\) 1.27384e13 2.16393e13i 0.650421 1.10490i
\(900\) 5.66041e12 0.287578
\(901\) −7.11400e12 1.62372e12i −0.359627 0.0820826i
\(902\) −2.58991e13 5.37801e13i −1.30273 2.70515i
\(903\) −1.02879e13 4.95438e12i −0.514910 0.247968i
\(904\) 7.64111e10 3.34779e11i 0.00380538 0.0166725i
\(905\) 2.67735e12 + 1.17302e13i 0.132674 + 0.581284i
\(906\) 2.94547e13 1.41847e13i 1.45237 0.699426i
\(907\) 1.46168e13 + 1.16565e13i 0.717164 + 0.571919i 0.912628 0.408792i \(-0.134050\pi\)
−0.195464 + 0.980711i \(0.562621\pi\)
\(908\) 1.13595e13 1.42444e13i 0.554591 0.695435i
\(909\) 2.81957e12 5.85490e12i 0.136976 0.284434i
\(910\) 1.36764e13 1.09065e13i 0.661126 0.527230i
\(911\) 1.62938e13i 0.783770i −0.920014 0.391885i \(-0.871823\pi\)
0.920014 0.391885i \(-0.128177\pi\)
\(912\) −1.28953e13 1.61703e13i −0.617243 0.773998i
\(913\) −4.27804e13 + 9.76434e12i −2.03763 + 0.465076i
\(914\) −2.67241e13 + 6.09959e12i −1.26661 + 0.289097i
\(915\) 5.06841e12 + 6.35559e12i 0.239044 + 0.299751i
\(916\) 1.79982e13i 0.844694i
\(917\) 2.09374e13 1.66970e13i 0.977825 0.779790i
\(918\) −5.39286e12 + 1.11984e13i −0.250627 + 0.520432i
\(919\) −6.14780e12 + 7.70910e12i −0.284315 + 0.356520i −0.903396 0.428807i \(-0.858934\pi\)
0.619081 + 0.785327i \(0.287505\pi\)
\(920\) 4.72135e11 + 3.76515e11i 0.0217281 + 0.0173276i
\(921\) −1.42328e13 + 6.85414e12i −0.651810 + 0.313895i
\(922\) −8.27957e12 3.62752e13i −0.377328 1.65318i
\(923\) 7.18161e12 3.14647e13i 0.325697 1.42697i
\(924\) 2.34581e13 + 1.12968e13i 1.05869 + 0.509839i
\(925\) −3.01384e12 6.25830e12i −0.135357 0.281073i
\(926\) 4.69088e13 + 1.07066e13i 2.09655 + 0.478523i
\(927\) 1.63904e13 0.729006
\(928\) 3.20438e13 4.55337e12i 1.41833 0.201543i
\(929\) −5.44286e12 −0.239749 −0.119874 0.992789i \(-0.538249\pi\)
−0.119874 + 0.992789i \(0.538249\pi\)
\(930\) −1.94367e13 4.43631e12i −0.852020 0.194468i
\(931\) 2.28107e12 + 4.73669e12i 0.0995097 + 0.206634i
\(932\) 2.83850e13 + 1.36695e13i 1.23230 + 0.593446i
\(933\) 3.88343e12 1.70144e13i 0.167783 0.735105i
\(934\) 1.45068e11 + 6.35583e11i 0.00623749 + 0.0273282i
\(935\) 1.13201e13 5.45148e12i 0.484394 0.233272i
\(936\) −1.02249e12 8.15413e11i −0.0435432 0.0347245i
\(937\) −1.93233e13 + 2.42307e13i −0.818944 + 1.02692i 0.180119 + 0.983645i \(0.442352\pi\)
−0.999063 + 0.0432782i \(0.986220\pi\)
\(938\) 5.02926e11 1.04434e12i 0.0212125 0.0440482i
\(939\) −4.07718e12 + 3.25144e12i −0.171145 + 0.136484i
\(940\) 2.35608e13i 0.984269i
\(941\) −8.26403e11 1.03628e12i −0.0343588 0.0430846i 0.764355 0.644795i \(-0.223057\pi\)
−0.798714 + 0.601711i \(0.794486\pi\)
\(942\) 3.33505e12 7.61202e11i 0.137998 0.0314971i
\(943\) −9.11281e12 + 2.07994e12i −0.375275 + 0.0856540i
\(944\) 2.02544e12 + 2.53982e12i 0.0830128 + 0.104095i
\(945\) 1.71705e13i 0.700389i
\(946\) 4.91714e13 3.92128e13i 1.99619 1.59191i
\(947\) −1.13751e13 + 2.36206e13i −0.459600 + 0.954369i 0.534425 + 0.845216i \(0.320528\pi\)
−0.994025 + 0.109153i \(0.965186\pi\)
\(948\) −8.35110e12 + 1.04719e13i −0.335820 + 0.421104i
\(949\) −1.40809e13 1.12291e13i −0.563550 0.449416i
\(950\) −2.48345e13 + 1.19597e13i −0.989235 + 0.476390i
\(951\) 4.92765e11 + 2.15894e12i 0.0195356 + 0.0855912i
\(952\) 2.28136e11 9.99531e11i 0.00900178 0.0394394i
\(953\) 3.80789e13 + 1.83378e13i 1.49543 + 0.720161i 0.989783 0.142580i \(-0.0455399\pi\)
0.505646 + 0.862741i \(0.331254\pi\)
\(954\) 8.86804e12 + 1.84147e13i 0.346625 + 0.719774i
\(955\) 4.70824e11 + 1.07463e11i 0.0183165 + 0.00418063i
\(956\) −3.69874e13 −1.43217
\(957\) −2.09083e13 + 2.21555e13i −0.805779 + 0.853844i
\(958\) −1.85150e13 −0.710199
\(959\) 1.78016e13 + 4.06311e12i 0.679636 + 0.155122i
\(960\) −6.19390e12 1.28618e13i −0.235366 0.488742i
\(961\) 1.53376e13 + 7.38619e12i 0.580098 + 0.279361i
\(962\) −5.02111e12 + 2.19989e13i −0.189022 + 0.828158i
\(963\) 2.73042e12 + 1.19627e13i 0.102308 + 0.448241i
\(964\) −2.90779e13 + 1.40032e13i −1.08447 + 0.522251i
\(965\) −1.74253e13 1.38962e13i −0.646857 0.515851i
\(966\) 4.90326e12 6.14849e12i 0.181171 0.227181i
\(967\) 4.09925e12 8.51218e12i 0.150760 0.313056i −0.811888 0.583813i \(-0.801560\pi\)
0.962648 + 0.270758i \(0.0872742\pi\)
\(968\) −5.61779e12 + 4.48004e12i −0.205649 + 0.164000i
\(969\) 1.16769e13i 0.425473i
\(970\) 1.68975e13 + 2.11888e13i 0.612844 + 0.768482i
\(971\) −2.87460e13 + 6.56108e12i −1.03774 + 0.236858i −0.707260 0.706953i \(-0.750069\pi\)
−0.330484 + 0.943812i \(0.607212\pi\)
\(972\) 2.86450e13 6.53802e12i 1.02932 0.234935i
\(973\) −8.92592e12 1.11927e13i −0.319260 0.400340i
\(974\) 6.01838e13i 2.14272i
\(975\) −5.40455e12 + 4.30998e12i −0.191531 + 0.152741i
\(976\) 9.14769e12 1.89954e13i 0.322691 0.670076i
\(977\) −1.31214e13 + 1.64537e13i −0.460739 + 0.577749i −0.956876 0.290495i \(-0.906180\pi\)
0.496137 + 0.868244i \(0.334751\pi\)
\(978\) −1.51026e13 1.20439e13i −0.527868 0.420961i
\(979\) 1.52755e13 7.35630e12i 0.531464 0.255939i
\(980\) 6.95512e11 + 3.04724e12i 0.0240873 + 0.105533i
\(981\) −1.24128e12 + 5.43839e12i −0.0427916 + 0.187482i
\(982\) −5.81531e12 2.80051e12i −0.199559 0.0961026i
\(983\) 1.17582e13 + 2.44162e13i 0.401653 + 0.834042i 0.999475 + 0.0324122i \(0.0103189\pi\)
−0.597821 + 0.801629i \(0.703967\pi\)
\(984\) −2.28696e12 5.21984e11i −0.0777644 0.0177492i
\(985\) −3.12441e13 −1.05756
\(986\) 1.45343e13 + 8.55588e12i 0.489720 + 0.288283i
\(987\) −2.18228e13 −0.731951
\(988\) 4.52581e13 + 1.03299e13i 1.51109 + 0.344896i
\(989\) −4.27307e12 8.87313e12i −0.142022 0.294913i
\(990\) −3.17076e13 1.52696e13i −1.04907 0.505207i
\(991\) 1.11042e13 4.86508e13i 0.365727 1.60236i −0.372653 0.927971i \(-0.621552\pi\)
0.738380 0.674385i \(-0.235591\pi\)
\(992\) 1.24660e13 + 5.46169e13i 0.408717 + 1.79071i
\(993\) 3.20564e13 1.54376e13i 1.04627 0.503857i
\(994\) −5.54054e13 4.41843e13i −1.80017 1.43559i
\(995\) −7.84396e12 + 9.83601e12i −0.253706 + 0.318138i
\(996\) −1.05197e13 + 2.18443e13i −0.338715 + 0.703349i
\(997\) −2.20099e12 + 1.75523e12i −0.0705488 + 0.0562608i −0.658129 0.752905i \(-0.728652\pi\)
0.587580 + 0.809166i \(0.300081\pi\)
\(998\) 1.97450e13i 0.630042i
\(999\) −1.38097e13 1.73168e13i −0.438670 0.550075i
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 29.10.e.a.4.4 132
29.22 even 14 inner 29.10.e.a.22.4 yes 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.10.e.a.4.4 132 1.1 even 1 trivial
29.10.e.a.22.4 yes 132 29.22 even 14 inner