Properties

Label 43.9.h.a.3.18
Level $43$
Weight $9$
Character 43.3
Analytic conductor $17.517$
Analytic rank $0$
Dimension $336$
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] = [43,9,Mod(3,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\), degree \(12\), 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: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 3.18
Character \(\chi\) \(=\) 43.3
Dual form 43.9.h.a.29.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.70483 - 7.69316i) q^{2} +(20.6613 + 1.54835i) q^{3} +(114.154 + 143.145i) q^{4} +(-181.686 + 589.011i) q^{5} +(88.4583 - 153.214i) q^{6} +(2375.79 - 1371.67i) q^{7} +(3655.28 - 834.293i) q^{8} +(-6063.23 - 913.884i) q^{9} +O(q^{10})\) \(q+(3.70483 - 7.69316i) q^{2} +(20.6613 + 1.54835i) q^{3} +(114.154 + 143.145i) q^{4} +(-181.686 + 589.011i) q^{5} +(88.4583 - 153.214i) q^{6} +(2375.79 - 1371.67i) q^{7} +(3655.28 - 834.293i) q^{8} +(-6063.23 - 913.884i) q^{9} +(3858.24 + 3579.93i) q^{10} +(-17515.6 + 21963.9i) q^{11} +(2136.94 + 3134.32i) q^{12} +(-22129.8 + 20533.5i) q^{13} +(-1750.53 - 23359.1i) q^{14} +(-4665.87 + 11888.4i) q^{15} +(-3305.93 + 14484.2i) q^{16} +(95601.8 - 29489.3i) q^{17} +(-29493.9 + 43259.6i) q^{18} +(-7179.70 - 47634.2i) q^{19} +(-105054. + 41230.8i) q^{20} +(51210.9 - 24661.8i) q^{21} +(104079. + 216123. i) q^{22} +(175654. + 447558. i) q^{23} +(76814.6 - 11577.9i) q^{24} +(8824.89 + 6016.71i) q^{25} +(75980.0 + 246321. i) q^{26} +(-256390. - 58519.3i) q^{27} +(467555. + 183502. i) q^{28} +(-874301. + 65519.8i) q^{29} +(74173.4 + 79939.9i) q^{30} +(695202. - 473981. i) q^{31} +(849596. + 677530. i) q^{32} +(-395903. + 426682. i) q^{33} +(127323. - 844732. i) q^{34} +(376278. + 1.64858e6i) q^{35} +(-561326. - 972246. i) q^{36} +(1.23942e6 + 715581. i) q^{37} +(-393057. - 121242. i) q^{38} +(-489024. + 389984. i) q^{39} +(-172704. + 2.30458e6i) q^{40} +(1.56977e6 + 755963. i) q^{41} -485341. i q^{42} +(-3.41822e6 + 62847.2i) q^{43} -5.14351e6 q^{44} +(1.63989e6 - 3.40527e6i) q^{45} +(4.09390e6 + 306796. i) q^{46} +(-2.32928e6 - 2.92083e6i) q^{47} +(-90731.5 + 294144. i) q^{48} +(880532. - 1.52513e6i) q^{49} +(78982.2 - 45600.4i) q^{50} +(2.02092e6 - 461261. i) q^{51} +(-5.46548e6 - 823789. i) q^{52} +(5.21502e6 + 4.83883e6i) q^{53} +(-1.40008e6 + 1.75564e6i) q^{54} +(-9.75463e6 - 1.43074e7i) q^{55} +(7.53982e6 - 6.99593e6i) q^{56} +(-74587.5 - 995302. i) q^{57} +(-2.73508e6 + 6.96888e6i) q^{58} +(1.08592e6 - 4.75773e6i) q^{59} +(-2.23440e6 + 689222. i) q^{60} +(1.02293e7 - 1.50036e7i) q^{61} +(-1.07080e6 - 7.10432e6i) q^{62} +(-1.56585e7 + 6.14552e6i) q^{63} +(4.93328e6 - 2.37574e6i) q^{64} +(-8.07377e6 - 1.67654e7i) q^{65} +(1.81578e6 + 4.62653e6i) q^{66} +(9.29438e6 - 1.40090e6i) q^{67} +(1.51346e7 + 1.03186e7i) q^{68} +(2.93626e6 + 9.51911e6i) q^{69} +(1.40768e7 + 3.21295e6i) q^{70} +(1.90411e6 + 747310. i) q^{71} +(-2.29252e7 + 1.71801e6i) q^{72} +(-1.17449e7 - 1.26580e7i) q^{73} +(1.00969e7 - 6.88397e6i) q^{74} +(173018. + 137977. i) q^{75} +(5.99901e6 - 6.46540e6i) q^{76} +(-1.14864e7 + 7.62072e7i) q^{77} +(1.18845e6 + 5.20696e6i) q^{78} +(-3.00323e7 - 5.20175e7i) q^{79} +(-7.93073e6 - 4.57881e6i) q^{80} +(3.32361e7 + 1.02520e7i) q^{81} +(1.16315e7 - 9.27580e6i) q^{82} +(3.65284e6 - 4.87438e7i) q^{83} +(9.37617e6 + 4.51533e6i) q^{84} +6.16683e7i q^{85} +(-1.21804e7 + 2.65298e7i) q^{86} -1.81657e7 q^{87} +(-4.57001e7 + 9.48972e7i) q^{88} +(9.50125e7 + 7.12020e6i) q^{89} +(-2.01218e7 - 2.52319e7i) q^{90} +(-2.44108e7 + 7.91380e7i) q^{91} +(-4.40141e7 + 7.62347e7i) q^{92} +(1.50977e7 - 8.71665e6i) q^{93} +(-3.11000e7 + 7.09837e6i) q^{94} +(2.93615e7 + 4.42554e6i) q^{95} +(1.65047e7 + 1.53141e7i) q^{96} +(-4.36382e7 + 5.47206e7i) q^{97} +(-8.47082e6 - 1.24244e7i) q^{98} +(1.26273e8 - 1.17165e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 336 q - 14 q^{2} + 70 q^{3} + 6460 q^{4} - 11 q^{5} - 1798 q^{6} + 5010 q^{7} + 5362 q^{8} - 40176 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 336 q - 14 q^{2} + 70 q^{3} + 6460 q^{4} - 11 q^{5} - 1798 q^{6} + 5010 q^{7} + 5362 q^{8} - 40176 q^{9} - 12505 q^{10} - 31942 q^{11} - 54796 q^{12} - 75596 q^{13} + 111780 q^{14} + 4037 q^{15} - 688224 q^{16} - 5977 q^{17} - 280532 q^{18} - 552290 q^{19} - 494171 q^{20} + 141291 q^{21} - 432782 q^{22} - 619546 q^{23} - 298136 q^{24} - 2392669 q^{25} - 113675 q^{26} - 14 q^{27} - 1143258 q^{28} + 4198855 q^{29} - 795576 q^{30} + 3391610 q^{31} + 3704176 q^{32} + 469240 q^{33} + 3670777 q^{34} - 2602743 q^{35} - 32236515 q^{36} + 7009521 q^{37} + 1762126 q^{38} - 573251 q^{39} - 41379997 q^{40} - 11003050 q^{41} + 7113655 q^{43} + 64459560 q^{44} + 11644332 q^{45} - 14793057 q^{46} + 9244886 q^{47} - 34730249 q^{48} + 82140290 q^{49} - 80542767 q^{50} - 7776902 q^{51} - 98888784 q^{52} + 39659528 q^{53} + 139217042 q^{54} + 96182224 q^{55} - 59364207 q^{56} - 94760066 q^{57} + 149491596 q^{58} - 74665213 q^{59} + 188098449 q^{60} + 55854238 q^{61} - 52173383 q^{62} + 40219829 q^{63} + 13742518 q^{64} + 87064978 q^{65} - 64965481 q^{66} + 210933441 q^{67} - 248367043 q^{68} + 405756759 q^{69} - 362301191 q^{70} - 34975301 q^{71} - 125412979 q^{72} - 216767388 q^{73} + 53341380 q^{74} + 436840145 q^{75} - 29249062 q^{76} - 59286141 q^{77} + 204702644 q^{78} + 71493313 q^{79} - 737037738 q^{80} - 235365082 q^{81} - 806662220 q^{82} + 254450510 q^{83} - 979300857 q^{84} + 50436244 q^{86} + 696609678 q^{87} + 65867942 q^{88} + 949059334 q^{89} + 1083992303 q^{90} - 184351501 q^{91} + 379980750 q^{92} - 271490850 q^{93} - 369651898 q^{94} - 1349611517 q^{95} - 1044343058 q^{96} - 850069303 q^{97} - 271546964 q^{98} + 148520290 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.70483 7.69316i 0.231552 0.480822i −0.752526 0.658563i \(-0.771165\pi\)
0.984077 + 0.177741i \(0.0568788\pi\)
\(3\) 20.6613 + 1.54835i 0.255078 + 0.0191154i 0.201655 0.979457i \(-0.435368\pi\)
0.0534226 + 0.998572i \(0.482987\pi\)
\(4\) 114.154 + 143.145i 0.445916 + 0.559161i
\(5\) −181.686 + 589.011i −0.290698 + 0.942418i 0.685964 + 0.727635i \(0.259381\pi\)
−0.976662 + 0.214783i \(0.931096\pi\)
\(6\) 88.4583 153.214i 0.0682549 0.118221i
\(7\) 2375.79 1371.67i 0.989502 0.571289i 0.0843766 0.996434i \(-0.473110\pi\)
0.905125 + 0.425145i \(0.139777\pi\)
\(8\) 3655.28 834.293i 0.892402 0.203685i
\(9\) −6063.23 913.884i −0.924131 0.139290i
\(10\) 3858.24 + 3579.93i 0.385824 + 0.357993i
\(11\) −17515.6 + 21963.9i −1.19634 + 1.50016i −0.377626 + 0.925958i \(0.623260\pi\)
−0.818713 + 0.574204i \(0.805312\pi\)
\(12\) 2136.94 + 3134.32i 0.103055 + 0.151153i
\(13\) −22129.8 + 20533.5i −0.774826 + 0.718934i −0.964837 0.262848i \(-0.915338\pi\)
0.190011 + 0.981782i \(0.439148\pi\)
\(14\) −1750.53 23359.1i −0.0455676 0.608058i
\(15\) −4665.87 + 11888.4i −0.0921653 + 0.234833i
\(16\) −3305.93 + 14484.2i −0.0504445 + 0.221012i
\(17\) 95601.8 29489.3i 1.14464 0.353076i 0.336282 0.941761i \(-0.390831\pi\)
0.808362 + 0.588686i \(0.200354\pi\)
\(18\) −29493.9 + 43259.6i −0.280958 + 0.412090i
\(19\) −7179.70 47634.2i −0.0550924 0.365514i −0.999342 0.0362826i \(-0.988448\pi\)
0.944249 0.329232i \(-0.106790\pi\)
\(20\) −105054. + 41230.8i −0.656590 + 0.257693i
\(21\) 51210.9 24661.8i 0.263321 0.126809i
\(22\) 104079. + 216123.i 0.444297 + 0.922592i
\(23\) 175654. + 447558.i 0.627691 + 1.59933i 0.790355 + 0.612649i \(0.209896\pi\)
−0.162665 + 0.986681i \(0.552009\pi\)
\(24\) 76814.6 11577.9i 0.231526 0.0348969i
\(25\) 8824.89 + 6016.71i 0.0225917 + 0.0154028i
\(26\) 75980.0 + 246321.i 0.166267 + 0.539024i
\(27\) −256390. 58519.3i −0.482443 0.110114i
\(28\) 467555. + 183502.i 0.760677 + 0.298544i
\(29\) −874301. + 65519.8i −1.23614 + 0.0926362i −0.676717 0.736243i \(-0.736598\pi\)
−0.559427 + 0.828880i \(0.688979\pi\)
\(30\) 74173.4 + 79939.9i 0.0915721 + 0.0986912i
\(31\) 695202. 473981.i 0.752773 0.513232i −0.125089 0.992146i \(-0.539922\pi\)
0.877862 + 0.478913i \(0.158969\pi\)
\(32\) 849596. + 677530.i 0.810238 + 0.646143i
\(33\) −395903. + 426682.i −0.333836 + 0.359790i
\(34\) 127323. 844732.i 0.0952776 0.632126i
\(35\) 376278. + 1.64858e6i 0.250748 + 1.09860i
\(36\) −561326. 972246.i −0.334199 0.578850i
\(37\) 1.23942e6 + 715581.i 0.661321 + 0.381814i 0.792780 0.609508i \(-0.208633\pi\)
−0.131459 + 0.991322i \(0.541966\pi\)
\(38\) −393057. 121242.i −0.188504 0.0581458i
\(39\) −489024. + 389984.i −0.211384 + 0.168573i
\(40\) −172704. + 2.30458e6i −0.0674627 + 0.900227i
\(41\) 1.56977e6 + 755963.i 0.555522 + 0.267525i 0.690511 0.723322i \(-0.257386\pi\)
−0.134989 + 0.990847i \(0.543100\pi\)
\(42\) 485341.i 0.155973i
\(43\) −3.41822e6 + 62847.2i −0.999831 + 0.0183828i
\(44\) −5.14351e6 −1.37230
\(45\) 1.63989e6 3.40527e6i 0.399913 0.830427i
\(46\) 4.09390e6 + 306796.i 0.914337 + 0.0685201i
\(47\) −2.32928e6 2.92083e6i −0.477343 0.598569i 0.483609 0.875284i \(-0.339326\pi\)
−0.960952 + 0.276715i \(0.910754\pi\)
\(48\) −90731.5 + 294144.i −0.0170920 + 0.0554110i
\(49\) 880532. 1.52513e6i 0.152743 0.264558i
\(50\) 78982.2 45600.4i 0.0126371 0.00729606i
\(51\) 2.02092e6 461261.i 0.298723 0.0681815i
\(52\) −5.46548e6 823789.i −0.747507 0.112669i
\(53\) 5.21502e6 + 4.83883e6i 0.660926 + 0.613250i 0.937601 0.347714i \(-0.113042\pi\)
−0.276675 + 0.960964i \(0.589232\pi\)
\(54\) −1.40008e6 + 1.75564e6i −0.164656 + 0.206472i
\(55\) −9.75463e6 1.43074e7i −1.06601 1.56354i
\(56\) 7.53982e6 6.99593e6i 0.766671 0.711366i
\(57\) −74587.5 995302.i −0.00706589 0.0942877i
\(58\) −2.73508e6 + 6.96888e6i −0.241690 + 0.615816i
\(59\) 1.08592e6 4.75773e6i 0.0896169 0.392637i −0.910149 0.414281i \(-0.864033\pi\)
0.999766 + 0.0216442i \(0.00689011\pi\)
\(60\) −2.23440e6 + 689222.i −0.172408 + 0.0531807i
\(61\) 1.02293e7 1.50036e7i 0.738800 1.08362i −0.254389 0.967102i \(-0.581874\pi\)
0.993189 0.116518i \(-0.0371732\pi\)
\(62\) −1.07080e6 7.10432e6i −0.0724674 0.480790i
\(63\) −1.56585e7 + 6.14552e6i −0.994005 + 0.390118i
\(64\) 4.93328e6 2.37574e6i 0.294046 0.141605i
\(65\) −8.07377e6 1.67654e7i −0.452296 0.939203i
\(66\) 1.81578e6 + 4.62653e6i 0.0956945 + 0.243826i
\(67\) 9.29438e6 1.40090e6i 0.461234 0.0695199i 0.0856849 0.996322i \(-0.472692\pi\)
0.375549 + 0.926802i \(0.377454\pi\)
\(68\) 1.51346e7 + 1.03186e7i 0.707841 + 0.482598i
\(69\) 2.93626e6 + 9.51911e6i 0.129538 + 0.419952i
\(70\) 1.40768e7 + 3.21295e6i 0.586291 + 0.133817i
\(71\) 1.90411e6 + 747310.i 0.0749307 + 0.0294081i 0.402510 0.915415i \(-0.368138\pi\)
−0.327580 + 0.944824i \(0.606233\pi\)
\(72\) −2.29252e7 + 1.71801e6i −0.853068 + 0.0639286i
\(73\) −1.17449e7 1.26580e7i −0.413579 0.445732i 0.491563 0.870842i \(-0.336426\pi\)
−0.905142 + 0.425110i \(0.860235\pi\)
\(74\) 1.00969e7 6.88397e6i 0.336715 0.229568i
\(75\) 173018. + 137977.i 0.00546822 + 0.00436076i
\(76\) 5.99901e6 6.46540e6i 0.179815 0.193794i
\(77\) −1.14864e7 + 7.62072e7i −0.326754 + 2.16787i
\(78\) 1.18845e6 + 5.20696e6i 0.0321073 + 0.140671i
\(79\) −3.00323e7 5.20175e7i −0.771046 1.33549i −0.936990 0.349355i \(-0.886401\pi\)
0.165944 0.986135i \(-0.446933\pi\)
\(80\) −7.93073e6 4.57881e6i −0.193621 0.111787i
\(81\) 3.32361e7 + 1.02520e7i 0.772094 + 0.238159i
\(82\) 1.16315e7 9.27580e6i 0.257264 0.205161i
\(83\) 3.65284e6 4.87438e7i 0.0769695 1.02709i −0.816319 0.577602i \(-0.803989\pi\)
0.893288 0.449485i \(-0.148392\pi\)
\(84\) 9.37617e6 + 4.51533e6i 0.188325 + 0.0906926i
\(85\) 6.16683e7i 1.18137i
\(86\) −1.21804e7 + 2.65298e7i −0.222674 + 0.484998i
\(87\) −1.81657e7 −0.317084
\(88\) −4.57001e7 + 9.48972e7i −0.762055 + 1.58242i
\(89\) 9.50125e7 + 7.12020e6i 1.51433 + 0.113483i 0.805796 0.592193i \(-0.201738\pi\)
0.708534 + 0.705677i \(0.249357\pi\)
\(90\) −2.01218e7 2.52319e7i −0.306687 0.384574i
\(91\) −2.44108e7 + 7.91380e7i −0.355973 + 1.15404i
\(92\) −4.40141e7 + 7.62347e7i −0.614386 + 1.06415i
\(93\) 1.50977e7 8.71665e6i 0.201827 0.116525i
\(94\) −3.11000e7 + 7.09837e6i −0.398335 + 0.0909174i
\(95\) 2.93615e7 + 4.42554e6i 0.360483 + 0.0543340i
\(96\) 1.65047e7 + 1.53141e7i 0.194322 + 0.180305i
\(97\) −4.36382e7 + 5.47206e7i −0.492924 + 0.618108i −0.964617 0.263656i \(-0.915072\pi\)
0.471693 + 0.881763i \(0.343643\pi\)
\(98\) −8.47082e6 1.24244e7i −0.0918377 0.134701i
\(99\) 1.26273e8 1.17165e8i 1.31453 1.21971i
\(100\) 146138. + 1.95007e6i 0.00146138 + 0.0195007i
\(101\) 4.30187e7 1.09610e8i 0.413401 1.05333i −0.560861 0.827910i \(-0.689530\pi\)
0.974262 0.225418i \(-0.0723748\pi\)
\(102\) 3.93860e6 1.72561e7i 0.0363866 0.159420i
\(103\) −2.32447e7 + 7.17003e6i −0.206526 + 0.0637048i −0.396292 0.918125i \(-0.629703\pi\)
0.189766 + 0.981829i \(0.439227\pi\)
\(104\) −6.37597e7 + 9.35183e7i −0.545020 + 0.799398i
\(105\) 5.22182e6 + 3.46445e7i 0.0429600 + 0.285021i
\(106\) 5.65467e7 2.21929e7i 0.447903 0.175789i
\(107\) 2.21498e8 1.06668e8i 1.68980 0.813763i 0.694224 0.719759i \(-0.255748\pi\)
0.995572 0.0940032i \(-0.0299664\pi\)
\(108\) −2.08913e7 4.33812e7i −0.153557 0.318865i
\(109\) 2.93776e7 + 7.48529e7i 0.208118 + 0.530277i 0.996375 0.0850699i \(-0.0271114\pi\)
−0.788257 + 0.615346i \(0.789016\pi\)
\(110\) −1.46208e8 + 2.20374e7i −0.998623 + 0.150518i
\(111\) 2.45001e7 + 1.67039e7i 0.161390 + 0.110034i
\(112\) 1.20133e7 + 3.89462e7i 0.0763467 + 0.247510i
\(113\) 2.04717e7 + 4.67254e6i 0.125557 + 0.0286575i 0.284838 0.958576i \(-0.408060\pi\)
−0.159281 + 0.987233i \(0.550917\pi\)
\(114\) −7.93335e6 3.11361e6i −0.0469718 0.0184351i
\(115\) −2.95531e8 + 2.21470e7i −1.68971 + 0.126626i
\(116\) −1.09184e8 1.17673e8i −0.603015 0.649895i
\(117\) 1.52943e8 1.04275e8i 0.816182 0.556463i
\(118\) −3.25788e7 2.59807e7i −0.168038 0.134006i
\(119\) 1.86681e8 2.01194e8i 0.930919 1.00329i
\(120\) −7.13660e6 + 4.73482e7i −0.0344165 + 0.228338i
\(121\) −1.27916e8 5.60436e8i −0.596737 2.61448i
\(122\) −7.75275e7 1.34282e8i −0.349958 0.606145i
\(123\) 3.12631e7 + 1.80497e7i 0.136588 + 0.0788589i
\(124\) 1.47208e8 + 4.54078e7i 0.622653 + 0.192063i
\(125\) −1.93396e8 + 1.54229e8i −0.792152 + 0.631720i
\(126\) −1.07337e7 + 1.43232e8i −0.0425861 + 0.568272i
\(127\) 2.96640e7 + 1.42854e7i 0.114029 + 0.0549134i 0.490029 0.871706i \(-0.336986\pi\)
−0.376000 + 0.926620i \(0.622701\pi\)
\(128\) 2.31434e8i 0.862160i
\(129\) −7.07223e7 3.99410e6i −0.255386 0.0144232i
\(130\) −1.58890e8 −0.556320
\(131\) −2.17739e8 + 4.52139e8i −0.739351 + 1.53528i 0.101997 + 0.994785i \(0.467477\pi\)
−0.841348 + 0.540493i \(0.818238\pi\)
\(132\) −1.06272e8 7.96395e6i −0.350043 0.0262321i
\(133\) −8.23957e7 1.03321e8i −0.263328 0.330203i
\(134\) 2.36567e7 7.66933e7i 0.0733729 0.237869i
\(135\) 8.10510e7 1.40384e8i 0.244019 0.422653i
\(136\) 3.24849e8 1.87551e8i 0.949566 0.548232i
\(137\) 3.75021e8 8.55960e7i 1.06457 0.242980i 0.345854 0.938288i \(-0.387589\pi\)
0.718712 + 0.695308i \(0.244732\pi\)
\(138\) 8.41104e7 + 1.26776e7i 0.231917 + 0.0349559i
\(139\) 2.47944e8 + 2.30059e8i 0.664194 + 0.616282i 0.938467 0.345370i \(-0.112246\pi\)
−0.274272 + 0.961652i \(0.588437\pi\)
\(140\) −1.93033e8 + 2.42055e8i −0.502480 + 0.630090i
\(141\) −4.36036e7 6.39547e7i −0.110318 0.161806i
\(142\) 1.28036e7 1.18800e7i 0.0314904 0.0292188i
\(143\) −6.33774e7 8.45712e8i −0.151562 2.02245i
\(144\) 3.32815e7 8.47999e7i 0.0774022 0.197218i
\(145\) 1.20256e8 5.26877e8i 0.272042 1.19189i
\(146\) −1.40893e8 + 4.34597e7i −0.310083 + 0.0956479i
\(147\) 2.05544e7 3.01477e7i 0.0440185 0.0645633i
\(148\) 3.90537e7 + 2.59104e8i 0.0813982 + 0.540042i
\(149\) −5.43788e8 + 2.13421e8i −1.10328 + 0.433005i −0.845919 0.533311i \(-0.820947\pi\)
−0.257359 + 0.966316i \(0.582852\pi\)
\(150\) 1.70248e6 819871.i 0.00336292 0.00161950i
\(151\) 3.66038e7 + 7.60085e7i 0.0704073 + 0.146202i 0.933202 0.359352i \(-0.117002\pi\)
−0.862795 + 0.505554i \(0.831288\pi\)
\(152\) −6.59847e7 1.68126e8i −0.123614 0.314964i
\(153\) −6.06605e8 + 9.14310e7i −1.10698 + 0.166851i
\(154\) 5.43719e8 + 3.70701e8i 0.966699 + 0.659084i
\(155\) 1.52872e8 + 4.95598e8i 0.264850 + 0.858623i
\(156\) −1.11649e8 2.54831e7i −0.188519 0.0430282i
\(157\) −1.31776e8 5.17181e7i −0.216889 0.0851225i 0.254409 0.967097i \(-0.418119\pi\)
−0.471298 + 0.881974i \(0.656214\pi\)
\(158\) −5.11443e8 + 3.83274e7i −0.820671 + 0.0615008i
\(159\) 1.00257e8 + 1.08051e8i 0.156865 + 0.169060i
\(160\) −5.53433e8 + 3.77324e8i −0.844471 + 0.575751i
\(161\) 1.03122e9 + 8.22368e8i 1.53478 + 1.22395i
\(162\) 2.02004e8 2.17709e8i 0.293292 0.316094i
\(163\) −1.67661e6 + 1.11236e7i −0.00237510 + 0.0157578i −0.989987 0.141159i \(-0.954917\pi\)
0.987612 + 0.156916i \(0.0501553\pi\)
\(164\) 7.09842e7 + 3.11002e8i 0.0981264 + 0.429920i
\(165\) −1.79391e8 3.10714e8i −0.242027 0.419203i
\(166\) −3.61461e8 2.08689e8i −0.476024 0.274832i
\(167\) 1.01415e9 + 3.12822e8i 1.30387 + 0.402191i 0.867437 0.497546i \(-0.165765\pi\)
0.436433 + 0.899737i \(0.356242\pi\)
\(168\) 1.66615e8 1.32871e8i 0.209159 0.166799i
\(169\) 7.14576e6 9.53535e7i 0.00875995 0.116893i
\(170\) 4.74424e8 + 2.28471e8i 0.568030 + 0.273549i
\(171\) 2.95378e8i 0.345457i
\(172\) −3.99202e8 4.82128e8i −0.456120 0.550869i
\(173\) 1.34513e9 1.50169 0.750846 0.660477i \(-0.229646\pi\)
0.750846 + 0.660477i \(0.229646\pi\)
\(174\) −6.73007e7 + 1.39751e8i −0.0734213 + 0.152461i
\(175\) 2.92190e7 + 2.18966e6i 0.0311540 + 0.00233467i
\(176\) −2.60224e8 3.26311e8i −0.271205 0.340080i
\(177\) 2.98032e7 9.66195e7i 0.0303647 0.0984400i
\(178\) 4.06782e8 7.04567e8i 0.405211 0.701846i
\(179\) −1.31838e9 + 7.61169e8i −1.28419 + 0.741428i −0.977612 0.210417i \(-0.932518\pi\)
−0.306580 + 0.951845i \(0.599185\pi\)
\(180\) 6.74649e8 1.53984e8i 0.642670 0.146685i
\(181\) −3.18901e8 4.80666e7i −0.297126 0.0447846i −0.00121267 0.999999i \(-0.500386\pi\)
−0.295914 + 0.955215i \(0.595624\pi\)
\(182\) 5.18383e8 + 4.80989e8i 0.472460 + 0.438379i
\(183\) 2.34582e8 2.94156e8i 0.209165 0.262285i
\(184\) 1.01546e9 + 1.48940e9i 0.885912 + 1.29939i
\(185\) −6.46671e8 + 6.00023e8i −0.552073 + 0.512249i
\(186\) −1.11242e7 1.48442e8i −0.00929433 0.124024i
\(187\) −1.02682e9 + 2.61631e9i −0.839711 + 2.13955i
\(188\) 1.52204e8 6.66851e8i 0.121842 0.533823i
\(189\) −6.89399e8 + 2.12651e8i −0.540285 + 0.166656i
\(190\) 1.42826e8 2.09487e8i 0.109595 0.160747i
\(191\) −1.66593e8 1.10528e9i −0.125177 0.830495i −0.960005 0.279984i \(-0.909671\pi\)
0.834828 0.550511i \(-0.185567\pi\)
\(192\) 1.05607e8 4.14475e7i 0.0777116 0.0304996i
\(193\) 5.50192e8 2.64959e8i 0.396538 0.190963i −0.224978 0.974364i \(-0.572231\pi\)
0.621517 + 0.783401i \(0.286517\pi\)
\(194\) 2.59302e8 + 5.38446e8i 0.183062 + 0.380133i
\(195\) −1.40856e8 3.58895e8i −0.0974175 0.248216i
\(196\) 3.18831e8 4.80561e7i 0.216041 0.0325630i
\(197\) −2.47490e8 1.68736e8i −0.164321 0.112032i 0.478367 0.878160i \(-0.341229\pi\)
−0.642689 + 0.766128i \(0.722181\pi\)
\(198\) −4.33545e8 1.40552e9i −0.282080 0.914482i
\(199\) −2.37631e9 5.42377e8i −1.51527 0.345851i −0.617592 0.786499i \(-0.711892\pi\)
−0.897680 + 0.440648i \(0.854749\pi\)
\(200\) 3.72771e7 + 1.46302e7i 0.0232982 + 0.00914387i
\(201\) 1.94203e8 1.45535e7i 0.118980 0.00891628i
\(202\) −6.83868e8 7.37035e8i −0.410740 0.442672i
\(203\) −1.98729e9 + 1.35491e9i −1.17024 + 0.797860i
\(204\) 2.96724e8 + 2.36630e8i 0.171330 + 0.136631i
\(205\) −7.30476e8 + 7.87266e8i −0.413610 + 0.445765i
\(206\) −3.09573e7 + 2.05389e8i −0.0171907 + 0.114053i
\(207\) −6.56011e8 2.87417e9i −0.357297 1.56542i
\(208\) −2.24252e8 3.88415e8i −0.119807 0.207512i
\(209\) 1.17199e9 + 6.76647e8i 0.614240 + 0.354631i
\(210\) 2.85871e8 + 8.81797e7i 0.146992 + 0.0453410i
\(211\) 1.99604e9 1.59179e9i 1.00702 0.803073i 0.0265334 0.999648i \(-0.491553\pi\)
0.980489 + 0.196574i \(0.0629817\pi\)
\(212\) −9.73376e7 + 1.29888e9i −0.0481878 + 0.643022i
\(213\) 3.81844e7 + 1.83886e7i 0.0185510 + 0.00893370i
\(214\) 2.09920e9i 1.00092i
\(215\) 5.84025e8 2.02479e9i 0.273324 0.947603i
\(216\) −9.85999e8 −0.452962
\(217\) 1.00151e9 2.07967e9i 0.451667 0.937896i
\(218\) 6.84694e8 + 5.13107e7i 0.303159 + 0.0227186i
\(219\) −2.23066e8 2.79716e8i −0.0969745 0.121602i
\(220\) 9.34503e8 3.02958e9i 0.398924 1.29328i
\(221\) −1.51013e9 + 2.61563e9i −0.633062 + 1.09650i
\(222\) 2.19275e8 1.26598e8i 0.0902769 0.0521214i
\(223\) 1.14265e9 2.60803e8i 0.462055 0.105461i 0.0148448 0.999890i \(-0.495275\pi\)
0.447211 + 0.894429i \(0.352417\pi\)
\(224\) 2.94781e9 + 4.44311e8i 1.17087 + 0.176480i
\(225\) −4.80087e7 4.45456e7i −0.0187323 0.0173810i
\(226\) 1.11791e8 1.40181e8i 0.0428521 0.0537349i
\(227\) 1.34430e9 + 1.97172e9i 0.506281 + 0.742578i 0.991256 0.131950i \(-0.0421238\pi\)
−0.484975 + 0.874528i \(0.661171\pi\)
\(228\) 1.33958e8 1.24295e8i 0.0495712 0.0459954i
\(229\) −1.99450e8 2.66147e9i −0.0725256 0.967787i −0.908193 0.418552i \(-0.862538\pi\)
0.835667 0.549236i \(-0.185081\pi\)
\(230\) −9.24511e8 + 2.35561e9i −0.330370 + 0.841769i
\(231\) −3.55319e8 + 1.55676e9i −0.124787 + 0.546729i
\(232\) −3.14115e9 + 9.68917e8i −1.08427 + 0.334453i
\(233\) −2.10999e9 + 3.09478e9i −0.715906 + 1.05004i 0.280031 + 0.959991i \(0.409655\pi\)
−0.995937 + 0.0900508i \(0.971297\pi\)
\(234\) −2.35575e8 1.56294e9i −0.0785716 0.521289i
\(235\) 2.14360e9 8.41300e8i 0.702865 0.275854i
\(236\) 8.05008e8 3.87671e8i 0.259509 0.124973i
\(237\) −5.39965e8 1.12125e9i −0.171148 0.355393i
\(238\) −8.56197e8 2.18155e9i −0.266849 0.679921i
\(239\) 8.30879e7 1.25235e7i 0.0254651 0.00383825i −0.136297 0.990668i \(-0.543520\pi\)
0.161762 + 0.986830i \(0.448282\pi\)
\(240\) −1.56770e8 1.06884e8i −0.0472517 0.0322157i
\(241\) −6.28486e8 2.03750e9i −0.186306 0.603990i −0.999750 0.0223468i \(-0.992886\pi\)
0.813444 0.581643i \(-0.197590\pi\)
\(242\) −4.78543e9 1.09224e9i −1.39527 0.318462i
\(243\) 2.27699e9 + 8.93653e8i 0.653034 + 0.256297i
\(244\) 3.31542e9 2.48456e8i 0.935360 0.0700956i
\(245\) 7.38336e8 + 7.95737e8i 0.204923 + 0.220854i
\(246\) 2.54684e8 1.73641e8i 0.0695442 0.0474144i
\(247\) 1.13698e9 + 9.06711e8i 0.305468 + 0.243602i
\(248\) 2.14572e9 2.31253e9i 0.567239 0.611338i
\(249\) 1.50945e8 1.00146e9i 0.0392664 0.260516i
\(250\) 4.70003e8 + 2.05922e9i 0.120321 + 0.527160i
\(251\) 1.34647e9 + 2.33215e9i 0.339236 + 0.587574i 0.984289 0.176564i \(-0.0564982\pi\)
−0.645053 + 0.764138i \(0.723165\pi\)
\(252\) −2.66719e9 1.53990e9i −0.661382 0.381849i
\(253\) −1.29068e10 3.98122e9i −3.15018 0.971703i
\(254\) 2.19800e8 1.75285e8i 0.0528072 0.0421123i
\(255\) −9.54842e7 + 1.27415e9i −0.0225824 + 0.301342i
\(256\) 3.04338e9 + 1.46561e9i 0.708592 + 0.341240i
\(257\) 8.12340e9i 1.86211i 0.364879 + 0.931055i \(0.381110\pi\)
−0.364879 + 0.931055i \(0.618890\pi\)
\(258\) −2.92741e8 + 5.29280e8i −0.0660701 + 0.119456i
\(259\) 3.92615e9 0.872505
\(260\) 1.47822e9 3.06956e9i 0.323479 0.671712i
\(261\) 5.36096e9 + 4.01749e8i 1.15526 + 0.0865750i
\(262\) 2.67169e9 + 3.35020e9i 0.566998 + 0.710993i
\(263\) −1.25594e9 + 4.07166e9i −0.262510 + 0.851037i 0.724346 + 0.689437i \(0.242142\pi\)
−0.986856 + 0.161601i \(0.948334\pi\)
\(264\) −1.09116e9 + 1.88994e9i −0.224632 + 0.389074i
\(265\) −3.79763e9 + 2.19256e9i −0.770067 + 0.444599i
\(266\) −1.10013e9 + 2.51097e8i −0.219743 + 0.0501550i
\(267\) 1.95206e9 + 2.94225e8i 0.384103 + 0.0578942i
\(268\) 1.26153e9 + 1.17053e9i 0.244544 + 0.226904i
\(269\) 1.98354e8 2.48728e8i 0.0378818 0.0475023i −0.762530 0.646953i \(-0.776043\pi\)
0.800412 + 0.599451i \(0.204614\pi\)
\(270\) −7.79720e8 1.14364e9i −0.146718 0.215196i
\(271\) −7.13041e8 + 6.61606e8i −0.132202 + 0.122665i −0.743503 0.668733i \(-0.766837\pi\)
0.611301 + 0.791398i \(0.290647\pi\)
\(272\) 1.11076e8 + 1.48221e9i 0.0202929 + 0.270791i
\(273\) −6.26893e8 + 1.59730e9i −0.112861 + 0.287565i
\(274\) 7.30884e8 3.20221e9i 0.129672 0.568130i
\(275\) −2.86723e8 + 8.84424e7i −0.0501340 + 0.0154643i
\(276\) −1.02743e9 + 1.50696e9i −0.177058 + 0.259696i
\(277\) 1.74403e8 + 1.15709e9i 0.0296234 + 0.196538i 0.998747 0.0500352i \(-0.0159334\pi\)
−0.969124 + 0.246574i \(0.920695\pi\)
\(278\) 2.68847e9 1.05515e9i 0.450118 0.176658i
\(279\) −4.64833e9 + 2.23852e9i −0.767150 + 0.369440i
\(280\) 2.75080e9 + 5.71210e9i 0.447535 + 0.929317i
\(281\) −6.64101e8 1.69210e9i −0.106514 0.271394i 0.867673 0.497136i \(-0.165615\pi\)
−0.974187 + 0.225741i \(0.927520\pi\)
\(282\) −6.53557e8 + 9.85079e7i −0.103344 + 0.0155767i
\(283\) 9.18909e9 + 6.26502e9i 1.43261 + 0.976734i 0.997065 + 0.0765659i \(0.0243956\pi\)
0.435542 + 0.900169i \(0.356557\pi\)
\(284\) 1.10389e8 + 3.57874e8i 0.0169689 + 0.0550119i
\(285\) 5.99795e8 + 1.36899e8i 0.0909125 + 0.0207502i
\(286\) −6.74100e9 2.64565e9i −1.00753 0.395428i
\(287\) 4.76639e9 3.57191e8i 0.702525 0.0526469i
\(288\) −4.53211e9 4.88445e9i −0.658765 0.709979i
\(289\) 2.50645e9 1.70887e9i 0.359308 0.244972i
\(290\) −3.60782e9 2.87714e9i −0.510097 0.406789i
\(291\) −9.86350e8 + 1.06303e9i −0.137550 + 0.148243i
\(292\) 4.71198e8 3.12620e9i 0.0648145 0.430016i
\(293\) 3.19557e8 + 1.40007e9i 0.0433588 + 0.189967i 0.991969 0.126479i \(-0.0403675\pi\)
−0.948611 + 0.316446i \(0.897510\pi\)
\(294\) −1.55781e8 2.69820e8i −0.0208509 0.0361148i
\(295\) 2.60506e9 + 1.50403e9i 0.343977 + 0.198595i
\(296\) 5.12744e9 + 1.58161e9i 0.667934 + 0.206030i
\(297\) 5.77613e9 4.60631e9i 0.742355 0.592008i
\(298\) −3.72760e8 + 4.97414e9i −0.0472677 + 0.630743i
\(299\) −1.30771e10 6.29760e9i −1.63616 0.787935i
\(300\) 4.05174e7i 0.00500214i
\(301\) −8.03479e9 + 4.83797e9i −0.978833 + 0.589383i
\(302\) 7.20356e8 0.0866003
\(303\) 1.05854e9 2.19807e9i 0.125584 0.260778i
\(304\) 7.13680e8 + 5.34829e7i 0.0835621 + 0.00626211i
\(305\) 6.97879e9 + 8.75112e9i 0.806456 + 1.01126i
\(306\) −1.54398e9 + 5.00545e9i −0.176098 + 0.570896i
\(307\) 3.94031e9 6.82482e9i 0.443585 0.768312i −0.554367 0.832272i \(-0.687040\pi\)
0.997952 + 0.0639600i \(0.0203730\pi\)
\(308\) −1.22199e10 + 7.05517e9i −1.35789 + 0.783979i
\(309\) −4.91367e8 + 1.12151e8i −0.0538979 + 0.0123018i
\(310\) 4.37907e9 + 6.60039e8i 0.474171 + 0.0714698i
\(311\) −2.77170e9 2.57176e9i −0.296281 0.274909i 0.517998 0.855382i \(-0.326677\pi\)
−0.814280 + 0.580473i \(0.802868\pi\)
\(312\) −1.46216e9 + 1.83349e9i −0.154304 + 0.193491i
\(313\) −4.63911e9 6.80432e9i −0.483345 0.708937i 0.504667 0.863314i \(-0.331615\pi\)
−0.988012 + 0.154377i \(0.950663\pi\)
\(314\) −8.86082e8 + 8.22164e8i −0.0911497 + 0.0845746i
\(315\) −7.74846e8 1.03396e10i −0.0786997 1.05017i
\(316\) 4.01773e9 1.02370e10i 0.402932 1.02666i
\(317\) −4.95939e7 + 2.17285e8i −0.00491124 + 0.0215175i −0.977324 0.211749i \(-0.932084\pi\)
0.972413 + 0.233266i \(0.0749413\pi\)
\(318\) 1.20269e9 3.70981e8i 0.117610 0.0362780i
\(319\) 1.38748e10 2.03507e10i 1.33988 1.96524i
\(320\) 5.03032e8 + 3.33740e9i 0.0479728 + 0.318279i
\(321\) 4.74159e9 1.86094e9i 0.446585 0.175272i
\(322\) 1.01471e10 4.88658e9i 0.943883 0.454550i
\(323\) −2.09109e9 4.34219e9i −0.192115 0.398932i
\(324\) 2.32653e9 + 5.92790e9i 0.211120 + 0.537924i
\(325\) −3.18837e8 + 4.80569e7i −0.0285782 + 0.00430747i
\(326\) 7.93641e7 + 5.41095e7i 0.00702673 + 0.00479075i
\(327\) 4.91081e8 + 1.59205e9i 0.0429499 + 0.139240i
\(328\) 6.36865e9 + 1.45360e9i 0.550240 + 0.125589i
\(329\) −9.54029e9 3.74429e9i −0.814288 0.319585i
\(330\) −3.05498e9 + 2.28939e8i −0.257604 + 0.0193047i
\(331\) −9.05178e9 9.75550e9i −0.754088 0.812714i 0.233070 0.972460i \(-0.425123\pi\)
−0.987158 + 0.159746i \(0.948932\pi\)
\(332\) 7.39443e9 5.04144e9i 0.608629 0.414956i
\(333\) −6.86094e9 5.47142e9i −0.557965 0.444962i
\(334\) 6.16383e9 6.64303e9i 0.495296 0.533802i
\(335\) −8.63511e8 + 5.72902e9i −0.0685628 + 0.454885i
\(336\) 1.87908e8 + 8.23280e8i 0.0147431 + 0.0645937i
\(337\) −8.03709e9 1.39207e10i −0.623131 1.07929i −0.988899 0.148588i \(-0.952527\pi\)
0.365768 0.930706i \(-0.380806\pi\)
\(338\) −7.07096e8 4.08242e8i −0.0541766 0.0312789i
\(339\) 4.15738e8 + 1.28238e8i 0.0314790 + 0.00970998i
\(340\) −8.82753e9 + 7.03972e9i −0.660577 + 0.526792i
\(341\) −1.76643e9 + 2.35714e10i −0.130641 + 1.74328i
\(342\) 2.27239e9 + 1.09433e9i 0.166103 + 0.0799912i
\(343\) 1.09836e10i 0.793537i
\(344\) −1.24421e10 + 3.08153e9i −0.888507 + 0.220055i
\(345\) −6.14034e9 −0.433427
\(346\) 4.98349e9 1.03483e10i 0.347720 0.722047i
\(347\) 4.03758e9 + 3.02575e8i 0.278486 + 0.0208696i 0.213241 0.977000i \(-0.431598\pi\)
0.0652449 + 0.997869i \(0.479217\pi\)
\(348\) −2.07369e9 2.60033e9i −0.141393 0.177301i
\(349\) −2.12568e9 + 6.89129e9i −0.143284 + 0.464514i −0.998559 0.0536593i \(-0.982912\pi\)
0.855276 + 0.518173i \(0.173388\pi\)
\(350\) 1.25097e8 2.16674e8i 0.00833632 0.0144389i
\(351\) 6.87546e9 3.96955e9i 0.452974 0.261525i
\(352\) −2.97624e10 + 6.79306e9i −1.93864 + 0.442481i
\(353\) −1.95447e9 2.94588e8i −0.125872 0.0189722i 0.0858040 0.996312i \(-0.472654\pi\)
−0.211676 + 0.977340i \(0.567892\pi\)
\(354\) −6.32893e8 5.87239e8i −0.0403011 0.0373940i
\(355\) −7.86125e8 + 9.85769e8i −0.0494969 + 0.0620672i
\(356\) 9.82688e9 + 1.44134e10i 0.611808 + 0.897358i
\(357\) 4.16859e9 3.86789e9i 0.256635 0.238123i
\(358\) 9.71408e8 + 1.29625e10i 0.0591384 + 0.789147i
\(359\) 4.12951e9 1.05218e10i 0.248611 0.633450i −0.751029 0.660269i \(-0.770442\pi\)
0.999640 + 0.0268185i \(0.00853760\pi\)
\(360\) 3.15327e9 1.38154e10i 0.187737 0.822531i
\(361\) 1.40116e10 4.32199e9i 0.825007 0.254481i
\(362\) −1.55126e9 + 2.27528e9i −0.0903336 + 0.132495i
\(363\) −1.77516e9 1.17774e10i −0.102238 0.678302i
\(364\) −1.41148e10 + 5.53966e9i −0.804026 + 0.315557i
\(365\) 9.58960e9 4.61811e9i 0.540292 0.260191i
\(366\) −1.39390e9 2.89447e9i −0.0776799 0.161304i
\(367\) 1.61818e9 + 4.12305e9i 0.0891994 + 0.227276i 0.968511 0.248970i \(-0.0800922\pi\)
−0.879312 + 0.476247i \(0.841997\pi\)
\(368\) −7.06323e9 + 1.06461e9i −0.385134 + 0.0580497i
\(369\) −8.82703e9 6.01816e9i −0.476112 0.324608i
\(370\) 2.22027e9 + 7.19793e9i 0.118467 + 0.384061i
\(371\) 1.90271e10 + 4.34281e9i 1.00433 + 0.229232i
\(372\) 2.97121e9 + 1.16612e9i 0.155154 + 0.0608933i
\(373\) −8.80252e9 + 6.59658e8i −0.454749 + 0.0340787i −0.300136 0.953896i \(-0.597032\pi\)
−0.154613 + 0.987975i \(0.549413\pi\)
\(374\) 1.63235e10 + 1.75925e10i 0.834306 + 0.899169i
\(375\) −4.23462e9 + 2.88712e9i −0.214136 + 0.145996i
\(376\) −1.09510e10 8.73313e9i −0.547901 0.436937i
\(377\) 1.80028e10 1.94024e10i 0.891198 0.960482i
\(378\) −9.18144e8 + 6.09149e9i −0.0449722 + 0.298371i
\(379\) 6.94973e9 + 3.04488e10i 0.336830 + 1.47575i 0.805616 + 0.592438i \(0.201835\pi\)
−0.468785 + 0.883312i \(0.655308\pi\)
\(380\) 2.71826e9 + 4.70816e9i 0.130363 + 0.225796i
\(381\) 5.90778e8 + 3.41086e8i 0.0280366 + 0.0161869i
\(382\) −9.12026e9 2.81323e9i −0.428306 0.132115i
\(383\) 1.48762e10 1.18634e10i 0.691348 0.551332i −0.213565 0.976929i \(-0.568507\pi\)
0.904913 + 0.425597i \(0.139936\pi\)
\(384\) −3.58342e8 + 4.78174e9i −0.0164806 + 0.219918i
\(385\) −4.28000e10 2.06114e10i −1.94805 0.938133i
\(386\) 5.21434e9i 0.234882i
\(387\) 2.07829e10 + 2.74280e9i 0.926536 + 0.122279i
\(388\) −1.28145e10 −0.565424
\(389\) −9.62035e9 + 1.99769e10i −0.420138 + 0.872426i 0.578260 + 0.815852i \(0.303732\pi\)
−0.998398 + 0.0565737i \(0.981982\pi\)
\(390\) −3.28288e9 2.46018e8i −0.141905 0.0106343i
\(391\) 2.99910e10 + 3.76075e10i 1.28317 + 1.60904i
\(392\) 1.94619e9 6.30938e9i 0.0824215 0.267204i
\(393\) −5.19884e9 + 9.00466e9i −0.217940 + 0.377483i
\(394\) −2.21502e9 + 1.27884e9i −0.0919164 + 0.0530680i
\(395\) 3.60953e10 8.23852e9i 1.48273 0.338424i
\(396\) 3.11862e10 + 4.70057e9i 1.26818 + 0.191148i
\(397\) 1.19855e10 + 1.11210e10i 0.482498 + 0.447693i 0.883532 0.468370i \(-0.155159\pi\)
−0.401034 + 0.916063i \(0.631349\pi\)
\(398\) −1.29764e10 + 1.62719e10i −0.517157 + 0.648494i
\(399\) −1.54243e9 2.26232e9i −0.0608573 0.0892612i
\(400\) −1.16322e8 + 1.07931e8i −0.00454382 + 0.00421605i
\(401\) −1.59387e9 2.12687e10i −0.0616418 0.822552i −0.939263 0.343198i \(-0.888490\pi\)
0.877621 0.479355i \(-0.159129\pi\)
\(402\) 6.07527e8 1.54795e9i 0.0232628 0.0592726i
\(403\) −5.65222e9 + 2.47640e10i −0.214289 + 0.938860i
\(404\) 2.06009e10 6.35453e9i 0.773322 0.238538i
\(405\) −1.20771e10 + 1.77138e10i −0.448892 + 0.658403i
\(406\) 3.06097e9 + 2.03082e10i 0.112656 + 0.747426i
\(407\) −3.74262e10 + 1.46887e10i −1.36395 + 0.535310i
\(408\) 7.00219e9 3.37208e9i 0.252693 0.121691i
\(409\) −1.85691e10 3.85592e10i −0.663588 1.37796i −0.912358 0.409393i \(-0.865741\pi\)
0.248770 0.968563i \(-0.419974\pi\)
\(410\) 3.35027e9 + 8.53636e9i 0.118562 + 0.302091i
\(411\) 7.88095e9 1.18786e9i 0.276192 0.0416293i
\(412\) −3.67984e9 2.50887e9i −0.127714 0.0870742i
\(413\) −3.94609e9 1.27929e10i −0.135633 0.439712i
\(414\) −2.45419e10 5.60152e9i −0.835423 0.190680i
\(415\) 2.80470e10 + 1.10076e10i 0.945570 + 0.371109i
\(416\) −3.27134e10 + 2.45153e9i −1.09233 + 0.0818586i
\(417\) 4.76665e9 + 5.13722e9i 0.157641 + 0.169896i
\(418\) 9.54757e9 6.50942e9i 0.312743 0.213225i
\(419\) −4.28676e9 3.41858e9i −0.139083 0.110915i 0.551477 0.834190i \(-0.314064\pi\)
−0.690560 + 0.723275i \(0.742636\pi\)
\(420\) −4.36310e9 + 4.70230e9i −0.140216 + 0.151117i
\(421\) −4.64277e8 + 3.08027e9i −0.0147791 + 0.0980530i −0.995004 0.0998324i \(-0.968169\pi\)
0.980225 + 0.197885i \(0.0634074\pi\)
\(422\) −4.85089e9 2.12531e10i −0.152958 0.670152i
\(423\) 1.14537e10 + 1.98383e10i 0.357753 + 0.619646i
\(424\) 2.30994e10 + 1.33364e10i 0.714721 + 0.412645i
\(425\) 1.02110e9 + 3.14969e8i 0.0312978 + 0.00965410i
\(426\) 2.82933e8 2.25632e8i 0.00859104 0.00685113i
\(427\) 3.72276e9 4.96767e10i 0.111983 1.49431i
\(428\) 4.05539e10 + 1.95297e10i 1.20853 + 0.581998i
\(429\) 1.75717e10i 0.518780i
\(430\) −1.34133e10 1.19945e10i −0.392340 0.350840i
\(431\) 1.75281e9 0.0507956 0.0253978 0.999677i \(-0.491915\pi\)
0.0253978 + 0.999677i \(0.491915\pi\)
\(432\) 1.69521e9 3.52015e9i 0.0486732 0.101071i
\(433\) −5.46106e10 4.09250e9i −1.55355 0.116423i −0.729914 0.683539i \(-0.760440\pi\)
−0.823638 + 0.567116i \(0.808059\pi\)
\(434\) −1.22888e10 1.54096e10i −0.346377 0.434343i
\(435\) 3.30044e9 1.06998e10i 0.0921755 0.298826i
\(436\) −7.36124e9 + 1.27500e10i −0.203707 + 0.352830i
\(437\) 2.00579e10 1.15805e10i 0.549997 0.317541i
\(438\) −2.97832e9 + 6.79783e8i −0.0809237 + 0.0184703i
\(439\) 3.68699e10 + 5.55724e9i 0.992690 + 0.149624i 0.625251 0.780424i \(-0.284997\pi\)
0.367439 + 0.930048i \(0.380235\pi\)
\(440\) −4.75925e10 4.41594e10i −1.26978 1.17818i
\(441\) −6.73265e9 + 8.44248e9i −0.178005 + 0.223211i
\(442\) 1.45276e10 + 2.13081e10i 0.380633 + 0.558286i
\(443\) 3.78823e10 3.51496e10i 0.983607 0.912654i −0.0125781 0.999921i \(-0.504004\pi\)
0.996185 + 0.0872671i \(0.0278134\pi\)
\(444\) 4.05716e8 + 5.41390e9i 0.0104397 + 0.139309i
\(445\) −2.14563e10 + 5.46698e10i −0.547161 + 1.39414i
\(446\) 2.22693e9 9.75682e9i 0.0562817 0.246586i
\(447\) −1.15658e10 + 3.56759e9i −0.289699 + 0.0893603i
\(448\) 8.46174e9 1.24111e10i 0.210062 0.308104i
\(449\) 3.19888e9 + 2.12232e10i 0.0787068 + 0.522185i 0.993092 + 0.117340i \(0.0374367\pi\)
−0.914385 + 0.404846i \(0.867325\pi\)
\(450\) −5.20560e8 + 2.04305e8i −0.0126947 + 0.00498229i
\(451\) −4.40994e10 + 2.12371e10i −1.06592 + 0.513322i
\(452\) 1.66809e9 + 3.46382e9i 0.0399636 + 0.0829854i
\(453\) 6.38594e8 + 1.62711e9i 0.0151646 + 0.0386389i
\(454\) 2.01492e10 3.03700e9i 0.474278 0.0714860i
\(455\) −4.21781e10 2.87565e10i −0.984104 0.670951i
\(456\) −1.10301e9 3.57588e9i −0.0255106 0.0827034i
\(457\) 6.45432e10 + 1.47316e10i 1.47974 + 0.337741i 0.884778 0.466013i \(-0.154310\pi\)
0.594962 + 0.803754i \(0.297167\pi\)
\(458\) −2.12140e10 8.32590e9i −0.482127 0.189221i
\(459\) −2.62370e10 + 1.96619e9i −0.591104 + 0.0442971i
\(460\) −3.69064e10 3.97756e10i −0.824271 0.888353i
\(461\) −7.35783e10 + 5.01649e10i −1.62909 + 1.11070i −0.720118 + 0.693852i \(0.755912\pi\)
−0.908977 + 0.416846i \(0.863135\pi\)
\(462\) 1.06600e10 + 8.50104e9i 0.233985 + 0.186597i
\(463\) −1.87065e10 + 2.01608e10i −0.407070 + 0.438717i −0.902997 0.429647i \(-0.858638\pi\)
0.495927 + 0.868364i \(0.334828\pi\)
\(464\) 1.94138e9 1.28802e10i 0.0418830 0.277875i
\(465\) 2.39117e9 + 1.04764e10i 0.0511444 + 0.224078i
\(466\) 1.59915e10 + 2.76981e10i 0.339114 + 0.587363i
\(467\) −1.71949e10 9.92747e9i −0.361520 0.208723i 0.308228 0.951313i \(-0.400264\pi\)
−0.669747 + 0.742589i \(0.733598\pi\)
\(468\) 3.23856e10 + 9.98964e9i 0.675101 + 0.208241i
\(469\) 2.01600e10 1.60770e10i 0.416676 0.332288i
\(470\) 1.46941e9 1.96079e10i 0.0301128 0.401828i
\(471\) −2.64258e9 1.27260e9i −0.0536963 0.0258588i
\(472\) 1.82968e10i 0.368644i
\(473\) 5.84919e10 7.61782e10i 1.16856 1.52190i
\(474\) −1.06264e10 −0.210511
\(475\) 2.23241e8 4.63564e8i 0.00438530 0.00910617i
\(476\) 5.01104e10 + 3.75526e9i 0.976113 + 0.0731496i
\(477\) −2.71977e10 3.41049e10i −0.525363 0.658784i
\(478\) 2.11481e8 6.85606e8i 0.00405098 0.0131330i
\(479\) 4.60247e10 7.97171e10i 0.874276 1.51429i 0.0167444 0.999860i \(-0.494670\pi\)
0.857532 0.514431i \(-0.171997\pi\)
\(480\) −1.20189e10 + 6.93910e9i −0.226412 + 0.130719i
\(481\) −4.21216e10 + 9.61397e9i −0.786908 + 0.179607i
\(482\) −1.80032e10 2.71355e9i −0.333551 0.0502748i
\(483\) 2.00330e10 + 1.85879e10i 0.368093 + 0.341540i
\(484\) 6.56216e10 8.22868e10i 1.19582 1.49951i
\(485\) −2.43026e10 3.56454e10i −0.439224 0.644223i
\(486\) 1.53109e10 1.42064e10i 0.274445 0.254647i
\(487\) −3.53790e9 4.72100e10i −0.0628969 0.839301i −0.936053 0.351860i \(-0.885549\pi\)
0.873156 0.487441i \(-0.162070\pi\)
\(488\) 2.48735e10 6.33767e10i 0.438589 1.11751i
\(489\) −5.18643e7 + 2.27232e8i −0.000907053 + 0.00397406i
\(490\) 8.85714e9 2.73207e9i 0.153642 0.0473922i
\(491\) −3.36338e10 + 4.93317e10i −0.578695 + 0.848790i −0.998262 0.0589346i \(-0.981230\pi\)
0.419567 + 0.907725i \(0.362182\pi\)
\(492\) 9.85086e8 + 6.53562e9i 0.0168118 + 0.111539i
\(493\) −8.16526e10 + 3.20463e10i −1.38224 + 0.542488i
\(494\) 1.11878e10 5.38776e9i 0.187861 0.0904691i
\(495\) 4.60692e10 + 9.56637e10i 0.767344 + 1.59341i
\(496\) 4.56696e9 + 1.16364e10i 0.0754571 + 0.192262i
\(497\) 5.54884e9 8.36354e8i 0.0909446 0.0137077i
\(498\) −7.14513e9 4.87147e9i −0.116170 0.0792031i
\(499\) −1.06132e9 3.44071e9i −0.0171176 0.0554940i 0.946611 0.322378i \(-0.104482\pi\)
−0.963729 + 0.266884i \(0.914006\pi\)
\(500\) −4.41541e10 1.00779e10i −0.706466 0.161246i
\(501\) 2.04692e10 + 8.03358e9i 0.324900 + 0.127514i
\(502\) 2.29301e10 1.71837e9i 0.361069 0.0270584i
\(503\) 2.10033e10 + 2.26362e10i 0.328107 + 0.353615i 0.875463 0.483284i \(-0.160556\pi\)
−0.547357 + 0.836899i \(0.684366\pi\)
\(504\) −5.21091e10 + 3.55274e10i −0.807591 + 0.550606i
\(505\) 5.67455e10 + 4.52530e10i 0.872501 + 0.695796i
\(506\) −7.84456e10 + 8.45442e10i −1.19665 + 1.28968i
\(507\) 2.95282e8 1.95906e9i 0.00446894 0.0296495i
\(508\) 1.34139e9 + 5.87700e9i 0.0201419 + 0.0882472i
\(509\) −8.31405e9 1.44004e10i −0.123863 0.214537i 0.797425 0.603418i \(-0.206195\pi\)
−0.921288 + 0.388881i \(0.872862\pi\)
\(510\) 9.44847e9 + 5.45508e9i 0.139663 + 0.0806344i
\(511\) −4.52661e10 1.39627e10i −0.663879 0.204780i
\(512\) −2.37709e10 + 1.89567e10i −0.345912 + 0.275856i
\(513\) −9.46718e8 + 1.26331e10i −0.0136695 + 0.182406i
\(514\) 6.24946e10 + 3.00958e10i 0.895344 + 0.431175i
\(515\) 1.49941e10i 0.213152i
\(516\) −7.50153e9 1.05795e10i −0.105816 0.149234i
\(517\) 1.04951e11 1.46901
\(518\) 1.45457e10 3.02045e10i 0.202030 0.419520i
\(519\) 2.77922e10 + 2.08274e9i 0.383049 + 0.0287055i
\(520\) −4.34991e10 5.45461e10i −0.594931 0.746020i
\(521\) −6.10882e9 + 1.98043e10i −0.0829099 + 0.268787i −0.987530 0.157432i \(-0.949679\pi\)
0.904620 + 0.426219i \(0.140155\pi\)
\(522\) 2.29522e10 3.97543e10i 0.309130 0.535430i
\(523\) 6.47385e10 3.73768e10i 0.865278 0.499568i −0.000498249 1.00000i \(-0.500159\pi\)
0.865776 + 0.500431i \(0.166825\pi\)
\(524\) −8.95774e10 + 2.04455e10i −1.18816 + 0.271189i
\(525\) 6.00313e8 + 9.04826e7i 0.00790206 + 0.00119104i
\(526\) 2.66709e10 + 2.47470e10i 0.348413 + 0.323280i
\(527\) 5.24852e10 6.58144e10i 0.680448 0.853254i
\(528\) −4.87133e9 7.14493e9i −0.0626776 0.0919311i
\(529\) −1.12048e11 + 1.03965e11i −1.43081 + 1.32760i
\(530\) 2.79816e9 + 3.73388e10i 0.0354624 + 0.473213i
\(531\) −1.09322e10 + 2.78548e10i −0.137508 + 0.350366i
\(532\) 5.38405e9 2.35891e10i 0.0672145 0.294486i
\(533\) −5.02613e10 + 1.55036e10i −0.622766 + 0.192098i
\(534\) 9.49556e9 1.39274e10i 0.116777 0.171280i
\(535\) 2.25855e10 + 1.49845e11i 0.275685 + 1.82905i
\(536\) 3.28048e10 1.28749e10i 0.397446 0.155986i
\(537\) −2.84181e10 + 1.36854e10i −0.341742 + 0.164574i
\(538\) −1.17863e9 2.44746e9i −0.0140686 0.0292137i
\(539\) 1.80746e10 + 4.60534e10i 0.214148 + 0.545640i
\(540\) 2.93477e10 4.42345e9i 0.345143 0.0520219i
\(541\) 3.81035e10 + 2.59785e10i 0.444812 + 0.303267i 0.764934 0.644109i \(-0.222772\pi\)
−0.320122 + 0.947376i \(0.603724\pi\)
\(542\) 2.44814e9 + 7.93667e9i 0.0283687 + 0.0919690i
\(543\) −6.51448e9 1.48689e9i −0.0749343 0.0171033i
\(544\) 1.01203e11 + 3.97192e10i 1.15557 + 0.453528i
\(545\) −4.94267e10 + 3.70402e9i −0.560242 + 0.0419843i
\(546\) 9.96573e9 + 1.07405e10i 0.112134 + 0.120852i
\(547\) 1.66728e10 1.13673e10i 0.186234 0.126972i −0.466614 0.884461i \(-0.654526\pi\)
0.652848 + 0.757489i \(0.273574\pi\)
\(548\) 5.50629e10 + 4.39112e10i 0.610572 + 0.486915i
\(549\) −7.57341e10 + 8.16220e10i −0.833686 + 0.898500i
\(550\) −3.81859e8 + 2.53347e9i −0.00417304 + 0.0276863i
\(551\) 9.39820e9 + 4.11762e10i 0.101962 + 0.446725i
\(552\) 1.86746e10 + 3.23453e10i 0.201138 + 0.348381i
\(553\) −1.42701e11 8.23885e10i −1.52590 0.880980i
\(554\) 9.54780e9 + 2.94511e9i 0.101359 + 0.0312652i
\(555\) −1.42901e10 + 1.13960e10i −0.150614 + 0.120110i
\(556\) −4.62785e9 + 6.17543e10i −0.0484261 + 0.646202i
\(557\) −1.16232e11 5.59742e10i −1.20755 0.581523i −0.281728 0.959494i \(-0.590908\pi\)
−0.925817 + 0.377971i \(0.876622\pi\)
\(558\) 4.40537e10i 0.454407i
\(559\) 7.43542e10 7.15788e10i 0.761479 0.733056i
\(560\) −2.51224e10 −0.255452
\(561\) −2.52665e10 + 5.24665e10i −0.255090 + 0.529700i
\(562\) −1.54780e10 1.15991e9i −0.155156 0.0116273i
\(563\) 2.05723e10 + 2.57969e10i 0.204762 + 0.256764i 0.873600 0.486645i \(-0.161779\pi\)
−0.668838 + 0.743408i \(0.733208\pi\)
\(564\) 4.17726e9 1.35423e10i 0.0412834 0.133837i
\(565\) −6.47160e9 + 1.12091e10i −0.0635065 + 0.109996i
\(566\) 8.22418e10 4.74823e10i 0.801358 0.462664i
\(567\) 9.30245e10 2.12322e10i 0.900046 0.205430i
\(568\) 7.58354e9 + 1.14304e9i 0.0728583 + 0.0109816i
\(569\) 5.12248e10 + 4.75297e10i 0.488687 + 0.453436i 0.885619 0.464413i \(-0.153735\pi\)
−0.396932 + 0.917848i \(0.629925\pi\)
\(570\) 3.27533e9 4.10713e9i 0.0310281 0.0389080i
\(571\) −5.31887e10 7.80135e10i −0.500351 0.733881i 0.490112 0.871660i \(-0.336956\pi\)
−0.990463 + 0.137779i \(0.956004\pi\)
\(572\) 1.13825e11 1.05614e11i 1.06329 0.986591i
\(573\) −1.73069e9 2.30944e10i −0.0160546 0.214234i
\(574\) 1.49107e10 3.79919e10i 0.137357 0.349980i
\(575\) −1.14270e9 + 5.00651e9i −0.0104535 + 0.0457998i
\(576\) −3.20828e10 + 9.89622e9i −0.291462 + 0.0899041i
\(577\) −2.66433e10 + 3.90786e10i −0.240373 + 0.352562i −0.927401 0.374069i \(-0.877962\pi\)
0.687028 + 0.726631i \(0.258915\pi\)
\(578\) −3.86062e9 2.56136e10i −0.0345896 0.229487i
\(579\) 1.17779e10 4.62250e9i 0.104798 0.0411304i
\(580\) 8.91478e10 4.29313e10i 0.787768 0.379369i
\(581\) −5.81818e10 1.20816e11i −0.510602 1.06028i
\(582\) 4.52382e9 + 1.15265e10i 0.0394288 + 0.100463i
\(583\) −1.97624e11 + 2.97870e10i −1.71067 + 0.257841i
\(584\) −5.34914e10 3.64698e10i −0.459868 0.313532i
\(585\) 3.36315e10 + 1.09031e11i 0.287159 + 0.930947i
\(586\) 1.19549e10 + 2.72862e9i 0.101380 + 0.0231394i
\(587\) −1.39786e11 5.48621e10i −1.17737 0.462083i −0.305675 0.952136i \(-0.598882\pi\)
−0.871693 + 0.490053i \(0.836977\pi\)
\(588\) 6.66188e9 4.99239e8i 0.0557298 0.00417637i
\(589\) −2.75690e10 2.97123e10i −0.229066 0.246874i
\(590\) 2.12220e10 1.44689e10i 0.175138 0.119407i
\(591\) −4.85221e9 3.86951e9i −0.0397731 0.0317180i
\(592\) −1.44621e10 + 1.55864e10i −0.117745 + 0.126899i
\(593\) 1.67424e9 1.11079e10i 0.0135394 0.0898280i −0.981041 0.193802i \(-0.937918\pi\)
0.994580 + 0.103974i \(0.0331560\pi\)
\(594\) −1.40375e10 6.15023e10i −0.112757 0.494021i
\(595\) 8.45883e10 + 1.46511e11i 0.674905 + 1.16897i
\(596\) −9.26261e10 5.34777e10i −0.734088 0.423826i
\(597\) −4.82579e10 1.48856e10i −0.379901 0.117184i
\(598\) −9.68969e10 + 7.72727e10i −0.757713 + 0.604256i
\(599\) 8.72049e9 1.16367e11i 0.0677382 0.903903i −0.855038 0.518566i \(-0.826466\pi\)
0.922776 0.385337i \(-0.125915\pi\)
\(600\) 7.47541e8 + 3.59997e8i 0.00576807 + 0.00277775i
\(601\) 1.85439e11i 1.42136i −0.703517 0.710678i \(-0.748388\pi\)
0.703517 0.710678i \(-0.251612\pi\)
\(602\) 7.45175e9 + 7.97368e10i 0.0567378 + 0.607117i
\(603\) −5.76342e10 −0.435924
\(604\) −6.70177e9 + 1.39164e10i −0.0503549 + 0.104563i
\(605\) 3.53344e11 + 2.64795e10i 2.63740 + 0.197646i
\(606\) −1.29884e10 1.62870e10i −0.0963088 0.120767i
\(607\) 1.40772e10 4.56371e10i 0.103696 0.336173i −0.888825 0.458246i \(-0.848478\pi\)
0.992521 + 0.122073i \(0.0389541\pi\)
\(608\) 2.61738e10 4.53343e10i 0.191537 0.331751i
\(609\) −4.31579e10 + 2.49172e10i −0.313755 + 0.181147i
\(610\) 9.31790e10 2.12675e10i 0.672975 0.153602i
\(611\) 1.11521e11 + 1.68091e10i 0.800189 + 0.120609i
\(612\) −8.23346e10 7.63954e10i −0.586917 0.544579i
\(613\) −4.73673e9 + 5.93968e9i −0.0335457 + 0.0420650i −0.798321 0.602232i \(-0.794278\pi\)
0.764776 + 0.644297i \(0.222850\pi\)
\(614\) −3.79062e10 5.55982e10i −0.266709 0.391190i
\(615\) −1.63116e10 + 1.51349e10i −0.114024 + 0.105799i
\(616\) 2.15932e10 + 2.88141e11i 0.149967 + 2.00116i
\(617\) 3.57639e10 9.11250e10i 0.246777 0.628777i −0.752788 0.658263i \(-0.771292\pi\)
0.999565 + 0.0294854i \(0.00938686\pi\)
\(618\) −9.57633e8 + 4.19566e9i −0.00656516 + 0.0287638i
\(619\) 7.40100e10 2.28291e10i 0.504113 0.155498i −0.0322598 0.999480i \(-0.510270\pi\)
0.536373 + 0.843981i \(0.319794\pi\)
\(620\) −5.34914e10 + 7.84575e10i −0.362007 + 0.530967i
\(621\) −1.88450e10 1.25029e11i −0.126716 0.840703i
\(622\) −3.00536e10 + 1.17952e10i −0.200787 + 0.0788030i
\(623\) 2.35497e11 1.13409e11i 1.56326 0.752829i
\(624\) −4.03193e9 8.37239e9i −0.0265935 0.0552219i
\(625\) −5.41807e10 1.38050e11i −0.355078 0.904725i
\(626\) −6.95338e10 + 1.04805e10i −0.452792 + 0.0682474i
\(627\) 2.31671e10 + 1.57951e10i 0.149900 + 0.102200i
\(628\) −7.63958e9 2.47669e10i −0.0491169 0.159233i
\(629\) 1.39593e11 + 3.18612e10i 0.891787 + 0.203545i
\(630\) −8.24149e10 3.23455e10i −0.523171 0.205329i
\(631\) 1.67777e11 1.25731e10i 1.05831 0.0793097i 0.465816 0.884881i \(-0.345761\pi\)
0.592498 + 0.805572i \(0.298142\pi\)
\(632\) −1.53174e11 1.65083e11i −0.960102 1.03474i
\(633\) 4.37054e10 2.97979e10i 0.272220 0.185597i
\(634\) 1.48787e9 + 1.18654e9i 0.00920891 + 0.00734386i
\(635\) −1.38038e10 + 1.48770e10i −0.0848993 + 0.0914997i
\(636\) −4.02225e9 + 2.66859e10i −0.0245833 + 0.163100i
\(637\) 1.18301e10 + 5.18311e10i 0.0718507 + 0.314799i
\(638\) −1.05157e11 1.82137e11i −0.634680 1.09930i
\(639\) −1.08621e10 6.27125e9i −0.0651495 0.0376141i
\(640\) −1.36317e11 4.20484e10i −0.812515 0.250628i
\(641\) −8.49282e10 + 6.77280e10i −0.503060 + 0.401177i −0.841872 0.539677i \(-0.818546\pi\)
0.338812 + 0.940854i \(0.389975\pi\)
\(642\) 3.25030e9 4.33723e10i 0.0191330 0.255313i
\(643\) −7.43431e10 3.58018e10i −0.434908 0.209440i 0.203603 0.979054i \(-0.434735\pi\)
−0.638511 + 0.769613i \(0.720449\pi\)
\(644\) 2.41491e11i 1.40397i
\(645\) 1.52018e10 4.09306e10i 0.0878328 0.236488i
\(646\) −4.11523e10 −0.236300
\(647\) −2.33754e10 + 4.85396e10i −0.133396 + 0.276999i −0.956958 0.290227i \(-0.906269\pi\)
0.823562 + 0.567226i \(0.191984\pi\)
\(648\) 1.30040e11 + 9.74518e9i 0.737528 + 0.0552701i
\(649\) 8.54775e10 + 1.07185e11i 0.481807 + 0.604167i
\(650\) −8.11527e8 + 2.63090e9i −0.00454621 + 0.0147384i
\(651\) 2.39126e10 4.14179e10i 0.133139 0.230603i
\(652\) −1.78368e9 + 1.02981e9i −0.00987023 + 0.00569858i
\(653\) −4.77397e10 + 1.08963e10i −0.262559 + 0.0599274i −0.351774 0.936085i \(-0.614421\pi\)
0.0892148 + 0.996012i \(0.471564\pi\)
\(654\) 1.40672e10 + 2.12029e9i 0.0768949 + 0.0115900i
\(655\) −2.26755e11 2.10398e11i −1.23195 1.14308i
\(656\) −1.61391e10 + 2.02378e10i −0.0871493 + 0.109282i
\(657\) 5.96441e10 + 8.74819e10i 0.320115 + 0.469523i
\(658\) −6.41506e10 + 5.95230e10i −0.342213 + 0.317528i
\(659\) −1.55086e10 2.06948e11i −0.0822303 1.09729i −0.873825 0.486241i \(-0.838368\pi\)
0.791595 0.611047i \(-0.209251\pi\)
\(660\) 2.39989e10 6.11482e10i 0.126478 0.322261i
\(661\) −4.72950e10 + 2.07213e11i −0.247747 + 1.08545i 0.686023 + 0.727580i \(0.259355\pi\)
−0.933770 + 0.357873i \(0.883502\pi\)
\(662\) −1.08586e11 + 3.34943e10i −0.565382 + 0.174397i
\(663\) −3.52512e10 + 5.17041e10i −0.182440 + 0.267591i
\(664\) −2.73145e10 1.81220e11i −0.140514 0.932252i
\(665\) 7.58273e10 2.97600e10i 0.387739 0.152176i
\(666\) −6.75111e10 + 3.25116e10i −0.343146 + 0.165250i
\(667\) −1.82898e11 3.79792e11i −0.924072 1.91886i
\(668\) 7.09902e10 + 1.80880e11i 0.356527 + 0.908416i
\(669\) 2.40125e10 3.61930e9i 0.119876 0.0180684i
\(670\) 4.08751e10 + 2.78682e10i 0.202843 + 0.138296i
\(671\) 1.50365e11 + 4.87473e11i 0.741750 + 2.40470i
\(672\) 6.02177e10 + 1.37443e10i 0.295289 + 0.0673977i
\(673\) 8.50563e10 + 3.33821e10i 0.414616 + 0.162725i 0.563474 0.826134i \(-0.309465\pi\)
−0.148858 + 0.988859i \(0.547560\pi\)
\(674\) −1.36870e11 + 1.02570e10i −0.663236 + 0.0497027i
\(675\) −1.91052e9 2.05905e9i −0.00920314 0.00991863i
\(676\) 1.44651e10 9.86215e9i 0.0692684 0.0472264i
\(677\) −2.14951e11 1.71417e11i −1.02326 0.816019i −0.0401745 0.999193i \(-0.512791\pi\)
−0.983081 + 0.183174i \(0.941363\pi\)
\(678\) 2.52679e9 2.72324e9i 0.0119578 0.0128874i
\(679\) −2.86171e10 + 1.89862e11i −0.134631 + 0.893221i
\(680\) 5.14495e10 + 2.25415e11i 0.240628 + 1.05426i
\(681\) 2.47220e10 + 4.28198e10i 0.114946 + 0.199093i
\(682\) 1.74794e11 + 1.00917e11i 0.807958 + 0.466475i
\(683\) 2.86444e11 + 8.83561e10i 1.31630 + 0.406026i 0.871849 0.489775i \(-0.162921\pi\)
0.444455 + 0.895801i \(0.353397\pi\)
\(684\) −4.22820e10 + 3.37188e10i −0.193166 + 0.154045i
\(685\) −1.77189e10 + 2.36443e11i −0.0804777 + 1.07390i
\(686\) 8.44984e10 + 4.06923e10i 0.381550 + 0.183745i
\(687\) 5.52983e10i 0.248248i
\(688\) 1.03901e10 4.97181e10i 0.0463732 0.221902i
\(689\) −2.14766e11 −0.952989
\(690\) −2.27489e10 + 4.72386e10i −0.100361 + 0.208402i
\(691\) −2.49662e11 1.87096e10i −1.09506 0.0820638i −0.485075 0.874473i \(-0.661208\pi\)
−0.609990 + 0.792409i \(0.708827\pi\)
\(692\) 1.53553e11 + 1.92549e11i 0.669629 + 0.839688i
\(693\) 1.39289e11 4.51564e11i 0.603927 1.95788i
\(694\) 1.72863e10 2.99407e10i 0.0745185 0.129070i
\(695\) −1.80555e11 + 1.04244e11i −0.773875 + 0.446797i
\(696\) −6.64005e10 + 1.51555e10i −0.282966 + 0.0645852i
\(697\) 1.72366e11 + 2.59800e10i 0.730332 + 0.110080i
\(698\) 4.51405e10 + 4.18842e10i 0.190171 + 0.176453i
\(699\) −4.83869e10 + 6.06753e10i −0.202684 + 0.254158i
\(700\) 3.02204e9 + 4.43252e9i 0.0125866 + 0.0184612i
\(701\) −1.76083e11 + 1.63381e11i −0.729196 + 0.676595i −0.954674 0.297653i \(-0.903796\pi\)
0.225478 + 0.974248i \(0.427606\pi\)
\(702\) −5.06596e9 6.76005e10i −0.0208600 0.278357i
\(703\) 2.51874e10 6.41766e10i 0.103125 0.262758i
\(704\) −3.42289e10 + 1.49966e11i −0.139348 + 0.610525i
\(705\) 4.55922e10 1.40633e10i 0.184558 0.0569287i
\(706\) −9.50728e9 + 1.39446e10i −0.0382681 + 0.0561291i
\(707\) −4.81444e10 3.19417e11i −0.192694 1.27844i
\(708\) 1.72328e10 6.76337e9i 0.0685839 0.0269172i
\(709\) 3.22449e11 1.55283e11i 1.27608 0.614526i 0.331697 0.943386i \(-0.392379\pi\)
0.944379 + 0.328860i \(0.106664\pi\)
\(710\) 4.67122e9 + 9.69989e9i 0.0183822 + 0.0381710i
\(711\) 1.34555e11 + 3.42840e11i 0.526527 + 1.34157i
\(712\) 3.53237e11 5.32420e10i 1.37451 0.207173i
\(713\) 3.34249e11 + 2.27887e11i 1.29334 + 0.881782i
\(714\) −1.43123e10 4.63995e10i −0.0550704 0.178534i
\(715\) 5.09649e11 + 1.16324e11i 1.95006 + 0.445087i
\(716\) −2.59457e11 1.01829e11i −0.987219 0.387455i
\(717\) 1.73610e9 1.30102e8i 0.00656897 0.000492276i
\(718\) −6.56468e10 7.07504e10i −0.247011 0.266214i
\(719\) −7.57307e10 + 5.16323e10i −0.283372 + 0.193200i −0.696662 0.717400i \(-0.745332\pi\)
0.413290 + 0.910600i \(0.364380\pi\)
\(720\) 4.39013e10 + 3.50101e10i 0.163361 + 0.130276i
\(721\) −4.53896e10 + 4.89184e10i −0.167964 + 0.181022i
\(722\) 1.86607e10 1.23805e11i 0.0686718 0.455607i
\(723\) −9.83058e9 4.30706e10i −0.0359771 0.157626i
\(724\) −2.95235e10 5.11361e10i −0.107452 0.186112i
\(725\) −8.10982e9 4.68221e9i −0.0293535 0.0169472i
\(726\) −9.71821e10 2.99767e10i −0.349816 0.107904i
\(727\) 3.89594e11 3.10691e11i 1.39468 1.11222i 0.415414 0.909632i \(-0.363637\pi\)
0.979264 0.202587i \(-0.0649348\pi\)
\(728\) −2.32041e10 + 3.09637e11i −0.0826112 + 1.10237i
\(729\) −1.59940e11 7.70228e10i −0.566299 0.272715i
\(730\) 9.08836e10i 0.320032i
\(731\) −3.24935e11 + 1.06809e11i −1.13796 + 0.374058i
\(732\) 6.88856e10 0.239930
\(733\) −4.33726e10 + 9.00641e10i −0.150245 + 0.311987i −0.962484 0.271338i \(-0.912534\pi\)
0.812239 + 0.583324i \(0.198248\pi\)
\(734\) 3.77143e10 + 2.82630e9i 0.129934 + 0.00973720i
\(735\) 1.40229e10 + 1.75842e10i 0.0480495 + 0.0602522i
\(736\) −1.54000e11 + 4.99254e11i −0.524817 + 1.70142i
\(737\) −1.32027e11 + 2.28678e11i −0.447501 + 0.775095i
\(738\) −7.90013e10 + 4.56114e10i −0.266323 + 0.153762i
\(739\) 1.99259e11 4.54796e10i 0.668098 0.152489i 0.124998 0.992157i \(-0.460108\pi\)
0.543100 + 0.839668i \(0.317250\pi\)
\(740\) −1.59711e11 2.40725e10i −0.532608 0.0802777i
\(741\) 2.20876e10 + 2.04943e10i 0.0732615 + 0.0679767i
\(742\) 1.03902e11 1.30289e11i 0.342774 0.429826i
\(743\) −4.90706e10 7.19734e10i −0.161015 0.236166i 0.737250 0.675620i \(-0.236124\pi\)
−0.898265 + 0.439455i \(0.855172\pi\)
\(744\) 4.79140e10 4.44577e10i 0.156376 0.145096i
\(745\) −2.69088e10 3.59073e11i −0.0873513 1.16562i
\(746\) −2.75370e10 + 7.01631e10i −0.0889121 + 0.226544i
\(747\) −6.66942e10 + 2.92207e11i −0.214193 + 0.938442i
\(748\) −4.91728e11 + 1.51678e11i −1.57079 + 0.484525i
\(749\) 3.79921e11 5.57241e11i 1.20716 1.77058i
\(750\) 6.52249e9 + 4.32739e10i 0.0206143 + 0.136767i
\(751\) −5.04845e11 + 1.98137e11i −1.58708 + 0.622882i −0.984532 0.175204i \(-0.943942\pi\)
−0.602544 + 0.798085i \(0.705846\pi\)
\(752\) 5.00064e10 2.40818e10i 0.156370 0.0753039i
\(753\) 2.42088e10 + 5.02702e10i 0.0752999 + 0.156362i
\(754\) −8.25683e10 2.10381e11i −0.255463 0.650909i
\(755\) −5.14202e10 + 7.75036e9i −0.158251 + 0.0238525i
\(756\) −1.09138e11 7.44090e10i −0.334109 0.227792i
\(757\) −5.75148e10 1.86458e11i −0.175144 0.567804i −0.999997 0.00245612i \(-0.999218\pi\)
0.824853 0.565348i \(-0.191258\pi\)
\(758\) 2.59995e11 + 5.93421e10i 0.787568 + 0.179757i
\(759\) −2.60507e11 1.02241e11i −0.784968 0.308077i
\(760\) 1.11017e11 8.31956e9i 0.332762 0.0249371i
\(761\) 2.28994e10 + 2.46797e10i 0.0682788 + 0.0735871i 0.766267 0.642522i \(-0.222112\pi\)
−0.697989 + 0.716109i \(0.745921\pi\)
\(762\) 4.81276e9 3.28128e9i 0.0142749 0.00973249i
\(763\) 1.72468e11 + 1.37539e11i 0.508875 + 0.405814i
\(764\) 1.39197e11 1.50019e11i 0.408562 0.440325i
\(765\) 5.63577e10 3.73909e11i 0.164554 1.09174i
\(766\) −3.61530e10 1.58397e11i −0.105010 0.460077i
\(767\) 7.36614e10 + 1.27585e11i 0.212843 + 0.368654i
\(768\) 6.06109e10 + 3.49937e10i 0.174223 + 0.100588i
\(769\) −5.39928e11 1.66546e11i −1.54394 0.476243i −0.598250 0.801310i \(-0.704137\pi\)
−0.945691 + 0.325067i \(0.894613\pi\)
\(770\) −3.17133e11 + 2.52905e11i −0.902150 + 0.719441i
\(771\) −1.25779e10 + 1.67840e11i −0.0355951 + 0.474983i
\(772\) 1.00734e11 + 4.85111e10i 0.283602 + 0.136575i
\(773\) 6.93305e11i 1.94181i −0.239469 0.970904i \(-0.576973\pi\)
0.239469 0.970904i \(-0.423027\pi\)
\(774\) 9.80979e10 1.49724e11i 0.273335 0.417185i
\(775\) 8.98688e9 0.0249116
\(776\) −1.13857e11 + 2.36426e11i −0.313987 + 0.652002i
\(777\) 8.11195e10 + 6.07906e9i 0.222557 + 0.0166783i
\(778\) 1.18043e11 + 1.48022e11i 0.322198 + 0.404024i
\(779\) 2.47392e10 8.02024e10i 0.0671793 0.217790i
\(780\) 3.52948e10 6.11324e10i 0.0953525 0.165155i
\(781\) −4.97655e10 + 2.87321e10i −0.133759 + 0.0772260i
\(782\) 4.00432e11 9.13959e10i 1.07078 0.244399i
\(783\) 2.27996e11 + 3.43649e10i 0.606569 + 0.0914256i
\(784\) 1.91793e10 + 1.77958e10i 0.0507655 + 0.0471035i
\(785\) 5.44044e10 6.82209e10i 0.143270 0.179655i
\(786\) 5.00134e10 + 7.33562e10i 0.131038 + 0.192197i
\(787\) −8.27490e10 + 7.67799e10i −0.215707 + 0.200147i −0.780624 0.625001i \(-0.785099\pi\)
0.564917 + 0.825148i \(0.308908\pi\)
\(788\) −4.09838e9 5.46890e10i −0.0106294 0.141839i
\(789\) −3.22538e10 + 8.21812e10i −0.0832285 + 0.212063i
\(790\) 7.03468e10 3.08209e11i 0.180608 0.791293i
\(791\) 5.50458e10 1.69794e10i 0.140611 0.0433726i
\(792\) 3.63815e11 5.33619e11i 0.924655 1.35622i
\(793\) 8.17040e10 + 5.42070e11i 0.206610 + 1.37076i
\(794\) 1.29960e11 5.10054e10i 0.326984 0.128332i
\(795\) −8.18588e10 + 3.94211e10i −0.204926 + 0.0986871i
\(796\) −1.93628e11 4.02072e11i −0.482297 1.00150i
\(797\) 2.22205e11 + 5.66169e11i 0.550707 + 1.40318i 0.887153 + 0.461475i \(0.152680\pi\)
−0.336447 + 0.941703i \(0.609225\pi\)
\(798\) −2.31188e10 + 3.48460e9i −0.0570104 + 0.00859294i
\(799\) −3.08817e11 2.10548e11i −0.757728 0.516610i
\(800\) 3.42109e9 + 1.10909e10i 0.00835226 + 0.0270774i
\(801\) −5.69575e11 1.30002e11i −1.38363 0.315805i
\(802\) −1.69529e11 6.65350e10i −0.409775 0.160825i
\(803\) 4.83738e11 3.62512e10i 1.16345 0.0871886i
\(804\) 2.42524e10 + 2.61379e10i 0.0580405 + 0.0625528i
\(805\) −6.71742e11 + 4.57986e11i −1.59963 + 1.09061i
\(806\) 1.69573e11 + 1.35230e11i 0.401806 + 0.320429i
\(807\) 4.48336e9 4.83192e9i 0.0105708 0.0113927i
\(808\) 6.57985e10 4.36544e11i 0.154373 1.02420i
\(809\) −1.67466e11 7.33718e11i −0.390961 1.71291i −0.661278 0.750141i \(-0.729986\pi\)
0.270317 0.962771i \(-0.412872\pi\)
\(810\) 9.15316e10 + 1.58537e11i 0.212633 + 0.368292i
\(811\) 1.00615e11 + 5.80898e10i 0.232583 + 0.134282i 0.611763 0.791041i \(-0.290461\pi\)
−0.379180 + 0.925323i \(0.623794\pi\)
\(812\) −4.20807e11 1.29802e11i −0.967963 0.298577i
\(813\) −1.57568e10 + 1.25656e10i −0.0360666 + 0.0287621i
\(814\) −2.56552e10 + 3.42344e11i −0.0584356 + 0.779768i
\(815\) −6.24731e9 3.00855e9i −0.0141600 0.00681909i
\(816\) 3.07963e10i 0.0694606i
\(817\) 2.75355e10 + 1.62373e11i 0.0618023 + 0.364440i
\(818\) −3.65438e11 −0.816207
\(819\) 2.20331e11 4.57523e11i 0.489712 1.01690i
\(820\) −1.96081e11 1.46942e10i −0.433690 0.0325005i
\(821\) 2.81120e11 + 3.52513e11i 0.618755 + 0.775894i 0.988169 0.153371i \(-0.0490129\pi\)
−0.369414 + 0.929265i \(0.620442\pi\)
\(822\) 2.00592e10 6.50302e10i 0.0439365 0.142439i
\(823\) 4.12609e10 7.14660e10i 0.0899373 0.155776i −0.817547 0.575862i \(-0.804667\pi\)
0.907484 + 0.420086i \(0.138000\pi\)
\(824\) −7.89838e10 + 4.56013e10i −0.171328 + 0.0989164i
\(825\) −6.06102e9 + 1.38339e9i −0.0130837 + 0.00298626i
\(826\) −1.13037e11 1.70376e10i −0.242830 0.0366007i
\(827\) −5.38493e11 4.99648e11i −1.15122 1.06817i −0.996781 0.0801721i \(-0.974453\pi\)
−0.154437 0.988003i \(-0.549357\pi\)
\(828\) 3.36537e11 4.22005e11i 0.715998 0.897834i
\(829\) 9.77260e10 + 1.43338e11i 0.206915 + 0.303489i 0.915642 0.401994i \(-0.131683\pi\)
−0.708727 + 0.705483i \(0.750730\pi\)
\(830\) 1.88593e11 1.74989e11i 0.397386 0.368720i
\(831\) 1.81182e9 + 2.41770e10i 0.00379936 + 0.0506989i
\(832\) −6.03903e10 + 1.53872e11i −0.126030 + 0.321119i
\(833\) 3.92056e10 1.71771e11i 0.0814270 0.356755i
\(834\) 5.71811e10 1.76380e10i 0.118192 0.0364574i
\(835\) −3.68512e11 + 5.40508e11i −0.758064 + 1.11188i
\(836\) 3.69288e10 + 2.45007e11i 0.0756032 + 0.501595i
\(837\) −2.05980e11 + 8.08411e10i −0.419684 + 0.164714i
\(838\) −4.21814e10 + 2.03135e10i −0.0855351 + 0.0411915i
\(839\) 3.18901e11 + 6.62205e11i 0.643588 + 1.33642i 0.926143 + 0.377174i \(0.123104\pi\)
−0.282554 + 0.959251i \(0.591182\pi\)
\(840\) 4.79909e10 + 1.22279e11i 0.0963921 + 0.245603i
\(841\) 2.65451e11 4.00103e10i 0.530640 0.0799811i
\(842\) 2.19770e10 + 1.49836e10i 0.0437240 + 0.0298105i
\(843\) −1.11012e10 3.59893e10i −0.0219817 0.0712628i
\(844\) 4.55713e11 + 1.04014e11i 0.898095 + 0.204984i
\(845\) 5.48660e10 + 2.15333e10i 0.107616 + 0.0422362i
\(846\) 1.95053e11 1.46172e10i 0.380778 0.0285354i
\(847\) −1.07263e12 1.15602e12i −2.08409 2.24612i
\(848\) −8.73273e10 + 5.95387e10i −0.168875 + 0.115137i
\(849\) 1.80158e11 + 1.43671e11i 0.346756 + 0.276528i
\(850\) 6.20612e9 6.68860e9i 0.0118890 0.0128133i
\(851\) −1.02555e11 + 6.80408e11i −0.195541 + 1.29733i
\(852\) 1.72668e9 + 7.56506e9i 0.00327682 + 0.0143567i
\(853\) 2.58794e11 + 4.48245e11i 0.488831 + 0.846679i 0.999917 0.0128497i \(-0.00409031\pi\)
−0.511087 + 0.859529i \(0.670757\pi\)
\(854\) −3.68379e11 2.12683e11i −0.692569 0.399855i
\(855\) −1.73981e11 5.36661e10i −0.325565 0.100424i
\(856\) 7.20644e11 5.74694e11i 1.34223 1.07039i
\(857\) −2.68852e10 + 3.58758e11i −0.0498413 + 0.665086i 0.915202 + 0.402995i \(0.132031\pi\)
−0.965043 + 0.262090i \(0.915588\pi\)
\(858\) −1.35181e11 6.51000e10i −0.249441 0.120125i
\(859\) 5.78401e11i 1.06232i −0.847270 0.531162i \(-0.821756\pi\)
0.847270 0.531162i \(-0.178244\pi\)
\(860\) 3.56508e11 1.47539e11i 0.651742 0.269719i
\(861\) 9.90328e10 0.180205
\(862\) 6.49387e9 1.34847e10i 0.0117618 0.0244237i
\(863\) −1.88606e11 1.41340e10i −0.340026 0.0254814i −0.0963768 0.995345i \(-0.530725\pi\)
−0.243649 + 0.969864i \(0.578344\pi\)
\(864\) −1.78179e11 2.23430e11i −0.319744 0.400946i
\(865\) −2.44392e11 + 7.92299e11i −0.436538 + 1.41522i
\(866\) −2.33807e11 + 4.04966e11i −0.415706 + 0.720024i
\(867\) 5.44324e10 3.14266e10i 0.0963344 0.0556187i
\(868\) 4.12021e11 9.40412e10i 0.725840 0.165668i
\(869\) 1.66854e12 + 2.51492e11i 2.92588 + 0.441006i
\(870\) −7.00875e10 6.50317e10i −0.122339 0.113514i
\(871\) −1.76918e11 + 2.21848e11i −0.307396 + 0.385463i
\(872\) 1.69833e11 + 2.49099e11i 0.293734 + 0.430829i
\(873\) 3.14597e11 2.91903e11i 0.541623 0.502553i
\(874\) −1.47790e10 1.97212e11i −0.0253280 0.337978i
\(875\) −2.47920e11 + 6.31690e11i −0.422941 + 1.07764i
\(876\) 1.45760e10 6.38617e10i 0.0247527 0.108449i
\(877\) 1.07817e11 3.32572e10i 0.182259 0.0562196i −0.202282 0.979327i \(-0.564836\pi\)
0.384541 + 0.923108i \(0.374360\pi\)
\(878\) 1.79349e11 2.63057e11i 0.301802 0.442662i
\(879\) 4.43466e9 + 2.94220e10i 0.00742856 + 0.0492853i
\(880\) 2.39480e11 9.39890e10i 0.399336 0.156728i
\(881\) 3.78570e11 1.82310e11i 0.628410 0.302626i −0.0924392 0.995718i \(-0.529466\pi\)
0.720849 + 0.693092i \(0.243752\pi\)
\(882\) 4.00060e10 + 8.30733e10i 0.0661075 + 0.137274i
\(883\) −1.70726e11 4.35003e11i −0.280839 0.715565i −0.999790 0.0205044i \(-0.993473\pi\)
0.718951 0.695061i \(-0.244622\pi\)
\(884\) −5.46803e11 + 8.24173e10i −0.895410 + 0.134961i
\(885\) 5.14952e10 + 3.51088e10i 0.0839447 + 0.0572325i
\(886\) −1.30064e11 4.21658e11i −0.211068 0.684267i
\(887\) −3.00687e10 6.86298e9i −0.0485758 0.0110871i 0.198164 0.980169i \(-0.436502\pi\)
−0.246740 + 0.969082i \(0.579359\pi\)
\(888\) 1.03491e11 + 4.06171e10i 0.166437 + 0.0653217i
\(889\) 9.00704e10 6.74984e9i 0.144203 0.0108065i
\(890\) 3.41091e11 + 3.67609e11i 0.543639 + 0.585904i
\(891\) −8.07324e11 + 5.50424e11i −1.28096 + 0.873346i
\(892\) 1.67771e11 + 1.33793e11i 0.265008 + 0.211337i
\(893\) −1.22408e11 + 1.31924e11i −0.192488 + 0.207452i
\(894\) −1.54034e10 + 1.02195e11i −0.0241139 + 0.159985i
\(895\) −2.08806e11 9.14837e11i −0.325424 1.42578i
\(896\) 3.17450e11 + 5.49840e11i 0.492543 + 0.853109i
\(897\) −2.60439e11 1.50365e11i −0.402287 0.232261i
\(898\) 1.75124e11 + 5.40187e10i 0.269303 + 0.0830690i
\(899\) −5.76761e11 + 4.59951e11i −0.882992 + 0.704163i
\(900\) 8.96075e8 1.19573e10i 0.00136576 0.0182248i
\(901\) 6.41259e11 + 3.08814e11i 0.973049 + 0.468596i
\(902\) 4.17943e11i 0.631381i
\(903\) −1.73500e11 + 8.75182e10i −0.260945 + 0.131628i
\(904\) 7.87281e10 0.117884
\(905\) 8.62515e10 1.79103e11i 0.128580 0.266999i
\(906\) 1.48835e10 + 1.11536e9i 0.0220898 + 0.00165540i
\(907\) −4.89430e11 6.13726e11i −0.723206 0.906871i 0.275309 0.961356i \(-0.411220\pi\)
−0.998515 + 0.0544847i \(0.982648\pi\)
\(908\) −1.28785e11 + 4.17510e11i −0.189462 + 0.614220i
\(909\) −3.61002e11 + 6.25275e11i −0.528755 + 0.915831i
\(910\) −3.77491e11 + 2.17945e11i −0.550479 + 0.317819i
\(911\) 2.02495e11 4.62181e10i 0.293995 0.0671025i −0.0729794 0.997333i \(-0.523251\pi\)
0.366975 + 0.930231i \(0.380394\pi\)
\(912\) 1.46628e10 + 2.21005e9i 0.0211951 + 0.00319465i
\(913\) 1.00662e12 + 9.34008e11i 1.44871 + 1.34421i
\(914\) 3.52454e11 4.41963e11i 0.505030 0.633288i
\(915\) 1.30641e11 + 1.91615e11i 0.186378 + 0.273367i
\(916\) 3.58209e11 3.32369e11i 0.508808 0.472105i
\(917\) 1.02881e11 + 1.37285e12i 0.145499 + 1.94154i
\(918\) −8.20775e10 + 2.09130e11i −0.115572 + 0.294473i
\(919\) −8.05939e10 + 3.53105e11i −0.112990 + 0.495041i 0.886489 + 0.462751i \(0.153137\pi\)
−0.999479 + 0.0322909i \(0.989720\pi\)
\(920\) −1.06177e12 + 3.27513e11i −1.48211 + 0.457169i
\(921\) 9.19792e10 1.34909e11i 0.127835 0.187500i
\(922\) 1.13331e11 + 7.51902e11i 0.156829 + 1.04049i
\(923\) −5.74826e10 + 2.25602e10i −0.0792007 + 0.0310840i
\(924\) −2.63403e11 + 1.26848e11i −0.361354 + 0.174019i
\(925\) 6.63232e9 + 1.37722e10i 0.00905939 + 0.0188120i
\(926\) 8.57961e10 + 2.18605e11i 0.116687 + 0.297314i
\(927\) 1.47490e11 2.22306e10i 0.199730 0.0301045i
\(928\) −7.87194e11 5.36700e11i −1.06143 0.723669i
\(929\) −5.98152e8 1.93916e9i −0.000803062 0.00260346i 0.955170 0.296057i \(-0.0956717\pi\)
−0.955973 + 0.293453i \(0.905196\pi\)
\(930\) 8.94554e10 + 2.04176e10i 0.119584 + 0.0272944i
\(931\) −7.89701e10 3.09935e10i −0.105115 0.0412545i
\(932\) −6.83868e11 + 5.12488e10i −0.906376 + 0.0679235i
\(933\) −5.32849e10 5.74275e10i −0.0703198 0.0757867i
\(934\) −1.40078e11 + 9.55034e10i −0.184069 + 0.125496i
\(935\) −1.35448e12 1.08016e12i −1.77225 1.41332i
\(936\) 4.72054e11 5.08754e11i 0.615019 0.662833i
\(937\) 1.62023e11 1.07495e12i 0.210193 1.39454i −0.596048 0.802949i \(-0.703263\pi\)
0.806240 0.591588i \(-0.201499\pi\)
\(938\) −4.89940e10 2.14657e11i −0.0632894 0.277289i
\(939\) −8.53146e10 1.47769e11i −0.109739 0.190073i
\(940\) 3.65129e11 + 2.10808e11i 0.467666 + 0.270007i
\(941\) 3.34332e11 + 1.03128e11i 0.426402 + 0.131528i 0.500526 0.865721i \(-0.333140\pi\)
−0.0741241 + 0.997249i \(0.523616\pi\)
\(942\) −1.95806e10 + 1.56150e10i −0.0248670 + 0.0198307i
\(943\) −6.26010e10 + 8.35352e11i −0.0791652 + 1.05639i
\(944\) 6.53220e10 + 3.14574e10i 0.0822568 + 0.0396128i
\(945\) 4.44699e11i 0.557621i
\(946\) −3.69349e11 7.32214e11i −0.461182 0.914268i
\(947\) −1.84752e11 −0.229715 −0.114858 0.993382i \(-0.536641\pi\)
−0.114858 + 0.993382i \(0.536641\pi\)
\(948\) 9.88620e10 2.05289e11i 0.122404 0.254175i
\(949\) 5.19826e11 + 3.89555e10i 0.640904 + 0.0480291i
\(950\) −2.73920e9 3.43485e9i −0.00336302 0.00421710i
\(951\) −1.36111e9 + 4.41260e9i −0.00166407 + 0.00539477i
\(952\) 5.14516e11 8.91167e11i 0.626398 1.08495i
\(953\) 3.38603e10 1.95493e10i 0.0410506 0.0237006i −0.479334 0.877632i \(-0.659122\pi\)
0.520385 + 0.853932i \(0.325788\pi\)
\(954\) −3.63137e11 + 8.28837e10i −0.438407 + 0.100063i
\(955\) 6.81288e11 + 1.02688e11i 0.819062 + 0.123454i
\(956\) 1.12775e10 + 1.04640e10i 0.0135015 + 0.0125276i
\(957\) 3.18182e11 3.98988e11i 0.379340 0.475677i
\(958\) −4.42762e11 6.49413e11i −0.525665 0.771008i
\(959\) 7.73563e11 7.17761e11i 0.914579 0.848605i
\(960\) 5.22583e9 + 6.97339e10i 0.00615277 + 0.0821030i
\(961\) −5.29480e10 + 1.34909e11i −0.0620806 + 0.158179i
\(962\) −8.20914e10 + 3.59666e11i −0.0958511 + 0.419951i
\(963\) −1.44047e12 + 4.44327e11i −1.67494 + 0.516651i
\(964\) 2.19914e11 3.22555e11i 0.254651 0.373504i
\(965\) 5.61014e10 + 3.72209e11i 0.0646941 + 0.429217i
\(966\) 2.17218e11 8.52519e10i 0.249453 0.0979029i
\(967\) 1.08074e12 5.20455e11i 1.23599 0.595219i 0.302266 0.953224i \(-0.402257\pi\)
0.933720 + 0.358004i \(0.116543\pi\)
\(968\) −9.35136e11 1.94183e12i −1.06506 2.21162i
\(969\) −3.64814e10 9.29531e10i −0.0413787 0.105431i
\(970\) −3.64263e11 + 5.49038e10i −0.411460 + 0.0620176i
\(971\) 9.72639e11 + 6.63134e11i 1.09414 + 0.745975i 0.969221 0.246192i \(-0.0791792\pi\)
0.124923 + 0.992166i \(0.460132\pi\)
\(972\) 1.32006e11 + 4.27955e11i 0.147887 + 0.479438i
\(973\) 9.04629e11 + 2.06476e11i 1.00930 + 0.230365i
\(974\) −3.76301e11 1.47687e11i −0.418119 0.164099i
\(975\) −6.66200e9 + 4.99248e8i −0.00737201 + 0.000552456i
\(976\) 1.83499e11 + 1.97764e11i 0.202224 + 0.217946i
\(977\) 9.01758e10 6.14808e10i 0.0989718 0.0674778i −0.512823 0.858494i \(-0.671400\pi\)
0.611795 + 0.791017i \(0.290448\pi\)
\(978\) 1.55598e9 + 1.24086e9i 0.00170079 + 0.00135633i
\(979\) −1.82059e12 + 1.96213e12i −1.98190 + 2.13598i
\(980\) −2.96216e10 + 1.96526e11i −0.0321147 + 0.213067i
\(981\) −1.09716e11 4.80698e11i −0.118466 0.519034i
\(982\) 2.54909e11 + 4.41516e11i 0.274119 + 0.474788i
\(983\) 4.00953e11 + 2.31490e11i 0.429417 + 0.247924i 0.699098 0.715026i \(-0.253585\pi\)
−0.269681 + 0.962950i \(0.586918\pi\)
\(984\) 1.29334e11 + 3.98943e10i 0.137953 + 0.0425530i
\(985\) 1.44353e11 1.15118e11i 0.153349 0.122292i
\(986\) −5.59719e10 + 7.46893e11i −0.0592192 + 0.790225i
\(987\) −1.91317e11 9.21336e10i −0.201598 0.0970844i
\(988\) 2.66258e11i 0.279432i
\(989\) −6.28551e11 1.51881e12i −0.656985 1.58752i
\(990\) 9.06634e11 0.943825
\(991\) −5.15779e11 + 1.07103e12i −0.534772 + 1.11047i 0.442164 + 0.896934i \(0.354211\pi\)
−0.976936 + 0.213531i \(0.931503\pi\)
\(992\) 9.11777e11 + 6.83282e10i 0.941547 + 0.0705592i
\(993\) −1.71917e11 2.15577e11i −0.176816 0.221720i
\(994\) 1.41233e10 4.57867e10i 0.0144674 0.0469022i
\(995\) 7.51208e11 1.30113e12i 0.766422 1.32748i
\(996\) 1.60585e11 9.27135e10i 0.163180 0.0942119i
\(997\) 1.27935e12 2.92003e11i 1.29482 0.295533i 0.481033 0.876702i \(-0.340262\pi\)
0.813783 + 0.581169i \(0.197404\pi\)
\(998\) −3.04019e10 4.58235e9i −0.0306464 0.00461920i
\(999\) −2.75900e11 2.55998e11i −0.277007 0.257025i
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 43.9.h.a.3.18 336
43.29 odd 42 inner 43.9.h.a.29.18 yes 336
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.9.h.a.3.18 336 1.1 even 1 trivial
43.9.h.a.29.18 yes 336 43.29 odd 42 inner