Properties

Label 29.10.d.a.7.5
Level $29$
Weight $10$
Character 29.7
Analytic conductor $14.936$
Analytic rank $0$
Dimension $126$
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] = [29,10,Mod(7,29)]
 
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([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.7");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.9360392488\)
Analytic rank: \(0\)
Dimension: \(126\)
Relative dimension: \(21\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 7.5
Character \(\chi\) \(=\) 29.7
Dual form 29.10.d.a.25.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.54005 - 24.2726i) q^{2} +(-131.756 - 63.4505i) q^{3} +(-97.1687 + 46.7940i) q^{4} +(-324.293 - 1420.82i) q^{5} +(-810.169 + 3549.58i) q^{6} +(-5845.17 - 2814.89i) q^{7} +(-6273.59 - 7866.83i) q^{8} +(1061.61 + 1331.22i) q^{9} +O(q^{10})\) \(q+(-5.54005 - 24.2726i) q^{2} +(-131.756 - 63.4505i) q^{3} +(-97.1687 + 46.7940i) q^{4} +(-324.293 - 1420.82i) q^{5} +(-810.169 + 3549.58i) q^{6} +(-5845.17 - 2814.89i) q^{7} +(-6273.59 - 7866.83i) q^{8} +(1061.61 + 1331.22i) q^{9} +(-32690.3 + 15742.8i) q^{10} +(-8679.31 + 10883.5i) q^{11} +15771.7 q^{12} +(38604.6 - 48408.7i) q^{13} +(-35941.9 + 157472. i) q^{14} +(-47424.1 + 207779. i) q^{15} +(-190620. + 239030. i) q^{16} +180166. q^{17} +(26430.6 - 33143.0i) q^{18} +(942957. - 454104. i) q^{19} +(97996.9 + 122884. i) q^{20} +(591533. + 741758. i) q^{21} +(312254. + 150374. i) q^{22} +(-13841.1 + 60641.9i) q^{23} +(327430. + 1.43457e6i) q^{24} +(-153859. + 74094.8i) q^{25} +(-1.38887e6 - 668847. i) q^{26} +(585099. + 2.56349e6i) q^{27} +699688. q^{28} +(-3.74168e6 - 712035. i) q^{29} +5.30605e6 q^{30} +(1.03651e6 + 4.54124e6i) q^{31} +(2.21634e6 + 1.06733e6i) q^{32} +(1.83412e6 - 883264. i) q^{33} +(-998128. - 4.37308e6i) q^{34} +(-2.10390e6 + 9.21779e6i) q^{35} +(-165448. - 79675.6i) q^{36} +(-3.06924e6 - 3.84871e6i) q^{37} +(-1.62463e7 - 2.03722e7i) q^{38} +(-8.15796e6 + 3.92867e6i) q^{39} +(-9.14287e6 + 1.14648e7i) q^{40} -1.78751e7 q^{41} +(1.47273e7 - 1.84674e7i) q^{42} +(4.26336e6 - 1.86790e7i) q^{43} +(334074. - 1.46368e6i) q^{44} +(1.54715e6 - 1.94006e6i) q^{45} +1.54861e6 q^{46} +(2.59221e7 - 3.25053e7i) q^{47} +(4.02820e7 - 1.93988e7i) q^{48} +(1.08241e6 + 1.35730e6i) q^{49} +(2.65086e6 + 3.32407e6i) q^{50} +(-2.37380e7 - 1.14316e7i) q^{51} +(-1.48593e6 + 6.51027e6i) q^{52} +(2.23167e6 + 9.77760e6i) q^{53} +(5.89809e7 - 2.84037e7i) q^{54} +(1.82781e7 + 8.80229e6i) q^{55} +(1.45260e7 + 6.36424e7i) q^{56} -1.53054e8 q^{57} +(3.44619e6 + 9.47648e7i) q^{58} -1.07273e8 q^{59} +(-5.11465e6 - 2.24087e7i) q^{60} +(4.44687e7 + 2.14150e7i) q^{61} +(1.04485e8 - 5.03175e7i) q^{62} +(-2.45807e6 - 1.07695e7i) q^{63} +(-2.12039e7 + 9.29005e7i) q^{64} +(-8.12993e7 - 3.91517e7i) q^{65} +(-3.16002e7 - 3.96254e7i) q^{66} +(6.83031e7 + 8.56494e7i) q^{67} +(-1.75065e7 + 8.43067e6i) q^{68} +(5.67141e6 - 7.11172e6i) q^{69} +2.35395e8 q^{70} +(-1.97967e8 + 2.48243e8i) q^{71} +(3.81235e6 - 1.67030e7i) q^{72} +(1.60102e7 - 7.01455e7i) q^{73} +(-7.64142e7 + 9.58204e7i) q^{74} +2.49733e7 q^{75} +(-7.03765e7 + 8.82494e7i) q^{76} +(8.13679e7 - 3.91847e7i) q^{77} +(1.40554e8 + 1.76250e8i) q^{78} +(-1.25769e7 - 1.57709e7i) q^{79} +(4.01436e8 + 1.93321e8i) q^{80} +(9.30216e7 - 4.07554e8i) q^{81} +(9.90287e7 + 4.33873e8i) q^{82} +(5.98140e8 - 2.88049e8i) q^{83} +(-9.21883e7 - 4.43955e7i) q^{84} +(-5.84265e7 - 2.55983e8i) q^{85} -4.77006e8 q^{86} +(4.47811e8 + 3.31226e8i) q^{87} +1.40069e8 q^{88} +(-1.42454e8 - 6.24130e8i) q^{89} +(-5.56615e7 - 2.68051e7i) q^{90} +(-3.61916e8 + 1.74290e8i) q^{91} +(-1.49275e6 - 6.54017e6i) q^{92} +(1.51578e8 - 6.64105e8i) q^{93} +(-9.32596e8 - 4.49115e8i) q^{94} +(-9.50994e8 - 1.19251e9i) q^{95} +(-2.24294e8 - 2.81256e8i) q^{96} +(-1.33511e9 + 6.42954e8i) q^{97} +(2.69485e7 - 3.37924e7i) q^{98} -2.37023e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 23 q^{2} - 5 q^{3} - 4699 q^{4} - 1031 q^{5} + 12781 q^{6} - 4959 q^{7} - 43354 q^{8} - 76050 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 23 q^{2} - 5 q^{3} - 4699 q^{4} - 1031 q^{5} + 12781 q^{6} - 4959 q^{7} - 43354 q^{8} - 76050 q^{9} + 8859 q^{10} - 195479 q^{11} + 141544 q^{12} - 68475 q^{13} - 271695 q^{14} + 322691 q^{15} - 916571 q^{16} - 587320 q^{17} - 3205692 q^{18} + 172239 q^{19} + 3022721 q^{20} + 4240955 q^{21} - 4806212 q^{22} + 4136729 q^{23} + 8763829 q^{24} + 3929026 q^{25} - 8916101 q^{26} - 22233347 q^{27} - 5636492 q^{28} - 8783106 q^{29} - 13875058 q^{30} + 4440751 q^{31} + 50266340 q^{32} - 13013201 q^{33} + 16498997 q^{34} + 2015357 q^{35} - 85629988 q^{36} + 3514043 q^{37} + 14330570 q^{38} - 72230993 q^{39} + 133179859 q^{40} + 16544588 q^{41} - 137066822 q^{42} + 51166115 q^{43} - 29984908 q^{44} + 263764053 q^{45} + 383616568 q^{46} - 97798039 q^{47} - 402814002 q^{48} + 35450702 q^{49} + 7192792 q^{50} + 57784388 q^{51} + 602315978 q^{52} + 137607435 q^{53} + 125382220 q^{54} - 411109327 q^{55} - 407148817 q^{56} - 138815986 q^{57} - 723336259 q^{58} - 899263700 q^{59} + 447938680 q^{60} + 666491883 q^{61} + 1037044473 q^{62} - 190916493 q^{63} + 65021266 q^{64} + 1392512087 q^{65} - 1056293177 q^{66} - 903332019 q^{67} - 1632042348 q^{68} - 527752591 q^{69} - 682041198 q^{70} + 1107000159 q^{71} + 430010561 q^{72} + 657123873 q^{73} - 198127908 q^{74} - 2404866172 q^{75} - 2839934913 q^{76} - 45301525 q^{77} + 2634791081 q^{78} + 1783807493 q^{79} + 3968800932 q^{80} + 2649824196 q^{81} + 3528483524 q^{82} - 1900496455 q^{83} - 3681471661 q^{84} + 183497446 q^{85} + 1213703072 q^{86} - 4480302165 q^{87} - 3448461606 q^{88} - 2924525111 q^{89} + 6284889126 q^{90} + 3601999725 q^{91} + 1893443670 q^{92} - 961083481 q^{93} + 1812573594 q^{94} + 837629545 q^{95} - 6708668090 q^{96} + 4263408987 q^{97} + 1842677548 q^{98} - 1747477852 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.54005 24.2726i −0.244838 1.07271i −0.936551 0.350533i \(-0.886001\pi\)
0.691713 0.722173i \(-0.256857\pi\)
\(3\) −131.756 63.4505i −0.939130 0.452261i −0.0992678 0.995061i \(-0.531650\pi\)
−0.839862 + 0.542800i \(0.817364\pi\)
\(4\) −97.1687 + 46.7940i −0.189783 + 0.0913945i
\(5\) −324.293 1420.82i −0.232045 1.01666i −0.947940 0.318448i \(-0.896838\pi\)
0.715895 0.698208i \(-0.246019\pi\)
\(6\) −810.169 + 3549.58i −0.255208 + 1.11814i
\(7\) −5845.17 2814.89i −0.920145 0.443119i −0.0870222 0.996206i \(-0.527735\pi\)
−0.833123 + 0.553088i \(0.813449\pi\)
\(8\) −6273.59 7866.83i −0.541516 0.679039i
\(9\) 1061.61 + 1331.22i 0.0539353 + 0.0676328i
\(10\) −32690.3 + 15742.8i −1.03376 + 0.497832i
\(11\) −8679.31 + 10883.5i −0.178738 + 0.224131i −0.863127 0.504986i \(-0.831498\pi\)
0.684389 + 0.729117i \(0.260069\pi\)
\(12\) 15771.7 0.219565
\(13\) 38604.6 48408.7i 0.374882 0.470087i −0.558223 0.829691i \(-0.688517\pi\)
0.933105 + 0.359604i \(0.117088\pi\)
\(14\) −35941.9 + 157472.i −0.250049 + 1.09554i
\(15\) −47424.1 + 207779.i −0.241874 + 1.05972i
\(16\) −190620. + 239030.i −0.727159 + 0.911828i
\(17\) 180166. 0.523181 0.261591 0.965179i \(-0.415753\pi\)
0.261591 + 0.965179i \(0.415753\pi\)
\(18\) 26430.6 33143.0i 0.0593446 0.0744158i
\(19\) 942957. 454104.i 1.65997 0.799400i 0.661181 0.750226i \(-0.270056\pi\)
0.998790 0.0491737i \(-0.0156588\pi\)
\(20\) 97996.9 + 122884.i 0.136955 + 0.171736i
\(21\) 591533. + 741758.i 0.663731 + 0.832292i
\(22\) 312254. + 150374.i 0.284188 + 0.136858i
\(23\) −13841.1 + 60641.9i −0.0103133 + 0.0451853i −0.979823 0.199869i \(-0.935948\pi\)
0.969509 + 0.245054i \(0.0788056\pi\)
\(24\) 327430. + 1.43457e6i 0.201451 + 0.882613i
\(25\) −153859. + 74094.8i −0.0787760 + 0.0379365i
\(26\) −1.38887e6 668847.i −0.596050 0.287043i
\(27\) 585099. + 2.56349e6i 0.211881 + 0.928313i
\(28\) 699688. 0.215126
\(29\) −3.74168e6 712035.i −0.982371 0.186943i
\(30\) 5.30605e6 1.19598
\(31\) 1.03651e6 + 4.54124e6i 0.201579 + 0.883176i 0.969976 + 0.243202i \(0.0781978\pi\)
−0.768397 + 0.639974i \(0.778945\pi\)
\(32\) 2.21634e6 + 1.06733e6i 0.373647 + 0.179939i
\(33\) 1.83412e6 883264.i 0.269224 0.129652i
\(34\) −998128. 4.37308e6i −0.128095 0.561219i
\(35\) −2.10390e6 + 9.21779e6i −0.236984 + 1.03829i
\(36\) −165448. 79675.6i −0.0164172 0.00790613i
\(37\) −3.06924e6 3.84871e6i −0.269230 0.337604i 0.628776 0.777586i \(-0.283556\pi\)
−0.898006 + 0.439982i \(0.854985\pi\)
\(38\) −1.62463e7 2.03722e7i −1.26394 1.58494i
\(39\) −8.15796e6 + 3.92867e6i −0.564665 + 0.271928i
\(40\) −9.14287e6 + 1.14648e7i −0.564693 + 0.708103i
\(41\) −1.78751e7 −0.987916 −0.493958 0.869486i \(-0.664450\pi\)
−0.493958 + 0.869486i \(0.664450\pi\)
\(42\) 1.47273e7 1.84674e7i 0.730298 0.915764i
\(43\) 4.26336e6 1.86790e7i 0.190171 0.833192i −0.786352 0.617779i \(-0.788033\pi\)
0.976523 0.215414i \(-0.0691101\pi\)
\(44\) 334074. 1.46368e6i 0.0134371 0.0588718i
\(45\) 1.54715e6 1.94006e6i 0.0562438 0.0705275i
\(46\) 1.54861e6 0.0509956
\(47\) 2.59221e7 3.25053e7i 0.774872 0.971659i −0.225125 0.974330i \(-0.572279\pi\)
0.999996 + 0.00267141i \(0.000850336\pi\)
\(48\) 4.02820e7 1.93988e7i 1.09528 0.527460i
\(49\) 1.08241e6 + 1.35730e6i 0.0268232 + 0.0336352i
\(50\) 2.65086e6 + 3.32407e6i 0.0599821 + 0.0752151i
\(51\) −2.37380e7 1.14316e7i −0.491335 0.236615i
\(52\) −1.48593e6 + 6.51027e6i −0.0281827 + 0.123476i
\(53\) 2.23167e6 + 9.77760e6i 0.0388498 + 0.170212i 0.990631 0.136565i \(-0.0436064\pi\)
−0.951781 + 0.306778i \(0.900749\pi\)
\(54\) 5.89809e7 2.84037e7i 0.943930 0.454573i
\(55\) 1.82781e7 + 8.80229e6i 0.269339 + 0.129707i
\(56\) 1.45260e7 + 6.36424e7i 0.197378 + 0.864770i
\(57\) −1.53054e8 −1.92047
\(58\) 3.44619e6 + 9.47648e7i 0.0399864 + 1.09957i
\(59\) −1.07273e8 −1.15254 −0.576269 0.817260i \(-0.695492\pi\)
−0.576269 + 0.817260i \(0.695492\pi\)
\(60\) −5.11465e6 2.24087e7i −0.0509489 0.223222i
\(61\) 4.44687e7 + 2.14150e7i 0.411216 + 0.198031i 0.628043 0.778179i \(-0.283856\pi\)
−0.216826 + 0.976210i \(0.569571\pi\)
\(62\) 1.04485e8 5.03175e7i 0.898033 0.432470i
\(63\) −2.45807e6 1.07695e7i −0.0196590 0.0861317i
\(64\) −2.12039e7 + 9.29005e7i −0.157982 + 0.692163i
\(65\) −8.12993e7 3.91517e7i −0.564906 0.272045i
\(66\) −3.16002e7 3.96254e7i −0.204994 0.257055i
\(67\) 6.83031e7 + 8.56494e7i 0.414099 + 0.519263i 0.944512 0.328475i \(-0.106535\pi\)
−0.530414 + 0.847739i \(0.677963\pi\)
\(68\) −1.75065e7 + 8.43067e6i −0.0992907 + 0.0478159i
\(69\) 5.67141e6 7.11172e6i 0.0301210 0.0377706i
\(70\) 2.35395e8 1.17181
\(71\) −1.97967e8 + 2.48243e8i −0.924549 + 1.15935i 0.0623572 + 0.998054i \(0.480138\pi\)
−0.986906 + 0.161294i \(0.948433\pi\)
\(72\) 3.81235e6 1.67030e7i 0.0167185 0.0732484i
\(73\) 1.60102e7 7.01455e7i 0.0659850 0.289099i −0.931160 0.364611i \(-0.881202\pi\)
0.997145 + 0.0755120i \(0.0240591\pi\)
\(74\) −7.64142e7 + 9.58204e7i −0.296232 + 0.371463i
\(75\) 2.49733e7 0.0911381
\(76\) −7.03765e7 + 8.82494e7i −0.241973 + 0.303424i
\(77\) 8.13679e7 3.91847e7i 0.263782 0.127031i
\(78\) 1.40554e8 + 1.76250e8i 0.429951 + 0.539141i
\(79\) −1.25769e7 1.57709e7i −0.0363288 0.0455549i 0.763335 0.646003i \(-0.223560\pi\)
−0.799664 + 0.600448i \(0.794989\pi\)
\(80\) 4.01436e8 + 1.93321e8i 1.09575 + 0.527685i
\(81\) 9.30216e7 4.07554e8i 0.240105 1.05197i
\(82\) 9.90287e7 + 4.33873e8i 0.241879 + 1.05974i
\(83\) 5.98140e8 2.88049e8i 1.38341 0.666215i 0.413687 0.910419i \(-0.364241\pi\)
0.969724 + 0.244204i \(0.0785266\pi\)
\(84\) −9.21883e7 4.43955e7i −0.202031 0.0972932i
\(85\) −5.84265e7 2.55983e8i −0.121402 0.531895i
\(86\) −4.77006e8 −0.940331
\(87\) 4.47811e8 + 3.31226e8i 0.838027 + 0.619852i
\(88\) 1.40069e8 0.248983
\(89\) −1.42454e8 6.24130e8i −0.240668 1.05444i −0.940411 0.340041i \(-0.889559\pi\)
0.699742 0.714395i \(-0.253298\pi\)
\(90\) −5.56615e7 2.68051e7i −0.0894259 0.0430652i
\(91\) −3.61916e8 + 1.74290e8i −0.553250 + 0.266431i
\(92\) −1.49275e6 6.54017e6i −0.00217241 0.00951796i
\(93\) 1.51578e8 6.64105e8i 0.210117 0.920584i
\(94\) −9.32596e8 4.49115e8i −1.23202 0.593310i
\(95\) −9.50994e8 1.19251e9i −1.19790 1.50212i
\(96\) −2.24294e8 2.81256e8i −0.269524 0.337972i
\(97\) −1.33511e9 + 6.42954e8i −1.53124 + 0.737407i −0.994341 0.106239i \(-0.966119\pi\)
−0.536900 + 0.843646i \(0.680405\pi\)
\(98\) 2.69485e7 3.37924e7i 0.0295133 0.0370085i
\(99\) −2.37023e7 −0.0247989
\(100\) 1.14831e7 1.43994e7i 0.0114831 0.0143994i
\(101\) −3.00901e8 + 1.31833e9i −0.287725 + 1.26061i 0.599913 + 0.800065i \(0.295202\pi\)
−0.887638 + 0.460541i \(0.847655\pi\)
\(102\) −1.45965e8 + 6.39513e8i −0.133520 + 0.584990i
\(103\) 6.66262e8 8.35466e8i 0.583280 0.731410i −0.399388 0.916782i \(-0.630777\pi\)
0.982669 + 0.185371i \(0.0593488\pi\)
\(104\) −6.23013e8 −0.522212
\(105\) 8.62076e8 1.08101e9i 0.692139 0.867915i
\(106\) 2.24964e8 1.08337e8i 0.173076 0.0833489i
\(107\) −5.10745e8 6.40454e8i −0.376684 0.472347i 0.556965 0.830536i \(-0.311966\pi\)
−0.933649 + 0.358189i \(0.883394\pi\)
\(108\) −1.76809e8 2.21712e8i −0.125054 0.156813i
\(109\) 2.02757e9 + 9.76426e8i 1.37580 + 0.662552i 0.968101 0.250562i \(-0.0806154\pi\)
0.407704 + 0.913114i \(0.366330\pi\)
\(110\) 1.12392e8 4.92422e8i 0.0731929 0.320679i
\(111\) 1.60190e8 + 7.01837e8i 0.100157 + 0.438816i
\(112\) 1.78705e9 8.60599e8i 1.07314 0.516797i
\(113\) −2.11558e9 1.01881e9i −1.22061 0.587815i −0.291129 0.956684i \(-0.594031\pi\)
−0.929481 + 0.368869i \(0.879745\pi\)
\(114\) 8.47925e8 + 3.71500e9i 0.470203 + 2.06010i
\(115\) 9.06497e7 0.0483311
\(116\) 3.96893e8 1.05900e8i 0.203522 0.0543046i
\(117\) 1.05425e8 0.0520127
\(118\) 5.94296e8 + 2.60378e9i 0.282185 + 1.23633i
\(119\) −1.05310e9 5.07146e8i −0.481403 0.231831i
\(120\) 1.93208e9 9.30440e8i 0.850568 0.409612i
\(121\) 4.81572e8 + 2.10991e9i 0.204234 + 0.894806i
\(122\) 2.73438e8 1.19801e9i 0.111748 0.489600i
\(123\) 2.35515e9 + 1.13418e9i 0.927782 + 0.446796i
\(124\) −3.13219e8 3.92764e8i −0.118974 0.149188i
\(125\) −1.61953e9 2.03083e9i −0.593328 0.744010i
\(126\) −2.47785e8 + 1.19327e8i −0.0875807 + 0.0421766i
\(127\) 1.40361e8 1.76007e8i 0.0478773 0.0600363i −0.757316 0.653048i \(-0.773490\pi\)
0.805194 + 0.593012i \(0.202061\pi\)
\(128\) 3.63190e9 1.19588
\(129\) −1.74692e9 + 2.19056e9i −0.555416 + 0.696469i
\(130\) −4.99909e8 + 2.19024e9i −0.153513 + 0.672585i
\(131\) 8.03288e7 3.51943e8i 0.0238314 0.104412i −0.961613 0.274408i \(-0.911518\pi\)
0.985445 + 0.169995i \(0.0543753\pi\)
\(132\) −1.36887e8 + 1.71651e8i −0.0392446 + 0.0492112i
\(133\) −6.79000e9 −1.88164
\(134\) 1.70053e9 2.13239e9i 0.455630 0.571341i
\(135\) 3.45251e9 1.66264e9i 0.894609 0.430821i
\(136\) −1.13029e9 1.41733e9i −0.283311 0.355260i
\(137\) −1.13673e9 1.42542e9i −0.275687 0.345701i 0.624641 0.780912i \(-0.285245\pi\)
−0.900328 + 0.435211i \(0.856674\pi\)
\(138\) −2.04040e8 9.82603e7i −0.0478915 0.0230633i
\(139\) −1.35956e9 + 5.95663e9i −0.308910 + 1.35342i 0.547361 + 0.836897i \(0.315633\pi\)
−0.856271 + 0.516527i \(0.827225\pi\)
\(140\) −2.26904e8 9.94130e8i −0.0499190 0.218709i
\(141\) −5.47788e9 + 2.63801e9i −1.16715 + 0.562069i
\(142\) 7.12223e9 + 3.42989e9i 1.47000 + 0.707916i
\(143\) 1.91795e8 + 8.40308e8i 0.0383552 + 0.168045i
\(144\) −5.20565e8 −0.100889
\(145\) 2.01726e8 + 5.54716e9i 0.0378971 + 1.04211i
\(146\) −1.79131e9 −0.326274
\(147\) −5.64931e7 2.47512e8i −0.00997855 0.0437189i
\(148\) 4.78331e8 + 2.30352e8i 0.0819503 + 0.0394652i
\(149\) 2.70497e9 1.30265e9i 0.449599 0.216515i −0.195362 0.980731i \(-0.562588\pi\)
0.644960 + 0.764216i \(0.276874\pi\)
\(150\) −1.38353e8 6.06165e8i −0.0223141 0.0977643i
\(151\) 1.99025e9 8.71986e9i 0.311538 1.36494i −0.540449 0.841377i \(-0.681746\pi\)
0.851988 0.523562i \(-0.175397\pi\)
\(152\) −9.48808e9 4.56922e9i −1.44172 0.694298i
\(153\) 1.91266e8 + 2.39839e8i 0.0282179 + 0.0353842i
\(154\) −1.40190e9 1.75792e9i −0.200850 0.251858i
\(155\) 6.11616e9 2.94539e9i 0.851111 0.409873i
\(156\) 6.08860e8 7.63487e8i 0.0823108 0.103215i
\(157\) −3.10294e9 −0.407591 −0.203796 0.979013i \(-0.565328\pi\)
−0.203796 + 0.979013i \(0.565328\pi\)
\(158\) −3.13124e8 + 3.92645e8i −0.0399723 + 0.0501236i
\(159\) 3.26356e8 1.42986e9i 0.0404953 0.177422i
\(160\) 7.97745e8 3.49515e9i 0.0962330 0.421624i
\(161\) 2.51604e8 3.15501e8i 0.0295121 0.0370070i
\(162\) −1.04077e10 −1.18724
\(163\) 3.17821e9 3.98535e9i 0.352645 0.442203i −0.573594 0.819140i \(-0.694451\pi\)
0.926239 + 0.376937i \(0.123023\pi\)
\(164\) 1.73690e9 8.36445e8i 0.187489 0.0902901i
\(165\) −1.84975e9 2.31951e9i −0.194283 0.243624i
\(166\) −1.03054e10 1.29226e10i −1.05336 1.32088i
\(167\) 1.39506e10 + 6.71827e9i 1.38794 + 0.668395i 0.970676 0.240392i \(-0.0772760\pi\)
0.417260 + 0.908787i \(0.362990\pi\)
\(168\) 2.12426e9 9.30697e9i 0.205738 0.901398i
\(169\) 1.50664e9 + 6.60102e9i 0.142076 + 0.622474i
\(170\) −5.88968e9 + 2.83632e9i −0.540843 + 0.260456i
\(171\) 1.60556e9 + 7.73198e8i 0.143597 + 0.0691525i
\(172\) 4.59799e8 + 2.01451e9i 0.0400581 + 0.175506i
\(173\) 8.35705e9 0.709326 0.354663 0.934994i \(-0.384596\pi\)
0.354663 + 0.934994i \(0.384596\pi\)
\(174\) 5.55882e9 1.27045e10i 0.459738 1.05072i
\(175\) 1.10790e9 0.0892957
\(176\) −9.47036e8 4.14924e9i −0.0743977 0.325958i
\(177\) 1.41339e10 + 6.80651e9i 1.08238 + 0.521248i
\(178\) −1.43600e10 + 6.91543e9i −1.07217 + 0.516332i
\(179\) 1.20914e9 + 5.29758e9i 0.0880314 + 0.385691i 0.999680 0.0252789i \(-0.00804737\pi\)
−0.911649 + 0.410970i \(0.865190\pi\)
\(180\) −5.95510e7 + 2.60910e8i −0.00422827 + 0.0185253i
\(181\) 5.05818e7 + 2.43589e7i 0.00350300 + 0.00168696i 0.435634 0.900124i \(-0.356524\pi\)
−0.432131 + 0.901811i \(0.642238\pi\)
\(182\) 6.23549e9 + 7.81905e9i 0.421259 + 0.528242i
\(183\) −4.50024e9 5.64312e9i −0.296624 0.371954i
\(184\) 5.63892e8 2.71556e8i 0.0362674 0.0174654i
\(185\) −4.47299e9 + 5.60895e9i −0.280753 + 0.352054i
\(186\) −1.69593e10 −1.03896
\(187\) −1.56371e9 + 1.96084e9i −0.0935126 + 0.117261i
\(188\) −9.97765e8 + 4.37149e9i −0.0582530 + 0.255223i
\(189\) 3.79592e9 1.66310e10i 0.216391 0.948071i
\(190\) −2.36767e10 + 2.96896e10i −1.31804 + 1.65277i
\(191\) 1.61550e10 0.878329 0.439164 0.898407i \(-0.355275\pi\)
0.439164 + 0.898407i \(0.355275\pi\)
\(192\) 8.68833e9 1.08948e10i 0.461404 0.578582i
\(193\) −2.14804e10 + 1.03444e10i −1.11438 + 0.536658i −0.898153 0.439684i \(-0.855090\pi\)
−0.216230 + 0.976342i \(0.569376\pi\)
\(194\) 2.30027e10 + 2.88445e10i 1.16593 + 1.46203i
\(195\) 8.22750e9 + 1.03170e10i 0.407485 + 0.510971i
\(196\) −1.68690e8 8.12368e7i −0.00816464 0.00393188i
\(197\) 4.62822e9 2.02775e10i 0.218935 0.959218i −0.739331 0.673342i \(-0.764858\pi\)
0.958267 0.285876i \(-0.0922845\pi\)
\(198\) 1.31312e8 + 5.75316e8i 0.00607172 + 0.0266019i
\(199\) −3.13227e10 + 1.50842e10i −1.41586 + 0.681842i −0.976310 0.216376i \(-0.930576\pi\)
−0.439550 + 0.898218i \(0.644862\pi\)
\(200\) 1.54814e9 + 7.45545e8i 0.0684188 + 0.0329488i
\(201\) −3.56487e9 1.56187e10i −0.154050 0.674937i
\(202\) 3.36664e10 1.42271
\(203\) 1.98665e10 + 1.46944e10i 0.821085 + 0.607322i
\(204\) 2.84152e9 0.114872
\(205\) 5.79675e9 + 2.53972e10i 0.229241 + 1.00437i
\(206\) −2.39700e10 1.15434e10i −0.927397 0.446611i
\(207\) −9.54212e7 + 4.59524e7i −0.00361226 + 0.00173957i
\(208\) 4.21232e9 + 1.84554e10i 0.156040 + 0.683656i
\(209\) −3.24197e9 + 1.42040e10i −0.117530 + 0.514934i
\(210\) −3.10148e10 1.49359e10i −1.10048 0.529963i
\(211\) −1.78624e9 2.23987e9i −0.0620396 0.0777951i 0.749843 0.661615i \(-0.230129\pi\)
−0.811883 + 0.583820i \(0.801557\pi\)
\(212\) −6.74381e8 8.45647e8i −0.0229295 0.0287527i
\(213\) 4.18345e10 2.01464e10i 1.39260 0.670641i
\(214\) −1.27159e10 + 1.59452e10i −0.414463 + 0.519720i
\(215\) −2.79221e10 −0.891198
\(216\) 1.64959e10 2.06851e10i 0.515624 0.646572i
\(217\) 6.72451e9 2.94620e10i 0.205870 0.901974i
\(218\) 1.24675e10 5.46238e10i 0.373874 1.63805i
\(219\) −6.56021e9 + 8.22625e9i −0.192717 + 0.241659i
\(220\) −2.18796e9 −0.0629704
\(221\) 6.95524e9 8.72159e9i 0.196131 0.245941i
\(222\) 1.61479e10 7.77642e9i 0.446198 0.214878i
\(223\) 2.45348e10 + 3.07657e10i 0.664372 + 0.833096i 0.993811 0.111081i \(-0.0354312\pi\)
−0.329440 + 0.944177i \(0.606860\pi\)
\(224\) −9.95047e9 1.24775e10i −0.264075 0.331140i
\(225\) −2.61975e8 1.26160e8i −0.00681456 0.00328172i
\(226\) −1.30087e10 + 5.69948e10i −0.331700 + 1.45327i
\(227\) −9.18974e8 4.02629e9i −0.0229714 0.100644i 0.962143 0.272546i \(-0.0878658\pi\)
−0.985114 + 0.171902i \(0.945009\pi\)
\(228\) 1.48720e10 7.16199e9i 0.364471 0.175520i
\(229\) 3.82534e8 + 1.84219e8i 0.00919201 + 0.00442664i 0.438474 0.898744i \(-0.355519\pi\)
−0.429282 + 0.903170i \(0.641233\pi\)
\(230\) −5.02204e8 2.20030e9i −0.0118333 0.0518450i
\(231\) −1.32070e10 −0.305176
\(232\) 1.78723e10 + 3.39022e10i 0.405027 + 0.768301i
\(233\) 5.38206e10 1.19632 0.598160 0.801377i \(-0.295899\pi\)
0.598160 + 0.801377i \(0.295899\pi\)
\(234\) −5.84063e8 2.55895e9i −0.0127347 0.0557943i
\(235\) −5.45905e10 2.62894e10i −1.16765 0.562310i
\(236\) 1.04235e10 5.01972e9i 0.218732 0.105336i
\(237\) 6.56411e8 + 2.87592e9i 0.0135148 + 0.0592120i
\(238\) −6.47551e9 + 2.83711e10i −0.130821 + 0.573164i
\(239\) −7.34420e8 3.53678e8i −0.0145598 0.00701161i 0.426590 0.904445i \(-0.359715\pi\)
−0.441149 + 0.897434i \(0.645429\pi\)
\(240\) −4.06254e10 5.09426e10i −0.790400 0.991130i
\(241\) −3.70733e10 4.64885e10i −0.707921 0.887705i 0.289666 0.957128i \(-0.406456\pi\)
−0.997587 + 0.0694228i \(0.977884\pi\)
\(242\) 4.85449e10 2.33780e10i 0.909859 0.438165i
\(243\) −5.84716e9 + 7.33210e9i −0.107576 + 0.134896i
\(244\) −5.32306e9 −0.0961407
\(245\) 1.57746e9 1.97807e9i 0.0279712 0.0350748i
\(246\) 1.44818e10 6.34490e10i 0.252124 1.10463i
\(247\) 1.44199e10 6.31778e10i 0.246506 1.08001i
\(248\) 2.92226e10 3.66439e10i 0.490553 0.615134i
\(249\) −9.70855e10 −1.60051
\(250\) −4.03212e10 + 5.05611e10i −0.652834 + 0.818628i
\(251\) −8.21839e10 + 3.95777e10i −1.30694 + 0.629388i −0.952171 0.305567i \(-0.901154\pi\)
−0.354767 + 0.934955i \(0.615440\pi\)
\(252\) 7.42795e8 + 9.31435e8i 0.0116029 + 0.0145496i
\(253\) −5.39865e8 6.76969e8i −0.00828405 0.0103879i
\(254\) −5.04975e9 2.43183e9i −0.0761234 0.0366591i
\(255\) −8.54420e9 + 3.74346e10i −0.126544 + 0.554424i
\(256\) −9.26449e9 4.05904e10i −0.134816 0.590668i
\(257\) −5.70835e10 + 2.74900e10i −0.816229 + 0.393075i −0.794932 0.606698i \(-0.792494\pi\)
−0.0212963 + 0.999773i \(0.506779\pi\)
\(258\) 6.28486e10 + 3.02663e10i 0.883093 + 0.425275i
\(259\) 7.10658e9 + 3.11359e10i 0.0981322 + 0.429945i
\(260\) 9.73180e9 0.132073
\(261\) −3.02433e9 5.73688e9i −0.0403410 0.0765233i
\(262\) −8.98759e9 −0.117839
\(263\) −2.45572e10 1.07592e11i −0.316503 1.38669i −0.843640 0.536909i \(-0.819592\pi\)
0.527137 0.849780i \(-0.323265\pi\)
\(264\) −1.84550e10 8.88745e9i −0.233828 0.112605i
\(265\) 1.31685e10 6.34161e9i 0.164032 0.0789938i
\(266\) 3.76169e10 + 1.64811e11i 0.460698 + 2.01845i
\(267\) −2.08322e10 + 9.12719e10i −0.250862 + 1.09910i
\(268\) −1.06448e10 5.12627e9i −0.126047 0.0607008i
\(269\) −3.34960e10 4.20027e10i −0.390039 0.489093i 0.547582 0.836752i \(-0.315548\pi\)
−0.937621 + 0.347659i \(0.886977\pi\)
\(270\) −5.94837e10 7.45902e10i −0.681178 0.854171i
\(271\) 1.28485e11 6.18752e10i 1.44707 0.696874i 0.464990 0.885316i \(-0.346058\pi\)
0.982084 + 0.188442i \(0.0603436\pi\)
\(272\) −3.43433e10 + 4.30651e10i −0.380436 + 0.477051i
\(273\) 5.87435e10 0.640070
\(274\) −2.83010e10 + 3.54883e10i −0.303336 + 0.380372i
\(275\) 5.28982e8 2.31762e9i 0.00557755 0.0244368i
\(276\) −2.18298e8 + 9.56424e8i −0.00226443 + 0.00992110i
\(277\) 6.08652e9 7.63225e9i 0.0621169 0.0778922i −0.749802 0.661662i \(-0.769851\pi\)
0.811919 + 0.583770i \(0.198423\pi\)
\(278\) 1.52115e11 1.52746
\(279\) −4.94501e9 + 6.20084e9i −0.0488594 + 0.0612677i
\(280\) 8.57138e10 4.12776e10i 0.833373 0.401331i
\(281\) −3.29820e10 4.13582e10i −0.315573 0.395715i 0.598595 0.801052i \(-0.295726\pi\)
−0.914168 + 0.405336i \(0.867154\pi\)
\(282\) 9.43789e10 + 1.18347e11i 0.888697 + 1.11439i
\(283\) 8.26017e10 + 3.97789e10i 0.765508 + 0.368649i 0.775538 0.631300i \(-0.217478\pi\)
−0.0100303 + 0.999950i \(0.503193\pi\)
\(284\) 7.61992e9 3.33851e10i 0.0695053 0.304523i
\(285\) 4.96342e10 + 2.17462e11i 0.445635 + 1.95245i
\(286\) 1.93339e10 9.31070e9i 0.170872 0.0822877i
\(287\) 1.04483e11 + 5.03163e10i 0.909026 + 0.437764i
\(288\) 9.32036e8 + 4.08352e9i 0.00798301 + 0.0349758i
\(289\) −8.61282e10 −0.726281
\(290\) 1.33526e11 3.56280e10i 1.10860 0.295801i
\(291\) 2.16705e11 1.77154
\(292\) 1.72669e9 + 7.56512e9i 0.0138993 + 0.0608966i
\(293\) −2.07696e11 1.00021e11i −1.64636 0.792845i −0.999544 0.0301973i \(-0.990386\pi\)
−0.646815 0.762647i \(-0.723899\pi\)
\(294\) −5.69478e9 + 2.74246e9i −0.0444544 + 0.0214081i
\(295\) 3.47878e10 + 1.52415e11i 0.267441 + 1.17173i
\(296\) −1.10220e10 + 4.82904e10i −0.0834539 + 0.365635i
\(297\) −3.29780e10 1.58814e10i −0.245935 0.118436i
\(298\) −4.66043e10 5.84399e10i −0.342336 0.429276i
\(299\) 2.40126e9 + 3.01109e9i 0.0173748 + 0.0217873i
\(300\) −2.42662e9 + 1.16860e9i −0.0172964 + 0.00832952i
\(301\) −7.74993e10 + 9.71811e10i −0.544188 + 0.682390i
\(302\) −2.22679e11 −1.54045
\(303\) 1.23295e11 1.54607e11i 0.840335 1.05375i
\(304\) −7.12021e10 + 3.11957e11i −0.478147 + 2.09490i
\(305\) 1.60060e10 7.01268e10i 0.105909 0.464018i
\(306\) 4.76190e9 5.97123e9i 0.0310480 0.0389329i
\(307\) −2.17689e11 −1.39866 −0.699332 0.714797i \(-0.746519\pi\)
−0.699332 + 0.714797i \(0.746519\pi\)
\(308\) −6.07280e9 + 7.61505e9i −0.0384513 + 0.0482164i
\(309\) −1.40795e11 + 6.78032e10i −0.878565 + 0.423094i
\(310\) −1.05376e11 1.32137e11i −0.648058 0.812639i
\(311\) −1.80801e11 2.26717e11i −1.09592 1.37424i −0.920958 0.389663i \(-0.872592\pi\)
−0.174961 0.984575i \(-0.555980\pi\)
\(312\) 8.20858e10 + 3.95305e10i 0.490425 + 0.236176i
\(313\) 4.48127e10 1.96337e11i 0.263908 1.15625i −0.653064 0.757303i \(-0.726517\pi\)
0.916972 0.398952i \(-0.130626\pi\)
\(314\) 1.71904e10 + 7.53162e10i 0.0997938 + 0.437225i
\(315\) −1.45044e10 + 6.98494e9i −0.0830045 + 0.0399729i
\(316\) 1.96006e9 + 9.43916e8i 0.0110580 + 0.00532527i
\(317\) −4.61068e10 2.02007e11i −0.256448 1.12357i −0.925018 0.379922i \(-0.875951\pi\)
0.668571 0.743648i \(-0.266906\pi\)
\(318\) −3.65144e10 −0.200236
\(319\) 4.02246e10 3.45426e10i 0.217487 0.186766i
\(320\) 1.38871e11 0.740350
\(321\) 2.66568e10 + 1.16791e11i 0.140131 + 0.613955i
\(322\) −9.05191e9 4.35917e9i −0.0469234 0.0225971i
\(323\) 1.69889e11 8.18140e10i 0.868466 0.418231i
\(324\) 1.00323e10 + 4.39544e10i 0.0505764 + 0.221590i
\(325\) −2.35286e9 + 1.03085e10i −0.0116982 + 0.0512533i
\(326\) −1.14342e11 5.50642e10i −0.560695 0.270016i
\(327\) −2.05190e11 2.57301e11i −0.992412 1.24445i
\(328\) 1.12141e11 + 1.40620e11i 0.534972 + 0.670834i
\(329\) −2.43018e11 + 1.17031e11i −1.14355 + 0.550707i
\(330\) −4.60528e10 + 5.77484e10i −0.213768 + 0.268057i
\(331\) 3.88744e11 1.78007 0.890037 0.455887i \(-0.150678\pi\)
0.890037 + 0.455887i \(0.150678\pi\)
\(332\) −4.46415e10 + 5.59786e10i −0.201659 + 0.252872i
\(333\) 1.86513e9 8.17165e9i 0.00831207 0.0364175i
\(334\) 8.57823e10 3.75837e11i 0.377171 1.65250i
\(335\) 9.95422e10 1.24822e11i 0.431823 0.541489i
\(336\) −2.90061e11 −1.24155
\(337\) 1.10251e11 1.38250e11i 0.465635 0.583888i −0.492461 0.870335i \(-0.663903\pi\)
0.958096 + 0.286446i \(0.0924740\pi\)
\(338\) 1.51877e11 7.31400e10i 0.632945 0.304810i
\(339\) 2.14097e11 + 2.68469e11i 0.880466 + 1.10407i
\(340\) 1.76557e10 + 2.21395e10i 0.0716522 + 0.0898490i
\(341\) −5.84208e10 2.81340e10i −0.233977 0.112677i
\(342\) 9.87259e9 4.32546e10i 0.0390224 0.170968i
\(343\) 5.57498e10 + 2.44256e11i 0.217480 + 0.952843i
\(344\) −1.73691e11 + 8.36452e10i −0.668751 + 0.322053i
\(345\) −1.19437e10 5.75177e9i −0.0453892 0.0218583i
\(346\) −4.62985e10 2.02847e11i −0.173670 0.760897i
\(347\) −3.38648e11 −1.25391 −0.626954 0.779057i \(-0.715698\pi\)
−0.626954 + 0.779057i \(0.715698\pi\)
\(348\) −5.90126e10 1.12300e10i −0.215694 0.0410462i
\(349\) −4.29713e11 −1.55047 −0.775236 0.631671i \(-0.782369\pi\)
−0.775236 + 0.631671i \(0.782369\pi\)
\(350\) −6.13784e9 2.68916e10i −0.0218630 0.0957880i
\(351\) 1.46683e11 + 7.06387e10i 0.515818 + 0.248405i
\(352\) −3.08526e10 + 1.48578e10i −0.107115 + 0.0515838i
\(353\) 9.86399e10 + 4.32170e11i 0.338117 + 1.48139i 0.802982 + 0.596004i \(0.203246\pi\)
−0.464865 + 0.885382i \(0.653897\pi\)
\(354\) 8.69090e10 3.80773e11i 0.294137 1.28870i
\(355\) 4.16907e11 + 2.00772e11i 1.39320 + 0.670928i
\(356\) 4.30476e10 + 5.39799e10i 0.142044 + 0.178118i
\(357\) 1.06574e11 + 1.33639e11i 0.347251 + 0.435439i
\(358\) 1.21887e11 5.86978e10i 0.392179 0.188864i
\(359\) 8.25037e10 1.03456e11i 0.262149 0.328724i −0.633285 0.773919i \(-0.718294\pi\)
0.895434 + 0.445194i \(0.146865\pi\)
\(360\) −2.49683e10 −0.0783479
\(361\) 4.81764e11 6.04114e11i 1.49297 1.87213i
\(362\) 3.11027e8 1.36270e9i 0.000951940 0.00417072i
\(363\) 7.04244e10 3.08549e11i 0.212884 0.932707i
\(364\) 2.70112e10 3.38710e10i 0.0806469 0.101128i
\(365\) −1.04856e11 −0.309226
\(366\) −1.12041e11 + 1.40496e11i −0.326373 + 0.409258i
\(367\) 3.45267e11 1.66272e11i 0.993478 0.478434i 0.134758 0.990879i \(-0.456974\pi\)
0.858720 + 0.512445i \(0.171260\pi\)
\(368\) −1.18568e10 1.48680e10i −0.0337019 0.0422608i
\(369\) −1.89763e10 2.37956e10i −0.0532836 0.0668155i
\(370\) 1.60924e11 + 7.74970e10i 0.446389 + 0.214970i
\(371\) 1.44783e10 6.34337e10i 0.0396767 0.173835i
\(372\) 1.63475e10 + 7.16231e10i 0.0442597 + 0.193914i
\(373\) −5.75731e11 + 2.77257e11i −1.54003 + 0.741640i −0.995288 0.0969621i \(-0.969087\pi\)
−0.544744 + 0.838602i \(0.683373\pi\)
\(374\) 5.62575e10 + 2.70922e10i 0.148682 + 0.0716015i
\(375\) 8.45265e10 + 3.70335e11i 0.220725 + 0.967061i
\(376\) −4.18338e11 −1.07940
\(377\) −1.78915e11 + 1.53642e11i −0.456153 + 0.391718i
\(378\) −4.24707e11 −1.06998
\(379\) 1.55859e11 + 6.82863e11i 0.388021 + 1.70003i 0.671459 + 0.741042i \(0.265668\pi\)
−0.283438 + 0.958991i \(0.591475\pi\)
\(380\) 1.48209e11 + 7.13737e10i 0.364627 + 0.175595i
\(381\) −2.96612e10 + 1.42841e10i −0.0721151 + 0.0347288i
\(382\) −8.94996e10 3.92123e11i −0.215048 0.942188i
\(383\) −1.26074e11 + 5.52365e11i −0.299385 + 1.31169i 0.571662 + 0.820489i \(0.306299\pi\)
−0.871046 + 0.491201i \(0.836558\pi\)
\(384\) −4.78525e11 2.30446e11i −1.12309 0.540852i
\(385\) −8.20615e10 1.02902e11i −0.190356 0.238699i
\(386\) 3.70088e11 + 4.64075e11i 0.848520 + 1.06401i
\(387\) 2.93918e10 1.41543e10i 0.0666080 0.0320767i
\(388\) 9.96443e10 1.24950e11i 0.223208 0.279894i
\(389\) −4.65233e11 −1.03014 −0.515072 0.857147i \(-0.672235\pi\)
−0.515072 + 0.857147i \(0.672235\pi\)
\(390\) 2.04838e11 2.56859e11i 0.448353 0.562217i
\(391\) −2.49369e9 + 1.09256e10i −0.00539570 + 0.0236401i
\(392\) 3.88705e9 1.70303e10i 0.00831444 0.0364279i
\(393\) −3.29148e10 + 4.12738e10i −0.0696025 + 0.0872787i
\(394\) −5.17828e11 −1.08256
\(395\) −1.83290e10 + 2.29839e10i −0.0378837 + 0.0475047i
\(396\) 2.30312e9 1.10913e9i 0.00470640 0.00226648i
\(397\) 5.00620e10 + 6.27757e10i 0.101146 + 0.126834i 0.829828 0.558019i \(-0.188438\pi\)
−0.728682 + 0.684852i \(0.759867\pi\)
\(398\) 5.39662e11 + 6.76715e11i 1.07807 + 1.35186i
\(399\) 8.94625e11 + 4.30829e11i 1.76711 + 0.850994i
\(400\) 1.16178e10 5.09010e10i 0.0226911 0.0994161i
\(401\) 3.66105e10 + 1.60401e11i 0.0707060 + 0.309783i 0.997898 0.0648031i \(-0.0206419\pi\)
−0.927192 + 0.374586i \(0.877785\pi\)
\(402\) −3.59357e11 + 1.73057e11i −0.686291 + 0.330500i
\(403\) 2.59850e11 + 1.25137e11i 0.490738 + 0.236327i
\(404\) −3.24519e10 1.42181e11i −0.0606072 0.265538i
\(405\) −6.09228e11 −1.12521
\(406\) 2.46609e11 5.63617e11i 0.450444 1.02948i
\(407\) 6.85263e10 0.123789
\(408\) 5.89917e10 + 2.58460e11i 0.105395 + 0.461766i
\(409\) 2.01760e11 + 9.71627e10i 0.356518 + 0.171690i 0.603565 0.797313i \(-0.293746\pi\)
−0.247048 + 0.969003i \(0.579460\pi\)
\(410\) 5.84342e11 2.81404e11i 1.02127 0.491816i
\(411\) 5.93283e10 + 2.59934e11i 0.102559 + 0.449340i
\(412\) −2.56450e10 + 1.12358e11i −0.0438496 + 0.192118i
\(413\) 6.27028e11 + 3.01961e11i 1.06050 + 0.510711i
\(414\) 1.64402e9 + 2.06154e9i 0.00275046 + 0.00344897i
\(415\) −6.03238e11 7.56437e11i −0.998326 1.25186i
\(416\) 1.37229e11 6.60861e10i 0.224660 0.108191i
\(417\) 5.57082e11 6.98558e11i 0.902208 1.13133i
\(418\) 3.62728e11 0.581149
\(419\) −5.30624e10 + 6.65382e10i −0.0841054 + 0.105465i −0.822104 0.569338i \(-0.807200\pi\)
0.737998 + 0.674802i \(0.235771\pi\)
\(420\) −3.31821e10 + 1.45380e11i −0.0520333 + 0.227973i
\(421\) 4.74035e10 2.07688e11i 0.0735430 0.322213i −0.924753 0.380568i \(-0.875728\pi\)
0.998296 + 0.0583552i \(0.0185856\pi\)
\(422\) −4.44716e10 + 5.57656e10i −0.0682616 + 0.0855974i
\(423\) 7.07907e10 0.107509
\(424\) 6.29181e10 7.88968e10i 0.0945430 0.118553i
\(425\) −2.77202e10 + 1.33493e10i −0.0412141 + 0.0198477i
\(426\) −7.20771e11 9.03818e11i −1.06036 1.32965i
\(427\) −1.99647e11 2.50349e11i −0.290627 0.364435i
\(428\) 7.95979e10 + 3.83323e10i 0.114658 + 0.0552164i
\(429\) 2.80478e10 1.22885e11i 0.0399798 0.175163i
\(430\) 1.54690e11 + 6.77740e11i 0.218199 + 0.955994i
\(431\) −8.45733e11 + 4.07283e11i −1.18055 + 0.568524i −0.918072 0.396413i \(-0.870255\pi\)
−0.262481 + 0.964937i \(0.584541\pi\)
\(432\) −7.24283e11 3.48796e11i −1.00053 0.481832i
\(433\) −2.49063e11 1.09121e12i −0.340497 1.49181i −0.798028 0.602620i \(-0.794124\pi\)
0.457532 0.889193i \(-0.348734\pi\)
\(434\) −7.52373e11 −1.01796
\(435\) 3.25391e11 7.43673e11i 0.435717 0.995819i
\(436\) −2.42707e11 −0.321657
\(437\) 1.44861e10 + 6.34680e10i 0.0190014 + 0.0832507i
\(438\) 2.36016e11 + 1.13659e11i 0.306414 + 0.147561i
\(439\) 6.73661e11 3.24418e11i 0.865667 0.416883i 0.0522983 0.998632i \(-0.483345\pi\)
0.813369 + 0.581748i \(0.197631\pi\)
\(440\) −4.54234e10 1.99013e11i −0.0577754 0.253130i
\(441\) −6.57762e8 + 2.88185e9i −0.000828124 + 0.00362825i
\(442\) −2.50228e11 1.20503e11i −0.311842 0.150175i
\(443\) 3.80044e11 + 4.76560e11i 0.468832 + 0.587897i 0.958885 0.283796i \(-0.0915938\pi\)
−0.490052 + 0.871693i \(0.663022\pi\)
\(444\) −4.84071e10 6.07006e10i −0.0591134 0.0741259i
\(445\) −8.40580e11 + 4.04802e11i −1.01615 + 0.489354i
\(446\) 6.10838e11 7.65967e11i 0.731003 0.916649i
\(447\) −4.39051e11 −0.520153
\(448\) 3.85445e11 4.83333e11i 0.452076 0.566885i
\(449\) 1.14764e11 5.02816e11i 0.133260 0.583849i −0.863566 0.504236i \(-0.831774\pi\)
0.996826 0.0796134i \(-0.0253686\pi\)
\(450\) −1.61088e9 + 7.05773e9i −0.00185185 + 0.00811350i
\(451\) 1.55143e11 1.94543e11i 0.176579 0.221422i
\(452\) 2.53243e11 0.285374
\(453\) −8.15507e11 + 1.02261e12i −0.909884 + 1.14096i
\(454\) −9.26371e10 + 4.46117e10i −0.102337 + 0.0492830i
\(455\) 3.65001e11 + 4.57697e11i 0.399248 + 0.500641i
\(456\) 9.60195e11 + 1.20405e12i 1.03996 + 1.30407i
\(457\) −6.71234e11 3.23249e11i −0.719865 0.346669i 0.0378240 0.999284i \(-0.487957\pi\)
−0.757689 + 0.652616i \(0.773672\pi\)
\(458\) 2.35220e9 1.03057e10i 0.00249793 0.0109441i
\(459\) 1.05415e11 + 4.61853e11i 0.110852 + 0.485676i
\(460\) −8.80832e9 + 4.24186e9i −0.00917239 + 0.00441719i
\(461\) −8.37659e11 4.03395e11i −0.863800 0.415984i −0.0511188 0.998693i \(-0.516279\pi\)
−0.812681 + 0.582708i \(0.801993\pi\)
\(462\) 7.31676e10 + 3.20568e11i 0.0747188 + 0.327365i
\(463\) 1.56011e12 1.57776 0.788882 0.614545i \(-0.210660\pi\)
0.788882 + 0.614545i \(0.210660\pi\)
\(464\) 8.83438e11 7.58646e11i 0.884800 0.759816i
\(465\) −9.92729e11 −0.984674
\(466\) −2.98169e11 1.30636e12i −0.292904 1.28330i
\(467\) −1.58888e12 7.65166e11i −1.54585 0.744440i −0.549972 0.835183i \(-0.685362\pi\)
−0.995874 + 0.0907428i \(0.971076\pi\)
\(468\) −1.02441e10 + 4.93328e9i −0.00987110 + 0.00475367i
\(469\) −1.58150e11 6.92901e11i −0.150936 0.661293i
\(470\) −3.35677e11 + 1.47070e12i −0.317308 + 1.39022i
\(471\) 4.08832e11 + 1.96883e11i 0.382781 + 0.184338i
\(472\) 6.72985e11 + 8.43896e11i 0.624117 + 0.782618i
\(473\) 1.66290e11 + 2.08521e11i 0.152753 + 0.191547i
\(474\) 6.61695e10 3.18655e10i 0.0602081 0.0289947i
\(475\) −1.11436e11 + 1.39736e11i −0.100439 + 0.125947i
\(476\) 1.26060e11 0.112550
\(477\) −1.06469e10 + 1.33508e10i −0.00941655 + 0.0118080i
\(478\) −4.51595e9 + 1.97857e10i −0.00395661 + 0.0173350i
\(479\) −1.54282e10 + 6.75955e10i −0.0133908 + 0.0586689i −0.981182 0.193086i \(-0.938150\pi\)
0.967791 + 0.251755i \(0.0810076\pi\)
\(480\) −3.26877e11 + 4.09891e11i −0.281060 + 0.352438i
\(481\) −3.04798e11 −0.259633
\(482\) −9.23006e11 + 1.15741e12i −0.778920 + 0.976735i
\(483\) −5.31691e10 + 2.56049e10i −0.0444526 + 0.0214072i
\(484\) −1.45525e11 1.82482e11i −0.120540 0.151153i
\(485\) 1.34649e12 + 1.68844e12i 1.10501 + 1.38563i
\(486\) 2.10362e11 + 1.01305e11i 0.171043 + 0.0823699i
\(487\) 2.41324e11 1.05731e12i 0.194411 0.851769i −0.779782 0.626051i \(-0.784670\pi\)
0.974193 0.225718i \(-0.0724728\pi\)
\(488\) −1.10510e11 4.84177e11i −0.0882090 0.386469i
\(489\) −6.71621e11 + 3.23436e11i −0.531171 + 0.255798i
\(490\) −5.67522e10 2.73304e10i −0.0444734 0.0214172i
\(491\) 3.14539e11 + 1.37809e12i 0.244235 + 1.07006i 0.937118 + 0.349014i \(0.113483\pi\)
−0.692882 + 0.721051i \(0.743659\pi\)
\(492\) −2.81920e11 −0.216911
\(493\) −6.74122e11 1.28284e11i −0.513958 0.0978053i
\(494\) −1.61337e12 −1.21889
\(495\) 7.68650e9 + 3.36767e10i 0.00575447 + 0.0252120i
\(496\) −1.28308e12 6.17896e11i −0.951885 0.458404i
\(497\) 1.85593e12 8.93767e11i 1.36445 0.657083i
\(498\) 5.37859e11 + 2.35651e12i 0.391865 + 1.71687i
\(499\) 3.31976e11 1.45448e12i 0.239693 1.05016i −0.701600 0.712571i \(-0.747531\pi\)
0.941293 0.337591i \(-0.109612\pi\)
\(500\) 2.52399e11 + 1.21549e11i 0.180602 + 0.0869732i
\(501\) −1.41181e12 1.77035e12i −1.00116 1.25542i
\(502\) 1.41595e12 + 1.77555e12i 0.995136 + 1.24786i
\(503\) 1.45240e12 6.99440e11i 1.01165 0.487186i 0.146775 0.989170i \(-0.453111\pi\)
0.864877 + 0.501984i \(0.167396\pi\)
\(504\) −6.93009e10 + 8.69006e10i −0.0478411 + 0.0599909i
\(505\) 1.97070e12 1.34837
\(506\) −1.34409e10 + 1.68543e10i −0.00911487 + 0.0114297i
\(507\) 2.20329e11 9.65323e11i 0.148093 0.648839i
\(508\) −5.40262e9 + 2.36704e10i −0.00359930 + 0.0157696i
\(509\) 8.35610e11 1.04782e12i 0.551790 0.691922i −0.425227 0.905087i \(-0.639806\pi\)
0.977016 + 0.213165i \(0.0683771\pi\)
\(510\) 9.55968e11 0.625717
\(511\) −2.91034e11 + 3.64945e11i −0.188821 + 0.236774i
\(512\) 7.41473e11 3.57075e11i 0.476849 0.229638i
\(513\) 1.71581e12 + 2.15156e12i 1.09381 + 1.37159i
\(514\) 9.83498e11 + 1.23327e12i 0.621497 + 0.779333i
\(515\) −1.40311e12 6.75702e11i −0.878940 0.423275i
\(516\) 6.72403e10 2.94599e11i 0.0417548 0.182940i
\(517\) 1.28786e11 + 5.64247e11i 0.0792793 + 0.347345i
\(518\) 7.16378e11 3.44990e11i 0.437178 0.210534i
\(519\) −1.10109e12 5.30259e11i −0.666149 0.320800i
\(520\) 2.02039e11 + 8.85189e11i 0.121177 + 0.530910i
\(521\) −3.86404e11 −0.229758 −0.114879 0.993379i \(-0.536648\pi\)
−0.114879 + 0.993379i \(0.536648\pi\)
\(522\) −1.22494e11 + 1.05191e11i −0.0722100 + 0.0620098i
\(523\) −1.89083e11 −0.110508 −0.0552542 0.998472i \(-0.517597\pi\)
−0.0552542 + 0.998472i \(0.517597\pi\)
\(524\) 8.66338e9 + 3.79568e10i 0.00501992 + 0.0219937i
\(525\) −1.45973e11 7.02970e10i −0.0838603 0.0403850i
\(526\) −2.47548e12 + 1.19213e12i −1.41002 + 0.679029i
\(527\) 1.86743e11 + 8.18177e11i 0.105462 + 0.462061i
\(528\) −1.38493e11 + 6.06778e11i −0.0775489 + 0.339764i
\(529\) 1.61930e12 + 7.79812e11i 0.899034 + 0.432952i
\(530\) −2.26881e11 2.84500e11i −0.124899 0.156618i
\(531\) −1.13882e11 1.42803e11i −0.0621625 0.0779493i
\(532\) 6.59775e11 3.17731e11i 0.357103 0.171972i
\(533\) −6.90060e11 + 8.65308e11i −0.370352 + 0.464407i
\(534\) 2.33081e12 1.24043
\(535\) −7.44340e11 + 9.33372e11i −0.392807 + 0.492564i
\(536\) 2.45284e11 1.07466e12i 0.128359 0.562378i
\(537\) 1.76823e11 7.74711e11i 0.0917600 0.402027i
\(538\) −8.33942e11 + 1.04573e12i −0.429156 + 0.538145i
\(539\) −2.41668e10 −0.0123330
\(540\) −2.57674e11 + 3.23114e11i −0.130407 + 0.163525i
\(541\) −5.06836e11 + 2.44079e11i −0.254378 + 0.122502i −0.556728 0.830695i \(-0.687943\pi\)
0.302350 + 0.953197i \(0.402229\pi\)
\(542\) −2.21368e12 2.77587e12i −1.10184 1.38166i
\(543\) −5.11888e9 6.41888e9i −0.00252683 0.00316855i
\(544\) 3.99308e11 + 1.92297e11i 0.195485 + 0.0941406i
\(545\) 7.29799e11 3.19746e12i 0.354339 1.55246i
\(546\) −3.25442e11 1.42585e12i −0.156714 0.686607i
\(547\) −3.61209e11 + 1.73949e11i −0.172511 + 0.0830768i −0.518146 0.855292i \(-0.673378\pi\)
0.345635 + 0.938369i \(0.387663\pi\)
\(548\) 1.77156e11 + 8.53138e10i 0.0839157 + 0.0404117i
\(549\) 1.87004e10 + 8.19318e10i 0.00878568 + 0.0384926i
\(550\) −5.91851e10 −0.0275791
\(551\) −3.85158e12 + 1.02769e12i −1.78015 + 0.474986i
\(552\) −9.15268e10 −0.0419587
\(553\) 2.91207e10 + 1.27586e11i 0.0132416 + 0.0580150i
\(554\) −2.18974e11 1.05452e11i −0.0987639 0.0475622i
\(555\) 9.45235e11 4.55201e11i 0.422884 0.203650i
\(556\) −1.46627e11 6.42417e11i −0.0650697 0.285089i
\(557\) −2.76236e11 + 1.21027e12i −0.121600 + 0.532763i 0.877030 + 0.480435i \(0.159521\pi\)
−0.998630 + 0.0523280i \(0.983336\pi\)
\(558\) 1.77906e11 + 8.56750e10i 0.0776849 + 0.0374111i
\(559\) −7.39640e11 9.27479e11i −0.320381 0.401746i
\(560\) −1.80229e12 2.25999e12i −0.774422 0.971094i
\(561\) 3.30445e11 1.59134e11i 0.140853 0.0678313i
\(562\) −8.21146e11 + 1.02969e12i −0.347222 + 0.435403i
\(563\) −3.70658e12 −1.55484 −0.777421 0.628981i \(-0.783472\pi\)
−0.777421 + 0.628981i \(0.783472\pi\)
\(564\) 4.08835e11 5.12663e11i 0.170135 0.213342i
\(565\) −7.61478e11 + 3.33626e12i −0.314369 + 1.37734i
\(566\) 5.07917e11 2.22533e12i 0.208027 0.911424i
\(567\) −1.69095e12 + 2.12038e12i −0.687078 + 0.861569i
\(568\) 3.19484e12 1.28790
\(569\) 1.41927e12 1.77971e12i 0.567623 0.711777i −0.412323 0.911038i \(-0.635283\pi\)
0.979947 + 0.199261i \(0.0638541\pi\)
\(570\) 5.00337e12 2.40950e12i 1.98530 0.956070i
\(571\) −1.72209e12 2.15943e12i −0.677943 0.850113i 0.317220 0.948352i \(-0.397251\pi\)
−0.995163 + 0.0982386i \(0.968679\pi\)
\(572\) −5.79578e10 7.26768e10i −0.0226376 0.0283866i
\(573\) −2.12852e12 1.02504e12i −0.824865 0.397234i
\(574\) 6.42464e11 2.81482e12i 0.247028 1.08230i
\(575\) −2.36366e9 1.03559e10i −0.000901736 0.00395077i
\(576\) −1.46181e11 + 7.03970e10i −0.0553337 + 0.0266473i
\(577\) −3.66122e12 1.76315e12i −1.37510 0.662213i −0.407151 0.913361i \(-0.633478\pi\)
−0.967949 + 0.251147i \(0.919192\pi\)
\(578\) 4.77155e11 + 2.09055e12i 0.177821 + 0.779086i
\(579\) 3.48654e12 1.28926
\(580\) −2.79175e11 5.29571e11i −0.102436 0.194311i
\(581\) −4.30706e12 −1.56815
\(582\) −1.20055e12 5.25998e12i −0.433739 1.90034i
\(583\) −1.25784e11 6.05743e10i −0.0450938 0.0217160i
\(584\) −6.52264e11 + 3.14114e11i −0.232041 + 0.111745i
\(585\) −3.41887e10 1.49791e11i −0.0120693 0.0528790i
\(586\) −1.27712e12 + 5.59544e12i −0.447397 + 1.96018i
\(587\) −7.63810e11 3.67832e11i −0.265530 0.127873i 0.296382 0.955069i \(-0.404220\pi\)
−0.561912 + 0.827197i \(0.689934\pi\)
\(588\) 1.70715e10 + 2.14069e10i 0.00588942 + 0.00738510i
\(589\) 3.03958e12 + 3.81151e12i 1.04063 + 1.30490i
\(590\) 3.50678e12 1.68878e12i 1.19145 0.573770i
\(591\) −1.89642e12 + 2.37803e12i −0.639426 + 0.801814i
\(592\) 1.50502e12 0.503610
\(593\) −5.14697e11 + 6.45409e11i −0.170925 + 0.214333i −0.859914 0.510438i \(-0.829483\pi\)
0.688990 + 0.724771i \(0.258055\pi\)
\(594\) −2.02782e11 + 8.88444e11i −0.0668328 + 0.292813i
\(595\) −3.79051e11 + 1.66073e12i −0.123986 + 0.543216i
\(596\) −2.01883e11 + 2.53153e11i −0.0655377 + 0.0821816i
\(597\) 5.08406e12 1.63805
\(598\) 5.97837e10 7.49663e10i 0.0191173 0.0239724i
\(599\) 5.09347e12 2.45289e12i 1.61657 0.778497i 0.616604 0.787274i \(-0.288508\pi\)
0.999961 + 0.00877683i \(0.00279379\pi\)
\(600\) −1.56672e11 1.96461e11i −0.0493527 0.0618863i
\(601\) −1.17370e12 1.47177e12i −0.366962 0.460156i 0.563730 0.825959i \(-0.309366\pi\)
−0.930692 + 0.365803i \(0.880794\pi\)
\(602\) 2.78818e12 + 1.34272e12i 0.865241 + 0.416678i
\(603\) −4.15066e10 + 1.81852e11i −0.0127847 + 0.0560133i
\(604\) 2.14647e11 + 9.40429e11i 0.0656233 + 0.287514i
\(605\) 2.84163e12 1.36846e12i 0.862319 0.415271i
\(606\) −4.43576e12 2.13615e12i −1.33611 0.643435i
\(607\) 1.25226e12 + 5.48653e12i 0.374409 + 1.64039i 0.714235 + 0.699906i \(0.246775\pi\)
−0.339825 + 0.940489i \(0.610368\pi\)
\(608\) 2.57459e12 0.764086
\(609\) −1.68517e12 3.19661e12i −0.496438 0.941699i
\(610\) −1.79083e12 −0.523685
\(611\) −5.72825e11 2.50971e12i −0.166279 0.728514i
\(612\) −2.98081e10 1.43548e10i −0.00858919 0.00413634i
\(613\) 2.46504e12 1.18710e12i 0.705103 0.339560i −0.0467355 0.998907i \(-0.514882\pi\)
0.751838 + 0.659348i \(0.229167\pi\)
\(614\) 1.20601e12 + 5.28386e12i 0.342446 + 1.50035i
\(615\) 8.47708e11 3.71405e12i 0.238951 1.04691i
\(616\) −8.18728e11 3.94279e11i −0.229101 0.110329i
\(617\) 2.96829e12 + 3.72211e12i 0.824560 + 1.03397i 0.998786 + 0.0492601i \(0.0156863\pi\)
−0.174226 + 0.984706i \(0.555742\pi\)
\(618\) 2.42577e12 + 3.04182e12i 0.668962 + 0.838852i
\(619\) 5.31947e12 2.56172e12i 1.45633 0.701332i 0.472650 0.881250i \(-0.343298\pi\)
0.983682 + 0.179918i \(0.0575833\pi\)
\(620\) −4.56473e11 + 5.72399e11i −0.124066 + 0.155574i
\(621\) −1.63553e11 −0.0441313
\(622\) −4.50135e12 + 5.64452e12i −1.20583 + 1.51206i
\(623\) −9.24190e11 + 4.04914e12i −0.245791 + 1.07688i
\(624\) 6.16003e11 2.69888e12i 0.162649 0.712613i
\(625\) −2.56820e12 + 3.22042e12i −0.673238 + 0.844214i
\(626\) −5.01388e12 −1.30494
\(627\) 1.32840e12 1.66576e12i 0.343261 0.430436i
\(628\) 3.01508e11 1.45199e11i 0.0773537 0.0372516i
\(629\) −5.52972e11 6.93406e11i −0.140856 0.176628i
\(630\) 2.49898e11 + 3.13362e11i 0.0632018 + 0.0792526i
\(631\) −6.41598e11 3.08978e11i −0.161113 0.0775880i 0.351589 0.936154i \(-0.385641\pi\)
−0.512703 + 0.858566i \(0.671356\pi\)
\(632\) −4.51649e10 + 1.97880e11i −0.0112609 + 0.0493373i
\(633\) 9.32273e10 + 4.08455e11i 0.0230795 + 0.101118i
\(634\) −4.64780e12 + 2.23826e12i −1.14247 + 0.550186i
\(635\) −2.95593e11 1.42350e11i −0.0721459 0.0347436i
\(636\) 3.51972e10 + 1.54209e11i 0.00853005 + 0.0373726i
\(637\) 1.07491e11 0.0258670
\(638\) −1.06128e12 7.84986e11i −0.253594 0.187572i
\(639\) −5.40628e11 −0.128276
\(640\) −1.17780e12 5.16027e12i −0.277499 1.21580i
\(641\) 4.19555e12 + 2.02047e12i 0.981585 + 0.472706i 0.854650 0.519205i \(-0.173772\pi\)
0.126935 + 0.991911i \(0.459486\pi\)
\(642\) 2.68714e12 1.29406e12i 0.624284 0.300639i
\(643\) 1.63514e12 + 7.16400e12i 0.377229 + 1.65275i 0.705907 + 0.708305i \(0.250540\pi\)
−0.328678 + 0.944442i \(0.606603\pi\)
\(644\) −9.68445e9 + 4.24304e10i −0.00221865 + 0.00972054i
\(645\) 3.67891e12 + 1.77167e12i 0.836951 + 0.403055i
\(646\) −2.92703e12 3.67037e12i −0.661272 0.829209i
\(647\) −1.39822e12 1.75332e12i −0.313695 0.393361i 0.599841 0.800119i \(-0.295231\pi\)
−0.913536 + 0.406758i \(0.866659\pi\)
\(648\) −3.78974e12 + 1.82504e12i −0.844349 + 0.406617i
\(649\) 9.31053e11 1.16750e12i 0.206003 0.258319i
\(650\) 2.63249e11 0.0578438
\(651\) −2.75538e12 + 3.45513e12i −0.601266 + 0.753964i
\(652\) −1.22332e11 + 5.35972e11i −0.0265110 + 0.116152i
\(653\) −6.77892e11 + 2.97004e12i −0.145899 + 0.639223i 0.848101 + 0.529835i \(0.177746\pi\)
−0.993999 + 0.109388i \(0.965111\pi\)
\(654\) −5.10858e12 + 6.40595e12i −1.09194 + 1.36925i
\(655\) −5.26098e11 −0.111681
\(656\) 3.40735e12 4.27268e12i 0.718372 0.900810i
\(657\) 1.10375e11 5.31540e10i 0.0231115 0.0111299i
\(658\) 4.18698e12 + 5.25031e12i 0.870732 + 1.09186i
\(659\) −2.64124e12 3.31201e12i −0.545537 0.684081i 0.430274 0.902698i \(-0.358417\pi\)
−0.975811 + 0.218617i \(0.929846\pi\)
\(660\) 2.88277e11 + 1.38827e11i 0.0591374 + 0.0284791i
\(661\) 9.48376e11 4.15511e12i 0.193230 0.846595i −0.781624 0.623750i \(-0.785608\pi\)
0.974854 0.222845i \(-0.0715345\pi\)
\(662\) −2.15366e12 9.43582e12i −0.435830 1.90950i
\(663\) −1.46979e12 + 7.07811e11i −0.295422 + 0.142268i
\(664\) −6.01851e12 2.89836e12i −1.20152 0.578624i
\(665\) 2.20195e12 + 9.64737e12i 0.436626 + 1.91298i
\(666\) −2.08680e11 −0.0411004
\(667\) 9.49681e10 2.17047e11i 0.0185785 0.0424607i
\(668\) −1.66994e12 −0.324494
\(669\) −1.28052e12 5.61032e12i −0.247155 1.08286i
\(670\) −3.58122e12 1.72462e12i −0.686584 0.330642i
\(671\) −6.19028e11 + 2.98108e11i −0.117885 + 0.0567705i
\(672\) 5.19334e11 + 2.27535e12i 0.0982392 + 0.430414i
\(673\) 1.29681e12 5.68168e12i 0.243673 1.06760i −0.693971 0.720003i \(-0.744140\pi\)
0.937644 0.347597i \(-0.113002\pi\)
\(674\) −3.96647e12 1.91015e12i −0.740346 0.356532i
\(675\) −2.79964e11 3.51064e11i −0.0519081 0.0650907i
\(676\) −4.55286e11 5.70911e11i −0.0838541 0.105150i
\(677\) 2.86794e12 1.38113e12i 0.524712 0.252688i −0.152725 0.988269i \(-0.548805\pi\)
0.677437 + 0.735581i \(0.263091\pi\)
\(678\) 5.33033e12 6.68402e12i 0.968769 1.21480i
\(679\) 9.61378e12 1.73572
\(680\) −1.64723e12 + 2.06556e12i −0.295437 + 0.370466i
\(681\) −1.34389e11 + 5.88798e11i −0.0239443 + 0.104907i
\(682\) −3.59229e11 + 1.57389e12i −0.0635832 + 0.278576i
\(683\) −1.96814e12 + 2.46797e12i −0.346070 + 0.433958i −0.924154 0.382019i \(-0.875229\pi\)
0.578085 + 0.815977i \(0.303800\pi\)
\(684\) −1.92191e11 −0.0335723
\(685\) −1.65663e12 + 2.07735e12i −0.287487 + 0.360497i
\(686\) 5.61986e12 2.70638e12i 0.968873 0.466585i
\(687\) −3.87125e10 4.85440e10i −0.00663050 0.00831438i
\(688\) 3.65216e12 + 4.57967e12i 0.621444 + 0.779266i
\(689\) 5.59474e11 + 2.69428e11i 0.0945787 + 0.0455467i
\(690\) −7.34416e10 + 3.21769e11i −0.0123345 + 0.0540409i
\(691\) −4.53690e11 1.98775e12i −0.0757022 0.331673i 0.922869 0.385114i \(-0.125838\pi\)
−0.998571 + 0.0534416i \(0.982981\pi\)
\(692\) −8.12044e11 + 3.91060e11i −0.134618 + 0.0648284i
\(693\) 1.38544e11 + 6.67194e10i 0.0228186 + 0.0109889i
\(694\) 1.87613e12 + 8.21984e12i 0.307004 + 1.34507i
\(695\) 8.90419e12 1.44765
\(696\) −2.03678e11 5.60083e12i −0.0329005 0.904713i
\(697\) −3.22047e12 −0.516859
\(698\) 2.38063e12 + 1.04302e13i 0.379615 + 1.66320i
\(699\) −7.09121e12 3.41495e12i −1.12350 0.541049i
\(700\) −1.07653e11 + 5.18432e10i −0.0169468 + 0.00816113i
\(701\) −1.12337e12 4.92179e12i −0.175707 0.769825i −0.983581 0.180469i \(-0.942239\pi\)
0.807873 0.589356i \(-0.200619\pi\)
\(702\) 9.01951e11 3.95171e12i 0.140174 0.614140i
\(703\) −4.64188e12 2.23541e12i −0.716795 0.345190i
\(704\) −8.27048e11 1.03708e12i −0.126898 0.159125i
\(705\) 5.52457e12 + 6.92759e12i 0.842263 + 1.05616i
\(706\) 9.94339e12 4.78848e12i 1.50631 0.725399i
\(707\) 5.46979e12 6.85889e12i 0.823347 1.03244i
\(708\) −1.69187e12 −0.253057
\(709\) 3.30021e12 4.13833e12i 0.490494 0.615060i −0.473562 0.880761i \(-0.657032\pi\)
0.964056 + 0.265701i \(0.0856034\pi\)
\(710\) 2.56356e12 1.12317e13i 0.378600 1.65876i
\(711\) 7.64275e9 3.34851e10i 0.00112160 0.00491403i
\(712\) −4.01623e12 + 5.03619e12i −0.585678 + 0.734417i
\(713\) −2.89736e11 −0.0419855
\(714\) 2.65335e12 3.32719e12i 0.382078 0.479111i
\(715\) 1.13173e12 5.45012e11i 0.161944 0.0779882i
\(716\) −3.65385e11 4.58179e11i −0.0519568 0.0651518i
\(717\) 7.43235e10 + 9.31987e10i 0.0105024 + 0.0131696i
\(718\) −2.96822e12 1.42942e12i −0.416809 0.200724i
\(719\) −3.72990e11 + 1.63418e12i −0.0520496 + 0.228044i −0.994262 0.106972i \(-0.965885\pi\)
0.942212 + 0.335016i \(0.108742\pi\)
\(720\) 1.68816e11 + 7.39630e11i 0.0234108 + 0.102569i
\(721\) −6.24616e12 + 3.00799e12i −0.860804 + 0.414541i
\(722\) −1.73324e13 8.34683e12i −2.37378 1.14315i
\(723\) 1.93493e12 + 8.47747e12i 0.263355 + 1.15384i
\(724\) −6.05481e9 −0.000818988
\(725\) 6.28450e11 1.67685e11i 0.0844792 0.0225411i
\(726\) −7.87944e12 −1.05264
\(727\) −3.30792e12 1.44929e13i −0.439188 1.92421i −0.377205 0.926130i \(-0.623115\pi\)
−0.0619827 0.998077i \(-0.519742\pi\)
\(728\) 3.64162e12 + 1.75371e12i 0.480511 + 0.231402i
\(729\) −6.17772e12 + 2.97503e12i −0.810129 + 0.390138i
\(730\) 5.80908e11 + 2.54513e12i 0.0757102 + 0.331708i
\(731\) 7.68111e11 3.36531e12i 0.0994938 0.435911i
\(732\) 7.01347e11 + 3.37751e11i 0.0902886 + 0.0434807i
\(733\) 4.63991e11 + 5.81826e11i 0.0593665 + 0.0744432i 0.810628 0.585561i \(-0.199126\pi\)
−0.751262 + 0.660004i \(0.770554\pi\)
\(734\) −5.94864e12 7.45936e12i −0.756459 0.948570i
\(735\) −3.33350e11 + 1.60533e11i −0.0421316 + 0.0202895i
\(736\) −9.54016e10 + 1.19630e11i −0.0119841 + 0.0150276i
\(737\) −1.52499e12 −0.190398
\(738\) −4.72449e11 + 5.92432e11i −0.0586275 + 0.0735166i
\(739\) −8.35869e11 + 3.66218e12i −0.103095 + 0.451689i 0.896861 + 0.442313i \(0.145842\pi\)
−0.999956 + 0.00937658i \(0.997015\pi\)
\(740\) 1.72169e11 7.54323e11i 0.0211064 0.0924730i
\(741\) −5.90858e12 + 7.40913e12i −0.719948 + 0.902787i
\(742\) −1.61991e12 −0.196188
\(743\) −2.74848e12 + 3.44649e12i −0.330859 + 0.414884i −0.919239 0.393701i \(-0.871195\pi\)
0.588380 + 0.808585i \(0.299766\pi\)
\(744\) −6.17533e12 + 2.97388e12i −0.738894 + 0.355833i
\(745\) −2.72803e12 3.42084e12i −0.324449 0.406846i
\(746\) 9.91932e12 + 1.24384e13i 1.17262 + 1.47042i
\(747\) 1.01845e12 + 4.90457e11i 0.119673 + 0.0576313i
\(748\) 6.01887e10 2.63704e11i 0.00703004 0.0308006i
\(749\) 1.18259e12 + 5.18126e12i 0.137298 + 0.601544i
\(750\) 8.52069e12 4.10335e12i 0.983330 0.473547i
\(751\) −1.03752e13 4.99643e12i −1.19019 0.573165i −0.269326 0.963049i \(-0.586801\pi\)
−0.920864 + 0.389884i \(0.872515\pi\)
\(752\) 2.82847e12 + 1.23923e13i 0.322531 + 1.41310i
\(753\) 1.33395e13 1.51203
\(754\) 4.72048e12 + 3.49154e12i 0.531882 + 0.393410i
\(755\) −1.30348e13 −1.45996
\(756\) 4.09387e11 + 1.79364e12i 0.0455812 + 0.199704i
\(757\) −1.61823e12 7.79300e11i −0.179106 0.0862528i 0.342182 0.939634i \(-0.388834\pi\)
−0.521288 + 0.853381i \(0.674548\pi\)
\(758\) 1.57114e13 7.56619e12i 1.72863 0.832465i
\(759\) 2.81766e10 + 1.23450e11i 0.00308177 + 0.0135021i
\(760\) −3.41512e12 + 1.49626e13i −0.371317 + 1.62685i
\(761\) 1.43307e12 + 6.90129e11i 0.154894 + 0.0745933i 0.509725 0.860337i \(-0.329747\pi\)
−0.354831 + 0.934931i \(0.615461\pi\)
\(762\) 5.11036e11 + 6.40818e11i 0.0549103 + 0.0688553i
\(763\) −9.10297e12 1.14148e13i −0.972350 1.21929i
\(764\) −1.56976e12 + 7.55957e11i −0.166692 + 0.0802744i
\(765\) 2.78743e11 3.49532e11i 0.0294257 0.0368987i
\(766\) 1.41058e13 1.48036
\(767\) −4.14122e12 + 5.19293e12i −0.432066 + 0.541793i
\(768\) −1.35483e12 + 5.93588e12i −0.140526 + 0.615686i
\(769\) 5.41287e11 2.37153e12i 0.0558161 0.244546i −0.939322 0.343037i \(-0.888544\pi\)
0.995138 + 0.0984908i \(0.0314015\pi\)
\(770\) −2.04307e12 + 2.56192e12i −0.209447 + 0.262638i
\(771\) 9.26537e12 0.944317
\(772\) 1.60317e12 2.01031e12i 0.162443 0.203697i
\(773\) 1.62740e13 7.83715e12i 1.63941 0.789497i 0.639624 0.768688i \(-0.279090\pi\)
0.999783 0.0208085i \(-0.00662402\pi\)
\(774\) −5.06394e11 6.34998e11i −0.0507171 0.0635972i
\(775\) −4.95959e11 6.21913e11i −0.0493842 0.0619258i
\(776\) 1.34339e13 + 6.46944e12i 1.32992 + 0.640455i
\(777\) 1.03925e12 4.55327e12i 0.102289 0.448156i
\(778\) 2.57742e12 + 1.12924e13i 0.252218 + 1.10504i
\(779\) −1.68554e13 + 8.11713e12i −1.63991 + 0.789740i
\(780\) −1.28223e12 6.17488e11i −0.124034 0.0597314i
\(781\) −9.83535e11 4.30915e12i −0.0945932 0.414440i
\(782\) 2.79007e11 0.0266799
\(783\) −3.63961e11 1.00084e13i −0.0346040 0.951557i
\(784\) −5.30766e11 −0.0501742
\(785\) 1.00626e12 + 4.40872e12i 0.0945795 + 0.414380i
\(786\) 1.18417e12 + 5.70267e11i 0.110666 + 0.0532938i
\(787\) −1.28987e13 + 6.21170e12i −1.19856 + 0.577197i −0.923266 0.384162i \(-0.874490\pi\)
−0.275296 + 0.961359i \(0.588776\pi\)
\(788\) 4.99149e11 + 2.18691e12i 0.0461171 + 0.202052i
\(789\) −3.59120e12 + 1.57341e13i −0.329908 + 1.44542i
\(790\) 6.59421e11 + 3.17560e11i 0.0602339 + 0.0290071i
\(791\) 9.49811e12 + 1.19103e13i 0.862667 + 1.08175i
\(792\) 1.48699e11 + 1.86462e11i 0.0134290 + 0.0168394i
\(793\) 2.75337e12 1.32595e12i 0.247250 0.119069i
\(794\) 1.24638e12 1.56291e12i 0.111291 0.139554i
\(795\) −2.13741e12 −0.189774
\(796\) 2.33774e12 2.93143e12i 0.206389 0.258804i
\(797\) −2.66676e12 + 1.16838e13i −0.234111 + 1.02571i 0.712080 + 0.702098i \(0.247753\pi\)
−0.946191 + 0.323609i \(0.895104\pi\)
\(798\) 5.50104e12 2.41017e13i 0.480211 2.10394i
\(799\) 4.67028e12 5.85634e12i 0.405398 0.508353i
\(800\) −4.20088e11 −0.0362607
\(801\) 6.79622e11 8.52219e11i 0.0583339 0.0731484i
\(802\) 3.69052e12 1.77726e12i 0.314995 0.151693i
\(803\) 6.24471e11 + 7.83061e11i 0.0530020 + 0.0664624i
\(804\) 1.07726e12 + 1.35084e12i 0.0909215 + 0.114012i
\(805\) −5.29864e11 2.55169e11i −0.0444716 0.0214164i
\(806\) 1.59781e12 7.00048e12i 0.133358 0.584279i
\(807\) 1.74822e12 + 7.65945e12i 0.145099 + 0.635721i
\(808\) 1.22588e13 5.90355e12i 1.01181 0.487261i
\(809\) 1.51717e13 + 7.30631e12i 1.24528 + 0.599694i 0.936242 0.351356i \(-0.114279\pi\)
0.309036 + 0.951050i \(0.399994\pi\)
\(810\) 3.37515e12 + 1.47875e13i 0.275493 + 1.20701i
\(811\) −1.52231e13 −1.23569 −0.617843 0.786301i \(-0.711993\pi\)
−0.617843 + 0.786301i \(0.711993\pi\)
\(812\) −2.61801e12 4.98202e11i −0.211334 0.0402164i
\(813\) −2.08547e13 −1.67416
\(814\) −3.79640e11 1.66331e12i −0.0303083 0.132789i
\(815\) −6.69313e12 3.22324e12i −0.531398 0.255908i
\(816\) 7.25744e12 3.49500e12i 0.573031 0.275957i
\(817\) −4.46204e12 1.95495e13i −0.350376 1.53510i
\(818\) 1.24062e12 5.43553e12i 0.0968836 0.424475i
\(819\) −6.16230e11 2.96761e11i −0.0478592 0.0230478i
\(820\) −1.75170e12 2.19656e12i −0.135300 0.169661i
\(821\) 3.55357e12 + 4.45604e12i 0.272974 + 0.342298i 0.899355 0.437218i \(-0.144036\pi\)
−0.626382 + 0.779516i \(0.715465\pi\)
\(822\) 5.98059e12 2.88010e12i 0.456900 0.220031i
\(823\) −8.65642e11 + 1.08548e12i −0.0657717 + 0.0824751i −0.813629 0.581384i \(-0.802511\pi\)
0.747857 + 0.663859i \(0.231083\pi\)
\(824\) −1.07523e13 −0.812512
\(825\) −2.16751e11 + 2.71797e11i −0.0162899 + 0.0204269i
\(826\) 3.85559e12 1.68924e13i 0.288191 1.26265i
\(827\) −1.07416e11 + 4.70620e11i −0.00798534 + 0.0349861i −0.978764 0.204992i \(-0.934283\pi\)
0.970778 + 0.239978i \(0.0771403\pi\)
\(828\) 7.12166e9 8.93028e9i 0.000526556 0.000660280i
\(829\) 2.02849e13 1.49168 0.745842 0.666123i \(-0.232048\pi\)
0.745842 + 0.666123i \(0.232048\pi\)
\(830\) −1.50187e13 + 1.88328e13i −1.09845 + 1.37741i
\(831\) −1.28621e12 + 6.19405e11i −0.0935635 + 0.0450578i
\(832\) 3.67862e12 + 4.61285e12i 0.266152 + 0.333744i
\(833\) 1.95013e11 + 2.44539e11i 0.0140334 + 0.0175973i
\(834\) −2.00421e13 9.65175e12i −1.43448 0.690810i
\(835\) 5.02136e12 2.20000e13i 0.357464 1.56615i
\(836\) −3.49643e11 1.53189e12i −0.0247569 0.108467i
\(837\) −1.10350e13 + 5.31416e12i −0.777153 + 0.374257i
\(838\) 1.90902e12 + 9.19336e11i 0.133725 + 0.0643985i
\(839\) −5.31977e12 2.33074e13i −0.370650 1.62392i −0.724956 0.688795i \(-0.758140\pi\)
0.354306 0.935130i \(-0.384717\pi\)
\(840\) −1.39124e13 −0.964152
\(841\) 1.34932e13 + 5.32841e12i 0.930104 + 0.367296i
\(842\) −5.30375e12 −0.363646
\(843\) 1.72140e12 + 7.54193e12i 0.117397 + 0.514350i
\(844\) 2.78379e11 + 1.34060e11i 0.0188841 + 0.00909409i
\(845\) 8.89027e12 4.28133e12i 0.599874 0.288884i
\(846\) −3.92184e11 1.71827e12i −0.0263223 0.115325i
\(847\) 3.12428e12 1.36883e13i 0.208581 0.913851i
\(848\) −2.76255e12 1.33037e12i −0.183454 0.0883470i
\(849\) −8.35930e12 1.04822e13i −0.552186 0.692419i
\(850\) 4.77594e11 + 5.98884e11i 0.0313815 + 0.0393511i
\(851\) 2.75875e11 1.32854e11i 0.0180314 0.00868345i
\(852\) −3.12227e12 + 3.91520e12i −0.202998 + 0.254552i
\(853\) 7.07680e12 0.457684 0.228842 0.973464i \(-0.426506\pi\)
0.228842 + 0.973464i \(0.426506\pi\)
\(854\) −4.97055e12 + 6.23288e12i −0.319775 + 0.400985i
\(855\) 5.77903e11 2.53196e12i 0.0369834 0.162035i
\(856\) −1.83414e12 + 8.03589e12i −0.116762 + 0.511567i
\(857\) 3.45261e12 4.32943e12i 0.218642 0.274168i −0.660399 0.750915i \(-0.729613\pi\)
0.879041 + 0.476747i \(0.158184\pi\)
\(858\) −3.13813e12 −0.197687
\(859\) −1.15271e13 + 1.44545e13i −0.722354 + 0.905804i −0.998469 0.0553211i \(-0.982382\pi\)
0.276114 + 0.961125i \(0.410953\pi\)
\(860\) 2.71315e12 1.30658e12i 0.169134 0.0814506i
\(861\) −1.05737e13 1.32590e13i −0.655710 0.822234i
\(862\) 1.45712e13 + 1.82717e13i 0.898903 + 1.12719i
\(863\) −5.27518e12 2.54039e12i −0.323734 0.155902i 0.264957 0.964260i \(-0.414642\pi\)
−0.588691 + 0.808358i \(0.700357\pi\)
\(864\) −1.43932e12 + 6.30606e12i −0.0878708 + 0.384987i
\(865\) −2.71013e12 1.18739e13i −0.164596 0.721140i
\(866\) −2.51067e13 + 1.20908e13i −1.51691 + 0.730505i
\(867\) 1.13479e13 + 5.46488e12i 0.682073 + 0.328469i
\(868\) 7.25233e11 + 3.17745e12i 0.0433649 + 0.189994i
\(869\) 2.80801e11 0.0167036
\(870\) −1.98535e13 3.77809e12i −1.17490 0.223581i
\(871\) 6.78299e12 0.399337
\(872\) −5.03876e12 2.20762e13i −0.295120 1.29301i
\(873\) −2.27327e12 1.09475e12i −0.132461 0.0637898i
\(874\) 1.46028e12 7.03232e11i 0.0846512 0.0407659i
\(875\) 3.74990e12 + 1.64294e13i 0.216263 + 0.947512i
\(876\) 2.52509e11 1.10631e12i 0.0144880 0.0634759i
\(877\) 1.86265e13 + 8.97006e12i 1.06325 + 0.512032i 0.881924 0.471392i \(-0.156248\pi\)
0.181321 + 0.983424i \(0.441963\pi\)
\(878\) −1.16066e13 1.45542e13i −0.659141 0.826537i
\(879\) 2.10189e13 + 2.63569e13i 1.18757 + 1.48917i
\(880\) −5.58820e12 + 2.69114e12i −0.314123 + 0.151274i
\(881\) −1.67973e13 + 2.10631e13i −0.939393 + 1.17796i 0.0444650 + 0.999011i \(0.485842\pi\)
−0.983858 + 0.178951i \(0.942730\pi\)
\(882\) 7.35938e10 0.00409480
\(883\) −6.34089e10 + 7.95122e10i −0.00351016 + 0.00440160i −0.783583 0.621287i \(-0.786610\pi\)
0.780073 + 0.625688i \(0.215182\pi\)
\(884\) −2.67713e11 + 1.17293e12i −0.0147447 + 0.0646006i
\(885\) 5.08731e12 2.22890e13i 0.278768 1.22136i
\(886\) 9.46188e12 1.18648e13i 0.515852 0.646858i
\(887\) −1.94333e13 −1.05412 −0.527061 0.849827i \(-0.676706\pi\)
−0.527061 + 0.849827i \(0.676706\pi\)
\(888\) 4.51627e12 5.66322e12i 0.243737 0.305636i
\(889\) −1.31588e12 + 6.33692e11i −0.0706573 + 0.0340267i
\(890\) 1.44824e13 + 1.81604e13i 0.773725 + 0.970221i
\(891\) 3.62826e12 + 4.54969e12i 0.192863 + 0.241842i
\(892\) −3.82367e12 1.84138e12i −0.202227 0.0973872i
\(893\) 9.68264e12 4.24224e13i 0.509521 2.23236i
\(894\) 2.43237e12 + 1.06569e13i 0.127353 + 0.557971i
\(895\) 7.13480e12 3.43594e12i 0.371688 0.178995i
\(896\) −2.12291e13 1.02234e13i −1.10039 0.529918i
\(897\) −1.25326e11 5.49091e11i −0.00646363 0.0283190i
\(898\) −1.28404e13 −0.658925
\(899\) −6.44760e11 1.77299e13i −0.0329215 0.905290i
\(900\) 3.13593e10 0.00159322
\(901\) 4.02071e11 + 1.76159e12i 0.0203255 + 0.0890518i
\(902\) −5.58156e12 2.68794e12i −0.280754 0.135204i
\(903\) 1.63772e13 7.88685e12i 0.819681 0.394738i
\(904\) 5.25748e12 + 2.30345e13i 0.261830 + 1.14715i
\(905\) 1.82063e10 7.97670e10i 0.000902201 0.00395280i
\(906\) 2.93394e13 + 1.41291e13i 1.44669 + 0.696687i
\(907\) −5.09738e12 6.39191e12i −0.250100 0.313616i 0.640895 0.767629i \(-0.278563\pi\)
−0.890995 + 0.454013i \(0.849992\pi\)
\(908\) 2.77701e11 + 3.48227e11i 0.0135579 + 0.0170010i
\(909\) −2.07443e12 + 9.98992e11i −0.100777 + 0.0485316i
\(910\) 9.08734e12 1.13952e13i 0.439289 0.550851i
\(911\) 1.23366e13 0.593422 0.296711 0.954967i \(-0.404110\pi\)
0.296711 + 0.954967i \(0.404110\pi\)
\(912\) 2.91751e13 3.65845e13i 1.39648 1.75114i
\(913\) −2.05646e12 + 9.00992e12i −0.0979492 + 0.429143i
\(914\) −4.12741e12 + 1.80834e13i −0.195623 + 0.857081i
\(915\) −6.55847e12 + 8.22406e12i −0.309320 + 0.387875i
\(916\) −4.57907e10 −0.00214905
\(917\) −1.46022e12 + 1.83105e12i −0.0681954 + 0.0855144i
\(918\) 1.06263e13 5.11738e12i 0.493846 0.237824i
\(919\) −1.45478e13 1.82424e13i −0.672787 0.843648i 0.321881 0.946780i \(-0.395685\pi\)
−0.994668 + 0.103132i \(0.967114\pi\)
\(920\) −5.68699e11 7.13126e11i −0.0261720 0.0328187i
\(921\) 2.86819e13 + 1.38125e13i 1.31353 + 0.632561i
\(922\) −5.15076e12 + 2.25670e13i −0.234737 + 1.02845i
\(923\) 4.37466e12 + 1.91666e13i 0.198398 + 0.869237i
\(924\) 1.28331e12 6.18009e11i 0.0579172 0.0278914i
\(925\) 7.57401e11 + 3.64745e11i 0.0340164 + 0.0163814i
\(926\) −8.64312e12 3.78680e13i −0.386297 1.69248i
\(927\) 1.81949e12 0.0809267
\(928\) −7.53285e12 5.57173e12i −0.333421 0.246618i
\(929\) 1.94074e13 0.854862 0.427431 0.904048i \(-0.359419\pi\)
0.427431 + 0.904048i \(0.359419\pi\)
\(930\) 5.49977e12 + 2.40961e13i 0.241086 + 1.05626i
\(931\) 1.63702e12 + 7.88349e11i 0.0714136 + 0.0343910i
\(932\) −5.22968e12 + 2.51848e12i −0.227041 + 0.109337i
\(933\) 9.43633e12 + 4.13433e13i 0.407695 + 1.78623i
\(934\) −9.77004e12 + 4.28053e13i −0.420083 + 1.84051i
\(935\) 3.29310e12 + 1.58587e12i 0.140913 + 0.0678603i
\(936\) −6.61396e11 8.29364e11i −0.0281657 0.0353186i
\(937\) 6.56544e12 + 8.23280e12i 0.278250 + 0.348915i 0.901244 0.433312i \(-0.142655\pi\)
−0.622994 + 0.782227i \(0.714084\pi\)
\(938\) −1.59423e13 + 7.67742e12i −0.672417 + 0.323819i
\(939\) −1.83621e13 + 2.30253e13i −0.770773 + 0.966519i
\(940\) 6.53468e12 0.272991
\(941\) 1.07752e12 1.35116e12i 0.0447992 0.0561764i −0.758927 0.651176i \(-0.774276\pi\)
0.803726 + 0.594999i \(0.202848\pi\)
\(942\) 2.51390e12 1.10141e13i 0.104021 0.455744i
\(943\) 2.47411e11 1.08398e12i 0.0101886 0.0446393i
\(944\) 2.04484e13 2.56414e13i 0.838078 1.05092i
\(945\) −2.48607e13 −1.01407
\(946\) 4.14008e12 5.19150e12i 0.168073 0.210757i
\(947\) −1.27911e13 + 6.15987e12i −0.516813 + 0.248884i −0.674062 0.738675i \(-0.735452\pi\)
0.157249 + 0.987559i \(0.449737\pi\)
\(948\) −1.98359e11 2.48734e11i −0.00797652 0.0100022i
\(949\) −2.77758e12 3.48298e12i −0.111165 0.139397i
\(950\) 4.00912e12 + 1.93069e12i 0.159695 + 0.0769053i
\(951\) −6.74259e12 + 2.95412e13i −0.267310 + 1.17116i
\(952\) 2.61708e12 + 1.14662e13i 0.103265 + 0.452431i
\(953\) −1.85005e13 + 8.90935e12i −0.726548 + 0.349887i −0.760326 0.649542i \(-0.774961\pi\)
0.0337772 + 0.999429i \(0.489246\pi\)
\(954\) 3.83043e11 + 1.84464e11i 0.0149720 + 0.00721014i
\(955\) −5.23896e12 2.29534e13i −0.203812 0.892958i
\(956\) 8.79127e10 0.00340401
\(957\) −7.49159e12 + 1.99893e12i −0.288716 + 0.0770362i
\(958\) 1.72619e12 0.0662130
\(959\) 2.63201e12 + 1.15316e13i 0.100486 + 0.440257i
\(960\) −1.82972e13 8.81144e12i −0.695285 0.334832i
\(961\) 4.27273e12 2.05764e12i 0.161603 0.0778240i
\(962\) 1.68860e12 + 7.39823e12i 0.0635679 + 0.278509i
\(963\) 3.10371e11 1.35982e12i 0.0116296 0.0509524i
\(964\) 5.77775e12 + 2.78242e12i 0.215482 + 0.103771i
\(965\) 2.16635e13 + 2.71652e13i 0.804184 + 1.00842i
\(966\) 9.16055e11 + 1.14870e12i 0.0338473 + 0.0424432i
\(967\) 6.73072e12 3.24134e12i 0.247538 0.119208i −0.306001 0.952031i \(-0.598991\pi\)
0.553539 + 0.832823i \(0.313277\pi\)
\(968\) 1.35771e13 1.70251e13i 0.497013 0.623234i
\(969\) −2.75750e13 −1.00475
\(970\) 3.35232e13 4.20368e13i 1.21583 1.52460i
\(971\) −6.66710e12 + 2.92105e13i −0.240686 + 1.05451i 0.699709 + 0.714428i \(0.253313\pi\)
−0.940395 + 0.340085i \(0.889544\pi\)
\(972\) 2.25062e11 9.86062e11i 0.00808732 0.0354329i
\(973\) 2.47141e13 3.09905e13i 0.883969 1.10846i
\(974\) −2.70006e13 −0.961297
\(975\) 9.64085e11 1.20892e12i 0.0341660 0.0428428i
\(976\) −1.35955e13 + 6.54724e12i −0.479590 + 0.230958i
\(977\) −1.11969e13 1.40405e13i −0.393163 0.493011i 0.545372 0.838194i \(-0.316388\pi\)
−0.938535 + 0.345183i \(0.887817\pi\)
\(978\) 1.15714e13 + 1.45101e13i 0.404447 + 0.507161i
\(979\) 8.02913e12 + 3.86662e12i 0.279348 + 0.134527i
\(980\) −6.07179e10 + 2.66023e11i −0.00210281 + 0.00921300i
\(981\) 8.52653e11 + 3.73572e12i 0.0293942 + 0.128784i
\(982\) 3.17071e13 1.52694e13i 1.08807 0.523985i
\(983\) 7.01206e12 + 3.37683e12i 0.239527 + 0.115350i 0.549797 0.835298i \(-0.314705\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(984\) −5.85284e12 2.56430e13i −0.199016 0.871947i
\(985\) −3.03116e13 −1.02600
\(986\) 6.20885e11 + 1.70734e13i 0.0209201 + 0.575272i
\(987\) 3.94448e13 1.32301
\(988\) 1.55518e12 + 6.81367e12i 0.0519246 + 0.227497i
\(989\) 1.07372e12 + 5.17076e11i 0.0356868 + 0.0171858i
\(990\) 7.74837e11 3.73142e11i 0.0256361 0.0123457i
\(991\) −4.20240e12 1.84119e13i −0.138410 0.606412i −0.995785 0.0917200i \(-0.970764\pi\)
0.857375 0.514692i \(-0.172094\pi\)
\(992\) −2.54976e12 + 1.11712e13i −0.0835983 + 0.366268i
\(993\) −5.12195e13 2.46660e13i −1.67172 0.805059i
\(994\) −3.19759e13 4.00966e13i −1.03893 1.30277i
\(995\) 3.15897e13 + 3.96122e13i 1.02174 + 1.28122i
\(996\) 9.43367e12 4.54302e12i 0.303748 0.146277i
\(997\) 4.94713e12 6.20350e12i 0.158571 0.198842i −0.696199 0.717849i \(-0.745127\pi\)
0.854770 + 0.519007i \(0.173698\pi\)
\(998\) −3.71432e13 −1.18520
\(999\) 8.07031e12 1.01198e13i 0.256357 0.321462i
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.d.a.7.5 126
29.25 even 7 inner 29.10.d.a.25.5 yes 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.10.d.a.7.5 126 1.1 even 1 trivial
29.10.d.a.25.5 yes 126 29.25 even 7 inner