Properties

Label 91.10.h.a.16.10
Level $91$
Weight $10$
Character 91.16
Analytic conductor $46.868$
Analytic rank $0$
Dimension $164$
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] = [91,10,Mod(16,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.16");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.h (of order \(3\), degree \(2\), 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: \(46.8682610909\)
Analytic rank: \(0\)
Dimension: \(164\)
Relative dimension: \(82\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.10
Character \(\chi\) \(=\) 91.16
Dual form 91.10.h.a.74.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-36.4163 q^{2} +(-91.6449 + 158.734i) q^{3} +814.145 q^{4} +(939.046 - 1626.48i) q^{5} +(3337.36 - 5780.49i) q^{6} +(6277.96 + 969.960i) q^{7} -11003.0 q^{8} +(-6956.07 - 12048.3i) q^{9} +O(q^{10})\) \(q-36.4163 q^{2} +(-91.6449 + 158.734i) q^{3} +814.145 q^{4} +(939.046 - 1626.48i) q^{5} +(3337.36 - 5780.49i) q^{6} +(6277.96 + 969.960i) q^{7} -11003.0 q^{8} +(-6956.07 - 12048.3i) q^{9} +(-34196.6 + 59230.2i) q^{10} +(-37266.1 + 64546.8i) q^{11} +(-74612.2 + 129232. i) q^{12} +(91879.7 + 46503.9i) q^{13} +(-228620. - 35322.3i) q^{14} +(172118. + 298116. i) q^{15} -16154.2 q^{16} +173176. q^{17} +(253314. + 438753. i) q^{18} +(-271004. - 469393. i) q^{19} +(764520. - 1.32419e6i) q^{20} +(-729308. + 907631. i) q^{21} +(1.35709e6 - 2.35055e6i) q^{22} +2.36268e6 q^{23} +(1.00837e6 - 1.74654e6i) q^{24} +(-787053. - 1.36322e6i) q^{25} +(-3.34592e6 - 1.69350e6i) q^{26} -1.05774e6 q^{27} +(5.11117e6 + 789688. i) q^{28} +(226914. + 393027. i) q^{29} +(-6.26788e6 - 1.08563e7i) q^{30} +(3.99021e6 + 6.91125e6i) q^{31} +6.22181e6 q^{32} +(-6.83050e6 - 1.18308e7i) q^{33} -6.30644e6 q^{34} +(7.47291e6 - 9.30011e6i) q^{35} +(-5.66325e6 - 9.80903e6i) q^{36} -1.72586e6 q^{37} +(9.86896e6 + 1.70935e7i) q^{38} +(-1.58020e7 + 1.03226e7i) q^{39} +(-1.03323e7 + 1.78961e7i) q^{40} +(-1.46523e7 - 2.53786e7i) q^{41} +(2.65587e7 - 3.30525e7i) q^{42} +(6.57912e6 - 1.13954e7i) q^{43} +(-3.03400e7 + 5.25505e7i) q^{44} -2.61283e7 q^{45} -8.60400e7 q^{46} +(1.46939e7 - 2.54506e7i) q^{47} +(1.48045e6 - 2.56422e6i) q^{48} +(3.84720e7 + 1.21787e7i) q^{49} +(2.86616e7 + 4.96433e7i) q^{50} +(-1.58707e7 + 2.74889e7i) q^{51} +(7.48034e7 + 3.78609e7i) q^{52} +(-7.12402e6 - 1.23392e7i) q^{53} +3.85190e7 q^{54} +(6.99892e7 + 1.21225e8i) q^{55} +(-6.90764e7 - 1.06725e7i) q^{56} +9.93445e7 q^{57} +(-8.26338e6 - 1.43126e7i) q^{58} +1.63741e7 q^{59} +(1.40129e8 + 2.42710e8i) q^{60} +(7.82834e7 + 1.35591e8i) q^{61} +(-1.45309e8 - 2.51682e8i) q^{62} +(-3.19836e7 - 8.23856e7i) q^{63} -2.18304e8 q^{64} +(1.61917e8 - 1.05771e8i) q^{65} +(2.48741e8 + 4.30833e8i) q^{66} +(-7.81745e7 + 1.35402e8i) q^{67} +1.40991e8 q^{68} +(-2.16528e8 + 3.75037e8i) q^{69} +(-2.72136e8 + 3.38675e8i) q^{70} +(1.69211e8 - 2.93083e8i) q^{71} +(7.65376e7 + 1.32567e8i) q^{72} +(-1.13252e8 - 1.96158e8i) q^{73} +6.28493e7 q^{74} +2.88518e8 q^{75} +(-2.20637e8 - 3.82154e8i) q^{76} +(-2.96563e8 + 3.69076e8i) q^{77} +(5.75451e8 - 3.75909e8i) q^{78} +(9.58541e7 - 1.66024e8i) q^{79} +(-1.51696e7 + 2.62745e7i) q^{80} +(2.33853e8 - 4.05045e8i) q^{81} +(5.33584e8 + 9.24194e8i) q^{82} -4.78611e8 q^{83} +(-5.93763e8 + 7.38943e8i) q^{84} +(1.62621e8 - 2.81667e8i) q^{85} +(-2.39587e8 + 4.14977e8i) q^{86} -8.31822e7 q^{87} +(4.10039e8 - 7.10208e8i) q^{88} +4.01254e8 q^{89} +9.51495e8 q^{90} +(5.31711e8 + 3.81069e8i) q^{91} +1.92356e9 q^{92} -1.46273e9 q^{93} +(-5.35097e8 + 9.26816e8i) q^{94} -1.01794e9 q^{95} +(-5.70197e8 + 9.87610e8i) q^{96} +(-5.66288e8 + 9.80839e8i) q^{97} +(-1.40101e9 - 4.43504e8i) q^{98} +1.03690e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −36.4163 −1.60939 −0.804694 0.593690i \(-0.797670\pi\)
−0.804694 + 0.593690i \(0.797670\pi\)
\(3\) −91.6449 + 158.734i −0.653225 + 1.13142i 0.329111 + 0.944291i \(0.393251\pi\)
−0.982336 + 0.187127i \(0.940082\pi\)
\(4\) 814.145 1.59013
\(5\) 939.046 1626.48i 0.671927 1.16381i −0.305430 0.952214i \(-0.598800\pi\)
0.977357 0.211597i \(-0.0678664\pi\)
\(6\) 3337.36 5780.49i 1.05129 1.82089i
\(7\) 6277.96 + 969.960i 0.988274 + 0.152691i
\(8\) −11003.0 −0.949743
\(9\) −6956.07 12048.3i −0.353405 0.612115i
\(10\) −34196.6 + 59230.2i −1.08139 + 1.87302i
\(11\) −37266.1 + 64546.8i −0.767445 + 1.32925i 0.171500 + 0.985184i \(0.445139\pi\)
−0.938944 + 0.344069i \(0.888195\pi\)
\(12\) −74612.2 + 129232.i −1.03871 + 1.79910i
\(13\) 91879.7 + 46503.9i 0.892226 + 0.451590i
\(14\) −228620. 35322.3i −1.59052 0.245738i
\(15\) 172118. + 298116.i 0.877838 + 1.52046i
\(16\) −16154.2 −0.0616235
\(17\) 173176. 0.502885 0.251443 0.967872i \(-0.419095\pi\)
0.251443 + 0.967872i \(0.419095\pi\)
\(18\) 253314. + 438753.i 0.568765 + 0.985130i
\(19\) −271004. 469393.i −0.477073 0.826314i 0.522582 0.852589i \(-0.324969\pi\)
−0.999655 + 0.0262749i \(0.991635\pi\)
\(20\) 764520. 1.32419e6i 1.06845 1.85061i
\(21\) −729308. + 907631.i −0.818322 + 1.01841i
\(22\) 1.35709e6 2.35055e6i 1.23512 2.13928i
\(23\) 2.36268e6 1.76047 0.880237 0.474534i \(-0.157383\pi\)
0.880237 + 0.474534i \(0.157383\pi\)
\(24\) 1.00837e6 1.74654e6i 0.620395 1.07456i
\(25\) −787053. 1.36322e6i −0.402971 0.697967i
\(26\) −3.34592e6 1.69350e6i −1.43594 0.726783i
\(27\) −1.05774e6 −0.383038
\(28\) 5.11117e6 + 789688.i 1.57148 + 0.242798i
\(29\) 226914. + 393027.i 0.0595760 + 0.103189i 0.894275 0.447518i \(-0.147692\pi\)
−0.834699 + 0.550706i \(0.814358\pi\)
\(30\) −6.26788e6 1.08563e7i −1.41278 2.44701i
\(31\) 3.99021e6 + 6.91125e6i 0.776012 + 1.34409i 0.934224 + 0.356687i \(0.116094\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(32\) 6.22181e6 1.04892
\(33\) −6.83050e6 1.18308e7i −1.00263 1.73660i
\(34\) −6.30644e6 −0.809337
\(35\) 7.47291e6 9.30011e6i 0.841751 1.04757i
\(36\) −5.66325e6 9.80903e6i −0.561959 0.973341i
\(37\) −1.72586e6 −0.151390 −0.0756950 0.997131i \(-0.524118\pi\)
−0.0756950 + 0.997131i \(0.524118\pi\)
\(38\) 9.86896e6 + 1.70935e7i 0.767795 + 1.32986i
\(39\) −1.58020e7 + 1.03226e7i −1.09376 + 0.714491i
\(40\) −1.03323e7 + 1.78961e7i −0.638157 + 1.10532i
\(41\) −1.46523e7 2.53786e7i −0.809804 1.40262i −0.913000 0.407960i \(-0.866240\pi\)
0.103196 0.994661i \(-0.467093\pi\)
\(42\) 2.65587e7 3.30525e7i 1.31700 1.63902i
\(43\) 6.57912e6 1.13954e7i 0.293467 0.508300i −0.681160 0.732135i \(-0.738524\pi\)
0.974627 + 0.223834i \(0.0718575\pi\)
\(44\) −3.03400e7 + 5.25505e7i −1.22033 + 2.11368i
\(45\) −2.61283e7 −0.949849
\(46\) −8.60400e7 −2.83328
\(47\) 1.46939e7 2.54506e7i 0.439235 0.760777i −0.558396 0.829575i \(-0.688583\pi\)
0.997631 + 0.0687975i \(0.0219162\pi\)
\(48\) 1.48045e6 2.56422e6i 0.0402540 0.0697219i
\(49\) 3.84720e7 + 1.21787e7i 0.953371 + 0.301800i
\(50\) 2.86616e7 + 4.96433e7i 0.648537 + 1.12330i
\(51\) −1.58707e7 + 2.74889e7i −0.328497 + 0.568973i
\(52\) 7.48034e7 + 3.78609e7i 1.41875 + 0.718085i
\(53\) −7.12402e6 1.23392e7i −0.124018 0.214805i 0.797331 0.603542i \(-0.206245\pi\)
−0.921349 + 0.388738i \(0.872911\pi\)
\(54\) 3.85190e7 0.616457
\(55\) 6.99892e7 + 1.21225e8i 1.03133 + 1.78632i
\(56\) −6.90764e7 1.06725e7i −0.938606 0.145017i
\(57\) 9.93445e7 1.24654
\(58\) −8.26338e6 1.43126e7i −0.0958808 0.166070i
\(59\) 1.63741e7 0.175923 0.0879617 0.996124i \(-0.471965\pi\)
0.0879617 + 0.996124i \(0.471965\pi\)
\(60\) 1.40129e8 + 2.42710e8i 1.39587 + 2.41773i
\(61\) 7.82834e7 + 1.35591e8i 0.723912 + 1.25385i 0.959420 + 0.281980i \(0.0909911\pi\)
−0.235509 + 0.971872i \(0.575676\pi\)
\(62\) −1.45309e8 2.51682e8i −1.24890 2.16316i
\(63\) −3.19836e7 8.23856e7i −0.255797 0.658899i
\(64\) −2.18304e8 −1.62649
\(65\) 1.61917e8 1.05771e8i 1.12508 0.734947i
\(66\) 2.48741e8 + 4.30833e8i 1.61362 + 2.79487i
\(67\) −7.81745e7 + 1.35402e8i −0.473945 + 0.820898i −0.999555 0.0298283i \(-0.990504\pi\)
0.525610 + 0.850726i \(0.323837\pi\)
\(68\) 1.40991e8 0.799651
\(69\) −2.16528e8 + 3.75037e8i −1.14999 + 1.99183i
\(70\) −2.72136e8 + 3.38675e8i −1.35470 + 1.68594i
\(71\) 1.69211e8 2.93083e8i 0.790254 1.36876i −0.135555 0.990770i \(-0.543282\pi\)
0.925809 0.377991i \(-0.123385\pi\)
\(72\) 7.65376e7 + 1.32567e8i 0.335644 + 0.581352i
\(73\) −1.13252e8 1.96158e8i −0.466758 0.808449i 0.532521 0.846417i \(-0.321245\pi\)
−0.999279 + 0.0379680i \(0.987911\pi\)
\(74\) 6.28493e7 0.243645
\(75\) 2.88518e8 1.05292
\(76\) −2.20637e8 3.82154e8i −0.758606 1.31394i
\(77\) −2.96563e8 + 3.69076e8i −0.961410 + 1.19648i
\(78\) 5.75451e8 3.75909e8i 1.76028 1.14989i
\(79\) 9.58541e7 1.66024e8i 0.276878 0.479567i −0.693729 0.720236i \(-0.744033\pi\)
0.970607 + 0.240669i \(0.0773668\pi\)
\(80\) −1.51696e7 + 2.62745e7i −0.0414065 + 0.0717181i
\(81\) 2.33853e8 4.05045e8i 0.603615 1.04549i
\(82\) 5.33584e8 + 9.24194e8i 1.30329 + 2.25736i
\(83\) −4.78611e8 −1.10696 −0.553479 0.832863i \(-0.686700\pi\)
−0.553479 + 0.832863i \(0.686700\pi\)
\(84\) −5.93763e8 + 7.38943e8i −1.30124 + 1.61940i
\(85\) 1.62621e8 2.81667e8i 0.337902 0.585263i
\(86\) −2.39587e8 + 4.14977e8i −0.472302 + 0.818052i
\(87\) −8.31822e7 −0.155666
\(88\) 4.10039e8 7.10208e8i 0.728875 1.26245i
\(89\) 4.01254e8 0.677898 0.338949 0.940805i \(-0.389929\pi\)
0.338949 + 0.940805i \(0.389929\pi\)
\(90\) 9.51495e8 1.52867
\(91\) 5.31711e8 + 3.81069e8i 0.812810 + 0.582529i
\(92\) 1.92356e9 2.79938
\(93\) −1.46273e9 −2.02764
\(94\) −5.35097e8 + 9.26816e8i −0.706899 + 1.22439i
\(95\) −1.01794e9 −1.28223
\(96\) −5.70197e8 + 9.87610e8i −0.685179 + 1.18677i
\(97\) −5.66288e8 + 9.80839e8i −0.649478 + 1.12493i 0.333770 + 0.942655i \(0.391679\pi\)
−0.983248 + 0.182274i \(0.941654\pi\)
\(98\) −1.40101e9 4.43504e8i −1.53434 0.485714i
\(99\) 1.03690e9 1.08487
\(100\) −6.40776e8 1.10986e9i −0.640776 1.10986i
\(101\) −6.77571e8 + 1.17359e9i −0.647901 + 1.12220i 0.335723 + 0.941961i \(0.391020\pi\)
−0.983623 + 0.180236i \(0.942314\pi\)
\(102\) 5.77953e8 1.00104e9i 0.528679 0.915698i
\(103\) 1.72261e8 2.98364e8i 0.150806 0.261204i −0.780718 0.624884i \(-0.785146\pi\)
0.931524 + 0.363680i \(0.118480\pi\)
\(104\) −1.01095e9 5.11682e8i −0.847385 0.428894i
\(105\) 7.91386e8 + 2.03851e9i 0.635385 + 1.63667i
\(106\) 2.59430e8 + 4.49346e8i 0.199592 + 0.345704i
\(107\) 2.26466e9 1.67023 0.835113 0.550079i \(-0.185402\pi\)
0.835113 + 0.550079i \(0.185402\pi\)
\(108\) −8.61154e8 −0.609079
\(109\) −5.38433e7 9.32593e7i −0.0365353 0.0632809i 0.847180 0.531307i \(-0.178299\pi\)
−0.883715 + 0.468026i \(0.844965\pi\)
\(110\) −2.54875e9 4.41456e9i −1.65981 2.87488i
\(111\) 1.58166e8 2.73952e8i 0.0988917 0.171285i
\(112\) −1.01416e8 1.56689e7i −0.0609009 0.00940933i
\(113\) −4.08937e8 + 7.08299e8i −0.235941 + 0.408661i −0.959546 0.281553i \(-0.909150\pi\)
0.723605 + 0.690214i \(0.242484\pi\)
\(114\) −3.61776e9 −2.00617
\(115\) 2.21867e9 3.84284e9i 1.18291 2.04886i
\(116\) 1.84741e8 + 3.19981e8i 0.0947333 + 0.164083i
\(117\) −7.88308e7 1.43048e9i −0.0388919 0.705739i
\(118\) −5.96284e8 −0.283129
\(119\) 1.08720e9 + 1.67974e8i 0.496988 + 0.0767859i
\(120\) −1.89381e9 3.28017e9i −0.833720 1.44405i
\(121\) −1.59855e9 2.76878e9i −0.677943 1.17423i
\(122\) −2.85079e9 4.93771e9i −1.16505 2.01793i
\(123\) 5.37125e9 2.11593
\(124\) 3.24861e9 + 5.62676e9i 1.23396 + 2.13728i
\(125\) 7.11831e8 0.260785
\(126\) 1.16472e9 + 3.00018e9i 0.411676 + 1.06042i
\(127\) 1.03575e9 + 1.79397e9i 0.353295 + 0.611924i 0.986825 0.161794i \(-0.0517280\pi\)
−0.633530 + 0.773718i \(0.718395\pi\)
\(128\) 4.76426e9 1.56874
\(129\) 1.20588e9 + 2.08865e9i 0.383400 + 0.664068i
\(130\) −5.89641e9 + 3.85178e9i −1.81068 + 1.18281i
\(131\) 1.37641e9 2.38402e9i 0.408346 0.707276i −0.586359 0.810052i \(-0.699439\pi\)
0.994705 + 0.102776i \(0.0327724\pi\)
\(132\) −5.56102e9 9.63196e9i −1.59431 2.76142i
\(133\) −1.24606e9 3.20969e9i −0.345308 0.889469i
\(134\) 2.84682e9 4.93084e9i 0.762762 1.32114i
\(135\) −9.93267e8 + 1.72039e9i −0.257374 + 0.445784i
\(136\) −1.90546e9 −0.477611
\(137\) −4.32934e8 −0.104998 −0.0524988 0.998621i \(-0.516719\pi\)
−0.0524988 + 0.998621i \(0.516719\pi\)
\(138\) 7.88513e9 1.36574e10i 1.85077 3.20563i
\(139\) −2.71127e9 + 4.69605e9i −0.616035 + 1.06700i 0.374167 + 0.927361i \(0.377929\pi\)
−0.990202 + 0.139643i \(0.955405\pi\)
\(140\) 6.08403e9 7.57164e9i 1.33849 1.66577i
\(141\) 2.69324e9 + 4.66483e9i 0.573838 + 0.993917i
\(142\) −6.16205e9 + 1.06730e10i −1.27183 + 2.20287i
\(143\) −6.42568e9 + 4.19753e9i −1.28501 + 0.839424i
\(144\) 1.12370e8 + 1.94630e8i 0.0217780 + 0.0377207i
\(145\) 8.52333e8 0.160123
\(146\) 4.12421e9 + 7.14333e9i 0.751195 + 1.30111i
\(147\) −5.45893e9 + 4.99067e9i −0.964228 + 0.881518i
\(148\) −1.40510e9 −0.240729
\(149\) −2.32467e9 4.02645e9i −0.386387 0.669243i 0.605573 0.795790i \(-0.292944\pi\)
−0.991961 + 0.126547i \(0.959611\pi\)
\(150\) −1.05067e10 −1.69456
\(151\) 8.24792e8 + 1.42858e9i 0.129107 + 0.223619i 0.923331 0.384006i \(-0.125456\pi\)
−0.794224 + 0.607625i \(0.792122\pi\)
\(152\) 2.98186e9 + 5.16472e9i 0.453096 + 0.784786i
\(153\) −1.20463e9 2.08648e9i −0.177722 0.307824i
\(154\) 1.07997e10 1.34404e10i 1.54728 1.92561i
\(155\) 1.49880e10 2.08569
\(156\) −1.28651e10 + 8.40406e9i −1.73922 + 1.13613i
\(157\) 3.67053e9 + 6.35755e9i 0.482148 + 0.835105i 0.999790 0.0204923i \(-0.00652337\pi\)
−0.517642 + 0.855597i \(0.673190\pi\)
\(158\) −3.49065e9 + 6.04598e9i −0.445604 + 0.771809i
\(159\) 2.61152e9 0.324045
\(160\) 5.84257e9 1.01196e10i 0.704797 1.22074i
\(161\) 1.48328e10 + 2.29170e9i 1.73983 + 0.268808i
\(162\) −8.51605e9 + 1.47502e10i −0.971450 + 1.68260i
\(163\) 6.31864e9 + 1.09442e10i 0.701099 + 1.21434i 0.968081 + 0.250637i \(0.0806401\pi\)
−0.266982 + 0.963701i \(0.586027\pi\)
\(164\) −1.19291e10 2.06619e10i −1.28769 2.23035i
\(165\) −2.56566e10 −2.69477
\(166\) 1.74292e10 1.78152
\(167\) 1.88149e9 + 3.25883e9i 0.187188 + 0.324219i 0.944312 0.329053i \(-0.106729\pi\)
−0.757124 + 0.653271i \(0.773396\pi\)
\(168\) 8.02457e9 9.98666e9i 0.777195 0.967227i
\(169\) 6.27928e9 + 8.54553e9i 0.592133 + 0.805840i
\(170\) −5.92204e9 + 1.02573e10i −0.543815 + 0.941915i
\(171\) −3.77024e9 + 6.53025e9i −0.337200 + 0.584047i
\(172\) 5.35636e9 9.27748e9i 0.466650 0.808262i
\(173\) 8.95431e9 + 1.55093e10i 0.760019 + 1.31639i 0.942840 + 0.333245i \(0.108144\pi\)
−0.182821 + 0.983146i \(0.558523\pi\)
\(174\) 3.02918e9 0.250527
\(175\) −3.61882e9 9.32163e9i −0.291673 0.751312i
\(176\) 6.02005e8 1.04270e9i 0.0472926 0.0819132i
\(177\) −1.50060e9 + 2.59912e9i −0.114917 + 0.199043i
\(178\) −1.46122e10 −1.09100
\(179\) 1.61085e8 2.79007e8i 0.0117278 0.0203131i −0.860102 0.510122i \(-0.829600\pi\)
0.871830 + 0.489809i \(0.162934\pi\)
\(180\) −2.12722e10 −1.51038
\(181\) −2.33915e10 −1.61996 −0.809982 0.586455i \(-0.800523\pi\)
−0.809982 + 0.586455i \(0.800523\pi\)
\(182\) −1.93629e10 1.38771e10i −1.30813 0.937515i
\(183\) −2.86971e10 −1.89151
\(184\) −2.59966e10 −1.67200
\(185\) −1.62066e9 + 2.80707e9i −0.101723 + 0.176189i
\(186\) 5.32672e10 3.26326
\(187\) −6.45362e9 + 1.11780e10i −0.385937 + 0.668462i
\(188\) 1.19630e10 2.07205e10i 0.698439 1.20973i
\(189\) −6.64045e9 1.02597e9i −0.378547 0.0584864i
\(190\) 3.70696e10 2.06361
\(191\) 1.86062e9 + 3.22269e9i 0.101160 + 0.175214i 0.912163 0.409828i \(-0.134411\pi\)
−0.811003 + 0.585042i \(0.801078\pi\)
\(192\) 2.00065e10 3.46522e10i 1.06246 1.84024i
\(193\) −2.52295e8 + 4.36987e8i −0.0130888 + 0.0226705i −0.872496 0.488622i \(-0.837500\pi\)
0.859407 + 0.511292i \(0.170833\pi\)
\(194\) 2.06221e10 3.57185e10i 1.04526 1.81045i
\(195\) 1.95055e9 + 3.53950e10i 0.0966054 + 1.75302i
\(196\) 3.13218e10 + 9.91526e9i 1.51598 + 0.479901i
\(197\) −1.38116e10 2.39225e10i −0.653352 1.13164i −0.982304 0.187292i \(-0.940029\pi\)
0.328952 0.944347i \(-0.393304\pi\)
\(198\) −3.77601e10 −1.74598
\(199\) 2.70942e10 1.22472 0.612360 0.790579i \(-0.290220\pi\)
0.612360 + 0.790579i \(0.290220\pi\)
\(200\) 8.65994e9 + 1.49995e10i 0.382719 + 0.662889i
\(201\) −1.43286e10 2.48178e10i −0.619186 1.07246i
\(202\) 2.46746e10 4.27377e10i 1.04272 1.80605i
\(203\) 1.04334e9 + 2.68751e9i 0.0431214 + 0.111075i
\(204\) −1.29211e10 + 2.23800e10i −0.522352 + 0.904740i
\(205\) −5.50369e10 −2.17651
\(206\) −6.27310e9 + 1.08653e10i −0.242705 + 0.420378i
\(207\) −1.64350e10 2.84662e10i −0.622160 1.07761i
\(208\) −1.48425e9 7.51234e8i −0.0549820 0.0278285i
\(209\) 4.03971e10 1.46451
\(210\) −2.88193e10 7.42349e10i −1.02258 2.63403i
\(211\) 1.52411e10 + 2.63983e10i 0.529353 + 0.916865i 0.999414 + 0.0342318i \(0.0108984\pi\)
−0.470061 + 0.882634i \(0.655768\pi\)
\(212\) −5.79998e9 1.00459e10i −0.197204 0.341567i
\(213\) 3.10147e10 + 5.37190e10i 1.03243 + 1.78822i
\(214\) −8.24703e10 −2.68804
\(215\) −1.23562e10 2.14016e10i −0.394377 0.683081i
\(216\) 1.16383e10 0.363788
\(217\) 1.83468e10 + 4.72589e10i 0.561682 + 1.44682i
\(218\) 1.96077e9 + 3.39616e9i 0.0587994 + 0.101843i
\(219\) 4.15158e10 1.21959
\(220\) 5.69814e10 + 9.86946e10i 1.63995 + 2.84048i
\(221\) 1.59114e10 + 8.05338e9i 0.448687 + 0.227098i
\(222\) −5.75982e9 + 9.97629e9i −0.159155 + 0.275665i
\(223\) 1.40657e9 + 2.43625e9i 0.0380881 + 0.0659706i 0.884441 0.466652i \(-0.154540\pi\)
−0.846353 + 0.532622i \(0.821207\pi\)
\(224\) 3.90603e10 + 6.03490e9i 1.03662 + 0.160160i
\(225\) −1.09496e10 + 1.89653e10i −0.284824 + 0.493330i
\(226\) 1.48920e10 2.57936e10i 0.379720 0.657695i
\(227\) 6.56906e10 1.64205 0.821026 0.570890i \(-0.193402\pi\)
0.821026 + 0.570890i \(0.193402\pi\)
\(228\) 8.08808e10 1.98216
\(229\) −1.12388e10 + 1.94661e10i −0.270059 + 0.467756i −0.968877 0.247544i \(-0.920377\pi\)
0.698818 + 0.715300i \(0.253710\pi\)
\(230\) −8.07955e10 + 1.39942e11i −1.90376 + 3.29741i
\(231\) −3.14062e10 8.08984e10i −0.725708 1.86933i
\(232\) −2.49674e9 4.32448e9i −0.0565818 0.0980026i
\(233\) −1.22974e10 + 2.12997e10i −0.273345 + 0.473448i −0.969716 0.244234i \(-0.921463\pi\)
0.696371 + 0.717682i \(0.254797\pi\)
\(234\) 2.87072e9 + 5.20926e10i 0.0625921 + 1.13581i
\(235\) −2.75965e10 4.77986e10i −0.590268 1.02237i
\(236\) 1.33309e10 0.279740
\(237\) 1.75691e10 + 3.04305e10i 0.361727 + 0.626530i
\(238\) −3.95916e10 6.11700e9i −0.799847 0.123578i
\(239\) 6.37909e10 1.26464 0.632322 0.774706i \(-0.282102\pi\)
0.632322 + 0.774706i \(0.282102\pi\)
\(240\) −2.78043e9 4.81584e9i −0.0540954 0.0936961i
\(241\) −5.64773e10 −1.07844 −0.539221 0.842164i \(-0.681281\pi\)
−0.539221 + 0.842164i \(0.681281\pi\)
\(242\) 5.82134e10 + 1.00829e11i 1.09107 + 1.88979i
\(243\) 3.24531e10 + 5.62104e10i 0.597073 + 1.03416i
\(244\) 6.37341e10 + 1.10391e11i 1.15111 + 1.99378i
\(245\) 5.59354e10 5.11373e10i 0.991834 0.906756i
\(246\) −1.95601e11 −3.40536
\(247\) −3.07120e9 5.57304e10i −0.0525015 0.952700i
\(248\) −4.39043e10 7.60444e10i −0.737011 1.27654i
\(249\) 4.38622e10 7.59716e10i 0.723092 1.25243i
\(250\) −2.59222e10 −0.419703
\(251\) 9.52805e9 1.65031e10i 0.151521 0.262442i −0.780266 0.625448i \(-0.784916\pi\)
0.931787 + 0.363006i \(0.118250\pi\)
\(252\) −2.60393e10 6.70738e10i −0.406749 1.04773i
\(253\) −8.80479e10 + 1.52503e11i −1.35107 + 2.34012i
\(254\) −3.77181e10 6.53296e10i −0.568588 0.984823i
\(255\) 2.98067e10 + 5.16267e10i 0.441452 + 0.764617i
\(256\) −6.17248e10 −0.898213
\(257\) −8.30998e10 −1.18823 −0.594116 0.804379i \(-0.702498\pi\)
−0.594116 + 0.804379i \(0.702498\pi\)
\(258\) −4.39138e10 7.60610e10i −0.617039 1.06874i
\(259\) −1.08349e10 1.67401e9i −0.149615 0.0231158i
\(260\) 1.31824e11 8.61128e10i 1.78901 1.16866i
\(261\) 3.15686e9 5.46785e9i 0.0421089 0.0729347i
\(262\) −5.01239e10 + 8.68171e10i −0.657187 + 1.13828i
\(263\) 1.87351e10 3.24501e10i 0.241465 0.418230i −0.719666 0.694320i \(-0.755705\pi\)
0.961132 + 0.276090i \(0.0890386\pi\)
\(264\) 7.51559e10 + 1.30174e11i 0.952238 + 1.64932i
\(265\) −2.67591e10 −0.333323
\(266\) 4.53769e10 + 1.16885e11i 0.555734 + 1.43150i
\(267\) −3.67729e10 + 6.36925e10i −0.442820 + 0.766986i
\(268\) −6.36453e10 + 1.10237e11i −0.753633 + 1.30533i
\(269\) 8.11335e10 0.944745 0.472373 0.881399i \(-0.343398\pi\)
0.472373 + 0.881399i \(0.343398\pi\)
\(270\) 3.61711e10 6.26502e10i 0.414214 0.717439i
\(271\) 6.81927e8 0.00768027 0.00384013 0.999993i \(-0.498778\pi\)
0.00384013 + 0.999993i \(0.498778\pi\)
\(272\) −2.79753e9 −0.0309895
\(273\) −1.09217e11 + 4.94773e10i −1.19003 + 0.539106i
\(274\) 1.57659e10 0.168982
\(275\) 1.17322e11 1.23703
\(276\) −1.76285e11 + 3.05334e11i −1.82862 + 3.16727i
\(277\) 1.85969e10 0.189793 0.0948967 0.995487i \(-0.469748\pi\)
0.0948967 + 0.995487i \(0.469748\pi\)
\(278\) 9.87342e10 1.71013e11i 0.991439 1.71722i
\(279\) 5.55124e10 9.61503e10i 0.548493 0.950017i
\(280\) −8.22244e10 + 1.02329e11i −0.799447 + 0.994920i
\(281\) 9.22103e9 0.0882269 0.0441135 0.999027i \(-0.485954\pi\)
0.0441135 + 0.999027i \(0.485954\pi\)
\(282\) −9.80779e10 1.69876e11i −0.923528 1.59960i
\(283\) 1.17767e10 2.03979e10i 0.109140 0.189037i −0.806282 0.591531i \(-0.798524\pi\)
0.915422 + 0.402495i \(0.131857\pi\)
\(284\) 1.37763e11 2.38612e11i 1.25660 2.17650i
\(285\) 9.32891e10 1.61581e11i 0.837585 1.45074i
\(286\) 2.33999e11 1.52858e11i 2.06808 1.35096i
\(287\) −6.73706e10 1.73538e11i −0.586141 1.50982i
\(288\) −4.32793e10 7.49620e10i −0.370693 0.642059i
\(289\) −8.85978e10 −0.747107
\(290\) −3.10388e10 −0.257700
\(291\) −1.03795e11 1.79778e11i −0.848510 1.46966i
\(292\) −9.22033e10 1.59701e11i −0.742205 1.28554i
\(293\) −7.28746e10 + 1.26222e11i −0.577659 + 1.00053i 0.418088 + 0.908406i \(0.362700\pi\)
−0.995747 + 0.0921284i \(0.970633\pi\)
\(294\) 1.98794e11 1.81742e11i 1.55182 1.41870i
\(295\) 1.53760e10 2.66321e10i 0.118208 0.204742i
\(296\) 1.89896e10 0.143782
\(297\) 3.94179e10 6.82738e10i 0.293961 0.509155i
\(298\) 8.46558e10 + 1.46628e11i 0.621847 + 1.07707i
\(299\) 2.17082e11 + 1.09874e11i 1.57074 + 0.795012i
\(300\) 2.34895e11 1.67428
\(301\) 5.23565e10 6.51582e10i 0.367639 0.457530i
\(302\) −3.00359e10 5.20236e10i −0.207782 0.359890i
\(303\) −1.24192e11 2.15106e11i −0.846449 1.46609i
\(304\) 4.37786e9 + 7.58267e9i 0.0293989 + 0.0509203i
\(305\) 2.94047e11 1.94566
\(306\) 4.38680e10 + 7.59817e10i 0.286024 + 0.495407i
\(307\) 7.91911e10 0.508808 0.254404 0.967098i \(-0.418121\pi\)
0.254404 + 0.967098i \(0.418121\pi\)
\(308\) −2.41445e11 + 3.00481e11i −1.52876 + 1.90256i
\(309\) 3.15736e10 + 5.46872e10i 0.197021 + 0.341250i
\(310\) −5.45806e11 −3.35669
\(311\) −5.07815e10 8.79562e10i −0.307811 0.533144i 0.670072 0.742296i \(-0.266263\pi\)
−0.977883 + 0.209152i \(0.932930\pi\)
\(312\) 1.73870e11 1.13579e11i 1.03879 0.678582i
\(313\) 2.16713e10 3.75357e10i 0.127625 0.221052i −0.795131 0.606437i \(-0.792598\pi\)
0.922756 + 0.385385i \(0.125931\pi\)
\(314\) −1.33667e11 2.31518e11i −0.775963 1.34401i
\(315\) −1.64032e11 2.53434e10i −0.938711 0.145033i
\(316\) 7.80392e10 1.35168e11i 0.440272 0.762573i
\(317\) −1.11422e11 + 1.92988e11i −0.619732 + 1.07341i 0.369802 + 0.929111i \(0.379425\pi\)
−0.989534 + 0.144297i \(0.953908\pi\)
\(318\) −9.51018e10 −0.521515
\(319\) −3.38249e10 −0.182885
\(320\) −2.04998e11 + 3.55066e11i −1.09288 + 1.89293i
\(321\) −2.07544e11 + 3.59477e11i −1.09103 + 1.88972i
\(322\) −5.40156e11 8.34553e10i −2.80006 0.432616i
\(323\) −4.69315e10 8.12878e10i −0.239913 0.415541i
\(324\) 1.90390e11 3.29765e11i 0.959824 1.66246i
\(325\) −8.91941e9 1.61853e11i −0.0443467 0.804722i
\(326\) −2.30101e11 3.98547e11i −1.12834 1.95434i
\(327\) 1.97378e10 0.0954629
\(328\) 1.61220e11 + 2.79241e11i 0.769105 + 1.33213i
\(329\) 1.16934e11 1.45525e11i 0.550248 0.684789i
\(330\) 9.34318e11 4.33693
\(331\) 1.17679e11 + 2.03827e11i 0.538858 + 0.933329i 0.998966 + 0.0454662i \(0.0144773\pi\)
−0.460108 + 0.887863i \(0.652189\pi\)
\(332\) −3.89659e11 −1.76020
\(333\) 1.20052e10 + 2.07936e10i 0.0535020 + 0.0926681i
\(334\) −6.85168e10 1.18675e11i −0.301258 0.521793i
\(335\) 1.46819e11 + 2.54298e11i 0.636913 + 1.10317i
\(336\) 1.17814e10 1.46621e10i 0.0504278 0.0627580i
\(337\) −3.51621e11 −1.48505 −0.742524 0.669819i \(-0.766372\pi\)
−0.742524 + 0.669819i \(0.766372\pi\)
\(338\) −2.28668e11 3.11196e11i −0.952972 1.29691i
\(339\) −7.49539e10 1.29824e11i −0.308245 0.533896i
\(340\) 1.32397e11 2.29318e11i 0.537307 0.930643i
\(341\) −5.94799e11 −2.38219
\(342\) 1.37298e11 2.37808e11i 0.542685 0.939957i
\(343\) 2.29713e11 + 1.13774e11i 0.896110 + 0.443832i
\(344\) −7.23900e10 + 1.25383e11i −0.278718 + 0.482754i
\(345\) 4.06659e11 + 7.04354e11i 1.54541 + 2.67673i
\(346\) −3.26082e11 5.64791e11i −1.22316 2.11858i
\(347\) −8.82983e10 −0.326941 −0.163471 0.986548i \(-0.552269\pi\)
−0.163471 + 0.986548i \(0.552269\pi\)
\(348\) −6.77223e10 −0.247529
\(349\) 2.34796e11 + 4.06679e11i 0.847181 + 1.46736i 0.883713 + 0.468028i \(0.155036\pi\)
−0.0365321 + 0.999332i \(0.511631\pi\)
\(350\) 1.31784e11 + 3.39459e11i 0.469415 + 1.20915i
\(351\) −9.71849e10 4.91890e10i −0.341757 0.172976i
\(352\) −2.31863e11 + 4.01598e11i −0.804987 + 1.39428i
\(353\) 7.29290e10 1.26317e11i 0.249985 0.432987i −0.713536 0.700618i \(-0.752908\pi\)
0.963521 + 0.267631i \(0.0862409\pi\)
\(354\) 5.46464e10 9.46503e10i 0.184947 0.320337i
\(355\) −3.17795e11 5.50436e11i −1.06199 1.83941i
\(356\) 3.26679e11 1.07794
\(357\) −1.26299e11 + 1.57180e11i −0.411522 + 0.512143i
\(358\) −5.86610e9 + 1.01604e10i −0.0188745 + 0.0326916i
\(359\) −1.50155e11 + 2.60076e11i −0.477106 + 0.826372i −0.999656 0.0262369i \(-0.991648\pi\)
0.522550 + 0.852609i \(0.324981\pi\)
\(360\) 2.87489e11 0.902112
\(361\) 1.44575e10 2.50412e10i 0.0448034 0.0776018i
\(362\) 8.51832e11 2.60715
\(363\) 5.85997e11 1.77140
\(364\) 4.32889e11 + 3.10246e11i 1.29247 + 0.926295i
\(365\) −4.25394e11 −1.25451
\(366\) 1.04504e12 3.04417
\(367\) 1.91175e11 3.31124e11i 0.550089 0.952782i −0.448179 0.893944i \(-0.647927\pi\)
0.998268 0.0588380i \(-0.0187396\pi\)
\(368\) −3.81673e10 −0.108487
\(369\) −2.03845e11 + 3.53071e11i −0.572377 + 0.991386i
\(370\) 5.90184e10 1.02223e11i 0.163712 0.283557i
\(371\) −3.27558e10 8.43747e10i −0.0897647 0.231222i
\(372\) −1.19087e12 −3.22421
\(373\) 1.07566e11 + 1.86311e11i 0.287731 + 0.498365i 0.973268 0.229673i \(-0.0737657\pi\)
−0.685537 + 0.728038i \(0.740432\pi\)
\(374\) 2.35017e11 4.07061e11i 0.621121 1.07581i
\(375\) −6.52357e10 + 1.12992e11i −0.170351 + 0.295057i
\(376\) −1.61677e11 + 2.80033e11i −0.417160 + 0.722543i
\(377\) 2.57154e9 + 4.66637e10i 0.00655629 + 0.118971i
\(378\) 2.41820e11 + 3.73618e10i 0.609228 + 0.0941272i
\(379\) 2.27678e11 + 3.94351e11i 0.566820 + 0.981762i 0.996878 + 0.0789602i \(0.0251600\pi\)
−0.430057 + 0.902802i \(0.641507\pi\)
\(380\) −8.28752e11 −2.03891
\(381\) −3.79684e11 −0.923123
\(382\) −6.77569e10 1.17358e11i −0.162805 0.281987i
\(383\) −6.93192e10 1.20064e11i −0.164611 0.285115i 0.771906 0.635737i \(-0.219304\pi\)
−0.936517 + 0.350622i \(0.885970\pi\)
\(384\) −4.36620e11 + 7.56248e11i −1.02474 + 1.77490i
\(385\) 3.21806e11 + 8.28932e11i 0.746485 + 1.92285i
\(386\) 9.18763e9 1.59134e10i 0.0210650 0.0364856i
\(387\) −1.83059e11 −0.414851
\(388\) −4.61040e11 + 7.98545e11i −1.03275 + 1.78878i
\(389\) 4.19606e11 + 7.26778e11i 0.929112 + 1.60927i 0.784810 + 0.619736i \(0.212760\pi\)
0.144302 + 0.989534i \(0.453906\pi\)
\(390\) −7.10318e10 1.28895e12i −0.155475 2.82128i
\(391\) 4.09161e11 0.885316
\(392\) −4.23307e11 1.34003e11i −0.905457 0.286633i
\(393\) 2.52283e11 + 4.36966e11i 0.533483 + 0.924020i
\(394\) 5.02968e11 + 8.71167e11i 1.05150 + 1.82124i
\(395\) −1.80023e11 3.11809e11i −0.372084 0.644468i
\(396\) 8.44189e11 1.72509
\(397\) −2.55930e11 4.43283e11i −0.517087 0.895621i −0.999803 0.0198438i \(-0.993683\pi\)
0.482716 0.875777i \(-0.339650\pi\)
\(398\) −9.86668e11 −1.97105
\(399\) 6.23681e11 + 9.63602e10i 1.23193 + 0.190335i
\(400\) 1.27142e10 + 2.20217e10i 0.0248325 + 0.0430111i
\(401\) 9.35853e11 1.80741 0.903707 0.428151i \(-0.140835\pi\)
0.903707 + 0.428151i \(0.140835\pi\)
\(402\) 5.21793e11 + 9.03773e11i 0.996509 + 1.72600i
\(403\) 4.52197e10 + 8.20564e11i 0.0853995 + 1.54967i
\(404\) −5.51641e11 + 9.55470e11i −1.03024 + 1.78444i
\(405\) −4.39197e11 7.60712e11i −0.811170 1.40499i
\(406\) −3.79945e10 9.78690e10i −0.0693991 0.178763i
\(407\) 6.43160e10 1.11399e11i 0.116183 0.201236i
\(408\) 1.74626e11 3.02460e11i 0.311988 0.540378i
\(409\) −6.35205e11 −1.12243 −0.561215 0.827670i \(-0.689666\pi\)
−0.561215 + 0.827670i \(0.689666\pi\)
\(410\) 2.00424e12 3.50286
\(411\) 3.96762e10 6.87212e10i 0.0685871 0.118796i
\(412\) 1.40245e11 2.42912e11i 0.239801 0.415347i
\(413\) 1.02796e11 + 1.58822e10i 0.173860 + 0.0268619i
\(414\) 5.98500e11 + 1.03663e12i 1.00130 + 1.73430i
\(415\) −4.49438e11 + 7.78449e11i −0.743795 + 1.28829i
\(416\) 5.71658e11 + 2.89338e11i 0.935872 + 0.473681i
\(417\) −4.96947e11 8.60738e11i −0.804818 1.39399i
\(418\) −1.47111e12 −2.35696
\(419\) −1.34488e11 2.32939e11i −0.213167 0.369215i 0.739537 0.673116i \(-0.235044\pi\)
−0.952704 + 0.303900i \(0.901711\pi\)
\(420\) 6.44303e11 + 1.65964e12i 1.01034 + 2.60251i
\(421\) 4.93938e11 0.766307 0.383154 0.923685i \(-0.374838\pi\)
0.383154 + 0.923685i \(0.374838\pi\)
\(422\) −5.55024e11 9.61329e11i −0.851933 1.47559i
\(423\) −4.08847e11 −0.620911
\(424\) 7.83855e10 + 1.35768e11i 0.117785 + 0.204009i
\(425\) −1.36299e11 2.36077e11i −0.202648 0.350997i
\(426\) −1.12944e12 1.95625e12i −1.66157 2.87793i
\(427\) 3.59943e11 + 9.27166e11i 0.523972 + 1.34968i
\(428\) 1.84376e12 2.65587
\(429\) −7.74077e10 1.40465e12i −0.110338 2.00222i
\(430\) 4.49966e11 + 7.79365e11i 0.634705 + 1.09934i
\(431\) −2.10604e11 + 3.64776e11i −0.293980 + 0.509189i −0.974747 0.223311i \(-0.928313\pi\)
0.680767 + 0.732500i \(0.261647\pi\)
\(432\) 1.70870e10 0.0236041
\(433\) 3.53261e10 6.11866e10i 0.0482948 0.0836490i −0.840867 0.541241i \(-0.817955\pi\)
0.889162 + 0.457592i \(0.151288\pi\)
\(434\) −6.68121e11 1.72099e12i −0.903964 2.32850i
\(435\) −7.81119e10 + 1.35294e11i −0.104596 + 0.181166i
\(436\) −4.38362e10 7.59266e10i −0.0580957 0.100625i
\(437\) −6.40296e11 1.10902e12i −0.839874 1.45470i
\(438\) −1.51185e12 −1.96280
\(439\) 5.68509e11 0.730545 0.365273 0.930901i \(-0.380976\pi\)
0.365273 + 0.930901i \(0.380976\pi\)
\(440\) −7.70091e11 1.33384e12i −0.979501 1.69655i
\(441\) −1.20881e11 5.48236e11i −0.152189 0.690231i
\(442\) −5.79434e11 2.93274e11i −0.722111 0.365488i
\(443\) 5.61420e11 9.72408e11i 0.692582 1.19959i −0.278407 0.960463i \(-0.589806\pi\)
0.970989 0.239124i \(-0.0768603\pi\)
\(444\) 1.28770e11 2.23036e11i 0.157250 0.272366i
\(445\) 3.76796e11 6.52630e11i 0.455498 0.788946i
\(446\) −5.12221e10 8.87192e10i −0.0612985 0.106172i
\(447\) 8.52176e11 1.00959
\(448\) −1.37050e12 2.11746e11i −1.60742 0.248350i
\(449\) 2.66002e11 4.60729e11i 0.308871 0.534979i −0.669245 0.743042i \(-0.733382\pi\)
0.978116 + 0.208062i \(0.0667157\pi\)
\(450\) 3.98743e11 6.90644e11i 0.458392 0.793959i
\(451\) 2.18414e12 2.48592
\(452\) −3.32934e11 + 5.76658e11i −0.375176 + 0.649824i
\(453\) −3.02352e11 −0.337342
\(454\) −2.39221e12 −2.64270
\(455\) 1.11910e12 5.06973e11i 1.22410 0.554541i
\(456\) −1.09309e12 −1.18389
\(457\) 1.68662e11 0.180882 0.0904410 0.995902i \(-0.471172\pi\)
0.0904410 + 0.995902i \(0.471172\pi\)
\(458\) 4.09274e11 7.08883e11i 0.434629 0.752800i
\(459\) −1.83176e11 −0.192624
\(460\) 1.80632e12 3.12863e12i 1.88098 3.25795i
\(461\) 5.09429e11 8.82357e11i 0.525327 0.909893i −0.474238 0.880397i \(-0.657276\pi\)
0.999565 0.0294961i \(-0.00939025\pi\)
\(462\) 1.14370e12 + 2.94602e12i 1.16795 + 3.00848i
\(463\) −8.67468e11 −0.877282 −0.438641 0.898662i \(-0.644540\pi\)
−0.438641 + 0.898662i \(0.644540\pi\)
\(464\) −3.66563e9 6.34905e9i −0.00367128 0.00635884i
\(465\) −1.37357e12 + 2.37910e12i −1.36243 + 2.35979i
\(466\) 4.47825e11 7.75656e11i 0.439918 0.761961i
\(467\) −8.51109e11 + 1.47416e12i −0.828055 + 1.43423i 0.0715064 + 0.997440i \(0.477219\pi\)
−0.899562 + 0.436794i \(0.856114\pi\)
\(468\) −6.41797e10 1.16461e12i −0.0618431 1.12221i
\(469\) −6.22111e11 + 7.74223e11i −0.593731 + 0.738905i
\(470\) 1.00496e12 + 1.74065e12i 0.949969 + 1.64539i
\(471\) −1.34554e12 −1.25980
\(472\) −1.80164e11 −0.167082
\(473\) 4.90356e11 + 8.49322e11i 0.450440 + 0.780185i
\(474\) −6.39800e11 1.10817e12i −0.582160 1.00833i
\(475\) −4.26589e11 + 7.38874e11i −0.384493 + 0.665962i
\(476\) 8.85134e11 + 1.36755e11i 0.790274 + 0.122099i
\(477\) −9.91103e10 + 1.71664e11i −0.0876569 + 0.151826i
\(478\) −2.32303e12 −2.03530
\(479\) 2.54865e11 4.41439e11i 0.221208 0.383143i −0.733967 0.679185i \(-0.762333\pi\)
0.955175 + 0.296042i \(0.0956668\pi\)
\(480\) 1.07088e12 + 1.85482e12i 0.920781 + 1.59484i
\(481\) −1.58571e11 8.02591e10i −0.135074 0.0683662i
\(482\) 2.05669e12 1.73563
\(483\) −1.72312e12 + 2.14444e12i −1.44063 + 1.79288i
\(484\) −1.30145e12 2.25419e12i −1.07802 1.86718i
\(485\) 1.06354e12 + 1.84211e12i 0.872803 + 1.51174i
\(486\) −1.18182e12 2.04697e12i −0.960922 1.66437i
\(487\) −1.45352e12 −1.17095 −0.585477 0.810689i \(-0.699093\pi\)
−0.585477 + 0.810689i \(0.699093\pi\)
\(488\) −8.61352e11 1.49191e12i −0.687530 1.19084i
\(489\) −2.31628e12 −1.83190
\(490\) −2.03696e12 + 1.86223e12i −1.59625 + 1.45932i
\(491\) 2.33677e11 + 4.04741e11i 0.181447 + 0.314275i 0.942373 0.334563i \(-0.108589\pi\)
−0.760927 + 0.648838i \(0.775255\pi\)
\(492\) 4.37297e12 3.36460
\(493\) 3.92962e10 + 6.80631e10i 0.0299599 + 0.0518920i
\(494\) 1.11842e11 + 2.02949e12i 0.0844952 + 1.53326i
\(495\) 9.73700e11 1.68650e12i 0.728957 1.26259i
\(496\) −6.44588e10 1.11646e11i −0.0478205 0.0828276i
\(497\) 1.34658e12 1.67583e12i 0.989985 1.23205i
\(498\) −1.59730e12 + 2.76660e12i −1.16374 + 2.01565i
\(499\) 2.05986e11 3.56778e11i 0.148726 0.257600i −0.782031 0.623239i \(-0.785816\pi\)
0.930757 + 0.365639i \(0.119150\pi\)
\(500\) 5.79534e11 0.414681
\(501\) −6.89715e11 −0.489103
\(502\) −3.46976e11 + 6.00980e11i −0.243856 + 0.422370i
\(503\) 2.43116e11 4.21089e11i 0.169339 0.293304i −0.768849 0.639431i \(-0.779170\pi\)
0.938188 + 0.346127i \(0.112503\pi\)
\(504\) 3.51915e11 + 9.06488e11i 0.242941 + 0.625785i
\(505\) 1.27254e12 + 2.20411e12i 0.870684 + 1.50807i
\(506\) 3.20638e12 5.55361e12i 2.17439 3.76615i
\(507\) −1.93193e12 + 2.13578e11i −1.29854 + 0.143556i
\(508\) 8.43248e11 + 1.46055e12i 0.561783 + 0.973037i
\(509\) −5.87752e11 −0.388118 −0.194059 0.980990i \(-0.562165\pi\)
−0.194059 + 0.980990i \(0.562165\pi\)
\(510\) −1.08545e12 1.88005e12i −0.710467 1.23056i
\(511\) −5.20725e11 1.34132e12i −0.337842 0.870239i
\(512\) −1.91514e11 −0.123164
\(513\) 2.86652e11 + 4.96496e11i 0.182737 + 0.316510i
\(514\) 3.02619e12 1.91232
\(515\) −3.23522e11 5.60356e11i −0.202661 0.351020i
\(516\) 9.81765e11 + 1.70047e12i 0.609655 + 1.05595i
\(517\) 1.09517e12 + 1.89689e12i 0.674177 + 1.16771i
\(518\) 3.94565e11 + 6.09613e10i 0.240788 + 0.0372023i
\(519\) −3.28246e12 −1.98585
\(520\) −1.78157e12 + 1.16380e12i −1.06853 + 0.698011i
\(521\) 6.39278e11 + 1.10726e12i 0.380119 + 0.658386i 0.991079 0.133276i \(-0.0425495\pi\)
−0.610960 + 0.791662i \(0.709216\pi\)
\(522\) −1.14961e11 + 1.99119e11i −0.0677695 + 0.117380i
\(523\) −1.99994e12 −1.16885 −0.584426 0.811447i \(-0.698680\pi\)
−0.584426 + 0.811447i \(0.698680\pi\)
\(524\) 1.12060e12 1.94094e12i 0.649322 1.12466i
\(525\) 1.81130e12 + 2.79851e11i 1.04058 + 0.160772i
\(526\) −6.82262e11 + 1.18171e12i −0.388611 + 0.673095i
\(527\) 6.91011e11 + 1.19687e12i 0.390245 + 0.675924i
\(528\) 1.10341e11 + 1.91117e11i 0.0617854 + 0.107015i
\(529\) 3.78110e12 2.09927
\(530\) 9.74467e11 0.536446
\(531\) −1.13899e11 1.97280e11i −0.0621722 0.107685i
\(532\) −1.01447e12 2.61315e12i −0.549084 1.41437i
\(533\) −1.66050e11 3.01317e12i −0.0891182 1.61715i
\(534\) 1.33913e12 2.31944e12i 0.712669 1.23438i
\(535\) 2.12662e12 3.68341e12i 1.12227 1.94383i
\(536\) 8.60153e11 1.48983e12i 0.450126 0.779641i
\(537\) 2.95252e10 + 5.11391e10i 0.0153217 + 0.0265380i
\(538\) −2.95458e12 −1.52046
\(539\) −2.21980e12 + 2.02939e12i −1.13283 + 1.03566i
\(540\) −8.08663e11 + 1.40065e12i −0.409257 + 0.708853i
\(541\) 1.16838e12 2.02369e12i 0.586401 1.01568i −0.408298 0.912849i \(-0.633878\pi\)
0.994699 0.102828i \(-0.0327891\pi\)
\(542\) −2.48332e10 −0.0123605
\(543\) 2.14371e12 3.71302e12i 1.05820 1.83286i
\(544\) 1.07747e12 0.527486
\(545\) −2.02245e11 −0.0981961
\(546\) 3.97728e12 1.80178e12i 1.91522 0.867630i
\(547\) 1.70239e12 0.813049 0.406525 0.913640i \(-0.366741\pi\)
0.406525 + 0.913640i \(0.366741\pi\)
\(548\) −3.52471e11 −0.166960
\(549\) 1.08909e12 1.88636e12i 0.511668 0.886235i
\(550\) −4.27242e12 −1.99086
\(551\) 1.22989e11 2.13024e11i 0.0568441 0.0984569i
\(552\) 2.38245e12 4.12653e12i 1.09219 1.89173i
\(553\) 7.62805e11 9.49319e11i 0.346857 0.431667i
\(554\) −6.77229e11 −0.305451
\(555\) −2.97050e11 5.14506e11i −0.132896 0.230183i
\(556\) −2.20736e12 + 3.82326e12i −0.979574 + 1.69667i
\(557\) 2.95868e11 5.12458e11i 0.130242 0.225585i −0.793528 0.608534i \(-0.791758\pi\)
0.923770 + 0.382949i \(0.125091\pi\)
\(558\) −2.02155e12 + 3.50143e12i −0.882737 + 1.52895i
\(559\) 1.13442e12 7.41049e11i 0.491382 0.320992i
\(560\) −1.20719e11 + 1.50236e11i −0.0518716 + 0.0645548i
\(561\) −1.18288e12 2.04881e12i −0.504207 0.873311i
\(562\) −3.35796e11 −0.141991
\(563\) −3.54244e12 −1.48599 −0.742993 0.669299i \(-0.766595\pi\)
−0.742993 + 0.669299i \(0.766595\pi\)
\(564\) 2.19269e12 + 3.79785e12i 0.912476 + 1.58045i
\(565\) 7.68021e11 + 1.33025e12i 0.317070 + 0.549181i
\(566\) −4.28864e11 + 7.42815e11i −0.175649 + 0.304233i
\(567\) 1.86100e12 2.31603e12i 0.756174 0.941066i
\(568\) −1.86183e12 + 3.22479e12i −0.750538 + 1.29997i
\(569\) −2.75518e12 −1.10191 −0.550953 0.834536i \(-0.685736\pi\)
−0.550953 + 0.834536i \(0.685736\pi\)
\(570\) −3.39724e12 + 5.88419e12i −1.34800 + 2.33480i
\(571\) −1.22082e12 2.11452e12i −0.480605 0.832433i 0.519147 0.854685i \(-0.326250\pi\)
−0.999752 + 0.0222522i \(0.992916\pi\)
\(572\) −5.23143e12 + 3.41739e12i −2.04333 + 1.33479i
\(573\) −6.82066e11 −0.264320
\(574\) 2.45339e12 + 6.31961e12i 0.943327 + 2.42989i
\(575\) −1.85956e12 3.22084e12i −0.709421 1.22875i
\(576\) 1.51854e12 + 2.63019e12i 0.574810 + 0.995601i
\(577\) −6.52405e11 1.13000e12i −0.245034 0.424411i 0.717107 0.696963i \(-0.245466\pi\)
−0.962141 + 0.272552i \(0.912132\pi\)
\(578\) 3.22640e12 1.20238
\(579\) −4.62430e10 8.00952e10i −0.0170999 0.0296178i
\(580\) 6.93922e11 0.254616
\(581\) −3.00470e12 4.64233e11i −1.09398 0.169022i
\(582\) 3.77982e12 + 6.54684e12i 1.36558 + 2.36526i
\(583\) 1.06194e12 0.380707
\(584\) 1.24611e12 + 2.15832e12i 0.443300 + 0.767818i
\(585\) −2.40066e12 1.21507e12i −0.847480 0.428942i
\(586\) 2.65382e12 4.59655e12i 0.929677 1.61025i
\(587\) −8.02910e11 1.39068e12i −0.279123 0.483455i 0.692044 0.721855i \(-0.256710\pi\)
−0.971167 + 0.238400i \(0.923377\pi\)
\(588\) −4.44436e12 + 4.06313e12i −1.53324 + 1.40173i
\(589\) 2.16273e12 3.74595e12i 0.740428 1.28246i
\(590\) −5.59938e11 + 9.69841e11i −0.190242 + 0.329508i
\(591\) 5.06306e12 1.70714
\(592\) 2.78799e10 0.00932918
\(593\) −1.87116e10 + 3.24095e10i −0.00621392 + 0.0107628i −0.869116 0.494609i \(-0.835311\pi\)
0.862902 + 0.505372i \(0.168645\pi\)
\(594\) −1.43545e12 + 2.48628e12i −0.473097 + 0.819427i
\(595\) 1.29413e12 1.61056e12i 0.423304 0.526806i
\(596\) −1.89262e12 3.27811e12i −0.614405 1.06418i
\(597\) −2.48304e12 + 4.30075e12i −0.800017 + 1.38567i
\(598\) −7.90533e12 4.00119e12i −2.52793 1.27948i
\(599\) 2.68642e12 + 4.65301e12i 0.852615 + 1.47677i 0.878840 + 0.477117i \(0.158318\pi\)
−0.0262245 + 0.999656i \(0.508348\pi\)
\(600\) −3.17456e12 −1.00001
\(601\) 2.01663e10 + 3.49290e10i 0.00630508 + 0.0109207i 0.869161 0.494530i \(-0.164660\pi\)
−0.862856 + 0.505450i \(0.831326\pi\)
\(602\) −1.90663e12 + 2.37282e12i −0.591673 + 0.736343i
\(603\) 2.17515e12 0.669978
\(604\) 6.71501e11 + 1.16307e12i 0.205296 + 0.355583i
\(605\) −6.00447e12 −1.82211
\(606\) 4.52260e12 + 7.83338e12i 1.36226 + 2.35951i
\(607\) 6.45956e11 + 1.11883e12i 0.193132 + 0.334514i 0.946286 0.323329i \(-0.104802\pi\)
−0.753155 + 0.657843i \(0.771469\pi\)
\(608\) −1.68614e12 2.92047e12i −0.500410 0.866736i
\(609\) −5.22214e11 8.06834e10i −0.153841 0.0237687i
\(610\) −1.07081e13 −3.13132
\(611\) 2.53362e12 1.65507e12i 0.735456 0.480431i
\(612\) −9.80741e11 1.69869e12i −0.282601 0.489479i
\(613\) −1.00893e12 + 1.74752e12i −0.288596 + 0.499863i −0.973475 0.228794i \(-0.926522\pi\)
0.684879 + 0.728657i \(0.259855\pi\)
\(614\) −2.88385e12 −0.818869
\(615\) 5.04385e12 8.73621e12i 1.42175 2.46255i
\(616\) 3.26308e12 4.06094e12i 0.913092 1.13635i
\(617\) 2.24918e12 3.89569e12i 0.624800 1.08218i −0.363780 0.931485i \(-0.618514\pi\)
0.988580 0.150700i \(-0.0481527\pi\)
\(618\) −1.14979e12 1.99150e12i −0.317082 0.549203i
\(619\) −5.63565e11 9.76123e11i −0.154289 0.267237i 0.778511 0.627631i \(-0.215975\pi\)
−0.932800 + 0.360394i \(0.882642\pi\)
\(620\) 1.22024e13 3.31652
\(621\) −2.49910e12 −0.674329
\(622\) 1.84927e12 + 3.20304e12i 0.495387 + 0.858035i
\(623\) 2.51906e12 + 3.89200e11i 0.669949 + 0.103509i
\(624\) 2.55270e11 1.66753e11i 0.0674013 0.0440294i
\(625\) 2.20566e12 3.82031e12i 0.578200 1.00147i
\(626\) −7.89187e11 + 1.36691e12i −0.205398 + 0.355759i
\(627\) −3.70219e12 + 6.41237e12i −0.956652 + 1.65697i
\(628\) 2.98834e12 + 5.17596e12i 0.766677 + 1.32792i
\(629\) −2.98878e11 −0.0761318
\(630\) 5.97344e12 + 9.22911e11i 1.51075 + 0.233414i
\(631\) 5.45292e11 9.44474e11i 0.136930 0.237169i −0.789403 0.613875i \(-0.789610\pi\)
0.926333 + 0.376706i \(0.122943\pi\)
\(632\) −1.05468e12 + 1.82676e12i −0.262963 + 0.455465i
\(633\) −5.58707e12 −1.38314
\(634\) 4.05757e12 7.02792e12i 0.997389 1.72753i
\(635\) 3.89046e12 0.949553
\(636\) 2.12615e12 0.515273
\(637\) 2.96844e12 + 2.90808e12i 0.714332 + 0.699807i
\(638\) 1.23178e12 0.294333
\(639\) −4.70818e12 −1.11712
\(640\) 4.47386e12 7.74895e12i 1.05408 1.82571i
\(641\) 2.91737e12 0.682543 0.341272 0.939965i \(-0.389142\pi\)
0.341272 + 0.939965i \(0.389142\pi\)
\(642\) 7.55798e12 1.30908e13i 1.75589 3.04130i
\(643\) 4.03060e12 6.98121e12i 0.929867 1.61058i 0.146326 0.989236i \(-0.453255\pi\)
0.783541 0.621341i \(-0.213412\pi\)
\(644\) 1.20761e13 + 1.86578e12i 2.76655 + 0.427439i
\(645\) 4.52953e12 1.03047
\(646\) 1.70907e12 + 2.96020e12i 0.386112 + 0.668766i
\(647\) −9.09630e11 + 1.57553e12i −0.204078 + 0.353473i −0.949838 0.312741i \(-0.898753\pi\)
0.745761 + 0.666214i \(0.232086\pi\)
\(648\) −2.57308e12 + 4.45671e12i −0.573279 + 0.992948i
\(649\) −6.10199e11 + 1.05690e12i −0.135011 + 0.233847i
\(650\) 3.24812e11 + 5.89408e12i 0.0713710 + 1.29511i
\(651\) −9.18296e12 1.41879e12i −2.00386 0.309602i
\(652\) 5.14429e12 + 8.91016e12i 1.11484 + 1.93095i
\(653\) −6.97913e12 −1.50208 −0.751039 0.660258i \(-0.770447\pi\)
−0.751039 + 0.660258i \(0.770447\pi\)
\(654\) −7.18779e11 −0.153637
\(655\) −2.58503e12 4.47741e12i −0.548757 0.950475i
\(656\) 2.36697e11 + 4.09972e11i 0.0499029 + 0.0864344i
\(657\) −1.57557e12 + 2.72897e12i −0.329909 + 0.571420i
\(658\) −4.25829e12 + 5.29949e12i −0.885562 + 1.10209i
\(659\) −9.76262e11 + 1.69094e12i −0.201643 + 0.349255i −0.949058 0.315102i \(-0.897961\pi\)
0.747415 + 0.664357i \(0.231295\pi\)
\(660\) −2.08882e13 −4.28503
\(661\) 4.10042e12 7.10214e12i 0.835453 1.44705i −0.0582073 0.998305i \(-0.518538\pi\)
0.893661 0.448743i \(-0.148128\pi\)
\(662\) −4.28544e12 7.42260e12i −0.867231 1.50209i
\(663\) −2.73654e12 + 1.78762e12i −0.550036 + 0.359307i
\(664\) 5.26615e12 1.05132
\(665\) −6.39059e12 9.87362e11i −1.26720 0.195785i
\(666\) −4.37184e11 7.57225e11i −0.0861054 0.149139i
\(667\) 5.36126e11 + 9.28598e11i 0.104882 + 0.181661i
\(668\) 1.53180e12 + 2.65316e12i 0.297652 + 0.515549i
\(669\) −5.15620e11 −0.0995204
\(670\) −5.34660e12 9.26058e12i −1.02504 1.77542i
\(671\) −1.16693e13 −2.22225
\(672\) −4.53762e12 + 5.64711e12i −0.858353 + 1.06823i
\(673\) 4.74419e12 + 8.21718e12i 0.891445 + 1.54403i 0.838144 + 0.545449i \(0.183641\pi\)
0.0533011 + 0.998578i \(0.483026\pi\)
\(674\) 1.28047e13 2.39002
\(675\) 8.32498e11 + 1.44193e12i 0.154353 + 0.267348i
\(676\) 5.11224e12 + 6.95730e12i 0.941567 + 1.28139i
\(677\) 1.12730e12 1.95253e12i 0.206248 0.357232i −0.744282 0.667866i \(-0.767208\pi\)
0.950530 + 0.310634i \(0.100541\pi\)
\(678\) 2.72954e12 + 4.72771e12i 0.496085 + 0.859245i
\(679\) −4.50651e12 + 5.60839e12i −0.813628 + 1.01257i
\(680\) −1.78931e12 + 3.09918e12i −0.320920 + 0.555850i
\(681\) −6.02021e12 + 1.04273e13i −1.07263 + 1.85785i
\(682\) 2.16604e13 3.83386
\(683\) 8.44847e12 1.48554 0.742771 0.669545i \(-0.233511\pi\)
0.742771 + 0.669545i \(0.233511\pi\)
\(684\) −3.06953e12 + 5.31657e12i −0.536190 + 0.928708i
\(685\) −4.06546e11 + 7.04157e11i −0.0705507 + 0.122197i
\(686\) −8.36528e12 4.14322e12i −1.44219 0.714298i
\(687\) −2.05995e12 3.56794e12i −0.352818 0.611099i
\(688\) −1.06281e11 + 1.84083e11i −0.0180845 + 0.0313232i
\(689\) −8.07341e10 1.46501e12i −0.0136480 0.247659i
\(690\) −1.48090e13 2.56499e13i −2.48717 4.30790i
\(691\) −6.77663e10 −0.0113074 −0.00565370 0.999984i \(-0.501800\pi\)
−0.00565370 + 0.999984i \(0.501800\pi\)
\(692\) 7.29010e12 + 1.26268e13i 1.20853 + 2.09323i
\(693\) 6.50963e12 + 1.00575e12i 1.07215 + 0.165650i
\(694\) 3.21550e12 0.526175
\(695\) 5.09201e12 + 8.81961e12i 0.827861 + 1.43390i
\(696\) 9.15253e11 0.147843
\(697\) −2.53744e12 4.39498e12i −0.407238 0.705357i
\(698\) −8.55040e12 1.48097e13i −1.36344 2.36155i
\(699\) −2.25399e12 3.90402e12i −0.357112 0.618536i
\(700\) −2.94625e12 7.58916e12i −0.463797 1.19468i
\(701\) 1.00876e12 0.157782 0.0788912 0.996883i \(-0.474862\pi\)
0.0788912 + 0.996883i \(0.474862\pi\)
\(702\) 3.53911e12 + 1.79128e12i 0.550019 + 0.278386i
\(703\) 4.67714e11 + 8.10105e11i 0.0722240 + 0.125096i
\(704\) 8.13535e12 1.40908e13i 1.24824 2.16202i
\(705\) 1.01163e13 1.54231
\(706\) −2.65580e12 + 4.59998e12i −0.402323 + 0.696843i
\(707\) −5.39209e12 + 6.71052e12i −0.811653 + 1.01011i
\(708\) −1.22171e12 + 2.11606e12i −0.182733 + 0.316503i
\(709\) −1.04124e12 1.80349e12i −0.154755 0.268043i 0.778215 0.627998i \(-0.216125\pi\)
−0.932970 + 0.359955i \(0.882792\pi\)
\(710\) 1.15729e13 + 2.00448e13i 1.70915 + 2.96033i
\(711\) −2.66707e12 −0.391401
\(712\) −4.41500e12 −0.643829
\(713\) 9.42759e12 + 1.63291e13i 1.36615 + 2.36624i
\(714\) 4.59934e12 5.72392e12i 0.662298 0.824237i
\(715\) 7.93164e11 + 1.43929e13i 0.113497 + 2.05954i
\(716\) 1.31146e11 2.27152e11i 0.0186487 0.0323004i
\(717\) −5.84611e12 + 1.01258e13i −0.826097 + 1.43084i
\(718\) 5.46809e12 9.47101e12i 0.767848 1.32995i
\(719\) 1.14377e12 + 1.98106e12i 0.159609 + 0.276451i 0.934728 0.355365i \(-0.115643\pi\)
−0.775119 + 0.631816i \(0.782310\pi\)
\(720\) 4.22082e11 0.0585330
\(721\) 1.37085e12 1.70603e12i 0.188921 0.235114i
\(722\) −5.26489e11 + 9.11905e11i −0.0721061 + 0.124891i
\(723\) 5.17585e12 8.96484e12i 0.704465 1.22017i
\(724\) −1.90441e13 −2.57595
\(725\) 3.57188e11 6.18667e11i 0.0480148 0.0831641i
\(726\) −2.13398e13 −2.85086
\(727\) −9.43893e12 −1.25319 −0.626597 0.779344i \(-0.715553\pi\)
−0.626597 + 0.779344i \(0.715553\pi\)
\(728\) −5.85041e12 4.19290e12i −0.771960 0.553253i
\(729\) −2.69078e12 −0.352862
\(730\) 1.54913e13 2.01899
\(731\) 1.13935e12 1.97341e12i 0.147580 0.255617i
\(732\) −2.33636e13 −3.00774
\(733\) 1.22092e12 2.11470e12i 0.156214 0.270571i −0.777286 0.629147i \(-0.783404\pi\)
0.933500 + 0.358576i \(0.116738\pi\)
\(734\) −6.96187e12 + 1.20583e13i −0.885306 + 1.53340i
\(735\) 2.99102e12 + 1.35653e13i 0.378030 + 1.71450i
\(736\) 1.47001e13 1.84659
\(737\) −5.82652e12 1.00918e13i −0.727454 1.25999i
\(738\) 7.42329e12 1.28575e13i 0.921176 1.59552i
\(739\) 2.89670e12 5.01723e12i 0.357276 0.618819i −0.630229 0.776409i \(-0.717039\pi\)
0.987505 + 0.157590i \(0.0503724\pi\)
\(740\) −1.31945e12 + 2.28536e12i −0.161752 + 0.280163i
\(741\) 9.12775e12 + 4.61991e12i 1.11220 + 0.562926i
\(742\) 1.19284e12 + 3.07261e12i 0.144466 + 0.372126i
\(743\) −5.17955e11 8.97125e11i −0.0623509 0.107995i 0.833165 0.553025i \(-0.186526\pi\)
−0.895516 + 0.445030i \(0.853193\pi\)
\(744\) 1.60944e13 1.92574
\(745\) −8.73189e12 −1.03850
\(746\) −3.91717e12 6.78474e12i −0.463071 0.802063i
\(747\) 3.32925e12 + 5.76643e12i 0.391204 + 0.677586i
\(748\) −5.25418e12 + 9.10051e12i −0.613688 + 1.06294i
\(749\) 1.42174e13 + 2.19662e12i 1.65064 + 0.255028i
\(750\) 2.37564e12 4.11473e12i 0.274161 0.474860i
\(751\) −1.06994e13 −1.22738 −0.613692 0.789545i \(-0.710317\pi\)
−0.613692 + 0.789545i \(0.710317\pi\)
\(752\) −2.37369e11 + 4.11135e11i −0.0270672 + 0.0468817i
\(753\) 1.74639e12 + 3.02484e12i 0.197954 + 0.342867i
\(754\) −9.36461e10 1.69932e12i −0.0105516 0.191471i
\(755\) 3.09807e12 0.347001
\(756\) −5.40629e12 8.35285e11i −0.601937 0.0930007i
\(757\) 1.03228e12 + 1.78795e12i 0.114252 + 0.197890i 0.917481 0.397781i \(-0.130219\pi\)
−0.803228 + 0.595671i \(0.796886\pi\)
\(758\) −8.29120e12 1.43608e13i −0.912234 1.58003i
\(759\) −1.61383e13 2.79523e13i −1.76510 3.05724i
\(760\) 1.12004e13 1.21779
\(761\) −6.29433e12 1.09021e13i −0.680328 1.17836i −0.974881 0.222728i \(-0.928504\pi\)
0.294552 0.955635i \(-0.404829\pi\)
\(762\) 1.38267e13 1.48566
\(763\) −2.47568e11 6.37704e11i −0.0264444 0.0681175i
\(764\) 1.51482e12 + 2.62374e12i 0.160857 + 0.278612i
\(765\) −4.52480e12 −0.477665
\(766\) 2.52435e12 + 4.37230e12i 0.264923 + 0.458860i
\(767\) 1.50445e12 + 7.61459e11i 0.156963 + 0.0794452i
\(768\) 5.65676e12 9.79779e12i 0.586735 1.01626i
\(769\) −3.77360e11 6.53606e11i −0.0389123 0.0673981i 0.845913 0.533320i \(-0.179056\pi\)
−0.884826 + 0.465922i \(0.845723\pi\)
\(770\) −1.17190e13 3.01866e13i −1.20138 3.09461i
\(771\) 7.61568e12 1.31907e13i 0.776182 1.34439i
\(772\) −2.05404e11 + 3.55771e11i −0.0208129 + 0.0360489i
\(773\) −5.92334e12 −0.596704 −0.298352 0.954456i \(-0.596437\pi\)
−0.298352 + 0.954456i \(0.596437\pi\)
\(774\) 6.66633e12 0.667656
\(775\) 6.28102e12 1.08790e13i 0.625421 1.08326i
\(776\) 6.23086e12 1.07922e13i 0.616837 1.06839i
\(777\) 1.25868e12 1.56644e12i 0.123886 0.154177i
\(778\) −1.52805e13 2.64666e13i −1.49530 2.58994i
\(779\) −7.94169e12 + 1.37554e13i −0.772670 + 1.33830i
\(780\) 1.58803e12 + 2.88167e13i 0.153615 + 2.78752i
\(781\) 1.26117e13 + 2.18441e13i 1.21295 + 2.10090i
\(782\) −1.49001e13 −1.42482
\(783\) −2.40017e11 4.15721e11i −0.0228199 0.0395252i
\(784\) −6.21485e11 1.96738e11i −0.0587500 0.0185980i
\(785\) 1.37872e13 1.29587
\(786\) −9.18719e12 1.59127e13i −0.858581 1.48711i
\(787\) −2.10589e13 −1.95681 −0.978407 0.206688i \(-0.933732\pi\)
−0.978407 + 0.206688i \(0.933732\pi\)
\(788\) −1.12447e13 1.94764e13i −1.03891 1.79945i
\(789\) 3.43395e12 + 5.94778e12i 0.315462 + 0.546397i
\(790\) 6.55576e12 + 1.13549e13i 0.598827 + 1.03720i
\(791\) −3.25431e12 + 4.05002e12i −0.295573 + 0.367844i
\(792\) −1.14090e13 −1.03035
\(793\) 8.87160e11 + 1.60985e13i 0.0796659 + 1.44563i
\(794\) 9.32001e12 + 1.61427e13i 0.832193 + 1.44140i
\(795\) 2.45234e12 4.24757e12i 0.217735 0.377128i
\(796\) 2.20586e13 1.94746
\(797\) 6.29784e12 1.09082e13i 0.552878 0.957613i −0.445187 0.895438i \(-0.646863\pi\)
0.998065 0.0621755i \(-0.0198038\pi\)
\(798\) −2.27121e13 3.50908e12i −1.98264 0.306323i
\(799\) 2.54464e12 4.40744e12i 0.220885 0.382584i
\(800\) −4.89690e12 8.48167e12i −0.422684 0.732110i
\(801\) −2.79115e12 4.83442e12i −0.239573 0.414952i
\(802\) −3.40803e13 −2.90883
\(803\) 1.68818e13 1.43284
\(804\) −1.16655e13 2.02053e13i −0.984584 1.70535i
\(805\) 1.76561e13 2.19732e13i 1.48188 1.84422i
\(806\) −1.64673e12 2.98819e13i −0.137441 2.49402i
\(807\) −7.43547e12 + 1.28786e13i −0.617131 + 1.06890i
\(808\) 7.45531e12 1.29130e13i 0.615339 1.06580i
\(809\) −8.14399e12 + 1.41058e13i −0.668450 + 1.15779i 0.309888 + 0.950773i \(0.399709\pi\)
−0.978338 + 0.207016i \(0.933625\pi\)
\(810\) 1.59939e13 + 2.77023e13i 1.30549 + 2.26117i
\(811\) 8.91726e12 0.723831 0.361916 0.932211i \(-0.382123\pi\)
0.361916 + 0.932211i \(0.382123\pi\)
\(812\) 8.49429e11 + 2.18802e12i 0.0685686 + 0.176624i
\(813\) −6.24951e10 + 1.08245e11i −0.00501694 + 0.00868959i
\(814\) −2.34215e12 + 4.05672e12i −0.186984 + 0.323866i
\(815\) 2.37340e13 1.88435
\(816\) 2.56379e11 4.44062e11i 0.0202431 0.0350621i
\(817\) −7.13187e12 −0.560021
\(818\) 2.31318e13 1.80642
\(819\) 8.92607e11 9.05693e12i 0.0693239 0.703402i
\(820\) −4.48080e13 −3.46093
\(821\) 2.76333e12 0.212270 0.106135 0.994352i \(-0.466152\pi\)
0.106135 + 0.994352i \(0.466152\pi\)
\(822\) −1.44486e12 + 2.50257e12i −0.110383 + 0.191189i
\(823\) 2.10364e12 0.159835 0.0799177 0.996801i \(-0.474534\pi\)
0.0799177 + 0.996801i \(0.474534\pi\)
\(824\) −1.89538e12 + 3.28290e12i −0.143227 + 0.248076i
\(825\) −1.07519e13 + 1.86229e13i −0.808060 + 1.39960i
\(826\) −3.74345e12 5.78371e11i −0.279809 0.0432311i
\(827\) −5.60638e12 −0.416781 −0.208391 0.978046i \(-0.566823\pi\)
−0.208391 + 0.978046i \(0.566823\pi\)
\(828\) −1.33804e13 2.31756e13i −0.989314 1.71354i
\(829\) −5.71792e12 + 9.90372e12i −0.420477 + 0.728288i −0.995986 0.0895077i \(-0.971471\pi\)
0.575509 + 0.817795i \(0.304804\pi\)
\(830\) 1.63668e13 2.83482e13i 1.19705 2.07336i
\(831\) −1.70431e12 + 2.95195e12i −0.123978 + 0.214736i
\(832\) −2.00577e13 1.01520e13i −1.45120 0.734507i
\(833\) 6.66244e12 + 2.10907e12i 0.479436 + 0.151771i
\(834\) 1.80970e13 + 3.13449e13i 1.29526 + 2.24346i
\(835\) 7.06722e12 0.503106
\(836\) 3.28891e13 2.32875
\(837\) −4.22061e12 7.31031e12i −0.297242 0.514839i
\(838\) 4.89754e12 + 8.48278e12i 0.343068 + 0.594211i
\(839\) −1.02878e13 + 1.78190e13i −0.716792 + 1.24152i 0.245472 + 0.969404i \(0.421057\pi\)
−0.962264 + 0.272116i \(0.912276\pi\)
\(840\) −8.70762e12 2.24297e13i −0.603452 1.55441i
\(841\) 7.15059e12 1.23852e13i 0.492901 0.853730i
\(842\) −1.79874e13 −1.23328
\(843\) −8.45061e11 + 1.46369e12i −0.0576320 + 0.0998216i
\(844\) 1.24085e13 + 2.14921e13i 0.841738 + 1.45793i
\(845\) 1.97956e13 2.18844e12i 1.33572 0.147666i
\(846\) 1.48887e13 0.999286
\(847\) −7.35006e12 1.89328e13i −0.490699 1.26398i
\(848\) 1.15083e11 + 1.99329e11i 0.00764240 + 0.0132370i
\(849\) 2.15855e12 + 3.73872e12i 0.142586 + 0.246967i
\(850\) 4.96351e12 + 8.59705e12i 0.326140 + 0.564890i
\(851\) −4.07765e12 −0.266518
\(852\) 2.52505e13 + 4.37351e13i 1.64169 + 2.84349i
\(853\) −7.62755e12 −0.493304 −0.246652 0.969104i \(-0.579330\pi\)
−0.246652 + 0.969104i \(0.579330\pi\)
\(854\) −1.31078e13 3.37639e13i −0.843273 2.17216i
\(855\) 7.08087e12 + 1.22644e13i 0.453147 + 0.784873i
\(856\) −2.49180e13 −1.58628
\(857\) −1.11324e13 1.92818e13i −0.704976 1.22105i −0.966700 0.255911i \(-0.917624\pi\)
0.261724 0.965143i \(-0.415709\pi\)
\(858\) 2.81890e12 + 5.11522e13i 0.177577 + 3.22234i
\(859\) −5.91009e12 + 1.02366e13i −0.370361 + 0.641484i −0.989621 0.143702i \(-0.954099\pi\)
0.619260 + 0.785186i \(0.287433\pi\)
\(860\) −1.00597e13 1.74240e13i −0.627109 1.08619i
\(861\) 3.37205e13 + 5.20989e12i 2.09112 + 0.323084i
\(862\) 7.66940e12 1.32838e13i 0.473128 0.819482i
\(863\) 2.03354e12 3.52220e12i 0.124797 0.216155i −0.796857 0.604169i \(-0.793505\pi\)
0.921654 + 0.388014i \(0.126839\pi\)
\(864\) −6.58106e12 −0.401776
\(865\) 3.36340e13 2.04271
\(866\) −1.28645e12 + 2.22819e12i −0.0777250 + 0.134624i
\(867\) 8.11953e12 1.40634e13i 0.488028 0.845290i
\(868\) 1.49369e13 + 3.84756e13i 0.893146 + 2.30063i
\(869\) 7.14422e12 + 1.23742e13i 0.424978 + 0.736083i
\(870\) 2.84454e12 4.92690e12i 0.168336 0.291566i
\(871\) −1.34794e13 + 8.80530e12i −0.793575 + 0.518397i
\(872\) 5.92437e11 + 1.02613e12i 0.0346991 + 0.0601006i
\(873\) 1.57565e13 0.918114
\(874\) 2.33172e13 + 4.03865e13i 1.35168 + 2.34118i
\(875\) 4.46885e12 + 6.90448e11i 0.257727 + 0.0398194i
\(876\) 3.37998e13 1.93931
\(877\) −8.76595e12 1.51831e13i −0.500381 0.866685i −1.00000 0.000439838i \(-0.999860\pi\)
0.499619 0.866245i \(-0.333473\pi\)
\(878\) −2.07030e13 −1.17573
\(879\) −1.33572e13 2.31353e13i −0.754682 1.30715i
\(880\) −1.13062e12 1.95829e12i −0.0635543 0.110079i
\(881\) −5.37255e12 9.30552e12i −0.300461 0.520414i 0.675779 0.737104i \(-0.263807\pi\)
−0.976240 + 0.216690i \(0.930474\pi\)
\(882\) 4.40203e12 + 1.99647e13i 0.244932 + 1.11085i
\(883\) −3.73309e12 −0.206655 −0.103327 0.994647i \(-0.532949\pi\)
−0.103327 + 0.994647i \(0.532949\pi\)
\(884\) 1.29542e13 + 6.55662e12i 0.713469 + 0.361114i
\(885\) 2.81827e12 + 4.88139e12i 0.154432 + 0.267485i
\(886\) −2.04448e13 + 3.54115e13i −1.11463 + 1.93060i
\(887\) 2.17771e13 1.18126 0.590628 0.806944i \(-0.298880\pi\)
0.590628 + 0.806944i \(0.298880\pi\)
\(888\) −1.74030e12 + 3.01429e12i −0.0939216 + 0.162677i
\(889\) 4.76230e12 + 1.22671e13i 0.255717 + 0.658694i
\(890\) −1.37215e13 + 2.37664e13i −0.733073 + 1.26972i
\(891\) 1.74296e13 + 3.01889e13i 0.926482 + 1.60471i
\(892\) 1.14515e12 + 1.98346e12i 0.0605650 + 0.104902i
\(893\) −1.59284e13 −0.838188
\(894\) −3.10331e13 −1.62482
\(895\) −3.02532e11 5.24001e11i −0.0157604 0.0272978i
\(896\) 2.99098e13 + 4.62114e12i 1.55034 + 0.239532i
\(897\) −3.73352e13 + 2.43889e13i −1.92554 + 1.25784i
\(898\) −9.68680e12 + 1.67780e13i −0.497092 + 0.860989i
\(899\) −1.81087e12 + 3.13652e12i −0.0924633 + 0.160151i
\(900\) −8.91456e12 + 1.54405e13i −0.452906 + 0.784457i
\(901\) −1.23371e12 2.13685e12i −0.0623666 0.108022i
\(902\) −7.95384e13 −4.00080
\(903\) 5.54459e12 + 1.42821e13i 0.277507 + 0.714823i
\(904\) 4.49953e12 7.79341e12i 0.224083 0.388123i
\(905\) −2.19657e13 + 3.80458e13i −1.08850 + 1.88533i
\(906\) 1.10105e13 0.542915
\(907\) −1.83740e13 + 3.18248e13i −0.901513 + 1.56147i −0.0759824 + 0.997109i \(0.524209\pi\)
−0.825531 + 0.564357i \(0.809124\pi\)
\(908\) 5.34817e13 2.61107
\(909\) 1.88529e13 0.915885
\(910\) −4.07535e13 + 1.84621e13i −1.97006 + 0.892470i
\(911\) −2.03724e13 −0.979963 −0.489981 0.871733i \(-0.662996\pi\)
−0.489981 + 0.871733i \(0.662996\pi\)
\(912\) −1.60483e12 −0.0768163
\(913\) 1.78360e13 3.08928e13i 0.849529 1.47143i
\(914\) −6.14205e12 −0.291109
\(915\) −2.69479e13 + 4.66752e13i −1.27095 + 2.20136i
\(916\) −9.14997e12 + 1.58482e13i −0.429428 + 0.743791i
\(917\) 1.09535e13 1.36317e13i 0.511552 0.636632i
\(918\) 6.67058e12 0.310007
\(919\) 1.51368e13 + 2.62177e13i 0.700025 + 1.21248i 0.968457 + 0.249180i \(0.0801611\pi\)
−0.268432 + 0.963299i \(0.586506\pi\)
\(920\) −2.44120e13 + 4.22828e13i −1.12346 + 1.94589i
\(921\) −7.25746e12 + 1.25703e13i −0.332366 + 0.575675i
\(922\) −1.85515e13 + 3.21322e13i −0.845454 + 1.46437i
\(923\) 2.91766e13 1.90594e13i 1.32320 0.864373i
\(924\) −2.55692e13 6.58630e13i −1.15397 2.97247i
\(925\) 1.35834e12 + 2.35272e12i 0.0610058 + 0.105665i
\(926\) 3.15900e13 1.41189
\(927\) −4.79303e12 −0.213182
\(928\) 1.41182e12 + 2.44534e12i 0.0624903 + 0.108236i
\(929\) −2.84077e12 4.92037e12i −0.125131 0.216734i 0.796653 0.604437i \(-0.206602\pi\)
−0.921784 + 0.387703i \(0.873269\pi\)
\(930\) 5.00203e13 8.66378e13i 2.19267 3.79782i
\(931\) −4.70945e12 2.13589e13i −0.205445 0.931765i
\(932\) −1.00119e13 + 1.73411e13i −0.434654 + 0.752842i
\(933\) 1.86155e13 0.804279
\(934\) 3.09942e13 5.36836e13i 1.33266 2.30824i
\(935\) 1.21205e13 + 2.09933e13i 0.518642 + 0.898315i
\(936\) 8.67374e11 + 1.57395e13i 0.0369373 + 0.670270i
\(937\) 3.77902e12 0.160159 0.0800795 0.996788i \(-0.474483\pi\)
0.0800795 + 0.996788i \(0.474483\pi\)
\(938\) 2.26550e13 2.81943e13i 0.955544 1.18918i
\(939\) 3.97212e12 + 6.87991e12i 0.166735 + 0.288794i
\(940\) −2.24676e13 3.89150e13i −0.938600 1.62570i
\(941\) −2.45300e12 4.24872e12i −0.101987 0.176647i 0.810516 0.585716i \(-0.199187\pi\)
−0.912503 + 0.409070i \(0.865853\pi\)
\(942\) 4.89996e13 2.02751
\(943\) −3.46188e13 5.99615e13i −1.42564 2.46928i
\(944\) −2.64511e11 −0.0108410
\(945\) −7.90440e12 + 9.83711e12i −0.322423 + 0.401258i
\(946\) −1.78570e13 3.09292e13i −0.724932 1.25562i
\(947\) −5.30841e11 −0.0214482 −0.0107241 0.999942i \(-0.503414\pi\)
−0.0107241 + 0.999942i \(0.503414\pi\)
\(948\) 1.43038e13 + 2.47749e13i 0.575193 + 0.996263i
\(949\) −1.28344e12 2.32896e13i −0.0513664 0.932102i
\(950\) 1.55348e13 2.69070e13i 0.618798 1.07179i
\(951\) −2.04225e13 3.53728e13i −0.809649 1.40235i
\(952\) −1.19624e13 1.84822e12i −0.472011 0.0729268i
\(953\) −1.83780e13 + 3.18316e13i −0.721737 + 1.25009i 0.238566 + 0.971126i \(0.423323\pi\)
−0.960303 + 0.278959i \(0.910011\pi\)
\(954\) 3.60923e12 6.25136e12i 0.141074 0.244347i
\(955\) 6.98884e12 0.271888
\(956\) 5.19351e13 2.01094
\(957\) 3.09988e12 5.36915e12i 0.119465 0.206920i
\(958\) −9.28123e12 + 1.60756e13i −0.356009 + 0.616625i
\(959\) −2.71795e12 4.19929e11i −0.103766 0.0160322i
\(960\) −3.75740e13 6.50800e13i −1.42780 2.47302i
\(961\) −1.86238e13 + 3.22573e13i −0.704389 + 1.22004i
\(962\) 5.77458e12 + 2.92274e12i 0.217386 + 0.110028i
\(963\) −1.57531e13 2.72852e13i −0.590266 1.02237i
\(964\) −4.59807e13 −1.71486
\(965\) 4.73833e11 + 8.20702e11i 0.0175894 + 0.0304658i
\(966\) 6.27497e13 7.80926e13i 2.31854 2.88545i
\(967\) −1.61423e11 −0.00593672 −0.00296836 0.999996i \(-0.500945\pi\)
−0.00296836 + 0.999996i \(0.500945\pi\)
\(968\) 1.75889e13 + 3.04648e13i 0.643871 + 1.11522i
\(969\) 1.72041e13 0.626868
\(970\) −3.87302e13 6.70827e13i −1.40468 2.43297i
\(971\) −1.51069e13 2.61660e13i −0.545368 0.944605i −0.998584 0.0532040i \(-0.983057\pi\)
0.453216 0.891401i \(-0.350277\pi\)
\(972\) 2.64215e13 + 4.57634e13i 0.949422 + 1.64445i
\(973\) −2.15762e13 + 2.68518e13i −0.771733 + 0.960429i
\(974\) 5.29317e13 1.88452
\(975\) 2.65089e13 + 1.34172e13i 0.939445 + 0.475489i
\(976\) −1.26461e12 2.19037e12i −0.0446100 0.0772667i
\(977\) 1.34810e13 2.33498e13i 0.473365 0.819892i −0.526170 0.850379i \(-0.676372\pi\)
0.999535 + 0.0304869i \(0.00970579\pi\)
\(978\) 8.43504e13 2.94824
\(979\) −1.49532e13 + 2.58997e13i −0.520250 + 0.901099i
\(980\) 4.55395e13 4.16332e13i 1.57714 1.44186i
\(981\) −7.49075e11 + 1.29744e12i −0.0258235 + 0.0447276i
\(982\) −8.50965e12 1.47392e13i −0.292018 0.505791i
\(983\) 1.00746e12 + 1.74497e12i 0.0344140 + 0.0596069i 0.882719 0.469900i \(-0.155710\pi\)
−0.848305 + 0.529507i \(0.822377\pi\)
\(984\) −5.90998e13 −2.00959
\(985\) −5.18791e13 −1.75602
\(986\) −1.43102e12 2.47860e12i −0.0482170 0.0835143i
\(987\) 1.23834e13 + 3.18980e13i 0.415348 + 1.06988i
\(988\) −2.50040e12 4.53726e13i −0.0834840 1.51491i
\(989\) 1.55444e13 2.69236e13i 0.516641 0.894849i
\(990\) −3.54585e13 + 6.14159e13i −1.17317 + 2.03200i
\(991\) −2.63769e13 + 4.56861e13i −0.868745 + 1.50471i −0.00546523 + 0.999985i \(0.501740\pi\)
−0.863280 + 0.504726i \(0.831594\pi\)
\(992\) 2.48263e13 + 4.30005e13i 0.813973 + 1.40984i
\(993\) −4.31388e13 −1.40798
\(994\) −4.90374e13 + 6.10276e13i −1.59327 + 1.98284i
\(995\) 2.54427e13 4.40680e13i 0.822922 1.42534i
\(996\) 3.57102e13 6.18519e13i 1.14981 1.99153i
\(997\) −5.13518e12 −0.164599 −0.0822995 0.996608i \(-0.526226\pi\)
−0.0822995 + 0.996608i \(0.526226\pi\)
\(998\) −7.50125e12 + 1.29925e13i −0.239357 + 0.414578i
\(999\) 1.82551e12 0.0579882
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 91.10.h.a.16.10 yes 164
7.4 even 3 91.10.g.a.81.73 yes 164
13.9 even 3 91.10.g.a.9.73 164
91.74 even 3 inner 91.10.h.a.74.10 yes 164
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.10.g.a.9.73 164 13.9 even 3
91.10.g.a.81.73 yes 164 7.4 even 3
91.10.h.a.16.10 yes 164 1.1 even 1 trivial
91.10.h.a.74.10 yes 164 91.74 even 3 inner