Properties

Label 14.14.c.a.9.3
Level $14$
Weight $14$
Character 14.9
Analytic conductor $15.012$
Analytic rank $0$
Dimension $8$
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] = [14,14,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.9");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 14.c (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: \(15.0123300533\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2 x^{7} + 692094 x^{6} + 445371928 x^{5} + 480078817147 x^{4} + 153633603309480 x^{3} + \cdots + 23\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14}\cdot 3\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.3
Root \(481.229 - 833.513i\) of defining polynomial
Character \(\chi\) \(=\) 14.9
Dual form 14.14.c.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-32.0000 + 55.4256i) q^{2} +(301.970 + 523.027i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(2521.96 - 4368.16i) q^{5} -38652.2 q^{6} +(302038. + 75247.5i) q^{7} +262144. q^{8} +(614790. - 1.06485e6i) q^{9} +O(q^{10})\) \(q+(-32.0000 + 55.4256i) q^{2} +(301.970 + 523.027i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(2521.96 - 4368.16i) q^{5} -38652.2 q^{6} +(302038. + 75247.5i) q^{7} +262144. q^{8} +(614790. - 1.06485e6i) q^{9} +(161406. + 279563. i) q^{10} +(542112. + 938966. i) q^{11} +(1.23687e6 - 2.14232e6i) q^{12} +4.14987e6 q^{13} +(-1.38358e7 + 1.43327e7i) q^{14} +3.04623e6 q^{15} +(-8.38861e6 + 1.45295e7i) q^{16} +(7.24847e7 + 1.25547e8i) q^{17} +(3.93465e7 + 6.81502e7i) q^{18} +(-1.39515e8 + 2.41647e8i) q^{19} -2.06599e7 q^{20} +(5.18498e7 + 1.80697e8i) q^{21} -6.93903e7 q^{22} +(-4.18856e7 + 7.25481e7i) q^{23} +(7.91596e7 + 1.37108e8i) q^{24} +(5.97631e8 + 1.03513e9i) q^{25} +(-1.32796e8 + 2.30009e8i) q^{26} +1.70547e9 q^{27} +(-3.51652e8 - 1.22551e9i) q^{28} +6.32895e8 q^{29} +(-9.74792e7 + 1.68839e8i) q^{30} +(-1.65733e9 - 2.87058e9i) q^{31} +(-5.36871e8 - 9.29888e8i) q^{32} +(-3.27403e8 + 5.67079e8i) q^{33} -9.27804e9 q^{34} +(1.09042e9 - 1.12958e9i) q^{35} -5.03636e9 q^{36} +(8.76684e9 - 1.51846e10i) q^{37} +(-8.92896e9 - 1.54654e10i) q^{38} +(1.25314e9 + 2.17049e9i) q^{39} +(6.61117e8 - 1.14509e9i) q^{40} +1.15568e10 q^{41} +(-1.16744e10 - 2.90848e9i) q^{42} +4.19323e10 q^{43} +(2.22049e9 - 3.84600e9i) q^{44} +(-3.10095e9 - 5.37101e9i) q^{45} +(-2.68068e9 - 4.64308e9i) q^{46} +(-2.47264e10 + 4.28274e10i) q^{47} -1.01324e10 q^{48} +(8.55646e10 + 4.54552e10i) q^{49} -7.64968e10 q^{50} +(-4.37764e10 + 7.58230e10i) q^{51} +(-8.49893e9 - 1.47206e10i) q^{52} +(1.09584e11 + 1.89805e11i) q^{53} +(-5.45750e10 + 9.45266e10i) q^{54} +5.46874e9 q^{55} +(7.91774e10 + 1.97257e10i) q^{56} -1.68517e11 q^{57} +(-2.02526e10 + 3.50786e10i) q^{58} +(-6.67539e10 - 1.15621e11i) q^{59} +(-6.23867e9 - 1.08057e10i) q^{60} +(6.84740e10 - 1.18600e11i) q^{61} +2.12138e11 q^{62} +(2.65817e11 - 2.75363e11i) q^{63} +6.87195e10 q^{64} +(1.04658e10 - 1.81273e10i) q^{65} +(-2.09538e10 - 3.62930e10i) q^{66} +(-4.61830e11 - 7.99913e11i) q^{67} +(2.96897e11 - 5.14241e11i) q^{68} -5.05928e10 q^{69} +(2.77142e10 + 9.65838e10i) q^{70} -9.00251e11 q^{71} +(1.61163e11 - 2.79143e11i) q^{72} +(-9.23524e11 - 1.59959e12i) q^{73} +(5.61077e11 + 9.71815e11i) q^{74} +(-3.60933e11 + 6.25155e11i) q^{75} +1.14291e12 q^{76} +(9.30835e10 + 3.24396e11i) q^{77} -1.60401e11 q^{78} +(-1.46285e12 + 2.53374e12i) q^{79} +(4.23115e10 + 7.32856e10i) q^{80} +(-4.65173e11 - 8.05704e11i) q^{81} +(-3.69819e11 + 6.40546e11i) q^{82} +4.12504e12 q^{83} +(5.34785e11 - 5.53990e11i) q^{84} +7.31215e11 q^{85} +(-1.34183e12 + 2.32412e12i) q^{86} +(1.91115e11 + 3.31021e11i) q^{87} +(1.42111e11 + 2.46144e11i) q^{88} +(-2.20056e12 + 3.81148e12i) q^{89} +3.96922e11 q^{90} +(1.25342e12 + 3.12267e11i) q^{91} +3.43127e11 q^{92} +(1.00093e12 - 1.73366e12i) q^{93} +(-1.58249e12 - 2.74095e12i) q^{94} +(7.03703e11 + 1.21885e12i) q^{95} +(3.24238e11 - 5.61596e11i) q^{96} +3.35398e12 q^{97} +(-5.25745e12 + 3.28791e12i) q^{98} +1.33314e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9} - 4121600 q^{10} - 1008790 q^{11} - 745472 q^{12} + 53807264 q^{13} + 23506560 q^{14} - 88888916 q^{15} - 67108864 q^{16} - 165333028 q^{17} - 254960128 q^{18} - 423405794 q^{19} + 527564800 q^{20} + 231089600 q^{21} + 129125120 q^{22} + 286233866 q^{23} - 47710208 q^{24} - 472017432 q^{25} - 1721832448 q^{26} - 10405941644 q^{27} - 1038557184 q^{28} + 18200674816 q^{29} + 2844445312 q^{30} + 1507094246 q^{31} - 4294967296 q^{32} - 16888935028 q^{33} + 21162627584 q^{34} - 4300332526 q^{35} + 32634896384 q^{36} - 18959705336 q^{37} - 27097970816 q^{38} + 35759388756 q^{39} - 16882073600 q^{40} + 113651910624 q^{41} + 25531294208 q^{42} - 91557619424 q^{43} - 4132003840 q^{44} - 119804452768 q^{45} + 18318967424 q^{46} - 81351201078 q^{47} + 6106906624 q^{48} - 60954502168 q^{49} + 60418231296 q^{50} + 14996824142 q^{51} - 110197276672 q^{52} + 87497947440 q^{53} + 332990132608 q^{54} + 701637410348 q^{55} - 29815209984 q^{56} - 1807326928264 q^{57} - 582421594112 q^{58} - 194140265102 q^{59} + 182044499968 q^{60} + 175816313120 q^{61} - 192908063488 q^{62} + 3245184239332 q^{63} + 549755813888 q^{64} - 1689866774568 q^{65} - 1080891841792 q^{66} - 243815218758 q^{67} - 677204082688 q^{68} + 6044157952784 q^{69} + 3010938632576 q^{70} - 3275394679072 q^{71} - 1044316684288 q^{72} - 3492491920596 q^{73} - 1213421141504 q^{74} - 2370218127424 q^{75} + 3468540264448 q^{76} + 6381735922240 q^{77} - 4577201760768 q^{78} - 1016380081246 q^{79} - 1080452710400 q^{80} + 17492694092 q^{81} - 3636861139968 q^{82} + 7027495743296 q^{83} - 2580545830912 q^{84} + 569114840528 q^{85} + 2929843821568 q^{86} - 9706955821052 q^{87} - 264448245760 q^{88} - 8034124428036 q^{89} + 15334969954304 q^{90} - 11436513503632 q^{91} - 2344827830272 q^{92} - 3388371390552 q^{93} - 5206476868992 q^{94} + 1429435505438 q^{95} - 195421011968 q^{96} + 54351131725632 q^{97} - 461748942592 q^{98} - 25837834576328 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −32.0000 + 55.4256i −0.353553 + 0.612372i
\(3\) 301.970 + 523.027i 0.239153 + 0.414225i 0.960471 0.278378i \(-0.0897970\pi\)
−0.721319 + 0.692603i \(0.756464\pi\)
\(4\) −2048.00 3547.24i −0.250000 0.433013i
\(5\) 2521.96 4368.16i 0.0721827 0.125024i −0.827675 0.561208i \(-0.810337\pi\)
0.899858 + 0.436184i \(0.143670\pi\)
\(6\) −38652.2 −0.338213
\(7\) 302038. + 75247.5i 0.970340 + 0.241743i
\(8\) 262144. 0.353553
\(9\) 614790. 1.06485e6i 0.385612 0.667899i
\(10\) 161406. + 279563.i 0.0510409 + 0.0884054i
\(11\) 542112. + 938966.i 0.0922649 + 0.159808i 0.908464 0.417963i \(-0.137256\pi\)
−0.816199 + 0.577771i \(0.803923\pi\)
\(12\) 1.23687e6 2.14232e6i 0.119576 0.207112i
\(13\) 4.14987e6 0.238453 0.119226 0.992867i \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)
\(14\) −1.38358e7 + 1.43327e7i −0.491104 + 0.508740i
\(15\) 3.04623e6 0.0690508
\(16\) −8.38861e6 + 1.45295e7i −0.125000 + 0.216506i
\(17\) 7.24847e7 + 1.25547e8i 0.728330 + 1.26151i 0.957588 + 0.288140i \(0.0930368\pi\)
−0.229258 + 0.973366i \(0.573630\pi\)
\(18\) 3.93465e7 + 6.81502e7i 0.272669 + 0.472276i
\(19\) −1.39515e8 + 2.41647e8i −0.680334 + 1.17837i 0.294545 + 0.955638i \(0.404832\pi\)
−0.974879 + 0.222736i \(0.928501\pi\)
\(20\) −2.06599e7 −0.0721827
\(21\) 5.18498e7 + 1.80697e8i 0.131923 + 0.459753i
\(22\) −6.93903e7 −0.130482
\(23\) −4.18856e7 + 7.25481e7i −0.0589976 + 0.102187i −0.894016 0.448036i \(-0.852124\pi\)
0.835018 + 0.550222i \(0.185457\pi\)
\(24\) 7.91596e7 + 1.37108e8i 0.0845533 + 0.146451i
\(25\) 5.97631e8 + 1.03513e9i 0.489579 + 0.847976i
\(26\) −1.32796e8 + 2.30009e8i −0.0843058 + 0.146022i
\(27\) 1.70547e9 0.847186
\(28\) −3.51652e8 1.22551e9i −0.137907 0.480605i
\(29\) 6.32895e8 0.197581 0.0987903 0.995108i \(-0.468503\pi\)
0.0987903 + 0.995108i \(0.468503\pi\)
\(30\) −9.74792e7 + 1.68839e8i −0.0244132 + 0.0422848i
\(31\) −1.65733e9 2.87058e9i −0.335396 0.580923i 0.648165 0.761500i \(-0.275537\pi\)
−0.983561 + 0.180577i \(0.942203\pi\)
\(32\) −5.36871e8 9.29888e8i −0.0883883 0.153093i
\(33\) −3.27403e8 + 5.67079e8i −0.0441308 + 0.0764369i
\(34\) −9.27804e9 −1.03001
\(35\) 1.09042e9 1.12958e9i 0.100266 0.103866i
\(36\) −5.03636e9 −0.385612
\(37\) 8.76684e9 1.51846e10i 0.561735 0.972954i −0.435610 0.900136i \(-0.643467\pi\)
0.997345 0.0728185i \(-0.0231994\pi\)
\(38\) −8.92896e9 1.54654e10i −0.481069 0.833236i
\(39\) 1.25314e9 + 2.17049e9i 0.0570267 + 0.0987731i
\(40\) 6.61117e8 1.14509e9i 0.0255205 0.0442027i
\(41\) 1.15568e10 0.379966 0.189983 0.981787i \(-0.439157\pi\)
0.189983 + 0.981787i \(0.439157\pi\)
\(42\) −1.16744e10 2.90848e9i −0.328182 0.0817609i
\(43\) 4.19323e10 1.01159 0.505794 0.862654i \(-0.331200\pi\)
0.505794 + 0.862654i \(0.331200\pi\)
\(44\) 2.22049e9 3.84600e9i 0.0461325 0.0799038i
\(45\) −3.10095e9 5.37101e9i −0.0556690 0.0964216i
\(46\) −2.68068e9 4.64308e9i −0.0417176 0.0722570i
\(47\) −2.47264e10 + 4.28274e10i −0.334599 + 0.579543i −0.983408 0.181409i \(-0.941934\pi\)
0.648808 + 0.760952i \(0.275268\pi\)
\(48\) −1.01324e10 −0.119576
\(49\) 8.55646e10 + 4.54552e10i 0.883120 + 0.469147i
\(50\) −7.64968e10 −0.692370
\(51\) −4.37764e10 + 7.58230e10i −0.348365 + 0.603385i
\(52\) −8.49893e9 1.47206e10i −0.0596132 0.103253i
\(53\) 1.09584e11 + 1.89805e11i 0.679132 + 1.17629i 0.975243 + 0.221138i \(0.0709770\pi\)
−0.296111 + 0.955154i \(0.595690\pi\)
\(54\) −5.45750e10 + 9.45266e10i −0.299526 + 0.518794i
\(55\) 5.46874e9 0.0266397
\(56\) 7.91774e10 + 1.97257e10i 0.343067 + 0.0854692i
\(57\) −1.68517e11 −0.650816
\(58\) −2.02526e10 + 3.50786e10i −0.0698553 + 0.120993i
\(59\) −6.67539e10 1.15621e11i −0.206034 0.356861i 0.744428 0.667703i \(-0.232722\pi\)
−0.950462 + 0.310842i \(0.899389\pi\)
\(60\) −6.23867e9 1.08057e10i −0.0172627 0.0298999i
\(61\) 6.84740e10 1.18600e11i 0.170170 0.294742i −0.768309 0.640079i \(-0.778902\pi\)
0.938479 + 0.345336i \(0.112235\pi\)
\(62\) 2.12138e11 0.474321
\(63\) 2.65817e11 2.75363e11i 0.535635 0.554870i
\(64\) 6.87195e10 0.125000
\(65\) 1.04658e10 1.81273e10i 0.0172122 0.0298124i
\(66\) −2.09538e10 3.62930e10i −0.0312052 0.0540490i
\(67\) −4.61830e11 7.99913e11i −0.623729 1.08033i −0.988785 0.149345i \(-0.952283\pi\)
0.365056 0.930986i \(-0.381050\pi\)
\(68\) 2.96897e11 5.14241e11i 0.364165 0.630753i
\(69\) −5.05928e10 −0.0564378
\(70\) 2.77142e10 + 9.65838e10i 0.0281556 + 0.0981222i
\(71\) −9.00251e11 −0.834035 −0.417017 0.908898i \(-0.636925\pi\)
−0.417017 + 0.908898i \(0.636925\pi\)
\(72\) 1.61163e11 2.79143e11i 0.136334 0.236138i
\(73\) −9.23524e11 1.59959e12i −0.714249 1.23711i −0.963249 0.268611i \(-0.913435\pi\)
0.249000 0.968503i \(-0.419898\pi\)
\(74\) 5.61077e11 + 9.71815e11i 0.397207 + 0.687982i
\(75\) −3.60933e11 + 6.25155e11i −0.234169 + 0.405592i
\(76\) 1.14291e12 0.680334
\(77\) 9.30835e10 + 3.24396e11i 0.0508959 + 0.177372i
\(78\) −1.60401e11 −0.0806479
\(79\) −1.46285e12 + 2.53374e12i −0.677056 + 1.17270i 0.298807 + 0.954314i \(0.403411\pi\)
−0.975863 + 0.218382i \(0.929922\pi\)
\(80\) 4.23115e10 + 7.32856e10i 0.0180457 + 0.0312560i
\(81\) −4.65173e11 8.05704e11i −0.183005 0.316973i
\(82\) −3.69819e11 + 6.40546e11i −0.134338 + 0.232681i
\(83\) 4.12504e12 1.38491 0.692453 0.721463i \(-0.256530\pi\)
0.692453 + 0.721463i \(0.256530\pi\)
\(84\) 5.34785e11 5.53990e11i 0.166098 0.172063i
\(85\) 7.31215e11 0.210292
\(86\) −1.34183e12 + 2.32412e12i −0.357650 + 0.619468i
\(87\) 1.91115e11 + 3.31021e11i 0.0472520 + 0.0818428i
\(88\) 1.42111e11 + 2.46144e11i 0.0326206 + 0.0565005i
\(89\) −2.20056e12 + 3.81148e12i −0.469351 + 0.812940i −0.999386 0.0350361i \(-0.988845\pi\)
0.530035 + 0.847976i \(0.322179\pi\)
\(90\) 3.96922e11 0.0787279
\(91\) 1.25342e12 + 3.12267e11i 0.231380 + 0.0576444i
\(92\) 3.43127e11 0.0589976
\(93\) 1.00093e12 1.73366e12i 0.160422 0.277859i
\(94\) −1.58249e12 2.74095e12i −0.236598 0.409799i
\(95\) 7.03703e11 + 1.21885e12i 0.0982168 + 0.170116i
\(96\) 3.24238e11 5.61596e11i 0.0422767 0.0732253i
\(97\) 3.35398e12 0.408832 0.204416 0.978884i \(-0.434471\pi\)
0.204416 + 0.978884i \(0.434471\pi\)
\(98\) −5.25745e12 + 3.28791e12i −0.599523 + 0.374930i
\(99\) 1.33314e12 0.142314
\(100\) 2.44790e12 4.23988e12i 0.244790 0.423988i
\(101\) 1.86598e12 + 3.23198e12i 0.174912 + 0.302956i 0.940131 0.340814i \(-0.110703\pi\)
−0.765219 + 0.643770i \(0.777369\pi\)
\(102\) −2.80169e12 4.85267e12i −0.246331 0.426658i
\(103\) −2.52549e12 + 4.37428e12i −0.208403 + 0.360965i −0.951212 0.308539i \(-0.900160\pi\)
0.742809 + 0.669504i \(0.233493\pi\)
\(104\) 1.08786e12 0.0843058
\(105\) 9.20075e11 + 2.29221e11i 0.0670028 + 0.0166926i
\(106\) −1.40268e13 −0.960438
\(107\) 5.60554e12 9.70909e12i 0.361096 0.625437i −0.627045 0.778983i \(-0.715736\pi\)
0.988142 + 0.153546i \(0.0490692\pi\)
\(108\) −3.49280e12 6.04970e12i −0.211797 0.366843i
\(109\) −1.53833e13 2.66446e13i −0.878571 1.52173i −0.852910 0.522058i \(-0.825164\pi\)
−0.0256606 0.999671i \(-0.508169\pi\)
\(110\) −1.75000e11 + 3.03108e11i −0.00941857 + 0.0163134i
\(111\) 1.05893e13 0.537362
\(112\) −3.62698e12 + 3.75723e12i −0.173632 + 0.179867i
\(113\) 2.36931e12 0.107056 0.0535281 0.998566i \(-0.482953\pi\)
0.0535281 + 0.998566i \(0.482953\pi\)
\(114\) 5.39255e12 9.34018e12i 0.230098 0.398542i
\(115\) 2.11268e11 + 3.65927e11i 0.00851722 + 0.0147522i
\(116\) −1.29617e12 2.24503e12i −0.0493952 0.0855549i
\(117\) 2.55130e12 4.41898e12i 0.0919502 0.159262i
\(118\) 8.54450e12 0.291376
\(119\) 1.24460e13 + 4.33743e13i 0.401768 + 1.40016i
\(120\) 7.98550e11 0.0244132
\(121\) 1.66736e13 2.88795e13i 0.482974 0.836536i
\(122\) 4.38234e12 + 7.59043e12i 0.120328 + 0.208414i
\(123\) 3.48982e12 + 6.04455e12i 0.0908699 + 0.157391i
\(124\) −6.78842e12 + 1.17579e13i −0.167698 + 0.290461i
\(125\) 1.21859e13 0.285722
\(126\) 6.75601e12 + 2.35447e13i 0.150412 + 0.524184i
\(127\) −3.93753e13 −0.832721 −0.416360 0.909200i \(-0.636694\pi\)
−0.416360 + 0.909200i \(0.636694\pi\)
\(128\) −2.19902e12 + 3.80882e12i −0.0441942 + 0.0765466i
\(129\) 1.26623e13 + 2.19317e13i 0.241924 + 0.419025i
\(130\) 6.69812e11 + 1.16015e12i 0.0121708 + 0.0210805i
\(131\) −4.20597e13 + 7.28495e13i −0.727114 + 1.25940i 0.230984 + 0.972958i \(0.425806\pi\)
−0.958098 + 0.286441i \(0.907528\pi\)
\(132\) 2.68209e12 0.0441308
\(133\) −6.03221e13 + 6.24884e13i −0.945020 + 0.978957i
\(134\) 5.91143e13 0.882087
\(135\) 4.30112e12 7.44976e12i 0.0611522 0.105919i
\(136\) 1.90014e13 + 3.29115e13i 0.257504 + 0.446010i
\(137\) −6.66096e13 1.15371e14i −0.860703 1.49078i −0.871251 0.490837i \(-0.836691\pi\)
0.0105480 0.999944i \(-0.496642\pi\)
\(138\) 1.61897e12 2.80414e12i 0.0199538 0.0345609i
\(139\) 4.32137e13 0.508189 0.254094 0.967179i \(-0.418223\pi\)
0.254094 + 0.967179i \(0.418223\pi\)
\(140\) −6.24007e12 1.55461e12i −0.0700418 0.0174497i
\(141\) −2.98665e13 −0.320082
\(142\) 2.88080e13 4.98970e13i 0.294876 0.510740i
\(143\) 2.24969e12 + 3.89658e12i 0.0220008 + 0.0381066i
\(144\) 1.03145e13 + 1.78652e13i 0.0964029 + 0.166975i
\(145\) 1.59614e12 2.76459e12i 0.0142619 0.0247024i
\(146\) 1.18211e14 1.01010
\(147\) 2.06365e12 + 5.84787e13i 0.0168684 + 0.478008i
\(148\) −7.18179e13 −0.561735
\(149\) 1.03951e14 1.80049e14i 0.778251 1.34797i −0.154699 0.987962i \(-0.549441\pi\)
0.932949 0.360008i \(-0.117226\pi\)
\(150\) −2.30997e13 4.00099e13i −0.165582 0.286797i
\(151\) −8.90723e13 1.54278e14i −0.611495 1.05914i −0.990989 0.133945i \(-0.957235\pi\)
0.379494 0.925194i \(-0.376098\pi\)
\(152\) −3.65730e13 + 6.33463e13i −0.240534 + 0.416618i
\(153\) 1.78251e14 1.12341
\(154\) −2.09585e13 5.22145e12i −0.126612 0.0315432i
\(155\) −1.67189e13 −0.0968392
\(156\) 5.13284e12 8.89035e12i 0.0285133 0.0493866i
\(157\) −1.40318e14 2.43037e14i −0.747764 1.29517i −0.948892 0.315601i \(-0.897794\pi\)
0.201128 0.979565i \(-0.435539\pi\)
\(158\) −9.36226e13 1.62159e14i −0.478751 0.829221i
\(159\) −6.61822e13 + 1.14631e14i −0.324833 + 0.562627i
\(160\) −5.41587e12 −0.0255205
\(161\) −1.81101e13 + 1.87605e13i −0.0819507 + 0.0848937i
\(162\) 5.95422e13 0.258808
\(163\) −1.56045e14 + 2.70278e14i −0.651674 + 1.12873i 0.331042 + 0.943616i \(0.392600\pi\)
−0.982717 + 0.185117i \(0.940734\pi\)
\(164\) −2.36684e13 4.09949e13i −0.0949914 0.164530i
\(165\) 1.65140e12 + 2.86030e12i 0.00637097 + 0.0110348i
\(166\) −1.32001e14 + 2.28633e14i −0.489638 + 0.848078i
\(167\) 5.39544e14 1.92473 0.962365 0.271762i \(-0.0876063\pi\)
0.962365 + 0.271762i \(0.0876063\pi\)
\(168\) 1.35921e13 + 4.73685e13i 0.0466420 + 0.162547i
\(169\) −2.85654e14 −0.943140
\(170\) −2.33989e13 + 4.05280e13i −0.0743493 + 0.128777i
\(171\) 1.71545e14 + 2.97124e14i 0.524690 + 0.908789i
\(172\) −8.58773e13 1.48744e14i −0.252897 0.438030i
\(173\) 7.54207e13 1.30632e14i 0.213890 0.370469i −0.739038 0.673663i \(-0.764720\pi\)
0.952929 + 0.303194i \(0.0980532\pi\)
\(174\) −2.44627e13 −0.0668244
\(175\) 1.02616e14 + 3.57618e14i 0.270066 + 0.941178i
\(176\) −1.81903e13 −0.0461325
\(177\) 4.03153e13 6.98282e13i 0.0985471 0.170689i
\(178\) −1.40836e14 2.43935e14i −0.331881 0.574835i
\(179\) 2.40641e14 + 4.16803e14i 0.546796 + 0.947079i 0.998491 + 0.0549068i \(0.0174862\pi\)
−0.451695 + 0.892172i \(0.649180\pi\)
\(180\) −1.27015e13 + 2.19996e13i −0.0278345 + 0.0482108i
\(181\) 9.46675e13 0.200120 0.100060 0.994981i \(-0.468097\pi\)
0.100060 + 0.994981i \(0.468097\pi\)
\(182\) −5.74170e13 + 5.94789e13i −0.117105 + 0.121311i
\(183\) 8.27084e13 0.162786
\(184\) −1.09801e13 + 1.90180e13i −0.0208588 + 0.0361285i
\(185\) −4.42192e13 7.65900e13i −0.0810952 0.140461i
\(186\) 6.40593e13 + 1.10954e14i 0.113435 + 0.196476i
\(187\) −7.85897e13 + 1.36121e14i −0.134399 + 0.232785i
\(188\) 2.02559e14 0.334599
\(189\) 5.15116e14 + 1.28332e14i 0.822059 + 0.204802i
\(190\) −9.00739e13 −0.138900
\(191\) −4.96741e13 + 8.60380e13i −0.0740309 + 0.128225i −0.900664 0.434515i \(-0.856920\pi\)
0.826634 + 0.562741i \(0.190253\pi\)
\(192\) 2.07512e13 + 3.59422e13i 0.0298941 + 0.0517781i
\(193\) −5.21901e14 9.03958e14i −0.726884 1.25900i −0.958194 0.286120i \(-0.907634\pi\)
0.231309 0.972880i \(-0.425699\pi\)
\(194\) −1.07327e14 + 1.85897e14i −0.144544 + 0.250357i
\(195\) 1.26414e13 0.0164654
\(196\) −1.39960e13 3.96611e14i −0.0176335 0.499689i
\(197\) −6.98238e14 −0.851085 −0.425543 0.904938i \(-0.639917\pi\)
−0.425543 + 0.904938i \(0.639917\pi\)
\(198\) −4.26605e13 + 7.38901e13i −0.0503155 + 0.0871490i
\(199\) −2.76476e14 4.78871e14i −0.315583 0.546605i 0.663979 0.747752i \(-0.268867\pi\)
−0.979561 + 0.201147i \(0.935533\pi\)
\(200\) 1.56665e14 + 2.71352e14i 0.173092 + 0.299805i
\(201\) 2.78918e14 4.83100e14i 0.298333 0.516729i
\(202\) −2.38846e14 −0.247362
\(203\) 1.91158e14 + 4.76237e13i 0.191720 + 0.0477638i
\(204\) 3.58616e14 0.348365
\(205\) 2.91459e13 5.04822e13i 0.0274270 0.0475049i
\(206\) −1.61631e14 2.79954e14i −0.147363 0.255241i
\(207\) 5.15017e13 + 8.92036e13i 0.0455003 + 0.0788089i
\(208\) −3.48116e13 + 6.02955e13i −0.0298066 + 0.0516266i
\(209\) −3.02531e14 −0.251084
\(210\) −4.21471e13 + 4.36607e13i −0.0339112 + 0.0351289i
\(211\) −1.28275e15 −1.00071 −0.500354 0.865821i \(-0.666797\pi\)
−0.500354 + 0.865821i \(0.666797\pi\)
\(212\) 4.48856e14 7.77442e14i 0.339566 0.588146i
\(213\) −2.71849e14 4.70856e14i −0.199462 0.345478i
\(214\) 3.58755e14 + 6.21382e14i 0.255334 + 0.442251i
\(215\) 1.05752e14 1.83167e14i 0.0730192 0.126473i
\(216\) 4.47078e14 0.299526
\(217\) −2.84572e14 9.91733e14i −0.185014 0.644772i
\(218\) 1.96906e15 1.24249
\(219\) 5.57753e14 9.66056e14i 0.341629 0.591719i
\(220\) −1.12000e13 1.93989e13i −0.00665993 0.0115353i
\(221\) 3.00802e14 + 5.21004e14i 0.173673 + 0.300810i
\(222\) −3.38857e14 + 5.86918e14i −0.189986 + 0.329066i
\(223\) −3.19482e15 −1.73966 −0.869830 0.493351i \(-0.835772\pi\)
−0.869830 + 0.493351i \(0.835772\pi\)
\(224\) −9.21836e13 3.21259e14i −0.0487575 0.169920i
\(225\) 1.46967e15 0.755150
\(226\) −7.58179e13 + 1.31320e14i −0.0378501 + 0.0655583i
\(227\) 1.82339e15 + 3.15821e15i 0.884530 + 1.53205i 0.846251 + 0.532784i \(0.178854\pi\)
0.0382789 + 0.999267i \(0.487812\pi\)
\(228\) 3.45123e14 + 5.97771e14i 0.162704 + 0.281811i
\(229\) 6.61331e14 1.14546e15i 0.303032 0.524866i −0.673789 0.738923i \(-0.735335\pi\)
0.976821 + 0.214057i \(0.0686679\pi\)
\(230\) −2.70423e13 −0.0120452
\(231\) −1.41559e14 + 1.46643e14i −0.0613000 + 0.0635014i
\(232\) 1.65910e14 0.0698553
\(233\) −1.95260e15 + 3.38200e15i −0.799464 + 1.38471i 0.120501 + 0.992713i \(0.461550\pi\)
−0.919965 + 0.391999i \(0.871784\pi\)
\(234\) 1.63283e14 + 2.82814e14i 0.0650186 + 0.112616i
\(235\) 1.24718e14 + 2.16018e14i 0.0483046 + 0.0836660i
\(236\) −2.73424e14 + 4.73584e14i −0.103017 + 0.178430i
\(237\) −1.76695e15 −0.647680
\(238\) −2.80232e15 6.98150e14i −0.999465 0.248999i
\(239\) 2.69308e15 0.934681 0.467341 0.884077i \(-0.345212\pi\)
0.467341 + 0.884077i \(0.345212\pi\)
\(240\) −2.55536e13 + 4.42601e13i −0.00863135 + 0.0149499i
\(241\) 1.46075e15 + 2.53010e15i 0.480248 + 0.831814i 0.999743 0.0226595i \(-0.00721335\pi\)
−0.519495 + 0.854473i \(0.673880\pi\)
\(242\) 1.06711e15 + 1.84829e15i 0.341514 + 0.591520i
\(243\) 1.64047e15 2.84138e15i 0.511125 0.885295i
\(244\) −5.60939e14 −0.170170
\(245\) 4.14346e14 2.59124e14i 0.122401 0.0765471i
\(246\) −4.46697e14 −0.128509
\(247\) −5.78969e14 + 1.00280e15i −0.162228 + 0.280987i
\(248\) −4.34459e14 7.52505e14i −0.118580 0.205387i
\(249\) 1.24564e15 + 2.15751e15i 0.331204 + 0.573662i
\(250\) −3.89950e14 + 6.75413e14i −0.101018 + 0.174968i
\(251\) −4.10252e15 −1.03555 −0.517776 0.855516i \(-0.673240\pi\)
−0.517776 + 0.855516i \(0.673240\pi\)
\(252\) −1.52117e15 3.78973e14i −0.374175 0.0932191i
\(253\) −9.08268e13 −0.0217736
\(254\) 1.26001e15 2.18240e15i 0.294411 0.509935i
\(255\) 2.20805e14 + 3.82445e14i 0.0502918 + 0.0871080i
\(256\) −1.40737e14 2.43764e14i −0.0312500 0.0541266i
\(257\) 2.72122e15 4.71329e15i 0.589113 1.02037i −0.405236 0.914212i \(-0.632811\pi\)
0.994349 0.106161i \(-0.0338559\pi\)
\(258\) −1.62077e15 −0.342132
\(259\) 3.79052e15 3.92664e15i 0.780280 0.808301i
\(260\) −8.57359e13 −0.0172122
\(261\) 3.89097e14 6.73936e14i 0.0761894 0.131964i
\(262\) −2.69182e15 4.66237e15i −0.514147 0.890529i
\(263\) −2.38641e15 4.13338e15i −0.444665 0.770182i 0.553364 0.832940i \(-0.313344\pi\)
−0.998029 + 0.0627574i \(0.980011\pi\)
\(264\) −8.58268e13 + 1.48656e14i −0.0156026 + 0.0270245i
\(265\) 1.10547e15 0.196086
\(266\) −1.53315e15 5.34302e15i −0.265371 0.924818i
\(267\) −2.65801e15 −0.448986
\(268\) −1.89166e15 + 3.27645e15i −0.311865 + 0.540165i
\(269\) 3.58399e15 + 6.20765e15i 0.576736 + 0.998936i 0.995851 + 0.0910026i \(0.0290072\pi\)
−0.419115 + 0.907933i \(0.637660\pi\)
\(270\) 2.75272e14 + 4.76785e14i 0.0432412 + 0.0748959i
\(271\) 4.94607e15 8.56684e15i 0.758508 1.31377i −0.185104 0.982719i \(-0.559262\pi\)
0.943612 0.331055i \(-0.107404\pi\)
\(272\) −2.43218e15 −0.364165
\(273\) 2.15170e14 + 7.49867e14i 0.0314575 + 0.109629i
\(274\) 8.52603e15 1.21722
\(275\) −6.47966e14 + 1.12231e15i −0.0903420 + 0.156477i
\(276\) 1.03614e14 + 1.79465e14i 0.0141094 + 0.0244383i
\(277\) 2.92957e15 + 5.07417e15i 0.389660 + 0.674911i 0.992404 0.123024i \(-0.0392592\pi\)
−0.602744 + 0.797935i \(0.705926\pi\)
\(278\) −1.38284e15 + 2.39514e15i −0.179672 + 0.311201i
\(279\) −4.07564e15 −0.517330
\(280\) 2.85847e14 2.96112e14i 0.0354492 0.0367223i
\(281\) −7.54166e15 −0.913852 −0.456926 0.889505i \(-0.651050\pi\)
−0.456926 + 0.889505i \(0.651050\pi\)
\(282\) 9.55730e14 1.65537e15i 0.113166 0.196009i
\(283\) −3.89732e14 6.75036e14i −0.0450977 0.0781116i 0.842595 0.538547i \(-0.181027\pi\)
−0.887693 + 0.460436i \(0.847693\pi\)
\(284\) 1.84371e15 + 3.19341e15i 0.208509 + 0.361148i
\(285\) −4.24994e14 + 7.36111e14i −0.0469777 + 0.0813677i
\(286\) −2.87961e14 −0.0311139
\(287\) 3.49061e15 + 8.69624e14i 0.368696 + 0.0918542i
\(288\) −1.32025e15 −0.136334
\(289\) −5.55578e15 + 9.62290e15i −0.560931 + 0.971560i
\(290\) 1.02153e14 + 1.76934e14i 0.0100847 + 0.0174672i
\(291\) 1.01280e15 + 1.75422e15i 0.0977732 + 0.169348i
\(292\) −3.78275e15 + 6.55192e15i −0.357124 + 0.618557i
\(293\) −1.10609e16 −1.02130 −0.510648 0.859790i \(-0.670595\pi\)
−0.510648 + 0.859790i \(0.670595\pi\)
\(294\) −3.30726e15 1.75694e15i −0.298683 0.158672i
\(295\) −6.73403e14 −0.0594883
\(296\) 2.29817e15 3.98055e15i 0.198603 0.343991i
\(297\) 9.24554e14 + 1.60138e15i 0.0781656 + 0.135387i
\(298\) 6.65289e15 + 1.15231e16i 0.550306 + 0.953158i
\(299\) −1.73820e14 + 3.01065e14i −0.0140681 + 0.0243667i
\(300\) 2.95677e15 0.234169
\(301\) 1.26651e16 + 3.15530e15i 0.981584 + 0.244545i
\(302\) 1.14013e16 0.864784
\(303\) −1.12694e15 + 1.95192e15i −0.0836613 + 0.144906i
\(304\) −2.34067e15 4.05416e15i −0.170084 0.294593i
\(305\) −3.45378e14 5.98212e14i −0.0245666 0.0425506i
\(306\) −5.70405e15 + 9.87970e15i −0.397186 + 0.687946i
\(307\) 1.05695e16 0.720536 0.360268 0.932849i \(-0.382685\pi\)
0.360268 + 0.932849i \(0.382685\pi\)
\(308\) 9.60074e14 9.94552e14i 0.0640804 0.0663816i
\(309\) −3.05049e15 −0.199361
\(310\) 5.35004e14 9.26654e14i 0.0342378 0.0593016i
\(311\) −1.12250e16 1.94423e16i −0.703467 1.21844i −0.967242 0.253856i \(-0.918301\pi\)
0.263775 0.964584i \(-0.415032\pi\)
\(312\) 3.28502e14 + 5.68982e14i 0.0201620 + 0.0349216i
\(313\) 4.10910e14 7.11717e14i 0.0247007 0.0427828i −0.853411 0.521239i \(-0.825470\pi\)
0.878111 + 0.478456i \(0.158803\pi\)
\(314\) 1.79607e16 1.05750
\(315\) −5.32450e14 1.85559e15i −0.0307086 0.107019i
\(316\) 1.19837e16 0.677056
\(317\) −1.74077e15 + 3.01510e15i −0.0963508 + 0.166885i −0.910172 0.414231i \(-0.864050\pi\)
0.813821 + 0.581116i \(0.197384\pi\)
\(318\) −4.23566e15 7.33638e15i −0.229691 0.397837i
\(319\) 3.43100e14 + 5.94266e14i 0.0182298 + 0.0315749i
\(320\) 1.73308e14 3.00178e14i 0.00902284 0.0156280i
\(321\) 6.77082e15 0.345429
\(322\) −4.60287e14 1.60410e15i −0.0230126 0.0801988i
\(323\) −4.04508e16 −1.98203
\(324\) −1.90535e15 + 3.30016e15i −0.0915024 + 0.158487i
\(325\) 2.48009e15 + 4.29564e15i 0.116742 + 0.202202i
\(326\) −9.98688e15 1.72978e16i −0.460803 0.798135i
\(327\) 9.29058e15 1.60918e16i 0.420225 0.727852i
\(328\) 3.02956e15 0.134338
\(329\) −1.06910e16 + 1.10749e16i −0.464776 + 0.481467i
\(330\) −2.11379e14 −0.00900991
\(331\) 9.67752e15 1.67620e16i 0.404466 0.700556i −0.589793 0.807554i \(-0.700791\pi\)
0.994259 + 0.106999i \(0.0341241\pi\)
\(332\) −8.44807e15 1.46325e16i −0.346226 0.599682i
\(333\) −1.07795e16 1.86707e16i −0.433223 0.750365i
\(334\) −1.72654e16 + 2.99045e16i −0.680494 + 1.17865i
\(335\) −4.65887e15 −0.180090
\(336\) −3.06038e15 7.62440e14i −0.116030 0.0289068i
\(337\) 3.60727e15 0.134148 0.0670740 0.997748i \(-0.478634\pi\)
0.0670740 + 0.997748i \(0.478634\pi\)
\(338\) 9.14092e15 1.58325e16i 0.333450 0.577553i
\(339\) 7.15460e14 + 1.23921e15i 0.0256028 + 0.0443453i
\(340\) −1.49753e15 2.59379e15i −0.0525729 0.0910589i
\(341\) 1.79692e15 3.11235e15i 0.0618905 0.107198i
\(342\) −2.19577e16 −0.742024
\(343\) 2.24234e16 + 2.01677e16i 0.743514 + 0.668721i
\(344\) 1.09923e16 0.357650
\(345\) −1.27593e14 + 2.20998e14i −0.00407383 + 0.00705609i
\(346\) 4.82692e15 + 8.36048e15i 0.151243 + 0.261961i
\(347\) −1.23542e16 2.13980e16i −0.379902 0.658010i 0.611145 0.791518i \(-0.290709\pi\)
−0.991048 + 0.133508i \(0.957376\pi\)
\(348\) 7.82808e14 1.35586e15i 0.0236260 0.0409214i
\(349\) 6.49301e16 1.92345 0.961725 0.274017i \(-0.0883525\pi\)
0.961725 + 0.274017i \(0.0883525\pi\)
\(350\) −2.31049e16 5.75619e15i −0.671834 0.167376i
\(351\) 7.07747e15 0.202014
\(352\) 5.82088e14 1.00821e15i 0.0163103 0.0282502i
\(353\) 2.68625e16 + 4.65273e16i 0.738944 + 1.27989i 0.952971 + 0.303061i \(0.0980084\pi\)
−0.214028 + 0.976828i \(0.568658\pi\)
\(354\) 2.58018e15 + 4.46901e15i 0.0696834 + 0.120695i
\(355\) −2.27040e15 + 3.93244e15i −0.0602029 + 0.104275i
\(356\) 1.80270e16 0.469351
\(357\) −1.89276e16 + 1.96073e16i −0.483897 + 0.501274i
\(358\) −3.08021e16 −0.773287
\(359\) −2.94150e14 + 5.09483e14i −0.00725195 + 0.0125607i −0.869629 0.493706i \(-0.835642\pi\)
0.862377 + 0.506267i \(0.168975\pi\)
\(360\) −8.12896e14 1.40798e15i −0.0196820 0.0340902i
\(361\) −1.79024e16 3.10078e16i −0.425710 0.737350i
\(362\) −3.02936e15 + 5.24701e15i −0.0707531 + 0.122548i
\(363\) 2.01397e16 0.462019
\(364\) −1.45931e15 5.08569e15i −0.0328843 0.114602i
\(365\) −9.31636e15 −0.206226
\(366\) −2.64667e15 + 4.58416e15i −0.0575536 + 0.0996858i
\(367\) 1.71940e16 + 2.97809e16i 0.367323 + 0.636221i 0.989146 0.146936i \(-0.0469412\pi\)
−0.621823 + 0.783158i \(0.713608\pi\)
\(368\) −7.02725e14 1.21715e15i −0.0147494 0.0255467i
\(369\) 7.10503e15 1.23063e16i 0.146519 0.253779i
\(370\) 5.66006e15 0.114686
\(371\) 1.88162e16 + 6.55743e16i 0.374628 + 1.30558i
\(372\) −8.19960e15 −0.160422
\(373\) −5.16753e15 + 8.95043e15i −0.0993518 + 0.172082i −0.911417 0.411485i \(-0.865010\pi\)
0.812065 + 0.583567i \(0.198344\pi\)
\(374\) −5.02974e15 8.71176e15i −0.0950342 0.164604i
\(375\) 3.67979e15 + 6.37358e15i 0.0683313 + 0.118353i
\(376\) −6.48188e15 + 1.12270e16i −0.118299 + 0.204899i
\(377\) 2.62643e15 0.0471137
\(378\) −2.35966e16 + 2.44440e16i −0.416057 + 0.430998i
\(379\) 1.03178e16 0.178827 0.0894137 0.995995i \(-0.471501\pi\)
0.0894137 + 0.995995i \(0.471501\pi\)
\(380\) 2.88237e15 4.99240e15i 0.0491084 0.0850582i
\(381\) −1.18901e16 2.05943e16i −0.199148 0.344934i
\(382\) −3.17914e15 5.50643e15i −0.0523477 0.0906689i
\(383\) −6.07099e16 + 1.05153e17i −0.982806 + 1.70227i −0.331499 + 0.943455i \(0.607554\pi\)
−0.651307 + 0.758815i \(0.725779\pi\)
\(384\) −2.65616e15 −0.0422767
\(385\) 1.65177e15 + 4.11509e14i 0.0258496 + 0.00643998i
\(386\) 6.68033e16 1.02797
\(387\) 2.57795e16 4.46515e16i 0.390080 0.675639i
\(388\) −6.86895e15 1.18974e16i −0.102208 0.177029i
\(389\) −4.72294e16 8.18038e16i −0.691099 1.19702i −0.971478 0.237129i \(-0.923793\pi\)
0.280379 0.959889i \(-0.409540\pi\)
\(390\) −4.04526e14 + 7.00660e14i −0.00582139 + 0.0100829i
\(391\) −1.21443e16 −0.171879
\(392\) 2.24303e16 + 1.19158e16i 0.312230 + 0.165868i
\(393\) −5.08031e16 −0.695566
\(394\) 2.23436e16 3.87003e16i 0.300904 0.521181i
\(395\) 7.37852e15 + 1.27800e16i 0.0977435 + 0.169297i
\(396\) −2.73027e15 4.72897e15i −0.0355784 0.0616237i
\(397\) 3.36900e16 5.83528e16i 0.431880 0.748037i −0.565156 0.824984i \(-0.691184\pi\)
0.997035 + 0.0769469i \(0.0245172\pi\)
\(398\) 3.53890e16 0.446301
\(399\) −5.08986e16 1.26805e16i −0.631513 0.157330i
\(400\) −2.00532e16 −0.244790
\(401\) 2.92556e16 5.06722e16i 0.351375 0.608599i −0.635116 0.772417i \(-0.719048\pi\)
0.986491 + 0.163818i \(0.0523810\pi\)
\(402\) 1.78507e16 + 3.09184e16i 0.210954 + 0.365382i
\(403\) −6.87770e15 1.19125e16i −0.0799761 0.138523i
\(404\) 7.64307e15 1.32382e16i 0.0874558 0.151478i
\(405\) −4.69260e15 −0.0528391
\(406\) −8.75663e15 + 9.07110e15i −0.0970327 + 0.100517i
\(407\) 1.90104e16 0.207314
\(408\) −1.14757e16 + 1.98765e16i −0.123166 + 0.213329i
\(409\) −7.39497e16 1.28085e17i −0.781151 1.35299i −0.931272 0.364325i \(-0.881300\pi\)
0.150121 0.988668i \(-0.452034\pi\)
\(410\) 1.86534e15 + 3.23086e15i 0.0193938 + 0.0335910i
\(411\) 4.02282e16 6.96773e16i 0.411679 0.713050i
\(412\) 2.06888e16 0.208403
\(413\) −1.14620e16 3.99450e16i −0.113654 0.396084i
\(414\) −6.59222e15 −0.0643472
\(415\) 1.04032e16 1.80188e16i 0.0999663 0.173147i
\(416\) −2.22794e15 3.85891e15i −0.0210765 0.0365055i
\(417\) 1.30492e16 + 2.26019e16i 0.121535 + 0.210504i
\(418\) 9.68099e15 1.67680e16i 0.0887716 0.153757i
\(419\) −6.30569e16 −0.569300 −0.284650 0.958631i \(-0.591877\pi\)
−0.284650 + 0.958631i \(0.591877\pi\)
\(420\) −1.07121e15 3.73317e15i −0.00952260 0.0331862i
\(421\) 4.32840e16 0.378873 0.189437 0.981893i \(-0.439334\pi\)
0.189437 + 0.981893i \(0.439334\pi\)
\(422\) 4.10482e16 7.10975e16i 0.353804 0.612807i
\(423\) 3.04031e16 + 5.26597e16i 0.258051 + 0.446957i
\(424\) 2.87268e16 + 4.97563e16i 0.240109 + 0.415882i
\(425\) −8.66382e16 + 1.50062e17i −0.713151 + 1.23521i
\(426\) 3.47966e16 0.282082
\(427\) 2.96061e16 3.06693e16i 0.236374 0.244863i
\(428\) −4.59206e16 −0.361096
\(429\) −1.35868e15 + 2.35330e15i −0.0105231 + 0.0182266i
\(430\) 6.76810e15 + 1.17227e16i 0.0516323 + 0.0894298i
\(431\) 7.05949e16 + 1.22274e17i 0.530482 + 0.918822i 0.999367 + 0.0355633i \(0.0113225\pi\)
−0.468885 + 0.883259i \(0.655344\pi\)
\(432\) −1.43065e16 + 2.47796e16i −0.105898 + 0.183421i
\(433\) −1.37045e17 −0.999293 −0.499646 0.866230i \(-0.666537\pi\)
−0.499646 + 0.866230i \(0.666537\pi\)
\(434\) 6.40737e16 + 1.59629e16i 0.460253 + 0.114664i
\(435\) 1.92794e15 0.0136431
\(436\) −6.30099e16 + 1.09136e17i −0.439285 + 0.760864i
\(437\) −1.16873e16 2.02431e16i −0.0802762 0.139042i
\(438\) 3.56962e16 + 6.18276e16i 0.241568 + 0.418409i
\(439\) −6.67396e16 + 1.15596e17i −0.445004 + 0.770770i −0.998053 0.0623790i \(-0.980131\pi\)
0.553048 + 0.833149i \(0.313465\pi\)
\(440\) 1.43360e15 0.00941857
\(441\) 1.01007e17 6.31679e16i 0.653884 0.408927i
\(442\) −3.85027e16 −0.245610
\(443\) −1.17690e17 + 2.03846e17i −0.739804 + 1.28138i 0.212779 + 0.977100i \(0.431748\pi\)
−0.952583 + 0.304278i \(0.901585\pi\)
\(444\) −2.16869e16 3.75627e16i −0.134341 0.232685i
\(445\) 1.10994e16 + 1.92248e16i 0.0677581 + 0.117360i
\(446\) 1.02234e17 1.77075e17i 0.615063 1.06532i
\(447\) 1.25561e17 0.744483
\(448\) 2.07559e16 + 5.17097e15i 0.121293 + 0.0302179i
\(449\) 2.96730e16 0.170907 0.0854536 0.996342i \(-0.472766\pi\)
0.0854536 + 0.996342i \(0.472766\pi\)
\(450\) −4.70294e16 + 8.14574e16i −0.266986 + 0.462433i
\(451\) 6.26511e15 + 1.08515e16i 0.0350575 + 0.0607214i
\(452\) −4.85234e15 8.40451e15i −0.0267640 0.0463567i
\(453\) 5.37943e16 9.31745e16i 0.292481 0.506593i
\(454\) −2.33395e17 −1.25091
\(455\) 4.52510e15 4.68761e15i 0.0239086 0.0247672i
\(456\) −4.41758e16 −0.230098
\(457\) −7.70400e16 + 1.33437e17i −0.395605 + 0.685207i −0.993178 0.116607i \(-0.962798\pi\)
0.597574 + 0.801814i \(0.296132\pi\)
\(458\) 4.23252e16 + 7.33093e16i 0.214276 + 0.371136i
\(459\) 1.23620e17 + 2.14117e17i 0.617032 + 1.06873i
\(460\) 8.65353e14 1.49884e15i 0.00425861 0.00737612i
\(461\) 2.83415e17 1.37520 0.687602 0.726088i \(-0.258664\pi\)
0.687602 + 0.726088i \(0.258664\pi\)
\(462\) −3.59788e15 1.25386e16i −0.0172137 0.0599896i
\(463\) 9.54079e15 0.0450099 0.0225049 0.999747i \(-0.492836\pi\)
0.0225049 + 0.999747i \(0.492836\pi\)
\(464\) −5.30910e15 + 9.19564e15i −0.0246976 + 0.0427775i
\(465\) −5.04860e15 8.74443e15i −0.0231594 0.0401132i
\(466\) −1.24966e17 2.16448e17i −0.565307 0.979140i
\(467\) 1.07577e17 1.86329e17i 0.479911 0.831230i −0.519823 0.854274i \(-0.674002\pi\)
0.999734 + 0.0230434i \(0.00733559\pi\)
\(468\) −2.09002e16 −0.0919502
\(469\) −7.92987e16 2.76356e17i −0.344067 1.19907i
\(470\) −1.59639e16 −0.0683130
\(471\) 8.47435e16 1.46780e17i 0.357660 0.619485i
\(472\) −1.74991e16 3.03094e16i −0.0728439 0.126169i
\(473\) 2.27320e16 + 3.93730e16i 0.0933340 + 0.161659i
\(474\) 5.65424e16 9.79344e16i 0.228989 0.396621i
\(475\) −3.33514e17 −1.33231
\(476\) 1.28370e17 1.32980e17i 0.505845 0.524010i
\(477\) 2.69485e17 1.04753
\(478\) −8.61787e16 + 1.49266e17i −0.330460 + 0.572373i
\(479\) −1.19781e17 2.07467e17i −0.453114 0.784816i 0.545464 0.838134i \(-0.316354\pi\)
−0.998578 + 0.0533184i \(0.983020\pi\)
\(480\) −1.63543e15 2.83265e15i −0.00610329 0.0105712i
\(481\) 3.63812e16 6.30141e16i 0.133947 0.232004i
\(482\) −1.86976e17 −0.679173
\(483\) −1.52809e16 3.80698e15i −0.0547638 0.0136435i
\(484\) −1.36590e17 −0.482974
\(485\) 8.45861e15 1.46507e16i 0.0295106 0.0511138i
\(486\) 1.04990e17 + 1.81848e17i 0.361420 + 0.625998i
\(487\) 3.20669e16 + 5.55414e16i 0.108923 + 0.188660i 0.915334 0.402695i \(-0.131927\pi\)
−0.806411 + 0.591355i \(0.798593\pi\)
\(488\) 1.79501e16 3.10904e16i 0.0601640 0.104207i
\(489\) −1.88484e17 −0.623399
\(490\) 1.10304e15 + 3.12574e16i 0.00360012 + 0.102018i
\(491\) 2.58459e17 0.832457 0.416228 0.909260i \(-0.363352\pi\)
0.416228 + 0.909260i \(0.363352\pi\)
\(492\) 1.42943e16 2.47585e16i 0.0454349 0.0786956i
\(493\) 4.58752e16 + 7.94582e16i 0.143904 + 0.249249i
\(494\) −3.70540e16 6.41794e16i −0.114712 0.198688i
\(495\) 3.36213e15 5.82337e15i 0.0102726 0.0177927i
\(496\) 5.56107e16 0.167698
\(497\) −2.71910e17 6.77416e16i −0.809298 0.201623i
\(498\) −1.59442e17 −0.468393
\(499\) 2.40740e15 4.16974e15i 0.00698064 0.0120908i −0.862514 0.506033i \(-0.831111\pi\)
0.869495 + 0.493942i \(0.164445\pi\)
\(500\) −2.49568e16 4.32265e16i −0.0714305 0.123721i
\(501\) 1.62926e17 + 2.82196e17i 0.460305 + 0.797271i
\(502\) 1.31281e17 2.27385e17i 0.366123 0.634144i
\(503\) −2.25171e17 −0.619899 −0.309949 0.950753i \(-0.600312\pi\)
−0.309949 + 0.950753i \(0.600312\pi\)
\(504\) 6.96823e16 7.21847e16i 0.189376 0.196176i
\(505\) 1.88237e16 0.0505024
\(506\) 2.90646e15 5.03413e15i 0.00769814 0.0133336i
\(507\) −8.62588e16 1.49405e17i −0.225555 0.390672i
\(508\) 8.06405e16 + 1.39674e17i 0.208180 + 0.360579i
\(509\) −4.46192e16 + 7.72828e16i −0.113725 + 0.196978i −0.917269 0.398267i \(-0.869612\pi\)
0.803544 + 0.595245i \(0.202945\pi\)
\(510\) −2.82630e16 −0.0711234
\(511\) −1.58574e17 5.52629e17i −0.394000 1.37309i
\(512\) 1.80144e16 0.0441942
\(513\) −2.37938e17 + 4.12121e17i −0.576370 + 0.998302i
\(514\) 1.74158e17 + 3.01651e17i 0.416566 + 0.721513i
\(515\) 1.27384e16 + 2.20635e16i 0.0300862 + 0.0521108i
\(516\) 5.18647e16 8.98324e16i 0.120962 0.209512i
\(517\) −5.36180e16 −0.123487
\(518\) 9.63400e16 + 3.35744e17i 0.219110 + 0.763599i
\(519\) 9.10992e16 0.204610
\(520\) 2.74355e15 4.75197e15i 0.00608542 0.0105403i
\(521\) 1.50346e17 + 2.60408e17i 0.329343 + 0.570438i 0.982382 0.186886i \(-0.0598396\pi\)
−0.653039 + 0.757324i \(0.726506\pi\)
\(522\) 2.49022e16 + 4.31319e16i 0.0538741 + 0.0933126i
\(523\) −1.87878e17 + 3.25414e17i −0.401435 + 0.695306i −0.993899 0.110291i \(-0.964822\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(524\) 3.44553e17 0.727114
\(525\) −1.56057e17 + 1.61661e17i −0.325272 + 0.336953i
\(526\) 3.05461e17 0.628851
\(527\) 2.40262e17 4.16146e17i 0.488558 0.846207i
\(528\) −5.49291e15 9.51400e15i −0.0110327 0.0191092i
\(529\) 2.48509e17 + 4.30431e17i 0.493039 + 0.853968i
\(530\) −3.53749e16 + 6.12712e16i −0.0693270 + 0.120078i
\(531\) −1.64158e17 −0.317796
\(532\) 3.45201e17 + 8.60009e16i 0.660156 + 0.164466i
\(533\) 4.79594e16 0.0906039
\(534\) 8.50563e16 1.47322e17i 0.158741 0.274947i
\(535\) −2.82739e16 4.89719e16i −0.0521299 0.0902916i
\(536\) −1.21066e17 2.09693e17i −0.220522 0.381955i
\(537\) −1.45333e17 + 2.51724e17i −0.261536 + 0.452993i
\(538\) −4.58751e17 −0.815628
\(539\) 3.70478e15 + 1.04984e17i 0.00650781 + 0.184415i
\(540\) −3.52348e16 −0.0611522
\(541\) 4.10437e17 7.10898e17i 0.703824 1.21906i −0.263290 0.964717i \(-0.584808\pi\)
0.967114 0.254343i \(-0.0818591\pi\)
\(542\) 3.16548e17 + 5.48278e17i 0.536346 + 0.928978i
\(543\) 2.85867e16 + 4.95137e16i 0.0478592 + 0.0828946i
\(544\) 7.78299e16 1.34805e17i 0.128752 0.223005i
\(545\) −1.55184e17 −0.253671
\(546\) −4.84473e16 1.20698e16i −0.0782559 0.0194961i
\(547\) 2.03903e17 0.325466 0.162733 0.986670i \(-0.447969\pi\)
0.162733 + 0.986670i \(0.447969\pi\)
\(548\) −2.72833e17 + 4.72561e17i −0.430352 + 0.745391i
\(549\) −8.41942e16 1.45829e17i −0.131239 0.227312i
\(550\) −4.14698e16 7.18278e16i −0.0638814 0.110646i
\(551\) −8.82983e16 + 1.52937e17i −0.134421 + 0.232824i
\(552\) −1.32626e16 −0.0199538
\(553\) −6.32494e17 + 6.55208e17i −0.940466 + 0.974240i
\(554\) −3.74985e17 −0.551062
\(555\) 2.67058e16 4.62557e16i 0.0387883 0.0671833i
\(556\) −8.85016e16 1.53289e17i −0.127047 0.220052i
\(557\) −3.39433e17 5.87916e17i −0.481610 0.834173i 0.518167 0.855279i \(-0.326615\pi\)
−0.999777 + 0.0211061i \(0.993281\pi\)
\(558\) 1.30420e17 2.25895e17i 0.182904 0.316799i
\(559\) 1.74013e17 0.241216
\(560\) 7.26511e15 + 2.53189e16i 0.00995451 + 0.0346914i
\(561\) −9.49269e16 −0.128567
\(562\) 2.41333e17 4.18001e17i 0.323095 0.559618i
\(563\) −2.22241e17 3.84933e17i −0.294117 0.509425i 0.680662 0.732597i \(-0.261692\pi\)
−0.974779 + 0.223172i \(0.928359\pi\)
\(564\) 6.11667e16 + 1.05944e17i 0.0800204 + 0.138599i
\(565\) 5.97530e15 1.03495e16i 0.00772761 0.0133846i
\(566\) 4.98858e16 0.0637778
\(567\) −7.98727e16 2.78356e17i −0.100951 0.351812i
\(568\) −2.35995e17 −0.294876
\(569\) 1.13051e17 1.95810e17i 0.139651 0.241883i −0.787714 0.616042i \(-0.788735\pi\)
0.927365 + 0.374159i \(0.122069\pi\)
\(570\) −2.71996e16 4.71111e16i −0.0332182 0.0575356i
\(571\) −4.84550e17 8.39266e17i −0.585065 1.01336i −0.994867 0.101188i \(-0.967736\pi\)
0.409802 0.912174i \(-0.365598\pi\)
\(572\) 9.21474e15 1.59604e16i 0.0110004 0.0190533i
\(573\) −6.00003e16 −0.0708188
\(574\) −1.59899e17 + 1.65641e17i −0.186603 + 0.193304i
\(575\) −1.00129e17 −0.115536
\(576\) 4.22480e16 7.31757e16i 0.0482015 0.0834874i
\(577\) 1.50341e17 + 2.60398e17i 0.169604 + 0.293762i 0.938281 0.345875i \(-0.112418\pi\)
−0.768677 + 0.639637i \(0.779085\pi\)
\(578\) −3.55570e17 6.15865e17i −0.396638 0.686997i
\(579\) 3.15197e17 5.45937e17i 0.347673 0.602187i
\(580\) −1.30755e16 −0.0142619
\(581\) 1.24592e18 + 3.10399e17i 1.34383 + 0.334792i
\(582\) −1.29639e17 −0.138272
\(583\) −1.18814e17 + 2.05791e17i −0.125320 + 0.217061i
\(584\) −2.42096e17 4.19323e17i −0.252525 0.437386i
\(585\) −1.28685e16 2.22890e16i −0.0132744 0.0229920i
\(586\) 3.53950e17 6.13059e17i 0.361083 0.625414i
\(587\) 1.77519e18 1.79101 0.895503 0.445055i \(-0.146816\pi\)
0.895503 + 0.445055i \(0.146816\pi\)
\(588\) 2.03212e17 1.27085e17i 0.202767 0.126806i
\(589\) 9.24889e17 0.912725
\(590\) 2.15489e16 3.73238e16i 0.0210323 0.0364290i
\(591\) −2.10847e17 3.65198e17i −0.203540 0.352541i
\(592\) 1.47083e17 + 2.54755e17i 0.140434 + 0.243238i
\(593\) −1.05330e18 + 1.82438e18i −0.994714 + 1.72289i −0.408427 + 0.912791i \(0.633923\pi\)
−0.586287 + 0.810104i \(0.699411\pi\)
\(594\) −1.18343e17 −0.110543
\(595\) 2.20854e17 + 5.50221e16i 0.204054 + 0.0508366i
\(596\) −8.51570e17 −0.778251
\(597\) 1.66975e17 2.89209e17i 0.150945 0.261444i
\(598\) −1.11245e16 1.92682e16i −0.00994768 0.0172299i
\(599\) −2.35210e17 4.07396e17i −0.208057 0.360365i 0.743046 0.669241i \(-0.233381\pi\)
−0.951102 + 0.308876i \(0.900047\pi\)
\(600\) −9.46165e16 + 1.63881e17i −0.0827911 + 0.143398i
\(601\) 1.26028e18 1.09090 0.545449 0.838144i \(-0.316359\pi\)
0.545449 + 0.838144i \(0.316359\pi\)
\(602\) −5.80169e17 + 6.01003e17i −0.496795 + 0.514635i
\(603\) −1.13571e18 −0.962070
\(604\) −3.64840e17 + 6.31922e17i −0.305747 + 0.529570i
\(605\) −8.41003e16 1.45666e17i −0.0697248 0.120767i
\(606\) −7.21243e16 1.24923e17i −0.0591574 0.102464i
\(607\) −1.46272e17 + 2.53351e17i −0.118696 + 0.205587i −0.919251 0.393672i \(-0.871205\pi\)
0.800555 + 0.599259i \(0.204538\pi\)
\(608\) 2.99606e17 0.240534
\(609\) 3.28155e16 + 1.14362e17i 0.0260655 + 0.0908383i
\(610\) 4.42083e16 0.0347424
\(611\) −1.02611e17 + 1.77728e17i −0.0797862 + 0.138194i
\(612\) −3.65059e17 6.32301e17i −0.280853 0.486451i
\(613\) 3.48094e17 + 6.02916e17i 0.264974 + 0.458949i 0.967557 0.252653i \(-0.0813033\pi\)
−0.702583 + 0.711602i \(0.747970\pi\)
\(614\) −3.38224e17 + 5.85822e17i −0.254748 + 0.441236i
\(615\) 3.52048e16 0.0262369
\(616\) 2.44013e16 + 8.50384e16i 0.0179944 + 0.0627105i
\(617\) −1.58841e18 −1.15907 −0.579535 0.814947i \(-0.696766\pi\)
−0.579535 + 0.814947i \(0.696766\pi\)
\(618\) 9.76157e16 1.69075e17i 0.0704847 0.122083i
\(619\) 7.74130e17 + 1.34083e18i 0.553127 + 0.958044i 0.998047 + 0.0624732i \(0.0198988\pi\)
−0.444920 + 0.895570i \(0.646768\pi\)
\(620\) 3.42403e16 + 5.93059e16i 0.0242098 + 0.0419326i
\(621\) −7.14346e16 + 1.23728e17i −0.0499820 + 0.0865713i
\(622\) 1.43680e18 0.994853
\(623\) −9.51456e17 + 9.85624e17i −0.651953 + 0.675365i
\(624\) −4.20483e16 −0.0285133
\(625\) −6.98798e17 + 1.21035e18i −0.468955 + 0.812254i
\(626\) 2.62982e16 + 4.55499e16i 0.0174660 + 0.0302520i
\(627\) −9.13553e16 1.58232e17i −0.0600474 0.104005i
\(628\) −5.74741e17 + 9.95481e17i −0.373882 + 0.647583i
\(629\) 2.54185e18 1.63652
\(630\) 1.19885e17 + 2.98674e16i 0.0763928 + 0.0190320i
\(631\) 1.59070e18 1.00322 0.501612 0.865092i \(-0.332740\pi\)
0.501612 + 0.865092i \(0.332740\pi\)
\(632\) −3.83478e17 + 6.64204e17i −0.239376 + 0.414611i
\(633\) −3.87353e17 6.70916e17i −0.239322 0.414519i
\(634\) −1.11409e17 1.92966e17i −0.0681303 0.118005i
\(635\) −9.93029e16 + 1.71998e17i −0.0601080 + 0.104110i
\(636\) 5.42165e17 0.324833
\(637\) 3.55082e17 + 1.88633e17i 0.210583 + 0.111869i
\(638\) −4.39168e16 −0.0257808
\(639\) −5.53465e17 + 9.58629e17i −0.321614 + 0.557051i
\(640\) 1.10917e16 + 1.92114e16i 0.00638011 + 0.0110507i
\(641\) −1.07230e18 1.85727e18i −0.610573 1.05754i −0.991144 0.132792i \(-0.957606\pi\)
0.380571 0.924752i \(-0.375728\pi\)
\(642\) −2.16666e17 + 3.75277e17i −0.122128 + 0.211531i
\(643\) −6.80973e17 −0.379978 −0.189989 0.981786i \(-0.560845\pi\)
−0.189989 + 0.981786i \(0.560845\pi\)
\(644\) 1.03637e17 + 2.58195e16i 0.0572477 + 0.0142623i
\(645\) 1.27735e17 0.0698510
\(646\) 1.29443e18 2.24201e18i 0.700754 1.21374i
\(647\) −9.40400e17 1.62882e18i −0.504005 0.872963i −0.999989 0.00463096i \(-0.998526\pi\)
0.495984 0.868332i \(-0.334807\pi\)
\(648\) −1.21942e17 2.11210e17i −0.0647019 0.112067i
\(649\) 7.23762e16 1.25359e17i 0.0380194 0.0658515i
\(650\) −3.17452e17 −0.165098
\(651\) 4.32771e17 4.48313e17i 0.222834 0.230837i
\(652\) 1.27832e18 0.651674
\(653\) 1.61072e18 2.78984e18i 0.812987 1.40813i −0.0977777 0.995208i \(-0.531173\pi\)
0.910764 0.412926i \(-0.135493\pi\)
\(654\) 5.94597e17 + 1.02987e18i 0.297144 + 0.514669i
\(655\) 2.12146e17 + 3.67447e17i 0.104970 + 0.181814i
\(656\) −9.69459e16 + 1.67915e17i −0.0474957 + 0.0822650i
\(657\) −2.27109e18 −1.10169
\(658\) −2.71722e17 9.46950e17i −0.130514 0.454840i
\(659\) −1.43576e18 −0.682853 −0.341426 0.939909i \(-0.610910\pi\)
−0.341426 + 0.939909i \(0.610910\pi\)
\(660\) 6.76412e15 1.17158e16i 0.00318548 0.00551742i
\(661\) −1.27907e18 2.21541e18i −0.596463 1.03310i −0.993339 0.115232i \(-0.963239\pi\)
0.396875 0.917872i \(-0.370094\pi\)
\(662\) 6.19361e17 + 1.07277e18i 0.286001 + 0.495368i
\(663\) −1.81666e17 + 3.14655e17i −0.0830686 + 0.143879i
\(664\) 1.08135e18 0.489638
\(665\) 1.20829e17 + 4.21090e17i 0.0541791 + 0.188814i
\(666\) 1.37978e18 0.612671
\(667\) −2.65092e16 + 4.59153e16i −0.0116568 + 0.0201901i
\(668\) −1.10499e18 1.91389e18i −0.481182 0.833432i
\(669\) −9.64739e17 1.67098e18i −0.416045 0.720611i
\(670\) 1.49084e17 2.58221e17i 0.0636714 0.110282i
\(671\) 1.48482e17 0.0628027
\(672\) 1.40191e17 1.45225e17i 0.0587245 0.0608334i
\(673\) −3.27500e18 −1.35867 −0.679334 0.733829i \(-0.737731\pi\)
−0.679334 + 0.733829i \(0.737731\pi\)
\(674\) −1.15433e17 + 1.99935e17i −0.0474285 + 0.0821486i
\(675\) 1.01924e18 + 1.76538e18i 0.414765 + 0.718394i
\(676\) 5.85019e17 + 1.01328e18i 0.235785 + 0.408392i
\(677\) 1.84721e18 3.19946e18i 0.737377 1.27717i −0.216295 0.976328i \(-0.569397\pi\)
0.953673 0.300847i \(-0.0972693\pi\)
\(678\) −9.15789e16 −0.0362078
\(679\) 1.01303e18 + 2.52379e17i 0.396706 + 0.0988324i
\(680\) 1.91684e17 0.0743493
\(681\) −1.10122e18 + 1.90737e18i −0.423076 + 0.732789i
\(682\) 1.15003e17 + 1.99190e17i 0.0437632 + 0.0758001i
\(683\) −4.10143e17 7.10389e17i −0.154597 0.267770i 0.778315 0.627874i \(-0.216075\pi\)
−0.932912 + 0.360104i \(0.882741\pi\)
\(684\) 7.02647e17 1.21702e18i 0.262345 0.454395i
\(685\) −6.71948e17 −0.248512
\(686\) −1.83536e18 + 5.97463e17i −0.672378 + 0.218879i
\(687\) 7.98808e17 0.289884
\(688\) −3.51753e17 + 6.09255e17i −0.126448 + 0.219015i
\(689\) 4.54759e17 + 7.87666e17i 0.161941 + 0.280490i
\(690\) −8.16596e15 1.41439e16i −0.00288064 0.00498941i
\(691\) −8.84769e16 + 1.53247e17i −0.0309188 + 0.0535529i −0.881071 0.472984i \(-0.843177\pi\)
0.850152 + 0.526537i \(0.176510\pi\)
\(692\) −6.17846e17 −0.213890
\(693\) 4.02659e17 + 1.00315e17i 0.138093 + 0.0344034i
\(694\) 1.58133e18 0.537263
\(695\) 1.08983e17 1.88764e17i 0.0366824 0.0635359i
\(696\) 5.00997e16 + 8.67752e16i 0.0167061 + 0.0289358i
\(697\) 8.37695e17 + 1.45093e18i 0.276741 + 0.479329i
\(698\) −2.07776e18 + 3.59879e18i −0.680042 + 1.17787i
\(699\) −2.35850e18 −0.764777
\(700\) 1.05840e18 1.09641e18i 0.340026 0.352236i
\(701\) 2.93632e17 0.0934624 0.0467312 0.998908i \(-0.485120\pi\)
0.0467312 + 0.998908i \(0.485120\pi\)
\(702\) −2.26479e17 + 3.92273e17i −0.0714228 + 0.123708i
\(703\) 2.44621e18 + 4.23696e18i 0.764335 + 1.32387i
\(704\) 3.72537e16 + 6.45252e16i 0.0115331 + 0.0199759i
\(705\) −7.53223e16 + 1.30462e17i −0.0231044 + 0.0400179i
\(706\) −3.43840e18 −1.04502
\(707\) 3.20399e17 + 1.11659e18i 0.0964862 + 0.336254i
\(708\) −3.30263e17 −0.0985471
\(709\) 1.26737e18 2.19514e18i 0.374716 0.649027i −0.615569 0.788083i \(-0.711074\pi\)
0.990284 + 0.139056i \(0.0444070\pi\)
\(710\) −1.45305e17 2.51676e17i −0.0425699 0.0737332i
\(711\) 1.79869e18 + 3.11543e18i 0.522162 + 0.904411i
\(712\) −5.76863e17 + 9.99156e17i −0.165941 + 0.287418i
\(713\) 2.77673e17 0.0791502
\(714\) −4.81065e17 1.67651e18i −0.135883 0.473552i
\(715\) 2.26946e16 0.00635232
\(716\) 9.85667e17 1.70723e18i 0.273398 0.473540i
\(717\) 8.13231e17 + 1.40856e18i 0.223532 + 0.387168i
\(718\) −1.88256e16 3.26069e16i −0.00512790 0.00888179i
\(719\) 2.44449e18 4.23397e18i 0.659857 1.14291i −0.320796 0.947148i \(-0.603950\pi\)
0.980652 0.195757i \(-0.0627164\pi\)
\(720\) 1.04051e17 0.0278345
\(721\) −1.09195e18 + 1.13116e18i −0.289483 + 0.299878i
\(722\) 2.29150e18 0.602044
\(723\) −8.82206e17 + 1.52803e18i −0.229705 + 0.397861i
\(724\) −1.93879e17 3.35808e17i −0.0500300 0.0866544i
\(725\) 3.78237e17 + 6.55126e17i 0.0967314 + 0.167544i
\(726\) −6.44470e17 + 1.11625e18i −0.163348 + 0.282928i
\(727\) −3.85989e18 −0.969618 −0.484809 0.874620i \(-0.661111\pi\)
−0.484809 + 0.874620i \(0.661111\pi\)
\(728\) 3.28576e17 + 8.18590e16i 0.0818053 + 0.0203804i
\(729\) 4.98217e17 0.122939
\(730\) 2.98124e17 5.16365e17i 0.0729118 0.126287i
\(731\) 3.03945e18 + 5.26448e18i 0.736770 + 1.27612i
\(732\) −1.69387e17 2.93387e17i −0.0406965 0.0704885i
\(733\) 2.53437e18 4.38966e18i 0.603524 1.04533i −0.388759 0.921340i \(-0.627096\pi\)
0.992283 0.123995i \(-0.0395706\pi\)
\(734\) −2.20083e18 −0.519473
\(735\) 2.60649e17 + 1.38467e17i 0.0609802 + 0.0323950i
\(736\) 8.99487e16 0.0208588
\(737\) 5.00727e17 8.67285e17i 0.115097 0.199353i
\(738\) 4.54722e17 + 7.87602e17i 0.103605 + 0.179449i
\(739\) 2.42667e18 + 4.20311e18i 0.548052 + 0.949254i 0.998408 + 0.0564049i \(0.0179638\pi\)
−0.450356 + 0.892849i \(0.648703\pi\)
\(740\) −1.81122e17 + 3.13712e17i −0.0405476 + 0.0702305i
\(741\) −6.99325e17 −0.155189
\(742\) −4.23661e18 1.05548e18i −0.931951 0.232180i
\(743\) 6.06538e17 0.132261 0.0661303 0.997811i \(-0.478935\pi\)
0.0661303 + 0.997811i \(0.478935\pi\)
\(744\) 2.62387e17 4.54468e17i 0.0567177 0.0982379i
\(745\) −5.24323e17 9.08153e17i −0.112353 0.194600i
\(746\) −3.30722e17 5.72827e17i −0.0702523 0.121681i
\(747\) 2.53603e18 4.39253e18i 0.534036 0.924977i
\(748\) 6.43807e17 0.134399
\(749\) 2.42367e18 2.51071e18i 0.501582 0.519594i
\(750\) −4.71013e17 −0.0966350
\(751\) −3.31064e18 + 5.73420e18i −0.673369 + 1.16631i 0.303574 + 0.952808i \(0.401820\pi\)
−0.976943 + 0.213501i \(0.931513\pi\)
\(752\) −4.14841e17 7.18525e17i −0.0836499 0.144886i
\(753\) −1.23884e18 2.14573e18i −0.247655 0.428951i
\(754\) −8.40457e16 + 1.45572e17i −0.0166572 + 0.0288511i
\(755\) −8.98548e17 −0.176557
\(756\) −5.99732e17 2.09006e18i −0.116833 0.407162i
\(757\) −3.07611e17 −0.0594127 −0.0297063 0.999559i \(-0.509457\pi\)
−0.0297063 + 0.999559i \(0.509457\pi\)
\(758\) −3.30171e17 + 5.71873e17i −0.0632251 + 0.109509i
\(759\) −2.74270e16 4.75049e16i −0.00520723 0.00901918i
\(760\) 1.84471e17 + 3.19514e17i 0.0347249 + 0.0601452i
\(761\) −1.60580e18 + 2.78132e18i −0.299702 + 0.519100i −0.976068 0.217467i \(-0.930221\pi\)
0.676365 + 0.736566i \(0.263554\pi\)
\(762\) 1.52194e18 0.281637
\(763\) −2.64139e18 9.20523e18i −0.484644 1.68898i
\(764\) 4.06930e17 0.0740309
\(765\) 4.49543e17 7.78632e17i 0.0810909 0.140454i
\(766\) −3.88544e18 6.72977e18i −0.694949 1.20369i
\(767\) −2.77020e17 4.79812e17i −0.0491293 0.0850945i
\(768\) 8.49970e16 1.47219e17i 0.0149471 0.0258891i
\(769\) −8.98488e18 −1.56672 −0.783359 0.621569i \(-0.786495\pi\)
−0.783359 + 0.621569i \(0.786495\pi\)
\(770\) −7.56647e16 + 7.83819e16i −0.0130829 + 0.0135527i
\(771\) 3.28691e18 0.563552
\(772\) −2.13770e18 + 3.70261e18i −0.363442 + 0.629500i
\(773\) 6.20424e17 + 1.07461e18i 0.104598 + 0.181168i 0.913574 0.406673i \(-0.133311\pi\)
−0.808976 + 0.587841i \(0.799978\pi\)
\(774\) 1.64989e18 + 2.85769e18i 0.275828 + 0.477749i
\(775\) 1.98094e18 3.43109e18i 0.328406 0.568815i
\(776\) 8.79226e17 0.144544
\(777\) 3.19836e18 + 7.96817e17i 0.521424 + 0.129904i
\(778\) 6.04537e18 0.977362
\(779\) −1.61235e18 + 2.79268e18i −0.258504 + 0.447742i
\(780\) −2.58897e16 4.48422e16i −0.00411634 0.00712971i
\(781\) −4.88037e17 8.45304e17i −0.0769522 0.133285i
\(782\) 3.88617e17 6.73104e17i 0.0607684 0.105254i
\(783\) 1.07938e18 0.167388
\(784\) −1.37821e18 + 8.61905e17i −0.211963 + 0.132558i
\(785\) −1.41550e18 −0.215903
\(786\) 1.62570e18 2.81579e18i 0.245920 0.425945i
\(787\) −5.90157e18 1.02218e19i −0.885385 1.53353i −0.845272 0.534336i \(-0.820562\pi\)
−0.0401124 0.999195i \(-0.512772\pi\)
\(788\) 1.42999e18 + 2.47682e18i 0.212771 + 0.368531i
\(789\) 1.44125e18 2.49632e18i 0.212686 0.368383i
\(790\) −9.44450e17 −0.138230
\(791\) 7.15621e17 + 1.78285e17i 0.103881 + 0.0258801i
\(792\) 3.49475e17 0.0503155
\(793\) 2.84158e17 4.92176e17i 0.0405774 0.0702822i
\(794\) 2.15616e18 + 3.73458e18i 0.305385 + 0.528942i
\(795\) 3.33818e17 + 5.78189e17i 0.0468946 + 0.0812239i
\(796\) −1.13245e18 + 1.96146e18i −0.157791 + 0.273303i
\(797\) 5.23046e18 0.722871 0.361436 0.932397i \(-0.382287\pi\)
0.361436 + 0.932397i \(0.382287\pi\)
\(798\) 2.33158e18 2.41531e18i 0.319618 0.331096i
\(799\) −7.16915e18 −0.974796
\(800\) 6.41701e17 1.11146e18i 0.0865462 0.149902i
\(801\) 2.70576e18 + 4.68651e18i 0.361974 + 0.626958i
\(802\) 1.87236e18 + 3.24302e18i 0.248459 + 0.430344i
\(803\) 1.00131e18 1.73431e18i 0.131800 0.228285i
\(804\) −2.28489e18 −0.298333
\(805\) 3.62758e16 + 1.26421e17i 0.00469834 + 0.0163737i
\(806\) 8.80345e17 0.113103
\(807\) −2.16451e18 + 3.74905e18i −0.275856 + 0.477797i
\(808\) 4.89156e17 + 8.47244e17i 0.0618406 + 0.107111i
\(809\) 1.01556e18 + 1.75901e18i 0.127362 + 0.220598i 0.922654 0.385629i \(-0.126016\pi\)
−0.795292 + 0.606227i \(0.792682\pi\)
\(810\) 1.50163e17 2.60090e17i 0.0186815 0.0323572i
\(811\) 2.48818e17 0.0307076 0.0153538 0.999882i \(-0.495113\pi\)
0.0153538 + 0.999882i \(0.495113\pi\)
\(812\) −2.22559e17 7.75617e17i −0.0272478 0.0949584i
\(813\) 5.97426e18 0.725597
\(814\) −6.08334e17 + 1.05366e18i −0.0732965 + 0.126953i
\(815\) 7.87079e17 + 1.36326e18i 0.0940793 + 0.162950i
\(816\) −7.34446e17 1.27210e18i −0.0870912 0.150846i
\(817\) −5.85018e18 + 1.01328e19i −0.688218 + 1.19203i
\(818\) 9.46556e18 1.10471
\(819\) 1.10310e18 1.14272e18i 0.127724 0.132310i
\(820\) −2.38763e17 −0.0274270
\(821\) −4.01984e18 + 6.96258e18i −0.458119 + 0.793486i −0.998862 0.0477022i \(-0.984810\pi\)
0.540742 + 0.841188i \(0.318143\pi\)
\(822\) 2.57461e18 + 4.45935e18i 0.291101 + 0.504202i
\(823\) −4.52962e17 7.84553e17i −0.0508116 0.0880082i 0.839501 0.543358i \(-0.182847\pi\)
−0.890313 + 0.455350i \(0.849514\pi\)
\(824\) −6.62042e17 + 1.14669e18i −0.0736816 + 0.127620i
\(825\) −7.82665e17 −0.0864222
\(826\) 2.58076e18 + 6.42952e17i 0.282734 + 0.0704382i
\(827\) −4.25212e18 −0.462189 −0.231095 0.972931i \(-0.574231\pi\)
−0.231095 + 0.972931i \(0.574231\pi\)
\(828\) 2.10951e17 3.65378e17i 0.0227502 0.0394044i
\(829\) 1.29722e17 + 2.24686e17i 0.0138807 + 0.0240420i 0.872882 0.487931i \(-0.162248\pi\)
−0.859002 + 0.511973i \(0.828915\pi\)
\(830\) 6.65804e17 + 1.15321e18i 0.0706868 + 0.122433i
\(831\) −1.76929e18 + 3.06449e18i −0.186377 + 0.322814i
\(832\) 2.85177e17 0.0298066
\(833\) 4.95358e17 + 1.40372e19i 0.0513721 + 1.45575i
\(834\) −1.67030e18 −0.171876
\(835\) 1.36071e18 2.35682e18i 0.138932 0.240638i
\(836\) 6.19583e17 + 1.07315e18i 0.0627710 + 0.108723i
\(837\) −2.82652e18 4.89568e18i −0.284143 0.492150i
\(838\) 2.01782e18 3.49497e18i 0.201278 0.348624i
\(839\) −8.59708e18 −0.850938 −0.425469 0.904973i \(-0.639891\pi\)
−0.425469 + 0.904973i \(0.639891\pi\)
\(840\) 2.41192e17 + 6.00889e16i 0.0236891 + 0.00590172i
\(841\) −9.86007e18 −0.960962
\(842\) −1.38509e18 + 2.39904e18i −0.133952 + 0.232011i
\(843\) −2.27735e18 3.94449e18i −0.218550 0.378540i
\(844\) 2.62708e18 + 4.55024e18i 0.250177 + 0.433320i
\(845\) −7.20407e17 + 1.24778e18i −0.0680784 + 0.117915i
\(846\) −3.89160e18 −0.364939
\(847\) 7.20916e18 7.46805e18i 0.670877 0.694969i
\(848\) −3.67703e18 −0.339566
\(849\) 2.35375e17 4.07681e17i 0.0215705 0.0373612i
\(850\) −5.54485e18 9.60396e18i −0.504274 0.873428i
\(851\) 7.34409e17 + 1.27203e18i 0.0662821 + 0.114804i
\(852\) −1.11349e18 + 1.92863e18i −0.0997309 + 0.172739i
\(853\) 2.04864e19 1.82095 0.910474 0.413566i \(-0.135717\pi\)
0.910474 + 0.413566i \(0.135717\pi\)
\(854\) 7.52471e17 + 2.62236e18i 0.0663763 + 0.231321i
\(855\) 1.73052e18 0.151494
\(856\) 1.46946e18 2.54518e18i 0.127667 0.221126i
\(857\) −1.73837e18 3.01094e18i −0.149888 0.259614i 0.781298 0.624158i \(-0.214558\pi\)
−0.931186 + 0.364545i \(0.881225\pi\)
\(858\) −8.69555e16 1.50611e17i −0.00744097 0.0128881i
\(859\) −6.11673e17 + 1.05945e18i −0.0519474 + 0.0899756i −0.890830 0.454337i \(-0.849876\pi\)
0.838882 + 0.544313i \(0.183209\pi\)
\(860\) −8.66317e17 −0.0730192
\(861\) 5.99221e17 + 2.08828e18i 0.0501264 + 0.174690i
\(862\) −9.03615e18 −0.750215
\(863\) 9.67599e18 1.67593e19i 0.797306 1.38097i −0.124058 0.992275i \(-0.539591\pi\)
0.921364 0.388700i \(-0.127076\pi\)
\(864\) −9.15616e17 1.58589e18i −0.0748814 0.129698i
\(865\) −3.80416e17 6.58900e17i −0.0308784 0.0534829i
\(866\) 4.38545e18 7.59582e18i 0.353303 0.611939i
\(867\) −6.71072e18 −0.536593
\(868\) −2.93511e18 + 3.04051e18i −0.232941 + 0.241306i
\(869\) −3.17212e18 −0.249874
\(870\) −6.16941e16 + 1.06857e17i −0.00482357 + 0.00835466i
\(871\) −1.91653e18 3.31954e18i −0.148730 0.257608i
\(872\) −4.03263e18 6.98473e18i −0.310622 0.538012i
\(873\) 2.06199e18 3.57148e18i 0.157650 0.273058i
\(874\) 1.49598e18 0.113528
\(875\) 3.68061e18 + 9.16961e17i 0.277248 + 0.0690715i
\(876\) −4.56911e18 −0.341629
\(877\) 2.56261e18 4.43857e18i 0.190189 0.329417i −0.755124 0.655582i \(-0.772423\pi\)
0.945313 + 0.326165i \(0.105757\pi\)
\(878\) −4.27134e18 7.39817e18i −0.314666 0.545017i
\(879\) −3.34007e18 5.78516e18i −0.244246 0.423046i
\(880\) −4.58751e16 + 7.94581e16i −0.00332997 + 0.00576767i
\(881\) 1.71952e19 1.23898 0.619491 0.785004i \(-0.287339\pi\)
0.619491 + 0.785004i \(0.287339\pi\)
\(882\) 2.68893e17 + 7.61975e18i 0.0192324 + 0.544998i
\(883\) 2.62825e19 1.86604 0.933021 0.359822i \(-0.117163\pi\)
0.933021 + 0.359822i \(0.117163\pi\)
\(884\) 1.23209e18 2.13403e18i 0.0868363 0.150405i
\(885\) −2.03347e17 3.52208e17i −0.0142268 0.0246415i
\(886\) −7.53218e18 1.30461e19i −0.523120 0.906071i
\(887\) 1.11566e18 1.93238e18i 0.0769179 0.133226i −0.825001 0.565132i \(-0.808825\pi\)
0.901919 + 0.431906i \(0.142159\pi\)
\(888\) 2.77592e18 0.189986
\(889\) −1.18928e19 2.96289e18i −0.808022 0.201305i
\(890\) −1.42073e18 −0.0958244
\(891\) 5.04352e17 8.73564e17i 0.0337698 0.0584911i
\(892\) 6.54299e18 + 1.13328e19i 0.434915 + 0.753295i
\(893\) −6.89941e18 1.19501e19i −0.455279 0.788566i
\(894\) −4.01794e18 + 6.95928e18i −0.263215 + 0.455901i
\(895\) 2.42755e18 0.157877
\(896\) −9.50792e17 + 9.84937e17i −0.0613880 + 0.0635925i
\(897\) −2.09954e17 −0.0134578
\(898\) −9.49537e17 + 1.64465e18i −0.0604248 + 0.104659i
\(899\) −1.04891e18 1.81677e18i −0.0662677 0.114779i
\(900\) −3.00988e18 5.21327e18i −0.188788 0.326990i
\(901\) −1.58863e19 + 2.75159e19i −0.989265 + 1.71346i
\(902\) −8.01934e17 −0.0495788
\(903\) 2.17418e18 + 7.57702e18i 0.133452 + 0.465080i
\(904\) 6.21100e17 0.0378501
\(905\) 2.38748e17 4.13523e17i 0.0144452 0.0250198i
\(906\) 3.44284e18 + 5.96317e18i 0.206816 + 0.358215i
\(907\) 4.08268e18 + 7.07142e18i 0.243500 + 0.421754i 0.961709 0.274074i \(-0.0883712\pi\)
−0.718209 + 0.695827i \(0.755038\pi\)
\(908\) 7.46862e18 1.29360e19i 0.442265 0.766026i
\(909\) 4.58875e18 0.269792
\(910\) 1.15010e17 + 4.00810e17i 0.00671378 + 0.0233975i
\(911\) −1.41341e19 −0.819218 −0.409609 0.912261i \(-0.634335\pi\)
−0.409609 + 0.912261i \(0.634335\pi\)
\(912\) 1.41363e18 2.44847e18i 0.0813520 0.140906i
\(913\) 2.23623e18 + 3.87327e18i 0.127778 + 0.221318i
\(914\) −4.93056e18 8.53999e18i −0.279735 0.484515i
\(915\) 2.08587e17 3.61284e17i 0.0117504 0.0203522i
\(916\) −5.41762e18 −0.303032
\(917\) −1.81854e19 + 1.88384e19i −1.01000 + 1.04627i
\(918\) −1.58234e19 −0.872615
\(919\) 6.47932e18 1.12225e19i 0.354796 0.614524i −0.632287 0.774734i \(-0.717884\pi\)
0.987083 + 0.160210i \(0.0512171\pi\)
\(920\) 5.53826e16 + 9.59255e16i 0.00301129 + 0.00521571i
\(921\) 3.19168e18 + 5.52814e18i 0.172318 + 0.298464i
\(922\) −9.06928e18 + 1.57085e19i −0.486208 + 0.842137i
\(923\) −3.73592e18 −0.198878
\(924\) 8.10091e17 + 2.01820e17i 0.0428219 + 0.0106683i
\(925\) 2.09573e19 1.10006
\(926\) −3.05305e17 + 5.28804e17i −0.0159134 + 0.0275628i
\(927\) 3.10529e18 + 5.37852e18i 0.160725 + 0.278384i
\(928\) −3.39783e17 5.88521e17i −0.0174638 0.0302482i
\(929\) −1.07171e19 + 1.85626e19i −0.546986 + 0.947408i 0.451493 + 0.892275i \(0.350892\pi\)
−0.998479 + 0.0551329i \(0.982442\pi\)
\(930\) 6.46221e17 0.0327523
\(931\) −2.29217e19 + 1.43348e19i −1.15365 + 0.721469i
\(932\) 1.59957e19 0.799464
\(933\) 6.77922e18 1.17420e19i 0.336472 0.582787i
\(934\) 6.88494e18 + 1.19251e19i 0.339348 + 0.587769i
\(935\) 3.96400e17 + 6.86585e17i 0.0194025 + 0.0336062i
\(936\) 6.68807e17 1.15841e18i 0.0325093 0.0563078i
\(937\) 3.52431e19 1.70124 0.850622 0.525778i \(-0.176226\pi\)
0.850622 + 0.525778i \(0.176226\pi\)
\(938\) 1.78547e19 + 4.44820e18i 0.855924 + 0.213239i
\(939\) 4.96330e17 0.0236289
\(940\) 5.10845e17 8.84810e17i 0.0241523 0.0418330i
\(941\) 1.92251e18 + 3.32988e18i 0.0902682 + 0.156349i 0.907624 0.419784i \(-0.137894\pi\)
−0.817356 + 0.576133i \(0.804561\pi\)
\(942\) 5.42358e18 + 9.39392e18i 0.252904 + 0.438042i
\(943\) −4.84066e17 + 8.38427e17i −0.0224171 + 0.0388275i
\(944\) 2.23989e18 0.103017
\(945\) 1.85968e18 1.92646e18i 0.0849436 0.0879941i
\(946\) −2.90969e18 −0.131994
\(947\) −7.78632e18 + 1.34863e19i −0.350798 + 0.607600i −0.986390 0.164425i \(-0.947423\pi\)
0.635591 + 0.772026i \(0.280756\pi\)
\(948\) 3.61872e18 + 6.26780e18i 0.161920 + 0.280454i
\(949\) −3.83250e18 6.63809e18i −0.170315 0.294994i
\(950\) 1.06724e19 1.84852e19i 0.471043 0.815870i
\(951\) −2.10264e18 −0.0921703
\(952\) 3.26265e18 + 1.13703e19i 0.142046 + 0.495031i
\(953\) −1.10796e19 −0.479095 −0.239548 0.970885i \(-0.576999\pi\)
−0.239548 + 0.970885i \(0.576999\pi\)
\(954\) −8.62351e18 + 1.49364e19i −0.370356 + 0.641476i
\(955\) 2.50552e17 + 4.33969e17i 0.0106875 + 0.0185113i
\(956\) −5.51544e18 9.55302e18i −0.233670 0.404729i
\(957\) −2.07212e17 + 3.58901e17i −0.00871940 + 0.0151024i
\(958\) 1.53320e19 0.640800
\(959\) −1.14372e19 3.98587e19i −0.474788 1.65463i
\(960\) 2.09335e17 0.00863135
\(961\) 6.71529e18 1.16312e19i 0.275019 0.476347i
\(962\) 2.32840e18 + 4.03290e18i 0.0947151 + 0.164051i
\(963\) −6.89246e18 1.19381e19i −0.278486 0.482352i
\(964\) 5.98324e18 1.03633e19i 0.240124 0.415907i
\(965\) −5.26485e18 −0.209874
\(966\) 6.99995e17 7.25133e17i 0.0277168 0.0287122i
\(967\) 2.18298e19 0.858574 0.429287 0.903168i \(-0.358765\pi\)
0.429287 + 0.903168i \(0.358765\pi\)
\(968\) 4.37088e18 7.57059e18i 0.170757 0.295760i
\(969\) −1.22149e19 2.11569e19i −0.474009 0.821007i
\(970\) 5.41351e17 + 9.37648e17i 0.0208671 + 0.0361429i
\(971\) −9.57047e18 + 1.65765e19i −0.366444 + 0.634700i −0.989007 0.147870i \(-0.952758\pi\)
0.622562 + 0.782570i \(0.286092\pi\)
\(972\) −1.34387e19 −0.511125
\(973\) 1.30522e19 + 3.25172e18i 0.493116 + 0.122851i
\(974\) −4.10456e18 −0.154040
\(975\) −1.49783e18 + 2.59431e18i −0.0558382 + 0.0967146i
\(976\) 1.14880e18 + 1.98979e18i 0.0425424 + 0.0736856i
\(977\) −2.00659e19 3.47551e19i −0.738148 1.27851i −0.953328 0.301935i \(-0.902367\pi\)
0.215181 0.976574i \(-0.430966\pi\)
\(978\) 6.03148e18 1.04468e19i 0.220405 0.381752i
\(979\) −4.77179e18 −0.173218
\(980\) −1.76776e18 9.39100e17i −0.0637460 0.0338643i
\(981\) −3.78299e19 −1.35515
\(982\) −8.27068e18 + 1.43252e19i −0.294318 + 0.509774i
\(983\) 1.99129e18 + 3.44902e18i 0.0703943 + 0.121926i 0.899074 0.437796i \(-0.144241\pi\)
−0.828680 + 0.559723i \(0.810908\pi\)
\(984\) 9.14836e17 + 1.58454e18i 0.0321274 + 0.0556462i
\(985\) −1.76093e18 + 3.05002e18i −0.0614337 + 0.106406i
\(986\) −5.87202e18 −0.203511
\(987\) −9.02083e18 2.24738e18i −0.310588 0.0773777i
\(988\) 4.74291e18 0.162228
\(989\) −1.75636e18 + 3.04211e18i −0.0596812 + 0.103371i
\(990\) 2.15176e17 + 3.72696e17i 0.00726382 + 0.0125813i
\(991\) 2.71104e19 + 4.69567e19i 0.909197 + 1.57478i 0.815182 + 0.579204i \(0.196637\pi\)
0.0940145 + 0.995571i \(0.470030\pi\)
\(992\) −1.77954e18 + 3.08226e18i −0.0592902 + 0.102694i
\(993\) 1.16893e19 0.386917
\(994\) 1.24557e19 1.29030e19i 0.409598 0.424307i
\(995\) −2.78905e18 −0.0911184
\(996\) 5.10213e18 8.83715e18i 0.165602 0.286831i
\(997\) −2.74343e19 4.75176e19i −0.884657 1.53227i −0.846106 0.533014i \(-0.821059\pi\)
−0.0385510 0.999257i \(-0.512274\pi\)
\(998\) 1.54074e17 + 2.66863e17i 0.00493606 + 0.00854950i
\(999\) 1.49516e19 2.58969e19i 0.475894 0.824273i
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 14.14.c.a.9.3 8
3.2 odd 2 126.14.g.d.37.2 8
7.2 even 3 98.14.a.l.1.2 4
7.3 odd 6 98.14.c.n.67.2 8
7.4 even 3 inner 14.14.c.a.11.3 yes 8
7.5 odd 6 98.14.a.k.1.3 4
7.6 odd 2 98.14.c.n.79.2 8
21.11 odd 6 126.14.g.d.109.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.14.c.a.9.3 8 1.1 even 1 trivial
14.14.c.a.11.3 yes 8 7.4 even 3 inner
98.14.a.k.1.3 4 7.5 odd 6
98.14.a.l.1.2 4 7.2 even 3
98.14.c.n.67.2 8 7.3 odd 6
98.14.c.n.79.2 8 7.6 odd 2
126.14.g.d.37.2 8 3.2 odd 2
126.14.g.d.109.2 8 21.11 odd 6