Properties

Label 7.10.c.a.4.1
Level $7$
Weight $10$
Character 7.4
Analytic conductor $3.605$
Analytic rank $0$
Dimension $10$
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] = [7,10,Mod(2,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 7.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: \(3.60525085315\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + 1399072384 x^{2} + 1034227200 x + 761760000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{3}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.1
Root \(-8.71912 + 15.1020i\) of defining polynomial
Character \(\chi\) \(=\) 7.4
Dual form 7.10.c.a.2.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-19.4382 - 33.6680i) q^{2} +(113.728 - 196.982i) q^{3} +(-499.691 + 865.489i) q^{4} +(-162.760 - 281.909i) q^{5} -8842.67 q^{6} +(5234.95 + 3598.46i) q^{7} +18947.7 q^{8} +(-16026.5 - 27758.7i) q^{9} +O(q^{10})\) \(q+(-19.4382 - 33.6680i) q^{2} +(113.728 - 196.982i) q^{3} +(-499.691 + 865.489i) q^{4} +(-162.760 - 281.909i) q^{5} -8842.67 q^{6} +(5234.95 + 3598.46i) q^{7} +18947.7 q^{8} +(-16026.5 - 27758.7i) q^{9} +(-6327.54 + 10959.6i) q^{10} +(24492.8 - 42422.7i) q^{11} +(113657. + 196860. i) q^{12} -108737. q^{13} +(19395.0 - 246198. i) q^{14} -74041.4 q^{15} +(-112468. - 194800. i) q^{16} +(114226. - 197845. i) q^{17} +(-623053. + 1.07916e6i) q^{18} +(28440.4 + 49260.3i) q^{19} +325319. q^{20} +(1.30419e6 - 621946. i) q^{21} -1.90439e6 q^{22} +(721856. + 1.25029e6i) q^{23} +(2.15487e6 - 3.73235e6i) q^{24} +(923581. - 1.59969e6i) q^{25} +(2.11367e6 + 3.66098e6i) q^{26} -2.81361e6 q^{27} +(-5.73029e6 + 2.73267e6i) q^{28} -266591. q^{29} +(1.43923e6 + 2.49283e6i) q^{30} +(-80792.9 + 139937. i) q^{31} +(478253. - 828358. i) q^{32} +(-5.57102e6 - 9.64928e6i) q^{33} -8.88141e6 q^{34} +(162398. - 2.06146e6i) q^{35} +3.20331e7 q^{36} +(3.04492e6 + 5.27396e6i) q^{37} +(1.10566e6 - 1.91507e6i) q^{38} +(-1.23665e7 + 2.14193e7i) q^{39} +(-3.08392e6 - 5.34151e6i) q^{40} +1.73177e7 q^{41} +(-4.62909e7 - 3.18200e7i) q^{42} +1.34512e7 q^{43} +(2.44776e7 + 4.23965e7i) q^{44} +(-5.21694e6 + 9.03601e6i) q^{45} +(2.80632e7 - 4.86069e7i) q^{46} +(-959805. - 1.66243e6i) q^{47} -5.11628e7 q^{48} +(1.44557e7 + 3.76755e7i) q^{49} -7.18111e7 q^{50} +(-2.59813e7 - 4.50010e7i) q^{51} +(5.43351e7 - 9.41111e7i) q^{52} +(-5.02699e7 + 8.70701e7i) q^{53} +(5.46916e7 + 9.47287e7i) q^{54} -1.59458e7 q^{55} +(9.91900e7 + 6.81825e7i) q^{56} +1.29379e7 q^{57} +(5.18206e6 + 8.97559e6i) q^{58} +(7.83622e7 - 1.35727e8i) q^{59} +(3.69978e7 - 6.40820e7i) q^{60} +(-3.73934e7 - 6.47672e7i) q^{61} +6.28189e6 q^{62} +(1.59908e7 - 2.02986e8i) q^{63} -1.52352e8 q^{64} +(1.76981e7 + 3.06541e7i) q^{65} +(-2.16581e8 + 3.75130e8i) q^{66} +(-6.10097e7 + 1.05672e8i) q^{67} +(1.14155e8 + 1.97723e8i) q^{68} +3.28380e8 q^{69} +(-7.25622e7 + 3.46036e7i) q^{70} -1.47012e8 q^{71} +(-3.03664e8 - 5.25962e8i) q^{72} +(-1.78170e8 + 3.08600e8i) q^{73} +(1.18376e8 - 2.05033e8i) q^{74} +(-2.10073e8 - 3.63858e8i) q^{75} -5.68456e7 q^{76} +(2.80875e8 - 1.33944e8i) q^{77} +9.61529e8 q^{78} +(2.81209e8 + 4.87068e8i) q^{79} +(-3.66105e7 + 6.34113e7i) q^{80} +(-4.53629e6 + 7.85709e6i) q^{81} +(-3.36626e8 - 5.83053e8i) q^{82} -2.10522e8 q^{83} +(-1.13404e8 + 1.43954e9i) q^{84} -7.43658e7 q^{85} +(-2.61468e8 - 4.52875e8i) q^{86} +(-3.03188e7 + 5.25136e7i) q^{87} +(4.64081e8 - 8.03812e8i) q^{88} +(2.74145e8 + 4.74833e8i) q^{89} +4.05633e8 q^{90} +(-5.69235e8 - 3.91288e8i) q^{91} -1.44282e9 q^{92} +(1.83768e7 + 3.18295e7i) q^{93} +(-3.73138e7 + 6.46295e7i) q^{94} +(9.25794e6 - 1.60352e7i) q^{95} +(-1.08781e8 - 1.88414e8i) q^{96} +9.75955e8 q^{97} +(9.87467e8 - 1.21904e9i) q^{98} -1.57013e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16} + 324681 q^{17} - 1012868 q^{18} - 16121 q^{19} - 350616 q^{20} - 1557857 q^{21} - 62692 q^{22} + 2638863 q^{23} + 8449728 q^{24} - 1304092 q^{25} + 4179252 q^{26} - 18331558 q^{27} - 22156316 q^{28} + 15292500 q^{29} + 20557942 q^{30} + 19179237 q^{31} - 6263520 q^{32} + 1689359 q^{33} - 62909700 q^{34} - 43746759 q^{35} + 71476528 q^{36} + 39566985 q^{37} + 67365270 q^{38} - 44299486 q^{39} + 5721744 q^{40} - 53436852 q^{41} - 183129856 q^{42} + 101835992 q^{43} + 99704916 q^{44} + 85098230 q^{45} - 14489202 q^{46} + 32509659 q^{47} - 185141600 q^{48} - 49024598 q^{49} + 3328464 q^{50} + 44168403 q^{51} + 103893272 q^{52} - 25714707 q^{53} + 51200926 q^{54} - 144695222 q^{55} + 115352832 q^{56} - 121710346 q^{57} - 46645516 q^{58} + 46776513 q^{59} + 132391756 q^{60} - 113075039 q^{61} + 467465628 q^{62} + 318071530 q^{63} - 192008960 q^{64} - 338113566 q^{65} - 836682602 q^{66} - 126707879 q^{67} + 32262636 q^{68} + 1323616182 q^{69} + 697712470 q^{70} - 1188736032 q^{71} - 950557728 q^{72} - 859257651 q^{73} + 591757530 q^{74} - 169061732 q^{75} + 1101475592 q^{76} + 1911891891 q^{77} + 519432424 q^{78} - 527065417 q^{79} - 1257352656 q^{80} + 551662715 q^{81} - 1341703076 q^{82} - 144863208 q^{83} + 486452204 q^{84} - 1197360222 q^{85} - 678648216 q^{86} - 340781350 q^{87} + 903700608 q^{88} + 1661554797 q^{89} + 1967758744 q^{90} + 726641384 q^{91} - 1301840952 q^{92} - 423057489 q^{93} - 272580882 q^{94} - 1197123495 q^{95} - 1441922272 q^{96} + 869770188 q^{97} - 2404833858 q^{98} - 1900777180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −19.4382 33.6680i −0.859057 1.48793i −0.872829 0.488025i \(-0.837717\pi\)
0.0137724 0.999905i \(-0.495616\pi\)
\(3\) 113.728 196.982i 0.810626 1.40405i −0.101800 0.994805i \(-0.532460\pi\)
0.912426 0.409241i \(-0.134206\pi\)
\(4\) −499.691 + 865.489i −0.975958 + 1.69041i
\(5\) −162.760 281.909i −0.116462 0.201718i 0.801901 0.597456i \(-0.203822\pi\)
−0.918363 + 0.395739i \(0.870489\pi\)
\(6\) −8842.67 −2.78550
\(7\) 5234.95 + 3598.46i 0.824083 + 0.566469i
\(8\) 18947.7 1.63550
\(9\) −16026.5 27758.7i −0.814229 1.41029i
\(10\) −6327.54 + 10959.6i −0.200094 + 0.346574i
\(11\) 24492.8 42422.7i 0.504395 0.873638i −0.495592 0.868556i \(-0.665049\pi\)
0.999987 0.00508275i \(-0.00161790\pi\)
\(12\) 113657. + 196860.i 1.58227 + 2.74058i
\(13\) −108737. −1.05593 −0.527964 0.849267i \(-0.677044\pi\)
−0.527964 + 0.849267i \(0.677044\pi\)
\(14\) 19395.0 246198.i 0.134931 1.71281i
\(15\) −74041.4 −0.377628
\(16\) −112468. 194800.i −0.429030 0.743102i
\(17\) 114226. 197845.i 0.331699 0.574520i −0.651146 0.758953i \(-0.725711\pi\)
0.982845 + 0.184432i \(0.0590447\pi\)
\(18\) −623053. + 1.07916e6i −1.39894 + 2.42303i
\(19\) 28440.4 + 49260.3i 0.0500662 + 0.0867172i 0.889972 0.456014i \(-0.150723\pi\)
−0.839906 + 0.542732i \(0.817390\pi\)
\(20\) 325319. 0.454647
\(21\) 1.30419e6 621946.i 1.46337 0.697856i
\(22\) −1.90439e6 −1.73322
\(23\) 721856. + 1.25029e6i 0.537867 + 0.931614i 0.999019 + 0.0442921i \(0.0141032\pi\)
−0.461151 + 0.887322i \(0.652563\pi\)
\(24\) 2.15487e6 3.73235e6i 1.32578 2.29632i
\(25\) 923581. 1.59969e6i 0.472873 0.819041i
\(26\) 2.11367e6 + 3.66098e6i 0.907102 + 1.57115i
\(27\) −2.81361e6 −1.01889
\(28\) −5.73029e6 + 2.73267e6i −1.76183 + 0.840188i
\(29\) −266591. −0.0699929 −0.0349965 0.999387i \(-0.511142\pi\)
−0.0349965 + 0.999387i \(0.511142\pi\)
\(30\) 1.43923e6 + 2.49283e6i 0.324404 + 0.561884i
\(31\) −80792.9 + 139937.i −0.0157125 + 0.0272149i −0.873775 0.486331i \(-0.838335\pi\)
0.858062 + 0.513546i \(0.171668\pi\)
\(32\) 478253. 828358.i 0.0806274 0.139651i
\(33\) −5.57102e6 9.64928e6i −0.817752 1.41639i
\(34\) −8.88141e6 −1.13979
\(35\) 162398. 2.06146e6i 0.0182925 0.232204i
\(36\) 3.20331e7 3.17861
\(37\) 3.04492e6 + 5.27396e6i 0.267097 + 0.462625i 0.968111 0.250522i \(-0.0806023\pi\)
−0.701014 + 0.713147i \(0.747269\pi\)
\(38\) 1.10566e6 1.91507e6i 0.0860195 0.148990i
\(39\) −1.23665e7 + 2.14193e7i −0.855962 + 1.48257i
\(40\) −3.08392e6 5.34151e6i −0.190473 0.329909i
\(41\) 1.73177e7 0.957113 0.478556 0.878057i \(-0.341160\pi\)
0.478556 + 0.878057i \(0.341160\pi\)
\(42\) −4.62909e7 3.18200e7i −2.29548 1.57790i
\(43\) 1.34512e7 0.600003 0.300001 0.953939i \(-0.403013\pi\)
0.300001 + 0.953939i \(0.403013\pi\)
\(44\) 2.44776e7 + 4.23965e7i 0.984537 + 1.70527i
\(45\) −5.21694e6 + 9.03601e6i −0.189653 + 0.328489i
\(46\) 2.80632e7 4.86069e7i 0.924118 1.60062i
\(47\) −959805. 1.66243e6i −0.0286908 0.0496939i 0.851323 0.524641i \(-0.175800\pi\)
−0.880014 + 0.474947i \(0.842467\pi\)
\(48\) −5.11628e7 −1.39113
\(49\) 1.44557e7 + 3.76755e7i 0.358227 + 0.933635i
\(50\) −7.18111e7 −1.62490
\(51\) −2.59813e7 4.50010e7i −0.537768 0.931442i
\(52\) 5.43351e7 9.41111e7i 1.03054 1.78495i
\(53\) −5.02699e7 + 8.70701e7i −0.875118 + 1.51575i −0.0184820 + 0.999829i \(0.505883\pi\)
−0.856636 + 0.515920i \(0.827450\pi\)
\(54\) 5.46916e7 + 9.47287e7i 0.875284 + 1.51604i
\(55\) −1.59458e7 −0.234971
\(56\) 9.91900e7 + 6.81825e7i 1.34779 + 0.926460i
\(57\) 1.29379e7 0.162340
\(58\) 5.18206e6 + 8.97559e6i 0.0601279 + 0.104145i
\(59\) 7.83622e7 1.35727e8i 0.841923 1.45825i −0.0463429 0.998926i \(-0.514757\pi\)
0.888266 0.459329i \(-0.151910\pi\)
\(60\) 3.69978e7 6.40820e7i 0.368549 0.638345i
\(61\) −3.73934e7 6.47672e7i −0.345788 0.598923i 0.639708 0.768618i \(-0.279055\pi\)
−0.985497 + 0.169695i \(0.945722\pi\)
\(62\) 6.28189e6 0.0539918
\(63\) 1.59908e7 2.02986e8i 0.127890 1.62343i
\(64\) −1.52352e8 −1.13511
\(65\) 1.76981e7 + 3.06541e7i 0.122975 + 0.212999i
\(66\) −2.16581e8 + 3.75130e8i −1.40499 + 2.43352i
\(67\) −6.10097e7 + 1.05672e8i −0.369881 + 0.640653i −0.989547 0.144213i \(-0.953935\pi\)
0.619665 + 0.784866i \(0.287268\pi\)
\(68\) 1.14155e8 + 1.97723e8i 0.647449 + 1.12142i
\(69\) 3.28380e8 1.74404
\(70\) −7.25622e7 + 3.46036e7i −0.361218 + 0.172258i
\(71\) −1.47012e8 −0.686578 −0.343289 0.939230i \(-0.611541\pi\)
−0.343289 + 0.939230i \(0.611541\pi\)
\(72\) −3.03664e8 5.25962e8i −1.33167 2.30652i
\(73\) −1.78170e8 + 3.08600e8i −0.734316 + 1.27187i 0.220707 + 0.975340i \(0.429163\pi\)
−0.955023 + 0.296532i \(0.904170\pi\)
\(74\) 1.18376e8 2.05033e8i 0.458903 0.794843i
\(75\) −2.10073e8 3.63858e8i −0.766647 1.32787i
\(76\) −5.68456e7 −0.195450
\(77\) 2.80875e8 1.33944e8i 0.910553 0.434227i
\(78\) 9.61529e8 2.94128
\(79\) 2.81209e8 + 4.87068e8i 0.812282 + 1.40691i 0.911263 + 0.411825i \(0.135109\pi\)
−0.0989804 + 0.995089i \(0.531558\pi\)
\(80\) −3.66105e7 + 6.34113e7i −0.0999312 + 0.173086i
\(81\) −4.53629e6 + 7.85709e6i −0.0117090 + 0.0202805i
\(82\) −3.36626e8 5.83053e8i −0.822214 1.42412i
\(83\) −2.10522e8 −0.486908 −0.243454 0.969912i \(-0.578280\pi\)
−0.243454 + 0.969912i \(0.578280\pi\)
\(84\) −1.13404e8 + 1.43954e9i −0.248527 + 3.15477i
\(85\) −7.43658e7 −0.154521
\(86\) −2.61468e8 4.52875e8i −0.515436 0.892762i
\(87\) −3.03188e7 + 5.25136e7i −0.0567381 + 0.0982733i
\(88\) 4.64081e8 8.03812e8i 0.824939 1.42884i
\(89\) 2.74145e8 + 4.74833e8i 0.463154 + 0.802206i 0.999116 0.0420359i \(-0.0133844\pi\)
−0.535962 + 0.844242i \(0.680051\pi\)
\(90\) 4.05633e8 0.651691
\(91\) −5.69235e8 3.91288e8i −0.870172 0.598150i
\(92\) −1.44282e9 −2.09974
\(93\) 1.83768e7 + 3.18295e7i 0.0254740 + 0.0441222i
\(94\) −3.73138e7 + 6.46295e7i −0.0492941 + 0.0853798i
\(95\) 9.25794e6 1.60352e7i 0.0116616 0.0201985i
\(96\) −1.08781e8 1.88414e8i −0.130717 0.226409i
\(97\) 9.75955e8 1.11933 0.559663 0.828720i \(-0.310930\pi\)
0.559663 + 0.828720i \(0.310930\pi\)
\(98\) 9.87467e8 1.21904e9i 1.08145 1.33506i
\(99\) −1.57013e9 −1.64277
\(100\) 9.23009e8 + 1.59870e9i 0.923009 + 1.59870i
\(101\) 2.80564e8 4.85951e8i 0.268278 0.464671i −0.700139 0.714006i \(-0.746879\pi\)
0.968417 + 0.249335i \(0.0802120\pi\)
\(102\) −1.01006e9 + 1.74948e9i −0.923947 + 1.60032i
\(103\) 4.12968e8 + 7.15282e8i 0.361534 + 0.626196i 0.988214 0.153082i \(-0.0489197\pi\)
−0.626679 + 0.779277i \(0.715586\pi\)
\(104\) −2.06032e9 −1.72697
\(105\) −3.87603e8 2.66435e8i −0.311197 0.213914i
\(106\) 3.90864e9 3.00711
\(107\) −8.35982e8 1.44796e9i −0.616552 1.06790i −0.990110 0.140293i \(-0.955196\pi\)
0.373558 0.927607i \(-0.378138\pi\)
\(108\) 1.40593e9 2.43515e9i 0.994393 1.72234i
\(109\) −9.48881e8 + 1.64351e9i −0.643862 + 1.11520i 0.340701 + 0.940172i \(0.389335\pi\)
−0.984563 + 0.175030i \(0.943998\pi\)
\(110\) 3.09958e8 + 5.36864e8i 0.201853 + 0.349620i
\(111\) 1.38517e9 0.866062
\(112\) 1.12217e8 1.42448e9i 0.0673874 0.855410i
\(113\) −2.80607e8 −0.161900 −0.0809499 0.996718i \(-0.525795\pi\)
−0.0809499 + 0.996718i \(0.525795\pi\)
\(114\) −2.51489e8 4.35592e8i −0.139459 0.241551i
\(115\) 2.34979e8 4.06995e8i 0.125282 0.216995i
\(116\) 1.33213e8 2.30732e8i 0.0683102 0.118317i
\(117\) 1.74268e9 + 3.01841e9i 0.859767 + 1.48916i
\(118\) −6.09289e9 −2.89304
\(119\) 1.30991e9 6.24671e8i 0.598796 0.285555i
\(120\) −1.40291e9 −0.617610
\(121\) −2.08191e7 3.60597e7i −0.00882931 0.0152928i
\(122\) −1.45372e9 + 2.51792e9i −0.594104 + 1.02902i
\(123\) 1.96950e9 3.41128e9i 0.775860 1.34383i
\(124\) −8.07429e7 1.39851e8i −0.0306695 0.0531212i
\(125\) −1.23707e9 −0.453210
\(126\) −7.14496e9 + 3.40731e9i −2.52541 + 1.20433i
\(127\) 4.35007e8 0.148381 0.0741907 0.997244i \(-0.476363\pi\)
0.0741907 + 0.997244i \(0.476363\pi\)
\(128\) 2.71660e9 + 4.70529e9i 0.894501 + 1.54932i
\(129\) 1.52977e9 2.64965e9i 0.486378 0.842431i
\(130\) 6.88041e8 1.19172e9i 0.211285 0.365957i
\(131\) −1.56383e9 2.70863e9i −0.463946 0.803578i 0.535207 0.844721i \(-0.320234\pi\)
−0.999153 + 0.0411427i \(0.986900\pi\)
\(132\) 1.11351e10 3.19237
\(133\) −2.83771e7 + 3.60217e8i −0.00786386 + 0.0998232i
\(134\) 4.74369e9 1.27100
\(135\) 4.57944e8 + 7.93182e8i 0.118662 + 0.205528i
\(136\) 2.16432e9 3.74870e9i 0.542495 0.939628i
\(137\) −7.30483e8 + 1.26523e9i −0.177161 + 0.306852i −0.940907 0.338665i \(-0.890025\pi\)
0.763746 + 0.645517i \(0.223358\pi\)
\(138\) −6.38313e9 1.10559e10i −1.49823 2.59501i
\(139\) −8.51599e9 −1.93494 −0.967472 0.252977i \(-0.918590\pi\)
−0.967472 + 0.252977i \(0.918590\pi\)
\(140\) 1.70303e9 + 1.17065e9i 0.374667 + 0.257543i
\(141\) −4.36625e8 −0.0930300
\(142\) 2.85765e9 + 4.94960e9i 0.589810 + 1.02158i
\(143\) −2.66328e9 + 4.61294e9i −0.532605 + 0.922499i
\(144\) −3.60492e9 + 6.24391e9i −0.698658 + 1.21011i
\(145\) 4.33904e7 + 7.51543e7i 0.00815150 + 0.0141188i
\(146\) 1.38533e10 2.52328
\(147\) 9.06542e9 + 1.43723e9i 1.60125 + 0.253862i
\(148\) −6.08608e9 −1.04270
\(149\) −2.90474e9 5.03116e9i −0.482802 0.836238i 0.517003 0.855984i \(-0.327048\pi\)
−0.999805 + 0.0197459i \(0.993714\pi\)
\(150\) −8.16692e9 + 1.41455e10i −1.31719 + 2.28143i
\(151\) −1.75822e8 + 3.04532e8i −0.0275218 + 0.0476691i −0.879458 0.475976i \(-0.842095\pi\)
0.851936 + 0.523645i \(0.175428\pi\)
\(152\) 5.38879e8 + 9.33367e8i 0.0818833 + 0.141826i
\(153\) −7.32256e9 −1.08032
\(154\) −9.96936e9 6.85287e9i −1.42832 0.981813i
\(155\) 5.25995e7 0.00731963
\(156\) −1.23588e10 2.14061e10i −1.67077 2.89385i
\(157\) 6.96496e9 1.20637e10i 0.914893 1.58464i 0.107835 0.994169i \(-0.465608\pi\)
0.807058 0.590472i \(-0.201058\pi\)
\(158\) 1.09324e10 1.89355e10i 1.39559 2.41724i
\(159\) 1.14342e10 + 1.98046e10i 1.41879 + 2.45741i
\(160\) −3.11362e8 −0.0375600
\(161\) −7.20249e8 + 9.14278e9i −0.0844824 + 1.07241i
\(162\) 3.52710e8 0.0402347
\(163\) 4.75825e9 + 8.24154e9i 0.527963 + 0.914459i 0.999469 + 0.0325955i \(0.0103773\pi\)
−0.471506 + 0.881863i \(0.656289\pi\)
\(164\) −8.65350e9 + 1.49883e10i −0.934102 + 1.61791i
\(165\) −1.81348e9 + 3.14104e9i −0.190474 + 0.329910i
\(166\) 4.09218e9 + 7.08787e9i 0.418282 + 0.724485i
\(167\) −9.07455e9 −0.902819 −0.451410 0.892317i \(-0.649079\pi\)
−0.451410 + 0.892317i \(0.649079\pi\)
\(168\) 2.47114e10 1.17844e10i 2.39334 1.14134i
\(169\) 1.21934e9 0.114983
\(170\) 1.44554e9 + 2.50375e9i 0.132742 + 0.229917i
\(171\) 9.11599e8 1.57894e9i 0.0815307 0.141215i
\(172\) −6.72144e9 + 1.16419e10i −0.585577 + 1.01425i
\(173\) −2.09018e9 3.62029e9i −0.177409 0.307281i 0.763583 0.645709i \(-0.223438\pi\)
−0.940992 + 0.338428i \(0.890105\pi\)
\(174\) 2.35737e9 0.194965
\(175\) 1.05913e10 5.05081e9i 0.853648 0.407090i
\(176\) −1.10186e10 −0.865603
\(177\) −1.78239e10 3.08719e10i −1.36497 2.36420i
\(178\) 1.06578e10 1.84598e10i 0.795751 1.37828i
\(179\) −4.79987e9 + 8.31362e9i −0.349455 + 0.605273i −0.986153 0.165840i \(-0.946966\pi\)
0.636698 + 0.771113i \(0.280300\pi\)
\(180\) −5.21371e9 9.03042e9i −0.370187 0.641182i
\(181\) 2.16308e10 1.49803 0.749013 0.662555i \(-0.230528\pi\)
0.749013 + 0.662555i \(0.230528\pi\)
\(182\) −2.10896e9 + 2.67710e10i −0.142478 + 1.80860i
\(183\) −1.70106e10 −1.12122
\(184\) 1.36775e10 + 2.36901e10i 0.879682 + 1.52365i
\(185\) 9.91185e8 1.71678e9i 0.0622131 0.107756i
\(186\) 7.14425e8 1.23742e9i 0.0437672 0.0758069i
\(187\) −5.59542e9 9.69156e9i −0.334615 0.579571i
\(188\) 1.91842e9 0.112004
\(189\) −1.47291e10 1.01247e10i −0.839650 0.577169i
\(190\) −7.19832e8 −0.0400719
\(191\) 5.37522e9 + 9.31016e9i 0.292245 + 0.506182i 0.974340 0.225081i \(-0.0722645\pi\)
−0.682096 + 0.731263i \(0.738931\pi\)
\(192\) −1.73267e10 + 3.00107e10i −0.920153 + 1.59375i
\(193\) −3.45029e9 + 5.97607e9i −0.178998 + 0.310033i −0.941538 0.336908i \(-0.890619\pi\)
0.762540 + 0.646941i \(0.223952\pi\)
\(194\) −1.89708e10 3.28585e10i −0.961565 1.66548i
\(195\) 8.05107e9 0.398747
\(196\) −3.98312e10 6.31482e9i −1.92784 0.305639i
\(197\) −1.85840e9 −0.0879104 −0.0439552 0.999034i \(-0.513996\pi\)
−0.0439552 + 0.999034i \(0.513996\pi\)
\(198\) 3.05206e10 + 5.28632e10i 1.41124 + 2.44433i
\(199\) 1.20595e10 2.08876e10i 0.545117 0.944170i −0.453483 0.891265i \(-0.649819\pi\)
0.998600 0.0529051i \(-0.0168481\pi\)
\(200\) 1.74997e10 3.03104e10i 0.773385 1.33954i
\(201\) 1.38770e10 + 2.40356e10i 0.599671 + 1.03866i
\(202\) −2.18147e10 −0.921865
\(203\) −1.39559e9 9.59317e8i −0.0576800 0.0396488i
\(204\) 5.19305e10 2.09936
\(205\) −2.81863e9 4.88202e9i −0.111467 0.193066i
\(206\) 1.60548e10 2.78077e10i 0.621157 1.07588i
\(207\) 2.31376e10 4.00755e10i 0.875895 1.51709i
\(208\) 1.22295e10 + 2.11820e10i 0.453025 + 0.784662i
\(209\) 2.78634e9 0.101013
\(210\) −1.43603e9 + 1.82288e10i −0.0509538 + 0.646803i
\(211\) 2.87100e10 0.997152 0.498576 0.866846i \(-0.333856\pi\)
0.498576 + 0.866846i \(0.333856\pi\)
\(212\) −5.02388e10 8.70162e10i −1.70816 2.95862i
\(213\) −1.67193e10 + 2.89587e10i −0.556558 + 0.963987i
\(214\) −3.25000e10 + 5.62917e10i −1.05931 + 1.83477i
\(215\) −2.18932e9 3.79201e9i −0.0698773 0.121031i
\(216\) −5.33113e10 −1.66639
\(217\) −9.26507e8 + 4.41835e8i −0.0283648 + 0.0135267i
\(218\) 7.37783e10 2.21246
\(219\) 4.05258e10 + 7.01928e10i 1.19051 + 2.06203i
\(220\) 7.96796e9 1.38009e10i 0.229322 0.397197i
\(221\) −1.24206e10 + 2.15132e10i −0.350251 + 0.606652i
\(222\) −2.69252e10 4.66359e10i −0.743997 1.28864i
\(223\) −5.06323e10 −1.37106 −0.685529 0.728046i \(-0.740429\pi\)
−0.685529 + 0.728046i \(0.740429\pi\)
\(224\) 5.48444e9 2.61543e9i 0.145551 0.0694109i
\(225\) −5.92070e10 −1.54011
\(226\) 5.45452e9 + 9.44750e9i 0.139081 + 0.240896i
\(227\) −2.59640e10 + 4.49710e10i −0.649016 + 1.12413i 0.334342 + 0.942452i \(0.391486\pi\)
−0.983358 + 0.181677i \(0.941848\pi\)
\(228\) −6.46492e9 + 1.11976e10i −0.158437 + 0.274421i
\(229\) 2.63620e9 + 4.56603e9i 0.0633459 + 0.109718i 0.895959 0.444137i \(-0.146490\pi\)
−0.832613 + 0.553855i \(0.813156\pi\)
\(230\) −1.82703e10 −0.430497
\(231\) 5.55861e9 7.05606e10i 0.128444 1.63045i
\(232\) −5.05127e9 −0.114473
\(233\) −7.65006e9 1.32503e10i −0.170045 0.294526i 0.768391 0.639981i \(-0.221058\pi\)
−0.938435 + 0.345455i \(0.887725\pi\)
\(234\) 6.77492e10 1.17345e11i 1.47718 2.55855i
\(235\) −3.12436e8 + 5.41155e8i −0.00668276 + 0.0115749i
\(236\) 7.83137e10 + 1.35643e11i 1.64336 + 2.84639i
\(237\) 1.27925e11 2.63383
\(238\) −4.64937e10 3.19594e10i −0.939286 0.645658i
\(239\) −8.20275e10 −1.62618 −0.813091 0.582137i \(-0.802217\pi\)
−0.813091 + 0.582137i \(0.802217\pi\)
\(240\) 8.32726e9 + 1.44232e10i 0.162014 + 0.280616i
\(241\) 7.98596e9 1.38321e10i 0.152493 0.264126i −0.779650 0.626215i \(-0.784603\pi\)
0.932143 + 0.362089i \(0.117936\pi\)
\(242\) −8.09372e8 + 1.40187e9i −0.0151698 + 0.0262748i
\(243\) −2.66583e10 4.61736e10i −0.490461 0.849504i
\(244\) 7.47404e10 1.34990
\(245\) 8.26825e9 1.02073e10i 0.146611 0.180993i
\(246\) −1.53135e11 −2.66603
\(247\) −3.09254e9 5.35644e9i −0.0528663 0.0915671i
\(248\) −1.53084e9 + 2.65149e9i −0.0256978 + 0.0445099i
\(249\) −2.39422e10 + 4.14691e10i −0.394700 + 0.683641i
\(250\) 2.40465e10 + 4.16497e10i 0.389333 + 0.674345i
\(251\) −1.58583e10 −0.252188 −0.126094 0.992018i \(-0.540244\pi\)
−0.126094 + 0.992018i \(0.540244\pi\)
\(252\) 1.67692e11 + 1.15270e11i 2.61944 + 1.80059i
\(253\) 7.07210e10 1.08519
\(254\) −8.45577e9 1.46458e10i −0.127468 0.220781i
\(255\) −8.45745e9 + 1.46487e10i −0.125259 + 0.216955i
\(256\) 6.66096e10 1.15371e11i 0.969297 1.67887i
\(257\) −4.88567e9 8.46223e9i −0.0698594 0.121000i 0.828980 0.559278i \(-0.188922\pi\)
−0.898839 + 0.438278i \(0.855588\pi\)
\(258\) −1.18944e11 −1.67130
\(259\) −3.03815e9 + 3.85660e10i −0.0419527 + 0.532544i
\(260\) −3.53744e10 −0.480074
\(261\) 4.27251e9 + 7.40020e9i 0.0569903 + 0.0987101i
\(262\) −6.07960e10 + 1.05302e11i −0.797112 + 1.38064i
\(263\) −2.82460e10 + 4.89235e10i −0.364046 + 0.630545i −0.988623 0.150418i \(-0.951938\pi\)
0.624577 + 0.780963i \(0.285271\pi\)
\(264\) −1.05558e11 1.82831e11i −1.33743 2.31650i
\(265\) 3.27278e10 0.407671
\(266\) 1.26794e10 6.04658e9i 0.155285 0.0740529i
\(267\) 1.24711e11 1.50178
\(268\) −6.09720e10 1.05607e11i −0.721977 1.25050i
\(269\) 7.11469e10 1.23230e11i 0.828459 1.43493i −0.0707884 0.997491i \(-0.522551\pi\)
0.899247 0.437441i \(-0.144115\pi\)
\(270\) 1.78032e10 3.08361e10i 0.203874 0.353120i
\(271\) −4.21917e10 7.30781e10i −0.475187 0.823048i 0.524409 0.851467i \(-0.324286\pi\)
−0.999596 + 0.0284182i \(0.990953\pi\)
\(272\) −5.13869e10 −0.569236
\(273\) −1.41814e11 + 6.76288e10i −1.54521 + 0.736886i
\(274\) 5.67973e10 0.608765
\(275\) −4.52421e10 7.83617e10i −0.477030 0.826241i
\(276\) −1.64088e11 + 2.84209e11i −1.70211 + 2.94814i
\(277\) −1.79902e10 + 3.11599e10i −0.183601 + 0.318007i −0.943104 0.332497i \(-0.892109\pi\)
0.759503 + 0.650504i \(0.225442\pi\)
\(278\) 1.65536e11 + 2.86717e11i 1.66223 + 2.87906i
\(279\) 5.17930e9 0.0511744
\(280\) 3.07706e9 3.90599e10i 0.0299175 0.379770i
\(281\) 9.07665e10 0.868454 0.434227 0.900803i \(-0.357022\pi\)
0.434227 + 0.900803i \(0.357022\pi\)
\(282\) 8.48723e9 + 1.47003e10i 0.0799181 + 0.138422i
\(283\) −4.68952e10 + 8.12249e10i −0.434600 + 0.752749i −0.997263 0.0739374i \(-0.976444\pi\)
0.562663 + 0.826686i \(0.309777\pi\)
\(284\) 7.34605e10 1.27237e11i 0.670071 1.16060i
\(285\) −2.10577e9 3.64730e9i −0.0189064 0.0327468i
\(286\) 2.07078e11 1.83015
\(287\) 9.06573e10 + 6.23171e10i 0.788741 + 0.542174i
\(288\) −3.06588e10 −0.262597
\(289\) 3.31988e10 + 5.75020e10i 0.279951 + 0.484889i
\(290\) 1.68686e9 2.92174e9i 0.0140052 0.0242577i
\(291\) 1.10993e11 1.92246e11i 0.907355 1.57159i
\(292\) −1.78060e11 3.08409e11i −1.43332 2.48259i
\(293\) −3.44893e10 −0.273389 −0.136694 0.990613i \(-0.543648\pi\)
−0.136694 + 0.990613i \(0.543648\pi\)
\(294\) −1.27827e11 3.33152e11i −0.997839 2.60064i
\(295\) −5.10170e10 −0.392207
\(296\) 5.76942e10 + 9.99293e10i 0.436837 + 0.756624i
\(297\) −6.89131e10 + 1.19361e11i −0.513923 + 0.890141i
\(298\) −1.12926e11 + 1.95594e11i −0.829509 + 1.43675i
\(299\) −7.84928e10 1.35953e11i −0.567949 0.983717i
\(300\) 4.19887e11 2.99286
\(301\) 7.04163e10 + 4.84037e10i 0.494452 + 0.339883i
\(302\) 1.36707e10 0.0945711
\(303\) −6.38157e10 1.10532e11i −0.434947 0.753349i
\(304\) 6.39726e9 1.10804e10i 0.0429598 0.0744086i
\(305\) −1.21723e10 + 2.10830e10i −0.0805422 + 0.139503i
\(306\) 1.42338e11 + 2.46536e11i 0.928054 + 1.60744i
\(307\) −1.33028e11 −0.854715 −0.427357 0.904083i \(-0.640555\pi\)
−0.427357 + 0.904083i \(0.640555\pi\)
\(308\) −2.44231e10 + 3.10025e11i −0.154641 + 1.96299i
\(309\) 1.87864e11 1.17228
\(310\) −1.02244e9 1.77092e9i −0.00628798 0.0108911i
\(311\) 7.32335e10 1.26844e11i 0.443903 0.768863i −0.554072 0.832469i \(-0.686927\pi\)
0.997975 + 0.0636062i \(0.0202601\pi\)
\(312\) −2.34316e11 + 4.05846e11i −1.39993 + 2.42474i
\(313\) −5.94129e10 1.02906e11i −0.349889 0.606026i 0.636340 0.771409i \(-0.280448\pi\)
−0.986230 + 0.165382i \(0.947114\pi\)
\(314\) −5.41546e11 −3.14378
\(315\) −5.98262e10 + 2.85301e10i −0.342368 + 0.163270i
\(316\) −5.62070e11 −3.17101
\(317\) 1.03199e11 + 1.78746e11i 0.573997 + 0.994192i 0.996150 + 0.0876676i \(0.0279413\pi\)
−0.422153 + 0.906525i \(0.638725\pi\)
\(318\) 4.44520e11 7.69931e11i 2.43764 4.22211i
\(319\) −6.52955e9 + 1.13095e10i −0.0353041 + 0.0611485i
\(320\) 2.47969e10 + 4.29495e10i 0.132197 + 0.228973i
\(321\) −3.80297e11 −1.99917
\(322\) 3.21820e11 1.53470e11i 1.66825 0.795559i
\(323\) 1.29945e10 0.0664277
\(324\) −4.53349e9 7.85223e9i −0.0228549 0.0395859i
\(325\) −1.00428e11 + 1.73946e11i −0.499320 + 0.864848i
\(326\) 1.84984e11 3.20402e11i 0.907100 1.57114i
\(327\) 2.15828e11 + 3.73825e11i 1.04386 + 1.80802i
\(328\) 3.28130e11 1.56536
\(329\) 9.57668e8 1.21566e10i 0.00450644 0.0572044i
\(330\) 1.41003e11 0.654511
\(331\) 6.11454e10 + 1.05907e11i 0.279987 + 0.484952i 0.971381 0.237526i \(-0.0763365\pi\)
−0.691394 + 0.722478i \(0.743003\pi\)
\(332\) 1.05196e11 1.82205e11i 0.475202 0.823073i
\(333\) 9.75988e10 1.69046e11i 0.434956 0.753366i
\(334\) 1.76393e11 + 3.05522e11i 0.775573 + 1.34333i
\(335\) 3.97198e10 0.172308
\(336\) −2.67834e11 1.84107e11i −1.14641 0.788033i
\(337\) −2.77263e11 −1.17100 −0.585500 0.810672i \(-0.699102\pi\)
−0.585500 + 0.810672i \(0.699102\pi\)
\(338\) −2.37018e10 4.10528e10i −0.0987772 0.171087i
\(339\) −3.19128e10 + 5.52747e10i −0.131240 + 0.227315i
\(340\) 3.71599e10 6.43628e10i 0.150806 0.261204i
\(341\) 3.95769e9 + 6.85492e9i 0.0158506 + 0.0274541i
\(342\) −7.08795e10 −0.280158
\(343\) −5.98990e10 + 2.49248e11i −0.233666 + 0.972317i
\(344\) 2.54869e11 0.981304
\(345\) −5.34472e10 9.25732e10i −0.203114 0.351803i
\(346\) −8.12587e10 + 1.40744e11i −0.304809 + 0.527944i
\(347\) 7.73905e10 1.34044e11i 0.286553 0.496324i −0.686432 0.727194i \(-0.740824\pi\)
0.972985 + 0.230870i \(0.0741573\pi\)
\(348\) −3.03000e10 5.24811e10i −0.110748 0.191821i
\(349\) 3.43353e11 1.23887 0.619435 0.785048i \(-0.287362\pi\)
0.619435 + 0.785048i \(0.287362\pi\)
\(350\) −3.75928e11 2.58410e11i −1.33905 0.920455i
\(351\) 3.05945e11 1.07587
\(352\) −2.34275e10 4.05776e10i −0.0813361 0.140878i
\(353\) −1.39016e10 + 2.40782e10i −0.0476516 + 0.0825351i −0.888867 0.458164i \(-0.848507\pi\)
0.841216 + 0.540700i \(0.181840\pi\)
\(354\) −6.92931e11 + 1.20019e12i −2.34517 + 4.06196i
\(355\) 2.39277e10 + 4.14440e10i 0.0799601 + 0.138495i
\(356\) −5.47951e11 −1.80807
\(357\) 2.59235e10 3.29070e11i 0.0844669 1.07221i
\(358\) 3.73204e11 1.20081
\(359\) 3.20996e10 + 5.55982e10i 0.101994 + 0.176659i 0.912506 0.409063i \(-0.134144\pi\)
−0.810512 + 0.585722i \(0.800811\pi\)
\(360\) −9.88489e10 + 1.71211e11i −0.310178 + 0.537243i
\(361\) 1.59726e11 2.76654e11i 0.494987 0.857342i
\(362\) −4.20465e11 7.28267e11i −1.28689 2.22896i
\(363\) −9.47081e9 −0.0286291
\(364\) 6.23097e11 2.97144e11i 1.86037 0.887178i
\(365\) 1.15996e11 0.342079
\(366\) 3.30657e11 + 5.72715e11i 0.963192 + 1.66830i
\(367\) 7.61178e10 1.31840e11i 0.219023 0.379358i −0.735487 0.677539i \(-0.763046\pi\)
0.954509 + 0.298181i \(0.0963798\pi\)
\(368\) 1.62371e11 2.81235e11i 0.461523 0.799381i
\(369\) −2.77542e11 4.80716e11i −0.779309 1.34980i
\(370\) −7.70675e10 −0.213778
\(371\) −5.76479e11 + 2.74913e11i −1.57980 + 0.753377i
\(372\) −3.67308e10 −0.0994460
\(373\) −1.88538e11 3.26557e11i −0.504322 0.873512i −0.999988 0.00499825i \(-0.998409\pi\)
0.495665 0.868514i \(-0.334924\pi\)
\(374\) −2.17530e11 + 3.76774e11i −0.574907 + 0.995769i
\(375\) −1.40689e11 + 2.43681e11i −0.367384 + 0.636327i
\(376\) −1.81861e10 3.14992e10i −0.0469238 0.0812744i
\(377\) 2.89884e10 0.0739075
\(378\) −5.45699e10 + 6.92705e11i −0.137480 + 1.74516i
\(379\) −9.07963e9 −0.0226043 −0.0113022 0.999936i \(-0.503598\pi\)
−0.0113022 + 0.999936i \(0.503598\pi\)
\(380\) 9.25221e9 + 1.60253e10i 0.0227625 + 0.0394257i
\(381\) 4.94723e10 8.56886e10i 0.120282 0.208334i
\(382\) 2.08970e11 3.61946e11i 0.502110 0.869679i
\(383\) 2.85906e11 + 4.95203e11i 0.678935 + 1.17595i 0.975302 + 0.220876i \(0.0708915\pi\)
−0.296367 + 0.955074i \(0.595775\pi\)
\(384\) 1.23581e12 2.90042
\(385\) −8.34754e10 5.73804e10i −0.193636 0.133104i
\(386\) 2.68270e11 0.615077
\(387\) −2.15575e11 3.73387e11i −0.488540 0.846175i
\(388\) −4.87675e11 + 8.44678e11i −1.09242 + 1.89212i
\(389\) 2.16995e11 3.75846e11i 0.480481 0.832218i −0.519268 0.854611i \(-0.673795\pi\)
0.999749 + 0.0223937i \(0.00712872\pi\)
\(390\) −1.56499e11 2.71064e11i −0.342547 0.593308i
\(391\) 3.29819e11 0.713641
\(392\) 2.73902e11 + 7.13863e11i 0.585880 + 1.52696i
\(393\) −7.11401e11 −1.50435
\(394\) 3.61239e10 + 6.25685e10i 0.0755200 + 0.130805i
\(395\) 9.15392e10 1.58551e11i 0.189200 0.327703i
\(396\) 7.84580e11 1.35893e12i 1.60328 2.77696i
\(397\) 7.92628e9 + 1.37287e10i 0.0160145 + 0.0277379i 0.873922 0.486067i \(-0.161569\pi\)
−0.857907 + 0.513805i \(0.828236\pi\)
\(398\) −9.37660e11 −1.87315
\(399\) 6.77290e10 + 4.65564e10i 0.133782 + 0.0919605i
\(400\) −4.15492e11 −0.811508
\(401\) 2.56105e11 + 4.43587e11i 0.494617 + 0.856702i 0.999981 0.00620472i \(-0.00197503\pi\)
−0.505364 + 0.862906i \(0.668642\pi\)
\(402\) 5.39488e11 9.34421e11i 1.03030 1.78454i
\(403\) 8.78522e9 1.52164e10i 0.0165913 0.0287369i
\(404\) 2.80390e11 + 4.85650e11i 0.523656 + 0.907000i
\(405\) 2.95331e9 0.00545459
\(406\) −5.17052e9 + 6.56342e10i −0.00944424 + 0.119884i
\(407\) 2.98315e11 0.538889
\(408\) −4.92285e11 8.52663e11i −0.879521 1.52337i
\(409\) −1.88162e11 + 3.25907e11i −0.332489 + 0.575888i −0.982999 0.183609i \(-0.941222\pi\)
0.650510 + 0.759498i \(0.274555\pi\)
\(410\) −1.09579e11 + 1.89796e11i −0.191513 + 0.331710i
\(411\) 1.66152e11 + 2.87784e11i 0.287222 + 0.497484i
\(412\) −8.25426e11 −1.41137
\(413\) 8.98632e11 4.28542e11i 1.51987 0.724800i
\(414\) −1.79902e12 −3.00977
\(415\) 3.42646e10 + 5.93481e10i 0.0567061 + 0.0982179i
\(416\) −5.20040e10 + 9.00735e10i −0.0851367 + 0.147461i
\(417\) −9.68504e11 + 1.67750e12i −1.56852 + 2.71675i
\(418\) −5.41616e10 9.38106e10i −0.0867756 0.150300i
\(419\) 6.65013e11 1.05406 0.527032 0.849845i \(-0.323305\pi\)
0.527032 + 0.849845i \(0.323305\pi\)
\(420\) 4.24278e11 2.02331e11i 0.665317 0.317278i
\(421\) −3.07333e11 −0.476804 −0.238402 0.971167i \(-0.576624\pi\)
−0.238402 + 0.971167i \(0.576624\pi\)
\(422\) −5.58071e11 9.66607e11i −0.856611 1.48369i
\(423\) −3.07646e10 + 5.32858e10i −0.0467218 + 0.0809245i
\(424\) −9.52498e11 + 1.64977e12i −1.43126 + 2.47901i
\(425\) −2.10994e11 3.65452e11i −0.313704 0.543351i
\(426\) 1.29998e12 1.91246
\(427\) 3.73101e10 4.73611e11i 0.0543127 0.689440i
\(428\) 1.67093e12 2.40692
\(429\) 6.05778e11 + 1.04924e12i 0.863487 + 1.49560i
\(430\) −8.51131e10 + 1.47420e11i −0.120057 + 0.207945i
\(431\) −2.46108e11 + 4.26272e11i −0.343541 + 0.595030i −0.985088 0.172054i \(-0.944960\pi\)
0.641547 + 0.767084i \(0.278293\pi\)
\(432\) 3.16440e11 + 5.48091e11i 0.437134 + 0.757139i
\(433\) −9.89860e10 −0.135325 −0.0676626 0.997708i \(-0.521554\pi\)
−0.0676626 + 0.997708i \(0.521554\pi\)
\(434\) 3.28854e10 + 2.26052e10i 0.0444937 + 0.0305847i
\(435\) 1.97387e10 0.0264313
\(436\) −9.48294e11 1.64249e12i −1.25676 2.17678i
\(437\) −4.10598e10 + 7.11176e10i −0.0538580 + 0.0932847i
\(438\) 1.57550e12 2.72885e12i 2.04543 3.54279i
\(439\) −5.90283e11 1.02240e12i −0.758525 1.31380i −0.943603 0.331079i \(-0.892587\pi\)
0.185078 0.982724i \(-0.440746\pi\)
\(440\) −3.02136e11 −0.384295
\(441\) 8.14148e11 1.00508e12i 1.02501 1.26539i
\(442\) 9.65742e11 1.20354
\(443\) −2.23839e11 3.87700e11i −0.276133 0.478277i 0.694287 0.719698i \(-0.255720\pi\)
−0.970420 + 0.241421i \(0.922386\pi\)
\(444\) −6.92155e11 + 1.19885e12i −0.845240 + 1.46400i
\(445\) 8.92398e10 1.54568e11i 0.107879 0.186853i
\(446\) 9.84203e11 + 1.70469e12i 1.17782 + 2.04004i
\(447\) −1.32140e12 −1.56549
\(448\) −7.97557e11 5.48235e11i −0.935429 0.643007i
\(449\) −1.56446e12 −1.81659 −0.908295 0.418330i \(-0.862616\pi\)
−0.908295 + 0.418330i \(0.862616\pi\)
\(450\) 1.15088e12 + 1.99338e12i 1.32304 + 2.29158i
\(451\) 4.24159e11 7.34665e11i 0.482763 0.836170i
\(452\) 1.40217e11 2.42863e11i 0.158007 0.273677i
\(453\) 3.99916e10 + 6.92675e10i 0.0446197 + 0.0772836i
\(454\) 2.01878e12 2.23017
\(455\) −1.76587e10 + 2.24158e11i −0.0193156 + 0.245191i
\(456\) 2.45142e11 0.265507
\(457\) 6.14225e11 + 1.06387e12i 0.658726 + 1.14095i 0.980946 + 0.194281i \(0.0622375\pi\)
−0.322220 + 0.946665i \(0.604429\pi\)
\(458\) 1.02486e11 1.77511e11i 0.108835 0.188509i
\(459\) −3.21387e11 + 5.56659e11i −0.337965 + 0.585372i
\(460\) 2.34833e11 + 4.06743e11i 0.244540 + 0.423555i
\(461\) −2.37095e11 −0.244494 −0.122247 0.992500i \(-0.539010\pi\)
−0.122247 + 0.992500i \(0.539010\pi\)
\(462\) −2.48368e12 + 1.18443e12i −2.53634 + 1.20954i
\(463\) 2.03876e11 0.206183 0.103091 0.994672i \(-0.467127\pi\)
0.103091 + 0.994672i \(0.467127\pi\)
\(464\) 2.99829e10 + 5.19318e10i 0.0300291 + 0.0520119i
\(465\) 5.98202e9 1.03612e10i 0.00593348 0.0102771i
\(466\) −2.97407e11 + 5.15125e11i −0.292156 + 0.506029i
\(467\) 7.59001e11 + 1.31463e12i 0.738442 + 1.27902i 0.953197 + 0.302351i \(0.0977715\pi\)
−0.214755 + 0.976668i \(0.568895\pi\)
\(468\) −3.48320e12 −3.35639
\(469\) −6.99639e11 + 3.33646e11i −0.667723 + 0.318425i
\(470\) 2.42928e10 0.0229635
\(471\) −1.58422e12 2.74395e12i −1.48327 2.56910i
\(472\) 1.48478e12 2.57172e12i 1.37697 2.38498i
\(473\) 3.29457e11 5.70637e11i 0.302638 0.524185i
\(474\) −2.48664e12 4.30698e12i −2.26261 3.91895i
\(475\) 1.05068e11 0.0946999
\(476\) −1.13901e11 + 1.44585e12i −0.101694 + 1.29090i
\(477\) 3.22260e12 2.85019
\(478\) 1.59447e12 + 2.76170e12i 1.39698 + 2.41965i
\(479\) 2.29691e11 3.97836e11i 0.199358 0.345298i −0.748962 0.662612i \(-0.769448\pi\)
0.948320 + 0.317314i \(0.102781\pi\)
\(480\) −3.54105e10 + 6.13327e10i −0.0304471 + 0.0527359i
\(481\) −3.31097e11 5.73477e11i −0.282035 0.488499i
\(482\) −6.20932e11 −0.524001
\(483\) 1.71905e12 + 1.18166e12i 1.43723 + 0.987942i
\(484\) 4.16123e10 0.0344681
\(485\) −1.58847e11 2.75130e11i −0.130359 0.225788i
\(486\) −1.03638e12 + 1.79507e12i −0.842669 + 1.45954i
\(487\) 5.62467e11 9.74222e11i 0.453124 0.784833i −0.545454 0.838140i \(-0.683643\pi\)
0.998578 + 0.0533072i \(0.0169763\pi\)
\(488\) −7.08517e11 1.22719e12i −0.565537 0.979538i
\(489\) 2.16458e12 1.71192
\(490\) −5.04379e11 7.99641e10i −0.395253 0.0626632i
\(491\) −2.10238e12 −1.63247 −0.816233 0.577723i \(-0.803942\pi\)
−0.816233 + 0.577723i \(0.803942\pi\)
\(492\) 1.96828e12 + 3.40917e12i 1.51441 + 2.62304i
\(493\) −3.04516e10 + 5.27437e10i −0.0232166 + 0.0402124i
\(494\) −1.20227e11 + 2.08239e11i −0.0908303 + 0.157323i
\(495\) 2.55555e11 + 4.42634e11i 0.191320 + 0.331376i
\(496\) 3.63464e10 0.0269646
\(497\) −7.69600e11 5.29017e11i −0.565798 0.388925i
\(498\) 1.86158e12 1.35628
\(499\) 1.92891e11 + 3.34096e11i 0.139270 + 0.241223i 0.927221 0.374516i \(-0.122191\pi\)
−0.787950 + 0.615739i \(0.788858\pi\)
\(500\) 6.18152e11 1.07067e12i 0.442314 0.766110i
\(501\) −1.03203e12 + 1.78752e12i −0.731849 + 1.26760i
\(502\) 3.08257e11 + 5.33916e11i 0.216644 + 0.375238i
\(503\) 4.76511e11 0.331907 0.165954 0.986134i \(-0.446930\pi\)
0.165954 + 0.986134i \(0.446930\pi\)
\(504\) 3.02988e11 3.84611e12i 0.209165 2.65512i
\(505\) −1.82658e11 −0.124977
\(506\) −1.37469e12 2.38104e12i −0.932241 1.61469i
\(507\) 1.38673e11 2.40188e11i 0.0932084 0.161442i
\(508\) −2.17369e11 + 3.76494e11i −0.144814 + 0.250825i
\(509\) 5.49065e11 + 9.51009e11i 0.362572 + 0.627993i 0.988383 0.151982i \(-0.0485655\pi\)
−0.625812 + 0.779974i \(0.715232\pi\)
\(510\) 6.57592e11 0.430418
\(511\) −2.04320e12 + 9.74366e11i −1.32561 + 0.632162i
\(512\) −2.39730e12 −1.54172
\(513\) −8.00202e10 1.38599e11i −0.0510119 0.0883552i
\(514\) −1.89938e11 + 3.28982e11i −0.120026 + 0.207892i
\(515\) 1.34430e11 2.32839e11i 0.0842098 0.145856i
\(516\) 1.52883e12 + 2.64801e12i 0.949368 + 1.64435i
\(517\) −9.40332e10 −0.0578860
\(518\) 1.35750e12 6.47366e11i 0.828428 0.395063i
\(519\) −9.50844e11 −0.575249
\(520\) 3.35338e11 + 5.80823e11i 0.201126 + 0.348360i
\(521\) 1.12572e12 1.94980e12i 0.669361 1.15937i −0.308722 0.951152i \(-0.599901\pi\)
0.978083 0.208215i \(-0.0667655\pi\)
\(522\) 1.66100e11 2.87694e11i 0.0979158 0.169595i
\(523\) 6.56384e11 + 1.13689e12i 0.383619 + 0.664448i 0.991577 0.129522i \(-0.0413442\pi\)
−0.607957 + 0.793970i \(0.708011\pi\)
\(524\) 3.12572e12 1.81117
\(525\) 2.09606e11 2.66072e12i 0.120417 1.52856i
\(526\) 2.19621e12 1.25094
\(527\) 1.84573e10 + 3.19690e10i 0.0104237 + 0.0180543i
\(528\) −1.25312e12 + 2.17047e12i −0.701681 + 1.21535i
\(529\) −1.41575e11 + 2.45216e11i −0.0786027 + 0.136144i
\(530\) −6.36170e11 1.10188e12i −0.350213 0.606586i
\(531\) −5.02348e12 −2.74207
\(532\) −2.97584e11 2.04557e11i −0.161067 0.110716i
\(533\) −1.88308e12 −1.01064
\(534\) −2.42417e12 4.19879e12i −1.29011 2.23454i
\(535\) −2.72129e11 + 4.71341e11i −0.143609 + 0.248739i
\(536\) −1.15599e12 + 2.00224e12i −0.604941 + 1.04779i
\(537\) 1.09176e12 + 1.89098e12i 0.566554 + 0.981300i
\(538\) −5.53188e12 −2.84677
\(539\) 1.95236e12 + 3.09527e11i 0.996347 + 0.157961i
\(540\) −9.15320e11 −0.463235
\(541\) −6.81130e10 1.17975e11i −0.0341855 0.0592111i 0.848426 0.529313i \(-0.177550\pi\)
−0.882612 + 0.470102i \(0.844217\pi\)
\(542\) −1.64026e12 + 2.84102e12i −0.816426 + 1.41409i
\(543\) 2.46002e12 4.26089e12i 1.21434 2.10330i
\(544\) −1.09258e11 1.89240e11i −0.0534881 0.0926441i
\(545\) 6.17760e11 0.299941
\(546\) 5.03355e12 + 3.46003e12i 2.42386 + 1.66614i
\(547\) 2.23412e12 1.06700 0.533499 0.845801i \(-0.320877\pi\)
0.533499 + 0.845801i \(0.320877\pi\)
\(548\) −7.30031e11 1.26445e12i −0.345803 0.598949i
\(549\) −1.19857e12 + 2.07598e12i −0.563102 + 0.975321i
\(550\) −1.75885e12 + 3.04643e12i −0.819592 + 1.41958i
\(551\) −7.58195e9 1.31323e10i −0.00350428 0.00606959i
\(552\) 6.22203e12 2.85237
\(553\) −2.80583e11 + 3.56170e12i −0.127585 + 1.61955i
\(554\) 1.39879e12 0.630897
\(555\) −2.25450e11 3.90491e11i −0.100863 0.174700i
\(556\) 4.25536e12 7.37050e12i 1.88842 3.27085i
\(557\) −1.35142e11 + 2.34072e11i −0.0594895 + 0.103039i −0.894236 0.447595i \(-0.852281\pi\)
0.834747 + 0.550634i \(0.185614\pi\)
\(558\) −1.00677e11 1.74377e11i −0.0439617 0.0761439i
\(559\) −1.46265e12 −0.633559
\(560\) −4.19837e11 + 2.00213e11i −0.180399 + 0.0860293i
\(561\) −2.54542e12 −1.08499
\(562\) −1.76434e12 3.05593e12i −0.746052 1.29220i
\(563\) −2.97806e11 + 5.15814e11i −0.124924 + 0.216374i −0.921703 0.387896i \(-0.873202\pi\)
0.796779 + 0.604270i \(0.206535\pi\)
\(564\) 2.18178e11 3.77895e11i 0.0907934 0.157259i
\(565\) 4.56717e10 + 7.91057e10i 0.0188551 + 0.0326580i
\(566\) 3.64624e12 1.49338
\(567\) −5.20207e10 + 2.48078e10i −0.0211374 + 0.0100801i
\(568\) −2.78553e12 −1.12290
\(569\) 7.88961e11 + 1.36652e12i 0.315537 + 0.546526i 0.979551 0.201194i \(-0.0644820\pi\)
−0.664015 + 0.747720i \(0.731149\pi\)
\(570\) −8.18648e10 + 1.41794e11i −0.0324833 + 0.0562628i
\(571\) 1.58417e12 2.74386e12i 0.623647 1.08019i −0.365154 0.930947i \(-0.618984\pi\)
0.988801 0.149241i \(-0.0476830\pi\)
\(572\) −2.66164e12 4.61009e12i −1.03960 1.80064i
\(573\) 2.44525e12 0.947604
\(574\) 3.35877e11 4.26359e12i 0.129145 1.63935i
\(575\) 2.66677e12 1.01737
\(576\) 2.44167e12 + 4.22910e12i 0.924243 + 1.60084i
\(577\) −9.47694e11 + 1.64145e12i −0.355940 + 0.616506i −0.987278 0.159001i \(-0.949173\pi\)
0.631338 + 0.775508i \(0.282506\pi\)
\(578\) 1.29065e12 2.23548e12i 0.480988 0.833095i
\(579\) 7.84787e11 + 1.35929e12i 0.290200 + 0.502642i
\(580\) −8.67270e10 −0.0318221
\(581\) −1.10207e12 7.57557e11i −0.401253 0.275818i
\(582\) −8.63004e12 −3.11788
\(583\) 2.46250e12 + 4.26518e12i 0.882811 + 1.52907i
\(584\) −3.37591e12 + 5.84725e12i −1.20097 + 2.08015i
\(585\) 5.67277e11 9.82553e11i 0.200260 0.346860i
\(586\) 6.70412e11 + 1.16119e12i 0.234856 + 0.406783i
\(587\) −4.26822e12 −1.48380 −0.741901 0.670510i \(-0.766075\pi\)
−0.741901 + 0.670510i \(0.766075\pi\)
\(588\) −5.77381e12 + 7.12786e12i −1.99189 + 2.45901i
\(589\) −9.19114e9 −0.00314667
\(590\) 9.91681e11 + 1.71764e12i 0.336929 + 0.583577i
\(591\) −2.11351e11 + 3.66071e11i −0.0712624 + 0.123430i
\(592\) 6.84911e11 1.18630e12i 0.229185 0.396960i
\(593\) −2.31308e12 4.00638e12i −0.768149 1.33047i −0.938566 0.345101i \(-0.887845\pi\)
0.170417 0.985372i \(-0.445489\pi\)
\(594\) 5.35820e12 1.76596
\(595\) −3.89301e11 2.67602e11i −0.127338 0.0875314i
\(596\) 5.80589e12 1.88478
\(597\) −2.74299e12 4.75100e12i −0.883772 1.53074i
\(598\) −3.05152e12 + 5.28539e12i −0.975801 + 1.69014i
\(599\) −3.92667e11 + 6.80119e11i −0.124625 + 0.215856i −0.921586 0.388174i \(-0.873106\pi\)
0.796962 + 0.604030i \(0.206439\pi\)
\(600\) −3.98040e12 6.89425e12i −1.25385 2.17173i
\(601\) 3.87598e12 1.21184 0.605921 0.795525i \(-0.292805\pi\)
0.605921 + 0.795525i \(0.292805\pi\)
\(602\) 2.60886e11 3.31166e12i 0.0809592 1.02769i
\(603\) 3.91108e12 1.20467
\(604\) −1.75713e11 3.04344e11i −0.0537202 0.0930461i
\(605\) −6.77702e9 + 1.17382e10i −0.00205655 + 0.00356205i
\(606\) −2.48093e12 + 4.29710e12i −0.747288 + 1.29434i
\(607\) −8.59263e11 1.48829e12i −0.256908 0.444977i 0.708504 0.705706i \(-0.249370\pi\)
−0.965412 + 0.260730i \(0.916037\pi\)
\(608\) 5.44068e10 0.0161468
\(609\) −3.47685e11 + 1.65805e11i −0.102426 + 0.0488450i
\(610\) 9.46432e11 0.276761
\(611\) 1.04367e11 + 1.80769e11i 0.0302954 + 0.0524732i
\(612\) 3.65901e12 6.33760e12i 1.05434 1.82618i
\(613\) −1.81276e12 + 3.13979e12i −0.518524 + 0.898109i 0.481245 + 0.876586i \(0.340185\pi\)
−0.999768 + 0.0215229i \(0.993149\pi\)
\(614\) 2.58584e12 + 4.47880e12i 0.734249 + 1.27176i
\(615\) −1.28223e12 −0.361432
\(616\) 5.32193e12 2.53793e12i 1.48921 0.710178i
\(617\) 1.30186e12 0.361644 0.180822 0.983516i \(-0.442124\pi\)
0.180822 + 0.983516i \(0.442124\pi\)
\(618\) −3.65174e12 6.32500e12i −1.00705 1.74427i
\(619\) 1.53034e12 2.65063e12i 0.418968 0.725674i −0.576868 0.816838i \(-0.695725\pi\)
0.995836 + 0.0911632i \(0.0290585\pi\)
\(620\) −2.62835e10 + 4.55243e10i −0.00714365 + 0.0123732i
\(621\) −2.03102e12 3.51783e12i −0.548027 0.949211i
\(622\) −5.69412e12 −1.52535
\(623\) −2.73535e11 + 3.47223e12i −0.0727472 + 0.923447i
\(624\) 5.56331e12 1.46894
\(625\) −1.60252e12 2.77565e12i −0.420092 0.727620i
\(626\) −2.30976e12 + 4.00063e12i −0.601150 + 1.04122i
\(627\) 3.16884e11 5.48859e11i 0.0818835 0.141826i
\(628\) 6.96065e12 + 1.20562e13i 1.78579 + 3.09309i
\(629\) 1.39124e12 0.354383
\(630\) 2.12347e12 + 1.45965e12i 0.537048 + 0.369163i
\(631\) 3.26960e12 0.821036 0.410518 0.911852i \(-0.365348\pi\)
0.410518 + 0.911852i \(0.365348\pi\)
\(632\) 5.32825e12 + 9.22880e12i 1.32849 + 2.30101i
\(633\) 3.26512e12 5.65535e12i 0.808318 1.40005i
\(634\) 4.01202e12 6.94903e12i 0.986193 1.70814i
\(635\) −7.08018e10 1.22632e11i −0.0172807 0.0299311i
\(636\) −2.28542e13 −5.53871
\(637\) −1.57188e12 4.09674e12i −0.378261 0.985851i
\(638\) 5.07692e11 0.121313
\(639\) 2.35608e12 + 4.08085e12i 0.559032 + 0.968272i
\(640\) 8.84308e11 1.53167e12i 0.208350 0.360873i
\(641\) −2.32593e12 + 4.02863e12i −0.544171 + 0.942533i 0.454487 + 0.890753i \(0.349823\pi\)
−0.998659 + 0.0517792i \(0.983511\pi\)
\(642\) 7.39231e12 + 1.28039e13i 1.71740 + 2.97463i
\(643\) 1.76017e12 0.406074 0.203037 0.979171i \(-0.434919\pi\)
0.203037 + 0.979171i \(0.434919\pi\)
\(644\) −7.55308e12 5.19193e12i −1.73036 1.18944i
\(645\) −9.95945e11 −0.226577
\(646\) −2.52591e11 4.37500e11i −0.0570652 0.0988399i
\(647\) −2.61427e12 + 4.52805e12i −0.586518 + 1.01588i 0.408166 + 0.912908i \(0.366168\pi\)
−0.994684 + 0.102972i \(0.967165\pi\)
\(648\) −8.59522e10 + 1.48874e11i −0.0191500 + 0.0331688i
\(649\) −3.83862e12 6.64868e12i −0.849325 1.47107i
\(650\) 7.80856e12 1.71578
\(651\) −1.83359e10 + 2.32754e11i −0.00400117 + 0.0507905i
\(652\) −9.51062e12 −2.06108
\(653\) −2.56788e12 4.44770e12i −0.552670 0.957252i −0.998081 0.0619256i \(-0.980276\pi\)
0.445411 0.895326i \(-0.353057\pi\)
\(654\) 8.39064e12 1.45330e13i 1.79347 3.10639i
\(655\) −5.09057e11 + 8.81713e11i −0.108064 + 0.187172i
\(656\) −1.94768e12 3.37349e12i −0.410630 0.711233i
\(657\) 1.14218e13 2.39160
\(658\) −4.27903e11 + 2.04059e11i −0.0889874 + 0.0424365i
\(659\) −6.45467e12 −1.33318 −0.666592 0.745423i \(-0.732248\pi\)
−0.666592 + 0.745423i \(0.732248\pi\)
\(660\) −1.81236e12 3.13909e12i −0.371788 0.643956i
\(661\) −3.39730e12 + 5.88430e12i −0.692194 + 1.19891i 0.278924 + 0.960313i \(0.410022\pi\)
−0.971118 + 0.238602i \(0.923311\pi\)
\(662\) 2.37712e12 4.11729e12i 0.481050 0.833203i
\(663\) 2.82514e12 + 4.89329e12i 0.567845 + 0.983536i
\(664\) −3.98891e12 −0.796338
\(665\) 1.06167e11 5.06292e10i 0.0210519 0.0100393i
\(666\) −7.58859e12 −1.49461
\(667\) −1.92440e11 3.33316e11i −0.0376469 0.0652064i
\(668\) 4.53447e12 7.85392e12i 0.881114 1.52613i
\(669\) −5.75829e12 + 9.97366e12i −1.11141 + 1.92503i
\(670\) −7.72083e11 1.33729e12i −0.148022 0.256382i
\(671\) −3.66347e12 −0.697656
\(672\) 1.08539e11 1.37778e12i 0.0205317 0.260627i
\(673\) 3.04579e12 0.572312 0.286156 0.958183i \(-0.407622\pi\)
0.286156 + 0.958183i \(0.407622\pi\)
\(674\) 5.38950e12 + 9.33489e12i 1.00596 + 1.74237i
\(675\) −2.59860e12 + 4.50090e12i −0.481806 + 0.834512i
\(676\) −6.09292e11 + 1.05533e12i −0.112219 + 0.194369i
\(677\) 4.09392e11 + 7.09087e11i 0.0749014 + 0.129733i 0.901043 0.433729i \(-0.142802\pi\)
−0.826142 + 0.563462i \(0.809469\pi\)
\(678\) 2.48132e12 0.450971
\(679\) 5.10907e12 + 3.51194e12i 0.922418 + 0.634063i
\(680\) −1.40906e12 −0.252719
\(681\) 5.90565e12 + 1.02289e13i 1.05222 + 1.82250i
\(682\) 1.53861e11 2.66495e11i 0.0272332 0.0471693i
\(683\) −1.05996e12 + 1.83591e12i −0.186379 + 0.322818i −0.944040 0.329830i \(-0.893009\pi\)
0.757661 + 0.652648i \(0.226342\pi\)
\(684\) 9.11035e11 + 1.57796e12i 0.159141 + 0.275641i
\(685\) 4.75574e11 0.0825298
\(686\) 9.55601e12 2.82826e12i 1.64747 0.487596i
\(687\) 1.19923e12 0.205399
\(688\) −1.51283e12 2.62029e12i −0.257419 0.445863i
\(689\) 5.46623e12 9.46778e12i 0.924062 1.60052i
\(690\) −2.07784e12 + 3.59892e12i −0.348972 + 0.604438i
\(691\) −5.59380e12 9.68875e12i −0.933374 1.61665i −0.777508 0.628873i \(-0.783516\pi\)
−0.155867 0.987778i \(-0.549817\pi\)
\(692\) 4.17777e12 0.692575
\(693\) −8.21956e12 5.65006e12i −1.35378 0.930580i
\(694\) −6.01734e12 −0.984661
\(695\) 1.38606e12 + 2.40073e12i 0.225347 + 0.390312i
\(696\) −5.74470e11 + 9.95010e11i −0.0927952 + 0.160726i
\(697\) 1.97813e12 3.42623e12i 0.317474 0.549881i
\(698\) −6.67417e12 1.15600e13i −1.06426 1.84335i
\(699\) −3.48009e12 −0.551371
\(700\) −9.20955e11 + 1.16905e13i −0.144976 + 1.84032i
\(701\) 4.84669e12 0.758079 0.379040 0.925380i \(-0.376254\pi\)
0.379040 + 0.925380i \(0.376254\pi\)
\(702\) −5.94703e12 1.03006e13i −0.924237 1.60082i
\(703\) −1.73198e11 + 2.99987e11i −0.0267450 + 0.0463238i
\(704\) −3.73154e12 + 6.46321e12i −0.572546 + 0.991680i
\(705\) 7.10652e10 + 1.23089e11i 0.0108344 + 0.0187658i
\(706\) 1.08089e12 0.163742
\(707\) 3.21741e12 1.53433e12i 0.484305 0.230957i
\(708\) 3.56257e13 5.32861
\(709\) 1.96400e12 + 3.40175e12i 0.291900 + 0.505586i 0.974259 0.225432i \(-0.0723792\pi\)
−0.682359 + 0.731017i \(0.739046\pi\)
\(710\) 9.30224e11 1.61120e12i 0.137380 0.237950i
\(711\) 9.01357e12 1.56120e13i 1.32277 2.29110i
\(712\) 5.19441e12 + 8.99698e12i 0.757488 + 1.31201i
\(713\) −2.33283e11 −0.0338050
\(714\) −1.15831e13 + 5.52376e12i −1.66794 + 0.795413i
\(715\) 1.73391e12 0.248112
\(716\) −4.79690e12 8.30847e12i −0.682106 1.18144i
\(717\) −9.32880e12 + 1.61580e13i −1.31823 + 2.28323i
\(718\) 1.24792e12 2.16146e12i 0.175237 0.303520i
\(719\) 1.24484e12 + 2.15613e12i 0.173714 + 0.300881i 0.939715 0.341957i \(-0.111090\pi\)
−0.766001 + 0.642839i \(0.777757\pi\)
\(720\) 2.34695e12 0.325468
\(721\) −4.12049e11 + 5.23052e12i −0.0567859 + 0.720835i
\(722\) −1.24192e13 −1.70089
\(723\) −1.81645e12 3.14618e12i −0.247230 0.428215i
\(724\) −1.08087e13 + 1.87213e13i −1.46201 + 2.53228i
\(725\) −2.46218e11 + 4.26462e11i −0.0330978 + 0.0573271i
\(726\) 1.84096e11 + 3.18863e11i 0.0245940 + 0.0425981i
\(727\) −2.66741e12 −0.354148 −0.177074 0.984198i \(-0.556663\pi\)
−0.177074 + 0.984198i \(0.556663\pi\)
\(728\) −1.07857e13 7.41399e12i −1.42317 0.978275i
\(729\) −1.23057e13 −1.61374
\(730\) −2.25476e12 3.90536e12i −0.293865 0.508989i
\(731\) 1.53648e12 2.66126e12i 0.199020 0.344714i
\(732\) 8.50005e12 1.47225e13i 1.09426 1.89532i
\(733\) −4.42523e12 7.66472e12i −0.566197 0.980683i −0.996937 0.0782065i \(-0.975081\pi\)
0.430740 0.902476i \(-0.358253\pi\)
\(734\) −5.91839e12 −0.752612
\(735\) −1.07032e12 2.78955e12i −0.135276 0.352566i
\(736\) 1.38092e12 0.173467
\(737\) 2.98860e12 + 5.17640e12i 0.373133 + 0.646285i
\(738\) −1.07898e13 + 1.86886e13i −1.33894 + 2.31912i
\(739\) 7.45321e12 1.29093e13i 0.919271 1.59222i 0.118746 0.992925i \(-0.462112\pi\)
0.800525 0.599300i \(-0.204554\pi\)
\(740\) 9.90571e11 + 1.71572e12i 0.121435 + 0.210331i
\(741\) −1.40683e12 −0.171419
\(742\) 2.04615e13 + 1.40651e13i 2.47811 + 1.70343i
\(743\) −5.88465e12 −0.708388 −0.354194 0.935172i \(-0.615245\pi\)
−0.354194 + 0.935172i \(0.615245\pi\)
\(744\) 3.48197e11 + 6.03095e11i 0.0416627 + 0.0721618i
\(745\) −9.45552e11 + 1.63774e12i −0.112456 + 0.194779i
\(746\) −7.32968e12 + 1.26954e13i −0.866483 + 1.50079i
\(747\) 3.37393e12 + 5.84382e12i 0.396454 + 0.686679i
\(748\) 1.11839e13 1.30628
\(749\) 8.34121e11 1.05883e13i 0.0968414 1.22930i
\(750\) 1.09390e13 1.26241
\(751\) −7.67766e12 1.32981e13i −0.880743 1.52549i −0.850516 0.525949i \(-0.823710\pi\)
−0.0302266 0.999543i \(-0.509623\pi\)
\(752\) −2.15894e11 + 3.73939e11i −0.0246184 + 0.0426404i
\(753\) −1.80352e12 + 3.12379e12i −0.204430 + 0.354083i
\(754\) −5.63484e11 9.75982e11i −0.0634907 0.109969i
\(755\) 1.14467e11 0.0128209
\(756\) 1.61228e13 7.68868e12i 1.79511 0.856059i
\(757\) 1.53062e13 1.69408 0.847042 0.531526i \(-0.178381\pi\)
0.847042 + 0.531526i \(0.178381\pi\)
\(758\) 1.76492e11 + 3.05693e11i 0.0194184 + 0.0336337i
\(759\) 8.04294e12 1.39308e13i 0.879684 1.52366i
\(760\) 1.75416e11 3.03830e11i 0.0190725 0.0330346i
\(761\) 5.84166e12 + 1.01180e13i 0.631401 + 1.09362i 0.987266 + 0.159081i \(0.0508530\pi\)
−0.355865 + 0.934537i \(0.615814\pi\)
\(762\) −3.84662e12 −0.413316
\(763\) −1.08815e13 + 5.18918e12i −1.16232 + 0.554291i
\(764\) −1.07438e13 −1.14087
\(765\) 1.19182e12 + 2.06429e12i 0.125816 + 0.217919i
\(766\) 1.11150e13 1.92518e13i 1.16649 2.02042i
\(767\) −8.52091e12 + 1.47586e13i −0.889010 + 1.53981i
\(768\) −1.51507e13 2.62418e13i −1.57148 2.72187i
\(769\) 1.46342e13 1.50904 0.754518 0.656279i \(-0.227871\pi\)
0.754518 + 0.656279i \(0.227871\pi\)
\(770\) −3.09268e11 + 3.92583e12i −0.0317050 + 0.402460i
\(771\) −2.22254e12 −0.226519
\(772\) −3.44815e12 5.97238e12i −0.349389 0.605159i
\(773\) 4.39512e12 7.61257e12i 0.442754 0.766873i −0.555139 0.831758i \(-0.687335\pi\)
0.997893 + 0.0648851i \(0.0206681\pi\)
\(774\) −8.38081e12 + 1.45160e13i −0.839367 + 1.45383i
\(775\) 1.49238e11 + 2.58487e11i 0.0148601 + 0.0257384i
\(776\) 1.84921e13 1.83066
\(777\) 7.25128e12 + 4.98448e12i 0.713707 + 0.490597i
\(778\) −1.68720e13 −1.65104
\(779\) 4.92523e11 + 8.53075e11i 0.0479190 + 0.0829982i
\(780\) −4.02304e12 + 6.96812e12i −0.389161 + 0.674046i
\(781\) −3.60073e12 + 6.23665e12i −0.346307 + 0.599821i
\(782\) −6.41110e12 1.11043e13i −0.613059 1.06185i
\(783\) 7.50082e11 0.0713150
\(784\) 5.71338e12 7.05325e12i 0.540096 0.666756i
\(785\) −4.53447e12 −0.426200
\(786\) 1.38284e13 + 2.39515e13i 1.29232 + 2.23836i
\(787\) −8.41564e12 + 1.45763e13i −0.781989 + 1.35445i 0.148792 + 0.988869i \(0.452461\pi\)
−0.930781 + 0.365577i \(0.880872\pi\)
\(788\) 9.28623e11 1.60842e12i 0.0857968 0.148604i
\(789\) 6.42470e12 + 1.11279e13i 0.590210 + 1.02227i
\(790\) −7.11745e12 −0.650133
\(791\) −1.46897e12 1.00976e12i −0.133419 0.0917112i
\(792\) −2.97503e13 −2.68676
\(793\) 4.06606e12 + 7.04262e12i 0.365127 + 0.632419i
\(794\) 3.08146e11 5.33725e11i 0.0275147 0.0476568i
\(795\) 3.72205e12 6.44679e12i 0.330469 0.572389i
\(796\) 1.20520e13 + 2.08747e13i 1.06402 + 1.84294i
\(797\) −2.51286e12 −0.220600 −0.110300 0.993898i \(-0.535181\pi\)
−0.110300 + 0.993898i \(0.535181\pi\)
\(798\) 2.50929e11 3.18527e12i 0.0219048 0.278057i
\(799\) −4.38539e11 −0.0380669
\(800\) −8.83410e11 1.53011e12i −0.0762531 0.132074i
\(801\) 8.78715e12 1.52198e13i 0.754227 1.30636i
\(802\) 9.95648e12 1.72451e13i 0.849808 1.47191i
\(803\) 8.72778e12 + 1.51170e13i 0.740771 + 1.28305i
\(804\) −2.77368e13 −2.34101
\(805\) 2.69466e12 1.28504e12i 0.226163 0.107853i
\(806\) −6.83077e11 −0.0570114
\(807\) −1.61827e13 2.80293e13i −1.34314 2.32639i
\(808\) 5.31603e12 9.20763e12i 0.438769 0.759970i
\(809\) 1.20294e13 2.08356e13i 0.987362 1.71016i 0.356429 0.934322i \(-0.383994\pi\)
0.630932 0.775838i \(-0.282673\pi\)
\(810\) −5.74072e10 9.94322e10i −0.00468580 0.00811604i
\(811\) −2.90243e12 −0.235596 −0.117798 0.993038i \(-0.537584\pi\)
−0.117798 + 0.993038i \(0.537584\pi\)
\(812\) 1.52764e12 7.28505e11i 0.123316 0.0588072i
\(813\) −1.91934e13 −1.54080
\(814\) −5.79871e12 1.00437e13i −0.462937 0.801830i
\(815\) 1.54891e12 2.68279e12i 0.122975 0.212999i
\(816\) −5.84412e12 + 1.01223e13i −0.461438 + 0.799234i
\(817\) 3.82558e11 + 6.62610e11i 0.0300399 + 0.0520306i
\(818\) 1.46302e13 1.14251
\(819\) −1.73880e12 + 2.20722e13i −0.135043 + 1.71422i
\(820\) 5.63378e12 0.435148
\(821\) −8.75599e12 1.51658e13i −0.672607 1.16499i −0.977162 0.212494i \(-0.931841\pi\)
0.304556 0.952494i \(-0.401492\pi\)
\(822\) 6.45942e12 1.11880e13i 0.493481 0.854734i
\(823\) −6.08213e12 + 1.05346e13i −0.462122 + 0.800419i −0.999067 0.0431987i \(-0.986245\pi\)
0.536944 + 0.843618i \(0.319578\pi\)
\(824\) 7.82479e12 + 1.35529e13i 0.591289 + 1.02414i
\(825\) −2.05811e13 −1.54677
\(826\) −3.18960e13 2.19251e13i −2.38411 1.63882i
\(827\) 2.07144e13 1.53992 0.769958 0.638095i \(-0.220277\pi\)
0.769958 + 0.638095i \(0.220277\pi\)
\(828\) 2.31233e13 + 4.00507e13i 1.70967 + 2.96124i
\(829\) −1.13364e13 + 1.96353e13i −0.833646 + 1.44392i 0.0614822 + 0.998108i \(0.480417\pi\)
−0.895128 + 0.445809i \(0.852916\pi\)
\(830\) 1.33209e12 2.30725e12i 0.0974276 0.168749i
\(831\) 4.09196e12 + 7.08748e12i 0.297664 + 0.515570i
\(832\) 1.65664e13 1.19860
\(833\) 9.10514e12 + 1.44353e12i 0.655216 + 0.103878i
\(834\) 7.53041e13 5.38978
\(835\) 1.47697e12 + 2.55820e12i 0.105144 + 0.182115i
\(836\) −1.39231e12 + 2.41155e12i −0.0985841 + 0.170753i
\(837\) 2.27320e11 3.93729e11i 0.0160093 0.0277289i
\(838\) −1.29267e13 2.23897e13i −0.905502 1.56838i
\(839\) −2.69030e13 −1.87444 −0.937222 0.348733i \(-0.886612\pi\)
−0.937222 + 0.348733i \(0.886612\pi\)
\(840\) −7.34416e12 5.04832e12i −0.508962 0.349857i
\(841\) −1.44361e13 −0.995101
\(842\) 5.97402e12 + 1.03473e13i 0.409602 + 0.709451i
\(843\) 1.03227e13 1.78794e13i 0.703992 1.21935i
\(844\) −1.43461e13 + 2.48482e13i −0.973179 + 1.68560i
\(845\) −1.98460e11 3.43743e11i −0.0133911 0.0231941i
\(846\) 2.39204e12 0.160547
\(847\) 2.07727e10 2.63687e11i 0.00138681 0.0176041i
\(848\) 2.26150e13 1.50181
\(849\) 1.06666e13 + 1.84750e13i 0.704596 + 1.22040i
\(850\) −8.20270e12 + 1.42075e13i −0.538979 + 0.933538i
\(851\) −4.39599e12 + 7.61408e12i −0.287325 + 0.497662i
\(852\) −1.67090e13 2.89408e13i −1.08635 1.88162i
\(853\) −2.44009e13 −1.57810 −0.789052 0.614327i \(-0.789428\pi\)
−0.789052 + 0.614327i \(0.789428\pi\)
\(854\) −1.66708e13 + 7.95001e12i −1.07250 + 0.511455i
\(855\) −5.93488e11 −0.0379808
\(856\) −1.58399e13 2.74355e13i −1.00837 1.74655i
\(857\) 2.61674e12 4.53233e12i 0.165710 0.287017i −0.771198 0.636596i \(-0.780342\pi\)
0.936907 + 0.349579i \(0.113675\pi\)
\(858\) 2.35505e13 4.07907e13i 1.48357 2.56962i
\(859\) −5.24957e12 9.09252e12i −0.328968 0.569790i 0.653339 0.757066i \(-0.273368\pi\)
−0.982307 + 0.187275i \(0.940034\pi\)
\(860\) 4.37593e12 0.272789
\(861\) 2.25856e13 1.07707e13i 1.40061 0.667927i
\(862\) 1.91356e13 1.18049
\(863\) 9.51997e12 + 1.64891e13i 0.584235 + 1.01192i 0.994970 + 0.100169i \(0.0319385\pi\)
−0.410736 + 0.911754i \(0.634728\pi\)
\(864\) −1.34562e12 + 2.33068e12i −0.0821503 + 0.142289i
\(865\) −6.80395e11 + 1.17848e12i −0.0413227 + 0.0715730i
\(866\) 1.92411e12 + 3.33266e12i 0.116252 + 0.201354i
\(867\) 1.51025e13 0.907742
\(868\) 8.05632e10 1.02266e12i 0.00481724 0.0611496i
\(869\) 2.75504e13 1.63885
\(870\) −3.83686e11 6.64564e11i −0.0227060 0.0393279i
\(871\) 6.63404e12 1.14905e13i 0.390568 0.676483i
\(872\) −1.79791e13 + 3.11407e13i −1.05304 + 1.82391i
\(873\) −1.56411e13 2.70912e13i −0.911388 1.57857i
\(874\) 3.19252e12 0.185068
\(875\) −6.47600e12 4.45155e12i −0.373483 0.256729i
\(876\) −8.10015e13 −4.64755
\(877\) 3.84858e12 + 6.66594e12i 0.219686 + 0.380508i 0.954712 0.297531i \(-0.0961633\pi\)
−0.735026 + 0.678039i \(0.762830\pi\)
\(878\) −2.29481e13 + 3.97473e13i −1.30323 + 2.25726i
\(879\) −3.92239e12 + 6.79378e12i −0.221616 + 0.383850i
\(880\) 1.79339e12 + 3.10624e12i 0.100810 + 0.174607i
\(881\) 3.36138e13 1.87986 0.939931 0.341364i \(-0.110889\pi\)
0.939931 + 0.341364i \(0.110889\pi\)
\(882\) −4.96646e13 7.87381e12i −2.76336 0.438103i
\(883\) 1.31382e13 0.727301 0.363651 0.931535i \(-0.381530\pi\)
0.363651 + 0.931535i \(0.381530\pi\)
\(884\) −1.24130e13 2.14999e13i −0.683660 1.18413i
\(885\) −5.80204e12 + 1.00494e13i −0.317934 + 0.550677i
\(886\) −8.70206e12 + 1.50724e13i −0.474428 + 0.821734i
\(887\) 1.47004e12 + 2.54618e12i 0.0797394 + 0.138113i 0.903137 0.429352i \(-0.141258\pi\)
−0.823398 + 0.567464i \(0.807925\pi\)
\(888\) 2.62457e13 1.41645
\(889\) 2.27724e12 + 1.56536e12i 0.122279 + 0.0840534i
\(890\) −6.93866e12 −0.370698
\(891\) 2.22213e11 + 3.84884e11i 0.0118119 + 0.0204588i
\(892\) 2.53005e13 4.38217e13i 1.33809 2.31765i
\(893\) 5.45945e10 9.45604e10i 0.00287288 0.00497597i
\(894\) 2.56856e13 + 4.44888e13i 1.34484 + 2.32934i
\(895\) 3.12491e12 0.162792
\(896\) −2.71055e12 + 3.44075e13i −0.140499 + 1.78348i
\(897\) −3.57072e13 −1.84158
\(898\) 3.04104e13 + 5.26724e13i 1.56055 + 2.70296i
\(899\) 2.15387e10 3.73060e10i 0.00109977 0.00190485i
\(900\) 2.95852e13 5.12430e13i 1.50308 2.60341i
\(901\) 1.14843e13 + 1.98913e13i 0.580553 + 1.00555i
\(902\) −3.29796e13 −1.65888
\(903\) 1.75429e13 8.36592e12i 0.878026 0.418715i
\(904\) −5.31686e12 −0.264787
\(905\) −3.52064e12 6.09792e12i −0.174463 0.302178i
\(906\) 1.55473e12 2.69288e12i 0.0766618 0.132782i
\(907\) 2.19229e12 3.79716e12i 0.107564 0.186306i −0.807219 0.590252i \(-0.799028\pi\)
0.914783 + 0.403946i \(0.132362\pi\)
\(908\) −2.59479e13 4.49431e13i −1.26682 2.19420i
\(909\) −1.79858e13 −0.873760
\(910\) 7.89023e12 3.76271e12i 0.381420 0.181892i
\(911\) −9.99239e12 −0.480659 −0.240329 0.970691i \(-0.577255\pi\)
−0.240329 + 0.970691i \(0.577255\pi\)
\(912\) −1.45509e12 2.52029e12i −0.0696487 0.120635i
\(913\) −5.15628e12 + 8.93093e12i −0.245594 + 0.425381i
\(914\) 2.38789e13 4.13595e13i 1.13177 1.96028i
\(915\) 2.76865e12 + 4.79545e12i 0.130579 + 0.226170i
\(916\) −5.26913e12 −0.247292
\(917\) 1.56034e12 1.98069e13i 0.0728716 0.925026i
\(918\) 2.49888e13 1.16132
\(919\) −7.17492e12 1.24273e13i −0.331816 0.574722i 0.651052 0.759033i \(-0.274328\pi\)
−0.982868 + 0.184311i \(0.940995\pi\)
\(920\) 4.45230e12 7.71161e12i 0.204899 0.354895i
\(921\) −1.51290e13 + 2.62042e13i −0.692854 + 1.20006i
\(922\) 4.60871e12 + 7.98251e12i 0.210034 + 0.363790i
\(923\) 1.59857e13 0.724977
\(924\) 5.82918e13 + 4.00694e13i 2.63078 + 1.80838i
\(925\) 1.12489e13 0.505212
\(926\) −3.96300e12 6.86411e12i −0.177123 0.306786i
\(927\) 1.32369e13 2.29269e13i 0.588743 1.01973i
\(928\) −1.27498e11 + 2.20833e11i −0.00564334 + 0.00977456i
\(929\) −1.63514e13 2.83215e13i −0.720254 1.24752i −0.960898 0.276903i \(-0.910692\pi\)
0.240644 0.970613i \(-0.422641\pi\)
\(930\) −4.65120e11 −0.0203888
\(931\) −1.44478e12 + 1.78360e12i −0.0630272 + 0.0778080i
\(932\) 1.52906e13 0.663826
\(933\) −1.66574e13 2.88514e13i −0.719679 1.24652i
\(934\) 2.95073e13 5.11081e13i 1.26873 2.19750i
\(935\) −1.82142e12 + 3.15480e12i −0.0779397 + 0.134996i
\(936\) 3.30197e13 + 5.71918e13i 1.40615 + 2.43552i
\(937\) −1.89684e13 −0.803901 −0.401951 0.915661i \(-0.631668\pi\)
−0.401951 + 0.915661i \(0.631668\pi\)
\(938\) 2.48329e13 + 1.70700e13i 1.04741 + 0.719980i
\(939\) −2.70275e13 −1.13452
\(940\) −3.12243e11 5.40820e11i −0.0130442 0.0225932i
\(941\) −6.19624e11 + 1.07322e12i −0.0257617 + 0.0446206i −0.878619 0.477524i \(-0.841534\pi\)
0.852857 + 0.522144i \(0.174868\pi\)
\(942\) −6.15888e13 + 1.06675e14i −2.54843 + 4.41401i
\(943\) 1.25009e13 + 2.16522e13i 0.514800 + 0.891659i
\(944\) −3.52529e13 −1.44484
\(945\) −4.56924e11 + 5.80016e12i −0.0186381 + 0.236590i
\(946\) −2.56163e13 −1.03993
\(947\) −9.20950e12 1.59513e13i −0.372101 0.644498i 0.617787 0.786345i \(-0.288029\pi\)
−0.989889 + 0.141847i \(0.954696\pi\)
\(948\) −6.39229e13 + 1.10718e14i −2.57051 + 4.45225i
\(949\) 1.93738e13 3.35564e13i 0.775384 1.34300i
\(950\) −2.04234e12 3.53744e12i −0.0813526 0.140907i
\(951\) 4.69464e13 1.86119
\(952\) 2.48196e13 1.18361e13i 0.979331 0.467026i
\(953\) −2.36101e13 −0.927213 −0.463606 0.886041i \(-0.653445\pi\)
−0.463606 + 0.886041i \(0.653445\pi\)
\(954\) −6.26416e13 1.08499e14i −2.44847 4.24088i
\(955\) 1.74974e12 3.03065e12i 0.0680706 0.117902i
\(956\) 4.09884e13 7.09940e13i 1.58709 2.74891i
\(957\) 1.48518e12 + 2.57241e12i 0.0572369 + 0.0991371i
\(958\) −1.78591e13 −0.685040
\(959\) −8.37694e12 + 3.99482e12i −0.319817 + 0.152515i
\(960\) 1.12804e13 0.428651
\(961\) 1.32068e13 + 2.28748e13i 0.499506 + 0.865170i
\(962\) −1.28719e13 + 2.22948e13i −0.484568 + 0.839296i
\(963\) −2.67957e13 + 4.64115e13i −1.00403 + 1.73903i
\(964\) 7.98102e12 + 1.38235e13i 0.297654 + 0.515552i
\(965\) 2.24628e12 0.0833855
\(966\) 6.36892e12 8.08465e13i 0.235325 2.98720i
\(967\) −1.39401e12 −0.0512682 −0.0256341 0.999671i \(-0.508160\pi\)
−0.0256341 + 0.999671i \(0.508160\pi\)
\(968\) −3.94472e11 6.83246e11i −0.0144403 0.0250114i
\(969\) 1.47784e12 2.55969e12i 0.0538481 0.0932676i
\(970\) −6.17539e12 + 1.06961e13i −0.223971 + 0.387929i
\(971\) 7.99479e12 + 1.38474e13i 0.288616 + 0.499898i 0.973480 0.228774i \(-0.0734715\pi\)
−0.684864 + 0.728671i \(0.740138\pi\)
\(972\) 5.32837e13 1.91468
\(973\) −4.45808e13 3.06445e13i −1.59456 1.09609i
\(974\) −4.37335e13 −1.55704
\(975\) 2.28429e13 + 3.95650e13i 0.809524 + 1.40214i
\(976\) −8.41109e12 + 1.45684e13i −0.296707 + 0.513912i
\(977\) 5.60793e11 9.71322e11i 0.0196914 0.0341065i −0.856012 0.516956i \(-0.827065\pi\)
0.875703 + 0.482850i \(0.160398\pi\)
\(978\) −4.20756e13 7.28772e13i −1.47064 2.54722i
\(979\) 2.68583e13 0.934451
\(980\) 4.70272e12 + 1.22566e13i 0.162867 + 0.424474i
\(981\) 6.08289e13 2.09700
\(982\) 4.08665e13 + 7.07829e13i 1.40238 + 2.42900i
\(983\) −2.13470e13 + 3.69741e13i −0.729200 + 1.26301i 0.228022 + 0.973656i \(0.426774\pi\)
−0.957222 + 0.289355i \(0.906559\pi\)
\(984\) 3.73175e13 6.46358e13i 1.26892 2.19783i
\(985\) 3.02473e11 + 5.23898e11i 0.0102382 + 0.0177331i
\(986\) 2.36770e12 0.0797776
\(987\) −2.28571e12 1.57118e12i −0.0766645 0.0526986i
\(988\) 6.18125e12 0.206381
\(989\) 9.70983e12 + 1.68179e13i 0.322722 + 0.558971i
\(990\) 9.93508e12 1.72081e13i 0.328710 0.569342i
\(991\) −4.69136e12 + 8.12568e12i −0.154514 + 0.267626i −0.932882 0.360182i \(-0.882714\pi\)
0.778368 + 0.627808i \(0.216048\pi\)
\(992\) 7.72789e10 + 1.33851e11i 0.00253372 + 0.00438853i
\(993\) 2.78157e13 0.907860
\(994\) −2.85129e12 + 3.61941e13i −0.0926410 + 1.17598i
\(995\) −7.85121e12 −0.253941
\(996\) −2.39274e13 4.14435e13i −0.770422 1.33441i
\(997\) 1.08546e13 1.88007e13i 0.347924 0.602622i −0.637957 0.770072i \(-0.720220\pi\)
0.985880 + 0.167451i \(0.0535535\pi\)
\(998\) 7.49891e12 1.29885e13i 0.239282 0.414449i
\(999\) −8.56723e12 1.48389e13i −0.272142 0.471364i
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 7.10.c.a.4.1 yes 10
3.2 odd 2 63.10.e.b.46.5 10
4.3 odd 2 112.10.i.c.81.1 10
7.2 even 3 inner 7.10.c.a.2.1 10
7.3 odd 6 49.10.a.f.1.5 5
7.4 even 3 49.10.a.e.1.5 5
7.5 odd 6 49.10.c.g.30.1 10
7.6 odd 2 49.10.c.g.18.1 10
21.2 odd 6 63.10.e.b.37.5 10
28.23 odd 6 112.10.i.c.65.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.10.c.a.2.1 10 7.2 even 3 inner
7.10.c.a.4.1 yes 10 1.1 even 1 trivial
49.10.a.e.1.5 5 7.4 even 3
49.10.a.f.1.5 5 7.3 odd 6
49.10.c.g.18.1 10 7.6 odd 2
49.10.c.g.30.1 10 7.5 odd 6
63.10.e.b.37.5 10 21.2 odd 6
63.10.e.b.46.5 10 3.2 odd 2
112.10.i.c.65.1 10 28.23 odd 6
112.10.i.c.81.1 10 4.3 odd 2