Properties

Label 98.13.d.a.31.2
Level $98$
Weight $13$
Character 98.31
Analytic conductor $89.571$
Analytic rank $0$
Dimension $16$
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] = [98,13,Mod(19,98)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(98, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("98.19");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 98.d (of order \(6\), degree \(2\), not 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: \(89.5713940931\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} - 2204556 x^{14} - 87623088 x^{13} + 1948666431190 x^{12} + 195028079162640 x^{11} + \cdots + 24\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{8}\cdot 7^{8} \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.2
Root \(468.905 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 98.31
Dual form 98.13.d.a.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-22.6274 - 39.1918i) q^{2} +(-702.607 - 405.650i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(18305.2 - 10568.5i) q^{5} +36715.3i q^{6} +92681.9 q^{8} +(63384.0 + 109784. i) q^{9} +O(q^{10})\) \(q+(-22.6274 - 39.1918i) q^{2} +(-702.607 - 405.650i) q^{3} +(-1024.00 + 1773.62i) q^{4} +(18305.2 - 10568.5i) q^{5} +36715.3i q^{6} +92681.9 q^{8} +(63384.0 + 109784. i) q^{9} +(-828399. - 478276. i) q^{10} +(651539. - 1.12850e6i) q^{11} +(1.43894e6 - 830772. i) q^{12} +7.09849e6i q^{13} -1.71485e7 q^{15} +(-2.09715e6 - 3.63237e6i) q^{16} +(2.79240e7 + 1.61219e7i) q^{17} +(2.86843e6 - 4.96827e6i) q^{18} +(2.32303e7 - 1.34120e7i) q^{19} +4.32886e7i q^{20} -5.89706e7 q^{22} +(6.22412e7 + 1.07805e8i) q^{23} +(-6.51190e7 - 3.75965e7i) q^{24} +(1.01317e8 - 1.75486e8i) q^{25} +(2.78203e8 - 1.60621e8i) q^{26} +3.28312e8i q^{27} -7.52793e8 q^{29} +(3.88026e8 + 6.72081e8i) q^{30} +(-9.46508e8 - 5.46467e8i) q^{31} +(-9.49063e7 + 1.64382e8i) q^{32} +(-9.15552e8 + 5.28594e8i) q^{33} -1.45919e9i q^{34} -2.59621e8 q^{36} +(-1.93585e9 - 3.35299e9i) q^{37} +(-1.05129e9 - 6.06960e8i) q^{38} +(2.87951e9 - 4.98745e9i) q^{39} +(1.69656e9 - 9.79510e8i) q^{40} -2.55800e9i q^{41} -4.36133e9 q^{43} +(1.33435e9 + 2.31116e9i) q^{44} +(2.32051e9 + 1.33975e9i) q^{45} +(2.81672e9 - 4.87869e9i) q^{46} +(-8.04169e9 + 4.64287e9i) q^{47} +3.40284e9i q^{48} -9.17013e9 q^{50} +(-1.30797e10 - 2.26548e10i) q^{51} +(-1.25900e10 - 7.26886e9i) q^{52} +(-1.09179e8 + 1.89104e8i) q^{53} +(1.28671e10 - 7.42884e9i) q^{54} -2.75432e10i q^{55} -2.17624e10 q^{57} +(1.70338e10 + 2.95033e10i) q^{58} +(-5.45224e10 - 3.14785e10i) q^{59} +(1.75600e10 - 3.04149e10i) q^{60} +(-4.19753e10 + 2.42344e10i) q^{61} +4.94605e10i q^{62} +8.58993e9 q^{64} +(7.50205e10 + 1.29939e11i) q^{65} +(4.14331e10 + 2.39214e10i) q^{66} +(-5.49220e10 + 9.51277e10i) q^{67} +(-5.71884e10 + 3.30177e10i) q^{68} -1.00993e11i q^{69} -7.43754e10 q^{71} +(5.87455e9 + 1.01750e10i) q^{72} +(2.26320e11 + 1.30666e11i) q^{73} +(-8.76065e10 + 1.51739e11i) q^{74} +(-1.42372e11 + 8.21982e10i) q^{75} +5.49357e10i q^{76} -2.60623e11 q^{78} +(-1.20639e11 - 2.08953e11i) q^{79} +(-7.67776e10 - 4.43276e10i) q^{80} +(1.66865e11 - 2.89018e11i) q^{81} +(-1.00253e11 + 5.78810e10i) q^{82} -2.09983e11i q^{83} +6.81540e11 q^{85} +(9.86855e10 + 1.70928e11i) q^{86} +(5.28918e11 + 3.05371e11i) q^{87} +(6.03859e10 - 1.04591e11i) q^{88} +(-1.79050e10 + 1.03374e10i) q^{89} -1.21260e11i q^{90} -2.54940e11 q^{92} +(4.43349e11 + 7.67903e11i) q^{93} +(3.63926e11 + 2.10113e11i) q^{94} +(2.83491e11 - 4.91020e11i) q^{95} +(1.33364e11 - 7.69975e10i) q^{96} +4.74911e11i q^{97} +1.65189e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16384 q^{4} - 18144 q^{5} + 2362248 q^{9} + 2290176 q^{10} + 2072088 q^{11} - 27163728 q^{15} - 33554432 q^{16} + 101561040 q^{17} - 4592640 q^{18} - 174931848 q^{19} + 62776320 q^{22} + 25630560 q^{23} - 242221056 q^{24} + 521205808 q^{25} + 1434682368 q^{26} + 532360944 q^{29} - 2151917568 q^{30} - 4583818344 q^{31} - 6054957720 q^{33} - 9675767808 q^{36} + 5764524040 q^{37} + 149506560 q^{38} + 10526083272 q^{39} - 4690280448 q^{40} - 66929432000 q^{43} + 4243636224 q^{44} - 57253352184 q^{45} + 7203213312 q^{46} - 18116171640 q^{47} - 99248080896 q^{50} - 23299256376 q^{51} - 8269578240 q^{52} + 39134161800 q^{53} - 105152205312 q^{54} - 328243960080 q^{57} + 29637396480 q^{58} - 201845459088 q^{59} + 27815657472 q^{60} - 336780254328 q^{61} + 137438953472 q^{64} + 158322703896 q^{65} - 268884080640 q^{66} + 107767119920 q^{67} - 207997009920 q^{68} - 1150259029344 q^{71} - 9405726720 q^{72} + 738414283320 q^{73} + 4902778368 q^{74} - 1537028640000 q^{75} - 786088888320 q^{78} + 227632064768 q^{79} + 76101451776 q^{80} - 391984178400 q^{81} + 302578053120 q^{82} + 710209696080 q^{85} - 38105192448 q^{86} - 1957017683880 q^{87} - 64282951680 q^{88} + 2485007442792 q^{89} - 104982773760 q^{92} - 458668768680 q^{93} + 2021298693120 q^{94} - 186503862960 q^{95} + 496068722688 q^{96} + 3921180354576 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.6274 39.1918i −0.353553 0.612372i
\(3\) −702.607 405.650i −0.963796 0.556448i −0.0664566 0.997789i \(-0.521169\pi\)
−0.897339 + 0.441342i \(0.854503\pi\)
\(4\) −1024.00 + 1773.62i −0.250000 + 0.433013i
\(5\) 18305.2 10568.5i 1.17153 0.676385i 0.217492 0.976062i \(-0.430212\pi\)
0.954041 + 0.299677i \(0.0968790\pi\)
\(6\) 36715.3i 0.786936i
\(7\) 0 0
\(8\) 92681.9 0.353553
\(9\) 63384.0 + 109784.i 0.119268 + 0.206579i
\(10\) −828399. 478276.i −0.828399 0.478276i
\(11\) 651539. 1.12850e6i 0.367777 0.637008i −0.621441 0.783461i \(-0.713452\pi\)
0.989218 + 0.146453i \(0.0467857\pi\)
\(12\) 1.43894e6 830772.i 0.481898 0.278224i
\(13\) 7.09849e6i 1.47064i 0.677720 + 0.735320i \(0.262968\pi\)
−0.677720 + 0.735320i \(0.737032\pi\)
\(14\) 0 0
\(15\) −1.71485e7 −1.50549
\(16\) −2.09715e6 3.63237e6i −0.125000 0.216506i
\(17\) 2.79240e7 + 1.61219e7i 1.15687 + 0.667919i 0.950552 0.310566i \(-0.100519\pi\)
0.206318 + 0.978485i \(0.433852\pi\)
\(18\) 2.86843e6 4.96827e6i 0.0843353 0.146073i
\(19\) 2.32303e7 1.34120e7i 0.493780 0.285084i −0.232361 0.972630i \(-0.574645\pi\)
0.726141 + 0.687545i \(0.241312\pi\)
\(20\) 4.32886e7i 0.676385i
\(21\) 0 0
\(22\) −5.89706e7 −0.520115
\(23\) 6.22412e7 + 1.07805e8i 0.420447 + 0.728235i 0.995983 0.0895411i \(-0.0285400\pi\)
−0.575536 + 0.817776i \(0.695207\pi\)
\(24\) −6.51190e7 3.75965e7i −0.340753 0.196734i
\(25\) 1.01317e8 1.75486e8i 0.414993 0.718789i
\(26\) 2.78203e8 1.60621e8i 0.900579 0.519950i
\(27\) 3.28312e8i 0.847429i
\(28\) 0 0
\(29\) −7.52793e8 −1.26557 −0.632787 0.774326i \(-0.718089\pi\)
−0.632787 + 0.774326i \(0.718089\pi\)
\(30\) 3.88026e8 + 6.72081e8i 0.532272 + 0.921921i
\(31\) −9.46508e8 5.46467e8i −1.06648 0.615735i −0.139265 0.990255i \(-0.544474\pi\)
−0.927219 + 0.374520i \(0.877807\pi\)
\(32\) −9.49063e7 + 1.64382e8i −0.0883883 + 0.153093i
\(33\) −9.15552e8 + 5.28594e8i −0.708923 + 0.409297i
\(34\) 1.45919e9i 0.944580i
\(35\) 0 0
\(36\) −2.59621e8 −0.119268
\(37\) −1.93585e9 3.35299e9i −0.754503 1.30684i −0.945621 0.325271i \(-0.894544\pi\)
0.191117 0.981567i \(-0.438789\pi\)
\(38\) −1.05129e9 6.06960e8i −0.349156 0.201585i
\(39\) 2.87951e9 4.98745e9i 0.818334 1.41740i
\(40\) 1.69656e9 9.79510e8i 0.414199 0.239138i
\(41\) 2.55800e9i 0.538516i −0.963068 0.269258i \(-0.913222\pi\)
0.963068 0.269258i \(-0.0867784\pi\)
\(42\) 0 0
\(43\) −4.36133e9 −0.689934 −0.344967 0.938615i \(-0.612110\pi\)
−0.344967 + 0.938615i \(0.612110\pi\)
\(44\) 1.33435e9 + 2.31116e9i 0.183888 + 0.318504i
\(45\) 2.32051e9 + 1.33975e9i 0.279453 + 0.161342i
\(46\) 2.81672e9 4.87869e9i 0.297301 0.514940i
\(47\) −8.04169e9 + 4.64287e9i −0.746037 + 0.430725i −0.824260 0.566211i \(-0.808409\pi\)
0.0782231 + 0.996936i \(0.475075\pi\)
\(48\) 3.40284e9i 0.278224i
\(49\) 0 0
\(50\) −9.17013e9 −0.586888
\(51\) −1.30797e10 2.26548e10i −0.743324 1.28747i
\(52\) −1.25900e10 7.26886e9i −0.636805 0.367660i
\(53\) −1.09179e8 + 1.89104e8i −0.00492590 + 0.00853191i −0.868478 0.495728i \(-0.834901\pi\)
0.863552 + 0.504260i \(0.168235\pi\)
\(54\) 1.28671e10 7.42884e9i 0.518942 0.299612i
\(55\) 2.75432e10i 0.995034i
\(56\) 0 0
\(57\) −2.17624e10 −0.634538
\(58\) 1.70338e10 + 2.95033e10i 0.447448 + 0.775003i
\(59\) −5.45224e10 3.14785e10i −1.29260 0.746280i −0.313482 0.949594i \(-0.601495\pi\)
−0.979114 + 0.203314i \(0.934829\pi\)
\(60\) 1.75600e10 3.04149e10i 0.376373 0.651897i
\(61\) −4.19753e10 + 2.42344e10i −0.814732 + 0.470386i −0.848596 0.529041i \(-0.822552\pi\)
0.0338645 + 0.999426i \(0.489219\pi\)
\(62\) 4.94605e10i 0.870780i
\(63\) 0 0
\(64\) 8.58993e9 0.125000
\(65\) 7.50205e10 + 1.29939e11i 0.994718 + 1.72290i
\(66\) 4.14331e10 + 2.39214e10i 0.501284 + 0.289417i
\(67\) −5.49220e10 + 9.51277e10i −0.607152 + 1.05162i 0.384556 + 0.923102i \(0.374355\pi\)
−0.991707 + 0.128516i \(0.958979\pi\)
\(68\) −5.71884e10 + 3.30177e10i −0.578435 + 0.333959i
\(69\) 1.00993e11i 0.935826i
\(70\) 0 0
\(71\) −7.43754e10 −0.580603 −0.290302 0.956935i \(-0.593756\pi\)
−0.290302 + 0.956935i \(0.593756\pi\)
\(72\) 5.87455e9 + 1.01750e10i 0.0421677 + 0.0730366i
\(73\) 2.26320e11 + 1.30666e11i 1.49550 + 0.863427i 0.999987 0.00517437i \(-0.00164706\pi\)
0.495512 + 0.868601i \(0.334980\pi\)
\(74\) −8.76065e10 + 1.51739e11i −0.533514 + 0.924074i
\(75\) −1.42372e11 + 8.21982e10i −0.799937 + 0.461844i
\(76\) 5.49357e10i 0.285084i
\(77\) 0 0
\(78\) −2.60623e11 −1.15730
\(79\) −1.20639e11 2.08953e11i −0.496279 0.859580i 0.503712 0.863871i \(-0.331967\pi\)
−0.999991 + 0.00429190i \(0.998634\pi\)
\(80\) −7.67776e10 4.43276e10i −0.292883 0.169096i
\(81\) 1.66865e11 2.89018e11i 0.590818 1.02333i
\(82\) −1.00253e11 + 5.78810e10i −0.329772 + 0.190394i
\(83\) 2.09983e11i 0.642268i −0.947034 0.321134i \(-0.895936\pi\)
0.947034 0.321134i \(-0.104064\pi\)
\(84\) 0 0
\(85\) 6.81540e11 1.80708
\(86\) 9.86855e10 + 1.70928e11i 0.243929 + 0.422497i
\(87\) 5.28918e11 + 3.05371e11i 1.21975 + 0.704226i
\(88\) 6.03859e10 1.04591e11i 0.130029 0.225216i
\(89\) −1.79050e10 + 1.03374e10i −0.0360275 + 0.0208005i −0.517906 0.855438i \(-0.673288\pi\)
0.481878 + 0.876238i \(0.339955\pi\)
\(90\) 1.21260e11i 0.228173i
\(91\) 0 0
\(92\) −2.54940e11 −0.420447
\(93\) 4.43349e11 + 7.67903e11i 0.685248 + 1.18689i
\(94\) 3.63926e11 + 2.10113e11i 0.527528 + 0.304568i
\(95\) 2.83491e11 4.91020e11i 0.385653 0.667971i
\(96\) 1.33364e11 7.69975e10i 0.170377 0.0983670i
\(97\) 4.74911e11i 0.570140i 0.958507 + 0.285070i \(0.0920169\pi\)
−0.958507 + 0.285070i \(0.907983\pi\)
\(98\) 0 0
\(99\) 1.65189e11 0.175456
\(100\) 2.07496e11 + 3.59394e11i 0.207496 + 0.359394i
\(101\) −9.97000e11 5.75618e11i −0.939219 0.542259i −0.0495038 0.998774i \(-0.515764\pi\)
−0.889715 + 0.456515i \(0.849097\pi\)
\(102\) −5.91921e11 + 1.02524e12i −0.525609 + 0.910382i
\(103\) −8.21363e11 + 4.74214e11i −0.687878 + 0.397147i −0.802817 0.596226i \(-0.796666\pi\)
0.114938 + 0.993373i \(0.463333\pi\)
\(104\) 6.57902e11i 0.519950i
\(105\) 0 0
\(106\) 9.88179e9 0.00696628
\(107\) 1.66978e11 + 2.89214e11i 0.111264 + 0.192715i 0.916280 0.400538i \(-0.131177\pi\)
−0.805016 + 0.593253i \(0.797843\pi\)
\(108\) −5.82300e11 3.36191e11i −0.366948 0.211857i
\(109\) 3.67785e11 6.37022e11i 0.219298 0.379835i −0.735295 0.677747i \(-0.762957\pi\)
0.954594 + 0.297911i \(0.0962899\pi\)
\(110\) −1.07947e12 + 6.23231e11i −0.609332 + 0.351798i
\(111\) 3.14111e12i 1.67937i
\(112\) 0 0
\(113\) −2.66369e12 −1.27942 −0.639709 0.768617i \(-0.720945\pi\)
−0.639709 + 0.768617i \(0.720945\pi\)
\(114\) 4.92427e11 + 8.52908e11i 0.224343 + 0.388574i
\(115\) 2.27868e12 + 1.31559e12i 0.985134 + 0.568768i
\(116\) 7.70860e11 1.33517e12i 0.316394 0.548010i
\(117\) −7.79303e11 + 4.49931e11i −0.303803 + 0.175400i
\(118\) 2.84911e12i 1.05540i
\(119\) 0 0
\(120\) −1.58935e12 −0.532272
\(121\) 7.20208e11 + 1.24744e12i 0.229481 + 0.397472i
\(122\) 1.89958e12 + 1.09673e12i 0.576102 + 0.332613i
\(123\) −1.03766e12 + 1.79727e12i −0.299656 + 0.519019i
\(124\) 1.93845e12 1.11916e12i 0.533242 0.307867i
\(125\) 8.77343e11i 0.229990i
\(126\) 0 0
\(127\) −2.69168e11 −0.0641506 −0.0320753 0.999485i \(-0.510212\pi\)
−0.0320753 + 0.999485i \(0.510212\pi\)
\(128\) −1.94368e11 3.36655e11i −0.0441942 0.0765466i
\(129\) 3.06430e12 + 1.76917e12i 0.664956 + 0.383912i
\(130\) 3.39504e12 5.88038e12i 0.703372 1.21828i
\(131\) −4.16356e12 + 2.40383e12i −0.823829 + 0.475638i −0.851735 0.523972i \(-0.824449\pi\)
0.0279059 + 0.999611i \(0.491116\pi\)
\(132\) 2.16512e12i 0.409297i
\(133\) 0 0
\(134\) 4.97097e12 0.858642
\(135\) 3.46976e12 + 6.00981e12i 0.573188 + 0.992791i
\(136\) 2.58805e12 + 1.49421e12i 0.409015 + 0.236145i
\(137\) −5.08937e12 + 8.81505e12i −0.769734 + 1.33322i 0.167973 + 0.985792i \(0.446278\pi\)
−0.937707 + 0.347427i \(0.887056\pi\)
\(138\) −3.95809e12 + 2.28520e12i −0.573074 + 0.330865i
\(139\) 3.81539e11i 0.0528994i −0.999650 0.0264497i \(-0.991580\pi\)
0.999650 0.0264497i \(-0.00842018\pi\)
\(140\) 0 0
\(141\) 7.53354e12 0.958703
\(142\) 1.68292e12 + 2.91491e12i 0.205274 + 0.355545i
\(143\) 8.01064e12 + 4.62495e12i 0.936809 + 0.540867i
\(144\) 2.65852e11 4.60469e11i 0.0298170 0.0516446i
\(145\) −1.37800e13 + 7.95590e12i −1.48266 + 0.856015i
\(146\) 1.18265e13i 1.22107i
\(147\) 0 0
\(148\) 7.92924e12 0.754503
\(149\) 1.01352e13 + 1.75546e13i 0.926218 + 1.60426i 0.789591 + 0.613634i \(0.210293\pi\)
0.136627 + 0.990623i \(0.456374\pi\)
\(150\) 6.44300e12 + 3.71987e12i 0.565641 + 0.326573i
\(151\) 9.98191e12 1.72892e13i 0.842077 1.45852i −0.0460585 0.998939i \(-0.514666\pi\)
0.888136 0.459582i \(-0.152001\pi\)
\(152\) 2.15303e12 1.24305e12i 0.174578 0.100793i
\(153\) 4.08749e12i 0.318646i
\(154\) 0 0
\(155\) −2.31014e13 −1.66589
\(156\) 5.89723e12 + 1.02143e13i 0.409167 + 0.708698i
\(157\) −6.85383e12 3.95706e12i −0.457652 0.264226i 0.253404 0.967360i \(-0.418450\pi\)
−0.711057 + 0.703135i \(0.751783\pi\)
\(158\) −5.45950e12 + 9.45613e12i −0.350922 + 0.607815i
\(159\) 1.53420e11 8.85774e10i 0.00949512 0.00548201i
\(160\) 4.01207e12i 0.239138i
\(161\) 0 0
\(162\) −1.51029e13 −0.835543
\(163\) −1.22758e13 2.12623e13i −0.654521 1.13366i −0.982014 0.188810i \(-0.939537\pi\)
0.327493 0.944854i \(-0.393796\pi\)
\(164\) 4.53693e12 + 2.61940e12i 0.233184 + 0.134629i
\(165\) −1.11729e13 + 1.93520e13i −0.553685 + 0.959010i
\(166\) −8.22964e12 + 4.75138e12i −0.393307 + 0.227076i
\(167\) 2.03607e13i 0.938629i 0.883031 + 0.469315i \(0.155499\pi\)
−0.883031 + 0.469315i \(0.844501\pi\)
\(168\) 0 0
\(169\) −2.70905e13 −1.16278
\(170\) −1.54215e13 2.67108e13i −0.638899 1.10661i
\(171\) 2.94486e12 + 1.70022e12i 0.117785 + 0.0680030i
\(172\) 4.46600e12 7.73533e12i 0.172484 0.298750i
\(173\) −1.88719e13 + 1.08957e13i −0.703945 + 0.406423i −0.808815 0.588063i \(-0.799891\pi\)
0.104870 + 0.994486i \(0.466557\pi\)
\(174\) 2.76390e13i 0.995926i
\(175\) 0 0
\(176\) −5.46550e12 −0.183888
\(177\) 2.55385e13 + 4.42340e13i 0.830532 + 1.43852i
\(178\) 8.10287e11 + 4.67819e11i 0.0254753 + 0.0147081i
\(179\) −5.29449e12 + 9.17033e12i −0.160956 + 0.278783i −0.935212 0.354089i \(-0.884791\pi\)
0.774256 + 0.632872i \(0.218124\pi\)
\(180\) −4.75241e12 + 2.74381e12i −0.139727 + 0.0806712i
\(181\) 5.35655e13i 1.52340i 0.647930 + 0.761700i \(0.275635\pi\)
−0.647930 + 0.761700i \(0.724365\pi\)
\(182\) 0 0
\(183\) 3.93229e13 1.04698
\(184\) 5.76863e12 + 9.99156e12i 0.148650 + 0.257470i
\(185\) −7.08722e13 4.09181e13i −1.76785 1.02067i
\(186\) 2.00637e13 3.47513e13i 0.484544 0.839255i
\(187\) 3.63872e13 2.10081e13i 0.850939 0.491290i
\(188\) 1.90172e13i 0.430725i
\(189\) 0 0
\(190\) −2.56586e13 −0.545396
\(191\) −3.11402e13 5.39365e13i −0.641390 1.11092i −0.985123 0.171852i \(-0.945025\pi\)
0.343733 0.939067i \(-0.388308\pi\)
\(192\) −6.03535e12 3.48451e12i −0.120474 0.0695560i
\(193\) 1.97810e13 3.42617e13i 0.382740 0.662926i −0.608713 0.793391i \(-0.708314\pi\)
0.991453 + 0.130465i \(0.0416471\pi\)
\(194\) 1.86126e13 1.07460e13i 0.349138 0.201575i
\(195\) 1.21728e14i 2.21403i
\(196\) 0 0
\(197\) 2.98938e12 0.0511427 0.0255713 0.999673i \(-0.491860\pi\)
0.0255713 + 0.999673i \(0.491860\pi\)
\(198\) −3.73779e12 6.47404e12i −0.0620332 0.107445i
\(199\) −5.16217e13 2.98038e13i −0.831216 0.479903i 0.0230526 0.999734i \(-0.492661\pi\)
−0.854269 + 0.519831i \(0.825995\pi\)
\(200\) 9.39022e12 1.62643e13i 0.146722 0.254130i
\(201\) 7.71771e13 4.45582e13i 1.17034 0.675697i
\(202\) 5.20990e13i 0.766869i
\(203\) 0 0
\(204\) 5.35746e13 0.743324
\(205\) −2.70343e13 4.68248e13i −0.364244 0.630889i
\(206\) 3.71706e13 + 2.14605e13i 0.486403 + 0.280825i
\(207\) −7.89019e12 + 1.36662e13i −0.100292 + 0.173711i
\(208\) 2.57844e13 1.48866e13i 0.318403 0.183830i
\(209\) 3.49539e13i 0.419389i
\(210\) 0 0
\(211\) 1.29666e14 1.46937 0.734684 0.678409i \(-0.237330\pi\)
0.734684 + 0.678409i \(0.237330\pi\)
\(212\) −2.23599e11 3.87286e11i −0.00246295 0.00426595i
\(213\) 5.22567e13 + 3.01704e13i 0.559583 + 0.323075i
\(214\) 7.55654e12 1.30883e13i 0.0786756 0.136270i
\(215\) −7.98349e13 + 4.60927e13i −0.808281 + 0.466661i
\(216\) 3.04285e13i 0.299612i
\(217\) 0 0
\(218\) −3.32881e13 −0.310134
\(219\) −1.06009e14 1.83614e14i −0.960904 1.66433i
\(220\) 4.88512e13 + 2.82042e13i 0.430863 + 0.248759i
\(221\) −1.14441e14 + 1.98218e14i −0.982268 + 1.70134i
\(222\) 1.23106e14 7.10753e13i 1.02840 0.593746i
\(223\) 1.05020e14i 0.853972i 0.904258 + 0.426986i \(0.140425\pi\)
−0.904258 + 0.426986i \(0.859575\pi\)
\(224\) 0 0
\(225\) 2.56874e13 0.197982
\(226\) 6.02724e13 + 1.04395e14i 0.452343 + 0.783481i
\(227\) −6.69859e13 3.86743e13i −0.489585 0.282662i 0.234817 0.972040i \(-0.424551\pi\)
−0.724402 + 0.689378i \(0.757884\pi\)
\(228\) 2.22847e13 3.85982e13i 0.158635 0.274763i
\(229\) 1.53002e14 8.83360e13i 1.06093 0.612526i 0.135238 0.990813i \(-0.456820\pi\)
0.925688 + 0.378287i \(0.123487\pi\)
\(230\) 1.19074e14i 0.804359i
\(231\) 0 0
\(232\) −6.97703e13 −0.447448
\(233\) −1.16414e14 2.01635e14i −0.727562 1.26017i −0.957911 0.287066i \(-0.907320\pi\)
0.230349 0.973108i \(-0.426013\pi\)
\(234\) 3.52672e13 + 2.03616e13i 0.214821 + 0.124027i
\(235\) −9.81366e13 + 1.69977e14i −0.582671 + 1.00922i
\(236\) 1.11662e14 6.44680e13i 0.646298 0.373140i
\(237\) 1.95749e14i 1.10461i
\(238\) 0 0
\(239\) 1.20020e14 0.643971 0.321986 0.946745i \(-0.395650\pi\)
0.321986 + 0.946745i \(0.395650\pi\)
\(240\) 3.59630e13 + 6.22897e13i 0.188186 + 0.325948i
\(241\) −4.44336e13 2.56537e13i −0.226782 0.130933i 0.382305 0.924036i \(-0.375131\pi\)
−0.609087 + 0.793104i \(0.708464\pi\)
\(242\) 3.25929e13 5.64526e13i 0.162267 0.281055i
\(243\) −8.33779e13 + 4.81383e13i −0.404961 + 0.233804i
\(244\) 9.92643e13i 0.470386i
\(245\) 0 0
\(246\) 9.39179e13 0.423777
\(247\) 9.52053e13 + 1.64900e14i 0.419256 + 0.726173i
\(248\) −8.77242e13 5.06476e13i −0.377059 0.217695i
\(249\) −8.51799e13 + 1.47536e14i −0.357389 + 0.619016i
\(250\) 3.43847e13 1.98520e13i 0.140840 0.0813138i
\(251\) 1.04293e14i 0.417073i −0.978015 0.208537i \(-0.933130\pi\)
0.978015 0.208537i \(-0.0668700\pi\)
\(252\) 0 0
\(253\) 1.62210e14 0.618522
\(254\) 6.09057e12 + 1.05492e13i 0.0226807 + 0.0392841i
\(255\) −4.78855e14 2.76467e14i −1.74166 1.00555i
\(256\) −8.79609e12 + 1.52353e13i −0.0312500 + 0.0541266i
\(257\) −2.30306e14 + 1.32967e14i −0.799295 + 0.461473i −0.843225 0.537561i \(-0.819346\pi\)
0.0439295 + 0.999035i \(0.486012\pi\)
\(258\) 1.60127e14i 0.542934i
\(259\) 0 0
\(260\) −3.07284e14 −0.994718
\(261\) −4.77150e13 8.26449e13i −0.150943 0.261440i
\(262\) 1.88421e14 + 1.08785e14i 0.582535 + 0.336327i
\(263\) 1.98352e14 3.43556e14i 0.599380 1.03816i −0.393533 0.919311i \(-0.628747\pi\)
0.992913 0.118846i \(-0.0379195\pi\)
\(264\) −8.48551e13 + 4.89911e13i −0.250642 + 0.144708i
\(265\) 4.61546e12i 0.0133272i
\(266\) 0 0
\(267\) 1.67735e13 0.0462975
\(268\) −1.12480e14 1.94821e14i −0.303576 0.525809i
\(269\) 5.98003e13 + 3.45257e13i 0.157830 + 0.0911232i 0.576835 0.816861i \(-0.304288\pi\)
−0.419005 + 0.907984i \(0.637621\pi\)
\(270\) 1.57024e14 2.71973e14i 0.405305 0.702010i
\(271\) 6.55851e14 3.78656e14i 1.65573 0.955936i 0.681078 0.732211i \(-0.261511\pi\)
0.974652 0.223726i \(-0.0718221\pi\)
\(272\) 1.35241e14i 0.333959i
\(273\) 0 0
\(274\) 4.60637e14 1.08857
\(275\) −1.32023e14 2.28671e14i −0.305249 0.528707i
\(276\) 1.79123e14 + 1.03416e14i 0.405225 + 0.233957i
\(277\) −1.16361e14 + 2.01543e14i −0.257590 + 0.446159i −0.965596 0.260047i \(-0.916262\pi\)
0.708006 + 0.706207i \(0.249595\pi\)
\(278\) −1.49532e13 + 8.63325e12i −0.0323941 + 0.0187028i
\(279\) 1.38549e14i 0.293750i
\(280\) 0 0
\(281\) −7.05866e14 −1.43379 −0.716893 0.697183i \(-0.754436\pi\)
−0.716893 + 0.697183i \(0.754436\pi\)
\(282\) −1.70464e14 2.95253e14i −0.338953 0.587083i
\(283\) −6.72043e14 3.88004e14i −1.30821 0.755297i −0.326414 0.945227i \(-0.605841\pi\)
−0.981798 + 0.189930i \(0.939174\pi\)
\(284\) 7.61604e13 1.31914e14i 0.145151 0.251409i
\(285\) −3.98365e14 + 2.29996e14i −0.743382 + 0.429192i
\(286\) 4.18602e14i 0.764901i
\(287\) 0 0
\(288\) −2.40622e13 −0.0421677
\(289\) 2.28522e14 + 3.95813e14i 0.392231 + 0.679364i
\(290\) 6.23613e14 + 3.60043e14i 1.04840 + 0.605294i
\(291\) 1.92648e14 3.33676e14i 0.317253 0.549499i
\(292\) −4.63504e14 + 2.67604e14i −0.747749 + 0.431713i
\(293\) 6.68824e14i 1.05708i 0.848910 + 0.528538i \(0.177260\pi\)
−0.848910 + 0.528538i \(0.822740\pi\)
\(294\) 0 0
\(295\) −1.33072e15 −2.01909
\(296\) −1.79418e14 3.10761e14i −0.266757 0.462037i
\(297\) 3.70499e14 + 2.13908e14i 0.539819 + 0.311665i
\(298\) 4.58665e14 7.94431e14i 0.654935 1.13438i
\(299\) −7.65253e14 + 4.41819e14i −1.07097 + 0.618325i
\(300\) 3.36684e14i 0.461844i
\(301\) 0 0
\(302\) −9.03459e14 −1.19088
\(303\) 4.67000e14 + 8.08867e14i 0.603477 + 1.04525i
\(304\) −9.74351e13 5.62542e13i −0.123445 0.0712711i
\(305\) −5.12244e14 + 8.87233e14i −0.636323 + 1.10214i
\(306\) 1.60196e14 9.24894e13i 0.195130 0.112658i
\(307\) 7.37934e14i 0.881429i 0.897647 + 0.440714i \(0.145275\pi\)
−0.897647 + 0.440714i \(0.854725\pi\)
\(308\) 0 0
\(309\) 7.69460e14 0.883965
\(310\) 5.22724e14 + 9.05385e14i 0.588983 + 1.02015i
\(311\) −4.21657e14 2.43444e14i −0.466012 0.269052i 0.248557 0.968617i \(-0.420044\pi\)
−0.714569 + 0.699565i \(0.753377\pi\)
\(312\) 2.66878e14 4.62247e14i 0.289325 0.501125i
\(313\) −2.88228e14 + 1.66408e14i −0.306528 + 0.176974i −0.645372 0.763869i \(-0.723297\pi\)
0.338844 + 0.940843i \(0.389964\pi\)
\(314\) 3.58152e14i 0.373671i
\(315\) 0 0
\(316\) 4.94138e14 0.496279
\(317\) 7.44042e14 + 1.28872e15i 0.733233 + 1.27000i 0.955494 + 0.295010i \(0.0953229\pi\)
−0.222261 + 0.974987i \(0.571344\pi\)
\(318\) −6.94302e12 4.00855e12i −0.00671407 0.00387637i
\(319\) −4.90474e14 + 8.49526e14i −0.465449 + 0.806181i
\(320\) 1.57240e14 9.07828e13i 0.146442 0.0845481i
\(321\) 2.70938e14i 0.247651i
\(322\) 0 0
\(323\) 8.64912e14 0.761653
\(324\) 3.41739e14 + 5.91909e14i 0.295409 + 0.511664i
\(325\) 1.24568e15 + 7.19195e14i 1.05708 + 0.610305i
\(326\) −5.55538e14 + 9.62221e14i −0.462816 + 0.801621i
\(327\) −5.16817e14 + 2.98384e14i −0.422717 + 0.244056i
\(328\) 2.37081e14i 0.190394i
\(329\) 0 0
\(330\) 1.01126e15 0.783028
\(331\) −1.12300e14 1.94510e14i −0.0853912 0.147902i 0.820167 0.572125i \(-0.193881\pi\)
−0.905558 + 0.424223i \(0.860547\pi\)
\(332\) 3.72431e14 + 2.15023e14i 0.278110 + 0.160567i
\(333\) 2.45404e14 4.25052e14i 0.179977 0.311728i
\(334\) 7.97974e14 4.60710e14i 0.574791 0.331856i
\(335\) 2.32177e15i 1.64267i
\(336\) 0 0
\(337\) 1.02994e15 0.703124 0.351562 0.936165i \(-0.385651\pi\)
0.351562 + 0.936165i \(0.385651\pi\)
\(338\) 6.12989e14 + 1.06173e15i 0.411105 + 0.712054i
\(339\) 1.87153e15 + 1.08053e15i 1.23310 + 0.711930i
\(340\) −6.97896e14 + 1.20879e15i −0.451770 + 0.782489i
\(341\) −1.23337e15 + 7.12089e14i −0.784456 + 0.452906i
\(342\) 1.53886e14i 0.0961707i
\(343\) 0 0
\(344\) −4.04216e14 −0.243929
\(345\) −1.06734e15 1.84869e15i −0.632979 1.09635i
\(346\) 8.54044e14 + 4.93083e14i 0.497764 + 0.287384i
\(347\) 4.36316e14 7.55722e14i 0.249934 0.432898i −0.713574 0.700580i \(-0.752925\pi\)
0.963507 + 0.267683i \(0.0862579\pi\)
\(348\) −1.08322e15 + 6.25399e14i −0.609877 + 0.352113i
\(349\) 2.50531e14i 0.138647i 0.997594 + 0.0693233i \(0.0220840\pi\)
−0.997594 + 0.0693233i \(0.977916\pi\)
\(350\) 0 0
\(351\) −2.33052e15 −1.24626
\(352\) 1.23670e14 + 2.14203e14i 0.0650144 + 0.112608i
\(353\) 2.45457e14 + 1.41714e14i 0.126861 + 0.0732430i 0.562087 0.827078i \(-0.309998\pi\)
−0.435227 + 0.900321i \(0.643332\pi\)
\(354\) 1.15574e15 2.00180e15i 0.587275 1.01719i
\(355\) −1.36146e15 + 7.86038e14i −0.680196 + 0.392711i
\(356\) 4.23422e13i 0.0208005i
\(357\) 0 0
\(358\) 4.79203e14 0.227626
\(359\) −2.96270e14 5.13154e14i −0.138395 0.239707i 0.788494 0.615042i \(-0.210861\pi\)
−0.926889 + 0.375335i \(0.877528\pi\)
\(360\) 2.15070e14 + 1.24171e14i 0.0988016 + 0.0570431i
\(361\) −7.46892e14 + 1.29365e15i −0.337454 + 0.584487i
\(362\) 2.09933e15 1.21205e15i 0.932888 0.538603i
\(363\) 1.16861e15i 0.510776i
\(364\) 0 0
\(365\) 5.52378e15 2.33603
\(366\) −8.89775e14 1.54113e15i −0.370163 0.641142i
\(367\) 4.05423e14 + 2.34071e14i 0.165925 + 0.0957969i 0.580663 0.814144i \(-0.302793\pi\)
−0.414738 + 0.909941i \(0.636127\pi\)
\(368\) 2.61059e14 4.52167e14i 0.105112 0.182059i
\(369\) 2.80829e14 1.62137e14i 0.111246 0.0642278i
\(370\) 3.70348e15i 1.44344i
\(371\) 0 0
\(372\) −1.81596e15 −0.685248
\(373\) 1.17094e15 + 2.02812e15i 0.434791 + 0.753081i 0.997279 0.0737253i \(-0.0234888\pi\)
−0.562487 + 0.826806i \(0.690155\pi\)
\(374\) −1.64669e15 9.50720e14i −0.601705 0.347394i
\(375\) 3.55895e14 6.16428e14i 0.127978 0.221664i
\(376\) −7.45320e14 + 4.30310e14i −0.263764 + 0.152284i
\(377\) 5.34370e15i 1.86120i
\(378\) 0 0
\(379\) −4.89878e15 −1.65292 −0.826461 0.562994i \(-0.809649\pi\)
−0.826461 + 0.562994i \(0.809649\pi\)
\(380\) 5.80589e14 + 1.00561e15i 0.192827 + 0.333986i
\(381\) 1.89119e14 + 1.09188e14i 0.0618281 + 0.0356965i
\(382\) −1.40925e15 + 2.44089e15i −0.453531 + 0.785539i
\(383\) 4.07029e15 2.34998e15i 1.28953 0.744513i 0.310963 0.950422i \(-0.399348\pi\)
0.978571 + 0.205909i \(0.0660150\pi\)
\(384\) 3.15382e14i 0.0983670i
\(385\) 0 0
\(386\) −1.79037e15 −0.541276
\(387\) −2.76438e14 4.78805e14i −0.0822872 0.142526i
\(388\) −8.42311e14 4.86309e14i −0.246878 0.142535i
\(389\) 1.04054e15 1.80226e15i 0.300303 0.520140i −0.675901 0.736992i \(-0.736246\pi\)
0.976205 + 0.216852i \(0.0695788\pi\)
\(390\) −4.77076e15 + 2.75440e15i −1.35581 + 0.782779i
\(391\) 4.01379e15i 1.12330i
\(392\) 0 0
\(393\) 3.90046e15 1.05867
\(394\) −6.76419e13 1.17159e14i −0.0180817 0.0313184i
\(395\) −4.41665e15 2.54995e15i −1.16281 0.671350i
\(396\) −1.69153e14 + 2.92982e14i −0.0438641 + 0.0759748i
\(397\) −5.98851e14 + 3.45747e14i −0.152959 + 0.0883110i −0.574526 0.818486i \(-0.694814\pi\)
0.421567 + 0.906797i \(0.361480\pi\)
\(398\) 2.69753e15i 0.678685i
\(399\) 0 0
\(400\) −8.49905e14 −0.207496
\(401\) 2.13958e15 + 3.70586e15i 0.514592 + 0.891299i 0.999857 + 0.0169316i \(0.00538977\pi\)
−0.485265 + 0.874367i \(0.661277\pi\)
\(402\) −3.49264e15 2.01648e15i −0.827556 0.477790i
\(403\) 3.87909e15 6.71878e15i 0.905524 1.56841i
\(404\) 2.04186e15 1.17887e15i 0.469610 0.271129i
\(405\) 7.05404e15i 1.59848i
\(406\) 0 0
\(407\) −5.04512e15 −1.10996
\(408\) −1.21226e15 2.09969e15i −0.262805 0.455191i
\(409\) 5.93554e13 + 3.42689e13i 0.0126800 + 0.00732082i 0.506327 0.862342i \(-0.331003\pi\)
−0.493647 + 0.869663i \(0.664336\pi\)
\(410\) −1.22343e15 + 2.11905e15i −0.257559 + 0.446106i
\(411\) 7.15166e15 4.12901e15i 1.48373 0.856633i
\(412\) 1.94238e15i 0.397147i
\(413\) 0 0
\(414\) 7.14139e14 0.141834
\(415\) −2.21921e15 3.84379e15i −0.434421 0.752439i
\(416\) −1.16687e15 6.73692e14i −0.225145 0.129987i
\(417\) −1.54772e14 + 2.68072e14i −0.0294357 + 0.0509842i
\(418\) −1.36991e15 + 7.90916e14i −0.256823 + 0.148277i
\(419\) 2.03797e15i 0.376628i 0.982109 + 0.188314i \(0.0603023\pi\)
−0.982109 + 0.188314i \(0.939698\pi\)
\(420\) 0 0
\(421\) −7.75234e15 −1.39232 −0.696162 0.717885i \(-0.745110\pi\)
−0.696162 + 0.717885i \(0.745110\pi\)
\(422\) −2.93400e15 5.08184e15i −0.519500 0.899801i
\(423\) −1.01943e15 5.88568e14i −0.177957 0.102744i
\(424\) −1.01190e13 + 1.75265e13i −0.00174157 + 0.00301649i
\(425\) 5.65833e15 3.26684e15i 0.960185 0.554363i
\(426\) 2.73071e15i 0.456897i
\(427\) 0 0
\(428\) −6.83940e14 −0.111264
\(429\) −3.75222e15 6.49904e15i −0.601928 1.04257i
\(430\) 3.61292e15 + 2.08592e15i 0.571541 + 0.329979i
\(431\) −3.20180e13 + 5.54569e13i −0.00499495 + 0.00865151i −0.868512 0.495668i \(-0.834923\pi\)
0.863517 + 0.504320i \(0.168257\pi\)
\(432\) 1.19255e15 6.88519e14i 0.183474 0.105929i
\(433\) 3.93012e14i 0.0596319i 0.999555 + 0.0298159i \(0.00949211\pi\)
−0.999555 + 0.0298159i \(0.990508\pi\)
\(434\) 0 0
\(435\) 1.29093e16 1.90531
\(436\) 7.53223e14 + 1.30462e15i 0.109649 + 0.189918i
\(437\) 2.89177e15 + 1.66956e15i 0.415217 + 0.239725i
\(438\) −4.79744e15 + 8.30941e15i −0.679461 + 1.17686i
\(439\) −6.94942e15 + 4.01225e15i −0.970871 + 0.560533i −0.899502 0.436917i \(-0.856070\pi\)
−0.0713694 + 0.997450i \(0.522737\pi\)
\(440\) 2.55276e15i 0.351798i
\(441\) 0 0
\(442\) 1.03581e16 1.38914
\(443\) −7.81118e14 1.35294e15i −0.103346 0.179001i 0.809715 0.586823i \(-0.199622\pi\)
−0.913061 + 0.407822i \(0.866288\pi\)
\(444\) −5.57114e15 3.21650e15i −0.727187 0.419842i
\(445\) −2.18503e14 + 3.78458e14i −0.0281382 + 0.0487369i
\(446\) 4.11593e15 2.37633e15i 0.522949 0.301925i
\(447\) 1.64453e16i 2.06157i
\(448\) 0 0
\(449\) −2.29552e15 −0.280158 −0.140079 0.990140i \(-0.544736\pi\)
−0.140079 + 0.990140i \(0.544736\pi\)
\(450\) −5.81240e14 1.00674e15i −0.0699971 0.121239i
\(451\) −2.88670e15 1.66664e15i −0.343039 0.198053i
\(452\) 2.72762e15 4.72437e15i 0.319855 0.554005i
\(453\) −1.40267e16 + 8.09833e15i −1.62318 + 0.937144i
\(454\) 3.50040e15i 0.399744i
\(455\) 0 0
\(456\) −2.01698e15 −0.224343
\(457\) −3.78307e15 6.55247e15i −0.415286 0.719296i 0.580173 0.814493i \(-0.302985\pi\)
−0.995458 + 0.0951976i \(0.969652\pi\)
\(458\) −6.92410e15 3.99763e15i −0.750188 0.433121i
\(459\) −5.29302e15 + 9.16777e15i −0.566014 + 0.980365i
\(460\) −4.66673e15 + 2.69434e15i −0.492567 + 0.284384i
\(461\) 3.83644e15i 0.399690i 0.979828 + 0.199845i \(0.0640439\pi\)
−0.979828 + 0.199845i \(0.935956\pi\)
\(462\) 0 0
\(463\) 4.62714e15 0.469707 0.234853 0.972031i \(-0.424539\pi\)
0.234853 + 0.972031i \(0.424539\pi\)
\(464\) 1.57872e15 + 2.73443e15i 0.158197 + 0.274005i
\(465\) 1.62312e16 + 9.37108e15i 1.60558 + 0.926983i
\(466\) −5.26830e15 + 9.12496e15i −0.514464 + 0.891078i
\(467\) 1.22742e16 7.08650e15i 1.18329 0.683173i 0.226517 0.974007i \(-0.427266\pi\)
0.956773 + 0.290834i \(0.0939328\pi\)
\(468\) 1.84292e15i 0.175400i
\(469\) 0 0
\(470\) 8.88231e15 0.824022
\(471\) 3.21037e15 + 5.56052e15i 0.294056 + 0.509319i
\(472\) −5.05324e15 2.91749e15i −0.457001 0.263850i
\(473\) −2.84157e15 + 4.92175e15i −0.253742 + 0.439494i
\(474\) 7.67177e15 4.42930e15i 0.676434 0.390539i
\(475\) 5.43545e15i 0.473232i
\(476\) 0 0
\(477\) −2.76809e13 −0.00235001
\(478\) −2.71575e15 4.70381e15i −0.227678 0.394350i
\(479\) −3.20508e15 1.85045e15i −0.265354 0.153202i 0.361421 0.932403i \(-0.382292\pi\)
−0.626774 + 0.779201i \(0.715625\pi\)
\(480\) 1.62750e15 2.81891e15i 0.133068 0.230480i
\(481\) 2.38012e16 1.37416e16i 1.92189 1.10960i
\(482\) 2.32191e15i 0.185167i
\(483\) 0 0
\(484\) −2.94997e15 −0.229481
\(485\) 5.01910e15 + 8.69334e15i 0.385634 + 0.667938i
\(486\) 3.77325e15 + 2.17849e15i 0.286351 + 0.165325i
\(487\) 8.57581e15 1.48537e16i 0.642838 1.11343i −0.341959 0.939715i \(-0.611090\pi\)
0.984796 0.173713i \(-0.0555764\pi\)
\(488\) −3.89035e15 + 2.24609e15i −0.288051 + 0.166306i
\(489\) 1.99187e16i 1.45683i
\(490\) 0 0
\(491\) −1.18747e16 −0.847487 −0.423744 0.905782i \(-0.639284\pi\)
−0.423744 + 0.905782i \(0.639284\pi\)
\(492\) −2.12512e15 3.68081e15i −0.149828 0.259510i
\(493\) −2.10210e16 1.21365e16i −1.46410 0.845301i
\(494\) 4.30850e15 7.46254e15i 0.296459 0.513482i
\(495\) 3.02381e15 1.74580e15i 0.205553 0.118676i
\(496\) 4.58410e15i 0.307867i
\(497\) 0 0
\(498\) 7.70960e15 0.505424
\(499\) 1.47725e15 + 2.55868e15i 0.0956868 + 0.165734i 0.909895 0.414839i \(-0.136162\pi\)
−0.814208 + 0.580573i \(0.802829\pi\)
\(500\) −1.55607e15 8.98399e14i −0.0995887 0.0574976i
\(501\) 8.25933e15 1.43056e16i 0.522298 0.904647i
\(502\) −4.08743e15 + 2.35988e15i −0.255404 + 0.147458i
\(503\) 3.88753e15i 0.240030i −0.992772 0.120015i \(-0.961706\pi\)
0.992772 0.120015i \(-0.0382943\pi\)
\(504\) 0 0
\(505\) −2.43337e16 −1.46710
\(506\) −3.67040e15 6.35732e15i −0.218681 0.378766i
\(507\) 1.90340e16 + 1.09893e16i 1.12068 + 0.647026i
\(508\) 2.75628e14 4.77402e14i 0.0160377 0.0277780i
\(509\) 2.28834e15 1.32117e15i 0.131587 0.0759719i −0.432761 0.901509i \(-0.642461\pi\)
0.564349 + 0.825537i \(0.309127\pi\)
\(510\) 2.50229e16i 1.42206i
\(511\) 0 0
\(512\) 7.96131e14 0.0441942
\(513\) 4.40333e15 + 7.62679e15i 0.241589 + 0.418444i
\(514\) 1.04225e16 + 6.01742e15i 0.565187 + 0.326311i
\(515\) −1.00235e16 + 1.73612e16i −0.537248 + 0.930541i
\(516\) −6.27568e15 + 3.62327e15i −0.332478 + 0.191956i
\(517\) 1.21001e16i 0.633642i
\(518\) 0 0
\(519\) 1.76794e16 0.904613
\(520\) 6.95305e15 + 1.20430e16i 0.351686 + 0.609138i
\(521\) 8.74947e15 + 5.05151e15i 0.437477 + 0.252578i 0.702527 0.711657i \(-0.252055\pi\)
−0.265050 + 0.964235i \(0.585388\pi\)
\(522\) −2.15934e15 + 3.74008e15i −0.106733 + 0.184866i
\(523\) −2.00319e16 + 1.15654e16i −0.978843 + 0.565135i −0.901921 0.431902i \(-0.857843\pi\)
−0.0769222 + 0.997037i \(0.524509\pi\)
\(524\) 9.84610e15i 0.475638i
\(525\) 0 0
\(526\) −1.79528e16 −0.847651
\(527\) −1.76202e16 3.05191e16i −0.822522 1.42465i
\(528\) 3.84010e15 + 2.21708e15i 0.177231 + 0.102324i
\(529\) 3.20938e15 5.55881e15i 0.146449 0.253657i
\(530\) 1.80888e14 1.04436e14i 0.00816122 0.00471188i
\(531\) 7.98093e15i 0.356030i
\(532\) 0 0
\(533\) 1.81580e16 0.791962
\(534\) −3.79542e14 6.57386e14i −0.0163686 0.0283513i
\(535\) 6.11311e15 + 3.52941e15i 0.260699 + 0.150515i
\(536\) −5.09027e15 + 8.81661e15i −0.214661 + 0.371803i
\(537\) 7.43989e15 4.29542e15i 0.310257 0.179127i
\(538\) 3.12491e15i 0.128868i
\(539\) 0 0
\(540\) −1.42122e16 −0.573188
\(541\) 1.20154e16 + 2.08113e16i 0.479243 + 0.830073i 0.999717 0.0238046i \(-0.00757796\pi\)
−0.520474 + 0.853878i \(0.674245\pi\)
\(542\) −2.96804e16 1.71360e16i −1.17078 0.675949i
\(543\) 2.17289e16 3.76355e16i 0.847692 1.46825i
\(544\) −5.30033e15 + 3.06015e15i −0.204508 + 0.118072i
\(545\) 1.55478e16i 0.593320i
\(546\) 0 0
\(547\) 2.61473e16 0.976119 0.488060 0.872810i \(-0.337705\pi\)
0.488060 + 0.872810i \(0.337705\pi\)
\(548\) −1.04230e16 1.80532e16i −0.384867 0.666609i
\(549\) −5.32112e15 3.07215e15i −0.194343 0.112204i
\(550\) −5.97470e15 + 1.03485e16i −0.215844 + 0.373853i
\(551\) −1.74876e16 + 1.00965e16i −0.624916 + 0.360795i
\(552\) 9.36019e15i 0.330865i
\(553\) 0 0
\(554\) 1.05318e16 0.364288
\(555\) 3.31969e16 + 5.74987e16i 1.13590 + 1.96743i
\(556\) 6.76706e14 + 3.90696e14i 0.0229061 + 0.0132248i
\(557\) 9.52588e15 1.64993e16i 0.318988 0.552503i −0.661289 0.750131i \(-0.729990\pi\)
0.980277 + 0.197628i \(0.0633238\pi\)
\(558\) −5.42999e15 + 3.13501e15i −0.179885 + 0.103856i
\(559\) 3.09588e16i 1.01464i
\(560\) 0 0
\(561\) −3.40878e16 −1.09351
\(562\) 1.59719e16 + 2.76642e16i 0.506920 + 0.878011i
\(563\) 1.49006e16 + 8.60286e15i 0.467900 + 0.270142i 0.715360 0.698756i \(-0.246263\pi\)
−0.247460 + 0.968898i \(0.579596\pi\)
\(564\) −7.71434e15 + 1.33616e16i −0.239676 + 0.415131i
\(565\) −4.87593e16 + 2.81512e16i −1.49888 + 0.865379i
\(566\) 3.51181e16i 1.06815i
\(567\) 0 0
\(568\) −6.89326e15 −0.205274
\(569\) −1.64180e16 2.84368e16i −0.483779 0.837930i 0.516048 0.856560i \(-0.327403\pi\)
−0.999826 + 0.0186304i \(0.994069\pi\)
\(570\) 1.80279e16 + 1.04084e16i 0.525651 + 0.303484i
\(571\) −2.21946e16 + 3.84422e16i −0.640369 + 1.10915i 0.344981 + 0.938610i \(0.387885\pi\)
−0.985350 + 0.170543i \(0.945448\pi\)
\(572\) −1.64058e16 + 9.47189e15i −0.468404 + 0.270433i
\(573\) 5.05282e16i 1.42760i
\(574\) 0 0
\(575\) 2.52243e16 0.697929
\(576\) 5.44464e14 + 9.43040e14i 0.0149085 + 0.0258223i
\(577\) 1.53625e16 + 8.86954e15i 0.416300 + 0.240351i 0.693493 0.720463i \(-0.256071\pi\)
−0.277193 + 0.960814i \(0.589404\pi\)
\(578\) 1.03417e16 1.79124e16i 0.277349 0.480383i
\(579\) −2.77965e16 + 1.60483e16i −0.737767 + 0.425950i
\(580\) 3.25874e16i 0.856015i
\(581\) 0 0
\(582\) −1.74365e16 −0.448664
\(583\) 1.42269e14 + 2.46418e14i 0.00362326 + 0.00627568i
\(584\) 2.09758e16 + 1.21104e16i 0.528739 + 0.305267i
\(585\) −9.51020e15 + 1.64722e16i −0.237276 + 0.410975i
\(586\) 2.62124e16 1.51338e16i 0.647324 0.373733i
\(587\) 1.42997e16i 0.349542i 0.984609 + 0.174771i \(0.0559185\pi\)
−0.984609 + 0.174771i \(0.944081\pi\)
\(588\) 0 0
\(589\) −2.93169e16 −0.702145
\(590\) 3.01108e16 + 5.21535e16i 0.713856 + 1.23644i
\(591\) −2.10036e15 1.21264e15i −0.0492911 0.0284582i
\(592\) −8.11954e15 + 1.40635e16i −0.188626 + 0.326710i
\(593\) −6.69933e15 + 3.86786e15i −0.154065 + 0.0889493i −0.575050 0.818118i \(-0.695018\pi\)
0.420986 + 0.907067i \(0.361684\pi\)
\(594\) 1.93607e16i 0.440761i
\(595\) 0 0
\(596\) −4.15136e16 −0.926218
\(597\) 2.41799e16 + 4.18807e16i 0.534082 + 0.925057i
\(598\) 3.46314e16 + 1.99944e16i 0.757291 + 0.437222i
\(599\) −1.42448e16 + 2.46727e16i −0.308387 + 0.534141i −0.978010 0.208560i \(-0.933122\pi\)
0.669623 + 0.742701i \(0.266456\pi\)
\(600\) −1.31953e16 + 7.61829e15i −0.282820 + 0.163286i
\(601\) 1.25771e16i 0.266892i 0.991056 + 0.133446i \(0.0426042\pi\)
−0.991056 + 0.133446i \(0.957396\pi\)
\(602\) 0 0
\(603\) −1.39247e16 −0.289656
\(604\) 2.04429e16 + 3.54082e16i 0.421039 + 0.729260i
\(605\) 2.63671e16 + 1.52231e16i 0.537688 + 0.310434i
\(606\) 2.11340e16 3.66051e16i 0.426723 0.739105i
\(607\) 3.41643e16 1.97248e16i 0.683030 0.394348i −0.117965 0.993018i \(-0.537637\pi\)
0.800996 + 0.598670i \(0.204304\pi\)
\(608\) 5.09155e15i 0.100793i
\(609\) 0 0
\(610\) 4.63630e16 0.899897
\(611\) −3.29574e16 5.70839e16i −0.633441 1.09715i
\(612\) −7.24966e15 4.18559e15i −0.137978 0.0796615i
\(613\) 1.23442e16 2.13807e16i 0.232648 0.402958i −0.725939 0.687759i \(-0.758594\pi\)
0.958586 + 0.284802i \(0.0919277\pi\)
\(614\) 2.89210e16 1.66975e16i 0.539763 0.311632i
\(615\) 4.38659e16i 0.810730i
\(616\) 0 0
\(617\) −4.97598e16 −0.901919 −0.450959 0.892545i \(-0.648918\pi\)
−0.450959 + 0.892545i \(0.648918\pi\)
\(618\) −1.74109e16 3.01566e16i −0.312529 0.541316i
\(619\) 1.68034e16 + 9.70147e15i 0.298713 + 0.172462i 0.641865 0.766818i \(-0.278161\pi\)
−0.343152 + 0.939280i \(0.611494\pi\)
\(620\) 2.36558e16 4.09730e16i 0.416474 0.721353i
\(621\) −3.53936e16 + 2.04345e16i −0.617128 + 0.356299i
\(622\) 2.20340e16i 0.380497i
\(623\) 0 0
\(624\) −2.41551e16 −0.409167
\(625\) 3.40077e16 + 5.89031e16i 0.570555 + 0.988230i
\(626\) 1.30437e16 + 7.53079e15i 0.216748 + 0.125139i
\(627\) −1.41791e16 + 2.45588e16i −0.233368 + 0.404206i
\(628\) 1.40366e16 8.10406e15i 0.228826 0.132113i
\(629\) 1.24839e17i 2.01579i
\(630\) 0 0
\(631\) 1.89698e16 0.300530 0.150265 0.988646i \(-0.451987\pi\)
0.150265 + 0.988646i \(0.451987\pi\)
\(632\) −1.11811e16 1.93662e16i −0.175461 0.303907i
\(633\) −9.11041e16 5.25990e16i −1.41617 0.817627i
\(634\) 3.36715e16 5.83208e16i 0.518474 0.898024i
\(635\) −4.92717e15 + 2.84470e15i −0.0751546 + 0.0433905i
\(636\) 3.62813e14i 0.00548201i
\(637\) 0 0
\(638\) 4.43926e16 0.658244
\(639\) −4.71421e15 8.16526e15i −0.0692475 0.119940i
\(640\) −7.11589e15 4.10836e15i −0.103550 0.0597845i
\(641\) −2.80509e16 + 4.85856e16i −0.404389 + 0.700422i −0.994250 0.107083i \(-0.965849\pi\)
0.589861 + 0.807505i \(0.299182\pi\)
\(642\) −1.06186e16 + 6.13063e15i −0.151655 + 0.0875578i
\(643\) 3.11805e15i 0.0441182i −0.999757 0.0220591i \(-0.992978\pi\)
0.999757 0.0220591i \(-0.00702220\pi\)
\(644\) 0 0
\(645\) 7.47901e16 1.03869
\(646\) −1.95707e16 3.38975e16i −0.269285 0.466415i
\(647\) −6.91898e16 3.99467e16i −0.943227 0.544572i −0.0522565 0.998634i \(-0.516641\pi\)
−0.890970 + 0.454061i \(0.849975\pi\)
\(648\) 1.54653e16 2.67867e16i 0.208886 0.361801i
\(649\) −7.10469e16 + 4.10189e16i −0.950773 + 0.548929i
\(650\) 6.50941e16i 0.863101i
\(651\) 0 0
\(652\) 5.02816e16 0.654521
\(653\) −6.87264e16 1.19038e17i −0.886430 1.53534i −0.844066 0.536240i \(-0.819844\pi\)
−0.0423648 0.999102i \(-0.513489\pi\)
\(654\) 2.33884e16 + 1.35033e16i 0.298906 + 0.172574i
\(655\) −5.08099e16 + 8.80053e16i −0.643429 + 1.11445i
\(656\) −9.29163e15 + 5.36453e15i −0.116592 + 0.0673144i
\(657\) 3.31285e16i 0.411917i
\(658\) 0 0
\(659\) −2.77636e15 −0.0338972 −0.0169486 0.999856i \(-0.505395\pi\)
−0.0169486 + 0.999856i \(0.505395\pi\)
\(660\) −2.28821e16 3.96330e16i −0.276842 0.479505i
\(661\) −1.34435e17 7.76164e16i −1.61178 0.930560i −0.988958 0.148195i \(-0.952654\pi\)
−0.622820 0.782365i \(-0.714013\pi\)
\(662\) −5.08213e15 + 8.80251e15i −0.0603807 + 0.104582i
\(663\) 1.60815e17 9.28465e16i 1.89341 1.09316i
\(664\) 1.94617e16i 0.227076i
\(665\) 0 0
\(666\) −2.22114e16 −0.254525
\(667\) −4.68547e16 8.11548e16i −0.532106 0.921635i
\(668\) −3.61122e16 2.08494e16i −0.406438 0.234657i
\(669\) 4.26015e16 7.37879e16i 0.475191 0.823054i
\(670\) 9.09946e16 5.25358e16i 1.00593 0.580773i
\(671\) 6.31587e16i 0.691988i
\(672\) 0 0
\(673\) 4.53293e15 0.0487852 0.0243926 0.999702i \(-0.492235\pi\)
0.0243926 + 0.999702i \(0.492235\pi\)
\(674\) −2.33048e16 4.03652e16i −0.248592 0.430574i
\(675\) 5.76139e16 + 3.32634e16i 0.609123 + 0.351677i
\(676\) 2.77407e16 4.80483e16i 0.290695 0.503498i
\(677\) 8.53907e16 4.93003e16i 0.886908 0.512057i 0.0139781 0.999902i \(-0.495550\pi\)
0.872930 + 0.487846i \(0.162217\pi\)
\(678\) 9.77981e16i 1.00682i
\(679\) 0 0
\(680\) 6.31664e16 0.638899
\(681\) 3.13765e16 + 5.43457e16i 0.314573 + 0.544857i
\(682\) 5.58161e16 + 3.22255e16i 0.554694 + 0.320253i
\(683\) −3.01263e16 + 5.21802e16i −0.296771 + 0.514022i −0.975395 0.220463i \(-0.929243\pi\)
0.678625 + 0.734485i \(0.262576\pi\)
\(684\) −6.03108e15 + 3.48205e15i −0.0588923 + 0.0340015i
\(685\) 2.15148e17i 2.08255i
\(686\) 0 0
\(687\) −1.43334e17 −1.36336
\(688\) 9.14636e15 + 1.58420e16i 0.0862418 + 0.149375i
\(689\) −1.34236e15 7.75010e14i −0.0125474 0.00724422i
\(690\) −4.83024e16 + 8.36622e16i −0.447584 + 0.775238i
\(691\) −1.24730e15 + 7.20129e14i −0.0114578 + 0.00661518i −0.505718 0.862699i \(-0.668772\pi\)
0.494260 + 0.869314i \(0.335439\pi\)
\(692\) 4.46288e16i 0.406423i
\(693\) 0 0
\(694\) −3.94909e16 −0.353460
\(695\) −4.03230e15 6.98415e15i −0.0357803 0.0619733i
\(696\) 4.90211e16 + 2.83023e16i 0.431248 + 0.248981i
\(697\) 4.12400e16 7.14298e16i 0.359685 0.622992i
\(698\) 9.81877e15 5.66887e15i 0.0849033 0.0490190i
\(699\) 1.88894e17i 1.61940i
\(700\) 0 0
\(701\) 1.76004e17 1.48325 0.741623 0.670817i \(-0.234056\pi\)
0.741623 + 0.670817i \(0.234056\pi\)
\(702\) 5.27336e16 + 9.13373e16i 0.440621 + 0.763177i
\(703\) −8.99409e16 5.19274e16i −0.745118 0.430194i
\(704\) 5.59668e15 9.69373e15i 0.0459721 0.0796260i
\(705\) 1.37903e17 7.96183e16i 1.12315 0.648452i
\(706\) 1.28265e16i 0.103581i
\(707\) 0 0
\(708\) −1.04606e17 −0.830532
\(709\) −7.39721e16 1.28123e17i −0.582358 1.00867i −0.995199 0.0978712i \(-0.968797\pi\)
0.412841 0.910803i \(-0.364537\pi\)
\(710\) 6.16125e16 + 3.55720e16i 0.480971 + 0.277689i
\(711\) 1.52932e16 2.64886e16i 0.118380 0.205041i
\(712\) −1.65947e15 + 9.58094e14i −0.0127376 + 0.00735407i
\(713\) 1.36051e17i 1.03553i
\(714\) 0 0
\(715\) 1.95515e17 1.46334
\(716\) −1.08431e16 1.87808e16i −0.0804778 0.139392i
\(717\) −8.43270e16 4.86862e16i −0.620657 0.358336i
\(718\) −1.34076e16 + 2.32227e16i −0.0978601 + 0.169499i
\(719\) 1.77523e16 1.02493e16i 0.128493 0.0741857i −0.434375 0.900732i \(-0.643031\pi\)
0.562869 + 0.826546i \(0.309698\pi\)
\(720\) 1.12386e16i 0.0806712i
\(721\) 0 0
\(722\) 6.76009e16 0.477232
\(723\) 2.08129e16 + 3.60490e16i 0.145714 + 0.252385i
\(724\) −9.50049e16 5.48511e16i −0.659651 0.380850i
\(725\) −7.62704e16 + 1.32104e17i −0.525204 + 0.909680i
\(726\) −4.58000e16 + 2.64427e16i −0.312785 + 0.180586i
\(727\) 9.52642e15i 0.0645243i −0.999479 0.0322621i \(-0.989729\pi\)
0.999479 0.0322621i \(-0.0102711\pi\)
\(728\) 0 0
\(729\) −9.92481e16 −0.661237
\(730\) −1.24989e17 2.16487e17i −0.825913 1.43052i
\(731\) −1.21786e17 7.03130e16i −0.798164 0.460820i
\(732\) −4.02666e16 + 6.97438e16i −0.261745 + 0.453356i
\(733\) −8.31903e16 + 4.80299e16i −0.536351 + 0.309662i −0.743599 0.668626i \(-0.766883\pi\)
0.207248 + 0.978288i \(0.433549\pi\)
\(734\) 2.11857e16i 0.135477i
\(735\) 0 0
\(736\) −2.36283e16 −0.148650
\(737\) 7.15676e16 + 1.23959e17i 0.446593 + 0.773521i
\(738\) −1.27089e16 7.33747e15i −0.0786626 0.0454159i
\(739\) −1.14442e17 + 1.98220e17i −0.702618 + 1.21697i 0.264926 + 0.964269i \(0.414653\pi\)
−0.967544 + 0.252702i \(0.918681\pi\)
\(740\) 1.45146e17 8.38003e16i 0.883926 0.510335i
\(741\) 1.54480e17i 0.933177i
\(742\) 0 0
\(743\) −1.73334e17 −1.03027 −0.515136 0.857109i \(-0.672258\pi\)
−0.515136 + 0.857109i \(0.672258\pi\)
\(744\) 4.10904e16 + 7.11707e16i 0.242272 + 0.419627i
\(745\) 3.71052e17 + 2.14227e17i 2.17019 + 1.25296i
\(746\) 5.29906e16 9.17824e16i 0.307444 0.532508i
\(747\) 2.30529e16 1.33096e16i 0.132679 0.0766022i
\(748\) 8.60493e16i 0.491290i
\(749\) 0 0
\(750\) −3.22119e16 −0.180988
\(751\) −5.91242e16 1.02406e17i −0.329553 0.570803i 0.652870 0.757470i \(-0.273565\pi\)
−0.982423 + 0.186667i \(0.940231\pi\)
\(752\) 3.37293e16 + 1.94736e16i 0.186509 + 0.107681i
\(753\) −4.23064e16 + 7.32769e16i −0.232079 + 0.401973i
\(754\) −2.09429e17 + 1.20914e17i −1.13975 + 0.658035i
\(755\) 4.21976e17i 2.27827i
\(756\) 0 0
\(757\) 2.23980e17 1.19024 0.595118 0.803638i \(-0.297105\pi\)
0.595118 + 0.803638i \(0.297105\pi\)
\(758\) 1.10847e17 + 1.91992e17i 0.584396 + 1.01220i
\(759\) −1.13970e17 6.58007e16i −0.596129 0.344175i
\(760\) 2.62745e16 4.55087e16i 0.136349 0.236163i
\(761\) −7.69944e16 + 4.44527e16i −0.396416 + 0.228871i −0.684936 0.728603i \(-0.740170\pi\)
0.288521 + 0.957474i \(0.406837\pi\)
\(762\) 9.88258e15i 0.0504824i
\(763\) 0 0
\(764\) 1.27550e17 0.641390
\(765\) 4.31987e16 + 7.48224e16i 0.215527 + 0.373304i
\(766\) −1.84200e17 1.06348e17i −0.911839 0.526450i
\(767\) 2.23450e17 3.87027e17i 1.09751 1.90094i
\(768\) 1.23604e16 7.13628e15i 0.0602372 0.0347780i
\(769\) 6.79519e16i 0.328582i −0.986412 0.164291i \(-0.947466\pi\)
0.986412 0.164291i \(-0.0525336\pi\)
\(770\) 0 0
\(771\) 2.15753e17 1.02714
\(772\) 4.05115e16 + 7.01679e16i 0.191370 + 0.331463i
\(773\) 1.75550e17 + 1.01354e17i 0.822856 + 0.475076i 0.851400 0.524516i \(-0.175754\pi\)
−0.0285441 + 0.999593i \(0.509087\pi\)
\(774\) −1.25102e16 + 2.16682e16i −0.0581859 + 0.100781i
\(775\) −1.91794e17 + 1.10732e17i −0.885166 + 0.511051i
\(776\) 4.40156e16i 0.201575i
\(777\) 0 0
\(778\) −9.41786e16 −0.424693
\(779\) −3.43081e16 5.94233e16i −0.153522 0.265908i
\(780\) 2.15900e17 + 1.24650e17i 0.958705 + 0.553509i
\(781\) −4.84585e16 + 8.39326e16i −0.213532 + 0.369849i
\(782\) 1.57308e17 9.08218e16i 0.687876 0.397145i
\(783\) 2.47151e17i 1.07248i
\(784\) 0 0
\(785\) −1.67281e17 −0.714873
\(786\) −8.82574e16 1.52866e17i −0.374297 0.648301i
\(787\) −5.94097e15 3.43002e15i −0.0250040 0.0144361i 0.487446 0.873153i \(-0.337929\pi\)
−0.512450 + 0.858717i \(0.671262\pi\)
\(788\) −3.06112e15 + 5.30202e15i −0.0127857 + 0.0221454i
\(789\) −2.78727e17 + 1.60923e17i −1.15536 + 0.667047i
\(790\) 2.30795e17i 0.949433i
\(791\) 0 0
\(792\) 1.53100e16 0.0620332
\(793\) −1.72028e17 2.97961e17i −0.691768 1.19818i
\(794\) 2.71009e16 + 1.56467e16i 0.108158 + 0.0624453i
\(795\) 1.87226e15 3.24285e15i 0.00741590 0.0128447i
\(796\) 1.05721e17 6.10382e16i 0.415608 0.239951i
\(797\) 3.49871e17i 1.36508i 0.730848 + 0.682540i \(0.239125\pi\)
−0.730848 + 0.682540i \(0.760875\pi\)
\(798\) 0 0
\(799\) −2.99408e17 −1.15076
\(800\) 1.92312e16 + 3.33093e16i 0.0733611 + 0.127065i
\(801\) −2.26978e15 1.31046e15i −0.00859386 0.00496167i
\(802\) 9.68264e16 1.67708e17i 0.363871 0.630243i
\(803\) 2.94913e17 1.70268e17i 1.10002 0.635096i
\(804\) 1.82511e17i 0.675697i
\(805\) 0 0
\(806\) −3.51095e17 −1.28060
\(807\) −2.80107e16 4.85160e16i −0.101411 0.175648i
\(808\) −9.24039e16 5.33494e16i −0.332064 0.191717i
\(809\) 2.06423e17 3.57535e17i 0.736320 1.27534i −0.217822 0.975989i \(-0.569895\pi\)
0.954142 0.299355i \(-0.0967714\pi\)
\(810\) −2.76461e17 + 1.59615e17i −0.978867 + 0.565149i
\(811\) 1.30953e17i 0.460246i −0.973162 0.230123i \(-0.926087\pi\)
0.973162 0.230123i \(-0.0739129\pi\)
\(812\) 0 0
\(813\) −6.14408e17 −2.12771
\(814\) 1.14158e17 + 1.97728e17i 0.392428 + 0.679706i
\(815\) −4.49421e17 2.59473e17i −1.53359 0.885416i
\(816\) −5.48604e16 + 9.50210e16i −0.185831 + 0.321869i
\(817\) −1.01315e17 + 5.84943e16i −0.340676 + 0.196689i
\(818\) 3.10166e15i 0.0103532i
\(819\) 0 0
\(820\) 1.10733e17 0.364244
\(821\) 2.28661e17 + 3.96053e17i 0.746679 + 1.29329i 0.949406 + 0.314050i \(0.101686\pi\)
−0.202728 + 0.979235i \(0.564981\pi\)
\(822\) −3.23647e17 1.86858e17i −1.04916 0.605731i
\(823\) −1.34881e17 + 2.33620e17i −0.434061 + 0.751816i −0.997218 0.0745339i \(-0.976253\pi\)
0.563157 + 0.826350i \(0.309586\pi\)
\(824\) −7.61254e16 + 4.39510e16i −0.243202 + 0.140413i
\(825\) 2.14221e17i 0.679421i
\(826\) 0 0
\(827\) 3.09486e17 0.967403 0.483702 0.875233i \(-0.339292\pi\)
0.483702 + 0.875233i \(0.339292\pi\)
\(828\) −1.61591e16 2.79884e16i −0.0501459 0.0868553i
\(829\) 3.48271e17 + 2.01074e17i 1.07298 + 0.619482i 0.928993 0.370098i \(-0.120676\pi\)
0.143982 + 0.989580i \(0.454009\pi\)
\(830\) −1.00430e17 + 1.73950e17i −0.307182 + 0.532054i
\(831\) 1.63512e17 9.44039e16i 0.496529 0.286671i
\(832\) 6.09756e16i 0.183830i
\(833\) 0 0
\(834\) 1.40083e16 0.0416284
\(835\) 2.15182e17 + 3.72707e17i 0.634875 + 1.09964i
\(836\) 6.19949e16 + 3.57928e16i 0.181601 + 0.104847i
\(837\) 1.79411e17 3.10750e17i 0.521792 0.903770i
\(838\) 7.98716e16 4.61139e16i 0.230637 0.133158i
\(839\) 6.07001e17i 1.74027i 0.492810 + 0.870137i \(0.335970\pi\)
−0.492810 + 0.870137i \(0.664030\pi\)
\(840\) 0 0
\(841\) 2.12882e17 0.601678
\(842\) 1.75415e17 + 3.03828e17i 0.492261 + 0.852620i
\(843\) 4.95947e17 + 2.86335e17i 1.38188 + 0.797827i
\(844\) −1.32778e17 + 2.29978e17i −0.367342 + 0.636255i
\(845\) −4.95898e17 + 2.86307e17i −1.36223 + 0.786487i
\(846\) 5.32711e16i 0.145301i
\(847\) 0 0
\(848\) 9.15863e14 0.00246295
\(849\) 3.14788e17 + 5.45229e17i 0.840566 + 1.45590i
\(850\) −2.56067e17 1.47840e17i −0.678953 0.391994i
\(851\) 2.40979e17 4.17388e17i 0.634457 1.09891i
\(852\) −1.07022e17 + 6.17890e16i −0.279791 + 0.161538i
\(853\) 9.20133e16i 0.238867i −0.992842 0.119434i \(-0.961892\pi\)
0.992842 0.119434i \(-0.0381078\pi\)
\(854\) 0 0
\(855\) 7.18751e16 0.183985
\(856\) 1.54758e16 + 2.68049e16i 0.0393378 + 0.0681351i
\(857\) 4.68450e17 + 2.70460e17i 1.18244 + 0.682681i 0.956577 0.291479i \(-0.0941473\pi\)
0.225860 + 0.974160i \(0.427481\pi\)
\(858\) −1.69806e17 + 2.94113e17i −0.425628 + 0.737209i
\(859\) 1.73078e16 9.99268e15i 0.0430808 0.0248727i −0.478305 0.878194i \(-0.658749\pi\)
0.521386 + 0.853321i \(0.325415\pi\)
\(860\) 1.88796e17i 0.466661i
\(861\) 0 0
\(862\) 2.89794e15 0.00706393
\(863\) −2.56860e17 4.44894e17i −0.621772 1.07694i −0.989156 0.146871i \(-0.953080\pi\)
0.367384 0.930069i \(-0.380254\pi\)
\(864\) −5.39687e16 3.11588e16i −0.129736 0.0749029i
\(865\) −2.30303e17 + 3.98896e17i −0.549797 + 0.952276i
\(866\) 1.54029e16 8.89285e15i 0.0365169 0.0210831i
\(867\) 3.70801e17i 0.873024i
\(868\) 0 0
\(869\) −3.14404e17 −0.730079
\(870\) −2.92103e17 5.05938e17i −0.673629 1.16676i
\(871\) −6.75263e17 3.89863e17i −1.54655 0.892901i
\(872\) 3.40870e16 5.90404e16i 0.0775336 0.134292i
\(873\) −5.21378e16 + 3.01017e16i −0.117779 + 0.0679996i
\(874\) 1.51112e17i 0.339023i
\(875\) 0 0
\(876\) 4.34215e17 0.960904
\(877\) 2.23428e17 + 3.86989e17i 0.491066 + 0.850551i 0.999947 0.0102854i \(-0.00327400\pi\)
−0.508881 + 0.860837i \(0.669941\pi\)
\(878\) 3.14495e17 + 1.81574e17i 0.686510 + 0.396356i
\(879\) 2.71309e17 4.69920e17i 0.588207 1.01880i
\(880\) −1.00047e17 + 5.77623e16i −0.215431 + 0.124379i
\(881\) 1.15011e17i 0.245971i 0.992408 + 0.122985i \(0.0392469\pi\)
−0.992408 + 0.122985i \(0.960753\pi\)
\(882\) 0 0
\(883\) 2.25816e16 0.0476421 0.0238210 0.999716i \(-0.492417\pi\)
0.0238210 + 0.999716i \(0.492417\pi\)
\(884\) −2.34376e17 4.05951e17i −0.491134 0.850669i
\(885\) 9.34976e17 + 5.39809e17i 1.94599 + 1.12352i
\(886\) −3.53494e16 + 6.12269e16i −0.0730767 + 0.126573i
\(887\) 3.28689e17 1.89769e17i 0.674907 0.389658i −0.123026 0.992403i \(-0.539260\pi\)
0.797933 + 0.602746i \(0.205927\pi\)
\(888\) 2.91124e17i 0.593746i
\(889\) 0 0
\(890\) 1.97766e16 0.0397935
\(891\) −2.17438e17 3.76613e17i −0.434579 0.752712i
\(892\) −1.86266e17 1.07541e17i −0.369781 0.213493i
\(893\) −1.24541e17 + 2.15711e17i −0.245586 + 0.425367i
\(894\) −6.44523e17 + 3.72115e17i −1.26245 + 0.728874i
\(895\) 2.23820e17i 0.435472i
\(896\) 0 0
\(897\) 7.16896e17 1.37626
\(898\) 5.19417e16 + 8.99656e16i 0.0990508 + 0.171561i
\(899\) 7.12525e17 + 4.11376e17i 1.34971 + 0.779258i
\(900\) −2.63039e16 + 4.55597e16i −0.0494954 + 0.0857286i
\(901\) −6.09746e15 + 3.52037e15i −0.0113972 + 0.00658020i
\(902\) 1.50847e17i 0.280090i
\(903\) 0 0
\(904\) −2.46876e17 −0.452343
\(905\) 5.66108e17 + 9.80527e17i 1.03040 + 1.78471i
\(906\) 6.34777e17 + 3.66489e17i 1.14776 + 0.662661i
\(907\) −2.02438e17 + 3.50632e17i −0.363620 + 0.629808i −0.988554 0.150870i \(-0.951793\pi\)
0.624934 + 0.780678i \(0.285126\pi\)
\(908\) 1.37187e17 7.92050e16i 0.244792 0.141331i
\(909\) 1.45940e17i 0.258697i
\(910\) 0 0
\(911\) 1.61744e17 0.282956 0.141478 0.989941i \(-0.454815\pi\)
0.141478 + 0.989941i \(0.454815\pi\)
\(912\) 4.56391e16 + 7.90492e16i 0.0793173 + 0.137382i
\(913\) −2.36966e17 1.36812e17i −0.409130 0.236211i
\(914\) −1.71202e17 + 2.96531e17i −0.293651 + 0.508619i
\(915\) 7.19813e17 4.15584e17i 1.22657 0.708161i
\(916\) 3.61824e17i 0.612526i
\(917\) 0 0
\(918\) 4.79069e17 0.800465
\(919\) −2.48909e17 4.31123e17i −0.413188 0.715662i 0.582049 0.813154i \(-0.302251\pi\)
−0.995236 + 0.0974921i \(0.968918\pi\)
\(920\) 2.11192e17 + 1.21932e17i 0.348298 + 0.201090i
\(921\) 2.99343e17 5.18478e17i 0.490469 0.849517i
\(922\) 1.50357e17 8.68088e16i 0.244759 0.141312i
\(923\) 5.27954e17i 0.853858i
\(924\) 0 0
\(925\) −7.84535e17 −1.25245
\(926\) −1.04700e17 1.81346e17i −0.166066 0.287636i
\(927\) −1.04122e17 6.01151e16i −0.164084 0.0947339i
\(928\) 7.14448e16 1.23746e17i 0.111862 0.193751i
\(929\) −2.35012e17 + 1.35684e17i −0.365591 + 0.211074i −0.671531 0.740977i \(-0.734363\pi\)
0.305939 + 0.952051i \(0.401030\pi\)
\(930\) 8.48173e17i 1.31095i
\(931\) 0 0
\(932\) 4.76832e17 0.727562
\(933\) 1.97506e17 + 3.42091e17i 0.299427 + 0.518623i
\(934\) −5.55466e17 3.20699e17i −0.836713 0.483076i
\(935\) 4.44050e17 7.69116e17i 0.664602 1.15112i
\(936\) −7.22273e16 + 4.17005e16i −0.107410 + 0.0620134i
\(937\) 1.19374e18i 1.76389i 0.471356 + 0.881943i \(0.343765\pi\)
−0.471356 + 0.881943i \(0.656235\pi\)
\(938\) 0 0
\(939\) 2.70015e17 0.393907
\(940\) −2.00984e17 3.48114e17i −0.291336 0.504608i
\(941\) 2.05289e17 + 1.18523e17i 0.295684 + 0.170713i 0.640502 0.767956i \(-0.278726\pi\)
−0.344819 + 0.938669i \(0.612060\pi\)
\(942\) 1.45285e17 2.51640e17i 0.207929 0.360143i
\(943\) 2.75766e17 1.59213e17i 0.392166 0.226417i
\(944\) 2.64061e17i 0.373140i
\(945\) 0 0
\(946\) 2.57190e17 0.358845
\(947\) −1.20199e17 2.08191e17i −0.166648 0.288643i 0.770591 0.637330i \(-0.219961\pi\)
−0.937239 + 0.348687i \(0.886628\pi\)
\(948\) −3.47185e17 2.00447e17i −0.478311 0.276153i
\(949\) −9.27532e17 + 1.60653e18i −1.26979 + 2.19934i
\(950\) −2.13025e17 + 1.22990e17i −0.289794 + 0.167313i
\(951\) 1.20728e18i 1.63202i
\(952\) 0 0
\(953\) 1.51022e17 0.201596 0.100798 0.994907i \(-0.467860\pi\)
0.100798 + 0.994907i \(0.467860\pi\)
\(954\) 6.26348e14 + 1.08487e15i 0.000830855 + 0.00143908i
\(955\) −1.14006e18 6.58212e17i −1.50282 0.867652i
\(956\) −1.22901e17 + 2.12870e17i −0.160993 + 0.278848i
\(957\) 6.89221e17 3.97922e17i 0.897195 0.517996i
\(958\) 1.67484e17i 0.216660i
\(959\) 0 0
\(960\) −1.47304e17 −0.188186
\(961\) 2.03421e17 + 3.52335e17i 0.258259 + 0.447317i
\(962\) −1.07712e18 6.21875e17i −1.35898 0.784607i
\(963\) −2.11674e16 + 3.66630e16i −0.0265406 + 0.0459696i
\(964\) 9.09999e16 5.25388e16i 0.113391 0.0654664i
\(965\) 8.36223e17i 1.03552i
\(966\) 0 0
\(967\) −1.07464e18 −1.31433 −0.657166 0.753746i \(-0.728245\pi\)
−0.657166 + 0.753746i \(0.728245\pi\)
\(968\) 6.67503e16 + 1.15615e17i 0.0811336 + 0.140528i
\(969\) −6.07694e17 3.50852e17i −0.734078 0.423820i
\(970\) 2.27139e17 3.93416e17i 0.272685 0.472303i
\(971\) −1.29510e18 + 7.47725e17i −1.54521 + 0.892127i −0.546712 + 0.837320i \(0.684121\pi\)
−0.998497 + 0.0548066i \(0.982546\pi\)
\(972\) 1.97174e17i 0.233804i
\(973\) 0 0
\(974\) −7.76194e17 −0.909110
\(975\) −5.83484e17 1.01062e18i −0.679205 1.17642i
\(976\) 1.76057e17 + 1.01647e17i 0.203683 + 0.117596i
\(977\) −4.73033e16 + 8.19317e16i −0.0543906 + 0.0942073i −0.891939 0.452156i \(-0.850655\pi\)
0.837548 + 0.546364i \(0.183988\pi\)
\(978\) 7.80650e17 4.50709e17i 0.892120 0.515066i
\(979\) 2.69410e16i 0.0305997i
\(980\) 0 0
\(981\) 9.32467e16 0.104621
\(982\) 2.68693e17 + 4.65391e17i 0.299632 + 0.518978i
\(983\) 1.78182e17 + 1.02873e17i 0.197488 + 0.114020i 0.595483 0.803368i \(-0.296961\pi\)
−0.397995 + 0.917388i \(0.630294\pi\)
\(984\) −9.61719e16 + 1.66575e17i −0.105944 + 0.183501i
\(985\) 5.47212e16 3.15933e16i 0.0599153 0.0345921i
\(986\) 1.09847e18i 1.19544i
\(987\) 0 0
\(988\) −3.89961e17 −0.419256
\(989\) −2.71454e17 4.70172e17i −0.290081 0.502434i
\(990\) −1.36842e17 7.90058e16i −0.145348 0.0839166i
\(991\) −4.00321e16 + 6.93377e16i −0.0422636 + 0.0732027i −0.886383 0.462952i \(-0.846790\pi\)
0.844120 + 0.536155i \(0.180124\pi\)
\(992\) 1.79659e17 1.03726e17i 0.188529 0.108848i
\(993\) 1.82219e17i 0.190063i
\(994\) 0 0
\(995\) −1.25993e18 −1.29840
\(996\) −1.74448e17 3.02153e17i −0.178694 0.309508i
\(997\) −9.46237e17 5.46310e17i −0.963449 0.556248i −0.0662163 0.997805i \(-0.521093\pi\)
−0.897233 + 0.441558i \(0.854426\pi\)
\(998\) 6.68529e16 1.15793e17i 0.0676608 0.117192i
\(999\) 1.10083e18 6.35562e17i 1.10745 0.639388i
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 98.13.d.a.31.2 16
7.2 even 3 14.13.d.a.5.3 yes 16
7.3 odd 6 98.13.b.c.97.11 16
7.4 even 3 98.13.b.c.97.14 16
7.5 odd 6 inner 98.13.d.a.19.2 16
7.6 odd 2 14.13.d.a.3.3 16
21.2 odd 6 126.13.n.a.19.8 16
21.20 even 2 126.13.n.a.73.8 16
28.23 odd 6 112.13.s.c.33.3 16
28.27 even 2 112.13.s.c.17.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.13.d.a.3.3 16 7.6 odd 2
14.13.d.a.5.3 yes 16 7.2 even 3
98.13.b.c.97.11 16 7.3 odd 6
98.13.b.c.97.14 16 7.4 even 3
98.13.d.a.19.2 16 7.5 odd 6 inner
98.13.d.a.31.2 16 1.1 even 1 trivial
112.13.s.c.17.3 16 28.27 even 2
112.13.s.c.33.3 16 28.23 odd 6
126.13.n.a.19.8 16 21.2 odd 6
126.13.n.a.73.8 16 21.20 even 2