Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,15,Mod(3,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.3");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.c (of order \(4\), 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: | \(12.4328968152\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} - 11690x^{3} + 819025x^{2} - 12217500x + 91125000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 5^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.3 | ||
Root | \(-23.8745 + 23.8745i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.3 |
Dual form | 10.15.c.a.7.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).
\(n\) | \(7\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −64.0000 | + | 64.0000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 1920.76 | + | 1920.76i | 0.878262 | + | 0.878262i | 0.993355 | − | 0.115093i | \(-0.0367165\pi\) |
−0.115093 | + | 0.993355i | \(0.536717\pi\) | |||||||
\(4\) | − | 8192.00i | − | 0.500000i | ||||||
\(5\) | −66391.4 | − | 41178.9i | −0.849809 | − | 0.527090i | ||||
\(6\) | −245857. | −0.878262 | ||||||||
\(7\) | −374464. | + | 374464.i | −0.454699 | + | 0.454699i | −0.896911 | − | 0.442212i | \(-0.854194\pi\) |
0.442212 | + | 0.896911i | \(0.354194\pi\) | |||||||
\(8\) | 524288. | + | 524288.i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.59566e6i | 0.542688i | ||||||||
\(10\) | 6.88450e6 | − | 1.61360e6i | 0.688450 | − | 0.161360i | ||||
\(11\) | −1.40802e7 | −0.722536 | −0.361268 | − | 0.932462i | \(-0.617656\pi\) | ||||
−0.361268 | + | 0.932462i | \(0.617656\pi\) | |||||||
\(12\) | 1.57349e7 | − | 1.57349e7i | 0.439131 | − | 0.439131i | ||||
\(13\) | −6.05534e7 | − | 6.05534e7i | −0.965017 | − | 0.965017i | 0.0343912 | − | 0.999408i | \(-0.489051\pi\) |
−0.999408 | + | 0.0343912i | \(0.989051\pi\) | |||||||
\(14\) | − | 4.79314e7i | − | 0.454699i | ||||||
\(15\) | −4.84270e7 | − | 2.06617e8i | −0.283432 | − | 1.20928i | ||||
\(16\) | −6.71089e7 | −0.250000 | ||||||||
\(17\) | 3.46706e8 | − | 3.46706e8i | 0.844928 | − | 0.844928i | −0.144567 | − | 0.989495i | \(-0.546179\pi\) |
0.989495 | + | 0.144567i | \(0.0461790\pi\) | |||||||
\(18\) | −1.66122e8 | − | 1.66122e8i | −0.271344 | − | 0.271344i | ||||
\(19\) | − | 1.12580e8i | − | 0.125946i | −0.998015 | − | 0.0629730i | \(-0.979942\pi\) | ||
0.998015 | − | 0.0629730i | \(-0.0200582\pi\) | |||||||
\(20\) | −3.37338e8 | + | 5.43878e8i | −0.263545 | + | 0.424905i | ||||
\(21\) | −1.43851e9 | −0.798689 | ||||||||
\(22\) | 9.01132e8 | − | 9.01132e8i | 0.361268 | − | 0.361268i | ||||
\(23\) | −3.26997e9 | − | 3.26997e9i | −0.960394 | − | 0.960394i | 0.0388509 | − | 0.999245i | \(-0.487630\pi\) |
−0.999245 | + | 0.0388509i | \(0.987630\pi\) | |||||||
\(24\) | 2.01406e9i | 0.439131i | ||||||||
\(25\) | 2.71211e9 | + | 5.46785e9i | 0.444352 | + | 0.895852i | ||||
\(26\) | 7.75084e9 | 0.965017 | ||||||||
\(27\) | 4.20129e9 | − | 4.20129e9i | 0.401640 | − | 0.401640i | ||||
\(28\) | 3.06761e9 | + | 3.06761e9i | 0.227349 | + | 0.227349i | ||||
\(29\) | 2.41211e10i | 1.39834i | 0.714958 | + | 0.699168i | \(0.246446\pi\) | ||||
−0.714958 | + | 0.699168i | \(0.753554\pi\) | |||||||
\(30\) | 1.63228e10 | + | 1.01241e10i | 0.746355 | + | 0.462923i | ||||
\(31\) | −3.63836e10 | −1.32243 | −0.661216 | − | 0.750196i | \(-0.729959\pi\) | ||||
−0.661216 | + | 0.750196i | \(0.729959\pi\) | |||||||
\(32\) | 4.29497e9 | − | 4.29497e9i | 0.125000 | − | 0.125000i | ||||
\(33\) | −2.70446e10 | − | 2.70446e10i | −0.634576 | − | 0.634576i | ||||
\(34\) | 4.43784e10i | 0.844928i | ||||||||
\(35\) | 4.02812e10 | − | 9.44115e9i | 0.626074 | − | 0.146740i | ||||
\(36\) | 2.12637e10 | 0.271344 | ||||||||
\(37\) | −4.43100e10 | + | 4.43100e10i | −0.466756 | + | 0.466756i | −0.900862 | − | 0.434106i | \(-0.857064\pi\) |
0.434106 | + | 0.900862i | \(0.357064\pi\) | |||||||
\(38\) | 7.20510e9 | + | 7.20510e9i | 0.0629730 | + | 0.0629730i | ||||
\(39\) | − | 2.32617e11i | − | 1.69508i | ||||||
\(40\) | −1.32186e10 | − | 5.63978e10i | −0.0806798 | − | 0.344225i | ||||
\(41\) | 2.75199e10 | 0.141306 | 0.0706528 | − | 0.997501i | \(-0.477492\pi\) | ||||
0.0706528 | + | 0.997501i | \(0.477492\pi\) | |||||||
\(42\) | 9.20646e10 | − | 9.20646e10i | 0.399345 | − | 0.399345i | ||||
\(43\) | −2.95811e11 | − | 2.95811e11i | −1.08827 | − | 1.08827i | −0.995707 | − | 0.0925605i | \(-0.970495\pi\) |
−0.0925605 | − | 0.995707i | \(-0.529505\pi\) | |||||||
\(44\) | 1.15345e11i | 0.361268i | ||||||||
\(45\) | 1.06886e11 | − | 1.72329e11i | 0.286046 | − | 0.461182i | ||||
\(46\) | 4.18557e11 | 0.960394 | ||||||||
\(47\) | −6.71176e11 | + | 6.71176e11i | −1.32480 | + | 1.32480i | −0.414965 | + | 0.909837i | \(0.636206\pi\) |
−0.909837 | + | 0.414965i | \(0.863794\pi\) | |||||||
\(48\) | −1.28900e11 | − | 1.28900e11i | −0.219565 | − | 0.219565i | ||||
\(49\) | 3.97777e11i | 0.586498i | ||||||||
\(50\) | −5.23517e11 | − | 1.76367e11i | −0.670102 | − | 0.225750i | ||||
\(51\) | 1.33188e12 | 1.48414 | ||||||||
\(52\) | −4.96053e11 | + | 4.96053e11i | −0.482509 | + | 0.482509i | ||||
\(53\) | 1.28292e12 | + | 1.28292e12i | 1.09211 | + | 1.09211i | 0.995303 | + | 0.0968099i | \(0.0308639\pi\) |
0.0968099 | + | 0.995303i | \(0.469136\pi\) | |||||||
\(54\) | 5.37765e11i | 0.401640i | ||||||||
\(55\) | 9.34802e11 | + | 5.79807e11i | 0.614018 | + | 0.380842i | ||||
\(56\) | −3.92654e11 | −0.227349 | ||||||||
\(57\) | 2.16238e11 | − | 2.16238e11i | 0.110614 | − | 0.110614i | ||||
\(58\) | −1.54375e12 | − | 1.54375e12i | −0.699168 | − | 0.699168i | ||||
\(59\) | − | 2.16199e12i | − | 0.868740i | −0.900735 | − | 0.434370i | \(-0.856971\pi\) | ||
0.900735 | − | 0.434370i | \(-0.143029\pi\) | |||||||
\(60\) | −1.69260e12 | + | 3.96714e11i | −0.604639 | + | 0.141716i | ||||
\(61\) | −1.39049e12 | −0.442445 | −0.221222 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221222 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(62\) | 2.32855e12 | − | 2.32855e12i | 0.661216 | − | 0.661216i | ||||
\(63\) | −9.71981e11 | − | 9.71981e11i | −0.246760 | − | 0.246760i | ||||
\(64\) | 5.49756e11i | 0.125000i | ||||||||
\(65\) | 1.52670e12 | + | 6.51375e12i | 0.311430 | + | 1.32873i | ||||
\(66\) | 3.46171e12 | 0.634576 | ||||||||
\(67\) | −7.20951e11 | + | 7.20951e11i | −0.118955 | + | 0.118955i | −0.764078 | − | 0.645123i | \(-0.776806\pi\) |
0.645123 | + | 0.764078i | \(0.276806\pi\) | |||||||
\(68\) | −2.84022e12 | − | 2.84022e12i | −0.422464 | − | 0.422464i | ||||
\(69\) | − | 1.25617e13i | − | 1.68696i | ||||||
\(70\) | −1.97376e12 | + | 3.18223e12i | −0.239667 | + | 0.386407i | ||||
\(71\) | 1.94287e12 | 0.213617 | 0.106808 | − | 0.994280i | \(-0.465937\pi\) | ||||
0.106808 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(72\) | −1.36087e12 | + | 1.36087e12i | −0.135672 | + | 0.135672i | ||||
\(73\) | −1.11254e13 | − | 1.11254e13i | −1.00706 | − | 1.00706i | −0.999975 | − | 0.00708939i | \(-0.997743\pi\) |
−0.00708939 | − | 0.999975i | \(-0.502257\pi\) | |||||||
\(74\) | − | 5.67168e12i | − | 0.466756i | ||||||
\(75\) | −5.29311e12 | + | 1.57117e13i | −0.396535 | + | 1.17705i | ||||
\(76\) | −9.22252e11 | −0.0629730 | ||||||||
\(77\) | 5.27252e12 | − | 5.27252e12i | 0.328536 | − | 0.328536i | ||||
\(78\) | 1.48875e13 | + | 1.48875e13i | 0.847538 | + | 0.847538i | ||||
\(79\) | 8.16132e11i | 0.0424982i | 0.999774 | + | 0.0212491i | \(0.00676431\pi\) | ||||
−0.999774 | + | 0.0212491i | \(0.993236\pi\) | |||||||
\(80\) | 4.45545e12 | + | 2.76347e12i | 0.212452 | + | 0.131773i | ||||
\(81\) | 2.85543e13 | 1.24818 | ||||||||
\(82\) | −1.76127e12 | + | 1.76127e12i | −0.0706528 | + | 0.0706528i | ||||
\(83\) | 8.01848e12 | + | 8.01848e12i | 0.295492 | + | 0.295492i | 0.839245 | − | 0.543753i | \(-0.182997\pi\) |
−0.543753 | + | 0.839245i | \(0.682997\pi\) | |||||||
\(84\) | 1.17843e13i | 0.399345i | ||||||||
\(85\) | −3.72953e13 | + | 8.74132e12i | −1.16338 | + | 0.272674i | ||||
\(86\) | 3.78639e13 | 1.08827 | ||||||||
\(87\) | −4.63308e13 | + | 4.63308e13i | −1.22810 | + | 1.22810i | ||||
\(88\) | −7.38207e12 | − | 7.38207e12i | −0.180634 | − | 0.180634i | ||||
\(89\) | − | 1.63791e13i | − | 0.370306i | −0.982710 | − | 0.185153i | \(-0.940722\pi\) | ||
0.982710 | − | 0.185153i | \(-0.0592780\pi\) | |||||||
\(90\) | 4.18835e12 | + | 1.78698e13i | 0.0875680 | + | 0.373614i | ||||
\(91\) | 4.53501e13 | 0.877584 | ||||||||
\(92\) | −2.67876e13 | + | 2.67876e13i | −0.480197 | + | 0.480197i | ||||
\(93\) | −6.98840e13 | − | 6.98840e13i | −1.16144 | − | 1.16144i | ||||
\(94\) | − | 8.59105e13i | − | 1.32480i | ||||||
\(95\) | −4.63591e12 | + | 7.47431e12i | −0.0663849 | + | 0.107030i | ||||
\(96\) | 1.64992e13 | 0.219565 | ||||||||
\(97\) | 3.07603e13 | − | 3.07603e13i | 0.380705 | − | 0.380705i | −0.490651 | − | 0.871356i | \(-0.663241\pi\) |
0.871356 | + | 0.490651i | \(0.163241\pi\) | |||||||
\(98\) | −2.54577e13 | − | 2.54577e13i | −0.293249 | − | 0.293249i | ||||
\(99\) | − | 3.65474e13i | − | 0.392112i | ||||||
\(100\) | 4.47926e13 | − | 2.22176e13i | 0.447926 | − | 0.222176i | ||||
\(101\) | 1.72852e14 | 1.61222 | 0.806110 | − | 0.591766i | \(-0.201569\pi\) | ||||
0.806110 | + | 0.591766i | \(0.201569\pi\) | |||||||
\(102\) | −8.52403e13 | + | 8.52403e13i | −0.742068 | + | 0.742068i | ||||
\(103\) | −8.23106e13 | − | 8.23106e13i | −0.669261 | − | 0.669261i | 0.288284 | − | 0.957545i | \(-0.406915\pi\) |
−0.957545 | + | 0.288284i | \(0.906915\pi\) | |||||||
\(104\) | − | 6.34948e13i | − | 0.482509i | ||||||
\(105\) | 9.55046e13 | + | 5.92363e13i | 0.678734 | + | 0.420981i | ||||
\(106\) | −1.64213e14 | −1.09211 | ||||||||
\(107\) | 5.29055e13 | − | 5.29055e13i | 0.329469 | − | 0.329469i | −0.522915 | − | 0.852385i | \(-0.675156\pi\) |
0.852385 | + | 0.522915i | \(0.175156\pi\) | |||||||
\(108\) | −3.44170e13 | − | 3.44170e13i | −0.200820 | − | 0.200820i | ||||
\(109\) | 2.43921e14i | 1.33433i | 0.744909 | + | 0.667166i | \(0.232493\pi\) | ||||
−0.744909 | + | 0.667166i | \(0.767507\pi\) | |||||||
\(110\) | −9.69350e13 | + | 2.27197e13i | −0.497430 | + | 0.116588i | ||||
\(111\) | −1.70218e14 | −0.819868 | ||||||||
\(112\) | 2.51299e13 | − | 2.51299e13i | 0.113675 | − | 0.113675i | ||||
\(113\) | 5.60583e13 | + | 5.60583e13i | 0.238282 | + | 0.238282i | 0.816138 | − | 0.577857i | \(-0.196111\pi\) |
−0.577857 | + | 0.816138i | \(0.696111\pi\) | |||||||
\(114\) | 2.76785e13i | 0.110614i | ||||||||
\(115\) | 8.24440e13 | + | 3.51752e14i | 0.309938 | + | 1.32237i | ||||
\(116\) | 1.97600e14 | 0.699168 | ||||||||
\(117\) | 1.57176e14 | − | 1.57176e14i | 0.523703 | − | 0.523703i | ||||
\(118\) | 1.38367e14 | + | 1.38367e14i | 0.434370 | + | 0.434370i | ||||
\(119\) | 2.59658e14i | 0.768375i | ||||||||
\(120\) | 8.29369e13 | − | 1.33716e14i | 0.231462 | − | 0.373178i | ||||
\(121\) | −1.81498e14 | −0.477942 | ||||||||
\(122\) | 8.89914e13 | − | 8.89914e13i | 0.221222 | − | 0.221222i | ||||
\(123\) | 5.28590e13 | + | 5.28590e13i | 0.124103 | + | 0.124103i | ||||
\(124\) | 2.98054e14i | 0.661216i | ||||||||
\(125\) | 4.50994e13 | − | 4.74700e14i | 0.0945803 | − | 0.995517i | ||||
\(126\) | 1.24414e14 | 0.246760 | ||||||||
\(127\) | −2.21935e14 | + | 2.21935e14i | −0.416485 | + | 0.416485i | −0.883990 | − | 0.467505i | \(-0.845153\pi\) |
0.467505 | + | 0.883990i | \(0.345153\pi\) | |||||||
\(128\) | −3.51844e13 | − | 3.51844e13i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 1.13636e15i | − | 1.91157i | ||||||
\(130\) | −5.14589e14 | − | 3.19171e14i | −0.820081 | − | 0.508651i | ||||
\(131\) | −4.64148e14 | −0.701064 | −0.350532 | − | 0.936551i | \(-0.613999\pi\) | ||||
−0.350532 | + | 0.936551i | \(0.613999\pi\) | |||||||
\(132\) | −2.21550e14 | + | 2.21550e14i | −0.317288 | + | 0.317288i | ||||
\(133\) | 4.21570e13 | + | 4.21570e13i | 0.0572675 | + | 0.0572675i | ||||
\(134\) | − | 9.22818e13i | − | 0.118955i | ||||||
\(135\) | −4.51934e14 | + | 1.05925e14i | −0.553017 | + | 0.129617i | ||||
\(136\) | 3.63548e14 | 0.422464 | ||||||||
\(137\) | 1.03604e15 | − | 1.03604e15i | 1.14375 | − | 1.14375i | 0.155992 | − | 0.987758i | \(-0.450143\pi\) |
0.987758 | − | 0.155992i | \(-0.0498573\pi\) | |||||||
\(138\) | 8.03947e14 | + | 8.03947e14i | 0.843478 | + | 0.843478i | ||||
\(139\) | 6.68729e14i | 0.667032i | 0.942744 | + | 0.333516i | \(0.108235\pi\) | ||||
−0.942744 | + | 0.333516i | \(0.891765\pi\) | |||||||
\(140\) | −7.73419e13 | − | 3.29984e14i | −0.0733700 | − | 0.313037i | ||||
\(141\) | −2.57833e15 | −2.32705 | ||||||||
\(142\) | −1.24344e14 | + | 1.24344e14i | −0.106808 | + | 0.106808i | ||||
\(143\) | 8.52603e14 | + | 8.52603e14i | 0.697260 | + | 0.697260i | ||||
\(144\) | − | 1.74192e14i | − | 0.135672i | ||||||
\(145\) | 9.93281e14 | − | 1.60143e15i | 0.737049 | − | 1.18832i | ||||
\(146\) | 1.42406e15 | 1.00706 | ||||||||
\(147\) | −7.64033e14 | + | 7.64033e14i | −0.515099 | + | 0.515099i | ||||
\(148\) | 3.62987e14 | + | 3.62987e14i | 0.233378 | + | 0.233378i | ||||
\(149\) | 1.29856e14i | 0.0796447i | 0.999207 | + | 0.0398223i | \(0.0126792\pi\) | ||||
−0.999207 | + | 0.0398223i | \(0.987321\pi\) | |||||||
\(150\) | −6.66792e14 | − | 1.34431e15i | −0.390258 | − | 0.786793i | ||||
\(151\) | −1.78301e15 | −0.996128 | −0.498064 | − | 0.867140i | \(-0.665955\pi\) | ||||
−0.498064 | + | 0.867140i | \(0.665955\pi\) | |||||||
\(152\) | 5.90242e13 | − | 5.90242e13i | 0.0314865 | − | 0.0314865i | ||||
\(153\) | 8.99932e14 | + | 8.99932e14i | 0.458532 | + | 0.458532i | ||||
\(154\) | 6.74883e14i | 0.328536i | ||||||||
\(155\) | 2.41555e15 | + | 1.49824e15i | 1.12382 | + | 0.697041i | ||||
\(156\) | −1.90560e15 | −0.847538 | ||||||||
\(157\) | 1.69865e15 | − | 1.69865e15i | 0.722448 | − | 0.722448i | −0.246655 | − | 0.969103i | \(-0.579332\pi\) |
0.969103 | + | 0.246655i | \(0.0793316\pi\) | |||||||
\(158\) | −5.22324e13 | − | 5.22324e13i | −0.0212491 | − | 0.0212491i | ||||
\(159\) | 4.92835e15i | 1.91832i | ||||||||
\(160\) | −4.62011e14 | + | 1.08287e14i | −0.172112 | + | 0.0403399i | ||||
\(161\) | 2.44897e15 | 0.873380 | ||||||||
\(162\) | −1.82748e15 | + | 1.82748e15i | −0.624089 | + | 0.624089i | ||||
\(163\) | −2.68393e15 | − | 2.68393e15i | −0.877926 | − | 0.877926i | 0.115393 | − | 0.993320i | \(-0.463187\pi\) |
−0.993320 | + | 0.115393i | \(0.963187\pi\) | |||||||
\(164\) | − | 2.25443e14i | − | 0.0706528i | ||||||
\(165\) | 6.81861e14 | + | 2.90920e15i | 0.204790 | + | 0.873747i | ||||
\(166\) | −1.02637e15 | −0.295492 | ||||||||
\(167\) | 3.63941e15 | − | 3.63941e15i | 1.00465 | − | 1.00465i | 0.00466162 | − | 0.999989i | \(-0.498516\pi\) |
0.999989 | − | 0.00466162i | \(-0.00148385\pi\) | |||||||
\(168\) | −7.54194e14 | − | 7.54194e14i | −0.199672 | − | 0.199672i | ||||
\(169\) | 3.39605e15i | 0.862517i | ||||||||
\(170\) | 1.82746e15 | − | 2.94634e15i | 0.445353 | − | 0.718027i | ||||
\(171\) | 2.92219e14 | 0.0683494 | ||||||||
\(172\) | −2.42329e15 | + | 2.42329e15i | −0.544134 | + | 0.544134i | ||||
\(173\) | −3.58641e15 | − | 3.58641e15i | −0.773281 | − | 0.773281i | 0.205398 | − | 0.978679i | \(-0.434151\pi\) |
−0.978679 | + | 0.205398i | \(0.934151\pi\) | |||||||
\(174\) | − | 5.93035e15i | − | 1.22810i | ||||||
\(175\) | −3.06310e15 | − | 1.03192e15i | −0.609389 | − | 0.205297i | ||||
\(176\) | 9.44905e14 | 0.180634 | ||||||||
\(177\) | 4.15266e15 | − | 4.15266e15i | 0.762981 | − | 0.762981i | ||||
\(178\) | 1.04826e15 | + | 1.04826e15i | 0.185153 | + | 0.185153i | ||||
\(179\) | − | 3.87998e15i | − | 0.658958i | −0.944163 | − | 0.329479i | \(-0.893127\pi\) | ||
0.944163 | − | 0.329479i | \(-0.106873\pi\) | |||||||
\(180\) | −1.41172e15 | − | 8.75614e14i | −0.230591 | − | 0.143023i | ||||
\(181\) | −7.20569e15 | −1.13221 | −0.566103 | − | 0.824335i | \(-0.691550\pi\) | ||||
−0.566103 | + | 0.824335i | \(0.691550\pi\) | |||||||
\(182\) | −2.90241e15 | + | 2.90241e15i | −0.438792 | + | 0.438792i | ||||
\(183\) | −2.67080e15 | − | 2.67080e15i | −0.388583 | − | 0.388583i | ||||
\(184\) | − | 3.42882e15i | − | 0.480197i | ||||||
\(185\) | 4.76644e15 | − | 1.11716e15i | 0.642676 | − | 0.150631i | ||||
\(186\) | 8.94516e15 | 1.16144 | ||||||||
\(187\) | −4.88169e15 | + | 4.88169e15i | −0.610491 | + | 0.610491i | ||||
\(188\) | 5.49827e15 | + | 5.49827e15i | 0.662401 | + | 0.662401i | ||||
\(189\) | 3.14646e15i | 0.365250i | ||||||||
\(190\) | −1.81658e14 | − | 7.75054e14i | −0.0203226 | − | 0.0867075i | ||||
\(191\) | 1.34097e16 | 1.44605 | 0.723026 | − | 0.690820i | \(-0.242751\pi\) | ||||
0.723026 | + | 0.690820i | \(0.242751\pi\) | |||||||
\(192\) | −1.05595e15 | + | 1.05595e15i | −0.109783 | + | 0.109783i | ||||
\(193\) | 3.17041e15 | + | 3.17041e15i | 0.317845 | + | 0.317845i | 0.847939 | − | 0.530094i | \(-0.177843\pi\) |
−0.530094 | + | 0.847939i | \(0.677843\pi\) | |||||||
\(194\) | 3.93732e15i | 0.380705i | ||||||||
\(195\) | −9.57891e15 | + | 1.54438e16i | −0.893458 | + | 1.44049i | ||||
\(196\) | 3.25859e15 | 0.293249 | ||||||||
\(197\) | −8.68419e15 | + | 8.68419e15i | −0.754164 | + | 0.754164i | −0.975253 | − | 0.221090i | \(-0.929039\pi\) |
0.221090 | + | 0.975253i | \(0.429039\pi\) | |||||||
\(198\) | 2.33903e15 | + | 2.33903e15i | 0.196056 | + | 0.196056i | ||||
\(199\) | − | 1.28217e16i | − | 1.03747i | −0.854936 | − | 0.518734i | \(-0.826404\pi\) | ||
0.854936 | − | 0.518734i | \(-0.173596\pi\) | |||||||
\(200\) | −1.44480e15 | + | 4.28865e15i | −0.112875 | + | 0.335051i | ||||
\(201\) | −2.76955e15 | −0.208947 | ||||||||
\(202\) | −1.10625e16 | + | 1.10625e16i | −0.806110 | + | 0.806110i | ||||
\(203\) | −9.03249e15 | − | 9.03249e15i | −0.635821 | − | 0.635821i | ||||
\(204\) | − | 1.09108e16i | − | 0.742068i | ||||||
\(205\) | −1.82708e15 | − | 1.13324e15i | −0.120083 | − | 0.0744808i | ||||
\(206\) | 1.05358e16 | 0.669261 | ||||||||
\(207\) | 8.48774e15 | − | 8.48774e15i | 0.521195 | − | 0.521195i | ||||
\(208\) | 4.06367e15 | + | 4.06367e15i | 0.241254 | + | 0.241254i | ||||
\(209\) | 1.58514e15i | 0.0910006i | ||||||||
\(210\) | −9.90342e15 | + | 2.32117e15i | −0.549857 | + | 0.128876i | ||||
\(211\) | 1.76128e16 | 0.945912 | 0.472956 | − | 0.881086i | \(-0.343187\pi\) | ||||
0.472956 | + | 0.881086i | \(0.343187\pi\) | |||||||
\(212\) | 1.05097e16 | − | 1.05097e16i | 0.546056 | − | 0.546056i | ||||
\(213\) | 3.73179e15 | + | 3.73179e15i | 0.187612 | + | 0.187612i | ||||
\(214\) | 6.77191e15i | 0.329469i | ||||||||
\(215\) | 7.45813e15 | + | 3.18205e16i | 0.351205 | + | 1.49844i | ||||
\(216\) | 4.40537e15 | 0.200820 | ||||||||
\(217\) | 1.36243e16 | − | 1.36243e16i | 0.601308 | − | 0.601308i | ||||
\(218\) | −1.56110e16 | − | 1.56110e16i | −0.667166 | − | 0.667166i | ||||
\(219\) | − | 4.27386e16i | − | 1.76893i | ||||||
\(220\) | 4.74978e15 | − | 7.65790e15i | 0.190421 | − | 0.307009i | ||||
\(221\) | −4.19885e16 | −1.63074 | ||||||||
\(222\) | 1.08939e16 | − | 1.08939e16i | 0.409934 | − | 0.409934i | ||||
\(223\) | −2.19749e16 | − | 2.19749e16i | −0.801297 | − | 0.801297i | 0.182002 | − | 0.983298i | \(-0.441742\pi\) |
−0.983298 | + | 0.182002i | \(0.941742\pi\) | |||||||
\(224\) | 3.21662e15i | 0.113675i | ||||||||
\(225\) | −1.41927e16 | + | 7.03972e15i | −0.486168 | + | 0.241145i | ||||
\(226\) | −7.17546e15 | −0.238282 | ||||||||
\(227\) | −7.99256e15 | + | 7.99256e15i | −0.257338 | + | 0.257338i | −0.823971 | − | 0.566632i | \(-0.808246\pi\) |
0.566632 | + | 0.823971i | \(0.308246\pi\) | |||||||
\(228\) | −1.77142e15 | − | 1.77142e15i | −0.0553068 | − | 0.0553068i | ||||
\(229\) | 3.55837e16i | 1.07746i | 0.842477 | + | 0.538732i | \(0.181096\pi\) | ||||
−0.842477 | + | 0.538732i | \(0.818904\pi\) | |||||||
\(230\) | −2.77885e16 | − | 1.72357e16i | −0.816152 | − | 0.506214i | ||||
\(231\) | 2.02545e16 | 0.577082 | ||||||||
\(232\) | −1.26464e16 | + | 1.26464e16i | −0.349584 | + | 0.349584i | ||||
\(233\) | 7.80283e15 | + | 7.80283e15i | 0.209296 | + | 0.209296i | 0.803968 | − | 0.594672i | \(-0.202718\pi\) |
−0.594672 | + | 0.803968i | \(0.702718\pi\) | |||||||
\(234\) | 2.01185e16i | 0.523703i | ||||||||
\(235\) | 7.21985e16 | − | 1.69220e16i | 1.82412 | − | 0.427539i | ||||
\(236\) | −1.77110e16 | −0.434370 | ||||||||
\(237\) | −1.56759e15 | + | 1.56759e15i | −0.0373246 | + | 0.0373246i | ||||
\(238\) | −1.66181e16 | − | 1.66181e16i | −0.384188 | − | 0.384188i | ||||
\(239\) | 1.50101e16i | 0.336975i | 0.985704 | + | 0.168487i | \(0.0538882\pi\) | ||||
−0.985704 | + | 0.168487i | \(0.946112\pi\) | |||||||
\(240\) | 3.24988e15 | + | 1.38658e16i | 0.0708580 | + | 0.302320i | ||||
\(241\) | 3.20749e16 | 0.679276 | 0.339638 | − | 0.940556i | \(-0.389695\pi\) | ||||
0.339638 | + | 0.940556i | \(0.389695\pi\) | |||||||
\(242\) | 1.16159e16 | − | 1.16159e16i | 0.238971 | − | 0.238971i | ||||
\(243\) | 3.47513e16 | + | 3.47513e16i | 0.694587 | + | 0.694587i | ||||
\(244\) | 1.13909e16i | 0.221222i | ||||||||
\(245\) | 1.63800e16 | − | 2.64089e16i | 0.309137 | − | 0.498412i | ||||
\(246\) | −6.76596e15 | −0.124103 | ||||||||
\(247\) | −6.81708e15 | + | 6.81708e15i | −0.121540 | + | 0.121540i | ||||
\(248\) | −1.90755e16 | − | 1.90755e16i | −0.330608 | − | 0.330608i | ||||
\(249\) | 3.08031e16i | 0.519039i | ||||||||
\(250\) | 2.74944e16 | + | 3.32671e16i | 0.450468 | + | 0.545049i | ||||
\(251\) | −8.14201e15 | −0.129723 | −0.0648613 | − | 0.997894i | \(-0.520660\pi\) | ||||
−0.0648613 | + | 0.997894i | \(0.520660\pi\) | |||||||
\(252\) | −7.96247e15 | + | 7.96247e15i | −0.123380 | + | 0.123380i | ||||
\(253\) | 4.60418e16 | + | 4.60418e16i | 0.693919 | + | 0.693919i | ||||
\(254\) | − | 2.84076e16i | − | 0.416485i | ||||||
\(255\) | −8.84253e16 | − | 5.48453e16i | −1.26123 | − | 0.782273i | ||||
\(256\) | 4.50360e15 | 0.0625000 | ||||||||
\(257\) | −9.79376e16 | + | 9.79376e16i | −1.32257 | + | 1.32257i | −0.410876 | + | 0.911691i | \(0.634777\pi\) |
−0.911691 | + | 0.410876i | \(0.865223\pi\) | |||||||
\(258\) | 7.27273e16 | + | 7.27273e16i | 0.955784 | + | 0.955784i | ||||
\(259\) | − | 3.31850e16i | − | 0.424466i | ||||||
\(260\) | 5.33606e16 | − | 1.25067e16i | 0.664366 | − | 0.155715i | ||||
\(261\) | −6.26102e16 | −0.758860 | ||||||||
\(262\) | 2.97055e16 | − | 2.97055e16i | 0.350532 | − | 0.350532i | ||||
\(263\) | −6.30626e16 | − | 6.30626e16i | −0.724573 | − | 0.724573i | 0.244960 | − | 0.969533i | \(-0.421225\pi\) |
−0.969533 | + | 0.244960i | \(0.921225\pi\) | |||||||
\(264\) | − | 2.83584e16i | − | 0.317288i | ||||||
\(265\) | −3.23455e16 | − | 1.38004e17i | −0.352446 | − | 1.50373i | ||||
\(266\) | −5.39610e15 | −0.0572675 | ||||||||
\(267\) | 3.14603e16 | − | 3.14603e16i | 0.325225 | − | 0.325225i | ||||
\(268\) | 5.90603e15 | + | 5.90603e15i | 0.0594774 | + | 0.0594774i | ||||
\(269\) | 1.05280e17i | 1.03295i | 0.856302 | + | 0.516476i | \(0.172756\pi\) | ||||
−0.856302 | + | 0.516476i | \(0.827244\pi\) | |||||||
\(270\) | 2.21446e16 | − | 3.57030e16i | 0.211700 | − | 0.341317i | ||||
\(271\) | 2.81984e16 | 0.262688 | 0.131344 | − | 0.991337i | \(-0.458071\pi\) | ||||
0.131344 | + | 0.991337i | \(0.458071\pi\) | |||||||
\(272\) | −2.32671e16 | + | 2.32671e16i | −0.211232 | + | 0.211232i | ||||
\(273\) | 8.71067e16 | + | 8.71067e16i | 0.770749 | + | 0.770749i | ||||
\(274\) | 1.32613e17i | 1.14375i | ||||||||
\(275\) | −3.81870e16 | − | 7.69883e16i | −0.321060 | − | 0.647285i | ||||
\(276\) | −1.02905e17 | −0.843478 | ||||||||
\(277\) | 1.53621e17 | − | 1.53621e17i | 1.22770 | − | 1.22770i | 0.262868 | − | 0.964832i | \(-0.415332\pi\) |
0.964832 | − | 0.262868i | \(-0.0846684\pi\) | |||||||
\(278\) | −4.27987e16 | − | 4.27987e16i | −0.333516 | − | 0.333516i | ||||
\(279\) | − | 9.44394e16i | − | 0.717668i | ||||||
\(280\) | 2.60688e16 | + | 1.61691e16i | 0.193204 | + | 0.119834i | ||||
\(281\) | −1.90956e17 | −1.38035 | −0.690176 | − | 0.723642i | \(-0.742467\pi\) | ||||
−0.690176 | + | 0.723642i | \(0.742467\pi\) | |||||||
\(282\) | 1.65013e17 | − | 1.65013e17i | 1.16352 | − | 1.16352i | ||||
\(283\) | −3.46761e16 | − | 3.46761e16i | −0.238520 | − | 0.238520i | 0.577717 | − | 0.816237i | \(-0.303944\pi\) |
−0.816237 | + | 0.577717i | \(0.803944\pi\) | |||||||
\(284\) | − | 1.59160e16i | − | 0.106808i | ||||||
\(285\) | −2.32608e16 | + | 5.45190e15i | −0.152304 | + | 0.0356972i | ||||
\(286\) | −1.09133e17 | −0.697260 | ||||||||
\(287\) | −1.03052e16 | + | 1.03052e16i | −0.0642515 | + | 0.0642515i | ||||
\(288\) | 1.11483e16 | + | 1.11483e16i | 0.0678360 | + | 0.0678360i | ||||
\(289\) | − | 7.20329e16i | − | 0.427805i | ||||||
\(290\) | 3.89217e16 | + | 1.66062e17i | 0.225635 | + | 0.962684i | ||||
\(291\) | 1.18166e17 | 0.668717 | ||||||||
\(292\) | −9.11396e16 | + | 9.11396e16i | −0.503532 | + | 0.503532i | ||||
\(293\) | 2.84928e16 | + | 2.84928e16i | 0.153696 | + | 0.153696i | 0.779766 | − | 0.626071i | \(-0.215338\pi\) |
−0.626071 | + | 0.779766i | \(0.715338\pi\) | |||||||
\(294\) | − | 9.77962e16i | − | 0.515099i | ||||||
\(295\) | −8.90284e16 | + | 1.43538e17i | −0.457904 | + | 0.738263i | ||||
\(296\) | −4.64624e16 | −0.233378 | ||||||||
\(297\) | −5.91550e16 | + | 5.91550e16i | −0.290199 | + | 0.290199i | ||||
\(298\) | −8.31076e15 | − | 8.31076e15i | −0.0398223 | − | 0.0398223i | ||||
\(299\) | 3.96016e17i | 1.85359i | ||||||||
\(300\) | 1.28710e17 | + | 4.33612e16i | 0.588525 | + | 0.198268i | ||||
\(301\) | 2.21541e17 | 0.989668 | ||||||||
\(302\) | 1.14113e17 | − | 1.14113e17i | 0.498064 | − | 0.498064i | ||||
\(303\) | 3.32007e17 | + | 3.32007e17i | 1.41595 | + | 1.41595i | ||||
\(304\) | 7.55509e15i | 0.0314865i | ||||||||
\(305\) | 9.23166e16 | + | 5.72589e16i | 0.375994 | + | 0.233208i | ||||
\(306\) | −1.15191e17 | −0.458532 | ||||||||
\(307\) | −2.26236e17 | + | 2.26236e17i | −0.880225 | + | 0.880225i | −0.993557 | − | 0.113332i | \(-0.963848\pi\) |
0.113332 | + | 0.993557i | \(0.463848\pi\) | |||||||
\(308\) | −4.31925e16 | − | 4.31925e16i | −0.164268 | − | 0.164268i | ||||
\(309\) | − | 3.16198e17i | − | 1.17557i | ||||||
\(310\) | −2.50483e17 | + | 5.87084e16i | −0.910428 | + | 0.213387i | ||||
\(311\) | −2.58062e16 | −0.0917068 | −0.0458534 | − | 0.998948i | \(-0.514601\pi\) | ||||
−0.0458534 | + | 0.998948i | \(0.514601\pi\) | |||||||
\(312\) | 1.21958e17 | − | 1.21958e17i | 0.423769 | − | 0.423769i | ||||
\(313\) | −1.70011e17 | − | 1.70011e17i | −0.577654 | − | 0.577654i | 0.356602 | − | 0.934256i | \(-0.383935\pi\) |
−0.934256 | + | 0.356602i | \(0.883935\pi\) | |||||||
\(314\) | 2.17427e17i | 0.722448i | ||||||||
\(315\) | 2.45060e16 | + | 1.04556e17i | 0.0796341 | + | 0.339763i | ||||
\(316\) | 6.68575e15 | 0.0212491 | ||||||||
\(317\) | 1.62728e17 | − | 1.62728e17i | 0.505879 | − | 0.505879i | −0.407380 | − | 0.913259i | \(-0.633557\pi\) |
0.913259 | + | 0.407380i | \(0.133557\pi\) | |||||||
\(318\) | −3.15414e17 | − | 3.15414e17i | −0.959161 | − | 0.959161i | ||||
\(319\) | − | 3.39630e17i | − | 1.01035i | ||||||
\(320\) | 2.26383e16 | − | 3.64990e16i | 0.0658863 | − | 0.106226i | ||||
\(321\) | 2.03238e17 | 0.578720 | ||||||||
\(322\) | −1.56734e17 | + | 1.56734e17i | −0.436690 | + | 0.436690i | ||||
\(323\) | −3.90321e16 | − | 3.90321e16i | −0.106415 | − | 0.106415i | ||||
\(324\) | − | 2.33917e17i | − | 0.624089i | ||||||
\(325\) | 1.66869e17 | − | 4.95324e17i | 0.435705 | − | 1.29332i | ||||
\(326\) | 3.43543e17 | 0.877926 | ||||||||
\(327\) | −4.68514e17 | + | 4.68514e17i | −1.17189 | + | 1.17189i | ||||
\(328\) | 1.44283e16 | + | 1.44283e16i | 0.0353264 | + | 0.0353264i | ||||
\(329\) | − | 5.02662e17i | − | 1.20477i | ||||||
\(330\) | −2.29828e17 | − | 1.42550e17i | −0.539269 | − | 0.334479i | ||||
\(331\) | 3.12172e17 | 0.717130 | 0.358565 | − | 0.933505i | \(-0.383266\pi\) | ||||
0.358565 | + | 0.933505i | \(0.383266\pi\) | |||||||
\(332\) | 6.56874e16 | − | 6.56874e16i | 0.147746 | − | 0.147746i | ||||
\(333\) | −1.15014e17 | − | 1.15014e17i | −0.253303 | − | 0.253303i | ||||
\(334\) | 4.65844e17i | 1.00465i | ||||||||
\(335\) | 7.75529e16 | − | 1.81769e16i | 0.163789 | − | 0.0383890i | ||||
\(336\) | 9.65368e16 | 0.199672 | ||||||||
\(337\) | −3.02174e17 | + | 3.02174e17i | −0.612136 | + | 0.612136i | −0.943502 | − | 0.331367i | \(-0.892490\pi\) |
0.331367 | + | 0.943502i | \(0.392490\pi\) | |||||||
\(338\) | −2.17347e17 | − | 2.17347e17i | −0.431258 | − | 0.431258i | ||||
\(339\) | 2.15349e17i | 0.418548i | ||||||||
\(340\) | 7.16089e16 | + | 3.05523e17i | 0.136337 | + | 0.581690i | ||||
\(341\) | 5.12287e17 | 0.955505 | ||||||||
\(342\) | −1.87020e16 | + | 1.87020e16i | −0.0341747 | + | 0.0341747i | ||||
\(343\) | −4.02923e17 | − | 4.02923e17i | −0.721379 | − | 0.721379i | ||||
\(344\) | − | 3.10181e17i | − | 0.544134i | ||||||
\(345\) | −5.17276e17 | + | 8.33986e17i | −0.889177 | + | 1.43359i | ||||
\(346\) | 4.59061e17 | 0.773281 | ||||||||
\(347\) | 1.78524e17 | − | 1.78524e17i | 0.294706 | − | 0.294706i | −0.544230 | − | 0.838936i | \(-0.683178\pi\) |
0.838936 | + | 0.544230i | \(0.183178\pi\) | |||||||
\(348\) | 3.79542e17 | + | 3.79542e17i | 0.614052 | + | 0.614052i | ||||
\(349\) | − | 3.20341e17i | − | 0.507965i | −0.967209 | − | 0.253983i | \(-0.918259\pi\) | ||
0.967209 | − | 0.253983i | \(-0.0817406\pi\) | |||||||
\(350\) | 2.62082e17 | − | 1.29995e17i | 0.407343 | − | 0.202046i | ||||
\(351\) | −5.08805e17 | −0.775178 | ||||||||
\(352\) | −6.04739e16 | + | 6.04739e16i | −0.0903170 | + | 0.0903170i | ||||
\(353\) | −2.56346e17 | − | 2.56346e17i | −0.375321 | − | 0.375321i | 0.494090 | − | 0.869411i | \(-0.335501\pi\) |
−0.869411 | + | 0.494090i | \(0.835501\pi\) | |||||||
\(354\) | 5.31541e17i | 0.762981i | ||||||||
\(355\) | −1.28990e17 | − | 8.00053e16i | −0.181534 | − | 0.112595i | ||||
\(356\) | −1.34178e17 | −0.185153 | ||||||||
\(357\) | −4.98741e17 | + | 4.98741e17i | −0.674835 | + | 0.674835i | ||||
\(358\) | 2.48318e17 | + | 2.48318e17i | 0.329479 | + | 0.329479i | ||||
\(359\) | 4.92845e17i | 0.641283i | 0.947201 | + | 0.320641i | \(0.103898\pi\) | ||||
−0.947201 | + | 0.320641i | \(0.896102\pi\) | |||||||
\(360\) | 1.46390e17 | − | 3.43110e16i | 0.186807 | − | 0.0437840i | ||||
\(361\) | 7.86333e17 | 0.984138 | ||||||||
\(362\) | 4.61164e17 | − | 4.61164e17i | 0.566103 | − | 0.566103i | ||||
\(363\) | −3.48614e17 | − | 3.48614e17i | −0.419758 | − | 0.419758i | ||||
\(364\) | − | 3.71508e17i | − | 0.438792i | ||||||
\(365\) | 2.80500e17 | + | 1.19677e18i | 0.324999 | + | 1.38663i | ||||
\(366\) | 3.41862e17 | 0.388583 | ||||||||
\(367\) | 5.44149e17 | − | 5.44149e17i | 0.606813 | − | 0.606813i | −0.335298 | − | 0.942112i | \(-0.608837\pi\) |
0.942112 | + | 0.335298i | \(0.108837\pi\) | |||||||
\(368\) | 2.19444e17 | + | 2.19444e17i | 0.240099 | + | 0.240099i | ||||
\(369\) | 7.14323e16i | 0.0766849i | ||||||||
\(370\) | −2.33554e17 | + | 3.76551e17i | −0.246022 | + | 0.396653i | ||||
\(371\) | −9.60812e17 | −0.993165 | ||||||||
\(372\) | −5.72490e17 | + | 5.72490e17i | −0.580721 | + | 0.580721i | ||||
\(373\) | 4.29023e17 | + | 4.29023e17i | 0.427089 | + | 0.427089i | 0.887636 | − | 0.460546i | \(-0.152346\pi\) |
−0.460546 | + | 0.887636i | \(0.652346\pi\) | |||||||
\(374\) | − | 6.24856e17i | − | 0.610491i | ||||||
\(375\) | 9.98409e17 | − | 8.25158e17i | 0.957391 | − | 0.791259i | ||||
\(376\) | −7.03779e17 | −0.662401 | ||||||||
\(377\) | 1.46062e18 | − | 1.46062e18i | 1.34942 | − | 1.34942i | ||||
\(378\) | −2.01374e17 | − | 2.01374e17i | −0.182625 | − | 0.182625i | ||||
\(379\) | 7.25584e17i | 0.645971i | 0.946404 | + | 0.322986i | \(0.104687\pi\) | ||||
−0.946404 | + | 0.322986i | \(0.895313\pi\) | |||||||
\(380\) | 6.12296e16 | + | 3.79774e16i | 0.0535151 | + | 0.0331925i | ||||
\(381\) | −8.52566e17 | −0.731566 | ||||||||
\(382\) | −8.58218e17 | + | 8.58218e17i | −0.723026 | + | 0.723026i | ||||
\(383\) | 4.13468e17 | + | 4.13468e17i | 0.342019 | + | 0.342019i | 0.857126 | − | 0.515107i | \(-0.172248\pi\) |
−0.515107 | + | 0.857126i | \(0.672248\pi\) | |||||||
\(384\) | − | 1.35161e17i | − | 0.109783i | ||||||
\(385\) | −5.67166e17 | + | 1.32933e17i | −0.452361 | + | 0.106025i | ||||
\(386\) | −4.05813e17 | −0.317845 | ||||||||
\(387\) | 7.67826e17 | − | 7.67826e17i | 0.590590 | − | 0.590590i | ||||
\(388\) | −2.51988e17 | − | 2.51988e17i | −0.190352 | − | 0.190352i | ||||
\(389\) | 1.91373e17i | 0.141982i | 0.997477 | + | 0.0709909i | \(0.0226161\pi\) | ||||
−0.997477 | + | 0.0709909i | \(0.977384\pi\) | |||||||
\(390\) | −3.75350e17 | − | 1.60145e18i | −0.273517 | − | 1.16697i | ||||
\(391\) | −2.26744e18 | −1.62293 | ||||||||
\(392\) | −2.08549e17 | + | 2.08549e17i | −0.146625 | + | 0.146625i | ||||
\(393\) | −8.91517e17 | − | 8.91517e17i | −0.615718 | − | 0.615718i | ||||
\(394\) | − | 1.11158e18i | − | 0.754164i | ||||||
\(395\) | 3.36074e16 | − | 5.41841e16i | 0.0224004 | − | 0.0361154i | ||||
\(396\) | −2.99396e17 | −0.196056 | ||||||||
\(397\) | 4.31783e17 | − | 4.31783e17i | 0.277800 | − | 0.277800i | −0.554430 | − | 0.832230i | \(-0.687064\pi\) |
0.832230 | + | 0.554430i | \(0.187064\pi\) | |||||||
\(398\) | 8.20590e17 | + | 8.20590e17i | 0.518734 | + | 0.518734i | ||||
\(399\) | 1.61947e17i | 0.100592i | ||||||||
\(400\) | −1.82007e17 | − | 3.66941e17i | −0.111088 | − | 0.223963i | ||||
\(401\) | 3.75207e17 | 0.225040 | 0.112520 | − | 0.993649i | \(-0.464108\pi\) | ||||
0.112520 | + | 0.993649i | \(0.464108\pi\) | |||||||
\(402\) | 1.77251e17 | − | 1.77251e17i | 0.104474 | − | 0.104474i | ||||
\(403\) | 2.20315e18 | + | 2.20315e18i | 1.27617 | + | 1.27617i | ||||
\(404\) | − | 1.41600e18i | − | 0.806110i | ||||||
\(405\) | −1.89576e18 | − | 1.17584e18i | −1.06071 | − | 0.657902i | ||||
\(406\) | 1.15616e18 | 0.635821 | ||||||||
\(407\) | 6.23893e17 | − | 6.23893e17i | 0.337248 | − | 0.337248i | ||||
\(408\) | 6.98288e17 | + | 6.98288e17i | 0.371034 | + | 0.371034i | ||||
\(409\) | 1.05253e18i | 0.549757i | 0.961479 | + | 0.274879i | \(0.0886376\pi\) | ||||
−0.961479 | + | 0.274879i | \(0.911362\pi\) | |||||||
\(410\) | 1.89460e17 | − | 4.44060e16i | 0.0972818 | − | 0.0228010i | ||||
\(411\) | 3.97995e18 | 2.00902 | ||||||||
\(412\) | −6.74289e17 | + | 6.74289e17i | −0.334630 | + | 0.334630i | ||||
\(413\) | 8.09588e17 | + | 8.09588e17i | 0.395015 | + | 0.395015i | ||||
\(414\) | 1.08643e18i | 0.521195i | ||||||||
\(415\) | −2.02166e17 | − | 8.62550e17i | −0.0953609 | − | 0.406863i | ||||
\(416\) | −5.20150e17 | −0.241254 | ||||||||
\(417\) | −1.28447e18 | + | 1.28447e18i | −0.585829 | + | 0.585829i | ||||
\(418\) | −1.01449e17 | − | 1.01449e17i | −0.0455003 | − | 0.0455003i | ||||
\(419\) | 1.24279e18i | 0.548151i | 0.961708 | + | 0.274075i | \(0.0883718\pi\) | ||||
−0.961708 | + | 0.274075i | \(0.911628\pi\) | |||||||
\(420\) | 4.85264e17 | − | 7.82374e17i | 0.210491 | − | 0.339367i | ||||
\(421\) | −2.61715e18 | −1.11649 | −0.558243 | − | 0.829677i | \(-0.688524\pi\) | ||||
−0.558243 | + | 0.829677i | \(0.688524\pi\) | |||||||
\(422\) | −1.12722e18 | + | 1.12722e18i | −0.472956 | + | 0.472956i | ||||
\(423\) | −1.74214e18 | − | 1.74214e18i | −0.718955 | − | 0.718955i | ||||
\(424\) | 1.34524e18i | 0.546056i | ||||||||
\(425\) | 2.83604e18 | + | 9.55432e17i | 1.13238 | + | 0.381485i | ||||
\(426\) | −4.77669e17 | −0.187612 | ||||||||
\(427\) | 5.20689e17 | − | 5.20689e17i | 0.201179 | − | 0.201179i | ||||
\(428\) | −4.33402e17 | − | 4.33402e17i | −0.164735 | − | 0.164735i | ||||
\(429\) | 3.27529e18i | 1.22475i | ||||||||
\(430\) | −2.51383e18 | − | 1.55919e18i | −0.924820 | − | 0.573615i | ||||
\(431\) | −5.14003e18 | −1.86048 | −0.930239 | − | 0.366954i | \(-0.880401\pi\) | ||||
−0.930239 | + | 0.366954i | \(0.880401\pi\) | |||||||
\(432\) | −2.81944e17 | + | 2.81944e17i | −0.100410 | + | 0.100410i | ||||
\(433\) | 1.03847e18 | + | 1.03847e18i | 0.363896 | + | 0.363896i | 0.865245 | − | 0.501349i | \(-0.167163\pi\) |
−0.501349 | + | 0.865245i | \(0.667163\pi\) | |||||||
\(434\) | 1.74391e18i | 0.601308i | ||||||||
\(435\) | 4.98382e18 | − | 1.16811e18i | 1.69098 | − | 0.396333i | ||||
\(436\) | 1.99820e18 | 0.667166 | ||||||||
\(437\) | −3.68132e17 | + | 3.68132e17i | −0.120958 | + | 0.120958i | ||||
\(438\) | 2.73527e18 | + | 2.73527e18i | 0.884466 | + | 0.884466i | ||||
\(439\) | − | 1.92845e18i | − | 0.613700i | −0.951758 | − | 0.306850i | \(-0.900725\pi\) | ||
0.951758 | − | 0.306850i | \(-0.0992749\pi\) | |||||||
\(440\) | 1.86120e17 | + | 7.94091e17i | 0.0582941 | + | 0.248715i | ||||
\(441\) | −1.03249e18 | −0.318286 | ||||||||
\(442\) | 2.68726e18 | − | 2.68726e18i | 0.815370 | − | 0.815370i | ||||
\(443\) | −1.31255e18 | − | 1.31255e18i | −0.392003 | − | 0.392003i | 0.483398 | − | 0.875401i | \(-0.339402\pi\) |
−0.875401 | + | 0.483398i | \(0.839402\pi\) | |||||||
\(444\) | 1.39442e18i | 0.409934i | ||||||||
\(445\) | −6.74474e17 | + | 1.08743e18i | −0.195184 | + | 0.314689i | ||||
\(446\) | 2.81279e18 | 0.801297 | ||||||||
\(447\) | −2.49421e17 | + | 2.49421e17i | −0.0699489 | + | 0.0699489i | ||||
\(448\) | −2.05864e17 | − | 2.05864e17i | −0.0568373 | − | 0.0568373i | ||||
\(449\) | − | 3.25445e18i | − | 0.884614i | −0.896864 | − | 0.442307i | \(-0.854160\pi\) | ||
0.896864 | − | 0.442307i | \(-0.145840\pi\) | |||||||
\(450\) | 4.57790e17 | − | 1.35887e18i | 0.122512 | − | 0.363657i | ||||
\(451\) | −3.87485e17 | −0.102098 | ||||||||
\(452\) | 4.59230e17 | − | 4.59230e17i | 0.119141 | − | 0.119141i | ||||
\(453\) | −3.42473e18 | − | 3.42473e18i | −0.874861 | − | 0.874861i | ||||
\(454\) | − | 1.02305e18i | − | 0.257338i | ||||||
\(455\) | −3.01086e18 | − | 1.86747e18i | −0.745779 | − | 0.462566i | ||||
\(456\) | 2.26742e17 | 0.0553068 | ||||||||
\(457\) | 1.44077e18 | − | 1.44077e18i | 0.346084 | − | 0.346084i | −0.512565 | − | 0.858649i | \(-0.671305\pi\) |
0.858649 | + | 0.512565i | \(0.171305\pi\) | |||||||
\(458\) | −2.27736e18 | − | 2.27736e18i | −0.538732 | − | 0.538732i | ||||
\(459\) | − | 2.91323e18i | − | 0.678713i | ||||||
\(460\) | 2.88155e18 | − | 6.75382e17i | 0.661183 | − | 0.154969i | ||||
\(461\) | −4.33161e18 | −0.978909 | −0.489455 | − | 0.872029i | \(-0.662804\pi\) | ||||
−0.489455 | + | 0.872029i | \(0.662804\pi\) | |||||||
\(462\) | −1.29629e18 | + | 1.29629e18i | −0.288541 | + | 0.288541i | ||||
\(463\) | −5.00335e18 | − | 5.00335e18i | −1.09697 | − | 1.09697i | −0.994763 | − | 0.102205i | \(-0.967410\pi\) |
−0.102205 | − | 0.994763i | \(-0.532590\pi\) | |||||||
\(464\) | − | 1.61874e18i | − | 0.349584i | ||||||
\(465\) | 1.76195e18 | + | 7.51745e18i | 0.374820 | + | 1.59919i | ||||
\(466\) | −9.98762e17 | −0.209296 | ||||||||
\(467\) | 2.03317e18 | − | 2.03317e18i | 0.419715 | − | 0.419715i | −0.465390 | − | 0.885106i | \(-0.654086\pi\) |
0.885106 | + | 0.465390i | \(0.154086\pi\) | |||||||
\(468\) | −1.28759e18 | − | 1.28759e18i | −0.261852 | − | 0.261852i | ||||
\(469\) | − | 5.39940e17i | − | 0.108177i | ||||||
\(470\) | −3.53770e18 | + | 5.70371e18i | −0.698290 | + | 1.12583i | ||||
\(471\) | 6.52540e18 | 1.26900 | ||||||||
\(472\) | 1.13351e18 | − | 1.13351e18i | 0.217185 | − | 0.217185i | ||||
\(473\) | 4.16508e18 | + | 4.16508e18i | 0.786312 | + | 0.786312i | ||||
\(474\) | − | 2.00652e17i | − | 0.0373246i | ||||||
\(475\) | 6.15568e17 | − | 3.05328e17i | 0.112829 | − | 0.0559644i | ||||
\(476\) | 2.12712e18 | 0.384188 | ||||||||
\(477\) | −3.33002e18 | + | 3.33002e18i | −0.592677 | + | 0.592677i | ||||
\(478\) | −9.60644e17 | − | 9.60644e17i | −0.168487 | − | 0.168487i | ||||
\(479\) | 4.68589e18i | 0.809923i | 0.914334 | + | 0.404961i | \(0.132715\pi\) | ||||
−0.914334 | + | 0.404961i | \(0.867285\pi\) | |||||||
\(480\) | −1.09540e18 | − | 6.79419e17i | −0.186589 | − | 0.115731i | ||||
\(481\) | 5.36624e18 | 0.900855 | ||||||||
\(482\) | −2.05279e18 | + | 2.05279e18i | −0.339638 | + | 0.339638i | ||||
\(483\) | 4.70389e18 | + | 4.70389e18i | 0.767056 | + | 0.767056i | ||||
\(484\) | 1.48683e18i | 0.238971i | ||||||||
\(485\) | −3.30889e18 | + | 7.75542e17i | −0.524192 | + | 0.122861i | ||||
\(486\) | −4.44816e18 | −0.694587 | ||||||||
\(487\) | −3.36110e18 | + | 3.36110e18i | −0.517343 | + | 0.517343i | −0.916767 | − | 0.399423i | \(-0.869210\pi\) |
0.399423 | + | 0.916767i | \(0.369210\pi\) | |||||||
\(488\) | −7.29017e17 | − | 7.29017e17i | −0.110611 | − | 0.110611i | ||||
\(489\) | − | 1.03104e19i | − | 1.54210i | ||||||
\(490\) | 6.41851e17 | + | 2.73849e18i | 0.0946371 | + | 0.403774i | ||||
\(491\) | 6.17759e18 | 0.897943 | 0.448971 | − | 0.893546i | \(-0.351791\pi\) | ||||
0.448971 | + | 0.893546i | \(0.351791\pi\) | |||||||
\(492\) | 4.33021e17 | − | 4.33021e17i | 0.0620517 | − | 0.0620517i | ||||
\(493\) | 8.36295e18 | + | 8.36295e18i | 1.18149 | + | 1.18149i | ||||
\(494\) | − | 8.72586e17i | − | 0.121540i | ||||||
\(495\) | −1.50498e18 | + | 2.42643e18i | −0.206678 | + | 0.333220i | ||||
\(496\) | 2.44166e18 | 0.330608 | ||||||||
\(497\) | −7.27535e17 | + | 7.27535e17i | −0.0971313 | + | 0.0971313i | ||||
\(498\) | −1.97140e18 | − | 1.97140e18i | −0.259519 | − | 0.259519i | ||||
\(499\) | 1.02637e19i | 1.33229i | 0.745823 | + | 0.666145i | \(0.232057\pi\) | ||||
−0.745823 | + | 0.666145i | \(0.767943\pi\) | |||||||
\(500\) | −3.88874e18 | − | 3.69454e17i | −0.497759 | − | 0.0472902i | ||||
\(501\) | 1.39808e19 | 1.76469 | ||||||||
\(502\) | 5.21088e17 | − | 5.21088e17i | 0.0648613 | − | 0.0648613i | ||||
\(503\) | −8.56568e18 | − | 8.56568e18i | −1.05144 | − | 1.05144i | −0.998603 | − | 0.0528411i | \(-0.983172\pi\) |
−0.0528411 | − | 0.998603i | \(-0.516828\pi\) | |||||||
\(504\) | − | 1.01920e18i | − | 0.123380i | ||||||
\(505\) | −1.14759e19 | − | 7.11785e18i | −1.37008 | − | 0.849785i | ||||
\(506\) | −5.89335e18 | −0.693919 | ||||||||
\(507\) | −6.52300e18 | + | 6.52300e18i | −0.757516 | + | 0.757516i | ||||
\(508\) | 1.81809e18 | + | 1.81809e18i | 0.208242 | + | 0.208242i | ||||
\(509\) | − | 6.56975e18i | − | 0.742206i | −0.928592 | − | 0.371103i | \(-0.878980\pi\) | ||
0.928592 | − | 0.371103i | \(-0.121020\pi\) | |||||||
\(510\) | 9.16932e18 | − | 2.14912e18i | 1.02175 | − | 0.239480i | ||||
\(511\) | 8.33215e18 | 0.915822 | ||||||||
\(512\) | −2.88230e17 | + | 2.88230e17i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −4.72980e17 | − | 4.72980e17i | −0.0505849 | − | 0.0505849i | ||||
\(514\) | − | 1.25360e19i | − | 1.32257i | ||||||
\(515\) | 2.07525e18 | + | 8.85418e18i | 0.215983 | + | 0.921505i | ||||
\(516\) | −9.30910e18 | −0.955784 | ||||||||
\(517\) | 9.45027e18 | − | 9.45027e18i | 0.957217 | − | 0.957217i | ||||
\(518\) | 2.12384e18 | + | 2.12384e18i | 0.212233 | + | 0.212233i | ||||
\(519\) | − | 1.37773e19i | − | 1.35829i | ||||||
\(520\) | −2.61465e18 | + | 4.21551e18i | −0.254326 | + | 0.410040i | ||||
\(521\) | −1.41790e19 | −1.36076 | −0.680380 | − | 0.732859i | \(-0.738185\pi\) | ||||
−0.680380 | + | 0.732859i | \(0.738185\pi\) | |||||||
\(522\) | 4.00705e18 | − | 4.00705e18i | 0.379430 | − | 0.379430i | ||||
\(523\) | 1.30117e18 | + | 1.30117e18i | 0.121569 | + | 0.121569i | 0.765274 | − | 0.643705i | \(-0.222603\pi\) |
−0.643705 | + | 0.765274i | \(0.722603\pi\) | |||||||
\(524\) | 3.80230e18i | 0.350532i | ||||||||
\(525\) | −3.90140e18 | − | 7.86555e18i | −0.354899 | − | 0.715508i | ||||
\(526\) | 8.07202e18 | 0.724573 | ||||||||
\(527\) | −1.26144e19 | + | 1.26144e19i | −1.11736 | + | 1.11736i | ||||
\(528\) | 1.81493e18 | + | 1.81493e18i | 0.158644 | + | 0.158644i | ||||
\(529\) | 9.79263e18i | 0.844714i | ||||||||
\(530\) | 1.09023e19 | + | 6.76213e18i | 0.928088 | + | 0.575642i | ||||
\(531\) | 5.61180e18 | 0.471455 | ||||||||
\(532\) | 3.45350e17 | − | 3.45350e17i | 0.0286338 | − | 0.0286338i | ||||
\(533\) | −1.66642e18 | − | 1.66642e18i | −0.136362 | − | 0.136362i | ||||
\(534\) | 4.02692e18i | 0.325225i | ||||||||
\(535\) | −5.69106e18 | + | 1.33388e18i | −0.453646 | + | 0.106326i | ||||
\(536\) | −7.55972e17 | −0.0594774 | ||||||||
\(537\) | 7.45250e18 | − | 7.45250e18i | 0.578738 | − | 0.578738i | ||||
\(538\) | −6.73792e18 | − | 6.73792e18i | −0.516476 | − | 0.516476i | ||||
\(539\) | − | 5.60077e18i | − | 0.423766i | ||||||
\(540\) | 8.67736e17 | + | 3.70224e18i | 0.0648084 | + | 0.276509i | ||||
\(541\) | −6.25252e18 | −0.460972 | −0.230486 | − | 0.973076i | \(-0.574032\pi\) | ||||
−0.230486 | + | 0.973076i | \(0.574032\pi\) | |||||||
\(542\) | −1.80470e18 | + | 1.80470e18i | −0.131344 | + | 0.131344i | ||||
\(543\) | −1.38404e19 | − | 1.38404e19i | −0.994373 | − | 0.994373i | ||||
\(544\) | − | 2.97819e18i | − | 0.211232i | ||||||
\(545\) | 1.00444e19 | − | 1.61943e19i | 0.703314 | − | 1.13393i | ||||
\(546\) | −1.11497e19 | −0.770749 | ||||||||
\(547\) | −5.53758e18 | + | 5.53758e18i | −0.377928 | + | 0.377928i | −0.870354 | − | 0.492426i | \(-0.836110\pi\) |
0.492426 | + | 0.870354i | \(0.336110\pi\) | |||||||
\(548\) | −8.48721e18 | − | 8.48721e18i | −0.571875 | − | 0.571875i | ||||
\(549\) | − | 3.60924e18i | − | 0.240110i | ||||||
\(550\) | 7.37122e18 | + | 2.48328e18i | 0.484173 | + | 0.163113i | ||||
\(551\) | 2.71555e18 | 0.176115 | ||||||||
\(552\) | 6.58593e18 | − | 6.58593e18i | 0.421739 | − | 0.421739i | ||||
\(553\) | −3.05612e17 | − | 3.05612e17i | −0.0193239 | − | 0.0193239i | ||||
\(554\) | 1.96635e19i | 1.22770i | ||||||||
\(555\) | 1.13010e19 | + | 7.00938e18i | 0.696731 | + | 0.432144i | ||||
\(556\) | 5.47823e18 | 0.333516 | ||||||||
\(557\) | 1.13109e19 | − | 1.13109e19i | 0.680001 | − | 0.680001i | −0.279999 | − | 0.960000i | \(-0.590334\pi\) |
0.960000 | + | 0.279999i | \(0.0903342\pi\) | |||||||
\(558\) | 6.04412e18 | + | 6.04412e18i | 0.358834 | + | 0.358834i | ||||
\(559\) | 3.58248e19i | 2.10039i | ||||||||
\(560\) | −2.70322e18 | + | 6.33585e17i | −0.156519 | + | 0.0366850i | ||||
\(561\) | −1.87531e19 | −1.07234 | ||||||||
\(562\) | 1.22212e19 | − | 1.22212e19i | 0.690176 | − | 0.690176i | ||||
\(563\) | 1.52642e19 | + | 1.52642e19i | 0.851361 | + | 0.851361i | 0.990301 | − | 0.138940i | \(-0.0443694\pi\) |
−0.138940 | + | 0.990301i | \(0.544369\pi\) | |||||||
\(564\) | 2.11217e19i | 1.16352i | ||||||||
\(565\) | −1.41337e18 | − | 6.03021e18i | −0.0768982 | − | 0.328090i | ||||
\(566\) | 4.43854e18 | 0.238520 | ||||||||
\(567\) | −1.06926e19 | + | 1.06926e19i | −0.567545 | + | 0.567545i | ||||
\(568\) | 1.01862e18 | + | 1.01862e18i | 0.0534042 | + | 0.0534042i | ||||
\(569\) | − | 6.51954e18i | − | 0.337622i | −0.985648 | − | 0.168811i | \(-0.946007\pi\) | ||
0.985648 | − | 0.168811i | \(-0.0539928\pi\) | |||||||
\(570\) | 1.13977e18 | − | 1.83761e18i | 0.0583034 | − | 0.0940005i | ||||
\(571\) | −1.91280e18 | −0.0966533 | −0.0483266 | − | 0.998832i | \(-0.515389\pi\) | ||||
−0.0483266 | + | 0.998832i | \(0.515389\pi\) | |||||||
\(572\) | 6.98452e18 | − | 6.98452e18i | 0.348630 | − | 0.348630i | ||||
\(573\) | 2.57567e19 | + | 2.57567e19i | 1.27001 | + | 1.27001i | ||||
\(574\) | − | 1.31907e18i | − | 0.0642515i | ||||||
\(575\) | 9.01119e18 | − | 2.67483e19i | 0.433618 | − | 1.28712i | ||||
\(576\) | −1.42698e18 | −0.0678360 | ||||||||
\(577\) | −1.52421e19 | + | 1.52421e19i | −0.715836 | + | 0.715836i | −0.967750 | − | 0.251913i | \(-0.918940\pi\) |
0.251913 | + | 0.967750i | \(0.418940\pi\) | |||||||
\(578\) | 4.61011e18 | + | 4.61011e18i | 0.213903 | + | 0.213903i | ||||
\(579\) | 1.21792e19i | 0.558302i | ||||||||
\(580\) | −1.31189e19 | − | 8.13696e18i | −0.594159 | − | 0.368524i | ||||
\(581\) | −6.00526e18 | −0.268720 | ||||||||
\(582\) | −7.56263e18 | + | 7.56263e18i | −0.334358 | + | 0.334358i | ||||
\(583\) | −1.80637e19 | − | 1.80637e19i | −0.789091 | − | 0.789091i | ||||
\(584\) | − | 1.16659e19i | − | 0.503532i | ||||||
\(585\) | −1.69075e19 | + | 3.96279e18i | −0.721087 | + | 0.169009i | ||||
\(586\) | −3.64708e18 | −0.153696 | ||||||||
\(587\) | −1.51055e18 | + | 1.51055e18i | −0.0629025 | + | 0.0629025i | −0.737858 | − | 0.674956i | \(-0.764163\pi\) |
0.674956 | + | 0.737858i | \(0.264163\pi\) | |||||||
\(588\) | 6.25896e18 | + | 6.25896e18i | 0.257550 | + | 0.257550i | ||||
\(589\) | 4.09605e18i | 0.166555i | ||||||||
\(590\) | −3.48858e18 | − | 1.48842e19i | −0.140180 | − | 0.598084i | ||||
\(591\) | −3.33605e19 | −1.32471 | ||||||||
\(592\) | 2.97359e18 | − | 2.97359e18i | 0.116689 | − | 0.116689i | ||||
\(593\) | 3.35516e19 | + | 3.35516e19i | 1.30116 | + | 1.30116i | 0.927611 | + | 0.373548i | \(0.121859\pi\) |
0.373548 | + | 0.927611i | \(0.378141\pi\) | |||||||
\(594\) | − | 7.57183e18i | − | 0.290199i | ||||||
\(595\) | 1.06924e19 | − | 1.72391e19i | 0.405003 | − | 0.652972i | ||||
\(596\) | 1.06378e18 | 0.0398223 | ||||||||
\(597\) | 2.46274e19 | − | 2.46274e19i | 0.911169 | − | 0.911169i | ||||
\(598\) | −2.53450e19 | − | 2.53450e19i | −0.926797 | − | 0.926797i | ||||
\(599\) | − | 4.16395e19i | − | 1.50493i | −0.658630 | − | 0.752467i | \(-0.728864\pi\) | ||
0.658630 | − | 0.752467i | \(-0.271136\pi\) | |||||||
\(600\) | −1.10126e19 | + | 5.46236e18i | −0.393396 | + | 0.195129i | ||||
\(601\) | 1.23890e19 | 0.437436 | 0.218718 | − | 0.975788i | \(-0.429812\pi\) | ||||
0.218718 | + | 0.975788i | \(0.429812\pi\) | |||||||
\(602\) | −1.41786e19 | + | 1.41786e19i | −0.494834 | + | 0.494834i | ||||
\(603\) | −1.87134e18 | − | 1.87134e18i | −0.0645554 | − | 0.0645554i | ||||
\(604\) | 1.46064e19i | 0.498064i | ||||||||
\(605\) | 1.20499e19 | + | 7.47390e18i | 0.406159 | + | 0.251918i | ||||
\(606\) | −4.24968e19 | −1.41595 | ||||||||
\(607\) | 2.87405e18 | − | 2.87405e18i | 0.0946614 | − | 0.0946614i | −0.658190 | − | 0.752852i | \(-0.728678\pi\) |
0.752852 | + | 0.658190i | \(0.228678\pi\) | |||||||
\(608\) | −4.83526e17 | − | 4.83526e17i | −0.0157433 | − | 0.0157433i | ||||
\(609\) | − | 3.46985e19i | − | 1.11684i | ||||||
\(610\) | −9.57283e18 | + | 2.24369e18i | −0.304601 | + | 0.0713928i | ||||
\(611\) | 8.12839e19 | 2.55691 | ||||||||
\(612\) | 7.37225e18 | − | 7.37225e18i | 0.229266 | − | 0.229266i | ||||
\(613\) | −1.19580e19 | − | 1.19580e19i | −0.367651 | − | 0.367651i | 0.498969 | − | 0.866620i | \(-0.333712\pi\) |
−0.866620 | + | 0.498969i | \(0.833712\pi\) | |||||||
\(614\) | − | 2.89583e19i | − | 0.880225i | ||||||
\(615\) | −1.33271e18 | − | 5.68606e18i | −0.0400505 | − | 0.170878i | ||||
\(616\) | 5.52864e18 | 0.164268 | ||||||||
\(617\) | −1.40098e19 | + | 1.40098e19i | −0.411563 | + | 0.411563i | −0.882283 | − | 0.470720i | \(-0.843994\pi\) |
0.470720 | + | 0.882283i | \(0.343994\pi\) | |||||||
\(618\) | 2.02367e19 | + | 2.02367e19i | 0.587786 | + | 0.587786i | ||||
\(619\) | 6.44748e18i | 0.185164i | 0.995705 | + | 0.0925818i | \(0.0295120\pi\) | ||||
−0.995705 | + | 0.0925818i | \(0.970488\pi\) | |||||||
\(620\) | 1.22735e19 | − | 1.97882e19i | 0.348520 | − | 0.561908i | ||||
\(621\) | −2.74762e19 | −0.771465 | ||||||||
\(622\) | 1.65160e18 | − | 1.65160e18i | 0.0458534 | − | 0.0458534i | ||||
\(623\) | 6.13339e18 | + | 6.13339e18i | 0.168378 | + | 0.168378i | ||||
\(624\) | 1.56107e19i | 0.423769i | ||||||||
\(625\) | −2.25418e19 | + | 2.96588e19i | −0.605103 | + | 0.796148i | ||||
\(626\) | 2.17615e19 | 0.577654 | ||||||||
\(627\) | −3.04468e18 | + | 3.04468e18i | −0.0799223 | + | 0.0799223i | ||||
\(628\) | −1.39153e19 | − | 1.39153e19i | −0.361224 | − | 0.361224i | ||||
\(629\) | 3.07251e19i | 0.788750i | ||||||||
\(630\) | −8.25999e18 | − | 5.12322e18i | −0.209699 | − | 0.130065i | ||||
\(631\) | −7.00444e19 | −1.75860 | −0.879301 | − | 0.476266i | \(-0.841990\pi\) | ||||
−0.879301 | + | 0.476266i | \(0.841990\pi\) | |||||||
\(632\) | −4.27888e17 | + | 4.27888e17i | −0.0106246 | + | 0.0106246i | ||||
\(633\) | 3.38299e19 | + | 3.38299e19i | 0.830759 | + | 0.830759i | ||||
\(634\) | 2.08291e19i | 0.505879i | ||||||||
\(635\) | 2.38736e19 | − | 5.59552e18i | 0.573458 | − | 0.134408i | ||||
\(636\) | 4.03730e19 | 0.959161 | ||||||||
\(637\) | 2.40867e19 | − | 2.40867e19i | 0.565981 | − | 0.565981i | ||||
\(638\) | 2.17363e19 | + | 2.17363e19i | 0.505174 | + | 0.505174i | ||||
\(639\) | 5.04303e18i | 0.115927i | ||||||||
\(640\) | 8.87084e17 | + | 3.78479e18i | 0.0201700 | + | 0.0860562i | ||||
\(641\) | −6.97876e19 | −1.56954 | −0.784770 | − | 0.619788i | \(-0.787219\pi\) | ||||
−0.784770 | + | 0.619788i | \(0.787219\pi\) | |||||||
\(642\) | −1.30072e19 | + | 1.30072e19i | −0.289360 | + | 0.289360i | ||||
\(643\) | −2.96862e19 | − | 2.96862e19i | −0.653247 | − | 0.653247i | 0.300526 | − | 0.953774i | \(-0.402838\pi\) |
−0.953774 | + | 0.300526i | \(0.902838\pi\) | |||||||
\(644\) | − | 2.00620e19i | − | 0.436690i | ||||||
\(645\) | −4.67943e19 | + | 7.54448e19i | −1.00757 | + | 1.62447i | ||||
\(646\) | 4.99611e18 | 0.106415 | ||||||||
\(647\) | 7.51188e18 | − | 7.51188e18i | 0.158277 | − | 0.158277i | −0.623526 | − | 0.781803i | \(-0.714300\pi\) |
0.781803 | + | 0.623526i | \(0.214300\pi\) | |||||||
\(648\) | 1.49707e19 | + | 1.49707e19i | 0.312044 | + | 0.312044i | ||||
\(649\) | 3.04412e19i | 0.627696i | ||||||||
\(650\) | 2.10211e19 | + | 4.23804e19i | 0.428807 | + | 0.864513i | ||||
\(651\) | 5.23381e19 | 1.05621 | ||||||||
\(652\) | −2.19868e19 | + | 2.19868e19i | −0.438963 | + | 0.438963i | ||||
\(653\) | −3.51026e19 | − | 3.51026e19i | −0.693342 | − | 0.693342i | 0.269624 | − | 0.962966i | \(-0.413101\pi\) |
−0.962966 | + | 0.269624i | \(0.913101\pi\) | |||||||
\(654\) | − | 5.99698e19i | − | 1.17189i | ||||||
\(655\) | 3.08154e19 | + | 1.91131e19i | 0.595771 | + | 0.369524i | ||||
\(656\) | −1.84683e18 | −0.0353264 | ||||||||
\(657\) | 2.88779e19 | − | 2.88779e19i | 0.546522 | − | 0.546522i | ||||
\(658\) | 3.21704e19 | + | 3.21704e19i | 0.602386 | + | 0.602386i | ||||
\(659\) | 1.01224e20i | 1.87536i | 0.347502 | + | 0.937679i | \(0.387030\pi\) | ||||
−0.347502 | + | 0.937679i | \(0.612970\pi\) | |||||||
\(660\) | 2.38322e19 | − | 5.58581e18i | 0.436874 | − | 0.102395i | ||||
\(661\) | 8.47972e19 | 1.53805 | 0.769027 | − | 0.639216i | \(-0.220741\pi\) | ||||
0.769027 | + | 0.639216i | \(0.220741\pi\) | |||||||
\(662\) | −1.99790e19 | + | 1.99790e19i | −0.358565 | + | 0.358565i | ||||
\(663\) | −8.06498e19 | − | 8.06498e19i | −1.43222 | − | 1.43222i | ||||
\(664\) | 8.40799e18i | 0.147746i | ||||||||
\(665\) | −1.06288e18 | − | 4.53484e18i | −0.0184813 | − | 0.0788516i | ||||
\(666\) | 1.47218e19 | 0.253303 | ||||||||
\(667\) | 7.88754e19 | − | 7.88754e19i | 1.34295 | − | 1.34295i | ||||
\(668\) | −2.98140e19 | − | 2.98140e19i | −0.502325 | − | 0.502325i | ||||
\(669\) | − | 8.44171e19i | − | 1.40750i | ||||||
\(670\) | −3.80006e18 | + | 6.12671e18i | −0.0626999 | + | 0.101089i | ||||
\(671\) | 1.95784e19 | 0.319682 | ||||||||
\(672\) | −6.17835e18 | + | 6.17835e18i | −0.0998362 | + | 0.0998362i | ||||
\(673\) | −3.99238e19 | − | 3.99238e19i | −0.638449 | − | 0.638449i | 0.311724 | − | 0.950173i | \(-0.399094\pi\) |
−0.950173 | + | 0.311724i | \(0.899094\pi\) | |||||||
\(674\) | − | 3.86783e19i | − | 0.612136i | ||||||
\(675\) | 3.43664e19 | + | 1.15777e19i | 0.538279 | + | 0.181340i | ||||
\(676\) | 2.78205e19 | 0.431258 | ||||||||
\(677\) | −5.58944e19 | + | 5.58944e19i | −0.857527 | + | 0.857527i | −0.991046 | − | 0.133520i | \(-0.957372\pi\) |
0.133520 | + | 0.991046i | \(0.457372\pi\) | |||||||
\(678\) | −1.37823e19 | − | 1.37823e19i | −0.209274 | − | 0.209274i | ||||
\(679\) | 2.30372e19i | 0.346212i | ||||||||
\(680\) | −2.41365e19 | − | 1.49705e19i | −0.359014 | − | 0.222676i | ||||
\(681\) | −3.07035e19 | −0.452021 | ||||||||
\(682\) | −3.27864e19 | + | 3.27864e19i | −0.477752 | + | 0.477752i | ||||
\(683\) | −6.59046e19 | − | 6.59046e19i | −0.950540 | − | 0.950540i | 0.0482928 | − | 0.998833i | \(-0.484622\pi\) |
−0.998833 | + | 0.0482928i | \(0.984622\pi\) | |||||||
\(684\) | − | 2.39385e18i | − | 0.0341747i | ||||||
\(685\) | −1.11447e20 | + | 2.61210e19i | −1.57483 | + | 0.369110i | ||||
\(686\) | 5.15742e19 | 0.721379 | ||||||||
\(687\) | −6.83477e19 | + | 6.83477e19i | −0.946295 | + | 0.946295i | ||||
\(688\) | 1.98516e19 | + | 1.98516e19i | 0.272067 | + | 0.272067i | ||||
\(689\) | − | 1.55370e20i | − | 2.10782i | ||||||
\(690\) | −2.02695e19 | − | 8.64807e19i | −0.272207 | − | 1.16138i | ||||
\(691\) | 7.64603e19 | 1.01646 | 0.508229 | − | 0.861222i | \(-0.330300\pi\) | ||||
0.508229 | + | 0.861222i | \(0.330300\pi\) | |||||||
\(692\) | −2.93799e19 | + | 2.93799e19i | −0.386640 | + | 0.386640i | ||||
\(693\) | 1.36857e19 | + | 1.36857e19i | 0.178293 | + | 0.178293i | ||||
\(694\) | 2.28510e19i | 0.294706i | ||||||||
\(695\) | 2.75375e19 | − | 4.43978e19i | 0.351586 | − | 0.566850i | ||||
\(696\) | −4.85814e19 | −0.614052 | ||||||||
\(697\) | 9.54132e18 | − | 9.54132e18i | 0.119393 | − | 0.119393i | ||||
\(698\) | 2.05018e19 | + | 2.05018e19i | 0.253983 | + | 0.253983i | ||||
\(699\) | 2.99747e19i | 0.367633i | ||||||||
\(700\) | −8.45353e18 | + | 2.50929e19i | −0.102648 | + | 0.304695i | ||||
\(701\) | 2.00952e19 | 0.241583 | 0.120791 | − | 0.992678i | \(-0.461457\pi\) | ||||
0.120791 | + | 0.992678i | \(0.461457\pi\) | |||||||
\(702\) | 3.25635e19 | − | 3.25635e19i | 0.387589 | − | 0.387589i | ||||
\(703\) | 4.98840e18 | + | 4.98840e18i | 0.0587860 | + | 0.0587860i | ||||
\(704\) | − | 7.74066e18i | − | 0.0903170i | ||||||
\(705\) | 1.71179e20 | + | 1.06173e20i | 1.97755 | + | 1.22656i | ||||
\(706\) | 3.28122e19 | 0.375321 | ||||||||
\(707\) | −6.47267e19 | + | 6.47267e19i | −0.733074 | + | 0.733074i | ||||
\(708\) | −3.40186e19 | − | 3.40186e19i | −0.381491 | − | 0.381491i | ||||
\(709\) | 1.14427e20i | 1.27059i | 0.772270 | + | 0.635294i | \(0.219121\pi\) | ||||
−0.772270 | + | 0.635294i | \(0.780879\pi\) | |||||||
\(710\) | 1.33757e19 | − | 3.13501e18i | 0.147064 | − | 0.0344691i | ||||
\(711\) | −2.11840e18 | −0.0230633 | ||||||||
\(712\) | 8.58737e18 | − | 8.58737e18i | 0.0925764 | − | 0.0925764i | ||||
\(713\) | 1.18973e20 | + | 1.18973e20i | 1.27006 | + | 1.27006i | ||||
\(714\) | − | 6.38388e19i | − | 0.674835i | ||||||
\(715\) | −2.14962e19 | − | 9.17147e19i | −0.225019 | − | 0.960057i | ||||
\(716\) | −3.17848e19 | −0.329479 | ||||||||
\(717\) | −2.88307e19 | + | 2.88307e19i | −0.295952 | + | 0.295952i | ||||
\(718\) | −3.15421e19 | − | 3.15421e19i | −0.320641 | − | 0.320641i | ||||
\(719\) | − | 9.01786e19i | − | 0.907823i | −0.891047 | − | 0.453912i | \(-0.850028\pi\) | ||
0.891047 | − | 0.453912i | \(-0.149972\pi\) | |||||||
\(720\) | −7.17303e18 | + | 1.15648e19i | −0.0715114 | + | 0.115295i | ||||
\(721\) | 6.16447e19 | 0.608624 | ||||||||
\(722\) | −5.03253e19 | + | 5.03253e19i | −0.492069 | + | 0.492069i | ||||
\(723\) | 6.16082e19 | + | 6.16082e19i | 0.596582 | + | 0.596582i | ||||
\(724\) | 5.90290e19i | 0.566103i | ||||||||
\(725\) | −1.31891e20 | + | 6.54191e19i | −1.25270 | + | 0.621353i | ||||
\(726\) | 4.46227e19 | 0.419758 | ||||||||
\(727\) | 1.40273e20 | − | 1.40273e20i | 1.30687 | − | 1.30687i | 0.383209 | − | 0.923662i | \(-0.374819\pi\) |
0.923662 | − | 0.383209i | \(-0.125181\pi\) | |||||||
\(728\) | 2.37765e19 | + | 2.37765e19i | 0.219396 | + | 0.219396i | ||||
\(729\) | − | 3.07667e18i | − | 0.0281182i | ||||||
\(730\) | −9.45450e19 | − | 5.86411e19i | −0.855813 | − | 0.530814i | ||||
\(731\) | −2.05119e20 | −1.83901 | ||||||||
\(732\) | −2.18792e19 | + | 2.18792e19i | −0.194291 | + | 0.194291i | ||||
\(733\) | 3.43695e19 | + | 3.43695e19i | 0.302305 | + | 0.302305i | 0.841915 | − | 0.539610i | \(-0.181428\pi\) |
−0.539610 | + | 0.841915i | \(0.681428\pi\) | |||||||
\(734\) | 6.96510e19i | 0.606813i | ||||||||
\(735\) | 8.21872e19 | − | 1.92631e19i | 0.709240 | − | 0.166232i | ||||
\(736\) | −2.80889e19 | −0.240099 | ||||||||
\(737\) | 1.01511e19 | − | 1.01511e19i | 0.0859492 | − | 0.0859492i | ||||
\(738\) | −4.57166e18 | − | 4.57166e18i | −0.0383424 | − | 0.0383424i | ||||
\(739\) | 4.71834e19i | 0.391993i | 0.980605 | + | 0.195996i | \(0.0627941\pi\) | ||||
−0.980605 | + | 0.195996i | \(0.937206\pi\) | |||||||
\(740\) | −9.15180e18 | − | 3.90467e19i | −0.0753155 | − | 0.321338i | ||||
\(741\) | −2.61879e19 | −0.213488 | ||||||||
\(742\) | 6.14920e19 | − | 6.14920e19i | 0.496582 | − | 0.496582i | ||||
\(743\) | 3.67311e19 | + | 3.67311e19i | 0.293841 | + | 0.293841i | 0.838596 | − | 0.544755i | \(-0.183377\pi\) |
−0.544755 | + | 0.838596i | \(0.683377\pi\) | |||||||
\(744\) | − | 7.32787e19i | − | 0.580721i | ||||||
\(745\) | 5.34731e18 | − | 8.62129e18i | 0.0419799 | − | 0.0676828i | ||||
\(746\) | −5.49149e19 | −0.427089 | ||||||||
\(747\) | −2.08133e19 | + | 2.08133e19i | −0.160360 | + | 0.160360i | ||||
\(748\) | 3.99908e19 | + | 3.99908e19i | 0.305245 | + | 0.305245i | ||||
\(749\) | 3.96224e19i | 0.299618i | ||||||||
\(750\) | −1.10880e19 | + | 1.16708e20i | −0.0830663 | + | 0.874325i | ||||
\(751\) | 6.76233e19 | 0.501900 | 0.250950 | − | 0.968000i | \(-0.419257\pi\) | ||||
0.250950 | + | 0.968000i | \(0.419257\pi\) | |||||||
\(752\) | 4.50418e19 | − | 4.50418e19i | 0.331201 | − | 0.331201i | ||||
\(753\) | −1.56388e19 | − | 1.56388e19i | −0.113930 | − | 0.113930i | ||||
\(754\) | 1.86959e20i | 1.34942i | ||||||||
\(755\) | 1.18376e20 | + | 7.34224e19i | 0.846519 | + | 0.525049i | ||||
\(756\) | 2.57758e19 | 0.182625 | ||||||||
\(757\) | 1.68997e20 | − | 1.68997e20i | 1.18634 | − | 1.18634i | 0.208262 | − | 0.978073i | \(-0.433219\pi\) |
0.978073 | − | 0.208262i | \(-0.0667807\pi\) | |||||||
\(758\) | −4.64374e19 | − | 4.64374e19i | −0.322986 | − | 0.322986i | ||||
\(759\) | 1.76871e20i | 1.21889i | ||||||||
\(760\) | −6.34924e18 | + | 1.48814e18i | −0.0433538 | + | 0.0101613i | ||||
\(761\) | −9.96683e19 | −0.674317 | −0.337159 | − | 0.941448i | \(-0.609466\pi\) | ||||
−0.337159 | + | 0.941448i | \(0.609466\pi\) | |||||||
\(762\) | 5.45642e19 | − | 5.45642e19i | 0.365783 | − | 0.365783i | ||||
\(763\) | −9.13397e19 | − | 9.13397e19i | −0.606719 | − | 0.606719i | ||||
\(764\) | − | 1.09852e20i | − | 0.723026i | ||||||
\(765\) | −2.26895e19 | − | 9.68060e19i | −0.147977 | − | 0.631353i | ||||
\(766\) | −5.29239e19 | −0.342019 | ||||||||
\(767\) | −1.30916e20 | + | 1.30916e20i | −0.838349 | + | 0.838349i | ||||
\(768\) | 8.65033e18 | + | 8.65033e18i | 0.0548914 | + | 0.0548914i | ||||
\(769\) | − | 3.05109e20i | − | 1.91854i | −0.282490 | − | 0.959270i | \(-0.591160\pi\) | ||
0.282490 | − | 0.959270i | \(-0.408840\pi\) | |||||||
\(770\) | 2.77909e19 | − | 4.48064e19i | 0.173168 | − | 0.279193i | ||||
\(771\) | −3.76229e20 | −2.32312 | ||||||||
\(772\) | 2.59720e19 | − | 2.59720e19i | 0.158922 | − | 0.158922i | ||||
\(773\) | −6.21534e19 | − | 6.21534e19i | −0.376885 | − | 0.376885i | 0.493092 | − | 0.869977i | \(-0.335866\pi\) |
−0.869977 | + | 0.493092i | \(0.835866\pi\) | |||||||
\(774\) | 9.82817e19i | 0.590590i | ||||||||
\(775\) | −9.86762e19 | − | 1.98940e20i | −0.587625 | − | 1.18470i | ||||
\(776\) | 3.22545e19 | 0.190352 | ||||||||
\(777\) | 6.37404e19 | − | 6.37404e19i | 0.372793 | − | 0.372793i | ||||
\(778\) | −1.22478e19 | − | 1.22478e19i | −0.0709909 | − | 0.0709909i | ||||
\(779\) | − | 3.09818e18i | − | 0.0177969i | ||||||
\(780\) | 1.26515e20 | + | 7.84705e19i | 0.720246 | + | 0.446729i | ||||
\(781\) | −2.73560e19 | −0.154346 | ||||||||
\(782\) | 1.45116e20 | − | 1.45116e20i | 0.811463 | − | 0.811463i | ||||
\(783\) | 1.01340e20 | + | 1.01340e20i | 0.561627 | + | 0.561627i | ||||
\(784\) | − | 2.66943e19i | − | 0.146625i | ||||||
\(785\) | −1.82724e20 | + | 4.28271e19i | −0.994738 | + | 0.233148i | ||||
\(786\) | 1.14114e20 | 0.615718 | ||||||||
\(787\) | −1.33787e20 | + | 1.33787e20i | −0.715469 | + | 0.715469i | −0.967674 | − | 0.252205i | \(-0.918844\pi\) |
0.252205 | + | 0.967674i | \(0.418844\pi\) | |||||||
\(788\) | 7.11409e19 | + | 7.11409e19i | 0.377082 | + | 0.377082i | ||||
\(789\) | − | 2.42256e20i | − | 1.27273i | ||||||
\(790\) | 1.31691e18 | + | 5.61866e18i | 0.00685750 | + | 0.0292579i | ||||
\(791\) | −4.19836e19 | −0.216693 | ||||||||
\(792\) | 1.91614e19 | − | 1.91614e19i | 0.0980279 | − | 0.0980279i | ||||
\(793\) | 8.41989e19 | + | 8.41989e19i | 0.426967 | + | 0.426967i | ||||
\(794\) | 5.52682e19i | 0.277800i | ||||||||
\(795\) | 2.02944e20 | − | 3.27200e20i | 1.01113 | − | 1.63021i | ||||
\(796\) | −1.05036e20 | −0.518734 | ||||||||
\(797\) | 1.52788e20 | − | 1.52788e20i | 0.747963 | − | 0.747963i | −0.226134 | − | 0.974096i | \(-0.572609\pi\) |
0.974096 | + | 0.226134i | \(0.0726086\pi\) | |||||||
\(798\) | −1.03646e19 | − | 1.03646e19i | −0.0502959 | − | 0.0502959i | ||||
\(799\) | 4.65402e20i | 2.23872i | ||||||||
\(800\) | 3.51327e19 | + | 1.18358e19i | 0.167526 | + | 0.0564375i | ||||
\(801\) | 4.25146e19 | 0.200961 | ||||||||
\(802\) | −2.40133e19 | + | 2.40133e19i | −0.112520 | + | 0.112520i | ||||
\(803\) | 1.56648e20 | + | 1.56648e20i | 0.727640 | + | 0.727640i | ||||
\(804\) | 2.26881e19i | 0.104474i | ||||||||
\(805\) | −1.62591e20 | − | 1.00846e20i | −0.742206 | − | 0.460350i | ||||
\(806\) | −2.82003e20 | −1.27617 | ||||||||
\(807\) | −2.02218e20 | + | 2.02218e20i | −0.907202 | + | 0.907202i | ||||
\(808\) | 9.06241e19 | + | 9.06241e19i | 0.403055 | + | 0.403055i | ||||
\(809\) | 1.32863e19i | 0.0585821i | 0.999571 | + | 0.0292911i | \(0.00932497\pi\) | ||||
−0.999571 | + | 0.0292911i | \(0.990675\pi\) | |||||||
\(810\) | 1.96582e20 | − | 4.60751e19i | 0.859308 | − | 0.201406i | ||||
\(811\) | 3.68640e20 | 1.59756 | 0.798778 | − | 0.601626i | \(-0.205480\pi\) | ||||
0.798778 | + | 0.601626i | \(0.205480\pi\) | |||||||
\(812\) | −7.39941e19 | + | 7.39941e19i | −0.317911 | + | 0.317911i | ||||
\(813\) | 5.41624e19 | + | 5.41624e19i | 0.230709 | + | 0.230709i | ||||
\(814\) | 7.98583e19i | 0.337248i | ||||||||
\(815\) | 6.76685e19 | + | 2.88711e20i | 0.283324 | + | 1.20882i | ||||
\(816\) | −8.93809e19 | −0.371034 | ||||||||
\(817\) | −3.33023e19 | + | 3.33023e19i | −0.137063 | + | 0.137063i | ||||
\(818\) | −6.73618e19 | − | 6.73618e19i | −0.274879 | − | 0.274879i | ||||
\(819\) | 1.17714e20i | 0.476255i | ||||||||
\(820\) | −9.28349e18 | + | 1.49675e19i | −0.0372404 | + | 0.0600414i | ||||
\(821\) | 2.35484e20 | 0.936612 | 0.468306 | − | 0.883566i | \(-0.344864\pi\) | ||||
0.468306 | + | 0.883566i | \(0.344864\pi\) | |||||||
\(822\) | −2.54717e20 | + | 2.54717e20i | −1.00451 | + | 1.00451i | ||||
\(823\) | −1.49715e20 | − | 1.49715e20i | −0.585418 | − | 0.585418i | 0.350969 | − | 0.936387i | \(-0.385852\pi\) |
−0.936387 | + | 0.350969i | \(0.885852\pi\) | |||||||
\(824\) | − | 8.63089e19i | − | 0.334630i | ||||||
\(825\) | 7.45279e19 | − | 2.21224e20i | 0.286511 | − | 0.850461i | ||||
\(826\) | −1.03627e20 | −0.395015 | ||||||||
\(827\) | −1.85395e20 | + | 1.85395e20i | −0.700743 | + | 0.700743i | −0.964570 | − | 0.263827i | \(-0.915015\pi\) |
0.263827 | + | 0.964570i | \(0.415015\pi\) | |||||||
\(828\) | −6.95316e19 | − | 6.95316e19i | −0.260597 | − | 0.260597i | ||||
\(829\) | 3.13386e20i | 1.16466i | 0.812954 | + | 0.582328i | \(0.197858\pi\) | ||||
−0.812954 | + | 0.582328i | \(0.802142\pi\) | |||||||
\(830\) | 6.81418e19 | + | 4.22646e19i | 0.251112 | + | 0.155751i | ||||
\(831\) | 5.90138e20 | 2.15648 | ||||||||
\(832\) | 3.32896e19 | − | 3.32896e19i | 0.120627 | − | 0.120627i | ||||
\(833\) | 1.37912e20 | + | 1.37912e20i | 0.495548 | + | 0.495548i | ||||
\(834\) | − | 1.64412e20i | − | 0.585829i | ||||||
\(835\) | −3.91492e20 | + | 9.17583e19i | −1.38330 | + | 0.324220i | ||||
\(836\) | 1.29855e19 | 0.0455003 | ||||||||
\(837\) | −1.52858e20 | + | 1.52858e20i | −0.531141 | + | 0.531141i | ||||
\(838\) | −7.95387e19 | − | 7.95387e19i | −0.274075 | − | 0.274075i | ||||
\(839\) | − | 4.39326e20i | − | 1.50125i | −0.660728 | − | 0.750626i | \(-0.729752\pi\) | ||
0.660728 | − | 0.750626i | \(-0.270248\pi\) | |||||||
\(840\) | 1.90151e19 | + | 8.11288e19i | 0.0644381 | + | 0.274929i | ||||
\(841\) | −2.84270e20 | −0.955342 | ||||||||
\(842\) | 1.67497e20 | − | 1.67497e20i | 0.558243 | − | 0.558243i | ||||
\(843\) | −3.66781e20 | − | 3.66781e20i | −1.21231 | − | 1.21231i | ||||
\(844\) | − | 1.44284e20i | − | 0.472956i | ||||||
\(845\) | 1.39846e20 | − | 2.25469e20i | 0.454624 | − | 0.732975i | ||||
\(846\) | 2.22994e20 | 0.718955 | ||||||||
\(847\) | 6.79646e19 | − | 6.79646e19i | 0.217320 | − | 0.217320i | ||||
\(848\) | −8.60951e19 | − | 8.60951e19i | −0.273028 | − | 0.273028i | ||||
\(849\) | − | 1.33209e20i | − | 0.418967i | ||||||
\(850\) | −2.42655e20 | + | 1.20359e20i | −0.756930 | + | 0.375445i | ||||
\(851\) | 2.89785e20 | 0.896539 | ||||||||
\(852\) | 3.05708e19 | − | 3.05708e19i | 0.0938058 | − | 0.0938058i | ||||
\(853\) | 1.93218e20 | + | 1.93218e20i | 0.588036 | + | 0.588036i | 0.937099 | − | 0.349063i | \(-0.113500\pi\) |
−0.349063 | + | 0.937099i | \(0.613500\pi\) | |||||||
\(854\) | 6.66481e19i | 0.201179i | ||||||||
\(855\) | −1.94008e19 | − | 1.20332e19i | −0.0580840 | − | 0.0360263i | ||||
\(856\) | 5.54755e19 | 0.164735 | ||||||||
\(857\) | −6.05233e19 | + | 6.05233e19i | −0.178261 | + | 0.178261i | −0.790598 | − | 0.612336i | \(-0.790230\pi\) |
0.612336 | + | 0.790598i | \(0.290230\pi\) | |||||||
\(858\) | −2.09619e20 | − | 2.09619e20i | −0.612377 | − | 0.612377i | ||||
\(859\) | − | 1.50678e20i | − | 0.436614i | −0.975880 | − | 0.218307i | \(-0.929947\pi\) | ||
0.975880 | − | 0.218307i | \(-0.0700534\pi\) | |||||||
\(860\) | 2.60674e20 | − | 6.10970e19i | 0.749218 | − | 0.175602i | ||||
\(861\) | −3.95876e19 | −0.112859 | ||||||||
\(862\) | 3.28962e20 | − | 3.28962e20i | 0.930239 | − | 0.930239i | ||||
\(863\) | −1.46564e20 | − | 1.46564e20i | −0.411105 | − | 0.411105i | 0.471018 | − | 0.882123i | \(-0.343887\pi\) |
−0.882123 | + | 0.471018i | \(0.843887\pi\) | |||||||
\(864\) | − | 3.60888e19i | − | 0.100410i | ||||||
\(865\) | 9.04222e19 | + | 3.85791e20i | 0.249553 | + | 1.06473i | ||||
\(866\) | −1.32924e20 | −0.363896 | ||||||||
\(867\) | 1.38358e20 | − | 1.38358e20i | 0.375725 | − | 0.375725i | ||||
\(868\) | −1.11611e20 | − | 1.11611e20i | −0.300654 | − | 0.300654i | ||||
\(869\) | − | 1.14913e19i | − | 0.0307065i | ||||||
\(870\) | −2.44205e20 | + | 3.93724e20i | −0.647322 | + | 1.04366i | ||||
\(871\) | 8.73121e19 | 0.229587 | ||||||||
\(872\) | −1.27885e20 | + | 1.27885e20i | −0.333583 | + | 0.333583i | ||||
\(873\) | 7.98433e19 | + | 7.98433e19i | 0.206604 | + | 0.206604i | ||||
\(874\) | − | 4.71210e19i | − | 0.120958i | ||||||
\(875\) | 1.60870e20 | + | 1.94646e20i | 0.409655 | + | 0.495666i | ||||
\(876\) | −3.50114e20 | −0.884466 | ||||||||
\(877\) | 3.49277e20 | − | 3.49277e20i | 0.875331 | − | 0.875331i | −0.117716 | − | 0.993047i | \(-0.537557\pi\) |
0.993047 | + | 0.117716i | \(0.0375573\pi\) | |||||||
\(878\) | 1.23421e20 | + | 1.23421e20i | 0.306850 | + | 0.306850i | ||||
\(879\) | 1.09456e20i | 0.269970i | ||||||||
\(880\) | −6.27335e19 | − | 3.89102e19i | −0.153504 | − | 0.0952104i | ||||
\(881\) | −3.27105e20 | −0.794063 | −0.397032 | − | 0.917805i | \(-0.629960\pi\) | ||||
−0.397032 | + | 0.917805i | \(0.629960\pi\) | |||||||
\(882\) | 6.60796e19 | − | 6.60796e19i | 0.159143 | − | 0.159143i | ||||
\(883\) | −3.55056e20 | − | 3.55056e20i | −0.848343 | − | 0.848343i | 0.141583 | − | 0.989926i | \(-0.454781\pi\) |
−0.989926 | + | 0.141583i | \(0.954781\pi\) | |||||||
\(884\) | 3.43970e20i | 0.815370i | ||||||||
\(885\) | −4.46703e20 | + | 1.04699e20i | −1.05055 | + | 0.246229i | ||||
\(886\) | 1.68006e20 | 0.392003 | ||||||||
\(887\) | 3.37013e20 | − | 3.37013e20i | 0.780157 | − | 0.780157i | −0.199700 | − | 0.979857i | \(-0.563997\pi\) |
0.979857 | + | 0.199700i | \(0.0639968\pi\) | |||||||
\(888\) | −8.92431e19 | − | 8.92431e19i | −0.204967 | − | 0.204967i | ||||
\(889\) | − | 1.66213e20i | − | 0.378750i | ||||||
\(890\) | −2.64293e19 | − | 1.12762e20i | −0.0597524 | − | 0.254937i | ||||
\(891\) | −4.02050e20 | −0.901853 | ||||||||
\(892\) | −1.80019e20 | + | 1.80019e20i | −0.400648 | + | 0.400648i | ||||
\(893\) | 7.55607e19 | + | 7.55607e19i | 0.166854 | + | 0.166854i | ||||
\(894\) | − | 3.19259e19i | − | 0.0699489i | ||||||
\(895\) | −1.59773e20 | + | 2.57597e20i | −0.347330 | + | 0.559989i | ||||
\(896\) | 2.63506e19 | 0.0568373 | ||||||||
\(897\) | −7.60652e20 | + | 7.60652e20i | −1.62794 | + | 1.62794i | ||||
\(898\) | 2.08285e20 | + | 2.08285e20i | 0.442307 | + | 0.442307i | ||||
\(899\) | − | 8.77612e20i | − | 1.84920i | ||||||
\(900\) | 5.76694e19 | + | 1.16266e20i | 0.120572 | + | 0.243084i | ||||
\(901\) | 8.89591e20 | 1.84551 | ||||||||
\(902\) | 2.47990e19 | − | 2.47990e19i | 0.0510492 | − | 0.0510492i | ||||
\(903\) | 4.25528e20 | + | 4.25528e20i | 0.869188 | + | 0.869188i | ||||
\(904\) | 5.87814e19i | 0.119141i | ||||||||
\(905\) | 4.78395e20 | + | 2.96722e20i | 0.962159 | + | 0.596775i | ||||
\(906\) | 4.38366e20 | 0.874861 | ||||||||
\(907\) | −4.24176e20 | + | 4.24176e20i | −0.840030 | + | 0.840030i | −0.988862 | − | 0.148832i | \(-0.952448\pi\) |
0.148832 | + | 0.988862i | \(0.452448\pi\) | |||||||
\(908\) | 6.54750e19 | + | 6.54750e19i | 0.128669 | + | 0.128669i | ||||
\(909\) | 4.48664e20i | 0.874932i | ||||||||
\(910\) | 3.12213e20 | − | 7.31768e19i | 0.604173 | − | 0.141607i | ||||
\(911\) | 1.83771e20 | 0.352897 | 0.176449 | − | 0.984310i | \(-0.443539\pi\) | ||||
0.176449 | + | 0.984310i | \(0.443539\pi\) | |||||||
\(912\) | −1.45115e19 | + | 1.45115e19i | −0.0276534 | + | 0.0276534i | ||||
\(913\) | −1.12902e20 | − | 1.12902e20i | −0.213503 | − | 0.213503i | ||||
\(914\) | 1.84419e20i | 0.346084i | ||||||||
\(915\) | 6.73373e19 | + | 2.87298e20i | 0.125403 | + | 0.535039i | ||||
\(916\) | 2.91502e20 | 0.538732 | ||||||||
\(917\) | 1.73807e20 | − | 1.73807e20i | 0.318773 | − | 0.318773i | ||||
\(918\) | 1.86447e20 | + | 1.86447e20i | 0.339356 | + | 0.339356i | ||||
\(919\) | 2.20334e19i | 0.0397991i | 0.999802 | + | 0.0198995i | \(0.00633464\pi\) | ||||
−0.999802 | + | 0.0198995i | \(0.993665\pi\) | |||||||
\(920\) | −1.41195e20 | + | 2.27644e20i | −0.253107 | + | 0.408076i | ||||
\(921\) | −8.69091e20 | −1.54614 | ||||||||
\(922\) | 2.77223e20 | − | 2.77223e20i | 0.489455 | − | 0.489455i | ||||
\(923\) | −1.17647e20 | − | 1.17647e20i | −0.206144 | − | 0.206144i | ||||
\(924\) | − | 1.65925e20i | − | 0.288541i | ||||||
\(925\) | −3.62454e20 | − | 1.22107e20i | −0.625548 | − | 0.210740i | ||||
\(926\) | 6.40429e20 | 1.09697 | ||||||||
\(927\) | 2.13650e20 | − | 2.13650e20i | 0.363200 | − | 0.363200i | ||||
\(928\) | 1.03599e20 | + | 1.03599e20i | 0.174792 | + | 0.174792i | ||||
\(929\) | − | 8.49853e20i | − | 1.42310i | −0.702638 | − | 0.711548i | \(-0.747995\pi\) | ||
0.702638 | − | 0.711548i | \(-0.252005\pi\) | |||||||
\(930\) | −5.93881e20 | − | 3.68352e20i | −0.987004 | − | 0.612184i | ||||
\(931\) | 4.47815e19 | 0.0738671 | ||||||||
\(932\) | 6.39208e19 | − | 6.39208e19i | 0.104648 | − | 0.104648i | ||||
\(933\) | −4.95675e19 | − | 4.95675e19i | −0.0805426 | − | 0.0805426i | ||||
\(934\) | 2.60245e20i | 0.419715i | ||||||||
\(935\) | 5.25125e20 | − | 1.23079e20i | 0.840584 | − | 0.197017i | ||||
\(936\) | 1.64811e20 | 0.261852 | ||||||||
\(937\) | −5.56457e20 | + | 5.56457e20i | −0.877515 | + | 0.877515i | −0.993277 | − | 0.115762i | \(-0.963069\pi\) |
0.115762 | + | 0.993277i | \(0.463069\pi\) | |||||||
\(938\) | 3.45562e19 | + | 3.45562e19i | 0.0540886 | + | 0.0540886i | ||||
\(939\) | − | 6.53102e20i | − | 1.01466i | ||||||
\(940\) | −1.38625e20 | − | 5.91450e20i | −0.213770 | − | 0.912060i | ||||
\(941\) | −8.73295e20 | −1.33670 | −0.668349 | − | 0.743848i | \(-0.732999\pi\) | ||||
−0.668349 | + | 0.743848i | \(0.732999\pi\) | |||||||
\(942\) | −4.17625e20 | + | 4.17625e20i | −0.634499 | + | 0.634499i | ||||
\(943\) | −8.99893e19 | − | 8.99893e19i | −0.135709 | − | 0.135709i | ||||
\(944\) | 1.45089e20i | 0.217185i | ||||||||
\(945\) | 1.29568e20 | − | 2.08898e20i | 0.192520 | − | 0.310393i | ||||
\(946\) | −5.33130e20 | −0.786312 | ||||||||
\(947\) | 2.29916e20 | − | 2.29916e20i | 0.336603 | − | 0.336603i | −0.518484 | − | 0.855087i | \(-0.673503\pi\) |
0.855087 | + | 0.518484i | \(0.173503\pi\) | |||||||
\(948\) | 1.28417e19 | + | 1.28417e19i | 0.0186623 | + | 0.0186623i | ||||
\(949\) | 1.34737e21i | 1.94367i | ||||||||
\(950\) | −1.98554e19 | + | 5.89374e19i | −0.0284323 | + | 0.0843967i | ||||
\(951\) | 6.25121e20 | 0.888589 | ||||||||
\(952\) | −1.36136e20 | + | 1.36136e20i | −0.192094 | + | 0.192094i | ||||
\(953\) | −8.80074e19 | − | 8.80074e19i | −0.123273 | − | 0.123273i | 0.642779 | − | 0.766052i | \(-0.277781\pi\) |
−0.766052 | + | 0.642779i | \(0.777781\pi\) | |||||||
\(954\) | − | 4.26242e20i | − | 0.592677i | ||||||
\(955\) | −8.90285e20 | − | 5.52195e20i | −1.22887 | − | 0.762200i | ||||
\(956\) | 1.22962e20 | 0.168487 | ||||||||
\(957\) | 6.52347e20 | − | 6.52347e20i | 0.887350 | − | 0.887350i | ||||
\(958\) | −2.99897e20 | − | 2.99897e20i | −0.404961 | − | 0.404961i | ||||
\(959\) | 7.75917e20i | 1.04012i | ||||||||
\(960\) | 1.13589e20 | − | 2.66230e19i | 0.151160 | − | 0.0354290i | ||||
\(961\) | 5.66820e20 | 0.748826 | ||||||||
\(962\) | −3.43439e20 | + | 3.43439e20i | −0.450427 | + | 0.450427i | ||||
\(963\) | 1.37325e20 | + | 1.37325e20i | 0.178799 | + | 0.178799i | ||||
\(964\) | − | 2.62758e20i | − | 0.339638i | ||||||
\(965\) | −7.99339e19 | − | 3.41042e20i | −0.102575 | − | 0.437640i | ||||
\(966\) | −6.02098e20 | −0.767056 | ||||||||
\(967\) | −2.60409e20 | + | 2.60409e20i | −0.329359 | + | 0.329359i | −0.852343 | − | 0.522984i | \(-0.824819\pi\) |
0.522984 | + | 0.852343i | \(0.324819\pi\) | |||||||
\(968\) | −9.51574e19 | − | 9.51574e19i | −0.119485 | − | 0.119485i | ||||
\(969\) | − | 1.49942e20i | − | 0.186921i | ||||||
\(970\) | 1.62134e20 | − | 2.61404e20i | 0.200666 | − | 0.323526i | ||||
\(971\) | −2.59376e20 | −0.318710 | −0.159355 | − | 0.987221i | \(-0.550941\pi\) | ||||
−0.159355 | + | 0.987221i | \(0.550941\pi\) | |||||||
\(972\) | 2.84683e20 | − | 2.84683e20i | 0.347294 | − | 0.347294i | ||||
\(973\) | −2.50415e20 | − | 2.50415e20i | −0.303299 | − | 0.303299i | ||||
\(974\) | − | 4.30221e20i | − | 0.517343i | ||||||
\(975\) | 1.27191e21 | − | 6.30883e20i | 1.51854 | − | 0.753210i | ||||
\(976\) | 9.33142e19 | 0.110611 | ||||||||
\(977\) | 5.36022e20 | − | 5.36022e20i | 0.630842 | − | 0.630842i | −0.317437 | − | 0.948279i | \(-0.602822\pi\) |
0.948279 | + | 0.317437i | \(0.102822\pi\) | |||||||
\(978\) | 6.59864e20 | + | 6.59864e20i | 0.771049 | + | 0.771049i | ||||
\(979\) | 2.30621e20i | 0.267559i | ||||||||
\(980\) | −2.16342e20 | − | 1.34185e20i | −0.249206 | − | 0.154569i | ||||
\(981\) | −6.33137e20 | −0.724127 | ||||||||
\(982\) | −3.95366e20 | + | 3.95366e20i | −0.448971 | + | 0.448971i | ||||
\(983\) | 3.43979e20 | + | 3.43979e20i | 0.387844 | + | 0.387844i | 0.873918 | − | 0.486074i | \(-0.161571\pi\) |
−0.486074 | + | 0.873918i | \(0.661571\pi\) | |||||||
\(984\) | 5.54267e19i | 0.0620517i | ||||||||
\(985\) | 9.34161e20 | − | 2.18950e20i | 1.03841 | − | 0.243383i | ||||
\(986\) | −1.07046e21 | −1.18149 | ||||||||
\(987\) | 9.65493e20 | − | 9.65493e20i | 1.05811 | − | 1.05811i | ||||
\(988\) | 5.58455e19 | + | 5.58455e19i | 0.0607701 | + | 0.0607701i | ||||
\(989\) | 1.93459e21i | 2.09033i | ||||||||
\(990\) | −5.89727e19 | − | 2.51610e20i | −0.0632710 | − | 0.269949i | ||||
\(991\) | −5.67452e20 | −0.604524 | −0.302262 | − | 0.953225i | \(-0.597742\pi\) | ||||
−0.302262 | + | 0.953225i | \(0.597742\pi\) | |||||||
\(992\) | −1.56266e20 | + | 1.56266e20i | −0.165304 | + | 0.165304i | ||||
\(993\) | 5.99607e20 | + | 5.99607e20i | 0.629828 | + | 0.629828i | ||||
\(994\) | − | 9.31245e19i | − | 0.0971313i | ||||||
\(995\) | −5.27984e20 | + | 8.51251e20i | −0.546839 | + | 0.881650i | ||||
\(996\) | 2.52339e20 | 0.259519 | ||||||||
\(997\) | 5.76322e20 | − | 5.76322e20i | 0.588571 | − | 0.588571i | −0.348673 | − | 0.937244i | \(-0.613368\pi\) |
0.937244 | + | 0.348673i | \(0.113368\pi\) | |||||||
\(998\) | −6.56874e20 | − | 6.56874e20i | −0.666145 | − | 0.666145i | ||||
\(999\) | 3.72318e20i | 0.374935i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 10.15.c.a.3.3 | ✓ | 6 | |
3.2 | odd | 2 | 90.15.g.a.73.3 | 6 | |||
4.3 | odd | 2 | 80.15.p.a.33.1 | 6 | |||
5.2 | odd | 4 | inner | 10.15.c.a.7.3 | yes | 6 | |
5.3 | odd | 4 | 50.15.c.b.7.1 | 6 | |||
5.4 | even | 2 | 50.15.c.b.43.1 | 6 | |||
15.2 | even | 4 | 90.15.g.a.37.3 | 6 | |||
20.7 | even | 4 | 80.15.p.a.17.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.15.c.a.3.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
10.15.c.a.7.3 | yes | 6 | 5.2 | odd | 4 | inner | |
50.15.c.b.7.1 | 6 | 5.3 | odd | 4 | |||
50.15.c.b.43.1 | 6 | 5.4 | even | 2 | |||
80.15.p.a.17.1 | 6 | 20.7 | even | 4 | |||
80.15.p.a.33.1 | 6 | 4.3 | odd | 2 | |||
90.15.g.a.37.3 | 6 | 15.2 | even | 4 | |||
90.15.g.a.73.3 | 6 | 3.2 | odd | 2 |