Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [342,7,Mod(145,342)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(342, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("342.145");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.m (of order \(6\), 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: | \(78.6784965980\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 112 x^{19} + 116318 x^{18} + 1860432 x^{17} + 7532794771 x^{16} - 134305195660 x^{15} + \cdots + 10\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{4}\cdot 19^{2} \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 217.10 | ||
Root | \(85.1965 - 147.565i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 342.217 |
Dual form | 342.7.m.a.145.10 |
$q$-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 \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.89898 | + | 2.82843i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | + | 27.7128i | 0.250000 | + | 0.433013i | ||||
\(5\) | 85.1965 | − | 147.565i | 0.681572 | − | 1.18052i | −0.292929 | − | 0.956134i | \(-0.594630\pi\) |
0.974501 | − | 0.224383i | \(-0.0720368\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 473.710 | 1.38108 | 0.690539 | − | 0.723295i | \(-0.257373\pi\) | ||||
0.690539 | + | 0.723295i | \(0.257373\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 834.752 | − | 481.944i | 0.834752 | − | 0.481944i | ||||
\(11\) | 2118.68 | 1.59179 | 0.795897 | − | 0.605432i | \(-0.207000\pi\) | ||||
0.795897 | + | 0.605432i | \(0.207000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2401.07 | − | 1386.26i | 1.09289 | − | 0.630978i | 0.158543 | − | 0.987352i | \(-0.449320\pi\) |
0.934344 | + | 0.356374i | \(0.115987\pi\) | |||||||
\(14\) | 2320.70 | + | 1339.85i | 0.845734 | + | 0.488285i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −512.000 | + | 886.810i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4199.48 | + | 7273.71i | −0.854769 | + | 1.48050i | 0.0220902 | + | 0.999756i | \(0.492968\pi\) |
−0.876859 | + | 0.480747i | \(0.840365\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6819.60 | + | 734.105i | 0.994256 | + | 0.107028i | ||||
\(20\) | 5452.58 | 0.681572 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10379.4 | + | 5992.52i | 0.974771 | + | 0.562784i | ||||
\(23\) | −3495.35 | − | 6054.13i | −0.287282 | − | 0.497586i | 0.685878 | − | 0.727716i | \(-0.259418\pi\) |
−0.973160 | + | 0.230130i | \(0.926085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6704.40 | − | 11612.4i | −0.429081 | − | 0.743191i | ||||
\(26\) | 15683.7 | 0.892338 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7579.36 | + | 13127.8i | 0.345270 | + | 0.598025i | ||||
\(29\) | −25424.0 | + | 14678.6i | −1.04244 | + | 0.601853i | −0.920523 | − | 0.390688i | \(-0.872237\pi\) |
−0.121916 | + | 0.992540i | \(0.538904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 38548.2i | − | 1.29395i | −0.762509 | − | 0.646977i | \(-0.776033\pi\) | ||
0.762509 | − | 0.646977i | \(-0.223967\pi\) | |||||||
\(32\) | −5016.55 | + | 2896.31i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −41146.3 | + | 23755.8i | −1.04687 | + | 0.604413i | ||||
\(35\) | 40358.4 | − | 69902.9i | 0.941305 | − | 1.63039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 49167.4i | 0.970671i | 0.874328 | + | 0.485335i | \(0.161302\pi\) | ||||
−0.874328 | + | 0.485335i | \(0.838698\pi\) | |||||||
\(38\) | 31332.7 | + | 22885.1i | 0.571015 | + | 0.417064i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 26712.1 | + | 15422.2i | 0.417376 | + | 0.240972i | ||||
\(41\) | −39559.5 | − | 22839.7i | −0.573983 | − | 0.331389i | 0.184756 | − | 0.982785i | \(-0.440851\pi\) |
−0.758739 | + | 0.651395i | \(0.774184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34060.1 | − | 58993.9i | 0.428392 | − | 0.741996i | −0.568339 | − | 0.822795i | \(-0.692414\pi\) |
0.996730 | + | 0.0807986i | \(0.0257471\pi\) | |||||||
\(44\) | 33898.8 | + | 58714.5i | 0.397948 | + | 0.689267i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 39545.4i | − | 0.406277i | ||||||
\(47\) | 79086.9 | + | 136983.i | 0.761748 | + | 1.31939i | 0.941949 | + | 0.335756i | \(0.108992\pi\) |
−0.180201 | + | 0.983630i | \(0.557675\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 106752. | 0.907378 | ||||||||
\(50\) | − | 75851.6i | − | 0.606813i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 76834.3 | + | 44360.3i | 0.546443 | + | 0.315489i | ||||
\(53\) | −60725.2 | + | 35059.7i | −0.407888 | + | 0.235494i | −0.689882 | − | 0.723922i | \(-0.742338\pi\) |
0.281994 | + | 0.959416i | \(0.409004\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 180504. | − | 312642.i | 1.08492 | − | 1.87914i | ||||
\(56\) | 85750.7i | 0.488285i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −166069. | −0.851148 | ||||||||
\(59\) | −214108. | − | 123615.i | −1.04250 | − | 0.601887i | −0.121959 | − | 0.992535i | \(-0.538918\pi\) |
−0.920540 | + | 0.390648i | \(0.872251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25917.8 | + | 44891.0i | 0.114185 | + | 0.197774i | 0.917454 | − | 0.397843i | \(-0.130241\pi\) |
−0.803269 | + | 0.595617i | \(0.796908\pi\) | |||||||
\(62\) | 109031. | − | 188847.i | 0.457482 | − | 0.792382i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | − | 472418.i | − | 1.72023i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −144770. | + | 83583.2i | −0.481344 | + | 0.277904i | −0.720976 | − | 0.692960i | \(-0.756306\pi\) |
0.239633 | + | 0.970864i | \(0.422973\pi\) | |||||||
\(68\) | −268767. | −0.854769 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 395430. | − | 228302.i | 1.15286 | − | 0.665603i | ||||
\(71\) | −2281.45 | − | 1317.20i | −0.00637435 | − | 0.00368023i | 0.496809 | − | 0.867860i | \(-0.334505\pi\) |
−0.503184 | + | 0.864179i | \(0.667838\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 115884. | − | 200716.i | 0.297889 | − | 0.515958i | −0.677764 | − | 0.735279i | \(-0.737051\pi\) |
0.975653 | + | 0.219321i | \(0.0703843\pi\) | |||||||
\(74\) | −139066. | + | 240870.i | −0.343184 | + | 0.594412i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 88769.5 | + | 200736.i | 0.202220 | + | 0.457282i | ||||
\(77\) | 1.00364e6 | 2.19839 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −376948. | − | 217631.i | −0.764540 | − | 0.441408i | 0.0663831 | − | 0.997794i | \(-0.478854\pi\) |
−0.830924 | + | 0.556387i | \(0.812187\pi\) | |||||||
\(80\) | 87241.2 | + | 151106.i | 0.170393 | + | 0.295129i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −129201. | − | 223782.i | −0.234328 | − | 0.405867i | ||||
\(83\) | 553204. | 0.967500 | 0.483750 | − | 0.875206i | \(-0.339274\pi\) | ||||
0.483750 | + | 0.875206i | \(0.339274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 715562. | + | 1.23939e6i | 1.16517 | + | 2.01814i | ||||
\(86\) | 333720. | − | 192673.i | 0.524670 | − | 0.302919i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 383522.i | 0.562784i | ||||||||
\(89\) | −324464. | + | 187330.i | −0.460254 | + | 0.265727i | −0.712151 | − | 0.702026i | \(-0.752279\pi\) |
0.251897 | + | 0.967754i | \(0.418945\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.13741e6 | − | 656685.i | 1.50936 | − | 0.871431i | ||||
\(92\) | 111851. | − | 193732.i | 0.143641 | − | 0.248793i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 894766.i | 1.07727i | ||||||||
\(95\) | 689334. | − | 943789.i | 0.804006 | − | 1.10079i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 274550. | + | 158512.i | 0.300820 | + | 0.173678i | 0.642811 | − | 0.766025i | \(-0.277768\pi\) |
−0.341991 | + | 0.939703i | \(0.611101\pi\) | |||||||
\(98\) | 522976. | + | 301940.i | 0.555653 | + | 0.320806i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 214541. | − | 371595.i | 0.214541 | − | 0.371595i | ||||
\(101\) | −56161.6 | − | 97274.8i | −0.0545099 | − | 0.0944139i | 0.837483 | − | 0.546464i | \(-0.184026\pi\) |
−0.891993 | + | 0.452050i | \(0.850693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 736462.i | 0.673967i | 0.941511 | + | 0.336983i | \(0.109407\pi\) | ||||
−0.941511 | + | 0.336983i | \(0.890593\pi\) | |||||||
\(104\) | 250940. | + | 434640.i | 0.223085 | + | 0.386394i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −396655. | −0.333039 | ||||||||
\(107\) | 110276.i | 0.0900184i | 0.998987 | + | 0.0450092i | \(0.0143317\pi\) | ||||
−0.998987 | + | 0.0450092i | \(0.985668\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −628454. | − | 362838.i | −0.485282 | − | 0.280177i | 0.237333 | − | 0.971428i | \(-0.423727\pi\) |
−0.722615 | + | 0.691251i | \(0.757060\pi\) | |||||||
\(110\) | 1.76857e6 | − | 1.02108e6i | 1.32875 | − | 0.767156i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −242539. | + | 420091.i | −0.172635 | + | 0.299012i | ||||
\(113\) | 1.72474e6i | 1.19533i | 0.801746 | + | 0.597665i | \(0.203905\pi\) | ||||
−0.801746 | + | 0.597665i | \(0.796095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.19117e6 | −0.783212 | ||||||||
\(116\) | −813570. | − | 469715.i | −0.521220 | − | 0.300926i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −699272. | − | 1.21118e6i | −0.425599 | − | 0.737159i | ||||
\(119\) | −1.98934e6 | + | 3.44563e6i | −1.18050 | + | 2.04469i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71723e6 | 1.53381 | ||||||||
\(122\) | 293227.i | 0.161482i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.06828e6 | − | 616771.i | 0.560299 | − | 0.323489i | ||||
\(125\) | 377626. | 0.193345 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.48410e6 | − | 856846.i | 0.724523 | − | 0.418304i | −0.0918919 | − | 0.995769i | \(-0.529291\pi\) |
0.816415 | + | 0.577465i | \(0.195958\pi\) | |||||||
\(128\) | −160530. | − | 92681.9i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.33620e6 | − | 2.31437e6i | 0.608193 | − | 1.05342i | ||||
\(131\) | 363251. | − | 629170.i | 0.161582 | − | 0.279868i | −0.773854 | − | 0.633364i | \(-0.781674\pi\) |
0.935436 | + | 0.353495i | \(0.115007\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23051e6 | + | 347753.i | 1.37315 | + | 0.147814i | ||||
\(134\) | −945636. | −0.393015 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.31668e6 | − | 760187.i | −0.523437 | − | 0.302206i | ||||
\(137\) | −1.24733e6 | − | 2.16044e6i | −0.485088 | − | 0.840197i | 0.514765 | − | 0.857331i | \(-0.327879\pi\) |
−0.999853 | + | 0.0171344i | \(0.994546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 76133.2 | + | 131867.i | 0.0283485 | + | 0.0491010i | 0.879852 | − | 0.475249i | \(-0.157642\pi\) |
−0.851503 | + | 0.524350i | \(0.824309\pi\) | |||||||
\(140\) | 2.58294e6 | 0.941305 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7451.18 | − | 12905.8i | −0.00260232 | − | 0.00450734i | ||||
\(143\) | 5.08710e6 | − | 2.93704e6i | 1.73965 | − | 1.00439i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.00226e6i | 1.64082i | ||||||||
\(146\) | 1.13542e6 | − | 655537.i | 0.364837 | − | 0.210639i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.36257e6 | + | 786678.i | −0.420313 | + | 0.242668i | ||||
\(149\) | −2.11509e6 | + | 3.66345e6i | −0.639397 | + | 1.10747i | 0.346169 | + | 0.938172i | \(0.387482\pi\) |
−0.985565 | + | 0.169295i | \(0.945851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.23909e6i | − | 0.359891i | −0.983677 | − | 0.179946i | \(-0.942408\pi\) | ||
0.983677 | − | 0.179946i | \(-0.0575922\pi\) | |||||||
\(152\) | −132887. | + | 1.23448e6i | −0.0378401 | + | 0.351523i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.91680e6 | + | 2.83872e6i | 1.34623 | + | 0.777249i | ||||
\(155\) | −5.68835e6 | − | 3.28417e6i | −1.52754 | − | 0.881923i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.26593e6 | − | 3.92470e6i | 0.585527 | − | 1.01416i | −0.409282 | − | 0.912408i | \(-0.634221\pi\) |
0.994809 | − | 0.101755i | \(-0.0324458\pi\) | |||||||
\(158\) | −1.23111e6 | − | 2.13234e6i | −0.312122 | − | 0.540612i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 987022.i | 0.240972i | ||||||||
\(161\) | −1.65578e6 | − | 2.86790e6i | −0.396758 | − | 0.687206i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.81695e6 | −0.881361 | −0.440681 | − | 0.897664i | \(-0.645263\pi\) | ||||
−0.440681 | + | 0.897664i | \(0.645263\pi\) | |||||||
\(164\) | − | 1.46174e6i | − | 0.331389i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.71013e6 | + | 1.56470e6i | 0.592470 | + | 0.342063i | ||||
\(167\) | 4.57438e6 | − | 2.64102e6i | 0.982161 | − | 0.567051i | 0.0792390 | − | 0.996856i | \(-0.474751\pi\) |
0.902922 | + | 0.429805i | \(0.141418\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.43003e6 | − | 2.47688e6i | 0.296267 | − | 0.513150i | ||||
\(170\) | 8.09566e6i | 1.64780i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.17985e6 | 0.428392 | ||||||||
\(173\) | −3.18607e6 | − | 1.83948e6i | −0.615342 | − | 0.355268i | 0.159711 | − | 0.987164i | \(-0.448944\pi\) |
−0.775053 | + | 0.631896i | \(0.782277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.17594e6 | − | 5.50089e6i | −0.592595 | − | 1.02640i | ||||
\(176\) | −1.08476e6 | + | 1.87886e6i | −0.198974 | + | 0.344633i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.11939e6 | −0.375795 | ||||||||
\(179\) | 580056.i | 0.101137i | 0.998721 | + | 0.0505686i | \(0.0161033\pi\) | ||||
−0.998721 | + | 0.0505686i | \(0.983897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.93034e6 | − | 4.57858e6i | 1.33738 | − | 0.772139i | 0.350965 | − | 0.936389i | \(-0.385854\pi\) |
0.986419 | + | 0.164250i | \(0.0525204\pi\) | |||||||
\(182\) | 7.42954e6 | 1.23239 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.09591e6 | − | 632727.i | 0.175923 | − | 0.101569i | ||||
\(185\) | 7.25537e6 | + | 4.18889e6i | 1.14589 | + | 0.661582i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.89734e6 | + | 1.54107e7i | −1.36062 | + | 2.35666i | ||||
\(188\) | −2.53078e6 | + | 4.38344e6i | −0.380874 | + | 0.659693i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.04647e6 | − | 2.67387e6i | 0.881539 | − | 0.389834i | ||||
\(191\) | −2.51336e6 | −0.360706 | −0.180353 | − | 0.983602i | \(-0.557724\pi\) | ||||
−0.180353 | + | 0.983602i | \(0.557724\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.97892e6 | + | 3.45193e6i | 0.831670 | + | 0.480165i | 0.854424 | − | 0.519576i | \(-0.173910\pi\) |
−0.0227540 | + | 0.999741i | \(0.507243\pi\) | |||||||
\(194\) | 896677. | + | 1.55309e6i | 0.122809 | + | 0.212712i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.70803e6 | + | 2.95840e6i | 0.226844 | + | 0.392906i | ||||
\(197\) | −9.83753e6 | −1.28673 | −0.643365 | − | 0.765560i | \(-0.722462\pi\) | ||||
−0.643365 | + | 0.765560i | \(0.722462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −747801. | − | 1.29523e6i | −0.0948914 | − | 0.164357i | 0.814672 | − | 0.579922i | \(-0.196917\pi\) |
−0.909563 | + | 0.415565i | \(0.863584\pi\) | |||||||
\(200\) | 2.10206e6 | − | 1.21363e6i | 0.262758 | − | 0.151703i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 635396.i | − | 0.0770887i | ||||||
\(203\) | −1.20436e7 | + | 6.95339e6i | −1.43969 | + | 0.831206i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.74066e6 | + | 3.89172e6i | −0.782422 | + | 0.451731i | ||||
\(206\) | −2.08303e6 | + | 3.60791e6i | −0.238283 | + | 0.412719i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.83906e6i | 0.315489i | ||||||||
\(209\) | 1.44485e7 | + | 1.55533e6i | 1.58265 | + | 0.170366i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.21782e6 | − | 703106.i | −0.129639 | − | 0.0748469i | 0.433778 | − | 0.901020i | \(-0.357180\pi\) |
−0.563417 | + | 0.826173i | \(0.690513\pi\) | |||||||
\(212\) | −1.94321e6 | − | 1.12191e6i | −0.203944 | − | 0.117747i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −311909. | + | 540242.i | −0.0318263 | + | 0.0551248i | ||||
\(215\) | −5.80361e6 | − | 1.00521e7i | −0.583960 | − | 1.01145i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.82607e7i | − | 1.78705i | ||||||
\(218\) | −2.05252e6 | − | 3.55507e6i | −0.198115 | − | 0.343146i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.15523e7 | 1.08492 | ||||||||
\(221\) | 2.32863e7i | 2.15736i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.31963e6 | − | 3.64864e6i | −0.569872 | − | 0.329016i | 0.187226 | − | 0.982317i | \(-0.440050\pi\) |
−0.757098 | + | 0.653301i | \(0.773384\pi\) | |||||||
\(224\) | −2.37639e6 | + | 1.37201e6i | −0.211434 | + | 0.122071i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.87829e6 | + | 8.44945e6i | −0.422613 | + | 0.731987i | ||||
\(227\) | − | 9.97093e6i | − | 0.852429i | −0.904622 | − | 0.426214i | \(-0.859847\pi\) | ||
0.904622 | − | 0.426214i | \(-0.140153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.78273e7 | −1.48450 | −0.742250 | − | 0.670123i | \(-0.766241\pi\) | ||||
−0.742250 | + | 0.670123i | \(0.766241\pi\) | |||||||
\(230\) | −5.83551e6 | − | 3.36913e6i | −0.479618 | − | 0.276907i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.65711e6 | − | 4.60224e6i | −0.212787 | − | 0.368558i | ||||
\(233\) | 4.52526e6 | − | 7.83799e6i | 0.357747 | − | 0.619636i | −0.629837 | − | 0.776727i | \(-0.716878\pi\) |
0.987584 | + | 0.157091i | \(0.0502117\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.69517e7 | 2.07674 | ||||||||
\(236\) | − | 7.91136e6i | − | 0.601887i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.94914e7 | + | 1.12534e7i | −1.44582 | + | 0.834742i | ||||
\(239\) | 1.07087e7 | 0.784407 | 0.392204 | − | 0.919878i | \(-0.371713\pi\) | ||||
0.392204 | + | 0.919878i | \(0.371713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.09983e6 | + | 634985.i | −0.0785730 | + | 0.0453641i | −0.538772 | − | 0.842452i | \(-0.681111\pi\) |
0.460199 | + | 0.887816i | \(0.347778\pi\) | |||||||
\(242\) | 1.33117e7 | + | 7.68550e6i | 0.939261 | + | 0.542283i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −829370. | + | 1.43651e6i | −0.0570925 | + | 0.0988871i | ||||
\(245\) | 9.09491e6 | − | 1.57528e7i | 0.618443 | − | 1.07118i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.73920e7 | − | 7.69110e6i | 1.15414 | − | 0.510385i | ||||
\(248\) | 6.97797e6 | 0.457482 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.84998e6 | + | 1.06809e6i | 0.118399 | + | 0.0683577i | ||||
\(251\) | 7.66607e6 | + | 1.32780e7i | 0.484788 | + | 0.839677i | 0.999847 | − | 0.0174776i | \(-0.00556356\pi\) |
−0.515060 | + | 0.857154i | \(0.672230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.40553e6 | − | 1.28268e7i | −0.457293 | − | 0.792055i | ||||
\(254\) | 9.69411e6 | 0.591571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −524288. | − | 908093.i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.98740e6 | − | 4.03418e6i | 0.411639 | − | 0.237660i | −0.279855 | − | 0.960042i | \(-0.590286\pi\) |
0.691494 | + | 0.722383i | \(0.256953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.32911e7i | 1.34057i | ||||||||
\(260\) | 1.30920e7 | − | 7.55869e6i | 0.744881 | − | 0.430057i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.55912e6 | − | 2.05486e6i | 0.197897 | − | 0.114256i | ||||
\(263\) | −319023. | + | 552564.i | −0.0175370 | + | 0.0303749i | −0.874661 | − | 0.484736i | \(-0.838916\pi\) |
0.857124 | + | 0.515111i | \(0.172249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.19479e7i | 0.642026i | ||||||||
\(266\) | 1.48426e7 | + | 1.08409e7i | 0.788616 | + | 0.575997i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.63265e6 | − | 2.67466e6i | −0.240672 | − | 0.138952i | ||||
\(269\) | −2.20327e7 | − | 1.27206e7i | −1.13191 | − | 0.653507i | −0.187493 | − | 0.982266i | \(-0.560036\pi\) |
−0.944414 | + | 0.328759i | \(0.893370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.57904e6 | − | 6.19908e6i | 0.179829 | − | 0.311472i | −0.761993 | − | 0.647585i | \(-0.775779\pi\) |
0.941822 | + | 0.336113i | \(0.109112\pi\) | |||||||
\(272\) | −4.30027e6 | − | 7.44828e6i | −0.213692 | − | 0.370126i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.41119e7i | − | 0.686018i | ||||||
\(275\) | −1.42045e7 | − | 2.46028e7i | −0.683009 | − | 1.18301i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.13300e7 | −1.00358 | −0.501788 | − | 0.864990i | \(-0.667324\pi\) | ||||
−0.501788 | + | 0.864990i | \(0.667324\pi\) | |||||||
\(278\) | 861349.i | 0.0400908i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.26538e7 | + | 7.30566e6i | 0.576429 | + | 0.332801i | ||||
\(281\) | −8.37820e6 | + | 4.83716e6i | −0.377600 | + | 0.218007i | −0.676773 | − | 0.736191i | \(-0.736622\pi\) |
0.299174 | + | 0.954199i | \(0.403289\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.92776e6 | + | 6.80308e6i | −0.173295 | + | 0.300155i | −0.939570 | − | 0.342357i | \(-0.888775\pi\) |
0.766275 | + | 0.642513i | \(0.222108\pi\) | |||||||
\(284\) | − | 84300.5i | − | 0.00368023i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.32288e7 | 1.42042 | ||||||||
\(287\) | −1.87397e7 | − | 1.08194e7i | −0.792716 | − | 0.457675i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.32025e7 | − | 4.01879e7i | −0.961260 | − | 1.66495i | ||||
\(290\) | −1.41485e7 | + | 2.45060e7i | −0.580119 | + | 1.00480i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.41656e6 | 0.297889 | ||||||||
\(293\) | − | 4.56689e7i | − | 1.81559i | −0.419415 | − | 0.907795i | \(-0.637765\pi\) | ||
0.419415 | − | 0.907795i | \(-0.362235\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.64824e7 | + | 2.10631e7i | −1.42108 | + | 0.820460i | ||||
\(296\) | −8.90025e6 | −0.343184 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.07236e7 | + | 1.19648e7i | −0.783098 | + | 0.452122i | ||||
\(299\) | −1.67852e7 | − | 9.69094e6i | −0.627932 | − | 0.362537i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.61346e7 | − | 2.79460e7i | 0.591642 | − | 1.02475i | ||||
\(302\) | 3.50467e6 | − | 6.07027e6i | 0.127241 | − | 0.220388i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.14265e6 | + | 5.67183e6i | −0.147454 | + | 0.201884i | ||||
\(305\) | 8.83243e6 | 0.311301 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.95527e7 | − | 2.28357e7i | −1.36698 | − | 0.789223i | −0.376435 | − | 0.926443i | \(-0.622850\pi\) |
−0.990541 | + | 0.137220i | \(0.956183\pi\) | |||||||
\(308\) | 1.60582e7 | + | 2.78136e7i | 0.549598 | + | 0.951932i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.85781e7 | − | 3.21782e7i | −0.623614 | − | 1.08013i | ||||
\(311\) | −5.28277e7 | −1.75623 | −0.878113 | − | 0.478453i | \(-0.841198\pi\) | ||||
−0.878113 | + | 0.478453i | \(0.841198\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.97271e7 | + | 3.41683e7i | 0.643324 | + | 1.11427i | 0.984686 | + | 0.174338i | \(0.0557787\pi\) |
−0.341361 | + | 0.939932i | \(0.610888\pi\) | |||||||
\(314\) | 2.22015e7 | − | 1.28180e7i | 0.717121 | − | 0.414030i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1.39284e7i | − | 0.441408i | ||||||
\(317\) | −2.25973e7 | + | 1.30466e7i | −0.709381 | + | 0.409561i | −0.810832 | − | 0.585279i | \(-0.800985\pi\) |
0.101451 | + | 0.994841i | \(0.467652\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.38654e7 | + | 3.10992e7i | −1.65935 | + | 0.958025i | ||||
\(320\) | −2.79172e6 | + | 4.83540e6i | −0.0851965 | + | 0.147565i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 1.87331e7i | − | 0.561101i | ||||||
\(323\) | −3.39784e7 | + | 4.65210e7i | −1.00831 | + | 1.38052i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.21955e7 | − | 1.85881e7i | −0.937875 | − | 0.541482i | ||||
\(326\) | −1.86992e7 | − | 1.07960e7i | −0.539721 | − | 0.311608i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.13442e6 | − | 7.16103e6i | 0.117164 | − | 0.202934i | ||||
\(329\) | 3.74643e7 | + | 6.48900e7i | 1.05203 | + | 1.82218i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.71670e7i | 0.749130i | 0.927201 | + | 0.374565i | \(0.122208\pi\) | ||||
−0.927201 | + | 0.374565i | \(0.877792\pi\) | |||||||
\(332\) | 8.85126e6 | + | 1.53308e7i | 0.241875 | + | 0.418940i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.98797e7 | 0.801931 | ||||||||
\(335\) | 2.84840e7i | 0.757646i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −774580. | − | 447204.i | −0.0202384 | − | 0.0116847i | 0.489847 | − | 0.871809i | \(-0.337053\pi\) |
−0.510085 | + | 0.860124i | \(0.670386\pi\) | |||||||
\(338\) | 1.40113e7 | − | 8.08945e6i | 0.362852 | − | 0.209493i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.28980e7 | + | 3.96605e7i | −0.582587 | + | 1.00907i | ||||
\(341\) | − | 8.16712e7i | − | 2.05971i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.16198e6 | −0.127919 | ||||||||
\(344\) | 1.06790e7 | + | 6.16554e6i | 0.262335 | + | 0.151459i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.04056e7 | − | 1.80231e7i | −0.251212 | − | 0.435112i | ||||
\(347\) | 1.55261e6 | − | 2.68920e6i | 0.0371599 | − | 0.0643628i | −0.846847 | − | 0.531836i | \(-0.821502\pi\) |
0.884007 | + | 0.467473i | \(0.154836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.85298e7 | −1.37690 | −0.688448 | − | 0.725286i | \(-0.741708\pi\) | ||||
−0.688448 | + | 0.725286i | \(0.741708\pi\) | |||||||
\(350\) | − | 3.59316e7i | − | 0.838056i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.06285e7 | + | 6.13635e6i | −0.243693 | + | 0.140696i | ||||
\(353\) | 1.20882e7 | 0.274814 | 0.137407 | − | 0.990515i | \(-0.456123\pi\) | ||||
0.137407 | + | 0.990515i | \(0.456123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −388743. | + | 224441.i | −0.00868916 | + | 0.00501669i | ||||
\(356\) | −1.03829e7 | − | 5.99455e6i | −0.230127 | − | 0.132864i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.64065e6 | + | 2.84168e6i | −0.0357574 | + | 0.0619336i | ||||
\(359\) | 1.11371e7 | − | 1.92901e7i | 0.240708 | − | 0.416918i | −0.720208 | − | 0.693758i | \(-0.755954\pi\) |
0.960916 | + | 0.276840i | \(0.0892871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.59681e7 | + | 1.00126e7i | 0.977090 | + | 0.212826i | ||||
\(362\) | 5.18007e7 | 1.09197 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.63972e7 | + | 2.10139e7i | 0.754681 | + | 0.435715i | ||||
\(365\) | −1.97458e7 | − | 3.42007e7i | −0.406065 | − | 0.703325i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.10044e7 | + | 7.10217e7i | 0.829530 | + | 1.43679i | 0.898407 | + | 0.439163i | \(0.144725\pi\) |
−0.0688770 | + | 0.997625i | \(0.521942\pi\) | |||||||
\(368\) | 7.15849e6 | 0.143641 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.36959e7 | + | 4.10426e7i | 0.467809 | + | 0.810269i | ||||
\(371\) | −2.87661e7 | + | 1.66081e7i | −0.563326 | + | 0.325236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.36821e7i | 0.649041i | 0.945879 | + | 0.324521i | \(0.105203\pi\) | ||||
−0.945879 | + | 0.324521i | \(0.894797\pi\) | |||||||
\(374\) | −8.71758e7 | + | 5.03310e7i | −1.66641 | + | 0.962101i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.47965e7 | + | 1.43163e7i | −0.466473 | + | 0.269318i | ||||
\(377\) | −4.06966e7 | + | 7.04887e7i | −0.759512 | + | 1.31551i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.05239e6i | − | 0.111175i | −0.998454 | − | 0.0555877i | \(-0.982297\pi\) | ||
0.998454 | − | 0.0555877i | \(-0.0177033\pi\) | |||||||
\(380\) | 3.71844e7 | + | 4.00276e6i | 0.677657 | + | 0.0729473i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.23129e7 | − | 7.10885e6i | −0.220887 | − | 0.127529i | ||||
\(383\) | 6.43303e6 | + | 3.71411e6i | 0.114504 | + | 0.0661087i | 0.556158 | − | 0.831077i | \(-0.312275\pi\) |
−0.441654 | + | 0.897185i | \(0.645608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.55065e7 | − | 1.48102e8i | 1.49836 | − | 2.59524i | ||||
\(386\) | 1.95271e7 | + | 3.38219e7i | 0.339528 | + | 0.588080i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.01447e7i | 0.173678i | ||||||||
\(389\) | 3.11660e7 | + | 5.39811e7i | 0.529459 | + | 0.917049i | 0.999410 | + | 0.0343568i | \(0.0109383\pi\) |
−0.469951 | + | 0.882693i | \(0.655728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.87147e7 | 0.982237 | ||||||||
\(392\) | 1.93242e7i | 0.320806i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.81938e7 | − | 2.78247e7i | −0.787958 | − | 0.454928i | ||||
\(395\) | −6.42294e7 | + | 3.70828e7i | −1.04218 | + | 0.601702i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.89353e7 | + | 1.02079e8i | −0.941898 | + | 1.63141i | −0.180051 | + | 0.983657i | \(0.557626\pi\) |
−0.761846 | + | 0.647758i | \(0.775707\pi\) | |||||||
\(398\) | − | 8.46040e6i | − | 0.134197i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.37306e7 | 0.214541 | ||||||||
\(401\) | −1.07712e8 | − | 6.21876e7i | −1.67044 | − | 0.964430i | −0.967390 | − | 0.253292i | \(-0.918487\pi\) |
−0.703052 | − | 0.711138i | \(-0.748180\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.34378e7 | − | 9.25570e7i | −0.816457 | − | 1.41415i | ||||
\(404\) | 1.79717e6 | − | 3.11279e6i | 0.0272550 | − | 0.0472070i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.86686e7 | −1.17550 | ||||||||
\(407\) | 1.04170e8i | 1.54511i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.42654e6 | + | 1.40096e6i | −0.0354664 | + | 0.0204765i | −0.517628 | − | 0.855606i | \(-0.673185\pi\) |
0.482162 | + | 0.876082i | \(0.339852\pi\) | |||||||
\(410\) | −4.40298e7 | −0.638845 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.04094e7 | + | 1.17834e7i | −0.291836 | + | 0.168492i | ||||
\(413\) | −1.01425e8 | − | 5.85577e7i | −1.43977 | − | 0.831254i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.71310e7 | − | 8.16334e7i | 0.659421 | − | 1.14215i | ||||
\(416\) | −8.03007e6 | + | 1.39085e7i | −0.111542 | + | 0.193197i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.63839e7 | + | 4.84862e7i | 0.908938 | + | 0.663879i | ||||
\(419\) | 7.84560e7 | 1.06656 | 0.533278 | − | 0.845940i | \(-0.320960\pi\) | ||||
0.533278 | + | 0.845940i | \(0.320960\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.89553e7 | − | 2.24909e7i | −0.522060 | − | 0.301412i | 0.215717 | − | 0.976456i | \(-0.430791\pi\) |
−0.737777 | + | 0.675044i | \(0.764125\pi\) | |||||||
\(422\) | −3.97737e6 | − | 6.88901e6i | −0.0529247 | − | 0.0916683i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.34648e6 | − | 1.09924e7i | −0.0832599 | − | 0.144210i | ||||
\(425\) | 1.12620e8 | 1.46706 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.22775e7 | + | 2.12653e7i | 0.157698 | + | 0.273142i | ||||
\(428\) | −3.05607e6 | + | 1.76442e6i | −0.0389791 | + | 0.0225046i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 6.56603e7i | − | 0.825844i | ||||||
\(431\) | 2.65195e7 | − | 1.53110e7i | 0.331233 | − | 0.191237i | −0.325155 | − | 0.945661i | \(-0.605417\pi\) |
0.656388 | + | 0.754423i | \(0.272083\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.86645e7 | − | 3.38700e7i | 0.722623 | − | 0.417207i | −0.0930943 | − | 0.995657i | \(-0.529676\pi\) |
0.815717 | + | 0.578451i | \(0.196342\pi\) | |||||||
\(434\) | 5.16489e7 | − | 8.94586e7i | 0.631818 | − | 1.09434i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 2.32216e7i | − | 0.280177i | ||||||
\(437\) | −1.93926e7 | − | 4.38527e7i | −0.232376 | − | 0.525475i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.04174e7 | + | 6.01448e6i | 0.123130 | + | 0.0710893i | 0.560300 | − | 0.828290i | \(-0.310686\pi\) |
−0.437170 | + | 0.899379i | \(0.644019\pi\) | |||||||
\(440\) | 5.65943e7 | + | 3.26747e7i | 0.664377 | + | 0.383578i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.58635e7 | + | 1.14079e8i | −0.762743 | + | 1.32111i | ||||
\(443\) | −4.34937e7 | − | 7.53334e7i | −0.500283 | − | 0.866515i | −1.00000 | 0.000326534i | \(-0.999896\pi\) | |
0.499717 | − | 0.866189i | \(-0.333437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.38393e7i | 0.724450i | ||||||||
\(446\) | −2.06398e7 | − | 3.57492e7i | −0.232649 | − | 0.402960i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.55225e7 | −0.172635 | ||||||||
\(449\) | 1.35990e8i | 1.50234i | 0.660109 | + | 0.751170i | \(0.270510\pi\) | ||||
−0.660109 | + | 0.751170i | \(0.729490\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.38138e7 | − | 4.83899e7i | −0.913663 | − | 0.527503i | ||||
\(452\) | −4.77973e7 | + | 2.75958e7i | −0.517593 | + | 0.298832i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.82020e7 | − | 4.88474e7i | 0.301379 | − | 0.522004i | ||||
\(455\) | − | 2.23789e8i | − | 2.37577i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.41239e8 | −1.47981 | −0.739907 | − | 0.672709i | \(-0.765131\pi\) | ||||
−0.739907 | + | 0.672709i | \(0.765131\pi\) | |||||||
\(458\) | −8.73358e7 | − | 5.04233e7i | −0.909067 | − | 0.524850i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.90587e7 | − | 3.30106e7i | −0.195803 | − | 0.339141i | ||||
\(461\) | −2.15628e7 | + | 3.73479e7i | −0.220091 | + | 0.381209i | −0.954835 | − | 0.297135i | \(-0.903969\pi\) |
0.734744 | + | 0.678344i | \(0.237302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.48353e8 | 1.49470 | 0.747350 | − | 0.664431i | \(-0.231326\pi\) | ||||
0.747350 | + | 0.664431i | \(0.231326\pi\) | |||||||
\(464\) | − | 3.00617e7i | − | 0.300926i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.43383e7 | − | 2.55988e7i | 0.438149 | − | 0.252965i | ||||
\(467\) | 1.76094e8 | 1.72900 | 0.864500 | − | 0.502634i | \(-0.167636\pi\) | ||||
0.864500 | + | 0.502634i | \(0.167636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.85791e7 | + | 3.95942e7i | −0.664773 | + | 0.383807i | ||||
\(470\) | 1.32036e8 | + | 7.62310e7i | 1.27174 | + | 0.734240i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.23767e7 | − | 3.87576e7i | 0.212799 | − | 0.368579i | ||||
\(473\) | 7.21624e7 | − | 1.24989e8i | 0.681911 | − | 1.18110i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.71966e7 | − | 8.41134e7i | −0.347075 | − | 0.784846i | ||||
\(476\) | −1.27317e8 | −1.18050 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.24615e7 | + | 3.02887e7i | 0.480349 | + | 0.277330i | ||||
\(479\) | −5.49533e7 | − | 9.51819e7i | −0.500020 | − | 0.866060i | −1.00000 | 2.30769e-5i | \(-0.999993\pi\) | |
0.499980 | − | 0.866037i | \(-0.333341\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.81587e7 | + | 1.18054e8i | 0.612472 | + | 1.06083i | ||||
\(482\) | −7.18404e6 | −0.0641546 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.34757e7 | + | 7.53022e7i | 0.383452 | + | 0.664158i | ||||
\(485\) | 4.67815e7 | − | 2.70093e7i | 0.410061 | − | 0.236749i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.17186e8i | 1.01458i | 0.861775 | + | 0.507291i | \(0.169353\pi\) | ||||
−0.861775 | + | 0.507291i | \(0.830647\pi\) | |||||||
\(488\) | −8.12614e6 | + | 4.69163e6i | −0.0699237 | + | 0.0403705i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.91115e7 | − | 5.14486e7i | 0.757435 | − | 0.437306i | ||||
\(491\) | 5.26780e7 | − | 9.12410e7i | 0.445026 | − | 0.770807i | −0.553028 | − | 0.833162i | \(-0.686528\pi\) |
0.998054 | + | 0.0623553i | \(0.0198612\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.46570e8i | − | 2.05778i | ||||||
\(494\) | 1.06957e8 | + | 1.15135e7i | 0.887213 | + | 0.0955051i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.41849e7 | + | 1.97367e7i | 0.280149 | + | 0.161744i | ||||
\(497\) | −1.08075e6 | − | 623968.i | −0.00880347 | − | 0.00508269i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.68864e7 | + | 1.67812e8i | −0.779761 | + | 1.35059i | 0.152319 | + | 0.988331i | \(0.451326\pi\) |
−0.932080 | + | 0.362254i | \(0.882007\pi\) | |||||||
\(500\) | 6.04202e6 | + | 1.04651e7i | 0.0483362 | + | 0.0837207i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.67317e7i | 0.685593i | ||||||||
\(503\) | 1.02650e8 | + | 1.77795e8i | 0.806595 | + | 1.39706i | 0.915209 | + | 0.402980i | \(0.132026\pi\) |
−0.108614 | + | 0.994084i | \(0.534641\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.91391e7 | −0.148610 | ||||||||
\(506\) | − | 8.37840e7i | − | 0.646710i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.74912e7 | + | 2.74191e7i | 0.362262 | + | 0.209152i | ||||
\(509\) | −4.03451e6 | + | 2.32933e6i | −0.0305941 | + | 0.0176635i | −0.515219 | − | 0.857059i | \(-0.672289\pi\) |
0.484625 | + | 0.874722i | \(0.338956\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.48953e7 | − | 9.50814e7i | 0.411407 | − | 0.712579i | ||||
\(512\) | − | 5.93164e6i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.56415e7 | 0.336101 | ||||||||
\(515\) | 1.08676e8 | + | 6.27440e7i | 0.795630 | + | 0.459357i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.67560e8 | + | 2.90222e8i | 1.21255 | + | 2.10019i | ||||
\(518\) | −6.58771e7 | + | 1.14102e8i | −0.473964 | + | 0.820929i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.55168e7 | 0.608193 | ||||||||
\(521\) | 1.51264e8i | 1.06960i | 0.844978 | + | 0.534801i | \(0.179613\pi\) | ||||
−0.844978 | + | 0.534801i | \(0.820387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.89523e8 | − | 1.09421e8i | 1.32482 | − | 0.764883i | 0.340324 | − | 0.940308i | \(-0.389463\pi\) |
0.984493 | + | 0.175425i | \(0.0561300\pi\) | |||||||
\(524\) | 2.32481e7 | 0.161582 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.12577e6 | + | 1.80467e6i | −0.0214783 | + | 0.0124005i | ||||
\(527\) | 2.80388e8 | + | 1.61882e8i | 1.91570 | + | 1.10603i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.95829e7 | − | 8.58802e7i | 0.334939 | − | 0.580131i | ||||
\(530\) | −3.37937e7 | + | 5.85323e7i | −0.226990 | + | 0.393159i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.20510e7 | + | 9.50906e7i | 0.279281 | + | 0.631543i | ||||
\(533\) | −1.26647e8 | −0.836398 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.62729e7 | + | 9.39517e6i | 0.106268 | + | 0.0613540i | ||||
\(536\) | −1.51302e7 | − | 2.62062e7i | −0.0982538 | − | 0.170181i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.19585e7 | − | 1.24636e8i | −0.462099 | − | 0.800379i | ||||
\(539\) | 2.26173e8 | 1.44436 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.56754e7 | + | 1.13753e8i | 0.414773 | + | 0.718409i | 0.995405 | − | 0.0957581i | \(-0.0305275\pi\) |
−0.580631 | + | 0.814167i | \(0.697194\pi\) | |||||||
\(542\) | 3.50673e7 | − | 2.02461e7i | 0.220244 | − | 0.127158i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 4.86520e7i | − | 0.302206i | ||||||
\(545\) | −1.07084e8 | + | 6.18251e7i | −0.661509 | + | 0.381922i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.10784e8 | − | 6.39611e7i | 0.676885 | − | 0.390800i | −0.121796 | − | 0.992555i | \(-0.538865\pi\) |
0.798680 | + | 0.601756i | \(0.205532\pi\) | |||||||
\(548\) | 3.99146e7 | − | 6.91341e7i | 0.242544 | − | 0.420098i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 1.60705e8i | − | 0.965921i | ||||||
\(551\) | −1.84158e8 | + | 8.14382e7i | −1.10087 | + | 0.486825i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.78564e8 | − | 1.03094e8i | −1.05589 | − | 0.609619i | ||||
\(554\) | −1.04495e8 | − | 6.03302e7i | −0.614563 | − | 0.354818i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.43626e6 | + | 4.21973e6i | −0.0141742 | + | 0.0245505i | ||||
\(557\) | 5.21712e7 | + | 9.03632e7i | 0.301902 | + | 0.522909i | 0.976567 | − | 0.215215i | \(-0.0690453\pi\) |
−0.674665 | + | 0.738124i | \(0.735712\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.88865e8i | − | 1.08122i | ||||||
\(560\) | 4.13270e7 | + | 7.15805e7i | 0.235326 | + | 0.407597i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.47262e7 | −0.308309 | ||||||||
\(563\) | − | 2.08088e8i | − | 1.16606i | −0.812450 | − | 0.583030i | \(-0.801867\pi\) | ||
0.812450 | − | 0.583030i | \(-0.198133\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.54510e8 | + | 1.46942e8i | 1.41111 | + | 0.814704i | ||||
\(566\) | −3.84840e7 | + | 2.22188e7i | −0.212242 | + | 0.122538i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 238438. | − | 412986.i | 0.00130116 | − | 0.00225367i | ||||
\(569\) | − | 1.74234e8i | − | 0.945792i | −0.881118 | − | 0.472896i | \(-0.843209\pi\) | ||
0.881118 | − | 0.472896i | \(-0.156791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.87430e8 | 1.54392 | 0.771958 | − | 0.635674i | \(-0.219278\pi\) | ||||
0.771958 | + | 0.635674i | \(0.219278\pi\) | |||||||
\(572\) | 1.62787e8 | + | 9.39852e7i | 0.869825 | + | 0.502194i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.12037e7 | − | 1.06008e8i | −0.323625 | − | 0.560535i | ||||
\(575\) | −4.68685e7 | + | 8.11786e7i | −0.246534 | + | 0.427010i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.22861e6 | −0.0376294 | −0.0188147 | − | 0.999823i | \(-0.505989\pi\) | ||||
−0.0188147 | + | 0.999823i | \(0.505989\pi\) | |||||||
\(578\) | − | 2.62506e8i | − | 1.35943i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.38627e8 | + | 8.00361e7i | −0.710498 | + | 0.410206i | ||||
\(581\) | 2.62058e8 | 1.33619 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.28657e8 | + | 7.42802e7i | −0.649274 | + | 0.374859i | ||||
\(584\) | 3.63336e7 | + | 2.09772e7i | 0.182419 | + | 0.105319i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.29171e8 | − | 2.23731e8i | 0.641908 | − | 1.11182i | ||||
\(587\) | −2.51761e7 | + | 4.36062e7i | −0.124473 | + | 0.215593i | −0.921527 | − | 0.388315i | \(-0.873057\pi\) |
0.797054 | + | 0.603908i | \(0.206391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.82984e7 | − | 2.62883e8i | 0.138489 | − | 1.28652i | ||||
\(590\) | −2.38302e8 | −1.16031 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.36021e7 | − | 2.51737e7i | −0.210156 | − | 0.121334i | ||||
\(593\) | 1.83196e8 | + | 3.17304e8i | 0.878520 | + | 1.52164i | 0.852966 | + | 0.521967i | \(0.174802\pi\) |
0.0255541 | + | 0.999673i | \(0.491865\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.38969e8 | + | 5.87111e8i | 1.60920 | + | 2.78721i | ||||
\(596\) | −1.35366e8 | −0.639397 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.48202e7 | − | 9.49514e7i | −0.256352 | − | 0.444015i | ||||
\(599\) | −1.99548e8 | + | 1.15209e8i | −0.928466 | + | 0.536050i | −0.886326 | − | 0.463061i | \(-0.846751\pi\) |
−0.0421401 | + | 0.999112i | \(0.513418\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.68476e8i | 1.23675i | 0.785884 | + | 0.618374i | \(0.212208\pi\) | ||||
−0.785884 | + | 0.618374i | \(0.787792\pi\) | |||||||
\(602\) | 1.58086e8 | − | 9.12712e7i | 0.724611 | − | 0.418354i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.43386e7 | − | 1.98254e7i | 0.155838 | − | 0.0899728i | ||||
\(605\) | 2.31499e8 | − | 4.00968e8i | 1.04540 | − | 1.81069i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.66029e7i | 0.431941i | 0.976400 | + | 0.215970i | \(0.0692915\pi\) | ||||
−0.976400 | + | 0.215970i | \(0.930709\pi\) | |||||||
\(608\) | −3.63371e7 | + | 1.60690e7i | −0.161674 | + | 0.0714954i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.32699e7 | + | 2.49819e7i | 0.190632 | + | 0.110062i | ||||
\(611\) | 3.79787e8 | + | 2.19270e8i | 1.66501 | + | 0.961293i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.38546e7 | + | 7.59583e7i | −0.190385 | + | 0.329757i | −0.945378 | − | 0.325976i | \(-0.894307\pi\) |
0.754993 | + | 0.655733i | \(0.227640\pi\) | |||||||
\(614\) | −1.29178e8 | − | 2.23744e8i | −0.558065 | − | 0.966597i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.81678e8i | 0.777249i | ||||||||
\(617\) | 5.96747e7 | + | 1.03360e8i | 0.254059 | + | 0.440043i | 0.964640 | − | 0.263573i | \(-0.0849009\pi\) |
−0.710580 | + | 0.703616i | \(0.751568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.57227e7 | −0.150617 | −0.0753083 | − | 0.997160i | \(-0.523994\pi\) | ||||
−0.0753083 | + | 0.997160i | \(0.523994\pi\) | |||||||
\(620\) | − | 2.10187e8i | − | 0.881923i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.58802e8 | − | 1.49419e8i | −1.07546 | − | 0.620920i | ||||
\(623\) | −1.53702e8 | + | 8.87399e7i | −0.635646 | + | 0.366991i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.36929e8 | − | 2.37167e8i | 0.560860 | − | 0.971438i | ||||
\(626\) | 2.23187e8i | 0.909798i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.45019e8 | 0.585527 | ||||||||
\(629\) | −3.57629e8 | − | 2.06477e8i | −1.43708 | − | 0.829699i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.05749e8 | − | 1.83162e8i | −0.420907 | − | 0.729032i | 0.575121 | − | 0.818068i | \(-0.304955\pi\) |
−0.996028 | + | 0.0890356i | \(0.971621\pi\) | |||||||
\(632\) | 3.93954e7 | − | 6.82349e7i | 0.156061 | − | 0.270306i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.47605e8 | −0.579207 | ||||||||
\(635\) | − | 2.92001e8i | − | 1.14042i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.56319e8 | − | 1.47986e8i | 0.991661 | − | 0.572536i | ||||
\(638\) | −3.51847e8 | −1.35485 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.73532e7 | + | 1.57924e7i | −0.104344 | + | 0.0602430i | ||||
\(641\) | 1.29393e7 | + | 7.47051e6i | 0.0491289 | + | 0.0283646i | 0.524363 | − | 0.851495i | \(-0.324303\pi\) |
−0.475234 | + | 0.879859i | \(0.657637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.07546e7 | + | 1.57192e8i | −0.341378 | + | 0.591284i | −0.984689 | − | 0.174321i | \(-0.944227\pi\) |
0.643311 | + | 0.765605i | \(0.277560\pi\) | |||||||
\(644\) | 5.29851e7 | − | 9.17729e7i | 0.198379 | − | 0.343603i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.98041e8 | + | 1.31800e8i | −1.10555 | + | 0.488896i | ||||
\(647\) | −4.57321e8 | −1.68853 | −0.844265 | − | 0.535927i | \(-0.819962\pi\) | ||||
−0.844265 | + | 0.535927i | \(0.819962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.53625e8 | − | 2.61900e8i | −1.65944 | − | 0.958081i | ||||
\(650\) | −1.05150e8 | − | 1.82125e8i | −0.382886 | − | 0.663177i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.10712e7 | − | 1.05778e8i | −0.220340 | − | 0.381641i | ||||
\(653\) | 2.28284e8 | 0.819852 | 0.409926 | − | 0.912119i | \(-0.365555\pi\) | ||||
0.409926 | + | 0.912119i | \(0.365555\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.18955e7 | − | 1.07206e8i | −0.220260 | − | 0.381501i | ||||
\(656\) | 4.05089e7 | − | 2.33878e7i | 0.143496 | − | 0.0828473i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.23860e8i | 1.48780i | ||||||||
\(659\) | −3.43814e8 | + | 1.98501e8i | −1.20134 | + | 0.693595i | −0.960854 | − | 0.277057i | \(-0.910641\pi\) |
−0.240489 | + | 0.970652i | \(0.577308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.88382e8 | + | 1.08763e8i | −0.652282 | + | 0.376595i | −0.789330 | − | 0.613969i | \(-0.789572\pi\) |
0.137048 | + | 0.990564i | \(0.456239\pi\) | |||||||
\(662\) | −7.68398e7 | + | 1.33090e8i | −0.264857 | + | 0.458746i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.00141e8i | 0.342063i | ||||||||
\(665\) | 3.26545e8 | − | 4.47082e8i | 1.11039 | − | 1.52028i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.77732e8 | + | 1.02614e8i | 0.598947 | + | 0.345802i | ||||
\(668\) | 1.46380e8 | + | 8.45126e7i | 0.491080 | + | 0.283525i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.05649e7 | + | 1.39542e8i | −0.267868 | + | 0.463962i | ||||
\(671\) | 5.49115e7 | + | 9.51095e7i | 0.181759 | + | 0.314816i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.63099e8i | − | 1.19119i | −0.803286 | − | 0.595593i | \(-0.796917\pi\) | ||
0.803286 | − | 0.595593i | \(-0.203083\pi\) | |||||||
\(674\) | −2.52977e6 | − | 4.38168e6i | −0.00826230 | − | 0.0143107i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.15217e7 | 0.296267 | ||||||||
\(677\) | 2.31011e8i | 0.744504i | 0.928132 | + | 0.372252i | \(0.121414\pi\) | ||||
−0.928132 | + | 0.372252i | \(0.878586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.30057e8 | + | 7.50885e7i | 0.415456 | + | 0.239864i | ||||
\(680\) | −2.24354e8 | + | 1.29531e8i | −0.713520 | + | 0.411951i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.31001e8 | − | 4.00105e8i | 0.728217 | − | 1.26131i | ||||
\(683\) | 1.93486e8i | 0.607276i | 0.952787 | + | 0.303638i | \(0.0982014\pi\) | ||||
−0.952787 | + | 0.303638i | \(0.901799\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.25073e8 | −1.32249 | ||||||||
\(686\) | −2.52884e7 | − | 1.46003e7i | −0.0783339 | − | 0.0452261i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.48776e7 | + | 6.04097e7i | 0.107098 | + | 0.185499i | ||||
\(689\) | −9.72037e7 | + | 1.68362e8i | −0.297184 | + | 0.514737i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.56808e8 | −0.475264 | −0.237632 | − | 0.971355i | \(-0.576371\pi\) | ||||
−0.237632 | + | 0.971355i | \(0.576371\pi\) | |||||||
\(692\) | − | 1.17726e8i | − | 0.355268i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.52124e7 | − | 8.78290e6i | 0.0455114 | − | 0.0262760i | ||||
\(695\) | 2.59451e7 | 0.0772861 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.32259e8 | − | 1.91830e8i | 0.981246 | − | 0.566523i | ||||
\(698\) | −2.86736e8 | − | 1.65547e8i | −0.843173 | − | 0.486806i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.01630e8 | − | 1.76028e8i | 0.296298 | − | 0.513202i | ||||
\(701\) | 7.57926e7 | − | 1.31277e8i | 0.220025 | − | 0.381095i | −0.734790 | − | 0.678295i | \(-0.762719\pi\) |
0.954815 | + | 0.297199i | \(0.0960526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.60940e7 | + | 3.35302e8i | −0.103889 | + | 0.965095i | ||||
\(704\) | −6.94248e7 | −0.198974 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.92200e7 | + | 3.41907e7i | 0.168289 | + | 0.0971614i | ||||
\(707\) | −2.66043e7 | − | 4.60800e7i | −0.0752825 | − | 0.130393i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.62778e7 | − | 1.66758e8i | −0.270139 | − | 0.467894i | 0.698758 | − | 0.715358i | \(-0.253736\pi\) |
−0.968897 | + | 0.247463i | \(0.920403\pi\) | |||||||
\(710\) | −2.53926e6 | −0.00709467 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.39103e7 | − | 5.87343e7i | −0.0939489 | − | 0.162724i | ||||
\(713\) | −2.33376e8 | + | 1.34740e8i | −0.643854 | + | 0.371729i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.00090e9i | − | 2.73825i | ||||||
\(716\) | −1.60750e7 | + | 9.28090e6i | −0.0437937 | + | 0.0252843i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.09121e8 | − | 6.30012e7i | 0.294806 | − | 0.170206i | ||||
\(719\) | 3.07401e8 | − | 5.32434e8i | 0.827024 | − | 1.43245i | −0.0733379 | − | 0.997307i | \(-0.523365\pi\) |
0.900362 | − | 0.435141i | \(-0.143301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.48869e8i | 0.930801i | ||||||||
\(722\) | 1.96877e8 | + | 1.79069e8i | 0.523098 | + | 0.475782i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.53771e8 | + | 1.46515e8i | 0.668692 | + | 0.386069i | ||||
\(725\) | 3.40906e8 | + | 1.96822e8i | 0.894582 | + | 0.516487i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.88645e8 | + | 4.99947e8i | −0.751208 | + | 1.30113i | 0.196030 | + | 0.980598i | \(0.437195\pi\) |
−0.947238 | + | 0.320532i | \(0.896138\pi\) | |||||||
\(728\) | 1.18873e8 | + | 2.05893e8i | 0.308097 | + | 0.533640i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 2.23398e8i | − | 0.574263i | ||||||
\(731\) | 2.86070e8 | + | 4.95487e8i | 0.732352 | + | 1.26847i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.47386e7 | −0.0374236 | −0.0187118 | − | 0.999825i | \(-0.505956\pi\) | ||||
−0.0187118 | + | 0.999825i | \(0.505956\pi\) | |||||||
\(734\) | 4.63912e8i | 1.17313i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.50693e7 | + | 2.02473e7i | 0.0879616 | + | 0.0507847i | ||||
\(737\) | −3.06722e8 | + | 1.77086e8i | −0.766200 | + | 0.442366i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.64418e7 | − | 1.15081e8i | 0.164630 | − | 0.285147i | −0.771894 | − | 0.635751i | \(-0.780690\pi\) |
0.936524 | + | 0.350604i | \(0.114024\pi\) | |||||||
\(740\) | 2.68089e8i | 0.661582i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.87900e8 | −0.459954 | ||||||||
\(743\) | 3.69572e8 | + | 2.13372e8i | 0.901016 | + | 0.520202i | 0.877530 | − | 0.479522i | \(-0.159190\pi\) |
0.0234864 | + | 0.999724i | \(0.492523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.60397e8 | + | 6.24226e8i | 0.871590 | + | 1.50964i | ||||
\(746\) | −9.52673e7 | + | 1.65008e8i | −0.229471 | + | 0.397455i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.69430e8 | −1.36062 | ||||||||
\(749\) | 5.22390e7i | 0.124322i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.55366e7 | − | 4.36111e7i | 0.178335 | − | 0.102962i | −0.408175 | − | 0.912904i | \(-0.633835\pi\) |
0.586510 | + | 0.809942i | \(0.300501\pi\) | |||||||
\(752\) | −1.61970e8 | −0.380874 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.98744e8 | + | 2.30215e8i | −0.930208 | + | 0.537056i | ||||
\(755\) | −1.82846e8 | − | 1.05566e8i | −0.424858 | − | 0.245292i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.60655e7 | + | 1.66390e8i | −0.221452 | + | 0.383566i | −0.955249 | − | 0.295802i | \(-0.904413\pi\) |
0.733797 | + | 0.679369i | \(0.237746\pi\) | |||||||
\(758\) | 1.71187e7 | − | 2.96505e7i | 0.0393065 | − | 0.0680808i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.70844e8 | + | 1.24783e8i | 0.389188 | + | 0.284259i | ||||
\(761\) | −3.89947e8 | −0.884814 | −0.442407 | − | 0.896814i | \(-0.645875\pi\) | ||||
−0.442407 | + | 0.896814i | \(0.645875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.97705e8 | − | 1.71880e8i | −0.670212 | − | 0.386947i | ||||
\(764\) | −4.02137e7 | − | 6.96522e7i | −0.0901766 | − | 0.156190i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.10102e7 | + | 3.63907e7i | 0.0467459 | + | 0.0809663i | ||||
\(767\) | −6.85450e8 | −1.51911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28041e8 | + | 2.21774e8i | 0.281560 | + | 0.487676i | 0.971769 | − | 0.235934i | \(-0.0758149\pi\) |
−0.690209 | + | 0.723610i | \(0.742482\pi\) | |||||||
\(770\) | 8.37789e8 | − | 4.83698e8i | 1.83511 | − | 1.05950i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.20924e8i | 0.480165i | ||||||||
\(773\) | 3.69690e7 | − | 2.13441e7i | 0.0800385 | − | 0.0462103i | −0.459447 | − | 0.888205i | \(-0.651952\pi\) |
0.539485 | + | 0.841995i | \(0.318619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.47635e8 | + | 2.58442e8i | −0.961655 | + | 0.555212i | ||||
\(776\) | −2.86937e7 | + | 4.96989e7i | −0.0614046 | + | 0.106356i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.52603e8i | 0.748768i | ||||||||
\(779\) | −2.53013e8 | − | 1.84798e8i | −0.535218 | − | 0.390918i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.83365e6 | − | 2.79071e6i | −0.0101466 | − | 0.00585817i | ||||
\(782\) | 2.87642e8 | + | 1.66070e8i | 0.601495 | + | 0.347273i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.46571e7 | + | 9.46688e7i | −0.113422 | + | 0.196453i | ||||
\(785\) | −3.86098e8 | − | 6.68742e8i | −0.798158 | − | 1.38245i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.52431e8i | 1.33847i | 0.743049 | + | 0.669237i | \(0.233379\pi\) | ||||
−0.743049 | + | 0.669237i | \(0.766621\pi\) | |||||||
\(788\) | −1.57400e8 | − | 2.72625e8i | −0.321682 | − | 0.557170i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.19544e8 | −0.850936 | ||||||||
\(791\) | 8.17025e8i | 1.65084i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.24461e8 | + | 7.18576e7i | 0.249582 | + | 0.144097i | ||||
\(794\) | −5.77445e8 | + | 3.33388e8i | −1.15358 | + | 0.666022i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.39296e7 | − | 4.14473e7i | 0.0474457 | − | 0.0821784i | ||||
\(797\) | − | 5.56853e8i | − | 1.09993i | −0.835187 | − | 0.549966i | \(-0.814641\pi\) | ||
0.835187 | − | 0.549966i | \(-0.185359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.32850e9 | −2.60447 | ||||||||
\(800\) | 6.72659e7 | + | 3.88360e7i | 0.131379 | + | 0.0758516i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.51786e8 | − | 6.09312e8i | −0.681955 | − | 1.18118i | ||||
\(803\) | 2.45520e8 | − | 4.25253e8i | 0.474177 | − | 0.821299i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.64268e8 | −1.08168 | ||||||||
\(806\) | − | 6.04580e8i | − | 1.15464i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.76086e7 | − | 1.01663e7i | 0.0333804 | − | 0.0192722i | ||||
\(809\) | 8.85849e8 | 1.67307 | 0.836535 | − | 0.547914i | \(-0.184578\pi\) | ||||
0.836535 | + | 0.547914i | \(0.184578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.91933e8 | + | 1.68547e8i | −0.547294 | + | 0.315980i | −0.748030 | − | 0.663665i | \(-0.769000\pi\) |
0.200736 | + | 0.979645i | \(0.435667\pi\) | |||||||
\(812\) | −3.85396e8 | − | 2.22508e8i | −0.719845 | − | 0.415603i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.94637e8 | + | 5.10326e8i | −0.546278 | + | 0.946181i | ||||
\(815\) | −3.25191e8 | + | 5.63247e8i | −0.600711 | + | 1.04046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.75584e8 | − | 3.77311e8i | 0.505345 | − | 0.691884i | ||||
\(818\) | −1.58501e7 | −0.0289582 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.15701e8 | − | 1.24535e8i | −0.391211 | − | 0.225866i | ||||
\(821\) | −3.08479e8 | − | 5.34300e8i | −0.557437 | − | 0.965508i | −0.997709 | − | 0.0676445i | \(-0.978452\pi\) |
0.440273 | − | 0.897864i | \(-0.354882\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.86716e8 | − | 3.23401e8i | −0.334951 | − | 0.580153i | 0.648524 | − | 0.761194i | \(-0.275387\pi\) |
−0.983475 | + | 0.181041i | \(0.942053\pi\) | |||||||
\(824\) | −1.33314e8 | −0.238283 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.31252e8 | − | 5.73746e8i | −0.587785 | − | 1.01807i | ||||
\(827\) | −2.92181e8 | + | 1.68691e8i | −0.516577 | + | 0.298246i | −0.735533 | − | 0.677489i | \(-0.763068\pi\) |
0.218956 | + | 0.975735i | \(0.429735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.99748e8i | − | 1.57927i | −0.613575 | − | 0.789637i | \(-0.710269\pi\) | ||
0.613575 | − | 0.789637i | \(-0.289731\pi\) | |||||||
\(830\) | 4.61788e8 | − | 2.66613e8i | 0.807623 | − | 0.466281i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.86783e7 | + | 4.54249e7i | −0.136611 | + | 0.0788723i | ||||
\(833\) | −4.48303e8 | + | 7.76484e8i | −0.775598 | + | 1.34338i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9.00022e8i | − | 1.54594i | ||||||
\(836\) | 1.88074e8 | + | 4.25295e8i | 0.321892 | + | 0.727899i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.84354e8 | + | 2.21907e8i | 0.653130 | + | 0.377085i | ||||
\(839\) | −2.08397e8 | − | 1.20318e8i | −0.352863 | − | 0.203726i | 0.313082 | − | 0.949726i | \(-0.398638\pi\) |
−0.665946 | + | 0.746000i | \(0.731972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.33510e8 | − | 2.31246e8i | 0.224453 | − | 0.388764i | ||||
\(842\) | −1.27228e8 | − | 2.20365e8i | −0.213130 | − | 0.369152i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.49988e7i | − | 0.0748469i | ||||||
\(845\) | −2.43667e8 | − | 4.22043e8i | −0.403855 | − | 0.699498i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.28718e9 | 2.11831 | ||||||||
\(848\) | − | 7.18023e7i | − | 0.117747i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.51723e8 | + | 3.18537e8i | 0.898388 | + | 0.518685i | ||||
\(851\) | 2.97666e8 | − | 1.71857e8i | 0.482992 | − | 0.278856i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.17202e8 | + | 7.22615e8i | −0.672201 | + | 1.16429i | 0.305077 | + | 0.952328i | \(0.401318\pi\) |
−0.977278 | + | 0.211959i | \(0.932016\pi\) | |||||||
\(854\) | 1.38904e8i | 0.223019i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.99622e7 | −0.0318263 | ||||||||
\(857\) | 3.04172e8 | + | 1.75614e8i | 0.483255 | + | 0.279007i | 0.721772 | − | 0.692131i | \(-0.243328\pi\) |
−0.238517 | + | 0.971138i | \(0.576661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.57849e8 | + | 7.93018e8i | 0.722342 | + | 1.25113i | 0.960059 | + | 0.279799i | \(0.0902678\pi\) |
−0.237716 | + | 0.971335i | \(0.576399\pi\) | |||||||
\(860\) | 1.85715e8 | − | 3.21669e8i | 0.291980 | − | 0.505724i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.73225e8 | 0.270451 | ||||||||
\(863\) | − | 1.32268e8i | − | 0.205789i | −0.994692 | − | 0.102895i | \(-0.967190\pi\) | ||
0.994692 | − | 0.102895i | \(-0.0328104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.42883e8 | + | 3.13434e8i | −0.838800 | + | 0.484281i | ||||
\(866\) | 3.83195e8 | 0.590019 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.06054e8 | − | 2.92171e8i | 0.773816 | − | 0.446763i | ||||
\(869\) | −7.98632e8 | − | 4.61090e8i | −1.21699 | − | 0.702630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.31736e8 | + | 4.01378e8i | −0.350703 | + | 0.607435i | ||||
\(872\) | 6.56807e7 | − | 1.13762e8i | 0.0990577 | − | 0.171573i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.90305e7 | − | 2.69684e8i | 0.0434830 | − | 0.403944i | ||||
\(875\) | 1.78885e8 | 0.267024 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.45547e8 | − | 1.41767e8i | −0.364029 | − | 0.210172i | 0.306818 | − | 0.951768i | \(-0.400736\pi\) |
−0.670847 | + | 0.741596i | \(0.734069\pi\) | |||||||
\(878\) | 3.40230e7 | + | 5.89296e7i | 0.0502677 | + | 0.0870663i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.84836e8 | + | 3.20145e8i | 0.271231 | + | 0.469785i | ||||
\(881\) | 2.29004e8 | 0.334901 | 0.167450 | − | 0.985881i | \(-0.446447\pi\) | ||||
0.167450 | + | 0.985881i | \(0.446447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.94334e7 | − | 1.54903e8i | −0.129902 | − | 0.224998i | 0.793736 | − | 0.608262i | \(-0.208133\pi\) |
−0.923639 | + | 0.383265i | \(0.874800\pi\) | |||||||
\(884\) | −6.45328e8 | + | 3.72580e8i | −0.934166 | + | 0.539341i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 4.92075e8i | − | 0.707507i | ||||||
\(887\) | −1.25755e8 | + | 7.26046e7i | −0.180200 | + | 0.104038i | −0.587386 | − | 0.809307i | \(-0.699843\pi\) |
0.407187 | + | 0.913345i | \(0.366510\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.03034e8 | − | 4.05897e8i | 1.00062 | − | 0.577710i | ||||
\(890\) | −1.80565e8 | + | 3.12748e8i | −0.256132 | + | 0.443633i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 2.33513e8i | − | 0.329016i | ||||||
\(893\) | 4.38782e8 | + | 9.92225e8i | 0.616161 | + | 1.39334i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.55958e7 | + | 4.94188e7i | 0.119394 | + | 0.0689323i | ||||
\(896\) | −7.60445e7 | − | 4.39043e7i | −0.105717 | − | 0.0610356i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.84638e8 | + | 6.66213e8i | −0.531158 | + | 0.919992i | ||||
\(899\) | 5.65833e8 | + | 9.80051e8i | 0.778770 | + | 1.34887i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.88930e8i | − | 0.805173i | ||||||
\(902\) | −2.73735e8 | − | 4.74122e8i | −0.373001 | − | 0.646057i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.12211e8 | −0.422613 | ||||||||
\(905\) | − | 1.56032e9i | − | 2.10507i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.02435e9 | − | 5.91408e8i | −1.37286 | − | 0.792621i | −0.381573 | − | 0.924339i | \(-0.624617\pi\) |
−0.991287 | + | 0.131718i | \(0.957951\pi\) | |||||||
\(908\) | 2.76322e8 | − | 1.59535e8i | 0.369112 | − | 0.213107i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.32971e8 | − | 1.09634e9i | 0.839962 | − | 1.45486i | ||||
\(911\) | − | 1.07316e8i | − | 0.141942i | −0.997478 | − | 0.0709708i | \(-0.977390\pi\) | ||
0.997478 | − | 0.0709708i | \(-0.0226097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.17206e9 | 1.54006 | ||||||||
\(914\) | −6.91929e8 | − | 3.99485e8i | −0.906198 | − | 0.523194i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.85237e8 | − | 4.94046e8i | −0.371125 | − | 0.642807i | ||||
\(917\) | 1.72076e8 | − | 2.98044e8i | 0.223158 | − | 0.386520i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.67281e7 | 0.111741 | 0.0558706 | − | 0.998438i | \(-0.482207\pi\) | ||||
0.0558706 | + | 0.998438i | \(0.482207\pi\) | |||||||
\(920\) | − | 2.15624e8i | − | 0.276907i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.11271e8 | + | 1.21978e8i | −0.269555 | + | 0.155628i | ||||
\(923\) | −7.30390e6 | −0.00928859 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.70949e8 | − | 3.29638e8i | 0.721393 | − | 0.416497i | ||||
\(926\) | 7.26779e8 | + | 4.19606e8i | 0.915313 | + | 0.528456i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.50274e7 | − | 1.47272e8i | 0.106393 | − | 0.184279i | ||||
\(929\) | 5.27852e8 | − | 9.14267e8i | 0.658362 | − | 1.14032i | −0.322677 | − | 0.946509i | \(-0.604583\pi\) |
0.981039 | − | 0.193808i | \(-0.0620839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.28007e8 | + | 7.83672e7i | 0.902166 | + | 0.0971148i | ||||
\(932\) | 2.89617e8 | 0.357747 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.62683e8 | + | 4.98070e8i | 1.05879 | + | 0.611293i | ||||
\(935\) | 1.51605e9 | + | 2.62587e9i | 1.85472 | + | 3.21246i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.34198e8 | + | 5.78847e8i | 0.406242 | + | 0.703632i | 0.994465 | − | 0.105067i | \(-0.0335057\pi\) |
−0.588223 | + | 0.808699i | \(0.700172\pi\) | |||||||
\(938\) | −4.47957e8 | −0.542785 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.31228e8 | + | 7.46908e8i | 0.519186 | + | 0.899257i | ||||
\(941\) | −7.92814e8 | + | 4.57731e8i | −0.951486 | + | 0.549341i | −0.893542 | − | 0.448979i | \(-0.851788\pi\) |
−0.0579438 | + | 0.998320i | \(0.518454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.19331e8i | 0.380808i | ||||||||
\(944\) | 2.19246e8 | − | 1.26582e8i | 0.260625 | − | 0.150472i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.07044e8 | − | 4.08212e8i | 0.835167 | − | 0.482184i | ||||
\(947\) | −2.84686e8 | + | 4.93091e8i | −0.335209 | + | 0.580600i | −0.983525 | − | 0.180772i | \(-0.942140\pi\) |
0.648316 | + | 0.761372i | \(0.275474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.42580e8i | − | 0.751845i | ||||||
\(950\) | 5.56830e7 | − | 5.17278e8i | 0.0649459 | − | 0.603327i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.23726e8 | − | 3.60108e8i | −0.722908 | − | 0.417371i | ||||
\(953\) | −1.37353e9 | − | 7.93011e8i | −1.58694 | − | 0.916221i | −0.993807 | − | 0.111118i | \(-0.964557\pi\) |
−0.593134 | − | 0.805104i | \(-0.702110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.14129e8 | + | 3.70883e8i | −0.245848 | + | 0.425820i | ||||
\(956\) | 1.71339e8 | + | 2.96767e8i | 0.196102 | + | 0.339658i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.21726e8i | − | 0.707135i | ||||||
\(959\) | −5.90873e8 | − | 1.02342e9i | −0.669944 | − | 1.16038i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.98459e8 | −0.674318 | ||||||||
\(962\) | 7.71128e8i | 0.866166i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.51945e7 | − | 2.03195e7i | −0.0392865 | − | 0.0226821i | ||||
\(965\) | 1.01877e9 | − | 5.88186e8i | 1.13369 | − | 0.654534i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.43965e8 | + | 2.49354e8i | −0.159212 | + | 0.275763i | −0.934585 | − | 0.355740i | \(-0.884229\pi\) |
0.775373 | + | 0.631504i | \(0.217562\pi\) | |||||||
\(968\) | 4.91872e8i | 0.542283i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.05575e8 | 0.334813 | ||||||||
\(971\) | 1.24333e9 | + | 7.17834e8i | 1.35809 | + | 0.784091i | 0.989366 | − | 0.145449i | \(-0.0464628\pi\) |
0.368720 | + | 0.929541i | \(0.379796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.60650e7 | + | 6.24665e7i | 0.0391515 | + | 0.0678123i | ||||
\(974\) | −3.31451e8 | + | 5.74090e8i | −0.358709 | + | 0.621302i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.30797e7 | −0.0570925 | ||||||||
\(977\) | − | 1.35543e9i | − | 1.45343i | −0.686940 | − | 0.726715i | \(-0.741046\pi\) | ||
0.686940 | − | 0.726715i | \(-0.258954\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.87436e8 | + | 3.96891e8i | −0.732629 | + | 0.422983i | ||||
\(980\) | 5.82074e8 | 0.618443 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.16137e8 | − | 2.97992e8i | 0.545043 | − | 0.314681i | ||||
\(983\) | −4.46227e8 | − | 2.57629e8i | −0.469781 | − | 0.271228i | 0.246367 | − | 0.969177i | \(-0.420763\pi\) |
−0.716148 | + | 0.697948i | \(0.754096\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.38123e8 | + | 1.45167e9i | −0.876999 | + | 1.51901i | ||||
\(986\) | 6.97404e8 | − | 1.20794e9i | 0.727535 | − | 1.26013i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.91414e8 | + | 3.58924e8i | 0.509538 | + | 0.372162i | ||||
\(989\) | −4.76209e8 | −0.492276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.51972e8 | − | 1.45476e8i | −0.258900 | − | 0.149476i | 0.364933 | − | 0.931034i | \(-0.381092\pi\) |
−0.623833 | + | 0.781558i | \(0.714425\pi\) | |||||||
\(992\) | 1.11647e8 | + | 1.93379e8i | 0.114370 | + | 0.198095i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.52970e6 | − | 6.11362e6i | −0.00359400 | − | 0.00622500i | ||||
\(995\) | −2.54840e8 | −0.258701 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.07050e8 | − | 1.39785e9i | −0.814357 | − | 1.41051i | −0.909789 | − | 0.415072i | \(-0.863756\pi\) |
0.0954314 | − | 0.995436i | \(-0.469577\pi\) | |||||||
\(998\) | −9.49289e8 | + | 5.48072e8i | −0.955008 | + | 0.551374i | ||||
\(999\) | 0 | 0 |
(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 | 342.7.m.a.217.10 | 20 | ||
3.2 | odd | 2 | 38.7.d.a.27.2 | ✓ | 20 | ||
19.12 | odd | 6 | inner | 342.7.m.a.145.10 | 20 | ||
57.50 | even | 6 | 38.7.d.a.31.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.7.d.a.27.2 | ✓ | 20 | 3.2 | odd | 2 | ||
38.7.d.a.31.2 | yes | 20 | 57.50 | even | 6 | ||
342.7.m.a.145.10 | 20 | 19.12 | odd | 6 | inner | ||
342.7.m.a.217.10 | 20 | 1.1 | even | 1 | trivial |