Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
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("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.6 | ||
Character | \(\chi\) | \(=\) | 76.29 |
Dual form | 76.7.j.a.21.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.99278 | + | 2.37490i | 0.0738066 | + | 0.0879593i | 0.801684 | − | 0.597748i | \(-0.203938\pi\) |
−0.727878 | + | 0.685707i | \(0.759493\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 187.566 | + | 68.2686i | 1.50053 | + | 0.546149i | 0.956198 | − | 0.292720i | \(-0.0945605\pi\) |
0.544333 | + | 0.838869i | \(0.316783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 84.5123 | − | 146.380i | 0.246391 | − | 0.426762i | −0.716130 | − | 0.697966i | \(-0.754088\pi\) |
0.962522 | + | 0.271204i | \(0.0874218\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 124.921 | − | 708.460i | 0.171359 | − | 0.971824i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 296.296 | + | 513.200i | 0.222612 | + | 0.385575i | 0.955600 | − | 0.294666i | \(-0.0952084\pi\) |
−0.732988 | + | 0.680241i | \(0.761875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1333.33 | + | 1589.00i | −0.606887 | + | 0.723260i | −0.978757 | − | 0.205025i | \(-0.934272\pi\) |
0.371870 | + | 0.928285i | \(0.378717\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 211.647 | + | 581.496i | 0.0627103 | + | 0.172295i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24.1897 | − | 137.187i | −0.00492362 | − | 0.0279232i | 0.982247 | − | 0.187592i | \(-0.0600684\pi\) |
−0.987171 | + | 0.159669i | \(0.948957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6582.58 | − | 1927.57i | 0.959700 | − | 0.281028i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 516.051 | − | 90.9937i | 0.0557231 | − | 0.00982548i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18497.1 | − | 6732.39i | 1.52027 | − | 0.553332i | 0.559052 | − | 0.829133i | \(-0.311165\pi\) |
0.961215 | + | 0.275801i | \(0.0889431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18551.1 | + | 15566.2i | 1.18727 | + | 0.996239i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3888.73 | − | 2245.16i | 0.197568 | − | 0.114066i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7132.30 | − | 1257.62i | −0.292439 | − | 0.0515649i | 0.0255038 | − | 0.999675i | \(-0.491881\pi\) |
−0.317943 | + | 0.948110i | \(0.602992\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17986.2 | + | 10384.3i | 0.603746 | + | 0.348573i | 0.770514 | − | 0.637423i | \(-0.220000\pi\) |
−0.166768 | + | 0.985996i | \(0.553333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −628.347 | + | 1726.37i | −0.0174847 | + | 0.0480388i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25844.8 | − | 21686.3i | 0.602794 | − | 0.505804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 24794.9i | 0.489505i | 0.969586 | + | 0.244752i | \(0.0787067\pi\) | ||||
−0.969586 | + | 0.244752i | \(0.921293\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6430.76 | −0.108410 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22011.1 | + | 26231.8i | 0.319367 | + | 0.380607i | 0.901714 | − | 0.432334i | \(-0.142310\pi\) |
−0.582346 | + | 0.812941i | \(0.697865\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43509.8 | + | 15836.3i | 0.547245 | + | 0.199181i | 0.600822 | − | 0.799383i | \(-0.294840\pi\) |
−0.0535770 | + | 0.998564i | \(0.517062\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 71796.4 | − | 124355.i | 0.787889 | − | 1.36466i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10510.6 | + | 59608.8i | −0.101236 | + | 0.574139i | 0.891421 | + | 0.453176i | \(0.149709\pi\) |
−0.992657 | + | 0.120963i | \(0.961402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44539.9 | + | 77145.3i | 0.378583 | + | 0.655724i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 277.600 | − | 330.831i | 0.00209271 | − | 0.00249400i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −86215.4 | − | 236875.i | −0.579105 | − | 1.59108i | −0.789693 | − | 0.613502i | \(-0.789760\pi\) |
0.210588 | − | 0.977575i | \(-0.432462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20539.8 | + | 116487.i | 0.123455 | + | 0.700146i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17695.4 | + | 11791.8i | 0.0955512 | + | 0.0636728i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −141003. | + | 24862.6i | −0.686549 | + | 0.121057i | −0.506032 | − | 0.862515i | \(-0.668888\pi\) |
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −220979. | + | 80429.6i | −0.973555 | + | 0.354345i | −0.779331 | − | 0.626612i | \(-0.784441\pi\) |
−0.194224 | + | 0.980957i | \(0.562219\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −93146.6 | − | 78159.3i | −0.372517 | − | 0.312579i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −358567. | + | 207019.i | −1.30566 | + | 0.753824i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −426049. | − | 75123.9i | −1.41656 | − | 0.249778i | −0.587630 | − | 0.809130i | \(-0.699939\pi\) |
−0.828930 | + | 0.559352i | \(0.811050\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 52849.4 | + | 30512.6i | 0.160876 | + | 0.0928820i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 112145. | − | 308115.i | 0.313332 | − | 0.860872i | −0.678647 | − | 0.734465i | \(-0.737433\pi\) |
0.991978 | − | 0.126407i | \(-0.0403445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 87636.5 | − | 73535.7i | 0.225277 | − | 0.189030i | −0.523163 | − | 0.852233i | \(-0.675248\pi\) |
0.748439 | + | 0.663203i | \(0.230804\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75077.1i | 0.177961i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 100163. | 0.219399 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 130394. | + | 155397.i | 0.264470 | + | 0.315183i | 0.881894 | − | 0.471447i | \(-0.156268\pi\) |
−0.617424 | + | 0.786630i | \(0.711824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −479726. | − | 174606.i | −0.902689 | − | 0.328552i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 410905. | − | 711708.i | 0.718633 | − | 1.24471i | −0.242909 | − | 0.970049i | \(-0.578102\pi\) |
0.961542 | − | 0.274660i | \(-0.0885652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4828.37 | − | 27383.0i | 0.00786219 | − | 0.0445887i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11226.4 | − | 19444.7i | −0.0170483 | − | 0.0295286i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −737289. | + | 878667.i | −1.04585 | + | 1.24639i | −0.0774434 | + | 0.996997i | \(0.524676\pi\) |
−0.968402 | + | 0.249394i | \(0.919769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 119915. | + | 329463.i | 0.159128 | + | 0.437202i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11180.7 | + | 63409.2i | 0.0139002 | + | 0.0788321i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36626e6 | + | 87836.5i | 1.59354 | + | 0.102448i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.56717e6 | + | 276335.i | −1.71712 | + | 0.302775i | −0.943623 | − | 0.331021i | \(-0.892607\pi\) |
−0.773500 | + | 0.633796i | \(0.781496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 400595. | − | 145805.i | 0.412857 | − | 0.150268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −637703. | − | 535096.i | −0.618948 | − | 0.519359i | 0.278525 | − | 0.960429i | \(-0.410155\pi\) |
−0.897473 | + | 0.441070i | \(0.854599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 163845. | − | 94595.9i | 0.149941 | − | 0.0865687i | −0.423152 | − | 0.906059i | \(-0.639076\pi\) |
0.573094 | + | 0.819490i | \(0.305743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 103006. | + | 18162.7i | 0.0889804 | + | 0.0156896i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 327641. | + | 189164.i | 0.267453 | + | 0.154414i | 0.627729 | − | 0.778432i | \(-0.283984\pi\) |
−0.360277 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 664905. | − | 1.82681e6i | 0.513429 | − | 1.41063i | −0.364213 | − | 0.931316i | \(-0.618662\pi\) |
0.877641 | − | 0.479318i | \(-0.159116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −58885.4 | + | 49410.7i | −0.0430565 | + | 0.0361287i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.99438e6i | 1.38220i | 0.722758 | + | 0.691101i | \(0.242874\pi\) | ||||
−0.722758 | + | 0.691101i | \(0.757126\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.92904e6 | 2.58341 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 959183. | + | 1.14311e6i | 0.598886 | + | 0.713724i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22125.7 | − | 8053.08i | −0.0131297 | − | 0.00477883i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 710198. | − | 1.23010e6i | 0.400888 | − | 0.694358i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18434.7 | + | 104548.i | −0.00990652 | + | 0.0561827i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 857474. | + | 1.48519e6i | 0.439027 | + | 0.760417i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.03813e6 | − | 1.23720e6i | 0.506805 | − | 0.603987i | −0.450603 | − | 0.892724i | \(-0.648791\pi\) |
0.957408 | + | 0.288737i | \(0.0932355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 49095.8 | + | 134890.i | 0.0228705 | + | 0.0628362i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 284582. | + | 1.61395e6i | 0.126588 | + | 0.717918i | 0.980352 | + | 0.197257i | \(0.0632034\pi\) |
−0.853763 | + | 0.520661i | \(0.825685\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 274152. | − | 1.12646e6i | 0.116530 | − | 0.478807i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 882668. | − | 155638.i | 0.358754 | − | 0.0632579i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −858669. | + | 312530.i | −0.333937 | + | 0.121543i | −0.503546 | − | 0.863968i | \(-0.667972\pi\) |
0.169609 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.81921e6 | − | 3.20470e6i | −1.42210 | − | 1.19328i | −0.950206 | − | 0.311623i | \(-0.899127\pi\) |
−0.471890 | − | 0.881657i | \(-0.656428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −162510. | + | 93825.5i | −0.0579728 | + | 0.0334706i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.21054e6 | − | 213450.i | −0.413971 | − | 0.0729943i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.25192e6 | − | 722799.i | −0.410652 | − | 0.237090i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −94454.4 | + | 259511.i | −0.0297352 | + | 0.0816967i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.50206e6 | + | 1.26038e6i | −0.454075 | + | 0.381014i | −0.840945 | − | 0.541120i | \(-0.818001\pi\) |
0.386870 | + | 0.922134i | \(0.373556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.65681e6i | 1.06212i | 0.847336 | + | 0.531058i | \(0.178205\pi\) | ||||
−0.847336 | + | 0.531058i | \(0.821795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −100213. | −0.0279802 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.66468e6 | + | 3.17565e6i | 0.715567 | + | 0.852780i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.32443e6 | − | 846024.i | −0.600645 | − | 0.218617i | 0.0237599 | − | 0.999718i | \(-0.492436\pi\) |
−0.624405 | + | 0.781101i | \(0.714658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 390746. | − | 676792.i | 0.0972083 | − | 0.168370i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 577746. | − | 3.27656e6i | 0.138439 | − | 0.785129i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −174377. | − | 302030.i | −0.0402650 | − | 0.0697410i | 0.845191 | − | 0.534465i | \(-0.179487\pi\) |
−0.885456 | + | 0.464724i | \(0.846154\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −235714. | + | 280912.i | −0.0524726 | + | 0.0625344i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −395539. | − | 1.08673e6i | −0.0849259 | − | 0.233332i | 0.889959 | − | 0.456040i | \(-0.150733\pi\) |
−0.974885 | + | 0.222708i | \(0.928510\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 91010.6 | + | 516147.i | 0.0188552 | + | 0.106933i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −543305. | − | 4.90428e6i | −0.108656 | − | 0.980816i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.62747e6 | + | 1.52126e6i | −1.66627 | + | 0.293808i | −0.925725 | − | 0.378198i | \(-0.876544\pi\) |
−0.740545 | + | 0.672007i | \(0.765433\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.84637e6 | − | 1.39997e6i | 0.717691 | − | 0.261218i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −340034. | − | 285322.i | −0.0613200 | − | 0.0514536i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.13141e6 | + | 653219.i | −0.197270 | + | 0.113894i | −0.595381 | − | 0.803443i | \(-0.702999\pi\) |
0.398112 | + | 0.917337i | \(0.369666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.35042e6 | − | 943424.i | −0.902303 | − | 0.159100i | −0.296796 | − | 0.954941i | \(-0.595918\pi\) |
−0.605506 | + | 0.795840i | \(0.707029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −631374. | − | 364524.i | −0.103023 | − | 0.0594802i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.69271e6 | + | 4.65069e6i | −0.267342 | + | 0.734517i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 63236.9 | − | 53062.1i | 0.00967044 | − | 0.00811446i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 758973.i | − | 0.112419i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.15444e6 | −0.883259 | −0.441630 | − | 0.897197i | \(-0.645599\pi\) | ||||
−0.441630 | + | 0.897197i | \(0.645599\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.66851e6 | − | 4.37196e6i | −0.510291 | − | 0.608141i | 0.447966 | − | 0.894051i | \(-0.352149\pi\) |
−0.958257 | + | 0.285910i | \(0.907704\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.20619e6 | − | 439019.i | −0.162672 | − | 0.0592078i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.56975e6 | + | 2.71888e6i | −0.205320 | + | 0.355624i | −0.950235 | − | 0.311535i | \(-0.899157\pi\) |
0.744915 | + | 0.667160i | \(0.232490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.40705e6 | + | 7.97976e6i | −0.178546 | + | 1.01258i | 0.755426 | + | 0.655235i | \(0.227430\pi\) |
−0.933971 | + | 0.357348i | \(0.883681\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −670610. | − | 1.16153e6i | −0.0825813 | − | 0.143035i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −786856. | + | 937739.i | −0.0940605 | + | 0.112097i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.33774e6 | + | 6.42288e6i | 0.271353 | + | 0.745535i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.45896e6 | − | 1.39454e7i | −0.277230 | − | 1.57225i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.93962e6 | + | 2.80705e6i | 0.321998 | + | 0.307476i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.71385e7 | − | 3.02198e6i | 1.82443 | − | 0.321695i | 0.846778 | − | 0.531947i | \(-0.178539\pi\) |
0.977647 | + | 0.210251i | \(0.0674282\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 955224. | − | 347673.i | 0.0988477 | − | 0.0359776i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.07986e6 | + | 5.94071e6i | 0.712376 | + | 0.597754i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.04011e6 | − | 1.75521e6i | 0.297516 | − | 0.171771i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 349280. | + | 61587.5i | 0.0332538 | + | 0.00586355i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 250243. | + | 144478.i | 0.0231838 | + | 0.0133852i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.34163e6 | + | 3.68610e6i | −0.120981 | + | 0.332393i | −0.985369 | − | 0.170432i | \(-0.945484\pi\) |
0.864388 | + | 0.502825i | \(0.167706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.33455e7 | − | 1.11982e7i | 1.17162 | − | 0.983104i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.15202e6i | − | 0.525945i | −0.964803 | − | 0.262973i | \(-0.915297\pi\) | ||
0.964803 | − | 0.262973i | \(-0.0847029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −728925. | −0.0606983 | −0.0303492 | − | 0.999539i | \(-0.509662\pi\) | ||||
−0.0303492 | + | 0.999539i | \(0.509662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 199602. | + | 237876.i | 0.0161931 | + | 0.0192981i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.24154e7 | + | 8.15853e6i | 1.77206 | + | 0.644977i | 0.999955 | + | 0.00948168i | \(0.00301816\pi\) |
0.772105 | + | 0.635495i | \(0.219204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.04085e6 | + | 1.04631e7i | −0.465473 | + | 0.806223i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −109207. | + | 619345.i | −0.00820364 | + | 0.0465251i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.89577e6 | − | 6.74766e6i | −0.285364 | − | 0.494265i | 0.687333 | − | 0.726342i | \(-0.258781\pi\) |
−0.972697 | + | 0.232077i | \(0.925448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.08206e7 | − | 1.28955e7i | 0.773040 | − | 0.921273i | −0.225557 | − | 0.974230i | \(-0.572420\pi\) |
0.998597 | + | 0.0529569i | \(0.0168646\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.66090e6 | − | 4.56328e6i | −0.115751 | − | 0.318023i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.08758e6 | + | 1.75105e7i | 0.209952 | + | 1.19070i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.71385e6 | + | 1.30298e7i | −0.379173 | + | 0.864664i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.50908e6 | − | 442419.i | 0.162524 | − | 0.0286573i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.65232e7 | + | 9.65365e6i | −1.67728 | + | 0.610479i | −0.992932 | − | 0.118681i | \(-0.962133\pi\) |
−0.684344 | + | 0.729160i | \(0.739911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.93568e6 | + | 7.49792e6i | 0.551780 | + | 0.462998i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 74653.9 | − | 43101.4i | 0.00450227 | − | 0.00259939i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.62831e7 | + | 2.87115e6i | 0.959262 | + | 0.169144i | 0.631293 | − | 0.775545i | \(-0.282525\pi\) |
0.327969 | + | 0.944688i | \(0.393636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.62946e6 | + | 2.09547e6i | 0.208902 | + | 0.120610i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.78194e6 | + | 4.89585e6i | −0.100224 | + | 0.275363i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −368254. | + | 309002.i | −0.0202433 | + | 0.0169861i | −0.652853 | − | 0.757485i | \(-0.726428\pi\) |
0.632610 | + | 0.774471i | \(0.281984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.03156e7i | − | 2.70374i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.55600e6 | −0.186822 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.53325e6 | − | 5.40252e6i | −0.232891 | − | 0.277549i | 0.636924 | − | 0.770927i | \(-0.280206\pi\) |
−0.869815 | + | 0.493378i | \(0.835762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.19906e7 | + | 4.36420e6i | 0.602464 | + | 0.219279i | 0.625203 | − | 0.780462i | \(-0.285016\pi\) |
−0.0227385 | + | 0.999741i | \(0.507239\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −543478. | + | 941331.i | −0.0267112 | + | 0.0462652i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.49197e6 | + | 1.41326e7i | −0.119824 | + | 0.679556i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.82226e6 | − | 1.35485e7i | −0.368038 | − | 0.637461i | 0.621221 | − | 0.783636i | \(-0.286637\pi\) |
−0.989259 | + | 0.146175i | \(0.953304\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.60373e6 | − | 1.14453e7i | 0.442209 | − | 0.527004i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.02735e7 | + | 2.82261e7i | 0.463018 | + | 1.27213i | 0.923204 | + | 0.384310i | \(0.125561\pi\) |
−0.460186 | + | 0.887823i | \(0.652217\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.38499e6 | − | 7.85468e6i | −0.0611065 | − | 0.346552i | −0.999997 | − | 0.00233709i | \(-0.999256\pi\) |
0.938891 | − | 0.344215i | \(-0.111855\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.51406e6 | + | 3.41978e6i | 0.108603 | + | 0.147728i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.70001e6 | − | 1.00507e6i | 0.241118 | − | 0.0425156i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.26637e7 | − | 8.24890e6i | 0.938937 | − | 0.341745i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.77930e6 | − | 3.17121e6i | −0.153367 | − | 0.128690i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.58074e6 | + | 4.37674e6i | −0.301376 | + | 0.174000i | −0.643061 | − | 0.765815i | \(-0.722336\pi\) |
0.341685 | + | 0.939815i | \(0.389002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.81447e7 | − | 4.96267e6i | −1.09630 | − | 0.193308i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.30443e6 | + | 1.33046e6i | 0.0879618 | + | 0.0507848i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.39650e7 | + | 3.83684e7i | −0.522427 | + | 1.43536i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.99522e6 | − | 5.03059e6i | 0.219839 | − | 0.184467i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.58081e6i | − | 0.0927744i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.69390e7 | −1.65437 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.22650e7 | − | 3.84519e7i | −1.11511 | − | 1.32893i | −0.938748 | − | 0.344605i | \(-0.888013\pi\) |
−0.176357 | − | 0.984326i | \(-0.556431\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 551163. | + | 200607.i | 0.0186812 | + | 0.00679940i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.83052e7 | + | 3.17055e7i | −0.608545 | + | 1.05403i | 0.382935 | + | 0.923775i | \(0.374913\pi\) |
−0.991480 | + | 0.130256i | \(0.958420\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.36773e6 | − | 2.47706e7i | 0.142437 | − | 0.807800i | −0.826952 | − | 0.562272i | \(-0.809927\pi\) |
0.969389 | − | 0.245528i | \(-0.0789614\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.21354e7 | − | 2.10191e7i | −0.388258 | − | 0.672483i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.48632e7 | + | 1.77133e7i | −0.466589 | + | 0.556060i | −0.947104 | − | 0.320927i | \(-0.896006\pi\) |
0.480514 | + | 0.876987i | \(0.340450\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.46787e6 | − | 4.03293e6i | −0.0452183 | − | 0.124236i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 203671. | + | 1.15508e6i | 0.00615764 | + | 0.0349217i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −423668. | − | 856416.i | −0.0125724 | − | 0.0254142i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.94695e7 | + | 8.72282e6i | −1.44108 | + | 0.254101i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.66351e6 | − | 2.06135e6i | 0.161973 | − | 0.0589533i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.83723e6 | + | 6.57622e6i | 0.220077 | + | 0.184667i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.39729e6 | − | 4.27083e6i | 0.203981 | − | 0.117768i | −0.394530 | − | 0.918883i | \(-0.629093\pi\) |
0.598511 | + | 0.801115i | \(0.295759\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.75662e7 | + | 3.09739e6i | 0.475713 | + | 0.0838810i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.47839e7 | − | 4.31765e7i | −1.98918 | − | 1.14845i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.66668e7 | + | 4.57917e7i | −0.435474 | + | 1.19646i | 0.506932 | + | 0.861986i | \(0.330779\pi\) |
−0.942406 | + | 0.334470i | \(0.891443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.73644e6 | + | 3.97435e6i | −0.121578 | + | 0.102016i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.23074e7i | 0.310386i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.49422e7 | 0.865901 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.82971e6 | + | 9.33109e6i | 0.190673 | + | 0.227235i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.66380e7 | + | 2.06146e7i | 1.35556 | + | 0.493384i | 0.914679 | − | 0.404180i | \(-0.132443\pi\) |
0.440883 | + | 0.897565i | \(0.354665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.92558e7 | − | 3.33520e7i | 0.452986 | − | 0.784595i | −0.545584 | − | 0.838056i | \(-0.683692\pi\) |
0.998570 | + | 0.0534611i | \(0.0170253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.61740e6 | + | 9.17273e6i | −0.0374021 | + | 0.212118i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.03009e7 | − | 1.78416e7i | −0.234180 | − | 0.405612i | 0.724854 | − | 0.688903i | \(-0.241907\pi\) |
−0.959034 | + | 0.283291i | \(0.908574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.20692e7 | − | 5.01361e7i | 0.940328 | − | 1.12064i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24966.3 | − | 68594.3i | −0.000548718 | − | 0.00150759i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.47367e6 | + | 5.37278e7i | 0.204755 | + | 1.16122i | 0.897825 | + | 0.440353i | \(0.145147\pi\) |
−0.693069 | + | 0.720871i | \(0.743742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.96148e7 | − | 2.53767e7i | 0.842047 | − | 0.539404i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.33663e6 | − | 764665.i | 0.0906635 | − | 0.0159864i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.14578e7 | − | 7.81002e6i | 0.441273 | − | 0.160610i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.89096e7 | − | 4.10400e7i | −0.989455 | − | 0.830251i | −0.00396620 | − | 0.999992i | \(-0.501262\pi\) |
−0.985489 | + | 0.169741i | \(0.945707\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.13338e7 | − | 1.23171e7i | 0.424610 | − | 0.245148i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.19599e7 | − | 7.39866e6i | −0.821698 | − | 0.144888i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.18440e7 | + | 6.83816e6i | 0.228230 | + | 0.131769i | 0.609755 | − | 0.792590i | \(-0.291268\pi\) |
−0.381525 | + | 0.924359i | \(0.624601\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.81842e6 | + | 4.99607e6i | −0.0344826 | + | 0.0947403i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.15081e7 | − | 9.65642e6i | 0.214773 | − | 0.180216i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.47237e7i | 1.55628i | 0.628092 | + | 0.778139i | \(0.283836\pi\) | ||||
−0.628092 | + | 0.778139i | \(0.716164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.00699e6 | 0.0905319 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.46108e7 | + | 6.50826e7i | 0.972035 | + | 1.15843i | 0.987352 | + | 0.158544i | \(0.0506798\pi\) |
−0.0153170 | + | 0.999883i | \(0.504876\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.87871e7 | + | 6.83796e6i | 0.329214 | + | 0.119824i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.66546e7 | − | 2.88467e7i | 0.287344 | − | 0.497694i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.07343e6 | − | 1.74303e7i | 0.0522125 | − | 0.296112i | −0.947509 | − | 0.319730i | \(-0.896408\pi\) |
0.999721 | + | 0.0236187i | \(0.00751876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.37103e6 | − | 2.37470e6i | −0.0229360 | − | 0.0397263i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.26585e6 | + | 3.89209e6i | −0.0538046 | + | 0.0641218i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.38487e7 | + | 3.80491e7i | 0.224708 | + | 0.617381i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.63087e6 | + | 2.05917e7i | 0.0580283 | + | 0.329095i | 0.999978 | − | 0.00665981i | \(-0.00211990\pi\) |
−0.941950 | + | 0.335754i | \(0.891009\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.22155e6 | − | 1.59370e6i | 0.0507162 | − | 0.0250892i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.06512e7 | − | 1.87810e6i | 0.165184 | − | 0.0291263i | −0.0904446 | − | 0.995901i | \(-0.528829\pi\) |
0.255628 | + | 0.966775i | \(0.417718\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.04823e7 | + | 1.47344e7i | −0.618515 | + | 0.225121i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.80603e7 | − | 6.55004e7i | −1.17507 | − | 0.986004i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.27247e7 | + | 7.34663e6i | −0.188741 | + | 0.108970i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.49726e6 | − | 1.67462e6i | −0.138812 | − | 0.0244764i | 0.103810 | − | 0.994597i | \(-0.466897\pi\) |
−0.242623 | + | 0.970121i | \(0.578008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.45337e6 | − | 1.41645e6i | −0.0353376 | − | 0.0204022i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.27709e6 | + | 2.27411e7i | −0.117497 | + | 0.322821i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.25659e8 | − | 1.05441e8i | 1.75813 | − | 1.47524i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.54565e7i | − | 0.213159i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.08867e8 | 1.47998 | 0.739990 | − | 0.672618i | \(-0.234830\pi\) | ||||
0.739990 | + | 0.672618i | \(0.234830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.75250e7 | + | 6.85556e7i | 0.770922 | + | 0.918749i | 0.998486 | − | 0.0550145i | \(-0.0175205\pi\) |
−0.227564 | + | 0.973763i | \(0.573076\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.09174e7 | + | 1.48927e7i | 0.540614 | + | 0.196767i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.68673e6 | − | 2.92151e6i | 0.0219725 | − | 0.0380575i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.90215e6 | + | 3.91440e7i | −0.0886544 | + | 0.502784i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.90541e6 | − | 3.30027e6i | −0.0241333 | − | 0.0418001i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.13629e7 | − | 8.50469e7i | 0.891334 | − | 1.06225i | −0.106357 | − | 0.994328i | \(-0.533919\pi\) |
0.997691 | − | 0.0679223i | \(-0.0216370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.69492e7 | + | 1.01517e8i | 0.455136 | + | 1.25048i | 0.929066 | + | 0.369914i | \(0.120613\pi\) |
−0.473930 | + | 0.880563i | \(0.657165\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −778233. | − | 4.41358e6i | −0.00945457 | − | 0.0536195i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.08781e8 | − | 7.99709e7i | 1.30350 | − | 0.958269i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.72273e7 | + | 1.18540e7i | −0.794606 | + | 0.140111i | −0.556193 | − | 0.831053i | \(-0.687738\pi\) |
−0.238414 | + | 0.971164i | \(0.576627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.02183e7 | − | 2.19177e7i | 0.702122 | − | 0.255551i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.33465e7 | − | 5.31540e7i | −0.728637 | − | 0.611399i | 0.201123 | − | 0.979566i | \(-0.435541\pi\) |
−0.929760 | + | 0.368167i | \(0.879985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.98276e8 | + | 1.14475e8i | −2.25004 | + | 1.29906i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.98654e6 | − | 1.05559e6i | −0.0670275 | − | 0.0118188i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.52064e6 | + | 3.18734e6i | 0.0609889 | + | 0.0352119i | 0.530184 | − | 0.847882i | \(-0.322123\pi\) |
−0.469196 | + | 0.883094i | \(0.655456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.94037e6 | + | 1.90685e7i | −0.0756576 | + | 0.207868i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.68456e6 | + | 7.28721e6i | −0.0934229 | + | 0.0783911i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.99825e7i | 0.742943i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.67794e6 | −0.0175803 | −0.00879017 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00879017 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −402073. | − | 479172.i | −0.00415783 | − | 0.00495511i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.50202e8 | − | 5.46692e7i | −1.53311 | − | 0.558008i | −0.568732 | − | 0.822523i | \(-0.692566\pi\) |
−0.964382 | + | 0.264515i | \(0.914788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.22230e7 | − | 7.31324e7i | 0.425408 | − | 0.736829i | −0.571050 | − | 0.820915i | \(-0.693464\pi\) |
0.996458 | + | 0.0840863i | \(0.0267971\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.23172e6 | + | 1.26567e7i | −0.0221963 | + | 0.125882i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.56441e7 | − | 1.13699e8i | −0.644533 | − | 1.11636i | −0.984409 | − | 0.175894i | \(-0.943719\pi\) |
0.339876 | − | 0.940470i | \(-0.389615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.70030e7 | + | 5.60159e7i | −0.455624 | + | 0.542992i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.62286e6 | − | 7.20624e6i | −0.0251022 | − | 0.0689677i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.76461e6 | + | 2.70215e7i | 0.0450240 | + | 0.255344i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.52119e8 | + | 6.67074e7i | 1.41939 | + | 0.622434i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.78586e8 | + | 3.14896e7i | −1.64548 | + | 0.290143i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.52120e7 | + | 2.00955e7i | −0.502374 | + | 0.182849i | −0.580761 | − | 0.814074i | \(-0.697245\pi\) |
0.0783877 | + | 0.996923i | \(0.475023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.93991e7 | − | 3.30598e7i | −0.354039 | − | 0.297074i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.93284e6 | − | 5.15737e6i | 0.0792771 | − | 0.0457707i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.12814e8 | − | 5.51575e7i | −2.74196 | − | 0.483481i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.20821e8 | − | 6.97559e7i | −1.04605 | − | 0.603940i | −0.124513 | − | 0.992218i | \(-0.539737\pi\) |
−0.921542 | + | 0.388278i | \(0.873070\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 369797. | − | 1.01601e6i | 0.00316255 | − | 0.00868902i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.05864e8 | − | 8.88307e7i | 0.894345 | − | 0.750445i | −0.0747319 | − | 0.997204i | \(-0.523810\pi\) |
0.969077 | + | 0.246759i | \(0.0793656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00888e6i | 0.00841973i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.50920e7 | 0.701574 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.56242e7 | − | 4.24552e7i | −0.290185 | − | 0.345830i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.49827e8 | + | 5.45326e7i | 1.20584 | + | 0.438889i | 0.865258 | − | 0.501327i | \(-0.167155\pi\) |
0.340579 | + | 0.940216i | \(0.389377\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.79267e6 | − | 3.10499e6i | 0.0142556 | − | 0.0246915i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.13421e7 | + | 1.21037e8i | −0.167700 | + | 0.951073i | 0.778537 | + | 0.627598i | \(0.215962\pi\) |
−0.946237 | + | 0.323474i | \(0.895149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.30813e7 | − | 1.43901e8i | −0.645104 | − | 1.11735i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.04443e6 | + | 1.24471e6i | −0.00801414 | + | 0.00955088i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.96389e7 | + | 2.46281e8i | 0.679740 | + | 1.86757i | 0.445068 | + | 0.895497i | \(0.353179\pi\) |
0.234672 | + | 0.972075i | \(0.424598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.35777e6 | − | 1.90429e7i | −0.0251645 | − | 0.142715i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.12702e7 | − | 2.22747e7i | 0.157550 | − | 0.164991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.71897e7 | − | 6.55755e6i | 0.272271 | − | 0.0480087i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.37055e7 | + | 1.22678e7i | −0.243910 | + | 0.0887759i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.08055e7 | − | 1.74579e7i | −0.148825 | − | 0.124879i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.60148e6 | − | 924617.i | 0.0113243 | − | 0.00653806i | −0.494327 | − | 0.869276i | \(-0.664586\pi\) |
0.505651 | + | 0.862738i | \(0.331252\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.97337e8 | − | 3.47958e7i | −1.37944 | − | 0.243233i | −0.565772 | − | 0.824562i | \(-0.691422\pi\) |
−0.813669 | + | 0.581329i | \(0.802533\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.09898e7 | + | 6.34494e6i | 0.0759469 | + | 0.0438480i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 989513. | − | 2.71866e6i | 0.00676067 | − | 0.0185748i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.83415e8 | − | 1.53903e8i | 1.23899 | − | 1.03964i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.03001e8i | 0.687949i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.10305e7 | −0.469098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.85405e7 | + | 5.78483e7i | 0.316988 | + | 0.377772i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.80598e6 | − | 1.38526e6i | −0.0245778 | − | 0.00894560i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.63940e7 | + | 4.57157e7i | −0.168554 | + | 0.291944i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.72537e7 | + | 1.54564e8i | −0.172121 | + | 0.976147i | 0.769294 | + | 0.638896i | \(0.220608\pi\) |
−0.941415 | + | 0.337252i | \(0.890503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.42167e6 | − | 1.45868e7i | −0.0526016 | − | 0.0911086i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.49428e8 | − | 2.97256e8i | 1.54083 | − | 1.83629i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.84055e7 | − | 2.42892e8i | −0.540154 | − | 1.48406i | −0.846630 | − | 0.532182i | \(-0.821372\pi\) |
0.306476 | − | 0.951878i | \(-0.400850\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.93764e7 | + | 1.66602e8i | 0.177534 | + | 1.00684i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.93731e7 | + | 5.46963e6i | −0.295145 | + | 0.0326966i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.37669e7 | − | 5.95401e6i | 0.199671 | − | 0.0352074i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.44181e7 | + | 5.24777e6i | −0.0843393 | + | 0.0306970i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.60018e7 | − | 7.21641e7i | −0.497671 | − | 0.417595i | 0.359095 | − | 0.933301i | \(-0.383085\pi\) |
−0.856766 | + | 0.515706i | \(0.827530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.31769e7 | + | 4.80222e7i | −0.476176 | + | 0.274920i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 252035. | + | 44440.5i | 0.00142748 | + | 0.000251704i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.23007e8 | − | 7.10184e7i | −0.689297 | − | 0.397966i | 0.114052 | − | 0.993475i | \(-0.463617\pi\) |
−0.803349 | + | 0.595509i | \(0.796950\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.36153e8 | + | 3.74078e8i | −0.754888 | + | 2.07404i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.61014e7 | + | 5.54657e7i | −0.362628 | + | 0.304281i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.88963e8i | − | 1.02575i | −0.858464 | − | 0.512874i | \(-0.828581\pi\) | ||
0.858464 | − | 0.512874i | \(-0.171419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.89687e7 | 0.101889 | 0.0509447 | − | 0.998701i | \(-0.483777\pi\) | ||||
0.0509447 | + | 0.998701i | \(0.483777\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.22644e7 | − | 1.46162e7i | −0.0651904 | − | 0.0776909i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.47939e8 | + | 1.63037e8i | 2.35622 | + | 0.857593i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.57382e7 | − | 7.92209e7i | 0.238096 | − | 0.412394i | −0.722072 | − | 0.691818i | \(-0.756810\pi\) |
0.960168 | + | 0.279424i | \(0.0901435\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.07244e6 | − | 1.74247e7i | 0.0158288 | − | 0.0897697i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.94530e7 | − | 1.20296e8i | −0.354130 | − | 0.613371i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.60189e7 | − | 1.14431e8i | 0.484564 | − | 0.577481i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.01872e8 | + | 2.79891e8i | 0.508847 | + | 1.39805i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.96959e7 | + | 2.25126e8i | 0.196260 | + | 1.11304i | 0.910614 | + | 0.413259i | \(0.135610\pi\) |
−0.714354 | + | 0.699785i | \(0.753279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.38412e8 | + | 3.36861e7i | 0.677374 | + | 0.164856i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.58523e6 | + | 1.69013e6i | −0.0464344 | + | 0.00818764i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.76079e8 | − | 1.00485e8i | 1.32394 | − | 0.481877i | 0.419225 | − | 0.907883i | \(-0.362302\pi\) |
0.904720 | + | 0.426006i | \(0.140080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.60026e6 | − | 3.02098e6i | −0.0170916 | − | 0.0143416i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.17551e7 | + | 1.25603e7i | −0.102244 | + | 0.0590306i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.49111e8 | + | 4.39250e7i | 1.15908 | + | 0.204376i | 0.719935 | − | 0.694041i | \(-0.244172\pi\) |
0.439141 | + | 0.898418i | \(0.355283\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.13035e8 | + | 6.52606e7i | 0.520700 | + | 0.300627i | 0.737221 | − | 0.675651i | \(-0.236138\pi\) |
−0.216521 | + | 0.976278i | \(0.569471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.06445e8 | + | 2.92454e8i | −0.485480 | + | 1.33385i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.17186e8 | − | 1.82241e8i | 0.980768 | − | 0.822962i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.00732e8i | − | 1.34466i | −0.740251 | − | 0.672331i | \(-0.765293\pi\) | ||
0.740251 | − | 0.672331i | \(-0.234707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.79507e6 | −0.0168023 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.07044e7 | − | 9.61797e7i | −0.353813 | − | 0.421658i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.76252e8 | + | 1.00547e8i | 1.19929 | + | 0.436505i | 0.862975 | − | 0.505246i | \(-0.168598\pi\) |
0.336312 | + | 0.941751i | \(0.390820\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.05951e7 | + | 1.83513e7i | −0.0455491 | + | 0.0788934i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.64889e7 | − | 4.33790e8i | 0.325644 | − | 1.84682i | −0.179467 | − | 0.983764i | \(-0.557437\pi\) |
0.505111 | − | 0.863054i | \(-0.331452\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.92713e7 | − | 3.33788e7i | −0.0812529 | − | 0.140734i | 0.822535 | − | 0.568714i | \(-0.192559\pi\) |
−0.903788 | + | 0.427980i | \(0.859225\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.68148e7 | − | 6.77093e7i | 0.237239 | − | 0.282731i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.63088e7 | + | 1.82182e8i | 0.274225 | + | 0.753427i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.26457e6 | − | 3.55281e7i | −0.0256597 | − | 0.145523i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −808450. | + | 1.25751e7i | −0.00327983 | + | 0.0510165i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.40153e6 | − | 599782.i | 0.0136686 | − | 0.00241013i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.78233e7 | + | 3.56048e7i | −0.389363 | + | 0.141716i | −0.529281 | − | 0.848447i | \(-0.677538\pi\) |
0.139918 | + | 0.990163i | \(0.455316\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.13302e7 | + | 3.46802e7i | 0.162951 | + | 0.136732i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.79180e8 | − | 1.61185e8i | 1.09034 | − | 0.629510i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.81970e8 | − | 3.20863e7i | −0.704016 | − | 0.124137i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.04278e8 | − | 1.17940e8i | −0.782924 | − | 0.452021i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.67173e8 | + | 4.59305e8i | −0.634735 | + | 1.74392i | 0.0329287 | + | 0.999458i | \(0.489517\pi\) |
−0.667664 | + | 0.744463i | \(0.732706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.36839e7 | − | 7.86101e7i | 0.352397 | − | 0.295696i | −0.449355 | − | 0.893353i | \(-0.648346\pi\) |
0.801752 | + | 0.597657i | \(0.203902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.86525e7i | 0.106778i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.29349e8 | −1.58525 | −0.792625 | − | 0.609709i | \(-0.791286\pi\) | ||||
−0.792625 | + | 0.609709i | \(0.791286\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.45381e7 | − | 6.49960e7i | −0.199510 | − | 0.237767i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.02267e7 | + | 3.72222e6i | 0.0370675 | + | 0.0134915i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.63126e8 | + | 2.82542e8i | −0.585845 | + | 1.01471i | 0.408924 | + | 0.912568i | \(0.365904\pi\) |
−0.994769 | + | 0.102145i | \(0.967429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.68037e7 | + | 3.22150e8i | −0.202140 | + | 1.14640i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.11495e7 | − | 7.12730e7i | −0.145100 | − | 0.251321i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.03667e8 | − | 1.23546e8i | 0.362230 | − | 0.431689i | −0.553892 | − | 0.832588i | \(-0.686858\pi\) |
0.916122 | + | 0.400900i | \(0.131302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.15617e8 | + | 3.17654e8i | 0.400328 | + | 1.09989i | 0.962123 | + | 0.272616i | \(0.0878889\pi\) |
−0.561795 | + | 0.827277i | \(0.689889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 155558. | + | 882215.i | 0.000533768 | + | 0.00302715i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.28323e8 | − | 1.92570e8i | 0.436356 | − | 0.654822i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.40394e8 | + | 2.47552e7i | −0.473118 | + | 0.0834235i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.14277e7 | + | 4.15934e6i | −0.0381663 | + | 0.0138914i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.06752e8 | − | 8.95752e7i | −0.353351 | − | 0.296497i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.44013e8 | + | 8.31457e7i | −0.472449 | + | 0.272769i | −0.717265 | − | 0.696801i | \(-0.754606\pi\) |
0.244815 | + | 0.969570i | \(0.421273\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.07089e8 | + | 1.88827e7i | 0.348203 | + | 0.0613976i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.81415e8 | − | 2.77945e8i | −1.55151 | − | 0.895763i | −0.998019 | − | 0.0629064i | \(-0.979963\pi\) |
−0.553488 | − | 0.832857i | \(-0.686704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.19955e7 | + | 2.52756e8i | −0.293871 | + | 0.807405i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.46105e7 | − | 1.22596e7i | 0.0462618 | − | 0.0388182i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.39407e8i | − | 1.06527i | −0.846346 | − | 0.532634i | \(-0.821202\pi\) | ||
0.846346 | − | 0.532634i | \(-0.178798\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.82394e8 | −0.567463 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.45259e6 | − | 1.73113e6i | −0.00447994 | − | 0.00533898i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.91348e8 | + | 1.78836e8i | 1.50221 | + | 0.546761i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.93924e8 | + | 3.35886e8i | −0.587757 | + | 1.01802i | 0.406769 | + | 0.913531i | \(0.366656\pi\) |
−0.994526 | + | 0.104494i | \(0.966678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.25124e7 | − | 7.09612e7i | 0.0375959 | − | 0.213217i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.97575e8 | − | 8.61825e8i | −1.48219 | − | 2.56723i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.06622e6 | − | 3.65418e6i | 0.00905534 | − | 0.0107917i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.52932e7 | + | 6.94925e7i | 0.0740580 | + | 0.203473i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.25117e7 | − | 4.67947e8i | −0.239531 | − | 1.35845i | −0.832858 | − | 0.553486i | \(-0.813297\pi\) |
0.593327 | − | 0.804961i | \(-0.297814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.77938e7 | + | 1.63214e8i | 0.137564 | + | 0.469778i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.68868e7 | + | 6.50414e6i | −0.105270 | + | 0.0185619i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.32221e8 | + | 4.81244e7i | −0.374146 | + | 0.136178i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.86887e8 | + | 1.56817e8i | 0.524374 | + | 0.440002i | 0.866153 | − | 0.499778i | \(-0.166585\pi\) |
−0.341779 | + | 0.939780i | \(0.611030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.26382e8 | − | 7.29665e7i | 0.351621 | − | 0.203009i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.02604e8 | + | 7.09899e7i | 1.11073 | + | 0.195852i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.12484e8 | − | 1.22678e8i | −0.581311 | − | 0.335620i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.26164e6 | − | 2.26987e7i | 0.0224134 | − | 0.0615804i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.71038e7 | + | 8.14798e7i | −0.261246 | + | 0.219211i | −0.763997 | − | 0.645220i | \(-0.776766\pi\) |
0.502751 | + | 0.864431i | \(0.332321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.19781e7i | − | 0.0853191i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.21888e7 | 0.138090 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.12736e8 | − | 1.34353e8i | −0.295834 | − | 0.352561i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.26275e8 | + | 1.18754e8i | 0.849143 | + | 0.309063i | 0.729691 | − | 0.683777i | \(-0.239664\pi\) |
0.119452 | + | 0.992840i | \(0.461886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.78555e8 | + | 3.09266e8i | −0.460881 | + | 0.798269i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.12004e6 | − | 6.35205e6i | 0.00286735 | − | 0.0162615i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.37119e7 | − | 5.83907e7i | −0.0855995 | − | 0.148263i | 0.820047 | − | 0.572296i | \(-0.193947\pi\) |
−0.905647 | + | 0.424033i | \(0.860614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.54329e7 | + | 4.22273e7i | −0.0892370 | + | 0.106349i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.76831e7 | − | 2.40907e8i | −0.219035 | − | 0.601794i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.22515e7 | + | 4.66471e8i | 0.203803 | + | 1.15582i | 0.899312 | + | 0.437307i | \(0.144068\pi\) |
−0.695510 | + | 0.718517i | \(0.744821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.23310e7 | + | 1.23957e7i | −0.104041 | + | 0.0304661i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.26825e8 | + | 3.99953e7i | −0.552998 | + | 0.0975085i | −0.443163 | − | 0.896441i | \(-0.646144\pi\) |
−0.109836 | + | 0.993950i | \(0.535032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.67780e8 | + | 1.33861e8i | −0.889444 | + | 0.323731i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.52886e8 | − | 3.80017e8i | −1.08649 | − | 0.911676i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.53793e7 | − | 3.19733e7i | 0.131796 | − | 0.0760925i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.60461e8 | − | 1.34090e8i | −1.79538 | − | 0.316575i | −0.826286 | − | 0.563250i | \(-0.809551\pi\) |
−0.969098 | + | 0.246676i | \(0.920662\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.57813e7 | − | 4.37524e7i | −0.177491 | − | 0.102475i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.49645e8 | + | 6.85895e8i | −0.580073 | + | 1.59374i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.90420e8 | − | 4.11511e8i | 1.13053 | − | 0.948623i | 0.131437 | − | 0.991324i | \(-0.458041\pi\) |
0.999088 | + | 0.0427013i | \(0.0135964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.61631e7i | 0.0827065i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.70113e8 | 0.839810 | 0.419905 | − | 0.907568i | \(-0.362063\pi\) | ||||
0.419905 | + | 0.907568i | \(0.362063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.11215e8 | − | 2.51716e8i | −0.475501 | − | 0.566680i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.87966e7 | − | 6.84140e6i | −0.0419851 | − | 0.0152813i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.48497e8 | − | 2.57204e8i | 0.329102 | − | 0.570022i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.42007e7 | + | 4.20813e8i | −0.163166 | + | 0.925359i | 0.787770 | + | 0.615970i | \(0.211236\pi\) |
−0.950935 | + | 0.309389i | \(0.899875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.56299e7 | + | 4.43923e7i | 0.0559221 | + | 0.0968600i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.24231e8 | − | 2.67228e8i | 0.485464 | − | 0.578553i | −0.466594 | − | 0.884472i | \(-0.654519\pi\) |
0.952058 | + | 0.305919i | \(0.0989635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.72019e8 | + | 4.72618e8i | 0.369548 | + | 1.01533i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.25618e6 | + | 1.27954e7i | 0.00480962 | + | 0.0272767i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.95454e8 | + | 1.30245e8i | 0.413458 | + | 0.275518i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.91353e8 | − | 3.37407e7i | 0.401682 | − | 0.0708273i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.05591e7 | + | 1.11226e7i | −0.0636584 | + | 0.0231698i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.78228e8 | − | 3.17371e8i | −0.781889 | − | 0.656083i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.43943e8 | + | 3.71781e8i | −1.32106 | + | 0.762716i | −0.983898 | − | 0.178730i | \(-0.942801\pi\) |
−0.337165 | + | 0.941446i | \(0.609468\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.46770e6 | − | 258795.i | −0.00298817 | − | 0.000526896i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.91936e8 | + | 1.68549e8i | 0.589872 | + | 0.340563i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.66835e8 | − | 4.58375e8i | 0.334555 | − | 0.919181i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.19494e8 | − | 1.00268e8i | 0.237819 | − | 0.199554i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.42302e8i | − | 0.478610i | −0.970944 | − | 0.239305i | \(-0.923080\pi\) | ||
0.970944 | − | 0.239305i | \(-0.0769195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.43179e6 | 0.0165303 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.30397e8 | + | 6.32103e8i | 1.03206 | + | 1.22996i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.37049e7 | + | 2.31867e7i | 0.123034 | + | 0.0447808i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.32052e8 | − | 5.75131e8i | 0.636530 | − | 1.10250i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.79668e6 | − | 2.15320e7i | 0.00722410 | − | 0.0409699i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.18836e8 | + | 5.52240e8i | 0.602173 | + | 1.04299i | 0.992491 | + | 0.122315i | \(0.0390317\pi\) |
−0.390318 | + | 0.920680i | \(0.627635\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.76612e8 | − | 6.87179e8i | 1.08099 | − | 1.28827i | 0.125869 | − | 0.992047i | \(-0.459828\pi\) |
0.955118 | − | 0.296224i | \(-0.0957276\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.35300e7 | + | 3.71733e7i | 0.0251782 | + | 0.0691766i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.20881e7 | − | 6.85553e7i | −0.0223299 | − | 0.126639i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.16932e8 | + | 2.03754e7i | 0.581166 | + | 0.0373629i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.48391e8 | − | 4.37980e7i | 0.452151 | − | 0.0797264i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.80064e8 | − | 1.01935e8i | 0.506090 | − | 0.184202i | −0.0763409 | − | 0.997082i | \(-0.524324\pi\) |
0.582431 | + | 0.812880i | \(0.302101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.30234e8 | + | 4.44919e8i | 0.951192 | + | 0.798145i | 0.979498 | − | 0.201454i | \(-0.0645667\pi\) |
−0.0283057 | + | 0.999599i | \(0.509011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.85296e7 | + | 2.22451e7i | −0.0686171 | + | 0.0396161i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.69801e7 | − | 1.18104e7i | −0.118421 | − | 0.0208808i | 0.114123 | − | 0.993467i | \(-0.463594\pi\) |
−0.232545 | + | 0.972586i | \(0.574705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.36993e8 | + | 4.25503e8i | 1.29360 | + | 0.746860i | 0.979290 | − | 0.202461i | \(-0.0648938\pi\) |
0.314309 | + | 0.949321i | \(0.398227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.65884e7 | − | 4.55763e7i | 0.0289070 | − | 0.0794212i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.50591e6 | − | 7.97640e6i | 0.0164459 | − | 0.0137998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 2.30838e8i | − | 0.396504i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.32579e7 | 0.159041 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.50452e8 | + | 4.17653e8i | 0.593394 | + | 0.707179i | 0.976254 | − | 0.216627i | \(-0.0695055\pi\) |
−0.382861 | + | 0.923806i | \(0.625061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.09663e8 | − | 1.85502e8i | −0.856831 | − | 0.311861i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.65615e7 | + | 8.06469e7i | −0.0777221 | + | 0.134619i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.81661e7 | + | 1.03025e8i | −0.0301086 | + | 0.170755i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.20041e8 | − | 2.07917e8i | −0.197551 | − | 0.342168i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.58941e7 | − | 1.89419e7i | 0.0259724 | − | 0.0309528i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.66929e8 | + | 4.58633e8i | 0.270859 | + | 0.744178i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.31021e8 | + | 7.43054e8i | 0.211102 | + | 1.19722i | 0.887544 | + | 0.460723i | \(0.152410\pi\) |
−0.676442 | + | 0.736496i | \(0.736479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.32903e8 | − | 9.56970e8i | 0.372629 | − | 1.53109i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.69949e8 | + | 1.00497e8i | −0.905510 | + | 0.159666i | −0.606964 | − | 0.794729i | \(-0.707613\pi\) |
−0.298546 | + | 0.954395i | \(0.596502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.10346e8 | − | 2.94942e8i | 1.27847 | − | 0.465325i | 0.388545 | − | 0.921430i | \(-0.372978\pi\) |
0.889926 | + | 0.456104i | \(0.150756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.37458e7 | + | 1.15341e7i | 0.0215358 | + | 0.0180707i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.76317e7 | − | 3.32737e7i | 0.0896662 | − | 0.0517688i | −0.454496 | − | 0.890749i | \(-0.650181\pi\) |
0.544163 | + | 0.838980i | \(0.316847\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.72208e9 | − | 3.03649e8i | −2.66075 | − | 0.469162i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.47540e7 | + | 3.73857e7i | 0.0993595 | + | 0.0573652i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.11147e7 | + | 1.12962e8i | −0.0626525 | + | 0.172136i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.87436e8 | − | 5.76828e8i | 1.04035 | − | 0.872954i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.14480e9i | 1.72062i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.89868e8 | 0.432690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.46555e8 | − | 2.93833e8i | −0.365524 | − | 0.435615i | 0.551666 | − | 0.834065i | \(-0.313992\pi\) |
−0.917190 | + | 0.398451i | \(0.869548\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.55011e7 | − | 9.28164e6i | −0.0375484 | − | 0.0136665i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.45035e8 | − | 4.24414e8i | 0.358345 | − | 0.620671i | −0.629340 | − | 0.777130i | \(-0.716675\pi\) |
0.987684 | + | 0.156459i | \(0.0500079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.74803e7 | + | 2.69274e8i | −0.0689655 | + | 0.391123i | 0.930713 | + | 0.365751i | \(0.119188\pi\) |
−0.999678 | + | 0.0253713i | \(0.991923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.43003e7 | − | 7.67304e7i | −0.0639112 | − | 0.110698i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.04177e8 | + | 6.00855e8i | −0.722457 | + | 0.860991i | −0.994867 | − | 0.101190i | \(-0.967735\pi\) |
0.272410 | + | 0.962181i | \(0.412179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.33654e7 | − | 2.56519e8i | −0.132886 | − | 0.365103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.25332e7 | − | 2.97930e8i | −0.0742678 | − | 0.421193i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.57129e7 | + | 4.12640e8i | 0.0641925 | + | 0.579451i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.56809e8 | + | 4.52823e7i | −0.358212 | + | 0.0631625i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.18950e8 | + | 4.32944e7i | −0.164812 | + | 0.0599866i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.15224e8 | − | 9.66840e7i | −0.158585 | − | 0.133069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.04106e7 | + | 1.75575e7i | −0.0415767 | + | 0.0240043i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.38943e7 | + | 4.21321e6i | 0.0324512 | + | 0.00572202i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.39153e8 | − | 5.42220e8i | −1.26704 | − | 0.731526i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.04149e8 | − | 1.11039e9i | 0.541651 | − | 1.48817i | −0.303071 | − | 0.952968i | \(-0.598012\pi\) |
0.844722 | − | 0.535206i | \(-0.179766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.58756e8 | + | 3.84942e8i | −0.610788 | + | 0.512512i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.02197e9i | 1.35171i | 0.737032 | + | 0.675857i | \(0.236227\pi\) | ||||
−0.737032 | + | 0.675857i | \(0.763773\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.86998e8 | 0.639905 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.35390e7 | − | 1.11475e8i | −0.122104 | − | 0.145518i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.60299e8 | + | 9.47412e7i | 0.337571 | + | 0.122866i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.53511e8 | − | 9.58710e8i | 0.713148 | − | 1.23521i | −0.250521 | − | 0.968111i | \(-0.580602\pi\) |
0.963669 | − | 0.267098i | \(-0.0860648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.70225e7 | − | 1.53252e8i | 0.0345897 | − | 0.196168i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.40070e8 | + | 5.89018e8i | 0.432477 | + | 0.749072i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.85963e8 | + | 4.59973e8i | −0.487664 | + | 0.581175i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.65498e7 | − | 1.27894e8i | −0.0584357 | − | 0.160551i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.76779e7 | + | 3.83820e8i | 0.0844111 | + | 0.478719i | 0.997482 | + | 0.0709186i | \(0.0225930\pi\) |
−0.913071 | + | 0.407801i | \(0.866296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.41890e8 | + | 4.21962e8i | 0.547602 | + | 0.522906i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.11776e8 | + | 1.97091e7i | −0.137627 | + | 0.0242673i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.54836e7 | − | 5.63557e6i | 0.0189425 | − | 0.00689450i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.04010e9 | − | 8.72746e8i | −1.26432 | − | 1.06089i | −0.995208 | − | 0.0977770i | \(-0.968827\pi\) |
−0.269108 | − | 0.963110i | \(-0.586729\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.75317e7 | − | 3.89895e7i | 0.0815663 | − | 0.0470923i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.31135e7 | − | 1.46552e7i | −0.0997477 | − | 0.0175882i | 0.123552 | − | 0.992338i | \(-0.460572\pi\) |
−0.223299 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.83744e8 | + | 3.37025e8i | 0.696125 | + | 0.401908i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.18140e7 | − | 1.42358e8i | 0.0613977 | − | 0.168689i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.57624e7 | + | 7.19632e7i | −0.100983 | + | 0.0847345i | −0.691881 | − | 0.722011i | \(-0.743218\pi\) |
0.590898 | + | 0.806746i | \(0.298773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.37302e8i | 0.277653i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.16864e7 | −0.0833480 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.91142e8 | + | 2.27794e8i | 0.220839 | + | 0.263186i | 0.865077 | − | 0.501639i | \(-0.167270\pi\) |
−0.644237 | + | 0.764826i | \(0.722825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.15437e9 | − | 4.20155e8i | −1.32536 | − | 0.482391i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.65267e6 | − | 1.15228e7i | 0.00759032 | − | 0.0131468i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.68201e7 | + | 1.52104e8i | −0.0304091 | + | 0.172459i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28083e8 | − | 3.95051e8i | −0.256994 | − | 0.445126i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.74944e8 | − | 2.08490e8i | 0.195893 | − | 0.233457i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.89622e8 | − | 1.07048e9i | −0.433572 | − | 1.19123i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.67980e8 | − | 9.52663e8i | −0.185771 | − | 1.05356i | −0.924960 | − | 0.380063i | \(-0.875902\pi\) |
0.739189 | − | 0.673498i | \(-0.235209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.18963e6 | − | 2.71282e6i | 0.00130749 | − | 0.00298160i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.91361e8 | + | 6.90075e7i | −0.427484 | + | 0.0753769i | −0.383251 | − | 0.923644i | \(-0.625196\pi\) |
−0.0442330 | + | 0.999021i | \(0.514084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.91872e8 | + | 2.88218e8i | −0.859640 | + | 0.312883i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.19298e8 | − | 1.00103e8i | −0.128712 | − | 0.108002i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.01224e8 | + | 3.47117e8i | −0.644692 | + | 0.372213i | −0.786420 | − | 0.617692i | \(-0.788068\pi\) |
0.141727 | + | 0.989906i | \(0.454734\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.69388e8 | − | 1.18031e8i | −0.713394 | − | 0.125791i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.21116e9 | − | 6.99265e8i | −1.28291 | − | 0.740687i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.33320e8 | + | 6.41041e8i | −0.245636 | + | 0.674878i | 0.754198 | + | 0.656647i | \(0.228026\pi\) |
−0.999834 | + | 0.0182314i | \(0.994196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.80046e8 | + | 4.02806e8i | −0.502312 | + | 0.421490i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.17176e7i | 0.0329875i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.11420e8 | 0.942171 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.36493e8 | + | 8.77718e8i | 0.756741 | + | 0.901849i | 0.997637 | − | 0.0687018i | \(-0.0218857\pi\) |
−0.240896 | + | 0.970551i | \(0.577441\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.48840e7 | + | 9.05702e6i | 0.0254139 | + | 0.00924992i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.08682e8 | + | 1.40068e9i | −0.820934 | + | 1.42190i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.68767e8 | + | 9.57124e8i | −0.170295 | + | 0.965791i | 0.773141 | + | 0.634235i | \(0.218685\pi\) |
−0.943436 | + | 0.331556i | \(0.892426\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.56684e7 | + | 9.64206e7i | 0.0558358 | + | 0.0967104i |
(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 | 76.7.j.a.29.6 | yes | 60 | |
19.2 | odd | 18 | inner | 76.7.j.a.21.6 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.21.6 | ✓ | 60 | 19.2 | odd | 18 | inner | |
76.7.j.a.29.6 | yes | 60 | 1.1 | even | 1 | trivial |