Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(11,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.11");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.e (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: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Character | \(\chi\) | \(=\) | 37.11 |
Dual form | 37.6.e.a.27.2 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.18598 | + | 5.30353i | −1.62387 | + | 0.937540i | −0.637994 | + | 0.770041i | \(0.720236\pi\) |
−0.985872 | + | 0.167498i | \(0.946431\pi\) | |||||||
\(3\) | −6.26292 | + | 10.8477i | −0.401766 | + | 0.695880i | −0.993939 | − | 0.109931i | \(-0.964937\pi\) |
0.592173 | + | 0.805811i | \(0.298270\pi\) | |||||||
\(4\) | 40.2548 | − | 69.7233i | 1.25796 | − | 2.17885i | ||||
\(5\) | 63.9646 | + | 36.9300i | 1.14423 | + | 0.660623i | 0.947475 | − | 0.319829i | \(-0.103625\pi\) |
0.196758 | + | 0.980452i | \(0.436959\pi\) | |||||||
\(6\) | − | 132.862i | − | 1.50669i | ||||||
\(7\) | 113.255 | − | 196.163i | 0.873596 | − | 1.51311i | 0.0153451 | − | 0.999882i | \(-0.495115\pi\) |
0.858251 | − | 0.513230i | \(-0.171551\pi\) | |||||||
\(8\) | 514.543i | 2.84248i | ||||||||
\(9\) | 43.0517 | + | 74.5678i | 0.177168 | + | 0.306863i | ||||
\(10\) | −783.436 | −2.47744 | ||||||||
\(11\) | 134.565 | 0.335314 | 0.167657 | − | 0.985845i | \(-0.446380\pi\) | ||||
0.167657 | + | 0.985845i | \(0.446380\pi\) | |||||||
\(12\) | 504.224 | + | 873.342i | 1.01081 | + | 1.75078i | ||||
\(13\) | −145.563 | − | 84.0406i | −0.238886 | − | 0.137921i | 0.375778 | − | 0.926710i | \(-0.377375\pi\) |
−0.614665 | + | 0.788788i | \(0.710709\pi\) | |||||||
\(14\) | 2402.59i | 3.27612i | ||||||||
\(15\) | −801.210 | + | 462.579i | −0.919429 | + | 0.530832i | ||||
\(16\) | −1440.74 | − | 2495.43i | −1.40697 | − | 2.43695i | ||||
\(17\) | 444.179 | − | 256.447i | 0.372766 | − | 0.215216i | −0.301900 | − | 0.953339i | \(-0.597621\pi\) |
0.674666 | + | 0.738123i | \(0.264288\pi\) | |||||||
\(18\) | −790.944 | − | 456.652i | −0.575393 | − | 0.332203i | ||||
\(19\) | 1944.69 | + | 1122.77i | 1.23585 | + | 0.713518i | 0.968243 | − | 0.250010i | \(-0.0804340\pi\) |
0.267606 | + | 0.963528i | \(0.413767\pi\) | |||||||
\(20\) | 5149.76 | − | 2973.21i | 2.87880 | − | 1.66208i | ||||
\(21\) | 1418.61 | + | 2457.10i | 0.701963 | + | 1.21584i | ||||
\(22\) | −1236.11 | + | 713.671i | −0.544505 | + | 0.314370i | ||||
\(23\) | − | 2768.93i | − | 1.09142i | −0.837973 | − | 0.545711i | \(-0.816260\pi\) | ||
0.837973 | − | 0.545711i | \(-0.183740\pi\) | |||||||
\(24\) | −5581.60 | − | 3222.54i | −1.97802 | − | 1.14201i | ||||
\(25\) | 1165.15 | + | 2018.09i | 0.372847 | + | 0.645789i | ||||
\(26\) | 1782.85 | 0.517226 | ||||||||
\(27\) | −4122.30 | −1.08825 | ||||||||
\(28\) | −9118.07 | − | 15793.0i | −2.19790 | − | 3.80687i | ||||
\(29\) | 8023.83i | 1.77169i | 0.463984 | + | 0.885843i | \(0.346419\pi\) | ||||
−0.463984 | + | 0.885843i | \(0.653581\pi\) | |||||||
\(30\) | 4906.60 | − | 8498.47i | 0.995353 | − | 1.72400i | ||||
\(31\) | 4034.07i | 0.753944i | 0.926225 | + | 0.376972i | \(0.123035\pi\) | ||||
−0.926225 | + | 0.376972i | \(0.876965\pi\) | |||||||
\(32\) | 12209.8 | + | 7049.31i | 2.10781 | + | 1.21695i | ||||
\(33\) | −842.772 | + | 1459.72i | −0.134718 | + | 0.233338i | ||||
\(34\) | −2720.14 | + | 4711.43i | −0.403548 | + | 0.698965i | ||||
\(35\) | 14488.6 | − | 8364.98i | 1.99920 | − | 1.15424i | ||||
\(36\) | 6932.15 | 0.891480 | ||||||||
\(37\) | 8084.81 | − | 1994.93i | 0.970880 | − | 0.239565i | ||||
\(38\) | −23818.5 | −2.67581 | ||||||||
\(39\) | 1823.29 | − | 1052.68i | 0.191953 | − | 0.110824i | ||||
\(40\) | −19002.1 | + | 32912.5i | −1.87781 | + | 3.25245i | ||||
\(41\) | −3293.83 | + | 5705.09i | −0.306014 | + | 0.530032i | −0.977487 | − | 0.210997i | \(-0.932329\pi\) |
0.671472 | + | 0.741030i | \(0.265662\pi\) | |||||||
\(42\) | −26062.6 | − | 15047.2i | −2.27979 | − | 1.31624i | ||||
\(43\) | 6097.29i | 0.502882i | 0.967873 | + | 0.251441i | \(0.0809044\pi\) | ||||
−0.967873 | + | 0.251441i | \(0.919096\pi\) | |||||||
\(44\) | 5416.90 | − | 9382.34i | 0.421812 | − | 0.730600i | ||||
\(45\) | 6359.60i | 0.468164i | ||||||||
\(46\) | 14685.1 | + | 25435.3i | 1.02325 | + | 1.77232i | ||||
\(47\) | 7386.71 | 0.487760 | 0.243880 | − | 0.969805i | \(-0.421580\pi\) | ||||
0.243880 | + | 0.969805i | \(0.421580\pi\) | |||||||
\(48\) | 36092.9 | 2.26110 | ||||||||
\(49\) | −17249.7 | − | 29877.3i | −1.02634 | − | 1.77767i | ||||
\(50\) | −21406.0 | − | 12358.8i | −1.21091 | − | 0.699117i | ||||
\(51\) | 6424.42i | 0.345867i | ||||||||
\(52\) | −11719.2 | + | 6766.07i | −0.601020 | + | 0.346999i | ||||
\(53\) | −6006.31 | − | 10403.2i | −0.293710 | − | 0.508720i | 0.680974 | − | 0.732307i | \(-0.261557\pi\) |
−0.974684 | + | 0.223587i | \(0.928223\pi\) | |||||||
\(54\) | 37867.3 | − | 21862.7i | 1.76718 | − | 1.02028i | ||||
\(55\) | 8607.42 | + | 4969.49i | 0.383677 | + | 0.221516i | ||||
\(56\) | 100934. | + | 58274.3i | 4.30098 | + | 2.48317i | ||||
\(57\) | −24358.8 | + | 14063.6i | −0.993045 | + | 0.573335i | ||||
\(58\) | −42554.6 | − | 73706.7i | −1.66103 | − | 2.87698i | ||||
\(59\) | 23166.7 | − | 13375.3i | 0.866433 | − | 0.500235i | 0.000271794 | − | 1.00000i | \(-0.499913\pi\) |
0.866161 | + | 0.499765i | \(0.166580\pi\) | |||||||
\(60\) | 74484.0i | 2.67107i | ||||||||
\(61\) | −29249.9 | − | 16887.4i | −1.00647 | − | 0.581084i | −0.0963120 | − | 0.995351i | \(-0.530705\pi\) |
−0.910155 | + | 0.414267i | \(0.864038\pi\) | |||||||
\(62\) | −21394.8 | − | 37056.9i | −0.706852 | − | 1.22430i | ||||
\(63\) | 19503.2 | 0.619092 | ||||||||
\(64\) | −57337.4 | −1.74980 | ||||||||
\(65\) | −6207.23 | − | 10751.2i | −0.182228 | − | 0.315628i | ||||
\(66\) | − | 17878.6i | − | 0.505213i | ||||||
\(67\) | −2015.93 | + | 3491.70i | −0.0548643 | + | 0.0950277i | −0.892153 | − | 0.451733i | \(-0.850806\pi\) |
0.837289 | + | 0.546761i | \(0.184139\pi\) | |||||||
\(68\) | − | 41292.8i | − | 1.08293i | ||||||
\(69\) | 30036.5 | + | 17341.6i | 0.759498 | + | 0.438497i | ||||
\(70\) | −88727.7 | + | 153681.i | −2.16428 | + | 3.74865i | ||||
\(71\) | 10113.5 | − | 17517.1i | 0.238098 | − | 0.412398i | −0.722071 | − | 0.691819i | \(-0.756809\pi\) |
0.960168 | + | 0.279422i | \(0.0901428\pi\) | |||||||
\(72\) | −38368.3 | + | 22152.0i | −0.872251 | + | 0.503595i | ||||
\(73\) | −11339.9 | −0.249058 | −0.124529 | − | 0.992216i | \(-0.539742\pi\) | ||||
−0.124529 | + | 0.992216i | \(0.539742\pi\) | |||||||
\(74\) | −63686.7 | + | 61203.4i | −1.35198 | + | 1.29926i | ||||
\(75\) | −29188.8 | −0.599189 | ||||||||
\(76\) | 156566. | − | 90393.3i | 3.10930 | − | 1.79516i | ||||
\(77\) | 15240.1 | − | 26396.7i | 0.292929 | − | 0.507368i | ||||
\(78\) | −11165.8 | + | 19339.8i | −0.207804 | + | 0.359927i | ||||
\(79\) | 29722.8 | + | 17160.5i | 0.535824 | + | 0.309358i | 0.743385 | − | 0.668864i | \(-0.233219\pi\) |
−0.207561 | + | 0.978222i | \(0.566552\pi\) | |||||||
\(80\) | − | 212826.i | − | 3.71791i | ||||||
\(81\) | 15356.0 | − | 26597.4i | 0.260056 | − | 0.450430i | ||||
\(82\) | − | 69875.7i | − | 1.14760i | ||||||
\(83\) | 45220.0 | + | 78323.4i | 0.720503 | + | 1.24795i | 0.960799 | + | 0.277247i | \(0.0894222\pi\) |
−0.240296 | + | 0.970700i | \(0.577244\pi\) | |||||||
\(84\) | 228423. | 3.53217 | ||||||||
\(85\) | 37882.3 | 0.568708 | ||||||||
\(86\) | −32337.1 | − | 56009.6i | −0.471472 | − | 0.816613i | ||||
\(87\) | −87040.1 | − | 50252.6i | −1.23288 | − | 0.711804i | ||||
\(88\) | 69239.7i | 0.953121i | ||||||||
\(89\) | −27293.3 | + | 15757.8i | −0.365243 | + | 0.210873i | −0.671378 | − | 0.741115i | \(-0.734297\pi\) |
0.306135 | + | 0.951988i | \(0.400964\pi\) | |||||||
\(90\) | −33728.3 | − | 58419.1i | −0.438923 | − | 0.760236i | ||||
\(91\) | −32971.3 | + | 19036.0i | −0.417380 | + | 0.240975i | ||||
\(92\) | −193059. | − | 111463.i | −2.37805 | − | 1.37297i | ||||
\(93\) | −43760.3 | − | 25265.0i | −0.524654 | − | 0.302909i | ||||
\(94\) | −67854.1 | + | 39175.6i | −0.792058 | + | 0.457295i | ||||
\(95\) | 82927.4 | + | 143634.i | 0.942733 | + | 1.63286i | ||||
\(96\) | −152937. | + | 88298.4i | −1.69370 | + | 0.977856i | ||||
\(97\) | 53658.9i | 0.579045i | 0.957171 | + | 0.289522i | \(0.0934965\pi\) | ||||
−0.957171 | + | 0.289522i | \(0.906504\pi\) | |||||||
\(98\) | 316911. | + | 182968.i | 3.33328 | + | 1.92447i | ||||
\(99\) | 5793.27 | + | 10034.2i | 0.0594068 | + | 0.102896i | ||||
\(100\) | 187611. | 1.87611 | ||||||||
\(101\) | −69763.3 | −0.680493 | −0.340246 | − | 0.940336i | \(-0.610510\pi\) | ||||
−0.340246 | + | 0.940336i | \(0.610510\pi\) | |||||||
\(102\) | −34072.1 | − | 59014.6i | −0.324264 | − | 0.561641i | ||||
\(103\) | − | 183425.i | − | 1.70360i | −0.523871 | − | 0.851798i | \(-0.675513\pi\) | ||
0.523871 | − | 0.851798i | \(-0.324487\pi\) | |||||||
\(104\) | 43242.5 | − | 74898.2i | 0.392037 | − | 0.679029i | ||||
\(105\) | 209557.i | 1.85493i | ||||||||
\(106\) | 110348. | + | 63709.3i | 0.953891 | + | 0.550729i | ||||
\(107\) | −45668.7 | + | 79100.5i | −0.385620 | + | 0.667913i | −0.991855 | − | 0.127372i | \(-0.959346\pi\) |
0.606235 | + | 0.795285i | \(0.292679\pi\) | |||||||
\(108\) | −165942. | + | 287420.i | −1.36898 | + | 2.37114i | ||||
\(109\) | 128674. | − | 74290.1i | 1.03735 | − | 0.598914i | 0.118269 | − | 0.992982i | \(-0.462266\pi\) |
0.919082 | + | 0.394067i | \(0.128932\pi\) | |||||||
\(110\) | −105423. | −0.830721 | ||||||||
\(111\) | −28994.1 | + | 100196.i | −0.223358 | + | 0.771865i | ||||
\(112\) | −652681. | −4.91650 | ||||||||
\(113\) | −132293. | + | 76379.6i | −0.974634 | + | 0.562705i | −0.900646 | − | 0.434554i | \(-0.856906\pi\) |
−0.0739884 | + | 0.997259i | \(0.523573\pi\) | |||||||
\(114\) | 149173. | − | 258375.i | 1.07505 | − | 1.86204i | ||||
\(115\) | 102257. | − | 177114.i | 0.721019 | − | 1.24884i | ||||
\(116\) | 559448. | + | 322997.i | 3.86024 | + | 2.22871i | ||||
\(117\) | − | 14472.4i | − | 0.0977406i | ||||||
\(118\) | −141873. | + | 245731.i | −0.937981 | + | 1.62463i | ||||
\(119\) | − | 116175.i | − | 0.752048i | ||||||
\(120\) | −238017. | − | 412257.i | −1.50888 | − | 2.61345i | ||||
\(121\) | −142943. | −0.887565 | ||||||||
\(122\) | 358252. | 2.17916 | ||||||||
\(123\) | −41258.0 | − | 71460.9i | −0.245893 | − | 0.425898i | ||||
\(124\) | 281269. | + | 162390.i | 1.64273 | + | 0.948432i | ||||
\(125\) | − | 58697.1i | − | 0.336002i | ||||||
\(126\) | −179156. | + | 103436.i | −1.00532 | + | 0.580423i | ||||
\(127\) | −132170. | − | 228925.i | −0.727147 | − | 1.25946i | −0.958084 | − | 0.286487i | \(-0.907512\pi\) |
0.230937 | − | 0.972969i | \(-0.425821\pi\) | |||||||
\(128\) | 135988. | − | 78512.5i | 0.733626 | − | 0.423559i | ||||
\(129\) | −66141.5 | − | 38186.8i | −0.349945 | − | 0.202041i | ||||
\(130\) | 114039. | + | 65840.4i | 0.591827 | + | 0.341692i | ||||
\(131\) | 19885.9 | − | 11481.2i | 0.101244 | − | 0.0584531i | −0.448523 | − | 0.893771i | \(-0.648050\pi\) |
0.549767 | + | 0.835318i | \(0.314717\pi\) | |||||||
\(132\) | 67851.1 | + | 117522.i | 0.338940 | + | 0.587061i | ||||
\(133\) | 440489. | − | 254317.i | 2.15927 | − | 1.24665i | ||||
\(134\) | − | 42766.2i | − | 0.205750i | ||||||
\(135\) | −263681. | − | 152236.i | −1.24521 | − | 0.718925i | ||||
\(136\) | 131953. | + | 228549.i | 0.611747 | + | 1.05958i | ||||
\(137\) | −168927. | −0.768950 | −0.384475 | − | 0.923135i | \(-0.625618\pi\) | ||||
−0.384475 | + | 0.923135i | \(0.625618\pi\) | |||||||
\(138\) | −367886. | −1.64443 | ||||||||
\(139\) | 59988.7 | + | 103904.i | 0.263350 | + | 0.456135i | 0.967130 | − | 0.254283i | \(-0.0818394\pi\) |
−0.703780 | + | 0.710418i | \(0.748506\pi\) | |||||||
\(140\) | − | 1.34692e6i | − | 5.80794i | ||||||
\(141\) | −46262.4 | + | 80128.8i | −0.195966 | + | 0.339422i | ||||
\(142\) | 214549.i | 0.892905i | ||||||||
\(143\) | −19587.7 | − | 11309.0i | −0.0801019 | − | 0.0462469i | ||||
\(144\) | 124053. | − | 214866.i | 0.498540 | − | 0.863496i | ||||
\(145\) | −296320. | + | 513241.i | −1.17042 | + | 2.02722i | ||||
\(146\) | 104168. | − | 60141.2i | 0.404437 | − | 0.233502i | ||||
\(147\) | 432134. | 1.64940 | ||||||||
\(148\) | 186359. | − | 644005.i | 0.699352 | − | 2.41677i | ||||
\(149\) | −17507.6 | −0.0646042 | −0.0323021 | − | 0.999478i | \(-0.510284\pi\) | ||||
−0.0323021 | + | 0.999478i | \(0.510284\pi\) | |||||||
\(150\) | 268128. | − | 154804.i | 0.973003 | − | 0.561763i | ||||
\(151\) | 171774. | − | 297521.i | 0.613075 | − | 1.06188i | −0.377643 | − | 0.925951i | \(-0.623265\pi\) |
0.990719 | − | 0.135927i | \(-0.0434012\pi\) | |||||||
\(152\) | −577711. | + | 1.00062e6i | −2.02816 | + | 3.51287i | ||||
\(153\) | 38245.4 | + | 22081.0i | 0.132084 | + | 0.0762587i | ||||
\(154\) | 323306.i | 1.09853i | ||||||||
\(155\) | −148978. | + | 258038.i | −0.498073 | + | 0.862688i | ||||
\(156\) | − | 169501.i | − | 0.557650i | ||||||
\(157\) | 95450.6 | + | 165325.i | 0.309050 | + | 0.535291i | 0.978155 | − | 0.207877i | \(-0.0666555\pi\) |
−0.669104 | + | 0.743168i | \(0.733322\pi\) | |||||||
\(158\) | −364044. | −1.16014 | ||||||||
\(159\) | 150468. | 0.472011 | ||||||||
\(160\) | 520661. | + | 901812.i | 1.60789 | + | 2.78494i | ||||
\(161\) | −543161. | − | 313594.i | −1.65144 | − | 0.953462i | ||||
\(162\) | 325764.i | 0.975250i | ||||||||
\(163\) | 271823. | − | 156937.i | 0.801341 | − | 0.462654i | −0.0425991 | − | 0.999092i | \(-0.513564\pi\) |
0.843940 | + | 0.536438i | \(0.180230\pi\) | |||||||
\(164\) | 265185. | + | 459314.i | 0.769909 | + | 1.33352i | ||||
\(165\) | −107815. | + | 62247.1i | −0.308297 | + | 0.177996i | ||||
\(166\) | −830780. | − | 479651.i | −2.34000 | − | 1.35100i | ||||
\(167\) | −231847. | − | 133857.i | −0.643296 | − | 0.371407i | 0.142587 | − | 0.989782i | \(-0.454458\pi\) |
−0.785883 | + | 0.618375i | \(0.787791\pi\) | |||||||
\(168\) | −1.26428e6 | + | 729935.i | −3.45598 | + | 1.99531i | ||||
\(169\) | −171521. | − | 297083.i | −0.461956 | − | 0.800130i | ||||
\(170\) | −347986. | + | 200910.i | −0.923505 | + | 0.533186i | ||||
\(171\) | 193348.i | 0.505649i | ||||||||
\(172\) | 425123. | + | 245445.i | 1.09571 | + | 0.632606i | ||||
\(173\) | −92575.0 | − | 160345.i | −0.235168 | − | 0.407323i | 0.724153 | − | 0.689639i | \(-0.242231\pi\) |
−0.959322 | + | 0.282316i | \(0.908897\pi\) | |||||||
\(174\) | 1.06606e6 | 2.66938 | ||||||||
\(175\) | 527832. | 1.30287 | ||||||||
\(176\) | −193874. | − | 335799.i | −0.471777 | − | 0.817142i | ||||
\(177\) | 335074.i | 0.803911i | ||||||||
\(178\) | 167144. | − | 289502.i | 0.395404 | − | 0.684859i | ||||
\(179\) | − | 451417.i | − | 1.05304i | −0.850162 | − | 0.526521i | \(-0.823496\pi\) | ||
0.850162 | − | 0.526521i | \(-0.176504\pi\) | |||||||
\(180\) | 443412. | + | 256004.i | 1.02006 | + | 0.588933i | ||||
\(181\) | −206734. | + | 358074.i | −0.469046 | + | 0.812411i | −0.999374 | − | 0.0353813i | \(-0.988735\pi\) |
0.530328 | + | 0.847793i | \(0.322069\pi\) | |||||||
\(182\) | 201915. | − | 349728.i | 0.451847 | − | 0.782621i | ||||
\(183\) | 366379. | − | 211529.i | 0.808729 | − | 0.466920i | ||||
\(184\) | 1.42473e6 | 3.10234 | ||||||||
\(185\) | 590815. | + | 170967.i | 1.26918 | + | 0.367268i | ||||
\(186\) | 535975. | 1.13596 | ||||||||
\(187\) | 59771.1 | − | 34508.9i | 0.124993 | − | 0.0721650i | ||||
\(188\) | 297350. | − | 515026.i | 0.613584 | − | 1.06276i | ||||
\(189\) | −466869. | + | 808640.i | −0.950693 | + | 1.64665i | ||||
\(190\) | −1.52354e6 | − | 879615.i | −3.06175 | − | 1.76770i | ||||
\(191\) | − | 376307.i | − | 0.746377i | −0.927755 | − | 0.373189i | \(-0.878264\pi\) | ||
0.927755 | − | 0.373189i | \(-0.121736\pi\) | |||||||
\(192\) | 359099. | − | 621978.i | 0.703010 | − | 1.21765i | ||||
\(193\) | − | 426538.i | − | 0.824261i | −0.911125 | − | 0.412130i | \(-0.864785\pi\) | ||
0.911125 | − | 0.412130i | \(-0.135215\pi\) | |||||||
\(194\) | −284581. | − | 492909.i | −0.542878 | − | 0.940292i | ||||
\(195\) | 155502. | 0.292852 | ||||||||
\(196\) | −2.77753e6 | −5.16438 | ||||||||
\(197\) | 178391. | + | 308983.i | 0.327497 | + | 0.567242i | 0.982015 | − | 0.188805i | \(-0.0604614\pi\) |
−0.654517 | + | 0.756047i | \(0.727128\pi\) | |||||||
\(198\) | −106434. | − | 61449.5i | −0.192937 | − | 0.111392i | ||||
\(199\) | 742232.i | 1.32864i | 0.747448 | + | 0.664320i | \(0.231279\pi\) | ||||
−0.747448 | + | 0.664320i | \(0.768721\pi\) | |||||||
\(200\) | −1.03839e6 | + | 599517.i | −1.83564 | + | 1.05981i | ||||
\(201\) | −25251.3 | − | 43736.5i | −0.0440852 | − | 0.0763578i | ||||
\(202\) | 640844. | − | 369991.i | 1.10503 | − | 0.637989i | ||||
\(203\) | 1.57398e6 | + | 908736.i | 2.68076 | + | 1.54774i | ||||
\(204\) | 447932. | + | 258614.i | 0.753592 | + | 0.435087i | ||||
\(205\) | −421377. | + | 243282.i | −0.700304 | + | 0.404321i | ||||
\(206\) | 972801. | + | 1.68494e6i | 1.59719 | + | 2.76641i | ||||
\(207\) | 206473. | − | 119207.i | 0.334917 | − | 0.193365i | ||||
\(208\) | 484322.i | 0.776205i | ||||||||
\(209\) | 261687. | + | 151085.i | 0.414398 | + | 0.239253i | ||||
\(210\) | −1.11139e6 | − | 1.92498e6i | −1.73907 | − | 3.01216i | ||||
\(211\) | −711408. | −1.10005 | −0.550025 | − | 0.835148i | \(-0.685382\pi\) | ||||
−0.550025 | + | 0.835148i | \(0.685382\pi\) | |||||||
\(212\) | −967131. | −1.47790 | ||||||||
\(213\) | 126680. | + | 219416.i | 0.191319 | + | 0.331375i | ||||
\(214\) | − | 968821.i | − | 1.44614i | ||||||
\(215\) | −225173. | + | 390011.i | −0.332215 | + | 0.575414i | ||||
\(216\) | − | 2.12110e6i | − | 3.09333i | ||||||
\(217\) | 791334. | + | 456877.i | 1.14080 | + | 0.658642i | ||||
\(218\) | −787999. | + | 1.36485e6i | −1.12301 | + | 1.94511i | ||||
\(219\) | 71020.6 | − | 123011.i | 0.100063 | − | 0.173314i | ||||
\(220\) | 692979. | − | 400092.i | 0.965302 | − | 0.557318i | ||||
\(221\) | −86207.8 | −0.118731 | ||||||||
\(222\) | −265051. | − | 1.07417e6i | −0.360950 | − | 1.46281i | ||||
\(223\) | −116431. | −0.156786 | −0.0783930 | − | 0.996923i | \(-0.524979\pi\) | ||||
−0.0783930 | + | 0.996923i | \(0.524979\pi\) | |||||||
\(224\) | 2.76562e6 | − | 1.59673e6i | 3.68275 | − | 2.12624i | ||||
\(225\) | −100323. | + | 173765.i | −0.132113 | + | 0.228826i | ||||
\(226\) | 810162. | − | 1.40324e6i | 1.05512 | − | 1.82752i | ||||
\(227\) | −496823. | − | 286841.i | −0.639937 | − | 0.369468i | 0.144653 | − | 0.989482i | \(-0.453793\pi\) |
−0.784590 | + | 0.620014i | \(0.787127\pi\) | |||||||
\(228\) | 2.26450e6i | 2.88493i | ||||||||
\(229\) | 452931. | − | 784500.i | 0.570747 | − | 0.988563i | −0.425742 | − | 0.904844i | \(-0.639987\pi\) |
0.996489 | − | 0.0837184i | \(-0.0266796\pi\) | |||||||
\(230\) | 2.16928e6i | 2.70394i | ||||||||
\(231\) | 190895. | + | 330641.i | 0.235378 | + | 0.407686i | ||||
\(232\) | −4.12861e6 | −5.03598 | ||||||||
\(233\) | 149372. | 0.180252 | 0.0901259 | − | 0.995930i | \(-0.471273\pi\) | ||||
0.0901259 | + | 0.995930i | \(0.471273\pi\) | |||||||
\(234\) | 76754.6 | + | 132943.i | 0.0916357 | + | 0.158718i | ||||
\(235\) | 472488. | + | 272791.i | 0.558112 | + | 0.322226i | ||||
\(236\) | − | 2.15368e6i | − | 2.51711i | ||||||
\(237\) | −372303. | + | 214949.i | −0.430552 | + | 0.248579i | ||||
\(238\) | 616138. | + | 1.06718e6i | 0.705075 | + | 1.22123i | ||||
\(239\) | −793127. | + | 457912.i | −0.898148 | + | 0.518546i | −0.876599 | − | 0.481222i | \(-0.840193\pi\) |
−0.0215492 | + | 0.999768i | \(0.506860\pi\) | |||||||
\(240\) | 2.30867e6 | + | 1.33291e6i | 2.58722 | + | 1.49373i | ||||
\(241\) | 321665. | + | 185713.i | 0.356748 | + | 0.205968i | 0.667653 | − | 0.744472i | \(-0.267299\pi\) |
−0.310905 | + | 0.950441i | \(0.600632\pi\) | |||||||
\(242\) | 1.31307e6 | − | 758103.i | 1.44129 | − | 0.832127i | ||||
\(243\) | −308512. | − | 534358.i | −0.335163 | − | 0.580520i | ||||
\(244\) | −2.35489e6 | + | 1.35960e6i | −2.53219 | + | 1.46196i | ||||
\(245\) | − | 2.54812e6i | − | 2.71210i | ||||||
\(246\) | 757990. | + | 437626.i | 0.798593 | + | 0.461068i | ||||
\(247\) | −188716. | − | 326865.i | −0.196818 | − | 0.340900i | ||||
\(248\) | −2.07570e6 | −2.14307 | ||||||||
\(249\) | −1.13284e6 | −1.15789 | ||||||||
\(250\) | 311302. | + | 539191.i | 0.315015 | + | 0.545622i | ||||
\(251\) | 456481.i | 0.457339i | 0.973504 | + | 0.228670i | \(0.0734375\pi\) | ||||
−0.973504 | + | 0.228670i | \(0.926562\pi\) | |||||||
\(252\) | 785098. | − | 1.35983e6i | 0.778793 | − | 1.34891i | ||||
\(253\) | − | 372602.i | − | 0.365969i | ||||||
\(254\) | 2.42821e6 | + | 1.40193e6i | 2.36158 | + | 1.36346i | ||||
\(255\) | −237254. | + | 410935.i | −0.228488 | + | 0.395752i | ||||
\(256\) | 84612.2 | − | 146553.i | 0.0806925 | − | 0.139764i | ||||
\(257\) | −116328. | + | 67162.0i | −0.109863 | + | 0.0634294i | −0.553925 | − | 0.832567i | \(-0.686870\pi\) |
0.444062 | + | 0.895996i | \(0.353537\pi\) | |||||||
\(258\) | 810099. | 0.757686 | ||||||||
\(259\) | 524311. | − | 1.81187e6i | 0.485668 | − | 1.67833i | ||||
\(260\) | −999483. | −0.916942 | ||||||||
\(261\) | −598320. | + | 345440.i | −0.543666 | + | 0.313886i | ||||
\(262\) | −121781. | + | 210931.i | −0.109604 | + | 0.189840i | ||||
\(263\) | 728850. | − | 1.26240e6i | 0.649753 | − | 1.12541i | −0.333428 | − | 0.942775i | \(-0.608206\pi\) |
0.983182 | − | 0.182630i | \(-0.0584612\pi\) | |||||||
\(264\) | −751090. | − | 433642.i | −0.663258 | − | 0.382932i | ||||
\(265\) | − | 887252.i | − | 0.776126i | ||||||
\(266\) | −2.69755e6 | + | 4.67229e6i | −2.33757 | + | 4.04880i | ||||
\(267\) | − | 394759.i | − | 0.338887i | ||||||
\(268\) | 162302. | + | 281115.i | 0.138034 | + | 0.239082i | ||||
\(269\) | 689118. | 0.580648 | 0.290324 | − | 0.956928i | \(-0.406237\pi\) | ||||
0.290324 | + | 0.956928i | \(0.406237\pi\) | |||||||
\(270\) | 3.22956e6 | 2.69608 | ||||||||
\(271\) | 260406. | + | 451036.i | 0.215391 | + | 0.373068i | 0.953393 | − | 0.301730i | \(-0.0975640\pi\) |
−0.738002 | + | 0.674798i | \(0.764231\pi\) | |||||||
\(272\) | −1.27989e6 | − | 738946.i | −1.04894 | − | 0.605606i | ||||
\(273\) | − | 476883.i | − | 0.387262i | ||||||
\(274\) | 1.55176e6 | − | 895910.i | 1.24867 | − | 0.720922i | ||||
\(275\) | 156788. | + | 271565.i | 0.125021 | + | 0.216542i | ||||
\(276\) | 2.41823e6 | − | 1.39616e6i | 1.91084 | − | 1.10322i | ||||
\(277\) | −204640. | − | 118149.i | −0.160248 | − | 0.0925190i | 0.417732 | − | 0.908570i | \(-0.362825\pi\) |
−0.577979 | + | 0.816051i | \(0.696159\pi\) | |||||||
\(278\) | −1.10211e6 | − | 636304.i | −0.855289 | − | 0.493801i | ||||
\(279\) | −300812. | + | 173674.i | −0.231358 | + | 0.133574i | ||||
\(280\) | 4.30414e6 | + | 7.45499e6i | 3.28089 | + | 5.68266i | ||||
\(281\) | −1.67872e6 | + | 969209.i | −1.26827 | + | 0.732237i | −0.974661 | − | 0.223688i | \(-0.928190\pi\) |
−0.293611 | + | 0.955925i | \(0.594857\pi\) | |||||||
\(282\) | − | 981414.i | − | 0.734902i | ||||||
\(283\) | −1.81483e6 | − | 1.04779e6i | −1.34701 | − | 0.777695i | −0.359183 | − | 0.933267i | \(-0.616945\pi\) |
−0.987825 | + | 0.155572i | \(0.950278\pi\) | |||||||
\(284\) | −814233. | − | 1.41029e6i | −0.599036 | − | 1.03756i | ||||
\(285\) | −2.07747e6 | −1.51503 | ||||||||
\(286\) | 239909. | 0.173433 | ||||||||
\(287\) | 746083. | + | 1.29225e6i | 0.534666 | + | 0.926068i | ||||
\(288\) | 1.21394e6i | 0.862414i | ||||||||
\(289\) | −578399. | + | 1.00182e6i | −0.407364 | + | 0.705575i | ||||
\(290\) | − | 6.28616e6i | − | 4.38925i | ||||||
\(291\) | −582075. | − | 336061.i | −0.402946 | − | 0.232641i | ||||
\(292\) | −456483. | + | 790652.i | −0.313305 | + | 0.542661i | ||||
\(293\) | −1.06980e6 | + | 1.85295e6i | −0.728006 | + | 1.26094i | 0.229719 | + | 0.973257i | \(0.426219\pi\) |
−0.957725 | + | 0.287686i | \(0.907114\pi\) | |||||||
\(294\) | −3.96957e6 | + | 2.29183e6i | −2.67840 | + | 1.54637i | ||||
\(295\) | 1.97580e6 | 1.32187 | ||||||||
\(296\) | 1.02648e6 | + | 4.15998e6i | 0.680959 | + | 2.75970i | ||||
\(297\) | −554718. | −0.364906 | ||||||||
\(298\) | 160824. | − | 92852.0i | 0.104909 | − | 0.0605690i | ||||
\(299\) | −232703. | + | 403053.i | −0.150530 | + | 0.260726i | ||||
\(300\) | −1.17499e6 | + | 2.03514e6i | −0.753756 | + | 1.30554i | ||||
\(301\) | 1.19606e6 | + | 690546.i | 0.760917 | + | 0.439315i | ||||
\(302\) | 3.64402e6i | 2.29913i | ||||||||
\(303\) | 436922. | − | 756770.i | 0.273399 | − | 0.473541i | ||||
\(304\) | − | 6.47045e6i | − | 4.01560i | ||||||
\(305\) | −1.24730e6 | − | 2.16040e6i | −0.767756 | − | 1.32979i | ||||
\(306\) | −468428. | −0.285982 | ||||||||
\(307\) | −1.78943e6 | −1.08360 | −0.541801 | − | 0.840507i | \(-0.682257\pi\) | ||||
−0.541801 | + | 0.840507i | \(0.682257\pi\) | |||||||
\(308\) | −1.22698e6 | − | 2.12519e6i | −0.736986 | − | 1.27650i | ||||
\(309\) | 1.98974e6 | + | 1.14878e6i | 1.18550 | + | 0.684447i | ||||
\(310\) | − | 3.16044e6i | − | 1.86785i | ||||||
\(311\) | 1.30466e6 | − | 753245.i | 0.764885 | − | 0.441606i | −0.0661622 | − | 0.997809i | \(-0.521075\pi\) |
0.831047 | + | 0.556203i | \(0.187742\pi\) | |||||||
\(312\) | 541648. | + | 938163.i | 0.315015 | + | 0.545622i | ||||
\(313\) | 991919. | − | 572685.i | 0.572289 | − | 0.330411i | −0.185774 | − | 0.982592i | \(-0.559479\pi\) |
0.758063 | + | 0.652181i | \(0.226146\pi\) | |||||||
\(314\) | −1.75361e6 | − | 1.01245e6i | −1.00371 | − | 0.579494i | ||||
\(315\) | 1.24752e6 | + | 720254.i | 0.708385 | + | 0.408987i | ||||
\(316\) | 2.39297e6 | − | 1.38158e6i | 1.34809 | − | 0.778321i | ||||
\(317\) | −1.46373e6 | − | 2.53525e6i | −0.818110 | − | 1.41701i | −0.907073 | − | 0.420973i | \(-0.861689\pi\) |
0.0889630 | − | 0.996035i | \(-0.471645\pi\) | |||||||
\(318\) | −1.38220e6 | + | 798012.i | −0.766482 | + | 0.442529i | ||||
\(319\) | 1.07973e6i | 0.594071i | ||||||||
\(320\) | −3.66756e6 | − | 2.11747e6i | −2.00218 | − | 1.15596i | ||||
\(321\) | −572039. | − | 990800.i | −0.309858 | − | 0.536690i | ||||
\(322\) | 6.65262e6 | 3.57563 | ||||||||
\(323\) | 1.15172e6 | 0.614243 | ||||||||
\(324\) | −1.23631e6 | − | 2.14134e6i | −0.654280 | − | 1.13325i | ||||
\(325\) | − | 391678.i | − | 0.205694i | ||||||
\(326\) | −1.66464e6 | + | 2.88324e6i | −0.867513 | + | 1.50258i | ||||
\(327\) | 1.86109e6i | 0.962494i | ||||||||
\(328\) | −2.93551e6 | − | 1.69482e6i | −1.50660 | − | 0.869838i | ||||
\(329\) | 836579. | − | 1.44900e6i | 0.426105 | − | 0.738036i | ||||
\(330\) | 660258. | − | 1.14360e6i | 0.333756 | − | 0.578082i | ||||
\(331\) | 661512. | − | 381924.i | 0.331870 | − | 0.191605i | −0.324801 | − | 0.945782i | \(-0.605297\pi\) |
0.656671 | + | 0.754177i | \(0.271964\pi\) | |||||||
\(332\) | 7.28129e6 | 3.62546 | ||||||||
\(333\) | 496823. | + | 516981.i | 0.245522 | + | 0.255484i | ||||
\(334\) | 2.83966e6 | 1.39284 | ||||||||
\(335\) | −257897. | + | 148897.i | −0.125555 | + | 0.0724892i | ||||
\(336\) | 4.08769e6 | − | 7.08008e6i | 1.97528 | − | 3.42129i | ||||
\(337\) | −759353. | + | 1.31524e6i | −0.364224 | + | 0.630855i | −0.988651 | − | 0.150228i | \(-0.951999\pi\) |
0.624427 | + | 0.781083i | \(0.285333\pi\) | |||||||
\(338\) | 3.15117e6 | + | 1.81933e6i | 1.50031 | + | 0.866203i | ||||
\(339\) | − | 1.91344e6i | − | 0.904304i | ||||||
\(340\) | 1.52494e6 | − | 2.64128e6i | 0.715412 | − | 1.23913i | ||||
\(341\) | 542846.i | 0.252808i | ||||||||
\(342\) | −1.02543e6 | − | 1.77609e6i | −0.474066 | − | 0.821107i | ||||
\(343\) | −4.00749e6 | −1.83923 | ||||||||
\(344\) | −3.13732e6 | −1.42943 | ||||||||
\(345\) | 1.28085e6 | + | 2.21850e6i | 0.579362 | + | 1.00348i | ||||
\(346\) | 1.70078e6 | + | 981947.i | 0.763763 | + | 0.440959i | ||||
\(347\) | 124642.i | 0.0555701i | 0.999614 | + | 0.0277850i | \(0.00884539\pi\) | ||||
−0.999614 | + | 0.0277850i | \(0.991155\pi\) | |||||||
\(348\) | −7.00755e6 | + | 4.04581e6i | −3.10183 | + | 1.79084i | ||||
\(349\) | 347320. | + | 601576.i | 0.152639 | + | 0.264379i | 0.932197 | − | 0.361952i | \(-0.117889\pi\) |
−0.779558 | + | 0.626330i | \(0.784556\pi\) | |||||||
\(350\) | −4.84865e6 | + | 2.79937e6i | −2.11569 | + | 1.22149i | ||||
\(351\) | 600052. | + | 346440.i | 0.259969 | + | 0.150093i | ||||
\(352\) | 1.64301e6 | + | 948592.i | 0.706779 | + | 0.408059i | ||||
\(353\) | −95622.3 | + | 55207.6i | −0.0408435 | + | 0.0235810i | −0.520283 | − | 0.853994i | \(-0.674173\pi\) |
0.479439 | + | 0.877575i | \(0.340840\pi\) | |||||||
\(354\) | −1.77707e6 | − | 3.07798e6i | −0.753698 | − | 1.30544i | ||||
\(355\) | 1.29381e6 | − | 746982.i | 0.544879 | − | 0.314586i | ||||
\(356\) | 2.53731e6i | 1.06108i | ||||||||
\(357\) | 1.26023e6 | + | 727595.i | 0.523335 | + | 0.302148i | ||||
\(358\) | 2.39410e6 | + | 4.14671e6i | 0.987268 | + | 1.71000i | ||||
\(359\) | −8173.01 | −0.00334692 | −0.00167346 | − | 0.999999i | \(-0.500533\pi\) | ||||
−0.00167346 | + | 0.999999i | \(0.500533\pi\) | |||||||
\(360\) | −3.27229e6 | −1.33075 | ||||||||
\(361\) | 1.28315e6 | + | 2.22249e6i | 0.518216 | + | 0.897576i | ||||
\(362\) | − | 4.38567e6i | − | 1.75900i | ||||||
\(363\) | 895241. | − | 1.55060e6i | 0.356594 | − | 0.617638i | ||||
\(364\) | 3.06515e6i | 1.21255i | ||||||||
\(365\) | −725349. | − | 418781.i | −0.284980 | − | 0.164534i | ||||
\(366\) | −2.24370e6 | + | 3.88620e6i | −0.875512 | + | 1.51643i | ||||
\(367\) | −1.69807e6 | + | 2.94114e6i | −0.658097 | + | 1.13986i | 0.323011 | + | 0.946395i | \(0.395305\pi\) |
−0.981108 | + | 0.193462i | \(0.938028\pi\) | |||||||
\(368\) | −6.90969e6 | + | 3.98931e6i | −2.65974 | + | 1.53560i | ||||
\(369\) | −567221. | −0.216863 | ||||||||
\(370\) | −6.33393e6 | + | 1.56290e6i | −2.40530 | + | 0.593510i | ||||
\(371\) | −2.72097e6 | −1.02633 | ||||||||
\(372\) | −3.52312e6 | + | 2.03408e6i | −1.31999 | + | 0.762096i | ||||
\(373\) | −705032. | + | 1.22115e6i | −0.262384 | + | 0.454462i | −0.966875 | − | 0.255251i | \(-0.917842\pi\) |
0.704491 | + | 0.709713i | \(0.251175\pi\) | |||||||
\(374\) | −366037. | + | 633995.i | −0.135315 | + | 0.234373i | ||||
\(375\) | 636728. | + | 367615.i | 0.233817 | + | 0.134994i | ||||
\(376\) | 3.80078e6i | 1.38645i | ||||||||
\(377\) | 674328. | − | 1.16797e6i | 0.244353 | − | 0.423232i | ||||
\(378\) | − | 9.90420e6i | − | 3.56525i | ||||||
\(379\) | −1.89819e6 | − | 3.28777e6i | −0.678801 | − | 1.17572i | −0.975342 | − | 0.220698i | \(-0.929166\pi\) |
0.296541 | − | 0.955020i | \(-0.404167\pi\) | |||||||
\(380\) | 1.33529e7 | 4.74369 | ||||||||
\(381\) | 3.31107e6 | 1.16857 | ||||||||
\(382\) | 1.99575e6 | + | 3.45674e6i | 0.699758 | + | 1.21202i | ||||
\(383\) | −1.38590e6 | − | 800150.i | −0.482765 | − | 0.278724i | 0.238803 | − | 0.971068i | \(-0.423245\pi\) |
−0.721568 | + | 0.692344i | \(0.756578\pi\) | |||||||
\(384\) | 1.96687e6i | 0.680687i | ||||||||
\(385\) | 1.94966e6 | − | 1.12564e6i | 0.670358 | − | 0.387031i | ||||
\(386\) | 2.26216e6 | + | 3.91817e6i | 0.772777 | + | 1.33849i | ||||
\(387\) | −454662. | + | 262499.i | −0.154316 | + | 0.0890944i | ||||
\(388\) | 3.74127e6 | + | 2.16003e6i | 1.26165 | + | 0.728416i | ||||
\(389\) | 3.99737e6 | + | 2.30788e6i | 1.33937 | + | 0.773284i | 0.986714 | − | 0.162469i | \(-0.0519458\pi\) |
0.352654 | + | 0.935754i | \(0.385279\pi\) | |||||||
\(390\) | −1.42843e6 | + | 824707.i | −0.475553 | + | 0.274560i | ||||
\(391\) | −710084. | − | 1.22990e6i | −0.234892 | − | 0.406845i | ||||
\(392\) | 1.53732e7 | − | 8.87571e6i | 5.05299 | − | 2.91735i | ||||
\(393\) | 287622.i | 0.0939379i | ||||||||
\(394\) | −3.27739e6 | − | 1.89220e6i | −1.06362 | − | 0.614084i | ||||
\(395\) | 1.26747e6 | + | 2.19532e6i | 0.408738 | + | 0.707956i | ||||
\(396\) | 932827. | 0.298926 | ||||||||
\(397\) | 2.88085e6 | 0.917370 | 0.458685 | − | 0.888599i | \(-0.348321\pi\) | ||||
0.458685 | + | 0.888599i | \(0.348321\pi\) | |||||||
\(398\) | −3.93645e6 | − | 6.81813e6i | −1.24565 | − | 2.15753i | ||||
\(399\) | 6.37105e6i | 2.00345i | ||||||||
\(400\) | 3.35734e6 | − | 5.81509e6i | 1.04917 | − | 1.81721i | ||||
\(401\) | 4.07705e6i | 1.26615i | 0.774091 | + | 0.633074i | \(0.218207\pi\) | ||||
−0.774091 | + | 0.633074i | \(0.781793\pi\) | |||||||
\(402\) | 463915. | + | 267841.i | 0.143177 | + | 0.0826633i | ||||
\(403\) | 339026. | − | 587210.i | 0.103985 | − | 0.180107i | ||||
\(404\) | −2.80830e6 | + | 4.86412e6i | −0.856033 | + | 1.48269i | ||||
\(405\) | 1.96448e6 | − | 1.13419e6i | 0.595129 | − | 0.343598i | ||||
\(406\) | −1.92780e7 | −5.80426 | ||||||||
\(407\) | 1.08794e6 | − | 268449.i | 0.325550 | − | 0.0803296i | ||||
\(408\) | −3.30564e6 | −0.983117 | ||||||||
\(409\) | −637323. | + | 367958.i | −0.188387 | + | 0.108765i | −0.591227 | − | 0.806505i | \(-0.701356\pi\) |
0.402840 | + | 0.915270i | \(0.368023\pi\) | |||||||
\(410\) | 2.58051e6 | − | 4.46957e6i | 0.758133 | − | 1.31313i | ||||
\(411\) | 1.05798e6 | − | 1.83247e6i | 0.308938 | − | 0.535097i | ||||
\(412\) | −1.27890e7 | − | 7.38374e6i | −3.71188 | − | 2.14306i | ||||
\(413\) | − | 6.05927e6i | − | 1.74801i | ||||||
\(414\) | −1.26444e6 | + | 2.19007e6i | −0.362574 | + | 0.627997i | ||||
\(415\) | 6.67990e6i | 1.90392i | ||||||||
\(416\) | −1.18486e6 | − | 2.05223e6i | −0.335685 | − | 0.581424i | ||||
\(417\) | −1.50282e6 | −0.423220 | ||||||||
\(418\) | −3.20514e6 | −0.897235 | ||||||||
\(419\) | −3.35788e6 | − | 5.81601e6i | −0.934393 | − | 1.61842i | −0.775713 | − | 0.631086i | \(-0.782610\pi\) |
−0.158680 | − | 0.987330i | \(-0.550724\pi\) | |||||||
\(420\) | 1.46110e7 | + | 8.43565e6i | 4.04162 | + | 2.33343i | ||||
\(421\) | − | 5.14495e6i | − | 1.41474i | −0.706845 | − | 0.707369i | \(-0.749882\pi\) | ||
0.706845 | − | 0.707369i | \(-0.250118\pi\) | |||||||
\(422\) | 6.53498e6 | − | 3.77297e6i | 1.78633 | − | 1.03134i | ||||
\(423\) | 318011. | + | 550811.i | 0.0864153 | + | 0.149676i | ||||
\(424\) | 5.35291e6 | − | 3.09051e6i | 1.44602 | − | 0.834863i | ||||
\(425\) | 1.03507e6 | + | 597596.i | 0.277969 | + | 0.160485i | ||||
\(426\) | −2.32736e6 | − | 1.34370e6i | −0.621354 | − | 0.358739i | ||||
\(427\) | −6.62537e6 | + | 3.82516e6i | −1.75849 | + | 1.01527i | ||||
\(428\) | 3.67677e6 | + | 6.36834e6i | 0.970189 | + | 1.68042i | ||||
\(429\) | 245352. | − | 141654.i | 0.0643645 | − | 0.0371609i | ||||
\(430\) | − | 4.77684e6i | − | 1.24586i | ||||||
\(431\) | −126738. | − | 73172.3i | −0.0328635 | − | 0.0189738i | 0.483478 | − | 0.875356i | \(-0.339373\pi\) |
−0.516342 | + | 0.856383i | \(0.672707\pi\) | |||||||
\(432\) | 5.93915e6 | + | 1.02869e7i | 1.53114 | + | 2.65201i | ||||
\(433\) | 6.24472e6 | 1.60064 | 0.800319 | − | 0.599575i | \(-0.204664\pi\) | ||||
0.800319 | + | 0.599575i | \(0.204664\pi\) | |||||||
\(434\) | −9.69223e6 | −2.47001 | ||||||||
\(435\) | −3.71165e6 | − | 6.42877e6i | −0.940469 | − | 1.62894i | ||||
\(436\) | − | 1.19621e7i | − | 3.01364i | ||||||
\(437\) | 3.10886e6 | − | 5.38471e6i | 0.778749 | − | 1.34883i | ||||
\(438\) | 1.50664e6i | 0.375253i | ||||||||
\(439\) | 4.40547e6 | + | 2.54350e6i | 1.09102 | + | 0.629898i | 0.933847 | − | 0.357674i | \(-0.116430\pi\) |
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(440\) | −2.55702e6 | + | 4.42889e6i | −0.629654 | + | 1.09059i | ||||
\(441\) | 1.48526e6 | − | 2.57254e6i | 0.363668 | − | 0.629892i | ||||
\(442\) | 791903. | − | 457205.i | 0.192804 | − | 0.111315i | ||||
\(443\) | −2.45729e6 | −0.594903 | −0.297452 | − | 0.954737i | \(-0.596137\pi\) | ||||
−0.297452 | + | 0.954737i | \(0.596137\pi\) | |||||||
\(444\) | 5.81882e6 | + | 6.05492e6i | 1.40080 | + | 1.45764i | ||||
\(445\) | −2.32774e6 | −0.557230 | ||||||||
\(446\) | 1.06953e6 | − | 617496.i | 0.254599 | − | 0.146993i | ||||
\(447\) | 109649. | − | 189917.i | 0.0259558 | − | 0.0449568i | ||||
\(448\) | −6.49372e6 | + | 1.12475e7i | −1.52862 | + | 2.64764i | ||||
\(449\) | 505510. | + | 291856.i | 0.118335 | + | 0.0683208i | 0.557999 | − | 0.829841i | \(-0.311569\pi\) |
−0.439664 | + | 0.898162i | \(0.644903\pi\) | |||||||
\(450\) | − | 2.12826e6i | − | 0.495444i | ||||||
\(451\) | −443236. | + | 767707.i | −0.102611 | + | 0.177727i | ||||
\(452\) | 1.22986e7i | 2.83145i | ||||||||
\(453\) | 2.15161e6 | + | 3.72669e6i | 0.492626 | + | 0.853254i | ||||
\(454\) | 6.08508e6 | 1.38556 | ||||||||
\(455\) | −2.81199e6 | −0.636774 | ||||||||
\(456\) | −7.23631e6 | − | 1.25337e7i | −1.62969 | − | 2.82271i | ||||
\(457\) | 19511.7 | + | 11265.1i | 0.00437022 | + | 0.00252315i | 0.502184 | − | 0.864761i | \(-0.332530\pi\) |
−0.497813 | + | 0.867284i | \(0.665864\pi\) | |||||||
\(458\) | 9.60853e6i | 2.14039i | ||||||||
\(459\) | −1.83104e6 | + | 1.05715e6i | −0.405663 | + | 0.234210i | ||||
\(460\) | −8.23263e6 | − | 1.42593e7i | −1.81403 | − | 3.14199i | ||||
\(461\) | −562023. | + | 324484.i | −0.123169 | + | 0.0711117i | −0.560319 | − | 0.828277i | \(-0.689321\pi\) |
0.437150 | + | 0.899389i | \(0.355988\pi\) | |||||||
\(462\) | −3.50712e6 | − | 2.02484e6i | −0.764445 | − | 0.441352i | ||||
\(463\) | −5.14770e6 | − | 2.97202e6i | −1.11599 | − | 0.644317i | −0.175616 | − | 0.984459i | \(-0.556192\pi\) |
−0.940374 | + | 0.340141i | \(0.889525\pi\) | |||||||
\(464\) | 2.00229e7 | − | 1.15603e7i | 4.31751 | − | 2.49271i | ||||
\(465\) | −1.86607e6 | − | 3.23214e6i | −0.400218 | − | 0.693198i | ||||
\(466\) | −1.37213e6 | + | 792198.i | −0.292705 | + | 0.168993i | ||||
\(467\) | 6.00001e6i | 1.27309i | 0.771239 | + | 0.636546i | \(0.219637\pi\) | ||||
−0.771239 | + | 0.636546i | \(0.780363\pi\) | |||||||
\(468\) | −1.00906e6 | − | 582582.i | −0.212962 | − | 0.122954i | ||||
\(469\) | 456628. | + | 790902.i | 0.0958584 | + | 0.166032i | ||||
\(470\) | −5.78702e6 | −1.20840 | ||||||||
\(471\) | −2.39120e6 | −0.496664 | ||||||||
\(472\) | 6.88218e6 | + | 1.19203e7i | 1.42191 | + | 2.46281i | ||||
\(473\) | 820484.i | 0.168623i | ||||||||
\(474\) | 2.27998e6 | − | 3.94904e6i | 0.466106 | − | 0.807319i | ||||
\(475\) | 5.23274e6i | 1.06413i | ||||||||
\(476\) | −8.10011e6 | − | 4.67660e6i | −1.63860 | − | 0.946048i | ||||
\(477\) | 517165. | − | 895755.i | 0.104072 | − | 0.180258i | ||||
\(478\) | 4.85710e6 | − | 8.41274e6i | 0.972315 | − | 1.68410i | ||||
\(479\) | 590037. | − | 340658.i | 0.117501 | − | 0.0678391i | −0.440098 | − | 0.897950i | \(-0.645056\pi\) |
0.557598 | + | 0.830111i | \(0.311723\pi\) | |||||||
\(480\) | −1.30434e7 | −2.58398 | ||||||||
\(481\) | −1.34450e6 | − | 389065.i | −0.264971 | − | 0.0766760i | ||||
\(482\) | −3.93974e6 | −0.772414 | ||||||||
\(483\) | 6.80355e6 | − | 3.92803e6i | 1.32699 | − | 0.766138i | ||||
\(484\) | −5.75414e6 | + | 9.96647e6i | −1.11652 | + | 1.93387i | ||||
\(485\) | −1.98162e6 | + | 3.43227e6i | −0.382531 | + | 0.662562i | ||||
\(486\) | 5.66797e6 | + | 3.27240e6i | 1.08852 | + | 0.628457i | ||||
\(487\) | 6.73116e6i | 1.28608i | 0.765833 | + | 0.643039i | \(0.222327\pi\) | ||||
−0.765833 | + | 0.643039i | \(0.777673\pi\) | |||||||
\(488\) | 8.68931e6 | − | 1.50503e7i | 1.65172 | − | 2.86086i | ||||
\(489\) | 3.93154e6i | 0.743516i | ||||||||
\(490\) | 1.35140e7 | + | 2.34070e7i | 2.54270 | + | 4.40408i | ||||
\(491\) | −2.18789e6 | −0.409565 | −0.204782 | − | 0.978808i | \(-0.565649\pi\) | ||||
−0.204782 | + | 0.978808i | \(0.565649\pi\) | |||||||
\(492\) | −6.64332e6 | −1.23729 | ||||||||
\(493\) | 2.05769e6 | + | 3.56402e6i | 0.381296 | + | 0.660424i | ||||
\(494\) | 3.46708e6 | + | 2.00172e6i | 0.639214 | + | 0.369050i | ||||
\(495\) | 855782.i | 0.156982i | ||||||||
\(496\) | 1.00668e7 | − | 5.81204e6i | 1.83732 | − | 1.06078i | ||||
\(497\) | −2.29080e6 | − | 3.96778e6i | −0.416003 | − | 0.720538i | ||||
\(498\) | 1.04062e7 | − | 6.00803e6i | 1.88027 | − | 1.08557i | ||||
\(499\) | −2.68701e6 | − | 1.55134e6i | −0.483078 | − | 0.278905i | 0.238620 | − | 0.971113i | \(-0.423305\pi\) |
−0.721698 | + | 0.692208i | \(0.756638\pi\) | |||||||
\(500\) | −4.09256e6 | − | 2.36284e6i | −0.732099 | − | 0.422678i | ||||
\(501\) | 2.90408e6 | − | 1.67667e6i | 0.516910 | − | 0.298438i | ||||
\(502\) | −2.42096e6 | − | 4.19322e6i | −0.428774 | − | 0.742658i | ||||
\(503\) | 8.04439e6 | − | 4.64443e6i | 1.41766 | − | 0.818489i | 0.421571 | − | 0.906795i | \(-0.361479\pi\) |
0.996093 | + | 0.0883065i | \(0.0281455\pi\) | |||||||
\(504\) | 1.00352e7i | 1.75975i | ||||||||
\(505\) | −4.46238e6 | − | 2.57636e6i | −0.778642 | − | 0.449549i | ||||
\(506\) | 1.97611e6 | + | 3.42272e6i | 0.343110 | + | 0.594285i | ||||
\(507\) | 4.29688e6 | 0.742393 | ||||||||
\(508\) | −2.12818e7 | −3.65889 | ||||||||
\(509\) | −5.45762e6 | − | 9.45287e6i | −0.933703 | − | 1.61722i | −0.776931 | − | 0.629586i | \(-0.783225\pi\) |
−0.156772 | − | 0.987635i | \(-0.550109\pi\) | |||||||
\(510\) | − | 5.03312e6i | − | 0.856865i | ||||||
\(511\) | −1.28429e6 | + | 2.22446e6i | −0.217576 | + | 0.376853i | ||||
\(512\) | 6.81977e6i | 1.14973i | ||||||||
\(513\) | −8.01657e6 | − | 4.62837e6i | −1.34492 | − | 0.776488i | ||||
\(514\) | 712391. | − | 1.23390e6i | 0.118935 | − | 0.206002i | ||||
\(515\) | 6.77389e6 | − | 1.17327e7i | 1.12543 | − | 1.94931i | ||||
\(516\) | −5.32502e6 | + | 3.07440e6i | −0.880435 | + | 0.508319i | ||||
\(517\) | 993995. | 0.163553 | ||||||||
\(518\) | 4.79301e6 | + | 1.94245e7i | 0.784846 | + | 3.18072i | ||||
\(519\) | 2.31916e6 | 0.377930 | ||||||||
\(520\) | 5.53198e6 | − | 3.19389e6i | 0.897164 | − | 0.517978i | ||||
\(521\) | 2.12272e6 | − | 3.67666e6i | 0.342609 | − | 0.593416i | −0.642307 | − | 0.766447i | \(-0.722023\pi\) |
0.984916 | + | 0.173031i | \(0.0553561\pi\) | |||||||
\(522\) | 3.66410e6 | − | 6.34641e6i | 0.588560 | − | 1.01942i | ||||
\(523\) | 6.78102e6 | + | 3.91502e6i | 1.08403 | + | 0.625864i | 0.931980 | − | 0.362509i | \(-0.118080\pi\) |
0.152048 | + | 0.988373i | \(0.451413\pi\) | |||||||
\(524\) | − | 1.84868e6i | − | 0.294127i | ||||||
\(525\) | −3.30577e6 | + | 5.72576e6i | −0.523449 | + | 0.906640i | ||||
\(526\) | 1.54619e7i | 2.43668i | ||||||||
\(527\) | 1.03452e6 | + | 1.79185e6i | 0.162261 | + | 0.281044i | ||||
\(528\) | 4.85686e6 | 0.758177 | ||||||||
\(529\) | −1.23064e6 | −0.191202 | ||||||||
\(530\) | 4.70556e6 | + | 8.15028e6i | 0.727649 | + | 1.26033i | ||||
\(531\) | 1.99474e6 | + | 1.15166e6i | 0.307008 | + | 0.177251i | ||||
\(532\) | − | 4.09498e7i | − | 6.27296i | ||||||
\(533\) | 958918. | − | 553631.i | 0.146205 | − | 0.0844117i | ||||
\(534\) | 2.09362e6 | + | 3.62625e6i | 0.317720 | + | 0.550307i | ||||
\(535\) | −5.84236e6 | + | 3.37309e6i | −0.882478 | + | 0.509499i | ||||
\(536\) | −1.79663e6 | − | 1.03729e6i | −0.270114 | − | 0.155950i | ||||
\(537\) | 4.89683e6 | + | 2.82719e6i | 0.732790 | + | 0.423076i | ||||
\(538\) | −6.33022e6 | + | 3.65475e6i | −0.942894 | + | 0.544380i | ||||
\(539\) | −2.32121e6 | − | 4.02046e6i | −0.344146 | − | 0.596078i | ||||
\(540\) | −2.12288e7 | + | 1.22565e7i | −3.13286 | + | 1.80876i | ||||
\(541\) | 160084.i | 0.0235156i | 0.999931 | + | 0.0117578i | \(0.00374270\pi\) | ||||
−0.999931 | + | 0.0117578i | \(0.996257\pi\) | |||||||
\(542\) | −4.78417e6 | − | 2.76214e6i | −0.699533 | − | 0.403875i | ||||
\(543\) | −2.58951e6 | − | 4.48517e6i | −0.376894 | − | 0.652799i | ||||
\(544\) | 7.23109e6 | 1.04763 | ||||||||
\(545\) | 1.09741e7 | 1.58263 | ||||||||
\(546\) | 2.52916e6 | + | 4.38063e6i | 0.363074 | + | 0.628862i | ||||
\(547\) | 8.75579e6i | 1.25120i | 0.780144 | + | 0.625600i | \(0.215146\pi\) | ||||
−0.780144 | + | 0.625600i | \(0.784854\pi\) | |||||||
\(548\) | −6.80013e6 | + | 1.17782e7i | −0.967310 | + | 1.67543i | ||||
\(549\) | − | 2.90813e6i | − | 0.411797i | ||||||
\(550\) | −2.88051e6 | − | 1.66306e6i | −0.406034 | − | 0.234424i | ||||
\(551\) | −9.00888e6 | + | 1.56038e7i | −1.26413 | + | 2.18954i | ||||
\(552\) | −8.92299e6 | + | 1.54551e7i | −1.24642 | + | 2.15886i | ||||
\(553\) | 6.73249e6 | − | 3.88700e6i | 0.936187 | − | 0.540508i | ||||
\(554\) | 2.50643e6 | 0.346961 | ||||||||
\(555\) | −5.55482e6 | + | 5.33822e6i | −0.765486 | + | 0.735638i | ||||
\(556\) | 9.65933e6 | 1.32513 | ||||||||
\(557\) | −1.19073e7 | + | 6.87469e6i | −1.62621 | + | 0.938891i | −0.640996 | + | 0.767544i | \(0.721479\pi\) |
−0.985211 | + | 0.171347i | \(0.945188\pi\) | |||||||
\(558\) | 1.84217e6 | − | 3.19072e6i | 0.250463 | − | 0.433814i | ||||
\(559\) | 512420. | − | 887538.i | 0.0693580 | − | 0.120132i | ||||
\(560\) | −4.17485e7 | − | 2.41035e7i | −5.62562 | − | 3.24795i | ||||
\(561\) | 864505.i | 0.115974i | ||||||||
\(562\) | 1.02804e7 | − | 1.78063e7i | 1.37300 | − | 2.37811i | ||||
\(563\) | − | 8.37169e6i | − | 1.11312i | −0.830807 | − | 0.556560i | \(-0.812121\pi\) | ||
0.830807 | − | 0.556560i | \(-0.187879\pi\) | |||||||
\(564\) | 3.72456e6 | + | 6.45113e6i | 0.493034 | + | 0.853961i | ||||
\(565\) | −1.12828e7 | −1.48695 | ||||||||
\(566\) | 2.22280e7 | 2.91648 | ||||||||
\(567\) | −3.47828e6 | − | 6.02456e6i | −0.454367 | − | 0.786987i | ||||
\(568\) | 9.01329e6 | + | 5.20383e6i | 1.17223 | + | 0.676787i | ||||
\(569\) | 8.29536e6i | 1.07412i | 0.843543 | + | 0.537062i | \(0.180466\pi\) | ||||
−0.843543 | + | 0.537062i | \(0.819534\pi\) | |||||||
\(570\) | 1.90836e7 | − | 1.10179e7i | 2.46021 | − | 1.42040i | ||||
\(571\) | 2.58783e6 | + | 4.48225e6i | 0.332159 | + | 0.575316i | 0.982935 | − | 0.183954i | \(-0.0588897\pi\) |
−0.650776 | + | 0.759270i | \(0.725556\pi\) | |||||||
\(572\) | −1.57699e6 | + | 910478.i | −0.201530 | + | 0.116354i | ||||
\(573\) | 4.08206e6 | + | 2.35678e6i | 0.519389 | + | 0.299869i | ||||
\(574\) | −1.37070e7 | − | 7.91374e6i | −1.73645 | − | 1.00254i | ||||
\(575\) | 5.58796e6 | − | 3.22621e6i | 0.704829 | − | 0.406933i | ||||
\(576\) | −2.46847e6 | − | 4.27552e6i | −0.310008 | − | 0.536949i | ||||
\(577\) | −6.74860e6 | + | 3.89631e6i | −0.843868 | + | 0.487207i | −0.858577 | − | 0.512685i | \(-0.828651\pi\) |
0.0147093 | + | 0.999892i | \(0.495318\pi\) | |||||||
\(578\) | − | 1.22702e7i | − | 1.52768i | ||||||
\(579\) | 4.62695e6 | + | 2.67137e6i | 0.573586 | + | 0.331160i | ||||
\(580\) | 2.38566e7 | + | 4.13208e7i | 2.94468 | + | 5.10034i | ||||
\(581\) | 2.04855e7 | 2.51771 | ||||||||
\(582\) | 7.12923e6 | 0.872440 | ||||||||
\(583\) | −808242. | − | 1.39992e6i | −0.0984850 | − | 0.170581i | ||||
\(584\) | − | 5.83485e6i | − | 0.707941i | ||||||
\(585\) | 534464. | − | 925720.i | 0.0645698 | − | 0.111838i | ||||
\(586\) | − | 2.26949e7i | − | 2.73014i | ||||||
\(587\) | −2.69447e6 | − | 1.55565e6i | −0.322758 | − | 0.186345i | 0.329863 | − | 0.944029i | \(-0.392997\pi\) |
−0.652621 | + | 0.757684i | \(0.726331\pi\) | |||||||
\(588\) | 1.73954e7 | − | 3.01298e7i | 2.07488 | − | 3.59379i | ||||
\(589\) | −4.52931e6 | + | 7.84500e6i | −0.537953 | + | 0.931761i | ||||
\(590\) | −1.81497e7 | + | 1.04787e7i | −2.14654 | + | 1.23930i | ||||
\(591\) | −4.46900e6 | −0.526310 | ||||||||
\(592\) | −1.66263e7 | − | 1.73009e7i | −1.94981 | − | 2.02892i | ||||
\(593\) | 7.93181e6 | 0.926266 | 0.463133 | − | 0.886289i | \(-0.346725\pi\) | ||||
0.463133 | + | 0.886289i | \(0.346725\pi\) | |||||||
\(594\) | 5.09563e6 | − | 2.94196e6i | 0.592559 | − | 0.342114i | ||||
\(595\) | 4.29034e6 | − | 7.43109e6i | 0.496821 | − | 0.860519i | ||||
\(596\) | −704764. | + | 1.22069e6i | −0.0812696 | + | 0.140763i | ||||
\(597\) | −8.05151e6 | − | 4.64854e6i | −0.924573 | − | 0.533803i | ||||
\(598\) | − | 4.93658e6i | − | 0.564512i | ||||||
\(599\) | 3.37674e6 | − | 5.84868e6i | 0.384530 | − | 0.666026i | −0.607174 | − | 0.794569i | \(-0.707697\pi\) |
0.991704 | + | 0.128543i | \(0.0410301\pi\) | |||||||
\(600\) | − | 1.50189e7i | − | 1.70318i | ||||||
\(601\) | −4.63664e6 | − | 8.03090e6i | −0.523622 | − | 0.906939i | −0.999622 | − | 0.0274940i | \(-0.991247\pi\) |
0.476000 | − | 0.879445i | \(-0.342086\pi\) | |||||||
\(602\) | −1.46493e7 | −1.64750 | ||||||||
\(603\) | −347158. | −0.0388807 | ||||||||
\(604\) | −1.38294e7 | − | 2.39532e7i | −1.54245 | − | 2.67160i | ||||
\(605\) | −9.14330e6 | − | 5.27889e6i | −1.01558 | − | 0.586346i | ||||
\(606\) | 9.26890e6i | 1.02529i | ||||||||
\(607\) | −4.13750e6 | + | 2.38879e6i | −0.455791 | + | 0.263151i | −0.710273 | − | 0.703926i | \(-0.751429\pi\) |
0.254482 | + | 0.967078i | \(0.418095\pi\) | |||||||
\(608\) | 1.58294e7 | + | 2.74174e7i | 1.73663 | + | 3.00793i | ||||
\(609\) | −1.97154e7 | + | 1.13827e7i | −2.15408 | + | 1.24366i | ||||
\(610\) | 2.29154e7 | + | 1.32302e7i | 2.49347 | + | 1.43960i | ||||
\(611\) | −1.07523e6 | − | 620784.i | −0.116519 | − | 0.0672724i | ||||
\(612\) | 3.07912e6 | − | 1.77773e6i | 0.332313 | − | 0.191861i | ||||
\(613\) | 786748. | + | 1.36269e6i | 0.0845638 | + | 0.146469i | 0.905205 | − | 0.424975i | \(-0.139717\pi\) |
−0.820641 | + | 0.571443i | \(0.806384\pi\) | |||||||
\(614\) | 1.64377e7 | − | 9.49031e6i | 1.75962 | − | 1.01592i | ||||
\(615\) | − | 6.09463e6i | − | 0.649770i | ||||||
\(616\) | 1.35822e7 | + | 7.84171e6i | 1.44218 | + | 0.832643i | ||||
\(617\) | −2.98931e6 | − | 5.17764e6i | −0.316124 | − | 0.547544i | 0.663551 | − | 0.748131i | \(-0.269048\pi\) |
−0.979676 | + | 0.200587i | \(0.935715\pi\) | |||||||
\(618\) | −2.43703e7 | −2.56679 | ||||||||
\(619\) | 3.24764e6 | 0.340676 | 0.170338 | − | 0.985386i | \(-0.445514\pi\) | ||||
0.170338 | + | 0.985386i | \(0.445514\pi\) | |||||||
\(620\) | 1.19942e7 | + | 2.07745e7i | 1.25311 | + | 2.17046i | ||||
\(621\) | 1.14144e7i | 1.18774i | ||||||||
\(622\) | −7.98971e6 | + | 1.38386e7i | −0.828047 | + | 1.43422i | ||||
\(623\) | 7.13858e6i | 0.736871i | ||||||||
\(624\) | −5.25378e6 | − | 3.03327e6i | −0.540145 | − | 0.311853i | ||||
\(625\) | 5.80876e6 | − | 1.00611e7i | 0.594817 | − | 1.03025i | ||||
\(626\) | −6.07450e6 | + | 1.05213e7i | −0.619547 | + | 1.07309i | ||||
\(627\) | −3.27785e6 | + | 1.89247e6i | −0.332982 | + | 0.192247i | ||||
\(628\) | 1.53694e7 | 1.55509 | ||||||||
\(629\) | 3.07951e6 | − | 2.95943e6i | 0.310352 | − | 0.298251i | ||||
\(630\) | −1.52795e7 | −1.53376 | ||||||||
\(631\) | −3.85963e6 | + | 2.22836e6i | −0.385898 | + | 0.222798i | −0.680381 | − | 0.732858i | \(-0.738186\pi\) |
0.294483 | + | 0.955657i | \(0.404852\pi\) | |||||||
\(632\) | −8.82980e6 | + | 1.52937e7i | −0.879343 | + | 1.52307i | ||||
\(633\) | 4.45549e6 | − | 7.71713e6i | 0.441963 | − | 0.765503i | ||||
\(634\) | 2.68915e7 | + | 1.55258e7i | 2.65700 | + | 1.53402i | ||||
\(635\) | − | 1.95241e7i | − | 1.92148i | ||||||
\(636\) | 6.05706e6 | − | 1.04911e7i | 0.593771 | − | 1.02844i | ||||
\(637\) | 5.79870e6i | 0.566216i | ||||||||
\(638\) | −5.72638e6 | − | 9.91837e6i | −0.556965 | − | 0.964692i | ||||
\(639\) | 1.74161e6 | 0.168733 | ||||||||
\(640\) | 1.15979e7 | 1.11925 | ||||||||
\(641\) | 5.07696e6 | + | 8.79355e6i | 0.488043 | + | 0.845316i | 0.999905 | − | 0.0137518i | \(-0.00437749\pi\) |
−0.511862 | + | 0.859068i | \(0.671044\pi\) | |||||||
\(642\) | 1.05095e7 | + | 6.06764e6i | 1.00634 | + | 0.581008i | ||||
\(643\) | − | 2.01143e6i | − | 0.191856i | −0.995388 | − | 0.0959282i | \(-0.969418\pi\) | ||
0.995388 | − | 0.0959282i | \(-0.0305819\pi\) | |||||||
\(644\) | −4.37296e7 | + | 2.52473e7i | −4.15491 | + | 2.39884i | ||||
\(645\) | −2.82048e6 | − | 4.88521e6i | −0.266946 | − | 0.462364i | ||||
\(646\) | −1.05797e7 | + | 6.10817e6i | −0.997448 | + | 0.575877i | ||||
\(647\) | −1.06646e7 | − | 6.15718e6i | −1.00157 | − | 0.578257i | −0.0928585 | − | 0.995679i | \(-0.529600\pi\) |
−0.908713 | + | 0.417422i | \(0.862934\pi\) | |||||||
\(648\) | 1.36855e7 | + | 7.90133e6i | 1.28033 | + | 0.739202i | ||||
\(649\) | 3.11744e6 | − | 1.79986e6i | 0.290527 | − | 0.167736i | ||||
\(650\) | 2.07728e6 | + | 3.59795e6i | 0.192846 | + | 0.334019i | ||||
\(651\) | −9.91212e6 | + | 5.72276e6i | −0.916672 | + | 0.529241i | ||||
\(652\) | − | 2.52699e7i | − | 2.32800i | ||||||
\(653\) | −6.35894e6 | − | 3.67134e6i | −0.583582 | − | 0.336931i | 0.178973 | − | 0.983854i | \(-0.442722\pi\) |
−0.762556 | + | 0.646923i | \(0.776056\pi\) | |||||||
\(654\) | −9.87034e6 | − | 1.70959e7i | −0.902377 | − | 1.56296i | ||||
\(655\) | 1.69599e6 | 0.154462 | ||||||||
\(656\) | 1.89822e7 | 1.72221 | ||||||||
\(657\) | −488201. | − | 845588.i | −0.0441250 | − | 0.0764268i | ||||
\(658\) | 1.77473e7i | 1.59796i | ||||||||
\(659\) | 8.68177e6 | − | 1.50373e7i | 0.778744 | − | 1.34882i | −0.153921 | − | 0.988083i | \(-0.549190\pi\) |
0.932666 | − | 0.360742i | \(-0.117476\pi\) | |||||||
\(660\) | 1.00230e7i | 0.895646i | ||||||||
\(661\) | 1.00432e7 | + | 5.79845e6i | 0.894064 | + | 0.516188i | 0.875270 | − | 0.483635i | \(-0.160684\pi\) |
0.0187944 | + | 0.999823i | \(0.494017\pi\) | |||||||
\(662\) | −4.05109e6 | + | 7.01669e6i | −0.359275 | + | 0.622283i | ||||
\(663\) | 539912. | − | 935156.i | 0.0477023 | − | 0.0826228i | ||||
\(664\) | −4.03007e7 | + | 2.32676e7i | −3.54726 | + | 2.04801i | ||||
\(665\) | 3.75676e7 | 3.29427 | ||||||||
\(666\) | −7.30563e6 | − | 2.11406e6i | −0.638222 | − | 0.184685i | ||||
\(667\) | 2.22175e7 | 1.93366 | ||||||||
\(668\) | −1.86659e7 | + | 1.07768e7i | −1.61848 | + | 0.934432i | ||||
\(669\) | 729199. | − | 1.26301e6i | 0.0629913 | − | 0.109104i | ||||
\(670\) | 1.57936e6 | − | 2.73553e6i | 0.135923 | − | 0.235426i | ||||
\(671\) | −3.93602e6 | − | 2.27246e6i | −0.337482 | − | 0.194846i | ||||
\(672\) | 4.00008e7i | 3.41700i | ||||||||
\(673\) | 4.77009e6 | − | 8.26204e6i | 0.405965 | − | 0.703153i | −0.588468 | − | 0.808521i | \(-0.700269\pi\) |
0.994433 | + | 0.105368i | \(0.0336020\pi\) | |||||||
\(674\) | − | 1.61090e7i | − | 1.36590i | ||||||
\(675\) | −4.80307e6 | − | 8.31917e6i | −0.405751 | − | 0.702782i | ||||
\(676\) | −2.76181e7 | −2.32449 | ||||||||
\(677\) | −1.66567e7 | −1.39674 | −0.698371 | − | 0.715736i | \(-0.746091\pi\) | ||||
−0.698371 | + | 0.715736i | \(0.746091\pi\) | |||||||
\(678\) | 1.01480e7 | + | 1.75768e7i | 0.847821 | + | 1.46847i | ||||
\(679\) | 1.05259e7 | + | 6.07711e6i | 0.876160 | + | 0.505851i | ||||
\(680\) | 1.94921e7i | 1.61654i | ||||||||
\(681\) | 6.22313e6 | − | 3.59292e6i | 0.514211 | − | 0.296880i | ||||
\(682\) | −2.87900e6 | − | 4.98657e6i | −0.237017 | − | 0.410526i | ||||
\(683\) | −9.63402e6 | + | 5.56220e6i | −0.790234 | + | 0.456242i | −0.840045 | − | 0.542517i | \(-0.817472\pi\) |
0.0498108 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(684\) | 1.34809e7 | + | 7.78318e6i | 1.10174 | + | 0.636087i | ||||
\(685\) | −1.08054e7 | − | 6.23848e6i | −0.879859 | − | 0.507987i | ||||
\(686\) | 3.68127e7 | − | 2.12538e7i | 2.98667 | − | 1.72435i | ||||
\(687\) | 5.67334e6 | + | 9.82652e6i | 0.458614 | + | 0.794342i | ||||
\(688\) | 1.52154e7 | − | 8.78461e6i | 1.22550 | − | 0.707540i | ||||
\(689\) | 2.01910e6i | 0.162035i | ||||||||
\(690\) | −2.35317e7 | − | 1.35860e7i | −1.88161 | − | 1.08635i | ||||
\(691\) | −3.31328e6 | − | 5.73878e6i | −0.263975 | − | 0.457219i | 0.703319 | − | 0.710874i | \(-0.251700\pi\) |
−0.967295 | + | 0.253655i | \(0.918367\pi\) | |||||||
\(692\) | −1.49063e7 | −1.18333 | ||||||||
\(693\) | 2.62446e6 | 0.207590 | ||||||||
\(694\) | −661042. | − | 1.14496e6i | −0.0520991 | − | 0.0902384i | ||||
\(695\) | 8.86153e6i | 0.695900i | ||||||||
\(696\) | 2.58571e7 | − | 4.47859e7i | 2.02329 | − | 3.50443i | ||||
\(697\) | 3.37877e6i | 0.263437i | ||||||||
\(698\) | −6.38095e6 | − | 3.68404e6i | −0.495731 | − | 0.286211i | ||||
\(699\) | −935505. | + | 1.62034e6i | −0.0724191 | + | 0.125434i | ||||
\(700\) | 2.12478e7 | − | 3.68022e7i | 1.63896 | − | 2.83876i | ||||
\(701\) | −1.68286e7 | + | 9.71599e6i | −1.29346 | + | 0.746779i | −0.979266 | − | 0.202580i | \(-0.935067\pi\) |
−0.314193 | + | 0.949359i | \(0.601734\pi\) | |||||||
\(702\) | −7.34942e6 | −0.562873 | ||||||||
\(703\) | 1.79623e7 | + | 5.19783e6i | 1.37080 | + | 0.396674i | ||||
\(704\) | −7.71563e6 | −0.586732 | ||||||||
\(705\) | −5.91831e6 | + | 3.41694e6i | −0.448461 | + | 0.258919i | ||||
\(706\) | 585589. | − | 1.01427e6i | 0.0442162 | − | 0.0765847i | ||||
\(707\) | −7.90101e6 | + | 1.36849e7i | −0.594476 | + | 1.02966i | ||||
\(708\) | 2.33625e7 | + | 1.34883e7i | 1.75160 | + | 1.01129i | ||||
\(709\) | 1.59173e7i | 1.18920i | 0.804022 | + | 0.594599i | \(0.202689\pi\) | ||||
−0.804022 | + | 0.594599i | \(0.797311\pi\) | |||||||
\(710\) | −7.92328e6 | + | 1.37235e7i | −0.589874 | + | 1.02169i | ||||
\(711\) | 2.95515e6i | 0.219233i | ||||||||
\(712\) | −8.10807e6 | − | 1.40436e7i | −0.599401 | − | 1.03819i | ||||
\(713\) | 1.11701e7 | 0.822871 | ||||||||
\(714\) | −1.54353e7 | −1.13310 | ||||||||
\(715\) | −835279. | − | 1.44675e6i | −0.0611035 | − | 0.105834i | ||||
\(716\) | −3.14743e7 | − | 1.81717e7i | −2.29442 | − | 1.32469i | ||||
\(717\) | − | 1.14715e7i | − | 0.833337i | ||||||
\(718\) | 75077.1 | − | 43345.8i | 0.00543496 | − | 0.00313787i | ||||
\(719\) | −3.98887e6 | − | 6.90892e6i | −0.287758 | − | 0.498412i | 0.685516 | − | 0.728057i | \(-0.259577\pi\) |
−0.973274 | + | 0.229646i | \(0.926243\pi\) | |||||||
\(720\) | 1.58700e7 | − | 9.16252e6i | 1.14089 | − | 0.658694i | ||||
\(721\) | −3.59812e7 | − | 2.07738e7i | −2.57773 | − | 1.48825i | ||||
\(722\) | −2.35740e7 | − | 1.36105e7i | −1.68303 | − | 0.971696i | ||||
\(723\) | −4.02912e6 | + | 2.32622e6i | −0.286659 | + | 0.165502i | ||||
\(724\) | 1.66440e7 | + | 2.88283e7i | 1.18008 | + | 2.04396i | ||||
\(725\) | −1.61928e7 | + | 9.34893e6i | −1.14414 | + | 0.660567i | ||||
\(726\) | 1.89917e7i | 1.33728i | ||||||||
\(727\) | 1.83970e7 | + | 1.06215e7i | 1.29095 | + | 0.745333i | 0.978824 | − | 0.204706i | \(-0.0656237\pi\) |
0.312131 | + | 0.950039i | \(0.398957\pi\) | |||||||
\(728\) | −9.79482e6 | − | 1.69651e7i | −0.684965 | − | 1.18639i | ||||
\(729\) | 1.51918e7 | 1.05874 | ||||||||
\(730\) | 8.88406e6 | 0.617027 | ||||||||
\(731\) | 1.56363e6 | + | 2.70829e6i | 0.108228 | + | 0.187457i | ||||
\(732\) | − | 3.40602e7i | − | 2.34947i | ||||||
\(733\) | −1.62321e6 | + | 2.81149e6i | −0.111588 | + | 0.193275i | −0.916410 | − | 0.400240i | \(-0.868927\pi\) |
0.804823 | + | 0.593515i | \(0.202260\pi\) | |||||||
\(734\) | − | 3.60230e7i | − | 2.46797i | ||||||
\(735\) | 2.76412e7 | + | 1.59587e7i | 1.88729 | + | 1.08963i | ||||
\(736\) | 1.95191e7 | − | 3.38080e7i | 1.32820 | − | 2.30051i | ||||
\(737\) | −271275. | + | 469862.i | −0.0183967 | + | 0.0318641i | ||||
\(738\) | 5.21048e6 | − | 3.00827e6i | 0.352157 | − | 0.203318i | ||||
\(739\) | 1.09288e7 | 0.736145 | 0.368072 | − | 0.929797i | \(-0.380018\pi\) | ||||
0.368072 | + | 0.929797i | \(0.380018\pi\) | |||||||
\(740\) | 3.57035e7 | − | 3.43113e7i | 2.39680 | − | 2.30334i | ||||
\(741\) | 4.72764e6 | 0.316300 | ||||||||
\(742\) | 2.49948e7 | − | 1.44307e7i | 1.66663 | − | 0.962229i | ||||
\(743\) | −4.74856e6 | + | 8.22475e6i | −0.315566 | + | 0.546576i | −0.979558 | − | 0.201164i | \(-0.935528\pi\) |
0.663992 | + | 0.747740i | \(0.268861\pi\) | |||||||
\(744\) | 1.29999e7 | − | 2.25166e7i | 0.861012 | − | 1.49132i | ||||
\(745\) | −1.11987e6 | − | 646555.i | −0.0739223 | − | 0.0426791i | ||||
\(746\) | − | 1.49566e7i | − | 0.983980i | ||||||
\(747\) | −3.89360e6 | + | 6.74392e6i | −0.255300 | + | 0.442192i | ||||
\(748\) | − | 5.55658e6i | − | 0.363123i | ||||||
\(749\) | 1.03444e7 | + | 1.79170e7i | 0.673752 | + | 1.16697i | ||||
\(750\) | −7.79863e6 | −0.506250 | ||||||||
\(751\) | −1.91857e7 | −1.24130 | −0.620652 | − | 0.784087i | \(-0.713132\pi\) | ||||
−0.620652 | + | 0.784087i | \(0.713132\pi\) | |||||||
\(752\) | −1.06423e7 | − | 1.84330e7i | −0.686265 | − | 1.18865i | ||||
\(753\) | −4.95176e6 | − | 2.85890e6i | −0.318253 | − | 0.183743i | ||||
\(754\) | 1.43053e7i | 0.916363i | ||||||||
\(755\) | 2.19748e7 | − | 1.26872e7i | 1.40300 | − | 0.810024i | ||||
\(756\) | 3.75874e7 | + | 6.51033e7i | 2.39187 | + | 4.14284i | ||||
\(757\) | 2.04277e7 | − | 1.17939e7i | 1.29562 | − | 0.748029i | 0.315979 | − | 0.948766i | \(-0.397667\pi\) |
0.979645 | + | 0.200737i | \(0.0643338\pi\) | |||||||
\(758\) | 3.48735e7 | + | 2.01342e7i | 2.20457 | + | 1.27281i | ||||
\(759\) | 4.04188e6 | + | 2.33358e6i | 0.254670 | + | 0.147034i | ||||
\(760\) | −7.39061e7 | + | 4.26697e7i | −4.64137 | + | 2.67970i | ||||
\(761\) | −1.82132e6 | − | 3.15461e6i | −0.114005 | − | 0.197462i | 0.803377 | − | 0.595471i | \(-0.203035\pi\) |
−0.917382 | + | 0.398009i | \(0.869701\pi\) | |||||||
\(762\) | −3.04154e7 | + | 1.75603e7i | −1.89761 | + | 1.09558i | ||||
\(763\) | − | 3.36548e7i | − | 2.09284i | ||||||
\(764\) | −2.62373e7 | − | 1.51481e7i | −1.62625 | − | 0.938914i | ||||
\(765\) | 1.63090e6 | + | 2.82480e6i | 0.100757 | + | 0.174516i | ||||
\(766\) | 1.69745e7 | 1.04526 | ||||||||
\(767\) | −4.49628e6 | −0.275972 | ||||||||
\(768\) | 1.05984e6 | + | 1.83569e6i | 0.0648391 | + | 0.112305i | ||||
\(769\) | 1.76578e7i | 1.07677i | 0.842700 | + | 0.538383i | \(0.180965\pi\) | ||||
−0.842700 | + | 0.538383i | \(0.819035\pi\) | |||||||
\(770\) | −1.19397e7 | + | 2.06801e7i | −0.725714 | + | 1.25697i | ||||
\(771\) | − | 1.68252e6i | − | 0.101935i | ||||||
\(772\) | −2.97396e7 | − | 1.71702e7i | −1.79594 | − | 1.03689i | ||||
\(773\) | −1.53213e7 | + | 2.65372e7i | −0.922244 | + | 1.59737i | −0.126310 | + | 0.991991i | \(0.540314\pi\) |
−0.795934 | + | 0.605383i | \(0.793020\pi\) | |||||||
\(774\) | 2.78434e6 | − | 4.82262e6i | 0.167059 | − | 0.289355i | ||||
\(775\) | −8.14112e6 | + | 4.70028e6i | −0.486889 | + | 0.281105i | ||||
\(776\) | −2.76098e7 | −1.64592 | ||||||||
\(777\) | 1.63709e7 | + | 1.70352e7i | 0.972794 | + | 1.01226i | ||||
\(778\) | −4.89596e7 | −2.89994 | ||||||||
\(779\) | −1.28109e7 | + | 7.39640e6i | −0.756375 | + | 0.436694i | ||||
\(780\) | 6.25968e6 | − | 1.08421e7i | 0.368397 | − | 0.638082i | ||||
\(781\) | 1.36093e6 | − | 2.35719e6i | 0.0798375 | − | 0.138283i | ||||
\(782\) | 1.30456e7 | + | 7.53190e6i | 0.762866 | + | 0.440441i | ||||
\(783\) | − | 3.30766e7i | − | 1.92804i | ||||||
\(784\) | −4.97046e7 | + | 8.60909e7i | −2.88806 | + | 5.00227i | ||||
\(785\) | 1.40999e7i | 0.816664i | ||||||||
\(786\) | −1.52541e6 | − | 2.64209e6i | −0.0880705 | − | 0.152543i | ||||
\(787\) | 2.96524e6 | 0.170657 | 0.0853283 | − | 0.996353i | \(-0.472806\pi\) | ||||
0.0853283 | + | 0.996353i | \(0.472806\pi\) | |||||||
\(788\) | 2.87244e7 | 1.64792 | ||||||||
\(789\) | 9.12945e6 | + | 1.58127e7i | 0.522098 | + | 0.904300i | ||||
\(790\) | −2.32859e7 | − | 1.34441e7i | −1.32747 | − | 0.766417i | ||||
\(791\) | 3.46013e7i | 1.96631i | ||||||||
\(792\) | −5.16305e6 | + | 2.98089e6i | −0.292478 | + | 0.168862i | ||||
\(793\) | 2.83846e6 | + | 4.91636e6i | 0.160288 | + | 0.277626i | ||||
\(794\) | −2.64634e7 | + | 1.52787e7i | −1.48969 | + | 0.860071i | ||||
\(795\) | 9.62464e6 | + | 5.55679e6i | 0.540090 | + | 0.311821i | ||||
\(796\) | 5.17509e7 | + | 2.98784e7i | 2.89491 | + | 1.67138i | ||||
\(797\) | 7.51156e6 | − | 4.33680e6i | 0.418875 | − | 0.241838i | −0.275721 | − | 0.961238i | \(-0.588917\pi\) |
0.694596 | + | 0.719400i | \(0.255583\pi\) | |||||||
\(798\) | −3.37891e7 | − | 5.85244e7i | −1.87832 | − | 3.25334i | ||||
\(799\) | 3.28102e6 | − | 1.89430e6i | 0.181820 | − | 0.104974i | ||||
\(800\) | 3.28539e7i | 1.81494i | ||||||||
\(801\) | −2.35005e6 | − | 1.35680e6i | −0.129418 | − | 0.0747197i | ||||
\(802\) | −2.16227e7 | − | 3.74516e7i | −1.18706 | − | 2.05606i | ||||
\(803\) | −1.52595e6 | −0.0835126 | ||||||||
\(804\) | −4.06593e6 | −0.221830 | ||||||||
\(805\) | −2.31621e7 | − | 4.01178e7i | −1.25976 | − | 2.18197i | ||||
\(806\) | 7.19212e6i | 0.389960i | ||||||||
\(807\) | −4.31589e6 | + | 7.47534e6i | −0.233285 | + | 0.404061i | ||||
\(808\) | − | 3.58962e7i | − | 1.93428i | ||||||
\(809\) | 5.59247e6 | + | 3.22881e6i | 0.300422 | + | 0.173449i | 0.642633 | − | 0.766174i | \(-0.277842\pi\) |
−0.342210 | + | 0.939623i | \(0.611176\pi\) | |||||||
\(810\) | −1.20305e7 | + | 2.08374e7i | −0.644273 | + | 1.11591i | ||||
\(811\) | 1.30787e7 | − | 2.26529e7i | 0.698251 | − | 1.20941i | −0.270822 | − | 0.962629i | \(-0.587295\pi\) |
0.969073 | − | 0.246776i | \(-0.0793712\pi\) | |||||||
\(812\) | 1.26720e8 | − | 7.31619e7i | 6.74459 | − | 3.89399i | ||||
\(813\) | −6.52360e6 | −0.346148 | ||||||||
\(814\) | −8.57002e6 | + | 8.23586e6i | −0.453337 | + | 0.435660i | ||||
\(815\) | 2.31827e7 | 1.22256 | ||||||||
\(816\) | 1.60317e7 | − | 9.25592e6i | 0.842858 | − | 0.486625i | ||||
\(817\) | −6.84583e6 | + | 1.18573e7i | −0.358815 | + | 0.621486i | ||||
\(818\) | 3.90295e6 | − | 6.76011e6i | 0.203944 | − | 0.353241i | ||||
\(819\) | −2.83894e6 | − | 1.63906e6i | −0.147893 | − | 0.0853858i | ||||
\(820\) | 3.91731e7i | 2.03448i | ||||||||
\(821\) | −4.41127e6 | + | 7.64054e6i | −0.228405 | + | 0.395609i | −0.957336 | − | 0.288979i | \(-0.906684\pi\) |
0.728931 | + | 0.684588i | \(0.240018\pi\) | |||||||
\(822\) | 2.24440e7i | 1.15857i | ||||||||
\(823\) | −9.14890e6 | − | 1.58464e7i | −0.470835 | − | 0.815511i | 0.528608 | − | 0.848866i | \(-0.322714\pi\) |
−0.999444 | + | 0.0333551i | \(0.989381\pi\) | |||||||
\(824\) | 9.43802e7 | 4.84243 | ||||||||
\(825\) | −3.92781e6 | −0.200916 | ||||||||
\(826\) | 3.21355e7 | + | 5.56603e7i | 1.63883 | + | 2.83854i | ||||
\(827\) | 2.88571e7 | + | 1.66606e7i | 1.46720 | + | 0.847087i | 0.999326 | − | 0.0367092i | \(-0.0116875\pi\) |
0.467872 | + | 0.883796i | \(0.345021\pi\) | |||||||
\(828\) | − | 1.91947e7i | − | 0.972981i | ||||||
\(829\) | 5.97327e6 | − | 3.44867e6i | 0.301874 | − | 0.174287i | −0.341410 | − | 0.939914i | \(-0.610905\pi\) |
0.643285 | + | 0.765627i | \(0.277571\pi\) | |||||||
\(830\) | −3.54270e7 | − | 6.13614e7i | −1.78500 | − | 3.09172i | ||||
\(831\) | 2.56329e6 | − | 1.47992e6i | 0.128764 | − | 0.0743421i | ||||
\(832\) | 8.34618e6 | + | 4.81867e6i | 0.418003 | + | 0.241334i | ||||
\(833\) | −1.53239e7 | − | 8.84726e6i | −0.765168 | − | 0.441770i | ||||
\(834\) | 1.38048e7 | − | 7.97023e6i | 0.687253 | − | 0.396786i | ||||
\(835\) | −9.88668e6 | − | 1.71242e7i | −0.490721 | − | 0.849953i | ||||
\(836\) | 2.10683e7 | − | 1.21638e7i | 1.04259 | − | 0.601941i | ||||
\(837\) | − | 1.66296e7i | − | 0.820482i | ||||||
\(838\) | 6.16907e7 | + | 3.56172e7i | 3.03466 | + | 1.75206i | ||||
\(839\) | −1.34486e7 | − | 2.32937e7i | −0.659587 | − | 1.14244i | −0.980723 | − | 0.195406i | \(-0.937398\pi\) |
0.321135 | − | 0.947033i | \(-0.395936\pi\) | |||||||
\(840\) | −1.07826e8 | −5.27260 | ||||||||
\(841\) | −4.38708e7 | −2.13887 | ||||||||
\(842\) | 2.72864e7 | + | 4.72614e7i | 1.32637 | + | 2.29734i | ||||
\(843\) | − | 2.42803e7i | − | 1.17675i | ||||||
\(844\) | −2.86376e7 | + | 4.96017e7i | −1.38382 | + | 2.39685i | ||||
\(845\) | − | 2.53370e7i | − | 1.22071i | ||||||
\(846\) | −5.84248e6 | − | 3.37316e6i | −0.280654 | − | 0.162036i | ||||
\(847\) | −1.61890e7 | + | 2.80401e7i | −0.775373 | + | 1.34299i | ||||
\(848\) | −1.73071e7 | + | 2.99767e7i | −0.826483 | + | 1.43151i | ||||
\(849\) | 2.27323e7 | − | 1.31245e7i | 1.08236 | − | 0.624904i | ||||
\(850\) | −1.26775e7 | −0.601845 | ||||||||
\(851\) | −5.52384e6 | − | 2.23863e7i | −0.261467 | − | 1.05964i | ||||
\(852\) | 2.03979e7 | 0.962689 | ||||||||
\(853\) | −3.91869e6 | + | 2.26245e6i | −0.184403 | + | 0.106465i | −0.589360 | − | 0.807871i | \(-0.700620\pi\) |
0.404957 | + | 0.914336i | \(0.367287\pi\) | |||||||
\(854\) | 4.05736e7 | − | 7.02756e7i | 1.90370 | − | 3.29731i | ||||
\(855\) | −7.14034e6 | + | 1.23674e7i | −0.334044 | + | 0.578581i | ||||
\(856\) | −4.07006e7 | − | 2.34985e7i | −1.89853 | − | 1.09611i | ||||
\(857\) | 2.18165e7i | 1.01469i | 0.861743 | + | 0.507346i | \(0.169373\pi\) | ||||
−0.861743 | + | 0.507346i | \(0.830627\pi\) | |||||||
\(858\) | −1.50253e6 | + | 2.60246e6i | −0.0696796 | + | 0.120689i | ||||
\(859\) | − | 1.92517e7i | − | 0.890195i | −0.895482 | − | 0.445097i | \(-0.853169\pi\) | ||
0.895482 | − | 0.445097i | \(-0.146831\pi\) | |||||||
\(860\) | 1.81286e7 | + | 3.13996e7i | 0.835828 | + | 1.44770i | ||||
\(861\) | −1.86906e7 | −0.859243 | ||||||||
\(862\) | 1.55229e6 | 0.0711547 | ||||||||
\(863\) | 3.87298e6 | + | 6.70820e6i | 0.177019 | + | 0.306605i | 0.940858 | − | 0.338801i | \(-0.110021\pi\) |
−0.763839 | + | 0.645406i | \(0.776688\pi\) | |||||||
\(864\) | −5.03322e7 | − | 2.90593e7i | −2.29383 | − | 1.32435i | ||||
\(865\) | − | 1.36752e7i | − | 0.621430i | ||||||
\(866\) | −5.73638e7 | + | 3.31190e7i | −2.59922 | + | 1.50066i | ||||
\(867\) | −7.24492e6 | − | 1.25486e7i | −0.327330 | − | 0.566953i | ||||
\(868\) | 6.37099e7 | − | 3.67829e7i | 2.87017 | − | 1.65709i | ||||
\(869\) | 3.99966e6 | + | 2.30920e6i | 0.179669 | + | 0.103732i | ||||
\(870\) | 6.81903e7 | + | 3.93697e7i | 3.05439 | + | 1.76345i | ||||
\(871\) | 586889. | − | 338841.i | 0.0262126 | − | 0.0151339i | ||||
\(872\) | 3.82254e7 | + | 6.62084e7i | 1.70240 | + | 2.94864i | ||||
\(873\) | −4.00122e6 | + | 2.31011e6i | −0.177688 | + | 0.102588i | ||||
\(874\) | 6.59517e7i | 2.92043i | ||||||||
\(875\) | −1.15142e7 | − | 6.64772e6i | −0.508409 | − | 0.293530i | ||||
\(876\) | −5.71783e6 | − | 9.90358e6i | −0.251751 | − | 0.436046i | ||||
\(877\) | 4.16977e7 | 1.83068 | 0.915341 | − | 0.402679i | \(-0.131921\pi\) | ||||
0.915341 | + | 0.402679i | \(0.131921\pi\) | |||||||
\(878\) | −5.39580e7 | −2.36222 | ||||||||
\(879\) | −1.34002e7 | − | 2.32098e7i | −0.584976 | − | 1.01321i | ||||
\(880\) | − | 2.86390e7i | − | 1.24667i | ||||||
\(881\) | −8.94056e6 | + | 1.54855e7i | −0.388083 | + | 0.672180i | −0.992192 | − | 0.124722i | \(-0.960196\pi\) |
0.604108 | + | 0.796902i | \(0.293529\pi\) | |||||||
\(882\) | 3.15084e7i | 1.36381i | ||||||||
\(883\) | 2.25539e7 | + | 1.30215e7i | 0.973464 | + | 0.562030i | 0.900291 | − | 0.435289i | \(-0.143354\pi\) |
0.0731736 | + | 0.997319i | \(0.476687\pi\) | |||||||
\(884\) | −3.47027e6 | + | 6.01069e6i | −0.149360 | + | 0.258698i | ||||
\(885\) | −1.23743e7 | + | 2.14329e7i | −0.531082 | + | 0.919862i | ||||
\(886\) | 2.25726e7 | − | 1.30323e7i | 0.966043 | − | 0.557745i | ||||
\(887\) | 3.90270e6 | 0.166554 | 0.0832772 | − | 0.996526i | \(-0.473461\pi\) | ||||
0.0832772 | + | 0.996526i | \(0.473461\pi\) | |||||||
\(888\) | −5.15550e7 | − | 1.49187e7i | −2.19401 | − | 0.634890i | ||||
\(889\) | −5.98753e7 | −2.54093 | ||||||||
\(890\) | 2.13826e7 | − | 1.23452e7i | 0.904868 | − | 0.522426i | ||||
\(891\) | 2.06639e6 | − | 3.57909e6i | 0.0872003 | − | 0.151035i | ||||
\(892\) | −4.68691e6 | + | 8.11796e6i | −0.197231 | + | 0.341613i | ||||
\(893\) | 1.43648e7 | + | 8.29354e6i | 0.602798 | + | 0.348026i | ||||
\(894\) | 2.32610e6i | 0.0973384i | ||||||||
\(895\) | 1.66708e7 | − | 2.88747e7i | 0.695664 | − | 1.20492i | ||||
\(896\) | − | 3.55676e7i | − | 1.48008i | ||||||
\(897\) | −2.91480e6 | − | 5.04857e6i | −0.120956 | − | 0.209502i | ||||
\(898\) | −6.19147e6 | −0.256214 | ||||||||
\(899\) | −3.23687e7 | −1.33575 | ||||||||
\(900\) | 8.07696e6 | + | 1.39897e7i | 0.332385 | + | 0.575708i | ||||
\(901\) | −5.33576e6 | − | 3.08060e6i | −0.218970 | − | 0.126422i | ||||
\(902\) | − | 9.40285e6i | − | 0.384807i | ||||||
\(903\) | −1.49817e7 | + | 8.64967e6i | −0.611421 | + | 0.353004i | ||||
\(904\) | −3.93006e7 | − | 6.80706e7i | −1.59948 | − | 2.77037i | ||||
\(905\) | −2.64473e7 | + | 1.52694e7i | −1.07340 | + | 0.619725i | ||||
\(906\) | −3.95292e7 | − | 2.28222e7i | −1.59992 | − | 0.923713i | ||||
\(907\) | −2.20014e7 | − | 1.27025e7i | −0.888039 | − | 0.512709i | −0.0147382 | − | 0.999891i | \(-0.504691\pi\) |
−0.873300 | + | 0.487182i | \(0.838025\pi\) | |||||||
\(908\) | −3.99990e7 | + | 2.30934e7i | −1.61003 | + | 0.929553i | ||||
\(909\) | −3.00343e6 | − | 5.20209e6i | −0.120561 | − | 0.208818i | ||||
\(910\) | 2.58309e7 | − | 1.49135e7i | 1.03404 | − | 0.597001i | ||||
\(911\) | 2.47187e6i | 0.0986802i | 0.998782 | + | 0.0493401i | \(0.0157118\pi\) | ||||
−0.998782 | + | 0.0493401i | \(0.984288\pi\) | |||||||
\(912\) | 7.01894e7 | + | 4.05239e7i | 2.79437 | + | 1.61333i | ||||
\(913\) | 6.08505e6 | + | 1.05396e7i | 0.241595 | + | 0.418454i | ||||
\(914\) | −238978. | −0.00946221 | ||||||||
\(915\) | 3.12471e7 | 1.23383 | ||||||||
\(916\) | −3.64653e7 | − | 6.31597e7i | −1.43596 | − | 2.48715i | ||||
\(917\) | − | 5.20117e6i | − | 0.204257i | ||||||
\(918\) | 1.12132e7 | − | 1.94219e7i | 0.439162 | − | 0.760650i | ||||
\(919\) | 3.59984e7i | 1.40603i | 0.711175 | + | 0.703015i | \(0.248164\pi\) | ||||
−0.711175 | + | 0.703015i | \(0.751836\pi\) | |||||||
\(920\) | 9.11326e7 | + | 5.26154e7i | 3.54980 | + | 2.04948i | ||||
\(921\) | 1.12071e7 | − | 1.94112e7i | 0.435355 | − | 0.754057i | ||||
\(922\) | 3.44182e6 | − | 5.96140e6i | 0.133340 | − | 0.230952i | ||||
\(923\) | −2.94429e6 | + | 1.69989e6i | −0.113757 | + | 0.0656774i | ||||
\(924\) | 3.07378e7 | 1.18439 | ||||||||
\(925\) | 1.34459e7 | + | 1.39915e7i | 0.516698 | + | 0.537663i | ||||
\(926\) | 6.30488e7 | 2.41629 | ||||||||
\(927\) | 1.36776e7 | − | 7.89678e6i | 0.522771 | − | 0.301822i | ||||
\(928\) | −5.65625e7 | + | 9.79691e7i | −2.15605 | + | 3.73438i | ||||
\(929\) | 1.69197e7 | − | 2.93057e7i | 0.643210 | − | 1.11407i | −0.341502 | − | 0.939881i | \(-0.610936\pi\) |
0.984712 | − | 0.174191i | \(-0.0557311\pi\) | |||||||
\(930\) | 3.42834e7 | + | 1.97935e7i | 1.29980 | + | 0.750440i | ||||
\(931\) | − | 7.74694e7i | − | 2.92925i | ||||||
\(932\) | 6.01294e6 | − | 1.04147e7i | 0.226750 | − | 0.392742i | ||||
\(933\) | 1.88700e7i | 0.709690i | ||||||||
\(934\) | −3.18212e7 | − | 5.51159e7i | −1.19357 | − | 2.06733i | ||||
\(935\) | 5.09765e6 | 0.190696 | ||||||||
\(936\) | 7.44666e6 | 0.277825 | ||||||||
\(937\) | −1.18068e6 | − | 2.04500e6i | −0.0439322 | − | 0.0760929i | 0.843223 | − | 0.537564i | \(-0.180655\pi\) |
−0.887155 | + | 0.461471i | \(0.847322\pi\) | |||||||
\(938\) | −8.38914e6 | − | 4.84347e6i | −0.311322 | − | 0.179742i | ||||
\(939\) | 1.43467e7i | 0.530992i | ||||||||
\(940\) | 3.80398e7 | − | 2.19623e7i | 1.40417 | − | 0.810695i | ||||
\(941\) | −1.74293e7 | − | 3.01884e7i | −0.641661 | − | 1.11139i | −0.985062 | − | 0.172200i | \(-0.944912\pi\) |
0.343401 | − | 0.939189i | \(-0.388421\pi\) | |||||||
\(942\) | 2.19655e7 | − | 1.26818e7i | 0.806516 | − | 0.465642i | ||||
\(943\) | 1.57970e7 | + | 9.12040e6i | 0.578489 | + | 0.333991i | ||||
\(944\) | −6.67545e7 | − | 3.85407e7i | −2.43809 | − | 1.40763i | ||||
\(945\) | −5.97261e7 | + | 3.44829e7i | −2.17563 | + | 1.25610i | ||||
\(946\) | −4.35146e6 | − | 7.53695e6i | −0.158091 | − | 0.273822i | ||||
\(947\) | −2.80675e7 | + | 1.62048e7i | −1.01702 | + | 0.587176i | −0.913239 | − | 0.407424i | \(-0.866427\pi\) |
−0.103780 | + | 0.994600i | \(0.533094\pi\) | |||||||
\(948\) | 3.46109e7i | 1.25081i | ||||||||
\(949\) | 1.65066e6 | + | 953009.i | 0.0594966 | + | 0.0343504i | ||||
\(950\) | −2.77520e7 | − | 4.80678e7i | −0.997665 | − | 1.72801i | ||||
\(951\) | 3.66688e7 | 1.31476 | ||||||||
\(952\) | 5.97771e7 | 2.13768 | ||||||||
\(953\) | −5.44960e6 | − | 9.43899e6i | −0.194371 | − | 0.336661i | 0.752323 | − | 0.658795i | \(-0.228933\pi\) |
−0.946694 | + | 0.322133i | \(0.895600\pi\) | |||||||
\(954\) | 1.09712e7i | 0.390286i | ||||||||
\(955\) | 1.38970e7 | − | 2.40703e7i | 0.493074 | − | 0.854030i | ||||
\(956\) | 7.37326e7i | 2.60924i | ||||||||
\(957\) | −1.17126e7 | − | 6.76226e6i | −0.413402 | − | 0.238678i | ||||
\(958\) | −3.61338e6 | + | 6.25855e6i | −0.127204 | + | 0.220323i | ||||
\(959\) | −1.91318e7 | + | 3.31372e7i | −0.671752 | + | 1.16351i | ||||
\(960\) | 4.59393e7 | − | 2.65231e7i | 1.60882 | − | 0.928850i | ||||
\(961\) | 1.23554e7 | 0.431568 | ||||||||
\(962\) | 1.44140e7 | − | 3.55666e6i | 0.502165 | − | 0.123909i | ||||
\(963\) | −7.86447e6 | −0.273277 | ||||||||
\(964\) | 2.58971e7 | − | 1.49517e7i | 0.897550 | − | 0.518201i | ||||
\(965\) | 1.57520e7 | − | 2.72833e7i | 0.544526 | − | 0.943146i | ||||
\(966\) | −4.16648e7 | + | 7.21656e7i | −1.43657 | + | 2.48821i | ||||
\(967\) | 4.77031e7 | + | 2.75414e7i | 1.64052 | + | 0.947152i | 0.980650 | + | 0.195768i | \(0.0627200\pi\) |
0.659865 | + | 0.751384i | \(0.270613\pi\) | |||||||
\(968\) | − | 7.35504e7i | − | 2.52288i | ||||||
\(969\) | −7.21312e6 | + | 1.24935e7i | −0.246782 | + | 0.427439i | ||||
\(970\) | − | 4.20383e7i | − | 1.43455i | ||||||
\(971\) | −3.90677e6 | − | 6.76673e6i | −0.132975 | − | 0.230319i | 0.791847 | − | 0.610719i | \(-0.209120\pi\) |
−0.924822 | + | 0.380400i | \(0.875786\pi\) | |||||||
\(972\) | −4.96763e7 | −1.68649 | ||||||||
\(973\) | 2.71760e7 | 0.920245 | ||||||||
\(974\) | −3.56989e7 | − | 6.18323e7i | −1.20575 | − | 2.08842i | ||||
\(975\) | 4.24880e6 | + | 2.45305e6i | 0.143138 | + | 0.0826408i | ||||
\(976\) | 9.73216e7i | 3.27028i | ||||||||
\(977\) | 4.13017e7 | − | 2.38456e7i | 1.38430 | − | 0.799229i | 0.391639 | − | 0.920119i | \(-0.371908\pi\) |
0.992666 | + | 0.120890i | \(0.0385749\pi\) | |||||||
\(978\) | −2.08510e7 | − | 3.61150e7i | −0.697075 | − | 1.20737i | ||||
\(979\) | −3.67274e6 | + | 2.12046e6i | −0.122471 | + | 0.0707086i | ||||
\(980\) | −1.77664e8 | − | 1.02574e8i | −5.90926 | − | 3.41171i | ||||
\(981\) | 1.10793e7 | + | 6.39664e6i | 0.367570 | + | 0.212217i | ||||
\(982\) | 2.00979e7 | − | 1.16036e7i | 0.665078 | − | 0.383983i | ||||
\(983\) | 2.76193e7 | + | 4.78381e7i | 0.911653 | + | 1.57903i | 0.811729 | + | 0.584034i | \(0.198527\pi\) |
0.0999238 | + | 0.994995i | \(0.468140\pi\) | |||||||
\(984\) | 3.67697e7 | − | 2.12290e7i | 1.21061 | − | 0.698943i | ||||
\(985\) | 2.63519e7i | 0.865410i | ||||||||
\(986\) | −3.78037e7 | − | 2.18260e7i | −1.23835 | − | 0.714960i | ||||
\(987\) | 1.04788e7 | + | 1.81499e7i | 0.342390 | + | 0.593036i | ||||
\(988\) | −3.03868e7 | −0.990360 | ||||||||
\(989\) | 1.68830e7 | 0.548856 | ||||||||
\(990\) | −4.53866e6 | − | 7.86119e6i | −0.147177 | − | 0.254918i | ||||
\(991\) | 2.55340e7i | 0.825913i | 0.910751 | + | 0.412957i | \(0.135504\pi\) | ||||
−0.910751 | + | 0.412957i | \(0.864496\pi\) | |||||||
\(992\) | −2.84374e7 | + | 4.92550e7i | −0.917510 | + | 1.58917i | ||||
\(993\) | 9.56784e6i | 0.307922i | ||||||||
\(994\) | 4.20864e7 | + | 2.42986e7i | 1.35107 | + | 0.780038i | ||||
\(995\) | −2.74106e7 | + | 4.74766e7i | −0.877730 | + | 1.52027i | ||||
\(996\) | −4.56021e7 | + | 7.89851e7i | −1.45659 | + | 2.52288i | ||||
\(997\) | 1.49861e7 | − | 8.65222e6i | 0.477474 | − | 0.275670i | −0.241889 | − | 0.970304i | \(-0.577767\pi\) |
0.719363 | + | 0.694634i | \(0.244434\pi\) | |||||||
\(998\) | 3.29104e7 | 1.04594 | ||||||||
\(999\) | −3.33280e7 | + | 8.22370e6i | −1.05656 | + | 0.260708i |
(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 | 37.6.e.a.11.2 | ✓ | 32 | |
37.27 | even | 6 | inner | 37.6.e.a.27.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.e.a.11.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
37.6.e.a.27.2 | yes | 32 | 37.27 | even | 6 | inner |