Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,5,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.c (of order \(2\), degree \(1\), 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: | \(31.0109889252\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 20 x^{14} - 108 x^{13} + 492 x^{12} - 2160 x^{11} + 7360 x^{10} - 39552 x^{9} + \cdots + 4294967296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.9 | ||
Root | \(-3.04390 + 2.59512i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.5.c.b.151.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.725488 | − | 3.93366i | −0.181372 | − | 0.983415i | ||||
\(3\) | − | 5.19615i | − | 0.577350i | ||||||
\(4\) | −14.9473 | + | 5.70765i | −0.934208 | + | 0.356728i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −20.4399 | + | 3.76975i | −0.567775 | + | 0.104715i | ||||
\(7\) | − | 36.7329i | − | 0.749650i | −0.927095 | − | 0.374825i | \(-0.877703\pi\) | ||
0.927095 | − | 0.374825i | \(-0.122297\pi\) | |||||||
\(8\) | 33.2960 | + | 54.6569i | 0.520251 | + | 0.854014i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 156.989i | 1.29743i | 0.761032 | + | 0.648715i | \(0.224693\pi\) | ||||
−0.761032 | + | 0.648715i | \(0.775307\pi\) | |||||||
\(12\) | 29.6578 | + | 77.6686i | 0.205957 | + | 0.539365i | ||||
\(13\) | 62.1869 | 0.367970 | 0.183985 | − | 0.982929i | \(-0.441100\pi\) | ||||
0.183985 | + | 0.982929i | \(0.441100\pi\) | |||||||
\(14\) | −144.495 | + | 26.6493i | −0.737217 | + | 0.135966i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 190.846 | − | 170.628i | 0.745490 | − | 0.666516i | ||||
\(17\) | 306.493 | 1.06053 | 0.530264 | − | 0.847832i | \(-0.322093\pi\) | ||||
0.530264 | + | 0.847832i | \(0.322093\pi\) | |||||||
\(18\) | 19.5882 | + | 106.209i | 0.0604574 | + | 0.327805i | ||||
\(19\) | 242.784i | 0.672532i | 0.941767 | + | 0.336266i | \(0.109164\pi\) | ||||
−0.941767 | + | 0.336266i | \(0.890836\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −190.870 | −0.432811 | ||||||||
\(22\) | 617.541 | − | 113.894i | 1.27591 | − | 0.235317i | ||||
\(23\) | 571.211i | 1.07979i | 0.841731 | + | 0.539897i | \(0.181537\pi\) | ||||
−0.841731 | + | 0.539897i | \(0.818463\pi\) | |||||||
\(24\) | 284.005 | − | 173.011i | 0.493065 | − | 0.300367i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −45.1158 | − | 244.622i | −0.0667394 | − | 0.361867i | ||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | 209.658 | + | 549.059i | 0.267421 | + | 0.700330i | ||||
\(29\) | −266.538 | −0.316930 | −0.158465 | − | 0.987365i | \(-0.550654\pi\) | ||||
−0.158465 | + | 0.987365i | \(0.550654\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 759.271i | − | 0.790084i | −0.918663 | − | 0.395042i | \(-0.870730\pi\) | ||
0.918663 | − | 0.395042i | \(-0.129270\pi\) | |||||||
\(32\) | −809.649 | − | 626.932i | −0.790673 | − | 0.612239i | ||||
\(33\) | 815.738 | 0.749071 | ||||||||
\(34\) | −222.357 | − | 1205.64i | −0.192350 | − | 1.04294i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 403.578 | − | 154.106i | 0.311403 | − | 0.118909i | ||||
\(37\) | 1214.97 | 0.887490 | 0.443745 | − | 0.896153i | \(-0.353650\pi\) | ||||
0.443745 | + | 0.896153i | \(0.353650\pi\) | |||||||
\(38\) | 955.029 | − | 176.137i | 0.661377 | − | 0.121978i | ||||
\(39\) | − | 323.132i | − | 0.212447i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2677.60 | 1.59286 | 0.796431 | − | 0.604730i | \(-0.206719\pi\) | ||||
0.796431 | + | 0.604730i | \(0.206719\pi\) | |||||||
\(42\) | 138.474 | + | 750.816i | 0.0784998 | + | 0.425633i | ||||
\(43\) | 2635.37i | 1.42530i | 0.701522 | + | 0.712648i | \(0.252504\pi\) | ||||
−0.701522 | + | 0.712648i | \(0.747496\pi\) | |||||||
\(44\) | −896.037 | − | 2346.57i | −0.462829 | − | 1.21207i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2246.95 | − | 414.407i | 1.06188 | − | 0.195844i | ||||
\(47\) | − | 2374.46i | − | 1.07490i | −0.843295 | − | 0.537451i | \(-0.819387\pi\) | ||
0.843295 | − | 0.537451i | \(-0.180613\pi\) | |||||||
\(48\) | −886.610 | − | 991.663i | −0.384813 | − | 0.430409i | ||||
\(49\) | 1051.70 | 0.438024 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1592.58i | − | 0.612297i | ||||||
\(52\) | −929.528 | + | 354.941i | −0.343760 | + | 0.131265i | ||||
\(53\) | 1396.48 | 0.497143 | 0.248572 | − | 0.968613i | \(-0.420039\pi\) | ||||
0.248572 | + | 0.968613i | \(0.420039\pi\) | |||||||
\(54\) | 551.877 | − | 101.783i | 0.189258 | − | 0.0349051i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2007.70 | − | 1223.06i | 0.640212 | − | 0.390006i | ||||
\(57\) | 1261.54 | 0.388286 | ||||||||
\(58\) | 193.370 | + | 1048.47i | 0.0574822 | + | 0.311673i | ||||
\(59\) | − | 2901.75i | − | 0.833597i | −0.908999 | − | 0.416798i | \(-0.863152\pi\) | ||
0.908999 | − | 0.416798i | \(-0.136848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4786.97 | −1.28647 | −0.643237 | − | 0.765667i | \(-0.722409\pi\) | ||||
−0.643237 | + | 0.765667i | \(0.722409\pi\) | |||||||
\(62\) | −2986.71 | + | 550.842i | −0.776980 | + | 0.143299i | ||||
\(63\) | 991.788i | 0.249883i | ||||||||
\(64\) | −1878.75 | + | 3639.72i | −0.458678 | + | 0.888602i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −591.809 | − | 3208.84i | −0.135861 | − | 0.736647i | ||||
\(67\) | − | 4656.43i | − | 1.03730i | −0.854987 | − | 0.518649i | \(-0.826435\pi\) | ||
0.854987 | − | 0.518649i | \(-0.173565\pi\) | |||||||
\(68\) | −4581.25 | + | 1749.35i | −0.990755 | + | 0.378320i | ||||
\(69\) | 2968.10 | 0.623419 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6767.57i | − | 1.34251i | −0.741228 | − | 0.671253i | \(-0.765756\pi\) | ||
0.741228 | − | 0.671253i | \(-0.234244\pi\) | |||||||
\(72\) | −898.993 | − | 1475.74i | −0.173417 | − | 0.284671i | ||||
\(73\) | −6581.94 | −1.23512 | −0.617559 | − | 0.786525i | \(-0.711878\pi\) | ||||
−0.617559 | + | 0.786525i | \(0.711878\pi\) | |||||||
\(74\) | −881.450 | − | 4779.29i | −0.160966 | − | 0.872771i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1385.72 | − | 3628.97i | −0.239911 | − | 0.628285i | ||||
\(77\) | 5766.65 | 0.972618 | ||||||||
\(78\) | −1271.09 | + | 234.429i | −0.208924 | + | 0.0385320i | ||||
\(79\) | 8545.74i | 1.36929i | 0.728876 | + | 0.684645i | \(0.240043\pi\) | ||||
−0.728876 | + | 0.684645i | \(0.759957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −1942.57 | − | 10532.8i | −0.288901 | − | 1.56644i | ||||
\(83\) | 2173.65i | 0.315525i | 0.987477 | + | 0.157763i | \(0.0504281\pi\) | ||||
−0.987477 | + | 0.157763i | \(0.949572\pi\) | |||||||
\(84\) | 2852.99 | − | 1089.42i | 0.404336 | − | 0.154396i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10366.6 | − | 1911.93i | 1.40166 | − | 0.258509i | ||||
\(87\) | 1384.97i | 0.182980i | ||||||||
\(88\) | −8580.52 | + | 5227.11i | −1.10802 | + | 0.674988i | ||||
\(89\) | 6633.68 | 0.837480 | 0.418740 | − | 0.908106i | \(-0.362472\pi\) | ||||
0.418740 | + | 0.908106i | \(0.362472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2284.30i | − | 0.275849i | ||||||
\(92\) | −3260.27 | − | 8538.08i | −0.385192 | − | 1.00875i | ||||
\(93\) | −3945.29 | −0.456155 | ||||||||
\(94\) | −9340.31 | + | 1722.64i | −1.05707 | + | 0.194957i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3257.64 | + | 4207.06i | −0.353476 | + | 0.456495i | ||||
\(97\) | 15704.1 | 1.66905 | 0.834525 | − | 0.550970i | \(-0.185742\pi\) | ||||
0.834525 | + | 0.550970i | \(0.185742\pi\) | |||||||
\(98\) | −762.993 | − | 4137.01i | −0.0794454 | − | 0.430759i | ||||
\(99\) | − | 4238.70i | − | 0.432476i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13188.7 | −1.29288 | −0.646440 | − | 0.762965i | \(-0.723743\pi\) | ||||
−0.646440 | + | 0.762965i | \(0.723743\pi\) | |||||||
\(102\) | −6264.68 | + | 1155.40i | −0.602141 | + | 0.111054i | ||||
\(103\) | − | 2187.77i | − | 0.206218i | −0.994670 | − | 0.103109i | \(-0.967121\pi\) | ||
0.994670 | − | 0.103109i | \(-0.0328791\pi\) | |||||||
\(104\) | 2070.58 | + | 3398.94i | 0.191436 | + | 0.314251i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1013.13 | − | 5493.26i | −0.0901680 | − | 0.488898i | ||||
\(107\) | 12415.4i | 1.08441i | 0.840246 | + | 0.542205i | \(0.182410\pi\) | ||||
−0.840246 | + | 0.542205i | \(0.817590\pi\) | |||||||
\(108\) | −800.761 | − | 2097.05i | −0.0686523 | − | 0.179788i | ||||
\(109\) | 13504.8 | 1.13667 | 0.568336 | − | 0.822797i | \(-0.307588\pi\) | ||||
0.568336 | + | 0.822797i | \(0.307588\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 6313.19i | − | 0.512393i | ||||||
\(112\) | −6267.66 | − | 7010.31i | −0.499654 | − | 0.558857i | ||||
\(113\) | 24496.4 | 1.91843 | 0.959213 | − | 0.282683i | \(-0.0912245\pi\) | ||||
0.959213 | + | 0.282683i | \(0.0912245\pi\) | |||||||
\(114\) | −915.234 | − | 4962.48i | −0.0704243 | − | 0.381846i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3984.03 | − | 1521.30i | 0.296079 | − | 0.113058i | ||||
\(117\) | −1679.05 | −0.122657 | ||||||||
\(118\) | −11414.5 | + | 2105.19i | −0.819771 | + | 0.151191i | ||||
\(119\) | − | 11258.4i | − | 0.795026i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10004.5 | −0.683322 | ||||||||
\(122\) | 3472.89 | + | 18830.3i | 0.233330 | + | 1.26514i | ||||
\(123\) | − | 13913.2i | − | 0.919639i | ||||||
\(124\) | 4333.65 | + | 11349.1i | 0.281845 | + | 0.738103i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3901.35 | − | 719.530i | 0.245739 | − | 0.0453219i | ||||
\(127\) | 6927.31i | 0.429494i | 0.976670 | + | 0.214747i | \(0.0688927\pi\) | ||||
−0.976670 | + | 0.214747i | \(0.931107\pi\) | |||||||
\(128\) | 15680.4 | + | 4749.78i | 0.957056 | + | 0.289903i | ||||
\(129\) | 13693.8 | 0.822895 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1893.13i | − | 0.110316i | −0.998478 | − | 0.0551579i | \(-0.982434\pi\) | ||
0.998478 | − | 0.0551579i | \(-0.0175662\pi\) | |||||||
\(132\) | −12193.1 | + | 4655.95i | −0.699788 | + | 0.267215i | ||||
\(133\) | 8918.15 | 0.504164 | ||||||||
\(134\) | −18316.8 | + | 3378.19i | −1.02009 | + | 0.188137i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10205.0 | + | 16751.9i | 0.551741 | + | 0.905706i | ||||
\(137\) | 35998.2 | 1.91796 | 0.958981 | − | 0.283470i | \(-0.0914857\pi\) | ||||
0.958981 | + | 0.283470i | \(0.0914857\pi\) | |||||||
\(138\) | −2153.32 | − | 11675.5i | −0.113071 | − | 0.613079i | ||||
\(139\) | 1899.55i | 0.0983155i | 0.998791 | + | 0.0491577i | \(0.0156537\pi\) | ||||
−0.998791 | + | 0.0491577i | \(0.984346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12338.0 | −0.620595 | ||||||||
\(142\) | −26621.3 | + | 4909.80i | −1.32024 | + | 0.243493i | ||||
\(143\) | 9762.65i | 0.477414i | ||||||||
\(144\) | −5152.83 | + | 4606.96i | −0.248497 | + | 0.222172i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4775.12 | + | 25891.1i | 0.224016 | + | 1.21463i | ||||
\(147\) | − | 5464.77i | − | 0.252893i | ||||||
\(148\) | −18160.6 | + | 6934.64i | −0.829101 | + | 0.316593i | ||||
\(149\) | 6118.77 | 0.275608 | 0.137804 | − | 0.990460i | \(-0.455996\pi\) | ||||
0.137804 | + | 0.990460i | \(0.455996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30282.1i | 1.32810i | 0.747687 | + | 0.664052i | \(0.231165\pi\) | ||||
−0.747687 | + | 0.664052i | \(0.768835\pi\) | |||||||
\(152\) | −13269.8 | + | 8083.74i | −0.574351 | + | 0.349885i | ||||
\(153\) | −8275.31 | −0.353510 | ||||||||
\(154\) | −4183.64 | − | 22684.0i | −0.176406 | − | 0.956487i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1844.33 | + | 4829.97i | 0.0757859 | + | 0.198470i | ||||
\(157\) | 11389.8 | 0.462078 | 0.231039 | − | 0.972945i | \(-0.425788\pi\) | ||||
0.231039 | + | 0.972945i | \(0.425788\pi\) | |||||||
\(158\) | 33616.0 | − | 6199.84i | 1.34658 | − | 0.248351i | ||||
\(159\) | − | 7256.30i | − | 0.287026i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20982.2 | 0.809468 | ||||||||
\(162\) | −528.881 | − | 2867.64i | −0.0201525 | − | 0.109268i | ||||
\(163\) | − | 10601.7i | − | 0.399027i | −0.979895 | − | 0.199513i | \(-0.936064\pi\) | ||
0.979895 | − | 0.199513i | \(-0.0639361\pi\) | |||||||
\(164\) | −40023.0 | + | 15282.8i | −1.48806 | + | 0.568218i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8550.41 | − | 1576.96i | 0.310292 | − | 0.0572275i | ||||
\(167\) | 15333.5i | 0.549803i | 0.961472 | + | 0.274902i | \(0.0886453\pi\) | ||||
−0.961472 | + | 0.274902i | \(0.911355\pi\) | |||||||
\(168\) | −6355.20 | − | 10432.3i | −0.225170 | − | 0.369626i | ||||
\(169\) | −24693.8 | −0.864598 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6555.17i | − | 0.224177i | ||||||
\(172\) | −15041.8 | − | 39391.8i | −0.508443 | − | 1.33152i | ||||
\(173\) | 37712.5 | 1.26007 | 0.630033 | − | 0.776568i | \(-0.283041\pi\) | ||||
0.630033 | + | 0.776568i | \(0.283041\pi\) | |||||||
\(174\) | 5448.01 | − | 1004.78i | 0.179945 | − | 0.0331874i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 26786.7 | + | 29960.6i | 0.864758 | + | 0.967221i | ||||
\(177\) | −15077.9 | −0.481277 | ||||||||
\(178\) | −4812.65 | − | 26094.6i | −0.151895 | − | 0.823590i | ||||
\(179\) | 26116.7i | 0.815101i | 0.913183 | + | 0.407551i | \(0.133617\pi\) | ||||
−0.913183 | + | 0.407551i | \(0.866383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −44004.0 | −1.34318 | −0.671591 | − | 0.740922i | \(-0.734389\pi\) | ||||
−0.671591 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(182\) | −8985.66 | + | 1657.23i | −0.271273 | + | 0.0500312i | ||||
\(183\) | 24873.8i | 0.742746i | ||||||||
\(184\) | −31220.6 | + | 19019.1i | −0.922158 | + | 0.561763i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2862.26 | + | 15519.4i | 0.0827338 | + | 0.448590i | ||||
\(187\) | 48116.0i | 1.37596i | ||||||||
\(188\) | 13552.6 | + | 35491.8i | 0.383448 | + | 1.00418i | ||||
\(189\) | 5153.48 | 0.144270 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 34103.8i | 0.934839i | 0.884036 | + | 0.467419i | \(0.154816\pi\) | ||||
−0.884036 | + | 0.467419i | \(0.845184\pi\) | |||||||
\(192\) | 18912.5 | + | 9762.25i | 0.513035 | + | 0.264818i | ||||
\(193\) | 27574.1 | 0.740263 | 0.370132 | − | 0.928979i | \(-0.379313\pi\) | ||||
0.370132 | + | 0.928979i | \(0.379313\pi\) | |||||||
\(194\) | −11393.1 | − | 61774.5i | −0.302719 | − | 1.64137i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15720.1 | + | 6002.71i | −0.409206 | + | 0.156255i | ||||
\(197\) | 45162.5 | 1.16371 | 0.581856 | − | 0.813292i | \(-0.302327\pi\) | ||||
0.581856 | + | 0.813292i | \(0.302327\pi\) | |||||||
\(198\) | −16673.6 | + | 3075.13i | −0.425304 | + | 0.0784391i | ||||
\(199\) | 56574.1i | 1.42860i | 0.699838 | + | 0.714302i | \(0.253255\pi\) | ||||
−0.699838 | + | 0.714302i | \(0.746745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24195.5 | −0.598885 | ||||||||
\(202\) | 9568.23 | + | 51879.7i | 0.234492 | + | 1.27144i | ||||
\(203\) | 9790.71i | 0.237587i | ||||||||
\(204\) | 9089.90 | + | 23804.9i | 0.218423 | + | 0.572013i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8605.94 | + | 1587.20i | −0.202798 | + | 0.0374023i | ||||
\(207\) | − | 15422.7i | − | 0.359931i | ||||||
\(208\) | 11868.1 | − | 10610.8i | 0.274318 | − | 0.245258i | ||||
\(209\) | −38114.4 | −0.872562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 75965.3i | 1.70628i | 0.521681 | + | 0.853140i | \(0.325305\pi\) | ||||
−0.521681 | + | 0.853140i | \(0.674695\pi\) | |||||||
\(212\) | −20873.6 | + | 7970.59i | −0.464436 | + | 0.177345i | ||||
\(213\) | −35165.3 | −0.775096 | ||||||||
\(214\) | 48838.0 | − | 9007.23i | 1.06642 | − | 0.196682i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7668.15 | + | 4671.31i | −0.164355 | + | 0.100122i | ||||
\(217\) | −27890.2 | −0.592287 | ||||||||
\(218\) | −9797.57 | − | 53123.2i | −0.206160 | − | 1.11782i | ||||
\(219\) | 34200.8i | 0.713096i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19059.8 | 0.390242 | ||||||||
\(222\) | −24833.9 | + | 4580.15i | −0.503895 | + | 0.0929338i | ||||
\(223\) | − | 92718.2i | − | 1.86447i | −0.361854 | − | 0.932235i | \(-0.617856\pi\) | ||
0.361854 | − | 0.932235i | \(-0.382144\pi\) | |||||||
\(224\) | −23029.0 | + | 29740.7i | −0.458965 | + | 0.592728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17771.8 | − | 96360.4i | −0.347949 | − | 1.88661i | ||||
\(227\) | − | 35666.1i | − | 0.692155i | −0.938206 | − | 0.346078i | \(-0.887513\pi\) | ||
0.938206 | − | 0.346078i | \(-0.112487\pi\) | |||||||
\(228\) | −18856.7 | + | 7200.44i | −0.362740 | + | 0.138513i | ||||
\(229\) | 103760. | 1.97861 | 0.989307 | − | 0.145850i | \(-0.0465916\pi\) | ||||
0.989307 | + | 0.145850i | \(0.0465916\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 29964.4i | − | 0.561541i | ||||||
\(232\) | −8874.66 | − | 14568.1i | −0.164883 | − | 0.270662i | ||||
\(233\) | 17612.7 | 0.324425 | 0.162213 | − | 0.986756i | \(-0.448137\pi\) | ||||
0.162213 | + | 0.986756i | \(0.448137\pi\) | |||||||
\(234\) | 1218.13 | + | 6604.79i | 0.0222465 | + | 0.120622i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16562.2 | + | 43373.4i | 0.297367 | + | 0.778753i | ||||
\(237\) | 44405.0 | 0.790560 | ||||||||
\(238\) | −44286.6 | + | 8167.81i | −0.781840 | + | 0.144196i | ||||
\(239\) | − | 57194.0i | − | 1.00128i | −0.865656 | − | 0.500639i | \(-0.833098\pi\) | ||
0.865656 | − | 0.500639i | \(-0.166902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −32787.4 | −0.564512 | −0.282256 | − | 0.959339i | \(-0.591083\pi\) | ||||
−0.282256 | + | 0.959339i | \(0.591083\pi\) | |||||||
\(242\) | 7258.16 | + | 39354.4i | 0.123936 | + | 0.671989i | ||||
\(243\) | − | 3788.00i | − | 0.0641500i | ||||||
\(244\) | 71552.4 | − | 27322.3i | 1.20183 | − | 0.458921i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −54729.8 | + | 10093.9i | −0.904386 | + | 0.166797i | ||||
\(247\) | 15098.0i | 0.247471i | ||||||||
\(248\) | 41499.4 | − | 25280.7i | 0.674743 | − | 0.411042i | ||||
\(249\) | 11294.6 | 0.182169 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 28803.4i | − | 0.457190i | −0.973522 | − | 0.228595i | \(-0.926587\pi\) | ||
0.973522 | − | 0.228595i | \(-0.0734131\pi\) | |||||||
\(252\) | −5660.77 | − | 14824.6i | −0.0891404 | − | 0.233443i | ||||
\(253\) | −89673.7 | −1.40096 | ||||||||
\(254\) | 27249.7 | − | 5025.69i | 0.422371 | − | 0.0778983i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7308.04 | − | 65127.3i | 0.111512 | − | 0.993763i | ||||
\(257\) | −97466.3 | −1.47567 | −0.737833 | − | 0.674983i | \(-0.764151\pi\) | ||||
−0.737833 | + | 0.674983i | \(0.764151\pi\) | |||||||
\(258\) | −9934.69 | − | 53866.7i | −0.149250 | − | 0.809247i | ||||
\(259\) | − | 44629.5i | − | 0.665308i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7196.53 | 0.105643 | ||||||||
\(262\) | −7446.93 | + | 1373.44i | −0.108486 | + | 0.0200082i | ||||
\(263\) | 82950.9i | 1.19925i | 0.800281 | + | 0.599625i | \(0.204684\pi\) | ||||
−0.800281 | + | 0.599625i | \(0.795316\pi\) | |||||||
\(264\) | 27160.9 | + | 44585.7i | 0.389705 | + | 0.639717i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6470.01 | − | 35081.0i | −0.0914412 | − | 0.495802i | ||||
\(267\) | − | 34469.6i | − | 0.483519i | ||||||
\(268\) | 26577.3 | + | 69601.3i | 0.370033 | + | 0.969053i | ||||
\(269\) | −76939.2 | −1.06327 | −0.531634 | − | 0.846974i | \(-0.678422\pi\) | ||||
−0.531634 | + | 0.846974i | \(0.678422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 73991.7i | − | 1.00750i | −0.863850 | − | 0.503749i | \(-0.831954\pi\) | ||
0.863850 | − | 0.503749i | \(-0.168046\pi\) | |||||||
\(272\) | 58492.8 | − | 52296.3i | 0.790614 | − | 0.706860i | ||||
\(273\) | −11869.6 | −0.159261 | ||||||||
\(274\) | −26116.3 | − | 141605.i | −0.347865 | − | 1.88615i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −44365.1 | + | 16940.9i | −0.582403 | + | 0.222391i | ||||
\(277\) | −40327.2 | −0.525580 | −0.262790 | − | 0.964853i | \(-0.584643\pi\) | ||||
−0.262790 | + | 0.964853i | \(0.584643\pi\) | |||||||
\(278\) | 7472.19 | − | 1378.10i | 0.0966849 | − | 0.0178317i | ||||
\(279\) | 20500.3i | 0.263361i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 39798.8 | 0.504031 | 0.252016 | − | 0.967723i | \(-0.418907\pi\) | ||||
0.252016 | + | 0.967723i | \(0.418907\pi\) | |||||||
\(282\) | 8951.11 | + | 48533.7i | 0.112559 | + | 0.610302i | ||||
\(283\) | − | 29271.4i | − | 0.365486i | −0.983161 | − | 0.182743i | \(-0.941502\pi\) | ||
0.983161 | − | 0.182743i | \(-0.0584976\pi\) | |||||||
\(284\) | 38626.9 | + | 101157.i | 0.478909 | + | 1.25418i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 38402.9 | − | 7082.69i | 0.469496 | − | 0.0865896i | ||||
\(287\) | − | 98356.0i | − | 1.19409i | ||||||
\(288\) | 21860.5 | + | 16927.2i | 0.263558 | + | 0.204080i | ||||
\(289\) | 10416.9 | 0.124722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 81600.8i | − | 0.963626i | ||||||
\(292\) | 98382.5 | − | 37567.4i | 1.15386 | − | 0.440601i | ||||
\(293\) | 14569.2 | 0.169707 | 0.0848535 | − | 0.996393i | \(-0.472958\pi\) | ||||
0.0848535 | + | 0.996393i | \(0.472958\pi\) | |||||||
\(294\) | −21496.5 | + | 3964.63i | −0.248699 | + | 0.0458678i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 40453.8 | + | 66406.7i | 0.461718 | + | 0.757929i | ||||
\(297\) | −22024.9 | −0.249690 | ||||||||
\(298\) | −4439.09 | − | 24069.1i | −0.0499875 | − | 0.271037i | ||||
\(299\) | 35521.8i | 0.397331i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 96804.8 | 1.06847 | ||||||||
\(302\) | 119119. | − | 21969.3i | 1.30608 | − | 0.240881i | ||||
\(303\) | 68530.3i | 0.746445i | ||||||||
\(304\) | 41425.8 | + | 46334.2i | 0.448253 | + | 0.501366i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6003.64 | + | 32552.2i | 0.0641168 | + | 0.347647i | ||||
\(307\) | 103447.i | 1.09759i | 0.835956 | + | 0.548796i | \(0.184914\pi\) | ||||
−0.835956 | + | 0.548796i | \(0.815086\pi\) | |||||||
\(308\) | −86196.1 | + | 32914.0i | −0.908628 | + | 0.346960i | ||||
\(309\) | −11368.0 | −0.119060 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 140701.i | − | 1.45471i | −0.686262 | − | 0.727354i | \(-0.740750\pi\) | ||
0.686262 | − | 0.727354i | \(-0.259250\pi\) | |||||||
\(312\) | 17661.4 | − | 10759.0i | 0.181433 | − | 0.110526i | ||||
\(313\) | −100063. | −1.02138 | −0.510688 | − | 0.859766i | \(-0.670609\pi\) | ||||
−0.510688 | + | 0.859766i | \(0.670609\pi\) | |||||||
\(314\) | −8263.14 | − | 44803.4i | −0.0838080 | − | 0.454414i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48776.1 | − | 127736.i | −0.488464 | − | 1.27920i | ||||
\(317\) | 15226.6 | 0.151525 | 0.0757623 | − | 0.997126i | \(-0.475861\pi\) | ||||
0.0757623 | + | 0.997126i | \(0.475861\pi\) | |||||||
\(318\) | −28543.8 | + | 5264.36i | −0.282265 | + | 0.0520585i | ||||
\(319\) | − | 41843.5i | − | 0.411194i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 64512.3 | 0.626084 | ||||||||
\(322\) | −15222.3 | − | 82536.8i | −0.146815 | − | 0.796042i | ||||
\(323\) | 74411.5i | 0.713239i | ||||||||
\(324\) | −10896.6 | + | 4160.87i | −0.103801 | + | 0.0396364i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −41703.6 | + | 7691.44i | −0.392409 | + | 0.0723723i | ||||
\(327\) | − | 70172.9i | − | 0.656257i | ||||||
\(328\) | 89153.5 | + | 146349.i | 0.828687 | + | 1.36033i | ||||
\(329\) | −87220.7 | −0.805801 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 174253.i | 1.59047i | 0.606304 | + | 0.795233i | \(0.292652\pi\) | ||||
−0.606304 | + | 0.795233i | \(0.707348\pi\) | |||||||
\(332\) | −12406.4 | − | 32490.3i | −0.112557 | − | 0.294766i | ||||
\(333\) | −32804.3 | −0.295830 | ||||||||
\(334\) | 60316.6 | − | 11124.2i | 0.540684 | − | 0.0997189i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −36426.6 | + | 32567.7i | −0.322656 | + | 0.288476i | ||||
\(337\) | −202345. | −1.78170 | −0.890848 | − | 0.454302i | \(-0.849889\pi\) | ||||
−0.890848 | + | 0.454302i | \(0.849889\pi\) | |||||||
\(338\) | 17915.1 | + | 97136.9i | 0.156814 | + | 0.850259i | ||||
\(339\) | − | 127287.i | − | 1.10760i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 119197. | 1.02508 | ||||||||
\(342\) | −25785.8 | + | 4755.70i | −0.220459 | + | 0.0406595i | ||||
\(343\) | − | 126827.i | − | 1.07802i | ||||||
\(344\) | −144041. | + | 87747.4i | −1.21722 | + | 0.741511i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27360.0 | − | 148348.i | −0.228541 | − | 1.23917i | ||||
\(347\) | − | 106576.i | − | 0.885115i | −0.896740 | − | 0.442558i | \(-0.854071\pi\) | ||
0.896740 | − | 0.442558i | \(-0.145929\pi\) | |||||||
\(348\) | −7904.93 | − | 20701.6i | −0.0652739 | − | 0.170941i | ||||
\(349\) | −192354. | −1.57925 | −0.789624 | − | 0.613590i | \(-0.789725\pi\) | ||||
−0.789624 | + | 0.613590i | \(0.789725\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8724.57i | 0.0708158i | ||||||||
\(352\) | 98421.4 | − | 127106.i | 0.794336 | − | 1.02584i | ||||
\(353\) | −76180.9 | −0.611360 | −0.305680 | − | 0.952134i | \(-0.598884\pi\) | ||||
−0.305680 | + | 0.952134i | \(0.598884\pi\) | |||||||
\(354\) | 10938.9 | + | 59311.4i | 0.0872902 | + | 0.473295i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −99155.8 | + | 37862.7i | −0.782380 | + | 0.298752i | ||||
\(357\) | −58500.2 | −0.459008 | ||||||||
\(358\) | 102734. | − | 18947.3i | 0.801582 | − | 0.147837i | ||||
\(359\) | − | 169799.i | − | 1.31749i | −0.752368 | − | 0.658743i | \(-0.771088\pi\) | ||
0.752368 | − | 0.658743i | \(-0.228912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 71377.0 | 0.547701 | ||||||||
\(362\) | 31924.4 | + | 173097.i | 0.243616 | + | 1.32091i | ||||
\(363\) | 51985.0i | 0.394516i | ||||||||
\(364\) | 13038.0 | + | 34144.2i | 0.0984029 | + | 0.257700i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 97845.1 | − | 18045.7i | 0.730427 | − | 0.134713i | ||||
\(367\) | − | 7980.18i | − | 0.0592489i | −0.999561 | − | 0.0296245i | \(-0.990569\pi\) | ||
0.999561 | − | 0.0296245i | \(-0.00943114\pi\) | |||||||
\(368\) | 97464.6 | + | 109013.i | 0.719700 | + | 0.804976i | ||||
\(369\) | −72295.2 | −0.530954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 51296.6i | − | 0.372684i | ||||||
\(372\) | 58971.5 | − | 22518.3i | 0.426144 | − | 0.162723i | ||||
\(373\) | 259277. | 1.86357 | 0.931786 | − | 0.363007i | \(-0.118250\pi\) | ||||
0.931786 | + | 0.363007i | \(0.118250\pi\) | |||||||
\(374\) | 189272. | − | 34907.6i | 1.35314 | − | 0.249561i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 129780. | − | 79060.1i | 0.917981 | − | 0.559219i | ||||
\(377\) | −16575.2 | −0.116621 | ||||||||
\(378\) | −3738.79 | − | 20272.0i | −0.0261666 | − | 0.141878i | ||||
\(379\) | 11693.1i | 0.0814048i | 0.999171 | + | 0.0407024i | \(0.0129596\pi\) | ||||
−0.999171 | + | 0.0407024i | \(0.987040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35995.4 | 0.247969 | ||||||||
\(382\) | 134153. | − | 24741.9i | 0.919334 | − | 0.169554i | ||||
\(383\) | 34931.5i | 0.238133i | 0.992886 | + | 0.119067i | \(0.0379902\pi\) | ||||
−0.992886 | + | 0.119067i | \(0.962010\pi\) | |||||||
\(384\) | 24680.6 | − | 81477.8i | 0.167376 | − | 0.552557i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20004.7 | − | 108467.i | −0.134263 | − | 0.727986i | ||||
\(387\) | − | 71155.0i | − | 0.475098i | ||||||
\(388\) | −234734. | + | 89633.4i | −1.55924 | + | 0.595397i | ||||
\(389\) | 110218. | 0.728375 | 0.364187 | − | 0.931326i | \(-0.381347\pi\) | ||||
0.364187 | + | 0.931326i | \(0.381347\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 175072.i | 1.14515i | ||||||||
\(392\) | 35017.3 | + | 57482.4i | 0.227882 | + | 0.374079i | ||||
\(393\) | −9836.99 | −0.0636909 | ||||||||
\(394\) | −32764.9 | − | 177654.i | −0.211065 | − | 1.14441i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 24193.0 | + | 63357.3i | 0.154276 | + | 0.404023i | ||||
\(397\) | −44836.0 | −0.284476 | −0.142238 | − | 0.989832i | \(-0.545430\pi\) | ||||
−0.142238 | + | 0.989832i | \(0.545430\pi\) | |||||||
\(398\) | 222543. | − | 41043.9i | 1.40491 | − | 0.259109i | ||||
\(399\) | − | 46340.1i | − | 0.291079i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 183752. | 1.14273 | 0.571364 | − | 0.820697i | \(-0.306414\pi\) | ||||
0.571364 | + | 0.820697i | \(0.306414\pi\) | |||||||
\(402\) | 17553.6 | + | 95177.0i | 0.108621 | + | 0.588952i | ||||
\(403\) | − | 47216.7i | − | 0.290727i | ||||||
\(404\) | 197135. | − | 75276.3i | 1.20782 | − | 0.461206i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 38513.3 | − | 7103.05i | 0.233646 | − | 0.0430916i | ||||
\(407\) | 190738.i | 1.15146i | ||||||||
\(408\) | 87045.6 | − | 53026.7i | 0.522910 | − | 0.318548i | ||||
\(409\) | −116120. | −0.694160 | −0.347080 | − | 0.937836i | \(-0.612827\pi\) | ||||
−0.347080 | + | 0.937836i | \(0.612827\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 187052.i | − | 1.10734i | ||||||
\(412\) | 12487.0 | + | 32701.3i | 0.0735638 | + | 0.192651i | ||||
\(413\) | −106590. | −0.624906 | ||||||||
\(414\) | −60667.6 | + | 11189.0i | −0.353961 | + | 0.0652815i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −50349.5 | − | 38987.0i | −0.290944 | − | 0.225285i | ||||
\(417\) | 9870.37 | 0.0567625 | ||||||||
\(418\) | 27651.5 | + | 149929.i | 0.158258 | + | 0.858090i | ||||
\(419\) | 26586.3i | 0.151436i | 0.997129 | + | 0.0757181i | \(0.0241249\pi\) | ||||
−0.997129 | + | 0.0757181i | \(0.975875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −41926.6 | −0.236551 | −0.118276 | − | 0.992981i | \(-0.537737\pi\) | ||||
−0.118276 | + | 0.992981i | \(0.537737\pi\) | |||||||
\(422\) | 298822. | − | 55112.0i | 1.67798 | − | 0.309472i | ||||
\(423\) | 64110.4i | 0.358301i | ||||||||
\(424\) | 46497.1 | + | 76327.0i | 0.258639 | + | 0.424567i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 25512.1 | + | 138328.i | 0.140581 | + | 0.762241i | ||||
\(427\) | 175839.i | 0.964406i | ||||||||
\(428\) | −70862.7 | − | 185577.i | −0.386839 | − | 1.01306i | ||||
\(429\) | 50728.2 | 0.275635 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 258465.i | − | 1.39138i | −0.718340 | − | 0.695692i | \(-0.755098\pi\) | ||
0.718340 | − | 0.695692i | \(-0.244902\pi\) | |||||||
\(432\) | 23938.5 | + | 26774.9i | 0.128271 | + | 0.143470i | ||||
\(433\) | −35539.8 | −0.189557 | −0.0947784 | − | 0.995498i | \(-0.530214\pi\) | ||||
−0.0947784 | + | 0.995498i | \(0.530214\pi\) | |||||||
\(434\) | 20234.0 | + | 109711.i | 0.107424 | + | 0.582464i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −201861. | + | 77080.6i | −1.06189 | + | 0.405482i | ||||
\(437\) | −138681. | −0.726195 | ||||||||
\(438\) | 134534. | − | 24812.3i | 0.701269 | − | 0.129336i | ||||
\(439\) | 238795.i | 1.23907i | 0.784969 | + | 0.619535i | \(0.212679\pi\) | ||||
−0.784969 | + | 0.619535i | \(0.787321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −28395.8 | −0.146008 | ||||||||
\(442\) | −13827.7 | − | 74974.8i | −0.0707791 | − | 0.383770i | ||||
\(443\) | − | 133181.i | − | 0.678632i | −0.940672 | − | 0.339316i | \(-0.889804\pi\) | ||
0.940672 | − | 0.339316i | \(-0.110196\pi\) | |||||||
\(444\) | 36033.5 | + | 94365.4i | 0.182785 | + | 0.478682i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −364722. | + | 67266.0i | −1.83355 | + | 0.338163i | ||||
\(447\) | − | 31794.0i | − | 0.159122i | ||||||
\(448\) | 133697. | + | 69011.8i | 0.666141 | + | 0.343848i | ||||
\(449\) | 190392. | 0.944398 | 0.472199 | − | 0.881492i | \(-0.343460\pi\) | ||||
0.472199 | + | 0.881492i | \(0.343460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 420354.i | 2.06662i | ||||||||
\(452\) | −366156. | + | 139817.i | −1.79221 | + | 0.684356i | ||||
\(453\) | 157350. | 0.766781 | ||||||||
\(454\) | −140298. | + | 25875.3i | −0.680675 | + | 0.125538i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 42004.4 | + | 68951.9i | 0.202006 | + | 0.331602i | ||||
\(457\) | 4305.85 | 0.0206171 | 0.0103085 | − | 0.999947i | \(-0.496719\pi\) | ||||
0.0103085 | + | 0.999947i | \(0.496719\pi\) | |||||||
\(458\) | −75277.0 | − | 408158.i | −0.358865 | − | 1.94580i | ||||
\(459\) | 42999.8i | 0.204099i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −346295. | −1.62946 | −0.814730 | − | 0.579840i | \(-0.803115\pi\) | ||||
−0.814730 | + | 0.579840i | \(0.803115\pi\) | |||||||
\(462\) | −117870. | + | 21738.8i | −0.552228 | + | 0.101848i | ||||
\(463\) | 148212.i | 0.691388i | 0.938347 | + | 0.345694i | \(0.112357\pi\) | ||||
−0.938347 | + | 0.345694i | \(0.887643\pi\) | |||||||
\(464\) | −50867.6 | + | 45478.9i | −0.236268 | + | 0.211239i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12777.8 | − | 69282.4i | −0.0588417 | − | 0.319044i | ||||
\(467\) | − | 171205.i | − | 0.785023i | −0.919747 | − | 0.392512i | \(-0.871606\pi\) | ||
0.919747 | − | 0.392512i | \(-0.128394\pi\) | |||||||
\(468\) | 25097.2 | − | 9583.40i | 0.114587 | − | 0.0437550i | ||||
\(469\) | −171044. | −0.777611 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 59182.9i | − | 0.266781i | ||||||
\(472\) | 158601. | − | 96616.8i | 0.711903 | − | 0.433679i | ||||
\(473\) | −413724. | −1.84922 | ||||||||
\(474\) | −32215.3 | − | 174674.i | −0.143386 | − | 0.777448i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 64258.8 | + | 168283.i | 0.283608 | + | 0.742720i | ||||
\(477\) | −37704.9 | −0.165714 | ||||||||
\(478\) | −224982. | + | 41493.6i | −0.984672 | + | 0.181604i | ||||
\(479\) | 55603.3i | 0.242342i | 0.992632 | + | 0.121171i | \(0.0386650\pi\) | ||||
−0.992632 | + | 0.121171i | \(0.961335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 75555.4 | 0.326569 | ||||||||
\(482\) | 23786.9 | + | 128975.i | 0.102387 | + | 0.555150i | ||||
\(483\) | − | 109027.i | − | 0.467346i | ||||||
\(484\) | 149541. | − | 57102.3i | 0.638365 | − | 0.243760i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14900.7 | + | 2748.15i | −0.0630861 | + | 0.0116350i | ||||
\(487\) | − | 191414.i | − | 0.807077i | −0.914963 | − | 0.403538i | \(-0.867780\pi\) | ||
0.914963 | − | 0.403538i | \(-0.132220\pi\) | |||||||
\(488\) | −159387. | − | 261641.i | −0.669289 | − | 1.09867i | ||||
\(489\) | −55088.3 | −0.230378 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 234139.i | 0.971206i | 0.874179 | + | 0.485603i | \(0.161400\pi\) | ||||
−0.874179 | + | 0.485603i | \(0.838600\pi\) | |||||||
\(492\) | 79411.7 | + | 207966.i | 0.328061 | + | 0.859134i | ||||
\(493\) | −81692.0 | −0.336113 | ||||||||
\(494\) | 59390.2 | − | 10953.4i | 0.243367 | − | 0.0448844i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −129553. | − | 144903.i | −0.526604 | − | 0.589000i | ||||
\(497\) | −248592. | −1.00641 | ||||||||
\(498\) | −8194.13 | − | 44429.2i | −0.0330403 | − | 0.179147i | ||||
\(499\) | 397603.i | 1.59679i | 0.602133 | + | 0.798396i | \(0.294318\pi\) | ||||
−0.602133 | + | 0.798396i | \(0.705682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 79675.0 | 0.317429 | ||||||||
\(502\) | −113303. | + | 20896.5i | −0.449607 | + | 0.0829215i | ||||
\(503\) | − | 34902.1i | − | 0.137948i | −0.997618 | − | 0.0689741i | \(-0.978027\pi\) | ||
0.997618 | − | 0.0689741i | \(-0.0219726\pi\) | |||||||
\(504\) | −54208.0 | + | 33022.6i | −0.213404 | + | 0.130002i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 65057.3 | + | 352746.i | 0.254094 | + | 1.37772i | ||||
\(507\) | 128313.i | 0.499176i | ||||||||
\(508\) | −39538.7 | − | 103545.i | −0.153213 | − | 0.401237i | ||||
\(509\) | 14871.2 | 0.0573997 | 0.0286999 | − | 0.999588i | \(-0.490863\pi\) | ||||
0.0286999 | + | 0.999588i | \(0.490863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 241774.i | 0.925907i | ||||||||
\(512\) | −261490. | + | 18501.7i | −0.997506 | + | 0.0705785i | ||||
\(513\) | −34061.6 | −0.129429 | ||||||||
\(514\) | 70710.7 | + | 383399.i | 0.267645 | + | 1.45119i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −204686. | + | 78159.3i | −0.768755 | + | 0.293550i | ||||
\(517\) | 372764. | 1.39461 | ||||||||
\(518\) | −175557. | + | 32378.2i | −0.654273 | + | 0.120668i | ||||
\(519\) | − | 195960.i | − | 0.727500i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −396677. | −1.46137 | −0.730687 | − | 0.682713i | \(-0.760800\pi\) | ||||
−0.730687 | + | 0.682713i | \(0.760800\pi\) | |||||||
\(522\) | −5221.00 | − | 28308.7i | −0.0191607 | − | 0.103891i | ||||
\(523\) | − | 492462.i | − | 1.80040i | −0.435474 | − | 0.900201i | \(-0.643419\pi\) | ||
0.435474 | − | 0.900201i | \(-0.356581\pi\) | |||||||
\(524\) | 10805.3 | + | 28297.2i | 0.0393527 | + | 0.103058i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 326301. | − | 60179.9i | 1.17936 | − | 0.217511i | ||||
\(527\) | − | 232711.i | − | 0.837907i | ||||||
\(528\) | 155680. | − | 139188.i | 0.558425 | − | 0.499268i | ||||
\(529\) | −46440.6 | −0.165954 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 78347.2i | 0.277866i | ||||||||
\(532\) | −133303. | + | 50901.7i | −0.470994 | + | 0.179849i | ||||
\(533\) | 166512. | 0.586125 | ||||||||
\(534\) | −135592. | + | 25007.3i | −0.475500 | + | 0.0876969i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 254506. | − | 155041.i | 0.885867 | − | 0.539655i | ||||
\(537\) | 135706. | 0.470599 | ||||||||
\(538\) | 55818.5 | + | 302653.i | 0.192847 | + | 1.04563i | ||||
\(539\) | 165105.i | 0.568305i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −350781. | −1.19851 | −0.599255 | − | 0.800559i | \(-0.704536\pi\) | ||||
−0.599255 | + | 0.800559i | \(0.704536\pi\) | |||||||
\(542\) | −291058. | + | 53680.1i | −0.990788 | + | 0.182732i | ||||
\(543\) | 228651.i | 0.775487i | ||||||||
\(544\) | −248152. | − | 192150.i | −0.838532 | − | 0.649297i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8611.24 | + | 46690.9i | 0.0288855 | + | 0.156620i | ||||
\(547\) | 426263.i | 1.42463i | 0.701858 | + | 0.712317i | \(0.252354\pi\) | ||||
−0.701858 | + | 0.712317i | \(0.747646\pi\) | |||||||
\(548\) | −538078. | + | 205465.i | −1.79178 | + | 0.684191i | ||||
\(549\) | 129248. | 0.428825 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 64711.1i | − | 0.213145i | ||||||
\(552\) | 98825.9 | + | 162227.i | 0.324334 | + | 0.532408i | ||||
\(553\) | 313910. | 1.02649 | ||||||||
\(554\) | 29256.9 | + | 158634.i | 0.0953255 | + | 0.516863i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10842.0 | − | 28393.3i | −0.0350719 | − | 0.0918471i | ||||
\(557\) | −46325.5 | −0.149317 | −0.0746585 | − | 0.997209i | \(-0.523787\pi\) | ||||
−0.0746585 | + | 0.997209i | \(0.523787\pi\) | |||||||
\(558\) | 80641.2 | − | 14872.7i | 0.258993 | − | 0.0477664i | ||||
\(559\) | 163885.i | 0.524465i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 250018. | 0.794411 | ||||||||
\(562\) | −28873.6 | − | 156555.i | −0.0914172 | − | 0.495672i | ||||
\(563\) | − | 155857.i | − | 0.491711i | −0.969306 | − | 0.245855i | \(-0.920931\pi\) | ||
0.969306 | − | 0.245855i | \(-0.0790689\pi\) | |||||||
\(564\) | 184421. | − | 70421.2i | 0.579765 | − | 0.221384i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −115144. | + | 21236.0i | −0.359424 | + | 0.0662889i | ||||
\(567\) | − | 26778.3i | − | 0.0832945i | ||||||
\(568\) | 369894. | − | 225333.i | 1.14652 | − | 0.698440i | ||||
\(569\) | 115079. | 0.355443 | 0.177722 | − | 0.984081i | \(-0.443127\pi\) | ||||
0.177722 | + | 0.984081i | \(0.443127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 297667.i | 0.912973i | 0.889730 | + | 0.456487i | \(0.150892\pi\) | ||||
−0.889730 | + | 0.456487i | \(0.849108\pi\) | |||||||
\(572\) | −55721.7 | − | 145926.i | −0.170307 | − | 0.446004i | ||||
\(573\) | 177209. | 0.539729 | ||||||||
\(574\) | −386899. | + | 71356.1i | −1.17428 | + | 0.216575i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 50726.2 | − | 98272.3i | 0.152893 | − | 0.296201i | ||||
\(577\) | 56864.8 | 0.170802 | 0.0854008 | − | 0.996347i | \(-0.472783\pi\) | ||||
0.0854008 | + | 0.996347i | \(0.472783\pi\) | |||||||
\(578\) | −7557.32 | − | 40976.4i | −0.0226210 | − | 0.122653i | ||||
\(579\) | − | 143279.i | − | 0.427391i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 79844.5 | 0.236534 | ||||||||
\(582\) | −320990. | + | 59200.5i | −0.947644 | + | 0.174775i | ||||
\(583\) | 219231.i | 0.645008i | ||||||||
\(584\) | −219153. | − | 359748.i | −0.642571 | − | 1.05481i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10569.8 | − | 57310.2i | −0.0307801 | − | 0.166892i | ||||
\(587\) | 265441.i | 0.770358i | 0.922842 | + | 0.385179i | \(0.125860\pi\) | ||||
−0.922842 | + | 0.385179i | \(0.874140\pi\) | |||||||
\(588\) | 31191.0 | + | 81683.8i | 0.0902141 | + | 0.236255i | ||||
\(589\) | 184339. | 0.531357 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 234671.i | − | 0.671870i | ||||||
\(592\) | 231872. | − | 207309.i | 0.661616 | − | 0.591527i | ||||
\(593\) | −16961.6 | −0.0482343 | −0.0241172 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241172 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(594\) | 15978.8 | + | 86638.6i | 0.0452869 | + | 0.245549i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −91459.2 | + | 34923.8i | −0.257475 | + | 0.0983170i | ||||
\(597\) | 293968. | 0.824804 | ||||||||
\(598\) | 139731. | − | 25770.6i | 0.390741 | − | 0.0720648i | ||||
\(599\) | − | 236573.i | − | 0.659342i | −0.944096 | − | 0.329671i | \(-0.893062\pi\) | ||
0.944096 | − | 0.329671i | \(-0.106938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 60822.4 | 0.168389 | 0.0841947 | − | 0.996449i | \(-0.473168\pi\) | ||||
0.0841947 | + | 0.996449i | \(0.473168\pi\) | |||||||
\(602\) | −70230.7 | − | 380797.i | −0.193791 | − | 1.05075i | ||||
\(603\) | 125724.i | 0.345766i | ||||||||
\(604\) | −172839. | − | 452636.i | −0.473772 | − | 1.24073i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 269575. | − | 49718.0i | 0.734065 | − | 0.135384i | ||||
\(607\) | 507342.i | 1.37697i | 0.725252 | + | 0.688484i | \(0.241723\pi\) | ||||
−0.725252 | + | 0.688484i | \(0.758277\pi\) | |||||||
\(608\) | 152209. | − | 196570.i | 0.411750 | − | 0.531753i | ||||
\(609\) | 50874.0 | 0.137171 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 147660.i | − | 0.395531i | ||||||
\(612\) | 123694. | − | 47232.5i | 0.330252 | − | 0.126107i | ||||
\(613\) | 73376.7 | 0.195271 | 0.0976354 | − | 0.995222i | \(-0.468872\pi\) | ||||
0.0976354 | + | 0.995222i | \(0.468872\pi\) | |||||||
\(614\) | 406925. | − | 75049.6i | 1.07939 | − | 0.199073i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 192007. | + | 315187.i | 0.506005 | + | 0.830629i | ||||
\(617\) | 288711. | 0.758391 | 0.379195 | − | 0.925317i | \(-0.376201\pi\) | ||||
0.379195 | + | 0.925317i | \(0.376201\pi\) | |||||||
\(618\) | 8247.34 | + | 44717.8i | 0.0215942 | + | 0.117086i | ||||
\(619\) | − | 241450.i | − | 0.630153i | −0.949066 | − | 0.315077i | \(-0.897970\pi\) | ||
0.949066 | − | 0.315077i | \(-0.102030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −80138.6 | −0.207806 | ||||||||
\(622\) | −553469. | + | 102077.i | −1.43058 | + | 0.263843i | ||||
\(623\) | − | 243674.i | − | 0.627817i | ||||||
\(624\) | −55135.5 | − | 61668.4i | −0.141600 | − | 0.158377i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 72594.6 | + | 393614.i | 0.185249 | + | 1.00444i | ||||
\(627\) | 198048.i | 0.503774i | ||||||||
\(628\) | −170247. | + | 65008.7i | −0.431677 | + | 0.164836i | ||||
\(629\) | 372381. | 0.941209 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 28166.1i | − | 0.0707404i | −0.999374 | − | 0.0353702i | \(-0.988739\pi\) | ||
0.999374 | − | 0.0353702i | \(-0.0112610\pi\) | |||||||
\(632\) | −467084. | + | 284539.i | −1.16939 | + | 0.712374i | ||||
\(633\) | 394727. | 0.985122 | ||||||||
\(634\) | −11046.7 | − | 59896.1i | −0.0274823 | − | 0.149011i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 41416.4 | + | 108462.i | 0.102390 | + | 0.268142i | ||||
\(637\) | 65401.7 | 0.161180 | ||||||||
\(638\) | −164598. | + | 30357.0i | −0.404374 | + | 0.0745791i | ||||
\(639\) | 182725.i | 0.447502i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −265522. | −0.646226 | −0.323113 | − | 0.946360i | \(-0.604729\pi\) | ||||
−0.323113 | + | 0.946360i | \(0.604729\pi\) | |||||||
\(642\) | −46803.0 | − | 253769.i | −0.113554 | − | 0.615700i | ||||
\(643\) | 38089.8i | 0.0921271i | 0.998939 | + | 0.0460635i | \(0.0146677\pi\) | ||||
−0.998939 | + | 0.0460635i | \(0.985332\pi\) | |||||||
\(644\) | −313628. | + | 119759.i | −0.756211 | + | 0.288760i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 292710. | − | 53984.7i | 0.701410 | − | 0.129362i | ||||
\(647\) | − | 290269.i | − | 0.693414i | −0.937974 | − | 0.346707i | \(-0.887300\pi\) | ||
0.937974 | − | 0.346707i | \(-0.112700\pi\) | |||||||
\(648\) | 24272.8 | + | 39844.9i | 0.0578056 | + | 0.0948904i | ||||
\(649\) | 455542. | 1.08153 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 144922.i | 0.341957i | ||||||||
\(652\) | 60511.0 | + | 158468.i | 0.142344 | + | 0.372774i | ||||
\(653\) | −145213. | −0.340549 | −0.170275 | − | 0.985397i | \(-0.554466\pi\) | ||||
−0.170275 | + | 0.985397i | \(0.554466\pi\) | |||||||
\(654\) | −276036. | + | 50909.7i | −0.645373 | + | 0.119027i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 511008. | − | 456874.i | 1.18746 | − | 1.06167i | ||||
\(657\) | 177712. | 0.411706 | ||||||||
\(658\) | 63277.6 | + | 343096.i | 0.146150 | + | 0.792436i | ||||
\(659\) | − | 27644.5i | − | 0.0636559i | −0.999493 | − | 0.0318279i | \(-0.989867\pi\) | ||
0.999493 | − | 0.0318279i | \(-0.0101329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −368306. | −0.842958 | −0.421479 | − | 0.906838i | \(-0.638489\pi\) | ||||
−0.421479 | + | 0.906838i | \(0.638489\pi\) | |||||||
\(662\) | 685452. | − | 126419.i | 1.56409 | − | 0.288466i | ||||
\(663\) | − | 99037.8i | − | 0.225307i | ||||||
\(664\) | −118805. | + | 72374.1i | −0.269463 | + | 0.164152i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23799.1 | + | 129041.i | 0.0536553 | + | 0.290924i | ||||
\(667\) | − | 152249.i | − | 0.342219i | ||||||
\(668\) | −87518.0 | − | 229194.i | −0.196130 | − | 0.513631i | ||||
\(669\) | −481778. | −1.07645 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 751501.i | − | 1.66911i | ||||||
\(672\) | 154537. | + | 119662.i | 0.342212 | + | 0.264984i | ||||
\(673\) | 560984. | 1.23857 | 0.619285 | − | 0.785166i | \(-0.287423\pi\) | ||||
0.619285 | + | 0.785166i | \(0.287423\pi\) | |||||||
\(674\) | 146799. | + | 795957.i | 0.323150 | + | 1.75215i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 369106. | − | 140943.i | 0.807715 | − | 0.308426i | ||||
\(677\) | 887674. | 1.93676 | 0.968381 | − | 0.249475i | \(-0.0802580\pi\) | ||||
0.968381 | + | 0.249475i | \(0.0802580\pi\) | |||||||
\(678\) | −500703. | + | 92345.2i | −1.08923 | + | 0.200888i | ||||
\(679\) | − | 576856.i | − | 1.25120i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −185326. | −0.399616 | ||||||||
\(682\) | −86476.1 | − | 468881.i | −0.185921 | − | 1.00808i | ||||
\(683\) | 673933.i | 1.44469i | 0.691532 | + | 0.722346i | \(0.256936\pi\) | ||||
−0.691532 | + | 0.722346i | \(0.743064\pi\) | |||||||
\(684\) | 37414.6 | + | 97982.2i | 0.0799703 | + | 0.209428i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −498896. | + | 92011.8i | −1.06014 | + | 0.195522i | ||||
\(687\) | − | 539155.i | − | 1.14235i | ||||||
\(688\) | 449669. | + | 502949.i | 0.949983 | + | 1.06254i | ||||
\(689\) | 86842.5 | 0.182934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 608132.i | − | 1.27363i | −0.771019 | − | 0.636813i | \(-0.780253\pi\) | ||
0.771019 | − | 0.636813i | \(-0.219747\pi\) | |||||||
\(692\) | −563702. | + | 215250.i | −1.17717 | + | 0.449501i | ||||
\(693\) | −155700. | −0.324206 | ||||||||
\(694\) | −419233. | + | 77319.5i | −0.870435 | + | 0.160535i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −75698.2 | + | 46114.1i | −0.156267 | + | 0.0951953i | ||||
\(697\) | 820665. | 1.68928 | ||||||||
\(698\) | 139551. | + | 756655.i | 0.286432 | + | 1.55306i | ||||
\(699\) | − | 91518.4i | − | 0.187307i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 429210. | 0.873442 | 0.436721 | − | 0.899597i | \(-0.356140\pi\) | ||||
0.436721 | + | 0.899597i | \(0.356140\pi\) | |||||||
\(702\) | 34319.5 | − | 6329.58i | 0.0696413 | − | 0.0128440i | ||||
\(703\) | 294976.i | 0.596865i | ||||||||
\(704\) | −571395. | − | 294942.i | −1.15290 | − | 0.595103i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 55268.4 | + | 299670.i | 0.110884 | + | 0.601220i | ||||
\(707\) | 484458.i | 0.969208i | ||||||||
\(708\) | 225375. | − | 86059.5i | 0.449613 | − | 0.171685i | ||||
\(709\) | 196746. | 0.391392 | 0.195696 | − | 0.980665i | \(-0.437303\pi\) | ||||
0.195696 | + | 0.980665i | \(0.437303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 230735.i | − | 0.456430i | ||||||
\(712\) | 220875. | + | 362576.i | 0.435699 | + | 0.715219i | ||||
\(713\) | 433704. | 0.853128 | ||||||||
\(714\) | 42441.2 | + | 230120.i | 0.0832513 | + | 0.451396i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −149065. | − | 390374.i | −0.290769 | − | 0.761474i | ||||
\(717\) | −297189. | −0.578089 | ||||||||
\(718\) | −667931. | + | 123187.i | −1.29564 | + | 0.238955i | ||||
\(719\) | − | 176676.i | − | 0.341758i | −0.985292 | − | 0.170879i | \(-0.945339\pi\) | ||
0.985292 | − | 0.170879i | \(-0.0546607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80363.1 | −0.154592 | ||||||||
\(722\) | −51783.2 | − | 280773.i | −0.0993377 | − | 0.538617i | ||||
\(723\) | 170369.i | 0.325921i | ||||||||
\(724\) | 657742. | − | 251159.i | 1.25481 | − | 0.479151i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 204491. | − | 37714.5i | 0.387973 | − | 0.0715542i | ||||
\(727\) | − | 773494.i | − | 1.46348i | −0.681582 | − | 0.731742i | \(-0.738708\pi\) | ||
0.681582 | − | 0.731742i | \(-0.261292\pi\) | |||||||
\(728\) | 124853. | − | 76058.2i | 0.235578 | − | 0.143510i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 807722.i | 1.51157i | ||||||||
\(732\) | −141971. | − | 371797.i | −0.264958 | − | 0.693880i | ||||
\(733\) | −405112. | −0.753992 | −0.376996 | − | 0.926215i | \(-0.623043\pi\) | ||||
−0.376996 | + | 0.926215i | \(0.623043\pi\) | |||||||
\(734\) | −31391.3 | + | 5789.53i | −0.0582663 | + | 0.0107461i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 358110. | − | 462480.i | 0.661091 | − | 0.853763i | ||||
\(737\) | 731008. | 1.34582 | ||||||||
\(738\) | 52449.3 | + | 284385.i | 0.0963002 | + | 0.522148i | ||||
\(739\) | − | 12430.2i | − | 0.0227609i | −0.999935 | − | 0.0113805i | \(-0.996377\pi\) | ||
0.999935 | − | 0.0113805i | \(-0.00362259\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 78451.3 | 0.142878 | ||||||||
\(742\) | −201783. | + | 37215.1i | −0.366503 | + | 0.0675945i | ||||
\(743\) | 642523.i | 1.16389i | 0.813229 | + | 0.581944i | \(0.197708\pi\) | ||||
−0.813229 | + | 0.581944i | \(0.802292\pi\) | |||||||
\(744\) | −131362. | − | 215637.i | −0.237315 | − | 0.389563i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −188102. | − | 1.01991e6i | −0.338000 | − | 1.83266i | ||||
\(747\) | − | 58688.6i | − | 0.105175i | ||||||
\(748\) | −274629. | − | 719206.i | −0.490844 | − | 1.28543i | ||||
\(749\) | 456054. | 0.812928 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.01784e6i | − | 1.80468i | −0.431022 | − | 0.902342i | \(-0.641847\pi\) | ||
0.431022 | − | 0.902342i | \(-0.358153\pi\) | |||||||
\(752\) | −405150. | − | 453155.i | −0.716440 | − | 0.801329i | ||||
\(753\) | −149667. | −0.263959 | ||||||||
\(754\) | 12025.1 | + | 65201.0i | 0.0211517 | + | 0.114686i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −77030.8 | + | 29414.2i | −0.134779 | + | 0.0514652i | ||||
\(757\) | −386917. | −0.675191 | −0.337595 | − | 0.941291i | \(-0.609614\pi\) | ||||
−0.337595 | + | 0.941291i | \(0.609614\pi\) | |||||||
\(758\) | 45996.5 | − | 8483.19i | 0.0800547 | − | 0.0147646i | ||||
\(759\) | 465958.i | 0.808842i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −424041. | −0.732215 | −0.366108 | − | 0.930572i | \(-0.619310\pi\) | ||||
−0.366108 | + | 0.930572i | \(0.619310\pi\) | |||||||
\(762\) | −26114.2 | − | 141594.i | −0.0449746 | − | 0.243856i | ||||
\(763\) | − | 496070.i | − | 0.852106i | ||||||
\(764\) | −194653. | − | 509762.i | −0.333483 | − | 0.873334i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 137409. | − | 25342.4i | 0.234183 | − | 0.0431907i | ||||
\(767\) | − | 180451.i | − | 0.306738i | ||||||
\(768\) | −338411. | − | 37973.7i | −0.573749 | − | 0.0643814i | ||||
\(769\) | −267929. | −0.453072 | −0.226536 | − | 0.974003i | \(-0.572740\pi\) | ||||
−0.226536 | + | 0.974003i | \(0.572740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 506450.i | 0.851977i | ||||||||
\(772\) | −412159. | + | 157383.i | −0.691560 | + | 0.264073i | ||||
\(773\) | −576873. | −0.965431 | −0.482715 | − | 0.875777i | \(-0.660349\pi\) | ||||
−0.482715 | + | 0.875777i | \(0.660349\pi\) | |||||||
\(774\) | −279900. | + | 51622.1i | −0.467219 | + | 0.0861696i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 522884. | + | 858336.i | 0.868324 | + | 1.42539i | ||||
\(777\) | −231902. | −0.384116 | ||||||||
\(778\) | −79962.2 | − | 433561.i | −0.132107 | − | 0.716294i | ||||
\(779\) | 650078.i | 1.07125i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06243e6 | 1.74181 | ||||||||
\(782\) | 688673. | − | 127013.i | 1.12616 | − | 0.207699i | ||||
\(783\) | − | 37394.3i | − | 0.0609932i | ||||||
\(784\) | 200711. | − | 179449.i | 0.326543 | − | 0.291950i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7136.62 | + | 38695.4i | 0.0115517 | + | 0.0626345i | ||||
\(787\) | − | 27874.2i | − | 0.0450043i | −0.999747 | − | 0.0225021i | \(-0.992837\pi\) | ||
0.999747 | − | 0.0225021i | \(-0.00716326\pi\) | |||||||
\(788\) | −675059. | + | 257772.i | −1.08715 | + | 0.415129i | ||||
\(789\) | 431026. | 0.692388 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 899823.i | − | 1.43815i | ||||||
\(792\) | 231674. | − | 141132.i | 0.369341 | − | 0.224996i | ||||
\(793\) | −297687. | −0.473383 | ||||||||
\(794\) | 32528.0 | + | 176370.i | 0.0515961 | + | 0.279758i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −322905. | − | 845632.i | −0.509623 | − | 1.33461i | ||||
\(797\) | −538595. | −0.847902 | −0.423951 | − | 0.905685i | \(-0.639357\pi\) | ||||
−0.423951 | + | 0.905685i | \(0.639357\pi\) | |||||||
\(798\) | −182286. | + | 33619.2i | −0.286251 | + | 0.0527936i | ||||
\(799\) | − | 727755.i | − | 1.13996i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −179109. | −0.279160 | ||||||||
\(802\) | −133310. | − | 722817.i | −0.207259 | − | 1.12378i | ||||
\(803\) | − | 1.03329e6i | − | 1.60248i | ||||||
\(804\) | 361659. | − | 138100.i | 0.559483 | − | 0.213639i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −185734. | + | 34255.1i | −0.285905 | + | 0.0527297i | ||||
\(807\) | 399788.i | 0.613879i | ||||||||
\(808\) | −439131. | − | 720851.i | −0.672622 | − | 1.10414i | ||||
\(809\) | −65846.2 | −0.100608 | −0.0503041 | − | 0.998734i | \(-0.516019\pi\) | ||||
−0.0503041 | + | 0.998734i | \(0.516019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42705.4i | 0.0649294i | 0.999473 | + | 0.0324647i | \(0.0103356\pi\) | ||||
−0.999473 | + | 0.0324647i | \(0.989664\pi\) | |||||||
\(812\) | −55881.9 | − | 146345.i | −0.0847538 | − | 0.221955i | ||||
\(813\) | −384472. | −0.581679 | ||||||||
\(814\) | 750296. | − | 138378.i | 1.13236 | − | 0.208842i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −271740. | − | 303937.i | −0.408106 | − | 0.456461i | ||||
\(817\) | −639826. | −0.958556 | ||||||||
\(818\) | 84243.5 | + | 456775.i | 0.125901 | + | 0.682647i | ||||
\(819\) | 61676.2i | 0.0919495i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −534742. | −0.793338 | −0.396669 | − | 0.917962i | \(-0.629834\pi\) | ||||
−0.396669 | + | 0.917962i | \(0.629834\pi\) | |||||||
\(822\) | −735800. | + | 135704.i | −1.08897 | + | 0.200840i | ||||
\(823\) | 281733.i | 0.415947i | 0.978134 | + | 0.207974i | \(0.0666869\pi\) | ||||
−0.978134 | + | 0.207974i | \(0.933313\pi\) | |||||||
\(824\) | 119577. | − | 72844.1i | 0.176113 | − | 0.107285i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 77329.5 | + | 419287.i | 0.113341 | + | 0.614542i | ||||
\(827\) | 44114.6i | 0.0645017i | 0.999480 | + | 0.0322509i | \(0.0102675\pi\) | ||||
−0.999480 | + | 0.0322509i | \(0.989732\pi\) | |||||||
\(828\) | 88027.3 | + | 230528.i | 0.128397 | + | 0.336251i | ||||
\(829\) | 597535. | 0.869470 | 0.434735 | − | 0.900558i | \(-0.356842\pi\) | ||||
0.434735 | + | 0.900558i | \(0.356842\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 209546.i | 0.303444i | ||||||||
\(832\) | −116833. | + | 226342.i | −0.168780 | + | 0.326979i | ||||
\(833\) | 322337. | 0.464537 | ||||||||
\(834\) | −7160.84 | − | 38826.7i | −0.0102951 | − | 0.0558210i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 569708. | − | 217543.i | 0.815155 | − | 0.311267i | ||||
\(837\) | 106523. | 0.152052 | ||||||||
\(838\) | 104581. | − | 19288.0i | 0.148925 | − | 0.0274663i | ||||
\(839\) | 607985.i | 0.863712i | 0.901943 | + | 0.431856i | \(0.142141\pi\) | ||||
−0.901943 | + | 0.431856i | \(0.857859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −636238. | −0.899555 | ||||||||
\(842\) | 30417.2 | + | 164925.i | 0.0429038 | + | 0.232628i | ||||
\(843\) | − | 206801.i | − | 0.291003i | ||||||
\(844\) | −433583. | − | 1.13548e6i | −0.608678 | − | 1.59402i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 252188. | − | 46511.3i | 0.352358 | − | 0.0649857i | ||||
\(847\) | 367495.i | 0.512253i | ||||||||
\(848\) | 266511. | − | 238278.i | 0.370616 | − | 0.331354i | ||||
\(849\) | −152099. | −0.211013 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 694006.i | 0.958306i | ||||||||
\(852\) | 525628. | − | 200711.i | 0.724102 | − | 0.276499i | ||||
\(853\) | 86914.1 | 0.119452 | 0.0597258 | − | 0.998215i | \(-0.480977\pi\) | ||||
0.0597258 | + | 0.998215i | \(0.480977\pi\) | |||||||
\(854\) | 691691. | − | 127569.i | 0.948411 | − | 0.174916i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −678587. | + | 413384.i | −0.926101 | + | 0.564165i | ||||
\(857\) | −864128. | −1.17657 | −0.588283 | − | 0.808655i | \(-0.700196\pi\) | ||||
−0.588283 | + | 0.808655i | \(0.700196\pi\) | |||||||
\(858\) | −36802.7 | − | 199547.i | −0.0499926 | − | 0.271064i | ||||
\(859\) | 276868.i | 0.375220i | 0.982244 | + | 0.187610i | \(0.0600741\pi\) | ||||
−0.982244 | + | 0.187610i | \(0.939926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −511073. | −0.689408 | ||||||||
\(862\) | −1.01671e6 | + | 187513.i | −1.36831 | + | 0.252358i | ||||
\(863\) | 537991.i | 0.722359i | 0.932496 | + | 0.361180i | \(0.117626\pi\) | ||||
−0.932496 | + | 0.361180i | \(0.882374\pi\) | |||||||
\(864\) | 87956.2 | − | 113591.i | 0.117825 | − | 0.152165i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25783.7 | + | 139801.i | 0.0343803 | + | 0.186413i | ||||
\(867\) | − | 54127.7i | − | 0.0720080i | ||||||
\(868\) | 416884. | − | 159187.i | 0.553319 | − | 0.211285i | ||||
\(869\) | −1.34159e6 | −1.77656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 289569.i | − | 0.381694i | ||||||
\(872\) | 449656. | + | 738130.i | 0.591354 | + | 0.970733i | ||||
\(873\) | −424010. | −0.556350 | ||||||||
\(874\) | 100611. | + | 545523.i | 0.131712 | + | 0.714151i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −195206. | − | 511210.i | −0.254381 | − | 0.666180i | ||||
\(877\) | 96844.0 | 0.125914 | 0.0629569 | − | 0.998016i | \(-0.479947\pi\) | ||||
0.0629569 | + | 0.998016i | \(0.479947\pi\) | |||||||
\(878\) | 939337. | − | 173243.i | 1.21852 | − | 0.224733i | ||||
\(879\) | − | 75703.7i | − | 0.0979804i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 792263. | 1.02075 | 0.510373 | − | 0.859953i | \(-0.329507\pi\) | ||||
0.510373 | + | 0.859953i | \(0.329507\pi\) | |||||||
\(882\) | 20600.8 | + | 111699.i | 0.0264818 | + | 0.143586i | ||||
\(883\) | − | 25402.5i | − | 0.0325803i | −0.999867 | − | 0.0162901i | \(-0.994814\pi\) | ||
0.999867 | − | 0.0162901i | \(-0.00518554\pi\) | |||||||
\(884\) | −284894. | + | 108787.i | −0.364568 | + | 0.139210i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −523888. | + | 96621.2i | −0.667377 | + | 0.123085i | ||||
\(887\) | − | 828735.i | − | 1.05334i | −0.850070 | − | 0.526670i | \(-0.823440\pi\) | ||
0.850070 | − | 0.526670i | \(-0.176560\pi\) | |||||||
\(888\) | 345059. | − | 210204.i | 0.437590 | − | 0.266573i | ||||
\(889\) | 254460. | 0.321971 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 114445.i | 0.144159i | ||||||||
\(892\) | 529203. | + | 1.38589e6i | 0.665108 | + | 1.74180i | ||||
\(893\) | 576480. | 0.722906 | ||||||||
\(894\) | −125067. | + | 23066.2i | −0.156483 | + | 0.0288603i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 174473. | − | 575986.i | 0.217326 | − | 0.717457i | ||||
\(897\) | 184577. | 0.229399 | ||||||||
\(898\) | −138127. | − | 748935.i | −0.171287 | − | 0.928735i | ||||
\(899\) | 202375.i | 0.250401i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 428010. | 0.527235 | ||||||||
\(902\) | 1.65353e6 | − | 304962.i | 2.03235 | − | 0.374828i | ||||
\(903\) | − | 503012.i | − | 0.616883i | ||||||
\(904\) | 815633. | + | 1.33890e6i | 0.998063 | + | 1.63836i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −114156. | − | 618962.i | −0.139073 | − | 0.754063i | ||||
\(907\) | − | 541780.i | − | 0.658580i | −0.944229 | − | 0.329290i | \(-0.893191\pi\) | ||
0.944229 | − | 0.329290i | \(-0.106809\pi\) | |||||||
\(908\) | 203569. | + | 533112.i | 0.246911 | + | 0.646617i | ||||
\(909\) | 356094. | 0.430960 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.33634e6i | 1.61020i | 0.593141 | + | 0.805099i | \(0.297888\pi\) | ||||
−0.593141 | + | 0.805099i | \(0.702112\pi\) | |||||||
\(912\) | 240760. | − | 215255.i | 0.289464 | − | 0.258799i | ||||
\(913\) | −341239. | −0.409372 | ||||||||
\(914\) | −3123.85 | − | 16937.8i | −0.00373936 | − | 0.0202751i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.55094e6 | + | 592228.i | −1.84844 | + | 0.705827i | ||||
\(917\) | −69540.1 | −0.0826983 | ||||||||
\(918\) | 169146. | − | 31195.8i | 0.200714 | − | 0.0370178i | ||||
\(919\) | − | 314921.i | − | 0.372881i | −0.982466 | − | 0.186440i | \(-0.940305\pi\) | ||
0.982466 | − | 0.186440i | \(-0.0596951\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 537526. | 0.633695 | ||||||||
\(922\) | 251233. | + | 1.36220e6i | 0.295539 | + | 1.60244i | ||||
\(923\) | − | 420854.i | − | 0.494001i | ||||||
\(924\) | 171026. | + | 447888.i | 0.200318 | + | 0.524597i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 583016. | − | 107526.i | 0.679921 | − | 0.125399i | ||||
\(927\) | 59069.8i | 0.0687394i | ||||||||
\(928\) | 215802. | + | 167101.i | 0.250588 | + | 0.194037i | ||||
\(929\) | −891827. | −1.03335 | −0.516677 | − | 0.856180i | \(-0.672831\pi\) | ||||
−0.516677 | + | 0.856180i | \(0.672831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 255335.i | 0.294585i | ||||||||
\(932\) | −263263. | + | 100527.i | −0.303081 | + | 0.115732i | ||||
\(933\) | −731103. | −0.839876 | ||||||||
\(934\) | −673462. | + | 124207.i | −0.772003 | + | 0.142381i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −55905.6 | − | 91771.3i | −0.0638121 | − | 0.104750i | ||||
\(937\) | 266527. | 0.303573 | 0.151786 | − | 0.988413i | \(-0.451497\pi\) | ||||
0.151786 | + | 0.988413i | \(0.451497\pi\) | |||||||
\(938\) | 124091. | + | 672829.i | 0.141037 | + | 0.764714i | ||||
\(939\) | 519943.i | 0.589691i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 710974. | 0.802924 | 0.401462 | − | 0.915876i | \(-0.368502\pi\) | ||||
0.401462 | + | 0.915876i | \(0.368502\pi\) | |||||||
\(942\) | −232805. | + | 42936.5i | −0.262356 | + | 0.0483866i | ||||
\(943\) | 1.52947e6i | 1.71996i | ||||||||
\(944\) | −495120. | − | 553786.i | −0.555606 | − | 0.621438i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 300152. | + | 1.62745e6i | 0.335397 | + | 1.81855i | ||||
\(947\) | 895332.i | 0.998353i | 0.866500 | + | 0.499177i | \(0.166364\pi\) | ||||
−0.866500 | + | 0.499177i | \(0.833636\pi\) | |||||||
\(948\) | −663736. | + | 253448.i | −0.738548 | + | 0.282015i | ||||
\(949\) | −409310. | −0.454486 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 79119.5i | − | 0.0874828i | ||||||
\(952\) | 615347. | − | 374859.i | 0.678963 | − | 0.413613i | ||||
\(953\) | 308910. | 0.340131 | 0.170066 | − | 0.985433i | \(-0.445602\pi\) | ||||
0.170066 | + | 0.985433i | \(0.445602\pi\) | |||||||
\(954\) | 27354.4 | + | 148318.i | 0.0300560 | + | 0.162966i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 326443. | + | 854899.i | 0.357184 | + | 0.935403i | ||||
\(957\) | −217425. | −0.237403 | ||||||||
\(958\) | 218724. | − | 40339.5i | 0.238323 | − | 0.0439541i | ||||
\(959\) | − | 1.32232e6i | − | 1.43780i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 347029. | 0.375767 | ||||||||
\(962\) | −54814.6 | − | 297209.i | −0.0592306 | − | 0.321153i | ||||
\(963\) | − | 335216.i | − | 0.361470i | ||||||
\(964\) | 490085. | − | 187139.i | 0.527372 | − | 0.201377i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −428874. | + | 79097.6i | −0.459595 | + | 0.0847636i | ||||
\(967\) | − | 845374.i | − | 0.904057i | −0.892003 | − | 0.452029i | \(-0.850700\pi\) | ||
0.892003 | − | 0.452029i | \(-0.149300\pi\) | |||||||
\(968\) | −333111. | − | 546816.i | −0.355499 | − | 0.583566i | ||||
\(969\) | 386654. | 0.411789 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.29869e6i | 1.37742i | 0.725036 | + | 0.688711i | \(0.241823\pi\) | ||||
−0.725036 | + | 0.688711i | \(0.758177\pi\) | |||||||
\(972\) | 21620.5 | + | 56620.4i | 0.0228841 | + | 0.0599295i | ||||
\(973\) | 69776.0 | 0.0737022 | ||||||||
\(974\) | −752956. | + | 138868.i | −0.793691 | + | 0.146381i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −913572. | + | 816792.i | −0.959054 | + | 0.857456i | ||||
\(977\) | −191660. | −0.200790 | −0.100395 | − | 0.994948i | \(-0.532011\pi\) | ||||
−0.100395 | + | 0.994948i | \(0.532011\pi\) | |||||||
\(978\) | 39965.9 | + | 216698.i | 0.0417842 | + | 0.226557i | ||||
\(979\) | 1.04141e6i | 1.08657i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −364629. | −0.378890 | ||||||||
\(982\) | 921024. | − | 169865.i | 0.955098 | − | 0.176150i | ||||
\(983\) | 69081.0i | 0.0714910i | 0.999361 | + | 0.0357455i | \(0.0113806\pi\) | ||||
−0.999361 | + | 0.0357455i | \(0.988619\pi\) | |||||||
\(984\) | 760453. | − | 463255.i | 0.785384 | − | 0.478443i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 59266.6 | + | 321348.i | 0.0609616 | + | 0.330539i | ||||
\(987\) | 453212.i | 0.465229i | ||||||||
\(988\) | −86173.9 | − | 225674.i | −0.0882799 | − | 0.231190i | ||||
\(989\) | −1.50535e6 | −1.53902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.79910e6i | − | 1.83192i | −0.401266 | − | 0.915962i | \(-0.631430\pi\) | ||
0.401266 | − | 0.915962i | \(-0.368570\pi\) | |||||||
\(992\) | −476011. | + | 614743.i | −0.483720 | + | 0.624698i | ||||
\(993\) | 905446. | 0.918256 | ||||||||
\(994\) | 180351. | + | 977878.i | 0.182535 | + | 0.989719i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −168825. | + | 64465.8i | −0.170183 | + | 0.0649846i | ||||
\(997\) | −1.95066e6 | −1.96241 | −0.981206 | − | 0.192963i | \(-0.938190\pi\) | ||||
−0.981206 | + | 0.192963i | \(0.938190\pi\) | |||||||
\(998\) | 1.56403e6 | − | 288456.i | 1.57031 | − | 0.289613i | ||||
\(999\) | 170456.i | 0.170798i |
(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 | 300.5.c.b.151.9 | ✓ | 16 | |
4.3 | odd | 2 | inner | 300.5.c.b.151.10 | yes | 16 | |
5.2 | odd | 4 | 300.5.f.c.199.31 | 32 | |||
5.3 | odd | 4 | 300.5.f.c.199.2 | 32 | |||
5.4 | even | 2 | 300.5.c.c.151.8 | yes | 16 | ||
20.3 | even | 4 | 300.5.f.c.199.32 | 32 | |||
20.7 | even | 4 | 300.5.f.c.199.1 | 32 | |||
20.19 | odd | 2 | 300.5.c.c.151.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.5.c.b.151.9 | ✓ | 16 | 1.1 | even | 1 | trivial | |
300.5.c.b.151.10 | yes | 16 | 4.3 | odd | 2 | inner | |
300.5.c.c.151.7 | yes | 16 | 20.19 | odd | 2 | ||
300.5.c.c.151.8 | yes | 16 | 5.4 | even | 2 | ||
300.5.f.c.199.1 | 32 | 20.7 | even | 4 | |||
300.5.f.c.199.2 | 32 | 5.3 | odd | 4 | |||
300.5.f.c.199.31 | 32 | 5.2 | odd | 4 | |||
300.5.f.c.199.32 | 32 | 20.3 | even | 4 |