Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,5,Mod(7,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.d (of order \(10\), degree \(4\), 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: | \(2.27413918784\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(0.809017 - 3.49146i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.13 |
Dual form | 22.5.d.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68999 | − | 0.874032i | −0.672499 | − | 0.218508i | ||||
\(3\) | 4.50928 | − | 3.27619i | 0.501032 | − | 0.364021i | −0.308379 | − | 0.951263i | \(-0.599787\pi\) |
0.809411 | + | 0.587243i | \(0.199787\pi\) | |||||||
\(4\) | 6.47214 | + | 4.70228i | 0.404508 | + | 0.293893i | ||||
\(5\) | −10.0117 | − | 30.8128i | −0.400467 | − | 1.23251i | −0.924621 | − | 0.380888i | \(-0.875618\pi\) |
0.524154 | − | 0.851624i | \(-0.324382\pi\) | |||||||
\(6\) | −14.9934 | + | 4.87166i | −0.416485 | + | 0.135324i | ||||
\(7\) | 50.5008 | − | 69.5083i | 1.03063 | − | 1.41854i | 0.126153 | − | 0.992011i | \(-0.459737\pi\) |
0.904475 | − | 0.426527i | \(-0.140263\pi\) | |||||||
\(8\) | −13.3001 | − | 18.3060i | −0.207813 | − | 0.286031i | ||||
\(9\) | −15.4301 | + | 47.4891i | −0.190495 | + | 0.586285i | ||||
\(10\) | 91.6368i | 0.916368i | ||||||||
\(11\) | −44.2851 | + | 112.605i | −0.365993 | + | 0.930618i | ||||
\(12\) | 44.5903 | 0.309655 | ||||||||
\(13\) | 97.9585 | + | 31.8286i | 0.579636 | + | 0.188335i | 0.584138 | − | 0.811655i | \(-0.301433\pi\) |
−0.00450146 | + | 0.999990i | \(0.501433\pi\) | |||||||
\(14\) | −196.599 | + | 142.838i | −1.00306 | + | 0.728764i | ||||
\(15\) | −146.094 | − | 106.144i | −0.649307 | − | 0.471749i | ||||
\(16\) | 19.7771 | + | 60.8676i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 121.020 | − | 39.3217i | 0.418754 | − | 0.136061i | −0.0920586 | − | 0.995754i | \(-0.529345\pi\) |
0.510812 | + | 0.859692i | \(0.329345\pi\) | |||||||
\(18\) | 83.0139 | − | 114.259i | 0.256216 | − | 0.352651i | ||||
\(19\) | 158.082 | + | 217.581i | 0.437900 | + | 0.602717i | 0.969744 | − | 0.244125i | \(-0.0785008\pi\) |
−0.531844 | + | 0.846842i | \(0.678501\pi\) | |||||||
\(20\) | 80.0935 | − | 246.502i | 0.200234 | − | 0.616256i | ||||
\(21\) | − | 478.883i | − | 1.08590i | ||||||
\(22\) | 217.547 | − | 264.199i | 0.449477 | − | 0.545867i | ||||
\(23\) | −446.426 | −0.843905 | −0.421953 | − | 0.906618i | \(-0.638655\pi\) | ||||
−0.421953 | + | 0.906618i | \(0.638655\pi\) | |||||||
\(24\) | −119.948 | − | 38.9733i | −0.208242 | − | 0.0676620i | ||||
\(25\) | −343.559 | + | 249.610i | −0.549694 | + | 0.399376i | ||||
\(26\) | −235.689 | − | 171.238i | −0.348652 | − | 0.253310i | ||||
\(27\) | 225.518 | + | 694.073i | 0.309353 | + | 0.952089i | ||||
\(28\) | 653.696 | − | 212.399i | 0.833796 | − | 0.270917i | ||||
\(29\) | 639.233 | − | 879.829i | 0.760087 | − | 1.04617i | −0.237120 | − | 0.971480i | \(-0.576203\pi\) |
0.997207 | − | 0.0746895i | \(-0.0237966\pi\) | |||||||
\(30\) | 300.219 | + | 413.216i | 0.333577 | + | 0.459129i | ||||
\(31\) | −155.334 | + | 478.068i | −0.161638 | + | 0.497470i | −0.998773 | − | 0.0495264i | \(-0.984229\pi\) |
0.837135 | + | 0.546996i | \(0.184229\pi\) | |||||||
\(32\) | − | 181.019i | − | 0.176777i | ||||||
\(33\) | 169.220 | + | 652.853i | 0.155390 | + | 0.599498i | ||||
\(34\) | −359.911 | −0.311342 | ||||||||
\(35\) | −2647.34 | − | 860.174i | −2.16110 | − | 0.702183i | ||||
\(36\) | −323.173 | + | 234.799i | −0.249362 | + | 0.181172i | ||||
\(37\) | 1568.75 | + | 1139.76i | 1.14591 | + | 0.832553i | 0.987932 | − | 0.154890i | \(-0.0495022\pi\) |
0.157979 | + | 0.987443i | \(0.449502\pi\) | |||||||
\(38\) | −235.066 | − | 723.460i | −0.162788 | − | 0.501011i | ||||
\(39\) | 545.999 | − | 177.406i | 0.358974 | − | 0.116638i | ||||
\(40\) | −430.902 | + | 593.086i | −0.269314 | + | 0.370678i | ||||
\(41\) | 951.709 | + | 1309.92i | 0.566157 | + | 0.779248i | 0.992093 | − | 0.125505i | \(-0.0400552\pi\) |
−0.425936 | + | 0.904753i | \(0.640055\pi\) | |||||||
\(42\) | −418.559 | + | 1288.19i | −0.237278 | + | 0.730268i | ||||
\(43\) | − | 1441.78i | − | 0.779763i | −0.920865 | − | 0.389881i | \(-0.872516\pi\) | ||
0.920865 | − | 0.389881i | \(-0.127484\pi\) | |||||||
\(44\) | −816.119 | + | 520.552i | −0.421549 | + | 0.268880i | ||||
\(45\) | 1617.75 | 0.798890 | ||||||||
\(46\) | 1200.88 | + | 390.191i | 0.567525 | + | 0.184400i | ||||
\(47\) | −2665.57 | + | 1936.65i | −1.20668 | + | 0.876708i | −0.994926 | − | 0.100614i | \(-0.967919\pi\) |
−0.211759 | + | 0.977322i | \(0.567919\pi\) | |||||||
\(48\) | 288.594 | + | 209.676i | 0.125258 | + | 0.0910052i | ||||
\(49\) | −1539.13 | − | 4736.96i | −0.641038 | − | 1.97291i | ||||
\(50\) | 1142.34 | − | 371.168i | 0.456935 | − | 0.148467i | ||||
\(51\) | 416.888 | − | 573.797i | 0.160280 | − | 0.220606i | ||||
\(52\) | 484.333 | + | 666.628i | 0.179117 | + | 0.246534i | ||||
\(53\) | 906.672 | − | 2790.45i | 0.322774 | − | 0.993396i | −0.649662 | − | 0.760223i | \(-0.725089\pi\) |
0.972435 | − | 0.233172i | \(-0.0749106\pi\) | |||||||
\(54\) | − | 2064.16i | − | 0.707875i | ||||||
\(55\) | 3913.04 | + | 237.186i | 1.29357 | + | 0.0784085i | ||||
\(56\) | −1944.08 | −0.619924 | ||||||||
\(57\) | 1425.67 | + | 463.229i | 0.438803 | + | 0.142576i | ||||
\(58\) | −2488.53 | + | 1808.02i | −0.739754 | + | 0.537463i | ||||
\(59\) | −1304.22 | − | 947.571i | −0.374668 | − | 0.272212i | 0.384476 | − | 0.923135i | \(-0.374382\pi\) |
−0.759144 | + | 0.650923i | \(0.774382\pi\) | |||||||
\(60\) | −446.424 | − | 1373.95i | −0.124007 | − | 0.381653i | ||||
\(61\) | −3170.81 | + | 1030.26i | −0.852138 | + | 0.276877i | −0.702341 | − | 0.711840i | \(-0.747862\pi\) |
−0.149797 | + | 0.988717i | \(0.547862\pi\) | |||||||
\(62\) | 835.694 | − | 1150.23i | 0.217402 | − | 0.299229i | ||||
\(63\) | 2521.65 | + | 3470.76i | 0.635337 | + | 0.874466i | ||||
\(64\) | −158.217 | + | 486.941i | −0.0386271 | + | 0.118882i | ||||
\(65\) | − | 3337.03i | − | 0.789830i | ||||||
\(66\) | 115.414 | − | 1904.07i | 0.0264954 | − | 0.437115i | ||||
\(67\) | −2147.45 | −0.478380 | −0.239190 | − | 0.970973i | \(-0.576882\pi\) | ||||
−0.239190 | + | 0.970973i | \(0.576882\pi\) | |||||||
\(68\) | 968.159 | + | 314.574i | 0.209377 | + | 0.0680307i | ||||
\(69\) | −2013.06 | + | 1462.57i | −0.422823 | + | 0.307199i | ||||
\(70\) | 6369.52 | + | 4627.73i | 1.29990 | + | 0.944434i | ||||
\(71\) | 1044.65 | + | 3215.10i | 0.207230 | + | 0.637789i | 0.999614 | + | 0.0277668i | \(0.00883957\pi\) |
−0.792384 | + | 0.610022i | \(0.791160\pi\) | |||||||
\(72\) | 1074.55 | − | 349.144i | 0.207283 | − | 0.0673503i | ||||
\(73\) | −4442.75 | + | 6114.92i | −0.833692 | + | 1.14748i | 0.153532 | + | 0.988144i | \(0.450935\pi\) |
−0.987224 | + | 0.159336i | \(0.949065\pi\) | |||||||
\(74\) | −3223.74 | − | 4437.10i | −0.588704 | − | 0.810281i | ||||
\(75\) | −731.435 | + | 2251.13i | −0.130033 | + | 0.400200i | ||||
\(76\) | 2151.56i | 0.372500i | ||||||||
\(77\) | 5590.54 | + | 8764.81i | 0.942914 | + | 1.47830i | ||||
\(78\) | −1623.79 | −0.266896 | ||||||||
\(79\) | −6155.63 | − | 2000.08i | −0.986320 | − | 0.320475i | −0.228934 | − | 0.973442i | \(-0.573524\pi\) |
−0.757386 | + | 0.652967i | \(0.773524\pi\) | |||||||
\(80\) | 1677.50 | − | 1218.77i | 0.262109 | − | 0.190434i | ||||
\(81\) | 18.7143 | + | 13.5967i | 0.00285236 | + | 0.00207236i | ||||
\(82\) | −1415.18 | − | 4355.49i | −0.210468 | − | 0.647753i | ||||
\(83\) | 3860.37 | − | 1254.31i | 0.560367 | − | 0.182074i | −0.0151193 | − | 0.999886i | \(-0.504813\pi\) |
0.575486 | + | 0.817811i | \(0.304813\pi\) | |||||||
\(84\) | 2251.84 | − | 3099.40i | 0.319139 | − | 0.439257i | ||||
\(85\) | −2423.22 | − | 3335.28i | −0.335394 | − | 0.461631i | ||||
\(86\) | −1260.16 | + | 3878.38i | −0.170384 | + | 0.524389i | ||||
\(87\) | − | 6061.65i | − | 0.800852i | ||||||
\(88\) | 2650.33 | − | 686.968i | 0.342243 | − | 0.0887097i | ||||
\(89\) | −6032.84 | −0.761626 | −0.380813 | − | 0.924652i | \(-0.624356\pi\) | ||||
−0.380813 | + | 0.924652i | \(0.624356\pi\) | |||||||
\(90\) | −4351.74 | − | 1413.97i | −0.537252 | − | 0.174564i | ||||
\(91\) | 7159.34 | − | 5201.56i | 0.864550 | − | 0.628132i | ||||
\(92\) | −2889.33 | − | 2099.22i | −0.341367 | − | 0.248018i | ||||
\(93\) | 865.797 | + | 2664.65i | 0.100104 | + | 0.308088i | ||||
\(94\) | 8863.05 | − | 2879.78i | 1.00306 | − | 0.325914i | ||||
\(95\) | 5121.61 | − | 7049.29i | 0.567491 | − | 0.781085i | ||||
\(96\) | −593.053 | − | 816.268i | −0.0643504 | − | 0.0885707i | ||||
\(97\) | 4241.03 | − | 13052.6i | 0.450742 | − | 1.38724i | −0.425320 | − | 0.905043i | \(-0.639839\pi\) |
0.876062 | − | 0.482198i | \(-0.160161\pi\) | |||||||
\(98\) | 14087.7i | 1.46685i | ||||||||
\(99\) | −4664.17 | − | 3840.56i | −0.475887 | − | 0.391854i | ||||
\(100\) | −3397.30 | −0.339730 | ||||||||
\(101\) | 9144.05 | + | 2971.08i | 0.896388 | + | 0.291254i | 0.720745 | − | 0.693200i | \(-0.243800\pi\) |
0.175643 | + | 0.984454i | \(0.443800\pi\) | |||||||
\(102\) | −1622.94 | + | 1179.14i | −0.155992 | + | 0.113335i | ||||
\(103\) | −893.689 | − | 649.303i | −0.0842387 | − | 0.0612030i | 0.544869 | − | 0.838521i | \(-0.316579\pi\) |
−0.629107 | + | 0.777318i | \(0.716579\pi\) | |||||||
\(104\) | −720.200 | − | 2216.55i | −0.0665865 | − | 0.204932i | ||||
\(105\) | −14755.7 | + | 4794.42i | −1.33839 | + | 0.434868i | ||||
\(106\) | −4877.88 | + | 6713.83i | −0.434130 | + | 0.597528i | ||||
\(107\) | 5677.54 | + | 7814.47i | 0.495898 | + | 0.682546i | 0.981462 | − | 0.191656i | \(-0.0613857\pi\) |
−0.485564 | + | 0.874201i | \(0.661386\pi\) | |||||||
\(108\) | −1804.14 | + | 5552.59i | −0.154676 | + | 0.476045i | ||||
\(109\) | − | 685.751i | − | 0.0577183i | −0.999583 | − | 0.0288591i | \(-0.990813\pi\) | ||
0.999583 | − | 0.0288591i | \(-0.00918742\pi\) | |||||||
\(110\) | −10318.7 | − | 4058.15i | −0.852788 | − | 0.335384i | ||||
\(111\) | 10808.0 | 0.877204 | ||||||||
\(112\) | 5229.57 | + | 1699.19i | 0.416898 | + | 0.135458i | ||||
\(113\) | −4633.79 | + | 3366.65i | −0.362894 | + | 0.263658i | −0.754258 | − | 0.656578i | \(-0.772003\pi\) |
0.391364 | + | 0.920236i | \(0.372003\pi\) | |||||||
\(114\) | −3430.17 | − | 2492.17i | −0.263941 | − | 0.191764i | ||||
\(115\) | 4469.47 | + | 13755.6i | 0.337956 | + | 1.04012i | ||||
\(116\) | 8274.41 | − | 2688.52i | 0.614923 | − | 0.199801i | ||||
\(117\) | −3023.02 | + | 4160.84i | −0.220836 | + | 0.303955i | ||||
\(118\) | 2680.14 | + | 3688.89i | 0.192483 | + | 0.264930i | ||||
\(119\) | 3378.41 | − | 10397.7i | 0.238571 | − | 0.734247i | ||||
\(120\) | 4086.11i | 0.283757i | ||||||||
\(121\) | −10718.7 | − | 9973.43i | −0.732098 | − | 0.681199i | ||||
\(122\) | 9429.93 | 0.633562 | ||||||||
\(123\) | 8583.06 | + | 2788.80i | 0.567325 | + | 0.184335i | ||||
\(124\) | −3253.35 | + | 2363.70i | −0.211587 | + | 0.153727i | ||||
\(125\) | −5251.04 | − | 3815.11i | −0.336067 | − | 0.244167i | ||||
\(126\) | −3749.68 | − | 11540.3i | −0.236185 | − | 0.726903i | ||||
\(127\) | −29557.9 | + | 9603.94i | −1.83259 | + | 0.595446i | −0.833516 | + | 0.552495i | \(0.813676\pi\) |
−0.999077 | + | 0.0429511i | \(0.986324\pi\) | |||||||
\(128\) | 851.204 | − | 1171.58i | 0.0519534 | − | 0.0715077i | ||||
\(129\) | −4723.54 | − | 6501.40i | −0.283850 | − | 0.390686i | ||||
\(130\) | −2916.67 | + | 8976.60i | −0.172584 | + | 0.531160i | ||||
\(131\) | 8729.96i | 0.508709i | 0.967111 | + | 0.254355i | \(0.0818630\pi\) | ||||
−0.967111 | + | 0.254355i | \(0.918137\pi\) | |||||||
\(132\) | −1974.69 | + | 5021.07i | −0.113331 | + | 0.288170i | ||||
\(133\) | 23106.9 | 1.30629 | ||||||||
\(134\) | 5776.62 | + | 1876.94i | 0.321710 | + | 0.104530i | ||||
\(135\) | 19128.5 | − | 13897.7i | 1.04958 | − | 0.762561i | ||||
\(136\) | −2329.39 | − | 1692.40i | −0.125940 | − | 0.0915011i | ||||
\(137\) | 8160.42 | + | 25115.2i | 0.434782 | + | 1.33812i | 0.893310 | + | 0.449441i | \(0.148377\pi\) |
−0.458528 | + | 0.888680i | \(0.651623\pi\) | |||||||
\(138\) | 6693.46 | − | 2174.84i | 0.351473 | − | 0.114201i | ||||
\(139\) | 10425.4 | − | 14349.3i | 0.539588 | − | 0.742679i | −0.448966 | − | 0.893549i | \(-0.648208\pi\) |
0.988554 | + | 0.150870i | \(0.0482076\pi\) | |||||||
\(140\) | −13089.2 | − | 18015.7i | −0.667816 | − | 0.919170i | ||||
\(141\) | −5674.98 | + | 17465.8i | −0.285447 | + | 0.878517i | ||||
\(142\) | − | 9561.64i | − | 0.474194i | ||||||
\(143\) | −7922.16 | + | 9621.06i | −0.387411 | + | 0.470490i | ||||
\(144\) | −3195.71 | −0.154114 | ||||||||
\(145\) | −33509.8 | − | 10888.0i | −1.59381 | − | 0.517859i | ||||
\(146\) | 17295.6 | − | 12566.0i | 0.811390 | − | 0.589510i | ||||
\(147\) | −22459.6 | − | 16317.8i | −1.03936 | − | 0.755141i | ||||
\(148\) | 4793.68 | + | 14753.4i | 0.218849 | + | 0.673549i | ||||
\(149\) | 17975.7 | − | 5840.66i | 0.809679 | − | 0.263081i | 0.125217 | − | 0.992129i | \(-0.460037\pi\) |
0.684462 | + | 0.729049i | \(0.260037\pi\) | |||||||
\(150\) | 3935.11 | − | 5416.22i | 0.174894 | − | 0.240721i | ||||
\(151\) | −264.180 | − | 363.612i | −0.0115863 | − | 0.0159472i | 0.803185 | − | 0.595730i | \(-0.203137\pi\) |
−0.814771 | + | 0.579783i | \(0.803137\pi\) | |||||||
\(152\) | 1880.53 | − | 5787.68i | 0.0813942 | − | 0.250505i | ||||
\(153\) | 6353.86i | 0.271428i | ||||||||
\(154\) | −7377.78 | − | 28463.6i | −0.311089 | − | 1.20019i | ||||
\(155\) | 16285.8 | 0.677868 | ||||||||
\(156\) | 4368.00 | + | 1419.25i | 0.179487 | + | 0.0583189i | ||||
\(157\) | 28892.7 | − | 20991.8i | 1.17217 | − | 0.851629i | 0.180900 | − | 0.983502i | \(-0.442099\pi\) |
0.991267 | + | 0.131873i | \(0.0420990\pi\) | |||||||
\(158\) | 14810.5 | + | 10760.4i | 0.593273 | + | 0.431038i | ||||
\(159\) | −5053.59 | − | 15553.4i | −0.199897 | − | 0.615219i | ||||
\(160\) | −5577.71 | + | 1812.31i | −0.217879 | + | 0.0707933i | ||||
\(161\) | −22544.8 | + | 31030.3i | −0.869752 | + | 1.19711i | ||||
\(162\) | −38.4574 | − | 52.9321i | −0.00146538 | − | 0.00201692i | ||||
\(163\) | −7301.42 | + | 22471.5i | −0.274810 | + | 0.845777i | 0.714460 | + | 0.699676i | \(0.246672\pi\) |
−0.989270 | + | 0.146101i | \(0.953328\pi\) | |||||||
\(164\) | 12953.2i | 0.481602i | ||||||||
\(165\) | 18422.1 | − | 11750.3i | 0.676660 | − | 0.431600i | ||||
\(166\) | −11480.7 | −0.416631 | ||||||||
\(167\) | −616.899 | − | 200.443i | −0.0221198 | − | 0.00718715i | 0.297936 | − | 0.954586i | \(-0.403702\pi\) |
−0.320056 | + | 0.947399i | \(0.603702\pi\) | |||||||
\(168\) | −8766.41 | + | 6369.17i | −0.310601 | + | 0.225665i | ||||
\(169\) | −14523.5 | − | 10552.0i | −0.508509 | − | 0.369454i | ||||
\(170\) | 3603.32 | + | 11089.9i | 0.124682 | + | 0.383732i | ||||
\(171\) | −12771.9 | + | 4149.85i | −0.436782 | + | 0.141919i | ||||
\(172\) | 6779.66 | − | 9331.40i | 0.229166 | − | 0.315421i | ||||
\(173\) | −13537.7 | − | 18633.0i | −0.452326 | − | 0.622573i | 0.520569 | − | 0.853819i | \(-0.325720\pi\) |
−0.972895 | + | 0.231246i | \(0.925720\pi\) | |||||||
\(174\) | −5298.07 | + | 16305.8i | −0.174993 | + | 0.538572i | ||||
\(175\) | 36485.7i | 1.19137i | ||||||||
\(176\) | −7729.81 | − | 468.537i | −0.249542 | − | 0.0151258i | ||||
\(177\) | −8985.52 | −0.286812 | ||||||||
\(178\) | 16228.3 | + | 5272.89i | 0.512192 | + | 0.166421i | ||||
\(179\) | −5194.85 | + | 3774.28i | −0.162131 | + | 0.117795i | −0.665893 | − | 0.746048i | \(-0.731949\pi\) |
0.503761 | + | 0.863843i | \(0.331949\pi\) | |||||||
\(180\) | 10470.3 | + | 7607.13i | 0.323158 | + | 0.234788i | ||||
\(181\) | 13260.0 | + | 40810.0i | 0.404749 | + | 1.24569i | 0.921105 | + | 0.389315i | \(0.127288\pi\) |
−0.516356 | + | 0.856374i | \(0.672712\pi\) | |||||||
\(182\) | −23804.9 | + | 7734.68i | −0.718660 | + | 0.233507i | ||||
\(183\) | −10922.8 | + | 15033.9i | −0.326159 | + | 0.448920i | ||||
\(184\) | 5937.49 | + | 8172.26i | 0.175375 | + | 0.241383i | ||||
\(185\) | 19413.5 | − | 59748.6i | 0.567231 | − | 1.74576i | ||||
\(186\) | − | 7924.63i | − | 0.229062i | ||||||
\(187\) | −931.567 | + | 15368.8i | −0.0266398 | + | 0.439497i | ||||
\(188\) | −26358.6 | −0.745772 | ||||||||
\(189\) | 59632.7 | + | 19375.8i | 1.66940 | + | 0.542422i | ||||
\(190\) | −19938.4 | + | 14486.1i | −0.552310 | + | 0.401277i | ||||
\(191\) | 20652.0 | + | 15004.5i | 0.566102 | + | 0.411298i | 0.833687 | − | 0.552237i | \(-0.186226\pi\) |
−0.267585 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(192\) | 881.866 | + | 2714.10i | 0.0239221 | + | 0.0736248i | ||||
\(193\) | 40117.2 | − | 13034.9i | 1.07700 | − | 0.349939i | 0.283790 | − | 0.958886i | \(-0.408408\pi\) |
0.793210 | + | 0.608948i | \(0.208408\pi\) | |||||||
\(194\) | −22816.7 | + | 31404.5i | −0.606247 | + | 0.834427i | ||||
\(195\) | −10932.7 | − | 15047.6i | −0.287515 | − | 0.395730i | ||||
\(196\) | 12313.1 | − | 37895.7i | 0.320519 | − | 0.986456i | ||||
\(197\) | − | 37597.4i | − | 0.968781i | −0.874852 | − | 0.484390i | \(-0.839041\pi\) | ||
0.874852 | − | 0.484390i | \(-0.160959\pi\) | |||||||
\(198\) | 9189.81 | + | 14407.7i | 0.234410 | + | 0.367507i | ||||
\(199\) | −37450.3 | −0.945690 | −0.472845 | − | 0.881146i | \(-0.656773\pi\) | ||||
−0.472845 | + | 0.881146i | \(0.656773\pi\) | |||||||
\(200\) | 9138.71 | + | 2969.35i | 0.228468 | + | 0.0742336i | ||||
\(201\) | −9683.44 | + | 7035.43i | −0.239683 | + | 0.174140i | ||||
\(202\) | −22000.6 | − | 15984.4i | −0.539178 | − | 0.391736i | ||||
\(203\) | −28873.7 | − | 88864.1i | −0.700665 | − | 2.15642i | ||||
\(204\) | 5396.31 | − | 1753.37i | 0.129669 | − | 0.0421320i | ||||
\(205\) | 30833.9 | − | 42439.3i | 0.733705 | − | 1.00986i | ||||
\(206\) | 1836.51 | + | 2527.73i | 0.0432771 | + | 0.0595658i | ||||
\(207\) | 6888.41 | − | 21200.3i | 0.160760 | − | 0.494769i | ||||
\(208\) | 6591.98i | 0.152366i | ||||||||
\(209\) | −31501.3 | + | 8165.16i | −0.721167 | + | 0.186927i | ||||
\(210\) | 43883.3 | 0.995086 | ||||||||
\(211\) | −31716.5 | − | 10305.3i | −0.712394 | − | 0.231471i | −0.0696716 | − | 0.997570i | \(-0.522195\pi\) |
−0.642722 | + | 0.766099i | \(0.722195\pi\) | |||||||
\(212\) | 18989.6 | − | 13796.7i | 0.422516 | − | 0.306976i | ||||
\(213\) | 15243.9 | + | 11075.3i | 0.335997 | + | 0.244116i | ||||
\(214\) | −8442.46 | − | 25983.2i | −0.184349 | − | 0.567369i | ||||
\(215\) | −44425.3 | + | 14434.7i | −0.961067 | + | 0.312269i | ||||
\(216\) | 9706.28 | − | 13359.5i | 0.208039 | − | 0.286341i | ||||
\(217\) | 25385.3 | + | 34939.8i | 0.539091 | + | 0.741995i | ||||
\(218\) | −599.368 | + | 1844.67i | −0.0126119 | + | 0.0388154i | ||||
\(219\) | 42129.2i | 0.878405i | ||||||||
\(220\) | 24210.4 | + | 19935.3i | 0.500215 | + | 0.411886i | ||||
\(221\) | 13106.5 | 0.268350 | ||||||||
\(222\) | −29073.5 | − | 9446.56i | −0.589918 | − | 0.191676i | ||||
\(223\) | 24842.4 | − | 18049.1i | 0.499556 | − | 0.362949i | −0.309291 | − | 0.950967i | \(-0.600092\pi\) |
0.808848 | + | 0.588018i | \(0.200092\pi\) | |||||||
\(224\) | −12582.4 | − | 9141.62i | −0.250764 | − | 0.182191i | ||||
\(225\) | −6552.59 | − | 20166.8i | −0.129434 | − | 0.398356i | ||||
\(226\) | 15407.4 | − | 5006.18i | 0.301657 | − | 0.0980143i | ||||
\(227\) | −5431.00 | + | 7475.12i | −0.105397 | + | 0.145066i | −0.858457 | − | 0.512885i | \(-0.828577\pi\) |
0.753060 | + | 0.657951i | \(0.228577\pi\) | |||||||
\(228\) | 7048.91 | + | 9701.99i | 0.135598 | + | 0.186634i | ||||
\(229\) | −23748.2 | + | 73089.5i | −0.452856 | + | 1.39375i | 0.420778 | + | 0.907164i | \(0.361757\pi\) |
−0.873634 | + | 0.486584i | \(0.838243\pi\) | |||||||
\(230\) | − | 40909.0i | − | 0.773327i | ||||||
\(231\) | 53924.5 | + | 21207.4i | 1.01056 | + | 0.397432i | ||||
\(232\) | −24608.0 | −0.457193 | ||||||||
\(233\) | −10685.0 | − | 3471.75i | −0.196816 | − | 0.0639495i | 0.208950 | − | 0.977926i | \(-0.432995\pi\) |
−0.405766 | + | 0.913977i | \(0.632995\pi\) | |||||||
\(234\) | 11768.6 | − | 8550.40i | 0.214928 | − | 0.156155i | ||||
\(235\) | 86360.3 | + | 62744.4i | 1.56379 | + | 1.13616i | ||||
\(236\) | −3985.34 | − | 12265.6i | −0.0715552 | − | 0.220224i | ||||
\(237\) | −34310.1 | + | 11148.0i | −0.610837 | + | 0.198473i | ||||
\(238\) | −18175.8 | + | 25016.8i | −0.320878 | + | 0.441650i | ||||
\(239\) | −16277.0 | − | 22403.4i | −0.284957 | − | 0.392210i | 0.642411 | − | 0.766360i | \(-0.277934\pi\) |
−0.927368 | + | 0.374151i | \(0.877934\pi\) | |||||||
\(240\) | 3571.39 | − | 10991.6i | 0.0620033 | − | 0.190826i | ||||
\(241\) | − | 39221.5i | − | 0.675289i | −0.941274 | − | 0.337644i | \(-0.890370\pi\) | ||
0.941274 | − | 0.337644i | \(-0.109630\pi\) | |||||||
\(242\) | 20116.0 | + | 36196.9i | 0.343488 | + | 0.618075i | ||||
\(243\) | −58984.2 | −0.998903 | ||||||||
\(244\) | −25366.5 | − | 8242.06i | −0.426069 | − | 0.138438i | ||||
\(245\) | −130550. | + | 94850.0i | −2.17492 | + | 1.58017i | ||||
\(246\) | −20650.9 | − | 15003.7i | −0.341246 | − | 0.247930i | ||||
\(247\) | 8560.15 | + | 26345.4i | 0.140310 | + | 0.431828i | ||||
\(248\) | 10817.5 | − | 3514.80i | 0.175882 | − | 0.0571476i | ||||
\(249\) | 13298.1 | − | 18303.3i | 0.214483 | − | 0.295210i | ||||
\(250\) | 10790.8 | + | 14852.2i | 0.172652 | + | 0.237635i | ||||
\(251\) | −25606.0 | + | 78807.1i | −0.406438 | + | 1.25089i | 0.513251 | + | 0.858238i | \(0.328441\pi\) |
−0.919689 | + | 0.392648i | \(0.871559\pi\) | |||||||
\(252\) | 34320.7i | 0.540450i | ||||||||
\(253\) | 19770.0 | − | 50269.7i | 0.308863 | − | 0.785353i | ||||
\(254\) | 87904.7 | 1.36253 | ||||||||
\(255\) | −21854.0 | − | 7100.80i | −0.336086 | − | 0.109201i | ||||
\(256\) | −3313.73 | + | 2407.57i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 4780.54 | + | 3473.26i | 0.0723786 | + | 0.0525861i | 0.623386 | − | 0.781914i | \(-0.285756\pi\) |
−0.551008 | + | 0.834500i | \(0.685756\pi\) | |||||||
\(258\) | 7023.87 | + | 21617.3i | 0.105521 | + | 0.324759i | ||||
\(259\) | 158446. | − | 51482.3i | 2.36201 | − | 0.767465i | ||||
\(260\) | 15691.7 | − | 21597.7i | 0.232125 | − | 0.319493i | ||||
\(261\) | 31918.8 | + | 43932.4i | 0.468560 | + | 0.644918i | ||||
\(262\) | 7630.26 | − | 23483.5i | 0.111157 | − | 0.342106i | ||||
\(263\) | − | 107951.i | − | 1.56069i | −0.625351 | − | 0.780344i | \(-0.715044\pi\) | ||
0.625351 | − | 0.780344i | \(-0.284956\pi\) | |||||||
\(264\) | 9700.47 | − | 11780.7i | 0.139183 | − | 0.169030i | ||||
\(265\) | −95058.8 | −1.35363 | ||||||||
\(266\) | −62157.5 | − | 20196.2i | −0.878477 | − | 0.285435i | ||||
\(267\) | −27203.8 | + | 19764.7i | −0.381599 | + | 0.277248i | ||||
\(268\) | −13898.6 | − | 10097.9i | −0.193509 | − | 0.140592i | ||||
\(269\) | −4826.05 | − | 14853.1i | −0.0666941 | − | 0.205263i | 0.912156 | − | 0.409844i | \(-0.134417\pi\) |
−0.978850 | + | 0.204581i | \(0.934417\pi\) | |||||||
\(270\) | −63602.6 | + | 20665.7i | −0.872464 | + | 0.283481i | ||||
\(271\) | −20136.9 | + | 27716.1i | −0.274192 | + | 0.377392i | −0.923799 | − | 0.382877i | \(-0.874933\pi\) |
0.649608 | + | 0.760270i | \(0.274933\pi\) | |||||||
\(272\) | 4786.84 | + | 6588.52i | 0.0647010 | + | 0.0890533i | ||||
\(273\) | 15242.2 | − | 46910.7i | 0.204514 | − | 0.629428i | ||||
\(274\) | − | 74692.2i | − | 0.994887i | ||||||
\(275\) | −12892.7 | − | 49740.4i | −0.170482 | − | 0.657724i | ||||
\(276\) | −19906.2 | −0.261319 | ||||||||
\(277\) | 68601.8 | + | 22290.1i | 0.894079 | + | 0.290504i | 0.719791 | − | 0.694191i | \(-0.244238\pi\) |
0.174288 | + | 0.984695i | \(0.444238\pi\) | |||||||
\(278\) | −40585.9 | + | 29487.4i | −0.525153 | + | 0.381546i | ||||
\(279\) | −20306.2 | − | 14753.3i | −0.260868 | − | 0.189531i | ||||
\(280\) | 19463.5 | + | 59902.6i | 0.248259 | + | 0.764063i | ||||
\(281\) | 96719.5 | − | 31426.1i | 1.22490 | − | 0.397995i | 0.376037 | − | 0.926605i | \(-0.377287\pi\) |
0.848865 | + | 0.528610i | \(0.177287\pi\) | |||||||
\(282\) | 30531.3 | − | 42022.8i | 0.383926 | − | 0.528429i | ||||
\(283\) | −1793.34 | − | 2468.33i | −0.0223919 | − | 0.0308198i | 0.797674 | − | 0.603089i | \(-0.206063\pi\) |
−0.820066 | + | 0.572269i | \(0.806063\pi\) | |||||||
\(284\) | −8357.18 | + | 25720.8i | −0.103615 | + | 0.318895i | ||||
\(285\) | − | 48566.6i | − | 0.597927i | ||||||
\(286\) | 29719.7 | − | 18956.4i | 0.363339 | − | 0.231752i | ||||
\(287\) | 139112. | 1.68889 | ||||||||
\(288\) | 8596.44 | + | 2793.15i | 0.103641 | + | 0.0336752i | ||||
\(289\) | −54470.3 | + | 39575.0i | −0.652175 | + | 0.473833i | ||||
\(290\) | 80624.7 | + | 58577.3i | 0.958676 | + | 0.696519i | ||||
\(291\) | −23638.6 | − | 72752.1i | −0.279149 | − | 0.859131i | ||||
\(292\) | −57508.1 | + | 18685.5i | −0.674471 | + | 0.219149i | ||||
\(293\) | 6804.87 | − | 9366.10i | 0.0792656 | − | 0.109100i | −0.767543 | − | 0.640997i | \(-0.778521\pi\) |
0.846809 | + | 0.531898i | \(0.178521\pi\) | |||||||
\(294\) | 46153.8 | + | 63525.3i | 0.533965 | + | 0.734940i | ||||
\(295\) | −16139.9 | + | 49673.4i | −0.185463 | + | 0.570795i | ||||
\(296\) | − | 43876.5i | − | 0.500781i | ||||||
\(297\) | −88143.0 | − | 5342.72i | −0.999252 | − | 0.0605689i | ||||
\(298\) | −53459.4 | −0.601993 | ||||||||
\(299\) | −43731.2 | − | 14209.1i | −0.489158 | − | 0.158937i | ||||
\(300\) | −15319.4 | + | 11130.2i | −0.170215 | + | 0.123669i | ||||
\(301\) | −100216. | − | 72811.1i | −1.10612 | − | 0.803645i | ||||
\(302\) | 392.833 | + | 1209.02i | 0.00430720 | + | 0.0132562i | ||||
\(303\) | 50967.0 | − | 16560.2i | 0.555141 | − | 0.180376i | ||||
\(304\) | −10117.2 | + | 13925.2i | −0.109475 | + | 0.150679i | ||||
\(305\) | 63490.2 | + | 87386.8i | 0.682507 | + | 0.939391i | ||||
\(306\) | 5553.47 | − | 17091.8i | 0.0593092 | − | 0.182535i | ||||
\(307\) | 26745.6i | 0.283776i | 0.989883 | + | 0.141888i | \(0.0453174\pi\) | ||||
−0.989883 | + | 0.141888i | \(0.954683\pi\) | |||||||
\(308\) | −5031.91 | + | 83015.3i | −0.0530434 | + | 0.875098i | ||||
\(309\) | −6157.13 | −0.0644854 | ||||||||
\(310\) | −43808.6 | − | 14234.3i | −0.455865 | − | 0.148120i | ||||
\(311\) | 32169.2 | − | 23372.3i | 0.332598 | − | 0.241646i | −0.408934 | − | 0.912564i | \(-0.634100\pi\) |
0.741532 | + | 0.670917i | \(0.234100\pi\) | |||||||
\(312\) | −10509.4 | − | 7635.54i | −0.107962 | − | 0.0784387i | ||||
\(313\) | −26400.8 | − | 81253.2i | −0.269481 | − | 0.829377i | −0.990627 | − | 0.136594i | \(-0.956384\pi\) |
0.721146 | − | 0.692783i | \(-0.243616\pi\) | |||||||
\(314\) | −96068.8 | + | 31214.6i | −0.974368 | + | 0.316591i | ||||
\(315\) | 81697.7 | − | 112447.i | 0.823358 | − | 1.13326i | ||||
\(316\) | −30435.1 | − | 41890.3i | −0.304790 | − | 0.419507i | ||||
\(317\) | 7585.16 | − | 23344.7i | 0.0754825 | − | 0.232311i | −0.906195 | − | 0.422859i | \(-0.861026\pi\) |
0.981678 | + | 0.190548i | \(0.0610265\pi\) | |||||||
\(318\) | 46255.4i | 0.457413i | ||||||||
\(319\) | 70764.4 | + | 110944.i | 0.695398 | + | 1.09024i | ||||
\(320\) | 16588.0 | 0.161992 | ||||||||
\(321\) | 51203.3 | + | 16637.0i | 0.496922 | + | 0.161460i | ||||
\(322\) | 87767.0 | − | 63766.5i | 0.846486 | − | 0.615008i | ||||
\(323\) | 27686.7 | + | 20115.6i | 0.265379 | + | 0.192809i | ||||
\(324\) | 57.1858 | + | 176.000i | 0.000544752 | + | 0.00167657i | ||||
\(325\) | −41599.3 | + | 13516.4i | −0.393839 | + | 0.127966i | ||||
\(326\) | 39281.5 | − | 54066.4i | 0.369618 | − | 0.508736i | ||||
\(327\) | −2246.65 | − | 3092.25i | −0.0210106 | − | 0.0289187i | ||||
\(328\) | 11321.5 | − | 34843.9i | 0.105234 | − | 0.323876i | ||||
\(329\) | 283081.i | 2.61529i | ||||||||
\(330\) | −59825.4 | + | 15506.8i | −0.549360 | + | 0.142395i | ||||
\(331\) | −88390.7 | −0.806772 | −0.403386 | − | 0.915030i | \(-0.632167\pi\) | ||||
−0.403386 | + | 0.915030i | \(0.632167\pi\) | |||||||
\(332\) | 30883.0 | + | 10034.5i | 0.280184 | + | 0.0910372i | ||||
\(333\) | −78332.4 | + | 56911.8i | −0.706404 | + | 0.513232i | ||||
\(334\) | 1484.26 | + | 1078.38i | 0.0133051 | + | 0.00966670i | ||||
\(335\) | 21499.5 | + | 66168.8i | 0.191575 | + | 0.589608i | ||||
\(336\) | 29148.5 | − | 9470.91i | 0.258189 | − | 0.0838906i | ||||
\(337\) | −59771.4 | + | 82268.3i | −0.526301 | + | 0.724391i | −0.986561 | − | 0.163393i | \(-0.947756\pi\) |
0.460260 | + | 0.887784i | \(0.347756\pi\) | |||||||
\(338\) | 29845.5 | + | 41078.7i | 0.261243 | + | 0.359570i | ||||
\(339\) | −9865.32 | + | 30362.3i | −0.0858444 | + | 0.264202i | ||||
\(340\) | − | 32981.1i | − | 0.285304i | ||||||
\(341\) | −46953.8 | − | 38662.7i | −0.403796 | − | 0.332493i | ||||
\(342\) | 37983.5 | 0.324745 | ||||||||
\(343\) | −210795. | − | 68491.6i | −1.79173 | − | 0.582169i | ||||
\(344\) | −26393.2 | + | 19175.8i | −0.223036 | + | 0.162045i | ||||
\(345\) | 65220.1 | + | 47385.2i | 0.547953 | + | 0.398111i | ||||
\(346\) | 20130.4 | + | 61955.0i | 0.168151 | + | 0.517516i | ||||
\(347\) | 35079.8 | − | 11398.1i | 0.291338 | − | 0.0946616i | −0.159702 | − | 0.987165i | \(-0.551053\pi\) |
0.451040 | + | 0.892504i | \(0.351053\pi\) | |||||||
\(348\) | 28503.6 | − | 39231.8i | 0.235364 | − | 0.323951i | ||||
\(349\) | −60796.7 | − | 83679.5i | −0.499148 | − | 0.687018i | 0.482894 | − | 0.875679i | \(-0.339585\pi\) |
−0.982042 | + | 0.188660i | \(0.939585\pi\) | |||||||
\(350\) | 31889.7 | − | 98146.3i | 0.260324 | − | 0.801194i | ||||
\(351\) | 75168.3i | 0.610127i | ||||||||
\(352\) | 20383.6 | + | 8016.47i | 0.164512 | + | 0.0646990i | ||||
\(353\) | 50438.5 | 0.404774 | 0.202387 | − | 0.979306i | \(-0.435130\pi\) | ||||
0.202387 | + | 0.979306i | \(0.435130\pi\) | |||||||
\(354\) | 24171.0 | + | 7853.63i | 0.192880 | + | 0.0626706i | ||||
\(355\) | 88607.4 | − | 64377.0i | 0.703094 | − | 0.510827i | ||||
\(356\) | −39045.3 | − | 28368.1i | −0.308084 | − | 0.223836i | ||||
\(357\) | −18830.5 | − | 57954.3i | −0.147749 | − | 0.454726i | ||||
\(358\) | 17273.0 | − | 5612.33i | 0.134772 | − | 0.0437902i | ||||
\(359\) | 51281.0 | − | 70582.2i | 0.397894 | − | 0.547654i | −0.562320 | − | 0.826920i | \(-0.690091\pi\) |
0.960214 | + | 0.279266i | \(0.0900910\pi\) | |||||||
\(360\) | −21516.2 | − | 29614.5i | −0.166020 | − | 0.228507i | ||||
\(361\) | 17919.8 | − | 55151.5i | 0.137505 | − | 0.423197i | ||||
\(362\) | − | 121368.i | − | 0.926165i | ||||||
\(363\) | −81008.3 | − | 9856.73i | −0.614775 | − | 0.0748031i | ||||
\(364\) | 70795.4 | 0.534321 | ||||||||
\(365\) | 232897. | + | 75672.8i | 1.74815 | + | 0.568008i | ||||
\(366\) | 42522.2 | − | 30894.2i | 0.317434 | − | 0.230630i | ||||
\(367\) | 41866.7 | + | 30417.9i | 0.310840 | + | 0.225838i | 0.732257 | − | 0.681029i | \(-0.238467\pi\) |
−0.421417 | + | 0.906867i | \(0.638467\pi\) | |||||||
\(368\) | −8829.00 | − | 27172.9i | −0.0651953 | − | 0.200650i | ||||
\(369\) | −76891.7 | + | 24983.6i | −0.564711 | + | 0.183486i | ||||
\(370\) | −104444. | + | 143755.i | −0.762924 | + | 1.05008i | ||||
\(371\) | −148172. | − | 203941.i | −1.07651 | − | 1.48169i | ||||
\(372\) | −6926.38 | + | 21317.2i | −0.0500519 | + | 0.154044i | ||||
\(373\) | − | 180034.i | − | 1.29401i | −0.762487 | − | 0.647003i | \(-0.776022\pi\) | ||
0.762487 | − | 0.647003i | \(-0.223978\pi\) | |||||||
\(374\) | 15938.7 | − | 40527.7i | 0.113949 | − | 0.289740i | ||||
\(375\) | −36177.5 | −0.257262 | ||||||||
\(376\) | 70904.4 | + | 23038.2i | 0.501531 | + | 0.162957i | ||||
\(377\) | 90622.1 | − | 65840.8i | 0.637604 | − | 0.463247i | ||||
\(378\) | −143477. | − | 104242.i | −1.00415 | − | 0.729556i | ||||
\(379\) | 57325.3 | + | 176429.i | 0.399087 | + | 1.22826i | 0.925732 | + | 0.378179i | \(0.123450\pi\) |
−0.526645 | + | 0.850085i | \(0.676550\pi\) | |||||||
\(380\) | 66295.5 | − | 21540.7i | 0.459110 | − | 0.149174i | ||||
\(381\) | −101821. | + | 140144.i | −0.701433 | + | 0.965439i | ||||
\(382\) | −42439.3 | − | 58412.6i | −0.290831 | − | 0.400295i | ||||
\(383\) | −1955.49 | + | 6018.39i | −0.0133309 | + | 0.0410283i | −0.957501 | − | 0.288431i | \(-0.906866\pi\) |
0.944170 | + | 0.329459i | \(0.106866\pi\) | |||||||
\(384\) | − | 8071.70i | − | 0.0547397i | ||||||
\(385\) | 214098. | − | 260011.i | 1.44441 | − | 1.75416i | ||||
\(386\) | −119308. | −0.800746 | ||||||||
\(387\) | 68468.8 | + | 22246.9i | 0.457163 | + | 0.148541i | ||||
\(388\) | 88825.3 | − | 64535.4i | 0.590029 | − | 0.428681i | ||||
\(389\) | −89160.2 | − | 64778.7i | −0.589212 | − | 0.428088i | 0.252821 | − | 0.967513i | \(-0.418642\pi\) |
−0.842034 | + | 0.539425i | \(0.818642\pi\) | |||||||
\(390\) | 16256.9 | + | 50033.6i | 0.106883 | + | 0.328952i | ||||
\(391\) | −54026.4 | + | 17554.2i | −0.353388 | + | 0.114823i | ||||
\(392\) | −66244.1 | + | 91177.2i | −0.431097 | + | 0.593354i | ||||
\(393\) | 28601.0 | + | 39365.9i | 0.185181 | + | 0.254879i | ||||
\(394\) | −32861.3 | + | 101137.i | −0.211686 | + | 0.651503i | ||||
\(395\) | 209696.i | 1.34399i | ||||||||
\(396\) | −12127.7 | − | 46788.9i | −0.0773372 | − | 0.298368i | ||||
\(397\) | −205760. | −1.30551 | −0.652755 | − | 0.757569i | \(-0.726387\pi\) | ||||
−0.652755 | + | 0.757569i | \(0.726387\pi\) | |||||||
\(398\) | 100741. | + | 32732.7i | 0.635975 | + | 0.206641i | ||||
\(399\) | 104196. | − | 75702.7i | 0.654492 | − | 0.475516i | ||||
\(400\) | −21987.8 | − | 15975.0i | −0.137424 | − | 0.0998440i | ||||
\(401\) | 40707.1 | + | 125284.i | 0.253152 | + | 0.779122i | 0.994188 | + | 0.107657i | \(0.0343347\pi\) |
−0.741036 | + | 0.671465i | \(0.765665\pi\) | |||||||
\(402\) | 32197.6 | − | 10461.6i | 0.199238 | − | 0.0647362i | ||||
\(403\) | −30432.5 | + | 41886.8i | −0.187382 | + | 0.257909i | ||||
\(404\) | 45210.7 | + | 62227.2i | 0.276999 | + | 0.381257i | ||||
\(405\) | 231.592 | − | 712.766i | 0.00141193 | − | 0.00434547i | ||||
\(406\) | 264280.i | 1.60329i | ||||||||
\(407\) | −197815. | + | 126174.i | −1.19418 | + | 0.761696i | ||||
\(408\) | −16048.5 | −0.0964084 | ||||||||
\(409\) | 75524.9 | + | 24539.5i | 0.451485 | + | 0.146696i | 0.525928 | − | 0.850529i | \(-0.323718\pi\) |
−0.0744433 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(410\) | −120036. | + | 87211.6i | −0.714077 | + | 0.518808i | ||||
\(411\) | 119080. | + | 86516.5i | 0.704943 | + | 0.512171i | ||||
\(412\) | −2730.87 | − | 8404.75i | −0.0160882 | − | 0.0495143i | ||||
\(413\) | −131728. | + | 42801.1i | −0.772287 | + | 0.250931i | ||||
\(414\) | −37059.6 | + | 51008.1i | −0.216222 | + | 0.297604i | ||||
\(415\) | −77297.6 | − | 106391.i | −0.448817 | − | 0.617744i | ||||
\(416\) | 5761.60 | − | 17732.4i | 0.0332933 | − | 0.102466i | ||||
\(417\) | − | 98860.5i | − | 0.568527i | ||||||
\(418\) | 91874.9 | + | 5568.93i | 0.525829 | + | 0.0318727i | ||||
\(419\) | 281150. | 1.60144 | 0.800718 | − | 0.599041i | \(-0.204451\pi\) | ||||
0.800718 | + | 0.599041i | \(0.204451\pi\) | |||||||
\(420\) | −118046. | − | 38355.4i | −0.669194 | − | 0.217434i | ||||
\(421\) | 268282. | − | 194918.i | 1.51366 | − | 1.09974i | 0.549136 | − | 0.835733i | \(-0.314957\pi\) |
0.964522 | − | 0.264004i | \(-0.0850433\pi\) | |||||||
\(422\) | 76310.0 | + | 55442.5i | 0.428506 | + | 0.311328i | ||||
\(423\) | −50839.5 | − | 156468.i | −0.284132 | − | 0.874469i | ||||
\(424\) | −63140.6 | + | 20515.6i | −0.351218 | + | 0.114118i | ||||
\(425\) | −31762.3 | + | 43717.1i | −0.175847 | + | 0.242032i | ||||
\(426\) | −31325.7 | − | 43116.2i | −0.172616 | − | 0.237586i | ||||
\(427\) | −88516.7 | + | 272426.i | −0.485478 | + | 1.49415i | ||||
\(428\) | 77273.7i | 0.421836i | ||||||||
\(429\) | −4202.90 | + | 69338.6i | −0.0228368 | + | 0.376756i | ||||
\(430\) | 132120. | 0.714549 | ||||||||
\(431\) | −118641. | − | 38548.8i | −0.638675 | − | 0.207518i | −0.0282608 | − | 0.999601i | \(-0.508997\pi\) |
−0.610414 | + | 0.792083i | \(0.708997\pi\) | |||||||
\(432\) | −37786.5 | + | 27453.5i | −0.202474 | + | 0.147106i | ||||
\(433\) | −20821.9 | − | 15128.0i | −0.111057 | − | 0.0806874i | 0.530871 | − | 0.847453i | \(-0.321865\pi\) |
−0.641927 | + | 0.766765i | \(0.721865\pi\) | |||||||
\(434\) | −37747.7 | − | 116175.i | −0.200406 | − | 0.616787i | ||||
\(435\) | −186776. | + | 60687.3i | −0.987059 | + | 0.320715i | ||||
\(436\) | 3224.59 | − | 4438.27i | 0.0169630 | − | 0.0233475i | ||||
\(437\) | −70571.8 | − | 97133.7i | −0.369546 | − | 0.508636i | ||||
\(438\) | 36822.2 | − | 113327.i | 0.191938 | − | 0.590726i | ||||
\(439\) | − | 123861.i | − | 0.642693i | −0.946962 | − | 0.321347i | \(-0.895865\pi\) | ||
0.946962 | − | 0.321347i | \(-0.104135\pi\) | |||||||
\(440\) | −47701.7 | − | 74786.5i | −0.246393 | − | 0.386294i | ||||
\(441\) | 248703. | 1.27880 | ||||||||
\(442\) | −35256.4 | − | 11455.5i | −0.180465 | − | 0.0586366i | ||||
\(443\) | 59932.0 | − | 43543.2i | 0.305388 | − | 0.221877i | −0.424527 | − | 0.905415i | \(-0.639560\pi\) |
0.729915 | + | 0.683538i | \(0.239560\pi\) | |||||||
\(444\) | 69951.0 | + | 50822.4i | 0.354836 | + | 0.257804i | ||||
\(445\) | 60398.9 | + | 185889.i | 0.305006 | + | 0.938713i | ||||
\(446\) | −82601.5 | + | 26838.9i | −0.415258 | + | 0.134926i | ||||
\(447\) | 61922.4 | − | 85228.9i | 0.309908 | − | 0.426552i | ||||
\(448\) | 25856.4 | + | 35588.3i | 0.128828 | + | 0.177317i | ||||
\(449\) | 71324.2 | − | 219513.i | 0.353789 | − | 1.08885i | −0.602920 | − | 0.797802i | \(-0.705996\pi\) |
0.956708 | − | 0.291048i | \(-0.0940040\pi\) | |||||||
\(450\) | 59975.7i | 0.296176i | ||||||||
\(451\) | −189649. | + | 49157.2i | −0.932391 | + | 0.241676i | ||||
\(452\) | −45821.4 | −0.224281 | ||||||||
\(453\) | −2382.53 | − | 774.129i | −0.0116102 | − | 0.00377239i | ||||
\(454\) | 21142.8 | − | 15361.2i | 0.102577 | − | 0.0745268i | ||||
\(455\) | −231952. | − | 168523.i | −1.12040 | − | 0.814021i | ||||
\(456\) | −10481.7 | − | 32259.3i | −0.0504082 | − | 0.155140i | ||||
\(457\) | 120027. | − | 38999.1i | 0.574706 | − | 0.186733i | −0.00722142 | − | 0.999974i | \(-0.502299\pi\) |
0.581928 | + | 0.813241i | \(0.302299\pi\) | |||||||
\(458\) | 127765. | − | 175854.i | 0.609090 | − | 0.838341i | ||||
\(459\) | 54584.3 | + | 75128.9i | 0.259085 | + | 0.356600i | ||||
\(460\) | −35755.8 | + | 110045.i | −0.168978 | + | 0.520062i | ||||
\(461\) | 65227.4i | 0.306922i | 0.988155 | + | 0.153461i | \(0.0490420\pi\) | ||||
−0.988155 | + | 0.153461i | \(0.950958\pi\) | |||||||
\(462\) | −126521. | − | 104179.i | −0.592758 | − | 0.488088i | ||||
\(463\) | 308377. | 1.43853 | 0.719267 | − | 0.694733i | \(-0.244478\pi\) | ||||
0.719267 | + | 0.694733i | \(0.244478\pi\) | |||||||
\(464\) | 66195.3 | + | 21508.1i | 0.307462 | + | 0.0999003i | ||||
\(465\) | 73437.2 | − | 53355.3i | 0.339633 | − | 0.246758i | ||||
\(466\) | 25708.0 | + | 18678.0i | 0.118385 | + | 0.0860119i | ||||
\(467\) | −115280. | − | 354796.i | −0.528592 | − | 1.62684i | −0.757102 | − | 0.653297i | \(-0.773385\pi\) |
0.228510 | − | 0.973542i | \(-0.426615\pi\) | |||||||
\(468\) | −39130.9 | + | 12714.4i | −0.178660 | + | 0.0580502i | ||||
\(469\) | −108448. | + | 149265.i | −0.493031 | + | 0.678599i | ||||
\(470\) | −177468. | − | 244264.i | −0.803386 | − | 1.10577i | ||||
\(471\) | 61512.5 | − | 189316.i | 0.277282 | − | 0.853386i | ||||
\(472\) | 36477.8i | 0.163736i | ||||||||
\(473\) | 162351. | + | 63849.5i | 0.725661 | + | 0.285388i | ||||
\(474\) | 102038. | 0.454155 | ||||||||
\(475\) | −108621. | − | 35293.0i | −0.481422 | − | 0.156423i | ||||
\(476\) | 70758.3 | − | 51408.9i | 0.312294 | − | 0.226895i | ||||
\(477\) | 118526. | + | 86113.9i | 0.520926 | + | 0.378475i | ||||
\(478\) | 24203.8 | + | 74491.7i | 0.105932 | + | 0.326026i | ||||
\(479\) | −243681. | + | 79176.8i | −1.06207 | + | 0.345086i | −0.787392 | − | 0.616452i | \(-0.788569\pi\) |
−0.274673 | + | 0.961538i | \(0.588569\pi\) | |||||||
\(480\) | −19214.0 | + | 26445.8i | −0.0833942 | + | 0.114782i | ||||
\(481\) | 117395. | + | 161581.i | 0.507412 | + | 0.698393i | ||||
\(482\) | −34280.8 | + | 105505.i | −0.147556 | + | 0.454131i | ||||
\(483\) | 213786.i | 0.916399i | ||||||||
\(484\) | −22474.7 | − | 114952.i | −0.0959408 | − | 0.490709i | ||||
\(485\) | −444645. | −1.89030 | ||||||||
\(486\) | 158667. | + | 51554.1i | 0.671761 | + | 0.218268i | ||||
\(487\) | −181763. | + | 132058.i | −0.766385 | + | 0.556811i | −0.900862 | − | 0.434105i | \(-0.857065\pi\) |
0.134477 | + | 0.990917i | \(0.457065\pi\) | |||||||
\(488\) | 61031.8 | + | 44342.2i | 0.256281 | + | 0.186199i | ||||
\(489\) | 40696.5 | + | 125251.i | 0.170192 | + | 0.523798i | ||||
\(490\) | 434080. | − | 141041.i | 1.80791 | − | 0.587427i | ||||
\(491\) | 58960.8 | − | 81152.6i | 0.244568 | − | 0.336620i | −0.669031 | − | 0.743234i | \(-0.733291\pi\) |
0.913600 | + | 0.406615i | \(0.133291\pi\) | |||||||
\(492\) | 42437.0 | + | 58409.5i | 0.175313 | + | 0.241298i | ||||
\(493\) | 42763.5 | − | 131612.i | 0.175946 | − | 0.541506i | ||||
\(494\) | − | 78350.9i | − | 0.321063i | ||||||
\(495\) | −71642.4 | + | 182167.i | −0.292388 | + | 0.743461i | ||||
\(496\) | −32170.9 | −0.130768 | ||||||||
\(497\) | 276231. | + | 89753.0i | 1.11831 | + | 0.363359i | ||||
\(498\) | −51769.6 | + | 37612.8i | −0.208745 | + | 0.151662i | ||||
\(499\) | −208468. | − | 151461.i | −0.837217 | − | 0.608274i | 0.0843746 | − | 0.996434i | \(-0.473111\pi\) |
−0.921592 | + | 0.388160i | \(0.873111\pi\) | |||||||
\(500\) | −16045.8 | − | 49383.8i | −0.0641831 | − | 0.197535i | ||||
\(501\) | −3438.46 | + | 1117.22i | −0.0136990 | + | 0.00445107i | ||||
\(502\) | 137760. | − | 189610.i | 0.546657 | − | 0.752409i | ||||
\(503\) | 238719. | + | 328568.i | 0.943518 | + | 1.29864i | 0.954347 | + | 0.298700i | \(0.0965529\pi\) |
−0.0108292 | + | 0.999941i | \(0.503447\pi\) | |||||||
\(504\) | 29997.4 | − | 92322.6i | 0.118093 | − | 0.363452i | ||||
\(505\) | − | 311499.i | − | 1.22145i | ||||||
\(506\) | −97118.6 | + | 117945.i | −0.379316 | + | 0.460660i | ||||
\(507\) | −100061. | −0.389268 | ||||||||
\(508\) | −236463. | − | 76831.6i | −0.916297 | − | 0.297723i | ||||
\(509\) | −263060. | + | 191124.i | −1.01536 | + | 0.737700i | −0.965326 | − | 0.261047i | \(-0.915932\pi\) |
−0.0500314 | + | 0.998748i | \(0.515932\pi\) | |||||||
\(510\) | 52580.9 | + | 38202.2i | 0.202156 | + | 0.146875i | ||||
\(511\) | 200676. | + | 617616.i | 0.768516 | + | 2.36525i | ||||
\(512\) | 11018.2 | − | 3580.04i | 0.0420312 | − | 0.0136568i | ||||
\(513\) | −115367. | + | 158789.i | −0.438375 | + | 0.603372i | ||||
\(514\) | −9823.87 | − | 13521.4i | −0.0371840 | − | 0.0511794i | ||||
\(515\) | −11059.5 | + | 34037.7i | −0.0416986 | + | 0.128335i | ||||
\(516\) | − | 64289.4i | − | 0.241457i | ||||||
\(517\) | −100031. | − | 385920.i | −0.374242 | − | 1.44383i | ||||
\(518\) | −471217. | −1.75615 | ||||||||
\(519\) | −122090. | − | 39669.6i | −0.453259 | − | 0.147273i | ||||
\(520\) | −61087.6 | + | 44382.7i | −0.225916 | + | 0.164137i | ||||
\(521\) | −322750. | − | 234492.i | −1.18903 | − | 0.863878i | −0.195865 | − | 0.980631i | \(-0.562751\pi\) |
−0.993161 | + | 0.116753i | \(0.962751\pi\) | |||||||
\(522\) | −47463.0 | − | 146076.i | −0.174186 | − | 0.536090i | ||||
\(523\) | 295038. | − | 95863.6i | 1.07863 | − | 0.350470i | 0.284790 | − | 0.958590i | \(-0.408076\pi\) |
0.793845 | + | 0.608120i | \(0.208076\pi\) | |||||||
\(524\) | −41050.7 | + | 56501.5i | −0.149506 | + | 0.205777i | ||||
\(525\) | 119534. | + | 164524.i | 0.433683 | + | 0.596914i | ||||
\(526\) | −94352.8 | + | 290388.i | −0.341023 | + | 1.04956i | ||||
\(527\) | 63963.8i | 0.230310i | ||||||||
\(528\) | −36390.9 | + | 23211.5i | −0.130535 | + | 0.0832600i | ||||
\(529\) | −80545.0 | −0.287824 | ||||||||
\(530\) | 255708. | + | 83084.4i | 0.910315 | + | 0.295779i | ||||
\(531\) | 65123.5 | − | 47315.0i | 0.230966 | − | 0.167807i | ||||
\(532\) | 149551. | + | 108655.i | 0.528405 | + | 0.383909i | ||||
\(533\) | 51535.2 | + | 158609.i | 0.181405 | + | 0.558307i | ||||
\(534\) | 90453.0 | − | 29390.0i | 0.317205 | − | 0.103066i | ||||
\(535\) | 183944. | − | 253177.i | 0.642654 | − | 0.884538i | ||||
\(536\) | 28561.2 | + | 39311.1i | 0.0994137 | + | 0.136831i | ||||
\(537\) | −11059.8 | + | 34038.6i | −0.0383530 | + | 0.118038i | ||||
\(538\) | 44172.8i | 0.152613i | ||||||||
\(539\) | 601565. | + | 36463.4i | 2.07064 | + | 0.125510i | ||||
\(540\) | 189153. | 0.648674 | ||||||||
\(541\) | −356881. | − | 115958.i | −1.21935 | − | 0.396191i | −0.372505 | − | 0.928030i | \(-0.621501\pi\) |
−0.846845 | + | 0.531839i | \(0.821501\pi\) | |||||||
\(542\) | 78392.9 | − | 56955.8i | 0.266857 | − | 0.193883i | ||||
\(543\) | 193494. | + | 140582.i | 0.656249 | + | 0.476792i | ||||
\(544\) | −7117.99 | − | 21906.9i | −0.0240525 | − | 0.0740259i | ||||
\(545\) | −21129.9 | + | 6865.52i | −0.0711384 | + | 0.0231143i | ||||
\(546\) | −82002.8 | + | 112867.i | −0.275070 | + | 0.378602i | ||||
\(547\) | −129542. | − | 178299.i | −0.432947 | − | 0.595901i | 0.535679 | − | 0.844422i | \(-0.320056\pi\) |
−0.968627 | + | 0.248521i | \(0.920056\pi\) | |||||||
\(548\) | −65283.3 | + | 200921.i | −0.217391 | + | 0.669060i | ||||
\(549\) | − | 166476.i | − | 0.552339i | ||||||
\(550\) | −8793.30 | + | 145070.i | −0.0290688 | + | 0.479570i | ||||
\(551\) | 292485. | 0.963386 | ||||||||
\(552\) | 53547.7 | + | 17398.7i | 0.175737 | + | 0.0571003i | ||||
\(553\) | −449886. | + | 326862.i | −1.47114 | + | 1.06884i | ||||
\(554\) | −165056. | − | 119920.i | −0.537789 | − | 0.390727i | ||||
\(555\) | −108207. | − | 333026.i | −0.351292 | − | 1.08116i | ||||
\(556\) | 134949. | − | 43847.5i | 0.436536 | − | 0.141839i | ||||
\(557\) | 252579. | − | 347646.i | 0.814118 | − | 1.12054i | −0.176557 | − | 0.984290i | \(-0.556496\pi\) |
0.990675 | − | 0.136247i | \(-0.0435040\pi\) | |||||||
\(558\) | 41728.7 | + | 57434.6i | 0.134019 | + | 0.184461i | ||||
\(559\) | 45889.9 | − | 141235.i | 0.146857 | − | 0.451979i | ||||
\(560\) | − | 178149.i | − | 0.568078i | ||||||
\(561\) | 46150.3 | + | 72354.2i | 0.146639 | + | 0.229899i | ||||
\(562\) | −287642. | −0.910710 | ||||||||
\(563\) | −438495. | − | 142476.i | −1.38340 | − | 0.449494i | −0.479615 | − | 0.877479i | \(-0.659224\pi\) |
−0.903786 | + | 0.427984i | \(0.859224\pi\) | |||||||
\(564\) | −118858. | + | 86355.6i | −0.373655 | + | 0.271477i | ||||
\(565\) | 150128. | + | 109074.i | 0.470288 | + | 0.341685i | ||||
\(566\) | 2666.69 | + | 8207.23i | 0.00832414 | + | 0.0256191i | ||||
\(567\) | 1890.17 | − | 614.155i | 0.00587944 | − | 0.00191034i | ||||
\(568\) | 44961.5 | − | 61884.2i | 0.139362 | − | 0.191815i | ||||
\(569\) | −98286.5 | − | 135280.i | −0.303577 | − | 0.417838i | 0.629788 | − | 0.776767i | \(-0.283142\pi\) |
−0.933365 | + | 0.358929i | \(0.883142\pi\) | |||||||
\(570\) | −42448.8 | + | 130644.i | −0.130652 | + | 0.402105i | ||||
\(571\) | − | 317894.i | − | 0.975012i | −0.873119 | − | 0.487506i | \(-0.837907\pi\) | ||
0.873119 | − | 0.487506i | \(-0.162093\pi\) | |||||||
\(572\) | −96514.2 | + | 25016.5i | −0.294985 | + | 0.0764602i | ||||
\(573\) | 142283. | 0.433356 | ||||||||
\(574\) | −374211. | − | 121588.i | −1.13578 | − | 0.369036i | ||||
\(575\) | 153374. | − | 111432.i | 0.463890 | − | 0.337036i | ||||
\(576\) | −20683.1 | − | 15027.1i | −0.0623404 | − | 0.0452930i | ||||
\(577\) | 93148.0 | + | 286680.i | 0.279783 | + | 0.861084i | 0.987914 | + | 0.155003i | \(0.0495388\pi\) |
−0.708131 | + | 0.706081i | \(0.750461\pi\) | |||||||
\(578\) | 181115. | − | 58847.7i | 0.542123 | − | 0.176146i | ||||
\(579\) | 138195. | − | 190209.i | 0.412226 | − | 0.567381i | ||||
\(580\) | −165681. | − | 228041.i | −0.492513 | − | 0.677886i | ||||
\(581\) | 107767. | − | 331671.i | 0.319251 | − | 0.982553i | ||||
\(582\) | 216364.i | 0.638761i | ||||||||
\(583\) | 274066. | + | 225671.i | 0.806339 | + | 0.663955i | ||||
\(584\) | 171028. | 0.501467 | ||||||||
\(585\) | 158473. | + | 51490.9i | 0.463065 | + | 0.150459i | ||||
\(586\) | −26491.3 | + | 19247.1i | −0.0771452 | + | 0.0560492i | ||||
\(587\) | 371096. | + | 269617.i | 1.07699 | + | 0.782477i | 0.977155 | − | 0.212528i | \(-0.0681695\pi\) |
0.0998318 | + | 0.995004i | \(0.468170\pi\) | |||||||
\(588\) | −68630.3 | − | 211222.i | −0.198500 | − | 0.610922i | ||||
\(589\) | −128574. | + | 41776.2i | −0.370615 | + | 0.120420i | ||||
\(590\) | 86832.3 | − | 119514.i | 0.249447 | − | 0.343334i | ||||
\(591\) | −123176. | − | 169537.i | −0.352656 | − | 0.485390i | ||||
\(592\) | −38349.4 | + | 118027.i | −0.109425 | + | 0.336775i | ||||
\(593\) | 32457.6i | 0.0923011i | 0.998934 | + | 0.0461506i | \(0.0146954\pi\) | ||||
−0.998934 | + | 0.0461506i | \(0.985305\pi\) | |||||||
\(594\) | 232435. | + | 91411.7i | 0.658761 | + | 0.259077i | ||||
\(595\) | −354205. | −1.00051 | ||||||||
\(596\) | 143806. | + | 46725.2i | 0.404840 | + | 0.131540i | ||||
\(597\) | −168874. | + | 122694.i | −0.473821 | + | 0.344251i | ||||
\(598\) | 105217. | + | 76445.0i | 0.294229 | + | 0.213770i | ||||
\(599\) | −213563. | − | 657279.i | −0.595213 | − | 1.83188i | −0.553664 | − | 0.832740i | \(-0.686771\pi\) |
−0.0415485 | − | 0.999136i | \(-0.513229\pi\) | |||||||
\(600\) | 50937.2 | − | 16550.5i | 0.141492 | − | 0.0459736i | ||||
\(601\) | −50232.0 | + | 69138.5i | −0.139070 | + | 0.191413i | −0.872871 | − | 0.487951i | \(-0.837744\pi\) |
0.733801 | + | 0.679364i | \(0.237744\pi\) | |||||||
\(602\) | 205941. | + | 283453.i | 0.568263 | + | 0.782147i | ||||
\(603\) | 33135.4 | − | 101980.i | 0.0911291 | − | 0.280467i | ||||
\(604\) | − | 3595.60i | − | 0.00985592i | ||||||
\(605\) | −199998. | + | 430123.i | −0.546404 | + | 1.17512i | ||||
\(606\) | −151575. | −0.412745 | ||||||||
\(607\) | 126369. | + | 41059.7i | 0.342975 | + | 0.111439i | 0.475439 | − | 0.879748i | \(-0.342289\pi\) |
−0.132465 | + | 0.991188i | \(0.542289\pi\) | |||||||
\(608\) | 39386.3 | − | 28615.9i | 0.106546 | − | 0.0774104i | ||||
\(609\) | −421335. | − | 306118.i | −1.13604 | − | 0.825380i | ||||
\(610\) | −94409.5 | − | 290562.i | −0.253721 | − | 0.780872i | ||||
\(611\) | −322756. | + | 104870.i | −0.864553 | + | 0.280910i | ||||
\(612\) | −29877.6 | + | 41123.0i | −0.0797707 | + | 0.109795i | ||||
\(613\) | 387238. | + | 532987.i | 1.03052 | + | 1.41839i | 0.904556 | + | 0.426355i | \(0.140203\pi\) |
0.125965 | + | 0.992035i | \(0.459797\pi\) | |||||||
\(614\) | 23376.5 | − | 71945.6i | 0.0620074 | − | 0.190839i | ||||
\(615\) | − | 292389.i | − | 0.773055i | ||||||
\(616\) | 86093.9 | − | 218913.i | 0.226888 | − | 0.576912i | ||||
\(617\) | 116511. | 0.306053 | 0.153026 | − | 0.988222i | \(-0.451098\pi\) | ||||
0.153026 | + | 0.988222i | \(0.451098\pi\) | |||||||
\(618\) | 16562.7 | + | 5381.53i | 0.0433664 | + | 0.0140906i | ||||
\(619\) | 102297. | − | 74322.9i | 0.266981 | − | 0.193973i | −0.446238 | − | 0.894914i | \(-0.647237\pi\) |
0.713219 | + | 0.700941i | \(0.247237\pi\) | |||||||
\(620\) | 105404. | + | 76580.3i | 0.274203 | + | 0.199220i | ||||
\(621\) | −100677. | − | 309852.i | −0.261064 | − | 0.803473i | ||||
\(622\) | −106963. | + | 34754.4i | −0.276473 | + | 0.0898315i | ||||
\(623\) | −304663. | + | 419333.i | −0.784953 | + | 1.08039i | ||||
\(624\) | 21596.6 | + | 29725.1i | 0.0554645 | + | 0.0763404i | ||||
\(625\) | −147000. | + | 452418.i | −0.376319 | + | 1.15819i | ||||
\(626\) | 241646.i | 0.616638i | ||||||||
\(627\) | −115298. | + | 140023.i | −0.293282 | + | 0.356176i | ||||
\(628\) | 285707. | 0.724439 | ||||||||
\(629\) | 234668. | + | 76248.1i | 0.593133 | + | 0.192720i | ||||
\(630\) | −318049. | + | 231076.i | −0.801333 | + | 0.582202i | ||||
\(631\) | 387143. | + | 281276.i | 0.972328 | + | 0.706437i | 0.955981 | − | 0.293429i | \(-0.0947965\pi\) |
0.0163467 | + | 0.999866i | \(0.494796\pi\) | |||||||
\(632\) | 45256.7 | + | 139286.i | 0.113305 | + | 0.348717i | ||||
\(633\) | −176781. | + | 57439.6i | −0.441192 | + | 0.143352i | ||||
\(634\) | −40808.1 | + | 56167.5i | −0.101524 | + | 0.139735i | ||||
\(635\) | 591849. | + | 814610.i | 1.46779 | + | 2.02024i | ||||
\(636\) | 40428.7 | − | 124427.i | 0.0999484 | − | 0.307609i | ||||
\(637\) | − | 513014.i | − | 1.26430i | ||||||
\(638\) | −93387.1 | − | 360289.i | −0.229428 | − | 0.885135i | ||||
\(639\) | −168801. | −0.413402 | ||||||||
\(640\) | −44621.7 | − | 14498.5i | −0.108940 | − | 0.0353966i | ||||
\(641\) | −562038. | + | 408345.i | −1.36789 | + | 0.993827i | −0.369986 | + | 0.929037i | \(0.620638\pi\) |
−0.997899 | + | 0.0647894i | \(0.979362\pi\) | |||||||
\(642\) | −123195. | − | 89506.7i | −0.298899 | − | 0.217163i | ||||
\(643\) | 74090.8 | + | 228028.i | 0.179202 | + | 0.551526i | 0.999800 | − | 0.0199785i | \(-0.00635978\pi\) |
−0.820599 | + | 0.571505i | \(0.806360\pi\) | |||||||
\(644\) | −291827. | + | 94820.2i | −0.703644 | + | 0.228628i | ||||
\(645\) | −153036. | + | 210636.i | −0.367852 | + | 0.506305i | ||||
\(646\) | −56895.4 | − | 78309.8i | −0.136336 | − | 0.187651i | ||||
\(647\) | −126061. | + | 387977.i | −0.301143 | + | 0.926824i | 0.679945 | + | 0.733263i | \(0.262004\pi\) |
−0.981088 | + | 0.193561i | \(0.937996\pi\) | |||||||
\(648\) | − | 523.421i | − | 0.00124653i | ||||||
\(649\) | 164459. | − | 104898.i | 0.390451 | − | 0.249045i | ||||
\(650\) | 123716. | 0.292818 | ||||||||
\(651\) | 228939. | + | 74386.7i | 0.540204 | + | 0.175523i | ||||
\(652\) | −152923. | + | 111105.i | −0.359731 | + | 0.261360i | ||||
\(653\) | 293149. | + | 212985.i | 0.687483 | + | 0.499486i | 0.875832 | − | 0.482617i | \(-0.160314\pi\) |
−0.188349 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(654\) | 3340.75 | + | 10281.8i | 0.00781067 | + | 0.0240388i | ||||
\(655\) | 268994. | − | 87401.6i | 0.626990 | − | 0.203721i | ||||
\(656\) | −60909.4 | + | 83834.6i | −0.141539 | + | 0.194812i | ||||
\(657\) | −221839. | − | 305336.i | −0.513935 | − | 0.707371i | ||||
\(658\) | 247422. | − | 761487.i | 0.571461 | − | 1.75878i | ||||
\(659\) | − | 56157.5i | − | 0.129311i | −0.997908 | − | 0.0646557i | \(-0.979405\pi\) | ||
0.997908 | − | 0.0646557i | \(-0.0205949\pi\) | |||||||
\(660\) | 174483. | + | 10576.2i | 0.400558 | + | 0.0242795i | ||||
\(661\) | −43617.9 | −0.0998301 | −0.0499150 | − | 0.998753i | \(-0.515895\pi\) | ||||
−0.0499150 | + | 0.998753i | \(0.515895\pi\) | |||||||
\(662\) | 237770. | + | 77256.3i | 0.542553 | + | 0.176286i | ||||
\(663\) | 59100.8 | − | 42939.3i | 0.134452 | − | 0.0976850i | ||||
\(664\) | −74304.5 | − | 53985.4i | −0.168531 | − | 0.122445i | ||||
\(665\) | −231339. | − | 711989.i | −0.523126 | − | 1.61002i | ||||
\(666\) | 260456. | − | 84627.4i | 0.587201 | − | 0.190793i | ||||
\(667\) | −285370. | + | 392778.i | −0.641441 | + | 0.882868i | ||||
\(668\) | −3050.12 | − | 4198.12i | −0.00683539 | − | 0.00940811i | ||||
\(669\) | 52889.5 | − | 162777.i | 0.118173 | − | 0.363698i | ||||
\(670\) | − | 196785.i | − | 0.438372i | ||||||
\(671\) | 24407.7 | − | 402673.i | 0.0542103 | − | 0.894350i | ||||
\(672\) | −86687.1 | −0.191962 | ||||||||
\(673\) | 2428.77 | + | 789.155i | 0.00536237 | + | 0.00174234i | 0.311697 | − | 0.950182i | \(-0.399103\pi\) |
−0.306335 | + | 0.951924i | \(0.599103\pi\) | |||||||
\(674\) | 232690. | − | 169059.i | 0.512222 | − | 0.372151i | ||||
\(675\) | −250726. | − | 182163.i | −0.550291 | − | 0.399810i | ||||
\(676\) | −44380.0 | − | 136587.i | −0.0971166 | − | 0.298894i | ||||
\(677\) | 460823. | − | 149731.i | 1.00544 | − | 0.326688i | 0.240404 | − | 0.970673i | \(-0.422720\pi\) |
0.765038 | + | 0.643985i | \(0.222720\pi\) | |||||||
\(678\) | 53075.3 | − | 73051.9i | 0.115460 | − | 0.158918i | ||||
\(679\) | −693086. | − | 953951.i | −1.50331 | − | 2.06912i | ||||
\(680\) | −28826.5 | + | 88718.9i | −0.0623411 | + | 0.191866i | ||||
\(681\) | 51500.4i | 0.111049i | ||||||||
\(682\) | 92513.0 | + | 145041.i | 0.198900 | + | 0.311834i | ||||
\(683\) | −498694. | −1.06904 | −0.534519 | − | 0.845157i | \(-0.679507\pi\) | ||||
−0.534519 | + | 0.845157i | \(0.679507\pi\) | |||||||
\(684\) | −102175. | − | 33198.8i | −0.218391 | − | 0.0709595i | ||||
\(685\) | 692169. | − | 502891.i | 1.47513 | − | 1.07175i | ||||
\(686\) | 507175. | + | 368484.i | 1.07773 | + | 0.783016i | ||||
\(687\) | 132367. | + | 407385.i | 0.280458 | + | 0.863161i | ||||
\(688\) | 87757.8 | − | 28514.2i | 0.185400 | − | 0.0602400i | ||||
\(689\) | 177632. | − | 244490.i | 0.374183 | − | 0.515018i | ||||
\(690\) | −134026. | − | 184470.i | −0.281507 | − | 0.387462i | ||||
\(691\) | 44449.9 | − | 136803.i | 0.0930924 | − | 0.286509i | −0.893659 | − | 0.448746i | \(-0.851871\pi\) |
0.986752 | + | 0.162237i | \(0.0518709\pi\) | |||||||
\(692\) | − | 184253.i | − | 0.384771i | ||||||
\(693\) | −502495. | + | 130247.i | −1.04632 | + | 0.271207i | ||||
\(694\) | −104327. | −0.216609 | ||||||||
\(695\) | −546517. | − | 177574.i | −1.13145 | − | 0.367630i | ||||
\(696\) | −110964. | + | 80620.3i | −0.229068 | + | 0.166428i | ||||
\(697\) | 166684. | + | 121103.i | 0.343106 | + | 0.249281i | ||||
\(698\) | 90404.2 | + | 278236.i | 0.185557 | + | 0.571087i | ||||
\(699\) | −59555.6 | + | 19350.8i | −0.121890 | + | 0.0396045i | ||||
\(700\) | −171566. | + | 236140.i | −0.350135 | + | 0.481919i | ||||
\(701\) | 271424. | + | 373582.i | 0.552346 | + | 0.760240i | 0.990328 | − | 0.138744i | \(-0.0443066\pi\) |
−0.437982 | + | 0.898984i | \(0.644307\pi\) | |||||||
\(702\) | 65699.5 | − | 202202.i | 0.133318 | − | 0.410310i | ||||
\(703\) | 521506.i | 1.05523i | ||||||||
\(704\) | −47825.2 | − | 39380.2i | −0.0964965 | − | 0.0794571i | ||||
\(705\) | 594986. | 1.19709 | ||||||||
\(706\) | −135679. | − | 44084.8i | −0.272210 | − | 0.0884464i | ||||
\(707\) | 668297. | − | 485546.i | 1.33700 | − | 0.971385i | ||||
\(708\) | −58155.5 | − | 42252.4i | −0.116018 | − | 0.0842918i | ||||
\(709\) | 88470.5 | + | 272284.i | 0.175997 | + | 0.541664i | 0.999678 | − | 0.0253903i | \(-0.00808286\pi\) |
−0.823680 | + | 0.567055i | \(0.808083\pi\) | |||||||
\(710\) | −294621. | + | 95728.1i | −0.584449 | + | 0.189899i | ||||
\(711\) | 189964. | − | 261463.i | 0.375779 | − | 0.517216i | ||||
\(712\) | 80237.1 | + | 110437.i | 0.158276 | + | 0.217848i | ||||
\(713\) | 69345.0 | − | 213422.i | 0.136407 | − | 0.419817i | ||||
\(714\) | 172355.i | 0.338087i | ||||||||
\(715\) | 375766. | + | 147781.i | 0.735030 | + | 0.289072i | ||||
\(716\) | −51369.5 | −0.100203 | ||||||||
\(717\) | −146795. | − | 47696.7i | −0.285545 | − | 0.0927792i | ||||
\(718\) | −199637. | + | 145044.i | −0.387250 | + | 0.281354i | ||||
\(719\) | −58393.7 | − | 42425.5i | −0.112956 | − | 0.0820672i | 0.529873 | − | 0.848077i | \(-0.322239\pi\) |
−0.642829 | + | 0.766010i | \(0.722239\pi\) | |||||||
\(720\) | 31994.4 | + | 98468.7i | 0.0617176 | + | 0.189947i | ||||
\(721\) | −90263.9 | + | 29328.5i | −0.173638 | + | 0.0564183i | ||||
\(722\) | −96408.4 | + | 132695.i | −0.184944 | + | 0.254554i | ||||
\(723\) | −128497. | − | 176861.i | −0.245819 | − | 0.338341i | ||||
\(724\) | −106080. | + | 326480.i | −0.202374 | + | 0.622844i | ||||
\(725\) | 461832.i | 0.878634i | ||||||||
\(726\) | 209297. | + | 97318.4i | 0.397090 | + | 0.184638i | ||||
\(727\) | −620396. | −1.17382 | −0.586908 | − | 0.809653i | \(-0.699655\pi\) | ||||
−0.586908 | + | 0.809653i | \(0.699655\pi\) | |||||||
\(728\) | −190439. | − | 61877.5i | −0.359330 | − | 0.116753i | ||||
\(729\) | −267492. | + | 194345.i | −0.503334 | + | 0.365694i | ||||
\(730\) | −560351. | − | 407119.i | −1.05151 | − | 0.763969i | ||||
\(731\) | −56693.3 | − | 174484.i | −0.106096 | − | 0.326529i | ||||
\(732\) | −141387. | + | 45939.5i | −0.263869 | + | 0.0857361i | ||||
\(733\) | 28232.2 | − | 38858.3i | 0.0525456 | − | 0.0723229i | −0.781936 | − | 0.623359i | \(-0.785767\pi\) |
0.834481 | + | 0.551036i | \(0.185767\pi\) | |||||||
\(734\) | −86034.9 | − | 118417.i | −0.159692 | − | 0.219797i | ||||
\(735\) | −277940. | + | 855411.i | −0.514489 | + | 1.58343i | ||||
\(736\) | 80811.7i | 0.149183i | ||||||||
\(737\) | 95099.9 | − | 241813.i | 0.175083 | − | 0.445188i | ||||
\(738\) | 228675. | 0.419861 | ||||||||
\(739\) | 41233.3 | + | 13397.5i | 0.0755021 | + | 0.0245321i | 0.346525 | − | 0.938041i | \(-0.387362\pi\) |
−0.271022 | + | 0.962573i | \(0.587362\pi\) | |||||||
\(740\) | 406601. | − | 295413.i | 0.742515 | − | 0.539469i | ||||
\(741\) | 124913. | + | 90754.4i | 0.227494 | + | 0.165284i | ||||
\(742\) | 220330. | + | 678107.i | 0.400190 | + | 1.23166i | ||||
\(743\) | 311459. | − | 101199.i | 0.564187 | − | 0.183315i | −0.0130172 | − | 0.999915i | \(-0.504144\pi\) |
0.577204 | + | 0.816600i | \(0.304144\pi\) | |||||||
\(744\) | 37263.8 | − | 51289.3i | 0.0673196 | − | 0.0926575i | ||||
\(745\) | −359934. | − | 495406.i | −0.648500 | − | 0.892584i | ||||
\(746\) | −157355. | + | 484290.i | −0.282751 | + | 0.870217i | ||||
\(747\) | 202679.i | 0.363219i | ||||||||
\(748\) | −78297.5 | + | 95088.3i | −0.139941 | + | 0.169951i | ||||
\(749\) | 829891. | 1.47930 | ||||||||
\(750\) | 97317.2 | + | 31620.3i | 0.173008 | + | 0.0562138i | ||||
\(751\) | 157605. | − | 114507.i | 0.279441 | − | 0.203026i | −0.439232 | − | 0.898374i | \(-0.644749\pi\) |
0.718674 | + | 0.695347i | \(0.244749\pi\) | |||||||
\(752\) | −170596. | − | 123945.i | −0.301671 | − | 0.219177i | ||||
\(753\) | 142722. | + | 439254.i | 0.251711 | + | 0.774685i | ||||
\(754\) | −301320. | + | 97904.7i | −0.530011 | + | 0.172211i | ||||
\(755\) | −8559.03 | + | 11780.5i | −0.0150152 | + | 0.0206666i | ||||
\(756\) | 294840. | + | 405813.i | 0.515874 | + | 0.710039i | ||||
\(757\) | 118949. | − | 366087.i | 0.207572 | − | 0.638841i | −0.792026 | − | 0.610487i | \(-0.790974\pi\) |
0.999598 | − | 0.0283533i | \(-0.00902635\pi\) | |||||||
\(758\) | − | 524698.i | − | 0.913210i | ||||||
\(759\) | −75544.2 | − | 291451.i | −0.131135 | − | 0.505919i | ||||
\(760\) | −197162. | −0.341347 | ||||||||
\(761\) | −263860. | − | 85733.3i | −0.455622 | − | 0.148040i | 0.0722100 | − | 0.997389i | \(-0.476995\pi\) |
−0.527832 | + | 0.849349i | \(0.676995\pi\) | |||||||
\(762\) | 396388. | − | 287992.i | 0.682669 | − | 0.495988i | ||||
\(763\) | −47665.4 | − | 34630.9i | −0.0818755 | − | 0.0594861i | ||||
\(764\) | 63106.8 | + | 194223.i | 0.108116 | + | 0.332747i | ||||
\(765\) | 195780. | − | 63612.8i | 0.334538 | − | 0.108698i | ||||
\(766\) | 10520.5 | − | 14480.3i | 0.0179300 | − | 0.0246785i | ||||
\(767\) | −97599.5 | − | 134334.i | −0.165904 | − | 0.228347i | ||||
\(768\) | −7054.92 | + | 21712.8i | −0.0119611 | + | 0.0368124i | ||||
\(769\) | 927410.i | 1.56826i | 0.620595 | + | 0.784131i | \(0.286891\pi\) | ||||
−0.620595 | + | 0.784131i | \(0.713109\pi\) | |||||||
\(770\) | −803179. | + | 512299.i | −1.35466 | + | 0.864056i | ||||
\(771\) | 32935.9 | 0.0554064 | ||||||||
\(772\) | 320938. | + | 104279.i | 0.538500 | + | 0.174969i | ||||
\(773\) | −82488.3 | + | 59931.2i | −0.138049 | + | 0.100298i | −0.654666 | − | 0.755918i | \(-0.727191\pi\) |
0.516618 | + | 0.856216i | \(0.327191\pi\) | |||||||
\(774\) | −164736. | − | 119688.i | −0.274984 | − | 0.199787i | ||||
\(775\) | −65964.4 | − | 203017.i | −0.109826 | − | 0.338010i | ||||
\(776\) | −295345. | + | 95963.6i | −0.490464 | + | 0.159361i | ||||
\(777\) | 545814. | − | 751248.i | 0.904071 | − | 1.24435i | ||||
\(778\) | 183222. | + | 252183.i | 0.302704 | + | 0.416636i | ||||
\(779\) | −134565. | + | 414148.i | −0.221746 | + | 0.682465i | ||||
\(780\) | − | 148799.i | − | 0.244575i | ||||||
\(781\) | −408297. | − | 24748.6i | −0.669383 | − | 0.0405741i | ||||
\(782\) | 160674. | 0.262743 | ||||||||
\(783\) | 754824. | + | 245257.i | 1.23118 | + | 0.400035i | ||||
\(784\) | 257888. | − | 187367.i | 0.419565 | − | 0.304832i | ||||
\(785\) | −936081. | − | 680103.i | −1.51906 | − | 1.10366i | ||||
\(786\) | −42529.4 | − | 130892.i | −0.0688406 | − | 0.211869i | ||||
\(787\) | −746565. | + | 242574.i | −1.20536 | + | 0.391646i | −0.841732 | − | 0.539896i | \(-0.818463\pi\) |
−0.363632 | + | 0.931543i | \(0.618463\pi\) | |||||||
\(788\) | 176794. | − | 243336.i | 0.284717 | − | 0.391880i | ||||
\(789\) | −353668. | − | 486783.i | −0.568123 | − | 0.781954i | ||||
\(790\) | 183281. | − | 564082.i | 0.293673 | − | 0.903832i | ||||
\(791\) | 492105.i | 0.786512i | ||||||||
\(792\) | −8271.53 | + | 136462.i | −0.0131867 | + | 0.217551i | ||||
\(793\) | −343399. | −0.546076 | ||||||||
\(794\) | 553494. | + | 179841.i | 0.877954 | + | 0.285264i | ||||
\(795\) | −428647. | + | 311430.i | −0.678212 | + | 0.492750i | ||||
\(796\) | −242383. | − | 176102.i | −0.382540 | − | 0.277931i | ||||
\(797\) | 146626. | + | 451268.i | 0.230831 | + | 0.710424i | 0.997647 | + | 0.0685576i | \(0.0218397\pi\) |
−0.766816 | + | 0.641867i | \(0.778160\pi\) | |||||||
\(798\) | −346453. | + | 112569.i | −0.544049 | + | 0.176772i | ||||
\(799\) | −246434. | + | 339187.i | −0.386018 | + | 0.531308i | ||||
\(800\) | 45184.2 | + | 62190.8i | 0.0706004 | + | 0.0971731i | ||||
\(801\) | 93087.4 | − | 286494.i | 0.145086 | − | 0.446529i | ||||
\(802\) | − | 372591.i | − | 0.579274i | ||||||
\(803\) | −491821. | − | 771074.i | −0.762739 | − | 1.19582i | ||||
\(804\) | −95755.2 | −0.148132 | ||||||||
\(805\) | 1.18184e6 | + | 384004.i | 1.82376 | + | 0.592576i | ||||
\(806\) | 118474. | − | 86076.2i | 0.182369 | − | 0.132499i | ||||
\(807\) | −70423.5 | − | 51165.7i | −0.108136 | − | 0.0785654i | ||||
\(808\) | −67227.9 | − | 206906.i | −0.102974 | − | 0.316921i | ||||
\(809\) | 325525. | − | 105770.i | 0.497379 | − | 0.161608i | −0.0495756 | − | 0.998770i | \(-0.515787\pi\) |
0.546955 | + | 0.837162i | \(0.315787\pi\) | |||||||
\(810\) | −1245.96 | + | 1714.92i | −0.00189904 | + | 0.00261381i | ||||
\(811\) | 267565. | + | 368272.i | 0.406807 | + | 0.559922i | 0.962436 | − | 0.271509i | \(-0.0875226\pi\) |
−0.555629 | + | 0.831430i | \(0.687523\pi\) | |||||||
\(812\) | 230990. | − | 710913.i | 0.350332 | − | 1.07821i | ||||
\(813\) | 190952.i | 0.288897i | ||||||||
\(814\) | 642402. | − | 166511.i | 0.969523 | − | 0.251301i | ||||
\(815\) | 765508. | 1.15248 | ||||||||
\(816\) | 43170.4 | + | 14026.9i | 0.0648345 | + | 0.0210660i | ||||
\(817\) | 313704. | − | 227919.i | 0.469976 | − | 0.341458i | ||||
\(818\) | −181713. | − | 132022.i | −0.271569 | − | 0.197306i | ||||
\(819\) | 136548. | + | 420251.i | 0.203571 | + | 0.626529i | ||||
\(820\) | 399123. | − | 129683.i | 0.593580 | − | 0.192866i | ||||
\(821\) | −233166. | + | 320925.i | −0.345923 | + | 0.476122i | −0.946160 | − | 0.323701i | \(-0.895073\pi\) |
0.600237 | + | 0.799822i | \(0.295073\pi\) | |||||||
\(822\) | −244705. | − | 336808.i | −0.362160 | − | 0.498470i | ||||
\(823\) | 300791. | − | 925738.i | 0.444083 | − | 1.36675i | −0.439402 | − | 0.898290i | \(-0.644810\pi\) |
0.883486 | − | 0.468458i | \(-0.155190\pi\) | |||||||
\(824\) | 24995.6i | 0.0368137i | ||||||||
\(825\) | −221096. | − | 182054.i | −0.324842 | − | 0.267481i | ||||
\(826\) | 391758. | 0.574192 | ||||||||
\(827\) | 136766. | + | 44438.1i | 0.199972 | + | 0.0649748i | 0.407290 | − | 0.913299i | \(-0.366474\pi\) |
−0.207319 | + | 0.978273i | \(0.566474\pi\) | |||||||
\(828\) | 144273. | − | 104820.i | 0.210438 | − | 0.152892i | ||||
\(829\) | 289762. | + | 210524.i | 0.421631 | + | 0.306333i | 0.778294 | − | 0.627901i | \(-0.216086\pi\) |
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(830\) | 114941. | + | 353752.i | 0.166847 | + | 0.513502i | ||||
\(831\) | 382371. | − | 124240.i | 0.553711 | − | 0.179912i | ||||
\(832\) | −30997.3 | + | 42664.2i | −0.0447793 | + | 0.0616335i | ||||
\(833\) | −372531. | − | 512745.i | −0.536874 | − | 0.738944i | ||||
\(834\) | −86407.3 | + | 265934.i | −0.124228 | + | 0.382333i | ||||
\(835\) | 21015.1i | 0.0301411i | ||||||||
\(836\) | −242276. | − | 95282.0i | −0.346655 | − | 0.136332i | ||||
\(837\) | −366845. | −0.523639 | ||||||||
\(838\) | −756291. | − | 245734.i | −1.07696 | − | 0.349927i | ||||
\(839\) | −1.09425e6 | + | 795018.i | −1.55451 | + | 1.12941i | −0.614166 | + | 0.789177i | \(0.710507\pi\) |
−0.940340 | + | 0.340237i | \(0.889493\pi\) | |||||||
\(840\) | 284019. | + | 206352.i | 0.402521 | + | 0.292448i | ||||
\(841\) | −146918. | − | 452167.i | −0.207722 | − | 0.639304i | ||||
\(842\) | −892043. | + | 289842.i | −1.25823 | + | 0.408825i | ||||
\(843\) | 333178. | − | 458580.i | 0.468836 | − | 0.645298i | ||||
\(844\) | −156815. | − | 215837.i | −0.220142 | − | 0.302999i | ||||
\(845\) | −179730. | + | 553153.i | −0.251714 | + | 0.774698i | ||||
\(846\) | 465333.i | 0.650165i | ||||||||
\(847\) | −1.23454e6 | + | 241370.i | −1.72083 | + | 0.336447i | ||||
\(848\) | 187779. | 0.261129 | ||||||||
\(849\) | −16173.4 | − | 5255.06i | −0.0224381 | − | 0.00729058i | ||||
\(850\) | 123651. | − | 89837.4i | 0.171143 | − | 0.124342i | ||||
\(851\) | −700331. | − | 508820.i | −0.967040 | − | 0.702596i | ||||
\(852\) | 46581.1 | + | 143362.i | 0.0641698 | + | 0.197494i | ||||
\(853\) | 691608. | − | 224717.i | 0.950521 | − | 0.308843i | 0.207594 | − | 0.978215i | \(-0.433437\pi\) |
0.742927 | + | 0.669372i | \(0.233437\pi\) | |||||||
\(854\) | 476219. | − | 655459.i | 0.652966 | − | 0.898731i | ||||
\(855\) | 255737. | + | 351992.i | 0.349834 | + | 0.481505i | ||||
\(856\) | 67539.7 | − | 207866.i | 0.0921746 | − | 0.283684i | ||||
\(857\) | 269066.i | 0.366351i | 0.983080 | + | 0.183175i | \(0.0586376\pi\) | ||||
−0.983080 | + | 0.183175i | \(0.941362\pi\) | |||||||
\(858\) | 71909.9 | − | 182847.i | 0.0976819 | − | 0.248378i | ||||
\(859\) | 919865. | 1.24663 | 0.623315 | − | 0.781971i | \(-0.285785\pi\) | ||||
0.623315 | + | 0.781971i | \(0.285785\pi\) | |||||||
\(860\) | −355402. | − | 115477.i | −0.480533 | − | 0.156135i | ||||
\(861\) | 627296. | − | 455757.i | 0.846187 | − | 0.614791i | ||||
\(862\) | 285450. | + | 207392.i | 0.384163 | + | 0.279111i | ||||
\(863\) | −89869.0 | − | 276588.i | −0.120667 | − | 0.371374i | 0.872420 | − | 0.488757i | \(-0.162550\pi\) |
−0.993087 | + | 0.117383i | \(0.962550\pi\) | |||||||
\(864\) | 125641. | − | 40823.1i | 0.168307 | − | 0.0546863i | ||||
\(865\) | −438600. | + | 603681.i | −0.586187 | + | 0.806817i | ||||
\(866\) | 42788.4 | + | 58893.2i | 0.0570546 | + | 0.0785289i | ||||
\(867\) | −115967. | + | 356910.i | −0.154275 | + | 0.474811i | ||||
\(868\) | 345504.i | 0.458578i | ||||||||
\(869\) | 497822. | − | 604579.i | 0.659226 | − | 0.800596i | ||||
\(870\) | 555470. | 0.733875 | ||||||||
\(871\) | −210361. | − | 68350.3i | −0.277286 | − | 0.0900957i | ||||
\(872\) | −12553.3 | + | 9120.53i | −0.0165092 | + | 0.0119946i | ||||
\(873\) | 554414. | + | 402805.i | 0.727454 | + | 0.528526i | ||||
\(874\) | 104940. | + | 322971.i | 0.137378 | + | 0.422806i | ||||
\(875\) | −530364. | + | 172326.i | −0.692720 | + | 0.225078i | ||||
\(876\) | −198103. | + | 272666.i | −0.258157 | + | 0.355322i | ||||
\(877\) | 6751.69 | + | 9292.90i | 0.00877835 | + | 0.0120824i | 0.813384 | − | 0.581728i | \(-0.197623\pi\) |
−0.804605 | + | 0.593810i | \(0.797623\pi\) | |||||||
\(878\) | −108258. | + | 333184.i | −0.140434 | + | 0.432210i | ||||
\(879\) | − | 64528.5i | − | 0.0835168i | ||||||
\(880\) | 62951.5 | + | 242868.i | 0.0812907 | + | 0.313621i | ||||
\(881\) | −742939. | −0.957197 | −0.478599 | − | 0.878034i | \(-0.658855\pi\) | ||||
−0.478599 | + | 0.878034i | \(0.658855\pi\) | |||||||
\(882\) | −669009. | − | 217374.i | −0.859993 | − | 0.279429i | ||||
\(883\) | 945222. | − | 686744.i | 1.21231 | − | 0.880792i | 0.216868 | − | 0.976201i | \(-0.430416\pi\) |
0.995438 | + | 0.0954091i | \(0.0304159\pi\) | |||||||
\(884\) | 84826.9 | + | 61630.4i | 0.108550 | + | 0.0788661i | ||||
\(885\) | 89960.2 | + | 276869.i | 0.114859 | + | 0.353499i | ||||
\(886\) | −199275. | + | 64748.4i | −0.253855 | + | 0.0824824i | ||||
\(887\) | −382008. | + | 525789.i | −0.485540 | + | 0.668289i | −0.979558 | − | 0.201163i | \(-0.935528\pi\) |
0.494018 | + | 0.869452i | \(0.335528\pi\) | |||||||
\(888\) | −143747. | − | 197851.i | −0.182295 | − | 0.250907i | ||||
\(889\) | −825143. | + | 2.53953e6i | −1.04406 | + | 3.21329i | ||||
\(890\) | − | 552830.i | − | 0.697929i | ||||||
\(891\) | −2359.82 | + | 1505.19i | −0.00297251 | + | 0.00189598i | ||||
\(892\) | 245656. | 0.308743 | ||||||||
\(893\) | −842755. | − | 273828.i | −1.05681 | − | 0.343379i | ||||
\(894\) | −241064. | + | 175143.i | −0.301618 | + | 0.219138i | ||||
\(895\) | 168305. | + | 122281.i | 0.210113 | + | 0.152656i | ||||
\(896\) | −38448.3 | − | 118332.i | −0.0478917 | − | 0.147396i | ||||
\(897\) | −243748. | + | 79198.6i | −0.302940 | + | 0.0984312i | ||||
\(898\) | −383723. | + | 528150.i | −0.475845 | + | 0.654944i | ||||
\(899\) | 321324. | + | 442264.i | 0.397579 | + | 0.547221i | ||||
\(900\) | 52420.7 | − | 161334.i | 0.0647169 | − | 0.199178i | ||||
\(901\) | − | 373351.i | − | 0.459905i | ||||||
\(902\) | 553120. | + | 33527.0i | 0.679840 | + | 0.0412080i | ||||
\(903\) | −690444. | −0.846746 | ||||||||
\(904\) | 123259. | + | 40049.4i | 0.150828 | + | 0.0490071i | ||||
\(905\) | 1.12472e6 | − | 817154.i | 1.37324 | − | 0.997715i | ||||
\(906\) | 5732.36 | + | 4164.81i | 0.00698357 | + | 0.00507386i | ||||
\(907\) | −68802.5 | − | 211752.i | −0.0836354 | − | 0.257403i | 0.900490 | − | 0.434876i | \(-0.143208\pi\) |
−0.984126 | + | 0.177473i | \(0.943208\pi\) | |||||||
\(908\) | −70300.3 | + | 22841.9i | −0.0852679 | + | 0.0277052i | ||||
\(909\) | −282188. | + | 388398.i | −0.341516 | + | 0.470056i | ||||
\(910\) | 476654. | + | 656058.i | 0.575600 | + | 0.792245i | ||||
\(911\) | 376111. | − | 1.15755e6i | 0.453189 | − | 1.39477i | −0.420060 | − | 0.907496i | \(-0.637991\pi\) |
0.873249 | − | 0.487275i | \(-0.162009\pi\) | |||||||
\(912\) | 95938.5i | 0.115346i | ||||||||
\(913\) | −29715.7 | + | 490243.i | −0.0356488 | + | 0.588125i | ||||
\(914\) | −356958. | −0.427292 | ||||||||
\(915\) | 572591. | + | 186046.i | 0.683915 | + | 0.222218i | ||||
\(916\) | −497389. | + | 361375.i | −0.592796 | + | 0.430692i | ||||
\(917\) | 606805. | + | 440870.i | 0.721623 | + | 0.524290i | ||||
\(918\) | −81166.5 | − | 249805.i | −0.0963144 | − | 0.296425i | ||||
\(919\) | 1.58795e6 | − | 515957.i | 1.88021 | − | 0.610917i | 0.893343 | − | 0.449375i | \(-0.148353\pi\) |
0.986866 | − | 0.161542i | \(-0.0516469\pi\) | |||||||
\(920\) | 192366. | − | 264769.i | 0.227275 | − | 0.312818i | ||||
\(921\) | 87623.7 | + | 120604.i | 0.103301 | + | 0.142181i | ||||
\(922\) | 57010.8 | − | 175461.i | 0.0670650 | − | 0.206405i | ||||
\(923\) | 348196.i | 0.408714i | ||||||||
\(924\) | 249283. | + | 390825.i | 0.291978 | + | 0.457761i | ||||
\(925\) | −823455. | −0.962402 | ||||||||
\(926\) | −829533. | − | 269532.i | −0.967412 | − | 0.314331i | ||||
\(927\) | 44624.5 | − | 32421.6i | 0.0519295 | − | 0.0377290i | ||||
\(928\) | −159266. | − | 115714.i | −0.184938 | − | 0.134366i | ||||
\(929\) | −95030.8 | − | 292475.i | −0.110112 | − | 0.338888i | 0.880785 | − | 0.473517i | \(-0.157016\pi\) |
−0.990896 | + | 0.134629i | \(0.957016\pi\) | |||||||
\(930\) | −244180. | + | 79338.8i | −0.282321 | + | 0.0917318i | ||||
\(931\) | 787364. | − | 1.08371e6i | 0.908398 | − | 1.25030i | ||||
\(932\) | −52829.3 | − | 72713.3i | −0.0608196 | − | 0.0837110i | ||||
\(933\) | 68488.0 | − | 210784.i | 0.0786776 | − | 0.242145i | ||||
\(934\) | 1.05516e6i | 1.20955i | ||||||||
\(935\) | 482881. | − | 125163.i | 0.552354 | − | 0.143170i | ||||
\(936\) | 116375. | 0.132833 | ||||||||
\(937\) | −1.12048e6 | − | 364066.i | −1.27622 | − | 0.414668i | −0.408971 | − | 0.912547i | \(-0.634112\pi\) |
−0.867247 | + | 0.497879i | \(0.834112\pi\) | |||||||
\(938\) | 422186. | − | 306736.i | 0.479842 | − | 0.348626i | ||||
\(939\) | −385249. | − | 279900.i | −0.436929 | − | 0.317447i | ||||
\(940\) | 263894. | + | 812181.i | 0.298657 | + | 0.919173i | ||||
\(941\) | −40929.6 | + | 13298.8i | −0.0462230 | + | 0.0150187i | −0.332037 | − | 0.943266i | \(-0.607736\pi\) |
0.285814 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(942\) | −330937. | + | 455495.i | −0.372943 | + | 0.513312i | ||||
\(943\) | −424868. | − | 584780.i | −0.477783 | − | 0.657611i | ||||
\(944\) | 31882.7 | − | 98124.9i | 0.0357776 | − | 0.110112i | ||||
\(945\) | − | 2.03144e6i | − | 2.27478i | ||||||
\(946\) | −380918. | − | 313655.i | −0.425646 | − | 0.350485i | ||||
\(947\) | −137993. | −0.153871 | −0.0769354 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769354 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(948\) | −274481. | − | 89184.3i | −0.305419 | − | 0.0992365i | ||||
\(949\) | −629834. | + | 457601.i | −0.699349 | + | 0.508107i | ||||
\(950\) | 261342. | + | 189876.i | 0.289576 | + | 0.210389i | ||||
\(951\) | −42278.0 | − | 130118.i | −0.0467470 | − | 0.143872i | ||||
\(952\) | −235272. | + | 76444.6i | −0.259595 | + | 0.0843477i | ||||
\(953\) | −813768. | + | 1.12006e6i | −0.896014 | + | 1.23326i | 0.0757081 | + | 0.997130i | \(0.475878\pi\) |
−0.971722 | + | 0.236127i | \(0.924122\pi\) | |||||||
\(954\) | −243567. | − | 335241.i | −0.267622 | − | 0.368350i | ||||
\(955\) | 255571. | − | 786566.i | 0.280223 | − | 0.862439i | ||||
\(956\) | − | 221537.i | − | 0.242399i | ||||||
\(957\) | 682570. | + | 268441.i | 0.745287 | + | 0.293106i | ||||
\(958\) | 724704. | 0.789641 | ||||||||
\(959\) | 2.15782e6 | + | 701119.i | 2.34627 | + | 0.762350i | ||||
\(960\) | 74800.1 | − | 54345.5i | 0.0811633 | − | 0.0589686i | ||||
\(961\) | 542723. | + | 394312.i | 0.587668 | + | 0.426966i | ||||
\(962\) | −174566. | − | 537259.i | −0.188629 | − | 0.580542i | ||||
\(963\) | −458707. | + | 149043.i | −0.494632 | + | 0.160716i | ||||
\(964\) | 184430. | − | 253847.i | 0.198462 | − | 0.273160i | ||||
\(965\) | −803281. | − | 1.10562e6i | −0.862607 | − | 1.18728i | ||||
\(966\) | 186856. | − | 575082.i | 0.200240 | − | 0.616277i | ||||
\(967\) | − | 1.79906e6i | − | 1.92394i | −0.273150 | − | 0.961972i | \(-0.588065\pi\) | ||
0.273150 | − | 0.961972i | \(-0.411935\pi\) | |||||||
\(968\) | −40014.5 | + | 328863.i | −0.0427038 | + | 0.350965i | ||||
\(969\) | 190749. | 0.203150 | ||||||||
\(970\) | 1.19609e6 | + | 388634.i | 1.27122 | + | 0.413045i | ||||
\(971\) | −1.07308e6 | + | 779641.i | −1.13814 | + | 0.826907i | −0.986859 | − | 0.161584i | \(-0.948340\pi\) |
−0.151280 | + | 0.988491i | \(0.548340\pi\) | |||||||
\(972\) | −381754. | − | 277360.i | −0.404065 | − | 0.293570i | ||||
\(973\) | −470906. | − | 1.44930e6i | −0.497404 | − | 1.53085i | ||||
\(974\) | 604364. | − | 196370.i | 0.637061 | − | 0.206994i | ||||
\(975\) | −143301. | + | 197236.i | −0.150744 | + | 0.207481i | ||||
\(976\) | −125419. | − | 172624.i | −0.131663 | − | 0.181218i | ||||
\(977\) | 422787. | − | 1.30120e6i | 0.442927 | − | 1.36319i | −0.441814 | − | 0.897107i | \(-0.645665\pi\) |
0.884741 | − | 0.466083i | \(-0.154335\pi\) | |||||||
\(978\) | − | 372495.i | − | 0.389441i | ||||||
\(979\) | 267165. | − | 679326.i | 0.278750 | − | 0.708782i | ||||
\(980\) | −1.29095e6 | −1.34418 | ||||||||
\(981\) | 32565.7 | + | 10581.2i | 0.0338393 | + | 0.0109951i | ||||
\(982\) | −229534. | + | 166766.i | −0.238026 | + | 0.172936i | ||||
\(983\) | 728116. | + | 529007.i | 0.753518 | + | 0.547463i | 0.896915 | − | 0.442202i | \(-0.145803\pi\) |
−0.143397 | + | 0.989665i | \(0.545803\pi\) | |||||||
\(984\) | −63103.4 | − | 194212.i | −0.0651723 | − | 0.200580i | ||||
\(985\) | −1.15848e6 | + | 376413.i | −1.19403 | + | 0.387965i | ||||
\(986\) | −230067. | + | 316660.i | −0.236647 | + | 0.325716i | ||||
\(987\) | 927427. | + | 1.27649e6i | 0.952019 | + | 1.31034i | ||||
\(988\) | −68481.2 | + | 210763.i | −0.0701548 | + | 0.215914i | ||||
\(989\) | 643648.i | 0.658046i | ||||||||
\(990\) | 351937. | − | 427409.i | 0.359083 | − | 0.436087i | ||||
\(991\) | 846524. | 0.861969 | 0.430985 | − | 0.902359i | \(-0.358166\pi\) | ||||
0.430985 | + | 0.902359i | \(0.358166\pi\) | |||||||
\(992\) | 86539.6 | + | 28118.4i | 0.0879411 | + | 0.0285738i | ||||
\(993\) | −398579. | + | 289584.i | −0.404218 | + | 0.293682i | ||||
\(994\) | −664614. | − | 482870.i | −0.672662 | − | 0.488717i | ||||
\(995\) | 374940. | + | 1.15395e6i | 0.378718 | + | 1.16557i | ||||
\(996\) | 172135. | − | 55930.0i | 0.173520 | − | 0.0563801i | ||||
\(997\) | 816248. | − | 1.12347e6i | 0.821167 | − | 1.13024i | −0.168336 | − | 0.985730i | \(-0.553839\pi\) |
0.989503 | − | 0.144510i | \(-0.0461607\pi\) | |||||||
\(998\) | 428396. | + | 589636.i | 0.430115 | + | 0.592002i | ||||
\(999\) | −437298. | + | 1.34587e6i | −0.438174 | + | 1.34856i |
(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 | 22.5.d.a.13.2 | ✓ | 16 | |
3.2 | odd | 2 | 198.5.j.a.145.4 | 16 | |||
4.3 | odd | 2 | 176.5.n.c.145.2 | 16 | |||
11.4 | even | 5 | 242.5.b.e.241.3 | 16 | |||
11.6 | odd | 10 | inner | 22.5.d.a.17.2 | yes | 16 | |
11.7 | odd | 10 | 242.5.b.e.241.11 | 16 | |||
33.17 | even | 10 | 198.5.j.a.127.4 | 16 | |||
44.39 | even | 10 | 176.5.n.c.17.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.d.a.13.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
22.5.d.a.17.2 | yes | 16 | 11.6 | odd | 10 | inner | |
176.5.n.c.17.2 | 16 | 44.39 | even | 10 | |||
176.5.n.c.145.2 | 16 | 4.3 | odd | 2 | |||
198.5.j.a.127.4 | 16 | 33.17 | even | 10 | |||
198.5.j.a.145.4 | 16 | 3.2 | odd | 2 | |||
242.5.b.e.241.3 | 16 | 11.4 | even | 5 | |||
242.5.b.e.241.11 | 16 | 11.7 | odd | 10 |