Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,5,Mod(3,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.65391940934\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(2.24452 + 1.72109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.11 |
Dual form | 16.5.f.a.3.1 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.96560 | − | 0.523430i | −0.991401 | − | 0.130858i | ||||
\(3\) | 5.54016 | + | 5.54016i | 0.615573 | + | 0.615573i | 0.944393 | − | 0.328820i | \(-0.106651\pi\) |
−0.328820 | + | 0.944393i | \(0.606651\pi\) | |||||||
\(4\) | 15.4520 | + | 4.15143i | 0.965753 | + | 0.259465i | ||||
\(5\) | 21.7374 | + | 21.7374i | 0.869495 | + | 0.869495i | 0.992416 | − | 0.122921i | \(-0.0392262\pi\) |
−0.122921 | + | 0.992416i | \(0.539226\pi\) | |||||||
\(6\) | −19.0702 | − | 24.8700i | −0.529727 | − | 0.690832i | ||||
\(7\) | −6.62054 | −0.135113 | −0.0675565 | − | 0.997715i | \(-0.521520\pi\) | ||||
−0.0675565 | + | 0.997715i | \(0.521520\pi\) | |||||||
\(8\) | −59.1037 | − | 24.5510i | −0.923495 | − | 0.383610i | ||||
\(9\) | − | 19.6133i | − | 0.242140i | ||||||
\(10\) | −74.8239 | − | 97.5799i | −0.748239 | − | 0.975799i | ||||
\(11\) | −90.9986 | + | 90.9986i | −0.752054 | + | 0.752054i | −0.974862 | − | 0.222808i | \(-0.928478\pi\) |
0.222808 | + | 0.974862i | \(0.428478\pi\) | |||||||
\(12\) | 62.6071 | + | 108.606i | 0.434772 | + | 0.754211i | ||||
\(13\) | 221.402 | − | 221.402i | 1.31007 | − | 1.31007i | 0.388707 | − | 0.921362i | \(-0.372922\pi\) |
0.921362 | − | 0.388707i | \(-0.127078\pi\) | |||||||
\(14\) | 26.2544 | + | 3.46539i | 0.133951 | + | 0.0176806i | ||||
\(15\) | 240.857i | 1.07048i | ||||||||
\(16\) | 221.531 | + | 128.296i | 0.865356 | + | 0.501157i | ||||
\(17\) | −132.575 | −0.458738 | −0.229369 | − | 0.973339i | \(-0.573666\pi\) | ||||
−0.229369 | + | 0.973339i | \(0.573666\pi\) | |||||||
\(18\) | −10.2662 | + | 77.7787i | −0.0316858 | + | 0.240058i | ||||
\(19\) | −402.520 | − | 402.520i | −1.11501 | − | 1.11501i | −0.992462 | − | 0.122552i | \(-0.960892\pi\) |
−0.122552 | − | 0.992462i | \(-0.539108\pi\) | |||||||
\(20\) | 245.646 | + | 426.128i | 0.614114 | + | 1.06532i | ||||
\(21\) | −36.6788 | − | 36.6788i | −0.0831720 | − | 0.0831720i | ||||
\(22\) | 408.496 | − | 313.233i | 0.843999 | − | 0.647175i | ||||
\(23\) | 27.5037 | 0.0519918 | 0.0259959 | − | 0.999662i | \(-0.491724\pi\) | ||||
0.0259959 | + | 0.999662i | \(0.491724\pi\) | |||||||
\(24\) | −191.427 | − | 463.460i | −0.332339 | − | 0.804618i | ||||
\(25\) | 320.028i | 0.512044i | ||||||||
\(26\) | −993.879 | + | 762.103i | −1.47024 | + | 1.12737i | ||||
\(27\) | 557.414 | − | 557.414i | 0.764628 | − | 0.764628i | ||||
\(28\) | −102.301 | − | 27.4847i | −0.130486 | − | 0.0350571i | ||||
\(29\) | 174.909 | − | 174.909i | 0.207978 | − | 0.207978i | −0.595430 | − | 0.803407i | \(-0.703018\pi\) |
0.803407 | + | 0.595430i | \(0.203018\pi\) | |||||||
\(30\) | 126.072 | − | 955.144i | 0.140080 | − | 1.06127i | ||||
\(31\) | 1083.96i | 1.12795i | 0.825791 | + | 0.563976i | \(0.190729\pi\) | ||||
−0.825791 | + | 0.563976i | \(0.809271\pi\) | |||||||
\(32\) | −811.351 | − | 624.728i | −0.792335 | − | 0.610086i | ||||
\(33\) | −1008.29 | −0.925888 | ||||||||
\(34\) | 525.742 | + | 69.3940i | 0.454794 | + | 0.0600294i | ||||
\(35\) | −143.913 | − | 143.913i | −0.117480 | − | 0.117480i | ||||
\(36\) | 81.4234 | − | 303.066i | 0.0628267 | − | 0.233847i | ||||
\(37\) | 553.474 | + | 553.474i | 0.404291 | + | 0.404291i | 0.879742 | − | 0.475451i | \(-0.157715\pi\) |
−0.475451 | + | 0.879742i | \(0.657715\pi\) | |||||||
\(38\) | 1385.54 | + | 1806.93i | 0.959518 | + | 1.25133i | ||||
\(39\) | 2453.20 | 1.61289 | ||||||||
\(40\) | −751.085 | − | 1818.43i | −0.469428 | − | 1.13652i | ||||
\(41\) | 1803.47i | 1.07285i | 0.843947 | + | 0.536427i | \(0.180226\pi\) | ||||
−0.843947 | + | 0.536427i | \(0.819774\pi\) | |||||||
\(42\) | 126.255 | + | 164.653i | 0.0715731 | + | 0.0933404i | ||||
\(43\) | 17.8633 | − | 17.8633i | 0.00966108 | − | 0.00966108i | −0.702260 | − | 0.711921i | \(-0.747825\pi\) |
0.711921 | + | 0.702260i | \(0.247825\pi\) | |||||||
\(44\) | −1783.89 | + | 1028.34i | −0.921430 | + | 0.531167i | ||||
\(45\) | 426.342 | − | 426.342i | 0.210539 | − | 0.210539i | ||||
\(46\) | −109.069 | − | 14.3963i | −0.0515448 | − | 0.00680352i | ||||
\(47\) | − | 2268.26i | − | 1.02683i | −0.858141 | − | 0.513414i | \(-0.828380\pi\) | ||
0.858141 | − | 0.513414i | \(-0.171620\pi\) | |||||||
\(48\) | 516.536 | + | 1938.10i | 0.224191 | + | 0.841189i | ||||
\(49\) | −2357.17 | −0.981744 | ||||||||
\(50\) | 167.512 | − | 1269.10i | 0.0670048 | − | 0.507641i | ||||
\(51\) | −734.489 | − | 734.489i | −0.282387 | − | 0.282387i | ||||
\(52\) | 4340.24 | − | 2501.97i | 1.60512 | − | 0.925285i | ||||
\(53\) | −822.415 | − | 822.415i | −0.292779 | − | 0.292779i | 0.545398 | − | 0.838177i | \(-0.316378\pi\) |
−0.838177 | + | 0.545398i | \(0.816378\pi\) | |||||||
\(54\) | −2502.25 | + | 1918.71i | −0.858110 | + | 0.657996i | ||||
\(55\) | −3956.14 | −1.30782 | ||||||||
\(56\) | 391.298 | + | 162.541i | 0.124776 | + | 0.0518307i | ||||
\(57\) | − | 4460.05i | − | 1.37275i | ||||||
\(58\) | −785.174 | + | 602.068i | −0.233405 | + | 0.178974i | ||||
\(59\) | −972.483 | + | 972.483i | −0.279369 | + | 0.279369i | −0.832857 | − | 0.553488i | \(-0.813296\pi\) |
0.553488 | + | 0.832857i | \(0.313296\pi\) | |||||||
\(60\) | −999.902 | + | 3721.73i | −0.277751 | + | 1.03381i | ||||
\(61\) | −2056.32 | + | 2056.32i | −0.552626 | + | 0.552626i | −0.927198 | − | 0.374572i | \(-0.877790\pi\) |
0.374572 | + | 0.927198i | \(0.377790\pi\) | |||||||
\(62\) | 567.378 | − | 4298.57i | 0.147601 | − | 1.11825i | ||||
\(63\) | 129.851i | 0.0327163i | ||||||||
\(64\) | 2890.50 | + | 2902.11i | 0.705687 | + | 0.708523i | ||||
\(65\) | 9625.38 | 2.27820 | ||||||||
\(66\) | 3998.49 | + | 527.771i | 0.917927 | + | 0.121159i | ||||
\(67\) | 4611.22 | + | 4611.22i | 1.02723 | + | 1.02723i | 0.999619 | + | 0.0276077i | \(0.00878893\pi\) |
0.0276077 | + | 0.999619i | \(0.491211\pi\) | |||||||
\(68\) | −2048.56 | − | 550.378i | −0.443028 | − | 0.119026i | ||||
\(69\) | 152.375 | + | 152.375i | 0.0320048 | + | 0.0320048i | ||||
\(70\) | 495.374 | + | 646.031i | 0.101097 | + | 0.131843i | ||||
\(71\) | −3105.84 | −0.616115 | −0.308058 | − | 0.951368i | \(-0.599679\pi\) | ||||
−0.308058 | + | 0.951368i | \(0.599679\pi\) | |||||||
\(72\) | −481.527 | + | 1159.22i | −0.0928872 | + | 0.223615i | ||||
\(73\) | − | 723.400i | − | 0.135748i | −0.997694 | − | 0.0678739i | \(-0.978378\pi\) | ||
0.997694 | − | 0.0678739i | \(-0.0216216\pi\) | |||||||
\(74\) | −1905.15 | − | 2484.56i | −0.347910 | − | 0.453719i | ||||
\(75\) | −1773.00 | + | 1773.00i | −0.315200 | + | 0.315200i | ||||
\(76\) | −4548.72 | − | 7890.79i | −0.787521 | − | 1.36613i | ||||
\(77\) | 602.460 | − | 602.460i | 0.101612 | − | 0.101612i | ||||
\(78\) | −9728.41 | − | 1284.08i | −1.59902 | − | 0.211058i | ||||
\(79\) | 3418.44i | 0.547739i | 0.961767 | + | 0.273869i | \(0.0883036\pi\) | ||||
−0.961767 | + | 0.273869i | \(0.911696\pi\) | |||||||
\(80\) | 2026.68 | + | 7604.33i | 0.316669 | + | 1.18818i | ||||
\(81\) | 4587.64 | 0.699228 | ||||||||
\(82\) | 943.989 | − | 7151.83i | 0.140391 | − | 1.06363i | ||||
\(83\) | −161.591 | − | 161.591i | −0.0234563 | − | 0.0234563i | 0.695281 | − | 0.718738i | \(-0.255280\pi\) |
−0.718738 | + | 0.695281i | \(0.755280\pi\) | |||||||
\(84\) | −414.493 | − | 719.033i | −0.0587434 | − | 0.101904i | ||||
\(85\) | −2881.84 | − | 2881.84i | −0.398871 | − | 0.398871i | ||||
\(86\) | −80.1892 | + | 61.4887i | −0.0108422 | + | 0.00831378i | ||||
\(87\) | 1938.05 | 0.256051 | ||||||||
\(88\) | 7612.46 | − | 3144.25i | 0.983014 | − | 0.406023i | ||||
\(89\) | 1464.04i | 0.184830i | 0.995721 | + | 0.0924150i | \(0.0294586\pi\) | ||||
−0.995721 | + | 0.0924150i | \(0.970541\pi\) | |||||||
\(90\) | −1913.87 | + | 1467.55i | −0.236280 | + | 0.181178i | ||||
\(91\) | −1465.80 | + | 1465.80i | −0.177007 | + | 0.177007i | ||||
\(92\) | 424.988 | + | 114.180i | 0.0502113 | + | 0.0134900i | ||||
\(93\) | −6005.32 | + | 6005.32i | −0.694337 | + | 0.694337i | ||||
\(94\) | −1187.28 | + | 8995.04i | −0.134368 | + | 1.01800i | ||||
\(95\) | − | 17499.5i | − | 1.93900i | ||||||
\(96\) | −1033.92 | − | 7956.10i | −0.112187 | − | 0.863293i | ||||
\(97\) | −8264.99 | −0.878413 | −0.439207 | − | 0.898386i | \(-0.644740\pi\) | ||||
−0.439207 | + | 0.898386i | \(0.644740\pi\) | |||||||
\(98\) | 9347.60 | + | 1233.81i | 0.973303 | + | 0.128469i | ||||
\(99\) | 1784.78 | + | 1784.78i | 0.182102 | + | 0.182102i | ||||
\(100\) | −1328.57 | + | 4945.08i | −0.132857 | + | 0.494508i | ||||
\(101\) | 5035.04 | + | 5035.04i | 0.493583 | + | 0.493583i | 0.909433 | − | 0.415850i | \(-0.136516\pi\) |
−0.415850 | + | 0.909433i | \(0.636516\pi\) | |||||||
\(102\) | 2528.24 | + | 3297.14i | 0.243006 | + | 0.316911i | ||||
\(103\) | 1427.24 | 0.134531 | 0.0672653 | − | 0.997735i | \(-0.478573\pi\) | ||||
0.0672653 | + | 0.997735i | \(0.478573\pi\) | |||||||
\(104\) | −18521.3 | + | 7650.02i | −1.71240 | + | 0.707287i | ||||
\(105\) | − | 1594.60i | − | 0.144635i | ||||||
\(106\) | 2830.90 | + | 3691.85i | 0.251949 | + | 0.328573i | ||||
\(107\) | 9978.53 | − | 9978.53i | 0.871564 | − | 0.871564i | −0.121079 | − | 0.992643i | \(-0.538635\pi\) |
0.992643 | + | 0.121079i | \(0.0386355\pi\) | |||||||
\(108\) | 10927.2 | − | 6299.11i | 0.936835 | − | 0.540047i | ||||
\(109\) | 9.47842 | − | 9.47842i | 0.000797780 | − | 0.000797780i | −0.706708 | − | 0.707506i | \(-0.749820\pi\) |
0.707506 | + | 0.706708i | \(0.249820\pi\) | |||||||
\(110\) | 15688.5 | + | 2070.76i | 1.29657 | + | 0.171137i | ||||
\(111\) | 6132.67i | 0.497741i | ||||||||
\(112\) | −1466.66 | − | 849.391i | −0.116921 | − | 0.0677129i | ||||
\(113\) | −13634.7 | −1.06780 | −0.533900 | − | 0.845548i | \(-0.679274\pi\) | ||||
−0.533900 | + | 0.845548i | \(0.679274\pi\) | |||||||
\(114\) | −2334.52 | + | 17686.8i | −0.179634 | + | 1.36094i | ||||
\(115\) | 597.858 | + | 597.858i | 0.0452067 | + | 0.0452067i | ||||
\(116\) | 3428.83 | − | 1976.58i | 0.254818 | − | 0.146892i | ||||
\(117\) | −4342.42 | − | 4342.42i | −0.317220 | − | 0.317220i | ||||
\(118\) | 4365.51 | − | 3347.46i | 0.313524 | − | 0.240409i | ||||
\(119\) | 877.721 | 0.0619816 | ||||||||
\(120\) | 5913.28 | − | 14235.5i | 0.410645 | − | 0.988579i | ||||
\(121\) | − | 1920.47i | − | 0.131171i | ||||||
\(122\) | 9230.89 | − | 7078.21i | 0.620189 | − | 0.475559i | ||||
\(123\) | −9991.49 | + | 9991.49i | −0.660419 | + | 0.660419i | ||||
\(124\) | −4500.00 | + | 16749.4i | −0.292664 | + | 1.08932i | ||||
\(125\) | 6629.30 | − | 6629.30i | 0.424275 | − | 0.424275i | ||||
\(126\) | 67.9678 | − | 514.937i | 0.00428117 | − | 0.0324349i | ||||
\(127\) | 8047.14i | 0.498923i | 0.968385 | + | 0.249462i | \(0.0802537\pi\) | ||||
−0.968385 | + | 0.249462i | \(0.919746\pi\) | |||||||
\(128\) | −9943.51 | − | 13021.6i | −0.606904 | − | 0.794775i | ||||
\(129\) | 197.931 | 0.0118942 | ||||||||
\(130\) | −38170.5 | − | 5038.21i | −2.25861 | − | 0.298119i | ||||
\(131\) | −15904.8 | − | 15904.8i | −0.926799 | − | 0.926799i | 0.0706991 | − | 0.997498i | \(-0.477477\pi\) |
−0.997498 | + | 0.0706991i | \(0.977477\pi\) | |||||||
\(132\) | −15580.2 | − | 4185.86i | −0.894179 | − | 0.240235i | ||||
\(133\) | 2664.90 | + | 2664.90i | 0.150653 | + | 0.150653i | ||||
\(134\) | −15872.6 | − | 20699.9i | −0.883973 | − | 1.15281i | ||||
\(135\) | 24233.4 | 1.32968 | ||||||||
\(136\) | 7835.70 | + | 3254.86i | 0.423643 | + | 0.175976i | ||||
\(137\) | 31169.3i | 1.66068i | 0.557257 | + | 0.830340i | \(0.311854\pi\) | ||||
−0.557257 | + | 0.830340i | \(0.688146\pi\) | |||||||
\(138\) | −524.500 | − | 684.015i | −0.0275415 | − | 0.0359176i | ||||
\(139\) | 21432.1 | − | 21432.1i | 1.10926 | − | 1.10926i | 0.116017 | − | 0.993247i | \(-0.462987\pi\) |
0.993247 | − | 0.116017i | \(-0.0370126\pi\) | |||||||
\(140\) | −1626.31 | − | 2821.20i | −0.0829748 | − | 0.143939i | ||||
\(141\) | 12566.5 | − | 12566.5i | 0.632088 | − | 0.632088i | ||||
\(142\) | 12316.5 | + | 1625.69i | 0.610818 | + | 0.0806233i | ||||
\(143\) | 40294.4i | 1.97048i | ||||||||
\(144\) | 2516.32 | − | 4344.96i | 0.121350 | − | 0.209537i | ||||
\(145\) | 7604.14 | 0.361671 | ||||||||
\(146\) | −378.649 | + | 2868.72i | −0.0177636 | + | 0.134581i | ||||
\(147\) | −13059.1 | − | 13059.1i | −0.604335 | − | 0.604335i | ||||
\(148\) | 6254.59 | + | 10850.0i | 0.285546 | + | 0.495344i | ||||
\(149\) | 11772.7 | + | 11772.7i | 0.530276 | + | 0.530276i | 0.920654 | − | 0.390378i | \(-0.127656\pi\) |
−0.390378 | + | 0.920654i | \(0.627656\pi\) | |||||||
\(150\) | 7959.07 | − | 6102.99i | 0.353736 | − | 0.271244i | ||||
\(151\) | −19454.9 | −0.853246 | −0.426623 | − | 0.904429i | \(-0.640297\pi\) | ||||
−0.426623 | + | 0.904429i | \(0.640297\pi\) | |||||||
\(152\) | 13908.2 | + | 33672.7i | 0.601980 | + | 1.45744i | ||||
\(153\) | 2600.25i | 0.111079i | ||||||||
\(154\) | −2704.46 | + | 2073.77i | −0.114035 | + | 0.0874419i | ||||
\(155\) | −23562.5 | + | 23562.5i | −0.980749 | + | 0.980749i | ||||
\(156\) | 37906.9 | + | 10184.3i | 1.55765 | + | 0.418487i | ||||
\(157\) | 18097.5 | − | 18097.5i | 0.734208 | − | 0.734208i | −0.237242 | − | 0.971450i | \(-0.576244\pi\) |
0.971450 | + | 0.237242i | \(0.0762436\pi\) | |||||||
\(158\) | 1789.31 | − | 13556.2i | 0.0716757 | − | 0.543029i | ||||
\(159\) | − | 9112.62i | − | 0.360453i | ||||||
\(160\) | −4056.69 | − | 31216.6i | −0.158464 | − | 1.21940i | ||||
\(161\) | −182.089 | −0.00702478 | ||||||||
\(162\) | −18192.8 | − | 2401.31i | −0.693216 | − | 0.0914993i | ||||
\(163\) | 17673.1 | + | 17673.1i | 0.665178 | + | 0.665178i | 0.956596 | − | 0.291418i | \(-0.0941270\pi\) |
−0.291418 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(164\) | −7486.97 | + | 27867.2i | −0.278367 | + | 1.03611i | ||||
\(165\) | −21917.6 | − | 21917.6i | −0.805056 | − | 0.805056i | ||||
\(166\) | 556.223 | + | 725.386i | 0.0201852 | + | 0.0263241i | ||||
\(167\) | −11374.1 | −0.407834 | −0.203917 | − | 0.978988i | \(-0.565367\pi\) | ||||
−0.203917 | + | 0.978988i | \(0.565367\pi\) | |||||||
\(168\) | 1267.35 | + | 3068.36i | 0.0449034 | + | 0.108714i | ||||
\(169\) | − | 69476.3i | − | 2.43256i | ||||||
\(170\) | 9919.80 | + | 12936.7i | 0.343246 | + | 0.447636i | ||||
\(171\) | −7894.76 | + | 7894.76i | −0.269989 | + | 0.269989i | ||||
\(172\) | 350.184 | − | 201.867i | 0.0118369 | − | 0.00682351i | ||||
\(173\) | −11289.3 | + | 11289.3i | −0.377204 | + | 0.377204i | −0.870092 | − | 0.492888i | \(-0.835941\pi\) |
0.492888 | + | 0.870092i | \(0.335941\pi\) | |||||||
\(174\) | −7685.54 | − | 1014.43i | −0.253849 | − | 0.0335062i | ||||
\(175\) | − | 2118.76i | − | 0.0691838i | ||||||
\(176\) | −31833.8 | + | 8484.24i | −1.02769 | + | 0.273897i | ||||
\(177\) | −10775.4 | −0.343944 | ||||||||
\(178\) | 766.322 | − | 5805.80i | 0.0241864 | − | 0.183241i | ||||
\(179\) | −25338.8 | − | 25338.8i | −0.790825 | − | 0.790825i | 0.190803 | − | 0.981628i | \(-0.438891\pi\) |
−0.981628 | + | 0.190803i | \(0.938891\pi\) | |||||||
\(180\) | 8357.79 | − | 4817.93i | 0.257957 | − | 0.148702i | ||||
\(181\) | 22579.8 | + | 22579.8i | 0.689228 | + | 0.689228i | 0.962061 | − | 0.272833i | \(-0.0879608\pi\) |
−0.272833 | + | 0.962061i | \(0.587961\pi\) | |||||||
\(182\) | 6580.02 | − | 5045.53i | 0.198648 | − | 0.152323i | ||||
\(183\) | −22784.7 | −0.680363 | ||||||||
\(184\) | −1625.57 | − | 675.243i | −0.0480142 | − | 0.0199446i | ||||
\(185\) | 24062.2i | 0.703058i | ||||||||
\(186\) | 26958.1 | − | 20671.4i | 0.779226 | − | 0.597507i | ||||
\(187\) | 12064.2 | − | 12064.2i | 0.344996 | − | 0.344996i | ||||
\(188\) | 9416.55 | − | 35049.3i | 0.266426 | − | 0.991663i | ||||
\(189\) | −3690.38 | + | 3690.38i | −0.103311 | + | 0.103311i | ||||
\(190\) | −9159.75 | + | 69396.0i | −0.253733 | + | 1.92233i | ||||
\(191\) | − | 62994.4i | − | 1.72677i | −0.504543 | − | 0.863386i | \(-0.668339\pi\) | ||
0.504543 | − | 0.863386i | \(-0.331661\pi\) | |||||||
\(192\) | −64.3511 | + | 32092.0i | −0.00174564 | + | 0.870550i | ||||
\(193\) | −25039.7 | −0.672225 | −0.336112 | − | 0.941822i | \(-0.609112\pi\) | ||||
−0.336112 | + | 0.941822i | \(0.609112\pi\) | |||||||
\(194\) | 32775.7 | + | 4326.14i | 0.870860 | + | 0.114947i | ||||
\(195\) | 53326.1 | + | 53326.1i | 1.40240 | + | 1.40240i | ||||
\(196\) | −36423.1 | − | 9785.63i | −0.948122 | − | 0.254728i | ||||
\(197\) | −6468.96 | − | 6468.96i | −0.166687 | − | 0.166687i | 0.618834 | − | 0.785521i | \(-0.287605\pi\) |
−0.785521 | + | 0.618834i | \(0.787605\pi\) | |||||||
\(198\) | −6143.54 | − | 8011.96i | −0.156707 | − | 0.204366i | ||||
\(199\) | 55793.6 | 1.40889 | 0.704446 | − | 0.709757i | \(-0.251195\pi\) | ||||
0.704446 | + | 0.709757i | \(0.251195\pi\) | |||||||
\(200\) | 7857.00 | − | 18914.8i | 0.196425 | − | 0.472870i | ||||
\(201\) | 51093.8i | 1.26467i | ||||||||
\(202\) | −17331.5 | − | 22602.5i | −0.424750 | − | 0.553928i | ||||
\(203\) | −1157.99 | + | 1157.99i | −0.0281005 | + | 0.0281005i | ||||
\(204\) | −8300.17 | − | 14398.5i | −0.199447 | − | 0.345985i | ||||
\(205\) | −39202.6 | + | 39202.6i | −0.932841 | + | 0.932841i | ||||
\(206\) | −5659.85 | − | 747.058i | −0.133374 | − | 0.0176044i | ||||
\(207\) | − | 539.439i | − | 0.0125893i | ||||||
\(208\) | 77452.3 | − | 20642.4i | 1.79023 | − | 0.477126i | ||||
\(209\) | 73257.5 | 1.67710 | ||||||||
\(210\) | −834.663 | + | 6323.57i | −0.0189266 | + | 0.143392i | ||||
\(211\) | −11403.6 | − | 11403.6i | −0.256139 | − | 0.256139i | 0.567343 | − | 0.823482i | \(-0.307971\pi\) |
−0.823482 | + | 0.567343i | \(0.807971\pi\) | |||||||
\(212\) | −9293.79 | − | 16122.2i | −0.206786 | − | 0.358717i | ||||
\(213\) | −17206.8 | − | 17206.8i | −0.379264 | − | 0.379264i | ||||
\(214\) | −44794.0 | + | 34347.9i | −0.978120 | + | 0.750019i | ||||
\(215\) | 776.604 | 0.0168005 | ||||||||
\(216\) | −46630.3 | + | 19260.1i | −0.999449 | + | 0.412812i | ||||
\(217\) | − | 7176.41i | − | 0.152401i | ||||||
\(218\) | −42.5490 | + | 32.6264i | −0.000895315 | + | 0.000686524i | ||||
\(219\) | 4007.75 | − | 4007.75i | 0.0835627 | − | 0.0835627i | ||||
\(220\) | −61130.5 | − | 16423.7i | −1.26303 | − | 0.339332i | ||||
\(221\) | −29352.4 | + | 29352.4i | −0.600979 | + | 0.600979i | ||||
\(222\) | 3210.02 | − | 24319.7i | 0.0651331 | − | 0.493461i | ||||
\(223\) | 15194.4i | 0.305545i | 0.988261 | + | 0.152772i | \(0.0488201\pi\) | ||||
−0.988261 | + | 0.152772i | \(0.951180\pi\) | |||||||
\(224\) | 5371.58 | + | 4136.04i | 0.107055 | + | 0.0824306i | ||||
\(225\) | 6276.81 | 0.123986 | ||||||||
\(226\) | 54070.0 | + | 7136.83i | 1.05862 | + | 0.139730i | ||||
\(227\) | 47509.0 | + | 47509.0i | 0.921986 | + | 0.921986i | 0.997170 | − | 0.0751841i | \(-0.0239544\pi\) |
−0.0751841 | + | 0.997170i | \(0.523954\pi\) | |||||||
\(228\) | 18515.6 | − | 68916.9i | 0.356179 | − | 1.32573i | ||||
\(229\) | 15628.9 | + | 15628.9i | 0.298028 | + | 0.298028i | 0.840241 | − | 0.542213i | \(-0.182413\pi\) |
−0.542213 | + | 0.840241i | \(0.682413\pi\) | |||||||
\(230\) | −2057.93 | − | 2683.81i | −0.0389023 | − | 0.0507336i | ||||
\(231\) | 6675.44 | 0.125100 | ||||||||
\(232\) | −14632.0 | + | 6043.59i | −0.271849 | + | 0.112284i | ||||
\(233\) | − | 63151.2i | − | 1.16324i | −0.813460 | − | 0.581621i | \(-0.802419\pi\) | ||
0.813460 | − | 0.581621i | \(-0.197581\pi\) | |||||||
\(234\) | 14947.4 | + | 19493.3i | 0.272981 | + | 0.356003i | ||||
\(235\) | 49306.1 | − | 49306.1i | 0.892823 | − | 0.892823i | ||||
\(236\) | −19064.1 | + | 10989.7i | −0.342288 | + | 0.197315i | ||||
\(237\) | −18938.7 | + | 18938.7i | −0.337173 | + | 0.337173i | ||||
\(238\) | −3480.69 | − | 459.426i | −0.0614486 | − | 0.00811075i | ||||
\(239\) | − | 33331.4i | − | 0.583522i | −0.956491 | − | 0.291761i | \(-0.905759\pi\) | ||
0.956491 | − | 0.291761i | \(-0.0942412\pi\) | |||||||
\(240\) | −30901.1 | + | 53357.3i | −0.536477 | + | 0.926343i | ||||
\(241\) | 5625.72 | 0.0968599 | 0.0484299 | − | 0.998827i | \(-0.484578\pi\) | ||||
0.0484299 | + | 0.998827i | \(0.484578\pi\) | |||||||
\(242\) | −1005.23 | + | 7615.84i | −0.0171647 | + | 0.130043i | ||||
\(243\) | −19734.3 | − | 19734.3i | −0.334202 | − | 0.334202i | ||||
\(244\) | −40311.0 | + | 23237.7i | −0.677087 | + | 0.390313i | ||||
\(245\) | −51238.7 | − | 51238.7i | −0.853622 | − | 0.853622i | ||||
\(246\) | 44852.1 | − | 34392.4i | 0.741162 | − | 0.568320i | ||||
\(247\) | −178237. | −2.92149 | ||||||||
\(248\) | 26612.4 | − | 64066.2i | 0.432693 | − | 1.04166i | ||||
\(249\) | − | 1790.47i | − | 0.0288782i | ||||||
\(250\) | −29759.2 | + | 22819.2i | −0.476147 | + | 0.365107i | ||||
\(251\) | −62195.0 | + | 62195.0i | −0.987206 | + | 0.987206i | −0.999919 | − | 0.0127130i | \(-0.995953\pi\) |
0.0127130 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(252\) | −539.067 | + | 2006.46i | −0.00848871 | + | 0.0315958i | ||||
\(253\) | −2502.80 | + | 2502.80i | −0.0391007 | + | 0.0391007i | ||||
\(254\) | 4212.11 | − | 31911.8i | 0.0652879 | − | 0.494633i | ||||
\(255\) | − | 31931.7i | − | 0.491068i | ||||||
\(256\) | 32616.1 | + | 56843.2i | 0.497683 | + | 0.867359i | ||||
\(257\) | 22791.9 | 0.345075 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(258\) | −784.918 | − | 103.603i | −0.0117919 | − | 0.00155645i | ||||
\(259\) | −3664.30 | − | 3664.30i | −0.0546250 | − | 0.0546250i | ||||
\(260\) | 148732. | + | 39959.1i | 2.20017 | + | 0.591111i | ||||
\(261\) | −3430.55 | − | 3430.55i | −0.0503597 | − | 0.0503597i | ||||
\(262\) | 54747.1 | + | 71397.2i | 0.797551 | + | 1.04011i | ||||
\(263\) | 126611. | 1.83047 | 0.915233 | − | 0.402926i | \(-0.132007\pi\) | ||||
0.915233 | + | 0.402926i | \(0.132007\pi\) | |||||||
\(264\) | 59593.8 | + | 24754.6i | 0.855054 | + | 0.355180i | ||||
\(265\) | − | 35754.3i | − | 0.509139i | ||||||
\(266\) | −9173.05 | − | 11962.8i | −0.129643 | − | 0.169072i | ||||
\(267\) | −8111.00 | + | 8111.00i | −0.113776 | + | 0.113776i | ||||
\(268\) | 52109.6 | + | 90395.9i | 0.725518 | + | 1.25858i | ||||
\(269\) | 65428.7 | − | 65428.7i | 0.904198 | − | 0.904198i | −0.0915982 | − | 0.995796i | \(-0.529198\pi\) |
0.995796 | + | 0.0915982i | \(0.0291975\pi\) | |||||||
\(270\) | −96100.2 | − | 12684.5i | −1.31825 | − | 0.173999i | ||||
\(271\) | 93429.2i | 1.27217i | 0.771621 | + | 0.636083i | \(0.219446\pi\) | ||||
−0.771621 | + | 0.636083i | \(0.780554\pi\) | |||||||
\(272\) | −29369.6 | − | 17008.9i | −0.396972 | − | 0.229900i | ||||
\(273\) | −16241.5 | −0.217922 | ||||||||
\(274\) | 16314.9 | − | 123605.i | 0.217312 | − | 1.64640i | ||||
\(275\) | −29122.0 | − | 29122.0i | −0.385085 | − | 0.385085i | ||||
\(276\) | 1721.93 | + | 2987.07i | 0.0226046 | + | 0.0392128i | ||||
\(277\) | 105271. | + | 105271.i | 1.37198 | + | 1.37198i | 0.857504 | + | 0.514477i | \(0.172014\pi\) |
0.514477 | + | 0.857504i | \(0.327986\pi\) | |||||||
\(278\) | −96209.4 | + | 73773.0i | −1.24488 | + | 0.954570i | ||||
\(279\) | 21260.1 | 0.273122 | ||||||||
\(280\) | 4972.59 | + | 12039.0i | 0.0634259 | + | 0.153559i | ||||
\(281\) | 42955.1i | 0.544004i | 0.962297 | + | 0.272002i | \(0.0876857\pi\) | ||||
−0.962297 | + | 0.272002i | \(0.912314\pi\) | |||||||
\(282\) | −56411.6 | + | 43256.2i | −0.709366 | + | 0.543939i | ||||
\(283\) | −36538.7 | + | 36538.7i | −0.456226 | + | 0.456226i | −0.897414 | − | 0.441189i | \(-0.854557\pi\) |
0.441189 | + | 0.897414i | \(0.354557\pi\) | |||||||
\(284\) | −47991.5 | − | 12893.7i | −0.595015 | − | 0.159860i | ||||
\(285\) | 96949.8 | − | 96949.8i | 1.19360 | − | 1.19360i | ||||
\(286\) | 21091.3 | − | 159792.i | 0.257853 | − | 1.95354i | ||||
\(287\) | − | 11939.9i | − | 0.144957i | ||||||
\(288\) | −12253.0 | + | 15913.3i | −0.147726 | + | 0.191856i | ||||
\(289\) | −65944.8 | −0.789559 | ||||||||
\(290\) | −30155.0 | − | 3980.24i | −0.358561 | − | 0.0473274i | ||||
\(291\) | −45789.3 | − | 45789.3i | −0.540727 | − | 0.540727i | ||||
\(292\) | 3003.15 | − | 11178.0i | 0.0352217 | − | 0.131099i | ||||
\(293\) | −45359.7 | − | 45359.7i | −0.528367 | − | 0.528367i | 0.391719 | − | 0.920085i | \(-0.371881\pi\) |
−0.920085 | + | 0.391719i | \(0.871881\pi\) | |||||||
\(294\) | 44951.6 | + | 58622.7i | 0.520057 | + | 0.678221i | ||||
\(295\) | −42278.5 | −0.485820 | ||||||||
\(296\) | −19124.0 | − | 46300.7i | −0.218271 | − | 0.528450i | ||||
\(297\) | 101448.i | 1.15008i | ||||||||
\(298\) | −40523.5 | − | 52847.9i | −0.456326 | − | 0.595107i | ||||
\(299\) | 6089.36 | − | 6089.36i | 0.0681129 | − | 0.0681129i | ||||
\(300\) | −34757.0 | + | 20036.0i | −0.386189 | + | 0.222622i | ||||
\(301\) | −118.265 | + | 118.265i | −0.00130534 | + | 0.00130534i | ||||
\(302\) | 77150.3 | + | 10183.3i | 0.845909 | + | 0.111654i | ||||
\(303\) | 55789.9i | 0.607673i | ||||||||
\(304\) | −37528.9 | − | 140813.i | −0.406087 | − | 1.52368i | ||||
\(305\) | −89398.0 | −0.961011 | ||||||||
\(306\) | 1361.05 | − | 10311.5i | 0.0145355 | − | 0.110124i | ||||
\(307\) | −10035.4 | − | 10035.4i | −0.106478 | − | 0.106478i | 0.651861 | − | 0.758339i | \(-0.273989\pi\) |
−0.758339 | + | 0.651861i | \(0.773989\pi\) | |||||||
\(308\) | 11810.3 | − | 6808.16i | 0.124497 | − | 0.0717676i | ||||
\(309\) | 7907.11 | + | 7907.11i | 0.0828134 | + | 0.0828134i | ||||
\(310\) | 105773. | − | 81106.2i | 1.10065 | − | 0.843977i | ||||
\(311\) | 102401. | 1.05873 | 0.529365 | − | 0.848394i | \(-0.322430\pi\) | ||||
0.529365 | + | 0.848394i | \(0.322430\pi\) | |||||||
\(312\) | −144993. | − | 60228.5i | −1.48949 | − | 0.618718i | ||||
\(313\) | − | 60933.1i | − | 0.621963i | −0.950416 | − | 0.310981i | \(-0.899342\pi\) | ||
0.950416 | − | 0.310981i | \(-0.100658\pi\) | |||||||
\(314\) | −81240.3 | + | 62294.7i | −0.823971 | + | 0.631818i | ||||
\(315\) | −2822.62 | + | 2822.62i | −0.0284466 | + | 0.0284466i | ||||
\(316\) | −14191.4 | + | 52821.8i | −0.142119 | + | 0.528980i | ||||
\(317\) | −10217.2 | + | 10217.2i | −0.101675 | + | 0.101675i | −0.756115 | − | 0.654439i | \(-0.772905\pi\) |
0.654439 | + | 0.756115i | \(0.272905\pi\) | |||||||
\(318\) | −4769.82 | + | 36137.0i | −0.0471680 | + | 0.357354i | ||||
\(319\) | 31833.0i | 0.312821i | ||||||||
\(320\) | −252.488 | + | 125916.i | −0.00246571 | + | 1.22965i | ||||
\(321\) | 110565. | 1.07302 | ||||||||
\(322\) | 722.094 | + | 95.3110i | 0.00696437 | + | 0.000919245i | ||||
\(323\) | 53364.3 | + | 53364.3i | 0.511500 | + | 0.511500i | ||||
\(324\) | 70888.4 | + | 19045.3i | 0.675282 | + | 0.181425i | ||||
\(325\) | 70854.6 | + | 70854.6i | 0.670813 | + | 0.670813i | ||||
\(326\) | −60834.0 | − | 79335.2i | −0.572415 | − | 0.746502i | ||||
\(327\) | 105.024 | 0.000982183 | ||||||||
\(328\) | 44276.9 | − | 106592.i | 0.411557 | − | 0.990775i | ||||
\(329\) | 15017.1i | 0.138738i | ||||||||
\(330\) | 75444.3 | + | 98389.0i | 0.692785 | + | 0.903481i | ||||
\(331\) | 123603. | − | 123603.i | 1.12817 | − | 1.12817i | 0.137692 | − | 0.990475i | \(-0.456032\pi\) |
0.990475 | − | 0.137692i | \(-0.0439684\pi\) | |||||||
\(332\) | −1826.07 | − | 3167.74i | −0.0165669 | − | 0.0287391i | ||||
\(333\) | 10855.5 | − | 10855.5i | 0.0978949 | − | 0.0978949i | ||||
\(334\) | 45105.1 | + | 5953.53i | 0.404327 | + | 0.0533681i | ||||
\(335\) | 200472.i | 1.78634i | ||||||||
\(336\) | −3419.75 | − | 12831.3i | −0.0302911 | − | 0.113656i | ||||
\(337\) | −102441. | −0.902018 | −0.451009 | − | 0.892519i | \(-0.648936\pi\) | ||||
−0.451009 | + | 0.892519i | \(0.648936\pi\) | |||||||
\(338\) | −36366.0 | + | 275515.i | −0.318318 | + | 2.41164i | ||||
\(339\) | −75538.6 | − | 75538.6i | −0.657309 | − | 0.657309i | ||||
\(340\) | −32566.6 | − | 56494.1i | −0.281718 | − | 0.488704i | ||||
\(341\) | −98639.0 | − | 98639.0i | −0.848281 | − | 0.848281i | ||||
\(342\) | 35439.9 | − | 27175.1i | 0.302998 | − | 0.232338i | ||||
\(343\) | 31501.6 | 0.267760 | ||||||||
\(344\) | −1494.35 | + | 617.227i | −0.0126280 | + | 0.00521588i | ||||
\(345\) | 6624.45i | 0.0556560i | ||||||||
\(346\) | 50678.2 | − | 38859.9i | 0.423320 | − | 0.324601i | ||||
\(347\) | 63342.4 | − | 63342.4i | 0.526061 | − | 0.526061i | −0.393335 | − | 0.919395i | \(-0.628679\pi\) |
0.919395 | + | 0.393335i | \(0.128679\pi\) | |||||||
\(348\) | 29946.8 | + | 8045.68i | 0.247282 | + | 0.0664362i | ||||
\(349\) | −114645. | + | 114645.i | −0.941247 | + | 0.941247i | −0.998367 | − | 0.0571205i | \(-0.981808\pi\) |
0.0571205 | + | 0.998367i | \(0.481808\pi\) | |||||||
\(350\) | −1109.02 | + | 8402.15i | −0.00905323 | + | 0.0685889i | ||||
\(351\) | − | 246824.i | − | 2.00343i | ||||||
\(352\) | 130681. | − | 16982.4i | 1.05470 | − | 0.137061i | ||||
\(353\) | −94430.7 | −0.757816 | −0.378908 | − | 0.925434i | \(-0.623700\pi\) | ||||
−0.378908 | + | 0.925434i | \(0.623700\pi\) | |||||||
\(354\) | 42731.1 | + | 5640.18i | 0.340986 | + | 0.0450076i | ||||
\(355\) | −67512.8 | − | 67512.8i | −0.535709 | − | 0.535709i | ||||
\(356\) | −6077.86 | + | 22622.4i | −0.0479568 | + | 0.178500i | ||||
\(357\) | 4862.71 | + | 4862.71i | 0.0381542 | + | 0.0381542i | ||||
\(358\) | 87220.7 | + | 113747.i | 0.680540 | + | 0.887511i | ||||
\(359\) | −59001.0 | −0.457794 | −0.228897 | − | 0.973451i | \(-0.573512\pi\) | ||||
−0.228897 | + | 0.973451i | \(0.573512\pi\) | |||||||
\(360\) | −35665.6 | + | 14731.3i | −0.275197 | + | 0.113667i | ||||
\(361\) | 193724.i | 1.48651i | ||||||||
\(362\) | −77723.6 | − | 101361.i | −0.593111 | − | 0.773492i | ||||
\(363\) | 10639.7 | − | 10639.7i | 0.0807453 | − | 0.0807453i | ||||
\(364\) | −28734.7 | + | 16564.4i | −0.216872 | + | 0.125018i | ||||
\(365\) | 15724.8 | − | 15724.8i | 0.118032 | − | 0.118032i | ||||
\(366\) | 90355.0 | + | 11926.2i | 0.674513 | + | 0.0890306i | ||||
\(367\) | − | 120112.i | − | 0.891775i | −0.895089 | − | 0.445888i | \(-0.852888\pi\) | ||
0.895089 | − | 0.445888i | \(-0.147112\pi\) | |||||||
\(368\) | 6092.92 | + | 3528.62i | 0.0449915 | + | 0.0260561i | ||||
\(369\) | 35372.0 | 0.259781 | ||||||||
\(370\) | 12594.9 | − | 95421.0i | 0.0920004 | − | 0.697012i | ||||
\(371\) | 5444.83 | + | 5444.83i | 0.0395582 | + | 0.0395582i | ||||
\(372\) | −117725. | + | 67863.8i | −0.850713 | + | 0.490402i | ||||
\(373\) | −113849. | − | 113849.i | −0.818300 | − | 0.818300i | 0.167562 | − | 0.985862i | \(-0.446411\pi\) |
−0.985862 | + | 0.167562i | \(0.946411\pi\) | |||||||
\(374\) | −54156.5 | + | 41527.0i | −0.387175 | + | 0.296884i | ||||
\(375\) | 73454.7 | 0.522345 | ||||||||
\(376\) | −55688.2 | + | 134063.i | −0.393901 | + | 0.948272i | ||||
\(377\) | − | 77450.4i | − | 0.544930i | ||||||
\(378\) | 16566.2 | − | 12702.9i | 0.115942 | − | 0.0889038i | ||||
\(379\) | −75841.4 | + | 75841.4i | −0.527993 | + | 0.527993i | −0.919973 | − | 0.391981i | \(-0.871790\pi\) |
0.391981 | + | 0.919973i | \(0.371790\pi\) | |||||||
\(380\) | 72647.9 | − | 270403.i | 0.503102 | − | 1.87259i | ||||
\(381\) | −44582.4 | + | 44582.4i | −0.307124 | + | 0.307124i | ||||
\(382\) | −32973.2 | + | 249811.i | −0.225961 | + | 1.71192i | ||||
\(383\) | 80282.4i | 0.547297i | 0.961830 | + | 0.273648i | \(0.0882304\pi\) | ||||
−0.961830 | + | 0.273648i | \(0.911770\pi\) | |||||||
\(384\) | 17053.1 | − | 127230.i | 0.115649 | − | 0.862836i | ||||
\(385\) | 26191.8 | 0.176703 | ||||||||
\(386\) | 99297.6 | + | 13106.5i | 0.666445 | + | 0.0879657i | ||||
\(387\) | −350.360 | − | 350.360i | −0.00233933 | − | 0.00233933i | ||||
\(388\) | −127711. | − | 34311.6i | −0.848330 | − | 0.227917i | ||||
\(389\) | 89476.2 | + | 89476.2i | 0.591301 | + | 0.591301i | 0.937983 | − | 0.346682i | \(-0.112692\pi\) |
−0.346682 | + | 0.937983i | \(0.612692\pi\) | |||||||
\(390\) | −183558. | − | 239383.i | −1.20682 | − | 1.57385i | ||||
\(391\) | −3646.31 | −0.0238507 | ||||||||
\(392\) | 139317. | + | 57870.9i | 0.906636 | + | 0.376607i | ||||
\(393\) | − | 176230.i | − | 1.14102i | ||||||
\(394\) | 22267.3 | + | 29039.4i | 0.143441 | + | 0.187066i | ||||
\(395\) | −74307.8 | + | 74307.8i | −0.476256 | + | 0.476256i | ||||
\(396\) | 20169.2 | + | 34988.0i | 0.128617 | + | 0.223115i | ||||
\(397\) | 128824. | − | 128824.i | 0.817363 | − | 0.817363i | −0.168362 | − | 0.985725i | \(-0.553848\pi\) |
0.985725 | + | 0.168362i | \(0.0538479\pi\) | |||||||
\(398\) | −221255. | − | 29204.0i | −1.39678 | − | 0.184364i | ||||
\(399\) | 29527.9i | 0.185476i | ||||||||
\(400\) | −41058.3 | + | 70896.1i | −0.256615 | + | 0.443101i | ||||
\(401\) | 71110.1 | 0.442224 | 0.221112 | − | 0.975248i | \(-0.429031\pi\) | ||||
0.221112 | + | 0.975248i | \(0.429031\pi\) | |||||||
\(402\) | 26744.0 | − | 202618.i | 0.165491 | − | 1.25379i | ||||
\(403\) | 239991. | + | 239991.i | 1.47769 | + | 1.47769i | ||||
\(404\) | 56899.1 | + | 98704.4i | 0.348612 | + | 0.604747i | ||||
\(405\) | 99723.2 | + | 99723.2i | 0.607976 | + | 0.607976i | ||||
\(406\) | 5198.27 | − | 3986.02i | 0.0315360 | − | 0.0241817i | ||||
\(407\) | −100731. | −0.608097 | ||||||||
\(408\) | 25378.6 | + | 61443.4i | 0.152457 | + | 0.369109i | ||||
\(409\) | − | 87416.4i | − | 0.522572i | −0.965261 | − | 0.261286i | \(-0.915853\pi\) | ||
0.965261 | − | 0.261286i | \(-0.0841466\pi\) | |||||||
\(410\) | 175982. | − | 134942.i | 1.04689 | − | 0.802750i | ||||
\(411\) | −172683. | + | 172683.i | −1.02227 | + | 1.02227i | ||||
\(412\) | 22053.7 | + | 5925.08i | 0.129923 | + | 0.0349059i | ||||
\(413\) | 6438.36 | − | 6438.36i | 0.0377464 | − | 0.0377464i | ||||
\(414\) | −282.358 | + | 2139.20i | −0.00164740 | + | 0.0124810i | ||||
\(415\) | − | 7025.11i | − | 0.0407903i | ||||||
\(416\) | −317950. | + | 41318.5i | −1.83727 | + | 0.238758i | ||||
\(417\) | 237474. | 1.36567 | ||||||||
\(418\) | −290510. | − | 38345.2i | −1.66268 | − | 0.219461i | ||||
\(419\) | 156666. | + | 156666.i | 0.892373 | + | 0.892373i | 0.994746 | − | 0.102373i | \(-0.0326436\pi\) |
−0.102373 | + | 0.994746i | \(0.532644\pi\) | |||||||
\(420\) | 6619.89 | − | 24639.9i | 0.0375277 | − | 0.139682i | ||||
\(421\) | 20636.7 | + | 20636.7i | 0.116433 | + | 0.116433i | 0.762923 | − | 0.646490i | \(-0.223764\pi\) |
−0.646490 | + | 0.762923i | \(0.723764\pi\) | |||||||
\(422\) | 39253.1 | + | 51191.0i | 0.220419 | + | 0.287454i | ||||
\(423\) | −44488.2 | −0.248636 | ||||||||
\(424\) | 28416.7 | + | 68798.9i | 0.158067 | + | 0.382692i | ||||
\(425\) | − | 42427.8i | − | 0.234894i | ||||||
\(426\) | 59228.9 | + | 77242.0i | 0.326373 | + | 0.425632i | ||||
\(427\) | 13614.0 | − | 13614.0i | 0.0746670 | − | 0.0746670i | ||||
\(428\) | 195614. | − | 112763.i | 1.06785 | − | 0.615575i | ||||
\(429\) | −223238. | + | 223238.i | −1.21298 | + | 1.21298i | ||||
\(430\) | −3079.71 | − | 406.498i | −0.0166561 | − | 0.00219848i | ||||
\(431\) | − | 294349.i | − | 1.58456i | −0.610160 | − | 0.792279i | \(-0.708895\pi\) | ||
0.610160 | − | 0.792279i | \(-0.291105\pi\) | |||||||
\(432\) | 194999. | − | 51970.4i | 1.04487 | − | 0.278477i | ||||
\(433\) | 240460. | 1.28253 | 0.641264 | − | 0.767321i | \(-0.278411\pi\) | ||||
0.641264 | + | 0.767321i | \(0.278411\pi\) | |||||||
\(434\) | −3756.35 | + | 28458.8i | −0.0199428 | + | 0.151091i | ||||
\(435\) | 42128.1 | + | 42128.1i | 0.222635 | + | 0.222635i | ||||
\(436\) | 185.810 | − | 107.112i | 0.000977454 | − | 0.000563462i | ||||
\(437\) | −11070.8 | − | 11070.8i | −0.0579716 | − | 0.0579716i | ||||
\(438\) | −17990.9 | + | 13795.4i | −0.0937789 | + | 0.0719093i | ||||
\(439\) | −294699. | −1.52915 | −0.764574 | − | 0.644536i | \(-0.777051\pi\) | ||||
−0.764574 | + | 0.644536i | \(0.777051\pi\) | |||||||
\(440\) | 233823. | + | 97127.2i | 1.20776 | + | 0.501690i | ||||
\(441\) | 46231.9i | 0.237719i | ||||||||
\(442\) | 131764. | − | 101036.i | 0.674454 | − | 0.517168i | ||||
\(443\) | 118964. | − | 118964.i | 0.606187 | − | 0.606187i | −0.335760 | − | 0.941948i | \(-0.608993\pi\) |
0.941948 | + | 0.335760i | \(0.108993\pi\) | |||||||
\(444\) | −25459.4 | + | 94762.2i | −0.129146 | + | 0.480695i | ||||
\(445\) | −31824.4 | + | 31824.4i | −0.160709 | + | 0.160709i | ||||
\(446\) | 7953.22 | − | 60255.1i | 0.0399828 | − | 0.302917i | ||||
\(447\) | 130445.i | 0.652847i | ||||||||
\(448\) | −19136.6 | − | 19213.5i | −0.0953476 | − | 0.0957308i | ||||
\(449\) | −82129.5 | −0.407386 | −0.203693 | − | 0.979035i | \(-0.565294\pi\) | ||||
−0.203693 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(450\) | −24891.3 | − | 3285.47i | −0.122920 | − | 0.0162245i | ||||
\(451\) | −164113. | − | 164113.i | −0.806844 | − | 0.806844i | ||||
\(452\) | −210684. | − | 56603.7i | −1.03123 | − | 0.277056i | ||||
\(453\) | −107783. | − | 107783.i | −0.525235 | − | 0.525235i | ||||
\(454\) | −163534. | − | 213270.i | −0.793409 | − | 1.03471i | ||||
\(455\) | −63725.2 | −0.307814 | ||||||||
\(456\) | −109499. | + | 263605.i | −0.526598 | + | 1.26772i | ||||
\(457\) | − | 172358.i | − | 0.825277i | −0.910895 | − | 0.412638i | \(-0.864607\pi\) | ||
0.910895 | − | 0.412638i | \(-0.135393\pi\) | |||||||
\(458\) | −53797.4 | − | 70158.6i | −0.256466 | − | 0.334465i | ||||
\(459\) | −73899.3 | + | 73899.3i | −0.350764 | + | 0.350764i | ||||
\(460\) | 6756.16 | + | 11720.1i | 0.0319289 | + | 0.0553880i | ||||
\(461\) | 96898.8 | − | 96898.8i | 0.455950 | − | 0.455950i | −0.441374 | − | 0.897323i | \(-0.645509\pi\) |
0.897323 | + | 0.441374i | \(0.145509\pi\) | |||||||
\(462\) | −26472.2 | − | 3494.13i | −0.124024 | − | 0.0163702i | ||||
\(463\) | − | 142244.i | − | 0.663549i | −0.943359 | − | 0.331775i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331775i | \(-0.107647\pi\) | |||||||
\(464\) | 61188.1 | − | 16307.7i | 0.284204 | − | 0.0757453i | ||||
\(465\) | −261080. | −1.20745 | ||||||||
\(466\) | −33055.2 | + | 250433.i | −0.152219 | + | 1.15324i | ||||
\(467\) | −139194. | − | 139194.i | −0.638246 | − | 0.638246i | 0.311877 | − | 0.950123i | \(-0.399042\pi\) |
−0.950123 | + | 0.311877i | \(0.899042\pi\) | |||||||
\(468\) | −49072.0 | − | 85126.5i | −0.224049 | − | 0.388663i | ||||
\(469\) | −30528.8 | − | 30528.8i | −0.138792 | − | 0.138792i | ||||
\(470\) | −221337. | + | 169720.i | −1.00198 | + | 0.768313i | ||||
\(471\) | 200526. | 0.903917 | ||||||||
\(472\) | 81352.8 | − | 33601.9i | 0.365164 | − | 0.150827i | ||||
\(473\) | 3251.08i | 0.0145313i | ||||||||
\(474\) | 85016.4 | − | 65190.2i | 0.378395 | − | 0.290152i | ||||
\(475\) | 128818. | − | 128818.i | 0.570936 | − | 0.570936i | ||||
\(476\) | 13562.6 | + | 3643.80i | 0.0598589 | + | 0.0160820i | ||||
\(477\) | −16130.3 | + | 16130.3i | −0.0708934 | + | 0.0708934i | ||||
\(478\) | −17446.6 | + | 132179.i | −0.0763582 | + | 0.578504i | ||||
\(479\) | 216764.i | 0.944749i | 0.881398 | + | 0.472374i | \(0.156603\pi\) | ||||
−0.881398 | + | 0.472374i | \(0.843397\pi\) | |||||||
\(480\) | 150470. | − | 195420.i | 0.653082 | − | 0.848175i | ||||
\(481\) | 245080. | 1.05930 | ||||||||
\(482\) | −22309.4 | − | 2944.67i | −0.0960270 | − | 0.0126748i | ||||
\(483\) | −1008.80 | − | 1008.80i | −0.00432426 | − | 0.00432426i | ||||
\(484\) | 7972.72 | − | 29675.2i | 0.0340342 | − | 0.126679i | ||||
\(485\) | −179659. | − | 179659.i | −0.763776 | − | 0.763776i | ||||
\(486\) | 67928.8 | + | 88587.8i | 0.287595 | + | 0.375061i | ||||
\(487\) | 146986. | 0.619752 | 0.309876 | − | 0.950777i | \(-0.399713\pi\) | ||||
0.309876 | + | 0.950777i | \(0.399713\pi\) | |||||||
\(488\) | 172021. | − | 71051.4i | 0.722340 | − | 0.298355i | ||||
\(489\) | 195824.i | 0.818931i | ||||||||
\(490\) | 176372. | + | 230012.i | 0.734579 | + | 0.957985i | ||||
\(491\) | −207292. | + | 207292.i | −0.859843 | + | 0.859843i | −0.991319 | − | 0.131476i | \(-0.958028\pi\) |
0.131476 | + | 0.991319i | \(0.458028\pi\) | |||||||
\(492\) | −195868. | + | 112910.i | −0.809157 | + | 0.466446i | ||||
\(493\) | −23188.7 | + | 23188.7i | −0.0954074 | + | 0.0954074i | ||||
\(494\) | 706818. | + | 93294.7i | 2.89637 | + | 0.382299i | ||||
\(495\) | 77593.1i | 0.316674i | ||||||||
\(496\) | −139068. | + | 240131.i | −0.565281 | + | 0.976080i | ||||
\(497\) | 20562.3 | 0.0832452 | ||||||||
\(498\) | −937.188 | + | 7100.31i | −0.00377892 | + | 0.0286298i | ||||
\(499\) | 5591.76 | + | 5591.76i | 0.0224568 | + | 0.0224568i | 0.718246 | − | 0.695789i | \(-0.244945\pi\) |
−0.695789 | + | 0.718246i | \(0.744945\pi\) | |||||||
\(500\) | 129957. | − | 74915.2i | 0.519829 | − | 0.299661i | ||||
\(501\) | −63014.2 | − | 63014.2i | −0.251051 | − | 0.251051i | ||||
\(502\) | 279195. | − | 214086.i | 1.10790 | − | 0.849534i | ||||
\(503\) | 154345. | 0.610037 | 0.305018 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305018 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(504\) | 3187.97 | − | 7674.67i | 0.0125503 | − | 0.0302133i | ||||
\(505\) | 218897.i | 0.858337i | ||||||||
\(506\) | 11235.1 | − | 8615.06i | 0.0438811 | − | 0.0336478i | ||||
\(507\) | 384909. | − | 384909.i | 1.49742 | − | 1.49742i | ||||
\(508\) | −33407.2 | + | 124345.i | −0.129453 | + | 0.481837i | ||||
\(509\) | −7996.84 | + | 7996.84i | −0.0308662 | + | 0.0308662i | −0.722371 | − | 0.691505i | \(-0.756948\pi\) |
0.691505 | + | 0.722371i | \(0.256948\pi\) | |||||||
\(510\) | −16714.0 | + | 126629.i | −0.0642600 | + | 0.486846i | ||||
\(511\) | 4789.30i | 0.0183413i | ||||||||
\(512\) | −99589.3 | − | 242490.i | −0.379903 | − | 0.925026i | ||||
\(513\) | −448740. | −1.70514 | ||||||||
\(514\) | −90383.6 | − | 11930.0i | −0.342108 | − | 0.0451557i | ||||
\(515\) | 31024.4 | + | 31024.4i | 0.116974 | + | 0.116974i | ||||
\(516\) | 3058.44 | + | 821.699i | 0.0114869 | + | 0.00308612i | ||||
\(517\) | 206409. | + | 206409.i | 0.772231 | + | 0.772231i | ||||
\(518\) | 12613.2 | + | 16449.2i | 0.0470072 | + | 0.0613033i | ||||
\(519\) | −125089. | −0.464393 | ||||||||
\(520\) | −568896. | − | 236313.i | −2.10390 | − | 0.873938i | ||||
\(521\) | 215831.i | 0.795130i | 0.917574 | + | 0.397565i | \(0.130145\pi\) | ||||
−0.917574 | + | 0.397565i | \(0.869855\pi\) | |||||||
\(522\) | 11808.6 | + | 15399.9i | 0.0433367 | + | 0.0565166i | ||||
\(523\) | −73690.2 | + | 73690.2i | −0.269405 | + | 0.269405i | −0.828861 | − | 0.559455i | \(-0.811010\pi\) |
0.559455 | + | 0.828861i | \(0.311010\pi\) | |||||||
\(524\) | −179734. | − | 311789.i | −0.654587 | − | 1.13553i | ||||
\(525\) | 11738.2 | − | 11738.2i | 0.0425877 | − | 0.0425877i | ||||
\(526\) | −502091. | − | 66272.3i | −1.81473 | − | 0.239530i | ||||
\(527\) | − | 143707.i | − | 0.517435i | ||||||
\(528\) | −223368. | − | 129360.i | −0.801223 | − | 0.464016i | ||||
\(529\) | −279085. | −0.997297 | ||||||||
\(530\) | −18714.9 | + | 141787.i | −0.0666247 | + | 0.504761i | ||||
\(531\) | 19073.6 | + | 19073.6i | 0.0676464 | + | 0.0676464i | ||||
\(532\) | 30115.0 | + | 52241.3i | 0.106404 | + | 0.184583i | ||||
\(533\) | 399290. | + | 399290.i | 1.40551 | + | 1.40551i | ||||
\(534\) | 36410.6 | − | 27919.5i | 0.127686 | − | 0.0979095i | ||||
\(535\) | 433814. | 1.51564 | ||||||||
\(536\) | −159330. | − | 385750.i | −0.554585 | − | 1.34269i | ||||
\(537\) | − | 280762.i | − | 0.973622i | ||||||
\(538\) | −293712. | + | 225217.i | −1.01474 | + | 0.778102i | ||||
\(539\) | 214499. | − | 214499.i | 0.738325 | − | 0.738325i | ||||
\(540\) | 374456. | + | 100603.i | 1.28414 | + | 0.345005i | ||||
\(541\) | 260589. | − | 260589.i | 0.890352 | − | 0.890352i | −0.104204 | − | 0.994556i | \(-0.533229\pi\) |
0.994556 | + | 0.104204i | \(0.0332294\pi\) | |||||||
\(542\) | 48903.6 | − | 370503.i | 0.166473 | − | 1.26123i | ||||
\(543\) | 250191.i | 0.848540i | ||||||||
\(544\) | 107565. | + | 82823.6i | 0.363475 | + | 0.279870i | ||||
\(545\) | 412.072 | 0.00138733 | ||||||||
\(546\) | 64407.4 | + | 8501.29i | 0.216048 | + | 0.0285167i | ||||
\(547\) | −87290.1 | − | 87290.1i | −0.291736 | − | 0.291736i | 0.546030 | − | 0.837766i | \(-0.316139\pi\) |
−0.837766 | + | 0.546030i | \(0.816139\pi\) | |||||||
\(548\) | −129397. | + | 481629.i | −0.430888 | + | 1.60381i | ||||
\(549\) | 40331.3 | + | 40331.3i | 0.133813 | + | 0.133813i | ||||
\(550\) | 100243. | + | 130730.i | 0.331382 | + | 0.432165i | ||||
\(551\) | −140809. | −0.463796 | ||||||||
\(552\) | −5264.96 | − | 12746.9i | −0.0172789 | − | 0.0418336i | ||||
\(553\) | − | 22631.9i | − | 0.0740066i | ||||||
\(554\) | −362360. | − | 472564.i | −1.18065 | − | 1.53972i | ||||
\(555\) | −133308. | + | 133308.i | −0.432783 | + | 0.432783i | ||||
\(556\) | 420143. | − | 242196.i | 1.35909 | − | 0.783460i | ||||
\(557\) | −342322. | + | 342322.i | −1.10338 | + | 1.10338i | −0.109377 | + | 0.994000i | \(0.534886\pi\) |
−0.994000 | + | 0.109377i | \(0.965114\pi\) | |||||||
\(558\) | −84309.2 | − | 11128.2i | −0.270774 | − | 0.0357401i | ||||
\(559\) | − | 7909.94i | − | 0.0253134i | ||||||
\(560\) | −13417.7 | − | 50344.8i | −0.0427862 | − | 0.160538i | ||||
\(561\) | 133675. | 0.424741 | ||||||||
\(562\) | 22484.0 | − | 170343.i | 0.0711870 | − | 0.539326i | ||||
\(563\) | −77521.3 | − | 77521.3i | −0.244571 | − | 0.244571i | 0.574167 | − | 0.818738i | \(-0.305326\pi\) |
−0.818738 | + | 0.574167i | \(0.805326\pi\) | |||||||
\(564\) | 246348. | − | 142010.i | 0.774445 | − | 0.446436i | ||||
\(565\) | −296383. | − | 296383.i | −0.928447 | − | 0.928447i | ||||
\(566\) | 164023. | − | 125772.i | 0.512003 | − | 0.392602i | ||||
\(567\) | −30372.6 | −0.0944749 | ||||||||
\(568\) | 183567. | + | 76251.5i | 0.568980 | + | 0.236348i | ||||
\(569\) | 304409.i | 0.940229i | 0.882605 | + | 0.470115i | \(0.155787\pi\) | ||||
−0.882605 | + | 0.470115i | \(0.844213\pi\) | |||||||
\(570\) | −435211. | + | 333718.i | −1.33952 | + | 1.02714i | ||||
\(571\) | −254051. | + | 254051.i | −0.779201 | + | 0.779201i | −0.979695 | − | 0.200494i | \(-0.935745\pi\) |
0.200494 | + | 0.979695i | \(0.435745\pi\) | |||||||
\(572\) | −167280. | + | 622631.i | −0.511271 | + | 1.90300i | ||||
\(573\) | 348999. | − | 348999.i | 1.06295 | − | 1.06295i | ||||
\(574\) | −6249.71 | + | 47349.0i | −0.0189686 | + | 0.143710i | ||||
\(575\) | 8801.94i | 0.0266221i | ||||||||
\(576\) | 56920.1 | − | 56692.2i | 0.171562 | − | 0.170875i | ||||
\(577\) | −486229. | −1.46046 | −0.730229 | − | 0.683202i | \(-0.760587\pi\) | ||||
−0.730229 | + | 0.683202i | \(0.760587\pi\) | |||||||
\(578\) | 261511. | + | 34517.5i | 0.782770 | + | 0.103320i | ||||
\(579\) | −138724. | − | 138724.i | −0.413803 | − | 0.413803i | ||||
\(580\) | 117499. | + | 31568.1i | 0.349285 | + | 0.0938409i | ||||
\(581\) | 1069.82 | + | 1069.82i | 0.00316926 | + | 0.00316926i | ||||
\(582\) | 157615. | + | 205550.i | 0.465320 | + | 0.606836i | ||||
\(583\) | 149677. | 0.440371 | ||||||||
\(584\) | −17760.2 | + | 42755.6i | −0.0520741 | + | 0.125362i | ||||
\(585\) | − | 188786.i | − | 0.551642i | ||||||
\(586\) | 156136. | + | 203621.i | 0.454682 | + | 0.592964i | ||||
\(587\) | −26612.4 | + | 26612.4i | −0.0772339 | + | 0.0772339i | −0.744668 | − | 0.667435i | \(-0.767392\pi\) |
0.667435 | + | 0.744668i | \(0.267392\pi\) | |||||||
\(588\) | −147576. | − | 256003.i | −0.426835 | − | 0.740442i | ||||
\(589\) | 436317. | − | 436317.i | 1.25768 | − | 1.25768i | ||||
\(590\) | 167660. | + | 22129.8i | 0.481642 | + | 0.0635732i | ||||
\(591\) | − | 71678.1i | − | 0.205216i | ||||||
\(592\) | 51603.1 | + | 193620.i | 0.147242 | + | 0.552469i | ||||
\(593\) | 301795. | 0.858228 | 0.429114 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429114 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(594\) | 53100.8 | − | 402301.i | 0.150497 | − | 1.14019i | ||||
\(595\) | 19079.4 | + | 19079.4i | 0.0538927 | + | 0.0538927i | ||||
\(596\) | 133038. | + | 230785.i | 0.374528 | + | 0.649703i | ||||
\(597\) | 309105. | + | 309105.i | 0.867276 | + | 0.867276i | ||||
\(598\) | −27335.3 | + | 20960.6i | −0.0764402 | + | 0.0586141i | ||||
\(599\) | −208748. | −0.581795 | −0.290897 | − | 0.956754i | \(-0.593954\pi\) | ||||
−0.290897 | + | 0.956754i | \(0.593954\pi\) | |||||||
\(600\) | 148320. | − | 61262.0i | 0.412000 | − | 0.170172i | ||||
\(601\) | 355946.i | 0.985451i | 0.870185 | + | 0.492725i | \(0.163999\pi\) | ||||
−0.870185 | + | 0.492725i | \(0.836001\pi\) | |||||||
\(602\) | 530.896 | − | 407.089i | 0.00146493 | − | 0.00112330i | ||||
\(603\) | 90441.4 | − | 90441.4i | 0.248733 | − | 0.248733i | ||||
\(604\) | −300617. | − | 80765.6i | −0.824025 | − | 0.221387i | ||||
\(605\) | 41746.1 | − | 41746.1i | 0.114053 | − | 0.114053i | ||||
\(606\) | 29202.1 | − | 221241.i | 0.0795186 | − | 0.602448i | ||||
\(607\) | 680696.i | 1.84746i | 0.383040 | + | 0.923732i | \(0.374877\pi\) | ||||
−0.383040 | + | 0.923732i | \(0.625123\pi\) | |||||||
\(608\) | 75119.4 | + | 578051.i | 0.203210 | + | 1.56372i | ||||
\(609\) | −12830.9 | −0.0345958 | ||||||||
\(610\) | 354517. | + | 46793.6i | 0.952747 | + | 0.125756i | ||||
\(611\) | −502197. | − | 502197.i | −1.34522 | − | 1.34522i | ||||
\(612\) | −10794.7 | + | 40179.1i | −0.0288210 | + | 0.107275i | ||||
\(613\) | −504818. | − | 504818.i | −1.34343 | − | 1.34343i | −0.892625 | − | 0.450800i | \(-0.851139\pi\) |
−0.450800 | − | 0.892625i | \(-0.648861\pi\) | |||||||
\(614\) | 34543.7 | + | 45049.4i | 0.0916289 | + | 0.119496i | ||||
\(615\) | −434378. | −1.14846 | ||||||||
\(616\) | −50398.6 | + | 20816.6i | −0.132818 | + | 0.0548591i | ||||
\(617\) | − | 601668.i | − | 1.58047i | −0.612803 | − | 0.790236i | \(-0.709958\pi\) | ||
0.612803 | − | 0.790236i | \(-0.290042\pi\) | |||||||
\(618\) | −27217.7 | − | 35495.3i | −0.0712646 | − | 0.0929381i | ||||
\(619\) | −34687.6 | + | 34687.6i | −0.0905300 | + | 0.0905300i | −0.750922 | − | 0.660391i | \(-0.770390\pi\) |
0.660391 | + | 0.750922i | \(0.270390\pi\) | |||||||
\(620\) | −461907. | + | 266271.i | −1.20163 | + | 0.692691i | ||||
\(621\) | 15330.9 | − | 15330.9i | 0.0397544 | − | 0.0397544i | ||||
\(622\) | −406084. | − | 53600.0i | −1.04963 | − | 0.138543i | ||||
\(623\) | − | 9692.72i | − | 0.0249729i | ||||||
\(624\) | 543460. | + | 314736.i | 1.39572 | + | 0.808309i | ||||
\(625\) | 488225. | 1.24985 | ||||||||
\(626\) | −31894.2 | + | 241636.i | −0.0813885 | + | 0.616615i | ||||
\(627\) | 405858. | + | 405858.i | 1.03238 | + | 1.03238i | ||||
\(628\) | 354774. | − | 204513.i | 0.899564 | − | 0.518562i | ||||
\(629\) | −73377.0 | − | 73377.0i | −0.185464 | − | 0.185464i | ||||
\(630\) | 12670.8 | − | 9715.94i | 0.0319245 | − | 0.0244796i | ||||
\(631\) | 557209. | 1.39946 | 0.699728 | − | 0.714409i | \(-0.253304\pi\) | ||||
0.699728 | + | 0.714409i | \(0.253304\pi\) | |||||||
\(632\) | 83926.1 | − | 202042.i | 0.210118 | − | 0.505834i | ||||
\(633\) | − | 126355.i | − | 0.315345i | ||||||
\(634\) | 45865.6 | − | 35169.5i | 0.114106 | − | 0.0874960i | ||||
\(635\) | −174924. | + | 174924.i | −0.433812 | + | 0.433812i | ||||
\(636\) | 37830.4 | − | 140809.i | 0.0935248 | − | 0.348109i | ||||
\(637\) | −521881. | + | 521881.i | −1.28615 | + | 1.28615i | ||||
\(638\) | 16662.3 | − | 126237.i | 0.0409350 | − | 0.310131i | ||||
\(639\) | 60915.8i | 0.149186i | ||||||||
\(640\) | 66909.6 | − | 499201.i | 0.163353 | − | 1.21875i | ||||
\(641\) | 354670. | 0.863193 | 0.431597 | − | 0.902067i | \(-0.357950\pi\) | ||||
0.431597 | + | 0.902067i | \(0.357950\pi\) | |||||||
\(642\) | −438458. | − | 57873.2i | −1.06380 | − | 0.140413i | ||||
\(643\) | −89105.3 | − | 89105.3i | −0.215517 | − | 0.215517i | 0.591089 | − | 0.806606i | \(-0.298698\pi\) |
−0.806606 | + | 0.591089i | \(0.798698\pi\) | |||||||
\(644\) | −2813.65 | − | 755.931i | −0.00678420 | − | 0.00182268i | ||||
\(645\) | 4302.51 | + | 4302.51i | 0.0103420 | + | 0.0103420i | ||||
\(646\) | −183689. | − | 239554.i | −0.440168 | − | 0.574035i | ||||
\(647\) | −669197. | −1.59862 | −0.799311 | − | 0.600918i | \(-0.794802\pi\) | ||||
−0.799311 | + | 0.600918i | \(0.794802\pi\) | |||||||
\(648\) | −271146. | − | 112631.i | −0.645734 | − | 0.268231i | ||||
\(649\) | − | 176989.i | − | 0.420201i | ||||||
\(650\) | −243894. | − | 318069.i | −0.577264 | − | 0.752825i | ||||
\(651\) | 39758.5 | − | 39758.5i | 0.0938140 | − | 0.0938140i | ||||
\(652\) | 199717. | + | 346455.i | 0.469807 | + | 0.814988i | ||||
\(653\) | 6136.50 | − | 6136.50i | 0.0143911 | − | 0.0143911i | −0.699875 | − | 0.714266i | \(-0.746761\pi\) |
0.714266 | + | 0.699875i | \(0.246761\pi\) | |||||||
\(654\) | −416.483 | − | 54.9727i | −0.000973738 | − | 0.000128526i | ||||
\(655\) | − | 691457.i | − | 1.61169i | ||||||
\(656\) | −231378. | + | 399524.i | −0.537668 | + | 0.928400i | ||||
\(657\) | −14188.3 | −0.0328700 | ||||||||
\(658\) | 7860.42 | − | 59552.0i | 0.0181549 | − | 0.137545i | ||||
\(659\) | 484888. | + | 484888.i | 1.11653 | + | 1.11653i | 0.992247 | + | 0.124283i | \(0.0396632\pi\) |
0.124283 | + | 0.992247i | \(0.460337\pi\) | |||||||
\(660\) | −247683. | − | 429662.i | −0.568601 | − | 0.986368i | ||||
\(661\) | −71185.1 | − | 71185.1i | −0.162924 | − | 0.162924i | 0.620937 | − | 0.783861i | \(-0.286752\pi\) |
−0.783861 | + | 0.620937i | \(0.786752\pi\) | |||||||
\(662\) | −554859. | + | 425463.i | −1.26610 | + | 0.970837i | ||||
\(663\) | −325234. | −0.739892 | ||||||||
\(664\) | 5583.39 | + | 13517.8i | 0.0126637 | + | 0.0306599i | ||||
\(665\) | 115856.i | 0.261984i | ||||||||
\(666\) | −48730.6 | + | 37366.4i | −0.109863 | + | 0.0842428i | ||||
\(667\) | 4810.65 | − | 4810.65i | 0.0108131 | − | 0.0108131i | ||||
\(668\) | −175753. | − | 47218.7i | −0.393867 | − | 0.105818i | ||||
\(669\) | −84179.5 | + | 84179.5i | −0.188085 | + | 0.188085i | ||||
\(670\) | 104933. | − | 794992.i | 0.233756 | − | 1.77098i | ||||
\(671\) | − | 374244.i | − | 0.831209i | ||||||
\(672\) | 6845.10 | + | 52673.7i | 0.0151580 | + | 0.116642i | ||||
\(673\) | 116807. | 0.257893 | 0.128947 | − | 0.991652i | \(-0.458840\pi\) | ||||
0.128947 | + | 0.991652i | \(0.458840\pi\) | |||||||
\(674\) | 406242. | + | 53620.9i | 0.894262 | + | 0.118036i | ||||
\(675\) | 178388. | + | 178388.i | 0.391523 | + | 0.391523i | ||||
\(676\) | 288426. | − | 1.07355e6i | 0.631163 | − | 2.34925i | ||||
\(677\) | 562443. | + | 562443.i | 1.22716 | + | 1.22716i | 0.965033 | + | 0.262127i | \(0.0844240\pi\) |
0.262127 | + | 0.965033i | \(0.415576\pi\) | |||||||
\(678\) | 260017. | + | 339095.i | 0.565643 | + | 0.737670i | ||||
\(679\) | 54718.7 | 0.118685 | ||||||||
\(680\) | 99575.4 | + | 241080.i | 0.215345 | + | 0.521366i | ||||
\(681\) | 526415.i | 1.13510i | ||||||||
\(682\) | 339533. | + | 442794.i | 0.729983 | + | 0.951991i | ||||
\(683\) | 392290. | − | 392290.i | 0.840941 | − | 0.840941i | −0.148040 | − | 0.988981i | \(-0.547297\pi\) |
0.988981 | + | 0.148040i | \(0.0472965\pi\) | |||||||
\(684\) | −154765. | + | 89215.6i | −0.330796 | + | 0.190690i | ||||
\(685\) | −677539. | + | 677539.i | −1.44395 | + | 1.44395i | ||||
\(686\) | −124923. | − | 16488.9i | −0.265457 | − | 0.0350384i | ||||
\(687\) | 173173.i | 0.366916i | ||||||||
\(688\) | 6249.09 | − | 1665.49i | 0.0132020 | − | 0.00351856i | ||||
\(689\) | −364168. | −0.767120 | ||||||||
\(690\) | 3467.44 | − | 26270.0i | 0.00728301 | − | 0.0551774i | ||||
\(691\) | 424716. | + | 424716.i | 0.889493 | + | 0.889493i | 0.994474 | − | 0.104981i | \(-0.0334781\pi\) |
−0.104981 | + | 0.994474i | \(0.533478\pi\) | |||||||
\(692\) | −221310. | + | 127576.i | −0.462157 | + | 0.266415i | ||||
\(693\) | −11816.2 | − | 11816.2i | −0.0246044 | − | 0.0246044i | ||||
\(694\) | −284346. | + | 218036.i | −0.590376 | + | 0.452698i | ||||
\(695\) | 931755. | 1.92900 | ||||||||
\(696\) | −114546. | − | 47581.1i | −0.236462 | − | 0.0982236i | ||||
\(697\) | − | 239095.i | − | 0.492159i | ||||||
\(698\) | 514645. | − | 394627.i | 1.05632 | − | 0.809984i | ||||
\(699\) | 349868. | − | 349868.i | 0.716060 | − | 0.716060i | ||||
\(700\) | 8795.87 | − | 32739.1i | 0.0179508 | − | 0.0668145i | ||||
\(701\) | −92393.5 | + | 92393.5i | −0.188021 | + | 0.188021i | −0.794840 | − | 0.606819i | \(-0.792445\pi\) |
0.606819 | + | 0.794840i | \(0.292445\pi\) | |||||||
\(702\) | −129195. | + | 978808.i | −0.262164 | + | 1.98620i | ||||
\(703\) | − | 445569.i | − | 0.901580i | ||||||
\(704\) | −527119. | − | 1056.98i | −1.06356 | − | 0.00213267i | ||||
\(705\) | 546327. | 1.09920 | ||||||||
\(706\) | 374475. | + | 49427.9i | 0.751300 | + | 0.0991659i | ||||
\(707\) | −33334.7 | − | 33334.7i | −0.0666896 | − | 0.0666896i | ||||
\(708\) | −166502. | − | 44733.4i | −0.332165 | − | 0.0892413i | ||||
\(709\) | 29997.3 | + | 29997.3i | 0.0596746 | + | 0.0596746i | 0.736314 | − | 0.676640i | \(-0.236565\pi\) |
−0.676640 | + | 0.736314i | \(0.736565\pi\) | |||||||
\(710\) | 232391. | + | 303067.i | 0.461001 | + | 0.601205i | ||||
\(711\) | 67046.9 | 0.132629 | ||||||||
\(712\) | 35943.6 | − | 86530.1i | 0.0709025 | − | 0.170690i | ||||
\(713\) | 29812.9i | 0.0586443i | ||||||||
\(714\) | −16738.3 | − | 21828.9i | −0.0328333 | − | 0.0428189i | ||||
\(715\) | −875896. | + | 875896.i | −1.71333 | + | 1.71333i | ||||
\(716\) | −286344. | − | 496729.i | −0.558551 | − | 0.968933i | ||||
\(717\) | 184661. | − | 184661.i | 0.359200 | − | 0.359200i | ||||
\(718\) | 233974. | + | 30882.9i | 0.453858 | + | 0.0599058i | ||||
\(719\) | − | 284133.i | − | 0.549622i | −0.961498 | − | 0.274811i | \(-0.911385\pi\) | ||
0.961498 | − | 0.274811i | \(-0.0886152\pi\) | |||||||
\(720\) | 149146. | − | 39750.0i | 0.287705 | − | 0.0766783i | ||||
\(721\) | −9449.07 | −0.0181769 | ||||||||
\(722\) | 101401. | − | 768232.i | 0.194521 | − | 1.47373i | ||||
\(723\) | 31167.4 | + | 31167.4i | 0.0596243 | + | 0.0596243i | ||||
\(724\) | 255165. | + | 442642.i | 0.486793 | + | 0.844454i | ||||
\(725\) | 55975.8 | + | 55975.8i | 0.106494 | + | 0.106494i | ||||
\(726\) | −47762.1 | + | 36623.8i | −0.0906171 | + | 0.0694848i | ||||
\(727\) | 39096.3 | 0.0739719 | 0.0369860 | − | 0.999316i | \(-0.488224\pi\) | ||||
0.0369860 | + | 0.999316i | \(0.488224\pi\) | |||||||
\(728\) | 122621. | − | 50647.3i | 0.231367 | − | 0.0955638i | ||||
\(729\) | − | 590261.i | − | 1.11068i | ||||||
\(730\) | −70589.3 | + | 54127.6i | −0.132463 | + | 0.101572i | ||||
\(731\) | −2368.24 | + | 2368.24i | −0.00443191 | + | 0.00443191i | ||||
\(732\) | −352070. | − | 94589.1i | −0.657062 | − | 0.176530i | ||||
\(733\) | 82927.3 | − | 82927.3i | 0.154344 | − | 0.154344i | −0.625711 | − | 0.780055i | \(-0.715191\pi\) |
0.780055 | + | 0.625711i | \(0.215191\pi\) | |||||||
\(734\) | −62870.4 | + | 476318.i | −0.116695 | + | 0.884107i | ||||
\(735\) | − | 567741.i | − | 1.05093i | ||||||
\(736\) | −22315.1 | − | 17182.3i | −0.0411950 | − | 0.0317195i | ||||
\(737\) | −839229. | −1.54506 | ||||||||
\(738\) | −140271. | − | 18514.8i | −0.257547 | − | 0.0339942i | ||||
\(739\) | −97643.8 | − | 97643.8i | −0.178795 | − | 0.178795i | 0.612035 | − | 0.790830i | \(-0.290351\pi\) |
−0.790830 | + | 0.612035i | \(0.790351\pi\) | |||||||
\(740\) | −99892.4 | + | 371809.i | −0.182419 | + | 0.678980i | ||||
\(741\) | −987462. | − | 987462.i | −1.79839 | − | 1.79839i | ||||
\(742\) | −18742.1 | − | 24442.0i | −0.0340416 | − | 0.0443945i | ||||
\(743\) | −552181. | −1.00024 | −0.500120 | − | 0.865956i | \(-0.666711\pi\) | ||||
−0.500120 | + | 0.865956i | \(0.666711\pi\) | |||||||
\(744\) | 502373. | − | 207500.i | 0.907571 | − | 0.374863i | ||||
\(745\) | 511813.i | 0.922145i | ||||||||
\(746\) | 391889. | + | 511073.i | 0.704182 | + | 0.918344i | ||||
\(747\) | −3169.33 | + | 3169.33i | −0.00567971 | + | 0.00567971i | ||||
\(748\) | 236500. | − | 136332.i | 0.422695 | − | 0.243667i | ||||
\(749\) | −66063.3 | + | 66063.3i | −0.117760 | + | 0.117760i | ||||
\(750\) | −291293. | − | 38448.4i | −0.517853 | − | 0.0683528i | ||||
\(751\) | 318447.i | 0.564621i | 0.959323 | + | 0.282310i | \(0.0911008\pi\) | ||||
−0.959323 | + | 0.282310i | \(0.908899\pi\) | |||||||
\(752\) | 291010. | − | 502491.i | 0.514603 | − | 0.888573i | ||||
\(753\) | −689140. | −1.21539 | ||||||||
\(754\) | −40539.9 | + | 307138.i | −0.0713082 | + | 0.540244i | ||||
\(755\) | −422898. | − | 422898.i | −0.741894 | − | 0.741894i | ||||
\(756\) | −72344.3 | + | 41703.5i | −0.126579 | + | 0.0729675i | ||||
\(757\) | −478701. | − | 478701.i | −0.835357 | − | 0.835357i | 0.152886 | − | 0.988244i | \(-0.451143\pi\) |
−0.988244 | + | 0.152886i | \(0.951143\pi\) | |||||||
\(758\) | 340455. | − | 261059.i | 0.592544 | − | 0.454361i | ||||
\(759\) | −27731.8 | −0.0481386 | ||||||||
\(760\) | −429630. | + | 1.03428e6i | −0.743819 | + | 1.79066i | ||||
\(761\) | − | 398315.i | − | 0.687793i | −0.939008 | − | 0.343896i | \(-0.888253\pi\) | ||
0.939008 | − | 0.343896i | \(-0.111747\pi\) | |||||||
\(762\) | 200132. | − | 153460.i | 0.344672 | − | 0.264293i | ||||
\(763\) | −62.7523 | + | 62.7523i | −0.000107790 | + | 0.000107790i | ||||
\(764\) | 261517. | − | 973392.i | 0.448036 | − | 1.66764i | ||||
\(765\) | −56522.5 | + | 56522.5i | −0.0965826 | + | 0.0965826i | ||||
\(766\) | 42022.2 | − | 318368.i | 0.0716179 | − | 0.542591i | ||||
\(767\) | 430619.i | 0.731985i | ||||||||
\(768\) | −134222. | + | 495619.i | −0.227563 | + | 0.840283i | ||||
\(769\) | 658868. | 1.11416 | 0.557078 | − | 0.830460i | \(-0.311922\pi\) | ||||
0.557078 | + | 0.830460i | \(0.311922\pi\) | |||||||
\(770\) | −103866. | − | 13709.6i | −0.175183 | − | 0.0231229i | ||||
\(771\) | 126271. | + | 126271.i | 0.212419 | + | 0.212419i | ||||
\(772\) | −386915. | − | 103951.i | −0.649203 | − | 0.174419i | ||||
\(773\) | 833367. | + | 833367.i | 1.39469 | + | 1.39469i | 0.814439 | + | 0.580250i | \(0.197045\pi\) |
0.580250 | + | 0.814439i | \(0.302955\pi\) | |||||||
\(774\) | 1206.00 | + | 1572.78i | 0.00201310 | + | 0.00262534i | ||||
\(775\) | −346898. | −0.577561 | ||||||||
\(776\) | 488491. | + | 202914.i | 0.811210 | + | 0.336968i | ||||
\(777\) | − | 40601.6i | − | 0.0672513i | ||||||
\(778\) | −307993. | − | 401662.i | −0.508840 | − | 0.663592i | ||||
\(779\) | 725932. | − | 725932.i | 1.19625 | − | 1.19625i | ||||
\(780\) | 602617. | + | 1.04538e6i | 0.990495 | + | 1.71824i | ||||
\(781\) | 282627. | − | 282627.i | 0.463352 | − | 0.463352i | ||||
\(782\) | 14459.8 | + | 1908.59i | 0.0236456 | + | 0.00312104i | ||||
\(783\) | − | 194994.i | − | 0.318051i | ||||||
\(784\) | −522186. | − | 302416.i | −0.849559 | − | 0.492008i | ||||
\(785\) | 786784. | 1.27678 | ||||||||
\(786\) | −92244.1 | + | 698859.i | −0.149312 | + | 1.13121i | ||||
\(787\) | −265518. | − | 265518.i | −0.428691 | − | 0.428691i | 0.459491 | − | 0.888182i | \(-0.348032\pi\) |
−0.888182 | + | 0.459491i | \(0.848032\pi\) | |||||||
\(788\) | −73103.2 | − | 126814.i | −0.117729 | − | 0.204228i | ||||
\(789\) | 701447. | + | 701447.i | 1.12679 | + | 1.12679i | ||||
\(790\) | 333571. | − | 255781.i | 0.534482 | − | 0.409839i | ||||
\(791\) | 90269.3 | 0.144274 | ||||||||
\(792\) | −61669.1 | − | 149306.i | −0.0983145 | − | 0.238027i | ||||
\(793\) | 910545.i | 1.44795i | ||||||||
\(794\) | −578294. | + | 443434.i | −0.917292 | + | 0.703376i | ||||
\(795\) | 198084. | − | 198084.i | 0.313412 | − | 0.313412i | ||||
\(796\) | 862124. | + | 231623.i | 1.36064 | + | 0.365558i | ||||
\(797\) | 51155.1 | − | 51155.1i | 0.0805327 | − | 0.0805327i | −0.665693 | − | 0.746226i | \(-0.731864\pi\) |
0.746226 | + | 0.665693i | \(0.231864\pi\) | |||||||
\(798\) | 15455.8 | − | 117096.i | 0.0242709 | − | 0.183881i | ||||
\(799\) | 300716.i | 0.471046i | ||||||||
\(800\) | 199930. | − | 259655.i | 0.312391 | − | 0.405710i | ||||
\(801\) | 28714.7 | 0.0447547 | ||||||||
\(802\) | −281994. | − | 37221.1i | −0.438421 | − | 0.0578683i | ||||
\(803\) | 65828.4 | + | 65828.4i | 0.102090 | + | 0.102090i | ||||
\(804\) | −212112. | + | 789503.i | −0.328136 | + | 1.22135i | ||||
\(805\) | −3958.14 | − | 3958.14i | −0.00610801 | − | 0.00610801i | ||||
\(806\) | −826090. | − | 1.07733e6i | −1.27162 | − | 1.65836i | ||||
\(807\) | 724970. | 1.11320 | ||||||||
\(808\) | −173974. | − | 421205.i | −0.266479 | − | 0.645165i | ||||
\(809\) | − | 608654.i | − | 0.929979i | −0.885316 | − | 0.464990i | \(-0.846058\pi\) | ||
0.885316 | − | 0.464990i | \(-0.153942\pi\) | |||||||
\(810\) | −343265. | − | 447661.i | −0.523190 | − | 0.682306i | ||||
\(811\) | −693367. | + | 693367.i | −1.05420 | + | 1.05420i | −0.0557512 | + | 0.998445i | \(0.517755\pi\) |
−0.998445 | + | 0.0557512i | \(0.982245\pi\) | |||||||
\(812\) | −22700.7 | + | 13086.0i | −0.0344292 | + | 0.0198471i | ||||
\(813\) | −517612. | + | 517612.i | −0.783111 | + | 0.783111i | ||||
\(814\) | 399458. | + | 52725.5i | 0.602868 | + | 0.0795741i | ||||
\(815\) | 768335.i | 1.15674i | ||||||||
\(816\) | −68480.0 | − | 256944.i | −0.102845 | − | 0.385886i | ||||
\(817\) | −14380.7 | −0.0215445 | ||||||||
\(818\) | −45756.4 | + | 346659.i | −0.0683825 | + | 0.518079i | ||||
\(819\) | 28749.2 | + | 28749.2i | 0.0428605 | + | 0.0428605i | ||||
\(820\) | −768508. | + | 443014.i | −1.14293 | + | 0.658854i | ||||
\(821\) | −843960. | − | 843960.i | −1.25209 | − | 1.25209i | −0.954781 | − | 0.297308i | \(-0.903911\pi\) |
−0.297308 | − | 0.954781i | \(-0.596089\pi\) | |||||||
\(822\) | 775179. | − | 594404.i | 1.14725 | − | 0.879708i | ||||
\(823\) | −562057. | −0.829815 | −0.414907 | − | 0.909864i | \(-0.636186\pi\) | ||||
−0.414907 | + | 0.909864i | \(0.636186\pi\) | |||||||
\(824\) | −84354.9 | − | 35040.1i | −0.124238 | − | 0.0516072i | ||||
\(825\) | − | 322681.i | − | 0.474096i | ||||||
\(826\) | −28902.0 | + | 22162.0i | −0.0423612 | + | 0.0324824i | ||||
\(827\) | 49278.3 | − | 49278.3i | 0.0720518 | − | 0.0720518i | −0.670163 | − | 0.742214i | \(-0.733776\pi\) |
0.742214 | + | 0.670163i | \(0.233776\pi\) | |||||||
\(828\) | 2239.44 | − | 8335.43i | 0.00326648 | − | 0.0121581i | ||||
\(829\) | 519755. | − | 519755.i | 0.756291 | − | 0.756291i | −0.219354 | − | 0.975645i | \(-0.570395\pi\) |
0.975645 | + | 0.219354i | \(0.0703949\pi\) | |||||||
\(830\) | −3677.16 | + | 27858.8i | −0.00533772 | + | 0.0404396i | ||||
\(831\) | 1.16643e6i | 1.68911i | ||||||||
\(832\) | 1.28249e6 | + | 2571.67i | 1.85271 | + | 0.00371508i | ||||
\(833\) | 312503. | 0.450364 | ||||||||
\(834\) | −941729. | − | 124301.i | −1.35392 | − | 0.178708i | ||||
\(835\) | −247243. | − | 247243.i | −0.354610 | − | 0.354610i | ||||
\(836\) | 1.13198e6 | + | 304124.i | 1.61967 | + | 0.435149i | ||||
\(837\) | 604215. | + | 604215.i | 0.862464 | + | 0.862464i | ||||
\(838\) | −539271. | − | 703278.i | −0.767926 | − | 1.00147i | ||||
\(839\) | −311968. | −0.443186 | −0.221593 | − | 0.975139i | \(-0.571126\pi\) | ||||
−0.221593 | + | 0.975139i | \(0.571126\pi\) | |||||||
\(840\) | −39149.1 | + | 94247.0i | −0.0554835 | + | 0.133570i | ||||
\(841\) | 646094.i | 0.913491i | ||||||||
\(842\) | −71035.0 | − | 92638.7i | −0.100196 | − | 0.130668i | ||||
\(843\) | −237978. | + | 237978.i | −0.334874 | + | 0.334874i | ||||
\(844\) | −128867. | − | 223550.i | −0.180908 | − | 0.313826i | ||||
\(845\) | 1.51023e6 | − | 1.51023e6i | 2.11510 | − | 2.11510i | ||||
\(846\) | 176423. | + | 23286.5i | 0.246498 | + | 0.0325359i | ||||
\(847\) | 12714.6i | 0.0177229i | ||||||||
\(848\) | −76677.8 | − | 287703.i | −0.106630 | − | 0.400086i | ||||
\(849\) | −404860. | −0.561681 | ||||||||
\(850\) | −22208.0 | + | 168252.i | −0.0307377 | + | 0.232874i | ||||
\(851\) | 15222.6 | + | 15222.6i | 0.0210198 | + | 0.0210198i | ||||
\(852\) | −194448. | − | 337314.i | −0.267870 | − | 0.464681i | ||||
\(853\) | 306461. | + | 306461.i | 0.421190 | + | 0.421190i | 0.885613 | − | 0.464424i | \(-0.153738\pi\) |
−0.464424 | + | 0.885613i | \(0.653738\pi\) | |||||||
\(854\) | −61113.5 | + | 46861.6i | −0.0837956 | + | 0.0642542i | ||||
\(855\) | −343223. | −0.469509 | ||||||||
\(856\) | −834751. | + | 344785.i | −1.13923 | + | 0.470545i | ||||
\(857\) | − | 16157.2i | − | 0.0219991i | −0.999940 | − | 0.0109995i | \(-0.996499\pi\) | ||
0.999940 | − | 0.0109995i | \(-0.00350133\pi\) | |||||||
\(858\) | 1.00212e6 | − | 768422.i | 1.36127 | − | 1.04382i | ||||
\(859\) | 74800.4 | − | 74800.4i | 0.101372 | − | 0.101372i | −0.654602 | − | 0.755974i | \(-0.727164\pi\) |
0.755974 | + | 0.654602i | \(0.227164\pi\) | |||||||
\(860\) | 12000.1 | + | 3224.02i | 0.0162252 | + | 0.00435914i | ||||
\(861\) | 66149.0 | − | 66149.0i | 0.0892313 | − | 0.0892313i | ||||
\(862\) | −154071. | + | 1.16727e6i | −0.207351 | + | 1.57093i | ||||
\(863\) | 902987.i | 1.21244i | 0.795297 | + | 0.606220i | \(0.207315\pi\) | ||||
−0.795297 | + | 0.606220i | \(0.792685\pi\) | |||||||
\(864\) | −800490. | + | 104026.i | −1.07233 | + | 0.139352i | ||||
\(865\) | −490801. | −0.655954 | ||||||||
\(866\) | −953568. | − | 125864.i | −1.27150 | − | 0.167828i | ||||
\(867\) | −365344. | − | 365344.i | −0.486031 | − | 0.486031i | ||||
\(868\) | 29792.4 | − | 110890.i | 0.0395427 | − | 0.147182i | ||||
\(869\) | −311073. | − | 311073.i | −0.411929 | − | 0.411929i | ||||
\(870\) | −145012. | − | 189115.i | −0.191587 | − | 0.249854i | ||||
\(871\) | 2.04186e6 | 2.69147 | ||||||||
\(872\) | −792.915 | + | 327.505i | −0.00104278 | + | 0.000430710i | ||||
\(873\) | 162104.i | 0.212699i | ||||||||
\(874\) | 38107.6 | + | 49697.1i | 0.0498871 | + | 0.0650592i | ||||
\(875\) | −43889.6 | + | 43889.6i | −0.0573251 | + | 0.0573251i | ||||
\(876\) | 78565.8 | − | 45290.0i | 0.102382 | − | 0.0590193i | ||||
\(877\) | 526163. | − | 526163.i | 0.684102 | − | 0.684102i | −0.276820 | − | 0.960922i | \(-0.589281\pi\) |
0.960922 | + | 0.276820i | \(0.0892805\pi\) | |||||||
\(878\) | 1.16866e6 | + | 154254.i | 1.51600 | + | 0.200100i | ||||
\(879\) | − | 502600.i | − | 0.650496i | ||||||
\(880\) | −876409. | − | 507558.i | −1.13173 | − | 0.655421i | ||||
\(881\) | −1.39036e6 | −1.79133 | −0.895664 | − | 0.444732i | \(-0.853299\pi\) | ||||
−0.895664 | + | 0.444732i | \(0.853299\pi\) | |||||||
\(882\) | 24199.2 | − | 183338.i | 0.0311074 | − | 0.235675i | ||||
\(883\) | −717884. | − | 717884.i | −0.920731 | − | 0.920731i | 0.0763499 | − | 0.997081i | \(-0.475673\pi\) |
−0.997081 | + | 0.0763499i | \(0.975673\pi\) | |||||||
\(884\) | −575409. | + | 331700.i | −0.736329 | + | 0.424464i | ||||
\(885\) | −234229. | − | 234229.i | −0.299058 | − | 0.299058i | ||||
\(886\) | −534032. | + | 409494.i | −0.680299 | + | 0.521651i | ||||
\(887\) | −398604. | −0.506633 | −0.253317 | − | 0.967383i | \(-0.581521\pi\) | ||||
−0.253317 | + | 0.967383i | \(0.581521\pi\) | |||||||
\(888\) | 150563. | − | 362463.i | 0.190938 | − | 0.459661i | ||||
\(889\) | − | 53276.4i | − | 0.0674111i | ||||||
\(890\) | 142861. | − | 109545.i | 0.180357 | − | 0.138297i | ||||
\(891\) | −417468. | + | 417468.i | −0.525858 | + | 0.525858i | ||||
\(892\) | −63078.7 | + | 234785.i | −0.0792780 | + | 0.295081i | ||||
\(893\) | −913022. | + | 913022.i | −1.14493 | + | 1.14493i | ||||
\(894\) | 68278.7 | − | 517292.i | 0.0854300 | − | 0.647233i | ||||
\(895\) | − | 1.10160e6i | − | 1.37524i | ||||||
\(896\) | 65831.4 | + | 86210.0i | 0.0820006 | + | 0.107385i | ||||
\(897\) | 67472.0 | 0.0838569 | ||||||||
\(898\) | 325693. | + | 42989.0i | 0.403883 | + | 0.0533096i | ||||
\(899\) | 189595. | + | 189595.i | 0.234589 | + | 0.234589i | ||||
\(900\) | 96989.5 | + | 26057.7i | 0.119740 | + | 0.0321701i | ||||
\(901\) | 109032. | + | 109032.i | 0.134309 | + | 0.134309i | ||||
\(902\) | 564905. | + | 736708.i | 0.694324 | + | 0.905487i | ||||
\(903\) | −1310.41 | −0.00160706 | ||||||||
\(904\) | 805863. | + | 334746.i | 0.986108 | + | 0.409618i | ||||
\(905\) | 981651.i | 1.19856i | ||||||||
\(906\) | 371008. | + | 483842.i | 0.451988 | + | 0.589450i | ||||
\(907\) | 954485. | − | 954485.i | 1.16026 | − | 1.16026i | 0.175840 | − | 0.984419i | \(-0.443736\pi\) |
0.984419 | − | 0.175840i | \(-0.0562640\pi\) | |||||||
\(908\) | 536881. | + | 931341.i | 0.651187 | + | 1.12963i | ||||
\(909\) | 98754.0 | − | 98754.0i | 0.119516 | − | 0.119516i | ||||
\(910\) | 252709. | + | 33355.7i | 0.305167 | + | 0.0402798i | ||||
\(911\) | − | 876782.i | − | 1.05646i | −0.849100 | − | 0.528232i | \(-0.822855\pi\) | ||
0.849100 | − | 0.528232i | \(-0.177145\pi\) | |||||||
\(912\) | 572208. | − | 988040.i | 0.687961 | − | 1.18791i | ||||
\(913\) | 29409.0 | 0.0352808 | ||||||||
\(914\) | −90217.5 | + | 683505.i | −0.107994 | + | 0.818180i | ||||
\(915\) | −495279. | − | 495279.i | −0.591572 | − | 0.591572i | ||||
\(916\) | 176616. | + | 306381.i | 0.210494 | + | 0.365149i | ||||
\(917\) | 105298. | + | 105298.i | 0.125223 | + | 0.125223i | ||||
\(918\) | 331737. | − | 254374.i | 0.393648 | − | 0.301848i | ||||
\(919\) | −146433. | −0.173384 | −0.0866920 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866920 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(920\) | −20657.6 | − | 50013.6i | −0.0244064 | − | 0.0590898i | ||||
\(921\) | − | 111196.i | − | 0.131090i | ||||||
\(922\) | −434982. | + | 333543.i | −0.511693 | + | 0.392364i | ||||
\(923\) | −687637. | + | 687637.i | −0.807153 | + | 0.807153i | ||||
\(924\) | 103149. | + | 27712.7i | 0.120815 | + | 0.0324589i | ||||
\(925\) | −177127. | + | 177127.i | −0.207015 | + | 0.207015i | ||||
\(926\) | −74455.0 | + | 564085.i | −0.0868304 | + | 0.657844i | ||||
\(927\) | − | 27992.8i | − | 0.0325752i | ||||||
\(928\) | −251184. | + | 32642.0i | −0.291672 | + | 0.0379037i | ||||
\(929\) | −357969. | −0.414776 | −0.207388 | − | 0.978259i | \(-0.566496\pi\) | ||||
−0.207388 | + | 0.978259i | \(0.566496\pi\) | |||||||
\(930\) | 1.03534e6 | + | 136657.i | 1.19706 | + | 0.158003i | ||||
\(931\) | 948808. | + | 948808.i | 1.09466 | + | 1.09466i | ||||
\(932\) | 262168. | − | 975815.i | 0.301820 | − | 1.12340i | ||||
\(933\) | 567320. | + | 567320.i | 0.651726 | + | 0.651726i | ||||
\(934\) | 479131. | + | 624848.i | 0.549238 | + | 0.716277i | ||||
\(935\) | 524487. | 0.599945 | ||||||||
\(936\) | 150042. | + | 363264.i | 0.171262 | + | 0.414639i | ||||
\(937\) | − | 1.49027e6i | − | 1.69740i | −0.528871 | − | 0.848702i | \(-0.677384\pi\) | ||
0.528871 | − | 0.848702i | \(-0.322616\pi\) | |||||||
\(938\) | 105085. | + | 137045.i | 0.119436 | + | 0.155760i | ||||
\(939\) | 337579. | − | 337579.i | 0.382863 | − | 0.382863i | ||||
\(940\) | 966572. | − | 557189.i | 1.09390 | − | 0.630590i | ||||
\(941\) | −977475. | + | 977475.i | −1.10389 | + | 1.10389i | −0.109954 | + | 0.993937i | \(0.535071\pi\) |
−0.993937 | + | 0.109954i | \(0.964929\pi\) | |||||||
\(942\) | −795207. | − | 104961.i | −0.896145 | − | 0.118284i | ||||
\(943\) | 49602.0i | 0.0557796i | ||||||||
\(944\) | −340201. | + | 90669.4i | −0.381761 | + | 0.101746i | ||||
\(945\) | −160438. | −0.179657 | ||||||||
\(946\) | 1701.71 | − | 12892.5i | 0.00190153 | − | 0.0144064i | ||||
\(947\) | 573883. | + | 573883.i | 0.639917 | + | 0.639917i | 0.950535 | − | 0.310618i | \(-0.100536\pi\) |
−0.310618 | + | 0.950535i | \(0.600536\pi\) | |||||||
\(948\) | −371264. | + | 214018.i | −0.413110 | + | 0.238141i | ||||
\(949\) | −160162. | − | 160162.i | −0.177839 | − | 0.177839i | ||||
\(950\) | −578266. | + | 443412.i | −0.640738 | + | 0.491316i | ||||
\(951\) | −113210. | −0.125177 | ||||||||
\(952\) | −51876.6 | − | 21548.9i | −0.0572397 | − | 0.0237767i | ||||
\(953\) | 356334.i | 0.392348i | 0.980569 | + | 0.196174i | \(0.0628517\pi\) | ||||
−0.980569 | + | 0.196174i | \(0.937148\pi\) | |||||||
\(954\) | 72409.5 | − | 55523.3i | 0.0795607 | − | 0.0610068i | ||||
\(955\) | 1.36933e6 | − | 1.36933e6i | 1.50142 | − | 1.50142i | ||||
\(956\) | 138373. | − | 515038.i | 0.151403 | − | 0.563538i | ||||
\(957\) | −176360. | + | 176360.i | −0.192564 | + | 0.192564i | ||||
\(958\) | 113461. | − | 859601.i | 0.123628 | − | 0.936625i | ||||
\(959\) | − | 206358.i | − | 0.224380i | ||||||
\(960\) | −698994. | + | 696196.i | −0.758457 | + | 0.755421i | ||||
\(961\) | −251453. | −0.272276 | ||||||||
\(962\) | −971890. | − | 128282.i | −1.05019 | − | 0.138617i | ||||
\(963\) | −195712. | − | 195712.i | −0.211040 | − | 0.211040i | ||||
\(964\) | 86928.8 | + | 23354.8i | 0.0935427 | + | 0.0251317i | ||||
\(965\) | −544298. | − | 544298.i | −0.584496 | − | 0.584496i | ||||
\(966\) | 3472.48 | + | 4528.55i | 0.00372122 | + | 0.00485294i | ||||
\(967\) | −1.37297e6 | −1.46828 | −0.734138 | − | 0.679001i | \(-0.762413\pi\) | ||||
−0.734138 | + | 0.679001i | \(0.762413\pi\) | |||||||
\(968\) | −47149.6 | + | 113507.i | −0.0503184 | + | 0.121136i | ||||
\(969\) | 591293.i | 0.629731i | ||||||||
\(970\) | 618418. | + | 806497.i | 0.657263 | + | 0.857154i | ||||
\(971\) | −424934. | + | 424934.i | −0.450696 | + | 0.450696i | −0.895585 | − | 0.444890i | \(-0.853243\pi\) |
0.444890 | + | 0.895585i | \(0.353243\pi\) | |||||||
\(972\) | −223009. | − | 386860.i | −0.236043 | − | 0.409470i | ||||
\(973\) | −141892. | + | 141892.i | −0.149876 | + | 0.149876i | ||||
\(974\) | −582888. | − | 76936.8i | −0.614422 | − | 0.0810992i | ||||
\(975\) | 785091.i | 0.825868i | ||||||||
\(976\) | −719357. | + | 191721.i | −0.755171 | + | 0.201266i | ||||
\(977\) | 985948. | 1.03292 | 0.516458 | − | 0.856313i | \(-0.327250\pi\) | ||||
0.516458 | + | 0.856313i | \(0.327250\pi\) | |||||||
\(978\) | 102500. | − | 776559.i | 0.107163 | − | 0.811889i | ||||
\(979\) | −133225. | − | 133225.i | −0.139002 | − | 0.139002i | ||||
\(980\) | −579028. | − | 1.00446e6i | −0.602903 | − | 1.04587i | ||||
\(981\) | −185.903 | − | 185.903i | −0.000193174 | − | 0.000193174i | ||||
\(982\) | 930541. | − | 713535.i | 0.964967 | − | 0.739933i | ||||
\(983\) | 92886.2 | 0.0961268 | 0.0480634 | − | 0.998844i | \(-0.484695\pi\) | ||||
0.0480634 | + | 0.998844i | \(0.484695\pi\) | |||||||
\(984\) | 835835. | − | 345233.i | 0.863238 | − | 0.356551i | ||||
\(985\) | − | 281236.i | − | 0.289867i | ||||||
\(986\) | 104095. | − | 79819.4i | 0.107072 | − | 0.0821022i | ||||
\(987\) | −83197.3 | + | 83197.3i | −0.0854034 | + | 0.0854034i | ||||
\(988\) | −2.75413e6 | − | 739940.i | −2.82144 | − | 0.758023i | ||||
\(989\) | 491.308 | − | 491.308i | 0.000502297 | − | 0.000502297i | ||||
\(990\) | 40614.6 | − | 307704.i | 0.0414392 | − | 0.313951i | ||||
\(991\) | − | 1.28759e6i | − | 1.31109i | −0.755157 | − | 0.655543i | \(-0.772440\pi\) | ||
0.755157 | − | 0.655543i | \(-0.227560\pi\) | |||||||
\(992\) | 677182. | − | 879474.i | 0.688148 | − | 0.893716i | ||||
\(993\) | 1.36956e6 | 1.38894 | ||||||||
\(994\) | −81542.1 | − | 10762.9i | −0.0825294 | − | 0.0108933i | ||||
\(995\) | 1.21281e6 | + | 1.21281e6i | 1.22503 | + | 1.22503i | ||||
\(996\) | 7433.04 | − | 27666.5i | 0.00749286 | − | 0.0278892i | ||||
\(997\) | −388032. | − | 388032.i | −0.390370 | − | 0.390370i | 0.484449 | − | 0.874819i | \(-0.339020\pi\) |
−0.874819 | + | 0.484449i | \(0.839020\pi\) | |||||||
\(998\) | −19247.8 | − | 25101.6i | −0.0193250 | − | 0.0252023i | ||||
\(999\) | 617028. | 0.618264 |
(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 | 16.5.f.a.11.1 | yes | 14 | |
3.2 | odd | 2 | 144.5.m.a.91.7 | 14 | |||
4.3 | odd | 2 | 64.5.f.a.15.2 | 14 | |||
8.3 | odd | 2 | 128.5.f.a.31.6 | 14 | |||
8.5 | even | 2 | 128.5.f.b.31.2 | 14 | |||
12.11 | even | 2 | 576.5.m.a.271.2 | 14 | |||
16.3 | odd | 4 | inner | 16.5.f.a.3.1 | ✓ | 14 | |
16.5 | even | 4 | 128.5.f.a.95.6 | 14 | |||
16.11 | odd | 4 | 128.5.f.b.95.2 | 14 | |||
16.13 | even | 4 | 64.5.f.a.47.2 | 14 | |||
48.29 | odd | 4 | 576.5.m.a.559.2 | 14 | |||
48.35 | even | 4 | 144.5.m.a.19.7 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.1 | ✓ | 14 | 16.3 | odd | 4 | inner | |
16.5.f.a.11.1 | yes | 14 | 1.1 | even | 1 | trivial | |
64.5.f.a.15.2 | 14 | 4.3 | odd | 2 | |||
64.5.f.a.47.2 | 14 | 16.13 | even | 4 | |||
128.5.f.a.31.6 | 14 | 8.3 | odd | 2 | |||
128.5.f.a.95.6 | 14 | 16.5 | even | 4 | |||
128.5.f.b.31.2 | 14 | 8.5 | even | 2 | |||
128.5.f.b.95.2 | 14 | 16.11 | odd | 4 | |||
144.5.m.a.19.7 | 14 | 48.35 | even | 4 | |||
144.5.m.a.91.7 | 14 | 3.2 | odd | 2 | |||
576.5.m.a.271.2 | 14 | 12.11 | even | 2 | |||
576.5.m.a.559.2 | 14 | 48.29 | odd | 4 |