Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.353");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.10 | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.4.c.a.353.9 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −3.04040 | + | 4.21378i | −0.585126 | + | 0.810942i | ||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | − | 12.5447i | − | 1.12203i | −0.827805 | − | 0.561016i | \(-0.810410\pi\) | ||
0.827805 | − | 0.561016i | \(-0.189590\pi\) | |||||||
\(6\) | 6.08081 | − | 8.42756i | 0.413747 | − | 0.573423i | ||||
\(7\) | −33.4405 | −1.80562 | −0.902810 | − | 0.430040i | \(-0.858499\pi\) | ||||
−0.902810 | + | 0.430040i | \(0.858499\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −8.51188 | − | 25.6232i | −0.315255 | − | 0.949007i | ||||
\(10\) | 25.0894i | 0.793397i | ||||||||
\(11\) | −55.6576 | −1.52558 | −0.762791 | − | 0.646645i | \(-0.776172\pi\) | ||||
−0.762791 | + | 0.646645i | \(0.776172\pi\) | |||||||
\(12\) | −12.1616 | + | 16.8551i | −0.292563 | + | 0.405471i | ||||
\(13\) | − | 53.4865i | − | 1.14111i | −0.821258 | − | 0.570557i | \(-0.806727\pi\) | ||
0.821258 | − | 0.570557i | \(-0.193273\pi\) | |||||||
\(14\) | 66.8811 | 1.27677 | ||||||||
\(15\) | 52.8606 | + | 38.1410i | 0.909904 | + | 0.656531i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 114.641i | 1.63556i | 0.575528 | + | 0.817782i | \(0.304797\pi\) | ||||
−0.575528 | + | 0.817782i | \(0.695203\pi\) | |||||||
\(18\) | 17.0238 | + | 51.2464i | 0.222919 | + | 0.671049i | ||||
\(19\) | 78.3915 | 0.946539 | 0.473269 | − | 0.880918i | \(-0.343074\pi\) | ||||
0.473269 | + | 0.880918i | \(0.343074\pi\) | |||||||
\(20\) | − | 50.1788i | − | 0.561016i | ||||||
\(21\) | 101.673 | − | 140.911i | 1.05652 | − | 1.46425i | ||||
\(22\) | 111.315 | 1.07875 | ||||||||
\(23\) | −163.867 | −1.48559 | −0.742795 | − | 0.669519i | \(-0.766500\pi\) | ||||
−0.742795 | + | 0.669519i | \(0.766500\pi\) | |||||||
\(24\) | 24.3232 | − | 33.7102i | 0.206873 | − | 0.286711i | ||||
\(25\) | −32.3697 | −0.258957 | ||||||||
\(26\) | 106.973i | 0.806889i | ||||||||
\(27\) | 133.850 | + | 42.0377i | 0.954054 | + | 0.299635i | ||||
\(28\) | −133.762 | −0.902810 | ||||||||
\(29\) | − | 76.0732i | − | 0.487119i | −0.969886 | − | 0.243559i | \(-0.921685\pi\) | ||
0.969886 | − | 0.243559i | \(-0.0783151\pi\) | |||||||
\(30\) | −105.721 | − | 76.2820i | −0.643399 | − | 0.464237i | ||||
\(31\) | − | 160.914i | − | 0.932289i | −0.884708 | − | 0.466145i | \(-0.845643\pi\) | ||
0.884708 | − | 0.466145i | \(-0.154357\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 169.222 | − | 234.529i | 0.892658 | − | 1.23716i | ||||
\(34\) | − | 229.283i | − | 1.15652i | ||||||
\(35\) | 419.502i | 2.02596i | ||||||||
\(36\) | −34.0475 | − | 102.493i | −0.157627 | − | 0.474504i | ||||
\(37\) | − | 83.0925i | − | 0.369198i | −0.982814 | − | 0.184599i | \(-0.940901\pi\) | ||
0.982814 | − | 0.184599i | \(-0.0590986\pi\) | |||||||
\(38\) | −156.783 | −0.669304 | ||||||||
\(39\) | 225.380 | + | 162.621i | 0.925378 | + | 0.667696i | ||||
\(40\) | 100.358i | 0.396698i | ||||||||
\(41\) | − | 70.9020i | − | 0.270074i | −0.990841 | − | 0.135037i | \(-0.956885\pi\) | ||
0.990841 | − | 0.135037i | \(-0.0431153\pi\) | |||||||
\(42\) | −203.346 | + | 281.822i | −0.747069 | + | 1.03538i | ||||
\(43\) | 257.980i | 0.914920i | 0.889230 | + | 0.457460i | \(0.151241\pi\) | ||||
−0.889230 | + | 0.457460i | \(0.848759\pi\) | |||||||
\(44\) | −222.631 | −0.762791 | ||||||||
\(45\) | −321.435 | + | 106.779i | −1.06482 | + | 0.353726i | ||||
\(46\) | 327.733 | 1.05047 | ||||||||
\(47\) | 497.485 | 1.54395 | 0.771975 | − | 0.635653i | \(-0.219269\pi\) | ||||
0.771975 | + | 0.635653i | \(0.219269\pi\) | |||||||
\(48\) | −48.6465 | + | 67.4205i | −0.146282 | + | 0.202736i | ||||
\(49\) | 775.270 | 2.26026 | ||||||||
\(50\) | 64.7393 | 0.183110 | ||||||||
\(51\) | −483.073 | − | 348.556i | −1.32635 | − | 0.957012i | ||||
\(52\) | − | 213.946i | − | 0.570557i | ||||||
\(53\) | 500.411i | 1.29692i | 0.761249 | + | 0.648459i | \(0.224586\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(54\) | −267.700 | − | 84.0753i | −0.674618 | − | 0.211874i | ||||
\(55\) | 698.209i | 1.71175i | ||||||||
\(56\) | 267.524 | 0.638383 | ||||||||
\(57\) | −238.342 | + | 330.324i | −0.553844 | + | 0.767588i | ||||
\(58\) | 152.146i | 0.344445i | ||||||||
\(59\) | −453.067 | + | 10.4364i | −0.999735 | + | 0.0230290i | ||||
\(60\) | 211.443 | + | 152.564i | 0.454952 | + | 0.328265i | ||||
\(61\) | 32.9911i | 0.0692472i | 0.999400 | + | 0.0346236i | \(0.0110232\pi\) | ||||
−0.999400 | + | 0.0346236i | \(0.988977\pi\) | |||||||
\(62\) | 321.828i | 0.659228i | ||||||||
\(63\) | 284.642 | + | 856.853i | 0.569230 | + | 1.71355i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −670.972 | −1.28037 | ||||||||
\(66\) | −338.443 | + | 469.058i | −0.631205 | + | 0.874804i | ||||
\(67\) | 1052.72i | 1.91956i | 0.280760 | + | 0.959778i | \(0.409414\pi\) | ||||
−0.280760 | + | 0.959778i | \(0.590586\pi\) | |||||||
\(68\) | 458.565i | 0.817782i | ||||||||
\(69\) | 498.221 | − | 690.498i | 0.869257 | − | 1.20473i | ||||
\(70\) | − | 839.004i | − | 1.43257i | ||||||
\(71\) | 470.752i | 0.786873i | 0.919352 | + | 0.393437i | \(0.128714\pi\) | ||||
−0.919352 | + | 0.393437i | \(0.871286\pi\) | |||||||
\(72\) | 68.0951 | + | 204.986i | 0.111459 | + | 0.335525i | ||||
\(73\) | − | 912.066i | − | 1.46232i | −0.682207 | − | 0.731159i | \(-0.738980\pi\) | ||
0.682207 | − | 0.731159i | \(-0.261020\pi\) | |||||||
\(74\) | 166.185i | 0.261062i | ||||||||
\(75\) | 98.4169 | − | 136.399i | 0.151523 | − | 0.209999i | ||||
\(76\) | 313.566 | 0.473269 | ||||||||
\(77\) | 1861.22 | 2.75462 | ||||||||
\(78\) | −450.761 | − | 325.241i | −0.654341 | − | 0.472132i | ||||
\(79\) | 674.923 | 0.961199 | 0.480600 | − | 0.876940i | \(-0.340419\pi\) | ||||
0.480600 | + | 0.876940i | \(0.340419\pi\) | |||||||
\(80\) | − | 200.715i | − | 0.280508i | ||||||
\(81\) | −584.096 | + | 436.203i | −0.801229 | + | 0.598358i | ||||
\(82\) | 141.804i | 0.190971i | ||||||||
\(83\) | −483.590 | −0.639528 | −0.319764 | − | 0.947497i | \(-0.603604\pi\) | ||||
−0.319764 | + | 0.947497i | \(0.603604\pi\) | |||||||
\(84\) | 406.691 | − | 563.644i | 0.528258 | − | 0.732127i | ||||
\(85\) | 1438.14 | 1.83516 | ||||||||
\(86\) | − | 515.960i | − | 0.646946i | ||||||
\(87\) | 320.556 | + | 231.293i | 0.395025 | + | 0.285026i | ||||
\(88\) | 445.261 | 0.539375 | ||||||||
\(89\) | −70.2848 | −0.0837098 | −0.0418549 | − | 0.999124i | \(-0.513327\pi\) | ||||
−0.0418549 | + | 0.999124i | \(0.513327\pi\) | |||||||
\(90\) | 642.871 | − | 213.558i | 0.752939 | − | 0.250122i | ||||
\(91\) | 1788.62i | 2.06042i | ||||||||
\(92\) | −655.467 | −0.742795 | ||||||||
\(93\) | 678.055 | + | 489.243i | 0.756033 | + | 0.545507i | ||||
\(94\) | −994.970 | −1.09174 | ||||||||
\(95\) | − | 983.398i | − | 1.06205i | ||||||
\(96\) | 97.2929 | − | 134.841i | 0.103437 | − | 0.143356i | ||||
\(97\) | − | 549.167i | − | 0.574840i | −0.957805 | − | 0.287420i | \(-0.907203\pi\) | ||
0.957805 | − | 0.287420i | \(-0.0927975\pi\) | |||||||
\(98\) | −1550.54 | −1.59825 | ||||||||
\(99\) | 473.751 | + | 1426.13i | 0.480947 | + | 1.44779i | ||||
\(100\) | −129.479 | −0.129479 | ||||||||
\(101\) | −1282.30 | −1.26330 | −0.631652 | − | 0.775252i | \(-0.717623\pi\) | ||||
−0.631652 | + | 0.775252i | \(0.717623\pi\) | |||||||
\(102\) | 966.146 | + | 697.112i | 0.937870 | + | 0.676709i | ||||
\(103\) | − | 1210.94i | − | 1.15842i | −0.815177 | − | 0.579212i | \(-0.803360\pi\) | ||
0.815177 | − | 0.579212i | \(-0.196640\pi\) | |||||||
\(104\) | 427.892i | 0.403445i | ||||||||
\(105\) | −1767.69 | − | 1275.46i | −1.64294 | − | 1.18544i | ||||
\(106\) | − | 1000.82i | − | 0.917060i | ||||||
\(107\) | − | 618.091i | − | 0.558440i | −0.960227 | − | 0.279220i | \(-0.909924\pi\) | ||
0.960227 | − | 0.279220i | \(-0.0900759\pi\) | |||||||
\(108\) | 535.400 | + | 168.151i | 0.477027 | + | 0.149818i | ||||
\(109\) | − | 14.7828i | − | 0.0129902i | −0.999979 | − | 0.00649512i | \(-0.997933\pi\) | ||
0.999979 | − | 0.00649512i | \(-0.00206748\pi\) | |||||||
\(110\) | − | 1396.42i | − | 1.21039i | ||||||
\(111\) | 350.133 | + | 252.635i | 0.299398 | + | 0.216027i | ||||
\(112\) | −535.049 | −0.451405 | ||||||||
\(113\) | 759.245 | 0.632068 | 0.316034 | − | 0.948748i | \(-0.397649\pi\) | ||||
0.316034 | + | 0.948748i | \(0.397649\pi\) | |||||||
\(114\) | 476.683 | − | 660.649i | 0.391627 | − | 0.542767i | ||||
\(115\) | 2055.66i | 1.66688i | ||||||||
\(116\) | − | 304.293i | − | 0.243559i | ||||||
\(117\) | −1370.49 | + | 455.271i | −1.08293 | + | 0.359742i | ||||
\(118\) | 906.135 | − | 20.8729i | 0.706919 | − | 0.0162839i | ||||
\(119\) | − | 3833.67i | − | 2.95321i | ||||||
\(120\) | −422.885 | − | 305.128i | −0.321700 | − | 0.232119i | ||||
\(121\) | 1766.77 | 1.32740 | ||||||||
\(122\) | − | 65.9823i | − | 0.0489652i | ||||||
\(123\) | 298.765 | + | 215.571i | 0.219014 | + | 0.158027i | ||||
\(124\) | − | 643.655i | − | 0.466145i | ||||||
\(125\) | − | 1162.02i | − | 0.831474i | ||||||
\(126\) | −569.284 | − | 1713.71i | −0.402507 | − | 1.21166i | ||||
\(127\) | −1634.61 | −1.14211 | −0.571055 | − | 0.820912i | \(-0.693466\pi\) | ||||
−0.571055 | + | 0.820912i | \(0.693466\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −1087.07 | − | 784.363i | −0.741947 | − | 0.535344i | ||||
\(130\) | 1341.94 | 0.905356 | ||||||||
\(131\) | 1341.04 | 0.894403 | 0.447201 | − | 0.894433i | \(-0.352421\pi\) | ||||
0.447201 | + | 0.894433i | \(0.352421\pi\) | |||||||
\(132\) | 676.887 | − | 938.116i | 0.446329 | − | 0.618580i | ||||
\(133\) | −2621.45 | −1.70909 | ||||||||
\(134\) | − | 2105.44i | − | 1.35733i | ||||||
\(135\) | 527.350 | − | 1679.11i | 0.336201 | − | 1.07048i | ||||
\(136\) | − | 917.130i | − | 0.578259i | ||||||
\(137\) | 2577.02i | 1.60708i | 0.595251 | + | 0.803540i | \(0.297053\pi\) | ||||
−0.595251 | + | 0.803540i | \(0.702947\pi\) | |||||||
\(138\) | −996.442 | + | 1381.00i | −0.614658 | + | 0.851871i | ||||
\(139\) | −280.345 | −0.171069 | −0.0855344 | − | 0.996335i | \(-0.527260\pi\) | ||||
−0.0855344 | + | 0.996335i | \(0.527260\pi\) | |||||||
\(140\) | 1678.01i | 1.01298i | ||||||||
\(141\) | −1512.56 | + | 2096.29i | −0.903406 | + | 1.25205i | ||||
\(142\) | − | 941.504i | − | 0.556403i | ||||||
\(143\) | 2976.93i | 1.74086i | ||||||||
\(144\) | −136.190 | − | 409.971i | −0.0788137 | − | 0.237252i | ||||
\(145\) | −954.316 | −0.546563 | ||||||||
\(146\) | 1824.13i | 1.03402i | ||||||||
\(147\) | −2357.13 | + | 3266.82i | −1.32254 | + | 1.83294i | ||||
\(148\) | − | 332.370i | − | 0.184599i | ||||||
\(149\) | 2428.29 | 1.33512 | 0.667562 | − | 0.744554i | \(-0.267338\pi\) | ||||
0.667562 | + | 0.744554i | \(0.267338\pi\) | |||||||
\(150\) | −196.834 | + | 272.797i | −0.107143 | + | 0.148492i | ||||
\(151\) | 477.528i | 0.257355i | 0.991686 | + | 0.128678i | \(0.0410733\pi\) | ||||
−0.991686 | + | 0.128678i | \(0.958927\pi\) | |||||||
\(152\) | −627.132 | −0.334652 | ||||||||
\(153\) | 2937.48 | − | 975.813i | 1.55216 | − | 0.515620i | ||||
\(154\) | −3722.44 | −1.94781 | ||||||||
\(155\) | −2018.62 | −1.04606 | ||||||||
\(156\) | 901.521 | + | 650.482i | 0.462689 | + | 0.333848i | ||||
\(157\) | 1193.03i | 0.606460i | 0.952917 | + | 0.303230i | \(0.0980650\pi\) | ||||
−0.952917 | + | 0.303230i | \(0.901935\pi\) | |||||||
\(158\) | −1349.85 | −0.679671 | ||||||||
\(159\) | −2108.62 | − | 1521.45i | −1.05173 | − | 0.758861i | ||||
\(160\) | 401.431i | 0.198349i | ||||||||
\(161\) | 5479.79 | 2.68241 | ||||||||
\(162\) | 1168.19 | − | 872.406i | 0.566554 | − | 0.423103i | ||||
\(163\) | −325.353 | −0.156341 | −0.0781707 | − | 0.996940i | \(-0.524908\pi\) | ||||
−0.0781707 | + | 0.996940i | \(0.524908\pi\) | |||||||
\(164\) | − | 283.608i | − | 0.135037i | ||||||
\(165\) | −2942.10 | − | 2122.84i | −1.38813 | − | 1.00159i | ||||
\(166\) | 967.179 | 0.452215 | ||||||||
\(167\) | − | 266.183i | − | 0.123340i | −0.998097 | − | 0.0616701i | \(-0.980357\pi\) | ||
0.998097 | − | 0.0616701i | \(-0.0196427\pi\) | |||||||
\(168\) | −813.382 | + | 1127.29i | −0.373535 | + | 0.517692i | ||||
\(169\) | −663.804 | −0.302141 | ||||||||
\(170\) | −2876.28 | −1.29765 | ||||||||
\(171\) | −667.259 | − | 2008.64i | −0.298401 | − | 0.898272i | ||||
\(172\) | 1031.92i | 0.457460i | ||||||||
\(173\) | 286.319 | 0.125829 | 0.0629144 | − | 0.998019i | \(-0.479960\pi\) | ||||
0.0629144 | + | 0.998019i | \(0.479960\pi\) | |||||||
\(174\) | −641.112 | − | 462.587i | −0.279325 | − | 0.201544i | ||||
\(175\) | 1082.46 | 0.467578 | ||||||||
\(176\) | −890.522 | −0.381396 | ||||||||
\(177\) | 1333.53 | − | 1940.86i | 0.566296 | − | 0.824202i | ||||
\(178\) | 140.570 | 0.0591918 | ||||||||
\(179\) | −2828.27 | −1.18098 | −0.590489 | − | 0.807046i | \(-0.701065\pi\) | ||||
−0.590489 | + | 0.807046i | \(0.701065\pi\) | |||||||
\(180\) | −1285.74 | + | 427.116i | −0.532408 | + | 0.176863i | ||||
\(181\) | 746.946 | 0.306741 | 0.153370 | − | 0.988169i | \(-0.450987\pi\) | ||||
0.153370 | + | 0.988169i | \(0.450987\pi\) | |||||||
\(182\) | − | 3577.23i | − | 1.45694i | ||||||
\(183\) | −139.017 | − | 100.306i | −0.0561555 | − | 0.0405184i | ||||
\(184\) | 1310.93 | 0.525235 | ||||||||
\(185\) | −1042.37 | −0.414252 | ||||||||
\(186\) | −1356.11 | − | 978.486i | −0.534596 | − | 0.385732i | ||||
\(187\) | − | 6380.66i | − | 2.49519i | ||||||
\(188\) | 1989.94 | 0.771975 | ||||||||
\(189\) | −4476.02 | − | 1405.76i | −1.72266 | − | 0.541027i | ||||
\(190\) | 1966.80i | 0.750981i | ||||||||
\(191\) | 769.440 | 0.291491 | 0.145745 | − | 0.989322i | \(-0.453442\pi\) | ||||
0.145745 | + | 0.989322i | \(0.453442\pi\) | |||||||
\(192\) | −194.586 | + | 269.682i | −0.0731408 | + | 0.101368i | ||||
\(193\) | 4249.52 | 1.58491 | 0.792453 | − | 0.609933i | \(-0.208804\pi\) | ||||
0.792453 | + | 0.609933i | \(0.208804\pi\) | |||||||
\(194\) | 1098.33i | 0.406473i | ||||||||
\(195\) | 2040.03 | − | 2827.33i | 0.749176 | − | 1.03830i | ||||
\(196\) | 3101.08 | 1.13013 | ||||||||
\(197\) | − | 2929.88i | − | 1.05962i | −0.848116 | − | 0.529810i | \(-0.822263\pi\) | ||
0.848116 | − | 0.529810i | \(-0.177737\pi\) | |||||||
\(198\) | −947.502 | − | 2852.25i | −0.340081 | − | 1.02374i | ||||
\(199\) | 1773.01 | 0.631583 | 0.315792 | − | 0.948829i | \(-0.397730\pi\) | ||||
0.315792 | + | 0.948829i | \(0.397730\pi\) | |||||||
\(200\) | 258.957 | 0.0915552 | ||||||||
\(201\) | −4435.93 | − | 3200.70i | −1.55665 | − | 1.12318i | ||||
\(202\) | 2564.60 | 0.893291 | ||||||||
\(203\) | 2543.93i | 0.879551i | ||||||||
\(204\) | −1932.29 | − | 1394.22i | −0.663174 | − | 0.478506i | ||||
\(205\) | −889.445 | −0.303032 | ||||||||
\(206\) | 2421.88i | 0.819129i | ||||||||
\(207\) | 1394.81 | + | 4198.79i | 0.468339 | + | 1.40984i | ||||
\(208\) | − | 855.784i | − | 0.285278i | ||||||
\(209\) | −4363.08 | −1.44402 | ||||||||
\(210\) | 3535.38 | + | 2550.91i | 1.16173 | + | 0.838236i | ||||
\(211\) | − | 796.189i | − | 0.259772i | −0.991529 | − | 0.129886i | \(-0.958539\pi\) | ||
0.991529 | − | 0.129886i | \(-0.0414611\pi\) | |||||||
\(212\) | 2001.64i | 0.648459i | ||||||||
\(213\) | −1983.65 | − | 1431.28i | −0.638109 | − | 0.460420i | ||||
\(214\) | 1236.18i | 0.394877i | ||||||||
\(215\) | 3236.28 | 1.02657 | ||||||||
\(216\) | −1070.80 | − | 336.301i | −0.337309 | − | 0.105937i | ||||
\(217\) | 5381.05i | 1.68336i | ||||||||
\(218\) | 29.5656i | 0.00918549i | ||||||||
\(219\) | 3843.25 | + | 2773.05i | 1.18586 | + | 0.855641i | ||||
\(220\) | 2792.83i | 0.855877i | ||||||||
\(221\) | 6131.76 | 1.86637 | ||||||||
\(222\) | −700.267 | − | 505.269i | −0.211706 | − | 0.152754i | ||||
\(223\) | 4107.19 | 1.23335 | 0.616677 | − | 0.787217i | \(-0.288479\pi\) | ||||
0.616677 | + | 0.787217i | \(0.288479\pi\) | |||||||
\(224\) | 1070.10 | 0.319191 | ||||||||
\(225\) | 275.527 | + | 829.414i | 0.0816376 | + | 0.245752i | ||||
\(226\) | −1518.49 | −0.446940 | ||||||||
\(227\) | 1090.69 | 0.318907 | 0.159454 | − | 0.987205i | \(-0.449027\pi\) | ||||
0.159454 | + | 0.987205i | \(0.449027\pi\) | |||||||
\(228\) | −953.367 | + | 1321.30i | −0.276922 | + | 0.383794i | ||||
\(229\) | − | 4974.89i | − | 1.43559i | −0.696254 | − | 0.717795i | \(-0.745151\pi\) | ||
0.696254 | − | 0.717795i | \(-0.254849\pi\) | |||||||
\(230\) | − | 4111.32i | − | 1.17866i | ||||||
\(231\) | −5658.87 | + | 7842.78i | −1.61180 | + | 2.23384i | ||||
\(232\) | 608.586i | 0.172222i | ||||||||
\(233\) | 434.162 | 0.122072 | 0.0610362 | − | 0.998136i | \(-0.480559\pi\) | ||||
0.0610362 | + | 0.998136i | \(0.480559\pi\) | |||||||
\(234\) | 2740.99 | − | 910.541i | 0.765744 | − | 0.254376i | ||||
\(235\) | − | 6240.81i | − | 1.73236i | ||||||
\(236\) | −1812.27 | + | 41.7457i | −0.499867 | + | 0.0115145i | ||||
\(237\) | −2052.04 | + | 2843.98i | −0.562423 | + | 0.779477i | ||||
\(238\) | 7667.33i | 2.08823i | ||||||||
\(239\) | 2563.30i | 0.693748i | 0.937912 | + | 0.346874i | \(0.112757\pi\) | ||||
−0.937912 | + | 0.346874i | \(0.887243\pi\) | |||||||
\(240\) | 845.770 | + | 610.256i | 0.227476 | + | 0.164133i | ||||
\(241\) | −3436.16 | −0.918434 | −0.459217 | − | 0.888324i | \(-0.651870\pi\) | ||||
−0.459217 | + | 0.888324i | \(0.651870\pi\) | |||||||
\(242\) | −3533.54 | −0.938615 | ||||||||
\(243\) | −62.1768 | − | 3787.48i | −0.0164142 | − | 0.999865i | ||||
\(244\) | 131.965i | 0.0346236i | ||||||||
\(245\) | − | 9725.54i | − | 2.53609i | ||||||
\(246\) | −597.531 | − | 431.141i | −0.154867 | − | 0.111742i | ||||
\(247\) | − | 4192.88i | − | 1.08011i | ||||||
\(248\) | 1287.31i | 0.329614i | ||||||||
\(249\) | 1470.31 | − | 2037.74i | 0.374205 | − | 0.518621i | ||||
\(250\) | 2324.04i | 0.587941i | ||||||||
\(251\) | − | 4517.63i | − | 1.13606i | −0.823009 | − | 0.568029i | \(-0.807706\pi\) | ||
0.823009 | − | 0.568029i | \(-0.192294\pi\) | |||||||
\(252\) | 1138.57 | + | 3427.41i | 0.284615 | + | 0.856773i | ||||
\(253\) | 9120.43 | 2.26639 | ||||||||
\(254\) | 3269.21 | 0.807594 | ||||||||
\(255\) | −4372.53 | + | 6060.01i | −1.07380 | + | 1.48821i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 6867.44i | 1.66685i | 0.552636 | + | 0.833423i | \(0.313622\pi\) | ||||
−0.552636 | + | 0.833423i | \(0.686378\pi\) | |||||||
\(258\) | 2174.14 | + | 1568.73i | 0.524636 | + | 0.378545i | ||||
\(259\) | 2778.66i | 0.666631i | ||||||||
\(260\) | −2683.89 | −0.640184 | ||||||||
\(261\) | −1949.24 | + | 647.526i | −0.462279 | + | 0.153567i | ||||
\(262\) | −2682.07 | −0.632438 | ||||||||
\(263\) | − | 2.40574i | − | 0.000564048i | −1.00000 | 0.000282024i | \(-0.999910\pi\) | |||
1.00000 | 0.000282024i | \(-8.97710e-5\pi\) | ||||||||
\(264\) | −1353.77 | + | 1876.23i | −0.315602 | + | 0.437402i | ||||
\(265\) | 6277.50 | 1.45518 | ||||||||
\(266\) | 5242.91 | 1.20851 | ||||||||
\(267\) | 213.694 | − | 296.165i | 0.0489808 | − | 0.0678838i | ||||
\(268\) | 4210.88i | 0.959778i | ||||||||
\(269\) | 827.485 | 0.187556 | 0.0937781 | − | 0.995593i | \(-0.470106\pi\) | ||||
0.0937781 | + | 0.995593i | \(0.470106\pi\) | |||||||
\(270\) | −1054.70 | + | 3358.22i | −0.237730 | + | 0.756943i | ||||
\(271\) | 2974.52 | 0.666750 | 0.333375 | − | 0.942794i | \(-0.391812\pi\) | ||||
0.333375 | + | 0.942794i | \(0.391812\pi\) | |||||||
\(272\) | 1834.26i | 0.408891i | ||||||||
\(273\) | −7536.84 | − | 5438.12i | −1.67088 | − | 1.20560i | ||||
\(274\) | − | 5154.04i | − | 1.13638i | ||||||
\(275\) | 1801.62 | 0.395061 | ||||||||
\(276\) | 1992.88 | − | 2761.99i | 0.434629 | − | 0.602364i | ||||
\(277\) | −5038.87 | −1.09298 | −0.546491 | − | 0.837465i | \(-0.684037\pi\) | ||||
−0.546491 | + | 0.837465i | \(0.684037\pi\) | |||||||
\(278\) | 560.690 | 0.120964 | ||||||||
\(279\) | −4123.13 | + | 1369.68i | −0.884749 | + | 0.293909i | ||||
\(280\) | − | 3356.01i | − | 0.716287i | ||||||
\(281\) | − | 2614.62i | − | 0.555073i | −0.960715 | − | 0.277536i | \(-0.910482\pi\) | ||
0.960715 | − | 0.277536i | \(-0.0895179\pi\) | |||||||
\(282\) | 3025.11 | − | 4192.59i | 0.638804 | − | 0.885336i | ||||
\(283\) | 8910.03i | 1.87154i | 0.352610 | + | 0.935770i | \(0.385294\pi\) | ||||
−0.352610 | + | 0.935770i | \(0.614706\pi\) | |||||||
\(284\) | 1883.01i | 0.393437i | ||||||||
\(285\) | 4143.82 | + | 2989.93i | 0.861259 | + | 0.621432i | ||||
\(286\) | − | 5953.86i | − | 1.23098i | ||||||
\(287\) | 2371.00i | 0.487651i | ||||||||
\(288\) | 272.380 | + | 819.942i | 0.0557297 | + | 0.167762i | ||||
\(289\) | −8229.63 | −1.67507 | ||||||||
\(290\) | 1908.63 | 0.386478 | ||||||||
\(291\) | 2314.07 | + | 1669.69i | 0.466162 | + | 0.336354i | ||||
\(292\) | − | 3648.26i | − | 0.731159i | ||||||
\(293\) | − | 1455.27i | − | 0.290162i | −0.989420 | − | 0.145081i | \(-0.953656\pi\) | ||
0.989420 | − | 0.145081i | \(-0.0463443\pi\) | |||||||
\(294\) | 4714.27 | − | 6533.63i | 0.935176 | − | 1.29609i | ||||
\(295\) | 130.922 | + | 5683.60i | 0.0258392 | + | 1.12174i | ||||
\(296\) | 664.740i | 0.130531i | ||||||||
\(297\) | −7449.78 | − | 2339.72i | −1.45549 | − | 0.457118i | ||||
\(298\) | −4856.58 | −0.944075 | ||||||||
\(299\) | 8764.65i | 1.69523i | ||||||||
\(300\) | 393.667 | − | 545.595i | 0.0757613 | − | 0.105000i | ||||
\(301\) | − | 8626.99i | − | 1.65200i | ||||||
\(302\) | − | 955.056i | − | 0.181978i | ||||||
\(303\) | 3898.71 | − | 5403.33i | 0.739192 | − | 1.02447i | ||||
\(304\) | 1254.26 | 0.236635 | ||||||||
\(305\) | 413.864 | 0.0776977 | ||||||||
\(306\) | −5874.95 | + | 1951.63i | −1.09754 | + | 0.364598i | ||||
\(307\) | 4945.35 | 0.919369 | 0.459684 | − | 0.888082i | \(-0.347963\pi\) | ||||
0.459684 | + | 0.888082i | \(0.347963\pi\) | |||||||
\(308\) | 7444.89 | 1.37731 | ||||||||
\(309\) | 5102.64 | + | 3681.75i | 0.939414 | + | 0.677824i | ||||
\(310\) | 4037.23 | 0.739676 | ||||||||
\(311\) | − | 6782.57i | − | 1.23667i | −0.785915 | − | 0.618335i | \(-0.787808\pi\) | ||
0.785915 | − | 0.618335i | \(-0.212192\pi\) | |||||||
\(312\) | −1803.04 | − | 1300.96i | −0.327170 | − | 0.236066i | ||||
\(313\) | 10189.2i | 1.84002i | 0.391891 | + | 0.920012i | \(0.371821\pi\) | ||||
−0.391891 | + | 0.920012i | \(0.628179\pi\) | |||||||
\(314\) | − | 2386.06i | − | 0.428832i | ||||||
\(315\) | 10749.0 | − | 3570.75i | 1.92265 | − | 0.638695i | ||||
\(316\) | 2699.69 | 0.480600 | ||||||||
\(317\) | 7339.51i | 1.30040i | 0.759762 | + | 0.650202i | \(0.225316\pi\) | ||||
−0.759762 | + | 0.650202i | \(0.774684\pi\) | |||||||
\(318\) | 4217.24 | + | 3042.90i | 0.743683 | + | 0.536596i | ||||
\(319\) | 4234.06i | 0.743140i | ||||||||
\(320\) | − | 802.861i | − | 0.140254i | ||||||
\(321\) | 2604.50 | + | 1879.25i | 0.452863 | + | 0.326758i | ||||
\(322\) | −10959.6 | −1.89675 | ||||||||
\(323\) | 8986.90i | 1.54813i | ||||||||
\(324\) | −2336.38 | + | 1744.81i | −0.400614 | + | 0.299179i | ||||
\(325\) | 1731.34i | 0.295500i | ||||||||
\(326\) | 650.707 | 0.110550 | ||||||||
\(327\) | 62.2915 | + | 44.9457i | 0.0105343 | + | 0.00760093i | ||||
\(328\) | 567.216i | 0.0954855i | ||||||||
\(329\) | −16636.2 | −2.78779 | ||||||||
\(330\) | 5884.20 | + | 4245.67i | 0.981558 | + | 0.708232i | ||||
\(331\) | −1887.25 | −0.313391 | −0.156696 | − | 0.987647i | \(-0.550084\pi\) | ||||
−0.156696 | + | 0.987647i | \(0.550084\pi\) | |||||||
\(332\) | −1934.36 | −0.319764 | ||||||||
\(333\) | −2129.09 | + | 707.273i | −0.350371 | + | 0.116391i | ||||
\(334\) | 532.365i | 0.0872147i | ||||||||
\(335\) | 13206.1 | 2.15380 | ||||||||
\(336\) | 1626.76 | − | 2254.58i | 0.264129 | − | 0.366063i | ||||
\(337\) | − | 2949.58i | − | 0.476778i | −0.971170 | − | 0.238389i | \(-0.923381\pi\) | ||
0.971170 | − | 0.238389i | \(-0.0766193\pi\) | |||||||
\(338\) | 1327.61 | 0.213646 | ||||||||
\(339\) | −2308.41 | + | 3199.29i | −0.369840 | + | 0.512571i | ||||
\(340\) | 5752.57 | 0.917578 | ||||||||
\(341\) | 8956.08i | 1.42228i | ||||||||
\(342\) | 1334.52 | + | 4017.28i | 0.211001 | + | 0.635174i | ||||
\(343\) | −14455.3 | −2.27556 | ||||||||
\(344\) | − | 2063.84i | − | 0.323473i | ||||||
\(345\) | −8662.10 | − | 6250.04i | −1.35174 | − | 0.975335i | ||||
\(346\) | −572.637 | −0.0889744 | ||||||||
\(347\) | −4174.20 | −0.645771 | −0.322886 | − | 0.946438i | \(-0.604653\pi\) | ||||
−0.322886 | + | 0.946438i | \(0.604653\pi\) | |||||||
\(348\) | 1282.22 | + | 925.173i | 0.197513 | + | 0.142513i | ||||
\(349\) | − | 5532.72i | − | 0.848595i | −0.905523 | − | 0.424297i | \(-0.860521\pi\) | ||
0.905523 | − | 0.424297i | \(-0.139479\pi\) | |||||||
\(350\) | −2164.92 | −0.330628 | ||||||||
\(351\) | 2248.45 | − | 7159.17i | 0.341918 | − | 1.08868i | ||||
\(352\) | 1781.04 | 0.269687 | ||||||||
\(353\) | 1343.96 | 0.202640 | 0.101320 | − | 0.994854i | \(-0.467693\pi\) | ||||
0.101320 | + | 0.994854i | \(0.467693\pi\) | |||||||
\(354\) | −2667.06 | + | 3881.71i | −0.400432 | + | 0.582799i | ||||
\(355\) | 5905.45 | 0.882897 | ||||||||
\(356\) | −281.139 | −0.0418549 | ||||||||
\(357\) | 16154.2 | + | 11655.9i | 2.39488 | + | 1.72800i | ||||
\(358\) | 5656.54 | 0.835077 | ||||||||
\(359\) | 1042.10i | 0.153204i | 0.997062 | + | 0.0766019i | \(0.0244071\pi\) | ||||
−0.997062 | + | 0.0766019i | \(0.975593\pi\) | |||||||
\(360\) | 2571.48 | − | 854.232i | 0.376470 | − | 0.125061i | ||||
\(361\) | −713.780 | −0.104065 | ||||||||
\(362\) | −1493.89 | −0.216898 | ||||||||
\(363\) | −5371.70 | + | 7444.79i | −0.776698 | + | 1.07645i | ||||
\(364\) | 7154.47i | 1.03021i | ||||||||
\(365\) | −11441.6 | −1.64077 | ||||||||
\(366\) | 278.035 | + | 200.613i | 0.0397079 | + | 0.0286508i | ||||
\(367\) | 3839.73i | 0.546137i | 0.961995 | + | 0.273069i | \(0.0880386\pi\) | ||||
−0.961995 | + | 0.273069i | \(0.911961\pi\) | |||||||
\(368\) | −2621.87 | −0.371397 | ||||||||
\(369\) | −1816.73 | + | 603.509i | −0.256302 | + | 0.0851421i | ||||
\(370\) | 2084.74 | 0.292920 | ||||||||
\(371\) | − | 16734.0i | − | 2.34174i | ||||||
\(372\) | 2712.22 | + | 1956.97i | 0.378016 | + | 0.272753i | ||||
\(373\) | −4156.50 | −0.576985 | −0.288492 | − | 0.957482i | \(-0.593154\pi\) | ||||
−0.288492 | + | 0.957482i | \(0.593154\pi\) | |||||||
\(374\) | 12761.3i | 1.76436i | ||||||||
\(375\) | 4896.50 | + | 3533.01i | 0.674278 | + | 0.486517i | ||||
\(376\) | −3979.88 | −0.545869 | ||||||||
\(377\) | −4068.89 | −0.555858 | ||||||||
\(378\) | 8952.04 | + | 2811.52i | 1.21810 | + | 0.382564i | ||||
\(379\) | 4195.10 | 0.568570 | 0.284285 | − | 0.958740i | \(-0.408244\pi\) | ||||
0.284285 | + | 0.958740i | \(0.408244\pi\) | |||||||
\(380\) | − | 3933.59i | − | 0.531024i | ||||||
\(381\) | 4969.87 | − | 6887.87i | 0.668278 | − | 0.926185i | ||||
\(382\) | −1538.88 | −0.206115 | ||||||||
\(383\) | 7774.39i | 1.03721i | 0.855013 | + | 0.518607i | \(0.173549\pi\) | ||||
−0.855013 | + | 0.518607i | \(0.826451\pi\) | |||||||
\(384\) | 389.172 | − | 539.364i | 0.0517183 | − | 0.0716779i | ||||
\(385\) | − | 23348.5i | − | 3.09078i | ||||||
\(386\) | −8499.03 | −1.12070 | ||||||||
\(387\) | 6610.27 | − | 2195.89i | 0.868266 | − | 0.288433i | ||||
\(388\) | − | 2196.67i | − | 0.287420i | ||||||
\(389\) | 4113.36i | 0.536133i | 0.963400 | + | 0.268066i | \(0.0863846\pi\) | ||||
−0.963400 | + | 0.268066i | \(0.913615\pi\) | |||||||
\(390\) | −4080.05 | + | 5654.66i | −0.529748 | + | 0.734192i | ||||
\(391\) | − | 18785.9i | − | 2.42978i | ||||||
\(392\) | −6202.16 | −0.799124 | ||||||||
\(393\) | −4077.29 | + | 5650.83i | −0.523338 | + | 0.725309i | ||||
\(394\) | 5859.76i | 0.749265i | ||||||||
\(395\) | − | 8466.71i | − | 1.07850i | ||||||
\(396\) | 1895.00 | + | 5704.50i | 0.240474 | + | 0.723894i | ||||
\(397\) | − | 856.145i | − | 0.108233i | −0.998535 | − | 0.0541167i | \(-0.982766\pi\) | ||
0.998535 | − | 0.0541167i | \(-0.0172343\pi\) | |||||||
\(398\) | −3546.01 | −0.446597 | ||||||||
\(399\) | 7970.28 | − | 11046.2i | 1.00003 | − | 1.38597i | ||||
\(400\) | −517.915 | −0.0647393 | ||||||||
\(401\) | 7604.09 | 0.946958 | 0.473479 | − | 0.880805i | \(-0.342998\pi\) | ||||
0.473479 | + | 0.880805i | \(0.342998\pi\) | |||||||
\(402\) | 8871.86 | + | 6401.39i | 1.10072 | + | 0.794210i | ||||
\(403\) | −8606.71 | −1.06385 | ||||||||
\(404\) | −5129.20 | −0.631652 | ||||||||
\(405\) | 5472.04 | + | 7327.31i | 0.671377 | + | 0.899005i | ||||
\(406\) | − | 5087.86i | − | 0.621937i | ||||||
\(407\) | 4624.73i | 0.563242i | ||||||||
\(408\) | 3864.59 | + | 2788.45i | 0.468935 | + | 0.338355i | ||||
\(409\) | 8859.06i | 1.07103i | 0.844525 | + | 0.535516i | \(0.179883\pi\) | ||||
−0.844525 | + | 0.535516i | \(0.820117\pi\) | |||||||
\(410\) | 1778.89 | 0.214276 | ||||||||
\(411\) | −10859.0 | − | 7835.19i | −1.30325 | − | 0.940344i | ||||
\(412\) | − | 4843.77i | − | 0.579212i | ||||||
\(413\) | 15150.8 | − | 349.000i | 1.80514 | − | 0.0415815i | ||||
\(414\) | −2789.63 | − | 8397.58i | −0.331166 | − | 0.996904i | ||||
\(415\) | 6066.49i | 0.717572i | ||||||||
\(416\) | 1711.57i | 0.201722i | ||||||||
\(417\) | 852.362 | − | 1181.31i | 0.100097 | − | 0.138727i | ||||
\(418\) | 8726.17 | 1.02108 | ||||||||
\(419\) | −5885.62 | −0.686232 | −0.343116 | − | 0.939293i | \(-0.611482\pi\) | ||||
−0.343116 | + | 0.939293i | \(0.611482\pi\) | |||||||
\(420\) | −7070.75 | − | 5101.82i | −0.821470 | − | 0.592722i | ||||
\(421\) | 9980.94i | 1.15544i | 0.816234 | + | 0.577721i | \(0.196058\pi\) | ||||
−0.816234 | + | 0.577721i | \(0.803942\pi\) | |||||||
\(422\) | 1592.38i | 0.183687i | ||||||||
\(423\) | −4234.53 | − | 12747.2i | −0.486738 | − | 1.46522i | ||||
\(424\) | − | 4003.28i | − | 0.458530i | ||||||
\(425\) | − | 3710.90i | − | 0.423541i | ||||||
\(426\) | 3967.29 | + | 2862.55i | 0.451211 | + | 0.325566i | ||||
\(427\) | − | 1103.24i | − | 0.125034i | ||||||
\(428\) | − | 2472.36i | − | 0.279220i | ||||||
\(429\) | −12544.1 | − | 9051.07i | −1.41174 | − | 1.01862i | ||||
\(430\) | −6472.56 | −0.725895 | ||||||||
\(431\) | 9150.70 | 1.02268 | 0.511339 | − | 0.859379i | \(-0.329150\pi\) | ||||
0.511339 | + | 0.859379i | \(0.329150\pi\) | |||||||
\(432\) | 2141.60 | + | 672.603i | 0.238513 | + | 0.0749088i | ||||
\(433\) | −7782.99 | −0.863803 | −0.431902 | − | 0.901921i | \(-0.642157\pi\) | ||||
−0.431902 | + | 0.901921i | \(0.642157\pi\) | |||||||
\(434\) | − | 10762.1i | − | 1.19032i | ||||||
\(435\) | 2901.51 | − | 4021.28i | 0.319808 | − | 0.443231i | ||||
\(436\) | − | 59.1312i | − | 0.00649512i | ||||||
\(437\) | −12845.7 | −1.40617 | ||||||||
\(438\) | −7686.49 | − | 5546.10i | −0.838527 | − | 0.605030i | ||||
\(439\) | −6307.27 | −0.685717 | −0.342858 | − | 0.939387i | \(-0.611395\pi\) | ||||
−0.342858 | + | 0.939387i | \(0.611395\pi\) | |||||||
\(440\) | − | 5585.67i | − | 0.605196i | ||||||
\(441\) | −6599.01 | − | 19864.9i | −0.712559 | − | 2.14501i | ||||
\(442\) | −12263.5 | −1.31972 | ||||||||
\(443\) | −2388.29 | −0.256142 | −0.128071 | − | 0.991765i | \(-0.540879\pi\) | ||||
−0.128071 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(444\) | 1400.53 | + | 1010.54i | 0.149699 | + | 0.108014i | ||||
\(445\) | 881.702i | 0.0939251i | ||||||||
\(446\) | −8214.38 | −0.872112 | ||||||||
\(447\) | −7382.99 | + | 10232.3i | −0.781216 | + | 1.08271i | ||||
\(448\) | −2140.19 | −0.225702 | ||||||||
\(449\) | − | 804.443i | − | 0.0845523i | −0.999106 | − | 0.0422762i | \(-0.986539\pi\) | ||
0.999106 | − | 0.0422762i | \(-0.0134609\pi\) | |||||||
\(450\) | −551.053 | − | 1658.83i | −0.0577265 | − | 0.173773i | ||||
\(451\) | 3946.24i | 0.412020i | ||||||||
\(452\) | 3036.98 | 0.316034 | ||||||||
\(453\) | −2012.20 | − | 1451.88i | −0.208700 | − | 0.150585i | ||||
\(454\) | −2181.39 | −0.225501 | ||||||||
\(455\) | 22437.7 | 2.31186 | ||||||||
\(456\) | 1906.73 | − | 2642.59i | 0.195814 | − | 0.271383i | ||||
\(457\) | 7628.94i | 0.780890i | 0.920626 | + | 0.390445i | \(0.127679\pi\) | ||||
−0.920626 | + | 0.390445i | \(0.872321\pi\) | |||||||
\(458\) | 9949.79i | 1.01512i | ||||||||
\(459\) | −4819.25 | + | 15344.7i | −0.490073 | + | 1.56042i | ||||
\(460\) | 8222.64i | 0.833440i | ||||||||
\(461\) | − | 1278.14i | − | 0.129130i | −0.997913 | − | 0.0645651i | \(-0.979434\pi\) | ||
0.997913 | − | 0.0645651i | \(-0.0205660\pi\) | |||||||
\(462\) | 11317.7 | − | 15685.6i | 1.13972 | − | 1.57956i | ||||
\(463\) | 7402.48i | 0.743029i | 0.928427 | + | 0.371514i | \(0.121161\pi\) | ||||
−0.928427 | + | 0.371514i | \(0.878839\pi\) | |||||||
\(464\) | − | 1217.17i | − | 0.121780i | ||||||
\(465\) | 6137.41 | − | 8506.01i | 0.612077 | − | 0.848294i | ||||
\(466\) | −868.323 | −0.0863182 | ||||||||
\(467\) | 12702.0 | 1.25862 | 0.629312 | − | 0.777153i | \(-0.283337\pi\) | ||||
0.629312 | + | 0.777153i | \(0.283337\pi\) | |||||||
\(468\) | −5481.98 | + | 1821.08i | −0.541463 | + | 0.179871i | ||||
\(469\) | − | 35203.5i | − | 3.46599i | ||||||
\(470\) | 12481.6i | 1.22497i | ||||||||
\(471\) | −5027.17 | − | 3627.29i | −0.491804 | − | 0.354855i | ||||
\(472\) | 3624.54 | − | 83.4915i | 0.353460 | − | 0.00814197i | ||||
\(473\) | − | 14358.6i | − | 1.39579i | ||||||
\(474\) | 4104.08 | − | 5687.95i | 0.397693 | − | 0.551174i | ||||
\(475\) | −2537.50 | −0.245113 | ||||||||
\(476\) | − | 15334.7i | − | 1.47660i | ||||||
\(477\) | 12822.1 | − | 4259.44i | 1.23078 | − | 0.408860i | ||||
\(478\) | − | 5126.59i | − | 0.490554i | ||||||
\(479\) | − | 2126.89i | − | 0.202881i | −0.994842 | − | 0.101441i | \(-0.967655\pi\) | ||
0.994842 | − | 0.101441i | \(-0.0323452\pi\) | |||||||
\(480\) | −1691.54 | − | 1220.51i | −0.160850 | − | 0.116059i | ||||
\(481\) | −4444.32 | −0.421297 | ||||||||
\(482\) | 6872.32 | 0.649431 | ||||||||
\(483\) | −16660.8 | + | 23090.6i | −1.56955 | + | 2.17528i | ||||
\(484\) | 7067.09 | 0.663701 | ||||||||
\(485\) | −6889.14 | −0.644989 | ||||||||
\(486\) | 124.354 | + | 7574.97i | 0.0116066 | + | 0.707012i | ||||
\(487\) | −15234.4 | −1.41753 | −0.708764 | − | 0.705446i | \(-0.750747\pi\) | ||||
−0.708764 | + | 0.705446i | \(0.750747\pi\) | |||||||
\(488\) | − | 263.929i | − | 0.0244826i | ||||||
\(489\) | 989.206 | − | 1370.97i | 0.0914794 | − | 0.126784i | ||||
\(490\) | 19451.1i | 1.79329i | ||||||||
\(491\) | 1651.33i | 0.151779i | 0.997116 | + | 0.0758895i | \(0.0241796\pi\) | ||||
−0.997116 | + | 0.0758895i | \(0.975820\pi\) | |||||||
\(492\) | 1195.06 | + | 862.283i | 0.109507 | + | 0.0790136i | ||||
\(493\) | 8721.13 | 0.796714 | ||||||||
\(494\) | 8385.77i | 0.763752i | ||||||||
\(495\) | 17890.3 | − | 5943.07i | 1.62447 | − | 0.539639i | ||||
\(496\) | − | 2574.62i | − | 0.233072i | ||||||
\(497\) | − | 15742.2i | − | 1.42079i | ||||||
\(498\) | −2940.62 | + | 4075.48i | −0.264603 | + | 0.366720i | ||||
\(499\) | 4317.55 | 0.387335 | 0.193667 | − | 0.981067i | \(-0.437962\pi\) | ||||
0.193667 | + | 0.981067i | \(0.437962\pi\) | |||||||
\(500\) | − | 4648.08i | − | 0.415737i | ||||||
\(501\) | 1121.63 | + | 809.303i | 0.100022 | + | 0.0721696i | ||||
\(502\) | 9035.27i | 0.803314i | ||||||||
\(503\) | 8677.03 | 0.769164 | 0.384582 | − | 0.923091i | \(-0.374346\pi\) | ||||
0.384582 | + | 0.923091i | \(0.374346\pi\) | |||||||
\(504\) | −2277.14 | − | 6854.83i | −0.201253 | − | 0.605830i | ||||
\(505\) | 16086.1i | 1.41747i | ||||||||
\(506\) | −18240.9 | −1.60258 | ||||||||
\(507\) | 2018.23 | − | 2797.12i | 0.176791 | − | 0.245019i | ||||
\(508\) | −6538.43 | −0.571055 | ||||||||
\(509\) | 12695.8 | 1.10557 | 0.552783 | − | 0.833325i | \(-0.313566\pi\) | ||||
0.552783 | + | 0.833325i | \(0.313566\pi\) | |||||||
\(510\) | 8745.06 | − | 12120.0i | 0.759290 | − | 1.05232i | ||||
\(511\) | 30500.0i | 2.64039i | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 10492.7 | + | 3295.39i | 0.903049 | + | 0.283616i | ||||
\(514\) | − | 13734.9i | − | 1.17864i | ||||||
\(515\) | −15190.9 | −1.29979 | ||||||||
\(516\) | −4348.28 | − | 3137.45i | −0.370974 | − | 0.267672i | ||||
\(517\) | −27688.8 | −2.35542 | ||||||||
\(518\) | − | 5557.31i | − | 0.471379i | ||||||
\(519\) | −870.524 | + | 1206.48i | −0.0736258 | + | 0.102040i | ||||
\(520\) | 5367.78 | 0.452678 | ||||||||
\(521\) | 12284.8i | 1.03303i | 0.856279 | + | 0.516513i | \(0.172770\pi\) | ||||
−0.856279 | + | 0.516513i | \(0.827230\pi\) | |||||||
\(522\) | 3898.48 | − | 1295.05i | 0.326881 | − | 0.108588i | ||||
\(523\) | 17854.6 | 1.49279 | 0.746395 | − | 0.665503i | \(-0.231783\pi\) | ||||
0.746395 | + | 0.665503i | \(0.231783\pi\) | |||||||
\(524\) | 5364.14 | 0.447201 | ||||||||
\(525\) | −3291.11 | + | 4561.24i | −0.273592 | + | 0.379179i | ||||
\(526\) | 4.81149i | 0.000398842i | ||||||||
\(527\) | 18447.4 | 1.52482 | ||||||||
\(528\) | 2707.55 | − | 3752.46i | 0.223165 | − | 0.309290i | ||||
\(529\) | 14685.3 | 1.20698 | ||||||||
\(530\) | −12555.0 | −1.02897 | ||||||||
\(531\) | 4123.87 | + | 11520.2i | 0.337026 | + | 0.941495i | ||||
\(532\) | −10485.8 | −0.854544 | ||||||||
\(533\) | −3792.30 | −0.308185 | ||||||||
\(534\) | −427.388 | + | 592.329i | −0.0346347 | + | 0.0480011i | ||||
\(535\) | −7753.77 | −0.626588 | ||||||||
\(536\) | − | 8421.76i | − | 0.678666i | ||||||
\(537\) | 8599.09 | − | 11917.7i | 0.691021 | − | 0.957704i | ||||
\(538\) | −1654.97 | −0.132622 | ||||||||
\(539\) | −43149.7 | −3.44822 | ||||||||
\(540\) | 2109.40 | − | 6716.44i | 0.168100 | − | 0.535240i | ||||
\(541\) | 6201.21i | 0.492811i | 0.969167 | + | 0.246405i | \(0.0792495\pi\) | ||||
−0.969167 | + | 0.246405i | \(0.920751\pi\) | |||||||
\(542\) | −5949.04 | −0.471463 | ||||||||
\(543\) | −2271.02 | + | 3147.47i | −0.179482 | + | 0.248749i | ||||
\(544\) | − | 3668.52i | − | 0.289130i | ||||||
\(545\) | −185.446 | −0.0145755 | ||||||||
\(546\) | 15073.7 | + | 10876.2i | 1.18149 | + | 0.852491i | ||||
\(547\) | 17428.0 | 1.36228 | 0.681142 | − | 0.732151i | \(-0.261484\pi\) | ||||
0.681142 | + | 0.732151i | \(0.261484\pi\) | |||||||
\(548\) | 10308.1i | 0.803540i | ||||||||
\(549\) | 845.338 | − | 280.817i | 0.0657161 | − | 0.0218305i | ||||
\(550\) | −3603.24 | −0.279350 | ||||||||
\(551\) | − | 5963.49i | − | 0.461077i | ||||||
\(552\) | −3985.77 | + | 5523.99i | −0.307329 | + | 0.425936i | ||||
\(553\) | −22569.8 | −1.73556 | ||||||||
\(554\) | 10077.7 | 0.772856 | ||||||||
\(555\) | 3169.23 | − | 4392.32i | 0.242390 | − | 0.335934i | ||||
\(556\) | −1121.38 | −0.0855344 | ||||||||
\(557\) | 5117.71i | 0.389308i | 0.980872 | + | 0.194654i | \(0.0623584\pi\) | ||||
−0.980872 | + | 0.194654i | \(0.937642\pi\) | |||||||
\(558\) | 8246.25 | − | 2739.36i | 0.625612 | − | 0.207825i | ||||
\(559\) | 13798.4 | 1.04403 | ||||||||
\(560\) | 6712.03i | 0.506491i | ||||||||
\(561\) | 26886.7 | + | 19399.8i | 2.02345 | + | 1.46000i | ||||
\(562\) | 5229.25i | 0.392496i | ||||||||
\(563\) | 5851.37 | 0.438021 | 0.219010 | − | 0.975723i | \(-0.429717\pi\) | ||||
0.219010 | + | 0.975723i | \(0.429717\pi\) | |||||||
\(564\) | −6050.22 | + | 8385.17i | −0.451703 | + | 0.626027i | ||||
\(565\) | − | 9524.50i | − | 0.709201i | ||||||
\(566\) | − | 17820.1i | − | 1.32338i | ||||||
\(567\) | 19532.5 | − | 14586.9i | 1.44671 | − | 1.08041i | ||||
\(568\) | − | 3766.02i | − | 0.278202i | ||||||
\(569\) | −19207.5 | −1.41515 | −0.707576 | − | 0.706637i | \(-0.750211\pi\) | ||||
−0.707576 | + | 0.706637i | \(0.750211\pi\) | |||||||
\(570\) | −8287.64 | − | 5979.85i | −0.609002 | − | 0.439418i | ||||
\(571\) | 449.899i | 0.0329732i | 0.999864 | + | 0.0164866i | \(0.00524808\pi\) | ||||
−0.999864 | + | 0.0164866i | \(0.994752\pi\) | |||||||
\(572\) | 11907.7i | 0.870432i | ||||||||
\(573\) | −2339.41 | + | 3242.25i | −0.170559 | + | 0.236382i | ||||
\(574\) | − | 4742.00i | − | 0.344821i | ||||||
\(575\) | 5304.31 | 0.384704 | ||||||||
\(576\) | −544.760 | − | 1639.88i | −0.0394069 | − | 0.118626i | ||||
\(577\) | −4649.13 | −0.335435 | −0.167717 | − | 0.985835i | \(-0.553640\pi\) | ||||
−0.167717 | + | 0.985835i | \(0.553640\pi\) | |||||||
\(578\) | 16459.3 | 1.18445 | ||||||||
\(579\) | −12920.2 | + | 17906.5i | −0.927370 | + | 1.28527i | ||||
\(580\) | −3817.26 | −0.273282 | ||||||||
\(581\) | 16171.5 | 1.15475 | ||||||||
\(582\) | −4628.14 | − | 3339.38i | −0.329626 | − | 0.237838i | ||||
\(583\) | − | 27851.7i | − | 1.97856i | ||||||
\(584\) | 7296.53i | 0.517008i | ||||||||
\(585\) | 5711.24 | + | 17192.4i | 0.403642 | + | 1.21508i | ||||
\(586\) | 2910.53i | 0.205176i | ||||||||
\(587\) | −13192.8 | −0.927641 | −0.463820 | − | 0.885929i | \(-0.653522\pi\) | ||||
−0.463820 | + | 0.885929i | \(0.653522\pi\) | |||||||
\(588\) | −9428.54 | + | 13067.3i | −0.661269 | + | 0.916471i | ||||
\(589\) | − | 12614.3i | − | 0.882448i | ||||||
\(590\) | −261.844 | − | 11367.2i | −0.0182711 | − | 0.793186i | ||||
\(591\) | 12345.9 | + | 8908.02i | 0.859291 | + | 0.620012i | ||||
\(592\) | − | 1329.48i | − | 0.0922994i | ||||||
\(593\) | − | 9442.45i | − | 0.653887i | −0.945044 | − | 0.326944i | \(-0.893981\pi\) | ||
0.945044 | − | 0.326944i | \(-0.106019\pi\) | |||||||
\(594\) | 14899.6 | + | 4679.43i | 1.02919 | + | 0.323231i | ||||
\(595\) | −48092.2 | −3.31360 | ||||||||
\(596\) | 9713.17 | 0.667562 | ||||||||
\(597\) | −5390.66 | + | 7471.06i | −0.369556 | + | 0.512178i | ||||
\(598\) | − | 17529.3i | − | 1.19871i | ||||||
\(599\) | 2266.84i | 0.154625i | 0.997007 | + | 0.0773127i | \(0.0246340\pi\) | ||||
−0.997007 | + | 0.0773127i | \(0.975366\pi\) | |||||||
\(600\) | −787.335 | + | 1091.19i | −0.0535714 | + | 0.0742460i | ||||
\(601\) | 28113.0i | 1.90807i | 0.299689 | + | 0.954037i | \(0.403117\pi\) | ||||
−0.299689 | + | 0.954037i | \(0.596883\pi\) | |||||||
\(602\) | 17254.0i | 1.16814i | ||||||||
\(603\) | 26974.1 | − | 8960.63i | 1.82167 | − | 0.605149i | ||||
\(604\) | 1910.11i | 0.128678i | ||||||||
\(605\) | − | 22163.6i | − | 1.48939i | ||||||
\(606\) | −7797.42 | + | 10806.7i | −0.522688 | + | 0.724407i | ||||
\(607\) | −22442.7 | −1.50069 | −0.750345 | − | 0.661046i | \(-0.770113\pi\) | ||||
−0.750345 | + | 0.661046i | \(0.770113\pi\) | |||||||
\(608\) | −2508.53 | −0.167326 | ||||||||
\(609\) | −10719.6 | − | 7734.58i | −0.713265 | − | 0.514648i | ||||
\(610\) | −827.728 | −0.0549405 | ||||||||
\(611\) | − | 26608.7i | − | 1.76182i | ||||||
\(612\) | 11749.9 | − | 3903.25i | 0.776081 | − | 0.257810i | ||||
\(613\) | 22313.5i | 1.47020i | 0.677958 | + | 0.735100i | \(0.262865\pi\) | ||||
−0.677958 | + | 0.735100i | \(0.737135\pi\) | |||||||
\(614\) | −9890.70 | −0.650092 | ||||||||
\(615\) | 2704.27 | − | 3747.92i | 0.177312 | − | 0.245741i | ||||
\(616\) | −14889.8 | −0.973906 | ||||||||
\(617\) | 13469.4i | 0.878861i | 0.898277 | + | 0.439431i | \(0.144820\pi\) | ||||
−0.898277 | + | 0.439431i | \(0.855180\pi\) | |||||||
\(618\) | −10205.3 | − | 7363.50i | −0.664266 | − | 0.479294i | ||||
\(619\) | 2388.74 | 0.155108 | 0.0775538 | − | 0.996988i | \(-0.475289\pi\) | ||||
0.0775538 | + | 0.996988i | \(0.475289\pi\) | |||||||
\(620\) | −8074.47 | −0.523030 | ||||||||
\(621\) | −21933.6 | − | 6888.57i | −1.41733 | − | 0.445135i | ||||
\(622\) | 13565.1i | 0.874457i | ||||||||
\(623\) | 2350.36 | 0.151148 | ||||||||
\(624\) | 3606.08 | + | 2601.93i | 0.231344 | + | 0.166924i | ||||
\(625\) | −18623.4 | −1.19190 | ||||||||
\(626\) | − | 20378.4i | − | 1.30109i | ||||||
\(627\) | 13265.5 | − | 18385.1i | 0.844935 | − | 1.17102i | ||||
\(628\) | 4772.12i | 0.303230i | ||||||||
\(629\) | 9525.83 | 0.603847 | ||||||||
\(630\) | −21498.0 | + | 7141.50i | −1.35952 | + | 0.451626i | ||||
\(631\) | −17418.9 | −1.09895 | −0.549474 | − | 0.835511i | \(-0.685172\pi\) | ||||
−0.549474 | + | 0.835511i | \(0.685172\pi\) | |||||||
\(632\) | −5399.38 | −0.339835 | ||||||||
\(633\) | 3354.96 | + | 2420.74i | 0.210660 | + | 0.151999i | ||||
\(634\) | − | 14679.0i | − | 0.919524i | ||||||
\(635\) | 20505.7i | 1.28148i | ||||||||
\(636\) | −8434.48 | − | 6085.80i | −0.525863 | − | 0.379430i | ||||
\(637\) | − | 41466.5i | − | 2.57922i | ||||||
\(638\) | − | 8468.11i | − | 0.525479i | ||||||
\(639\) | 12062.2 | − | 4006.99i | 0.746748 | − | 0.248066i | ||||
\(640\) | 1605.72i | 0.0991746i | ||||||||
\(641\) | 21873.3i | 1.34780i | 0.738821 | + | 0.673902i | \(0.235383\pi\) | ||||
−0.738821 | + | 0.673902i | \(0.764617\pi\) | |||||||
\(642\) | −5209.00 | − | 3758.49i | −0.320222 | − | 0.231053i | ||||
\(643\) | 19302.9 | 1.18388 | 0.591939 | − | 0.805983i | \(-0.298363\pi\) | ||||
0.591939 | + | 0.805983i | \(0.298363\pi\) | |||||||
\(644\) | 21919.2 | 1.34121 | ||||||||
\(645\) | −9839.61 | + | 13637.0i | −0.600673 | + | 0.832489i | ||||
\(646\) | − | 17973.8i | − | 1.09469i | ||||||
\(647\) | 5086.48i | 0.309073i | 0.987987 | + | 0.154537i | \(0.0493884\pi\) | ||||
−0.987987 | + | 0.154537i | \(0.950612\pi\) | |||||||
\(648\) | 4672.77 | − | 3489.63i | 0.283277 | − | 0.211552i | ||||
\(649\) | 25216.7 | − | 580.867i | 1.52518 | − | 0.0351326i | ||||
\(650\) | − | 3462.68i | − | 0.208950i | ||||||
\(651\) | −22674.5 | − | 16360.6i | −1.36511 | − | 0.984978i | ||||
\(652\) | −1301.41 | −0.0781707 | ||||||||
\(653\) | − | 8037.99i | − | 0.481701i | −0.970562 | − | 0.240851i | \(-0.922574\pi\) | ||
0.970562 | − | 0.240851i | \(-0.0774264\pi\) | |||||||
\(654\) | −124.583 | − | 89.8914i | −0.00744890 | − | 0.00537467i | ||||
\(655\) | − | 16822.9i | − | 1.00355i | ||||||
\(656\) | − | 1134.43i | − | 0.0675185i | ||||||
\(657\) | −23370.0 | + | 7763.40i | −1.38775 | + | 0.461003i | ||||
\(658\) | 33272.3 | 1.97126 | ||||||||
\(659\) | −10316.1 | −0.609798 | −0.304899 | − | 0.952385i | \(-0.598623\pi\) | ||||
−0.304899 | + | 0.952385i | \(0.598623\pi\) | |||||||
\(660\) | −11768.4 | − | 8491.35i | −0.694067 | − | 0.500796i | ||||
\(661\) | 18597.1 | 1.09432 | 0.547160 | − | 0.837028i | \(-0.315709\pi\) | ||||
0.547160 | + | 0.837028i | \(0.315709\pi\) | |||||||
\(662\) | 3774.50 | 0.221601 | ||||||||
\(663\) | −18643.0 | + | 25837.9i | −1.09206 | + | 1.51351i | ||||
\(664\) | 3868.72 | 0.226107 | ||||||||
\(665\) | 32885.4i | 1.91765i | ||||||||
\(666\) | 4258.19 | − | 1414.55i | 0.247750 | − | 0.0823011i | ||||
\(667\) | 12465.9i | 0.723659i | ||||||||
\(668\) | − | 1064.73i | − | 0.0616701i | ||||||
\(669\) | −12487.5 | + | 17306.8i | −0.721667 | + | 1.00018i | ||||
\(670\) | −26412.1 | −1.52297 | ||||||||
\(671\) | − | 1836.21i | − | 0.105642i | ||||||
\(672\) | −3253.53 | + | 4509.16i | −0.186767 | + | 0.258846i | ||||
\(673\) | − | 8336.73i | − | 0.477500i | −0.971081 | − | 0.238750i | \(-0.923262\pi\) | ||
0.971081 | − | 0.238750i | \(-0.0767376\pi\) | |||||||
\(674\) | 5899.17i | 0.337133i | ||||||||
\(675\) | −4332.68 | − | 1360.74i | −0.247059 | − | 0.0775927i | ||||
\(676\) | −2655.22 | −0.151071 | ||||||||
\(677\) | − | 324.448i | − | 0.0184188i | −0.999958 | − | 0.00920942i | \(-0.997069\pi\) | ||
0.999958 | − | 0.00920942i | \(-0.00293149\pi\) | |||||||
\(678\) | 4616.82 | − | 6398.58i | 0.261516 | − | 0.362442i | ||||
\(679\) | 18364.4i | 1.03794i | ||||||||
\(680\) | −11505.1 | −0.648826 | ||||||||
\(681\) | −3316.15 | + | 4595.95i | −0.186601 | + | 0.258615i | ||||
\(682\) | − | 17912.2i | − | 1.00571i | ||||||
\(683\) | −21486.8 | −1.20376 | −0.601882 | − | 0.798585i | \(-0.705582\pi\) | ||||
−0.601882 | + | 0.798585i | \(0.705582\pi\) | |||||||
\(684\) | −2669.04 | − | 8034.56i | −0.149200 | − | 0.449136i | ||||
\(685\) | 32328.0 | 1.80320 | ||||||||
\(686\) | 28910.7 | 1.60906 | ||||||||
\(687\) | 20963.1 | + | 15125.7i | 1.16418 | + | 0.840002i | ||||
\(688\) | 4127.68i | 0.228730i | ||||||||
\(689\) | 26765.2 | 1.47993 | ||||||||
\(690\) | 17324.2 | + | 12500.1i | 0.955827 | + | 0.689666i | ||||
\(691\) | 23522.7i | 1.29500i | 0.762064 | + | 0.647501i | \(0.224186\pi\) | ||||
−0.762064 | + | 0.647501i | \(0.775814\pi\) | |||||||
\(692\) | 1145.27 | 0.0629144 | ||||||||
\(693\) | −15842.5 | − | 47690.4i | −0.868408 | − | 2.61416i | ||||
\(694\) | 8348.39 | 0.456629 | ||||||||
\(695\) | 3516.85i | 0.191945i | ||||||||
\(696\) | −2564.45 | − | 1850.35i | −0.139662 | − | 0.100772i | ||||
\(697\) | 8128.29 | 0.441723 | ||||||||
\(698\) | 11065.4i | 0.600047i | ||||||||
\(699\) | −1320.03 | + | 1829.46i | −0.0714278 | + | 0.0989937i | ||||
\(700\) | 4329.84 | 0.233789 | ||||||||
\(701\) | −4275.19 | −0.230345 | −0.115172 | − | 0.993346i | \(-0.536742\pi\) | ||||
−0.115172 | + | 0.993346i | \(0.536742\pi\) | |||||||
\(702\) | −4496.89 | + | 14318.3i | −0.241773 | + | 0.769816i | ||||
\(703\) | − | 6513.74i | − | 0.349460i | ||||||
\(704\) | −3562.09 | −0.190698 | ||||||||
\(705\) | 26297.4 | + | 18974.6i | 1.40485 | + | 1.01365i | ||||
\(706\) | −2687.92 | −0.143288 | ||||||||
\(707\) | 42880.8 | 2.28105 | ||||||||
\(708\) | 5334.13 | − | 7763.43i | 0.283148 | − | 0.412101i | ||||
\(709\) | −3259.59 | −0.172661 | −0.0863305 | − | 0.996267i | \(-0.527514\pi\) | ||||
−0.0863305 | + | 0.996267i | \(0.527514\pi\) | |||||||
\(710\) | −11810.9 | −0.624303 | ||||||||
\(711\) | −5744.86 | − | 17293.7i | −0.303023 | − | 0.912185i | ||||
\(712\) | 562.278 | 0.0295959 | ||||||||
\(713\) | 26368.4i | 1.38500i | ||||||||
\(714\) | −32308.5 | − | 23311.8i | −1.69344 | − | 1.22188i | ||||
\(715\) | 37344.7 | 1.95331 | ||||||||
\(716\) | −11313.1 | −0.590489 | ||||||||
\(717\) | −10801.2 | − | 7793.45i | −0.562590 | − | 0.405930i | ||||
\(718\) | − | 2084.21i | − | 0.108332i | ||||||
\(719\) | 14322.0 | 0.742865 | 0.371433 | − | 0.928460i | \(-0.378867\pi\) | ||||
0.371433 | + | 0.928460i | \(0.378867\pi\) | |||||||
\(720\) | −5142.97 | + | 1708.46i | −0.266204 | + | 0.0884316i | ||||
\(721\) | 40494.5i | 2.09167i | ||||||||
\(722\) | 1427.56 | 0.0735848 | ||||||||
\(723\) | 10447.3 | − | 14479.2i | 0.537400 | − | 0.744797i | ||||
\(724\) | 2987.78 | 0.153370 | ||||||||
\(725\) | 2462.46i | 0.126143i | ||||||||
\(726\) | 10743.4 | − | 14889.6i | 0.549208 | − | 0.761163i | ||||
\(727\) | 27243.3 | 1.38982 | 0.694909 | − | 0.719098i | \(-0.255445\pi\) | ||||
0.694909 | + | 0.719098i | \(0.255445\pi\) | |||||||
\(728\) | − | 14308.9i | − | 0.728468i | ||||||
\(729\) | 16148.7 | + | 11253.5i | 0.820437 | + | 0.571736i | ||||
\(730\) | 22883.2 | 1.16020 | ||||||||
\(731\) | −29575.1 | −1.49641 | ||||||||
\(732\) | −556.070 | − | 401.226i | −0.0280778 | − | 0.0202592i | ||||
\(733\) | 20545.8 | 1.03530 | 0.517652 | − | 0.855591i | \(-0.326806\pi\) | ||||
0.517652 | + | 0.855591i | \(0.326806\pi\) | |||||||
\(734\) | − | 7679.47i | − | 0.386178i | ||||||
\(735\) | 40981.3 | + | 29569.6i | 2.05662 | + | 1.48393i | ||||
\(736\) | 5243.73 | 0.262618 | ||||||||
\(737\) | − | 58591.9i | − | 2.92844i | ||||||
\(738\) | 3633.47 | − | 1207.02i | 0.181233 | − | 0.0602046i | ||||
\(739\) | − | 3615.91i | − | 0.179991i | −0.995942 | − | 0.0899956i | \(-0.971315\pi\) | ||
0.995942 | − | 0.0899956i | \(-0.0286853\pi\) | |||||||
\(740\) | −4169.48 | −0.207126 | ||||||||
\(741\) | 17667.9 | + | 12748.1i | 0.875906 | + | 0.632000i | ||||
\(742\) | 33468.0i | 1.65586i | ||||||||
\(743\) | − | 36180.7i | − | 1.78646i | −0.449600 | − | 0.893230i | \(-0.648434\pi\) | ||
0.449600 | − | 0.893230i | \(-0.351566\pi\) | |||||||
\(744\) | −5424.44 | − | 3913.94i | −0.267298 | − | 0.192866i | ||||
\(745\) | − | 30462.2i | − | 1.49805i | ||||||
\(746\) | 8313.00 | 0.407990 | ||||||||
\(747\) | 4116.26 | + | 12391.1i | 0.201614 | + | 0.606917i | ||||
\(748\) | − | 25522.7i | − | 1.24759i | ||||||
\(749\) | 20669.3i | 1.00833i | ||||||||
\(750\) | −9793.00 | − | 7066.02i | −0.476786 | − | 0.344020i | ||||
\(751\) | 13254.4i | 0.644019i | 0.946736 | + | 0.322009i | \(0.104358\pi\) | ||||
−0.946736 | + | 0.322009i | \(0.895642\pi\) | |||||||
\(752\) | 7959.76 | 0.385988 | ||||||||
\(753\) | 19036.3 | + | 13735.4i | 0.921277 | + | 0.664737i | ||||
\(754\) | 8137.78 | 0.393051 | ||||||||
\(755\) | 5990.45 | 0.288761 | ||||||||
\(756\) | −17904.1 | − | 5623.05i | −0.861329 | − | 0.270514i | ||||
\(757\) | −19347.1 | −0.928904 | −0.464452 | − | 0.885598i | \(-0.653749\pi\) | ||||
−0.464452 | + | 0.885598i | \(0.653749\pi\) | |||||||
\(758\) | −8390.20 | −0.402039 | ||||||||
\(759\) | −27729.8 | + | 38431.5i | −1.32612 | + | 1.83791i | ||||
\(760\) | 7867.18i | 0.375490i | ||||||||
\(761\) | − | 24236.4i | − | 1.15449i | −0.816570 | − | 0.577247i | \(-0.804127\pi\) | ||
0.816570 | − | 0.577247i | \(-0.195873\pi\) | |||||||
\(762\) | −9939.73 | + | 13775.7i | −0.472544 | + | 0.654912i | ||||
\(763\) | 494.345i | 0.0234554i | ||||||||
\(764\) | 3077.76 | 0.145745 | ||||||||
\(765\) | −12241.3 | − | 36849.8i | −0.578542 | − | 1.74158i | ||||
\(766\) | − | 15548.8i | − | 0.733421i | ||||||
\(767\) | 558.208 | + | 24233.0i | 0.0262787 | + | 1.14081i | ||||
\(768\) | −778.344 | + | 1078.73i | −0.0365704 | + | 0.0506839i | ||||
\(769\) | 23437.6i | 1.09907i | 0.835472 | + | 0.549533i | \(0.185195\pi\) | ||||
−0.835472 | + | 0.549533i | \(0.814805\pi\) | |||||||
\(770\) | 46697.0i | 2.18551i | ||||||||
\(771\) | −28937.9 | − | 20879.8i | −1.35172 | − | 0.975315i | ||||
\(772\) | 16998.1 | 0.792453 | ||||||||
\(773\) | −2034.21 | −0.0946514 | −0.0473257 | − | 0.998880i | \(-0.515070\pi\) | ||||
−0.0473257 | + | 0.998880i | \(0.515070\pi\) | |||||||
\(774\) | −13220.5 | + | 4391.79i | −0.613957 | + | 0.203953i | ||||
\(775\) | 5208.73i | 0.241423i | ||||||||
\(776\) | 4393.33i | 0.203236i | ||||||||
\(777\) | −11708.6 | − | 8448.24i | −0.540599 | − | 0.390063i | ||||
\(778\) | − | 8226.72i | − | 0.379103i | ||||||
\(779\) | − | 5558.11i | − | 0.255635i | ||||||
\(780\) | 8160.11 | − | 11309.3i | 0.374588 | − | 0.519152i | ||||
\(781\) | − | 26200.9i | − | 1.20044i | ||||||
\(782\) | 37571.8i | 1.71811i | ||||||||
\(783\) | 3197.94 | − | 10182.4i | 0.145958 | − | 0.464737i | ||||
\(784\) | 12404.3 | 0.565066 | ||||||||
\(785\) | 14966.2 | 0.680468 | ||||||||
\(786\) | 8154.58 | − | 11301.7i | 0.370056 | − | 0.512871i | ||||
\(787\) | −23012.9 | −1.04234 | −0.521170 | − | 0.853453i | \(-0.674504\pi\) | ||||
−0.521170 | + | 0.853453i | \(0.674504\pi\) | |||||||
\(788\) | − | 11719.5i | − | 0.529810i | ||||||
\(789\) | 10.1373 | + | 7.31443i | 0.000457410 | + | 0.000330039i | ||||
\(790\) | 16933.4i | 0.762613i | ||||||||
\(791\) | −25389.6 | −1.14128 | ||||||||
\(792\) | −3790.01 | − | 11409.0i | −0.170041 | − | 0.511871i | ||||
\(793\) | 1764.58 | 0.0790190 | ||||||||
\(794\) | 1712.29i | 0.0765326i | ||||||||
\(795\) | −19086.1 | + | 26452.0i | −0.851467 | + | 1.18007i | ||||
\(796\) | 7092.03 | 0.315792 | ||||||||
\(797\) | −8204.42 | −0.364637 | −0.182318 | − | 0.983240i | \(-0.558360\pi\) | ||||
−0.182318 | + | 0.983240i | \(0.558360\pi\) | |||||||
\(798\) | −15940.6 | + | 22092.5i | −0.707130 | + | 0.980030i | ||||
\(799\) | 57032.3i | 2.52523i | ||||||||
\(800\) | 1035.83 | 0.0457776 | ||||||||
\(801\) | 598.256 | + | 1800.92i | 0.0263899 | + | 0.0794412i | ||||
\(802\) | −15208.2 | −0.669600 | ||||||||
\(803\) | 50763.4i | 2.23089i | ||||||||
\(804\) | −17743.7 | − | 12802.8i | −0.778325 | − | 0.561591i | ||||
\(805\) | − | 68742.4i | − | 3.00975i | ||||||
\(806\) | 17213.4 | 0.752254 | ||||||||
\(807\) | −2515.89 | + | 3486.84i | −0.109744 | + | 0.152097i | ||||
\(808\) | 10258.4 | 0.446645 | ||||||||
\(809\) | 17732.7 | 0.770640 | 0.385320 | − | 0.922783i | \(-0.374091\pi\) | ||||
0.385320 | + | 0.922783i | \(0.374091\pi\) | |||||||
\(810\) | −10944.1 | − | 14654.6i | −0.474736 | − | 0.635692i | ||||
\(811\) | − | 13848.3i | − | 0.599604i | −0.954001 | − | 0.299802i | \(-0.903079\pi\) | ||
0.954001 | − | 0.299802i | \(-0.0969206\pi\) | |||||||
\(812\) | 10175.7i | 0.439776i | ||||||||
\(813\) | −9043.74 | + | 12534.0i | −0.390133 | + | 0.540696i | ||||
\(814\) | − | 9249.46i | − | 0.398272i | ||||||
\(815\) | 4081.46i | 0.175420i | ||||||||
\(816\) | −7729.17 | − | 5576.89i | −0.331587 | − | 0.239253i | ||||
\(817\) | 20223.4i | 0.866007i | ||||||||
\(818\) | − | 17718.1i | − | 0.757335i | ||||||
\(819\) | 45830.1 | − | 15224.5i | 1.95535 | − | 0.649557i | ||||
\(820\) | −3557.78 | −0.151516 | ||||||||
\(821\) | −16741.1 | −0.711653 | −0.355827 | − | 0.934552i | \(-0.615801\pi\) | ||||
−0.355827 | + | 0.934552i | \(0.615801\pi\) | |||||||
\(822\) | 21718.0 | + | 15670.4i | 0.921536 | + | 0.664924i | ||||
\(823\) | 25986.4i | 1.10064i | 0.834953 | + | 0.550322i | \(0.185495\pi\) | ||||
−0.834953 | + | 0.550322i | \(0.814505\pi\) | |||||||
\(824\) | 9687.53i | 0.409564i | ||||||||
\(825\) | −5477.65 | + | 7591.62i | −0.231160 | + | 0.320371i | ||||
\(826\) | −30301.6 | + | 698.000i | −1.27643 | + | 0.0294026i | ||||
\(827\) | − | 36797.3i | − | 1.54724i | −0.633649 | − | 0.773620i | \(-0.718444\pi\) | ||
0.633649 | − | 0.773620i | \(-0.281556\pi\) | |||||||
\(828\) | 5579.26 | + | 16795.2i | 0.234170 | + | 0.704918i | ||||
\(829\) | −4459.84 | −0.186848 | −0.0934238 | − | 0.995626i | \(-0.529781\pi\) | ||||
−0.0934238 | + | 0.995626i | \(0.529781\pi\) | |||||||
\(830\) | − | 12133.0i | − | 0.507400i | ||||||
\(831\) | 15320.2 | − | 21232.7i | 0.639533 | − | 0.886346i | ||||
\(832\) | − | 3423.14i | − | 0.142639i | ||||||
\(833\) | 88878.0i | 3.69681i | ||||||||
\(834\) | −1704.72 | + | 2362.62i | −0.0707791 | + | 0.0980947i | ||||
\(835\) | −3339.18 | −0.138392 | ||||||||
\(836\) | −17452.3 | −0.722011 | ||||||||
\(837\) | 6764.44 | − | 21538.3i | 0.279347 | − | 0.889454i | ||||
\(838\) | 11771.2 | 0.485240 | ||||||||
\(839\) | 236.762 | 0.00974249 | 0.00487124 | − | 0.999988i | \(-0.498449\pi\) | ||||
0.00487124 | + | 0.999988i | \(0.498449\pi\) | |||||||
\(840\) | 14141.5 | + | 10203.6i | 0.580867 | + | 0.419118i | ||||
\(841\) | 18601.9 | 0.762715 | ||||||||
\(842\) | − | 19961.9i | − | 0.817021i | ||||||
\(843\) | 11017.5 | + | 7949.52i | 0.450132 | + | 0.324788i | ||||
\(844\) | − | 3184.76i | − | 0.129886i | ||||||
\(845\) | 8327.23i | 0.339012i | ||||||||
\(846\) | 8469.07 | + | 25494.3i | 0.344176 | + | 1.03607i | ||||
\(847\) | −59081.8 | −2.39678 | ||||||||
\(848\) | 8006.57i | 0.324230i | ||||||||
\(849\) | −37544.9 | − | 27090.1i | −1.51771 | − | 1.09509i | ||||
\(850\) | 7421.80i | 0.299489i | ||||||||
\(851\) | 13616.1i | 0.548476i | ||||||||
\(852\) | −7934.58 | − | 5725.11i | −0.319054 | − | 0.230210i | ||||
\(853\) | 23034.2 | 0.924590 | 0.462295 | − | 0.886726i | \(-0.347026\pi\) | ||||
0.462295 | + | 0.886726i | \(0.347026\pi\) | |||||||
\(854\) | 2206.48i | 0.0884125i | ||||||||
\(855\) | −25197.8 | + | 8370.57i | −1.00789 | + | 0.334816i | ||||
\(856\) | 4944.73i | 0.197438i | ||||||||
\(857\) | −31941.4 | −1.27316 | −0.636579 | − | 0.771211i | \(-0.719651\pi\) | ||||
−0.636579 | + | 0.771211i | \(0.719651\pi\) | |||||||
\(858\) | 25088.3 | + | 18102.1i | 0.998251 | + | 0.720276i | ||||
\(859\) | − | 48871.3i | − | 1.94117i | −0.240757 | − | 0.970585i | \(-0.577396\pi\) | ||
0.240757 | − | 0.970585i | \(-0.422604\pi\) | |||||||
\(860\) | 12945.1 | 0.513285 | ||||||||
\(861\) | −9990.88 | − | 7208.80i | −0.395457 | − | 0.285337i | ||||
\(862\) | −18301.4 | −0.723142 | ||||||||
\(863\) | 5868.09 | 0.231463 | 0.115731 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115731 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(864\) | −4283.20 | − | 1345.21i | −0.168654 | − | 0.0529685i | ||||
\(865\) | − | 3591.78i | − | 0.141184i | ||||||
\(866\) | 15566.0 | 0.610801 | ||||||||
\(867\) | 25021.4 | − | 34677.8i | 0.980128 | − | 1.35839i | ||||
\(868\) | 21524.2i | 0.841680i | ||||||||
\(869\) | −37564.6 | −1.46639 | ||||||||
\(870\) | −5803.01 | + | 8042.56i | −0.226139 | + | 0.313412i | ||||
\(871\) | 56306.3 | 2.19043 | ||||||||
\(872\) | 118.262i | 0.00459274i | ||||||||
\(873\) | −14071.4 | + | 4674.44i | −0.545527 | + | 0.181221i | ||||
\(874\) | 25691.5 | 0.994311 | ||||||||
\(875\) | 38858.6i | 1.50133i | ||||||||
\(876\) | 15373.0 | + | 11092.2i | 0.592928 | + | 0.427820i | ||||
\(877\) | 17315.4 | 0.666705 | 0.333353 | − | 0.942802i | \(-0.391820\pi\) | ||||
0.333353 | + | 0.942802i | \(0.391820\pi\) | |||||||
\(878\) | 12614.5 | 0.484875 | ||||||||
\(879\) | 6132.17 | + | 4424.60i | 0.235305 | + | 0.169782i | ||||
\(880\) | 11171.3i | 0.427938i | ||||||||
\(881\) | 31653.0 | 1.21046 | 0.605231 | − | 0.796050i | \(-0.293081\pi\) | ||||
0.605231 | + | 0.796050i | \(0.293081\pi\) | |||||||
\(882\) | 13198.0 | + | 39729.8i | 0.503855 | + | 1.51675i | ||||
\(883\) | −32748.3 | −1.24810 | −0.624048 | − | 0.781386i | \(-0.714513\pi\) | ||||
−0.624048 | + | 0.781386i | \(0.714513\pi\) | |||||||
\(884\) | 24527.0 | 0.933183 | ||||||||
\(885\) | −24347.5 | − | 16728.8i | −0.924782 | − | 0.635402i | ||||
\(886\) | 4776.58 | 0.181120 | ||||||||
\(887\) | 24272.6 | 0.918823 | 0.459411 | − | 0.888224i | \(-0.348060\pi\) | ||||
0.459411 | + | 0.888224i | \(0.348060\pi\) | |||||||
\(888\) | −2801.07 | − | 2021.08i | −0.105853 | − | 0.0763772i | ||||
\(889\) | 54662.2 | 2.06222 | ||||||||
\(890\) | − | 1763.40i | − | 0.0664151i | ||||||
\(891\) | 32509.4 | − | 24278.0i | 1.22234 | − | 0.912845i | ||||
\(892\) | 16428.8 | 0.616677 | ||||||||
\(893\) | 38998.6 | 1.46141 | ||||||||
\(894\) | 14766.0 | − | 20464.6i | 0.552403 | − | 0.765590i | ||||
\(895\) | 35479.8i | 1.32510i | ||||||||
\(896\) | 4280.39 | 0.159596 | ||||||||
\(897\) | −36932.3 | − | 26648.1i | −1.37473 | − | 0.991922i | ||||
\(898\) | 1608.89i | 0.0597875i | ||||||||
\(899\) | −12241.2 | −0.454136 | ||||||||
\(900\) | 1102.11 | + | 3317.66i | 0.0408188 | + | 0.122876i | ||||
\(901\) | −57367.7 | −2.12119 | ||||||||
\(902\) | − | 7892.47i | − | 0.291342i | ||||||
\(903\) | 36352.2 | + | 26229.5i | 1.33967 | + | 0.966627i | ||||
\(904\) | −6073.96 | −0.223470 | ||||||||
\(905\) | − | 9370.22i | − | 0.344173i | ||||||
\(906\) | 4024.40 | + | 2903.76i | 0.147573 | + | 0.106480i | ||||
\(907\) | −24434.5 | −0.894524 | −0.447262 | − | 0.894403i | \(-0.647601\pi\) | ||||
−0.447262 | + | 0.894403i | \(0.647601\pi\) | |||||||
\(908\) | 4362.78 | 0.159454 | ||||||||
\(909\) | 10914.8 | + | 32856.6i | 0.398263 | + | 1.19888i | ||||
\(910\) | −44875.4 | −1.63473 | ||||||||
\(911\) | 27512.4i | 1.00058i | 0.865859 | + | 0.500289i | \(0.166773\pi\) | ||||
−0.865859 | + | 0.500289i | \(0.833227\pi\) | |||||||
\(912\) | −3813.47 | + | 5285.19i | −0.138461 | + | 0.191897i | ||||
\(913\) | 26915.5 | 0.975653 | ||||||||
\(914\) | − | 15257.9i | − | 0.552173i | ||||||
\(915\) | −1258.31 | + | 1743.93i | −0.0454629 | + | 0.0630083i | ||||
\(916\) | − | 19899.6i | − | 0.717795i | ||||||
\(917\) | −44844.9 | −1.61495 | ||||||||
\(918\) | 9638.50 | − | 30689.5i | 0.346534 | − | 1.10338i | ||||
\(919\) | 6767.64i | 0.242920i | 0.992596 | + | 0.121460i | \(0.0387577\pi\) | ||||
−0.992596 | + | 0.121460i | \(0.961242\pi\) | |||||||
\(920\) | − | 16445.3i | − | 0.589331i | ||||||
\(921\) | −15035.9 | + | 20838.6i | −0.537947 | + | 0.745555i | ||||
\(922\) | 2556.29i | 0.0913089i | ||||||||
\(923\) | 25178.9 | 0.897912 | ||||||||
\(924\) | −22635.5 | + | 31371.1i | −0.805901 | + | 1.11692i | ||||
\(925\) | 2689.67i | 0.0956064i | ||||||||
\(926\) | − | 14805.0i | − | 0.525401i | ||||||
\(927\) | −31028.2 | + | 10307.4i | −1.09935 | + | 0.365199i | ||||
\(928\) | 2434.34i | 0.0861112i | ||||||||
\(929\) | 47152.2 | 1.66525 | 0.832623 | − | 0.553841i | \(-0.186838\pi\) | ||||
0.832623 | + | 0.553841i | \(0.186838\pi\) | |||||||
\(930\) | −12274.8 | + | 17012.0i | −0.432803 | + | 0.599834i | ||||
\(931\) | 60774.6 | 2.13943 | ||||||||
\(932\) | 1736.65 | 0.0610362 | ||||||||
\(933\) | 28580.2 | + | 20621.7i | 1.00287 | + | 0.723607i | ||||
\(934\) | −25403.9 | −0.889981 | ||||||||
\(935\) | −80043.5 | −2.79968 | ||||||||
\(936\) | 10964.0 | − | 3642.17i | 0.382872 | − | 0.127188i | ||||
\(937\) | − | 21544.1i | − | 0.751136i | −0.926795 | − | 0.375568i | \(-0.877448\pi\) | ||
0.926795 | − | 0.375568i | \(-0.122552\pi\) | |||||||
\(938\) | 70407.1i | 2.45082i | ||||||||
\(939\) | −42935.0 | − | 30979.3i | −1.49215 | − | 1.07665i | ||||
\(940\) | − | 24963.2i | − | 0.866181i | ||||||
\(941\) | −3628.62 | −0.125706 | −0.0628532 | − | 0.998023i | \(-0.520020\pi\) | ||||
−0.0628532 | + | 0.998023i | \(0.520020\pi\) | |||||||
\(942\) | 10054.3 | + | 7254.59i | 0.347758 | + | 0.250921i | ||||
\(943\) | 11618.5i | 0.401219i | ||||||||
\(944\) | −7249.08 | + | 166.983i | −0.249934 | + | 0.00575724i | ||||
\(945\) | −17634.9 | + | 56150.3i | −0.607050 | + | 1.93288i | ||||
\(946\) | 28717.1i | 0.986970i | ||||||||
\(947\) | − | 34650.5i | − | 1.18901i | −0.804093 | − | 0.594503i | \(-0.797349\pi\) | ||
0.804093 | − | 0.594503i | \(-0.202651\pi\) | |||||||
\(948\) | −8208.15 | + | 11375.9i | −0.281211 | + | 0.389739i | ||||
\(949\) | −48783.2 | −1.66867 | ||||||||
\(950\) | 5075.01 | 0.173321 | ||||||||
\(951\) | −30927.1 | − | 22315.1i | −1.05455 | − | 0.760900i | ||||
\(952\) | 30669.3i | 1.04412i | ||||||||
\(953\) | − | 29717.0i | − | 1.01010i | −0.863089 | − | 0.505052i | \(-0.831473\pi\) | ||
0.863089 | − | 0.505052i | \(-0.168527\pi\) | |||||||
\(954\) | −25644.2 | + | 8518.87i | −0.870296 | + | 0.289108i | ||||
\(955\) | − | 9652.40i | − | 0.327062i | ||||||
\(956\) | 10253.2i | 0.346874i | ||||||||
\(957\) | −17841.4 | − | 12873.2i | −0.602643 | − | 0.434830i | ||||
\(958\) | 4253.78i | 0.143459i | ||||||||
\(959\) | − | 86177.0i | − | 2.90177i | ||||||
\(960\) | 3383.08 | + | 2441.02i | 0.113738 | + | 0.0820663i | ||||
\(961\) | 3897.75 | 0.130836 | ||||||||
\(962\) | 8888.65 | 0.297902 | ||||||||
\(963\) | −15837.5 | + | 5261.12i | −0.529964 | + | 0.176051i | ||||
\(964\) | −13744.6 | −0.459217 | ||||||||
\(965\) | − | 53308.9i | − | 1.77832i | ||||||
\(966\) | 33321.6 | − | 46181.3i | 1.10984 | − | 1.53816i | ||||
\(967\) | − | 4345.44i | − | 0.144509i | −0.997386 | − | 0.0722544i | \(-0.976981\pi\) | ||
0.997386 | − | 0.0722544i | \(-0.0230193\pi\) | |||||||
\(968\) | −14134.2 | −0.469308 | ||||||||
\(969\) | −37868.8 | − | 27323.8i | −1.25544 | − | 0.905848i | ||||
\(970\) | 13778.3 | 0.456076 | ||||||||
\(971\) | 46728.5i | 1.54438i | 0.635394 | + | 0.772188i | \(0.280838\pi\) | ||||
−0.635394 | + | 0.772188i | \(0.719162\pi\) | |||||||
\(972\) | −248.707 | − | 15149.9i | −0.00820708 | − | 0.499933i | ||||
\(973\) | 9374.89 | 0.308885 | ||||||||
\(974\) | 30468.8 | 1.00234 | ||||||||
\(975\) | −7295.48 | − | 5263.97i | −0.239633 | − | 0.172905i | ||||
\(976\) | 527.858i | 0.0173118i | ||||||||
\(977\) | −23068.5 | −0.755399 | −0.377700 | − | 0.925928i | \(-0.623285\pi\) | ||||
−0.377700 | + | 0.925928i | \(0.623285\pi\) | |||||||
\(978\) | −1978.41 | + | 2741.93i | −0.0646857 | + | 0.0896497i | ||||
\(979\) | 3911.89 | 0.127706 | ||||||||
\(980\) | − | 38902.1i | − | 1.26804i | ||||||
\(981\) | −378.783 | + | 125.830i | −0.0123278 | + | 0.00409524i | ||||
\(982\) | − | 3302.66i | − | 0.107324i | ||||||
\(983\) | −9487.51 | −0.307838 | −0.153919 | − | 0.988083i | \(-0.549189\pi\) | ||||
−0.153919 | + | 0.988083i | \(0.549189\pi\) | |||||||
\(984\) | −2390.12 | − | 1724.57i | −0.0774333 | − | 0.0558711i | ||||
\(985\) | −36754.5 | −1.18893 | ||||||||
\(986\) | −17442.3 | −0.563362 | ||||||||
\(987\) | 50580.7 | − | 70101.2i | 1.63121 | − | 2.26073i | ||||
\(988\) | − | 16771.5i | − | 0.540054i | ||||||
\(989\) | − | 42274.3i | − | 1.35920i | ||||||
\(990\) | −35780.7 | + | 11886.1i | −1.14867 | + | 0.381582i | ||||
\(991\) | − | 24894.2i | − | 0.797973i | −0.916957 | − | 0.398987i | \(-0.869362\pi\) | ||
0.916957 | − | 0.398987i | \(-0.130638\pi\) | |||||||
\(992\) | 5149.24i | 0.164807i | ||||||||
\(993\) | 5738.00 | − | 7952.45i | 0.183373 | − | 0.254142i | ||||
\(994\) | 31484.4i | 1.00465i | ||||||||
\(995\) | − | 22241.8i | − | 0.708657i | ||||||
\(996\) | 5881.23 | − | 8150.96i | 0.187102 | − | 0.259310i | ||||
\(997\) | 43927.8 | 1.39540 | 0.697698 | − | 0.716392i | \(-0.254208\pi\) | ||||
0.697698 | + | 0.716392i | \(0.254208\pi\) | |||||||
\(998\) | −8635.09 | −0.273887 | ||||||||
\(999\) | 3493.01 | − | 11121.9i | 0.110625 | − | 0.352234i |
(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 | 354.4.c.a.353.10 | yes | 30 | |
3.2 | odd | 2 | 354.4.c.b.353.9 | yes | 30 | ||
59.58 | odd | 2 | 354.4.c.b.353.10 | yes | 30 | ||
177.176 | even | 2 | inner | 354.4.c.a.353.9 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.c.a.353.9 | ✓ | 30 | 177.176 | even | 2 | inner | |
354.4.c.a.353.10 | yes | 30 | 1.1 | even | 1 | trivial | |
354.4.c.b.353.9 | yes | 30 | 3.2 | odd | 2 | ||
354.4.c.b.353.10 | yes | 30 | 59.58 | odd | 2 |