Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,4,Mod(9,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("100.9");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.i (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.90019100057\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 9.3 | ||
Character | \(\chi\) | \(=\) | 100.9 |
Dual form | 100.4.i.a.89.3 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.71349 | + | 1.53150i | −0.907111 | + | 0.294738i | −0.725169 | − | 0.688571i | \(-0.758238\pi\) |
−0.181942 | + | 0.983309i | \(0.558238\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.20187 | + | 10.7121i | 0.286384 | + | 0.958115i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 16.8592i | − | 0.910309i | −0.890412 | − | 0.455155i | \(-0.849584\pi\) | ||
0.890412 | − | 0.455155i | \(-0.150416\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.97201 | + | 1.43275i | −0.0730373 | + | 0.0530647i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −47.8389 | − | 34.7570i | −1.31127 | − | 0.952693i | −0.999997 | − | 0.00237169i | \(-0.999245\pi\) |
−0.311272 | − | 0.950321i | \(-0.600755\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.71191 | − | 5.10901i | −0.0791922 | − | 0.108999i | 0.767583 | − | 0.640949i | \(-0.221459\pi\) |
−0.846775 | + | 0.531951i | \(0.821459\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.4975 | − | 45.5874i | −0.542175 | − | 0.784708i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −125.140 | − | 40.6606i | −1.78535 | − | 0.580097i | −0.786078 | − | 0.618128i | \(-0.787891\pi\) |
−0.999277 | + | 0.0380312i | \(0.987891\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.3925 | + | 78.1500i | −0.306602 | + | 0.943623i | 0.672473 | + | 0.740122i | \(0.265232\pi\) |
−0.979075 | + | 0.203501i | \(0.934768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25.8199 | + | 79.4654i | 0.268303 | + | 0.825752i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 93.7224 | − | 128.998i | 0.849672 | − | 1.16947i | −0.134262 | − | 0.990946i | \(-0.542866\pi\) |
0.983935 | − | 0.178528i | \(-0.0571335\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.496 | + | 68.5972i | −0.835968 | + | 0.548777i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 85.7543 | − | 118.031i | 0.611238 | − | 0.841297i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.4646 | + | 47.5950i | 0.0990240 | + | 0.304765i | 0.988281 | − | 0.152642i | \(-0.0487783\pi\) |
−0.889257 | + | 0.457407i | \(0.848778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.8066 | + | 42.4924i | −0.0799917 | + | 0.246189i | −0.983053 | − | 0.183323i | \(-0.941315\pi\) |
0.903061 | + | 0.429512i | \(0.141315\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 278.718 | + | 90.5611i | 1.47026 | + | 0.477717i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 180.596 | − | 53.9808i | 0.872181 | − | 0.260698i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.1117 | + | 60.7145i | 0.195998 | + | 0.269768i | 0.895692 | − | 0.444674i | \(-0.146681\pi\) |
−0.699695 | + | 0.714442i | \(0.746681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 25.3205 | + | 18.3964i | 0.103962 | + | 0.0755330i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −286.091 | + | 207.857i | −1.08975 | + | 0.791752i | −0.979357 | − | 0.202136i | \(-0.935212\pi\) |
−0.110395 | + | 0.993888i | \(0.535212\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79.3703i | 0.281485i | 0.990046 | + | 0.140743i | \(0.0449490\pi\) | ||||
−0.990046 | + | 0.140743i | \(0.955051\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21.6618 | − | 16.5368i | −0.0717588 | − | 0.0547812i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −289.874 | + | 94.1857i | −0.899626 | + | 0.292306i | −0.722083 | − | 0.691807i | \(-0.756815\pi\) |
−0.177543 | + | 0.984113i | \(0.556815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 58.7686 | 0.171337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 652.120 | 1.79049 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 322.676 | − | 104.844i | 0.836282 | − | 0.271725i | 0.140593 | − | 0.990067i | \(-0.455099\pi\) |
0.695689 | + | 0.718343i | \(0.255099\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 219.145 | − | 623.740i | 0.537263 | − | 1.52918i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 407.248i | − | 0.946338i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −636.533 | + | 462.468i | −1.40457 | + | 1.02048i | −0.410483 | + | 0.911868i | \(0.634640\pi\) |
−0.994084 | + | 0.108610i | \(0.965360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 675.055 | + | 490.456i | 1.41692 | + | 1.02945i | 0.992271 | + | 0.124090i | \(0.0396011\pi\) |
0.424645 | + | 0.905360i | \(0.360399\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.1549 | + | 33.2464i | 0.0483053 | + | 0.0664865i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 42.8429 | − | 56.1206i | 0.0817540 | − | 0.107091i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −578.147 | − | 187.851i | −1.05421 | − | 0.342533i | −0.269889 | − | 0.962891i | \(-0.586987\pi\) |
−0.784318 | + | 0.620359i | \(0.786987\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −244.198 | + | 751.566i | −0.426059 | + | 1.31127i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −18.9894 | − | 58.4435i | −0.0317413 | − | 0.0976897i | 0.933931 | − | 0.357454i | \(-0.116355\pi\) |
−0.965672 | + | 0.259764i | \(0.916355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −23.2607 | + | 32.0156i | −0.0372940 | + | 0.0513307i | −0.827257 | − | 0.561824i | \(-0.810100\pi\) |
0.789963 | + | 0.613155i | \(0.210100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 387.484 | − | 483.368i | 0.596570 | − | 0.744194i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −585.973 | + | 806.523i | −0.867245 | + | 1.19366i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −178.592 | − | 549.648i | −0.254343 | − | 0.782788i | −0.993958 | − | 0.109758i | \(-0.964992\pi\) |
0.739615 | − | 0.673030i | \(-0.235008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −203.100 | + | 625.077i | −0.278601 | + | 0.857445i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 50.7554 | + | 16.4914i | 0.0671220 | + | 0.0218093i | 0.342386 | − | 0.939560i | \(-0.388765\pi\) |
−0.275264 | + | 0.961369i | \(0.588765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34.8749 | − | 1470.70i | 0.0445026 | − | 1.87670i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −145.784 | − | 200.654i | −0.179652 | − | 0.247269i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1170.83 | − | 850.656i | −1.39447 | − | 1.01314i | −0.995359 | − | 0.0962343i | \(-0.969320\pi\) |
−0.399107 | − | 0.916904i | \(-0.630680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −86.1336 | + | 62.5797i | −0.0992226 | + | 0.0720894i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 221.432i | − | 0.246898i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −918.450 | − | 21.7793i | −0.991905 | − | 0.0235212i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.9127 | − | 16.5425i | 0.0532928 | − | 0.0173159i | −0.282249 | − | 0.959341i | \(-0.591081\pi\) |
0.335542 | + | 0.942025i | \(0.391081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 144.136 | 0.146326 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −47.2102 | −0.0465108 | −0.0232554 | − | 0.999730i | \(-0.507403\pi\) | ||||
−0.0232554 | + | 0.999730i | \(0.507403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 139.952 | − | 45.4731i | 0.133882 | − | 0.0435009i | −0.241310 | − | 0.970448i | \(-0.577577\pi\) |
0.375192 | + | 0.926947i | \(0.377577\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −768.566 | + | 531.022i | −0.714327 | + | 0.493547i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1350.74i | − | 1.22038i | −0.792254 | − | 0.610192i | \(-0.791092\pi\) | ||
0.792254 | − | 0.610192i | \(-0.208908\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 220.694 | − | 160.344i | 0.193933 | − | 0.140900i | −0.486582 | − | 0.873635i | \(-0.661756\pi\) |
0.680514 | + | 0.732735i | \(0.261756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −300.904 | − | 218.620i | −0.257302 | − | 0.186941i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 371.744 | + | 511.662i | 0.309476 | + | 0.425957i | 0.935218 | − | 0.354073i | \(-0.115204\pi\) |
−0.625742 | + | 0.780030i | \(0.715204\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1681.92 | + | 590.925i | 1.36382 | + | 0.479165i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.6398 | + | 4.75677i | 0.0115680 | + | 0.00375866i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −685.504 | + | 2109.76i | −0.528067 | + | 1.62522i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 669.208 | + | 2059.61i | 0.502786 | + | 1.54742i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1030.15 | − | 1417.88i | 0.755167 | − | 1.03940i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1069.40 | − | 899.728i | −0.765200 | − | 0.643793i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −538.581 | + | 741.293i | −0.376310 | + | 0.517946i | −0.954602 | − | 0.297884i | \(-0.903719\pi\) |
0.578293 | + | 0.815829i | \(0.303719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −121.556 | − | 374.111i | −0.0829644 | − | 0.255338i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 202.335 | − | 622.722i | 0.134947 | − | 0.415324i | −0.860635 | − | 0.509223i | \(-0.829933\pi\) |
0.995582 | + | 0.0938986i | \(0.0299330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1317.54 | + | 428.096i | 0.858989 | + | 0.279102i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1538.93 | + | 540.686i | 0.981108 | + | 0.344702i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 333.970 | + | 459.671i | 0.208270 | + | 0.286659i | 0.900354 | − | 0.435158i | \(-0.143307\pi\) |
−0.692084 | + | 0.721817i | \(0.743307\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2079.69 | + | 1510.98i | 1.26904 | + | 0.922014i | 0.999164 | − | 0.0408805i | \(-0.0130163\pi\) |
0.269879 | + | 0.962894i | \(0.413016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1222.07 | − | 887.886i | 0.729907 | − | 0.530308i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 373.424i | 0.218373i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −460.325 | + | 318.050i | −0.263641 | + | 0.182156i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −277.005 | + | 90.0044i | −0.155422 | + | 0.0504996i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3146.97 | 1.73027 | 0.865134 | − | 0.501541i | \(-0.167233\pi\) | ||||
0.865134 | + | 0.501541i | \(0.167233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1560.39 | −0.840946 | −0.420473 | − | 0.907305i | \(-0.638136\pi\) | ||||
−0.420473 | + | 0.907305i | \(0.638136\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 305.034 | − | 99.1116i | 0.161180 | − | 0.0523706i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −499.388 | − | 11.8421i | −0.258786 | − | 0.00613663i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2777.66i | − | 1.41198i | −0.708219 | − | 0.705992i | \(-0.750501\pi\) | ||
0.708219 | − | 0.705992i | \(-0.249499\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1360.36 | + | 988.360i | −0.678513 | + | 0.492969i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2174.79 | − | 1580.08i | −1.06458 | − | 0.773465i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −319.367 | − | 439.571i | −0.153465 | − | 0.211226i | 0.725361 | − | 0.688368i | \(-0.241673\pi\) |
−0.878826 | + | 0.477142i | \(0.841673\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −77.6750 | + | 3275.61i | −0.0366484 | + | 1.54549i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 458.479 | + | 148.969i | 0.212444 | + | 0.0690273i | 0.413306 | − | 0.910592i | \(-0.364374\pi\) |
−0.200862 | + | 0.979620i | \(0.564374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 666.587 | − | 2051.54i | 0.303408 | − | 0.933793i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −61.8950 | − | 190.493i | −0.0276797 | − | 0.0851893i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2069.40 | + | 2848.28i | −0.909442 | + | 1.25174i | 0.0579150 | + | 0.998322i | \(0.481555\pi\) |
−0.967357 | + | 0.253418i | \(0.918445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1156.49 | + | 1761.72i | 0.499557 | + | 0.760990i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2292.02 | − | 3154.69i | 0.973325 | − | 1.33967i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −468.991 | − | 1443.41i | −0.195833 | − | 0.602711i | −0.999966 | − | 0.00826192i | \(-0.997370\pi\) |
0.804133 | − | 0.594449i | \(-0.202630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1017.44 | − | 3131.37i | 0.417823 | − | 1.28593i | −0.491879 | − | 0.870664i | \(-0.663690\pi\) |
0.909702 | − | 0.415262i | \(-0.136310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3933.00 | − | 1277.91i | −1.58872 | − | 0.516206i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −509.137 | + | 666.926i | −0.202338 | + | 0.265045i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4573.34 | + | 6294.66i | 1.78843 | + | 2.46156i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1989.90 | − | 1445.75i | −0.765841 | − | 0.556416i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3404.02 | + | 2473.17i | −1.28956 | + | 0.936922i | −0.999796 | − | 0.0201762i | \(-0.993577\pi\) |
−0.289765 | + | 0.957098i | \(0.593577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1843.42i | − | 0.687524i | −0.939057 | − | 0.343762i | \(-0.888299\pi\) | ||
0.939057 | − | 0.343762i | \(-0.111701\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −115.991 | + | 330.138i | −0.0425962 | + | 0.121239i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3542.01 | + | 1150.87i | −1.28101 | + | 0.416224i | −0.868934 | − | 0.494928i | \(-0.835195\pi\) |
−0.412071 | + | 0.911152i | \(0.635195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 324.095 | 0.115450 | 0.0577248 | − | 0.998333i | \(-0.481615\pi\) | ||||
0.0577248 | + | 0.998333i | \(0.481615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3012.78 | 1.05724 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 802.412 | − | 260.720i | 0.277430 | − | 0.0901425i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3142.60 | − | 2399.09i | −1.07068 | − | 0.817363i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 388.665i | 0.130503i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3931.00 | − | 2856.04i | 1.30102 | − | 0.945246i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3043.05 | − | 2210.91i | −0.992855 | − | 0.721352i | −0.0323107 | − | 0.999478i | \(-0.510287\pi\) |
−0.960545 | + | 0.278126i | \(0.910287\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 179.013 | + | 246.390i | 0.0575858 | + | 0.0792600i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −850.219 | + | 254.133i | −0.269695 | + | 0.0806128i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 716.387 | + | 232.768i | 0.224108 | + | 0.0728172i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 60.6070 | − | 186.529i | 0.0187006 | − | 0.0575546i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 256.775 | + | 790.272i | 0.0781564 | + | 0.240541i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1628.08 | + | 2240.86i | −0.488898 | + | 0.672911i | −0.980184 | − | 0.198088i | \(-0.936527\pi\) |
0.491286 | + | 0.870998i | \(0.336527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 107.785 | − | 284.990i | 0.0319362 | − | 0.0844416i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1038.20 | + | 1428.96i | −0.303559 | + | 0.417813i | −0.933359 | − | 0.358945i | \(-0.883137\pi\) |
0.629800 | + | 0.776757i | \(0.283137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −332.536 | − | 1023.44i | −0.0959588 | − | 0.295331i | 0.891544 | − | 0.452935i | \(-0.149623\pi\) |
−0.987502 | + | 0.157604i | \(0.949623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1526.78 | − | 4698.96i | 0.434870 | − | 1.33839i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3225.67 | − | 1048.08i | −0.906955 | − | 0.294688i | −0.181850 | − | 0.983326i | \(-0.558209\pi\) |
−0.725105 | + | 0.688639i | \(0.758209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1937.06 | − | 2803.57i | −0.537702 | − | 0.778234i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1683.58 | + | 2317.25i | 0.461435 | + | 0.635111i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3460.57 | − | 2514.25i | −0.936594 | − | 0.680475i | 0.0110046 | − | 0.999939i | \(-0.496497\pi\) |
−0.947598 | + | 0.319464i | \(0.896497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1761.89 | + | 1280.09i | −0.470927 | + | 0.342149i | −0.797803 | − | 0.602919i | \(-0.794004\pi\) |
0.326875 | + | 0.945067i | \(0.394004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 681.796i | 0.179989i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 188.169 | + | 629.532i | 0.0490682 | + | 0.164161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 493.523 | − | 160.355i | 0.127134 | − | 0.0413084i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −264.492 | −0.0673152 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3829.18 | 0.962931 | 0.481465 | − | 0.876465i | \(-0.340105\pi\) | ||||
0.481465 | + | 0.876465i | \(0.340105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8967.14 | + | 2913.60i | −2.22830 | + | 0.724018i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2088.00 | + | 6985.54i | 0.512768 | + | 1.71550i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1052.72i | − | 0.255513i | −0.991806 | − | 0.127757i | \(-0.959222\pi\) | ||
0.991806 | − | 0.127757i | \(-0.0407776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1023.60 | − | 743.686i | 0.245572 | − | 0.178419i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −98.6878 | − | 71.7009i | −0.0234047 | − | 0.0170045i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2377.23 | − | 3271.97i | −0.557361 | − | 0.767142i | 0.433627 | − | 0.901093i | \(-0.357234\pi\) |
−0.990988 | + | 0.133951i | \(0.957234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2156.26 | + | 3120.83i | 0.499841 | + | 0.723437i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6821.46 | + | 2216.43i | 1.56355 | + | 0.508027i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1125.70 | − | 3464.56i | 0.255150 | − | 0.785272i | −0.738650 | − | 0.674090i | \(-0.764536\pi\) |
0.993800 | − | 0.111182i | \(-0.0354638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −893.315 | − | 2749.34i | −0.200240 | − | 0.616275i | −0.999875 | − | 0.0157892i | \(-0.994974\pi\) |
0.799635 | − | 0.600486i | \(-0.205026\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 310.148 | − | 426.883i | 0.0687584 | − | 0.0946378i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7383.20 | + | 350.355i | 1.61900 | + | 0.0768262i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2661.63 | − | 3663.41i | 0.577334 | − | 0.794633i | −0.416066 | − | 0.909335i | \(-0.636591\pi\) |
0.993400 | + | 0.114702i | \(0.0365913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.6541 | − | 103.577i | −0.00722158 | − | 0.0222257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 934.864 | − | 2877.21i | 0.198467 | − | 0.610819i | −0.801451 | − | 0.598060i | \(-0.795938\pi\) |
0.999919 | − | 0.0127594i | \(-0.00406156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5425.06 | + | 1762.71i | 1.13953 | + | 0.370255i | 0.817189 | − | 0.576370i | \(-0.195531\pi\) |
0.322338 | + | 0.946625i | \(0.395531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4362.46 | − | 1303.95i | 0.906700 | − | 0.271016i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3504.30 | + | 4823.25i | 0.720739 | + | 0.992012i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10032.2 | + | 7288.78i | 2.04196 | + | 1.48357i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −214.641 | + | 155.946i | −0.0432388 | + | 0.0314148i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6874.37i | 1.37067i | 0.728230 | + | 0.685333i | \(0.240343\pi\) | ||||
−0.728230 | + | 0.685333i | \(0.759657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6992.08 | − | 5337.81i | −1.37998 | − | 1.05349i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8204.78 | + | 2665.89i | −1.60300 | + | 0.520845i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1006.94 | −0.194759 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1338.12 | 0.256238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 222.524 | − | 72.3026i | 0.0421904 | − | 0.0137085i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3092.35 | + | 8801.59i | −0.580549 | + | 1.65239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4653.22i | − | 0.865060i | −0.901620 | − | 0.432530i | \(-0.857621\pi\) | ||
0.901620 | − | 0.432530i | \(-0.142379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −590.018 | + | 428.674i | −0.108625 | + | 0.0789203i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4202.31 | − | 3053.16i | −0.766210 | − | 0.556684i | 0.134599 | − | 0.990900i | \(-0.457025\pi\) |
−0.900809 | + | 0.434216i | \(0.857025\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2799.64 | + | 3853.37i | 0.505574 | + | 0.695863i | 0.983165 | − | 0.182719i | \(-0.0584899\pi\) |
−0.477591 | + | 0.878582i | \(0.658490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −278.796 | + | 365.199i | −0.0498679 | + | 0.0653227i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5960.65 | + | 1936.73i | 1.05610 | + | 0.343148i | 0.785060 | − | 0.619420i | \(-0.212632\pi\) |
0.271040 | + | 0.962568i | \(0.412632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 914.452 | − | 2814.39i | 0.160500 | − | 0.493968i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2068.67 | + | 6366.70i | 0.359694 | + | 1.10702i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6355.25 | − | 8747.25i | 1.09478 | − | 1.50684i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 738.344 | + | 279.245i | 0.126018 | + | 0.0476606i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −794.671 | + | 1093.77i | −0.134390 | + | 0.184971i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1587.89 | + | 4887.03i | 0.266089 | + | 0.818938i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2918.94 | + | 8983.56i | −0.484711 | + | 1.49179i | 0.347688 | + | 0.937610i | \(0.386967\pi\) |
−0.832399 | + | 0.554176i | \(0.813033\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −173.977 | − | 56.5285i | −0.0286303 | − | 0.00930254i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 161.122 | − | 6794.61i | 0.0262777 | − | 1.10815i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6480.14 | − | 8919.14i | −1.04746 | − | 1.44171i | −0.890987 | − | 0.454030i | \(-0.849986\pi\) |
−0.156478 | − | 0.987681i | \(-0.550014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2535.83 | − | 1842.39i | −0.406275 | − | 0.295176i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2137.40 | − | 1552.91i | 0.339433 | − | 0.246613i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6773.48i | − | 1.06628i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8832.70 | − | 209.451i | −1.37837 | − | 0.0326854i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9594.55 | + | 3117.46i | −1.48433 | + | 0.482288i | −0.935404 | − | 0.353582i | \(-0.884964\pi\) |
−0.548927 | + | 0.835870i | \(0.684964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7071.09 | −1.08455 | −0.542273 | − | 0.840202i | \(-0.682436\pi\) | ||||
−0.542273 | + | 0.840202i | \(0.682436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −921.332 | −0.140106 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9680.64 | − | 3145.43i | 1.45963 | − | 0.474262i | 0.531671 | − | 0.846951i | \(-0.321564\pi\) |
0.927956 | + | 0.372689i | \(0.121564\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 565.248 | − | 390.544i | 0.0845078 | − | 0.0583886i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 10994.2i | − | 1.62990i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2756.36 | + | 2002.61i | −0.405223 | + | 0.294412i | −0.771665 | − | 0.636029i | \(-0.780576\pi\) |
0.366442 | + | 0.930441i | \(0.380576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 86.4079 | + | 62.7790i | 0.0125977 | + | 0.00915280i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6308.61 | − | 8683.05i | −0.912165 | − | 1.25549i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −417.431 | − | 146.660i | −0.0598611 | − | 0.0210316i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6336.96 | + | 2059.00i | 0.901326 | + | 0.292859i | 0.722784 | − | 0.691074i | \(-0.242862\pi\) |
0.178542 | + | 0.983932i | \(0.442862\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 266.366 | − | 819.791i | 0.0375785 | − | 0.115655i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1767.58 | − | 5440.05i | −0.247353 | − | 0.761275i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3602.45 | + | 4958.34i | −0.500074 | + | 0.688293i | −0.982206 | − | 0.187805i | \(-0.939863\pi\) |
0.482132 | + | 0.876099i | \(0.339863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6418.54 | + | 2603.07i | 0.883872 | + | 0.358458i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 185.760 | − | 255.677i | 0.0253770 | − | 0.0349285i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3610.91 | + | 11113.2i | 0.489393 | + | 1.50620i | 0.825517 | + | 0.564378i | \(0.190884\pi\) |
−0.336124 | + | 0.941818i | \(0.609116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1403.30 | − | 4318.91i | 0.188696 | − | 0.580747i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9743.83 | + | 3165.96i | 1.29996 | + | 0.422384i | 0.875569 | − | 0.483093i | \(-0.160487\pi\) |
0.424395 | + | 0.905477i | \(0.360487\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10515.7 | − | 3694.59i | −1.39203 | − | 0.489075i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −113.718 | − | 156.519i | −0.0149369 | − | 0.0205589i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3651.69 | − | 2653.11i | −0.475960 | − | 0.345805i | 0.323800 | − | 0.946126i | \(-0.395040\pi\) |
−0.799759 | + | 0.600321i | \(0.795040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16973.6 | + | 12332.0i | −2.19537 | + | 1.59503i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3245.07i | 0.416519i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5316.03 | − | 3672.98i | 0.677161 | − | 0.467868i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11189.7 | + | 3635.76i | −1.41460 | + | 0.459631i | −0.913881 | − | 0.405981i | \(-0.866930\pi\) |
−0.500716 | + | 0.865612i | \(0.666930\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6865.85 | −0.861460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6156.96 | 0.766743 | 0.383371 | − | 0.923594i | \(-0.374763\pi\) | ||||
0.383371 | + | 0.923594i | \(0.374763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 268.343 | − | 87.1900i | 0.0331690 | − | 0.0107773i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7346.16 | − | 174.201i | −0.901317 | − | 0.0213731i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4437.70i | − | 0.540463i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4636.63 | − | 3368.71i | 0.560554 | − | 0.407266i | −0.271108 | − | 0.962549i | \(-0.587390\pi\) |
0.831662 | + | 0.555283i | \(0.187390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2278.15 | − | 1655.17i | −0.273413 | − | 0.198647i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7796.82 | + | 10731.4i | 0.928951 | + | 1.27859i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.1448 | + | 596.498i | −0.00167312 | + | 0.0705564i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12116.7 | − | 3936.94i | −1.42292 | − | 0.462333i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −484.018 | + | 1489.65i | −0.0564339 | + | 0.173686i | −0.975300 | − | 0.220883i | \(-0.929106\pi\) |
0.918866 | + | 0.394569i | \(0.129106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4904.78 | + | 15095.4i | 0.567801 | + | 1.74751i | 0.659479 | + | 0.751723i | \(0.270777\pi\) |
−0.0916782 | + | 0.995789i | \(0.529223\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 436.689 | − | 601.050i | 0.0501951 | − | 0.0690876i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15865.9 | − | 4335.41i | 1.81084 | − | 0.494820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8268.68 | − | 11380.9i | 0.937118 | − | 1.28983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −571.900 | − | 1760.13i | −0.0643627 | − | 0.198088i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3851.68 | − | 11854.2i | 0.430461 | − | 1.32482i | −0.467206 | − | 0.884149i | \(-0.654739\pi\) |
0.897667 | − | 0.440674i | \(-0.145261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13943.4 | − | 4530.50i | −1.54753 | − | 0.502822i | −0.594086 | − | 0.804401i | \(-0.702486\pi\) |
−0.953441 | + | 0.301579i | \(0.902486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1682.64 | − | 2204.12i | 0.185463 | − | 0.242941i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7701.33 | + | 10600.0i | 0.843031 | + | 1.16033i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3142.95 | + | 2283.49i | 0.341697 | + | 0.248257i | 0.745377 | − | 0.666643i | \(-0.232269\pi\) |
−0.403681 | + | 0.914900i | \(0.632269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −115.892 | + | 84.2005i | −0.0125140 | + | 0.00909194i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4840.23i | − | 0.519111i | −0.965728 | − | 0.259556i | \(-0.916424\pi\) | ||
0.965728 | − | 0.259556i | \(-0.0835761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5363.43 | − | 15265.7i | 0.571351 | − | 1.62621i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14833.2 | + | 4819.60i | −1.56955 | + | 0.509976i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9780.24 | −1.02797 | −0.513985 | − | 0.857799i | \(-0.671831\pi\) | ||||
−0.513985 | + | 0.857799i | \(0.671831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20910.7 | 2.18325 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7354.88 | − | 2389.75i | 0.762831 | − | 0.247859i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −946.146 | − | 722.295i | −0.0974857 | − | 0.0744214i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3537.61i | − | 0.362106i | −0.983473 | − | 0.181053i | \(-0.942050\pi\) | ||
0.983473 | − | 0.181053i | \(-0.0579505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15530.5 | + | 11283.6i | −1.57931 | + | 1.14744i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9138.35 | + | 6639.40i | 0.923243 | + | 0.670776i | 0.944329 | − | 0.329002i | \(-0.106712\pi\) |
−0.0210859 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1174.11 | + | 1616.02i | 0.117852 | + | 0.162209i | 0.863867 | − | 0.503719i | \(-0.168035\pi\) |
−0.746015 | + | 0.665929i | \(0.768035\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2372.00 | − | 708.998i | 0.236556 | − | 0.0707075i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10886.4 | − | 3537.19i | −1.07872 | − | 0.350496i | −0.284840 | − | 0.958575i | \(-0.591941\pi\) |
−0.793877 | + | 0.608079i | \(0.791941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3167.02 | + | 9747.07i | −0.311811 | + | 0.959655i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4254.00 | + | 13092.5i | 0.416166 | + | 1.28083i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2758.67 | − | 3796.98i | 0.268169 | − | 0.369103i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2707.46 | − | 9908.21i | −0.261530 | − | 0.957095i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −486.105 | + | 669.065i | −0.0466608 | + | 0.0642231i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1357.34 | + | 4177.45i | 0.129474 | + | 0.398481i | 0.994690 | − | 0.102919i | \(-0.0328183\pi\) |
−0.865215 | + | 0.501401i | \(0.832818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 146.452 | − | 450.734i | 0.0138828 | − | 0.0427270i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12670.8 | + | 4116.98i | 1.19366 | + | 0.387845i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 340.220 | + | 492.412i | 0.0318528 | + | 0.0461016i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4407.69 | + | 6066.67i | 0.410127 | + | 0.564491i | 0.963249 | − | 0.268609i | \(-0.0865640\pi\) |
−0.553123 | + | 0.833100i | \(0.686564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2178.54 | + | 1582.80i | 0.201466 | + | 0.146374i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −348.167 | + | 252.958i | −0.0320011 | + | 0.0232502i | −0.603671 | − | 0.797234i | \(-0.706296\pi\) |
0.571670 | + | 0.820484i | \(0.306296\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6584.86i | − | 0.601556i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 461.506 | + | 1544.00i | 0.0419054 | + | 0.140197i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −985.309 | + | 320.146i | −0.0889278 | + | 0.0288944i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1063.14 | 0.0953765 | 0.0476883 | − | 0.998862i | \(-0.484815\pi\) | ||||
0.0476883 | + | 0.998862i | \(0.484815\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2389.18 | −0.213055 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2601.15 | − | 845.164i | 0.230575 | − | 0.0749185i | −0.191450 | − | 0.981502i | \(-0.561319\pi\) |
0.422026 | + | 0.906584i | \(0.361319\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −151.161 | − | 505.718i | −0.0133199 | − | 0.0445626i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10690.8i | 0.936480i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7550.83 | − | 5486.00i | 0.657533 | − | 0.477726i | −0.208296 | − | 0.978066i | \(-0.566792\pi\) |
0.865829 | + | 0.500340i | \(0.166792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 539.757 | + | 392.156i | 0.0467269 | + | 0.0339490i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7046.58 | + | 9698.79i | 0.606460 | + | 0.834721i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 935.217 | + | 1353.57i | 0.0800206 | + | 0.115816i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17140.8 | + | 5569.40i | 1.45813 | + | 0.473775i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5391.92 | − | 16594.6i | 0.456029 | − | 1.40351i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6778.80 | + | 20863.0i | 0.570028 | + | 1.75437i | 0.652517 | + | 0.757774i | \(0.273713\pi\) |
−0.0824889 | + | 0.996592i | \(0.526287\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5930.64 | + | 8162.82i | −0.495848 | + | 0.682477i | −0.981453 | − | 0.191702i | \(-0.938599\pi\) |
0.485605 | + | 0.874178i | \(0.338599\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8149.18 | − | 6532.65i | −0.677447 | − | 0.543064i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3455.54 | − | 4756.14i | 0.285627 | − | 0.393132i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4096.74 | − | 12608.5i | −0.336709 | − | 1.03628i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 592.647 | − | 1823.98i | 0.0484344 | − | 0.149066i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2123.89 | + | 690.093i | 0.172600 | + | 0.0560811i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14469.2 | − | 4324.90i | 1.16927 | − | 0.349498i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4421.17 | + | 6085.22i | 0.355284 | + | 0.489007i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2811.42 | − | 2042.62i | −0.224669 | − | 0.163232i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3988.34 | − | 2897.70i | 0.316954 | − | 0.230281i | −0.417920 | − | 0.908484i | \(-0.637241\pi\) |
0.734875 | + | 0.678203i | \(0.237241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16317.9i | 1.28963i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2424.24 | + | 1850.69i | 0.190538 | + | 0.145458i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15836.7 | + | 5145.67i | −1.23790 | + | 0.402217i | −0.853569 | − | 0.520979i | \(-0.825567\pi\) |
−0.384328 | + | 0.923196i | \(0.625567\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2033.91 | −0.158115 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4112.23 | −0.317944 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9266.61 | + | 3010.90i | −0.712579 | + | 0.231531i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1378.41 | − | 3923.29i | 0.105424 | − | 0.300062i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13982.7i | − | 1.06367i | −0.846847 | − | 0.531836i | \(-0.821502\pi\) | ||
0.846847 | − | 0.531836i | \(-0.178498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 405.504 | − | 294.616i | 0.0306815 | − | 0.0222914i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31196.7 | − | 22665.7i | −2.34782 | − | 1.70579i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5828.84 | − | 8022.71i | −0.436334 | − | 0.600563i | 0.533058 | − | 0.846079i | \(-0.321043\pi\) |
−0.969393 | + | 0.245516i | \(0.921043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4290.68 | + | 5620.42i | −0.319487 | + | 0.418501i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10538.3 | + | 3424.09i | 0.780540 | + | 0.253613i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2562.12 | + | 7885.39i | −0.188769 | + | 0.580972i | −0.999993 | − | 0.00376415i | \(-0.998802\pi\) |
0.811224 | + | 0.584736i | \(0.198802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1824.42 | + | 5614.99i | 0.133712 | + | 0.411524i | 0.995387 | − | 0.0959364i | \(-0.0305845\pi\) |
−0.861675 | + | 0.507460i | \(0.830585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12257.1 | − | 16870.5i | 0.893629 | − | 1.22997i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −944.734 | + | 19908.9i | −0.0685185 | + | 1.44392i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3535.47 | − | 4866.15i | 0.255084 | − | 0.351093i | −0.662200 | − | 0.749327i | \(-0.730377\pi\) |
0.917284 | + | 0.398234i | \(0.130377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2823.20 | + | 8688.92i | 0.202639 | + | 0.623660i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 278.032 | − | 855.694i | 0.0198532 | − | 0.0611018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19080.5 | − | 6199.63i | −1.35546 | − | 0.440416i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.07992 | + | 172.053i | −0.000288349 | + | 0.0121599i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5035.76 | − | 6931.13i | −0.354085 | − | 0.487357i | 0.594404 | − | 0.804167i | \(-0.297388\pi\) |
−0.948489 | + | 0.316810i | \(0.897388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2970.20 | − | 2157.97i | −0.207784 | − | 0.150964i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14932.7 | − | 10849.2i | 1.03934 | − | 0.755123i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19704.6i | − | 1.36453i | −0.731103 | − | 0.682267i | \(-0.760994\pi\) | ||
0.731103 | − | 0.682267i | \(-0.239006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24794.8 | − | 587.962i | −1.70838 | − | 0.0405111i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1527.62 | + | 496.353i | −0.104726 | + | 0.0340274i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2540.05 | 0.173262 | 0.0866308 | − | 0.996240i | \(-0.472390\pi\) | ||||
0.0866308 | + | 0.996240i | \(0.472390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18593.4 | −1.26197 | −0.630983 | − | 0.775797i | \(-0.717348\pi\) | ||||
−0.630983 | + | 0.775797i | \(0.717348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1409.25 | − | 457.894i | 0.0951728 | − | 0.0309235i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19919.9 | + | 13763.2i | −1.33861 | + | 0.924882i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22878.6i | − | 1.52984i | −0.644123 | − | 0.764922i | \(-0.722778\pi\) | ||
0.644123 | − | 0.764922i | \(-0.277222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3382.87 | + | 2457.80i | −0.225091 | + | 0.163538i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1557.18 | + | 1131.36i | 0.103104 | + | 0.0749098i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8498.54 | − | 11697.2i | −0.559956 | − | 0.770713i | 0.431365 | − | 0.902178i | \(-0.358032\pi\) |
−0.991321 | + | 0.131464i | \(0.958032\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18486.8 | + | 6495.16i | 1.21213 | + | 0.425870i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18583.9 | − | 6038.28i | −1.21258 | − | 0.393990i | −0.368203 | − | 0.929745i | \(-0.620027\pi\) |
−0.844373 | + | 0.535755i | \(0.820027\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5737.53 | + | 17658.3i | −0.372553 | + | 1.14660i | 0.572561 | + | 0.819862i | \(0.305950\pi\) |
−0.945114 | + | 0.326740i | \(0.894050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7188.60 | − | 22124.2i | −0.464523 | − | 1.42965i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14341.3 | + | 19739.2i | −0.922270 | + | 1.26940i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6213.85 | − | 14336.3i | 0.397687 | − | 0.917521i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14154.7 | + | 19482.3i | −0.901569 | + | 1.24090i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3051.47 | − | 9391.45i | −0.193434 | − | 0.595328i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1938.92 | + | 5967.39i | −0.122325 | + | 0.376479i | −0.993404 | − | 0.114664i | \(-0.963421\pi\) |
0.871079 | + | 0.491143i | \(0.163421\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17729.4 | + | 5760.63i | 1.11324 | + | 0.361714i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9665.23 | − | 3395.78i | −0.604021 | − | 0.212217i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −218.144 | − | 300.249i | −0.0135686 | − | 0.0186755i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 121.182 | + | 88.0439i | 0.00750217 | + | 0.00545065i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5365.30 | + | 3898.12i | −0.330603 | + | 0.240197i | −0.740687 | − | 0.671851i | \(-0.765500\pi\) |
0.410083 | + | 0.912048i | \(0.365500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12509.7i | 0.767240i | 0.923491 | + | 0.383620i | \(0.125323\pi\) | ||||
−0.923491 | + | 0.383620i | \(0.874677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3618.29 | − | 2499.97i | 0.220884 | − | 0.152614i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24076.1 | − | 7822.81i | 1.46295 | − | 0.475342i | 0.533982 | − | 0.845496i | \(-0.320695\pi\) |
0.928970 | + | 0.370154i | \(0.120695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46525.0 | 2.81397 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3733.17 | −0.224753 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −862.934 | + | 280.384i | −0.0517140 | + | 0.0168029i | −0.334760 | − | 0.942304i | \(-0.608655\pi\) |
0.283046 | + | 0.959106i | \(0.408655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7318.48 | + | 173.544i | 0.436575 | + | 0.0103526i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 96.4617i | − | 0.00572805i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9417.94 | − | 6842.54i | 0.556709 | − | 0.404473i | −0.273544 | − | 0.961859i | \(-0.588196\pi\) |
0.830253 | + | 0.557387i | \(0.188196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16022.0 | + | 11640.7i | 0.942791 | + | 0.684977i | 0.949091 | − | 0.315003i | \(-0.102005\pi\) |
−0.00630023 | + | 0.999980i | \(0.502005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2420.61 | − | 3331.69i | −0.141793 | − | 0.195161i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −367.181 | + | 15484.3i | −0.0214116 | + | 0.902940i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7589.03 | + | 2465.82i | 0.440552 | + | 0.143144i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4242.05 | − | 13055.7i | 0.245152 | − | 0.754502i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15247.1 | − | 46925.7i | −0.877209 | − | 2.69977i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2320.74 | + | 3194.22i | −0.132924 | + | 0.182954i | −0.870291 | − | 0.492538i | \(-0.836069\pi\) |
0.737367 | + | 0.675493i | \(0.236069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −864.415 | + | 18216.3i | −0.0492909 | + | 1.03873i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14742.6 | + | 20291.5i | −0.836935 | + | 1.15194i | 0.149657 | + | 0.988738i | \(0.452183\pi\) |
−0.986592 | + | 0.163204i | \(0.947817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −278.893 | − | 858.345i | −0.0157628 | − | 0.0485129i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2705.09 | − | 8325.40i | 0.152216 | − | 0.468473i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7011.29 | − | 2278.10i | −0.392796 | − | 0.127627i | 0.105959 | − | 0.994371i | \(-0.466209\pi\) |
−0.498754 | + | 0.866744i | \(0.666209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3854.69 | + | 5049.31i | −0.215007 | + | 0.281641i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3134.80 | + | 4314.69i | 0.174091 | + | 0.239615i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1733.39 | − | 1259.38i | −0.0958447 | − | 0.0696353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24373.2 | + | 17708.2i | −1.34183 | + | 0.974894i | −0.342452 | + | 0.939535i | \(0.611257\pi\) |
−0.999375 | + | 0.0353584i | \(0.988743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 2430.02i | − | 0.133202i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9526.83 | + | 27115.7i | −0.519962 | + | 1.47994i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 44253.1 | − | 14378.7i | 2.40489 | − | 0.781395i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16809.3 | 0.909564 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 275.799 | 0.0148599 | 0.00742994 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00742994 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5864.94 | + | 1905.63i | −0.314652 | + | 0.102237i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13424.0 | + | 10248.0i | 0.717130 | + | 0.547463i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 795.924i | 0.0423392i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3614.00 | + | 2625.72i | −0.191434 | + | 0.139085i | −0.679374 | − | 0.733792i | \(-0.737748\pi\) |
0.487940 | + | 0.872877i | \(0.337748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1139.69 | + | 828.033i | 0.0601149 | + | 0.0436760i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4187.44 | + | 5763.52i | 0.219945 | + | 0.302728i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4000.14 | + | 1195.65i | −0.209226 | + | 0.0625384i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20162.0 | + | 6551.02i | 1.05016 | + | 0.341217i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1471.37 | + | 4528.41i | −0.0763183 | + | 0.234883i | −0.981937 | − | 0.189210i | \(-0.939407\pi\) |
0.905618 | + | 0.424094i | \(0.139407\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −766.638 | − | 2359.47i | −0.0395993 | − | 0.121874i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6344.19 | − | 8732.03i | 0.326339 | − | 0.449167i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4880.87 | − | 3912.67i | −0.250029 | − | 0.200431i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11696.4 | − | 16098.8i | 0.596694 | − | 0.821279i | −0.398707 | − | 0.917079i | \(-0.630541\pi\) |
0.995401 | + | 0.0957995i | \(0.0305408\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6527.87 | − | 20090.7i | −0.331650 | − | 1.02071i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3227.24 | − | 9932.44i | 0.163289 | − | 0.502551i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21893.7 | − | 7113.68i | −1.10322 | − | 0.358458i | −0.299879 | − | 0.953977i | \(-0.596946\pi\) |
−0.803341 | + | 0.595519i | \(0.796946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1851.07 | − | 2679.11i | −0.0928947 | − | 0.134450i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21128.7 | + | 29081.2i | 1.05602 | + | 1.45349i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3899.72 | − | 2833.31i | −0.194119 | − | 0.141035i | 0.486481 | − | 0.873691i | \(-0.338280\pi\) |
−0.680599 | + | 0.732656i | \(0.738280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2080.63 | + | 1511.67i | −0.103150 | + | 0.0749426i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11267.6i | 0.556348i | 0.960531 | + | 0.278174i | \(0.0897291\pi\) | ||||
−0.960531 | + | 0.278174i | \(0.910271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10076.2 | + | 33710.5i | 0.495521 | + | 1.65780i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −123.718 | + | 40.1984i | −0.00605971 | + | 0.00196892i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22772.4 | −1.11093 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21124.7 | 1.02643 | 0.513216 | − | 0.858259i | \(-0.328454\pi\) | ||||
0.513216 | + | 0.858259i | \(0.328454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18048.8 | + | 5864.41i | −0.873485 | + | 0.283813i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4996.17 | − | 16715.0i | −0.240833 | − | 0.805723i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25198.7i | 1.20986i | 0.796279 | + | 0.604929i | \(0.206799\pi\) | ||||
−0.796279 | + | 0.604929i | \(0.793201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37804.3 | − | 27466.4i | 1.80792 | − | 1.31353i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7499.45 | − | 5448.67i | −0.357234 | − | 0.259546i | 0.394664 | − | 0.918826i | \(-0.370861\pi\) |
−0.751897 | + | 0.659280i | \(0.770861\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2703.26 | − | 3720.72i | −0.128263 | − | 0.176539i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2038.37 | + | 2950.20i | 0.0963364 | + | 0.139431i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4725.51 | + | 1535.41i | 0.222462 | + | 0.0722822i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2189.37 | − | 6738.20i | 0.102667 | − | 0.315976i | −0.886509 | − | 0.462712i | \(-0.846877\pi\) |
0.989176 | + | 0.146735i | \(0.0468766\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1612.25 | + | 4961.98i | 0.0753095 | + | 0.231779i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7895.59 | + | 10867.3i | −0.367380 | + | 0.505655i | −0.952186 | − | 0.305518i | \(-0.901170\pi\) |
0.584806 | + | 0.811173i | \(0.301170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1472.12 | − | 5387.39i | −0.0682325 | − | 0.249704i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3685.75 | + | 5073.00i | −0.170174 | + | 0.234225i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8979.47 | − | 27636.0i | −0.412995 | − | 1.27107i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1122.89 | + | 3455.89i | −0.0514469 | + | 0.158337i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6943.83 | + | 2256.19i | 0.316925 | + | 0.102975i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29754.5 | − | 8893.71i | 1.35284 | − | 0.404370i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7420.09 | − | 10212.9i | −0.336084 | − | 0.462579i | 0.607209 | − | 0.794542i | \(-0.292289\pi\) |
−0.943292 | + | 0.331963i | \(0.892289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16216.1 | + | 11781.7i | 0.731695 | + | 0.531607i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8626.20 | − | 6267.30i | 0.387753 | − | 0.281719i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5269.39i | − | 0.235967i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14943.1 | − | 11407.7i | −0.666636 | − | 0.508915i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19301.2 | + | 6271.34i | −0.857822 | + | 0.278723i | −0.704718 | − | 0.709487i | \(-0.748927\pi\) |
−0.153103 | + | 0.988210i | \(0.548927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40104.6 | 1.77572 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3527.65 | 0.155610 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2225.53 | − | 723.119i | 0.0978048 | − | 0.0317787i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9962.50 | − | 28355.7i | 0.436189 | − | 1.24150i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18054.2i | 0.787531i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34293.3 | + | 24915.5i | −1.49034 | + | 1.08280i | −0.516308 | + | 0.856403i | \(0.672694\pi\) |
−0.974036 | + | 0.226395i | \(0.927306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18821.8 | + | 13674.9i | 0.814949 | + | 0.592095i | 0.915261 | − | 0.402861i | \(-0.131984\pi\) |
−0.100312 | + | 0.994956i | \(0.531984\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8421.25 | + | 11590.9i | 0.363280 | + | 0.500011i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3686.14 | − | 4828.53i | 0.158429 | − | 0.207529i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6202.79 | − | 2015.41i | −0.265616 | − | 0.0863038i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 80.1951 | − | 246.815i | 0.00342154 | − | 0.0105304i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6419.92 | − | 19758.5i | −0.272907 | − | 0.839921i | −0.989766 | − | 0.142703i | \(-0.954421\pi\) |
0.716859 | − | 0.697219i | \(-0.245579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1454.67 | − | 2002.18i | 0.0616120 | − | 0.0848017i | −0.777099 | − | 0.629378i | \(-0.783310\pi\) |
0.838711 | + | 0.544577i | \(0.183310\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35337.2 | + | 9656.02i | −1.49125 | + | 0.407490i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6256.34 | + | 8611.12i | −0.263064 | + | 0.362077i | −0.920033 | − | 0.391841i | \(-0.871838\pi\) |
0.656969 | + | 0.753918i | \(0.271838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6995.29 | + | 21529.3i | 0.293072 | + | 0.901982i | 0.983862 | + | 0.178927i | \(0.0572626\pi\) |
−0.690791 | + | 0.723055i | \(0.742737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6935.00 | + | 21343.8i | −0.289498 | + | 0.890983i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7354.33 | − | 2389.57i | −0.305897 | − | 0.0993920i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −127.772 | + | 5388.23i | −0.00529548 | + | 0.223314i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3831.43 | + | 5273.52i | 0.158224 | + | 0.217777i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27328.7 | − | 19855.5i | −1.12454 | − | 0.817029i | −0.139653 | − | 0.990201i | \(-0.544599\pi\) |
−0.984892 | + | 0.173171i | \(0.944599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17705.0 | − | 12863.4i | 0.725941 | − | 0.527427i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14993.5i | 0.612577i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24110.6 | + | 571.737i | 0.981572 | + | 0.0232762i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34723.3 | − | 11282.3i | 1.40863 | − | 0.457691i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28270.5 | −1.14281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11966.3 | 0.482020 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35704.6 | + | 11601.1i | −1.43318 | + | 0.465669i | −0.919764 | − | 0.392471i | \(-0.871620\pi\) |
−0.513416 | + | 0.858140i | \(0.671620\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1842.39 | − | 1272.96i | 0.0736942 | − | 0.0509172i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24120.1i | 0.961408i | 0.876883 | + | 0.480704i | \(0.159619\pi\) | ||||
−0.876883 | + | 0.480704i | \(0.840381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5422.85 | + | 3939.93i | −0.215396 | + | 0.156494i | −0.690252 | − | 0.723569i | \(-0.742500\pi\) |
0.474856 | + | 0.880064i | \(0.342500\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23904.3 | − | 17367.5i | −0.946174 | − | 0.687436i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18359.9 | − | 25270.2i | −0.724193 | − | 0.996766i | −0.999374 | − | 0.0353735i | \(-0.988738\pi\) |
0.275181 | − | 0.961392i | \(-0.411262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37136.9 | − | 13047.7i | −1.45976 | − | 0.512872i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −58449.2 | − | 18991.3i | −2.28955 | − | 0.743920i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10560.5 | + | 32501.8i | −0.412244 | + | 1.26876i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1186.30 | + | 3651.04i | 0.0461494 | + | 0.142033i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −76.6988 | + | 105.567i | −0.00297350 | + | 0.00409267i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15168.7 | + | 18029.2i | −0.586051 | + | 0.696569i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14264.4 | − | 19633.2i | 0.549228 | − | 0.755948i | −0.440679 | − | 0.897665i | \(-0.645262\pi\) |
0.989907 | + | 0.141717i | \(0.0452623\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10528.1 | − | 32402.3i | −0.403988 | − | 1.24335i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1004.56 | − | 3091.71i | 0.0384159 | − | 0.118232i | −0.930010 | − | 0.367535i | \(-0.880202\pi\) |
0.968425 | + | 0.249304i | \(0.0802017\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11569.0 | − | 3759.01i | −0.440916 | − | 0.143262i | 0.0801422 | − | 0.996783i | \(-0.474463\pi\) |
−0.521058 | + | 0.853521i | \(0.674463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41131.9 | + | 14451.3i | 1.56230 | + | 0.548898i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7631.43 | − | 10503.8i | −0.288882 | − | 0.397612i | 0.639768 | − | 0.768568i | \(-0.279030\pi\) |
−0.928651 | + | 0.370956i | \(0.879030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12497.6 | + | 9080.02i | 0.471491 | + | 0.342558i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31441.9 | − | 22843.8i | 1.18220 | − | 0.858920i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 25045.2i | − | 0.938529i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13960.2 | − | 9645.46i | 0.521383 | − | 0.360237i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4746.20 | − | 1542.13i | 0.176668 | − | 0.0574028i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2235.94 | −0.0829509 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44642.8 | −1.65069 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6307.20 | + | 2049.33i | −0.232437 | + | 0.0755233i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36801.1 | + | 872.669i | 1.35172 | + | 0.0320536i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 34569.1i | − | 1.26554i | −0.774339 | − | 0.632771i | \(-0.781917\pi\) | ||
0.774339 | − | 0.632771i | \(-0.218083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 93.0987 | − | 67.6402i | 0.00339702 | − | 0.00246808i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7607.64 | − | 5527.27i | −0.276676 | − | 0.201017i | 0.440790 | − | 0.897610i | \(-0.354698\pi\) |
−0.717466 | + | 0.696593i | \(0.754698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1854.89 | − | 2553.03i | −0.0672375 | − | 0.0925445i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1096.07 | − | 46222.2i | 0.0396011 | − | 1.67001i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10498.6 | − | 3411.19i | −0.378073 | − | 0.122843i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12428.8 | − | 38251.9i | 0.446124 | − | 1.37303i | −0.435121 | − | 0.900372i | \(-0.643295\pi\) |
0.881246 | − | 0.472658i | \(-0.156705\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7126.43 | + | 21932.9i | 0.254966 | + | 0.784705i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −228.101 | + | 313.954i | −0.00813439 | + | 0.0111960i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8774.34 | − | 3318.49i | −0.311890 | − | 0.117958i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −210.834 | + | 290.189i | −0.00747002 | + | 0.0102816i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4084.78 | − | 12571.7i | −0.144260 | − | 0.443986i | 0.852655 | − | 0.522474i | \(-0.174991\pi\) |
−0.996915 | + | 0.0784880i | \(0.974991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1492.28 | + | 4592.76i | −0.0525322 | + | 0.161677i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24483.5 | + | 7955.16i | 0.859114 | + | 0.279143i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −52785.5 | + | 69144.5i | −1.84628 | + | 2.41847i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3967.34 | − | 5460.58i | −0.138322 | − | 0.190384i | 0.734236 | − | 0.678894i | \(-0.237540\pi\) |
−0.872558 | + | 0.488510i | \(0.837540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19097.5 | − | 13875.1i | −0.663709 | − | 0.482213i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19548.5 | + | 14202.8i | −0.677219 | + | 0.492028i | −0.872434 | − | 0.488732i | \(-0.837460\pi\) |
0.195215 | + | 0.980760i | \(0.437460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56385.9i | 1.94717i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9115.51 | − | 25945.0i | 0.313786 | − | 0.893112i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2569.36 | + | 834.834i | −0.0881656 | + | 0.0286467i | −0.352768 | − | 0.935711i | \(-0.614759\pi\) |
0.264602 | + | 0.964358i | \(0.414759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 249.910 | 0.00854838 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31061.6 | −1.05914 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33842.8 | − | 10996.2i | 1.15034 | − | 0.373768i | 0.329069 | − | 0.944306i | \(-0.393265\pi\) |
0.821272 | + | 0.570537i | \(0.193265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37391.9 | − | 28545.3i | −1.26699 | − | 0.967229i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14666.1i | 0.495389i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7749.66 | − | 5630.46i | 0.260948 | − | 0.189590i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22486.4 | + | 16337.4i | 0.754807 | + | 0.548399i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1935.27 | + | 2663.67i | 0.0647593 | + | 0.0891335i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19746.8 | − | 5902.38i | 0.658727 | − | 0.196896i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5597.59 | − | 1818.77i | −0.186149 | − | 0.0604836i | 0.214459 | − | 0.976733i | \(-0.431201\pi\) |
−0.400608 | + | 0.916249i | \(0.631201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16558.9 | + | 50963.1i | −0.548967 | + | 1.68955i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12777.2 | + | 39324.0i | 0.422285 | + | 1.29966i | 0.905570 | + | 0.424196i | \(0.139443\pi\) |
−0.483286 | + | 0.875463i | \(0.660557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25473.9 | − | 35061.8i | 0.839318 | − | 1.15522i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3907.84 | − | 185.439i | −0.128360 | − | 0.00609106i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16220.0 | + | 22324.9i | −0.531141 | + | 0.731052i | −0.987304 | − | 0.158844i | \(-0.949223\pi\) |
0.456163 | + | 0.889896i | \(0.349223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26444.8 | + | 81388.8i | 0.863310 | + | 2.65699i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −205.478 | + | 632.397i | −0.00668748 | + | 0.0205819i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53965.8 | + | 17534.5i | 1.75101 | + | 0.568937i | 0.996207 | − | 0.0870170i | \(-0.0277335\pi\) |
0.754801 | + | 0.655954i | \(0.227733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23669.3 | − | 34257.3i | −0.765650 | − | 1.10815i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14969.0 | − | 20603.1i | −0.482745 | − | 0.664441i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10238.6 | + | 7438.77i | 0.329189 | + | 0.239170i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14200.8 | + | 10317.5i | −0.455200 | + | 0.330722i | −0.791646 | − | 0.610981i | \(-0.790775\pi\) |
0.336445 | + | 0.941703i | \(0.390775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 46814.3i | − | 1.49608i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1037.71 | + | 3471.72i | 0.0330629 | + | 0.110614i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20217.4 | − | 6569.04i | 0.642219 | − | 0.208669i | 0.0302386 | − | 0.999543i | \(-0.490373\pi\) |
0.611980 | + | 0.790873i | \(0.290373\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10948.9 | 0.346756 |
(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 | 100.4.i.a.9.3 | ✓ | 32 | |
5.2 | odd | 4 | 500.4.g.b.201.12 | 64 | |||
5.3 | odd | 4 | 500.4.g.b.201.5 | 64 | |||
5.4 | even | 2 | 500.4.i.a.49.6 | 32 | |||
25.2 | odd | 20 | 500.4.g.b.301.12 | 64 | |||
25.8 | odd | 20 | 2500.4.a.g.1.9 | 32 | |||
25.11 | even | 5 | 500.4.i.a.449.6 | 32 | |||
25.14 | even | 10 | inner | 100.4.i.a.89.3 | yes | 32 | |
25.17 | odd | 20 | 2500.4.a.g.1.24 | 32 | |||
25.23 | odd | 20 | 500.4.g.b.301.5 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.i.a.9.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
100.4.i.a.89.3 | yes | 32 | 25.14 | even | 10 | inner | |
500.4.g.b.201.5 | 64 | 5.3 | odd | 4 | |||
500.4.g.b.201.12 | 64 | 5.2 | odd | 4 | |||
500.4.g.b.301.5 | 64 | 25.23 | odd | 20 | |||
500.4.g.b.301.12 | 64 | 25.2 | odd | 20 | |||
500.4.i.a.49.6 | 32 | 5.4 | even | 2 | |||
500.4.i.a.449.6 | 32 | 25.11 | even | 5 | |||
2500.4.a.g.1.9 | 32 | 25.8 | odd | 20 | |||
2500.4.a.g.1.24 | 32 | 25.17 | odd | 20 |