Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,3,Mod(114,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.114");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.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: | \(3.13352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 6 x^{18} - 827 x^{16} - 12720 x^{14} + 346250 x^{12} + 9668500 x^{10} + 216406250 x^{8} - 4968750000 x^{6} - 201904296875 x^{4} + \cdots + 95367431640625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 114.17 | ||
Root | \(4.94294 - 0.753214i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.114 |
Dual form | 115.3.c.c.114.3 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.38977i | 1.69489i | 0.530886 | + | 0.847443i | \(0.321859\pi\) | ||||
−0.530886 | + | 0.847443i | \(0.678141\pi\) | |||||||
\(3\) | − | 3.81595i | − | 1.27198i | −0.771696 | − | 0.635992i | \(-0.780591\pi\) | ||
0.771696 | − | 0.635992i | \(-0.219409\pi\) | |||||||
\(4\) | −7.49055 | −1.87264 | ||||||||
\(5\) | −4.94294 | − | 0.753214i | −0.988588 | − | 0.150643i | ||||
\(6\) | 12.9352 | 2.15587 | ||||||||
\(7\) | −7.85531 | −1.12219 | −0.561093 | − | 0.827753i | \(-0.689619\pi\) | ||||
−0.561093 | + | 0.827753i | \(0.689619\pi\) | |||||||
\(8\) | − | 11.8322i | − | 1.47902i | ||||||
\(9\) | −5.56149 | −0.617944 | ||||||||
\(10\) | 2.55323 | − | 16.7554i | 0.255323 | − | 1.67554i | ||||
\(11\) | − | 14.6318i | − | 1.33016i | −0.746772 | − | 0.665080i | \(-0.768397\pi\) | ||
0.746772 | − | 0.665080i | \(-0.231603\pi\) | |||||||
\(12\) | 28.5836i | 2.38197i | ||||||||
\(13\) | − | 7.02001i | − | 0.540001i | −0.962860 | − | 0.270000i | \(-0.912976\pi\) | ||
0.962860 | − | 0.270000i | \(-0.0870238\pi\) | |||||||
\(14\) | − | 26.6277i | − | 1.90198i | ||||||
\(15\) | −2.87423 | + | 18.8620i | −0.191615 | + | 1.25747i | ||||
\(16\) | 10.1462 | 0.634137 | ||||||||
\(17\) | −15.0008 | −0.882402 | −0.441201 | − | 0.897408i | \(-0.645447\pi\) | ||||
−0.441201 | + | 0.897408i | \(0.645447\pi\) | |||||||
\(18\) | − | 18.8522i | − | 1.04734i | ||||||
\(19\) | 19.6736i | 1.03545i | 0.855546 | + | 0.517726i | \(0.173221\pi\) | ||||
−0.855546 | + | 0.517726i | \(0.826779\pi\) | |||||||
\(20\) | 37.0254 | + | 5.64199i | 1.85127 | + | 0.282100i | ||||
\(21\) | 29.9755i | 1.42740i | ||||||||
\(22\) | 49.5984 | 2.25447 | ||||||||
\(23\) | 3.89296 | + | 22.6681i | 0.169259 | + | 0.985572i | ||||
\(24\) | −45.1511 | −1.88129 | ||||||||
\(25\) | 23.8653 | + | 7.44619i | 0.954613 | + | 0.297848i | ||||
\(26\) | 23.7962 | 0.915240 | ||||||||
\(27\) | − | 13.1212i | − | 0.485970i | ||||||
\(28\) | 58.8406 | 2.10145 | ||||||||
\(29\) | −36.8947 | −1.27223 | −0.636115 | − | 0.771594i | \(-0.719460\pi\) | ||||
−0.636115 | + | 0.771594i | \(0.719460\pi\) | |||||||
\(30\) | −63.9380 | − | 9.74299i | −2.13127 | − | 0.324766i | ||||
\(31\) | −12.6964 | −0.409563 | −0.204781 | − | 0.978808i | \(-0.565648\pi\) | ||||
−0.204781 | + | 0.978808i | \(0.565648\pi\) | |||||||
\(32\) | − | 12.9355i | − | 0.404233i | ||||||
\(33\) | −55.8341 | −1.69194 | ||||||||
\(34\) | − | 50.8494i | − | 1.49557i | ||||||
\(35\) | 38.8283 | + | 5.91673i | 1.10938 | + | 0.169049i | ||||
\(36\) | 41.6587 | 1.15719 | ||||||||
\(37\) | −1.40335 | −0.0379283 | −0.0189642 | − | 0.999820i | \(-0.506037\pi\) | ||||
−0.0189642 | + | 0.999820i | \(0.506037\pi\) | |||||||
\(38\) | −66.6890 | −1.75497 | ||||||||
\(39\) | −26.7880 | −0.686872 | ||||||||
\(40\) | −8.91217 | + | 58.4858i | −0.222804 | + | 1.46214i | ||||
\(41\) | 5.88082 | 0.143435 | 0.0717173 | − | 0.997425i | \(-0.477152\pi\) | ||||
0.0717173 | + | 0.997425i | \(0.477152\pi\) | |||||||
\(42\) | −101.610 | −2.41929 | ||||||||
\(43\) | 81.8367 | 1.90318 | 0.951589 | − | 0.307373i | \(-0.0994499\pi\) | ||||
0.951589 | + | 0.307373i | \(0.0994499\pi\) | |||||||
\(44\) | 109.600i | 2.49091i | ||||||||
\(45\) | 27.4901 | + | 4.18900i | 0.610892 | + | 0.0930888i | ||||
\(46\) | −76.8398 | + | 13.1962i | −1.67043 | + | 0.286875i | ||||
\(47\) | − | 65.3796i | − | 1.39106i | −0.718499 | − | 0.695528i | \(-0.755171\pi\) | ||
0.718499 | − | 0.695528i | \(-0.244829\pi\) | |||||||
\(48\) | − | 38.7174i | − | 0.806612i | ||||||
\(49\) | 12.7059 | 0.259303 | ||||||||
\(50\) | −25.2409 | + | 80.8980i | −0.504818 | + | 1.61796i | ||||
\(51\) | 57.2425i | 1.12240i | ||||||||
\(52\) | 52.5838i | 1.01123i | ||||||||
\(53\) | −59.2189 | −1.11734 | −0.558668 | − | 0.829391i | \(-0.688688\pi\) | ||||
−0.558668 | + | 0.829391i | \(0.688688\pi\) | |||||||
\(54\) | 44.4778 | 0.823663 | ||||||||
\(55\) | −11.0209 | + | 72.3240i | −0.200379 | + | 1.31498i | ||||
\(56\) | 92.9454i | 1.65974i | ||||||||
\(57\) | 75.0735 | 1.31708 | ||||||||
\(58\) | − | 125.065i | − | 2.15629i | ||||||
\(59\) | −16.2369 | −0.275202 | −0.137601 | − | 0.990488i | \(-0.543939\pi\) | ||||
−0.137601 | + | 0.990488i | \(0.543939\pi\) | |||||||
\(60\) | 21.5296 | − | 141.287i | 0.358826 | − | 2.35478i | ||||
\(61\) | − | 108.080i | − | 1.77181i | −0.463870 | − | 0.885903i | \(-0.653539\pi\) | ||
0.463870 | − | 0.885903i | \(-0.346461\pi\) | |||||||
\(62\) | − | 43.0381i | − | 0.694162i | ||||||
\(63\) | 43.6872 | 0.693448 | ||||||||
\(64\) | 84.4330 | 1.31927 | ||||||||
\(65\) | −5.28757 | + | 34.6995i | −0.0813473 | + | 0.533838i | ||||
\(66\) | − | 189.265i | − | 2.86765i | ||||||
\(67\) | 95.6533 | 1.42766 | 0.713830 | − | 0.700319i | \(-0.246959\pi\) | ||||
0.713830 | + | 0.700319i | \(0.246959\pi\) | |||||||
\(68\) | 112.365 | 1.65242 | ||||||||
\(69\) | 86.5006 | − | 14.8554i | 1.25363 | − | 0.215295i | ||||
\(70\) | −20.0564 | + | 131.619i | −0.286520 | + | 1.88027i | ||||
\(71\) | −89.4921 | −1.26045 | −0.630226 | − | 0.776412i | \(-0.717038\pi\) | ||||
−0.630226 | + | 0.776412i | \(0.717038\pi\) | |||||||
\(72\) | 65.8046i | 0.913953i | ||||||||
\(73\) | − | 58.6284i | − | 0.803129i | −0.915831 | − | 0.401564i | \(-0.868467\pi\) | ||
0.915831 | − | 0.401564i | \(-0.131533\pi\) | |||||||
\(74\) | − | 4.75703i | − | 0.0642842i | ||||||
\(75\) | 28.4143 | − | 91.0690i | 0.378857 | − | 1.21425i | ||||
\(76\) | − | 147.366i | − | 1.93903i | ||||||
\(77\) | 114.937i | 1.49269i | ||||||||
\(78\) | − | 90.8053i | − | 1.16417i | ||||||
\(79\) | 42.3986i | 0.536691i | 0.963323 | + | 0.268345i | \(0.0864768\pi\) | ||||
−0.963323 | + | 0.268345i | \(0.913523\pi\) | |||||||
\(80\) | −50.1520 | − | 7.64226i | −0.626900 | − | 0.0955282i | ||||
\(81\) | −100.123 | −1.23609 | ||||||||
\(82\) | 19.9346i | 0.243105i | ||||||||
\(83\) | 57.2277 | 0.689490 | 0.344745 | − | 0.938696i | \(-0.387965\pi\) | ||||
0.344745 | + | 0.938696i | \(0.387965\pi\) | |||||||
\(84\) | − | 224.533i | − | 2.67301i | ||||||
\(85\) | 74.1482 | + | 11.2988i | 0.872332 | + | 0.132928i | ||||
\(86\) | 277.408i | 3.22567i | ||||||||
\(87\) | 140.788i | 1.61826i | ||||||||
\(88\) | −173.126 | −1.96734 | ||||||||
\(89\) | − | 21.1091i | − | 0.237181i | −0.992943 | − | 0.118591i | \(-0.962162\pi\) | ||
0.992943 | − | 0.118591i | \(-0.0378376\pi\) | |||||||
\(90\) | −14.1997 | + | 93.1853i | −0.157775 | + | 1.03539i | ||||
\(91\) | 55.1443i | 0.605982i | ||||||||
\(92\) | −29.1604 | − | 169.797i | −0.316961 | − | 1.84562i | ||||
\(93\) | 48.4490i | 0.520957i | ||||||||
\(94\) | 221.622 | 2.35768 | ||||||||
\(95\) | 14.8184 | − | 97.2455i | 0.155984 | − | 1.02364i | ||||
\(96\) | −49.3611 | −0.514178 | ||||||||
\(97\) | −101.231 | −1.04362 | −0.521811 | − | 0.853061i | \(-0.674743\pi\) | ||||
−0.521811 | + | 0.853061i | \(0.674743\pi\) | |||||||
\(98\) | 43.0699i | 0.439489i | ||||||||
\(99\) | 81.3745i | 0.821964i | ||||||||
\(100\) | −178.765 | − | 55.7761i | −1.78765 | − | 0.557761i | ||||
\(101\) | 10.8200 | 0.107129 | 0.0535644 | − | 0.998564i | \(-0.482942\pi\) | ||||
0.0535644 | + | 0.998564i | \(0.482942\pi\) | |||||||
\(102\) | −194.039 | −1.90234 | ||||||||
\(103\) | −78.3852 | −0.761021 | −0.380511 | − | 0.924777i | \(-0.624252\pi\) | ||||
−0.380511 | + | 0.924777i | \(0.624252\pi\) | |||||||
\(104\) | −83.0620 | −0.798674 | ||||||||
\(105\) | 22.5780 | − | 148.167i | 0.215028 | − | 1.41111i | ||||
\(106\) | − | 200.738i | − | 1.89376i | ||||||
\(107\) | −129.231 | −1.20776 | −0.603881 | − | 0.797074i | \(-0.706380\pi\) | ||||
−0.603881 | + | 0.797074i | \(0.706380\pi\) | |||||||
\(108\) | 98.2849i | 0.910045i | ||||||||
\(109\) | 0.761552i | 0.00698671i | 0.999994 | + | 0.00349336i | \(0.00111197\pi\) | ||||
−0.999994 | + | 0.00349336i | \(0.998888\pi\) | |||||||
\(110\) | −245.162 | − | 37.3582i | −2.22874 | − | 0.339620i | ||||
\(111\) | 5.35511i | 0.0482442i | ||||||||
\(112\) | −79.7015 | −0.711620 | ||||||||
\(113\) | 82.8256 | 0.732970 | 0.366485 | − | 0.930424i | \(-0.380561\pi\) | ||||
0.366485 | + | 0.930424i | \(0.380561\pi\) | |||||||
\(114\) | 254.482i | 2.23230i | ||||||||
\(115\) | −2.16870 | − | 114.980i | −0.0188582 | − | 0.999822i | ||||
\(116\) | 276.362 | 2.38243 | ||||||||
\(117\) | 39.0417i | 0.333690i | ||||||||
\(118\) | − | 55.0395i | − | 0.466436i | ||||||
\(119\) | 117.836 | 0.990220 | ||||||||
\(120\) | 223.179 | + | 34.0084i | 1.85983 | + | 0.283404i | ||||
\(121\) | −93.0886 | −0.769327 | ||||||||
\(122\) | 366.367 | 3.00301 | ||||||||
\(123\) | − | 22.4409i | − | 0.182447i | ||||||
\(124\) | 95.1034 | 0.766963 | ||||||||
\(125\) | −112.356 | − | 54.7818i | −0.898851 | − | 0.438254i | ||||
\(126\) | 148.090i | 1.17532i | ||||||||
\(127\) | 202.484i | 1.59436i | 0.603739 | + | 0.797182i | \(0.293677\pi\) | ||||
−0.603739 | + | 0.797182i | \(0.706323\pi\) | |||||||
\(128\) | 234.467i | 1.83177i | ||||||||
\(129\) | − | 312.285i | − | 2.42081i | ||||||
\(130\) | −117.623 | − | 17.9237i | −0.904795 | − | 0.137874i | ||||
\(131\) | 161.376 | 1.23188 | 0.615938 | − | 0.787795i | \(-0.288777\pi\) | ||||
0.615938 | + | 0.787795i | \(0.288777\pi\) | |||||||
\(132\) | 418.229 | 3.16840 | ||||||||
\(133\) | − | 154.542i | − | 1.16197i | ||||||
\(134\) | 324.243i | 2.41972i | ||||||||
\(135\) | −9.88306 | + | 64.8572i | −0.0732079 | + | 0.480424i | ||||
\(136\) | 177.493i | 1.30509i | ||||||||
\(137\) | −207.622 | −1.51549 | −0.757745 | − | 0.652551i | \(-0.773699\pi\) | ||||
−0.757745 | + | 0.652551i | \(0.773699\pi\) | |||||||
\(138\) | 50.3563 | + | 293.217i | 0.364900 | + | 2.12476i | ||||
\(139\) | −139.793 | −1.00570 | −0.502852 | − | 0.864372i | \(-0.667716\pi\) | ||||
−0.502852 | + | 0.864372i | \(0.667716\pi\) | |||||||
\(140\) | −290.846 | − | 44.3196i | −2.07747 | − | 0.316569i | ||||
\(141\) | −249.485 | −1.76940 | ||||||||
\(142\) | − | 303.358i | − | 2.13632i | ||||||
\(143\) | −102.715 | −0.718288 | ||||||||
\(144\) | −56.4280 | −0.391861 | ||||||||
\(145\) | 182.368 | + | 27.7896i | 1.25771 | + | 0.191652i | ||||
\(146\) | 198.737 | 1.36121 | ||||||||
\(147\) | − | 48.4849i | − | 0.329829i | ||||||
\(148\) | 10.5118 | 0.0710260 | ||||||||
\(149\) | − | 153.810i | − | 1.03228i | −0.856504 | − | 0.516140i | \(-0.827368\pi\) | ||
0.856504 | − | 0.516140i | \(-0.172632\pi\) | |||||||
\(150\) | 308.703 | + | 96.3180i | 2.05802 | + | 0.642120i | ||||
\(151\) | 89.8082 | 0.594756 | 0.297378 | − | 0.954760i | \(-0.403888\pi\) | ||||
0.297378 | + | 0.954760i | \(0.403888\pi\) | |||||||
\(152\) | 232.782 | 1.53146 | ||||||||
\(153\) | 83.4270 | 0.545275 | ||||||||
\(154\) | −389.610 | −2.52994 | ||||||||
\(155\) | 62.7578 | + | 9.56315i | 0.404889 | + | 0.0616977i | ||||
\(156\) | 200.657 | 1.28626 | ||||||||
\(157\) | 98.8554 | 0.629652 | 0.314826 | − | 0.949149i | \(-0.398054\pi\) | ||||
0.314826 | + | 0.949149i | \(0.398054\pi\) | |||||||
\(158\) | −143.721 | −0.909629 | ||||||||
\(159\) | 225.976i | 1.42123i | ||||||||
\(160\) | −9.74318 | + | 63.9392i | −0.0608949 | + | 0.399620i | ||||
\(161\) | −30.5804 | − | 178.065i | −0.189940 | − | 1.10600i | ||||
\(162\) | − | 339.395i | − | 2.09503i | ||||||
\(163\) | 64.0772i | 0.393112i | 0.980493 | + | 0.196556i | \(0.0629757\pi\) | ||||
−0.980493 | + | 0.196556i | \(0.937024\pi\) | |||||||
\(164\) | −44.0506 | −0.268601 | ||||||||
\(165\) | 275.985 | + | 42.0551i | 1.67264 | + | 0.254879i | ||||
\(166\) | 193.989i | 1.16861i | ||||||||
\(167\) | − | 154.332i | − | 0.924143i | −0.886843 | − | 0.462072i | \(-0.847106\pi\) | ||
0.886843 | − | 0.462072i | \(-0.152894\pi\) | |||||||
\(168\) | 354.675 | 2.11116 | ||||||||
\(169\) | 119.719 | 0.708399 | ||||||||
\(170\) | −38.3005 | + | 251.346i | −0.225297 | + | 1.47850i | ||||
\(171\) | − | 109.415i | − | 0.639852i | ||||||
\(172\) | −613.002 | −3.56397 | ||||||||
\(173\) | − | 115.869i | − | 0.669761i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||
0.942261 | − | 0.334880i | \(-0.108696\pi\) | |||||||
\(174\) | −477.241 | −2.74276 | ||||||||
\(175\) | −187.470 | − | 58.4921i | −1.07125 | − | 0.334241i | ||||
\(176\) | − | 148.457i | − | 0.843504i | ||||||
\(177\) | 61.9593i | 0.350053i | ||||||||
\(178\) | 71.5551 | 0.401995 | ||||||||
\(179\) | −69.9062 | −0.390538 | −0.195269 | − | 0.980750i | \(-0.562558\pi\) | ||||
−0.195269 | + | 0.980750i | \(0.562558\pi\) | |||||||
\(180\) | −205.916 | − | 31.3779i | −1.14398 | − | 0.174322i | ||||
\(181\) | 198.065i | 1.09428i | 0.837041 | + | 0.547141i | \(0.184284\pi\) | ||||
−0.837041 | + | 0.547141i | \(0.815716\pi\) | |||||||
\(182\) | −186.927 | −1.02707 | ||||||||
\(183\) | −412.429 | −2.25371 | ||||||||
\(184\) | 268.214 | − | 46.0622i | 1.45768 | − | 0.250338i | ||||
\(185\) | 6.93666 | + | 1.05702i | 0.0374955 | + | 0.00571363i | ||||
\(186\) | −164.231 | −0.882964 | ||||||||
\(187\) | 219.489i | 1.17374i | ||||||||
\(188\) | 489.729i | 2.60494i | ||||||||
\(189\) | 103.071i | 0.545349i | ||||||||
\(190\) | 329.640 | + | 50.2311i | 1.73495 | + | 0.264374i | ||||
\(191\) | 54.6601i | 0.286179i | 0.989710 | + | 0.143089i | \(0.0457036\pi\) | ||||
−0.989710 | + | 0.143089i | \(0.954296\pi\) | |||||||
\(192\) | − | 322.192i | − | 1.67809i | ||||||
\(193\) | − | 234.294i | − | 1.21396i | −0.794718 | − | 0.606979i | \(-0.792381\pi\) | ||
0.794718 | − | 0.606979i | \(-0.207619\pi\) | |||||||
\(194\) | − | 343.151i | − | 1.76882i | ||||||
\(195\) | 132.412 | + | 20.1771i | 0.679034 | + | 0.103472i | ||||
\(196\) | −95.1739 | −0.485581 | ||||||||
\(197\) | 103.313i | 0.524430i | 0.965009 | + | 0.262215i | \(0.0844530\pi\) | ||||
−0.965009 | + | 0.262215i | \(0.915547\pi\) | |||||||
\(198\) | −275.841 | −1.39314 | ||||||||
\(199\) | 104.822i | 0.526743i | 0.964694 | + | 0.263372i | \(0.0848345\pi\) | ||||
−0.964694 | + | 0.263372i | \(0.915165\pi\) | |||||||
\(200\) | 88.1047 | − | 282.379i | 0.440523 | − | 1.41190i | ||||
\(201\) | − | 365.008i | − | 1.81596i | ||||||
\(202\) | 36.6774i | 0.181571i | ||||||||
\(203\) | 289.819 | 1.42768 | ||||||||
\(204\) | − | 428.778i | − | 2.10185i | ||||||
\(205\) | −29.0685 | − | 4.42952i | −0.141798 | − | 0.0216074i | ||||
\(206\) | − | 265.708i | − | 1.28984i | ||||||
\(207\) | −21.6507 | − | 126.069i | −0.104593 | − | 0.609028i | ||||
\(208\) | − | 71.2264i | − | 0.342434i | ||||||
\(209\) | 287.860 | 1.37732 | ||||||||
\(210\) | 502.252 | + | 76.5341i | 2.39168 | + | 0.364448i | ||||
\(211\) | −325.637 | −1.54330 | −0.771651 | − | 0.636046i | \(-0.780569\pi\) | ||||
−0.771651 | + | 0.636046i | \(0.780569\pi\) | |||||||
\(212\) | 443.582 | 2.09237 | ||||||||
\(213\) | 341.497i | 1.60327i | ||||||||
\(214\) | − | 438.062i | − | 2.04702i | ||||||
\(215\) | −404.514 | − | 61.6406i | −1.88146 | − | 0.286700i | ||||
\(216\) | −155.252 | −0.718760 | ||||||||
\(217\) | 99.7345 | 0.459606 | ||||||||
\(218\) | −2.58149 | −0.0118417 | ||||||||
\(219\) | −223.723 | −1.02157 | ||||||||
\(220\) | 82.5523 | − | 541.747i | 0.375238 | − | 2.46248i | ||||
\(221\) | 105.306i | 0.476498i | ||||||||
\(222\) | −18.1526 | −0.0817684 | ||||||||
\(223\) | − | 83.1916i | − | 0.373056i | −0.982450 | − | 0.186528i | \(-0.940276\pi\) | ||
0.982450 | − | 0.186528i | \(-0.0597236\pi\) | |||||||
\(224\) | 101.612i | 0.453625i | ||||||||
\(225\) | −132.727 | − | 41.4119i | −0.589897 | − | 0.184053i | ||||
\(226\) | 280.760i | 1.24230i | ||||||||
\(227\) | 20.1827 | 0.0889106 | 0.0444553 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444553 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(228\) | −562.342 | −2.46641 | ||||||||
\(229\) | − | 31.8770i | − | 0.139201i | −0.997575 | − | 0.0696004i | \(-0.977828\pi\) | ||
0.997575 | − | 0.0696004i | \(-0.0221724\pi\) | |||||||
\(230\) | 389.754 | − | 7.35139i | 1.69458 | − | 0.0319626i | ||||
\(231\) | 438.594 | 1.89868 | ||||||||
\(232\) | 436.545i | 1.88166i | ||||||||
\(233\) | − | 70.1772i | − | 0.301190i | −0.988596 | − | 0.150595i | \(-0.951881\pi\) | ||
0.988596 | − | 0.150595i | \(-0.0481189\pi\) | |||||||
\(234\) | −132.343 | −0.565567 | ||||||||
\(235\) | −49.2449 | + | 323.168i | −0.209553 | + | 1.37518i | ||||
\(236\) | 121.624 | 0.515354 | ||||||||
\(237\) | 161.791 | 0.682662 | ||||||||
\(238\) | 399.438i | 1.67831i | ||||||||
\(239\) | 102.474 | 0.428763 | 0.214382 | − | 0.976750i | \(-0.431226\pi\) | ||||
0.214382 | + | 0.976750i | \(0.431226\pi\) | |||||||
\(240\) | −29.1625 | + | 191.378i | −0.121510 | + | 0.797407i | ||||
\(241\) | − | 146.746i | − | 0.608903i | −0.952528 | − | 0.304452i | \(-0.901527\pi\) | ||
0.952528 | − | 0.304452i | \(-0.0984732\pi\) | |||||||
\(242\) | − | 315.549i | − | 1.30392i | ||||||
\(243\) | 263.975i | 1.08632i | ||||||||
\(244\) | 809.581i | 3.31795i | ||||||||
\(245\) | −62.8043 | − | 9.57023i | −0.256344 | − | 0.0390622i | ||||
\(246\) | 76.0696 | 0.309226 | ||||||||
\(247\) | 138.109 | 0.559145 | ||||||||
\(248\) | 150.227i | 0.605753i | ||||||||
\(249\) | − | 218.378i | − | 0.877020i | ||||||
\(250\) | 185.698 | − | 380.863i | 0.742791 | − | 1.52345i | ||||
\(251\) | 244.758i | 0.975133i | 0.873086 | + | 0.487566i | \(0.162115\pi\) | ||||
−0.873086 | + | 0.487566i | \(0.837885\pi\) | |||||||
\(252\) | −327.242 | −1.29858 | ||||||||
\(253\) | 331.675 | − | 56.9609i | 1.31097 | − | 0.225142i | ||||
\(254\) | −686.375 | −2.70226 | ||||||||
\(255\) | 43.1158 | − | 282.946i | 0.169082 | − | 1.10959i | ||||
\(256\) | −457.057 | −1.78538 | ||||||||
\(257\) | 102.219i | 0.397738i | 0.980026 | + | 0.198869i | \(0.0637268\pi\) | ||||
−0.980026 | + | 0.198869i | \(0.936273\pi\) | |||||||
\(258\) | 1058.57 | 4.10300 | ||||||||
\(259\) | 11.0237 | 0.0425626 | ||||||||
\(260\) | 39.6068 | − | 259.918i | 0.152334 | − | 0.999686i | ||||
\(261\) | 205.190 | 0.786167 | ||||||||
\(262\) | 547.027i | 2.08789i | ||||||||
\(263\) | −331.315 | −1.25975 | −0.629876 | − | 0.776696i | \(-0.716894\pi\) | ||||
−0.629876 | + | 0.776696i | \(0.716894\pi\) | |||||||
\(264\) | 660.640i | 2.50242i | ||||||||
\(265\) | 292.715 | + | 44.6045i | 1.10459 | + | 0.168319i | ||||
\(266\) | 523.863 | 1.96941 | ||||||||
\(267\) | −80.5514 | −0.301691 | ||||||||
\(268\) | −716.496 | −2.67349 | ||||||||
\(269\) | −45.6414 | −0.169671 | −0.0848353 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848353 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(270\) | −219.851 | − | 33.5013i | −0.814264 | − | 0.124079i | ||||
\(271\) | 272.196 | 1.00441 | 0.502206 | − | 0.864748i | \(-0.332522\pi\) | ||||
0.502206 | + | 0.864748i | \(0.332522\pi\) | |||||||
\(272\) | −152.201 | −0.559564 | ||||||||
\(273\) | 210.428 | 0.770799 | ||||||||
\(274\) | − | 703.791i | − | 2.56858i | ||||||
\(275\) | 108.951 | − | 349.192i | 0.396185 | − | 1.26979i | ||||
\(276\) | −647.937 | + | 111.275i | −2.34760 | + | 0.403170i | ||||
\(277\) | 347.550i | 1.25469i | 0.778740 | + | 0.627347i | \(0.215859\pi\) | ||||
−0.778740 | + | 0.627347i | \(0.784141\pi\) | |||||||
\(278\) | − | 473.866i | − | 1.70455i | ||||||
\(279\) | 70.6112 | 0.253087 | ||||||||
\(280\) | 70.0079 | − | 459.424i | 0.250028 | − | 1.64080i | ||||
\(281\) | − | 339.063i | − | 1.20663i | −0.797503 | − | 0.603316i | \(-0.793846\pi\) | ||
0.797503 | − | 0.603316i | \(-0.206154\pi\) | |||||||
\(282\) | − | 845.699i | − | 2.99893i | ||||||
\(283\) | 214.943 | 0.759517 | 0.379758 | − | 0.925086i | \(-0.376007\pi\) | ||||
0.379758 | + | 0.925086i | \(0.376007\pi\) | |||||||
\(284\) | 670.345 | 2.36037 | ||||||||
\(285\) | −371.084 | − | 56.5465i | −1.30205 | − | 0.198409i | ||||
\(286\) | − | 348.181i | − | 1.21742i | ||||||
\(287\) | −46.1956 | −0.160960 | ||||||||
\(288\) | 71.9405i | 0.249793i | ||||||||
\(289\) | −63.9751 | −0.221367 | ||||||||
\(290\) | −94.2005 | + | 618.187i | −0.324829 | + | 2.13168i | ||||
\(291\) | 386.294i | 1.32747i | ||||||||
\(292\) | 439.159i | 1.50397i | ||||||||
\(293\) | −164.482 | −0.561371 | −0.280686 | − | 0.959800i | \(-0.590562\pi\) | ||||
−0.280686 | + | 0.959800i | \(0.590562\pi\) | |||||||
\(294\) | 164.353 | 0.559023 | ||||||||
\(295\) | 80.2581 | + | 12.2299i | 0.272062 | + | 0.0414572i | ||||
\(296\) | 16.6047i | 0.0560968i | ||||||||
\(297\) | −191.986 | −0.646418 | ||||||||
\(298\) | 521.380 | 1.74960 | ||||||||
\(299\) | 159.131 | − | 27.3286i | 0.532209 | − | 0.0914000i | ||||
\(300\) | −212.839 | + | 682.157i | −0.709463 | + | 2.27386i | ||||
\(301\) | −642.852 | −2.13572 | ||||||||
\(302\) | 304.429i | 1.00804i | ||||||||
\(303\) | − | 41.2887i | − | 0.136266i | ||||||
\(304\) | 199.612i | 0.656619i | ||||||||
\(305\) | −81.4076 | + | 534.234i | −0.266910 | + | 1.75159i | ||||
\(306\) | 282.799i | 0.924178i | ||||||||
\(307\) | − | 485.528i | − | 1.58152i | −0.612124 | − | 0.790762i | \(-0.709685\pi\) | ||
0.612124 | − | 0.790762i | \(-0.290315\pi\) | |||||||
\(308\) | − | 860.942i | − | 2.79527i | ||||||
\(309\) | 299.114i | 0.968007i | ||||||||
\(310\) | −32.4169 | + | 212.735i | −0.104571 | + | 0.686241i | ||||
\(311\) | −239.365 | −0.769663 | −0.384832 | − | 0.922987i | \(-0.625741\pi\) | ||||
−0.384832 | + | 0.922987i | \(0.625741\pi\) | |||||||
\(312\) | 316.961i | 1.01590i | ||||||||
\(313\) | −72.9249 | −0.232987 | −0.116493 | − | 0.993191i | \(-0.537165\pi\) | ||||
−0.116493 | + | 0.993191i | \(0.537165\pi\) | |||||||
\(314\) | 335.097i | 1.06719i | ||||||||
\(315\) | −215.943 | − | 32.9059i | −0.685535 | − | 0.104463i | ||||
\(316\) | − | 317.589i | − | 1.00503i | ||||||
\(317\) | − | 151.052i | − | 0.476503i | −0.971203 | − | 0.238252i | \(-0.923426\pi\) | ||
0.971203 | − | 0.238252i | \(-0.0765743\pi\) | |||||||
\(318\) | −766.008 | −2.40883 | ||||||||
\(319\) | 539.834i | 1.69227i | ||||||||
\(320\) | −417.348 | − | 63.5962i | −1.30421 | − | 0.198738i | ||||
\(321\) | 493.138i | 1.53625i | ||||||||
\(322\) | 603.601 | − | 103.661i | 1.87454 | − | 0.321927i | ||||
\(323\) | − | 295.120i | − | 0.913685i | ||||||
\(324\) | 749.979 | 2.31475 | ||||||||
\(325\) | 52.2723 | − | 167.535i | 0.160838 | − | 0.515492i | ||||
\(326\) | −217.207 | −0.666279 | ||||||||
\(327\) | 2.90605 | 0.00888699 | ||||||||
\(328\) | − | 69.5829i | − | 0.212143i | ||||||
\(329\) | 513.577i | 1.56102i | ||||||||
\(330\) | −142.557 | + | 935.526i | −0.431991 | + | 2.83493i | ||||
\(331\) | 544.555 | 1.64518 | 0.822590 | − | 0.568634i | \(-0.192528\pi\) | ||||
0.822590 | + | 0.568634i | \(0.192528\pi\) | |||||||
\(332\) | −428.667 | −1.29117 | ||||||||
\(333\) | 7.80471 | 0.0234376 | ||||||||
\(334\) | 523.150 | 1.56632 | ||||||||
\(335\) | −472.808 | − | 72.0474i | −1.41137 | − | 0.215067i | ||||
\(336\) | 304.137i | 0.905170i | ||||||||
\(337\) | 90.1232 | 0.267428 | 0.133714 | − | 0.991020i | \(-0.457310\pi\) | ||||
0.133714 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(338\) | 405.822i | 1.20066i | ||||||||
\(339\) | − | 316.059i | − | 0.932326i | ||||||
\(340\) | −555.411 | − | 84.6346i | −1.63356 | − | 0.248925i | ||||
\(341\) | 185.771i | 0.544784i | ||||||||
\(342\) | 370.891 | 1.08448 | ||||||||
\(343\) | 285.102 | 0.831200 | ||||||||
\(344\) | − | 968.307i | − | 2.81484i | ||||||
\(345\) | −438.756 | + | 8.27565i | −1.27176 | + | 0.0239874i | ||||
\(346\) | 392.768 | 1.13517 | ||||||||
\(347\) | 435.423i | 1.25482i | 0.778689 | + | 0.627411i | \(0.215885\pi\) | ||||
−0.778689 | + | 0.627411i | \(0.784115\pi\) | |||||||
\(348\) | − | 1054.58i | − | 3.03041i | ||||||
\(349\) | 191.631 | 0.549085 | 0.274543 | − | 0.961575i | \(-0.411474\pi\) | ||||
0.274543 | + | 0.961575i | \(0.411474\pi\) | |||||||
\(350\) | 198.275 | − | 635.479i | 0.566500 | − | 1.81565i | ||||
\(351\) | −92.1108 | −0.262424 | ||||||||
\(352\) | −189.269 | −0.537695 | ||||||||
\(353\) | 174.369i | 0.493962i | 0.969020 | + | 0.246981i | \(0.0794386\pi\) | ||||
−0.969020 | + | 0.246981i | \(0.920561\pi\) | |||||||
\(354\) | −210.028 | −0.593299 | ||||||||
\(355\) | 442.354 | + | 67.4067i | 1.24607 | + | 0.189878i | ||||
\(356\) | 158.119i | 0.444155i | ||||||||
\(357\) | − | 449.657i | − | 1.25954i | ||||||
\(358\) | − | 236.966i | − | 0.661917i | ||||||
\(359\) | − | 490.103i | − | 1.36519i | −0.730797 | − | 0.682594i | \(-0.760852\pi\) | ||
0.730797 | − | 0.682594i | \(-0.239148\pi\) | |||||||
\(360\) | 49.5650 | − | 325.268i | 0.137681 | − | 0.903523i | ||||
\(361\) | −26.0507 | −0.0721626 | ||||||||
\(362\) | −671.395 | −1.85468 | ||||||||
\(363\) | 355.222i | 0.978572i | ||||||||
\(364\) | − | 413.062i | − | 1.13478i | ||||||
\(365\) | −44.1598 | + | 289.797i | −0.120986 | + | 0.793964i | ||||
\(366\) | − | 1398.04i | − | 3.81978i | ||||||
\(367\) | 443.384 | 1.20813 | 0.604065 | − | 0.796935i | \(-0.293547\pi\) | ||||
0.604065 | + | 0.796935i | \(0.293547\pi\) | |||||||
\(368\) | 39.4987 | + | 229.995i | 0.107333 | + | 0.624987i | ||||
\(369\) | −32.7061 | −0.0886345 | ||||||||
\(370\) | −3.58306 | + | 23.5137i | −0.00968395 | + | 0.0635506i | ||||
\(371\) | 465.182 | 1.25386 | ||||||||
\(372\) | − | 362.910i | − | 0.975565i | ||||||
\(373\) | −379.967 | −1.01868 | −0.509339 | − | 0.860566i | \(-0.670110\pi\) | ||||
−0.509339 | + | 0.860566i | \(0.670110\pi\) | |||||||
\(374\) | −744.016 | −1.98935 | ||||||||
\(375\) | −209.045 | + | 428.747i | −0.557453 | + | 1.14332i | ||||
\(376\) | −773.584 | −2.05740 | ||||||||
\(377\) | 259.001i | 0.687005i | ||||||||
\(378\) | −349.387 | −0.924304 | ||||||||
\(379\) | − | 219.444i | − | 0.579008i | −0.957177 | − | 0.289504i | \(-0.906510\pi\) | ||
0.957177 | − | 0.289504i | \(-0.0934904\pi\) | |||||||
\(380\) | −110.998 | + | 728.422i | −0.292101 | + | 1.91690i | ||||
\(381\) | 772.670 | 2.02801 | ||||||||
\(382\) | −185.285 | −0.485040 | ||||||||
\(383\) | 188.650 | 0.492558 | 0.246279 | − | 0.969199i | \(-0.420792\pi\) | ||||
0.246279 | + | 0.969199i | \(0.420792\pi\) | |||||||
\(384\) | 894.715 | 2.32999 | ||||||||
\(385\) | 86.5722 | − | 568.127i | 0.224863 | − | 1.47565i | ||||
\(386\) | 794.202 | 2.05752 | ||||||||
\(387\) | −455.134 | −1.17606 | ||||||||
\(388\) | 758.279 | 1.95433 | ||||||||
\(389\) | 139.634i | 0.358955i | 0.983762 | + | 0.179478i | \(0.0574408\pi\) | ||||
−0.983762 | + | 0.179478i | \(0.942559\pi\) | |||||||
\(390\) | −68.3958 | + | 448.845i | −0.175374 | + | 1.15089i | ||||
\(391\) | −58.3976 | − | 340.041i | −0.149355 | − | 0.869670i | ||||
\(392\) | − | 150.338i | − | 0.383515i | ||||||
\(393\) | − | 615.802i | − | 1.56693i | ||||||
\(394\) | −350.207 | −0.888850 | ||||||||
\(395\) | 31.9352 | − | 209.574i | 0.0808486 | − | 0.530566i | ||||
\(396\) | − | 609.540i | − | 1.53924i | ||||||
\(397\) | − | 572.066i | − | 1.44097i | −0.693470 | − | 0.720486i | \(-0.743919\pi\) | ||
0.693470 | − | 0.720486i | \(-0.256081\pi\) | |||||||
\(398\) | −355.322 | −0.892769 | ||||||||
\(399\) | −589.726 | −1.47801 | ||||||||
\(400\) | 242.142 | + | 75.5505i | 0.605356 | + | 0.188876i | ||||
\(401\) | − | 401.445i | − | 1.00111i | −0.865705 | − | 0.500555i | \(-0.833129\pi\) | ||
0.865705 | − | 0.500555i | \(-0.166871\pi\) | |||||||
\(402\) | 1237.30 | 3.07785 | ||||||||
\(403\) | 89.1292i | 0.221164i | ||||||||
\(404\) | −81.0479 | −0.200614 | ||||||||
\(405\) | 494.903 | + | 75.4143i | 1.22198 | + | 0.186208i | ||||
\(406\) | 982.421i | 2.41976i | ||||||||
\(407\) | 20.5334i | 0.0504507i | ||||||||
\(408\) | 677.303 | 1.66006 | ||||||||
\(409\) | −106.927 | −0.261436 | −0.130718 | − | 0.991420i | \(-0.541728\pi\) | ||||
−0.130718 | + | 0.991420i | \(0.541728\pi\) | |||||||
\(410\) | 15.0151 | − | 98.5357i | 0.0366221 | − | 0.240331i | ||||
\(411\) | 792.276i | 1.92768i | ||||||||
\(412\) | 587.148 | 1.42512 | ||||||||
\(413\) | 127.546 | 0.308828 | ||||||||
\(414\) | 427.344 | − | 73.3908i | 1.03223 | − | 0.177273i | ||||
\(415\) | −282.873 | − | 43.1047i | −0.681622 | − | 0.103867i | ||||
\(416\) | −90.8071 | −0.218286 | ||||||||
\(417\) | 533.443i | 1.27924i | ||||||||
\(418\) | 975.778i | 2.33440i | ||||||||
\(419\) | − | 704.907i | − | 1.68236i | −0.540758 | − | 0.841178i | \(-0.681863\pi\) | ||
0.540758 | − | 0.841178i | \(-0.318137\pi\) | |||||||
\(420\) | −169.121 | + | 1109.85i | −0.402670 | + | 2.64251i | ||||
\(421\) | 579.217i | 1.37581i | 0.725800 | + | 0.687906i | \(0.241470\pi\) | ||||
−0.725800 | + | 0.687906i | \(0.758530\pi\) | |||||||
\(422\) | − | 1103.83i | − | 2.61572i | ||||||
\(423\) | 363.608i | 0.859594i | ||||||||
\(424\) | 700.688i | 1.65257i | ||||||||
\(425\) | −358.000 | − | 111.699i | −0.842353 | − | 0.262821i | ||||
\(426\) | −1157.60 | −2.71737 | ||||||||
\(427\) | 849.003i | 1.98830i | ||||||||
\(428\) | 968.009 | 2.26170 | ||||||||
\(429\) | 391.956i | 0.913650i | ||||||||
\(430\) | 208.947 | − | 1371.21i | 0.485924 | − | 3.18886i | ||||
\(431\) | − | 366.876i | − | 0.851220i | −0.904907 | − | 0.425610i | \(-0.860060\pi\) | ||
0.904907 | − | 0.425610i | \(-0.139940\pi\) | |||||||
\(432\) | − | 133.130i | − | 0.308171i | ||||||
\(433\) | −684.534 | −1.58091 | −0.790455 | − | 0.612520i | \(-0.790156\pi\) | ||||
−0.790455 | + | 0.612520i | \(0.790156\pi\) | |||||||
\(434\) | 338.077i | 0.778980i | ||||||||
\(435\) | 106.044 | − | 695.909i | 0.243779 | − | 1.59979i | ||||
\(436\) | − | 5.70445i | − | 0.0130836i | ||||||
\(437\) | −445.964 | + | 76.5886i | −1.02051 | + | 0.175260i | ||||
\(438\) | − | 758.371i | − | 1.73144i | ||||||
\(439\) | 354.150 | 0.806720 | 0.403360 | − | 0.915041i | \(-0.367842\pi\) | ||||
0.403360 | + | 0.915041i | \(0.367842\pi\) | |||||||
\(440\) | 855.750 | + | 130.401i | 1.94489 | + | 0.296365i | ||||
\(441\) | −70.6635 | −0.160235 | ||||||||
\(442\) | −356.963 | −0.807609 | ||||||||
\(443\) | 269.078i | 0.607399i | 0.952768 | + | 0.303700i | \(0.0982220\pi\) | ||||
−0.952768 | + | 0.303700i | \(0.901778\pi\) | |||||||
\(444\) | − | 40.1127i | − | 0.0903440i | ||||||
\(445\) | −15.8997 | + | 104.341i | −0.0357297 | + | 0.234474i | ||||
\(446\) | 282.001 | 0.632288 | ||||||||
\(447\) | −586.931 | −1.31304 | ||||||||
\(448\) | −663.247 | −1.48046 | ||||||||
\(449\) | 101.610 | 0.226303 | 0.113152 | − | 0.993578i | \(-0.463905\pi\) | ||||
0.113152 | + | 0.993578i | \(0.463905\pi\) | |||||||
\(450\) | 140.377 | − | 449.914i | 0.311949 | − | 0.999809i | ||||
\(451\) | − | 86.0468i | − | 0.190791i | ||||||
\(452\) | −620.410 | −1.37259 | ||||||||
\(453\) | − | 342.704i | − | 0.756520i | ||||||
\(454\) | 68.4148i | 0.150693i | ||||||||
\(455\) | 41.5355 | − | 272.575i | 0.0912868 | − | 0.599066i | ||||
\(456\) | − | 888.284i | − | 1.94799i | ||||||
\(457\) | −486.800 | −1.06521 | −0.532604 | − | 0.846364i | \(-0.678787\pi\) | ||||
−0.532604 | + | 0.846364i | \(0.678787\pi\) | |||||||
\(458\) | 108.056 | 0.235929 | ||||||||
\(459\) | 196.829i | 0.428820i | ||||||||
\(460\) | 16.2447 | + | 861.261i | 0.0353147 | + | 1.87231i | ||||
\(461\) | −110.762 | −0.240264 | −0.120132 | − | 0.992758i | \(-0.538332\pi\) | ||||
−0.120132 | + | 0.992758i | \(0.538332\pi\) | |||||||
\(462\) | 1486.73i | 3.21804i | ||||||||
\(463\) | 110.728i | 0.239154i | 0.992825 | + | 0.119577i | \(0.0381539\pi\) | ||||
−0.992825 | + | 0.119577i | \(0.961846\pi\) | |||||||
\(464\) | −374.341 | −0.806768 | ||||||||
\(465\) | 36.4925 | − | 239.481i | 0.0784785 | − | 0.515012i | ||||
\(466\) | 237.885 | 0.510482 | ||||||||
\(467\) | 559.817 | 1.19875 | 0.599376 | − | 0.800468i | \(-0.295416\pi\) | ||||
0.599376 | + | 0.800468i | \(0.295416\pi\) | |||||||
\(468\) | − | 292.444i | − | 0.624881i | ||||||
\(469\) | −751.386 | −1.60210 | ||||||||
\(470\) | −1095.46 | − | 166.929i | −2.33078 | − | 0.355168i | ||||
\(471\) | − | 377.228i | − | 0.800908i | ||||||
\(472\) | 192.118i | 0.407030i | ||||||||
\(473\) | − | 1197.41i | − | 2.53153i | ||||||
\(474\) | 548.434i | 1.15703i | ||||||||
\(475\) | −146.493 | + | 469.517i | −0.308407 | + | 0.988457i | ||||
\(476\) | −882.658 | −1.85432 | ||||||||
\(477\) | 329.345 | 0.690451 | ||||||||
\(478\) | 347.365i | 0.726705i | ||||||||
\(479\) | − | 389.448i | − | 0.813044i | −0.913641 | − | 0.406522i | \(-0.866741\pi\) | ||
0.913641 | − | 0.406522i | \(-0.133259\pi\) | |||||||
\(480\) | 243.989 | + | 37.1795i | 0.508311 | + | 0.0774573i | ||||
\(481\) | 9.85151i | 0.0204813i | ||||||||
\(482\) | 497.434 | 1.03202 | ||||||||
\(483\) | −679.489 | + | 116.693i | −1.40681 | + | 0.241601i | ||||
\(484\) | 697.285 | 1.44067 | ||||||||
\(485\) | 500.381 | + | 76.2489i | 1.03171 | + | 0.157214i | ||||
\(486\) | −894.815 | −1.84118 | ||||||||
\(487\) | 303.721i | 0.623657i | 0.950138 | + | 0.311828i | \(0.100941\pi\) | ||||
−0.950138 | + | 0.311828i | \(0.899059\pi\) | |||||||
\(488\) | −1278.83 | −2.62054 | ||||||||
\(489\) | 244.515 | 0.500032 | ||||||||
\(490\) | 32.4409 | − | 212.892i | 0.0662059 | − | 0.434474i | ||||
\(491\) | 893.361 | 1.81947 | 0.909736 | − | 0.415187i | \(-0.136284\pi\) | ||||
0.909736 | + | 0.415187i | \(0.136284\pi\) | |||||||
\(492\) | 168.095i | 0.341656i | ||||||||
\(493\) | 553.451 | 1.12262 | ||||||||
\(494\) | 468.158i | 0.947687i | ||||||||
\(495\) | 61.2924 | − | 402.229i | 0.123823 | − | 0.812584i | ||||
\(496\) | −128.821 | −0.259719 | ||||||||
\(497\) | 702.988 | 1.41446 | ||||||||
\(498\) | 740.252 | 1.48645 | ||||||||
\(499\) | −373.121 | −0.747737 | −0.373868 | − | 0.927482i | \(-0.621969\pi\) | ||||
−0.373868 | + | 0.927482i | \(0.621969\pi\) | |||||||
\(500\) | 841.612 | + | 410.346i | 1.68322 | + | 0.820692i | ||||
\(501\) | −588.923 | −1.17550 | ||||||||
\(502\) | −829.675 | −1.65274 | ||||||||
\(503\) | −572.051 | −1.13728 | −0.568639 | − | 0.822587i | \(-0.692530\pi\) | ||||
−0.568639 | + | 0.822587i | \(0.692530\pi\) | |||||||
\(504\) | − | 516.915i | − | 1.02563i | ||||||
\(505\) | −53.4827 | − | 8.14979i | −0.105906 | − | 0.0161382i | ||||
\(506\) | 193.084 | + | 1124.30i | 0.381590 | + | 2.22194i | ||||
\(507\) | − | 456.844i | − | 0.901073i | ||||||
\(508\) | − | 1516.72i | − | 2.98567i | ||||||
\(509\) | −172.246 | −0.338400 | −0.169200 | − | 0.985582i | \(-0.554118\pi\) | ||||
−0.169200 | + | 0.985582i | \(0.554118\pi\) | |||||||
\(510\) | 959.123 | + | 146.153i | 1.88063 | + | 0.286574i | ||||
\(511\) | 460.544i | 0.901261i | ||||||||
\(512\) | − | 611.452i | − | 1.19424i | ||||||
\(513\) | 258.141 | 0.503199 | ||||||||
\(514\) | −346.498 | −0.674120 | ||||||||
\(515\) | 387.453 | + | 59.0408i | 0.752337 | + | 0.114642i | ||||
\(516\) | 2339.19i | 4.53331i | ||||||||
\(517\) | −956.619 | −1.85033 | ||||||||
\(518\) | 37.3679i | 0.0721388i | ||||||||
\(519\) | −442.149 | −0.851925 | ||||||||
\(520\) | 410.571 | + | 62.5635i | 0.789559 | + | 0.120314i | ||||
\(521\) | − | 190.011i | − | 0.364704i | −0.983233 | − | 0.182352i | \(-0.941629\pi\) | ||
0.983233 | − | 0.182352i | \(-0.0583711\pi\) | |||||||
\(522\) | 695.546i | 1.33246i | ||||||||
\(523\) | 255.175 | 0.487906 | 0.243953 | − | 0.969787i | \(-0.421556\pi\) | ||||
0.243953 | + | 0.969787i | \(0.421556\pi\) | |||||||
\(524\) | −1208.79 | −2.30686 | ||||||||
\(525\) | −223.203 | + | 715.375i | −0.425149 | + | 1.36262i | ||||
\(526\) | − | 1123.08i | − | 2.13513i | ||||||
\(527\) | 190.457 | 0.361399 | ||||||||
\(528\) | −566.504 | −1.07292 | ||||||||
\(529\) | −498.690 | + | 176.492i | −0.942703 | + | 0.333634i | ||||
\(530\) | −151.199 | + | 992.238i | −0.285281 | + | 1.87215i | ||||
\(531\) | 90.3015 | 0.170059 | ||||||||
\(532\) | 1157.61i | 2.17595i | ||||||||
\(533\) | − | 41.2834i | − | 0.0774548i | ||||||
\(534\) | − | 273.051i | − | 0.511331i | ||||||
\(535\) | 638.779 | + | 97.3383i | 1.19398 | + | 0.181941i | ||||
\(536\) | − | 1131.79i | − | 2.11154i | ||||||
\(537\) | 266.759i | 0.496758i | ||||||||
\(538\) | − | 154.714i | − | 0.287572i | ||||||
\(539\) | − | 185.909i | − | 0.344915i | ||||||
\(540\) | 74.0296 | − | 485.817i | 0.137092 | − | 0.899660i | ||||
\(541\) | 275.118 | 0.508537 | 0.254268 | − | 0.967134i | \(-0.418165\pi\) | ||||
0.254268 | + | 0.967134i | \(0.418165\pi\) | |||||||
\(542\) | 922.681i | 1.70236i | ||||||||
\(543\) | 755.806 | 1.39191 | ||||||||
\(544\) | 194.043i | 0.356696i | ||||||||
\(545\) | 0.573612 | − | 3.76431i | 0.00105250 | − | 0.00690698i | ||||
\(546\) | 713.303i | 1.30642i | ||||||||
\(547\) | − | 310.599i | − | 0.567823i | −0.958850 | − | 0.283912i | \(-0.908368\pi\) | ||
0.958850 | − | 0.283912i | \(-0.0916323\pi\) | |||||||
\(548\) | 1555.20 | 2.83796 | ||||||||
\(549\) | 601.087i | 1.09488i | ||||||||
\(550\) | 1183.68 | + | 369.319i | 2.15215 | + | 0.671489i | ||||
\(551\) | − | 725.851i | − | 1.31733i | ||||||
\(552\) | −175.771 | − | 1023.49i | −0.318426 | − | 1.85415i | ||||
\(553\) | − | 333.054i | − | 0.602267i | ||||||
\(554\) | −1178.12 | −2.12656 | ||||||||
\(555\) | 4.03354 | − | 26.4700i | 0.00726765 | − | 0.0476937i | ||||
\(556\) | 1047.13 | 1.88332 | ||||||||
\(557\) | 99.9420 | 0.179429 | 0.0897146 | − | 0.995968i | \(-0.471405\pi\) | ||||
0.0897146 | + | 0.995968i | \(0.471405\pi\) | |||||||
\(558\) | 239.356i | 0.428953i | ||||||||
\(559\) | − | 574.494i | − | 1.02772i | ||||||
\(560\) | 393.960 | + | 60.0323i | 0.703499 | + | 0.107201i | ||||
\(561\) | 837.558 | 1.49297 | ||||||||
\(562\) | 1149.35 | 2.04510 | ||||||||
\(563\) | 469.692 | 0.834266 | 0.417133 | − | 0.908846i | \(-0.363035\pi\) | ||||
0.417133 | + | 0.908846i | \(0.363035\pi\) | |||||||
\(564\) | 1868.78 | 3.31345 | ||||||||
\(565\) | −409.402 | − | 62.3854i | −0.724606 | − | 0.110417i | ||||
\(566\) | 728.609i | 1.28729i | ||||||||
\(567\) | 786.499 | 1.38712 | ||||||||
\(568\) | 1058.89i | 1.86424i | ||||||||
\(569\) | − | 299.605i | − | 0.526547i | −0.964721 | − | 0.263274i | \(-0.915198\pi\) | ||
0.964721 | − | 0.263274i | \(-0.0848022\pi\) | |||||||
\(570\) | 191.680 | − | 1257.89i | 0.336280 | − | 2.20683i | ||||
\(571\) | − | 833.584i | − | 1.45987i | −0.683518 | − | 0.729933i | \(-0.739551\pi\) | ||
0.683518 | − | 0.729933i | \(-0.260449\pi\) | |||||||
\(572\) | 769.393 | 1.34509 | ||||||||
\(573\) | 208.580 | 0.364015 | ||||||||
\(574\) | − | 156.593i | − | 0.272810i | ||||||
\(575\) | −75.8845 | + | 569.971i | −0.131973 | + | 0.991253i | ||||
\(576\) | −469.574 | −0.815232 | ||||||||
\(577\) | 372.711i | 0.645947i | 0.946408 | + | 0.322974i | \(0.104682\pi\) | ||||
−0.946408 | + | 0.322974i | \(0.895318\pi\) | |||||||
\(578\) | − | 216.861i | − | 0.375192i | ||||||
\(579\) | −894.054 | −1.54413 | ||||||||
\(580\) | −1366.04 | − | 208.160i | −2.35524 | − | 0.358896i | ||||
\(581\) | −449.541 | −0.773736 | ||||||||
\(582\) | −1309.45 | −2.24991 | ||||||||
\(583\) | 866.476i | 1.48624i | ||||||||
\(584\) | −693.702 | −1.18785 | ||||||||
\(585\) | 29.4068 | − | 192.981i | 0.0502680 | − | 0.329882i | ||||
\(586\) | − | 557.556i | − | 0.951460i | ||||||
\(587\) | − | 478.228i | − | 0.814698i | −0.913273 | − | 0.407349i | \(-0.866453\pi\) | ||
0.913273 | − | 0.407349i | \(-0.133547\pi\) | |||||||
\(588\) | 363.179i | 0.617651i | ||||||||
\(589\) | − | 249.785i | − | 0.424083i | ||||||
\(590\) | −41.4565 | + | 272.057i | −0.0702653 | + | 0.461113i | ||||
\(591\) | 394.237 | 0.667067 | ||||||||
\(592\) | −14.2386 | −0.0240517 | ||||||||
\(593\) | 685.488i | 1.15597i | 0.816049 | + | 0.577983i | \(0.196160\pi\) | ||||
−0.816049 | + | 0.577983i | \(0.803840\pi\) | |||||||
\(594\) | − | 650.789i | − | 1.09560i | ||||||
\(595\) | −582.457 | − | 88.7559i | −0.978919 | − | 0.149170i | ||||
\(596\) | 1152.12i | 1.93309i | ||||||||
\(597\) | 399.995 | 0.670009 | ||||||||
\(598\) | 92.6378 | + | 539.416i | 0.154913 | + | 0.902034i | ||||
\(599\) | 806.008 | 1.34559 | 0.672795 | − | 0.739829i | \(-0.265094\pi\) | ||||
0.672795 | + | 0.739829i | \(0.265094\pi\) | |||||||
\(600\) | −1077.55 | − | 336.203i | −1.79591 | − | 0.560339i | ||||
\(601\) | −162.773 | −0.270836 | −0.135418 | − | 0.990789i | \(-0.543238\pi\) | ||||
−0.135418 | + | 0.990789i | \(0.543238\pi\) | |||||||
\(602\) | − | 2179.12i | − | 3.61980i | ||||||
\(603\) | −531.975 | −0.882214 | ||||||||
\(604\) | −672.713 | −1.11376 | ||||||||
\(605\) | 460.131 | + | 70.1156i | 0.760548 | + | 0.115894i | ||||
\(606\) | 139.959 | 0.230956 | ||||||||
\(607\) | − | 862.711i | − | 1.42127i | −0.703561 | − | 0.710635i | \(-0.748408\pi\) | ||
0.703561 | − | 0.710635i | \(-0.251592\pi\) | |||||||
\(608\) | 254.487 | 0.418564 | ||||||||
\(609\) | − | 1105.94i | − | 1.81599i | ||||||
\(610\) | −1810.93 | − | 275.953i | −2.96874 | − | 0.452382i | ||||
\(611\) | −458.965 | −0.751171 | ||||||||
\(612\) | −624.915 | −1.02110 | ||||||||
\(613\) | 31.4095 | 0.0512390 | 0.0256195 | − | 0.999672i | \(-0.491844\pi\) | ||||
0.0256195 | + | 0.999672i | \(0.491844\pi\) | |||||||
\(614\) | 1645.83 | 2.68050 | ||||||||
\(615\) | −16.9028 | + | 110.924i | −0.0274843 | + | 0.180364i | ||||
\(616\) | 1359.96 | 2.20772 | ||||||||
\(617\) | 356.586 | 0.577935 | 0.288968 | − | 0.957339i | \(-0.406688\pi\) | ||||
0.288968 | + | 0.957339i | \(0.406688\pi\) | |||||||
\(618\) | −1013.93 | −1.64066 | ||||||||
\(619\) | 150.564i | 0.243238i | 0.992577 | + | 0.121619i | \(0.0388086\pi\) | ||||
−0.992577 | + | 0.121619i | \(0.961191\pi\) | |||||||
\(620\) | −470.091 | − | 71.6333i | −0.758211 | − | 0.115538i | ||||
\(621\) | 297.433 | − | 51.0802i | 0.478958 | − | 0.0822548i | ||||
\(622\) | − | 811.394i | − | 1.30449i | ||||||
\(623\) | 165.819i | 0.266162i | ||||||||
\(624\) | −271.796 | −0.435571 | ||||||||
\(625\) | 514.109 | + | 355.412i | 0.822574 | + | 0.568659i | ||||
\(626\) | − | 247.199i | − | 0.394886i | ||||||
\(627\) | − | 1098.46i | − | 1.75193i | ||||||
\(628\) | −740.482 | −1.17911 | ||||||||
\(629\) | 21.0514 | 0.0334680 | ||||||||
\(630\) | 111.543 | − | 731.999i | 0.177053 | − | 1.16190i | ||||
\(631\) | − | 251.228i | − | 0.398143i | −0.979985 | − | 0.199072i | \(-0.936207\pi\) | ||
0.979985 | − | 0.199072i | \(-0.0637927\pi\) | |||||||
\(632\) | 501.668 | 0.793778 | ||||||||
\(633\) | 1242.61i | 1.96306i | ||||||||
\(634\) | 512.030 | 0.807619 | ||||||||
\(635\) | 152.514 | − | 1000.87i | 0.240180 | − | 1.57617i | ||||
\(636\) | − | 1692.69i | − | 2.66146i | ||||||
\(637\) | − | 89.1952i | − | 0.140024i | ||||||
\(638\) | −1829.92 | −2.86821 | ||||||||
\(639\) | 497.710 | 0.778888 | ||||||||
\(640\) | 176.604 | − | 1158.96i | 0.275944 | − | 1.81087i | ||||
\(641\) | 601.005i | 0.937605i | 0.883303 | + | 0.468803i | \(0.155314\pi\) | ||||
−0.883303 | + | 0.468803i | \(0.844686\pi\) | |||||||
\(642\) | −1671.62 | −2.60378 | ||||||||
\(643\) | −532.541 | −0.828214 | −0.414107 | − | 0.910228i | \(-0.635906\pi\) | ||||
−0.414107 | + | 0.910228i | \(0.635906\pi\) | |||||||
\(644\) | 229.064 | + | 1333.81i | 0.355690 | + | 2.07113i | ||||
\(645\) | −235.217 | + | 1543.61i | −0.364678 | + | 2.39319i | ||||
\(646\) | 1000.39 | 1.54859 | ||||||||
\(647\) | − | 627.608i | − | 0.970028i | −0.874506 | − | 0.485014i | \(-0.838815\pi\) | ||
0.874506 | − | 0.485014i | \(-0.161185\pi\) | |||||||
\(648\) | 1184.68i | 1.82820i | ||||||||
\(649\) | 237.575i | 0.366063i | ||||||||
\(650\) | 567.905 | + | 177.191i | 0.873700 | + | 0.272602i | ||||
\(651\) | − | 380.582i | − | 0.584612i | ||||||
\(652\) | − | 479.974i | − | 0.736156i | ||||||
\(653\) | 243.613i | 0.373068i | 0.982449 | + | 0.186534i | \(0.0597254\pi\) | ||||
−0.982449 | + | 0.186534i | \(0.940275\pi\) | |||||||
\(654\) | 9.85083i | 0.0150624i | ||||||||
\(655\) | −797.670 | − | 121.550i | −1.21782 | − | 0.185573i | ||||
\(656\) | 59.6679 | 0.0909572 | ||||||||
\(657\) | 326.061i | 0.496288i | ||||||||
\(658\) | −1740.91 | −2.64576 | ||||||||
\(659\) | 568.999i | 0.863427i | 0.902011 | + | 0.431714i | \(0.142091\pi\) | ||||
−0.902011 | + | 0.431714i | \(0.857909\pi\) | |||||||
\(660\) | −2067.28 | − | 315.016i | −3.13224 | − | 0.477297i | ||||
\(661\) | − | 165.702i | − | 0.250683i | −0.992114 | − | 0.125342i | \(-0.959997\pi\) | ||
0.992114 | − | 0.125342i | \(-0.0400027\pi\) | |||||||
\(662\) | 1845.92i | 2.78839i | ||||||||
\(663\) | 401.843 | 0.606097 | ||||||||
\(664\) | − | 677.128i | − | 1.01977i | ||||||
\(665\) | −116.403 | + | 763.893i | −0.175043 | + | 1.14871i | ||||
\(666\) | 26.4562i | 0.0397240i | ||||||||
\(667\) | −143.630 | − | 836.334i | −0.215337 | − | 1.25387i | ||||
\(668\) | 1156.03i | 1.73059i | ||||||||
\(669\) | −317.455 | −0.474522 | ||||||||
\(670\) | 244.224 | − | 1602.71i | 0.364514 | − | 2.39211i | ||||
\(671\) | −1581.40 | −2.35679 | ||||||||
\(672\) | 387.747 | 0.577004 | ||||||||
\(673\) | − | 787.294i | − | 1.16983i | −0.811095 | − | 0.584914i | \(-0.801128\pi\) | ||
0.811095 | − | 0.584914i | \(-0.198872\pi\) | |||||||
\(674\) | 305.497i | 0.453260i | ||||||||
\(675\) | 97.7028 | − | 313.141i | 0.144745 | − | 0.463913i | ||||
\(676\) | −896.765 | −1.32658 | ||||||||
\(677\) | 640.320 | 0.945820 | 0.472910 | − | 0.881111i | \(-0.343204\pi\) | ||||
0.472910 | + | 0.881111i | \(0.343204\pi\) | |||||||
\(678\) | 1071.37 | 1.58019 | ||||||||
\(679\) | 795.203 | 1.17114 | ||||||||
\(680\) | 133.690 | − | 877.335i | 0.196603 | − | 1.29020i | ||||
\(681\) | − | 77.0162i | − | 0.113093i | ||||||
\(682\) | −629.723 | −0.923347 | ||||||||
\(683\) | 1135.46i | 1.66246i | 0.555930 | + | 0.831229i | \(0.312362\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(684\) | 819.576i | 1.19821i | ||||||||
\(685\) | 1026.26 | + | 156.384i | 1.49819 | + | 0.228298i | ||||
\(686\) | 966.430i | 1.40879i | ||||||||
\(687\) | −121.641 | −0.177061 | ||||||||
\(688\) | 830.330 | 1.20688 | ||||||||
\(689\) | 415.717i | 0.603363i | ||||||||
\(690\) | −28.0526 | − | 1487.28i | −0.0406559 | − | 2.15548i | ||||
\(691\) | −584.766 | −0.846261 | −0.423131 | − | 0.906069i | \(-0.639069\pi\) | ||||
−0.423131 | + | 0.906069i | \(0.639069\pi\) | |||||||
\(692\) | 867.920i | 1.25422i | ||||||||
\(693\) | − | 639.221i | − | 0.922397i | ||||||
\(694\) | −1475.98 | −2.12678 | ||||||||
\(695\) | 690.988 | + | 105.294i | 0.994228 | + | 0.151502i | ||||
\(696\) | 1665.83 | 2.39344 | ||||||||
\(697\) | −88.2172 | −0.126567 | ||||||||
\(698\) | 649.585i | 0.930637i | ||||||||
\(699\) | −267.793 | −0.383109 | ||||||||
\(700\) | 1404.25 | + | 438.138i | 2.00607 | + | 0.625912i | ||||
\(701\) | 789.534i | 1.12630i | 0.826356 | + | 0.563148i | \(0.190410\pi\) | ||||
−0.826356 | + | 0.563148i | \(0.809590\pi\) | |||||||
\(702\) | − | 312.235i | − | 0.444779i | ||||||
\(703\) | − | 27.6089i | − | 0.0392730i | ||||||
\(704\) | − | 1235.40i | − | 1.75484i | ||||||
\(705\) | 1233.19 | + | 187.916i | 1.74921 | + | 0.266548i | ||||
\(706\) | −591.070 | −0.837210 | ||||||||
\(707\) | −84.9946 | −0.120219 | ||||||||
\(708\) | − | 464.110i | − | 0.655522i | ||||||
\(709\) | 1356.27i | 1.91294i | 0.291836 | + | 0.956468i | \(0.405734\pi\) | ||||
−0.291836 | + | 0.956468i | \(0.594266\pi\) | |||||||
\(710\) | −228.493 | + | 1499.48i | −0.321822 | + | 2.11194i | ||||
\(711\) | − | 235.799i | − | 0.331645i | ||||||
\(712\) | −249.767 | −0.350796 | ||||||||
\(713\) | −49.4268 | − | 287.805i | −0.0693223 | − | 0.403654i | ||||
\(714\) | 1524.23 | 2.13478 | ||||||||
\(715\) | 507.715 | + | 77.3665i | 0.710091 | + | 0.108205i | ||||
\(716\) | 523.637 | 0.731336 | ||||||||
\(717\) | − | 391.038i | − | 0.545380i | ||||||
\(718\) | 1661.34 | 2.31384 | ||||||||
\(719\) | 1205.36 | 1.67644 | 0.838221 | − | 0.545330i | \(-0.183596\pi\) | ||||
0.838221 | + | 0.545330i | \(0.183596\pi\) | |||||||
\(720\) | 278.920 | + | 42.5024i | 0.387389 | + | 0.0590311i | ||||
\(721\) | 615.740 | 0.854008 | ||||||||
\(722\) | − | 88.3059i | − | 0.122307i | ||||||
\(723\) | −559.974 | −0.774515 | ||||||||
\(724\) | − | 1483.62i | − | 2.04919i | ||||||
\(725\) | −880.504 | − | 274.725i | −1.21449 | − | 0.378931i | ||||
\(726\) | −1204.12 | −1.65857 | ||||||||
\(727\) | −949.180 | −1.30561 | −0.652806 | − | 0.757525i | \(-0.726408\pi\) | ||||
−0.652806 | + | 0.757525i | \(0.726408\pi\) | |||||||
\(728\) | 652.478 | 0.896261 | ||||||||
\(729\) | 106.207 | 0.145688 | ||||||||
\(730\) | −982.345 | − | 149.692i | −1.34568 | − | 0.205057i | ||||
\(731\) | −1227.62 | −1.67937 | ||||||||
\(732\) | 3089.32 | 4.22039 | ||||||||
\(733\) | −24.1006 | −0.0328794 | −0.0164397 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164397 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(734\) | 1502.97i | 2.04764i | ||||||||
\(735\) | −36.5195 | + | 239.658i | −0.0496865 | + | 0.326066i | ||||
\(736\) | 293.223 | − | 50.3572i | 0.398401 | − | 0.0684202i | ||||
\(737\) | − | 1399.58i | − | 1.89902i | ||||||
\(738\) | − | 110.866i | − | 0.150225i | ||||||
\(739\) | −49.6986 | −0.0672512 | −0.0336256 | − | 0.999435i | \(-0.510705\pi\) | ||||
−0.0336256 | + | 0.999435i | \(0.510705\pi\) | |||||||
\(740\) | −51.9595 | − | 7.91768i | −0.0702155 | − | 0.0106996i | ||||
\(741\) | − | 527.017i | − | 0.711224i | ||||||
\(742\) | 1576.86i | 2.12515i | ||||||||
\(743\) | 728.213 | 0.980099 | 0.490049 | − | 0.871695i | \(-0.336979\pi\) | ||||
0.490049 | + | 0.871695i | \(0.336979\pi\) | |||||||
\(744\) | 573.258 | 0.770508 | ||||||||
\(745\) | −115.852 | + | 760.272i | −0.155506 | + | 1.02050i | ||||
\(746\) | − | 1288.00i | − | 1.72654i | ||||||
\(747\) | −318.271 | −0.426066 | ||||||||
\(748\) | − | 1644.09i | − | 2.19798i | ||||||
\(749\) | 1015.15 | 1.35533 | ||||||||
\(750\) | −1453.35 | − | 708.614i | −1.93780 | − | 0.944819i | ||||
\(751\) | 832.335i | 1.10830i | 0.832416 | + | 0.554151i | \(0.186957\pi\) | ||||
−0.832416 | + | 0.554151i | \(0.813043\pi\) | |||||||
\(752\) | − | 663.354i | − | 0.882120i | ||||||
\(753\) | 933.986 | 1.24035 | ||||||||
\(754\) | −877.955 | −1.16440 | ||||||||
\(755\) | −443.917 | − | 67.6448i | −0.587969 | − | 0.0895958i | ||||
\(756\) | − | 772.058i | − | 1.02124i | ||||||
\(757\) | −83.6711 | −0.110530 | −0.0552649 | − | 0.998472i | \(-0.517600\pi\) | ||||
−0.0552649 | + | 0.998472i | \(0.517600\pi\) | |||||||
\(758\) | 743.865 | 0.981353 | ||||||||
\(759\) | −217.360 | − | 1265.66i | −0.286377 | − | 1.66753i | ||||
\(760\) | −1150.63 | − | 175.335i | −1.51398 | − | 0.230703i | ||||
\(761\) | −1113.77 | −1.46356 | −0.731782 | − | 0.681539i | \(-0.761311\pi\) | ||||
−0.731782 | + | 0.681539i | \(0.761311\pi\) | |||||||
\(762\) | 2619.18i | 3.43724i | ||||||||
\(763\) | − | 5.98222i | − | 0.00784040i | ||||||
\(764\) | − | 409.434i | − | 0.535909i | ||||||
\(765\) | −412.375 | − | 62.8384i | −0.539052 | − | 0.0821417i | ||||
\(766\) | 639.480i | 0.834830i | ||||||||
\(767\) | 113.983i | 0.148609i | ||||||||
\(768\) | 1744.11i | 2.27097i | ||||||||
\(769\) | − | 945.642i | − | 1.22970i | −0.788643 | − | 0.614852i | \(-0.789216\pi\) | ||
0.788643 | − | 0.614852i | \(-0.210784\pi\) | |||||||
\(770\) | 1925.82 | + | 293.460i | 2.50107 | + | 0.381117i | ||||
\(771\) | 390.061 | 0.505916 | ||||||||
\(772\) | 1754.99i | 2.27330i | ||||||||
\(773\) | −966.297 | −1.25006 | −0.625030 | − | 0.780601i | \(-0.714913\pi\) | ||||
−0.625030 | + | 0.780601i | \(0.714913\pi\) | |||||||
\(774\) | − | 1542.80i | − | 1.99328i | ||||||
\(775\) | −303.005 | − | 94.5402i | −0.390974 | − | 0.121987i | ||||
\(776\) | 1197.79i | 1.54354i | ||||||||
\(777\) | − | 42.0660i | − | 0.0541390i | ||||||
\(778\) | −473.326 | −0.608388 | ||||||||
\(779\) | 115.697i | 0.148520i | ||||||||
\(780\) | −991.836 | − | 151.138i | −1.27159 | − | 0.193766i | ||||
\(781\) | 1309.43i | 1.67660i | ||||||||
\(782\) | 1152.66 | − | 197.955i | 1.47399 | − | 0.253139i | ||||
\(783\) | 484.102i | 0.618265i | ||||||||
\(784\) | 128.916 | 0.164434 | ||||||||
\(785\) | −488.636 | − | 74.4593i | −0.622467 | − | 0.0948526i | ||||
\(786\) | 2087.43 | 2.65576 | ||||||||
\(787\) | −156.202 | −0.198477 | −0.0992386 | − | 0.995064i | \(-0.531641\pi\) | ||||
−0.0992386 | + | 0.995064i | \(0.531641\pi\) | |||||||
\(788\) | − | 773.870i | − | 0.982069i | ||||||
\(789\) | 1264.28i | 1.60238i | ||||||||
\(790\) | 710.407 | + | 108.253i | 0.899249 | + | 0.137029i | ||||
\(791\) | −650.621 | −0.822529 | ||||||||
\(792\) | 962.838 | 1.21570 | ||||||||
\(793\) | −758.724 | −0.956777 | ||||||||
\(794\) | 1939.17 | 2.44228 | ||||||||
\(795\) | 170.209 | − | 1116.99i | 0.214099 | − | 1.40502i | ||||
\(796\) | − | 785.174i | − | 0.986399i | ||||||
\(797\) | 559.866 | 0.702467 | 0.351233 | − | 0.936288i | \(-0.385762\pi\) | ||||
0.351233 | + | 0.936288i | \(0.385762\pi\) | |||||||
\(798\) | − | 1999.04i | − | 2.50506i | ||||||
\(799\) | 980.748i | 1.22747i | ||||||||
\(800\) | 96.3199 | − | 308.709i | 0.120400 | − | 0.385886i | ||||
\(801\) | 117.398i | 0.146565i | ||||||||
\(802\) | 1360.81 | 1.69677 | ||||||||
\(803\) | −857.837 | −1.06829 | ||||||||
\(804\) | 2734.11i | 3.40064i | ||||||||
\(805\) | 17.0358 | + | 903.200i | 0.0211625 | + | 1.12199i | ||||
\(806\) | −302.128 | −0.374848 | ||||||||
\(807\) | 174.165i | 0.215818i | ||||||||
\(808\) | − | 128.024i | − | 0.158446i | ||||||
\(809\) | 1289.52 | 1.59396 | 0.796981 | − | 0.604004i | \(-0.206429\pi\) | ||||
0.796981 | + | 0.604004i | \(0.206429\pi\) | |||||||
\(810\) | −255.637 | + | 1677.61i | −0.315601 | + | 2.07112i | ||||
\(811\) | −1091.91 | −1.34637 | −0.673185 | − | 0.739474i | \(-0.735074\pi\) | ||||
−0.673185 | + | 0.739474i | \(0.735074\pi\) | |||||||
\(812\) | −2170.91 | −2.67353 | ||||||||
\(813\) | − | 1038.69i | − | 1.27760i | ||||||
\(814\) | −69.6037 | −0.0855082 | ||||||||
\(815\) | 48.2639 | − | 316.730i | 0.0592195 | − | 0.388625i | ||||
\(816\) | 580.793i | 0.711756i | ||||||||
\(817\) | 1610.02i | 1.97065i | ||||||||
\(818\) | − | 362.459i | − | 0.443104i | ||||||
\(819\) | − | 306.685i | − | 0.374463i | ||||||
\(820\) | 217.739 | + | 33.1795i | 0.265536 | + | 0.0404629i | ||||
\(821\) | −950.992 | −1.15833 | −0.579167 | − | 0.815209i | \(-0.696622\pi\) | ||||
−0.579167 | + | 0.815209i | \(0.696622\pi\) | |||||||
\(822\) | −2685.63 | −3.26719 | ||||||||
\(823\) | − | 472.254i | − | 0.573820i | −0.957957 | − | 0.286910i | \(-0.907372\pi\) | ||
0.957957 | − | 0.286910i | \(-0.0926281\pi\) | |||||||
\(824\) | 927.468i | 1.12557i | ||||||||
\(825\) | −1332.50 | − | 415.751i | −1.61515 | − | 0.503941i | ||||
\(826\) | 432.352i | 0.523428i | ||||||||
\(827\) | −1539.15 | −1.86113 | −0.930565 | − | 0.366126i | \(-0.880684\pi\) | ||||
−0.930565 | + | 0.366126i | \(0.880684\pi\) | |||||||
\(828\) | 162.176 | + | 944.325i | 0.195864 | + | 1.14049i | ||||
\(829\) | −175.844 | −0.212116 | −0.106058 | − | 0.994360i | \(-0.533823\pi\) | ||||
−0.106058 | + | 0.994360i | \(0.533823\pi\) | |||||||
\(830\) | 146.115 | − | 958.875i | 0.176042 | − | 1.15527i | ||||
\(831\) | 1326.23 | 1.59595 | ||||||||
\(832\) | − | 592.721i | − | 0.712405i | ||||||
\(833\) | −190.598 | −0.228810 | ||||||||
\(834\) | −1808.25 | −2.16817 | ||||||||
\(835\) | −116.245 | + | 762.854i | −0.139216 | + | 0.913597i | ||||
\(836\) | −2156.23 | −2.57922 | ||||||||
\(837\) | 166.592i | 0.199035i | ||||||||
\(838\) | 2389.47 | 2.85140 | ||||||||
\(839\) | 1603.02i | 1.91063i | 0.295596 | + | 0.955313i | \(0.404482\pi\) | ||||
−0.295596 | + | 0.955313i | \(0.595518\pi\) | |||||||
\(840\) | −1753.14 | − | 267.147i | −2.08707 | − | 0.318032i | ||||
\(841\) | 520.218 | 0.618571 | ||||||||
\(842\) | −1963.41 | −2.33185 | ||||||||
\(843\) | −1293.85 | −1.53482 | ||||||||
\(844\) | 2439.20 | 2.89005 | ||||||||
\(845\) | −591.766 | − | 90.1744i | −0.700315 | − | 0.106715i | ||||
\(846\) | −1232.55 | −1.45691 | ||||||||
\(847\) | 731.239 | 0.863329 | ||||||||
\(848\) | −600.846 | −0.708545 | ||||||||
\(849\) | − | 820.213i | − | 0.966093i | ||||||
\(850\) | 378.634 | − | 1213.54i | 0.445452 | − | 1.42769i | ||||
\(851\) | −5.46317 | − | 31.8113i | −0.00641971 | − | 0.0373811i | ||||
\(852\) | − | 2558.01i | − | 3.00235i | ||||||
\(853\) | − | 480.409i | − | 0.563200i | −0.959532 | − | 0.281600i | \(-0.909135\pi\) | ||
0.959532 | − | 0.281600i | \(-0.0908651\pi\) | |||||||
\(854\) | −2877.93 | −3.36994 | ||||||||
\(855\) | −82.4127 | + | 540.830i | −0.0963891 | + | 0.632550i | ||||
\(856\) | 1529.08i | 1.78631i | ||||||||
\(857\) | 30.1380i | 0.0351669i | 0.999845 | + | 0.0175834i | \(0.00559727\pi\) | ||||
−0.999845 | + | 0.0175834i | \(0.994403\pi\) | |||||||
\(858\) | −1328.64 | −1.54853 | ||||||||
\(859\) | −548.892 | −0.638990 | −0.319495 | − | 0.947588i | \(-0.603513\pi\) | ||||
−0.319495 | + | 0.947588i | \(0.603513\pi\) | |||||||
\(860\) | 3030.03 | + | 461.722i | 3.52329 | + | 0.536886i | ||||
\(861\) | 176.280i | 0.204739i | ||||||||
\(862\) | 1243.62 | 1.44272 | ||||||||
\(863\) | 514.023i | 0.595624i | 0.954625 | + | 0.297812i | \(0.0962569\pi\) | ||||
−0.954625 | + | 0.297812i | \(0.903743\pi\) | |||||||
\(864\) | −169.729 | −0.196445 | ||||||||
\(865\) | −87.2739 | + | 572.732i | −0.100895 | + | 0.662118i | ||||
\(866\) | − | 2320.41i | − | 2.67946i | ||||||
\(867\) | 244.126i | 0.281576i | ||||||||
\(868\) | −747.067 | −0.860676 | ||||||||
\(869\) | 620.366 | 0.713885 | ||||||||
\(870\) | 2358.97 | + | 359.464i | 2.71146 | + | 0.413178i | ||||
\(871\) | − | 671.487i | − | 0.770938i | ||||||
\(872\) | 9.01082 | 0.0103335 | ||||||||
\(873\) | 562.997 | 0.644900 | ||||||||
\(874\) | −259.618 | − | 1511.72i | −0.297045 | − | 1.72965i | ||||
\(875\) | 882.594 | + | 430.328i | 1.00868 | + | 0.491803i | ||||
\(876\) | 1675.81 | 1.91303 | ||||||||
\(877\) | − | 474.355i | − | 0.540883i | −0.962736 | − | 0.270442i | \(-0.912830\pi\) | ||
0.962736 | − | 0.270442i | \(-0.0871697\pi\) | |||||||
\(878\) | 1200.49i | 1.36730i | ||||||||
\(879\) | 627.655i | 0.714055i | ||||||||
\(880\) | −111.820 | + | 733.813i | −0.127068 | + | 0.833878i | ||||
\(881\) | − | 884.227i | − | 1.00366i | −0.864966 | − | 0.501831i | \(-0.832660\pi\) | ||
0.864966 | − | 0.501831i | \(-0.167340\pi\) | |||||||
\(882\) | − | 239.533i | − | 0.271580i | ||||||
\(883\) | − | 1166.30i | − | 1.32083i | −0.750899 | − | 0.660417i | \(-0.770380\pi\) | ||
0.750899 | − | 0.660417i | \(-0.229620\pi\) | |||||||
\(884\) | − | 788.800i | − | 0.892308i | ||||||
\(885\) | 46.6687 | − | 306.261i | 0.0527329 | − | 0.346058i | ||||
\(886\) | −912.113 | −1.02947 | ||||||||
\(887\) | − | 40.5530i | − | 0.0457193i | −0.999739 | − | 0.0228596i | \(-0.992723\pi\) | ||
0.999739 | − | 0.0228596i | \(-0.00727708\pi\) | |||||||
\(888\) | 63.3626 | 0.0713543 | ||||||||
\(889\) | − | 1590.58i | − | 1.78917i | ||||||
\(890\) | −353.693 | − | 53.8963i | −0.397408 | − | 0.0605577i | ||||
\(891\) | 1464.98i | 1.64420i | ||||||||
\(892\) | 623.151i | 0.698600i | ||||||||
\(893\) | 1286.25 | 1.44037 | ||||||||
\(894\) | − | 1989.56i | − | 2.22546i | ||||||
\(895\) | 345.542 | + | 52.6544i | 0.386081 | + | 0.0588317i | ||||
\(896\) | − | 1841.81i | − | 2.05559i | ||||||
\(897\) | −104.285 | − | 607.235i | −0.116259 | − | 0.676962i | ||||
\(898\) | 344.435i | 0.383558i | ||||||||
\(899\) | 468.432 | 0.521058 | ||||||||
\(900\) | 994.198 | + | 310.198i | 1.10466 | + | 0.344665i | ||||
\(901\) | 888.332 | 0.985940 | ||||||||
\(902\) | 291.679 | 0.323369 | ||||||||
\(903\) | 2453.09i | 2.71660i | ||||||||
\(904\) | − | 980.008i | − | 1.08408i | ||||||
\(905\) | 149.185 | − | 979.023i | 0.164846 | − | 1.08179i | ||||
\(906\) | 1161.69 | 1.28222 | ||||||||
\(907\) | 699.890 | 0.771654 | 0.385827 | − | 0.922571i | \(-0.373916\pi\) | ||||
0.385827 | + | 0.922571i | \(0.373916\pi\) | |||||||
\(908\) | −151.180 | −0.166497 | ||||||||
\(909\) | −60.1755 | −0.0661996 | ||||||||
\(910\) | 923.968 | + | 140.796i | 1.01535 | + | 0.154721i | ||||
\(911\) | − | 1678.86i | − | 1.84287i | −0.388531 | − | 0.921436i | \(-0.627017\pi\) | ||
0.388531 | − | 0.921436i | \(-0.372983\pi\) | |||||||
\(912\) | 761.710 | 0.835209 | ||||||||
\(913\) | − | 837.342i | − | 0.917132i | ||||||
\(914\) | − | 1650.14i | − | 1.80541i | ||||||
\(915\) | 2038.61 | + | 310.647i | 2.22799 | + | 0.339505i | ||||
\(916\) | 238.776i | 0.260673i | ||||||||
\(917\) | −1267.66 | −1.38239 | ||||||||
\(918\) | −667.204 | −0.726802 | ||||||||
\(919\) | 392.082i | 0.426640i | 0.976982 | + | 0.213320i | \(0.0684277\pi\) | ||||
−0.976982 | + | 0.213320i | \(0.931572\pi\) | |||||||
\(920\) | −1360.46 | + | 25.6604i | −1.47876 | + | 0.0278918i | ||||
\(921\) | −1852.75 | −2.01167 | ||||||||
\(922\) | − | 375.458i | − | 0.407221i | ||||||
\(923\) | 628.235i | 0.680645i | ||||||||
\(924\) | −3285.31 | −3.55553 | ||||||||
\(925\) | −33.4914 | − | 10.4496i | −0.0362069 | − | 0.0112969i | ||||
\(926\) | −375.344 | −0.405339 | ||||||||
\(927\) | 435.939 | 0.470268 | ||||||||
\(928\) | 477.250i | 0.514278i | ||||||||
\(929\) | −1172.07 | −1.26165 | −0.630823 | − | 0.775927i | \(-0.717282\pi\) | ||||
−0.630823 | + | 0.775927i | \(0.717282\pi\) | |||||||
\(930\) | 811.785 | + | 123.701i | 0.872887 | + | 0.133012i | ||||
\(931\) | 249.970i | 0.268496i | ||||||||
\(932\) | 525.666i | 0.564020i | ||||||||
\(933\) | 913.407i | 0.979000i | ||||||||
\(934\) | 1897.65i | 2.03175i | ||||||||
\(935\) | 165.322 | − | 1084.92i | 0.176815 | − | 1.16034i | ||||
\(936\) | 461.949 | 0.493535 | ||||||||
\(937\) | −183.235 | −0.195555 | −0.0977773 | − | 0.995208i | \(-0.531173\pi\) | ||||
−0.0977773 | + | 0.995208i | \(0.531173\pi\) | |||||||
\(938\) | − | 2547.03i | − | 2.71538i | ||||||
\(939\) | 278.278i | 0.296356i | ||||||||
\(940\) | 368.871 | − | 2420.70i | 0.392416 | − | 2.57522i | ||||
\(941\) | 808.527i | 0.859221i | 0.903014 | + | 0.429611i | \(0.141349\pi\) | ||||
−0.903014 | + | 0.429611i | \(0.858651\pi\) | |||||||
\(942\) | 1278.72 | 1.35745 | ||||||||
\(943\) | 22.8938 | + | 133.307i | 0.0242776 | + | 0.141365i | ||||
\(944\) | −164.743 | −0.174516 | ||||||||
\(945\) | 77.6345 | − | 509.473i | 0.0821529 | − | 0.539125i | ||||
\(946\) | 4058.96 | 4.29066 | ||||||||
\(947\) | 171.842i | 0.181460i | 0.995876 | + | 0.0907298i | \(0.0289199\pi\) | ||||
−0.995876 | + | 0.0907298i | \(0.971080\pi\) | |||||||
\(948\) | −1211.90 | −1.27838 | ||||||||
\(949\) | −411.572 | −0.433690 | ||||||||
\(950\) | −1591.56 | − | 496.579i | −1.67532 | − | 0.522715i | ||||
\(951\) | −576.405 | −0.606104 | ||||||||
\(952\) | − | 1394.26i | − | 1.46456i | ||||||
\(953\) | −500.502 | −0.525185 | −0.262593 | − | 0.964907i | \(-0.584578\pi\) | ||||
−0.262593 | + | 0.964907i | \(0.584578\pi\) | |||||||
\(954\) | 1116.41i | 1.17024i | ||||||||
\(955\) | 41.1708 | − | 270.182i | 0.0431108 | − | 0.282913i | ||||
\(956\) | −767.591 | −0.802919 | ||||||||
\(957\) | 2059.98 | 2.15254 | ||||||||
\(958\) | 1320.14 | 1.37802 | ||||||||
\(959\) | 1630.93 | 1.70066 | ||||||||
\(960\) | −242.680 | + | 1592.58i | −0.252792 | + | 1.65894i | ||||
\(961\) | −799.800 | −0.832258 | ||||||||
\(962\) | −33.3944 | −0.0347135 | ||||||||
\(963\) | 718.715 | 0.746329 | ||||||||
\(964\) | 1099.21i | 1.14026i | ||||||||
\(965\) | −176.473 | + | 1158.10i | −0.182874 | + | 1.20010i | ||||
\(966\) | −395.564 | − | 2303.31i | −0.409486 | − | 2.38438i | ||||
\(967\) | 881.587i | 0.911672i | 0.890064 | + | 0.455836i | \(0.150660\pi\) | ||||
−0.890064 | + | 0.455836i | \(0.849340\pi\) | |||||||
\(968\) | 1101.44i | 1.13785i | ||||||||
\(969\) | −1126.17 | −1.16219 | ||||||||
\(970\) | −258.466 | + | 1696.18i | −0.266460 | + | 1.74864i | ||||
\(971\) | 918.528i | 0.945961i | 0.881073 | + | 0.472980i | \(0.156822\pi\) | ||||
−0.881073 | + | 0.472980i | \(0.843178\pi\) | |||||||
\(972\) | − | 1977.32i | − | 2.03428i | ||||||
\(973\) | 1098.12 | 1.12859 | ||||||||
\(974\) | −1029.54 | −1.05703 | ||||||||
\(975\) | −639.305 | − | 199.469i | −0.655698 | − | 0.204583i | ||||
\(976\) | − | 1096.60i | − | 1.12357i | ||||||
\(977\) | 410.684 | 0.420352 | 0.210176 | − | 0.977664i | \(-0.432596\pi\) | ||||
0.210176 | + | 0.977664i | \(0.432596\pi\) | |||||||
\(978\) | 828.852i | 0.847497i | ||||||||
\(979\) | −308.864 | −0.315489 | ||||||||
\(980\) | 470.439 | + | 71.6863i | 0.480040 | + | 0.0731493i | ||||
\(981\) | − | 4.23537i | − | 0.00431740i | ||||||
\(982\) | 3028.29i | 3.08380i | ||||||||
\(983\) | 1275.13 | 1.29719 | 0.648594 | − | 0.761135i | \(-0.275358\pi\) | ||||
0.648594 | + | 0.761135i | \(0.275358\pi\) | |||||||
\(984\) | −265.525 | −0.269843 | ||||||||
\(985\) | 77.8167 | − | 510.669i | 0.0790017 | − | 0.518446i | ||||
\(986\) | 1876.07i | 1.90271i | ||||||||
\(987\) | 1959.78 | 1.98560 | ||||||||
\(988\) | −1034.51 | −1.04708 | ||||||||
\(989\) | 318.587 | + | 1855.09i | 0.322130 | + | 1.87572i | ||||
\(990\) | 1363.47 | + | 207.767i | 1.37724 | + | 0.209866i | ||||
\(991\) | −1260.06 | −1.27151 | −0.635754 | − | 0.771892i | \(-0.719311\pi\) | ||||
−0.635754 | + | 0.771892i | \(0.719311\pi\) | |||||||
\(992\) | 164.234i | 0.165559i | ||||||||
\(993\) | − | 2078.00i | − | 2.09264i | ||||||
\(994\) | 2382.97i | 2.39735i | ||||||||
\(995\) | 78.9533 | − | 518.128i | 0.0793501 | − | 0.520732i | ||||
\(996\) | 1635.77i | 1.64234i | ||||||||
\(997\) | − | 951.919i | − | 0.954783i | −0.878691 | − | 0.477392i | \(-0.841582\pi\) | ||
0.878691 | − | 0.477392i | \(-0.158418\pi\) | |||||||
\(998\) | − | 1264.79i | − | 1.26733i | ||||||
\(999\) | 18.4136i | 0.0184320i |
(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 | 115.3.c.c.114.17 | yes | 20 | |
5.2 | odd | 4 | 575.3.d.i.551.3 | 20 | |||
5.3 | odd | 4 | 575.3.d.i.551.18 | 20 | |||
5.4 | even | 2 | inner | 115.3.c.c.114.4 | yes | 20 | |
23.22 | odd | 2 | inner | 115.3.c.c.114.18 | yes | 20 | |
115.22 | even | 4 | 575.3.d.i.551.4 | 20 | |||
115.68 | even | 4 | 575.3.d.i.551.17 | 20 | |||
115.114 | odd | 2 | inner | 115.3.c.c.114.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.3.c.c.114.3 | ✓ | 20 | 115.114 | odd | 2 | inner | |
115.3.c.c.114.4 | yes | 20 | 5.4 | even | 2 | inner | |
115.3.c.c.114.17 | yes | 20 | 1.1 | even | 1 | trivial | |
115.3.c.c.114.18 | yes | 20 | 23.22 | odd | 2 | inner | |
575.3.d.i.551.3 | 20 | 5.2 | odd | 4 | |||
575.3.d.i.551.4 | 20 | 115.22 | even | 4 | |||
575.3.d.i.551.17 | 20 | 115.68 | even | 4 | |||
575.3.d.i.551.18 | 20 | 5.3 | odd | 4 |