Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,4,Mod(4,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.e (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.12103629011\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 4.2 | ||
Character | \(\chi\) | \(=\) | 19.4 |
Dual form | 19.4.e.a.5.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.16911 | − | 0.789492i | −0.766897 | − | 0.279128i | −0.0711991 | − | 0.997462i | \(-0.522683\pi\) |
−0.695698 | + | 0.718334i | \(0.744905\pi\) | |||||||
\(3\) | −0.930433 | − | 5.27675i | −0.179062 | − | 1.01551i | −0.933350 | − | 0.358967i | \(-0.883129\pi\) |
0.754288 | − | 0.656543i | \(-0.227982\pi\) | |||||||
\(4\) | −2.04660 | − | 1.71731i | −0.255826 | − | 0.214663i | ||||
\(5\) | 6.28846 | − | 5.27664i | 0.562457 | − | 0.471957i | −0.316676 | − | 0.948534i | \(-0.602567\pi\) |
0.879133 | + | 0.476576i | \(0.158122\pi\) | |||||||
\(6\) | −2.14774 | + | 12.1804i | −0.146135 | + | 0.828773i | ||||
\(7\) | −1.44586 | + | 2.50430i | −0.0780691 | + | 0.135220i | −0.902417 | − | 0.430864i | \(-0.858209\pi\) |
0.824348 | + | 0.566084i | \(0.191542\pi\) | |||||||
\(8\) | 12.3168 | + | 21.3333i | 0.544331 | + | 0.942809i | ||||
\(9\) | −1.60664 | + | 0.584768i | −0.0595051 | + | 0.0216581i | ||||
\(10\) | −17.8062 | + | 6.48094i | −0.563083 | + | 0.204945i | ||||
\(11\) | 14.1179 | + | 24.4529i | 0.386973 | + | 0.670257i | 0.992041 | − | 0.125917i | \(-0.0401872\pi\) |
−0.605068 | + | 0.796174i | \(0.706854\pi\) | |||||||
\(12\) | −7.15756 | + | 12.3972i | −0.172184 | + | 0.298231i | ||||
\(13\) | 14.7989 | − | 83.9287i | 0.315729 | − | 1.79059i | −0.252374 | − | 0.967630i | \(-0.581211\pi\) |
0.568103 | − | 0.822957i | \(-0.307677\pi\) | |||||||
\(14\) | 5.11336 | − | 4.29062i | 0.0976145 | − | 0.0819083i | ||||
\(15\) | −33.6945 | − | 28.2730i | −0.579992 | − | 0.486671i | ||||
\(16\) | −6.16261 | − | 34.9499i | −0.0962908 | − | 0.546092i | ||||
\(17\) | 33.2517 | + | 12.1026i | 0.474396 | + | 0.172666i | 0.568143 | − | 0.822930i | \(-0.307662\pi\) |
−0.0937467 | + | 0.995596i | \(0.529884\pi\) | |||||||
\(18\) | 3.94665 | 0.0516797 | ||||||||
\(19\) | −70.3411 | + | 43.7165i | −0.849335 | + | 0.527855i | ||||
\(20\) | −21.9316 | −0.245203 | ||||||||
\(21\) | 14.5598 | + | 5.29935i | 0.151296 | + | 0.0550673i | ||||
\(22\) | −11.3179 | − | 64.1871i | −0.109681 | − | 0.622033i | ||||
\(23\) | 131.166 | + | 110.062i | 1.18913 | + | 0.997801i | 0.999874 | + | 0.0158739i | \(0.00505302\pi\) |
0.189259 | + | 0.981927i | \(0.439391\pi\) | |||||||
\(24\) | 101.111 | − | 84.8419i | 0.859963 | − | 0.721595i | ||||
\(25\) | −10.0043 | + | 56.7370i | −0.0800341 | + | 0.453896i | ||||
\(26\) | −98.3615 | + | 170.367i | −0.741934 | + | 1.28507i | ||||
\(27\) | −67.7545 | − | 117.354i | −0.482939 | − | 0.836475i | ||||
\(28\) | 7.25975 | − | 2.64233i | 0.0489987 | − | 0.0178341i | ||||
\(29\) | −62.1167 | + | 22.6086i | −0.397751 | + | 0.144770i | −0.533148 | − | 0.846022i | \(-0.678991\pi\) |
0.135397 | + | 0.990791i | \(0.456769\pi\) | |||||||
\(30\) | 50.7658 | + | 87.9290i | 0.308951 | + | 0.535119i | ||||
\(31\) | −76.2433 | + | 132.057i | −0.441732 | + | 0.765102i | −0.997818 | − | 0.0660223i | \(-0.978969\pi\) |
0.556086 | + | 0.831125i | \(0.312302\pi\) | |||||||
\(32\) | 19.9954 | − | 113.399i | 0.110460 | − | 0.626449i | ||||
\(33\) | 115.896 | − | 97.2483i | 0.611361 | − | 0.512993i | ||||
\(34\) | −62.5718 | − | 52.5040i | −0.315617 | − | 0.264834i | ||||
\(35\) | 4.12208 | + | 23.3775i | 0.0199074 | + | 0.112901i | ||||
\(36\) | 4.29238 | + | 1.56230i | 0.0198721 | + | 0.00723286i | ||||
\(37\) | 129.616 | 0.575912 | 0.287956 | − | 0.957644i | \(-0.407024\pi\) | ||||
0.287956 | + | 0.957644i | \(0.407024\pi\) | |||||||
\(38\) | 187.092 | − | 39.2921i | 0.798691 | − | 0.167738i | ||||
\(39\) | −456.640 | −1.87489 | ||||||||
\(40\) | 190.022 | + | 69.1624i | 0.751128 | + | 0.273388i | ||||
\(41\) | −27.0433 | − | 153.370i | −0.103011 | − | 0.584206i | −0.991996 | − | 0.126269i | \(-0.959700\pi\) |
0.888985 | − | 0.457937i | \(-0.151411\pi\) | |||||||
\(42\) | −27.3981 | − | 22.9898i | −0.100658 | − | 0.0844619i | ||||
\(43\) | 242.696 | − | 203.646i | 0.860715 | − | 0.722226i | −0.101407 | − | 0.994845i | \(-0.532334\pi\) |
0.962122 | + | 0.272619i | \(0.0878899\pi\) | |||||||
\(44\) | 13.0994 | − | 74.2902i | 0.0448819 | − | 0.254538i | ||||
\(45\) | −7.01766 | + | 12.1550i | −0.0232474 | + | 0.0402656i | ||||
\(46\) | −197.622 | − | 342.291i | −0.633429 | − | 1.09713i | ||||
\(47\) | −450.304 | + | 163.897i | −1.39752 | + | 0.508657i | −0.927442 | − | 0.373966i | \(-0.877998\pi\) |
−0.470082 | + | 0.882623i | \(0.655776\pi\) | |||||||
\(48\) | −178.688 | + | 65.0370i | −0.537320 | + | 0.195568i | ||||
\(49\) | 167.319 | + | 289.805i | 0.487810 | + | 0.844912i | ||||
\(50\) | 66.4938 | − | 115.171i | 0.188073 | − | 0.325752i | ||||
\(51\) | 32.9241 | − | 186.722i | 0.0903979 | − | 0.512672i | ||||
\(52\) | −174.419 | + | 146.355i | −0.465145 | + | 0.390303i | ||||
\(53\) | 518.579 | + | 435.139i | 1.34401 | + | 1.12775i | 0.980578 | + | 0.196132i | \(0.0628381\pi\) |
0.363428 | + | 0.931622i | \(0.381606\pi\) | |||||||
\(54\) | 54.3168 | + | 308.046i | 0.136881 | + | 0.776292i | ||||
\(55\) | 217.809 | + | 79.2761i | 0.533989 | + | 0.194356i | ||||
\(56\) | −71.2335 | −0.169982 | ||||||||
\(57\) | 296.128 | + | 330.497i | 0.688125 | + | 0.767989i | ||||
\(58\) | 152.588 | 0.345444 | ||||||||
\(59\) | −202.212 | − | 73.5992i | −0.446200 | − | 0.162403i | 0.109141 | − | 0.994026i | \(-0.465190\pi\) |
−0.555341 | + | 0.831623i | \(0.687412\pi\) | |||||||
\(60\) | 20.4059 | + | 115.727i | 0.0439065 | + | 0.249006i | ||||
\(61\) | −164.334 | − | 137.893i | −0.344932 | − | 0.289432i | 0.453819 | − | 0.891094i | \(-0.350061\pi\) |
−0.798751 | + | 0.601662i | \(0.794506\pi\) | |||||||
\(62\) | 269.638 | − | 226.253i | 0.552324 | − | 0.463455i | ||||
\(63\) | 0.858536 | − | 4.86900i | 0.00171691 | − | 0.00973708i | ||||
\(64\) | −274.856 | + | 476.065i | −0.536829 | + | 0.929815i | ||||
\(65\) | −349.800 | − | 605.871i | −0.667497 | − | 1.15614i | ||||
\(66\) | −328.168 | + | 119.444i | −0.612042 | + | 0.222765i | ||||
\(67\) | −417.529 | + | 151.968i | −0.761332 | + | 0.277102i | −0.693366 | − | 0.720585i | \(-0.743873\pi\) |
−0.0679659 | + | 0.997688i | \(0.521651\pi\) | |||||||
\(68\) | −47.2692 | − | 81.8727i | −0.0842976 | − | 0.146008i | ||||
\(69\) | 458.726 | − | 794.536i | 0.800349 | − | 1.38624i | ||||
\(70\) | 9.51509 | − | 53.9628i | 0.0162467 | − | 0.0921398i | ||||
\(71\) | 178.870 | − | 150.090i | 0.298986 | − | 0.250879i | −0.480936 | − | 0.876756i | \(-0.659703\pi\) |
0.779922 | + | 0.625877i | \(0.215259\pi\) | |||||||
\(72\) | −32.2637 | − | 27.0725i | −0.0528099 | − | 0.0443128i | ||||
\(73\) | −140.645 | − | 797.639i | −0.225497 | − | 1.27886i | −0.861732 | − | 0.507363i | \(-0.830620\pi\) |
0.636235 | − | 0.771495i | \(-0.280491\pi\) | |||||||
\(74\) | −281.152 | − | 102.331i | −0.441666 | − | 0.160753i | ||||
\(75\) | 308.695 | 0.475267 | ||||||||
\(76\) | 219.035 | + | 31.3269i | 0.330593 | + | 0.0472821i | ||||
\(77\) | −81.6500 | −0.120843 | ||||||||
\(78\) | 990.503 | + | 360.514i | 1.43785 | + | 0.523335i | ||||
\(79\) | 17.1116 | + | 97.0449i | 0.0243697 | + | 0.138208i | 0.994565 | − | 0.104116i | \(-0.0332014\pi\) |
−0.970195 | + | 0.242324i | \(0.922090\pi\) | |||||||
\(80\) | −223.171 | − | 187.263i | −0.311892 | − | 0.261708i | ||||
\(81\) | −591.570 | + | 496.386i | −0.811482 | + | 0.680914i | ||||
\(82\) | −62.4247 | + | 354.028i | −0.0840690 | + | 0.476779i | ||||
\(83\) | 143.051 | − | 247.772i | 0.189180 | − | 0.327669i | −0.755797 | − | 0.654806i | \(-0.772750\pi\) |
0.944977 | + | 0.327137i | \(0.106084\pi\) | |||||||
\(84\) | −20.6976 | − | 35.8494i | −0.0268845 | − | 0.0465653i | ||||
\(85\) | 272.964 | − | 99.3506i | 0.348318 | − | 0.126778i | ||||
\(86\) | −687.211 | + | 250.125i | −0.861673 | + | 0.313623i | ||||
\(87\) | 177.096 | + | 306.738i | 0.218237 | + | 0.377998i | ||||
\(88\) | −347.775 | + | 602.363i | −0.421283 | + | 0.729684i | ||||
\(89\) | −71.1994 | + | 403.792i | −0.0847992 | + | 0.480920i | 0.912601 | + | 0.408852i | \(0.134071\pi\) |
−0.997400 | + | 0.0720677i | \(0.977040\pi\) | |||||||
\(90\) | 24.8183 | − | 20.8251i | 0.0290676 | − | 0.0243906i | ||||
\(91\) | 188.786 | + | 158.410i | 0.217474 | + | 0.182482i | ||||
\(92\) | −79.4362 | − | 450.505i | −0.0900195 | − | 0.510526i | ||||
\(93\) | 767.772 | + | 279.446i | 0.856067 | + | 0.311583i | ||||
\(94\) | 1106.16 | 1.21374 | ||||||||
\(95\) | −211.661 | + | 646.074i | −0.228589 | + | 0.697745i | ||||
\(96\) | −616.984 | −0.655944 | ||||||||
\(97\) | −841.874 | − | 306.417i | −0.881231 | − | 0.320742i | −0.138524 | − | 0.990359i | \(-0.544236\pi\) |
−0.742706 | + | 0.669617i | \(0.766458\pi\) | |||||||
\(98\) | −134.135 | − | 760.717i | −0.138262 | − | 0.784122i | ||||
\(99\) | −36.9816 | − | 31.0313i | −0.0375434 | − | 0.0315026i | ||||
\(100\) | 117.910 | − | 98.9379i | 0.117910 | − | 0.0989379i | ||||
\(101\) | −52.7103 | + | 298.935i | −0.0519294 | + | 0.294506i | −0.999701 | − | 0.0244429i | \(-0.992219\pi\) |
0.947772 | + | 0.318949i | \(0.103330\pi\) | |||||||
\(102\) | −218.831 | + | 379.027i | −0.212427 | + | 0.367934i | ||||
\(103\) | 379.896 | + | 658.000i | 0.363421 | + | 0.629463i | 0.988521 | − | 0.151081i | \(-0.0482755\pi\) |
−0.625101 | + | 0.780544i | \(0.714942\pi\) | |||||||
\(104\) | 1972.75 | − | 718.023i | 1.86004 | − | 0.677000i | ||||
\(105\) | 119.522 | − | 43.5024i | 0.111087 | − | 0.0404323i | ||||
\(106\) | −781.317 | − | 1353.28i | −0.715926 | − | 1.24002i | ||||
\(107\) | −79.2465 | + | 137.259i | −0.0715986 | + | 0.124012i | −0.899602 | − | 0.436711i | \(-0.856143\pi\) |
0.828003 | + | 0.560723i | \(0.189477\pi\) | |||||||
\(108\) | −62.8663 | + | 356.533i | −0.0560122 | + | 0.317661i | ||||
\(109\) | −929.528 | + | 779.967i | −0.816813 | + | 0.685388i | −0.952224 | − | 0.305402i | \(-0.901209\pi\) |
0.135410 | + | 0.990790i | \(0.456765\pi\) | |||||||
\(110\) | −409.865 | − | 343.917i | −0.355264 | − | 0.298102i | ||||
\(111\) | −120.599 | − | 683.951i | −0.103124 | − | 0.584845i | ||||
\(112\) | 96.4354 | + | 35.0996i | 0.0813597 | + | 0.0296125i | ||||
\(113\) | −1431.94 | −1.19209 | −0.596044 | − | 0.802951i | \(-0.703262\pi\) | ||||
−0.596044 | + | 0.802951i | \(0.703262\pi\) | |||||||
\(114\) | −381.411 | − | 950.676i | −0.313354 | − | 0.781044i | ||||
\(115\) | 1405.59 | 1.13976 | ||||||||
\(116\) | 165.954 | + | 60.4025i | 0.132832 | + | 0.0483468i | ||||
\(117\) | 25.3024 | + | 143.497i | 0.0199932 | + | 0.113387i | ||||
\(118\) | 380.515 | + | 319.290i | 0.296858 | + | 0.249093i | ||||
\(119\) | −78.3860 | + | 65.7737i | −0.0603835 | + | 0.0506678i | ||||
\(120\) | 188.150 | − | 1067.05i | 0.143130 | − | 0.811732i | ||||
\(121\) | 266.870 | − | 462.232i | 0.200503 | − | 0.347282i | ||||
\(122\) | 247.594 | + | 428.845i | 0.183739 | + | 0.318244i | ||||
\(123\) | −784.135 | + | 285.402i | −0.574822 | + | 0.209218i | ||||
\(124\) | 382.822 | − | 139.336i | 0.277246 | − | 0.100909i | ||||
\(125\) | 749.532 | + | 1298.23i | 0.536322 | + | 0.928936i | ||||
\(126\) | −5.70630 | + | 9.88360i | −0.00403458 | + | 0.00698810i | ||||
\(127\) | 249.705 | − | 1416.15i | 0.174470 | − | 0.989470i | −0.764283 | − | 0.644881i | \(-0.776907\pi\) |
0.938754 | − | 0.344589i | \(-0.111982\pi\) | |||||||
\(128\) | 266.372 | − | 223.512i | 0.183939 | − | 0.154343i | ||||
\(129\) | −1300.40 | − | 1091.17i | −0.887549 | − | 0.744742i | ||||
\(130\) | 280.424 | + | 1590.37i | 0.189191 | + | 1.07296i | ||||
\(131\) | −50.0440 | − | 18.2145i | −0.0333769 | − | 0.0121482i | 0.325278 | − | 0.945619i | \(-0.394542\pi\) |
−0.358655 | + | 0.933470i | \(0.616764\pi\) | |||||||
\(132\) | −404.199 | −0.266522 | ||||||||
\(133\) | −7.77585 | − | 239.363i | −0.00506956 | − | 0.156056i | ||||
\(134\) | 1025.64 | 0.661210 | ||||||||
\(135\) | −1045.31 | − | 380.461i | −0.666413 | − | 0.242554i | ||||
\(136\) | 151.365 | + | 858.436i | 0.0954374 | + | 0.541252i | ||||
\(137\) | −427.730 | − | 358.908i | −0.266740 | − | 0.223822i | 0.499600 | − | 0.866256i | \(-0.333480\pi\) |
−0.766341 | + | 0.642434i | \(0.777925\pi\) | |||||||
\(138\) | −1622.31 | + | 1361.28i | −1.00072 | + | 0.839708i | ||||
\(139\) | −5.07488 | + | 28.7811i | −0.00309673 | + | 0.0175624i | −0.986317 | − | 0.164860i | \(-0.947283\pi\) |
0.983220 | + | 0.182422i | \(0.0583939\pi\) | |||||||
\(140\) | 31.7100 | − | 54.9234i | 0.0191428 | − | 0.0331562i | ||||
\(141\) | 1283.82 | + | 2223.65i | 0.766790 | + | 1.32812i | ||||
\(142\) | −506.485 | + | 184.345i | −0.299319 | + | 0.108943i | ||||
\(143\) | 2261.23 | − | 823.021i | 1.32233 | − | 0.481290i | ||||
\(144\) | 30.3387 | + | 52.5481i | 0.0175571 | + | 0.0304098i | ||||
\(145\) | −271.321 | + | 469.942i | −0.155393 | + | 0.269148i | ||||
\(146\) | −324.655 | + | 1841.21i | −0.184032 | + | 1.04370i | ||||
\(147\) | 1373.55 | − | 1152.54i | 0.770669 | − | 0.646668i | ||||
\(148\) | −265.273 | − | 222.590i | −0.147333 | − | 0.123627i | ||||
\(149\) | 377.120 | + | 2138.75i | 0.207348 | + | 1.17593i | 0.893702 | + | 0.448661i | \(0.148099\pi\) |
−0.686354 | + | 0.727267i | \(0.740790\pi\) | |||||||
\(150\) | −669.594 | − | 243.712i | −0.364481 | − | 0.132660i | ||||
\(151\) | −849.862 | −0.458018 | −0.229009 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229009 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(152\) | −1798.99 | − | 962.163i | −0.959985 | − | 0.513432i | ||||
\(153\) | −60.5008 | −0.0319686 | ||||||||
\(154\) | 177.108 | + | 64.4620i | 0.0926738 | + | 0.0337305i | ||||
\(155\) | 217.366 | + | 1232.75i | 0.112640 | + | 0.638816i | ||||
\(156\) | 934.561 | + | 784.190i | 0.479646 | + | 0.402471i | ||||
\(157\) | 1340.48 | − | 1124.80i | 0.681416 | − | 0.571776i | −0.235004 | − | 0.971994i | \(-0.575510\pi\) |
0.916420 | + | 0.400219i | \(0.131066\pi\) | |||||||
\(158\) | 39.4992 | − | 224.011i | 0.0198885 | − | 0.112793i | ||||
\(159\) | 1813.62 | − | 3141.28i | 0.904586 | − | 1.56679i | ||||
\(160\) | −472.628 | − | 818.616i | −0.233528 | − | 0.404483i | ||||
\(161\) | −465.275 | + | 169.346i | −0.227757 | + | 0.0828967i | ||||
\(162\) | 1675.08 | − | 609.678i | 0.812385 | − | 0.295684i | ||||
\(163\) | −1661.85 | − | 2878.40i | −0.798563 | − | 1.38315i | −0.920552 | − | 0.390621i | \(-0.872260\pi\) |
0.121988 | − | 0.992532i | \(-0.461073\pi\) | |||||||
\(164\) | −208.037 | + | 360.330i | −0.0990546 | + | 0.171568i | ||||
\(165\) | 215.663 | − | 1223.08i | 0.101754 | − | 0.577073i | ||||
\(166\) | −505.909 | + | 424.508i | −0.236543 | + | 0.198483i | ||||
\(167\) | 2146.56 | + | 1801.18i | 0.994644 | + | 0.834605i | 0.986233 | − | 0.165359i | \(-0.0528783\pi\) |
0.00841064 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(168\) | 66.2779 | + | 375.881i | 0.0304372 | + | 0.172618i | ||||
\(169\) | −4760.51 | − | 1732.69i | −2.16682 | − | 0.788660i | ||||
\(170\) | −670.525 | −0.302511 | ||||||||
\(171\) | 87.4487 | − | 111.370i | 0.0391074 | − | 0.0498050i | ||||
\(172\) | −846.425 | −0.375228 | ||||||||
\(173\) | −3146.61 | − | 1145.27i | −1.38285 | − | 0.503314i | −0.459806 | − | 0.888020i | \(-0.652081\pi\) |
−0.923039 | + | 0.384705i | \(0.874303\pi\) | |||||||
\(174\) | −141.972 | − | 805.166i | −0.0618558 | − | 0.350801i | ||||
\(175\) | −127.622 | − | 107.087i | −0.0551275 | − | 0.0462574i | ||||
\(176\) | 767.624 | − | 644.113i | 0.328760 | − | 0.275863i | ||||
\(177\) | −200.219 | + | 1135.50i | −0.0850249 | + | 0.482200i | ||||
\(178\) | 473.230 | − | 819.659i | 0.199270 | − | 0.345146i | ||||
\(179\) | 1167.62 | + | 2022.37i | 0.487552 | + | 0.844465i | 0.999898 | − | 0.0143143i | \(-0.00455654\pi\) |
−0.512345 | + | 0.858780i | \(0.671223\pi\) | |||||||
\(180\) | 35.2361 | − | 12.8249i | 0.0145908 | − | 0.00531062i | ||||
\(181\) | 4318.67 | − | 1571.87i | 1.77350 | − | 0.645503i | 0.773574 | − | 0.633706i | \(-0.218467\pi\) |
0.999930 | − | 0.0117973i | \(-0.00375530\pi\) | |||||||
\(182\) | −284.434 | − | 492.654i | −0.115844 | − | 0.200648i | ||||
\(183\) | −574.723 | + | 995.449i | −0.232157 | + | 0.402108i | ||||
\(184\) | −732.430 | + | 4153.82i | −0.293454 | + | 1.66426i | ||||
\(185\) | 815.086 | − | 683.938i | 0.323926 | − | 0.271806i | ||||
\(186\) | −1444.76 | − | 1212.30i | −0.569544 | − | 0.477904i | ||||
\(187\) | 173.500 | + | 983.966i | 0.0678479 | + | 0.384785i | ||||
\(188\) | 1203.06 | + | 437.877i | 0.466712 | + | 0.169869i | ||||
\(189\) | 391.854 | 0.150810 | ||||||||
\(190\) | 969.187 | − | 1234.30i | 0.370064 | − | 0.471293i | ||||
\(191\) | 375.808 | 0.142369 | 0.0711845 | − | 0.997463i | \(-0.477322\pi\) | ||||
0.0711845 | + | 0.997463i | \(0.477322\pi\) | |||||||
\(192\) | 2767.81 | + | 1007.40i | 1.04036 | + | 0.378661i | ||||
\(193\) | 502.800 | + | 2851.52i | 0.187525 | + | 1.06351i | 0.922668 | + | 0.385595i | \(0.126004\pi\) |
−0.735143 | + | 0.677912i | \(0.762885\pi\) | |||||||
\(194\) | 1584.21 | + | 1329.31i | 0.586285 | + | 0.491952i | ||||
\(195\) | −2871.56 | + | 2409.53i | −1.05455 | + | 0.884870i | ||||
\(196\) | 155.248 | − | 880.454i | 0.0565772 | − | 0.320865i | ||||
\(197\) | −770.856 | + | 1335.16i | −0.278788 | + | 0.482875i | −0.971084 | − | 0.238739i | \(-0.923266\pi\) |
0.692296 | + | 0.721614i | \(0.256599\pi\) | |||||||
\(198\) | 55.7184 | + | 96.5071i | 0.0199987 | + | 0.0346387i | ||||
\(199\) | −508.048 | + | 184.914i | −0.180978 | + | 0.0658705i | −0.430920 | − | 0.902390i | \(-0.641811\pi\) |
0.249942 | + | 0.968261i | \(0.419589\pi\) | |||||||
\(200\) | −1333.61 | + | 485.394i | −0.471502 | + | 0.171613i | ||||
\(201\) | 1190.38 | + | 2061.80i | 0.417726 | + | 0.723522i | ||||
\(202\) | 350.341 | − | 606.809i | 0.122029 | − | 0.211361i | ||||
\(203\) | 33.1932 | − | 188.248i | 0.0114764 | − | 0.0650858i | ||||
\(204\) | −388.041 | + | 325.605i | −0.133178 | + | 0.111749i | ||||
\(205\) | −979.342 | − | 821.766i | −0.333660 | − | 0.279974i | ||||
\(206\) | −304.552 | − | 1727.20i | −0.103006 | − | 0.584174i | ||||
\(207\) | −275.097 | − | 100.127i | −0.0923699 | − | 0.0336199i | ||||
\(208\) | −3024.50 | −1.00823 | ||||||||
\(209\) | −2062.06 | − | 1102.86i | −0.682468 | − | 0.365007i | ||||
\(210\) | −293.601 | −0.0964780 | ||||||||
\(211\) | 2783.24 | + | 1013.02i | 0.908085 | + | 0.330516i | 0.753488 | − | 0.657462i | \(-0.228370\pi\) |
0.154597 | + | 0.987978i | \(0.450592\pi\) | |||||||
\(212\) | −314.059 | − | 1781.12i | −0.101744 | − | 0.577017i | ||||
\(213\) | −958.414 | − | 804.205i | −0.308307 | − | 0.258701i | ||||
\(214\) | 280.260 | − | 235.166i | 0.0895241 | − | 0.0751196i | ||||
\(215\) | 451.616 | − | 2561.24i | 0.143255 | − | 0.812442i | ||||
\(216\) | 1669.04 | − | 2890.86i | 0.525757 | − | 0.910638i | ||||
\(217\) | −220.474 | − | 381.872i | −0.0689712 | − | 0.119462i | ||||
\(218\) | 2632.03 | − | 957.980i | 0.817722 | − | 0.297627i | ||||
\(219\) | −4078.08 | + | 1484.30i | −1.25832 | + | 0.457989i | ||||
\(220\) | −309.628 | − | 536.292i | −0.0948869 | − | 0.164349i | ||||
\(221\) | 1507.85 | − | 2611.67i | 0.458954 | − | 0.794932i | ||||
\(222\) | −278.381 | + | 1578.78i | −0.0841610 | + | 0.477301i | ||||
\(223\) | −2355.31 | + | 1976.34i | −0.707280 | + | 0.593479i | −0.923835 | − | 0.382792i | \(-0.874963\pi\) |
0.216554 | + | 0.976271i | \(0.430518\pi\) | |||||||
\(224\) | 255.076 | + | 214.034i | 0.0760847 | + | 0.0638426i | ||||
\(225\) | −17.1048 | − | 97.0060i | −0.00506808 | − | 0.0287425i | ||||
\(226\) | 3106.05 | + | 1130.51i | 0.914209 | + | 0.332745i | ||||
\(227\) | 1339.90 | 0.391773 | 0.195886 | − | 0.980627i | \(-0.437242\pi\) | ||||
0.195886 | + | 0.980627i | \(0.437242\pi\) | |||||||
\(228\) | −38.4934 | − | 1184.94i | −0.0111811 | − | 0.344186i | ||||
\(229\) | 5397.19 | 1.55745 | 0.778726 | − | 0.627364i | \(-0.215866\pi\) | ||||
0.778726 | + | 0.627364i | \(0.215866\pi\) | |||||||
\(230\) | −3048.88 | − | 1109.70i | −0.874075 | − | 0.318137i | ||||
\(231\) | 75.9698 | + | 430.846i | 0.0216383 | + | 0.122717i | ||||
\(232\) | −1247.40 | − | 1046.69i | −0.352998 | − | 0.296201i | ||||
\(233\) | 279.243 | − | 234.312i | 0.0785141 | − | 0.0658812i | −0.602686 | − | 0.797978i | \(-0.705903\pi\) |
0.681200 | + | 0.732097i | \(0.261458\pi\) | |||||||
\(234\) | 58.4060 | − | 331.237i | 0.0163168 | − | 0.0925369i | ||||
\(235\) | −1966.89 | + | 3406.76i | −0.545983 | + | 0.945670i | ||||
\(236\) | 287.456 | + | 497.888i | 0.0792872 | + | 0.137330i | ||||
\(237\) | 496.160 | − | 180.587i | 0.135988 | − | 0.0494954i | ||||
\(238\) | 221.956 | − | 80.7854i | 0.0604507 | − | 0.0220023i | ||||
\(239\) | −2227.54 | − | 3858.21i | −0.602876 | − | 1.04421i | −0.992383 | − | 0.123188i | \(-0.960688\pi\) |
0.389507 | − | 0.921023i | \(-0.372645\pi\) | |||||||
\(240\) | −780.494 | + | 1351.85i | −0.209919 | + | 0.363591i | ||||
\(241\) | 980.954 | − | 5563.26i | 0.262194 | − | 1.48698i | −0.514714 | − | 0.857362i | \(-0.672102\pi\) |
0.776908 | − | 0.629614i | \(-0.216787\pi\) | |||||||
\(242\) | −943.800 | + | 791.942i | −0.250701 | + | 0.210363i | ||||
\(243\) | 366.962 | + | 307.918i | 0.0968751 | + | 0.0812879i | ||||
\(244\) | 99.5231 | + | 564.424i | 0.0261119 | + | 0.148088i | ||||
\(245\) | 2581.38 | + | 939.544i | 0.673135 | + | 0.245001i | ||||
\(246\) | 1926.20 | 0.499228 | ||||||||
\(247\) | 2628.09 | + | 6550.59i | 0.677011 | + | 1.68747i | ||||
\(248\) | −3756.29 | −0.961794 | ||||||||
\(249\) | −1440.53 | − | 524.310i | −0.366626 | − | 0.133441i | ||||
\(250\) | −600.879 | − | 3407.75i | −0.152012 | − | 0.862101i | ||||
\(251\) | −3436.36 | − | 2883.45i | −0.864149 | − | 0.725107i | 0.0987089 | − | 0.995116i | \(-0.468529\pi\) |
−0.962858 | + | 0.270009i | \(0.912973\pi\) | |||||||
\(252\) | −10.1186 | + | 8.49055i | −0.00252942 | + | 0.00212244i | ||||
\(253\) | −839.534 | + | 4761.24i | −0.208621 | + | 1.18315i | ||||
\(254\) | −1659.67 | + | 2874.64i | −0.409989 | + | 0.710122i | ||||
\(255\) | −778.222 | − | 1347.92i | −0.191114 | − | 0.331020i | ||||
\(256\) | 3378.24 | − | 1229.58i | 0.824764 | − | 0.300190i | ||||
\(257\) | −3832.00 | + | 1394.73i | −0.930091 | + | 0.338525i | −0.762246 | − | 0.647288i | \(-0.775903\pi\) |
−0.167845 | + | 0.985813i | \(0.553681\pi\) | |||||||
\(258\) | 1959.25 | + | 3393.52i | 0.472781 | + | 0.818880i | ||||
\(259\) | −187.407 | + | 324.598i | −0.0449610 | + | 0.0778747i | ||||
\(260\) | −324.563 | + | 1840.69i | −0.0774176 | + | 0.439057i | ||||
\(261\) | 86.5783 | − | 72.6478i | 0.0205328 | − | 0.0172291i | ||||
\(262\) | 94.1709 | + | 79.0188i | 0.0222057 | + | 0.0186328i | ||||
\(263\) | −964.755 | − | 5471.40i | −0.226195 | − | 1.28282i | −0.860387 | − | 0.509641i | \(-0.829778\pi\) |
0.634192 | − | 0.773176i | \(-0.281333\pi\) | |||||||
\(264\) | 3502.10 | + | 1274.66i | 0.816437 | + | 0.297159i | ||||
\(265\) | 5557.14 | 1.28820 | ||||||||
\(266\) | −172.109 | + | 525.345i | −0.0396717 | + | 0.121094i | ||||
\(267\) | 2196.95 | 0.503563 | ||||||||
\(268\) | 1115.49 | + | 406.006i | 0.254252 | + | 0.0925401i | ||||
\(269\) | 103.353 | + | 586.146i | 0.0234259 | + | 0.132855i | 0.994278 | − | 0.106825i | \(-0.0340686\pi\) |
−0.970852 | + | 0.239680i | \(0.922957\pi\) | |||||||
\(270\) | 1967.02 | + | 1650.52i | 0.443366 | + | 0.372029i | ||||
\(271\) | −2709.72 | + | 2273.72i | −0.607394 | + | 0.509664i | −0.893813 | − | 0.448441i | \(-0.851980\pi\) |
0.286419 | + | 0.958104i | \(0.407535\pi\) | |||||||
\(272\) | 218.069 | − | 1236.73i | 0.0486116 | − | 0.275690i | ||||
\(273\) | 660.237 | − | 1143.56i | 0.146371 | − | 0.253522i | ||||
\(274\) | 644.439 | + | 1116.20i | 0.142088 | + | 0.246103i | ||||
\(275\) | −1528.62 | + | 556.374i | −0.335198 | + | 0.122002i | ||||
\(276\) | −2303.29 | + | 838.329i | −0.502325 | + | 0.182831i | ||||
\(277\) | 1518.38 | + | 2629.91i | 0.329353 | + | 0.570456i | 0.982384 | − | 0.186876i | \(-0.0598361\pi\) |
−0.653031 | + | 0.757331i | \(0.726503\pi\) | |||||||
\(278\) | 33.7304 | − | 58.4228i | 0.00727704 | − | 0.0126042i | ||||
\(279\) | 45.2724 | − | 256.753i | 0.00971466 | − | 0.0550946i | ||||
\(280\) | −447.949 | + | 375.874i | −0.0956074 | + | 0.0802241i | ||||
\(281\) | 2615.44 | + | 2194.62i | 0.555247 | + | 0.465907i | 0.876713 | − | 0.481014i | \(-0.159731\pi\) |
−0.321466 | + | 0.946921i | \(0.604176\pi\) | |||||||
\(282\) | −1029.20 | − | 5836.91i | −0.217334 | − | 1.23256i | ||||
\(283\) | −5101.09 | − | 1856.64i | −1.07148 | − | 0.389986i | −0.254749 | − | 0.967007i | \(-0.581993\pi\) |
−0.816729 | + | 0.577021i | \(0.804215\pi\) | |||||||
\(284\) | −623.828 | −0.130343 | ||||||||
\(285\) | 3606.11 | + | 515.753i | 0.749499 | + | 0.107195i | ||||
\(286\) | −5554.63 | −1.14843 | ||||||||
\(287\) | 423.187 | + | 154.027i | 0.0870381 | + | 0.0316793i | ||||
\(288\) | 34.1870 | + | 193.884i | 0.00699476 | + | 0.0396692i | ||||
\(289\) | −2804.37 | − | 2353.15i | −0.570806 | − | 0.478963i | ||||
\(290\) | 959.541 | − | 805.150i | 0.194297 | − | 0.163035i | ||||
\(291\) | −833.578 | + | 4727.46i | −0.167922 | + | 0.952331i | ||||
\(292\) | −1081.95 | + | 1873.98i | −0.216836 | + | 0.375571i | ||||
\(293\) | −2004.32 | − | 3471.59i | −0.399637 | − | 0.692192i | 0.594044 | − | 0.804433i | \(-0.297531\pi\) |
−0.993681 | + | 0.112241i | \(0.964197\pi\) | |||||||
\(294\) | −3889.30 | + | 1415.59i | −0.771527 | + | 0.280813i | ||||
\(295\) | −1659.96 | + | 604.176i | −0.327616 | + | 0.119242i | ||||
\(296\) | 1596.46 | + | 2765.14i | 0.313487 | + | 0.542975i | ||||
\(297\) | 1913.10 | − | 3313.59i | 0.373769 | − | 0.647387i | ||||
\(298\) | 870.513 | − | 4936.92i | 0.169220 | − | 0.959692i | ||||
\(299\) | 11178.4 | − | 9379.82i | 2.16209 | − | 1.81421i | ||||
\(300\) | −631.777 | − | 530.124i | −0.121586 | − | 0.102022i | ||||
\(301\) | 159.087 | + | 902.227i | 0.0304639 | + | 0.172769i | ||||
\(302\) | 1843.45 | + | 670.960i | 0.351253 | + | 0.127846i | ||||
\(303\) | 1626.45 | 0.308373 | ||||||||
\(304\) | 1961.37 | + | 2189.01i | 0.370040 | + | 0.412987i | ||||
\(305\) | −1761.02 | −0.330609 | ||||||||
\(306\) | 131.233 | + | 47.7649i | 0.0245166 | + | 0.00892332i | ||||
\(307\) | −791.199 | − | 4487.11i | −0.147088 | − | 0.834179i | −0.965667 | − | 0.259784i | \(-0.916348\pi\) |
0.818578 | − | 0.574395i | \(-0.194763\pi\) | |||||||
\(308\) | 167.105 | + | 140.218i | 0.0309146 | + | 0.0259405i | ||||
\(309\) | 3118.63 | − | 2616.84i | 0.574151 | − | 0.481770i | ||||
\(310\) | 501.751 | − | 2845.57i | 0.0919276 | − | 0.521347i | ||||
\(311\) | −1659.45 | + | 2874.24i | −0.302568 | + | 0.524063i | −0.976717 | − | 0.214533i | \(-0.931177\pi\) |
0.674149 | + | 0.738595i | \(0.264510\pi\) | |||||||
\(312\) | −5624.34 | − | 9741.64i | −1.02056 | − | 1.76767i | ||||
\(313\) | −825.518 | + | 300.464i | −0.149077 | + | 0.0542595i | −0.415481 | − | 0.909602i | \(-0.636387\pi\) |
0.266404 | + | 0.963861i | \(0.414164\pi\) | |||||||
\(314\) | −3795.68 | + | 1381.52i | −0.682174 | + | 0.248291i | ||||
\(315\) | −20.2931 | − | 35.1487i | −0.00362980 | − | 0.00628700i | ||||
\(316\) | 131.635 | − | 227.998i | 0.0234337 | − | 0.0405883i | ||||
\(317\) | −173.100 | + | 981.701i | −0.0306697 | + | 0.173936i | −0.996295 | − | 0.0860016i | \(-0.972591\pi\) |
0.965625 | + | 0.259938i | \(0.0837021\pi\) | |||||||
\(318\) | −6413.95 | + | 5381.94i | −1.13106 | + | 0.949071i | ||||
\(319\) | −1429.81 | − | 1199.75i | −0.250952 | − | 0.210574i | ||||
\(320\) | 783.603 | + | 4444.04i | 0.136890 | + | 0.776341i | ||||
\(321\) | 798.014 | + | 290.453i | 0.138756 | + | 0.0505032i | ||||
\(322\) | 1142.93 | 0.197805 | ||||||||
\(323\) | −2868.05 | + | 602.335i | −0.494064 | + | 0.103761i | ||||
\(324\) | 2063.16 | 0.353765 | ||||||||
\(325\) | 4613.81 | + | 1679.29i | 0.787472 | + | 0.286616i | ||||
\(326\) | 1332.25 | + | 7555.59i | 0.226340 | + | 1.28364i | ||||
\(327\) | 4980.55 | + | 4179.18i | 0.842278 | + | 0.706755i | ||||
\(328\) | 2938.81 | − | 2465.96i | 0.494722 | − | 0.415121i | ||||
\(329\) | 240.628 | − | 1364.67i | 0.0403230 | − | 0.228683i | ||||
\(330\) | −1433.41 | + | 2482.74i | −0.239111 | + | 0.414153i | ||||
\(331\) | −2105.07 | − | 3646.09i | −0.349562 | − | 0.605459i | 0.636610 | − | 0.771186i | \(-0.280336\pi\) |
−0.986172 | + | 0.165727i | \(0.947003\pi\) | |||||||
\(332\) | −718.270 | + | 261.429i | −0.118736 | + | 0.0432162i | ||||
\(333\) | −208.246 | + | 75.7954i | −0.0342697 | + | 0.0124732i | ||||
\(334\) | −3234.11 | − | 5601.64i | −0.529828 | − | 0.917689i | ||||
\(335\) | −1823.73 | + | 3158.80i | −0.297436 | + | 0.515174i | ||||
\(336\) | 95.4851 | − | 541.523i | 0.0155034 | − | 0.0879241i | ||||
\(337\) | −6894.59 | + | 5785.24i | −1.11446 | + | 0.935140i | −0.998311 | − | 0.0580918i | \(-0.981498\pi\) |
−0.116146 | + | 0.993232i | \(0.537054\pi\) | |||||||
\(338\) | 8958.15 | + | 7516.78i | 1.44159 | + | 1.20964i | ||||
\(339\) | 1332.33 | + | 7556.01i | 0.213458 | + | 1.21058i | ||||
\(340\) | −729.264 | − | 265.430i | −0.116323 | − | 0.0423382i | ||||
\(341\) | −4305.58 | −0.683754 | ||||||||
\(342\) | −277.612 | + | 172.533i | −0.0438933 | + | 0.0272794i | ||||
\(343\) | −1959.54 | −0.308470 | ||||||||
\(344\) | 7333.68 | + | 2669.24i | 1.14944 | + | 0.418360i | ||||
\(345\) | −1307.81 | − | 7416.94i | −0.204087 | − | 1.15743i | ||||
\(346\) | 5921.16 | + | 4968.45i | 0.920011 | + | 0.771981i | ||||
\(347\) | 8596.78 | − | 7213.55i | 1.32997 | − | 1.11598i | 0.345884 | − | 0.938277i | \(-0.387579\pi\) |
0.984085 | − | 0.177699i | \(-0.0568653\pi\) | |||||||
\(348\) | 164.319 | − | 931.899i | 0.0253116 | − | 0.143549i | ||||
\(349\) | −1836.77 | + | 3181.37i | −0.281719 | + | 0.487951i | −0.971808 | − | 0.235773i | \(-0.924238\pi\) |
0.690089 | + | 0.723724i | \(0.257571\pi\) | |||||||
\(350\) | 192.281 | + | 333.041i | 0.0293654 | + | 0.0508623i | ||||
\(351\) | −10852.1 | + | 3949.83i | −1.65026 | + | 0.600645i | ||||
\(352\) | 3055.24 | − | 1112.02i | 0.462627 | − | 0.168382i | ||||
\(353\) | 5820.93 | + | 10082.1i | 0.877668 | + | 1.52016i | 0.853894 | + | 0.520447i | \(0.174235\pi\) |
0.0237739 | + | 0.999717i | \(0.492432\pi\) | |||||||
\(354\) | 1330.77 | − | 2304.96i | 0.199801 | − | 0.346065i | ||||
\(355\) | 332.847 | − | 1887.67i | 0.0497625 | − | 0.282217i | ||||
\(356\) | 839.151 | − | 704.132i | 0.124930 | − | 0.104828i | ||||
\(357\) | 420.004 | + | 352.425i | 0.0622660 | + | 0.0522474i | ||||
\(358\) | −936.046 | − | 5308.58i | −0.138189 | − | 0.783707i | ||||
\(359\) | 847.286 | + | 308.387i | 0.124563 | + | 0.0453372i | 0.403550 | − | 0.914958i | \(-0.367776\pi\) |
−0.278987 | + | 0.960295i | \(0.589999\pi\) | |||||||
\(360\) | −345.741 | −0.0506170 | ||||||||
\(361\) | 3036.74 | − | 6150.13i | 0.442738 | − | 0.896651i | ||||
\(362\) | −10608.7 | −1.54027 | ||||||||
\(363\) | −2687.39 | − | 978.129i | −0.388571 | − | 0.141428i | ||||
\(364\) | −114.331 | − | 648.405i | −0.0164632 | − | 0.0933672i | ||||
\(365\) | −5093.30 | − | 4273.79i | −0.730399 | − | 0.612878i | ||||
\(366\) | 2032.54 | − | 1705.50i | 0.290280 | − | 0.243574i | ||||
\(367\) | −38.0243 | + | 215.646i | −0.00540831 | + | 0.0306721i | −0.987392 | − | 0.158291i | \(-0.949402\pi\) |
0.981984 | + | 0.188963i | \(0.0605127\pi\) | |||||||
\(368\) | 3038.31 | − | 5262.51i | 0.430389 | − | 0.745455i | ||||
\(369\) | 133.135 | + | 230.597i | 0.0187825 | + | 0.0325322i | ||||
\(370\) | −2307.98 | + | 840.035i | −0.324287 | + | 0.118031i | ||||
\(371\) | −1839.51 | + | 669.528i | −0.257420 | + | 0.0936931i | ||||
\(372\) | −1091.43 | − | 1890.41i | −0.152118 | − | 0.263477i | ||||
\(373\) | 1916.57 | − | 3319.60i | 0.266049 | − | 0.460811i | −0.701789 | − | 0.712385i | \(-0.747615\pi\) |
0.967838 | + | 0.251574i | \(0.0809483\pi\) | |||||||
\(374\) | 400.493 | − | 2271.31i | 0.0553717 | − | 0.314028i | ||||
\(375\) | 6153.03 | − | 5163.01i | 0.847310 | − | 0.710977i | ||||
\(376\) | −9042.78 | − | 7587.80i | −1.24028 | − | 1.04072i | ||||
\(377\) | 978.255 | + | 5547.96i | 0.133641 | + | 0.757916i | ||||
\(378\) | −849.975 | − | 309.366i | −0.115656 | − | 0.0420954i | ||||
\(379\) | −3205.78 | −0.434486 | −0.217243 | − | 0.976118i | \(-0.569706\pi\) | ||||
−0.217243 | + | 0.976118i | \(0.569706\pi\) | |||||||
\(380\) | 1542.69 | − | 958.772i | 0.208259 | − | 0.129431i | ||||
\(381\) | −7704.98 | −1.03606 | ||||||||
\(382\) | −815.169 | − | 296.697i | −0.109182 | − | 0.0397391i | ||||
\(383\) | 711.867 | + | 4037.20i | 0.0949731 | + | 0.538619i | 0.994756 | + | 0.102280i | \(0.0326139\pi\) |
−0.899783 | + | 0.436339i | \(0.856275\pi\) | |||||||
\(384\) | −1427.26 | − | 1197.61i | −0.189673 | − | 0.159155i | ||||
\(385\) | −513.453 | + | 430.838i | −0.0679688 | + | 0.0570326i | ||||
\(386\) | 1160.62 | − | 6582.22i | 0.153042 | − | 0.867944i | ||||
\(387\) | −270.839 | + | 469.106i | −0.0355749 | + | 0.0616176i | ||||
\(388\) | 1196.77 | + | 2072.87i | 0.156590 | + | 0.271222i | ||||
\(389\) | 1309.99 | − | 476.798i | 0.170743 | − | 0.0621455i | −0.255234 | − | 0.966879i | \(-0.582153\pi\) |
0.425977 | + | 0.904734i | \(0.359930\pi\) | |||||||
\(390\) | 8131.04 | − | 2959.46i | 1.05572 | − | 0.384251i | ||||
\(391\) | 3029.47 | + | 5247.20i | 0.391834 | + | 0.678676i | ||||
\(392\) | −4121.67 | + | 7138.94i | −0.531061 | + | 0.919824i | ||||
\(393\) | −49.5509 | + | 281.017i | −0.00636008 | + | 0.0360698i | ||||
\(394\) | 2726.17 | − | 2287.53i | 0.348585 | − | 0.292498i | ||||
\(395\) | 619.677 | + | 519.971i | 0.0789351 | + | 0.0662344i | ||||
\(396\) | 22.3966 | + | 127.018i | 0.00284210 | + | 0.0161184i | ||||
\(397\) | 2430.12 | + | 884.491i | 0.307215 | + | 0.111817i | 0.491027 | − | 0.871144i | \(-0.336622\pi\) |
−0.183812 | + | 0.982961i | \(0.558844\pi\) | |||||||
\(398\) | 1248.00 | 0.157178 | ||||||||
\(399\) | −1255.82 | + | 263.743i | −0.157569 | + | 0.0330918i | ||||
\(400\) | 2044.61 | 0.255576 | ||||||||
\(401\) | −3379.27 | − | 1229.95i | −0.420830 | − | 0.153170i | 0.122920 | − | 0.992417i | \(-0.460774\pi\) |
−0.543751 | + | 0.839247i | \(0.682996\pi\) | |||||||
\(402\) | −954.293 | − | 5412.06i | −0.118398 | − | 0.671466i | ||||
\(403\) | 9955.07 | + | 8353.30i | 1.23052 | + | 1.03252i | ||||
\(404\) | 621.240 | − | 521.282i | 0.0765045 | − | 0.0641949i | ||||
\(405\) | −1100.81 | + | 6243.01i | −0.135061 | + | 0.765970i | ||||
\(406\) | −220.620 | + | 382.125i | −0.0269685 | + | 0.0467108i | ||||
\(407\) | 1829.91 | + | 3169.49i | 0.222863 | + | 0.386010i | ||||
\(408\) | 4388.91 | − | 1597.43i | 0.532558 | − | 0.193835i | ||||
\(409\) | −5497.35 | + | 2000.87i | −0.664612 | + | 0.241899i | −0.652226 | − | 0.758024i | \(-0.726165\pi\) |
−0.0123857 | + | 0.999923i | \(0.503943\pi\) | |||||||
\(410\) | 1475.53 | + | 2555.69i | 0.177734 | + | 0.307845i | ||||
\(411\) | −1495.89 | + | 2590.96i | −0.179530 | + | 0.310956i | ||||
\(412\) | 352.489 | − | 1999.06i | 0.0421502 | − | 0.239046i | ||||
\(413\) | 476.685 | − | 399.986i | 0.0567945 | − | 0.0476562i | ||||
\(414\) | 517.667 | + | 434.374i | 0.0614540 | + | 0.0515660i | ||||
\(415\) | −407.833 | − | 2312.94i | −0.0482403 | − | 0.273585i | ||||
\(416\) | −9221.55 | − | 3356.37i | −1.08684 | − | 0.395576i | ||||
\(417\) | 156.592 | 0.0183893 | ||||||||
\(418\) | 3602.15 | + | 4020.21i | 0.421499 | + | 0.470419i | ||||
\(419\) | 7193.31 | 0.838702 | 0.419351 | − | 0.907824i | \(-0.362258\pi\) | ||||
0.419351 | + | 0.907824i | \(0.362258\pi\) | |||||||
\(420\) | −319.321 | − | 116.223i | −0.0370982 | − | 0.0135026i | ||||
\(421\) | −129.270 | − | 733.127i | −0.0149649 | − | 0.0848704i | 0.976411 | − | 0.215922i | \(-0.0692757\pi\) |
−0.991376 | + | 0.131052i | \(0.958165\pi\) | |||||||
\(422\) | −5237.39 | − | 4394.69i | −0.604152 | − | 0.506944i | ||||
\(423\) | 627.634 | − | 526.647i | 0.0721433 | − | 0.0605354i | ||||
\(424\) | −2895.74 | + | 16422.5i | −0.331673 | + | 1.88101i | ||||
\(425\) | −1019.33 | + | 1765.53i | −0.116340 | + | 0.201507i | ||||
\(426\) | 1443.99 | + | 2501.07i | 0.164229 | + | 0.284454i | ||||
\(427\) | 582.929 | − | 212.169i | 0.0660654 | − | 0.0240458i | ||||
\(428\) | 397.902 | − | 144.824i | 0.0449377 | − | 0.0163560i | ||||
\(429\) | −6446.79 | − | 11166.2i | −0.725534 | − | 1.25666i | ||||
\(430\) | −3001.68 | + | 5199.07i | −0.336637 | + | 0.583073i | ||||
\(431\) | 207.779 | − | 1178.37i | 0.0232213 | − | 0.131694i | −0.970993 | − | 0.239107i | \(-0.923145\pi\) |
0.994215 | + | 0.107412i | \(0.0342565\pi\) | |||||||
\(432\) | −3683.97 | + | 3091.22i | −0.410290 | + | 0.344274i | ||||
\(433\) | −2731.59 | − | 2292.07i | −0.303168 | − | 0.254388i | 0.478494 | − | 0.878091i | \(-0.341183\pi\) |
−0.781661 | + | 0.623703i | \(0.785627\pi\) | |||||||
\(434\) | 176.748 | + | 1002.39i | 0.0195488 | + | 0.110867i | ||||
\(435\) | 2732.21 | + | 994.442i | 0.301148 | + | 0.109609i | ||||
\(436\) | 3241.82 | 0.356089 | ||||||||
\(437\) | −14037.9 | − | 2007.73i | −1.53667 | − | 0.219777i | ||||
\(438\) | 10017.7 | 1.09284 | ||||||||
\(439\) | −1894.29 | − | 689.465i | −0.205944 | − | 0.0749576i | 0.236988 | − | 0.971513i | \(-0.423840\pi\) |
−0.442933 | + | 0.896555i | \(0.646062\pi\) | |||||||
\(440\) | 991.491 | + | 5623.02i | 0.107426 | + | 0.609243i | ||||
\(441\) | −438.290 | − | 367.769i | −0.0473264 | − | 0.0397116i | ||||
\(442\) | −5332.59 | + | 4474.57i | −0.573858 | + | 0.481524i | ||||
\(443\) | 1948.81 | − | 11052.3i | 0.209009 | − | 1.18535i | −0.681997 | − | 0.731355i | \(-0.738888\pi\) |
0.891006 | − | 0.453992i | \(-0.150000\pi\) | |||||||
\(444\) | −927.735 | + | 1606.88i | −0.0991629 | + | 0.171755i | ||||
\(445\) | 1682.93 | + | 2914.92i | 0.179278 | + | 0.310518i | ||||
\(446\) | 6669.25 | − | 2427.41i | 0.708068 | − | 0.257716i | ||||
\(447\) | 10934.8 | − | 3979.93i | 1.15704 | − | 0.421128i | ||||
\(448\) | −794.807 | − | 1376.65i | −0.0838194 | − | 0.145180i | ||||
\(449\) | 2795.84 | − | 4842.55i | 0.293862 | − | 0.508984i | −0.680857 | − | 0.732416i | \(-0.738393\pi\) |
0.974720 | + | 0.223432i | \(0.0717260\pi\) | |||||||
\(450\) | −39.4833 | + | 223.921i | −0.00413614 | + | 0.0234572i | ||||
\(451\) | 3368.56 | − | 2826.56i | 0.351706 | − | 0.295116i | ||||
\(452\) | 2930.62 | + | 2459.09i | 0.304967 | + | 0.255898i | ||||
\(453\) | 790.739 | + | 4484.51i | 0.0820136 | + | 0.465122i | ||||
\(454\) | −2906.40 | − | 1057.84i | −0.300449 | − | 0.109355i | ||||
\(455\) | 2023.04 | 0.208444 | ||||||||
\(456\) | −3403.25 | + | 10388.1i | −0.349499 | + | 1.06681i | ||||
\(457\) | 11052.0 | 1.13127 | 0.565635 | − | 0.824655i | \(-0.308631\pi\) | ||||
0.565635 | + | 0.824655i | \(0.308631\pi\) | |||||||
\(458\) | −11707.1 | − | 4261.04i | −1.19441 | − | 0.434728i | ||||
\(459\) | −832.658 | − | 4722.24i | −0.0846735 | − | 0.480207i | ||||
\(460\) | −2876.69 | − | 2413.83i | −0.291579 | − | 0.244664i | ||||
\(461\) | −12252.0 | + | 10280.7i | −1.23782 | + | 1.03865i | −0.240127 | + | 0.970742i | \(0.577189\pi\) |
−0.997691 | + | 0.0679113i | \(0.978367\pi\) | |||||||
\(462\) | 175.363 | − | 994.532i | 0.0176593 | − | 0.100151i | ||||
\(463\) | 7314.72 | − | 12669.5i | 0.734220 | − | 1.27171i | −0.220845 | − | 0.975309i | \(-0.570881\pi\) |
0.955065 | − | 0.296397i | \(-0.0957852\pi\) | |||||||
\(464\) | 1172.97 | + | 2031.65i | 0.117357 | + | 0.203269i | ||||
\(465\) | 6302.64 | − | 2293.97i | 0.628555 | − | 0.228775i | ||||
\(466\) | −790.697 | + | 287.790i | −0.0786015 | + | 0.0286086i | ||||
\(467\) | −1918.37 | − | 3322.72i | −0.190089 | − | 0.329244i | 0.755190 | − | 0.655505i | \(-0.227544\pi\) |
−0.945280 | + | 0.326261i | \(0.894211\pi\) | |||||||
\(468\) | 194.644 | − | 337.133i | 0.0192253 | − | 0.0332991i | ||||
\(469\) | 223.114 | − | 1265.34i | 0.0219668 | − | 0.124580i | ||||
\(470\) | 6956.02 | − | 5836.79i | 0.682675 | − | 0.572832i | ||||
\(471\) | −7182.51 | − | 6026.84i | −0.702660 | − | 0.589601i | ||||
\(472\) | −920.491 | − | 5220.36i | −0.0897649 | − | 0.509082i | ||||
\(473\) | 8406.09 | + | 3059.57i | 0.817151 | + | 0.297419i | ||||
\(474\) | −1218.80 | −0.118104 | ||||||||
\(475\) | −1776.63 | − | 4428.30i | −0.171616 | − | 0.427756i | ||||
\(476\) | 273.379 | 0.0263241 | ||||||||
\(477\) | −1087.62 | − | 395.863i | −0.104400 | − | 0.0379986i | ||||
\(478\) | 1785.75 | + | 10127.5i | 0.170875 | + | 0.969082i | ||||
\(479\) | 1570.98 | + | 1318.20i | 0.149853 | + | 0.125742i | 0.714632 | − | 0.699500i | \(-0.246594\pi\) |
−0.564779 | + | 0.825242i | \(0.691039\pi\) | |||||||
\(480\) | −3879.88 | + | 3255.60i | −0.368940 | + | 0.309578i | ||||
\(481\) | 1918.18 | − | 10878.5i | 0.181832 | − | 1.03122i | ||||
\(482\) | −6519.95 | + | 11292.9i | −0.616132 | + | 1.06717i | ||||
\(483\) | 1326.51 | + | 2297.57i | 0.124965 | + | 0.216446i | ||||
\(484\) | −1339.97 | + | 487.710i | −0.125843 | + | 0.0458029i | ||||
\(485\) | −6910.95 | + | 2515.38i | −0.647031 | + | 0.235500i | ||||
\(486\) | −552.884 | − | 957.623i | −0.0516035 | − | 0.0893799i | ||||
\(487\) | −1689.16 | + | 2925.72i | −0.157173 | + | 0.272232i | −0.933848 | − | 0.357670i | \(-0.883571\pi\) |
0.776675 | + | 0.629901i | \(0.216905\pi\) | |||||||
\(488\) | 917.639 | − | 5204.19i | 0.0851221 | − | 0.482751i | ||||
\(489\) | −13642.4 | + | 11447.3i | −1.26161 | + | 1.05862i | ||||
\(490\) | −4857.53 | − | 4075.95i | −0.447839 | − | 0.375781i | ||||
\(491\) | −3674.60 | − | 20839.7i | −0.337744 | − | 1.91544i | −0.398259 | − | 0.917273i | \(-0.630385\pi\) |
0.0605149 | − | 0.998167i | \(-0.480726\pi\) | |||||||
\(492\) | 2094.94 | + | 762.494i | 0.191965 | + | 0.0698697i | ||||
\(493\) | −2339.11 | −0.213688 | ||||||||
\(494\) | −528.989 | − | 16283.8i | −0.0481788 | − | 1.48309i | ||||
\(495\) | −396.299 | −0.0359844 | ||||||||
\(496\) | 5085.24 | + | 1850.88i | 0.460351 | + | 0.167554i | ||||
\(497\) | 117.249 | + | 664.955i | 0.0105822 | + | 0.0600147i | ||||
\(498\) | 2710.73 | + | 2274.58i | 0.243917 | + | 0.204671i | ||||
\(499\) | −12405.1 | + | 10409.2i | −1.11289 | + | 0.933823i | −0.998223 | − | 0.0595812i | \(-0.981023\pi\) |
−0.114664 | + | 0.993404i | \(0.536579\pi\) | |||||||
\(500\) | 695.458 | − | 3944.14i | 0.0622036 | − | 0.352774i | ||||
\(501\) | 7507.12 | − | 13002.7i | 0.669448 | − | 1.15952i | ||||
\(502\) | 5177.40 | + | 8967.51i | 0.460316 | + | 0.797290i | ||||
\(503\) | 16004.5 | − | 5825.17i | 1.41870 | − | 0.516365i | 0.485030 | − | 0.874497i | \(-0.338809\pi\) |
0.933671 | + | 0.358132i | \(0.116586\pi\) | |||||||
\(504\) | 114.446 | − | 41.6551i | 0.0101148 | − | 0.00368148i | ||||
\(505\) | 1245.91 | + | 2157.97i | 0.109786 | + | 0.190156i | ||||
\(506\) | 5580.00 | − | 9664.85i | 0.490240 | − | 0.849121i | ||||
\(507\) | −4713.60 | + | 26732.2i | −0.412896 | + | 2.34165i | ||||
\(508\) | −2943.00 | + | 2469.47i | −0.257037 | + | 0.215679i | ||||
\(509\) | 4582.39 | + | 3845.08i | 0.399039 | + | 0.334833i | 0.820122 | − | 0.572189i | \(-0.193906\pi\) |
−0.421083 | + | 0.907022i | \(0.638350\pi\) | |||||||
\(510\) | 623.879 | + | 3538.19i | 0.0541683 | + | 0.307203i | ||||
\(511\) | 2200.88 | + | 801.056i | 0.190531 | + | 0.0693476i | ||||
\(512\) | −11080.3 | −0.956416 | ||||||||
\(513\) | 9896.23 | + | 5292.84i | 0.851714 | + | 0.455525i | ||||
\(514\) | 9413.16 | 0.807776 | ||||||||
\(515\) | 5861.00 | + | 2133.23i | 0.501488 | + | 0.182527i | ||||
\(516\) | 787.541 | + | 4466.37i | 0.0671891 | + | 0.381048i | ||||
\(517\) | −10365.1 | − | 8697.37i | −0.881736 | − | 0.739864i | ||||
\(518\) | 662.774 | − | 556.133i | 0.0562174 | − | 0.0471720i | ||||
\(519\) | −3115.60 | + | 17669.4i | −0.263506 | + | 1.49442i | ||||
\(520\) | 8616.83 | − | 14924.8i | 0.726679 | − | 1.25864i | ||||
\(521\) | 11626.8 | + | 20138.2i | 0.977695 | + | 1.69342i | 0.670740 | + | 0.741693i | \(0.265977\pi\) |
0.306955 | + | 0.951724i | \(0.400690\pi\) | |||||||
\(522\) | −245.153 | + | 89.2284i | −0.0205557 | + | 0.00748165i | ||||
\(523\) | 6686.10 | − | 2433.54i | 0.559011 | − | 0.203463i | −0.0470348 | − | 0.998893i | \(-0.514977\pi\) |
0.606045 | + | 0.795430i | \(0.292755\pi\) | |||||||
\(524\) | 71.1404 | + | 123.219i | 0.00593089 | + | 0.0102726i | ||||
\(525\) | −446.330 | + | 773.066i | −0.0371037 | + | 0.0642655i | ||||
\(526\) | −2226.96 | + | 12629.7i | −0.184601 | + | 1.04693i | ||||
\(527\) | −4133.46 | + | 3468.39i | −0.341663 | + | 0.286689i | ||||
\(528\) | −4113.04 | − | 3451.25i | −0.339010 | − | 0.284463i | ||||
\(529\) | 2978.26 | + | 16890.6i | 0.244782 | + | 1.38823i | ||||
\(530\) | −12054.1 | − | 4387.32i | −0.987915 | − | 0.359572i | ||||
\(531\) | 367.920 | 0.0300685 | ||||||||
\(532\) | −395.146 | + | 503.235i | −0.0322025 | + | 0.0410113i | ||||
\(533\) | −13272.4 | −1.07860 | ||||||||
\(534\) | −4765.44 | − | 1734.48i | −0.386181 | − | 0.140558i | ||||
\(535\) | 225.928 | + | 1281.30i | 0.0182575 | + | 0.103543i | ||||
\(536\) | −8384.60 | − | 7035.52i | −0.675671 | − | 0.566955i | ||||
\(537\) | 9585.16 | − | 8042.90i | 0.770261 | − | 0.646326i | ||||
\(538\) | 238.573 | − | 1353.01i | 0.0191182 | − | 0.108425i | ||||
\(539\) | −4724.38 | + | 8182.87i | −0.377539 | + | 0.653917i | ||||
\(540\) | 1485.96 | + | 2573.76i | 0.118418 | + | 0.205106i | ||||
\(541\) | −3361.41 | + | 1223.45i | −0.267132 | + | 0.0972279i | −0.472113 | − | 0.881538i | \(-0.656509\pi\) |
0.204982 | + | 0.978766i | \(0.434286\pi\) | |||||||
\(542\) | 7672.77 | − | 2792.66i | 0.608070 | − | 0.221319i | ||||
\(543\) | −12312.6 | − | 21326.0i | −0.973082 | − | 1.68543i | ||||
\(544\) | 2037.31 | − | 3528.73i | 0.160568 | − | 0.278112i | ||||
\(545\) | −1729.69 | + | 9809.58i | −0.135948 | + | 0.771002i | ||||
\(546\) | −2334.96 | + | 1959.27i | −0.183017 | + | 0.153569i | ||||
\(547\) | 6284.63 | + | 5273.43i | 0.491246 | + | 0.412204i | 0.854473 | − | 0.519497i | \(-0.173881\pi\) |
−0.363227 | + | 0.931701i | \(0.618325\pi\) | |||||||
\(548\) | 259.040 | + | 1469.09i | 0.0201927 | + | 0.114519i | ||||
\(549\) | 344.661 | + | 125.446i | 0.0267937 | + | 0.00975212i | ||||
\(550\) | 3755.01 | 0.291117 | ||||||||
\(551\) | 3380.99 | − | 4305.84i | 0.261407 | − | 0.332913i | ||||
\(552\) | 22600.1 | 1.74262 | ||||||||
\(553\) | −267.771 | − | 97.4606i | −0.0205909 | − | 0.00749448i | ||||
\(554\) | −1217.24 | − | 6903.33i | −0.0933497 | − | 0.529412i | ||||
\(555\) | −4367.35 | − | 3664.64i | −0.334025 | − | 0.280280i | ||||
\(556\) | 59.8122 | − | 50.1884i | 0.00456223 | − | 0.00382817i | ||||
\(557\) | 2975.28 | − | 16873.6i | 0.226331 | − | 1.28359i | −0.633792 | − | 0.773503i | \(-0.718503\pi\) |
0.860124 | − | 0.510086i | \(-0.170386\pi\) | |||||||
\(558\) | −300.905 | + | 521.183i | −0.0228286 | + | 0.0395402i | ||||
\(559\) | −13500.1 | − | 23382.9i | −1.02146 | − | 1.76921i | ||||
\(560\) | 791.638 | − | 288.133i | 0.0597372 | − | 0.0217426i | ||||
\(561\) | 5030.71 | − | 1831.03i | 0.378604 | − | 0.137800i | ||||
\(562\) | −3940.56 | − | 6825.25i | −0.295769 | − | 0.512288i | ||||
\(563\) | −2994.16 | + | 5186.04i | −0.224137 | + | 0.388216i | −0.956060 | − | 0.293171i | \(-0.905290\pi\) |
0.731923 | + | 0.681387i | \(0.238623\pi\) | |||||||
\(564\) | 1191.20 | − | 6755.64i | 0.0889337 | − | 0.504368i | ||||
\(565\) | −9004.73 | + | 7555.86i | −0.670499 | + | 0.562615i | ||||
\(566\) | 9599.03 | + | 8054.54i | 0.712857 | + | 0.598158i | ||||
\(567\) | −387.774 | − | 2199.18i | −0.0287213 | − | 0.162887i | ||||
\(568\) | 5405.03 | + | 1967.27i | 0.399278 | + | 0.145325i | ||||
\(569\) | −2828.73 | −0.208413 | −0.104206 | − | 0.994556i | \(-0.533230\pi\) | ||||
−0.104206 | + | 0.994556i | \(0.533230\pi\) | |||||||
\(570\) | −7414.87 | − | 3965.72i | −0.544868 | − | 0.291414i | ||||
\(571\) | −14475.6 | −1.06092 | −0.530459 | − | 0.847711i | \(-0.677980\pi\) | ||||
−0.530459 | + | 0.847711i | \(0.677980\pi\) | |||||||
\(572\) | −6041.22 | − | 2198.83i | −0.441602 | − | 0.160730i | ||||
\(573\) | −349.664 | − | 1983.04i | −0.0254929 | − | 0.144577i | ||||
\(574\) | −796.336 | − | 668.206i | −0.0579067 | − | 0.0485895i | ||||
\(575\) | −7556.79 | + | 6340.90i | −0.548069 | + | 0.459885i | ||||
\(576\) | 163.207 | − | 925.591i | 0.0118060 | − | 0.0669554i | ||||
\(577\) | 8589.46 | − | 14877.4i | 0.619729 | − | 1.07340i | −0.369805 | − | 0.929109i | \(-0.620576\pi\) |
0.989535 | − | 0.144294i | \(-0.0460910\pi\) | |||||||
\(578\) | 4225.21 | + | 7318.27i | 0.304058 | + | 0.526644i | ||||
\(579\) | 14578.9 | − | 5306.29i | 1.04642 | − | 0.380867i | ||||
\(580\) | 1362.32 | − | 495.844i | 0.0975297 | − | 0.0354979i | ||||
\(581\) | 413.664 | + | 716.488i | 0.0295382 | + | 0.0511616i | ||||
\(582\) | 5540.42 | − | 9596.28i | 0.394601 | − | 0.683468i | ||||
\(583\) | −3319.18 | + | 18824.0i | −0.235792 | + | 1.33724i | ||||
\(584\) | 15284.0 | − | 12824.8i | 1.08297 | − | 0.908723i | ||||
\(585\) | 916.295 | + | 768.863i | 0.0647592 | + | 0.0543395i | ||||
\(586\) | 1606.81 | + | 9112.66i | 0.113271 | + | 0.642390i | ||||
\(587\) | −18207.6 | − | 6627.03i | −1.28025 | − | 0.465974i | −0.389737 | − | 0.920926i | \(-0.627434\pi\) |
−0.890516 | + | 0.454952i | \(0.849656\pi\) | |||||||
\(588\) | −4790.38 | −0.335973 | ||||||||
\(589\) | −410.037 | − | 12622.1i | −0.0286847 | − | 0.882998i | ||||
\(590\) | 4077.63 | 0.284531 | ||||||||
\(591\) | 7762.53 | + | 2825.33i | 0.540284 | + | 0.196647i | ||||
\(592\) | −798.774 | − | 4530.07i | −0.0554551 | − | 0.314501i | ||||
\(593\) | 7818.84 | + | 6560.79i | 0.541453 | + | 0.454333i | 0.872034 | − | 0.489445i | \(-0.162800\pi\) |
−0.330582 | + | 0.943777i | \(0.607245\pi\) | |||||||
\(594\) | −6765.78 | + | 5677.17i | −0.467346 | + | 0.392150i | ||||
\(595\) | −145.863 | + | 827.231i | −0.0100501 | + | 0.0569969i | ||||
\(596\) | 2901.07 | − | 5024.81i | 0.199384 | − | 0.345343i | ||||
\(597\) | 1448.45 | + | 2508.79i | 0.0992984 | + | 0.171990i | ||||
\(598\) | −31652.6 | + | 11520.6i | −2.16450 | + | 0.787813i | ||||
\(599\) | −1493.84 | + | 543.713i | −0.101898 | + | 0.0370877i | −0.392466 | − | 0.919767i | \(-0.628378\pi\) |
0.290568 | + | 0.956854i | \(0.406156\pi\) | |||||||
\(600\) | 3802.14 | + | 6585.49i | 0.258703 | + | 0.448086i | ||||
\(601\) | −457.078 | + | 791.682i | −0.0310226 | + | 0.0537327i | −0.881120 | − | 0.472893i | \(-0.843210\pi\) |
0.850097 | + | 0.526626i | \(0.176543\pi\) | |||||||
\(602\) | 367.224 | − | 2082.63i | 0.0248620 | − | 0.140999i | ||||
\(603\) | 581.951 | − | 488.315i | 0.0393016 | − | 0.0329780i | ||||
\(604\) | 1739.33 | + | 1459.47i | 0.117173 | + | 0.0983197i | ||||
\(605\) | −760.835 | − | 4314.91i | −0.0511278 | − | 0.289960i | ||||
\(606\) | −3527.95 | − | 1284.07i | −0.236490 | − | 0.0860754i | ||||
\(607\) | 8012.94 | 0.535807 | 0.267904 | − | 0.963446i | \(-0.413669\pi\) | ||||
0.267904 | + | 0.963446i | \(0.413669\pi\) | |||||||
\(608\) | 3550.92 | + | 8850.76i | 0.236857 | + | 0.590371i | ||||
\(609\) | −1024.22 | −0.0681503 | ||||||||
\(610\) | 3819.85 | + | 1390.31i | 0.253543 | + | 0.0922821i | ||||
\(611\) | 7091.69 | + | 40219.0i | 0.469556 | + | 2.66299i | ||||
\(612\) | 123.821 | + | 103.898i | 0.00817839 | + | 0.00686248i | ||||
\(613\) | 2659.88 | − | 2231.90i | 0.175255 | − | 0.147056i | −0.550941 | − | 0.834544i | \(-0.685731\pi\) |
0.726196 | + | 0.687488i | \(0.241287\pi\) | |||||||
\(614\) | −1826.34 | + | 10357.7i | −0.120041 | + | 0.680786i | ||||
\(615\) | −3425.04 | + | 5932.34i | −0.224570 | + | 0.388967i | ||||
\(616\) | −1005.67 | − | 1741.87i | −0.0657784 | − | 0.113931i | ||||
\(617\) | −4629.25 | + | 1684.91i | −0.302053 | + | 0.109938i | −0.488600 | − | 0.872508i | \(-0.662492\pi\) |
0.186547 | + | 0.982446i | \(0.440270\pi\) | |||||||
\(618\) | −8830.64 | + | 3214.09i | −0.574790 | + | 0.209207i | ||||
\(619\) | 4647.29 | + | 8049.34i | 0.301762 | + | 0.522666i | 0.976535 | − | 0.215359i | \(-0.0690920\pi\) |
−0.674774 | + | 0.738025i | \(0.735759\pi\) | |||||||
\(620\) | 1672.14 | − | 2896.23i | 0.108314 | − | 0.187605i | ||||
\(621\) | 4029.08 | − | 22850.1i | 0.260357 | − | 1.47656i | ||||
\(622\) | 5868.72 | − | 4924.44i | 0.378319 | − | 0.317447i | ||||
\(623\) | −908.273 | − | 762.132i | −0.0584096 | − | 0.0490115i | ||||
\(624\) | 2814.09 | + | 15959.5i | 0.180535 | + | 1.02386i | ||||
\(625\) | 4796.46 | + | 1745.77i | 0.306974 | + | 0.111729i | ||||
\(626\) | 2027.86 | 0.129472 | ||||||||
\(627\) | −3900.91 | + | 11907.1i | −0.248464 | + | 0.758412i | ||||
\(628\) | −4675.07 | −0.297063 | ||||||||
\(629\) | 4309.96 | + | 1568.70i | 0.273211 | + | 0.0994405i | ||||
\(630\) | 16.2684 | + | 92.2628i | 0.00102881 | + | 0.00583466i | ||||
\(631\) | 16192.7 | + | 13587.3i | 1.02159 | + | 0.857212i | 0.989826 | − | 0.142284i | \(-0.0454445\pi\) |
0.0317593 | + | 0.999496i | \(0.489889\pi\) | |||||||
\(632\) | −1859.53 | + | 1560.33i | −0.117038 | + | 0.0982067i | ||||
\(633\) | 2755.81 | − | 15629.0i | 0.173039 | − | 0.981353i | ||||
\(634\) | 1150.52 | − | 1992.76i | 0.0720709 | − | 0.124830i | ||||
\(635\) | −5902.24 | − | 10223.0i | −0.368856 | − | 0.638877i | ||||
\(636\) | −9106.29 | + | 3314.42i | −0.567748 | + | 0.206643i | ||||
\(637\) | 26799.1 | − | 9754.07i | 1.66691 | − | 0.606704i | ||||
\(638\) | 2154.22 | + | 3731.21i | 0.133677 | + | 0.231536i | ||||
\(639\) | −199.612 | + | 345.738i | −0.0123576 | + | 0.0214041i | ||||
\(640\) | 495.673 | − | 2811.10i | 0.0306143 | − | 0.173623i | ||||
\(641\) | 5782.43 | − | 4852.03i | 0.356306 | − | 0.298976i | −0.447010 | − | 0.894529i | \(-0.647511\pi\) |
0.803316 | + | 0.595552i | \(0.203067\pi\) | |||||||
\(642\) | −1501.67 | − | 1260.05i | −0.0923151 | − | 0.0774615i | ||||
\(643\) | −3213.94 | − | 18227.2i | −0.197116 | − | 1.11790i | −0.909373 | − | 0.415981i | \(-0.863438\pi\) |
0.712257 | − | 0.701918i | \(-0.247673\pi\) | |||||||
\(644\) | 1243.05 | + | 452.435i | 0.0760609 | + | 0.0276839i | ||||
\(645\) | −13935.2 | −0.850695 | ||||||||
\(646\) | 6696.66 | + | 957.771i | 0.407858 | + | 0.0583328i | ||||
\(647\) | 6739.57 | 0.409521 | 0.204760 | − | 0.978812i | \(-0.434359\pi\) | ||||
0.204760 | + | 0.978812i | \(0.434359\pi\) | |||||||
\(648\) | −17875.8 | − | 6506.27i | −1.08369 | − | 0.394430i | ||||
\(649\) | −1055.09 | − | 5983.74i | −0.0638153 | − | 0.361914i | ||||
\(650\) | −8682.09 | − | 7285.14i | −0.523907 | − | 0.439610i | ||||
\(651\) | −1809.91 | + | 1518.69i | −0.108964 | + | 0.0914320i | ||||
\(652\) | −1541.95 | + | 8744.85i | −0.0926189 | + | 0.525268i | ||||
\(653\) | −10072.9 | + | 17446.7i | −0.603647 | + | 1.04555i | 0.388617 | + | 0.921399i | \(0.372953\pi\) |
−0.992264 | + | 0.124147i | \(0.960380\pi\) | |||||||
\(654\) | −7503.94 | − | 12997.2i | −0.448666 | − | 0.777112i | ||||
\(655\) | −410.812 | + | 149.523i | −0.0245065 | + | 0.00891963i | ||||
\(656\) | −5193.62 | + | 1890.32i | −0.309111 | + | 0.112507i | ||||
\(657\) | 692.400 | + | 1199.27i | 0.0411159 | + | 0.0712147i | ||||
\(658\) | −1599.35 | + | 2770.15i | −0.0947554 | + | 0.164121i | ||||
\(659\) | 874.078 | − | 4957.14i | 0.0516681 | − | 0.293024i | −0.948014 | − | 0.318228i | \(-0.896912\pi\) |
0.999682 | + | 0.0252036i | \(0.00802341\pi\) | |||||||
\(660\) | −2541.79 | + | 2132.81i | −0.149907 | + | 0.125787i | ||||
\(661\) | −13584.8 | − | 11399.0i | −0.799377 | − | 0.670757i | 0.148670 | − | 0.988887i | \(-0.452501\pi\) |
−0.948047 | + | 0.318130i | \(0.896945\pi\) | |||||||
\(662\) | 1687.57 | + | 9570.71i | 0.0990777 | + | 0.561897i | ||||
\(663\) | −15184.1 | − | 5526.55i | −0.889442 | − | 0.323731i | ||||
\(664\) | 7047.74 | 0.411906 | ||||||||
\(665\) | −1311.93 | − | 1464.20i | −0.0765031 | − | 0.0853821i | ||||
\(666\) | 511.549 | 0.0297630 | ||||||||
\(667\) | −10636.0 | − | 3871.18i | −0.617431 | − | 0.224726i | ||||
\(668\) | −1299.99 | − | 7372.59i | −0.0752964 | − | 0.427027i | ||||
\(669\) | 12620.1 | + | 10589.5i | 0.729331 | + | 0.611981i | ||||
\(670\) | 6449.72 | − | 5411.96i | 0.371902 | − | 0.312063i | ||||
\(671\) | 1051.83 | − | 5965.20i | 0.0605146 | − | 0.343195i | ||||
\(672\) | 892.072 | − | 1545.11i | 0.0512090 | − | 0.0886965i | ||||
\(673\) | 57.3669 | + | 99.3624i | 0.00328578 | + | 0.00569114i | 0.867664 | − | 0.497152i | \(-0.165621\pi\) |
−0.864378 | + | 0.502843i | \(0.832287\pi\) | |||||||
\(674\) | 19522.5 | − | 7105.62i | 1.11570 | − | 0.406081i | ||||
\(675\) | 7336.16 | − | 2670.14i | 0.418324 | − | 0.152258i | ||||
\(676\) | 6767.34 | + | 11721.4i | 0.385033 | + | 0.666897i | ||||
\(677\) | −15180.1 | + | 26292.8i | −0.861773 | + | 1.49263i | 0.00844344 | + | 0.999964i | \(0.497312\pi\) |
−0.870216 | + | 0.492670i | \(0.836021\pi\) | |||||||
\(678\) | 3075.44 | − | 17441.7i | 0.174206 | − | 0.987971i | ||||
\(679\) | 1984.59 | − | 1665.27i | 0.112167 | − | 0.0941197i | ||||
\(680\) | 5481.52 | + | 4599.54i | 0.309127 | + | 0.259389i | ||||
\(681\) | −1246.69 | − | 7070.32i | −0.0701515 | − | 0.397849i | ||||
\(682\) | 9339.28 | + | 3399.22i | 0.524369 | + | 0.190855i | ||||
\(683\) | −11815.2 | −0.661925 | −0.330962 | − | 0.943644i | \(-0.607373\pi\) | ||||
−0.330962 | + | 0.943644i | \(0.607373\pi\) | |||||||
\(684\) | −370.229 | + | 77.7538i | −0.0206960 | + | 0.00434648i | ||||
\(685\) | −4583.59 | −0.255664 | ||||||||
\(686\) | 4250.46 | + | 1547.04i | 0.236565 | + | 0.0861025i | ||||
\(687\) | −5021.72 | − | 28479.6i | −0.278880 | − | 1.58161i | ||||
\(688\) | −8613.04 | − | 7227.20i | −0.477281 | − | 0.400486i | ||||
\(689\) | 44195.1 | − | 37084.1i | 2.44368 | − | 2.05049i | ||||
\(690\) | −3018.84 | + | 17120.7i | −0.166558 | + | 0.944599i | ||||
\(691\) | −7277.33 | + | 12604.7i | −0.400641 | + | 0.693930i | −0.993803 | − | 0.111153i | \(-0.964546\pi\) |
0.593163 | + | 0.805083i | \(0.297879\pi\) | |||||||
\(692\) | 4473.08 | + | 7747.61i | 0.245724 | + | 0.425607i | ||||
\(693\) | 131.182 | − | 47.7463i | 0.00719075 | − | 0.00261722i | ||||
\(694\) | −24342.4 | + | 8859.92i | −1.33145 | + | 0.484608i | ||||
\(695\) | 119.954 | + | 207.767i | 0.00654695 | + | 0.0113396i | ||||
\(696\) | −4362.50 | + | 7556.07i | −0.237586 | + | 0.411512i | ||||
\(697\) | 956.950 | − | 5427.13i | 0.0520044 | − | 0.294931i | ||||
\(698\) | 6495.82 | − | 5450.64i | 0.352250 | − | 0.295573i | ||||
\(699\) | −1496.22 | − | 1255.48i | −0.0809619 | − | 0.0679351i | ||||
\(700\) | 77.2897 | + | 438.331i | 0.00417325 | + | 0.0236677i | ||||
\(701\) | 28341.4 | + | 10315.4i | 1.52702 | + | 0.555789i | 0.962889 | − | 0.269897i | \(-0.0869898\pi\) |
0.564129 | + | 0.825687i | \(0.309212\pi\) | |||||||
\(702\) | 26657.7 | 1.43324 | ||||||||
\(703\) | −9117.34 | + | 5666.36i | −0.489142 | + | 0.303998i | ||||
\(704\) | −15521.6 | −0.830954 | ||||||||
\(705\) | 19806.7 | + | 7209.03i | 1.05810 | + | 0.385118i | ||||
\(706\) | −4666.47 | − | 26464.9i | −0.248761 | − | 1.41079i | ||||
\(707\) | −672.412 | − | 564.220i | −0.0357689 | − | 0.0300137i | ||||
\(708\) | 2359.77 | − | 1980.08i | 0.125262 | − | 0.105107i | ||||
\(709\) | −1539.66 | + | 8731.85i | −0.0815560 | + | 0.462527i | 0.916491 | + | 0.400056i | \(0.131009\pi\) |
−0.998047 | + | 0.0624711i | \(0.980102\pi\) | |||||||
\(710\) | −2212.29 | + | 3831.79i | −0.116937 | + | 0.202542i | ||||
\(711\) | −84.2410 | − | 145.910i | −0.00444344 | − | 0.00769626i | ||||
\(712\) | −9491.18 | + | 3454.51i | −0.499574 | + | 0.181830i | ||||
\(713\) | −24535.0 | + | 8930.00i | −1.28870 | + | 0.469048i | ||||
\(714\) | −632.799 | − | 1096.04i | −0.0331679 | − | 0.0574485i | ||||
\(715\) | 9876.87 | − | 17107.2i | 0.516607 | − | 0.894790i | ||||
\(716\) | 1083.38 | − | 6144.15i | 0.0565472 | − | 0.320695i | ||||
\(717\) | −18286.2 | + | 15343.9i | −0.952456 | + | 0.799205i | ||||
\(718\) | −1594.39 | − | 1337.85i | −0.0828720 | − | 0.0695379i | ||||
\(719\) | 1324.91 | + | 7513.95i | 0.0687217 | + | 0.389740i | 0.999696 | + | 0.0246554i | \(0.00784886\pi\) |
−0.930974 | + | 0.365085i | \(0.881040\pi\) | |||||||
\(720\) | 468.061 | + | 170.360i | 0.0242272 | + | 0.00881800i | ||||
\(721\) | −2197.11 | −0.113488 | ||||||||
\(722\) | −11442.5 | + | 10942.8i | −0.589815 | + | 0.564058i | ||||
\(723\) | −30268.6 | −1.55699 | ||||||||
\(724\) | −11538.0 | − | 4199.49i | −0.592274 | − | 0.215570i | ||||
\(725\) | −661.315 | − | 3750.50i | −0.0338767 | − | 0.192124i | ||||
\(726\) | 5057.02 | + | 4243.34i | 0.258517 | + | 0.216922i | ||||
\(727\) | −5040.04 | + | 4229.10i | −0.257118 | + | 0.215748i | −0.762230 | − | 0.647306i | \(-0.775896\pi\) |
0.505112 | + | 0.863054i | \(0.331451\pi\) | |||||||
\(728\) | −1054.18 | + | 5978.53i | −0.0536681 | + | 0.304367i | ||||
\(729\) | −9141.87 | + | 15834.2i | −0.464455 | + | 0.804460i | ||||
\(730\) | 7673.82 | + | 13291.5i | 0.389070 | + | 0.673889i | ||||
\(731\) | 10534.7 | − | 3834.32i | 0.533024 | − | 0.194005i | ||||
\(732\) | 2885.72 | − | 1050.32i | 0.145709 | − | 0.0530339i | ||||
\(733\) | 3341.60 | + | 5787.83i | 0.168383 | + | 0.291648i | 0.937852 | − | 0.347037i | \(-0.112812\pi\) |
−0.769468 | + | 0.638685i | \(0.779479\pi\) | |||||||
\(734\) | 252.730 | − | 437.741i | 0.0127090 | − | 0.0220127i | ||||
\(735\) | 2555.94 | − | 14495.5i | 0.128268 | − | 0.727446i | ||||
\(736\) | 15103.6 | − | 12673.4i | 0.756423 | − | 0.634714i | ||||
\(737\) | −9610.69 | − | 8064.33i | −0.480345 | − | 0.403057i | ||||
\(738\) | −106.731 | − | 605.299i | −0.00532359 | − | 0.0301916i | ||||
\(739\) | 11769.3 | + | 4283.68i | 0.585848 | + | 0.213231i | 0.617902 | − | 0.786255i | \(-0.287983\pi\) |
−0.0320543 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(740\) | −2842.69 | −0.141215 | ||||||||
\(741\) | 32120.5 | − | 19962.7i | 1.59241 | − | 0.989672i | ||||
\(742\) | 4518.70 | 0.223567 | ||||||||
\(743\) | 14254.7 | + | 5188.28i | 0.703841 | + | 0.256177i | 0.669050 | − | 0.743217i | \(-0.266701\pi\) |
0.0347911 | + | 0.999395i | \(0.488923\pi\) | |||||||
\(744\) | 3494.98 | + | 19821.0i | 0.172221 | + | 0.976711i | ||||
\(745\) | 13656.9 | + | 11459.5i | 0.671612 | + | 0.563550i | ||||
\(746\) | −6778.06 | + | 5687.47i | −0.332657 | + | 0.279133i | ||||
\(747\) | −84.9424 | + | 481.732i | −0.00416048 | + | 0.0235953i | ||||
\(748\) | 1334.68 | − | 2311.74i | 0.0652419 | − | 0.113002i | ||||
\(749\) | −229.159 | − | 396.915i | −0.0111793 | − | 0.0193631i | ||||
\(750\) | −17422.8 | + | 6341.37i | −0.848253 | + | 0.308739i | ||||
\(751\) | −16800.1 | + | 6114.75i | −0.816306 | + | 0.297111i | −0.716226 | − | 0.697868i | \(-0.754132\pi\) |
−0.100080 | + | 0.994979i | \(0.531910\pi\) | |||||||
\(752\) | 8503.24 | + | 14728.1i | 0.412342 | + | 0.714198i | ||||
\(753\) | −12017.9 | + | 20815.7i | −0.581617 | + | 1.00739i | ||||
\(754\) | 2258.13 | − | 12806.5i | 0.109067 | − | 0.618547i | ||||
\(755\) | −5344.32 | + | 4484.42i | −0.257616 | + | 0.216165i | ||||
\(756\) | −801.970 | − | 672.932i | −0.0385812 | − | 0.0323734i | ||||
\(757\) | −431.651 | − | 2448.01i | −0.0207247 | − | 0.117536i | 0.972690 | − | 0.232107i | \(-0.0745618\pi\) |
−0.993415 | + | 0.114571i | \(0.963451\pi\) | |||||||
\(758\) | 6953.71 | + | 2530.94i | 0.333206 | + | 0.121277i | ||||
\(759\) | 25905.0 | 1.23885 | ||||||||
\(760\) | −16389.9 | + | 3442.13i | −0.782269 | + | 0.164289i | ||||
\(761\) | −8995.52 | −0.428498 | −0.214249 | − | 0.976779i | \(-0.568730\pi\) | ||||
−0.214249 | + | 0.976779i | \(0.568730\pi\) | |||||||
\(762\) | 16713.0 | + | 6083.02i | 0.794550 | + | 0.289192i | ||||
\(763\) | −609.305 | − | 3455.54i | −0.0289100 | − | 0.163957i | ||||
\(764\) | −769.130 | − | 645.376i | −0.0364216 | − | 0.0305614i | ||||
\(765\) | −380.457 | + | 319.241i | −0.0179810 | + | 0.0150878i | ||||
\(766\) | 1643.22 | − | 9319.15i | 0.0775089 | − | 0.439575i | ||||
\(767\) | −9169.60 | + | 15882.2i | −0.431675 | + | 0.747684i | ||||
\(768\) | −9631.39 | − | 16682.0i | −0.452530 | − | 0.783804i | ||||
\(769\) | 7137.38 | − | 2597.80i | 0.334695 | − | 0.121819i | −0.169205 | − | 0.985581i | \(-0.554120\pi\) |
0.503900 | + | 0.863762i | \(0.331898\pi\) | |||||||
\(770\) | 1453.88 | − | 529.169i | 0.0680444 | − | 0.0247661i | ||||
\(771\) | 10925.1 | + | 18922.8i | 0.510320 | + | 0.883900i | ||||
\(772\) | 3867.90 | − | 6699.39i | 0.180322 | − | 0.312327i | ||||
\(773\) | 746.091 | − | 4231.29i | 0.0347154 | − | 0.196881i | −0.962518 | − | 0.271219i | \(-0.912573\pi\) |
0.997233 | + | 0.0743379i | \(0.0236843\pi\) | |||||||
\(774\) | 957.835 | − | 803.719i | 0.0444815 | − | 0.0373244i | ||||
\(775\) | −6729.78 | − | 5646.95i | −0.311923 | − | 0.261735i | ||||
\(776\) | −3832.30 | − | 21734.1i | −0.177283 | − | 1.00542i | ||||
\(777\) | 1887.19 | + | 686.881i | 0.0871333 | + | 0.0317139i | ||||
\(778\) | −3217.95 | −0.148289 | ||||||||
\(779\) | 8607.07 | + | 9606.01i | 0.395867 | + | 0.441811i | ||||
\(780\) | 10014.8 | 0.459729 | ||||||||
\(781\) | 6195.41 | + | 2254.95i | 0.283853 | + | 0.103314i | ||||
\(782\) | −2428.64 | − | 13773.5i | −0.111059 | − | 0.629846i | ||||
\(783\) | 6861.91 | + | 5757.82i | 0.313186 | + | 0.262794i | ||||
\(784\) | 9097.53 | − | 7633.73i | 0.414428 | − | 0.347747i | ||||
\(785\) | 2494.41 | − | 14146.5i | 0.113413 | − | 0.643199i | ||||
\(786\) | 329.342 | − | 570.438i | 0.0149456 | − | 0.0258866i | ||||
\(787\) | −12826.2 | − | 22215.6i | −0.580945 | − | 1.00623i | −0.995368 | − | 0.0961423i | \(-0.969350\pi\) |
0.414422 | − | 0.910085i | \(-0.363984\pi\) | |||||||
\(788\) | 3870.52 | − | 1408.75i | 0.174976 | − | 0.0636862i | ||||
\(789\) | −27973.5 | + | 10181.5i | −1.26221 | + | 0.459407i | ||||
\(790\) | −933.637 | − | 1617.11i | −0.0420472 | − | 0.0728279i | ||||
\(791\) | 2070.39 | − | 3586.02i | 0.0930653 | − | 0.161194i | ||||
\(792\) | 206.505 | − | 1171.15i | 0.00926494 | − | 0.0525441i | ||||
\(793\) | −14005.1 | + | 11751.7i | −0.627158 | + | 0.526248i | ||||
\(794\) | −4572.90 | − | 3837.12i | −0.204391 | − | 0.171504i | ||||
\(795\) | −5170.54 | − | 29323.6i | −0.230667 | − | 1.30818i | ||||
\(796\) | 1357.33 | + | 494.027i | 0.0604387 | + | 0.0219979i | ||||
\(797\) | −19912.2 | −0.884978 | −0.442489 | − | 0.896774i | \(-0.645904\pi\) | ||||
−0.442489 | + | 0.896774i | \(0.645904\pi\) | |||||||
\(798\) | 2932.25 | + | 419.376i | 0.130076 | + | 0.0186037i | ||||
\(799\) | −16957.0 | −0.750808 | ||||||||
\(800\) | 6233.90 | + | 2268.95i | 0.275502 | + | 0.100275i | ||||
\(801\) | −121.733 | − | 690.383i | −0.00536982 | − | 0.0304538i | ||||
\(802\) | 6358.98 | + | 5335.82i | 0.279979 | + | 0.234931i | ||||
\(803\) | 17519.0 | − | 14700.2i | 0.769903 | − | 0.646025i | ||||
\(804\) | 1104.50 | − | 6263.93i | 0.0484486 | − | 0.274766i | ||||
\(805\) | −2032.29 | + | 3520.02i | −0.0889797 | + | 0.154117i | ||||
\(806\) | −14998.8 | − | 25978.7i | −0.655472 | − | 1.13531i | ||||
\(807\) | 2996.78 | − | 1090.74i | 0.130721 | − | 0.0475784i | ||||
\(808\) | −7026.50 | + | 2557.44i | −0.305930 | + | 0.111349i | ||||
\(809\) | −12817.7 | − | 22200.9i | −0.557040 | − | 0.964822i | −0.997742 | − | 0.0671685i | \(-0.978603\pi\) |
0.440701 | − | 0.897654i | \(-0.354730\pi\) | |||||||
\(810\) | 7316.59 | − | 12672.7i | 0.317381 | − | 0.549721i | ||||
\(811\) | −184.217 | + | 1044.74i | −0.00797623 | + | 0.0452354i | −0.988536 | − | 0.150985i | \(-0.951756\pi\) |
0.980560 | + | 0.196220i | \(0.0628667\pi\) | |||||||
\(812\) | −391.213 | + | 328.266i | −0.0169075 | + | 0.0141871i | ||||
\(813\) | 14519.1 | + | 12182.9i | 0.626330 | + | 0.525553i | ||||
\(814\) | −1466.98 | − | 8319.68i | −0.0631668 | − | 0.358237i | ||||
\(815\) | −25638.8 | − | 9331.74i | −1.10195 | − | 0.401076i | ||||
\(816\) | −6728.80 | −0.288671 | ||||||||
\(817\) | −8168.81 | + | 24934.5i | −0.349805 | + | 1.06774i | ||||
\(818\) | 13504.0 | 0.577210 | ||||||||
\(819\) | −395.943 | − | 144.112i | −0.0168930 | − | 0.00614856i | ||||
\(820\) | 593.104 | + | 3363.66i | 0.0252586 | + | 0.143249i | ||||
\(821\) | −29115.3 | − | 24430.6i | −1.23768 | − | 1.03853i | −0.997702 | − | 0.0677532i | \(-0.978417\pi\) |
−0.239973 | − | 0.970780i | \(-0.577139\pi\) | |||||||
\(822\) | 5290.31 | − | 4439.09i | 0.224478 | − | 0.188359i | ||||
\(823\) | −6311.23 | + | 35792.8i | −0.267309 | + | 1.51599i | 0.495068 | + | 0.868854i | \(0.335143\pi\) |
−0.762377 | + | 0.647133i | \(0.775968\pi\) | |||||||
\(824\) | −9358.22 | + | 16208.9i | −0.395642 | + | 0.685272i | ||||
\(825\) | 4358.13 | + | 7548.50i | 0.183916 | + | 0.318551i | ||||
\(826\) | −1349.77 | + | 491.276i | −0.0568577 | + | 0.0206945i | ||||
\(827\) | 36176.5 | − | 13167.2i | 1.52114 | − | 0.553648i | 0.559704 | − | 0.828693i | \(-0.310915\pi\) |
0.961432 | + | 0.275044i | \(0.0886926\pi\) | |||||||
\(828\) | 391.066 | + | 677.347i | 0.0164136 | + | 0.0284293i | ||||
\(829\) | 10889.6 | − | 18861.4i | 0.456227 | − | 0.790208i | −0.542531 | − | 0.840036i | \(-0.682534\pi\) |
0.998758 | + | 0.0498281i | \(0.0158673\pi\) | |||||||
\(830\) | −941.410 | + | 5339.00i | −0.0393697 | + | 0.223276i | ||||
\(831\) | 12464.6 | − | 10459.1i | 0.520329 | − | 0.436608i | ||||
\(832\) | 35888.0 | + | 30113.6i | 1.49542 | + | 1.25481i | ||||
\(833\) | 2056.24 | + | 11661.5i | 0.0855277 | + | 0.485051i | ||||
\(834\) | −339.666 | − | 123.628i | −0.0141027 | − | 0.00513298i | ||||
\(835\) | 23002.7 | 0.953343 | ||||||||
\(836\) | 2326.28 | + | 5798.31i | 0.0962393 | + | 0.239879i | ||||
\(837\) | 20663.3 | 0.853319 | ||||||||
\(838\) | −15603.1 | − | 5679.06i | −0.643198 | − | 0.234105i | ||||
\(839\) | 3543.68 | + | 20097.2i | 0.145818 | + | 0.826976i | 0.966707 | + | 0.255887i | \(0.0823676\pi\) |
−0.820888 | + | 0.571089i | \(0.806521\pi\) | |||||||
\(840\) | 2400.18 | + | 2013.99i | 0.0985880 | + | 0.0827252i | ||||
\(841\) | −15335.7 | + | 12868.2i | −0.628797 | + | 0.527623i | ||||
\(842\) | −298.397 | + | 1692.29i | −0.0122131 | + | 0.0692640i | ||||
\(843\) | 9146.95 | − | 15843.0i | 0.373710 | − | 0.647285i | ||||
\(844\) | −3956.53 | − | 6852.91i | −0.161362 | − | 0.279487i | ||||
\(845\) | −39079.1 | + | 14223.6i | −1.59096 | + | 0.579062i | ||||
\(846\) | −1777.19 | + | 646.845i | −0.0722236 | + | 0.0262872i | ||||
\(847\) | 771.713 | + | 1336.65i | 0.0313062 | + | 0.0542240i | ||||
\(848\) | 12012.3 | − | 20805.9i | 0.486442 | − | 0.842543i | ||||
\(849\) | −5050.82 | + | 28644.6i | −0.204174 | + | 1.15793i | ||||
\(850\) | 3604.91 | − | 3024.88i | 0.145467 | − | 0.122062i | ||||
\(851\) | 17001.3 | + | 14265.8i | 0.684837 | + | 0.574646i | ||||
\(852\) | 580.429 | + | 3291.78i | 0.0233394 | + | 0.132364i | ||||
\(853\) | 33402.0 | + | 12157.3i | 1.34075 | + | 0.487995i | 0.910050 | − | 0.414498i | \(-0.136043\pi\) |
0.430705 | + | 0.902493i | \(0.358265\pi\) | |||||||
\(854\) | −1431.94 | −0.0573772 | ||||||||
\(855\) | −37.7411 | − | 1161.78i | −0.00150961 | − | 0.0464702i | ||||
\(856\) | −3904.25 | −0.155893 | ||||||||
\(857\) | −13505.0 | − | 4915.41i | −0.538298 | − | 0.195925i | 0.0585415 | − | 0.998285i | \(-0.481355\pi\) |
−0.596840 | + | 0.802360i | \(0.703577\pi\) | |||||||
\(858\) | 5168.21 | + | 29310.4i | 0.205641 | + | 1.16625i | ||||
\(859\) | 13143.2 | + | 11028.5i | 0.522049 | + | 0.438051i | 0.865345 | − | 0.501176i | \(-0.167099\pi\) |
−0.343296 | + | 0.939227i | \(0.611543\pi\) | |||||||
\(860\) | −5322.71 | + | 4466.28i | −0.211050 | + | 0.177092i | ||||
\(861\) | 419.017 | − | 2376.36i | 0.0165854 | − | 0.0940606i | ||||
\(862\) | −1381.01 | + | 2391.98i | −0.0545678 | + | 0.0945143i | ||||
\(863\) | −16963.8 | − | 29382.1i | −0.669123 | − | 1.15895i | −0.978150 | − | 0.207901i | \(-0.933337\pi\) |
0.309027 | − | 0.951053i | \(-0.399997\pi\) | |||||||
\(864\) | −14662.7 | + | 5336.77i | −0.577354 | + | 0.210140i | ||||
\(865\) | −25830.5 | + | 9401.54i | −1.01533 | + | 0.369551i | ||||
\(866\) | 4115.54 | + | 7128.33i | 0.161492 | + | 0.279712i | ||||
\(867\) | −9807.68 | + | 16987.4i | −0.384183 | + | 0.665424i | ||||
\(868\) | −204.568 | + | 1160.16i | −0.00799942 | + | 0.0453669i | ||||
\(869\) | −2131.45 | + | 1788.50i | −0.0832043 | + | 0.0698167i | ||||
\(870\) | −5141.36 | − | 4314.12i | −0.200355 | − | 0.168117i | ||||
\(871\) | 6575.51 | + | 37291.6i | 0.255801 | + | 1.45072i | ||||
\(872\) | −28088.1 | − | 10223.2i | −1.09081 | − | 0.397021i | ||||
\(873\) | 1531.77 | 0.0593844 | ||||||||
\(874\) | 28864.7 | + | 15437.8i | 1.11712 | + | 0.597473i | ||||
\(875\) | −4334.87 | −0.167481 | ||||||||
\(876\) | 10895.2 | + | 3965.53i | 0.420223 | + | 0.152949i | ||||
\(877\) | −6443.83 | − | 36544.8i | −0.248110 | − | 1.40710i | −0.813157 | − | 0.582044i | \(-0.802253\pi\) |
0.565047 | − | 0.825059i | \(-0.308858\pi\) | |||||||
\(878\) | 3564.60 | + | 2991.06i | 0.137015 | + | 0.114970i | ||||
\(879\) | −16453.8 | + | 13806.4i | −0.631368 | + | 0.529781i | ||||
\(880\) | 1428.42 | − | 8100.96i | 0.0547181 | − | 0.310322i | ||||
\(881\) | 12253.3 | − | 21223.4i | 0.468587 | − | 0.811616i | −0.530769 | − | 0.847517i | \(-0.678097\pi\) |
0.999355 | + | 0.0359006i | \(0.0114300\pi\) | |||||||
\(882\) | 660.349 | + | 1143.76i | 0.0252099 | + | 0.0436648i | ||||
\(883\) | 35378.6 | − | 12876.8i | 1.34834 | − | 0.490756i | 0.435912 | − | 0.899989i | \(-0.356426\pi\) |
0.912430 | + | 0.409233i | \(0.134204\pi\) | |||||||
\(884\) | −7571.00 | + | 2755.62i | −0.288055 | + | 0.104843i | ||||
\(885\) | 4732.56 | + | 8197.04i | 0.179755 | + | 0.311345i | ||||
\(886\) | −12952.9 | + | 22435.0i | −0.491151 | + | 0.850699i | ||||
\(887\) | −2593.78 | + | 14710.1i | −0.0981856 | + | 0.556838i | 0.895539 | + | 0.444983i | \(0.146790\pi\) |
−0.993725 | + | 0.111855i | \(0.964321\pi\) | |||||||
\(888\) | 13105.6 | − | 10996.9i | 0.495263 | − | 0.415575i | ||||
\(889\) | 3185.42 | + | 2672.89i | 0.120175 | + | 0.100839i | ||||
\(890\) | −1349.16 | − | 7651.46i | −0.0508134 | − | 0.288177i | ||||
\(891\) | −20489.8 | − | 7457.68i | −0.770409 | − | 0.280406i | ||||
\(892\) | 8214.38 | 0.308338 | ||||||||
\(893\) | 24509.9 | − | 31214.4i | 0.918468 | − | 1.16971i | ||||
\(894\) | −26860.8 | −1.00488 | ||||||||
\(895\) | 18013.9 | + | 6556.51i | 0.672779 | + | 0.244871i | ||||
\(896\) | 174.607 | + | 990.243i | 0.00651026 | + | 0.0369215i | ||||
\(897\) | −59895.7 | − | 50258.5i | −2.22950 | − | 1.87077i | ||||
\(898\) | −9887.66 | + | 8296.73i | −0.367434 | + | 0.308313i | ||||
\(899\) | 1750.35 | − | 9926.72i | 0.0649359 | − | 0.368270i | ||||
\(900\) | −131.582 | + | 227.907i | −0.00487342 | + | 0.00844100i | ||||
\(901\) | 11977.3 | + | 20745.3i | 0.442866 | + | 0.767066i | ||||
\(902\) | −9538.33 | + | 3471.67i | −0.352097 | + | 0.128153i | ||||
\(903\) | 4612.80 | − | 1678.92i | 0.169994 | − | 0.0618727i | ||||
\(904\) | −17637.0 | − | 30548.1i | −0.648891 | − | 1.12391i | ||||
\(905\) | 18863.6 | − | 32672.7i | 0.692870 | − | 1.20009i | ||||
\(906\) | 1825.28 | − | 10351.7i | 0.0669325 | − | 0.379593i | ||||
\(907\) | 3979.99 | − | 3339.61i | 0.145704 | − | 0.122260i | −0.567022 | − | 0.823702i | \(-0.691905\pi\) |
0.712726 | + | 0.701442i | \(0.247460\pi\) | |||||||
\(908\) | −2742.25 | − | 2301.02i | −0.100225 | − | 0.0840992i | ||||
\(909\) | −90.1213 | − | 511.103i | −0.00328838 | − | 0.0186493i | ||||
\(910\) | −4388.21 | − | 1597.18i | −0.159855 | − | 0.0581824i | ||||
\(911\) | 46091.3 | 1.67626 | 0.838130 | − | 0.545470i | \(-0.183649\pi\) | ||||
0.838130 | + | 0.545470i | \(0.183649\pi\) | |||||||
\(912\) | 9725.91 | − | 12386.4i | 0.353133 | − | 0.449730i | ||||
\(913\) | 8078.34 | 0.292830 | ||||||||
\(914\) | −23973.0 | − | 8725.47i | −0.867568 | − | 0.315769i | ||||
\(915\) | 1638.51 | + | 9292.45i | 0.0591994 | + | 0.335737i | ||||
\(916\) | −11045.9 | − | 9268.63i | −0.398436 | − | 0.334328i | ||||
\(917\) | 117.971 | − | 98.9897i | 0.00424837 | − | 0.00356481i | ||||
\(918\) | −1922.04 | + | 10900.4i | −0.0691033 | + | 0.391904i | ||||
\(919\) | 14318.6 | − | 24800.5i | 0.513957 | − | 0.890200i | −0.485912 | − | 0.874008i | \(-0.661512\pi\) |
0.999869 | − | 0.0161922i | \(-0.00515436\pi\) | |||||||
\(920\) | 17312.4 | + | 29985.9i | 0.620404 | + | 1.07457i | ||||
\(921\) | −22941.2 | + | 8349.91i | −0.820780 | + | 0.298739i | ||||
\(922\) | 34692.6 | − | 12627.1i | 1.23920 | − | 0.451030i | ||||
\(923\) | −9949.78 | − | 17233.5i | −0.354822 | − | 0.614570i | ||||
\(924\) | 584.414 | − | 1012.24i | 0.0208072 | − | 0.0360391i | ||||
\(925\) | −1296.71 | + | 7354.03i | −0.0460927 | + | 0.261404i | ||||
\(926\) | −25868.9 | + | 21706.6i | −0.918039 | + | 0.770327i | ||||
\(927\) | −995.134 | − | 835.016i | −0.0352583 | − | 0.0295853i | ||||
\(928\) | 1321.76 | + | 7496.07i | 0.0467552 | + | 0.265162i | ||||
\(929\) | 18005.8 | + | 6553.57i | 0.635899 | + | 0.231448i | 0.639797 | − | 0.768544i | \(-0.279018\pi\) |
−0.00389775 | + | 0.999992i | \(0.501241\pi\) | |||||||
\(930\) | −15482.2 | −0.545894 | ||||||||
\(931\) | −24438.6 | − | 13070.6i | −0.860305 | − | 0.460120i | ||||
\(932\) | −973.885 | −0.0342282 | ||||||||
\(933\) | 16710.7 | + | 6082.18i | 0.586369 | + | 0.213421i | ||||
\(934\) | 1537.90 | + | 8721.89i | 0.0538777 | + | 0.305556i | ||||
\(935\) | 6283.09 | + | 5272.14i | 0.219764 | + | 0.184403i | ||||
\(936\) | −2749.62 | + | 2307.21i | −0.0960195 | + | 0.0805699i | ||||
\(937\) | 6334.38 | − | 35924.1i | 0.220849 | − | 1.25250i | −0.649615 | − | 0.760263i | \(-0.725070\pi\) |
0.870464 | − | 0.492232i | \(-0.163819\pi\) | |||||||
\(938\) | −1482.94 | + | 2568.52i | −0.0516201 | + | 0.0894086i | ||||
\(939\) | 2353.56 | + | 4076.49i | 0.0817951 | + | 0.141673i | ||||
\(940\) | 9875.89 | − | 3594.53i | 0.342677 | − | 0.124724i | ||||
\(941\) | −11897.6 | + | 4330.37i | −0.412168 | + | 0.150017i | −0.539778 | − | 0.841807i | \(-0.681492\pi\) |
0.127610 | + | 0.991824i | \(0.459270\pi\) | |||||||
\(942\) | 10821.5 | + | 18743.4i | 0.374294 | + | 0.648295i | ||||
\(943\) | 13333.0 | − | 23093.5i | 0.460427 | − | 0.797483i | ||||
\(944\) | −1326.13 | + | 7520.85i | −0.0457223 | + | 0.259304i | ||||
\(945\) | 2464.16 | − | 2067.67i | 0.0848244 | − | 0.0711761i | ||||
\(946\) | −15818.3 | − | 13273.1i | −0.543653 | − | 0.456179i | ||||
\(947\) | −486.150 | − | 2757.10i | −0.0166819 | − | 0.0946078i | 0.975330 | − | 0.220752i | \(-0.0708510\pi\) |
−0.992012 | + | 0.126144i | \(0.959740\pi\) | |||||||
\(948\) | −1325.57 | − | 482.467i | −0.0454140 | − | 0.0165293i | ||||
\(949\) | −69026.2 | −2.36110 | ||||||||
\(950\) | 357.604 | + | 11008.1i | 0.0122129 | + | 0.375948i | ||||
\(951\) | 5341.24 | 0.182126 | ||||||||
\(952\) | −2368.64 | − | 862.113i | −0.0806386 | − | 0.0293501i | ||||
\(953\) | 1703.59 | + | 9661.53i | 0.0579062 | + | 0.328402i | 0.999975 | − | 0.00701619i | \(-0.00223334\pi\) |
−0.942069 | + | 0.335419i | \(0.891122\pi\) | |||||||
\(954\) | 2046.65 | + | 1717.34i | 0.0694577 | + | 0.0582820i | ||||
\(955\) | 2363.25 | − | 1983.00i | 0.0800765 | − | 0.0671921i | ||||
\(956\) | −2066.83 | + | 11721.6i | −0.0699227 | + | 0.396551i | ||||
\(957\) | −5000.43 | + | 8661.00i | −0.168904 | + | 0.292550i | ||||
\(958\) | −2366.91 | − | 4099.61i | −0.0798240 | − | 0.138259i | ||||
\(959\) | 1517.25 | − | 552.235i | 0.0510893 | − | 0.0185950i | ||||
\(960\) | 22721.0 | − | 8269.75i | 0.763870 | − | 0.278026i | ||||
\(961\) | 3269.43 | + | 5662.81i | 0.109745 | + | 0.190085i | ||||
\(962\) | −12749.2 | + | 22082.3i | −0.427289 | + | 0.740086i | ||||
\(963\) | 47.0557 | − | 266.866i | 0.00157461 | − | 0.00893006i | ||||
\(964\) | −11561.4 | + | 9701.21i | −0.386275 | + | 0.324123i | ||||
\(965\) | 18208.3 | + | 15278.6i | 0.607405 | + | 0.509673i | ||||
\(966\) | −1063.42 | − | 6030.96i | −0.0354193 | − | 0.200873i | ||||
\(967\) | 3374.58 | + | 1228.25i | 0.112223 | + | 0.0408457i | 0.397521 | − | 0.917593i | \(-0.369871\pi\) |
−0.285299 | + | 0.958439i | \(0.592093\pi\) | |||||||
\(968\) | 13147.9 | 0.436561 | ||||||||
\(969\) | 5846.89 | + | 14573.5i | 0.193838 | + | 0.483147i | ||||
\(970\) | 16976.5 | 0.561941 | ||||||||
\(971\) | −22358.1 | − | 8137.68i | −0.738935 | − | 0.268950i | −0.0549927 | − | 0.998487i | \(-0.517514\pi\) |
−0.683942 | + | 0.729537i | \(0.739736\pi\) | |||||||
\(972\) | −222.238 | − | 1260.37i | −0.00733362 | − | 0.0415910i | ||||
\(973\) | −64.7390 | − | 54.3224i | −0.00213303 | − | 0.00178982i | ||||
\(974\) | 5973.82 | − | 5012.63i | 0.196523 | − | 0.164902i | ||||
\(975\) | 4568.35 | − | 25908.4i | 0.150056 | − | 0.851007i | ||||
\(976\) | −3806.61 | + | 6593.24i | −0.124843 | + | 0.216234i | ||||
\(977\) | 3207.81 | + | 5556.09i | 0.105043 | + | 0.181940i | 0.913756 | − | 0.406264i | \(-0.133169\pi\) |
−0.808713 | + | 0.588204i | \(0.799835\pi\) | |||||||
\(978\) | 38629.4 | − | 14059.9i | 1.26302 | − | 0.459701i | ||||
\(979\) | −10879.1 | + | 3959.66i | −0.355155 | + | 0.129266i | ||||
\(980\) | −3669.57 | − | 6355.89i | −0.119612 | − | 0.207175i | ||||
\(981\) | 1037.31 | − | 1796.68i | 0.0337604 | − | 0.0584747i | ||||
\(982\) | −8482.15 | + | 48104.7i | −0.275638 | + | 1.56322i | ||||
\(983\) | 849.162 | − | 712.531i | 0.0275525 | − | 0.0231193i | −0.628907 | − | 0.777480i | \(-0.716498\pi\) |
0.656460 | + | 0.754361i | \(0.272053\pi\) | |||||||
\(984\) | −15746.6 | − | 13213.0i | −0.510146 | − | 0.428063i | ||||
\(985\) | 2197.68 | + | 12463.6i | 0.0710901 | + | 0.403172i | ||||
\(986\) | 5073.80 | + | 1846.71i | 0.163877 | + | 0.0596464i | ||||
\(987\) | −7424.91 | −0.239450 | ||||||||
\(988\) | 5870.70 | − | 17919.7i | 0.189040 | − | 0.577026i | ||||
\(989\) | 54247.1 | 1.74414 | ||||||||
\(990\) | 859.616 | + | 312.875i | 0.0275964 | + | 0.0100443i | ||||
\(991\) | 31.9956 | + | 181.456i | 0.00102560 | + | 0.00581648i | 0.985316 | − | 0.170739i | \(-0.0546156\pi\) |
−0.984291 | + | 0.176556i | \(0.943504\pi\) | |||||||
\(992\) | 13450.7 | + | 11286.5i | 0.430504 | + | 0.361236i | ||||
\(993\) | −17280.8 | + | 14500.4i | −0.552257 | + | 0.463399i | ||||
\(994\) | 270.649 | − | 1534.93i | 0.00863630 | − | 0.0489789i | ||||
\(995\) | −2219.11 | + | 3843.62i | −0.0707041 | + | 0.122463i | ||||
\(996\) | 2047.80 | + | 3546.89i | 0.0651475 | + | 0.112839i | ||||
\(997\) | 12241.5 | − | 4455.53i | 0.388858 | − | 0.141533i | −0.140190 | − | 0.990125i | \(-0.544771\pi\) |
0.529048 | + | 0.848592i | \(0.322549\pi\) | |||||||
\(998\) | 35126.1 | − | 12784.9i | 1.11413 | − | 0.405509i | ||||
\(999\) | −8782.07 | − | 15211.0i | −0.278131 | − | 0.481736i |
(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 | 19.4.e.a.4.2 | ✓ | 24 | |
3.2 | odd | 2 | 171.4.u.b.118.3 | 24 | |||
19.5 | even | 9 | inner | 19.4.e.a.5.2 | yes | 24 | |
19.9 | even | 9 | 361.4.a.n.1.8 | 12 | |||
19.10 | odd | 18 | 361.4.a.m.1.5 | 12 | |||
57.5 | odd | 18 | 171.4.u.b.100.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.4.e.a.4.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
19.4.e.a.5.2 | yes | 24 | 19.5 | even | 9 | inner | |
171.4.u.b.100.3 | 24 | 57.5 | odd | 18 | |||
171.4.u.b.118.3 | 24 | 3.2 | odd | 2 | |||
361.4.a.m.1.5 | 12 | 19.10 | odd | 18 | |||
361.4.a.n.1.8 | 12 | 19.9 | even | 9 |