Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.64000000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 511.1 | ||
Root | \(1.14412 + 0.831254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.511 |
Dual form | 605.2.g.l.251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.746033 | − | 2.29605i | −0.527525 | − | 1.62356i | −0.759268 | − | 0.650778i | \(-0.774443\pi\) |
0.231743 | − | 0.972777i | \(-0.425557\pi\) | |||||||
\(3\) | 2.28825 | + | 1.66251i | 1.32112 | + | 0.959849i | 0.999918 | + | 0.0128385i | \(0.00408672\pi\) |
0.321202 | + | 0.947011i | \(0.395913\pi\) | |||||||
\(4\) | −3.09726 | + | 2.25029i | −1.54863 | + | 1.12515i | ||||
\(5\) | −0.309017 | + | 0.951057i | −0.138197 | + | 0.425325i | ||||
\(6\) | 2.11010 | − | 6.49422i | 0.861445 | − | 2.65125i | ||||
\(7\) | −1.61803 | + | 1.17557i | −0.611559 | + | 0.444324i | −0.849963 | − | 0.526842i | \(-0.823376\pi\) |
0.238404 | + | 0.971166i | \(0.423376\pi\) | |||||||
\(8\) | 3.57117 | + | 2.59461i | 1.26260 | + | 0.917333i | ||||
\(9\) | 1.54508 | + | 4.75528i | 0.515028 | + | 1.58509i | ||||
\(10\) | 2.41421 | 0.763441 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −10.8284 | −3.12590 | ||||||||
\(13\) | 0.362036 | + | 1.11423i | 0.100411 | + | 0.309032i | 0.988626 | − | 0.150395i | \(-0.0480546\pi\) |
−0.888215 | + | 0.459428i | \(0.848055\pi\) | |||||||
\(14\) | 3.90628 | + | 2.83808i | 1.04400 | + | 0.758508i | ||||
\(15\) | −2.28825 | + | 1.66251i | −0.590822 | + | 0.429258i | ||||
\(16\) | 0.927051 | − | 2.85317i | 0.231763 | − | 0.713292i | ||||
\(17\) | −2.11010 | + | 6.49422i | −0.511774 | + | 1.57508i | 0.277301 | + | 0.960783i | \(0.410560\pi\) |
−0.789075 | + | 0.614297i | \(0.789440\pi\) | |||||||
\(18\) | 9.76570 | − | 7.09520i | 2.30180 | − | 1.67235i | ||||
\(19\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(20\) | −1.18305 | − | 3.64105i | −0.264538 | − | 0.814164i | ||||
\(21\) | −5.65685 | −1.23443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 3.85816 | + | 11.8742i | 0.787544 | + | 2.42381i | ||||
\(25\) | −0.809017 | − | 0.587785i | −0.161803 | − | 0.117557i | ||||
\(26\) | 2.28825 | − | 1.66251i | 0.448762 | − | 0.326045i | ||||
\(27\) | −1.74806 | + | 5.37999i | −0.336415 | + | 1.03538i | ||||
\(28\) | 2.36610 | − | 7.28210i | 0.447151 | − | 1.37619i | ||||
\(29\) | −2.95846 | + | 2.14944i | −0.549372 | + | 0.399142i | −0.827554 | − | 0.561386i | \(-0.810268\pi\) |
0.278182 | + | 0.960528i | \(0.410268\pi\) | |||||||
\(30\) | 5.52431 | + | 4.01365i | 1.00860 | + | 0.732789i | ||||
\(31\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 16.4853 | 2.82720 | ||||||||
\(35\) | −0.618034 | − | 1.90211i | −0.104467 | − | 0.321516i | ||||
\(36\) | −15.4863 | − | 11.2515i | −2.58105 | − | 1.87524i | ||||
\(37\) | 6.19453 | − | 4.50059i | 1.01837 | − | 0.739892i | 0.0524248 | − | 0.998625i | \(-0.483305\pi\) |
0.965949 | + | 0.258733i | \(0.0833050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.02399 | + | 3.15152i | −0.163970 | + | 0.504648i | ||||
\(40\) | −3.57117 | + | 2.59461i | −0.564652 | + | 0.410244i | ||||
\(41\) | 4.85410 | + | 3.52671i | 0.758083 | + | 0.550780i | 0.898322 | − | 0.439338i | \(-0.144787\pi\) |
−0.140238 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(42\) | 4.22020 | + | 12.9884i | 0.651191 | + | 2.00416i | ||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.00000 | −0.745356 | ||||||||
\(46\) | 2.11010 | + | 6.49422i | 0.311117 | + | 0.957521i | ||||
\(47\) | −2.28825 | − | 1.66251i | −0.333775 | − | 0.242502i | 0.408256 | − | 0.912868i | \(-0.366137\pi\) |
−0.742031 | + | 0.670366i | \(0.766137\pi\) | |||||||
\(48\) | 6.86474 | − | 4.98752i | 0.990839 | − | 0.719887i | ||||
\(49\) | −0.927051 | + | 2.85317i | −0.132436 | + | 0.407596i | ||||
\(50\) | −0.746033 | + | 2.29605i | −0.105505 | + | 0.324711i | ||||
\(51\) | −15.6251 | + | 11.3523i | −2.18795 | + | 1.58964i | ||||
\(52\) | −3.62867 | − | 2.63638i | −0.503206 | − | 0.365600i | ||||
\(53\) | 3.60217 | + | 11.0863i | 0.494796 | + | 1.52282i | 0.817275 | + | 0.576248i | \(0.195484\pi\) |
−0.322480 | + | 0.946576i | \(0.604516\pi\) | |||||||
\(54\) | 13.6569 | 1.85846 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.82843 | −1.17975 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.14235 | + | 5.18922i | 0.937836 | + | 0.681378i | ||||
\(59\) | −1.34042 | + | 0.973874i | −0.174508 | + | 0.126788i | −0.671611 | − | 0.740904i | \(-0.734397\pi\) |
0.497103 | + | 0.867692i | \(0.334397\pi\) | |||||||
\(60\) | 3.34617 | − | 10.2984i | 0.431988 | − | 1.32952i | ||||
\(61\) | 2.87809 | − | 8.85786i | 0.368502 | − | 1.13413i | −0.579257 | − | 0.815145i | \(-0.696657\pi\) |
0.947759 | − | 0.318988i | \(-0.103343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.09017 | − | 5.87785i | −1.01927 | − | 0.740540i | ||||
\(64\) | −3.03715 | − | 9.34739i | −0.379644 | − | 1.16842i | ||||
\(65\) | −1.17157 | −0.145316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853 | 1.52532 | 0.762660 | − | 0.646800i | \(-0.223893\pi\) | ||||
0.762660 | + | 0.646800i | \(0.223893\pi\) | |||||||
\(68\) | −8.07836 | − | 24.8626i | −0.979646 | − | 3.01504i | ||||
\(69\) | −6.47214 | − | 4.70228i | −0.779154 | − | 0.566088i | ||||
\(70\) | −3.90628 | + | 2.83808i | −0.466890 | + | 0.339215i | ||||
\(71\) | 3.49613 | − | 10.7600i | 0.414914 | − | 1.27697i | −0.497414 | − | 0.867513i | \(-0.665717\pi\) |
0.912328 | − | 0.409461i | \(-0.134283\pi\) | |||||||
\(72\) | −6.82034 | + | 20.9908i | −0.803784 | + | 2.47379i | ||||
\(73\) | −0.947822 | + | 0.688633i | −0.110934 | + | 0.0805984i | −0.641869 | − | 0.766814i | \(-0.721841\pi\) |
0.530935 | + | 0.847413i | \(0.321841\pi\) | |||||||
\(74\) | −14.9549 | − | 10.8654i | −1.73847 | − | 1.26307i | ||||
\(75\) | −0.874032 | − | 2.68999i | −0.100925 | − | 0.310614i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.00000 | 0.905822 | ||||||||
\(79\) | −1.23607 | − | 3.80423i | −0.139069 | − | 0.428009i | 0.857132 | − | 0.515097i | \(-0.172244\pi\) |
−0.996201 | + | 0.0870877i | \(0.972244\pi\) | |||||||
\(80\) | 2.42705 | + | 1.76336i | 0.271353 | + | 0.197149i | ||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 4.47620 | − | 13.7763i | 0.494313 | − | 1.52134i | ||||
\(83\) | 1.85410 | − | 5.70634i | 0.203514 | − | 0.626352i | −0.796257 | − | 0.604959i | \(-0.793190\pi\) |
0.999771 | − | 0.0213936i | \(-0.00681031\pi\) | |||||||
\(84\) | 17.5208 | − | 12.7296i | 1.91167 | − | 1.38891i | ||||
\(85\) | −5.52431 | − | 4.01365i | −0.599196 | − | 0.435341i | ||||
\(86\) | −4.47620 | − | 13.7763i | −0.482681 | − | 1.48554i | ||||
\(87\) | −10.3431 | −1.10890 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3137 | −1.41125 | −0.705625 | − | 0.708585i | \(-0.749334\pi\) | ||||
−0.705625 | + | 0.708585i | \(0.749334\pi\) | |||||||
\(90\) | 3.73017 | + | 11.4803i | 0.393194 | + | 1.21013i | ||||
\(91\) | −1.89564 | − | 1.37727i | −0.198718 | − | 0.144377i | ||||
\(92\) | 8.76038 | − | 6.36479i | 0.913333 | − | 0.663575i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.11010 | + | 6.49422i | −0.217640 | + | 0.669828i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.62867 | + | 2.63638i | 0.370349 | + | 0.269075i | ||||
\(97\) | 1.13003 | + | 3.47788i | 0.114737 | + | 0.353125i | 0.991892 | − | 0.127083i | \(-0.0405614\pi\) |
−0.877155 | + | 0.480207i | \(0.840561\pi\) | |||||||
\(98\) | 7.24264 | 0.731617 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.82843 | 0.382843 | ||||||||
\(101\) | −2.87809 | − | 8.85786i | −0.286381 | − | 0.881390i | −0.985981 | − | 0.166856i | \(-0.946639\pi\) |
0.699600 | − | 0.714534i | \(-0.253361\pi\) | |||||||
\(102\) | 37.7224 | + | 27.4069i | 3.73507 | + | 2.71369i | ||||
\(103\) | −5.52431 | + | 4.01365i | −0.544327 | + | 0.395477i | −0.825689 | − | 0.564125i | \(-0.809214\pi\) |
0.281363 | + | 0.959602i | \(0.409214\pi\) | |||||||
\(104\) | −1.59810 | + | 4.91846i | −0.156707 | + | 0.482294i | ||||
\(105\) | 1.74806 | − | 5.37999i | 0.170594 | − | 0.525033i | ||||
\(106\) | 22.7675 | − | 16.5415i | 2.21137 | − | 1.60666i | ||||
\(107\) | 6.19453 | + | 4.50059i | 0.598847 | + | 0.435088i | 0.845470 | − | 0.534024i | \(-0.179321\pi\) |
−0.246622 | + | 0.969112i | \(0.579321\pi\) | |||||||
\(108\) | −6.69234 | − | 20.5969i | −0.643970 | − | 1.98194i | ||||
\(109\) | 7.65685 | 0.733394 | 0.366697 | − | 0.930341i | \(-0.380489\pi\) | ||||
0.366697 | + | 0.930341i | \(0.380489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.6569 | 2.05558 | ||||||||
\(112\) | 1.85410 | + | 5.70634i | 0.175196 | + | 0.539198i | ||||
\(113\) | −15.9027 | − | 11.5540i | −1.49600 | − | 1.08691i | −0.971940 | − | 0.235230i | \(-0.924416\pi\) |
−0.524063 | − | 0.851679i | \(-0.675584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.874032 | − | 2.68999i | 0.0815039 | − | 0.250843i | ||||
\(116\) | 4.32624 | − | 13.3148i | 0.401681 | − | 1.23625i | ||||
\(117\) | −4.73911 | + | 3.44317i | −0.438131 | + | 0.318321i | ||||
\(118\) | 3.23607 | + | 2.35114i | 0.297904 | + | 0.216440i | ||||
\(119\) | −4.22020 | − | 12.9884i | −0.386865 | − | 1.19065i | ||||
\(120\) | −12.4853 | −1.13975 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −22.4853 | −2.03572 | ||||||||
\(123\) | 5.24419 | + | 16.1400i | 0.472853 | + | 1.45529i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.809017 | − | 0.587785i | 0.0723607 | − | 0.0525731i | ||||
\(126\) | −7.46033 | + | 22.9605i | −0.664619 | + | 2.04549i | ||||
\(127\) | −1.34211 | + | 4.13058i | −0.119093 | + | 0.366529i | −0.992779 | − | 0.119961i | \(-0.961723\pi\) |
0.873686 | + | 0.486490i | \(0.161723\pi\) | |||||||
\(128\) | −16.6304 | + | 12.0827i | −1.46994 | + | 1.06797i | ||||
\(129\) | 13.7295 | + | 9.97505i | 1.20881 | + | 0.878254i | ||||
\(130\) | 0.874032 | + | 2.68999i | 0.0766577 | + | 0.235928i | ||||
\(131\) | 11.3137 | 0.988483 | 0.494242 | − | 0.869325i | \(-0.335446\pi\) | ||||
0.494242 | + | 0.869325i | \(0.335446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.31443 | − | 28.6669i | −0.804644 | − | 2.47644i | ||||
\(135\) | −4.57649 | − | 3.32502i | −0.393882 | − | 0.286172i | ||||
\(136\) | −24.3855 | + | 17.7171i | −2.09104 | + | 1.51923i | ||||
\(137\) | −3.39009 | + | 10.4336i | −0.289635 | + | 0.891405i | 0.695336 | + | 0.718685i | \(0.255256\pi\) |
−0.984971 | + | 0.172720i | \(0.944744\pi\) | |||||||
\(138\) | −5.96826 | + | 18.3684i | −0.508052 | + | 1.56362i | ||||
\(139\) | −3.23607 | + | 2.35114i | −0.274480 | + | 0.199421i | −0.716506 | − | 0.697581i | \(-0.754260\pi\) |
0.442026 | + | 0.897002i | \(0.354260\pi\) | |||||||
\(140\) | 6.19453 | + | 4.50059i | 0.523533 | + | 0.380369i | ||||
\(141\) | −2.47214 | − | 7.60845i | −0.208191 | − | 0.640747i | ||||
\(142\) | −27.3137 | −2.29212 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 15.0000 | 1.25000 | ||||||||
\(145\) | −1.13003 | − | 3.47788i | −0.0938439 | − | 0.288822i | ||||
\(146\) | 2.28825 | + | 1.66251i | 0.189377 | + | 0.137590i | ||||
\(147\) | −6.86474 | + | 4.98752i | −0.566194 | + | 0.411364i | ||||
\(148\) | −9.05843 | + | 27.8790i | −0.744599 | + | 2.29164i | ||||
\(149\) | −0.106038 | + | 0.326351i | −0.00868696 | + | 0.0267357i | −0.955306 | − | 0.295619i | \(-0.904474\pi\) |
0.946619 | + | 0.322354i | \(0.104474\pi\) | |||||||
\(150\) | −5.52431 | + | 4.01365i | −0.451058 | + | 0.327713i | ||||
\(151\) | −9.70820 | − | 7.05342i | −0.790042 | − | 0.573999i | 0.117934 | − | 0.993021i | \(-0.462373\pi\) |
−0.907976 | + | 0.419022i | \(0.862373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.1421 | −2.76023 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.92028 | − | 12.0654i | −0.313874 | − | 0.966004i | ||||
\(157\) | 11.3262 | + | 8.22899i | 0.903932 | + | 0.656745i | 0.939473 | − | 0.342623i | \(-0.111315\pi\) |
−0.0355408 | + | 0.999368i | \(0.511315\pi\) | |||||||
\(158\) | −7.81256 | + | 5.67616i | −0.621534 | + | 0.451571i | ||||
\(159\) | −10.1885 | + | 31.3569i | −0.807998 | + | 2.48676i | ||||
\(160\) | −0.490035 | + | 1.50817i | −0.0387407 | + | 0.119232i | ||||
\(161\) | 4.57649 | − | 3.32502i | 0.360678 | − | 0.262048i | ||||
\(162\) | 1.95314 | + | 1.41904i | 0.153453 | + | 0.111490i | ||||
\(163\) | 5.09423 | + | 15.6784i | 0.399011 | + | 1.22803i | 0.925794 | + | 0.378030i | \(0.123398\pi\) |
−0.526782 | + | 0.850000i | \(0.676602\pi\) | |||||||
\(164\) | −22.9706 | −1.79370 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4853 | −1.12428 | ||||||||
\(167\) | 7.09829 | + | 21.8463i | 0.549283 | + | 1.69052i | 0.710584 | + | 0.703613i | \(0.248431\pi\) |
−0.161301 | + | 0.986905i | \(0.551569\pi\) | |||||||
\(168\) | −20.2016 | − | 14.6773i | −1.55859 | − | 1.13238i | ||||
\(169\) | 9.40678 | − | 6.83442i | 0.723598 | − | 0.525725i | ||||
\(170\) | −5.09423 | + | 15.6784i | −0.390710 | + | 1.20248i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.5836 | + | 13.5018i | −1.41698 | + | 1.02950i | ||||
\(173\) | −17.9134 | − | 13.0148i | −1.36193 | − | 0.989499i | −0.998320 | − | 0.0579465i | \(-0.981545\pi\) |
−0.363608 | − | 0.931552i | \(-0.618455\pi\) | |||||||
\(174\) | 7.71633 | + | 23.7484i | 0.584973 | + | 1.80036i | ||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.68629 | −0.352243 | ||||||||
\(178\) | 9.93247 | + | 30.5690i | 0.744470 | + | 2.29124i | ||||
\(179\) | −7.81256 | − | 5.67616i | −0.583938 | − | 0.424256i | 0.256204 | − | 0.966623i | \(-0.417528\pi\) |
−0.840142 | + | 0.542367i | \(0.817528\pi\) | |||||||
\(180\) | 15.4863 | − | 11.2515i | 1.15428 | − | 0.838635i | ||||
\(181\) | 6.58630 | − | 20.2705i | 0.489556 | − | 1.50670i | −0.335717 | − | 0.941963i | \(-0.608979\pi\) |
0.825273 | − | 0.564735i | \(-0.191021\pi\) | |||||||
\(182\) | −1.74806 | + | 5.37999i | −0.129575 | + | 0.398791i | ||||
\(183\) | 21.3121 | − | 15.4841i | 1.57543 | − | 1.14462i | ||||
\(184\) | −10.1008 | − | 7.33866i | −0.744641 | − | 0.541014i | ||||
\(185\) | 2.36610 | + | 7.28210i | 0.173959 | + | 0.535391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.8284 | 0.789744 | ||||||||
\(189\) | −3.49613 | − | 10.7600i | −0.254306 | − | 0.782673i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.68085 | + | 1.94775i | −0.193979 | + | 0.140934i | −0.680536 | − | 0.732715i | \(-0.738253\pi\) |
0.486556 | + | 0.873649i | \(0.338253\pi\) | |||||||
\(192\) | 8.59036 | − | 26.4384i | 0.619956 | − | 1.90803i | ||||
\(193\) | 0.362036 | − | 1.11423i | 0.0260599 | − | 0.0802042i | −0.937181 | − | 0.348844i | \(-0.886574\pi\) |
0.963241 | + | 0.268640i | \(0.0865742\pi\) | |||||||
\(194\) | 7.14235 | − | 5.18922i | 0.512791 | − | 0.372564i | ||||
\(195\) | −2.68085 | − | 1.94775i | −0.191979 | − | 0.139481i | ||||
\(196\) | −3.54915 | − | 10.9232i | −0.253511 | − | 0.780225i | ||||
\(197\) | 10.8284 | 0.771493 | 0.385747 | − | 0.922605i | \(-0.373944\pi\) | ||||
0.385747 | + | 0.922605i | \(0.373944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3431 | 0.733206 | 0.366603 | − | 0.930377i | \(-0.380521\pi\) | ||||
0.366603 | + | 0.930377i | \(0.380521\pi\) | |||||||
\(200\) | −1.36407 | − | 4.19817i | −0.0964541 | − | 0.296855i | ||||
\(201\) | 28.5694 | + | 20.7569i | 2.01513 | + | 1.46408i | ||||
\(202\) | −18.1910 | + | 13.2165i | −1.27991 | + | 0.929911i | ||||
\(203\) | 2.26006 | − | 6.95575i | 0.158625 | − | 0.488198i | ||||
\(204\) | 22.8491 | − | 70.3222i | 1.59975 | − | 4.92354i | ||||
\(205\) | −4.85410 | + | 3.52671i | −0.339025 | + | 0.246316i | ||||
\(206\) | 13.3369 | + | 9.68981i | 0.929224 | + | 0.675121i | ||||
\(207\) | −4.37016 | − | 13.4500i | −0.303747 | − | 0.934838i | ||||
\(208\) | 3.51472 | 0.243702 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −13.6569 | −0.942412 | ||||||||
\(211\) | 4.94427 | + | 15.2169i | 0.340378 | + | 1.04757i | 0.964012 | + | 0.265859i | \(0.0856555\pi\) |
−0.623634 | + | 0.781716i | \(0.714345\pi\) | |||||||
\(212\) | −36.1043 | − | 26.2313i | −2.47966 | − | 1.80158i | ||||
\(213\) | 25.8885 | − | 18.8091i | 1.77385 | − | 1.28878i | ||||
\(214\) | 5.71227 | − | 17.5805i | 0.390482 | − | 1.20178i | ||||
\(215\) | −1.85410 | + | 5.70634i | −0.126449 | + | 0.389169i | ||||
\(216\) | −20.2016 | + | 14.6773i | −1.37455 | + | 0.998666i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.71227 | − | 17.5805i | −0.386883 | − | 1.19070i | ||||
\(219\) | −3.31371 | −0.223920 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | −16.1567 | − | 49.7253i | −1.08437 | − | 3.33734i | ||||
\(223\) | 8.76038 | + | 6.36479i | 0.586639 | + | 0.426218i | 0.841111 | − | 0.540862i | \(-0.181902\pi\) |
−0.254473 | + | 0.967080i | \(0.581902\pi\) | |||||||
\(224\) | −2.56586 | + | 1.86420i | −0.171438 | + | 0.124557i | ||||
\(225\) | 1.54508 | − | 4.75528i | 0.103006 | − | 0.317019i | ||||
\(226\) | −14.6647 | + | 45.1332i | −0.975479 | + | 3.00222i | ||||
\(227\) | 20.4792 | − | 14.8790i | 1.35925 | − | 0.987556i | 0.360762 | − | 0.932658i | \(-0.382517\pi\) |
0.998492 | − | 0.0548975i | \(-0.0174832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.405958 | + | 1.24941i | 0.0268265 | + | 0.0825634i | 0.963573 | − | 0.267444i | \(-0.0861791\pi\) |
−0.936747 | + | 0.350007i | \(0.886179\pi\) | |||||||
\(230\) | −6.82843 | −0.450253 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.1421 | −1.05978 | ||||||||
\(233\) | 1.89802 | + | 5.84152i | 0.124344 | + | 0.382691i | 0.993781 | − | 0.111353i | \(-0.0355184\pi\) |
−0.869437 | + | 0.494043i | \(0.835518\pi\) | |||||||
\(234\) | 11.4412 | + | 8.31254i | 0.747936 | + | 0.543408i | ||||
\(235\) | 2.28825 | − | 1.66251i | 0.149269 | − | 0.108450i | ||||
\(236\) | 1.96014 | − | 6.03269i | 0.127594 | − | 0.392695i | ||||
\(237\) | 3.49613 | − | 10.7600i | 0.227098 | − | 0.698936i | ||||
\(238\) | −26.6737 | + | 19.3796i | −1.72900 | + | 1.25619i | ||||
\(239\) | −18.8612 | − | 13.7035i | −1.22003 | − | 0.886403i | −0.223926 | − | 0.974606i | \(-0.571887\pi\) |
−0.996102 | + | 0.0882033i | \(0.971887\pi\) | |||||||
\(240\) | 2.62210 | + | 8.06998i | 0.169256 | + | 0.520915i | ||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1421 | 0.907218 | ||||||||
\(244\) | 11.0186 | + | 33.9117i | 0.705392 | + | 2.17097i | ||||
\(245\) | −2.42705 | − | 1.76336i | −0.155059 | − | 0.112657i | ||||
\(246\) | 33.1459 | − | 24.0819i | 2.11330 | − | 1.53541i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7295 | − | 9.97505i | 0.870070 | − | 0.632143i | ||||
\(250\) | −1.95314 | − | 1.41904i | −0.123527 | − | 0.0897479i | ||||
\(251\) | 3.70820 | + | 11.4127i | 0.234060 | + | 0.720362i | 0.997245 | + | 0.0741818i | \(0.0236345\pi\) |
−0.763185 | + | 0.646180i | \(0.776365\pi\) | |||||||
\(252\) | 38.2843 | 2.41168 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.4853 | 0.657905 | ||||||||
\(255\) | −5.96826 | − | 18.3684i | −0.373747 | − | 1.15028i | ||||
\(256\) | 24.2467 | + | 17.6163i | 1.51542 | + | 1.10102i | ||||
\(257\) | 7.53495 | − | 5.47446i | 0.470017 | − | 0.341487i | −0.327431 | − | 0.944875i | \(-0.606183\pi\) |
0.797448 | + | 0.603388i | \(0.206183\pi\) | |||||||
\(258\) | 12.6606 | − | 38.9653i | 0.788215 | − | 2.42587i | ||||
\(259\) | −4.73220 | + | 14.5642i | −0.294044 | + | 0.904975i | ||||
\(260\) | 3.62867 | − | 2.63638i | 0.225040 | − | 0.163501i | ||||
\(261\) | −14.7923 | − | 10.7472i | −0.915620 | − | 0.665237i | ||||
\(262\) | −8.44040 | − | 25.9769i | −0.521450 | − | 1.60486i | ||||
\(263\) | 10.9706 | 0.676474 | 0.338237 | − | 0.941061i | \(-0.390169\pi\) | ||||
0.338237 | + | 0.941061i | \(0.390169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6569 | −0.716075 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.4650 | − | 22.1341i | −1.86443 | − | 1.35459i | ||||
\(268\) | −38.6702 | + | 28.0955i | −2.36216 | + | 1.71621i | ||||
\(269\) | 5.35023 | − | 16.4663i | 0.326209 | − | 1.00397i | −0.644683 | − | 0.764450i | \(-0.723010\pi\) |
0.970892 | − | 0.239519i | \(-0.0769896\pi\) | |||||||
\(270\) | −4.22020 | + | 12.9884i | −0.256833 | + | 0.790451i | ||||
\(271\) | 5.91691 | − | 4.29889i | 0.359427 | − | 0.261139i | −0.393386 | − | 0.919373i | \(-0.628696\pi\) |
0.752813 | + | 0.658234i | \(0.228696\pi\) | |||||||
\(272\) | 16.5729 | + | 12.0409i | 1.00488 | + | 0.730090i | ||||
\(273\) | −2.04798 | − | 6.30305i | −0.123950 | − | 0.381478i | ||||
\(274\) | 26.4853 | 1.60003 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 30.6274 | 1.84355 | ||||||||
\(277\) | −2.11010 | − | 6.49422i | −0.126784 | − | 0.390200i | 0.867438 | − | 0.497545i | \(-0.165765\pi\) |
−0.994222 | + | 0.107345i | \(0.965765\pi\) | |||||||
\(278\) | 7.81256 | + | 5.67616i | 0.468566 | + | 0.340433i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.72813 | − | 8.39633i | 0.163037 | − | 0.501777i | ||||
\(281\) | −5.35023 | + | 16.4663i | −0.319168 | + | 0.982298i | 0.654837 | + | 0.755770i | \(0.272737\pi\) |
−0.974005 | + | 0.226528i | \(0.927263\pi\) | |||||||
\(282\) | −15.6251 | + | 11.3523i | −0.930462 | + | 0.676020i | ||||
\(283\) | 26.3961 | + | 19.1779i | 1.56909 | + | 1.14001i | 0.928024 | + | 0.372521i | \(0.121507\pi\) |
0.641064 | + | 0.767488i | \(0.278493\pi\) | |||||||
\(284\) | 13.3847 | + | 41.1938i | 0.794234 | + | 2.44440i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 2.45017 | + | 7.54086i | 0.144378 | + | 0.444350i | ||||
\(289\) | −23.9691 | − | 17.4146i | −1.40995 | − | 1.02439i | ||||
\(290\) | −7.14235 | + | 5.18922i | −0.419413 | + | 0.304721i | ||||
\(291\) | −3.19621 | + | 9.83692i | −0.187365 | + | 0.576650i | ||||
\(292\) | 1.38603 | − | 4.26576i | 0.0811112 | − | 0.249634i | ||||
\(293\) | −7.41996 | + | 5.39092i | −0.433479 | + | 0.314941i | −0.783038 | − | 0.621973i | \(-0.786331\pi\) |
0.349560 | + | 0.936914i | \(0.386331\pi\) | |||||||
\(294\) | 16.5729 | + | 12.0409i | 0.966554 | + | 0.702242i | ||||
\(295\) | −0.511996 | − | 1.57576i | −0.0298096 | − | 0.0917444i | ||||
\(296\) | 33.7990 | 1.96453 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.828427 | 0.0479895 | ||||||||
\(299\) | −1.02399 | − | 3.15152i | −0.0592190 | − | 0.182257i | ||||
\(300\) | 8.76038 | + | 6.36479i | 0.505781 | + | 0.367471i | ||||
\(301\) | −9.70820 | + | 7.05342i | −0.559572 | + | 0.406553i | ||||
\(302\) | −8.95240 | + | 27.5526i | −0.515153 | + | 1.58548i | ||||
\(303\) | 8.14048 | − | 25.0538i | 0.467658 | − | 1.43930i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.53495 | + | 5.47446i | 0.431450 | + | 0.313467i | ||||
\(306\) | 25.4712 | + | 78.3922i | 1.45609 | + | 4.48138i | ||||
\(307\) | 16.3431 | 0.932753 | 0.466376 | − | 0.884586i | \(-0.345559\pi\) | ||||
0.466376 | + | 0.884586i | \(0.345559\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3137 | −1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.79129 | − | 2.75453i | −0.214984 | − | 0.156195i | 0.475082 | − | 0.879942i | \(-0.342419\pi\) |
−0.690066 | + | 0.723746i | \(0.742419\pi\) | |||||||
\(312\) | −11.8338 | + | 8.59778i | −0.669959 | + | 0.486753i | ||||
\(313\) | −0.405958 | + | 1.24941i | −0.0229461 | + | 0.0706209i | −0.961874 | − | 0.273493i | \(-0.911821\pi\) |
0.938928 | + | 0.344114i | \(0.111821\pi\) | |||||||
\(314\) | 10.4445 | − | 32.1447i | 0.589415 | − | 1.81403i | ||||
\(315\) | 8.09017 | − | 5.87785i | 0.455829 | − | 0.331179i | ||||
\(316\) | 12.3891 | + | 9.00117i | 0.696939 | + | 0.506355i | ||||
\(317\) | −0.405958 | − | 1.24941i | −0.0228009 | − | 0.0701739i | 0.939009 | − | 0.343894i | \(-0.111746\pi\) |
−0.961810 | + | 0.273720i | \(0.911746\pi\) | |||||||
\(318\) | 79.5980 | 4.46363 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.82843 | 0.549426 | ||||||||
\(321\) | 6.69234 | + | 20.5969i | 0.373530 | + | 1.14961i | ||||
\(322\) | −11.0486 | − | 8.02730i | −0.615716 | − | 0.447344i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.18305 | − | 3.64105i | 0.0657249 | − | 0.202281i | ||||
\(325\) | 0.362036 | − | 1.11423i | 0.0200821 | − | 0.0618065i | ||||
\(326\) | 32.1981 | − | 23.3933i | 1.78329 | − | 1.29563i | ||||
\(327\) | 17.5208 | + | 12.7296i | 0.968900 | + | 0.703947i | ||||
\(328\) | 8.18440 | + | 25.1890i | 0.451908 | + | 1.39083i | ||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.31371 | −0.401998 | −0.200999 | − | 0.979591i | \(-0.564419\pi\) | ||||
−0.200999 | + | 0.979591i | \(0.564419\pi\) | |||||||
\(332\) | 7.09829 | + | 21.8463i | 0.389570 | + | 1.19897i | ||||
\(333\) | 30.9726 | + | 22.5029i | 1.69729 | + | 1.23315i | ||||
\(334\) | 44.8647 | − | 32.5961i | 2.45489 | − | 1.78358i | ||||
\(335\) | −3.85816 | + | 11.8742i | −0.210794 | + | 0.648757i | ||||
\(336\) | −5.24419 | + | 16.1400i | −0.286094 | + | 0.880507i | ||||
\(337\) | −16.5729 | + | 12.0409i | −0.902786 | + | 0.655912i | −0.939180 | − | 0.343425i | \(-0.888413\pi\) |
0.0363944 | + | 0.999338i | \(0.488413\pi\) | |||||||
\(338\) | −22.7100 | − | 16.4998i | −1.23526 | − | 0.897469i | ||||
\(339\) | −17.1807 | − | 52.8768i | −0.933129 | − | 2.87187i | ||||
\(340\) | 26.1421 | 1.41776 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.18034 | − | 19.0211i | −0.333707 | − | 1.02704i | ||||
\(344\) | 21.4270 | + | 15.5677i | 1.15527 | + | 0.839352i | ||||
\(345\) | 6.47214 | − | 4.70228i | 0.348448 | − | 0.253162i | ||||
\(346\) | −16.5188 | + | 50.8395i | −0.888054 | + | 2.73315i | ||||
\(347\) | −3.39009 | + | 10.4336i | −0.181990 | + | 0.560106i | −0.999884 | − | 0.0152627i | \(-0.995142\pi\) |
0.817894 | + | 0.575369i | \(0.195142\pi\) | |||||||
\(348\) | 32.0354 | − | 23.2751i | 1.71728 | − | 1.24768i | ||||
\(349\) | 21.8196 | + | 15.8529i | 1.16798 | + | 0.848586i | 0.990766 | − | 0.135586i | \(-0.0432918\pi\) |
0.177213 | + | 0.984172i | \(0.443292\pi\) | |||||||
\(350\) | −1.49207 | − | 4.59211i | −0.0797543 | − | 0.245458i | ||||
\(351\) | −6.62742 | −0.353745 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.3137 | 1.13441 | 0.567207 | − | 0.823575i | \(-0.308024\pi\) | ||||
0.567207 | + | 0.823575i | \(0.308024\pi\) | |||||||
\(354\) | 3.49613 | + | 10.7600i | 0.185817 | + | 0.571886i | ||||
\(355\) | 9.15298 | + | 6.65003i | 0.485790 | + | 0.352947i | ||||
\(356\) | 41.2361 | − | 29.9597i | 2.18551 | − | 1.58786i | ||||
\(357\) | 11.9365 | − | 36.7369i | 0.631748 | − | 1.94432i | ||||
\(358\) | −7.20433 | + | 22.1727i | −0.380761 | + | 1.17186i | ||||
\(359\) | 0.555221 | − | 0.403392i | 0.0293035 | − | 0.0212902i | −0.573037 | − | 0.819529i | \(-0.694235\pi\) |
0.602341 | + | 0.798239i | \(0.294235\pi\) | |||||||
\(360\) | −17.8559 | − | 12.9730i | −0.941087 | − | 0.683740i | ||||
\(361\) | −5.87132 | − | 18.0701i | −0.309017 | − | 0.951057i | ||||
\(362\) | −51.4558 | −2.70446 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.97056 | 0.470185 | ||||||||
\(365\) | −0.362036 | − | 1.11423i | −0.0189498 | − | 0.0583216i | ||||
\(366\) | −51.4518 | − | 37.3820i | −2.68943 | − | 1.95399i | ||||
\(367\) | 6.86474 | − | 4.98752i | 0.358336 | − | 0.260347i | −0.394022 | − | 0.919101i | \(-0.628916\pi\) |
0.752358 | + | 0.658755i | \(0.228916\pi\) | |||||||
\(368\) | −2.62210 | + | 8.06998i | −0.136686 | + | 0.420677i | ||||
\(369\) | −9.27051 | + | 28.5317i | −0.482603 | + | 1.48530i | ||||
\(370\) | 14.9549 | − | 10.8654i | 0.777469 | − | 0.564864i | ||||
\(371\) | −18.8612 | − | 13.7035i | −0.979224 | − | 0.711448i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.7990 | −1.85360 | −0.926801 | − | 0.375554i | \(-0.877453\pi\) | ||||
−0.926801 | + | 0.375554i | \(0.877453\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.82843 | 0.146059 | ||||||||
\(376\) | −3.85816 | − | 11.8742i | −0.198970 | − | 0.612366i | ||||
\(377\) | −3.46605 | − | 2.51823i | −0.178511 | − | 0.129696i | ||||
\(378\) | −22.0973 | + | 16.0546i | −1.13656 | + | 0.825759i | ||||
\(379\) | 10.4005 | − | 32.0096i | 0.534240 | − | 1.64422i | −0.211046 | − | 0.977476i | \(-0.567687\pi\) |
0.745286 | − | 0.666745i | \(-0.232313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.93818 | + | 7.22051i | −0.509149 | + | 0.369918i | ||||
\(382\) | 6.47214 | + | 4.70228i | 0.331143 | + | 0.240590i | ||||
\(383\) | −1.81018 | − | 5.57116i | −0.0924959 | − | 0.284673i | 0.894097 | − | 0.447873i | \(-0.147818\pi\) |
−0.986593 | + | 0.163200i | \(0.947818\pi\) | |||||||
\(384\) | −58.1421 | −2.96705 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.82843 | −0.143963 | ||||||||
\(387\) | 9.27051 | + | 28.5317i | 0.471246 | + | 1.45035i | ||||
\(388\) | −11.3262 | − | 8.22899i | −0.575003 | − | 0.417764i | ||||
\(389\) | −16.6879 | + | 12.1245i | −0.846112 | + | 0.614736i | −0.924071 | − | 0.382220i | \(-0.875160\pi\) |
0.0779595 | + | 0.996957i | \(0.475160\pi\) | |||||||
\(390\) | −2.47214 | + | 7.60845i | −0.125181 | + | 0.385269i | ||||
\(391\) | 5.96826 | − | 18.3684i | 0.301828 | − | 0.928931i | ||||
\(392\) | −10.7135 | + | 7.78383i | −0.541115 | + | 0.393143i | ||||
\(393\) | 25.8885 | + | 18.8091i | 1.30590 | + | 0.948795i | ||||
\(394\) | −8.07836 | − | 24.8626i | −0.406982 | − | 1.25256i | ||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.31371 | −0.467442 | −0.233721 | − | 0.972304i | \(-0.575090\pi\) | ||||
−0.233721 | + | 0.972304i | \(0.575090\pi\) | |||||||
\(398\) | −7.71633 | − | 23.7484i | −0.386785 | − | 1.19040i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.42705 | + | 1.76336i | −0.121353 | + | 0.0881678i | ||||
\(401\) | −1.64203 | + | 5.05364i | −0.0819989 | + | 0.252367i | −0.983648 | − | 0.180102i | \(-0.942357\pi\) |
0.901649 | + | 0.432468i | \(0.142357\pi\) | |||||||
\(402\) | 26.3452 | − | 81.0822i | 1.31398 | − | 4.04401i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 28.8470 | + | 20.9586i | 1.43519 | + | 1.04273i | ||||
\(405\) | −0.309017 | − | 0.951057i | −0.0153552 | − | 0.0472584i | ||||
\(406\) | −17.6569 | −0.876295 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −85.2548 | −4.22074 | ||||||||
\(409\) | −0.318114 | − | 0.979053i | −0.0157297 | − | 0.0484111i | 0.942884 | − | 0.333122i | \(-0.108102\pi\) |
−0.958613 | + | 0.284711i | \(0.908102\pi\) | |||||||
\(410\) | 11.7188 | + | 8.51423i | 0.578752 | + | 0.420488i | ||||
\(411\) | −25.1033 | + | 18.2386i | −1.23826 | + | 0.899646i | ||||
\(412\) | 8.07836 | − | 24.8626i | 0.397992 | − | 1.22489i | ||||
\(413\) | 1.02399 | − | 3.15152i | 0.0503874 | − | 0.155076i | ||||
\(414\) | −27.6216 | + | 20.0682i | −1.35753 | + | 0.986300i | ||||
\(415\) | 4.85410 | + | 3.52671i | 0.238278 | + | 0.173119i | ||||
\(416\) | 0.574112 | + | 1.76693i | 0.0281481 | + | 0.0866311i | ||||
\(417\) | −11.3137 | −0.554035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.6569 | −1.25342 | −0.626710 | − | 0.779253i | \(-0.715599\pi\) | ||||
−0.626710 | + | 0.779253i | \(0.715599\pi\) | |||||||
\(420\) | 6.69234 | + | 20.5969i | 0.326553 | + | 1.00503i | ||||
\(421\) | 4.85410 | + | 3.52671i | 0.236574 | + | 0.171881i | 0.699756 | − | 0.714382i | \(-0.253292\pi\) |
−0.463181 | + | 0.886264i | \(0.653292\pi\) | |||||||
\(422\) | 31.2502 | − | 22.7046i | 1.52124 | − | 1.10524i | ||||
\(423\) | 4.37016 | − | 13.4500i | 0.212484 | − | 0.653960i | ||||
\(424\) | −15.9007 | + | 48.9374i | −0.772208 | + | 2.37661i | ||||
\(425\) | 5.52431 | − | 4.01365i | 0.267969 | − | 0.194691i | ||||
\(426\) | −62.5005 | − | 45.4093i | −3.02816 | − | 2.20009i | ||||
\(427\) | 5.75619 | + | 17.7157i | 0.278561 | + | 0.857324i | ||||
\(428\) | −29.3137 | −1.41693 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.4853 | 0.698542 | ||||||||
\(431\) | 3.49613 | + | 10.7600i | 0.168403 | + | 0.518290i | 0.999271 | − | 0.0381792i | \(-0.0121558\pi\) |
−0.830868 | + | 0.556469i | \(0.812156\pi\) | |||||||
\(432\) | 13.7295 | + | 9.97505i | 0.660560 | + | 0.479925i | ||||
\(433\) | 6.19453 | − | 4.50059i | 0.297690 | − | 0.216284i | −0.428907 | − | 0.903349i | \(-0.641101\pi\) |
0.726596 | + | 0.687065i | \(0.241101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.19621 | − | 9.83692i | 0.153246 | − | 0.471644i | ||||
\(436\) | −23.7153 | + | 17.2302i | −1.13576 | + | 0.825175i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.47214 | + | 7.60845i | 0.118123 | + | 0.363546i | ||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 5.96826 | + | 18.3684i | 0.283881 | + | 0.873697i | ||||
\(443\) | 21.7047 | + | 15.7694i | 1.03122 | + | 0.749225i | 0.968552 | − | 0.248810i | \(-0.0800394\pi\) |
0.0626669 | + | 0.998035i | \(0.480039\pi\) | |||||||
\(444\) | −67.0770 | + | 48.7343i | −3.18333 | + | 2.31283i | ||||
\(445\) | 4.11416 | − | 12.6621i | 0.195030 | − | 0.600241i | ||||
\(446\) | 8.07836 | − | 24.8626i | 0.382522 | − | 1.17728i | ||||
\(447\) | −0.785202 | + | 0.570482i | −0.0371388 | + | 0.0269829i | ||||
\(448\) | 15.9027 | + | 11.5540i | 0.751333 | + | 0.545876i | ||||
\(449\) | 8.84636 | + | 27.2263i | 0.417485 | + | 1.28489i | 0.910009 | + | 0.414589i | \(0.136075\pi\) |
−0.492523 | + | 0.870299i | \(0.663925\pi\) | |||||||
\(450\) | −12.0711 | −0.569036 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 75.2548 | 3.53969 | ||||||||
\(453\) | −10.4884 | − | 32.2799i | −0.492787 | − | 1.51664i | ||||
\(454\) | −49.4412 | − | 35.9211i | −2.32039 | − | 1.68586i | ||||
\(455\) | 1.89564 | − | 1.37727i | 0.0888692 | − | 0.0645673i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.149960 | + | 0.461530i | −0.00701484 | + | 0.0215895i | −0.954503 | − | 0.298202i | \(-0.903613\pi\) |
0.947488 | + | 0.319792i | \(0.103613\pi\) | |||||||
\(458\) | 2.56586 | − | 1.86420i | 0.119895 | − | 0.0871085i | ||||
\(459\) | −31.2502 | − | 22.7046i | −1.45864 | − | 1.05976i | ||||
\(460\) | 3.34617 | + | 10.2984i | 0.156016 | + | 0.480168i | ||||
\(461\) | −12.6274 | −0.588117 | −0.294059 | − | 0.955787i | \(-0.595006\pi\) | ||||
−0.294059 | + | 0.955787i | \(0.595006\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.14214 | −0.285449 | −0.142725 | − | 0.989762i | \(-0.545586\pi\) | ||||
−0.142725 | + | 0.989762i | \(0.545586\pi\) | |||||||
\(464\) | 3.39009 | + | 10.4336i | 0.157381 | + | 0.484369i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.9964 | − | 8.71593i | 0.555725 | − | 0.403758i | ||||
\(467\) | −4.58224 | + | 14.1027i | −0.212041 | + | 0.652594i | 0.787310 | + | 0.616557i | \(0.211473\pi\) |
−0.999350 | + | 0.0360364i | \(0.988527\pi\) | |||||||
\(468\) | 6.93014 | − | 21.3288i | 0.320346 | − | 0.985923i | ||||
\(469\) | −20.2016 | + | 14.6773i | −0.932824 | + | 0.677736i | ||||
\(470\) | −5.52431 | − | 4.01365i | −0.254818 | − | 0.185136i | ||||
\(471\) | 12.2364 | + | 37.6599i | 0.563826 | + | 1.73528i | ||||
\(472\) | −7.31371 | −0.336641 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −27.3137 | −1.25456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 42.2989 | + | 30.7319i | 1.93877 | + | 1.40860i | ||||
\(477\) | −47.1530 | + | 34.2586i | −2.15899 | + | 1.56860i | ||||
\(478\) | −17.3928 | + | 53.5295i | −0.795528 | + | 2.44838i | ||||
\(479\) | 11.1246 | − | 34.2380i | 0.508296 | − | 1.56438i | −0.286861 | − | 0.957972i | \(-0.592612\pi\) |
0.795157 | − | 0.606403i | \(-0.207388\pi\) | |||||||
\(480\) | −3.62867 | + | 2.63638i | −0.165625 | + | 0.120334i | ||||
\(481\) | 7.25734 | + | 5.27276i | 0.330906 | + | 0.240417i | ||||
\(482\) | 4.47620 | + | 13.7763i | 0.203885 | + | 0.627494i | ||||
\(483\) | 16.0000 | 0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.65685 | −0.166049 | ||||||||
\(486\) | −10.5505 | − | 32.4711i | −0.478580 | − | 1.47292i | ||||
\(487\) | 19.8090 | + | 14.3921i | 0.897632 | + | 0.652168i | 0.937857 | − | 0.347023i | \(-0.112807\pi\) |
−0.0402248 | + | 0.999191i | \(0.512807\pi\) | |||||||
\(488\) | 33.2609 | − | 24.1654i | 1.50565 | − | 1.09392i | ||||
\(489\) | −14.4087 | + | 44.3453i | −0.651582 | + | 2.00536i | ||||
\(490\) | −2.23810 | + | 6.88816i | −0.101107 | + | 0.311175i | ||||
\(491\) | −0.555221 | + | 0.403392i | −0.0250568 | + | 0.0182048i | −0.600243 | − | 0.799818i | \(-0.704930\pi\) |
0.575186 | + | 0.818022i | \(0.304930\pi\) | |||||||
\(492\) | −52.5623 | − | 38.1887i | −2.36969 | − | 1.72168i | ||||
\(493\) | −7.71633 | − | 23.7484i | −0.347526 | − | 1.06957i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.99226 | + | 21.5200i | 0.313646 | + | 0.965302i | ||||
\(498\) | −33.1459 | − | 24.0819i | −1.48530 | − | 1.07914i | ||||
\(499\) | −7.81256 | + | 5.67616i | −0.349738 | + | 0.254100i | −0.748759 | − | 0.662842i | \(-0.769350\pi\) |
0.399021 | + | 0.916942i | \(0.369350\pi\) | |||||||
\(500\) | −1.18305 | + | 3.64105i | −0.0529076 | + | 0.162833i | ||||
\(501\) | −20.0770 | + | 61.7907i | −0.896975 | + | 2.76060i | ||||
\(502\) | 23.4377 | − | 17.0285i | 1.04607 | − | 0.760018i | ||||
\(503\) | 13.4519 | + | 9.77335i | 0.599789 | + | 0.435772i | 0.845804 | − | 0.533494i | \(-0.179121\pi\) |
−0.246015 | + | 0.969266i | \(0.579121\pi\) | |||||||
\(504\) | −13.6407 | − | 41.9817i | −0.607604 | − | 1.87001i | ||||
\(505\) | 9.31371 | 0.414455 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.8873 | 1.46058 | ||||||||
\(508\) | −5.13815 | − | 15.8136i | −0.227969 | − | 0.701616i | ||||
\(509\) | 10.7710 | + | 7.82560i | 0.477417 | + | 0.346864i | 0.800325 | − | 0.599567i | \(-0.204660\pi\) |
−0.322908 | + | 0.946430i | \(0.604660\pi\) | |||||||
\(510\) | −37.7224 | + | 27.4069i | −1.67037 | + | 1.21360i | ||||
\(511\) | 0.724072 | − | 2.22846i | 0.0320311 | − | 0.0985814i | ||||
\(512\) | 9.65451 | − | 29.7135i | 0.426673 | − | 1.31316i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.1910 | − | 13.2165i | −0.802369 | − | 0.582956i | ||||
\(515\) | −2.11010 | − | 6.49422i | −0.0929821 | − | 0.286170i | ||||
\(516\) | −64.9706 | −2.86017 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 36.9706 | 1.62439 | ||||||||
\(519\) | −19.3529 | − | 59.5622i | −0.849500 | − | 2.61449i | ||||
\(520\) | −4.18389 | − | 3.03977i | −0.183476 | − | 0.133303i | ||||
\(521\) | −20.4792 | + | 14.8790i | −0.897211 | + | 0.651862i | −0.937748 | − | 0.347316i | \(-0.887093\pi\) |
0.0405372 | + | 0.999178i | \(0.487093\pi\) | |||||||
\(522\) | −13.6407 | + | 41.9817i | −0.597036 | + | 1.83749i | ||||
\(523\) | 12.8545 | − | 39.5620i | 0.562087 | − | 1.72993i | −0.114364 | − | 0.993439i | \(-0.536483\pi\) |
0.676451 | − | 0.736488i | \(-0.263517\pi\) | |||||||
\(524\) | −35.0415 | + | 25.4592i | −1.53080 | + | 1.11219i | ||||
\(525\) | 4.57649 | + | 3.32502i | 0.199734 | + | 0.145116i | ||||
\(526\) | −8.18440 | − | 25.1890i | −0.356857 | − | 1.09829i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 8.69640 | + | 26.7648i | 0.377747 | + | 1.16259i | ||||
\(531\) | −6.70212 | − | 4.86937i | −0.290847 | − | 0.211313i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.17222 | + | 6.68539i | −0.0940891 | + | 0.289576i | ||||
\(534\) | −28.0933 | + | 86.4622i | −1.21571 | + | 3.74158i | ||||
\(535\) | −6.19453 | + | 4.50059i | −0.267813 | + | 0.194577i | ||||
\(536\) | 44.5871 | + | 32.3944i | 1.92587 | + | 1.39923i | ||||
\(537\) | −8.44040 | − | 25.9769i | −0.364230 | − | 1.12099i | ||||
\(538\) | −41.7990 | −1.80208 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 21.6569 | 0.931963 | ||||||||
\(541\) | −1.85410 | − | 5.70634i | −0.0797141 | − | 0.245335i | 0.903255 | − | 0.429103i | \(-0.141170\pi\) |
−0.982970 | + | 0.183768i | \(0.941170\pi\) | |||||||
\(542\) | −14.2847 | − | 10.3784i | −0.613580 | − | 0.445792i | ||||
\(543\) | 48.7710 | − | 35.4342i | 2.09296 | − | 1.52063i | ||||
\(544\) | −3.34617 | + | 10.2984i | −0.143466 | + | 0.441542i | ||||
\(545\) | −2.36610 | + | 7.28210i | −0.101353 | + | 0.311931i | ||||
\(546\) | −12.9443 | + | 9.40456i | −0.553964 | + | 0.402478i | ||||
\(547\) | −27.5066 | − | 19.9847i | −1.17610 | − | 0.854484i | −0.184370 | − | 0.982857i | \(-0.559025\pi\) |
−0.991726 | + | 0.128373i | \(0.959025\pi\) | |||||||
\(548\) | −12.9787 | − | 39.9444i | −0.554423 | − | 1.70634i | ||||
\(549\) | 46.5685 | 1.98750 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −10.9125 | − | 33.5853i | −0.464468 | − | 1.42949i | ||||
\(553\) | 6.47214 | + | 4.70228i | 0.275223 | + | 0.199961i | ||||
\(554\) | −13.3369 | + | 9.68981i | −0.566629 | + | 0.411680i | ||||
\(555\) | −6.69234 | + | 20.5969i | −0.284074 | + | 0.874289i | ||||
\(556\) | 4.73220 | − | 14.5642i | 0.200690 | − | 0.617660i | ||||
\(557\) | 7.97518 | − | 5.79431i | 0.337919 | − | 0.245513i | −0.405864 | − | 0.913933i | \(-0.633029\pi\) |
0.743783 | + | 0.668421i | \(0.233029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.17222 | + | 6.68539i | 0.0918749 | + | 0.282762i | ||||
\(560\) | −6.00000 | −0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 41.7990 | 1.76318 | ||||||||
\(563\) | −0.106038 | − | 0.326351i | −0.00446896 | − | 0.0137541i | 0.948797 | − | 0.315886i | \(-0.102302\pi\) |
−0.953266 | + | 0.302132i | \(0.902302\pi\) | |||||||
\(564\) | 24.7781 | + | 18.0023i | 1.04335 | + | 0.758035i | ||||
\(565\) | 15.9027 | − | 11.5540i | 0.669033 | − | 0.486081i | ||||
\(566\) | 24.3411 | − | 74.9143i | 1.02313 | − | 3.14888i | ||||
\(567\) | 0.618034 | − | 1.90211i | 0.0259550 | − | 0.0798812i | ||||
\(568\) | 40.4032 | − | 29.3547i | 1.69528 | − | 1.23169i | ||||
\(569\) | 25.6109 | + | 18.6074i | 1.07367 | + | 0.780064i | 0.976568 | − | 0.215211i | \(-0.0690438\pi\) |
0.0970985 | + | 0.995275i | \(0.469044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9411 | 0.918208 | 0.459104 | − | 0.888383i | \(-0.348171\pi\) | ||||
0.459104 | + | 0.888383i | \(0.348171\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.37258 | −0.391545 | ||||||||
\(574\) | 8.95240 | + | 27.5526i | 0.373666 | + | 1.15003i | ||||
\(575\) | 2.28825 | + | 1.66251i | 0.0954264 | + | 0.0693314i | ||||
\(576\) | 39.7568 | − | 28.8850i | 1.65653 | − | 1.20354i | ||||
\(577\) | −8.33436 | + | 25.6505i | −0.346964 | + | 1.06785i | 0.613560 | + | 0.789648i | \(0.289737\pi\) |
−0.960524 | + | 0.278197i | \(0.910263\pi\) | |||||||
\(578\) | −22.1030 | + | 68.0261i | −0.919365 | + | 2.82951i | ||||
\(579\) | 2.68085 | − | 1.94775i | 0.111412 | − | 0.0809457i | ||||
\(580\) | 11.3262 | + | 8.22899i | 0.470296 | + | 0.341690i | ||||
\(581\) | 3.70820 | + | 11.4127i | 0.153842 | + | 0.473478i | ||||
\(582\) | 24.9706 | 1.03506 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.17157 | −0.214001 | ||||||||
\(585\) | −1.81018 | − | 5.57116i | −0.0748417 | − | 0.230339i | ||||
\(586\) | 17.9134 | + | 13.0148i | 0.739994 | + | 0.537637i | ||||
\(587\) | 1.73302 | − | 1.25912i | 0.0715296 | − | 0.0519693i | −0.551446 | − | 0.834211i | \(-0.685924\pi\) |
0.622975 | + | 0.782241i | \(0.285924\pi\) | |||||||
\(588\) | 10.0385 | − | 30.8953i | 0.413981 | − | 1.27410i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.23607 | + | 2.35114i | −0.133227 | + | 0.0967949i | ||||
\(591\) | 24.7781 | + | 18.0023i | 1.01923 | + | 0.740517i | ||||
\(592\) | −7.09829 | − | 21.8463i | −0.291738 | − | 0.897878i | ||||
\(593\) | −3.51472 | −0.144332 | −0.0721661 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721661 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.6569 | 0.559876 | ||||||||
\(596\) | −0.405958 | − | 1.24941i | −0.0166287 | − | 0.0511779i | ||||
\(597\) | 23.6677 | + | 17.1956i | 0.968653 | + | 0.703767i | ||||
\(598\) | −6.47214 | + | 4.70228i | −0.264665 | + | 0.192291i | ||||
\(599\) | −1.74806 | + | 5.37999i | −0.0714240 | + | 0.219820i | −0.980396 | − | 0.197036i | \(-0.936868\pi\) |
0.908972 | + | 0.416857i | \(0.136868\pi\) | |||||||
\(600\) | 3.85816 | − | 11.8742i | 0.157509 | − | 0.484763i | ||||
\(601\) | 19.3688 | − | 14.0722i | 0.790069 | − | 0.574019i | −0.117915 | − | 0.993024i | \(-0.537621\pi\) |
0.907984 | + | 0.419005i | \(0.137621\pi\) | |||||||
\(602\) | 23.4377 | + | 17.0285i | 0.955248 | + | 0.694029i | ||||
\(603\) | 19.2908 | + | 59.3710i | 0.785583 | + | 2.41778i | ||||
\(604\) | 45.9411 | 1.86932 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −63.5980 | −2.58349 | ||||||||
\(607\) | −11.8305 | − | 36.4105i | −0.480185 | − | 1.47786i | −0.838835 | − | 0.544385i | \(-0.816763\pi\) |
0.358651 | − | 0.933472i | \(-0.383237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.7356 | − | 12.1591i | 0.678159 | − | 0.492711i | ||||
\(610\) | 6.94833 | − | 21.3848i | 0.281330 | − | 0.865844i | ||||
\(611\) | 1.02399 | − | 3.15152i | 0.0414263 | − | 0.127497i | ||||
\(612\) | 105.747 | − | 76.8298i | 4.27458 | − | 3.10566i | ||||
\(613\) | −20.5942 | − | 14.9626i | −0.831792 | − | 0.604333i | 0.0882735 | − | 0.996096i | \(-0.471865\pi\) |
−0.920066 | + | 0.391764i | \(0.871865\pi\) | |||||||
\(614\) | −12.1925 | − | 37.5247i | −0.492050 | − | 1.51438i | ||||
\(615\) | −16.9706 | −0.684319 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.343146 | 0.0138145 | 0.00690726 | − | 0.999976i | \(-0.497801\pi\) | ||||
0.00690726 | + | 0.999976i | \(0.497801\pi\) | |||||||
\(618\) | 14.4087 | + | 44.3453i | 0.579601 | + | 1.78383i | ||||
\(619\) | 11.6038 | + | 8.43069i | 0.466398 | + | 0.338858i | 0.796036 | − | 0.605249i | \(-0.206927\pi\) |
−0.329638 | + | 0.944107i | \(0.606927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.94427 | − | 15.2169i | 0.198407 | − | 0.610633i | ||||
\(622\) | −3.49613 | + | 10.7600i | −0.140182 | + | 0.431436i | ||||
\(623\) | 21.5420 | − | 15.6512i | 0.863063 | − | 0.627052i | ||||
\(624\) | 8.04254 | + | 5.84325i | 0.321959 | + | 0.233917i | ||||
\(625\) | 0.309017 | + | 0.951057i | 0.0123607 | + | 0.0380423i | ||||
\(626\) | 3.17157 | 0.126762 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −53.5980 | −2.13879 | ||||||||
\(629\) | 16.1567 | + | 49.7253i | 0.644211 | + | 1.98268i | ||||
\(630\) | −19.5314 | − | 14.1904i | −0.778150 | − | 0.565359i | ||||
\(631\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(632\) | 5.45627 | − | 16.7927i | 0.217039 | − | 0.667976i | ||||
\(633\) | −13.9845 | + | 43.0399i | −0.555834 | + | 1.71068i | ||||
\(634\) | −2.56586 | + | 1.86420i | −0.101903 | + | 0.0740370i | ||||
\(635\) | −3.51368 | − | 2.55284i | −0.139436 | − | 0.101306i | ||||
\(636\) | −39.0058 | − | 120.047i | −1.54668 | − | 4.76019i | ||||
\(637\) | −3.51472 | −0.139258 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 56.5685 | 2.23782 | ||||||||
\(640\) | −6.35226 | − | 19.5502i | −0.251095 | − | 0.772791i | ||||
\(641\) | −24.2705 | − | 17.6336i | −0.958628 | − | 0.696484i | −0.00579592 | − | 0.999983i | \(-0.501845\pi\) |
−0.952832 | + | 0.303500i | \(0.901845\pi\) | |||||||
\(642\) | 42.2989 | − | 30.7319i | 1.66940 | − | 1.21289i | ||||
\(643\) | −0.449881 | + | 1.38459i | −0.0177416 | + | 0.0546029i | −0.959535 | − | 0.281588i | \(-0.909139\pi\) |
0.941794 | + | 0.336191i | \(0.109139\pi\) | |||||||
\(644\) | −6.69234 | + | 20.5969i | −0.263715 | + | 0.811631i | ||||
\(645\) | −13.7295 | + | 9.97505i | −0.540597 | + | 0.392767i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.37828 | + | 25.7857i | 0.329384 | + | 1.01374i | 0.969422 | + | 0.245398i | \(0.0789185\pi\) |
−0.640038 | + | 0.768343i | \(0.721081\pi\) | |||||||
\(648\) | −4.41421 | −0.173407 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.82843 | −0.110940 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −51.0592 | − | 37.0967i | −1.99963 | − | 1.45282i | ||||
\(653\) | −9.43059 | + | 6.85173i | −0.369048 | + | 0.268129i | −0.756816 | − | 0.653628i | \(-0.773246\pi\) |
0.387768 | + | 0.921757i | \(0.373246\pi\) | |||||||
\(654\) | 16.1567 | − | 49.7253i | 0.631778 | − | 1.94441i | ||||
\(655\) | −3.49613 | + | 10.7600i | −0.136605 | + | 0.420427i | ||||
\(656\) | 14.5623 | − | 10.5801i | 0.568563 | − | 0.413085i | ||||
\(657\) | −4.73911 | − | 3.44317i | −0.184890 | − | 0.134331i | ||||
\(658\) | −4.22020 | − | 12.9884i | −0.164521 | − | 0.506342i | ||||
\(659\) | −45.9411 | −1.78961 | −0.894806 | − | 0.446455i | \(-0.852686\pi\) | ||||
−0.894806 | + | 0.446455i | \(0.852686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.6274 | 1.73581 | 0.867903 | − | 0.496734i | \(-0.165468\pi\) | ||||
0.867903 | + | 0.496734i | \(0.165468\pi\) | |||||||
\(662\) | 5.45627 | + | 16.7927i | 0.212064 | + | 0.652666i | ||||
\(663\) | −18.3060 | − | 13.3001i | −0.710945 | − | 0.516532i | ||||
\(664\) | 21.4270 | − | 15.5677i | 0.831531 | − | 0.604142i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.5613 | − | 87.9027i | 1.10673 | − | 3.40616i | ||||
\(667\) | 8.36778 | − | 6.07955i | 0.324002 | − | 0.235401i | ||||
\(668\) | −71.1459 | − | 51.6905i | −2.75272 | − | 1.99997i | ||||
\(669\) | 9.46439 | + | 29.1284i | 0.365915 | + | 1.12617i | ||||
\(670\) | 30.1421 | 1.16449 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.97056 | −0.346047 | ||||||||
\(673\) | 3.85816 | + | 11.8742i | 0.148721 | + | 0.457717i | 0.997471 | − | 0.0710781i | \(-0.0226440\pi\) |
−0.848749 | + | 0.528795i | \(0.822644\pi\) | |||||||
\(674\) | 40.0106 | + | 29.0694i | 1.54115 | + | 1.11971i | ||||
\(675\) | 4.57649 | − | 3.32502i | 0.176149 | − | 0.127980i | ||||
\(676\) | −13.7558 | + | 42.3360i | −0.529069 | + | 1.62831i | ||||
\(677\) | −7.05437 | + | 21.7111i | −0.271122 | + | 0.834426i | 0.719098 | + | 0.694909i | \(0.244555\pi\) |
−0.990220 | + | 0.139518i | \(0.955445\pi\) | |||||||
\(678\) | −108.591 | + | 78.8957i | −4.17040 | + | 3.02997i | ||||
\(679\) | −5.91691 | − | 4.29889i | −0.227070 | − | 0.164976i | ||||
\(680\) | −9.31443 | − | 28.6669i | −0.357192 | − | 1.09932i | ||||
\(681\) | 71.5980 | 2.74364 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.79899 | −0.298420 | −0.149210 | − | 0.988806i | \(-0.547673\pi\) | ||||
−0.149210 | + | 0.988806i | \(0.547673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.87537 | − | 6.44833i | −0.339111 | − | 0.246378i | ||||
\(686\) | −39.0628 | + | 28.3808i | −1.49142 | + | 1.08358i | ||||
\(687\) | −1.14822 | + | 3.53387i | −0.0438075 | + | 0.134825i | ||||
\(688\) | 5.56231 | − | 17.1190i | 0.212061 | − | 0.652656i | ||||
\(689\) | −11.0486 | + | 8.02730i | −0.420919 | + | 0.305816i | ||||
\(690\) | −15.6251 | − | 11.3523i | −0.594838 | − | 0.432175i | ||||
\(691\) | −12.1486 | − | 37.3896i | −0.462155 | − | 1.42237i | −0.862526 | − | 0.506013i | \(-0.831119\pi\) |
0.400371 | − | 0.916353i | \(-0.368881\pi\) | |||||||
\(692\) | 84.7696 | 3.22245 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.4853 | 1.00537 | ||||||||
\(695\) | −1.23607 | − | 3.80423i | −0.0468867 | − | 0.144303i | ||||
\(696\) | −36.9372 | − | 26.8364i | −1.40010 | − | 1.01723i | ||||
\(697\) | −33.1459 | + | 24.0819i | −1.25549 | + | 0.912167i | ||||
\(698\) | 20.1209 | − | 61.9259i | 0.761588 | − | 2.34393i | ||||
\(699\) | −5.36842 | + | 16.5223i | −0.203052 | + | 0.624931i | ||||
\(700\) | −6.19453 | + | 4.50059i | −0.234131 | + | 0.170106i | ||||
\(701\) | −10.2158 | − | 7.42221i | −0.385845 | − | 0.280333i | 0.377906 | − | 0.925844i | \(-0.376644\pi\) |
−0.763751 | + | 0.645511i | \(0.776644\pi\) | |||||||
\(702\) | 4.94427 | + | 15.2169i | 0.186610 | + | 0.574325i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | −15.9007 | − | 48.9374i | −0.598432 | − | 1.84178i | ||||
\(707\) | 15.0699 | + | 10.9489i | 0.566762 | + | 0.411777i | ||||
\(708\) | 14.5147 | − | 10.5455i | 0.545495 | − | 0.396325i | ||||
\(709\) | 7.61029 | − | 23.4221i | 0.285810 | − | 0.879634i | −0.700344 | − | 0.713805i | \(-0.746970\pi\) |
0.986155 | − | 0.165829i | \(-0.0530299\pi\) | |||||||
\(710\) | 8.44040 | − | 25.9769i | 0.316763 | − | 0.974895i | ||||
\(711\) | 16.1803 | − | 11.7557i | 0.606810 | − | 0.440873i | ||||
\(712\) | −47.5456 | − | 34.5439i | −1.78185 | − | 1.29459i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −93.2548 | −3.48997 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36.9706 | 1.38165 | ||||||||
\(717\) | −20.3769 | − | 62.7137i | −0.760990 | − | 2.34209i | ||||
\(718\) | −1.34042 | − | 0.973874i | −0.0500242 | − | 0.0363447i | ||||
\(719\) | −14.8399 | + | 10.7818i | −0.553436 | + | 0.402094i | −0.829051 | − | 0.559174i | \(-0.811118\pi\) |
0.275615 | + | 0.961268i | \(0.411118\pi\) | |||||||
\(720\) | −4.63525 | + | 14.2658i | −0.172746 | + | 0.531657i | ||||
\(721\) | 4.22020 | − | 12.9884i | 0.157168 | − | 0.483715i | ||||
\(722\) | −37.1097 | + | 26.9617i | −1.38108 | + | 1.00341i | ||||
\(723\) | −13.7295 | − | 9.97505i | −0.510605 | − | 0.370976i | ||||
\(724\) | 25.2152 | + | 77.6043i | 0.937114 | + | 2.88414i | ||||
\(725\) | 3.65685 | 0.135812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5147 | −0.723761 | −0.361880 | − | 0.932225i | \(-0.617865\pi\) | ||||
−0.361880 | + | 0.932225i | \(0.617865\pi\) | |||||||
\(728\) | −3.19621 | − | 9.83692i | −0.118459 | − | 0.364580i | ||||
\(729\) | 34.7877 | + | 25.2748i | 1.28843 | + | 0.936102i | ||||
\(730\) | −2.28825 | + | 1.66251i | −0.0846918 | + | 0.0615322i | ||||
\(731\) | −12.6606 | + | 38.9653i | −0.468269 | + | 1.44118i | ||||
\(732\) | −31.1652 | + | 95.9167i | −1.15190 | + | 3.54518i | ||||
\(733\) | −14.1221 | + | 10.2603i | −0.521611 | + | 0.378972i | −0.817210 | − | 0.576340i | \(-0.804481\pi\) |
0.295600 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(734\) | −16.5729 | − | 12.0409i | −0.611718 | − | 0.444439i | ||||
\(735\) | −2.62210 | − | 8.06998i | −0.0967175 | − | 0.297666i | ||||
\(736\) | −4.48528 | −0.165330 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 72.4264 | 2.66605 | ||||||||
\(739\) | −9.25232 | − | 28.4757i | −0.340352 | − | 1.04750i | −0.964025 | − | 0.265811i | \(-0.914360\pi\) |
0.623673 | − | 0.781685i | \(-0.285640\pi\) | |||||||
\(740\) | −23.7153 | − | 17.2302i | −0.871791 | − | 0.633393i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.3928 | + | 53.5295i | −0.638510 | + | 1.96513i | ||||
\(743\) | 15.3266 | − | 47.1705i | 0.562279 | − | 1.73052i | −0.113621 | − | 0.993524i | \(-0.536245\pi\) |
0.675900 | − | 0.736993i | \(-0.263755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.277611 | − | 0.201696i | −0.0101709 | − | 0.00738957i | ||||
\(746\) | 26.7072 | + | 82.1964i | 0.977821 | + | 3.00942i | ||||
\(747\) | 30.0000 | 1.09764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.3137 | −0.559551 | ||||||||
\(750\) | −2.11010 | − | 6.49422i | −0.0770500 | − | 0.237135i | ||||
\(751\) | 12.9443 | + | 9.40456i | 0.472343 | + | 0.343177i | 0.798354 | − | 0.602189i | \(-0.205705\pi\) |
−0.326011 | + | 0.945366i | \(0.605705\pi\) | |||||||
\(752\) | −6.86474 | + | 4.98752i | −0.250331 | + | 0.181876i | ||||
\(753\) | −10.4884 | + | 32.2799i | −0.382218 | + | 1.17635i | ||||
\(754\) | −3.19621 | + | 9.83692i | −0.116399 | + | 0.358239i | ||||
\(755\) | 9.70820 | − | 7.05342i | 0.353318 | − | 0.256700i | ||||
\(756\) | 35.0415 | + | 25.4592i | 1.27445 | + | 0.925941i | ||||
\(757\) | 4.11416 | + | 12.6621i | 0.149532 | + | 0.460211i | 0.997566 | − | 0.0697302i | \(-0.0222138\pi\) |
−0.848034 | + | 0.529942i | \(0.822214\pi\) | |||||||
\(758\) | −81.2548 | −2.95131 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.27051 | + | 28.5317i | 0.336056 | + | 1.03427i | 0.966200 | + | 0.257795i | \(0.0829959\pi\) |
−0.630144 | + | 0.776478i | \(0.717004\pi\) | |||||||
\(762\) | 23.9929 | + | 17.4319i | 0.869171 | + | 0.631490i | ||||
\(763\) | −12.3891 | + | 9.00117i | −0.448514 | + | 0.325864i | ||||
\(764\) | 3.92028 | − | 12.0654i | 0.141831 | − | 0.436510i | ||||
\(765\) | 10.5505 | − | 32.4711i | 0.381454 | − | 1.17400i | ||||
\(766\) | −11.4412 | + | 8.31254i | −0.413388 | + | 0.300344i | ||||
\(767\) | −1.57040 | − | 1.14096i | −0.0567040 | − | 0.0411979i | ||||
\(768\) | 26.1952 | + | 80.6206i | 0.945239 | + | 2.90915i | ||||
\(769\) | 18.9706 | 0.684096 | 0.342048 | − | 0.939682i | \(-0.388879\pi\) | ||||
0.342048 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.3431 | 0.948725 | ||||||||
\(772\) | 1.38603 | + | 4.26576i | 0.0498842 | + | 0.153528i | ||||
\(773\) | −21.2644 | − | 15.4495i | −0.764828 | − | 0.555680i | 0.135559 | − | 0.990769i | \(-0.456717\pi\) |
−0.900387 | + | 0.435089i | \(0.856717\pi\) | |||||||
\(774\) | 58.5942 | − | 42.5712i | 2.10612 | − | 1.53019i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.98819 | + | 15.3521i | −0.179066 | + | 0.551108i | ||||
\(777\) | −35.0415 | + | 25.4592i | −1.25711 | + | 0.913342i | ||||
\(778\) | 40.2882 | + | 29.2711i | 1.44440 | + | 1.04942i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 12.6863 | 0.454242 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −46.6274 | −1.66739 | ||||||||
\(783\) | −6.39242 | − | 19.6738i | −0.228446 | − | 0.703085i | ||||
\(784\) | 7.28115 | + | 5.29007i | 0.260041 | + | 0.188931i | ||||
\(785\) | −11.3262 | + | 8.22899i | −0.404251 | + | 0.293705i | ||||
\(786\) | 23.8731 | − | 73.4737i | 0.851524 | − | 2.62072i | ||||
\(787\) | 4.62616 | − | 14.2379i | 0.164905 | − | 0.507525i | −0.834125 | − | 0.551576i | \(-0.814027\pi\) |
0.999029 | + | 0.0440516i | \(0.0140266\pi\) | |||||||
\(788\) | −33.5385 | + | 24.3671i | −1.19476 | + | 0.868043i | ||||
\(789\) | 25.1033 | + | 18.2386i | 0.893703 | + | 0.649313i | ||||
\(790\) | −2.98413 | − | 9.18421i | −0.106171 | − | 0.326760i | ||||
\(791\) | 39.3137 | 1.39783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9117 | 0.387485 | ||||||||
\(794\) | 6.94833 | + | 21.3848i | 0.246587 | + | 0.758917i | ||||
\(795\) | −26.6737 | − | 19.3796i | −0.946020 | − | 0.687324i | ||||
\(796\) | −32.0354 | + | 23.2751i | −1.13547 | + | 0.824964i | ||||
\(797\) | 10.0824 | − | 31.0305i | 0.357138 | − | 1.09916i | −0.597622 | − | 0.801778i | \(-0.703887\pi\) |
0.954759 | − | 0.297379i | \(-0.0961125\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.6251 | − | 11.3523i | 0.552777 | − | 0.401616i | ||||
\(800\) | −1.28293 | − | 0.932102i | −0.0453584 | − | 0.0329548i | ||||
\(801\) | −20.5708 | − | 63.3104i | −0.726834 | − | 2.23696i | ||||
\(802\) | 12.8284 | 0.452988 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −135.196 | −4.76799 | ||||||||
\(805\) | 1.74806 | + | 5.37999i | 0.0616112 | + | 0.189620i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.6180 | − | 28.7842i | 1.39462 | − | 1.01325i | ||||
\(808\) | 12.7045 | − | 39.1005i | 0.446944 | − | 1.37555i | ||||
\(809\) | 3.39009 | − | 10.4336i | 0.119189 | − | 0.366827i | −0.873608 | − | 0.486629i | \(-0.838226\pi\) |
0.992798 | + | 0.119803i | \(0.0382262\pi\) | |||||||
\(810\) | −1.95314 | + | 1.41904i | −0.0686263 | + | 0.0498600i | ||||
\(811\) | 43.6393 | + | 31.7058i | 1.53238 | + | 1.11334i | 0.954896 | + | 0.296941i | \(0.0959665\pi\) |
0.577487 | + | 0.816400i | \(0.304033\pi\) | |||||||
\(812\) | 8.65248 | + | 26.6296i | 0.303642 | + | 0.934515i | ||||
\(813\) | 20.6863 | 0.725500 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.4853 | −0.577454 | ||||||||
\(816\) | 17.9048 | + | 55.1053i | 0.626793 | + | 1.92907i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.01063 | + | 1.46081i | −0.0703002 | + | 0.0510761i | ||||
\(819\) | 3.62036 | − | 11.1423i | 0.126506 | − | 0.389344i | ||||
\(820\) | 7.09829 | − | 21.8463i | 0.247883 | − | 0.762906i | ||||
\(821\) | −33.4235 | + | 24.2836i | −1.16649 | + | 0.847503i | −0.990584 | − | 0.136904i | \(-0.956285\pi\) |
−0.175904 | + | 0.984407i | \(0.556285\pi\) | |||||||
\(822\) | 60.6048 | + | 44.0320i | 2.11384 | + | 1.53579i | ||||
\(823\) | 6.03038 | + | 18.5596i | 0.210206 | + | 0.646947i | 0.999459 | + | 0.0328795i | \(0.0104678\pi\) |
−0.789254 | + | 0.614068i | \(0.789532\pi\) | |||||||
\(824\) | −30.1421 | −1.05005 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | −6.88622 | − | 21.1936i | −0.239457 | − | 0.736974i | −0.996499 | − | 0.0836070i | \(-0.973356\pi\) |
0.757042 | − | 0.653367i | \(-0.226644\pi\) | |||||||
\(828\) | 43.8019 | + | 31.8239i | 1.52222 | + | 1.10596i | ||||
\(829\) | −14.5623 | + | 10.5801i | −0.505770 | + | 0.367463i | −0.811217 | − | 0.584746i | \(-0.801194\pi\) |
0.305447 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(830\) | 4.47620 | − | 13.7763i | 0.155371 | − | 0.478183i | ||||
\(831\) | 5.96826 | − | 18.3684i | 0.207037 | − | 0.637194i | ||||
\(832\) | 9.31560 | − | 6.76818i | 0.322960 | − | 0.234644i | ||||
\(833\) | −16.5729 | − | 12.0409i | −0.574218 | − | 0.417194i | ||||
\(834\) | 8.44040 | + | 25.9769i | 0.292267 | + | 0.899506i | ||||
\(835\) | −22.9706 | −0.794929 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.1409 | + | 58.9095i | 0.661210 | + | 2.03500i | ||||
\(839\) | −21.3121 | − | 15.4841i | −0.735774 | − | 0.534571i | 0.155611 | − | 0.987818i | \(-0.450265\pi\) |
−0.891385 | + | 0.453247i | \(0.850265\pi\) | |||||||
\(840\) | 20.2016 | − | 14.6773i | 0.697022 | − | 0.506416i | ||||
\(841\) | −4.82914 | + | 14.8626i | −0.166522 | + | 0.512502i | ||||
\(842\) | 4.47620 | − | 13.7763i | 0.154260 | − | 0.474763i | ||||
\(843\) | −39.6180 | + | 28.7842i | −1.36452 | + | 0.991380i | ||||
\(844\) | −49.5562 | − | 36.0047i | −1.70579 | − | 1.23933i | ||||
\(845\) | 3.59307 | + | 11.0583i | 0.123605 | + | 0.380418i | ||||
\(846\) | −34.1421 | −1.17383 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 34.9706 | 1.20089 | ||||||||
\(849\) | 28.5174 | + | 87.7676i | 0.978715 | + | 3.01217i | ||||
\(850\) | −13.3369 | − | 9.68981i | −0.457451 | − | 0.332358i | ||||
\(851\) | −17.5208 | + | 12.7296i | −0.600604 | + | 0.436364i | ||||
\(852\) | −37.8576 | + | 116.514i | −1.29698 | + | 3.99169i | ||||
\(853\) | 4.79431 | − | 14.7554i | 0.164154 | − | 0.505214i | −0.834819 | − | 0.550525i | \(-0.814428\pi\) |
0.998973 | + | 0.0453103i | \(0.0144277\pi\) | |||||||
\(854\) | 36.3819 | − | 26.4330i | 1.24496 | − | 0.904520i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.4445 | + | 32.1447i | 0.356984 | + | 1.09868i | ||||
\(857\) | −24.7696 | −0.846112 | −0.423056 | − | 0.906104i | \(-0.639043\pi\) | ||||
−0.423056 | + | 0.906104i | \(0.639043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.2843 | 0.828569 | 0.414284 | − | 0.910148i | \(-0.364032\pi\) | ||||
0.414284 | + | 0.910148i | \(0.364032\pi\) | |||||||
\(860\) | −7.09829 | − | 21.8463i | −0.242050 | − | 0.744953i | ||||
\(861\) | −27.4589 | − | 19.9501i | −0.935798 | − | 0.679897i | ||||
\(862\) | 22.0973 | − | 16.0546i | 0.752635 | − | 0.546822i | ||||
\(863\) | −2.83417 | + | 8.72268i | −0.0964763 | + | 0.296924i | −0.987636 | − | 0.156767i | \(-0.949893\pi\) |
0.891159 | + | 0.453691i | \(0.149893\pi\) | |||||||
\(864\) | −2.77206 | + | 8.53151i | −0.0943073 | + | 0.290248i | ||||
\(865\) | 17.9134 | − | 13.0148i | 0.609073 | − | 0.442517i | ||||
\(866\) | −14.9549 | − | 10.8654i | −0.508188 | − | 0.369220i | ||||
\(867\) | −25.8953 | − | 79.6976i | −0.879451 | − | 2.70667i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −24.9706 | −0.846581 | ||||||||
\(871\) | 4.52012 | + | 13.9115i | 0.153158 | + | 0.471373i | ||||
\(872\) | 27.3440 | + | 19.8665i | 0.925983 | + | 0.672766i | ||||
\(873\) | −14.7923 | + | 10.7472i | −0.500643 | + | 0.363738i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.618034 | + | 1.90211i | −0.0208934 | + | 0.0643032i | ||||
\(876\) | 10.2634 | − | 7.45682i | 0.346769 | − | 0.251942i | ||||
\(877\) | −40.0106 | − | 29.0694i | −1.35106 | − | 0.981604i | −0.998958 | − | 0.0456438i | \(-0.985466\pi\) |
−0.352105 | − | 0.935961i | \(-0.614534\pi\) | |||||||
\(878\) | −11.9365 | − | 36.7369i | −0.402838 | − | 1.23981i | ||||
\(879\) | −25.9411 | −0.874972 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.37258 | −0.248389 | −0.124194 | − | 0.992258i | \(-0.539635\pi\) | ||||
−0.124194 | + | 0.992258i | \(0.539635\pi\) | |||||||
\(882\) | 11.1905 | + | 34.4408i | 0.376804 | + | 1.15968i | ||||
\(883\) | −30.0724 | − | 21.8489i | −1.01202 | − | 0.735274i | −0.0473866 | − | 0.998877i | \(-0.515089\pi\) |
−0.964631 | + | 0.263603i | \(0.915089\pi\) | |||||||
\(884\) | 24.7781 | − | 18.0023i | 0.833378 | − | 0.605484i | ||||
\(885\) | 1.44814 | − | 4.45693i | 0.0486788 | − | 0.149818i | ||||
\(886\) | 20.0149 | − | 61.5995i | 0.672413 | − | 2.06948i | ||||
\(887\) | 30.9726 | − | 22.5029i | 1.03996 | − | 0.755574i | 0.0696815 | − | 0.997569i | \(-0.477802\pi\) |
0.970278 | + | 0.241995i | \(0.0778017\pi\) | |||||||
\(888\) | 77.3404 | + | 56.1911i | 2.59537 | + | 1.88565i | ||||
\(889\) | −2.68421 | − | 8.26115i | −0.0900256 | − | 0.277070i | ||||
\(890\) | −32.1421 | −1.07741 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −41.4558 | −1.38804 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 1.89564 | + | 1.37727i | 0.0633998 | + | 0.0460627i | ||||
\(895\) | 7.81256 | − | 5.67616i | 0.261145 | − | 0.189733i | ||||
\(896\) | 12.7045 | − | 39.1005i | 0.424428 | − | 1.30626i | ||||
\(897\) | 2.89629 | − | 8.91386i | 0.0967042 | − | 0.297625i | ||||
\(898\) | 55.9133 | − | 40.6234i | 1.86585 | − | 1.35562i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.91525 | + | 18.2053i | 0.197175 | + | 0.606842i | ||||
\(901\) | −79.5980 | −2.65179 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.9411 | −1.12949 | ||||||||
\(904\) | −26.8133 | − | 82.5227i | −0.891796 | − | 2.74467i | ||||
\(905\) | 17.2432 | + | 12.5279i | 0.573182 | + | 0.416441i | ||||
\(906\) | −66.2918 | + | 48.1638i | −2.20240 | + | 1.60013i | ||||
\(907\) | −8.50252 | + | 26.1681i | −0.282321 | + | 0.868896i | 0.704867 | + | 0.709339i | \(0.251007\pi\) |
−0.987189 | + | 0.159557i | \(0.948993\pi\) | |||||||
\(908\) | −29.9474 | + | 92.1685i | −0.993838 | + | 3.05872i | ||||
\(909\) | 37.6747 | − | 27.3723i | 1.24959 | − | 0.907882i | ||||
\(910\) | −4.57649 | − | 3.32502i | −0.151709 | − | 0.110223i | ||||
\(911\) | −3.07198 | − | 9.45457i | −0.101779 | − | 0.313244i | 0.887182 | − | 0.461420i | \(-0.152660\pi\) |
−0.988961 | + | 0.148176i | \(0.952660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.17157 | 0.0387522 | ||||||||
\(915\) | 8.14048 | + | 25.0538i | 0.269116 | + | 0.828254i | ||||
\(916\) | −4.06890 | − | 2.95623i | −0.134440 | − | 0.0976766i | ||||
\(917\) | −18.3060 | + | 13.3001i | −0.604516 | + | 0.439207i | ||||
\(918\) | −28.8173 | + | 88.6906i | −0.951114 | + | 2.92723i | ||||
\(919\) | 9.88854 | − | 30.4338i | 0.326193 | − | 1.00392i | −0.644706 | − | 0.764430i | \(-0.723020\pi\) |
0.970899 | − | 0.239488i | \(-0.0769797\pi\) | |||||||
\(920\) | 10.1008 | − | 7.33866i | 0.333014 | − | 0.241949i | ||||
\(921\) | 37.3971 | + | 27.1706i | 1.23228 | + | 0.895302i | ||||
\(922\) | 9.42047 | + | 28.9932i | 0.310247 | + | 0.954841i | ||||
\(923\) | 13.2548 | 0.436288 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.65685 | −0.251756 | ||||||||
\(926\) | 4.58224 | + | 14.1027i | 0.150582 | + | 0.463443i | ||||
\(927\) | −27.6216 | − | 20.0682i | −0.907211 | − | 0.659128i | ||||
\(928\) | −4.69148 | + | 3.40856i | −0.154005 | + | 0.111891i | ||||
\(929\) | 1.64203 | − | 5.05364i | 0.0538731 | − | 0.165804i | −0.920500 | − | 0.390743i | \(-0.872218\pi\) |
0.974373 | + | 0.224939i | \(0.0722181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −19.0238 | − | 13.8216i | −0.623146 | − | 0.452742i | ||||
\(933\) | −4.09597 | − | 12.6061i | −0.134096 | − | 0.412705i | ||||
\(934\) | 35.7990 | 1.17138 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25.8579 | −0.845191 | ||||||||
\(937\) | 0.449881 | + | 1.38459i | 0.0146970 | + | 0.0452326i | 0.958136 | − | 0.286313i | \(-0.0924298\pi\) |
−0.943439 | + | 0.331546i | \(0.892430\pi\) | |||||||
\(938\) | 48.7710 | + | 35.4342i | 1.59243 | + | 1.15697i | ||||
\(939\) | −3.00609 | + | 2.18405i | −0.0981000 | + | 0.0712738i | ||||
\(940\) | −3.34617 | + | 10.2984i | −0.109140 | + | 0.335898i | ||||
\(941\) | 2.06618 | − | 6.35904i | 0.0673555 | − | 0.207299i | −0.911714 | − | 0.410826i | \(-0.865240\pi\) |
0.979069 | + | 0.203527i | \(0.0652405\pi\) | |||||||
\(942\) | 77.3404 | − | 56.1911i | 2.51989 | − | 1.83080i | ||||
\(943\) | −13.7295 | − | 9.97505i | −0.447093 | − | 0.324832i | ||||
\(944\) | 1.53599 | + | 4.72729i | 0.0499922 | + | 0.153860i | ||||
\(945\) | 11.3137 | 0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.1716 | 1.33790 | 0.668948 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668948 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(948\) | 13.3847 | + | 41.1938i | 0.434714 | + | 1.33791i | ||||
\(949\) | −1.11044 | − | 0.806784i | −0.0360465 | − | 0.0261893i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.14822 | − | 3.53387i | 0.0372337 | − | 0.114594i | ||||
\(952\) | 18.6289 | − | 57.3337i | 0.603765 | − | 1.85820i | ||||
\(953\) | 43.0167 | − | 31.2535i | 1.39345 | − | 1.01240i | 0.397971 | − | 0.917398i | \(-0.369715\pi\) |
0.995477 | − | 0.0950009i | \(-0.0302854\pi\) | |||||||
\(954\) | 113.837 | + | 82.7077i | 3.68562 | + | 2.67776i | ||||
\(955\) | −1.02399 | − | 3.15152i | −0.0331356 | − | 0.101981i | ||||
\(956\) | 89.2548 | 2.88671 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −86.9117 | −2.80799 | ||||||||
\(959\) | −6.78018 | − | 20.8673i | −0.218943 | − | 0.673839i | ||||
\(960\) | 22.4899 | + | 16.3398i | 0.725857 | + | 0.527366i | ||||
\(961\) | 25.0795 | − | 18.2213i | 0.809017 | − | 0.587785i | ||||
\(962\) | 6.69234 | − | 20.5969i | 0.215770 | − | 0.664070i | ||||
\(963\) | −11.8305 | + | 36.4105i | −0.381232 | + | 1.17331i | ||||
\(964\) | 18.5836 | − | 13.5018i | 0.598537 | − | 0.434862i | ||||
\(965\) | 0.947822 | + | 0.688633i | 0.0305115 | + | 0.0221679i | ||||
\(966\) | −11.9365 | − | 36.7369i | −0.384052 | − | 1.18199i | ||||
\(967\) | 14.9706 | 0.481421 | 0.240710 | − | 0.970597i | \(-0.422620\pi\) | ||||
0.240710 | + | 0.970597i | \(0.422620\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.72813 | + | 8.39633i | 0.0875951 | + | 0.269590i | ||||
\(971\) | 7.02736 | + | 5.10567i | 0.225519 | + | 0.163849i | 0.694807 | − | 0.719196i | \(-0.255490\pi\) |
−0.469289 | + | 0.883045i | \(0.655490\pi\) | |||||||
\(972\) | −43.8019 | + | 31.8239i | −1.40495 | + | 1.02075i | ||||
\(973\) | 2.47214 | − | 7.60845i | 0.0792530 | − | 0.243916i | ||||
\(974\) | 18.2668 | − | 56.2195i | 0.585307 | − | 1.80139i | ||||
\(975\) | 2.68085 | − | 1.94775i | 0.0858558 | − | 0.0623779i | ||||
\(976\) | −22.6048 | − | 16.4234i | −0.723563 | − | 0.525700i | ||||
\(977\) | 9.99458 | + | 30.7602i | 0.319755 | + | 0.984105i | 0.973753 | + | 0.227608i | \(0.0730906\pi\) |
−0.653998 | + | 0.756496i | \(0.726909\pi\) | |||||||
\(978\) | 112.569 | 3.59955 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 11.4853 | 0.366884 | ||||||||
\(981\) | 11.8305 | + | 36.4105i | 0.377718 | + | 1.16250i | ||||
\(982\) | 1.34042 | + | 0.973874i | 0.0427746 | + | 0.0310776i | ||||
\(983\) | 17.6834 | − | 12.8477i | 0.564012 | − | 0.409779i | −0.268913 | − | 0.963165i | \(-0.586664\pi\) |
0.832925 | + | 0.553386i | \(0.186664\pi\) | |||||||
\(984\) | −23.1490 | + | 71.2452i | −0.737963 | + | 2.27122i | ||||
\(985\) | −3.34617 | + | 10.2984i | −0.106618 | + | 0.328136i | ||||
\(986\) | −48.7710 | + | 35.4342i | −1.55319 | + | 1.12845i | ||||
\(987\) | 12.9443 | + | 9.40456i | 0.412021 | + | 0.299351i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.9706 | −0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9411 | −1.84056 | −0.920280 | − | 0.391260i | \(-0.872039\pi\) | ||||
−0.920280 | + | 0.391260i | \(0.872039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.7356 | − | 12.1591i | −0.531087 | − | 0.385857i | ||||
\(994\) | 44.1945 | − | 32.1092i | 1.40176 | − | 1.01844i | ||||
\(995\) | −3.19621 | + | 9.83692i | −0.101327 | + | 0.311851i | ||||
\(996\) | −20.0770 | + | 61.7907i | −0.636164 | + | 1.95791i | ||||
\(997\) | −33.5385 | + | 24.3671i | −1.06217 | + | 0.771715i | −0.974489 | − | 0.224433i | \(-0.927947\pi\) |
−0.0876850 | + | 0.996148i | \(0.527947\pi\) | |||||||
\(998\) | 18.8612 | + | 13.7035i | 0.597040 | + | 0.433775i | ||||
\(999\) | 13.3847 | + | 41.1938i | 0.423472 | + | 1.30331i |
(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 | 605.2.g.l.511.1 | 8 | ||
11.2 | odd | 10 | 605.2.g.f.251.2 | 8 | |||
11.3 | even | 5 | 605.2.a.d.1.1 | 2 | |||
11.4 | even | 5 | inner | 605.2.g.l.366.2 | 8 | ||
11.5 | even | 5 | inner | 605.2.g.l.81.2 | 8 | ||
11.6 | odd | 10 | 605.2.g.f.81.1 | 8 | |||
11.7 | odd | 10 | 605.2.g.f.366.1 | 8 | |||
11.8 | odd | 10 | 55.2.a.b.1.2 | ✓ | 2 | ||
11.9 | even | 5 | inner | 605.2.g.l.251.1 | 8 | ||
11.10 | odd | 2 | 605.2.g.f.511.2 | 8 | |||
33.8 | even | 10 | 495.2.a.b.1.1 | 2 | |||
33.14 | odd | 10 | 5445.2.a.y.1.2 | 2 | |||
44.3 | odd | 10 | 9680.2.a.bn.1.2 | 2 | |||
44.19 | even | 10 | 880.2.a.m.1.2 | 2 | |||
55.8 | even | 20 | 275.2.b.d.199.1 | 4 | |||
55.14 | even | 10 | 3025.2.a.o.1.2 | 2 | |||
55.19 | odd | 10 | 275.2.a.c.1.1 | 2 | |||
55.52 | even | 20 | 275.2.b.d.199.4 | 4 | |||
77.41 | even | 10 | 2695.2.a.f.1.2 | 2 | |||
88.19 | even | 10 | 3520.2.a.bo.1.1 | 2 | |||
88.85 | odd | 10 | 3520.2.a.bn.1.2 | 2 | |||
132.107 | odd | 10 | 7920.2.a.ch.1.2 | 2 | |||
143.129 | odd | 10 | 9295.2.a.g.1.1 | 2 | |||
165.8 | odd | 20 | 2475.2.c.l.199.4 | 4 | |||
165.74 | even | 10 | 2475.2.a.x.1.2 | 2 | |||
165.107 | odd | 20 | 2475.2.c.l.199.1 | 4 | |||
220.19 | even | 10 | 4400.2.a.bn.1.1 | 2 | |||
220.63 | odd | 20 | 4400.2.b.q.4049.3 | 4 | |||
220.107 | odd | 20 | 4400.2.b.q.4049.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.2 | ✓ | 2 | 11.8 | odd | 10 | ||
275.2.a.c.1.1 | 2 | 55.19 | odd | 10 | |||
275.2.b.d.199.1 | 4 | 55.8 | even | 20 | |||
275.2.b.d.199.4 | 4 | 55.52 | even | 20 | |||
495.2.a.b.1.1 | 2 | 33.8 | even | 10 | |||
605.2.a.d.1.1 | 2 | 11.3 | even | 5 | |||
605.2.g.f.81.1 | 8 | 11.6 | odd | 10 | |||
605.2.g.f.251.2 | 8 | 11.2 | odd | 10 | |||
605.2.g.f.366.1 | 8 | 11.7 | odd | 10 | |||
605.2.g.f.511.2 | 8 | 11.10 | odd | 2 | |||
605.2.g.l.81.2 | 8 | 11.5 | even | 5 | inner | ||
605.2.g.l.251.1 | 8 | 11.9 | even | 5 | inner | ||
605.2.g.l.366.2 | 8 | 11.4 | even | 5 | inner | ||
605.2.g.l.511.1 | 8 | 1.1 | even | 1 | trivial | ||
880.2.a.m.1.2 | 2 | 44.19 | even | 10 | |||
2475.2.a.x.1.2 | 2 | 165.74 | even | 10 | |||
2475.2.c.l.199.1 | 4 | 165.107 | odd | 20 | |||
2475.2.c.l.199.4 | 4 | 165.8 | odd | 20 | |||
2695.2.a.f.1.2 | 2 | 77.41 | even | 10 | |||
3025.2.a.o.1.2 | 2 | 55.14 | even | 10 | |||
3520.2.a.bn.1.2 | 2 | 88.85 | odd | 10 | |||
3520.2.a.bo.1.1 | 2 | 88.19 | even | 10 | |||
4400.2.a.bn.1.1 | 2 | 220.19 | even | 10 | |||
4400.2.b.q.4049.2 | 4 | 220.107 | odd | 20 | |||
4400.2.b.q.4049.3 | 4 | 220.63 | odd | 20 | |||
5445.2.a.y.1.2 | 2 | 33.14 | odd | 10 | |||
7920.2.a.ch.1.2 | 2 | 132.107 | odd | 10 | |||
9295.2.a.g.1.1 | 2 | 143.129 | odd | 10 | |||
9680.2.a.bn.1.2 | 2 | 44.3 | odd | 10 |