Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.h.122.4 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.52434i | − | 1.26217i | −0.775714 | − | 0.631084i | \(-0.782610\pi\) | ||
0.775714 | − | 0.631084i | \(-0.217390\pi\) | |||||||
\(3\) | −2.68614 | + | 1.33591i | −0.895380 | + | 0.445302i | ||||
\(4\) | −2.37228 | −0.593070 | ||||||||
\(5\) | 0.792287i | 0.158457i | 0.996856 | + | 0.0792287i | \(0.0252457\pi\) | ||||
−0.996856 | + | 0.0792287i | \(0.974754\pi\) | |||||||
\(6\) | 3.37228 | + | 6.78073i | 0.562047 | + | 1.13012i | ||||
\(7\) | −6.74456 | −0.963509 | −0.481754 | − | 0.876306i | \(-0.660000\pi\) | ||||
−0.481754 | + | 0.876306i | \(0.660000\pi\) | |||||||
\(8\) | − | 4.10891i | − | 0.513614i | ||||||
\(9\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(10\) | 2.00000 | 0.200000 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.37228 | − | 3.16915i | 0.531023 | − | 0.264096i | ||||
\(13\) | −9.48913 | −0.729933 | −0.364966 | − | 0.931021i | \(-0.618920\pi\) | ||||
−0.364966 | + | 0.931021i | \(0.618920\pi\) | |||||||
\(14\) | 17.0256i | 1.21611i | ||||||||
\(15\) | −1.05842 | − | 2.12819i | −0.0705615 | − | 0.141880i | ||||
\(16\) | −19.8614 | −1.24134 | ||||||||
\(17\) | 29.2974i | 1.72338i | 0.507439 | + | 0.861688i | \(0.330592\pi\) | ||||
−0.507439 | + | 0.861688i | \(0.669408\pi\) | |||||||
\(18\) | −18.1168 | − | 13.7089i | −1.00649 | − | 0.761607i | ||||
\(19\) | 26.2337 | 1.38072 | 0.690360 | − | 0.723466i | \(-0.257452\pi\) | ||||
0.690360 | + | 0.723466i | \(0.257452\pi\) | |||||||
\(20\) | − | 1.87953i | − | 0.0939764i | ||||||
\(21\) | 18.1168 | − | 9.01011i | 0.862707 | − | 0.429053i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 26.9205i | 1.17046i | 0.810868 | + | 0.585229i | \(0.198995\pi\) | ||||
−0.810868 | + | 0.585229i | \(0.801005\pi\) | |||||||
\(24\) | 5.48913 | + | 11.0371i | 0.228714 | + | 0.459880i | ||||
\(25\) | 24.3723 | 0.974891 | ||||||||
\(26\) | 23.9538i | 0.921298i | ||||||||
\(27\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(28\) | 16.0000 | 0.571429 | ||||||||
\(29\) | 25.9431i | 0.894589i | 0.894387 | + | 0.447295i | \(0.147612\pi\) | ||||
−0.894387 | + | 0.447295i | \(0.852388\pi\) | |||||||
\(30\) | −5.37228 | + | 2.67181i | −0.179076 | + | 0.0890605i | ||||
\(31\) | −2.86141 | −0.0923034 | −0.0461517 | − | 0.998934i | \(-0.514696\pi\) | ||||
−0.0461517 | + | 0.998934i | \(0.514696\pi\) | |||||||
\(32\) | 33.7013i | 1.05316i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 73.9565 | 2.17519 | ||||||||
\(35\) | − | 5.34363i | − | 0.152675i | ||||||
\(36\) | −12.8832 | + | 17.0256i | −0.357865 | + | 0.472932i | ||||
\(37\) | −2.39403 | −0.0647035 | −0.0323518 | − | 0.999477i | \(-0.510300\pi\) | ||||
−0.0323518 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(38\) | − | 66.2227i | − | 1.74270i | ||||||
\(39\) | 25.4891 | − | 12.6766i | 0.653567 | − | 0.325041i | ||||
\(40\) | 3.25544 | 0.0813859 | ||||||||
\(41\) | 17.6155i | 0.429645i | 0.976653 | + | 0.214823i | \(0.0689174\pi\) | ||||
−0.976653 | + | 0.214823i | \(0.931083\pi\) | |||||||
\(42\) | −22.7446 | − | 45.7330i | −0.541537 | − | 1.08888i | ||||
\(43\) | −12.5109 | −0.290951 | −0.145475 | − | 0.989362i | \(-0.546471\pi\) | ||||
−0.145475 | + | 0.989362i | \(0.546471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.68614 | + | 4.30268i | 0.126359 | + | 0.0956150i | ||||
\(46\) | 67.9565 | 1.47732 | ||||||||
\(47\) | − | 41.6790i | − | 0.886788i | −0.896327 | − | 0.443394i | \(-0.853774\pi\) | ||
0.896327 | − | 0.443394i | \(-0.146226\pi\) | |||||||
\(48\) | 53.3505 | − | 26.5330i | 1.11147 | − | 0.552771i | ||||
\(49\) | −3.51087 | −0.0716505 | ||||||||
\(50\) | − | 61.5239i | − | 1.23048i | ||||||
\(51\) | −39.1386 | − | 78.6969i | −0.767423 | − | 1.54308i | ||||
\(52\) | 22.5109 | 0.432901 | ||||||||
\(53\) | 89.5865i | 1.69031i | 0.534520 | + | 0.845156i | \(0.320493\pi\) | ||||
−0.534520 | + | 0.845156i | \(0.679507\pi\) | |||||||
\(54\) | 66.9783 | + | 12.6217i | 1.24034 | + | 0.233735i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 27.7128i | 0.494872i | ||||||||
\(57\) | −70.4674 | + | 35.0458i | −1.23627 | + | 0.614838i | ||||
\(58\) | 65.4891 | 1.12912 | ||||||||
\(59\) | 14.7585i | 0.250144i | 0.992148 | + | 0.125072i | \(0.0399162\pi\) | ||||
−0.992148 | + | 0.125072i | \(0.960084\pi\) | |||||||
\(60\) | 2.51087 | + | 5.04868i | 0.0418479 | + | 0.0841446i | ||||
\(61\) | 63.4456 | 1.04009 | 0.520046 | − | 0.854138i | \(-0.325915\pi\) | ||||
0.520046 | + | 0.854138i | \(0.325915\pi\) | |||||||
\(62\) | 7.22316i | 0.116503i | ||||||||
\(63\) | −36.6277 | + | 48.4048i | −0.581392 | + | 0.768331i | ||||
\(64\) | 5.62772 | 0.0879331 | ||||||||
\(65\) | − | 7.51811i | − | 0.115663i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.3288 | −0.945206 | −0.472603 | − | 0.881276i | \(-0.656685\pi\) | ||||
−0.472603 | + | 0.881276i | \(0.656685\pi\) | |||||||
\(68\) | − | 69.5016i | − | 1.02208i | ||||||
\(69\) | −35.9633 | − | 72.3123i | −0.521208 | − | 1.04800i | ||||
\(70\) | −13.4891 | −0.192702 | ||||||||
\(71\) | − | 4.55134i | − | 0.0641034i | −0.999486 | − | 0.0320517i | \(-0.989796\pi\) | ||
0.999486 | − | 0.0320517i | \(-0.0102041\pi\) | |||||||
\(72\) | −29.4891 | − | 22.3143i | −0.409571 | − | 0.309921i | ||||
\(73\) | 53.7663 | 0.736525 | 0.368262 | − | 0.929722i | \(-0.379953\pi\) | ||||
0.368262 | + | 0.929722i | \(0.379953\pi\) | |||||||
\(74\) | 6.04334i | 0.0816668i | ||||||||
\(75\) | −65.4674 | + | 32.5591i | −0.872898 | + | 0.434121i | ||||
\(76\) | −62.2337 | −0.818864 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −32.0000 | − | 64.3432i | −0.410256 | − | 0.824912i | ||||
\(79\) | −55.6793 | −0.704801 | −0.352401 | − | 0.935849i | \(-0.614635\pi\) | ||||
−0.352401 | + | 0.935849i | \(0.614635\pi\) | |||||||
\(80\) | − | 15.7359i | − | 0.196699i | ||||||
\(81\) | −22.0149 | − | 77.9509i | −0.271789 | − | 0.962357i | ||||
\(82\) | 44.4674 | 0.542285 | ||||||||
\(83\) | 65.3378i | 0.787203i | 0.919281 | + | 0.393601i | \(0.128771\pi\) | ||||
−0.919281 | + | 0.393601i | \(0.871229\pi\) | |||||||
\(84\) | −42.9783 | + | 21.3745i | −0.511646 | + | 0.254459i | ||||
\(85\) | −23.2119 | −0.273082 | ||||||||
\(86\) | 31.5817i | 0.367229i | ||||||||
\(87\) | −34.6576 | − | 69.6868i | −0.398363 | − | 0.800998i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.1341i | − | 0.158810i | −0.996842 | − | 0.0794052i | \(-0.974698\pi\) | ||
0.996842 | − | 0.0794052i | \(-0.0253021\pi\) | |||||||
\(90\) | 10.8614 | − | 14.3537i | 0.120682 | − | 0.159486i | ||||
\(91\) | 64.0000 | 0.703297 | ||||||||
\(92\) | − | 63.8631i | − | 0.694164i | ||||||
\(93\) | 7.68614 | − | 3.82257i | 0.0826467 | − | 0.0411029i | ||||
\(94\) | −105.212 | −1.11928 | ||||||||
\(95\) | 20.7846i | 0.218785i | ||||||||
\(96\) | −45.0217 | − | 90.5263i | −0.468977 | − | 0.942982i | ||||
\(97\) | 149.285 | 1.53902 | 0.769512 | − | 0.638633i | \(-0.220500\pi\) | ||||
0.769512 | + | 0.638633i | \(0.220500\pi\) | |||||||
\(98\) | 8.86263i | 0.0904350i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −57.8179 | −0.578179 | ||||||||
\(101\) | 20.0096i | 0.198114i | 0.995082 | + | 0.0990572i | \(0.0315827\pi\) | ||||
−0.995082 | + | 0.0990572i | \(0.968417\pi\) | |||||||
\(102\) | −198.658 | + | 98.7990i | −1.94762 | + | 0.968618i | ||||
\(103\) | −180.424 | −1.75169 | −0.875844 | − | 0.482594i | \(-0.839695\pi\) | ||||
−0.875844 | + | 0.482594i | \(0.839695\pi\) | |||||||
\(104\) | 38.9900i | 0.374904i | ||||||||
\(105\) | 7.13859 | + | 14.3537i | 0.0679866 | + | 0.136702i | ||||
\(106\) | 226.147 | 2.13346 | ||||||||
\(107\) | − | 64.5283i | − | 0.603068i | −0.953455 | − | 0.301534i | \(-0.902501\pi\) | ||
0.953455 | − | 0.301534i | \(-0.0974987\pi\) | |||||||
\(108\) | 11.8614 | − | 62.9437i | 0.109828 | − | 0.582812i | ||||
\(109\) | −110.277 | −1.01172 | −0.505859 | − | 0.862616i | \(-0.668824\pi\) | ||||
−0.505859 | + | 0.862616i | \(0.668824\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.43070 | − | 3.19820i | 0.0579343 | − | 0.0288126i | ||||
\(112\) | 133.957 | 1.19604 | ||||||||
\(113\) | 125.239i | 1.10831i | 0.832412 | + | 0.554157i | \(0.186959\pi\) | ||||
−0.832412 | + | 0.554157i | \(0.813041\pi\) | |||||||
\(114\) | 88.4674 | + | 177.883i | 0.776030 | + | 1.56038i | ||||
\(115\) | −21.3288 | −0.185468 | ||||||||
\(116\) | − | 61.5443i | − | 0.530554i | ||||||
\(117\) | −51.5326 | + | 68.1022i | −0.440450 | + | 0.582070i | ||||
\(118\) | 37.2554 | 0.315724 | ||||||||
\(119\) | − | 197.598i | − | 1.66049i | ||||||
\(120\) | −8.74456 | + | 4.34896i | −0.0728714 | + | 0.0362414i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 160.158i | − | 1.31277i | ||||||
\(123\) | −23.5326 | − | 47.3176i | −0.191322 | − | 0.384696i | ||||
\(124\) | 6.78806 | 0.0547424 | ||||||||
\(125\) | 39.1170i | 0.312936i | ||||||||
\(126\) | 122.190 | + | 92.4607i | 0.969763 | + | 0.733815i | ||||
\(127\) | −192.848 | −1.51849 | −0.759243 | − | 0.650807i | \(-0.774431\pi\) | ||||
−0.759243 | + | 0.650807i | \(0.774431\pi\) | |||||||
\(128\) | 120.599i | 0.942178i | ||||||||
\(129\) | 33.6060 | − | 16.7134i | 0.260511 | − | 0.129561i | ||||
\(130\) | −18.9783 | −0.145987 | ||||||||
\(131\) | − | 106.098i | − | 0.809905i | −0.914338 | − | 0.404952i | \(-0.867288\pi\) | ||
0.914338 | − | 0.404952i | \(-0.132712\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −176.935 | −1.33034 | ||||||||
\(134\) | 159.863i | 1.19301i | ||||||||
\(135\) | −21.0217 | − | 3.96143i | −0.155717 | − | 0.0293440i | ||||
\(136\) | 120.380 | 0.885150 | ||||||||
\(137\) | 195.297i | 1.42552i | 0.701407 | + | 0.712761i | \(0.252556\pi\) | ||||
−0.701407 | + | 0.712761i | \(0.747444\pi\) | |||||||
\(138\) | −182.541 | + | 90.7836i | −1.32276 | + | 0.657852i | ||||
\(139\) | −6.93475 | −0.0498903 | −0.0249452 | − | 0.999689i | \(-0.507941\pi\) | ||||
−0.0249452 | + | 0.999689i | \(0.507941\pi\) | |||||||
\(140\) | 12.6766i | 0.0905471i | ||||||||
\(141\) | 55.6793 | + | 111.956i | 0.394889 | + | 0.794012i | ||||
\(142\) | −11.4891 | −0.0809093 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −107.861 | + | 142.543i | −0.749038 | + | 0.989880i | ||||
\(145\) | −20.5544 | −0.141754 | ||||||||
\(146\) | − | 135.724i | − | 0.929619i | ||||||
\(147\) | 9.43070 | − | 4.69020i | 0.0641544 | − | 0.0319061i | ||||
\(148\) | 5.67931 | 0.0383737 | ||||||||
\(149\) | 67.6975i | 0.454345i | 0.973854 | + | 0.227173i | \(0.0729482\pi\) | ||||
−0.973854 | + | 0.227173i | \(0.927052\pi\) | |||||||
\(150\) | 82.1902 | + | 165.262i | 0.547935 | + | 1.10175i | ||||
\(151\) | −28.2337 | −0.186978 | −0.0934890 | − | 0.995620i | \(-0.529802\pi\) | ||||
−0.0934890 | + | 0.995620i | \(0.529802\pi\) | |||||||
\(152\) | − | 107.792i | − | 0.709157i | ||||||
\(153\) | 210.264 | + | 159.105i | 1.37427 | + | 1.03990i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.26706i | − | 0.0146262i | ||||||
\(156\) | −60.4674 | + | 30.0724i | −0.387611 | + | 0.192772i | ||||
\(157\) | −67.7962 | −0.431823 | −0.215911 | − | 0.976413i | \(-0.569272\pi\) | ||||
−0.215911 | + | 0.976413i | \(0.569272\pi\) | |||||||
\(158\) | 140.553i | 0.889578i | ||||||||
\(159\) | −119.679 | − | 240.642i | −0.752700 | − | 1.51347i | ||||
\(160\) | −26.7011 | −0.166882 | ||||||||
\(161\) | − | 181.567i | − | 1.12775i | ||||||
\(162\) | −196.774 | + | 55.5731i | −1.21466 | + | 0.343044i | ||||
\(163\) | −67.8695 | −0.416377 | −0.208189 | − | 0.978089i | \(-0.566757\pi\) | ||||
−0.208189 | + | 0.978089i | \(0.566757\pi\) | |||||||
\(164\) | − | 41.7888i | − | 0.254810i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 164.935 | 0.993583 | ||||||||
\(167\) | 56.2351i | 0.336737i | 0.985724 | + | 0.168369i | \(0.0538499\pi\) | ||||
−0.985724 | + | 0.168369i | \(0.946150\pi\) | |||||||
\(168\) | −37.0217 | − | 74.4405i | −0.220368 | − | 0.443098i | ||||
\(169\) | −78.9565 | −0.467198 | ||||||||
\(170\) | 58.5948i | 0.344675i | ||||||||
\(171\) | 142.467 | − | 188.276i | 0.833143 | − | 1.10103i | ||||
\(172\) | 29.6793 | 0.172554 | ||||||||
\(173\) | − | 224.536i | − | 1.29789i | −0.760833 | − | 0.648947i | \(-0.775209\pi\) | ||
0.760833 | − | 0.648947i | \(-0.224791\pi\) | |||||||
\(174\) | −175.913 | + | 87.4874i | −1.01099 | + | 0.502801i | ||||
\(175\) | −164.380 | −0.939316 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.7160 | − | 39.6434i | −0.111390 | − | 0.223974i | ||||
\(178\) | −35.6793 | −0.200446 | ||||||||
\(179\) | 140.461i | 0.784697i | 0.919817 | + | 0.392349i | \(0.128337\pi\) | ||||
−0.919817 | + | 0.392349i | \(0.871663\pi\) | |||||||
\(180\) | −13.4891 | − | 10.2072i | −0.0749396 | − | 0.0567064i | ||||
\(181\) | 130.861 | 0.722991 | 0.361496 | − | 0.932374i | \(-0.382266\pi\) | ||||
0.361496 | + | 0.932374i | \(0.382266\pi\) | |||||||
\(182\) | − | 161.558i | − | 0.887679i | ||||||
\(183\) | −170.424 | + | 84.7575i | −0.931278 | + | 0.463156i | ||||
\(184\) | 110.614 | 0.601163 | ||||||||
\(185\) | − | 1.89676i | − | 0.0102528i | ||||||
\(186\) | −9.64947 | − | 19.4024i | −0.0518789 | − | 0.104314i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 98.8744i | 0.525928i | ||||||||
\(189\) | 33.7228 | − | 178.953i | 0.178428 | − | 0.946844i | ||||
\(190\) | 52.4674 | 0.276144 | ||||||||
\(191\) | − | 351.401i | − | 1.83979i | −0.392160 | − | 0.919897i | \(-0.628272\pi\) | ||
0.392160 | − | 0.919897i | \(-0.371728\pi\) | |||||||
\(192\) | −15.1168 | + | 7.51811i | −0.0787336 | + | 0.0391568i | ||||
\(193\) | 245.505 | 1.27205 | 0.636024 | − | 0.771669i | \(-0.280578\pi\) | ||||
0.636024 | + | 0.771669i | \(0.280578\pi\) | |||||||
\(194\) | − | 376.846i | − | 1.94251i | ||||||
\(195\) | 10.0435 | + | 20.1947i | 0.0515051 | + | 0.103563i | ||||
\(196\) | 8.32878 | 0.0424938 | ||||||||
\(197\) | − | 6.15315i | − | 0.0312343i | −0.999878 | − | 0.0156171i | \(-0.995029\pi\) | ||
0.999878 | − | 0.0156171i | \(-0.00497129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 193.272 | 0.971214 | 0.485607 | − | 0.874177i | \(-0.338599\pi\) | ||||
0.485607 | + | 0.874177i | \(0.338599\pi\) | |||||||
\(200\) | − | 100.144i | − | 0.500718i | ||||||
\(201\) | 170.110 | − | 84.6014i | 0.846318 | − | 0.420902i | ||||
\(202\) | 50.5109 | 0.250054 | ||||||||
\(203\) | − | 174.975i | − | 0.861945i | ||||||
\(204\) | 92.8478 | + | 186.691i | 0.455136 | + | 0.915153i | ||||
\(205\) | −13.9565 | −0.0680805 | ||||||||
\(206\) | 455.451i | 2.21093i | ||||||||
\(207\) | 193.205 | + | 146.197i | 0.933358 | + | 0.706268i | ||||
\(208\) | 188.467 | 0.906093 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 36.2337 | − | 18.0202i | 0.172541 | − | 0.0858106i | ||||
\(211\) | 106.788 | 0.506105 | 0.253052 | − | 0.967453i | \(-0.418566\pi\) | ||||
0.253052 | + | 0.967453i | \(0.418566\pi\) | |||||||
\(212\) | − | 212.524i | − | 1.00247i | ||||||
\(213\) | 6.08017 | + | 12.2255i | 0.0285454 | + | 0.0573969i | ||||
\(214\) | −162.891 | −0.761174 | ||||||||
\(215\) | − | 9.91220i | − | 0.0461033i | ||||||
\(216\) | 109.022 | + | 20.5446i | 0.504730 | + | 0.0951137i | ||||
\(217\) | 19.2989 | 0.0889352 | ||||||||
\(218\) | 278.377i | 1.27696i | ||||||||
\(219\) | −144.424 | + | 71.8268i | −0.659470 | + | 0.327976i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 278.007i | − | 1.25795i | ||||||
\(222\) | −8.07335 | − | 16.2333i | −0.0363664 | − | 0.0731228i | ||||
\(223\) | 76.7309 | 0.344085 | 0.172042 | − | 0.985090i | \(-0.444963\pi\) | ||||
0.172042 | + | 0.985090i | \(0.444963\pi\) | |||||||
\(224\) | − | 227.300i | − | 1.01473i | ||||||
\(225\) | 132.359 | − | 174.917i | 0.588261 | − | 0.777408i | ||||
\(226\) | 316.147 | 1.39888 | ||||||||
\(227\) | − | 48.2433i | − | 0.212526i | −0.994338 | − | 0.106263i | \(-0.966111\pi\) | ||
0.994338 | − | 0.106263i | \(-0.0338885\pi\) | |||||||
\(228\) | 167.168 | − | 83.1384i | 0.733195 | − | 0.364642i | ||||
\(229\) | −15.4158 | −0.0673178 | −0.0336589 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336589 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(230\) | 53.8411i | 0.234092i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 106.598 | 0.459474 | ||||||||
\(233\) | − | 173.205i | − | 0.743369i | −0.928359 | − | 0.371685i | \(-0.878780\pi\) | ||
0.928359 | − | 0.371685i | \(-0.121220\pi\) | |||||||
\(234\) | 171.913 | + | 130.086i | 0.734671 | + | 0.555922i | ||||
\(235\) | 33.0217 | 0.140518 | ||||||||
\(236\) | − | 35.0113i | − | 0.148353i | ||||||
\(237\) | 149.562 | − | 74.3824i | 0.631065 | − | 0.313850i | ||||
\(238\) | −498.804 | −2.09582 | ||||||||
\(239\) | 296.397i | 1.24016i | 0.784540 | + | 0.620078i | \(0.212899\pi\) | ||||
−0.784540 | + | 0.620078i | \(0.787101\pi\) | |||||||
\(240\) | 21.0217 | + | 42.2689i | 0.0875906 | + | 0.176121i | ||||
\(241\) | −46.7011 | −0.193780 | −0.0968902 | − | 0.995295i | \(-0.530890\pi\) | ||||
−0.0968902 | + | 0.995295i | \(0.530890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 163.270 | + | 179.977i | 0.671894 | + | 0.740647i | ||||
\(244\) | −150.511 | −0.616848 | ||||||||
\(245\) | − | 2.78162i | − | 0.0113536i | ||||||
\(246\) | −119.446 | + | 59.4043i | −0.485551 | + | 0.241481i | ||||
\(247\) | −248.935 | −1.00783 | ||||||||
\(248\) | 11.7573i | 0.0474083i | ||||||||
\(249\) | −87.2853 | − | 175.507i | −0.350543 | − | 0.704846i | ||||
\(250\) | 98.7446 | 0.394978 | ||||||||
\(251\) | − | 207.788i | − | 0.827841i | −0.910313 | − | 0.413920i | \(-0.864159\pi\) | ||
0.910313 | − | 0.413920i | \(-0.135841\pi\) | |||||||
\(252\) | 86.8913 | − | 114.830i | 0.344807 | − | 0.455674i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 486.813i | 1.91659i | ||||||||
\(255\) | 62.3505 | − | 31.0090i | 0.244512 | − | 0.121604i | ||||
\(256\) | 326.943 | 1.27712 | ||||||||
\(257\) | 199.738i | 0.777191i | 0.921408 | + | 0.388595i | \(0.127040\pi\) | ||||
−0.921408 | + | 0.388595i | \(0.872960\pi\) | |||||||
\(258\) | −42.1902 | − | 84.8328i | −0.163528 | − | 0.328809i | ||||
\(259\) | 16.1467 | 0.0623424 | ||||||||
\(260\) | 17.8351i | 0.0685964i | ||||||||
\(261\) | 186.190 | + | 140.889i | 0.713372 | + | 0.539805i | ||||
\(262\) | −267.826 | −1.02224 | ||||||||
\(263\) | 99.7592i | 0.379313i | 0.981851 | + | 0.189656i | \(0.0607374\pi\) | ||||
−0.981851 | + | 0.189656i | \(0.939263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −70.9783 | −0.267842 | ||||||||
\(266\) | 446.643i | 1.67911i | ||||||||
\(267\) | 18.8819 | + | 37.9663i | 0.0707187 | + | 0.142196i | ||||
\(268\) | 150.234 | 0.560573 | ||||||||
\(269\) | 50.3770i | 0.187275i | 0.995606 | + | 0.0936375i | \(0.0298495\pi\) | ||||
−0.995606 | + | 0.0936375i | \(0.970151\pi\) | |||||||
\(270\) | −10.0000 | + | 53.0660i | −0.0370370 | + | 0.196541i | ||||
\(271\) | 124.380 | 0.458968 | 0.229484 | − | 0.973312i | \(-0.426296\pi\) | ||||
0.229484 | + | 0.973312i | \(0.426296\pi\) | |||||||
\(272\) | − | 581.887i | − | 2.13929i | ||||||
\(273\) | −171.913 | + | 85.4981i | −0.629718 | + | 0.313180i | ||||
\(274\) | 492.994 | 1.79925 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 85.3151 | + | 171.545i | 0.309113 | + | 0.621540i | ||||
\(277\) | −293.723 | −1.06037 | −0.530186 | − | 0.847882i | \(-0.677878\pi\) | ||||
−0.530186 | + | 0.847882i | \(0.677878\pi\) | |||||||
\(278\) | 17.5057i | 0.0629700i | ||||||||
\(279\) | −15.5395 | + | 20.5359i | −0.0556970 | + | 0.0736055i | ||||
\(280\) | −21.9565 | −0.0784161 | ||||||||
\(281\) | 263.676i | 0.938350i | 0.883105 | + | 0.469175i | \(0.155449\pi\) | ||||
−0.883105 | + | 0.469175i | \(0.844551\pi\) | |||||||
\(282\) | 282.614 | − | 140.553i | 1.00218 | − | 0.498416i | ||||
\(283\) | −398.788 | −1.40915 | −0.704573 | − | 0.709632i | \(-0.748861\pi\) | ||||
−0.704573 | + | 0.709632i | \(0.748861\pi\) | |||||||
\(284\) | 10.7971i | 0.0380178i | ||||||||
\(285\) | −27.7663 | − | 55.8304i | −0.0974257 | − | 0.195896i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 118.809i | − | 0.413967i | ||||||
\(288\) | 241.870 | + | 183.022i | 0.839825 | + | 0.635491i | ||||
\(289\) | −569.337 | −1.97002 | ||||||||
\(290\) | 51.8862i | 0.178918i | ||||||||
\(291\) | −401.001 | + | 199.431i | −1.37801 | + | 0.685331i | ||||
\(292\) | −127.549 | −0.436811 | ||||||||
\(293\) | 348.839i | 1.19058i | 0.803512 | + | 0.595288i | \(0.202962\pi\) | ||||
−0.803512 | + | 0.595288i | \(0.797038\pi\) | |||||||
\(294\) | −11.8397 | − | 23.8063i | −0.0402709 | − | 0.0809737i | ||||
\(295\) | −11.6930 | −0.0396372 | ||||||||
\(296\) | 9.83686i | 0.0332326i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 170.891 | 0.573461 | ||||||||
\(299\) | − | 255.452i | − | 0.854355i | ||||||
\(300\) | 155.307 | − | 77.2394i | 0.517690 | − | 0.257465i | ||||
\(301\) | 84.3804 | 0.280333 | ||||||||
\(302\) | 71.2714i | 0.235998i | ||||||||
\(303\) | −26.7309 | − | 53.7485i | −0.0882208 | − | 0.177388i | ||||
\(304\) | −521.038 | −1.71394 | ||||||||
\(305\) | 50.2671i | 0.164810i | ||||||||
\(306\) | 401.636 | − | 530.776i | 1.31254 | − | 1.73456i | ||||
\(307\) | 398.527 | 1.29813 | 0.649067 | − | 0.760731i | \(-0.275160\pi\) | ||||
0.649067 | + | 0.760731i | \(0.275160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 484.644 | − | 241.030i | 1.56843 | − | 0.780031i | ||||
\(310\) | −5.72281 | −0.0184607 | ||||||||
\(311\) | 440.346i | 1.41590i | 0.706261 | + | 0.707951i | \(0.250380\pi\) | ||||
−0.706261 | + | 0.707951i | \(0.749620\pi\) | |||||||
\(312\) | −52.0870 | − | 104.733i | −0.166946 | − | 0.335681i | ||||
\(313\) | 529.899 | 1.69297 | 0.846485 | − | 0.532413i | \(-0.178715\pi\) | ||||
0.846485 | + | 0.532413i | \(0.178715\pi\) | |||||||
\(314\) | 171.140i | 0.545033i | ||||||||
\(315\) | −38.3505 | − | 29.0197i | −0.121748 | − | 0.0921259i | ||||
\(316\) | 132.087 | 0.417997 | ||||||||
\(317\) | − | 368.426i | − | 1.16223i | −0.813822 | − | 0.581114i | \(-0.802617\pi\) | ||
0.813822 | − | 0.581114i | \(-0.197383\pi\) | |||||||
\(318\) | −607.462 | + | 302.111i | −1.91026 | + | 0.950035i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.45877i | 0.0139337i | ||||||||
\(321\) | 86.2038 | + | 173.332i | 0.268548 | + | 0.539975i | ||||
\(322\) | −458.337 | −1.42341 | ||||||||
\(323\) | 768.579i | 2.37950i | ||||||||
\(324\) | 52.2256 | + | 184.921i | 0.161190 | + | 0.570745i | ||||
\(325\) | −231.272 | −0.711605 | ||||||||
\(326\) | 171.326i | 0.525539i | ||||||||
\(327\) | 296.220 | − | 147.320i | 0.905872 | − | 0.450520i | ||||
\(328\) | 72.3804 | 0.220672 | ||||||||
\(329\) | 281.107i | 0.854428i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −115.649 | −0.349394 | −0.174697 | − | 0.984622i | \(-0.555895\pi\) | ||||
−0.174697 | + | 0.984622i | \(0.555895\pi\) | |||||||
\(332\) | − | 155.000i | − | 0.466867i | ||||||
\(333\) | −13.0013 | + | 17.1816i | −0.0390429 | + | 0.0515965i | ||||
\(334\) | 141.957 | 0.425019 | ||||||||
\(335\) | − | 50.1746i | − | 0.149775i | ||||||
\(336\) | −359.826 | + | 178.953i | −1.07091 | + | 0.532600i | ||||
\(337\) | 53.2716 | 0.158076 | 0.0790380 | − | 0.996872i | \(-0.474815\pi\) | ||||
0.0790380 | + | 0.996872i | \(0.474815\pi\) | |||||||
\(338\) | 199.313i | 0.589683i | ||||||||
\(339\) | −167.308 | − | 336.411i | −0.493535 | − | 0.992362i | ||||
\(340\) | 55.0652 | 0.161957 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −475.272 | − | 359.636i | −1.38968 | − | 1.05157i | ||||
\(343\) | 354.163 | 1.03254 | ||||||||
\(344\) | 51.4061i | 0.149436i | ||||||||
\(345\) | 57.2921 | − | 28.4933i | 0.166064 | − | 0.0825892i | ||||
\(346\) | −566.804 | −1.63816 | ||||||||
\(347\) | − | 11.2082i | − | 0.0323004i | −0.999870 | − | 0.0161502i | \(-0.994859\pi\) | ||
0.999870 | − | 0.0161502i | \(-0.00514099\pi\) | |||||||
\(348\) | 82.2175 | + | 165.317i | 0.236257 | + | 0.475048i | ||||
\(349\) | 214.016 | 0.613227 | 0.306613 | − | 0.951834i | \(-0.400804\pi\) | ||||
0.306613 | + | 0.951834i | \(0.400804\pi\) | |||||||
\(350\) | 414.952i | 1.18558i | ||||||||
\(351\) | 47.4456 | − | 251.775i | 0.135173 | − | 0.717308i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 531.528i | 1.50574i | 0.658167 | + | 0.752872i | \(0.271332\pi\) | ||||
−0.658167 | + | 0.752872i | \(0.728668\pi\) | |||||||
\(354\) | −100.073 | + | 49.7698i | −0.282693 | + | 0.140593i | ||||
\(355\) | 3.60597 | 0.0101577 | ||||||||
\(356\) | 33.5301i | 0.0941858i | ||||||||
\(357\) | 263.973 | + | 530.776i | 0.739419 | + | 1.48677i | ||||
\(358\) | 354.571 | 0.990421 | ||||||||
\(359\) | 175.194i | 0.488007i | 0.969774 | + | 0.244003i | \(0.0784608\pi\) | ||||
−0.969774 | + | 0.244003i | \(0.921539\pi\) | |||||||
\(360\) | 17.6793 | − | 23.3639i | 0.0491092 | − | 0.0648996i | ||||
\(361\) | 327.206 | 0.906389 | ||||||||
\(362\) | − | 330.338i | − | 0.912537i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −151.826 | −0.417104 | ||||||||
\(365\) | 42.5983i | 0.116708i | ||||||||
\(366\) | 213.957 | + | 430.207i | 0.584581 | + | 1.17543i | ||||
\(367\) | 139.035 | 0.378843 | 0.189422 | − | 0.981896i | \(-0.439339\pi\) | ||||
0.189422 | + | 0.981896i | \(0.439339\pi\) | |||||||
\(368\) | − | 534.680i | − | 1.45293i | ||||||
\(369\) | 126.424 | + | 95.6643i | 0.342612 | + | 0.259253i | ||||
\(370\) | −4.78806 | −0.0129407 | ||||||||
\(371\) | − | 604.222i | − | 1.62863i | ||||||
\(372\) | −18.2337 | + | 9.06822i | −0.0490153 | + | 0.0243769i | ||||
\(373\) | −149.081 | −0.399682 | −0.199841 | − | 0.979828i | \(-0.564043\pi\) | ||||
−0.199841 | + | 0.979828i | \(0.564043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −52.2567 | − | 105.074i | −0.139351 | − | 0.280197i | ||||
\(376\) | −171.255 | −0.455467 | ||||||||
\(377\) | − | 246.177i | − | 0.652990i | ||||||
\(378\) | −451.739 | − | 85.1278i | −1.19508 | − | 0.225206i | ||||
\(379\) | 270.394 | 0.713441 | 0.356720 | − | 0.934211i | \(-0.383895\pi\) | ||||
0.356720 | + | 0.934211i | \(0.383895\pi\) | |||||||
\(380\) | − | 49.3069i | − | 0.129755i | ||||||
\(381\) | 518.016 | − | 257.627i | 1.35962 | − | 0.676186i | ||||
\(382\) | −887.054 | −2.32213 | ||||||||
\(383\) | 631.801i | 1.64961i | 0.565416 | + | 0.824806i | \(0.308716\pi\) | ||||
−0.565416 | + | 0.824806i | \(0.691284\pi\) | |||||||
\(384\) | −161.109 | − | 323.945i | −0.419554 | − | 0.843607i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 619.738i | − | 1.60554i | ||||||
\(387\) | −67.9428 | + | 89.7889i | −0.175563 | + | 0.232013i | ||||
\(388\) | −354.147 | −0.912749 | ||||||||
\(389\) | − | 459.996i | − | 1.18251i | −0.806485 | − | 0.591254i | \(-0.798633\pi\) | ||
0.806485 | − | 0.591254i | \(-0.201367\pi\) | |||||||
\(390\) | 50.9783 | − | 25.3532i | 0.130713 | − | 0.0650082i | ||||
\(391\) | −788.701 | −2.01714 | ||||||||
\(392\) | 14.4259i | 0.0368007i | ||||||||
\(393\) | 141.736 | + | 284.993i | 0.360653 | + | 0.725173i | ||||
\(394\) | −15.5326 | −0.0394229 | ||||||||
\(395\) | − | 44.1140i | − | 0.111681i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −561.272 | −1.41378 | −0.706891 | − | 0.707322i | \(-0.749903\pi\) | ||||
−0.706891 | + | 0.707322i | \(0.749903\pi\) | |||||||
\(398\) | − | 487.883i | − | 1.22584i | ||||||
\(399\) | 475.272 | − | 236.368i | 1.19116 | − | 0.592402i | ||||
\(400\) | −484.068 | −1.21017 | ||||||||
\(401\) | 179.845i | 0.448491i | 0.974533 | + | 0.224245i | \(0.0719917\pi\) | ||||
−0.974533 | + | 0.224245i | \(0.928008\pi\) | |||||||
\(402\) | −213.562 | − | 429.415i | −0.531250 | − | 1.06820i | ||||
\(403\) | 27.1522 | 0.0673753 | ||||||||
\(404\) | − | 47.4683i | − | 0.117496i | ||||||
\(405\) | 61.7595 | − | 17.4421i | 0.152493 | − | 0.0430670i | ||||
\(406\) | −441.696 | −1.08792 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −323.359 | + | 160.817i | −0.792546 | + | 0.394159i | ||||
\(409\) | −135.696 | −0.331774 | −0.165887 | − | 0.986145i | \(-0.553049\pi\) | ||||
−0.165887 | + | 0.986145i | \(0.553049\pi\) | |||||||
\(410\) | 35.2309i | 0.0859291i | ||||||||
\(411\) | −260.898 | − | 524.594i | −0.634789 | − | 1.27638i | ||||
\(412\) | 428.016 | 1.03887 | ||||||||
\(413\) | − | 99.5396i | − | 0.241016i | ||||||
\(414\) | 369.052 | − | 487.715i | 0.891429 | − | 1.17806i | ||||
\(415\) | −51.7663 | −0.124738 | ||||||||
\(416\) | − | 319.795i | − | 0.768739i | ||||||
\(417\) | 18.6277 | − | 9.26419i | 0.0446708 | − | 0.0222163i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 50.3361i | 0.120134i | 0.998194 | + | 0.0600669i | \(0.0191314\pi\) | ||||
−0.998194 | + | 0.0600669i | \(0.980869\pi\) | |||||||
\(420\) | −16.9348 | − | 34.0511i | −0.0403208 | − | 0.0810741i | ||||
\(421\) | −52.6849 | −0.125142 | −0.0625711 | − | 0.998041i | \(-0.519930\pi\) | ||||
−0.0625711 | + | 0.998041i | \(0.519930\pi\) | |||||||
\(422\) | − | 269.569i | − | 0.638789i | ||||||
\(423\) | −299.125 | − | 226.346i | −0.707151 | − | 0.535098i | ||||
\(424\) | 368.103 | 0.868168 | ||||||||
\(425\) | 714.044i | 1.68010i | ||||||||
\(426\) | 30.8614 | − | 15.3484i | 0.0724446 | − | 0.0360291i | ||||
\(427\) | −427.913 | −1.00214 | ||||||||
\(428\) | 153.079i | 0.357662i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.0217 | −0.0581901 | ||||||||
\(431\) | 496.807i | 1.15268i | 0.817209 | + | 0.576342i | \(0.195520\pi\) | ||||
−0.817209 | + | 0.576342i | \(0.804480\pi\) | |||||||
\(432\) | 99.3070 | − | 526.983i | 0.229877 | − | 1.21987i | ||||
\(433\) | 515.622 | 1.19081 | 0.595407 | − | 0.803424i | \(-0.296991\pi\) | ||||
0.595407 | + | 0.803424i | \(0.296991\pi\) | |||||||
\(434\) | − | 48.7170i | − | 0.112251i | ||||||
\(435\) | 55.2119 | − | 27.4587i | 0.126924 | − | 0.0631235i | ||||
\(436\) | 261.609 | 0.600020 | ||||||||
\(437\) | 706.225i | 1.61607i | ||||||||
\(438\) | 181.315 | + | 364.575i | 0.413961 | + | 0.832362i | ||||
\(439\) | 25.1087 | 0.0571953 | 0.0285977 | − | 0.999591i | \(-0.490896\pi\) | ||||
0.0285977 | + | 0.999591i | \(0.490896\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.0665 | + | 25.1971i | −0.0432347 | + | 0.0571363i | ||||
\(442\) | −701.783 | −1.58774 | ||||||||
\(443\) | − | 870.420i | − | 1.96483i | −0.186711 | − | 0.982415i | \(-0.559783\pi\) | ||
0.186711 | − | 0.982415i | \(-0.440217\pi\) | |||||||
\(444\) | −15.2554 | + | 7.58704i | −0.0343591 | + | 0.0170879i | ||||
\(445\) | 11.1983 | 0.0251647 | ||||||||
\(446\) | − | 193.695i | − | 0.434293i | ||||||
\(447\) | −90.4375 | − | 181.845i | −0.202321 | − | 0.406812i | ||||
\(448\) | −37.9565 | −0.0847243 | ||||||||
\(449\) | 575.642i | 1.28205i | 0.767519 | + | 0.641026i | \(0.221491\pi\) | ||||
−0.767519 | + | 0.641026i | \(0.778509\pi\) | |||||||
\(450\) | −441.549 | − | 334.118i | −0.981220 | − | 0.742484i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 297.103i | − | 0.657308i | ||||||
\(453\) | 75.8397 | − | 37.7176i | 0.167416 | − | 0.0832618i | ||||
\(454\) | −121.783 | −0.268243 | ||||||||
\(455\) | 50.7064i | 0.111443i | ||||||||
\(456\) | 144.000 | + | 289.544i | 0.315789 | + | 0.634965i | ||||
\(457\) | −25.5923 | −0.0560007 | −0.0280003 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280003 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(458\) | 38.9146i | 0.0849665i | ||||||||
\(459\) | −777.348 | − | 146.487i | −1.69357 | − | 0.319144i | ||||
\(460\) | 50.5979 | 0.109995 | ||||||||
\(461\) | − | 289.365i | − | 0.627691i | −0.949474 | − | 0.313845i | \(-0.898383\pi\) | ||
0.949474 | − | 0.313845i | \(-0.101617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −201.052 | −0.434237 | −0.217118 | − | 0.976145i | \(-0.569666\pi\) | ||||
−0.217118 | + | 0.976145i | \(0.569666\pi\) | |||||||
\(464\) | − | 515.266i | − | 1.11049i | ||||||
\(465\) | 3.02858 | + | 6.08963i | 0.00651307 | + | 0.0130960i | ||||
\(466\) | −437.228 | −0.938258 | ||||||||
\(467\) | − | 110.319i | − | 0.236230i | −0.993000 | − | 0.118115i | \(-0.962315\pi\) | ||
0.993000 | − | 0.118115i | \(-0.0376852\pi\) | |||||||
\(468\) | 122.250 | − | 161.558i | 0.261218 | − | 0.345209i | ||||
\(469\) | 427.125 | 0.910714 | ||||||||
\(470\) | − | 83.3581i | − | 0.177358i | ||||||
\(471\) | 182.110 | − | 90.5694i | 0.386645 | − | 0.192292i | ||||
\(472\) | 60.6414 | 0.128477 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −187.766 | − | 377.546i | −0.396131 | − | 0.796511i | ||||
\(475\) | 639.375 | 1.34605 | ||||||||
\(476\) | 468.758i | 0.984786i | ||||||||
\(477\) | 642.951 | + | 486.518i | 1.34791 | + | 1.01995i | ||||
\(478\) | 748.206 | 1.56529 | ||||||||
\(479\) | − | 683.532i | − | 1.42700i | −0.700656 | − | 0.713499i | \(-0.747109\pi\) | ||
0.700656 | − | 0.713499i | \(-0.252891\pi\) | |||||||
\(480\) | 71.7228 | − | 35.6701i | 0.149423 | − | 0.0743128i | ||||
\(481\) | 22.7173 | 0.0472292 | ||||||||
\(482\) | 117.889i | 0.244584i | ||||||||
\(483\) | 242.557 | + | 487.715i | 0.502188 | + | 1.00976i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 118.277i | 0.243870i | ||||||||
\(486\) | 454.323 | − | 412.150i | 0.934821 | − | 0.848044i | ||||
\(487\) | −130.101 | −0.267147 | −0.133574 | − | 0.991039i | \(-0.542645\pi\) | ||||
−0.133574 | + | 0.991039i | \(0.542645\pi\) | |||||||
\(488\) | − | 260.692i | − | 0.534206i | ||||||
\(489\) | 182.307 | − | 90.6674i | 0.372816 | − | 0.185414i | ||||
\(490\) | −7.02175 | −0.0143301 | ||||||||
\(491\) | − | 796.580i | − | 1.62236i | −0.584795 | − | 0.811181i | \(-0.698825\pi\) | ||
0.584795 | − | 0.811181i | \(-0.301175\pi\) | |||||||
\(492\) | 55.8260 | + | 112.251i | 0.113467 | + | 0.228152i | ||||
\(493\) | −760.065 | −1.54171 | ||||||||
\(494\) | 628.395i | 1.27206i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 56.8316 | 0.114580 | ||||||||
\(497\) | 30.6968i | 0.0617642i | ||||||||
\(498\) | −443.038 | + | 220.338i | −0.889634 | + | 0.442445i | ||||
\(499\) | 490.032 | 0.982029 | 0.491014 | − | 0.871151i | \(-0.336626\pi\) | ||||
0.491014 | + | 0.871151i | \(0.336626\pi\) | |||||||
\(500\) | − | 92.7966i | − | 0.185593i | ||||||
\(501\) | −75.1249 | − | 151.056i | −0.149950 | − | 0.301508i | ||||
\(502\) | −524.527 | −1.04487 | ||||||||
\(503\) | − | 283.281i | − | 0.563183i | −0.959534 | − | 0.281592i | \(-0.909138\pi\) | ||
0.959534 | − | 0.281592i | \(-0.0908624\pi\) | |||||||
\(504\) | 198.891 | + | 150.500i | 0.394626 | + | 0.298611i | ||||
\(505\) | −15.8533 | −0.0313927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 212.088 | − | 105.479i | 0.418320 | − | 0.208045i | ||||
\(508\) | 457.489 | 0.900569 | ||||||||
\(509\) | − | 243.650i | − | 0.478683i | −0.970935 | − | 0.239342i | \(-0.923068\pi\) | ||
0.970935 | − | 0.239342i | \(-0.0769316\pi\) | |||||||
\(510\) | −78.2772 | − | 157.394i | −0.153485 | − | 0.308615i | ||||
\(511\) | −362.630 | −0.709648 | ||||||||
\(512\) | − | 342.919i | − | 0.669764i | ||||||
\(513\) | −131.168 | + | 696.058i | −0.255689 | + | 1.35684i | ||||
\(514\) | 504.206 | 0.980946 | ||||||||
\(515\) | − | 142.947i | − | 0.277568i | ||||||
\(516\) | −79.7228 | + | 39.6488i | −0.154502 | + | 0.0768388i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 40.7597i | − | 0.0786867i | ||||||
\(519\) | 299.959 | + | 603.135i | 0.577956 | + | 1.16211i | ||||
\(520\) | −30.8913 | −0.0594063 | ||||||||
\(521\) | 376.274i | 0.722215i | 0.932524 | + | 0.361107i | \(0.117601\pi\) | ||||
−0.932524 | + | 0.361107i | \(0.882399\pi\) | |||||||
\(522\) | 355.652 | − | 470.007i | 0.681326 | − | 0.900396i | ||||
\(523\) | −555.842 | −1.06280 | −0.531398 | − | 0.847122i | \(-0.678333\pi\) | ||||
−0.531398 | + | 0.847122i | \(0.678333\pi\) | |||||||
\(524\) | 251.693i | 0.480331i | ||||||||
\(525\) | 441.549 | − | 219.597i | 0.841045 | − | 0.418280i | ||||
\(526\) | 251.826 | 0.478757 | ||||||||
\(527\) | − | 83.8317i | − | 0.159074i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −195.715 | −0.369971 | ||||||||
\(530\) | 179.173i | 0.338062i | ||||||||
\(531\) | 105.920 | + | 80.1490i | 0.199472 | + | 0.150940i | ||||
\(532\) | 419.739 | 0.788983 | ||||||||
\(533\) | − | 167.155i | − | 0.313612i | ||||||
\(534\) | 95.8397 | − | 47.6643i | 0.179475 | − | 0.0892589i | ||||
\(535\) | 51.1249 | 0.0955606 | ||||||||
\(536\) | 260.212i | 0.485471i | ||||||||
\(537\) | −187.643 | − | 377.298i | −0.349428 | − | 0.702602i | ||||
\(538\) | 127.168 | 0.236373 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 49.8695 | + | 9.39764i | 0.0923509 | + | 0.0174030i | ||||
\(541\) | −932.206 | −1.72312 | −0.861559 | − | 0.507658i | \(-0.830511\pi\) | ||||
−0.861559 | + | 0.507658i | \(0.830511\pi\) | |||||||
\(542\) | − | 313.978i | − | 0.579295i | ||||||
\(543\) | −351.512 | + | 174.819i | −0.647352 | + | 0.321950i | ||||
\(544\) | −987.359 | −1.81500 | ||||||||
\(545\) | − | 87.3712i | − | 0.160314i | ||||||
\(546\) | 215.826 | + | 433.966i | 0.395286 | + | 0.794810i | ||||
\(547\) | −736.983 | −1.34732 | −0.673659 | − | 0.739042i | \(-0.735278\pi\) | ||||
−0.673659 | + | 0.739042i | \(0.735278\pi\) | |||||||
\(548\) | − | 463.298i | − | 0.845435i | ||||||
\(549\) | 344.554 | − | 455.341i | 0.627604 | − | 0.829401i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 680.583i | 1.23518i | ||||||||
\(552\) | −297.125 | + | 147.770i | −0.538270 | + | 0.267700i | ||||
\(553\) | 375.533 | 0.679083 | ||||||||
\(554\) | 741.456i | 1.33837i | ||||||||
\(555\) | 2.53389 | + | 5.09496i | 0.00456558 | + | 0.00918011i | ||||
\(556\) | 16.4512 | 0.0295885 | ||||||||
\(557\) | − | 635.659i | − | 1.14122i | −0.821221 | − | 0.570610i | \(-0.806707\pi\) | ||
0.821221 | − | 0.570610i | \(-0.193293\pi\) | |||||||
\(558\) | 51.8397 | + | 39.2268i | 0.0929026 | + | 0.0702990i | ||||
\(559\) | 118.717 | 0.212374 | ||||||||
\(560\) | 106.132i | 0.189521i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 665.609 | 1.18436 | ||||||||
\(563\) | 800.352i | 1.42158i | 0.703402 | + | 0.710792i | \(0.251663\pi\) | ||||
−0.703402 | + | 0.710792i | \(0.748337\pi\) | |||||||
\(564\) | −132.087 | − | 265.590i | −0.234197 | − | 0.470905i | ||||
\(565\) | −99.2256 | −0.175621 | ||||||||
\(566\) | 1006.68i | 1.77858i | ||||||||
\(567\) | 148.481 | + | 525.745i | 0.261871 | + | 0.927239i | ||||
\(568\) | −18.7011 | −0.0329244 | ||||||||
\(569\) | − | 52.5450i | − | 0.0923463i | −0.998933 | − | 0.0461731i | \(-0.985297\pi\) | ||
0.998933 | − | 0.0461731i | \(-0.0147026\pi\) | |||||||
\(570\) | −140.935 | + | 70.0916i | −0.247254 | + | 0.122968i | ||||
\(571\) | −10.1143 | −0.0177133 | −0.00885666 | − | 0.999961i | \(-0.502819\pi\) | ||||
−0.00885666 | + | 0.999961i | \(0.502819\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 469.439 | + | 943.912i | 0.819265 | + | 1.64732i | ||||
\(574\) | −299.913 | −0.522497 | ||||||||
\(575\) | 656.115i | 1.14107i | ||||||||
\(576\) | 30.5625 | − | 40.3894i | 0.0530598 | − | 0.0701205i | ||||
\(577\) | −88.2959 | −0.153026 | −0.0765129 | − | 0.997069i | \(-0.524379\pi\) | ||||
−0.0765129 | + | 0.997069i | \(0.524379\pi\) | |||||||
\(578\) | 1437.20i | 2.48650i | ||||||||
\(579\) | −659.462 | + | 327.972i | −1.13897 | + | 0.566446i | ||||
\(580\) | 48.7608 | 0.0840703 | ||||||||
\(581\) | − | 440.675i | − | 0.758477i | ||||||
\(582\) | 503.432 | + | 1012.26i | 0.865003 | + | 1.73928i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 220.921i | − | 0.378289i | ||||||
\(585\) | −53.9565 | − | 40.8286i | −0.0922333 | − | 0.0697925i | ||||
\(586\) | 880.587 | 1.50271 | ||||||||
\(587\) | − | 752.212i | − | 1.28145i | −0.767770 | − | 0.640726i | \(-0.778634\pi\) | ||
0.767770 | − | 0.640726i | \(-0.221366\pi\) | |||||||
\(588\) | −22.3723 | + | 11.1265i | −0.0380481 | + | 0.0189226i | ||||
\(589\) | −75.0652 | −0.127445 | ||||||||
\(590\) | 29.5170i | 0.0500288i | ||||||||
\(591\) | 8.22004 | + | 16.5282i | 0.0139087 | + | 0.0279665i | ||||
\(592\) | 47.5488 | 0.0803189 | ||||||||
\(593\) | − | 656.836i | − | 1.10765i | −0.832633 | − | 0.553825i | \(-0.813168\pi\) | ||
0.832633 | − | 0.553825i | \(-0.186832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 156.554 | 0.263117 | ||||||||
\(596\) | − | 160.597i | − | 0.269459i | ||||||
\(597\) | −519.155 | + | 258.193i | −0.869606 | + | 0.432484i | ||||
\(598\) | −644.848 | −1.07834 | ||||||||
\(599\) | 403.922i | 0.674327i | 0.941446 | + | 0.337164i | \(0.109468\pi\) | ||||
−0.941446 | + | 0.337164i | \(0.890532\pi\) | |||||||
\(600\) | 133.783 | + | 269.000i | 0.222971 | + | 0.448333i | ||||
\(601\) | 826.761 | 1.37564 | 0.687821 | − | 0.725880i | \(-0.258567\pi\) | ||||
0.687821 | + | 0.725880i | \(0.258567\pi\) | |||||||
\(602\) | − | 213.005i | − | 0.353828i | ||||||
\(603\) | −343.920 | + | 454.502i | −0.570348 | + | 0.753735i | ||||
\(604\) | 66.9783 | 0.110891 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −135.679 | + | 67.4778i | −0.223893 | + | 0.111350i | ||||
\(607\) | 1156.44 | 1.90517 | 0.952587 | − | 0.304268i | \(-0.0984118\pi\) | ||||
0.952587 | + | 0.304268i | \(0.0984118\pi\) | |||||||
\(608\) | 884.108i | 1.45413i | ||||||||
\(609\) | 233.750 | + | 470.007i | 0.383826 | + | 0.771768i | ||||
\(610\) | 126.891 | 0.208018 | ||||||||
\(611\) | 395.497i | 0.647295i | ||||||||
\(612\) | −498.804 | − | 377.443i | −0.815040 | − | 0.616737i | ||||
\(613\) | 898.250 | 1.46533 | 0.732667 | − | 0.680587i | \(-0.238275\pi\) | ||||
0.732667 | + | 0.680587i | \(0.238275\pi\) | |||||||
\(614\) | − | 1006.02i | − | 1.63846i | ||||||
\(615\) | 37.4891 | − | 18.6446i | 0.0609579 | − | 0.0303164i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 713.002i | − | 1.15560i | −0.816180 | − | 0.577798i | \(-0.803912\pi\) | ||
0.816180 | − | 0.577798i | \(-0.196088\pi\) | |||||||
\(618\) | −608.440 | − | 1223.40i | −0.984531 | − | 1.97962i | ||||
\(619\) | −40.4102 | −0.0652831 | −0.0326415 | − | 0.999467i | \(-0.510392\pi\) | ||||
−0.0326415 | + | 0.999467i | \(0.510392\pi\) | |||||||
\(620\) | 5.37809i | 0.00867434i | ||||||||
\(621\) | −714.282 | − | 134.603i | −1.15021 | − | 0.216751i | ||||
\(622\) | 1111.58 | 1.78711 | ||||||||
\(623\) | 95.3285i | 0.153015i | ||||||||
\(624\) | −506.250 | + | 251.775i | −0.811298 | + | 0.403485i | ||||
\(625\) | 578.315 | 0.925304 | ||||||||
\(626\) | − | 1337.64i | − | 2.13681i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 160.832 | 0.256101 | ||||||||
\(629\) | − | 70.1388i | − | 0.111508i | ||||||
\(630\) | −73.2554 | + | 96.8097i | −0.116278 | + | 0.153666i | ||||
\(631\) | −748.502 | −1.18622 | −0.593108 | − | 0.805123i | \(-0.702099\pi\) | ||||
−0.593108 | + | 0.805123i | \(0.702099\pi\) | |||||||
\(632\) | 228.781i | 0.361996i | ||||||||
\(633\) | −286.848 | + | 142.659i | −0.453156 | + | 0.225370i | ||||
\(634\) | −930.032 | −1.46693 | ||||||||
\(635\) | − | 152.791i | − | 0.240615i | ||||||
\(636\) | 283.913 | + | 570.871i | 0.446404 | + | 0.897595i | ||||
\(637\) | 33.3151 | 0.0523000 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.6644 | − | 24.7170i | −0.0511180 | − | 0.0386807i | ||||
\(640\) | −95.5488 | −0.149295 | ||||||||
\(641\) | 122.303i | 0.190800i | 0.995439 | + | 0.0954000i | \(0.0304130\pi\) | ||||
−0.995439 | + | 0.0954000i | \(0.969587\pi\) | |||||||
\(642\) | 437.549 | − | 217.608i | 0.681540 | − | 0.338953i | ||||
\(643\) | −629.313 | −0.978713 | −0.489357 | − | 0.872084i | \(-0.662768\pi\) | ||||
−0.489357 | + | 0.872084i | \(0.662768\pi\) | |||||||
\(644\) | 430.728i | 0.668833i | ||||||||
\(645\) | 13.2418 | + | 26.6256i | 0.0205299 | + | 0.0412800i | ||||
\(646\) | 1940.15 | 3.00333 | ||||||||
\(647\) | − | 185.830i | − | 0.287218i | −0.989635 | − | 0.143609i | \(-0.954129\pi\) | ||
0.989635 | − | 0.143609i | \(-0.0458707\pi\) | |||||||
\(648\) | −320.293 | + | 90.4574i | −0.494280 | + | 0.139595i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 583.808i | 0.898166i | ||||||||
\(651\) | −51.8397 | + | 25.7816i | −0.0796308 | + | 0.0396031i | ||||
\(652\) | 161.006 | 0.246941 | ||||||||
\(653\) | 202.416i | 0.309979i | 0.987916 | + | 0.154990i | \(0.0495344\pi\) | ||||
−0.987916 | + | 0.154990i | \(0.950466\pi\) | |||||||
\(654\) | −371.886 | − | 747.759i | −0.568633 | − | 1.14336i | ||||
\(655\) | 84.0597 | 0.128335 | ||||||||
\(656\) | − | 349.868i | − | 0.533335i | ||||||
\(657\) | 291.989 | − | 385.874i | 0.444428 | − | 0.587327i | ||||
\(658\) | 709.609 | 1.07843 | ||||||||
\(659\) | 1094.02i | 1.66012i | 0.557674 | + | 0.830060i | \(0.311694\pi\) | ||||
−0.557674 | + | 0.830060i | \(0.688306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1024.53 | 1.54997 | 0.774985 | − | 0.631980i | \(-0.217758\pi\) | ||||
0.774985 | + | 0.631980i | \(0.217758\pi\) | |||||||
\(662\) | 291.938i | 0.440994i | ||||||||
\(663\) | 371.391 | + | 746.765i | 0.560167 | + | 1.12634i | ||||
\(664\) | 268.467 | 0.404318 | ||||||||
\(665\) | − | 140.183i | − | 0.210802i | ||||||
\(666\) | 43.3723 | + | 32.8196i | 0.0651235 | + | 0.0492787i | ||||
\(667\) | −698.402 | −1.04708 | ||||||||
\(668\) | − | 133.406i | − | 0.199709i | ||||||
\(669\) | −206.110 | + | 102.505i | −0.308087 | + | 0.153222i | ||||
\(670\) | −126.658 | −0.189041 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 303.652 | + | 610.560i | 0.451863 | + | 0.908572i | ||||
\(673\) | −259.489 | −0.385571 | −0.192785 | − | 0.981241i | \(-0.561752\pi\) | ||||
−0.192785 | + | 0.981241i | \(0.561752\pi\) | |||||||
\(674\) | − | 134.476i | − | 0.199519i | ||||||
\(675\) | −121.861 | + | 646.670i | −0.180535 | + | 0.958029i | ||||
\(676\) | 187.307 | 0.277081 | ||||||||
\(677\) | 116.565i | 0.172179i | 0.996287 | + | 0.0860895i | \(0.0274371\pi\) | ||||
−0.996287 | + | 0.0860895i | \(0.972563\pi\) | |||||||
\(678\) | −849.214 | + | 422.343i | −1.25253 | + | 0.622924i | ||||
\(679\) | −1006.86 | −1.48286 | ||||||||
\(680\) | 95.3758i | 0.140259i | ||||||||
\(681\) | 64.4486 | + | 129.588i | 0.0946382 | + | 0.190291i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 739.385i | − | 1.08255i | −0.840844 | − | 0.541277i | \(-0.817941\pi\) | ||
0.840844 | − | 0.541277i | \(-0.182059\pi\) | |||||||
\(684\) | −337.973 | + | 446.643i | −0.494112 | + | 0.652987i | ||||
\(685\) | −154.731 | −0.225885 | ||||||||
\(686\) | − | 894.027i | − | 1.30325i | ||||||
\(687\) | 41.4090 | − | 20.5941i | 0.0602750 | − | 0.0299768i | ||||
\(688\) | 248.484 | 0.361168 | ||||||||
\(689\) | − | 850.098i | − | 1.23381i | ||||||
\(690\) | −71.9267 | − | 144.625i | −0.104242 | − | 0.209601i | ||||
\(691\) | 389.024 | 0.562987 | 0.281494 | − | 0.959563i | \(-0.409170\pi\) | ||||
0.281494 | + | 0.959563i | \(0.409170\pi\) | |||||||
\(692\) | 532.662i | 0.769743i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.2934 | −0.0407686 | ||||||||
\(695\) | − | 5.49431i | − | 0.00790549i | ||||||
\(696\) | −286.337 | + | 142.405i | −0.411404 | + | 0.204605i | ||||
\(697\) | −516.087 | −0.740440 | ||||||||
\(698\) | − | 540.249i | − | 0.773996i | ||||||
\(699\) | 231.386 | + | 465.253i | 0.331024 | + | 0.665598i | ||||
\(700\) | 389.957 | 0.557081 | ||||||||
\(701\) | 1164.12i | 1.66066i | 0.557271 | + | 0.830330i | \(0.311848\pi\) | ||||
−0.557271 | + | 0.830330i | \(0.688152\pi\) | |||||||
\(702\) | −635.565 | − | 119.769i | −0.905363 | − | 0.170611i | ||||
\(703\) | −62.8043 | −0.0893375 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −88.7011 | + | 44.1140i | −0.125817 | + | 0.0625730i | ||||
\(706\) | 1341.76 | 1.90050 | ||||||||
\(707\) | − | 134.956i | − | 0.190885i | ||||||
\(708\) | 46.7719 | + | 94.0453i | 0.0660620 | + | 0.132832i | ||||
\(709\) | 1329.93 | 1.87579 | 0.937893 | − | 0.346926i | \(-0.112774\pi\) | ||||
0.937893 | + | 0.346926i | \(0.112774\pi\) | |||||||
\(710\) | − | 9.10268i | − | 0.0128207i | ||||||
\(711\) | −302.378 | + | 399.603i | −0.425285 | + | 0.562030i | ||||
\(712\) | −58.0759 | −0.0815673 | ||||||||
\(713\) | − | 77.0306i | − | 0.108037i | ||||||
\(714\) | 1339.86 | − | 666.356i | 1.87655 | − | 0.933272i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 333.213i | − | 0.465381i | ||||||
\(717\) | −395.959 | − | 796.164i | −0.552244 | − | 1.11041i | ||||
\(718\) | 442.250 | 0.615947 | ||||||||
\(719\) | − | 838.618i | − | 1.16637i | −0.812340 | − | 0.583184i | \(-0.801807\pi\) | ||
0.812340 | − | 0.583184i | \(-0.198193\pi\) | |||||||
\(720\) | −112.935 | − | 85.4572i | −0.156854 | − | 0.118691i | ||||
\(721\) | 1216.88 | 1.68777 | ||||||||
\(722\) | − | 825.979i | − | 1.14402i | ||||||
\(723\) | 125.446 | − | 62.3883i | 0.173507 | − | 0.0862909i | ||||
\(724\) | −310.440 | −0.428785 | ||||||||
\(725\) | 632.292i | 0.872127i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 154.628 | 0.212693 | 0.106346 | − | 0.994329i | \(-0.466085\pi\) | ||||
0.106346 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(728\) | − | 262.970i | − | 0.361223i | ||||||
\(729\) | −679.000 | − | 265.330i | −0.931413 | − | 0.363964i | ||||
\(730\) | 107.533 | 0.147305 | ||||||||
\(731\) | − | 366.536i | − | 0.501417i | ||||||
\(732\) | 404.293 | − | 201.069i | 0.552313 | − | 0.274684i | ||||
\(733\) | −445.022 | −0.607124 | −0.303562 | − | 0.952812i | \(-0.598176\pi\) | ||||
−0.303562 | + | 0.952812i | \(0.598176\pi\) | |||||||
\(734\) | − | 350.972i | − | 0.478164i | ||||||
\(735\) | 3.71599 | + | 7.47182i | 0.00505576 | + | 0.0101657i | ||||
\(736\) | −907.255 | −1.23268 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 241.489 | − | 319.137i | 0.327221 | − | 0.432434i | ||||
\(739\) | −61.3586 | −0.0830293 | −0.0415146 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415146 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(740\) | 4.49965i | 0.00608060i | ||||||||
\(741\) | 668.674 | − | 332.554i | 0.902394 | − | 0.448790i | ||||
\(742\) | −1525.26 | −2.05561 | ||||||||
\(743\) | − | 723.250i | − | 0.973419i | −0.873564 | − | 0.486709i | \(-0.838197\pi\) | ||
0.873564 | − | 0.486709i | \(-0.161803\pi\) | |||||||
\(744\) | −15.7066 | − | 31.5817i | −0.0211110 | − | 0.0424485i | ||||
\(745\) | −53.6358 | −0.0719944 | ||||||||
\(746\) | 376.332i | 0.504466i | ||||||||
\(747\) | 468.921 | + | 354.830i | 0.627739 | + | 0.475007i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 435.215i | 0.581062i | ||||||||
\(750\) | −265.242 | + | 131.914i | −0.353656 | + | 0.175885i | ||||
\(751\) | 1286.37 | 1.71287 | 0.856436 | − | 0.516253i | \(-0.172674\pi\) | ||||
0.856436 | + | 0.516253i | \(0.172674\pi\) | |||||||
\(752\) | 827.804i | 1.10080i | ||||||||
\(753\) | 277.585 | + | 558.148i | 0.368639 | + | 0.741232i | ||||
\(754\) | −621.435 | −0.824184 | ||||||||
\(755\) | − | 22.3692i | − | 0.0296281i | ||||||
\(756\) | −80.0000 | + | 424.528i | −0.105820 | + | 0.561545i | ||||
\(757\) | −272.717 | −0.360261 | −0.180130 | − | 0.983643i | \(-0.557652\pi\) | ||||
−0.180130 | + | 0.983643i | \(0.557652\pi\) | |||||||
\(758\) | − | 682.566i | − | 0.900483i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 85.4021 | 0.112371 | ||||||||
\(761\) | − | 476.634i | − | 0.626326i | −0.949699 | − | 0.313163i | \(-0.898611\pi\) | ||
0.949699 | − | 0.313163i | \(-0.101389\pi\) | |||||||
\(762\) | −650.337 | − | 1307.65i | −0.853460 | − | 1.71607i | ||||
\(763\) | 743.771 | 0.974799 | ||||||||
\(764\) | 833.621i | 1.09113i | ||||||||
\(765\) | −126.057 | + | 166.589i | −0.164781 | + | 0.217763i | ||||
\(766\) | 1594.88 | 2.08209 | ||||||||
\(767\) | − | 140.045i | − | 0.182588i | ||||||
\(768\) | −878.214 | + | 436.765i | −1.14351 | + | 0.568705i | ||||
\(769\) | 22.4401 | 0.0291808 | 0.0145904 | − | 0.999894i | \(-0.495356\pi\) | ||||
0.0145904 | + | 0.999894i | \(0.495356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −266.832 | − | 536.525i | −0.346085 | − | 0.695881i | ||||
\(772\) | −582.408 | −0.754414 | ||||||||
\(773\) | − | 1227.79i | − | 1.58834i | −0.607694 | − | 0.794171i | \(-0.707905\pi\) | ||
0.607694 | − | 0.794171i | \(-0.292095\pi\) | |||||||
\(774\) | 226.658 | + | 171.511i | 0.292839 | + | 0.221590i | ||||
\(775\) | −69.7390 | −0.0899858 | ||||||||
\(776\) | − | 613.400i | − | 0.790464i | ||||||
\(777\) | −43.3723 | + | 21.5705i | −0.0558202 | + | 0.0277612i | ||||
\(778\) | −1161.18 | −1.49253 | ||||||||
\(779\) | 462.119i | 0.593220i | ||||||||
\(780\) | −23.8260 | − | 47.9075i | −0.0305462 | − | 0.0614199i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1990.95i | 2.54597i | ||||||||
\(783\) | −688.348 | − | 129.715i | −0.879116 | − | 0.165665i | ||||
\(784\) | 69.7309 | 0.0889425 | ||||||||
\(785\) | − | 53.7140i | − | 0.0684255i | ||||||
\(786\) | 719.418 | − | 357.791i | 0.915290 | − | 0.455204i | ||||
\(787\) | −872.277 | −1.10836 | −0.554179 | − | 0.832398i | \(-0.686968\pi\) | ||||
−0.554179 | + | 0.832398i | \(0.686968\pi\) | |||||||
\(788\) | 14.5970i | 0.0185241i | ||||||||
\(789\) | −133.269 | − | 267.967i | −0.168909 | − | 0.339629i | ||||
\(790\) | −111.359 | −0.140960 | ||||||||
\(791\) | − | 844.685i | − | 1.06787i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −602.043 | −0.759197 | ||||||||
\(794\) | 1416.84i | 1.78443i | ||||||||
\(795\) | 190.658 | − | 94.8204i | 0.239821 | − | 0.119271i | ||||
\(796\) | −458.495 | −0.575998 | ||||||||
\(797\) | − | 55.7659i | − | 0.0699697i | −0.999388 | − | 0.0349849i | \(-0.988862\pi\) | ||
0.999388 | − | 0.0349849i | \(-0.0111383\pi\) | |||||||
\(798\) | −596.674 | − | 1199.75i | −0.747711 | − | 1.50344i | ||||
\(799\) | 1221.09 | 1.52827 | ||||||||
\(800\) | 821.376i | 1.02672i | ||||||||
\(801\) | −101.439 | − | 76.7583i | −0.126640 | − | 0.0958280i | ||||
\(802\) | 453.989 | 0.566071 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −403.549 | + | 200.698i | −0.501926 | + | 0.249625i | ||||
\(805\) | 143.853 | 0.178700 | ||||||||
\(806\) | − | 68.5414i | − | 0.0850390i | ||||||
\(807\) | −67.2989 | − | 135.320i | −0.0833940 | − | 0.167682i | ||||
\(808\) | 82.2175 | 0.101754 | ||||||||
\(809\) | − | 1325.11i | − | 1.63796i | −0.573819 | − | 0.818982i | \(-0.694539\pi\) | ||
0.573819 | − | 0.818982i | \(-0.305461\pi\) | |||||||
\(810\) | −44.0298 | − | 155.902i | −0.0543578 | − | 0.192471i | ||||
\(811\) | 1028.13 | 1.26773 | 0.633866 | − | 0.773443i | \(-0.281467\pi\) | ||||
0.633866 | + | 0.773443i | \(0.281467\pi\) | |||||||
\(812\) | 415.089i | 0.511194i | ||||||||
\(813\) | −334.103 | + | 166.161i | −0.410951 | + | 0.204380i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 53.7721i | − | 0.0659781i | ||||||
\(816\) | 777.348 | + | 1563.03i | 0.952632 | + | 1.91548i | ||||
\(817\) | −328.206 | −0.401721 | ||||||||
\(818\) | 342.541i | 0.418755i | ||||||||
\(819\) | 347.565 | − | 459.320i | 0.424377 | − | 0.560830i | ||||
\(820\) | 33.1087 | 0.0403765 | ||||||||
\(821\) | 892.085i | 1.08658i | 0.839544 | + | 0.543292i | \(0.182822\pi\) | ||||
−0.839544 | + | 0.543292i | \(0.817178\pi\) | |||||||
\(822\) | −1324.25 | + | 658.595i | −1.61101 | + | 0.801210i | ||||
\(823\) | −415.301 | −0.504619 | −0.252310 | − | 0.967647i | \(-0.581190\pi\) | ||||
−0.252310 | + | 0.967647i | \(0.581190\pi\) | |||||||
\(824\) | 741.346i | 0.899691i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −251.272 | −0.304203 | ||||||||
\(827\) | − | 464.560i | − | 0.561741i | −0.959746 | − | 0.280871i | \(-0.909377\pi\) | ||
0.959746 | − | 0.280871i | \(-0.0906232\pi\) | |||||||
\(828\) | −458.337 | − | 346.821i | −0.553547 | − | 0.418866i | ||||
\(829\) | −886.193 | −1.06899 | −0.534495 | − | 0.845172i | \(-0.679498\pi\) | ||||
−0.534495 | + | 0.845172i | \(0.679498\pi\) | |||||||
\(830\) | 130.676i | 0.157441i | ||||||||
\(831\) | 788.981 | − | 392.386i | 0.949435 | − | 0.472186i | ||||
\(832\) | −53.4021 | −0.0641852 | ||||||||
\(833\) | − | 102.859i | − | 0.123481i | ||||||
\(834\) | −23.3859 | − | 47.0227i | −0.0280407 | − | 0.0563821i | ||||
\(835\) | −44.5544 | −0.0533585 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.3070 | − | 75.9217i | 0.0170932 | − | 0.0907069i | ||||
\(838\) | 127.065 | 0.151629 | ||||||||
\(839\) | 163.482i | 0.194854i | 0.995243 | + | 0.0974270i | \(0.0310612\pi\) | ||||
−0.995243 | + | 0.0974270i | \(0.968939\pi\) | |||||||
\(840\) | 58.9783 | − | 29.3319i | 0.0702122 | − | 0.0349189i | ||||
\(841\) | 167.956 | 0.199710 | ||||||||
\(842\) | 132.994i | 0.157951i | ||||||||
\(843\) | −352.247 | − | 708.272i | −0.417850 | − | 0.840180i | ||||
\(844\) | −253.331 | −0.300156 | ||||||||
\(845\) | − | 62.5562i | − | 0.0740310i | ||||||
\(846\) | −571.375 | + | 755.092i | −0.675384 | + | 0.892544i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 1779.31i | − | 2.09825i | ||||||
\(849\) | 1071.20 | − | 532.744i | 1.26172 | − | 0.627496i | ||||
\(850\) | 1802.49 | 2.12057 | ||||||||
\(851\) | − | 64.4486i | − | 0.0757327i | ||||||
\(852\) | −14.4239 | − | 29.0024i | −0.0169294 | − | 0.0340404i | ||||
\(853\) | 451.647 | 0.529481 | 0.264740 | − | 0.964320i | \(-0.414714\pi\) | ||||
0.264740 | + | 0.964320i | \(0.414714\pi\) | |||||||
\(854\) | 1080.20i | 1.26487i | ||||||||
\(855\) | 149.168 | + | 112.875i | 0.174466 | + | 0.132018i | ||||
\(856\) | −265.141 | −0.309744 | ||||||||
\(857\) | 233.720i | 0.272719i | 0.990659 | + | 0.136360i | \(0.0435402\pi\) | ||||
−0.990659 | + | 0.136360i | \(0.956460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −694.225 | −0.808178 | −0.404089 | − | 0.914720i | \(-0.632411\pi\) | ||||
−0.404089 | + | 0.914720i | \(0.632411\pi\) | |||||||
\(860\) | 23.5145i | 0.0273425i | ||||||||
\(861\) | 158.717 | + | 319.137i | 0.184341 | + | 0.370658i | ||||
\(862\) | 1254.11 | 1.45488 | ||||||||
\(863\) | − | 1143.39i | − | 1.32490i | −0.749106 | − | 0.662450i | \(-0.769517\pi\) | ||
0.749106 | − | 0.662450i | \(-0.230483\pi\) | |||||||
\(864\) | −894.195 | − | 168.506i | −1.03495 | − | 0.195030i | ||||
\(865\) | 177.897 | 0.205661 | ||||||||
\(866\) | − | 1301.60i | − | 1.50301i | ||||||
\(867\) | 1529.32 | − | 760.581i | 1.76392 | − | 0.877256i | ||||
\(868\) | −45.7825 | −0.0527448 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −69.3151 | − | 139.374i | −0.0796726 | − | 0.160200i | ||||
\(871\) | 600.935 | 0.689937 | ||||||||
\(872\) | 453.119i | 0.519632i | ||||||||
\(873\) | 810.724 | − | 1071.40i | 0.928664 | − | 1.22726i | ||||
\(874\) | 1782.75 | 2.03976 | ||||||||
\(875\) | − | 263.827i | − | 0.301517i | ||||||
\(876\) | 342.614 | − | 170.393i | 0.391112 | − | 0.194513i | ||||
\(877\) | 1080.36 | 1.23188 | 0.615940 | − | 0.787793i | \(-0.288777\pi\) | ||||
0.615940 | + | 0.787793i | \(0.288777\pi\) | |||||||
\(878\) | − | 63.3830i | − | 0.0721902i | ||||||
\(879\) | −466.016 | − | 937.030i | −0.530166 | − | 1.06602i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 638.008i | − | 0.724186i | −0.932142 | − | 0.362093i | \(-0.882062\pi\) | ||
0.932142 | − | 0.362093i | \(-0.117938\pi\) | |||||||
\(882\) | 63.6060 | + | 48.1303i | 0.0721156 | + | 0.0545695i | ||||
\(883\) | −972.195 | −1.10101 | −0.550507 | − | 0.834831i | \(-0.685566\pi\) | ||||
−0.550507 | + | 0.834831i | \(0.685566\pi\) | |||||||
\(884\) | 659.510i | 0.746052i | ||||||||
\(885\) | 31.4090 | − | 15.6207i | 0.0354903 | − | 0.0176505i | ||||
\(886\) | −2197.23 | −2.47995 | ||||||||
\(887\) | 525.975i | 0.592982i | 0.955036 | + | 0.296491i | \(0.0958165\pi\) | ||||
−0.955036 | + | 0.296491i | \(0.904183\pi\) | |||||||
\(888\) | −13.1411 | − | 26.4232i | −0.0147986 | − | 0.0297558i | ||||
\(889\) | 1300.67 | 1.46308 | ||||||||
\(890\) | − | 28.2683i | − | 0.0317621i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −182.027 | −0.204066 | ||||||||
\(893\) | − | 1093.39i | − | 1.22441i | ||||||
\(894\) | −459.038 | + | 228.295i | −0.513465 | + | 0.255363i | ||||
\(895\) | −111.285 | −0.124341 | ||||||||
\(896\) | − | 813.386i | − | 0.907797i | ||||||
\(897\) | 341.261 | + | 686.181i | 0.380447 | + | 0.764973i | ||||
\(898\) | 1453.11 | 1.61817 | ||||||||
\(899\) | − | 74.2337i | − | 0.0825737i | ||||||
\(900\) | −313.992 | + | 414.952i | −0.348880 | + | 0.461057i | ||||
\(901\) | −2624.65 | −2.91304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −226.658 | + | 112.724i | −0.251005 | + | 0.124833i | ||||
\(904\) | 514.598 | 0.569245 | ||||||||
\(905\) | 103.680i | 0.114563i | ||||||||
\(906\) | −95.2119 | − | 191.445i | −0.105090 | − | 0.211308i | ||||
\(907\) | −574.706 | −0.633634 | −0.316817 | − | 0.948487i | \(-0.602614\pi\) | ||||
−0.316817 | + | 0.948487i | \(0.602614\pi\) | |||||||
\(908\) | 114.447i | 0.126043i | ||||||||
\(909\) | 143.606 | + | 108.666i | 0.157982 | + | 0.119545i | ||||
\(910\) | 128.000 | 0.140659 | ||||||||
\(911\) | 1279.17i | 1.40413i | 0.712111 | + | 0.702067i | \(0.247739\pi\) | ||||
−0.712111 | + | 0.702067i | \(0.752261\pi\) | |||||||
\(912\) | 1399.58 | − | 696.058i | 1.53463 | − | 0.763222i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 64.6037i | 0.0706823i | ||||||||
\(915\) | −67.1522 | − | 135.025i | −0.0733904 | − | 0.147568i | ||||
\(916\) | 36.5706 | 0.0399242 | ||||||||
\(917\) | 715.581i | 0.780351i | ||||||||
\(918\) | −369.783 | + | 1962.29i | −0.402813 | + | 2.13757i | ||||
\(919\) | 481.929 | 0.524406 | 0.262203 | − | 0.965013i | \(-0.415551\pi\) | ||||
0.262203 | + | 0.965013i | \(0.415551\pi\) | |||||||
\(920\) | 87.6381i | 0.0952588i | ||||||||
\(921\) | −1070.50 | + | 532.395i | −1.16232 | + | 0.578062i | ||||
\(922\) | −730.456 | −0.792252 | ||||||||
\(923\) | 43.1883i | 0.0467912i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.3480 | −0.0630789 | ||||||||
\(926\) | 507.522i | 0.548080i | ||||||||
\(927\) | −979.829 | + | 1294.88i | −1.05699 | + | 1.39685i | ||||
\(928\) | −874.315 | −0.942149 | ||||||||
\(929\) | 1112.26i | 1.19726i | 0.801024 | + | 0.598632i | \(0.204289\pi\) | ||||
−0.801024 | + | 0.598632i | \(0.795711\pi\) | |||||||
\(930\) | 15.3723 | − | 7.64515i | 0.0165293 | − | 0.00822059i | ||||
\(931\) | −92.1032 | −0.0989293 | ||||||||
\(932\) | 410.891i | 0.440870i | ||||||||
\(933\) | −588.261 | − | 1182.83i | −0.630505 | − | 1.26777i | ||||
\(934\) | −278.484 | −0.298162 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 279.826 | + | 211.743i | 0.298959 | + | 0.226221i | ||||
\(937\) | −1743.58 | −1.86081 | −0.930406 | − | 0.366530i | \(-0.880546\pi\) | ||||
−0.930406 | + | 0.366530i | \(0.880546\pi\) | |||||||
\(938\) | − | 1078.21i | − | 1.14948i | ||||||
\(939\) | −1423.38 | + | 707.896i | −1.51585 | + | 0.753883i | ||||
\(940\) | −78.3369 | −0.0833371 | ||||||||
\(941\) | 836.194i | 0.888623i | 0.895872 | + | 0.444311i | \(0.146552\pi\) | ||||
−0.895872 | + | 0.444311i | \(0.853448\pi\) | |||||||
\(942\) | −228.628 | − | 459.707i | −0.242705 | − | 0.488012i | ||||
\(943\) | −474.217 | −0.502882 | ||||||||
\(944\) | − | 293.125i | − | 0.310513i | ||||||
\(945\) | 141.783 | + | 26.7181i | 0.150034 | + | 0.0282732i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 114.725i | 0.121145i | 0.998164 | + | 0.0605726i | \(0.0192927\pi\) | ||||
−0.998164 | + | 0.0605726i | \(0.980707\pi\) | |||||||
\(948\) | −354.804 | + | 176.456i | −0.374266 | + | 0.186135i | ||||
\(949\) | −510.195 | −0.537614 | ||||||||
\(950\) | − | 1614.00i | − | 1.69895i | ||||||
\(951\) | 492.183 | + | 989.645i | 0.517543 | + | 1.04064i | ||||
\(952\) | −811.913 | −0.852850 | ||||||||
\(953\) | 327.059i | 0.343189i | 0.985168 | + | 0.171595i | \(0.0548919\pi\) | ||||
−0.985168 | + | 0.171595i | \(0.945108\pi\) | |||||||
\(954\) | 1228.14 | − | 1623.03i | 1.28735 | − | 1.70128i | ||||
\(955\) | 278.410 | 0.291529 | ||||||||
\(956\) | − | 703.137i | − | 0.735499i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1725.47 | −1.80111 | ||||||||
\(959\) | − | 1317.19i | − | 1.37350i | ||||||
\(960\) | −5.95650 | − | 11.9769i | −0.00620469 | − | 0.0124759i | ||||
\(961\) | −952.812 | −0.991480 | ||||||||
\(962\) | − | 57.3460i | − | 0.0596113i | ||||||
\(963\) | −463.111 | − | 350.434i | −0.480905 | − | 0.363898i | ||||
\(964\) | 110.788 | 0.114925 | ||||||||
\(965\) | 194.511i | 0.201565i | ||||||||
\(966\) | 1231.16 | − | 612.296i | 1.27449 | − | 0.633846i | ||||
\(967\) | −168.674 | −0.174430 | −0.0872150 | − | 0.996190i | \(-0.527797\pi\) | ||||
−0.0872150 | + | 0.996190i | \(0.527797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1026.75 | − | 2064.51i | −1.05960 | − | 2.13056i | ||||
\(970\) | 298.571 | 0.307805 | ||||||||
\(971\) | − | 81.7370i | − | 0.0841782i | −0.999114 | − | 0.0420891i | \(-0.986599\pi\) | ||
0.999114 | − | 0.0420891i | \(-0.0134013\pi\) | |||||||
\(972\) | −387.323 | − | 426.957i | −0.398481 | − | 0.439256i | ||||
\(973\) | 46.7719 | 0.0480698 | ||||||||
\(974\) | 328.418i | 0.337185i | ||||||||
\(975\) | 621.228 | − | 308.957i | 0.637157 | − | 0.316879i | ||||
\(976\) | −1260.12 | −1.29111 | ||||||||
\(977\) | − | 20.3562i | − | 0.0208354i | −0.999946 | − | 0.0104177i | \(-0.996684\pi\) | ||
0.999946 | − | 0.0104177i | \(-0.00331612\pi\) | |||||||
\(978\) | −228.875 | − | 460.205i | −0.234024 | − | 0.470557i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.59879i | 0.00673346i | ||||||||
\(981\) | −598.883 | + | 791.445i | −0.610482 | + | 0.806774i | ||||
\(982\) | −2010.84 | −2.04770 | ||||||||
\(983\) | 797.407i | 0.811197i | 0.914051 | + | 0.405598i | \(0.132937\pi\) | ||||
−0.914051 | + | 0.405598i | \(0.867063\pi\) | |||||||
\(984\) | −194.424 | + | 96.6935i | −0.197585 | + | 0.0982657i | ||||
\(985\) | 4.87506 | 0.00494930 | ||||||||
\(986\) | 1918.66i | 1.94590i | ||||||||
\(987\) | −375.533 | − | 755.092i | −0.380479 | − | 0.765038i | ||||
\(988\) | 590.543 | 0.597716 | ||||||||
\(989\) | − | 336.799i | − | 0.340545i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 609.620 | 0.615156 | 0.307578 | − | 0.951523i | \(-0.400481\pi\) | ||||
0.307578 | + | 0.951523i | \(0.400481\pi\) | |||||||
\(992\) | − | 96.4330i | − | 0.0972107i | ||||||
\(993\) | 310.651 | − | 154.497i | 0.312841 | − | 0.155586i | ||||
\(994\) | 77.4891 | 0.0779569 | ||||||||
\(995\) | 153.127i | 0.153896i | ||||||||
\(996\) | 207.065 | + | 416.351i | 0.207897 | + | 0.418023i | ||||
\(997\) | −1771.28 | −1.77661 | −0.888303 | − | 0.459257i | \(-0.848116\pi\) | ||||
−0.888303 | + | 0.459257i | \(0.848116\pi\) | |||||||
\(998\) | − | 1237.01i | − | 1.23949i | ||||||
\(999\) | 11.9702 | − | 63.5208i | 0.0119821 | − | 0.0635844i |
(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 | 363.3.b.h.122.1 | 4 | ||
3.2 | odd | 2 | inner | 363.3.b.h.122.4 | 4 | ||
11.2 | odd | 10 | 363.3.h.m.323.4 | 16 | |||
11.3 | even | 5 | 363.3.h.l.251.1 | 16 | |||
11.4 | even | 5 | 363.3.h.l.269.4 | 16 | |||
11.5 | even | 5 | 363.3.h.l.245.4 | 16 | |||
11.6 | odd | 10 | 363.3.h.m.245.1 | 16 | |||
11.7 | odd | 10 | 363.3.h.m.269.1 | 16 | |||
11.8 | odd | 10 | 363.3.h.m.251.4 | 16 | |||
11.9 | even | 5 | 363.3.h.l.323.1 | 16 | |||
11.10 | odd | 2 | 33.3.b.b.23.4 | yes | 4 | ||
33.2 | even | 10 | 363.3.h.m.323.1 | 16 | |||
33.5 | odd | 10 | 363.3.h.l.245.1 | 16 | |||
33.8 | even | 10 | 363.3.h.m.251.1 | 16 | |||
33.14 | odd | 10 | 363.3.h.l.251.4 | 16 | |||
33.17 | even | 10 | 363.3.h.m.245.4 | 16 | |||
33.20 | odd | 10 | 363.3.h.l.323.4 | 16 | |||
33.26 | odd | 10 | 363.3.h.l.269.1 | 16 | |||
33.29 | even | 10 | 363.3.h.m.269.4 | 16 | |||
33.32 | even | 2 | 33.3.b.b.23.1 | ✓ | 4 | ||
44.43 | even | 2 | 528.3.i.d.353.3 | 4 | |||
132.131 | odd | 2 | 528.3.i.d.353.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.b.23.1 | ✓ | 4 | 33.32 | even | 2 | ||
33.3.b.b.23.4 | yes | 4 | 11.10 | odd | 2 | ||
363.3.b.h.122.1 | 4 | 1.1 | even | 1 | trivial | ||
363.3.b.h.122.4 | 4 | 3.2 | odd | 2 | inner | ||
363.3.h.l.245.1 | 16 | 33.5 | odd | 10 | |||
363.3.h.l.245.4 | 16 | 11.5 | even | 5 | |||
363.3.h.l.251.1 | 16 | 11.3 | even | 5 | |||
363.3.h.l.251.4 | 16 | 33.14 | odd | 10 | |||
363.3.h.l.269.1 | 16 | 33.26 | odd | 10 | |||
363.3.h.l.269.4 | 16 | 11.4 | even | 5 | |||
363.3.h.l.323.1 | 16 | 11.9 | even | 5 | |||
363.3.h.l.323.4 | 16 | 33.20 | odd | 10 | |||
363.3.h.m.245.1 | 16 | 11.6 | odd | 10 | |||
363.3.h.m.245.4 | 16 | 33.17 | even | 10 | |||
363.3.h.m.251.1 | 16 | 33.8 | even | 10 | |||
363.3.h.m.251.4 | 16 | 11.8 | odd | 10 | |||
363.3.h.m.269.1 | 16 | 11.7 | odd | 10 | |||
363.3.h.m.269.4 | 16 | 33.29 | even | 10 | |||
363.3.h.m.323.1 | 16 | 33.2 | even | 10 | |||
363.3.h.m.323.4 | 16 | 11.2 | odd | 10 | |||
528.3.i.d.353.3 | 4 | 44.43 | even | 2 | |||
528.3.i.d.353.4 | 4 | 132.131 | odd | 2 |