Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(251,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 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("560.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bc (of order \(4\), degree \(2\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(64\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 251.20 | ||
Character | \(\chi\) | \(=\) | 560.251 |
Dual form | 560.2.bc.a.531.20 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.883798 | + | 1.10404i | −0.624939 | + | 0.780673i | ||||
\(3\) | 1.16174 | − | 1.16174i | 0.670731 | − | 0.670731i | −0.287153 | − | 0.957885i | \(-0.592709\pi\) |
0.957885 | + | 0.287153i | \(0.0927090\pi\) | |||||||
\(4\) | −0.437803 | − | 1.95149i | −0.218902 | − | 0.975747i | ||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | 0.255863 | + | 2.30935i | 0.104456 | + | 0.942788i | ||||
\(7\) | 2.48811 | + | 0.899608i | 0.940418 | + | 0.340020i | ||||
\(8\) | 2.54145 | + | 1.24137i | 0.898540 | + | 0.438892i | ||||
\(9\) | 0.300718i | 0.100239i | ||||||||
\(10\) | 0.155734 | + | 1.40561i | 0.0492474 | + | 0.444494i | ||||
\(11\) | −3.08981 | + | 3.08981i | −0.931613 | + | 0.931613i | −0.997807 | − | 0.0661940i | \(-0.978914\pi\) |
0.0661940 | + | 0.997807i | \(0.478914\pi\) | |||||||
\(12\) | −2.77574 | − | 1.75852i | −0.801288 | − | 0.507640i | ||||
\(13\) | 3.64354 | + | 3.64354i | 1.01054 | + | 1.01054i | 0.999944 | + | 0.0105914i | \(0.00337140\pi\) |
0.0105914 | + | 0.999944i | \(0.496629\pi\) | |||||||
\(14\) | −3.19219 | + | 1.95190i | −0.853149 | + | 0.521668i | ||||
\(15\) | − | 1.64295i | − | 0.424208i | ||||||
\(16\) | −3.61666 | + | 1.70874i | −0.904164 | + | 0.427185i | ||||
\(17\) | − | 1.90479i | − | 0.461979i | −0.972956 | − | 0.230989i | \(-0.925804\pi\) | ||
0.972956 | − | 0.230989i | \(-0.0741963\pi\) | |||||||
\(18\) | −0.332005 | − | 0.265774i | −0.0782543 | − | 0.0626436i | ||||
\(19\) | 2.96251 | − | 2.96251i | 0.679647 | − | 0.679647i | −0.280273 | − | 0.959920i | \(-0.590425\pi\) |
0.959920 | + | 0.280273i | \(0.0904250\pi\) | |||||||
\(20\) | −1.68949 | − | 1.07034i | −0.377781 | − | 0.239335i | ||||
\(21\) | 3.93565 | − | 1.84543i | 0.858830 | − | 0.402706i | ||||
\(22\) | −0.680503 | − | 6.14204i | −0.145084 | − | 1.30949i | ||||
\(23\) | 0.655690 | 0.136721 | 0.0683604 | − | 0.997661i | \(-0.478223\pi\) | ||||
0.0683604 | + | 0.997661i | \(0.478223\pi\) | |||||||
\(24\) | 4.39466 | − | 1.51036i | 0.897057 | − | 0.308300i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | −7.24276 | + | 0.802457i | −1.42042 | + | 0.157375i | ||||
\(27\) | 3.83458 | + | 3.83458i | 0.737965 | + | 0.737965i | ||||
\(28\) | 0.666275 | − | 5.24939i | 0.125914 | − | 0.992041i | ||||
\(29\) | 2.68009 | − | 2.68009i | 0.497680 | − | 0.497680i | −0.413035 | − | 0.910715i | \(-0.635531\pi\) |
0.910715 | + | 0.413035i | \(0.135531\pi\) | |||||||
\(30\) | 1.81388 | + | 1.45203i | 0.331168 | + | 0.265104i | ||||
\(31\) | 3.01437 | 0.541398 | 0.270699 | − | 0.962664i | \(-0.412745\pi\) | ||||
0.270699 | + | 0.962664i | \(0.412745\pi\) | |||||||
\(32\) | 1.30988 | − | 5.50311i | 0.231555 | − | 0.972822i | ||||
\(33\) | 7.17911i | 1.24972i | ||||||||
\(34\) | 2.10296 | + | 1.68345i | 0.360654 | + | 0.288709i | ||||
\(35\) | 2.39548 | − | 1.12324i | 0.404910 | − | 0.189863i | ||||
\(36\) | 0.586850 | − | 0.131656i | 0.0978084 | − | 0.0219426i | ||||
\(37\) | −6.08074 | − | 6.08074i | −0.999667 | − | 0.999667i | 0.000333113 | − | 1.00000i | \(-0.499894\pi\) |
−1.00000 | 0.000333113i | \(0.999894\pi\) | ||||||||
\(38\) | 0.652467 | + | 5.88899i | 0.105844 | + | 0.955321i | ||||
\(39\) | 8.46569 | 1.35559 | ||||||||
\(40\) | 2.67486 | − | 0.919296i | 0.422933 | − | 0.145353i | ||||
\(41\) | 7.27882 | 1.13676 | 0.568380 | − | 0.822766i | \(-0.307570\pi\) | ||||
0.568380 | + | 0.822766i | \(0.307570\pi\) | |||||||
\(42\) | −1.44089 | + | 5.97610i | −0.222335 | + | 0.922132i | ||||
\(43\) | −0.168678 | + | 0.168678i | −0.0257232 | + | 0.0257232i | −0.719851 | − | 0.694128i | \(-0.755790\pi\) |
0.694128 | + | 0.719851i | \(0.255790\pi\) | |||||||
\(44\) | 7.38247 | + | 4.67702i | 1.11295 | + | 0.705087i | ||||
\(45\) | 0.212640 | + | 0.212640i | 0.0316985 | + | 0.0316985i | ||||
\(46\) | −0.579497 | + | 0.723907i | −0.0854422 | + | 0.106734i | ||||
\(47\) | −8.95609 | −1.30638 | −0.653190 | − | 0.757194i | \(-0.726570\pi\) | ||||
−0.653190 | + | 0.757194i | \(0.726570\pi\) | |||||||
\(48\) | −2.21650 | + | 6.18673i | −0.319924 | + | 0.892978i | ||||
\(49\) | 5.38141 | + | 4.47665i | 0.768773 | + | 0.639522i | ||||
\(50\) | 1.10404 | + | 0.883798i | 0.156135 | + | 0.124988i | ||||
\(51\) | −2.21287 | − | 2.21287i | −0.309864 | − | 0.309864i | ||||
\(52\) | 5.51519 | − | 8.70549i | 0.764819 | − | 1.20723i | ||||
\(53\) | −6.49178 | − | 6.49178i | −0.891714 | − | 0.891714i | 0.102971 | − | 0.994684i | \(-0.467165\pi\) |
−0.994684 | + | 0.102971i | \(0.967165\pi\) | |||||||
\(54\) | −7.62251 | + | 0.844532i | −1.03729 | + | 0.114926i | ||||
\(55\) | 4.36965i | 0.589204i | ||||||||
\(56\) | 5.20668 | + | 5.37499i | 0.695771 | + | 0.718263i | ||||
\(57\) | − | 6.88334i | − | 0.911721i | ||||||
\(58\) | 0.590266 | + | 5.32758i | 0.0775057 | + | 0.699545i | ||||
\(59\) | −7.08273 | − | 7.08273i | −0.922094 | − | 0.922094i | 0.0750837 | − | 0.997177i | \(-0.476078\pi\) |
−0.997177 | + | 0.0750837i | \(0.976078\pi\) | |||||||
\(60\) | −3.20620 | + | 0.719289i | −0.413919 | + | 0.0928598i | ||||
\(61\) | 3.27600 | + | 3.27600i | 0.419448 | + | 0.419448i | 0.885014 | − | 0.465565i | \(-0.154149\pi\) |
−0.465565 | + | 0.885014i | \(0.654149\pi\) | |||||||
\(62\) | −2.66410 | + | 3.32799i | −0.338341 | + | 0.422655i | ||||
\(63\) | −0.270529 | + | 0.748222i | −0.0340834 | + | 0.0942671i | ||||
\(64\) | 4.91798 | + | 6.30979i | 0.614748 | + | 0.788724i | ||||
\(65\) | 5.15274 | 0.639119 | ||||||||
\(66\) | −7.92602 | − | 6.34488i | −0.975626 | − | 0.781001i | ||||
\(67\) | −0.886744 | − | 0.886744i | −0.108333 | − | 0.108333i | 0.650863 | − | 0.759196i | \(-0.274407\pi\) |
−0.759196 | + | 0.650863i | \(0.774407\pi\) | |||||||
\(68\) | −3.71718 | + | 0.833922i | −0.450774 | + | 0.101128i | ||||
\(69\) | 0.761741 | − | 0.761741i | 0.0917029 | − | 0.0917029i | ||||
\(70\) | −0.877017 | + | 3.63742i | −0.104824 | + | 0.434755i | ||||
\(71\) | −15.5247 | −1.84244 | −0.921222 | − | 0.389038i | \(-0.872807\pi\) | ||||
−0.921222 | + | 0.389038i | \(0.872807\pi\) | |||||||
\(72\) | −0.373304 | + | 0.764262i | −0.0439943 | + | 0.0900692i | ||||
\(73\) | 6.26678 | 0.733471 | 0.366736 | − | 0.930325i | \(-0.380475\pi\) | ||||
0.366736 | + | 0.930325i | \(0.380475\pi\) | |||||||
\(74\) | 12.0875 | − | 1.33923i | 1.40514 | − | 0.155682i | ||||
\(75\) | −1.16174 | − | 1.16174i | −0.134146 | − | 0.134146i | ||||
\(76\) | −7.07832 | − | 4.48433i | −0.811940 | − | 0.514388i | ||||
\(77\) | −10.4674 | + | 4.90818i | −1.19287 | + | 0.559339i | ||||
\(78\) | −7.48195 | + | 9.34645i | −0.847165 | + | 1.05828i | ||||
\(79\) | 12.3148i | 1.38552i | 0.721168 | + | 0.692760i | \(0.243605\pi\) | ||||
−0.721168 | + | 0.692760i | \(0.756395\pi\) | |||||||
\(80\) | −1.34910 | + | 3.76562i | −0.150834 | + | 0.421010i | ||||
\(81\) | 8.00741 | 0.889713 | ||||||||
\(82\) | −6.43300 | + | 8.03610i | −0.710406 | + | 0.887439i | ||||
\(83\) | −2.44679 | + | 2.44679i | −0.268570 | + | 0.268570i | −0.828524 | − | 0.559954i | \(-0.810819\pi\) |
0.559954 | + | 0.828524i | \(0.310819\pi\) | |||||||
\(84\) | −5.32439 | − | 6.87247i | −0.580938 | − | 0.749847i | ||||
\(85\) | −1.34689 | − | 1.34689i | −0.146091 | − | 0.146091i | ||||
\(86\) | −0.0371499 | − | 0.335305i | −0.00400598 | − | 0.0361568i | ||||
\(87\) | − | 6.22713i | − | 0.667619i | ||||||
\(88\) | −11.6882 | + | 4.01700i | −1.24597 | + | 0.428214i | ||||
\(89\) | 12.5968 | 1.33525 | 0.667627 | − | 0.744496i | \(-0.267310\pi\) | ||||
0.667627 | + | 0.744496i | \(0.267310\pi\) | |||||||
\(90\) | −0.422694 | + | 0.0468321i | −0.0445558 | + | 0.00493654i | ||||
\(91\) | 5.78778 | + | 12.3433i | 0.606724 | + | 1.29393i | ||||
\(92\) | −0.287063 | − | 1.27957i | −0.0299284 | − | 0.133405i | ||||
\(93\) | 3.50192 | − | 3.50192i | 0.363132 | − | 0.363132i | ||||
\(94\) | 7.91537 | − | 9.88787i | 0.816408 | − | 1.01986i | ||||
\(95\) | − | 4.18963i | − | 0.429847i | ||||||
\(96\) | −4.87145 | − | 7.91492i | −0.497190 | − | 0.807813i | ||||
\(97\) | 13.2440i | 1.34472i | 0.740222 | + | 0.672362i | \(0.234720\pi\) | ||||
−0.740222 | + | 0.672362i | \(0.765280\pi\) | |||||||
\(98\) | −9.69848 | + | 1.98483i | −0.979694 | + | 0.200498i | ||||
\(99\) | −0.929163 | − | 0.929163i | −0.0933844 | − | 0.0933844i | ||||
\(100\) | −1.95149 | + | 0.437803i | −0.195149 | + | 0.0437803i | ||||
\(101\) | −1.62825 | + | 1.62825i | −0.162017 | + | 0.162017i | −0.783460 | − | 0.621443i | \(-0.786547\pi\) |
0.621443 | + | 0.783460i | \(0.286547\pi\) | |||||||
\(102\) | 4.39882 | − | 0.487365i | 0.435548 | − | 0.0482563i | ||||
\(103\) | − | 17.7281i | − | 1.74680i | −0.487001 | − | 0.873401i | \(-0.661909\pi\) | ||
0.487001 | − | 0.873401i | \(-0.338091\pi\) | |||||||
\(104\) | 4.73689 | + | 13.7829i | 0.464491 | + | 1.35152i | ||||
\(105\) | 1.47801 | − | 4.08784i | 0.144239 | − | 0.398933i | ||||
\(106\) | 12.9046 | − | 1.42976i | 1.25340 | − | 0.138870i | ||||
\(107\) | −9.36421 | + | 9.36421i | −0.905272 | + | 0.905272i | −0.995886 | − | 0.0906139i | \(-0.971117\pi\) |
0.0906139 | + | 0.995886i | \(0.471117\pi\) | |||||||
\(108\) | 5.80436 | − | 9.16195i | 0.558525 | − | 0.881609i | ||||
\(109\) | 2.52170 | − | 2.52170i | 0.241535 | − | 0.241535i | −0.575950 | − | 0.817485i | \(-0.695368\pi\) |
0.817485 | + | 0.575950i | \(0.195368\pi\) | |||||||
\(110\) | −4.82426 | − | 3.86189i | −0.459976 | − | 0.368217i | ||||
\(111\) | −14.1285 | −1.34102 | ||||||||
\(112\) | −10.5358 | + | 0.997969i | −0.995544 | + | 0.0942992i | ||||
\(113\) | 1.25495 | 0.118056 | 0.0590279 | − | 0.998256i | \(-0.481200\pi\) | ||||
0.0590279 | + | 0.998256i | \(0.481200\pi\) | |||||||
\(114\) | 7.59948 | + | 6.08348i | 0.711756 | + | 0.569770i | ||||
\(115\) | 0.463643 | − | 0.463643i | 0.0432349 | − | 0.0432349i | ||||
\(116\) | −6.40353 | − | 4.05682i | −0.594553 | − | 0.376667i | ||||
\(117\) | −1.09568 | + | 1.09568i | −0.101296 | + | 0.101296i | ||||
\(118\) | 14.0793 | − | 1.55991i | 1.29611 | − | 0.143601i | ||||
\(119\) | 1.71356 | − | 4.73933i | 0.157082 | − | 0.434453i | ||||
\(120\) | 2.03951 | − | 4.17548i | 0.186181 | − | 0.381167i | ||||
\(121\) | − | 8.09385i | − | 0.735805i | ||||||
\(122\) | −6.51214 | + | 0.721509i | −0.589582 | + | 0.0653224i | ||||
\(123\) | 8.45610 | − | 8.45610i | 0.762461 | − | 0.762461i | ||||
\(124\) | −1.31970 | − | 5.88253i | −0.118513 | − | 0.528267i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −0.586973 | − | 0.959951i | −0.0522917 | − | 0.0855192i | ||||
\(127\) | − | 12.2925i | − | 1.09078i | −0.838183 | − | 0.545389i | \(-0.816382\pi\) | ||
0.838183 | − | 0.545389i | \(-0.183618\pi\) | |||||||
\(128\) | −11.3128 | − | 0.146933i | −0.999916 | − | 0.0129871i | ||||
\(129\) | 0.391921i | 0.0345067i | ||||||||
\(130\) | −4.55398 | + | 5.68882i | −0.399410 | + | 0.498943i | ||||
\(131\) | 6.73342 | − | 6.73342i | 0.588302 | − | 0.588302i | −0.348870 | − | 0.937171i | \(-0.613434\pi\) |
0.937171 | + | 0.348870i | \(0.113434\pi\) | |||||||
\(132\) | 14.0100 | − | 3.14304i | 1.21941 | − | 0.273567i | ||||
\(133\) | 10.0362 | − | 4.70597i | 0.870246 | − | 0.408059i | ||||
\(134\) | 1.76270 | − | 0.195298i | 0.152274 | − | 0.0168711i | ||||
\(135\) | 5.42291 | 0.466730 | ||||||||
\(136\) | 2.36455 | − | 4.84093i | 0.202759 | − | 0.415106i | ||||
\(137\) | 17.0309i | 1.45505i | 0.686080 | + | 0.727526i | \(0.259330\pi\) | ||||
−0.686080 | + | 0.727526i | \(0.740670\pi\) | |||||||
\(138\) | 0.167767 | + | 1.51422i | 0.0142813 | + | 0.128899i | ||||
\(139\) | −10.9977 | − | 10.9977i | −0.932812 | − | 0.932812i | 0.0650691 | − | 0.997881i | \(-0.479273\pi\) |
−0.997881 | + | 0.0650691i | \(0.979273\pi\) | |||||||
\(140\) | −3.24075 | − | 4.18301i | −0.273893 | − | 0.353529i | ||||
\(141\) | −10.4047 | + | 10.4047i | −0.876230 | + | 0.876230i | ||||
\(142\) | 13.7207 | − | 17.1399i | 1.15142 | − | 1.43835i | ||||
\(143\) | −22.5157 | −1.88286 | ||||||||
\(144\) | −0.513850 | − | 1.08760i | −0.0428208 | − | 0.0906330i | ||||
\(145\) | − | 3.79022i | − | 0.314760i | ||||||
\(146\) | −5.53857 | + | 6.91877i | −0.458375 | + | 0.572602i | ||||
\(147\) | 11.4525 | − | 1.05109i | 0.944587 | − | 0.0866928i | ||||
\(148\) | −9.20435 | + | 14.5287i | −0.756593 | + | 1.19425i | ||||
\(149\) | −0.189559 | − | 0.189559i | −0.0155293 | − | 0.0155293i | 0.699299 | − | 0.714829i | \(-0.253495\pi\) |
−0.714829 | + | 0.699299i | \(0.753495\pi\) | |||||||
\(150\) | 2.30935 | − | 0.255863i | 0.188558 | − | 0.0208911i | ||||
\(151\) | −8.33315 | −0.678142 | −0.339071 | − | 0.940761i | \(-0.610113\pi\) | ||||
−0.339071 | + | 0.940761i | \(0.610113\pi\) | |||||||
\(152\) | 11.2067 | − | 3.85151i | 0.908982 | − | 0.312398i | ||||
\(153\) | 0.572805 | 0.0463085 | ||||||||
\(154\) | 3.83226 | − | 15.8943i | 0.308812 | − | 1.28080i | ||||
\(155\) | 2.13148 | − | 2.13148i | 0.171205 | − | 0.171205i | ||||
\(156\) | −3.70631 | − | 16.5207i | −0.296742 | − | 1.32272i | ||||
\(157\) | −15.2438 | − | 15.2438i | −1.21659 | − | 1.21659i | −0.968819 | − | 0.247770i | \(-0.920302\pi\) |
−0.247770 | − | 0.968819i | \(-0.579698\pi\) | |||||||
\(158\) | −13.5960 | − | 10.8838i | −1.08164 | − | 0.865866i | ||||
\(159\) | −15.0835 | −1.19620 | ||||||||
\(160\) | −2.96507 | − | 4.81751i | −0.234409 | − | 0.380857i | ||||
\(161\) | 1.63143 | + | 0.589864i | 0.128575 | + | 0.0464878i | ||||
\(162\) | −7.07693 | + | 8.84049i | −0.556016 | + | 0.694575i | ||||
\(163\) | −5.83870 | − | 5.83870i | −0.457323 | − | 0.457323i | 0.440453 | − | 0.897776i | \(-0.354818\pi\) |
−0.897776 | + | 0.440453i | \(0.854818\pi\) | |||||||
\(164\) | −3.18669 | − | 14.2046i | −0.248839 | − | 1.10919i | ||||
\(165\) | 5.07640 | + | 5.07640i | 0.395197 | + | 0.395197i | ||||
\(166\) | −0.538884 | − | 4.86382i | −0.0418255 | − | 0.377505i | ||||
\(167\) | 4.19425i | 0.324561i | 0.986745 | + | 0.162281i | \(0.0518850\pi\) | ||||
−0.986745 | + | 0.162281i | \(0.948115\pi\) | |||||||
\(168\) | 12.2931 | + | 0.195537i | 0.948437 | + | 0.0150860i | ||||
\(169\) | 13.5507i | 1.04236i | ||||||||
\(170\) | 2.67739 | − | 0.296640i | 0.205347 | − | 0.0227513i | ||||
\(171\) | 0.890883 | + | 0.890883i | 0.0681275 | + | 0.0681275i | ||||
\(172\) | 0.403022 | + | 0.255327i | 0.0307302 | + | 0.0194685i | ||||
\(173\) | −15.7848 | − | 15.7848i | −1.20010 | − | 1.20010i | −0.974137 | − | 0.225959i | \(-0.927448\pi\) |
−0.225959 | − | 0.974137i | \(-0.572552\pi\) | |||||||
\(174\) | 6.87500 | + | 5.50353i | 0.521192 | + | 0.417221i | ||||
\(175\) | 0.899608 | − | 2.48811i | 0.0680040 | − | 0.188084i | ||||
\(176\) | 5.89509 | − | 16.4545i | 0.444359 | − | 1.24030i | ||||
\(177\) | −16.4566 | −1.23695 | ||||||||
\(178\) | −11.1330 | + | 13.9073i | −0.834453 | + | 1.04240i | ||||
\(179\) | 4.18280 | + | 4.18280i | 0.312637 | + | 0.312637i | 0.845930 | − | 0.533293i | \(-0.179046\pi\) |
−0.533293 | + | 0.845930i | \(0.679046\pi\) | |||||||
\(180\) | 0.321871 | − | 0.508060i | 0.0239909 | − | 0.0378686i | ||||
\(181\) | 5.91259 | − | 5.91259i | 0.439479 | − | 0.439479i | −0.452357 | − | 0.891837i | \(-0.649417\pi\) |
0.891837 | + | 0.452357i | \(0.149417\pi\) | |||||||
\(182\) | −18.7427 | − | 4.51904i | −1.38930 | − | 0.334973i | ||||
\(183\) | 7.61171 | 0.562674 | ||||||||
\(184\) | 1.66641 | + | 0.813956i | 0.122849 | + | 0.0600056i | ||||
\(185\) | −8.59946 | −0.632245 | ||||||||
\(186\) | 0.771267 | + | 6.96124i | 0.0565520 | + | 0.510423i | ||||
\(187\) | 5.88543 | + | 5.88543i | 0.430385 | + | 0.430385i | ||||
\(188\) | 3.92101 | + | 17.4778i | 0.285969 | + | 1.27470i | ||||
\(189\) | 6.09125 | + | 12.9905i | 0.443073 | + | 0.944918i | ||||
\(190\) | 4.62551 | + | 3.70278i | 0.335570 | + | 0.268628i | ||||
\(191\) | 14.8787i | 1.07659i | 0.842758 | + | 0.538293i | \(0.180930\pi\) | ||||
−0.842758 | + | 0.538293i | \(0.819070\pi\) | |||||||
\(192\) | 13.0438 | + | 1.61692i | 0.941352 | + | 0.116691i | ||||
\(193\) | −4.17202 | −0.300309 | −0.150154 | − | 0.988663i | \(-0.547977\pi\) | ||||
−0.150154 | + | 0.988663i | \(0.547977\pi\) | |||||||
\(194\) | −14.6219 | − | 11.7050i | −1.04979 | − | 0.840371i | ||||
\(195\) | 5.98615 | − | 5.98615i | 0.428677 | − | 0.428677i | ||||
\(196\) | 6.38016 | − | 12.4617i | 0.455726 | − | 0.890120i | ||||
\(197\) | 11.7586 | + | 11.7586i | 0.837765 | + | 0.837765i | 0.988564 | − | 0.150799i | \(-0.0481847\pi\) |
−0.150799 | + | 0.988564i | \(0.548185\pi\) | |||||||
\(198\) | 1.84702 | − | 0.204640i | 0.131262 | − | 0.0145431i | ||||
\(199\) | 20.0732i | 1.42295i | 0.702711 | + | 0.711476i | \(0.251973\pi\) | ||||
−0.702711 | + | 0.711476i | \(0.748027\pi\) | |||||||
\(200\) | 1.24137 | − | 2.54145i | 0.0877784 | − | 0.179708i | ||||
\(201\) | −2.06033 | −0.145325 | ||||||||
\(202\) | −0.358608 | − | 3.23670i | −0.0252316 | − | 0.227733i | ||||
\(203\) | 9.07939 | − | 4.25733i | 0.637248 | − | 0.298806i | ||||
\(204\) | −3.34960 | + | 5.28720i | −0.234519 | + | 0.370178i | ||||
\(205\) | 5.14690 | − | 5.14690i | 0.359475 | − | 0.359475i | ||||
\(206\) | 19.5725 | + | 15.6681i | 1.36368 | + | 1.09165i | ||||
\(207\) | 0.197178i | 0.0137048i | ||||||||
\(208\) | −19.4033 | − | 6.95156i | −1.34538 | − | 0.482004i | ||||
\(209\) | 18.3072i | 1.26634i | ||||||||
\(210\) | 3.20688 | + | 5.24461i | 0.221295 | + | 0.361912i | ||||
\(211\) | −5.82363 | − | 5.82363i | −0.400915 | − | 0.400915i | 0.477640 | − | 0.878555i | \(-0.341492\pi\) |
−0.878555 | + | 0.477640i | \(0.841492\pi\) | |||||||
\(212\) | −9.82654 | + | 15.5108i | −0.674889 | + | 1.06528i | ||||
\(213\) | −18.0357 | + | 18.0357i | −1.23578 | + | 1.23578i | ||||
\(214\) | −2.06238 | − | 18.6145i | −0.140982 | − | 1.27246i | ||||
\(215\) | 0.238547i | 0.0162688i | ||||||||
\(216\) | 4.98526 | + | 14.5055i | 0.339204 | + | 0.986978i | ||||
\(217\) | 7.50010 | + | 2.71175i | 0.509140 | + | 0.184086i | ||||
\(218\) | 0.555382 | + | 5.01273i | 0.0376152 | + | 0.339505i | ||||
\(219\) | 7.28038 | − | 7.28038i | 0.491962 | − | 0.491962i | ||||
\(220\) | 8.52735 | − | 1.91305i | 0.574914 | − | 0.128978i | ||||
\(221\) | 6.94016 | − | 6.94016i | 0.466846 | − | 0.466846i | ||||
\(222\) | 12.4867 | − | 15.5984i | 0.838053 | − | 1.04689i | ||||
\(223\) | −13.0612 | −0.874642 | −0.437321 | − | 0.899305i | \(-0.644073\pi\) | ||||
−0.437321 | + | 0.899305i | \(0.644073\pi\) | |||||||
\(224\) | 8.20976 | − | 12.5140i | 0.548538 | − | 0.836126i | ||||
\(225\) | 0.300718 | 0.0200479 | ||||||||
\(226\) | −1.10912 | + | 1.38551i | −0.0737777 | + | 0.0921630i | ||||
\(227\) | −6.47580 | + | 6.47580i | −0.429814 | + | 0.429814i | −0.888565 | − | 0.458751i | \(-0.848297\pi\) |
0.458751 | + | 0.888565i | \(0.348297\pi\) | |||||||
\(228\) | −13.4328 | + | 3.01355i | −0.889609 | + | 0.199577i | ||||
\(229\) | 16.6199 | − | 16.6199i | 1.09827 | − | 1.09827i | 0.103660 | − | 0.994613i | \(-0.466945\pi\) |
0.994613 | − | 0.103660i | \(-0.0330552\pi\) | |||||||
\(230\) | 0.102113 | + | 0.921646i | 0.00673314 | + | 0.0607715i | ||||
\(231\) | −6.45839 | + | 17.8624i | −0.424931 | + | 1.17526i | ||||
\(232\) | 10.1383 | − | 3.48433i | 0.665613 | − | 0.228758i | ||||
\(233\) | − | 20.6706i | − | 1.35418i | −0.735902 | − | 0.677088i | \(-0.763242\pi\) | ||
0.735902 | − | 0.677088i | \(-0.236758\pi\) | |||||||
\(234\) | −0.241314 | − | 2.17803i | −0.0157752 | − | 0.142382i | ||||
\(235\) | −6.33291 | + | 6.33291i | −0.413114 | + | 0.413114i | ||||
\(236\) | −10.7211 | + | 16.9228i | −0.697882 | + | 1.10158i | ||||
\(237\) | 14.3066 | + | 14.3066i | 0.929311 | + | 0.929311i | ||||
\(238\) | 3.71796 | + | 6.08044i | 0.240999 | + | 0.394137i | ||||
\(239\) | 4.70064i | 0.304059i | 0.988376 | + | 0.152030i | \(0.0485809\pi\) | ||||
−0.988376 | + | 0.152030i | \(0.951419\pi\) | |||||||
\(240\) | 2.80738 | + | 5.94198i | 0.181215 | + | 0.383553i | ||||
\(241\) | 3.80524i | 0.245117i | 0.992461 | + | 0.122558i | \(0.0391099\pi\) | ||||
−0.992461 | + | 0.122558i | \(0.960890\pi\) | |||||||
\(242\) | 8.93593 | + | 7.15333i | 0.574423 | + | 0.459833i | ||||
\(243\) | −2.20120 | + | 2.20120i | −0.141207 | + | 0.141207i | ||||
\(244\) | 4.95884 | − | 7.82733i | 0.317457 | − | 0.501093i | ||||
\(245\) | 6.97070 | − | 0.639761i | 0.445342 | − | 0.0408728i | ||||
\(246\) | 1.86238 | + | 16.8093i | 0.118741 | + | 1.07172i | ||||
\(247\) | 21.5881 | 1.37361 | ||||||||
\(248\) | 7.66089 | + | 3.74196i | 0.486467 | + | 0.237615i | ||||
\(249\) | 5.68507i | 0.360277i | ||||||||
\(250\) | 1.40561 | − | 0.155734i | 0.0888987 | − | 0.00984949i | ||||
\(251\) | −8.25157 | − | 8.25157i | −0.520835 | − | 0.520835i | 0.396989 | − | 0.917823i | \(-0.370055\pi\) |
−0.917823 | + | 0.396989i | \(0.870055\pi\) | |||||||
\(252\) | 1.57859 | + | 0.200361i | 0.0994417 | + | 0.0126216i | ||||
\(253\) | −2.02596 | + | 2.02596i | −0.127371 | + | 0.127371i | ||||
\(254\) | 13.5713 | + | 10.8640i | 0.851542 | + | 0.681671i | ||||
\(255\) | −3.12947 | −0.195975 | ||||||||
\(256\) | 10.1604 | − | 12.3599i | 0.635025 | − | 0.772491i | ||||
\(257\) | 10.3771i | 0.647307i | 0.946176 | + | 0.323654i | \(0.104911\pi\) | ||||
−0.946176 | + | 0.323654i | \(0.895089\pi\) | |||||||
\(258\) | −0.432696 | − | 0.346379i | −0.0269385 | − | 0.0215646i | ||||
\(259\) | −9.65928 | − | 20.5998i | −0.600198 | − | 1.28001i | ||||
\(260\) | −2.25589 | − | 10.0555i | −0.139904 | − | 0.623618i | ||||
\(261\) | 0.805952 | + | 0.805952i | 0.0498872 | + | 0.0498872i | ||||
\(262\) | 1.48298 | + | 13.3849i | 0.0916186 | + | 0.826924i | ||||
\(263\) | −24.4187 | −1.50572 | −0.752862 | − | 0.658178i | \(-0.771327\pi\) | ||||
−0.752862 | + | 0.658178i | \(0.771327\pi\) | |||||||
\(264\) | −8.91196 | + | 18.2454i | −0.548493 | + | 1.12293i | ||||
\(265\) | −9.18076 | −0.563969 | ||||||||
\(266\) | −3.67437 | + | 15.2394i | −0.225290 | + | 0.934390i | ||||
\(267\) | 14.6342 | − | 14.6342i | 0.895597 | − | 0.895597i | ||||
\(268\) | −1.34226 | + | 2.11870i | −0.0819913 | + | 0.129420i | ||||
\(269\) | −13.6160 | − | 13.6160i | −0.830183 | − | 0.830183i | 0.157359 | − | 0.987541i | \(-0.449702\pi\) |
−0.987541 | + | 0.157359i | \(0.949702\pi\) | |||||||
\(270\) | −4.79276 | + | 5.98711i | −0.291678 | + | 0.364364i | ||||
\(271\) | −5.57441 | −0.338621 | −0.169311 | − | 0.985563i | \(-0.554154\pi\) | ||||
−0.169311 | + | 0.985563i | \(0.554154\pi\) | |||||||
\(272\) | 3.25479 | + | 6.88896i | 0.197351 | + | 0.417705i | ||||
\(273\) | 21.0636 | + | 7.61580i | 1.27483 | + | 0.460929i | ||||
\(274\) | −18.8028 | − | 15.0519i | −1.13592 | − | 0.909319i | ||||
\(275\) | 3.08981 | + | 3.08981i | 0.186323 | + | 0.186323i | ||||
\(276\) | −1.82003 | − | 1.15304i | −0.109553 | − | 0.0694049i | ||||
\(277\) | 10.7412 | + | 10.7412i | 0.645377 | + | 0.645377i | 0.951872 | − | 0.306496i | \(-0.0991564\pi\) |
−0.306496 | + | 0.951872i | \(0.599156\pi\) | |||||||
\(278\) | 21.8616 | − | 2.42214i | 1.31117 | − | 0.145271i | ||||
\(279\) | 0.906478i | 0.0542694i | ||||||||
\(280\) | 7.48237 | + | 0.119016i | 0.447157 | + | 0.00711257i | ||||
\(281\) | 8.61214i | 0.513757i | 0.966444 | + | 0.256879i | \(0.0826941\pi\) | ||||
−0.966444 | + | 0.256879i | \(0.917306\pi\) | |||||||
\(282\) | −2.29153 | − | 20.6828i | −0.136459 | − | 1.23164i | ||||
\(283\) | 3.17809 | + | 3.17809i | 0.188918 | + | 0.188918i | 0.795228 | − | 0.606310i | \(-0.207351\pi\) |
−0.606310 | + | 0.795228i | \(0.707351\pi\) | |||||||
\(284\) | 6.79677 | + | 30.2964i | 0.403314 | + | 1.79776i | ||||
\(285\) | −4.86726 | − | 4.86726i | −0.288311 | − | 0.288311i | ||||
\(286\) | 19.8993 | − | 24.8582i | 1.17667 | − | 1.46989i | ||||
\(287\) | 18.1105 | + | 6.54809i | 1.06903 | + | 0.386521i | ||||
\(288\) | 1.65489 | + | 0.393904i | 0.0975152 | + | 0.0232110i | ||||
\(289\) | 13.3718 | 0.786576 | ||||||||
\(290\) | 4.18455 | + | 3.34978i | 0.245725 | + | 0.196706i | ||||
\(291\) | 15.3861 | + | 15.3861i | 0.901949 | + | 0.901949i | ||||
\(292\) | −2.74362 | − | 12.2296i | −0.160558 | − | 0.715683i | ||||
\(293\) | −2.49809 | + | 2.49809i | −0.145940 | + | 0.145940i | −0.776302 | − | 0.630362i | \(-0.782907\pi\) |
0.630362 | + | 0.776302i | \(0.282907\pi\) | |||||||
\(294\) | −8.96125 | + | 13.5730i | −0.522631 | + | 0.791592i | ||||
\(295\) | −10.0165 | −0.583183 | ||||||||
\(296\) | −7.90545 | − | 23.0024i | −0.459495 | − | 1.33699i | ||||
\(297\) | −23.6962 | −1.37500 | ||||||||
\(298\) | 0.376813 | − | 0.0417488i | 0.0218282 | − | 0.00241844i | ||||
\(299\) | 2.38903 | + | 2.38903i | 0.138161 | + | 0.138161i | ||||
\(300\) | −1.75852 | + | 2.77574i | −0.101528 | + | 0.160258i | ||||
\(301\) | −0.571435 | + | 0.267946i | −0.0329370 | + | 0.0154442i | ||||
\(302\) | 7.36482 | − | 9.20012i | 0.423798 | − | 0.529407i | ||||
\(303\) | 3.78321i | 0.217340i | ||||||||
\(304\) | −5.65222 | + | 15.7766i | −0.324177 | + | 0.904848i | ||||
\(305\) | 4.63296 | 0.265282 | ||||||||
\(306\) | −0.506243 | + | 0.632399i | −0.0289400 | + | 0.0361518i | ||||
\(307\) | 6.43361 | − | 6.43361i | 0.367185 | − | 0.367185i | −0.499264 | − | 0.866450i | \(-0.666396\pi\) |
0.866450 | + | 0.499264i | \(0.166396\pi\) | |||||||
\(308\) | 14.1609 | + | 18.2783i | 0.806895 | + | 1.04150i | ||||
\(309\) | −20.5955 | − | 20.5955i | −1.17163 | − | 1.17163i | ||||
\(310\) | 0.469441 | + | 4.23704i | 0.0266624 | + | 0.240648i | ||||
\(311\) | 1.47719i | 0.0837637i | 0.999123 | + | 0.0418818i | \(0.0133353\pi\) | ||||
−0.999123 | + | 0.0418818i | \(0.986665\pi\) | |||||||
\(312\) | 21.5152 | + | 10.5091i | 1.21806 | + | 0.594960i | ||||
\(313\) | 26.5456 | 1.50045 | 0.750224 | − | 0.661184i | \(-0.229946\pi\) | ||||
0.750224 | + | 0.661184i | \(0.229946\pi\) | |||||||
\(314\) | 30.3022 | − | 3.35732i | 1.71005 | − | 0.189464i | ||||
\(315\) | 0.337780 | + | 0.720365i | 0.0190317 | + | 0.0405880i | ||||
\(316\) | 24.0322 | − | 5.39145i | 1.35192 | − | 0.303293i | ||||
\(317\) | −5.52565 | + | 5.52565i | −0.310352 | + | 0.310352i | −0.845046 | − | 0.534694i | \(-0.820427\pi\) |
0.534694 | + | 0.845046i | \(0.320427\pi\) | |||||||
\(318\) | 13.3308 | − | 16.6528i | 0.747553 | − | 0.933842i | ||||
\(319\) | 16.5619i | 0.927290i | ||||||||
\(320\) | 7.93923 | + | 0.984156i | 0.443817 | + | 0.0550160i | ||||
\(321\) | 21.7576i | 1.21439i | ||||||||
\(322\) | −2.09309 | + | 1.27984i | −0.116643 | + | 0.0713228i | ||||
\(323\) | −5.64296 | − | 5.64296i | −0.313983 | − | 0.313983i | ||||
\(324\) | −3.50567 | − | 15.6264i | −0.194760 | − | 0.868134i | ||||
\(325\) | 3.64354 | − | 3.64354i | 0.202107 | − | 0.202107i | ||||
\(326\) | 11.6064 | − | 1.28592i | 0.642818 | − | 0.0712207i | ||||
\(327\) | − | 5.85912i | − | 0.324010i | ||||||
\(328\) | 18.4988 | + | 9.03574i | 1.02142 | + | 0.498915i | ||||
\(329\) | −22.2838 | − | 8.05697i | −1.22854 | − | 0.444195i | ||||
\(330\) | −10.0911 | + | 1.11803i | −0.555494 | + | 0.0615457i | ||||
\(331\) | −14.7924 | + | 14.7924i | −0.813062 | + | 0.813062i | −0.985092 | − | 0.172029i | \(-0.944968\pi\) |
0.172029 | + | 0.985092i | \(0.444968\pi\) | |||||||
\(332\) | 5.84611 | + | 3.70368i | 0.320847 | + | 0.203266i | ||||
\(333\) | 1.82859 | − | 1.82859i | 0.100206 | − | 0.100206i | ||||
\(334\) | −4.63062 | − | 3.70687i | −0.253376 | − | 0.202831i | ||||
\(335\) | −1.25405 | −0.0685158 | ||||||||
\(336\) | −11.0805 | + | 13.3993i | −0.604493 | + | 0.730992i | ||||
\(337\) | −29.0873 | −1.58449 | −0.792244 | − | 0.610204i | \(-0.791087\pi\) | ||||
−0.792244 | + | 0.610204i | \(0.791087\pi\) | |||||||
\(338\) | −14.9605 | − | 11.9761i | −0.813745 | − | 0.651414i | ||||
\(339\) | 1.45793 | − | 1.45793i | 0.0791837 | − | 0.0791837i | ||||
\(340\) | −2.03877 | + | 3.21812i | −0.110568 | + | 0.174527i | ||||
\(341\) | −9.31384 | + | 9.31384i | −0.504373 | + | 0.504373i | ||||
\(342\) | −1.77093 | + | 0.196209i | −0.0957609 | + | 0.0106098i | ||||
\(343\) | 9.36233 | + | 15.9796i | 0.505518 | + | 0.862816i | ||||
\(344\) | −0.638081 | + | 0.219295i | −0.0344030 | + | 0.0118236i | ||||
\(345\) | − | 1.07726i | − | 0.0579980i | ||||||
\(346\) | 31.3776 | − | 3.47646i | 1.68687 | − | 0.186896i | ||||
\(347\) | −7.32687 | + | 7.32687i | −0.393327 | + | 0.393327i | −0.875872 | − | 0.482544i | \(-0.839713\pi\) |
0.482544 | + | 0.875872i | \(0.339713\pi\) | |||||||
\(348\) | −12.1522 | + | 2.72626i | −0.651427 | + | 0.146143i | ||||
\(349\) | 8.65818 | + | 8.65818i | 0.463462 | + | 0.463462i | 0.899788 | − | 0.436327i | \(-0.143721\pi\) |
−0.436327 | + | 0.899788i | \(0.643721\pi\) | |||||||
\(350\) | 1.95190 | + | 3.19219i | 0.104334 | + | 0.170630i | ||||
\(351\) | 27.9429i | 1.49148i | ||||||||
\(352\) | 12.9563 | + | 21.0508i | 0.690573 | + | 1.12201i | ||||
\(353\) | − | 8.56359i | − | 0.455794i | −0.973685 | − | 0.227897i | \(-0.926815\pi\) | ||
0.973685 | − | 0.227897i | \(-0.0731850\pi\) | |||||||
\(354\) | 14.5443 | − | 18.1687i | 0.773021 | − | 0.965657i | ||||
\(355\) | −10.9776 | + | 10.9776i | −0.582632 | + | 0.582632i | ||||
\(356\) | −5.51491 | − | 24.5825i | −0.292290 | − | 1.30287i | ||||
\(357\) | −3.51515 | − | 7.49658i | −0.186042 | − | 0.396761i | ||||
\(358\) | −8.31473 | + | 0.921225i | −0.439447 | + | 0.0486883i | ||||
\(359\) | 2.20627 | 0.116443 | 0.0582213 | − | 0.998304i | \(-0.481457\pi\) | ||||
0.0582213 | + | 0.998304i | \(0.481457\pi\) | |||||||
\(360\) | 0.276449 | + | 0.804381i | 0.0145702 | + | 0.0423946i | ||||
\(361\) | 1.44703i | 0.0761595i | ||||||||
\(362\) | 1.30220 | + | 11.7533i | 0.0684419 | + | 0.617738i | ||||
\(363\) | −9.40295 | − | 9.40295i | −0.493527 | − | 0.493527i | ||||
\(364\) | 21.5539 | − | 16.6987i | 1.12973 | − | 0.875252i | ||||
\(365\) | 4.43128 | − | 4.43128i | 0.231944 | − | 0.231944i | ||||
\(366\) | −6.72721 | + | 8.40363i | −0.351637 | + | 0.439265i | ||||
\(367\) | −9.33617 | −0.487344 | −0.243672 | − | 0.969858i | \(-0.578352\pi\) | ||||
−0.243672 | + | 0.969858i | \(0.578352\pi\) | |||||||
\(368\) | −2.37140 | + | 1.12040i | −0.123618 | + | 0.0584051i | ||||
\(369\) | 2.18888i | 0.113948i | ||||||||
\(370\) | 7.60018 | − | 9.49414i | 0.395115 | − | 0.493577i | ||||
\(371\) | −10.3122 | − | 21.9923i | −0.535384 | − | 1.14178i | ||||
\(372\) | −8.36713 | − | 5.30082i | −0.433815 | − | 0.274835i | ||||
\(373\) | −4.81520 | − | 4.81520i | −0.249321 | − | 0.249321i | 0.571371 | − | 0.820692i | \(-0.306412\pi\) |
−0.820692 | + | 0.571371i | \(0.806412\pi\) | |||||||
\(374\) | −11.6993 | + | 1.29621i | −0.604955 | + | 0.0670256i | ||||
\(375\) | −1.64295 | −0.0848415 | ||||||||
\(376\) | −22.7615 | − | 11.1179i | −1.17383 | − | 0.573360i | ||||
\(377\) | 19.5300 | 1.00585 | ||||||||
\(378\) | −19.7254 | − | 4.75598i | −1.01457 | − | 0.244621i | ||||
\(379\) | 21.6084 | − | 21.6084i | 1.10995 | − | 1.10995i | 0.116791 | − | 0.993156i | \(-0.462739\pi\) |
0.993156 | − | 0.116791i | \(-0.0372608\pi\) | |||||||
\(380\) | −8.17603 | + | 1.83423i | −0.419421 | + | 0.0940942i | ||||
\(381\) | −14.2806 | − | 14.2806i | −0.731619 | − | 0.731619i | ||||
\(382\) | −16.4267 | − | 13.1498i | −0.840461 | − | 0.672800i | ||||
\(383\) | 33.5735 | 1.71553 | 0.857764 | − | 0.514044i | \(-0.171853\pi\) | ||||
0.857764 | + | 0.514044i | \(0.171853\pi\) | |||||||
\(384\) | −13.3132 | + | 12.9718i | −0.679385 | + | 0.661964i | ||||
\(385\) | −3.93097 | + | 10.8722i | −0.200341 | + | 0.554098i | ||||
\(386\) | 3.68723 | − | 4.60608i | 0.187675 | − | 0.234443i | ||||
\(387\) | −0.0507247 | − | 0.0507247i | −0.00257848 | − | 0.00257848i | ||||
\(388\) | 25.8456 | − | 5.79827i | 1.31211 | − | 0.294363i | ||||
\(389\) | −22.3390 | − | 22.3390i | −1.13263 | − | 1.13263i | −0.989738 | − | 0.142896i | \(-0.954359\pi\) |
−0.142896 | − | 0.989738i | \(-0.545641\pi\) | |||||||
\(390\) | 1.31840 | + | 11.8995i | 0.0667596 | + | 0.602553i | ||||
\(391\) | − | 1.24895i | − | 0.0631621i | ||||||
\(392\) | 8.11941 | + | 18.0576i | 0.410092 | + | 0.912044i | ||||
\(393\) | − | 15.6450i | − | 0.789184i | ||||||
\(394\) | −23.3742 | + | 2.58973i | −1.17757 | + | 0.130469i | ||||
\(395\) | 8.70786 | + | 8.70786i | 0.438140 | + | 0.438140i | ||||
\(396\) | −1.40647 | + | 2.22005i | −0.0706775 | + | 0.111562i | ||||
\(397\) | −13.8135 | − | 13.8135i | −0.693282 | − | 0.693282i | 0.269671 | − | 0.962953i | \(-0.413085\pi\) |
−0.962953 | + | 0.269671i | \(0.913085\pi\) | |||||||
\(398\) | −22.1616 | − | 17.7407i | −1.11086 | − | 0.889258i | ||||
\(399\) | 6.19231 | − | 17.1265i | 0.310003 | − | 0.857399i | ||||
\(400\) | 1.70874 | + | 3.61666i | 0.0854371 | + | 0.180833i | ||||
\(401\) | 2.34938 | 0.117322 | 0.0586611 | − | 0.998278i | \(-0.481317\pi\) | ||||
0.0586611 | + | 0.998278i | \(0.481317\pi\) | |||||||
\(402\) | 1.82092 | − | 2.27469i | 0.0908191 | − | 0.113451i | ||||
\(403\) | 10.9830 | + | 10.9830i | 0.547101 | + | 0.547101i | ||||
\(404\) | 3.89038 | + | 2.46467i | 0.193554 | + | 0.122622i | ||||
\(405\) | 5.66210 | − | 5.66210i | 0.281352 | − | 0.281352i | ||||
\(406\) | −3.32408 | + | 13.7866i | −0.164971 | + | 0.684218i | ||||
\(407\) | 37.5766 | 1.86260 | ||||||||
\(408\) | −2.87691 | − | 8.37090i | −0.142428 | − | 0.414421i | ||||
\(409\) | −31.3208 | −1.54871 | −0.774356 | − | 0.632750i | \(-0.781926\pi\) | ||||
−0.774356 | + | 0.632750i | \(0.781926\pi\) | |||||||
\(410\) | 1.13356 | + | 10.2312i | 0.0559825 | + | 0.505283i | ||||
\(411\) | 19.7855 | + | 19.7855i | 0.975948 | + | 0.975948i | ||||
\(412\) | −34.5963 | + | 7.76143i | −1.70444 | + | 0.382378i | ||||
\(413\) | −11.2510 | − | 23.9943i | −0.553623 | − | 1.18068i | ||||
\(414\) | −0.217692 | − | 0.174265i | −0.0106990 | − | 0.00856468i | ||||
\(415\) | 3.46028i | 0.169859i | ||||||||
\(416\) | 24.8234 | − | 15.2782i | 1.21707 | − | 0.749076i | ||||
\(417\) | −25.5529 | −1.25133 | ||||||||
\(418\) | −20.2119 | − | 16.1799i | −0.988595 | − | 0.791383i | ||||
\(419\) | 10.4710 | − | 10.4710i | 0.511544 | − | 0.511544i | −0.403455 | − | 0.914999i | \(-0.632191\pi\) |
0.914999 | + | 0.403455i | \(0.132191\pi\) | |||||||
\(420\) | −8.62448 | − | 1.09466i | −0.420831 | − | 0.0534137i | ||||
\(421\) | 20.6186 | + | 20.6186i | 1.00489 | + | 1.00489i | 0.999988 | + | 0.00490286i | \(0.00156064\pi\) |
0.00490286 | + | 0.999988i | \(0.498439\pi\) | |||||||
\(422\) | 11.5764 | − | 1.28260i | 0.563531 | − | 0.0624361i | ||||
\(423\) | − | 2.69326i | − | 0.130951i | ||||||
\(424\) | −8.43983 | − | 24.5573i | −0.409875 | − | 1.19261i | ||||
\(425\) | −1.90479 | −0.0923958 | ||||||||
\(426\) | −3.97220 | − | 35.8520i | −0.192454 | − | 1.73703i | ||||
\(427\) | 5.20394 | + | 11.0982i | 0.251836 | + | 0.537078i | ||||
\(428\) | 22.3739 | + | 14.1745i | 1.08148 | + | 0.685151i | ||||
\(429\) | −26.1574 | + | 26.1574i | −1.26289 | + | 1.26289i | ||||
\(430\) | −0.263365 | − | 0.210827i | −0.0127006 | − | 0.0101670i | ||||
\(431\) | − | 18.8920i | − | 0.909997i | −0.890492 | − | 0.454999i | \(-0.849640\pi\) | ||
0.890492 | − | 0.454999i | \(-0.150360\pi\) | |||||||
\(432\) | −20.4207 | − | 7.31605i | −0.982489 | − | 0.351994i | ||||
\(433\) | − | 25.8925i | − | 1.24431i | −0.782892 | − | 0.622157i | \(-0.786256\pi\) | ||
0.782892 | − | 0.622157i | \(-0.213744\pi\) | |||||||
\(434\) | −9.62246 | + | 5.88376i | −0.461893 | + | 0.282430i | ||||
\(435\) | −4.40325 | − | 4.40325i | −0.211120 | − | 0.211120i | ||||
\(436\) | −6.02509 | − | 3.81707i | −0.288549 | − | 0.182805i | ||||
\(437\) | 1.94249 | − | 1.94249i | 0.0929219 | − | 0.0929219i | ||||
\(438\) | 1.60344 | + | 14.4722i | 0.0766153 | + | 0.691508i | ||||
\(439\) | − | 2.69090i | − | 0.128430i | −0.997936 | − | 0.0642148i | \(-0.979546\pi\) | ||
0.997936 | − | 0.0642148i | \(-0.0204543\pi\) | |||||||
\(440\) | −5.42437 | + | 11.1053i | −0.258597 | + | 0.529423i | ||||
\(441\) | −1.34621 | + | 1.61829i | −0.0641053 | + | 0.0770614i | ||||
\(442\) | 1.52851 | + | 13.7959i | 0.0727038 | + | 0.656204i | ||||
\(443\) | 23.8127 | − | 23.8127i | 1.13138 | − | 1.13138i | 0.141429 | − | 0.989948i | \(-0.454830\pi\) |
0.989948 | − | 0.141429i | \(-0.0451697\pi\) | |||||||
\(444\) | 6.18549 | + | 27.5716i | 0.293551 | + | 1.30849i | ||||
\(445\) | 8.90726 | − | 8.90726i | 0.422245 | − | 0.422245i | ||||
\(446\) | 11.5435 | − | 14.4201i | 0.546598 | − | 0.682810i | ||||
\(447\) | −0.440438 | −0.0208320 | ||||||||
\(448\) | 6.56016 | + | 20.1237i | 0.309938 | + | 0.950757i | ||||
\(449\) | 12.6452 | 0.596763 | 0.298381 | − | 0.954447i | \(-0.403553\pi\) | ||||
0.298381 | + | 0.954447i | \(0.403553\pi\) | |||||||
\(450\) | −0.265774 | + | 0.332005i | −0.0125287 | + | 0.0156509i | ||||
\(451\) | −22.4902 | + | 22.4902i | −1.05902 | + | 1.05902i | ||||
\(452\) | −0.549421 | − | 2.44903i | −0.0258426 | − | 0.115193i | ||||
\(453\) | −9.68096 | + | 9.68096i | −0.454851 | + | 0.454851i | ||||
\(454\) | −1.42624 | − | 12.8728i | −0.0669367 | − | 0.604152i | ||||
\(455\) | 12.8206 | + | 4.63545i | 0.601039 | + | 0.217313i | ||||
\(456\) | 8.54480 | − | 17.4937i | 0.400147 | − | 0.819218i | ||||
\(457\) | − | 35.0394i | − | 1.63907i | −0.573027 | − | 0.819536i | \(-0.694231\pi\) | ||
0.573027 | − | 0.819536i | \(-0.305769\pi\) | |||||||
\(458\) | 3.66038 | + | 33.0376i | 0.171038 | + | 1.54375i | ||||
\(459\) | 7.30406 | − | 7.30406i | 0.340924 | − | 0.340924i | ||||
\(460\) | −1.10778 | − | 0.701811i | −0.0516505 | − | 0.0327221i | ||||
\(461\) | −21.7115 | − | 21.7115i | −1.01120 | − | 1.01120i | −0.999937 | − | 0.0112676i | \(-0.996413\pi\) |
−0.0112676 | − | 0.999937i | \(-0.503587\pi\) | |||||||
\(462\) | −14.0129 | − | 22.9171i | −0.651940 | − | 1.06620i | ||||
\(463\) | 0.418425i | 0.0194459i | 0.999953 | + | 0.00972294i | \(0.00309496\pi\) | ||||
−0.999953 | + | 0.00972294i | \(0.996905\pi\) | |||||||
\(464\) | −5.11338 | + | 14.2725i | −0.237383 | + | 0.662586i | ||||
\(465\) | − | 4.95246i | − | 0.229665i | ||||||
\(466\) | 22.8211 | + | 18.2686i | 1.05717 | + | 0.846277i | ||||
\(467\) | 18.9158 | − | 18.9158i | 0.875320 | − | 0.875320i | −0.117726 | − | 0.993046i | \(-0.537560\pi\) |
0.993046 | + | 0.117726i | \(0.0375604\pi\) | |||||||
\(468\) | 2.61790 | + | 1.65852i | 0.121013 | + | 0.0766650i | ||||
\(469\) | −1.40860 | − | 3.00404i | −0.0650430 | − | 0.138714i | ||||
\(470\) | −1.39477 | − | 12.5888i | −0.0643359 | − | 0.580678i | ||||
\(471\) | −35.4187 | −1.63201 | ||||||||
\(472\) | −9.20813 | − | 26.7928i | −0.423838 | − | 1.23324i | ||||
\(473\) | − | 1.04237i | − | 0.0479281i | ||||||
\(474\) | −28.4391 | + | 3.15089i | −1.30625 | + | 0.144725i | ||||
\(475\) | −2.96251 | − | 2.96251i | −0.135929 | − | 0.135929i | ||||
\(476\) | −9.99897 | − | 1.26911i | −0.458302 | − | 0.0581697i | ||||
\(477\) | 1.95220 | − | 1.95220i | 0.0893850 | − | 0.0893850i | ||||
\(478\) | −5.18969 | − | 4.15442i | −0.237371 | − | 0.190019i | ||||
\(479\) | 26.0182 | 1.18880 | 0.594401 | − | 0.804169i | \(-0.297389\pi\) | ||||
0.594401 | + | 0.804169i | \(0.297389\pi\) | |||||||
\(480\) | −9.04133 | − | 2.15206i | −0.412678 | − | 0.0982276i | ||||
\(481\) | − | 44.3108i | − | 2.02040i | ||||||
\(482\) | −4.20113 | − | 3.36306i | −0.191356 | − | 0.153183i | ||||
\(483\) | 2.58057 | − | 1.21003i | 0.117420 | − | 0.0550582i | ||||
\(484\) | −15.7951 | + | 3.54352i | −0.717959 | + | 0.161069i | ||||
\(485\) | 9.36492 | + | 9.36492i | 0.425239 | + | 0.425239i | ||||
\(486\) | −0.484795 | − | 4.37562i | −0.0219907 | − | 0.198482i | ||||
\(487\) | −10.0152 | −0.453831 | −0.226915 | − | 0.973914i | \(-0.572864\pi\) | ||||
−0.226915 | + | 0.973914i | \(0.572864\pi\) | |||||||
\(488\) | 4.25906 | + | 12.3925i | 0.192799 | + | 0.560983i | ||||
\(489\) | −13.5661 | −0.613481 | ||||||||
\(490\) | −5.45437 | + | 8.26135i | −0.246403 | + | 0.373210i | ||||
\(491\) | −27.3123 | + | 27.3123i | −1.23259 | + | 1.23259i | −0.269619 | + | 0.962967i | \(0.586898\pi\) |
−0.962967 | + | 0.269619i | \(0.913102\pi\) | |||||||
\(492\) | −20.2041 | − | 12.7999i | −0.910873 | − | 0.577065i | ||||
\(493\) | −5.10500 | − | 5.10500i | −0.229918 | − | 0.229918i | ||||
\(494\) | −19.0795 | + | 23.8340i | −0.858426 | + | 1.07234i | ||||
\(495\) | −1.31403 | −0.0590615 | ||||||||
\(496\) | −10.9020 | + | 5.15079i | −0.489512 | + | 0.231277i | ||||
\(497\) | −38.6272 | − | 13.9661i | −1.73267 | − | 0.626467i | ||||
\(498\) | −6.27654 | − | 5.02445i | −0.281258 | − | 0.225151i | ||||
\(499\) | 18.1053 | + | 18.1053i | 0.810503 | + | 0.810503i | 0.984709 | − | 0.174206i | \(-0.0557358\pi\) |
−0.174206 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(500\) | −1.07034 | + | 1.68949i | −0.0478671 | + | 0.0755562i | ||||
\(501\) | 4.87263 | + | 4.87263i | 0.217693 | + | 0.217693i | ||||
\(502\) | 16.4028 | − | 1.81734i | 0.732092 | − | 0.0811117i | ||||
\(503\) | − | 2.52704i | − | 0.112675i | −0.998412 | − | 0.0563375i | \(-0.982058\pi\) | ||
0.998412 | − | 0.0563375i | \(-0.0179423\pi\) | |||||||
\(504\) | −1.61636 | + | 1.56574i | −0.0719984 | + | 0.0697438i | ||||
\(505\) | 2.30270i | 0.102469i | ||||||||
\(506\) | −0.446199 | − | 4.02727i | −0.0198360 | − | 0.179034i | ||||
\(507\) | 15.7424 | + | 15.7424i | 0.699145 | + | 0.699145i | ||||
\(508\) | −23.9886 | + | 5.38168i | −1.06432 | + | 0.238773i | ||||
\(509\) | 25.0178 | + | 25.0178i | 1.10889 | + | 1.10889i | 0.993296 | + | 0.115597i | \(0.0368781\pi\) |
0.115597 | + | 0.993296i | \(0.463122\pi\) | |||||||
\(510\) | 2.76582 | − | 3.45505i | 0.122472 | − | 0.152992i | ||||
\(511\) | 15.5925 | + | 5.63765i | 0.689770 | + | 0.249395i | ||||
\(512\) | 4.66602 | + | 22.1411i | 0.206211 | + | 0.978508i | ||||
\(513\) | 22.7200 | 1.00311 | ||||||||
\(514\) | −11.4567 | − | 9.17128i | −0.505335 | − | 0.404528i | ||||
\(515\) | −12.5357 | − | 12.5357i | −0.552387 | − | 0.552387i | ||||
\(516\) | 0.764831 | − | 0.171584i | 0.0336698 | − | 0.00755357i | ||||
\(517\) | 27.6726 | − | 27.6726i | 1.21704 | − | 1.21704i | ||||
\(518\) | 31.2799 | + | 7.54187i | 1.37436 | + | 0.331371i | ||||
\(519\) | −36.6757 | −1.60988 | ||||||||
\(520\) | 13.0955 | + | 6.39647i | 0.574274 | + | 0.280504i | ||||
\(521\) | 3.39271 | 0.148637 | 0.0743187 | − | 0.997235i | \(-0.476322\pi\) | ||||
0.0743187 | + | 0.997235i | \(0.476322\pi\) | |||||||
\(522\) | −1.60210 | + | 0.177504i | −0.0701221 | + | 0.00776913i | ||||
\(523\) | 23.0833 | + | 23.0833i | 1.00936 | + | 1.00936i | 0.999956 | + | 0.00940786i | \(0.00299466\pi\) |
0.00940786 | + | 0.999956i | \(0.497005\pi\) | |||||||
\(524\) | −16.0881 | − | 10.1923i | −0.702814 | − | 0.445253i | ||||
\(525\) | −1.84543 | − | 3.93565i | −0.0805412 | − | 0.171766i | ||||
\(526\) | 21.5812 | − | 26.9592i | 0.940986 | − | 1.17548i | ||||
\(527\) | − | 5.74174i | − | 0.250114i | ||||||
\(528\) | −12.2673 | − | 25.9644i | −0.533864 | − | 1.12995i | ||||
\(529\) | −22.5701 | −0.981307 | ||||||||
\(530\) | 8.11393 | − | 10.1359i | 0.352447 | − | 0.440276i | ||||
\(531\) | 2.12991 | − | 2.12991i | 0.0924302 | − | 0.0924302i | ||||
\(532\) | −13.5775 | − | 17.5252i | −0.588661 | − | 0.759815i | ||||
\(533\) | 26.5206 | + | 26.5206i | 1.14874 | + | 1.14874i | ||||
\(534\) | 3.22305 | + | 29.0903i | 0.139475 | + | 1.25886i | ||||
\(535\) | 13.2430i | 0.572544i | ||||||||
\(536\) | −1.15284 | − | 3.35440i | −0.0497951 | − | 0.144888i | ||||
\(537\) | 9.71866 | 0.419391 | ||||||||
\(538\) | 27.0664 | − | 2.99881i | 1.16692 | − | 0.129288i | ||||
\(539\) | −30.4595 | + | 2.79553i | −1.31199 | + | 0.120412i | ||||
\(540\) | −2.37417 | − | 10.5828i | −0.102168 | − | 0.455410i | ||||
\(541\) | −6.72937 | + | 6.72937i | −0.289318 | + | 0.289318i | −0.836811 | − | 0.547492i | \(-0.815583\pi\) |
0.547492 | + | 0.836811i | \(0.315583\pi\) | |||||||
\(542\) | 4.92665 | − | 6.15436i | 0.211618 | − | 0.264353i | ||||
\(543\) | − | 13.7378i | − | 0.589545i | ||||||
\(544\) | −10.4823 | − | 2.49503i | −0.449423 | − | 0.106974i | ||||
\(545\) | − | 3.56622i | − | 0.152760i | ||||||
\(546\) | −27.0241 | + | 16.5242i | −1.15652 | + | 0.707170i | ||||
\(547\) | 11.9959 | + | 11.9959i | 0.512908 | + | 0.512908i | 0.915416 | − | 0.402508i | \(-0.131862\pi\) |
−0.402508 | + | 0.915416i | \(0.631862\pi\) | |||||||
\(548\) | 33.2358 | − | 7.45621i | 1.41976 | − | 0.318513i | ||||
\(549\) | −0.985153 | + | 0.985153i | −0.0420453 | + | 0.0420453i | ||||
\(550\) | −6.14204 | + | 0.680503i | −0.261897 | + | 0.0290168i | ||||
\(551\) | − | 15.8796i | − | 0.676493i | ||||||
\(552\) | 2.88154 | − | 0.990325i | 0.122646 | − | 0.0421510i | ||||
\(553\) | −11.0785 | + | 30.6405i | −0.471104 | + | 1.30297i | ||||
\(554\) | −21.3518 | + | 2.36566i | −0.907150 | + | 0.100507i | ||||
\(555\) | −9.99034 | + | 9.99034i | −0.424066 | + | 0.424066i | ||||
\(556\) | −16.6471 | + | 26.2767i | −0.705994 | + | 1.11438i | ||||
\(557\) | 1.78658 | − | 1.78658i | 0.0756996 | − | 0.0756996i | −0.668243 | − | 0.743943i | \(-0.732953\pi\) |
0.743943 | + | 0.668243i | \(0.232953\pi\) | |||||||
\(558\) | −1.00079 | − | 0.801143i | −0.0423667 | − | 0.0339151i | ||||
\(559\) | −1.22917 | −0.0519884 | ||||||||
\(560\) | −6.74430 | + | 8.15564i | −0.284999 | + | 0.344639i | ||||
\(561\) | 13.6747 | 0.577346 | ||||||||
\(562\) | −9.50814 | − | 7.61139i | −0.401077 | − | 0.321067i | ||||
\(563\) | 25.1096 | − | 25.1096i | 1.05824 | − | 1.05824i | 0.0600469 | − | 0.998196i | \(-0.480875\pi\) |
0.998196 | − | 0.0600469i | \(-0.0191250\pi\) | |||||||
\(564\) | 24.8598 | + | 15.7494i | 1.04679 | + | 0.663170i | ||||
\(565\) | 0.887384 | − | 0.887384i | 0.0373325 | − | 0.0373325i | ||||
\(566\) | −6.31752 | + | 0.699946i | −0.265545 | + | 0.0294209i | ||||
\(567\) | 19.9233 | + | 7.20353i | 0.836702 | + | 0.302520i | ||||
\(568\) | −39.4553 | − | 19.2720i | −1.65551 | − | 0.808633i | ||||
\(569\) | 16.9846i | 0.712030i | 0.934480 | + | 0.356015i | \(0.115865\pi\) | ||||
−0.934480 | + | 0.356015i | \(0.884135\pi\) | |||||||
\(570\) | 9.67531 | − | 1.07197i | 0.405254 | − | 0.0448999i | ||||
\(571\) | 24.7972 | − | 24.7972i | 1.03773 | − | 1.03773i | 0.0384723 | − | 0.999260i | \(-0.487751\pi\) |
0.999260 | − | 0.0384723i | \(-0.0122491\pi\) | |||||||
\(572\) | 9.85744 | + | 43.9392i | 0.412160 | + | 1.83719i | ||||
\(573\) | 17.2852 | + | 17.2852i | 0.722099 | + | 0.722099i | ||||
\(574\) | −23.2354 | + | 14.2075i | −0.969826 | + | 0.593011i | ||||
\(575\) | − | 0.655690i | − | 0.0273441i | ||||||
\(576\) | −1.89747 | + | 1.47893i | −0.0790613 | + | 0.0616220i | ||||
\(577\) | 38.0906i | 1.58573i | 0.609397 | + | 0.792865i | \(0.291412\pi\) | ||||
−0.609397 | + | 0.792865i | \(0.708588\pi\) | |||||||
\(578\) | −11.8180 | + | 14.7630i | −0.491562 | + | 0.614059i | ||||
\(579\) | −4.84681 | + | 4.84681i | −0.201427 | + | 0.201427i | ||||
\(580\) | −7.39659 | + | 1.65937i | −0.307126 | + | 0.0689016i | ||||
\(581\) | −8.28904 | + | 3.88674i | −0.343887 | + | 0.161249i | ||||
\(582\) | −30.5850 | + | 3.38865i | −1.26779 | + | 0.140464i | ||||
\(583\) | 40.1167 | 1.66146 | ||||||||
\(584\) | 15.9267 | + | 7.77942i | 0.659053 | + | 0.321915i | ||||
\(585\) | 1.54952i | 0.0640649i | ||||||||
\(586\) | −0.550183 | − | 4.96580i | −0.0227278 | − | 0.205135i | ||||
\(587\) | −19.8295 | − | 19.8295i | −0.818450 | − | 0.818450i | 0.167434 | − | 0.985883i | \(-0.446452\pi\) |
−0.985883 | + | 0.167434i | \(0.946452\pi\) | |||||||
\(588\) | −7.06515 | − | 21.8893i | −0.291362 | − | 0.902701i | ||||
\(589\) | 8.93012 | − | 8.93012i | 0.367959 | − | 0.367959i | ||||
\(590\) | 8.85256 | − | 11.0586i | 0.364454 | − | 0.455276i | ||||
\(591\) | 27.3209 | 1.12383 | ||||||||
\(592\) | 32.3823 | + | 11.6015i | 1.33091 | + | 0.476820i | ||||
\(593\) | − | 5.85503i | − | 0.240437i | −0.992747 | − | 0.120219i | \(-0.961640\pi\) | ||
0.992747 | − | 0.120219i | \(-0.0383595\pi\) | |||||||
\(594\) | 20.9427 | − | 26.1616i | 0.859288 | − | 1.07342i | ||||
\(595\) | −2.13954 | − | 4.56288i | −0.0877125 | − | 0.187060i | ||||
\(596\) | −0.286934 | + | 0.452914i | −0.0117533 | + | 0.0185521i | ||||
\(597\) | 23.3199 | + | 23.3199i | 0.954418 | + | 0.954418i | ||||
\(598\) | −4.74900 | + | 0.526163i | −0.194201 | + | 0.0215164i | ||||
\(599\) | 16.4465 | 0.671985 | 0.335992 | − | 0.941865i | \(-0.390928\pi\) | ||||
0.335992 | + | 0.941865i | \(0.390928\pi\) | |||||||
\(600\) | −1.51036 | − | 4.39466i | −0.0616601 | − | 0.179411i | ||||
\(601\) | −7.56096 | −0.308418 | −0.154209 | − | 0.988038i | \(-0.549283\pi\) | ||||
−0.154209 | + | 0.988038i | \(0.549283\pi\) | |||||||
\(602\) | 0.209210 | − | 0.867696i | 0.00852675 | − | 0.0353647i | ||||
\(603\) | 0.266660 | − | 0.266660i | 0.0108592 | − | 0.0108592i | ||||
\(604\) | 3.64828 | + | 16.2621i | 0.148446 | + | 0.661695i | ||||
\(605\) | −5.72322 | − | 5.72322i | −0.232682 | − | 0.232682i | ||||
\(606\) | −4.17681 | − | 3.34359i | −0.169671 | − | 0.135824i | ||||
\(607\) | −28.9016 | −1.17308 | −0.586540 | − | 0.809920i | \(-0.699510\pi\) | ||||
−0.586540 | + | 0.809920i | \(0.699510\pi\) | |||||||
\(608\) | −12.4225 | − | 20.1836i | −0.503800 | − | 0.818551i | ||||
\(609\) | 5.60198 | − | 15.4938i | 0.227004 | − | 0.627841i | ||||
\(610\) | −4.09460 | + | 5.11497i | −0.165785 | + | 0.207099i | ||||
\(611\) | −32.6319 | − | 32.6319i | −1.32014 | − | 1.32014i | ||||
\(612\) | −0.250776 | − | 1.11782i | −0.0101370 | − | 0.0451854i | ||||
\(613\) | −31.1495 | − | 31.1495i | −1.25811 | − | 1.25811i | −0.951992 | − | 0.306122i | \(-0.900968\pi\) |
−0.306122 | − | 0.951992i | \(-0.599032\pi\) | |||||||
\(614\) | 1.41695 | + | 12.7890i | 0.0571832 | + | 0.516120i | ||||
\(615\) | − | 11.9587i | − | 0.482223i | ||||||
\(616\) | −32.6953 | − | 0.520059i | −1.31733 | − | 0.0209538i | ||||
\(617\) | 4.76961i | 0.192017i | 0.995381 | + | 0.0960085i | \(0.0306076\pi\) | ||||
−0.995381 | + | 0.0960085i | \(0.969392\pi\) | |||||||
\(618\) | 40.9404 | − | 4.53597i | 1.64686 | − | 0.182463i | ||||
\(619\) | 33.1839 | + | 33.1839i | 1.33377 | + | 1.33377i | 0.901966 | + | 0.431807i | \(0.142124\pi\) |
0.431807 | + | 0.901966i | \(0.357876\pi\) | |||||||
\(620\) | −5.09275 | − | 3.22641i | −0.204530 | − | 0.129576i | ||||
\(621\) | 2.51429 | + | 2.51429i | 0.100895 | + | 0.100895i | ||||
\(622\) | −1.63087 | − | 1.30554i | −0.0653921 | − | 0.0523472i | ||||
\(623\) | 31.3422 | + | 11.3322i | 1.25570 | + | 0.454013i | ||||
\(624\) | −30.6175 | + | 14.4657i | −1.22568 | + | 0.579090i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −23.4610 | + | 29.3074i | −0.937689 | + | 1.17136i | ||||
\(627\) | 21.2682 | + | 21.2682i | 0.849371 | + | 0.849371i | ||||
\(628\) | −23.0744 | + | 36.4220i | −0.920769 | + | 1.45340i | ||||
\(629\) | −11.5825 | + | 11.5825i | −0.461825 | + | 0.461825i | ||||
\(630\) | −1.09384 | − | 0.263735i | −0.0435796 | − | 0.0105075i | ||||
\(631\) | 12.8457 | 0.511380 | 0.255690 | − | 0.966759i | \(-0.417697\pi\) | ||||
0.255690 | + | 0.966759i | \(0.417697\pi\) | |||||||
\(632\) | −15.2872 | + | 31.2974i | −0.608093 | + | 1.24494i | ||||
\(633\) | −13.5311 | −0.537812 | ||||||||
\(634\) | −1.21698 | − | 10.9841i | −0.0483323 | − | 0.436234i | ||||
\(635\) | −8.69208 | − | 8.69208i | −0.344935 | − | 0.344935i | ||||
\(636\) | 6.60362 | + | 29.4354i | 0.261850 | + | 1.16719i | ||||
\(637\) | 3.29652 | + | 35.9182i | 0.130613 | + | 1.42313i | ||||
\(638\) | −18.2850 | − | 14.6374i | −0.723910 | − | 0.579500i | ||||
\(639\) | − | 4.66857i | − | 0.184686i | ||||||
\(640\) | −8.10322 | + | 7.89543i | −0.320308 | + | 0.312094i | ||||
\(641\) | 39.7192 | 1.56881 | 0.784407 | − | 0.620246i | \(-0.212967\pi\) | ||||
0.784407 | + | 0.620246i | \(0.212967\pi\) | |||||||
\(642\) | −24.0212 | − | 19.2293i | −0.948041 | − | 0.758919i | ||||
\(643\) | −21.0735 | + | 21.0735i | −0.831057 | + | 0.831057i | −0.987661 | − | 0.156605i | \(-0.949945\pi\) |
0.156605 | + | 0.987661i | \(0.449945\pi\) | |||||||
\(644\) | 0.436870 | − | 3.44197i | 0.0172151 | − | 0.135633i | ||||
\(645\) | 0.277130 | + | 0.277130i | 0.0109120 | + | 0.0109120i | ||||
\(646\) | 11.2173 | − | 1.24281i | 0.441338 | − | 0.0488978i | ||||
\(647\) | − | 21.7509i | − | 0.855117i | −0.903988 | − | 0.427559i | \(-0.859374\pi\) | ||
0.903988 | − | 0.427559i | \(-0.140626\pi\) | |||||||
\(648\) | 20.3505 | + | 9.94019i | 0.799442 | + | 0.390488i | ||||
\(649\) | 43.7686 | 1.71807 | ||||||||
\(650\) | 0.802457 | + | 7.24276i | 0.0314749 | + | 0.284084i | ||||
\(651\) | 11.8635 | − | 5.56282i | 0.464968 | − | 0.218024i | ||||
\(652\) | −8.83799 | + | 13.9504i | −0.346122 | + | 0.546340i | ||||
\(653\) | −12.1669 | + | 12.1669i | −0.476129 | + | 0.476129i | −0.903891 | − | 0.427762i | \(-0.859302\pi\) |
0.427762 | + | 0.903891i | \(0.359302\pi\) | |||||||
\(654\) | 6.46870 | + | 5.17828i | 0.252946 | + | 0.202487i | ||||
\(655\) | − | 9.52249i | − | 0.372075i | ||||||
\(656\) | −26.3250 | + | 12.4376i | −1.02782 | + | 0.485608i | ||||
\(657\) | 1.88454i | 0.0735228i | ||||||||
\(658\) | 28.5896 | − | 17.4814i | 1.11454 | − | 0.681496i | ||||
\(659\) | −5.00285 | − | 5.00285i | −0.194883 | − | 0.194883i | 0.602919 | − | 0.797802i | \(-0.294004\pi\) |
−0.797802 | + | 0.602919i | \(0.794004\pi\) | |||||||
\(660\) | 7.68410 | − | 12.1290i | 0.299103 | − | 0.472122i | ||||
\(661\) | −14.4182 | + | 14.4182i | −0.560804 | + | 0.560804i | −0.929536 | − | 0.368732i | \(-0.879792\pi\) |
0.368732 | + | 0.929536i | \(0.379792\pi\) | |||||||
\(662\) | −3.25789 | − | 29.4048i | −0.126621 | − | 1.14285i | ||||
\(663\) | − | 16.1253i | − | 0.626256i | ||||||
\(664\) | −9.25579 | + | 3.18102i | −0.359194 | + | 0.123448i | ||||
\(665\) | 3.76902 | − | 10.4243i | 0.146156 | − | 0.404236i | ||||
\(666\) | 0.402731 | + | 3.63494i | 0.0156055 | + | 0.140851i | ||||
\(667\) | 1.75731 | − | 1.75731i | 0.0680432 | − | 0.0680432i | ||||
\(668\) | 8.18506 | − | 1.83626i | 0.316689 | − | 0.0710470i | ||||
\(669\) | −15.1737 | + | 15.1737i | −0.586650 | + | 0.586650i | ||||
\(670\) | 1.10832 | − | 1.38451i | 0.0428182 | − | 0.0534885i | ||||
\(671\) | −20.2444 | −0.781527 | ||||||||
\(672\) | −5.00039 | − | 24.0756i | −0.192894 | − | 0.928737i | ||||
\(673\) | 6.26349 | 0.241440 | 0.120720 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120720 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(674\) | 25.7073 | − | 32.1136i | 0.990209 | − | 1.23697i | ||||
\(675\) | 3.83458 | − | 3.83458i | 0.147593 | − | 0.147593i | ||||
\(676\) | 26.4441 | − | 5.93255i | 1.01708 | − | 0.228175i | ||||
\(677\) | −27.7880 | + | 27.7880i | −1.06798 | + | 1.06798i | −0.0704674 | + | 0.997514i | \(0.522449\pi\) |
−0.997514 | + | 0.0704674i | \(0.977551\pi\) | |||||||
\(678\) | 0.321095 | + | 2.89812i | 0.0123316 | + | 0.111302i | ||||
\(679\) | −11.9144 | + | 32.9526i | −0.457233 | + | 1.26460i | ||||
\(680\) | −1.75106 | − | 5.09505i | −0.0671502 | − | 0.195386i | ||||
\(681\) | 15.0464i | 0.576580i | ||||||||
\(682\) | −2.05129 | − | 18.5144i | −0.0785480 | − | 0.708953i | ||||
\(683\) | 1.81836 | − | 1.81836i | 0.0695774 | − | 0.0695774i | −0.671462 | − | 0.741039i | \(-0.734333\pi\) |
0.741039 | + | 0.671462i | \(0.234333\pi\) | |||||||
\(684\) | 1.34852 | − | 2.12858i | 0.0515620 | − | 0.0813884i | ||||
\(685\) | 12.0427 | + | 12.0427i | 0.460128 | + | 0.460128i | ||||
\(686\) | −25.9165 | − | 3.78634i | −0.989496 | − | 0.144563i | ||||
\(687\) | − | 38.6160i | − | 1.47329i | ||||||
\(688\) | 0.321824 | − | 0.898279i | 0.0122694 | − | 0.0342466i | ||||
\(689\) | − | 47.3060i | − | 1.80222i | ||||||
\(690\) | 1.18934 | + | 0.952084i | 0.0452775 | + | 0.0362452i | ||||
\(691\) | −19.4464 | + | 19.4464i | −0.739776 | + | 0.739776i | −0.972535 | − | 0.232759i | \(-0.925225\pi\) |
0.232759 | + | 0.972535i | \(0.425225\pi\) | |||||||
\(692\) | −23.8933 | + | 37.7146i | −0.908287 | + | 1.43369i | ||||
\(693\) | −1.47598 | − | 3.14774i | −0.0560678 | − | 0.119573i | ||||
\(694\) | −1.61368 | − | 14.5646i | −0.0612544 | − | 0.552866i | ||||
\(695\) | −15.5531 | −0.589962 | ||||||||
\(696\) | 7.73020 | − | 15.8260i | 0.293012 | − | 0.599882i | ||||
\(697\) | − | 13.8646i | − | 0.525159i | ||||||
\(698\) | −17.2110 | + | 1.90689i | −0.651448 | + | 0.0721768i | ||||
\(699\) | −24.0139 | − | 24.0139i | −0.908288 | − | 0.908288i | ||||
\(700\) | −5.24939 | − | 0.666275i | −0.198408 | − | 0.0251828i | ||||
\(701\) | 25.1291 | − | 25.1291i | 0.949115 | − | 0.949115i | −0.0496520 | − | 0.998767i | \(-0.515811\pi\) |
0.998767 | + | 0.0496520i | \(0.0158112\pi\) | |||||||
\(702\) | −30.8500 | − | 24.6958i | −1.16436 | − | 0.932084i | ||||
\(703\) | −36.0285 | −1.35884 | ||||||||
\(704\) | −34.6917 | − | 4.30042i | −1.30749 | − | 0.162078i | ||||
\(705\) | 14.7144i | 0.554177i | ||||||||
\(706\) | 9.45454 | + | 7.56848i | 0.355826 | + | 0.284844i | ||||
\(707\) | −5.51606 | + | 2.58649i | −0.207453 | + | 0.0972748i | ||||
\(708\) | 7.20476 | + | 32.1150i | 0.270771 | + | 1.20695i | ||||
\(709\) | −13.5498 | − | 13.5498i | −0.508873 | − | 0.508873i | 0.405307 | − | 0.914180i | \(-0.367164\pi\) |
−0.914180 | + | 0.405307i | \(0.867164\pi\) | |||||||
\(710\) | −2.41772 | − | 21.8217i | −0.0907356 | − | 0.818955i | ||||
\(711\) | −3.70328 | −0.138884 | ||||||||
\(712\) | 32.0141 | + | 15.6373i | 1.19978 | + | 0.586032i | ||||
\(713\) | 1.97649 | 0.0740203 | ||||||||
\(714\) | 11.3832 | + | 2.74460i | 0.426005 | + | 0.102714i | ||||
\(715\) | −15.9210 | + | 15.9210i | −0.595411 | + | 0.595411i | ||||
\(716\) | 6.33147 | − | 9.99396i | 0.236618 | − | 0.373492i | ||||
\(717\) | 5.46093 | + | 5.46093i | 0.203942 | + | 0.203942i | ||||
\(718\) | −1.94990 | + | 2.43581i | −0.0727695 | + | 0.0909036i | ||||
\(719\) | 47.9742 | 1.78914 | 0.894568 | − | 0.446931i | \(-0.147483\pi\) | ||||
0.894568 | + | 0.446931i | \(0.147483\pi\) | |||||||
\(720\) | −1.13239 | − | 0.405699i | −0.0422018 | − | 0.0151195i | ||||
\(721\) | 15.9483 | − | 44.1095i | 0.593948 | − | 1.64272i | ||||
\(722\) | −1.59758 | − | 1.27888i | −0.0594557 | − | 0.0475951i | ||||
\(723\) | 4.42070 | + | 4.42070i | 0.164407 | + | 0.164407i | ||||
\(724\) | −14.1269 | − | 8.94983i | −0.525024 | − | 0.332618i | ||||
\(725\) | −2.68009 | − | 2.68009i | −0.0995360 | − | 0.0995360i | ||||
\(726\) | 18.6915 | − | 2.07092i | 0.693708 | − | 0.0768590i | ||||
\(727\) | − | 12.6465i | − | 0.469034i | −0.972112 | − | 0.234517i | \(-0.924649\pi\) | ||
0.972112 | − | 0.234517i | \(-0.0753509\pi\) | |||||||
\(728\) | −0.613259 | + | 38.5547i | −0.0227289 | + | 1.42893i | ||||
\(729\) | 29.1367i | 1.07914i | ||||||||
\(730\) | 0.975951 | + | 8.80867i | 0.0361216 | + | 0.326023i | ||||
\(731\) | 0.321296 | + | 0.321296i | 0.0118836 | + | 0.0118836i | ||||
\(732\) | −3.33243 | − | 14.8542i | −0.123170 | − | 0.549027i | ||||
\(733\) | 18.8835 | + | 18.8835i | 0.697477 | + | 0.697477i | 0.963866 | − | 0.266389i | \(-0.0858305\pi\) |
−0.266389 | + | 0.963866i | \(0.585830\pi\) | |||||||
\(734\) | 8.25129 | − | 10.3075i | 0.304561 | − | 0.380457i | ||||
\(735\) | 7.35491 | − | 8.84138i | 0.271290 | − | 0.326119i | ||||
\(736\) | 0.858872 | − | 3.60833i | 0.0316584 | − | 0.133005i | ||||
\(737\) | 5.47974 | 0.201849 | ||||||||
\(738\) | −2.41660 | − | 1.93452i | −0.0889564 | − | 0.0712108i | ||||
\(739\) | −5.82858 | − | 5.82858i | −0.214408 | − | 0.214408i | 0.591729 | − | 0.806137i | \(-0.298445\pi\) |
−0.806137 | + | 0.591729i | \(0.798445\pi\) | |||||||
\(740\) | 3.76487 | + | 16.7818i | 0.138399 | + | 0.616911i | ||||
\(741\) | 25.0797 | − | 25.0797i | 0.921326 | − | 0.921326i | ||||
\(742\) | 33.3943 | + | 8.05167i | 1.22594 | + | 0.295586i | ||||
\(743\) | 3.18943 | 0.117009 | 0.0585043 | − | 0.998287i | \(-0.481367\pi\) | ||||
0.0585043 | + | 0.998287i | \(0.481367\pi\) | |||||||
\(744\) | 13.2472 | − | 4.55278i | 0.485665 | − | 0.166913i | ||||
\(745\) | −0.268078 | −0.00982160 | ||||||||
\(746\) | 9.57182 | − | 1.06050i | 0.350449 | − | 0.0388278i | ||||
\(747\) | −0.735795 | − | 0.735795i | −0.0269213 | − | 0.0269213i | ||||
\(748\) | 8.90872 | − | 14.0620i | 0.325735 | − | 0.514159i | ||||
\(749\) | −31.7233 | + | 14.8751i | −1.15915 | + | 0.543524i | ||||
\(750\) | 1.45203 | − | 1.81388i | 0.0530208 | − | 0.0662335i | ||||
\(751\) | − | 18.1496i | − | 0.662287i | −0.943580 | − | 0.331144i | \(-0.892566\pi\) | ||
0.943580 | − | 0.331144i | \(-0.107434\pi\) | |||||||
\(752\) | 32.3911 | − | 15.3036i | 1.18118 | − | 0.558067i | ||||
\(753\) | −19.1724 | −0.698680 | ||||||||
\(754\) | −17.2606 | + | 21.5619i | −0.628593 | + | 0.785237i | ||||
\(755\) | −5.89243 | + | 5.89243i | −0.214447 | + | 0.214447i | ||||
\(756\) | 22.6841 | − | 17.5743i | 0.825012 | − | 0.639171i | ||||
\(757\) | −13.7316 | − | 13.7316i | −0.499085 | − | 0.499085i | 0.412068 | − | 0.911153i | \(-0.364807\pi\) |
−0.911153 | + | 0.412068i | \(0.864807\pi\) | |||||||
\(758\) | 4.75905 | + | 42.9539i | 0.172857 | + | 1.56016i | ||||
\(759\) | 4.70727i | 0.170863i | ||||||||
\(760\) | 5.20089 | − | 10.6477i | 0.188656 | − | 0.386234i | ||||
\(761\) | 49.6904 | 1.80128 | 0.900638 | − | 0.434571i | \(-0.143100\pi\) | ||||
0.900638 | + | 0.434571i | \(0.143100\pi\) | |||||||
\(762\) | 28.3876 | − | 3.14519i | 1.02837 | − | 0.113938i | ||||
\(763\) | 8.54281 | − | 4.00573i | 0.309271 | − | 0.145017i | ||||
\(764\) | 29.0357 | − | 6.51395i | 1.05047 | − | 0.235666i | ||||
\(765\) | 0.405034 | − | 0.405034i | 0.0146440 | − | 0.0146440i | ||||
\(766\) | −29.6722 | + | 37.0665i | −1.07210 | + | 1.33927i | ||||
\(767\) | − | 51.6124i | − | 1.86362i | ||||||
\(768\) | −2.55520 | − | 26.1627i | −0.0922027 | − | 0.944065i | ||||
\(769\) | − | 3.60667i | − | 0.130060i | −0.997883 | − | 0.0650298i | \(-0.979286\pi\) | ||
0.997883 | − | 0.0650298i | \(-0.0207143\pi\) | |||||||
\(770\) | −8.52913 | − | 13.9488i | −0.307369 | − | 0.502678i | ||||
\(771\) | 12.0555 | + | 12.0555i | 0.434169 | + | 0.434169i | ||||
\(772\) | 1.82653 | + | 8.14168i | 0.0657381 | + | 0.293026i | ||||
\(773\) | 21.3669 | − | 21.3669i | 0.768515 | − | 0.768515i | −0.209330 | − | 0.977845i | \(-0.567128\pi\) |
0.977845 | + | 0.209330i | \(0.0671283\pi\) | |||||||
\(774\) | 0.100832 | − | 0.0111717i | 0.00362434 | − | 0.000401557i | ||||
\(775\) | − | 3.01437i | − | 0.108280i | ||||||
\(776\) | −16.4408 | + | 33.6590i | −0.590189 | + | 1.20829i | ||||
\(777\) | −35.1532 | − | 12.7101i | −1.26112 | − | 0.455972i | ||||
\(778\) | 44.4063 | − | 4.91997i | 1.59204 | − | 0.176390i | ||||
\(779\) | 21.5636 | − | 21.5636i | 0.772596 | − | 0.772596i | ||||
\(780\) | −14.3027 | − | 9.06117i | −0.512118 | − | 0.324442i | ||||
\(781\) | 47.9684 | − | 47.9684i | 1.71644 | − | 1.71644i | ||||
\(782\) | 1.37889 | + | 1.10382i | 0.0493089 | + | 0.0394725i | ||||
\(783\) | 20.5540 | 0.734541 | ||||||||
\(784\) | −27.1122 | − | 6.99507i | −0.968291 | − | 0.249824i | ||||
\(785\) | −21.5580 | −0.769438 | ||||||||
\(786\) | 17.2727 | + | 13.8270i | 0.616095 | + | 0.493192i | ||||
\(787\) | −16.9931 | + | 16.9931i | −0.605738 | + | 0.605738i | −0.941829 | − | 0.336091i | \(-0.890895\pi\) |
0.336091 | + | 0.941829i | \(0.390895\pi\) | |||||||
\(788\) | 17.7989 | − | 28.0948i | 0.634058 | − | 1.00083i | ||||
\(789\) | −28.3682 | + | 28.3682i | −1.00994 | + | 1.00994i | ||||
\(790\) | −17.3098 | + | 1.91783i | −0.615855 | + | 0.0682333i | ||||
\(791\) | 3.12246 | + | 1.12896i | 0.111022 | + | 0.0401413i | ||||
\(792\) | −1.20799 | − | 3.51486i | −0.0429240 | − | 0.124895i | ||||
\(793\) | 23.8724i | 0.847735i | ||||||||
\(794\) | 27.4591 | − | 3.04231i | 0.974486 | − | 0.107968i | ||||
\(795\) | −10.6657 | + | 10.6657i | −0.378272 | + | 0.378272i | ||||
\(796\) | 39.1727 | − | 8.78812i | 1.38844 | − | 0.311487i | ||||
\(797\) | 16.5746 | + | 16.5746i | 0.587104 | + | 0.587104i | 0.936846 | − | 0.349742i | \(-0.113731\pi\) |
−0.349742 | + | 0.936846i | \(0.613731\pi\) | |||||||
\(798\) | 13.4356 | + | 21.9729i | 0.475615 | + | 0.777834i | ||||
\(799\) | 17.0595i | 0.603520i | ||||||||
\(800\) | −5.50311 | − | 1.30988i | −0.194564 | − | 0.0463111i | ||||
\(801\) | 3.78808i | 0.133845i | ||||||||
\(802\) | −2.07637 | + | 2.59380i | −0.0733193 | + | 0.0915904i | ||||
\(803\) | −19.3632 | + | 19.3632i | −0.683311 | + | 0.683311i | ||||
\(804\) | 0.902021 | + | 4.02073i | 0.0318118 | + | 0.141800i | ||||
\(805\) | 1.57069 | − | 0.736498i | 0.0553596 | − | 0.0259582i | ||||
\(806\) | −21.8324 | + | 2.41891i | −0.769013 | + | 0.0852023i | ||||
\(807\) | −31.6365 | −1.11366 | ||||||||
\(808\) | −6.15940 | + | 2.11686i | −0.216687 | + | 0.0744709i | ||||
\(809\) | 25.7007i | 0.903588i | 0.892122 | + | 0.451794i | \(0.149216\pi\) | ||||
−0.892122 | + | 0.451794i | \(0.850784\pi\) | |||||||
\(810\) | 1.24703 | + | 11.2553i | 0.0438161 | + | 0.395472i | ||||
\(811\) | 1.45385 | + | 1.45385i | 0.0510514 | + | 0.0510514i | 0.732172 | − | 0.681120i | \(-0.238507\pi\) |
−0.681120 | + | 0.732172i | \(0.738507\pi\) | |||||||
\(812\) | −12.2831 | − | 15.8545i | −0.431054 | − | 0.556384i | ||||
\(813\) | −6.47602 | + | 6.47602i | −0.227124 | + | 0.227124i | ||||
\(814\) | −33.2101 | + | 41.4861i | −1.16401 | + | 1.45409i | ||||
\(815\) | −8.25717 | −0.289236 | ||||||||
\(816\) | 11.7844 | + | 4.22196i | 0.412537 | + | 0.147798i | ||||
\(817\) | 0.999423i | 0.0349654i | ||||||||
\(818\) | 27.6812 | − | 34.5793i | 0.967851 | − | 1.20904i | ||||
\(819\) | −3.71185 | + | 1.74049i | −0.129703 | + | 0.0608177i | ||||
\(820\) | −12.2975 | − | 7.79082i | −0.429447 | − | 0.272067i | ||||
\(821\) | −10.1678 | − | 10.1678i | −0.354859 | − | 0.354859i | 0.507055 | − | 0.861914i | \(-0.330734\pi\) |
−0.861914 | + | 0.507055i | \(0.830734\pi\) | |||||||
\(822\) | −39.3304 | + | 4.35759i | −1.37181 | + | 0.151988i | ||||
\(823\) | −46.5085 | −1.62119 | −0.810593 | − | 0.585610i | \(-0.800855\pi\) | ||||
−0.810593 | + | 0.585610i | \(0.800855\pi\) | |||||||
\(824\) | 22.0072 | − | 45.0552i | 0.766657 | − | 1.56957i | ||||
\(825\) | 7.17911 | 0.249945 | ||||||||
\(826\) | 36.4342 | + | 8.78464i | 1.26771 | + | 0.305657i | ||||
\(827\) | −17.9248 | + | 17.9248i | −0.623305 | + | 0.623305i | −0.946375 | − | 0.323070i | \(-0.895285\pi\) |
0.323070 | + | 0.946375i | \(0.395285\pi\) | |||||||
\(828\) | 0.384792 | − | 0.0863252i | 0.0133724 | − | 0.00300001i | ||||
\(829\) | −14.2329 | − | 14.2329i | −0.494331 | − | 0.494331i | 0.415337 | − | 0.909668i | \(-0.363664\pi\) |
−0.909668 | + | 0.415337i | \(0.863664\pi\) | |||||||
\(830\) | −3.82029 | − | 3.05819i | −0.132604 | − | 0.106151i | ||||
\(831\) | 24.9570 | 0.865748 | ||||||||
\(832\) | −5.07110 | + | 40.9088i | −0.175809 | + | 1.41826i | ||||
\(833\) | 8.52707 | − | 10.2504i | 0.295445 | − | 0.355157i | ||||
\(834\) | 22.5836 | − | 28.2114i | 0.782006 | − | 0.976881i | ||||
\(835\) | 2.96579 | + | 2.96579i | 0.102635 | + | 0.102635i | ||||
\(836\) | 35.7264 | − | 8.01496i | 1.23562 | − | 0.277203i | ||||
\(837\) | 11.5589 | + | 11.5589i | 0.399532 | + | 0.399532i | ||||
\(838\) | 2.30616 | + | 20.8147i | 0.0796648 | + | 0.719033i | ||||
\(839\) | 43.8985i | 1.51554i | 0.652519 | + | 0.757772i | \(0.273712\pi\) | ||||
−0.652519 | + | 0.757772i | \(0.726288\pi\) | |||||||
\(840\) | 8.83084 | − | 8.55430i | 0.304693 | − | 0.295152i | ||||
\(841\) | 14.6343i | 0.504629i | ||||||||
\(842\) | −40.9865 | + | 4.54107i | −1.41249 | + | 0.156496i | ||||
\(843\) | 10.0051 | + | 10.0051i | 0.344593 | + | 0.344593i | ||||
\(844\) | −8.81517 | + | 13.9144i | −0.303431 | + | 0.478953i | ||||
\(845\) | 9.58181 | + | 9.58181i | 0.329624 | + | 0.329624i | ||||
\(846\) | 2.97347 | + | 2.38030i | 0.102230 | + | 0.0818364i | ||||
\(847\) | 7.28129 | − | 20.1384i | 0.250188 | − | 0.691964i | ||||
\(848\) | 34.5713 | + | 12.3858i | 1.18718 | + | 0.425329i | ||||
\(849\) | 7.38423 | 0.253426 | ||||||||
\(850\) | 1.68345 | − | 2.10296i | 0.0577417 | − | 0.0721309i | ||||
\(851\) | −3.98708 | − | 3.98708i | −0.136675 | − | 0.136675i | ||||
\(852\) | 43.0926 | + | 27.3004i | 1.47633 | + | 0.935297i | ||||
\(853\) | −8.35675 | + | 8.35675i | −0.286130 | + | 0.286130i | −0.835548 | − | 0.549418i | \(-0.814849\pi\) |
0.549418 | + | 0.835548i | \(0.314849\pi\) | |||||||
\(854\) | −16.8520 | − | 4.06318i | −0.576664 | − | 0.139039i | ||||
\(855\) | 1.25990 | 0.0430876 | ||||||||
\(856\) | −35.4232 | + | 12.1742i | −1.21074 | + | 0.416107i | ||||
\(857\) | 25.7773 | 0.880535 | 0.440267 | − | 0.897867i | \(-0.354884\pi\) | ||||
0.440267 | + | 0.897867i | \(0.354884\pi\) | |||||||
\(858\) | −5.76093 | − | 51.9966i | −0.196675 | − | 1.77513i | ||||
\(859\) | −3.99405 | − | 3.99405i | −0.136275 | − | 0.136275i | 0.635679 | − | 0.771954i | \(-0.280720\pi\) |
−0.771954 | + | 0.635679i | \(0.780720\pi\) | |||||||
\(860\) | 0.465523 | − | 0.104437i | 0.0158742 | − | 0.00356126i | ||||
\(861\) | 28.6469 | − | 13.4326i | 0.976284 | − | 0.457780i | ||||
\(862\) | 20.8575 | + | 16.6967i | 0.710411 | + | 0.568693i | ||||
\(863\) | − | 4.95262i | − | 0.168589i | −0.996441 | − | 0.0842945i | \(-0.973136\pi\) | ||
0.996441 | − | 0.0842945i | \(-0.0268636\pi\) | |||||||
\(864\) | 26.1249 | − | 16.0793i | 0.888788 | − | 0.547028i | ||||
\(865\) | −22.3231 | −0.759007 | ||||||||
\(866\) | 28.5863 | + | 22.8837i | 0.971403 | + | 0.777621i | ||||
\(867\) | 15.5345 | − | 15.5345i | 0.527581 | − | 0.527581i | ||||
\(868\) | 2.00840 | − | 15.8236i | 0.0681696 | − | 0.537089i | ||||
\(869\) | −38.0503 | − | 38.0503i | −1.29077 | − | 1.29077i | ||||
\(870\) | 8.75294 | − | 0.969777i | 0.296752 | − | 0.0328785i | ||||
\(871\) | − | 6.46177i | − | 0.218949i | ||||||
\(872\) | 9.53916 | − | 3.27841i | 0.323037 | − | 0.111021i | ||||
\(873\) | −3.98272 | −0.134795 | ||||||||
\(874\) | 0.427816 | + | 3.86135i | 0.0144711 | + | 0.130612i | ||||
\(875\) | −1.12324 | − | 2.39548i | −0.0379725 | − | 0.0809820i | ||||
\(876\) | −17.3950 | − | 11.0202i | −0.587722 | − | 0.372339i | ||||
\(877\) | 20.9265 | − | 20.9265i | 0.706637 | − | 0.706637i | −0.259190 | − | 0.965826i | \(-0.583455\pi\) |
0.965826 | + | 0.259190i | \(0.0834555\pi\) | |||||||
\(878\) | 2.97086 | + | 2.37821i | 0.100262 | + | 0.0802607i | ||||
\(879\) | 5.80427i | 0.195773i | ||||||||
\(880\) | −7.46660 | − | 15.8035i | −0.251699 | − | 0.532737i | ||||
\(881\) | 10.0400i | 0.338257i | 0.985594 | + | 0.169128i | \(0.0540953\pi\) | ||||
−0.985594 | + | 0.169128i | \(0.945905\pi\) | |||||||
\(882\) | −0.596876 | − | 2.91651i | −0.0200978 | − | 0.0982040i | ||||
\(883\) | 22.3597 | + | 22.3597i | 0.752465 | + | 0.752465i | 0.974939 | − | 0.222474i | \(-0.0714131\pi\) |
−0.222474 | + | 0.974939i | \(0.571413\pi\) | |||||||
\(884\) | −16.5821 | − | 10.5053i | −0.557717 | − | 0.353330i | ||||
\(885\) | −11.6366 | + | 11.6366i | −0.391159 | + | 0.391159i | ||||
\(886\) | 5.24455 | + | 47.3358i | 0.176194 | + | 1.59028i | ||||
\(887\) | − | 25.9525i | − | 0.871400i | −0.900092 | − | 0.435700i | \(-0.856501\pi\) | ||
0.900092 | − | 0.435700i | \(-0.143499\pi\) | |||||||
\(888\) | −35.9069 | − | 17.5387i | −1.20496 | − | 0.588561i | ||||
\(889\) | 11.0584 | − | 30.5850i | 0.370887 | − | 1.02579i | ||||
\(890\) | 1.96175 | + | 17.7062i | 0.0657578 | + | 0.593512i | ||||
\(891\) | −24.7414 | + | 24.7414i | −0.828868 | + | 0.828868i | ||||
\(892\) | 5.71824 | + | 25.4888i | 0.191461 | + | 0.853429i | ||||
\(893\) | −26.5325 | + | 26.5325i | −0.887878 | + | 0.887878i | ||||
\(894\) | 0.389258 | − | 0.486260i | 0.0130187 | − | 0.0162630i | ||||
\(895\) | 5.91537 | 0.197729 | ||||||||
\(896\) | −28.0152 | − | 10.5426i | −0.935923 | − | 0.352205i | ||||
\(897\) | 5.55086 | 0.185338 | ||||||||
\(898\) | −11.1758 | + | 13.9608i | −0.372941 | + | 0.465877i | ||||
\(899\) | 8.07879 | − | 8.07879i | 0.269443 | − | 0.269443i | ||||
\(900\) | −0.131656 | − | 0.586850i | −0.00438852 | − | 0.0195617i | ||||
\(901\) | −12.3655 | + | 12.3655i | −0.411953 | + | 0.411953i | ||||
\(902\) | −4.95326 | − | 44.7068i | −0.164926 | − | 1.48857i | ||||
\(903\) | −0.352575 | + | 0.975143i | −0.0117330 | + | 0.0324507i | ||||
\(904\) | 3.18940 | + | 1.55786i | 0.106078 | + | 0.0518137i | ||||
\(905\) | − | 8.36167i | − | 0.277951i | ||||||
\(906\) | −2.13215 | − | 19.2442i | −0.0708358 | − | 0.639344i | ||||
\(907\) | −23.5825 | + | 23.5825i | −0.783045 | + | 0.783045i | −0.980343 | − | 0.197298i | \(-0.936783\pi\) |
0.197298 | + | 0.980343i | \(0.436783\pi\) | |||||||
\(908\) | 15.4726 | + | 9.80236i | 0.513477 | + | 0.325303i | ||||
\(909\) | −0.489646 | − | 0.489646i | −0.0162405 | − | 0.0162405i | ||||
\(910\) | −16.4485 | + | 10.0576i | −0.545263 | + | 0.333408i | ||||
\(911\) | − | 24.0854i | − | 0.797984i | −0.916954 | − | 0.398992i | \(-0.869360\pi\) | ||
0.916954 | − | 0.398992i | \(-0.130640\pi\) | |||||||
\(912\) | 11.7619 | + | 24.8947i | 0.389474 | + | 0.824345i | ||||
\(913\) | − | 15.1202i | − | 0.500407i | ||||||
\(914\) | 38.6848 | + | 30.9677i | 1.27958 | + | 1.02432i | ||||
\(915\) | 5.38229 | − | 5.38229i | 0.177933 | − | 0.177933i | ||||
\(916\) | −39.7098 | − | 25.1573i | −1.31205 | − | 0.831222i | ||||
\(917\) | 22.8109 | − | 10.6961i | 0.753284 | − | 0.353215i | ||||
\(918\) | 1.60865 | + | 14.5193i | 0.0530935 | + | 0.479207i | ||||
\(919\) | 21.0056 | 0.692909 | 0.346455 | − | 0.938067i | \(-0.387385\pi\) | ||||
0.346455 | + | 0.938067i | \(0.387385\pi\) | |||||||
\(920\) | 1.75388 | − | 0.602773i | 0.0578237 | − | 0.0198728i | ||||
\(921\) | − | 14.9484i | − | 0.492565i | ||||||
\(922\) | 43.1589 | − | 4.78176i | 1.42136 | − | 0.157479i | ||||
\(923\) | −56.5648 | − | 56.5648i | −1.86185 | − | 1.86185i | ||||
\(924\) | 37.6860 | + | 4.78326i | 1.23978 | + | 0.157358i | ||||
\(925\) | −6.08074 | + | 6.08074i | −0.199933 | + | 0.199933i | ||||
\(926\) | −0.461958 | − | 0.369803i | −0.0151809 | − | 0.0121525i | ||||
\(927\) | 5.33117 | 0.175099 | ||||||||
\(928\) | −11.2382 | − | 18.2594i | −0.368913 | − | 0.599394i | ||||
\(929\) | 2.00319i | 0.0657224i | 0.999460 | + | 0.0328612i | \(0.0104619\pi\) | ||||
−0.999460 | + | 0.0328612i | \(0.989538\pi\) | |||||||
\(930\) | 5.46771 | + | 4.37697i | 0.179293 | + | 0.143527i | ||||
\(931\) | 29.2046 | − | 2.68036i | 0.957144 | − | 0.0878452i | ||||
\(932\) | −40.3385 | + | 9.04966i | −1.32133 | + | 0.296431i | ||||
\(933\) | 1.71611 | + | 1.71611i | 0.0561829 | + | 0.0561829i | ||||
\(934\) | 4.16604 | + | 37.6016i | 0.136317 | + | 1.23036i | ||||
\(935\) | 8.32326 | 0.272200 | ||||||||
\(936\) | −4.14476 | + | 1.42447i | −0.135476 | + | 0.0465603i | ||||
\(937\) | −48.2490 | −1.57623 | −0.788113 | − | 0.615531i | \(-0.788942\pi\) | ||||
−0.788113 | + | 0.615531i | \(0.788942\pi\) | |||||||
\(938\) | 4.56149 | + | 1.09982i | 0.148938 | + | 0.0359104i | ||||
\(939\) | 30.8391 | − | 30.8391i | 1.00640 | − | 1.00640i | ||||
\(940\) | 15.1312 | + | 9.58607i | 0.493526 | + | 0.312663i | ||||
\(941\) | 4.58268 | + | 4.58268i | 0.149391 | + | 0.149391i | 0.777846 | − | 0.628455i | \(-0.216312\pi\) |
−0.628455 | + | 0.777846i | \(0.716312\pi\) | |||||||
\(942\) | 31.3030 | − | 39.1036i | 1.01991 | − | 1.27406i | ||||
\(943\) | 4.77265 | 0.155419 | ||||||||
\(944\) | 37.7184 | + | 13.5133i | 1.22763 | + | 0.439819i | ||||
\(945\) | 13.4928 | + | 4.87850i | 0.438921 | + | 0.158697i | ||||
\(946\) | 1.15081 | + | 0.921242i | 0.0374162 | + | 0.0299522i | ||||
\(947\) | 2.50849 | + | 2.50849i | 0.0815151 | + | 0.0815151i | 0.746689 | − | 0.665174i | \(-0.231642\pi\) |
−0.665174 | + | 0.746689i | \(0.731642\pi\) | |||||||
\(948\) | 21.6557 | − | 34.1826i | 0.703345 | − | 1.11020i | ||||
\(949\) | 22.8333 | + | 22.8333i | 0.741199 | + | 0.741199i | ||||
\(950\) | 5.88899 | − | 0.652467i | 0.191064 | − | 0.0211688i | ||||
\(951\) | 12.8387i | 0.416325i | ||||||||
\(952\) | 10.2382 | − | 9.91761i | 0.331822 | − | 0.321432i | ||||
\(953\) | − | 2.28997i | − | 0.0741795i | −0.999312 | − | 0.0370897i | \(-0.988191\pi\) | ||
0.999312 | − | 0.0370897i | \(-0.0118087\pi\) | |||||||
\(954\) | 0.429954 | + | 3.88065i | 0.0139203 | + | 0.125641i | ||||
\(955\) | 10.5208 | + | 10.5208i | 0.340446 | + | 0.340446i | ||||
\(956\) | 9.17327 | − | 2.05796i | 0.296685 | − | 0.0665591i | ||||
\(957\) | 19.2407 | + | 19.2407i | 0.621962 | + | 0.621962i | ||||
\(958\) | −22.9948 | + | 28.7251i | −0.742929 | + | 0.928066i | ||||
\(959\) | −15.3212 | + | 42.3749i | −0.494746 | + | 1.36836i | ||||
\(960\) | 10.3667 | − | 8.08000i | 0.334583 | − | 0.260781i | ||||
\(961\) | −21.9135 | −0.706889 | ||||||||
\(962\) | 48.9208 | + | 39.1618i | 1.57727 | + | 1.26263i | ||||
\(963\) | −2.81599 | − | 2.81599i | −0.0907440 | − | 0.0907440i | ||||
\(964\) | 7.42589 | − | 1.66595i | 0.239172 | − | 0.0536565i | ||||
\(965\) | −2.95007 | + | 2.95007i | −0.0949660 | + | 0.0949660i | ||||
\(966\) | −0.944779 | + | 3.91847i | −0.0303978 | + | 0.126075i | ||||
\(967\) | 30.3317 | 0.975402 | 0.487701 | − | 0.873011i | \(-0.337836\pi\) | ||||
0.487701 | + | 0.873011i | \(0.337836\pi\) | |||||||
\(968\) | 10.0475 | − | 20.5702i | 0.322939 | − | 0.661150i | ||||
\(969\) | −13.1113 | −0.421196 | ||||||||
\(970\) | −18.6159 | + | 2.06254i | −0.597722 | + | 0.0662242i | ||||
\(971\) | 11.5680 | + | 11.5680i | 0.371236 | + | 0.371236i | 0.867927 | − | 0.496691i | \(-0.165452\pi\) |
−0.496691 | + | 0.867927i | \(0.665452\pi\) | |||||||
\(972\) | 5.25932 | + | 3.33193i | 0.168693 | + | 0.106872i | ||||
\(973\) | −17.4699 | − | 37.2571i | −0.560059 | − | 1.19441i | ||||
\(974\) | 8.85138 | − | 11.0571i | 0.283617 | − | 0.354293i | ||||
\(975\) | − | 8.46569i | − | 0.271119i | ||||||
\(976\) | −17.4460 | − | 6.25032i | −0.558432 | − | 0.200068i | ||||
\(977\) | −0.542253 | −0.0173482 | −0.00867410 | − | 0.999962i | \(-0.502761\pi\) | ||||
−0.00867410 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(978\) | 11.9897 | − | 14.9775i | 0.383388 | − | 0.478928i | ||||
\(979\) | −38.9216 | + | 38.9216i | −1.24394 | + | 1.24394i | ||||
\(980\) | −4.30029 | − | 13.3232i | −0.137368 | − | 0.425594i | ||||
\(981\) | 0.758322 | + | 0.758322i | 0.0242113 | + | 0.0242113i | ||||
\(982\) | −6.01529 | − | 54.2924i | −0.191956 | − | 1.73254i | ||||
\(983\) | − | 11.7834i | − | 0.375832i | −0.982185 | − | 0.187916i | \(-0.939827\pi\) | ||
0.982185 | − | 0.187916i | \(-0.0601733\pi\) | |||||||
\(984\) | 31.9880 | − | 10.9936i | 1.01974 | − | 0.350464i | ||||
\(985\) | 16.6292 | 0.529849 | ||||||||
\(986\) | 10.1479 | − | 1.12433i | 0.323175 | − | 0.0358060i | ||||
\(987\) | −35.2481 | + | 16.5278i | −1.12196 | + | 0.526087i | ||||
\(988\) | −9.45132 | − | 42.1289i | −0.300687 | − | 1.34030i | ||||
\(989\) | −0.110601 | + | 0.110601i | −0.00351689 | + | 0.00351689i | ||||
\(990\) | 1.16134 | − | 1.45075i | 0.0369098 | − | 0.0461077i | ||||
\(991\) | 31.4105i | 0.997788i | 0.866663 | + | 0.498894i | \(0.166260\pi\) | ||||
−0.866663 | + | 0.498894i | \(0.833740\pi\) | |||||||
\(992\) | 3.94845 | − | 16.5884i | 0.125364 | − | 0.526683i | ||||
\(993\) | 34.3698i | 1.09069i | ||||||||
\(994\) | 49.5578 | − | 30.3027i | 1.57188 | − | 0.961143i | ||||
\(995\) | 14.1939 | + | 14.1939i | 0.449977 | + | 0.449977i | ||||
\(996\) | 11.0944 | − | 2.48894i | 0.351539 | − | 0.0788652i | ||||
\(997\) | −17.6622 | + | 17.6622i | −0.559368 | + | 0.559368i | −0.929128 | − | 0.369759i | \(-0.879440\pi\) |
0.369759 | + | 0.929128i | \(0.379440\pi\) | |||||||
\(998\) | −35.9903 | + | 3.98753i | −1.13925 | + | 0.126223i | ||||
\(999\) | − | 46.6341i | − | 1.47544i |
(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 | 560.2.bc.a.251.20 | yes | 128 | |
7.6 | odd | 2 | inner | 560.2.bc.a.251.19 | ✓ | 128 | |
16.3 | odd | 4 | inner | 560.2.bc.a.531.19 | yes | 128 | |
112.83 | even | 4 | inner | 560.2.bc.a.531.20 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bc.a.251.19 | ✓ | 128 | 7.6 | odd | 2 | inner | |
560.2.bc.a.251.20 | yes | 128 | 1.1 | even | 1 | trivial | |
560.2.bc.a.531.19 | yes | 128 | 16.3 | odd | 4 | inner | |
560.2.bc.a.531.20 | yes | 128 | 112.83 | even | 4 | inner |