Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [574,2,Mod(155,574)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(574, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("574.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 574 = 2 \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 574.f (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: | \(4.58341307602\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 40 x^{18} + 666 x^{16} + 6052 x^{14} + 33033 x^{12} + 112020 x^{10} + 235396 x^{8} + \cdots + 8464 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 155.4 | ||
Root | \(1.98313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 574.155 |
Dual form | 574.2.f.a.337.4 |
$q$-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 \(\left(\mathbb{Z}/574\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(493\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.40228 | + | 1.40228i | −0.809609 | + | 0.809609i | −0.984575 | − | 0.174965i | \(-0.944019\pi\) |
0.174965 | + | 0.984575i | \(0.444019\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.58615i | 0.709348i | 0.934990 | + | 0.354674i | \(0.115408\pi\) | ||||
−0.934990 | + | 0.354674i | \(0.884592\pi\) | |||||||
\(6\) | 1.40228 | + | 1.40228i | 0.572480 | + | 0.572480i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | − | 0.932805i | − | 0.310935i | ||||||
\(10\) | 1.58615 | 0.501585 | ||||||||
\(11\) | −1.52386 | + | 1.52386i | −0.459462 | + | 0.459462i | −0.898479 | − | 0.439017i | \(-0.855327\pi\) |
0.439017 | + | 0.898479i | \(0.355327\pi\) | |||||||
\(12\) | 1.40228 | − | 1.40228i | 0.404805 | − | 0.404805i | ||||
\(13\) | −1.17480 | + | 1.17480i | −0.325831 | + | 0.325831i | −0.850999 | − | 0.525168i | \(-0.824003\pi\) |
0.525168 | + | 0.850999i | \(0.324003\pi\) | |||||||
\(14\) | −0.707107 | − | 0.707107i | −0.188982 | − | 0.188982i | ||||
\(15\) | −2.22424 | − | 2.22424i | −0.574295 | − | 0.574295i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.81650 | − | 2.81650i | −0.683101 | − | 0.683101i | 0.277597 | − | 0.960698i | \(-0.410462\pi\) |
−0.960698 | + | 0.277597i | \(0.910462\pi\) | |||||||
\(18\) | −0.932805 | −0.219864 | ||||||||
\(19\) | −5.01036 | − | 5.01036i | −1.14946 | − | 1.14946i | −0.986660 | − | 0.162795i | \(-0.947949\pi\) |
−0.162795 | − | 0.986660i | \(-0.552051\pi\) | |||||||
\(20\) | − | 1.58615i | − | 0.354674i | ||||||
\(21\) | 1.98313i | 0.432754i | ||||||||
\(22\) | 1.52386 | + | 1.52386i | 0.324889 | + | 0.324889i | ||||
\(23\) | 6.10702 | 1.27340 | 0.636701 | − | 0.771111i | \(-0.280299\pi\) | ||||
0.636701 | + | 0.771111i | \(0.280299\pi\) | |||||||
\(24\) | −1.40228 | − | 1.40228i | −0.286240 | − | 0.286240i | ||||
\(25\) | 2.48412 | 0.496825 | ||||||||
\(26\) | 1.17480 | + | 1.17480i | 0.230397 | + | 0.230397i | ||||
\(27\) | −2.89880 | − | 2.89880i | −0.557874 | − | 0.557874i | ||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | −7.06728 | + | 7.06728i | −1.31236 | + | 1.31236i | −0.392691 | + | 0.919670i | \(0.628456\pi\) |
−0.919670 | + | 0.392691i | \(0.871544\pi\) | |||||||
\(30\) | −2.22424 | + | 2.22424i | −0.406088 | + | 0.406088i | ||||
\(31\) | −9.34523 | −1.67845 | −0.839226 | − | 0.543782i | \(-0.816992\pi\) | ||||
−0.839226 | + | 0.543782i | \(0.816992\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 4.27378i | − | 0.743970i | ||||||
\(34\) | −2.81650 | + | 2.81650i | −0.483025 | + | 0.483025i | ||||
\(35\) | 1.12158 | + | 1.12158i | 0.189581 | + | 0.189581i | ||||
\(36\) | 0.932805i | 0.155467i | ||||||||
\(37\) | −2.74728 | −0.451650 | −0.225825 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225825 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(38\) | −5.01036 | + | 5.01036i | −0.812787 | + | 0.812787i | ||||
\(39\) | − | 3.29481i | − | 0.527592i | ||||||
\(40\) | −1.58615 | −0.250793 | ||||||||
\(41\) | −4.76951 | + | 4.27221i | −0.744872 | + | 0.667207i | ||||
\(42\) | 1.98313 | 0.306004 | ||||||||
\(43\) | 7.14760i | 1.09000i | 0.838437 | + | 0.544999i | \(0.183470\pi\) | ||||
−0.838437 | + | 0.544999i | \(0.816530\pi\) | |||||||
\(44\) | 1.52386 | − | 1.52386i | 0.229731 | − | 0.229731i | ||||
\(45\) | 1.47957 | 0.220561 | ||||||||
\(46\) | − | 6.10702i | − | 0.900431i | ||||||
\(47\) | −5.02180 | − | 5.02180i | −0.732504 | − | 0.732504i | 0.238611 | − | 0.971115i | \(-0.423308\pi\) |
−0.971115 | + | 0.238611i | \(0.923308\pi\) | |||||||
\(48\) | −1.40228 | + | 1.40228i | −0.202402 | + | 0.202402i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | − | 2.48412i | − | 0.351308i | ||||||
\(51\) | 7.89906 | 1.10609 | ||||||||
\(52\) | 1.17480 | − | 1.17480i | 0.162916 | − | 0.162916i | ||||
\(53\) | −7.43800 | + | 7.43800i | −1.02169 | + | 1.02169i | −0.0219276 | + | 0.999760i | \(0.506980\pi\) |
−0.999760 | + | 0.0219276i | \(0.993020\pi\) | |||||||
\(54\) | −2.89880 | + | 2.89880i | −0.394476 | + | 0.394476i | ||||
\(55\) | −2.41708 | − | 2.41708i | −0.325919 | − | 0.325919i | ||||
\(56\) | 0.707107 | + | 0.707107i | 0.0944911 | + | 0.0944911i | ||||
\(57\) | 14.0519 | 1.86122 | ||||||||
\(58\) | 7.06728 | + | 7.06728i | 0.927980 | + | 0.927980i | ||||
\(59\) | 10.7381 | 1.39798 | 0.698990 | − | 0.715131i | \(-0.253633\pi\) | ||||
0.698990 | + | 0.715131i | \(0.253633\pi\) | |||||||
\(60\) | 2.22424 | + | 2.22424i | 0.287148 | + | 0.287148i | ||||
\(61\) | − | 12.4049i | − | 1.58829i | −0.607731 | − | 0.794143i | \(-0.707920\pi\) | ||
0.607731 | − | 0.794143i | \(-0.292080\pi\) | |||||||
\(62\) | 9.34523i | 1.18685i | ||||||||
\(63\) | −0.659593 | − | 0.659593i | −0.0831009 | − | 0.0831009i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.86341 | − | 1.86341i | −0.231128 | − | 0.231128i | ||||
\(66\) | −4.27378 | −0.526066 | ||||||||
\(67\) | −6.07639 | − | 6.07639i | −0.742349 | − | 0.742349i | 0.230680 | − | 0.973030i | \(-0.425905\pi\) |
−0.973030 | + | 0.230680i | \(0.925905\pi\) | |||||||
\(68\) | 2.81650 | + | 2.81650i | 0.341551 | + | 0.341551i | ||||
\(69\) | −8.56378 | + | 8.56378i | −1.03096 | + | 1.03096i | ||||
\(70\) | 1.12158 | − | 1.12158i | 0.134054 | − | 0.134054i | ||||
\(71\) | 6.10702 | − | 6.10702i | 0.724770 | − | 0.724770i | −0.244803 | − | 0.969573i | \(-0.578723\pi\) |
0.969573 | + | 0.244803i | \(0.0787232\pi\) | |||||||
\(72\) | 0.932805 | 0.109932 | ||||||||
\(73\) | 16.1050i | 1.88495i | 0.334280 | + | 0.942474i | \(0.391507\pi\) | ||||
−0.334280 | + | 0.942474i | \(0.608493\pi\) | |||||||
\(74\) | 2.74728i | 0.319365i | ||||||||
\(75\) | −3.48345 | + | 3.48345i | −0.402234 | + | 0.402234i | ||||
\(76\) | 5.01036 | + | 5.01036i | 0.574728 | + | 0.574728i | ||||
\(77\) | 2.15507i | 0.245593i | ||||||||
\(78\) | −3.29481 | −0.373064 | ||||||||
\(79\) | 2.49677 | − | 2.49677i | 0.280908 | − | 0.280908i | −0.552563 | − | 0.833471i | \(-0.686350\pi\) |
0.833471 | + | 0.552563i | \(0.186350\pi\) | |||||||
\(80\) | 1.58615i | 0.177337i | ||||||||
\(81\) | 10.9283 | 1.21425 | ||||||||
\(82\) | 4.27221 | + | 4.76951i | 0.471787 | + | 0.526704i | ||||
\(83\) | −2.01947 | −0.221666 | −0.110833 | − | 0.993839i | \(-0.535352\pi\) | ||||
−0.110833 | + | 0.993839i | \(0.535352\pi\) | |||||||
\(84\) | − | 1.98313i | − | 0.216377i | ||||||
\(85\) | 4.46739 | − | 4.46739i | 0.484557 | − | 0.484557i | ||||
\(86\) | 7.14760 | 0.770745 | ||||||||
\(87\) | − | 19.8207i | − | 2.12500i | ||||||
\(88\) | −1.52386 | − | 1.52386i | −0.162444 | − | 0.162444i | ||||
\(89\) | 12.2966 | − | 12.2966i | 1.30343 | − | 1.30343i | 0.377374 | − | 0.926061i | \(-0.376827\pi\) |
0.926061 | − | 0.377374i | \(-0.123173\pi\) | |||||||
\(90\) | − | 1.47957i | − | 0.155960i | ||||||
\(91\) | 1.66142i | 0.174164i | ||||||||
\(92\) | −6.10702 | −0.636701 | ||||||||
\(93\) | 13.1047 | − | 13.1047i | 1.35889 | − | 1.35889i | ||||
\(94\) | −5.02180 | + | 5.02180i | −0.517959 | + | 0.517959i | ||||
\(95\) | 7.94719 | − | 7.94719i | 0.815364 | − | 0.815364i | ||||
\(96\) | 1.40228 | + | 1.40228i | 0.143120 | + | 0.143120i | ||||
\(97\) | 3.70310 | + | 3.70310i | 0.375993 | + | 0.375993i | 0.869654 | − | 0.493661i | \(-0.164342\pi\) |
−0.493661 | + | 0.869654i | \(0.664342\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.42147 | + | 1.42147i | 0.142863 | + | 0.142863i | ||||
\(100\) | −2.48412 | −0.248412 | ||||||||
\(101\) | 11.2599 | + | 11.2599i | 1.12040 | + | 1.12040i | 0.991680 | + | 0.128724i | \(0.0410881\pi\) |
0.128724 | + | 0.991680i | \(0.458912\pi\) | |||||||
\(102\) | − | 7.89906i | − | 0.782124i | ||||||
\(103\) | 3.35643i | 0.330719i | 0.986233 | + | 0.165359i | \(0.0528784\pi\) | ||||
−0.986233 | + | 0.165359i | \(0.947122\pi\) | |||||||
\(104\) | −1.17480 | − | 1.17480i | −0.115199 | − | 0.115199i | ||||
\(105\) | −3.14554 | −0.306974 | ||||||||
\(106\) | 7.43800 | + | 7.43800i | 0.722442 | + | 0.722442i | ||||
\(107\) | 1.29895 | 0.125574 | 0.0627872 | − | 0.998027i | \(-0.480001\pi\) | ||||
0.0627872 | + | 0.998027i | \(0.480001\pi\) | |||||||
\(108\) | 2.89880 | + | 2.89880i | 0.278937 | + | 0.278937i | ||||
\(109\) | −4.52106 | − | 4.52106i | −0.433039 | − | 0.433039i | 0.456622 | − | 0.889661i | \(-0.349059\pi\) |
−0.889661 | + | 0.456622i | \(0.849059\pi\) | |||||||
\(110\) | −2.41708 | + | 2.41708i | −0.230459 | + | 0.230459i | ||||
\(111\) | 3.85247 | − | 3.85247i | 0.365660 | − | 0.365660i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −10.6539 | −1.00223 | −0.501116 | − | 0.865380i | \(-0.667077\pi\) | ||||
−0.501116 | + | 0.865380i | \(0.667077\pi\) | |||||||
\(114\) | − | 14.0519i | − | 1.31608i | ||||||
\(115\) | 9.68666i | 0.903286i | ||||||||
\(116\) | 7.06728 | − | 7.06728i | 0.656181 | − | 0.656181i | ||||
\(117\) | 1.09586 | + | 1.09586i | 0.101312 | + | 0.101312i | ||||
\(118\) | − | 10.7381i | − | 0.988522i | ||||||
\(119\) | −3.98313 | −0.365133 | ||||||||
\(120\) | 2.22424 | − | 2.22424i | 0.203044 | − | 0.203044i | ||||
\(121\) | 6.35568i | 0.577789i | ||||||||
\(122\) | −12.4049 | −1.12309 | ||||||||
\(123\) | 0.697359 | − | 12.6791i | 0.0628788 | − | 1.14323i | ||||
\(124\) | 9.34523 | 0.839226 | ||||||||
\(125\) | 11.8710i | 1.06177i | ||||||||
\(126\) | −0.659593 | + | 0.659593i | −0.0587612 | + | 0.0587612i | ||||
\(127\) | −4.16613 | −0.369684 | −0.184842 | − | 0.982768i | \(-0.559177\pi\) | ||||
−0.184842 | + | 0.982768i | \(0.559177\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −10.0230 | − | 10.0230i | −0.882473 | − | 0.882473i | ||||
\(130\) | −1.86341 | + | 1.86341i | −0.163432 | + | 0.163432i | ||||
\(131\) | 7.24503i | 0.633002i | 0.948592 | + | 0.316501i | \(0.102508\pi\) | ||||
−0.948592 | + | 0.316501i | \(0.897492\pi\) | |||||||
\(132\) | 4.27378i | 0.371985i | ||||||||
\(133\) | −7.08572 | −0.614410 | ||||||||
\(134\) | −6.07639 | + | 6.07639i | −0.524920 | + | 0.524920i | ||||
\(135\) | 4.59793 | − | 4.59793i | 0.395727 | − | 0.395727i | ||||
\(136\) | 2.81650 | − | 2.81650i | 0.241513 | − | 0.241513i | ||||
\(137\) | 4.97206 | + | 4.97206i | 0.424792 | + | 0.424792i | 0.886850 | − | 0.462058i | \(-0.152889\pi\) |
−0.462058 | + | 0.886850i | \(0.652889\pi\) | |||||||
\(138\) | 8.56378 | + | 8.56378i | 0.728997 | + | 0.728997i | ||||
\(139\) | −6.66802 | −0.565574 | −0.282787 | − | 0.959183i | \(-0.591259\pi\) | ||||
−0.282787 | + | 0.959183i | \(0.591259\pi\) | |||||||
\(140\) | −1.12158 | − | 1.12158i | −0.0947907 | − | 0.0947907i | ||||
\(141\) | 14.0840 | 1.18608 | ||||||||
\(142\) | −6.10702 | − | 6.10702i | −0.512490 | − | 0.512490i | ||||
\(143\) | − | 3.58047i | − | 0.299414i | ||||||
\(144\) | − | 0.932805i | − | 0.0777337i | ||||||
\(145\) | −11.2098 | − | 11.2098i | −0.930922 | − | 0.930922i | ||||
\(146\) | 16.1050 | 1.33286 | ||||||||
\(147\) | 1.40228 | + | 1.40228i | 0.115658 | + | 0.115658i | ||||
\(148\) | 2.74728 | 0.225825 | ||||||||
\(149\) | 15.2358 | + | 15.2358i | 1.24817 | + | 1.24817i | 0.956528 | + | 0.291639i | \(0.0942006\pi\) |
0.291639 | + | 0.956528i | \(0.405799\pi\) | |||||||
\(150\) | 3.48345 | + | 3.48345i | 0.284422 | + | 0.284422i | ||||
\(151\) | 2.64895 | − | 2.64895i | 0.215568 | − | 0.215568i | −0.591060 | − | 0.806628i | \(-0.701290\pi\) |
0.806628 | + | 0.591060i | \(0.201290\pi\) | |||||||
\(152\) | 5.01036 | − | 5.01036i | 0.406394 | − | 0.406394i | ||||
\(153\) | −2.62724 | + | 2.62724i | −0.212400 | + | 0.212400i | ||||
\(154\) | 2.15507 | 0.173660 | ||||||||
\(155\) | − | 14.8229i | − | 1.19061i | ||||||
\(156\) | 3.29481i | 0.263796i | ||||||||
\(157\) | −13.4802 | + | 13.4802i | −1.07584 | + | 1.07584i | −0.0789590 | + | 0.996878i | \(0.525160\pi\) |
−0.996878 | + | 0.0789590i | \(0.974840\pi\) | |||||||
\(158\) | −2.49677 | − | 2.49677i | −0.198632 | − | 0.198632i | ||||
\(159\) | − | 20.8604i | − | 1.65434i | ||||||
\(160\) | 1.58615 | 0.125396 | ||||||||
\(161\) | 4.31832 | − | 4.31832i | 0.340331 | − | 0.340331i | ||||
\(162\) | − | 10.9283i | − | 0.858608i | ||||||
\(163\) | −17.2081 | −1.34784 | −0.673922 | − | 0.738802i | \(-0.735392\pi\) | ||||
−0.673922 | + | 0.738802i | \(0.735392\pi\) | |||||||
\(164\) | 4.76951 | − | 4.27221i | 0.372436 | − | 0.333603i | ||||
\(165\) | 6.77886 | 0.527734 | ||||||||
\(166\) | 2.01947i | 0.156741i | ||||||||
\(167\) | −4.93231 | + | 4.93231i | −0.381673 | + | 0.381673i | −0.871705 | − | 0.490032i | \(-0.836985\pi\) |
0.490032 | + | 0.871705i | \(0.336985\pi\) | |||||||
\(168\) | −1.98313 | −0.153002 | ||||||||
\(169\) | 10.2397i | 0.787668i | ||||||||
\(170\) | −4.46739 | − | 4.46739i | −0.342633 | − | 0.342633i | ||||
\(171\) | −4.67369 | + | 4.67369i | −0.357406 | + | 0.357406i | ||||
\(172\) | − | 7.14760i | − | 0.544999i | ||||||
\(173\) | 0.436899i | 0.0332168i | 0.999862 | + | 0.0166084i | \(0.00528686\pi\) | ||||
−0.999862 | + | 0.0166084i | \(0.994713\pi\) | |||||||
\(174\) | −19.8207 | −1.50260 | ||||||||
\(175\) | 1.75654 | − | 1.75654i | 0.132782 | − | 0.132782i | ||||
\(176\) | −1.52386 | + | 1.52386i | −0.114865 | + | 0.114865i | ||||
\(177\) | −15.0579 | + | 15.0579i | −1.13182 | + | 1.13182i | ||||
\(178\) | −12.2966 | − | 12.2966i | −0.921668 | − | 0.921668i | ||||
\(179\) | −3.35925 | − | 3.35925i | −0.251082 | − | 0.251082i | 0.570332 | − | 0.821414i | \(-0.306815\pi\) |
−0.821414 | + | 0.570332i | \(0.806815\pi\) | |||||||
\(180\) | −1.47957 | −0.110281 | ||||||||
\(181\) | −6.46558 | − | 6.46558i | −0.480583 | − | 0.480583i | 0.424735 | − | 0.905318i | \(-0.360367\pi\) |
−0.905318 | + | 0.424735i | \(0.860367\pi\) | |||||||
\(182\) | 1.66142 | 0.123153 | ||||||||
\(183\) | 17.3952 | + | 17.3952i | 1.28589 | + | 1.28589i | ||||
\(184\) | 6.10702i | 0.450216i | ||||||||
\(185\) | − | 4.35760i | − | 0.320377i | ||||||
\(186\) | −13.1047 | − | 13.1047i | −0.960881 | − | 0.960881i | ||||
\(187\) | 8.58392 | 0.627718 | ||||||||
\(188\) | 5.02180 | + | 5.02180i | 0.366252 | + | 0.366252i | ||||
\(189\) | −4.09952 | −0.298196 | ||||||||
\(190\) | −7.94719 | − | 7.94719i | −0.576549 | − | 0.576549i | ||||
\(191\) | 15.5425 | + | 15.5425i | 1.12462 | + | 1.12462i | 0.991038 | + | 0.133577i | \(0.0426462\pi\) |
0.133577 | + | 0.991038i | \(0.457354\pi\) | |||||||
\(192\) | 1.40228 | − | 1.40228i | 0.101201 | − | 0.101201i | ||||
\(193\) | 5.09221 | − | 5.09221i | 0.366545 | − | 0.366545i | −0.499670 | − | 0.866216i | \(-0.666545\pi\) |
0.866216 | + | 0.499670i | \(0.166545\pi\) | |||||||
\(194\) | 3.70310 | − | 3.70310i | 0.265867 | − | 0.265867i | ||||
\(195\) | 5.22607 | 0.374247 | ||||||||
\(196\) | 1.00000i | 0.0714286i | ||||||||
\(197\) | 5.17834i | 0.368942i | 0.982838 | + | 0.184471i | \(0.0590571\pi\) | ||||
−0.982838 | + | 0.184471i | \(0.940943\pi\) | |||||||
\(198\) | 1.42147 | − | 1.42147i | 0.101019 | − | 0.101019i | ||||
\(199\) | 4.18223 | + | 4.18223i | 0.296470 | + | 0.296470i | 0.839630 | − | 0.543159i | \(-0.182772\pi\) |
−0.543159 | + | 0.839630i | \(0.682772\pi\) | |||||||
\(200\) | 2.48412i | 0.175654i | ||||||||
\(201\) | 17.0417 | 1.20203 | ||||||||
\(202\) | 11.2599 | − | 11.2599i | 0.792245 | − | 0.792245i | ||||
\(203\) | 9.99465i | 0.701487i | ||||||||
\(204\) | −7.89906 | −0.553045 | ||||||||
\(205\) | −6.77637 | − | 7.56517i | −0.473282 | − | 0.528374i | ||||
\(206\) | 3.35643 | 0.233853 | ||||||||
\(207\) | − | 5.69666i | − | 0.395945i | ||||||
\(208\) | −1.17480 | + | 1.17480i | −0.0814578 | + | 0.0814578i | ||||
\(209\) | 15.2702 | 1.05626 | ||||||||
\(210\) | 3.14554i | 0.217063i | ||||||||
\(211\) | −15.7282 | − | 15.7282i | −1.08277 | − | 1.08277i | −0.996250 | − | 0.0865241i | \(-0.972424\pi\) |
−0.0865241 | − | 0.996250i | \(-0.527576\pi\) | |||||||
\(212\) | 7.43800 | − | 7.43800i | 0.510844 | − | 0.510844i | ||||
\(213\) | 17.1276i | 1.17356i | ||||||||
\(214\) | − | 1.29895i | − | 0.0887945i | ||||||
\(215\) | −11.3372 | −0.773188 | ||||||||
\(216\) | 2.89880 | − | 2.89880i | 0.197238 | − | 0.197238i | ||||
\(217\) | −6.60807 | + | 6.60807i | −0.448585 | + | 0.448585i | ||||
\(218\) | −4.52106 | + | 4.52106i | −0.306205 | + | 0.306205i | ||||
\(219\) | −22.5838 | − | 22.5838i | −1.52607 | − | 1.52607i | ||||
\(220\) | 2.41708 | + | 2.41708i | 0.162959 | + | 0.162959i | ||||
\(221\) | 6.61765 | 0.445151 | ||||||||
\(222\) | −3.85247 | − | 3.85247i | −0.258561 | − | 0.258561i | ||||
\(223\) | 14.3426 | 0.960455 | 0.480227 | − | 0.877144i | \(-0.340554\pi\) | ||||
0.480227 | + | 0.877144i | \(0.340554\pi\) | |||||||
\(224\) | −0.707107 | − | 0.707107i | −0.0472456 | − | 0.0472456i | ||||
\(225\) | − | 2.31720i | − | 0.154480i | ||||||
\(226\) | 10.6539i | 0.708685i | ||||||||
\(227\) | 12.3679 | + | 12.3679i | 0.820889 | + | 0.820889i | 0.986236 | − | 0.165347i | \(-0.0528743\pi\) |
−0.165347 | + | 0.986236i | \(0.552874\pi\) | |||||||
\(228\) | −14.0519 | −0.930610 | ||||||||
\(229\) | −3.41290 | − | 3.41290i | −0.225531 | − | 0.225531i | 0.585292 | − | 0.810823i | \(-0.300980\pi\) |
−0.810823 | + | 0.585292i | \(0.800980\pi\) | |||||||
\(230\) | 9.68666 | 0.638719 | ||||||||
\(231\) | −3.02202 | − | 3.02202i | −0.198834 | − | 0.198834i | ||||
\(232\) | −7.06728 | − | 7.06728i | −0.463990 | − | 0.463990i | ||||
\(233\) | −7.39952 | + | 7.39952i | −0.484759 | + | 0.484759i | −0.906647 | − | 0.421889i | \(-0.861367\pi\) |
0.421889 | + | 0.906647i | \(0.361367\pi\) | |||||||
\(234\) | 1.09586 | − | 1.09586i | 0.0716386 | − | 0.0716386i | ||||
\(235\) | 7.96533 | − | 7.96533i | 0.519601 | − | 0.519601i | ||||
\(236\) | −10.7381 | −0.698990 | ||||||||
\(237\) | 7.00235i | 0.454852i | ||||||||
\(238\) | 3.98313i | 0.258188i | ||||||||
\(239\) | 6.93393 | − | 6.93393i | 0.448519 | − | 0.448519i | −0.446343 | − | 0.894862i | \(-0.647274\pi\) |
0.894862 | + | 0.446343i | \(0.147274\pi\) | |||||||
\(240\) | −2.22424 | − | 2.22424i | −0.143574 | − | 0.143574i | ||||
\(241\) | − | 5.96031i | − | 0.383938i | −0.981401 | − | 0.191969i | \(-0.938513\pi\) | ||
0.981401 | − | 0.191969i | \(-0.0614872\pi\) | |||||||
\(242\) | 6.35568 | 0.408559 | ||||||||
\(243\) | −6.62819 | + | 6.62819i | −0.425198 | + | 0.425198i | ||||
\(244\) | 12.4049i | 0.794143i | ||||||||
\(245\) | 1.58615 | 0.101335 | ||||||||
\(246\) | −12.6791 | − | 0.697359i | −0.808388 | − | 0.0444620i | ||||
\(247\) | 11.7724 | 0.749057 | ||||||||
\(248\) | − | 9.34523i | − | 0.593423i | ||||||
\(249\) | 2.83187 | − | 2.83187i | 0.179462 | − | 0.179462i | ||||
\(250\) | 11.8710 | 0.750785 | ||||||||
\(251\) | − | 7.29974i | − | 0.460755i | −0.973101 | − | 0.230378i | \(-0.926004\pi\) | ||
0.973101 | − | 0.230378i | \(-0.0739962\pi\) | |||||||
\(252\) | 0.659593 | + | 0.659593i | 0.0415504 | + | 0.0415504i | ||||
\(253\) | −9.30626 | + | 9.30626i | −0.585080 | + | 0.585080i | ||||
\(254\) | 4.16613i | 0.261406i | ||||||||
\(255\) | 12.5291i | 0.784603i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.0144 | + | 17.0144i | −1.06133 | + | 1.06133i | −0.0633353 | + | 0.997992i | \(0.520174\pi\) |
−0.997992 | + | 0.0633353i | \(0.979826\pi\) | |||||||
\(258\) | −10.0230 | + | 10.0230i | −0.624002 | + | 0.624002i | ||||
\(259\) | −1.94262 | + | 1.94262i | −0.120708 | + | 0.120708i | ||||
\(260\) | 1.86341 | + | 1.86341i | 0.115564 | + | 0.115564i | ||||
\(261\) | 6.59240 | + | 6.59240i | 0.408059 | + | 0.408059i | ||||
\(262\) | 7.24503 | 0.447600 | ||||||||
\(263\) | −10.1034 | − | 10.1034i | −0.623002 | − | 0.623002i | 0.323296 | − | 0.946298i | \(-0.395209\pi\) |
−0.946298 | + | 0.323296i | \(0.895209\pi\) | |||||||
\(264\) | 4.27378 | 0.263033 | ||||||||
\(265\) | −11.7978 | − | 11.7978i | −0.724732 | − | 0.724732i | ||||
\(266\) | 7.08572i | 0.434453i | ||||||||
\(267\) | 34.4866i | 2.11055i | ||||||||
\(268\) | 6.07639 | + | 6.07639i | 0.371175 | + | 0.371175i | ||||
\(269\) | −7.51023 | −0.457907 | −0.228953 | − | 0.973437i | \(-0.573530\pi\) | ||||
−0.228953 | + | 0.973437i | \(0.573530\pi\) | |||||||
\(270\) | −4.59793 | − | 4.59793i | −0.279821 | − | 0.279821i | ||||
\(271\) | −11.9601 | −0.726522 | −0.363261 | − | 0.931687i | \(-0.618337\pi\) | ||||
−0.363261 | + | 0.931687i | \(0.618337\pi\) | |||||||
\(272\) | −2.81650 | − | 2.81650i | −0.170775 | − | 0.170775i | ||||
\(273\) | −2.32978 | − | 2.32978i | −0.141005 | − | 0.141005i | ||||
\(274\) | 4.97206 | − | 4.97206i | 0.300373 | − | 0.300373i | ||||
\(275\) | −3.78547 | + | 3.78547i | −0.228272 | + | 0.228272i | ||||
\(276\) | 8.56378 | − | 8.56378i | 0.515479 | − | 0.515479i | ||||
\(277\) | 18.8642 | 1.13344 | 0.566721 | − | 0.823909i | \(-0.308212\pi\) | ||||
0.566721 | + | 0.823909i | \(0.308212\pi\) | |||||||
\(278\) | 6.66802i | 0.399921i | ||||||||
\(279\) | 8.71727i | 0.521890i | ||||||||
\(280\) | −1.12158 | + | 1.12158i | −0.0670271 | + | 0.0670271i | ||||
\(281\) | 18.3632 | + | 18.3632i | 1.09546 | + | 1.09546i | 0.994935 | + | 0.100520i | \(0.0320507\pi\) |
0.100520 | + | 0.994935i | \(0.467949\pi\) | |||||||
\(282\) | − | 14.0840i | − | 0.838688i | ||||||
\(283\) | 2.10610 | 0.125195 | 0.0625974 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625974 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(284\) | −6.10702 | + | 6.10702i | −0.362385 | + | 0.362385i | ||||
\(285\) | 22.2884i | 1.32025i | ||||||||
\(286\) | −3.58047 | −0.211718 | ||||||||
\(287\) | −0.351646 | + | 6.39346i | −0.0207570 | + | 0.377394i | ||||
\(288\) | −0.932805 | −0.0549661 | ||||||||
\(289\) | − | 1.13467i | − | 0.0667456i | ||||||
\(290\) | −11.2098 | + | 11.2098i | −0.658261 | + | 0.658261i | ||||
\(291\) | −10.3856 | −0.608815 | ||||||||
\(292\) | − | 16.1050i | − | 0.942474i | ||||||
\(293\) | 1.42089 | + | 1.42089i | 0.0830090 | + | 0.0830090i | 0.747392 | − | 0.664383i | \(-0.231306\pi\) |
−0.664383 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(294\) | 1.40228 | − | 1.40228i | 0.0817829 | − | 0.0817829i | ||||
\(295\) | 17.0322i | 0.991655i | ||||||||
\(296\) | − | 2.74728i | − | 0.159682i | ||||||
\(297\) | 8.83474 | 0.512643 | ||||||||
\(298\) | 15.2358 | − | 15.2358i | 0.882588 | − | 0.882588i | ||||
\(299\) | −7.17454 | + | 7.17454i | −0.414914 | + | 0.414914i | ||||
\(300\) | 3.48345 | − | 3.48345i | 0.201117 | − | 0.201117i | ||||
\(301\) | 5.05411 | + | 5.05411i | 0.291314 | + | 0.291314i | ||||
\(302\) | −2.64895 | − | 2.64895i | −0.152430 | − | 0.152430i | ||||
\(303\) | −31.5792 | −1.81418 | ||||||||
\(304\) | −5.01036 | − | 5.01036i | −0.287364 | − | 0.287364i | ||||
\(305\) | 19.6761 | 1.12665 | ||||||||
\(306\) | 2.62724 | + | 2.62724i | 0.150190 | + | 0.150190i | ||||
\(307\) | 25.3910i | 1.44914i | 0.689201 | + | 0.724570i | \(0.257962\pi\) | ||||
−0.689201 | + | 0.724570i | \(0.742038\pi\) | |||||||
\(308\) | − | 2.15507i | − | 0.122796i | ||||||
\(309\) | −4.70667 | − | 4.70667i | −0.267753 | − | 0.267753i | ||||
\(310\) | −14.8229 | −0.841887 | ||||||||
\(311\) | 4.91679 | + | 4.91679i | 0.278805 | + | 0.278805i | 0.832632 | − | 0.553827i | \(-0.186833\pi\) |
−0.553827 | + | 0.832632i | \(0.686833\pi\) | |||||||
\(312\) | 3.29481 | 0.186532 | ||||||||
\(313\) | −19.8081 | − | 19.8081i | −1.11962 | − | 1.11962i | −0.991797 | − | 0.127822i | \(-0.959201\pi\) |
−0.127822 | − | 0.991797i | \(-0.540799\pi\) | |||||||
\(314\) | 13.4802 | + | 13.4802i | 0.760732 | + | 0.760732i | ||||
\(315\) | 1.04621 | − | 1.04621i | 0.0589475 | − | 0.0589475i | ||||
\(316\) | −2.49677 | + | 2.49677i | −0.140454 | + | 0.140454i | ||||
\(317\) | 5.92813 | − | 5.92813i | 0.332957 | − | 0.332957i | −0.520751 | − | 0.853708i | \(-0.674348\pi\) |
0.853708 | + | 0.520751i | \(0.174348\pi\) | |||||||
\(318\) | −20.8604 | −1.16979 | ||||||||
\(319\) | − | 21.5391i | − | 1.20596i | ||||||
\(320\) | − | 1.58615i | − | 0.0886685i | ||||||
\(321\) | −1.82150 | + | 1.82150i | −0.101666 | + | 0.101666i | ||||
\(322\) | −4.31832 | − | 4.31832i | −0.240650 | − | 0.240650i | ||||
\(323\) | 28.2233i | 1.57039i | ||||||||
\(324\) | −10.9283 | −0.607127 | ||||||||
\(325\) | −2.91835 | + | 2.91835i | −0.161881 | + | 0.161881i | ||||
\(326\) | 17.2081i | 0.953070i | ||||||||
\(327\) | 12.6796 | 0.701185 | ||||||||
\(328\) | −4.27221 | − | 4.76951i | −0.235893 | − | 0.263352i | ||||
\(329\) | −7.10189 | −0.391540 | ||||||||
\(330\) | − | 6.77886i | − | 0.373164i | ||||||
\(331\) | −0.234595 | + | 0.234595i | −0.0128945 | + | 0.0128945i | −0.713525 | − | 0.700630i | \(-0.752902\pi\) |
0.700630 | + | 0.713525i | \(0.252902\pi\) | |||||||
\(332\) | 2.01947 | 0.110833 | ||||||||
\(333\) | 2.56267i | 0.140434i | ||||||||
\(334\) | 4.93231 | + | 4.93231i | 0.269884 | + | 0.269884i | ||||
\(335\) | 9.63807 | − | 9.63807i | 0.526584 | − | 0.526584i | ||||
\(336\) | 1.98313i | 0.108189i | ||||||||
\(337\) | − | 33.2342i | − | 1.81038i | −0.425004 | − | 0.905191i | \(-0.639727\pi\) | ||
0.425004 | − | 0.905191i | \(-0.360273\pi\) | |||||||
\(338\) | 10.2397 | 0.556965 | ||||||||
\(339\) | 14.9398 | − | 14.9398i | 0.811417 | − | 0.811417i | ||||
\(340\) | −4.46739 | + | 4.46739i | −0.242278 | + | 0.242278i | ||||
\(341\) | 14.2408 | − | 14.2408i | 0.771185 | − | 0.771185i | ||||
\(342\) | 4.67369 | + | 4.67369i | 0.252724 | + | 0.252724i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −7.14760 | −0.385373 | ||||||||
\(345\) | −13.5835 | − | 13.5835i | −0.731308 | − | 0.731308i | ||||
\(346\) | 0.436899 | 0.0234878 | ||||||||
\(347\) | 5.66767 | + | 5.66767i | 0.304257 | + | 0.304257i | 0.842677 | − | 0.538420i | \(-0.180979\pi\) |
−0.538420 | + | 0.842677i | \(0.680979\pi\) | |||||||
\(348\) | 19.8207i | 1.06250i | ||||||||
\(349\) | 23.7758i | 1.27269i | 0.771405 | + | 0.636344i | \(0.219554\pi\) | ||||
−0.771405 | + | 0.636344i | \(0.780446\pi\) | |||||||
\(350\) | −1.75654 | − | 1.75654i | −0.0938911 | − | 0.0938911i | ||||
\(351\) | 6.81102 | 0.363545 | ||||||||
\(352\) | 1.52386 | + | 1.52386i | 0.0812222 | + | 0.0812222i | ||||
\(353\) | 4.33345 | 0.230646 | 0.115323 | − | 0.993328i | \(-0.463210\pi\) | ||||
0.115323 | + | 0.993328i | \(0.463210\pi\) | |||||||
\(354\) | 15.0579 | + | 15.0579i | 0.800316 | + | 0.800316i | ||||
\(355\) | 9.68666 | + | 9.68666i | 0.514115 | + | 0.514115i | ||||
\(356\) | −12.2966 | + | 12.2966i | −0.651717 | + | 0.651717i | ||||
\(357\) | 5.58548 | − | 5.58548i | 0.295615 | − | 0.295615i | ||||
\(358\) | −3.35925 | + | 3.35925i | −0.177542 | + | 0.177542i | ||||
\(359\) | −30.4102 | −1.60499 | −0.802495 | − | 0.596659i | \(-0.796495\pi\) | ||||
−0.802495 | + | 0.596659i | \(0.796495\pi\) | |||||||
\(360\) | 1.47957i | 0.0779802i | ||||||||
\(361\) | 31.2074i | 1.64249i | ||||||||
\(362\) | −6.46558 | + | 6.46558i | −0.339823 | + | 0.339823i | ||||
\(363\) | −8.91248 | − | 8.91248i | −0.467784 | − | 0.467784i | ||||
\(364\) | − | 1.66142i | − | 0.0870821i | ||||||
\(365\) | −25.5450 | −1.33708 | ||||||||
\(366\) | 17.3952 | − | 17.3952i | 0.909262 | − | 0.909262i | ||||
\(367\) | 6.73610i | 0.351622i | 0.984424 | + | 0.175811i | \(0.0562547\pi\) | ||||
−0.984424 | + | 0.175811i | \(0.943745\pi\) | |||||||
\(368\) | 6.10702 | 0.318350 | ||||||||
\(369\) | 3.98514 | + | 4.44902i | 0.207458 | + | 0.231607i | ||||
\(370\) | −4.35760 | −0.226541 | ||||||||
\(371\) | 10.5189i | 0.546115i | ||||||||
\(372\) | −13.1047 | + | 13.1047i | −0.679445 | + | 0.679445i | ||||
\(373\) | −5.69811 | −0.295037 | −0.147518 | − | 0.989059i | \(-0.547129\pi\) | ||||
−0.147518 | + | 0.989059i | \(0.547129\pi\) | |||||||
\(374\) | − | 8.58392i | − | 0.443864i | ||||||
\(375\) | −16.6465 | − | 16.6465i | −0.859619 | − | 0.859619i | ||||
\(376\) | 5.02180 | − | 5.02180i | 0.258979 | − | 0.258979i | ||||
\(377\) | − | 16.6053i | − | 0.855217i | ||||||
\(378\) | 4.09952i | 0.210856i | ||||||||
\(379\) | −9.74441 | −0.500537 | −0.250268 | − | 0.968177i | \(-0.580519\pi\) | ||||
−0.250268 | + | 0.968177i | \(0.580519\pi\) | |||||||
\(380\) | −7.94719 | + | 7.94719i | −0.407682 | + | 0.407682i | ||||
\(381\) | 5.84210 | − | 5.84210i | 0.299300 | − | 0.299300i | ||||
\(382\) | 15.5425 | − | 15.5425i | 0.795223 | − | 0.795223i | ||||
\(383\) | −15.1746 | − | 15.1746i | −0.775388 | − | 0.775388i | 0.203655 | − | 0.979043i | \(-0.434718\pi\) |
−0.979043 | + | 0.203655i | \(0.934718\pi\) | |||||||
\(384\) | −1.40228 | − | 1.40228i | −0.0715600 | − | 0.0715600i | ||||
\(385\) | −3.41826 | −0.174211 | ||||||||
\(386\) | −5.09221 | − | 5.09221i | −0.259187 | − | 0.259187i | ||||
\(387\) | 6.66731 | 0.338919 | ||||||||
\(388\) | −3.70310 | − | 3.70310i | −0.187997 | − | 0.187997i | ||||
\(389\) | 13.9321i | 0.706388i | 0.935550 | + | 0.353194i | \(0.114904\pi\) | ||||
−0.935550 | + | 0.353194i | \(0.885096\pi\) | |||||||
\(390\) | − | 5.22607i | − | 0.264632i | ||||||
\(391\) | −17.2004 | − | 17.2004i | −0.869862 | − | 0.869862i | ||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −10.1596 | − | 10.1596i | −0.512484 | − | 0.512484i | ||||
\(394\) | 5.17834 | 0.260881 | ||||||||
\(395\) | 3.96025 | + | 3.96025i | 0.199262 | + | 0.199262i | ||||
\(396\) | −1.42147 | − | 1.42147i | −0.0714314 | − | 0.0714314i | ||||
\(397\) | −1.31578 | + | 1.31578i | −0.0660373 | + | 0.0660373i | −0.739354 | − | 0.673317i | \(-0.764869\pi\) |
0.673317 | + | 0.739354i | \(0.264869\pi\) | |||||||
\(398\) | 4.18223 | − | 4.18223i | 0.209636 | − | 0.209636i | ||||
\(399\) | 9.93619 | − | 9.93619i | 0.497432 | − | 0.497432i | ||||
\(400\) | 2.48412 | 0.124206 | ||||||||
\(401\) | − | 30.3808i | − | 1.51714i | −0.651589 | − | 0.758572i | \(-0.725897\pi\) | ||
0.651589 | − | 0.758572i | \(-0.274103\pi\) | |||||||
\(402\) | − | 17.0417i | − | 0.849961i | ||||||
\(403\) | 10.9788 | − | 10.9788i | 0.546892 | − | 0.546892i | ||||
\(404\) | −11.2599 | − | 11.2599i | −0.560202 | − | 0.560202i | ||||
\(405\) | 17.3339i | 0.861329i | ||||||||
\(406\) | 9.99465 | 0.496026 | ||||||||
\(407\) | 4.18647 | − | 4.18647i | 0.207516 | − | 0.207516i | ||||
\(408\) | 7.89906i | 0.391062i | ||||||||
\(409\) | 28.4107 | 1.40482 | 0.702409 | − | 0.711773i | \(-0.252108\pi\) | ||||
0.702409 | + | 0.711773i | \(0.252108\pi\) | |||||||
\(410\) | −7.56517 | + | 6.77637i | −0.373617 | + | 0.334661i | ||||
\(411\) | −13.9445 | −0.687831 | ||||||||
\(412\) | − | 3.35643i | − | 0.165359i | ||||||
\(413\) | 7.59298 | − | 7.59298i | 0.373626 | − | 0.373626i | ||||
\(414\) | −5.69666 | −0.279975 | ||||||||
\(415\) | − | 3.20318i | − | 0.157238i | ||||||
\(416\) | 1.17480 | + | 1.17480i | 0.0575994 | + | 0.0575994i | ||||
\(417\) | 9.35046 | − | 9.35046i | 0.457894 | − | 0.457894i | ||||
\(418\) | − | 15.2702i | − | 0.746890i | ||||||
\(419\) | − | 35.4270i | − | 1.73072i | −0.501147 | − | 0.865362i | \(-0.667088\pi\) | ||
0.501147 | − | 0.865362i | \(-0.332912\pi\) | |||||||
\(420\) | 3.14554 | 0.153487 | ||||||||
\(421\) | 14.7557 | − | 14.7557i | 0.719148 | − | 0.719148i | −0.249282 | − | 0.968431i | \(-0.580195\pi\) |
0.968431 | + | 0.249282i | \(0.0801948\pi\) | |||||||
\(422\) | −15.7282 | + | 15.7282i | −0.765637 | + | 0.765637i | ||||
\(423\) | −4.68435 | + | 4.68435i | −0.227761 | + | 0.227761i | ||||
\(424\) | −7.43800 | − | 7.43800i | −0.361221 | − | 0.361221i | ||||
\(425\) | −6.99653 | − | 6.99653i | −0.339382 | − | 0.339382i | ||||
\(426\) | 17.1276 | 0.829833 | ||||||||
\(427\) | −8.77159 | − | 8.77159i | −0.424487 | − | 0.424487i | ||||
\(428\) | −1.29895 | −0.0627872 | ||||||||
\(429\) | 5.02084 | + | 5.02084i | 0.242409 | + | 0.242409i | ||||
\(430\) | 11.3372i | 0.546727i | ||||||||
\(431\) | 28.8932i | 1.39173i | 0.718170 | + | 0.695867i | \(0.244980\pi\) | ||||
−0.718170 | + | 0.695867i | \(0.755020\pi\) | |||||||
\(432\) | −2.89880 | − | 2.89880i | −0.139468 | − | 0.139468i | ||||
\(433\) | −13.9634 | −0.671039 | −0.335520 | − | 0.942033i | \(-0.608912\pi\) | ||||
−0.335520 | + | 0.942033i | \(0.608912\pi\) | |||||||
\(434\) | 6.60807 | + | 6.60807i | 0.317198 | + | 0.317198i | ||||
\(435\) | 31.4386 | 1.50737 | ||||||||
\(436\) | 4.52106 | + | 4.52106i | 0.216520 | + | 0.216520i | ||||
\(437\) | −30.5984 | − | 30.5984i | −1.46372 | − | 1.46372i | ||||
\(438\) | −22.5838 | + | 22.5838i | −1.07910 | + | 1.07910i | ||||
\(439\) | −5.52443 | + | 5.52443i | −0.263667 | + | 0.263667i | −0.826542 | − | 0.562875i | \(-0.809695\pi\) |
0.562875 | + | 0.826542i | \(0.309695\pi\) | |||||||
\(440\) | 2.41708 | − | 2.41708i | 0.115230 | − | 0.115230i | ||||
\(441\) | −0.932805 | −0.0444193 | ||||||||
\(442\) | − | 6.61765i | − | 0.314770i | ||||||
\(443\) | 25.7874i | 1.22520i | 0.790394 | + | 0.612599i | \(0.209876\pi\) | ||||
−0.790394 | + | 0.612599i | \(0.790124\pi\) | |||||||
\(444\) | −3.85247 | + | 3.85247i | −0.182830 | + | 0.182830i | ||||
\(445\) | 19.5042 | + | 19.5042i | 0.924589 | + | 0.924589i | ||||
\(446\) | − | 14.3426i | − | 0.679144i | ||||||
\(447\) | −42.7299 | −2.02106 | ||||||||
\(448\) | −0.707107 | + | 0.707107i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | − | 34.6856i | − | 1.63691i | −0.574567 | − | 0.818457i | \(-0.694830\pi\) | ||
0.574567 | − | 0.818457i | \(-0.305170\pi\) | |||||||
\(450\) | −2.31720 | −0.109234 | ||||||||
\(451\) | 0.757821 | − | 13.7783i | 0.0356844 | − | 0.648797i | ||||
\(452\) | 10.6539 | 0.501116 | ||||||||
\(453\) | 7.42916i | 0.349052i | ||||||||
\(454\) | 12.3679 | − | 12.3679i | 0.580456 | − | 0.580456i | ||||
\(455\) | −2.63526 | −0.123543 | ||||||||
\(456\) | 14.0519i | 0.658040i | ||||||||
\(457\) | −21.6838 | − | 21.6838i | −1.01432 | − | 1.01432i | −0.999896 | − | 0.0144284i | \(-0.995407\pi\) |
−0.0144284 | − | 0.999896i | \(-0.504593\pi\) | |||||||
\(458\) | −3.41290 | + | 3.41290i | −0.159474 | + | 0.159474i | ||||
\(459\) | 16.3289i | 0.762168i | ||||||||
\(460\) | − | 9.68666i | − | 0.451643i | ||||||
\(461\) | 36.3096 | 1.69111 | 0.845554 | − | 0.533891i | \(-0.179271\pi\) | ||||
0.845554 | + | 0.533891i | \(0.179271\pi\) | |||||||
\(462\) | −3.02202 | + | 3.02202i | −0.140597 | + | 0.140597i | ||||
\(463\) | −1.00359 | + | 1.00359i | −0.0466408 | + | 0.0466408i | −0.730043 | − | 0.683402i | \(-0.760500\pi\) |
0.683402 | + | 0.730043i | \(0.260500\pi\) | |||||||
\(464\) | −7.06728 | + | 7.06728i | −0.328090 | + | 0.328090i | ||||
\(465\) | 20.7860 | + | 20.7860i | 0.963927 | + | 0.963927i | ||||
\(466\) | 7.39952 | + | 7.39952i | 0.342776 | + | 0.342776i | ||||
\(467\) | 18.2854 | 0.846146 | 0.423073 | − | 0.906096i | \(-0.360951\pi\) | ||||
0.423073 | + | 0.906096i | \(0.360951\pi\) | |||||||
\(468\) | −1.09586 | − | 1.09586i | −0.0506562 | − | 0.0506562i | ||||
\(469\) | −8.59331 | −0.396802 | ||||||||
\(470\) | −7.96533 | − | 7.96533i | −0.367413 | − | 0.367413i | ||||
\(471\) | − | 37.8061i | − | 1.74202i | ||||||
\(472\) | 10.7381i | 0.494261i | ||||||||
\(473\) | −10.8920 | − | 10.8920i | −0.500813 | − | 0.500813i | ||||
\(474\) | 7.00235 | 0.321629 | ||||||||
\(475\) | −12.4464 | − | 12.4464i | −0.571078 | − | 0.571078i | ||||
\(476\) | 3.98313 | 0.182566 | ||||||||
\(477\) | 6.93820 | + | 6.93820i | 0.317678 | + | 0.317678i | ||||
\(478\) | −6.93393 | − | 6.93393i | −0.317151 | − | 0.317151i | ||||
\(479\) | −20.1039 | + | 20.1039i | −0.918571 | + | 0.918571i | −0.996926 | − | 0.0783546i | \(-0.975033\pi\) |
0.0783546 | + | 0.996926i | \(0.475033\pi\) | |||||||
\(480\) | −2.22424 | + | 2.22424i | −0.101522 | + | 0.101522i | ||||
\(481\) | 3.22751 | − | 3.22751i | 0.147162 | − | 0.147162i | ||||
\(482\) | −5.96031 | −0.271485 | ||||||||
\(483\) | 12.1110i | 0.551070i | ||||||||
\(484\) | − | 6.35568i | − | 0.288895i | ||||||
\(485\) | −5.87368 | + | 5.87368i | −0.266710 | + | 0.266710i | ||||
\(486\) | 6.62819 | + | 6.62819i | 0.300661 | + | 0.300661i | ||||
\(487\) | − | 18.1781i | − | 0.823730i | −0.911245 | − | 0.411865i | \(-0.864878\pi\) | ||
0.911245 | − | 0.411865i | \(-0.135122\pi\) | |||||||
\(488\) | 12.4049 | 0.561544 | ||||||||
\(489\) | 24.1307 | − | 24.1307i | 1.09123 | − | 1.09123i | ||||
\(490\) | − | 1.58615i | − | 0.0716550i | ||||||
\(491\) | 8.40653 | 0.379382 | 0.189691 | − | 0.981844i | \(-0.439251\pi\) | ||||
0.189691 | + | 0.981844i | \(0.439251\pi\) | |||||||
\(492\) | −0.697359 | + | 12.6791i | −0.0314394 | + | 0.571616i | ||||
\(493\) | 39.8100 | 1.79295 | ||||||||
\(494\) | − | 11.7724i | − | 0.529663i | ||||||
\(495\) | −2.25466 | + | 2.25466i | −0.101339 | + | 0.101339i | ||||
\(496\) | −9.34523 | −0.419613 | ||||||||
\(497\) | − | 8.63663i | − | 0.387406i | ||||||
\(498\) | −2.83187 | − | 2.83187i | −0.126899 | − | 0.126899i | ||||
\(499\) | 11.0199 | − | 11.0199i | 0.493320 | − | 0.493320i | −0.416030 | − | 0.909351i | \(-0.636579\pi\) |
0.909351 | + | 0.416030i | \(0.136579\pi\) | |||||||
\(500\) | − | 11.8710i | − | 0.530885i | ||||||
\(501\) | − | 13.8330i | − | 0.618013i | ||||||
\(502\) | −7.29974 | −0.325803 | ||||||||
\(503\) | −13.8985 | + | 13.8985i | −0.619701 | + | 0.619701i | −0.945455 | − | 0.325753i | \(-0.894382\pi\) |
0.325753 | + | 0.945455i | \(0.394382\pi\) | |||||||
\(504\) | 0.659593 | − | 0.659593i | 0.0293806 | − | 0.0293806i | ||||
\(505\) | −17.8599 | + | 17.8599i | −0.794757 | + | 0.794757i | ||||
\(506\) | 9.30626 | + | 9.30626i | 0.413714 | + | 0.413714i | ||||
\(507\) | −14.3590 | − | 14.3590i | −0.637703 | − | 0.637703i | ||||
\(508\) | 4.16613 | 0.184842 | ||||||||
\(509\) | −2.42818 | − | 2.42818i | −0.107627 | − | 0.107627i | 0.651243 | − | 0.758870i | \(-0.274248\pi\) |
−0.758870 | + | 0.651243i | \(0.774248\pi\) | |||||||
\(510\) | 12.5291 | 0.554798 | ||||||||
\(511\) | 11.3880 | + | 11.3880i | 0.503773 | + | 0.503773i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 29.0480i | 1.28250i | ||||||||
\(514\) | 17.0144 | + | 17.0144i | 0.750472 | + | 0.750472i | ||||
\(515\) | −5.32380 | −0.234595 | ||||||||
\(516\) | 10.0230 | + | 10.0230i | 0.441236 | + | 0.441236i | ||||
\(517\) | 15.3051 | 0.673116 | ||||||||
\(518\) | 1.94262 | + | 1.94262i | 0.0853538 | + | 0.0853538i | ||||
\(519\) | −0.612656 | − | 0.612656i | −0.0268926 | − | 0.0268926i | ||||
\(520\) | 1.86341 | − | 1.86341i | 0.0817160 | − | 0.0817160i | ||||
\(521\) | −8.69534 | + | 8.69534i | −0.380950 | + | 0.380950i | −0.871444 | − | 0.490494i | \(-0.836816\pi\) |
0.490494 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(522\) | 6.59240 | − | 6.59240i | 0.288541 | − | 0.288541i | ||||
\(523\) | −2.07808 | −0.0908682 | −0.0454341 | − | 0.998967i | \(-0.514467\pi\) | ||||
−0.0454341 | + | 0.998967i | \(0.514467\pi\) | |||||||
\(524\) | − | 7.24503i | − | 0.316501i | ||||||
\(525\) | 4.92634i | 0.215003i | ||||||||
\(526\) | −10.1034 | + | 10.1034i | −0.440529 | + | 0.440529i | ||||
\(527\) | 26.3208 | + | 26.3208i | 1.14655 | + | 1.14655i | ||||
\(528\) | − | 4.27378i | − | 0.185992i | ||||||
\(529\) | 14.2957 | 0.621552 | ||||||||
\(530\) | −11.7978 | + | 11.7978i | −0.512463 | + | 0.512463i | ||||
\(531\) | − | 10.0165i | − | 0.434681i | ||||||
\(532\) | 7.08572 | 0.307205 | ||||||||
\(533\) | 0.584231 | − | 10.6222i | 0.0253059 | − | 0.460100i | ||||
\(534\) | 34.4866 | 1.49238 | ||||||||
\(535\) | 2.06033i | 0.0890760i | ||||||||
\(536\) | 6.07639 | − | 6.07639i | 0.262460 | − | 0.262460i | ||||
\(537\) | 9.42125 | 0.406557 | ||||||||
\(538\) | 7.51023i | 0.323789i | ||||||||
\(539\) | 1.52386 | + | 1.52386i | 0.0656374 | + | 0.0656374i | ||||
\(540\) | −4.59793 | + | 4.59793i | −0.197863 | + | 0.197863i | ||||
\(541\) | − | 17.8201i | − | 0.766148i | −0.923718 | − | 0.383074i | \(-0.874866\pi\) | ||
0.923718 | − | 0.383074i | \(-0.125134\pi\) | |||||||
\(542\) | 11.9601i | 0.513729i | ||||||||
\(543\) | 18.1332 | 0.778169 | ||||||||
\(544\) | −2.81650 | + | 2.81650i | −0.120756 | + | 0.120756i | ||||
\(545\) | 7.17109 | − | 7.17109i | 0.307176 | − | 0.307176i | ||||
\(546\) | −2.32978 | + | 2.32978i | −0.0997055 | + | 0.0997055i | ||||
\(547\) | 10.5511 | + | 10.5511i | 0.451131 | + | 0.451131i | 0.895730 | − | 0.444599i | \(-0.146654\pi\) |
−0.444599 | + | 0.895730i | \(0.646654\pi\) | |||||||
\(548\) | −4.97206 | − | 4.97206i | −0.212396 | − | 0.212396i | ||||
\(549\) | −11.5714 | −0.493853 | ||||||||
\(550\) | 3.78547 | + | 3.78547i | 0.161413 | + | 0.161413i | ||||
\(551\) | 70.8193 | 3.01700 | ||||||||
\(552\) | −8.56378 | − | 8.56378i | −0.364499 | − | 0.364499i | ||||
\(553\) | − | 3.53096i | − | 0.150152i | ||||||
\(554\) | − | 18.8642i | − | 0.801465i | ||||||
\(555\) | 6.11059 | + | 6.11059i | 0.259380 | + | 0.259380i | ||||
\(556\) | 6.66802 | 0.282787 | ||||||||
\(557\) | 4.79505 | + | 4.79505i | 0.203173 | + | 0.203173i | 0.801358 | − | 0.598185i | \(-0.204111\pi\) |
−0.598185 | + | 0.801358i | \(0.704111\pi\) | |||||||
\(558\) | 8.71727 | 0.369032 | ||||||||
\(559\) | −8.39700 | − | 8.39700i | −0.355155 | − | 0.355155i | ||||
\(560\) | 1.12158 | + | 1.12158i | 0.0473953 | + | 0.0473953i | ||||
\(561\) | −12.0371 | + | 12.0371i | −0.508206 | + | 0.508206i | ||||
\(562\) | 18.3632 | − | 18.3632i | 0.774604 | − | 0.774604i | ||||
\(563\) | 9.34570 | − | 9.34570i | 0.393875 | − | 0.393875i | −0.482191 | − | 0.876066i | \(-0.660159\pi\) |
0.876066 | + | 0.482191i | \(0.160159\pi\) | |||||||
\(564\) | −14.0840 | −0.593042 | ||||||||
\(565\) | − | 16.8987i | − | 0.710932i | ||||||
\(566\) | − | 2.10610i | − | 0.0885260i | ||||||
\(567\) | 7.72747 | − | 7.72747i | 0.324523 | − | 0.324523i | ||||
\(568\) | 6.10702 | + | 6.10702i | 0.256245 | + | 0.256245i | ||||
\(569\) | − | 3.73057i | − | 0.156394i | −0.996938 | − | 0.0781968i | \(-0.975084\pi\) | ||
0.996938 | − | 0.0781968i | \(-0.0249162\pi\) | |||||||
\(570\) | 22.2884 | 0.933560 | ||||||||
\(571\) | −12.1834 | + | 12.1834i | −0.509859 | + | 0.509859i | −0.914483 | − | 0.404624i | \(-0.867402\pi\) |
0.404624 | + | 0.914483i | \(0.367402\pi\) | |||||||
\(572\) | 3.58047i | 0.149707i | ||||||||
\(573\) | −43.5900 | −1.82100 | ||||||||
\(574\) | 6.39346 | + | 0.351646i | 0.266858 | + | 0.0146774i | ||||
\(575\) | 15.1706 | 0.632658 | ||||||||
\(576\) | 0.932805i | 0.0388669i | ||||||||
\(577\) | −17.0798 | + | 17.0798i | −0.711043 | + | 0.711043i | −0.966753 | − | 0.255710i | \(-0.917691\pi\) |
0.255710 | + | 0.966753i | \(0.417691\pi\) | |||||||
\(578\) | −1.13467 | −0.0471963 | ||||||||
\(579\) | 14.2815i | 0.593517i | ||||||||
\(580\) | 11.2098 | + | 11.2098i | 0.465461 | + | 0.465461i | ||||
\(581\) | −1.42798 | + | 1.42798i | −0.0592426 | + | 0.0592426i | ||||
\(582\) | 10.3856i | 0.430497i | ||||||||
\(583\) | − | 22.6690i | − | 0.938853i | ||||||
\(584\) | −16.1050 | −0.666430 | ||||||||
\(585\) | −1.73820 | + | 1.73820i | −0.0718657 | + | 0.0718657i | ||||
\(586\) | 1.42089 | − | 1.42089i | 0.0586962 | − | 0.0586962i | ||||
\(587\) | −12.5201 | + | 12.5201i | −0.516759 | + | 0.516759i | −0.916589 | − | 0.399830i | \(-0.869069\pi\) |
0.399830 | + | 0.916589i | \(0.369069\pi\) | |||||||
\(588\) | −1.40228 | − | 1.40228i | −0.0578292 | − | 0.0578292i | ||||
\(589\) | 46.8229 | + | 46.8229i | 1.92931 | + | 1.92931i | ||||
\(590\) | 17.0322 | 0.701206 | ||||||||
\(591\) | −7.26151 | − | 7.26151i | −0.298699 | − | 0.298699i | ||||
\(592\) | −2.74728 | −0.112912 | ||||||||
\(593\) | 24.6510 | + | 24.6510i | 1.01230 | + | 1.01230i | 0.999923 | + | 0.0123729i | \(0.00393852\pi\) |
0.0123729 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(594\) | − | 8.83474i | − | 0.362494i | ||||||
\(595\) | − | 6.31785i | − | 0.259006i | ||||||
\(596\) | −15.2358 | − | 15.2358i | −0.624084 | − | 0.624084i | ||||
\(597\) | −11.7293 | −0.480050 | ||||||||
\(598\) | 7.17454 | + | 7.17454i | 0.293389 | + | 0.293389i | ||||
\(599\) | −14.9728 | −0.611773 | −0.305886 | − | 0.952068i | \(-0.598953\pi\) | ||||
−0.305886 | + | 0.952068i | \(0.598953\pi\) | |||||||
\(600\) | −3.48345 | − | 3.48345i | −0.142211 | − | 0.142211i | ||||
\(601\) | 4.64267 | + | 4.64267i | 0.189379 | + | 0.189379i | 0.795427 | − | 0.606049i | \(-0.207246\pi\) |
−0.606049 | + | 0.795427i | \(0.707246\pi\) | |||||||
\(602\) | 5.05411 | − | 5.05411i | 0.205990 | − | 0.205990i | ||||
\(603\) | −5.66809 | + | 5.66809i | −0.230822 | + | 0.230822i | ||||
\(604\) | −2.64895 | + | 2.64895i | −0.107784 | + | 0.107784i | ||||
\(605\) | −10.0811 | −0.409854 | ||||||||
\(606\) | 31.5792i | 1.28282i | ||||||||
\(607\) | 30.9530i | 1.25634i | 0.778075 | + | 0.628172i | \(0.216196\pi\) | ||||
−0.778075 | + | 0.628172i | \(0.783804\pi\) | |||||||
\(608\) | −5.01036 | + | 5.01036i | −0.203197 | + | 0.203197i | ||||
\(609\) | −14.0153 | − | 14.0153i | −0.567930 | − | 0.567930i | ||||
\(610\) | − | 19.6761i | − | 0.796660i | ||||||
\(611\) | 11.7992 | 0.477345 | ||||||||
\(612\) | 2.62724 | − | 2.62724i | 0.106200 | − | 0.106200i | ||||
\(613\) | − | 10.1505i | − | 0.409974i | −0.978765 | − | 0.204987i | \(-0.934285\pi\) | ||
0.978765 | − | 0.204987i | \(-0.0657152\pi\) | |||||||
\(614\) | 25.3910 | 1.02470 | ||||||||
\(615\) | 20.1109 | + | 1.10612i | 0.810950 | + | 0.0446030i | ||||
\(616\) | −2.15507 | −0.0868302 | ||||||||
\(617\) | − | 3.09595i | − | 0.124638i | −0.998056 | − | 0.0623191i | \(-0.980150\pi\) | ||
0.998056 | − | 0.0623191i | \(-0.0198496\pi\) | |||||||
\(618\) | −4.70667 | + | 4.70667i | −0.189330 | + | 0.189330i | ||||
\(619\) | 21.9289 | 0.881398 | 0.440699 | − | 0.897655i | \(-0.354731\pi\) | ||||
0.440699 | + | 0.897655i | \(0.354731\pi\) | |||||||
\(620\) | 14.8229i | 0.595304i | ||||||||
\(621\) | −17.7030 | − | 17.7030i | −0.710397 | − | 0.710397i | ||||
\(622\) | 4.91679 | − | 4.91679i | 0.197145 | − | 0.197145i | ||||
\(623\) | − | 17.3900i | − | 0.696715i | ||||||
\(624\) | − | 3.29481i | − | 0.131898i | ||||||
\(625\) | −6.40850 | −0.256340 | ||||||||
\(626\) | −19.8081 | + | 19.8081i | −0.791690 | + | 0.791690i | ||||
\(627\) | −21.4132 | + | 21.4132i | −0.855160 | + | 0.855160i | ||||
\(628\) | 13.4802 | − | 13.4802i | 0.537918 | − | 0.537918i | ||||
\(629\) | 7.73770 | + | 7.73770i | 0.308522 | + | 0.308522i | ||||
\(630\) | −1.04621 | − | 1.04621i | −0.0416822 | − | 0.0416822i | ||||
\(631\) | 27.7002 | 1.10273 | 0.551364 | − | 0.834265i | \(-0.314108\pi\) | ||||
0.551364 | + | 0.834265i | \(0.314108\pi\) | |||||||
\(632\) | 2.49677 | + | 2.49677i | 0.0993160 | + | 0.0993160i | ||||
\(633\) | 44.1108 | 1.75325 | ||||||||
\(634\) | −5.92813 | − | 5.92813i | −0.235436 | − | 0.235436i | ||||
\(635\) | − | 6.60811i | − | 0.262235i | ||||||
\(636\) | 20.8604i | 0.827168i | ||||||||
\(637\) | 1.17480 | + | 1.17480i | 0.0465473 | + | 0.0465473i | ||||
\(638\) | −21.5391 | −0.852743 | ||||||||
\(639\) | −5.69666 | − | 5.69666i | −0.225356 | − | 0.225356i | ||||
\(640\) | −1.58615 | −0.0626981 | ||||||||
\(641\) | −31.8489 | − | 31.8489i | −1.25795 | − | 1.25795i | −0.952068 | − | 0.305887i | \(-0.901047\pi\) |
−0.305887 | − | 0.952068i | \(-0.598953\pi\) | |||||||
\(642\) | 1.82150 | + | 1.82150i | 0.0718889 | + | 0.0718889i | ||||
\(643\) | 17.3075 | − | 17.3075i | 0.682540 | − | 0.682540i | −0.278032 | − | 0.960572i | \(-0.589682\pi\) |
0.960572 | + | 0.278032i | \(0.0896822\pi\) | |||||||
\(644\) | −4.31832 | + | 4.31832i | −0.170165 | + | 0.170165i | ||||
\(645\) | 15.8979 | − | 15.8979i | 0.625981 | − | 0.625981i | ||||
\(646\) | 28.2233 | 1.11043 | ||||||||
\(647\) | − | 18.1376i | − | 0.713062i | −0.934283 | − | 0.356531i | \(-0.883959\pi\) | ||
0.934283 | − | 0.356531i | \(-0.116041\pi\) | |||||||
\(648\) | 10.9283i | 0.429304i | ||||||||
\(649\) | −16.3634 | + | 16.3634i | −0.642319 | + | 0.642319i | ||||
\(650\) | 2.91835 | + | 2.91835i | 0.114467 | + | 0.114467i | ||||
\(651\) | − | 18.5328i | − | 0.726358i | ||||||
\(652\) | 17.2081 | 0.673922 | ||||||||
\(653\) | 13.1212 | − | 13.1212i | 0.513474 | − | 0.513474i | −0.402115 | − | 0.915589i | \(-0.631725\pi\) |
0.915589 | + | 0.402115i | \(0.131725\pi\) | |||||||
\(654\) | − | 12.6796i | − | 0.495813i | ||||||
\(655\) | −11.4917 | −0.449019 | ||||||||
\(656\) | −4.76951 | + | 4.27221i | −0.186218 | + | 0.166802i | ||||
\(657\) | 15.0228 | 0.586096 | ||||||||
\(658\) | 7.10189i | 0.276861i | ||||||||
\(659\) | −6.83367 | + | 6.83367i | −0.266202 | + | 0.266202i | −0.827568 | − | 0.561366i | \(-0.810276\pi\) |
0.561366 | + | 0.827568i | \(0.310276\pi\) | |||||||
\(660\) | −6.77886 | −0.263867 | ||||||||
\(661\) | − | 10.3391i | − | 0.402146i | −0.979576 | − | 0.201073i | \(-0.935557\pi\) | ||
0.979576 | − | 0.201073i | \(-0.0644429\pi\) | |||||||
\(662\) | 0.234595 | + | 0.234595i | 0.00911778 | + | 0.00911778i | ||||
\(663\) | −9.27983 | + | 9.27983i | −0.360399 | + | 0.360399i | ||||
\(664\) | − | 2.01947i | − | 0.0783706i | ||||||
\(665\) | − | 11.2390i | − | 0.435830i | ||||||
\(666\) | 2.56267 | 0.0993016 | ||||||||
\(667\) | −43.1600 | + | 43.1600i | −1.67116 | + | 1.67116i | ||||
\(668\) | 4.93231 | − | 4.93231i | 0.190837 | − | 0.190837i | ||||
\(669\) | −20.1125 | + | 20.1125i | −0.777593 | + | 0.777593i | ||||
\(670\) | −9.63807 | − | 9.63807i | −0.372351 | − | 0.372351i | ||||
\(671\) | 18.9034 | + | 18.9034i | 0.729757 | + | 0.729757i | ||||
\(672\) | 1.98313 | 0.0765009 | ||||||||
\(673\) | −20.8609 | − | 20.8609i | −0.804127 | − | 0.804127i | 0.179610 | − | 0.983738i | \(-0.442516\pi\) |
−0.983738 | + | 0.179610i | \(0.942516\pi\) | |||||||
\(674\) | −33.2342 | −1.28013 | ||||||||
\(675\) | −7.20097 | − | 7.20097i | −0.277165 | − | 0.277165i | ||||
\(676\) | − | 10.2397i | − | 0.393834i | ||||||
\(677\) | 23.0766i | 0.886906i | 0.896298 | + | 0.443453i | \(0.146247\pi\) | ||||
−0.896298 | + | 0.443453i | \(0.853753\pi\) | |||||||
\(678\) | −14.9398 | − | 14.9398i | −0.573758 | − | 0.573758i | ||||
\(679\) | 5.23698 | 0.200977 | ||||||||
\(680\) | 4.46739 | + | 4.46739i | 0.171317 | + | 0.171317i | ||||
\(681\) | −34.6867 | −1.32920 | ||||||||
\(682\) | −14.2408 | − | 14.2408i | −0.545310 | − | 0.545310i | ||||
\(683\) | −22.5184 | − | 22.5184i | −0.861644 | − | 0.861644i | 0.129885 | − | 0.991529i | \(-0.458539\pi\) |
−0.991529 | + | 0.129885i | \(0.958539\pi\) | |||||||
\(684\) | 4.67369 | − | 4.67369i | 0.178703 | − | 0.178703i | ||||
\(685\) | −7.88644 | + | 7.88644i | −0.301326 | + | 0.301326i | ||||
\(686\) | −0.707107 | + | 0.707107i | −0.0269975 | + | 0.0269975i | ||||
\(687\) | 9.57172 | 0.365184 | ||||||||
\(688\) | 7.14760i | 0.272500i | ||||||||
\(689\) | − | 17.4763i | − | 0.665795i | ||||||
\(690\) | −13.5835 | + | 13.5835i | −0.517113 | + | 0.517113i | ||||
\(691\) | −19.3661 | − | 19.3661i | −0.736720 | − | 0.736720i | 0.235221 | − | 0.971942i | \(-0.424418\pi\) |
−0.971942 | + | 0.235221i | \(0.924418\pi\) | |||||||
\(692\) | − | 0.436899i | − | 0.0166084i | ||||||
\(693\) | 2.01026 | 0.0763634 | ||||||||
\(694\) | 5.66767 | − | 5.66767i | 0.215142 | − | 0.215142i | ||||
\(695\) | − | 10.5765i | − | 0.401189i | ||||||
\(696\) | 19.8207 | 0.751301 | ||||||||
\(697\) | 25.4660 | + | 1.40065i | 0.964593 | + | 0.0530534i | ||||
\(698\) | 23.7758 | 0.899926 | ||||||||
\(699\) | − | 20.7525i | − | 0.784930i | ||||||
\(700\) | −1.75654 | + | 1.75654i | −0.0663910 | + | 0.0663910i | ||||
\(701\) | −14.9924 | −0.566253 | −0.283127 | − | 0.959083i | \(-0.591372\pi\) | ||||
−0.283127 | + | 0.959083i | \(0.591372\pi\) | |||||||
\(702\) | − | 6.81102i | − | 0.257065i | ||||||
\(703\) | 13.7648 | + | 13.7648i | 0.519151 | + | 0.519151i | ||||
\(704\) | 1.52386 | − | 1.52386i | 0.0574327 | − | 0.0574327i | ||||
\(705\) | 22.3393i | 0.841347i | ||||||||
\(706\) | − | 4.33345i | − | 0.163091i | ||||||
\(707\) | 15.9239 | 0.598881 | ||||||||
\(708\) | 15.0579 | − | 15.0579i | 0.565909 | − | 0.565909i | ||||
\(709\) | 34.3676 | − | 34.3676i | 1.29070 | − | 1.29070i | 0.356350 | − | 0.934353i | \(-0.384021\pi\) |
0.934353 | − | 0.356350i | \(-0.115979\pi\) | |||||||
\(710\) | 9.68666 | − | 9.68666i | 0.363534 | − | 0.363534i | ||||
\(711\) | −2.32899 | − | 2.32899i | −0.0873441 | − | 0.0873441i | ||||
\(712\) | 12.2966 | + | 12.2966i | 0.460834 | + | 0.460834i | ||||
\(713\) | −57.0715 | −2.13734 | ||||||||
\(714\) | −5.58548 | − | 5.58548i | −0.209031 | − | 0.209031i | ||||
\(715\) | 5.67917 | 0.212389 | ||||||||
\(716\) | 3.35925 | + | 3.35925i | 0.125541 | + | 0.125541i | ||||
\(717\) | 19.4467i | 0.726250i | ||||||||
\(718\) | 30.4102i | 1.13490i | ||||||||
\(719\) | −12.6627 | − | 12.6627i | −0.472239 | − | 0.472239i | 0.430400 | − | 0.902638i | \(-0.358373\pi\) |
−0.902638 | + | 0.430400i | \(0.858373\pi\) | |||||||
\(720\) | 1.47957 | 0.0551403 | ||||||||
\(721\) | 2.37335 | + | 2.37335i | 0.0883883 | + | 0.0883883i | ||||
\(722\) | 31.2074 | 1.16142 | ||||||||
\(723\) | 8.35806 | + | 8.35806i | 0.310839 | + | 0.310839i | ||||
\(724\) | 6.46558 | + | 6.46558i | 0.240291 | + | 0.240291i | ||||
\(725\) | −17.5560 | + | 17.5560i | −0.652014 | + | 0.652014i | ||||
\(726\) | −8.91248 | + | 8.91248i | −0.330773 | + | 0.330773i | ||||
\(727\) | 2.96258 | − | 2.96258i | 0.109876 | − | 0.109876i | −0.650031 | − | 0.759907i | \(-0.725244\pi\) |
0.759907 | + | 0.650031i | \(0.225244\pi\) | |||||||
\(728\) | −1.66142 | −0.0615763 | ||||||||
\(729\) | 14.1957i | 0.525765i | ||||||||
\(730\) | 25.5450i | 0.945461i | ||||||||
\(731\) | 20.1312 | − | 20.1312i | 0.744579 | − | 0.744579i | ||||
\(732\) | −17.3952 | − | 17.3952i | −0.642945 | − | 0.642945i | ||||
\(733\) | 11.1209i | 0.410761i | 0.978682 | + | 0.205380i | \(0.0658431\pi\) | ||||
−0.978682 | + | 0.205380i | \(0.934157\pi\) | |||||||
\(734\) | 6.73610 | 0.248634 | ||||||||
\(735\) | −2.22424 | + | 2.22424i | −0.0820422 | + | 0.0820422i | ||||
\(736\) | − | 6.10702i | − | 0.225108i | ||||||
\(737\) | 18.5192 | 0.682163 | ||||||||
\(738\) | 4.44902 | − | 3.98514i | 0.163771 | − | 0.146695i | ||||
\(739\) | −23.2928 | −0.856838 | −0.428419 | − | 0.903580i | \(-0.640929\pi\) | ||||
−0.428419 | + | 0.903580i | \(0.640929\pi\) | |||||||
\(740\) | 4.35760i | 0.160188i | ||||||||
\(741\) | −16.5082 | + | 16.5082i | −0.606443 | + | 0.606443i | ||||
\(742\) | 10.5189 | 0.386161 | ||||||||
\(743\) | − | 23.5886i | − | 0.865383i | −0.901542 | − | 0.432691i | \(-0.857564\pi\) | ||
0.901542 | − | 0.432691i | \(-0.142436\pi\) | |||||||
\(744\) | 13.1047 | + | 13.1047i | 0.480441 | + | 0.480441i | ||||
\(745\) | −24.1663 | + | 24.1663i | −0.885386 | + | 0.885386i | ||||
\(746\) | 5.69811i | 0.208623i | ||||||||
\(747\) | 1.88377i | 0.0689236i | ||||||||
\(748\) | −8.58392 | −0.313859 | ||||||||
\(749\) | 0.918498 | − | 0.918498i | 0.0335612 | − | 0.0335612i | ||||
\(750\) | −16.6465 | + | 16.6465i | −0.607843 | + | 0.607843i | ||||
\(751\) | −1.98972 | + | 1.98972i | −0.0726058 | + | 0.0726058i | −0.742477 | − | 0.669871i | \(-0.766349\pi\) |
0.669871 | + | 0.742477i | \(0.266349\pi\) | |||||||
\(752\) | −5.02180 | − | 5.02180i | −0.183126 | − | 0.183126i | ||||
\(753\) | 10.2363 | + | 10.2363i | 0.373032 | + | 0.373032i | ||||
\(754\) | −16.6053 | −0.604730 | ||||||||
\(755\) | 4.20163 | + | 4.20163i | 0.152913 | + | 0.152913i | ||||
\(756\) | 4.09952 | 0.149098 | ||||||||
\(757\) | 3.09270 | + | 3.09270i | 0.112406 | + | 0.112406i | 0.761073 | − | 0.648667i | \(-0.224673\pi\) |
−0.648667 | + | 0.761073i | \(0.724673\pi\) | |||||||
\(758\) | 9.74441i | 0.353933i | ||||||||
\(759\) | − | 26.1001i | − | 0.947372i | ||||||
\(760\) | 7.94719 | + | 7.94719i | 0.288275 | + | 0.288275i | ||||
\(761\) | −23.7013 | −0.859173 | −0.429587 | − | 0.903026i | \(-0.641341\pi\) | ||||
−0.429587 | + | 0.903026i | \(0.641341\pi\) | |||||||
\(762\) | −5.84210 | − | 5.84210i | −0.211637 | − | 0.211637i | ||||
\(763\) | −6.39375 | −0.231469 | ||||||||
\(764\) | −15.5425 | − | 15.5425i | −0.562308 | − | 0.562308i | ||||
\(765\) | −4.16721 | − | 4.16721i | −0.150666 | − | 0.150666i | ||||
\(766\) | −15.1746 | + | 15.1746i | −0.548282 | + | 0.548282i | ||||
\(767\) | −12.6151 | + | 12.6151i | −0.455506 | + | 0.455506i | ||||
\(768\) | −1.40228 | + | 1.40228i | −0.0506006 | + | 0.0506006i | ||||
\(769\) | −50.7910 | −1.83157 | −0.915785 | − | 0.401669i | \(-0.868430\pi\) | ||||
−0.915785 | + | 0.401669i | \(0.868430\pi\) | |||||||
\(770\) | 3.41826i | 0.123186i | ||||||||
\(771\) | − | 47.7180i | − | 1.71852i | ||||||
\(772\) | −5.09221 | + | 5.09221i | −0.183273 | + | 0.183273i | ||||
\(773\) | −22.9512 | − | 22.9512i | −0.825498 | − | 0.825498i | 0.161392 | − | 0.986890i | \(-0.448401\pi\) |
−0.986890 | + | 0.161392i | \(0.948401\pi\) | |||||||
\(774\) | − | 6.66731i | − | 0.239652i | ||||||
\(775\) | −23.2147 | −0.833897 | ||||||||
\(776\) | −3.70310 | + | 3.70310i | −0.132934 | + | 0.132934i | ||||
\(777\) | − | 5.44821i | − | 0.195453i | ||||||
\(778\) | 13.9321 | 0.499491 | ||||||||
\(779\) | 45.3023 | + | 2.49166i | 1.62312 | + | 0.0892731i | ||||
\(780\) | −5.22607 | −0.187123 | ||||||||
\(781\) | 18.6125i | 0.666009i | ||||||||
\(782\) | −17.2004 | + | 17.2004i | −0.615086 | + | 0.615086i | ||||
\(783\) | 40.9732 | 1.46426 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −21.3816 | − | 21.3816i | −0.763143 | − | 0.763143i | ||||
\(786\) | −10.1596 | + | 10.1596i | −0.362381 | + | 0.362381i | ||||
\(787\) | 37.8952i | 1.35082i | 0.737443 | + | 0.675409i | \(0.236033\pi\) | ||||
−0.737443 | + | 0.675409i | \(0.763967\pi\) | |||||||
\(788\) | − | 5.17834i | − | 0.184471i | ||||||
\(789\) | 28.3357 | 1.00878 | ||||||||
\(790\) | 3.96025 | − | 3.96025i | 0.140899 | − | 0.140899i | ||||
\(791\) | −7.53343 | + | 7.53343i | −0.267858 | + | 0.267858i | ||||
\(792\) | −1.42147 | + | 1.42147i | −0.0505096 | + | 0.0505096i | ||||
\(793\) | 14.5733 | + | 14.5733i | 0.517513 | + | 0.517513i | ||||
\(794\) | 1.31578 | + | 1.31578i | 0.0466954 | + | 0.0466954i | ||||
\(795\) | 33.0877 | 1.17350 | ||||||||
\(796\) | −4.18223 | − | 4.18223i | −0.148235 | − | 0.148235i | ||||
\(797\) | −16.9168 | −0.599223 | −0.299612 | − | 0.954061i | \(-0.596857\pi\) | ||||
−0.299612 | + | 0.954061i | \(0.596857\pi\) | |||||||
\(798\) | −9.93619 | − | 9.93619i | −0.351737 | − | 0.351737i | ||||
\(799\) | 28.2878i | 1.00075i | ||||||||
\(800\) | − | 2.48412i | − | 0.0878271i | ||||||
\(801\) | −11.4703 | − | 11.4703i | −0.405283 | − | 0.405283i | ||||
\(802\) | −30.3808 | −1.07278 | ||||||||
\(803\) | −24.5418 | − | 24.5418i | −0.866062 | − | 0.866062i | ||||
\(804\) | −17.0417 | −0.601013 | ||||||||
\(805\) | 6.84950 | + | 6.84950i | 0.241413 | + | 0.241413i | ||||
\(806\) | −10.9788 | − | 10.9788i | −0.386711 | − | 0.386711i | ||||
\(807\) | 10.5315 | − | 10.5315i | 0.370726 | − | 0.370726i | ||||
\(808\) | −11.2599 | + | 11.2599i | −0.396123 | + | 0.396123i | ||||
\(809\) | −30.4167 | + | 30.4167i | −1.06939 | + | 1.06939i | −0.0719882 | + | 0.997405i | \(0.522934\pi\) |
−0.997405 | + | 0.0719882i | \(0.977066\pi\) | |||||||
\(810\) | 17.3339 | 0.609052 | ||||||||
\(811\) | − | 35.2170i | − | 1.23664i | −0.785928 | − | 0.618318i | \(-0.787814\pi\) | ||
0.785928 | − | 0.618318i | \(-0.212186\pi\) | |||||||
\(812\) | − | 9.99465i | − | 0.350743i | ||||||
\(813\) | 16.7714 | − | 16.7714i | 0.588199 | − | 0.588199i | ||||
\(814\) | −4.18647 | − | 4.18647i | −0.146736 | − | 0.146736i | ||||
\(815\) | − | 27.2947i | − | 0.956091i | ||||||
\(816\) | 7.89906 | 0.276523 | ||||||||
\(817\) | 35.8120 | − | 35.8120i | 1.25290 | − | 1.25290i | ||||
\(818\) | − | 28.4107i | − | 0.993357i | ||||||
\(819\) | 1.54978 | 0.0541537 | ||||||||
\(820\) | 6.77637 | + | 7.56517i | 0.236641 | + | 0.264187i | ||||
\(821\) | −5.93171 | −0.207018 | −0.103509 | − | 0.994629i | \(-0.533007\pi\) | ||||
−0.103509 | + | 0.994629i | \(0.533007\pi\) | |||||||
\(822\) | 13.9445i | 0.486370i | ||||||||
\(823\) | −22.6843 | + | 22.6843i | −0.790726 | + | 0.790726i | −0.981612 | − | 0.190886i | \(-0.938864\pi\) |
0.190886 | + | 0.981612i | \(0.438864\pi\) | |||||||
\(824\) | −3.35643 | −0.116927 | ||||||||
\(825\) | − | 10.6166i | − | 0.369623i | ||||||
\(826\) | −7.59298 | − | 7.59298i | −0.264194 | − | 0.264194i | ||||
\(827\) | −15.1027 | + | 15.1027i | −0.525172 | + | 0.525172i | −0.919129 | − | 0.393957i | \(-0.871106\pi\) |
0.393957 | + | 0.919129i | \(0.371106\pi\) | |||||||
\(828\) | 5.69666i | 0.197973i | ||||||||
\(829\) | − | 27.4318i | − | 0.952745i | −0.879243 | − | 0.476373i | \(-0.841951\pi\) | ||
0.879243 | − | 0.476373i | \(-0.158049\pi\) | |||||||
\(830\) | −3.20318 | −0.111184 | ||||||||
\(831\) | −26.4530 | + | 26.4530i | −0.917646 | + | 0.917646i | ||||
\(832\) | 1.17480 | − | 1.17480i | 0.0407289 | − | 0.0407289i | ||||
\(833\) | −2.81650 | + | 2.81650i | −0.0975859 | + | 0.0975859i | ||||
\(834\) | −9.35046 | − | 9.35046i | −0.323780 | − | 0.323780i | ||||
\(835\) | −7.82338 | − | 7.82338i | −0.270739 | − | 0.270739i | ||||
\(836\) | −15.2702 | −0.528131 | ||||||||
\(837\) | 27.0899 | + | 27.0899i | 0.936364 | + | 0.936364i | ||||
\(838\) | −35.4270 | −1.22381 | ||||||||
\(839\) | 10.1075 | + | 10.1075i | 0.348951 | + | 0.348951i | 0.859719 | − | 0.510768i | \(-0.170639\pi\) |
−0.510768 | + | 0.859719i | \(0.670639\pi\) | |||||||
\(840\) | − | 3.14554i | − | 0.108532i | ||||||
\(841\) | − | 70.8930i | − | 2.44459i | ||||||
\(842\) | −14.7557 | − | 14.7557i | −0.508515 | − | 0.508515i | ||||
\(843\) | −51.5008 | −1.77378 | ||||||||
\(844\) | 15.7282 | + | 15.7282i | 0.541387 | + | 0.541387i | ||||
\(845\) | −16.2417 | −0.558731 | ||||||||
\(846\) | 4.68435 | + | 4.68435i | 0.161051 | + | 0.161051i | ||||
\(847\) | 4.49415 | + | 4.49415i | 0.154421 | + | 0.154421i | ||||
\(848\) | −7.43800 | + | 7.43800i | −0.255422 | + | 0.255422i | ||||
\(849\) | −2.95335 | + | 2.95335i | −0.101359 | + | 0.101359i | ||||
\(850\) | −6.99653 | + | 6.99653i | −0.239979 | + | 0.239979i | ||||
\(851\) | −16.7777 | −0.575132 | ||||||||
\(852\) | − | 17.1276i | − | 0.586781i | ||||||
\(853\) | 30.5661i | 1.04656i | 0.852160 | + | 0.523282i | \(0.175292\pi\) | ||||
−0.852160 | + | 0.523282i | \(0.824708\pi\) | |||||||
\(854\) | −8.77159 | + | 8.77159i | −0.300158 | + | 0.300158i | ||||
\(855\) | −7.41317 | − | 7.41317i | −0.253525 | − | 0.253525i | ||||
\(856\) | 1.29895i | 0.0443973i | ||||||||
\(857\) | −14.8307 | −0.506607 | −0.253304 | − | 0.967387i | \(-0.581517\pi\) | ||||
−0.253304 | + | 0.967387i | \(0.581517\pi\) | |||||||
\(858\) | 5.02084 | − | 5.02084i | 0.171409 | − | 0.171409i | ||||
\(859\) | − | 3.22363i | − | 0.109989i | −0.998487 | − | 0.0549943i | \(-0.982486\pi\) | ||
0.998487 | − | 0.0549943i | \(-0.0175141\pi\) | |||||||
\(860\) | 11.3372 | 0.386594 | ||||||||
\(861\) | −8.47235 | − | 9.45856i | −0.288737 | − | 0.322347i | ||||
\(862\) | 28.8932 | 0.984105 | ||||||||
\(863\) | 3.49816i | 0.119079i | 0.998226 | + | 0.0595394i | \(0.0189632\pi\) | ||||
−0.998226 | + | 0.0595394i | \(0.981037\pi\) | |||||||
\(864\) | −2.89880 | + | 2.89880i | −0.0986190 | + | 0.0986190i | ||||
\(865\) | −0.692987 | −0.0235623 | ||||||||
\(866\) | 13.9634i | 0.474497i | ||||||||
\(867\) | 1.59114 | + | 1.59114i | 0.0540379 | + | 0.0540379i | ||||
\(868\) | 6.60807 | − | 6.60807i | 0.224293 | − | 0.224293i | ||||
\(869\) | 7.60946i | 0.258133i | ||||||||
\(870\) | − | 31.4386i | − | 1.06587i | ||||||
\(871\) | 14.2771 | 0.483761 | ||||||||
\(872\) | 4.52106 | − | 4.52106i | 0.153102 | − | 0.153102i | ||||
\(873\) | 3.45427 | − | 3.45427i | 0.116909 | − | 0.116909i | ||||
\(874\) | −30.5984 | + | 30.5984i | −1.03501 | + | 1.03501i | ||||
\(875\) | 8.39403 | + | 8.39403i | 0.283770 | + | 0.283770i | ||||
\(876\) | 22.5838 | + | 22.5838i | 0.763036 | + | 0.763036i | ||||
\(877\) | −35.8719 | −1.21131 | −0.605654 | − | 0.795728i | \(-0.707089\pi\) | ||||
−0.605654 | + | 0.795728i | \(0.707089\pi\) | |||||||
\(878\) | 5.52443 | + | 5.52443i | 0.186441 | + | 0.186441i | ||||
\(879\) | −3.98497 | −0.134410 | ||||||||
\(880\) | −2.41708 | − | 2.41708i | −0.0814797 | − | 0.0814797i | ||||
\(881\) | − | 14.6893i | − | 0.494896i | −0.968901 | − | 0.247448i | \(-0.920408\pi\) | ||
0.968901 | − | 0.247448i | \(-0.0795919\pi\) | |||||||
\(882\) | 0.932805i | 0.0314092i | ||||||||
\(883\) | 29.1455 | + | 29.1455i | 0.980824 | + | 0.980824i | 0.999820 | − | 0.0189952i | \(-0.00604672\pi\) |
−0.0189952 | + | 0.999820i | \(0.506047\pi\) | |||||||
\(884\) | −6.61765 | −0.222576 | ||||||||
\(885\) | −23.8840 | − | 23.8840i | −0.802854 | − | 0.802854i | ||||
\(886\) | 25.7874 | 0.866345 | ||||||||
\(887\) | 18.9492 | + | 18.9492i | 0.636251 | + | 0.636251i | 0.949629 | − | 0.313378i | \(-0.101461\pi\) |
−0.313378 | + | 0.949629i | \(0.601461\pi\) | |||||||
\(888\) | 3.85247 | + | 3.85247i | 0.129280 | + | 0.129280i | ||||
\(889\) | −2.94590 | + | 2.94590i | −0.0988023 | + | 0.0988023i | ||||
\(890\) | 19.5042 | − | 19.5042i | 0.653783 | − | 0.653783i | ||||
\(891\) | −16.6532 | + | 16.6532i | −0.557904 | + | 0.557904i | ||||
\(892\) | −14.3426 | −0.480227 | ||||||||
\(893\) | 50.3220i | 1.68396i | ||||||||
\(894\) | 42.7299i | 1.42910i | ||||||||
\(895\) | 5.32828 | − | 5.32828i | 0.178105 | − | 0.178105i | ||||
\(896\) | 0.707107 | + | 0.707107i | 0.0236228 | + | 0.0236228i | ||||
\(897\) | − | 20.1215i | − | 0.671837i | ||||||
\(898\) | −34.6856 | −1.15747 | ||||||||
\(899\) | 66.0454 | − | 66.0454i | 2.20274 | − | 2.20274i | ||||
\(900\) | 2.31720i | 0.0772401i | ||||||||
\(901\) | 41.8982 | 1.39583 | ||||||||
\(902\) | −13.7783 | − | 0.757821i | −0.458769 | − | 0.0252327i | ||||
\(903\) | −14.1746 | −0.471702 | ||||||||
\(904\) | − | 10.6539i | − | 0.354343i | ||||||
\(905\) | 10.2554 | − | 10.2554i | 0.340901 | − | 0.340901i | ||||
\(906\) | 7.42916 | 0.246817 | ||||||||
\(907\) | − | 42.7081i | − | 1.41810i | −0.705159 | − | 0.709049i | \(-0.749125\pi\) | ||
0.705159 | − | 0.709049i | \(-0.250875\pi\) | |||||||
\(908\) | −12.3679 | − | 12.3679i | −0.410444 | − | 0.410444i | ||||
\(909\) | 10.5033 | − | 10.5033i | 0.348373 | − | 0.348373i | ||||
\(910\) | 2.63526i | 0.0873581i | ||||||||
\(911\) | 40.6781i | 1.34773i | 0.738857 | + | 0.673863i | \(0.235366\pi\) | ||||
−0.738857 | + | 0.673863i | \(0.764634\pi\) | |||||||
\(912\) | 14.0519 | 0.465305 | ||||||||
\(913\) | 3.07739 | − | 3.07739i | 0.101847 | − | 0.101847i | ||||
\(914\) | −21.6838 | + | 21.6838i | −0.717236 | + | 0.717236i | ||||
\(915\) | −27.5914 | + | 27.5914i | −0.912145 | + | 0.912145i | ||||
\(916\) | 3.41290 | + | 3.41290i | 0.112765 | + | 0.112765i | ||||
\(917\) | 5.12301 | + | 5.12301i | 0.169177 | + | 0.169177i | ||||
\(918\) | 16.3289 | 0.538934 | ||||||||
\(919\) | 40.2775 | + | 40.2775i | 1.32863 | + | 1.32863i | 0.906565 | + | 0.422066i | \(0.138695\pi\) |
0.422066 | + | 0.906565i | \(0.361305\pi\) | |||||||
\(920\) | −9.68666 | −0.319360 | ||||||||
\(921\) | −35.6054 | − | 35.6054i | −1.17324 | − | 1.17324i | ||||
\(922\) | − | 36.3096i | − | 1.19579i | ||||||
\(923\) | 14.3491i | 0.472306i | ||||||||
\(924\) | 3.02202 | + | 3.02202i | 0.0994171 | + | 0.0994171i | ||||
\(925\) | −6.82458 | −0.224391 | ||||||||
\(926\) | 1.00359 | + | 1.00359i | 0.0329800 | + | 0.0329800i | ||||
\(927\) | 3.13089 | 0.102832 | ||||||||
\(928\) | 7.06728 | + | 7.06728i | 0.231995 | + | 0.231995i | ||||
\(929\) | 14.1784 | + | 14.1784i | 0.465177 | + | 0.465177i | 0.900348 | − | 0.435171i | \(-0.143312\pi\) |
−0.435171 | + | 0.900348i | \(0.643312\pi\) | |||||||
\(930\) | 20.7860 | − | 20.7860i | 0.681599 | − | 0.681599i | ||||
\(931\) | −5.01036 | + | 5.01036i | −0.164208 | + | 0.164208i | ||||
\(932\) | 7.39952 | − | 7.39952i | 0.242379 | − | 0.242379i | ||||
\(933\) | −13.7895 | −0.451447 | ||||||||
\(934\) | − | 18.2854i | − | 0.598315i | ||||||
\(935\) | 13.6154i | 0.445271i | ||||||||
\(936\) | −1.09586 | + | 1.09586i | −0.0358193 | + | 0.0358193i | ||||
\(937\) | −21.0233 | − | 21.0233i | −0.686800 | − | 0.686800i | 0.274723 | − | 0.961523i | \(-0.411414\pi\) |
−0.961523 | + | 0.274723i | \(0.911414\pi\) | |||||||
\(938\) | 8.59331i | 0.280582i | ||||||||
\(939\) | 55.5531 | 1.81291 | ||||||||
\(940\) | −7.96533 | + | 7.96533i | −0.259800 | + | 0.259800i | ||||
\(941\) | − | 5.03135i | − | 0.164017i | −0.996632 | − | 0.0820086i | \(-0.973867\pi\) | ||
0.996632 | − | 0.0820086i | \(-0.0261335\pi\) | |||||||
\(942\) | −37.8061 | −1.23179 | ||||||||
\(943\) | −29.1275 | + | 26.0905i | −0.948522 | + | 0.849622i | ||||
\(944\) | 10.7381 | 0.349495 | ||||||||
\(945\) | − | 6.50245i | − | 0.211525i | ||||||
\(946\) | −10.8920 | + | 10.8920i | −0.354128 | + | 0.354128i | ||||
\(947\) | −2.59221 | −0.0842357 | −0.0421178 | − | 0.999113i | \(-0.513410\pi\) | ||||
−0.0421178 | + | 0.999113i | \(0.513410\pi\) | |||||||
\(948\) | − | 7.00235i | − | 0.227426i | ||||||
\(949\) | −18.9202 | − | 18.9202i | −0.614175 | − | 0.614175i | ||||
\(950\) | −12.4464 | + | 12.4464i | −0.403813 | + | 0.403813i | ||||
\(951\) | 16.6259i | 0.539131i | ||||||||
\(952\) | − | 3.98313i | − | 0.129094i | ||||||
\(953\) | −3.81977 | −0.123734 | −0.0618672 | − | 0.998084i | \(-0.519706\pi\) | ||||
−0.0618672 | + | 0.998084i | \(0.519706\pi\) | |||||||
\(954\) | 6.93820 | − | 6.93820i | 0.224632 | − | 0.224632i | ||||
\(955\) | −24.6527 | + | 24.6527i | −0.797744 | + | 0.797744i | ||||
\(956\) | −6.93393 | + | 6.93393i | −0.224259 | + | 0.224259i | ||||
\(957\) | 30.2040 | + | 30.2040i | 0.976357 | + | 0.976357i | ||||
\(958\) | 20.1039 | + | 20.1039i | 0.649528 | + | 0.649528i | ||||
\(959\) | 7.03156 | 0.227061 | ||||||||
\(960\) | 2.22424 | + | 2.22424i | 0.0717869 | + | 0.0717869i | ||||
\(961\) | 56.3333 | 1.81720 | ||||||||
\(962\) | −3.22751 | − | 3.22751i | −0.104059 | − | 0.104059i | ||||
\(963\) | − | 1.21167i | − | 0.0390455i | ||||||
\(964\) | 5.96031i | 0.191969i | ||||||||
\(965\) | 8.07702 | + | 8.07702i | 0.260008 | + | 0.260008i | ||||
\(966\) | 12.1110 | 0.389666 | ||||||||
\(967\) | 1.19772 | + | 1.19772i | 0.0385162 | + | 0.0385162i | 0.726103 | − | 0.687586i | \(-0.241330\pi\) |
−0.687586 | + | 0.726103i | \(0.741330\pi\) | |||||||
\(968\) | −6.35568 | −0.204279 | ||||||||
\(969\) | −39.5771 | − | 39.5771i | −1.27140 | − | 1.27140i | ||||
\(970\) | 5.87368 | + | 5.87368i | 0.188592 | + | 0.188592i | ||||
\(971\) | 22.5633 | − | 22.5633i | 0.724091 | − | 0.724091i | −0.245345 | − | 0.969436i | \(-0.578901\pi\) |
0.969436 | + | 0.245345i | \(0.0789011\pi\) | |||||||
\(972\) | 6.62819 | − | 6.62819i | 0.212599 | − | 0.212599i | ||||
\(973\) | −4.71500 | + | 4.71500i | −0.151156 | + | 0.151156i | ||||
\(974\) | −18.1781 | −0.582465 | ||||||||
\(975\) | − | 8.18472i | − | 0.262121i | ||||||
\(976\) | − | 12.4049i | − | 0.397071i | ||||||
\(977\) | 11.0051 | − | 11.0051i | 0.352085 | − | 0.352085i | −0.508800 | − | 0.860885i | \(-0.669911\pi\) |
0.860885 | + | 0.508800i | \(0.169911\pi\) | |||||||
\(978\) | −24.1307 | − | 24.1307i | −0.771615 | − | 0.771615i | ||||
\(979\) | 37.4766i | 1.19776i | ||||||||
\(980\) | −1.58615 | −0.0506677 | ||||||||
\(981\) | −4.21727 | + | 4.21727i | −0.134647 | + | 0.134647i | ||||
\(982\) | − | 8.40653i | − | 0.268263i | ||||||
\(983\) | 14.1424 | 0.451073 | 0.225537 | − | 0.974235i | \(-0.427586\pi\) | ||||
0.225537 | + | 0.974235i | \(0.427586\pi\) | |||||||
\(984\) | 12.6791 | + | 0.697359i | 0.404194 | + | 0.0222310i | ||||
\(985\) | −8.21363 | −0.261708 | ||||||||
\(986\) | − | 39.8100i | − | 1.26781i | ||||||
\(987\) | 9.95887 | − | 9.95887i | 0.316994 | − | 0.316994i | ||||
\(988\) | −11.7724 | −0.374528 | ||||||||
\(989\) | 43.6505i | 1.38801i | ||||||||
\(990\) | 2.25466 | + | 2.25466i | 0.0716578 | + | 0.0716578i | ||||
\(991\) | −27.7803 | + | 27.7803i | −0.882470 | + | 0.882470i | −0.993785 | − | 0.111315i | \(-0.964494\pi\) |
0.111315 | + | 0.993785i | \(0.464494\pi\) | |||||||
\(992\) | 9.34523i | 0.296711i | ||||||||
\(993\) | − | 0.657937i | − | 0.0208790i | ||||||
\(994\) | −8.63663 | −0.273937 | ||||||||
\(995\) | −6.63364 | + | 6.63364i | −0.210301 | + | 0.210301i | ||||
\(996\) | −2.83187 | + | 2.83187i | −0.0897312 | + | 0.0897312i | ||||
\(997\) | 5.77370 | − | 5.77370i | 0.182855 | − | 0.182855i | −0.609744 | − | 0.792599i | \(-0.708728\pi\) |
0.792599 | + | 0.609744i | \(0.208728\pi\) | |||||||
\(998\) | −11.0199 | − | 11.0199i | −0.348830 | − | 0.348830i | ||||
\(999\) | 7.96380 | + | 7.96380i | 0.251963 | + | 0.251963i |
(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 | 574.2.f.a.155.4 | ✓ | 20 | |
41.9 | even | 4 | inner | 574.2.f.a.337.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.f.a.155.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
574.2.f.a.337.4 | yes | 20 | 41.9 | even | 4 | inner |