Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.8 | ||
Root | \(-0.157845 - 1.72484i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.b.551.16 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.72484 | − | 0.157845i | 0.995839 | − | 0.0911321i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.157845 | − | 1.72484i | −0.0644401 | − | 0.704164i | ||||
\(7\) | 4.77029i | 1.80300i | 0.432780 | + | 0.901500i | \(0.357533\pi\) | ||||
−0.432780 | + | 0.901500i | \(0.642467\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.95017 | − | 0.544517i | 0.983390 | − | 0.181506i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | 5.68772 | 1.71491 | 0.857455 | − | 0.514558i | \(-0.172044\pi\) | ||||
0.857455 | + | 0.514558i | \(0.172044\pi\) | |||||||
\(12\) | −1.72484 | + | 0.157845i | −0.497919 | + | 0.0455660i | ||||
\(13\) | −5.86303 | −1.62611 | −0.813056 | − | 0.582185i | \(-0.802198\pi\) | ||||
−0.813056 | + | 0.582185i | \(0.802198\pi\) | |||||||
\(14\) | 4.77029 | 1.27491 | ||||||||
\(15\) | 1.72484 | − | 0.157845i | 0.445353 | − | 0.0407555i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.96521 | −0.476634 | −0.238317 | − | 0.971187i | \(-0.576596\pi\) | ||||
−0.238317 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(18\) | −0.544517 | − | 2.95017i | −0.128344 | − | 0.695362i | ||||
\(19\) | 3.08903i | 0.708673i | 0.935118 | + | 0.354337i | \(0.115293\pi\) | ||||
−0.935118 | + | 0.354337i | \(0.884707\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0.752968 | + | 8.22800i | 0.164311 | + | 1.79550i | ||||
\(22\) | − | 5.68772i | − | 1.21262i | ||||||
\(23\) | −1.22009 | + | 4.63804i | −0.254405 | + | 0.967098i | ||||
\(24\) | 0.157845 | + | 1.72484i | 0.0322201 | + | 0.352082i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.86303i | 1.14984i | ||||||||
\(27\) | 5.00263 | − | 1.40488i | 0.962757 | − | 0.270369i | ||||
\(28\) | − | 4.77029i | − | 0.901500i | ||||||
\(29\) | − | 4.66722i | − | 0.866681i | −0.901230 | − | 0.433341i | \(-0.857335\pi\) | ||
0.901230 | − | 0.433341i | \(-0.142665\pi\) | |||||||
\(30\) | −0.157845 | − | 1.72484i | −0.0288185 | − | 0.314912i | ||||
\(31\) | 7.74501 | 1.39105 | 0.695523 | − | 0.718504i | \(-0.255173\pi\) | ||||
0.695523 | + | 0.718504i | \(0.255173\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 9.81042 | − | 0.897780i | 1.70777 | − | 0.156283i | ||||
\(34\) | 1.96521i | 0.337031i | ||||||||
\(35\) | 4.77029i | 0.806326i | ||||||||
\(36\) | −2.95017 | + | 0.544517i | −0.491695 | + | 0.0907529i | ||||
\(37\) | 3.13987i | 0.516192i | 0.966119 | + | 0.258096i | \(0.0830950\pi\) | ||||
−0.966119 | + | 0.258096i | \(0.916905\pi\) | |||||||
\(38\) | 3.08903 | 0.501108 | ||||||||
\(39\) | −10.1128 | + | 0.925453i | −1.61935 | + | 0.148191i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | − | 8.70541i | − | 1.35956i | −0.733417 | − | 0.679779i | \(-0.762076\pi\) | ||
0.733417 | − | 0.679779i | \(-0.237924\pi\) | |||||||
\(42\) | 8.22800 | − | 0.752968i | 1.26961 | − | 0.116185i | ||||
\(43\) | − | 7.75780i | − | 1.18305i | −0.806285 | − | 0.591527i | \(-0.798525\pi\) | ||
0.806285 | − | 0.591527i | \(-0.201475\pi\) | |||||||
\(44\) | −5.68772 | −0.857455 | ||||||||
\(45\) | 2.95017 | − | 0.544517i | 0.439785 | − | 0.0811718i | ||||
\(46\) | 4.63804 | + | 1.22009i | 0.683841 | + | 0.179892i | ||||
\(47\) | − | 8.55477i | − | 1.24784i | −0.781488 | − | 0.623921i | \(-0.785539\pi\) | ||
0.781488 | − | 0.623921i | \(-0.214461\pi\) | |||||||
\(48\) | 1.72484 | − | 0.157845i | 0.248960 | − | 0.0227830i | ||||
\(49\) | −15.7556 | −2.25081 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | −3.38968 | + | 0.310200i | −0.474651 | + | 0.0434366i | ||||
\(52\) | 5.86303 | 0.813056 | ||||||||
\(53\) | −2.37670 | −0.326465 | −0.163233 | − | 0.986588i | \(-0.552192\pi\) | ||||
−0.163233 | + | 0.986588i | \(0.552192\pi\) | |||||||
\(54\) | −1.40488 | − | 5.00263i | −0.191180 | − | 0.680772i | ||||
\(55\) | 5.68772 | 0.766931 | ||||||||
\(56\) | −4.77029 | −0.637456 | ||||||||
\(57\) | 0.487590 | + | 5.32810i | 0.0645829 | + | 0.705724i | ||||
\(58\) | −4.66722 | −0.612836 | ||||||||
\(59\) | − | 2.47606i | − | 0.322355i | −0.986925 | − | 0.161178i | \(-0.948471\pi\) | ||
0.986925 | − | 0.161178i | \(-0.0515292\pi\) | |||||||
\(60\) | −1.72484 | + | 0.157845i | −0.222676 | + | 0.0203778i | ||||
\(61\) | − | 2.31175i | − | 0.295989i | −0.988988 | − | 0.147994i | \(-0.952718\pi\) | ||
0.988988 | − | 0.147994i | \(-0.0472818\pi\) | |||||||
\(62\) | − | 7.74501i | − | 0.983618i | ||||||
\(63\) | 2.59750 | + | 14.0732i | 0.327255 | + | 1.77305i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.86303 | −0.727220 | ||||||||
\(66\) | −0.897780 | − | 9.81042i | −0.110509 | − | 1.20758i | ||||
\(67\) | − | 9.67337i | − | 1.18179i | −0.806748 | − | 0.590895i | \(-0.798775\pi\) | ||
0.806748 | − | 0.590895i | \(-0.201225\pi\) | |||||||
\(68\) | 1.96521 | 0.238317 | ||||||||
\(69\) | −1.37236 | + | 8.19247i | −0.165213 | + | 0.986258i | ||||
\(70\) | 4.77029 | 0.570158 | ||||||||
\(71\) | − | 1.59802i | − | 0.189650i | −0.995494 | − | 0.0948252i | \(-0.969771\pi\) | ||
0.995494 | − | 0.0948252i | \(-0.0302292\pi\) | |||||||
\(72\) | 0.544517 | + | 2.95017i | 0.0641720 | + | 0.347681i | ||||
\(73\) | 3.25573 | 0.381054 | 0.190527 | − | 0.981682i | \(-0.438980\pi\) | ||||
0.190527 | + | 0.981682i | \(0.438980\pi\) | |||||||
\(74\) | 3.13987 | 0.365003 | ||||||||
\(75\) | 1.72484 | − | 0.157845i | 0.199168 | − | 0.0182264i | ||||
\(76\) | − | 3.08903i | − | 0.354337i | ||||||
\(77\) | 27.1320i | 3.09198i | ||||||||
\(78\) | 0.925453 | + | 10.1128i | 0.104787 | + | 1.14505i | ||||
\(79\) | 6.19457i | 0.696944i | 0.937319 | + | 0.348472i | \(0.113299\pi\) | ||||
−0.937319 | + | 0.348472i | \(0.886701\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.40700 | − | 3.21284i | 0.934111 | − | 0.356982i | ||||
\(82\) | −8.70541 | −0.961352 | ||||||||
\(83\) | −14.7833 | −1.62268 | −0.811339 | − | 0.584576i | \(-0.801261\pi\) | ||||
−0.811339 | + | 0.584576i | \(0.801261\pi\) | |||||||
\(84\) | −0.752968 | − | 8.22800i | −0.0821555 | − | 0.897748i | ||||
\(85\) | −1.96521 | −0.213157 | ||||||||
\(86\) | −7.75780 | −0.836546 | ||||||||
\(87\) | −0.736699 | − | 8.05022i | −0.0789824 | − | 0.863075i | ||||
\(88\) | 5.68772i | 0.606312i | ||||||||
\(89\) | −7.42799 | −0.787366 | −0.393683 | − | 0.919246i | \(-0.628799\pi\) | ||||
−0.393683 | + | 0.919246i | \(0.628799\pi\) | |||||||
\(90\) | −0.544517 | − | 2.95017i | −0.0573971 | − | 0.310975i | ||||
\(91\) | − | 27.9683i | − | 2.93188i | ||||||
\(92\) | 1.22009 | − | 4.63804i | 0.127203 | − | 0.483549i | ||||
\(93\) | 13.3589 | − | 1.22251i | 1.38526 | − | 0.126769i | ||||
\(94\) | −8.55477 | −0.882357 | ||||||||
\(95\) | 3.08903i | 0.316928i | ||||||||
\(96\) | −0.157845 | − | 1.72484i | −0.0161100 | − | 0.176041i | ||||
\(97\) | − | 6.65323i | − | 0.675533i | −0.941230 | − | 0.337767i | \(-0.890329\pi\) | ||
0.941230 | − | 0.337767i | \(-0.109671\pi\) | |||||||
\(98\) | 15.7556i | 1.59156i | ||||||||
\(99\) | 16.7797 | − | 3.09706i | 1.68643 | − | 0.311266i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | − | 7.33256i | − | 0.729617i | −0.931083 | − | 0.364808i | \(-0.881135\pi\) | ||
0.931083 | − | 0.364808i | \(-0.118865\pi\) | |||||||
\(102\) | 0.310200 | + | 3.38968i | 0.0307143 | + | 0.335629i | ||||
\(103\) | 9.24100i | 0.910543i | 0.890353 | + | 0.455271i | \(0.150458\pi\) | ||||
−0.890353 | + | 0.455271i | \(0.849542\pi\) | |||||||
\(104\) | − | 5.86303i | − | 0.574918i | ||||||
\(105\) | 0.752968 | + | 8.22800i | 0.0734821 | + | 0.802970i | ||||
\(106\) | 2.37670i | 0.230846i | ||||||||
\(107\) | −4.05749 | −0.392252 | −0.196126 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196126 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(108\) | −5.00263 | + | 1.40488i | −0.481378 | + | 0.135184i | ||||
\(109\) | 12.2955i | 1.17769i | 0.808245 | + | 0.588846i | \(0.200418\pi\) | ||||
−0.808245 | + | 0.588846i | \(0.799582\pi\) | |||||||
\(110\) | − | 5.68772i | − | 0.542302i | ||||||
\(111\) | 0.495614 | + | 5.41579i | 0.0470416 | + | 0.514044i | ||||
\(112\) | 4.77029i | 0.450750i | ||||||||
\(113\) | 16.8426 | 1.58442 | 0.792208 | − | 0.610251i | \(-0.208931\pi\) | ||||
0.792208 | + | 0.610251i | \(0.208931\pi\) | |||||||
\(114\) | 5.32810 | − | 0.487590i | 0.499022 | − | 0.0456670i | ||||
\(115\) | −1.22009 | + | 4.63804i | −0.113774 | + | 0.432499i | ||||
\(116\) | 4.66722i | 0.433341i | ||||||||
\(117\) | −17.2969 | + | 3.19252i | −1.59910 | + | 0.295149i | ||||
\(118\) | −2.47606 | −0.227940 | ||||||||
\(119\) | − | 9.37463i | − | 0.859370i | ||||||
\(120\) | 0.157845 | + | 1.72484i | 0.0144092 | + | 0.157456i | ||||
\(121\) | 21.3501 | 1.94092 | ||||||||
\(122\) | −2.31175 | −0.209296 | ||||||||
\(123\) | −1.37411 | − | 15.0155i | −0.123899 | − | 1.35390i | ||||
\(124\) | −7.74501 | −0.695523 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 14.0732 | − | 2.59750i | 1.25374 | − | 0.231404i | ||||
\(127\) | −1.86527 | −0.165516 | −0.0827580 | − | 0.996570i | \(-0.526373\pi\) | ||||
−0.0827580 | + | 0.996570i | \(0.526373\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.22453 | − | 13.3810i | −0.107814 | − | 1.17813i | ||||
\(130\) | 5.86303i | 0.514222i | ||||||||
\(131\) | 16.7197i | 1.46081i | 0.683016 | + | 0.730403i | \(0.260668\pi\) | ||||
−0.683016 | + | 0.730403i | \(0.739332\pi\) | |||||||
\(132\) | −9.81042 | + | 0.897780i | −0.853887 | + | 0.0781417i | ||||
\(133\) | −14.7356 | −1.27774 | ||||||||
\(134\) | −9.67337 | −0.835652 | ||||||||
\(135\) | 5.00263 | − | 1.40488i | 0.430558 | − | 0.120913i | ||||
\(136\) | − | 1.96521i | − | 0.168516i | ||||||
\(137\) | 8.27644 | 0.707104 | 0.353552 | − | 0.935415i | \(-0.384974\pi\) | ||||
0.353552 | + | 0.935415i | \(0.384974\pi\) | |||||||
\(138\) | 8.19247 | + | 1.37236i | 0.697390 | + | 0.116823i | ||||
\(139\) | 1.92339 | 0.163140 | 0.0815698 | − | 0.996668i | \(-0.474007\pi\) | ||||
0.0815698 | + | 0.996668i | \(0.474007\pi\) | |||||||
\(140\) | − | 4.77029i | − | 0.403163i | ||||||
\(141\) | −1.35033 | − | 14.7556i | −0.113718 | − | 1.24265i | ||||
\(142\) | −1.59802 | −0.134103 | ||||||||
\(143\) | −33.3473 | −2.78864 | ||||||||
\(144\) | 2.95017 | − | 0.544517i | 0.245847 | − | 0.0453764i | ||||
\(145\) | − | 4.66722i | − | 0.387592i | ||||||
\(146\) | − | 3.25573i | − | 0.269446i | ||||||
\(147\) | −27.1760 | + | 2.48695i | −2.24144 | + | 0.205121i | ||||
\(148\) | − | 3.13987i | − | 0.258096i | ||||||
\(149\) | −15.1957 | −1.24488 | −0.622439 | − | 0.782669i | \(-0.713858\pi\) | ||||
−0.622439 | + | 0.782669i | \(0.713858\pi\) | |||||||
\(150\) | −0.157845 | − | 1.72484i | −0.0128880 | − | 0.140833i | ||||
\(151\) | 8.73197 | 0.710598 | 0.355299 | − | 0.934753i | \(-0.384379\pi\) | ||||
0.355299 | + | 0.934753i | \(0.384379\pi\) | |||||||
\(152\) | −3.08903 | −0.250554 | ||||||||
\(153\) | −5.79771 | + | 1.07009i | −0.468717 | + | 0.0865118i | ||||
\(154\) | 27.1320 | 2.18636 | ||||||||
\(155\) | 7.74501 | 0.622095 | ||||||||
\(156\) | 10.1128 | − | 0.925453i | 0.809673 | − | 0.0740955i | ||||
\(157\) | − | 1.95674i | − | 0.156165i | −0.996947 | − | 0.0780826i | \(-0.975120\pi\) | ||
0.996947 | − | 0.0780826i | \(-0.0248798\pi\) | |||||||
\(158\) | 6.19457 | 0.492813 | ||||||||
\(159\) | −4.09944 | + | 0.375151i | −0.325107 | + | 0.0297514i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | −22.1248 | − | 5.82016i | −1.74368 | − | 0.458693i | ||||
\(162\) | −3.21284 | − | 8.40700i | −0.252424 | − | 0.660516i | ||||
\(163\) | −10.7116 | −0.839001 | −0.419500 | − | 0.907755i | \(-0.637795\pi\) | ||||
−0.419500 | + | 0.907755i | \(0.637795\pi\) | |||||||
\(164\) | 8.70541i | 0.679779i | ||||||||
\(165\) | 9.81042 | − | 0.897780i | 0.763740 | − | 0.0698921i | ||||
\(166\) | 14.7833i | 1.14741i | ||||||||
\(167\) | 0.164537i | 0.0127323i | 0.999980 | + | 0.00636614i | \(0.00202642\pi\) | ||||
−0.999980 | + | 0.00636614i | \(0.997974\pi\) | |||||||
\(168\) | −8.22800 | + | 0.752968i | −0.634804 | + | 0.0580927i | ||||
\(169\) | 21.3751 | 1.64424 | ||||||||
\(170\) | 1.96521i | 0.150725i | ||||||||
\(171\) | 1.68203 | + | 9.11318i | 0.128628 | + | 0.696902i | ||||
\(172\) | 7.75780i | 0.591527i | ||||||||
\(173\) | 4.40561i | 0.334953i | 0.985876 | + | 0.167476i | \(0.0535618\pi\) | ||||
−0.985876 | + | 0.167476i | \(0.946438\pi\) | |||||||
\(174\) | −8.05022 | + | 0.736699i | −0.610286 | + | 0.0558490i | ||||
\(175\) | 4.77029i | 0.360600i | ||||||||
\(176\) | 5.68772 | 0.428728 | ||||||||
\(177\) | −0.390834 | − | 4.27081i | −0.0293769 | − | 0.321014i | ||||
\(178\) | 7.42799i | 0.556752i | ||||||||
\(179\) | 21.8808i | 1.63545i | 0.575612 | + | 0.817723i | \(0.304764\pi\) | ||||
−0.575612 | + | 0.817723i | \(0.695236\pi\) | |||||||
\(180\) | −2.95017 | + | 0.544517i | −0.219893 | + | 0.0405859i | ||||
\(181\) | 13.0668i | 0.971248i | 0.874168 | + | 0.485624i | \(0.161408\pi\) | ||||
−0.874168 | + | 0.485624i | \(0.838592\pi\) | |||||||
\(182\) | −27.9683 | −2.07315 | ||||||||
\(183\) | −0.364899 | − | 3.98740i | −0.0269741 | − | 0.294757i | ||||
\(184\) | −4.63804 | − | 1.22009i | −0.341921 | − | 0.0899459i | ||||
\(185\) | 3.13987i | 0.230848i | ||||||||
\(186\) | −1.22251 | − | 13.3589i | −0.0896391 | − | 0.979525i | ||||
\(187\) | −11.1776 | −0.817385 | ||||||||
\(188\) | 8.55477i | 0.623921i | ||||||||
\(189\) | 6.70167 | + | 23.8640i | 0.487475 | + | 1.73585i | ||||
\(190\) | 3.08903 | 0.224102 | ||||||||
\(191\) | −6.15903 | −0.445652 | −0.222826 | − | 0.974858i | \(-0.571528\pi\) | ||||
−0.222826 | + | 0.974858i | \(0.571528\pi\) | |||||||
\(192\) | −1.72484 | + | 0.157845i | −0.124480 | + | 0.0113915i | ||||
\(193\) | 7.16580 | 0.515806 | 0.257903 | − | 0.966171i | \(-0.416969\pi\) | ||||
0.257903 | + | 0.966171i | \(0.416969\pi\) | |||||||
\(194\) | −6.65323 | −0.477674 | ||||||||
\(195\) | −10.1128 | + | 0.925453i | −0.724194 | + | 0.0662730i | ||||
\(196\) | 15.7556 | 1.12540 | ||||||||
\(197\) | 5.95934i | 0.424585i | 0.977206 | + | 0.212293i | \(0.0680930\pi\) | ||||
−0.977206 | + | 0.212293i | \(0.931907\pi\) | |||||||
\(198\) | −3.09706 | − | 16.7797i | −0.220098 | − | 1.19248i | ||||
\(199\) | − | 13.4932i | − | 0.956509i | −0.878221 | − | 0.478254i | \(-0.841270\pi\) | ||
0.878221 | − | 0.478254i | \(-0.158730\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −1.52690 | − | 16.6851i | −0.107699 | − | 1.17687i | ||||
\(202\) | −7.33256 | −0.515917 | ||||||||
\(203\) | 22.2640 | 1.56263 | ||||||||
\(204\) | 3.38968 | − | 0.310200i | 0.237325 | − | 0.0217183i | ||||
\(205\) | − | 8.70541i | − | 0.608013i | ||||||
\(206\) | 9.24100 | 0.643851 | ||||||||
\(207\) | −1.07397 | + | 14.3474i | −0.0746460 | + | 0.997210i | ||||
\(208\) | −5.86303 | −0.406528 | ||||||||
\(209\) | 17.5695i | 1.21531i | ||||||||
\(210\) | 8.22800 | − | 0.752968i | 0.567786 | − | 0.0519597i | ||||
\(211\) | −6.51146 | −0.448268 | −0.224134 | − | 0.974558i | \(-0.571955\pi\) | ||||
−0.224134 | + | 0.974558i | \(0.571955\pi\) | |||||||
\(212\) | 2.37670 | 0.163233 | ||||||||
\(213\) | −0.252241 | − | 2.75634i | −0.0172832 | − | 0.188861i | ||||
\(214\) | 4.05749i | 0.277364i | ||||||||
\(215\) | − | 7.75780i | − | 0.529078i | ||||||
\(216\) | 1.40488 | + | 5.00263i | 0.0955898 | + | 0.340386i | ||||
\(217\) | 36.9459i | 2.50805i | ||||||||
\(218\) | 12.2955 | 0.832755 | ||||||||
\(219\) | 5.61562 | − | 0.513902i | 0.379468 | − | 0.0347263i | ||||
\(220\) | −5.68772 | −0.383466 | ||||||||
\(221\) | 11.5221 | 0.775060 | ||||||||
\(222\) | 5.41579 | − | 0.495614i | 0.363484 | − | 0.0332634i | ||||
\(223\) | −6.93854 | −0.464639 | −0.232319 | − | 0.972640i | \(-0.574631\pi\) | ||||
−0.232319 | + | 0.972640i | \(0.574631\pi\) | |||||||
\(224\) | 4.77029 | 0.318728 | ||||||||
\(225\) | 2.95017 | − | 0.544517i | 0.196678 | − | 0.0363011i | ||||
\(226\) | − | 16.8426i | − | 1.12035i | ||||||
\(227\) | −8.24167 | −0.547019 | −0.273509 | − | 0.961869i | \(-0.588184\pi\) | ||||
−0.273509 | + | 0.961869i | \(0.588184\pi\) | |||||||
\(228\) | −0.487590 | − | 5.32810i | −0.0322914 | − | 0.352862i | ||||
\(229\) | − | 18.1323i | − | 1.19821i | −0.800669 | − | 0.599107i | \(-0.795522\pi\) | ||
0.800669 | − | 0.599107i | \(-0.204478\pi\) | |||||||
\(230\) | 4.63804 | + | 1.22009i | 0.305823 | + | 0.0804501i | ||||
\(231\) | 4.28267 | + | 46.7985i | 0.281779 | + | 3.07912i | ||||
\(232\) | 4.66722 | 0.306418 | ||||||||
\(233\) | − | 9.01790i | − | 0.590782i | −0.955376 | − | 0.295391i | \(-0.904550\pi\) | ||
0.955376 | − | 0.295391i | \(-0.0954500\pi\) | |||||||
\(234\) | 3.19252 | + | 17.2969i | 0.208702 | + | 1.13074i | ||||
\(235\) | − | 8.55477i | − | 0.558052i | ||||||
\(236\) | 2.47606i | 0.161178i | ||||||||
\(237\) | 0.977784 | + | 10.6847i | 0.0635139 | + | 0.694043i | ||||
\(238\) | −9.37463 | −0.607667 | ||||||||
\(239\) | − | 26.2916i | − | 1.70066i | −0.526247 | − | 0.850331i | \(-0.676401\pi\) | ||
0.526247 | − | 0.850331i | \(-0.323599\pi\) | |||||||
\(240\) | 1.72484 | − | 0.157845i | 0.111338 | − | 0.0101889i | ||||
\(241\) | 6.09867i | 0.392850i | 0.980519 | + | 0.196425i | \(0.0629332\pi\) | ||||
−0.980519 | + | 0.196425i | \(0.937067\pi\) | |||||||
\(242\) | − | 21.3501i | − | 1.37244i | ||||||
\(243\) | 13.9936 | − | 6.86865i | 0.897692 | − | 0.440624i | ||||
\(244\) | 2.31175i | 0.147994i | ||||||||
\(245\) | −15.7556 | −1.00659 | ||||||||
\(246\) | −15.0155 | + | 1.37411i | −0.957352 | + | 0.0876100i | ||||
\(247\) | − | 18.1111i | − | 1.15238i | ||||||
\(248\) | 7.74501i | 0.491809i | ||||||||
\(249\) | −25.4989 | + | 2.33347i | −1.61593 | + | 0.147878i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −13.8819 | −0.876215 | −0.438107 | − | 0.898923i | \(-0.644351\pi\) | ||||
−0.438107 | + | 0.898923i | \(0.644351\pi\) | |||||||
\(252\) | −2.59750 | − | 14.0732i | −0.163627 | − | 0.886526i | ||||
\(253\) | −6.93950 | + | 26.3798i | −0.436283 | + | 1.65849i | ||||
\(254\) | 1.86527i | 0.117038i | ||||||||
\(255\) | −3.38968 | + | 0.310200i | −0.212270 | + | 0.0194255i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.6251i | − | 0.912286i | −0.889907 | − | 0.456143i | \(-0.849231\pi\) | ||
0.889907 | − | 0.456143i | \(-0.150769\pi\) | |||||||
\(258\) | −13.3810 | + | 1.22453i | −0.833065 | + | 0.0762361i | ||||
\(259\) | −14.9781 | −0.930693 | ||||||||
\(260\) | 5.86303 | 0.363610 | ||||||||
\(261\) | −2.54138 | − | 13.7691i | −0.157308 | − | 0.852285i | ||||
\(262\) | 16.7197 | 1.03295 | ||||||||
\(263\) | 13.7157 | 0.845744 | 0.422872 | − | 0.906189i | \(-0.361022\pi\) | ||||
0.422872 | + | 0.906189i | \(0.361022\pi\) | |||||||
\(264\) | 0.897780 | + | 9.81042i | 0.0552545 | + | 0.603790i | ||||
\(265\) | −2.37670 | −0.146000 | ||||||||
\(266\) | 14.7356i | 0.903496i | ||||||||
\(267\) | −12.8121 | + | 1.17247i | −0.784089 | + | 0.0717543i | ||||
\(268\) | 9.67337i | 0.590895i | ||||||||
\(269\) | − | 31.3415i | − | 1.91092i | −0.295116 | − | 0.955462i | \(-0.595358\pi\) | ||
0.295116 | − | 0.955462i | \(-0.404642\pi\) | |||||||
\(270\) | −1.40488 | − | 5.00263i | −0.0854981 | − | 0.304450i | ||||
\(271\) | −4.59208 | −0.278949 | −0.139475 | − | 0.990226i | \(-0.544541\pi\) | ||||
−0.139475 | + | 0.990226i | \(0.544541\pi\) | |||||||
\(272\) | −1.96521 | −0.119158 | ||||||||
\(273\) | −4.41467 | − | 48.2410i | −0.267188 | − | 2.91968i | ||||
\(274\) | − | 8.27644i | − | 0.499998i | ||||||
\(275\) | 5.68772 | 0.342982 | ||||||||
\(276\) | 1.37236 | − | 8.19247i | 0.0826066 | − | 0.493129i | ||||
\(277\) | −14.1389 | −0.849524 | −0.424762 | − | 0.905305i | \(-0.639642\pi\) | ||||
−0.424762 | + | 0.905305i | \(0.639642\pi\) | |||||||
\(278\) | − | 1.92339i | − | 0.115357i | ||||||
\(279\) | 22.8491 | − | 4.21729i | 1.36794 | − | 0.252483i | ||||
\(280\) | −4.77029 | −0.285079 | ||||||||
\(281\) | −6.36108 | −0.379470 | −0.189735 | − | 0.981835i | \(-0.560763\pi\) | ||||
−0.189735 | + | 0.981835i | \(0.560763\pi\) | |||||||
\(282\) | −14.7556 | + | 1.35033i | −0.878685 | + | 0.0804110i | ||||
\(283\) | − | 26.0151i | − | 1.54644i | −0.634141 | − | 0.773218i | \(-0.718646\pi\) | ||
0.634141 | − | 0.773218i | \(-0.281354\pi\) | |||||||
\(284\) | 1.59802i | 0.0948252i | ||||||||
\(285\) | 0.487590 | + | 5.32810i | 0.0288823 | + | 0.315609i | ||||
\(286\) | 33.3473i | 1.97186i | ||||||||
\(287\) | 41.5273 | 2.45128 | ||||||||
\(288\) | −0.544517 | − | 2.95017i | −0.0320860 | − | 0.173840i | ||||
\(289\) | −13.1379 | −0.772820 | ||||||||
\(290\) | −4.66722 | −0.274069 | ||||||||
\(291\) | −1.05018 | − | 11.4758i | −0.0615627 | − | 0.672722i | ||||
\(292\) | −3.25573 | −0.190527 | ||||||||
\(293\) | −8.44627 | −0.493437 | −0.246718 | − | 0.969087i | \(-0.579352\pi\) | ||||
−0.246718 | + | 0.969087i | \(0.579352\pi\) | |||||||
\(294\) | 2.48695 | + | 27.1760i | 0.145042 | + | 1.58494i | ||||
\(295\) | − | 2.47606i | − | 0.144162i | ||||||
\(296\) | −3.13987 | −0.182501 | ||||||||
\(297\) | 28.4535 | − | 7.99054i | 1.65104 | − | 0.463658i | ||||
\(298\) | 15.1957i | 0.880261i | ||||||||
\(299\) | 7.15340 | − | 27.1930i | 0.413692 | − | 1.57261i | ||||
\(300\) | −1.72484 | + | 0.157845i | −0.0995839 | + | 0.00911321i | ||||
\(301\) | 37.0070 | 2.13305 | ||||||||
\(302\) | − | 8.73197i | − | 0.502469i | ||||||
\(303\) | −1.15741 | − | 12.6475i | −0.0664915 | − | 0.726581i | ||||
\(304\) | 3.08903i | 0.177168i | ||||||||
\(305\) | − | 2.31175i | − | 0.132370i | ||||||
\(306\) | 1.07009 | + | 5.79771i | 0.0611731 | + | 0.331433i | ||||
\(307\) | −8.46953 | −0.483381 | −0.241691 | − | 0.970353i | \(-0.577702\pi\) | ||||
−0.241691 | + | 0.970353i | \(0.577702\pi\) | |||||||
\(308\) | − | 27.1320i | − | 1.54599i | ||||||
\(309\) | 1.45865 | + | 15.9393i | 0.0829796 | + | 0.906754i | ||||
\(310\) | − | 7.74501i | − | 0.439887i | ||||||
\(311\) | 16.1616i | 0.916443i | 0.888838 | + | 0.458221i | \(0.151513\pi\) | ||||
−0.888838 | + | 0.458221i | \(0.848487\pi\) | |||||||
\(312\) | −0.925453 | − | 10.1128i | −0.0523934 | − | 0.572525i | ||||
\(313\) | − | 6.86741i | − | 0.388169i | −0.980985 | − | 0.194084i | \(-0.937826\pi\) | ||
0.980985 | − | 0.194084i | \(-0.0621735\pi\) | |||||||
\(314\) | −1.95674 | −0.110425 | ||||||||
\(315\) | 2.59750 | + | 14.0732i | 0.146353 | + | 0.792933i | ||||
\(316\) | − | 6.19457i | − | 0.348472i | ||||||
\(317\) | 18.7231i | 1.05159i | 0.850610 | + | 0.525797i | \(0.176233\pi\) | ||||
−0.850610 | + | 0.525797i | \(0.823767\pi\) | |||||||
\(318\) | 0.375151 | + | 4.09944i | 0.0210374 | + | 0.229885i | ||||
\(319\) | − | 26.5458i | − | 1.48628i | ||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.99854 | + | 0.640456i | −0.390620 | + | 0.0357468i | ||||
\(322\) | −5.82016 | + | 22.1248i | −0.324345 | + | 1.23297i | ||||
\(323\) | − | 6.07061i | − | 0.337778i | ||||||
\(324\) | −8.40700 | + | 3.21284i | −0.467056 | + | 0.178491i | ||||
\(325\) | −5.86303 | −0.325223 | ||||||||
\(326\) | 10.7116i | 0.593263i | ||||||||
\(327\) | 1.94078 | + | 21.2078i | 0.107326 | + | 1.17279i | ||||
\(328\) | 8.70541 | 0.480676 | ||||||||
\(329\) | 40.8087 | 2.24986 | ||||||||
\(330\) | −0.897780 | − | 9.81042i | −0.0494211 | − | 0.540046i | ||||
\(331\) | 13.5890 | 0.746918 | 0.373459 | − | 0.927647i | \(-0.378172\pi\) | ||||
0.373459 | + | 0.927647i | \(0.378172\pi\) | |||||||
\(332\) | 14.7833 | 0.811339 | ||||||||
\(333\) | 1.70971 | + | 9.26315i | 0.0936917 | + | 0.507618i | ||||
\(334\) | 0.164537 | 0.00900308 | ||||||||
\(335\) | − | 9.67337i | − | 0.528513i | ||||||
\(336\) | 0.752968 | + | 8.22800i | 0.0410778 | + | 0.448874i | ||||
\(337\) | 4.53301i | 0.246929i | 0.992349 | + | 0.123464i | \(0.0394005\pi\) | ||||
−0.992349 | + | 0.123464i | \(0.960599\pi\) | |||||||
\(338\) | − | 21.3751i | − | 1.16265i | ||||||
\(339\) | 29.0508 | − | 2.65852i | 1.57782 | − | 0.144391i | ||||
\(340\) | 1.96521 | 0.106579 | ||||||||
\(341\) | 44.0514 | 2.38552 | ||||||||
\(342\) | 9.11318 | − | 1.68203i | 0.492784 | − | 0.0909539i | ||||
\(343\) | − | 41.7669i | − | 2.25520i | ||||||
\(344\) | 7.75780 | 0.418273 | ||||||||
\(345\) | −1.37236 | + | 8.19247i | −0.0738856 | + | 0.441068i | ||||
\(346\) | 4.40561 | 0.236847 | ||||||||
\(347\) | 7.21414i | 0.387275i | 0.981073 | + | 0.193638i | \(0.0620286\pi\) | ||||
−0.981073 | + | 0.193638i | \(0.937971\pi\) | |||||||
\(348\) | 0.736699 | + | 8.05022i | 0.0394912 | + | 0.431537i | ||||
\(349\) | −0.988122 | −0.0528930 | −0.0264465 | − | 0.999650i | \(-0.508419\pi\) | ||||
−0.0264465 | + | 0.999650i | \(0.508419\pi\) | |||||||
\(350\) | 4.77029 | 0.254983 | ||||||||
\(351\) | −29.3306 | + | 8.23684i | −1.56555 | + | 0.439650i | ||||
\(352\) | − | 5.68772i | − | 0.303156i | ||||||
\(353\) | 12.2940i | 0.654342i | 0.944965 | + | 0.327171i | \(0.106095\pi\) | ||||
−0.944965 | + | 0.327171i | \(0.893905\pi\) | |||||||
\(354\) | −4.27081 | + | 0.390834i | −0.226991 | + | 0.0207726i | ||||
\(355\) | − | 1.59802i | − | 0.0848143i | ||||||
\(356\) | 7.42799 | 0.393683 | ||||||||
\(357\) | −1.47974 | − | 16.1698i | −0.0783162 | − | 0.855794i | ||||
\(358\) | 21.8808 | 1.15644 | ||||||||
\(359\) | −0.189672 | −0.0100105 | −0.00500526 | − | 0.999987i | \(-0.501593\pi\) | ||||
−0.00500526 | + | 0.999987i | \(0.501593\pi\) | |||||||
\(360\) | 0.544517 | + | 2.95017i | 0.0286986 | + | 0.155488i | ||||
\(361\) | 9.45787 | 0.497782 | ||||||||
\(362\) | 13.0668 | 0.686776 | ||||||||
\(363\) | 36.8256 | − | 3.37002i | 1.93284 | − | 0.176880i | ||||
\(364\) | 27.9683i | 1.46594i | ||||||||
\(365\) | 3.25573 | 0.170413 | ||||||||
\(366\) | −3.98740 | + | 0.364899i | −0.208425 | + | 0.0190736i | ||||
\(367\) | − | 20.2545i | − | 1.05728i | −0.848847 | − | 0.528638i | \(-0.822703\pi\) | ||
0.848847 | − | 0.528638i | \(-0.177297\pi\) | |||||||
\(368\) | −1.22009 | + | 4.63804i | −0.0636014 | + | 0.241774i | ||||
\(369\) | −4.74025 | − | 25.6824i | −0.246767 | − | 1.33697i | ||||
\(370\) | 3.13987 | 0.163234 | ||||||||
\(371\) | − | 11.3375i | − | 0.588616i | ||||||
\(372\) | −13.3589 | + | 1.22251i | −0.692629 | + | 0.0633844i | ||||
\(373\) | 31.1346i | 1.61209i | 0.591854 | + | 0.806045i | \(0.298396\pi\) | ||||
−0.591854 | + | 0.806045i | \(0.701604\pi\) | |||||||
\(374\) | 11.1776i | 0.577978i | ||||||||
\(375\) | 1.72484 | − | 0.157845i | 0.0890705 | − | 0.00815110i | ||||
\(376\) | 8.55477 | 0.441179 | ||||||||
\(377\) | 27.3641i | 1.40932i | ||||||||
\(378\) | 23.8640 | − | 6.70167i | 1.22743 | − | 0.344697i | ||||
\(379\) | − | 21.8934i | − | 1.12459i | −0.826937 | − | 0.562295i | \(-0.809919\pi\) | ||
0.826937 | − | 0.562295i | \(-0.190081\pi\) | |||||||
\(380\) | − | 3.08903i | − | 0.158464i | ||||||
\(381\) | −3.21730 | + | 0.294424i | −0.164827 | + | 0.0150838i | ||||
\(382\) | 6.15903i | 0.315123i | ||||||||
\(383\) | 20.5229 | 1.04867 | 0.524334 | − | 0.851512i | \(-0.324314\pi\) | ||||
0.524334 | + | 0.851512i | \(0.324314\pi\) | |||||||
\(384\) | 0.157845 | + | 1.72484i | 0.00805501 | + | 0.0880205i | ||||
\(385\) | 27.1320i | 1.38278i | ||||||||
\(386\) | − | 7.16580i | − | 0.364730i | ||||||
\(387\) | −4.22426 | − | 22.8868i | −0.214731 | − | 1.16340i | ||||
\(388\) | 6.65323i | 0.337767i | ||||||||
\(389\) | −6.78101 | −0.343811 | −0.171905 | − | 0.985113i | \(-0.554992\pi\) | ||||
−0.171905 | + | 0.985113i | \(0.554992\pi\) | |||||||
\(390\) | 0.925453 | + | 10.1128i | 0.0468621 | + | 0.512082i | ||||
\(391\) | 2.39773 | − | 9.11473i | 0.121258 | − | 0.460952i | ||||
\(392\) | − | 15.7556i | − | 0.795780i | ||||||
\(393\) | 2.63913 | + | 28.8388i | 0.133126 | + | 1.45473i | ||||
\(394\) | 5.95934 | 0.300227 | ||||||||
\(395\) | 6.19457i | 0.311683i | ||||||||
\(396\) | −16.7797 | + | 3.09706i | −0.843213 | + | 0.155633i | ||||
\(397\) | −10.4669 | −0.525320 | −0.262660 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262660 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(398\) | −13.4932 | −0.676354 | ||||||||
\(399\) | −25.4166 | + | 2.32594i | −1.27242 | + | 0.116443i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 6.92220 | 0.345678 | 0.172839 | − | 0.984950i | \(-0.444706\pi\) | ||||
0.172839 | + | 0.984950i | \(0.444706\pi\) | |||||||
\(402\) | −16.6851 | + | 1.52690i | −0.832175 | + | 0.0761547i | ||||
\(403\) | −45.4093 | −2.26200 | ||||||||
\(404\) | 7.33256i | 0.364808i | ||||||||
\(405\) | 8.40700 | − | 3.21284i | 0.417747 | − | 0.159647i | ||||
\(406\) | − | 22.2640i | − | 1.10494i | ||||||
\(407\) | 17.8587i | 0.885223i | ||||||||
\(408\) | −0.310200 | − | 3.38968i | −0.0153572 | − | 0.167814i | ||||
\(409\) | −0.551195 | −0.0272549 | −0.0136274 | − | 0.999907i | \(-0.504338\pi\) | ||||
−0.0136274 | + | 0.999907i | \(0.504338\pi\) | |||||||
\(410\) | −8.70541 | −0.429930 | ||||||||
\(411\) | 14.2756 | − | 1.30640i | 0.704162 | − | 0.0644399i | ||||
\(412\) | − | 9.24100i | − | 0.455271i | ||||||
\(413\) | 11.8115 | 0.581206 | ||||||||
\(414\) | 14.3474 | + | 1.07397i | 0.705134 | + | 0.0527827i | ||||
\(415\) | −14.7833 | −0.725683 | ||||||||
\(416\) | 5.86303i | 0.287459i | ||||||||
\(417\) | 3.31754 | − | 0.303598i | 0.162461 | − | 0.0148673i | ||||
\(418\) | 17.5695 | 0.859355 | ||||||||
\(419\) | 29.7594 | 1.45384 | 0.726921 | − | 0.686721i | \(-0.240951\pi\) | ||||
0.726921 | + | 0.686721i | \(0.240951\pi\) | |||||||
\(420\) | −0.752968 | − | 8.22800i | −0.0367411 | − | 0.401485i | ||||
\(421\) | 25.4818i | 1.24191i | 0.783847 | + | 0.620953i | \(0.213254\pi\) | ||||
−0.783847 | + | 0.620953i | \(0.786746\pi\) | |||||||
\(422\) | 6.51146i | 0.316973i | ||||||||
\(423\) | −4.65822 | − | 25.2380i | −0.226490 | − | 1.22711i | ||||
\(424\) | − | 2.37670i | − | 0.115423i | ||||||
\(425\) | −1.96521 | −0.0953268 | ||||||||
\(426\) | −2.75634 | + | 0.252241i | −0.133545 | + | 0.0122211i | ||||
\(427\) | 11.0277 | 0.533668 | ||||||||
\(428\) | 4.05749 | 0.196126 | ||||||||
\(429\) | −57.5188 | + | 5.26371i | −2.77703 | + | 0.254134i | ||||
\(430\) | −7.75780 | −0.374115 | ||||||||
\(431\) | 25.7344 | 1.23958 | 0.619791 | − | 0.784767i | \(-0.287217\pi\) | ||||
0.619791 | + | 0.784767i | \(0.287217\pi\) | |||||||
\(432\) | 5.00263 | − | 1.40488i | 0.240689 | − | 0.0675922i | ||||
\(433\) | 39.5558i | 1.90093i | 0.310827 | + | 0.950466i | \(0.399394\pi\) | ||||
−0.310827 | + | 0.950466i | \(0.600606\pi\) | |||||||
\(434\) | 36.9459 | 1.77346 | ||||||||
\(435\) | −0.736699 | − | 8.05022i | −0.0353220 | − | 0.385979i | ||||
\(436\) | − | 12.2955i | − | 0.588846i | ||||||
\(437\) | −14.3271 | − | 3.76889i | −0.685356 | − | 0.180290i | ||||
\(438\) | −0.513902 | − | 5.61562i | −0.0245552 | − | 0.268325i | ||||
\(439\) | 12.4645 | 0.594900 | 0.297450 | − | 0.954737i | \(-0.403864\pi\) | ||||
0.297450 | + | 0.954737i | \(0.403864\pi\) | |||||||
\(440\) | 5.68772i | 0.271151i | ||||||||
\(441\) | −46.4818 | + | 8.57922i | −2.21342 | + | 0.408534i | ||||
\(442\) | − | 11.5221i | − | 0.548050i | ||||||
\(443\) | 12.1118i | 0.575450i | 0.957713 | + | 0.287725i | \(0.0928989\pi\) | ||||
−0.957713 | + | 0.287725i | \(0.907101\pi\) | |||||||
\(444\) | −0.495614 | − | 5.41579i | −0.0235208 | − | 0.257022i | ||||
\(445\) | −7.42799 | −0.352121 | ||||||||
\(446\) | 6.93854i | 0.328549i | ||||||||
\(447\) | −26.2101 | + | 2.39857i | −1.23970 | + | 0.113448i | ||||
\(448\) | − | 4.77029i | − | 0.225375i | ||||||
\(449\) | 15.0035i | 0.708060i | 0.935234 | + | 0.354030i | \(0.115189\pi\) | ||||
−0.935234 | + | 0.354030i | \(0.884811\pi\) | |||||||
\(450\) | −0.544517 | − | 2.95017i | −0.0256688 | − | 0.139072i | ||||
\(451\) | − | 49.5139i | − | 2.33152i | ||||||
\(452\) | −16.8426 | −0.792208 | ||||||||
\(453\) | 15.0613 | − | 1.37830i | 0.707641 | − | 0.0647583i | ||||
\(454\) | 8.24167i | 0.386801i | ||||||||
\(455\) | − | 27.9683i | − | 1.31118i | ||||||
\(456\) | −5.32810 | + | 0.487590i | −0.249511 | + | 0.0228335i | ||||
\(457\) | 1.63920i | 0.0766785i | 0.999265 | + | 0.0383392i | \(0.0122068\pi\) | ||||
−0.999265 | + | 0.0383392i | \(0.987793\pi\) | |||||||
\(458\) | −18.1323 | −0.847266 | ||||||||
\(459\) | −9.83123 | + | 2.76088i | −0.458883 | + | 0.128867i | ||||
\(460\) | 1.22009 | − | 4.63804i | 0.0568868 | − | 0.216250i | ||||
\(461\) | 11.3693i | 0.529520i | 0.964314 | + | 0.264760i | \(0.0852928\pi\) | ||||
−0.964314 | + | 0.264760i | \(0.914707\pi\) | |||||||
\(462\) | 46.7985 | − | 4.28267i | 2.17726 | − | 0.199248i | ||||
\(463\) | 33.7826 | 1.57001 | 0.785006 | − | 0.619488i | \(-0.212660\pi\) | ||||
0.785006 | + | 0.619488i | \(0.212660\pi\) | |||||||
\(464\) | − | 4.66722i | − | 0.216670i | ||||||
\(465\) | 13.3589 | − | 1.22251i | 0.619506 | − | 0.0566928i | ||||
\(466\) | −9.01790 | −0.417746 | ||||||||
\(467\) | 16.9801 | 0.785747 | 0.392873 | − | 0.919593i | \(-0.371481\pi\) | ||||
0.392873 | + | 0.919593i | \(0.371481\pi\) | |||||||
\(468\) | 17.2969 | − | 3.19252i | 0.799551 | − | 0.147574i | ||||
\(469\) | 46.1448 | 2.13077 | ||||||||
\(470\) | −8.55477 | −0.394602 | ||||||||
\(471\) | −0.308863 | − | 3.37508i | −0.0142317 | − | 0.155515i | ||||
\(472\) | 2.47606 | 0.113970 | ||||||||
\(473\) | − | 44.1242i | − | 2.02883i | ||||||
\(474\) | 10.6847 | − | 0.977784i | 0.490763 | − | 0.0449111i | ||||
\(475\) | 3.08903i | 0.141735i | ||||||||
\(476\) | 9.37463i | 0.429685i | ||||||||
\(477\) | −7.01167 | + | 1.29415i | −0.321042 | + | 0.0592553i | ||||
\(478\) | −26.2916 | −1.20255 | ||||||||
\(479\) | −21.1756 | −0.967540 | −0.483770 | − | 0.875195i | \(-0.660733\pi\) | ||||
−0.483770 | + | 0.875195i | \(0.660733\pi\) | |||||||
\(480\) | −0.157845 | − | 1.72484i | −0.00720462 | − | 0.0787280i | ||||
\(481\) | − | 18.4092i | − | 0.839386i | ||||||
\(482\) | 6.09867 | 0.277787 | ||||||||
\(483\) | −39.0804 | − | 6.54657i | −1.77822 | − | 0.297879i | ||||
\(484\) | −21.3501 | −0.970459 | ||||||||
\(485\) | − | 6.65323i | − | 0.302108i | ||||||
\(486\) | −6.86865 | − | 13.9936i | −0.311568 | − | 0.634764i | ||||
\(487\) | 14.8247 | 0.671772 | 0.335886 | − | 0.941903i | \(-0.390964\pi\) | ||||
0.335886 | + | 0.941903i | \(0.390964\pi\) | |||||||
\(488\) | 2.31175 | 0.104648 | ||||||||
\(489\) | −18.4759 | + | 1.69078i | −0.835509 | + | 0.0764599i | ||||
\(490\) | 15.7556i | 0.711767i | ||||||||
\(491\) | − | 39.8929i | − | 1.80034i | −0.435536 | − | 0.900171i | \(-0.643441\pi\) | ||
0.435536 | − | 0.900171i | \(-0.356559\pi\) | |||||||
\(492\) | 1.37411 | + | 15.0155i | 0.0619496 | + | 0.676950i | ||||
\(493\) | 9.17208i | 0.413090i | ||||||||
\(494\) | −18.1111 | −0.814857 | ||||||||
\(495\) | 16.7797 | − | 3.09706i | 0.754193 | − | 0.139202i | ||||
\(496\) | 7.74501 | 0.347761 | ||||||||
\(497\) | 7.62303 | 0.341940 | ||||||||
\(498\) | 2.33347 | + | 25.4989i | 0.104566 | + | 1.14263i | ||||
\(499\) | −19.4748 | −0.871811 | −0.435906 | − | 0.899992i | \(-0.643572\pi\) | ||||
−0.435906 | + | 0.899992i | \(0.643572\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0.0259715 | + | 0.283801i | 0.00116032 | + | 0.0126793i | ||||
\(502\) | 13.8819i | 0.619577i | ||||||||
\(503\) | −30.4466 | −1.35755 | −0.678774 | − | 0.734348i | \(-0.737488\pi\) | ||||
−0.678774 | + | 0.734348i | \(0.737488\pi\) | |||||||
\(504\) | −14.0732 | + | 2.59750i | −0.626868 | + | 0.115702i | ||||
\(505\) | − | 7.33256i | − | 0.326294i | ||||||
\(506\) | 26.3798 | + | 6.93950i | 1.17273 | + | 0.308498i | ||||
\(507\) | 36.8688 | − | 3.37397i | 1.63740 | − | 0.149843i | ||||
\(508\) | 1.86527 | 0.0827580 | ||||||||
\(509\) | − | 3.89849i | − | 0.172798i | −0.996261 | − | 0.0863988i | \(-0.972464\pi\) | ||
0.996261 | − | 0.0863988i | \(-0.0275359\pi\) | |||||||
\(510\) | 0.310200 | + | 3.38968i | 0.0137359 | + | 0.150098i | ||||
\(511\) | 15.5308i | 0.687040i | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.33972 | + | 15.4533i | 0.191603 | + | 0.682280i | ||||
\(514\) | −14.6251 | −0.645083 | ||||||||
\(515\) | 9.24100i | 0.407207i | ||||||||
\(516\) | 1.22453 | + | 13.3810i | 0.0539071 | + | 0.589066i | ||||
\(517\) | − | 48.6571i | − | 2.13994i | ||||||
\(518\) | 14.9781i | 0.658099i | ||||||||
\(519\) | 0.695406 | + | 7.59899i | 0.0305249 | + | 0.333559i | ||||
\(520\) | − | 5.86303i | − | 0.257111i | ||||||
\(521\) | −13.7197 | −0.601072 | −0.300536 | − | 0.953770i | \(-0.597166\pi\) | ||||
−0.300536 | + | 0.953770i | \(0.597166\pi\) | |||||||
\(522\) | −13.7691 | + | 2.54138i | −0.602657 | + | 0.111233i | ||||
\(523\) | 23.2611i | 1.01714i | 0.861022 | + | 0.508568i | \(0.169825\pi\) | ||||
−0.861022 | + | 0.508568i | \(0.830175\pi\) | |||||||
\(524\) | − | 16.7197i | − | 0.730403i | ||||||
\(525\) | 0.752968 | + | 8.22800i | 0.0328622 | + | 0.359099i | ||||
\(526\) | − | 13.7157i | − | 0.598031i | ||||||
\(527\) | −15.2206 | −0.663020 | ||||||||
\(528\) | 9.81042 | − | 0.897780i | 0.426944 | − | 0.0390708i | ||||
\(529\) | −20.0228 | − | 11.3176i | −0.870556 | − | 0.492070i | ||||
\(530\) | 2.37670i | 0.103237i | ||||||||
\(531\) | −1.34826 | − | 7.30479i | −0.0585093 | − | 0.317001i | ||||
\(532\) | 14.7356 | 0.638868 | ||||||||
\(533\) | 51.0401i | 2.21079i | ||||||||
\(534\) | 1.17247 | + | 12.8121i | 0.0507379 | + | 0.554435i | ||||
\(535\) | −4.05749 | −0.175421 | ||||||||
\(536\) | 9.67337 | 0.417826 | ||||||||
\(537\) | 3.45378 | + | 37.7409i | 0.149042 | + | 1.62864i | ||||
\(538\) | −31.3415 | −1.35123 | ||||||||
\(539\) | −89.6136 | −3.85993 | ||||||||
\(540\) | −5.00263 | + | 1.40488i | −0.215279 | + | 0.0604563i | ||||
\(541\) | −20.3714 | −0.875837 | −0.437918 | − | 0.899015i | \(-0.644284\pi\) | ||||
−0.437918 | + | 0.899015i | \(0.644284\pi\) | |||||||
\(542\) | 4.59208i | 0.197247i | ||||||||
\(543\) | 2.06254 | + | 22.5382i | 0.0885119 | + | 0.967207i | ||||
\(544\) | 1.96521i | 0.0842578i | ||||||||
\(545\) | 12.2955i | 0.526680i | ||||||||
\(546\) | −48.2410 | + | 4.41467i | −2.06453 | + | 0.188931i | ||||
\(547\) | 22.9836 | 0.982706 | 0.491353 | − | 0.870960i | \(-0.336502\pi\) | ||||
0.491353 | + | 0.870960i | \(0.336502\pi\) | |||||||
\(548\) | −8.27644 | −0.353552 | ||||||||
\(549\) | −1.25879 | − | 6.82005i | −0.0537237 | − | 0.291072i | ||||
\(550\) | − | 5.68772i | − | 0.242525i | ||||||
\(551\) | 14.4172 | 0.614194 | ||||||||
\(552\) | −8.19247 | − | 1.37236i | −0.348695 | − | 0.0584117i | ||||
\(553\) | −29.5499 | −1.25659 | ||||||||
\(554\) | 14.1389i | 0.600704i | ||||||||
\(555\) | 0.495614 | + | 5.41579i | 0.0210377 | + | 0.229887i | ||||
\(556\) | −1.92339 | −0.0815698 | ||||||||
\(557\) | −28.2412 | −1.19662 | −0.598310 | − | 0.801265i | \(-0.704161\pi\) | ||||
−0.598310 | + | 0.801265i | \(0.704161\pi\) | |||||||
\(558\) | −4.21729 | − | 22.8491i | −0.178532 | − | 0.967280i | ||||
\(559\) | 45.4843i | 1.92378i | ||||||||
\(560\) | 4.77029i | 0.201581i | ||||||||
\(561\) | −19.2796 | + | 1.76433i | −0.813983 | + | 0.0744900i | ||||
\(562\) | 6.36108i | 0.268326i | ||||||||
\(563\) | 26.5126 | 1.11737 | 0.558687 | − | 0.829379i | \(-0.311305\pi\) | ||||
0.558687 | + | 0.829379i | \(0.311305\pi\) | |||||||
\(564\) | 1.35033 | + | 14.7556i | 0.0568592 | + | 0.621324i | ||||
\(565\) | 16.8426 | 0.708573 | ||||||||
\(566\) | −26.0151 | −1.09349 | ||||||||
\(567\) | 15.3262 | + | 40.1038i | 0.643638 | + | 1.68420i | ||||
\(568\) | 1.59802 | 0.0670516 | ||||||||
\(569\) | 27.8748 | 1.16857 | 0.584285 | − | 0.811548i | \(-0.301375\pi\) | ||||
0.584285 | + | 0.811548i | \(0.301375\pi\) | |||||||
\(570\) | 5.32810 | − | 0.487590i | 0.223170 | − | 0.0204229i | ||||
\(571\) | 40.1603i | 1.68066i | 0.542077 | + | 0.840329i | \(0.317638\pi\) | ||||
−0.542077 | + | 0.840329i | \(0.682362\pi\) | |||||||
\(572\) | 33.3473 | 1.39432 | ||||||||
\(573\) | −10.6234 | + | 0.972175i | −0.443797 | + | 0.0406132i | ||||
\(574\) | − | 41.5273i | − | 1.73332i | ||||||
\(575\) | −1.22009 | + | 4.63804i | −0.0508811 | + | 0.193420i | ||||
\(576\) | −2.95017 | + | 0.544517i | −0.122924 | + | 0.0226882i | ||||
\(577\) | 12.9838 | 0.540523 | 0.270261 | − | 0.962787i | \(-0.412890\pi\) | ||||
0.270261 | + | 0.962787i | \(0.412890\pi\) | |||||||
\(578\) | 13.1379i | 0.546466i | ||||||||
\(579\) | 12.3599 | − | 1.13109i | 0.513660 | − | 0.0470065i | ||||
\(580\) | 4.66722i | 0.193796i | ||||||||
\(581\) | − | 70.5206i | − | 2.92569i | ||||||
\(582\) | −11.4758 | + | 1.05018i | −0.475686 | + | 0.0435314i | ||||
\(583\) | −13.5180 | −0.559858 | ||||||||
\(584\) | 3.25573i | 0.134723i | ||||||||
\(585\) | −17.2969 | + | 3.19252i | −0.715140 | + | 0.131995i | ||||
\(586\) | 8.44627i | 0.348912i | ||||||||
\(587\) | 26.6529i | 1.10008i | 0.835137 | + | 0.550041i | \(0.185388\pi\) | ||||
−0.835137 | + | 0.550041i | \(0.814612\pi\) | |||||||
\(588\) | 27.1760 | − | 2.48695i | 1.12072 | − | 0.102560i | ||||
\(589\) | 23.9246i | 0.985797i | ||||||||
\(590\) | −2.47606 | −0.101938 | ||||||||
\(591\) | 0.940654 | + | 10.2789i | 0.0386933 | + | 0.422818i | ||||
\(592\) | 3.13987i | 0.129048i | ||||||||
\(593\) | − | 13.5281i | − | 0.555534i | −0.960648 | − | 0.277767i | \(-0.910406\pi\) | ||
0.960648 | − | 0.277767i | \(-0.0895943\pi\) | |||||||
\(594\) | −7.99054 | − | 28.4535i | −0.327856 | − | 1.16746i | ||||
\(595\) | − | 9.37463i | − | 0.384322i | ||||||
\(596\) | 15.1957 | 0.622439 | ||||||||
\(597\) | −2.12984 | − | 23.2737i | −0.0871686 | − | 0.952529i | ||||
\(598\) | −27.1930 | − | 7.15340i | −1.11200 | − | 0.292524i | ||||
\(599\) | 8.13093i | 0.332221i | 0.986107 | + | 0.166110i | \(0.0531208\pi\) | ||||
−0.986107 | + | 0.166110i | \(0.946879\pi\) | |||||||
\(600\) | 0.157845 | + | 1.72484i | 0.00644401 | + | 0.0704164i | ||||
\(601\) | −1.00715 | −0.0410827 | −0.0205413 | − | 0.999789i | \(-0.506539\pi\) | ||||
−0.0205413 | + | 0.999789i | \(0.506539\pi\) | |||||||
\(602\) | − | 37.0070i | − | 1.50829i | ||||||
\(603\) | −5.26732 | − | 28.5381i | −0.214502 | − | 1.16216i | ||||
\(604\) | −8.73197 | −0.355299 | ||||||||
\(605\) | 21.3501 | 0.868005 | ||||||||
\(606\) | −12.6475 | + | 1.15741i | −0.513770 | + | 0.0470166i | ||||
\(607\) | −32.1949 | −1.30675 | −0.653375 | − | 0.757034i | \(-0.726648\pi\) | ||||
−0.653375 | + | 0.757034i | \(0.726648\pi\) | |||||||
\(608\) | 3.08903 | 0.125277 | ||||||||
\(609\) | 38.4019 | − | 3.51427i | 1.55612 | − | 0.142405i | ||||
\(610\) | −2.31175 | −0.0935999 | ||||||||
\(611\) | 50.1569i | 2.02913i | ||||||||
\(612\) | 5.79771 | − | 1.07009i | 0.234358 | − | 0.0432559i | ||||
\(613\) | − | 24.0591i | − | 0.971739i | −0.874031 | − | 0.485869i | \(-0.838503\pi\) | ||
0.874031 | − | 0.485869i | \(-0.161497\pi\) | |||||||
\(614\) | 8.46953i | 0.341802i | ||||||||
\(615\) | −1.37411 | − | 15.0155i | −0.0554094 | − | 0.605482i | ||||
\(616\) | −27.1320 | −1.09318 | ||||||||
\(617\) | −10.6333 | −0.428081 | −0.214041 | − | 0.976825i | \(-0.568662\pi\) | ||||
−0.214041 | + | 0.976825i | \(0.568662\pi\) | |||||||
\(618\) | 15.9393 | − | 1.45865i | 0.641172 | − | 0.0586755i | ||||
\(619\) | 12.3292i | 0.495553i | 0.968817 | + | 0.247776i | \(0.0796999\pi\) | ||||
−0.968817 | + | 0.247776i | \(0.920300\pi\) | |||||||
\(620\) | −7.74501 | −0.311047 | ||||||||
\(621\) | 0.412237 | + | 24.9165i | 0.0165425 | + | 0.999863i | ||||
\(622\) | 16.1616 | 0.648023 | ||||||||
\(623\) | − | 35.4337i | − | 1.41962i | ||||||
\(624\) | −10.1128 | + | 0.925453i | −0.404837 | + | 0.0370478i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.86741 | −0.274477 | ||||||||
\(627\) | 2.77327 | + | 30.3047i | 0.110754 | + | 1.21025i | ||||
\(628\) | 1.95674i | 0.0780826i | ||||||||
\(629\) | − | 6.17051i | − | 0.246034i | ||||||
\(630\) | 14.0732 | − | 2.59750i | 0.560688 | − | 0.103487i | ||||
\(631\) | 9.73351i | 0.387485i | 0.981052 | + | 0.193742i | \(0.0620626\pi\) | ||||
−0.981052 | + | 0.193742i | \(0.937937\pi\) | |||||||
\(632\) | −6.19457 | −0.246407 | ||||||||
\(633\) | −11.2313 | + | 1.02780i | −0.446402 | + | 0.0408516i | ||||
\(634\) | 18.7231 | 0.743589 | ||||||||
\(635\) | −1.86527 | −0.0740210 | ||||||||
\(636\) | 4.09944 | − | 0.375151i | 0.162553 | − | 0.0148757i | ||||
\(637\) | 92.3758 | 3.66006 | ||||||||
\(638\) | −26.5458 | −1.05096 | ||||||||
\(639\) | −0.870151 | − | 4.71444i | −0.0344226 | − | 0.186500i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | −37.1576 | −1.46764 | −0.733819 | − | 0.679345i | \(-0.762264\pi\) | ||||
−0.733819 | + | 0.679345i | \(0.762264\pi\) | |||||||
\(642\) | 0.640456 | + | 6.99854i | 0.0252768 | + | 0.276210i | ||||
\(643\) | − | 20.5307i | − | 0.809652i | −0.914394 | − | 0.404826i | \(-0.867332\pi\) | ||
0.914394 | − | 0.404826i | \(-0.132668\pi\) | |||||||
\(644\) | 22.1248 | + | 5.82016i | 0.871838 | + | 0.229346i | ||||
\(645\) | −1.22453 | − | 13.3810i | −0.0482160 | − | 0.526876i | ||||
\(646\) | −6.07061 | −0.238845 | ||||||||
\(647\) | 10.6897i | 0.420254i | 0.977674 | + | 0.210127i | \(0.0673878\pi\) | ||||
−0.977674 | + | 0.210127i | \(0.932612\pi\) | |||||||
\(648\) | 3.21284 | + | 8.40700i | 0.126212 | + | 0.330258i | ||||
\(649\) | − | 14.0831i | − | 0.552810i | ||||||
\(650\) | 5.86303i | 0.229967i | ||||||||
\(651\) | 5.83175 | + | 63.7260i | 0.228564 | + | 2.49762i | ||||
\(652\) | 10.7116 | 0.419500 | ||||||||
\(653\) | 5.99567i | 0.234629i | 0.993095 | + | 0.117314i | \(0.0374285\pi\) | ||||
−0.993095 | + | 0.117314i | \(0.962572\pi\) | |||||||
\(654\) | 21.2078 | − | 1.94078i | 0.829289 | − | 0.0758907i | ||||
\(655\) | 16.7197i | 0.653292i | ||||||||
\(656\) | − | 8.70541i | − | 0.339889i | ||||||
\(657\) | 9.60495 | − | 1.77280i | 0.374725 | − | 0.0691635i | ||||
\(658\) | − | 40.8087i | − | 1.59089i | ||||||
\(659\) | −5.16327 | −0.201132 | −0.100566 | − | 0.994930i | \(-0.532065\pi\) | ||||
−0.100566 | + | 0.994930i | \(0.532065\pi\) | |||||||
\(660\) | −9.81042 | + | 0.897780i | −0.381870 | + | 0.0349460i | ||||
\(661\) | 0.430476i | 0.0167436i | 0.999965 | + | 0.00837179i | \(0.00266485\pi\) | ||||
−0.999965 | + | 0.00837179i | \(0.997335\pi\) | |||||||
\(662\) | − | 13.5890i | − | 0.528151i | ||||||
\(663\) | 19.8738 | − | 1.81871i | 0.771835 | − | 0.0706329i | ||||
\(664\) | − | 14.7833i | − | 0.573703i | ||||||
\(665\) | −14.7356 | −0.571421 | ||||||||
\(666\) | 9.26315 | − | 1.70971i | 0.358940 | − | 0.0662501i | ||||
\(667\) | 21.6467 | + | 5.69441i | 0.838165 | + | 0.220488i | ||||
\(668\) | − | 0.164537i | − | 0.00636614i | ||||||
\(669\) | −11.9679 | + | 1.09522i | −0.462705 | + | 0.0423435i | ||||
\(670\) | −9.67337 | −0.373715 | ||||||||
\(671\) | − | 13.1486i | − | 0.507594i | ||||||
\(672\) | 8.22800 | − | 0.752968i | 0.317402 | − | 0.0290464i | ||||
\(673\) | 43.9112 | 1.69265 | 0.846327 | − | 0.532664i | \(-0.178809\pi\) | ||||
0.846327 | + | 0.532664i | \(0.178809\pi\) | |||||||
\(674\) | 4.53301 | 0.174605 | ||||||||
\(675\) | 5.00263 | − | 1.40488i | 0.192551 | − | 0.0540738i | ||||
\(676\) | −21.3751 | −0.822121 | ||||||||
\(677\) | 27.5574 | 1.05912 | 0.529558 | − | 0.848274i | \(-0.322358\pi\) | ||||
0.529558 | + | 0.848274i | \(0.322358\pi\) | |||||||
\(678\) | −2.65852 | − | 29.0508i | −0.102100 | − | 1.11569i | ||||
\(679\) | 31.7378 | 1.21799 | ||||||||
\(680\) | − | 1.96521i | − | 0.0753624i | ||||||
\(681\) | −14.2156 | + | 1.30091i | −0.544742 | + | 0.0498509i | ||||
\(682\) | − | 44.0514i | − | 1.68682i | ||||||
\(683\) | − | 26.2484i | − | 1.00437i | −0.864761 | − | 0.502184i | \(-0.832530\pi\) | ||
0.864761 | − | 0.502184i | \(-0.167470\pi\) | |||||||
\(684\) | −1.68203 | − | 9.11318i | −0.0643141 | − | 0.348451i | ||||
\(685\) | 8.27644 | 0.316227 | ||||||||
\(686\) | −41.7669 | −1.59467 | ||||||||
\(687\) | −2.86210 | − | 31.2753i | −0.109196 | − | 1.19323i | ||||
\(688\) | − | 7.75780i | − | 0.295764i | ||||||
\(689\) | 13.9347 | 0.530869 | ||||||||
\(690\) | 8.19247 | + | 1.37236i | 0.311882 | + | 0.0522450i | ||||
\(691\) | −38.6282 | −1.46948 | −0.734742 | − | 0.678347i | \(-0.762697\pi\) | ||||
−0.734742 | + | 0.678347i | \(0.762697\pi\) | |||||||
\(692\) | − | 4.40561i | − | 0.167476i | ||||||
\(693\) | 14.7739 | + | 80.0441i | 0.561212 | + | 3.04062i | ||||
\(694\) | 7.21414 | 0.273845 | ||||||||
\(695\) | 1.92339 | 0.0729583 | ||||||||
\(696\) | 8.05022 | − | 0.736699i | 0.305143 | − | 0.0279245i | ||||
\(697\) | 17.1080i | 0.648011i | ||||||||
\(698\) | 0.988122i | 0.0374010i | ||||||||
\(699\) | −1.42343 | − | 15.5545i | −0.0538392 | − | 0.588324i | ||||
\(700\) | − | 4.77029i | − | 0.180300i | ||||||
\(701\) | −33.5349 | −1.26659 | −0.633297 | − | 0.773909i | \(-0.718299\pi\) | ||||
−0.633297 | + | 0.773909i | \(0.718299\pi\) | |||||||
\(702\) | 8.23684 | + | 29.3306i | 0.310880 | + | 1.10701i | ||||
\(703\) | −9.69917 | −0.365811 | ||||||||
\(704\) | −5.68772 | −0.214364 | ||||||||
\(705\) | −1.35033 | − | 14.7556i | −0.0508564 | − | 0.555729i | ||||
\(706\) | 12.2940 | 0.462690 | ||||||||
\(707\) | 34.9784 | 1.31550 | ||||||||
\(708\) | 0.390834 | + | 4.27081i | 0.0146884 | + | 0.160507i | ||||
\(709\) | 38.3106i | 1.43879i | 0.694604 | + | 0.719393i | \(0.255580\pi\) | ||||
−0.694604 | + | 0.719393i | \(0.744420\pi\) | |||||||
\(710\) | −1.59802 | −0.0599727 | ||||||||
\(711\) | 3.37305 | + | 18.2750i | 0.126499 | + | 0.685367i | ||||
\(712\) | − | 7.42799i | − | 0.278376i | ||||||
\(713\) | −9.44958 | + | 35.9217i | −0.353890 | + | 1.34528i | ||||
\(714\) | −16.1698 | + | 1.47974i | −0.605138 | + | 0.0553779i | ||||
\(715\) | −33.3473 | −1.24712 | ||||||||
\(716\) | − | 21.8808i | − | 0.817723i | ||||||
\(717\) | −4.15001 | − | 45.3489i | −0.154985 | − | 1.69359i | ||||
\(718\) | 0.189672i | 0.00707851i | ||||||||
\(719\) | − | 17.1239i | − | 0.638612i | −0.947652 | − | 0.319306i | \(-0.896550\pi\) | ||
0.947652 | − | 0.319306i | \(-0.103450\pi\) | |||||||
\(720\) | 2.95017 | − | 0.544517i | 0.109946 | − | 0.0202930i | ||||
\(721\) | −44.0822 | −1.64171 | ||||||||
\(722\) | − | 9.45787i | − | 0.351985i | ||||||
\(723\) | 0.962646 | + | 10.5192i | 0.0358012 | + | 0.391215i | ||||
\(724\) | − | 13.0668i | − | 0.485624i | ||||||
\(725\) | − | 4.66722i | − | 0.173336i | ||||||
\(726\) | −3.37002 | − | 36.8256i | −0.125073 | − | 1.36673i | ||||
\(727\) | − | 29.1589i | − | 1.08144i | −0.841201 | − | 0.540722i | \(-0.818151\pi\) | ||
0.841201 | − | 0.540722i | \(-0.181849\pi\) | |||||||
\(728\) | 27.9683 | 1.03658 | ||||||||
\(729\) | 23.0526 | − | 14.0562i | 0.853801 | − | 0.520599i | ||||
\(730\) | − | 3.25573i | − | 0.120500i | ||||||
\(731\) | 15.2457i | 0.563884i | ||||||||
\(732\) | 0.364899 | + | 3.98740i | 0.0134870 | + | 0.147379i | ||||
\(733\) | − | 19.6633i | − | 0.726282i | −0.931734 | − | 0.363141i | \(-0.881704\pi\) | ||
0.931734 | − | 0.363141i | \(-0.118296\pi\) | |||||||
\(734\) | −20.2545 | −0.747607 | ||||||||
\(735\) | −27.1760 | + | 2.48695i | −1.00240 | + | 0.0917327i | ||||
\(736\) | 4.63804 | + | 1.22009i | 0.170960 | + | 0.0449729i | ||||
\(737\) | − | 55.0194i | − | 2.02667i | ||||||
\(738\) | −25.6824 | + | 4.74025i | −0.945384 | + | 0.174491i | ||||
\(739\) | 2.45920 | 0.0904632 | 0.0452316 | − | 0.998977i | \(-0.485597\pi\) | ||||
0.0452316 | + | 0.998977i | \(0.485597\pi\) | |||||||
\(740\) | − | 3.13987i | − | 0.115424i | ||||||
\(741\) | −2.85876 | − | 31.2388i | −0.105019 | − | 1.14759i | ||||
\(742\) | −11.3375 | −0.416214 | ||||||||
\(743\) | −30.2633 | −1.11025 | −0.555127 | − | 0.831765i | \(-0.687330\pi\) | ||||
−0.555127 | + | 0.831765i | \(0.687330\pi\) | |||||||
\(744\) | 1.22251 | + | 13.3589i | 0.0448196 | + | 0.489762i | ||||
\(745\) | −15.1957 | −0.556726 | ||||||||
\(746\) | 31.1346 | 1.13992 | ||||||||
\(747\) | −43.6132 | + | 8.04976i | −1.59572 | + | 0.294525i | ||||
\(748\) | 11.1776 | 0.408692 | ||||||||
\(749\) | − | 19.3554i | − | 0.707231i | ||||||
\(750\) | −0.157845 | − | 1.72484i | −0.00576370 | − | 0.0629824i | ||||
\(751\) | 20.4106i | 0.744794i | 0.928074 | + | 0.372397i | \(0.121464\pi\) | ||||
−0.928074 | + | 0.372397i | \(0.878536\pi\) | |||||||
\(752\) | − | 8.55477i | − | 0.311960i | ||||||
\(753\) | −23.9440 | + | 2.19119i | −0.872569 | + | 0.0798513i | ||||
\(754\) | 27.3641 | 0.996540 | ||||||||
\(755\) | 8.73197 | 0.317789 | ||||||||
\(756\) | −6.70167 | − | 23.8640i | −0.243737 | − | 0.867925i | ||||
\(757\) | 14.2385i | 0.517507i | 0.965943 | + | 0.258754i | \(0.0833118\pi\) | ||||
−0.965943 | + | 0.258754i | \(0.916688\pi\) | |||||||
\(758\) | −21.8934 | −0.795205 | ||||||||
\(759\) | −7.80561 | + | 46.5965i | −0.283326 | + | 1.69134i | ||||
\(760\) | −3.08903 | −0.112051 | ||||||||
\(761\) | − | 26.2699i | − | 0.952284i | −0.879368 | − | 0.476142i | \(-0.842035\pi\) | ||
0.879368 | − | 0.476142i | \(-0.157965\pi\) | |||||||
\(762\) | 0.294424 | + | 3.21730i | 0.0106659 | + | 0.116551i | ||||
\(763\) | −58.6529 | −2.12338 | ||||||||
\(764\) | 6.15903 | 0.222826 | ||||||||
\(765\) | −5.79771 | + | 1.07009i | −0.209617 | + | 0.0386892i | ||||
\(766\) | − | 20.5229i | − | 0.741521i | ||||||
\(767\) | 14.5172i | 0.524186i | ||||||||
\(768\) | 1.72484 | − | 0.157845i | 0.0622399 | − | 0.00569576i | ||||
\(769\) | − | 16.3030i | − | 0.587902i | −0.955820 | − | 0.293951i | \(-0.905030\pi\) | ||
0.955820 | − | 0.293951i | \(-0.0949703\pi\) | |||||||
\(770\) | 27.1320 | 0.977771 | ||||||||
\(771\) | −2.30850 | − | 25.2259i | −0.0831385 | − | 0.908489i | ||||
\(772\) | −7.16580 | −0.257903 | ||||||||
\(773\) | 17.7749 | 0.639320 | 0.319660 | − | 0.947532i | \(-0.396431\pi\) | ||||
0.319660 | + | 0.947532i | \(0.396431\pi\) | |||||||
\(774\) | −22.8868 | + | 4.22426i | −0.822650 | + | 0.151838i | ||||
\(775\) | 7.74501 | 0.278209 | ||||||||
\(776\) | 6.65323 | 0.238837 | ||||||||
\(777\) | −25.8349 | + | 2.36422i | −0.926820 | + | 0.0848160i | ||||
\(778\) | 6.78101i | 0.243111i | ||||||||
\(779\) | 26.8913 | 0.963482 | ||||||||
\(780\) | 10.1128 | − | 0.925453i | 0.362097 | − | 0.0331365i | ||||
\(781\) | − | 9.08910i | − | 0.325234i | ||||||
\(782\) | −9.11473 | − | 2.39773i | −0.325942 | − | 0.0857425i | ||||
\(783\) | −6.55687 | − | 23.3484i | −0.234324 | − | 0.834403i | ||||
\(784\) | −15.7556 | −0.562701 | ||||||||
\(785\) | − | 1.95674i | − | 0.0698392i | ||||||
\(786\) | 28.8388 | − | 2.63913i | 1.02865 | − | 0.0941345i | ||||
\(787\) | 19.0599i | 0.679413i | 0.940531 | + | 0.339707i | \(0.110328\pi\) | ||||
−0.940531 | + | 0.339707i | \(0.889672\pi\) | |||||||
\(788\) | − | 5.95934i | − | 0.212293i | ||||||
\(789\) | 23.6574 | − | 2.16495i | 0.842225 | − | 0.0770744i | ||||
\(790\) | 6.19457 | 0.220393 | ||||||||
\(791\) | 80.3440i | 2.85670i | ||||||||
\(792\) | 3.09706 | + | 16.7797i | 0.110049 | + | 0.596242i | ||||
\(793\) | 13.5538i | 0.481311i | ||||||||
\(794\) | 10.4669i | 0.371457i | ||||||||
\(795\) | −4.09944 | + | 0.375151i | −0.145392 | + | 0.0133052i | ||||
\(796\) | 13.4932i | 0.478254i | ||||||||
\(797\) | −33.4483 | −1.18480 | −0.592399 | − | 0.805645i | \(-0.701819\pi\) | ||||
−0.592399 | + | 0.805645i | \(0.701819\pi\) | |||||||
\(798\) | 2.32594 | + | 25.4166i | 0.0823375 | + | 0.899737i | ||||
\(799\) | 16.8119i | 0.594764i | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −21.9138 | + | 4.04467i | −0.774287 | + | 0.142911i | ||||
\(802\) | − | 6.92220i | − | 0.244431i | ||||||
\(803\) | 18.5177 | 0.653474 | ||||||||
\(804\) | 1.52690 | + | 16.6851i | 0.0538495 | + | 0.588436i | ||||
\(805\) | −22.1248 | − | 5.82016i | −0.779796 | − | 0.205134i | ||||
\(806\) | 45.4093i | 1.59947i | ||||||||
\(807\) | −4.94711 | − | 54.0591i | −0.174146 | − | 1.90297i | ||||
\(808\) | 7.33256 | 0.257958 | ||||||||
\(809\) | 28.3635i | 0.997208i | 0.866830 | + | 0.498604i | \(0.166154\pi\) | ||||
−0.866830 | + | 0.498604i | \(0.833846\pi\) | |||||||
\(810\) | −3.21284 | − | 8.40700i | −0.112888 | − | 0.295392i | ||||
\(811\) | −3.46425 | −0.121646 | −0.0608232 | − | 0.998149i | \(-0.519373\pi\) | ||||
−0.0608232 | + | 0.998149i | \(0.519373\pi\) | |||||||
\(812\) | −22.2640 | −0.781313 | ||||||||
\(813\) | −7.92063 | + | 0.724839i | −0.277788 | + | 0.0254212i | ||||
\(814\) | 17.8587 | 0.625947 | ||||||||
\(815\) | −10.7116 | −0.375213 | ||||||||
\(816\) | −3.38968 | + | 0.310200i | −0.118663 | + | 0.0108592i | ||||
\(817\) | 23.9641 | 0.838399 | ||||||||
\(818\) | 0.551195i | 0.0192721i | ||||||||
\(819\) | −15.2292 | − | 82.5114i | −0.532153 | − | 2.88318i | ||||
\(820\) | 8.70541i | 0.304006i | ||||||||
\(821\) | − | 5.03757i | − | 0.175812i | −0.996129 | − | 0.0879062i | \(-0.971982\pi\) | ||
0.996129 | − | 0.0879062i | \(-0.0280176\pi\) | |||||||
\(822\) | −1.30640 | − | 14.2756i | −0.0455659 | − | 0.497918i | ||||
\(823\) | −8.76482 | −0.305522 | −0.152761 | − | 0.988263i | \(-0.548817\pi\) | ||||
−0.152761 | + | 0.988263i | \(0.548817\pi\) | |||||||
\(824\) | −9.24100 | −0.321925 | ||||||||
\(825\) | 9.81042 | − | 0.897780i | 0.341555 | − | 0.0312567i | ||||
\(826\) | − | 11.8115i | − | 0.410975i | ||||||
\(827\) | 35.4433 | 1.23249 | 0.616243 | − | 0.787556i | \(-0.288654\pi\) | ||||
0.616243 | + | 0.787556i | \(0.288654\pi\) | |||||||
\(828\) | 1.07397 | − | 14.3474i | 0.0373230 | − | 0.498605i | ||||
\(829\) | 36.1702 | 1.25624 | 0.628121 | − | 0.778116i | \(-0.283824\pi\) | ||||
0.628121 | + | 0.778116i | \(0.283824\pi\) | |||||||
\(830\) | 14.7833i | 0.513136i | ||||||||
\(831\) | −24.3874 | + | 2.23176i | −0.845989 | + | 0.0774189i | ||||
\(832\) | 5.86303 | 0.203264 | ||||||||
\(833\) | 30.9632 | 1.07281 | ||||||||
\(834\) | −0.303598 | − | 3.31754i | −0.0105127 | − | 0.114877i | ||||
\(835\) | 0.164537i | 0.00569405i | ||||||||
\(836\) | − | 17.5695i | − | 0.607656i | ||||||
\(837\) | 38.7455 | − | 10.8808i | 1.33924 | − | 0.376095i | ||||
\(838\) | − | 29.7594i | − | 1.02802i | ||||||
\(839\) | −36.2195 | −1.25044 | −0.625219 | − | 0.780450i | \(-0.714990\pi\) | ||||
−0.625219 | + | 0.780450i | \(0.714990\pi\) | |||||||
\(840\) | −8.22800 | + | 0.752968i | −0.283893 | + | 0.0259799i | ||||
\(841\) | 7.21706 | 0.248864 | ||||||||
\(842\) | 25.4818 | 0.878161 | ||||||||
\(843\) | −10.9719 | + | 1.00407i | −0.377891 | + | 0.0345819i | ||||
\(844\) | 6.51146 | 0.224134 | ||||||||
\(845\) | 21.3751 | 0.735327 | ||||||||
\(846\) | −25.2380 | + | 4.65822i | −0.867701 | + | 0.160153i | ||||
\(847\) | 101.846i | 3.49947i | ||||||||
\(848\) | −2.37670 | −0.0816163 | ||||||||
\(849\) | −4.10636 | − | 44.8719i | −0.140930 | − | 1.54000i | ||||
\(850\) | 1.96521i | 0.0674062i | ||||||||
\(851\) | −14.5628 | − | 3.83091i | −0.499208 | − | 0.131322i | ||||
\(852\) | 0.252241 | + | 2.75634i | 0.00864162 | + | 0.0944306i | ||||
\(853\) | 30.6307 | 1.04878 | 0.524388 | − | 0.851479i | \(-0.324294\pi\) | ||||
0.524388 | + | 0.851479i | \(0.324294\pi\) | |||||||
\(854\) | − | 11.0277i | − | 0.377360i | ||||||
\(855\) | 1.68203 | + | 9.11318i | 0.0575243 | + | 0.311664i | ||||
\(856\) | − | 4.05749i | − | 0.138682i | ||||||
\(857\) | 46.9029i | 1.60217i | 0.598548 | + | 0.801087i | \(0.295745\pi\) | ||||
−0.598548 | + | 0.801087i | \(0.704255\pi\) | |||||||
\(858\) | 5.26371 | + | 57.5188i | 0.179700 | + | 1.96366i | ||||
\(859\) | 41.8557 | 1.42810 | 0.714049 | − | 0.700096i | \(-0.246860\pi\) | ||||
0.714049 | + | 0.700096i | \(0.246860\pi\) | |||||||
\(860\) | 7.75780i | 0.264539i | ||||||||
\(861\) | 71.6281 | − | 6.55490i | 2.44108 | − | 0.223390i | ||||
\(862\) | − | 25.7344i | − | 0.876517i | ||||||
\(863\) | 36.8163i | 1.25324i | 0.779325 | + | 0.626620i | \(0.215562\pi\) | ||||
−0.779325 | + | 0.626620i | \(0.784438\pi\) | |||||||
\(864\) | −1.40488 | − | 5.00263i | −0.0477949 | − | 0.170193i | ||||
\(865\) | 4.40561i | 0.149795i | ||||||||
\(866\) | 39.5558 | 1.34416 | ||||||||
\(867\) | −22.6609 | + | 2.07376i | −0.769604 | + | 0.0704287i | ||||
\(868\) | − | 36.9459i | − | 1.25403i | ||||||
\(869\) | 35.2329i | 1.19520i | ||||||||
\(870\) | −8.05022 | + | 0.736699i | −0.272928 | + | 0.0249764i | ||||
\(871\) | 56.7153i | 1.92172i | ||||||||
\(872\) | −12.2955 | −0.416377 | ||||||||
\(873\) | −3.62280 | − | 19.6282i | −0.122613 | − | 0.664313i | ||||
\(874\) | −3.76889 | + | 14.3271i | −0.127484 | + | 0.484620i | ||||
\(875\) | 4.77029i | 0.161265i | ||||||||
\(876\) | −5.61562 | + | 0.513902i | −0.189734 | + | 0.0173631i | ||||
\(877\) | −25.1591 | −0.849563 | −0.424781 | − | 0.905296i | \(-0.639649\pi\) | ||||
−0.424781 | + | 0.905296i | \(0.639649\pi\) | |||||||
\(878\) | − | 12.4645i | − | 0.420658i | ||||||
\(879\) | −14.5685 | + | 1.33321i | −0.491383 | + | 0.0449679i | ||||
\(880\) | 5.68772 | 0.191733 | ||||||||
\(881\) | −57.3451 | −1.93201 | −0.966003 | − | 0.258529i | \(-0.916762\pi\) | ||||
−0.966003 | + | 0.258529i | \(0.916762\pi\) | |||||||
\(882\) | 8.57922 | + | 46.4818i | 0.288877 | + | 1.56512i | ||||
\(883\) | 28.7600 | 0.967851 | 0.483925 | − | 0.875109i | \(-0.339211\pi\) | ||||
0.483925 | + | 0.875109i | \(0.339211\pi\) | |||||||
\(884\) | −11.5221 | −0.387530 | ||||||||
\(885\) | −0.390834 | − | 4.27081i | −0.0131377 | − | 0.143562i | ||||
\(886\) | 12.1118 | 0.406905 | ||||||||
\(887\) | 29.1696i | 0.979421i | 0.871885 | + | 0.489710i | \(0.162898\pi\) | ||||
−0.871885 | + | 0.489710i | \(0.837102\pi\) | |||||||
\(888\) | −5.41579 | + | 0.495614i | −0.181742 | + | 0.0166317i | ||||
\(889\) | − | 8.89788i | − | 0.298425i | ||||||
\(890\) | 7.42799i | 0.248987i | ||||||||
\(891\) | 47.8166 | − | 18.2737i | 1.60192 | − | 0.612192i | ||||
\(892\) | 6.93854 | 0.232319 | ||||||||
\(893\) | 26.4260 | 0.884312 | ||||||||
\(894\) | 2.39857 | + | 26.2101i | 0.0802200 | + | 0.876598i | ||||
\(895\) | 21.8808i | 0.731394i | ||||||||
\(896\) | −4.77029 | −0.159364 | ||||||||
\(897\) | 8.04621 | − | 48.0327i | 0.268655 | − | 1.60377i | ||||
\(898\) | 15.0035 | 0.500674 | ||||||||
\(899\) | − | 36.1477i | − | 1.20559i | ||||||
\(900\) | −2.95017 | + | 0.544517i | −0.0983390 | + | 0.0181506i | ||||
\(901\) | 4.67072 | 0.155604 | ||||||||
\(902\) | −49.5139 | −1.64863 | ||||||||
\(903\) | 63.8312 | − | 5.84138i | 2.12417 | − | 0.194389i | ||||
\(904\) | 16.8426i | 0.560176i | ||||||||
\(905\) | 13.0668i | 0.434355i | ||||||||
\(906\) | −1.37830 | − | 15.0613i | −0.0457910 | − | 0.500378i | ||||
\(907\) | − | 55.0564i | − | 1.82812i | −0.405583 | − | 0.914058i | \(-0.632931\pi\) | ||
0.405583 | − | 0.914058i | \(-0.367069\pi\) | |||||||
\(908\) | 8.24167 | 0.273509 | ||||||||
\(909\) | −3.99270 | − | 21.6323i | −0.132430 | − | 0.717498i | ||||
\(910\) | −27.9683 | −0.927142 | ||||||||
\(911\) | −24.5235 | −0.812499 | −0.406249 | − | 0.913762i | \(-0.633164\pi\) | ||||
−0.406249 | + | 0.913762i | \(0.633164\pi\) | |||||||
\(912\) | 0.487590 | + | 5.32810i | 0.0161457 | + | 0.176431i | ||||
\(913\) | −84.0832 | −2.78275 | ||||||||
\(914\) | 1.63920 | 0.0542199 | ||||||||
\(915\) | −0.364899 | − | 3.98740i | −0.0120632 | − | 0.131819i | ||||
\(916\) | 18.1323i | 0.599107i | ||||||||
\(917\) | −79.7577 | −2.63383 | ||||||||
\(918\) | 2.76088 | + | 9.83123i | 0.0911227 | + | 0.324479i | ||||
\(919\) | 3.64383i | 0.120199i | 0.998192 | + | 0.0600994i | \(0.0191418\pi\) | ||||
−0.998192 | + | 0.0600994i | \(0.980858\pi\) | |||||||
\(920\) | −4.63804 | − | 1.22009i | −0.152912 | − | 0.0402250i | ||||
\(921\) | −14.6086 | + | 1.33688i | −0.481370 | + | 0.0440516i | ||||
\(922\) | 11.3693 | 0.374428 | ||||||||
\(923\) | 9.36926i | 0.308393i | ||||||||
\(924\) | −4.28267 | − | 46.7985i | −0.140889 | − | 1.53956i | ||||
\(925\) | 3.13987i | 0.103238i | ||||||||
\(926\) | − | 33.7826i | − | 1.11017i | ||||||
\(927\) | 5.03188 | + | 27.2625i | 0.165269 | + | 0.895418i | ||||
\(928\) | −4.66722 | −0.153209 | ||||||||
\(929\) | 39.8886i | 1.30870i | 0.756191 | + | 0.654351i | \(0.227058\pi\) | ||||
−0.756191 | + | 0.654351i | \(0.772942\pi\) | |||||||
\(930\) | −1.22251 | − | 13.3589i | −0.0400878 | − | 0.438057i | ||||
\(931\) | − | 48.6697i | − | 1.59509i | ||||||
\(932\) | 9.01790i | 0.295391i | ||||||||
\(933\) | 2.55104 | + | 27.8763i | 0.0835173 | + | 0.912629i | ||||
\(934\) | − | 16.9801i | − | 0.555607i | ||||||
\(935\) | −11.1776 | −0.365545 | ||||||||
\(936\) | −3.19252 | − | 17.2969i | −0.104351 | − | 0.565368i | ||||
\(937\) | 0.738216i | 0.0241165i | 0.999927 | + | 0.0120582i | \(0.00383835\pi\) | ||||
−0.999927 | + | 0.0120582i | \(0.996162\pi\) | |||||||
\(938\) | − | 46.1448i | − | 1.50668i | ||||||
\(939\) | −1.08399 | − | 11.8452i | −0.0353746 | − | 0.386553i | ||||
\(940\) | 8.55477i | 0.279026i | ||||||||
\(941\) | 13.4338 | 0.437929 | 0.218965 | − | 0.975733i | \(-0.429732\pi\) | ||||
0.218965 | + | 0.975733i | \(0.429732\pi\) | |||||||
\(942\) | −3.37508 | + | 0.308863i | −0.109966 | + | 0.0100633i | ||||
\(943\) | 40.3760 | + | 10.6214i | 1.31482 | + | 0.345879i | ||||
\(944\) | − | 2.47606i | − | 0.0805888i | ||||||
\(945\) | 6.70167 | + | 23.8640i | 0.218005 | + | 0.776296i | ||||
\(946\) | −44.1242 | −1.43460 | ||||||||
\(947\) | 5.38503i | 0.174990i | 0.996165 | + | 0.0874950i | \(0.0278862\pi\) | ||||
−0.996165 | + | 0.0874950i | \(0.972114\pi\) | |||||||
\(948\) | −0.977784 | − | 10.6847i | −0.0317570 | − | 0.347022i | ||||
\(949\) | −19.0884 | −0.619637 | ||||||||
\(950\) | 3.08903 | 0.100222 | ||||||||
\(951\) | 2.95535 | + | 32.2944i | 0.0958339 | + | 1.04722i | ||||
\(952\) | 9.37463 | 0.303833 | ||||||||
\(953\) | −24.6835 | −0.799577 | −0.399788 | − | 0.916607i | \(-0.630916\pi\) | ||||
−0.399788 | + | 0.916607i | \(0.630916\pi\) | |||||||
\(954\) | 1.29415 | + | 7.01167i | 0.0418998 | + | 0.227011i | ||||
\(955\) | −6.15903 | −0.199302 | ||||||||
\(956\) | 26.2916i | 0.850331i | ||||||||
\(957\) | −4.19014 | − | 45.7874i | −0.135448 | − | 1.48010i | ||||
\(958\) | 21.1756i | 0.684154i | ||||||||
\(959\) | 39.4810i | 1.27491i | ||||||||
\(960\) | −1.72484 | + | 0.157845i | −0.0556691 | + | 0.00509444i | ||||
\(961\) | 28.9853 | 0.935008 | ||||||||
\(962\) | −18.4092 | −0.593535 | ||||||||
\(963\) | −11.9703 | + | 2.20937i | −0.385737 | + | 0.0711961i | ||||
\(964\) | − | 6.09867i | − | 0.196425i | ||||||
\(965\) | 7.16580 | 0.230675 | ||||||||
\(966\) | −6.54657 | + | 39.0804i | −0.210632 | + | 1.25739i | ||||
\(967\) | 40.9958 | 1.31834 | 0.659168 | − | 0.751996i | \(-0.270909\pi\) | ||||
0.659168 | + | 0.751996i | \(0.270909\pi\) | |||||||
\(968\) | 21.3501i | 0.686218i | ||||||||
\(969\) | −0.958217 | − | 10.4708i | −0.0307824 | − | 0.336372i | ||||
\(970\) | −6.65323 | −0.213622 | ||||||||
\(971\) | 9.66722 | 0.310236 | 0.155118 | − | 0.987896i | \(-0.450424\pi\) | ||||
0.155118 | + | 0.987896i | \(0.450424\pi\) | |||||||
\(972\) | −13.9936 | + | 6.86865i | −0.448846 | + | 0.220312i | ||||
\(973\) | 9.17511i | 0.294141i | ||||||||
\(974\) | − | 14.8247i | − | 0.475015i | ||||||
\(975\) | −10.1128 | + | 0.925453i | −0.323869 | + | 0.0296382i | ||||
\(976\) | − | 2.31175i | − | 0.0739972i | ||||||
\(977\) | 34.0227 | 1.08848 | 0.544241 | − | 0.838929i | \(-0.316818\pi\) | ||||
0.544241 | + | 0.838929i | \(0.316818\pi\) | |||||||
\(978\) | 1.69078 | + | 18.4759i | 0.0540653 | + | 0.590794i | ||||
\(979\) | −42.2483 | −1.35026 | ||||||||
\(980\) | 15.7556 | 0.503295 | ||||||||
\(981\) | 6.69510 | + | 36.2737i | 0.213758 | + | 1.15813i | ||||
\(982\) | −39.8929 | −1.27303 | ||||||||
\(983\) | −14.8967 | −0.475131 | −0.237566 | − | 0.971371i | \(-0.576350\pi\) | ||||
−0.237566 | + | 0.971371i | \(0.576350\pi\) | |||||||
\(984\) | 15.0155 | − | 1.37411i | 0.478676 | − | 0.0438050i | ||||
\(985\) | 5.95934i | 0.189880i | ||||||||
\(986\) | 9.17208 | 0.292098 | ||||||||
\(987\) | 70.3886 | − | 6.44147i | 2.24049 | − | 0.205034i | ||||
\(988\) | 18.1111i | 0.576191i | ||||||||
\(989\) | 35.9810 | + | 9.46518i | 1.14413 | + | 0.300975i | ||||
\(990\) | −3.09706 | − | 16.7797i | −0.0984310 | − | 0.533295i | ||||
\(991\) | −15.1230 | −0.480398 | −0.240199 | − | 0.970724i | \(-0.577213\pi\) | ||||
−0.240199 | + | 0.970724i | \(0.577213\pi\) | |||||||
\(992\) | − | 7.74501i | − | 0.245904i | ||||||
\(993\) | 23.4389 | − | 2.14496i | 0.743810 | − | 0.0680682i | ||||
\(994\) | − | 7.62303i | − | 0.241788i | ||||||
\(995\) | − | 13.4932i | − | 0.427764i | ||||||
\(996\) | 25.4989 | − | 2.33347i | 0.807963 | − | 0.0739390i | ||||
\(997\) | 0.414730 | 0.0131346 | 0.00656731 | − | 0.999978i | \(-0.497910\pi\) | ||||
0.00656731 | + | 0.999978i | \(0.497910\pi\) | |||||||
\(998\) | 19.4748i | 0.616464i | ||||||||
\(999\) | 4.41113 | + | 15.7076i | 0.139562 | + | 0.496967i |
(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 | 690.2.e.b.551.8 | yes | 16 | |
3.2 | odd | 2 | 690.2.e.a.551.16 | yes | 16 | ||
23.22 | odd | 2 | 690.2.e.a.551.8 | ✓ | 16 | ||
69.68 | even | 2 | inner | 690.2.e.b.551.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.8 | ✓ | 16 | 23.22 | odd | 2 | ||
690.2.e.a.551.16 | yes | 16 | 3.2 | odd | 2 | ||
690.2.e.b.551.8 | yes | 16 | 1.1 | even | 1 | trivial | |
690.2.e.b.551.16 | yes | 16 | 69.68 | even | 2 | inner |