Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(301,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.n (of order \(5\), degree \(4\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 9 x^{14} - 15 x^{13} + 44 x^{12} - 61 x^{11} + 208 x^{10} - 281 x^{9} + 851 x^{8} - 1252 x^{7} + 1929 x^{6} - 1320 x^{5} + 1261 x^{4} + 45 x^{3} + 640 x^{2} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 751.1 | ||
Root | \(-0.624800 + 1.92294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.751 |
Dual form | 825.2.n.n.301.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.63575 | + | 1.18844i | −1.15665 | + | 0.840354i | −0.989351 | − | 0.145553i | \(-0.953504\pi\) |
−0.167297 | + | 0.985906i | \(0.553504\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 0.645245 | − | 1.98586i | 0.322623 | − | 0.992931i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.63575 | + | 1.18844i | 0.667791 | + | 0.485179i | ||||
\(7\) | −0.404805 | + | 1.24586i | −0.153002 | + | 0.470891i | −0.997953 | − | 0.0639522i | \(-0.979629\pi\) |
0.844951 | + | 0.534844i | \(0.179629\pi\) | |||||||
\(8\) | 0.0550187 | + | 0.169330i | 0.0194520 | + | 0.0598672i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.83030 | − | 1.72900i | 0.853366 | − | 0.521312i | ||||
\(12\) | −2.08806 | −0.602770 | ||||||||
\(13\) | −1.57642 | + | 1.14533i | −0.437220 | + | 0.317659i | −0.784529 | − | 0.620092i | \(-0.787095\pi\) |
0.347310 | + | 0.937751i | \(0.387095\pi\) | |||||||
\(14\) | −0.818473 | − | 2.51900i | −0.218746 | − | 0.673231i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.08731 | + | 2.24306i | 0.771828 | + | 0.560766i | ||||
\(17\) | −2.45542 | − | 1.78397i | −0.595527 | − | 0.432675i | 0.248762 | − | 0.968565i | \(-0.419976\pi\) |
−0.844288 | + | 0.535889i | \(0.819976\pi\) | |||||||
\(18\) | 0.624800 | − | 1.92294i | 0.147267 | − | 0.453240i | ||||
\(19\) | −0.322858 | − | 0.993654i | −0.0740686 | − | 0.227960i | 0.907168 | − | 0.420770i | \(-0.138240\pi\) |
−0.981236 | + | 0.192810i | \(0.938240\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30998 | 0.285860 | ||||||||
\(22\) | −2.57484 | + | 6.19184i | −0.548958 | + | 1.32010i | ||||
\(23\) | 1.23786 | 0.258111 | 0.129056 | − | 0.991637i | \(-0.458805\pi\) | ||||
0.129056 | + | 0.991637i | \(0.458805\pi\) | |||||||
\(24\) | 0.144041 | − | 0.104652i | 0.0294022 | − | 0.0213620i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.21746 | − | 3.74696i | 0.238764 | − | 0.734839i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | 2.21291 | + | 1.60777i | 0.418201 | + | 0.303841i | ||||
\(29\) | 0.158207 | − | 0.486912i | 0.0293784 | − | 0.0904174i | −0.935292 | − | 0.353876i | \(-0.884863\pi\) |
0.964671 | + | 0.263459i | \(0.0848634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02947 | + | 0.747953i | −0.184898 | + | 0.134336i | −0.676384 | − | 0.736549i | \(-0.736454\pi\) |
0.491486 | + | 0.870886i | \(0.336454\pi\) | |||||||
\(32\) | −8.07190 | −1.42692 | ||||||||
\(33\) | −2.51898 | − | 2.15748i | −0.438498 | − | 0.375570i | ||||
\(34\) | 6.13658 | 1.05242 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.645245 | + | 1.98586i | 0.107541 | + | 0.330977i | ||||
\(37\) | −0.679912 | + | 2.09255i | −0.111777 | + | 0.344014i | −0.991261 | − | 0.131914i | \(-0.957888\pi\) |
0.879484 | + | 0.475928i | \(0.157888\pi\) | |||||||
\(38\) | 1.70901 | + | 1.24167i | 0.277238 | + | 0.201425i | ||||
\(39\) | 1.57642 | + | 1.14533i | 0.252429 | + | 0.183400i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.66786 | − | 11.2885i | −0.572823 | − | 1.76297i | −0.643476 | − | 0.765466i | \(-0.722508\pi\) |
0.0706535 | − | 0.997501i | \(-0.477492\pi\) | |||||||
\(42\) | −2.14279 | + | 1.55683i | −0.330640 | + | 0.240224i | ||||
\(43\) | 3.33759 | 0.508978 | 0.254489 | − | 0.967076i | \(-0.418093\pi\) | ||||
0.254489 | + | 0.967076i | \(0.418093\pi\) | |||||||
\(44\) | −1.60731 | − | 6.73620i | −0.242311 | − | 1.01552i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.02482 | + | 1.47112i | −0.298544 | + | 0.216905i | ||||
\(47\) | −4.02739 | − | 12.3950i | −0.587455 | − | 1.80800i | −0.589179 | − | 0.808003i | \(-0.700549\pi\) |
0.00172330 | − | 0.999999i | \(-0.499451\pi\) | |||||||
\(48\) | 1.17925 | − | 3.62935i | 0.170210 | − | 0.523852i | ||||
\(49\) | 4.27482 | + | 3.10583i | 0.610688 | + | 0.443691i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.937887 | + | 2.88652i | −0.131330 | + | 0.404193i | ||||
\(52\) | 1.25730 | + | 3.86957i | 0.174356 | + | 0.536613i | ||||
\(53\) | 8.19681 | − | 5.95533i | 1.12592 | − | 0.818028i | 0.140823 | − | 0.990035i | \(-0.455025\pi\) |
0.985096 | + | 0.172007i | \(0.0550253\pi\) | |||||||
\(54\) | −2.02189 | −0.275145 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.233234 | −0.0311672 | ||||||||
\(57\) | −0.845252 | + | 0.614112i | −0.111956 | + | 0.0813411i | ||||
\(58\) | 0.319879 | + | 0.984486i | 0.0420021 | + | 0.129269i | ||||
\(59\) | 0.989277 | − | 3.04468i | 0.128793 | − | 0.396384i | −0.865780 | − | 0.500425i | \(-0.833177\pi\) |
0.994573 | + | 0.104041i | \(0.0331772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.32395 | − | 5.32116i | −0.937735 | − | 0.681305i | 0.0101391 | − | 0.999949i | \(-0.496773\pi\) |
−0.947874 | + | 0.318644i | \(0.896773\pi\) | |||||||
\(62\) | 0.795054 | − | 2.44693i | 0.100972 | − | 0.310760i | ||||
\(63\) | −0.404805 | − | 1.24586i | −0.0510006 | − | 0.156964i | ||||
\(64\) | 7.02896 | − | 5.10684i | 0.878620 | − | 0.638355i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.68446 | + | 0.535438i | 0.822800 | + | 0.0659079i | ||||
\(67\) | 9.53414 | 1.16478 | 0.582390 | − | 0.812909i | \(-0.302118\pi\) | ||||
0.582390 | + | 0.812909i | \(0.302118\pi\) | |||||||
\(68\) | −5.12706 | + | 3.72503i | −0.621747 | + | 0.451726i | ||||
\(69\) | −0.382520 | − | 1.17727i | −0.0460499 | − | 0.141727i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.37823 | − | 2.45443i | −0.400922 | − | 0.291287i | 0.368994 | − | 0.929432i | \(-0.379702\pi\) |
−0.769916 | + | 0.638145i | \(0.779702\pi\) | |||||||
\(72\) | −0.144041 | − | 0.104652i | −0.0169754 | − | 0.0123333i | ||||
\(73\) | 4.04828 | − | 12.4593i | 0.473815 | − | 1.45825i | −0.373734 | − | 0.927536i | \(-0.621923\pi\) |
0.847549 | − | 0.530717i | \(-0.178077\pi\) | |||||||
\(74\) | −1.37471 | − | 4.23093i | −0.159807 | − | 0.491835i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.18158 | −0.250245 | ||||||||
\(77\) | 1.00837 | + | 4.22606i | 0.114914 | + | 0.481605i | ||||
\(78\) | −3.93978 | −0.446093 | ||||||||
\(79\) | −0.889024 | + | 0.645914i | −0.100023 | + | 0.0726710i | −0.636673 | − | 0.771134i | \(-0.719690\pi\) |
0.536650 | + | 0.843805i | \(0.319690\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 19.4154 | + | 14.1061i | 2.14407 | + | 1.55776i | ||||
\(83\) | 4.01823 | + | 2.91942i | 0.441058 | + | 0.320447i | 0.786055 | − | 0.618156i | \(-0.212120\pi\) |
−0.344997 | + | 0.938604i | \(0.612120\pi\) | |||||||
\(84\) | 0.845256 | − | 2.60143i | 0.0922250 | − | 0.283839i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.45946 | + | 3.96653i | −0.588709 | + | 0.427722i | ||||
\(87\) | −0.511970 | −0.0548890 | ||||||||
\(88\) | 0.448490 | + | 0.384127i | 0.0478092 | + | 0.0409481i | ||||
\(89\) | 7.38928 | 0.783263 | 0.391631 | − | 0.920122i | \(-0.371911\pi\) | ||||
0.391631 | + | 0.920122i | \(0.371911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.788787 | − | 2.42764i | −0.0826873 | − | 0.254485i | ||||
\(92\) | 0.798723 | − | 2.45822i | 0.0832726 | − | 0.256287i | ||||
\(93\) | 1.02947 | + | 0.747953i | 0.106751 | + | 0.0775592i | ||||
\(94\) | 21.3185 | + | 15.4888i | 2.19884 | + | 1.59755i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.49435 | + | 7.67683i | 0.254579 | + | 0.783514i | ||||
\(97\) | 12.0147 | − | 8.72918i | 1.21991 | − | 0.886314i | 0.223814 | − | 0.974632i | \(-0.428149\pi\) |
0.996092 | + | 0.0883182i | \(0.0281492\pi\) | |||||||
\(98\) | −10.6836 | −1.07921 | ||||||||
\(99\) | −1.27348 | + | 3.06239i | −0.127990 | + | 0.307782i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.84831 | − | 4.24905i | 0.581929 | − | 0.422796i | −0.257490 | − | 0.966281i | \(-0.582895\pi\) |
0.839419 | + | 0.543485i | \(0.182895\pi\) | |||||||
\(102\) | −1.89631 | − | 5.83624i | −0.187762 | − | 0.577873i | ||||
\(103\) | 2.73642 | − | 8.42184i | 0.269628 | − | 0.829829i | −0.720963 | − | 0.692973i | \(-0.756300\pi\) |
0.990591 | − | 0.136856i | \(-0.0436996\pi\) | |||||||
\(104\) | −0.280672 | − | 0.203920i | −0.0275222 | − | 0.0199960i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.33035 | + | 19.4828i | −0.614858 | + | 1.89234i | ||||
\(107\) | −1.27605 | − | 3.92727i | −0.123360 | − | 0.379663i | 0.870239 | − | 0.492630i | \(-0.163965\pi\) |
−0.993599 | + | 0.112967i | \(0.963965\pi\) | |||||||
\(108\) | 1.68927 | − | 1.22733i | 0.162551 | − | 0.118100i | ||||
\(109\) | −13.6437 | −1.30683 | −0.653414 | − | 0.757001i | \(-0.726664\pi\) | ||||
−0.653414 | + | 0.757001i | \(0.726664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.20024 | 0.208838 | ||||||||
\(112\) | −4.04431 | + | 2.93836i | −0.382151 | + | 0.277649i | ||||
\(113\) | 4.77495 | + | 14.6958i | 0.449190 | + | 1.38246i | 0.877823 | + | 0.478985i | \(0.158995\pi\) |
−0.428633 | + | 0.903479i | \(0.641005\pi\) | |||||||
\(114\) | 0.652784 | − | 2.00906i | 0.0611388 | − | 0.188166i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.864858 | − | 0.628356i | −0.0803001 | − | 0.0583414i | ||||
\(117\) | 0.602138 | − | 1.85319i | 0.0556677 | − | 0.171328i | ||||
\(118\) | 2.00021 | + | 6.15603i | 0.184135 | + | 0.566708i | ||||
\(119\) | 3.21654 | − | 2.33695i | 0.294860 | − | 0.214228i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.02115 | − | 9.78714i | 0.456468 | − | 0.889740i | ||||
\(122\) | 18.3040 | 1.65717 | ||||||||
\(123\) | −9.60257 | + | 6.97667i | −0.865835 | + | 0.629066i | ||||
\(124\) | 0.821071 | + | 2.52700i | 0.0737344 | + | 0.226931i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.14279 | + | 1.55683i | 0.190895 | + | 0.138693i | ||||
\(127\) | 6.86545 | + | 4.98804i | 0.609210 | + | 0.442617i | 0.849136 | − | 0.528174i | \(-0.177123\pi\) |
−0.239926 | + | 0.970791i | \(0.577123\pi\) | |||||||
\(128\) | −0.439723 | + | 1.35333i | −0.0388664 | + | 0.119618i | ||||
\(129\) | −1.03137 | − | 3.17424i | −0.0908073 | − | 0.279476i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.09703 | −0.620070 | −0.310035 | − | 0.950725i | \(-0.600341\pi\) | ||||
−0.310035 | + | 0.950725i | \(0.600341\pi\) | |||||||
\(132\) | −5.90982 | + | 3.61024i | −0.514384 | + | 0.314231i | ||||
\(133\) | 1.36865 | 0.118677 | ||||||||
\(134\) | −15.5954 | + | 11.3308i | −1.34724 | + | 0.978828i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.166985 | − | 0.513928i | 0.0143189 | − | 0.0440690i | ||||
\(137\) | −1.00875 | − | 0.732897i | −0.0861831 | − | 0.0626157i | 0.543859 | − | 0.839176i | \(-0.316963\pi\) |
−0.630042 | + | 0.776561i | \(0.716963\pi\) | |||||||
\(138\) | 2.02482 | + | 1.47112i | 0.172365 | + | 0.125230i | ||||
\(139\) | −4.15401 | + | 12.7847i | −0.352338 | + | 1.08439i | 0.605198 | + | 0.796075i | \(0.293094\pi\) |
−0.957537 | + | 0.288311i | \(0.906906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5438 | + | 7.66055i | −0.887952 | + | 0.645135i | ||||
\(142\) | 8.44287 | 0.708510 | ||||||||
\(143\) | −2.48145 | + | 5.96726i | −0.207509 | + | 0.499007i | ||||
\(144\) | −3.81613 | −0.318011 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.18519 | + | 25.1914i | 0.677411 | + | 2.08486i | ||||
\(147\) | 1.63283 | − | 5.02535i | 0.134674 | − | 0.414484i | ||||
\(148\) | 3.71681 | + | 2.70042i | 0.305520 | + | 0.221973i | ||||
\(149\) | 11.6912 | + | 8.49414i | 0.957778 | + | 0.695867i | 0.952634 | − | 0.304120i | \(-0.0983624\pi\) |
0.00514473 | + | 0.999987i | \(0.498362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.97241 | − | 18.3812i | −0.486028 | − | 1.49584i | −0.830487 | − | 0.557039i | \(-0.811937\pi\) |
0.344459 | − | 0.938802i | \(-0.388063\pi\) | |||||||
\(152\) | 0.150492 | − | 0.109339i | 0.0122065 | − | 0.00886857i | ||||
\(153\) | 3.03507 | 0.245370 | ||||||||
\(154\) | −6.67186 | − | 5.71438i | −0.537634 | − | 0.460478i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.29165 | − | 2.39153i | 0.263543 | − | 0.191475i | ||||
\(157\) | −6.91721 | − | 21.2890i | −0.552053 | − | 1.69905i | −0.703601 | − | 0.710595i | \(-0.748426\pi\) |
0.151548 | − | 0.988450i | \(-0.451574\pi\) | |||||||
\(158\) | 0.686589 | − | 2.11310i | 0.0546221 | − | 0.168109i | ||||
\(159\) | −8.19681 | − | 5.95533i | −0.650049 | − | 0.472288i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.501092 | + | 1.54220i | −0.0394915 | + | 0.121542i | ||||
\(162\) | 0.624800 | + | 1.92294i | 0.0490889 | + | 0.151080i | ||||
\(163\) | −9.30657 | + | 6.76162i | −0.728947 | + | 0.529611i | −0.889230 | − | 0.457460i | \(-0.848759\pi\) |
0.160283 | + | 0.987071i | \(0.448759\pi\) | |||||||
\(164\) | −24.7841 | −1.93531 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.0424 | −0.779438 | ||||||||
\(167\) | −12.5779 | + | 9.13840i | −0.973310 | + | 0.707151i | −0.956203 | − | 0.292703i | \(-0.905445\pi\) |
−0.0171062 | + | 0.999854i | \(0.505445\pi\) | |||||||
\(168\) | 0.0720732 | + | 0.221818i | 0.00556057 | + | 0.0171137i | ||||
\(169\) | −2.84392 | + | 8.75268i | −0.218763 | + | 0.673283i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.845252 | + | 0.614112i | 0.0646381 | + | 0.0469623i | ||||
\(172\) | 2.15357 | − | 6.62800i | 0.164208 | − | 0.505380i | ||||
\(173\) | −4.19647 | − | 12.9154i | −0.319052 | − | 0.981940i | −0.974054 | − | 0.226314i | \(-0.927333\pi\) |
0.655003 | − | 0.755627i | \(-0.272667\pi\) | |||||||
\(174\) | 0.837454 | − | 0.608446i | 0.0634872 | − | 0.0461261i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.6163 | + | 1.01059i | 0.950986 | + | 0.0761759i | ||||
\(177\) | −3.20137 | −0.240630 | ||||||||
\(178\) | −12.0870 | + | 8.78172i | −0.905959 | + | 0.658218i | ||||
\(179\) | −7.59067 | − | 23.3617i | −0.567353 | − | 1.74613i | −0.660855 | − | 0.750514i | \(-0.729806\pi\) |
0.0935018 | − | 0.995619i | \(-0.470194\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.21301 | − | 1.60785i | −0.164492 | − | 0.119510i | 0.502494 | − | 0.864581i | \(-0.332416\pi\) |
−0.666986 | + | 0.745070i | \(0.732416\pi\) | |||||||
\(182\) | 4.17535 | + | 3.03357i | 0.309498 | + | 0.224863i | ||||
\(183\) | −2.79750 | + | 8.60982i | −0.206797 | + | 0.636456i | ||||
\(184\) | 0.0681054 | + | 0.209607i | 0.00502080 | + | 0.0154524i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.57285 | −0.188650 | ||||||||
\(187\) | −10.0340 | − | 0.803746i | −0.733761 | − | 0.0587757i | ||||
\(188\) | −27.2135 | −1.98475 | ||||||||
\(189\) | −1.05979 | + | 0.769985i | −0.0770886 | + | 0.0560082i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.747926 | + | 2.30188i | −0.0541181 | + | 0.166558i | −0.974462 | − | 0.224551i | \(-0.927909\pi\) |
0.920344 | + | 0.391109i | \(0.127909\pi\) | |||||||
\(192\) | −7.02896 | − | 5.10684i | −0.507272 | − | 0.368554i | ||||
\(193\) | 14.9746 | + | 10.8797i | 1.07790 | + | 0.783137i | 0.977315 | − | 0.211791i | \(-0.0679298\pi\) |
0.100581 | + | 0.994929i | \(0.467930\pi\) | |||||||
\(194\) | −9.27888 | + | 28.5575i | −0.666185 | + | 2.05031i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.92606 | − | 6.48516i | 0.637576 | − | 0.463226i | ||||
\(197\) | −23.5986 | −1.68133 | −0.840664 | − | 0.541557i | \(-0.817835\pi\) | ||||
−0.840664 | + | 0.541557i | \(0.817835\pi\) | |||||||
\(198\) | −1.55638 | − | 6.52275i | −0.110607 | − | 0.463552i | ||||
\(199\) | −25.4697 | −1.80550 | −0.902751 | − | 0.430164i | \(-0.858456\pi\) | ||||
−0.902751 | + | 0.430164i | \(0.858456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.94621 | − | 9.06751i | −0.207810 | − | 0.639573i | ||||
\(202\) | −4.51662 | + | 13.9007i | −0.317789 | + | 0.978053i | ||||
\(203\) | 0.542582 | + | 0.394209i | 0.0380818 | + | 0.0276681i | ||||
\(204\) | 5.12706 | + | 3.72503i | 0.358966 | + | 0.260804i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.53276 | + | 17.0281i | 0.385485 | + | 1.18640i | ||||
\(207\) | −1.00145 | + | 0.727595i | −0.0696055 | + | 0.0505714i | ||||
\(208\) | −7.43596 | −0.515591 | ||||||||
\(209\) | −2.63181 | − | 2.25412i | −0.182046 | − | 0.155920i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.84006 | − | 2.78996i | 0.264360 | − | 0.192069i | −0.447707 | − | 0.894180i | \(-0.647759\pi\) |
0.712067 | + | 0.702111i | \(0.247759\pi\) | |||||||
\(212\) | −6.53751 | − | 20.1204i | −0.448998 | − | 1.38187i | ||||
\(213\) | −1.29037 | + | 3.97135i | −0.0884146 | + | 0.272112i | ||||
\(214\) | 6.75461 | + | 4.90751i | 0.461736 | + | 0.335471i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.0550187 | + | 0.169330i | −0.00374355 | + | 0.0115215i | ||||
\(217\) | −0.515112 | − | 1.58535i | −0.0349681 | − | 0.107621i | ||||
\(218\) | 22.3176 | − | 16.2147i | 1.51154 | − | 1.09820i | ||||
\(219\) | −13.1005 | −0.885250 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.91401 | 0.397819 | ||||||||
\(222\) | −3.59904 | + | 2.61486i | −0.241552 | + | 0.175498i | ||||
\(223\) | −0.157853 | − | 0.485822i | −0.0105706 | − | 0.0325331i | 0.945632 | − | 0.325238i | \(-0.105445\pi\) |
−0.956203 | + | 0.292705i | \(0.905445\pi\) | |||||||
\(224\) | 3.26755 | − | 10.0565i | 0.218322 | − | 0.671926i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.2757 | − | 18.3639i | −1.68131 | − | 1.22155i | ||||
\(227\) | 3.17203 | − | 9.76250i | 0.210535 | − | 0.647960i | −0.788906 | − | 0.614514i | \(-0.789352\pi\) |
0.999441 | − | 0.0334456i | \(-0.0106481\pi\) | |||||||
\(228\) | 0.674146 | + | 2.07481i | 0.0446464 | + | 0.137407i | ||||
\(229\) | 17.7739 | − | 12.9135i | 1.17453 | − | 0.853346i | 0.182986 | − | 0.983116i | \(-0.441424\pi\) |
0.991544 | + | 0.129770i | \(0.0414238\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.70762 | − | 2.26494i | 0.243944 | − | 0.149022i | ||||
\(232\) | 0.0911533 | 0.00598451 | ||||||||
\(233\) | −6.52071 | + | 4.73757i | −0.427186 | + | 0.310369i | −0.780523 | − | 0.625128i | \(-0.785047\pi\) |
0.353337 | + | 0.935496i | \(0.385047\pi\) | |||||||
\(234\) | 1.21746 | + | 3.74696i | 0.0795878 | + | 0.244946i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.40799 | − | 3.92914i | −0.352030 | − | 0.255765i | ||||
\(237\) | 0.889024 | + | 0.645914i | 0.0577483 | + | 0.0419566i | ||||
\(238\) | −2.48412 | + | 7.64533i | −0.161022 | + | 0.495573i | ||||
\(239\) | 4.57556 | + | 14.0821i | 0.295969 | + | 0.910898i | 0.982894 | + | 0.184170i | \(0.0589598\pi\) |
−0.686926 | + | 0.726728i | \(0.741040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7412 | 1.14281 | 0.571404 | − | 0.820669i | \(-0.306399\pi\) | ||||
0.571404 | + | 0.820669i | \(0.306399\pi\) | |||||||
\(242\) | 3.41809 | + | 21.9766i | 0.219723 | + | 1.41271i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −15.2928 | + | 11.1109i | −0.979023 | + | 0.711302i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.41602 | − | 22.8242i | 0.472828 | − | 1.45521i | ||||
\(247\) | 1.64702 | + | 1.19663i | 0.104798 | + | 0.0761400i | ||||
\(248\) | −0.183291 | − | 0.133169i | −0.0116390 | − | 0.00845623i | ||||
\(249\) | 1.53483 | − | 4.72371i | 0.0972657 | − | 0.299353i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.75951 | + | 4.18453i | −0.363537 | + | 0.264125i | −0.754526 | − | 0.656270i | \(-0.772133\pi\) |
0.390989 | + | 0.920395i | \(0.372133\pi\) | |||||||
\(252\) | −2.73531 | −0.172308 | ||||||||
\(253\) | 3.50351 | − | 2.14025i | 0.220264 | − | 0.134557i | ||||
\(254\) | −17.1581 | −1.07660 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.48057 | + | 13.7898i | 0.280036 | + | 0.861862i | ||||
\(257\) | −6.04078 | + | 18.5916i | −0.376813 | + | 1.15971i | 0.565434 | + | 0.824794i | \(0.308709\pi\) |
−0.942247 | + | 0.334918i | \(0.891291\pi\) | |||||||
\(258\) | 5.45946 | + | 3.96653i | 0.339891 | + | 0.246945i | ||||
\(259\) | −2.33180 | − | 1.69415i | −0.144891 | − | 0.105270i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.158207 | + | 0.486912i | 0.00979280 | + | 0.0301391i | ||||
\(262\) | 11.6089 | − | 8.43439i | 0.717203 | − | 0.521078i | ||||
\(263\) | −26.8455 | −1.65537 | −0.827683 | − | 0.561197i | \(-0.810341\pi\) | ||||
−0.827683 | + | 0.561197i | \(0.810341\pi\) | |||||||
\(264\) | 0.226736 | − | 0.545241i | 0.0139546 | − | 0.0335573i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.23876 | + | 1.62656i | −0.137267 | + | 0.0997306i | ||||
\(267\) | −2.28341 | − | 7.02763i | −0.139743 | − | 0.430084i | ||||
\(268\) | 6.15186 | − | 18.9335i | 0.375785 | − | 1.15655i | ||||
\(269\) | 14.8387 | + | 10.7810i | 0.904734 | + | 0.657328i | 0.939677 | − | 0.342062i | \(-0.111125\pi\) |
−0.0349437 | + | 0.999389i | \(0.511125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.00793 | + | 15.4128i | −0.304210 | + | 0.936262i | 0.675761 | + | 0.737121i | \(0.263815\pi\) |
−0.979971 | + | 0.199141i | \(0.936185\pi\) | |||||||
\(272\) | −3.57910 | − | 11.0153i | −0.217015 | − | 0.667902i | ||||
\(273\) | −2.06507 | + | 1.50036i | −0.124984 | + | 0.0908060i | ||||
\(274\) | 2.52106 | 0.152303 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.58472 | −0.155582 | ||||||||
\(277\) | −15.2048 | + | 11.0469i | −0.913566 | + | 0.663745i | −0.941914 | − | 0.335853i | \(-0.890975\pi\) |
0.0283479 | + | 0.999598i | \(0.490975\pi\) | |||||||
\(278\) | −8.39897 | − | 25.8494i | −0.503737 | − | 1.55034i | ||||
\(279\) | 0.393222 | − | 1.21021i | 0.0235416 | − | 0.0724536i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.9177 | + | 18.1038i | 1.48647 | + | 1.07998i | 0.975400 | + | 0.220441i | \(0.0707495\pi\) |
0.511067 | + | 0.859541i | \(0.329250\pi\) | |||||||
\(282\) | 8.14296 | − | 25.0615i | 0.484906 | − | 1.49239i | ||||
\(283\) | 5.85955 | + | 18.0339i | 0.348314 | + | 1.07200i | 0.959785 | + | 0.280734i | \(0.0905780\pi\) |
−0.611471 | + | 0.791267i | \(0.709422\pi\) | |||||||
\(284\) | −7.05394 | + | 5.12499i | −0.418574 | + | 0.304112i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.03270 | − | 12.7100i | −0.179327 | − | 0.751557i | ||||
\(287\) | 15.5487 | 0.917809 | ||||||||
\(288\) | 6.53030 | − | 4.74454i | 0.384802 | − | 0.279575i | ||||
\(289\) | −2.40674 | − | 7.40719i | −0.141573 | − | 0.435717i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0147 | − | 8.72918i | −0.704313 | − | 0.511713i | ||||
\(292\) | −22.1303 | − | 16.0786i | −1.29508 | − | 0.940931i | ||||
\(293\) | −0.907237 | + | 2.79219i | −0.0530013 | + | 0.163121i | −0.974053 | − | 0.226318i | \(-0.927331\pi\) |
0.921052 | + | 0.389439i | \(0.127331\pi\) | |||||||
\(294\) | 3.30142 | + | 10.1607i | 0.192543 | + | 0.592585i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.391740 | −0.0227695 | ||||||||
\(297\) | 3.30604 | + | 0.264820i | 0.191836 | + | 0.0153664i | ||||
\(298\) | −29.2186 | −1.69259 | ||||||||
\(299\) | −1.95138 | + | 1.41776i | −0.112851 | + | 0.0819914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.35107 | + | 4.15818i | −0.0778746 | + | 0.239674i | ||||
\(302\) | 31.6143 | + | 22.9691i | 1.81920 | + | 1.32172i | ||||
\(303\) | −5.84831 | − | 4.24905i | −0.335977 | − | 0.244102i | ||||
\(304\) | 1.23207 | − | 3.79191i | 0.0706639 | − | 0.217481i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.96460 | + | 3.60699i | −0.283807 | + | 0.206198i | ||||
\(307\) | 18.4893 | 1.05524 | 0.527621 | − | 0.849480i | \(-0.323084\pi\) | ||||
0.527621 | + | 0.849480i | \(0.323084\pi\) | |||||||
\(308\) | 9.04302 | + | 0.724364i | 0.515274 | + | 0.0412745i | ||||
\(309\) | −8.85525 | −0.503757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.17840 | + | 22.0928i | 0.407050 | + | 1.25277i | 0.919171 | + | 0.393858i | \(0.128860\pi\) |
−0.512122 | + | 0.858913i | \(0.671140\pi\) | |||||||
\(312\) | −0.107207 | + | 0.329950i | −0.00606941 | + | 0.0186797i | ||||
\(313\) | −1.81604 | − | 1.31943i | −0.102649 | − | 0.0745785i | 0.535277 | − | 0.844677i | \(-0.320207\pi\) |
−0.637926 | + | 0.770098i | \(0.720207\pi\) | |||||||
\(314\) | 36.6155 | + | 26.6027i | 2.06633 | + | 1.50128i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.709057 | + | 2.18225i | 0.0398875 | + | 0.122761i | ||||
\(317\) | −5.16486 | + | 3.75249i | −0.290088 | + | 0.210761i | −0.723305 | − | 0.690528i | \(-0.757378\pi\) |
0.433218 | + | 0.901289i | \(0.357378\pi\) | |||||||
\(318\) | 20.4855 | 1.14877 | ||||||||
\(319\) | −0.394095 | − | 1.65165i | −0.0220651 | − | 0.0924744i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.34073 | + | 2.42719i | −0.186462 | + | 0.135472i | ||||
\(322\) | −1.01315 | − | 3.11817i | −0.0564609 | − | 0.173769i | ||||
\(323\) | −0.979894 | + | 3.01580i | −0.0545228 | + | 0.167804i | ||||
\(324\) | −1.68927 | − | 1.22733i | −0.0938486 | − | 0.0681850i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.18742 | − | 22.1206i | 0.398074 | − | 1.22515i | ||||
\(327\) | 4.21613 | + | 12.9759i | 0.233153 | + | 0.717570i | ||||
\(328\) | 1.70968 | − | 1.24216i | 0.0944014 | − | 0.0685866i | ||||
\(329\) | 17.0728 | 0.941254 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3804 | −0.845383 | −0.422691 | − | 0.906274i | \(-0.638915\pi\) | ||||
−0.422691 | + | 0.906274i | \(0.638915\pi\) | |||||||
\(332\) | 8.39030 | − | 6.09591i | 0.460478 | − | 0.334556i | ||||
\(333\) | −0.679912 | − | 2.09255i | −0.0372590 | − | 0.114671i | ||||
\(334\) | 9.71388 | − | 29.8962i | 0.531520 | − | 1.63585i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.04431 | + | 2.93836i | 0.220635 | + | 0.160301i | ||||
\(337\) | 3.34175 | − | 10.2848i | 0.182037 | − | 0.560251i | −0.817848 | − | 0.575434i | \(-0.804833\pi\) |
0.999885 | + | 0.0151830i | \(0.00483309\pi\) | |||||||
\(338\) | −5.75010 | − | 17.6970i | −0.312764 | − | 0.962590i | ||||
\(339\) | 12.5010 | − | 9.08250i | 0.678960 | − | 0.493294i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.62050 | + | 3.89688i | −0.0877548 | + | 0.211028i | ||||
\(342\) | −2.11245 | −0.114228 | ||||||||
\(343\) | −13.0185 | + | 9.45846i | −0.702931 | + | 0.510709i | ||||
\(344\) | 0.183630 | + | 0.565155i | 0.00990067 | + | 0.0304711i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.2136 | + | 16.1391i | 1.19421 | + | 0.867643i | ||||
\(347\) | 14.4919 | + | 10.5290i | 0.777966 | + | 0.565226i | 0.904368 | − | 0.426754i | \(-0.140343\pi\) |
−0.126402 | + | 0.991979i | \(0.540343\pi\) | |||||||
\(348\) | −0.330346 | + | 1.01670i | −0.0177084 | + | 0.0545009i | ||||
\(349\) | 1.71595 | + | 5.28114i | 0.0918525 | + | 0.282693i | 0.986421 | − | 0.164239i | \(-0.0525167\pi\) |
−0.894568 | + | 0.446932i | \(0.852517\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.94856 | −0.104006 | ||||||||
\(352\) | −22.8459 | + | 13.9563i | −1.21769 | + | 0.743872i | ||||
\(353\) | 28.1513 | 1.49834 | 0.749171 | − | 0.662376i | \(-0.230452\pi\) | ||||
0.749171 | + | 0.662376i | \(0.230452\pi\) | |||||||
\(354\) | 5.23663 | − | 3.80463i | 0.278324 | − | 0.202214i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.76790 | − | 14.6741i | 0.252698 | − | 0.777725i | ||||
\(357\) | −3.21654 | − | 2.33695i | −0.170237 | − | 0.123685i | ||||
\(358\) | 40.1803 | + | 29.1927i | 2.12360 | + | 1.54288i | ||||
\(359\) | 1.85030 | − | 5.69463i | 0.0976549 | − | 0.300551i | −0.890282 | − | 0.455411i | \(-0.849493\pi\) |
0.987936 | + | 0.154860i | \(0.0494925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4882 | − | 10.5263i | 0.762537 | − | 0.554016i | ||||
\(362\) | 5.53075 | 0.290690 | ||||||||
\(363\) | −10.8597 | − | 1.75101i | −0.569989 | − | 0.0919041i | ||||
\(364\) | −5.32991 | −0.279363 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.65625 | − | 17.4081i | −0.295657 | − | 0.909938i | ||||
\(367\) | −5.45626 | + | 16.7926i | −0.284814 | + | 0.876568i | 0.701640 | + | 0.712532i | \(0.252451\pi\) |
−0.986454 | + | 0.164036i | \(0.947549\pi\) | |||||||
\(368\) | 3.82166 | + | 2.77660i | 0.199218 | + | 0.144740i | ||||
\(369\) | 9.60257 | + | 6.97667i | 0.499890 | + | 0.363191i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.10141 | + | 12.6228i | 0.212934 | + | 0.655345i | ||||
\(372\) | 2.14959 | − | 1.56177i | 0.111451 | − | 0.0809740i | ||||
\(373\) | 3.01742 | 0.156236 | 0.0781179 | − | 0.996944i | \(-0.475109\pi\) | ||||
0.0781179 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(374\) | 17.3683 | − | 10.6101i | 0.898096 | − | 0.548636i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.87727 | − | 1.36392i | 0.0968129 | − | 0.0703387i | ||||
\(377\) | 0.308277 | + | 0.948778i | 0.0158771 | + | 0.0488646i | ||||
\(378\) | 0.818473 | − | 2.51900i | 0.0420977 | − | 0.129563i | ||||
\(379\) | −19.0938 | − | 13.8724i | −0.980781 | − | 0.712579i | −0.0228981 | − | 0.999738i | \(-0.507289\pi\) |
−0.957883 | + | 0.287159i | \(0.907289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.62237 | − | 8.07082i | 0.134348 | − | 0.413480i | ||||
\(382\) | −1.51223 | − | 4.65416i | −0.0773723 | − | 0.238128i | ||||
\(383\) | 6.71771 | − | 4.88071i | 0.343259 | − | 0.249392i | −0.402776 | − | 0.915298i | \(-0.631955\pi\) |
0.746036 | + | 0.665906i | \(0.231955\pi\) | |||||||
\(384\) | 1.42297 | 0.0726158 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −37.4245 | −1.90486 | ||||||||
\(387\) | −2.70017 | + | 1.96179i | −0.137257 | + | 0.0997233i | ||||
\(388\) | −9.58252 | − | 29.4920i | −0.486479 | − | 1.49723i | ||||
\(389\) | 9.22384 | − | 28.3881i | 0.467667 | − | 1.43933i | −0.387929 | − | 0.921689i | \(-0.626809\pi\) |
0.855597 | − | 0.517643i | \(-0.173191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.03946 | − | 2.20830i | −0.153712 | − | 0.111678i | ||||
\(392\) | −0.290717 | + | 0.894734i | −0.0146834 | + | 0.0451909i | ||||
\(393\) | 2.19310 | + | 6.74967i | 0.110627 | + | 0.340476i | ||||
\(394\) | 38.6013 | − | 28.0455i | 1.94471 | − | 1.41291i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.25978 | + | 4.50495i | 0.264314 | + | 0.226382i | ||||
\(397\) | 10.4162 | 0.522772 | 0.261386 | − | 0.965234i | \(-0.415820\pi\) | ||||
0.261386 | + | 0.965234i | \(0.415820\pi\) | |||||||
\(398\) | 41.6621 | − | 30.2693i | 2.08833 | − | 1.51726i | ||||
\(399\) | −0.422936 | − | 1.30166i | −0.0211733 | − | 0.0651647i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.8199 | − | 19.4858i | −1.33932 | − | 0.973075i | −0.999469 | − | 0.0325971i | \(-0.989622\pi\) |
−0.339854 | − | 0.940478i | \(-0.610378\pi\) | |||||||
\(402\) | 15.5954 | + | 11.3308i | 0.777830 | + | 0.565127i | ||||
\(403\) | 0.766217 | − | 2.35817i | 0.0381680 | − | 0.117469i | ||||
\(404\) | −4.66442 | − | 14.3556i | −0.232064 | − | 0.714219i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.35602 | −0.0672982 | ||||||||
\(407\) | 1.69366 | + | 7.09811i | 0.0839518 | + | 0.351840i | ||||
\(408\) | −0.540376 | −0.0267526 | ||||||||
\(409\) | 20.2486 | − | 14.7115i | 1.00123 | − | 0.727436i | 0.0388783 | − | 0.999244i | \(-0.487622\pi\) |
0.962352 | + | 0.271808i | \(0.0876215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.385307 | + | 1.18585i | −0.0190058 | + | 0.0584938i | ||||
\(412\) | −14.9589 | − | 10.8683i | −0.736974 | − | 0.535443i | ||||
\(413\) | 3.39279 | + | 2.46501i | 0.166948 | + | 0.121295i | ||||
\(414\) | 0.773414 | − | 2.38032i | 0.0380112 | − | 0.116987i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.7247 | − | 9.24503i | 0.623879 | − | 0.453275i | ||||
\(417\) | 13.4427 | 0.658290 | ||||||||
\(418\) | 6.98385 | + | 0.559420i | 0.341591 | + | 0.0273621i | ||||
\(419\) | −4.38157 | −0.214054 | −0.107027 | − | 0.994256i | \(-0.534133\pi\) | ||||
−0.107027 | + | 0.994256i | \(0.534133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.97933 | + | 30.7132i | 0.486363 | + | 1.49687i | 0.829997 | + | 0.557768i | \(0.188342\pi\) |
−0.343634 | + | 0.939104i | \(0.611658\pi\) | |||||||
\(422\) | −2.96566 | + | 9.12735i | −0.144366 | + | 0.444313i | ||||
\(423\) | 10.5438 | + | 7.66055i | 0.512659 | + | 0.372469i | ||||
\(424\) | 1.45939 | + | 1.06031i | 0.0708745 | + | 0.0514933i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.60899 | − | 8.02965i | −0.126406 | − | 0.389038i | ||||
\(427\) | 9.59420 | − | 6.97059i | 0.464296 | − | 0.337331i | ||||
\(428\) | −8.62237 | −0.416778 | ||||||||
\(429\) | 6.44201 | + | 0.516018i | 0.311023 | + | 0.0249136i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.04370 | + | 2.21138i | −0.146610 | + | 0.106518i | −0.658672 | − | 0.752430i | \(-0.728882\pi\) |
0.512062 | + | 0.858948i | \(0.328882\pi\) | |||||||
\(432\) | 1.17925 | + | 3.62935i | 0.0567366 | + | 0.174617i | ||||
\(433\) | 5.53863 | − | 17.0461i | 0.266169 | − | 0.819185i | −0.725252 | − | 0.688483i | \(-0.758277\pi\) |
0.991422 | − | 0.130702i | \(-0.0417232\pi\) | |||||||
\(434\) | 2.72669 | + | 1.98106i | 0.130885 | + | 0.0950937i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.80352 | + | 27.0945i | −0.421612 | + | 1.29759i | ||||
\(437\) | −0.399652 | − | 1.23000i | −0.0191180 | − | 0.0588390i | ||||
\(438\) | 21.4291 | − | 15.5692i | 1.02392 | − | 0.743923i | ||||
\(439\) | 0.249655 | 0.0119154 | 0.00595768 | − | 0.999982i | \(-0.498104\pi\) | ||||
0.00595768 | + | 0.999982i | \(0.498104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.28396 | −0.251617 | ||||||||
\(442\) | −9.67382 | + | 7.02844i | −0.460137 | + | 0.334309i | ||||
\(443\) | 7.50802 | + | 23.1073i | 0.356717 | + | 1.09786i | 0.955007 | + | 0.296582i | \(0.0958468\pi\) |
−0.598291 | + | 0.801279i | \(0.704153\pi\) | |||||||
\(444\) | 1.41970 | − | 4.36938i | 0.0673758 | − | 0.207361i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.835578 | + | 0.607083i | 0.0395658 | + | 0.0287462i | ||||
\(447\) | 4.46563 | − | 13.7438i | 0.211217 | − | 0.650060i | ||||
\(448\) | 3.51706 | + | 10.8244i | 0.166165 | + | 0.511404i | ||||
\(449\) | 13.2783 | − | 9.64725i | 0.626641 | − | 0.455282i | −0.228594 | − | 0.973522i | \(-0.573413\pi\) |
0.855235 | + | 0.518240i | \(0.173413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.8989 | − | 25.6081i | −1.40788 | − | 1.20584i | ||||
\(452\) | 32.2648 | 1.51761 | ||||||||
\(453\) | −15.6360 | + | 11.3602i | −0.734642 | + | 0.533749i | ||||
\(454\) | 6.41351 | + | 19.7388i | 0.301001 | + | 0.926386i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.150492 | − | 0.109339i | −0.00704745 | − | 0.00512027i | ||||
\(457\) | −11.5208 | − | 8.37034i | −0.538920 | − | 0.391548i | 0.284764 | − | 0.958598i | \(-0.408085\pi\) |
−0.823684 | + | 0.567050i | \(0.808085\pi\) | |||||||
\(458\) | −13.7267 | + | 42.2463i | −0.641405 | + | 1.97404i | ||||
\(459\) | −0.937887 | − | 2.88652i | −0.0437768 | − | 0.134731i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.34050 | −0.341881 | −0.170940 | − | 0.985281i | \(-0.554681\pi\) | ||||
−0.170940 | + | 0.985281i | \(0.554681\pi\) | |||||||
\(462\) | −3.37298 | + | 8.11116i | −0.156925 | + | 0.377365i | ||||
\(463\) | 29.1159 | 1.35313 | 0.676566 | − | 0.736382i | \(-0.263467\pi\) | ||||
0.676566 | + | 0.736382i | \(0.263467\pi\) | |||||||
\(464\) | 1.58061 | − | 1.14838i | 0.0733781 | − | 0.0533123i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.03591 | − | 15.4989i | 0.233284 | − | 0.717974i | ||||
\(467\) | −13.8158 | − | 10.0377i | −0.639317 | − | 0.464491i | 0.220298 | − | 0.975433i | \(-0.429297\pi\) |
−0.859615 | + | 0.510942i | \(0.829297\pi\) | |||||||
\(468\) | −3.29165 | − | 2.39153i | −0.152157 | − | 0.110548i | ||||
\(469\) | −3.85947 | + | 11.8782i | −0.178214 | + | 0.548485i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.1095 | + | 13.1573i | −0.834441 | + | 0.606257i | ||||
\(472\) | 0.569985 | 0.0262357 | ||||||||
\(473\) | 9.44638 | − | 5.77068i | 0.434345 | − | 0.265336i | ||||
\(474\) | −2.22185 | −0.102053 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.56541 | − | 7.89551i | −0.117585 | − | 0.361890i | ||||
\(477\) | −3.13090 | + | 9.63593i | −0.143354 | + | 0.441199i | ||||
\(478\) | −24.2202 | − | 17.5970i | −1.10781 | − | 0.804870i | ||||
\(479\) | −0.898607 | − | 0.652876i | −0.0410584 | − | 0.0298307i | 0.567067 | − | 0.823672i | \(-0.308078\pi\) |
−0.608125 | + | 0.793841i | \(0.708078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.32485 | − | 4.07747i | −0.0604079 | − | 0.185917i | ||||
\(482\) | −29.0200 | + | 21.0843i | −1.32183 | + | 0.960363i | ||||
\(483\) | 1.62157 | 0.0737838 | ||||||||
\(484\) | −16.1960 | − | 16.2864i | −0.736183 | − | 0.740292i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.63575 | − | 1.18844i | 0.0741990 | − | 0.0539087i | ||||
\(487\) | 8.27334 | + | 25.4627i | 0.374901 | + | 1.15383i | 0.943546 | + | 0.331243i | \(0.107468\pi\) |
−0.568645 | + | 0.822583i | \(0.692532\pi\) | |||||||
\(488\) | 0.498079 | − | 1.53293i | 0.0225470 | − | 0.0693924i | ||||
\(489\) | 9.30657 | + | 6.76162i | 0.420858 | + | 0.305771i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.91454 | − | 30.5138i | 0.447437 | − | 1.37707i | −0.432352 | − | 0.901705i | \(-0.642316\pi\) |
0.879789 | − | 0.475364i | \(-0.157684\pi\) | |||||||
\(492\) | 7.65869 | + | 23.5710i | 0.345281 | + | 1.06266i | ||||
\(493\) | −1.25710 | + | 0.913337i | −0.0566170 | + | 0.0411347i | ||||
\(494\) | −4.11624 | −0.185199 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.85600 | −0.218041 | ||||||||
\(497\) | 4.42540 | − | 3.21524i | 0.198506 | − | 0.144223i | ||||
\(498\) | 3.10326 | + | 9.55085i | 0.139060 | + | 0.427984i | ||||
\(499\) | −6.27290 | + | 19.3060i | −0.280814 | + | 0.864255i | 0.706809 | + | 0.707405i | \(0.250134\pi\) |
−0.987622 | + | 0.156851i | \(0.949866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.5779 | + | 9.13840i | 0.561941 | + | 0.408274i | ||||
\(502\) | 4.44804 | − | 13.6897i | 0.198526 | − | 0.611000i | ||||
\(503\) | −6.52282 | − | 20.0752i | −0.290838 | − | 0.895108i | −0.984588 | − | 0.174892i | \(-0.944042\pi\) |
0.693749 | − | 0.720217i | \(-0.255958\pi\) | |||||||
\(504\) | 0.188690 | − | 0.137091i | 0.00840492 | − | 0.00610653i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.18729 | + | 7.66462i | −0.141692 | + | 0.340734i | ||||
\(507\) | 9.20311 | 0.408725 | ||||||||
\(508\) | 14.3355 | − | 10.4153i | 0.636033 | − | 0.462105i | ||||
\(509\) | −2.83208 | − | 8.71625i | −0.125530 | − | 0.386341i | 0.868467 | − | 0.495746i | \(-0.165105\pi\) |
−0.993997 | + | 0.109405i | \(0.965105\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8838 | + | 10.0872i | 0.614184 | + | 0.446231i | ||||
\(512\) | −26.0198 | − | 18.9045i | −1.14993 | − | 0.835470i | ||||
\(513\) | 0.322858 | − | 0.993654i | 0.0142545 | − | 0.0438709i | ||||
\(514\) | −12.2138 | − | 37.5903i | −0.538728 | − | 1.65804i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.96909 | −0.306797 | ||||||||
\(517\) | −32.8297 | − | 28.1183i | −1.44385 | − | 1.23664i | ||||
\(518\) | 5.82764 | 0.256052 | ||||||||
\(519\) | −10.9865 | + | 7.98216i | −0.482254 | + | 0.350378i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.03826 | + | 12.4285i | −0.176919 | + | 0.544502i | −0.999716 | − | 0.0238341i | \(-0.992413\pi\) |
0.822796 | + | 0.568336i | \(0.192413\pi\) | |||||||
\(522\) | −0.837454 | − | 0.608446i | −0.0366543 | − | 0.0266309i | ||||
\(523\) | −12.4336 | − | 9.03354i | −0.543684 | − | 0.395009i | 0.281768 | − | 0.959483i | \(-0.409079\pi\) |
−0.825451 | + | 0.564473i | \(0.809079\pi\) | |||||||
\(524\) | −4.57932 | + | 14.0937i | −0.200049 | + | 0.615687i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.9125 | − | 31.9043i | 1.91467 | − | 1.39109i | ||||
\(527\) | 3.86210 | 0.168236 | ||||||||
\(528\) | −2.93751 | − | 12.3111i | −0.127839 | − | 0.535770i | ||||
\(529\) | −21.4677 | −0.933378 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.989277 | + | 3.04468i | 0.0429310 | + | 0.132128i | ||||
\(532\) | 0.883115 | − | 2.71795i | 0.0382879 | − | 0.117838i | ||||
\(533\) | 18.7112 | + | 13.5945i | 0.810471 | + | 0.588842i | ||||
\(534\) | 12.0870 | + | 8.78172i | 0.523056 | + | 0.380022i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.524556 | + | 1.61442i | 0.0226574 | + | 0.0697322i | ||||
\(537\) | −19.8726 | + | 14.4383i | −0.857567 | + | 0.623059i | ||||
\(538\) | −37.0850 | −1.59885 | ||||||||
\(539\) | 17.4690 | + | 1.39930i | 0.752442 | + | 0.0602721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.7031 | − | 12.8621i | 0.761116 | − | 0.552983i | −0.138136 | − | 0.990413i | \(-0.544111\pi\) |
0.899252 | + | 0.437430i | \(0.144111\pi\) | |||||||
\(542\) | −10.1255 | − | 31.1631i | −0.434927 | − | 1.33857i | ||||
\(543\) | −0.845294 | + | 2.60155i | −0.0362750 | + | 0.111643i | ||||
\(544\) | 19.8199 | + | 14.4000i | 0.849771 | + | 0.617395i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.59484 | − | 4.90842i | 0.0682530 | − | 0.210061i | ||||
\(547\) | 0.0925567 | + | 0.284860i | 0.00395744 | + | 0.0121797i | 0.953016 | − | 0.302921i | \(-0.0979618\pi\) |
−0.949058 | + | 0.315101i | \(0.897962\pi\) | |||||||
\(548\) | −2.10632 | + | 1.53033i | −0.0899776 | + | 0.0653726i | ||||
\(549\) | 9.05290 | 0.386368 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.534901 | −0.0227875 | ||||||||
\(552\) | 0.178302 | − | 0.129544i | 0.00758905 | − | 0.00551377i | ||||
\(553\) | −0.444838 | − | 1.36907i | −0.0189164 | − | 0.0582188i | ||||
\(554\) | 11.7426 | − | 36.1399i | 0.498894 | − | 1.53544i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.7083 | + | 16.4986i | 0.963048 | + | 0.699695i | ||||
\(557\) | −4.60835 | + | 14.1830i | −0.195262 | + | 0.600954i | 0.804712 | + | 0.593666i | \(0.202320\pi\) |
−0.999973 | + | 0.00728838i | \(0.997680\pi\) | |||||||
\(558\) | 0.795054 | + | 2.44693i | 0.0336573 | + | 0.103587i | ||||
\(559\) | −5.26144 | + | 3.82266i | −0.222535 | + | 0.161681i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.33628 | + | 9.79130i | 0.0986378 | + | 0.413389i | ||||
\(562\) | −62.2744 | −2.62689 | ||||||||
\(563\) | −25.4635 | + | 18.5003i | −1.07316 | + | 0.779696i | −0.976478 | − | 0.215619i | \(-0.930823\pi\) |
−0.0966820 | + | 0.995315i | \(0.530823\pi\) | |||||||
\(564\) | 8.40943 | + | 25.8815i | 0.354101 | + | 1.08981i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −31.0169 | − | 22.5351i | −1.30374 | − | 0.947221i | ||||
\(567\) | 1.05979 | + | 0.769985i | 0.0445071 | + | 0.0323363i | ||||
\(568\) | 0.229743 | − | 0.707076i | 0.00963979 | − | 0.0296682i | ||||
\(569\) | 6.85188 | + | 21.0879i | 0.287246 | + | 0.884052i | 0.985717 | + | 0.168413i | \(0.0538642\pi\) |
−0.698471 | + | 0.715639i | \(0.746136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.6015 | 1.78282 | 0.891409 | − | 0.453200i | \(-0.149718\pi\) | ||||
0.891409 | + | 0.453200i | \(0.149718\pi\) | |||||||
\(572\) | 10.2490 | + | 8.77816i | 0.428532 | + | 0.367033i | ||||
\(573\) | 2.42034 | 0.101111 | ||||||||
\(574\) | −25.4337 | + | 18.4787i | −1.06158 | + | 0.771284i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.68482 | + | 8.26304i | −0.111868 | + | 0.344293i | ||||
\(577\) | 5.07173 | + | 3.68483i | 0.211139 | + | 0.153401i | 0.688329 | − | 0.725399i | \(-0.258345\pi\) |
−0.477190 | + | 0.878800i | \(0.658345\pi\) | |||||||
\(578\) | 12.7398 | + | 9.25602i | 0.529907 | + | 0.385000i | ||||
\(579\) | 5.71979 | − | 17.6037i | 0.237706 | − | 0.731585i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.26379 | + | 3.82437i | −0.218379 | + | 0.158661i | ||||
\(582\) | 30.0271 | 1.24466 | ||||||||
\(583\) | 12.9027 | − | 31.0276i | 0.534374 | − | 1.28503i | ||||
\(584\) | 2.33247 | 0.0965182 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.83434 | − | 5.64551i | −0.0757758 | − | 0.233214i | ||||
\(587\) | 0.230368 | − | 0.709000i | 0.00950831 | − | 0.0292636i | −0.946190 | − | 0.323612i | \(-0.895103\pi\) |
0.955698 | + | 0.294349i | \(0.0951027\pi\) | |||||||
\(588\) | −8.92606 | − | 6.48516i | −0.368105 | − | 0.267444i | ||||
\(589\) | 1.07558 | + | 0.781454i | 0.0443185 | + | 0.0321992i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.29236 | + | 22.4436i | 0.299968 | + | 0.923205i | ||||
\(592\) | −6.79284 | + | 4.93529i | −0.279184 | + | 0.202839i | ||||
\(593\) | −31.7760 | −1.30488 | −0.652441 | − | 0.757840i | \(-0.726255\pi\) | ||||
−0.652441 | + | 0.757840i | \(0.726255\pi\) | |||||||
\(594\) | −5.72256 | + | 3.49585i | −0.234800 | + | 0.143436i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.4119 | − | 17.7363i | 0.999949 | − | 0.726505i | ||||
\(597\) | 7.87058 | + | 24.2232i | 0.322121 | + | 0.991388i | ||||
\(598\) | 1.50704 | − | 4.63820i | 0.0616276 | − | 0.189670i | ||||
\(599\) | −14.7282 | − | 10.7006i | −0.601776 | − | 0.437216i | 0.244733 | − | 0.969591i | \(-0.421300\pi\) |
−0.846509 | + | 0.532374i | \(0.821300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.07978 | + | 27.9447i | −0.370372 | + | 1.13989i | 0.576176 | + | 0.817325i | \(0.304544\pi\) |
−0.946548 | + | 0.322562i | \(0.895456\pi\) | |||||||
\(602\) | −2.73173 | − | 8.40740i | −0.111337 | − | 0.342660i | ||||
\(603\) | −7.71328 | + | 5.60403i | −0.314109 | + | 0.228214i | ||||
\(604\) | −40.3562 | −1.64207 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.6161 | 0.593739 | ||||||||
\(607\) | 22.7962 | − | 16.5624i | 0.925268 | − | 0.672247i | −0.0195615 | − | 0.999809i | \(-0.506227\pi\) |
0.944830 | + | 0.327562i | \(0.106227\pi\) | |||||||
\(608\) | 2.60608 | + | 8.02067i | 0.105690 | + | 0.325281i | ||||
\(609\) | 0.207248 | − | 0.637844i | 0.00839811 | − | 0.0258467i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.5453 | + | 14.9270i | 0.831174 | + | 0.603884i | ||||
\(612\) | 1.95836 | − | 6.02722i | 0.0791621 | − | 0.243636i | ||||
\(613\) | −13.1272 | − | 40.4013i | −0.530201 | − | 1.63179i | −0.753795 | − | 0.657110i | \(-0.771779\pi\) |
0.223593 | − | 0.974683i | \(-0.428221\pi\) | |||||||
\(614\) | −30.2439 | + | 21.9735i | −1.22054 | + | 0.886776i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.660121 | + | 0.403260i | −0.0265970 | + | 0.0162478i | ||||
\(617\) | 1.38228 | 0.0556484 | 0.0278242 | − | 0.999613i | \(-0.491142\pi\) | ||||
0.0278242 | + | 0.999613i | \(0.491142\pi\) | |||||||
\(618\) | 14.4849 | − | 10.5239i | 0.582670 | − | 0.423335i | ||||
\(619\) | 11.5409 | + | 35.5193i | 0.463868 | + | 1.42764i | 0.860400 | + | 0.509619i | \(0.170214\pi\) |
−0.396532 | + | 0.918021i | \(0.629786\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00145 | + | 0.727595i | 0.0401868 | + | 0.0291974i | ||||
\(622\) | −37.9981 | − | 27.6072i | −1.52358 | − | 1.10695i | ||||
\(623\) | −2.99122 | + | 9.20602i | −0.119841 | + | 0.368832i | ||||
\(624\) | 2.29784 | + | 7.07201i | 0.0919871 | + | 0.283107i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.53864 | 0.181401 | ||||||||
\(627\) | −1.33052 | + | 3.19956i | −0.0531358 | + | 0.127778i | ||||
\(628\) | −46.7402 | −1.86514 | ||||||||
\(629\) | 5.40252 | − | 3.92516i | 0.215412 | − | 0.156506i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6311 | + | 35.7967i | −0.463025 | + | 1.42504i | 0.398424 | + | 0.917201i | \(0.369557\pi\) |
−0.861449 | + | 0.507843i | \(0.830443\pi\) | |||||||
\(632\) | −0.158286 | − | 0.115001i | −0.00629626 | − | 0.00457450i | ||||
\(633\) | −3.84006 | − | 2.78996i | −0.152629 | − | 0.110891i | ||||
\(634\) | 3.98880 | − | 12.2763i | 0.158415 | − | 0.487552i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −17.1154 | + | 12.4351i | −0.678670 | + | 0.493083i | ||||
\(637\) | −10.2961 | −0.407947 | ||||||||
\(638\) | 2.60752 | + | 2.23332i | 0.103233 | + | 0.0884179i | ||||
\(639\) | 4.17572 | 0.165189 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.46046 | − | 13.7279i | −0.176178 | − | 0.542219i | 0.823508 | − | 0.567305i | \(-0.192014\pi\) |
−0.999685 | + | 0.0250860i | \(0.992014\pi\) | |||||||
\(642\) | 2.58003 | − | 7.94052i | 0.101826 | − | 0.313387i | ||||
\(643\) | −22.4030 | − | 16.2767i | −0.883488 | − | 0.641891i | 0.0506841 | − | 0.998715i | \(-0.483860\pi\) |
−0.934172 | + | 0.356823i | \(0.883860\pi\) | |||||||
\(644\) | 2.73927 | + | 1.99020i | 0.107942 | + | 0.0784247i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.98124 | − | 6.09764i | −0.0779510 | − | 0.239908i | ||||
\(647\) | −7.00966 | + | 5.09282i | −0.275578 | + | 0.200219i | −0.716986 | − | 0.697087i | \(-0.754479\pi\) |
0.441408 | + | 0.897306i | \(0.354479\pi\) | |||||||
\(648\) | 0.178044 | 0.00699424 | ||||||||
\(649\) | −2.46429 | − | 10.3278i | −0.0967320 | − | 0.405402i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.34858 | + | 0.979801i | −0.0528551 | + | 0.0384014i | ||||
\(652\) | 7.42262 | + | 22.8445i | 0.290692 | + | 0.894658i | ||||
\(653\) | −0.669921 | + | 2.06180i | −0.0262160 | + | 0.0806847i | −0.963309 | − | 0.268397i | \(-0.913506\pi\) |
0.937092 | + | 0.349081i | \(0.113506\pi\) | |||||||
\(654\) | −22.3176 | − | 16.2147i | −0.872688 | − | 0.634045i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.9970 | − | 43.0784i | 0.546491 | − | 1.68193i | ||||
\(657\) | 4.04828 | + | 12.4593i | 0.157938 | + | 0.486084i | ||||
\(658\) | −27.9268 | + | 20.2900i | −1.08870 | + | 0.790987i | ||||
\(659\) | −48.3550 | −1.88364 | −0.941822 | − | 0.336112i | \(-0.890888\pi\) | ||||
−0.941822 | + | 0.336112i | \(0.890888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.3261 | 1.49071 | 0.745356 | − | 0.666667i | \(-0.232280\pi\) | ||||
0.745356 | + | 0.666667i | \(0.232280\pi\) | |||||||
\(662\) | 25.1584 | − | 18.2787i | 0.977810 | − | 0.710421i | ||||
\(663\) | −1.82753 | − | 5.62455i | −0.0709753 | − | 0.218440i | ||||
\(664\) | −0.273267 | + | 0.841030i | −0.0106048 | + | 0.0326383i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.59904 | + | 2.61486i | 0.139460 | + | 0.101324i | ||||
\(667\) | 0.195839 | − | 0.602729i | 0.00758290 | − | 0.0233378i | ||||
\(668\) | 10.0317 | + | 30.8745i | 0.388140 | + | 1.19457i | ||||
\(669\) | −0.413265 | + | 0.300255i | −0.0159777 | + | 0.0116085i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.9292 | − | 2.39739i | −1.15540 | − | 0.0925501i | ||||
\(672\) | −10.5740 | −0.407901 | ||||||||
\(673\) | 15.0694 | − | 10.9485i | 0.580882 | − | 0.422035i | −0.258160 | − | 0.966102i | \(-0.583116\pi\) |
0.839042 | + | 0.544067i | \(0.183116\pi\) | |||||||
\(674\) | 6.75666 | + | 20.7949i | 0.260257 | + | 0.800989i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.5466 | + | 11.2953i | 0.597946 | + | 0.434433i | ||||
\(677\) | 2.98496 | + | 2.16870i | 0.114721 | + | 0.0833498i | 0.643667 | − | 0.765306i | \(-0.277412\pi\) |
−0.528945 | + | 0.848656i | \(0.677412\pi\) | |||||||
\(678\) | −9.65445 | + | 29.7133i | −0.370777 | + | 1.14113i | ||||
\(679\) | 6.01174 | + | 18.5022i | 0.230710 | + | 0.710051i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.2649 | −0.393352 | ||||||||
\(682\) | −1.98048 | − | 8.30017i | −0.0758366 | − | 0.317830i | ||||
\(683\) | −1.43352 | −0.0548521 | −0.0274260 | − | 0.999624i | \(-0.508731\pi\) | ||||
−0.0274260 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(684\) | 1.76494 | − | 1.28230i | 0.0674840 | − | 0.0490300i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0541 | − | 30.9433i | 0.383867 | − | 1.18142i | ||||
\(687\) | −17.7739 | − | 12.9135i | −0.678115 | − | 0.492679i | ||||
\(688\) | 10.3042 | + | 7.48644i | 0.392844 | + | 0.285418i | ||||
\(689\) | −6.10075 | + | 18.7762i | −0.232420 | + | 0.715315i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0832 | − | 12.4117i | 0.649876 | − | 0.472163i | −0.213353 | − | 0.976975i | \(-0.568438\pi\) |
0.863229 | + | 0.504812i | \(0.168438\pi\) | |||||||
\(692\) | −28.3560 | −1.07793 | ||||||||
\(693\) | −3.29981 | − | 2.82625i | −0.125349 | − | 0.107360i | ||||
\(694\) | −36.2182 | −1.37482 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.0281679 | − | 0.0866920i | −0.00106770 | − | 0.00328605i | ||||
\(697\) | −11.1322 | + | 34.2613i | −0.421661 | + | 1.29774i | ||||
\(698\) | −9.08317 | − | 6.59931i | −0.343803 | − | 0.249788i | ||||
\(699\) | 6.52071 | + | 4.73757i | 0.246636 | + | 0.179191i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.61516 | − | 4.97094i | −0.0610036 | − | 0.187750i | 0.915910 | − | 0.401383i | \(-0.131470\pi\) |
−0.976914 | + | 0.213633i | \(0.931470\pi\) | |||||||
\(702\) | 3.18735 | − | 2.31575i | 0.120299 | − | 0.0874022i | ||||
\(703\) | 2.29879 | 0.0867005 | ||||||||
\(704\) | 11.0643 | − | 26.6069i | 0.417003 | − | 1.00279i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −46.0484 | + | 33.4561i | −1.73305 | + | 1.25914i | ||||
\(707\) | 2.92630 | + | 9.00623i | 0.110055 | + | 0.338714i | ||||
\(708\) | −2.06567 | + | 6.35747i | −0.0776326 | + | 0.238929i | ||||
\(709\) | −14.8032 | − | 10.7551i | −0.555944 | − | 0.403917i | 0.274028 | − | 0.961722i | \(-0.411644\pi\) |
−0.829972 | + | 0.557805i | \(0.811644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.339577 | − | 1.04511i | 0.0127351 | − | 0.0391947i | ||||
\(712\) | 0.406549 | + | 1.25123i | 0.0152361 | + | 0.0468918i | ||||
\(713\) | −1.27434 | + | 0.925861i | −0.0477243 | + | 0.0346738i | ||||
\(714\) | 8.03878 | 0.300844 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51.2909 | −1.91683 | ||||||||
\(717\) | 11.9790 | − | 8.70324i | 0.447363 | − | 0.325028i | ||||
\(718\) | 3.74111 | + | 11.5139i | 0.139617 | + | 0.429696i | ||||
\(719\) | −6.11462 | + | 18.8189i | −0.228037 | + | 0.701826i | 0.769932 | + | 0.638126i | \(0.220290\pi\) |
−0.997969 | + | 0.0636999i | \(0.979710\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.38473 | + | 6.81841i | 0.349506 | + | 0.253931i | ||||
\(722\) | −11.1892 | + | 34.4367i | −0.416418 | + | 1.28160i | ||||
\(723\) | −5.48232 | − | 16.8728i | −0.203890 | − | 0.627508i | ||||
\(724\) | −4.62089 | + | 3.35727i | −0.171734 | + | 0.124772i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.8448 | − | 10.0419i | 0.736508 | − | 0.372691i | ||||
\(727\) | 7.17943 | 0.266270 | 0.133135 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133135 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(728\) | 0.367674 | − | 0.267131i | 0.0136269 | − | 0.00990052i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.19519 | − | 5.95416i | −0.303110 | − | 0.220222i | ||||
\(732\) | 15.2928 | + | 11.1109i | 0.565239 | + | 0.410670i | ||||
\(733\) | 6.22921 | − | 19.1715i | 0.230081 | − | 0.708117i | −0.767655 | − | 0.640864i | \(-0.778576\pi\) |
0.997736 | − | 0.0672534i | \(-0.0214236\pi\) | |||||||
\(734\) | −11.0320 | − | 33.9529i | −0.407198 | − | 1.25323i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.99188 | −0.368305 | ||||||||
\(737\) | 26.9844 | − | 16.4845i | 0.993985 | − | 0.607214i | ||||
\(738\) | −23.9987 | −0.883406 | ||||||||
\(739\) | −14.7561 | + | 10.7210i | −0.542813 | + | 0.394377i | −0.825129 | − | 0.564945i | \(-0.808897\pi\) |
0.282316 | + | 0.959322i | \(0.408897\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.629108 | − | 1.93619i | 0.0231108 | − | 0.0711279i | ||||
\(742\) | −21.7103 | − | 15.7735i | −0.797012 | − | 0.579063i | ||||
\(743\) | 0.601874 | + | 0.437287i | 0.0220806 | + | 0.0160425i | 0.598771 | − | 0.800920i | \(-0.295656\pi\) |
−0.576690 | + | 0.816963i | \(0.695656\pi\) | |||||||
\(744\) | −0.0700110 | + | 0.215472i | −0.00256673 | + | 0.00789957i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.93573 | + | 3.58602i | −0.180710 | + | 0.131293i | ||||
\(747\) | −4.96681 | −0.181726 | ||||||||
\(748\) | −8.07054 | + | 19.4076i | −0.295088 | + | 0.709612i | ||||
\(749\) | 5.40938 | 0.197655 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.44667 | − | 13.6855i | −0.162261 | − | 0.499389i | 0.836563 | − | 0.547871i | \(-0.184562\pi\) |
−0.998824 | + | 0.0484819i | \(0.984562\pi\) | |||||||
\(752\) | 15.3690 | − | 47.3011i | 0.560451 | − | 1.72489i | ||||
\(753\) | 5.75951 | + | 4.18453i | 0.209888 | + | 0.152493i | ||||
\(754\) | −1.63183 | − | 1.18559i | −0.0594277 | − | 0.0431767i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.845256 | + | 2.60143i | 0.0307417 | + | 0.0946131i | ||||
\(757\) | 16.8803 | − | 12.2643i | 0.613525 | − | 0.445752i | −0.237129 | − | 0.971478i | \(-0.576206\pi\) |
0.850654 | + | 0.525726i | \(0.176206\pi\) | |||||||
\(758\) | 47.7191 | 1.73324 | ||||||||
\(759\) | −3.11814 | − | 2.67066i | −0.113181 | − | 0.0969388i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.33612 | + | 2.42384i | −0.120934 | + | 0.0878640i | −0.646608 | − | 0.762822i | \(-0.723813\pi\) |
0.525674 | + | 0.850686i | \(0.323813\pi\) | |||||||
\(762\) | 5.30215 | + | 16.3183i | 0.192077 | + | 0.591151i | ||||
\(763\) | 5.52303 | − | 16.9981i | 0.199947 | − | 0.615374i | ||||
\(764\) | 4.08862 | + | 2.97056i | 0.147921 | + | 0.107471i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.18806 | + | 15.9672i | −0.187452 | + | 0.576918i | ||||
\(767\) | 1.92767 | + | 5.93275i | 0.0696040 | + | 0.214219i | ||||
\(768\) | 11.7303 | − | 8.52256i | 0.423281 | − | 0.307531i | ||||
\(769\) | 43.9189 | 1.58375 | 0.791877 | − | 0.610680i | \(-0.209104\pi\) | ||||
0.791877 | + | 0.610680i | \(0.209104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5484 | 0.704017 | ||||||||
\(772\) | 31.2679 | − | 22.7174i | 1.12535 | − | 0.817618i | ||||
\(773\) | 7.91042 | + | 24.3458i | 0.284518 | + | 0.875657i | 0.986543 | + | 0.163504i | \(0.0522797\pi\) |
−0.702025 | + | 0.712153i | \(0.747720\pi\) | |||||||
\(774\) | 2.08533 | − | 6.41798i | 0.0749556 | − | 0.230690i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.13915 | + | 1.55418i | 0.0767908 | + | 0.0557918i | ||||
\(777\) | −0.890669 | + | 2.74120i | −0.0319526 | + | 0.0983399i | ||||
\(778\) | 18.6496 | + | 57.3977i | 0.668622 | + | 2.05781i | ||||
\(779\) | −10.0327 | + | 7.28916i | −0.359457 | + | 0.261161i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8051 | − | 1.10581i | −0.493985 | − | 0.0395692i | ||||
\(782\) | 7.59622 | 0.271640 | ||||||||
\(783\) | 0.414193 | − | 0.300928i | 0.0148020 | − | 0.0107543i | ||||
\(784\) | 6.23111 | + | 19.1774i | 0.222540 | + | 0.684906i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.6089 | − | 8.43439i | −0.414077 | − | 0.300845i | ||||
\(787\) | 1.55087 | + | 1.12677i | 0.0552825 | + | 0.0401651i | 0.615083 | − | 0.788462i | \(-0.289122\pi\) |
−0.559801 | + | 0.828627i | \(0.689122\pi\) | |||||||
\(788\) | −15.2269 | + | 46.8635i | −0.542435 | + | 1.66944i | ||||
\(789\) | 8.29572 | + | 25.5316i | 0.295335 | + | 0.908949i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.2418 | −0.719717 | ||||||||
\(792\) | −0.588621 | − | 0.0471497i | −0.0209157 | − | 0.00167539i | ||||
\(793\) | 17.6401 | 0.626419 | ||||||||
\(794\) | −17.0382 | + | 12.3790i | −0.604663 | + | 0.439313i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.4342 | + | 50.5794i | −0.582496 | + | 1.79274i | ||||
\(797\) | −20.7262 | − | 15.0585i | −0.734161 | − | 0.533399i | 0.156716 | − | 0.987644i | \(-0.449909\pi\) |
−0.890877 | + | 0.454244i | \(0.849909\pi\) | |||||||
\(798\) | 2.23876 | + | 1.62656i | 0.0792514 | + | 0.0575795i | ||||
\(799\) | −12.2234 | + | 37.6197i | −0.432433 | + | 1.33089i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.97806 | + | 4.34331i | −0.211224 | + | 0.153463i | ||||
\(802\) | 67.0283 | 2.36685 | ||||||||
\(803\) | −10.0843 | − | 42.2630i | −0.355866 | − | 1.49143i | ||||
\(804\) | −19.9078 | −0.702095 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.54921 | + | 4.76798i | 0.0545686 | + | 0.167945i | ||||
\(807\) | 5.66789 | − | 17.4440i | 0.199519 | − | 0.614057i | ||||
\(808\) | 1.04126 | + | 0.756519i | 0.0366314 | + | 0.0266142i | ||||
\(809\) | −5.42843 | − | 3.94399i | −0.190853 | − | 0.138663i | 0.488255 | − | 0.872701i | \(-0.337634\pi\) |
−0.679109 | + | 0.734038i | \(0.737634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.45747 | − | 22.9517i | −0.261867 | − | 0.805945i | −0.992399 | − | 0.123065i | \(-0.960728\pi\) |
0.730531 | − | 0.682879i | \(-0.239272\pi\) | |||||||
\(812\) | 1.13294 | − | 0.823132i | 0.0397585 | − | 0.0288863i | ||||
\(813\) | 16.2060 | 0.568369 | ||||||||
\(814\) | −11.2061 | − | 9.59790i | −0.392773 | − | 0.336406i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.37020 | + | 6.80785i | −0.328023 | + | 0.238322i | ||||
\(817\) | −1.07757 | − | 3.31641i | −0.0376993 | − | 0.116027i | ||||
\(818\) | −15.6379 | + | 48.1285i | −0.546767 | + | 1.68277i | ||||
\(819\) | 2.06507 | + | 1.50036i | 0.0721594 | + | 0.0524269i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.17008 | − | 3.60115i | 0.0408362 | − | 0.125681i | −0.928560 | − | 0.371182i | \(-0.878953\pi\) |
0.969396 | + | 0.245501i | \(0.0789525\pi\) | |||||||
\(822\) | −0.779050 | − | 2.39767i | −0.0271725 | − | 0.0836283i | ||||
\(823\) | −33.1638 | + | 24.0949i | −1.15602 | + | 0.839896i | −0.989269 | − | 0.146104i | \(-0.953327\pi\) |
−0.166748 | + | 0.986000i | \(0.553327\pi\) | |||||||
\(824\) | 1.57663 | 0.0549244 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.47925 | −0.295031 | ||||||||
\(827\) | 36.6611 | − | 26.6358i | 1.27483 | − | 0.926219i | 0.275447 | − | 0.961316i | \(-0.411174\pi\) |
0.999384 | + | 0.0350975i | \(0.0111742\pi\) | |||||||
\(828\) | 0.798723 | + | 2.45822i | 0.0277575 | + | 0.0854289i | ||||
\(829\) | 9.58044 | − | 29.4856i | 0.332743 | − | 1.02408i | −0.635081 | − | 0.772446i | \(-0.719033\pi\) |
0.967823 | − | 0.251630i | \(-0.0809668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.2048 | + | 11.0469i | 0.527448 | + | 0.383213i | ||||
\(832\) | −5.23154 | + | 16.1010i | −0.181371 | + | 0.558203i | ||||
\(833\) | −4.95576 | − | 15.2523i | −0.171707 | − | 0.528459i | ||||
\(834\) | −21.9888 | + | 15.9758i | −0.761409 | + | 0.553196i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.17452 | + | 3.77194i | −0.213550 | + | 0.130455i | ||||
\(837\) | −1.27249 | −0.0439838 | ||||||||
\(838\) | 7.16715 | − | 5.20724i | 0.247585 | − | 0.179881i | ||||
\(839\) | 0.696077 | + | 2.14230i | 0.0240312 | + | 0.0739606i | 0.962353 | − | 0.271803i | \(-0.0876199\pi\) |
−0.938322 | + | 0.345764i | \(0.887620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2494 | + | 16.8917i | 0.801705 | + | 0.582473i | ||||
\(842\) | −52.8245 | − | 38.3792i | −1.82045 | − | 1.32264i | ||||
\(843\) | 9.51773 | − | 29.2925i | 0.327808 | − | 1.00889i | ||||
\(844\) | −3.06270 | − | 9.42603i | −0.105423 | − | 0.324457i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −26.3512 | −0.905972 | ||||||||
\(847\) | 10.1608 | + | 10.2175i | 0.349130 | + | 0.351079i | ||||
\(848\) | 38.6643 | 1.32774 | ||||||||
\(849\) | 15.3405 | − | 11.1455i | 0.526485 | − | 0.382514i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.841636 | + | 2.59029i | −0.0288509 | + | 0.0887939i | ||||
\(852\) | 7.05394 | + | 5.12499i | 0.241664 | + | 0.175579i | ||||
\(853\) | 3.95242 | + | 2.87160i | 0.135328 | + | 0.0983218i | 0.653390 | − | 0.757022i | \(-0.273346\pi\) |
−0.518062 | + | 0.855343i | \(0.673346\pi\) | |||||||
\(854\) | −7.40955 | + | 22.8043i | −0.253550 | + | 0.780345i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.594799 | − | 0.432146i | 0.0203298 | − | 0.0147705i | ||||
\(857\) | 21.9877 | 0.751086 | 0.375543 | − | 0.926805i | \(-0.377456\pi\) | ||||
0.375543 | + | 0.926805i | \(0.377456\pi\) | |||||||
\(858\) | −11.1508 | + | 6.81186i | −0.380680 | + | 0.232553i | ||||
\(859\) | 3.07460 | 0.104904 | 0.0524520 | − | 0.998623i | \(-0.483296\pi\) | ||||
0.0524520 | + | 0.998623i | \(0.483296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.80480 | − | 14.7877i | −0.163747 | − | 0.503962i | ||||
\(862\) | 2.35064 | − | 7.23452i | 0.0800630 | − | 0.246409i | ||||
\(863\) | −23.0306 | − | 16.7327i | −0.783971 | − | 0.569589i | 0.122197 | − | 0.992506i | \(-0.461006\pi\) |
−0.906168 | + | 0.422917i | \(0.861006\pi\) | |||||||
\(864\) | −6.53030 | − | 4.74454i | −0.222165 | − | 0.161413i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.1985 | + | 34.4655i | 0.380541 | + | 1.17119i | ||||
\(867\) | −6.30093 | + | 4.57790i | −0.213991 | + | 0.155473i | ||||
\(868\) | −3.48066 | −0.118141 | ||||||||
\(869\) | −1.39942 | + | 3.36525i | −0.0474721 | + | 0.114158i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.0298 | + | 10.9198i | −0.509265 | + | 0.370003i | ||||
\(872\) | −0.750658 | − | 2.31029i | −0.0254205 | − | 0.0782362i | ||||
\(873\) | −4.58920 | + | 14.1241i | −0.155321 | + | 0.478029i | ||||
\(874\) | 2.11552 | + | 1.53701i | 0.0715584 | + | 0.0519902i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.45304 | + | 26.0158i | −0.285602 | + | 0.878991i | ||||
\(877\) | −1.20130 | − | 3.69721i | −0.0405649 | − | 0.124846i | 0.928723 | − | 0.370774i | \(-0.120907\pi\) |
−0.969288 | + | 0.245928i | \(0.920907\pi\) | |||||||
\(878\) | −0.408372 | + | 0.296700i | −0.0137819 | + | 0.0100131i | ||||
\(879\) | 2.93588 | 0.0990248 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.09160 | 0.104159 | 0.0520793 | − | 0.998643i | \(-0.483415\pi\) | ||||
0.0520793 | + | 0.998643i | \(0.483415\pi\) | |||||||
\(882\) | 8.64323 | − | 6.27967i | 0.291033 | − | 0.211448i | ||||
\(883\) | 12.5339 | + | 38.5753i | 0.421799 | + | 1.29816i | 0.906026 | + | 0.423221i | \(0.139101\pi\) |
−0.484227 | + | 0.874942i | \(0.660899\pi\) | |||||||
\(884\) | 3.81599 | − | 11.7444i | 0.128345 | − | 0.395007i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.7429 | − | 28.8749i | −1.33519 | − | 0.970071i | ||||
\(887\) | −4.82010 | + | 14.8348i | −0.161843 | + | 0.498102i | −0.998790 | − | 0.0491822i | \(-0.984338\pi\) |
0.836947 | + | 0.547285i | \(0.184338\pi\) | |||||||
\(888\) | 0.121054 | + | 0.372567i | 0.00406232 | + | 0.0125025i | ||||
\(889\) | −8.99357 | + | 6.53421i | −0.301635 | + | 0.219150i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.769762 | − | 3.22606i | −0.0257880 | − | 0.108077i | ||||
\(892\) | −1.06663 | −0.0357134 | ||||||||
\(893\) | −11.0161 | + | 8.00366i | −0.368640 | + | 0.267832i | ||||
\(894\) | 9.02904 | + | 27.7885i | 0.301976 | + | 0.929387i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.50806 | − | 1.09567i | −0.0503807 | − | 0.0366037i | ||||
\(897\) | 1.95138 | + | 1.41776i | 0.0651548 | + | 0.0473377i | ||||
\(898\) | −10.2548 | + | 31.5609i | −0.342206 | + | 1.05320i | ||||
\(899\) | 0.201318 | + | 0.619593i | 0.00671433 | + | 0.0206646i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.7507 | −1.02445 | ||||||||
\(902\) | 79.3407 | + | 6.35534i | 2.64176 | + | 0.211610i | ||||
\(903\) | 4.37217 | 0.145497 | ||||||||
\(904\) | −2.22573 | + | 1.61709i | −0.0740266 | + | 0.0537835i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.0756 | − | 37.1648i | 0.401185 | − | 1.23472i | ||||
\(907\) | 7.61986 | + | 5.53615i | 0.253013 | + | 0.183825i | 0.707061 | − | 0.707152i | \(-0.250021\pi\) |
−0.454048 | + | 0.890977i | \(0.650021\pi\) | |||||||
\(908\) | −17.3402 | − | 12.5984i | −0.575456 | − | 0.418093i | ||||
\(909\) | −2.23386 | + | 6.87511i | −0.0740924 | + | 0.228033i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.59196 | + | 2.60971i | −0.119007 | + | 0.0864637i | −0.645697 | − | 0.763594i | \(-0.723433\pi\) |
0.526690 | + | 0.850058i | \(0.323433\pi\) | |||||||
\(912\) | −3.98705 | −0.132024 | ||||||||
\(913\) | 16.4204 | + | 1.31531i | 0.543437 | + | 0.0435304i | ||||
\(914\) | 28.7927 | 0.952380 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.1758 | − | 43.6288i | −0.468383 | − | 1.44154i | ||||
\(917\) | 2.87291 | − | 8.84191i | 0.0948719 | − | 0.291986i | ||||
\(918\) | 4.96460 | + | 3.60699i | 0.163856 | + | 0.119048i | ||||
\(919\) | −24.8246 | − | 18.0361i | −0.818888 | − | 0.594957i | 0.0975057 | − | 0.995235i | \(-0.468914\pi\) |
−0.916394 | + | 0.400278i | \(0.868914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.71352 | − | 17.5844i | −0.188267 | − | 0.579425i | ||||
\(922\) | 12.0072 | − | 8.72374i | 0.395436 | − | 0.287301i | ||||
\(923\) | 8.13664 | 0.267821 | ||||||||
\(924\) | −2.10554 | − | 8.82426i | −0.0692671 | − | 0.290297i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −47.6263 | + | 34.6025i | −1.56510 | + | 1.13711i | ||||
\(927\) | 2.73642 | + | 8.42184i | 0.0898759 | + | 0.276610i | ||||
\(928\) | −1.27703 | + | 3.93031i | −0.0419207 | + | 0.129019i | ||||
\(929\) | 16.7900 | + | 12.1986i | 0.550861 | + | 0.400224i | 0.828103 | − | 0.560576i | \(-0.189420\pi\) |
−0.277242 | + | 0.960800i | \(0.589420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.70597 | − | 5.25043i | 0.0559108 | − | 0.172076i | ||||
\(932\) | 5.20070 | + | 16.0061i | 0.170355 | + | 0.524298i | ||||
\(933\) | 18.7933 | − | 13.6541i | 0.615265 | − | 0.447016i | ||||
\(934\) | 34.5283 | 1.12980 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.346930 | 0.0113398 | ||||||||
\(937\) | −4.95966 | + | 3.60340i | −0.162025 | + | 0.117718i | −0.665843 | − | 0.746092i | \(-0.731928\pi\) |
0.503818 | + | 0.863810i | \(0.331928\pi\) | |||||||
\(938\) | −7.80344 | − | 24.0165i | −0.254791 | − | 0.784167i | ||||
\(939\) | −0.693665 | + | 2.13488i | −0.0226369 | + | 0.0696692i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.7733 | + | 30.3501i | 1.36177 | + | 0.989385i | 0.998330 | + | 0.0577680i | \(0.0183984\pi\) |
0.363442 | + | 0.931617i | \(0.381602\pi\) | |||||||
\(942\) | 13.9859 | − | 43.0441i | 0.455684 | − | 1.40245i | ||||
\(943\) | −4.54029 | − | 13.9736i | −0.147852 | − | 0.455042i | ||||
\(944\) | 9.88363 | − | 7.18088i | 0.321685 | − | 0.233718i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.59378 | + | 20.6658i | −0.279408 | + | 0.671904i | ||||
\(947\) | 23.2475 | 0.755444 | 0.377722 | − | 0.925919i | \(-0.376708\pi\) | ||||
0.377722 | + | 0.925919i | \(0.376708\pi\) | |||||||
\(948\) | 1.85633 | − | 1.34871i | 0.0602909 | − | 0.0438039i | ||||
\(949\) | 7.88831 | + | 24.2777i | 0.256065 | + | 0.788088i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.16486 | + | 3.75249i | 0.167482 | + | 0.121683i | ||||
\(952\) | 0.572687 | + | 0.416081i | 0.0185609 | + | 0.0134853i | ||||
\(953\) | 6.43507 | − | 19.8051i | 0.208453 | − | 0.641551i | −0.791101 | − | 0.611685i | \(-0.790492\pi\) |
0.999554 | − | 0.0298658i | \(-0.00950800\pi\) | |||||||
\(954\) | −6.33035 | − | 19.4828i | −0.204953 | − | 0.630780i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 30.9175 | 0.999945 | ||||||||
\(957\) | −1.44903 | + | 0.885194i | −0.0468404 | + | 0.0286142i | ||||
\(958\) | 2.24580 | 0.0725584 | ||||||||
\(959\) | 1.32143 | − | 0.960078i | 0.0426713 | − | 0.0310025i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.07915 | + | 27.9428i | −0.292876 | + | 0.901379i | ||||
\(962\) | 7.01294 | + | 5.09520i | 0.226106 | + | 0.164276i | ||||
\(963\) | 3.34073 | + | 2.42719i | 0.107654 | + | 0.0782150i | ||||
\(964\) | 11.4474 | − | 35.2315i | 0.368696 | − | 1.13473i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.65247 | + | 1.92713i | −0.0853419 | + | 0.0620045i | ||||
\(967\) | 26.7093 | 0.858913 | 0.429456 | − | 0.903088i | \(-0.358705\pi\) | ||||
0.429456 | + | 0.903088i | \(0.358705\pi\) | |||||||
\(968\) | 1.93351 | + | 0.311757i | 0.0621455 | + | 0.0100203i | ||||
\(969\) | 3.17100 | 0.101867 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.00422 | − | 27.7121i | −0.288959 | − | 0.889324i | −0.985184 | − | 0.171501i | \(-0.945138\pi\) |
0.696225 | − | 0.717824i | \(-0.254862\pi\) | |||||||
\(972\) | −0.645245 | + | 1.98586i | −0.0206963 | + | 0.0636965i | ||||
\(973\) | −14.2464 | − | 10.3506i | −0.456720 | − | 0.331826i | ||||
\(974\) | −43.7940 | − | 31.8182i | −1.40325 | − | 1.01952i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.6756 | − | 32.8562i | −0.341718 | − | 1.05170i | ||||
\(977\) | −20.5646 | + | 14.9411i | −0.657921 | + | 0.478008i | −0.865960 | − | 0.500113i | \(-0.833292\pi\) |
0.208039 | + | 0.978121i | \(0.433292\pi\) | |||||||
\(978\) | −23.2590 | −0.743740 | ||||||||
\(979\) | 20.9139 | − | 12.7760i | 0.668410 | − | 0.408324i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0380 | − | 8.01956i | 0.352415 | − | 0.256045i | ||||
\(982\) | 20.0462 | + | 61.6957i | 0.639698 | + | 1.96879i | ||||
\(983\) | 13.5014 | − | 41.5530i | 0.430627 | − | 1.32534i | −0.466874 | − | 0.884324i | \(-0.654620\pi\) |
0.897502 | − | 0.441011i | \(-0.145380\pi\) | |||||||
\(984\) | −1.70968 | − | 1.24216i | −0.0545027 | − | 0.0395985i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.970853 | − | 2.98798i | 0.0309183 | − | 0.0951566i | ||||
\(987\) | −5.27579 | − | 16.2372i | −0.167930 | − | 0.516836i | ||||
\(988\) | 3.43908 | − | 2.49864i | 0.109412 | − | 0.0794923i | ||||
\(989\) | 4.13147 | 0.131373 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.9993 | 1.74711 | 0.873555 | − | 0.486725i | \(-0.161809\pi\) | ||||
0.873555 | + | 0.486725i | \(0.161809\pi\) | |||||||
\(992\) | 8.30978 | − | 6.03741i | 0.263836 | − | 0.191688i | ||||
\(993\) | 4.75280 | + | 14.6276i | 0.150826 | + | 0.464193i | ||||
\(994\) | −3.41772 | + | 10.5186i | −0.108403 | + | 0.333631i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.39030 | − | 6.09591i | −0.265857 | − | 0.193156i | ||||
\(997\) | −4.71321 | + | 14.5058i | −0.149269 | + | 0.459402i | −0.997535 | − | 0.0701677i | \(-0.977647\pi\) |
0.848266 | + | 0.529570i | \(0.177647\pi\) | |||||||
\(998\) | −12.6831 | − | 39.0347i | −0.401478 | − | 1.23562i | ||||
\(999\) | −1.78003 | + | 1.29327i | −0.0563178 | + | 0.0409172i |
(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 | 825.2.n.n.751.1 | yes | 16 | |
5.2 | odd | 4 | 825.2.bx.j.124.2 | 32 | |||
5.3 | odd | 4 | 825.2.bx.j.124.7 | 32 | |||
5.4 | even | 2 | 825.2.n.m.751.4 | yes | 16 | ||
11.2 | odd | 10 | 9075.2.a.dt.1.2 | 8 | |||
11.4 | even | 5 | inner | 825.2.n.n.301.1 | yes | 16 | |
11.9 | even | 5 | 9075.2.a.dv.1.7 | 8 | |||
55.4 | even | 10 | 825.2.n.m.301.4 | ✓ | 16 | ||
55.9 | even | 10 | 9075.2.a.du.1.2 | 8 | |||
55.24 | odd | 10 | 9075.2.a.dw.1.7 | 8 | |||
55.37 | odd | 20 | 825.2.bx.j.499.7 | 32 | |||
55.48 | odd | 20 | 825.2.bx.j.499.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.m.301.4 | ✓ | 16 | 55.4 | even | 10 | ||
825.2.n.m.751.4 | yes | 16 | 5.4 | even | 2 | ||
825.2.n.n.301.1 | yes | 16 | 11.4 | even | 5 | inner | |
825.2.n.n.751.1 | yes | 16 | 1.1 | even | 1 | trivial | |
825.2.bx.j.124.2 | 32 | 5.2 | odd | 4 | |||
825.2.bx.j.124.7 | 32 | 5.3 | odd | 4 | |||
825.2.bx.j.499.2 | 32 | 55.48 | odd | 20 | |||
825.2.bx.j.499.7 | 32 | 55.37 | odd | 20 | |||
9075.2.a.dt.1.2 | 8 | 11.2 | odd | 10 | |||
9075.2.a.du.1.2 | 8 | 55.9 | even | 10 | |||
9075.2.a.dv.1.7 | 8 | 11.9 | even | 5 | |||
9075.2.a.dw.1.7 | 8 | 55.24 | odd | 10 |