Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(36,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.36");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.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: | \(3.07424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
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 | 36.2 | ||
Root | \(1.69513 - 1.23158i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 385.36 |
Dual form | 385.2.n.c.246.2 |
$q$-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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93376 | − | 1.40496i | 1.36737 | − | 0.993455i | 0.369437 | − | 0.929256i | \(-0.379551\pi\) |
0.997937 | − | 0.0641992i | \(-0.0204493\pi\) | |||||||
\(3\) | −0.456498 | − | 1.40496i | −0.263559 | − | 0.811153i | −0.992022 | − | 0.126067i | \(-0.959765\pi\) |
0.728462 | − | 0.685086i | \(-0.240235\pi\) | |||||||
\(4\) | 1.14748 | − | 3.53158i | 0.573741 | − | 1.76579i | ||||
\(5\) | −0.809017 | − | 0.587785i | −0.361803 | − | 0.262866i | ||||
\(6\) | −2.85666 | − | 2.07549i | −1.16623 | − | 0.847314i | ||||
\(7\) | 0.309017 | − | 0.951057i | 0.116797 | − | 0.359466i | ||||
\(8\) | −1.26552 | − | 3.89486i | −0.447427 | − | 1.37704i | ||||
\(9\) | 0.661536 | − | 0.480634i | 0.220512 | − | 0.160211i | ||||
\(10\) | −2.39026 | −0.755866 | ||||||||
\(11\) | 1.20381 | + | 3.09044i | 0.362964 | + | 0.931803i | ||||
\(12\) | −5.48555 | −1.58354 | ||||||||
\(13\) | −3.12889 | + | 2.27327i | −0.867797 | + | 0.630491i | −0.929995 | − | 0.367572i | \(-0.880189\pi\) |
0.0621978 | + | 0.998064i | \(0.480189\pi\) | |||||||
\(14\) | −0.738630 | − | 2.27327i | −0.197407 | − | 0.607557i | ||||
\(15\) | −0.456498 | + | 1.40496i | −0.117867 | + | 0.362759i | ||||
\(16\) | −1.91102 | − | 1.38844i | −0.477755 | − | 0.347109i | ||||
\(17\) | 1.23192 | + | 0.895044i | 0.298785 | + | 0.217080i | 0.727069 | − | 0.686564i | \(-0.240882\pi\) |
−0.428284 | + | 0.903644i | \(0.640882\pi\) | |||||||
\(18\) | 0.603980 | − | 1.85886i | 0.142359 | − | 0.438137i | ||||
\(19\) | −0.261370 | − | 0.804414i | −0.0599624 | − | 0.184545i | 0.916589 | − | 0.399832i | \(-0.130931\pi\) |
−0.976551 | + | 0.215287i | \(0.930931\pi\) | |||||||
\(20\) | −3.00415 | + | 2.18264i | −0.671747 | + | 0.488053i | ||||
\(21\) | −1.47726 | −0.322365 | ||||||||
\(22\) | 6.66983 | + | 4.28486i | 1.42201 | + | 0.913535i | ||||
\(23\) | −0.986585 | −0.205717 | −0.102859 | − | 0.994696i | \(-0.532799\pi\) | ||||
−0.102859 | + | 0.994696i | \(0.532799\pi\) | |||||||
\(24\) | −4.89440 | + | 3.55599i | −0.999066 | + | 0.725864i | ||||
\(25\) | 0.309017 | + | 0.951057i | 0.0618034 | + | 0.190211i | ||||
\(26\) | −2.85666 | + | 8.79191i | −0.560238 | + | 1.72423i | ||||
\(27\) | −4.56265 | − | 3.31496i | −0.878082 | − | 0.637964i | ||||
\(28\) | −3.00415 | − | 2.18264i | −0.567730 | − | 0.412480i | ||||
\(29\) | 2.01820 | − | 6.21138i | 0.374770 | − | 1.15342i | −0.568863 | − | 0.822432i | \(-0.692617\pi\) |
0.943634 | − | 0.330992i | \(-0.107383\pi\) | |||||||
\(30\) | 1.09115 | + | 3.35821i | 0.199216 | + | 0.613122i | ||||
\(31\) | 6.88769 | − | 5.00420i | 1.23707 | − | 0.898781i | 0.239667 | − | 0.970855i | \(-0.422962\pi\) |
0.997399 | + | 0.0720737i | \(0.0229617\pi\) | |||||||
\(32\) | 2.54445 | 0.449799 | ||||||||
\(33\) | 3.79240 | − | 3.10209i | 0.660172 | − | 0.540005i | ||||
\(34\) | 3.63974 | 0.624210 | ||||||||
\(35\) | −0.809017 | + | 0.587785i | −0.136749 | + | 0.0993538i | ||||
\(36\) | −0.938299 | − | 2.88779i | −0.156383 | − | 0.481298i | ||||
\(37\) | −2.92705 | + | 9.00854i | −0.481204 | + | 1.48099i | 0.356200 | + | 0.934410i | \(0.384072\pi\) |
−0.837404 | + | 0.546584i | \(0.815928\pi\) | |||||||
\(38\) | −1.63559 | − | 1.18833i | −0.265328 | − | 0.192772i | ||||
\(39\) | 4.62218 | + | 3.35821i | 0.740141 | + | 0.537744i | ||||
\(40\) | −1.26552 | + | 3.89486i | −0.200096 | + | 0.615831i | ||||
\(41\) | −1.02613 | − | 3.15810i | −0.160255 | − | 0.493213i | 0.838401 | − | 0.545054i | \(-0.183491\pi\) |
−0.998655 | + | 0.0518415i | \(0.983491\pi\) | |||||||
\(42\) | −2.85666 | + | 2.07549i | −0.440793 | + | 0.320255i | ||||
\(43\) | 3.28155 | 0.500431 | 0.250216 | − | 0.968190i | \(-0.419498\pi\) | ||||
0.250216 | + | 0.968190i | \(0.419498\pi\) | |||||||
\(44\) | 12.2955 | − | 0.705148i | 1.85362 | − | 0.106305i | ||||
\(45\) | −0.817703 | −0.121896 | ||||||||
\(46\) | −1.90782 | + | 1.38611i | −0.281292 | + | 0.204371i | ||||
\(47\) | 4.13757 | + | 12.7341i | 0.603527 | + | 1.85747i | 0.506615 | + | 0.862172i | \(0.330896\pi\) |
0.0969117 | + | 0.995293i | \(0.469104\pi\) | |||||||
\(48\) | −1.07832 | + | 3.31872i | −0.155642 | + | 0.479016i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 1.93376 | + | 1.40496i | 0.273475 | + | 0.198691i | ||||
\(51\) | 0.695128 | − | 2.13939i | 0.0973375 | − | 0.299574i | ||||
\(52\) | 4.43790 | + | 13.6585i | 0.615427 | + | 1.89409i | ||||
\(53\) | 2.52368 | − | 1.83356i | 0.346655 | − | 0.251859i | −0.400810 | − | 0.916161i | \(-0.631271\pi\) |
0.747464 | + | 0.664302i | \(0.231271\pi\) | |||||||
\(54\) | −13.4804 | −1.83445 | ||||||||
\(55\) | 0.842610 | − | 3.20780i | 0.113617 | − | 0.432540i | ||||
\(56\) | −4.09529 | −0.547257 | ||||||||
\(57\) | −1.01085 | + | 0.734428i | −0.133891 | + | 0.0972773i | ||||
\(58\) | −4.82402 | − | 14.8468i | −0.633424 | − | 1.94948i | ||||
\(59\) | −1.96735 | + | 6.05488i | −0.256127 | + | 0.788279i | 0.737478 | + | 0.675371i | \(0.236016\pi\) |
−0.993605 | + | 0.112908i | \(0.963984\pi\) | |||||||
\(60\) | 4.43790 | + | 3.22433i | 0.572931 | + | 0.416259i | ||||
\(61\) | 0.372697 | + | 0.270780i | 0.0477189 | + | 0.0346698i | 0.611389 | − | 0.791330i | \(-0.290611\pi\) |
−0.563670 | + | 0.826000i | \(0.690611\pi\) | |||||||
\(62\) | 6.28844 | − | 19.3538i | 0.798633 | − | 2.45794i | ||||
\(63\) | −0.252684 | − | 0.777682i | −0.0318352 | − | 0.0979787i | ||||
\(64\) | 8.74238 | − | 6.35171i | 1.09280 | − | 0.793964i | ||||
\(65\) | 3.86752 | 0.479706 | ||||||||
\(66\) | 2.97528 | − | 11.3269i | 0.366232 | − | 1.39424i | ||||
\(67\) | −10.1146 | −1.23569 | −0.617845 | − | 0.786300i | \(-0.711994\pi\) | ||||
−0.617845 | + | 0.786300i | \(0.711994\pi\) | |||||||
\(68\) | 4.57453 | − | 3.32359i | 0.554744 | − | 0.403045i | ||||
\(69\) | 0.450375 | + | 1.38611i | 0.0542187 | + | 0.166868i | ||||
\(70\) | −0.738630 | + | 2.27327i | −0.0882832 | + | 0.271708i | ||||
\(71\) | 4.65897 | + | 3.38494i | 0.552918 | + | 0.401719i | 0.828860 | − | 0.559456i | \(-0.188990\pi\) |
−0.275942 | + | 0.961174i | \(0.588990\pi\) | |||||||
\(72\) | −2.70918 | − | 1.96834i | −0.319280 | − | 0.231971i | ||||
\(73\) | −1.66165 | + | 5.11404i | −0.194482 | + | 0.598553i | 0.805501 | + | 0.592595i | \(0.201897\pi\) |
−0.999982 | + | 0.00595804i | \(0.998103\pi\) | |||||||
\(74\) | 6.99640 | + | 21.5327i | 0.813315 | + | 2.50313i | ||||
\(75\) | 1.19513 | − | 0.868312i | 0.138002 | − | 0.100264i | ||||
\(76\) | −3.14077 | −0.360271 | ||||||||
\(77\) | 3.31118 | − | 0.189896i | 0.377344 | − | 0.0216407i | ||||
\(78\) | 13.6563 | 1.54627 | ||||||||
\(79\) | 4.63426 | − | 3.36698i | 0.521394 | − | 0.378815i | −0.295735 | − | 0.955270i | \(-0.595564\pi\) |
0.817129 | + | 0.576455i | \(0.195564\pi\) | |||||||
\(80\) | 0.729944 | + | 2.24654i | 0.0816102 | + | 0.251170i | ||||
\(81\) | −1.81648 | + | 5.59055i | −0.201831 | + | 0.621172i | ||||
\(82\) | −6.42129 | − | 4.66534i | −0.709113 | − | 0.515200i | ||||
\(83\) | −9.90175 | − | 7.19404i | −1.08686 | − | 0.789649i | −0.107992 | − | 0.994152i | \(-0.534442\pi\) |
−0.978866 | + | 0.204503i | \(0.934442\pi\) | |||||||
\(84\) | −1.69513 | + | 5.21707i | −0.184954 | + | 0.569229i | ||||
\(85\) | −0.470553 | − | 1.44821i | −0.0510386 | − | 0.157081i | ||||
\(86\) | 6.34572 | − | 4.61044i | 0.684277 | − | 0.497156i | ||||
\(87\) | −9.64803 | −1.03438 | ||||||||
\(88\) | 10.5134 | − | 8.59969i | 1.12073 | − | 0.916730i | ||||
\(89\) | −8.86318 | −0.939496 | −0.469748 | − | 0.882801i | \(-0.655655\pi\) | ||||
−0.469748 | + | 0.882801i | \(0.655655\pi\) | |||||||
\(90\) | −1.58124 | + | 1.14884i | −0.166677 | + | 0.121098i | ||||
\(91\) | 1.19513 | + | 3.67823i | 0.125284 | + | 0.385583i | ||||
\(92\) | −1.13209 | + | 3.48421i | −0.118028 | + | 0.363254i | ||||
\(93\) | −10.1749 | − | 7.39251i | −1.05509 | − | 0.766568i | ||||
\(94\) | 25.8920 | + | 18.8116i | 2.67056 | + | 1.94027i | ||||
\(95\) | −0.261370 | + | 0.804414i | −0.0268160 | + | 0.0825312i | ||||
\(96\) | −1.16154 | − | 3.57484i | −0.118549 | − | 0.364855i | ||||
\(97\) | −5.14077 | + | 3.73499i | −0.521967 | + | 0.379231i | −0.817344 | − | 0.576150i | \(-0.804555\pi\) |
0.295378 | + | 0.955381i | \(0.404555\pi\) | |||||||
\(98\) | −2.39026 | −0.241452 | ||||||||
\(99\) | 2.28174 | + | 1.46584i | 0.229323 | + | 0.147323i | ||||
\(100\) | 3.71333 | 0.371333 | ||||||||
\(101\) | 6.06813 | − | 4.40875i | 0.603802 | − | 0.438687i | −0.243425 | − | 0.969920i | \(-0.578271\pi\) |
0.847226 | + | 0.531232i | \(0.178271\pi\) | |||||||
\(102\) | −1.66154 | − | 5.11368i | −0.164517 | − | 0.506330i | ||||
\(103\) | −1.97568 | + | 6.08051i | −0.194669 | + | 0.599130i | 0.805311 | + | 0.592852i | \(0.201998\pi\) |
−0.999980 | + | 0.00627773i | \(0.998002\pi\) | |||||||
\(104\) | 12.8137 | + | 9.30971i | 1.25649 | + | 0.912892i | ||||
\(105\) | 1.19513 | + | 0.868312i | 0.116633 | + | 0.0847385i | ||||
\(106\) | 2.30412 | − | 7.09134i | 0.223796 | − | 0.688772i | ||||
\(107\) | 4.41773 | + | 13.5964i | 0.427078 | + | 1.31441i | 0.900991 | + | 0.433838i | \(0.142841\pi\) |
−0.473913 | + | 0.880572i | \(0.657159\pi\) | |||||||
\(108\) | −16.9426 | + | 12.3095i | −1.63030 | + | 1.18448i | ||||
\(109\) | −15.6231 | −1.49642 | −0.748210 | − | 0.663462i | \(-0.769087\pi\) | ||||
−0.748210 | + | 0.663462i | \(0.769087\pi\) | |||||||
\(110\) | −2.87743 | − | 7.38695i | −0.274352 | − | 0.704318i | ||||
\(111\) | 13.9928 | 1.32814 | ||||||||
\(112\) | −1.91102 | + | 1.38844i | −0.180574 | + | 0.131195i | ||||
\(113\) | −4.44486 | − | 13.6799i | −0.418137 | − | 1.28689i | −0.909415 | − | 0.415890i | \(-0.863470\pi\) |
0.491278 | − | 0.871003i | \(-0.336530\pi\) | |||||||
\(114\) | −0.922906 | + | 2.84041i | −0.0864380 | + | 0.266029i | ||||
\(115\) | 0.798164 | + | 0.579900i | 0.0744292 | + | 0.0540760i | ||||
\(116\) | −19.6202 | − | 14.2549i | −1.82169 | − | 1.32353i | ||||
\(117\) | −0.977260 | + | 3.00770i | −0.0903477 | + | 0.278062i | ||||
\(118\) | 4.70248 | + | 14.4727i | 0.432898 | + | 1.33232i | ||||
\(119\) | 1.23192 | − | 0.895044i | 0.112930 | − | 0.0820486i | ||||
\(120\) | 6.04981 | 0.552270 | ||||||||
\(121\) | −8.10166 | + | 7.44064i | −0.736515 | + | 0.676422i | ||||
\(122\) | 1.10114 | 0.0996925 | ||||||||
\(123\) | −3.96857 | + | 2.88334i | −0.357834 | + | 0.259982i | ||||
\(124\) | −9.76927 | − | 30.0667i | −0.877306 | − | 2.70007i | ||||
\(125\) | 0.309017 | − | 0.951057i | 0.0276393 | − | 0.0850651i | ||||
\(126\) | −1.58124 | − | 1.14884i | −0.140868 | − | 0.102347i | ||||
\(127\) | 5.10556 | + | 3.70941i | 0.453045 | + | 0.329157i | 0.790797 | − | 0.612078i | \(-0.209666\pi\) |
−0.337752 | + | 0.941235i | \(0.609666\pi\) | |||||||
\(128\) | 6.40921 | − | 19.7255i | 0.566500 | − | 1.74351i | ||||
\(129\) | −1.49802 | − | 4.61044i | −0.131893 | − | 0.405926i | ||||
\(130\) | 7.47884 | − | 5.43370i | 0.655938 | − | 0.476567i | ||||
\(131\) | 11.9054 | 1.04018 | 0.520091 | − | 0.854111i | \(-0.325898\pi\) | ||||
0.520091 | + | 0.854111i | \(0.325898\pi\) | |||||||
\(132\) | −6.60358 | − | 16.9528i | −0.574768 | − | 1.47555i | ||||
\(133\) | −0.845811 | −0.0733411 | ||||||||
\(134\) | −19.5591 | + | 14.2105i | −1.68965 | + | 1.22760i | ||||
\(135\) | 1.74278 | + | 5.36371i | 0.149994 | + | 0.461635i | ||||
\(136\) | 1.92705 | − | 5.93085i | 0.165243 | − | 0.508566i | ||||
\(137\) | −17.5849 | − | 12.7762i | −1.50238 | − | 1.09154i | −0.969422 | − | 0.245401i | \(-0.921080\pi\) |
−0.532958 | − | 0.846142i | \(-0.678920\pi\) | |||||||
\(138\) | 2.81834 | + | 2.04765i | 0.239913 | + | 0.174307i | ||||
\(139\) | −2.30938 | + | 7.10753i | −0.195879 | + | 0.602853i | 0.804086 | + | 0.594513i | \(0.202655\pi\) |
−0.999965 | + | 0.00834062i | \(0.997345\pi\) | |||||||
\(140\) | 1.14748 | + | 3.53158i | 0.0969799 | + | 0.298473i | ||||
\(141\) | 16.0021 | − | 11.6262i | 1.34762 | − | 0.979105i | ||||
\(142\) | 13.7650 | 1.15514 | ||||||||
\(143\) | −10.7920 | − | 6.93305i | −0.902473 | − | 0.579771i | ||||
\(144\) | −1.93154 | −0.160961 | ||||||||
\(145\) | −5.28371 | + | 3.83884i | −0.438789 | + | 0.318799i | ||||
\(146\) | 3.97178 | + | 12.2239i | 0.328706 | + | 1.01165i | ||||
\(147\) | −0.456498 | + | 1.40496i | −0.0376514 | + | 0.115879i | ||||
\(148\) | 28.4557 | + | 20.6743i | 2.33904 | + | 1.69941i | ||||
\(149\) | −7.71644 | − | 5.60632i | −0.632155 | − | 0.459288i | 0.224991 | − | 0.974361i | \(-0.427765\pi\) |
−0.857146 | + | 0.515073i | \(0.827765\pi\) | |||||||
\(150\) | 1.09115 | − | 3.35821i | 0.0890919 | − | 0.274197i | ||||
\(151\) | 3.36874 | + | 10.3679i | 0.274144 | + | 0.843729i | 0.989445 | + | 0.144912i | \(0.0462899\pi\) |
−0.715300 | + | 0.698817i | \(0.753710\pi\) | |||||||
\(152\) | −2.80231 | + | 2.03600i | −0.227297 | + | 0.165141i | ||||
\(153\) | 1.24515 | 0.100664 | ||||||||
\(154\) | 6.13623 | − | 5.01929i | 0.494472 | − | 0.404466i | ||||
\(155\) | −8.51366 | −0.683834 | ||||||||
\(156\) | 17.1637 | − | 12.4701i | 1.37419 | − | 0.998410i | ||||
\(157\) | 0.0187111 | + | 0.0575868i | 0.00149331 | + | 0.00459593i | 0.951800 | − | 0.306718i | \(-0.0992309\pi\) |
−0.950307 | + | 0.311314i | \(0.899231\pi\) | |||||||
\(158\) | 4.23106 | − | 13.0219i | 0.336605 | − | 1.03596i | ||||
\(159\) | −3.72814 | − | 2.70865i | −0.295661 | − | 0.214810i | ||||
\(160\) | −2.05850 | − | 1.49559i | −0.162739 | − | 0.118237i | ||||
\(161\) | −0.304872 | + | 0.938298i | −0.0240272 | + | 0.0739483i | ||||
\(162\) | 4.34185 | + | 13.3629i | 0.341128 | + | 1.04988i | ||||
\(163\) | −10.3353 | + | 7.50905i | −0.809525 | + | 0.588154i | −0.913693 | − | 0.406406i | \(-0.866782\pi\) |
0.104168 | + | 0.994560i | \(0.466782\pi\) | |||||||
\(164\) | −12.3306 | −0.962856 | ||||||||
\(165\) | −4.89148 | + | 0.280526i | −0.380801 | + | 0.0218389i | ||||
\(166\) | −29.2549 | −2.27062 | ||||||||
\(167\) | 16.2555 | − | 11.8103i | 1.25788 | − | 0.913907i | 0.259233 | − | 0.965815i | \(-0.416530\pi\) |
0.998652 | + | 0.0519079i | \(0.0165302\pi\) | |||||||
\(168\) | 1.86950 | + | 5.75372i | 0.144235 | + | 0.443909i | ||||
\(169\) | 0.604958 | − | 1.86187i | 0.0465353 | − | 0.143221i | ||||
\(170\) | −2.94461 | − | 2.13939i | −0.225841 | − | 0.164083i | ||||
\(171\) | −0.559534 | − | 0.406525i | −0.0427886 | − | 0.0310878i | ||||
\(172\) | 3.76552 | − | 11.5891i | 0.287118 | − | 0.883658i | ||||
\(173\) | 2.27957 | + | 7.01579i | 0.173312 | + | 0.533401i | 0.999552 | − | 0.0299175i | \(-0.00952445\pi\) |
−0.826240 | + | 0.563318i | \(0.809524\pi\) | |||||||
\(174\) | −18.6570 | + | 13.5551i | −1.41438 | + | 1.02761i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 1.99037 | − | 7.57731i | 0.150030 | − | 0.571161i | ||||
\(177\) | 9.40495 | 0.706919 | ||||||||
\(178\) | −17.1393 | + | 12.4524i | −1.28464 | + | 0.933347i | ||||
\(179\) | 3.01247 | + | 9.27143i | 0.225163 | + | 0.692979i | 0.998275 | + | 0.0587103i | \(0.0186988\pi\) |
−0.773112 | + | 0.634269i | \(0.781301\pi\) | |||||||
\(180\) | −0.938299 | + | 2.88779i | −0.0699367 | + | 0.215243i | ||||
\(181\) | 4.27682 | + | 3.10729i | 0.317893 | + | 0.230963i | 0.735276 | − | 0.677768i | \(-0.237053\pi\) |
−0.417383 | + | 0.908731i | \(0.637053\pi\) | |||||||
\(182\) | 7.47884 | + | 5.43370i | 0.554369 | + | 0.402772i | ||||
\(183\) | 0.210299 | − | 0.647233i | 0.0155457 | − | 0.0478449i | ||||
\(184\) | 1.24854 | + | 3.84261i | 0.0920435 | + | 0.283281i | ||||
\(185\) | 7.66312 | − | 5.56758i | 0.563404 | − | 0.409337i | ||||
\(186\) | −30.0620 | −2.20425 | ||||||||
\(187\) | −1.28308 | + | 4.88465i | −0.0938278 | + | 0.357201i | ||||
\(188\) | 49.7195 | 3.62617 | ||||||||
\(189\) | −4.56265 | + | 3.31496i | −0.331884 | + | 0.241128i | ||||
\(190\) | 0.624741 | + | 1.92276i | 0.0453235 | + | 0.139491i | ||||
\(191\) | −3.75647 | + | 11.5612i | −0.271809 | + | 0.836541i | 0.718238 | + | 0.695798i | \(0.244949\pi\) |
−0.990046 | + | 0.140743i | \(0.955051\pi\) | |||||||
\(192\) | −12.9148 | − | 9.38313i | −0.932043 | − | 0.677169i | ||||
\(193\) | −4.23741 | − | 3.07866i | −0.305015 | − | 0.221607i | 0.424739 | − | 0.905316i | \(-0.360366\pi\) |
−0.729755 | + | 0.683709i | \(0.760366\pi\) | |||||||
\(194\) | −4.69351 | + | 14.4451i | −0.336974 | + | 1.03710i | ||||
\(195\) | −1.76552 | − | 5.43370i | −0.126431 | − | 0.389115i | ||||
\(196\) | −3.00415 | + | 2.18264i | −0.214582 | + | 0.155903i | ||||
\(197\) | −3.51610 | −0.250512 | −0.125256 | − | 0.992124i | \(-0.539975\pi\) | ||||
−0.125256 | + | 0.992124i | \(0.539975\pi\) | |||||||
\(198\) | 6.47178 | − | 0.371156i | 0.459929 | − | 0.0263769i | ||||
\(199\) | 7.63650 | 0.541337 | 0.270669 | − | 0.962673i | \(-0.412755\pi\) | ||||
0.270669 | + | 0.962673i | \(0.412755\pi\) | |||||||
\(200\) | 3.31316 | − | 2.40715i | 0.234276 | − | 0.170211i | ||||
\(201\) | 4.61728 | + | 14.2105i | 0.325678 | + | 1.00233i | ||||
\(202\) | 5.54018 | − | 17.0509i | 0.389806 | − | 1.19970i | ||||
\(203\) | −5.28371 | − | 3.83884i | −0.370844 | − | 0.269434i | ||||
\(204\) | −6.75777 | − | 4.90981i | −0.473139 | − | 0.343755i | ||||
\(205\) | −1.02613 | + | 3.15810i | −0.0716680 | + | 0.220571i | ||||
\(206\) | 4.72237 | + | 14.5340i | 0.329023 | + | 1.01263i | ||||
\(207\) | −0.652661 | + | 0.474186i | −0.0453631 | + | 0.0329582i | ||||
\(208\) | 9.13565 | 0.633443 | ||||||||
\(209\) | 2.17135 | − | 1.77611i | 0.150196 | − | 0.122856i | ||||
\(210\) | 3.53103 | 0.243664 | ||||||||
\(211\) | −17.2971 | + | 12.5671i | −1.19078 | + | 0.865153i | −0.993347 | − | 0.115163i | \(-0.963261\pi\) |
−0.197435 | + | 0.980316i | \(0.563261\pi\) | |||||||
\(212\) | −3.57951 | − | 11.0166i | −0.245841 | − | 0.756622i | ||||
\(213\) | 2.62889 | − | 8.09088i | 0.180128 | − | 0.554378i | ||||
\(214\) | 27.6451 | + | 20.0854i | 1.88978 | + | 1.37301i | ||||
\(215\) | −2.65483 | − | 1.92885i | −0.181058 | − | 0.131546i | ||||
\(216\) | −7.13718 | + | 21.9660i | −0.485623 | + | 1.49460i | ||||
\(217\) | −2.63087 | − | 8.09697i | −0.178595 | − | 0.549658i | ||||
\(218\) | −30.2113 | + | 21.9498i | −2.04617 | + | 1.48663i | ||||
\(219\) | 7.94355 | 0.536775 | ||||||||
\(220\) | −10.3618 | − | 6.65664i | −0.698589 | − | 0.448791i | ||||
\(221\) | −5.88922 | −0.396152 | ||||||||
\(222\) | 27.0587 | − | 19.6593i | 1.81606 | − | 1.31945i | ||||
\(223\) | 7.54759 | + | 23.2291i | 0.505424 | + | 1.55554i | 0.800056 | + | 0.599925i | \(0.204803\pi\) |
−0.294632 | + | 0.955611i | \(0.595197\pi\) | |||||||
\(224\) | 0.786277 | − | 2.41991i | 0.0525353 | − | 0.161687i | ||||
\(225\) | 0.661536 | + | 0.480634i | 0.0441024 | + | 0.0320422i | ||||
\(226\) | −27.8149 | − | 20.2087i | −1.85022 | − | 1.34426i | ||||
\(227\) | 7.37202 | − | 22.6888i | 0.489298 | − | 1.50591i | −0.336359 | − | 0.941734i | \(-0.609196\pi\) |
0.825657 | − | 0.564172i | \(-0.190804\pi\) | |||||||
\(228\) | 1.43376 | + | 4.41265i | 0.0949530 | + | 0.292235i | ||||
\(229\) | −0.776952 | + | 0.564489i | −0.0513424 | + | 0.0373025i | −0.613160 | − | 0.789958i | \(-0.710102\pi\) |
0.561818 | + | 0.827261i | \(0.310102\pi\) | |||||||
\(230\) | 2.35819 | 0.155495 | ||||||||
\(231\) | −1.77835 | − | 4.56539i | −0.117007 | − | 0.300380i | ||||
\(232\) | −26.7465 | −1.75599 | ||||||||
\(233\) | 20.6239 | − | 14.9842i | 1.35112 | − | 0.981644i | 0.352163 | − | 0.935939i | \(-0.385446\pi\) |
0.998955 | − | 0.0457057i | \(-0.0145537\pi\) | |||||||
\(234\) | 2.33590 | + | 7.18917i | 0.152703 | + | 0.469971i | ||||
\(235\) | 4.13757 | − | 12.7341i | 0.269905 | − | 0.830684i | ||||
\(236\) | 19.1258 | + | 13.8957i | 1.24499 | + | 0.904535i | ||||
\(237\) | −6.84600 | − | 4.97391i | −0.444695 | − | 0.323090i | ||||
\(238\) | 1.12474 | − | 3.46160i | 0.0729062 | − | 0.224382i | ||||
\(239\) | −7.25580 | − | 22.3310i | −0.469338 | − | 1.44448i | −0.853443 | − | 0.521186i | \(-0.825490\pi\) |
0.384105 | − | 0.923289i | \(-0.374510\pi\) | |||||||
\(240\) | 2.82307 | − | 2.05108i | 0.182228 | − | 0.132397i | ||||
\(241\) | −13.0860 | −0.842942 | −0.421471 | − | 0.906842i | \(-0.638486\pi\) | ||||
−0.421471 | + | 0.906842i | \(0.638486\pi\) | |||||||
\(242\) | −5.21288 | + | 25.7709i | −0.335096 | + | 1.65662i | ||||
\(243\) | −8.23551 | −0.528308 | ||||||||
\(244\) | 1.38394 | − | 1.00549i | 0.0885980 | − | 0.0643702i | ||||
\(245\) | 0.309017 | + | 0.951057i | 0.0197424 | + | 0.0607608i | ||||
\(246\) | −3.62330 | + | 11.1514i | −0.231013 | + | 0.710985i | ||||
\(247\) | 2.64645 | + | 1.92276i | 0.168389 | + | 0.122342i | ||||
\(248\) | −28.2071 | − | 20.4937i | −1.79115 | − | 1.30135i | ||||
\(249\) | −5.58719 | + | 17.1956i | −0.354074 | + | 1.08973i | ||||
\(250\) | −0.738630 | − | 2.27327i | −0.0467151 | − | 0.143774i | ||||
\(251\) | 10.0246 | − | 7.28327i | 0.632745 | − | 0.459716i | −0.224605 | − | 0.974450i | \(-0.572109\pi\) |
0.857350 | + | 0.514734i | \(0.172109\pi\) | |||||||
\(252\) | −3.03640 | −0.191275 | ||||||||
\(253\) | −1.18767 | − | 3.04898i | −0.0746679 | − | 0.191688i | ||||
\(254\) | 15.0845 | 0.946485 | ||||||||
\(255\) | −1.81987 | + | 1.32221i | −0.113965 | + | 0.0828002i | ||||
\(256\) | −8.64108 | − | 26.5945i | −0.540067 | − | 1.66216i | ||||
\(257\) | 5.68644 | − | 17.5011i | 0.354711 | − | 1.09169i | −0.601467 | − | 0.798898i | \(-0.705417\pi\) |
0.956177 | − | 0.292789i | \(-0.0945833\pi\) | |||||||
\(258\) | −9.37428 | − | 6.81081i | −0.583617 | − | 0.424023i | ||||
\(259\) | 7.66312 | + | 5.56758i | 0.476163 | + | 0.345953i | ||||
\(260\) | 4.43790 | − | 13.6585i | 0.275227 | − | 0.847062i | ||||
\(261\) | −1.65029 | − | 5.07906i | −0.102150 | − | 0.314386i | ||||
\(262\) | 23.0222 | − | 16.7266i | 1.42232 | − | 1.03337i | ||||
\(263\) | −9.82776 | −0.606006 | −0.303003 | − | 0.952990i | \(-0.597989\pi\) | ||||
−0.303003 | + | 0.952990i | \(0.597989\pi\) | |||||||
\(264\) | −16.8815 | − | 10.8451i | −1.03899 | − | 0.667471i | ||||
\(265\) | −3.11945 | −0.191626 | ||||||||
\(266\) | −1.63559 | + | 1.18833i | −0.100285 | + | 0.0728611i | ||||
\(267\) | 4.04603 | + | 12.4524i | 0.247613 | + | 0.762074i | ||||
\(268\) | −11.6063 | + | 35.7204i | −0.708965 | + | 2.18197i | ||||
\(269\) | 7.25368 | + | 5.27011i | 0.442265 | + | 0.321324i | 0.786534 | − | 0.617547i | \(-0.211873\pi\) |
−0.344269 | + | 0.938871i | \(0.611873\pi\) | |||||||
\(270\) | 10.9059 | + | 7.92360i | 0.663712 | + | 0.482215i | ||||
\(271\) | −2.38438 | + | 7.33836i | −0.144841 | + | 0.445774i | −0.996990 | − | 0.0775243i | \(-0.975298\pi\) |
0.852150 | + | 0.523298i | \(0.175298\pi\) | |||||||
\(272\) | −1.11152 | − | 3.42089i | −0.0673955 | − | 0.207422i | ||||
\(273\) | 4.62218 | − | 3.35821i | 0.279747 | − | 0.203248i | ||||
\(274\) | −51.9549 | −3.13871 | ||||||||
\(275\) | −2.56719 | + | 2.09989i | −0.154807 | + | 0.126628i | ||||
\(276\) | 5.41196 | 0.325762 | ||||||||
\(277\) | −2.36959 | + | 1.72160i | −0.142375 | + | 0.103441i | −0.656693 | − | 0.754158i | \(-0.728045\pi\) |
0.514318 | + | 0.857600i | \(0.328045\pi\) | |||||||
\(278\) | 5.52001 | + | 16.9888i | 0.331068 | + | 1.01892i | ||||
\(279\) | 2.15127 | − | 6.62092i | 0.128793 | − | 0.396384i | ||||
\(280\) | 3.31316 | + | 2.40715i | 0.197999 | + | 0.143855i | ||||
\(281\) | −23.2945 | − | 16.9245i | −1.38964 | − | 1.00963i | −0.995905 | − | 0.0904031i | \(-0.971184\pi\) |
−0.393730 | − | 0.919226i | \(-0.628816\pi\) | |||||||
\(282\) | 14.6099 | − | 44.9646i | 0.870007 | − | 2.67761i | ||||
\(283\) | −8.94098 | − | 27.5175i | −0.531486 | − | 1.63575i | −0.751122 | − | 0.660164i | \(-0.770487\pi\) |
0.219636 | − | 0.975582i | \(-0.429513\pi\) | |||||||
\(284\) | 17.3003 | − | 12.5694i | 1.02658 | − | 0.745857i | ||||
\(285\) | 1.24948 | 0.0740130 | ||||||||
\(286\) | −30.6098 | + | 1.75547i | −1.80999 | + | 0.103803i | ||||
\(287\) | −3.32063 | −0.196010 | ||||||||
\(288\) | 1.68324 | − | 1.22295i | 0.0991859 | − | 0.0720628i | ||||
\(289\) | −4.53676 | − | 13.9627i | −0.266868 | − | 0.821336i | ||||
\(290\) | −4.82402 | + | 14.8468i | −0.283276 | + | 0.871834i | ||||
\(291\) | 7.59426 | + | 5.51755i | 0.445183 | + | 0.323445i | ||||
\(292\) | 16.1539 | + | 11.7365i | 0.945338 | + | 0.686828i | ||||
\(293\) | 5.98638 | − | 18.4242i | 0.349728 | − | 1.07635i | −0.609276 | − | 0.792958i | \(-0.708540\pi\) |
0.959004 | − | 0.283394i | \(-0.0914603\pi\) | |||||||
\(294\) | 1.09115 | + | 3.35821i | 0.0636371 | + | 0.195855i | ||||
\(295\) | 5.15059 | − | 3.74212i | 0.299879 | − | 0.217875i | ||||
\(296\) | 38.7912 | 2.25469 | ||||||||
\(297\) | 4.75210 | − | 18.0912i | 0.275745 | − | 1.04976i | ||||
\(298\) | −22.7984 | −1.32067 | ||||||||
\(299\) | 3.08691 | − | 2.24277i | 0.178521 | − | 0.129703i | ||||
\(300\) | −1.69513 | − | 5.21707i | −0.0978683 | − | 0.301208i | ||||
\(301\) | 1.01405 | − | 3.12094i | 0.0584491 | − | 0.179888i | ||||
\(302\) | 21.0808 | + | 15.3161i | 1.21306 | + | 0.881343i | ||||
\(303\) | −8.96421 | − | 6.51288i | −0.514980 | − | 0.374155i | ||||
\(304\) | −0.617395 | + | 1.90015i | −0.0354100 | + | 0.108981i | ||||
\(305\) | −0.142357 | − | 0.438131i | −0.00815136 | − | 0.0250873i | ||||
\(306\) | 2.40782 | − | 1.74938i | 0.137646 | − | 0.100005i | ||||
\(307\) | −17.2849 | −0.986504 | −0.493252 | − | 0.869886i | \(-0.664192\pi\) | ||||
−0.493252 | + | 0.869886i | \(0.664192\pi\) | |||||||
\(308\) | 3.12889 | − | 11.9116i | 0.178285 | − | 0.678728i | ||||
\(309\) | 9.44475 | 0.537293 | ||||||||
\(310\) | −16.4634 | + | 11.9613i | −0.935056 | + | 0.679358i | ||||
\(311\) | 6.12194 | + | 18.8414i | 0.347143 | + | 1.06840i | 0.960426 | + | 0.278534i | \(0.0898484\pi\) |
−0.613283 | + | 0.789863i | \(0.710152\pi\) | |||||||
\(312\) | 7.23030 | − | 22.2526i | 0.409335 | − | 1.25980i | ||||
\(313\) | 24.6269 | + | 17.8925i | 1.39199 | + | 1.01134i | 0.995643 | + | 0.0932427i | \(0.0297233\pi\) |
0.396350 | + | 0.918100i | \(0.370277\pi\) | |||||||
\(314\) | 0.117090 | + | 0.0850707i | 0.00660776 | + | 0.00480082i | ||||
\(315\) | −0.252684 | + | 0.777682i | −0.0142371 | + | 0.0438174i | ||||
\(316\) | −6.57307 | − | 20.2298i | −0.369764 | − | 1.13802i | ||||
\(317\) | 3.52112 | − | 2.55825i | 0.197766 | − | 0.143685i | −0.484495 | − | 0.874794i | \(-0.660997\pi\) |
0.682261 | + | 0.731109i | \(0.260997\pi\) | |||||||
\(318\) | −11.0149 | −0.617683 | ||||||||
\(319\) | 21.6254 | − | 1.24022i | 1.21079 | − | 0.0694390i | ||||
\(320\) | −10.8062 | −0.604084 | ||||||||
\(321\) | 17.0856 | − | 12.4134i | 0.953627 | − | 0.692850i | ||||
\(322\) | 0.728721 | + | 2.24277i | 0.0406101 | + | 0.124985i | ||||
\(323\) | 0.397999 | − | 1.22491i | 0.0221452 | − | 0.0681560i | ||||
\(324\) | 17.6591 | + | 12.8301i | 0.981063 | + | 0.712784i | ||||
\(325\) | −3.12889 | − | 2.27327i | −0.173559 | − | 0.126098i | ||||
\(326\) | −9.43611 | + | 29.0414i | −0.522618 | + | 1.60845i | ||||
\(327\) | 7.13192 | + | 21.9498i | 0.394396 | + | 1.21383i | ||||
\(328\) | −11.0018 | + | 7.99326i | −0.607471 | + | 0.441354i | ||||
\(329\) | 13.3895 | 0.738185 | ||||||||
\(330\) | −9.06481 | + | 7.41479i | −0.499001 | + | 0.408171i | ||||
\(331\) | 7.44787 | 0.409372 | 0.204686 | − | 0.978828i | \(-0.434383\pi\) | ||||
0.204686 | + | 0.978828i | \(0.434383\pi\) | |||||||
\(332\) | −36.7684 | + | 26.7138i | −2.01793 | + | 1.46611i | ||||
\(333\) | 2.39346 | + | 7.36631i | 0.131161 | + | 0.403671i | ||||
\(334\) | 14.8412 | − | 45.6765i | 0.812073 | − | 2.49930i | ||||
\(335\) | 8.18285 | + | 5.94519i | 0.447077 | + | 0.324820i | ||||
\(336\) | 2.82307 | + | 2.05108i | 0.154011 | + | 0.111896i | ||||
\(337\) | 7.23174 | − | 22.2570i | 0.393938 | − | 1.21242i | −0.535848 | − | 0.844315i | \(-0.680008\pi\) |
0.929786 | − | 0.368101i | \(-0.119992\pi\) | |||||||
\(338\) | −1.44601 | − | 4.45035i | −0.0786524 | − | 0.242067i | ||||
\(339\) | −17.1906 | + | 12.4897i | −0.933663 | + | 0.678346i | ||||
\(340\) | −5.65443 | −0.306655 | ||||||||
\(341\) | 23.7567 | + | 15.2619i | 1.28650 | + | 0.826478i | ||||
\(342\) | −1.65315 | −0.0893924 | ||||||||
\(343\) | −0.809017 | + | 0.587785i | −0.0436828 | + | 0.0317374i | ||||
\(344\) | −4.15285 | − | 12.7812i | −0.223907 | − | 0.689114i | ||||
\(345\) | 0.450375 | − | 1.38611i | 0.0242474 | − | 0.0746257i | ||||
\(346\) | 14.2650 | + | 10.3642i | 0.766893 | + | 0.557180i | ||||
\(347\) | 18.9241 | + | 13.7492i | 1.01590 | + | 0.738094i | 0.965438 | − | 0.260633i | \(-0.0839311\pi\) |
0.0504605 | + | 0.998726i | \(0.483931\pi\) | |||||||
\(348\) | −11.0709 | + | 34.0728i | −0.593464 | + | 1.82650i | ||||
\(349\) | −0.633499 | − | 1.94971i | −0.0339104 | − | 0.104366i | 0.932669 | − | 0.360734i | \(-0.117474\pi\) |
−0.966579 | + | 0.256369i | \(0.917474\pi\) | |||||||
\(350\) | 1.93376 | − | 1.40496i | 0.103364 | − | 0.0750982i | ||||
\(351\) | 21.8118 | 1.16423 | ||||||||
\(352\) | 3.06304 | + | 7.86346i | 0.163261 | + | 0.419124i | ||||
\(353\) | −19.3842 | −1.03172 | −0.515858 | − | 0.856674i | \(-0.672527\pi\) | ||||
−0.515858 | + | 0.856674i | \(0.672527\pi\) | |||||||
\(354\) | 18.1869 | − | 13.2136i | 0.966623 | − | 0.702293i | ||||
\(355\) | −1.77957 | − | 5.47695i | −0.0944497 | − | 0.290686i | ||||
\(356\) | −10.1703 | + | 31.3011i | −0.539027 | + | 1.65895i | ||||
\(357\) | −1.81987 | − | 1.32221i | −0.0963177 | − | 0.0699789i | ||||
\(358\) | 18.8514 | + | 13.6963i | 0.996325 | + | 0.723873i | ||||
\(359\) | 2.67339 | − | 8.22784i | 0.141096 | − | 0.434249i | −0.855392 | − | 0.517981i | \(-0.826684\pi\) |
0.996488 | + | 0.0837318i | \(0.0266839\pi\) | |||||||
\(360\) | 1.03482 | + | 3.18484i | 0.0545396 | + | 0.167856i | ||||
\(361\) | 14.7926 | − | 10.7474i | 0.778556 | − | 0.565654i | ||||
\(362\) | 12.6359 | 0.664131 | ||||||||
\(363\) | 14.1522 | + | 7.98585i | 0.742797 | + | 0.419149i | ||||
\(364\) | 14.3614 | 0.752740 | ||||||||
\(365\) | 4.35026 | − | 3.16065i | 0.227703 | − | 0.165436i | ||||
\(366\) | −0.502668 | − | 1.54705i | −0.0262749 | − | 0.0808658i | ||||
\(367\) | −3.37879 | + | 10.3988i | −0.176371 | + | 0.542815i | −0.999693 | − | 0.0247595i | \(-0.992118\pi\) |
0.823322 | + | 0.567574i | \(0.192118\pi\) | |||||||
\(368\) | 1.88538 | + | 1.36981i | 0.0982823 | + | 0.0714063i | ||||
\(369\) | −2.19671 | − | 1.59600i | −0.114356 | − | 0.0830847i | ||||
\(370\) | 6.99640 | − | 21.5327i | 0.363726 | − | 1.11943i | ||||
\(371\) | −0.963962 | − | 2.96677i | −0.0500464 | − | 0.154027i | ||||
\(372\) | −37.7828 | + | 27.4508i | −1.95895 | + | 1.42326i | ||||
\(373\) | −29.2848 | −1.51631 | −0.758154 | − | 0.652076i | \(-0.773898\pi\) | ||||
−0.758154 | + | 0.652076i | \(0.773898\pi\) | |||||||
\(374\) | 4.38157 | + | 11.2484i | 0.226566 | + | 0.581641i | ||||
\(375\) | −1.47726 | −0.0762854 | ||||||||
\(376\) | 44.3615 | − | 32.2305i | 2.28777 | − | 1.66216i | ||||
\(377\) | 7.80542 | + | 24.0226i | 0.402000 | + | 1.23723i | ||||
\(378\) | −4.16568 | + | 12.8206i | −0.214260 | + | 0.659423i | ||||
\(379\) | −26.3901 | − | 19.1736i | −1.35557 | − | 0.984879i | −0.998713 | − | 0.0507203i | \(-0.983848\pi\) |
−0.356857 | − | 0.934159i | \(-0.616152\pi\) | |||||||
\(380\) | 2.54094 | + | 1.84610i | 0.130347 | + | 0.0947030i | ||||
\(381\) | 2.88088 | − | 8.86644i | 0.147592 | − | 0.454241i | ||||
\(382\) | 8.97893 | + | 27.6343i | 0.459402 | + | 1.41389i | ||||
\(383\) | 15.3328 | − | 11.1400i | 0.783471 | − | 0.569225i | −0.122548 | − | 0.992463i | \(-0.539106\pi\) |
0.906019 | + | 0.423238i | \(0.139106\pi\) | |||||||
\(384\) | −30.6393 | −1.56356 | ||||||||
\(385\) | −2.79042 | − | 1.79264i | −0.142213 | − | 0.0913612i | ||||
\(386\) | −12.5195 | −0.637226 | ||||||||
\(387\) | 2.17086 | − | 1.57722i | 0.110351 | − | 0.0801747i | ||||
\(388\) | 7.29149 | + | 22.4409i | 0.370170 | + | 1.13926i | ||||
\(389\) | −12.0031 | + | 36.9416i | −0.608580 | + | 1.87302i | −0.138574 | + | 0.990352i | \(0.544252\pi\) |
−0.470006 | + | 0.882663i | \(0.655748\pi\) | |||||||
\(390\) | −11.0482 | − | 8.02698i | −0.559447 | − | 0.406462i | ||||
\(391\) | −1.21540 | − | 0.883037i | −0.0614652 | − | 0.0446571i | ||||
\(392\) | −1.26552 | + | 3.89486i | −0.0639182 | + | 0.196720i | ||||
\(393\) | −5.43481 | − | 16.7266i | −0.274150 | − | 0.843746i | ||||
\(394\) | −6.79930 | + | 4.93998i | −0.342544 | + | 0.248873i | ||||
\(395\) | −5.72825 | −0.288220 | ||||||||
\(396\) | 7.79500 | − | 6.37612i | 0.391714 | − | 0.320412i | ||||
\(397\) | −7.29557 | −0.366154 | −0.183077 | − | 0.983099i | \(-0.558606\pi\) | ||||
−0.183077 | + | 0.983099i | \(0.558606\pi\) | |||||||
\(398\) | 14.7672 | − | 10.7290i | 0.740211 | − | 0.537794i | ||||
\(399\) | 0.386111 | + | 1.18833i | 0.0193297 | + | 0.0594909i | ||||
\(400\) | 0.729944 | − | 2.24654i | 0.0364972 | − | 0.112327i | ||||
\(401\) | 30.4424 | + | 22.1177i | 1.52022 | + | 1.10451i | 0.961377 | + | 0.275236i | \(0.0887559\pi\) |
0.558847 | + | 0.829271i | \(0.311244\pi\) | |||||||
\(402\) | 28.8939 | + | 20.9926i | 1.44110 | + | 1.04702i | ||||
\(403\) | −10.1749 | + | 31.3152i | −0.506849 | + | 1.55992i | ||||
\(404\) | −8.60682 | − | 26.4891i | −0.428205 | − | 1.31788i | ||||
\(405\) | 4.75561 | − | 3.45515i | 0.236308 | − | 0.171688i | ||||
\(406\) | −15.6108 | −0.774753 | ||||||||
\(407\) | −31.3640 | + | 1.79872i | −1.55466 | + | 0.0891595i | ||||
\(408\) | −9.21229 | −0.456077 | ||||||||
\(409\) | 15.6164 | − | 11.3460i | 0.772182 | − | 0.561023i | −0.130440 | − | 0.991456i | \(-0.541639\pi\) |
0.902623 | + | 0.430433i | \(0.141639\pi\) | |||||||
\(410\) | 2.45271 | + | 7.54868i | 0.121131 | + | 0.372803i | ||||
\(411\) | −9.92251 | + | 30.5383i | −0.489441 | + | 1.50635i | ||||
\(412\) | 19.2068 | + | 13.9545i | 0.946250 | + | 0.687491i | ||||
\(413\) | 5.15059 | + | 3.74212i | 0.253444 | + | 0.184138i | ||||
\(414\) | −0.595878 | + | 1.83392i | −0.0292858 | + | 0.0901324i | ||||
\(415\) | 3.78213 | + | 11.6402i | 0.185658 | + | 0.571395i | ||||
\(416\) | −7.96128 | + | 5.78421i | −0.390334 | + | 0.283594i | ||||
\(417\) | 11.0400 | 0.540632 | ||||||||
\(418\) | 1.70351 | − | 6.48524i | 0.0833214 | − | 0.317203i | ||||
\(419\) | 18.1588 | 0.887114 | 0.443557 | − | 0.896246i | \(-0.353716\pi\) | ||||
0.443557 | + | 0.896246i | \(0.353716\pi\) | |||||||
\(420\) | 4.43790 | − | 3.22433i | 0.216548 | − | 0.157331i | ||||
\(421\) | −6.04678 | − | 18.6101i | −0.294702 | − | 0.907000i | −0.983321 | − | 0.181877i | \(-0.941783\pi\) |
0.688619 | − | 0.725123i | \(-0.258217\pi\) | |||||||
\(422\) | −15.7922 | + | 48.6034i | −0.768752 | + | 2.36598i | ||||
\(423\) | 8.85761 | + | 6.43543i | 0.430672 | + | 0.312901i | ||||
\(424\) | −10.3352 | − | 7.50898i | −0.501923 | − | 0.364668i | ||||
\(425\) | −0.470553 | + | 1.44821i | −0.0228252 | + | 0.0702486i | ||||
\(426\) | −6.28371 | − | 19.3393i | −0.304447 | − | 0.936991i | ||||
\(427\) | 0.372697 | − | 0.270780i | 0.0180360 | − | 0.0131040i | ||||
\(428\) | 53.0860 | 2.56601 | ||||||||
\(429\) | −4.81411 | + | 18.3272i | −0.232427 | + | 0.884847i | ||||
\(430\) | −7.84374 | −0.378259 | ||||||||
\(431\) | 24.5407 | − | 17.8299i | 1.18209 | − | 0.858835i | 0.189680 | − | 0.981846i | \(-0.439255\pi\) |
0.992405 | + | 0.123011i | \(0.0392550\pi\) | |||||||
\(432\) | 4.11669 | + | 12.6699i | 0.198065 | + | 0.609580i | ||||
\(433\) | −2.55622 | + | 7.86723i | −0.122844 | + | 0.378075i | −0.993502 | − | 0.113814i | \(-0.963693\pi\) |
0.870658 | + | 0.491889i | \(0.163693\pi\) | |||||||
\(434\) | −16.4634 | − | 11.9613i | −0.790267 | − | 0.574162i | ||||
\(435\) | 7.80542 | + | 5.67097i | 0.374241 | + | 0.271902i | ||||
\(436\) | −17.9272 | + | 55.1743i | −0.858557 | + | 2.64237i | ||||
\(437\) | 0.257864 | + | 0.793623i | 0.0123353 | + | 0.0379641i | ||||
\(438\) | 15.3609 | − | 11.1604i | 0.733973 | − | 0.533262i | ||||
\(439\) | −2.08907 | −0.0997059 | −0.0498530 | − | 0.998757i | \(-0.515875\pi\) | ||||
−0.0498530 | + | 0.998757i | \(0.515875\pi\) | |||||||
\(440\) | −13.5603 | + | 0.777682i | −0.646461 | + | 0.0370745i | ||||
\(441\) | −0.817703 | −0.0389382 | ||||||||
\(442\) | −11.3883 | + | 8.27411i | −0.541688 | + | 0.393559i | ||||
\(443\) | 5.07973 | + | 15.6338i | 0.241345 | + | 0.742784i | 0.996216 | + | 0.0869107i | \(0.0276995\pi\) |
−0.754871 | + | 0.655873i | \(0.772301\pi\) | |||||||
\(444\) | 16.0565 | − | 49.4168i | 0.762007 | − | 2.34522i | ||||
\(445\) | 7.17047 | + | 5.20965i | 0.339913 | + | 0.246961i | ||||
\(446\) | 47.2311 | + | 34.3154i | 2.23646 | + | 1.62488i | ||||
\(447\) | −4.35410 | + | 13.4005i | −0.205942 | + | 0.633824i | ||||
\(448\) | −3.33929 | − | 10.2773i | −0.157767 | − | 0.485556i | ||||
\(449\) | 7.20106 | − | 5.23188i | 0.339839 | − | 0.246908i | −0.404755 | − | 0.914425i | \(-0.632643\pi\) |
0.744594 | + | 0.667518i | \(0.232643\pi\) | |||||||
\(450\) | 1.95452 | 0.0921370 | ||||||||
\(451\) | 8.52466 | − | 6.97296i | 0.401411 | − | 0.328344i | ||||
\(452\) | −53.4120 | −2.51229 | ||||||||
\(453\) | 13.0287 | − | 9.46587i | 0.612140 | − | 0.444746i | ||||
\(454\) | −17.6210 | − | 54.2319i | −0.826996 | − | 2.54523i | ||||
\(455\) | 1.19513 | − | 3.67823i | 0.0560285 | − | 0.172438i | ||||
\(456\) | 4.13974 | + | 3.00770i | 0.193861 | + | 0.140848i | ||||
\(457\) | −5.34400 | − | 3.88265i | −0.249982 | − | 0.181623i | 0.455737 | − | 0.890115i | \(-0.349376\pi\) |
−0.705719 | + | 0.708492i | \(0.749376\pi\) | |||||||
\(458\) | −0.709355 | + | 2.18317i | −0.0331460 | + | 0.102013i | ||||
\(459\) | −2.65379 | − | 8.16754i | −0.123868 | − | 0.381228i | ||||
\(460\) | 2.96385 | − | 2.15336i | 0.138190 | − | 0.100401i | ||||
\(461\) | 19.8327 | 0.923701 | 0.461851 | − | 0.886958i | \(-0.347186\pi\) | ||||
0.461851 | + | 0.886958i | \(0.347186\pi\) | |||||||
\(462\) | −9.85307 | − | 6.32985i | −0.458406 | − | 0.294491i | ||||
\(463\) | 10.7257 | 0.498465 | 0.249233 | − | 0.968444i | \(-0.419822\pi\) | ||||
0.249233 | + | 0.968444i | \(0.419822\pi\) | |||||||
\(464\) | −12.4809 | + | 9.06792i | −0.579412 | + | 0.420968i | ||||
\(465\) | 3.88647 | + | 11.9613i | 0.180231 | + | 0.554693i | ||||
\(466\) | 18.8296 | − | 57.9515i | 0.872263 | − | 2.68455i | ||||
\(467\) | −15.5123 | − | 11.2703i | −0.717823 | − | 0.521529i | 0.167865 | − | 0.985810i | \(-0.446313\pi\) |
−0.885688 | + | 0.464281i | \(0.846313\pi\) | |||||||
\(468\) | 9.50055 | + | 6.90255i | 0.439163 | + | 0.319071i | ||||
\(469\) | −3.12557 | + | 9.61951i | −0.144325 | + | 0.444188i | ||||
\(470\) | −9.88986 | − | 30.4379i | −0.456185 | − | 1.40399i | ||||
\(471\) | 0.0723654 | − | 0.0525766i | 0.00333442 | − | 0.00242260i | ||||
\(472\) | 26.0726 | 1.20009 | ||||||||
\(473\) | 3.95037 | + | 10.1414i | 0.181638 | + | 0.466304i | ||||
\(474\) | −20.2266 | −0.929040 | ||||||||
\(475\) | 0.684276 | − | 0.497155i | 0.0313967 | − | 0.0228110i | ||||
\(476\) | −1.74732 | − | 5.37769i | −0.0800881 | − | 0.246486i | ||||
\(477\) | 0.788234 | − | 2.42594i | 0.0360908 | − | 0.111076i | ||||
\(478\) | −45.4051 | − | 32.9888i | −2.07678 | − | 1.50887i | ||||
\(479\) | 1.39074 | + | 1.01043i | 0.0635446 | + | 0.0461679i | 0.619104 | − | 0.785309i | \(-0.287496\pi\) |
−0.555559 | + | 0.831477i | \(0.687496\pi\) | |||||||
\(480\) | −1.16154 | + | 3.57484i | −0.0530166 | + | 0.163168i | ||||
\(481\) | −11.3204 | − | 34.8407i | −0.516167 | − | 1.58860i | ||||
\(482\) | −25.3051 | + | 18.3852i | −1.15262 | + | 0.837425i | ||||
\(483\) | 1.45744 | 0.0663159 | ||||||||
\(484\) | 16.9807 | + | 37.1497i | 0.771851 | + | 1.68862i | ||||
\(485\) | 6.35435 | 0.288536 | ||||||||
\(486\) | −15.9255 | + | 11.5705i | −0.722395 | + | 0.524851i | ||||
\(487\) | −4.98472 | − | 15.3414i | −0.225879 | − | 0.695185i | −0.998201 | − | 0.0599537i | \(-0.980905\pi\) |
0.772322 | − | 0.635231i | \(-0.219095\pi\) | |||||||
\(488\) | 0.582995 | − | 1.79428i | 0.0263910 | − | 0.0812230i | ||||
\(489\) | 15.2680 | + | 11.0928i | 0.690441 | + | 0.501635i | ||||
\(490\) | 1.93376 | + | 1.40496i | 0.0873583 | + | 0.0634695i | ||||
\(491\) | −5.57370 | + | 17.1541i | −0.251538 | + | 0.774154i | 0.742954 | + | 0.669342i | \(0.233424\pi\) |
−0.994492 | + | 0.104812i | \(0.966576\pi\) | |||||||
\(492\) | 5.62889 | + | 17.3239i | 0.253770 | + | 0.781023i | ||||
\(493\) | 8.04572 | − | 5.84556i | 0.362361 | − | 0.263271i | ||||
\(494\) | 7.81898 | 0.351793 | ||||||||
\(495\) | −0.984362 | − | 2.52706i | −0.0442438 | − | 0.113583i | ||||
\(496\) | −20.1105 | −0.902989 | ||||||||
\(497\) | 4.65897 | − | 3.38494i | 0.208984 | − | 0.151835i | ||||
\(498\) | 13.3548 | + | 41.1019i | 0.598444 | + | 1.84182i | ||||
\(499\) | −2.27763 | + | 7.00981i | −0.101961 | + | 0.313802i | −0.989005 | − | 0.147882i | \(-0.952755\pi\) |
0.887045 | + | 0.461684i | \(0.152755\pi\) | |||||||
\(500\) | −3.00415 | − | 2.18264i | −0.134349 | − | 0.0976106i | ||||
\(501\) | −24.0135 | − | 17.4469i | −1.07285 | − | 0.779468i | ||||
\(502\) | 9.15240 | − | 28.1682i | 0.408492 | − | 1.25721i | ||||
\(503\) | −11.1260 | − | 34.2424i | −0.496086 | − | 1.52680i | −0.815258 | − | 0.579098i | \(-0.803405\pi\) |
0.319172 | − | 0.947697i | \(-0.396595\pi\) | |||||||
\(504\) | −2.70918 | + | 1.96834i | −0.120677 | + | 0.0876767i | ||||
\(505\) | −7.50062 | −0.333773 | ||||||||
\(506\) | −6.58035 | − | 4.22738i | −0.292532 | − | 0.187930i | ||||
\(507\) | −2.89201 | −0.128439 | ||||||||
\(508\) | 18.9586 | − | 13.7743i | 0.841153 | − | 0.611134i | ||||
\(509\) | −10.5385 | − | 32.4340i | −0.467109 | − | 1.43761i | −0.856311 | − | 0.516461i | \(-0.827249\pi\) |
0.389202 | − | 0.921153i | \(-0.372751\pi\) | |||||||
\(510\) | −1.66154 | + | 5.11368i | −0.0735740 | + | 0.226438i | ||||
\(511\) | 4.35026 | + | 3.16065i | 0.192444 | + | 0.139819i | ||||
\(512\) | −20.5148 | − | 14.9049i | −0.906637 | − | 0.658710i | ||||
\(513\) | −1.47406 | + | 4.53669i | −0.0650813 | + | 0.200300i | ||||
\(514\) | −13.5921 | − | 41.8321i | −0.599520 | − | 1.84513i | ||||
\(515\) | 5.17239 | − | 3.75796i | 0.227923 | − | 0.165596i | ||||
\(516\) | −18.0011 | −0.792454 | ||||||||
\(517\) | −34.3732 | + | 28.1165i | −1.51173 | + | 1.23656i | ||||
\(518\) | 22.6408 | 0.994781 | ||||||||
\(519\) | 8.81627 | − | 6.40540i | 0.386991 | − | 0.281166i | ||||
\(520\) | −4.89440 | − | 15.0634i | −0.214634 | − | 0.660575i | ||||
\(521\) | 10.6919 | − | 32.9064i | 0.468422 | − | 1.44165i | −0.386206 | − | 0.922413i | \(-0.626215\pi\) |
0.854628 | − | 0.519242i | \(-0.173785\pi\) | |||||||
\(522\) | −10.3271 | − | 7.50310i | −0.452006 | − | 0.328402i | ||||
\(523\) | 34.5295 | + | 25.0871i | 1.50987 | + | 1.09698i | 0.966235 | + | 0.257661i | \(0.0829517\pi\) |
0.543633 | + | 0.839323i | \(0.317048\pi\) | |||||||
\(524\) | 13.6613 | − | 42.0450i | 0.596795 | − | 1.83675i | ||||
\(525\) | −0.456498 | − | 1.40496i | −0.0199232 | − | 0.0613174i | ||||
\(526\) | −19.0045 | + | 13.8076i | −0.828636 | + | 0.602039i | ||||
\(527\) | 12.9641 | 0.564725 | ||||||||
\(528\) | −11.5544 | + | 0.662645i | −0.502841 | + | 0.0288379i | ||||
\(529\) | −22.0266 | −0.957680 | ||||||||
\(530\) | −6.03225 | + | 4.38269i | −0.262024 | + | 0.190372i | ||||
\(531\) | 1.60871 | + | 4.95110i | 0.0698120 | + | 0.214859i | ||||
\(532\) | −0.970553 | + | 2.98705i | −0.0420788 | + | 0.129505i | ||||
\(533\) | 10.3899 | + | 7.54868i | 0.450035 | + | 0.326969i | ||||
\(534\) | 25.3191 | + | 18.3954i | 1.09567 | + | 0.796048i | ||||
\(535\) | 4.41773 | − | 13.5964i | 0.190995 | − | 0.587822i | ||||
\(536\) | 12.8001 | + | 39.3947i | 0.552881 | + | 1.70159i | ||||
\(537\) | 11.6508 | − | 8.46479i | 0.502768 | − | 0.365283i | ||||
\(538\) | 21.4312 | 0.923963 | ||||||||
\(539\) | 0.842610 | − | 3.20780i | 0.0362938 | − | 0.138170i | ||||
\(540\) | 20.9422 | 0.901209 | ||||||||
\(541\) | −11.4549 | + | 8.32250i | −0.492486 | + | 0.357812i | −0.806140 | − | 0.591725i | \(-0.798447\pi\) |
0.313653 | + | 0.949538i | \(0.398447\pi\) | |||||||
\(542\) | 5.69927 | + | 17.5406i | 0.244805 | + | 0.753432i | ||||
\(543\) | 2.41325 | − | 7.42722i | 0.103563 | − | 0.318733i | ||||
\(544\) | 3.13456 | + | 2.27739i | 0.134393 | + | 0.0976423i | ||||
\(545\) | 12.6393 | + | 9.18302i | 0.541410 | + | 0.393357i | ||||
\(546\) | 4.22004 | − | 12.9879i | 0.180601 | − | 0.555832i | ||||
\(547\) | −12.2499 | − | 37.7012i | −0.523767 | − | 1.61199i | −0.766741 | − | 0.641956i | \(-0.778123\pi\) |
0.242974 | − | 0.970033i | \(-0.421877\pi\) | |||||||
\(548\) | −65.2985 | + | 47.4421i | −2.78941 | + | 2.02663i | ||||
\(549\) | 0.376698 | 0.0160771 | ||||||||
\(550\) | −2.01405 | + | 7.66748i | −0.0858796 | + | 0.326942i | ||||
\(551\) | −5.52402 | −0.235331 | ||||||||
\(552\) | 4.82874 | − | 3.50829i | 0.205525 | − | 0.149323i | ||||
\(553\) | −1.77013 | − | 5.44789i | −0.0752735 | − | 0.231668i | ||||
\(554\) | −2.16342 | + | 6.65833i | −0.0919151 | + | 0.282886i | ||||
\(555\) | −11.3204 | − | 8.22477i | −0.480525 | − | 0.349122i | ||||
\(556\) | 22.4509 | + | 16.3115i | 0.952130 | + | 0.691763i | ||||
\(557\) | −6.76188 | + | 20.8109i | −0.286510 | + | 0.881787i | 0.699432 | + | 0.714699i | \(0.253436\pi\) |
−0.985942 | + | 0.167088i | \(0.946564\pi\) | |||||||
\(558\) | −5.14208 | − | 15.8257i | −0.217682 | − | 0.669955i | ||||
\(559\) | −10.2676 | + | 7.45984i | −0.434273 | + | 0.315518i | ||||
\(560\) | 2.36215 | 0.0998190 | ||||||||
\(561\) | 7.44845 | − | 0.427169i | 0.314474 | − | 0.0180351i | ||||
\(562\) | −68.8242 | −2.90317 | ||||||||
\(563\) | −11.1289 | + | 8.08563i | −0.469028 | + | 0.340769i | −0.797062 | − | 0.603897i | \(-0.793614\pi\) |
0.328034 | + | 0.944666i | \(0.393614\pi\) | |||||||
\(564\) | −22.6969 | − | 69.8538i | −0.955710 | − | 2.94137i | ||||
\(565\) | −4.44486 | + | 13.6799i | −0.186996 | + | 0.575516i | ||||
\(566\) | −55.9506 | − | 40.6505i | −2.35178 | − | 1.70867i | ||||
\(567\) | 4.75561 | + | 3.45515i | 0.199717 | + | 0.145103i | ||||
\(568\) | 7.28786 | − | 22.4297i | 0.305792 | − | 0.941130i | ||||
\(569\) | −4.55812 | − | 14.0284i | −0.191086 | − | 0.588103i | −1.00000 | 0.000175504i | \(-0.999944\pi\) | |
0.808914 | − | 0.587927i | \(-0.200056\pi\) | |||||||
\(570\) | 2.41620 | − | 1.75547i | 0.101203 | − | 0.0735286i | ||||
\(571\) | 32.3734 | 1.35478 | 0.677392 | − | 0.735622i | \(-0.263110\pi\) | ||||
0.677392 | + | 0.735622i | \(0.263110\pi\) | |||||||
\(572\) | −36.8683 | + | 30.1573i | −1.54154 | + | 1.26094i | ||||
\(573\) | 17.9579 | 0.750200 | ||||||||
\(574\) | −6.42129 | + | 4.66534i | −0.268019 | + | 0.194727i | ||||
\(575\) | −0.304872 | − | 0.938298i | −0.0127140 | − | 0.0391297i | ||||
\(576\) | 2.73055 | − | 8.40377i | 0.113773 | − | 0.350157i | ||||
\(577\) | −4.82741 | − | 3.50732i | −0.200968 | − | 0.146011i | 0.482750 | − | 0.875758i | \(-0.339638\pi\) |
−0.683718 | + | 0.729747i | \(0.739638\pi\) | |||||||
\(578\) | −28.3900 | − | 20.6266i | −1.18087 | − | 0.857952i | ||||
\(579\) | −2.39101 | + | 7.35878i | −0.0993671 | + | 0.305820i | ||||
\(580\) | 7.49424 | + | 23.0649i | 0.311181 | + | 0.957717i | ||||
\(581\) | −9.90175 | + | 7.19404i | −0.410794 | + | 0.298459i | ||||
\(582\) | 22.4374 | 0.930060 | ||||||||
\(583\) | 8.70457 | + | 5.59203i | 0.360506 | + | 0.231598i | ||||
\(584\) | 22.0213 | 0.911248 | ||||||||
\(585\) | 2.55850 | − | 1.85886i | 0.105781 | − | 0.0768544i | ||||
\(586\) | −14.3090 | − | 44.0385i | −0.591099 | − | 1.81921i | ||||
\(587\) | −11.8278 | + | 36.4023i | −0.488186 | + | 1.50248i | 0.339127 | + | 0.940741i | \(0.389868\pi\) |
−0.827313 | + | 0.561741i | \(0.810132\pi\) | |||||||
\(588\) | 4.43790 | + | 3.22433i | 0.183016 | + | 0.132969i | ||||
\(589\) | −5.82569 | − | 4.23261i | −0.240043 | − | 0.174402i | ||||
\(590\) | 4.70248 | − | 14.4727i | 0.193598 | − | 0.595833i | ||||
\(591\) | 1.60510 | + | 4.93998i | 0.0660248 | + | 0.203204i | ||||
\(592\) | 18.1014 | − | 13.1515i | 0.743964 | − | 0.540522i | ||||
\(593\) | −46.1732 | −1.89611 | −0.948053 | − | 0.318112i | \(-0.896951\pi\) | ||||
−0.948053 | + | 0.318112i | \(0.896951\pi\) | |||||||
\(594\) | −16.2279 | − | 41.6605i | −0.665840 | − | 1.70935i | ||||
\(595\) | −1.52274 | −0.0624263 | ||||||||
\(596\) | −28.6537 | + | 20.8181i | −1.17370 | + | 0.852743i | ||||
\(597\) | −3.48605 | − | 10.7290i | −0.142675 | − | 0.439107i | ||||
\(598\) | 2.81834 | − | 8.67397i | 0.115251 | − | 0.354705i | ||||
\(599\) | −26.6274 | − | 19.3459i | −1.08797 | − | 0.790454i | −0.108911 | − | 0.994051i | \(-0.534736\pi\) |
−0.979055 | + | 0.203598i | \(0.934736\pi\) | |||||||
\(600\) | −4.89440 | − | 3.55599i | −0.199813 | − | 0.145173i | ||||
\(601\) | 0.971287 | − | 2.98931i | 0.0396196 | − | 0.121937i | −0.929290 | − | 0.369350i | \(-0.879580\pi\) |
0.968910 | + | 0.247413i | \(0.0795805\pi\) | |||||||
\(602\) | −2.42385 | − | 7.45984i | −0.0987887 | − | 0.304040i | ||||
\(603\) | −6.69114 | + | 4.86140i | −0.272484 | + | 0.197971i | ||||
\(604\) | 40.4807 | 1.64714 | ||||||||
\(605\) | 10.9279 | − | 1.25756i | 0.444281 | − | 0.0511272i | ||||
\(606\) | −26.4849 | −1.07588 | ||||||||
\(607\) | −8.21766 | + | 5.97048i | −0.333545 | + | 0.242334i | −0.741933 | − | 0.670474i | \(-0.766091\pi\) |
0.408389 | + | 0.912808i | \(0.366091\pi\) | |||||||
\(608\) | −0.665042 | − | 2.04679i | −0.0269710 | − | 0.0830082i | ||||
\(609\) | −2.98141 | + | 9.17582i | −0.120813 | + | 0.371823i | ||||
\(610\) | −0.890840 | − | 0.647233i | −0.0360691 | − | 0.0262057i | ||||
\(611\) | −41.8941 | − | 30.4379i | −1.69485 | − | 1.23138i | ||||
\(612\) | 1.42879 | − | 4.39735i | 0.0577552 | − | 0.177752i | ||||
\(613\) | 2.82963 | + | 8.70870i | 0.114288 | + | 0.351741i | 0.991798 | − | 0.127817i | \(-0.0407970\pi\) |
−0.877510 | + | 0.479558i | \(0.840797\pi\) | |||||||
\(614\) | −33.4249 | + | 24.2846i | −1.34892 | + | 0.980048i | ||||
\(615\) | 4.90543 | 0.197806 | ||||||||
\(616\) | −4.92997 | − | 12.6563i | −0.198634 | − | 0.509936i | ||||
\(617\) | 37.1224 | 1.49449 | 0.747245 | − | 0.664548i | \(-0.231376\pi\) | ||||
0.747245 | + | 0.664548i | \(0.231376\pi\) | |||||||
\(618\) | 18.2639 | − | 13.2695i | 0.734680 | − | 0.533777i | ||||
\(619\) | 1.05262 | + | 3.23963i | 0.0423084 | + | 0.130212i | 0.969980 | − | 0.243186i | \(-0.0781926\pi\) |
−0.927671 | + | 0.373398i | \(0.878193\pi\) | |||||||
\(620\) | −9.76927 | + | 30.0667i | −0.392343 | + | 1.20751i | ||||
\(621\) | 4.50144 | + | 3.27049i | 0.180636 | + | 0.131240i | ||||
\(622\) | 38.3097 | + | 27.8336i | 1.53608 | + | 1.11603i | ||||
\(623\) | −2.73887 | + | 8.42939i | −0.109731 | + | 0.337716i | ||||
\(624\) | −4.17041 | − | 12.8352i | −0.166950 | − | 0.513819i | ||||
\(625\) | −0.809017 | + | 0.587785i | −0.0323607 | + | 0.0235114i | ||||
\(626\) | 72.7606 | 2.90810 | ||||||||
\(627\) | −3.48659 | − | 2.23987i | −0.139241 | − | 0.0894517i | ||||
\(628\) | 0.224843 | 0.00897222 | ||||||||
\(629\) | −11.6689 | + | 8.47798i | −0.465271 | + | 0.338039i | ||||
\(630\) | 0.603980 | + | 1.85886i | 0.0240631 | + | 0.0740587i | ||||
\(631\) | −3.00580 | + | 9.25090i | −0.119659 | + | 0.368273i | −0.992890 | − | 0.119033i | \(-0.962020\pi\) |
0.873231 | + | 0.487306i | \(0.162020\pi\) | |||||||
\(632\) | −18.9786 | − | 13.7888i | −0.754930 | − | 0.548488i | ||||
\(633\) | 25.5523 | + | 18.5648i | 1.01561 | + | 0.737886i | ||||
\(634\) | 3.21477 | − | 9.89406i | 0.127675 | − | 0.392943i | ||||
\(635\) | −1.95015 | − | 6.00195i | −0.0773894 | − | 0.238180i | ||||
\(636\) | −13.8438 | + | 10.0581i | −0.548942 | + | 0.398830i | ||||
\(637\) | 3.86752 | 0.153237 | ||||||||
\(638\) | 40.0759 | − | 32.7811i | 1.58662 | − | 1.29782i | ||||
\(639\) | 4.70899 | 0.186285 | ||||||||
\(640\) | −16.7795 | + | 12.1910i | −0.663269 | + | 0.481893i | ||||
\(641\) | −5.44029 | − | 16.7435i | −0.214879 | − | 0.661329i | −0.999162 | − | 0.0409260i | \(-0.986969\pi\) |
0.784283 | − | 0.620403i | \(-0.213031\pi\) | |||||||
\(642\) | 15.5991 | − | 48.0092i | 0.615648 | − | 1.89477i | ||||
\(643\) | −30.8947 | − | 22.4463i | −1.21837 | − | 0.885196i | −0.222405 | − | 0.974954i | \(-0.571391\pi\) |
−0.995964 | + | 0.0897579i | \(0.971391\pi\) | |||||||
\(644\) | 2.96385 | + | 2.15336i | 0.116792 | + | 0.0848543i | ||||
\(645\) | −1.49802 | + | 4.61044i | −0.0589845 | + | 0.181536i | ||||
\(646\) | −0.951319 | − | 2.92786i | −0.0374291 | − | 0.115195i | ||||
\(647\) | 15.2665 | − | 11.0917i | 0.600186 | − | 0.436061i | −0.245759 | − | 0.969331i | \(-0.579037\pi\) |
0.845945 | + | 0.533270i | \(0.179037\pi\) | |||||||
\(648\) | 24.0732 | 0.945684 | ||||||||
\(649\) | −21.0806 | + | 1.20897i | −0.827486 | + | 0.0474563i | ||||
\(650\) | −9.24436 | −0.362594 | ||||||||
\(651\) | −10.1749 | + | 7.39251i | −0.398786 | + | 0.289735i | ||||
\(652\) | 14.6593 | + | 45.1165i | 0.574101 | + | 1.76690i | ||||
\(653\) | 5.05751 | − | 15.5654i | 0.197916 | − | 0.609122i | −0.802014 | − | 0.597305i | \(-0.796238\pi\) |
0.999930 | − | 0.0118173i | \(-0.00376165\pi\) | |||||||
\(654\) | 44.6299 | + | 32.4255i | 1.74517 | + | 1.26794i | ||||
\(655\) | −9.63169 | − | 6.99783i | −0.376341 | − | 0.273428i | ||||
\(656\) | −2.42387 | + | 7.45991i | −0.0946363 | + | 0.291260i | ||||
\(657\) | 1.35874 | + | 4.18176i | 0.0530094 | + | 0.163146i | ||||
\(658\) | 25.8920 | − | 18.8116i | 1.00938 | − | 0.733354i | ||||
\(659\) | −5.42317 | −0.211257 | −0.105628 | − | 0.994406i | \(-0.533685\pi\) | ||||
−0.105628 | + | 0.994406i | \(0.533685\pi\) | |||||||
\(660\) | −4.62218 | + | 17.5966i | −0.179918 | + | 0.684946i | ||||
\(661\) | −17.4333 | −0.678077 | −0.339039 | − | 0.940772i | \(-0.610102\pi\) | ||||
−0.339039 | + | 0.940772i | \(0.610102\pi\) | |||||||
\(662\) | 14.4024 | − | 10.4639i | 0.559765 | − | 0.406693i | ||||
\(663\) | 2.68842 | + | 8.27411i | 0.104410 | + | 0.321340i | ||||
\(664\) | −15.4889 | + | 47.6701i | −0.601087 | + | 1.84996i | ||||
\(665\) | 0.684276 | + | 0.497155i | 0.0265351 | + | 0.0192789i | ||||
\(666\) | 14.9777 | + | 10.8819i | 0.580375 | + | 0.421667i | ||||
\(667\) | −1.99113 | + | 6.12805i | −0.0770967 | + | 0.237279i | ||||
\(668\) | −23.0562 | − | 70.9596i | −0.892070 | − | 2.74551i | ||||
\(669\) | 29.1904 | − | 21.2081i | 1.12857 | − | 0.819952i | ||||
\(670\) | 24.1764 | 0.934015 | ||||||||
\(671\) | −0.388172 | + | 1.47777i | −0.0149852 | + | 0.0570485i | ||||
\(672\) | −3.75881 | −0.144999 | ||||||||
\(673\) | 1.98747 | − | 1.44398i | 0.0766115 | − | 0.0556615i | −0.548820 | − | 0.835940i | \(-0.684923\pi\) |
0.625432 | + | 0.780279i | \(0.284923\pi\) | |||||||
\(674\) | −17.2857 | − | 53.1999i | −0.665821 | − | 2.04919i | ||||
\(675\) | 1.74278 | − | 5.36371i | 0.0670795 | − | 0.206449i | ||||
\(676\) | −5.88118 | − | 4.27292i | −0.226199 | − | 0.164343i | ||||
\(677\) | −17.8596 | − | 12.9758i | −0.686401 | − | 0.498700i | 0.189074 | − | 0.981963i | \(-0.439451\pi\) |
−0.875475 | + | 0.483263i | \(0.839451\pi\) | |||||||
\(678\) | −15.6949 | + | 48.3040i | −0.602760 | + | 1.85510i | ||||
\(679\) | 1.96360 | + | 6.04334i | 0.0753561 | + | 0.231922i | ||||
\(680\) | −5.04508 | + | 3.66547i | −0.193470 | + | 0.140564i | ||||
\(681\) | −35.2421 | −1.35048 | ||||||||
\(682\) | 67.3820 | − | 3.86436i | 2.58019 | − | 0.147974i | ||||
\(683\) | 0.861150 | 0.0329510 | 0.0164755 | − | 0.999864i | \(-0.494755\pi\) | ||||
0.0164755 | + | 0.999864i | \(0.494755\pi\) | |||||||
\(684\) | −2.07773 | + | 1.50956i | −0.0794441 | + | 0.0577195i | ||||
\(685\) | 6.71683 | + | 20.6723i | 0.256637 | + | 0.789848i | ||||
\(686\) | −0.738630 | + | 2.27327i | −0.0282010 | + | 0.0867938i | ||||
\(687\) | 1.14776 | + | 0.833896i | 0.0437898 | + | 0.0318151i | ||||
\(688\) | −6.27110 | − | 4.55622i | −0.239083 | − | 0.173704i | ||||
\(689\) | −3.72814 | + | 11.4740i | −0.142031 | + | 0.437126i | ||||
\(690\) | −1.07651 | − | 3.31316i | −0.0409821 | − | 0.126130i | ||||
\(691\) | −19.4307 | + | 14.1172i | −0.739179 | + | 0.537045i | −0.892454 | − | 0.451139i | \(-0.851018\pi\) |
0.153275 | + | 0.988184i | \(0.451018\pi\) | |||||||
\(692\) | 27.3926 | 1.04131 | ||||||||
\(693\) | 2.09920 | − | 1.71709i | 0.0797418 | − | 0.0652269i | ||||
\(694\) | 55.9116 | 2.12238 | ||||||||
\(695\) | 6.04603 | − | 4.39270i | 0.229339 | − | 0.166625i | ||||
\(696\) | 12.2097 | + | 37.5777i | 0.462809 | + | 1.42438i | ||||
\(697\) | 1.56253 | − | 4.80897i | 0.0591850 | − | 0.182153i | ||||
\(698\) | −3.96430 | − | 2.88023i | −0.150051 | − | 0.109018i | ||||
\(699\) | −30.4669 | − | 22.1355i | −1.15236 | − | 0.837241i | ||||
\(700\) | 1.14748 | − | 3.53158i | 0.0433707 | − | 0.133481i | ||||
\(701\) | 3.50582 | + | 10.7898i | 0.132413 | + | 0.407526i | 0.995179 | − | 0.0980786i | \(-0.0312697\pi\) |
−0.862766 | + | 0.505604i | \(0.831270\pi\) | |||||||
\(702\) | 42.1787 | − | 30.6446i | 1.59193 | − | 1.15661i | ||||
\(703\) | 8.01164 | 0.302165 | ||||||||
\(704\) | 30.1538 | + | 19.3715i | 1.13646 | + | 0.730092i | ||||
\(705\) | −19.7797 | −0.744947 | ||||||||
\(706\) | −37.4844 | + | 27.2340i | −1.41074 | + | 1.02496i | ||||
\(707\) | −2.31782 | − | 7.13351i | −0.0871706 | − | 0.268283i | ||||
\(708\) | 10.7920 | − | 33.2144i | 0.405588 | − | 1.24827i | ||||
\(709\) | 35.5355 | + | 25.8181i | 1.33457 | + | 0.969618i | 0.999625 | + | 0.0273790i | \(0.00871609\pi\) |
0.334940 | + | 0.942239i | \(0.391284\pi\) | |||||||
\(710\) | −11.1361 | − | 8.09088i | −0.417932 | − | 0.303645i | ||||
\(711\) | 1.44744 | − | 4.45476i | 0.0542832 | − | 0.167066i | ||||
\(712\) | 11.2165 | + | 34.5208i | 0.420356 | + | 1.29372i | ||||
\(713\) | −6.79530 | + | 4.93707i | −0.254486 | + | 0.184895i | ||||
\(714\) | −5.37684 | −0.201223 | ||||||||
\(715\) | 4.65577 | + | 11.9523i | 0.174116 | + | 0.446992i | ||||
\(716\) | 36.1996 | 1.35284 | ||||||||
\(717\) | −28.0619 | + | 20.3882i | −1.04799 | + | 0.761410i | ||||
\(718\) | −6.39008 | − | 19.6667i | −0.238476 | − | 0.733953i | ||||
\(719\) | −3.02238 | + | 9.30193i | −0.112716 | + | 0.346903i | −0.991464 | − | 0.130383i | \(-0.958379\pi\) |
0.878748 | + | 0.477286i | \(0.158379\pi\) | |||||||
\(720\) | 1.56265 | + | 1.13533i | 0.0582364 | + | 0.0423112i | ||||
\(721\) | 5.17239 | + | 3.75796i | 0.192630 | + | 0.139954i | ||||
\(722\) | 13.5056 | − | 41.5658i | 0.502625 | − | 1.54692i | ||||
\(723\) | 5.97373 | + | 18.3852i | 0.222165 | + | 0.683755i | ||||
\(724\) | 15.8812 | − | 11.5384i | 0.590221 | − | 0.428821i | ||||
\(725\) | 6.53103 | 0.242556 | ||||||||
\(726\) | 38.5867 | − | 4.44050i | 1.43209 | − | 0.164802i | ||||
\(727\) | 1.08785 | 0.0403460 | 0.0201730 | − | 0.999797i | \(-0.493578\pi\) | ||||
0.0201730 | + | 0.999797i | \(0.493578\pi\) | |||||||
\(728\) | 12.8137 | − | 9.30971i | 0.474908 | − | 0.345041i | ||||
\(729\) | 9.20894 | + | 28.3422i | 0.341072 | + | 1.04971i | ||||
\(730\) | 3.97178 | − | 12.2239i | 0.147002 | − | 0.452426i | ||||
\(731\) | 4.04261 | + | 2.93713i | 0.149521 | + | 0.108634i | ||||
\(732\) | −2.04445 | − | 1.48538i | −0.0755649 | − | 0.0549011i | ||||
\(733\) | −2.60001 | + | 8.00200i | −0.0960334 | + | 0.295561i | −0.987522 | − | 0.157483i | \(-0.949662\pi\) |
0.891488 | + | 0.453044i | \(0.149662\pi\) | |||||||
\(734\) | 8.07617 | + | 24.8559i | 0.298097 | + | 0.917447i | ||||
\(735\) | 1.19513 | − | 0.868312i | 0.0440830 | − | 0.0320282i | ||||
\(736\) | −2.51031 | −0.0925313 | ||||||||
\(737\) | −12.1760 | − | 31.2584i | −0.448510 | − | 1.15142i | ||||
\(738\) | −6.49023 | −0.238909 | ||||||||
\(739\) | 2.15958 | − | 1.56903i | 0.0794416 | − | 0.0577177i | −0.547356 | − | 0.836900i | \(-0.684365\pi\) |
0.626797 | + | 0.779182i | \(0.284365\pi\) | |||||||
\(740\) | −10.8691 | − | 33.4517i | −0.399556 | − | 1.22971i | ||||
\(741\) | 1.49329 | − | 4.59588i | 0.0548575 | − | 0.168834i | ||||
\(742\) | −6.03225 | − | 4.38269i | −0.221451 | − | 0.160894i | ||||
\(743\) | −14.0794 | − | 10.2293i | −0.516524 | − | 0.375277i | 0.298769 | − | 0.954326i | \(-0.403424\pi\) |
−0.815293 | + | 0.579049i | \(0.803424\pi\) | |||||||
\(744\) | −15.9162 | + | 48.9852i | −0.583518 | + | 1.79588i | ||||
\(745\) | 2.94742 | + | 9.07122i | 0.107985 | + | 0.332344i | ||||
\(746\) | −56.6297 | + | 41.1439i | −2.07336 | + | 1.50638i | ||||
\(747\) | −10.0081 | −0.366176 | ||||||||
\(748\) | 15.7783 | + | 10.1363i | 0.576910 | + | 0.370621i | ||||
\(749\) | 14.2961 | 0.522367 | ||||||||
\(750\) | −2.85666 | + | 2.07549i | −0.104311 | + | 0.0757861i | ||||
\(751\) | 7.20446 | + | 22.1731i | 0.262895 | + | 0.809106i | 0.992171 | + | 0.124887i | \(0.0398569\pi\) |
−0.729276 | + | 0.684219i | \(0.760143\pi\) | |||||||
\(752\) | 9.77356 | − | 30.0799i | 0.356405 | − | 1.09690i | ||||
\(753\) | −14.8089 | − | 10.7593i | −0.539666 | − | 0.392090i | ||||
\(754\) | 48.8446 | + | 35.4876i | 1.77881 | + | 1.29238i | ||||
\(755\) | 3.36874 | − | 10.3679i | 0.122601 | − | 0.377327i | ||||
\(756\) | 6.47150 | + | 19.9172i | 0.235366 | + | 0.724382i | ||||
\(757\) | −10.5266 | + | 7.64801i | −0.382595 | + | 0.277972i | −0.762415 | − | 0.647089i | \(-0.775986\pi\) |
0.379819 | + | 0.925061i | \(0.375986\pi\) | |||||||
\(758\) | −77.9702 | −2.83200 | ||||||||
\(759\) | −3.74153 | + | 3.06048i | −0.135809 | + | 0.111088i | ||||
\(760\) | 3.46385 | 0.125647 | ||||||||
\(761\) | −11.1301 | + | 8.08650i | −0.403466 | + | 0.293135i | −0.770951 | − | 0.636894i | \(-0.780219\pi\) |
0.367485 | + | 0.930029i | \(0.380219\pi\) | |||||||
\(762\) | −6.88605 | − | 21.1931i | −0.249455 | − | 0.767744i | ||||
\(763\) | −4.82780 | + | 14.8584i | −0.174778 | + | 0.537912i | ||||
\(764\) | 36.5190 | + | 26.5326i | 1.32121 | + | 0.959915i | ||||
\(765\) | −1.00735 | − | 0.731880i | −0.0364207 | − | 0.0264612i | ||||
\(766\) | 13.9988 | − | 43.0840i | 0.505798 | − | 1.55669i | ||||
\(767\) | −7.60876 | − | 23.4174i | −0.274737 | − | 0.845552i | ||||
\(768\) | −33.4195 | + | 24.2807i | −1.20592 | + | 0.876154i | ||||
\(769\) | −32.1927 | −1.16090 | −0.580450 | − | 0.814296i | \(-0.697123\pi\) | ||||
−0.580450 | + | 0.814296i | \(0.697123\pi\) | |||||||
\(770\) | −7.91458 | + | 0.453901i | −0.285222 | + | 0.0163575i | ||||
\(771\) | −27.1841 | −0.979012 | ||||||||
\(772\) | −15.7349 | + | 11.4321i | −0.566311 | + | 0.411449i | ||||
\(773\) | 2.92829 | + | 9.01237i | 0.105323 | + | 0.324152i | 0.989806 | − | 0.142421i | \(-0.0454886\pi\) |
−0.884483 | + | 0.466573i | \(0.845489\pi\) | |||||||
\(774\) | 1.98199 | − | 6.09993i | 0.0712411 | − | 0.219258i | ||||
\(775\) | 6.88769 | + | 5.00420i | 0.247413 | + | 0.179756i | ||||
\(776\) | 21.0530 | + | 15.2959i | 0.755758 | + | 0.549090i | ||||
\(777\) | 4.32402 | − | 13.3080i | 0.155123 | − | 0.477420i | ||||
\(778\) | 28.6904 | + | 88.3000i | 1.02860 | + | 3.16571i | ||||
\(779\) | −2.27222 | + | 1.65087i | −0.0814108 | + | 0.0591484i | ||||
\(780\) | −21.2155 | −0.759635 | ||||||||
\(781\) | −4.85243 | + | 18.4731i | −0.173634 | + | 0.661021i | ||||
\(782\) | −3.59091 | −0.128411 | ||||||||
\(783\) | −29.7988 | + | 21.6501i | −1.06492 | + | 0.773711i | ||||
\(784\) | 0.729944 | + | 2.24654i | 0.0260694 | + | 0.0802335i | ||||
\(785\) | 0.0187111 | − | 0.0575868i | 0.000667827 | − | 0.00205536i | ||||
\(786\) | −34.0098 | − | 24.7096i | −1.21309 | − | 0.881361i | ||||
\(787\) | −29.3084 | − | 21.2938i | −1.04473 | − | 0.759042i | −0.0735280 | − | 0.997293i | \(-0.523426\pi\) |
−0.971204 | + | 0.238251i | \(0.923426\pi\) | |||||||
\(788\) | −4.03466 | + | 12.4174i | −0.143729 | + | 0.442352i | ||||
\(789\) | 4.48636 | + | 13.8076i | 0.159719 | + | 0.491563i | ||||
\(790\) | −11.0771 | + | 8.04796i | −0.394104 | + | 0.286333i | ||||
\(791\) | −14.3839 | −0.511431 | ||||||||
\(792\) | 2.82168 | − | 10.7421i | 0.100264 | − | 0.381703i | ||||
\(793\) | −1.78168 | −0.0632693 | ||||||||
\(794\) | −14.1079 | + | 10.2500i | −0.500670 | + | 0.363758i | ||||
\(795\) | 1.42402 | + | 4.38269i | 0.0505049 | + | 0.155438i | ||||
\(796\) | 8.76275 | − | 26.9690i | 0.310587 | − | 0.955890i | ||||
\(797\) | −8.04935 | − | 5.84819i | −0.285122 | − | 0.207154i | 0.436026 | − | 0.899934i | \(-0.356386\pi\) |
−0.721149 | + | 0.692780i | \(0.756386\pi\) | |||||||
\(798\) | 2.41620 | + | 1.75547i | 0.0855325 | + | 0.0621430i | ||||
\(799\) | −6.30045 | + | 19.3908i | −0.222894 | + | 0.685997i | ||||
\(800\) | 0.786277 | + | 2.41991i | 0.0277991 | + | 0.0855568i | ||||
\(801\) | −5.86331 | + | 4.25994i | −0.207170 | + | 0.150518i | ||||
\(802\) | 89.9428 | 3.17599 | ||||||||
\(803\) | −17.8050 | + | 1.02111i | −0.628323 | + | 0.0360344i | ||||
\(804\) | 55.4839 | 1.95677 | ||||||||
\(805\) | 0.798164 | − | 0.579900i | 0.0281316 | − | 0.0204388i | ||||
\(806\) | 24.3207 | + | 74.8513i | 0.856659 | + | 2.63652i | ||||
\(807\) | 4.09299 | − | 12.5969i | 0.144080 | − | 0.443432i | ||||
\(808\) | −24.8508 | − | 18.0551i | −0.874247 | − | 0.635178i | ||||
\(809\) | −10.5350 | − | 7.65414i | −0.370392 | − | 0.269105i | 0.386982 | − | 0.922087i | \(-0.373518\pi\) |
−0.757373 | + | 0.652982i | \(0.773518\pi\) | |||||||
\(810\) | 4.34185 | − | 13.3629i | 0.152557 | − | 0.469523i | ||||
\(811\) | −9.69373 | − | 29.8342i | −0.340393 | − | 1.04762i | −0.964004 | − | 0.265887i | \(-0.914335\pi\) |
0.623611 | − | 0.781735i | \(-0.285665\pi\) | |||||||
\(812\) | −19.6202 | + | 14.2549i | −0.688533 | + | 0.500248i | ||||
\(813\) | 11.3985 | 0.399765 | ||||||||
\(814\) | −58.1232 | + | 47.5434i | −2.03722 | + | 1.66639i | ||||
\(815\) | 12.7752 | 0.447494 | ||||||||
\(816\) | −4.29880 | + | 3.12326i | −0.150488 | + | 0.109336i | ||||
\(817\) | −0.857698 | − | 2.63972i | −0.0300071 | − | 0.0923522i | ||||
\(818\) | 14.2577 | − | 43.8808i | 0.498510 | − | 1.53426i | ||||
\(819\) | 2.55850 | + | 1.85886i | 0.0894012 | + | 0.0649538i | ||||
\(820\) | 9.97564 | + | 7.24773i | 0.348365 | + | 0.253102i | ||||
\(821\) | 3.32495 | − | 10.2331i | 0.116042 | − | 0.357139i | −0.876121 | − | 0.482091i | \(-0.839878\pi\) |
0.992163 | + | 0.124952i | \(0.0398776\pi\) | |||||||
\(822\) | 23.7173 | + | 72.9945i | 0.827238 | + | 2.54598i | ||||
\(823\) | 38.3465 | − | 27.8604i | 1.33668 | − | 0.971152i | 0.337117 | − | 0.941463i | \(-0.390548\pi\) |
0.999559 | − | 0.0296896i | \(-0.00945187\pi\) | |||||||
\(824\) | 26.1829 | 0.912126 | ||||||||
\(825\) | 4.12218 | + | 2.64819i | 0.143516 | + | 0.0921981i | ||||
\(826\) | 15.2175 | 0.529486 | ||||||||
\(827\) | 37.1648 | − | 27.0018i | 1.29235 | − | 0.938945i | 0.292498 | − | 0.956266i | \(-0.405514\pi\) |
0.999850 | + | 0.0173209i | \(0.00551368\pi\) | |||||||
\(828\) | 0.925712 | + | 2.84905i | 0.0321707 | + | 0.0990113i | ||||
\(829\) | −16.2560 | + | 50.0307i | −0.564593 | + | 1.73764i | 0.104564 | + | 0.994518i | \(0.466655\pi\) |
−0.669157 | + | 0.743121i | \(0.733345\pi\) | |||||||
\(830\) | 23.6677 | + | 17.1956i | 0.821519 | + | 0.596868i | ||||
\(831\) | 3.50049 | + | 2.54326i | 0.121431 | + | 0.0882246i | ||||
\(832\) | −12.9148 | + | 39.7476i | −0.447739 | + | 1.37800i | ||||
\(833\) | −0.470553 | − | 1.44821i | −0.0163037 | − | 0.0501776i | ||||
\(834\) | 21.3487 | − | 15.5107i | 0.739246 | − | 0.537093i | ||||
\(835\) | −20.0928 | −0.695342 | ||||||||
\(836\) | −3.78091 | − | 9.70638i | −0.130765 | − | 0.335702i | ||||
\(837\) | −48.0148 | −1.65964 | ||||||||
\(838\) | 35.1147 | − | 25.5123i | 1.21302 | − | 0.881308i | ||||
\(839\) | −9.22859 | − | 28.4027i | −0.318606 | − | 0.980570i | −0.974244 | − | 0.225494i | \(-0.927600\pi\) |
0.655638 | − | 0.755075i | \(-0.272400\pi\) | |||||||
\(840\) | 1.86950 | − | 5.75372i | 0.0645037 | − | 0.198522i | ||||
\(841\) | −11.0466 | − | 8.02583i | −0.380918 | − | 0.276753i | ||||
\(842\) | −37.8394 | − | 27.4919i | −1.30403 | − | 0.947435i | ||||
\(843\) | −13.1442 | + | 40.4538i | −0.452712 | + | 1.39330i | ||||
\(844\) | 24.5336 | + | 75.5066i | 0.844481 | + | 2.59905i | ||||
\(845\) | −1.58380 | + | 1.15070i | −0.0544844 | + | 0.0395853i | ||||
\(846\) | 26.1700 | 0.899742 | ||||||||
\(847\) | 4.57291 | + | 10.0044i | 0.157127 | + | 0.343756i | ||||
\(848\) | −7.36859 | −0.253039 | ||||||||
\(849\) | −34.5794 | + | 25.1234i | −1.18676 | + | 0.862233i | ||||
\(850\) | 1.12474 | + | 3.46160i | 0.0385783 | + | 0.118732i | ||||
\(851\) | 2.88778 | − | 8.88769i | 0.0989920 | − | 0.304666i | ||||
\(852\) | −25.5570 | − | 18.5683i | −0.875570 | − | 0.636139i | ||||
\(853\) | 42.6200 | + | 30.9652i | 1.45928 | + | 1.06023i | 0.983550 | + | 0.180638i | \(0.0578163\pi\) |
0.475731 | + | 0.879591i | \(0.342184\pi\) | |||||||
\(854\) | 0.340271 | − | 1.04725i | 0.0116438 | − | 0.0358360i | ||||
\(855\) | 0.213723 | + | 0.657772i | 0.00730917 | + | 0.0224953i | ||||
\(856\) | 47.3652 | − | 34.4128i | 1.61891 | − | 1.17621i | ||||
\(857\) | −0.0751683 | −0.00256770 | −0.00128385 | − | 0.999999i | \(-0.500409\pi\) | ||||
−0.00128385 | + | 0.999999i | \(0.500409\pi\) | |||||||
\(858\) | 16.4397 | + | 42.2041i | 0.561241 | + | 1.44082i | ||||
\(859\) | 32.9785 | 1.12521 | 0.562606 | − | 0.826725i | \(-0.309799\pi\) | ||||
0.562606 | + | 0.826725i | \(0.309799\pi\) | |||||||
\(860\) | −9.85825 | + | 7.16244i | −0.336163 | + | 0.244237i | ||||
\(861\) | 1.51586 | + | 4.66534i | 0.0516604 | + | 0.158994i | ||||
\(862\) | 22.4056 | − | 68.9574i | 0.763138 | − | 2.34870i | ||||
\(863\) | 41.3308 | + | 30.0285i | 1.40692 | + | 1.02218i | 0.993762 | + | 0.111522i | \(0.0355726\pi\) |
0.413153 | + | 0.910662i | \(0.364427\pi\) | |||||||
\(864\) | −11.6094 | − | 8.43473i | −0.394960 | − | 0.286955i | ||||
\(865\) | 2.27957 | − | 7.01579i | 0.0775077 | − | 0.238544i | ||||
\(866\) | 6.11001 | + | 18.8047i | 0.207627 | + | 0.639009i | ||||
\(867\) | −17.5460 | + | 12.7479i | −0.595893 | + | 0.432942i | ||||
\(868\) | −31.6140 | −1.07305 | ||||||||
\(869\) | 15.9842 | + | 10.2687i | 0.542229 | + | 0.348341i | ||||
\(870\) | 23.0613 | 0.781850 | ||||||||
\(871\) | 31.6473 | − | 22.9931i | 1.07233 | − | 0.779092i | ||||
\(872\) | 19.7713 | + | 60.8497i | 0.669539 | + | 2.06063i | ||||
\(873\) | −1.60564 | + | 4.94166i | −0.0543428 | + | 0.167250i | ||||
\(874\) | 1.61365 | + | 1.17239i | 0.0545826 | + | 0.0396566i | ||||
\(875\) | −0.809017 | − | 0.587785i | −0.0273498 | − | 0.0198708i | ||||
\(876\) | 9.11508 | − | 28.0533i | 0.307970 | − | 0.947834i | ||||
\(877\) | 6.68017 | + | 20.5594i | 0.225573 | + | 0.694243i | 0.998233 | + | 0.0594226i | \(0.0189259\pi\) |
−0.772660 | + | 0.634820i | \(0.781074\pi\) | |||||||
\(878\) | −4.03976 | + | 2.93506i | −0.136335 | + | 0.0990534i | ||||
\(879\) | −28.6180 | −0.965260 | ||||||||
\(880\) | −6.06407 | + | 4.96026i | −0.204420 | + | 0.167210i | ||||
\(881\) | 12.2075 | 0.411280 | 0.205640 | − | 0.978628i | \(-0.434072\pi\) | ||||
0.205640 | + | 0.978628i | \(0.434072\pi\) | |||||||
\(882\) | −1.58124 | + | 1.14884i | −0.0532431 | + | 0.0386834i | ||||
\(883\) | 0.732936 | + | 2.25574i | 0.0246652 | + | 0.0759118i | 0.962631 | − | 0.270815i | \(-0.0872931\pi\) |
−0.937966 | + | 0.346727i | \(0.887293\pi\) | |||||||
\(884\) | −6.75777 | + | 20.7983i | −0.227289 | + | 0.699522i | ||||
\(885\) | −7.60876 | − | 5.52809i | −0.255766 | − | 0.185825i | ||||
\(886\) | 31.7878 | + | 23.0952i | 1.06793 | + | 0.775898i | ||||
\(887\) | −3.14139 | + | 9.66819i | −0.105477 | + | 0.324626i | −0.989842 | − | 0.142170i | \(-0.954592\pi\) |
0.884365 | + | 0.466796i | \(0.154592\pi\) | |||||||
\(888\) | −17.7081 | − | 54.5000i | −0.594245 | − | 1.82890i | ||||
\(889\) | 5.10556 | − | 3.70941i | 0.171235 | − | 0.124410i | ||||
\(890\) | 21.1853 | 0.710132 | ||||||||
\(891\) | −19.4640 | + | 1.11626i | −0.652068 | + | 0.0373961i | ||||
\(892\) | 90.6962 | 3.03674 | ||||||||
\(893\) | 9.16208 | − | 6.65664i | 0.306597 | − | 0.222756i | ||||
\(894\) | 10.4074 | + | 32.0308i | 0.348076 | + | 1.07127i | ||||
\(895\) | 3.01247 | − | 9.27143i | 0.100696 | − | 0.309910i | ||||
\(896\) | −16.7795 | − | 12.1910i | −0.560565 | − | 0.407274i | ||||
\(897\) | −4.56017 | − | 3.31316i | −0.152260 | − | 0.110623i | ||||
\(898\) | 6.57455 | − | 20.2344i | 0.219396 | − | 0.675230i | ||||
\(899\) | −17.1823 | − | 52.8816i | −0.573061 | − | 1.76370i | ||||
\(900\) | 2.45650 | − | 1.78475i | 0.0818833 | − | 0.0594917i | ||||
\(901\) | 4.75010 | 0.158249 | ||||||||
\(902\) | 6.68792 | − | 25.4608i | 0.222683 | − | 0.847753i | ||||
\(903\) | −4.84770 | −0.161321 | ||||||||
\(904\) | −47.6560 | + | 34.6241i | −1.58502 | + | 1.15158i | ||||
\(905\) | −1.63360 | − | 5.02770i | −0.0543027 | − | 0.167126i | ||||
\(906\) | 11.8951 | − | 36.6094i | 0.395189 | − | 1.21627i | ||||
\(907\) | 27.2434 | + | 19.7935i | 0.904601 | + | 0.657231i | 0.939644 | − | 0.342155i | \(-0.111157\pi\) |
−0.0350426 | + | 0.999386i | \(0.511157\pi\) | |||||||
\(908\) | −71.6680 | − | 52.0698i | −2.37839 | − | 1.72800i | ||||
\(909\) | 1.89529 | − | 5.83310i | 0.0628627 | − | 0.193472i | ||||
\(910\) | −2.85666 | − | 8.79191i | −0.0946975 | − | 0.291449i | ||||
\(911\) | −37.8360 | + | 27.4894i | −1.25356 | + | 0.910766i | −0.998423 | − | 0.0561389i | \(-0.982121\pi\) |
−0.255138 | + | 0.966905i | \(0.582121\pi\) | |||||||
\(912\) | 2.95146 | 0.0977328 | ||||||||
\(913\) | 10.3129 | − | 39.2611i | 0.341307 | − | 1.29935i | ||||
\(914\) | −15.7890 | −0.522253 | ||||||||
\(915\) | −0.550570 | + | 0.400012i | −0.0182013 | + | 0.0132240i | ||||
\(916\) | 1.10200 | + | 3.39161i | 0.0364112 | + | 0.112062i | ||||
\(917\) | 3.67898 | − | 11.3227i | 0.121491 | − | 0.373910i | ||||
\(918\) | −16.6068 | − | 12.0656i | −0.548107 | − | 0.398223i | ||||
\(919\) | 4.46730 | + | 3.24568i | 0.147362 | + | 0.107065i | 0.659024 | − | 0.752122i | \(-0.270970\pi\) |
−0.511661 | + | 0.859187i | \(0.670970\pi\) | |||||||
\(920\) | 1.24854 | − | 3.84261i | 0.0411631 | − | 0.126687i | ||||
\(921\) | 7.89055 | + | 24.2846i | 0.260003 | + | 0.800205i | ||||
\(922\) | 38.3517 | − | 27.8641i | 1.26304 | − | 0.917656i | ||||
\(923\) | −22.2723 | −0.733101 | ||||||||
\(924\) | −18.1637 | + | 1.04169i | −0.597541 | + | 0.0342690i | ||||
\(925\) | −9.47214 | −0.311442 | ||||||||
\(926\) | 20.7409 | − | 15.0692i | 0.681589 | − | 0.495203i | ||||
\(927\) | 1.61552 | + | 4.97205i | 0.0530605 | + | 0.163303i | ||||
\(928\) | 5.13520 | − | 15.8045i | 0.168571 | − | 0.518809i | ||||
\(929\) | 3.73103 | + | 2.71075i | 0.122411 | + | 0.0889370i | 0.647306 | − | 0.762230i | \(-0.275895\pi\) |
−0.524895 | + | 0.851167i | \(0.675895\pi\) | |||||||
\(930\) | 24.3207 | + | 17.6700i | 0.797506 | + | 0.579422i | ||||
\(931\) | −0.261370 | + | 0.804414i | −0.00856606 | + | 0.0263636i | ||||
\(932\) | −29.2522 | − | 90.0291i | −0.958189 | − | 2.94900i | ||||
\(933\) | 23.6767 | − | 17.2021i | 0.775140 | − | 0.563172i | ||||
\(934\) | −45.8314 | −1.49965 | ||||||||
\(935\) | 3.90916 | − | 3.19759i | 0.127843 | − | 0.104572i | ||||
\(936\) | 12.9513 | 0.423326 | ||||||||
\(937\) | 0.647948 | − | 0.470762i | 0.0211676 | − | 0.0153791i | −0.577151 | − | 0.816637i | \(-0.695836\pi\) |
0.598319 | + | 0.801258i | \(0.295836\pi\) | |||||||
\(938\) | 7.47091 | + | 22.9931i | 0.243934 | + | 0.750752i | ||||
\(939\) | 13.8960 | − | 42.7676i | 0.453480 | − | 1.39567i | ||||
\(940\) | −40.2239 | − | 29.2244i | −1.31196 | − | 0.953194i | ||||
\(941\) | −0.455276 | − | 0.330777i | −0.0148416 | − | 0.0107830i | 0.580340 | − | 0.814374i | \(-0.302920\pi\) |
−0.595181 | + | 0.803591i | \(0.702920\pi\) | |||||||
\(942\) | 0.0660694 | − | 0.203341i | 0.00215266 | − | 0.00662520i | ||||
\(943\) | 1.01236 | + | 3.11574i | 0.0329671 | + | 0.101462i | ||||
\(944\) | 12.1665 | − | 8.83945i | 0.395985 | − | 0.287700i | ||||
\(945\) | 5.63974 | 0.183461 | ||||||||
\(946\) | 21.8874 | + | 14.0610i | 0.711619 | + | 0.457162i | ||||
\(947\) | 43.8097 | 1.42362 | 0.711812 | − | 0.702370i | \(-0.247875\pi\) | ||||
0.711812 | + | 0.702370i | \(0.247875\pi\) | |||||||
\(948\) | −25.4214 | + | 18.4698i | −0.825650 | + | 0.599870i | ||||
\(949\) | −6.42647 | − | 19.7786i | −0.208612 | − | 0.642042i | ||||
\(950\) | 0.624741 | − | 1.92276i | 0.0202693 | − | 0.0623825i | ||||
\(951\) | −5.20161 | − | 3.77919i | −0.168674 | − | 0.122549i | ||||
\(952\) | −5.04508 | − | 3.66547i | −0.163512 | − | 0.118799i | ||||
\(953\) | −8.26625 | + | 25.4409i | −0.267770 | + | 0.824112i | 0.723272 | + | 0.690563i | \(0.242637\pi\) |
−0.991042 | + | 0.133549i | \(0.957363\pi\) | |||||||
\(954\) | −1.88408 | − | 5.79861i | −0.0609994 | − | 0.187737i | ||||
\(955\) | 9.83456 | − | 7.14523i | 0.318239 | − | 0.231214i | ||||
\(956\) | −87.1899 | −2.81992 | ||||||||
\(957\) | −11.6144 | − | 29.8167i | −0.375441 | − | 0.963836i | ||||
\(958\) | 4.10897 | 0.132755 | ||||||||
\(959\) | −17.5849 | + | 12.7762i | −0.567846 | + | 0.412564i | ||||
\(960\) | 4.93300 | + | 15.1822i | 0.159212 | + | 0.490004i | ||||
\(961\) | 12.8188 | − | 39.4521i | 0.413509 | − | 1.27265i | ||||
\(962\) | −70.8406 | − | 51.4687i | −2.28399 | − | 1.65942i | ||||
\(963\) | 9.45735 | + | 6.87117i | 0.304759 | + | 0.221420i | ||||
\(964\) | −15.0159 | + | 46.2142i | −0.483630 | + | 1.48846i | ||||
\(965\) | 1.61855 | + | 4.98137i | 0.0521028 | + | 0.160356i | ||||
\(966\) | 2.81834 | − | 2.04765i | 0.0906787 | − | 0.0658819i | ||||
\(967\) | −10.8617 | −0.349290 | −0.174645 | − | 0.984631i | \(-0.555878\pi\) | ||||
−0.174645 | + | 0.984631i | \(0.555878\pi\) | |||||||
\(968\) | 39.2330 | + | 22.1386i | 1.26100 | + | 0.711560i | ||||
\(969\) | −1.90264 | −0.0611215 | ||||||||
\(970\) | 12.2878 | − | 8.92759i | 0.394537 | − | 0.286648i | ||||
\(971\) | −16.3248 | − | 50.2425i | −0.523887 | − | 1.61236i | −0.766506 | − | 0.642237i | \(-0.778007\pi\) |
0.242619 | − | 0.970122i | \(-0.421993\pi\) | |||||||
\(972\) | −9.45010 | + | 29.0844i | −0.303112 | + | 0.932883i | ||||
\(973\) | 6.04603 | + | 4.39270i | 0.193827 | + | 0.140823i | ||||
\(974\) | −31.1933 | − | 22.6632i | −0.999497 | − | 0.726177i | ||||
\(975\) | −1.76552 | + | 5.43370i | −0.0565417 | + | 0.174018i | ||||
\(976\) | −0.336269 | − | 1.03493i | −0.0107637 | − | 0.0331273i | ||||
\(977\) | 10.4529 | − | 7.59446i | 0.334417 | − | 0.242968i | −0.407885 | − | 0.913033i | \(-0.633734\pi\) |
0.742303 | + | 0.670065i | \(0.233734\pi\) | |||||||
\(978\) | 45.1095 | 1.44244 | ||||||||
\(979\) | −10.6696 | − | 27.3912i | −0.341003 | − | 0.875425i | ||||
\(980\) | 3.71333 | 0.118618 | ||||||||
\(981\) | −10.3352 | + | 7.50898i | −0.329978 | + | 0.239743i | ||||
\(982\) | 13.3226 | + | 41.0027i | 0.425141 | + | 1.30845i | ||||
\(983\) | −10.3136 | + | 31.7421i | −0.328954 | + | 1.01242i | 0.640670 | + | 0.767816i | \(0.278657\pi\) |
−0.969624 | + | 0.244600i | \(0.921343\pi\) | |||||||
\(984\) | 16.2525 | + | 11.8081i | 0.518110 | + | 0.376429i | ||||
\(985\) | 2.84459 | + | 2.06671i | 0.0906361 | + | 0.0658510i | ||||
\(986\) | 7.34572 | − | 22.6078i | 0.233935 | − | 0.719979i | ||||
\(987\) | −6.11227 | − | 18.8116i | −0.194556 | − | 0.598781i | ||||
\(988\) | 9.82713 | − | 7.13983i | 0.312643 | − | 0.227148i | ||||
\(989\) | −3.23753 | −0.102947 | ||||||||
\(990\) | −5.45394 | − | 3.50374i | −0.173337 | − | 0.111356i | ||||
\(991\) | 21.2540 | 0.675157 | 0.337579 | − | 0.941297i | \(-0.390392\pi\) | ||||
0.337579 | + | 0.941297i | \(0.390392\pi\) | |||||||
\(992\) | 17.5254 | − | 12.7329i | 0.556431 | − | 0.404271i | ||||
\(993\) | −3.39994 | − | 10.4639i | −0.107894 | − | 0.332063i | ||||
\(994\) | 4.25363 | − | 13.0913i | 0.134917 | − | 0.415232i | ||||
\(995\) | −6.17806 | − | 4.48862i | −0.195858 | − | 0.142299i | ||||
\(996\) | 54.3165 | + | 39.4633i | 1.72109 | + | 1.25044i | ||||
\(997\) | 4.03120 | − | 12.4068i | 0.127669 | − | 0.392926i | −0.866709 | − | 0.498815i | \(-0.833769\pi\) |
0.994378 | + | 0.105889i | \(0.0337687\pi\) | |||||||
\(998\) | 5.44411 | + | 16.7552i | 0.172330 | + | 0.530378i | ||||
\(999\) | 43.2180 | − | 31.3997i | 1.36736 | − | 0.993443i |
(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 | 385.2.n.c.36.2 | ✓ | 8 | |
11.2 | odd | 10 | 4235.2.a.t.1.4 | 4 | |||
11.4 | even | 5 | inner | 385.2.n.c.246.2 | yes | 8 | |
11.9 | even | 5 | 4235.2.a.w.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.n.c.36.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
385.2.n.c.246.2 | yes | 8 | 11.4 | even | 5 | inner | |
4235.2.a.t.1.4 | 4 | 11.2 | odd | 10 | |||
4235.2.a.w.1.1 | 4 | 11.9 | even | 5 |