Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(123,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.123");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 123.15 | ||
Character | \(\chi\) | \(=\) | 349.123 |
Dual form | 349.2.e.a.227.15 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0377450 | + | 0.0217921i | −0.0266898 | + | 0.0154093i | −0.513286 | − | 0.858218i | \(-0.671572\pi\) |
0.486596 | + | 0.873627i | \(0.338238\pi\) | |||||||
\(3\) | 1.71622 | − | 2.97259i | 0.990862 | − | 1.71622i | 0.378622 | − | 0.925551i | \(-0.376398\pi\) |
0.612240 | − | 0.790672i | \(-0.290269\pi\) | |||||||
\(4\) | −0.999050 | + | 1.73041i | −0.499525 | + | 0.865203i | ||||
\(5\) | 1.73771 | − | 3.00980i | 0.777127 | − | 1.34602i | −0.156464 | − | 0.987684i | \(-0.550010\pi\) |
0.933591 | − | 0.358340i | \(-0.116657\pi\) | |||||||
\(6\) | 0.149601i | 0.0610741i | ||||||||
\(7\) | −2.79927 | + | 1.61616i | −1.05802 | + | 0.610850i | −0.924885 | − | 0.380248i | \(-0.875839\pi\) |
−0.133138 | + | 0.991097i | \(0.542505\pi\) | |||||||
\(8\) | − | 0.174254i | − | 0.0616081i | ||||||
\(9\) | −4.39085 | − | 7.60517i | −1.46362 | − | 2.53506i | ||||
\(10\) | 0.151473i | 0.0479001i | ||||||||
\(11\) | 0.153470i | 0.0462730i | 0.999732 | + | 0.0231365i | \(0.00736523\pi\) | ||||
−0.999732 | + | 0.0231365i | \(0.992635\pi\) | |||||||
\(12\) | 3.42919 | + | 5.93953i | 0.989921 | + | 1.71459i | ||||
\(13\) | 2.06169 | − | 1.19032i | 0.571810 | − | 0.330135i | −0.186062 | − | 0.982538i | \(-0.559573\pi\) |
0.757872 | + | 0.652403i | \(0.226239\pi\) | |||||||
\(14\) | 0.0704389 | − | 0.122004i | 0.0188256 | − | 0.0326069i | ||||
\(15\) | −5.96459 | − | 10.3310i | −1.54005 | − | 2.66745i | ||||
\(16\) | −1.99430 | − | 3.45423i | −0.498576 | − | 0.863559i | ||||
\(17\) | 5.10067 | 1.23709 | 0.618547 | − | 0.785748i | \(-0.287722\pi\) | ||||
0.618547 | + | 0.785748i | \(0.287722\pi\) | |||||||
\(18\) | 0.331465 | + | 0.191372i | 0.0781271 | + | 0.0451067i | ||||
\(19\) | −2.56067 | + | 4.43522i | −0.587459 | + | 1.01751i | 0.407105 | + | 0.913381i | \(0.366538\pi\) |
−0.994564 | + | 0.104127i | \(0.966795\pi\) | |||||||
\(20\) | 3.47212 | + | 6.01388i | 0.776389 | + | 1.34475i | ||||
\(21\) | 11.0947i | 2.42107i | ||||||||
\(22\) | −0.00334444 | − | 0.00579273i | −0.000713036 | − | 0.00123501i | ||||
\(23\) | 2.19639 | + | 3.80426i | 0.457979 | + | 0.793244i | 0.998854 | − | 0.0478596i | \(-0.0152400\pi\) |
−0.540875 | + | 0.841103i | \(0.681907\pi\) | |||||||
\(24\) | −0.517985 | − | 0.299059i | −0.105733 | − | 0.0610451i | ||||
\(25\) | −3.53927 | − | 6.13019i | −0.707853 | − | 1.22604i | ||||
\(26\) | −0.0518790 | + | 0.0898571i | −0.0101743 | + | 0.0176224i | ||||
\(27\) | −19.8454 | −3.81924 | ||||||||
\(28\) | − | 6.45849i | − | 1.22054i | ||||||
\(29\) | 2.29456 | − | 3.97429i | 0.426089 | − | 0.738007i | −0.570433 | − | 0.821344i | \(-0.693225\pi\) |
0.996521 | + | 0.0833373i | \(0.0265579\pi\) | |||||||
\(30\) | 0.450268 | + | 0.259962i | 0.0822073 | + | 0.0474624i | ||||
\(31\) | 5.19023 | 0.932193 | 0.466096 | − | 0.884734i | \(-0.345660\pi\) | ||||
0.466096 | + | 0.884734i | \(0.345660\pi\) | |||||||
\(32\) | 0.452367 | + | 0.261174i | 0.0799679 | + | 0.0461695i | ||||
\(33\) | 0.456203 | + | 0.263389i | 0.0794147 | + | 0.0458501i | ||||
\(34\) | −0.192525 | + | 0.111154i | −0.0330177 | + | 0.0190628i | ||||
\(35\) | 11.2336i | 1.89883i | ||||||||
\(36\) | 17.5467 | 2.92445 | ||||||||
\(37\) | −1.35934 | −0.223474 | −0.111737 | − | 0.993738i | \(-0.535641\pi\) | ||||
−0.111737 | + | 0.993738i | \(0.535641\pi\) | |||||||
\(38\) | − | 0.223210i | − | 0.0362094i | ||||||
\(39\) | − | 8.17140i | − | 1.30847i | ||||||
\(40\) | −0.524470 | − | 0.302803i | −0.0829260 | − | 0.0478773i | ||||
\(41\) | 7.68887 | 1.20080 | 0.600400 | − | 0.799700i | \(-0.295008\pi\) | ||||
0.600400 | + | 0.799700i | \(0.295008\pi\) | |||||||
\(42\) | −0.241778 | − | 0.418772i | −0.0373071 | − | 0.0646179i | ||||
\(43\) | 1.29737 | + | 0.749037i | 0.197847 | + | 0.114227i | 0.595651 | − | 0.803243i | \(-0.296894\pi\) |
−0.397804 | + | 0.917471i | \(0.630228\pi\) | |||||||
\(44\) | −0.265565 | − | 0.153324i | −0.0400355 | − | 0.0231145i | ||||
\(45\) | −30.5201 | −4.54966 | ||||||||
\(46\) | −0.165806 | − | 0.0957280i | −0.0244467 | − | 0.0141143i | ||||
\(47\) | − | 2.44212i | − | 0.356219i | −0.984011 | − | 0.178110i | \(-0.943002\pi\) | ||
0.984011 | − | 0.178110i | \(-0.0569982\pi\) | |||||||
\(48\) | −13.6907 | −1.97608 | ||||||||
\(49\) | 1.72393 | − | 2.98593i | 0.246275 | − | 0.426561i | ||||
\(50\) | 0.267179 | + | 0.154256i | 0.0377849 | + | 0.0218151i | ||||
\(51\) | 8.75388 | − | 15.1622i | 1.22579 | − | 2.12313i | ||||
\(52\) | 4.75675i | 0.659642i | ||||||||
\(53\) | 6.29968i | 0.865328i | 0.901555 | + | 0.432664i | \(0.142426\pi\) | ||||
−0.901555 | + | 0.432664i | \(0.857574\pi\) | |||||||
\(54\) | 0.749063 | − | 0.432472i | 0.101935 | − | 0.0588520i | ||||
\(55\) | 0.461914 | + | 0.266686i | 0.0622845 | + | 0.0359600i | ||||
\(56\) | 0.281622 | + | 0.487783i | 0.0376333 | + | 0.0651828i | ||||
\(57\) | 8.78937 | + | 15.2236i | 1.16418 | + | 2.01642i | ||||
\(58\) | 0.200013i | 0.0262630i | ||||||||
\(59\) | −7.84880 | − | 4.53151i | −1.02183 | − | 0.589952i | −0.107195 | − | 0.994238i | \(-0.534187\pi\) |
−0.914633 | + | 0.404286i | \(0.867520\pi\) | |||||||
\(60\) | 23.8357 | 3.07718 | ||||||||
\(61\) | 4.70242i | 0.602083i | 0.953611 | + | 0.301041i | \(0.0973342\pi\) | ||||
−0.953611 | + | 0.301041i | \(0.902666\pi\) | |||||||
\(62\) | −0.195905 | + | 0.113106i | −0.0248800 | + | 0.0143645i | ||||
\(63\) | 24.5823 | + | 14.1926i | 3.09708 | + | 1.78810i | ||||
\(64\) | 7.95445 | 0.994306 | ||||||||
\(65\) | − | 8.27370i | − | 1.02623i | ||||||
\(66\) | −0.0229592 | −0.00282608 | ||||||||
\(67\) | 5.98833 | 0.731590 | 0.365795 | − | 0.930695i | \(-0.380797\pi\) | ||||
0.365795 | + | 0.930695i | \(0.380797\pi\) | |||||||
\(68\) | −5.09582 | + | 8.82622i | −0.617959 | + | 1.07034i | ||||
\(69\) | 15.0780 | 1.81518 | ||||||||
\(70\) | −0.244805 | − | 0.424014i | −0.0292598 | − | 0.0506794i | ||||
\(71\) | 8.67606 | − | 5.00912i | 1.02966 | − | 0.594474i | 0.112772 | − | 0.993621i | \(-0.464027\pi\) |
0.916887 | + | 0.399147i | \(0.130694\pi\) | |||||||
\(72\) | −1.32523 | + | 0.765123i | −0.156180 | + | 0.0901706i | ||||
\(73\) | 2.31215 | − | 4.00477i | 0.270617 | − | 0.468723i | −0.698403 | − | 0.715705i | \(-0.746106\pi\) |
0.969020 | + | 0.246982i | \(0.0794389\pi\) | |||||||
\(74\) | 0.0513082 | − | 0.0296228i | 0.00596446 | − | 0.00344358i | ||||
\(75\) | −24.2967 | −2.80554 | ||||||||
\(76\) | −5.11648 | − | 8.86201i | −0.586901 | − | 1.01654i | ||||
\(77\) | −0.248032 | − | 0.429604i | −0.0282658 | − | 0.0489579i | ||||
\(78\) | 0.178072 | + | 0.308430i | 0.0201627 | + | 0.0349228i | ||||
\(79\) | 9.12273i | 1.02639i | 0.858273 | + | 0.513194i | \(0.171538\pi\) | ||||
−0.858273 | + | 0.513194i | \(0.828462\pi\) | |||||||
\(80\) | −13.8621 | −1.54983 | ||||||||
\(81\) | −20.8865 | + | 36.1765i | −2.32072 | + | 4.01961i | ||||
\(82\) | −0.290217 | + | 0.167557i | −0.0320491 | + | 0.0185035i | ||||
\(83\) | 2.69012 | + | 4.65943i | 0.295279 | + | 0.511439i | 0.975050 | − | 0.221986i | \(-0.0712540\pi\) |
−0.679770 | + | 0.733425i | \(0.737921\pi\) | |||||||
\(84\) | −19.1984 | − | 11.0842i | −2.09472 | − | 1.20939i | ||||
\(85\) | 8.86347 | − | 15.3520i | 0.961379 | − | 1.66516i | ||||
\(86\) | −0.0652924 | −0.00704066 | ||||||||
\(87\) | −7.87594 | − | 13.6415i | −0.844390 | − | 1.46253i | ||||
\(88\) | 0.0267428 | 0.00285079 | ||||||||
\(89\) | −0.728326 | − | 0.420499i | −0.0772024 | − | 0.0445728i | 0.460902 | − | 0.887451i | \(-0.347526\pi\) |
−0.538104 | + | 0.842878i | \(0.680859\pi\) | |||||||
\(90\) | 1.15198 | − | 0.665096i | 0.121429 | − | 0.0701073i | ||||
\(91\) | −3.84748 | + | 6.66403i | −0.403325 | + | 0.698580i | ||||
\(92\) | −8.77722 | −0.915089 | ||||||||
\(93\) | 8.90759 | − | 15.4284i | 0.923674 | − | 1.59985i | ||||
\(94\) | 0.0532188 | + | 0.0921777i | 0.00548910 | + | 0.00950741i | ||||
\(95\) | 8.89941 | + | 15.4142i | 0.913060 | + | 1.58147i | ||||
\(96\) | 1.55273 | − | 0.896467i | 0.158474 | − | 0.0914952i | ||||
\(97\) | −13.5267 | + | 7.80965i | −1.37343 | + | 0.792950i | −0.991358 | − | 0.131183i | \(-0.958122\pi\) |
−0.382071 | + | 0.924133i | \(0.624789\pi\) | |||||||
\(98\) | 0.150272i | 0.0151798i | ||||||||
\(99\) | 1.16717 | − | 0.673863i | 0.117305 | − | 0.0677258i | ||||
\(100\) | 14.1436 | 1.41436 | ||||||||
\(101\) | − | 8.83219i | − | 0.878836i | −0.898283 | − | 0.439418i | \(-0.855185\pi\) | ||
0.898283 | − | 0.439418i | \(-0.144815\pi\) | |||||||
\(102\) | 0.763062i | 0.0755544i | ||||||||
\(103\) | 13.9242i | 1.37199i | 0.727607 | + | 0.685994i | \(0.240633\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(104\) | −0.207418 | − | 0.359258i | −0.0203390 | − | 0.0352281i | ||||
\(105\) | 33.3930 | + | 19.2794i | 3.25882 | + | 1.88148i | ||||
\(106\) | −0.137283 | − | 0.237782i | −0.0133341 | − | 0.0230954i | ||||
\(107\) | −7.56872 | + | 4.36980i | −0.731696 | + | 0.422445i | −0.819042 | − | 0.573733i | \(-0.805495\pi\) |
0.0873463 | + | 0.996178i | \(0.472161\pi\) | |||||||
\(108\) | 19.8265 | − | 34.3405i | 1.90781 | − | 3.30442i | ||||
\(109\) | −2.56617 | + | 4.44473i | −0.245794 | + | 0.425728i | −0.962355 | − | 0.271797i | \(-0.912382\pi\) |
0.716560 | + | 0.697525i | \(0.245715\pi\) | |||||||
\(110\) | −0.0232466 | −0.00221648 | ||||||||
\(111\) | −2.33293 | + | 4.04075i | −0.221431 | + | 0.383531i | ||||
\(112\) | 11.1652 | + | 6.44621i | 1.05501 | + | 0.609110i | ||||
\(113\) | −6.95228 | + | 4.01390i | −0.654015 | + | 0.377596i | −0.789993 | − | 0.613116i | \(-0.789916\pi\) |
0.135978 | + | 0.990712i | \(0.456583\pi\) | |||||||
\(114\) | −0.663511 | − | 0.383078i | −0.0621435 | − | 0.0358785i | ||||
\(115\) | 15.2668 | 1.42363 | ||||||||
\(116\) | 4.58476 | + | 7.94103i | 0.425684 | + | 0.737306i | ||||
\(117\) | −18.1051 | − | 10.4530i | −1.67382 | − | 0.966380i | ||||
\(118\) | 0.395005 | 0.0363631 | ||||||||
\(119\) | −14.2781 | + | 8.24348i | −1.30887 | + | 0.755678i | ||||
\(120\) | −1.80022 | + | 1.03935i | −0.164336 | + | 0.0948797i | ||||
\(121\) | 10.9764 | 0.997859 | ||||||||
\(122\) | −0.102476 | − | 0.177493i | −0.00927770 | − | 0.0160694i | ||||
\(123\) | 13.1958 | − | 22.8558i | 1.18983 | − | 2.06084i | ||||
\(124\) | −5.18530 | + | 8.98120i | −0.465654 | + | 0.806536i | ||||
\(125\) | −7.22377 | −0.646114 | ||||||||
\(126\) | −1.23715 | −0.110214 | ||||||||
\(127\) | − | 7.06750i | − | 0.627139i | −0.949565 | − | 0.313569i | \(-0.898475\pi\) | ||
0.949565 | − | 0.313569i | \(-0.101525\pi\) | |||||||
\(128\) | −1.20497 | + | 0.695693i | −0.106506 | + | 0.0614911i | ||||
\(129\) | 4.45316 | − | 2.57103i | 0.392079 | − | 0.226367i | ||||
\(130\) | 0.180301 | + | 0.312291i | 0.0158135 | + | 0.0273897i | ||||
\(131\) | 21.5664i | 1.88427i | 0.335234 | + | 0.942135i | \(0.391184\pi\) | ||||
−0.335234 | + | 0.942135i | \(0.608816\pi\) | |||||||
\(132\) | −0.911539 | + | 0.526278i | −0.0793393 | + | 0.0458066i | ||||
\(133\) | − | 16.5538i | − | 1.43540i | ||||||
\(134\) | −0.226030 | + | 0.130498i | −0.0195260 | + | 0.0112733i | ||||
\(135\) | −34.4854 | + | 59.7305i | −2.96803 | + | 5.14079i | ||||
\(136\) | − | 0.888812i | − | 0.0762150i | ||||||
\(137\) | −13.4902 | − | 7.78856i | −1.15254 | − | 0.665422i | −0.203039 | − | 0.979171i | \(-0.565082\pi\) |
−0.949506 | + | 0.313749i | \(0.898415\pi\) | |||||||
\(138\) | −0.569120 | + | 0.328581i | −0.0484467 | + | 0.0279707i | ||||
\(139\) | 3.54489 | 0.300674 | 0.150337 | − | 0.988635i | \(-0.451964\pi\) | ||||
0.150337 | + | 0.988635i | \(0.451964\pi\) | |||||||
\(140\) | −19.4388 | − | 11.2230i | −1.64288 | − | 0.948514i | ||||
\(141\) | −7.25940 | − | 4.19122i | −0.611352 | − | 0.352964i | ||||
\(142\) | −0.218319 | + | 0.378139i | −0.0183209 | + | 0.0317327i | ||||
\(143\) | 0.182678 | + | 0.316408i | 0.0152763 | + | 0.0264593i | ||||
\(144\) | −17.5134 | + | 30.3340i | −1.45945 | + | 2.52784i | ||||
\(145\) | −7.97454 | − | 13.8123i | −0.662250 | − | 1.14705i | ||||
\(146\) | 0.201547i | 0.0166801i | ||||||||
\(147\) | −5.91729 | − | 10.2490i | −0.488050 | − | 0.845327i | ||||
\(148\) | 1.35805 | − | 2.35220i | 0.111631 | − | 0.193350i | ||||
\(149\) | −3.56236 | + | 2.05673i | −0.291840 | + | 0.168494i | −0.638771 | − | 0.769397i | \(-0.720557\pi\) |
0.346932 | + | 0.937890i | \(0.387224\pi\) | |||||||
\(150\) | 0.917079 | − | 0.529476i | 0.0748792 | − | 0.0432315i | ||||
\(151\) | 10.3680 | − | 17.9579i | 0.843737 | − | 1.46140i | −0.0429765 | − | 0.999076i | \(-0.513684\pi\) |
0.886714 | − | 0.462319i | \(-0.152983\pi\) | |||||||
\(152\) | 0.772854 | + | 0.446208i | 0.0626868 | + | 0.0361922i | ||||
\(153\) | −22.3962 | − | 38.7914i | −1.81063 | − | 3.13610i | ||||
\(154\) | 0.0187239 | + | 0.0108103i | 0.00150882 | + | 0.000871116i | ||||
\(155\) | 9.01911 | − | 15.6216i | 0.724432 | − | 1.25475i | ||||
\(156\) | 14.1398 | + | 8.16364i | 1.13209 | + | 0.653614i | ||||
\(157\) | 9.75898 | − | 16.9031i | 0.778852 | − | 1.34901i | −0.153753 | − | 0.988109i | \(-0.549136\pi\) |
0.932604 | − | 0.360901i | \(-0.117531\pi\) | |||||||
\(158\) | −0.198804 | − | 0.344338i | −0.0158160 | − | 0.0273941i | ||||
\(159\) | 18.7264 | + | 10.8117i | 1.48510 | + | 0.857421i | ||||
\(160\) | 1.57216 | − | 0.907690i | 0.124291 | − | 0.0717592i | ||||
\(161\) | −12.2966 | − | 7.09943i | −0.969106 | − | 0.559513i | ||||
\(162\) | − | 1.82064i | − | 0.143043i | ||||||
\(163\) | − | 8.83252i | − | 0.691817i | −0.938268 | − | 0.345908i | \(-0.887571\pi\) | ||
0.938268 | − | 0.345908i | \(-0.112429\pi\) | |||||||
\(164\) | −7.68157 | + | 13.3049i | −0.599830 | + | 1.03894i | ||||
\(165\) | 1.58550 | − | 0.915387i | 0.123431 | − | 0.0712628i | ||||
\(166\) | −0.203078 | − | 0.117247i | −0.0157619 | − | 0.00910012i | ||||
\(167\) | − | 3.25894i | − | 0.252184i | −0.992019 | − | 0.126092i | \(-0.959757\pi\) | ||
0.992019 | − | 0.126092i | \(-0.0402435\pi\) | |||||||
\(168\) | 1.93330 | 0.149158 | ||||||||
\(169\) | −3.66629 | + | 6.35020i | −0.282022 | + | 0.488477i | ||||
\(170\) | 0.772615i | 0.0592569i | ||||||||
\(171\) | 44.9741 | 3.43925 | ||||||||
\(172\) | −2.59228 | + | 1.49665i | −0.197659 | + | 0.114119i | ||||
\(173\) | −5.29351 | + | 3.05621i | −0.402458 | + | 0.232359i | −0.687544 | − | 0.726143i | \(-0.741311\pi\) |
0.285086 | + | 0.958502i | \(0.407978\pi\) | |||||||
\(174\) | 0.594556 | + | 0.343267i | 0.0450731 | + | 0.0260230i | ||||
\(175\) | 19.8147 | + | 11.4400i | 1.49785 | + | 0.864784i | ||||
\(176\) | 0.530122 | − | 0.306066i | 0.0399594 | − | 0.0230706i | ||||
\(177\) | −26.9406 | + | 15.5542i | −2.02498 | + | 1.16912i | ||||
\(178\) | 0.0366542 | 0.00274735 | ||||||||
\(179\) | 1.55969i | 0.116576i | 0.998300 | + | 0.0582882i | \(0.0185642\pi\) | ||||
−0.998300 | + | 0.0582882i | \(0.981436\pi\) | |||||||
\(180\) | 30.4911 | − | 52.8121i | 2.27267 | − | 3.93638i | ||||
\(181\) | −4.33550 | −0.322255 | −0.161127 | − | 0.986934i | \(-0.551513\pi\) | ||||
−0.161127 | + | 0.986934i | \(0.551513\pi\) | |||||||
\(182\) | − | 0.335379i | − | 0.0248599i | ||||||
\(183\) | 13.9783 | + | 8.07040i | 1.03331 | + | 0.596581i | ||||
\(184\) | 0.662908 | − | 0.382730i | 0.0488702 | − | 0.0282152i | ||||
\(185\) | −2.36213 | + | 4.09133i | −0.173667 | + | 0.300801i | ||||
\(186\) | 0.776461i | 0.0569329i | ||||||||
\(187\) | 0.782800i | 0.0572440i | ||||||||
\(188\) | 4.22585 | + | 2.43980i | 0.308202 | + | 0.177940i | ||||
\(189\) | 55.5524 | − | 32.0732i | 4.04084 | − | 2.33298i | ||||
\(190\) | −0.671817 | − | 0.387874i | −0.0487387 | − | 0.0281393i | ||||
\(191\) | −7.30153 | − | 12.6466i | −0.528320 | − | 0.915078i | −0.999455 | − | 0.0330162i | \(-0.989489\pi\) |
0.471135 | − | 0.882061i | \(-0.343845\pi\) | |||||||
\(192\) | 13.6516 | − | 23.6453i | 0.985220 | − | 1.70645i | ||||
\(193\) | −1.45959 | − | 0.842697i | −0.105064 | − | 0.0606587i | 0.446547 | − | 0.894760i | \(-0.352653\pi\) |
−0.551611 | + | 0.834101i | \(0.685987\pi\) | |||||||
\(194\) | 0.340377 | − | 0.589551i | 0.0244377 | − | 0.0423273i | ||||
\(195\) | −24.5943 | − | 14.1995i | −1.76123 | − | 1.01685i | ||||
\(196\) | 3.44458 | + | 5.96619i | 0.246041 | + | 0.426156i | ||||
\(197\) | −19.5668 | − | 11.2969i | −1.39407 | − | 0.804869i | −0.400310 | − | 0.916380i | \(-0.631098\pi\) |
−0.993763 | + | 0.111511i | \(0.964431\pi\) | |||||||
\(198\) | −0.0293698 | + | 0.0508700i | −0.00208722 | + | 0.00361517i | ||||
\(199\) | −14.4447 | + | 8.33963i | −1.02395 | + | 0.591181i | −0.915247 | − | 0.402893i | \(-0.868005\pi\) |
−0.108708 | + | 0.994074i | \(0.534671\pi\) | |||||||
\(200\) | −1.06821 | + | 0.616732i | −0.0755339 | + | 0.0436095i | ||||
\(201\) | 10.2773 | − | 17.8008i | 0.724905 | − | 1.25557i | ||||
\(202\) | 0.192472 | + | 0.333371i | 0.0135423 | + | 0.0234559i | ||||
\(203\) | 14.8335i | 1.04110i | ||||||||
\(204\) | 17.4911 | + | 30.2955i | 1.22462 | + | 2.12111i | ||||
\(205\) | 13.3610 | − | 23.1420i | 0.933174 | − | 1.61630i | ||||
\(206\) | −0.303437 | − | 0.525568i | −0.0211414 | − | 0.0366181i | ||||
\(207\) | 19.2880 | − | 33.4079i | 1.34061 | − | 2.32201i | ||||
\(208\) | −8.22327 | − | 4.74771i | −0.570181 | − | 0.329194i | ||||
\(209\) | −0.680673 | − | 0.392987i | −0.0470831 | − | 0.0271835i | ||||
\(210\) | −1.68056 | −0.115970 | ||||||||
\(211\) | −20.3484 | + | 11.7481i | −1.40084 | + | 0.808775i | −0.994479 | − | 0.104938i | \(-0.966536\pi\) |
−0.406360 | + | 0.913713i | \(0.633202\pi\) | |||||||
\(212\) | −10.9010 | − | 6.29370i | −0.748684 | − | 0.432253i | ||||
\(213\) | − | 34.3871i | − | 2.35617i | ||||||
\(214\) | 0.190454 | − | 0.329877i | 0.0130192 | − | 0.0225499i | ||||
\(215\) | 4.50891 | − | 2.60322i | 0.307505 | − | 0.177538i | ||||
\(216\) | 3.45813i | 0.235296i | ||||||||
\(217\) | −14.5288 | + | 8.38822i | −0.986281 | + | 0.569430i | ||||
\(218\) | − | 0.223689i | − | 0.0151501i | ||||||
\(219\) | −7.93634 | − | 13.7461i | −0.536288 | − | 0.928879i | ||||
\(220\) | −0.922951 | + | 0.532866i | −0.0622254 | + | 0.0359258i | ||||
\(221\) | 10.5160 | − | 6.07141i | 0.707382 | − | 0.408407i | ||||
\(222\) | − | 0.203357i | − | 0.0136485i | ||||||
\(223\) | −12.2642 | −0.821273 | −0.410637 | − | 0.911799i | \(-0.634694\pi\) | ||||
−0.410637 | + | 0.911799i | \(0.634694\pi\) | |||||||
\(224\) | −1.68839 | −0.112811 | ||||||||
\(225\) | −31.0807 | + | 53.8334i | −2.07205 | + | 3.58890i | ||||
\(226\) | 0.174943 | − | 0.303010i | 0.0116370 | − | 0.0201559i | ||||
\(227\) | −2.56741 | − | 4.44689i | −0.170405 | − | 0.295150i | 0.768156 | − | 0.640262i | \(-0.221174\pi\) |
−0.938562 | + | 0.345112i | \(0.887841\pi\) | |||||||
\(228\) | −35.1241 | −2.32615 | ||||||||
\(229\) | −9.63795 | + | 5.56447i | −0.636894 | + | 0.367711i | −0.783417 | − | 0.621496i | \(-0.786525\pi\) |
0.146523 | + | 0.989207i | \(0.453192\pi\) | |||||||
\(230\) | −0.576245 | + | 0.332695i | −0.0379964 | + | 0.0219373i | ||||
\(231\) | −1.70271 | −0.112030 | ||||||||
\(232\) | −0.692536 | − | 0.399836i | −0.0454672 | − | 0.0262505i | ||||
\(233\) | 8.54545 | + | 14.8012i | 0.559831 | + | 0.969656i | 0.997510 | + | 0.0705246i | \(0.0224673\pi\) |
−0.437679 | + | 0.899131i | \(0.644199\pi\) | |||||||
\(234\) | 0.911171 | 0.0595651 | ||||||||
\(235\) | −7.35028 | − | 4.24369i | −0.479479 | − | 0.276828i | ||||
\(236\) | 15.6827 | − | 9.05441i | 1.02086 | − | 0.589392i | ||||
\(237\) | 27.1181 | + | 15.6566i | 1.76151 | + | 1.01701i | ||||
\(238\) | 0.359285 | − | 0.622301i | 0.0232890 | − | 0.0403378i | ||||
\(239\) | 0.513859 | 0.0332388 | 0.0166194 | − | 0.999862i | \(-0.494710\pi\) | ||||
0.0166194 | + | 0.999862i | \(0.494710\pi\) | |||||||
\(240\) | −23.7904 | + | 41.2062i | −1.53566 | + | 2.65985i | ||||
\(241\) | 1.70481 | − | 2.95282i | 0.109817 | − | 0.190208i | −0.805879 | − | 0.592080i | \(-0.798307\pi\) |
0.915696 | + | 0.401872i | \(0.131640\pi\) | |||||||
\(242\) | −0.414306 | + | 0.239200i | −0.0266326 | + | 0.0153764i | ||||
\(243\) | 41.9238 | + | 72.6142i | 2.68942 | + | 4.65820i | ||||
\(244\) | −8.13709 | − | 4.69795i | −0.520924 | − | 0.300755i | ||||
\(245\) | −5.99137 | − | 10.3774i | −0.382774 | − | 0.662985i | ||||
\(246\) | 1.15026i | 0.0733378i | ||||||||
\(247\) | 12.1921i | 0.775762i | ||||||||
\(248\) | − | 0.904418i | − | 0.0574306i | ||||||
\(249\) | 18.4674 | 1.17032 | ||||||||
\(250\) | 0.272661 | − | 0.157421i | 0.0172446 | − | 0.00995619i | ||||
\(251\) | 14.1782i | 0.894919i | 0.894304 | + | 0.447459i | \(0.147671\pi\) | ||||
−0.894304 | + | 0.447459i | \(0.852329\pi\) | |||||||
\(252\) | −49.1179 | + | 28.3582i | −3.09414 | + | 1.78640i | ||||
\(253\) | −0.583840 | + | 0.337080i | −0.0367057 | + | 0.0211921i | ||||
\(254\) | 0.154016 | + | 0.266763i | 0.00966380 | + | 0.0167382i | ||||
\(255\) | −30.4234 | − | 52.6949i | −1.90519 | − | 3.29988i | ||||
\(256\) | −7.92412 | + | 13.7250i | −0.495258 | + | 0.857812i | ||||
\(257\) | 1.16555 | 0.0727051 | 0.0363525 | − | 0.999339i | \(-0.488426\pi\) | ||||
0.0363525 | + | 0.999339i | \(0.488426\pi\) | |||||||
\(258\) | −0.112056 | + | 0.194087i | −0.00697632 | + | 0.0120833i | ||||
\(259\) | 3.80514 | − | 2.19690i | 0.236440 | − | 0.136509i | ||||
\(260\) | 14.3169 | + | 8.26584i | 0.887894 | + | 0.512626i | ||||
\(261\) | −40.3002 | −2.49452 | ||||||||
\(262\) | −0.469978 | − | 0.814026i | −0.0290354 | − | 0.0502907i | ||||
\(263\) | 13.8050 | 0.851252 | 0.425626 | − | 0.904899i | \(-0.360054\pi\) | ||||
0.425626 | + | 0.904899i | \(0.360054\pi\) | |||||||
\(264\) | 0.0458966 | − | 0.0794952i | 0.00282474 | − | 0.00489259i | ||||
\(265\) | 18.9608 | + | 10.9470i | 1.16475 | + | 0.672470i | ||||
\(266\) | 0.360742 | + | 0.624824i | 0.0221185 | + | 0.0383104i | ||||
\(267\) | −2.49994 | + | 1.44334i | −0.152994 | + | 0.0883310i | ||||
\(268\) | −5.98264 | + | 10.3622i | −0.365448 | + | 0.632974i | ||||
\(269\) | 16.8251 | 1.02585 | 0.512923 | − | 0.858434i | \(-0.328562\pi\) | ||||
0.512923 | + | 0.858434i | \(0.328562\pi\) | |||||||
\(270\) | − | 3.00604i | − | 0.182942i | ||||||
\(271\) | −7.24870 | − | 12.5551i | −0.440327 | − | 0.762669i | 0.557386 | − | 0.830253i | \(-0.311804\pi\) |
−0.997714 | + | 0.0675842i | \(0.978471\pi\) | |||||||
\(272\) | −10.1723 | − | 17.6189i | −0.616785 | − | 1.06830i | ||||
\(273\) | 13.2063 | + | 22.8739i | 0.799280 | + | 1.38439i | ||||
\(274\) | 0.678917 | 0.0410149 | ||||||||
\(275\) | 0.940801 | − | 0.543171i | 0.0567324 | − | 0.0327545i | ||||
\(276\) | −15.0637 | + | 26.0911i | −0.906727 | + | 1.57050i | ||||
\(277\) | 16.6258 | − | 9.59892i | 0.998949 | − | 0.576743i | 0.0910115 | − | 0.995850i | \(-0.470990\pi\) |
0.907937 | + | 0.419107i | \(0.137657\pi\) | |||||||
\(278\) | −0.133802 | + | 0.0772507i | −0.00802492 | + | 0.00463319i | ||||
\(279\) | −22.7895 | − | 39.4726i | −1.36437 | − | 2.36316i | ||||
\(280\) | 1.95751 | 0.116983 | ||||||||
\(281\) | −9.04315 | + | 15.6632i | −0.539469 | + | 0.934388i | 0.459464 | + | 0.888197i | \(0.348042\pi\) |
−0.998933 | + | 0.0461911i | \(0.985292\pi\) | |||||||
\(282\) | 0.365342 | 0.0217558 | ||||||||
\(283\) | −19.8833 | −1.18194 | −0.590970 | − | 0.806693i | \(-0.701255\pi\) | ||||
−0.590970 | + | 0.806693i | \(0.701255\pi\) | |||||||
\(284\) | 20.0175i | 1.18782i | ||||||||
\(285\) | 61.0935 | 3.61887 | ||||||||
\(286\) | −0.0137904 | − | 0.00796188i | −0.000815442 | − | 0.000470796i | ||||
\(287\) | −21.5232 | + | 12.4264i | −1.27047 | + | 0.733508i | ||||
\(288\) | − | 4.58710i | − | 0.270298i | ||||||
\(289\) | 9.01679 | 0.530399 | ||||||||
\(290\) | 0.601999 | + | 0.347564i | 0.0353506 | + | 0.0204097i | ||||
\(291\) | 53.6124i | 3.14281i | ||||||||
\(292\) | 4.61991 | + | 8.00193i | 0.270360 | + | 0.468277i | ||||
\(293\) | −4.54943 | − | 7.87984i | −0.265780 | − | 0.460345i | 0.701987 | − | 0.712189i | \(-0.252296\pi\) |
−0.967768 | + | 0.251844i | \(0.918963\pi\) | |||||||
\(294\) | 0.446697 | + | 0.257900i | 0.0260519 | + | 0.0150411i | ||||
\(295\) | −27.2779 | + | 15.7489i | −1.58818 | + | 0.916936i | ||||
\(296\) | 0.236870i | 0.0137678i | ||||||||
\(297\) | − | 3.04567i | − | 0.176728i | ||||||
\(298\) | 0.0896409 | − | 0.155263i | 0.00519276 | − | 0.00899412i | ||||
\(299\) | 9.05656 | + | 5.22881i | 0.523754 | + | 0.302390i | ||||
\(300\) | 24.2736 | − | 42.0431i | 1.40144 | − | 2.42736i | ||||
\(301\) | −4.84225 | −0.279103 | ||||||||
\(302\) | 0.903764i | 0.0520057i | ||||||||
\(303\) | −26.2545 | − | 15.1580i | −1.50828 | − | 0.870805i | ||||
\(304\) | 20.4270 | 1.17157 | ||||||||
\(305\) | 14.1533 | + | 8.17143i | 0.810418 | + | 0.467895i | ||||
\(306\) | 1.69069 | + | 0.976122i | 0.0966505 | + | 0.0558012i | ||||
\(307\) | −7.56181 | − | 13.0974i | −0.431575 | − | 0.747510i | 0.565434 | − | 0.824794i | \(-0.308709\pi\) |
−0.997009 | + | 0.0772833i | \(0.975375\pi\) | |||||||
\(308\) | 0.991185 | 0.0564780 | ||||||||
\(309\) | 41.3908 | + | 23.8970i | 2.35464 | + | 1.35945i | ||||
\(310\) | 0.786181i | 0.0446521i | ||||||||
\(311\) | − | 4.62828i | − | 0.262446i | −0.991353 | − | 0.131223i | \(-0.958110\pi\) | ||
0.991353 | − | 0.131223i | \(-0.0418903\pi\) | |||||||
\(312\) | −1.42390 | −0.0806125 | ||||||||
\(313\) | −24.2089 | −1.36837 | −0.684185 | − | 0.729309i | \(-0.739842\pi\) | ||||
−0.684185 | + | 0.729309i | \(0.739842\pi\) | |||||||
\(314\) | 0.850675i | 0.0480064i | ||||||||
\(315\) | 85.4337 | − | 49.3252i | 4.81365 | − | 2.77916i | ||||
\(316\) | −15.7860 | − | 9.11407i | −0.888034 | − | 0.512706i | ||||
\(317\) | 2.51279 | + | 1.45076i | 0.141132 | + | 0.0814827i | 0.568903 | − | 0.822404i | \(-0.307368\pi\) |
−0.427771 | + | 0.903887i | \(0.640701\pi\) | |||||||
\(318\) | −0.942436 | −0.0528492 | ||||||||
\(319\) | 0.609934 | + | 0.352146i | 0.0341498 | + | 0.0197164i | ||||
\(320\) | 13.8225 | − | 23.9413i | 0.772702 | − | 1.33836i | ||||
\(321\) | 29.9982i | 1.67434i | ||||||||
\(322\) | 0.618846 | 0.0344869 | ||||||||
\(323\) | −13.0611 | + | 22.6226i | −0.726741 | + | 1.25875i | ||||
\(324\) | −41.7334 | − | 72.2843i | −2.31852 | − | 4.01579i | ||||
\(325\) | −14.5937 | − | 8.42570i | −0.809515 | − | 0.467374i | ||||
\(326\) | 0.192479 | + | 0.333384i | 0.0106604 | + | 0.0184644i | ||||
\(327\) | 8.80824 | + | 15.2563i | 0.487097 | + | 0.843676i | ||||
\(328\) | − | 1.33982i | − | 0.0739790i | ||||||
\(329\) | 3.94684 | + | 6.83613i | 0.217596 | + | 0.376888i | ||||
\(330\) | −0.0398964 | + | 0.0691026i | −0.00219623 | + | 0.00380397i | ||||
\(331\) | −7.88875 | − | 4.55457i | −0.433605 | − | 0.250342i | 0.267276 | − | 0.963620i | \(-0.413876\pi\) |
−0.700881 | + | 0.713278i | \(0.747210\pi\) | |||||||
\(332\) | −10.7503 | −0.589998 | ||||||||
\(333\) | 5.96864 | + | 10.3380i | 0.327079 | + | 0.566518i | ||||
\(334\) | 0.0710191 | + | 0.123009i | 0.00388599 | + | 0.00673073i | ||||
\(335\) | 10.4060 | − | 18.0237i | 0.568539 | − | 0.984738i | ||||
\(336\) | 38.3239 | − | 22.1263i | 2.09074 | − | 1.20709i | ||||
\(337\) | 6.47887 | + | 11.2217i | 0.352927 | + | 0.611287i | 0.986761 | − | 0.162182i | \(-0.0518532\pi\) |
−0.633834 | + | 0.773469i | \(0.718520\pi\) | |||||||
\(338\) | − | 0.319585i | − | 0.0173831i | ||||||
\(339\) | 27.5550i | 1.49658i | ||||||||
\(340\) | 17.7101 | + | 30.6748i | 0.960466 | + | 1.66358i | ||||
\(341\) | 0.796545i | 0.0431353i | ||||||||
\(342\) | −1.69755 | + | 0.980080i | −0.0917929 | + | 0.0529967i | ||||
\(343\) | − | 11.4817i | − | 0.619951i | ||||||
\(344\) | 0.130523 | − | 0.226072i | 0.00703732 | − | 0.0121890i | ||||
\(345\) | 26.2012 | − | 45.3818i | 1.41062 | − | 2.44327i | ||||
\(346\) | 0.133203 | − | 0.230714i | 0.00716101 | − | 0.0124032i | ||||
\(347\) | 31.0899 | − | 17.9497i | 1.66899 | − | 0.963592i | 0.700807 | − | 0.713351i | \(-0.252823\pi\) |
0.968183 | − | 0.250242i | \(-0.0805101\pi\) | |||||||
\(348\) | 31.4739 | 1.68718 | ||||||||
\(349\) | 13.4876 | + | 12.9261i | 0.721975 | + | 0.691919i | ||||
\(350\) | −0.997209 | −0.0533030 | ||||||||
\(351\) | −40.9150 | + | 23.6223i | −2.18388 | + | 1.26086i | ||||
\(352\) | −0.0400824 | + | 0.0694248i | −0.00213640 | + | 0.00370035i | ||||
\(353\) | −12.1970 | + | 21.1259i | −0.649183 | + | 1.12442i | 0.334136 | + | 0.942525i | \(0.391556\pi\) |
−0.983318 | + | 0.181893i | \(0.941778\pi\) | |||||||
\(354\) | 0.677916 | − | 1.17419i | 0.0360308 | − | 0.0624072i | ||||
\(355\) | − | 34.8176i | − | 1.84793i | ||||||
\(356\) | 1.45527 | − | 0.840199i | 0.0771290 | − | 0.0445305i | ||||
\(357\) | 56.5906i | 2.99509i | ||||||||
\(358\) | −0.0339889 | − | 0.0588704i | −0.00179637 | − | 0.00311140i | ||||
\(359\) | 37.6526i | 1.98723i | 0.112826 | + | 0.993615i | \(0.464010\pi\) | ||||
−0.112826 | + | 0.993615i | \(0.535990\pi\) | |||||||
\(360\) | 5.31824i | 0.280296i | ||||||||
\(361\) | −3.61409 | − | 6.25980i | −0.190216 | − | 0.329463i | ||||
\(362\) | 0.163644 | − | 0.0944796i | 0.00860091 | − | 0.00496574i | ||||
\(363\) | 18.8380 | − | 32.6284i | 0.988740 | − | 1.71255i | ||||
\(364\) | −7.68765 | − | 13.3154i | −0.402942 | − | 0.697917i | ||||
\(365\) | −8.03570 | − | 13.9182i | −0.420608 | − | 0.728514i | ||||
\(366\) | −0.703484 | −0.0367717 | ||||||||
\(367\) | 9.90695 | + | 5.71978i | 0.517138 | + | 0.298570i | 0.735763 | − | 0.677239i | \(-0.236824\pi\) |
−0.218625 | + | 0.975809i | \(0.570157\pi\) | |||||||
\(368\) | 8.76054 | − | 15.1737i | 0.456675 | − | 0.790984i | ||||
\(369\) | −33.7606 | − | 58.4751i | −1.75751 | − | 3.04409i | ||||
\(370\) | − | 0.205903i | − | 0.0107044i | ||||||
\(371\) | −10.1813 | − | 17.6345i | −0.528586 | − | 0.915537i | ||||
\(372\) | 17.7983 | + | 30.8275i | 0.922797 | + | 1.59833i | ||||
\(373\) | −1.76180 | − | 1.01718i | −0.0912227 | − | 0.0526675i | 0.453695 | − | 0.891157i | \(-0.350106\pi\) |
−0.544917 | + | 0.838490i | \(0.683439\pi\) | |||||||
\(374\) | −0.0170589 | − | 0.0295468i | −0.000882092 | − | 0.00152783i | ||||
\(375\) | −12.3976 | + | 21.4733i | −0.640210 | + | 1.10888i | ||||
\(376\) | −0.425549 | −0.0219460 | ||||||||
\(377\) | − | 10.9250i | − | 0.562666i | ||||||
\(378\) | −1.39789 | + | 2.42121i | −0.0718995 | + | 0.124534i | ||||
\(379\) | −25.8662 | − | 14.9338i | −1.32866 | − | 0.767100i | −0.343564 | − | 0.939129i | \(-0.611634\pi\) |
−0.985092 | + | 0.172029i | \(0.944968\pi\) | |||||||
\(380\) | −35.5638 | −1.82439 | ||||||||
\(381\) | −21.0087 | − | 12.1294i | −1.07631 | − | 0.621408i | ||||
\(382\) | 0.551193 | + | 0.318231i | 0.0282015 | + | 0.0162821i | ||||
\(383\) | 1.70520 | − | 0.984500i | 0.0871319 | − | 0.0503056i | −0.455801 | − | 0.890082i | \(-0.650647\pi\) |
0.542933 | + | 0.839776i | \(0.317314\pi\) | |||||||
\(384\) | 4.77586i | 0.243717i | ||||||||
\(385\) | −1.72403 | −0.0878646 | ||||||||
\(386\) | 0.0734566 | 0.00373884 | ||||||||
\(387\) | − | 13.1556i | − | 0.668738i | ||||||
\(388\) | − | 31.2089i | − | 1.58439i | ||||||
\(389\) | −2.76192 | − | 1.59459i | −0.140035 | − | 0.0808491i | 0.428346 | − | 0.903615i | \(-0.359097\pi\) |
−0.568381 | + | 0.822766i | \(0.692430\pi\) | |||||||
\(390\) | 1.23775 | 0.0626759 | ||||||||
\(391\) | 11.2031 | + | 19.4043i | 0.566563 | + | 0.981316i | ||||
\(392\) | −0.520310 | − | 0.300401i | −0.0262796 | − | 0.0151726i | ||||
\(393\) | 64.1081 | + | 37.0128i | 3.23383 | + | 1.86705i | ||||
\(394\) | 0.984730 | 0.0496100 | ||||||||
\(395\) | 27.4576 | + | 15.8527i | 1.38154 | + | 0.797634i | ||||
\(396\) | 2.69289i | 0.135323i | ||||||||
\(397\) | 11.8828 | 0.596383 | 0.298192 | − | 0.954506i | \(-0.403617\pi\) | ||||
0.298192 | + | 0.954506i | \(0.403617\pi\) | |||||||
\(398\) | 0.363476 | − | 0.629559i | 0.0182194 | − | 0.0315569i | ||||
\(399\) | −49.2076 | − | 28.4100i | −2.46346 | − | 1.42228i | ||||
\(400\) | −14.1167 | + | 24.4509i | −0.705837 | + | 1.22255i | ||||
\(401\) | 6.23113i | 0.311168i | 0.987823 | + | 0.155584i | \(0.0497259\pi\) | ||||
−0.987823 | + | 0.155584i | \(0.950274\pi\) | |||||||
\(402\) | 0.895857i | 0.0446813i | ||||||||
\(403\) | 10.7006 | − | 6.17802i | 0.533037 | − | 0.307749i | ||||
\(404\) | 15.2833 | + | 8.82380i | 0.760371 | + | 0.439001i | ||||
\(405\) | 72.5894 | + | 125.729i | 3.60700 | + | 6.24750i | ||||
\(406\) | −0.323252 | − | 0.559889i | −0.0160427 | − | 0.0277868i | ||||
\(407\) | − | 0.208617i | − | 0.0103408i | ||||||
\(408\) | −2.64207 | − | 1.52540i | −0.130802 | − | 0.0755185i | ||||
\(409\) | 17.8181 | 0.881050 | 0.440525 | − | 0.897740i | \(-0.354792\pi\) | ||||
0.440525 | + | 0.897740i | \(0.354792\pi\) | |||||||
\(410\) | 1.16466i | 0.0575184i | ||||||||
\(411\) | −46.3044 | + | 26.7338i | −2.28403 | + | 1.31868i | ||||
\(412\) | −24.0945 | − | 13.9109i | −1.18705 | − | 0.685343i | ||||
\(413\) | 29.2945 | 1.44149 | ||||||||
\(414\) | 1.68131i | 0.0826318i | ||||||||
\(415\) | 18.6986 | 0.917878 | ||||||||
\(416\) | 1.24352 | 0.0609686 | ||||||||
\(417\) | 6.08383 | − | 10.5375i | 0.297926 | − | 0.516024i | ||||
\(418\) | 0.0342560 | 0.00167552 | ||||||||
\(419\) | −8.27828 | − | 14.3384i | −0.404420 | − | 0.700477i | 0.589833 | − | 0.807525i | \(-0.299193\pi\) |
−0.994254 | + | 0.107048i | \(0.965860\pi\) | |||||||
\(420\) | −66.7225 | + | 38.5223i | −3.25573 | + | 1.87969i | ||||
\(421\) | 19.1881 | − | 11.0783i | 0.935173 | − | 0.539923i | 0.0467292 | − | 0.998908i | \(-0.485120\pi\) |
0.888444 | + | 0.458985i | \(0.151787\pi\) | |||||||
\(422\) | 0.512033 | − | 0.886867i | 0.0249254 | − | 0.0431720i | ||||
\(423\) | −18.5727 | + | 10.7230i | −0.903036 | + | 0.521368i | ||||
\(424\) | 1.09775 | 0.0533112 | ||||||||
\(425\) | −18.0526 | − | 31.2680i | −0.875680 | − | 1.51672i | ||||
\(426\) | 0.749367 | + | 1.29794i | 0.0363070 | + | 0.0628855i | ||||
\(427\) | −7.59984 | − | 13.1633i | −0.367782 | − | 0.637017i | ||||
\(428\) | − | 17.4626i | − | 0.844087i | ||||||
\(429\) | 1.25407 | 0.0605469 | ||||||||
\(430\) | −0.113459 | + | 0.196517i | −0.00547149 | + | 0.00947690i | ||||
\(431\) | 17.7796 | − | 10.2651i | 0.856414 | − | 0.494451i | −0.00639581 | − | 0.999980i | \(-0.502036\pi\) |
0.862810 | + | 0.505529i | \(0.168703\pi\) | |||||||
\(432\) | 39.5776 | + | 68.5505i | 1.90418 | + | 3.29814i | ||||
\(433\) | 9.52497 | + | 5.49925i | 0.457741 | + | 0.264277i | 0.711094 | − | 0.703097i | \(-0.248200\pi\) |
−0.253353 | + | 0.967374i | \(0.581533\pi\) | |||||||
\(434\) | 0.365594 | − | 0.633228i | 0.0175491 | − | 0.0303959i | ||||
\(435\) | −54.7444 | −2.62479 | ||||||||
\(436\) | −5.12746 | − | 8.88102i | −0.245561 | − | 0.425324i | ||||
\(437\) | −22.4970 | −1.07618 | ||||||||
\(438\) | 0.599115 | + | 0.345899i | 0.0286268 | + | 0.0165277i | ||||
\(439\) | −0.460783 | + | 0.266033i | −0.0219920 | + | 0.0126971i | −0.510956 | − | 0.859607i | \(-0.670708\pi\) |
0.488964 | + | 0.872304i | \(0.337375\pi\) | |||||||
\(440\) | 0.0464712 | − | 0.0804904i | 0.00221543 | − | 0.00383723i | ||||
\(441\) | −30.2780 | −1.44181 | ||||||||
\(442\) | −0.264618 | + | 0.458331i | −0.0125866 | + | 0.0218006i | ||||
\(443\) | −1.01879 | − | 1.76459i | −0.0484041 | − | 0.0838383i | 0.840808 | − | 0.541333i | \(-0.182080\pi\) |
−0.889212 | + | 0.457495i | \(0.848747\pi\) | |||||||
\(444\) | −4.66142 | − | 8.07381i | −0.221221 | − | 0.383166i | ||||
\(445\) | −2.53124 | + | 1.46141i | −0.119992 | + | 0.0692775i | ||||
\(446\) | 0.462914 | − | 0.267263i | 0.0219196 | − | 0.0126553i | ||||
\(447\) | 14.1192i | 0.667816i | ||||||||
\(448\) | −22.2666 | + | 12.8556i | −1.05200 | + | 0.607372i | ||||
\(449\) | −7.90622 | −0.373117 | −0.186559 | − | 0.982444i | \(-0.559733\pi\) | ||||
−0.186559 | + | 0.982444i | \(0.559733\pi\) | |||||||
\(450\) | − | 2.70926i | − | 0.127716i | ||||||
\(451\) | 1.18001i | 0.0555646i | ||||||||
\(452\) | − | 16.0404i | − | 0.754475i | ||||||
\(453\) | −35.5877 | − | 61.6396i | −1.67205 | − | 2.89608i | ||||
\(454\) | 0.193814 | + | 0.111899i | 0.00909615 | + | 0.00525167i | ||||
\(455\) | 13.3716 | + | 23.1603i | 0.626870 | + | 1.08577i | ||||
\(456\) | 2.65278 | − | 1.53158i | 0.124228 | − | 0.0717230i | ||||
\(457\) | −6.59094 | + | 11.4158i | −0.308311 | + | 0.534011i | −0.977993 | − | 0.208637i | \(-0.933097\pi\) |
0.669682 | + | 0.742648i | \(0.266430\pi\) | |||||||
\(458\) | 0.242523 | − | 0.420063i | 0.0113324 | − | 0.0196282i | ||||
\(459\) | −101.225 | −4.72476 | ||||||||
\(460\) | −15.2523 | + | 26.4177i | −0.711140 | + | 1.23173i | ||||
\(461\) | 15.8446 | + | 9.14790i | 0.737958 | + | 0.426060i | 0.821326 | − | 0.570459i | \(-0.193235\pi\) |
−0.0833684 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(462\) | 0.0642689 | − | 0.0371057i | 0.00299006 | − | 0.00172631i | ||||
\(463\) | 27.0568 | + | 15.6213i | 1.25744 | + | 0.725982i | 0.972576 | − | 0.232586i | \(-0.0747187\pi\) |
0.284863 | + | 0.958568i | \(0.408052\pi\) | |||||||
\(464\) | −18.3042 | −0.849750 | ||||||||
\(465\) | −30.9576 | − | 53.6201i | −1.43562 | − | 2.48657i | ||||
\(466\) | −0.645097 | − | 0.372447i | −0.0298835 | − | 0.0172533i | ||||
\(467\) | 36.2994 | 1.67973 | 0.839867 | − | 0.542792i | \(-0.182633\pi\) | ||||
0.839867 | + | 0.542792i | \(0.182633\pi\) | |||||||
\(468\) | 36.1759 | − | 20.8861i | 1.67223 | − | 0.965462i | ||||
\(469\) | −16.7629 | + | 9.67807i | −0.774040 | + | 0.446892i | ||||
\(470\) | 0.369915 | 0.0170629 | ||||||||
\(471\) | −33.4972 | − | 58.0188i | −1.54347 | − | 2.67337i | ||||
\(472\) | −0.789634 | + | 1.36769i | −0.0363458 | + | 0.0629529i | ||||
\(473\) | −0.114955 | + | 0.199108i | −0.00528563 | + | 0.00915498i | ||||
\(474\) | −1.36477 | −0.0626858 | ||||||||
\(475\) | 36.2516 | 1.66334 | ||||||||
\(476\) | − | 32.9426i | − | 1.50992i | ||||||
\(477\) | 47.9102 | − | 27.6609i | 2.19366 | − | 1.26651i | ||||
\(478\) | −0.0193956 | + | 0.0111981i | −0.000887135 | + | 0.000512188i | ||||
\(479\) | 7.67071 | + | 13.2861i | 0.350484 | + | 0.607056i | 0.986334 | − | 0.164756i | \(-0.0526838\pi\) |
−0.635850 | + | 0.771812i | \(0.719350\pi\) | |||||||
\(480\) | − | 6.23119i | − | 0.284414i | ||||||
\(481\) | −2.80253 | + | 1.61804i | −0.127784 | + | 0.0737764i | ||||
\(482\) | 0.148606i | 0.00676880i | ||||||||
\(483\) | −42.2073 | + | 24.3684i | −1.92050 | + | 1.10880i | ||||
\(484\) | −10.9660 | + | 18.9937i | −0.498456 | + | 0.863350i | ||||
\(485\) | 54.2836i | 2.46489i | ||||||||
\(486\) | −3.16483 | − | 1.82722i | −0.143560 | − | 0.0828843i | ||||
\(487\) | 1.13023 | − | 0.652541i | 0.0512158 | − | 0.0295695i | −0.474173 | − | 0.880431i | \(-0.657253\pi\) |
0.525389 | + | 0.850862i | \(0.323920\pi\) | |||||||
\(488\) | 0.819415 | 0.0370932 | ||||||||
\(489\) | −26.2554 | − | 15.1586i | −1.18731 | − | 0.685495i | ||||
\(490\) | 0.452289 | + | 0.261129i | 0.0204323 | + | 0.0117966i | ||||
\(491\) | −3.83732 | + | 6.64643i | −0.173176 | + | 0.299949i | −0.939528 | − | 0.342471i | \(-0.888736\pi\) |
0.766353 | + | 0.642420i | \(0.222070\pi\) | |||||||
\(492\) | 26.3666 | + | 45.6682i | 1.18870 | + | 2.05888i | ||||
\(493\) | 11.7038 | − | 20.2715i | 0.527111 | − | 0.912983i | ||||
\(494\) | −0.265691 | − | 0.460190i | −0.0119540 | − | 0.0207049i | ||||
\(495\) | − | 4.68391i | − | 0.210526i | ||||||
\(496\) | −10.3509 | − | 17.9283i | −0.464769 | − | 0.805003i | ||||
\(497\) | −16.1911 | + | 28.0437i | −0.726268 | + | 1.25793i | ||||
\(498\) | −0.697053 | + | 0.402444i | −0.0312357 | + | 0.0180339i | ||||
\(499\) | 37.6940 | − | 21.7626i | 1.68742 | − | 0.974230i | 0.730929 | − | 0.682454i | \(-0.239087\pi\) |
0.956487 | − | 0.291776i | \(-0.0942462\pi\) | |||||||
\(500\) | 7.21691 | − | 12.5001i | 0.322750 | − | 0.559019i | ||||
\(501\) | −9.68747 | − | 5.59306i | −0.432804 | − | 0.249880i | ||||
\(502\) | −0.308972 | − | 0.535156i | −0.0137901 | − | 0.0238852i | ||||
\(503\) | −37.4705 | − | 21.6336i | −1.67073 | − | 0.964596i | −0.967231 | − | 0.253899i | \(-0.918287\pi\) |
−0.703498 | − | 0.710697i | \(-0.748380\pi\) | |||||||
\(504\) | 2.47312 | − | 4.28356i | 0.110161 | − | 0.190805i | ||||
\(505\) | −26.5831 | − | 15.3478i | −1.18293 | − | 0.682967i | ||||
\(506\) | 0.0146914 | − | 0.0254462i | 0.000653112 | − | 0.00113122i | ||||
\(507\) | 12.5843 | + | 21.7967i | 0.558890 | + | 0.968027i | ||||
\(508\) | 12.2296 | + | 7.06078i | 0.542602 | + | 0.313272i | ||||
\(509\) | 18.2933 | − | 10.5617i | 0.810838 | − | 0.468138i | −0.0364086 | − | 0.999337i | \(-0.511592\pi\) |
0.847247 | + | 0.531199i | \(0.178258\pi\) | |||||||
\(510\) | 2.29666 | + | 1.32598i | 0.101698 | + | 0.0587154i | ||||
\(511\) | 14.9472i | 0.661226i | ||||||||
\(512\) | − | 3.47350i | − | 0.153509i | ||||||
\(513\) | 50.8175 | − | 88.0184i | 2.24365 | − | 3.88611i | ||||
\(514\) | −0.0439938 | + | 0.0253998i | −0.00194048 | + | 0.00112034i | ||||
\(515\) | 41.9090 | + | 24.1961i | 1.84673 | + | 1.06621i | ||||
\(516\) | 10.2744i | 0.452303i | ||||||||
\(517\) | 0.374792 | 0.0164833 | ||||||||
\(518\) | −0.0957502 | + | 0.165844i | −0.00420702 | + | 0.00728678i | ||||
\(519\) | 20.9806i | 0.920944i | ||||||||
\(520\) | −1.44173 | −0.0632239 | ||||||||
\(521\) | 12.9141 | − | 7.45598i | 0.565778 | − | 0.326652i | −0.189683 | − | 0.981845i | \(-0.560746\pi\) |
0.755461 | + | 0.655193i | \(0.227413\pi\) | |||||||
\(522\) | 1.52113 | − | 0.878226i | 0.0665781 | − | 0.0384389i | ||||
\(523\) | −24.8498 | − | 14.3471i | −1.08661 | − | 0.627353i | −0.153936 | − | 0.988081i | \(-0.549195\pi\) |
−0.932671 | + | 0.360728i | \(0.882528\pi\) | |||||||
\(524\) | −37.3187 | − | 21.5460i | −1.63028 | − | 0.941240i | ||||
\(525\) | 68.0129 | − | 39.2673i | 2.96833 | − | 1.71376i | ||||
\(526\) | −0.521070 | + | 0.300840i | −0.0227197 | + | 0.0131172i | ||||
\(527\) | 26.4736 | 1.15321 | ||||||||
\(528\) | − | 2.10111i | − | 0.0914390i | ||||||
\(529\) | 1.85172 | − | 3.20728i | 0.0805097 | − | 0.139447i | ||||
\(530\) | −0.954234 | −0.0414493 | ||||||||
\(531\) | 79.5886i | 3.45385i | ||||||||
\(532\) | 28.6448 | + | 16.5381i | 1.24191 | + | 0.717017i | ||||
\(533\) | 15.8521 | − | 9.15219i | 0.686629 | − | 0.396425i | ||||
\(534\) | 0.0629069 | − | 0.108958i | 0.00272225 | − | 0.00471507i | ||||
\(535\) | 30.3738i | 1.31317i | ||||||||
\(536\) | − | 1.04349i | − | 0.0450719i | ||||||
\(537\) | 4.63630 | + | 2.67677i | 0.200071 | + | 0.115511i | ||||
\(538\) | −0.635066 | + | 0.366655i | −0.0273796 | + | 0.0158076i | ||||
\(539\) | 0.458251 | + | 0.264571i | 0.0197383 | + | 0.0113959i | ||||
\(540\) | −68.9054 | − | 119.348i | −2.96522 | − | 5.13590i | ||||
\(541\) | 12.8923 | − | 22.3300i | 0.554282 | − | 0.960044i | −0.443677 | − | 0.896187i | \(-0.646326\pi\) |
0.997959 | − | 0.0638573i | \(-0.0203402\pi\) | |||||||
\(542\) | 0.547205 | + | 0.315929i | 0.0235045 | + | 0.0135703i | ||||
\(543\) | −7.44068 | + | 12.8876i | −0.319310 | + | 0.553062i | ||||
\(544\) | 2.30737 | + | 1.33216i | 0.0989278 | + | 0.0571160i | ||||
\(545\) | 8.91851 | + | 15.4473i | 0.382027 | + | 0.661690i | ||||
\(546\) | −0.996942 | − | 0.575585i | −0.0426652 | − | 0.0246328i | ||||
\(547\) | −2.18920 | + | 3.79181i | −0.0936035 | + | 0.162126i | −0.909025 | − | 0.416742i | \(-0.863172\pi\) |
0.815421 | + | 0.578868i | \(0.196505\pi\) | |||||||
\(548\) | 26.9548 | − | 15.5623i | 1.15145 | − | 0.664790i | ||||
\(549\) | 35.7627 | − | 20.6476i | 1.52631 | − | 0.881217i | ||||
\(550\) | −0.0236737 | + | 0.0410041i | −0.00100945 | + | 0.00174842i | ||||
\(551\) | 11.7512 | + | 20.3537i | 0.500619 | + | 0.867097i | ||||
\(552\) | − | 2.62740i | − | 0.111830i | ||||||
\(553\) | −14.7438 | − | 25.5370i | −0.626969 | − | 1.08594i | ||||
\(554\) | −0.418361 | + | 0.724623i | −0.0177745 | + | 0.0307863i | ||||
\(555\) | 8.10789 | + | 14.0433i | 0.344161 | + | 0.596104i | ||||
\(556\) | −3.54153 | + | 6.13410i | −0.150194 | + | 0.260144i | ||||
\(557\) | −2.49880 | − | 1.44268i | −0.105878 | − | 0.0611285i | 0.446126 | − | 0.894970i | \(-0.352803\pi\) |
−0.552004 | + | 0.833842i | \(0.686137\pi\) | |||||||
\(558\) | 1.72038 | + | 0.993262i | 0.0728295 | + | 0.0420481i | ||||
\(559\) | 3.56637 | 0.150841 | ||||||||
\(560\) | 38.8036 | − | 22.4033i | 1.63975 | − | 0.946712i | ||||
\(561\) | 2.32694 | + | 1.34346i | 0.0982434 | + | 0.0567209i | ||||
\(562\) | − | 0.788277i | − | 0.0332515i | ||||||
\(563\) | 0.704029 | − | 1.21941i | 0.0296713 | − | 0.0513922i | −0.850808 | − | 0.525476i | \(-0.823887\pi\) |
0.880480 | + | 0.474084i | \(0.157221\pi\) | |||||||
\(564\) | 14.5050 | − | 8.37447i | 0.610771 | − | 0.352629i | ||||
\(565\) | 27.9000i | 1.17376i | ||||||||
\(566\) | 0.750496 | − | 0.433299i | 0.0315457 | − | 0.0182129i | ||||
\(567\) | − | 135.024i | − | 5.67046i | ||||||
\(568\) | −0.872860 | − | 1.51184i | −0.0366244 | − | 0.0634353i | ||||
\(569\) | 18.2195 | − | 10.5190i | 0.763801 | − | 0.440981i | −0.0668580 | − | 0.997763i | \(-0.521297\pi\) |
0.830659 | + | 0.556782i | \(0.187964\pi\) | |||||||
\(570\) | −2.30598 | + | 1.33136i | −0.0965867 | + | 0.0557644i | ||||
\(571\) | 16.2009i | 0.677986i | 0.940789 | + | 0.338993i | \(0.110086\pi\) | ||||
−0.940789 | + | 0.338993i | \(0.889914\pi\) | |||||||
\(572\) | −0.730018 | −0.0305236 | ||||||||
\(573\) | −50.1242 | −2.09397 | ||||||||
\(574\) | 0.541596 | − | 0.938071i | 0.0226058 | − | 0.0391543i | ||||
\(575\) | 15.5472 | − | 26.9286i | 0.648364 | − | 1.12300i | ||||
\(576\) | −34.9267 | − | 60.4949i | −1.45528 | − | 2.52062i | ||||
\(577\) | −6.87072 | −0.286032 | −0.143016 | − | 0.989720i | \(-0.545680\pi\) | ||||
−0.143016 | + | 0.989720i | \(0.545680\pi\) | |||||||
\(578\) | −0.340339 | + | 0.196495i | −0.0141562 | + | 0.00817311i | ||||
\(579\) | −5.00998 | + | 2.89251i | −0.208208 | + | 0.120209i | ||||
\(580\) | 31.8679 | 1.32324 | ||||||||
\(581\) | −15.0607 | − | 8.69532i | −0.624825 | − | 0.360743i | ||||
\(582\) | −1.16833 | − | 2.02360i | −0.0484287 | − | 0.0838810i | ||||
\(583\) | −0.966813 | −0.0400413 | ||||||||
\(584\) | −0.697847 | − | 0.402902i | −0.0288771 | − | 0.0166722i | ||||
\(585\) | −62.9229 | + | 36.3285i | −2.60154 | + | 1.50200i | ||||
\(586\) | 0.343437 | + | 0.198283i | 0.0141872 | + | 0.00819100i | ||||
\(587\) | −9.02221 | + | 15.6269i | −0.372386 | + | 0.644992i | −0.989932 | − | 0.141543i | \(-0.954794\pi\) |
0.617546 | + | 0.786535i | \(0.288127\pi\) | |||||||
\(588\) | 23.6467 | 0.975172 | ||||||||
\(589\) | −13.2905 | + | 23.0198i | −0.547625 | + | 0.948514i | ||||
\(590\) | 0.686403 | − | 1.18888i | 0.0282588 | − | 0.0489456i | ||||
\(591\) | −67.1618 | + | 38.7759i | −2.76267 | + | 1.59503i | ||||
\(592\) | 2.71093 | + | 4.69547i | 0.111418 | + | 0.192982i | ||||
\(593\) | −16.4537 | − | 9.49956i | −0.675674 | − | 0.390100i | 0.122549 | − | 0.992462i | \(-0.460893\pi\) |
−0.798223 | + | 0.602362i | \(0.794226\pi\) | |||||||
\(594\) | 0.0663715 | + | 0.114959i | 0.00272326 | + | 0.00471682i | ||||
\(595\) | 57.2991i | 2.34903i | ||||||||
\(596\) | − | 8.21910i | − | 0.336667i | ||||||
\(597\) | 57.2507i | 2.34311i | ||||||||
\(598\) | −0.455787 | −0.0186385 | ||||||||
\(599\) | 10.2888 | − | 5.94021i | 0.420387 | − | 0.242711i | −0.274856 | − | 0.961485i | \(-0.588630\pi\) |
0.695243 | + | 0.718775i | \(0.255297\pi\) | |||||||
\(600\) | 4.23380i | 0.172844i | ||||||||
\(601\) | 38.1423 | − | 22.0215i | 1.55586 | − | 0.898274i | 0.558211 | − | 0.829699i | \(-0.311488\pi\) |
0.997646 | − | 0.0685752i | \(-0.0218453\pi\) | |||||||
\(602\) | 0.182771 | − | 0.105523i | 0.00744918 | − | 0.00430079i | ||||
\(603\) | −26.2938 | − | 45.5422i | −1.07077 | − | 1.85462i | ||||
\(604\) | 20.7163 | + | 35.8817i | 0.842936 | + | 1.46001i | ||||
\(605\) | 19.0739 | − | 33.0369i | 0.775463 | − | 1.34314i | ||||
\(606\) | 1.32130 | 0.0536742 | ||||||||
\(607\) | −0.350397 | + | 0.606905i | −0.0142222 | + | 0.0246335i | −0.873049 | − | 0.487633i | \(-0.837861\pi\) |
0.858827 | + | 0.512266i | \(0.171194\pi\) | |||||||
\(608\) | −2.31673 | + | 1.33756i | −0.0939557 | + | 0.0542454i | ||||
\(609\) | 44.0937 | + | 25.4575i | 1.78677 | + | 1.03159i | ||||
\(610\) | −0.712291 | −0.0288398 | ||||||||
\(611\) | −2.90689 | − | 5.03488i | −0.117600 | − | 0.203690i | ||||
\(612\) | 89.4999 | 3.61782 | ||||||||
\(613\) | 15.2102 | − | 26.3449i | 0.614336 | − | 1.06406i | −0.376165 | − | 0.926553i | \(-0.622757\pi\) |
0.990501 | − | 0.137508i | \(-0.0439092\pi\) | |||||||
\(614\) | 0.570842 | + | 0.329576i | 0.0230373 | + | 0.0133006i | ||||
\(615\) | −45.8610 | − | 79.4336i | −1.84929 | − | 3.20307i | ||||
\(616\) | −0.0748602 | + | 0.0432205i | −0.00301620 | + | 0.00174141i | ||||
\(617\) | −12.6704 | + | 21.9458i | −0.510092 | + | 0.883506i | 0.489839 | + | 0.871813i | \(0.337055\pi\) |
−0.999932 | + | 0.0116932i | \(0.996278\pi\) | |||||||
\(618\) | −2.08306 | −0.0837930 | ||||||||
\(619\) | 33.7826i | 1.35784i | 0.734214 | + | 0.678918i | \(0.237551\pi\) | ||||
−0.734214 | + | 0.678918i | \(0.762449\pi\) | |||||||
\(620\) | 18.0211 | + | 31.2134i | 0.723744 | + | 1.25356i | ||||
\(621\) | −43.5882 | − | 75.4969i | −1.74913 | − | 3.02959i | ||||
\(622\) | 0.100860 | + | 0.174695i | 0.00404412 | + | 0.00700462i | ||||
\(623\) | 2.71837 | 0.108909 | ||||||||
\(624\) | −28.2259 | + | 16.2963i | −1.12994 | + | 0.652372i | ||||
\(625\) | 5.14352 | − | 8.90884i | 0.205741 | − | 0.356353i | ||||
\(626\) | 0.913767 | − | 0.527564i | 0.0365215 | − | 0.0210857i | ||||
\(627\) | −2.33637 | + | 1.34891i | −0.0933058 | + | 0.0538701i | ||||
\(628\) | 19.4994 | + | 33.7740i | 0.778112 | + | 1.34773i | ||||
\(629\) | −6.93352 | −0.276458 | ||||||||
\(630\) | −2.14980 | + | 3.72356i | −0.0856501 | + | 0.148350i | ||||
\(631\) | −22.4495 | −0.893701 | −0.446851 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446851 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(632\) | 1.58967 | 0.0632338 | ||||||||
\(633\) | 80.6497i | 3.20554i | ||||||||
\(634\) | −0.126460 | −0.00502238 | ||||||||
\(635\) | −21.2718 | − | 12.2813i | −0.844144 | − | 0.487367i | ||||
\(636\) | −37.4171 | + | 21.6028i | −1.48369 | + | 0.856606i | ||||
\(637\) | − | 8.20808i | − | 0.325216i | ||||||
\(638\) | −0.0306960 | −0.00121527 | ||||||||
\(639\) | −76.1904 | − | 43.9886i | −3.01405 | − | 1.74016i | ||||
\(640\) | 4.83565i | 0.191146i | ||||||||
\(641\) | 15.2130 | + | 26.3497i | 0.600878 | + | 1.04075i | 0.992688 | + | 0.120705i | \(0.0385156\pi\) |
−0.391810 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(642\) | −0.653725 | − | 1.13228i | −0.0258005 | − | 0.0446877i | ||||
\(643\) | −6.05668 | − | 3.49683i | −0.238852 | − | 0.137901i | 0.375797 | − | 0.926702i | \(-0.377369\pi\) |
−0.614649 | + | 0.788801i | \(0.710702\pi\) | |||||||
\(644\) | 24.5698 | − | 14.1854i | 0.968185 | − | 0.558982i | ||||
\(645\) | − | 17.8708i | − | 0.703663i | ||||||
\(646\) | − | 1.13852i | − | 0.0447944i | ||||||
\(647\) | 0.325177 | − | 0.563224i | 0.0127840 | − | 0.0221426i | −0.859563 | − | 0.511030i | \(-0.829264\pi\) |
0.872347 | + | 0.488888i | \(0.162597\pi\) | |||||||
\(648\) | 6.30390 | + | 3.63956i | 0.247641 | + | 0.142975i | ||||
\(649\) | 0.695451 | − | 1.20456i | 0.0272988 | − | 0.0472830i | ||||
\(650\) | 0.734455 | 0.0288077 | ||||||||
\(651\) | 57.5843i | 2.25691i | ||||||||
\(652\) | 15.2839 | + | 8.82414i | 0.598562 | + | 0.345580i | ||||
\(653\) | −8.60111 | −0.336587 | −0.168294 | − | 0.985737i | \(-0.553826\pi\) | ||||
−0.168294 | + | 0.985737i | \(0.553826\pi\) | |||||||
\(654\) | −0.664934 | − | 0.383900i | −0.0260010 | − | 0.0150117i | ||||
\(655\) | 64.9107 | + | 37.4762i | 2.53627 | + | 1.46432i | ||||
\(656\) | −15.3339 | − | 26.5592i | −0.598690 | − | 1.03696i | ||||
\(657\) | −40.6092 | −1.58432 | ||||||||
\(658\) | −0.297947 | − | 0.172020i | −0.0116152 | − | 0.00670604i | ||||
\(659\) | − | 1.04842i | − | 0.0408406i | −0.999791 | − | 0.0204203i | \(-0.993500\pi\) | ||
0.999791 | − | 0.0204203i | \(-0.00650043\pi\) | |||||||
\(660\) | 3.65807i | 0.142390i | ||||||||
\(661\) | −6.85802 | −0.266746 | −0.133373 | − | 0.991066i | \(-0.542581\pi\) | ||||
−0.133373 | + | 0.991066i | \(0.542581\pi\) | |||||||
\(662\) | 0.397015 | 0.0154304 | ||||||||
\(663\) | − | 41.6796i | − | 1.61870i | ||||||
\(664\) | 0.811925 | − | 0.468765i | 0.0315088 | − | 0.0181916i | ||||
\(665\) | −49.8236 | − | 28.7657i | −1.93208 | − | 1.11549i | ||||
\(666\) | −0.450573 | − | 0.260138i | −0.0174593 | − | 0.0100802i | ||||
\(667\) | 20.1590 | 0.780559 | ||||||||
\(668\) | 5.63928 | + | 3.25584i | 0.218190 | + | 0.125972i | ||||
\(669\) | −21.0482 | + | 36.4565i | −0.813769 | + | 1.40949i | ||||
\(670\) | 0.907072i | 0.0350432i | ||||||||
\(671\) | −0.721680 | −0.0278602 | ||||||||
\(672\) | −2.89766 | + | 5.01890i | −0.111780 | + | 0.193608i | ||||
\(673\) | 1.38508 | + | 2.39903i | 0.0533910 | + | 0.0924759i | 0.891486 | − | 0.453049i | \(-0.149664\pi\) |
−0.838095 | + | 0.545525i | \(0.816330\pi\) | |||||||
\(674\) | −0.489091 | − | 0.282377i | −0.0188391 | − | 0.0108767i | ||||
\(675\) | 70.2380 | + | 121.656i | 2.70346 | + | 4.68253i | ||||
\(676\) | −7.32562 | − | 12.6883i | −0.281754 | − | 0.488013i | ||||
\(677\) | 31.0863i | 1.19474i | 0.801965 | + | 0.597371i | \(0.203788\pi\) | ||||
−0.801965 | + | 0.597371i | \(0.796212\pi\) | |||||||
\(678\) | −0.600482 | − | 1.04006i | −0.0230614 | − | 0.0399434i | ||||
\(679\) | 25.2432 | − | 43.7226i | 0.968746 | − | 1.67792i | ||||
\(680\) | −2.67515 | − | 1.54450i | −0.102587 | − | 0.0592287i | ||||
\(681\) | −17.6250 | −0.675392 | ||||||||
\(682\) | −0.0173584 | − | 0.0300656i | −0.000664687 | − | 0.00115127i | ||||
\(683\) | −10.7592 | − | 18.6355i | −0.411691 | − | 0.713069i | 0.583384 | − | 0.812196i | \(-0.301728\pi\) |
−0.995075 | + | 0.0991272i | \(0.968395\pi\) | |||||||
\(684\) | −44.9314 | + | 77.8234i | −1.71799 | + | 2.97565i | ||||
\(685\) | −46.8841 | + | 27.0685i | −1.79135 | + | 1.03423i | ||||
\(686\) | 0.250209 | + | 0.433375i | 0.00955304 | + | 0.0165463i | ||||
\(687\) | 38.1995i | 1.45740i | ||||||||
\(688\) | − | 5.97523i | − | 0.227804i | ||||||
\(689\) | 7.49862 | + | 12.9880i | 0.285675 | + | 0.494803i | ||||
\(690\) | 2.28392i | 0.0869472i | ||||||||
\(691\) | −12.7097 | + | 7.33796i | −0.483501 | + | 0.279149i | −0.721874 | − | 0.692024i | \(-0.756719\pi\) |
0.238374 | + | 0.971174i | \(0.423386\pi\) | |||||||
\(692\) | − | 12.2132i | − | 0.464277i | ||||||
\(693\) | −2.17814 | + | 3.77265i | −0.0827406 | + | 0.143311i | ||||
\(694\) | −0.782325 | + | 1.35503i | −0.0296967 | + | 0.0514361i | ||||
\(695\) | 6.15999 | − | 10.6694i | 0.233662 | − | 0.404714i | ||||
\(696\) | −2.37709 | + | 1.37242i | −0.0901035 | + | 0.0520213i | ||||
\(697\) | 39.2183 | 1.48550 | ||||||||
\(698\) | −0.790777 | − | 0.193974i | −0.0299314 | − | 0.00734201i | ||||
\(699\) | 58.6636 | 2.21886 | ||||||||
\(700\) | −39.5918 | + | 22.8583i | −1.49643 | + | 0.863963i | ||||
\(701\) | −6.99985 | + | 12.1241i | −0.264381 | + | 0.457921i | −0.967401 | − | 0.253249i | \(-0.918501\pi\) |
0.703020 | + | 0.711170i | \(0.251834\pi\) | |||||||
\(702\) | 1.02956 | − | 1.78325i | 0.0388582 | − | 0.0673043i | ||||
\(703\) | 3.48082 | − | 6.02895i | 0.131281 | − | 0.227386i | ||||
\(704\) | 1.22077i | 0.0460095i | ||||||||
\(705\) | −25.2294 | + | 14.5662i | −0.950196 | + | 0.548596i | ||||
\(706\) | − | 1.06320i | − | 0.0400139i | ||||||
\(707\) | 14.2742 | + | 24.7237i | 0.536837 | + | 0.929829i | ||||
\(708\) | − | 62.1576i | − | 2.33602i | ||||||
\(709\) | − | 46.1829i | − | 1.73444i | −0.497929 | − | 0.867218i | \(-0.665906\pi\) | ||
0.497929 | − | 0.867218i | \(-0.334094\pi\) | |||||||
\(710\) | 0.758749 | + | 1.31419i | 0.0284753 | + | 0.0493207i | ||||
\(711\) | 69.3799 | − | 40.0565i | 2.60195 | − | 1.50224i | ||||
\(712\) | −0.0732737 | + | 0.126914i | −0.00274605 | + | 0.00475629i | ||||
\(713\) | 11.3998 | + | 19.7450i | 0.426925 | + | 0.739456i | ||||
\(714\) | −1.23323 | − | 2.13601i | −0.0461524 | − | 0.0799383i | ||||
\(715\) | 1.26977 | 0.0474865 | ||||||||
\(716\) | −2.69889 | − | 1.55821i | −0.100862 | − | 0.0582329i | ||||
\(717\) | 0.881897 | − | 1.52749i | 0.0329350 | − | 0.0570452i | ||||
\(718\) | −0.820530 | − | 1.42120i | −0.0306219 | − | 0.0530387i | ||||
\(719\) | − | 6.76173i | − | 0.252170i | −0.992019 | − | 0.126085i | \(-0.959759\pi\) | ||
0.992019 | − | 0.126085i | \(-0.0402412\pi\) | |||||||
\(720\) | 60.8662 | + | 105.423i | 2.26835 | + | 3.92890i | ||||
\(721\) | −22.5036 | − | 38.9774i | −0.838079 | − | 1.45160i | ||||
\(722\) | 0.272828 | + | 0.157517i | 0.0101536 | + | 0.00586219i | ||||
\(723\) | −5.85167 | − | 10.1354i | −0.217626 | − | 0.376939i | ||||
\(724\) | 4.33138 | − | 7.50217i | 0.160974 | − | 0.278816i | ||||
\(725\) | −32.4842 | −1.20643 | ||||||||
\(726\) | 1.64208i | 0.0609434i | ||||||||
\(727\) | −19.8092 | + | 34.3106i | −0.734684 | + | 1.27251i | 0.220178 | + | 0.975460i | \(0.429336\pi\) |
−0.954862 | + | 0.297050i | \(0.903997\pi\) | |||||||
\(728\) | 1.16123 | + | 0.670439i | 0.0430382 | + | 0.0248481i | ||||
\(729\) | 162.484 | 6.01791 | ||||||||
\(730\) | 0.606616 | + | 0.350230i | 0.0224518 | + | 0.0129626i | ||||
\(731\) | 6.61745 | + | 3.82059i | 0.244755 | + | 0.141310i | ||||
\(732\) | −27.9301 | + | 16.1255i | −1.03233 | + | 0.596014i | ||||
\(733\) | − | 28.2153i | − | 1.04215i | −0.853510 | − | 0.521077i | \(-0.825530\pi\) | ||
0.853510 | − | 0.521077i | \(-0.174470\pi\) | |||||||
\(734\) | −0.498584 | −0.0184031 | ||||||||
\(735\) | −41.1301 | −1.51711 | ||||||||
\(736\) | 2.29456i | 0.0845787i | ||||||||
\(737\) | 0.919029i | 0.0338529i | ||||||||
\(738\) | 2.54859 | + | 1.47143i | 0.0938150 | + | 0.0541641i | ||||
\(739\) | 10.3735 | 0.381594 | 0.190797 | − | 0.981629i | \(-0.438893\pi\) | ||||
0.190797 | + | 0.981629i | \(0.438893\pi\) | |||||||
\(740\) | −4.71978 | − | 8.17489i | −0.173502 | − | 0.300515i | ||||
\(741\) | 36.2419 | + | 20.9243i | 1.33138 | + | 0.768673i | ||||
\(742\) | 0.768585 | + | 0.443743i | 0.0282157 | + | 0.0162903i | ||||
\(743\) | 17.1978 | 0.630926 | 0.315463 | − | 0.948938i | \(-0.397840\pi\) | ||||
0.315463 | + | 0.948938i | \(0.397840\pi\) | |||||||
\(744\) | −2.68846 | − | 1.55218i | −0.0985638 | − | 0.0569058i | ||||
\(745\) | 14.2960i | 0.523764i | ||||||||
\(746\) | 0.0886658 | 0.00324629 | ||||||||
\(747\) | 23.6238 | − | 40.9177i | 0.864351 | − | 1.49710i | ||||
\(748\) | −1.35456 | − | 0.782056i | −0.0495276 | − | 0.0285948i | ||||
\(749\) | 14.1246 | − | 24.4645i | 0.516101 | − | 0.893913i | ||||
\(750\) | − | 1.08068i | − | 0.0394608i | ||||||
\(751\) | − | 20.9053i | − | 0.762846i | −0.924401 | − | 0.381423i | \(-0.875434\pi\) | ||
0.924401 | − | 0.381423i | \(-0.124566\pi\) | |||||||
\(752\) | −8.43564 | + | 4.87032i | −0.307616 | + | 0.177602i | ||||
\(753\) | 42.1459 | + | 24.3329i | 1.53588 | + | 0.886741i | ||||
\(754\) | 0.238079 | + | 0.412365i | 0.00867032 | + | 0.0150174i | ||||
\(755\) | −36.0332 | − | 62.4113i | −1.31138 | − | 2.27138i | ||||
\(756\) | 128.171i | 4.66153i | ||||||||
\(757\) | −18.7721 | − | 10.8381i | −0.682283 | − | 0.393916i | 0.118432 | − | 0.992962i | \(-0.462213\pi\) |
−0.800715 | + | 0.599046i | \(0.795547\pi\) | |||||||
\(758\) | 1.30176 | 0.0472820 | ||||||||
\(759\) | 2.31402i | 0.0839937i | ||||||||
\(760\) | 2.68599 | − | 1.55076i | 0.0974312 | − | 0.0562519i | ||||
\(761\) | 7.19378 | + | 4.15333i | 0.260774 | + | 0.150558i | 0.624688 | − | 0.780875i | \(-0.285226\pi\) |
−0.363913 | + | 0.931433i | \(0.618560\pi\) | |||||||
\(762\) | 1.05730 | 0.0383020 | ||||||||
\(763\) | − | 16.5893i | − | 0.600574i | ||||||
\(764\) | 29.1784 | 1.05564 | ||||||||
\(765\) | −155.673 | −5.62835 | ||||||||
\(766\) | −0.0429087 | + | 0.0743200i | −0.00155035 | + | 0.00268529i | ||||
\(767\) | −21.5757 | −0.779055 | ||||||||
\(768\) | 27.1991 | + | 47.1103i | 0.981464 | + | 1.69995i | ||||
\(769\) | −41.8215 | + | 24.1457i | −1.50812 | + | 0.870715i | −0.508167 | + | 0.861259i | \(0.669677\pi\) |
−0.999955 | + | 0.00945575i | \(0.996990\pi\) | |||||||
\(770\) | 0.0650735 | − | 0.0375702i | 0.00234509 | − | 0.00135394i | ||||
\(771\) | 2.00035 | − | 3.46470i | 0.0720407 | − | 0.124778i | ||||
\(772\) | 2.91642 | − | 1.68379i | 0.104964 | − | 0.0606010i | ||||
\(773\) | −32.0059 | −1.15117 | −0.575586 | − | 0.817741i | \(-0.695226\pi\) | ||||
−0.575586 | + | 0.817741i | \(0.695226\pi\) | |||||||
\(774\) | 0.286689 | + | 0.496560i | 0.0103048 | + | 0.0178485i | ||||
\(775\) | −18.3696 | − | 31.8171i | −0.659856 | − | 1.14290i | ||||
\(776\) | 1.36086 | + | 2.35708i | 0.0488521 | + | 0.0846144i | ||||
\(777\) | − | 15.0815i | − | 0.541046i | ||||||
\(778\) | 0.138998 | 0.00498333 | ||||||||
\(779\) | −19.6887 | + | 34.1018i | −0.705420 | + | 1.22182i | ||||
\(780\) | 49.1419 | − | 28.3721i | 1.75956 | − | 1.01588i | ||||
\(781\) | 0.768750 | + | 1.33151i | 0.0275081 | + | 0.0476453i | ||||
\(782\) | −0.845720 | − | 0.488277i | −0.0302429 | − | 0.0174607i | ||||
\(783\) | −45.5363 | + | 78.8712i | −1.62733 | + | 2.81863i | ||||
\(784\) | −13.7521 | −0.491148 | ||||||||
\(785\) | −33.9165 | − | 58.7452i | −1.21053 | − | 2.09671i | ||||
\(786\) | −3.22635 | −0.115080 | ||||||||
\(787\) | −24.1844 | − | 13.9629i | −0.862081 | − | 0.497723i | 0.00262765 | − | 0.999997i | \(-0.499164\pi\) |
−0.864709 | + | 0.502274i | \(0.832497\pi\) | |||||||
\(788\) | 39.0963 | − | 22.5723i | 1.39275 | − | 0.804104i | ||||
\(789\) | 23.6924 | − | 41.0365i | 0.843473 | − | 1.46094i | ||||
\(790\) | −1.38185 | −0.0491641 | ||||||||
\(791\) | 12.9742 | − | 22.4720i | 0.461309 | − | 0.799011i | ||||
\(792\) | −0.117423 | − | 0.203383i | −0.00417246 | − | 0.00722691i | ||||
\(793\) | 5.59737 | + | 9.69492i | 0.198768 | + | 0.344277i | ||||
\(794\) | −0.448519 | + | 0.258952i | −0.0159173 | + | 0.00918987i | ||||
\(795\) | 65.0819 | − | 37.5751i | 2.30822 | − | 1.33265i | ||||
\(796\) | − | 33.3268i | − | 1.18124i | ||||||
\(797\) | 36.6442 | − | 21.1565i | 1.29800 | − | 0.749402i | 0.317944 | − | 0.948110i | \(-0.397008\pi\) |
0.980059 | + | 0.198707i | \(0.0636743\pi\) | |||||||
\(798\) | 2.47646 | 0.0876656 | ||||||||
\(799\) | − | 12.4564i | − | 0.440676i | ||||||
\(800\) | − | 3.69746i | − | 0.130725i | ||||||
\(801\) | 7.38539i | 0.260950i | ||||||||
\(802\) | −0.135789 | − | 0.235194i | −0.00479489 | − | 0.00830499i | ||||
\(803\) | 0.614612 | + | 0.354846i | 0.0216892 | + | 0.0125223i | ||||
\(804\) | 20.5351 | + | 35.5678i | 0.724217 | + | 1.25438i | ||||
\(805\) | −42.7357 | + | 24.6735i | −1.50624 | + | 0.869626i | ||||
\(806\) | −0.269264 | + | 0.466379i | −0.00948442 | + | 0.0164275i | ||||
\(807\) | 28.8757 | − | 50.0142i | 1.01647 | − | 1.76058i | ||||
\(808\) | −1.53905 | −0.0541434 | ||||||||
\(809\) | −20.1639 | + | 34.9248i | −0.708923 | + | 1.22789i | 0.256333 | + | 0.966588i | \(0.417486\pi\) |
−0.965257 | + | 0.261303i | \(0.915848\pi\) | |||||||
\(810\) | −5.47978 | − | 3.16375i | −0.192540 | − | 0.111163i | ||||
\(811\) | −29.3237 | + | 16.9301i | −1.02970 | + | 0.594495i | −0.916897 | − | 0.399123i | \(-0.869315\pi\) |
−0.112798 | + | 0.993618i | \(0.535981\pi\) | |||||||
\(812\) | −25.6679 | − | 14.8194i | −0.900767 | − | 0.520058i | ||||
\(813\) | −49.7616 | −1.74521 | ||||||||
\(814\) | 0.00454621 | + | 0.00787427i | 0.000159345 | + | 0.000275993i | ||||
\(815\) | −26.5841 | − | 15.3484i | −0.931202 | − | 0.537630i | ||||
\(816\) | −69.8316 | −2.44459 | ||||||||
\(817\) | −6.64429 | + | 3.83608i | −0.232454 | + | 0.134207i | ||||
\(818\) | −0.672546 | + | 0.388295i | −0.0235150 | + | 0.0135764i | ||||
\(819\) | 67.5748 | 2.36125 | ||||||||
\(820\) | 26.6967 | + | 46.2400i | 0.932288 | + | 1.61477i | ||||
\(821\) | −12.8795 | + | 22.3080i | −0.449499 | + | 0.778555i | −0.998353 | − | 0.0573629i | \(-0.981731\pi\) |
0.548854 | + | 0.835918i | \(0.315064\pi\) | |||||||
\(822\) | 1.16517 | − | 2.01814i | 0.0406401 | − | 0.0703907i | ||||
\(823\) | 26.3297 | 0.917794 | 0.458897 | − | 0.888489i | \(-0.348245\pi\) | ||||
0.458897 | + | 0.888489i | \(0.348245\pi\) | |||||||
\(824\) | 2.42634 | 0.0845256 | ||||||||
\(825\) | − | 3.72881i | − | 0.129821i | ||||||
\(826\) | −1.10572 | + | 0.638389i | −0.0384730 | + | 0.0222124i | ||||
\(827\) | 38.2686 | − | 22.0944i | 1.33073 | − | 0.768297i | 0.345318 | − | 0.938486i | \(-0.387771\pi\) |
0.985412 | + | 0.170189i | \(0.0544377\pi\) | |||||||
\(828\) | 38.5394 | + | 66.7523i | 1.33934 | + | 2.31980i | ||||
\(829\) | − | 37.7758i | − | 1.31201i | −0.754758 | − | 0.656004i | \(-0.772245\pi\) | ||
0.754758 | − | 0.656004i | \(-0.227755\pi\) | |||||||
\(830\) | −0.705780 | + | 0.407482i | −0.0244980 | + | 0.0141439i | ||||
\(831\) | − | 65.8956i | − | 2.28589i | ||||||
\(832\) | 16.3996 | − | 9.46831i | 0.568554 | − | 0.328255i | ||||
\(833\) | 8.79318 | − | 15.2302i | 0.304665 | − | 0.527696i | ||||
\(834\) | 0.530318i | 0.0183634i | ||||||||
\(835\) | −9.80875 | − | 5.66308i | −0.339446 | − | 0.195979i | ||||
\(836\) | 1.36005 | − | 0.785227i | 0.0470384 | − | 0.0271576i | ||||
\(837\) | −103.002 | −3.56027 | ||||||||
\(838\) | 0.624928 | + | 0.360802i | 0.0215878 | + | 0.0124637i | ||||
\(839\) | 37.3588 | + | 21.5691i | 1.28977 | + | 0.744649i | 0.978613 | − | 0.205710i | \(-0.0659502\pi\) |
0.311157 | + | 0.950359i | \(0.399284\pi\) | |||||||
\(840\) | 3.35952 | − | 5.81886i | 0.115914 | − | 0.200770i | ||||
\(841\) | 3.97002 | + | 6.87627i | 0.136897 | + | 0.237113i | ||||
\(842\) | −0.482838 | + | 0.836300i | −0.0166397 | + | 0.0288208i | ||||
\(843\) | 31.0401 | + | 53.7631i | 1.06908 | + | 1.85170i | ||||
\(844\) | − | 46.9479i | − | 1.61601i | ||||||
\(845\) | 12.7419 | + | 22.0696i | 0.438334 | + | 0.759217i | ||||
\(846\) | 0.467351 | − | 0.809476i | 0.0160679 | − | 0.0278304i | ||||
\(847\) | −30.7260 | + | 17.7397i | −1.05576 | + | 0.609542i | ||||
\(848\) | 21.7606 | − | 12.5635i | 0.747262 | − | 0.431432i | ||||
\(849\) | −34.1242 | + | 59.1049i | −1.17114 | + | 2.02847i | ||||
\(850\) | 1.36279 | + | 0.786809i | 0.0467434 | + | 0.0269873i | ||||
\(851\) | −2.98564 | − | 5.17127i | −0.102346 | − | 0.177269i | ||||
\(852\) | 59.5036 | + | 34.3544i | 2.03856 | + | 1.17696i | ||||
\(853\) | −6.59669 | + | 11.4258i | −0.225866 | + | 0.391212i | −0.956579 | − | 0.291473i | \(-0.905855\pi\) |
0.730713 | + | 0.682685i | \(0.239188\pi\) | |||||||
\(854\) | 0.573713 | + | 0.331233i | 0.0196320 | + | 0.0113346i | ||||
\(855\) | 78.1519 | − | 135.363i | 2.67274 | − | 4.62932i | ||||
\(856\) | 0.761456 | + | 1.31888i | 0.0260260 | + | 0.0450784i | ||||
\(857\) | 10.2273 | + | 5.90473i | 0.349358 | + | 0.201702i | 0.664402 | − | 0.747375i | \(-0.268686\pi\) |
−0.315045 | + | 0.949077i | \(0.602019\pi\) | |||||||
\(858\) | −0.0473347 | + | 0.0273287i | −0.00161598 | + | 0.000932987i | ||||
\(859\) | 9.96916 | + | 5.75570i | 0.340143 | + | 0.196382i | 0.660335 | − | 0.750971i | \(-0.270414\pi\) |
−0.320192 | + | 0.947353i | \(0.603747\pi\) | |||||||
\(860\) | 10.4030i | 0.354739i | ||||||||
\(861\) | 85.3060i | 2.90722i | ||||||||
\(862\) | −0.447395 | + | 0.774911i | −0.0152383 | + | 0.0263936i | ||||
\(863\) | −15.6693 | + | 9.04665i | −0.533388 | + | 0.307952i | −0.742395 | − | 0.669963i | \(-0.766310\pi\) |
0.209007 | + | 0.977914i | \(0.432977\pi\) | |||||||
\(864\) | −8.97738 | − | 5.18309i | −0.305417 | − | 0.176332i | ||||
\(865\) | 21.2432i | 0.722291i | ||||||||
\(866\) | −0.479361 | −0.0162893 | ||||||||
\(867\) | 15.4748 | − | 26.8032i | 0.525553 | − | 0.910284i | ||||
\(868\) | − | 33.5210i | − | 1.13778i | ||||||
\(869\) | −1.40007 | −0.0474940 | ||||||||
\(870\) | 2.06633 | − | 1.19300i | 0.0700551 | − | 0.0404464i | ||||
\(871\) | 12.3461 | − | 7.12801i | 0.418331 | − | 0.241523i | ||||
\(872\) | 0.774513 | + | 0.447165i | 0.0262283 | + | 0.0151429i | ||||
\(873\) | 118.787 | + | 68.5819i | 4.02034 | + | 2.32115i | ||||
\(874\) | 0.849149 | − | 0.490256i | 0.0287229 | − | 0.0165832i | ||||
\(875\) | 20.2213 | − | 11.6747i | 0.683603 | − | 0.394678i | ||||
\(876\) | 31.7152 | 1.07156 | ||||||||
\(877\) | − | 9.53162i | − | 0.321860i | −0.986966 | − | 0.160930i | \(-0.948551\pi\) | ||
0.986966 | − | 0.160930i | \(-0.0514493\pi\) | |||||||
\(878\) | 0.0115948 | − | 0.0200829i | 0.000391307 | − | 0.000677763i | ||||
\(879\) | −31.2313 | −1.05341 | ||||||||
\(880\) | − | 2.12741i | − | 0.0717151i | ||||||
\(881\) | 1.81420 | + | 1.04743i | 0.0611221 | + | 0.0352888i | 0.530250 | − | 0.847842i | \(-0.322098\pi\) |
−0.469128 | + | 0.883130i | \(0.655432\pi\) | |||||||
\(882\) | 1.14284 | − | 0.659821i | 0.0384816 | − | 0.0222173i | ||||
\(883\) | −20.0918 | + | 34.8001i | −0.676144 | + | 1.17112i | 0.299989 | + | 0.953943i | \(0.403017\pi\) |
−0.976133 | + | 0.217174i | \(0.930316\pi\) | |||||||
\(884\) | 24.2626i | 0.816039i | ||||||||
\(885\) | 108.114i | 3.63423i | ||||||||
\(886\) | 0.0769083 | + | 0.0444031i | 0.00258379 | + | 0.00149175i | ||||
\(887\) | −27.2470 | + | 15.7311i | −0.914864 | + | 0.528197i | −0.881993 | − | 0.471263i | \(-0.843798\pi\) |
−0.0328711 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(888\) | 0.704116 | + | 0.406522i | 0.0236286 | + | 0.0136420i | ||||
\(889\) | 11.4222 | + | 19.7838i | 0.383088 | + | 0.663527i | ||||
\(890\) | 0.0636944 | − | 0.110322i | 0.00213504 | − | 0.00369800i | ||||
\(891\) | −5.55201 | − | 3.20546i | −0.185999 | − | 0.107387i | ||||
\(892\) | 12.2526 | − | 21.2221i | 0.410247 | − | 0.710568i | ||||
\(893\) | 10.8313 | + | 6.25346i | 0.362456 | + | 0.209264i | ||||
\(894\) | −0.307688 | − | 0.532930i | −0.0102906 | − | 0.0178239i | ||||
\(895\) | 4.69435 | + | 2.71028i | 0.156915 | + | 0.0905947i | ||||
\(896\) | 2.24870 | − | 3.89486i | 0.0751237 | − | 0.130118i | ||||
\(897\) | 31.0862 | − | 17.9476i | 1.03794 | − | 0.599253i | ||||
\(898\) | 0.298420 | − | 0.172293i | 0.00995842 | − | 0.00574950i | ||||
\(899\) | 11.9093 | − | 20.6275i | 0.397197 | − | 0.687965i | ||||
\(900\) | −62.1025 | − | 107.565i | −2.07008 | − | 3.58549i | ||||
\(901\) | 32.1326i | 1.07049i | ||||||||
\(902\) | −0.0257149 | − | 0.0445396i | −0.000856213 | − | 0.00148301i | ||||
\(903\) | −8.31038 | + | 14.3940i | −0.276552 | + | 0.479002i | ||||
\(904\) | 0.699438 | + | 1.21146i | 0.0232630 | + | 0.0402927i | ||||
\(905\) | −7.53383 | + | 13.0490i | −0.250433 | + | 0.433763i | ||||
\(906\) | 2.68651 | + | 1.55106i | 0.0892535 | + | 0.0515305i | ||||
\(907\) | −40.5522 | − | 23.4128i | −1.34651 | − | 0.777410i | −0.358760 | − | 0.933430i | \(-0.616800\pi\) |
−0.987754 | + | 0.156020i | \(0.950134\pi\) | |||||||
\(908\) | 10.2599 | 0.340487 | ||||||||
\(909\) | −67.1703 | + | 38.7808i | −2.22790 | + | 1.28628i | ||||
\(910\) | −1.00942 | − | 0.582791i | −0.0334620 | − | 0.0193193i | ||||
\(911\) | − | 35.4798i | − | 1.17550i | −0.809043 | − | 0.587750i | \(-0.800014\pi\) | ||
0.809043 | − | 0.587750i | \(-0.199986\pi\) | |||||||
\(912\) | 35.0574 | − | 60.7211i | 1.16087 | − | 2.01068i | ||||
\(913\) | −0.715083 | + | 0.412853i | −0.0236658 | + | 0.0136635i | ||||
\(914\) | − | 0.574522i | − | 0.0190035i | ||||||
\(915\) | 48.5806 | − | 28.0480i | 1.60602 | − | 0.927238i | ||||
\(916\) | − | 22.2368i | − | 0.734723i | ||||||
\(917\) | −34.8548 | − | 60.3702i | −1.15101 | − | 1.99360i | ||||
\(918\) | 3.82072 | − | 2.20590i | 0.126103 | − | 0.0728054i | ||||
\(919\) | −48.1720 | + | 27.8121i | −1.58905 | + | 0.917438i | −0.595585 | + | 0.803293i | \(0.703080\pi\) |
−0.993464 | + | 0.114145i | \(0.963587\pi\) | |||||||
\(920\) | − | 2.66030i | − | 0.0877073i | ||||||
\(921\) | −51.9110 | −1.71053 | ||||||||
\(922\) | −0.797408 | −0.0262612 | ||||||||
\(923\) | 11.9249 | − | 20.6545i | 0.392513 | − | 0.679852i | ||||
\(924\) | 1.70109 | − | 2.94638i | 0.0559619 | − | 0.0969288i | ||||
\(925\) | 4.81105 | + | 8.33299i | 0.158186 | + | 0.273987i | ||||
\(926\) | −1.36168 | −0.0447477 | ||||||||
\(927\) | 105.896 | − | 61.1389i | 3.47807 | − | 2.00806i | ||||
\(928\) | 2.07596 | − | 1.19856i | 0.0681468 | − | 0.0393446i | ||||
\(929\) | −17.2028 | −0.564404 | −0.282202 | − | 0.959355i | \(-0.591065\pi\) | ||||
−0.282202 | + | 0.959355i | \(0.591065\pi\) | |||||||
\(930\) | 2.33699 | + | 1.34926i | 0.0766330 | + | 0.0442441i | ||||
\(931\) | 8.82883 | + | 15.2920i | 0.289353 | + | 0.501174i | ||||
\(932\) | −34.1493 | −1.11860 | ||||||||
\(933\) | −13.7580 | − | 7.94316i | −0.450416 | − | 0.260048i | ||||
\(934\) | −1.37012 | + | 0.791040i | −0.0448317 | + | 0.0258836i | ||||
\(935\) | 2.35607 | + | 1.36028i | 0.0770517 | + | 0.0444858i | ||||
\(936\) | −1.82148 | + | 3.15489i | −0.0595369 | + | 0.103121i | ||||
\(937\) | 3.17941 | 0.103867 | 0.0519334 | − | 0.998651i | \(-0.483462\pi\) | ||||
0.0519334 | + | 0.998651i | \(0.483462\pi\) | |||||||
\(938\) | 0.421811 | − | 0.730599i | 0.0137726 | − | 0.0238549i | ||||
\(939\) | −41.5479 | + | 71.9631i | −1.35587 | + | 2.34843i | ||||
\(940\) | 14.6866 | − | 8.47931i | 0.479024 | − | 0.276565i | ||||
\(941\) | −11.7882 | − | 20.4178i | −0.384286 | − | 0.665603i | 0.607384 | − | 0.794408i | \(-0.292219\pi\) |
−0.991670 | + | 0.128806i | \(0.958886\pi\) | |||||||
\(942\) | 2.52871 | + | 1.45995i | 0.0823897 | + | 0.0475677i | ||||
\(943\) | 16.8878 | + | 29.2505i | 0.549941 | + | 0.952527i | ||||
\(944\) | 36.1488i | 1.17654i | ||||||||
\(945\) | − | 222.936i | − | 7.25210i | ||||||
\(946\) | − | 0.0100204i | − | 0.000325792i | ||||||
\(947\) | −35.8512 | −1.16501 | −0.582503 | − | 0.812828i | \(-0.697927\pi\) | ||||
−0.582503 | + | 0.812828i | \(0.697927\pi\) | |||||||
\(948\) | −54.1847 | + | 31.2836i | −1.75984 | + | 1.01604i | ||||
\(949\) | − | 11.0088i | − | 0.357360i | ||||||
\(950\) | −1.36832 | + | 0.789999i | −0.0443941 | + | 0.0256310i | ||||
\(951\) | 8.62501 | − | 4.97965i | 0.279685 | − | 0.161476i | ||||
\(952\) | 1.43646 | + | 2.48802i | 0.0465559 | + | 0.0806372i | ||||
\(953\) | 8.51296 | + | 14.7449i | 0.275762 | + | 0.477634i | 0.970327 | − | 0.241796i | \(-0.0777365\pi\) |
−0.694565 | + | 0.719430i | \(0.744403\pi\) | |||||||
\(954\) | −1.20558 | + | 2.08813i | −0.0390321 | + | 0.0676056i | ||||
\(955\) | −50.7518 | −1.64229 | ||||||||
\(956\) | −0.513371 | + | 0.889184i | −0.0166036 | + | 0.0287583i | ||||
\(957\) | 2.09357 | − | 1.20872i | 0.0676754 | − | 0.0390724i | ||||
\(958\) | −0.579063 | − | 0.334322i | −0.0187087 | − | 0.0108015i | ||||
\(959\) | 50.3502 | 1.62589 | ||||||||
\(960\) | −47.4450 | − | 82.1772i | −1.53128 | − | 2.65226i | ||||
\(961\) | −4.06153 | −0.131017 | ||||||||
\(962\) | 0.0705211 | − | 0.122146i | 0.00227369 | − | 0.00393815i | ||||
\(963\) | 66.4662 | + | 38.3743i | 2.14184 | + | 1.23659i | ||||
\(964\) | 3.40638 | + | 5.90003i | 0.109712 | + | 0.190027i | ||||
\(965\) | −5.07270 | + | 2.92872i | −0.163296 | + | 0.0942790i | ||||
\(966\) | 1.06208 | − | 1.83957i | 0.0341718 | − | 0.0591873i | ||||
\(967\) | −18.6195 | −0.598762 | −0.299381 | − | 0.954134i | \(-0.596780\pi\) | ||||
−0.299381 | + | 0.954134i | \(0.596780\pi\) | |||||||
\(968\) | − | 1.91269i | − | 0.0614762i | ||||||
\(969\) | 44.8317 | + | 77.6507i | 1.44020 | + | 2.49450i | ||||
\(970\) | −1.18295 | − | 2.04894i | −0.0379824 | − | 0.0657874i | ||||
\(971\) | 0.808954 | + | 1.40115i | 0.0259606 | + | 0.0449650i | 0.878714 | − | 0.477349i | \(-0.158402\pi\) |
−0.852753 | + | 0.522314i | \(0.825069\pi\) | |||||||
\(972\) | −167.536 | −5.37372 | ||||||||
\(973\) | −9.92310 | + | 5.72911i | −0.318120 | + | 0.183667i | ||||
\(974\) | −0.0284405 | + | 0.0492604i | −0.000911293 | + | 0.00157840i | ||||
\(975\) | −50.0922 | + | 28.9208i | −1.60424 | + | 0.926206i | ||||
\(976\) | 16.2432 | − | 9.37804i | 0.519934 | − | 0.300184i | ||||
\(977\) | 6.42665 | + | 11.1313i | 0.205607 | + | 0.356122i | 0.950326 | − | 0.311257i | \(-0.100750\pi\) |
−0.744719 | + | 0.667378i | \(0.767417\pi\) | |||||||
\(978\) | 1.32135 | 0.0422521 | ||||||||
\(979\) | 0.0645340 | − | 0.111776i | 0.00206252 | − | 0.00357238i | ||||
\(980\) | 23.9427 | 0.764822 | ||||||||
\(981\) | 45.0706 | 1.43899 | ||||||||
\(982\) | − | 0.334493i | − | 0.0106741i | ||||||
\(983\) | −20.3939 | −0.650463 | −0.325231 | − | 0.945634i | \(-0.605442\pi\) | ||||
−0.325231 | + | 0.945634i | \(0.605442\pi\) | |||||||
\(984\) | −3.98272 | − | 2.29942i | −0.126964 | − | 0.0733030i | ||||
\(985\) | −68.0026 | + | 39.2613i | −2.16674 | + | 1.25097i | ||||
\(986\) | 1.02020i | 0.0324898i | ||||||||
\(987\) | 27.0947 | 0.862432 | ||||||||
\(988\) | −21.0972 | − | 12.1805i | −0.671191 | − | 0.387512i | ||||
\(989\) | 6.58072i | 0.209255i | ||||||||
\(990\) | 0.102072 | + | 0.176795i | 0.00324407 | + | 0.00561890i | ||||
\(991\) | −1.83244 | − | 3.17387i | −0.0582093 | − | 0.100821i | 0.835452 | − | 0.549563i | \(-0.185206\pi\) |
−0.893662 | + | 0.448741i | \(0.851872\pi\) | |||||||
\(992\) | 2.34789 | + | 1.35555i | 0.0745455 | + | 0.0430389i | ||||
\(993\) | −27.0777 | + | 15.6333i | −0.859285 | + | 0.496109i | ||||
\(994\) | − | 1.41135i | − | 0.0447653i | ||||||
\(995\) | 57.9674i | 1.83769i | ||||||||
\(996\) | −18.4499 | + | 31.9561i | −0.584606 | + | 1.01257i | ||||
\(997\) | 23.3751 | + | 13.4956i | 0.740297 | + | 0.427411i | 0.822177 | − | 0.569231i | \(-0.192759\pi\) |
−0.0818800 | + | 0.996642i | \(0.526092\pi\) | |||||||
\(998\) | −0.948508 | + | 1.64286i | −0.0300245 | + | 0.0520039i | ||||
\(999\) | 26.9765 | 0.853499 |
(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 | 349.2.e.a.123.15 | ✓ | 58 | |
349.227 | even | 6 | inner | 349.2.e.a.227.15 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.e.a.123.15 | ✓ | 58 | 1.1 | even | 1 | trivial | |
349.2.e.a.227.15 | yes | 58 | 349.227 | even | 6 | inner |