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 | 227.15 | ||
Character | \(\chi\) | \(=\) | 349.227 |
Dual form | 349.2.e.a.123.15 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0.486596 | − | 0.873627i | \(-0.338238\pi\) |
−0.513286 | + | 0.858218i | \(0.671572\pi\) | |||||||
\(3\) | 1.71622 | + | 2.97259i | 0.990862 | + | 1.71622i | 0.612240 | + | 0.790672i | \(0.290269\pi\) |
0.378622 | + | 0.925551i | \(0.376398\pi\) | |||||||
\(4\) | −0.999050 | − | 1.73041i | −0.499525 | − | 0.865203i | ||||
\(5\) | 1.73771 | + | 3.00980i | 0.777127 | + | 1.34602i | 0.933591 | + | 0.358340i | \(0.116657\pi\) |
−0.156464 | + | 0.987684i | \(0.550010\pi\) | |||||||
\(6\) | − | 0.149601i | − | 0.0610741i | ||||||
\(7\) | −2.79927 | − | 1.61616i | −1.05802 | − | 0.610850i | −0.133138 | − | 0.991097i | \(-0.542505\pi\) |
−0.924885 | + | 0.380248i | \(0.875839\pi\) | |||||||
\(8\) | 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 | \(-0.992635\pi\) | ||
0.999732 | − | 0.0231365i | \(-0.00736523\pi\) | |||||||
\(12\) | 3.42919 | − | 5.93953i | 0.989921 | − | 1.71459i | ||||
\(13\) | 2.06169 | + | 1.19032i | 0.571810 | + | 0.330135i | 0.757872 | − | 0.652403i | \(-0.226239\pi\) |
−0.186062 | + | 0.982538i | \(0.559573\pi\) | |||||||
\(14\) | 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 | −0.994564 | − | 0.104127i | \(-0.966795\pi\) |
0.407105 | − | 0.913381i | \(-0.366538\pi\) | |||||||
\(20\) | 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 | −0.540875 | − | 0.841103i | \(-0.681907\pi\) |
0.998854 | + | 0.0478596i | \(0.0152400\pi\) | |||||||
\(24\) | −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 | 0.996521 | − | 0.0833373i | \(-0.0265579\pi\) |
−0.570433 | + | 0.821344i | \(0.693225\pi\) | |||||||
\(30\) | 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 | −0.397804 | − | 0.917471i | \(-0.630228\pi\) |
0.595651 | + | 0.803243i | \(0.296894\pi\) | |||||||
\(44\) | −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 | \(0.0569982\pi\) | ||||
−0.984011 | + | 0.178110i | \(0.943002\pi\) | |||||||
\(48\) | −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 | \(-0.857574\pi\) | ||
0.901555 | − | 0.432664i | \(-0.142426\pi\) | |||||||
\(54\) | 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 | −0.914633 | − | 0.404286i | \(-0.867520\pi\) |
−0.107195 | + | 0.994238i | \(0.534187\pi\) | |||||||
\(60\) | 23.8357 | 3.07718 | ||||||||
\(61\) | − | 4.70242i | − | 0.602083i | −0.953611 | − | 0.301041i | \(-0.902666\pi\) | ||
0.953611 | − | 0.301041i | \(-0.0973342\pi\) | |||||||
\(62\) | −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 | 0.916887 | − | 0.399147i | \(-0.130694\pi\) |
0.112772 | + | 0.993621i | \(0.464027\pi\) | |||||||
\(72\) | −1.32523 | − | 0.765123i | −0.156180 | − | 0.0901706i | ||||
\(73\) | 2.31215 | + | 4.00477i | 0.270617 | + | 0.468723i | 0.969020 | − | 0.246982i | \(-0.0794389\pi\) |
−0.698403 | + | 0.715705i | \(0.746106\pi\) | |||||||
\(74\) | 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 | \(-0.828462\pi\) | ||
0.858273 | − | 0.513194i | \(-0.171538\pi\) | |||||||
\(80\) | −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 | −0.679770 | − | 0.733425i | \(-0.737921\pi\) |
0.975050 | + | 0.221986i | \(0.0712540\pi\) | |||||||
\(84\) | −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 | −0.538104 | − | 0.842878i | \(-0.680859\pi\) |
0.460902 | + | 0.887451i | \(0.347526\pi\) | |||||||
\(90\) | 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 | −0.382071 | − | 0.924133i | \(-0.624789\pi\) |
−0.991358 | + | 0.131183i | \(0.958122\pi\) | |||||||
\(98\) | − | 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 | \(0.144815\pi\) | ||||
−0.898283 | + | 0.439418i | \(0.855185\pi\) | |||||||
\(102\) | − | 0.763062i | − | 0.0755544i | ||||||
\(103\) | − | 13.9242i | − | 1.37199i | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||
0.727607 | − | 0.685994i | \(-0.240633\pi\) | |||||||
\(104\) | −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 | 0.0873463 | − | 0.996178i | \(-0.472161\pi\) |
−0.819042 | + | 0.573733i | \(0.805495\pi\) | |||||||
\(108\) | 19.8265 | + | 34.3405i | 1.90781 | + | 3.30442i | ||||
\(109\) | −2.56617 | − | 4.44473i | −0.245794 | − | 0.425728i | 0.716560 | − | 0.697525i | \(-0.245715\pi\) |
−0.962355 | + | 0.271797i | \(0.912382\pi\) | |||||||
\(110\) | −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 | 0.135978 | − | 0.990712i | \(-0.456583\pi\) |
−0.789993 | + | 0.613116i | \(0.789916\pi\) | |||||||
\(114\) | −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 | \(0.101525\pi\) | ||||
−0.949565 | + | 0.313569i | \(0.898475\pi\) | |||||||
\(128\) | −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 | \(-0.608816\pi\) | ||
0.335234 | − | 0.942135i | \(-0.391184\pi\) | |||||||
\(132\) | −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 | −0.949506 | − | 0.313749i | \(-0.898415\pi\) |
−0.203039 | + | 0.979171i | \(0.565082\pi\) | |||||||
\(138\) | −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 | 0.346932 | − | 0.937890i | \(-0.387224\pi\) |
−0.638771 | + | 0.769397i | \(0.720557\pi\) | |||||||
\(150\) | 0.917079 | + | 0.529476i | 0.0748792 | + | 0.0432315i | ||||
\(151\) | 10.3680 | + | 17.9579i | 0.843737 | + | 1.46140i | 0.886714 | + | 0.462319i | \(0.152983\pi\) |
−0.0429765 | + | 0.999076i | \(0.513684\pi\) | |||||||
\(152\) | 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 | 0.932604 | + | 0.360901i | \(0.117531\pi\) |
−0.153753 | + | 0.988109i | \(0.549136\pi\) | |||||||
\(158\) | −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 | \(0.112429\pi\) | ||||
−0.938268 | + | 0.345908i | \(0.887571\pi\) | |||||||
\(164\) | −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 | \(0.0402435\pi\) | ||||
−0.992019 | + | 0.126092i | \(0.959757\pi\) | |||||||
\(168\) | 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 | 0.285086 | − | 0.958502i | \(-0.407978\pi\) |
−0.687544 | + | 0.726143i | \(0.741311\pi\) | |||||||
\(174\) | 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 | \(-0.981436\pi\) | ||
0.998300 | − | 0.0582882i | \(-0.0185642\pi\) | |||||||
\(180\) | 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 | 0.471135 | + | 0.882061i | \(0.343845\pi\) |
−0.999455 | + | 0.0330162i | \(0.989489\pi\) | |||||||
\(192\) | 13.6516 | + | 23.6453i | 0.985220 | + | 1.70645i | ||||
\(193\) | −1.45959 | + | 0.842697i | −0.105064 | + | 0.0606587i | −0.551611 | − | 0.834101i | \(-0.685987\pi\) |
0.446547 | + | 0.894760i | \(0.352653\pi\) | |||||||
\(194\) | 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 | −0.993763 | − | 0.111511i | \(-0.964431\pi\) |
−0.400310 | + | 0.916380i | \(0.631098\pi\) | |||||||
\(198\) | −0.0293698 | − | 0.0508700i | −0.00208722 | − | 0.00361517i | ||||
\(199\) | −14.4447 | − | 8.33963i | −1.02395 | − | 0.591181i | −0.108708 | − | 0.994074i | \(-0.534671\pi\) |
−0.915247 | + | 0.402893i | \(0.868005\pi\) | |||||||
\(200\) | −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 | −0.406360 | − | 0.913713i | \(-0.633202\pi\) |
−0.994479 | + | 0.104938i | \(0.966536\pi\) | |||||||
\(212\) | −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 | −0.938562 | − | 0.345112i | \(-0.887841\pi\) |
0.768156 | + | 0.640262i | \(0.221174\pi\) | |||||||
\(228\) | −35.1241 | −2.32615 | ||||||||
\(229\) | −9.63795 | − | 5.56447i | −0.636894 | − | 0.367711i | 0.146523 | − | 0.989207i | \(-0.453192\pi\) |
−0.783417 | + | 0.621496i | \(0.786525\pi\) | |||||||
\(230\) | −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 | −0.437679 | − | 0.899131i | \(-0.644199\pi\) |
0.997510 | − | 0.0705246i | \(-0.0224673\pi\) | |||||||
\(234\) | 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 | 0.915696 | − | 0.401872i | \(-0.131640\pi\) |
−0.805879 | + | 0.592080i | \(0.798307\pi\) | |||||||
\(242\) | −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 | \(-0.852329\pi\) | ||
0.894304 | − | 0.447459i | \(-0.147671\pi\) | |||||||
\(252\) | −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 | −0.997714 | − | 0.0675842i | \(-0.978471\pi\) |
0.557386 | + | 0.830253i | \(0.311804\pi\) | |||||||
\(272\) | −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 | 0.907937 | − | 0.419107i | \(-0.137657\pi\) |
0.0910115 | + | 0.995850i | \(0.470990\pi\) | |||||||
\(278\) | −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 | −0.998933 | − | 0.0461911i | \(-0.985292\pi\) |
0.459464 | − | 0.888197i | \(-0.348042\pi\) | |||||||
\(282\) | 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 | −0.967768 | − | 0.251844i | \(-0.918963\pi\) |
0.701987 | + | 0.712189i | \(0.252296\pi\) | |||||||
\(294\) | 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 | −0.997009 | − | 0.0772833i | \(-0.975375\pi\) |
0.565434 | + | 0.824794i | \(0.308709\pi\) | |||||||
\(308\) | 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 | \(0.0418903\pi\) | ||||
−0.991353 | + | 0.131223i | \(0.958110\pi\) | |||||||
\(312\) | −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 | −0.427771 | − | 0.903887i | \(-0.640701\pi\) |
0.568903 | + | 0.822404i | \(0.307368\pi\) | |||||||
\(318\) | −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 | −0.700881 | − | 0.713278i | \(-0.747210\pi\) |
0.267276 | + | 0.963620i | \(0.413876\pi\) | |||||||
\(332\) | −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 | −0.633834 | − | 0.773469i | \(-0.718520\pi\) |
0.986761 | + | 0.162182i | \(0.0518532\pi\) | |||||||
\(338\) | 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 | 0.968183 | + | 0.250242i | \(0.0805101\pi\) |
0.700807 | + | 0.713351i | \(0.252823\pi\) | |||||||
\(348\) | 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 | −0.983318 | − | 0.181893i | \(-0.941778\pi\) |
0.334136 | − | 0.942525i | \(-0.391556\pi\) | |||||||
\(354\) | 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 | \(-0.535990\pi\) | ||
0.112826 | − | 0.993615i | \(-0.464010\pi\) | |||||||
\(360\) | − | 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 | −0.218625 | − | 0.975809i | \(-0.570157\pi\) |
0.735763 | + | 0.677239i | \(0.236824\pi\) | |||||||
\(368\) | 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 | −0.544917 | − | 0.838490i | \(-0.683439\pi\) |
0.453695 | + | 0.891157i | \(0.350106\pi\) | |||||||
\(374\) | −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 | −0.985092 | − | 0.172029i | \(-0.944968\pi\) |
−0.343564 | + | 0.939129i | \(0.611634\pi\) | |||||||
\(380\) | −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 | 0.542933 | − | 0.839776i | \(-0.317314\pi\) |
−0.455801 | + | 0.890082i | \(0.650647\pi\) | |||||||
\(384\) | − | 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 | −0.568381 | − | 0.822766i | \(-0.692430\pi\) |
0.428346 | + | 0.903615i | \(0.359097\pi\) | |||||||
\(390\) | 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 | \(-0.950274\pi\) | ||
0.987823 | − | 0.155584i | \(-0.0497259\pi\) | |||||||
\(402\) | − | 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 | −0.994254 | − | 0.107048i | \(-0.965860\pi\) |
0.589833 | + | 0.807525i | \(0.299193\pi\) | |||||||
\(420\) | −66.7225 | − | 38.5223i | −3.25573 | − | 1.87969i | ||||
\(421\) | 19.1881 | + | 11.0783i | 0.935173 | + | 0.539923i | 0.888444 | − | 0.458985i | \(-0.151787\pi\) |
0.0467292 | + | 0.998908i | \(0.485120\pi\) | |||||||
\(422\) | 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 | 0.862810 | − | 0.505529i | \(-0.168703\pi\) |
−0.00639581 | + | 0.999980i | \(0.502036\pi\) | |||||||
\(432\) | 39.5776 | − | 68.5505i | 1.90418 | − | 3.29814i | ||||
\(433\) | 9.52497 | − | 5.49925i | 0.457741 | − | 0.264277i | −0.253353 | − | 0.967374i | \(-0.581533\pi\) |
0.711094 | + | 0.703097i | \(0.248200\pi\) | |||||||
\(434\) | 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 | 0.488964 | − | 0.872304i | \(-0.337375\pi\) |
−0.510956 | + | 0.859607i | \(0.670708\pi\) | |||||||
\(440\) | 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 | −0.889212 | − | 0.457495i | \(-0.848747\pi\) |
0.840808 | + | 0.541333i | \(0.182080\pi\) | |||||||
\(444\) | −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 | 0.669682 | − | 0.742648i | \(-0.266430\pi\) |
−0.977993 | + | 0.208637i | \(0.933097\pi\) | |||||||
\(458\) | 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 | −0.0833684 | − | 0.996519i | \(-0.526568\pi\) |
0.821326 | + | 0.570459i | \(0.193235\pi\) | |||||||
\(462\) | 0.0642689 | + | 0.0371057i | 0.00299006 | + | 0.00172631i | ||||
\(463\) | 27.0568 | − | 15.6213i | 1.25744 | − | 0.725982i | 0.284863 | − | 0.958568i | \(-0.408052\pi\) |
0.972576 | + | 0.232586i | \(0.0747187\pi\) | |||||||
\(464\) | −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 | −0.635850 | − | 0.771812i | \(-0.719350\pi\) |
0.986334 | + | 0.164756i | \(0.0526838\pi\) | |||||||
\(480\) | 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 | 0.525389 | − | 0.850862i | \(-0.323920\pi\) |
−0.474173 | + | 0.880431i | \(0.657253\pi\) | |||||||
\(488\) | 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 | 0.766353 | − | 0.642420i | \(-0.222070\pi\) |
−0.939528 | + | 0.342471i | \(0.888736\pi\) | |||||||
\(492\) | 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 | 0.956487 | + | 0.291776i | \(0.0942462\pi\) |
0.730929 | + | 0.682454i | \(0.239087\pi\) | |||||||
\(500\) | 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 | −0.703498 | + | 0.710697i | \(0.748380\pi\) |
−0.967231 | + | 0.253899i | \(0.918287\pi\) | |||||||
\(504\) | 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 | 0.847247 | − | 0.531199i | \(-0.178258\pi\) |
−0.0364086 | + | 0.999337i | \(0.511592\pi\) | |||||||
\(510\) | 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 | 0.755461 | − | 0.655193i | \(-0.227413\pi\) |
−0.189683 | + | 0.981845i | \(0.560746\pi\) | |||||||
\(522\) | 1.52113 | + | 0.878226i | 0.0665781 | + | 0.0384389i | ||||
\(523\) | −24.8498 | + | 14.3471i | −1.08661 | + | 0.627353i | −0.932671 | − | 0.360728i | \(-0.882528\pi\) |
−0.153936 | + | 0.988081i | \(0.549195\pi\) | |||||||
\(524\) | −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 | 0.997959 | + | 0.0638573i | \(0.0203402\pi\) |
−0.443677 | + | 0.896187i | \(0.646326\pi\) | |||||||
\(542\) | 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 | 0.815421 | − | 0.578868i | \(-0.196505\pi\) |
−0.909025 | + | 0.416742i | \(0.863172\pi\) | |||||||
\(548\) | 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 | −0.552004 | − | 0.833842i | \(-0.686137\pi\) |
0.446126 | + | 0.894970i | \(0.352803\pi\) | |||||||
\(558\) | 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 | 0.880480 | − | 0.474084i | \(-0.157221\pi\) |
−0.850808 | + | 0.525476i | \(0.823887\pi\) | |||||||
\(564\) | 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 | 0.830659 | − | 0.556782i | \(-0.187964\pi\) |
−0.0668580 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(570\) | −2.30598 | − | 1.33136i | −0.0965867 | − | 0.0557644i | ||||
\(571\) | − | 16.2009i | − | 0.677986i | −0.940789 | − | 0.338993i | \(-0.889914\pi\) | ||
0.940789 | − | 0.338993i | \(-0.110086\pi\) | |||||||
\(572\) | −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 | 0.617546 | − | 0.786535i | \(-0.288127\pi\) |
−0.989932 | + | 0.141543i | \(0.954794\pi\) | |||||||
\(588\) | 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 | −0.798223 | − | 0.602362i | \(-0.794226\pi\) |
0.122549 | + | 0.992462i | \(0.460893\pi\) | |||||||
\(594\) | 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 | 0.695243 | − | 0.718775i | \(-0.255297\pi\) |
−0.274856 | + | 0.961485i | \(0.588630\pi\) | |||||||
\(600\) | − | 4.23380i | − | 0.172844i | ||||||
\(601\) | 38.1423 | + | 22.0215i | 1.55586 | + | 0.898274i | 0.997646 | + | 0.0685752i | \(0.0218453\pi\) |
0.558211 | + | 0.829699i | \(0.311488\pi\) | |||||||
\(602\) | 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 | 0.858827 | − | 0.512266i | \(-0.171194\pi\) |
−0.873049 | + | 0.487633i | \(0.837861\pi\) | |||||||
\(608\) | −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 | 0.990501 | + | 0.137508i | \(0.0439092\pi\) |
−0.376165 | + | 0.926553i | \(0.622757\pi\) | |||||||
\(614\) | 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 | −0.999932 | − | 0.0116932i | \(-0.996278\pi\) |
0.489839 | − | 0.871813i | \(-0.337055\pi\) | |||||||
\(618\) | −2.08306 | −0.0837930 | ||||||||
\(619\) | − | 33.7826i | − | 1.35784i | −0.734214 | − | 0.678918i | \(-0.762449\pi\) | ||
0.734214 | − | 0.678918i | \(-0.237551\pi\) | |||||||
\(620\) | 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 | −0.391810 | − | 0.920046i | \(-0.628151\pi\) |
0.992688 | − | 0.120705i | \(-0.0385156\pi\) | |||||||
\(642\) | −0.653725 | + | 1.13228i | −0.0258005 | + | 0.0446877i | ||||
\(643\) | −6.05668 | + | 3.49683i | −0.238852 | + | 0.137901i | −0.614649 | − | 0.788801i | \(-0.710702\pi\) |
0.375797 | + | 0.926702i | \(0.377369\pi\) | |||||||
\(644\) | 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 | 0.872347 | − | 0.488888i | \(-0.162597\pi\) |
−0.859563 | + | 0.511030i | \(0.829264\pi\) | |||||||
\(648\) | 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 | \(0.00650043\pi\) | ||||
−0.999791 | + | 0.0204203i | \(0.993500\pi\) | |||||||
\(660\) | − | 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 | −0.838095 | − | 0.545525i | \(-0.816330\pi\) |
0.891486 | + | 0.453049i | \(0.149664\pi\) | |||||||
\(674\) | −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 | \(-0.796212\pi\) | ||
0.801965 | − | 0.597371i | \(-0.203788\pi\) | |||||||
\(678\) | −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 | −0.995075 | − | 0.0991272i | \(-0.968395\pi\) |
0.583384 | + | 0.812196i | \(0.301728\pi\) | |||||||
\(684\) | −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 | 0.238374 | − | 0.971174i | \(-0.423386\pi\) |
−0.721874 | + | 0.692024i | \(0.756719\pi\) | |||||||
\(692\) | 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 | 0.703020 | − | 0.711170i | \(-0.251834\pi\) |
−0.967401 | + | 0.253249i | \(0.918501\pi\) | |||||||
\(702\) | 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 | \(0.334094\pi\) | ||||
−0.497929 | + | 0.867218i | \(0.665906\pi\) | |||||||
\(710\) | 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 | \(0.0402412\pi\) | ||||
−0.992019 | + | 0.126085i | \(0.959759\pi\) | |||||||
\(720\) | 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 | −0.954862 | − | 0.297050i | \(-0.903997\pi\) |
0.220178 | − | 0.975460i | \(-0.429336\pi\) | |||||||
\(728\) | 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 | \(0.174470\pi\) | ||||
−0.853510 | + | 0.521077i | \(0.825530\pi\) | |||||||
\(734\) | −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 | \(0.124566\pi\) | ||||
−0.924401 | + | 0.381423i | \(0.875434\pi\) | |||||||
\(752\) | −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 | −0.800715 | − | 0.599046i | \(-0.795547\pi\) |
0.118432 | + | 0.992962i | \(0.462213\pi\) | |||||||
\(758\) | 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 | −0.363913 | − | 0.931433i | \(-0.618560\pi\) |
0.624688 | + | 0.780875i | \(0.285226\pi\) | |||||||
\(762\) | 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 | −0.999955 | − | 0.00945575i | \(-0.996990\pi\) |
−0.508167 | − | 0.861259i | \(-0.669677\pi\) | |||||||
\(770\) | 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 | −0.864709 | − | 0.502274i | \(-0.832497\pi\) |
0.00262765 | + | 0.999997i | \(0.499164\pi\) | |||||||
\(788\) | 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 | 0.980059 | − | 0.198707i | \(-0.0636743\pi\) |
0.317944 | + | 0.948110i | \(0.397008\pi\) | |||||||
\(798\) | 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 | −0.965257 | − | 0.261303i | \(-0.915848\pi\) |
0.256333 | − | 0.966588i | \(-0.417486\pi\) | |||||||
\(810\) | −5.47978 | + | 3.16375i | −0.192540 | + | 0.111163i | ||||
\(811\) | −29.3237 | − | 16.9301i | −1.02970 | − | 0.594495i | −0.112798 | − | 0.993618i | \(-0.535981\pi\) |
−0.916897 | + | 0.399123i | \(0.869315\pi\) | |||||||
\(812\) | −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 | 0.548854 | − | 0.835918i | \(-0.315064\pi\) |
−0.998353 | + | 0.0573629i | \(0.981731\pi\) | |||||||
\(822\) | 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 | 0.985412 | − | 0.170189i | \(-0.0544377\pi\) |
0.345318 | + | 0.938486i | \(0.387771\pi\) | |||||||
\(828\) | 38.5394 | − | 66.7523i | 1.33934 | − | 2.31980i | ||||
\(829\) | 37.7758i | 1.31201i | 0.754758 | + | 0.656004i | \(0.227755\pi\) | ||||
−0.754758 | + | 0.656004i | \(0.772245\pi\) | |||||||
\(830\) | −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 | 0.311157 | − | 0.950359i | \(-0.399284\pi\) |
0.978613 | + | 0.205710i | \(0.0659502\pi\) | |||||||
\(840\) | 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 | 0.730713 | − | 0.682685i | \(-0.239188\pi\) |
−0.956579 | + | 0.291473i | \(0.905855\pi\) | |||||||
\(854\) | 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 | −0.315045 | − | 0.949077i | \(-0.602019\pi\) |
0.664402 | + | 0.747375i | \(0.268686\pi\) | |||||||
\(858\) | −0.0473347 | − | 0.0273287i | −0.00161598 | − | 0.000932987i | ||||
\(859\) | 9.96916 | − | 5.75570i | 0.340143 | − | 0.196382i | −0.320192 | − | 0.947353i | \(-0.603747\pi\) |
0.660335 | + | 0.750971i | \(0.270414\pi\) | |||||||
\(860\) | − | 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 | 0.209007 | − | 0.977914i | \(-0.432977\pi\) |
−0.742395 | + | 0.669963i | \(0.766310\pi\) | |||||||
\(864\) | −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 | \(0.0514493\pi\) | ||||
−0.986966 | + | 0.160930i | \(0.948551\pi\) | |||||||
\(878\) | 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 | −0.469128 | − | 0.883130i | \(-0.655432\pi\) |
0.530250 | + | 0.847842i | \(0.322098\pi\) | |||||||
\(882\) | 1.14284 | + | 0.659821i | 0.0384816 | + | 0.0222173i | ||||
\(883\) | −20.0918 | − | 34.8001i | −0.676144 | − | 1.17112i | −0.976133 | − | 0.217174i | \(-0.930316\pi\) |
0.299989 | − | 0.953943i | \(-0.403017\pi\) | |||||||
\(884\) | − | 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 | −0.0328711 | − | 0.999460i | \(-0.510465\pi\) |
−0.881993 | + | 0.471263i | \(0.843798\pi\) | |||||||
\(888\) | 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 | −0.987754 | − | 0.156020i | \(-0.950134\pi\) |
−0.358760 | + | 0.933430i | \(0.616800\pi\) | |||||||
\(908\) | 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 | \(0.199986\pi\) | ||||
−0.809043 | + | 0.587750i | \(0.800014\pi\) | |||||||
\(912\) | 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 | −0.993464 | − | 0.114145i | \(-0.963587\pi\) |
−0.595585 | − | 0.803293i | \(-0.703080\pi\) | |||||||
\(920\) | 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 | −0.991670 | − | 0.128806i | \(-0.958886\pi\) |
0.607384 | + | 0.794408i | \(0.292219\pi\) | |||||||
\(942\) | 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 | −0.694565 | − | 0.719430i | \(-0.744403\pi\) |
0.970327 | + | 0.241796i | \(0.0777365\pi\) | |||||||
\(954\) | −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 | −0.852753 | − | 0.522314i | \(-0.825069\pi\) |
0.878714 | + | 0.477349i | \(0.158402\pi\) | |||||||
\(972\) | −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 | −0.744719 | − | 0.667378i | \(-0.767417\pi\) |
0.950326 | + | 0.311257i | \(0.100750\pi\) | |||||||
\(978\) | 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 | −0.893662 | − | 0.448741i | \(-0.851872\pi\) |
0.835452 | + | 0.549563i | \(0.185206\pi\) | |||||||
\(992\) | 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 | −0.0818800 | − | 0.996642i | \(-0.526092\pi\) |
0.822177 | + | 0.569231i | \(0.192759\pi\) | |||||||
\(998\) | −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.227.15 | yes | 58 | |
349.123 | even | 6 | inner | 349.2.e.a.123.15 | ✓ | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.e.a.123.15 | ✓ | 58 | 349.123 | even | 6 | inner | |
349.2.e.a.227.15 | yes | 58 | 1.1 | even | 1 | trivial |