Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,2,Mod(77,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.k (of order \(4\), 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: | \(2.42745222145\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.28 | ||
Character | \(\chi\) | \(=\) | 304.77 |
Dual form | 304.2.k.b.229.28 |
$q$-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 \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16214 | + | 0.805879i | 0.821754 | + | 0.569843i | ||||
\(3\) | −1.57596 | − | 1.57596i | −0.909883 | − | 0.909883i | 0.0863796 | − | 0.996262i | \(-0.472470\pi\) |
−0.996262 | + | 0.0863796i | \(0.972470\pi\) | |||||||
\(4\) | 0.701117 | + | 1.87308i | 0.350559 | + | 0.936541i | ||||
\(5\) | −1.57740 | + | 1.57740i | −0.705436 | + | 0.705436i | −0.965572 | − | 0.260136i | \(-0.916233\pi\) |
0.260136 | + | 0.965572i | \(0.416233\pi\) | |||||||
\(6\) | −0.561447 | − | 3.10152i | −0.229210 | − | 1.26619i | ||||
\(7\) | 1.68609i | 0.637281i | 0.947876 | + | 0.318641i | \(0.103226\pi\) | ||||
−0.947876 | + | 0.318641i | \(0.896774\pi\) | |||||||
\(8\) | −0.694684 | + | 2.74179i | −0.245608 | + | 0.969369i | ||||
\(9\) | 1.96732i | 0.655773i | ||||||||
\(10\) | −3.10435 | + | 0.561960i | −0.981682 | + | 0.177707i | ||||
\(11\) | −2.67034 | + | 2.67034i | −0.805137 | + | 0.805137i | −0.983893 | − | 0.178757i | \(-0.942792\pi\) |
0.178757 | + | 0.983893i | \(0.442792\pi\) | |||||||
\(12\) | 1.84697 | − | 4.05684i | 0.533175 | − | 1.17111i | ||||
\(13\) | 4.96054 | + | 4.96054i | 1.37581 | + | 1.37581i | 0.851579 | + | 0.524226i | \(0.175645\pi\) |
0.524226 | + | 0.851579i | \(0.324355\pi\) | |||||||
\(14\) | −1.35878 | + | 1.95946i | −0.363150 | + | 0.523688i | ||||
\(15\) | 4.97186 | 1.28373 | ||||||||
\(16\) | −3.01687 | + | 2.62650i | −0.754217 | + | 0.656625i | ||||
\(17\) | 0.745156 | 0.180727 | 0.0903635 | − | 0.995909i | \(-0.471197\pi\) | ||||
0.0903635 | + | 0.995909i | \(0.471197\pi\) | |||||||
\(18\) | −1.58542 | + | 2.28629i | −0.373687 | + | 0.538884i | ||||
\(19\) | −0.707107 | − | 0.707107i | −0.162221 | − | 0.162221i | ||||
\(20\) | −4.06055 | − | 1.84866i | −0.907966 | − | 0.413373i | ||||
\(21\) | 2.65721 | − | 2.65721i | 0.579851 | − | 0.579851i | ||||
\(22\) | −5.25526 | + | 0.951324i | −1.12043 | + | 0.202823i | ||||
\(23\) | − | 9.28569i | − | 1.93620i | −0.250563 | − | 0.968100i | \(-0.580616\pi\) | ||
0.250563 | − | 0.968100i | \(-0.419384\pi\) | |||||||
\(24\) | 5.41576 | − | 3.22616i | 1.10549 | − | 0.658538i | ||||
\(25\) | 0.0235982i | 0.00471964i | ||||||||
\(26\) | 1.76722 | + | 9.76241i | 0.346581 | + | 1.91457i | ||||
\(27\) | −1.62747 | + | 1.62747i | −0.313206 | + | 0.313206i | ||||
\(28\) | −3.15818 | + | 1.18215i | −0.596840 | + | 0.223405i | ||||
\(29\) | −2.38928 | − | 2.38928i | −0.443678 | − | 0.443678i | 0.449568 | − | 0.893246i | \(-0.351578\pi\) |
−0.893246 | + | 0.449568i | \(0.851578\pi\) | |||||||
\(30\) | 5.77797 | + | 4.00672i | 1.05491 | + | 0.731523i | ||||
\(31\) | 4.12358 | 0.740616 | 0.370308 | − | 0.928909i | \(-0.379252\pi\) | ||||
0.370308 | + | 0.928909i | \(0.379252\pi\) | |||||||
\(32\) | −5.62265 | + | 0.621117i | −0.993954 | + | 0.109799i | ||||
\(33\) | 8.41670 | 1.46516 | ||||||||
\(34\) | 0.865973 | + | 0.600506i | 0.148513 | + | 0.102986i | ||||
\(35\) | −2.65964 | − | 2.65964i | −0.449561 | − | 0.449561i | ||||
\(36\) | −3.68495 | + | 1.37932i | −0.614158 | + | 0.229887i | ||||
\(37\) | −4.56212 | + | 4.56212i | −0.750008 | + | 0.750008i | −0.974480 | − | 0.224473i | \(-0.927934\pi\) |
0.224473 | + | 0.974480i | \(0.427934\pi\) | |||||||
\(38\) | −0.251911 | − | 1.39160i | −0.0408654 | − | 0.225747i | ||||
\(39\) | − | 15.6352i | − | 2.50364i | ||||||
\(40\) | −3.22911 | − | 5.42071i | −0.510567 | − | 0.857089i | ||||
\(41\) | 2.33941i | 0.365355i | 0.983173 | + | 0.182678i | \(0.0584764\pi\) | ||||
−0.983173 | + | 0.182678i | \(0.941524\pi\) | |||||||
\(42\) | 5.22943 | − | 0.946648i | 0.806919 | − | 0.146071i | ||||
\(43\) | −2.19419 | + | 2.19419i | −0.334611 | + | 0.334611i | −0.854335 | − | 0.519723i | \(-0.826035\pi\) |
0.519723 | + | 0.854335i | \(0.326035\pi\) | |||||||
\(44\) | −6.87398 | − | 3.12954i | −1.03629 | − | 0.471796i | ||||
\(45\) | −3.10326 | − | 3.10326i | −0.462606 | − | 0.462606i | ||||
\(46\) | 7.48315 | − | 10.7912i | 1.10333 | − | 1.59108i | ||||
\(47\) | 6.33222 | 0.923649 | 0.461824 | − | 0.886971i | \(-0.347195\pi\) | ||||
0.461824 | + | 0.886971i | \(0.347195\pi\) | |||||||
\(48\) | 8.89374 | + | 0.615207i | 1.28370 | + | 0.0887975i | ||||
\(49\) | 4.15711 | 0.593873 | ||||||||
\(50\) | −0.0190173 | + | 0.0274243i | −0.00268945 | + | 0.00387839i | ||||
\(51\) | −1.17434 | − | 1.17434i | −0.164440 | − | 0.164440i | ||||
\(52\) | −5.81357 | + | 12.7694i | −0.806197 | + | 1.77080i | ||||
\(53\) | 7.24655 | − | 7.24655i | 0.995391 | − | 0.995391i | −0.00459887 | − | 0.999989i | \(-0.501464\pi\) |
0.999989 | + | 0.00459887i | \(0.00146387\pi\) | |||||||
\(54\) | −3.20288 | + | 0.579795i | −0.435857 | + | 0.0789001i | ||||
\(55\) | − | 8.42439i | − | 1.13594i | ||||||
\(56\) | −4.62290 | − | 1.17130i | −0.617761 | − | 0.156521i | ||||
\(57\) | 2.22875i | 0.295205i | ||||||||
\(58\) | −0.851195 | − | 4.70214i | −0.111767 | − | 0.617421i | ||||
\(59\) | 8.10520 | − | 8.10520i | 1.05521 | − | 1.05521i | 0.0568228 | − | 0.998384i | \(-0.481903\pi\) |
0.998384 | − | 0.0568228i | \(-0.0180970\pi\) | |||||||
\(60\) | 3.48586 | + | 9.31270i | 0.450022 | + | 1.20226i | ||||
\(61\) | 2.83217 | + | 2.83217i | 0.362622 | + | 0.362622i | 0.864777 | − | 0.502155i | \(-0.167459\pi\) |
−0.502155 | + | 0.864777i | \(0.667459\pi\) | |||||||
\(62\) | 4.79215 | + | 3.32310i | 0.608604 | + | 0.422035i | ||||
\(63\) | −3.31707 | −0.417912 | ||||||||
\(64\) | −7.03483 | − | 3.80936i | −0.879353 | − | 0.476170i | ||||
\(65\) | −15.6495 | −1.94109 | ||||||||
\(66\) | 9.78135 | + | 6.78284i | 1.20400 | + | 0.834910i | ||||
\(67\) | −3.09338 | − | 3.09338i | −0.377917 | − | 0.377917i | 0.492433 | − | 0.870350i | \(-0.336108\pi\) |
−0.870350 | + | 0.492433i | \(0.836108\pi\) | |||||||
\(68\) | 0.522442 | + | 1.39574i | 0.0633554 | + | 0.169258i | ||||
\(69\) | −14.6339 | + | 14.6339i | −1.76172 | + | 1.76172i | ||||
\(70\) | −0.947513 | − | 5.23421i | −0.113250 | − | 0.625608i | ||||
\(71\) | 4.16634i | 0.494454i | 0.968958 | + | 0.247227i | \(0.0795193\pi\) | ||||
−0.968958 | + | 0.247227i | \(0.920481\pi\) | |||||||
\(72\) | −5.39398 | − | 1.36667i | −0.635686 | − | 0.161063i | ||||
\(73\) | − | 8.32181i | − | 0.973994i | −0.873404 | − | 0.486997i | \(-0.838092\pi\) | ||
0.873404 | − | 0.486997i | \(-0.161908\pi\) | |||||||
\(74\) | −8.97832 | + | 1.62528i | −1.04371 | + | 0.188935i | ||||
\(75\) | 0.0371899 | − | 0.0371899i | 0.00429432 | − | 0.00429432i | ||||
\(76\) | 0.828704 | − | 1.82023i | 0.0950588 | − | 0.208795i | ||||
\(77\) | −4.50242 | − | 4.50242i | −0.513098 | − | 0.513098i | ||||
\(78\) | 12.6001 | − | 18.1703i | 1.42668 | − | 2.05738i | ||||
\(79\) | 5.53927 | 0.623216 | 0.311608 | − | 0.950211i | \(-0.399132\pi\) | ||||
0.311608 | + | 0.950211i | \(0.399132\pi\) | |||||||
\(80\) | 0.615769 | − | 8.90187i | 0.0688451 | − | 0.995259i | ||||
\(81\) | 11.0316 | 1.22573 | ||||||||
\(82\) | −1.88529 | + | 2.71872i | −0.208195 | + | 0.300232i | ||||
\(83\) | 5.44587 | + | 5.44587i | 0.597762 | + | 0.597762i | 0.939716 | − | 0.341955i | \(-0.111089\pi\) |
−0.341955 | + | 0.939716i | \(0.611089\pi\) | |||||||
\(84\) | 6.84019 | + | 3.11416i | 0.746326 | + | 0.339782i | ||||
\(85\) | −1.17541 | + | 1.17541i | −0.127491 | + | 0.127491i | ||||
\(86\) | −4.31820 | + | 0.781695i | −0.465644 | + | 0.0842923i | ||||
\(87\) | 7.53083i | 0.807390i | ||||||||
\(88\) | −5.46646 | − | 9.17654i | −0.582727 | − | 0.978223i | ||||
\(89\) | 12.5226i | 1.32739i | 0.748004 | + | 0.663694i | \(0.231012\pi\) | ||||
−0.748004 | + | 0.663694i | \(0.768988\pi\) | |||||||
\(90\) | −1.10555 | − | 6.10725i | −0.116536 | − | 0.643761i | ||||
\(91\) | −8.36390 | + | 8.36390i | −0.876775 | + | 0.876775i | ||||
\(92\) | 17.3929 | − | 6.51036i | 1.81333 | − | 0.678752i | ||||
\(93\) | −6.49860 | − | 6.49860i | −0.673874 | − | 0.673874i | ||||
\(94\) | 7.35889 | + | 5.10300i | 0.759012 | + | 0.526334i | ||||
\(95\) | 2.23079 | 0.228874 | ||||||||
\(96\) | 9.83995 | + | 7.88223i | 1.00429 | + | 0.804477i | ||||
\(97\) | 3.33008 | 0.338118 | 0.169059 | − | 0.985606i | \(-0.445927\pi\) | ||||
0.169059 | + | 0.985606i | \(0.445927\pi\) | |||||||
\(98\) | 4.83112 | + | 3.35013i | 0.488017 | + | 0.338414i | ||||
\(99\) | −5.25340 | − | 5.25340i | −0.527987 | − | 0.527987i | ||||
\(100\) | −0.0442014 | + | 0.0165451i | −0.00442014 | + | 0.00165451i | ||||
\(101\) | 5.75972 | − | 5.75972i | 0.573114 | − | 0.573114i | −0.359883 | − | 0.932997i | \(-0.617184\pi\) |
0.932997 | + | 0.359883i | \(0.117184\pi\) | |||||||
\(102\) | −0.418366 | − | 2.31112i | −0.0414244 | − | 0.228835i | ||||
\(103\) | 17.1116i | 1.68606i | 0.537869 | + | 0.843028i | \(0.319229\pi\) | ||||
−0.537869 | + | 0.843028i | \(0.680771\pi\) | |||||||
\(104\) | −17.0468 | + | 10.1547i | −1.67157 | + | 0.995755i | ||||
\(105\) | 8.38299i | 0.818096i | ||||||||
\(106\) | 14.2613 | − | 2.58163i | 1.38518 | − | 0.250750i | ||||
\(107\) | −6.09993 | + | 6.09993i | −0.589702 | + | 0.589702i | −0.937551 | − | 0.347849i | \(-0.886912\pi\) |
0.347849 | + | 0.937551i | \(0.386912\pi\) | |||||||
\(108\) | −4.18942 | − | 1.90733i | −0.403127 | − | 0.183533i | ||||
\(109\) | 8.30961 | + | 8.30961i | 0.795916 | + | 0.795916i | 0.982449 | − | 0.186533i | \(-0.0597250\pi\) |
−0.186533 | + | 0.982449i | \(0.559725\pi\) | |||||||
\(110\) | 6.78904 | − | 9.79029i | 0.647310 | − | 0.933467i | ||||
\(111\) | 14.3795 | 1.36484 | ||||||||
\(112\) | −4.42851 | − | 5.08671i | −0.418455 | − | 0.480649i | ||||
\(113\) | −8.64423 | −0.813181 | −0.406590 | − | 0.913611i | \(-0.633282\pi\) | ||||
−0.406590 | + | 0.913611i | \(0.633282\pi\) | |||||||
\(114\) | −1.79610 | + | 2.59011i | −0.168220 | + | 0.242586i | ||||
\(115\) | 14.6473 | + | 14.6473i | 1.36587 | + | 1.36587i | ||||
\(116\) | 2.80015 | − | 6.15048i | 0.259987 | − | 0.571058i | ||||
\(117\) | −9.75896 | + | 9.75896i | −0.902216 | + | 0.902216i | ||||
\(118\) | 15.9512 | − | 2.88753i | 1.46842 | − | 0.265818i | ||||
\(119\) | 1.25640i | 0.115174i | ||||||||
\(120\) | −3.45387 | + | 13.6318i | −0.315294 | + | 1.24441i | ||||
\(121\) | − | 3.26139i | − | 0.296490i | ||||||
\(122\) | 1.00898 | + | 5.57375i | 0.0913485 | + | 0.504623i | ||||
\(123\) | 3.68683 | − | 3.68683i | 0.332430 | − | 0.332430i | ||||
\(124\) | 2.89111 | + | 7.72380i | 0.259629 | + | 0.693617i | ||||
\(125\) | −7.92424 | − | 7.92424i | −0.708766 | − | 0.708766i | ||||
\(126\) | −3.85489 | − | 2.67316i | −0.343421 | − | 0.238144i | ||||
\(127\) | −18.5183 | −1.64323 | −0.821617 | − | 0.570040i | \(-0.806928\pi\) | ||||
−0.821617 | + | 0.570040i | \(0.806928\pi\) | |||||||
\(128\) | −5.10554 | − | 10.0962i | −0.451270 | − | 0.892387i | ||||
\(129\) | 6.91593 | 0.608914 | ||||||||
\(130\) | −18.1869 | − | 12.6116i | −1.59509 | − | 1.10611i | ||||
\(131\) | 7.55135 | + | 7.55135i | 0.659764 | + | 0.659764i | 0.955324 | − | 0.295560i | \(-0.0955062\pi\) |
−0.295560 | + | 0.955324i | \(0.595506\pi\) | |||||||
\(132\) | 5.90110 | + | 15.7652i | 0.513624 | + | 1.37218i | ||||
\(133\) | 1.19224 | − | 1.19224i | 0.103381 | − | 0.103381i | ||||
\(134\) | −1.10204 | − | 6.08782i | −0.0952014 | − | 0.525908i | ||||
\(135\) | − | 5.13434i | − | 0.441894i | ||||||
\(136\) | −0.517648 | + | 2.04306i | −0.0443880 | + | 0.175191i | ||||
\(137\) | − | 7.22190i | − | 0.617009i | −0.951223 | − | 0.308504i | \(-0.900172\pi\) | ||
0.951223 | − | 0.308504i | \(-0.0998284\pi\) | |||||||
\(138\) | −28.7997 | + | 5.21342i | −2.45160 | + | 0.443796i | ||||
\(139\) | −2.08768 | + | 2.08768i | −0.177075 | + | 0.177075i | −0.790079 | − | 0.613005i | \(-0.789961\pi\) |
0.613005 | + | 0.790079i | \(0.289961\pi\) | |||||||
\(140\) | 3.11700 | − | 6.84644i | 0.263435 | − | 0.578630i | ||||
\(141\) | −9.97934 | − | 9.97934i | −0.840412 | − | 0.840412i | ||||
\(142\) | −3.35757 | + | 4.84185i | −0.281761 | + | 0.406319i | ||||
\(143\) | −26.4926 | −2.21542 | ||||||||
\(144\) | −5.16716 | − | 5.93514i | −0.430597 | − | 0.494595i | ||||
\(145\) | 7.53771 | 0.625973 | ||||||||
\(146\) | 6.70637 | − | 9.67107i | 0.555023 | − | 0.800383i | ||||
\(147\) | −6.55145 | − | 6.55145i | −0.540354 | − | 0.540354i | ||||
\(148\) | −11.7438 | − | 5.34664i | −0.965334 | − | 0.439491i | ||||
\(149\) | 4.10195 | − | 4.10195i | 0.336045 | − | 0.336045i | −0.518831 | − | 0.854877i | \(-0.673633\pi\) |
0.854877 | + | 0.518831i | \(0.173633\pi\) | |||||||
\(150\) | 0.0731903 | − | 0.0132491i | 0.00597596 | − | 0.00108179i | ||||
\(151\) | − | 17.3656i | − | 1.41319i | −0.707619 | − | 0.706594i | \(-0.750231\pi\) | ||
0.707619 | − | 0.706594i | \(-0.249769\pi\) | |||||||
\(152\) | 2.42995 | − | 1.44752i | 0.197095 | − | 0.117410i | ||||
\(153\) | 1.46596i | 0.118516i | ||||||||
\(154\) | −1.60402 | − | 8.86083i | −0.129255 | − | 0.714026i | ||||
\(155\) | −6.50454 | + | 6.50454i | −0.522457 | + | 0.522457i | ||||
\(156\) | 29.2861 | − | 10.9621i | 2.34476 | − | 0.877674i | ||||
\(157\) | −4.68861 | − | 4.68861i | −0.374192 | − | 0.374192i | 0.494809 | − | 0.869001i | \(-0.335238\pi\) |
−0.869001 | + | 0.494809i | \(0.835238\pi\) | |||||||
\(158\) | 6.43738 | + | 4.46398i | 0.512130 | + | 0.355135i | ||||
\(159\) | −22.8406 | −1.81138 | ||||||||
\(160\) | 7.88944 | − | 9.84894i | 0.623715 | − | 0.778627i | ||||
\(161\) | 15.6565 | 1.23390 | ||||||||
\(162\) | 12.8202 | + | 8.89015i | 1.00725 | + | 0.698476i | ||||
\(163\) | −9.42345 | − | 9.42345i | −0.738101 | − | 0.738101i | 0.234109 | − | 0.972210i | \(-0.424783\pi\) |
−0.972210 | + | 0.234109i | \(0.924783\pi\) | |||||||
\(164\) | −4.38191 | + | 1.64020i | −0.342170 | + | 0.128078i | ||||
\(165\) | −13.2765 | + | 13.2765i | −1.03358 | + | 1.03358i | ||||
\(166\) | 1.94012 | + | 10.7176i | 0.150583 | + | 0.831843i | ||||
\(167\) | 2.49387i | 0.192982i | 0.995334 | + | 0.0964909i | \(0.0307619\pi\) | ||||
−0.995334 | + | 0.0964909i | \(0.969238\pi\) | |||||||
\(168\) | 5.43960 | + | 9.13144i | 0.419674 | + | 0.704506i | ||||
\(169\) | 36.2138i | 2.78568i | ||||||||
\(170\) | −2.31323 | + | 0.418748i | −0.177417 | + | 0.0321165i | ||||
\(171\) | 1.39110 | − | 1.39110i | 0.106380 | − | 0.106380i | ||||
\(172\) | −5.64829 | − | 2.57152i | −0.430678 | − | 0.196076i | ||||
\(173\) | −1.03148 | − | 1.03148i | −0.0784222 | − | 0.0784222i | 0.666808 | − | 0.745230i | \(-0.267660\pi\) |
−0.745230 | + | 0.666808i | \(0.767660\pi\) | |||||||
\(174\) | −6.06894 | + | 8.75184i | −0.460085 | + | 0.663476i | ||||
\(175\) | −0.0397887 | −0.00300774 | ||||||||
\(176\) | 1.04242 | − | 15.0697i | 0.0785750 | − | 1.13592i | ||||
\(177\) | −25.5470 | −1.92023 | ||||||||
\(178\) | −10.0917 | + | 14.5529i | −0.756403 | + | 1.09079i | ||||
\(179\) | 0.977829 | + | 0.977829i | 0.0730864 | + | 0.0730864i | 0.742705 | − | 0.669619i | \(-0.233542\pi\) |
−0.669619 | + | 0.742705i | \(0.733542\pi\) | |||||||
\(180\) | 3.63690 | − | 7.98840i | 0.271079 | − | 0.595420i | ||||
\(181\) | 9.98191 | − | 9.98191i | 0.741949 | − | 0.741949i | −0.231004 | − | 0.972953i | \(-0.574201\pi\) |
0.972953 | + | 0.231004i | \(0.0742009\pi\) | |||||||
\(182\) | −16.4603 | + | 2.97969i | −1.22012 | + | 0.220869i | ||||
\(183\) | − | 8.92678i | − | 0.659887i | ||||||
\(184\) | 25.4594 | + | 6.45062i | 1.87689 | + | 0.475546i | ||||
\(185\) | − | 14.3926i | − | 1.05817i | ||||||
\(186\) | −2.31517 | − | 12.7893i | −0.169756 | − | 0.937761i | ||||
\(187\) | −1.98982 | + | 1.98982i | −0.145510 | + | 0.145510i | ||||
\(188\) | 4.43963 | + | 11.8608i | 0.323793 | + | 0.865035i | ||||
\(189\) | −2.74405 | − | 2.74405i | −0.199600 | − | 0.199600i | ||||
\(190\) | 2.59247 | + | 1.79774i | 0.188078 | + | 0.130422i | ||||
\(191\) | 7.18058 | 0.519569 | 0.259784 | − | 0.965667i | \(-0.416349\pi\) | ||||
0.259784 | + | 0.965667i | \(0.416349\pi\) | |||||||
\(192\) | 5.08322 | + | 17.0900i | 0.366850 | + | 1.23337i | ||||
\(193\) | 13.9809 | 1.00637 | 0.503183 | − | 0.864180i | \(-0.332162\pi\) | ||||
0.503183 | + | 0.864180i | \(0.332162\pi\) | |||||||
\(194\) | 3.87000 | + | 2.68364i | 0.277850 | + | 0.192674i | ||||
\(195\) | 24.6631 | + | 24.6631i | 1.76616 | + | 1.76616i | ||||
\(196\) | 2.91462 | + | 7.78660i | 0.208187 | + | 0.556186i | ||||
\(197\) | 3.17726 | − | 3.17726i | 0.226371 | − | 0.226371i | −0.584804 | − | 0.811175i | \(-0.698829\pi\) |
0.811175 | + | 0.584804i | \(0.198829\pi\) | |||||||
\(198\) | −1.87156 | − | 10.3388i | −0.133006 | − | 0.734745i | ||||
\(199\) | − | 3.42039i | − | 0.242465i | −0.992624 | − | 0.121233i | \(-0.961315\pi\) | ||
0.992624 | − | 0.121233i | \(-0.0386847\pi\) | |||||||
\(200\) | −0.0647014 | − | 0.0163933i | −0.00457508 | − | 0.00115918i | ||||
\(201\) | 9.75011i | 0.687720i | ||||||||
\(202\) | 11.3352 | − | 2.05194i | 0.797543 | − | 0.144374i | ||||
\(203\) | 4.02853 | − | 4.02853i | 0.282748 | − | 0.282748i | ||||
\(204\) | 1.37628 | − | 3.02298i | 0.0963591 | − | 0.211651i | ||||
\(205\) | −3.69020 | − | 3.69020i | −0.257735 | − | 0.257735i | ||||
\(206\) | −13.7899 | + | 19.8860i | −0.960787 | + | 1.38552i | ||||
\(207\) | 18.2679 | 1.26971 | ||||||||
\(208\) | −27.9941 | − | 1.93644i | −1.94104 | − | 0.134268i | ||||
\(209\) | 3.77643 | 0.261221 | ||||||||
\(210\) | −6.75568 | + | 9.74217i | −0.466186 | + | 0.672274i | ||||
\(211\) | 9.02544 | + | 9.02544i | 0.621337 | + | 0.621337i | 0.945873 | − | 0.324536i | \(-0.105208\pi\) |
−0.324536 | + | 0.945873i | \(0.605208\pi\) | |||||||
\(212\) | 18.6541 | + | 8.49270i | 1.28117 | + | 0.583281i | ||||
\(213\) | 6.56600 | − | 6.56600i | 0.449895 | − | 0.449895i | ||||
\(214\) | −12.0047 | + | 2.17314i | −0.820627 | + | 0.148553i | ||||
\(215\) | − | 6.92225i | − | 0.472094i | ||||||
\(216\) | −3.33160 | − | 5.59275i | −0.226686 | − | 0.380538i | ||||
\(217\) | 6.95271i | 0.471981i | ||||||||
\(218\) | 2.96035 | + | 16.3534i | 0.200500 | + | 1.10759i | ||||
\(219\) | −13.1149 | + | 13.1149i | −0.886220 | + | 0.886220i | ||||
\(220\) | 15.7796 | − | 5.90649i | 1.06386 | − | 0.398215i | ||||
\(221\) | 3.69638 | + | 3.69638i | 0.248645 | + | 0.248645i | ||||
\(222\) | 16.7109 | + | 11.5881i | 1.12156 | + | 0.777743i | ||||
\(223\) | 10.1714 | 0.681130 | 0.340565 | − | 0.940221i | \(-0.389382\pi\) | ||||
0.340565 | + | 0.940221i | \(0.389382\pi\) | |||||||
\(224\) | −1.04726 | − | 9.48029i | −0.0699728 | − | 0.633428i | ||||
\(225\) | −0.0464252 | −0.00309502 | ||||||||
\(226\) | −10.0458 | − | 6.96621i | −0.668235 | − | 0.463385i | ||||
\(227\) | −10.2101 | − | 10.2101i | −0.677668 | − | 0.677668i | 0.281804 | − | 0.959472i | \(-0.409067\pi\) |
−0.959472 | + | 0.281804i | \(0.909067\pi\) | |||||||
\(228\) | −4.17463 | + | 1.56261i | −0.276471 | + | 0.103487i | ||||
\(229\) | 15.8958 | − | 15.8958i | 1.05042 | − | 1.05042i | 0.0517648 | − | 0.998659i | \(-0.483515\pi\) |
0.998659 | − | 0.0517648i | \(-0.0164846\pi\) | |||||||
\(230\) | 5.21818 | + | 28.8261i | 0.344077 | + | 1.90073i | ||||
\(231\) | 14.1913i | 0.933719i | ||||||||
\(232\) | 8.21070 | − | 4.89111i | 0.539059 | − | 0.321117i | ||||
\(233\) | − | 14.4046i | − | 0.943674i | −0.881686 | − | 0.471837i | \(-0.843591\pi\) | ||
0.881686 | − | 0.471837i | \(-0.156409\pi\) | |||||||
\(234\) | −19.2058 | + | 3.47669i | −1.25552 | + | 0.227278i | ||||
\(235\) | −9.98846 | + | 9.98846i | −0.651575 | + | 0.651575i | ||||
\(236\) | 20.8644 | + | 9.49900i | 1.35816 | + | 0.618332i | ||||
\(237\) | −8.72968 | − | 8.72968i | −0.567054 | − | 0.567054i | ||||
\(238\) | −1.01251 | + | 1.46011i | −0.0656310 | + | 0.0946446i | ||||
\(239\) | 4.89457 | 0.316603 | 0.158302 | − | 0.987391i | \(-0.449398\pi\) | ||||
0.158302 | + | 0.987391i | \(0.449398\pi\) | |||||||
\(240\) | −14.9994 | + | 13.0586i | −0.968210 | + | 0.842928i | ||||
\(241\) | 13.5680 | 0.873990 | 0.436995 | − | 0.899464i | \(-0.356043\pi\) | ||||
0.436995 | + | 0.899464i | \(0.356043\pi\) | |||||||
\(242\) | 2.62828 | − | 3.79017i | 0.168953 | − | 0.243642i | ||||
\(243\) | −12.5030 | − | 12.5030i | −0.802069 | − | 0.802069i | ||||
\(244\) | −3.31920 | + | 7.29056i | −0.212490 | + | 0.466730i | ||||
\(245\) | −6.55743 | + | 6.55743i | −0.418939 | + | 0.418939i | ||||
\(246\) | 7.25574 | − | 1.31346i | 0.462609 | − | 0.0837429i | ||||
\(247\) | − | 7.01526i | − | 0.446370i | ||||||
\(248\) | −2.86458 | + | 11.3060i | −0.181901 | + | 0.717931i | ||||
\(249\) | − | 17.1650i | − | 1.08779i | ||||||
\(250\) | −2.82306 | − | 15.5950i | −0.178546 | − | 0.986316i | ||||
\(251\) | −16.3192 | + | 16.3192i | −1.03006 | + | 1.03006i | −0.0305248 | + | 0.999534i | \(0.509718\pi\) |
−0.999534 | + | 0.0305248i | \(0.990282\pi\) | |||||||
\(252\) | −2.32566 | − | 6.21315i | −0.146503 | − | 0.391392i | ||||
\(253\) | 24.7959 | + | 24.7959i | 1.55891 | + | 1.55891i | ||||
\(254\) | −21.5208 | − | 14.9235i | −1.35033 | − | 0.936385i | ||||
\(255\) | 3.70481 | 0.232004 | ||||||||
\(256\) | 2.20300 | − | 15.8476i | 0.137687 | − | 0.990476i | ||||
\(257\) | −25.3775 | −1.58301 | −0.791503 | − | 0.611165i | \(-0.790701\pi\) | ||||
−0.791503 | + | 0.611165i | \(0.790701\pi\) | |||||||
\(258\) | 8.03725 | + | 5.57341i | 0.500377 | + | 0.346985i | ||||
\(259\) | −7.69213 | − | 7.69213i | −0.477966 | − | 0.477966i | ||||
\(260\) | −10.9722 | − | 29.3129i | −0.680464 | − | 1.81791i | ||||
\(261\) | 4.70047 | − | 4.70047i | 0.290952 | − | 0.290952i | ||||
\(262\) | 2.69021 | + | 14.8612i | 0.166202 | + | 0.918126i | ||||
\(263\) | 9.72484i | 0.599659i | 0.953993 | + | 0.299830i | \(0.0969299\pi\) | ||||
−0.953993 | + | 0.299830i | \(0.903070\pi\) | |||||||
\(264\) | −5.84695 | + | 23.0768i | −0.359855 | + | 1.42028i | ||||
\(265\) | 22.8615i | 1.40437i | ||||||||
\(266\) | 2.34635 | − | 0.424744i | 0.143864 | − | 0.0260427i | ||||
\(267\) | 19.7351 | − | 19.7351i | 1.20777 | − | 1.20777i | ||||
\(268\) | 3.62533 | − | 7.96298i | 0.221452 | − | 0.486416i | ||||
\(269\) | −19.6767 | − | 19.6767i | −1.19971 | − | 1.19971i | −0.974254 | − | 0.225453i | \(-0.927614\pi\) |
−0.225453 | − | 0.974254i | \(-0.572386\pi\) | |||||||
\(270\) | 4.13766 | − | 5.96680i | 0.251810 | − | 0.363128i | ||||
\(271\) | 20.8174 | 1.26457 | 0.632285 | − | 0.774736i | \(-0.282117\pi\) | ||||
0.632285 | + | 0.774736i | \(0.282117\pi\) | |||||||
\(272\) | −2.24804 | + | 1.95715i | −0.136307 | + | 0.118670i | ||||
\(273\) | 26.3624 | 1.59552 | ||||||||
\(274\) | 5.81998 | − | 8.39283i | 0.351598 | − | 0.507029i | ||||
\(275\) | −0.0630152 | − | 0.0630152i | −0.00379996 | − | 0.00379996i | ||||
\(276\) | −37.6706 | − | 17.1504i | −2.26750 | − | 1.03233i | ||||
\(277\) | 19.8793 | − | 19.8793i | 1.19443 | − | 1.19443i | 0.218618 | − | 0.975810i | \(-0.429845\pi\) |
0.975810 | − | 0.218618i | \(-0.0701549\pi\) | |||||||
\(278\) | −4.10858 | + | 0.743748i | −0.246416 | + | 0.0446071i | ||||
\(279\) | 8.11239i | 0.485676i | ||||||||
\(280\) | 9.13979 | − | 5.44457i | 0.546207 | − | 0.325375i | ||||
\(281\) | 1.38015i | 0.0823329i | 0.999152 | + | 0.0411664i | \(0.0131074\pi\) | ||||
−0.999152 | + | 0.0411664i | \(0.986893\pi\) | |||||||
\(282\) | −3.55520 | − | 19.6395i | −0.211709 | − | 1.16951i | ||||
\(283\) | 2.30064 | − | 2.30064i | 0.136759 | − | 0.136759i | −0.635413 | − | 0.772172i | \(-0.719170\pi\) |
0.772172 | + | 0.635413i | \(0.219170\pi\) | |||||||
\(284\) | −7.80390 | + | 2.92109i | −0.463076 | + | 0.173335i | ||||
\(285\) | −3.51563 | − | 3.51563i | −0.208248 | − | 0.208248i | ||||
\(286\) | −30.7880 | − | 21.3498i | −1.82053 | − | 1.26244i | ||||
\(287\) | −3.94446 | −0.232834 | ||||||||
\(288\) | −1.22194 | − | 11.0616i | −0.0720032 | − | 0.651808i | ||||
\(289\) | −16.4447 | −0.967338 | ||||||||
\(290\) | 8.75984 | + | 6.07449i | 0.514396 | + | 0.356706i | ||||
\(291\) | −5.24808 | − | 5.24808i | −0.307648 | − | 0.307648i | ||||
\(292\) | 15.5874 | − | 5.83456i | 0.912185 | − | 0.341442i | ||||
\(293\) | −17.2518 | + | 17.2518i | −1.00786 | + | 1.00786i | −0.00789162 | + | 0.999969i | \(0.502512\pi\) |
−0.999969 | + | 0.00789162i | \(0.997488\pi\) | |||||||
\(294\) | −2.33399 | − | 12.8933i | −0.136121 | − | 0.751955i | ||||
\(295\) | 25.5703i | 1.48876i | ||||||||
\(296\) | −9.33914 | − | 15.6776i | −0.542827 | − | 0.911242i | ||||
\(297\) | − | 8.69177i | − | 0.504347i | ||||||
\(298\) | 8.07270 | − | 1.46135i | 0.467639 | − | 0.0846535i | ||||
\(299\) | 46.0620 | − | 46.0620i | 2.66383 | − | 2.66383i | ||||
\(300\) | 0.0957343 | + | 0.0435853i | 0.00552722 | + | 0.00251640i | ||||
\(301\) | −3.69960 | − | 3.69960i | −0.213242 | − | 0.213242i | ||||
\(302\) | 13.9945 | − | 20.1811i | 0.805295 | − | 1.16129i | ||||
\(303\) | −18.1542 | −1.04293 | ||||||||
\(304\) | 3.99046 | + | 0.276032i | 0.228869 | + | 0.0158315i | ||||
\(305\) | −8.93494 | −0.511613 | ||||||||
\(306\) | −1.18139 | + | 1.70364i | −0.0675354 | + | 0.0973909i | ||||
\(307\) | −0.402763 | − | 0.402763i | −0.0229869 | − | 0.0229869i | 0.695520 | − | 0.718507i | \(-0.255174\pi\) |
−0.718507 | + | 0.695520i | \(0.755174\pi\) | |||||||
\(308\) | 5.27668 | − | 11.5901i | 0.300667 | − | 0.660409i | ||||
\(309\) | 26.9673 | − | 26.9673i | 1.53411 | − | 1.53411i | ||||
\(310\) | −12.8010 | + | 2.31728i | −0.727050 | + | 0.131613i | ||||
\(311\) | 15.7246i | 0.891658i | 0.895118 | + | 0.445829i | \(0.147091\pi\) | ||||
−0.895118 | + | 0.445829i | \(0.852909\pi\) | |||||||
\(312\) | 42.8686 | + | 10.8616i | 2.42695 | + | 0.614915i | ||||
\(313\) | − | 17.1622i | − | 0.970063i | −0.874497 | − | 0.485031i | \(-0.838808\pi\) | ||
0.874497 | − | 0.485031i | \(-0.161192\pi\) | |||||||
\(314\) | −1.67035 | − | 9.22726i | −0.0942632 | − | 0.520724i | ||||
\(315\) | 5.23236 | − | 5.23236i | 0.294810 | − | 0.294810i | ||||
\(316\) | 3.88368 | + | 10.3755i | 0.218474 | + | 0.583667i | ||||
\(317\) | 1.89706 | + | 1.89706i | 0.106550 | + | 0.106550i | 0.758372 | − | 0.651822i | \(-0.225995\pi\) |
−0.651822 | + | 0.758372i | \(0.725995\pi\) | |||||||
\(318\) | −26.5439 | − | 18.4068i | −1.48851 | − | 1.03220i | ||||
\(319\) | 12.7604 | 0.714443 | ||||||||
\(320\) | 17.1057 | − | 5.08787i | 0.956235 | − | 0.284421i | ||||
\(321\) | 19.2265 | 1.07312 | ||||||||
\(322\) | 18.1950 | + | 12.6172i | 1.01397 | + | 0.703131i | ||||
\(323\) | −0.526905 | − | 0.526905i | −0.0293178 | − | 0.0293178i | ||||
\(324\) | 7.73446 | + | 20.6631i | 0.429692 | + | 1.14795i | ||||
\(325\) | −0.117060 | + | 0.117060i | −0.00649331 | + | 0.00649331i | ||||
\(326\) | −3.35716 | − | 18.5455i | −0.185936 | − | 1.02714i | ||||
\(327\) | − | 26.1913i | − | 1.44838i | ||||||
\(328\) | −6.41418 | − | 1.62515i | −0.354164 | − | 0.0897341i | ||||
\(329\) | 10.6767i | 0.588624i | ||||||||
\(330\) | −26.1284 | + | 4.72985i | −1.43832 | + | 0.260369i | ||||
\(331\) | 3.76461 | − | 3.76461i | 0.206922 | − | 0.206922i | −0.596036 | − | 0.802958i | \(-0.703258\pi\) |
0.802958 | + | 0.596036i | \(0.203258\pi\) | |||||||
\(332\) | −6.38236 | + | 14.0188i | −0.350278 | + | 0.769379i | ||||
\(333\) | −8.97514 | − | 8.97514i | −0.491835 | − | 0.491835i | ||||
\(334\) | −2.00976 | + | 2.89822i | −0.109969 | + | 0.158584i | ||||
\(335\) | 9.75902 | 0.533192 | ||||||||
\(336\) | −1.03729 | + | 14.9956i | −0.0565890 | + | 0.818079i | ||||
\(337\) | 1.11886 | 0.0609480 | 0.0304740 | − | 0.999536i | \(-0.490298\pi\) | ||||
0.0304740 | + | 0.999536i | \(0.490298\pi\) | |||||||
\(338\) | −29.1840 | + | 42.0854i | −1.58740 | + | 2.28914i | ||||
\(339\) | 13.6230 | + | 13.6230i | 0.739899 | + | 0.739899i | ||||
\(340\) | −3.02574 | − | 1.37754i | −0.164094 | − | 0.0747076i | ||||
\(341\) | −11.0113 | + | 11.0113i | −0.596297 | + | 0.596297i | ||||
\(342\) | 2.73771 | − | 0.495590i | 0.148039 | − | 0.0267984i | ||||
\(343\) | 18.8119i | 1.01575i | ||||||||
\(344\) | −4.49175 | − | 7.54029i | −0.242179 | − | 0.406545i | ||||
\(345\) | − | 46.1671i | − | 2.48556i | ||||||
\(346\) | −0.367472 | − | 2.02997i | −0.0197554 | − | 0.109132i | ||||
\(347\) | −22.6290 | + | 22.6290i | −1.21479 | + | 1.21479i | −0.245354 | + | 0.969434i | \(0.578904\pi\) |
−0.969434 | + | 0.245354i | \(0.921096\pi\) | |||||||
\(348\) | −14.1059 | + | 5.28000i | −0.756153 | + | 0.283037i | ||||
\(349\) | −18.5059 | − | 18.5059i | −0.990597 | − | 0.990597i | 0.00935911 | − | 0.999956i | \(-0.497021\pi\) |
−0.999956 | + | 0.00935911i | \(0.997021\pi\) | |||||||
\(350\) | −0.0462398 | − | 0.0320649i | −0.00247162 | − | 0.00171394i | ||||
\(351\) | −16.1462 | −0.861821 | ||||||||
\(352\) | 13.3558 | − | 16.6730i | 0.711865 | − | 0.888672i | ||||
\(353\) | −20.2998 | −1.08045 | −0.540225 | − | 0.841521i | \(-0.681661\pi\) | ||||
−0.540225 | + | 0.841521i | \(0.681661\pi\) | |||||||
\(354\) | −29.6891 | − | 20.5878i | −1.57796 | − | 1.09423i | ||||
\(355\) | −6.57200 | − | 6.57200i | −0.348806 | − | 0.348806i | ||||
\(356\) | −23.4558 | + | 8.77979i | −1.24315 | + | 0.465328i | ||||
\(357\) | 1.98004 | − | 1.98004i | 0.104795 | − | 0.104795i | ||||
\(358\) | 0.348358 | + | 1.92438i | 0.0184113 | + | 0.101707i | ||||
\(359\) | − | 0.916087i | − | 0.0483492i | −0.999708 | − | 0.0241746i | \(-0.992304\pi\) | ||
0.999708 | − | 0.0241746i | \(-0.00769577\pi\) | |||||||
\(360\) | 10.6643 | − | 6.35269i | 0.562056 | − | 0.334816i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 19.6445 | − | 3.55612i | 1.03249 | − | 0.186905i | ||||
\(363\) | −5.13983 | + | 5.13983i | −0.269771 | + | 0.269771i | ||||
\(364\) | −21.5303 | − | 9.80219i | −1.12850 | − | 0.513774i | ||||
\(365\) | 13.1268 | + | 13.1268i | 0.687090 | + | 0.687090i | ||||
\(366\) | 7.19391 | − | 10.3741i | 0.376032 | − | 0.542264i | ||||
\(367\) | 14.7129 | 0.768005 | 0.384003 | − | 0.923332i | \(-0.374545\pi\) | ||||
0.384003 | + | 0.923332i | \(0.374545\pi\) | |||||||
\(368\) | 24.3889 | + | 28.0137i | 1.27136 | + | 1.46032i | ||||
\(369\) | −4.60238 | −0.239590 | ||||||||
\(370\) | 11.5987 | − | 16.7262i | 0.602988 | − | 0.869551i | ||||
\(371\) | 12.2183 | + | 12.2183i | 0.634344 | + | 0.634344i | ||||
\(372\) | 7.61613 | − | 16.7287i | 0.394878 | − | 0.867343i | ||||
\(373\) | −10.0488 | + | 10.0488i | −0.520308 | + | 0.520308i | −0.917664 | − | 0.397356i | \(-0.869928\pi\) |
0.397356 | + | 0.917664i | \(0.369928\pi\) | |||||||
\(374\) | −3.91599 | + | 0.708885i | −0.202491 | + | 0.0366556i | ||||
\(375\) | 24.9766i | 1.28979i | ||||||||
\(376\) | −4.39889 | + | 17.3616i | −0.226855 | + | 0.895357i | ||||
\(377\) | − | 23.7042i | − | 1.22083i | ||||||
\(378\) | −0.977585 | − | 5.40033i | −0.0502816 | − | 0.277763i | ||||
\(379\) | −10.4995 | + | 10.4995i | −0.539325 | + | 0.539325i | −0.923331 | − | 0.384006i | \(-0.874544\pi\) |
0.384006 | + | 0.923331i | \(0.374544\pi\) | |||||||
\(380\) | 1.56404 | + | 4.17844i | 0.0802337 | + | 0.214350i | ||||
\(381\) | 29.1842 | + | 29.1842i | 1.49515 | + | 1.49515i | ||||
\(382\) | 8.34481 | + | 5.78668i | 0.426958 | + | 0.296072i | ||||
\(383\) | 1.23106 | 0.0629044 | 0.0314522 | − | 0.999505i | \(-0.489987\pi\) | ||||
0.0314522 | + | 0.999505i | \(0.489987\pi\) | |||||||
\(384\) | −7.86511 | + | 23.9574i | −0.401365 | + | 1.22257i | ||||
\(385\) | 14.2043 | 0.723916 | ||||||||
\(386\) | 16.2477 | + | 11.2669i | 0.826984 | + | 0.573470i | ||||
\(387\) | −4.31668 | − | 4.31668i | −0.219429 | − | 0.219429i | ||||
\(388\) | 2.33477 | + | 6.23750i | 0.118530 | + | 0.316661i | ||||
\(389\) | 2.75220 | − | 2.75220i | 0.139542 | − | 0.139542i | −0.633885 | − | 0.773427i | \(-0.718541\pi\) |
0.773427 | + | 0.633885i | \(0.218541\pi\) | |||||||
\(390\) | 8.78638 | + | 48.5373i | 0.444916 | + | 2.45778i | ||||
\(391\) | − | 6.91929i | − | 0.349924i | ||||||
\(392\) | −2.88788 | + | 11.3979i | −0.145860 | + | 0.575682i | ||||
\(393\) | − | 23.8013i | − | 1.20062i | ||||||
\(394\) | 6.25290 | − | 1.13192i | 0.315017 | − | 0.0570253i | ||||
\(395\) | −8.73766 | + | 8.73766i | −0.439639 | + | 0.439639i | ||||
\(396\) | 6.15680 | − | 13.5233i | 0.309391 | − | 0.679572i | ||||
\(397\) | −9.87588 | − | 9.87588i | −0.495656 | − | 0.495656i | 0.414427 | − | 0.910083i | \(-0.363982\pi\) |
−0.910083 | + | 0.414427i | \(0.863982\pi\) | |||||||
\(398\) | 2.75642 | − | 3.97496i | 0.138167 | − | 0.199247i | ||||
\(399\) | −3.75787 | −0.188129 | ||||||||
\(400\) | −0.0619807 | − | 0.0711927i | −0.00309904 | − | 0.00355964i | ||||
\(401\) | −11.5469 | −0.576625 | −0.288312 | − | 0.957536i | \(-0.593094\pi\) | ||||
−0.288312 | + | 0.957536i | \(0.593094\pi\) | |||||||
\(402\) | −7.85741 | + | 11.3309i | −0.391892 | + | 0.565136i | ||||
\(403\) | 20.4552 | + | 20.4552i | 1.01894 | + | 1.01894i | ||||
\(404\) | 14.8267 | + | 6.75019i | 0.737655 | + | 0.335834i | ||||
\(405\) | −17.4013 | + | 17.4013i | −0.864678 | + | 0.864678i | ||||
\(406\) | 7.92821 | − | 1.43519i | 0.393471 | − | 0.0712273i | ||||
\(407\) | − | 24.3648i | − | 1.20772i | ||||||
\(408\) | 4.03559 | − | 2.40400i | 0.199791 | − | 0.119016i | ||||
\(409\) | − | 36.8887i | − | 1.82403i | −0.410156 | − | 0.912015i | \(-0.634526\pi\) | ||
0.410156 | − | 0.912015i | \(-0.365474\pi\) | |||||||
\(410\) | −1.31466 | − | 7.26237i | −0.0649263 | − | 0.358663i | ||||
\(411\) | −11.3815 | + | 11.3815i | −0.561406 | + | 0.561406i | ||||
\(412\) | −32.0514 | + | 11.9972i | −1.57906 | + | 0.591062i | ||||
\(413\) | 13.6661 | + | 13.6661i | 0.672464 | + | 0.672464i | ||||
\(414\) | 21.2298 | + | 14.7217i | 1.04339 | + | 0.723534i | ||||
\(415\) | −17.1807 | −0.843366 | ||||||||
\(416\) | −30.9724 | − | 24.8103i | −1.51855 | − | 1.21642i | ||||
\(417\) | 6.58021 | 0.322234 | ||||||||
\(418\) | 4.38872 | + | 3.04334i | 0.214659 | + | 0.148855i | ||||
\(419\) | 17.8976 | + | 17.8976i | 0.874355 | + | 0.874355i | 0.992943 | − | 0.118589i | \(-0.0378370\pi\) |
−0.118589 | + | 0.992943i | \(0.537837\pi\) | |||||||
\(420\) | −15.7020 | + | 5.87746i | −0.766180 | + | 0.286791i | ||||
\(421\) | 20.8204 | − | 20.8204i | 1.01473 | − | 1.01473i | 0.0148362 | − | 0.999890i | \(-0.495277\pi\) |
0.999890 | − | 0.0148362i | \(-0.00472269\pi\) | |||||||
\(422\) | 3.21537 | + | 17.7622i | 0.156522 | + | 0.864650i | ||||
\(423\) | 12.4575i | 0.605704i | ||||||||
\(424\) | 14.8345 | + | 24.9026i | 0.720425 | + | 1.20938i | ||||
\(425\) | 0.0175844i | 0.000852967i | ||||||||
\(426\) | 12.9220 | − | 2.33918i | 0.626072 | − | 0.113334i | ||||
\(427\) | −4.77528 | + | 4.77528i | −0.231092 | + | 0.231092i | ||||
\(428\) | −15.7024 | − | 7.14889i | −0.759005 | − | 0.345555i | ||||
\(429\) | 41.7514 | + | 41.7514i | 2.01577 | + | 2.01577i | ||||
\(430\) | 5.57850 | − | 8.04460i | 0.269019 | − | 0.387945i | ||||
\(431\) | 5.86431 | 0.282474 | 0.141237 | − | 0.989976i | \(-0.454892\pi\) | ||||
0.141237 | + | 0.989976i | \(0.454892\pi\) | |||||||
\(432\) | 0.635312 | − | 9.18439i | 0.0305665 | − | 0.441884i | ||||
\(433\) | −1.10457 | −0.0530822 | −0.0265411 | − | 0.999648i | \(-0.508449\pi\) | ||||
−0.0265411 | + | 0.999648i | \(0.508449\pi\) | |||||||
\(434\) | −5.60305 | + | 8.07999i | −0.268955 | + | 0.387852i | ||||
\(435\) | −11.8792 | − | 11.8792i | −0.569562 | − | 0.569562i | ||||
\(436\) | −9.73856 | + | 21.3906i | −0.466393 | + | 1.02442i | ||||
\(437\) | −6.56598 | + | 6.56598i | −0.314093 | + | 0.314093i | ||||
\(438\) | −25.8102 | + | 4.67225i | −1.23326 | + | 0.223249i | ||||
\(439\) | 20.5982i | 0.983100i | 0.870849 | + | 0.491550i | \(0.163569\pi\) | ||||
−0.870849 | + | 0.491550i | \(0.836431\pi\) | |||||||
\(440\) | 23.0979 | + | 5.85229i | 1.10115 | + | 0.278997i | ||||
\(441\) | 8.17836i | 0.389446i | ||||||||
\(442\) | 1.31686 | + | 7.27452i | 0.0626365 | + | 0.346014i | ||||
\(443\) | 25.4691 | − | 25.4691i | 1.21007 | − | 1.21007i | 0.239071 | − | 0.971002i | \(-0.423157\pi\) |
0.971002 | − | 0.239071i | \(-0.0768429\pi\) | |||||||
\(444\) | 10.0817 | + | 26.9339i | 0.478456 | + | 1.27823i | ||||
\(445\) | −19.7531 | − | 19.7531i | −0.936388 | − | 0.936388i | ||||
\(446\) | 11.8206 | + | 8.19695i | 0.559721 | + | 0.388137i | ||||
\(447\) | −12.9291 | −0.611523 | ||||||||
\(448\) | 6.42291 | − | 11.8613i | 0.303454 | − | 0.560396i | ||||
\(449\) | −18.4747 | −0.871874 | −0.435937 | − | 0.899977i | \(-0.643583\pi\) | ||||
−0.435937 | + | 0.899977i | \(0.643583\pi\) | |||||||
\(450\) | −0.0539524 | − | 0.0374131i | −0.00254334 | − | 0.00176367i | ||||
\(451\) | −6.24702 | − | 6.24702i | −0.294161 | − | 0.294161i | ||||
\(452\) | −6.06062 | − | 16.1914i | −0.285068 | − | 0.761577i | ||||
\(453\) | −27.3675 | + | 27.3675i | −1.28584 | + | 1.28584i | ||||
\(454\) | −3.63741 | − | 20.0936i | −0.170712 | − | 0.943040i | ||||
\(455\) | − | 26.3865i | − | 1.23702i | ||||||
\(456\) | −6.11076 | − | 1.54828i | −0.286163 | − | 0.0725047i | ||||
\(457\) | − | 0.505944i | − | 0.0236671i | −0.999930 | − | 0.0118335i | \(-0.996233\pi\) | ||
0.999930 | − | 0.0118335i | \(-0.00376682\pi\) | |||||||
\(458\) | 31.2832 | − | 5.66298i | 1.46177 | − | 0.264614i | ||||
\(459\) | −1.21272 | + | 1.21272i | −0.0566048 | + | 0.0566048i | ||||
\(460\) | −17.1661 | + | 37.7050i | −0.800373 | + | 1.75801i | ||||
\(461\) | 8.39485 | + | 8.39485i | 0.390987 | + | 0.390987i | 0.875039 | − | 0.484052i | \(-0.160835\pi\) |
−0.484052 | + | 0.875039i | \(0.660835\pi\) | |||||||
\(462\) | −11.4365 | + | 16.4922i | −0.532073 | + | 0.767287i | ||||
\(463\) | −6.77587 | −0.314901 | −0.157451 | − | 0.987527i | \(-0.550327\pi\) | ||||
−0.157451 | + | 0.987527i | \(0.550327\pi\) | |||||||
\(464\) | 13.4836 | + | 0.932700i | 0.625960 | + | 0.0432995i | ||||
\(465\) | 20.5018 | 0.950750 | ||||||||
\(466\) | 11.6083 | − | 16.7401i | 0.537746 | − | 0.775468i | ||||
\(467\) | 12.2684 | + | 12.2684i | 0.567716 | + | 0.567716i | 0.931488 | − | 0.363772i | \(-0.118511\pi\) |
−0.363772 | + | 0.931488i | \(0.618511\pi\) | |||||||
\(468\) | −25.1215 | − | 11.4372i | −1.16124 | − | 0.528682i | ||||
\(469\) | 5.21571 | − | 5.21571i | 0.240839 | − | 0.240839i | ||||
\(470\) | −19.6574 | + | 3.55845i | −0.906730 | + | 0.164139i | ||||
\(471\) | 14.7782i | 0.680942i | ||||||||
\(472\) | 16.5922 | + | 27.8533i | 0.763718 | + | 1.28205i | ||||
\(473\) | − | 11.7185i | − | 0.538816i | ||||||
\(474\) | −3.11000 | − | 17.1801i | −0.142847 | − | 0.789110i | ||||
\(475\) | 0.0166865 | − | 0.0166865i | 0.000765627 | − | 0.000765627i | ||||
\(476\) | −2.35334 | + | 0.880883i | −0.107865 | + | 0.0403752i | ||||
\(477\) | 14.2563 | + | 14.2563i | 0.652750 | + | 0.652750i | ||||
\(478\) | 5.68815 | + | 3.94443i | 0.260170 | + | 0.180414i | ||||
\(479\) | 4.99002 | 0.228000 | 0.114000 | − | 0.993481i | \(-0.463634\pi\) | ||||
0.114000 | + | 0.993481i | \(0.463634\pi\) | |||||||
\(480\) | −27.9550 | + | 3.08810i | −1.27597 | + | 0.140952i | ||||
\(481\) | −45.2611 | −2.06373 | ||||||||
\(482\) | 15.7678 | + | 10.9341i | 0.718205 | + | 0.498037i | ||||
\(483\) | −24.6741 | − | 24.6741i | −1.12271 | − | 1.12271i | ||||
\(484\) | 6.10884 | − | 2.28662i | 0.277675 | − | 0.103937i | ||||
\(485\) | −5.25287 | + | 5.25287i | −0.238521 | + | 0.238521i | ||||
\(486\) | −4.45428 | − | 24.6061i | −0.202050 | − | 1.11616i | ||||
\(487\) | 9.95097i | 0.450922i | 0.974252 | + | 0.225461i | \(0.0723888\pi\) | ||||
−0.974252 | + | 0.225461i | \(0.927611\pi\) | |||||||
\(488\) | −9.73267 | + | 5.79775i | −0.440577 | + | 0.262452i | ||||
\(489\) | 29.7020i | 1.34317i | ||||||||
\(490\) | −12.9051 | + | 2.33613i | −0.582994 | + | 0.105535i | ||||
\(491\) | 10.1145 | − | 10.1145i | 0.456463 | − | 0.456463i | −0.441030 | − | 0.897493i | \(-0.645387\pi\) |
0.897493 | + | 0.441030i | \(0.145387\pi\) | |||||||
\(492\) | 9.49064 | + | 4.32083i | 0.427871 | + | 0.194798i | ||||
\(493\) | −1.78039 | − | 1.78039i | −0.0801846 | − | 0.0801846i | ||||
\(494\) | 5.65345 | − | 8.15268i | 0.254361 | − | 0.366806i | ||||
\(495\) | 16.5735 | 0.744922 | ||||||||
\(496\) | −12.4403 | + | 10.8306i | −0.558586 | + | 0.486307i | ||||
\(497\) | −7.02482 | −0.315106 | ||||||||
\(498\) | 13.8329 | − | 19.9480i | 0.619867 | − | 0.893893i | ||||
\(499\) | −21.1075 | − | 21.1075i | −0.944903 | − | 0.944903i | 0.0536568 | − | 0.998559i | \(-0.482912\pi\) |
−0.998559 | + | 0.0536568i | \(0.982912\pi\) | |||||||
\(500\) | 9.28693 | − | 20.3986i | 0.415324 | − | 0.912252i | ||||
\(501\) | 3.93025 | − | 3.93025i | 0.175591 | − | 0.175591i | ||||
\(502\) | −32.1164 | + | 5.81382i | −1.43343 | + | 0.259483i | ||||
\(503\) | − | 20.9971i | − | 0.936214i | −0.883672 | − | 0.468107i | \(-0.844936\pi\) | ||
0.883672 | − | 0.468107i | \(-0.155064\pi\) | |||||||
\(504\) | 2.30432 | − | 9.09472i | 0.102642 | − | 0.405111i | ||||
\(505\) | 18.1708i | 0.808590i | ||||||||
\(506\) | 8.83370 | + | 48.7987i | 0.392706 | + | 2.16937i | ||||
\(507\) | 57.0717 | − | 57.0717i | 2.53464 | − | 2.53464i | ||||
\(508\) | −12.9835 | − | 34.6863i | −0.576050 | − | 1.53896i | ||||
\(509\) | 30.7064 | + | 30.7064i | 1.36104 | + | 1.36104i | 0.872595 | + | 0.488444i | \(0.162435\pi\) |
0.488444 | + | 0.872595i | \(0.337565\pi\) | |||||||
\(510\) | 4.30549 | + | 2.98563i | 0.190650 | + | 0.132206i | ||||
\(511\) | 14.0313 | 0.620708 | ||||||||
\(512\) | 15.3314 | − | 16.6417i | 0.677560 | − | 0.735467i | ||||
\(513\) | 2.30159 | 0.101617 | ||||||||
\(514\) | −29.4921 | − | 20.4512i | −1.30084 | − | 0.902064i | ||||
\(515\) | −26.9919 | − | 26.9919i | −1.18941 | − | 1.18941i | ||||
\(516\) | 4.84888 | + | 12.9541i | 0.213460 | + | 0.570273i | ||||
\(517\) | −16.9091 | + | 16.9091i | −0.743663 | + | 0.743663i | ||||
\(518\) | −2.74037 | − | 15.1382i | −0.120405 | − | 0.665136i | ||||
\(519\) | 3.25116i | 0.142710i | ||||||||
\(520\) | 10.8715 | − | 42.9077i | 0.476746 | − | 1.88163i | ||||
\(521\) | − | 6.56275i | − | 0.287519i | −0.989613 | − | 0.143760i | \(-0.954081\pi\) | ||
0.989613 | − | 0.143760i | \(-0.0459192\pi\) | |||||||
\(522\) | 9.25060 | − | 1.67457i | 0.404888 | − | 0.0732941i | ||||
\(523\) | −13.0317 | + | 13.0317i | −0.569837 | + | 0.569837i | −0.932083 | − | 0.362246i | \(-0.882010\pi\) |
0.362246 | + | 0.932083i | \(0.382010\pi\) | |||||||
\(524\) | −8.84991 | + | 19.4387i | −0.386610 | + | 0.849182i | ||||
\(525\) | 0.0627055 | + | 0.0627055i | 0.00273669 | + | 0.00273669i | ||||
\(526\) | −7.83705 | + | 11.3016i | −0.341711 | + | 0.492772i | ||||
\(527\) | 3.07271 | 0.133849 | ||||||||
\(528\) | −25.3921 | + | 22.1065i | −1.10505 | + | 0.962060i | ||||
\(529\) | −63.2241 | −2.74887 | ||||||||
\(530\) | −18.4236 | + | 26.5681i | −0.800269 | + | 1.15405i | ||||
\(531\) | 15.9455 | + | 15.9455i | 0.691976 | + | 0.691976i | ||||
\(532\) | 3.06907 | + | 1.39727i | 0.133061 | + | 0.0605792i | ||||
\(533\) | −11.6048 | + | 11.6048i | −0.502658 | + | 0.502658i | ||||
\(534\) | 38.8390 | − | 7.03075i | 1.68073 | − | 0.304250i | ||||
\(535\) | − | 19.2441i | − | 0.831994i | ||||||
\(536\) | 10.6303 | − | 6.33248i | 0.459160 | − | 0.273522i | ||||
\(537\) | − | 3.08205i | − | 0.133000i | ||||||
\(538\) | −7.00993 | − | 38.7239i | −0.302220 | − | 1.66951i | ||||
\(539\) | −11.1009 | + | 11.1009i | −0.478148 | + | 0.478148i | ||||
\(540\) | 9.61704 | − | 3.59978i | 0.413852 | − | 0.154910i | ||||
\(541\) | 28.8515 | + | 28.8515i | 1.24042 | + | 1.24042i | 0.959826 | + | 0.280595i | \(0.0905318\pi\) |
0.280595 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(542\) | 24.1927 | + | 16.7763i | 1.03917 | + | 0.720606i | ||||
\(543\) | −31.4622 | −1.35017 | ||||||||
\(544\) | −4.18976 | + | 0.462829i | −0.179634 | + | 0.0198436i | ||||
\(545\) | −26.2152 | −1.12294 | ||||||||
\(546\) | 30.6367 | + | 21.2449i | 1.31113 | + | 0.909198i | ||||
\(547\) | 0.123183 | + | 0.123183i | 0.00526694 | + | 0.00526694i | 0.709735 | − | 0.704468i | \(-0.248815\pi\) |
−0.704468 | + | 0.709735i | \(0.748815\pi\) | |||||||
\(548\) | 13.5272 | − | 5.06340i | 0.577854 | − | 0.216298i | ||||
\(549\) | −5.57178 | + | 5.57178i | −0.237798 | + | 0.237798i | ||||
\(550\) | −0.0224495 | − | 0.124015i | −0.000957252 | − | 0.00528801i | ||||
\(551\) | 3.37895i | 0.143948i | ||||||||
\(552\) | −29.9572 | − | 50.2890i | −1.27506 | − | 2.14044i | ||||
\(553\) | 9.33969i | 0.397164i | ||||||||
\(554\) | 39.1227 | − | 7.08211i | 1.66216 | − | 0.300890i | ||||
\(555\) | −22.6822 | + | 22.6822i | −0.962806 | + | 0.962806i | ||||
\(556\) | −5.37410 | − | 2.44668i | −0.227913 | − | 0.103763i | ||||
\(557\) | 4.64693 | + | 4.64693i | 0.196897 | + | 0.196897i | 0.798668 | − | 0.601772i | \(-0.205538\pi\) |
−0.601772 | + | 0.798668i | \(0.705538\pi\) | |||||||
\(558\) | −6.53761 | + | 9.42770i | −0.276759 | + | 0.399106i | ||||
\(559\) | −21.7687 | −0.920720 | ||||||||
\(560\) | 15.0093 | + | 1.03824i | 0.634260 | + | 0.0438737i | ||||
\(561\) | 6.27176 | 0.264794 | ||||||||
\(562\) | −1.11223 | + | 1.60392i | −0.0469168 | + | 0.0676573i | ||||
\(563\) | 0.0253124 | + | 0.0253124i | 0.00106679 | + | 0.00106679i | 0.707640 | − | 0.706573i | \(-0.249760\pi\) |
−0.706573 | + | 0.707640i | \(0.749760\pi\) | |||||||
\(564\) | 11.6954 | − | 25.6888i | 0.492466 | − | 1.08169i | ||||
\(565\) | 13.6354 | − | 13.6354i | 0.573647 | − | 0.573647i | ||||
\(566\) | 4.52770 | − | 0.819618i | 0.190313 | − | 0.0344511i | ||||
\(567\) | 18.6003i | 0.781138i | ||||||||
\(568\) | −11.4232 | − | 2.89429i | −0.479308 | − | 0.121442i | ||||
\(569\) | 35.4165i | 1.48474i | 0.669992 | + | 0.742369i | \(0.266298\pi\) | ||||
−0.669992 | + | 0.742369i | \(0.733702\pi\) | |||||||
\(570\) | −1.25247 | − | 6.91882i | −0.0524601 | − | 0.289798i | ||||
\(571\) | −8.52660 | + | 8.52660i | −0.356827 | + | 0.356827i | −0.862642 | − | 0.505815i | \(-0.831192\pi\) |
0.505815 | + | 0.862642i | \(0.331192\pi\) | |||||||
\(572\) | −18.5744 | − | 49.6228i | −0.776636 | − | 2.07483i | ||||
\(573\) | −11.3163 | − | 11.3163i | −0.472747 | − | 0.472747i | ||||
\(574\) | −4.58399 | − | 3.17876i | −0.191332 | − | 0.132679i | ||||
\(575\) | 0.219126 | 0.00913818 | ||||||||
\(576\) | 7.49422 | − | 13.8398i | 0.312259 | − | 0.576656i | ||||
\(577\) | −17.8216 | −0.741924 | −0.370962 | − | 0.928648i | \(-0.620972\pi\) | ||||
−0.370962 | + | 0.928648i | \(0.620972\pi\) | |||||||
\(578\) | −19.1110 | − | 13.2525i | −0.794913 | − | 0.551230i | ||||
\(579\) | −22.0333 | − | 22.0333i | −0.915674 | − | 0.915674i | ||||
\(580\) | 5.28482 | + | 14.1187i | 0.219440 | + | 0.586249i | ||||
\(581\) | −9.18221 | + | 9.18221i | −0.380942 | + | 0.380942i | ||||
\(582\) | −1.86966 | − | 10.3283i | −0.0774999 | − | 0.428121i | ||||
\(583\) | 38.7015i | 1.60285i | ||||||||
\(584\) | 22.8166 | + | 5.78103i | 0.944160 | + | 0.239221i | ||||
\(585\) | − | 30.7876i | − | 1.27291i | ||||||
\(586\) | −33.9518 | + | 6.14606i | −1.40254 | + | 0.253891i | ||||
\(587\) | 22.0917 | − | 22.0917i | 0.911821 | − | 0.911821i | −0.0845949 | − | 0.996415i | \(-0.526960\pi\) |
0.996415 | + | 0.0845949i | \(0.0269596\pi\) | |||||||
\(588\) | 7.67806 | − | 16.8647i | 0.316638 | − | 0.695490i | ||||
\(589\) | −2.91581 | − | 2.91581i | −0.120144 | − | 0.120144i | ||||
\(590\) | −20.6066 | + | 29.7162i | −0.848360 | + | 1.22340i | ||||
\(591\) | −10.0145 | −0.411941 | ||||||||
\(592\) | 1.78091 | − | 25.7457i | 0.0731949 | − | 1.05814i | ||||
\(593\) | 18.7487 | 0.769917 | 0.384958 | − | 0.922934i | \(-0.374216\pi\) | ||||
0.384958 | + | 0.922934i | \(0.374216\pi\) | |||||||
\(594\) | 7.00451 | − | 10.1010i | 0.287399 | − | 0.414449i | ||||
\(595\) | −1.98185 | − | 1.98185i | −0.0812479 | − | 0.0812479i | ||||
\(596\) | 10.5592 | + | 4.80734i | 0.432523 | + | 0.196916i | ||||
\(597\) | −5.39041 | + | 5.39041i | −0.220615 | + | 0.220615i | ||||
\(598\) | 90.6507 | − | 16.4099i | 3.70698 | − | 0.671050i | ||||
\(599\) | 12.6985i | 0.518846i | 0.965764 | + | 0.259423i | \(0.0835323\pi\) | ||||
−0.965764 | + | 0.259423i | \(0.916468\pi\) | |||||||
\(600\) | 0.0761317 | + | 0.127802i | 0.00310806 | + | 0.00521750i | ||||
\(601\) | 40.7759i | 1.66328i | 0.555312 | + | 0.831642i | \(0.312599\pi\) | ||||
−0.555312 | + | 0.831642i | \(0.687401\pi\) | |||||||
\(602\) | −1.31801 | − | 7.28087i | −0.0537179 | − | 0.296746i | ||||
\(603\) | 6.08567 | − | 6.08567i | 0.247828 | − | 0.247828i | ||||
\(604\) | 32.5271 | − | 12.1753i | 1.32351 | − | 0.495406i | ||||
\(605\) | 5.14452 | + | 5.14452i | 0.209155 | + | 0.209155i | ||||
\(606\) | −21.0977 | − | 14.6301i | −0.857034 | − | 0.594308i | ||||
\(607\) | 23.2677 | 0.944405 | 0.472202 | − | 0.881490i | \(-0.343459\pi\) | ||||
0.472202 | + | 0.881490i | \(0.343459\pi\) | |||||||
\(608\) | 4.41501 | + | 3.53662i | 0.179052 | + | 0.143429i | ||||
\(609\) | −12.6976 | −0.514534 | ||||||||
\(610\) | −10.3836 | − | 7.20048i | −0.420420 | − | 0.291539i | ||||
\(611\) | 31.4112 | + | 31.4112i | 1.27076 | + | 1.27076i | ||||
\(612\) | −2.74586 | + | 1.02781i | −0.110995 | + | 0.0415468i | ||||
\(613\) | 13.5213 | − | 13.5213i | 0.546120 | − | 0.546120i | −0.379196 | − | 0.925316i | \(-0.623799\pi\) |
0.925316 | + | 0.379196i | \(0.123799\pi\) | |||||||
\(614\) | −0.143487 | − | 0.792644i | −0.00579066 | − | 0.0319885i | ||||
\(615\) | 11.6312i | 0.469017i | ||||||||
\(616\) | 15.4725 | − | 9.21693i | 0.623403 | − | 0.371361i | ||||
\(617\) | 20.0366i | 0.806642i | 0.915059 | + | 0.403321i | \(0.132144\pi\) | ||||
−0.915059 | + | 0.403321i | \(0.867856\pi\) | |||||||
\(618\) | 53.0720 | − | 9.60725i | 2.13487 | − | 0.386460i | ||||
\(619\) | 22.2313 | − | 22.2313i | 0.893552 | − | 0.893552i | −0.101304 | − | 0.994856i | \(-0.532301\pi\) |
0.994856 | + | 0.101304i | \(0.0323013\pi\) | |||||||
\(620\) | −16.7440 | − | 7.62309i | −0.672455 | − | 0.306151i | ||||
\(621\) | 15.1122 | + | 15.1122i | 0.606430 | + | 0.606430i | ||||
\(622\) | −12.6721 | + | 18.2741i | −0.508105 | + | 0.732723i | ||||
\(623\) | −21.1141 | −0.845920 | ||||||||
\(624\) | 41.0660 | + | 47.1695i | 1.64395 | + | 1.88829i | ||||
\(625\) | 24.8815 | 0.995258 | ||||||||
\(626\) | 13.8306 | − | 19.9448i | 0.552783 | − | 0.797153i | ||||
\(627\) | −5.95151 | − | 5.95151i | −0.237680 | − | 0.237680i | ||||
\(628\) | 5.49489 | − | 12.0694i | 0.219270 | − | 0.481622i | ||||
\(629\) | −3.39949 | + | 3.39949i | −0.135547 | + | 0.135547i | ||||
\(630\) | 10.2974 | − | 1.86406i | 0.410257 | − | 0.0742660i | ||||
\(631\) | − | 35.8471i | − | 1.42705i | −0.700629 | − | 0.713526i | \(-0.747097\pi\) | ||
0.700629 | − | 0.713526i | \(-0.252903\pi\) | |||||||
\(632\) | −3.84804 | + | 15.1875i | −0.153067 | + | 0.604127i | ||||
\(633\) | − | 28.4475i | − | 1.13069i | ||||||
\(634\) | 0.675841 | + | 3.73345i | 0.0268411 | + | 0.148274i | ||||
\(635\) | 29.2108 | − | 29.2108i | 1.15920 | − | 1.15920i | ||||
\(636\) | −16.0139 | − | 42.7823i | −0.634994 | − | 1.69643i | ||||
\(637\) | 20.6215 | + | 20.6215i | 0.817053 | + | 0.817053i | ||||
\(638\) | 14.8293 | + | 10.2833i | 0.587096 | + | 0.407120i | ||||
\(639\) | −8.19652 | −0.324249 | ||||||||
\(640\) | 23.9793 | + | 7.87230i | 0.947865 | + | 0.311180i | ||||
\(641\) | −35.8583 | −1.41632 | −0.708158 | − | 0.706054i | \(-0.750474\pi\) | ||||
−0.708158 | + | 0.706054i | \(0.750474\pi\) | |||||||
\(642\) | 22.3438 | + | 15.4943i | 0.881840 | + | 0.611509i | ||||
\(643\) | −23.4956 | − | 23.4956i | −0.926574 | − | 0.926574i | 0.0709085 | − | 0.997483i | \(-0.477410\pi\) |
−0.997483 | + | 0.0709085i | \(0.977410\pi\) | |||||||
\(644\) | 10.9770 | + | 29.3259i | 0.432556 | + | 1.15560i | ||||
\(645\) | −10.9092 | + | 10.9092i | −0.429550 | + | 0.429550i | ||||
\(646\) | −0.187713 | − | 1.03696i | −0.00738548 | − | 0.0407985i | ||||
\(647\) | − | 28.2637i | − | 1.11116i | −0.831463 | − | 0.555580i | \(-0.812496\pi\) | ||
0.831463 | − | 0.555580i | \(-0.187504\pi\) | |||||||
\(648\) | −7.66349 | + | 30.2464i | −0.301050 | + | 1.18819i | ||||
\(649\) | 43.2872i | 1.69917i | ||||||||
\(650\) | −0.230376 | + | 0.0417033i | −0.00903607 | + | 0.00163574i | ||||
\(651\) | 10.9572 | − | 10.9572i | 0.429447 | − | 0.429447i | ||||
\(652\) | 11.0439 | − | 24.2578i | 0.432514 | − | 0.950010i | ||||
\(653\) | −24.1245 | − | 24.1245i | −0.944066 | − | 0.944066i | 0.0544504 | − | 0.998516i | \(-0.482659\pi\) |
−0.998516 | + | 0.0544504i | \(0.982659\pi\) | |||||||
\(654\) | 21.1070 | − | 30.4378i | 0.825349 | − | 1.19021i | ||||
\(655\) | −23.8230 | −0.930843 | ||||||||
\(656\) | −6.14447 | − | 7.05771i | −0.239901 | − | 0.275557i | ||||
\(657\) | 16.3717 | 0.638719 | ||||||||
\(658\) | −8.60411 | + | 12.4077i | −0.335423 | + | 0.483704i | ||||
\(659\) | −33.1834 | − | 33.1834i | −1.29264 | − | 1.29264i | −0.933146 | − | 0.359497i | \(-0.882948\pi\) |
−0.359497 | − | 0.933146i | \(-0.617052\pi\) | |||||||
\(660\) | −34.1764 | − | 15.5596i | −1.33032 | − | 0.605657i | ||||
\(661\) | 7.71340 | − | 7.71340i | 0.300017 | − | 0.300017i | −0.541004 | − | 0.841020i | \(-0.681955\pi\) |
0.841020 | + | 0.541004i | \(0.181955\pi\) | |||||||
\(662\) | 7.40881 | − | 1.34117i | 0.287951 | − | 0.0521259i | ||||
\(663\) | − | 11.6507i | − | 0.452476i | ||||||
\(664\) | −18.7146 | + | 11.1483i | −0.726267 | + | 0.432637i | ||||
\(665\) | 3.76130i | 0.145857i | ||||||||
\(666\) | −3.19745 | − | 17.6632i | −0.123899 | − | 0.684436i | ||||
\(667\) | −22.1861 | + | 22.1861i | −0.859049 | + | 0.859049i | ||||
\(668\) | −4.67123 | + | 1.74850i | −0.180735 | + | 0.0676514i | ||||
\(669\) | −16.0298 | − | 16.0298i | −0.619748 | − | 0.619748i | ||||
\(670\) | 11.3413 | + | 7.86459i | 0.438153 | + | 0.303836i | ||||
\(671\) | −15.1257 | −0.583920 | ||||||||
\(672\) | −13.2901 | + | 16.5910i | −0.512678 | + | 0.640012i | ||||
\(673\) | 17.0920 | 0.658848 | 0.329424 | − | 0.944182i | \(-0.393145\pi\) | ||||
0.329424 | + | 0.944182i | \(0.393145\pi\) | |||||||
\(674\) | 1.30026 | + | 0.901663i | 0.0500842 | + | 0.0347307i | ||||
\(675\) | −0.0384053 | − | 0.0384053i | −0.00147822 | − | 0.00147822i | ||||
\(676\) | −67.8315 | + | 25.3902i | −2.60890 | + | 0.976545i | ||||
\(677\) | 33.0966 | − | 33.0966i | 1.27200 | − | 1.27200i | 0.326970 | − | 0.945035i | \(-0.393972\pi\) |
0.945035 | − | 0.326970i | \(-0.106028\pi\) | |||||||
\(678\) | 4.85327 | + | 26.8102i | 0.186389 | + | 1.02964i | ||||
\(679\) | 5.61480i | 0.215476i | ||||||||
\(680\) | −2.40619 | − | 4.03927i | −0.0922733 | − | 0.154899i | ||||
\(681\) | 32.1815i | 1.23320i | ||||||||
\(682\) | −21.6705 | + | 3.92286i | −0.829805 | + | 0.150214i | ||||
\(683\) | −29.7256 | + | 29.7256i | −1.13742 | + | 1.13742i | −0.148508 | + | 0.988911i | \(0.547447\pi\) |
−0.988911 | + | 0.148508i | \(0.952553\pi\) | |||||||
\(684\) | 3.58098 | + | 1.63032i | 0.136922 | + | 0.0623370i | ||||
\(685\) | 11.3919 | + | 11.3919i | 0.435260 | + | 0.435260i | ||||
\(686\) | −15.1601 | + | 21.8619i | −0.578815 | + | 0.834692i | ||||
\(687\) | −50.1024 | −1.91153 | ||||||||
\(688\) | 0.856544 | − | 12.3826i | 0.0326555 | − | 0.472084i | ||||
\(689\) | 71.8936 | 2.73893 | ||||||||
\(690\) | 37.2051 | − | 53.6525i | 1.41638 | − | 2.04251i | ||||
\(691\) | −20.7907 | − | 20.7907i | −0.790915 | − | 0.790915i | 0.190728 | − | 0.981643i | \(-0.438915\pi\) |
−0.981643 | + | 0.190728i | \(0.938915\pi\) | |||||||
\(692\) | 1.20886 | − | 2.65524i | 0.0459540 | − | 0.100937i | ||||
\(693\) | 8.85770 | − | 8.85770i | 0.336476 | − | 0.336476i | ||||
\(694\) | −44.5342 | + | 8.06171i | −1.69049 | + | 0.306018i | ||||
\(695\) | − | 6.58622i | − | 0.249830i | ||||||
\(696\) | −20.6480 | − | 5.23155i | −0.782659 | − | 0.198301i | ||||
\(697\) | 1.74323i | 0.0660295i | ||||||||
\(698\) | −6.59283 | − | 36.4198i | −0.249542 | − | 1.37851i | ||||
\(699\) | −22.7011 | + | 22.7011i | −0.858633 | + | 0.858633i | ||||
\(700\) | −0.0278965 | − | 0.0745274i | −0.00105439 | − | 0.00281687i | ||||
\(701\) | 0.922831 | + | 0.922831i | 0.0348548 | + | 0.0348548i | 0.724319 | − | 0.689465i | \(-0.242154\pi\) |
−0.689465 | + | 0.724319i | \(0.742154\pi\) | |||||||
\(702\) | −18.7641 | − | 13.0119i | −0.708205 | − | 0.491103i | ||||
\(703\) | 6.45181 | 0.243335 | ||||||||
\(704\) | 28.9576 | − | 8.61309i | 1.09138 | − | 0.324618i | ||||
\(705\) | 31.4829 | 1.18571 | ||||||||
\(706\) | −23.5911 | − | 16.3592i | −0.887864 | − | 0.615686i | ||||
\(707\) | 9.71140 | + | 9.71140i | 0.365235 | + | 0.365235i | ||||
\(708\) | −17.9114 | − | 47.8516i | −0.673153 | − | 1.79837i | ||||
\(709\) | 13.2315 | − | 13.2315i | 0.496920 | − | 0.496920i | −0.413558 | − | 0.910478i | \(-0.635714\pi\) |
0.910478 | + | 0.413558i | \(0.135714\pi\) | |||||||
\(710\) | −2.34132 | − | 12.9338i | −0.0878680 | − | 0.485397i | ||||
\(711\) | 10.8975i | 0.408688i | ||||||||
\(712\) | −34.3342 | − | 8.69922i | −1.28673 | − | 0.326017i | ||||
\(713\) | − | 38.2903i | − | 1.43398i | ||||||
\(714\) | 3.89675 | − | 0.705401i | 0.145832 | − | 0.0263990i | ||||
\(715\) | 41.7895 | − | 41.7895i | 1.56284 | − | 1.56284i | ||||
\(716\) | −1.14598 | + | 2.51713i | −0.0428273 | + | 0.0940695i | ||||
\(717\) | −7.71366 | − | 7.71366i | −0.288072 | − | 0.288072i | ||||
\(718\) | 0.738256 | − | 1.06462i | 0.0275515 | − | 0.0397312i | ||||
\(719\) | −8.61798 | −0.321396 | −0.160698 | − | 0.987004i | \(-0.551375\pi\) | ||||
−0.160698 | + | 0.987004i | \(0.551375\pi\) | |||||||
\(720\) | 17.5128 | + | 1.21141i | 0.652664 | + | 0.0451467i | ||||
\(721\) | −28.8517 | −1.07449 | ||||||||
\(722\) | −0.805879 | + | 1.16214i | −0.0299917 | + | 0.0432502i | ||||
\(723\) | −21.3826 | − | 21.3826i | −0.795229 | − | 0.795229i | ||||
\(724\) | 25.6954 | + | 11.6984i | 0.954963 | + | 0.434769i | ||||
\(725\) | 0.0563827 | − | 0.0563827i | 0.00209400 | − | 0.00209400i | ||||
\(726\) | −10.1153 | + | 1.83109i | −0.375412 | + | 0.0679583i | ||||
\(727\) | − | 2.92019i | − | 0.108304i | −0.998533 | − | 0.0541519i | \(-0.982754\pi\) | ||
0.998533 | − | 0.0541519i | \(-0.0172455\pi\) | |||||||
\(728\) | −17.1218 | − | 28.7423i | −0.634576 | − | 1.06526i | ||||
\(729\) | 6.31374i | 0.233842i | ||||||||
\(730\) | 4.67652 | + | 25.8338i | 0.173086 | + | 0.956153i | ||||
\(731\) | −1.63502 | + | 1.63502i | −0.0604733 | + | 0.0604733i | ||||
\(732\) | 16.7206 | − | 6.25872i | 0.618011 | − | 0.231329i | ||||
\(733\) | −17.0882 | − | 17.0882i | −0.631166 | − | 0.631166i | 0.317195 | − | 0.948360i | \(-0.397259\pi\) |
−0.948360 | + | 0.317195i | \(0.897259\pi\) | |||||||
\(734\) | 17.0983 | + | 11.8568i | 0.631111 | + | 0.437642i | ||||
\(735\) | 20.6686 | 0.762371 | ||||||||
\(736\) | 5.76750 | + | 52.2102i | 0.212593 | + | 1.92449i | ||||
\(737\) | 16.5207 | 0.608549 | ||||||||
\(738\) | −5.34858 | − | 3.70896i | −0.196884 | − | 0.136529i | ||||
\(739\) | 10.2614 | + | 10.2614i | 0.377470 | + | 0.377470i | 0.870189 | − | 0.492719i | \(-0.163997\pi\) |
−0.492719 | + | 0.870189i | \(0.663997\pi\) | |||||||
\(740\) | 26.9585 | − | 10.0909i | 0.991015 | − | 0.370949i | ||||
\(741\) | −11.0558 | + | 11.0558i | −0.406145 | + | 0.406145i | ||||
\(742\) | 4.35285 | + | 24.0458i | 0.159798 | + | 0.882751i | ||||
\(743\) | 24.2443i | 0.889436i | 0.895671 | + | 0.444718i | \(0.146696\pi\) | ||||
−0.895671 | + | 0.444718i | \(0.853304\pi\) | |||||||
\(744\) | 22.3323 | − | 13.3033i | 0.818741 | − | 0.487724i | ||||
\(745\) | 12.9409i | 0.474117i | ||||||||
\(746\) | −19.7762 | + | 3.57996i | −0.724059 | + | 0.131071i | ||||
\(747\) | −10.7138 | + | 10.7138i | −0.391996 | + | 0.391996i | ||||
\(748\) | −5.12219 | − | 2.33200i | −0.187286 | − | 0.0852662i | ||||
\(749\) | −10.2850 | − | 10.2850i | −0.375806 | − | 0.375806i | ||||
\(750\) | −20.1281 | + | 29.0262i | −0.734976 | + | 1.05989i | ||||
\(751\) | −38.6250 | −1.40944 | −0.704722 | − | 0.709483i | \(-0.748928\pi\) | ||||
−0.704722 | + | 0.709483i | \(0.748928\pi\) | |||||||
\(752\) | −19.1035 | + | 16.6316i | −0.696632 | + | 0.606491i | ||||
\(753\) | 51.4369 | 1.87447 | ||||||||
\(754\) | 19.1027 | − | 27.5475i | 0.695680 | − | 1.00322i | ||||
\(755\) | 27.3925 | + | 27.3925i | 0.996915 | + | 0.996915i | ||||
\(756\) | 3.21593 | − | 7.06374i | 0.116962 | − | 0.256906i | ||||
\(757\) | −1.87274 | + | 1.87274i | −0.0680660 | + | 0.0680660i | −0.740320 | − | 0.672254i | \(-0.765326\pi\) |
0.672254 | + | 0.740320i | \(0.265326\pi\) | |||||||
\(758\) | −20.6632 | + | 3.74052i | −0.750522 | + | 0.135862i | ||||
\(759\) | − | 78.1549i | − | 2.83684i | ||||||
\(760\) | −1.54969 | + | 6.11634i | −0.0562132 | + | 0.221863i | ||||
\(761\) | 20.5292i | 0.744181i | 0.928196 | + | 0.372091i | \(0.121359\pi\) | ||||
−0.928196 | + | 0.372091i | \(0.878641\pi\) | |||||||
\(762\) | 10.3970 | + | 57.4349i | 0.376645 | + | 2.08065i | ||||
\(763\) | −14.0107 | + | 14.0107i | −0.507222 | + | 0.507222i | ||||
\(764\) | 5.03443 | + | 13.4498i | 0.182139 | + | 0.486597i | ||||
\(765\) | −2.31241 | − | 2.31241i | −0.0836054 | − | 0.0836054i | ||||
\(766\) | 1.43066 | + | 0.992088i | 0.0516919 | + | 0.0358456i | ||||
\(767\) | 80.4123 | 2.90352 | ||||||||
\(768\) | −28.4471 | + | 21.5034i | −1.02650 | + | 0.775938i | ||||
\(769\) | −31.5640 | −1.13823 | −0.569113 | − | 0.822259i | \(-0.692713\pi\) | ||||
−0.569113 | + | 0.822259i | \(0.692713\pi\) | |||||||
\(770\) | 16.5073 | + | 11.4469i | 0.594881 | + | 0.412518i | ||||
\(771\) | 39.9940 | + | 39.9940i | 1.44035 | + | 1.44035i | ||||
\(772\) | 9.80223 | + | 26.1873i | 0.352790 | + | 0.942502i | ||||
\(773\) | −24.0804 | + | 24.0804i | −0.866113 | + | 0.866113i | −0.992040 | − | 0.125927i | \(-0.959810\pi\) |
0.125927 | + | 0.992040i | \(0.459810\pi\) | |||||||
\(774\) | −1.53784 | − | 8.49529i | −0.0552766 | − | 0.305357i | ||||
\(775\) | 0.0973091i | 0.00349545i | ||||||||
\(776\) | −2.31335 | + | 9.13037i | −0.0830445 | + | 0.327761i | ||||
\(777\) | 24.2450i | 0.869786i | ||||||||
\(778\) | 5.41636 | − | 0.980487i | 0.194186 | − | 0.0351522i | ||||
\(779\) | 1.65422 | − | 1.65422i | 0.0592684 | − | 0.0592684i | ||||
\(780\) | −28.9043 | + | 63.4877i | −1.03494 | + | 2.27322i | ||||
\(781\) | −11.1255 | − | 11.1255i | −0.398103 | − | 0.398103i | ||||
\(782\) | 5.57611 | − | 8.04116i | 0.199401 | − | 0.287551i | ||||
\(783\) | 7.77694 | 0.277925 | ||||||||
\(784\) | −12.5414 | + | 10.9186i | −0.447909 | + | 0.389952i | ||||
\(785\) | 14.7917 | 0.527937 | ||||||||
\(786\) | 19.1810 | − | 27.6603i | 0.684162 | − | 0.986611i | ||||
\(787\) | −9.26918 | − | 9.26918i | −0.330410 | − | 0.330410i | 0.522332 | − | 0.852742i | \(-0.325062\pi\) |
−0.852742 | + | 0.522332i | \(0.825062\pi\) | |||||||
\(788\) | 8.17891 | + | 3.72364i | 0.291362 | + | 0.132649i | ||||
\(789\) | 15.3260 | − | 15.3260i | 0.545620 | − | 0.545620i | ||||
\(790\) | −17.1958 | + | 3.11284i | −0.611800 | + | 0.110750i | ||||
\(791\) | − | 14.5749i | − | 0.518225i | ||||||
\(792\) | 18.0532 | − | 10.7543i | 0.641492 | − | 0.382136i | ||||
\(793\) | 28.0981i | 0.997794i | ||||||||
\(794\) | −3.51834 | − | 19.4359i | −0.124861 | − | 0.689753i | ||||
\(795\) | 36.0288 | − | 36.0288i | 1.27781 | − | 1.27781i | ||||
\(796\) | 6.40668 | − | 2.39810i | 0.227079 | − | 0.0849983i | ||||
\(797\) | 3.18216 | + | 3.18216i | 0.112718 | + | 0.112718i | 0.761216 | − | 0.648498i | \(-0.224603\pi\) |
−0.648498 | + | 0.761216i | \(0.724603\pi\) | |||||||
\(798\) | −4.36715 | − | 3.02839i | −0.154595 | − | 0.107204i | ||||
\(799\) | 4.71849 | 0.166928 | ||||||||
\(800\) | −0.0146573 | − | 0.132685i | −0.000518212 | − | 0.00469111i | ||||
\(801\) | −24.6359 | −0.870466 | ||||||||
\(802\) | −13.4191 | − | 9.30541i | −0.473844 | − | 0.328585i | ||||
\(803\) | 22.2220 | + | 22.2220i | 0.784198 | + | 0.784198i | ||||
\(804\) | −18.2628 | + | 6.83597i | −0.644078 | + | 0.241086i | ||||
\(805\) | −24.6966 | + | 24.6966i | −0.870441 | + | 0.870441i | ||||
\(806\) | 7.28727 | + | 40.2560i | 0.256683 | + | 1.41796i | ||||
\(807\) | 62.0194i | 2.18318i | ||||||||
\(808\) | 11.7908 | + | 19.7931i | 0.414798 | + | 0.696320i | ||||
\(809\) | − | 49.6396i | − | 1.74524i | −0.488402 | − | 0.872619i | \(-0.662420\pi\) | ||
0.488402 | − | 0.872619i | \(-0.337580\pi\) | |||||||
\(810\) | −34.2460 | + | 6.19932i | −1.20328 | + | 0.217822i | ||||
\(811\) | 34.5423 | − | 34.5423i | 1.21294 | − | 1.21294i | 0.242891 | − | 0.970053i | \(-0.421904\pi\) |
0.970053 | − | 0.242891i | \(-0.0780959\pi\) | |||||||
\(812\) | 10.3702 | + | 4.72130i | 0.363924 | + | 0.165685i | ||||
\(813\) | −32.8075 | − | 32.8075i | −1.15061 | − | 1.15061i | ||||
\(814\) | 19.6351 | − | 28.3152i | 0.688209 | − | 0.992446i | ||||
\(815\) | 29.7291 | 1.04137 | ||||||||
\(816\) | 6.62723 | + | 0.458425i | 0.231999 | + | 0.0160481i | ||||
\(817\) | 3.10306 | 0.108562 | ||||||||
\(818\) | 29.7279 | − | 42.8697i | 1.03941 | − | 1.49890i | ||||
\(819\) | −16.4545 | − | 16.4545i | −0.574965 | − | 0.574965i | ||||
\(820\) | 4.32478 | − | 9.49931i | 0.151028 | − | 0.331730i | ||||
\(821\) | 29.9868 | − | 29.9868i | 1.04655 | − | 1.04655i | 0.0476858 | − | 0.998862i | \(-0.484815\pi\) |
0.998862 | − | 0.0476858i | \(-0.0151846\pi\) | |||||||
\(822\) | −22.3989 | + | 4.05471i | −0.781250 | + | 0.141424i | ||||
\(823\) | 18.6588i | 0.650404i | 0.945645 | + | 0.325202i | \(0.105432\pi\) | ||||
−0.945645 | + | 0.325202i | \(0.894568\pi\) | |||||||
\(824\) | −46.9164 | − | 11.8872i | −1.63441 | − | 0.414109i | ||||
\(825\) | 0.198619i | 0.00691503i | ||||||||
\(826\) | 4.86863 | + | 26.8950i | 0.169401 | + | 0.935798i | ||||
\(827\) | 33.8005 | − | 33.8005i | 1.17536 | − | 1.17536i | 0.194443 | − | 0.980914i | \(-0.437710\pi\) |
0.980914 | − | 0.194443i | \(-0.0622900\pi\) | |||||||
\(828\) | 12.8080 | + | 34.2173i | 0.445107 | + | 1.18913i | ||||
\(829\) | 15.0301 | + | 15.0301i | 0.522018 | + | 0.522018i | 0.918181 | − | 0.396162i | \(-0.129658\pi\) |
−0.396162 | + | 0.918181i | \(0.629658\pi\) | |||||||
\(830\) | −19.9663 | − | 13.8455i | −0.693039 | − | 0.480586i | ||||
\(831\) | −62.6579 | −2.17358 | ||||||||
\(832\) | −16.0001 | − | 53.7930i | −0.554703 | − | 1.86494i | ||||
\(833\) | 3.09770 | 0.107329 | ||||||||
\(834\) | 7.64709 | + | 5.30285i | 0.264797 | + | 0.183623i | ||||
\(835\) | −3.93385 | − | 3.93385i | −0.136136 | − | 0.136136i | ||||
\(836\) | 2.64772 | + | 7.07355i | 0.0915732 | + | 0.244644i | ||||
\(837\) | −6.71098 | + | 6.71098i | −0.231966 | + | 0.231966i | ||||
\(838\) | 6.37613 | + | 35.2227i | 0.220260 | + | 1.21675i | ||||
\(839\) | 23.2106i | 0.801321i | 0.916227 | + | 0.400660i | \(0.131219\pi\) | ||||
−0.916227 | + | 0.400660i | \(0.868781\pi\) | |||||||
\(840\) | −22.9844 | − | 5.82353i | −0.793037 | − | 0.200931i | ||||
\(841\) | − | 17.5827i | − | 0.606300i | ||||||
\(842\) | 40.9749 | − | 7.41741i | 1.41209 | − | 0.255621i | ||||
\(843\) | 2.17507 | − | 2.17507i | 0.0749133 | − | 0.0749133i | ||||
\(844\) | −10.5775 | + | 23.2333i | −0.364092 | + | 0.799722i | ||||
\(845\) | −57.1238 | − | 57.1238i | −1.96512 | − | 1.96512i | ||||
\(846\) | −10.0392 | + | 14.4773i | −0.345156 | + | 0.497740i | ||||
\(847\) | 5.49899 | 0.188947 | ||||||||
\(848\) | −2.82883 | + | 40.8950i | −0.0971424 | + | 1.40434i | ||||
\(849\) | −7.25145 | −0.248869 | ||||||||
\(850\) | −0.0141709 | + | 0.0204354i | −0.000486057 | + | 0.000700929i | ||||
\(851\) | 42.3624 | + | 42.3624i | 1.45217 | + | 1.45217i | ||||
\(852\) | 16.9022 | + | 7.69512i | 0.579059 | + | 0.263630i | ||||
\(853\) | −7.73580 | + | 7.73580i | −0.264869 | + | 0.264869i | −0.827029 | − | 0.562160i | \(-0.809971\pi\) |
0.562160 | + | 0.827029i | \(0.309971\pi\) | |||||||
\(854\) | −9.39783 | + | 1.70122i | −0.321587 | + | 0.0582147i | ||||
\(855\) | 4.38867i | 0.150089i | ||||||||
\(856\) | −12.4872 | − | 20.9622i | −0.426804 | − | 0.716475i | ||||
\(857\) | − | 35.5955i | − | 1.21592i | −0.793968 | − | 0.607959i | \(-0.791988\pi\) | ||
0.793968 | − | 0.607959i | \(-0.208012\pi\) | |||||||
\(858\) | 14.8742 | + | 82.1673i | 0.507796 | + | 2.80514i | ||||
\(859\) | 15.6464 | − | 15.6464i | 0.533848 | − | 0.533848i | −0.387867 | − | 0.921715i | \(-0.626788\pi\) |
0.921715 | + | 0.387867i | \(0.126788\pi\) | |||||||
\(860\) | 12.9659 | − | 4.85331i | 0.442135 | − | 0.165497i | ||||
\(861\) | 6.21632 | + | 6.21632i | 0.211852 | + | 0.211852i | ||||
\(862\) | 6.81512 | + | 4.72592i | 0.232124 | + | 0.160966i | ||||
\(863\) | 12.0054 | 0.408668 | 0.204334 | − | 0.978901i | \(-0.434497\pi\) | ||||
0.204334 | + | 0.978901i | \(0.434497\pi\) | |||||||
\(864\) | 8.13983 | − | 10.1615i | 0.276923 | − | 0.345702i | ||||
\(865\) | 3.25413 | 0.110644 | ||||||||
\(866\) | −1.28366 | − | 0.890149i | −0.0436205 | − | 0.0302485i | ||||
\(867\) | 25.9163 | + | 25.9163i | 0.880164 | + | 0.880164i | ||||
\(868\) | −13.0230 | + | 4.87467i | −0.442029 | + | 0.165457i | ||||
\(869\) | −14.7917 | + | 14.7917i | −0.501774 | + | 0.501774i | ||||
\(870\) | −4.23202 | − | 23.3784i | −0.143479 | − | 0.792600i | ||||
\(871\) | − | 30.6897i | − | 1.03988i | ||||||
\(872\) | −28.5558 | + | 17.0106i | −0.967020 | + | 0.576053i | ||||
\(873\) | 6.55132i | 0.221729i | ||||||||
\(874\) | −12.9219 | + | 2.33917i | −0.437091 | + | 0.0791236i | ||||
\(875\) | 13.3610 | − | 13.3610i | 0.451683 | − | 0.451683i | ||||
\(876\) | −33.7603 | − | 15.3701i | −1.14065 | − | 0.519309i | ||||
\(877\) | 16.1952 | + | 16.1952i | 0.546872 | + | 0.546872i | 0.925535 | − | 0.378663i | \(-0.123616\pi\) |
−0.378663 | + | 0.925535i | \(0.623616\pi\) | |||||||
\(878\) | −16.5997 | + | 23.9379i | −0.560212 | + | 0.807866i | ||||
\(879\) | 54.3764 | 1.83407 | ||||||||
\(880\) | 22.1267 | + | 25.4153i | 0.745890 | + | 0.856749i | ||||
\(881\) | 27.9754 | 0.942517 | 0.471258 | − | 0.881995i | \(-0.343800\pi\) | ||||
0.471258 | + | 0.881995i | \(0.343800\pi\) | |||||||
\(882\) | −6.59077 | + | 9.50436i | −0.221923 | + | 0.320028i | ||||
\(883\) | −5.09457 | − | 5.09457i | −0.171446 | − | 0.171446i | 0.616169 | − | 0.787614i | \(-0.288684\pi\) |
−0.787614 | + | 0.616169i | \(0.788684\pi\) | |||||||
\(884\) | −4.33202 | + | 9.51521i | −0.145702 | + | 0.320031i | ||||
\(885\) | 40.2979 | − | 40.2979i | 1.35460 | − | 1.35460i | ||||
\(886\) | 50.1235 | − | 9.07352i | 1.68393 | − | 0.304831i | ||||
\(887\) | 5.03188i | 0.168954i | 0.996425 | + | 0.0844769i | \(0.0269219\pi\) | ||||
−0.996425 | + | 0.0844769i | \(0.973078\pi\) | |||||||
\(888\) | −9.98918 | + | 39.4255i | −0.335215 | + | 1.32303i | ||||
\(889\) | − | 31.2235i | − | 1.04720i | ||||||
\(890\) | −7.03717 | − | 38.8744i | −0.235887 | − | 1.30307i | ||||
\(891\) | −29.4581 | + | 29.4581i | −0.986884 | + | 0.986884i | ||||
\(892\) | 7.13137 | + | 19.0519i | 0.238776 | + | 0.637906i | ||||
\(893\) | −4.47755 | − | 4.47755i | −0.149836 | − | 0.149836i | ||||
\(894\) | −15.0253 | − | 10.4193i | −0.502522 | − | 0.348472i | ||||
\(895\) | −3.08486 | −0.103116 | ||||||||
\(896\) | 17.0231 | − | 8.60839i | 0.568702 | − | 0.287586i | ||||
\(897\) | −145.184 | −4.84755 | ||||||||
\(898\) | −21.4701 | − | 14.8884i | −0.716466 | − | 0.496831i | ||||
\(899\) | −9.85237 | − | 9.85237i | −0.328595 | − | 0.328595i | ||||
\(900\) | −0.0325495 | − | 0.0869583i | −0.00108498 | − | 0.00289861i | ||||
\(901\) | 5.39982 | − | 5.39982i | 0.179894 | − | 0.179894i | ||||
\(902\) | −2.22554 | − | 12.2942i | −0.0741024 | − | 0.409353i | ||||
\(903\) | 11.6609i | 0.388050i | ||||||||
\(904\) | 6.00501 | − | 23.7007i | 0.199724 | − | 0.788273i | ||||
\(905\) | 31.4910i | 1.04680i | ||||||||
\(906\) | −53.8596 | + | 9.74983i | −1.78936 | + | 0.323916i | ||||
\(907\) | −21.1793 | + | 21.1793i | −0.703248 | + | 0.703248i | −0.965106 | − | 0.261858i | \(-0.915665\pi\) |
0.261858 | + | 0.965106i | \(0.415665\pi\) | |||||||
\(908\) | 11.9659 | − | 26.2828i | 0.397101 | − | 0.872226i | ||||
\(909\) | 11.3312 | + | 11.3312i | 0.375833 | + | 0.375833i | ||||
\(910\) | 21.2643 | − | 30.6647i | 0.704905 | − | 1.01652i | ||||
\(911\) | −8.55091 | −0.283304 | −0.141652 | − | 0.989916i | \(-0.545241\pi\) | ||||
−0.141652 | + | 0.989916i | \(0.545241\pi\) | |||||||
\(912\) | −5.85381 | − | 6.72384i | −0.193839 | − | 0.222649i | ||||
\(913\) | −29.0846 | −0.962560 | ||||||||
\(914\) | 0.407730 | − | 0.587976i | 0.0134865 | − | 0.0194485i | ||||
\(915\) | 14.0811 | + | 14.0811i | 0.465508 | + | 0.465508i | ||||
\(916\) | 40.9190 | + | 18.6293i | 1.35200 | + | 0.615530i | ||||
\(917\) | −12.7322 | + | 12.7322i | −0.420455 | + | 0.420455i | ||||
\(918\) | −2.38665 | + | 0.432038i | −0.0787710 | + | 0.0142594i | ||||
\(919\) | 5.69492i | 0.187858i | 0.995579 | + | 0.0939291i | \(0.0299427\pi\) | ||||
−0.995579 | + | 0.0939291i | \(0.970057\pi\) | |||||||
\(920\) | −50.3350 | + | 29.9845i | −1.65950 | + | 0.988561i | ||||
\(921\) | 1.26948i | 0.0418308i | ||||||||
\(922\) | 2.99072 | + | 16.5212i | 0.0984941 | + | 0.544097i | ||||
\(923\) | −20.6673 | + | 20.6673i | −0.680272 | + | 0.680272i | ||||
\(924\) | −26.5815 | + | 9.94977i | −0.874466 | + | 0.327323i | ||||
\(925\) | −0.107658 | − | 0.107658i | −0.00353977 | − | 0.00353977i | ||||
\(926\) | −7.87447 | − | 5.46053i | −0.258771 | − | 0.179444i | ||||
\(927\) | −33.6640 | −1.10567 | ||||||||
\(928\) | 14.9181 | + | 11.9501i | 0.489711 | + | 0.392280i | ||||
\(929\) | 49.3534 | 1.61923 | 0.809616 | − | 0.586960i | \(-0.199676\pi\) | ||||
0.809616 | + | 0.586960i | \(0.199676\pi\) | |||||||
\(930\) | 23.8259 | + | 16.5220i | 0.781282 | + | 0.541778i | ||||
\(931\) | −2.93952 | − | 2.93952i | −0.0963388 | − | 0.0963388i | ||||
\(932\) | 26.9809 | − | 10.0993i | 0.883790 | − | 0.330813i | ||||
\(933\) | 24.7813 | − | 24.7813i | 0.811304 | − | 0.811304i | ||||
\(934\) | 4.37071 | + | 24.1445i | 0.143014 | + | 0.790031i | ||||
\(935\) | − | 6.27749i | − | 0.205296i | ||||||
\(936\) | −19.9776 | − | 33.5364i | −0.652989 | − | 1.09617i | ||||
\(937\) | − | 16.8032i | − | 0.548936i | −0.961596 | − | 0.274468i | \(-0.911498\pi\) | ||
0.961596 | − | 0.274468i | \(-0.0885017\pi\) | |||||||
\(938\) | 10.2646 | − | 1.85813i | 0.335151 | − | 0.0606701i | ||||
\(939\) | −27.0469 | + | 27.0469i | −0.882643 | + | 0.882643i | ||||
\(940\) | −25.7123 | − | 11.7061i | −0.838642 | − | 0.381811i | ||||
\(941\) | 29.3410 | + | 29.3410i | 0.956489 | + | 0.956489i | 0.999092 | − | 0.0426033i | \(-0.0135651\pi\) |
−0.0426033 | + | 0.999092i | \(0.513565\pi\) | |||||||
\(942\) | −11.9094 | + | 17.1742i | −0.388030 | + | 0.559566i | ||||
\(943\) | 21.7231 | 0.707401 | ||||||||
\(944\) | −3.16402 | + | 45.7406i | −0.102980 | + | 1.48873i | ||||
\(945\) | 8.65695 | 0.281611 | ||||||||
\(946\) | 9.44367 | − | 13.6184i | 0.307040 | − | 0.442774i | ||||
\(947\) | −6.93921 | − | 6.93921i | −0.225494 | − | 0.225494i | 0.585313 | − | 0.810807i | \(-0.300972\pi\) |
−0.810807 | + | 0.585313i | \(0.800972\pi\) | |||||||
\(948\) | 10.2309 | − | 22.4719i | 0.332283 | − | 0.729854i | ||||
\(949\) | 41.2806 | − | 41.2806i | 1.34003 | − | 1.34003i | ||||
\(950\) | 0.0328392 | − | 0.00594466i | 0.00106544 | − | 0.000192870i | ||||
\(951\) | − | 5.97941i | − | 0.193896i | ||||||
\(952\) | −3.44478 | − | 0.872801i | −0.111646 | − | 0.0282876i | ||||
\(953\) | 58.9341i | 1.90906i | 0.298108 | + | 0.954532i | \(0.403644\pi\) | ||||
−0.298108 | + | 0.954532i | \(0.596356\pi\) | |||||||
\(954\) | 5.07889 | + | 28.0566i | 0.164435 | + | 0.908365i | ||||
\(955\) | −11.3267 | + | 11.3267i | −0.366523 | + | 0.366523i | ||||
\(956\) | 3.43167 | + | 9.16793i | 0.110988 | + | 0.296512i | ||||
\(957\) | −20.1098 | − | 20.1098i | −0.650059 | − | 0.650059i | ||||
\(958\) | 5.79908 | + | 4.02135i | 0.187360 | + | 0.129924i | ||||
\(959\) | 12.1768 | 0.393208 | ||||||||
\(960\) | −34.9762 | − | 18.9396i | −1.12885 | − | 0.611272i | ||||
\(961\) | −13.9961 | −0.451488 | ||||||||
\(962\) | −52.5995 | − | 36.4750i | −1.69588 | − | 1.17600i | ||||
\(963\) | −12.0005 | − | 12.0005i | −0.386711 | − | 0.386711i | ||||
\(964\) | 9.51274 | + | 25.4139i | 0.306385 | + | 0.818527i | ||||
\(965\) | −22.0535 | + | 22.0535i | −0.709926 | + | 0.709926i | ||||
\(966\) | −8.79028 | − | 48.5589i | −0.282823 | − | 1.56236i | ||||
\(967\) | − | 53.4092i | − | 1.71752i | −0.512375 | − | 0.858762i | \(-0.671234\pi\) | ||
0.512375 | − | 0.858762i | \(-0.328766\pi\) | |||||||
\(968\) | 8.94204 | + | 2.26563i | 0.287408 | + | 0.0728202i | ||||
\(969\) | 1.66077i | 0.0533515i | ||||||||
\(970\) | −10.3377 | + | 1.87137i | −0.331925 | + | 0.0600860i | ||||
\(971\) | −26.3394 | + | 26.3394i | −0.845270 | + | 0.845270i | −0.989539 | − | 0.144268i | \(-0.953917\pi\) |
0.144268 | + | 0.989539i | \(0.453917\pi\) | |||||||
\(972\) | 14.6531 | − | 32.1852i | 0.469998 | − | 1.03234i | ||||
\(973\) | −3.52001 | − | 3.52001i | −0.112846 | − | 0.112846i | ||||
\(974\) | −8.01928 | + | 11.5644i | −0.256954 | + | 0.370547i | ||||
\(975\) | 0.368964 | 0.0118163 | ||||||||
\(976\) | −15.9830 | − | 1.10559i | −0.511602 | − | 0.0353891i | ||||
\(977\) | −6.77662 | −0.216803 | −0.108402 | − | 0.994107i | \(-0.534573\pi\) | ||||
−0.108402 | + | 0.994107i | \(0.534573\pi\) | |||||||
\(978\) | −23.9362 | + | 34.5178i | −0.765396 | + | 1.10376i | ||||
\(979\) | −33.4394 | − | 33.4394i | −1.06873 | − | 1.06873i | ||||
\(980\) | −16.8801 | − | 7.68508i | −0.539216 | − | 0.245491i | ||||
\(981\) | −16.3477 | + | 16.3477i | −0.521940 | + | 0.521940i | ||||
\(982\) | 19.9056 | − | 3.60337i | 0.635212 | − | 0.114988i | ||||
\(983\) | 26.6344i | 0.849505i | 0.905310 | + | 0.424752i | \(0.139639\pi\) | ||||
−0.905310 | + | 0.424752i | \(0.860361\pi\) | |||||||
\(984\) | 7.54733 | + | 12.6697i | 0.240600 | + | 0.403895i | ||||
\(985\) | 10.0237i | 0.319380i | ||||||||
\(986\) | −0.634274 | − | 3.50383i | −0.0201994 | − | 0.111585i | ||||
\(987\) | 16.8260 | − | 16.8260i | 0.535579 | − | 0.535579i | ||||
\(988\) | 13.1402 | − | 4.91852i | 0.418044 | − | 0.156479i | ||||
\(989\) | 20.3746 | + | 20.3746i | 0.647874 | + | 0.647874i | ||||
\(990\) | 19.2606 | + | 13.3562i | 0.612143 | + | 0.424488i | ||||
\(991\) | −21.3636 | −0.678638 | −0.339319 | − | 0.940671i | \(-0.610197\pi\) | ||||
−0.339319 | + | 0.940671i | \(0.610197\pi\) | |||||||
\(992\) | −23.1854 | + | 2.56122i | −0.736138 | + | 0.0813189i | ||||
\(993\) | −11.8658 | −0.376549 | ||||||||
\(994\) | −8.16379 | − | 5.66115i | −0.258940 | − | 0.179561i | ||||
\(995\) | 5.39534 | + | 5.39534i | 0.171044 | + | 0.171044i | ||||
\(996\) | 32.1514 | − | 12.0347i | 1.01876 | − | 0.381333i | ||||
\(997\) | −13.3210 | + | 13.3210i | −0.421880 | + | 0.421880i | −0.885851 | − | 0.463970i | \(-0.846424\pi\) |
0.463970 | + | 0.885851i | \(0.346424\pi\) | |||||||
\(998\) | −7.51969 | − | 41.5399i | −0.238032 | − | 1.31492i | ||||
\(999\) | − | 14.8494i | − | 0.469814i |
(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 | 304.2.k.b.77.28 | ✓ | 68 | |
4.3 | odd | 2 | 1216.2.k.b.913.28 | 68 | |||
16.5 | even | 4 | inner | 304.2.k.b.229.28 | yes | 68 | |
16.11 | odd | 4 | 1216.2.k.b.305.28 | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.k.b.77.28 | ✓ | 68 | 1.1 | even | 1 | trivial | |
304.2.k.b.229.28 | yes | 68 | 16.5 | even | 4 | inner | |
1216.2.k.b.305.28 | 68 | 16.11 | odd | 4 | |||
1216.2.k.b.913.28 | 68 | 4.3 | odd | 2 |