Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(311,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.t (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 311.8 | ||
Character | \(\chi\) | \(=\) | 630.311 |
Dual form | 630.2.t.b.551.8 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −1.51897 | + | 0.832312i | −0.876975 | + | 0.480536i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.73162 | − | 0.0386792i | −0.706930 | − | 0.0157907i | ||||
\(7\) | 2.13731 | + | 1.55945i | 0.807829 | + | 0.589417i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.61451 | − | 2.52851i | 0.538171 | − | 0.842836i | ||||
\(10\) | −0.866025 | − | 0.500000i | −0.273861 | − | 0.158114i | ||||
\(11\) | − | 0.450472i | − | 0.135823i | −0.997691 | − | 0.0679113i | \(-0.978367\pi\) | ||
0.997691 | − | 0.0679113i | \(-0.0216335\pi\) | |||||||
\(12\) | −1.48029 | − | 0.899307i | −0.427322 | − | 0.259607i | ||||
\(13\) | 4.26160 | + | 2.46044i | 1.18196 | + | 0.682403i | 0.956466 | − | 0.291843i | \(-0.0942684\pi\) |
0.225490 | + | 0.974246i | \(0.427602\pi\) | |||||||
\(14\) | 1.07124 | + | 2.41918i | 0.286302 | + | 0.646553i | ||||
\(15\) | 1.51897 | − | 0.832312i | 0.392195 | − | 0.214902i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.93285 | + | 6.81190i | −0.953857 | + | 1.65213i | −0.216894 | + | 0.976195i | \(0.569593\pi\) |
−0.736963 | + | 0.675933i | \(0.763741\pi\) | |||||||
\(18\) | 2.66246 | − | 1.38250i | 0.627548 | − | 0.325857i | ||||
\(19\) | −4.75019 | + | 2.74252i | −1.08977 | + | 0.629178i | −0.933515 | − | 0.358539i | \(-0.883275\pi\) |
−0.156254 | + | 0.987717i | \(0.549942\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | −4.54446 | − | 0.589839i | −0.991682 | − | 0.128713i | ||||
\(22\) | 0.225236 | − | 0.390121i | 0.0480205 | − | 0.0831740i | ||||
\(23\) | − | 4.86229i | − | 1.01386i | −0.861988 | − | 0.506929i | \(-0.830781\pi\) | ||
0.861988 | − | 0.506929i | \(-0.169219\pi\) | |||||||
\(24\) | −0.832312 | − | 1.51897i | −0.169895 | − | 0.310058i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.46044 | + | 4.26160i | 0.482532 | + | 0.835769i | ||||
\(27\) | −0.347881 | + | 5.18449i | −0.0669498 | + | 0.997756i | ||||
\(28\) | −0.281867 | + | 2.63069i | −0.0532678 | + | 0.497154i | ||||
\(29\) | −8.05558 | + | 4.65089i | −1.49588 | + | 0.863648i | −0.999989 | − | 0.00473444i | \(-0.998493\pi\) |
−0.495894 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(30\) | 1.73162 | + | 0.0386792i | 0.316149 | + | 0.00706182i | ||||
\(31\) | 0.497185 | − | 0.287050i | 0.0892970 | − | 0.0515557i | −0.454687 | − | 0.890652i | \(-0.650249\pi\) |
0.543984 | + | 0.839096i | \(0.316915\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0.374934 | + | 0.684252i | 0.0652676 | + | 0.119113i | ||||
\(34\) | −6.81190 | + | 3.93285i | −1.16823 | + | 0.674479i | ||||
\(35\) | −2.13731 | − | 1.55945i | −0.361272 | − | 0.263595i | ||||
\(36\) | 2.99701 | + | 0.133955i | 0.499501 | + | 0.0223259i | ||||
\(37\) | −0.721812 | − | 1.25022i | −0.118665 | − | 0.205534i | 0.800574 | − | 0.599234i | \(-0.204528\pi\) |
−0.919239 | + | 0.393700i | \(0.871195\pi\) | |||||||
\(38\) | −5.48505 | −0.889792 | ||||||||
\(39\) | −8.52108 | − | 0.190335i | −1.36446 | − | 0.0304781i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 0.956724 | − | 1.65709i | 0.149415 | − | 0.258795i | −0.781596 | − | 0.623785i | \(-0.785594\pi\) |
0.931011 | + | 0.364990i | \(0.118928\pi\) | |||||||
\(42\) | −3.64070 | − | 2.78304i | −0.561772 | − | 0.429433i | ||||
\(43\) | −0.459119 | − | 0.795218i | −0.0700151 | − | 0.121270i | 0.828893 | − | 0.559408i | \(-0.188971\pi\) |
−0.898908 | + | 0.438138i | \(0.855638\pi\) | |||||||
\(44\) | 0.390121 | − | 0.225236i | 0.0588129 | − | 0.0339556i | ||||
\(45\) | −1.61451 | + | 2.52851i | −0.240677 | + | 0.376928i | ||||
\(46\) | 2.43115 | − | 4.21087i | 0.358453 | − | 0.620858i | ||||
\(47\) | 3.71305 | − | 6.43119i | 0.541604 | − | 0.938085i | −0.457209 | − | 0.889359i | \(-0.651151\pi\) |
0.998812 | − | 0.0487254i | \(-0.0155159\pi\) | |||||||
\(48\) | 0.0386792 | − | 1.73162i | 0.00558286 | − | 0.249938i | ||||
\(49\) | 2.13623 | + | 6.66607i | 0.305175 | + | 0.952296i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 0.304239 | − | 13.6204i | 0.0426020 | − | 1.90724i | ||||
\(52\) | 4.92088i | 0.682403i | ||||||||
\(53\) | 8.30591 | + | 4.79542i | 1.14090 | + | 0.658701i | 0.946654 | − | 0.322251i | \(-0.104439\pi\) |
0.194250 | + | 0.980952i | \(0.437773\pi\) | |||||||
\(54\) | −2.89352 | + | 4.31596i | −0.393758 | + | 0.587328i | ||||
\(55\) | 0.450472i | 0.0607417i | ||||||||
\(56\) | −1.55945 | + | 2.13731i | −0.208390 | + | 0.285611i | ||||
\(57\) | 4.93274 | − | 8.11944i | 0.653357 | − | 1.07545i | ||||
\(58\) | −9.30178 | −1.22138 | ||||||||
\(59\) | 4.43278 | + | 7.67779i | 0.577098 | + | 0.999564i | 0.995810 | + | 0.0914445i | \(0.0291484\pi\) |
−0.418712 | + | 0.908119i | \(0.637518\pi\) | |||||||
\(60\) | 1.48029 | + | 0.899307i | 0.191104 | + | 0.116100i | ||||
\(61\) | 8.54152 | + | 4.93145i | 1.09363 | + | 0.631407i | 0.934540 | − | 0.355857i | \(-0.115811\pi\) |
0.159089 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(62\) | 0.574100 | 0.0729107 | ||||||||
\(63\) | 7.39380 | − | 2.88646i | 0.931532 | − | 0.363660i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.26160 | − | 2.46044i | −0.528587 | − | 0.305180i | ||||
\(66\) | −0.0174239 | + | 0.780047i | −0.00214473 | + | 0.0960171i | ||||
\(67\) | 2.32102 | + | 4.02013i | 0.283558 | + | 0.491137i | 0.972258 | − | 0.233909i | \(-0.0751518\pi\) |
−0.688700 | + | 0.725046i | \(0.741818\pi\) | |||||||
\(68\) | −7.86570 | −0.953857 | ||||||||
\(69\) | 4.04694 | + | 7.38565i | 0.487195 | + | 0.889128i | ||||
\(70\) | −1.07124 | − | 2.41918i | −0.128038 | − | 0.289147i | ||||
\(71\) | − | 3.88571i | − | 0.461149i | −0.973055 | − | 0.230575i | \(-0.925939\pi\) | ||
0.973055 | − | 0.230575i | \(-0.0740606\pi\) | |||||||
\(72\) | 2.52851 | + | 1.61451i | 0.297987 | + | 0.190272i | ||||
\(73\) | 4.91339 | + | 2.83675i | 0.575069 | + | 0.332016i | 0.759171 | − | 0.650891i | \(-0.225604\pi\) |
−0.184102 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(74\) | − | 1.44362i | − | 0.167818i | ||||||
\(75\) | −1.51897 | + | 0.832312i | −0.175395 | + | 0.0961071i | ||||
\(76\) | −4.75019 | − | 2.74252i | −0.544884 | − | 0.314589i | ||||
\(77\) | 0.702489 | − | 0.962801i | 0.0800561 | − | 0.109721i | ||||
\(78\) | −7.28430 | − | 4.42538i | −0.824785 | − | 0.501075i | ||||
\(79\) | 1.00320 | − | 1.73760i | 0.112869 | − | 0.195495i | −0.804057 | − | 0.594552i | \(-0.797329\pi\) |
0.916926 | + | 0.399058i | \(0.130663\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −3.78670 | − | 8.16461i | −0.420744 | − | 0.907179i | ||||
\(82\) | 1.65709 | − | 0.956724i | 0.182995 | − | 0.105652i | ||||
\(83\) | −4.76689 | − | 8.25650i | −0.523234 | − | 0.906268i | −0.999634 | − | 0.0270398i | \(-0.991392\pi\) |
0.476400 | − | 0.879229i | \(-0.341941\pi\) | |||||||
\(84\) | −1.76141 | − | 4.23053i | −0.192186 | − | 0.461589i | ||||
\(85\) | 3.93285 | − | 6.81190i | 0.426578 | − | 0.738854i | ||||
\(86\) | − | 0.918239i | − | 0.0990162i | ||||||
\(87\) | 8.36515 | − | 13.7693i | 0.896838 | − | 1.47622i | ||||
\(88\) | 0.450472 | 0.0480205 | ||||||||
\(89\) | −1.98445 | − | 3.43716i | −0.210351 | − | 0.364339i | 0.741473 | − | 0.670982i | \(-0.234127\pi\) |
−0.951824 | + | 0.306644i | \(0.900794\pi\) | |||||||
\(90\) | −2.66246 | + | 1.38250i | −0.280648 | + | 0.145728i | ||||
\(91\) | 5.27146 | + | 11.9045i | 0.552599 | + | 1.24793i | ||||
\(92\) | 4.21087 | − | 2.43115i | 0.439013 | − | 0.253464i | ||||
\(93\) | −0.516292 | + | 0.849832i | −0.0535369 | + | 0.0881235i | ||||
\(94\) | 6.43119 | − | 3.71305i | 0.663326 | − | 0.382972i | ||||
\(95\) | 4.75019 | − | 2.74252i | 0.487359 | − | 0.281377i | ||||
\(96\) | 0.899307 | − | 1.48029i | 0.0917851 | − | 0.151081i | ||||
\(97\) | −8.69468 | + | 5.01988i | −0.882811 | + | 0.509691i | −0.871584 | − | 0.490246i | \(-0.836907\pi\) |
−0.0112270 | + | 0.999937i | \(0.503574\pi\) | |||||||
\(98\) | −1.48301 | + | 6.84110i | −0.149807 | + | 0.691056i | ||||
\(99\) | −1.13902 | − | 0.727293i | −0.114476 | − | 0.0730957i | ||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −5.49909 | −0.547180 | −0.273590 | − | 0.961846i | \(-0.588211\pi\) | ||||
−0.273590 | + | 0.961846i | \(0.588211\pi\) | |||||||
\(102\) | 7.07368 | − | 11.6435i | 0.700399 | − | 1.15288i | ||||
\(103\) | − | 15.5075i | − | 1.52800i | −0.645216 | − | 0.764000i | \(-0.723233\pi\) | ||
0.645216 | − | 0.764000i | \(-0.276767\pi\) | |||||||
\(104\) | −2.46044 | + | 4.26160i | −0.241266 | + | 0.417885i | ||||
\(105\) | 4.54446 | + | 0.589839i | 0.443494 | + | 0.0575623i | ||||
\(106\) | 4.79542 | + | 8.30591i | 0.465772 | + | 0.806741i | ||||
\(107\) | 8.60043 | − | 4.96546i | 0.831435 | − | 0.480029i | −0.0229088 | − | 0.999738i | \(-0.507293\pi\) |
0.854344 | + | 0.519708i | \(0.173959\pi\) | |||||||
\(108\) | −4.66384 | + | 2.29097i | −0.448779 | + | 0.220449i | ||||
\(109\) | 2.22823 | − | 3.85941i | 0.213426 | − | 0.369665i | −0.739359 | − | 0.673312i | \(-0.764871\pi\) |
0.952784 | + | 0.303647i | \(0.0982045\pi\) | |||||||
\(110\) | −0.225236 | + | 0.390121i | −0.0214754 | + | 0.0371965i | ||||
\(111\) | 2.13698 | + | 1.29826i | 0.202833 | + | 0.123225i | ||||
\(112\) | −2.41918 | + | 1.07124i | −0.228591 | + | 0.101223i | ||||
\(113\) | 17.4964 | + | 10.1015i | 1.64592 | + | 0.950271i | 0.978671 | + | 0.205435i | \(0.0658610\pi\) |
0.667247 | + | 0.744836i | \(0.267472\pi\) | |||||||
\(114\) | 8.33160 | − | 4.56527i | 0.780326 | − | 0.427577i | ||||
\(115\) | 4.86229i | 0.453411i | ||||||||
\(116\) | −8.05558 | − | 4.65089i | −0.747942 | − | 0.431824i | ||||
\(117\) | 13.1016 | − | 6.80309i | 1.21125 | − | 0.628946i | ||||
\(118\) | 8.86555i | 0.816140i | ||||||||
\(119\) | −19.0286 | + | 8.42608i | −1.74435 | + | 0.772418i | ||||
\(120\) | 0.832312 | + | 1.51897i | 0.0759794 | + | 0.138662i | ||||
\(121\) | 10.7971 | 0.981552 | ||||||||
\(122\) | 4.93145 | + | 8.54152i | 0.446472 | + | 0.773313i | ||||
\(123\) | −0.0740106 | + | 3.31336i | −0.00667331 | + | 0.298756i | ||||
\(124\) | 0.497185 | + | 0.287050i | 0.0446485 | + | 0.0257778i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 7.84645 | + | 1.19715i | 0.699018 | + | 0.106651i | ||||
\(127\) | 3.08808 | 0.274023 | 0.137012 | − | 0.990569i | \(-0.456250\pi\) | ||||
0.137012 | + | 0.990569i | \(0.456250\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 1.35926 | + | 0.825778i | 0.119676 | + | 0.0727057i | ||||
\(130\) | −2.46044 | − | 4.26160i | −0.215795 | − | 0.373767i | ||||
\(131\) | −15.7084 | −1.37245 | −0.686227 | − | 0.727388i | \(-0.740734\pi\) | ||||
−0.686227 | + | 0.727388i | \(0.740734\pi\) | |||||||
\(132\) | −0.405113 | + | 0.666828i | −0.0352605 | + | 0.0580399i | ||||
\(133\) | −14.4295 | − | 1.54605i | −1.25120 | − | 0.134060i | ||||
\(134\) | 4.64204i | 0.401012i | ||||||||
\(135\) | 0.347881 | − | 5.18449i | 0.0299409 | − | 0.446210i | ||||
\(136\) | −6.81190 | − | 3.93285i | −0.584116 | − | 0.337239i | ||||
\(137\) | − | 13.0632i | − | 1.11606i | −0.829821 | − | 0.558030i | \(-0.811557\pi\) | ||
0.829821 | − | 0.558030i | \(-0.188443\pi\) | |||||||
\(138\) | −0.188069 | + | 8.41963i | −0.0160095 | + | 0.716727i | ||||
\(139\) | −0.567606 | − | 0.327707i | −0.0481437 | − | 0.0277958i | 0.475735 | − | 0.879589i | \(-0.342182\pi\) |
−0.523879 | + | 0.851793i | \(0.675515\pi\) | |||||||
\(140\) | 0.281867 | − | 2.63069i | 0.0238221 | − | 0.222334i | ||||
\(141\) | −0.287235 | + | 12.8592i | −0.0241896 | + | 1.08294i | ||||
\(142\) | 1.94286 | − | 3.36513i | 0.163041 | − | 0.282395i | ||||
\(143\) | 1.10836 | − | 1.91973i | 0.0926857 | − | 0.160536i | ||||
\(144\) | 1.38250 | + | 2.66246i | 0.115208 | + | 0.221872i | ||||
\(145\) | 8.05558 | − | 4.65089i | 0.668979 | − | 0.386235i | ||||
\(146\) | 2.83675 | + | 4.91339i | 0.234771 | + | 0.406635i | ||||
\(147\) | −8.79311 | − | 8.34753i | −0.725244 | − | 0.688492i | ||||
\(148\) | 0.721812 | − | 1.25022i | 0.0593326 | − | 0.102767i | ||||
\(149\) | − | 4.62313i | − | 0.378741i | −0.981906 | − | 0.189371i | \(-0.939355\pi\) | ||
0.981906 | − | 0.189371i | \(-0.0606448\pi\) | |||||||
\(150\) | −1.73162 | − | 0.0386792i | −0.141386 | − | 0.00315814i | ||||
\(151\) | 12.3019 | 1.00112 | 0.500559 | − | 0.865703i | \(-0.333128\pi\) | ||||
0.500559 | + | 0.865703i | \(0.333128\pi\) | |||||||
\(152\) | −2.74252 | − | 4.75019i | −0.222448 | − | 0.385291i | ||||
\(153\) | 10.8743 | + | 20.9421i | 0.879135 | + | 1.69307i | ||||
\(154\) | 1.08977 | − | 0.482566i | 0.0878165 | − | 0.0388862i | ||||
\(155\) | −0.497185 | + | 0.287050i | −0.0399349 | + | 0.0230564i | ||||
\(156\) | −4.09570 | − | 7.47464i | −0.327919 | − | 0.598450i | ||||
\(157\) | 16.6593 | − | 9.61826i | 1.32956 | − | 0.767620i | 0.344326 | − | 0.938850i | \(-0.388107\pi\) |
0.985231 | + | 0.171230i | \(0.0547740\pi\) | |||||||
\(158\) | 1.73760 | − | 1.00320i | 0.138236 | − | 0.0798104i | ||||
\(159\) | −16.6077 | − | 0.370966i | −1.31707 | − | 0.0294195i | ||||
\(160\) | 0.866025 | − | 0.500000i | 0.0684653 | − | 0.0395285i | ||||
\(161\) | 7.58250 | − | 10.3922i | 0.597585 | − | 0.819024i | ||||
\(162\) | 0.802930 | − | 8.96411i | 0.0630841 | − | 0.704287i | ||||
\(163\) | 3.11468 | + | 5.39478i | 0.243960 | + | 0.422551i | 0.961839 | − | 0.273617i | \(-0.0882200\pi\) |
−0.717879 | + | 0.696168i | \(0.754887\pi\) | |||||||
\(164\) | 1.91345 | 0.149415 | ||||||||
\(165\) | −0.374934 | − | 0.684252i | −0.0291885 | − | 0.0532689i | ||||
\(166\) | − | 9.53378i | − | 0.739965i | ||||||
\(167\) | −3.60660 | + | 6.24681i | −0.279087 | + | 0.483393i | −0.971158 | − | 0.238437i | \(-0.923365\pi\) |
0.692071 | + | 0.721829i | \(0.256698\pi\) | |||||||
\(168\) | 0.589839 | − | 4.54446i | 0.0455070 | − | 0.350612i | ||||
\(169\) | 5.60751 | + | 9.71249i | 0.431347 | + | 0.747114i | ||||
\(170\) | 6.81190 | − | 3.93285i | 0.522449 | − | 0.301636i | ||||
\(171\) | −0.734751 | + | 16.4387i | −0.0561878 | + | 1.25710i | ||||
\(172\) | 0.459119 | − | 0.795218i | 0.0350075 | − | 0.0606348i | ||||
\(173\) | 7.80001 | − | 13.5100i | 0.593024 | − | 1.02715i | −0.400798 | − | 0.916166i | \(-0.631267\pi\) |
0.993822 | − | 0.110982i | \(-0.0353994\pi\) | |||||||
\(174\) | 14.1291 | − | 7.74198i | 1.07112 | − | 0.586918i | ||||
\(175\) | 2.13731 | + | 1.55945i | 0.161566 | + | 0.117883i | ||||
\(176\) | 0.390121 | + | 0.225236i | 0.0294064 | + | 0.0169778i | ||||
\(177\) | −13.1236 | − | 7.97285i | −0.986427 | − | 0.599276i | ||||
\(178\) | − | 3.96890i | − | 0.297481i | ||||||
\(179\) | −3.30274 | − | 1.90684i | −0.246858 | − | 0.142524i | 0.371466 | − | 0.928446i | \(-0.378855\pi\) |
−0.618325 | + | 0.785923i | \(0.712188\pi\) | |||||||
\(180\) | −2.99701 | − | 0.133955i | −0.223384 | − | 0.00998443i | ||||
\(181\) | − | 4.59480i | − | 0.341529i | −0.985312 | − | 0.170764i | \(-0.945376\pi\) | ||
0.985312 | − | 0.170764i | \(-0.0546237\pi\) | |||||||
\(182\) | −1.38703 | + | 12.9453i | −0.102814 | + | 0.959571i | ||||
\(183\) | −17.0788 | − | 0.381489i | −1.26250 | − | 0.0282005i | ||||
\(184\) | 4.86229 | 0.358453 | ||||||||
\(185\) | 0.721812 | + | 1.25022i | 0.0530687 | + | 0.0919177i | ||||
\(186\) | −0.872038 | + | 0.477830i | −0.0639409 | + | 0.0350362i | ||||
\(187\) | 3.06857 | + | 1.77164i | 0.224396 | + | 0.129555i | ||||
\(188\) | 7.42609 | 0.541604 | ||||||||
\(189\) | −8.82849 | + | 10.5384i | −0.642178 | + | 0.766555i | ||||
\(190\) | 5.48505 | 0.397927 | ||||||||
\(191\) | −21.7317 | − | 12.5468i | −1.57245 | − | 0.907855i | −0.995868 | − | 0.0908162i | \(-0.971052\pi\) |
−0.576583 | − | 0.817039i | \(-0.695614\pi\) | |||||||
\(192\) | 1.51897 | − | 0.832312i | 0.109622 | − | 0.0600670i | ||||
\(193\) | 8.95240 | + | 15.5060i | 0.644408 | + | 1.11615i | 0.984438 | + | 0.175733i | \(0.0562295\pi\) |
−0.340030 | + | 0.940415i | \(0.610437\pi\) | |||||||
\(194\) | −10.0398 | −0.720812 | ||||||||
\(195\) | 8.52108 | + | 0.190335i | 0.610207 | + | 0.0136302i | ||||
\(196\) | −4.70487 | + | 5.18306i | −0.336062 | + | 0.370219i | ||||
\(197\) | 12.6523i | 0.901439i | 0.892666 | + | 0.450720i | \(0.148833\pi\) | ||||
−0.892666 | + | 0.450720i | \(0.851167\pi\) | |||||||
\(198\) | −0.622776 | − | 1.19937i | −0.0442588 | − | 0.0852352i | ||||
\(199\) | −18.2922 | − | 10.5610i | −1.29670 | − | 0.748648i | −0.316865 | − | 0.948471i | \(-0.602630\pi\) |
−0.979832 | + | 0.199823i | \(0.935963\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −6.87155 | − | 4.17462i | −0.484682 | − | 0.294455i | ||||
\(202\) | −4.76235 | − | 2.74955i | −0.335078 | − | 0.193457i | ||||
\(203\) | −24.4701 | − | 2.62186i | −1.71747 | − | 0.184019i | ||||
\(204\) | 11.9477 | − | 6.54672i | 0.836509 | − | 0.458362i | ||||
\(205\) | −0.956724 | + | 1.65709i | −0.0668205 | + | 0.115736i | ||||
\(206\) | 7.75376 | − | 13.4299i | 0.540230 | − | 0.935705i | ||||
\(207\) | −12.2943 | − | 7.85023i | −0.854515 | − | 0.545629i | ||||
\(208\) | −4.26160 | + | 2.46044i | −0.295489 | + | 0.170601i | ||||
\(209\) | 1.23543 | + | 2.13983i | 0.0854566 | + | 0.148015i | ||||
\(210\) | 3.64070 | + | 2.78304i | 0.251232 | + | 0.192048i | ||||
\(211\) | 10.0132 | − | 17.3434i | 0.689338 | − | 1.19397i | −0.282714 | − | 0.959204i | \(-0.591235\pi\) |
0.972052 | − | 0.234764i | \(-0.0754318\pi\) | |||||||
\(212\) | 9.59084i | 0.658701i | ||||||||
\(213\) | 3.23413 | + | 5.90226i | 0.221599 | + | 0.404416i | ||||
\(214\) | 9.93092 | 0.678864 | ||||||||
\(215\) | 0.459119 | + | 0.795218i | 0.0313117 | + | 0.0542334i | ||||
\(216\) | −5.18449 | − | 0.347881i | −0.352760 | − | 0.0236703i | ||||
\(217\) | 1.51028 | + | 0.161819i | 0.102525 | + | 0.0109850i | ||||
\(218\) | 3.85941 | − | 2.22823i | 0.261392 | − | 0.150915i | ||||
\(219\) | −9.82433 | − | 0.219446i | −0.663867 | − | 0.0148288i | ||||
\(220\) | −0.390121 | + | 0.225236i | −0.0263019 | + | 0.0151854i | ||||
\(221\) | −33.5205 | + | 19.3531i | −2.25483 | + | 1.30183i | ||||
\(222\) | 1.20155 | + | 2.19282i | 0.0806425 | + | 0.147172i | ||||
\(223\) | 2.43988 | − | 1.40867i | 0.163387 | − | 0.0943313i | −0.416077 | − | 0.909329i | \(-0.636595\pi\) |
0.579464 | + | 0.814998i | \(0.303262\pi\) | |||||||
\(224\) | −2.63069 | − | 0.281867i | −0.175771 | − | 0.0188330i | ||||
\(225\) | 1.61451 | − | 2.52851i | 0.107634 | − | 0.168567i | ||||
\(226\) | 10.1015 | + | 17.4964i | 0.671943 | + | 1.16384i | ||||
\(227\) | −2.59017 | −0.171915 | −0.0859577 | − | 0.996299i | \(-0.527395\pi\) | ||||
−0.0859577 | + | 0.996299i | \(0.527395\pi\) | |||||||
\(228\) | 9.49801 | + | 0.212157i | 0.629021 | + | 0.0140505i | ||||
\(229\) | 21.5183i | 1.42197i | 0.703206 | + | 0.710986i | \(0.251751\pi\) | ||||
−0.703206 | + | 0.710986i | \(0.748249\pi\) | |||||||
\(230\) | −2.43115 | + | 4.21087i | −0.160305 | + | 0.277656i | ||||
\(231\) | −0.265706 | + | 2.04715i | −0.0174822 | + | 0.134693i | ||||
\(232\) | −4.65089 | − | 8.05558i | −0.305346 | − | 0.528875i | ||||
\(233\) | −2.79452 | + | 1.61342i | −0.183075 | + | 0.105699i | −0.588737 | − | 0.808325i | \(-0.700375\pi\) |
0.405661 | + | 0.914023i | \(0.367041\pi\) | |||||||
\(234\) | 14.7479 | + | 0.659177i | 0.964101 | + | 0.0430918i | ||||
\(235\) | −3.71305 | + | 6.43119i | −0.242212 | + | 0.419524i | ||||
\(236\) | −4.43278 | + | 7.67779i | −0.288549 | + | 0.499782i | ||||
\(237\) | −0.0776060 | + | 3.47432i | −0.00504105 | + | 0.225682i | ||||
\(238\) | −20.6923 | − | 2.21708i | −1.34128 | − | 0.143712i | ||||
\(239\) | 13.9417 | + | 8.04923i | 0.901812 | + | 0.520661i | 0.877788 | − | 0.479050i | \(-0.159019\pi\) |
0.0240242 | + | 0.999711i | \(0.492352\pi\) | |||||||
\(240\) | −0.0386792 | + | 1.73162i | −0.00249673 | + | 0.111776i | ||||
\(241\) | − | 25.6376i | − | 1.65147i | −0.564061 | − | 0.825733i | \(-0.690762\pi\) | ||
0.564061 | − | 0.825733i | \(-0.309238\pi\) | |||||||
\(242\) | 9.35054 | + | 5.39854i | 0.601076 | + | 0.347031i | ||||
\(243\) | 12.5474 | + | 9.25005i | 0.804914 | + | 0.593391i | ||||
\(244\) | 9.86290i | 0.631407i | ||||||||
\(245\) | −2.13623 | − | 6.66607i | −0.136479 | − | 0.425880i | ||||
\(246\) | −1.72078 | + | 2.83245i | −0.109713 | + | 0.180590i | ||||
\(247\) | −26.9912 | −1.71741 | ||||||||
\(248\) | 0.287050 | + | 0.497185i | 0.0182277 | + | 0.0315713i | ||||
\(249\) | 14.1127 | + | 8.57379i | 0.894358 | + | 0.543342i | ||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | 12.7547 | 0.805068 | 0.402534 | − | 0.915405i | \(-0.368129\pi\) | ||||
0.402534 | + | 0.915405i | \(0.368129\pi\) | |||||||
\(252\) | 6.19665 | + | 4.95999i | 0.390352 | + | 0.312450i | ||||
\(253\) | −2.19033 | −0.137705 | ||||||||
\(254\) | 2.67436 | + | 1.54404i | 0.167804 | + | 0.0968818i | ||||
\(255\) | −0.304239 | + | 13.6204i | −0.0190522 | + | 0.852943i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 27.0776 | 1.68906 | 0.844528 | − | 0.535512i | \(-0.179881\pi\) | ||||
0.844528 | + | 0.535512i | \(0.179881\pi\) | |||||||
\(258\) | 0.764261 | + | 1.39477i | 0.0475808 | + | 0.0868348i | ||||
\(259\) | 0.406909 | − | 3.79773i | 0.0252841 | − | 0.235980i | ||||
\(260\) | − | 4.92088i | − | 0.305180i | ||||||
\(261\) | −1.24602 | + | 27.8775i | −0.0771268 | + | 1.72557i | ||||
\(262\) | −13.6039 | − | 7.85422i | −0.840453 | − | 0.485235i | ||||
\(263\) | 13.3334i | 0.822172i | 0.911597 | + | 0.411086i | \(0.134850\pi\) | ||||
−0.911597 | + | 0.411086i | \(0.865150\pi\) | |||||||
\(264\) | −0.684252 | + | 0.374934i | −0.0421128 | + | 0.0230756i | ||||
\(265\) | −8.30591 | − | 4.79542i | −0.510228 | − | 0.294580i | ||||
\(266\) | −11.7233 | − | 8.55366i | −0.718800 | − | 0.524459i | ||||
\(267\) | 5.87510 | + | 3.56925i | 0.359550 | + | 0.218435i | ||||
\(268\) | −2.32102 | + | 4.02013i | −0.141779 | + | 0.245568i | ||||
\(269\) | −7.58415 | + | 13.1361i | −0.462414 | + | 0.800924i | −0.999081 | − | 0.0428702i | \(-0.986350\pi\) |
0.536667 | + | 0.843794i | \(0.319683\pi\) | |||||||
\(270\) | 2.89352 | − | 4.31596i | 0.176094 | − | 0.262661i | ||||
\(271\) | 22.7711 | − | 13.1469i | 1.38325 | − | 0.798617i | 0.390703 | − | 0.920517i | \(-0.372232\pi\) |
0.992542 | + | 0.121900i | \(0.0388986\pi\) | |||||||
\(272\) | −3.93285 | − | 6.81190i | −0.238464 | − | 0.413032i | ||||
\(273\) | −17.9154 | − | 13.6950i | −1.08429 | − | 0.828860i | ||||
\(274\) | 6.53158 | − | 11.3130i | 0.394587 | − | 0.683445i | ||||
\(275\) | − | 0.450472i | − | 0.0271645i | ||||||
\(276\) | −4.37269 | + | 7.19758i | −0.263205 | + | 0.433244i | ||||
\(277\) | 23.2800 | 1.39876 | 0.699381 | − | 0.714749i | \(-0.253459\pi\) | ||||
0.699381 | + | 0.714749i | \(0.253459\pi\) | |||||||
\(278\) | −0.327707 | − | 0.567606i | −0.0196546 | − | 0.0340427i | ||||
\(279\) | 0.0769037 | − | 1.72058i | 0.00460410 | − | 0.103009i | ||||
\(280\) | 1.55945 | − | 2.13731i | 0.0931950 | − | 0.127729i | ||||
\(281\) | −3.40387 | + | 1.96523i | −0.203058 | + | 0.117236i | −0.598081 | − | 0.801436i | \(-0.704070\pi\) |
0.395023 | + | 0.918671i | \(0.370737\pi\) | |||||||
\(282\) | −6.67833 | + | 10.9927i | −0.397689 | + | 0.654608i | ||||
\(283\) | −25.0227 | + | 14.4469i | −1.48745 | + | 0.858778i | −0.999898 | − | 0.0143172i | \(-0.995443\pi\) |
−0.487550 | + | 0.873095i | \(0.662109\pi\) | |||||||
\(284\) | 3.36513 | − | 1.94286i | 0.199683 | − | 0.115287i | ||||
\(285\) | −4.93274 | + | 8.11944i | −0.292190 | + | 0.480954i | ||||
\(286\) | 1.91973 | − | 1.10836i | 0.113516 | − | 0.0655387i | ||||
\(287\) | 4.62898 | − | 2.04977i | 0.273240 | − | 0.120994i | ||||
\(288\) | −0.133955 | + | 2.99701i | −0.00789339 | + | 0.176600i | ||||
\(289\) | −22.4347 | − | 38.8580i | −1.31969 | − | 2.28576i | ||||
\(290\) | 9.30178 | 0.546219 | ||||||||
\(291\) | 9.02882 | − | 14.8617i | 0.529279 | − | 0.871209i | ||||
\(292\) | 5.67350i | 0.332016i | ||||||||
\(293\) | 2.16359 | − | 3.74744i | 0.126398 | − | 0.218928i | −0.795880 | − | 0.605454i | \(-0.792992\pi\) |
0.922279 | + | 0.386526i | \(0.126325\pi\) | |||||||
\(294\) | −3.44129 | − | 11.6257i | −0.200700 | − | 0.678026i | ||||
\(295\) | −4.43278 | − | 7.67779i | −0.258086 | − | 0.447018i | ||||
\(296\) | 1.25022 | − | 0.721812i | 0.0726673 | − | 0.0419545i | ||||
\(297\) | 2.33547 | + | 0.156711i | 0.135518 | + | 0.00909329i | ||||
\(298\) | 2.31156 | − | 4.00375i | 0.133905 | − | 0.231931i | ||||
\(299\) | 11.9634 | − | 20.7212i | 0.691859 | − | 1.19834i | ||||
\(300\) | −1.48029 | − | 0.899307i | −0.0854644 | − | 0.0519215i | ||||
\(301\) | 0.258821 | − | 2.41561i | 0.0149182 | − | 0.139233i | ||||
\(302\) | 10.6538 | + | 6.15097i | 0.613057 | + | 0.353948i | ||||
\(303\) | 8.35293 | − | 4.57696i | 0.479864 | − | 0.262940i | ||||
\(304\) | − | 5.48505i | − | 0.314589i | ||||||
\(305\) | −8.54152 | − | 4.93145i | −0.489086 | − | 0.282374i | ||||
\(306\) | −1.05365 | + | 23.5736i | −0.0602333 | + | 1.34761i | ||||
\(307\) | − | 0.419882i | − | 0.0239639i | −0.999928 | − | 0.0119820i | \(-0.996186\pi\) | ||
0.999928 | − | 0.0119820i | \(-0.00381407\pi\) | |||||||
\(308\) | 1.18506 | + | 0.126973i | 0.0675248 | + | 0.00723496i | ||||
\(309\) | 12.9071 | + | 23.5554i | 0.734259 | + | 1.34002i | ||||
\(310\) | −0.574100 | −0.0326067 | ||||||||
\(311\) | −3.14218 | − | 5.44241i | −0.178177 | − | 0.308611i | 0.763079 | − | 0.646305i | \(-0.223686\pi\) |
−0.941256 | + | 0.337694i | \(0.890353\pi\) | |||||||
\(312\) | 0.190335 | − | 8.52108i | 0.0107756 | − | 0.482411i | ||||
\(313\) | −4.92258 | − | 2.84206i | −0.278241 | − | 0.160642i | 0.354386 | − | 0.935099i | \(-0.384690\pi\) |
−0.632627 | + | 0.774457i | \(0.718023\pi\) | |||||||
\(314\) | 19.2365 | 1.08558 | ||||||||
\(315\) | −7.39380 | + | 2.88646i | −0.416594 | + | 0.162634i | ||||
\(316\) | 2.00640 | 0.112869 | ||||||||
\(317\) | −8.68744 | − | 5.01570i | −0.487935 | − | 0.281710i | 0.235782 | − | 0.971806i | \(-0.424235\pi\) |
−0.723718 | + | 0.690096i | \(0.757568\pi\) | |||||||
\(318\) | −14.1972 | − | 8.62510i | −0.796139 | − | 0.483672i | ||||
\(319\) | 2.09510 | + | 3.62881i | 0.117303 | + | 0.203175i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −8.93094 | + | 14.7006i | −0.498477 | + | 0.820508i | ||||
\(322\) | 11.7628 | − | 5.20870i | 0.655513 | − | 0.290269i | ||||
\(323\) | − | 43.1438i | − | 2.40058i | ||||||
\(324\) | 5.17741 | − | 7.36168i | 0.287634 | − | 0.408982i | ||||
\(325\) | 4.26160 | + | 2.46044i | 0.236391 | + | 0.136481i | ||||
\(326\) | 6.22935i | 0.345012i | ||||||||
\(327\) | −0.172372 | + | 7.71690i | −0.00953222 | + | 0.426745i | ||||
\(328\) | 1.65709 | + | 0.956724i | 0.0914977 | + | 0.0528262i | ||||
\(329\) | 17.9651 | − | 7.95515i | 0.990446 | − | 0.438582i | ||||
\(330\) | 0.0174239 | − | 0.780047i | 0.000959155 | − | 0.0429401i | ||||
\(331\) | −15.8516 | + | 27.4558i | −0.871282 | + | 1.50910i | −0.0106106 | + | 0.999944i | \(0.503378\pi\) |
−0.860671 | + | 0.509161i | \(0.829956\pi\) | |||||||
\(332\) | 4.76689 | − | 8.25650i | 0.261617 | − | 0.453134i | ||||
\(333\) | −4.32655 | − | 0.193381i | −0.237094 | − | 0.0105972i | ||||
\(334\) | −6.24681 | + | 3.60660i | −0.341810 | + | 0.197344i | ||||
\(335\) | −2.32102 | − | 4.02013i | −0.126811 | − | 0.219643i | ||||
\(336\) | 2.78304 | − | 3.64070i | 0.151827 | − | 0.198616i | ||||
\(337\) | −7.09612 | + | 12.2908i | −0.386550 | + | 0.669525i | −0.991983 | − | 0.126372i | \(-0.959667\pi\) |
0.605433 | + | 0.795897i | \(0.293000\pi\) | |||||||
\(338\) | 11.2150i | 0.610016i | ||||||||
\(339\) | −34.9840 | − | 0.781437i | −1.90007 | − | 0.0424419i | ||||
\(340\) | 7.86570 | 0.426578 | ||||||||
\(341\) | −0.129308 | − | 0.223968i | −0.00700242 | − | 0.0121286i | ||||
\(342\) | −8.85568 | + | 13.8690i | −0.478860 | + | 0.749949i | ||||
\(343\) | −5.82962 | + | 17.5788i | −0.314770 | + | 0.949168i | ||||
\(344\) | 0.795218 | − | 0.459119i | 0.0428753 | − | 0.0247541i | ||||
\(345\) | −4.04694 | − | 7.38565i | −0.217880 | − | 0.397630i | ||||
\(346\) | 13.5100 | − | 7.80001i | 0.726303 | − | 0.419331i | ||||
\(347\) | 0.634656 | − | 0.366419i | 0.0340701 | − | 0.0196704i | −0.482868 | − | 0.875693i | \(-0.660405\pi\) |
0.516938 | + | 0.856023i | \(0.327072\pi\) | |||||||
\(348\) | 16.1071 | + | 0.359785i | 0.863433 | + | 0.0192865i | ||||
\(349\) | −23.1243 | + | 13.3508i | −1.23782 | + | 0.714653i | −0.968647 | − | 0.248440i | \(-0.920082\pi\) |
−0.269169 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(350\) | 1.07124 | + | 2.41918i | 0.0572604 | + | 0.129311i | ||||
\(351\) | −14.2387 | + | 21.2383i | −0.760003 | + | 1.13362i | ||||
\(352\) | 0.225236 | + | 0.390121i | 0.0120051 | + | 0.0207935i | ||||
\(353\) | 6.00317 | 0.319516 | 0.159758 | − | 0.987156i | \(-0.448929\pi\) | ||||
0.159758 | + | 0.987156i | \(0.448929\pi\) | |||||||
\(354\) | −7.37891 | − | 13.4665i | −0.392185 | − | 0.715735i | ||||
\(355\) | 3.88571i | 0.206232i | ||||||||
\(356\) | 1.98445 | − | 3.43716i | 0.105176 | − | 0.182169i | ||||
\(357\) | 21.8906 | − | 28.6366i | 1.15857 | − | 1.51561i | ||||
\(358\) | −1.90684 | − | 3.30274i | −0.100780 | − | 0.174555i | ||||
\(359\) | 25.3873 | − | 14.6574i | 1.33989 | − | 0.773587i | 0.353101 | − | 0.935585i | \(-0.385127\pi\) |
0.986791 | + | 0.161998i | \(0.0517938\pi\) | |||||||
\(360\) | −2.52851 | − | 1.61451i | −0.133264 | − | 0.0850923i | ||||
\(361\) | 5.54288 | − | 9.60055i | 0.291730 | − | 0.505292i | ||||
\(362\) | 2.29740 | − | 3.97921i | 0.120749 | − | 0.209143i | ||||
\(363\) | −16.4004 | + | 8.98654i | −0.860797 | + | 0.471671i | ||||
\(364\) | −7.67386 | + | 10.5175i | −0.402220 | + | 0.551265i | ||||
\(365\) | −4.91339 | − | 2.83675i | −0.257179 | − | 0.148482i | ||||
\(366\) | −14.5999 | − | 8.86977i | −0.763150 | − | 0.463630i | ||||
\(367\) | − | 20.0340i | − | 1.04576i | −0.852405 | − | 0.522882i | \(-0.824857\pi\) | ||
0.852405 | − | 0.522882i | \(-0.175143\pi\) | |||||||
\(368\) | 4.21087 | + | 2.43115i | 0.219507 | + | 0.126732i | ||||
\(369\) | −2.64533 | − | 5.09448i | −0.137710 | − | 0.265208i | ||||
\(370\) | 1.44362i | 0.0750505i | ||||||||
\(371\) | 10.2741 | + | 23.2020i | 0.533406 | + | 1.20459i | ||||
\(372\) | −0.994122 | − | 0.0222057i | −0.0515428 | − | 0.00115131i | ||||
\(373\) | −6.86717 | −0.355568 | −0.177784 | − | 0.984069i | \(-0.556893\pi\) | ||||
−0.177784 | + | 0.984069i | \(0.556893\pi\) | |||||||
\(374\) | 1.77164 | + | 3.06857i | 0.0916094 | + | 0.158672i | ||||
\(375\) | 1.51897 | − | 0.832312i | 0.0784390 | − | 0.0429804i | ||||
\(376\) | 6.43119 | + | 3.71305i | 0.331663 | + | 0.191486i | ||||
\(377\) | −45.7729 | −2.35742 | ||||||||
\(378\) | −12.9149 | + | 4.71227i | −0.664271 | + | 0.242373i | ||||
\(379\) | 0.682216 | 0.0350431 | 0.0175216 | − | 0.999846i | \(-0.494422\pi\) | ||||
0.0175216 | + | 0.999846i | \(0.494422\pi\) | |||||||
\(380\) | 4.75019 | + | 2.74252i | 0.243680 | + | 0.140689i | ||||
\(381\) | −4.69069 | + | 2.57025i | −0.240312 | + | 0.131678i | ||||
\(382\) | −12.5468 | − | 21.7317i | −0.641950 | − | 1.11189i | ||||
\(383\) | 31.6323 | 1.61634 | 0.808168 | − | 0.588952i | \(-0.200459\pi\) | ||||
0.808168 | + | 0.588952i | \(0.200459\pi\) | |||||||
\(384\) | 1.73162 | + | 0.0386792i | 0.0883663 | + | 0.00197384i | ||||
\(385\) | −0.702489 | + | 0.962801i | −0.0358022 | + | 0.0490689i | ||||
\(386\) | 17.9048i | 0.911331i | ||||||||
\(387\) | −2.75197 | − | 0.123003i | −0.139890 | − | 0.00625259i | ||||
\(388\) | −8.69468 | − | 5.01988i | −0.441406 | − | 0.254846i | ||||
\(389\) | 28.0321i | 1.42128i | 0.703554 | + | 0.710641i | \(0.251595\pi\) | ||||
−0.703554 | + | 0.710641i | \(0.748405\pi\) | |||||||
\(390\) | 7.28430 | + | 4.42538i | 0.368855 | + | 0.224088i | ||||
\(391\) | 33.1214 | + | 19.1227i | 1.67502 | + | 0.967075i | ||||
\(392\) | −6.66607 | + | 2.13623i | −0.336688 | + | 0.107896i | ||||
\(393\) | 23.8606 | − | 13.0743i | 1.20361 | − | 0.659513i | ||||
\(394\) | −6.32615 | + | 10.9572i | −0.318707 | + | 0.552017i | ||||
\(395\) | −1.00320 | + | 1.73760i | −0.0504765 | + | 0.0874279i | ||||
\(396\) | 0.0603431 | − | 1.35007i | 0.00303236 | − | 0.0678435i | ||||
\(397\) | −25.3210 | + | 14.6191i | −1.27083 | + | 0.733711i | −0.975143 | − | 0.221575i | \(-0.928880\pi\) |
−0.295682 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(398\) | −10.5610 | − | 18.2922i | −0.529374 | − | 0.916903i | ||||
\(399\) | 23.2047 | − | 9.66144i | 1.16169 | − | 0.483677i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 11.5694i | 0.577750i | 0.957367 | + | 0.288875i | \(0.0932812\pi\) | ||||
−0.957367 | + | 0.288875i | \(0.906719\pi\) | |||||||
\(402\) | −3.86363 | − | 7.05111i | −0.192700 | − | 0.351677i | ||||
\(403\) | 2.82507 | 0.140727 | ||||||||
\(404\) | −2.74955 | − | 4.76235i | −0.136795 | − | 0.236936i | ||||
\(405\) | 3.78670 | + | 8.16461i | 0.188163 | + | 0.405703i | ||||
\(406\) | −19.8808 | − | 14.5057i | −0.986669 | − | 0.719904i | ||||
\(407\) | −0.563188 | + | 0.325157i | −0.0279162 | + | 0.0161174i | ||||
\(408\) | 13.6204 | + | 0.304239i | 0.674310 | + | 0.0150621i | ||||
\(409\) | −1.79921 | + | 1.03878i | −0.0889653 | + | 0.0513641i | −0.543823 | − | 0.839200i | \(-0.683024\pi\) |
0.454857 | + | 0.890564i | \(0.349690\pi\) | |||||||
\(410\) | −1.65709 | + | 0.956724i | −0.0818380 | + | 0.0472492i | ||||
\(411\) | 10.8726 | + | 19.8425i | 0.536307 | + | 0.978757i | ||||
\(412\) | 13.4299 | − | 7.75376i | 0.661644 | − | 0.382000i | ||||
\(413\) | −2.49890 | + | 23.3226i | −0.122963 | + | 1.14763i | ||||
\(414\) | −6.72209 | − | 12.9457i | −0.330373 | − | 0.636245i | ||||
\(415\) | 4.76689 | + | 8.25650i | 0.233998 | + | 0.405296i | ||||
\(416\) | −4.92088 | −0.241266 | ||||||||
\(417\) | 1.13493 | + | 0.0253509i | 0.0555777 | + | 0.00124144i | ||||
\(418\) | 2.47086i | 0.120854i | ||||||||
\(419\) | −3.15211 | + | 5.45962i | −0.153991 | + | 0.266720i | −0.932691 | − | 0.360676i | \(-0.882546\pi\) |
0.778700 | + | 0.627396i | \(0.215879\pi\) | |||||||
\(420\) | 1.76141 | + | 4.23053i | 0.0859482 | + | 0.206429i | ||||
\(421\) | −1.30121 | − | 2.25376i | −0.0634172 | − | 0.109842i | 0.832574 | − | 0.553914i | \(-0.186867\pi\) |
−0.895991 | + | 0.444073i | \(0.853533\pi\) | |||||||
\(422\) | 17.3434 | − | 10.0132i | 0.844263 | − | 0.487436i | ||||
\(423\) | −10.2665 | − | 19.7717i | −0.499176 | − | 0.961333i | ||||
\(424\) | −4.79542 | + | 8.30591i | −0.232886 | + | 0.403371i | ||||
\(425\) | −3.93285 | + | 6.81190i | −0.190771 | + | 0.330426i | ||||
\(426\) | −0.150296 | + | 6.72857i | −0.00728187 | + | 0.326000i | ||||
\(427\) | 10.5656 | + | 23.8601i | 0.511303 | + | 1.15467i | ||||
\(428\) | 8.60043 | + | 4.96546i | 0.415717 | + | 0.240015i | ||||
\(429\) | −0.0857409 | + | 3.83851i | −0.00413961 | + | 0.185325i | ||||
\(430\) | 0.918239i | 0.0442814i | ||||||||
\(431\) | −8.46126 | − | 4.88511i | −0.407564 | − | 0.235307i | 0.282178 | − | 0.959362i | \(-0.408943\pi\) |
−0.689743 | + | 0.724055i | \(0.742276\pi\) | |||||||
\(432\) | −4.31596 | − | 2.89352i | −0.207652 | − | 0.139215i | ||||
\(433\) | − | 34.4543i | − | 1.65577i | −0.560898 | − | 0.827885i | \(-0.689544\pi\) | ||
0.560898 | − | 0.827885i | \(-0.310456\pi\) | |||||||
\(434\) | 1.22703 | + | 0.895280i | 0.0588994 | + | 0.0429748i | ||||
\(435\) | −8.36515 | + | 13.7693i | −0.401078 | + | 0.660187i | ||||
\(436\) | 4.45646 | 0.213426 | ||||||||
\(437\) | 13.3349 | + | 23.0968i | 0.637897 | + | 1.10487i | ||||
\(438\) | −8.39840 | − | 5.10221i | −0.401291 | − | 0.243793i | ||||
\(439\) | −17.9508 | − | 10.3639i | −0.856745 | − | 0.494642i | 0.00617595 | − | 0.999981i | \(-0.498034\pi\) |
−0.862921 | + | 0.505339i | \(0.831367\pi\) | |||||||
\(440\) | −0.450472 | −0.0214754 | ||||||||
\(441\) | 20.3042 | + | 5.36099i | 0.966866 | + | 0.255285i | ||||
\(442\) | −38.7061 | −1.84106 | ||||||||
\(443\) | 8.25856 | + | 4.76808i | 0.392376 | + | 0.226538i | 0.683189 | − | 0.730241i | \(-0.260592\pi\) |
−0.290813 | + | 0.956780i | \(0.593926\pi\) | |||||||
\(444\) | −0.0558382 | + | 2.49981i | −0.00264997 | + | 0.118636i | ||||
\(445\) | 1.98445 | + | 3.43716i | 0.0940719 | + | 0.162937i | ||||
\(446\) | 2.81733 | 0.133405 | ||||||||
\(447\) | 3.84789 | + | 7.02237i | 0.181999 | + | 0.332147i | ||||
\(448\) | −2.13731 | − | 1.55945i | −0.100979 | − | 0.0736771i | ||||
\(449\) | − | 2.23000i | − | 0.105240i | −0.998615 | − | 0.0526200i | \(-0.983243\pi\) | ||
0.998615 | − | 0.0526200i | \(-0.0167572\pi\) | |||||||
\(450\) | 2.66246 | − | 1.38250i | 0.125510 | − | 0.0651715i | ||||
\(451\) | −0.746475 | − | 0.430978i | −0.0351501 | − | 0.0202939i | ||||
\(452\) | 20.2030i | 0.950271i | ||||||||
\(453\) | −18.6862 | + | 10.2390i | −0.877955 | + | 0.481073i | ||||
\(454\) | −2.24315 | − | 1.29508i | −0.105276 | − | 0.0607813i | ||||
\(455\) | −5.27146 | − | 11.9045i | −0.247130 | − | 0.558091i | ||||
\(456\) | 8.11944 | + | 4.93274i | 0.380228 | + | 0.230997i | ||||
\(457\) | −6.43820 | + | 11.1513i | −0.301166 | + | 0.521635i | −0.976400 | − | 0.215968i | \(-0.930709\pi\) |
0.675234 | + | 0.737603i | \(0.264043\pi\) | |||||||
\(458\) | −10.7592 | + | 18.6354i | −0.502743 | + | 0.870776i | ||||
\(459\) | −33.9481 | − | 22.7596i | −1.58456 | − | 1.06233i | ||||
\(460\) | −4.21087 | + | 2.43115i | −0.196333 | + | 0.113353i | ||||
\(461\) | 1.56738 | + | 2.71478i | 0.0730000 | + | 0.126440i | 0.900215 | − | 0.435446i | \(-0.143409\pi\) |
−0.827215 | + | 0.561886i | \(0.810076\pi\) | |||||||
\(462\) | −1.25368 | + | 1.64003i | −0.0583267 | + | 0.0763012i | ||||
\(463\) | −7.25355 | + | 12.5635i | −0.337101 | + | 0.583877i | −0.983886 | − | 0.178796i | \(-0.942780\pi\) |
0.646785 | + | 0.762672i | \(0.276113\pi\) | |||||||
\(464\) | − | 9.30178i | − | 0.431824i | ||||||
\(465\) | 0.516292 | − | 0.849832i | 0.0239425 | − | 0.0394100i | ||||
\(466\) | −3.22684 | −0.149480 | ||||||||
\(467\) | 4.83041 | + | 8.36651i | 0.223525 | + | 0.387156i | 0.955876 | − | 0.293771i | \(-0.0949104\pi\) |
−0.732351 | + | 0.680927i | \(0.761577\pi\) | |||||||
\(468\) | 12.4425 | + | 7.94482i | 0.575153 | + | 0.367249i | ||||
\(469\) | −1.30844 | + | 12.2118i | −0.0604180 | + | 0.563888i | ||||
\(470\) | −6.43119 | + | 3.71305i | −0.296648 | + | 0.171270i | ||||
\(471\) | −17.2995 | + | 28.4755i | −0.797120 | + | 1.31208i | ||||
\(472\) | −7.67779 | + | 4.43278i | −0.353399 | + | 0.204035i | ||||
\(473\) | −0.358224 | + | 0.206821i | −0.0164711 | + | 0.00950962i | ||||
\(474\) | −1.80437 | + | 2.97005i | −0.0828775 | + | 0.136419i | ||||
\(475\) | −4.75019 | + | 2.74252i | −0.217954 | + | 0.125836i | ||||
\(476\) | −16.8115 | − | 12.2662i | −0.770553 | − | 0.562219i | ||||
\(477\) | 25.5352 | − | 13.2593i | 1.16918 | − | 0.607101i | ||||
\(478\) | 8.04923 | + | 13.9417i | 0.368163 | + | 0.637677i | ||||
\(479\) | 35.7357 | 1.63280 | 0.816402 | − | 0.577483i | \(-0.195965\pi\) | ||||
0.816402 | + | 0.577483i | \(0.195965\pi\) | |||||||
\(480\) | −0.899307 | + | 1.48029i | −0.0410475 | + | 0.0675655i | ||||
\(481\) | − | 7.10390i | − | 0.323910i | ||||||
\(482\) | 12.8188 | − | 22.2029i | 0.583881 | − | 1.01131i | ||||
\(483\) | −2.86797 | + | 22.0965i | −0.130497 | + | 1.00542i | ||||
\(484\) | 5.39854 | + | 9.35054i | 0.245388 | + | 0.425025i | ||||
\(485\) | 8.69468 | − | 5.01988i | 0.394805 | − | 0.227941i | ||||
\(486\) | 6.24132 | + | 14.2845i | 0.283112 | + | 0.647957i | ||||
\(487\) | −9.42060 | + | 16.3170i | −0.426888 | + | 0.739392i | −0.996595 | − | 0.0824564i | \(-0.973723\pi\) |
0.569707 | + | 0.821848i | \(0.307057\pi\) | |||||||
\(488\) | −4.93145 | + | 8.54152i | −0.223236 | + | 0.386656i | ||||
\(489\) | −9.22122 | − | 5.60210i | −0.416998 | − | 0.253336i | ||||
\(490\) | 1.48301 | − | 6.84110i | 0.0669955 | − | 0.309050i | ||||
\(491\) | −13.9486 | − | 8.05323i | −0.629492 | − | 0.363437i | 0.151064 | − | 0.988524i | \(-0.451730\pi\) |
−0.780555 | + | 0.625087i | \(0.785064\pi\) | |||||||
\(492\) | −2.90646 | + | 1.59259i | −0.131033 | + | 0.0717993i | ||||
\(493\) | − | 73.1650i | − | 3.29519i | ||||||
\(494\) | −23.3751 | − | 13.4956i | −1.05170 | − | 0.607197i | ||||
\(495\) | 1.13902 | + | 0.727293i | 0.0511953 | + | 0.0326894i | ||||
\(496\) | 0.574100i | 0.0257778i | ||||||||
\(497\) | 6.05958 | − | 8.30499i | 0.271809 | − | 0.372530i | ||||
\(498\) | 7.93508 | + | 14.4815i | 0.355580 | + | 0.648931i | ||||
\(499\) | 1.35262 | 0.0605518 | 0.0302759 | − | 0.999542i | \(-0.490361\pi\) | ||||
0.0302759 | + | 0.999542i | \(0.490361\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 0.279000 | − | 12.4905i | 0.0124648 | − | 0.558034i | ||||
\(502\) | 11.0459 | + | 6.37734i | 0.493002 | + | 0.284635i | ||||
\(503\) | 39.9065 | 1.77934 | 0.889671 | − | 0.456603i | \(-0.150934\pi\) | ||||
0.889671 | + | 0.456603i | \(0.150934\pi\) | |||||||
\(504\) | 2.88646 | + | 7.39380i | 0.128573 | + | 0.329346i | ||||
\(505\) | 5.49909 | 0.244706 | ||||||||
\(506\) | −1.89688 | − | 1.09516i | −0.0843266 | − | 0.0486860i | ||||
\(507\) | −16.6014 | − | 10.0857i | −0.737296 | − | 0.447923i | ||||
\(508\) | 1.54404 | + | 2.67436i | 0.0685058 | + | 0.118656i | ||||
\(509\) | −10.8798 | −0.482240 | −0.241120 | − | 0.970495i | \(-0.577515\pi\) | ||||
−0.241120 | + | 0.970495i | \(0.577515\pi\) | |||||||
\(510\) | −7.07368 | + | 11.6435i | −0.313228 | + | 0.515583i | ||||
\(511\) | 6.07770 | + | 13.7252i | 0.268861 | + | 0.607168i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −12.5661 | − | 25.5814i | −0.554807 | − | 1.12945i | ||||
\(514\) | 23.4499 | + | 13.5388i | 1.03433 | + | 0.597171i | ||||
\(515\) | 15.5075i | 0.683343i | ||||||||
\(516\) | −0.0355167 | + | 1.59004i | −0.00156354 | + | 0.0699976i | ||||
\(517\) | −2.89707 | − | 1.67263i | −0.127413 | − | 0.0735620i | ||||
\(518\) | 2.25126 | − | 3.08548i | 0.0989147 | − | 0.135568i | ||||
\(519\) | −0.603396 | + | 27.0133i | −0.0264862 | + | 1.18575i | ||||
\(520\) | 2.46044 | − | 4.26160i | 0.107897 | − | 0.186884i | ||||
\(521\) | 19.6042 | − | 33.9555i | 0.858877 | − | 1.48762i | −0.0141243 | − | 0.999900i | \(-0.504496\pi\) |
0.873001 | − | 0.487718i | \(-0.162171\pi\) | |||||||
\(522\) | −15.0178 | + | 23.5196i | −0.657313 | + | 1.02943i | ||||
\(523\) | 13.7286 | − | 7.92622i | 0.600310 | − | 0.346589i | −0.168853 | − | 0.985641i | \(-0.554006\pi\) |
0.769164 | + | 0.639052i | \(0.220673\pi\) | |||||||
\(524\) | −7.85422 | − | 13.6039i | −0.343113 | − | 0.594290i | ||||
\(525\) | −4.54446 | − | 0.589839i | −0.198336 | − | 0.0257427i | ||||
\(526\) | −6.66669 | + | 11.5471i | −0.290682 | + | 0.503475i | ||||
\(527\) | 4.51570i | 0.196707i | ||||||||
\(528\) | −0.780047 | − | 0.0174239i | −0.0339472 | − | 0.000758278i | ||||
\(529\) | −0.641865 | −0.0279072 | ||||||||
\(530\) | −4.79542 | − | 8.30591i | −0.208300 | − | 0.360786i | ||||
\(531\) | 26.5701 | + | 1.18759i | 1.15305 | + | 0.0515369i | ||||
\(532\) | −5.87582 | − | 13.2693i | −0.254749 | − | 0.575298i | ||||
\(533\) | 8.15435 | − | 4.70792i | 0.353204 | − | 0.203923i | ||||
\(534\) | 3.30336 | + | 6.02862i | 0.142950 | + | 0.260884i | ||||
\(535\) | −8.60043 | + | 4.96546i | −0.371829 | + | 0.214676i | ||||
\(536\) | −4.02013 | + | 2.32102i | −0.173643 | + | 0.100253i | ||||
\(537\) | 6.60383 | + | 0.147510i | 0.284976 | + | 0.00636552i | ||||
\(538\) | −13.1361 | + | 7.58415i | −0.566339 | + | 0.326976i | ||||
\(539\) | 3.00288 | − | 0.962312i | 0.129343 | − | 0.0414497i | ||||
\(540\) | 4.66384 | − | 2.29097i | 0.200700 | − | 0.0985878i | ||||
\(541\) | −8.42008 | − | 14.5840i | −0.362007 | − | 0.627015i | 0.626284 | − | 0.779595i | \(-0.284575\pi\) |
−0.988291 | + | 0.152580i | \(0.951242\pi\) | |||||||
\(542\) | 26.2938 | 1.12942 | ||||||||
\(543\) | 3.82431 | + | 6.97934i | 0.164117 | + | 0.299512i | ||||
\(544\) | − | 7.86570i | − | 0.337239i | ||||||
\(545\) | −2.22823 | + | 3.85941i | −0.0954470 | + | 0.165319i | ||||
\(546\) | −8.66770 | − | 20.8179i | −0.370943 | − | 0.890925i | ||||
\(547\) | −13.5255 | − | 23.4268i | −0.578307 | − | 1.00166i | −0.995674 | − | 0.0929192i | \(-0.970380\pi\) |
0.417366 | − | 0.908738i | \(-0.362953\pi\) | |||||||
\(548\) | 11.3130 | − | 6.53158i | 0.483268 | − | 0.279015i | ||||
\(549\) | 26.2596 | − | 13.6354i | 1.12073 | − | 0.581945i | ||||
\(550\) | 0.225236 | − | 0.390121i | 0.00960410 | − | 0.0166348i | ||||
\(551\) | 25.5104 | − | 44.1852i | 1.08678 | − | 1.88235i | ||||
\(552\) | −7.38565 | + | 4.04694i | −0.314354 | + | 0.172249i | ||||
\(553\) | 4.85385 | − | 2.14935i | 0.206407 | − | 0.0913995i | ||||
\(554\) | 20.1611 | + | 11.6400i | 0.856563 | + | 0.494537i | ||||
\(555\) | −2.13698 | − | 1.29826i | −0.0907097 | − | 0.0551081i | ||||
\(556\) | − | 0.655415i | − | 0.0277958i | ||||||
\(557\) | 31.3474 | + | 18.0984i | 1.32823 | + | 0.766854i | 0.985026 | − | 0.172406i | \(-0.0551542\pi\) |
0.343205 | + | 0.939261i | \(0.388487\pi\) | |||||||
\(558\) | 0.926891 | − | 1.45162i | 0.0392384 | − | 0.0614518i | ||||
\(559\) | − | 4.51854i | − | 0.191114i | ||||||
\(560\) | 2.41918 | − | 1.07124i | 0.102229 | − | 0.0452683i | ||||
\(561\) | −6.13562 | − | 0.137051i | −0.259046 | − | 0.00578631i | ||||
\(562\) | −3.93045 | −0.165796 | ||||||||
\(563\) | 7.00932 | + | 12.1405i | 0.295408 | + | 0.511661i | 0.975080 | − | 0.221855i | \(-0.0712111\pi\) |
−0.679672 | + | 0.733516i | \(0.737878\pi\) | |||||||
\(564\) | −11.2800 | + | 6.18083i | −0.474973 | + | 0.260260i | ||||
\(565\) | −17.4964 | − | 10.1015i | −0.736077 | − | 0.424974i | ||||
\(566\) | −28.8938 | −1.21450 | ||||||||
\(567\) | 4.63895 | − | 23.3555i | 0.194817 | − | 0.980840i | ||||
\(568\) | 3.88571 | 0.163041 | ||||||||
\(569\) | −22.2561 | − | 12.8496i | −0.933024 | − | 0.538682i | −0.0452575 | − | 0.998975i | \(-0.514411\pi\) |
−0.887767 | + | 0.460294i | \(0.847744\pi\) | |||||||
\(570\) | −8.33160 | + | 4.56527i | −0.348972 | + | 0.191218i | ||||
\(571\) | −7.82510 | − | 13.5535i | −0.327470 | − | 0.567195i | 0.654539 | − | 0.756028i | \(-0.272863\pi\) |
−0.982009 | + | 0.188833i | \(0.939530\pi\) | |||||||
\(572\) | 2.21672 | 0.0926857 | ||||||||
\(573\) | 43.4526 | + | 0.970600i | 1.81526 | + | 0.0405474i | ||||
\(574\) | 5.03369 | + | 0.539337i | 0.210102 | + | 0.0225115i | ||||
\(575\) | − | 4.86229i | − | 0.202772i | ||||||
\(576\) | −1.61451 | + | 2.52851i | −0.0672714 | + | 0.105354i | ||||
\(577\) | −26.9592 | − | 15.5649i | −1.12233 | − | 0.647976i | −0.180334 | − | 0.983605i | \(-0.557718\pi\) |
−0.941994 | + | 0.335629i | \(0.891051\pi\) | |||||||
\(578\) | − | 44.8693i | − | 1.86632i | ||||||
\(579\) | −26.5042 | − | 16.1019i | −1.10148 | − | 0.669173i | ||||
\(580\) | 8.05558 | + | 4.65089i | 0.334490 | + | 0.193118i | ||||
\(581\) | 2.68725 | − | 25.0805i | 0.111486 | − | 1.04051i | ||||
\(582\) | 15.2500 | − | 8.35621i | 0.632135 | − | 0.346376i | ||||
\(583\) | 2.16020 | − | 3.74158i | 0.0894665 | − | 0.154961i | ||||
\(584\) | −2.83675 | + | 4.91339i | −0.117385 | + | 0.203318i | ||||
\(585\) | −13.1016 | + | 6.80309i | −0.541686 | + | 0.281273i | ||||
\(586\) | 3.74744 | − | 2.16359i | 0.154805 | − | 0.0893770i | ||||
\(587\) | −2.19821 | − | 3.80741i | −0.0907299 | − | 0.157149i | 0.817089 | − | 0.576512i | \(-0.195587\pi\) |
−0.907818 | + | 0.419363i | \(0.862253\pi\) | |||||||
\(588\) | 2.83262 | − | 11.7888i | 0.116815 | − | 0.486163i | ||||
\(589\) | −1.57448 | + | 2.72708i | −0.0648754 | + | 0.112368i | ||||
\(590\) | − | 8.86555i | − | 0.364989i | ||||||
\(591\) | −10.5307 | − | 19.2184i | −0.433174 | − | 0.790540i | ||||
\(592\) | 1.44362 | 0.0593326 | ||||||||
\(593\) | 8.99345 | + | 15.5771i | 0.369317 | + | 0.639675i | 0.989459 | − | 0.144814i | \(-0.0462584\pi\) |
−0.620142 | + | 0.784489i | \(0.712925\pi\) | |||||||
\(594\) | 1.94422 | + | 1.30345i | 0.0797724 | + | 0.0534813i | ||||
\(595\) | 19.0286 | − | 8.42608i | 0.780095 | − | 0.345436i | ||||
\(596\) | 4.00375 | − | 2.31156i | 0.164000 | − | 0.0946853i | ||||
\(597\) | 36.5752 | + | 0.816981i | 1.49692 | + | 0.0334368i | ||||
\(598\) | 20.7212 | − | 11.9634i | 0.847351 | − | 0.489218i | ||||
\(599\) | −1.19486 | + | 0.689852i | −0.0488206 | + | 0.0281866i | −0.524212 | − | 0.851588i | \(-0.675640\pi\) |
0.475391 | + | 0.879775i | \(0.342307\pi\) | |||||||
\(600\) | −0.832312 | − | 1.51897i | −0.0339790 | − | 0.0620115i | ||||
\(601\) | −40.5777 | + | 23.4275i | −1.65520 | + | 0.955630i | −0.680314 | + | 0.732921i | \(0.738157\pi\) |
−0.974885 | + | 0.222709i | \(0.928510\pi\) | |||||||
\(602\) | 1.43195 | − | 1.96257i | 0.0583618 | − | 0.0799882i | ||||
\(603\) | 13.9122 | + | 0.621826i | 0.566550 | + | 0.0253227i | ||||
\(604\) | 6.15097 | + | 10.6538i | 0.250279 | + | 0.433496i | ||||
\(605\) | −10.7971 | −0.438964 | ||||||||
\(606\) | 9.52233 | + | 0.212701i | 0.386818 | + | 0.00864037i | ||||
\(607\) | 22.5955i | 0.917121i | 0.888663 | + | 0.458561i | \(0.151635\pi\) | ||||
−0.888663 | + | 0.458561i | \(0.848365\pi\) | |||||||
\(608\) | 2.74252 | − | 4.75019i | 0.111224 | − | 0.192646i | ||||
\(609\) | 39.3515 | − | 16.3843i | 1.59460 | − | 0.663924i | ||||
\(610\) | −4.93145 | − | 8.54152i | −0.199668 | − | 0.345836i | ||||
\(611\) | 31.6471 | − | 18.2714i | 1.28030 | − | 0.739183i | ||||
\(612\) | −12.6993 | + | 19.8885i | −0.513338 | + | 0.803945i | ||||
\(613\) | 10.4551 | − | 18.1088i | 0.422279 | − | 0.731409i | −0.573883 | − | 0.818938i | \(-0.694563\pi\) |
0.996162 | + | 0.0875282i | \(0.0278968\pi\) | |||||||
\(614\) | 0.209941 | − | 0.363629i | 0.00847253 | − | 0.0146749i | ||||
\(615\) | 0.0740106 | − | 3.31336i | 0.00298440 | − | 0.133608i | ||||
\(616\) | 0.962801 | + | 0.702489i | 0.0387924 | + | 0.0283041i | ||||
\(617\) | −8.43544 | − | 4.87020i | −0.339598 | − | 0.196067i | 0.320496 | − | 0.947250i | \(-0.396150\pi\) |
−0.660094 | + | 0.751183i | \(0.729484\pi\) | |||||||
\(618\) | −0.599818 | + | 26.8531i | −0.0241282 | + | 1.08019i | ||||
\(619\) | − | 18.2795i | − | 0.734715i | −0.930080 | − | 0.367358i | \(-0.880263\pi\) | ||
0.930080 | − | 0.367358i | \(-0.119737\pi\) | |||||||
\(620\) | −0.497185 | − | 0.287050i | −0.0199674 | − | 0.0115282i | ||||
\(621\) | 25.2085 | + | 1.69150i | 1.01158 | + | 0.0678775i | ||||
\(622\) | − | 6.28435i | − | 0.251980i | ||||||
\(623\) | 1.11870 | − | 10.4410i | 0.0448197 | − | 0.418308i | ||||
\(624\) | 4.42538 | − | 7.28430i | 0.177157 | − | 0.291606i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.84206 | − | 4.92258i | −0.113591 | − | 0.196746i | ||||
\(627\) | −3.65758 | − | 2.22206i | −0.146070 | − | 0.0887407i | ||||
\(628\) | 16.6593 | + | 9.61826i | 0.664779 | + | 0.383810i | ||||
\(629\) | 11.3551 | 0.452758 | ||||||||
\(630\) | −7.84645 | − | 1.19715i | −0.312610 | − | 0.0476957i | ||||
\(631\) | 23.4168 | 0.932209 | 0.466104 | − | 0.884730i | \(-0.345657\pi\) | ||||
0.466104 | + | 0.884730i | \(0.345657\pi\) | |||||||
\(632\) | 1.73760 | + | 1.00320i | 0.0691178 | + | 0.0399052i | ||||
\(633\) | −0.774606 | + | 34.6781i | −0.0307878 | + | 1.37833i | ||||
\(634\) | −5.01570 | − | 8.68744i | −0.199199 | − | 0.345022i | ||||
\(635\) | −3.08808 | −0.122547 | ||||||||
\(636\) | −7.98257 | − | 14.5682i | −0.316530 | − | 0.577665i | ||||
\(637\) | −7.29770 | + | 33.6642i | −0.289146 | + | 1.33382i | ||||
\(638\) | 4.19019i | 0.165891i | ||||||||
\(639\) | −9.82505 | − | 6.27353i | −0.388673 | − | 0.248177i | ||||
\(640\) | 0.866025 | + | 0.500000i | 0.0342327 | + | 0.0197642i | ||||
\(641\) | − | 3.99917i | − | 0.157958i | −0.996876 | − | 0.0789788i | \(-0.974834\pi\) | ||
0.996876 | − | 0.0789788i | \(-0.0251659\pi\) | |||||||
\(642\) | −15.0847 | + | 8.26563i | −0.595347 | + | 0.326218i | ||||
\(643\) | −14.6262 | − | 8.44444i | −0.576801 | − | 0.333016i | 0.183060 | − | 0.983102i | \(-0.441400\pi\) |
−0.759861 | + | 0.650085i | \(0.774733\pi\) | |||||||
\(644\) | 12.7912 | + | 1.37052i | 0.504044 | + | 0.0540059i | ||||
\(645\) | −1.35926 | − | 0.825778i | −0.0535207 | − | 0.0325150i | ||||
\(646\) | 21.5719 | − | 37.3636i | 0.848734 | − | 1.47005i | ||||
\(647\) | −14.0753 | + | 24.3792i | −0.553358 | + | 0.958443i | 0.444672 | + | 0.895694i | \(0.353320\pi\) |
−0.998029 | + | 0.0627498i | \(0.980013\pi\) | |||||||
\(648\) | 8.16461 | − | 3.78670i | 0.320736 | − | 0.148756i | ||||
\(649\) | 3.45863 | − | 1.99684i | 0.135763 | − | 0.0783830i | ||||
\(650\) | 2.46044 | + | 4.26160i | 0.0965063 | + | 0.167154i | ||||
\(651\) | −2.42875 | + | 1.01123i | −0.0951902 | + | 0.0396331i | ||||
\(652\) | −3.11468 | + | 5.39478i | −0.121980 | + | 0.211276i | ||||
\(653\) | 23.4509i | 0.917704i | 0.888513 | + | 0.458852i | \(0.151739\pi\) | ||||
−0.888513 | + | 0.458852i | \(0.848261\pi\) | |||||||
\(654\) | −4.00773 | + | 6.59684i | −0.156715 | + | 0.257957i | ||||
\(655\) | 15.7084 | 0.613780 | ||||||||
\(656\) | 0.956724 | + | 1.65709i | 0.0373538 | + | 0.0646987i | ||||
\(657\) | 15.1055 | − | 7.84358i | 0.589321 | − | 0.306007i | ||||
\(658\) | 19.5358 | + | 2.09317i | 0.761584 | + | 0.0816002i | ||||
\(659\) | 13.7094 | − | 7.91513i | 0.534043 | − | 0.308330i | −0.208618 | − | 0.977997i | \(-0.566897\pi\) |
0.742661 | + | 0.669667i | \(0.233563\pi\) | |||||||
\(660\) | 0.405113 | − | 0.666828i | 0.0157690 | − | 0.0259563i | ||||
\(661\) | 10.3009 | − | 5.94725i | 0.400660 | − | 0.231321i | −0.286109 | − | 0.958197i | \(-0.592362\pi\) |
0.686769 | + | 0.726876i | \(0.259028\pi\) | |||||||
\(662\) | −27.4558 | + | 15.8516i | −1.06710 | + | 0.616089i | ||||
\(663\) | 34.8087 | − | 57.2962i | 1.35186 | − | 2.22520i | ||||
\(664\) | 8.25650 | − | 4.76689i | 0.320414 | − | 0.184991i | ||||
\(665\) | 14.4295 | + | 1.54605i | 0.559551 | + | 0.0599533i | ||||
\(666\) | −3.65022 | − | 2.33075i | −0.141443 | − | 0.0903147i | ||||
\(667\) | 22.6140 | + | 39.1686i | 0.875617 | + | 1.51661i | ||||
\(668\) | −7.21319 | −0.279087 | ||||||||
\(669\) | −2.53365 | + | 4.17046i | −0.0979565 | + | 0.161239i | ||||
\(670\) | − | 4.64204i | − | 0.179338i | ||||||
\(671\) | 2.22148 | − | 3.84772i | 0.0857593 | − | 0.148540i | ||||
\(672\) | 4.23053 | − | 1.76141i | 0.163196 | − | 0.0679480i | ||||
\(673\) | −2.58993 | − | 4.48588i | −0.0998343 | − | 0.172918i | 0.811782 | − | 0.583961i | \(-0.198498\pi\) |
−0.911616 | + | 0.411043i | \(0.865165\pi\) | |||||||
\(674\) | −12.2908 | + | 7.09612i | −0.473425 | + | 0.273332i | ||||
\(675\) | −0.347881 | + | 5.18449i | −0.0133900 | + | 0.199551i | ||||
\(676\) | −5.60751 | + | 9.71249i | −0.215673 | + | 0.373557i | ||||
\(677\) | −5.58197 | + | 9.66826i | −0.214533 | + | 0.371582i | −0.953128 | − | 0.302568i | \(-0.902156\pi\) |
0.738595 | + | 0.674149i | \(0.235490\pi\) | |||||||
\(678\) | −29.9063 | − | 18.1687i | −1.14854 | − | 0.697766i | ||||
\(679\) | −26.4115 | − | 2.82987i | −1.01358 | − | 0.108600i | ||||
\(680\) | 6.81190 | + | 3.93285i | 0.261224 | + | 0.150818i | ||||
\(681\) | 3.93437 | − | 2.15583i | 0.150766 | − | 0.0826115i | ||||
\(682\) | − | 0.258616i | − | 0.00990292i | ||||||
\(683\) | −31.3199 | − | 18.0825i | −1.19842 | − | 0.691909i | −0.238219 | − | 0.971211i | \(-0.576564\pi\) |
−0.960203 | + | 0.279302i | \(0.909897\pi\) | |||||||
\(684\) | −14.6037 | + | 7.58305i | −0.558388 | + | 0.289945i | ||||
\(685\) | 13.0632i | 0.499117i | ||||||||
\(686\) | −13.8380 | + | 12.3089i | −0.528338 | + | 0.469956i | ||||
\(687\) | −17.9100 | − | 32.6856i | −0.683308 | − | 1.24703i | ||||
\(688\) | 0.918239 | 0.0350075 | ||||||||
\(689\) | 23.5977 | + | 40.8723i | 0.898999 | + | 1.55711i | ||||
\(690\) | 0.188069 | − | 8.41963i | 0.00715968 | − | 0.320530i | ||||
\(691\) | 5.80724 | + | 3.35281i | 0.220918 | + | 0.127547i | 0.606375 | − | 0.795179i | \(-0.292623\pi\) |
−0.385457 | + | 0.922726i | \(0.625956\pi\) | |||||||
\(692\) | 15.6000 | 0.593024 | ||||||||
\(693\) | −1.30027 | − | 3.33070i | −0.0493932 | − | 0.126523i | ||||
\(694\) | 0.732838 | 0.0278181 | ||||||||
\(695\) | 0.567606 | + | 0.327707i | 0.0215305 | + | 0.0124306i | ||||
\(696\) | 13.7693 | + | 8.36515i | 0.521924 | + | 0.317080i | ||||
\(697\) | 7.52531 | + | 13.0342i | 0.285041 | + | 0.493706i | ||||
\(698\) | −26.7017 | −1.01067 | ||||||||
\(699\) | 2.90192 | − | 4.77665i | 0.109761 | − | 0.180669i | ||||
\(700\) | −0.281867 | + | 2.63069i | −0.0106536 | + | 0.0994309i | ||||
\(701\) | − | 1.39464i | − | 0.0526749i | −0.999653 | − | 0.0263375i | \(-0.991616\pi\) | ||
0.999653 | − | 0.0263375i | \(-0.00838445\pi\) | |||||||
\(702\) | −22.9502 | + | 11.2736i | −0.866199 | + | 0.425494i | ||||
\(703\) | 6.85749 | + | 3.95918i | 0.258635 | + | 0.149323i | ||||
\(704\) | 0.450472i | 0.0169778i | ||||||||
\(705\) | 0.287235 | − | 12.8592i | 0.0108179 | − | 0.484304i | ||||
\(706\) | 5.19889 | + | 3.00158i | 0.195663 | + | 0.112966i | ||||
\(707\) | −11.7533 | − | 8.57557i | −0.442028 | − | 0.322517i | ||||
\(708\) | 0.342912 | − | 15.3518i | 0.0128874 | − | 0.576954i | ||||
\(709\) | 24.8056 | − | 42.9645i | 0.931593 | − | 1.61357i | 0.150994 | − | 0.988535i | \(-0.451753\pi\) |
0.780599 | − | 0.625032i | \(-0.214914\pi\) | |||||||
\(710\) | −1.94286 | + | 3.36513i | −0.0729141 | + | 0.126291i | ||||
\(711\) | −2.77384 | − | 5.34197i | −0.104027 | − | 0.200340i | ||||
\(712\) | 3.43716 | − | 1.98445i | 0.128813 | − | 0.0743703i | ||||
\(713\) | −1.39572 | − | 2.41746i | −0.0522701 | − | 0.0905345i | ||||
\(714\) | 33.2761 | − | 13.8548i | 1.24533 | − | 0.518501i | ||||
\(715\) | −1.10836 | + | 1.91973i | −0.0414503 | + | 0.0717940i | ||||
\(716\) | − | 3.81368i | − | 0.142524i | ||||||
\(717\) | −27.8764 | − | 0.622675i | −1.04106 | − | 0.0232542i | ||||
\(718\) | 29.3148 | 1.09402 | ||||||||
\(719\) | −10.4343 | − | 18.0727i | −0.389133 | − | 0.673998i | 0.603200 | − | 0.797590i | \(-0.293892\pi\) |
−0.992333 | + | 0.123592i | \(0.960559\pi\) | |||||||
\(720\) | −1.38250 | − | 2.66246i | −0.0515226 | − | 0.0992241i | ||||
\(721\) | 24.1832 | − | 33.1444i | 0.900629 | − | 1.23436i | ||||
\(722\) | 9.60055 | − | 5.54288i | 0.357295 | − | 0.206285i | ||||
\(723\) | 21.3385 | + | 38.9427i | 0.793588 | + | 1.44829i | ||||
\(724\) | 3.97921 | − | 2.29740i | 0.147886 | − | 0.0853821i | ||||
\(725\) | −8.05558 | + | 4.65089i | −0.299177 | + | 0.172730i | ||||
\(726\) | −18.6964 | − | 0.417622i | −0.693889 | − | 0.0154994i | ||||
\(727\) | −32.1908 | + | 18.5854i | −1.19389 | + | 0.689293i | −0.959187 | − | 0.282773i | \(-0.908746\pi\) |
−0.234704 | + | 0.972067i | \(0.575412\pi\) | |||||||
\(728\) | −11.9045 | + | 5.27146i | −0.441210 | + | 0.195373i | ||||
\(729\) | −26.7580 | − | 3.60718i | −0.991035 | − | 0.133599i | ||||
\(730\) | −2.83675 | − | 4.91339i | −0.104993 | − | 0.181853i | ||||
\(731\) | 7.22260 | 0.267137 | ||||||||
\(732\) | −8.20901 | − | 14.9814i | −0.303414 | − | 0.553728i | ||||
\(733\) | − | 11.9964i | − | 0.443096i | −0.975149 | − | 0.221548i | \(-0.928889\pi\) | ||
0.975149 | − | 0.221548i | \(-0.0711109\pi\) | |||||||
\(734\) | 10.0170 | − | 17.3499i | 0.369733 | − | 0.640397i | ||||
\(735\) | 8.79311 | + | 8.34753i | 0.324339 | + | 0.307903i | ||||
\(736\) | 2.43115 | + | 4.21087i | 0.0896132 | + | 0.155215i | ||||
\(737\) | 1.81096 | − | 1.04556i | 0.0667075 | − | 0.0385136i | ||||
\(738\) | 0.256316 | − | 5.73462i | 0.00943513 | − | 0.211094i | ||||
\(739\) | 16.6995 | − | 28.9243i | 0.614300 | − | 1.06400i | −0.376207 | − | 0.926535i | \(-0.622772\pi\) |
0.990507 | − | 0.137463i | \(-0.0438947\pi\) | |||||||
\(740\) | −0.721812 | + | 1.25022i | −0.0265343 | + | 0.0459588i | ||||
\(741\) | 40.9988 | − | 22.4651i | 1.50613 | − | 0.825278i | ||||
\(742\) | −2.70334 | + | 25.2306i | −0.0992426 | + | 0.926243i | ||||
\(743\) | −42.2679 | − | 24.4034i | −1.55066 | − | 0.895273i | −0.998088 | − | 0.0618062i | \(-0.980314\pi\) |
−0.552570 | − | 0.833467i | \(-0.686353\pi\) | |||||||
\(744\) | −0.849832 | − | 0.516292i | −0.0311563 | − | 0.0189282i | ||||
\(745\) | 4.62313i | 0.169378i | ||||||||
\(746\) | −5.94714 | − | 3.43358i | −0.217740 | − | 0.125712i | ||||
\(747\) | −28.5728 | − | 1.27710i | −1.04542 | − | 0.0467267i | ||||
\(748\) | 3.54328i | 0.129555i | ||||||||
\(749\) | 26.1252 | + | 2.79919i | 0.954595 | + | 0.102280i | ||||
\(750\) | 1.73162 | + | 0.0386792i | 0.0632298 | + | 0.00141236i | ||||
\(751\) | 10.6219 | 0.387599 | 0.193799 | − | 0.981041i | \(-0.437919\pi\) | ||||
0.193799 | + | 0.981041i | \(0.437919\pi\) | |||||||
\(752\) | 3.71305 | + | 6.43119i | 0.135401 | + | 0.234521i | ||||
\(753\) | −19.3739 | + | 10.6159i | −0.706025 | + | 0.386864i | ||||
\(754\) | −39.6405 | − | 22.8864i | −1.44362 | − | 0.833475i | ||||
\(755\) | −12.3019 | −0.447713 | ||||||||
\(756\) | −13.5408 | − | 2.37650i | −0.492473 | − | 0.0864326i | ||||
\(757\) | −41.0132 | −1.49065 | −0.745326 | − | 0.666701i | \(-0.767706\pi\) | ||||
−0.745326 | + | 0.666701i | \(0.767706\pi\) | |||||||
\(758\) | 0.590817 | + | 0.341108i | 0.0214594 | + | 0.0123896i | ||||
\(759\) | 3.32703 | − | 1.82304i | 0.120764 | − | 0.0661720i | ||||
\(760\) | 2.74252 | + | 4.75019i | 0.0994818 | + | 0.172308i | ||||
\(761\) | 1.62266 | 0.0588212 | 0.0294106 | − | 0.999567i | \(-0.490637\pi\) | ||||
0.0294106 | + | 0.999567i | \(0.490637\pi\) | |||||||
\(762\) | −5.34739 | − | 0.119445i | −0.193715 | − | 0.00432702i | ||||
\(763\) | 10.7810 | − | 4.77396i | 0.390298 | − | 0.172829i | ||||
\(764\) | − | 25.0936i | − | 0.907855i | ||||||
\(765\) | −10.8743 | − | 20.9421i | −0.393161 | − | 0.757165i | ||||
\(766\) | 27.3944 | + | 15.8162i | 0.989799 | + | 0.571461i | ||||
\(767\) | 43.6263i | 1.57525i | ||||||||
\(768\) | 1.48029 | + | 0.899307i | 0.0534152 | + | 0.0324509i | ||||
\(769\) | −15.4016 | − | 8.89210i | −0.555395 | − | 0.320657i | 0.195900 | − | 0.980624i | \(-0.437237\pi\) |
−0.751295 | + | 0.659966i | \(0.770570\pi\) | |||||||
\(770\) | −1.08977 | + | 0.482566i | −0.0392727 | + | 0.0173905i | ||||
\(771\) | −41.1300 | + | 22.5370i | −1.48126 | + | 0.811651i | ||||
\(772\) | −8.95240 | + | 15.5060i | −0.322204 | + | 0.558074i | ||||
\(773\) | −13.0759 | + | 22.6481i | −0.470307 | + | 0.814596i | −0.999423 | − | 0.0339536i | \(-0.989190\pi\) |
0.529116 | + | 0.848549i | \(0.322523\pi\) | |||||||
\(774\) | −2.32177 | − | 1.48251i | −0.0834544 | − | 0.0532877i | ||||
\(775\) | 0.497185 | − | 0.287050i | 0.0178594 | − | 0.0103111i | ||||
\(776\) | −5.01988 | − | 8.69468i | −0.180203 | − | 0.312121i | ||||
\(777\) | 2.54282 | + | 6.10730i | 0.0912231 | + | 0.219098i | ||||
\(778\) | −14.0160 | + | 24.2765i | −0.502499 | + | 0.870355i | ||||
\(779\) | 10.4954i | 0.376035i | ||||||||
\(780\) | 4.09570 | + | 7.47464i | 0.146650 | + | 0.267635i | ||||
\(781\) | −1.75041 | −0.0626344 | ||||||||
\(782\) | 19.1227 | + | 33.1214i | 0.683825 | + | 1.18442i | ||||
\(783\) | −21.3101 | − | 43.3820i | −0.761562 | − | 1.55035i | ||||
\(784\) | −6.84110 | − | 1.48301i | −0.244325 | − | 0.0529646i | ||||
\(785\) | −16.6593 | + | 9.61826i | −0.594596 | + | 0.343290i | ||||
\(786\) | 27.2010 | + | 0.607590i | 0.970229 | + | 0.0216720i | ||||
\(787\) | 19.8282 | − | 11.4478i | 0.706800 | − | 0.408071i | −0.103075 | − | 0.994674i | \(-0.532868\pi\) |
0.809875 | + | 0.586603i | \(0.199535\pi\) | |||||||
\(788\) | −10.9572 | + | 6.32615i | −0.390335 | + | 0.225360i | ||||
\(789\) | −11.0975 | − | 20.2530i | −0.395083 | − | 0.721024i | ||||
\(790\) | −1.73760 | + | 1.00320i | −0.0618209 | + | 0.0356923i | ||||
\(791\) | 21.6424 | + | 48.8748i | 0.769514 | + | 1.73779i | ||||
\(792\) | 0.727293 | − | 1.13902i | 0.0258432 | − | 0.0404734i | ||||
\(793\) | 24.2670 | + | 42.0317i | 0.861748 | + | 1.49259i | ||||
\(794\) | −29.2382 | −1.03762 | ||||||||
\(795\) | 16.6077 | + | 0.370966i | 0.589014 | + | 0.0131568i | ||||
\(796\) | − | 21.1220i | − | 0.748648i | ||||||
\(797\) | −8.74751 | + | 15.1511i | −0.309853 | + | 0.536681i | −0.978330 | − | 0.207052i | \(-0.933613\pi\) |
0.668477 | + | 0.743733i | \(0.266946\pi\) | |||||||
\(798\) | 24.9266 | + | 3.23529i | 0.882391 | + | 0.114528i | ||||
\(799\) | 29.2057 | + | 50.5858i | 1.03322 | + | 1.78960i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | −11.8948 | − | 0.531654i | −0.420283 | − | 0.0187851i | ||||
\(802\) | −5.78471 | + | 10.0194i | −0.204265 | + | 0.353798i | ||||
\(803\) | 1.27788 | − | 2.21335i | 0.0450953 | − | 0.0781073i | ||||
\(804\) | 0.179551 | − | 8.03825i | 0.00633226 | − | 0.283487i | ||||
\(805\) | −7.58250 | + | 10.3922i | −0.267248 | + | 0.366278i | ||||
\(806\) | 2.44658 | + | 1.41254i | 0.0861773 | + | 0.0497545i | ||||
\(807\) | 0.586697 | − | 26.2657i | 0.0206527 | − | 0.924597i | ||||
\(808\) | − | 5.49909i | − | 0.193457i | ||||||
\(809\) | −3.79610 | − | 2.19168i | −0.133464 | − | 0.0770553i | 0.431782 | − | 0.901978i | \(-0.357885\pi\) |
−0.565245 | + | 0.824923i | \(0.691218\pi\) | |||||||
\(810\) | −0.802930 | + | 8.96411i | −0.0282121 | + | 0.314967i | ||||
\(811\) | − | 55.5831i | − | 1.95179i | −0.218247 | − | 0.975893i | \(-0.570034\pi\) | ||
0.218247 | − | 0.975893i | \(-0.429966\pi\) | |||||||
\(812\) | −9.96447 | − | 22.5027i | −0.349684 | − | 0.789690i | ||||
\(813\) | −23.6462 | + | 38.9223i | −0.829308 | + | 1.36507i | ||||
\(814\) | −0.650313 | −0.0227935 | ||||||||
\(815\) | −3.11468 | − | 5.39478i | −0.109102 | − | 0.188971i | ||||
\(816\) | 11.6435 | + | 7.07368i | 0.407604 | + | 0.247628i | ||||
\(817\) | 4.36181 | + | 2.51829i | 0.152600 | + | 0.0881039i | ||||
\(818\) | −2.07755 | −0.0726398 | ||||||||
\(819\) | 38.6114 | + | 5.89103i | 1.34919 | + | 0.205849i | ||||
\(820\) | −1.91345 | −0.0668205 | ||||||||
\(821\) | −13.1066 | − | 7.56707i | −0.457422 | − | 0.264093i | 0.253538 | − | 0.967325i | \(-0.418406\pi\) |
−0.710960 | + | 0.703233i | \(0.751739\pi\) | |||||||
\(822\) | −0.505272 | + | 22.6204i | −0.0176234 | + | 0.788977i | ||||
\(823\) | 18.1011 | + | 31.3520i | 0.630964 | + | 1.09286i | 0.987355 | + | 0.158525i | \(0.0506739\pi\) |
−0.356391 | + | 0.934337i | \(0.615993\pi\) | |||||||
\(824\) | 15.5075 | 0.540230 | ||||||||
\(825\) | 0.374934 | + | 0.684252i | 0.0130535 | + | 0.0238226i | ||||
\(826\) | −13.8254 | + | 18.9485i | −0.481047 | + | 0.659302i | ||||
\(827\) | 3.78131i | 0.131489i | 0.997836 | + | 0.0657446i | \(0.0209422\pi\) | ||||
−0.997836 | + | 0.0657446i | \(0.979058\pi\) | |||||||
\(828\) | 0.651329 | − | 14.5723i | 0.0226353 | − | 0.506423i | ||||
\(829\) | 24.5988 | + | 14.2021i | 0.854352 | + | 0.493260i | 0.862117 | − | 0.506710i | \(-0.169138\pi\) |
−0.00776491 | + | 0.999970i | \(0.502472\pi\) | |||||||
\(830\) | 9.53378i | 0.330922i | ||||||||
\(831\) | −35.3616 | + | 19.3763i | −1.22668 | + | 0.672155i | ||||
\(832\) | −4.26160 | − | 2.46044i | −0.147745 | − | 0.0853003i | ||||
\(833\) | −53.8101 | − | 11.6649i | −1.86441 | − | 0.404165i | ||||
\(834\) | 0.970201 | + | 0.589419i | 0.0335953 | + | 0.0204099i | ||||
\(835\) | 3.60660 | − | 6.24681i | 0.124811 | − | 0.216180i | ||||
\(836\) | −1.23543 | + | 2.13983i | −0.0427283 | + | 0.0740076i | ||||
\(837\) | 1.31525 | + | 2.67751i | 0.0454616 | + | 0.0925483i | ||||
\(838\) | −5.45962 | + | 3.15211i | −0.188600 | + | 0.108888i | ||||
\(839\) | 13.6621 | + | 23.6634i | 0.471667 | + | 0.816951i | 0.999475 | − | 0.0324131i | \(-0.0103192\pi\) |
−0.527808 | + | 0.849364i | \(0.676986\pi\) | |||||||
\(840\) | −0.589839 | + | 4.54446i | −0.0203514 | + | 0.156799i | ||||
\(841\) | 28.7615 | − | 49.8165i | 0.991777 | − | 1.71781i | ||||
\(842\) | − | 2.60242i | − | 0.0896854i | ||||||
\(843\) | 3.53468 | − | 5.81820i | 0.121741 | − | 0.200389i | ||||
\(844\) | 20.0264 | 0.689338 | ||||||||
\(845\) | −5.60751 | − | 9.71249i | −0.192904 | − | 0.334120i | ||||
\(846\) | 0.994764 | − | 22.2561i | 0.0342007 | − | 0.765179i | ||||
\(847\) | 23.0767 | + | 16.8375i | 0.792926 | + | 0.578544i | ||||
\(848\) | −8.30591 | + | 4.79542i | −0.285226 | + | 0.164675i | ||||
\(849\) | 25.9844 | − | 42.7710i | 0.891781 | − | 1.46790i | ||||
\(850\) | −6.81190 | + | 3.93285i | −0.233646 | + | 0.134896i | ||||
\(851\) | −6.07891 | + | 3.50966i | −0.208382 | + | 0.120310i | ||||
\(852\) | −3.49445 | + | 5.75197i | −0.119718 | + | 0.197059i | ||||
\(853\) | −7.91557 | + | 4.57006i | −0.271024 | + | 0.156476i | −0.629353 | − | 0.777120i | \(-0.716680\pi\) |
0.358329 | + | 0.933595i | \(0.383347\pi\) | |||||||
\(854\) | −2.78002 | + | 25.9463i | −0.0951303 | + | 0.887863i | ||||
\(855\) | 0.734751 | − | 16.4387i | 0.0251280 | − | 0.562193i | ||||
\(856\) | 4.96546 | + | 8.60043i | 0.169716 | + | 0.293957i | ||||
\(857\) | 0.951997 | 0.0325196 | 0.0162598 | − | 0.999868i | \(-0.494824\pi\) | ||||
0.0162598 | + | 0.999868i | \(0.494824\pi\) | |||||||
\(858\) | −1.99351 | + | 3.28138i | −0.0680573 | + | 0.112024i | ||||
\(859\) | − | 35.4135i | − | 1.20829i | −0.796873 | − | 0.604147i | \(-0.793514\pi\) | ||
0.796873 | − | 0.604147i | \(-0.206486\pi\) | |||||||
\(860\) | −0.459119 | + | 0.795218i | −0.0156558 | + | 0.0271167i | ||||
\(861\) | −5.32521 | + | 6.96628i | −0.181483 | + | 0.237410i | ||||
\(862\) | −4.88511 | − | 8.46126i | −0.166388 | − | 0.288192i | ||||
\(863\) | −22.9444 | + | 13.2469i | −0.781036 | + | 0.450931i | −0.836797 | − | 0.547513i | \(-0.815575\pi\) |
0.0557615 | + | 0.998444i | \(0.482241\pi\) | |||||||
\(864\) | −2.29097 | − | 4.66384i | −0.0779405 | − | 0.158667i | ||||
\(865\) | −7.80001 | + | 13.5100i | −0.265208 | + | 0.459354i | ||||
\(866\) | 17.2272 | − | 29.8383i | 0.585403 | − | 1.01395i | ||||
\(867\) | 66.4194 | + | 40.3513i | 2.25572 | + | 1.37040i | ||||
\(868\) | 0.615001 | + | 1.38885i | 0.0208745 | + | 0.0471407i | ||||
\(869\) | −0.782739 | − | 0.451915i | −0.0265526 | − | 0.0153301i | ||||
\(870\) | −14.1291 | + | 7.74198i | −0.479021 | + | 0.262478i | ||||
\(871\) | 22.8429i | 0.774003i | ||||||||
\(872\) | 3.85941 | + | 2.22823i | 0.130696 | + | 0.0754575i | ||||
\(873\) | −1.34488 | + | 30.0892i | −0.0455172 | + | 1.01837i | ||||
\(874\) | 26.6699i | 0.902123i | ||||||||
\(875\) | −2.13731 | − | 1.55945i | −0.0722544 | − | 0.0527191i | ||||
\(876\) | −4.72212 | − | 8.61785i | −0.159546 | − | 0.291170i | ||||
\(877\) | 12.5178 | 0.422697 | 0.211349 | − | 0.977411i | \(-0.432214\pi\) | ||||
0.211349 | + | 0.977411i | \(0.432214\pi\) | |||||||
\(878\) | −10.3639 | − | 17.9508i | −0.349765 | − | 0.605810i | ||||
\(879\) | −0.167372 | + | 7.49302i | −0.00564530 | + | 0.252733i | ||||
\(880\) | −0.390121 | − | 0.225236i | −0.0131510 | − | 0.00759271i | ||||
\(881\) | −32.3516 | −1.08995 | −0.544977 | − | 0.838451i | \(-0.683462\pi\) | ||||
−0.544977 | + | 0.838451i | \(0.683462\pi\) | |||||||
\(882\) | 14.9034 | + | 14.7948i | 0.501825 | + | 0.498168i | ||||
\(883\) | 24.9749 | 0.840473 | 0.420237 | − | 0.907415i | \(-0.361947\pi\) | ||||
0.420237 | + | 0.907415i | \(0.361947\pi\) | |||||||
\(884\) | −33.5205 | − | 19.3531i | −1.12742 | − | 0.650914i | ||||
\(885\) | 13.1236 | + | 7.97285i | 0.441144 | + | 0.268004i | ||||
\(886\) | 4.76808 | + | 8.25856i | 0.160187 | + | 0.277452i | ||||
\(887\) | −0.411815 | −0.0138274 | −0.00691370 | − | 0.999976i | \(-0.502201\pi\) | ||||
−0.00691370 | + | 0.999976i | \(0.502201\pi\) | |||||||
\(888\) | −1.29826 | + | 2.13698i | −0.0435668 | + | 0.0717123i | ||||
\(889\) | 6.60021 | + | 4.81572i | 0.221364 | + | 0.161514i | ||||
\(890\) | 3.96890i | 0.133038i | ||||||||
\(891\) | −3.67793 | + | 1.70580i | −0.123215 | + | 0.0571466i | ||||
\(892\) | 2.43988 | + | 1.40867i | 0.0816933 | + | 0.0471657i | ||||
\(893\) | 40.7325i | 1.36306i | ||||||||
\(894\) | −0.178819 | + | 8.00550i | −0.00598060 | + | 0.267744i | ||||
\(895\) | 3.30274 | + | 1.90684i | 0.110398 | + | 0.0637386i | ||||
\(896\) | −1.07124 | − | 2.41918i | −0.0357877 | − | 0.0808192i | ||||
\(897\) | −0.925466 | + | 41.4320i | −0.0309004 | + | 1.38337i | ||||
\(898\) | 1.11500 | − | 1.93123i | 0.0372080 | − | 0.0644461i | ||||
\(899\) | −2.67007 | + | 4.62470i | −0.0890520 | + | 0.154243i | ||||
\(900\) | 2.99701 | + | 0.133955i | 0.0999003 | + | 0.00446517i | ||||
\(901\) | −65.3318 | + | 37.7193i | −2.17652 | + | 1.25661i | ||||
\(902\) | −0.430978 | − | 0.746475i | −0.0143500 | − | 0.0248549i | ||||
\(903\) | 1.61740 | + | 3.88464i | 0.0538236 | + | 0.129273i | ||||
\(904\) | −10.1015 | + | 17.4964i | −0.335972 | + | 0.581920i | ||||
\(905\) | 4.59480i | 0.152736i | ||||||||
\(906\) | −21.3023 | − | 0.475829i | −0.707720 | − | 0.0158084i | ||||
\(907\) | −40.4316 | −1.34251 | −0.671254 | − | 0.741227i | \(-0.734244\pi\) | ||||
−0.671254 | + | 0.741227i | \(0.734244\pi\) | |||||||
\(908\) | −1.29508 | − | 2.24315i | −0.0429789 | − | 0.0744416i | ||||
\(909\) | −8.87836 | + | 13.9045i | −0.294476 | + | 0.461183i | ||||
\(910\) | 1.38703 | − | 12.9453i | 0.0459796 | − | 0.429133i | ||||
\(911\) | −24.9849 | + | 14.4250i | −0.827786 | + | 0.477923i | −0.853094 | − | 0.521757i | \(-0.825277\pi\) |
0.0253077 | + | 0.999680i | \(0.491943\pi\) | |||||||
\(912\) | 4.56527 | + | 8.33160i | 0.151171 | + | 0.275887i | ||||
\(913\) | −3.71932 | + | 2.14735i | −0.123092 | + | 0.0710670i | ||||
\(914\) | −11.1513 | + | 6.43820i | −0.368852 | + | 0.212957i | ||||
\(915\) | 17.0788 | + | 0.381489i | 0.564607 | + | 0.0126116i | ||||
\(916\) | −18.6354 | + | 10.7592i | −0.615732 | + | 0.355493i | ||||
\(917\) | −33.5739 | − | 24.4965i | −1.10871 | − | 0.808947i | ||||
\(918\) | −18.0201 | − | 36.6844i | −0.594752 | − | 1.21077i | ||||
\(919\) | 1.99289 | + | 3.45179i | 0.0657394 | + | 0.113864i | 0.897022 | − | 0.441986i | \(-0.145726\pi\) |
−0.831282 | + | 0.555850i | \(0.812393\pi\) | |||||||
\(920\) | −4.86229 | −0.160305 | ||||||||
\(921\) | 0.349473 | + | 0.637786i | 0.0115155 | + | 0.0210158i | ||||
\(922\) | 3.13475i | 0.103238i | ||||||||
\(923\) | 9.56055 | − | 16.5594i | 0.314689 | − | 0.545058i | ||||
\(924\) | −1.90574 | + | 0.793468i | −0.0626942 | + | 0.0261032i | ||||
\(925\) | −0.721812 | − | 1.25022i | −0.0237330 | − | 0.0411068i | ||||
\(926\) | −12.5635 | + | 7.25355i | −0.412863 | + | 0.238367i | ||||
\(927\) | −39.2109 | − | 25.0371i | −1.28785 | − | 0.822325i | ||||
\(928\) | 4.65089 | − | 8.05558i | 0.152673 | − | 0.264437i | ||||
\(929\) | −21.0976 | + | 36.5422i | −0.692191 | + | 1.19891i | 0.278927 | + | 0.960312i | \(0.410021\pi\) |
−0.971118 | + | 0.238598i | \(0.923312\pi\) | |||||||
\(930\) | 0.872038 | − | 0.477830i | 0.0285952 | − | 0.0156687i | ||||
\(931\) | −28.4294 | − | 25.8065i | −0.931735 | − | 0.845773i | ||||
\(932\) | −2.79452 | − | 1.61342i | −0.0915377 | − | 0.0528493i | ||||
\(933\) | 9.30264 | + | 5.65156i | 0.304555 | + | 0.185024i | ||||
\(934\) | 9.66081i | 0.316111i | ||||||||
\(935\) | −3.06857 | − | 1.77164i | −0.100353 | − | 0.0579389i | ||||
\(936\) | 6.80309 | + | 13.1016i | 0.222366 | + | 0.428241i | ||||
\(937\) | − | 41.8456i | − | 1.36704i | −0.729933 | − | 0.683519i | \(-0.760449\pi\) | ||
0.729933 | − | 0.683519i | \(-0.239551\pi\) | |||||||
\(938\) | −7.23904 | + | 9.92151i | −0.236363 | + | 0.323949i | ||||
\(939\) | 9.84271 | + | 0.219857i | 0.321205 | + | 0.00717476i | ||||
\(940\) | −7.42609 | −0.242212 | ||||||||
\(941\) | −17.1592 | − | 29.7207i | −0.559375 | − | 0.968866i | −0.997549 | − | 0.0699758i | \(-0.977708\pi\) |
0.438174 | − | 0.898890i | \(-0.355626\pi\) | |||||||
\(942\) | −29.2196 | + | 16.0108i | −0.952026 | + | 0.521660i | ||||
\(943\) | −8.05727 | − | 4.65187i | −0.262381 | − | 0.151486i | ||||
\(944\) | −8.86555 | −0.288549 | ||||||||
\(945\) | 8.82849 | − | 10.5384i | 0.287191 | − | 0.342814i | ||||
\(946\) | −0.413641 | −0.0134486 | ||||||||
\(947\) | −21.0886 | − | 12.1755i | −0.685289 | − | 0.395652i | 0.116556 | − | 0.993184i | \(-0.462815\pi\) |
−0.801845 | + | 0.597532i | \(0.796148\pi\) | |||||||
\(948\) | −3.04766 | + | 1.66995i | −0.0989833 | + | 0.0542376i | ||||
\(949\) | 13.9593 | + | 24.1782i | 0.453138 | + | 0.784857i | ||||
\(950\) | −5.48505 | −0.177958 | ||||||||
\(951\) | 17.3705 | + | 0.388006i | 0.563279 | + | 0.0125820i | ||||
\(952\) | −8.42608 | − | 19.0286i | −0.273091 | − | 0.616719i | ||||
\(953\) | 39.1967i | 1.26970i | 0.772634 | + | 0.634852i | \(0.218939\pi\) | ||||
−0.772634 | + | 0.634852i | \(0.781061\pi\) | |||||||
\(954\) | 28.7438 | + | 1.28474i | 0.930615 | + | 0.0415951i | ||||
\(955\) | 21.7317 | + | 12.5468i | 0.703221 | + | 0.406005i | ||||
\(956\) | 16.0985i | 0.520661i | ||||||||
\(957\) | −6.20269 | − | 3.76827i | −0.200504 | − | 0.121811i | ||||
\(958\) | 30.9480 | + | 17.8678i | 0.999885 | + | 0.577284i | ||||
\(959\) | 20.3713 | − | 27.9201i | 0.657825 | − | 0.901586i | ||||
\(960\) | −1.51897 | + | 0.832312i | −0.0490244 | + | 0.0268628i | ||||
\(961\) | −15.3352 | + | 26.5614i | −0.494684 | + | 0.856818i | ||||
\(962\) | 3.55195 | − | 6.15215i | 0.114519 | − | 0.198353i | ||||
\(963\) | 1.33030 | − | 29.7630i | 0.0428683 | − | 0.959101i | ||||
\(964\) | 22.2029 | − | 12.8188i | 0.715106 | − | 0.412867i | ||||
\(965\) | −8.95240 | − | 15.5060i | −0.288188 | − | 0.499156i | ||||
\(966\) | −13.5320 | + | 17.7021i | −0.435384 | + | 0.569556i | ||||
\(967\) | 7.42308 | − | 12.8572i | 0.238710 | − | 0.413458i | −0.721634 | − | 0.692275i | \(-0.756609\pi\) |
0.960344 | + | 0.278816i | \(0.0899421\pi\) | |||||||
\(968\) | 10.7971i | 0.347031i | ||||||||
\(969\) | 35.9091 | + | 65.5339i | 1.15357 | + | 2.10525i | ||||
\(970\) | 10.0398 | 0.322357 | ||||||||
\(971\) | 21.8681 | + | 37.8766i | 0.701780 | + | 1.21552i | 0.967841 | + | 0.251562i | \(0.0809444\pi\) |
−0.266061 | + | 0.963956i | \(0.585722\pi\) | |||||||
\(972\) | −1.73709 | + | 15.4914i | −0.0557173 | + | 0.496886i | ||||
\(973\) | −0.702109 | − | 1.58557i | −0.0225086 | − | 0.0508309i | ||||
\(974\) | −16.3170 | + | 9.42060i | −0.522829 | + | 0.301855i | ||||
\(975\) | −8.52108 | − | 0.190335i | −0.272893 | − | 0.00609561i | ||||
\(976\) | −8.54152 | + | 4.93145i | −0.273407 | + | 0.157852i | ||||
\(977\) | 36.7089 | − | 21.1939i | 1.17442 | − | 0.678052i | 0.219704 | − | 0.975567i | \(-0.429491\pi\) |
0.954717 | + | 0.297514i | \(0.0961576\pi\) | |||||||
\(978\) | −5.18476 | − | 9.46217i | −0.165790 | − | 0.302567i | ||||
\(979\) | −1.54835 | + | 0.893939i | −0.0494854 | + | 0.0285704i | ||||
\(980\) | 4.70487 | − | 5.18306i | 0.150292 | − | 0.165567i | ||||
\(981\) | −6.16104 | − | 11.8652i | −0.196707 | − | 0.378826i | ||||
\(982\) | −8.05323 | − | 13.9486i | −0.256989 | − | 0.445118i | ||||
\(983\) | 57.2841 | 1.82708 | 0.913540 | − | 0.406748i | \(-0.133337\pi\) | ||||
0.913540 | + | 0.406748i | \(0.133337\pi\) | |||||||
\(984\) | −3.31336 | − | 0.0740106i | −0.105626 | − | 0.00235937i | ||||
\(985\) | − | 12.6523i | − | 0.403136i | ||||||
\(986\) | 36.5825 | − | 63.3628i | 1.16502 | − | 2.01788i | ||||
\(987\) | −20.6671 | + | 27.0361i | −0.657842 | + | 0.860570i | ||||
\(988\) | −13.4956 | − | 23.3751i | −0.429353 | − | 0.743661i | ||||
\(989\) | −3.86658 | + | 2.23237i | −0.122950 | + | 0.0709853i | ||||
\(990\) | 0.622776 | + | 1.19937i | 0.0197931 | + | 0.0381184i | ||||
\(991\) | −13.4576 | + | 23.3093i | −0.427496 | + | 0.740445i | −0.996650 | − | 0.0817862i | \(-0.973938\pi\) |
0.569154 | + | 0.822231i | \(0.307271\pi\) | |||||||
\(992\) | −0.287050 | + | 0.497185i | −0.00911384 | + | 0.0157856i | ||||
\(993\) | 1.22625 | − | 54.8978i | 0.0389140 | − | 1.74213i | ||||
\(994\) | 9.40024 | − | 4.16254i | 0.298158 | − | 0.132028i | ||||
\(995\) | 18.2922 | + | 10.5610i | 0.579900 | + | 0.334806i | ||||
\(996\) | −0.368759 | + | 16.5089i | −0.0116846 | + | 0.523104i | ||||
\(997\) | 59.1431i | 1.87308i | 0.350561 | + | 0.936540i | \(0.385991\pi\) | ||||
−0.350561 | + | 0.936540i | \(0.614009\pi\) | |||||||
\(998\) | 1.17141 | + | 0.676312i | 0.0370802 | + | 0.0214083i | ||||
\(999\) | 6.73284 | − | 3.30730i | 0.213018 | − | 0.104638i |
(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 | 630.2.t.b.311.8 | ✓ | 28 | |
3.2 | odd | 2 | 1890.2.t.b.1151.5 | 28 | |||
7.5 | odd | 6 | 630.2.bk.b.131.3 | yes | 28 | ||
9.2 | odd | 6 | 630.2.bk.b.101.10 | yes | 28 | ||
9.7 | even | 3 | 1890.2.bk.b.521.9 | 28 | |||
21.5 | even | 6 | 1890.2.bk.b.341.9 | 28 | |||
63.47 | even | 6 | inner | 630.2.t.b.551.8 | yes | 28 | |
63.61 | odd | 6 | 1890.2.t.b.1601.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.8 | ✓ | 28 | 1.1 | even | 1 | trivial | |
630.2.t.b.551.8 | yes | 28 | 63.47 | even | 6 | inner | |
630.2.bk.b.101.10 | yes | 28 | 9.2 | odd | 6 | ||
630.2.bk.b.131.3 | yes | 28 | 7.5 | odd | 6 | ||
1890.2.t.b.1151.5 | 28 | 3.2 | odd | 2 | |||
1890.2.t.b.1601.5 | 28 | 63.61 | odd | 6 | |||
1890.2.bk.b.341.9 | 28 | 21.5 | even | 6 | |||
1890.2.bk.b.521.9 | 28 | 9.7 | even | 3 |