Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Character | \(\chi\) | \(=\) | 475.24 |
Dual form | 475.2.u.b.99.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.429906 | − | 1.18116i | −0.303989 | − | 0.835204i | −0.993797 | − | 0.111211i | \(-0.964527\pi\) |
0.689807 | − | 0.723993i | \(-0.257695\pi\) | |||||||
\(3\) | −2.96649 | − | 0.523072i | −1.71270 | − | 0.301996i | −0.770600 | − | 0.637319i | \(-0.780043\pi\) |
−0.942103 | + | 0.335323i | \(0.891155\pi\) | |||||||
\(4\) | 0.321776 | − | 0.270002i | 0.160888 | − | 0.135001i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.657481 | + | 3.72876i | 0.268416 | + | 1.52226i | ||||
\(7\) | 3.22501 | − | 1.86196i | 1.21894 | − | 0.703754i | 0.254247 | − | 0.967139i | \(-0.418172\pi\) |
0.964691 | + | 0.263385i | \(0.0848389\pi\) | |||||||
\(8\) | −2.63437 | − | 1.52095i | −0.931390 | − | 0.537738i | ||||
\(9\) | 5.70738 | + | 2.07732i | 1.90246 | + | 0.692439i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.67794 | − | 2.90627i | 0.505917 | − | 0.876275i | −0.494059 | − | 0.869428i | \(-0.664487\pi\) |
0.999977 | − | 0.00684646i | \(-0.00217931\pi\) | |||||||
\(12\) | −1.09578 | + | 0.632646i | −0.316323 | + | 0.182629i | ||||
\(13\) | 4.76776 | − | 0.840684i | 1.32234 | − | 0.233164i | 0.532474 | − | 0.846446i | \(-0.321262\pi\) |
0.789864 | + | 0.613282i | \(0.210151\pi\) | |||||||
\(14\) | −3.58572 | − | 3.00877i | −0.958323 | − | 0.804129i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.518073 | + | 2.93814i | −0.129518 | + | 0.734534i | ||||
\(17\) | 0.914991 | + | 2.51392i | 0.221918 | + | 0.609715i | 0.999826 | − | 0.0186637i | \(-0.00594120\pi\) |
−0.777908 | + | 0.628378i | \(0.783719\pi\) | |||||||
\(18\) | − | 7.63436i | − | 1.79944i | ||||||
\(19\) | −0.961823 | − | 4.25146i | −0.220657 | − | 0.975351i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.5409 | + | 3.83657i | −2.30021 | + | 0.837208i | ||||
\(22\) | −4.15412 | − | 0.732484i | −0.885662 | − | 0.156166i | ||||
\(23\) | −1.20653 | − | 1.43789i | −0.251579 | − | 0.299820i | 0.625443 | − | 0.780270i | \(-0.284918\pi\) |
−0.877023 | + | 0.480449i | \(0.840474\pi\) | |||||||
\(24\) | 7.01926 | + | 5.88986i | 1.43280 | + | 1.20226i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.04267 | − | 5.27006i | −0.596716 | − | 1.03354i | ||||
\(27\) | −8.01823 | − | 4.62933i | −1.54311 | − | 0.890914i | ||||
\(28\) | 0.534997 | − | 1.46989i | 0.101105 | − | 0.277783i | ||||
\(29\) | −4.93461 | − | 1.79605i | −0.916335 | − | 0.333519i | −0.159555 | − | 0.987189i | \(-0.551006\pi\) |
−0.756779 | + | 0.653670i | \(0.773228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.55945 | + | 2.70105i | 0.280086 | + | 0.485124i | 0.971406 | − | 0.237426i | \(-0.0763036\pi\) |
−0.691319 | + | 0.722549i | \(0.742970\pi\) | |||||||
\(32\) | −2.29826 | + | 0.405246i | −0.406279 | + | 0.0716380i | ||||
\(33\) | −6.49778 | + | 7.74375i | −1.13112 | + | 1.34801i | ||||
\(34\) | 2.57597 | − | 2.16150i | 0.441776 | − | 0.370694i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.39738 | − | 0.872573i | 0.399563 | − | 0.145429i | ||||
\(37\) | 0.992927i | 0.163236i | 0.996664 | + | 0.0816181i | \(0.0260088\pi\) | ||||
−0.996664 | + | 0.0816181i | \(0.973991\pi\) | |||||||
\(38\) | −4.60815 | + | 2.96379i | −0.747540 | + | 0.480790i | ||||
\(39\) | −14.5832 | −2.33519 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0723041 | − | 0.410057i | 0.0112920 | − | 0.0640401i | −0.978641 | − | 0.205576i | \(-0.934093\pi\) |
0.989933 | + | 0.141536i | \(0.0452042\pi\) | |||||||
\(42\) | 9.06319 | + | 10.8011i | 1.39848 | + | 1.66664i | ||||
\(43\) | −4.64013 | + | 5.52990i | −0.707614 | + | 0.843301i | −0.993365 | − | 0.115003i | \(-0.963312\pi\) |
0.285751 | + | 0.958304i | \(0.407757\pi\) | |||||||
\(44\) | −0.244780 | − | 1.38822i | −0.0369020 | − | 0.209281i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.17968 | + | 2.04326i | −0.173934 | + | 0.301262i | ||||
\(47\) | 0.766421 | − | 2.10572i | 0.111794 | − | 0.307151i | −0.871161 | − | 0.490997i | \(-0.836633\pi\) |
0.982955 | + | 0.183846i | \(0.0588547\pi\) | |||||||
\(48\) | 3.07372 | − | 8.44496i | 0.443653 | − | 1.21893i | ||||
\(49\) | 3.43378 | − | 5.94749i | 0.490540 | − | 0.849641i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.39935 | − | 7.93612i | −0.195948 | − | 1.11128i | ||||
\(52\) | 1.30716 | − | 1.55782i | 0.181271 | − | 0.216030i | ||||
\(53\) | −0.167287 | − | 0.199365i | −0.0229786 | − | 0.0273848i | 0.754433 | − | 0.656377i | \(-0.227912\pi\) |
−0.777411 | + | 0.628993i | \(0.783468\pi\) | |||||||
\(54\) | −2.02088 | + | 11.4610i | −0.275007 | + | 1.55964i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.3278 | −1.51374 | ||||||||
\(57\) | 0.629417 | + | 13.1150i | 0.0833683 | + | 1.73713i | ||||
\(58\) | 6.60069i | 0.866713i | ||||||||
\(59\) | −4.87590 | + | 1.77468i | −0.634789 | + | 0.231044i | −0.639314 | − | 0.768946i | \(-0.720782\pi\) |
0.00452556 | + | 0.999990i | \(0.498559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.589041 | − | 0.494264i | 0.0754189 | − | 0.0632840i | −0.604299 | − | 0.796758i | \(-0.706547\pi\) |
0.679718 | + | 0.733474i | \(0.262102\pi\) | |||||||
\(62\) | 2.51995 | − | 3.00316i | 0.320034 | − | 0.381402i | ||||
\(63\) | 22.2742 | − | 3.92754i | 2.80629 | − | 0.494824i | ||||
\(64\) | 4.45016 | + | 7.70790i | 0.556270 | + | 0.963488i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.9400 | + | 4.34581i | 1.46971 | + | 0.534933i | ||||
\(67\) | 3.68611 | − | 10.1275i | 0.450330 | − | 1.23727i | −0.482162 | − | 0.876082i | \(-0.660148\pi\) |
0.932492 | − | 0.361190i | \(-0.117629\pi\) | |||||||
\(68\) | 0.973185 | + | 0.561868i | 0.118016 | + | 0.0681366i | ||||
\(69\) | 2.82704 | + | 4.89658i | 0.340336 | + | 0.589479i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.53320 | + | 1.28651i | 0.181958 | + | 0.152681i | 0.729217 | − | 0.684282i | \(-0.239884\pi\) |
−0.547259 | + | 0.836963i | \(0.684329\pi\) | |||||||
\(72\) | −11.8758 | − | 14.1531i | −1.39958 | − | 1.66796i | ||||
\(73\) | −4.49331 | − | 0.792291i | −0.525902 | − | 0.0927307i | −0.0956071 | − | 0.995419i | \(-0.530479\pi\) |
−0.430295 | + | 0.902688i | \(0.641590\pi\) | |||||||
\(74\) | 1.17280 | − | 0.426865i | 0.136336 | − | 0.0496221i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.45739 | − | 1.10832i | −0.167174 | − | 0.127133i | ||||
\(77\) | − | 12.4970i | − | 1.42417i | ||||||
\(78\) | 6.26942 | + | 17.2251i | 0.709872 | + | 1.95036i | ||||
\(79\) | 2.09282 | − | 11.8690i | 0.235460 | − | 1.33536i | −0.606181 | − | 0.795326i | \(-0.707299\pi\) |
0.841642 | − | 0.540036i | \(-0.181589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.40643 | + | 6.21473i | 0.822937 | + | 0.690526i | ||||
\(82\) | −0.515426 | + | 0.0908835i | −0.0569192 | + | 0.0100364i | ||||
\(83\) | 11.7529 | − | 6.78553i | 1.29005 | − | 0.744809i | 0.311384 | − | 0.950284i | \(-0.399207\pi\) |
0.978662 | + | 0.205475i | \(0.0658741\pi\) | |||||||
\(84\) | −2.35592 | + | 4.08058i | −0.257052 | + | 0.445227i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.52650 | + | 3.10339i | 0.919436 | + | 0.334647i | ||||
\(87\) | 13.6990 | + | 7.90913i | 1.46869 | + | 0.847948i | ||||
\(88\) | −8.84062 | + | 5.10413i | −0.942413 | + | 0.544102i | ||||
\(89\) | 1.33178 | + | 7.55289i | 0.141168 | + | 0.800605i | 0.970364 | + | 0.241647i | \(0.0776876\pi\) |
−0.829196 | + | 0.558958i | \(0.811201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.8107 | − | 11.5886i | 1.44776 | − | 1.21481i | ||||
\(92\) | −0.776465 | − | 0.136912i | −0.0809521 | − | 0.0142740i | ||||
\(93\) | −3.21326 | − | 8.82836i | −0.333199 | − | 0.915458i | ||||
\(94\) | −2.81668 | −0.290518 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.02975 | 0.717471 | ||||||||
\(97\) | 2.47244 | + | 6.79298i | 0.251039 | + | 0.689723i | 0.999643 | + | 0.0267064i | \(0.00850192\pi\) |
−0.748605 | + | 0.663017i | \(0.769276\pi\) | |||||||
\(98\) | −8.50112 | − | 1.49898i | −0.858743 | − | 0.151420i | ||||
\(99\) | 15.6139 | − | 13.1016i | 1.56925 | − | 1.31676i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.779999 | + | 4.42360i | 0.0776128 | + | 0.440164i | 0.998708 | + | 0.0508257i | \(0.0161853\pi\) |
−0.921095 | + | 0.389339i | \(0.872704\pi\) | |||||||
\(102\) | −8.77221 | + | 5.06464i | −0.868578 | + | 0.501474i | ||||
\(103\) | 9.30504 | + | 5.37227i | 0.916853 | + | 0.529345i | 0.882630 | − | 0.470069i | \(-0.155771\pi\) |
0.0342231 | + | 0.999414i | \(0.489104\pi\) | |||||||
\(104\) | −13.8387 | − | 5.03686i | −1.35699 | − | 0.493905i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.163563 | + | 0.283300i | −0.0158867 | + | 0.0275165i | ||||
\(107\) | 1.19393 | − | 0.689315i | 0.115421 | − | 0.0666386i | −0.441178 | − | 0.897420i | \(-0.645439\pi\) |
0.556599 | + | 0.830781i | \(0.312106\pi\) | |||||||
\(108\) | −3.83000 | + | 0.675332i | −0.368542 | + | 0.0649839i | ||||
\(109\) | −7.27648 | − | 6.10570i | −0.696961 | − | 0.584820i | 0.223946 | − | 0.974601i | \(-0.428106\pi\) |
−0.920907 | + | 0.389782i | \(0.872550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.519372 | − | 2.94551i | 0.0492966 | − | 0.279575i | ||||
\(112\) | 3.79990 | + | 10.4401i | 0.359057 | + | 0.986501i | ||||
\(113\) | 17.0436i | 1.60333i | 0.597772 | + | 0.801666i | \(0.296053\pi\) | ||||
−0.597772 | + | 0.801666i | \(0.703947\pi\) | |||||||
\(114\) | 15.2203 | − | 6.38166i | 1.42551 | − | 0.597697i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.07278 | + | 0.754429i | −0.192453 | + | 0.0700470i | ||||
\(117\) | 28.9578 | + | 5.10603i | 2.67715 | + | 0.472053i | ||||
\(118\) | 4.19236 | + | 4.99626i | 0.385938 | + | 0.459943i | ||||
\(119\) | 7.63167 | + | 6.40373i | 0.699594 | + | 0.587029i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.130955 | − | 0.226821i | −0.0119050 | − | 0.0206201i | ||||
\(122\) | −0.837035 | − | 0.483263i | −0.0757816 | − | 0.0437525i | ||||
\(123\) | −0.428979 | + | 1.17861i | −0.0386797 | + | 0.106272i | ||||
\(124\) | 1.23108 | + | 0.448078i | 0.110555 | + | 0.0402386i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −14.2149 | − | 24.6209i | −1.26636 | − | 2.19340i | ||||
\(127\) | −19.5581 | + | 3.44862i | −1.73550 | + | 0.306016i | −0.949862 | − | 0.312669i | \(-0.898777\pi\) |
−0.785640 | + | 0.618685i | \(0.787666\pi\) | |||||||
\(128\) | 4.19092 | − | 4.99455i | 0.370429 | − | 0.441460i | ||||
\(129\) | 16.6574 | − | 13.9773i | 1.46661 | − | 1.23063i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.09611 | + | 1.85483i | −0.445249 | + | 0.162057i | −0.554908 | − | 0.831912i | \(-0.687246\pi\) |
0.109659 | + | 0.993969i | \(0.465024\pi\) | |||||||
\(132\) | 4.24616i | 0.369581i | ||||||||
\(133\) | −11.0179 | − | 11.9201i | −0.955375 | − | 1.03360i | ||||
\(134\) | −13.5469 | −1.17027 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.41313 | − | 8.01425i | 0.121175 | − | 0.687216i | ||||
\(137\) | −11.9311 | − | 14.2189i | −1.01934 | − | 1.21480i | −0.976455 | − | 0.215723i | \(-0.930789\pi\) |
−0.0428860 | − | 0.999080i | \(-0.513655\pi\) | |||||||
\(138\) | 4.56827 | − | 5.44425i | 0.388877 | − | 0.463446i | ||||
\(139\) | 1.82551 | + | 10.3530i | 0.154838 | + | 0.878128i | 0.958934 | + | 0.283629i | \(0.0915385\pi\) |
−0.804096 | + | 0.594499i | \(0.797350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.37502 | + | 5.84571i | −0.284228 | + | 0.492298i | ||||
\(142\) | 0.860438 | − | 2.36404i | 0.0722064 | − | 0.198385i | ||||
\(143\) | 5.55674 | − | 15.2670i | 0.464678 | − | 1.27669i | ||||
\(144\) | −9.06027 | + | 15.6929i | −0.755023 | + | 1.30774i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.995879 | + | 5.64791i | 0.0824196 | + | 0.467425i | ||||
\(147\) | −13.2972 | + | 15.8470i | −1.09674 | + | 1.30704i | ||||
\(148\) | 0.268092 | + | 0.319500i | 0.0220370 | + | 0.0262627i | ||||
\(149\) | −2.62919 | + | 14.9109i | −0.215392 | + | 1.22155i | 0.664834 | + | 0.746992i | \(0.268502\pi\) |
−0.880225 | + | 0.474556i | \(0.842609\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3432 | 0.923095 | 0.461548 | − | 0.887115i | \(-0.347294\pi\) | ||||
0.461548 | + | 0.887115i | \(0.347294\pi\) | |||||||
\(152\) | −3.93248 | + | 12.6628i | −0.318966 | + | 1.02709i | ||||
\(153\) | 16.2486i | 1.31362i | ||||||||
\(154\) | −14.7609 | + | 5.37254i | −1.18947 | + | 0.432932i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.69253 | + | 3.93750i | −0.375703 | + | 0.315253i | ||||
\(157\) | 2.70953 | − | 3.22909i | 0.216244 | − | 0.257710i | −0.647007 | − | 0.762484i | \(-0.723980\pi\) |
0.863252 | + | 0.504774i | \(0.168424\pi\) | |||||||
\(158\) | −14.9188 | + | 2.63059i | −1.18688 | + | 0.209279i | ||||
\(159\) | 0.391972 | + | 0.678916i | 0.0310854 | + | 0.0538415i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.56836 | − | 2.39069i | −0.517659 | − | 0.188413i | ||||
\(162\) | 4.15651 | − | 11.4199i | 0.326566 | − | 0.897233i | ||||
\(163\) | −12.0426 | − | 6.95280i | −0.943249 | − | 0.544585i | −0.0522718 | − | 0.998633i | \(-0.516646\pi\) |
−0.890977 | + | 0.454048i | \(0.849980\pi\) | |||||||
\(164\) | −0.0874505 | − | 0.151469i | −0.00682873 | − | 0.0118277i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.0674 | − | 10.9649i | −1.01423 | − | 0.851038i | ||||
\(167\) | 11.3273 | + | 13.4994i | 0.876537 | + | 1.04462i | 0.998642 | + | 0.0520984i | \(0.0165910\pi\) |
−0.122105 | + | 0.992517i | \(0.538965\pi\) | |||||||
\(168\) | 33.6038 | + | 5.92526i | 2.59259 | + | 0.457144i | ||||
\(169\) | 9.80875 | − | 3.57009i | 0.754519 | − | 0.274623i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.34214 | − | 26.2627i | 0.255580 | − | 2.00836i | ||||
\(172\) | 3.03223i | 0.231206i | ||||||||
\(173\) | −4.55510 | − | 12.5150i | −0.346317 | − | 0.951499i | −0.983519 | − | 0.180803i | \(-0.942131\pi\) |
0.637202 | − | 0.770697i | \(-0.280092\pi\) | |||||||
\(174\) | 3.45264 | − | 19.5809i | 0.261744 | − | 1.48442i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.66974 | + | 6.43567i | 0.578128 | + | 0.485107i | ||||
\(177\) | 15.3926 | − | 2.71413i | 1.15698 | − | 0.204007i | ||||
\(178\) | 8.34861 | − | 4.82007i | 0.625755 | − | 0.361280i | ||||
\(179\) | 7.31322 | − | 12.6669i | 0.546616 | − | 0.946767i | −0.451887 | − | 0.892075i | \(-0.649249\pi\) |
0.998503 | − | 0.0546916i | \(-0.0174176\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.25497 | + | 3.00456i | 0.613587 | + | 0.223328i | 0.630072 | − | 0.776537i | \(-0.283025\pi\) |
−0.0164849 | + | 0.999864i | \(0.505248\pi\) | |||||||
\(182\) | −19.6253 | − | 11.3306i | −1.45472 | − | 0.839883i | ||||
\(183\) | −2.00592 | + | 1.15812i | −0.148282 | + | 0.0856105i | ||||
\(184\) | 0.991488 | + | 5.62301i | 0.0730934 | + | 0.414533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.04628 | + | 7.59073i | −0.663305 | + | 0.556579i | ||||
\(187\) | 8.84144 | + | 1.55898i | 0.646550 | + | 0.114004i | ||||
\(188\) | −0.321934 | − | 0.884506i | −0.0234794 | − | 0.0645092i | ||||
\(189\) | −34.4785 | −2.50794 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.70737 | −0.702401 | −0.351200 | − | 0.936300i | \(-0.614226\pi\) | ||||
−0.351200 | + | 0.936300i | \(0.614226\pi\) | |||||||
\(192\) | −9.16956 | − | 25.1932i | −0.661756 | − | 1.81816i | ||||
\(193\) | 19.9469 | + | 3.51718i | 1.43581 | + | 0.253172i | 0.836774 | − | 0.547549i | \(-0.184439\pi\) |
0.599038 | + | 0.800721i | \(0.295550\pi\) | |||||||
\(194\) | 6.96066 | − | 5.84069i | 0.499747 | − | 0.419337i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500925 | − | 2.84089i | −0.0357803 | − | 0.202920i | ||||
\(197\) | −8.02097 | + | 4.63091i | −0.571470 | + | 0.329939i | −0.757736 | − | 0.652561i | \(-0.773695\pi\) |
0.186266 | + | 0.982499i | \(0.440361\pi\) | |||||||
\(198\) | −22.1875 | − | 12.8100i | −1.57680 | − | 0.910366i | ||||
\(199\) | 17.0574 | + | 6.20837i | 1.20916 | + | 0.440100i | 0.866414 | − | 0.499327i | \(-0.166419\pi\) |
0.342750 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2322 | + | 28.1150i | −1.14493 | + | 1.98308i | ||||
\(202\) | 4.88964 | − | 2.82303i | 0.344034 | − | 0.198628i | ||||
\(203\) | −19.2583 | + | 3.39577i | −1.35167 | + | 0.238336i | ||||
\(204\) | −2.59304 | − | 2.17582i | −0.181549 | − | 0.152338i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.34520 | − | 13.3003i | 0.163398 | − | 0.926675i | ||||
\(207\) | −3.89918 | − | 10.7129i | −0.271012 | − | 0.744599i | ||||
\(208\) | 14.4439i | 1.00150i | ||||||||
\(209\) | −13.9698 | − | 4.33836i | −0.966310 | − | 0.300091i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3337 | + | 5.94498i | −1.12446 | + | 0.409269i | −0.836277 | − | 0.548307i | \(-0.815273\pi\) |
−0.288181 | + | 0.957576i | \(0.593050\pi\) | |||||||
\(212\) | −0.107658 | − | 0.0189829i | −0.00739396 | − | 0.00130375i | ||||
\(213\) | −3.87530 | − | 4.61840i | −0.265531 | − | 0.316448i | ||||
\(214\) | −1.32747 | − | 1.11388i | −0.0907438 | − | 0.0761431i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.0820 | + | 24.3907i | 0.958157 | + | 1.65958i | ||||
\(217\) | 10.0585 | + | 5.80728i | 0.682816 | + | 0.394224i | ||||
\(218\) | −4.08358 | + | 11.2195i | −0.276575 | + | 0.759884i | ||||
\(219\) | 12.9149 | + | 4.70065i | 0.872710 | + | 0.317640i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47587 | + | 11.2165i | 0.435614 | + | 0.754505i | ||||
\(222\) | −3.70239 | + | 0.652831i | −0.248488 | + | 0.0438151i | ||||
\(223\) | −5.60941 | + | 6.68504i | −0.375634 | + | 0.447663i | −0.920431 | − | 0.390905i | \(-0.872162\pi\) |
0.544797 | + | 0.838568i | \(0.316607\pi\) | |||||||
\(224\) | −6.65737 | + | 5.58619i | −0.444814 | + | 0.373243i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.1312 | − | 7.32717i | 1.33911 | − | 0.487396i | ||||
\(227\) | − | 20.1154i | − | 1.33510i | −0.744563 | − | 0.667552i | \(-0.767342\pi\) | ||
0.744563 | − | 0.667552i | \(-0.232658\pi\) | |||||||
\(228\) | 3.74361 | + | 4.05015i | 0.247927 | + | 0.268228i | ||||
\(229\) | 20.8410 | 1.37721 | 0.688607 | − | 0.725135i | \(-0.258222\pi\) | ||||
0.688607 | + | 0.725135i | \(0.258222\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.53684 | + | 37.0723i | −0.430092 | + | 2.43918i | ||||
\(232\) | 10.2679 | + | 12.2368i | 0.674119 | + | 0.803384i | ||||
\(233\) | 0.349709 | − | 0.416767i | 0.0229102 | − | 0.0273033i | −0.754468 | − | 0.656337i | \(-0.772105\pi\) |
0.777378 | + | 0.629034i | \(0.216549\pi\) | |||||||
\(234\) | −6.41809 | − | 36.3988i | −0.419563 | − | 2.37946i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.08978 | + | 1.88755i | −0.0709386 | + | 0.122869i | ||||
\(237\) | −12.4166 | + | 34.1145i | −0.806548 | + | 2.21597i | ||||
\(238\) | 4.28291 | − | 11.7672i | 0.277620 | − | 0.762754i | ||||
\(239\) | −11.1117 | + | 19.2461i | −0.718758 | + | 1.24493i | 0.242733 | + | 0.970093i | \(0.421956\pi\) |
−0.961492 | + | 0.274833i | \(0.911377\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.77399 | + | 21.4034i | 0.243104 | + | 1.37871i | 0.824854 | + | 0.565345i | \(0.191257\pi\) |
−0.581750 | + | 0.813368i | \(0.697632\pi\) | |||||||
\(242\) | −0.211613 | + | 0.252190i | −0.0136030 | + | 0.0162114i | ||||
\(243\) | −0.866300 | − | 1.03242i | −0.0555732 | − | 0.0662295i | ||||
\(244\) | 0.0560868 | − | 0.318084i | 0.00359059 | − | 0.0203633i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.57654 | 0.100517 | ||||||||
\(247\) | −8.15987 | − | 19.4613i | −0.519200 | − | 1.23829i | ||||
\(248\) | − | 9.48743i | − | 0.602452i | ||||||
\(249\) | −38.4141 | + | 13.9816i | −2.43440 | + | 0.886048i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.6539 | − | 11.4570i | 0.861828 | − | 0.723160i | −0.100533 | − | 0.994934i | \(-0.532055\pi\) |
0.962361 | + | 0.271774i | \(0.0876104\pi\) | |||||||
\(252\) | 6.10686 | − | 7.27787i | 0.384696 | − | 0.458463i | ||||
\(253\) | −6.20338 | + | 1.09382i | −0.390003 | + | 0.0687681i | ||||
\(254\) | 12.4815 | + | 21.6186i | 0.783160 | + | 1.35647i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.02608 | + | 3.28522i | 0.564130 | + | 0.205326i | ||||
\(257\) | 5.37788 | − | 14.7756i | 0.335463 | − | 0.921678i | −0.651201 | − | 0.758906i | \(-0.725734\pi\) |
0.986664 | − | 0.162772i | \(-0.0520434\pi\) | |||||||
\(258\) | −23.6705 | − | 13.6662i | −1.47366 | − | 0.850817i | ||||
\(259\) | 1.84879 | + | 3.20220i | 0.114878 | + | 0.198975i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.4327 | − | 20.5015i | −1.51235 | − | 1.26901i | ||||
\(262\) | 4.38170 | + | 5.22190i | 0.270702 | + | 0.322610i | ||||
\(263\) | 29.9878 | + | 5.28766i | 1.84913 | + | 0.326051i | 0.984366 | − | 0.176133i | \(-0.0563589\pi\) |
0.864761 | + | 0.502184i | \(0.167470\pi\) | |||||||
\(264\) | 28.8954 | − | 10.5171i | 1.77839 | − | 0.647281i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.34285 | + | 18.1384i | −0.572847 | + | 1.11214i | ||||
\(267\) | − | 23.1022i | − | 1.41383i | ||||||
\(268\) | −1.54835 | − | 4.25404i | −0.0945802 | − | 0.259857i | ||||
\(269\) | −0.453555 | + | 2.57224i | −0.0276537 | + | 0.156832i | −0.995508 | − | 0.0946808i | \(-0.969817\pi\) |
0.967854 | + | 0.251513i | \(0.0809281\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.36033 | − | 6.17605i | −0.447108 | − | 0.375168i | 0.391253 | − | 0.920283i | \(-0.372042\pi\) |
−0.838361 | + | 0.545115i | \(0.816486\pi\) | |||||||
\(272\) | −7.86027 | + | 1.38598i | −0.476599 | + | 0.0840372i | ||||
\(273\) | −47.0311 | + | 27.1534i | −2.84645 | + | 1.64340i | ||||
\(274\) | −11.6655 | + | 20.2053i | −0.704740 | + | 1.22064i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.23176 | + | 0.812295i | 0.134336 | + | 0.0488944i | ||||
\(277\) | −17.3787 | − | 10.0336i | −1.04418 | − | 0.602860i | −0.123168 | − | 0.992386i | \(-0.539305\pi\) |
−0.921015 | + | 0.389526i | \(0.872639\pi\) | |||||||
\(278\) | 11.4437 | − | 6.60702i | 0.686348 | − | 0.396263i | ||||
\(279\) | 3.28945 | + | 18.6554i | 0.196934 | + | 1.11687i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3428 | − | 17.0696i | 1.21355 | − | 1.01829i | 0.214410 | − | 0.976744i | \(-0.431217\pi\) |
0.999137 | − | 0.0415429i | \(-0.0132273\pi\) | |||||||
\(282\) | 8.35565 | + | 1.47333i | 0.497572 | + | 0.0877353i | ||||
\(283\) | −5.73869 | − | 15.7669i | −0.341130 | − | 0.937247i | −0.985067 | − | 0.172169i | \(-0.944923\pi\) |
0.643938 | − | 0.765078i | \(-0.277300\pi\) | |||||||
\(284\) | 0.840709 | 0.0498869 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.4216 | −1.20756 | ||||||||
\(287\) | −0.530328 | − | 1.45706i | −0.0313043 | − | 0.0860078i | ||||
\(288\) | −13.9589 | − | 2.46133i | −0.822535 | − | 0.145035i | ||||
\(289\) | 7.54018 | − | 6.32696i | 0.443540 | − | 0.372174i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.78126 | − | 21.4446i | −0.221661 | − | 1.25710i | ||||
\(292\) | −1.65976 | + | 0.958262i | −0.0971300 | + | 0.0560780i | ||||
\(293\) | 11.5864 | + | 6.68939i | 0.676883 | + | 0.390799i | 0.798680 | − | 0.601757i | \(-0.205532\pi\) |
−0.121797 | + | 0.992555i | \(0.538866\pi\) | |||||||
\(294\) | 24.4344 | + | 8.89340i | 1.42504 | + | 0.518674i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.51020 | − | 2.61574i | 0.0877783 | − | 0.152037i | ||||
\(297\) | −26.9082 | + | 15.5355i | −1.56137 | + | 0.901458i | ||||
\(298\) | 18.7424 | − | 3.30479i | 1.08572 | − | 0.191441i | ||||
\(299\) | −6.96126 | − | 5.84119i | −0.402580 | − | 0.337805i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.66803 | + | 26.4737i | −0.269061 | + | 1.52592i | ||||
\(302\) | −4.87650 | − | 13.3981i | −0.280611 | − | 0.770973i | ||||
\(303\) | − | 13.5305i | − | 0.777310i | ||||||
\(304\) | 12.9897 | − | 0.623401i | 0.745008 | − | 0.0357545i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 19.1922 | − | 6.98537i | 1.09714 | − | 0.399327i | ||||
\(307\) | 27.5473 | + | 4.85734i | 1.57221 | + | 0.277223i | 0.890702 | − | 0.454588i | \(-0.150213\pi\) |
0.681508 | + | 0.731811i | \(0.261325\pi\) | |||||||
\(308\) | −3.37422 | − | 4.02124i | −0.192264 | − | 0.229131i | ||||
\(309\) | −24.7932 | − | 20.8040i | −1.41044 | − | 1.18350i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4175 | − | 21.5078i | −0.704132 | − | 1.21959i | −0.967004 | − | 0.254762i | \(-0.918003\pi\) |
0.262871 | − | 0.964831i | \(-0.415331\pi\) | |||||||
\(312\) | 38.4176 | + | 22.1804i | 2.17497 | + | 1.25572i | ||||
\(313\) | 7.61769 | − | 20.9294i | 0.430577 | − | 1.18300i | −0.514882 | − | 0.857261i | \(-0.672164\pi\) |
0.945459 | − | 0.325741i | \(-0.105614\pi\) | |||||||
\(314\) | −4.97891 | − | 1.81218i | −0.280976 | − | 0.102267i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.53122 | − | 4.38421i | −0.142393 | − | 0.246631i | ||||
\(317\) | 13.8618 | − | 2.44421i | 0.778557 | − | 0.137281i | 0.229772 | − | 0.973244i | \(-0.426202\pi\) |
0.548785 | + | 0.835964i | \(0.315091\pi\) | |||||||
\(318\) | 0.633395 | − | 0.754851i | 0.0355190 | − | 0.0423299i | ||||
\(319\) | −13.4998 | + | 11.3277i | −0.755844 | + | 0.634228i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.90234 | + | 1.42034i | −0.217807 | + | 0.0792754i | ||||
\(322\) | 8.78604i | 0.489627i | ||||||||
\(323\) | 9.80776 | − | 6.30799i | 0.545718 | − | 0.350986i | ||||
\(324\) | 4.06120 | 0.225622 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.03516 | + | 17.2133i | −0.168102 | + | 0.953354i | ||||
\(327\) | 18.3919 | + | 21.9186i | 1.01707 | + | 1.21210i | ||||
\(328\) | −0.814153 | + | 0.970270i | −0.0449541 | + | 0.0535742i | ||||
\(329\) | −1.44906 | − | 8.21802i | −0.0798892 | − | 0.453074i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.64274 | − | 4.57737i | 0.145258 | − | 0.251595i | −0.784211 | − | 0.620494i | \(-0.786932\pi\) |
0.929469 | + | 0.368899i | \(0.120265\pi\) | |||||||
\(332\) | 1.94969 | − | 5.35672i | 0.107003 | − | 0.293988i | ||||
\(333\) | −2.06262 | + | 5.66701i | −0.113031 | + | 0.310550i | ||||
\(334\) | 11.0752 | − | 19.1829i | 0.606009 | − | 1.04964i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.81142 | − | 32.9582i | −0.317039 | − | 1.79802i | ||||
\(337\) | −15.3550 | + | 18.2993i | −0.836438 | + | 0.996828i | 0.163509 | + | 0.986542i | \(0.447719\pi\) |
−0.999947 | + | 0.0102861i | \(0.996726\pi\) | |||||||
\(338\) | −8.43368 | − | 10.0509i | −0.458732 | − | 0.546695i | ||||
\(339\) | 8.91506 | − | 50.5598i | 0.484200 | − | 2.74603i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4667 | 0.566802 | ||||||||
\(342\) | −32.4572 | + | 7.34290i | −1.75508 | + | 0.397059i | ||||
\(343\) | 0.493173i | 0.0266288i | ||||||||
\(344\) | 20.6345 | − | 7.51036i | 1.11254 | − | 0.404931i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.8239 | + | 10.7606i | −0.689419 | + | 0.578492i | ||||
\(347\) | 5.63534 | − | 6.71594i | 0.302521 | − | 0.360531i | −0.593272 | − | 0.805002i | \(-0.702164\pi\) |
0.895793 | + | 0.444472i | \(0.146609\pi\) | |||||||
\(348\) | 6.54349 | − | 1.15379i | 0.350768 | − | 0.0618499i | ||||
\(349\) | 1.02005 | + | 1.76679i | 0.0546023 | + | 0.0945739i | 0.892035 | − | 0.451967i | \(-0.149278\pi\) |
−0.837432 | + | 0.546541i | \(0.815944\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −42.1208 | − | 15.3307i | −2.24824 | − | 0.818293i | ||||
\(352\) | −2.67859 | + | 7.35936i | −0.142769 | + | 0.392255i | ||||
\(353\) | 7.85009 | + | 4.53225i | 0.417818 | + | 0.241227i | 0.694143 | − | 0.719837i | \(-0.255783\pi\) |
−0.276325 | + | 0.961064i | \(0.589117\pi\) | |||||||
\(354\) | −9.82319 | − | 17.0143i | −0.522097 | − | 0.904298i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.46783 | + | 2.07076i | 0.130795 | + | 0.109750i | ||||
\(357\) | −19.2896 | − | 22.9885i | −1.02092 | − | 1.21668i | ||||
\(358\) | −18.1056 | − | 3.19250i | −0.956909 | − | 0.168729i | ||||
\(359\) | −22.1964 | + | 8.07884i | −1.17148 | + | 0.426385i | −0.853186 | − | 0.521606i | \(-0.825333\pi\) |
−0.318297 | + | 0.947991i | \(0.603111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1498 | + | 8.17830i | −0.902621 | + | 0.430437i | ||||
\(362\) | − | 11.0421i | − | 0.580360i | ||||||
\(363\) | 0.269833 | + | 0.741361i | 0.0141626 | + | 0.0389113i | ||||
\(364\) | 1.31502 | − | 7.45785i | 0.0689258 | − | 0.390898i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.23028 | + | 1.87142i | 0.116578 | + | 0.0978208i | ||||
\(367\) | −10.2628 | + | 1.80960i | −0.535713 | + | 0.0944606i | −0.434958 | − | 0.900451i | \(-0.643237\pi\) |
−0.100755 | + | 0.994911i | \(0.532126\pi\) | |||||||
\(368\) | 4.84978 | − | 2.80002i | 0.252812 | − | 0.145961i | ||||
\(369\) | 1.26448 | − | 2.19015i | 0.0658264 | − | 0.114015i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.910709 | − | 0.331471i | −0.0472817 | − | 0.0172091i | ||||
\(372\) | −3.41762 | − | 1.97317i | −0.177195 | − | 0.102304i | ||||
\(373\) | −7.97137 | + | 4.60227i | −0.412742 | + | 0.238297i | −0.691967 | − | 0.721929i | \(-0.743256\pi\) |
0.279225 | + | 0.960226i | \(0.409922\pi\) | |||||||
\(374\) | −1.95958 | − | 11.1133i | −0.101328 | − | 0.574657i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.22174 | + | 4.38156i | −0.269291 | + | 0.225962i | ||||
\(377\) | −25.0370 | − | 4.41469i | −1.28947 | − | 0.227368i | ||||
\(378\) | 14.8225 | + | 40.7245i | 0.762387 | + | 2.09464i | ||||
\(379\) | −12.6143 | −0.647954 | −0.323977 | − | 0.946065i | \(-0.605020\pi\) | ||||
−0.323977 | + | 0.946065i | \(0.605020\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 59.8228 | 3.06482 | ||||||||
\(382\) | 4.17326 | + | 11.4659i | 0.213522 | + | 0.586648i | ||||
\(383\) | −0.521688 | − | 0.0919877i | −0.0266570 | − | 0.00470035i | 0.160304 | − | 0.987068i | \(-0.448753\pi\) |
−0.186961 | + | 0.982367i | \(0.559864\pi\) | |||||||
\(384\) | −15.0448 | + | 12.6241i | −0.767754 | + | 0.644222i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.42096 | − | 25.0725i | −0.225021 | − | 1.27616i | ||||
\(387\) | −37.9703 | + | 21.9222i | −1.93014 | + | 1.11437i | ||||
\(388\) | 2.62969 | + | 1.51825i | 0.133502 | + | 0.0770776i | ||||
\(389\) | 28.5541 | + | 10.3928i | 1.44775 | + | 0.526938i | 0.941962 | − | 0.335720i | \(-0.108980\pi\) |
0.505788 | + | 0.862658i | \(0.331202\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.51077 | − | 4.34878i | 0.126975 | − | 0.219927i | ||||
\(392\) | −18.0917 | + | 10.4452i | −0.913769 | + | 0.527565i | ||||
\(393\) | 16.0878 | − | 2.83671i | 0.811521 | − | 0.143093i | ||||
\(394\) | 8.91809 | + | 7.48317i | 0.449287 | + | 0.376997i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.48671 | − | 8.43156i | 0.0747100 | − | 0.423702i | ||||
\(397\) | 4.14727 | + | 11.3945i | 0.208146 | + | 0.571875i | 0.999205 | − | 0.0398640i | \(-0.0126925\pi\) |
−0.791060 | + | 0.611739i | \(0.790470\pi\) | |||||||
\(398\) | − | 22.8164i | − | 1.14368i | ||||||
\(399\) | 26.4495 | + | 41.1241i | 1.32413 | + | 2.05878i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.8916 | − | 3.96422i | 0.543900 | − | 0.197963i | −0.0554341 | − | 0.998462i | \(-0.517654\pi\) |
0.599334 | + | 0.800499i | \(0.295432\pi\) | |||||||
\(402\) | 40.1866 | + | 7.08598i | 2.00433 | + | 0.353417i | ||||
\(403\) | 9.70583 | + | 11.5670i | 0.483482 | + | 0.576191i | ||||
\(404\) | 1.44536 | + | 1.21280i | 0.0719096 | + | 0.0603393i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.2902 | + | 21.2873i | 0.609953 | + | 1.05647i | ||||
\(407\) | 2.88572 | + | 1.66607i | 0.143040 | + | 0.0825840i | ||||
\(408\) | −8.38406 | + | 23.0350i | −0.415073 | + | 1.14040i | ||||
\(409\) | 4.54489 | + | 1.65420i | 0.224730 | + | 0.0817952i | 0.451931 | − | 0.892053i | \(-0.350735\pi\) |
−0.227201 | + | 0.973848i | \(0.572957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.9559 | + | 48.4210i | 1.37896 | + | 2.38843i | ||||
\(412\) | 4.44466 | − | 0.783713i | 0.218973 | − | 0.0386108i | ||||
\(413\) | −12.4204 | + | 14.8021i | −0.611170 | + | 0.728364i | ||||
\(414\) | −10.9774 | + | 9.21110i | −0.539508 | + | 0.452701i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.6169 | + | 3.86423i | −0.520535 | + | 0.189459i | ||||
\(417\) | − | 31.6669i | − | 1.55073i | ||||||
\(418\) | 0.881404 | + | 18.3656i | 0.0431109 | + | 0.898291i | ||||
\(419\) | −12.4329 | −0.607385 | −0.303693 | − | 0.952770i | \(-0.598220\pi\) | ||||
−0.303693 | + | 0.952770i | \(0.598220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.79547 | − | 27.1965i | 0.233717 | − | 1.32547i | −0.611582 | − | 0.791181i | \(-0.709467\pi\) |
0.845299 | − | 0.534294i | \(-0.179422\pi\) | |||||||
\(422\) | 14.0439 | + | 16.7369i | 0.683647 | + | 0.814738i | ||||
\(423\) | 8.74850 | − | 10.4261i | 0.425367 | − | 0.506932i | ||||
\(424\) | 0.137471 | + | 0.779635i | 0.00667617 | + | 0.0378624i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.78904 | + | 6.56281i | −0.183580 | + | 0.317969i | ||||
\(427\) | 0.979362 | − | 2.69077i | 0.0473946 | − | 0.130216i | ||||
\(428\) | 0.198061 | − | 0.544168i | 0.00957364 | − | 0.0263034i | ||||
\(429\) | −24.4698 | + | 42.3829i | −1.18141 | + | 2.04627i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.23145 | + | 6.98391i | 0.0593170 | + | 0.336403i | 0.999996 | − | 0.00289506i | \(-0.000921529\pi\) |
−0.940679 | + | 0.339298i | \(0.889810\pi\) | |||||||
\(432\) | 17.7556 | − | 21.1603i | 0.854268 | − | 1.01808i | ||||
\(433\) | 4.23203 | + | 5.04353i | 0.203378 | + | 0.242377i | 0.858087 | − | 0.513505i | \(-0.171653\pi\) |
−0.654709 | + | 0.755881i | \(0.727209\pi\) | |||||||
\(434\) | 2.53510 | − | 14.3773i | 0.121689 | − | 0.690131i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.98995 | −0.191084 | ||||||||
\(437\) | −4.95265 | + | 6.51251i | −0.236917 | + | 0.311536i | ||||
\(438\) | − | 17.2754i | − | 0.825450i | ||||||
\(439\) | 4.16119 | − | 1.51455i | 0.198603 | − | 0.0722855i | −0.240804 | − | 0.970574i | \(-0.577411\pi\) |
0.439407 | + | 0.898288i | \(0.355189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 31.9527 | − | 26.8115i | 1.52156 | − | 1.27674i | ||||
\(442\) | 10.4645 | − | 12.4711i | 0.497744 | − | 0.593188i | ||||
\(443\) | −2.73002 | + | 0.481376i | −0.129707 | + | 0.0228709i | −0.238125 | − | 0.971235i | \(-0.576533\pi\) |
0.108418 | + | 0.994105i | \(0.465422\pi\) | |||||||
\(444\) | −0.628171 | − | 1.08802i | −0.0298117 | − | 0.0516353i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.3076 | + | 3.75166i | 0.488079 | + | 0.177646i | ||||
\(447\) | 15.5989 | − | 42.8577i | 0.737805 | − | 2.02710i | ||||
\(448\) | 28.7036 | + | 16.5720i | 1.35612 | + | 0.782955i | ||||
\(449\) | 13.1785 | + | 22.8258i | 0.621930 | + | 1.07721i | 0.989126 | + | 0.147071i | \(0.0469845\pi\) |
−0.367196 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07042 | − | 0.898186i | −0.0504039 | − | 0.0422939i | ||||
\(452\) | 4.60182 | + | 5.48423i | 0.216451 | + | 0.257957i | ||||
\(453\) | −33.6494 | − | 5.93330i | −1.58099 | − | 0.278771i | ||||
\(454\) | −23.7594 | + | 8.64772i | −1.11508 | + | 0.405857i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.2892 | − | 35.5071i | 0.856470 | − | 1.66277i | ||||
\(457\) | 33.5784i | 1.57073i | 0.619032 | + | 0.785366i | \(0.287525\pi\) | ||||
−0.619032 | + | 0.785366i | \(0.712475\pi\) | |||||||
\(458\) | −8.95969 | − | 24.6165i | −0.418659 | − | 1.15026i | ||||
\(459\) | 4.30114 | − | 24.3930i | 0.200760 | − | 1.13857i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3279 | + | 19.5745i | 1.08649 | + | 0.911674i | 0.996443 | − | 0.0842639i | \(-0.0268539\pi\) |
0.0900469 | + | 0.995938i | \(0.471298\pi\) | |||||||
\(462\) | 46.5984 | − | 8.21655i | 2.16795 | − | 0.382269i | ||||
\(463\) | 24.7477 | − | 14.2881i | 1.15013 | − | 0.664025i | 0.201208 | − | 0.979549i | \(-0.435513\pi\) |
0.948918 | + | 0.315523i | \(0.102180\pi\) | |||||||
\(464\) | 7.83354 | − | 13.5681i | 0.363663 | − | 0.629883i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.642610 | − | 0.233891i | −0.0297683 | − | 0.0108348i | ||||
\(467\) | 9.71443 | + | 5.60863i | 0.449530 | + | 0.259536i | 0.707632 | − | 0.706581i | \(-0.249764\pi\) |
−0.258101 | + | 0.966118i | \(0.583097\pi\) | |||||||
\(468\) | 10.6965 | − | 6.17565i | 0.494448 | − | 0.285470i | ||||
\(469\) | −6.96927 | − | 39.5247i | −0.321811 | − | 1.82508i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.72684 | + | 8.16179i | −0.448189 | + | 0.376075i | ||||
\(472\) | 15.5441 | + | 2.74085i | 0.715477 | + | 0.126158i | ||||
\(473\) | 8.28554 | + | 22.7643i | 0.380969 | + | 1.04670i | ||||
\(474\) | 45.6325 | 2.09597 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.18470 | 0.191806 | ||||||||
\(477\) | −0.540625 | − | 1.48536i | −0.0247535 | − | 0.0680098i | ||||
\(478\) | 27.5097 | + | 4.85070i | 1.25826 | + | 0.221866i | ||||
\(479\) | 13.3219 | − | 11.1784i | 0.608695 | − | 0.510755i | −0.285532 | − | 0.958369i | \(-0.592170\pi\) |
0.894227 | + | 0.447614i | \(0.147726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.834738 | + | 4.73403i | 0.0380608 | + | 0.215853i | ||||
\(482\) | 23.6583 | − | 13.6591i | 1.07761 | − | 0.622156i | ||||
\(483\) | 18.2345 | + | 10.5277i | 0.829697 | + | 0.479026i | ||||
\(484\) | −0.103380 | − | 0.0376273i | −0.00469910 | − | 0.00171033i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.847018 | + | 1.46708i | −0.0384215 | + | 0.0665480i | ||||
\(487\) | 13.2911 | − | 7.67364i | 0.602278 | − | 0.347726i | −0.167659 | − | 0.985845i | \(-0.553621\pi\) |
0.769937 | + | 0.638119i | \(0.220287\pi\) | |||||||
\(488\) | −2.30350 | + | 0.406170i | −0.104275 | + | 0.0183864i | ||||
\(489\) | 32.0874 | + | 26.9246i | 1.45104 | + | 1.21757i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.45066 | − | 8.22710i | 0.0654673 | − | 0.371284i | −0.934419 | − | 0.356177i | \(-0.884080\pi\) |
0.999886 | − | 0.0151068i | \(-0.00480884\pi\) | |||||||
\(492\) | 0.180192 | + | 0.495073i | 0.00812368 | + | 0.0223196i | ||||
\(493\) | − | 14.0486i | − | 0.632717i | ||||||
\(494\) | −19.4789 | + | 18.0046i | −0.876398 | + | 0.810067i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.74398 | + | 3.18255i | −0.392616 | + | 0.142901i | ||||
\(497\) | 7.34003 | + | 1.29425i | 0.329245 | + | 0.0580548i | ||||
\(498\) | 33.0289 | + | 39.3623i | 1.48006 | + | 1.76387i | ||||
\(499\) | −0.207470 | − | 0.174088i | −0.00928764 | − | 0.00779325i | 0.638132 | − | 0.769927i | \(-0.279707\pi\) |
−0.647420 | + | 0.762134i | \(0.724152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.5413 | − | 45.9709i | −1.18578 | − | 2.05383i | ||||
\(502\) | −19.4024 | − | 11.2020i | −0.865973 | − | 0.499970i | ||||
\(503\) | −14.2279 | + | 39.0907i | −0.634389 | + | 1.74297i | 0.0342827 | + | 0.999412i | \(0.489085\pi\) |
−0.668672 | + | 0.743558i | \(0.733137\pi\) | |||||||
\(504\) | −64.6521 | − | 23.5314i | −2.87983 | − | 1.04817i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.95885 | + | 6.85693i | 0.175992 | + | 0.304828i | ||||
\(507\) | −30.9650 | + | 5.45996i | −1.37520 | + | 0.242485i | ||||
\(508\) | −5.36219 | + | 6.39041i | −0.237909 | + | 0.283529i | ||||
\(509\) | −1.24694 | + | 1.04631i | −0.0552696 | + | 0.0463767i | −0.670004 | − | 0.742357i | \(-0.733708\pi\) |
0.614734 | + | 0.788734i | \(0.289263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.9662 | + | 5.81121i | −0.706301 | + | 0.257073i | ||||
\(512\) | − | 25.1134i | − | 1.10987i | ||||||
\(513\) | −11.9693 | + | 38.5418i | −0.528456 | + | 1.70166i | ||||
\(514\) | −19.7643 | −0.871766 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.58608 | − | 8.99508i | 0.0698231 | − | 0.395987i | ||||
\(517\) | −4.83380 | − | 5.76070i | −0.212590 | − | 0.253355i | ||||
\(518\) | 2.98749 | − | 3.56035i | 0.131263 | − | 0.156433i | ||||
\(519\) | 6.96638 | + | 39.5083i | 0.305790 | + | 1.73422i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.57062 | − | 7.91655i | 0.200243 | − | 0.346830i | −0.748364 | − | 0.663288i | \(-0.769160\pi\) |
0.948607 | + | 0.316458i | \(0.102494\pi\) | |||||||
\(522\) | −13.7117 | + | 37.6726i | −0.600145 | + | 1.64889i | ||||
\(523\) | −12.7572 | + | 35.0501i | −0.557833 | + | 1.53263i | 0.264942 | + | 0.964264i | \(0.414647\pi\) |
−0.822774 | + | 0.568368i | \(0.807575\pi\) | |||||||
\(524\) | −1.13900 | + | 1.97280i | −0.0497573 | + | 0.0861822i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.64638 | − | 37.6935i | −0.289796 | − | 1.64351i | ||||
\(527\) | −5.36334 | + | 6.39178i | −0.233631 | + | 0.278430i | ||||
\(528\) | −19.3859 | − | 23.1032i | −0.843662 | − | 1.00544i | ||||
\(529\) | 3.38210 | − | 19.1809i | 0.147048 | − | 0.833951i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.5152 | −1.36764 | ||||||||
\(532\) | −6.76376 | − | 0.860742i | −0.293246 | − | 0.0373179i | ||||
\(533\) | − | 2.01584i | − | 0.0873156i | ||||||
\(534\) | −27.2873 | + | 9.93177i | −1.18084 | + | 0.429790i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.1140 | + | 21.0732i | −1.08476 | + | 0.910223i | ||||
\(537\) | −28.3203 | + | 33.7508i | −1.22211 | + | 1.45645i | ||||
\(538\) | 3.23320 | − | 0.570101i | 0.139393 | − | 0.0245788i | ||||
\(539\) | −11.5234 | − | 19.9590i | −0.496346 | − | 0.859696i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0583 | + | 12.3962i | 1.46428 | + | 0.532955i | 0.946541 | − | 0.322582i | \(-0.104551\pi\) |
0.517741 | + | 0.855538i | \(0.326773\pi\) | |||||||
\(542\) | −4.13063 | + | 11.3488i | −0.177426 | + | 0.487474i | ||||
\(543\) | −22.9167 | − | 13.2310i | −0.983449 | − | 0.567795i | ||||
\(544\) | −3.12165 | − | 5.40685i | −0.133839 | − | 0.231817i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 52.2914 | + | 43.8777i | 2.23786 | + | 1.87779i | ||||
\(547\) | −9.70823 | − | 11.5698i | −0.415094 | − | 0.494690i | 0.517466 | − | 0.855704i | \(-0.326875\pi\) |
−0.932561 | + | 0.361014i | \(0.882431\pi\) | |||||||
\(548\) | −7.67826 | − | 1.35388i | −0.327999 | − | 0.0578351i | ||||
\(549\) | 4.38862 | − | 1.59733i | 0.187302 | − | 0.0681722i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.88962 | + | 22.7068i | −0.123102 | + | 0.967342i | ||||
\(552\) | − | 17.1992i | − | 0.732047i | ||||||
\(553\) | −15.3502 | − | 42.1742i | −0.652755 | − | 1.79343i | ||||
\(554\) | −4.38004 | + | 24.8404i | −0.186090 | + | 1.05537i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.38273 | + | 2.83845i | 0.143460 | + | 0.120377i | ||||
\(557\) | 9.22051 | − | 1.62582i | 0.390685 | − | 0.0688884i | 0.0251450 | − | 0.999684i | \(-0.491995\pi\) |
0.365541 | + | 0.930795i | \(0.380884\pi\) | |||||||
\(558\) | 20.6208 | − | 11.9054i | 0.872949 | − | 0.503997i | ||||
\(559\) | −17.4741 | + | 30.2661i | −0.739077 | + | 1.28012i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.4126 | − | 9.24942i | −1.07292 | − | 0.390511i | ||||
\(562\) | −28.9073 | − | 16.6897i | −1.21938 | − | 0.704011i | ||||
\(563\) | 12.5101 | − | 7.22271i | 0.527238 | − | 0.304401i | −0.212653 | − | 0.977128i | \(-0.568210\pi\) |
0.739891 | + | 0.672727i | \(0.234877\pi\) | |||||||
\(564\) | 0.492353 | + | 2.79227i | 0.0207318 | + | 0.117576i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.1561 | + | 13.5566i | −0.679092 | + | 0.569826i | ||||
\(567\) | 35.4574 | + | 6.25209i | 1.48907 | + | 0.262563i | ||||
\(568\) | −2.08230 | − | 5.72108i | −0.0873715 | − | 0.240051i | ||||
\(569\) | 37.8642 | 1.58735 | 0.793675 | − | 0.608342i | \(-0.208165\pi\) | ||||
0.793675 | + | 0.608342i | \(0.208165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.5203 | −0.775048 | −0.387524 | − | 0.921860i | \(-0.626670\pi\) | ||||
−0.387524 | + | 0.921860i | \(0.626670\pi\) | |||||||
\(572\) | −2.33410 | − | 6.41289i | −0.0975937 | − | 0.268136i | ||||
\(573\) | 28.7968 | + | 5.07766i | 1.20300 | + | 0.212122i | ||||
\(574\) | −1.49303 | + | 1.25280i | −0.0623179 | + | 0.0522909i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.38699 | + | 53.2363i | 0.391125 | + | 2.21818i | ||||
\(577\) | −7.86434 | + | 4.54048i | −0.327397 | + | 0.189022i | −0.654685 | − | 0.755902i | \(-0.727199\pi\) |
0.327288 | + | 0.944925i | \(0.393865\pi\) | |||||||
\(578\) | −10.7147 | − | 6.18614i | −0.445673 | − | 0.257309i | ||||
\(579\) | −57.3326 | − | 20.8674i | −2.38266 | − | 0.867218i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.2688 | − | 43.7668i | 1.04832 | − | 1.81575i | ||||
\(582\) | −23.7038 | + | 13.6854i | −0.982556 | + | 0.567279i | ||||
\(583\) | −0.860105 | + | 0.151660i | −0.0356219 | + | 0.00628110i | ||||
\(584\) | 10.6320 | + | 8.92130i | 0.439955 | + | 0.369166i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.92017 | − | 16.5611i | 0.120631 | − | 0.684134i | ||||
\(587\) | 7.87923 | + | 21.6480i | 0.325211 | + | 0.893509i | 0.989305 | + | 0.145860i | \(0.0465950\pi\) |
−0.664094 | + | 0.747649i | \(0.731183\pi\) | |||||||
\(588\) | 8.68948i | 0.358348i | ||||||||
\(589\) | 9.98350 | − | 9.22789i | 0.411363 | − | 0.380229i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.2164 | − | 9.54200i | 1.07840 | − | 0.392505i | ||||
\(592\) | −2.91735 | − | 0.514408i | −0.119903 | − | 0.0211421i | ||||
\(593\) | −25.8678 | − | 30.8280i | −1.06226 | − | 1.26596i | −0.962598 | − | 0.270935i | \(-0.912667\pi\) |
−0.0996654 | − | 0.995021i | \(-0.531777\pi\) | |||||||
\(594\) | 29.9178 | + | 25.1040i | 1.22754 | + | 1.03003i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.17996 | + | 5.50785i | 0.130256 | + | 0.225610i | ||||
\(597\) | −47.3530 | − | 27.3393i | −1.93803 | − | 1.11892i | ||||
\(598\) | −3.90668 | + | 10.7335i | −0.159756 | + | 0.438926i | ||||
\(599\) | −35.4913 | − | 12.9178i | −1.45014 | − | 0.527807i | −0.507507 | − | 0.861647i | \(-0.669433\pi\) |
−0.942629 | + | 0.333841i | \(0.891655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.9195 | − | 37.9656i | −0.894113 | − | 1.54865i | −0.834898 | − | 0.550404i | \(-0.814474\pi\) |
−0.0592147 | − | 0.998245i | \(-0.518860\pi\) | |||||||
\(602\) | 33.2764 | − | 5.86753i | 1.35625 | − | 0.239143i | ||||
\(603\) | 42.0760 | − | 50.1443i | 1.71347 | − | 2.04203i | ||||
\(604\) | 3.64996 | − | 3.06268i | 0.148515 | − | 0.124619i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.9817 | + | 5.81686i | −0.649212 | + | 0.236294i | ||||
\(607\) | − | 7.80810i | − | 0.316921i | −0.987365 | − | 0.158461i | \(-0.949347\pi\) | ||
0.987365 | − | 0.158461i | \(-0.0506531\pi\) | |||||||
\(608\) | 3.93341 | + | 9.38120i | 0.159521 | + | 0.380458i | ||||
\(609\) | 58.9059 | 2.38699 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.88386 | − | 10.6839i | 0.0762128 | − | 0.432224i | ||||
\(612\) | 4.38715 | + | 5.22841i | 0.177340 | + | 0.211346i | ||||
\(613\) | −25.0017 | + | 29.7958i | −1.00981 | + | 1.20344i | −0.0308202 | + | 0.999525i | \(0.509812\pi\) |
−0.978988 | + | 0.203918i | \(0.934633\pi\) | |||||||
\(614\) | −6.10549 | − | 34.6259i | −0.246397 | − | 1.39739i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.0074 | + | 32.9217i | −0.765829 | + | 1.32645i | ||||
\(617\) | 4.26208 | − | 11.7100i | 0.171585 | − | 0.471426i | −0.823857 | − | 0.566798i | \(-0.808182\pi\) |
0.995442 | + | 0.0953722i | \(0.0304041\pi\) | |||||||
\(618\) | −13.9140 | + | 38.2284i | −0.559704 | + | 1.53777i | ||||
\(619\) | −1.37870 | + | 2.38799i | −0.0554148 | + | 0.0959813i | −0.892402 | − | 0.451241i | \(-0.850981\pi\) |
0.836987 | + | 0.547222i | \(0.184315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.01779 | + | 17.1147i | 0.121100 | + | 0.686791i | ||||
\(622\) | −20.0657 | + | 23.9133i | −0.804561 | + | 0.958838i | ||||
\(623\) | 18.3582 | + | 21.8784i | 0.735505 | + | 0.876540i | ||||
\(624\) | 7.55518 | − | 42.8476i | 0.302449 | − | 1.71527i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.9958 | −1.11894 | ||||||||
\(627\) | 39.1719 | + | 20.1769i | 1.56438 | + | 0.805789i | ||||
\(628\) | − | 1.77062i | − | 0.0706555i | ||||||
\(629\) | −2.49614 | + | 0.908519i | −0.0995275 | + | 0.0362250i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.5821 | + | 25.6614i | −1.21745 | + | 1.02156i | −0.218498 | + | 0.975837i | \(0.570116\pi\) |
−0.998954 | + | 0.0457265i | \(0.985440\pi\) | |||||||
\(632\) | −23.5654 | + | 28.0841i | −0.937381 | + | 1.11713i | ||||
\(633\) | 51.5634 | − | 9.09201i | 2.04946 | − | 0.361375i | ||||
\(634\) | −8.84628 | − | 15.3222i | −0.351331 | − | 0.608522i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.309436 | + | 0.112625i | 0.0122699 | + | 0.00446589i | ||||
\(637\) | 11.3715 | − | 31.2429i | 0.450555 | − | 1.23789i | ||||
\(638\) | 19.1834 | + | 11.0755i | 0.759479 | + | 0.438485i | ||||
\(639\) | 6.07809 | + | 10.5276i | 0.240445 | + | 0.416464i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.83994 | − | 3.22209i | −0.151668 | − | 0.127265i | 0.563796 | − | 0.825914i | \(-0.309340\pi\) |
−0.715464 | + | 0.698649i | \(0.753785\pi\) | |||||||
\(642\) | 3.35528 | + | 3.99866i | 0.132422 | + | 0.157815i | ||||
\(643\) | −49.2161 | − | 8.67812i | −1.94089 | − | 0.342232i | −0.999994 | − | 0.00354380i | \(-0.998872\pi\) |
−0.940899 | − | 0.338688i | \(-0.890017\pi\) | |||||||
\(644\) | −2.75903 | + | 1.00420i | −0.108721 | + | 0.0395712i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.6671 | − | 8.87266i | −0.459038 | − | 0.349090i | ||||
\(647\) | 32.7681i | 1.28825i | 0.764922 | + | 0.644123i | \(0.222777\pi\) | ||||
−0.764922 | + | 0.644123i | \(0.777223\pi\) | |||||||
\(648\) | −10.0589 | − | 27.6367i | −0.395153 | − | 1.08567i | ||||
\(649\) | −3.02375 | + | 17.1485i | −0.118693 | + | 0.673139i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.8008 | − | 22.4886i | −1.05041 | − | 0.881396i | ||||
\(652\) | −5.75229 | + | 1.01428i | −0.225277 | + | 0.0397224i | ||||
\(653\) | −13.6828 | + | 7.89978i | −0.535450 | + | 0.309142i | −0.743233 | − | 0.669033i | \(-0.766709\pi\) |
0.207783 | + | 0.978175i | \(0.433375\pi\) | |||||||
\(654\) | 17.9825 | − | 31.1467i | 0.703173 | − | 1.21793i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.16734 | + | 0.424879i | 0.0455772 | + | 0.0165887i | ||||
\(657\) | −23.9992 | − | 13.8559i | −0.936296 | − | 0.540571i | ||||
\(658\) | −9.08381 | + | 5.24454i | −0.354124 | + | 0.204453i | ||||
\(659\) | 2.35267 | + | 13.3426i | 0.0916468 | + | 0.519755i | 0.995723 | + | 0.0923845i | \(0.0294489\pi\) |
−0.904077 | + | 0.427370i | \(0.859440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.80202 | − | 2.35117i | 0.108986 | − | 0.0914501i | −0.586666 | − | 0.809829i | \(-0.699560\pi\) |
0.695652 | + | 0.718379i | \(0.255115\pi\) | |||||||
\(662\) | −6.54272 | − | 1.15366i | −0.254290 | − | 0.0448382i | ||||
\(663\) | −13.3435 | − | 36.6611i | −0.518220 | − | 1.42380i | ||||
\(664\) | −41.2819 | −1.60205 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.58036 | 0.293733 | ||||||||
\(667\) | 3.37124 | + | 9.26242i | 0.130535 | + | 0.358642i | ||||
\(668\) | 7.28973 | + | 1.28538i | 0.282048 | + | 0.0497327i | ||||
\(669\) | 20.1370 | − | 16.8970i | 0.778542 | − | 0.653275i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.448092 | − | 2.54126i | −0.0172984 | − | 0.0981042i | ||||
\(672\) | 22.6710 | − | 13.0891i | 0.874552 | − | 0.504923i | ||||
\(673\) | −23.3223 | − | 13.4651i | −0.899009 | − | 0.519043i | −0.0221303 | − | 0.999755i | \(-0.507045\pi\) |
−0.876878 | + | 0.480712i | \(0.840378\pi\) | |||||||
\(674\) | 28.2156 | + | 10.2696i | 1.08682 | + | 0.395571i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.19229 | − | 3.79715i | 0.0843187 | − | 0.146044i | ||||
\(677\) | 17.9209 | − | 10.3467i | 0.688757 | − | 0.397654i | −0.114389 | − | 0.993436i | \(-0.536491\pi\) |
0.803146 | + | 0.595782i | \(0.203158\pi\) | |||||||
\(678\) | −63.5517 | + | 11.2059i | −2.44069 | + | 0.430359i | ||||
\(679\) | 20.6219 | + | 17.3038i | 0.791396 | + | 0.664060i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5218 | + | 59.6720i | −0.403196 | + | 2.28664i | ||||
\(682\) | −4.49969 | − | 12.3628i | −0.172302 | − | 0.473396i | ||||
\(683\) | − | 26.9573i | − | 1.03149i | −0.856742 | − | 0.515745i | \(-0.827515\pi\) | ||
0.856742 | − | 0.515745i | \(-0.172485\pi\) | |||||||
\(684\) | −6.01556 | − | 9.35308i | −0.230011 | − | 0.357624i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.582515 | − | 0.212018i | 0.0222405 | − | 0.00809489i | ||||
\(687\) | −61.8247 | − | 10.9014i | −2.35876 | − | 0.415913i | ||||
\(688\) | −13.8437 | − | 16.4982i | −0.527785 | − | 0.628989i | ||||
\(689\) | −0.965185 | − | 0.809886i | −0.0367706 | − | 0.0308542i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.35021 | − | 7.53479i | −0.165490 | − | 0.286637i | 0.771339 | − | 0.636424i | \(-0.219587\pi\) |
−0.936829 | + | 0.349787i | \(0.886254\pi\) | |||||||
\(692\) | −4.84480 | − | 2.79715i | −0.184172 | − | 0.106332i | ||||
\(693\) | 25.9602 | − | 71.3252i | 0.986148 | − | 2.70942i | ||||
\(694\) | −10.3553 | − | 3.76900i | −0.393080 | − | 0.143069i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −24.0588 | − | 41.6711i | −0.911948 | − | 1.57954i | ||||
\(697\) | 1.09701 | − | 0.193432i | 0.0415521 | − | 0.00732676i | ||||
\(698\) | 1.64832 | − | 1.96440i | 0.0623900 | − | 0.0743535i | ||||
\(699\) | −1.25541 | + | 1.05341i | −0.0474839 | + | 0.0398437i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.378762 | − | 0.137858i | 0.0143056 | − | 0.00520683i | −0.334857 | − | 0.942269i | \(-0.608688\pi\) |
0.349163 | + | 0.937062i | \(0.386466\pi\) | |||||||
\(702\) | 56.3420i | 2.12649i | ||||||||
\(703\) | 4.22139 | − | 0.955019i | 0.159213 | − | 0.0360192i | ||||
\(704\) | 29.8684 | 1.12571 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.97850 | − | 11.2206i | 0.0744618 | − | 0.422294i | ||||
\(707\) | 10.7521 | + | 12.8138i | 0.404373 | + | 0.481913i | ||||
\(708\) | 4.22015 | − | 5.02938i | 0.158603 | − | 0.189016i | ||||
\(709\) | −6.95535 | − | 39.4457i | −0.261214 | − | 1.48142i | −0.779604 | − | 0.626272i | \(-0.784580\pi\) |
0.518391 | − | 0.855144i | \(-0.326531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 36.6001 | − | 63.3932i | 1.37261 | − | 2.37743i | ||||
\(712\) | 7.97920 | − | 21.9227i | 0.299033 | − | 0.821587i | ||||
\(713\) | 2.00228 | − | 5.50123i | 0.0749861 | − | 0.206023i | ||||
\(714\) | −18.8603 | + | 32.6670i | −0.705829 | + | 1.22253i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.06686 | − | 6.05048i | −0.0398705 | − | 0.226117i | ||||
\(717\) | 43.0299 | − | 51.2811i | 1.60698 | − | 1.91513i | ||||
\(718\) | 19.0848 | + | 22.7443i | 0.712237 | + | 0.848811i | ||||
\(719\) | −3.13880 | + | 17.8010i | −0.117058 | + | 0.663867i | 0.868653 | + | 0.495421i | \(0.164986\pi\) |
−0.985711 | + | 0.168446i | \(0.946125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.0118 | 1.49012 | ||||||||
\(722\) | 17.0327 | + | 16.7407i | 0.633890 | + | 0.623024i | ||||
\(723\) | − | 65.4670i | − | 2.43474i | ||||||
\(724\) | 3.46749 | − | 1.26206i | 0.128868 | − | 0.0469042i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.759660 | − | 0.637431i | 0.0281936 | − | 0.0236573i | ||||
\(727\) | −16.9448 | + | 20.1940i | −0.628446 | + | 0.748953i | −0.982498 | − | 0.186273i | \(-0.940359\pi\) |
0.354052 | + | 0.935226i | \(0.384804\pi\) | |||||||
\(728\) | −54.0083 | + | 9.52311i | −2.00168 | + | 0.352950i | ||||
\(729\) | −12.4728 | − | 21.6035i | −0.461954 | − | 0.800129i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1474 | − | 6.60511i | −0.671205 | − | 0.244299i | ||||
\(732\) | −0.332762 | + | 0.914256i | −0.0122992 | + | 0.0337919i | ||||
\(733\) | −2.86584 | − | 1.65460i | −0.105852 | − | 0.0611139i | 0.446139 | − | 0.894964i | \(-0.352799\pi\) |
−0.551992 | + | 0.833850i | \(0.686132\pi\) | |||||||
\(734\) | 6.54946 | + | 11.3440i | 0.241745 | + | 0.418714i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.35562 | + | 2.81570i | 0.123690 | + | 0.103788i | ||||
\(737\) | −23.2482 | − | 27.7062i | −0.856360 | − | 1.02057i | ||||
\(738\) | −3.13052 | − | 0.551996i | −0.115236 | − | 0.0203192i | ||||
\(739\) | 16.6272 | − | 6.05179i | 0.611640 | − | 0.222619i | −0.0175807 | − | 0.999845i | \(-0.505596\pi\) |
0.629221 | + | 0.777227i | \(0.283374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.0265 | + | 62.0000i | 0.515276 | + | 2.27763i | ||||
\(742\) | 1.21819i | 0.0447212i | ||||||||
\(743\) | 12.7413 | + | 35.0065i | 0.467434 | + | 1.28427i | 0.919784 | + | 0.392425i | \(0.128364\pi\) |
−0.452350 | + | 0.891841i | \(0.649414\pi\) | |||||||
\(744\) | −4.96261 | + | 28.1444i | −0.181938 | + | 1.03182i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.86295 | + | 7.43689i | 0.324496 | + | 0.272284i | ||||
\(747\) | 81.1738 | − | 14.3131i | 2.96999 | − | 0.523690i | ||||
\(748\) | 3.26589 | − | 1.88556i | 0.119413 | − | 0.0689430i | ||||
\(749\) | 2.56695 | − | 4.44609i | 0.0937944 | − | 0.162457i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7466 | + | 4.63939i | 0.465131 | + | 0.169294i | 0.563945 | − | 0.825812i | \(-0.309283\pi\) |
−0.0988146 | + | 0.995106i | \(0.531505\pi\) | |||||||
\(752\) | 5.78984 | + | 3.34277i | 0.211134 | + | 0.121898i | ||||
\(753\) | −46.4971 | + | 26.8451i | −1.69445 | + | 0.978289i | ||||
\(754\) | 5.54909 | + | 31.4705i | 0.202086 | + | 1.14609i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.0943 | + | 9.30925i | −0.403497 | + | 0.338574i | ||||
\(757\) | 12.3465 | + | 2.17703i | 0.448743 | + | 0.0791255i | 0.393453 | − | 0.919345i | \(-0.371281\pi\) |
0.0552901 | + | 0.998470i | \(0.482392\pi\) | |||||||
\(758\) | 5.42297 | + | 14.8995i | 0.196971 | + | 0.541174i | ||||
\(759\) | 18.9744 | 0.688728 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2282 | −0.987022 | −0.493511 | − | 0.869740i | \(-0.664287\pi\) | ||||
−0.493511 | + | 0.869740i | \(0.664287\pi\) | |||||||
\(762\) | −25.7182 | − | 70.6601i | −0.931672 | − | 2.55975i | ||||
\(763\) | −34.8353 | − | 6.14240i | −1.26112 | − | 0.222370i | ||||
\(764\) | −3.12360 | + | 2.62101i | −0.113008 | + | 0.0948248i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.115625 | + | 0.655742i | 0.00417770 | + | 0.0236929i | ||||
\(767\) | −21.7552 | + | 12.5604i | −0.785534 | + | 0.453528i | ||||
\(768\) | −25.0574 | − | 14.4669i | −0.904179 | − | 0.522028i | ||||
\(769\) | −0.864690 | − | 0.314721i | −0.0311815 | − | 0.0113491i | 0.326382 | − | 0.945238i | \(-0.394170\pi\) |
−0.357564 | + | 0.933889i | \(0.616393\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.6821 | + | 41.0187i | −0.852892 | + | 1.47725i | ||||
\(772\) | 7.36809 | − | 4.25397i | 0.265183 | − | 0.153104i | ||||
\(773\) | −1.80207 | + | 0.317753i | −0.0648158 | + | 0.0114288i | −0.205962 | − | 0.978560i | \(-0.566032\pi\) |
0.141146 | + | 0.989989i | \(0.454921\pi\) | |||||||
\(774\) | 42.2172 | + | 35.4245i | 1.51747 | + | 1.27331i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.81848 | − | 21.6557i | 0.137076 | − | 0.777394i | ||||
\(777\) | −3.80943 | − | 10.4663i | −0.136663 | − | 0.375478i | ||||
\(778\) | − | 38.1948i | − | 1.36935i | ||||||
\(779\) | −1.81288 | + | 0.0870041i | −0.0649533 | + | 0.00311725i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.31158 | − | 2.29723i | 0.225846 | − | 0.0822013i | ||||
\(782\) | −6.21598 | − | 1.09605i | −0.222283 | − | 0.0391945i | ||||
\(783\) | 31.2524 | + | 37.2451i | 1.11687 | + | 1.33103i | ||||
\(784\) | 15.6956 | + | 13.1702i | 0.560556 | + | 0.470363i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.2668 | − | 17.7827i | −0.366206 | − | 0.634287i | ||||
\(787\) | 2.51571 | + | 1.45244i | 0.0896752 | + | 0.0517740i | 0.544167 | − | 0.838977i | \(-0.316846\pi\) |
−0.454492 | + | 0.890751i | \(0.650179\pi\) | |||||||
\(788\) | −1.33060 | + | 3.65579i | −0.0474006 | + | 0.130232i | ||||
\(789\) | −86.1927 | − | 31.3716i | −3.06854 | − | 1.11686i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.7346 | + | 54.9659i | 1.12835 | + | 1.95436i | ||||
\(792\) | −61.0596 | + | 10.7665i | −2.16966 | + | 0.382570i | ||||
\(793\) | 2.39288 | − | 2.85173i | 0.0849737 | − | 0.101268i | ||||
\(794\) | 11.6758 | − | 9.79716i | 0.414358 | − | 0.347688i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.16491 | − | 2.60782i | 0.253954 | − | 0.0924316i | ||||
\(797\) | 19.9042i | 0.705044i | 0.935804 | + | 0.352522i | \(0.114676\pi\) | ||||
−0.935804 | + | 0.352522i | \(0.885324\pi\) | |||||||
\(798\) | 37.2032 | − | 48.9205i | 1.31698 | − | 1.73177i | ||||
\(799\) | 5.99488 | 0.212084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.08878 | + | 45.8737i | −0.285803 | + | 1.62087i | ||||
\(802\) | −9.36472 | − | 11.1604i | −0.330680 | − | 0.394089i | ||||
\(803\) | −9.84211 | + | 11.7294i | −0.347320 | + | 0.413920i | ||||
\(804\) | 2.36798 | + | 13.4295i | 0.0835121 | + | 0.473621i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.48980 | − | 16.4368i | 0.334264 | − | 0.578962i | ||||
\(807\) | 2.69093 | − | 7.39327i | 0.0947252 | − | 0.260255i | ||||
\(808\) | 4.67328 | − | 12.8397i | 0.164405 | − | 0.451700i | ||||
\(809\) | 22.2093 | − | 38.4677i | 0.780838 | − | 1.35245i | −0.150616 | − | 0.988592i | \(-0.548126\pi\) |
0.931454 | − | 0.363859i | \(-0.118541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.91262 | + | 33.5322i | 0.207620 | + | 1.17747i | 0.893263 | + | 0.449535i | \(0.148410\pi\) |
−0.685642 | + | 0.727939i | \(0.740479\pi\) | |||||||
\(812\) | −5.28001 | + | 6.29247i | −0.185292 | + | 0.220822i | ||||
\(813\) | 18.6038 | + | 22.1712i | 0.652464 | + | 0.777577i | ||||
\(814\) | 0.727303 | − | 4.12474i | 0.0254920 | − | 0.144572i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 24.0424 | 0.841651 | ||||||||
\(817\) | 27.9731 | + | 14.4086i | 0.978655 | + | 0.504092i | ||||
\(818\) | − | 6.07938i | − | 0.212561i | ||||||
\(819\) | 102.896 | − | 37.4512i | 3.59548 | − | 1.30865i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.5350 | + | 17.2309i | −0.716675 | + | 0.601362i | −0.926463 | − | 0.376385i | \(-0.877167\pi\) |
0.209788 | + | 0.977747i | \(0.432723\pi\) | |||||||
\(822\) | 45.1744 | − | 53.8368i | 1.57564 | − | 1.87777i | ||||
\(823\) | 10.8729 | − | 1.91719i | 0.379006 | − | 0.0668290i | 0.0191001 | − | 0.999818i | \(-0.493920\pi\) |
0.359906 | + | 0.932989i | \(0.382809\pi\) | |||||||
\(824\) | −16.3419 | − | 28.3051i | −0.569298 | − | 0.986054i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.8232 | + | 8.30698i | 0.794122 | + | 0.289037i | ||||
\(827\) | 4.06958 | − | 11.1811i | 0.141513 | − | 0.388804i | −0.848607 | − | 0.529023i | \(-0.822558\pi\) |
0.990121 | + | 0.140219i | \(0.0447807\pi\) | |||||||
\(828\) | −4.14717 | − | 2.39437i | −0.144124 | − | 0.0832101i | ||||
\(829\) | 5.60968 | + | 9.71626i | 0.194832 | + | 0.337460i | 0.946846 | − | 0.321689i | \(-0.104250\pi\) |
−0.752013 | + | 0.659148i | \(0.770917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 46.3054 | + | 38.8548i | 1.60632 | + | 1.34786i | ||||
\(832\) | 27.6972 | + | 33.0082i | 0.960227 | + | 1.14435i | ||||
\(833\) | 18.0934 | + | 3.19035i | 0.626898 | + | 0.110539i | ||||
\(834\) | −37.4036 | + | 13.6138i | −1.29518 | + | 0.471407i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.66651 | + | 2.37589i | −0.195980 | + | 0.0821718i | ||||
\(837\) | − | 28.8769i | − | 0.998132i | ||||||
\(838\) | 5.34496 | + | 14.6852i | 0.184639 | + | 0.507291i | ||||
\(839\) | 6.22171 | − | 35.2851i | 0.214797 | − | 1.21818i | −0.666460 | − | 0.745540i | \(-0.732191\pi\) |
0.881258 | − | 0.472636i | \(-0.156697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.09068 | − | 0.915188i | −0.0376096 | − | 0.0315582i | ||||
\(842\) | −34.1849 | + | 6.02772i | −1.17809 | + | 0.207729i | ||||
\(843\) | −69.2752 | + | 39.9960i | −2.38596 | + | 1.37754i | ||||
\(844\) | −3.65063 | + | 6.32308i | −0.125660 | + | 0.217649i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16.0759 | − | 5.85113i | −0.552699 | − | 0.201166i | ||||
\(847\) | −0.844662 | − | 0.487666i | −0.0290229 | − | 0.0167564i | ||||
\(848\) | 0.672427 | − | 0.388226i | 0.0230912 | − | 0.0133317i | ||||
\(849\) | 8.77653 | + | 49.7742i | 0.301210 | + | 1.70825i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.42772 | − | 1.19800i | 0.0489415 | − | 0.0410668i | ||||
\(852\) | −2.49395 | − | 0.439751i | −0.0854415 | − | 0.0150656i | ||||
\(853\) | 4.46788 | + | 12.2754i | 0.152977 | + | 0.420302i | 0.992381 | − | 0.123207i | \(-0.0393178\pi\) |
−0.839404 | + | 0.543509i | \(0.817096\pi\) | |||||||
\(854\) | −3.59926 | −0.123164 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.19366 | −0.143337 | ||||||||
\(857\) | 8.27355 | + | 22.7314i | 0.282619 | + | 0.776489i | 0.997048 | + | 0.0767813i | \(0.0244643\pi\) |
−0.714429 | + | 0.699708i | \(0.753313\pi\) | |||||||
\(858\) | 60.5806 | + | 10.6820i | 2.06819 | + | 0.364677i | ||||
\(859\) | −41.4832 | + | 34.8086i | −1.41539 | + | 1.18765i | −0.461633 | + | 0.887071i | \(0.652736\pi\) |
−0.953756 | + | 0.300581i | \(0.902819\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.811063 | + | 4.59977i | 0.0276409 | + | 0.156760i | ||||
\(862\) | 7.71969 | − | 4.45696i | 0.262934 | − | 0.151805i | ||||
\(863\) | 43.0287 | + | 24.8426i | 1.46471 | + | 0.845653i | 0.999224 | − | 0.0394004i | \(-0.0125448\pi\) |
0.465490 | + | 0.885053i | \(0.345878\pi\) | |||||||
\(864\) | 20.3040 | + | 7.39006i | 0.690757 | + | 0.251415i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.13783 | − | 7.16693i | 0.140609 | − | 0.243542i | ||||
\(867\) | −25.6773 | + | 14.8248i | −0.872048 | + | 0.503477i | ||||
\(868\) | 4.80456 | − | 0.847174i | 0.163077 | − | 0.0287549i | ||||
\(869\) | −30.9828 | − | 25.9977i | −1.05102 | − | 0.881911i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.06045 | − | 51.3843i | 0.307001 | − | 1.74109i | ||||
\(872\) | 9.88246 | + | 27.1518i | 0.334662 | + | 0.919478i | ||||
\(873\) | 43.9062i | 1.48600i | ||||||||
\(874\) | 9.82147 | + | 3.05009i | 0.332216 | + | 0.103171i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.42489 | − | 1.97450i | 0.183290 | − | 0.0667122i | ||||
\(877\) | −8.14572 | − | 1.43631i | −0.275061 | − | 0.0485007i | 0.0344159 | − | 0.999408i | \(-0.489043\pi\) |
−0.309477 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(878\) | −3.57784 | − | 4.26391i | −0.120746 | − | 0.143900i | ||||
\(879\) | −30.8718 | − | 25.9045i | −1.04128 | − | 0.873738i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.2596 | + | 21.2343i | 0.413037 | + | 0.715402i | 0.995220 | − | 0.0976562i | \(-0.0311346\pi\) |
−0.582183 | + | 0.813058i | \(0.697801\pi\) | |||||||
\(882\) | −45.4053 | − | 26.2147i | −1.52887 | − | 0.882696i | ||||
\(883\) | −16.8217 | + | 46.2172i | −0.566095 | + | 1.55533i | 0.244454 | + | 0.969661i | \(0.421391\pi\) |
−0.810549 | + | 0.585671i | \(0.800831\pi\) | |||||||
\(884\) | 5.11226 | + | 1.86071i | 0.171944 | + | 0.0625825i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.74223 | + | 3.01764i | 0.0585315 | + | 0.101380i | ||||
\(887\) | −21.3177 | + | 3.75889i | −0.715779 | + | 0.126211i | −0.519665 | − | 0.854370i | \(-0.673943\pi\) |
−0.196114 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(888\) | −5.84820 | + | 6.96961i | −0.196253 | + | 0.233885i | ||||
\(889\) | −56.6539 | + | 47.5382i | −1.90011 | + | 1.59438i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.4893 | − | 11.0972i | 1.02143 | − | 0.371770i | ||||
\(892\) | 3.66564i | 0.122735i | ||||||||
\(893\) | −9.68955 | − | 1.23307i | −0.324249 | − | 0.0412632i | ||||
\(894\) | −57.3278 | −1.91733 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.21612 | − | 23.9108i | 0.140851 | − | 0.798803i | ||||
\(897\) | 17.5951 | + | 20.9691i | 0.587484 | + | 0.700137i | ||||
\(898\) | 21.2953 | − | 25.3788i | 0.710634 | − | 0.846900i | ||||
\(899\) | −2.84407 | − | 16.1295i | −0.0948550 | − | 0.537950i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.348120 | − | 0.602962i | 0.0115976 | − | 0.0200876i | ||||
\(902\) | −0.600720 | + | 1.65047i | −0.0200018 | + | 0.0549545i | ||||
\(903\) | 27.6953 | − | 76.0922i | 0.921642 | − | 2.53219i | ||||
\(904\) | 25.9226 | − | 44.8993i | 0.862173 | − | 1.49333i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.45793 | + | 42.2960i | 0.247773 | + | 1.40519i | ||||
\(907\) | −8.67336 | + | 10.3365i | −0.287994 | + | 0.343218i | −0.890572 | − | 0.454842i | \(-0.849696\pi\) |
0.602578 | + | 0.798060i | \(0.294140\pi\) | |||||||
\(908\) | −5.43119 | − | 6.47264i | −0.180240 | − | 0.214802i | ||||
\(909\) | −4.73745 | + | 26.8674i | −0.157131 | + | 0.891137i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.2069 | 0.536958 | 0.268479 | − | 0.963286i | \(-0.413479\pi\) | ||||
0.268479 | + | 0.963286i | \(0.413479\pi\) | |||||||
\(912\) | −38.8598 | − | 4.94522i | −1.28678 | − | 0.163752i | ||||
\(913\) | − | 45.5428i | − | 1.50725i | ||||||
\(914\) | 39.6614 | − | 14.4356i | 1.31188 | − | 0.477486i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.70614 | − | 5.62712i | 0.221577 | − | 0.185925i | ||||
\(917\) | −12.9814 | + | 15.4706i | −0.428683 | + | 0.510884i | ||||
\(918\) | −30.6610 | + | 5.40636i | −1.01196 | + | 0.178437i | ||||
\(919\) | 9.86867 | + | 17.0930i | 0.325537 | + | 0.563847i | 0.981621 | − | 0.190841i | \(-0.0611215\pi\) |
−0.656084 | + | 0.754688i | \(0.727788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −79.1782 | − | 28.8185i | −2.60901 | − | 0.949602i | ||||
\(922\) | 13.0917 | − | 35.9691i | 0.431152 | − | 1.18458i | ||||
\(923\) | 8.39150 | + | 4.84483i | 0.276210 | + | 0.159470i | ||||
\(924\) | 7.90618 | + | 13.6939i | 0.260094 | + | 0.450497i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −27.5157 | − | 23.0884i | −0.904223 | − | 0.758733i | ||||
\(927\) | 41.9475 | + | 49.9911i | 1.37774 | + | 1.64192i | ||||
\(928\) | 12.0689 | + | 2.12807i | 0.396181 | + | 0.0698573i | ||||
\(929\) | 6.09658 | − | 2.21897i | 0.200022 | − | 0.0728022i | −0.240066 | − | 0.970756i | \(-0.577169\pi\) |
0.440089 | + | 0.897954i | \(0.354947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.5882 | − | 8.87816i | −0.936940 | − | 0.290970i | ||||
\(932\) | − | 0.228528i | − | 0.00748568i | ||||||
\(933\) | 25.5863 | + | 70.2978i | 0.837658 | + | 2.30145i | ||||
\(934\) | 2.44838 | − | 13.8855i | 0.0801135 | − | 0.454346i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −68.5194 | − | 57.4946i | −2.23963 | − | 1.87927i | ||||
\(937\) | 7.28885 | − | 1.28522i | 0.238116 | − | 0.0419863i | −0.0533164 | − | 0.998578i | \(-0.516979\pi\) |
0.291433 | + | 0.956591i | \(0.405868\pi\) | |||||||
\(938\) | −43.6887 | + | 25.2237i | −1.42649 | + | 0.823583i | ||||
\(939\) | −33.5454 | + | 58.1024i | −1.09471 | + | 1.89610i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.8981 | − | 18.1614i | −1.62663 | − | 0.592046i | −0.642002 | − | 0.766703i | \(-0.721896\pi\) |
−0.984629 | + | 0.174657i | \(0.944118\pi\) | |||||||
\(942\) | 13.8220 | + | 7.98013i | 0.450345 | + | 0.260007i | ||||
\(943\) | −0.676853 | + | 0.390781i | −0.0220414 | + | 0.0127256i | ||||
\(944\) | −2.68819 | − | 15.2455i | −0.0874932 | − | 0.496198i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.3262 | − | 19.5730i | 0.758402 | − | 0.636375i | ||||
\(947\) | 15.0450 | + | 2.65283i | 0.488896 | + | 0.0862055i | 0.412661 | − | 0.910884i | \(-0.364599\pi\) |
0.0762341 | + | 0.997090i | \(0.475710\pi\) | |||||||
\(948\) | 5.21559 | + | 14.3297i | 0.169395 | + | 0.465408i | ||||
\(949\) | −22.0891 | −0.717041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.3994 | −1.37490 | ||||||||
\(952\) | −10.3649 | − | 28.4772i | −0.335927 | − | 0.922951i | ||||
\(953\) | 16.6552 | + | 2.93675i | 0.539514 | + | 0.0951308i | 0.436763 | − | 0.899576i | \(-0.356125\pi\) |
0.102750 | + | 0.994707i | \(0.467236\pi\) | |||||||
\(954\) | −1.52202 | + | 1.27713i | −0.0492772 | + | 0.0413485i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.62099 | + | 9.19312i | 0.0524267 | + | 0.297327i | ||||
\(957\) | 45.9722 | − | 26.5421i | 1.48607 | − | 0.857983i | ||||
\(958\) | −18.9307 | − | 10.9296i | −0.611622 | − | 0.353120i | ||||
\(959\) | −64.9528 | − | 23.6409i | −2.09744 | − | 0.763404i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6362 | − | 18.4224i | 0.343103 | − | 0.594272i | ||||
\(962\) | 5.23278 | − | 3.02115i | 0.168712 | − | 0.0974057i | ||||
\(963\) | 8.24613 | − | 1.45401i | 0.265728 | − | 0.0468550i | ||||
\(964\) | 6.99333 | + | 5.86810i | 0.225240 | + | 0.188999i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.59573 | − | 26.0637i | 0.147865 | − | 0.838585i | ||||
\(967\) | −4.96803 | − | 13.6496i | −0.159761 | − | 0.438940i | 0.833823 | − | 0.552031i | \(-0.186147\pi\) |
−0.993585 | + | 0.113091i | \(0.963925\pi\) | |||||||
\(968\) | 0.796706i | 0.0256071i | ||||||||
\(969\) | −32.3941 | + | 13.5824i | −1.04065 | + | 0.436330i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.7590 | + | 10.4674i | −0.922920 | + | 0.335915i | −0.759400 | − | 0.650625i | \(-0.774507\pi\) |
−0.163520 | + | 0.986540i | \(0.552285\pi\) | |||||||
\(972\) | −0.557509 | − | 0.0983038i | −0.0178821 | − | 0.00315310i | ||||
\(973\) | 25.1641 | + | 29.9894i | 0.806724 | + | 0.961417i | ||||
\(974\) | −14.7777 | − | 12.4000i | −0.473508 | − | 0.397321i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.14705 | + | 1.98675i | 0.0367161 | + | 0.0635942i | ||||
\(977\) | 38.1064 | + | 22.0007i | 1.21913 | + | 0.703865i | 0.964732 | − | 0.263234i | \(-0.0847892\pi\) |
0.254399 | + | 0.967099i | \(0.418122\pi\) | |||||||
\(978\) | 18.0075 | − | 49.4753i | 0.575818 | − | 1.58205i | ||||
\(979\) | 24.1854 | + | 8.80277i | 0.772970 | + | 0.281338i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.8462 | − | 49.9631i | −0.920988 | − | 1.59520i | ||||
\(982\) | −10.3411 | + | 1.82342i | −0.329999 | + | 0.0581878i | ||||
\(983\) | 22.7302 | − | 27.0888i | 0.724982 | − | 0.864000i | −0.270123 | − | 0.962826i | \(-0.587064\pi\) |
0.995105 | + | 0.0988259i | \(0.0315087\pi\) | |||||||
\(984\) | 2.92270 | − | 2.45244i | 0.0931722 | − | 0.0781808i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.5936 | + | 6.03957i | −0.528448 | + | 0.192339i | ||||
\(987\) | 25.1366i | 0.800108i | ||||||||
\(988\) | −7.88025 | − | 4.05900i | −0.250704 | − | 0.129134i | ||||
\(989\) | 13.5498 | 0.430860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.58302 | − | 31.6629i | 0.177350 | − | 1.00580i | −0.758045 | − | 0.652202i | \(-0.773845\pi\) |
0.935396 | − | 0.353602i | \(-0.115043\pi\) | |||||||
\(992\) | −4.67863 | − | 5.57577i | −0.148547 | − | 0.177031i | ||||
\(993\) | −10.2340 | + | 12.1964i | −0.324765 | + | 0.387040i | ||||
\(994\) | −1.62682 | − | 9.22613i | −0.0515995 | − | 0.292635i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.58568 | + | 14.8708i | −0.272048 | + | 0.471200i | ||||
\(997\) | −2.84338 | + | 7.81213i | −0.0900509 | + | 0.247413i | −0.976540 | − | 0.215337i | \(-0.930915\pi\) |
0.886489 | + | 0.462750i | \(0.153137\pi\) | |||||||
\(998\) | −0.116433 | + | 0.319896i | −0.00368561 | + | 0.0101261i | ||||
\(999\) | 4.59658 | − | 7.96151i | 0.145429 | − | 0.251891i |
(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 | 475.2.u.b.24.2 | 36 | ||
5.2 | odd | 4 | 475.2.l.c.176.2 | 18 | |||
5.3 | odd | 4 | 95.2.k.a.81.2 | yes | 18 | ||
5.4 | even | 2 | inner | 475.2.u.b.24.5 | 36 | ||
15.8 | even | 4 | 855.2.bs.c.271.2 | 18 | |||
19.4 | even | 9 | inner | 475.2.u.b.99.5 | 36 | ||
95.2 | even | 36 | 9025.2.a.cf.1.6 | 9 | |||
95.4 | even | 18 | inner | 475.2.u.b.99.2 | 36 | ||
95.17 | odd | 36 | 9025.2.a.cc.1.4 | 9 | |||
95.23 | odd | 36 | 95.2.k.a.61.2 | ✓ | 18 | ||
95.42 | odd | 36 | 475.2.l.c.251.2 | 18 | |||
95.78 | even | 36 | 1805.2.a.s.1.4 | 9 | |||
95.93 | odd | 36 | 1805.2.a.v.1.6 | 9 | |||
285.23 | even | 36 | 855.2.bs.c.631.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.61.2 | ✓ | 18 | 95.23 | odd | 36 | ||
95.2.k.a.81.2 | yes | 18 | 5.3 | odd | 4 | ||
475.2.l.c.176.2 | 18 | 5.2 | odd | 4 | |||
475.2.l.c.251.2 | 18 | 95.42 | odd | 36 | |||
475.2.u.b.24.2 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.b.24.5 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.b.99.2 | 36 | 95.4 | even | 18 | inner | ||
475.2.u.b.99.5 | 36 | 19.4 | even | 9 | inner | ||
855.2.bs.c.271.2 | 18 | 15.8 | even | 4 | |||
855.2.bs.c.631.2 | 18 | 285.23 | even | 36 | |||
1805.2.a.s.1.4 | 9 | 95.78 | even | 36 | |||
1805.2.a.v.1.6 | 9 | 95.93 | odd | 36 | |||
9025.2.a.cc.1.4 | 9 | 95.17 | odd | 36 | |||
9025.2.a.cf.1.6 | 9 | 95.2 | even | 36 |