Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(49,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([14, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 499.3 | ||
Character | \(\chi\) | \(=\) | 675.499 |
Dual form | 675.2.u.b.349.3 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03831 | − | 0.183082i | 0.734194 | − | 0.129458i | 0.205964 | − | 0.978560i | \(-0.433967\pi\) |
0.528230 | + | 0.849101i | \(0.322856\pi\) | |||||||
\(3\) | 0.0916693 | − | 1.72962i | 0.0529253 | − | 0.998598i | ||||
\(4\) | −0.834822 | + | 0.303850i | −0.417411 | + | 0.151925i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.221481 | − | 1.81266i | −0.0904194 | − | 0.740017i | ||||
\(7\) | −0.841112 | + | 2.31094i | −0.317910 | + | 0.873452i | 0.673086 | + | 0.739564i | \(0.264968\pi\) |
−0.990997 | + | 0.133888i | \(0.957254\pi\) | |||||||
\(8\) | −2.63732 | + | 1.52266i | −0.932432 | + | 0.538340i | ||||
\(9\) | −2.98319 | − | 0.317107i | −0.994398 | − | 0.105702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.960783 | + | 0.806193i | −0.289687 | + | 0.243076i | −0.776036 | − | 0.630688i | \(-0.782773\pi\) |
0.486349 | + | 0.873764i | \(0.338328\pi\) | |||||||
\(12\) | 0.449019 | + | 1.47178i | 0.129621 | + | 0.424867i | ||||
\(13\) | −4.47992 | − | 0.789931i | −1.24251 | − | 0.219087i | −0.486517 | − | 0.873671i | \(-0.661733\pi\) |
−0.755989 | + | 0.654584i | \(0.772844\pi\) | |||||||
\(14\) | −0.450243 | + | 2.55345i | −0.120332 | + | 0.682439i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.09847 | + | 0.921724i | −0.274617 | + | 0.230431i | ||||
\(17\) | −5.75662 | − | 3.32358i | −1.39618 | − | 0.806088i | −0.402194 | − | 0.915554i | \(-0.631752\pi\) |
−0.993990 | + | 0.109467i | \(0.965086\pi\) | |||||||
\(18\) | −3.15553 | + | 0.216914i | −0.743765 | + | 0.0511270i | ||||
\(19\) | 0.124578 | + | 0.215776i | 0.0285802 | + | 0.0495023i | 0.879962 | − | 0.475045i | \(-0.157568\pi\) |
−0.851382 | + | 0.524547i | \(0.824235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.91994 | + | 1.66665i | 0.855402 | + | 0.363693i | ||||
\(22\) | −0.849989 | + | 1.01298i | −0.181218 | + | 0.215967i | ||||
\(23\) | −0.287981 | − | 0.791222i | −0.0600483 | − | 0.164981i | 0.906041 | − | 0.423190i | \(-0.139090\pi\) |
−0.966089 | + | 0.258209i | \(0.916868\pi\) | |||||||
\(24\) | 2.39186 | + | 4.70115i | 0.488236 | + | 0.959617i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.79615 | −0.940603 | ||||||||
\(27\) | −0.821942 | + | 5.13073i | −0.158183 | + | 0.987410i | ||||
\(28\) | − | 2.18479i | − | 0.412887i | ||||||
\(29\) | 0.0889744 | + | 0.504599i | 0.0165221 | + | 0.0937016i | 0.991954 | − | 0.126601i | \(-0.0404067\pi\) |
−0.975432 | + | 0.220302i | \(0.929296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.770551 | − | 0.280458i | 0.138395 | − | 0.0503717i | −0.271894 | − | 0.962327i | \(-0.587650\pi\) |
0.410289 | + | 0.911956i | \(0.365428\pi\) | |||||||
\(32\) | 2.94318 | − | 3.50754i | 0.520286 | − | 0.620052i | ||||
\(33\) | 1.30634 | + | 1.73570i | 0.227404 | + | 0.302146i | ||||
\(34\) | −6.58563 | − | 2.39697i | −1.12943 | − | 0.411077i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.58679 | − | 0.641717i | 0.431131 | − | 0.106953i | ||||
\(37\) | 2.25865 | + | 1.30403i | 0.371319 | + | 0.214381i | 0.674035 | − | 0.738700i | \(-0.264560\pi\) |
−0.302715 | + | 0.953081i | \(0.597893\pi\) | |||||||
\(38\) | 0.168855 | + | 0.201233i | 0.0273919 | + | 0.0326444i | ||||
\(39\) | −1.77695 | + | 7.67616i | −0.284540 | + | 1.22917i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.41572 | + | 8.02895i | −0.221099 | + | 1.25391i | 0.648906 | + | 0.760869i | \(0.275227\pi\) |
−0.870005 | + | 0.493044i | \(0.835884\pi\) | |||||||
\(42\) | 4.37524 | + | 1.01282i | 0.675114 | + | 0.156282i | ||||
\(43\) | 2.78143 | + | 3.31478i | 0.424165 | + | 0.505500i | 0.935229 | − | 0.354042i | \(-0.115193\pi\) |
−0.511065 | + | 0.859542i | \(0.670749\pi\) | |||||||
\(44\) | 0.557121 | − | 0.964962i | 0.0839891 | − | 0.145473i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.443871 | − | 0.768808i | −0.0654452 | − | 0.113354i | ||||
\(47\) | 1.81351 | − | 4.98256i | 0.264527 | − | 0.726782i | −0.734321 | − | 0.678802i | \(-0.762499\pi\) |
0.998848 | − | 0.0479798i | \(-0.0152783\pi\) | |||||||
\(48\) | 1.49354 | + | 1.98443i | 0.215574 | + | 0.286428i | ||||
\(49\) | 0.729356 | + | 0.612002i | 0.104194 | + | 0.0874289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.27625 | + | 9.65211i | −0.878851 | + | 1.35157i | ||||
\(52\) | 3.97996 | − | 0.701774i | 0.551921 | − | 0.0973185i | ||||
\(53\) | − | 10.4841i | − | 1.44010i | −0.693920 | − | 0.720052i | \(-0.744118\pi\) | ||
0.693920 | − | 0.720052i | \(-0.255882\pi\) | |||||||
\(54\) | 0.0859140 | + | 5.47776i | 0.0116914 | + | 0.745429i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.30048 | − | 7.37539i | −0.173784 | − | 0.985578i | ||||
\(57\) | 0.384630 | − | 0.195693i | 0.0509456 | − | 0.0259202i | ||||
\(58\) | 0.184765 | + | 0.507639i | 0.0242609 | + | 0.0666563i | ||||
\(59\) | 2.30289 | + | 1.93235i | 0.299810 | + | 0.251571i | 0.780265 | − | 0.625449i | \(-0.215084\pi\) |
−0.480455 | + | 0.877019i | \(0.659529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.70930 | − | 0.986103i | −0.346890 | − | 0.126258i | 0.162699 | − | 0.986676i | \(-0.447980\pi\) |
−0.509589 | + | 0.860418i | \(0.670202\pi\) | |||||||
\(62\) | 0.748722 | − | 0.432275i | 0.0950878 | − | 0.0548990i | ||||
\(63\) | 3.24201 | − | 6.62725i | 0.408455 | − | 0.834955i | ||||
\(64\) | 3.84771 | − | 6.66442i | 0.480963 | − | 0.833053i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.67415 | + | 1.56302i | 0.206074 | + | 0.192394i | ||||
\(67\) | −9.93303 | − | 1.75146i | −1.21351 | − | 0.213975i | −0.469982 | − | 0.882676i | \(-0.655739\pi\) |
−0.743531 | + | 0.668701i | \(0.766851\pi\) | |||||||
\(68\) | 5.81562 | + | 1.02545i | 0.705248 | + | 0.124354i | ||||
\(69\) | −1.39492 | + | 0.425568i | −0.167928 | + | 0.0512324i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0447378 | + | 0.0774882i | −0.00530940 | + | 0.00919615i | −0.868668 | − | 0.495395i | \(-0.835023\pi\) |
0.863358 | + | 0.504591i | \(0.168357\pi\) | |||||||
\(72\) | 8.35047 | − | 3.70607i | 0.984112 | − | 0.436764i | ||||
\(73\) | −4.60824 | + | 2.66057i | −0.539354 | + | 0.311396i | −0.744817 | − | 0.667269i | \(-0.767463\pi\) |
0.205463 | + | 0.978665i | \(0.434130\pi\) | |||||||
\(74\) | 2.58391 | + | 0.940468i | 0.300374 | + | 0.109327i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.169564 | − | 0.142281i | −0.0194503 | − | 0.0163208i | ||||
\(77\) | −1.05493 | − | 2.89841i | −0.120221 | − | 0.330304i | ||||
\(78\) | −0.439660 | + | 8.29554i | −0.0497817 | + | 0.939285i | ||||
\(79\) | −0.829503 | − | 4.70435i | −0.0933264 | − | 0.529280i | −0.995247 | − | 0.0973792i | \(-0.968954\pi\) |
0.901921 | − | 0.431901i | \(-0.142157\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.79889 | + | 1.89198i | 0.977654 | + | 0.210220i | ||||
\(82\) | 8.59571i | 0.949238i | ||||||||
\(83\) | −7.91851 | + | 1.39625i | −0.869169 | + | 0.153258i | −0.590410 | − | 0.807103i | \(-0.701034\pi\) |
−0.278759 | + | 0.960361i | \(0.589923\pi\) | |||||||
\(84\) | −3.77887 | − | 0.200278i | −0.412308 | − | 0.0218522i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.49486 | + | 2.93254i | 0.376860 | + | 0.316223i | ||||
\(87\) | 0.880922 | − | 0.107636i | 0.0944448 | − | 0.0115398i | ||||
\(88\) | 1.30634 | − | 3.58913i | 0.139256 | − | 0.382602i | ||||
\(89\) | 3.35189 | + | 5.80564i | 0.355299 | + | 0.615396i | 0.987169 | − | 0.159678i | \(-0.0510457\pi\) |
−0.631870 | + | 0.775074i | \(0.717712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.59359 | − | 9.68839i | 0.586368 | − | 1.01562i | ||||
\(92\) | 0.480826 | + | 0.573026i | 0.0501296 | + | 0.0597421i | ||||
\(93\) | −0.414450 | − | 1.35847i | −0.0429765 | − | 0.140867i | ||||
\(94\) | 0.970760 | − | 5.50545i | 0.100126 | − | 0.567844i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.79693 | − | 5.41213i | −0.591647 | − | 0.552373i | ||||
\(97\) | −3.52928 | − | 4.20603i | −0.358344 | − | 0.427057i | 0.556511 | − | 0.830840i | \(-0.312140\pi\) |
−0.914855 | + | 0.403783i | \(0.867695\pi\) | |||||||
\(98\) | 0.869342 | + | 0.501915i | 0.0878168 | + | 0.0507010i | ||||
\(99\) | 3.12185 | − | 2.10036i | 0.313758 | − | 0.211094i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.70360 | − | 1.71197i | −0.468025 | − | 0.170347i | 0.0972322 | − | 0.995262i | \(-0.469001\pi\) |
−0.565258 | + | 0.824914i | \(0.691223\pi\) | |||||||
\(102\) | −4.74956 | + | 11.1709i | −0.470276 | + | 1.10609i | ||||
\(103\) | −7.46865 | + | 8.90079i | −0.735908 | + | 0.877021i | −0.996072 | − | 0.0885431i | \(-0.971779\pi\) |
0.260164 | + | 0.965564i | \(0.416223\pi\) | |||||||
\(104\) | 13.0178 | − | 4.73808i | 1.27650 | − | 0.464607i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.91945 | − | 10.8857i | −0.186433 | − | 1.05732i | ||||
\(107\) | − | 19.4581i | − | 1.88109i | −0.339673 | − | 0.940544i | \(-0.610316\pi\) | ||
0.339673 | − | 0.940544i | \(-0.389684\pi\) | |||||||
\(108\) | −0.872799 | − | 4.53300i | −0.0839852 | − | 0.436188i | ||||
\(109\) | −6.31515 | −0.604881 | −0.302441 | − | 0.953168i | \(-0.597801\pi\) | ||||
−0.302441 | + | 0.953168i | \(0.597801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.46253 | − | 3.78707i | 0.233733 | − | 0.359453i | ||||
\(112\) | −1.20611 | − | 3.31376i | −0.113967 | − | 0.313121i | ||||
\(113\) | 4.44534 | − | 5.29775i | 0.418183 | − | 0.498371i | −0.515292 | − | 0.857015i | \(-0.672316\pi\) |
0.933474 | + | 0.358644i | \(0.116761\pi\) | |||||||
\(114\) | 0.363537 | − | 0.273608i | 0.0340483 | − | 0.0256258i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.227600 | − | 0.394215i | −0.0211322 | − | 0.0366020i | ||||
\(117\) | 13.1140 | + | 3.77713i | 1.21239 | + | 0.349196i | ||||
\(118\) | 2.74488 | + | 1.58476i | 0.252687 | + | 0.145889i | ||||
\(119\) | 12.5226 | − | 10.5077i | 1.14794 | − | 0.963236i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.63697 | + | 9.28373i | −0.148816 | + | 0.843976i | ||||
\(122\) | −2.99362 | − | 0.527856i | −0.271030 | − | 0.0477898i | ||||
\(123\) | 13.7573 | + | 3.18467i | 1.24045 | + | 0.287152i | ||||
\(124\) | −0.558056 | + | 0.468265i | −0.0501149 | + | 0.0420514i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.15288 | − | 7.47467i | 0.191794 | − | 0.665897i | ||||
\(127\) | −10.4124 | + | 6.01162i | −0.923954 | + | 0.533445i | −0.884894 | − | 0.465792i | \(-0.845770\pi\) |
−0.0390598 | + | 0.999237i | \(0.512436\pi\) | |||||||
\(128\) | −0.357098 | + | 0.981117i | −0.0315633 | + | 0.0867194i | ||||
\(129\) | 5.98830 | − | 4.50697i | 0.527240 | − | 0.396817i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2354 | − | 4.81728i | 1.15638 | − | 0.420888i | 0.308577 | − | 0.951199i | \(-0.400147\pi\) |
0.847803 | + | 0.530311i | \(0.177925\pi\) | |||||||
\(132\) | −1.61795 | − | 1.05207i | −0.140824 | − | 0.0915706i | ||||
\(133\) | −0.603428 | + | 0.106401i | −0.0523238 | + | 0.00922610i | ||||
\(134\) | −10.6342 | −0.918655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.2427 | 1.73580 | ||||||||
\(137\) | 2.22383 | − | 0.392122i | 0.189995 | − | 0.0335012i | −0.0778409 | − | 0.996966i | \(-0.524803\pi\) |
0.267836 | + | 0.963465i | \(0.413692\pi\) | |||||||
\(138\) | −1.37044 | + | 0.697254i | −0.116659 | + | 0.0593542i | ||||
\(139\) | −7.49414 | + | 2.72764i | −0.635644 | + | 0.231356i | −0.639686 | − | 0.768636i | \(-0.720936\pi\) |
0.00404179 | + | 0.999992i | \(0.498713\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.45172 | − | 3.59343i | −0.711763 | − | 0.302621i | ||||
\(142\) | −0.0322649 | + | 0.0886472i | −0.00270761 | + | 0.00743911i | ||||
\(143\) | 4.94107 | − | 2.85273i | 0.413193 | − | 0.238557i | ||||
\(144\) | 3.56923 | − | 2.40135i | 0.297436 | − | 0.200113i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.29767 | + | 3.60617i | −0.355678 | + | 0.298449i | ||||
\(147\) | 1.12539 | − | 1.20541i | 0.0928208 | − | 0.0994204i | ||||
\(148\) | −2.28180 | − | 0.402343i | −0.187563 | − | 0.0330724i | ||||
\(149\) | 0.0185697 | − | 0.105314i | 0.00152129 | − | 0.00862764i | −0.984038 | − | 0.177960i | \(-0.943050\pi\) |
0.985559 | + | 0.169333i | \(0.0541612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5196 | + | 13.0225i | −1.26297 | + | 1.05976i | −0.267609 | + | 0.963528i | \(0.586233\pi\) |
−0.995359 | + | 0.0962282i | \(0.969322\pi\) | |||||||
\(152\) | −0.657104 | − | 0.379379i | −0.0532982 | − | 0.0307717i | ||||
\(153\) | 16.1192 | + | 11.7404i | 1.30316 | + | 0.949152i | ||||
\(154\) | −1.62599 | − | 2.81630i | −0.131026 | − | 0.226944i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.848964 | − | 6.94816i | −0.0679716 | − | 0.556298i | ||||
\(157\) | −13.3377 | + | 15.8953i | −1.06447 | + | 1.26858i | −0.102701 | + | 0.994712i | \(0.532748\pi\) |
−0.961767 | + | 0.273871i | \(0.911696\pi\) | |||||||
\(158\) | −1.72256 | − | 4.73269i | −0.137039 | − | 0.376513i | ||||
\(159\) | −18.1336 | − | 0.961071i | −1.43809 | − | 0.0762179i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07069 | 0.163193 | ||||||||
\(162\) | 9.48234 | + | 0.353543i | 0.745003 | + | 0.0277770i | ||||
\(163\) | − | 20.1346i | − | 1.57706i | −0.614995 | − | 0.788531i | \(-0.710842\pi\) | ||
0.614995 | − | 0.788531i | \(-0.289158\pi\) | |||||||
\(164\) | −1.25773 | − | 7.13292i | −0.0982119 | − | 0.556987i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.96622 | + | 2.89947i | −0.618298 | + | 0.225042i | ||||
\(167\) | −12.7674 | + | 15.2156i | −0.987974 | + | 1.17742i | −0.00383999 | + | 0.999993i | \(0.501222\pi\) |
−0.984134 | + | 0.177429i | \(0.943222\pi\) | |||||||
\(168\) | −12.8759 | + | 1.57325i | −0.993395 | + | 0.121378i | ||||
\(169\) | 7.22968 | + | 2.63139i | 0.556130 | + | 0.202415i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.303217 | − | 0.683205i | −0.0231876 | − | 0.0522460i | ||||
\(172\) | −3.32920 | − | 1.92212i | −0.253849 | − | 0.146560i | ||||
\(173\) | 12.1648 | + | 14.4975i | 0.924875 | + | 1.10222i | 0.994509 | + | 0.104650i | \(0.0333724\pi\) |
−0.0696342 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(174\) | 0.894962 | − | 0.273040i | 0.0678469 | − | 0.0206991i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.312302 | − | 1.77115i | 0.0235407 | − | 0.133506i | ||||
\(177\) | 3.55334 | − | 3.80599i | 0.267085 | − | 0.286075i | ||||
\(178\) | 4.54319 | + | 5.41436i | 0.340527 | + | 0.405824i | ||||
\(179\) | 5.45683 | − | 9.45151i | 0.407863 | − | 0.706439i | −0.586787 | − | 0.809741i | \(-0.699608\pi\) |
0.994650 | + | 0.103302i | \(0.0329409\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.97393 | + | 15.5433i | 0.667027 | + | 1.15532i | 0.978731 | + | 0.205146i | \(0.0657668\pi\) |
−0.311704 | + | 0.950179i | \(0.600900\pi\) | |||||||
\(182\) | 4.03410 | − | 11.0836i | 0.299028 | − | 0.821572i | ||||
\(183\) | −1.95395 | + | 4.59567i | −0.144440 | + | 0.339721i | ||||
\(184\) | 1.96426 | + | 1.64821i | 0.144807 | + | 0.121507i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.679038 | − | 1.33463i | −0.0497895 | − | 0.0978601i | ||||
\(187\) | 8.21031 | − | 1.44770i | 0.600397 | − | 0.105866i | ||||
\(188\) | 4.71059i | 0.343555i | ||||||||
\(189\) | −11.1654 | − | 6.21498i | −0.812167 | − | 0.452073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.68261 | − | 26.5564i | −0.338822 | − | 1.92155i | −0.385641 | − | 0.922649i | \(-0.626020\pi\) |
0.0468192 | − | 0.998903i | \(-0.485092\pi\) | |||||||
\(192\) | −11.1742 | − | 7.26601i | −0.806430 | − | 0.524379i | ||||
\(193\) | 5.86729 | + | 16.1202i | 0.422337 | + | 1.16036i | 0.950366 | + | 0.311135i | \(0.100709\pi\) |
−0.528029 | + | 0.849226i | \(0.677069\pi\) | |||||||
\(194\) | −4.43452 | − | 3.72100i | −0.318380 | − | 0.267152i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.794839 | − | 0.289298i | −0.0567742 | − | 0.0206641i | ||||
\(197\) | −2.17567 | + | 1.25612i | −0.155010 | + | 0.0894951i | −0.575499 | − | 0.817803i | \(-0.695192\pi\) |
0.420489 | + | 0.907298i | \(0.361859\pi\) | |||||||
\(198\) | 2.85690 | − | 2.75237i | 0.203031 | − | 0.195602i | ||||
\(199\) | 9.26942 | − | 16.0551i | 0.657092 | − | 1.13812i | −0.324273 | − | 0.945964i | \(-0.605120\pi\) |
0.981365 | − | 0.192153i | \(-0.0615470\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.93992 | + | 17.0198i | −0.277901 | + | 1.20049i | ||||
\(202\) | −5.19721 | − | 0.916408i | −0.365674 | − | 0.0644783i | ||||
\(203\) | −1.24093 | − | 0.218810i | −0.0870964 | − | 0.0153574i | ||||
\(204\) | 2.30676 | − | 9.96484i | 0.161505 | − | 0.697678i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.12519 | + | 10.6091i | −0.426762 | + | 0.739173i | ||||
\(207\) | 0.608202 | + | 2.45169i | 0.0422730 | + | 0.170404i | ||||
\(208\) | 5.64915 | − | 3.26154i | 0.391698 | − | 0.226147i | ||||
\(209\) | −0.293649 | − | 0.106880i | −0.0203121 | − | 0.00739301i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.82761 | − | 2.37264i | −0.194661 | − | 0.163340i | 0.540248 | − | 0.841506i | \(-0.318330\pi\) |
−0.734908 | + | 0.678166i | \(0.762775\pi\) | |||||||
\(212\) | 3.18560 | + | 8.75237i | 0.218788 | + | 0.601115i | ||||
\(213\) | 0.129924 | + | 0.0844829i | 0.00890226 | + | 0.00578867i | ||||
\(214\) | −3.56242 | − | 20.2035i | −0.243522 | − | 1.38108i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.64462 | − | 14.7829i | −0.384067 | − | 1.00585i | ||||
\(217\) | 2.01659i | 0.136895i | ||||||||
\(218\) | −6.55706 | + | 1.15619i | −0.444100 | + | 0.0783069i | ||||
\(219\) | 4.17935 | + | 8.21441i | 0.282414 | + | 0.555079i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.1638 | + | 19.4367i | 1.55816 | + | 1.30746i | ||||
\(222\) | 1.86352 | − | 4.38299i | 0.125071 | − | 0.294167i | ||||
\(223\) | −7.26487 | + | 19.9601i | −0.486491 | + | 1.33662i | 0.417346 | + | 0.908748i | \(0.362960\pi\) |
−0.903837 | + | 0.427876i | \(0.859262\pi\) | |||||||
\(224\) | 5.63017 | + | 9.75174i | 0.376181 | + | 0.651565i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.64571 | − | 6.31456i | 0.242509 | − | 0.420038i | ||||
\(227\) | 9.21761 | + | 10.9851i | 0.611794 | + | 0.729108i | 0.979636 | − | 0.200781i | \(-0.0643478\pi\) |
−0.367842 | + | 0.929888i | \(0.619903\pi\) | |||||||
\(228\) | −0.261637 | + | 0.280239i | −0.0173273 | + | 0.0185593i | ||||
\(229\) | −2.93219 | + | 16.6293i | −0.193765 | + | 1.09889i | 0.720403 | + | 0.693556i | \(0.243957\pi\) |
−0.914167 | + | 0.405337i | \(0.867154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.10985 | + | 1.55894i | −0.336204 | + | 0.102571i | ||||
\(232\) | −1.00298 | − | 1.19531i | −0.0658491 | − | 0.0784759i | ||||
\(233\) | −4.84926 | − | 2.79972i | −0.317686 | − | 0.183416i | 0.332675 | − | 0.943042i | \(-0.392049\pi\) |
−0.650361 | + | 0.759626i | \(0.725382\pi\) | |||||||
\(234\) | 14.3079 | + | 1.52089i | 0.935334 | + | 0.0994238i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.50964 | − | 0.913436i | −0.163364 | − | 0.0594596i | ||||
\(237\) | −8.21279 | + | 1.00348i | −0.533478 | + | 0.0651833i | ||||
\(238\) | 11.0785 | − | 13.2028i | 0.718112 | − | 0.855813i | ||||
\(239\) | −4.95620 | + | 1.80391i | −0.320590 | + | 0.116685i | −0.497302 | − | 0.867577i | \(-0.665676\pi\) |
0.176712 | + | 0.984263i | \(0.443454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.54590 | − | 8.76723i | −0.0995801 | − | 0.564747i | −0.993247 | − | 0.116017i | \(-0.962987\pi\) |
0.893667 | − | 0.448730i | \(-0.148124\pi\) | |||||||
\(242\) | 9.93907i | 0.638907i | ||||||||
\(243\) | 4.07900 | − | 15.0453i | 0.261668 | − | 0.965158i | ||||
\(244\) | 2.56141 | 0.163977 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.8673 | + | 0.787963i | 0.947908 | + | 0.0502387i | ||||
\(247\) | −0.387652 | − | 1.06507i | −0.0246657 | − | 0.0677685i | ||||
\(248\) | −1.60515 | + | 1.91294i | −0.101927 | + | 0.121472i | ||||
\(249\) | 1.68910 | + | 13.8240i | 0.107042 | + | 0.876062i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.89010 | + | 6.73786i | 0.245541 | + | 0.425290i | 0.962284 | − | 0.272048i | \(-0.0877010\pi\) |
−0.716742 | + | 0.697338i | \(0.754368\pi\) | |||||||
\(252\) | −0.692812 | + | 6.51766i | −0.0436431 | + | 0.410574i | ||||
\(253\) | 0.914565 | + | 0.528024i | 0.0574982 | + | 0.0331966i | ||||
\(254\) | −9.71069 | + | 8.14824i | −0.609303 | + | 0.511266i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.86374 | + | 16.2411i | −0.178984 | + | 1.01507i | ||||
\(257\) | 20.1261 | + | 3.54877i | 1.25543 | + | 0.221366i | 0.761517 | − | 0.648145i | \(-0.224455\pi\) |
0.493913 | + | 0.869511i | \(0.335566\pi\) | |||||||
\(258\) | 5.39255 | − | 5.77597i | 0.335726 | − | 0.359596i | ||||
\(259\) | −4.91331 | + | 4.12275i | −0.305298 | + | 0.256175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.105416 | − | 1.53353i | −0.00652510 | − | 0.0949231i | ||||
\(262\) | 12.8604 | − | 7.42498i | 0.794520 | − | 0.458717i | ||||
\(263\) | 3.85792 | − | 10.5996i | 0.237890 | − | 0.653596i | −0.762092 | − | 0.647469i | \(-0.775827\pi\) |
0.999981 | − | 0.00612723i | \(-0.00195037\pi\) | |||||||
\(264\) | −6.08809 | − | 2.58848i | −0.374696 | − | 0.159310i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.607063 | + | 0.220953i | −0.0372214 | + | 0.0135475i | ||||
\(267\) | 10.3488 | − | 5.26530i | 0.633338 | − | 0.322231i | ||||
\(268\) | 8.82450 | − | 1.55600i | 0.539042 | − | 0.0950476i | ||||
\(269\) | 0.307761 | 0.0187645 | 0.00938226 | − | 0.999956i | \(-0.497013\pi\) | ||||
0.00938226 | + | 0.999956i | \(0.497013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.22251 | −0.135008 | −0.0675040 | − | 0.997719i | \(-0.521504\pi\) | ||||
−0.0675040 | + | 0.997719i | \(0.521504\pi\) | |||||||
\(272\) | 9.38689 | − | 1.65516i | 0.569164 | − | 0.100359i | ||||
\(273\) | −16.2445 | − | 10.5629i | −0.983162 | − | 0.639298i | ||||
\(274\) | 2.23723 | − | 0.814286i | 0.135156 | − | 0.0491928i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.03520 | − | 0.779119i | 0.0623115 | − | 0.0468975i | ||||
\(277\) | 7.97924 | − | 21.9228i | 0.479426 | − | 1.31721i | −0.430556 | − | 0.902564i | \(-0.641683\pi\) |
0.909982 | − | 0.414648i | \(-0.136095\pi\) | |||||||
\(278\) | −7.28184 | + | 4.20417i | −0.436735 | + | 0.252149i | ||||
\(279\) | −2.38764 | + | 0.592313i | −0.142944 | + | 0.0354608i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.53502 | − | 4.64443i | 0.330192 | − | 0.277064i | −0.462586 | − | 0.886574i | \(-0.653078\pi\) |
0.792778 | + | 0.609511i | \(0.208634\pi\) | |||||||
\(282\) | −9.43337 | − | 2.18373i | −0.561749 | − | 0.130039i | ||||
\(283\) | 7.01212 | + | 1.23643i | 0.416827 | + | 0.0734979i | 0.378129 | − | 0.925753i | \(-0.376568\pi\) |
0.0386985 | + | 0.999251i | \(0.487679\pi\) | |||||||
\(284\) | 0.0138033 | − | 0.0782824i | 0.000819076 | − | 0.00464521i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.60806 | − | 3.86662i | 0.272480 | − | 0.228638i | ||||
\(287\) | −17.3636 | − | 10.0249i | −1.02494 | − | 0.591751i | ||||
\(288\) | −9.89234 | + | 9.53038i | −0.582912 | + | 0.561583i | ||||
\(289\) | 13.5924 | + | 23.5428i | 0.799555 | + | 1.38487i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.59837 | + | 5.71875i | −0.445424 | + | 0.335239i | ||||
\(292\) | 3.03865 | − | 3.62132i | 0.177823 | − | 0.211922i | ||||
\(293\) | −0.188961 | − | 0.519166i | −0.0110392 | − | 0.0303300i | 0.934051 | − | 0.357141i | \(-0.116248\pi\) |
−0.945090 | + | 0.326811i | \(0.894026\pi\) | |||||||
\(294\) | 0.947815 | − | 1.45762i | 0.0552777 | − | 0.0850103i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.94236 | −0.461640 | ||||||||
\(297\) | −3.34665 | − | 5.59216i | −0.194192 | − | 0.324490i | ||||
\(298\) | − | 0.112748i | − | 0.00653131i | ||||||
\(299\) | 0.665122 | + | 3.77210i | 0.0384650 | + | 0.218146i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.99975 | + | 3.63961i | −0.576376 | + | 0.209784i | ||||
\(302\) | −13.7299 | + | 16.3627i | −0.790069 | + | 0.941568i | ||||
\(303\) | −3.39224 | + | 7.97852i | −0.194879 | + | 0.458354i | ||||
\(304\) | −0.335731 | − | 0.122196i | −0.0192555 | − | 0.00700842i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.8861 | + | 9.23898i | 1.07965 | + | 0.528157i | ||||
\(307\) | 5.82728 | + | 3.36438i | 0.332580 | + | 0.192015i | 0.656986 | − | 0.753903i | \(-0.271831\pi\) |
−0.324406 | + | 0.945918i | \(0.605164\pi\) | |||||||
\(308\) | 1.76136 | + | 2.09911i | 0.100363 | + | 0.119608i | ||||
\(309\) | 14.7104 | + | 13.7339i | 0.836844 | + | 0.781293i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.67825 | − | 15.1891i | 0.151870 | − | 0.861297i | −0.809722 | − | 0.586814i | \(-0.800382\pi\) |
0.961592 | − | 0.274483i | \(-0.0885068\pi\) | |||||||
\(312\) | −7.00176 | − | 22.9502i | −0.396397 | − | 1.29930i | ||||
\(313\) | −15.1446 | − | 18.0487i | −0.856025 | − | 1.02017i | −0.999534 | − | 0.0305223i | \(-0.990283\pi\) |
0.143509 | − | 0.989649i | \(-0.454162\pi\) | |||||||
\(314\) | −10.9385 | + | 18.9461i | −0.617297 | + | 1.06919i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.12191 | + | 3.67525i | 0.119367 | + | 0.206749i | ||||
\(317\) | −2.48034 | + | 6.81469i | −0.139310 | + | 0.382751i | −0.989654 | − | 0.143477i | \(-0.954172\pi\) |
0.850344 | + | 0.526228i | \(0.176394\pi\) | |||||||
\(318\) | −19.0042 | + | 2.32204i | −1.06570 | + | 0.130213i | ||||
\(319\) | −0.492289 | − | 0.413079i | −0.0275629 | − | 0.0231280i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.6552 | − | 1.78371i | −1.87845 | − | 0.0995571i | ||||
\(322\) | 2.15001 | − | 0.379105i | 0.119815 | − | 0.0211267i | ||||
\(323\) | − | 1.65618i | − | 0.0921525i | ||||||
\(324\) | −7.92038 | + | 1.09408i | −0.440021 | + | 0.0607821i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.68627 | − | 20.9059i | −0.204164 | − | 1.15787i | ||||
\(327\) | −0.578905 | + | 10.9228i | −0.0320135 | + | 0.604034i | ||||
\(328\) | −8.49163 | − | 23.3306i | −0.468872 | − | 1.28821i | ||||
\(329\) | 9.98903 | + | 8.38179i | 0.550713 | + | 0.462103i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.2835 | − | 9.93037i | −1.49964 | − | 0.545823i | −0.543669 | − | 0.839300i | \(-0.682965\pi\) |
−0.955966 | + | 0.293477i | \(0.905188\pi\) | |||||||
\(332\) | 6.18629 | − | 3.57166i | 0.339517 | − | 0.196020i | ||||
\(333\) | −6.32447 | − | 4.60641i | −0.346579 | − | 0.252430i | ||||
\(334\) | −10.4708 | + | 18.1360i | −0.572938 | + | 0.992357i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.84213 | + | 1.78235i | −0.318714 | + | 0.0972351i | ||||
\(337\) | 1.14149 | + | 0.201275i | 0.0621807 | + | 0.0109641i | 0.204652 | − | 0.978835i | \(-0.434394\pi\) |
−0.142471 | + | 0.989799i | \(0.545505\pi\) | |||||||
\(338\) | 7.98839 | + | 1.40857i | 0.434511 | + | 0.0766161i | ||||
\(339\) | −8.75561 | − | 8.17441i | −0.475540 | − | 0.443973i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.514230 | + | 0.890672i | −0.0278471 | + | 0.0482326i | ||||
\(342\) | −0.439914 | − | 0.653863i | −0.0237878 | − | 0.0353569i | ||||
\(343\) | −16.9362 | + | 9.77810i | −0.914467 | + | 0.527968i | ||||
\(344\) | −12.3828 | − | 4.50697i | −0.667636 | − | 0.243000i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.2851 | + | 12.8257i | 0.821730 | + | 0.689513i | ||||
\(347\) | 2.01440 | + | 5.53452i | 0.108139 | + | 0.297108i | 0.981945 | − | 0.189165i | \(-0.0605781\pi\) |
−0.873807 | + | 0.486273i | \(0.838356\pi\) | |||||||
\(348\) | −0.702708 | + | 0.357525i | −0.0376691 | + | 0.0191654i | ||||
\(349\) | 5.31237 | + | 30.1279i | 0.284364 | + | 1.61271i | 0.707547 | + | 0.706666i | \(0.249802\pi\) |
−0.423183 | + | 0.906044i | \(0.639087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.73516 | − | 22.3360i | 0.412872 | − | 1.19221i | ||||
\(352\) | 5.74276i | 0.306090i | ||||||||
\(353\) | −36.3997 | + | 6.41826i | −1.93736 | + | 0.341609i | −0.999978 | − | 0.00668455i | \(-0.997872\pi\) |
−0.937385 | + | 0.348294i | \(0.886761\pi\) | |||||||
\(354\) | 2.99265 | − | 4.60233i | 0.159058 | − | 0.244611i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.56227 | − | 3.82820i | −0.241800 | − | 0.202894i | ||||
\(357\) | −17.0264 | − | 22.6225i | −0.901131 | − | 1.19731i | ||||
\(358\) | 3.93547 | − | 10.8126i | 0.207996 | − | 0.571464i | ||||
\(359\) | −13.1880 | − | 22.8423i | −0.696037 | − | 1.20557i | −0.969830 | − | 0.243783i | \(-0.921611\pi\) |
0.273792 | − | 0.961789i | \(-0.411722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.46896 | − | 16.4007i | 0.498366 | − | 0.863196i | ||||
\(362\) | 12.1634 | + | 14.4958i | 0.639294 | + | 0.761881i | ||||
\(363\) | 15.9073 | + | 3.68238i | 0.834917 | + | 0.193275i | ||||
\(364\) | −1.72583 | + | 9.78769i | −0.0904583 | + | 0.513015i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.18741 | + | 5.12944i | −0.0620671 | + | 0.268120i | ||||
\(367\) | 7.27194 | + | 8.66636i | 0.379592 | + | 0.452380i | 0.921685 | − | 0.387938i | \(-0.126813\pi\) |
−0.542093 | + | 0.840318i | \(0.682368\pi\) | |||||||
\(368\) | 1.04563 | + | 0.603693i | 0.0545071 | + | 0.0314697i | ||||
\(369\) | 6.76941 | − | 23.5030i | 0.352401 | − | 1.22352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2281 | + | 8.81831i | 1.25786 | + | 0.457824i | ||||
\(372\) | 0.758765 | + | 1.00815i | 0.0393401 | + | 0.0522703i | ||||
\(373\) | −3.75650 | + | 4.47682i | −0.194504 | + | 0.231801i | −0.854478 | − | 0.519487i | \(-0.826123\pi\) |
0.659974 | + | 0.751289i | \(0.270567\pi\) | |||||||
\(374\) | 8.25978 | − | 3.00631i | 0.427103 | − | 0.155453i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.80394 | + | 15.9019i | 0.144602 | + | 0.820080i | ||||
\(377\) | − | 2.33085i | − | 0.120045i | ||||||
\(378\) | −12.7310 | − | 4.40887i | −0.654813 | − | 0.226768i | ||||
\(379\) | −24.3265 | −1.24957 | −0.624783 | − | 0.780798i | \(-0.714813\pi\) | ||||
−0.624783 | + | 0.780798i | \(0.714813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.44334 | + | 18.5607i | 0.483797 | + | 0.950892i | ||||
\(382\) | −9.72397 | − | 26.7164i | −0.497522 | − | 1.36693i | ||||
\(383\) | 2.45291 | − | 2.92326i | 0.125338 | − | 0.149372i | −0.699726 | − | 0.714411i | \(-0.746695\pi\) |
0.825064 | + | 0.565039i | \(0.191139\pi\) | |||||||
\(384\) | 1.66423 | + | 0.707583i | 0.0849273 | + | 0.0361087i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.04337 | + | 15.6636i | 0.460295 | + | 0.797255i | ||||
\(387\) | −7.24642 | − | 10.7707i | −0.368356 | − | 0.547503i | ||||
\(388\) | 4.22432 | + | 2.43891i | 0.214457 | + | 0.123817i | ||||
\(389\) | −8.30534 | + | 6.96901i | −0.421097 | + | 0.353343i | −0.828580 | − | 0.559870i | \(-0.810851\pi\) |
0.407483 | + | 0.913213i | \(0.366407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.971896 | + | 5.51189i | −0.0491509 | + | 0.278748i | ||||
\(392\) | −2.85541 | − | 0.503486i | −0.144220 | − | 0.0254299i | ||||
\(393\) | −7.11881 | − | 23.3338i | −0.359096 | − | 1.17704i | ||||
\(394\) | −2.02904 | + | 1.70257i | −0.102222 | + | 0.0857741i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.96799 | + | 2.70200i | −0.0988955 | + | 0.135781i | ||||
\(397\) | 9.10124 | − | 5.25461i | 0.456778 | − | 0.263721i | −0.253910 | − | 0.967228i | \(-0.581717\pi\) |
0.710689 | + | 0.703507i | \(0.248383\pi\) | |||||||
\(398\) | 6.68511 | − | 18.3672i | 0.335094 | − | 0.920665i | ||||
\(399\) | 0.128717 | + | 1.05346i | 0.00644392 | + | 0.0527388i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4992 | + | 4.91332i | −0.674119 | + | 0.245359i | −0.656320 | − | 0.754482i | \(-0.727888\pi\) |
−0.0177987 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(402\) | −0.974829 | + | 18.3932i | −0.0486201 | + | 0.917367i | ||||
\(403\) | −3.67355 | + | 0.647746i | −0.182993 | + | 0.0322665i | ||||
\(404\) | 4.44685 | 0.221239 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.32853 | −0.0659338 | ||||||||
\(407\) | −3.22137 | + | 0.568014i | −0.159677 | + | 0.0281554i | ||||
\(408\) | 1.85563 | − | 35.0122i | 0.0918675 | − | 1.73336i | ||||
\(409\) | 16.6159 | − | 6.04769i | 0.821603 | − | 0.299039i | 0.103195 | − | 0.994661i | \(-0.467093\pi\) |
0.718408 | + | 0.695622i | \(0.244871\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.474366 | − | 3.88234i | −0.0233988 | − | 0.191502i | ||||
\(412\) | 3.53049 | − | 9.69993i | 0.173935 | − | 0.477881i | ||||
\(413\) | −6.40252 | + | 3.69650i | −0.315047 | + | 0.181893i | ||||
\(414\) | 1.08036 | + | 2.43426i | 0.0530968 | + | 0.119637i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.9559 | + | 13.3886i | −0.782303 | + | 0.656431i | ||||
\(417\) | 4.03081 | + | 13.2121i | 0.197390 | + | 0.646998i | ||||
\(418\) | −0.324466 | − | 0.0572121i | −0.0158701 | − | 0.00279833i | ||||
\(419\) | −1.58606 | + | 8.99500i | −0.0774842 | + | 0.439435i | 0.921243 | + | 0.388988i | \(0.127175\pi\) |
−0.998727 | + | 0.0504461i | \(0.983936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5344 | − | 15.5522i | 0.903310 | − | 0.757967i | −0.0675243 | − | 0.997718i | \(-0.521510\pi\) |
0.970835 | + | 0.239750i | \(0.0770656\pi\) | |||||||
\(422\) | −3.37031 | − | 1.94585i | −0.164064 | − | 0.0947226i | ||||
\(423\) | −6.99004 | + | 14.2889i | −0.339867 | + | 0.694749i | ||||
\(424\) | 15.9637 | + | 27.6499i | 0.775265 | + | 1.34280i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.150369 | + | 0.0639324i | 0.00728538 | + | 0.00309754i | ||||
\(427\) | 4.55764 | − | 5.43159i | 0.220560 | − | 0.262853i | ||||
\(428\) | 5.91236 | + | 16.2441i | 0.285785 | + | 0.785187i | ||||
\(429\) | −4.48120 | − | 8.80769i | −0.216354 | − | 0.425239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.5332 | −1.42256 | −0.711282 | − | 0.702907i | \(-0.751885\pi\) | ||||
−0.711282 | + | 0.702907i | \(0.751885\pi\) | |||||||
\(432\) | −3.82624 | − | 6.39355i | −0.184090 | − | 0.307610i | ||||
\(433\) | 0.669754i | 0.0321863i | 0.999870 | + | 0.0160932i | \(0.00512283\pi\) | ||||
−0.999870 | + | 0.0160932i | \(0.994877\pi\) | |||||||
\(434\) | 0.369201 | + | 2.09384i | 0.0177222 | + | 0.100508i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.27203 | − | 1.91886i | 0.252484 | − | 0.0918967i | ||||
\(437\) | 0.134850 | − | 0.160708i | 0.00645076 | − | 0.00768772i | ||||
\(438\) | 5.84336 | + | 7.76392i | 0.279206 | + | 0.370975i | ||||
\(439\) | −5.96599 | − | 2.17144i | −0.284741 | − | 0.103637i | 0.195701 | − | 0.980664i | \(-0.437302\pi\) |
−0.480442 | + | 0.877026i | \(0.659524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.98174 | − | 2.05700i | −0.0943685 | − | 0.0979526i | ||||
\(442\) | 27.6096 | + | 15.9404i | 1.31326 | + | 0.758209i | ||||
\(443\) | 9.86931 | + | 11.7618i | 0.468905 | + | 0.558819i | 0.947723 | − | 0.319095i | \(-0.103379\pi\) |
−0.478818 | + | 0.877914i | \(0.658934\pi\) | |||||||
\(444\) | −0.905072 | + | 3.90977i | −0.0429528 | + | 0.185550i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.88884 | + | 22.0547i | −0.184142 | + | 1.04432i | ||||
\(447\) | −0.180451 | − | 0.0417726i | −0.00853503 | − | 0.00197577i | ||||
\(448\) | 12.1647 | + | 14.4973i | 0.574728 | + | 0.684934i | ||||
\(449\) | −16.0199 | + | 27.7473i | −0.756027 | + | 1.30948i | 0.188836 | + | 0.982009i | \(0.439529\pi\) |
−0.944862 | + | 0.327468i | \(0.893805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.11268 | − | 8.85543i | −0.240747 | − | 0.416986i | ||||
\(452\) | −2.10135 | + | 5.77340i | −0.0988390 | + | 0.271558i | ||||
\(453\) | 21.1013 | + | 28.0368i | 0.991428 | + | 1.31729i | ||||
\(454\) | 11.5819 | + | 9.71835i | 0.543565 | + | 0.456105i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.716419 | + | 1.10176i | −0.0335494 | + | 0.0515949i | ||||
\(457\) | 18.8768 | − | 3.32849i | 0.883021 | − | 0.155700i | 0.286291 | − | 0.958143i | \(-0.407578\pi\) |
0.596730 | + | 0.802442i | \(0.296466\pi\) | |||||||
\(458\) | 17.8031i | 0.831886i | ||||||||
\(459\) | 21.7840 | − | 26.8039i | 1.01679 | − | 1.25110i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.906494 | − | 5.14098i | −0.0422196 | − | 0.239440i | 0.956394 | − | 0.292080i | \(-0.0943474\pi\) |
−0.998614 | + | 0.0526405i | \(0.983236\pi\) | |||||||
\(462\) | −5.02019 | + | 2.55418i | −0.233560 | + | 0.118831i | ||||
\(463\) | −0.580541 | − | 1.59502i | −0.0269800 | − | 0.0741271i | 0.925471 | − | 0.378818i | \(-0.123669\pi\) |
−0.952451 | + | 0.304690i | \(0.901447\pi\) | |||||||
\(464\) | −0.562837 | − | 0.472276i | −0.0261290 | − | 0.0219249i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.54760 | − | 2.01916i | −0.256988 | − | 0.0935359i | ||||
\(467\) | −17.0457 | + | 9.84136i | −0.788783 | + | 0.455404i | −0.839534 | − | 0.543307i | \(-0.817172\pi\) |
0.0507511 | + | 0.998711i | \(0.483838\pi\) | |||||||
\(468\) | −12.0955 | + | 0.831456i | −0.559115 | + | 0.0384341i | ||||
\(469\) | 12.4023 | − | 21.4814i | 0.572685 | − | 0.991920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.2702 | + | 24.5264i | 1.21047 | + | 1.13012i | ||||
\(472\) | −9.01574 | − | 1.58972i | −0.414983 | − | 0.0731727i | ||||
\(473\) | −5.34471 | − | 0.942416i | −0.245750 | − | 0.0433324i | ||||
\(474\) | −8.34368 | + | 2.54554i | −0.383238 | + | 0.116920i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.26134 | + | 12.5770i | −0.332823 | + | 0.576467i | ||||
\(477\) | −3.32458 | + | 31.2761i | −0.152222 | + | 1.43204i | ||||
\(478\) | −4.81579 | + | 2.78040i | −0.220269 | + | 0.127173i | ||||
\(479\) | −27.4892 | − | 10.0053i | −1.25601 | − | 0.457152i | −0.373585 | − | 0.927596i | \(-0.621872\pi\) |
−0.882430 | + | 0.470444i | \(0.844094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.08847 | − | 7.62613i | −0.414398 | − | 0.347722i | ||||
\(482\) | −3.21024 | − | 8.82005i | −0.146222 | − | 0.401742i | ||||
\(483\) | 0.189818 | − | 3.58151i | 0.00863704 | − | 0.162964i | ||||
\(484\) | −1.45429 | − | 8.24766i | −0.0661039 | − | 0.374894i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.48074 | − | 16.3685i | 0.0671675 | − | 0.742488i | ||||
\(487\) | 20.5056i | 0.929199i | 0.885521 | + | 0.464600i | \(0.153802\pi\) | ||||
−0.885521 | + | 0.464600i | \(0.846198\pi\) | |||||||
\(488\) | 8.64677 | − | 1.52466i | 0.391421 | − | 0.0690180i | ||||
\(489\) | −34.8252 | − | 1.84572i | −1.57485 | − | 0.0834664i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4265 | + | 11.2661i | 0.605927 | + | 0.508433i | 0.893345 | − | 0.449372i | \(-0.148352\pi\) |
−0.287417 | + | 0.957805i | \(0.592797\pi\) | |||||||
\(492\) | −12.4526 | + | 1.52152i | −0.561404 | + | 0.0685955i | ||||
\(493\) | 1.16489 | − | 3.20050i | 0.0524638 | − | 0.144143i | ||||
\(494\) | −0.597496 | − | 1.03489i | −0.0268826 | − | 0.0465620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.587922 | + | 1.01831i | −0.0263985 | + | 0.0457235i | ||||
\(497\) | −0.141441 | − | 0.168562i | −0.00634448 | − | 0.00756106i | ||||
\(498\) | 4.28473 | + | 14.0443i | 0.192003 | + | 0.629342i | ||||
\(499\) | 3.31772 | − | 18.8157i | 0.148522 | − | 0.842307i | −0.815950 | − | 0.578122i | \(-0.803786\pi\) |
0.964472 | − | 0.264185i | \(-0.0851031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.1469 | + | 23.4777i | 1.12348 | + | 1.04890i | ||||
\(502\) | 5.27270 | + | 6.28376i | 0.235332 | + | 0.280458i | ||||
\(503\) | 9.49824 | + | 5.48381i | 0.423506 | + | 0.244511i | 0.696576 | − | 0.717483i | \(-0.254706\pi\) |
−0.273070 | + | 0.961994i | \(0.588039\pi\) | |||||||
\(504\) | 1.54080 | + | 22.4146i | 0.0686327 | + | 0.998426i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.04627 | + | 0.380811i | 0.0465124 | + | 0.0169291i | ||||
\(507\) | 5.21405 | − | 12.2634i | 0.231564 | − | 0.544637i | ||||
\(508\) | 6.86590 | − | 8.18246i | 0.304625 | − | 0.363038i | ||||
\(509\) | −18.6993 | + | 6.80598i | −0.828831 | + | 0.301670i | −0.721379 | − | 0.692540i | \(-0.756491\pi\) |
−0.107452 | + | 0.994210i | \(0.534269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.27236 | − | 12.8872i | −0.100523 | − | 0.570096i | ||||
\(512\) | 15.2994i | 0.676143i | ||||||||
\(513\) | −1.20948 | + | 0.461822i | −0.0534000 | + | 0.0203899i | ||||
\(514\) | 21.5468 | 0.950387 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.62972 | + | 5.58207i | −0.159790 | + | 0.245737i | ||||
\(517\) | 2.27452 | + | 6.24920i | 0.100033 | + | 0.274839i | ||||
\(518\) | −4.34672 | + | 5.18022i | −0.190984 | + | 0.227606i | ||||
\(519\) | 26.1903 | − | 19.7116i | 1.14963 | − | 0.865243i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5583 | − | 30.4119i | −0.769244 | − | 1.33237i | −0.937973 | − | 0.346708i | \(-0.887300\pi\) |
0.168729 | − | 0.985662i | \(-0.446034\pi\) | |||||||
\(522\) | −0.390216 | − | 1.57298i | −0.0170793 | − | 0.0688473i | ||||
\(523\) | 12.3369 | + | 7.12269i | 0.539453 | + | 0.311453i | 0.744857 | − | 0.667224i | \(-0.232518\pi\) |
−0.205404 | + | 0.978677i | \(0.565851\pi\) | |||||||
\(524\) | −9.58545 | + | 8.04315i | −0.418742 | + | 0.351367i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.06513 | − | 11.7119i | 0.0900437 | − | 0.510663i | ||||
\(527\) | −5.36789 | − | 0.946505i | −0.233829 | − | 0.0412304i | ||||
\(528\) | −3.03480 | − | 0.702526i | −0.132073 | − | 0.0305735i | ||||
\(529\) | 17.0759 | − | 14.3284i | 0.742431 | − | 0.622974i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.25719 | − | 6.49483i | −0.271539 | − | 0.281852i | ||||
\(532\) | 0.471425 | − | 0.272177i | 0.0204389 | − | 0.0118004i | ||||
\(533\) | 12.6846 | − | 34.8507i | 0.549433 | − | 1.50955i | ||||
\(534\) | 9.78128 | − | 7.36168i | 0.423277 | − | 0.318571i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 28.8634 | − | 10.5054i | 1.24671 | − | 0.453765i | ||||
\(537\) | −15.8473 | − | 10.3047i | −0.683862 | − | 0.444679i | ||||
\(538\) | 0.319550 | − | 0.0563454i | 0.0137768 | − | 0.00242922i | ||||
\(539\) | −1.19414 | −0.0514354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.2368 | −0.569094 | −0.284547 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284547 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(542\) | −2.30765 | + | 0.406901i | −0.0991222 | + | 0.0174779i | ||||
\(543\) | 27.7067 | − | 14.0967i | 1.18901 | − | 0.604946i | ||||
\(544\) | −28.6004 | + | 10.4097i | −1.22623 | + | 0.446312i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.8007 | − | 7.99350i | −0.804594 | − | 0.342090i | ||||
\(547\) | 5.57661 | − | 15.3216i | 0.238439 | − | 0.655105i | −0.761537 | − | 0.648121i | \(-0.775555\pi\) |
0.999976 | − | 0.00698326i | \(-0.00222286\pi\) | |||||||
\(548\) | −1.73736 | + | 1.00306i | −0.0742163 | + | 0.0428488i | ||||
\(549\) | 7.76965 | + | 3.80087i | 0.331601 | + | 0.162217i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0977958 | + | 0.0820605i | −0.00416624 | + | 0.00349589i | ||||
\(552\) | 3.03084 | − | 3.24633i | 0.129001 | − | 0.138173i | ||||
\(553\) | 11.5692 | + | 2.03995i | 0.491970 | + | 0.0867476i | ||||
\(554\) | 4.27124 | − | 24.2234i | 0.181468 | − | 1.02915i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.42748 | − | 4.55419i | 0.230176 | − | 0.193141i | ||||
\(557\) | 26.7577 | + | 15.4486i | 1.13376 | + | 0.654577i | 0.944878 | − | 0.327422i | \(-0.106180\pi\) |
0.188883 | + | 0.982000i | \(0.439513\pi\) | |||||||
\(558\) | −2.37066 | + | 1.05214i | −0.100358 | + | 0.0445404i | ||||
\(559\) | −9.84215 | − | 17.0471i | −0.416279 | − | 0.721016i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75134 | − | 14.3335i | −0.0739417 | − | 0.605159i | ||||
\(562\) | 4.89674 | − | 5.83571i | 0.206557 | − | 0.246165i | ||||
\(563\) | −9.15791 | − | 25.1612i | −0.385960 | − | 1.06042i | −0.968803 | − | 0.247832i | \(-0.920282\pi\) |
0.582843 | − | 0.812585i | \(-0.301940\pi\) | |||||||
\(564\) | 8.14755 | + | 0.431816i | 0.343074 | + | 0.0181827i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.50710 | 0.315547 | ||||||||
\(567\) | −11.7731 | + | 18.7423i | −0.494423 | + | 0.787102i | ||||
\(568\) | − | 0.272481i | − | 0.0114331i | ||||||
\(569\) | −3.30985 | − | 18.7711i | −0.138756 | − | 0.786924i | −0.972170 | − | 0.234275i | \(-0.924728\pi\) |
0.833414 | − | 0.552649i | \(-0.186383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6420 | − | 6.42116i | 0.738294 | − | 0.268717i | 0.0546227 | − | 0.998507i | \(-0.482604\pi\) |
0.683671 | + | 0.729790i | \(0.260382\pi\) | |||||||
\(572\) | −3.25811 | + | 3.88286i | −0.136228 | + | 0.162351i | ||||
\(573\) | −46.3618 | + | 5.66474i | −1.93679 | + | 0.236648i | ||||
\(574\) | −19.8641 | − | 7.22996i | −0.829113 | − | 0.301773i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.5918 | + | 18.6611i | −0.566324 | + | 0.777547i | ||||
\(577\) | −4.20856 | − | 2.42981i | −0.175204 | − | 0.101154i | 0.409833 | − | 0.912161i | \(-0.365587\pi\) |
−0.585038 | + | 0.811006i | \(0.698920\pi\) | |||||||
\(578\) | 18.4234 | + | 21.9561i | 0.766311 | + | 0.913254i | ||||
\(579\) | 28.4198 | − | 8.67047i | 1.18109 | − | 0.360332i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43371 | − | 19.4736i | 0.142454 | − | 0.807899i | ||||
\(582\) | −6.84244 | + | 7.32894i | −0.283628 | + | 0.303795i | ||||
\(583\) | 8.45221 | + | 10.0730i | 0.350055 | + | 0.417179i | ||||
\(584\) | 8.10226 | − | 14.0335i | 0.335274 | − | 0.580712i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.291249 | − | 0.504459i | −0.0120314 | − | 0.0208390i | ||||
\(587\) | 11.2174 | − | 30.8194i | 0.462990 | − | 1.27205i | −0.460236 | − | 0.887796i | \(-0.652235\pi\) |
0.923226 | − | 0.384257i | \(-0.125542\pi\) | |||||||
\(588\) | −0.573239 | + | 1.34825i | −0.0236400 | + | 0.0556010i | ||||
\(589\) | 0.156510 | + | 0.131327i | 0.00644887 | + | 0.00541125i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.97318 | + | 3.87824i | 0.0811657 | + | 0.159529i | ||||
\(592\) | −3.68301 | + | 0.649414i | −0.151371 | + | 0.0266908i | ||||
\(593\) | 17.3446i | 0.712258i | 0.934437 | + | 0.356129i | \(0.115904\pi\) | ||||
−0.934437 | + | 0.356129i | \(0.884096\pi\) | |||||||
\(594\) | −4.49867 | − | 5.19367i | −0.184583 | − | 0.213099i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0164973 | + | 0.0935607i | 0.000675754 | + | 0.00383239i | ||||
\(597\) | −26.9196 | − | 17.5044i | −1.10174 | − | 0.716406i | ||||
\(598\) | 1.38120 | + | 3.79482i | 0.0564816 | + | 0.155182i | ||||
\(599\) | −18.6975 | − | 15.6891i | −0.763961 | − | 0.641039i | 0.175194 | − | 0.984534i | \(-0.443945\pi\) |
−0.939155 | + | 0.343495i | \(0.888389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.39563 | − | 2.69179i | −0.301674 | − | 0.109800i | 0.186748 | − | 0.982408i | \(-0.440205\pi\) |
−0.488422 | + | 0.872607i | \(0.662427\pi\) | |||||||
\(602\) | −9.71647 | + | 5.60981i | −0.396014 | + | 0.228639i | ||||
\(603\) | 29.0768 | + | 8.37478i | 1.18410 | + | 0.341047i | ||||
\(604\) | 8.99922 | − | 15.5871i | 0.366173 | − | 0.634230i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.06147 | + | 8.90521i | −0.0837413 | + | 0.361749i | ||||
\(607\) | 10.0819 | + | 1.77772i | 0.409213 | + | 0.0721553i | 0.374466 | − | 0.927241i | \(-0.377826\pi\) |
0.0347476 | + | 0.999396i | \(0.488937\pi\) | |||||||
\(608\) | 1.12350 | + | 0.198103i | 0.0455639 | + | 0.00803414i | ||||
\(609\) | −0.492214 | + | 2.12629i | −0.0199455 | + | 0.0861615i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0602 | + | 20.8889i | −0.487905 | + | 0.845076i | ||||
\(612\) | −17.0240 | − | 4.90329i | −0.688153 | − | 0.198204i | ||||
\(613\) | 1.93563 | − | 1.11753i | 0.0781792 | − | 0.0451368i | −0.460401 | − | 0.887711i | \(-0.652294\pi\) |
0.538580 | + | 0.842574i | \(0.318961\pi\) | |||||||
\(614\) | 6.66646 | + | 2.42639i | 0.269036 | + | 0.0979213i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.19547 | + | 6.03771i | 0.289914 | + | 0.243266i | ||||
\(617\) | 11.6204 | + | 31.9267i | 0.467818 | + | 1.28532i | 0.919482 | + | 0.393132i | \(0.128609\pi\) |
−0.451664 | + | 0.892188i | \(0.649169\pi\) | |||||||
\(618\) | 17.7883 | + | 11.5668i | 0.715551 | + | 0.465285i | ||||
\(619\) | 5.01079 | + | 28.4176i | 0.201401 | + | 1.14220i | 0.903004 | + | 0.429632i | \(0.141357\pi\) |
−0.701604 | + | 0.712567i | \(0.747532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.29625 | − | 0.827216i | 0.172403 | − | 0.0331950i | ||||
\(622\) | − | 16.2613i | − | 0.652020i | ||||||
\(623\) | −16.2358 | + | 2.86280i | −0.650472 | + | 0.114696i | ||||
\(624\) | −5.12338 | − | 10.0699i | −0.205099 | − | 0.403118i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.0292 | − | 15.9674i | −0.760558 | − | 0.638184i | ||||
\(627\) | −0.211780 | + | 0.498105i | −0.00845768 | + | 0.0198924i | ||||
\(628\) | 6.30485 | − | 17.3224i | 0.251591 | − | 0.691240i | ||||
\(629\) | −8.66811 | − | 15.0136i | −0.345620 | − | 0.598632i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.57039 | − | 2.71999i | 0.0625162 | − | 0.108281i | −0.833073 | − | 0.553163i | \(-0.813421\pi\) |
0.895590 | + | 0.444881i | \(0.146754\pi\) | |||||||
\(632\) | 9.35076 | + | 11.1438i | 0.371953 | + | 0.443277i | ||||
\(633\) | −4.36299 | + | 4.67320i | −0.173413 | + | 0.185743i | ||||
\(634\) | −1.32772 | + | 7.52985i | −0.0527303 | + | 0.299049i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.4303 | − | 4.70757i | 0.611852 | − | 0.186667i | ||||
\(637\) | −2.78402 | − | 3.31786i | −0.110307 | − | 0.131458i | ||||
\(638\) | −0.586774 | − | 0.338774i | −0.0232306 | − | 0.0134122i | ||||
\(639\) | 0.158034 | − | 0.216976i | 0.00625171 | − | 0.00858342i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.9034 | + | 10.8839i | 1.18111 | + | 0.429890i | 0.856595 | − | 0.515989i | \(-0.172576\pi\) |
0.324518 | + | 0.945879i | \(0.394798\pi\) | |||||||
\(642\) | −35.2710 | + | 4.30961i | −1.39204 | + | 0.170087i | ||||
\(643\) | 8.25794 | − | 9.84142i | 0.325661 | − | 0.388108i | −0.578228 | − | 0.815876i | \(-0.696255\pi\) |
0.903889 | + | 0.427768i | \(0.140700\pi\) | |||||||
\(644\) | −1.72866 | + | 0.629179i | −0.0681186 | + | 0.0247931i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.303217 | − | 1.71963i | −0.0119299 | − | 0.0676578i | ||||
\(647\) | − | 28.2444i | − | 1.11040i | −0.831717 | − | 0.555200i | \(-0.812642\pi\) | ||
0.831717 | − | 0.555200i | \(-0.187358\pi\) | |||||||
\(648\) | −26.0863 | + | 8.40792i | −1.02477 | + | 0.330294i | ||||
\(649\) | −3.77042 | −0.148002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.48794 | + | 0.184859i | 0.136703 | + | 0.00724521i | ||||
\(652\) | 6.11790 | + | 16.8088i | 0.239595 | + | 0.658283i | ||||
\(653\) | −16.7064 | + | 19.9099i | −0.653771 | + | 0.779134i | −0.986477 | − | 0.163897i | \(-0.947594\pi\) |
0.332707 | + | 0.943030i | \(0.392038\pi\) | |||||||
\(654\) | 1.39869 | + | 11.4472i | 0.0546930 | + | 0.447622i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.84536 | − | 10.1245i | −0.228223 | − | 0.395294i | ||||
\(657\) | 14.5910 | − | 6.47569i | 0.569248 | − | 0.252641i | ||||
\(658\) | 11.9062 | + | 6.87407i | 0.464153 | + | 0.267979i | ||||
\(659\) | 36.4774 | − | 30.6081i | 1.42096 | − | 1.19232i | 0.470131 | − | 0.882597i | \(-0.344207\pi\) |
0.950826 | − | 0.309727i | \(-0.100238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.152204 | + | 0.863192i | −0.00592005 | + | 0.0335743i | −0.987625 | − | 0.156836i | \(-0.949871\pi\) |
0.981705 | + | 0.190410i | \(0.0609818\pi\) | |||||||
\(662\) | −30.1467 | − | 5.31568i | −1.17168 | − | 0.206600i | ||||
\(663\) | 35.7416 | − | 38.2829i | 1.38809 | − | 1.48678i | ||||
\(664\) | 18.7576 | − | 15.7395i | 0.727936 | − | 0.610811i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.41009 | − | 3.62497i | −0.287135 | − | 0.140465i | ||||
\(667\) | 0.373627 | − | 0.215714i | 0.0144669 | − | 0.00835246i | ||||
\(668\) | 6.03526 | − | 16.5817i | 0.233511 | − | 0.641567i | ||||
\(669\) | 33.8574 | + | 14.3952i | 1.30900 | + | 0.556551i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.39803 | − | 1.23678i | 0.131180 | − | 0.0477455i | ||||
\(672\) | 17.3829 | − | 8.84413i | 0.670562 | − | 0.341170i | ||||
\(673\) | −36.7722 | + | 6.48393i | −1.41746 | + | 0.249937i | −0.829299 | − | 0.558805i | \(-0.811260\pi\) |
−0.588164 | + | 0.808742i | \(0.700149\pi\) | |||||||
\(674\) | 1.22206 | 0.0470721 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.83505 | −0.262886 | ||||||||
\(677\) | −13.5107 | + | 2.38231i | −0.519260 | + | 0.0915596i | −0.427135 | − | 0.904188i | \(-0.640477\pi\) |
−0.0921251 | + | 0.995747i | \(0.529366\pi\) | |||||||
\(678\) | −10.5876 | − | 6.88456i | −0.406614 | − | 0.264400i | ||||
\(679\) | 12.6884 | − | 4.61819i | 0.486935 | − | 0.177230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8451 | − | 14.9360i | 0.760465 | − | 0.572348i | ||||
\(682\) | −0.370863 | + | 1.01894i | −0.0142011 | + | 0.0390171i | ||||
\(683\) | 43.2914 | − | 24.9943i | 1.65650 | − | 0.956381i | 0.682190 | − | 0.731175i | \(-0.261028\pi\) |
0.974311 | − | 0.225206i | \(-0.0723056\pi\) | |||||||
\(684\) | 0.460724 | + | 0.478222i | 0.0176162 | + | 0.0182853i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7947 | + | 13.2534i | −0.603046 | + | 0.506016i | ||||
\(687\) | 28.4936 | + | 6.59598i | 1.08710 | + | 0.251652i | ||||
\(688\) | −6.11064 | − | 1.07747i | −0.232966 | − | 0.0410782i | ||||
\(689\) | −8.28172 | + | 46.9680i | −0.315509 | + | 1.78934i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.2434 | − | 15.3080i | 0.694011 | − | 0.582345i | −0.226052 | − | 0.974115i | \(-0.572582\pi\) |
0.920063 | + | 0.391771i | \(0.128137\pi\) | |||||||
\(692\) | −14.5605 | − | 8.40653i | −0.553508 | − | 0.319568i | ||||
\(693\) | 2.22797 | + | 8.98103i | 0.0846335 | + | 0.341161i | ||||
\(694\) | 3.10483 | + | 5.37773i | 0.117858 | + | 0.204136i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.15938 | + | 1.62521i | −0.0818510 | + | 0.0616035i | ||||
\(697\) | 34.8347 | − | 41.5144i | 1.31946 | − | 1.57247i | ||||
\(698\) | 11.0317 | + | 30.3094i | 0.417557 | + | 1.14723i | ||||
\(699\) | −5.28700 | + | 8.13075i | −0.199973 | + | 0.307533i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.4493 | 1.30113 | 0.650565 | − | 0.759450i | \(-0.274532\pi\) | ||||
0.650565 | + | 0.759450i | \(0.274532\pi\) | |||||||
\(702\) | 3.94216 | − | 24.6078i | 0.148787 | − | 0.928761i | ||||
\(703\) | 0.649815i | 0.0245082i | ||||||||
\(704\) | 1.67600 | + | 9.50506i | 0.0631665 | + | 0.358235i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.6191 | + | 13.3282i | −1.37818 | + | 0.501615i | ||||
\(707\) | 7.91250 | − | 9.42975i | 0.297580 | − | 0.354642i | ||||
\(708\) | −1.80996 | + | 4.25701i | −0.0680224 | + | 0.159988i | ||||
\(709\) | 14.5871 | + | 5.30927i | 0.547830 | + | 0.199394i | 0.601082 | − | 0.799187i | \(-0.294736\pi\) |
−0.0532520 | + | 0.998581i | \(0.516959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.982789 | + | 14.2970i | 0.0368575 | + | 0.536180i | ||||
\(712\) | −17.6800 | − | 10.2075i | −0.662585 | − | 0.382543i | ||||
\(713\) | −0.443809 | − | 0.528911i | −0.0166208 | − | 0.0198079i | ||||
\(714\) | −21.8204 | − | 20.3719i | −0.816607 | − | 0.762400i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.68364 | + | 9.54839i | −0.0629205 | + | 0.356840i | ||||
\(717\) | 2.66575 | + | 8.73772i | 0.0995543 | + | 0.326316i | ||||
\(718\) | −17.8752 | − | 21.3029i | −0.667098 | − | 0.795016i | ||||
\(719\) | 6.02686 | − | 10.4388i | 0.224764 | − | 0.389303i | −0.731485 | − | 0.681858i | \(-0.761172\pi\) |
0.956249 | + | 0.292555i | \(0.0945056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2872 | − | 24.7461i | −0.532083 | − | 0.921594i | ||||
\(722\) | 6.82902 | − | 18.7626i | 0.254150 | − | 0.698271i | ||||
\(723\) | −15.3057 | + | 1.87014i | −0.569226 | + | 0.0695512i | ||||
\(724\) | −12.2145 | − | 10.2492i | −0.453947 | − | 0.380907i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.1908 | + | 0.911107i | 0.638012 | + | 0.0338144i | ||||
\(727\) | −31.1497 | + | 5.49253i | −1.15528 | + | 0.203707i | −0.718279 | − | 0.695755i | \(-0.755070\pi\) |
−0.437000 | + | 0.899462i | \(0.643959\pi\) | |||||||
\(728\) | 34.0685i | 1.26266i | ||||||||
\(729\) | −25.6488 | − | 8.43433i | −0.949956 | − | 0.312383i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.99469 | − | 28.3263i | −0.184735 | − | 1.04769i | ||||
\(732\) | 0.234802 | − | 4.43027i | 0.00867855 | − | 0.163748i | ||||
\(733\) | 6.50891 | + | 17.8831i | 0.240412 | + | 0.660527i | 0.999949 | + | 0.0100630i | \(0.00320322\pi\) |
−0.759537 | + | 0.650464i | \(0.774575\pi\) | |||||||
\(734\) | 9.13716 | + | 7.66699i | 0.337259 | + | 0.282994i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.62283 | − | 1.31860i | −0.133539 | − | 0.0486043i | ||||
\(737\) | 10.9555 | − | 6.32516i | 0.403551 | − | 0.232990i | ||||
\(738\) | 2.72576 | − | 25.6427i | 0.100337 | − | 0.943920i | ||||
\(739\) | 8.30036 | − | 14.3767i | 0.305334 | − | 0.528854i | −0.672002 | − | 0.740550i | \(-0.734565\pi\) |
0.977336 | + | 0.211696i | \(0.0678986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.87770 | + | 0.572858i | −0.0689789 | + | 0.0210445i | ||||
\(742\) | 26.7707 | + | 4.72040i | 0.982783 | + | 0.173291i | ||||
\(743\) | −32.7976 | − | 5.78310i | −1.20323 | − | 0.212161i | −0.464134 | − | 0.885765i | \(-0.653634\pi\) |
−0.739093 | + | 0.673604i | \(0.764745\pi\) | |||||||
\(744\) | 3.16152 | + | 2.95166i | 0.115907 | + | 0.108213i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.08078 | + | 5.33606i | −0.112795 | + | 0.195367i | ||||
\(747\) | 24.0652 | − | 1.65426i | 0.880499 | − | 0.0605263i | ||||
\(748\) | −6.41426 | + | 3.70328i | −0.234529 | + | 0.135405i | ||||
\(749\) | 44.9665 | + | 16.3665i | 1.64304 | + | 0.598017i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2819 | + | 17.8577i | 0.776589 | + | 0.651636i | 0.942387 | − | 0.334524i | \(-0.108576\pi\) |
−0.165798 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(752\) | 2.60047 | + | 7.14474i | 0.0948295 | + | 0.260542i | ||||
\(753\) | 12.0106 | − | 6.11076i | 0.437689 | − | 0.222688i | ||||
\(754\) | −0.426735 | − | 2.42013i | −0.0155408 | − | 0.0881361i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.2096 | + | 1.79577i | 0.407689 | + | 0.0653116i | ||||
\(757\) | 3.12036i | 0.113411i | 0.998391 | + | 0.0567057i | \(0.0180597\pi\) | ||||
−0.998391 | + | 0.0567057i | \(0.981940\pi\) | |||||||
\(758\) | −25.2583 | + | 4.45373i | −0.917424 | + | 0.161767i | ||||
\(759\) | 0.997121 | − | 1.53345i | 0.0361932 | − | 0.0556607i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.6747 | − | 28.2564i | −1.22071 | − | 1.02429i | −0.998787 | − | 0.0492297i | \(-0.984323\pi\) |
−0.221919 | − | 0.975065i | \(-0.571232\pi\) | |||||||
\(762\) | 13.2032 | + | 17.5428i | 0.478302 | + | 0.635508i | ||||
\(763\) | 5.31175 | − | 14.5939i | 0.192298 | − | 0.528335i | ||||
\(764\) | 11.9783 | + | 20.7470i | 0.433360 | + | 0.750602i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.01168 | − | 3.48433i | 0.0726849 | − | 0.125894i | ||||
\(767\) | −8.79032 | − | 10.4759i | −0.317400 | − | 0.378263i | ||||
\(768\) | 27.8284 | + | 6.44200i | 1.00417 | + | 0.232456i | ||||
\(769\) | −0.644731 | + | 3.65645i | −0.0232496 | + | 0.131855i | −0.994223 | − | 0.107331i | \(-0.965769\pi\) |
0.970974 | + | 0.239186i | \(0.0768806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.98298 | − | 34.4852i | 0.287500 | − | 1.24195i | ||||
\(772\) | −9.79629 | − | 11.6748i | −0.352576 | − | 0.420184i | ||||
\(773\) | 7.76741 | + | 4.48452i | 0.279374 | + | 0.161297i | 0.633140 | − | 0.774037i | \(-0.281766\pi\) |
−0.353766 | + | 0.935334i | \(0.615099\pi\) | |||||||
\(774\) | −9.49592 | − | 9.85656i | −0.341324 | − | 0.354287i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.7121 | + | 5.71875i | 0.564033 | + | 0.205291i | ||||
\(777\) | 6.68041 | + | 8.87610i | 0.239658 | + | 0.318428i | ||||
\(778\) | −7.34760 | + | 8.75652i | −0.263424 | + | 0.313937i | ||||
\(779\) | −1.90882 | + | 0.694754i | −0.0683906 | + | 0.0248921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0194871 | − | 0.110517i | −0.000697302 | − | 0.00395459i | ||||
\(782\) | 5.90098i | 0.211018i | ||||||||
\(783\) | −2.66209 | + | 0.0417527i | −0.0951354 | + | 0.00149212i | ||||
\(784\) | −1.36527 | −0.0487597 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.6635 | − | 22.9243i | −0.416023 | − | 0.817684i | ||||
\(787\) | 14.9981 | + | 41.2069i | 0.534624 | + | 1.46887i | 0.853512 | + | 0.521074i | \(0.174468\pi\) |
−0.318888 | + | 0.947792i | \(0.603309\pi\) | |||||||
\(788\) | 1.43462 | − | 1.70972i | 0.0511063 | − | 0.0609062i | ||||
\(789\) | −17.9796 | − | 7.64441i | −0.640090 | − | 0.272148i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.50374 | + | 14.7289i | 0.302358 | + | 0.523699i | ||||
\(792\) | −5.03519 | + | 10.2928i | −0.178918 | + | 0.365739i | ||||
\(793\) | 11.3585 | + | 6.55782i | 0.403351 | + | 0.232875i | ||||
\(794\) | 8.48787 | − | 7.12217i | 0.301223 | − | 0.252756i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.85997 | + | 16.2197i | −0.101369 | + | 0.574891i | ||||
\(797\) | −11.8335 | − | 2.08656i | −0.419163 | − | 0.0739097i | −0.0399111 | − | 0.999203i | \(-0.512707\pi\) |
−0.379252 | + | 0.925294i | \(0.623819\pi\) | |||||||
\(798\) | 0.326516 | + | 1.07025i | 0.0115586 | + | 0.0378863i | ||||
\(799\) | −26.9996 | + | 22.6554i | −0.955178 | + | 0.801490i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.15832 | − | 18.3822i | −0.288260 | − | 0.649504i | ||||
\(802\) | −13.1168 | + | 7.57299i | −0.463171 | + | 0.267412i | ||||
\(803\) | 2.28259 | − | 6.27136i | 0.0805508 | − | 0.221311i | ||||
\(804\) | −1.88235 | − | 15.4057i | −0.0663855 | − | 0.543317i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.69568 | + | 1.34512i | −0.130175 | + | 0.0473798i | ||||
\(807\) | 0.0282122 | − | 0.532311i | 0.000993117 | − | 0.0187382i | ||||
\(808\) | 15.0116 | − | 2.64695i | 0.528107 | − | 0.0931195i | ||||
\(809\) | 8.02937 | 0.282298 | 0.141149 | − | 0.989988i | \(-0.454920\pi\) | ||||
0.141149 | + | 0.989988i | \(0.454920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8345 | −0.450681 | −0.225341 | − | 0.974280i | \(-0.572349\pi\) | ||||
−0.225341 | + | 0.974280i | \(0.572349\pi\) | |||||||
\(812\) | 1.10244 | − | 0.194391i | 0.0386882 | − | 0.00682177i | ||||
\(813\) | −0.203736 | + | 3.84411i | −0.00714534 | + | 0.134819i | ||||
\(814\) | −3.24078 | + | 1.17955i | −0.113589 | + | 0.0413431i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00232 | − | 16.3875i | −0.0700951 | − | 0.573678i | ||||
\(817\) | −0.368744 | + | 1.01312i | −0.0129007 | + | 0.0354444i | ||||
\(818\) | 16.1452 | − | 9.32142i | 0.564503 | − | 0.325916i | ||||
\(819\) | −19.7590 | + | 27.1286i | −0.690436 | + | 0.947949i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.7250 | + | 19.0685i | −0.793108 | + | 0.665497i | −0.946513 | − | 0.322667i | \(-0.895421\pi\) |
0.153404 | + | 0.988163i | \(0.450976\pi\) | |||||||
\(822\) | −1.20332 | − | 3.94422i | −0.0419707 | − | 0.137570i | ||||
\(823\) | 48.7881 | + | 8.60266i | 1.70065 | + | 0.299870i | 0.937920 | − | 0.346852i | \(-0.112749\pi\) |
0.762726 | + | 0.646722i | \(0.223861\pi\) | |||||||
\(824\) | 6.14436 | − | 34.8464i | 0.214049 | − | 1.21393i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.97102 | + | 5.01028i | −0.207758 | + | 0.174330i | ||||
\(827\) | 35.3711 | + | 20.4215i | 1.22997 | + | 0.710126i | 0.967025 | − | 0.254683i | \(-0.0819712\pi\) |
0.262950 | + | 0.964809i | \(0.415305\pi\) | |||||||
\(828\) | −1.25269 | − | 1.86192i | −0.0435339 | − | 0.0647063i | ||||
\(829\) | −4.72638 | − | 8.18633i | −0.164154 | − | 0.284323i | 0.772201 | − | 0.635379i | \(-0.219156\pi\) |
−0.936355 | + | 0.351056i | \(0.885823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.1867 | − | 15.8107i | −1.28999 | − | 0.548468i | ||||
\(832\) | −22.5018 | + | 26.8167i | −0.780111 | + | 0.929700i | ||||
\(833\) | −2.16458 | − | 5.94714i | −0.0749983 | − | 0.206056i | ||||
\(834\) | 6.60411 | + | 12.9802i | 0.228682 | + | 0.449468i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.277620 | 0.00960170 | ||||||||
\(837\) | 0.805605 | + | 4.18401i | 0.0278458 | + | 0.144621i | ||||
\(838\) | 9.62995i | 0.332661i | ||||||||
\(839\) | 2.13360 | + | 12.1002i | 0.0736599 | + | 0.417746i | 0.999232 | + | 0.0391756i | \(0.0124732\pi\) |
−0.925572 | + | 0.378571i | \(0.876416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0044 | − | 9.82879i | 0.931186 | − | 0.338924i | ||||
\(842\) | 16.3971 | − | 19.5413i | 0.565080 | − | 0.673436i | ||||
\(843\) | −7.52573 | − | 9.99925i | −0.259200 | − | 0.344392i | ||||
\(844\) | 3.08148 | + | 1.12157i | 0.106069 | + | 0.0386059i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.64178 | + | 16.1160i | −0.159588 | + | 0.554079i | ||||
\(847\) | −20.0772 | − | 11.5916i | −0.689862 | − | 0.398292i | ||||
\(848\) | 9.66346 | + | 11.5165i | 0.331845 | + | 0.395477i | ||||
\(849\) | 2.78135 | − | 12.0150i | 0.0954556 | − | 0.412353i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.381330 | − | 2.16263i | 0.0130718 | − | 0.0741339i | ||||
\(852\) | −0.134134 | − | 0.0310506i | −0.00459535 | − | 0.00106378i | ||||
\(853\) | −19.8402 | − | 23.6446i | −0.679315 | − | 0.809576i | 0.310704 | − | 0.950507i | \(-0.399435\pi\) |
−0.990020 | + | 0.140930i | \(0.954991\pi\) | |||||||
\(854\) | 3.73781 | − | 6.47408i | 0.127905 | − | 0.221538i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6280 | + | 51.3172i | 1.01266 | + | 1.75399i | ||||
\(857\) | −3.81217 | + | 10.4738i | −0.130221 | + | 0.357780i | −0.987618 | − | 0.156876i | \(-0.949858\pi\) |
0.857397 | + | 0.514655i | \(0.172080\pi\) | |||||||
\(858\) | −6.26539 | − | 8.32466i | −0.213897 | − | 0.284199i | ||||
\(859\) | −3.17807 | − | 2.66672i | −0.108434 | − | 0.0909872i | 0.586958 | − | 0.809617i | \(-0.300325\pi\) |
−0.695393 | + | 0.718630i | \(0.744770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.9310 | + | 29.1135i | −0.645167 | + | 0.992187i | ||||
\(862\) | −30.6645 | + | 5.40698i | −1.04444 | + | 0.184163i | ||||
\(863\) | − | 47.2534i | − | 1.60852i | −0.594275 | − | 0.804262i | \(-0.702561\pi\) | ||
0.594275 | − | 0.804262i | \(-0.297439\pi\) | |||||||
\(864\) | 15.5771 | + | 17.9837i | 0.529945 | + | 0.611817i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.122620 | + | 0.695411i | 0.00416678 | + | 0.0236310i | ||||
\(867\) | 41.9662 | − | 21.3516i | 1.42525 | − | 0.725140i | ||||
\(868\) | −0.612742 | − | 1.68349i | −0.0207978 | − | 0.0571415i | ||||
\(869\) | 4.58958 | + | 3.85112i | 0.155691 | + | 0.130640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.1156 | + | 15.6928i | 1.46092 | + | 0.531731i | ||||
\(872\) | 16.6550 | − | 9.61579i | 0.564011 | − | 0.325632i | ||||
\(873\) | 9.19475 | + | 13.6665i | 0.311195 | + | 0.462543i | ||||
\(874\) | 0.110593 | − | 0.191553i | 0.00374087 | − | 0.00647938i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.98497 | − | 5.58768i | −0.202213 | − | 0.188790i | ||||
\(877\) | −34.6164 | − | 6.10381i | −1.16891 | − | 0.206111i | −0.444695 | − | 0.895682i | \(-0.646688\pi\) |
−0.724218 | + | 0.689571i | \(0.757799\pi\) | |||||||
\(878\) | −6.59208 | − | 1.16236i | −0.222472 | − | 0.0392278i | ||||
\(879\) | −0.915284 | + | 0.279240i | −0.0308718 | + | 0.00941852i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.67981 | − | 16.7659i | 0.326121 | − | 0.564858i | −0.655618 | − | 0.755093i | \(-0.727592\pi\) |
0.981739 | + | 0.190235i | \(0.0609250\pi\) | |||||||
\(882\) | −2.43425 | − | 1.77298i | −0.0819656 | − | 0.0596994i | ||||
\(883\) | −11.9391 | + | 6.89302i | −0.401781 | + | 0.231969i | −0.687252 | − | 0.726419i | \(-0.741183\pi\) |
0.285471 | + | 0.958387i | \(0.407850\pi\) | |||||||
\(884\) | −25.2435 | − | 9.18788i | −0.849031 | − | 0.309022i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.4007 | + | 10.4055i | 0.416611 | + | 0.349578i | ||||
\(887\) | −10.1982 | − | 28.0192i | −0.342421 | − | 0.940794i | −0.984690 | − | 0.174315i | \(-0.944229\pi\) |
0.642269 | − | 0.766479i | \(-0.277993\pi\) | |||||||
\(888\) | −0.728070 | + | 13.7373i | −0.0244324 | + | 0.460993i | ||||
\(889\) | −5.13445 | − | 29.1189i | −0.172204 | − | 0.976617i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.97912 | + | 5.27581i | −0.334313 | + | 0.176746i | ||||
\(892\) | − | 18.8705i | − | 0.631832i | ||||||
\(893\) | 1.30104 | − | 0.229408i | 0.0435376 | − | 0.00767685i | ||||
\(894\) | −0.195011 | − | 0.0103355i | −0.00652215 | − | 0.000345671i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.96694 | − | 1.65046i | −0.0657109 | − | 0.0551380i | ||||
\(897\) | 6.58528 | − | 0.804626i | 0.219876 | − | 0.0268657i | ||||
\(898\) | −11.5536 | + | 31.7432i | −0.385548 | + | 1.05928i | ||||
\(899\) | 0.210078 | + | 0.363866i | 0.00700649 | + | 0.0121356i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.8448 | + | 60.3530i | −1.16085 | + | 2.01065i | ||||
\(902\) | −6.92980 | − | 8.25862i | −0.230737 | − | 0.274982i | ||||
\(903\) | 5.37849 | + | 17.6294i | 0.178985 | + | 0.586671i | ||||
\(904\) | −3.65712 | + | 20.7406i | −0.121634 | + | 0.689821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27.0427 | + | 25.2476i | 0.898434 | + | 0.838795i | ||||
\(907\) | 4.00558 | + | 4.77366i | 0.133003 | + | 0.158507i | 0.828435 | − | 0.560085i | \(-0.189231\pi\) |
−0.695432 | + | 0.718592i | \(0.744787\pi\) | |||||||
\(908\) | −11.0329 | − | 6.36984i | −0.366139 | − | 0.211391i | ||||
\(909\) | 13.4889 | + | 6.59868i | 0.447397 | + | 0.218864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.7314 | + | 10.8213i | 0.985044 | + | 0.358527i | 0.783799 | − | 0.621014i | \(-0.213279\pi\) |
0.201245 | + | 0.979541i | \(0.435501\pi\) | |||||||
\(912\) | −0.242129 | + | 0.569486i | −0.00801770 | + | 0.0188576i | ||||
\(913\) | 6.48232 | − | 7.72533i | 0.214534 | − | 0.255671i | ||||
\(914\) | 18.9906 | − | 6.91200i | 0.628152 | − | 0.228629i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.60496 | − | 14.7734i | −0.0860701 | − | 0.488128i | ||||
\(917\) | 34.6380i | 1.14385i | ||||||||
\(918\) | 17.7112 | − | 31.8189i | 0.584557 | − | 1.05018i | ||||
\(919\) | −36.0031 | −1.18763 | −0.593816 | − | 0.804601i | \(-0.702379\pi\) | ||||
−0.593816 | + | 0.804601i | \(0.702379\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.35329 | − | 9.77058i | 0.209348 | − | 0.321952i | ||||
\(922\) | −1.88244 | − | 5.17196i | −0.0619948 | − | 0.170329i | ||||
\(923\) | 0.261632 | − | 0.311801i | 0.00861173 | − | 0.0102631i | ||||
\(924\) | 3.79213 | − | 2.85407i | 0.124752 | − | 0.0938921i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.894800 | − | 1.54984i | −0.0294049 | − | 0.0509309i | ||||
\(927\) | 25.1029 | − | 24.1844i | 0.824489 | − | 0.794321i | ||||
\(928\) | 2.03177 | + | 1.17304i | 0.0666961 | + | 0.0385070i | ||||
\(929\) | −19.4941 | + | 16.3575i | −0.639580 | + | 0.536672i | −0.903889 | − | 0.427767i | \(-0.859301\pi\) |
0.264309 | + | 0.964438i | \(0.414856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0411934 | + | 0.233619i | −0.00135006 | + | 0.00765656i | ||||
\(932\) | 4.89897 | + | 0.863820i | 0.160471 | + | 0.0282954i | ||||
\(933\) | −26.0260 | − | 6.02475i | −0.852052 | − | 0.197241i | ||||
\(934\) | −15.8969 | + | 13.3391i | −0.520164 | + | 0.436469i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −40.3370 | + | 10.0066i | −1.31846 | + | 0.327075i | ||||
\(937\) | −24.5127 | + | 14.1524i | −0.800794 | + | 0.462338i | −0.843749 | − | 0.536739i | \(-0.819656\pi\) |
0.0429549 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(938\) | 8.94455 | − | 24.5750i | 0.292050 | − | 0.802401i | ||||
\(939\) | −32.6057 | + | 24.5400i | −1.06405 | + | 0.800833i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.79422 | + | 2.83687i | −0.254084 | + | 0.0924792i | −0.465922 | − | 0.884826i | \(-0.654277\pi\) |
0.211838 | + | 0.977305i | \(0.432055\pi\) | |||||||
\(942\) | 31.7669 | + | 20.6563i | 1.03502 | + | 0.673019i | ||||
\(943\) | 6.76039 | − | 1.19204i | 0.220149 | − | 0.0388181i | ||||
\(944\) | −4.31074 | −0.140303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.72199 | −0.186038 | ||||||||
\(947\) | −43.7753 | + | 7.71877i | −1.42251 | + | 0.250826i | −0.831358 | − | 0.555737i | \(-0.812436\pi\) |
−0.591148 | + | 0.806563i | \(0.701325\pi\) | |||||||
\(948\) | 6.55131 | − | 3.33319i | 0.212777 | − | 0.108257i | ||||
\(949\) | 22.7462 | − | 8.27895i | 0.738373 | − | 0.268746i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5595 | + | 4.91476i | 0.374842 | + | 0.159372i | ||||
\(952\) | −17.0264 | + | 46.7796i | −0.551828 | + | 1.51613i | ||||
\(953\) | −8.37576 | + | 4.83574i | −0.271317 | + | 0.156645i | −0.629486 | − | 0.777012i | \(-0.716735\pi\) |
0.358169 | + | 0.933657i | \(0.383401\pi\) | |||||||
\(954\) | 2.27415 | + | 33.0829i | 0.0736283 | + | 1.07110i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.58942 | − | 3.01188i | 0.116090 | − | 0.0974113i | ||||
\(957\) | −0.759599 | + | 0.813608i | −0.0245544 | + | 0.0263002i | ||||
\(958\) | −30.3740 | − | 5.35576i | −0.981341 | − | 0.173037i | ||||
\(959\) | −0.964325 | + | 5.46896i | −0.0311397 | + | 0.176602i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2323 | + | 19.4942i | −0.749429 | + | 0.628845i | ||||
\(962\) | −10.8328 | − | 6.25433i | −0.349264 | − | 0.201648i | ||||
\(963\) | −6.17030 | + | 58.0473i | −0.198835 | + | 1.87055i | ||||
\(964\) | 3.95448 | + | 6.84936i | 0.127365 | + | 0.220603i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.458619 | − | 3.75346i | −0.0147558 | − | 0.120766i | ||||
\(967\) | −21.2860 | + | 25.3676i | −0.684510 | + | 0.815768i | −0.990680 | − | 0.136209i | \(-0.956508\pi\) |
0.306170 | + | 0.951977i | \(0.400953\pi\) | |||||||
\(968\) | −9.81871 | − | 26.9767i | −0.315585 | − | 0.867064i | ||||
\(969\) | −2.86457 | − | 0.151821i | −0.0920234 | − | 0.00487720i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4309 | −0.880298 | −0.440149 | − | 0.897925i | \(-0.645074\pi\) | ||||
−0.440149 | + | 0.897925i | \(0.645074\pi\) | |||||||
\(972\) | 1.16629 | + | 13.7996i | 0.0374087 | + | 0.442622i | ||||
\(973\) | − | 19.6127i | − | 0.628755i | ||||||
\(974\) | 3.75420 | + | 21.2912i | 0.120292 | + | 0.682213i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.88499 | − | 1.41402i | 0.124356 | − | 0.0452617i | ||||
\(977\) | 23.3831 | − | 27.8668i | 0.748090 | − | 0.891539i | −0.248943 | − | 0.968518i | \(-0.580083\pi\) |
0.997033 | + | 0.0769792i | \(0.0245275\pi\) | |||||||
\(978\) | −36.4972 | + | 4.45943i | −1.16705 | + | 0.142597i | ||||
\(979\) | −7.90089 | − | 2.87569i | −0.252514 | − | 0.0919075i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8393 | + | 2.00258i | 0.601493 | + | 0.0639373i | ||||
\(982\) | 16.0034 | + | 9.23957i | 0.510689 | + | 0.294847i | ||||
\(983\) | 27.0853 | + | 32.2790i | 0.863886 | + | 1.02954i | 0.999249 | + | 0.0387434i | \(0.0123355\pi\) |
−0.135363 | + | 0.990796i | \(0.543220\pi\) | |||||||
\(984\) | −41.1315 | + | 12.5486i | −1.31122 | + | 0.400035i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.623557 | − | 3.53637i | 0.0198581 | − | 0.112621i | ||||
\(987\) | 15.4130 | − | 16.5089i | 0.490602 | − | 0.525484i | ||||
\(988\) | 0.647241 | + | 0.771352i | 0.0205915 | + | 0.0245400i | ||||
\(989\) | 1.82173 | − | 3.15533i | 0.0579276 | − | 0.100334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7705 | − | 22.1191i | −0.405667 | − | 0.702635i | 0.588732 | − | 0.808328i | \(-0.299627\pi\) |
−0.994399 | + | 0.105693i | \(0.966294\pi\) | |||||||
\(992\) | 1.28415 | − | 3.52818i | 0.0407719 | − | 0.112020i | ||||
\(993\) | −19.6769 | + | 46.2798i | −0.624426 | + | 1.46865i | ||||
\(994\) | −0.177720 | − | 0.149124i | −0.00563692 | − | 0.00472994i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.61053 | − | 11.0274i | −0.177776 | − | 0.349416i | ||||
\(997\) | 23.1754 | − | 4.08644i | 0.733971 | − | 0.129419i | 0.205845 | − | 0.978585i | \(-0.434006\pi\) |
0.528126 | + | 0.849166i | \(0.322895\pi\) | |||||||
\(998\) | − | 20.1439i | − | 0.637644i | ||||||
\(999\) | −8.54711 | + | 10.5167i | −0.270419 | + | 0.332733i |
(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 | 675.2.u.b.499.3 | 24 | ||
5.2 | odd | 4 | 27.2.e.a.13.2 | ✓ | 12 | ||
5.3 | odd | 4 | 675.2.l.c.526.1 | 12 | |||
5.4 | even | 2 | inner | 675.2.u.b.499.2 | 24 | ||
15.2 | even | 4 | 81.2.e.a.10.1 | 12 | |||
20.7 | even | 4 | 432.2.u.c.337.2 | 12 | |||
27.25 | even | 9 | inner | 675.2.u.b.349.2 | 24 | ||
45.2 | even | 12 | 243.2.e.b.109.1 | 12 | |||
45.7 | odd | 12 | 243.2.e.c.109.2 | 12 | |||
45.22 | odd | 12 | 243.2.e.d.190.1 | 12 | |||
45.32 | even | 12 | 243.2.e.a.190.2 | 12 | |||
135.2 | even | 36 | 81.2.e.a.73.1 | 12 | |||
135.7 | odd | 36 | 243.2.e.c.136.2 | 12 | |||
135.22 | odd | 36 | 729.2.a.a.1.5 | 6 | |||
135.32 | even | 36 | 729.2.a.d.1.2 | 6 | |||
135.47 | even | 36 | 243.2.e.b.136.1 | 12 | |||
135.52 | odd | 36 | 27.2.e.a.25.2 | yes | 12 | ||
135.67 | odd | 36 | 729.2.c.e.244.2 | 12 | |||
135.77 | even | 36 | 729.2.c.b.487.5 | 12 | |||
135.79 | even | 18 | inner | 675.2.u.b.349.3 | 24 | ||
135.92 | even | 36 | 243.2.e.a.55.2 | 12 | |||
135.97 | odd | 36 | 243.2.e.d.55.1 | 12 | |||
135.112 | odd | 36 | 729.2.c.e.487.2 | 12 | |||
135.122 | even | 36 | 729.2.c.b.244.5 | 12 | |||
135.133 | odd | 36 | 675.2.l.c.376.1 | 12 | |||
540.187 | even | 36 | 432.2.u.c.241.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.2 | ✓ | 12 | 5.2 | odd | 4 | ||
27.2.e.a.25.2 | yes | 12 | 135.52 | odd | 36 | ||
81.2.e.a.10.1 | 12 | 15.2 | even | 4 | |||
81.2.e.a.73.1 | 12 | 135.2 | even | 36 | |||
243.2.e.a.55.2 | 12 | 135.92 | even | 36 | |||
243.2.e.a.190.2 | 12 | 45.32 | even | 12 | |||
243.2.e.b.109.1 | 12 | 45.2 | even | 12 | |||
243.2.e.b.136.1 | 12 | 135.47 | even | 36 | |||
243.2.e.c.109.2 | 12 | 45.7 | odd | 12 | |||
243.2.e.c.136.2 | 12 | 135.7 | odd | 36 | |||
243.2.e.d.55.1 | 12 | 135.97 | odd | 36 | |||
243.2.e.d.190.1 | 12 | 45.22 | odd | 12 | |||
432.2.u.c.241.2 | 12 | 540.187 | even | 36 | |||
432.2.u.c.337.2 | 12 | 20.7 | even | 4 | |||
675.2.l.c.376.1 | 12 | 135.133 | odd | 36 | |||
675.2.l.c.526.1 | 12 | 5.3 | odd | 4 | |||
675.2.u.b.349.2 | 24 | 27.25 | even | 9 | inner | ||
675.2.u.b.349.3 | 24 | 135.79 | even | 18 | inner | ||
675.2.u.b.499.2 | 24 | 5.4 | even | 2 | inner | ||
675.2.u.b.499.3 | 24 | 1.1 | even | 1 | trivial | ||
729.2.a.a.1.5 | 6 | 135.22 | odd | 36 | |||
729.2.a.d.1.2 | 6 | 135.32 | even | 36 | |||
729.2.c.b.244.5 | 12 | 135.122 | even | 36 | |||
729.2.c.b.487.5 | 12 | 135.77 | even | 36 | |||
729.2.c.e.244.2 | 12 | 135.67 | odd | 36 | |||
729.2.c.e.487.2 | 12 | 135.112 | odd | 36 |