Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(76,675)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.l (of order \(9\), degree \(6\), 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: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.1952986685049.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 526.1 | ||
Root | \(0.500000 + 1.00210i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.526 |
Dual form | 675.2.l.c.376.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.183082 | − | 1.03831i | −0.129458 | − | 0.734194i | −0.978560 | − | 0.205964i | \(-0.933967\pi\) |
0.849101 | − | 0.528230i | \(-0.177144\pi\) | |||||||
\(3\) | 1.72962 | + | 0.0916693i | 0.998598 | + | 0.0529253i | ||||
\(4\) | 0.834822 | − | 0.303850i | 0.417411 | − | 0.151925i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.221481 | − | 1.81266i | −0.0904194 | − | 0.740017i | ||||
\(7\) | 2.31094 | + | 0.841112i | 0.873452 | + | 0.317910i | 0.739564 | − | 0.673086i | \(-0.235032\pi\) |
0.133888 | + | 0.990997i | \(0.457254\pi\) | |||||||
\(8\) | −1.52266 | − | 2.63732i | −0.538340 | − | 0.932432i | ||||
\(9\) | 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 | \(0.338328\pi\) | |||||||
\(12\) | 1.47178 | − | 0.449019i | 0.424867 | − | 0.129621i | ||||
\(13\) | 0.789931 | − | 4.47992i | 0.219087 | − | 1.24251i | −0.654584 | − | 0.755989i | \(-0.727156\pi\) |
0.873671 | − | 0.486517i | \(-0.161733\pi\) | |||||||
\(14\) | 0.450243 | − | 2.55345i | 0.120332 | − | 0.682439i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.09847 | + | 0.921724i | −0.274617 | + | 0.230431i | ||||
\(17\) | −3.32358 | + | 5.75662i | −0.806088 | + | 1.39618i | 0.109467 | + | 0.993990i | \(0.465086\pi\) |
−0.915554 | + | 0.402194i | \(0.868248\pi\) | |||||||
\(18\) | −0.216914 | − | 3.15553i | −0.0511270 | − | 0.743765i | ||||
\(19\) | −0.124578 | − | 0.215776i | −0.0285802 | − | 0.0495023i | 0.851382 | − | 0.524547i | \(-0.175765\pi\) |
−0.879962 | + | 0.475045i | \(0.842432\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.91994 | + | 1.66665i | 0.855402 | + | 0.363693i | ||||
\(22\) | 1.01298 | + | 0.849989i | 0.215967 | + | 0.181218i | ||||
\(23\) | 0.791222 | − | 0.287981i | 0.164981 | − | 0.0600483i | −0.258209 | − | 0.966089i | \(-0.583132\pi\) |
0.423190 | + | 0.906041i | \(0.360910\pi\) | |||||||
\(24\) | −2.39186 | − | 4.70115i | −0.488236 | − | 0.959617i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.79615 | −0.940603 | ||||||||
\(27\) | 5.13073 | + | 0.821942i | 0.987410 | + | 0.158183i | ||||
\(28\) | 2.18479 | 0.412887 | ||||||||
\(29\) | −0.0889744 | − | 0.504599i | −0.0165221 | − | 0.0937016i | 0.975432 | − | 0.220302i | \(-0.0707044\pi\) |
−0.991954 | + | 0.126601i | \(0.959593\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.770551 | − | 0.280458i | 0.138395 | − | 0.0503717i | −0.271894 | − | 0.962327i | \(-0.587650\pi\) |
0.410289 | + | 0.911956i | \(0.365428\pi\) | |||||||
\(32\) | −3.50754 | − | 2.94318i | −0.620052 | − | 0.520286i | ||||
\(33\) | −1.73570 | + | 1.30634i | −0.302146 | + | 0.227404i | ||||
\(34\) | 6.58563 | + | 2.39697i | 1.12943 | + | 0.411077i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.58679 | − | 0.641717i | 0.431131 | − | 0.106953i | ||||
\(37\) | 1.30403 | − | 2.25865i | 0.214381 | − | 0.371319i | −0.738700 | − | 0.674035i | \(-0.764560\pi\) |
0.953081 | + | 0.302715i | \(0.0978931\pi\) | |||||||
\(38\) | −0.201233 | + | 0.168855i | −0.0326444 | + | 0.0273919i | ||||
\(39\) | 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 | \(0.835884\pi\) | |||||||
\(42\) | 1.01282 | − | 4.37524i | 0.156282 | − | 0.675114i | ||||
\(43\) | −3.31478 | + | 2.78143i | −0.505500 | + | 0.424165i | −0.859542 | − | 0.511065i | \(-0.829251\pi\) |
0.354042 | + | 0.935229i | \(0.384807\pi\) | |||||||
\(44\) | −0.557121 | + | 0.964962i | −0.0839891 | + | 0.145473i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.443871 | − | 0.768808i | −0.0654452 | − | 0.113354i | ||||
\(47\) | −4.98256 | − | 1.81351i | −0.726782 | − | 0.264527i | −0.0479798 | − | 0.998848i | \(-0.515278\pi\) |
−0.678802 | + | 0.734321i | \(0.737501\pi\) | |||||||
\(48\) | −1.98443 | + | 1.49354i | −0.286428 | + | 0.215574i | ||||
\(49\) | −0.729356 | − | 0.612002i | −0.104194 | − | 0.0874289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.27625 | + | 9.65211i | −0.878851 | + | 1.35157i | ||||
\(52\) | −0.701774 | − | 3.97996i | −0.0973185 | − | 0.551921i | ||||
\(53\) | 10.4841 | 1.44010 | 0.720052 | − | 0.693920i | \(-0.244118\pi\) | ||||
0.720052 | + | 0.693920i | \(0.244118\pi\) | |||||||
\(54\) | −0.0859140 | − | 5.47776i | −0.0116914 | − | 0.745429i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.30048 | − | 7.37539i | −0.173784 | − | 0.985578i | ||||
\(57\) | −0.195693 | − | 0.384630i | −0.0259202 | − | 0.0509456i | ||||
\(58\) | −0.507639 | + | 0.184765i | −0.0666563 | + | 0.0242609i | ||||
\(59\) | −2.30289 | − | 1.93235i | −0.299810 | − | 0.251571i | 0.480455 | − | 0.877019i | \(-0.340471\pi\) |
−0.780265 | + | 0.625449i | \(0.784916\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.70930 | − | 0.986103i | −0.346890 | − | 0.126258i | 0.162699 | − | 0.986676i | \(-0.447980\pi\) |
−0.509589 | + | 0.860418i | \(0.670202\pi\) | |||||||
\(62\) | −0.432275 | − | 0.748722i | −0.0548990 | − | 0.0950878i | ||||
\(63\) | 6.62725 | + | 3.24201i | 0.834955 | + | 0.408455i | ||||
\(64\) | −3.84771 | + | 6.66442i | −0.480963 | + | 0.833053i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.67415 | + | 1.56302i | 0.206074 | + | 0.192394i | ||||
\(67\) | −1.75146 | + | 9.93303i | −0.213975 | + | 1.21351i | 0.668701 | + | 0.743531i | \(0.266851\pi\) |
−0.882676 | + | 0.469982i | \(0.844261\pi\) | |||||||
\(68\) | −1.02545 | + | 5.81562i | −0.124354 | + | 0.705248i | ||||
\(69\) | 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 | \(0.168357\pi\) | |||||||
\(72\) | −3.70607 | − | 8.35047i | −0.436764 | − | 0.984112i | ||||
\(73\) | −2.66057 | − | 4.60824i | −0.311396 | − | 0.539354i | 0.667269 | − | 0.744817i | \(-0.267463\pi\) |
−0.978665 | + | 0.205463i | \(0.934130\pi\) | |||||||
\(74\) | −2.58391 | − | 0.940468i | −0.300374 | − | 0.109327i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.169564 | − | 0.142281i | −0.0194503 | − | 0.0163208i | ||||
\(77\) | −2.89841 | + | 1.05493i | −0.330304 | + | 0.120221i | ||||
\(78\) | −8.29554 | − | 0.439660i | −0.939285 | − | 0.0497817i | ||||
\(79\) | 0.829503 | + | 4.70435i | 0.0933264 | + | 0.529280i | 0.995247 | + | 0.0973792i | \(0.0310460\pi\) |
−0.901921 | + | 0.431901i | \(0.857843\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.79889 | + | 1.89198i | 0.977654 | + | 0.210220i | ||||
\(82\) | 8.59571 | 0.949238 | ||||||||
\(83\) | −1.39625 | − | 7.91851i | −0.153258 | − | 0.869169i | −0.960361 | − | 0.278759i | \(-0.910077\pi\) |
0.807103 | − | 0.590410i | \(-0.201034\pi\) | |||||||
\(84\) | 3.77887 | + | 0.200278i | 0.412308 | + | 0.0218522i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.49486 | + | 2.93254i | 0.376860 | + | 0.316223i | ||||
\(87\) | −0.107636 | − | 0.880922i | −0.0115398 | − | 0.0944448i | ||||
\(88\) | 3.58913 | + | 1.30634i | 0.382602 | + | 0.139256i | ||||
\(89\) | −3.35189 | − | 5.80564i | −0.355299 | − | 0.615396i | 0.631870 | − | 0.775074i | \(-0.282288\pi\) |
−0.987169 | + | 0.159678i | \(0.948954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.59359 | − | 9.68839i | 0.586368 | − | 1.01562i | ||||
\(92\) | 0.573026 | − | 0.480826i | 0.0597421 | − | 0.0501296i | ||||
\(93\) | 1.35847 | − | 0.414450i | 0.140867 | − | 0.0429765i | ||||
\(94\) | −0.970760 | + | 5.50545i | −0.100126 | + | 0.567844i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.79693 | − | 5.41213i | −0.591647 | − | 0.552373i | ||||
\(97\) | −4.20603 | + | 3.52928i | −0.427057 | + | 0.358344i | −0.830840 | − | 0.556511i | \(-0.812140\pi\) |
0.403783 | + | 0.914855i | \(0.367695\pi\) | |||||||
\(98\) | −0.501915 | + | 0.869342i | −0.0507010 | + | 0.0878168i | ||||
\(99\) | −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 | \(0.691223\pi\) | |||||||
\(102\) | 11.1709 | + | 4.74956i | 1.10609 | + | 0.470276i | ||||
\(103\) | −8.90079 | − | 7.46865i | −0.877021 | − | 0.735908i | 0.0885431 | − | 0.996072i | \(-0.471779\pi\) |
−0.965564 | + | 0.260164i | \(0.916223\pi\) | |||||||
\(104\) | −13.0178 | + | 4.73808i | −1.27650 | + | 0.464607i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.91945 | − | 10.8857i | −0.186433 | − | 1.05732i | ||||
\(107\) | −19.4581 | −1.88109 | −0.940544 | − | 0.339673i | \(-0.889684\pi\) | ||||
−0.940544 | + | 0.339673i | \(0.889684\pi\) | |||||||
\(108\) | 4.53300 | − | 0.872799i | 0.436188 | − | 0.0839852i | ||||
\(109\) | 6.31515 | 0.604881 | 0.302441 | − | 0.953168i | \(-0.402199\pi\) | ||||
0.302441 | + | 0.953168i | \(0.402199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.46253 | − | 3.78707i | 0.233733 | − | 0.359453i | ||||
\(112\) | −3.31376 | + | 1.20611i | −0.313121 | + | 0.113967i | ||||
\(113\) | 5.29775 | + | 4.44534i | 0.498371 | + | 0.418183i | 0.857015 | − | 0.515292i | \(-0.172316\pi\) |
−0.358644 | + | 0.933474i | \(0.616761\pi\) | |||||||
\(114\) | −0.363537 | + | 0.273608i | −0.0340483 | + | 0.0256258i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.227600 | − | 0.394215i | −0.0211322 | − | 0.0366020i | ||||
\(117\) | 3.77713 | − | 13.1140i | 0.349196 | − | 1.21239i | ||||
\(118\) | −1.58476 | + | 2.74488i | −0.145889 | + | 0.252687i | ||||
\(119\) | −12.5226 | + | 10.5077i | −1.14794 | + | 0.963236i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.63697 | + | 9.28373i | −0.148816 | + | 0.843976i | ||||
\(122\) | −0.527856 | + | 2.99362i | −0.0477898 | + | 0.271030i | ||||
\(123\) | −3.18467 | + | 13.7573i | −0.287152 | + | 1.24045i | ||||
\(124\) | 0.558056 | − | 0.468265i | 0.0501149 | − | 0.0420514i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.15288 | − | 7.47467i | 0.191794 | − | 0.665897i | ||||
\(127\) | 6.01162 | + | 10.4124i | 0.533445 | + | 0.923954i | 0.999237 | + | 0.0390598i | \(0.0124363\pi\) |
−0.465792 | + | 0.884894i | \(0.654230\pi\) | |||||||
\(128\) | −0.981117 | − | 0.357098i | −0.0867194 | − | 0.0315633i | ||||
\(129\) | −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 | \(0.177925\pi\) | |||||||
\(132\) | −1.05207 | + | 1.61795i | −0.0915706 | + | 0.140824i | ||||
\(133\) | −0.106401 | − | 0.603428i | −0.00922610 | − | 0.0523238i | ||||
\(134\) | 10.6342 | 0.918655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.2427 | 1.73580 | ||||||||
\(137\) | −0.392122 | − | 2.22383i | −0.0335012 | − | 0.189995i | 0.963465 | − | 0.267836i | \(-0.0863085\pi\) |
−0.996966 | + | 0.0778409i | \(0.975197\pi\) | |||||||
\(138\) | −0.697254 | − | 1.37044i | −0.0593542 | − | 0.116659i | ||||
\(139\) | 7.49414 | − | 2.72764i | 0.635644 | − | 0.231356i | −0.00404179 | − | 0.999992i | \(-0.501287\pi\) |
0.639686 | + | 0.768636i | \(0.279064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.45172 | − | 3.59343i | −0.711763 | − | 0.302621i | ||||
\(142\) | 0.0886472 | + | 0.0322649i | 0.00743911 | + | 0.00270761i | ||||
\(143\) | 2.85273 | + | 4.94107i | 0.238557 | + | 0.413193i | ||||
\(144\) | −3.56923 | + | 2.40135i | −0.297436 | + | 0.200113i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.29767 | + | 3.60617i | −0.355678 | + | 0.298449i | ||||
\(147\) | −1.20541 | − | 1.12539i | −0.0994204 | − | 0.0928208i | ||||
\(148\) | 0.402343 | − | 2.28180i | 0.0330724 | − | 0.187563i | ||||
\(149\) | −0.0185697 | + | 0.105314i | −0.00152129 | + | 0.00862764i | −0.985559 | − | 0.169333i | \(-0.945839\pi\) |
0.984038 | + | 0.177960i | \(0.0569499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5196 | + | 13.0225i | −1.26297 | + | 1.05976i | −0.267609 | + | 0.963528i | \(0.586233\pi\) |
−0.995359 | + | 0.0962282i | \(0.969322\pi\) | |||||||
\(152\) | −0.379379 | + | 0.657104i | −0.0307717 | + | 0.0532982i | ||||
\(153\) | −11.7404 | + | 16.1192i | −0.949152 | + | 1.30316i | ||||
\(154\) | 1.62599 | + | 2.81630i | 0.131026 | + | 0.226944i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.848964 | − | 6.94816i | −0.0679716 | − | 0.556298i | ||||
\(157\) | 15.8953 | + | 13.3377i | 1.26858 | + | 1.06447i | 0.994712 | + | 0.102701i | \(0.0327485\pi\) |
0.273871 | + | 0.961767i | \(0.411696\pi\) | |||||||
\(158\) | 4.73269 | − | 1.72256i | 0.376513 | − | 0.137039i | ||||
\(159\) | 18.1336 | + | 0.961071i | 1.43809 | + | 0.0762179i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.07069 | 0.163193 | ||||||||
\(162\) | 0.353543 | − | 9.48234i | 0.0277770 | − | 0.745003i | ||||
\(163\) | 20.1346 | 1.57706 | 0.788531 | − | 0.614995i | \(-0.210842\pi\) | ||||
0.788531 | + | 0.614995i | \(0.210842\pi\) | |||||||
\(164\) | 1.25773 | + | 7.13292i | 0.0982119 | + | 0.556987i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.96622 | + | 2.89947i | −0.618298 | + | 0.225042i | ||||
\(167\) | 15.2156 | + | 12.7674i | 1.17742 | + | 0.987974i | 0.999993 | + | 0.00383999i | \(0.00122231\pi\) |
0.177429 | + | 0.984134i | \(0.443222\pi\) | |||||||
\(168\) | −1.57325 | − | 12.8759i | −0.121378 | − | 0.993395i | ||||
\(169\) | −7.22968 | − | 2.63139i | −0.556130 | − | 0.202415i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.303217 | − | 0.683205i | −0.0231876 | − | 0.0522460i | ||||
\(172\) | −1.92212 | + | 3.32920i | −0.146560 | + | 0.253849i | ||||
\(173\) | −14.4975 | + | 12.1648i | −1.10222 | + | 0.924875i | −0.997573 | − | 0.0696342i | \(-0.977817\pi\) |
−0.104650 | + | 0.994509i | \(0.533372\pi\) | |||||||
\(174\) | −0.894962 | + | 0.273040i | −0.0678469 | + | 0.0206991i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.312302 | − | 1.77115i | 0.0235407 | − | 0.133506i | ||||
\(177\) | −3.80599 | − | 3.55334i | −0.286075 | − | 0.267085i | ||||
\(178\) | −5.41436 | + | 4.54319i | −0.405824 | + | 0.340527i | ||||
\(179\) | −5.45683 | + | 9.45151i | −0.407863 | + | 0.706439i | −0.994650 | − | 0.103302i | \(-0.967059\pi\) |
0.586787 | + | 0.809741i | \(0.300392\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.97393 | + | 15.5433i | 0.667027 | + | 1.15532i | 0.978731 | + | 0.205146i | \(0.0657668\pi\) |
−0.311704 | + | 0.950179i | \(0.600900\pi\) | |||||||
\(182\) | −11.0836 | − | 4.03410i | −0.821572 | − | 0.299028i | ||||
\(183\) | −4.59567 | − | 1.95395i | −0.339721 | − | 0.144440i | ||||
\(184\) | −1.96426 | − | 1.64821i | −0.144807 | − | 0.121507i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.679038 | − | 1.33463i | −0.0497895 | − | 0.0978601i | ||||
\(187\) | −1.44770 | − | 8.21031i | −0.105866 | − | 0.600397i | ||||
\(188\) | −4.71059 | −0.343555 | ||||||||
\(189\) | 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 | \(-0.485092\pi\) | |||||||
\(192\) | −7.26601 | + | 11.1742i | −0.524379 | + | 0.806430i | ||||
\(193\) | −16.1202 | + | 5.86729i | −1.16036 | + | 0.422337i | −0.849226 | − | 0.528029i | \(-0.822931\pi\) |
−0.311135 | + | 0.950366i | \(0.600709\pi\) | |||||||
\(194\) | 4.43452 | + | 3.72100i | 0.318380 | + | 0.267152i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.794839 | − | 0.289298i | −0.0567742 | − | 0.0206641i | ||||
\(197\) | 1.25612 | + | 2.17567i | 0.0894951 | + | 0.155010i | 0.907298 | − | 0.420489i | \(-0.138141\pi\) |
−0.817803 | + | 0.575499i | \(0.804808\pi\) | |||||||
\(198\) | 2.75237 | + | 2.85690i | 0.195602 | + | 0.203031i | ||||
\(199\) | −9.26942 | + | 16.0551i | −0.657092 | + | 1.13812i | 0.324273 | + | 0.945964i | \(0.394880\pi\) |
−0.981365 | + | 0.192153i | \(0.938453\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.93992 | + | 17.0198i | −0.277901 | + | 1.20049i | ||||
\(202\) | −0.916408 | + | 5.19721i | −0.0644783 | + | 0.365674i | ||||
\(203\) | 0.218810 | − | 1.24093i | 0.0153574 | − | 0.0870964i | ||||
\(204\) | −2.30676 | + | 9.96484i | −0.161505 | + | 0.697678i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.12519 | + | 10.6091i | −0.426762 | + | 0.739173i | ||||
\(207\) | 2.45169 | − | 0.608202i | 0.170404 | − | 0.0422730i | ||||
\(208\) | 3.26154 | + | 5.64915i | 0.226147 | + | 0.391698i | ||||
\(209\) | 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 | \(0.762775\pi\) | |||||||
\(212\) | 8.75237 | − | 3.18560i | 0.601115 | − | 0.218788i | ||||
\(213\) | −0.0844829 | + | 0.129924i | −0.00578867 | + | 0.00890226i | ||||
\(214\) | 3.56242 | + | 20.2035i | 0.243522 | + | 1.38108i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.64462 | − | 14.7829i | −0.384067 | − | 1.00585i | ||||
\(217\) | 2.01659 | 0.136895 | ||||||||
\(218\) | −1.15619 | − | 6.55706i | −0.0783069 | − | 0.444100i | ||||
\(219\) | −4.17935 | − | 8.21441i | −0.282414 | − | 0.555079i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.1638 | + | 19.4367i | 1.55816 | + | 1.30746i | ||||
\(222\) | −4.38299 | − | 1.86352i | −0.294167 | − | 0.125071i | ||||
\(223\) | −19.9601 | − | 7.26487i | −1.33662 | − | 0.486491i | −0.427876 | − | 0.903837i | \(-0.640738\pi\) |
−0.908748 | + | 0.417346i | \(0.862960\pi\) | |||||||
\(224\) | −5.63017 | − | 9.75174i | −0.376181 | − | 0.651565i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.64571 | − | 6.31456i | 0.242509 | − | 0.420038i | ||||
\(227\) | 10.9851 | − | 9.21761i | 0.729108 | − | 0.611794i | −0.200781 | − | 0.979636i | \(-0.564348\pi\) |
0.929888 | + | 0.367842i | \(0.119903\pi\) | |||||||
\(228\) | −0.280239 | − | 0.261637i | −0.0185593 | − | 0.0173273i | ||||
\(229\) | 2.93219 | − | 16.6293i | 0.193765 | − | 1.09889i | −0.720403 | − | 0.693556i | \(-0.756043\pi\) |
0.914167 | − | 0.405337i | \(-0.132846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.10985 | + | 1.55894i | −0.336204 | + | 0.102571i | ||||
\(232\) | −1.19531 | + | 1.00298i | −0.0784759 | + | 0.0658491i | ||||
\(233\) | 2.79972 | − | 4.84926i | 0.183416 | − | 0.317686i | −0.759626 | − | 0.650361i | \(-0.774618\pi\) |
0.943042 | + | 0.332675i | \(0.107951\pi\) | |||||||
\(234\) | −14.3079 | − | 1.52089i | −0.935334 | − | 0.0994238i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.50964 | − | 0.913436i | −0.163364 | − | 0.0594596i | ||||
\(237\) | 1.00348 | + | 8.21279i | 0.0651833 | + | 0.533478i | ||||
\(238\) | 13.2028 | + | 11.0785i | 0.855813 | + | 0.718112i | ||||
\(239\) | 4.95620 | − | 1.80391i | 0.320590 | − | 0.116685i | −0.176712 | − | 0.984263i | \(-0.556546\pi\) |
0.497302 | + | 0.867577i | \(0.334324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.54590 | − | 8.76723i | −0.0995801 | − | 0.564747i | −0.993247 | − | 0.116017i | \(-0.962987\pi\) |
0.893667 | − | 0.448730i | \(-0.148124\pi\) | |||||||
\(242\) | 9.93907 | 0.638907 | ||||||||
\(243\) | 15.0453 | + | 4.07900i | 0.965158 | + | 0.261668i | ||||
\(244\) | −2.56141 | −0.163977 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.8673 | + | 0.787963i | 0.947908 | + | 0.0502387i | ||||
\(247\) | −1.06507 | + | 0.387652i | −0.0677685 | + | 0.0246657i | ||||
\(248\) | −1.91294 | − | 1.60515i | −0.121472 | − | 0.101927i | ||||
\(249\) | −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 | \(0.754368\pi\) | |||||||
\(252\) | 6.51766 | + | 0.692812i | 0.410574 | + | 0.0436431i | ||||
\(253\) | −0.528024 | + | 0.914565i | −0.0331966 | + | 0.0574982i | ||||
\(254\) | 9.71069 | − | 8.14824i | 0.609303 | − | 0.511266i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.86374 | + | 16.2411i | −0.178984 | + | 1.01507i | ||||
\(257\) | 3.54877 | − | 20.1261i | 0.221366 | − | 1.25543i | −0.648145 | − | 0.761517i | \(-0.724455\pi\) |
0.869511 | − | 0.493913i | \(-0.164434\pi\) | |||||||
\(258\) | 5.77597 | + | 5.39255i | 0.359596 | + | 0.335726i | ||||
\(259\) | 4.91331 | − | 4.12275i | 0.305298 | − | 0.256175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.105416 | − | 1.53353i | −0.00652510 | − | 0.0949231i | ||||
\(262\) | −7.42498 | − | 12.8604i | −0.458717 | − | 0.794520i | ||||
\(263\) | 10.5996 | + | 3.85792i | 0.653596 | + | 0.237890i | 0.647469 | − | 0.762092i | \(-0.275827\pi\) |
0.00612723 | + | 0.999981i | \(0.498050\pi\) | |||||||
\(264\) | 6.08809 | + | 2.58848i | 0.374696 | + | 0.159310i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.607063 | + | 0.220953i | −0.0372214 | + | 0.0135475i | ||||
\(267\) | −5.26530 | − | 10.3488i | −0.322231 | − | 0.633338i | ||||
\(268\) | 1.55600 | + | 8.82450i | 0.0950476 | + | 0.539042i | ||||
\(269\) | −0.307761 | −0.0187645 | −0.00938226 | − | 0.999956i | \(-0.502987\pi\) | ||||
−0.00938226 | + | 0.999956i | \(0.502987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.22251 | −0.135008 | −0.0675040 | − | 0.997719i | \(-0.521504\pi\) | ||||
−0.0675040 | + | 0.997719i | \(0.521504\pi\) | |||||||
\(272\) | −1.65516 | − | 9.38689i | −0.100359 | − | 0.569164i | ||||
\(273\) | 10.5629 | − | 16.2445i | 0.639298 | − | 0.983162i | ||||
\(274\) | −2.23723 | + | 0.814286i | −0.135156 | + | 0.0491928i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.03520 | − | 0.779119i | 0.0623115 | − | 0.0468975i | ||||
\(277\) | −21.9228 | − | 7.97924i | −1.31721 | − | 0.479426i | −0.414648 | − | 0.909982i | \(-0.636095\pi\) |
−0.902564 | + | 0.430556i | \(0.858317\pi\) | |||||||
\(278\) | −4.20417 | − | 7.28184i | −0.252149 | − | 0.436735i | ||||
\(279\) | 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 | \(0.208634\pi\) | |||||||
\(282\) | −2.18373 | + | 9.43337i | −0.130039 | + | 0.561749i | ||||
\(283\) | −1.23643 | + | 7.01212i | −0.0734979 | + | 0.416827i | 0.925753 | + | 0.378129i | \(0.123432\pi\) |
−0.999251 | + | 0.0386985i | \(0.987679\pi\) | |||||||
\(284\) | −0.0138033 | + | 0.0782824i | −0.000819076 | + | 0.00464521i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.60806 | − | 3.86662i | 0.272480 | − | 0.228638i | ||||
\(287\) | −10.0249 | + | 17.3636i | −0.591751 | + | 1.02494i | ||||
\(288\) | −9.53038 | − | 9.89234i | −0.561583 | − | 0.582912i | ||||
\(289\) | −13.5924 | − | 23.5428i | −0.799555 | − | 1.38487i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.59837 | + | 5.71875i | −0.445424 | + | 0.335239i | ||||
\(292\) | −3.62132 | − | 3.03865i | −0.211922 | − | 0.177823i | ||||
\(293\) | 0.519166 | − | 0.188961i | 0.0303300 | − | 0.0110392i | −0.326811 | − | 0.945090i | \(-0.605974\pi\) |
0.357141 | + | 0.934051i | \(0.383752\pi\) | |||||||
\(294\) | −0.947815 | + | 1.45762i | −0.0552777 | + | 0.0850103i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.94236 | −0.461640 | ||||||||
\(297\) | −5.59216 | + | 3.34665i | −0.324490 | + | 0.194192i | ||||
\(298\) | 0.112748 | 0.00653131 | ||||||||
\(299\) | −0.665122 | − | 3.77210i | −0.0384650 | − | 0.218146i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.99975 | + | 3.63961i | −0.576376 | + | 0.209784i | ||||
\(302\) | 16.3627 | + | 13.7299i | 0.941568 | + | 0.790069i | ||||
\(303\) | −7.97852 | − | 3.39224i | −0.458354 | − | 0.194879i | ||||
\(304\) | 0.335731 | + | 0.122196i | 0.0192555 | + | 0.00700842i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.8861 | + | 9.23898i | 1.07965 | + | 0.528157i | ||||
\(307\) | 3.36438 | − | 5.82728i | 0.192015 | − | 0.332580i | −0.753903 | − | 0.656986i | \(-0.771831\pi\) |
0.945918 | + | 0.324406i | \(0.105164\pi\) | |||||||
\(308\) | −2.09911 | + | 1.76136i | −0.119608 | + | 0.100363i | ||||
\(309\) | −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 | \(-0.0885068\pi\) | |||||||
\(312\) | −22.9502 | + | 7.00176i | −1.29930 | + | 0.396397i | ||||
\(313\) | 18.0487 | − | 15.1446i | 1.02017 | − | 0.856025i | 0.0305223 | − | 0.999534i | \(-0.490283\pi\) |
0.989649 | + | 0.143509i | \(0.0458385\pi\) | |||||||
\(314\) | 10.9385 | − | 18.9461i | 0.617297 | − | 1.06919i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.12191 | + | 3.67525i | 0.119367 | + | 0.206749i | ||||
\(317\) | 6.81469 | + | 2.48034i | 0.382751 | + | 0.139310i | 0.526228 | − | 0.850344i | \(-0.323606\pi\) |
−0.143477 | + | 0.989654i | \(0.545828\pi\) | |||||||
\(318\) | −2.32204 | − | 19.0042i | −0.130213 | − | 1.06570i | ||||
\(319\) | 0.492289 | + | 0.413079i | 0.0275629 | + | 0.0231280i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.6552 | − | 1.78371i | −1.87845 | − | 0.0995571i | ||||
\(322\) | −0.379105 | − | 2.15001i | −0.0211267 | − | 0.119815i | ||||
\(323\) | 1.65618 | 0.0921525 | ||||||||
\(324\) | 7.92038 | − | 1.09408i | 0.440021 | − | 0.0607821i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.68627 | − | 20.9059i | −0.204164 | − | 1.15787i | ||||
\(327\) | 10.9228 | + | 0.578905i | 0.604034 | + | 0.0320135i | ||||
\(328\) | 23.3306 | − | 8.49163i | 1.28821 | − | 0.468872i | ||||
\(329\) | −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 | \(0.905188\pi\) | |||||||
\(332\) | −3.57166 | − | 6.18629i | −0.196020 | − | 0.339517i | ||||
\(333\) | 4.60641 | − | 6.32447i | 0.252430 | − | 0.346579i | ||||
\(334\) | 10.4708 | − | 18.1360i | 0.572938 | − | 0.992357i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.84213 | + | 1.78235i | −0.318714 | + | 0.0972351i | ||||
\(337\) | 0.201275 | − | 1.14149i | 0.0109641 | − | 0.0621807i | −0.978835 | − | 0.204652i | \(-0.934394\pi\) |
0.989799 | + | 0.142471i | \(0.0455049\pi\) | |||||||
\(338\) | −1.40857 | + | 7.98839i | −0.0766161 | + | 0.434511i | ||||
\(339\) | 8.75561 | + | 8.17441i | 0.475540 | + | 0.443973i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.514230 | + | 0.890672i | −0.0278471 | + | 0.0482326i | ||||
\(342\) | −0.653863 | + | 0.439914i | −0.0353569 | + | 0.0237878i | ||||
\(343\) | −9.77810 | − | 16.9362i | −0.527968 | − | 0.914467i | ||||
\(344\) | 12.3828 | + | 4.50697i | 0.667636 | + | 0.243000i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.2851 | + | 12.8257i | 0.821730 | + | 0.689513i | ||||
\(347\) | 5.53452 | − | 2.01440i | 0.297108 | − | 0.108139i | −0.189165 | − | 0.981945i | \(-0.560578\pi\) |
0.486273 | + | 0.873807i | \(0.338356\pi\) | |||||||
\(348\) | −0.357525 | − | 0.702708i | −0.0191654 | − | 0.0376691i | ||||
\(349\) | −5.31237 | − | 30.1279i | −0.284364 | − | 1.61271i | −0.707547 | − | 0.706666i | \(-0.750198\pi\) |
0.423183 | − | 0.906044i | \(-0.360913\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.73516 | − | 22.3360i | 0.412872 | − | 1.19221i | ||||
\(352\) | 5.74276 | 0.306090 | ||||||||
\(353\) | −6.41826 | − | 36.3997i | −0.341609 | − | 1.93736i | −0.348294 | − | 0.937385i | \(-0.613239\pi\) |
0.00668455 | − | 0.999978i | \(-0.497872\pi\) | |||||||
\(354\) | −2.99265 | + | 4.60233i | −0.159058 | + | 0.244611i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.56227 | − | 3.82820i | −0.241800 | − | 0.202894i | ||||
\(357\) | −22.6225 | + | 17.0264i | −1.19731 | + | 0.901131i | ||||
\(358\) | 10.8126 | + | 3.93547i | 0.571464 | + | 0.207996i | ||||
\(359\) | 13.1880 | + | 22.8423i | 0.696037 | + | 1.20557i | 0.969830 | + | 0.243783i | \(0.0783886\pi\) |
−0.273792 | + | 0.961789i | \(0.588278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.46896 | − | 16.4007i | 0.498366 | − | 0.863196i | ||||
\(362\) | 14.4958 | − | 12.1634i | 0.761881 | − | 0.639294i | ||||
\(363\) | −3.68238 | + | 15.9073i | −0.193275 | + | 0.834917i | ||||
\(364\) | 1.72583 | − | 9.78769i | 0.0904583 | − | 0.513015i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.18741 | + | 5.12944i | −0.0620671 | + | 0.268120i | ||||
\(367\) | 8.66636 | − | 7.27194i | 0.452380 | − | 0.379592i | −0.387938 | − | 0.921685i | \(-0.626813\pi\) |
0.840318 | + | 0.542093i | \(0.182368\pi\) | |||||||
\(368\) | −0.603693 | + | 1.04563i | −0.0314697 | + | 0.0545071i | ||||
\(369\) | −6.76941 | + | 23.5030i | −0.352401 | + | 1.22352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2281 | + | 8.81831i | 1.25786 | + | 0.457824i | ||||
\(372\) | 1.00815 | − | 0.758765i | 0.0522703 | − | 0.0393401i | ||||
\(373\) | −4.47682 | − | 3.75650i | −0.231801 | − | 0.194504i | 0.519487 | − | 0.854478i | \(-0.326123\pi\) |
−0.751289 | + | 0.659974i | \(0.770567\pi\) | |||||||
\(374\) | −8.25978 | + | 3.00631i | −0.427103 | + | 0.155453i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.80394 | + | 15.9019i | 0.144602 | + | 0.820080i | ||||
\(377\) | −2.33085 | −0.120045 | ||||||||
\(378\) | 4.40887 | − | 12.7310i | 0.226768 | − | 0.654813i | ||||
\(379\) | 24.3265 | 1.24957 | 0.624783 | − | 0.780798i | \(-0.285187\pi\) | ||||
0.624783 | + | 0.780798i | \(0.285187\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.44334 | + | 18.5607i | 0.483797 | + | 0.950892i | ||||
\(382\) | −26.7164 | + | 9.72397i | −1.36693 | + | 0.497522i | ||||
\(383\) | 2.92326 | + | 2.45291i | 0.149372 | + | 0.125338i | 0.714411 | − | 0.699726i | \(-0.246695\pi\) |
−0.565039 | + | 0.825064i | \(0.691139\pi\) | |||||||
\(384\) | −1.66423 | − | 0.707583i | −0.0849273 | − | 0.0361087i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.04337 | + | 15.6636i | 0.460295 | + | 0.797255i | ||||
\(387\) | −10.7707 | + | 7.24642i | −0.547503 | + | 0.368356i | ||||
\(388\) | −2.43891 | + | 4.22432i | −0.123817 | + | 0.214457i | ||||
\(389\) | 8.30534 | − | 6.96901i | 0.421097 | − | 0.353343i | −0.407483 | − | 0.913213i | \(-0.633593\pi\) |
0.828580 | + | 0.559870i | \(0.189149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.971896 | + | 5.51189i | −0.0491509 | + | 0.278748i | ||||
\(392\) | −0.503486 | + | 2.85541i | −0.0254299 | + | 0.144220i | ||||
\(393\) | 23.3338 | − | 7.11881i | 1.17704 | − | 0.359096i | ||||
\(394\) | 2.02904 | − | 1.70257i | 0.102222 | − | 0.0857741i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.96799 | + | 2.70200i | −0.0988955 | + | 0.135781i | ||||
\(397\) | −5.25461 | − | 9.10124i | −0.263721 | − | 0.456778i | 0.703507 | − | 0.710689i | \(-0.251617\pi\) |
−0.967228 | + | 0.253910i | \(0.918283\pi\) | |||||||
\(398\) | 18.3672 | + | 6.68511i | 0.920665 | + | 0.335094i | ||||
\(399\) | −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 | \(0.505666\pi\) | |||||||
\(402\) | 18.3932 | + | 0.974829i | 0.917367 | + | 0.0486201i | ||||
\(403\) | −0.647746 | − | 3.67355i | −0.0322665 | − | 0.182993i | ||||
\(404\) | −4.44685 | −0.221239 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.32853 | −0.0659338 | ||||||||
\(407\) | 0.568014 | + | 3.22137i | 0.0281554 | + | 0.159677i | ||||
\(408\) | 35.0122 | + | 1.85563i | 1.73336 | + | 0.0918675i | ||||
\(409\) | −16.6159 | + | 6.04769i | −0.821603 | + | 0.299039i | −0.718408 | − | 0.695622i | \(-0.755129\pi\) |
−0.103195 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.474366 | − | 3.88234i | −0.0233988 | − | 0.191502i | ||||
\(412\) | −9.69993 | − | 3.53049i | −0.477881 | − | 0.173935i | ||||
\(413\) | −3.69650 | − | 6.40252i | −0.181893 | − | 0.315047i | ||||
\(414\) | −1.08036 | − | 2.43426i | −0.0530968 | − | 0.119637i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.9559 | + | 13.3886i | −0.782303 | + | 0.656431i | ||||
\(417\) | 13.2121 | − | 4.03081i | 0.646998 | − | 0.197390i | ||||
\(418\) | 0.0572121 | − | 0.324466i | 0.00279833 | − | 0.0158701i | ||||
\(419\) | 1.58606 | − | 8.99500i | 0.0774842 | − | 0.439435i | −0.921243 | − | 0.388988i | \(-0.872825\pi\) |
0.998727 | − | 0.0504461i | \(-0.0160643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5344 | − | 15.5522i | 0.903310 | − | 0.757967i | −0.0675243 | − | 0.997718i | \(-0.521510\pi\) |
0.970835 | + | 0.239750i | \(0.0770656\pi\) | |||||||
\(422\) | −1.94585 | + | 3.37031i | −0.0947226 | + | 0.164064i | ||||
\(423\) | −14.2889 | − | 6.99004i | −0.694749 | − | 0.339867i | ||||
\(424\) | −15.9637 | − | 27.6499i | −0.775265 | − | 1.34280i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.150369 | + | 0.0639324i | 0.00728538 | + | 0.00309754i | ||||
\(427\) | −5.43159 | − | 4.55764i | −0.262853 | − | 0.220560i | ||||
\(428\) | −16.2441 | + | 5.91236i | −0.785187 | + | 0.285785i | ||||
\(429\) | 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 | \(0.751885\pi\) | |||||||
\(432\) | −6.39355 | + | 3.82624i | −0.307610 | + | 0.184090i | ||||
\(433\) | −0.669754 | −0.0321863 | −0.0160932 | − | 0.999870i | \(-0.505123\pi\) | ||||
−0.0160932 | + | 0.999870i | \(0.505123\pi\) | |||||||
\(434\) | −0.369201 | − | 2.09384i | −0.0177222 | − | 0.100508i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.27203 | − | 1.91886i | 0.252484 | − | 0.0918967i | ||||
\(437\) | −0.160708 | − | 0.134850i | −0.00768772 | − | 0.00645076i | ||||
\(438\) | −7.76392 | + | 5.84336i | −0.370975 | + | 0.279206i | ||||
\(439\) | 5.96599 | + | 2.17144i | 0.284741 | + | 0.103637i | 0.480442 | − | 0.877026i | \(-0.340476\pi\) |
−0.195701 | + | 0.980664i | \(0.562698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.98174 | − | 2.05700i | −0.0943685 | − | 0.0979526i | ||||
\(442\) | 15.9404 | − | 27.6096i | 0.758209 | − | 1.31326i | ||||
\(443\) | −11.7618 | + | 9.86931i | −0.558819 | + | 0.468905i | −0.877914 | − | 0.478818i | \(-0.841066\pi\) |
0.319095 | + | 0.947723i | \(0.396621\pi\) | |||||||
\(444\) | 0.905072 | − | 3.90977i | 0.0429528 | − | 0.185550i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.88884 | + | 22.0547i | −0.184142 | + | 1.04432i | ||||
\(447\) | −0.0417726 | + | 0.180451i | −0.00197577 | + | 0.00853503i | ||||
\(448\) | −14.4973 | + | 12.1647i | −0.684934 | + | 0.574728i | ||||
\(449\) | 16.0199 | − | 27.7473i | 0.756027 | − | 1.30948i | −0.188836 | − | 0.982009i | \(-0.560471\pi\) |
0.944862 | − | 0.327468i | \(-0.106195\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.11268 | − | 8.85543i | −0.240747 | − | 0.416986i | ||||
\(452\) | 5.77340 | + | 2.10135i | 0.271558 | + | 0.0988390i | ||||
\(453\) | −28.0368 | + | 21.1013i | −1.31729 | + | 0.991428i | ||||
\(454\) | −11.5819 | − | 9.71835i | −0.543565 | − | 0.456105i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.716419 | + | 1.10176i | −0.0335494 | + | 0.0515949i | ||||
\(457\) | −3.32849 | − | 18.8768i | −0.155700 | − | 0.883021i | −0.958143 | − | 0.286291i | \(-0.907578\pi\) |
0.802442 | − | 0.596730i | \(-0.203534\pi\) | |||||||
\(458\) | −17.8031 | −0.831886 | ||||||||
\(459\) | −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 | \(0.983236\pi\) | |||||||
\(462\) | 2.55418 | + | 5.02019i | 0.118831 | + | 0.233560i | ||||
\(463\) | 1.59502 | − | 0.580541i | 0.0741271 | − | 0.0269800i | −0.304690 | − | 0.952451i | \(-0.598553\pi\) |
0.378818 | + | 0.925471i | \(0.376331\pi\) | |||||||
\(464\) | 0.562837 | + | 0.472276i | 0.0261290 | + | 0.0219249i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.54760 | − | 2.01916i | −0.256988 | − | 0.0935359i | ||||
\(467\) | 9.84136 | + | 17.0457i | 0.455404 | + | 0.788783i | 0.998711 | − | 0.0507511i | \(-0.0161615\pi\) |
−0.543307 | + | 0.839534i | \(0.682828\pi\) | |||||||
\(468\) | −0.831456 | − | 12.0955i | −0.0384341 | − | 0.559115i | ||||
\(469\) | −12.4023 | + | 21.4814i | −0.572685 | + | 0.991920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.2702 | + | 24.5264i | 1.21047 | + | 1.13012i | ||||
\(472\) | −1.58972 | + | 9.01574i | −0.0731727 | + | 0.414983i | ||||
\(473\) | 0.942416 | − | 5.34471i | 0.0433324 | − | 0.245750i | ||||
\(474\) | 8.34368 | − | 2.54554i | 0.383238 | − | 0.116920i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.26134 | + | 12.5770i | −0.332823 | + | 0.576467i | ||||
\(477\) | 31.2761 | + | 3.32458i | 1.43204 | + | 0.152222i | ||||
\(478\) | −2.78040 | − | 4.81579i | −0.127173 | − | 0.220269i | ||||
\(479\) | 27.4892 | + | 10.0053i | 1.25601 | + | 0.457152i | 0.882430 | − | 0.470444i | \(-0.155906\pi\) |
0.373585 | + | 0.927596i | \(0.378128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.08847 | − | 7.62613i | −0.414398 | − | 0.347722i | ||||
\(482\) | −8.82005 | + | 3.21024i | −0.401742 | + | 0.146222i | ||||
\(483\) | 3.58151 | + | 0.189818i | 0.162964 | + | 0.00863704i | ||||
\(484\) | 1.45429 | + | 8.24766i | 0.0661039 | + | 0.374894i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.48074 | − | 16.3685i | 0.0671675 | − | 0.742488i | ||||
\(487\) | 20.5056 | 0.929199 | 0.464600 | − | 0.885521i | \(-0.346198\pi\) | ||||
0.464600 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(488\) | 1.52466 | + | 8.64677i | 0.0690180 | + | 0.391421i | ||||
\(489\) | 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 | \(0.592797\pi\) | |||||||
\(492\) | 1.52152 | + | 12.4526i | 0.0685955 | + | 0.561404i | ||||
\(493\) | 3.20050 | + | 1.16489i | 0.144143 | + | 0.0524638i | ||||
\(494\) | 0.597496 | + | 1.03489i | 0.0268826 | + | 0.0465620i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.587922 | + | 1.01831i | −0.0263985 | + | 0.0457235i | ||||
\(497\) | −0.168562 | + | 0.141441i | −0.00756106 | + | 0.00634448i | ||||
\(498\) | −14.0443 | + | 4.28473i | −0.629342 | + | 0.192003i | ||||
\(499\) | −3.31772 | + | 18.8157i | −0.148522 | + | 0.842307i | 0.815950 | + | 0.578122i | \(0.196214\pi\) |
−0.964472 | + | 0.264185i | \(0.914897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.1469 | + | 23.4777i | 1.12348 | + | 1.04890i | ||||
\(502\) | 6.28376 | − | 5.27270i | 0.280458 | − | 0.235332i | ||||
\(503\) | −5.48381 | + | 9.49824i | −0.244511 | + | 0.423506i | −0.961994 | − | 0.273070i | \(-0.911961\pi\) |
0.717483 | + | 0.696576i | \(0.245294\pi\) | |||||||
\(504\) | −1.54080 | − | 22.4146i | −0.0686327 | − | 0.998426i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.04627 | + | 0.380811i | 0.0465124 | + | 0.0169291i | ||||
\(507\) | −12.2634 | − | 5.21405i | −0.544637 | − | 0.231564i | ||||
\(508\) | 8.18246 | + | 6.86590i | 0.363038 | + | 0.304625i | ||||
\(509\) | 18.6993 | − | 6.80598i | 0.828831 | − | 0.301670i | 0.107452 | − | 0.994210i | \(-0.465731\pi\) |
0.721379 | + | 0.692540i | \(0.243509\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.27236 | − | 12.8872i | −0.100523 | − | 0.570096i | ||||
\(512\) | 15.2994 | 0.676143 | ||||||||
\(513\) | −0.461822 | − | 1.20948i | −0.0203899 | − | 0.0534000i | ||||
\(514\) | −21.5468 | −0.950387 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.62972 | + | 5.58207i | −0.159790 | + | 0.245737i | ||||
\(517\) | 6.24920 | − | 2.27452i | 0.274839 | − | 0.100033i | ||||
\(518\) | −5.18022 | − | 4.34672i | −0.227606 | − | 0.190984i | ||||
\(519\) | −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 | \(-0.446034\pi\) | |||||||
\(522\) | −1.57298 | + | 0.390216i | −0.0688473 | + | 0.0170793i | ||||
\(523\) | −7.12269 | + | 12.3369i | −0.311453 | + | 0.539453i | −0.978677 | − | 0.205404i | \(-0.934149\pi\) |
0.667224 | + | 0.744857i | \(0.267482\pi\) | |||||||
\(524\) | 9.58545 | − | 8.04315i | 0.418742 | − | 0.351367i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.06513 | − | 11.7119i | 0.0900437 | − | 0.510663i | ||||
\(527\) | −0.946505 | + | 5.36789i | −0.0412304 | + | 0.233829i | ||||
\(528\) | 0.702526 | − | 3.03480i | 0.0305735 | − | 0.132073i | ||||
\(529\) | −17.0759 | + | 14.3284i | −0.742431 | + | 0.622974i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.25719 | − | 6.49483i | −0.271539 | − | 0.281852i | ||||
\(532\) | −0.272177 | − | 0.471425i | −0.0118004 | − | 0.0204389i | ||||
\(533\) | 34.8507 | + | 12.6846i | 1.50955 | + | 0.549433i | ||||
\(534\) | −9.78128 | + | 7.36168i | −0.423277 | + | 0.318571i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 28.8634 | − | 10.5054i | 1.24671 | − | 0.453765i | ||||
\(537\) | −10.3047 | + | 15.8473i | −0.444679 | + | 0.683862i | ||||
\(538\) | 0.0563454 | + | 0.319550i | 0.00242922 | + | 0.0137768i | ||||
\(539\) | 1.19414 | 0.0514354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.2368 | −0.569094 | −0.284547 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284547 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(542\) | 0.406901 | + | 2.30765i | 0.0174779 | + | 0.0991222i | ||||
\(543\) | 14.0967 | + | 27.7067i | 0.604946 | + | 1.18901i | ||||
\(544\) | 28.6004 | − | 10.4097i | 1.22623 | − | 0.446312i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.8007 | − | 7.99350i | −0.804594 | − | 0.342090i | ||||
\(547\) | −15.3216 | − | 5.57661i | −0.655105 | − | 0.238439i | −0.00698326 | − | 0.999976i | \(-0.502223\pi\) |
−0.648121 | + | 0.761537i | \(0.724445\pi\) | |||||||
\(548\) | −1.00306 | − | 1.73736i | −0.0428488 | − | 0.0742163i | ||||
\(549\) | −7.76965 | − | 3.80087i | −0.331601 | − | 0.162217i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0977958 | + | 0.0820605i | −0.00416624 | + | 0.00349589i | ||||
\(552\) | −3.24633 | − | 3.03084i | −0.138173 | − | 0.129001i | ||||
\(553\) | −2.03995 | + | 11.5692i | −0.0867476 | + | 0.491970i | ||||
\(554\) | −4.27124 | + | 24.2234i | −0.181468 | + | 1.02915i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.42748 | − | 4.55419i | 0.230176 | − | 0.193141i | ||||
\(557\) | 15.4486 | − | 26.7577i | 0.654577 | − | 1.13376i | −0.327422 | − | 0.944878i | \(-0.606180\pi\) |
0.982000 | − | 0.188883i | \(-0.0604867\pi\) | |||||||
\(558\) | −1.05214 | − | 2.37066i | −0.0445404 | − | 0.100358i | ||||
\(559\) | 9.84215 | + | 17.0471i | 0.416279 | + | 0.721016i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.75134 | − | 14.3335i | −0.0739417 | − | 0.605159i | ||||
\(562\) | −5.83571 | − | 4.89674i | −0.246165 | − | 0.206557i | ||||
\(563\) | 25.1612 | − | 9.15791i | 1.06042 | − | 0.385960i | 0.247832 | − | 0.968803i | \(-0.420282\pi\) |
0.812585 | + | 0.582843i | \(0.198060\pi\) | |||||||
\(564\) | −8.14755 | − | 0.431816i | −0.343074 | − | 0.0181827i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.50710 | 0.315547 | ||||||||
\(567\) | 18.7423 | + | 11.7731i | 0.787102 | + | 0.494423i | ||||
\(568\) | 0.272481 | 0.0114331 | ||||||||
\(569\) | 3.30985 | + | 18.7711i | 0.138756 | + | 0.786924i | 0.972170 | + | 0.234275i | \(0.0752717\pi\) |
−0.833414 | + | 0.552649i | \(0.813617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.6420 | − | 6.42116i | 0.738294 | − | 0.268717i | 0.0546227 | − | 0.998507i | \(-0.482604\pi\) |
0.683671 | + | 0.729790i | \(0.260382\pi\) | |||||||
\(572\) | 3.88286 | + | 3.25811i | 0.162351 | + | 0.136228i | ||||
\(573\) | −5.66474 | − | 46.3618i | −0.236648 | − | 1.93679i | ||||
\(574\) | 19.8641 | + | 7.22996i | 0.829113 | + | 0.301773i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.5918 | + | 18.6611i | −0.566324 | + | 0.777547i | ||||
\(577\) | −2.42981 | + | 4.20856i | −0.101154 | + | 0.175204i | −0.912161 | − | 0.409833i | \(-0.865587\pi\) |
0.811006 | + | 0.585038i | \(0.198920\pi\) | |||||||
\(578\) | −21.9561 | + | 18.4234i | −0.913254 | + | 0.766311i | ||||
\(579\) | −28.4198 | + | 8.67047i | −1.18109 | + | 0.360332i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43371 | − | 19.4736i | 0.142454 | − | 0.807899i | ||||
\(582\) | 7.32894 | + | 6.84244i | 0.303795 | + | 0.283628i | ||||
\(583\) | −10.0730 | + | 8.45221i | −0.417179 | + | 0.350055i | ||||
\(584\) | −8.10226 | + | 14.0335i | −0.335274 | + | 0.580712i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.291249 | − | 0.504459i | −0.0120314 | − | 0.0208390i | ||||
\(587\) | −30.8194 | − | 11.2174i | −1.27205 | − | 0.462990i | −0.384257 | − | 0.923226i | \(-0.625542\pi\) |
−0.887796 | + | 0.460236i | \(0.847765\pi\) | |||||||
\(588\) | −1.34825 | − | 0.573239i | −0.0556010 | − | 0.0236400i | ||||
\(589\) | −0.156510 | − | 0.131327i | −0.00644887 | − | 0.00541125i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.97318 | + | 3.87824i | 0.0811657 | + | 0.159529i | ||||
\(592\) | 0.649414 | + | 3.68301i | 0.0266908 | + | 0.151371i | ||||
\(593\) | −17.3446 | −0.712258 | −0.356129 | − | 0.934437i | \(-0.615904\pi\) | ||||
−0.356129 | + | 0.934437i | \(0.615904\pi\) | |||||||
\(594\) | 4.49867 | + | 5.19367i | 0.184583 | + | 0.213099i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0164973 | + | 0.0935607i | 0.000675754 | + | 0.00383239i | ||||
\(597\) | −17.5044 | + | 26.9196i | −0.716406 | + | 1.10174i | ||||
\(598\) | −3.79482 | + | 1.38120i | −0.155182 | + | 0.0564816i | ||||
\(599\) | 18.6975 | + | 15.6891i | 0.763961 | + | 0.641039i | 0.939155 | − | 0.343495i | \(-0.111611\pi\) |
−0.175194 | + | 0.984534i | \(0.556055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.39563 | − | 2.69179i | −0.301674 | − | 0.109800i | 0.186748 | − | 0.982408i | \(-0.440205\pi\) |
−0.488422 | + | 0.872607i | \(0.662427\pi\) | |||||||
\(602\) | 5.60981 | + | 9.71647i | 0.228639 | + | 0.396014i | ||||
\(603\) | −8.37478 | + | 29.0768i | −0.341047 | + | 1.18410i | ||||
\(604\) | −8.99922 | + | 15.5871i | −0.366173 | + | 0.634230i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.06147 | + | 8.90521i | −0.0837413 | + | 0.361749i | ||||
\(607\) | 1.77772 | − | 10.0819i | 0.0721553 | − | 0.409213i | −0.927241 | − | 0.374466i | \(-0.877826\pi\) |
0.999396 | − | 0.0347476i | \(-0.0110627\pi\) | |||||||
\(608\) | −0.198103 | + | 1.12350i | −0.00803414 | + | 0.0455639i | ||||
\(609\) | 0.492214 | − | 2.12629i | 0.0199455 | − | 0.0861615i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0602 | + | 20.8889i | −0.487905 | + | 0.845076i | ||||
\(612\) | −4.90329 | + | 17.0240i | −0.198204 | + | 0.688153i | ||||
\(613\) | 1.11753 | + | 1.93563i | 0.0451368 | + | 0.0781792i | 0.887711 | − | 0.460401i | \(-0.152294\pi\) |
−0.842574 | + | 0.538580i | \(0.818961\pi\) | |||||||
\(614\) | −6.66646 | − | 2.42639i | −0.269036 | − | 0.0979213i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.19547 | + | 6.03771i | 0.289914 | + | 0.243266i | ||||
\(617\) | 31.9267 | − | 11.6204i | 1.28532 | − | 0.467818i | 0.393132 | − | 0.919482i | \(-0.371391\pi\) |
0.892188 | + | 0.451664i | \(0.149169\pi\) | |||||||
\(618\) | −11.5668 | + | 17.7883i | −0.465285 | + | 0.715551i | ||||
\(619\) | −5.01079 | − | 28.4176i | −0.201401 | − | 1.14220i | −0.903004 | − | 0.429632i | \(-0.858643\pi\) |
0.701604 | − | 0.712567i | \(-0.252468\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.29625 | − | 0.827216i | 0.172403 | − | 0.0331950i | ||||
\(622\) | −16.2613 | −0.652020 | ||||||||
\(623\) | −2.86280 | − | 16.2358i | −0.114696 | − | 0.650472i | ||||
\(624\) | 5.12338 | + | 10.0699i | 0.205099 | + | 0.403118i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.0292 | − | 15.9674i | −0.760558 | − | 0.638184i | ||||
\(627\) | 0.498105 | + | 0.211780i | 0.0198924 | + | 0.00845768i | ||||
\(628\) | 17.3224 | + | 6.30485i | 0.691240 | + | 0.251591i | ||||
\(629\) | 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 | \(0.146754\pi\) | |||||||
\(632\) | 11.1438 | − | 9.35076i | 0.443277 | − | 0.371953i | ||||
\(633\) | −4.67320 | − | 4.36299i | −0.185743 | − | 0.173413i | ||||
\(634\) | 1.32772 | − | 7.52985i | 0.0527303 | − | 0.299049i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.4303 | − | 4.70757i | 0.611852 | − | 0.186667i | ||||
\(637\) | −3.31786 | + | 2.78402i | −0.131458 | + | 0.110307i | ||||
\(638\) | 0.338774 | − | 0.586774i | 0.0134122 | − | 0.0232306i | ||||
\(639\) | −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 | \(0.394798\pi\) | |||||||
\(642\) | 4.30961 | + | 35.2710i | 0.170087 | + | 1.39204i | ||||
\(643\) | 9.84142 | + | 8.25794i | 0.388108 | + | 0.325661i | 0.815876 | − | 0.578228i | \(-0.196255\pi\) |
−0.427768 | + | 0.903889i | \(0.640700\pi\) | |||||||
\(644\) | 1.72866 | − | 0.629179i | 0.0681186 | − | 0.0247931i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.303217 | − | 1.71963i | −0.0119299 | − | 0.0676578i | ||||
\(647\) | −28.2444 | −1.11040 | −0.555200 | − | 0.831717i | \(-0.687358\pi\) | ||||
−0.555200 | + | 0.831717i | \(0.687358\pi\) | |||||||
\(648\) | −8.40792 | − | 26.0863i | −0.330294 | − | 1.02477i | ||||
\(649\) | 3.77042 | 0.148002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.48794 | + | 0.184859i | 0.136703 | + | 0.00724521i | ||||
\(652\) | 16.8088 | − | 6.11790i | 0.658283 | − | 0.239595i | ||||
\(653\) | −19.9099 | − | 16.7064i | −0.779134 | − | 0.653771i | 0.163897 | − | 0.986477i | \(-0.447594\pi\) |
−0.943030 | + | 0.332707i | \(0.892038\pi\) | |||||||
\(654\) | −1.39869 | − | 11.4472i | −0.0546930 | − | 0.447622i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.84536 | − | 10.1245i | −0.228223 | − | 0.395294i | ||||
\(657\) | −6.47569 | − | 14.5910i | −0.252641 | − | 0.569248i | ||||
\(658\) | −6.87407 | + | 11.9062i | −0.267979 | + | 0.464153i | ||||
\(659\) | −36.4774 | + | 30.6081i | −1.42096 | + | 1.19232i | −0.470131 | + | 0.882597i | \(0.655793\pi\) |
−0.950826 | + | 0.309727i | \(0.899762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.152204 | + | 0.863192i | −0.00592005 | + | 0.0335743i | −0.987625 | − | 0.156836i | \(-0.949871\pi\) |
0.981705 | + | 0.190410i | \(0.0609818\pi\) | |||||||
\(662\) | −5.31568 | + | 30.1467i | −0.206600 | + | 1.17168i | ||||
\(663\) | 38.2829 | + | 35.7416i | 1.48678 | + | 1.38809i | ||||
\(664\) | −18.7576 | + | 15.7395i | −0.727936 | + | 0.610811i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.41009 | − | 3.62497i | −0.287135 | − | 0.140465i | ||||
\(667\) | −0.215714 | − | 0.373627i | −0.00835246 | − | 0.0144669i | ||||
\(668\) | 16.5817 | + | 6.03526i | 0.641567 | + | 0.233511i | ||||
\(669\) | −33.8574 | − | 14.3952i | −1.30900 | − | 0.556551i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.39803 | − | 1.23678i | 0.131180 | − | 0.0477455i | ||||
\(672\) | −8.84413 | − | 17.3829i | −0.341170 | − | 0.670562i | ||||
\(673\) | −6.48393 | − | 36.7722i | −0.249937 | − | 1.41746i | −0.808742 | − | 0.588164i | \(-0.799851\pi\) |
0.558805 | − | 0.829299i | \(-0.311260\pi\) | |||||||
\(674\) | −1.22206 | −0.0470721 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.83505 | −0.262886 | ||||||||
\(677\) | 2.38231 | + | 13.5107i | 0.0915596 | + | 0.519260i | 0.995747 | + | 0.0921251i | \(0.0293660\pi\) |
−0.904188 | + | 0.427135i | \(0.859523\pi\) | |||||||
\(678\) | 6.88456 | − | 10.5876i | 0.264400 | − | 0.406614i | ||||
\(679\) | −12.6884 | + | 4.61819i | −0.486935 | + | 0.177230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8451 | − | 14.9360i | 0.760465 | − | 0.572348i | ||||
\(682\) | 1.01894 | + | 0.370863i | 0.0390171 | + | 0.0142011i | ||||
\(683\) | 24.9943 | + | 43.2914i | 0.956381 | + | 1.65650i | 0.731175 | + | 0.682190i | \(0.238972\pi\) |
0.225206 | + | 0.974311i | \(0.427694\pi\) | |||||||
\(684\) | −0.460724 | − | 0.478222i | −0.0176162 | − | 0.0182853i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7947 | + | 13.2534i | −0.603046 | + | 0.506016i | ||||
\(687\) | 6.59598 | − | 28.4936i | 0.251652 | − | 1.08710i | ||||
\(688\) | 1.07747 | − | 6.11064i | 0.0410782 | − | 0.232966i | ||||
\(689\) | 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 | \(0.128137\pi\) | |||||||
\(692\) | −8.40653 | + | 14.5605i | −0.319568 | + | 0.553508i | ||||
\(693\) | −8.98103 | + | 2.22797i | −0.341161 | + | 0.0846335i | ||||
\(694\) | −3.10483 | − | 5.37773i | −0.117858 | − | 0.204136i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.15938 | + | 1.62521i | −0.0818510 | + | 0.0616035i | ||||
\(697\) | −41.5144 | − | 34.8347i | −1.57247 | − | 1.31946i | ||||
\(698\) | −30.3094 | + | 11.0317i | −1.14723 | + | 0.417557i | ||||
\(699\) | 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 | \(0.274532\pi\) | |||||||
\(702\) | −24.6078 | − | 3.94216i | −0.928761 | − | 0.148787i | ||||
\(703\) | −0.649815 | −0.0245082 | ||||||||
\(704\) | −1.67600 | − | 9.50506i | −0.0631665 | − | 0.358235i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.6191 | + | 13.3282i | −1.37818 | + | 0.501615i | ||||
\(707\) | −9.42975 | − | 7.91250i | −0.354642 | − | 0.297580i | ||||
\(708\) | −4.25701 | − | 1.80996i | −0.159988 | − | 0.0680224i | ||||
\(709\) | −14.5871 | − | 5.30927i | −0.547830 | − | 0.199394i | 0.0532520 | − | 0.998581i | \(-0.483041\pi\) |
−0.601082 | + | 0.799187i | \(0.705264\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.982789 | + | 14.2970i | 0.0368575 | + | 0.536180i | ||||
\(712\) | −10.2075 | + | 17.6800i | −0.382543 | + | 0.662585i | ||||
\(713\) | 0.528911 | − | 0.443809i | 0.0198079 | − | 0.0166208i | ||||
\(714\) | 21.8204 | + | 20.3719i | 0.816607 | + | 0.762400i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.68364 | + | 9.54839i | −0.0629205 | + | 0.356840i | ||||
\(717\) | 8.73772 | − | 2.66575i | 0.326316 | − | 0.0995543i | ||||
\(718\) | 21.3029 | − | 17.8752i | 0.795016 | − | 0.667098i | ||||
\(719\) | −6.02686 | + | 10.4388i | −0.224764 | + | 0.389303i | −0.956249 | − | 0.292555i | \(-0.905494\pi\) |
0.731485 | + | 0.681858i | \(0.238828\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.2872 | − | 24.7461i | −0.532083 | − | 0.921594i | ||||
\(722\) | −18.7626 | − | 6.82902i | −0.698271 | − | 0.254150i | ||||
\(723\) | −1.87014 | − | 15.3057i | −0.0695512 | − | 0.569226i | ||||
\(724\) | 12.2145 | + | 10.2492i | 0.453947 | + | 0.380907i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.1908 | + | 0.911107i | 0.638012 | + | 0.0338144i | ||||
\(727\) | 5.49253 | + | 31.1497i | 0.203707 | + | 1.15528i | 0.899462 | + | 0.437000i | \(0.143959\pi\) |
−0.695755 | + | 0.718279i | \(0.744930\pi\) | |||||||
\(728\) | −34.0685 | −1.26266 | ||||||||
\(729\) | 25.6488 | + | 8.43433i | 0.949956 | + | 0.312383i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.99469 | − | 28.3263i | −0.184735 | − | 1.04769i | ||||
\(732\) | −4.43027 | − | 0.234802i | −0.163748 | − | 0.00867855i | ||||
\(733\) | −17.8831 | + | 6.50891i | −0.660527 | + | 0.240412i | −0.650464 | − | 0.759537i | \(-0.725425\pi\) |
−0.0100630 | + | 0.999949i | \(0.503203\pi\) | |||||||
\(734\) | −9.13716 | − | 7.66699i | −0.337259 | − | 0.282994i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.62283 | − | 1.31860i | −0.133539 | − | 0.0486043i | ||||
\(737\) | −6.32516 | − | 10.9555i | −0.232990 | − | 0.403551i | ||||
\(738\) | 25.6427 | + | 2.72576i | 0.943920 | + | 0.100337i | ||||
\(739\) | −8.30036 | + | 14.3767i | −0.305334 | + | 0.528854i | −0.977336 | − | 0.211696i | \(-0.932101\pi\) |
0.672002 | + | 0.740550i | \(0.265435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.87770 | + | 0.572858i | −0.0689789 | + | 0.0210445i | ||||
\(742\) | 4.72040 | − | 26.7707i | 0.173291 | − | 0.982783i | ||||
\(743\) | 5.78310 | − | 32.7976i | 0.212161 | − | 1.20323i | −0.673604 | − | 0.739093i | \(-0.735255\pi\) |
0.885765 | − | 0.464134i | \(-0.153634\pi\) | |||||||
\(744\) | −3.16152 | − | 2.95166i | −0.115907 | − | 0.108213i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.08078 | + | 5.33606i | −0.112795 | + | 0.195367i | ||||
\(747\) | −1.65426 | − | 24.0652i | −0.0605263 | − | 0.880499i | ||||
\(748\) | −3.70328 | − | 6.41426i | −0.135405 | − | 0.234529i | ||||
\(749\) | −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 | \(0.553020\pi\) | |||||||
\(752\) | 7.14474 | − | 2.60047i | 0.260542 | − | 0.0948295i | ||||
\(753\) | 6.11076 | + | 12.0106i | 0.222688 | + | 0.437689i | ||||
\(754\) | 0.426735 | + | 2.42013i | 0.0155408 | + | 0.0881361i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.2096 | + | 1.79577i | 0.407689 | + | 0.0653116i | ||||
\(757\) | 3.12036 | 0.113411 | 0.0567057 | − | 0.998391i | \(-0.481940\pi\) | ||||
0.0567057 | + | 0.998391i | \(0.481940\pi\) | |||||||
\(758\) | −4.45373 | − | 25.2583i | −0.161767 | − | 0.917424i | ||||
\(759\) | −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 | \(-0.571232\pi\) | |||||||
\(762\) | 17.5428 | − | 13.2032i | 0.635508 | − | 0.478302i | ||||
\(763\) | 14.5939 | + | 5.31175i | 0.528335 | + | 0.192298i | ||||
\(764\) | −11.9783 | − | 20.7470i | −0.433360 | − | 0.750602i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.01168 | − | 3.48433i | 0.0726849 | − | 0.125894i | ||||
\(767\) | −10.4759 | + | 8.79032i | −0.378263 | + | 0.317400i | ||||
\(768\) | −6.44200 | + | 27.8284i | −0.232456 | + | 1.00417i | ||||
\(769\) | 0.644731 | − | 3.65645i | 0.0232496 | − | 0.131855i | −0.970974 | − | 0.239186i | \(-0.923119\pi\) |
0.994223 | + | 0.107331i | \(0.0342305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.98298 | − | 34.4852i | 0.287500 | − | 1.24195i | ||||
\(772\) | −11.6748 | + | 9.79629i | −0.420184 | + | 0.352576i | ||||
\(773\) | −4.48452 | + | 7.76741i | −0.161297 | + | 0.279374i | −0.935334 | − | 0.353766i | \(-0.884901\pi\) |
0.774037 | + | 0.633140i | \(0.218234\pi\) | |||||||
\(774\) | 9.49592 | + | 9.85656i | 0.341324 | + | 0.354287i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.7121 | + | 5.71875i | 0.564033 | + | 0.205291i | ||||
\(777\) | 8.87610 | − | 6.68041i | 0.318428 | − | 0.239658i | ||||
\(778\) | −8.75652 | − | 7.34760i | −0.313937 | − | 0.263424i | ||||
\(779\) | 1.90882 | − | 0.694754i | 0.0683906 | − | 0.0248921i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0194871 | − | 0.110517i | −0.000697302 | − | 0.00395459i | ||||
\(782\) | 5.90098 | 0.211018 | ||||||||
\(783\) | −0.0417527 | − | 2.66209i | −0.00149212 | − | 0.0951354i | ||||
\(784\) | 1.36527 | 0.0487597 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.6635 | − | 22.9243i | −0.416023 | − | 0.817684i | ||||
\(787\) | 41.2069 | − | 14.9981i | 1.46887 | − | 0.534624i | 0.521074 | − | 0.853512i | \(-0.325532\pi\) |
0.947792 | + | 0.318888i | \(0.103309\pi\) | |||||||
\(788\) | 1.70972 | + | 1.43462i | 0.0609062 | + | 0.0511063i | ||||
\(789\) | 17.9796 | + | 7.64441i | 0.640090 | + | 0.272148i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.50374 | + | 14.7289i | 0.302358 | + | 0.523699i | ||||
\(792\) | 10.2928 | + | 5.03519i | 0.365739 | + | 0.178918i | ||||
\(793\) | −6.55782 | + | 11.3585i | −0.232875 | + | 0.403351i | ||||
\(794\) | −8.48787 | + | 7.12217i | −0.301223 | + | 0.252756i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.85997 | + | 16.2197i | −0.101369 | + | 0.574891i | ||||
\(797\) | −2.08656 | + | 11.8335i | −0.0739097 | + | 0.419163i | 0.925294 | + | 0.379252i | \(0.123819\pi\) |
−0.999203 | + | 0.0399111i | \(0.987293\pi\) | |||||||
\(798\) | −1.07025 | + | 0.326516i | −0.0378863 | + | 0.0115586i | ||||
\(799\) | 26.9996 | − | 22.6554i | 0.955178 | − | 0.801490i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.15832 | − | 18.3822i | −0.288260 | − | 0.649504i | ||||
\(802\) | 7.57299 | + | 13.1168i | 0.267412 | + | 0.463171i | ||||
\(803\) | 6.27136 | + | 2.28259i | 0.221311 | + | 0.0805508i | ||||
\(804\) | 1.88235 | + | 15.4057i | 0.0663855 | + | 0.543317i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.69568 | + | 1.34512i | −0.130175 | + | 0.0473798i | ||||
\(807\) | −0.532311 | − | 0.0282122i | −0.0187382 | − | 0.000993117i | ||||
\(808\) | 2.64695 | + | 15.0116i | 0.0931195 | + | 0.528107i | ||||
\(809\) | −8.02937 | −0.282298 | −0.141149 | − | 0.989988i | \(-0.545080\pi\) | ||||
−0.141149 | + | 0.989988i | \(0.545080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8345 | −0.450681 | −0.225341 | − | 0.974280i | \(-0.572349\pi\) | ||||
−0.225341 | + | 0.974280i | \(0.572349\pi\) | |||||||
\(812\) | −0.194391 | − | 1.10244i | −0.00682177 | − | 0.0386882i | ||||
\(813\) | −3.84411 | − | 0.203736i | −0.134819 | − | 0.00714534i | ||||
\(814\) | 3.24078 | − | 1.17955i | 0.113589 | − | 0.0413431i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00232 | − | 16.3875i | −0.0700951 | − | 0.573678i | ||||
\(817\) | 1.01312 | + | 0.368744i | 0.0354444 | + | 0.0129007i | ||||
\(818\) | 9.32142 | + | 16.1452i | 0.325916 | + | 0.564503i | ||||
\(819\) | 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 | \(0.450976\pi\) | |||||||
\(822\) | −3.94422 | + | 1.20332i | −0.137570 | + | 0.0419707i | ||||
\(823\) | −8.60266 | + | 48.7881i | −0.299870 | + | 1.70065i | 0.346852 | + | 0.937920i | \(0.387251\pi\) |
−0.646722 | + | 0.762726i | \(0.723861\pi\) | |||||||
\(824\) | −6.14436 | + | 34.8464i | −0.214049 | + | 1.21393i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.97102 | + | 5.01028i | −0.207758 | + | 0.174330i | ||||
\(827\) | 20.4215 | − | 35.3711i | 0.710126 | − | 1.22997i | −0.254683 | − | 0.967025i | \(-0.581971\pi\) |
0.964809 | − | 0.262950i | \(-0.0846955\pi\) | |||||||
\(828\) | 1.86192 | − | 1.25269i | 0.0647063 | − | 0.0435339i | ||||
\(829\) | 4.72638 | + | 8.18633i | 0.164154 | + | 0.284323i | 0.936355 | − | 0.351056i | \(-0.114177\pi\) |
−0.772201 | + | 0.635379i | \(0.780844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.1867 | − | 15.8107i | −1.28999 | − | 0.548468i | ||||
\(832\) | 26.8167 | + | 22.5018i | 0.929700 | + | 0.780111i | ||||
\(833\) | 5.94714 | − | 2.16458i | 0.206056 | − | 0.0749983i | ||||
\(834\) | −6.60411 | − | 12.9802i | −0.228682 | − | 0.449468i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.277620 | 0.00960170 | ||||||||
\(837\) | 4.18401 | − | 0.805605i | 0.144621 | − | 0.0278458i | ||||
\(838\) | −9.62995 | −0.332661 | ||||||||
\(839\) | −2.13360 | − | 12.1002i | −0.0736599 | − | 0.417746i | −0.999232 | − | 0.0391756i | \(-0.987527\pi\) |
0.925572 | − | 0.378571i | \(-0.123584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0044 | − | 9.82879i | 0.931186 | − | 0.338924i | ||||
\(842\) | −19.5413 | − | 16.3971i | −0.673436 | − | 0.565080i | ||||
\(843\) | 9.99925 | − | 7.52573i | 0.344392 | − | 0.259200i | ||||
\(844\) | −3.08148 | − | 1.12157i | −0.106069 | − | 0.0386059i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.64178 | + | 16.1160i | −0.159588 | + | 0.554079i | ||||
\(847\) | −11.5916 | + | 20.0772i | −0.398292 | + | 0.689862i | ||||
\(848\) | −11.5165 | + | 9.66346i | −0.395477 | + | 0.331845i | ||||
\(849\) | −2.78135 | + | 12.0150i | −0.0954556 | + | 0.412353i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.381330 | − | 2.16263i | 0.0130718 | − | 0.0741339i | ||||
\(852\) | −0.0310506 | + | 0.134134i | −0.00106378 | + | 0.00459535i | ||||
\(853\) | 23.6446 | − | 19.8402i | 0.809576 | − | 0.679315i | −0.140930 | − | 0.990020i | \(-0.545009\pi\) |
0.950507 | + | 0.310704i | \(0.100565\pi\) | |||||||
\(854\) | −3.73781 | + | 6.47408i | −0.127905 | + | 0.221538i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6280 | + | 51.3172i | 1.01266 | + | 1.75399i | ||||
\(857\) | 10.4738 | + | 3.81217i | 0.357780 | + | 0.130221i | 0.514655 | − | 0.857397i | \(-0.327920\pi\) |
−0.156876 | + | 0.987618i | \(0.550142\pi\) | |||||||
\(858\) | 8.32466 | − | 6.26539i | 0.284199 | − | 0.213897i | ||||
\(859\) | 3.17807 | + | 2.66672i | 0.108434 | + | 0.0909872i | 0.695393 | − | 0.718630i | \(-0.255230\pi\) |
−0.586958 | + | 0.809617i | \(0.699675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.9310 | + | 29.1135i | −0.645167 | + | 0.992187i | ||||
\(862\) | 5.40698 | + | 30.6645i | 0.184163 | + | 1.04444i | ||||
\(863\) | 47.2534 | 1.60852 | 0.804262 | − | 0.594275i | \(-0.202561\pi\) | ||||
0.804262 | + | 0.594275i | \(0.202561\pi\) | |||||||
\(864\) | −15.5771 | − | 17.9837i | −0.529945 | − | 0.611817i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.122620 | + | 0.695411i | 0.00416678 | + | 0.0236310i | ||||
\(867\) | −21.3516 | − | 41.9662i | −0.725140 | − | 1.42525i | ||||
\(868\) | 1.68349 | − | 0.612742i | 0.0571415 | − | 0.0207978i | ||||
\(869\) | −4.58958 | − | 3.85112i | −0.155691 | − | 0.130640i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.1156 | + | 15.6928i | 1.46092 | + | 0.531731i | ||||
\(872\) | −9.61579 | − | 16.6550i | −0.325632 | − | 0.564011i | ||||
\(873\) | −13.6665 | + | 9.19475i | −0.462543 | + | 0.311195i | ||||
\(874\) | −0.110593 | + | 0.191553i | −0.00374087 | + | 0.00647938i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.98497 | − | 5.58768i | −0.202213 | − | 0.188790i | ||||
\(877\) | −6.10381 | + | 34.6164i | −0.206111 | + | 1.16891i | 0.689571 | + | 0.724218i | \(0.257799\pi\) |
−0.895682 | + | 0.444695i | \(0.853312\pi\) | |||||||
\(878\) | 1.16236 | − | 6.59208i | 0.0392278 | − | 0.222472i | ||||
\(879\) | 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 | \(0.0609250\pi\) | |||||||
\(882\) | −1.77298 | + | 2.43425i | −0.0596994 | + | 0.0819656i | ||||
\(883\) | −6.89302 | − | 11.9391i | −0.231969 | − | 0.401781i | 0.726419 | − | 0.687252i | \(-0.241183\pi\) |
−0.958387 | + | 0.285471i | \(0.907850\pi\) | |||||||
\(884\) | 25.2435 | + | 9.18788i | 0.849031 | + | 0.309022i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.4007 | + | 10.4055i | 0.416611 | + | 0.349578i | ||||
\(887\) | −28.0192 | + | 10.1982i | −0.940794 | + | 0.342421i | −0.766479 | − | 0.642269i | \(-0.777993\pi\) |
−0.174315 | + | 0.984690i | \(0.555771\pi\) | |||||||
\(888\) | −13.7373 | − | 0.728070i | −0.460993 | − | 0.0244324i | ||||
\(889\) | 5.13445 | + | 29.1189i | 0.172204 | + | 0.976617i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.97912 | + | 5.27581i | −0.334313 | + | 0.176746i | ||||
\(892\) | −18.8705 | −0.631832 | ||||||||
\(893\) | 0.229408 | + | 1.30104i | 0.00767685 | + | 0.0435376i | ||||
\(894\) | 0.195011 | + | 0.0103355i | 0.00652215 | + | 0.000345671i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.96694 | − | 1.65046i | −0.0657109 | − | 0.0551380i | ||||
\(897\) | −0.804626 | − | 6.58528i | −0.0268657 | − | 0.219876i | ||||
\(898\) | −31.7432 | − | 11.5536i | −1.05928 | − | 0.385548i | ||||
\(899\) | −0.210078 | − | 0.363866i | −0.00700649 | − | 0.0121356i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.8448 | + | 60.3530i | −1.16085 | + | 2.01065i | ||||
\(902\) | −8.25862 | + | 6.92980i | −0.274982 | + | 0.230737i | ||||
\(903\) | −17.6294 | + | 5.37849i | −0.586671 | + | 0.178985i | ||||
\(904\) | 3.65712 | − | 20.7406i | 0.121634 | − | 0.689821i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27.0427 | + | 25.2476i | 0.898434 | + | 0.838795i | ||||
\(907\) | 4.77366 | − | 4.00558i | 0.158507 | − | 0.133003i | −0.560085 | − | 0.828435i | \(-0.689231\pi\) |
0.718592 | + | 0.695432i | \(0.244787\pi\) | |||||||
\(908\) | 6.36984 | − | 11.0329i | 0.211391 | − | 0.366139i | ||||
\(909\) | −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 | \(0.435501\pi\) | |||||||
\(912\) | 0.569486 | + | 0.242129i | 0.0188576 | + | 0.00801770i | ||||
\(913\) | 7.72533 | + | 6.48232i | 0.255671 | + | 0.214534i | ||||
\(914\) | −18.9906 | + | 6.91200i | −0.628152 | + | 0.228629i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.60496 | − | 14.7734i | −0.0860701 | − | 0.488128i | ||||
\(917\) | 34.6380 | 1.14385 | ||||||||
\(918\) | 31.8189 | + | 17.7112i | 1.05018 | + | 0.584557i | ||||
\(919\) | 36.0031 | 1.18763 | 0.593816 | − | 0.804601i | \(-0.297621\pi\) | ||||
0.593816 | + | 0.804601i | \(0.297621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.35329 | − | 9.77058i | 0.209348 | − | 0.321952i | ||||
\(922\) | −5.17196 | + | 1.88244i | −0.170329 | + | 0.0619948i | ||||
\(923\) | 0.311801 | + | 0.261632i | 0.0102631 | + | 0.00861173i | ||||
\(924\) | −3.79213 | + | 2.85407i | −0.124752 | + | 0.0938921i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.894800 | − | 1.54984i | −0.0294049 | − | 0.0509309i | ||||
\(927\) | −24.1844 | − | 25.1029i | −0.794321 | − | 0.824489i | ||||
\(928\) | −1.17304 | + | 2.03177i | −0.0385070 | + | 0.0666961i | ||||
\(929\) | 19.4941 | − | 16.3575i | 0.639580 | − | 0.536672i | −0.264309 | − | 0.964438i | \(-0.585144\pi\) |
0.903889 | + | 0.427767i | \(0.140699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0411934 | + | 0.233619i | −0.00135006 | + | 0.00765656i | ||||
\(932\) | 0.863820 | − | 4.89897i | 0.0282954 | − | 0.160471i | ||||
\(933\) | 6.02475 | − | 26.0260i | 0.197241 | − | 0.852052i | ||||
\(934\) | 15.8969 | − | 13.3391i | 0.520164 | − | 0.436469i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −40.3370 | + | 10.0066i | −1.31846 | + | 0.327075i | ||||
\(937\) | 14.1524 | + | 24.5127i | 0.462338 | + | 0.800794i | 0.999077 | − | 0.0429549i | \(-0.0136772\pi\) |
−0.536739 | + | 0.843749i | \(0.680344\pi\) | |||||||
\(938\) | 24.5750 | + | 8.94455i | 0.802401 | + | 0.292050i | ||||
\(939\) | 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 | \(0.432055\pi\) | |||||||
\(942\) | 20.6563 | − | 31.7669i | 0.673019 | − | 1.03502i | ||||
\(943\) | 1.19204 | + | 6.76039i | 0.0388181 | + | 0.220149i | ||||
\(944\) | 4.31074 | 0.140303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.72199 | −0.186038 | ||||||||
\(947\) | 7.71877 | + | 43.7753i | 0.250826 | + | 1.42251i | 0.806563 | + | 0.591148i | \(0.201325\pi\) |
−0.555737 | + | 0.831358i | \(0.687564\pi\) | |||||||
\(948\) | 3.33319 | + | 6.55131i | 0.108257 | + | 0.212777i | ||||
\(949\) | −22.7462 | + | 8.27895i | −0.738373 | + | 0.268746i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5595 | + | 4.91476i | 0.374842 | + | 0.159372i | ||||
\(952\) | 46.7796 | + | 17.0264i | 1.51613 | + | 0.551828i | ||||
\(953\) | −4.83574 | − | 8.37576i | −0.156645 | − | 0.271317i | 0.777012 | − | 0.629486i | \(-0.216735\pi\) |
−0.933657 | + | 0.358169i | \(0.883401\pi\) | |||||||
\(954\) | −2.27415 | − | 33.0829i | −0.0736283 | − | 1.07110i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.58942 | − | 3.01188i | 0.116090 | − | 0.0974113i | ||||
\(957\) | 0.813608 | + | 0.759599i | 0.0263002 | + | 0.0245544i | ||||
\(958\) | 5.35576 | − | 30.3740i | 0.173037 | − | 0.981341i | ||||
\(959\) | 0.964325 | − | 5.46896i | 0.0311397 | − | 0.176602i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2323 | + | 19.4942i | −0.749429 | + | 0.628845i | ||||
\(962\) | −6.25433 | + | 10.8328i | −0.201648 | + | 0.349264i | ||||
\(963\) | −58.0473 | − | 6.17030i | −1.87055 | − | 0.198835i | ||||
\(964\) | −3.95448 | − | 6.84936i | −0.127365 | − | 0.220603i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.458619 | − | 3.75346i | −0.0147558 | − | 0.120766i | ||||
\(967\) | 25.3676 | + | 21.2860i | 0.815768 | + | 0.684510i | 0.951977 | − | 0.306170i | \(-0.0990475\pi\) |
−0.136209 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(968\) | 26.9767 | − | 9.81871i | 0.867064 | − | 0.315585i | ||||
\(969\) | 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 | \(0.645074\pi\) | |||||||
\(972\) | 13.7996 | − | 1.16629i | 0.442622 | − | 0.0374087i | ||||
\(973\) | 19.6127 | 0.628755 | ||||||||
\(974\) | −3.75420 | − | 21.2912i | −0.120292 | − | 0.682213i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.88499 | − | 1.41402i | 0.124356 | − | 0.0452617i | ||||
\(977\) | −27.8668 | − | 23.3831i | −0.891539 | − | 0.748090i | 0.0769792 | − | 0.997033i | \(-0.475473\pi\) |
−0.968518 | + | 0.248943i | \(0.919917\pi\) | |||||||
\(978\) | −4.45943 | − | 36.4972i | −0.142597 | − | 1.16705i | ||||
\(979\) | 7.90089 | + | 2.87569i | 0.252514 | + | 0.0919075i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8393 | + | 2.00258i | 0.601493 | + | 0.0639373i | ||||
\(982\) | 9.23957 | − | 16.0034i | 0.294847 | − | 0.510689i | ||||
\(983\) | −32.2790 | + | 27.0853i | −1.02954 | + | 0.863886i | −0.990796 | − | 0.135363i | \(-0.956780\pi\) |
−0.0387434 | + | 0.999249i | \(0.512335\pi\) | |||||||
\(984\) | 41.1315 | − | 12.5486i | 1.31122 | − | 0.400035i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.623557 | − | 3.53637i | 0.0198581 | − | 0.112621i | ||||
\(987\) | −16.5089 | − | 15.4130i | −0.525484 | − | 0.490602i | ||||
\(988\) | −0.771352 | + | 0.647241i | −0.0245400 | + | 0.0205915i | ||||
\(989\) | −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 | \(0.966294\pi\) | |||||||
\(992\) | −3.52818 | − | 1.28415i | −0.112020 | − | 0.0407719i | ||||
\(993\) | −46.2798 | − | 19.6769i | −1.46865 | − | 0.624426i | ||||
\(994\) | 0.177720 | + | 0.149124i | 0.00563692 | + | 0.00472994i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.61053 | − | 11.0274i | −0.177776 | − | 0.349416i | ||||
\(997\) | −4.08644 | − | 23.1754i | −0.129419 | − | 0.733971i | −0.978585 | − | 0.205845i | \(-0.934006\pi\) |
0.849166 | − | 0.528126i | \(-0.177105\pi\) | |||||||
\(998\) | 20.1439 | 0.637644 | ||||||||
\(999\) | 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.l.c.526.1 | 12 | ||
5.2 | odd | 4 | 675.2.u.b.499.3 | 24 | |||
5.3 | odd | 4 | 675.2.u.b.499.2 | 24 | |||
5.4 | even | 2 | 27.2.e.a.13.2 | ✓ | 12 | ||
15.14 | odd | 2 | 81.2.e.a.10.1 | 12 | |||
20.19 | odd | 2 | 432.2.u.c.337.2 | 12 | |||
27.25 | even | 9 | inner | 675.2.l.c.376.1 | 12 | ||
45.4 | even | 6 | 243.2.e.d.190.1 | 12 | |||
45.14 | odd | 6 | 243.2.e.a.190.2 | 12 | |||
45.29 | odd | 6 | 243.2.e.b.109.1 | 12 | |||
45.34 | even | 6 | 243.2.e.c.109.2 | 12 | |||
135.4 | even | 18 | 729.2.c.e.487.2 | 12 | |||
135.14 | odd | 18 | 729.2.c.b.244.5 | 12 | |||
135.29 | odd | 18 | 81.2.e.a.73.1 | 12 | |||
135.34 | even | 18 | 243.2.e.c.136.2 | 12 | |||
135.49 | even | 18 | 729.2.a.a.1.5 | 6 | |||
135.52 | odd | 36 | 675.2.u.b.349.2 | 24 | |||
135.59 | odd | 18 | 729.2.a.d.1.2 | 6 | |||
135.74 | odd | 18 | 243.2.e.b.136.1 | 12 | |||
135.79 | even | 18 | 27.2.e.a.25.2 | yes | 12 | ||
135.94 | even | 18 | 729.2.c.e.244.2 | 12 | |||
135.104 | odd | 18 | 729.2.c.b.487.5 | 12 | |||
135.119 | odd | 18 | 243.2.e.a.55.2 | 12 | |||
135.124 | even | 18 | 243.2.e.d.55.1 | 12 | |||
135.133 | odd | 36 | 675.2.u.b.349.3 | 24 | |||
540.79 | odd | 18 | 432.2.u.c.241.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.2.e.a.13.2 | ✓ | 12 | 5.4 | even | 2 | ||
27.2.e.a.25.2 | yes | 12 | 135.79 | even | 18 | ||
81.2.e.a.10.1 | 12 | 15.14 | odd | 2 | |||
81.2.e.a.73.1 | 12 | 135.29 | odd | 18 | |||
243.2.e.a.55.2 | 12 | 135.119 | odd | 18 | |||
243.2.e.a.190.2 | 12 | 45.14 | odd | 6 | |||
243.2.e.b.109.1 | 12 | 45.29 | odd | 6 | |||
243.2.e.b.136.1 | 12 | 135.74 | odd | 18 | |||
243.2.e.c.109.2 | 12 | 45.34 | even | 6 | |||
243.2.e.c.136.2 | 12 | 135.34 | even | 18 | |||
243.2.e.d.55.1 | 12 | 135.124 | even | 18 | |||
243.2.e.d.190.1 | 12 | 45.4 | even | 6 | |||
432.2.u.c.241.2 | 12 | 540.79 | odd | 18 | |||
432.2.u.c.337.2 | 12 | 20.19 | odd | 2 | |||
675.2.l.c.376.1 | 12 | 27.25 | even | 9 | inner | ||
675.2.l.c.526.1 | 12 | 1.1 | even | 1 | trivial | ||
675.2.u.b.349.2 | 24 | 135.52 | odd | 36 | |||
675.2.u.b.349.3 | 24 | 135.133 | odd | 36 | |||
675.2.u.b.499.2 | 24 | 5.3 | odd | 4 | |||
675.2.u.b.499.3 | 24 | 5.2 | odd | 4 | |||
729.2.a.a.1.5 | 6 | 135.49 | even | 18 | |||
729.2.a.d.1.2 | 6 | 135.59 | odd | 18 | |||
729.2.c.b.244.5 | 12 | 135.14 | odd | 18 | |||
729.2.c.b.487.5 | 12 | 135.104 | odd | 18 | |||
729.2.c.e.244.2 | 12 | 135.94 | even | 18 | |||
729.2.c.e.487.2 | 12 | 135.4 | even | 18 |