Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(406,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.406");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 285) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 406.3 | ||
Root | \(0.145349 - 0.251751i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.406 |
Dual form | 855.2.k.i.676.3 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.145349 | − | 0.251751i | −0.102777 | − | 0.178015i | 0.810051 | − | 0.586360i | \(-0.199439\pi\) |
−0.912828 | + | 0.408345i | \(0.866106\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.957748 | − | 1.65887i | 0.478874 | − | 0.829434i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.486575 | −0.183908 | −0.0919539 | − | 0.995763i | \(-0.529311\pi\) | ||||
−0.0919539 | + | 0.995763i | \(0.529311\pi\) | |||||||
\(8\) | −1.13822 | −0.402423 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.145349 | − | 0.251751i | 0.0459633 | − | 0.0796107i | ||||
\(11\) | −5.34764 | −1.61237 | −0.806187 | − | 0.591661i | \(-0.798472\pi\) | ||||
−0.806187 | + | 0.591661i | \(0.798472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.24329 | − | 2.15344i | 0.344826 | − | 0.597256i | −0.640496 | − | 0.767961i | \(-0.721271\pi\) |
0.985322 | + | 0.170705i | \(0.0546046\pi\) | |||||||
\(14\) | 0.0707229 | + | 0.122496i | 0.0189015 | + | 0.0327384i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.75006 | − | 3.03119i | −0.437514 | − | 0.757796i | ||||
\(17\) | −1.70780 | − | 2.95800i | −0.414203 | − | 0.717421i | 0.581141 | − | 0.813803i | \(-0.302606\pi\) |
−0.995344 | + | 0.0963817i | \(0.969273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.46291 | − | 3.59640i | −0.565029 | − | 0.825071i | ||||
\(20\) | 1.91550 | 0.428318 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.777272 | + | 1.34627i | 0.165715 | + | 0.287027i | ||||
\(23\) | 3.20619 | − | 5.55329i | 0.668537 | − | 1.15794i | −0.309776 | − | 0.950810i | \(-0.600254\pi\) |
0.978313 | − | 0.207131i | \(-0.0664126\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −0.722840 | −0.141761 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.466016 | + | 0.807163i | −0.0880687 | + | 0.152539i | ||||
\(29\) | 1.38312 | − | 2.39564i | 0.256839 | − | 0.444859i | −0.708554 | − | 0.705656i | \(-0.750652\pi\) |
0.965393 | + | 0.260798i | \(0.0839856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83099 | 0.867671 | 0.433836 | − | 0.900992i | \(-0.357160\pi\) | ||||
0.433836 | + | 0.900992i | \(0.357160\pi\) | |||||||
\(32\) | −1.64696 | + | 2.85262i | −0.291144 | + | 0.504276i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.496454 | + | 0.859883i | −0.0851411 | + | 0.147469i | ||||
\(35\) | −0.243287 | − | 0.421386i | −0.0411231 | − | 0.0712272i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.31756 | −1.03860 | −0.519301 | − | 0.854592i | \(-0.673808\pi\) | ||||
−0.519301 | + | 0.854592i | \(0.673808\pi\) | |||||||
\(38\) | −0.547418 | + | 1.14277i | −0.0888030 | + | 0.185382i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.569112 | − | 0.985730i | −0.0899845 | − | 0.155858i | ||||
\(41\) | 1.29070 | + | 2.23555i | 0.201573 | + | 0.349135i | 0.949035 | − | 0.315169i | \(-0.102061\pi\) |
−0.747462 | + | 0.664304i | \(0.768728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.24329 | + | 2.15344i | 0.189600 | + | 0.328396i | 0.945117 | − | 0.326733i | \(-0.105948\pi\) |
−0.755517 | + | 0.655129i | \(0.772614\pi\) | |||||||
\(44\) | −5.12169 | + | 8.87102i | −0.772123 | + | 1.33736i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.86406 | −0.274841 | ||||||||
\(47\) | 5.55533 | − | 9.62211i | 0.810328 | − | 1.40353i | −0.102306 | − | 0.994753i | \(-0.532622\pi\) |
0.912634 | − | 0.408777i | \(-0.134044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.76325 | −0.966178 | ||||||||
\(50\) | 0.290697 | 0.0411108 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.38151 | − | 4.12490i | −0.330256 | − | 0.572020i | ||||
\(53\) | 1.49839 | − | 2.59529i | 0.205820 | − | 0.356490i | −0.744574 | − | 0.667540i | \(-0.767347\pi\) |
0.950394 | + | 0.311050i | \(0.100681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.67382 | − | 4.63119i | −0.360538 | − | 0.624470i | ||||
\(56\) | 0.553831 | 0.0740087 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.804139 | −0.105589 | ||||||||
\(59\) | 6.36659 | + | 11.0273i | 0.828859 | + | 1.43563i | 0.898934 | + | 0.438084i | \(0.144343\pi\) |
−0.0700752 | + | 0.997542i | \(0.522324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.92742 | + | 10.2666i | −0.758929 | + | 1.31450i | 0.184469 | + | 0.982838i | \(0.440944\pi\) |
−0.943397 | + | 0.331664i | \(0.892390\pi\) | |||||||
\(62\) | −0.702178 | − | 1.21621i | −0.0891767 | − | 0.154458i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.04269 | −0.755336 | ||||||||
\(65\) | 2.48657 | 0.308422 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.58770 | − | 13.1423i | 0.926985 | − | 1.60559i | 0.138649 | − | 0.990342i | \(-0.455724\pi\) |
0.788336 | − | 0.615244i | \(-0.210943\pi\) | |||||||
\(68\) | −6.54258 | −0.793404 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0707229 | + | 0.122496i | −0.00845301 | + | 0.0146410i | ||||
\(71\) | −4.96452 | − | 8.59879i | −0.589180 | − | 1.02049i | −0.994340 | − | 0.106244i | \(-0.966118\pi\) |
0.405160 | − | 0.914246i | \(-0.367216\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.50642 | + | 9.53740i | 0.644478 | + | 1.11627i | 0.984422 | + | 0.175823i | \(0.0562585\pi\) |
−0.339944 | + | 0.940446i | \(0.610408\pi\) | |||||||
\(74\) | 0.918249 | + | 1.59045i | 0.106744 | + | 0.184887i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.32479 | + | 0.641189i | −0.954919 | + | 0.0735494i | ||||
\(77\) | 2.60202 | 0.296528 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.06636 | − | 7.04314i | −0.457501 | − | 0.792415i | 0.541327 | − | 0.840812i | \(-0.317922\pi\) |
−0.998828 | + | 0.0483971i | \(0.984589\pi\) | |||||||
\(80\) | 1.75006 | − | 3.03119i | 0.195662 | − | 0.338897i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.375202 | − | 0.649869i | 0.0414341 | − | 0.0717660i | ||||
\(83\) | 5.86106 | 0.643335 | 0.321668 | − | 0.946853i | \(-0.395757\pi\) | ||||
0.321668 | + | 0.946853i | \(0.395757\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.70780 | − | 2.95800i | 0.185237 | − | 0.320840i | ||||
\(86\) | 0.361420 | − | 0.625998i | 0.0389729 | − | 0.0675031i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.08681 | 0.648856 | ||||||||
\(89\) | −3.25521 | + | 5.63820i | −0.345052 | + | 0.597647i | −0.985363 | − | 0.170468i | \(-0.945472\pi\) |
0.640311 | + | 0.768116i | \(0.278805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.604952 | + | 1.04781i | −0.0634162 | + | 0.109840i | ||||
\(92\) | −6.14145 | − | 10.6373i | −0.640290 | − | 1.10901i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.22984 | −0.333132 | ||||||||
\(95\) | 1.88312 | − | 3.93114i | 0.193204 | − | 0.403326i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 0.983028 | + | 1.70265i | 0.0993008 | + | 0.171994i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.957748 | + | 1.65887i | 0.0957748 | + | 0.165887i | ||||
\(101\) | 0.758324 | − | 1.31346i | 0.0754561 | − | 0.130694i | −0.825828 | − | 0.563921i | \(-0.809292\pi\) |
0.901285 | + | 0.433228i | \(0.142625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.15478 | −0.902047 | −0.451023 | − | 0.892512i | \(-0.648941\pi\) | ||||
−0.451023 | + | 0.892512i | \(0.648941\pi\) | |||||||
\(104\) | −1.41514 | + | 2.45109i | −0.138766 | + | 0.240349i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.871155 | −0.0846140 | ||||||||
\(107\) | −0.138936 | −0.0134315 | −0.00671574 | − | 0.999977i | \(-0.502138\pi\) | ||||
−0.00671574 | + | 0.999977i | \(0.502138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.86497 | + | 13.6225i | 0.753328 | + | 1.30480i | 0.946201 | + | 0.323579i | \(0.104886\pi\) |
−0.192873 | + | 0.981224i | \(0.561781\pi\) | |||||||
\(110\) | −0.777272 | + | 1.34627i | −0.0741099 | + | 0.128362i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.851533 | + | 1.47490i | 0.0804623 | + | 0.139365i | ||||
\(113\) | −14.8011 | −1.39237 | −0.696187 | − | 0.717860i | \(-0.745122\pi\) | ||||
−0.696187 | + | 0.717860i | \(0.745122\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.41238 | 0.597958 | ||||||||
\(116\) | −2.64936 | − | 4.58883i | −0.245987 | − | 0.426062i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.85075 | − | 3.20559i | 0.170375 | − | 0.295099i | ||||
\(119\) | 0.830974 | + | 1.43929i | 0.0761752 | + | 0.131939i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5972 | 1.59975 | ||||||||
\(122\) | 3.44617 | 0.312002 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.62687 | − | 8.01397i | 0.415505 | − | 0.719676i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.91550 | − | 8.51389i | 0.436180 | − | 0.755485i | −0.561211 | − | 0.827672i | \(-0.689665\pi\) |
0.997391 | + | 0.0721871i | \(0.0229979\pi\) | |||||||
\(128\) | 4.17222 | + | 7.22649i | 0.368775 | + | 0.638738i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.361420 | − | 0.625998i | −0.0316986 | − | 0.0549037i | ||||
\(131\) | 7.11459 | + | 12.3228i | 0.621605 | + | 1.07665i | 0.989187 | + | 0.146660i | \(0.0468524\pi\) |
−0.367582 | + | 0.929991i | \(0.619814\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.19839 | + | 1.74992i | 0.103913 | + | 0.151737i | ||||
\(134\) | −4.41145 | −0.381091 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.94386 | + | 3.36687i | 0.166685 | + | 0.288707i | ||||
\(137\) | 3.29220 | − | 5.70225i | 0.281271 | − | 0.487176i | −0.690427 | − | 0.723402i | \(-0.742577\pi\) |
0.971698 | + | 0.236226i | \(0.0759106\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.116878 | + | 0.202439i | −0.00991347 | + | 0.0171706i | −0.870940 | − | 0.491390i | \(-0.836489\pi\) |
0.861026 | + | 0.508561i | \(0.169822\pi\) | |||||||
\(140\) | −0.932031 | −0.0787710 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.44317 | + | 2.49965i | −0.121108 | + | 0.209766i | ||||
\(143\) | −6.64865 | + | 11.5158i | −0.555988 | + | 0.963000i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.76624 | 0.229724 | ||||||||
\(146\) | 1.60070 | − | 2.77250i | 0.132475 | − | 0.229453i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.05063 | + | 10.4800i | −0.497359 | + | 0.861451i | ||||
\(149\) | −1.33650 | − | 2.31488i | −0.109490 | − | 0.189642i | 0.806074 | − | 0.591815i | \(-0.201588\pi\) |
−0.915564 | + | 0.402173i | \(0.868255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.95266 | 0.484421 | 0.242210 | − | 0.970224i | \(-0.422128\pi\) | ||||
0.242210 | + | 0.970224i | \(0.422128\pi\) | |||||||
\(152\) | 2.80334 | + | 4.09351i | 0.227381 | + | 0.332027i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.378201 | − | 0.655063i | −0.0304763 | − | 0.0527865i | ||||
\(155\) | 2.41550 | + | 4.18376i | 0.194017 | + | 0.336048i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.60424 | + | 6.24273i | 0.287650 | + | 0.498224i | 0.973248 | − | 0.229756i | \(-0.0737928\pi\) |
−0.685599 | + | 0.727980i | \(0.740459\pi\) | |||||||
\(158\) | −1.18208 | + | 2.04742i | −0.0940411 | + | 0.162884i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.29392 | −0.260407 | ||||||||
\(161\) | −1.56005 | + | 2.70209i | −0.122949 | + | 0.212954i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1756 | 1.11032 | 0.555161 | − | 0.831743i | \(-0.312657\pi\) | ||||
0.555161 | + | 0.831743i | \(0.312657\pi\) | |||||||
\(164\) | 4.94465 | 0.386112 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.851897 | − | 1.47553i | −0.0661201 | − | 0.114523i | ||||
\(167\) | 6.27817 | − | 10.8741i | 0.485819 | − | 0.841464i | −0.514048 | − | 0.857762i | \(-0.671855\pi\) |
0.999867 | + | 0.0162977i | \(0.00518794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.40847 | + | 5.90365i | 0.262190 | + | 0.454127i | ||||
\(170\) | −0.992907 | −0.0761525 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.76302 | 0.363177 | ||||||||
\(173\) | 1.09482 | + | 1.89628i | 0.0832376 | + | 0.144172i | 0.904639 | − | 0.426179i | \(-0.140141\pi\) |
−0.821401 | + | 0.570351i | \(0.806807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.243287 | − | 0.421386i | 0.0183908 | − | 0.0318538i | ||||
\(176\) | 9.35867 | + | 16.2097i | 0.705436 | + | 1.22185i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.89256 | 0.141854 | ||||||||
\(179\) | −7.50421 | −0.560891 | −0.280445 | − | 0.959870i | \(-0.590482\pi\) | ||||
−0.280445 | + | 0.959870i | \(0.590482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.33260 | − | 10.9684i | 0.470699 | − | 0.815274i | −0.528740 | − | 0.848784i | \(-0.677335\pi\) |
0.999438 | + | 0.0335101i | \(0.0106686\pi\) | |||||||
\(182\) | 0.351716 | 0.0260709 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.64936 | + | 6.32088i | −0.269035 | + | 0.465982i | ||||
\(185\) | −3.15878 | − | 5.47117i | −0.232238 | − | 0.402249i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.13272 | + | 15.8183i | 0.667850 | + | 1.15675i | ||||
\(188\) | −10.6412 | − | 18.4311i | −0.776090 | − | 1.34423i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.26338 | + | 0.0973074i | −0.0916551 | + | 0.00705942i | ||||
\(191\) | −8.15777 | −0.590276 | −0.295138 | − | 0.955455i | \(-0.595366\pi\) | ||||
−0.295138 | + | 0.955455i | \(0.595366\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.68252 | + | 2.91422i | 0.121111 | + | 0.209770i | 0.920206 | − | 0.391435i | \(-0.128021\pi\) |
−0.799095 | + | 0.601204i | \(0.794688\pi\) | |||||||
\(194\) | −0.290697 | + | 0.503502i | −0.0208708 | + | 0.0361494i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.47748 | + | 11.2193i | −0.462677 | + | 0.801381i | ||||
\(197\) | −3.83399 | −0.273160 | −0.136580 | − | 0.990629i | \(-0.543611\pi\) | ||||
−0.136580 | + | 0.990629i | \(0.543611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.34925 | + | 10.9972i | −0.450086 | + | 0.779572i | −0.998391 | − | 0.0567063i | \(-0.981940\pi\) |
0.548305 | + | 0.836279i | \(0.315273\pi\) | |||||||
\(200\) | 0.569112 | − | 0.985730i | 0.0402423 | − | 0.0697017i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.440885 | −0.0310206 | ||||||||
\(203\) | −0.672992 | + | 1.16566i | −0.0472348 | + | 0.0818130i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.29070 | + | 2.23555i | −0.0901462 | + | 0.156138i | ||||
\(206\) | 1.33063 | + | 2.30473i | 0.0927097 | + | 0.160578i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.70329 | −0.603465 | ||||||||
\(209\) | 13.1707 | + | 19.2323i | 0.911038 | + | 1.33032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.57828 | + | 7.92982i | 0.315182 | + | 0.545911i | 0.979476 | − | 0.201560i | \(-0.0646011\pi\) |
−0.664294 | + | 0.747471i | \(0.731268\pi\) | |||||||
\(212\) | −2.87016 | − | 4.97126i | −0.197123 | − | 0.341427i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.0201942 | + | 0.0349774i | 0.00138045 | + | 0.00239100i | ||||
\(215\) | −1.24329 | + | 2.15344i | −0.0847915 | + | 0.146863i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.35064 | −0.159572 | ||||||||
\(218\) | 2.28633 | − | 3.96003i | 0.154850 | − | 0.268207i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.2434 | −0.690608 | ||||||||
\(221\) | −8.49316 | −0.571312 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.44877 | − | 9.43754i | −0.364876 | − | 0.631984i | 0.623880 | − | 0.781520i | \(-0.285555\pi\) |
−0.988756 | + | 0.149536i | \(0.952222\pi\) | |||||||
\(224\) | 0.801369 | − | 1.38801i | 0.0535437 | − | 0.0927404i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.15133 | + | 3.72620i | 0.143104 | + | 0.247863i | ||||
\(227\) | 24.6351 | 1.63509 | 0.817545 | − | 0.575864i | \(-0.195334\pi\) | ||||
0.817545 | + | 0.575864i | \(0.195334\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1676 | 1.13447 | 0.567234 | − | 0.823557i | \(-0.308013\pi\) | ||||
0.567234 | + | 0.823557i | \(0.308013\pi\) | |||||||
\(230\) | −0.932031 | − | 1.61433i | −0.0614563 | − | 0.106445i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.57430 | + | 2.72677i | −0.103358 | + | 0.179021i | ||||
\(233\) | 14.2316 | + | 24.6498i | 0.932341 | + | 1.61486i | 0.779309 | + | 0.626640i | \(0.215570\pi\) |
0.153032 | + | 0.988221i | \(0.451096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.1107 | 0.724780 | ||||||||
\(236\) | 24.3903 | 1.58768 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.241562 | − | 0.418397i | 0.0156581 | − | 0.0271207i | ||||
\(239\) | −4.07741 | −0.263746 | −0.131873 | − | 0.991267i | \(-0.542099\pi\) | ||||
−0.131873 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.33421 | − | 10.9712i | 0.408023 | − | 0.706716i | −0.586646 | − | 0.809844i | \(-0.699552\pi\) |
0.994668 | + | 0.103128i | \(0.0328852\pi\) | |||||||
\(242\) | −2.55773 | − | 4.43012i | −0.164417 | − | 0.284779i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.3539 | + | 19.6656i | 0.726862 | + | 1.25896i | ||||
\(245\) | −3.38162 | − | 5.85714i | −0.216044 | − | 0.374199i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.8067 | + | 0.832351i | −0.687615 | + | 0.0529612i | ||||
\(248\) | −5.49875 | −0.349171 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.145349 | + | 0.251751i | 0.00919265 | + | 0.0159221i | ||||
\(251\) | −5.81204 | + | 10.0668i | −0.366853 | + | 0.635408i | −0.989072 | − | 0.147436i | \(-0.952898\pi\) |
0.622219 | + | 0.782843i | \(0.286231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.1456 | + | 29.6970i | −1.07793 | + | 1.86703i | ||||
\(254\) | −2.85784 | −0.179317 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.82984 | + | 8.36553i | −0.301865 | + | 0.522845i | ||||
\(257\) | 5.27416 | − | 9.13512i | 0.328993 | − | 0.569833i | −0.653319 | − | 0.757083i | \(-0.726624\pi\) |
0.982312 | + | 0.187250i | \(0.0599574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.07397 | 0.191007 | ||||||||
\(260\) | 2.38151 | − | 4.12490i | 0.147695 | − | 0.255815i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.06819 | − | 3.58221i | 0.127773 | − | 0.221310i | ||||
\(263\) | 11.8967 | + | 20.6058i | 0.733585 | + | 1.27061i | 0.955341 | + | 0.295504i | \(0.0954876\pi\) |
−0.221757 | + | 0.975102i | \(0.571179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.99678 | 0.184091 | ||||||||
\(266\) | 0.266360 | − | 0.556043i | 0.0163316 | − | 0.0340932i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.5342 | − | 25.1740i | −0.887818 | − | 1.53775i | ||||
\(269\) | −2.11377 | − | 3.66115i | −0.128879 | − | 0.223224i | 0.794364 | − | 0.607442i | \(-0.207804\pi\) |
−0.923242 | + | 0.384218i | \(0.874471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5736 | − | 26.9742i | −0.946027 | − | 1.63857i | −0.753682 | − | 0.657239i | \(-0.771724\pi\) |
−0.192344 | − | 0.981328i | \(-0.561609\pi\) | |||||||
\(272\) | −5.97750 | + | 10.3533i | −0.362439 | + | 0.627763i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.91406 | −0.115633 | ||||||||
\(275\) | 2.67382 | − | 4.63119i | 0.161237 | − | 0.279271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.05393 | 0.0633243 | 0.0316621 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316621 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(278\) | 0.0679523 | 0.00407551 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.276915 | + | 0.479631i | 0.0165489 | + | 0.0286635i | ||||
\(281\) | 12.8177 | − | 22.2009i | 0.764638 | − | 1.32439i | −0.175799 | − | 0.984426i | \(-0.556251\pi\) |
0.940437 | − | 0.339967i | \(-0.110416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7056 | − | 25.4708i | −0.874157 | − | 1.51408i | −0.857658 | − | 0.514220i | \(-0.828082\pi\) |
−0.0164983 | − | 0.999864i | \(-0.505252\pi\) | |||||||
\(284\) | −19.0190 | −1.12857 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.86549 | 0.228571 | ||||||||
\(287\) | −0.628020 | − | 1.08776i | −0.0370709 | − | 0.0642086i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.66681 | − | 4.61906i | 0.156871 | − | 0.271709i | ||||
\(290\) | −0.402070 | − | 0.696405i | −0.0236103 | − | 0.0408943i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.0950 | 1.23449 | ||||||||
\(293\) | 10.8548 | 0.634147 | 0.317073 | − | 0.948401i | \(-0.397300\pi\) | ||||
0.317073 | + | 0.948401i | \(0.397300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.36659 | + | 11.0273i | −0.370677 | + | 0.642031i | ||||
\(296\) | 7.19080 | 0.417957 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.388516 | + | 0.672929i | −0.0225061 | + | 0.0389817i | ||||
\(299\) | −7.97244 | − | 13.8087i | −0.461058 | − | 0.798576i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.604952 | − | 1.04781i | −0.0348688 | − | 0.0603946i | ||||
\(302\) | −0.865211 | − | 1.49859i | −0.0497873 | − | 0.0862341i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.59114 | + | 13.7594i | −0.378028 | + | 0.789157i | ||||
\(305\) | −11.8548 | −0.678806 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8445 | − | 29.1756i | −0.961368 | − | 1.66514i | −0.719072 | − | 0.694936i | \(-0.755433\pi\) |
−0.242296 | − | 0.970202i | \(-0.577901\pi\) | |||||||
\(308\) | 2.49208 | − | 4.31641i | 0.142000 | − | 0.245950i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.702178 | − | 1.21621i | 0.0398810 | − | 0.0690759i | ||||
\(311\) | 11.7221 | 0.664701 | 0.332350 | − | 0.943156i | \(-0.392158\pi\) | ||||
0.332350 | + | 0.943156i | \(0.392158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.23928 | + | 3.87855i | −0.126572 | + | 0.219229i | −0.922346 | − | 0.386364i | \(-0.873731\pi\) |
0.795775 | + | 0.605593i | \(0.207064\pi\) | |||||||
\(314\) | 1.04774 | − | 1.81474i | 0.0591275 | − | 0.102412i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5782 | −0.876341 | ||||||||
\(317\) | 6.19367 | − | 10.7277i | 0.347871 | − | 0.602530i | −0.638000 | − | 0.770036i | \(-0.720238\pi\) |
0.985871 | + | 0.167506i | \(0.0535714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.39644 | + | 12.8110i | −0.414121 | + | 0.717278i | ||||
\(320\) | −3.02135 | − | 5.23312i | −0.168898 | − | 0.292541i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.907005 | 0.0505454 | ||||||||
\(323\) | −6.43200 | + | 13.4272i | −0.357886 | + | 0.747111i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.24329 | + | 2.15344i | 0.0689652 | + | 0.119451i | ||||
\(326\) | −2.06041 | − | 3.56873i | −0.114115 | − | 0.197654i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.46910 | − | 2.54456i | −0.0811176 | − | 0.140500i | ||||
\(329\) | −2.70308 | + | 4.68188i | −0.149026 | + | 0.258120i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5058 | 1.34696 | 0.673480 | − | 0.739206i | \(-0.264799\pi\) | ||||
0.673480 | + | 0.739206i | \(0.264799\pi\) | |||||||
\(332\) | 5.61342 | − | 9.72273i | 0.308076 | − | 0.533604i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.65009 | −0.199724 | ||||||||
\(335\) | 15.1754 | 0.829121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.25038 | − | 9.09392i | −0.286006 | − | 0.495378i | 0.686846 | − | 0.726803i | \(-0.258995\pi\) |
−0.972853 | + | 0.231425i | \(0.925661\pi\) | |||||||
\(338\) | 0.990834 | − | 1.71617i | 0.0538942 | − | 0.0933476i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.27129 | − | 5.66604i | −0.177411 | − | 0.307284i | ||||
\(341\) | −25.8344 | −1.39901 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.69684 | 0.361596 | ||||||||
\(344\) | −1.41514 | − | 2.45109i | −0.0762992 | − | 0.132154i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.318261 | − | 0.551244i | 0.0171098 | − | 0.0296351i | ||||
\(347\) | −0.727562 | − | 1.26017i | −0.0390576 | − | 0.0676497i | 0.845836 | − | 0.533443i | \(-0.179102\pi\) |
−0.884893 | + | 0.465794i | \(0.845769\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7332 | 1.27041 | 0.635204 | − | 0.772345i | \(-0.280916\pi\) | ||||
0.635204 | + | 0.772345i | \(0.280916\pi\) | |||||||
\(350\) | −0.141446 | −0.00756060 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.80735 | − | 15.2548i | 0.469433 | − | 0.813082i | ||||
\(353\) | 7.39055 | 0.393359 | 0.196680 | − | 0.980468i | \(-0.436984\pi\) | ||||
0.196680 | + | 0.980468i | \(0.436984\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.96452 | − | 8.59879i | 0.263489 | − | 0.456377i | ||||
\(356\) | 6.23535 | + | 10.7999i | 0.330473 | + | 0.572395i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.09073 | + | 1.88919i | 0.0576467 | + | 0.0998469i | ||||
\(359\) | 1.17934 | + | 2.04268i | 0.0622433 | + | 0.107808i | 0.895468 | − | 0.445126i | \(-0.146841\pi\) |
−0.833225 | + | 0.552935i | \(0.813508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.86820 | + | 17.7152i | −0.361484 | + | 0.932378i | ||||
\(362\) | −3.68174 | −0.193508 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.15878 | + | 2.00707i | 0.0607367 | + | 0.105199i | ||||
\(365\) | −5.50642 | + | 9.53740i | −0.288219 | + | 0.499210i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0743 | − | 19.1812i | 0.578073 | − | 1.00125i | −0.417628 | − | 0.908618i | \(-0.637138\pi\) |
0.995700 | − | 0.0926329i | \(-0.0295283\pi\) | |||||||
\(368\) | −22.4441 | −1.16998 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.918249 | + | 1.59045i | −0.0477375 | + | 0.0826838i | ||||
\(371\) | −0.729078 | + | 1.26280i | −0.0378518 | + | 0.0655613i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.1738 | 1.61412 | 0.807060 | − | 0.590469i | \(-0.201057\pi\) | ||||
0.807060 | + | 0.590469i | \(0.201057\pi\) | |||||||
\(374\) | 2.65485 | − | 4.59834i | 0.137279 | − | 0.237775i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.32321 | + | 10.9521i | −0.326094 | + | 0.564812i | ||||
\(377\) | −3.43924 | − | 5.95693i | −0.177130 | − | 0.306798i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0349 | −1.33732 | −0.668662 | − | 0.743567i | \(-0.733132\pi\) | ||||
−0.668662 | + | 0.743567i | \(0.733132\pi\) | |||||||
\(380\) | −4.71768 | − | 6.88889i | −0.242012 | − | 0.353393i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.18572 | + | 2.05373i | 0.0606668 | + | 0.105078i | ||||
\(383\) | −1.06647 | − | 1.84718i | −0.0544941 | − | 0.0943865i | 0.837492 | − | 0.546450i | \(-0.184021\pi\) |
−0.891986 | + | 0.452064i | \(0.850688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.30101 | + | 2.25342i | 0.0663057 | + | 0.114845i | ||||
\(386\) | 0.489105 | − | 0.847154i | 0.0248948 | − | 0.0431190i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.83099 | −0.194489 | ||||||||
\(389\) | −6.52135 | + | 11.2953i | −0.330645 | + | 0.572695i | −0.982639 | − | 0.185530i | \(-0.940600\pi\) |
0.651993 | + | 0.758225i | \(0.273933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.9022 | −1.10764 | ||||||||
\(392\) | 7.69808 | 0.388812 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.557265 | + | 0.965211i | 0.0280746 | + | 0.0486266i | ||||
\(395\) | 4.06636 | − | 7.04314i | 0.204601 | − | 0.354379i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0143214 | − | 0.0248054i | −0.000718770 | − | 0.00124495i | 0.865666 | − | 0.500622i | \(-0.166895\pi\) |
−0.866385 | + | 0.499377i | \(0.833562\pi\) | |||||||
\(398\) | 3.69142 | 0.185034 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.50011 | 0.175006 | ||||||||
\(401\) | −13.6596 | − | 23.6591i | −0.682126 | − | 1.18148i | −0.974331 | − | 0.225122i | \(-0.927722\pi\) |
0.292204 | − | 0.956356i | \(-0.405611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00631 | − | 10.4032i | 0.299196 | − | 0.518222i | ||||
\(404\) | −1.45257 | − | 2.51592i | −0.0722679 | − | 0.125172i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.391274 | 0.0194186 | ||||||||
\(407\) | 33.7841 | 1.67461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.36958 | − | 5.83629i | 0.166615 | − | 0.288586i | −0.770612 | − | 0.637304i | \(-0.780050\pi\) |
0.937228 | + | 0.348718i | \(0.113383\pi\) | |||||||
\(410\) | 0.750404 | 0.0370598 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.76796 | + | 15.1866i | −0.431967 | + | 0.748188i | ||||
\(413\) | −3.09782 | − | 5.36558i | −0.152434 | − | 0.264023i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.93053 | + | 5.07583i | 0.143854 | + | 0.249163i | ||||
\(416\) | 4.09529 | + | 7.09325i | 0.200788 | + | 0.347775i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.92739 | − | 6.11113i | 0.143184 | − | 0.298905i | ||||
\(419\) | −26.4076 | −1.29010 | −0.645048 | − | 0.764142i | \(-0.723163\pi\) | ||||
−0.645048 | + | 0.764142i | \(0.723163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9448 | − | 32.8133i | −0.923311 | − | 1.59922i | −0.794255 | − | 0.607584i | \(-0.792139\pi\) |
−0.129056 | − | 0.991637i | \(-0.541195\pi\) | |||||||
\(422\) | 1.33089 | − | 2.30518i | 0.0647869 | − | 0.112214i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.70550 | + | 2.95401i | −0.0828265 | + | 0.143460i | ||||
\(425\) | 3.41561 | 0.165681 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.88413 | − | 4.99546i | 0.139573 | − | 0.241747i | ||||
\(428\) | −0.133066 | + | 0.230477i | −0.00643198 | + | 0.0111405i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.722840 | 0.0348585 | ||||||||
\(431\) | −9.60285 | + | 16.6326i | −0.462553 | + | 0.801165i | −0.999087 | − | 0.0427131i | \(-0.986400\pi\) |
0.536534 | + | 0.843879i | \(0.319733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.47562 | + | 14.6802i | −0.407312 | + | 0.705485i | −0.994588 | − | 0.103902i | \(-0.966867\pi\) |
0.587275 | + | 0.809387i | \(0.300201\pi\) | |||||||
\(434\) | 0.341662 | + | 0.591776i | 0.0164003 | + | 0.0284061i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.1306 | 1.44300 | ||||||||
\(437\) | −27.8684 | + | 2.14647i | −1.33313 | + | 0.102680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.55143 | − | 9.61536i | −0.264955 | − | 0.458916i | 0.702597 | − | 0.711588i | \(-0.252024\pi\) |
−0.967552 | + | 0.252672i | \(0.918691\pi\) | |||||||
\(440\) | 3.04340 | + | 5.27133i | 0.145089 | + | 0.251301i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.23447 | + | 2.13816i | 0.0587177 | + | 0.101702i | ||||
\(443\) | −6.94708 | + | 12.0327i | −0.330066 | + | 0.571691i | −0.982524 | − | 0.186133i | \(-0.940404\pi\) |
0.652459 | + | 0.757824i | \(0.273738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.51043 | −0.308624 | ||||||||
\(446\) | −1.58394 | + | 2.74347i | −0.0750018 | + | 0.129907i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.94022 | 0.138912 | ||||||||
\(449\) | −27.8675 | −1.31515 | −0.657573 | − | 0.753391i | \(-0.728417\pi\) | ||||
−0.657573 | + | 0.753391i | \(0.728417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.90218 | − | 11.9549i | −0.325011 | − | 0.562936i | ||||
\(452\) | −14.1758 | + | 24.5531i | −0.666772 | + | 1.15488i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.58068 | − | 6.20192i | −0.168050 | − | 0.291071i | ||||
\(455\) | −1.20990 | −0.0567212 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.5660 | −1.71048 | −0.855242 | − | 0.518229i | \(-0.826591\pi\) | ||||
−0.855242 | + | 0.518229i | \(0.826591\pi\) | |||||||
\(458\) | −2.49529 | − | 4.32197i | −0.116597 | − | 0.201952i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.14145 | − | 10.6373i | 0.286346 | − | 0.495966i | ||||
\(461\) | 10.9590 | + | 18.9816i | 0.510412 | + | 0.884059i | 0.999927 | + | 0.0120646i | \(0.00384039\pi\) |
−0.489515 | + | 0.871995i | \(0.662826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.0255 | −0.651821 | −0.325910 | − | 0.945401i | \(-0.605671\pi\) | ||||
−0.325910 | + | 0.945401i | \(0.605671\pi\) | |||||||
\(464\) | −9.68216 | −0.449483 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.13707 | − | 7.16562i | 0.191646 | − | 0.331941i | ||||
\(467\) | −33.9294 | −1.57007 | −0.785033 | − | 0.619453i | \(-0.787354\pi\) | ||||
−0.785033 | + | 0.619453i | \(0.787354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.69198 | + | 6.39470i | −0.170480 | + | 0.295280i | ||||
\(470\) | −1.61492 | − | 2.79712i | −0.0744906 | − | 0.129022i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.24660 | − | 12.5515i | −0.333552 | − | 0.577728i | ||||
\(473\) | −6.64865 | − | 11.5158i | −0.305705 | − | 0.529497i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.34603 | − | 0.334738i | 0.199409 | − | 0.0153588i | ||||
\(476\) | 3.18345 | 0.145913 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.592646 | + | 1.02649i | 0.0271070 | + | 0.0469507i | ||||
\(479\) | 15.9748 | − | 27.6692i | 0.729909 | − | 1.26424i | −0.227012 | − | 0.973892i | \(-0.572896\pi\) |
0.956921 | − | 0.290348i | \(-0.0937711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.85455 | + | 13.6045i | −0.358137 | + | 0.620311i | ||||
\(482\) | −3.68268 | −0.167741 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.8537 | − | 29.1915i | 0.766078 | − | 1.32689i | ||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.6229 | 1.70486 | 0.852428 | − | 0.522844i | \(-0.175129\pi\) | ||||
0.852428 | + | 0.522844i | \(0.175129\pi\) | |||||||
\(488\) | 6.74673 | − | 11.6857i | 0.305410 | − | 0.528986i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.983028 | + | 1.70265i | −0.0444087 | + | 0.0769181i | ||||
\(491\) | −20.0421 | − | 34.7139i | −0.904487 | − | 1.56662i | −0.821604 | − | 0.570059i | \(-0.806920\pi\) |
−0.0828838 | − | 0.996559i | \(-0.526413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.44840 | −0.425535 | ||||||||
\(494\) | 1.78029 | + | 2.59962i | 0.0800989 | + | 0.116963i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.45450 | − | 14.6436i | −0.379618 | − | 0.657518i | ||||
\(497\) | 2.41561 | + | 4.18395i | 0.108355 | + | 0.187676i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1533 | + | 26.2464i | 0.678357 | + | 1.17495i | 0.975475 | + | 0.220108i | \(0.0706410\pi\) |
−0.297118 | + | 0.954841i | \(0.596026\pi\) | |||||||
\(500\) | −0.957748 | + | 1.65887i | −0.0428318 | + | 0.0741868i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.37909 | 0.150816 | ||||||||
\(503\) | −8.64393 | + | 14.9717i | −0.385414 | + | 0.667556i | −0.991827 | − | 0.127594i | \(-0.959275\pi\) |
0.606413 | + | 0.795150i | \(0.292608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.51665 | 0.0674899 | ||||||||
\(506\) | 9.96833 | 0.443146 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.41561 | − | 16.3083i | −0.417750 | − | 0.723564i | ||||
\(509\) | 2.80412 | − | 4.85688i | 0.124291 | − | 0.215278i | −0.797165 | − | 0.603762i | \(-0.793668\pi\) |
0.921455 | + | 0.388484i | \(0.127001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.67928 | − | 4.64066i | −0.118525 | − | 0.205291i | ||||
\(512\) | 19.4969 | 0.861650 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.06637 | −0.135252 | ||||||||
\(515\) | −4.57739 | − | 7.92827i | −0.201704 | − | 0.349361i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.7079 | + | 51.4556i | −1.30655 | + | 2.26301i | ||||
\(518\) | −0.446797 | − | 0.773874i | −0.0196311 | − | 0.0340021i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.83028 | −0.124116 | ||||||||
\(521\) | −13.7128 | −0.600767 | −0.300384 | − | 0.953818i | \(-0.597115\pi\) | ||||
−0.300384 | + | 0.953818i | \(0.597115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.6171 | − | 30.5137i | 0.770341 | − | 1.33427i | −0.167035 | − | 0.985951i | \(-0.553419\pi\) |
0.937376 | − | 0.348319i | \(-0.113247\pi\) | |||||||
\(524\) | 27.2559 | 1.19068 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.45835 | − | 5.99004i | 0.150791 | − | 0.261178i | ||||
\(527\) | −8.25038 | − | 14.2901i | −0.359392 | − | 0.622486i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.05934 | − | 15.6912i | −0.393884 | − | 0.682228i | ||||
\(530\) | −0.435577 | − | 0.754442i | −0.0189203 | − | 0.0327709i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.05063 | − | 0.311986i | 0.175617 | − | 0.0135263i | ||||
\(533\) | 6.41883 | 0.278030 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.0694682 | − | 0.120322i | −0.00300337 | − | 0.00520199i | ||||
\(536\) | −8.63650 | + | 14.9589i | −0.373040 | + | 0.646124i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.614466 | + | 1.06429i | −0.0264915 | + | 0.0458847i | ||||
\(539\) | 36.1674 | 1.55784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1179 | + | 26.1849i | −0.649968 | + | 1.12578i | 0.333162 | + | 0.942869i | \(0.391884\pi\) |
−0.983130 | + | 0.182908i | \(0.941449\pi\) | |||||||
\(542\) | −4.52719 | + | 7.84133i | −0.194460 | + | 0.336814i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11.2507 | 0.482371 | ||||||||
\(545\) | −7.86497 | + | 13.6225i | −0.336899 | + | 0.583525i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4766 | + | 30.2703i | −0.747244 | + | 1.29426i | 0.201895 | + | 0.979407i | \(0.435290\pi\) |
−0.949139 | + | 0.314858i | \(0.898043\pi\) | |||||||
\(548\) | −6.30619 | − | 10.9226i | −0.269387 | − | 0.466592i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.55454 | −0.0662860 | ||||||||
\(551\) | −12.0222 | + | 0.925967i | −0.512162 | + | 0.0394475i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.97859 | + | 3.42701i | 0.0841380 | + | 0.145731i | ||||
\(554\) | −0.153187 | − | 0.265327i | −0.00650828 | − | 0.0112727i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.223879 | + | 0.387771i | 0.00949460 | + | 0.0164451i | ||||
\(557\) | 1.58139 | − | 2.73906i | 0.0670058 | − | 0.116058i | −0.830576 | − | 0.556905i | \(-0.811989\pi\) |
0.897582 | + | 0.440848i | \(0.145322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.18305 | 0.261515 | ||||||||
\(560\) | −0.851533 | + | 1.47490i | −0.0359838 | + | 0.0623258i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.45213 | −0.314349 | ||||||||
\(563\) | 29.0570 | 1.22460 | 0.612302 | − | 0.790624i | \(-0.290244\pi\) | ||||
0.612302 | + | 0.790624i | \(0.290244\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.40057 | − | 12.8182i | −0.311344 | − | 0.539264i | ||||
\(566\) | −4.27487 | + | 7.40430i | −0.179686 | + | 0.311226i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.65073 | + | 9.78735i | 0.237099 | + | 0.410668i | ||||
\(569\) | 31.3398 | 1.31383 | 0.656916 | − | 0.753964i | \(-0.271861\pi\) | ||||
0.656916 | + | 0.753964i | \(0.271861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.56556 | 0.107365 | 0.0536827 | − | 0.998558i | \(-0.482904\pi\) | ||||
0.0536827 | + | 0.998558i | \(0.482904\pi\) | |||||||
\(572\) | 12.7355 | + | 22.0585i | 0.532496 | + | 0.922311i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.182564 | + | 0.316210i | −0.00762006 | + | 0.0131983i | ||||
\(575\) | 3.20619 | + | 5.55329i | 0.133707 | + | 0.231588i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.12153 | 0.129951 | 0.0649755 | − | 0.997887i | \(-0.479303\pi\) | ||||
0.0649755 | + | 0.997887i | \(0.479303\pi\) | |||||||
\(578\) | −1.55047 | −0.0644911 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.64936 | − | 4.58883i | 0.110009 | − | 0.190541i | ||||
\(581\) | −2.85184 | −0.118314 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.01284 | + | 13.8786i | −0.331858 | + | 0.574795i | ||||
\(584\) | −6.26754 | − | 10.8557i | −0.259353 | − | 0.449212i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.57774 | − | 2.73272i | −0.0651757 | − | 0.112888i | ||||
\(587\) | −4.63985 | − | 8.03646i | −0.191507 | − | 0.331700i | 0.754243 | − | 0.656596i | \(-0.228004\pi\) |
−0.945750 | + | 0.324896i | \(0.894671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8983 | − | 17.3742i | −0.490260 | − | 0.715891i | ||||
\(590\) | 3.70150 | 0.152388 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.0561 | + | 19.1497i | 0.454403 | + | 0.787048i | ||||
\(593\) | 17.0224 | − | 29.4836i | 0.699025 | − | 1.21075i | −0.269780 | − | 0.962922i | \(-0.586951\pi\) |
0.968805 | − | 0.247825i | \(-0.0797157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.830974 | + | 1.43929i | −0.0340666 | + | 0.0590051i | ||||
\(596\) | −5.12010 | −0.209728 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.31756 | + | 4.01414i | −0.0947723 | + | 0.164150i | ||||
\(599\) | 12.5366 | − | 21.7140i | 0.512231 | − | 0.887210i | −0.487669 | − | 0.873029i | \(-0.662153\pi\) |
0.999899 | − | 0.0141810i | \(-0.00451411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0225 | −1.06148 | −0.530739 | − | 0.847535i | \(-0.678086\pi\) | ||||
−0.530739 | + | 0.847535i | \(0.678086\pi\) | |||||||
\(602\) | −0.175858 | + | 0.304595i | −0.00716743 | + | 0.0124144i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.70115 | − | 9.87468i | 0.231976 | − | 0.401795i | ||||
\(605\) | 8.79862 | + | 15.2397i | 0.357715 | + | 0.619580i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.54650 | −0.306303 | −0.153151 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153151 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(608\) | 14.3155 | − | 1.10260i | 0.580569 | − | 0.0447163i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.72308 | + | 2.98447i | 0.0697657 | + | 0.120838i | ||||
\(611\) | −13.8137 | − | 23.9261i | −0.558844 | − | 0.967946i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.1345 | + | 33.1419i | 0.772836 | + | 1.33859i | 0.936003 | + | 0.351992i | \(0.114496\pi\) |
−0.163167 | + | 0.986598i | \(0.552171\pi\) | |||||||
\(614\) | −4.89666 | + | 8.48126i | −0.197613 | + | 0.342276i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.96169 | −0.119330 | ||||||||
\(617\) | −5.82540 | + | 10.0899i | −0.234522 | + | 0.406203i | −0.959134 | − | 0.282954i | \(-0.908686\pi\) |
0.724612 | + | 0.689157i | \(0.242019\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.47710 | −0.0995630 | −0.0497815 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497815 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(620\) | 9.25374 | 0.371639 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.70379 | − | 2.95106i | −0.0683159 | − | 0.118327i | ||||
\(623\) | 1.58390 | − | 2.74340i | 0.0634578 | − | 0.109912i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 1.30191 | 0.0520346 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.8078 | 0.550991 | ||||||||
\(629\) | 10.7892 | + | 18.6874i | 0.430192 | + | 0.745114i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8279 | − | 37.8070i | 0.868954 | − | 1.50507i | 0.00588756 | − | 0.999983i | \(-0.498126\pi\) |
0.863067 | − | 0.505090i | \(-0.168541\pi\) | |||||||
\(632\) | 4.62842 | + | 8.01666i | 0.184109 | + | 0.318886i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.60096 | −0.143012 | ||||||||
\(635\) | 9.83099 | 0.390131 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.40866 | + | 14.5642i | −0.333163 | + | 0.577055i | ||||
\(638\) | 4.30025 | 0.170248 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.17222 | + | 7.22649i | −0.164921 | + | 0.285652i | ||||
\(641\) | 12.1163 | + | 20.9860i | 0.478564 | + | 0.828897i | 0.999698 | − | 0.0245776i | \(-0.00782407\pi\) |
−0.521134 | + | 0.853475i | \(0.674491\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.15878 | − | 7.20322i | −0.164006 | − | 0.284067i | 0.772296 | − | 0.635263i | \(-0.219108\pi\) |
−0.936302 | + | 0.351196i | \(0.885775\pi\) | |||||||
\(644\) | 2.98827 | + | 5.17584i | 0.117754 | + | 0.203957i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.31520 | − | 0.332364i | 0.169779 | − | 0.0130767i | ||||
\(647\) | 10.9164 | 0.429170 | 0.214585 | − | 0.976705i | \(-0.431160\pi\) | ||||
0.214585 | + | 0.976705i | \(0.431160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34.0462 | − | 58.9697i | −1.33643 | − | 2.31476i | ||||
\(650\) | 0.361420 | − | 0.625998i | 0.0141761 | − | 0.0245537i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.5767 | − | 23.5155i | 0.531704 | − | 0.920938i | ||||
\(653\) | 21.8452 | 0.854868 | 0.427434 | − | 0.904047i | \(-0.359418\pi\) | ||||
0.427434 | + | 0.904047i | \(0.359418\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.11459 | + | 12.3228i | −0.277990 | + | 0.481493i | ||||
\(656\) | 4.51758 | − | 7.82469i | 0.176382 | − | 0.305503i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.57156 | 0.0612657 | ||||||||
\(659\) | −13.2094 | + | 22.8794i | −0.514566 | + | 0.891254i | 0.485291 | + | 0.874352i | \(0.338714\pi\) |
−0.999857 | + | 0.0169015i | \(0.994620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.30721 | + | 16.1206i | −0.362008 | + | 0.627017i | −0.988291 | − | 0.152579i | \(-0.951242\pi\) |
0.626283 | + | 0.779596i | \(0.284576\pi\) | |||||||
\(662\) | −3.56188 | − | 6.16936i | −0.138436 | − | 0.239779i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.67120 | −0.258893 | ||||||||
\(665\) | −0.916279 | + | 1.91279i | −0.0355318 | + | 0.0741749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.86911 | − | 15.3617i | −0.343413 | − | 0.594809i | ||||
\(668\) | −12.0258 | − | 20.8293i | −0.465292 | − | 0.805910i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.20572 | − | 3.82043i | −0.0852146 | − | 0.147596i | ||||
\(671\) | 31.6977 | − | 54.9020i | 1.22368 | − | 2.11947i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.98693 | 0.230779 | 0.115390 | − | 0.993320i | \(-0.463188\pi\) | ||||
0.115390 | + | 0.993320i | \(0.463188\pi\) | |||||||
\(674\) | −1.52627 | + | 2.64358i | −0.0587898 | + | 0.101827i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0578 | 0.502224 | ||||||||
\(677\) | −33.7287 | −1.29630 | −0.648150 | − | 0.761512i | \(-0.724457\pi\) | ||||
−0.648150 | + | 0.761512i | \(0.724457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.486575 | + | 0.842772i | 0.0186730 | + | 0.0323426i | ||||
\(680\) | −1.94386 | + | 3.36687i | −0.0745437 | + | 0.129113i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.75499 | + | 6.50384i | 0.143786 | + | 0.249045i | ||||
\(683\) | −11.4959 | −0.439880 | −0.219940 | − | 0.975513i | \(-0.570586\pi\) | ||||
−0.219940 | + | 0.975513i | \(0.570586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.58439 | 0.251577 | ||||||||
\(686\) | −0.973377 | − | 1.68594i | −0.0371637 | − | 0.0643694i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.35164 | − | 7.53727i | 0.165905 | − | 0.287356i | ||||
\(689\) | −3.72586 | − | 6.45337i | −0.141944 | − | 0.245854i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.3039 | 1.38107 | 0.690533 | − | 0.723301i | \(-0.257376\pi\) | ||||
0.690533 | + | 0.723301i | \(0.257376\pi\) | |||||||
\(692\) | 4.19424 | 0.159441 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.211500 | + | 0.366329i | −0.00802844 | + | 0.0139057i | ||||
\(695\) | −0.233756 | −0.00886688 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.40851 | − | 7.63577i | 0.166984 | − | 0.289225i | ||||
\(698\) | −3.44958 | − | 5.97485i | −0.130569 | − | 0.226152i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.466016 | − | 0.807163i | −0.0176137 | − | 0.0305079i | ||||
\(701\) | 6.76373 | + | 11.7151i | 0.255463 | + | 0.442474i | 0.965021 | − | 0.262172i | \(-0.0844389\pi\) |
−0.709558 | + | 0.704647i | \(0.751106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5596 | + | 22.7205i | 0.586840 | + | 0.856920i | ||||
\(704\) | 32.3141 | 1.21788 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.07421 | − | 1.86058i | −0.0404283 | − | 0.0700239i | ||||
\(707\) | −0.368981 | + | 0.639094i | −0.0138770 | + | 0.0240356i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.496778 | − | 0.860444i | 0.0186569 | − | 0.0323147i | −0.856546 | − | 0.516070i | \(-0.827394\pi\) |
0.875203 | + | 0.483756i | \(0.160728\pi\) | |||||||
\(710\) | −2.88634 | −0.108322 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.70516 | − | 6.41753i | 0.138857 | − | 0.240507i | ||||
\(713\) | 15.4891 | − | 26.8279i | 0.580071 | − | 1.00471i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.2973 | −0.497291 | ||||||||
\(716\) | −7.18714 | + | 12.4485i | −0.268596 | + | 0.465222i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.342831 | − | 0.593801i | 0.0127943 | − | 0.0221605i | ||||
\(719\) | −0.700670 | − | 1.21360i | −0.0261306 | − | 0.0452595i | 0.852664 | − | 0.522459i | \(-0.174985\pi\) |
−0.878795 | + | 0.477200i | \(0.841652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.45448 | 0.165894 | ||||||||
\(722\) | 5.45810 | − | 0.845801i | 0.203130 | − | 0.0314775i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.1301 | − | 21.0099i | −0.450810 | − | 0.780827i | ||||
\(725\) | 1.38312 | + | 2.39564i | 0.0513679 | + | 0.0889717i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.4834 | + | 40.6745i | 0.870953 | + | 1.50853i | 0.861013 | + | 0.508584i | \(0.169831\pi\) |
0.00993990 | + | 0.999951i | \(0.496836\pi\) | |||||||
\(728\) | 0.688570 | − | 1.19264i | 0.0255201 | − | 0.0442021i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.20140 | 0.118489 | ||||||||
\(731\) | 4.24658 | − | 7.35529i | 0.157065 | − | 0.272045i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.6068 | −0.798066 | −0.399033 | − | 0.916937i | \(-0.630654\pi\) | ||||
−0.399033 | + | 0.916937i | \(0.630654\pi\) | |||||||
\(734\) | −6.43852 | −0.237650 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.5609 | + | 18.2921i | 0.389281 | + | 0.674255i | ||||
\(737\) | −40.5763 | + | 70.2802i | −1.49465 | + | 2.58880i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.4063 | + | 26.6845i | 0.566729 | + | 0.981603i | 0.996887 | + | 0.0788496i | \(0.0251247\pi\) |
−0.430158 | + | 0.902754i | \(0.641542\pi\) | |||||||
\(740\) | −12.1013 | −0.444851 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.423882 | 0.0155612 | ||||||||
\(743\) | 22.2143 | + | 38.4763i | 0.814964 | + | 1.41156i | 0.909354 | + | 0.416024i | \(0.136577\pi\) |
−0.0943897 | + | 0.995535i | \(0.530090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.33650 | − | 2.31488i | 0.0489654 | − | 0.0848106i | ||||
\(746\) | −4.53107 | − | 7.84805i | −0.165894 | − | 0.287338i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 34.9873 | 1.27926 | ||||||||
\(749\) | 0.0676029 | 0.00247016 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.43935 | + | 12.8853i | −0.271466 | + | 0.470192i | −0.969237 | − | 0.246128i | \(-0.920842\pi\) |
0.697772 | + | 0.716320i | \(0.254175\pi\) | |||||||
\(752\) | −38.8886 | −1.41812 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.999776 | + | 1.73166i | −0.0364097 | + | 0.0630634i | ||||
\(755\) | 2.97633 | + | 5.15516i | 0.108320 | + | 0.187615i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.7204 | − | 20.3004i | −0.425986 | − | 0.737829i | 0.570526 | − | 0.821279i | \(-0.306739\pi\) |
−0.996512 | + | 0.0834503i | \(0.973406\pi\) | |||||||
\(758\) | 3.78414 | + | 6.55432i | 0.137446 | + | 0.238063i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.14341 | + | 4.47451i | −0.0777498 | + | 0.162308i | ||||
\(761\) | −36.3224 | −1.31669 | −0.658344 | − | 0.752717i | \(-0.728743\pi\) | ||||
−0.658344 | + | 0.752717i | \(0.728743\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.82690 | − | 6.62838i | −0.138543 | − | 0.239963i | ||||
\(764\) | −7.81309 | + | 13.5327i | −0.282668 | + | 0.489595i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.310020 | + | 0.536970i | −0.0112015 | + | 0.0194015i | ||||
\(767\) | 31.6620 | 1.14325 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.4052 | + | 18.0223i | −0.375220 | + | 0.649901i | −0.990360 | − | 0.138517i | \(-0.955766\pi\) |
0.615140 | + | 0.788418i | \(0.289100\pi\) | |||||||
\(770\) | 0.378201 | − | 0.655063i | 0.0136294 | − | 0.0236068i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.44573 | 0.231987 | ||||||||
\(773\) | 1.78351 | − | 3.08913i | 0.0641484 | − | 0.111108i | −0.832168 | − | 0.554524i | \(-0.812900\pi\) |
0.896316 | + | 0.443416i | \(0.146234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.41550 | + | 4.18376i | −0.0867671 | + | 0.150285i | ||||
\(776\) | 1.13822 | + | 1.97146i | 0.0408598 | + | 0.0707713i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.79147 | 0.135931 | ||||||||
\(779\) | 4.86108 | − | 10.1478i | 0.174166 | − | 0.363583i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.5484 | + | 45.9832i | 0.949978 | + | 1.64541i | ||||
\(782\) | 3.18345 | + | 5.51390i | 0.113840 | + | 0.197177i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.8361 | + | 20.5007i | 0.422716 | + | 0.732166i | ||||
\(785\) | −3.60424 | + | 6.24273i | −0.128641 | + | 0.222812i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.5660 | 1.58860 | 0.794302 | − | 0.607523i | \(-0.207837\pi\) | ||||
0.794302 | + | 0.607523i | \(0.207837\pi\) | |||||||
\(788\) | −3.67199 | + | 6.36008i | −0.130809 | + | 0.226568i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.36416 | −0.0841129 | ||||||||
\(791\) | 7.20186 | 0.256069 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.7390 | + | 25.5287i | 0.523396 | + | 0.906549i | ||||
\(794\) | −0.00416319 | + | 0.00721085i | −0.000147746 | + | 0.000255904i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1620 | + | 21.0651i | 0.431069 | + | 0.746634i | ||||
\(797\) | 44.7396 | 1.58476 | 0.792378 | − | 0.610030i | \(-0.208843\pi\) | ||||
0.792378 | + | 0.610030i | \(0.208843\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.9496 | −1.34256 | ||||||||
\(800\) | −1.64696 | − | 2.85262i | −0.0582288 | − | 0.100855i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.97080 | + | 6.87762i | −0.140214 | + | 0.242857i | ||||
\(803\) | −29.4463 | − | 51.0026i | −1.03914 | − | 1.79984i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.12010 | −0.109969 | ||||||||
\(806\) | −3.49203 | −0.123002 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.863142 | + | 1.49501i | −0.0303652 | + | 0.0525941i | ||||
\(809\) | −8.67442 | −0.304976 | −0.152488 | − | 0.988305i | \(-0.548729\pi\) | ||||
−0.152488 | + | 0.988305i | \(0.548729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3651 | + | 23.1490i | −0.469312 | + | 0.812872i | −0.999384 | − | 0.0350805i | \(-0.988831\pi\) |
0.530073 | + | 0.847952i | \(0.322165\pi\) | |||||||
\(812\) | 1.28911 | + | 2.23281i | 0.0452390 | + | 0.0783562i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.91046 | − | 8.50517i | −0.172112 | − | 0.298106i | ||||
\(815\) | 7.08781 | + | 12.2765i | 0.248275 | + | 0.430025i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.68252 | − | 9.77507i | 0.163821 | − | 0.341986i | ||||
\(818\) | −1.95906 | −0.0684968 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.47232 | + | 4.28219i | 0.0863373 | + | 0.149541i | ||||
\(821\) | −4.72432 | + | 8.18275i | −0.164880 | + | 0.285580i | −0.936613 | − | 0.350367i | \(-0.886057\pi\) |
0.771733 | + | 0.635947i | \(0.219390\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.73340 | − | 16.8587i | 0.339285 | − | 0.587659i | −0.645014 | − | 0.764171i | \(-0.723148\pi\) |
0.984298 | + | 0.176513i | \(0.0564816\pi\) | |||||||
\(824\) | 10.4202 | 0.363004 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.900527 | + | 1.55976i | −0.0313333 | + | 0.0542709i | ||||
\(827\) | −18.5009 | + | 32.0445i | −0.643340 | + | 1.11430i | 0.341342 | + | 0.939939i | \(0.389118\pi\) |
−0.984682 | + | 0.174358i | \(0.944215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5418 | 0.713448 | 0.356724 | − | 0.934210i | \(-0.383894\pi\) | ||||
0.356724 | + | 0.934210i | \(0.383894\pi\) | |||||||
\(830\) | 0.851897 | − | 1.47553i | 0.0295698 | − | 0.0512164i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.51280 | + | 13.0126i | −0.260459 | + | 0.451129i | ||||
\(833\) | 11.5503 | + | 20.0057i | 0.400194 | + | 0.693156i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.5563 | 0.434530 | ||||||||
\(836\) | 44.5180 | − | 3.42885i | 1.53969 | − | 0.118589i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.83831 | + | 6.64814i | 0.132592 | + | 0.229656i | ||||
\(839\) | −23.8946 | − | 41.3866i | −0.824932 | − | 1.42882i | −0.901972 | − | 0.431795i | \(-0.857880\pi\) |
0.0770401 | − | 0.997028i | \(-0.475453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6739 | + | 18.4878i | 0.368067 | + | 0.637511i | ||||
\(842\) | −5.50719 | + | 9.53873i | −0.189790 | + | 0.328726i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.5394 | 0.603730 | ||||||||
\(845\) | −3.40847 | + | 5.90365i | −0.117255 | + | 0.203092i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.56237 | −0.294206 | ||||||||
\(848\) | −10.4891 | −0.360196 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.496454 | − | 0.859883i | −0.0170282 | − | 0.0294937i | ||||
\(851\) | −20.2553 | + | 35.0833i | −0.694344 | + | 1.20264i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.71632 | − | 9.90096i | −0.195723 | − | 0.339003i | 0.751414 | − | 0.659831i | \(-0.229372\pi\) |
−0.947137 | + | 0.320828i | \(0.896039\pi\) | |||||||
\(854\) | −1.67682 | −0.0573795 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.158141 | 0.00540513 | ||||||||
\(857\) | 2.78522 | + | 4.82414i | 0.0951412 | + | 0.164789i | 0.909668 | − | 0.415337i | \(-0.136336\pi\) |
−0.814526 | + | 0.580127i | \(0.803003\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.50709 | − | 14.7347i | 0.290258 | − | 0.502742i | −0.683612 | − | 0.729845i | \(-0.739592\pi\) |
0.973871 | + | 0.227103i | \(0.0729255\pi\) | |||||||
\(860\) | 2.38151 | + | 4.12490i | 0.0812088 | + | 0.140658i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.58304 | 0.190159 | ||||||||
\(863\) | −46.8850 | −1.59598 | −0.797992 | − | 0.602668i | \(-0.794104\pi\) | ||||
−0.797992 | + | 0.602668i | \(0.794104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09482 | + | 1.89628i | −0.0372250 | + | 0.0644756i | ||||
\(866\) | 4.92768 | 0.167449 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.25132 | + | 3.89939i | −0.0764147 | + | 0.132354i | ||||
\(869\) | 21.7454 | + | 37.6642i | 0.737662 | + | 1.27767i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.8674 | − | 32.6793i | −0.639297 | − | 1.10730i | ||||
\(872\) | −8.95210 | − | 15.5055i | −0.303156 | − | 0.525082i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.59101 | + | 6.70391i | 0.155293 | + | 0.226763i | ||||
\(875\) | 0.486575 | 0.0164492 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.8922 | + | 25.7940i | 0.502873 | + | 0.871002i | 0.999994 | + | 0.00332078i | \(0.00105704\pi\) |
−0.497121 | + | 0.867681i | \(0.665610\pi\) | |||||||
\(878\) | −1.61379 | + | 2.79516i | −0.0544626 | + | 0.0943321i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.35867 | + | 16.2097i | −0.315481 | + | 0.546428i | ||||
\(881\) | 20.4884 | 0.690271 | 0.345135 | − | 0.938553i | \(-0.387833\pi\) | ||||
0.345135 | + | 0.938553i | \(0.387833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7402 | + | 27.2628i | −0.529699 | + | 0.917466i | 0.469701 | + | 0.882826i | \(0.344362\pi\) |
−0.999400 | + | 0.0346401i | \(0.988972\pi\) | |||||||
\(884\) | −8.13430 | + | 14.0890i | −0.273586 | + | 0.473865i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.03900 | 0.135693 | ||||||||
\(887\) | −16.8051 | + | 29.1074i | −0.564262 | + | 0.977330i | 0.432856 | + | 0.901463i | \(0.357506\pi\) |
−0.997118 | + | 0.0758670i | \(0.975828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.39175 | + | 4.14264i | −0.0802169 | + | 0.138940i | ||||
\(890\) | 0.946281 | + | 1.63901i | 0.0317194 | + | 0.0549397i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.8742 | −0.698919 | ||||||||
\(893\) | −48.2872 | + | 3.71916i | −1.61587 | + | 0.124457i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.75210 | − | 6.49883i | −0.125419 | − | 0.217232i | ||||
\(896\) | −2.03009 | − | 3.51623i | −0.0678207 | − | 0.117469i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.05050 | + | 7.01567i | 0.135167 | + | 0.234116i | ||||
\(899\) | 6.68185 | − | 11.5733i | 0.222852 | − | 0.385991i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2358 | −0.341004 | ||||||||
\(902\) | −2.00644 | + | 3.47526i | −0.0668073 | + | 0.115714i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.8470 | 0.560323 | ||||||||
\(905\) | 12.6652 | 0.421006 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.9747 | − | 19.0088i | −0.364410 | − | 0.631176i | 0.624272 | − | 0.781207i | \(-0.285396\pi\) |
−0.988681 | + | 0.150031i | \(0.952063\pi\) | |||||||
\(908\) | 23.5942 | − | 40.8664i | 0.783002 | − | 1.35620i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.175858 | + | 0.304595i | 0.00582963 | + | 0.0100972i | ||||
\(911\) | −21.2865 | −0.705253 | −0.352626 | − | 0.935764i | \(-0.614711\pi\) | ||||
−0.352626 | + | 0.935764i | \(0.614711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.3428 | −1.03730 | ||||||||
\(914\) | 5.31481 | + | 9.20552i | 0.175798 | + | 0.304492i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.4422 | − | 28.4788i | 0.543267 | − | 0.940966i | ||||
\(917\) | −3.46178 | − | 5.99598i | −0.114318 | − | 0.198005i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.61948 | −0.0864087 | −0.0432043 | − | 0.999066i | \(-0.513757\pi\) | ||||
−0.0432043 | + | 0.999066i | \(0.513757\pi\) | |||||||
\(920\) | −7.29873 | −0.240632 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.18575 | − | 5.51789i | 0.104917 | − | 0.181722i | ||||
\(923\) | −24.6893 | −0.812658 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.15878 | − | 5.47117i | 0.103860 | − | 0.179891i | ||||
\(926\) | 2.03859 | + | 3.53094i | 0.0669921 | + | 0.116034i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.55589 | + | 7.89104i | 0.149554 | + | 0.259036i | ||||
\(929\) | 1.91237 | + | 3.31232i | 0.0627428 | + | 0.108674i | 0.895691 | − | 0.444678i | \(-0.146682\pi\) |
−0.832948 | + | 0.553352i | \(0.813349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.6572 | + | 24.3233i | 0.545919 | + | 0.797165i | ||||
\(932\) | 54.5210 | 1.78589 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.93160 | + | 8.54177i | 0.161367 | + | 0.279495i | ||||
\(935\) | −9.13272 | + | 15.8183i | −0.298672 | + | 0.517315i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.69584 | − | 6.40138i | 0.120738 | − | 0.209124i | −0.799321 | − | 0.600904i | \(-0.794807\pi\) |
0.920059 | + | 0.391780i | \(0.128141\pi\) | |||||||
\(938\) | 2.14650 | 0.0700856 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.6412 | − | 18.4311i | 0.347078 | − | 0.601157i | ||||
\(941\) | 24.3057 | − | 42.0988i | 0.792344 | − | 1.37238i | −0.132168 | − | 0.991227i | \(-0.542194\pi\) |
0.924512 | − | 0.381153i | \(-0.124473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.5529 | 0.539036 | ||||||||
\(944\) | 22.2838 | − | 38.5966i | 0.725275 | − | 1.25621i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.93274 | + | 3.34761i | −0.0628389 | + | 0.108840i | ||||
\(947\) | −18.0103 | − | 31.1948i | −0.585257 | − | 1.01370i | −0.994843 | − | 0.101424i | \(-0.967660\pi\) |
0.409586 | − | 0.912271i | \(-0.365673\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.3843 | 0.888930 | ||||||||
\(950\) | −0.715960 | − | 1.04546i | −0.0232288 | − | 0.0339193i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.945834 | − | 1.63823i | −0.0306546 | − | 0.0530954i | ||||
\(953\) | 5.60605 | + | 9.70996i | 0.181598 | + | 0.314537i | 0.942425 | − | 0.334418i | \(-0.108540\pi\) |
−0.760827 | + | 0.648955i | \(0.775206\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.07889 | − | 7.06484i | −0.131990 | − | 0.228613i | ||||
\(956\) | −3.90513 | + | 6.76389i | −0.126301 | + | 0.218760i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.28769 | −0.300072 | ||||||||
\(959\) | −1.60190 | + | 2.77457i | −0.0517280 | + | 0.0895955i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.66153 | −0.247146 | ||||||||
\(962\) | 4.56659 | 0.147233 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.1332 | − | 21.0152i | −0.390783 | − | 0.676855i | ||||
\(965\) | −1.68252 | + | 2.91422i | −0.0541623 | + | 0.0938119i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.02307 | + | 8.70021i | 0.161531 | + | 0.279780i | 0.935418 | − | 0.353544i | \(-0.115023\pi\) |
−0.773887 | + | 0.633324i | \(0.781690\pi\) | |||||||
\(968\) | −20.0296 | −0.643775 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.581394 | −0.0186674 | ||||||||
\(971\) | −18.9495 | − | 32.8214i | −0.608117 | − | 1.05329i | −0.991551 | − | 0.129721i | \(-0.958592\pi\) |
0.383434 | − | 0.923568i | \(-0.374742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0568699 | − | 0.0985016i | 0.00182317 | − | 0.00315782i | ||||
\(974\) | −5.46844 | − | 9.47161i | −0.175220 | − | 0.303490i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41.4933 | 1.32817 | ||||||||
\(977\) | −44.6435 | −1.42827 | −0.714135 | − | 0.700008i | \(-0.753180\pi\) | ||||
−0.714135 | + | 0.700008i | \(0.753180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.4077 | − | 30.1510i | 0.556353 | − | 0.963631i | ||||
\(980\) | −12.9550 | −0.413831 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.82618 | + | 10.0912i | −0.185921 | + | 0.322025i | ||||
\(983\) | −6.25454 | − | 10.8332i | −0.199489 | − | 0.345525i | 0.748874 | − | 0.662712i | \(-0.230595\pi\) |
−0.948363 | + | 0.317188i | \(0.897262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.91699 | − | 3.32033i | −0.0610805 | − | 0.105795i | ||||
\(986\) | 1.37331 | + | 2.37865i | 0.0437352 | + | 0.0757515i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.96935 | + | 18.7241i | −0.285353 | + | 0.595693i | ||||
\(989\) | 15.9449 | 0.507017 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.1503 | − | 43.5617i | −0.798927 | − | 1.38378i | −0.920315 | − | 0.391177i | \(-0.872068\pi\) |
0.121388 | − | 0.992605i | \(-0.461265\pi\) | |||||||
\(992\) | −7.95645 | + | 13.7810i | −0.252617 | + | 0.437546i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.702210 | − | 1.21626i | 0.0222728 | − | 0.0385775i | ||||
\(995\) | −12.6985 | −0.402569 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.46875 | + | 11.2042i | −0.204867 | + | 0.354841i | −0.950090 | − | 0.311975i | \(-0.899010\pi\) |
0.745223 | + | 0.666815i | \(0.232343\pi\) | |||||||
\(998\) | 4.40504 | − | 7.62975i | 0.139439 | − | 0.241515i | ||||
\(999\) | 0 | 0 |
(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 | 855.2.k.i.406.3 | 10 | ||
3.2 | odd | 2 | 285.2.i.f.121.3 | yes | 10 | ||
19.11 | even | 3 | inner | 855.2.k.i.676.3 | 10 | ||
57.11 | odd | 6 | 285.2.i.f.106.3 | ✓ | 10 | ||
57.26 | odd | 6 | 5415.2.a.y.1.3 | 5 | |||
57.50 | even | 6 | 5415.2.a.z.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.i.f.106.3 | ✓ | 10 | 57.11 | odd | 6 | ||
285.2.i.f.121.3 | yes | 10 | 3.2 | odd | 2 | ||
855.2.k.i.406.3 | 10 | 1.1 | even | 1 | trivial | ||
855.2.k.i.676.3 | 10 | 19.11 | even | 3 | inner | ||
5415.2.a.y.1.3 | 5 | 57.26 | odd | 6 | |||
5415.2.a.z.1.3 | 5 | 57.50 | even | 6 |