Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5415,2,Mod(1,5415)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5415, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5415.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5415 = 3 \cdot 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5415.a (trivial) |
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: | yes |
Analytic conductor: | \(43.2389926945\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.8797896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - x^{4} - 8x^{3} + 5x^{2} + 13x - 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 285) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.290697\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5415.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.290697 | 0.205554 | 0.102777 | − | 0.994704i | \(-0.467227\pi\) | ||||
0.102777 | + | 0.994704i | \(0.467227\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.91550 | −0.957748 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.290697 | 0.118677 | ||||||||
\(7\) | −0.486575 | −0.183908 | −0.0919539 | − | 0.995763i | \(-0.529311\pi\) | ||||
−0.0919539 | + | 0.995763i | \(0.529311\pi\) | |||||||
\(8\) | −1.13822 | −0.402423 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.290697 | 0.0919265 | ||||||||
\(11\) | 5.34764 | 1.61237 | 0.806187 | − | 0.591661i | \(-0.201528\pi\) | ||||
0.806187 | + | 0.591661i | \(0.201528\pi\) | |||||||
\(12\) | −1.91550 | −0.552956 | ||||||||
\(13\) | 2.48657 | 0.689652 | 0.344826 | − | 0.938667i | \(-0.387938\pi\) | ||||
0.344826 | + | 0.938667i | \(0.387938\pi\) | |||||||
\(14\) | −0.141446 | −0.0378030 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 3.50011 | 0.875028 | ||||||||
\(17\) | −3.41561 | −0.828406 | −0.414203 | − | 0.910184i | \(-0.635940\pi\) | ||||
−0.414203 | + | 0.910184i | \(0.635940\pi\) | |||||||
\(18\) | 0.290697 | 0.0685180 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.91550 | −0.428318 | ||||||||
\(21\) | −0.486575 | −0.106179 | ||||||||
\(22\) | 1.55454 | 0.331430 | ||||||||
\(23\) | 6.41238 | 1.33707 | 0.668537 | − | 0.743679i | \(-0.266921\pi\) | ||||
0.668537 | + | 0.743679i | \(0.266921\pi\) | |||||||
\(24\) | −1.13822 | −0.232339 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.722840 | 0.141761 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.932031 | 0.176137 | ||||||||
\(29\) | −2.76624 | −0.513679 | −0.256839 | − | 0.966454i | \(-0.582681\pi\) | ||||
−0.256839 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(30\) | 0.290697 | 0.0530738 | ||||||||
\(31\) | −4.83099 | −0.867671 | −0.433836 | − | 0.900992i | \(-0.642840\pi\) | ||||
−0.433836 | + | 0.900992i | \(0.642840\pi\) | |||||||
\(32\) | 3.29392 | 0.582288 | ||||||||
\(33\) | 5.34764 | 0.930904 | ||||||||
\(34\) | −0.992907 | −0.170282 | ||||||||
\(35\) | −0.486575 | −0.0822461 | ||||||||
\(36\) | −1.91550 | −0.319249 | ||||||||
\(37\) | 6.31756 | 1.03860 | 0.519301 | − | 0.854592i | \(-0.326192\pi\) | ||||
0.519301 | + | 0.854592i | \(0.326192\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.48657 | 0.398171 | ||||||||
\(40\) | −1.13822 | −0.179969 | ||||||||
\(41\) | −2.58139 | −0.403146 | −0.201573 | − | 0.979473i | \(-0.564605\pi\) | ||||
−0.201573 | + | 0.979473i | \(0.564605\pi\) | |||||||
\(42\) | −0.141446 | −0.0218256 | ||||||||
\(43\) | −2.48657 | −0.379199 | −0.189600 | − | 0.981862i | \(-0.560719\pi\) | ||||
−0.189600 | + | 0.981862i | \(0.560719\pi\) | |||||||
\(44\) | −10.2434 | −1.54425 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.86406 | 0.274841 | ||||||||
\(47\) | 11.1107 | 1.62066 | 0.810328 | − | 0.585976i | \(-0.199289\pi\) | ||||
0.810328 | + | 0.585976i | \(0.199289\pi\) | |||||||
\(48\) | 3.50011 | 0.505198 | ||||||||
\(49\) | −6.76325 | −0.966178 | ||||||||
\(50\) | 0.290697 | 0.0411108 | ||||||||
\(51\) | −3.41561 | −0.478281 | ||||||||
\(52\) | −4.76302 | −0.660512 | ||||||||
\(53\) | −2.99678 | −0.411639 | −0.205820 | − | 0.978590i | \(-0.565986\pi\) | ||||
−0.205820 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(54\) | 0.290697 | 0.0395589 | ||||||||
\(55\) | 5.34764 | 0.721075 | ||||||||
\(56\) | 0.553831 | 0.0740087 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.804139 | −0.105589 | ||||||||
\(59\) | −12.7332 | −1.65772 | −0.828859 | − | 0.559458i | \(-0.811009\pi\) | ||||
−0.828859 | + | 0.559458i | \(0.811009\pi\) | |||||||
\(60\) | −1.91550 | −0.247289 | ||||||||
\(61\) | 11.8548 | 1.51786 | 0.758929 | − | 0.651174i | \(-0.225723\pi\) | ||||
0.758929 | + | 0.651174i | \(0.225723\pi\) | |||||||
\(62\) | −1.40436 | −0.178353 | ||||||||
\(63\) | −0.486575 | −0.0613026 | ||||||||
\(64\) | −6.04269 | −0.755336 | ||||||||
\(65\) | 2.48657 | 0.308422 | ||||||||
\(66\) | 1.55454 | 0.191351 | ||||||||
\(67\) | 15.1754 | 1.85397 | 0.926985 | − | 0.375097i | \(-0.122391\pi\) | ||||
0.926985 | + | 0.375097i | \(0.122391\pi\) | |||||||
\(68\) | 6.54258 | 0.793404 | ||||||||
\(69\) | 6.41238 | 0.771960 | ||||||||
\(70\) | −0.141446 | −0.0169060 | ||||||||
\(71\) | 9.92903 | 1.17836 | 0.589180 | − | 0.808002i | \(-0.299451\pi\) | ||||
0.589180 | + | 0.808002i | \(0.299451\pi\) | |||||||
\(72\) | −1.13822 | −0.134141 | ||||||||
\(73\) | −11.0128 | −1.28896 | −0.644478 | − | 0.764623i | \(-0.722925\pi\) | ||||
−0.644478 | + | 0.764623i | \(0.722925\pi\) | |||||||
\(74\) | 1.83650 | 0.213489 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.60202 | −0.296528 | ||||||||
\(78\) | 0.722840 | 0.0818455 | ||||||||
\(79\) | −8.13272 | −0.915002 | −0.457501 | − | 0.889209i | \(-0.651255\pi\) | ||||
−0.457501 | + | 0.889209i | \(0.651255\pi\) | |||||||
\(80\) | 3.50011 | 0.391324 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.750404 | −0.0828683 | ||||||||
\(83\) | −5.86106 | −0.643335 | −0.321668 | − | 0.946853i | \(-0.604243\pi\) | ||||
−0.321668 | + | 0.946853i | \(0.604243\pi\) | |||||||
\(84\) | 0.932031 | 0.101693 | ||||||||
\(85\) | −3.41561 | −0.370475 | ||||||||
\(86\) | −0.722840 | −0.0779459 | ||||||||
\(87\) | −2.76624 | −0.296572 | ||||||||
\(88\) | −6.08681 | −0.648856 | ||||||||
\(89\) | 6.51043 | 0.690104 | 0.345052 | − | 0.938584i | \(-0.387861\pi\) | ||||
0.345052 | + | 0.938584i | \(0.387861\pi\) | |||||||
\(90\) | 0.290697 | 0.0306422 | ||||||||
\(91\) | −1.20990 | −0.126832 | ||||||||
\(92\) | −12.2829 | −1.28058 | ||||||||
\(93\) | −4.83099 | −0.500950 | ||||||||
\(94\) | 3.22984 | 0.333132 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.29392 | 0.336184 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −1.96606 | −0.198602 | ||||||||
\(99\) | 5.34764 | 0.537458 | ||||||||
\(100\) | −1.91550 | −0.191550 | ||||||||
\(101\) | 1.51665 | 0.150912 | 0.0754561 | − | 0.997149i | \(-0.475959\pi\) | ||||
0.0754561 | + | 0.997149i | \(0.475959\pi\) | |||||||
\(102\) | −0.992907 | −0.0983125 | ||||||||
\(103\) | 9.15478 | 0.902047 | 0.451023 | − | 0.892512i | \(-0.351059\pi\) | ||||
0.451023 | + | 0.892512i | \(0.351059\pi\) | |||||||
\(104\) | −2.83028 | −0.277532 | ||||||||
\(105\) | −0.486575 | −0.0474848 | ||||||||
\(106\) | −0.871155 | −0.0846140 | ||||||||
\(107\) | −0.138936 | −0.0134315 | −0.00671574 | − | 0.999977i | \(-0.502138\pi\) | ||||
−0.00671574 | + | 0.999977i | \(0.502138\pi\) | |||||||
\(108\) | −1.91550 | −0.184319 | ||||||||
\(109\) | 15.7299 | 1.50666 | 0.753328 | − | 0.657645i | \(-0.228447\pi\) | ||||
0.753328 | + | 0.657645i | \(0.228447\pi\) | |||||||
\(110\) | 1.55454 | 0.148220 | ||||||||
\(111\) | 6.31756 | 0.599637 | ||||||||
\(112\) | −1.70307 | −0.160925 | ||||||||
\(113\) | −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 | ||||||||
\(116\) | 5.29873 | 0.491974 | ||||||||
\(117\) | 2.48657 | 0.229884 | ||||||||
\(118\) | −3.70150 | −0.340750 | ||||||||
\(119\) | 1.66195 | 0.152350 | ||||||||
\(120\) | −1.13822 | −0.103905 | ||||||||
\(121\) | 17.5972 | 1.59975 | ||||||||
\(122\) | 3.44617 | 0.312002 | ||||||||
\(123\) | −2.58139 | −0.232756 | ||||||||
\(124\) | 9.25374 | 0.831010 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.141446 | −0.0126010 | ||||||||
\(127\) | 9.83099 | 0.872359 | 0.436180 | − | 0.899860i | \(-0.356331\pi\) | ||||
0.436180 | + | 0.899860i | \(0.356331\pi\) | |||||||
\(128\) | −8.34443 | −0.737551 | ||||||||
\(129\) | −2.48657 | −0.218931 | ||||||||
\(130\) | 0.722840 | 0.0633973 | ||||||||
\(131\) | 14.2292 | 1.24321 | 0.621605 | − | 0.783331i | \(-0.286481\pi\) | ||||
0.621605 | + | 0.783331i | \(0.286481\pi\) | |||||||
\(132\) | −10.2434 | −0.891571 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.41145 | 0.381091 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 3.88772 | 0.333370 | ||||||||
\(137\) | 6.58439 | 0.562543 | 0.281271 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281271 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(138\) | 1.86406 | 0.158680 | ||||||||
\(139\) | 0.233756 | 0.0198269 | 0.00991347 | − | 0.999951i | \(-0.496844\pi\) | ||||
0.00991347 | + | 0.999951i | \(0.496844\pi\) | |||||||
\(140\) | 0.932031 | 0.0787710 | ||||||||
\(141\) | 11.1107 | 0.935686 | ||||||||
\(142\) | 2.88634 | 0.242216 | ||||||||
\(143\) | 13.2973 | 1.11198 | ||||||||
\(144\) | 3.50011 | 0.291676 | ||||||||
\(145\) | −2.76624 | −0.229724 | ||||||||
\(146\) | −3.20140 | −0.264950 | ||||||||
\(147\) | −6.76325 | −0.557823 | ||||||||
\(148\) | −12.1013 | −0.994718 | ||||||||
\(149\) | −2.67299 | −0.218980 | −0.109490 | − | 0.993988i | \(-0.534922\pi\) | ||||
−0.109490 | + | 0.993988i | \(0.534922\pi\) | |||||||
\(150\) | 0.290697 | 0.0237353 | ||||||||
\(151\) | −5.95266 | −0.484421 | −0.242210 | − | 0.970224i | \(-0.577872\pi\) | ||||
−0.242210 | + | 0.970224i | \(0.577872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.41561 | −0.276135 | ||||||||
\(154\) | −0.756401 | −0.0609525 | ||||||||
\(155\) | −4.83099 | −0.388034 | ||||||||
\(156\) | −4.76302 | −0.381347 | ||||||||
\(157\) | −7.20848 | −0.575299 | −0.287650 | − | 0.957736i | \(-0.592874\pi\) | ||||
−0.287650 | + | 0.957736i | \(0.592874\pi\) | |||||||
\(158\) | −2.36416 | −0.188082 | ||||||||
\(159\) | −2.99678 | −0.237660 | ||||||||
\(160\) | 3.29392 | 0.260407 | ||||||||
\(161\) | −3.12010 | −0.245899 | ||||||||
\(162\) | 0.290697 | 0.0228393 | ||||||||
\(163\) | 14.1756 | 1.11032 | 0.555161 | − | 0.831743i | \(-0.312657\pi\) | ||||
0.555161 | + | 0.831743i | \(0.312657\pi\) | |||||||
\(164\) | 4.94465 | 0.386112 | ||||||||
\(165\) | 5.34764 | 0.416313 | ||||||||
\(166\) | −1.70379 | −0.132240 | ||||||||
\(167\) | −12.5563 | −0.971639 | −0.485819 | − | 0.874059i | \(-0.661479\pi\) | ||||
−0.485819 | + | 0.874059i | \(0.661479\pi\) | |||||||
\(168\) | 0.553831 | 0.0427290 | ||||||||
\(169\) | −6.81695 | −0.524381 | ||||||||
\(170\) | −0.992907 | −0.0761525 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.76302 | 0.363177 | ||||||||
\(173\) | −2.18964 | −0.166475 | −0.0832376 | − | 0.996530i | \(-0.526526\pi\) | ||||
−0.0832376 | + | 0.996530i | \(0.526526\pi\) | |||||||
\(174\) | −0.804139 | −0.0609616 | ||||||||
\(175\) | −0.486575 | −0.0367816 | ||||||||
\(176\) | 18.7173 | 1.41087 | ||||||||
\(177\) | −12.7332 | −0.957084 | ||||||||
\(178\) | 1.89256 | 0.141854 | ||||||||
\(179\) | −7.50421 | −0.560891 | −0.280445 | − | 0.959870i | \(-0.590482\pi\) | ||||
−0.280445 | + | 0.959870i | \(0.590482\pi\) | |||||||
\(180\) | −1.91550 | −0.142773 | ||||||||
\(181\) | 12.6652 | 0.941397 | 0.470699 | − | 0.882294i | \(-0.344002\pi\) | ||||
0.470699 | + | 0.882294i | \(0.344002\pi\) | |||||||
\(182\) | −0.351716 | −0.0260709 | ||||||||
\(183\) | 11.8548 | 0.876335 | ||||||||
\(184\) | −7.29873 | −0.538069 | ||||||||
\(185\) | 6.31756 | 0.464477 | ||||||||
\(186\) | −1.40436 | −0.102972 | ||||||||
\(187\) | −18.2654 | −1.33570 | ||||||||
\(188\) | −21.2824 | −1.55218 | ||||||||
\(189\) | −0.486575 | −0.0353931 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.15777 | 0.590276 | 0.295138 | − | 0.955455i | \(-0.404634\pi\) | ||||
0.295138 | + | 0.955455i | \(0.404634\pi\) | |||||||
\(192\) | −6.04269 | −0.436094 | ||||||||
\(193\) | 3.36505 | 0.242221 | 0.121111 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121111 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(194\) | −0.581394 | −0.0417417 | ||||||||
\(195\) | 2.48657 | 0.178067 | ||||||||
\(196\) | 12.9550 | 0.925355 | ||||||||
\(197\) | 3.83399 | 0.273160 | 0.136580 | − | 0.990629i | \(-0.456389\pi\) | ||||
0.136580 | + | 0.990629i | \(0.456389\pi\) | |||||||
\(198\) | 1.55454 | 0.110477 | ||||||||
\(199\) | 12.6985 | 0.900173 | 0.450086 | − | 0.892985i | \(-0.351393\pi\) | ||||
0.450086 | + | 0.892985i | \(0.351393\pi\) | |||||||
\(200\) | −1.13822 | −0.0804846 | ||||||||
\(201\) | 15.1754 | 1.07039 | ||||||||
\(202\) | 0.440885 | 0.0310206 | ||||||||
\(203\) | 1.34598 | 0.0944695 | ||||||||
\(204\) | 6.54258 | 0.458072 | ||||||||
\(205\) | −2.58139 | −0.180292 | ||||||||
\(206\) | 2.66127 | 0.185419 | ||||||||
\(207\) | 6.41238 | 0.445692 | ||||||||
\(208\) | 8.70329 | 0.603465 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.141446 | −0.00976069 | ||||||||
\(211\) | 9.15657 | 0.630364 | 0.315182 | − | 0.949031i | \(-0.397934\pi\) | ||||
0.315182 | + | 0.949031i | \(0.397934\pi\) | |||||||
\(212\) | 5.74031 | 0.394246 | ||||||||
\(213\) | 9.92903 | 0.680326 | ||||||||
\(214\) | −0.0403884 | −0.00276089 | ||||||||
\(215\) | −2.48657 | −0.169583 | ||||||||
\(216\) | −1.13822 | −0.0774463 | ||||||||
\(217\) | 2.35064 | 0.159572 | ||||||||
\(218\) | 4.57265 | 0.309699 | ||||||||
\(219\) | −11.0128 | −0.744179 | ||||||||
\(220\) | −10.2434 | −0.690608 | ||||||||
\(221\) | −8.49316 | −0.571312 | ||||||||
\(222\) | 1.83650 | 0.123258 | ||||||||
\(223\) | −10.8975 | −0.729753 | −0.364876 | − | 0.931056i | \(-0.618889\pi\) | ||||
−0.364876 | + | 0.931056i | \(0.618889\pi\) | |||||||
\(224\) | −1.60274 | −0.107087 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −4.30265 | −0.286208 | ||||||||
\(227\) | 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 | \(0.308013\pi\) | |||||||
\(230\) | 1.86406 | 0.122913 | ||||||||
\(231\) | −2.60202 | −0.171201 | ||||||||
\(232\) | 3.14860 | 0.206716 | ||||||||
\(233\) | 28.4631 | 1.86468 | 0.932341 | − | 0.361581i | \(-0.117763\pi\) | ||||
0.932341 | + | 0.361581i | \(0.117763\pi\) | |||||||
\(234\) | 0.722840 | 0.0472535 | ||||||||
\(235\) | 11.1107 | 0.724780 | ||||||||
\(236\) | 24.3903 | 1.58768 | ||||||||
\(237\) | −8.13272 | −0.528277 | ||||||||
\(238\) | 0.483123 | 0.0313162 | ||||||||
\(239\) | 4.07741 | 0.263746 | 0.131873 | − | 0.991267i | \(-0.457901\pi\) | ||||
0.131873 | + | 0.991267i | \(0.457901\pi\) | |||||||
\(240\) | 3.50011 | 0.225931 | ||||||||
\(241\) | 12.6684 | 0.816045 | 0.408023 | − | 0.912972i | \(-0.366218\pi\) | ||||
0.408023 | + | 0.912972i | \(0.366218\pi\) | |||||||
\(242\) | 5.11547 | 0.328835 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −22.7079 | −1.45372 | ||||||||
\(245\) | −6.76325 | −0.432088 | ||||||||
\(246\) | −0.750404 | −0.0478440 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.49875 | 0.349171 | ||||||||
\(249\) | −5.86106 | −0.371430 | ||||||||
\(250\) | 0.290697 | 0.0183853 | ||||||||
\(251\) | −11.6241 | −0.733706 | −0.366853 | − | 0.930279i | \(-0.619565\pi\) | ||||
−0.366853 | + | 0.930279i | \(0.619565\pi\) | |||||||
\(252\) | 0.932031 | 0.0587124 | ||||||||
\(253\) | 34.2911 | 2.15586 | ||||||||
\(254\) | 2.85784 | 0.179317 | ||||||||
\(255\) | −3.41561 | −0.213894 | ||||||||
\(256\) | 9.65968 | 0.603730 | ||||||||
\(257\) | −10.5483 | −0.657986 | −0.328993 | − | 0.944332i | \(-0.606709\pi\) | ||||
−0.328993 | + | 0.944332i | \(0.606709\pi\) | |||||||
\(258\) | −0.722840 | −0.0450021 | ||||||||
\(259\) | −3.07397 | −0.191007 | ||||||||
\(260\) | −4.76302 | −0.295390 | ||||||||
\(261\) | −2.76624 | −0.171226 | ||||||||
\(262\) | 4.13639 | 0.255547 | ||||||||
\(263\) | 23.7935 | 1.46717 | 0.733585 | − | 0.679598i | \(-0.237846\pi\) | ||||
0.733585 | + | 0.679598i | \(0.237846\pi\) | |||||||
\(264\) | −6.08681 | −0.374617 | ||||||||
\(265\) | −2.99678 | −0.184091 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.51043 | 0.398432 | ||||||||
\(268\) | −29.0684 | −1.77564 | ||||||||
\(269\) | 4.22754 | 0.257757 | 0.128879 | − | 0.991660i | \(-0.458862\pi\) | ||||
0.128879 | + | 0.991660i | \(0.458862\pi\) | |||||||
\(270\) | 0.290697 | 0.0176913 | ||||||||
\(271\) | 31.1471 | 1.89205 | 0.946027 | − | 0.324089i | \(-0.105058\pi\) | ||||
0.946027 | + | 0.324089i | \(0.105058\pi\) | |||||||
\(272\) | −11.9550 | −0.724879 | ||||||||
\(273\) | −1.20990 | −0.0732267 | ||||||||
\(274\) | 1.91406 | 0.115633 | ||||||||
\(275\) | 5.34764 | 0.322475 | ||||||||
\(276\) | −12.2829 | −0.739343 | ||||||||
\(277\) | 1.05393 | 0.0633243 | 0.0316621 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316621 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(278\) | 0.0679523 | 0.00407551 | ||||||||
\(279\) | −4.83099 | −0.289224 | ||||||||
\(280\) | 0.553831 | 0.0330977 | ||||||||
\(281\) | −25.6354 | −1.52928 | −0.764638 | − | 0.644459i | \(-0.777082\pi\) | ||||
−0.764638 | + | 0.644459i | \(0.777082\pi\) | |||||||
\(282\) | 3.22984 | 0.192334 | ||||||||
\(283\) | 29.4112 | 1.74831 | 0.874157 | − | 0.485644i | \(-0.161415\pi\) | ||||
0.874157 | + | 0.485644i | \(0.161415\pi\) | |||||||
\(284\) | −19.0190 | −1.12857 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.86549 | 0.228571 | ||||||||
\(287\) | 1.25604 | 0.0741417 | ||||||||
\(288\) | 3.29392 | 0.194096 | ||||||||
\(289\) | −5.33363 | −0.313743 | ||||||||
\(290\) | −0.804139 | −0.0472207 | ||||||||
\(291\) | −2.00000 | −0.117242 | ||||||||
\(292\) | 21.0950 | 1.23449 | ||||||||
\(293\) | 10.8548 | 0.634147 | 0.317073 | − | 0.948401i | \(-0.397300\pi\) | ||||
0.317073 | + | 0.948401i | \(0.397300\pi\) | |||||||
\(294\) | −1.96606 | −0.114663 | ||||||||
\(295\) | −12.7332 | −0.741354 | ||||||||
\(296\) | −7.19080 | −0.417957 | ||||||||
\(297\) | 5.34764 | 0.310301 | ||||||||
\(298\) | −0.777031 | −0.0450122 | ||||||||
\(299\) | 15.9449 | 0.922116 | ||||||||
\(300\) | −1.91550 | −0.110591 | ||||||||
\(301\) | 1.20990 | 0.0697377 | ||||||||
\(302\) | −1.73042 | −0.0995746 | ||||||||
\(303\) | 1.51665 | 0.0871291 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.8548 | 0.678806 | ||||||||
\(306\) | −0.992907 | −0.0567607 | ||||||||
\(307\) | −33.6891 | −1.92274 | −0.961368 | − | 0.275266i | \(-0.911234\pi\) | ||||
−0.961368 | + | 0.275266i | \(0.911234\pi\) | |||||||
\(308\) | 4.98417 | 0.283999 | ||||||||
\(309\) | 9.15478 | 0.520797 | ||||||||
\(310\) | −1.40436 | −0.0797620 | ||||||||
\(311\) | −11.7221 | −0.664701 | −0.332350 | − | 0.943156i | \(-0.607842\pi\) | ||||
−0.332350 | + | 0.943156i | \(0.607842\pi\) | |||||||
\(312\) | −2.83028 | −0.160233 | ||||||||
\(313\) | 4.47856 | 0.253143 | 0.126572 | − | 0.991957i | \(-0.459603\pi\) | ||||
0.126572 | + | 0.991957i | \(0.459603\pi\) | |||||||
\(314\) | −2.09548 | −0.118255 | ||||||||
\(315\) | −0.486575 | −0.0274154 | ||||||||
\(316\) | 15.5782 | 0.876341 | ||||||||
\(317\) | −12.3873 | −0.695742 | −0.347871 | − | 0.937542i | \(-0.613095\pi\) | ||||
−0.347871 | + | 0.937542i | \(0.613095\pi\) | |||||||
\(318\) | −0.871155 | −0.0488519 | ||||||||
\(319\) | −14.7929 | −0.828242 | ||||||||
\(320\) | −6.04269 | −0.337797 | ||||||||
\(321\) | −0.138936 | −0.00775467 | ||||||||
\(322\) | −0.907005 | −0.0505454 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.91550 | −0.106416 | ||||||||
\(325\) | 2.48657 | 0.137930 | ||||||||
\(326\) | 4.12082 | 0.228231 | ||||||||
\(327\) | 15.7299 | 0.869868 | ||||||||
\(328\) | 2.93820 | 0.162235 | ||||||||
\(329\) | −5.40616 | −0.298051 | ||||||||
\(330\) | 1.55454 | 0.0855748 | ||||||||
\(331\) | −24.5058 | −1.34696 | −0.673480 | − | 0.739206i | \(-0.735201\pi\) | ||||
−0.673480 | + | 0.739206i | \(0.735201\pi\) | |||||||
\(332\) | 11.2268 | 0.616153 | ||||||||
\(333\) | 6.31756 | 0.346200 | ||||||||
\(334\) | −3.65009 | −0.199724 | ||||||||
\(335\) | 15.1754 | 0.829121 | ||||||||
\(336\) | −1.70307 | −0.0929098 | ||||||||
\(337\) | −10.5008 | −0.572013 | −0.286006 | − | 0.958228i | \(-0.592328\pi\) | ||||
−0.286006 | + | 0.958228i | \(0.592328\pi\) | |||||||
\(338\) | −1.98167 | −0.107788 | ||||||||
\(339\) | −14.8011 | −0.803888 | ||||||||
\(340\) | 6.54258 | 0.354821 | ||||||||
\(341\) | −25.8344 | −1.39901 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.69684 | 0.361596 | ||||||||
\(344\) | 2.83028 | 0.152598 | ||||||||
\(345\) | 6.41238 | 0.345231 | ||||||||
\(346\) | −0.636522 | −0.0342196 | ||||||||
\(347\) | −1.45512 | −0.0781151 | −0.0390576 | − | 0.999237i | \(-0.512436\pi\) | ||||
−0.0390576 | + | 0.999237i | \(0.512436\pi\) | |||||||
\(348\) | 5.29873 | 0.284042 | ||||||||
\(349\) | 23.7332 | 1.27041 | 0.635204 | − | 0.772345i | \(-0.280916\pi\) | ||||
0.635204 | + | 0.772345i | \(0.280916\pi\) | |||||||
\(350\) | −0.141446 | −0.00756060 | ||||||||
\(351\) | 2.48657 | 0.132724 | ||||||||
\(352\) | 17.6147 | 0.938866 | ||||||||
\(353\) | −7.39055 | −0.393359 | −0.196680 | − | 0.980468i | \(-0.563016\pi\) | ||||
−0.196680 | + | 0.980468i | \(0.563016\pi\) | |||||||
\(354\) | −3.70150 | −0.196732 | ||||||||
\(355\) | 9.92903 | 0.526978 | ||||||||
\(356\) | −12.4707 | −0.660945 | ||||||||
\(357\) | 1.66195 | 0.0879596 | ||||||||
\(358\) | −2.18145 | −0.115293 | ||||||||
\(359\) | 2.35868 | 0.124487 | 0.0622433 | − | 0.998061i | \(-0.480175\pi\) | ||||
0.0622433 | + | 0.998061i | \(0.480175\pi\) | |||||||
\(360\) | −1.13822 | −0.0599896 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 3.68174 | 0.193508 | ||||||||
\(363\) | 17.5972 | 0.923615 | ||||||||
\(364\) | 2.31756 | 0.121473 | ||||||||
\(365\) | −11.0128 | −0.576438 | ||||||||
\(366\) | 3.44617 | 0.180134 | ||||||||
\(367\) | −22.1486 | −1.15615 | −0.578073 | − | 0.815985i | \(-0.696195\pi\) | ||||
−0.578073 | + | 0.815985i | \(0.696195\pi\) | |||||||
\(368\) | 22.4441 | 1.16998 | ||||||||
\(369\) | −2.58139 | −0.134382 | ||||||||
\(370\) | 1.83650 | 0.0954750 | ||||||||
\(371\) | 1.45816 | 0.0757037 | ||||||||
\(372\) | 9.25374 | 0.479784 | ||||||||
\(373\) | −31.1738 | −1.61412 | −0.807060 | − | 0.590469i | \(-0.798943\pi\) | ||||
−0.807060 | + | 0.590469i | \(0.798943\pi\) | |||||||
\(374\) | −5.30971 | −0.274559 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −12.6464 | −0.652189 | ||||||||
\(377\) | −6.87847 | −0.354259 | ||||||||
\(378\) | −0.141446 | −0.00727519 | ||||||||
\(379\) | 26.0349 | 1.33732 | 0.668662 | − | 0.743567i | \(-0.266868\pi\) | ||||
0.668662 | + | 0.743567i | \(0.266868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.83099 | 0.503657 | ||||||||
\(382\) | 2.37144 | 0.121334 | ||||||||
\(383\) | 2.13294 | 0.108988 | 0.0544941 | − | 0.998514i | \(-0.482645\pi\) | ||||
0.0544941 | + | 0.998514i | \(0.482645\pi\) | |||||||
\(384\) | −8.34443 | −0.425825 | ||||||||
\(385\) | −2.60202 | −0.132611 | ||||||||
\(386\) | 0.978209 | 0.0497895 | ||||||||
\(387\) | −2.48657 | −0.126400 | ||||||||
\(388\) | 3.83099 | 0.194489 | ||||||||
\(389\) | −13.0427 | −0.661291 | −0.330645 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330645 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(390\) | 0.722840 | 0.0366024 | ||||||||
\(391\) | −21.9022 | −1.10764 | ||||||||
\(392\) | 7.69808 | 0.388812 | ||||||||
\(393\) | 14.2292 | 0.717768 | ||||||||
\(394\) | 1.11453 | 0.0561492 | ||||||||
\(395\) | −8.13272 | −0.409201 | ||||||||
\(396\) | −10.2434 | −0.514749 | ||||||||
\(397\) | 0.0286428 | 0.00143754 | 0.000718770 | − | 1.00000i | \(-0.499771\pi\) | ||||
0.000718770 | 1.00000i | \(0.499771\pi\) | ||||||||
\(398\) | 3.69142 | 0.185034 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.50011 | 0.175006 | ||||||||
\(401\) | 27.3191 | 1.36425 | 0.682126 | − | 0.731234i | \(-0.261055\pi\) | ||||
0.682126 | + | 0.731234i | \(0.261055\pi\) | |||||||
\(402\) | 4.41145 | 0.220023 | ||||||||
\(403\) | −12.0126 | −0.598391 | ||||||||
\(404\) | −2.90513 | −0.144536 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0.391274 | 0.0194186 | ||||||||
\(407\) | 33.7841 | 1.67461 | ||||||||
\(408\) | 3.88772 | 0.192471 | ||||||||
\(409\) | 6.73917 | 0.333230 | 0.166615 | − | 0.986022i | \(-0.446716\pi\) | ||||
0.166615 | + | 0.986022i | \(0.446716\pi\) | |||||||
\(410\) | −0.750404 | −0.0370598 | ||||||||
\(411\) | 6.58439 | 0.324784 | ||||||||
\(412\) | −17.5359 | −0.863933 | ||||||||
\(413\) | 6.19564 | 0.304867 | ||||||||
\(414\) | 1.86406 | 0.0916137 | ||||||||
\(415\) | −5.86106 | −0.287708 | ||||||||
\(416\) | 8.19058 | 0.401576 | ||||||||
\(417\) | 0.233756 | 0.0114471 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.4076 | 1.29010 | 0.645048 | − | 0.764142i | \(-0.276837\pi\) | ||||
0.645048 | + | 0.764142i | \(0.276837\pi\) | |||||||
\(420\) | 0.932031 | 0.0454785 | ||||||||
\(421\) | −37.8895 | −1.84662 | −0.923311 | − | 0.384053i | \(-0.874528\pi\) | ||||
−0.923311 | + | 0.384053i | \(0.874528\pi\) | |||||||
\(422\) | 2.66179 | 0.129574 | ||||||||
\(423\) | 11.1107 | 0.540219 | ||||||||
\(424\) | 3.41100 | 0.165653 | ||||||||
\(425\) | −3.41561 | −0.165681 | ||||||||
\(426\) | 2.88634 | 0.139844 | ||||||||
\(427\) | −5.76826 | −0.279146 | ||||||||
\(428\) | 0.266132 | 0.0128640 | ||||||||
\(429\) | 13.2973 | 0.642000 | ||||||||
\(430\) | −0.722840 | −0.0348585 | ||||||||
\(431\) | 19.2057 | 0.925106 | 0.462553 | − | 0.886592i | \(-0.346933\pi\) | ||||
0.462553 | + | 0.886592i | \(0.346933\pi\) | |||||||
\(432\) | 3.50011 | 0.168399 | ||||||||
\(433\) | −16.9512 | −0.814624 | −0.407312 | − | 0.913289i | \(-0.633534\pi\) | ||||
−0.407312 | + | 0.913289i | \(0.633534\pi\) | |||||||
\(434\) | 0.683323 | 0.0328006 | ||||||||
\(435\) | −2.76624 | −0.132631 | ||||||||
\(436\) | −30.1306 | −1.44300 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.20140 | −0.152969 | ||||||||
\(439\) | −11.1029 | −0.529911 | −0.264955 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264955 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(440\) | −6.08681 | −0.290177 | ||||||||
\(441\) | −6.76325 | −0.322059 | ||||||||
\(442\) | −2.46894 | −0.117435 | ||||||||
\(443\) | −13.8942 | −0.660132 | −0.330066 | − | 0.943958i | \(-0.607071\pi\) | ||||
−0.330066 | + | 0.943958i | \(0.607071\pi\) | |||||||
\(444\) | −12.1013 | −0.574301 | ||||||||
\(445\) | 6.51043 | 0.308624 | ||||||||
\(446\) | −3.16788 | −0.150004 | ||||||||
\(447\) | −2.67299 | −0.126428 | ||||||||
\(448\) | 2.94022 | 0.138912 | ||||||||
\(449\) | −27.8675 | −1.31515 | −0.657573 | − | 0.753391i | \(-0.728417\pi\) | ||||
−0.657573 | + | 0.753391i | \(0.728417\pi\) | |||||||
\(450\) | 0.290697 | 0.0137036 | ||||||||
\(451\) | −13.8044 | −0.650022 | ||||||||
\(452\) | 28.3515 | 1.33354 | ||||||||
\(453\) | −5.95266 | −0.279680 | ||||||||
\(454\) | 7.16136 | 0.336099 | ||||||||
\(455\) | −1.20990 | −0.0567212 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.5660 | −1.71048 | −0.855242 | − | 0.518229i | \(-0.826591\pi\) | ||||
−0.855242 | + | 0.518229i | \(0.826591\pi\) | |||||||
\(458\) | 4.99058 | 0.233194 | ||||||||
\(459\) | −3.41561 | −0.159427 | ||||||||
\(460\) | −12.2829 | −0.572693 | ||||||||
\(461\) | 21.9180 | 1.02082 | 0.510412 | − | 0.859930i | \(-0.329493\pi\) | ||||
0.510412 | + | 0.859930i | \(0.329493\pi\) | |||||||
\(462\) | −0.756401 | −0.0351910 | ||||||||
\(463\) | −14.0255 | −0.651821 | −0.325910 | − | 0.945401i | \(-0.605671\pi\) | ||||
−0.325910 | + | 0.945401i | \(0.605671\pi\) | |||||||
\(464\) | −9.68216 | −0.449483 | ||||||||
\(465\) | −4.83099 | −0.224032 | ||||||||
\(466\) | 8.27415 | 0.383293 | ||||||||
\(467\) | 33.9294 | 1.57007 | 0.785033 | − | 0.619453i | \(-0.212646\pi\) | ||||
0.785033 | + | 0.619453i | \(0.212646\pi\) | |||||||
\(468\) | −4.76302 | −0.220171 | ||||||||
\(469\) | −7.38397 | −0.340960 | ||||||||
\(470\) | 3.22984 | 0.148981 | ||||||||
\(471\) | −7.20848 | −0.332149 | ||||||||
\(472\) | 14.4932 | 0.667103 | ||||||||
\(473\) | −13.2973 | −0.611411 | ||||||||
\(474\) | −2.36416 | −0.108589 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.18345 | −0.145913 | ||||||||
\(477\) | −2.99678 | −0.137213 | ||||||||
\(478\) | 1.18529 | 0.0542140 | ||||||||
\(479\) | 31.9497 | 1.45982 | 0.729909 | − | 0.683544i | \(-0.239562\pi\) | ||||
0.729909 | + | 0.683544i | \(0.239562\pi\) | |||||||
\(480\) | 3.29392 | 0.150346 | ||||||||
\(481\) | 15.7091 | 0.716273 | ||||||||
\(482\) | 3.68268 | 0.167741 | ||||||||
\(483\) | −3.12010 | −0.141970 | ||||||||
\(484\) | −33.7074 | −1.53216 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0.290697 | 0.0131863 | ||||||||
\(487\) | −37.6229 | −1.70486 | −0.852428 | − | 0.522844i | \(-0.824871\pi\) | ||||
−0.852428 | + | 0.522844i | \(0.824871\pi\) | |||||||
\(488\) | −13.4935 | −0.610820 | ||||||||
\(489\) | 14.1756 | 0.641044 | ||||||||
\(490\) | −1.96606 | −0.0888174 | ||||||||
\(491\) | −40.0842 | −1.80897 | −0.904487 | − | 0.426500i | \(-0.859746\pi\) | ||||
−0.904487 | + | 0.426500i | \(0.859746\pi\) | |||||||
\(492\) | 4.94465 | 0.222922 | ||||||||
\(493\) | 9.44840 | 0.425535 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.34764 | 0.240358 | ||||||||
\(496\) | −16.9090 | −0.759237 | ||||||||
\(497\) | −4.83121 | −0.216710 | ||||||||
\(498\) | −1.70379 | −0.0763489 | ||||||||
\(499\) | −30.3067 | −1.35671 | −0.678357 | − | 0.734732i | \(-0.737308\pi\) | ||||
−0.678357 | + | 0.734732i | \(0.737308\pi\) | |||||||
\(500\) | −1.91550 | −0.0856635 | ||||||||
\(501\) | −12.5563 | −0.560976 | ||||||||
\(502\) | −3.37909 | −0.150816 | ||||||||
\(503\) | −17.2879 | −0.770827 | −0.385414 | − | 0.922744i | \(-0.625941\pi\) | ||||
−0.385414 | + | 0.922744i | \(0.625941\pi\) | |||||||
\(504\) | 0.553831 | 0.0246696 | ||||||||
\(505\) | 1.51665 | 0.0674899 | ||||||||
\(506\) | 9.96833 | 0.443146 | ||||||||
\(507\) | −6.81695 | −0.302751 | ||||||||
\(508\) | −18.8312 | −0.835500 | ||||||||
\(509\) | −5.60825 | −0.248581 | −0.124291 | − | 0.992246i | \(-0.539665\pi\) | ||||
−0.124291 | + | 0.992246i | \(0.539665\pi\) | |||||||
\(510\) | −0.992907 | −0.0439667 | ||||||||
\(511\) | 5.35857 | 0.237049 | ||||||||
\(512\) | 19.4969 | 0.861650 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.06637 | −0.135252 | ||||||||
\(515\) | 9.15478 | 0.403408 | ||||||||
\(516\) | 4.76302 | 0.209680 | ||||||||
\(517\) | 59.4158 | 2.61310 | ||||||||
\(518\) | −0.893593 | −0.0392622 | ||||||||
\(519\) | −2.18964 | −0.0961145 | ||||||||
\(520\) | −2.83028 | −0.124116 | ||||||||
\(521\) | −13.7128 | −0.600767 | −0.300384 | − | 0.953818i | \(-0.597115\pi\) | ||||
−0.300384 | + | 0.953818i | \(0.597115\pi\) | |||||||
\(522\) | −0.804139 | −0.0351962 | ||||||||
\(523\) | 35.2342 | 1.54068 | 0.770341 | − | 0.637632i | \(-0.220086\pi\) | ||||
0.770341 | + | 0.637632i | \(0.220086\pi\) | |||||||
\(524\) | −27.2559 | −1.19068 | ||||||||
\(525\) | −0.486575 | −0.0212359 | ||||||||
\(526\) | 6.91670 | 0.301583 | ||||||||
\(527\) | 16.5008 | 0.718785 | ||||||||
\(528\) | 18.7173 | 0.814567 | ||||||||
\(529\) | 18.1187 | 0.787769 | ||||||||
\(530\) | −0.871155 | −0.0378405 | ||||||||
\(531\) | −12.7332 | −0.552573 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.41883 | −0.278030 | ||||||||
\(534\) | 1.89256 | 0.0818992 | ||||||||
\(535\) | −0.138936 | −0.00600674 | ||||||||
\(536\) | −17.2730 | −0.746080 | ||||||||
\(537\) | −7.50421 | −0.323830 | ||||||||
\(538\) | 1.22893 | 0.0529830 | ||||||||
\(539\) | −36.1674 | −1.55784 | ||||||||
\(540\) | −1.91550 | −0.0824298 | ||||||||
\(541\) | 30.2357 | 1.29994 | 0.649968 | − | 0.759962i | \(-0.274782\pi\) | ||||
0.649968 | + | 0.759962i | \(0.274782\pi\) | |||||||
\(542\) | 9.05438 | 0.388919 | ||||||||
\(543\) | 12.6652 | 0.543516 | ||||||||
\(544\) | −11.2507 | −0.482371 | ||||||||
\(545\) | 15.7299 | 0.673797 | ||||||||
\(546\) | −0.351716 | −0.0150520 | ||||||||
\(547\) | −34.9531 | −1.49449 | −0.747244 | − | 0.664550i | \(-0.768623\pi\) | ||||
−0.747244 | + | 0.664550i | \(0.768623\pi\) | |||||||
\(548\) | −12.6124 | −0.538774 | ||||||||
\(549\) | 11.8548 | 0.505952 | ||||||||
\(550\) | 1.55454 | 0.0662860 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −7.29873 | −0.310654 | ||||||||
\(553\) | 3.95717 | 0.168276 | ||||||||
\(554\) | 0.306373 | 0.0130166 | ||||||||
\(555\) | 6.31756 | 0.268166 | ||||||||
\(556\) | −0.447759 | −0.0189892 | ||||||||
\(557\) | 3.16279 | 0.134012 | 0.0670058 | − | 0.997753i | \(-0.478655\pi\) | ||||
0.0670058 | + | 0.997753i | \(0.478655\pi\) | |||||||
\(558\) | −1.40436 | −0.0594511 | ||||||||
\(559\) | −6.18305 | −0.261515 | ||||||||
\(560\) | −1.70307 | −0.0719676 | ||||||||
\(561\) | −18.2654 | −0.771167 | ||||||||
\(562\) | −7.45213 | −0.314349 | ||||||||
\(563\) | 29.0570 | 1.22460 | 0.612302 | − | 0.790624i | \(-0.290244\pi\) | ||||
0.612302 | + | 0.790624i | \(0.290244\pi\) | |||||||
\(564\) | −21.2824 | −0.896151 | ||||||||
\(565\) | −14.8011 | −0.622689 | ||||||||
\(566\) | 8.54975 | 0.359373 | ||||||||
\(567\) | −0.486575 | −0.0204342 | ||||||||
\(568\) | −11.3015 | −0.474199 | ||||||||
\(569\) | 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 | \(0.482904\pi\) | |||||||
\(572\) | −25.4709 | −1.06499 | ||||||||
\(573\) | 8.15777 | 0.340796 | ||||||||
\(574\) | 0.365128 | 0.0152401 | ||||||||
\(575\) | 6.41238 | 0.267415 | ||||||||
\(576\) | −6.04269 | −0.251779 | ||||||||
\(577\) | 3.12153 | 0.129951 | 0.0649755 | − | 0.997887i | \(-0.479303\pi\) | ||||
0.0649755 | + | 0.997887i | \(0.479303\pi\) | |||||||
\(578\) | −1.55047 | −0.0644911 | ||||||||
\(579\) | 3.36505 | 0.139847 | ||||||||
\(580\) | 5.29873 | 0.220018 | ||||||||
\(581\) | 2.85184 | 0.118314 | ||||||||
\(582\) | −0.581394 | −0.0240996 | ||||||||
\(583\) | −16.0257 | −0.663716 | ||||||||
\(584\) | 12.5351 | 0.518705 | ||||||||
\(585\) | 2.48657 | 0.102807 | ||||||||
\(586\) | 3.15547 | 0.130351 | ||||||||
\(587\) | −9.27970 | −0.383014 | −0.191507 | − | 0.981491i | \(-0.561338\pi\) | ||||
−0.191507 | + | 0.981491i | \(0.561338\pi\) | |||||||
\(588\) | 12.9550 | 0.534254 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.70150 | −0.152388 | ||||||||
\(591\) | 3.83399 | 0.157709 | ||||||||
\(592\) | 22.1122 | 0.908805 | ||||||||
\(593\) | 34.0447 | 1.39805 | 0.699025 | − | 0.715097i | \(-0.253618\pi\) | ||||
0.699025 | + | 0.715097i | \(0.253618\pi\) | |||||||
\(594\) | 1.55454 | 0.0637837 | ||||||||
\(595\) | 1.66195 | 0.0681332 | ||||||||
\(596\) | 5.12010 | 0.209728 | ||||||||
\(597\) | 12.6985 | 0.519715 | ||||||||
\(598\) | 4.63513 | 0.189545 | ||||||||
\(599\) | −25.0732 | −1.02446 | −0.512231 | − | 0.858848i | \(-0.671181\pi\) | ||||
−0.512231 | + | 0.858848i | \(0.671181\pi\) | |||||||
\(600\) | −1.13822 | −0.0464678 | ||||||||
\(601\) | 26.0225 | 1.06148 | 0.530739 | − | 0.847535i | \(-0.321914\pi\) | ||||
0.530739 | + | 0.847535i | \(0.321914\pi\) | |||||||
\(602\) | 0.351716 | 0.0143349 | ||||||||
\(603\) | 15.1754 | 0.617990 | ||||||||
\(604\) | 11.4023 | 0.463953 | ||||||||
\(605\) | 17.5972 | 0.715429 | ||||||||
\(606\) | 0.440885 | 0.0179097 | ||||||||
\(607\) | 7.54650 | 0.306303 | 0.153151 | − | 0.988203i | \(-0.451058\pi\) | ||||
0.153151 | + | 0.988203i | \(0.451058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.34598 | 0.0545420 | ||||||||
\(610\) | 3.44617 | 0.139531 | ||||||||
\(611\) | 27.6275 | 1.11769 | ||||||||
\(612\) | 6.54258 | 0.264468 | ||||||||
\(613\) | −38.2690 | −1.54567 | −0.772836 | − | 0.634606i | \(-0.781162\pi\) | ||||
−0.772836 | + | 0.634606i | \(0.781162\pi\) | |||||||
\(614\) | −9.79331 | −0.395226 | ||||||||
\(615\) | −2.58139 | −0.104092 | ||||||||
\(616\) | 2.96169 | 0.119330 | ||||||||
\(617\) | −11.6508 | −0.469043 | −0.234522 | − | 0.972111i | \(-0.575352\pi\) | ||||
−0.234522 | + | 0.972111i | \(0.575352\pi\) | |||||||
\(618\) | 2.66127 | 0.107052 | ||||||||
\(619\) | −2.47710 | −0.0995630 | −0.0497815 | − | 0.998760i | \(-0.515852\pi\) | ||||
−0.0497815 | + | 0.998760i | \(0.515852\pi\) | |||||||
\(620\) | 9.25374 | 0.371639 | ||||||||
\(621\) | 6.41238 | 0.257320 | ||||||||
\(622\) | −3.40759 | −0.136632 | ||||||||
\(623\) | −3.16781 | −0.126916 | ||||||||
\(624\) | 8.70329 | 0.348410 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.30191 | 0.0520346 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.8078 | 0.550991 | ||||||||
\(629\) | −21.5783 | −0.860384 | ||||||||
\(630\) | −0.141446 | −0.00563534 | ||||||||
\(631\) | −43.6558 | −1.73791 | −0.868954 | − | 0.494893i | \(-0.835207\pi\) | ||||
−0.868954 | + | 0.494893i | \(0.835207\pi\) | |||||||
\(632\) | 9.25685 | 0.368218 | ||||||||
\(633\) | 9.15657 | 0.363941 | ||||||||
\(634\) | −3.60096 | −0.143012 | ||||||||
\(635\) | 9.83099 | 0.390131 | ||||||||
\(636\) | 5.74031 | 0.227618 | ||||||||
\(637\) | −16.8173 | −0.666326 | ||||||||
\(638\) | −4.30025 | −0.170248 | ||||||||
\(639\) | 9.92903 | 0.392786 | ||||||||
\(640\) | −8.34443 | −0.329843 | ||||||||
\(641\) | −24.2326 | −0.957128 | −0.478564 | − | 0.878053i | \(-0.658843\pi\) | ||||
−0.478564 | + | 0.878053i | \(0.658843\pi\) | |||||||
\(642\) | −0.0403884 | −0.00159400 | ||||||||
\(643\) | 8.31756 | 0.328013 | 0.164006 | − | 0.986459i | \(-0.447558\pi\) | ||||
0.164006 | + | 0.986459i | \(0.447558\pi\) | |||||||
\(644\) | 5.97654 | 0.235509 | ||||||||
\(645\) | −2.48657 | −0.0979088 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.9164 | −0.429170 | −0.214585 | − | 0.976705i | \(-0.568840\pi\) | ||||
−0.214585 | + | 0.976705i | \(0.568840\pi\) | |||||||
\(648\) | −1.13822 | −0.0447136 | ||||||||
\(649\) | −68.0924 | −2.67286 | ||||||||
\(650\) | 0.722840 | 0.0283521 | ||||||||
\(651\) | 2.35064 | 0.0921287 | ||||||||
\(652\) | −27.1534 | −1.06341 | ||||||||
\(653\) | −21.8452 | −0.854868 | −0.427434 | − | 0.904047i | \(-0.640582\pi\) | ||||
−0.427434 | + | 0.904047i | \(0.640582\pi\) | |||||||
\(654\) | 4.57265 | 0.178805 | ||||||||
\(655\) | 14.2292 | 0.555980 | ||||||||
\(656\) | −9.03517 | −0.352764 | ||||||||
\(657\) | −11.0128 | −0.429652 | ||||||||
\(658\) | −1.57156 | −0.0612657 | ||||||||
\(659\) | 26.4188 | 1.02913 | 0.514566 | − | 0.857451i | \(-0.327953\pi\) | ||||
0.514566 | + | 0.857451i | \(0.327953\pi\) | |||||||
\(660\) | −10.2434 | −0.398723 | ||||||||
\(661\) | −18.6144 | −0.724017 | −0.362008 | − | 0.932175i | \(-0.617909\pi\) | ||||
−0.362008 | + | 0.932175i | \(0.617909\pi\) | |||||||
\(662\) | −7.12376 | −0.276873 | ||||||||
\(663\) | −8.49316 | −0.329847 | ||||||||
\(664\) | 6.67120 | 0.258893 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.83650 | 0.0711629 | ||||||||
\(667\) | −17.7382 | −0.686827 | ||||||||
\(668\) | 24.0516 | 0.930585 | ||||||||
\(669\) | −10.8975 | −0.421323 | ||||||||
\(670\) | 4.41145 | 0.170429 | ||||||||
\(671\) | 63.3954 | 2.44735 | ||||||||
\(672\) | −1.60274 | −0.0618269 | ||||||||
\(673\) | −5.98693 | −0.230779 | −0.115390 | − | 0.993320i | \(-0.536812\pi\) | ||||
−0.115390 | + | 0.993320i | \(0.536812\pi\) | |||||||
\(674\) | −3.05254 | −0.117580 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 13.0578 | 0.502224 | ||||||||
\(677\) | −33.7287 | −1.29630 | −0.648150 | − | 0.761512i | \(-0.724457\pi\) | ||||
−0.648150 | + | 0.761512i | \(0.724457\pi\) | |||||||
\(678\) | −4.30265 | −0.165242 | ||||||||
\(679\) | 0.973149 | 0.0373460 | ||||||||
\(680\) | 3.88772 | 0.149087 | ||||||||
\(681\) | 24.6351 | 0.944020 | ||||||||
\(682\) | −7.50998 | −0.287572 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | 1.94675 | 0.0743274 | ||||||||
\(687\) | 17.1676 | 0.654985 | ||||||||
\(688\) | −8.70329 | −0.331810 | ||||||||
\(689\) | −7.45171 | −0.283888 | ||||||||
\(690\) | 1.86406 | 0.0709636 | ||||||||
\(691\) | 36.3039 | 1.38107 | 0.690533 | − | 0.723301i | \(-0.257376\pi\) | ||||
0.690533 | + | 0.723301i | \(0.257376\pi\) | |||||||
\(692\) | 4.19424 | 0.159441 | ||||||||
\(693\) | −2.60202 | −0.0988427 | ||||||||
\(694\) | −0.423000 | −0.0160569 | ||||||||
\(695\) | 0.233756 | 0.00886688 | ||||||||
\(696\) | 3.14860 | 0.119348 | ||||||||
\(697\) | 8.81703 | 0.333969 | ||||||||
\(698\) | 6.89917 | 0.261137 | ||||||||
\(699\) | 28.4631 | 1.07657 | ||||||||
\(700\) | 0.932031 | 0.0352275 | ||||||||
\(701\) | 13.5275 | 0.510925 | 0.255463 | − | 0.966819i | \(-0.417772\pi\) | ||||
0.255463 | + | 0.966819i | \(0.417772\pi\) | |||||||
\(702\) | 0.722840 | 0.0272818 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −32.3141 | −1.21788 | ||||||||
\(705\) | 11.1107 | 0.418452 | ||||||||
\(706\) | −2.14841 | −0.0808566 | ||||||||
\(707\) | −0.737962 | −0.0277539 | ||||||||
\(708\) | 24.3903 | 0.916645 | ||||||||
\(709\) | −0.993555 | −0.0373137 | −0.0186569 | − | 0.999826i | \(-0.505939\pi\) | ||||
−0.0186569 | + | 0.999826i | \(0.505939\pi\) | |||||||
\(710\) | 2.88634 | 0.108322 | ||||||||
\(711\) | −8.13272 | −0.305001 | ||||||||
\(712\) | −7.41032 | −0.277714 | ||||||||
\(713\) | −30.9782 | −1.16014 | ||||||||
\(714\) | 0.483123 | 0.0180804 | ||||||||
\(715\) | 13.2973 | 0.497291 | ||||||||
\(716\) | 14.3743 | 0.537192 | ||||||||
\(717\) | 4.07741 | 0.152274 | ||||||||
\(718\) | 0.685662 | 0.0255887 | ||||||||
\(719\) | −1.40134 | −0.0522612 | −0.0261306 | − | 0.999659i | \(-0.508319\pi\) | ||||
−0.0261306 | + | 0.999659i | \(0.508319\pi\) | |||||||
\(720\) | 3.50011 | 0.130441 | ||||||||
\(721\) | −4.45448 | −0.165894 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.6684 | 0.471144 | ||||||||
\(724\) | −24.2601 | −0.901621 | ||||||||
\(725\) | −2.76624 | −0.102736 | ||||||||
\(726\) | 5.11547 | 0.189853 | ||||||||
\(727\) | −46.9669 | −1.74191 | −0.870953 | − | 0.491367i | \(-0.836497\pi\) | ||||
−0.870953 | + | 0.491367i | \(0.836497\pi\) | |||||||
\(728\) | 1.37714 | 0.0510402 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.20140 | −0.118489 | ||||||||
\(731\) | 8.49316 | 0.314131 | ||||||||
\(732\) | −22.7079 | −0.839308 | ||||||||
\(733\) | −21.6068 | −0.798066 | −0.399033 | − | 0.916937i | \(-0.630654\pi\) | ||||
−0.399033 | + | 0.916937i | \(0.630654\pi\) | |||||||
\(734\) | −6.43852 | −0.237650 | ||||||||
\(735\) | −6.76325 | −0.249466 | ||||||||
\(736\) | 21.1219 | 0.778563 | ||||||||
\(737\) | 81.1526 | 2.98929 | ||||||||
\(738\) | −0.750404 | −0.0276228 | ||||||||
\(739\) | −30.8126 | −1.13346 | −0.566729 | − | 0.823904i | \(-0.691791\pi\) | ||||
−0.566729 | + | 0.823904i | \(0.691791\pi\) | |||||||
\(740\) | −12.1013 | −0.444851 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.423882 | 0.0155612 | ||||||||
\(743\) | −44.4286 | −1.62993 | −0.814964 | − | 0.579512i | \(-0.803243\pi\) | ||||
−0.814964 | + | 0.579512i | \(0.803243\pi\) | |||||||
\(744\) | 5.49875 | 0.201594 | ||||||||
\(745\) | −2.67299 | −0.0979308 | ||||||||
\(746\) | −9.06215 | −0.331789 | ||||||||
\(747\) | −5.86106 | −0.214445 | ||||||||
\(748\) | 34.9873 | 1.27926 | ||||||||
\(749\) | 0.0676029 | 0.00247016 | ||||||||
\(750\) | 0.290697 | 0.0106148 | ||||||||
\(751\) | −14.8787 | −0.542931 | −0.271466 | − | 0.962448i | \(-0.587508\pi\) | ||||
−0.271466 | + | 0.962448i | \(0.587508\pi\) | |||||||
\(752\) | 38.8886 | 1.41812 | ||||||||
\(753\) | −11.6241 | −0.423605 | ||||||||
\(754\) | −1.99955 | −0.0728194 | ||||||||
\(755\) | −5.95266 | −0.216640 | ||||||||
\(756\) | 0.932031 | 0.0338976 | ||||||||
\(757\) | 23.4408 | 0.851972 | 0.425986 | − | 0.904730i | \(-0.359927\pi\) | ||||
0.425986 | + | 0.904730i | \(0.359927\pi\) | |||||||
\(758\) | 7.56827 | 0.274892 | ||||||||
\(759\) | 34.2911 | 1.24469 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.3224 | 1.31669 | 0.658344 | − | 0.752717i | \(-0.271257\pi\) | ||||
0.658344 | + | 0.752717i | \(0.271257\pi\) | |||||||
\(762\) | 2.85784 | 0.103529 | ||||||||
\(763\) | −7.65379 | −0.277086 | ||||||||
\(764\) | −15.6262 | −0.565335 | ||||||||
\(765\) | −3.41561 | −0.123492 | ||||||||
\(766\) | 0.620039 | 0.0224029 | ||||||||
\(767\) | −31.6620 | −1.14325 | ||||||||
\(768\) | 9.65968 | 0.348564 | ||||||||
\(769\) | 20.8104 | 0.750441 | 0.375220 | − | 0.926936i | \(-0.377567\pi\) | ||||
0.375220 | + | 0.926936i | \(0.377567\pi\) | |||||||
\(770\) | −0.756401 | −0.0272588 | ||||||||
\(771\) | −10.5483 | −0.379889 | ||||||||
\(772\) | −6.44573 | −0.231987 | ||||||||
\(773\) | −3.56702 | −0.128297 | −0.0641484 | − | 0.997940i | \(-0.520433\pi\) | ||||
−0.0641484 | + | 0.997940i | \(0.520433\pi\) | |||||||
\(774\) | −0.722840 | −0.0259820 | ||||||||
\(775\) | −4.83099 | −0.173534 | ||||||||
\(776\) | 2.27645 | 0.0817197 | ||||||||
\(777\) | −3.07397 | −0.110278 | ||||||||
\(778\) | −3.79147 | −0.135931 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −4.76302 | −0.170544 | ||||||||
\(781\) | 53.0969 | 1.89996 | ||||||||
\(782\) | −6.36690 | −0.227680 | ||||||||
\(783\) | −2.76624 | −0.0988575 | ||||||||
\(784\) | −23.6721 | −0.845433 | ||||||||
\(785\) | −7.20848 | −0.257282 | ||||||||
\(786\) | 4.13639 | 0.147540 | ||||||||
\(787\) | −44.5660 | −1.58860 | −0.794302 | − | 0.607523i | \(-0.792163\pi\) | ||||
−0.794302 | + | 0.607523i | \(0.792163\pi\) | |||||||
\(788\) | −7.34399 | −0.261619 | ||||||||
\(789\) | 23.7935 | 0.847071 | ||||||||
\(790\) | −2.36416 | −0.0841129 | ||||||||
\(791\) | 7.20186 | 0.256069 | ||||||||
\(792\) | −6.08681 | −0.216285 | ||||||||
\(793\) | 29.4779 | 1.04679 | ||||||||
\(794\) | 0.00832637 | 0.000295492 0 | ||||||||
\(795\) | −2.99678 | −0.106285 | ||||||||
\(796\) | −24.3239 | −0.862138 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 3.29392 | 0.116458 | ||||||||
\(801\) | 6.51043 | 0.230035 | ||||||||
\(802\) | 7.94160 | 0.280428 | ||||||||
\(803\) | −58.8927 | −2.07828 | ||||||||
\(804\) | −29.0684 | −1.02516 | ||||||||
\(805\) | −3.12010 | −0.109969 | ||||||||
\(806\) | −3.49203 | −0.123002 | ||||||||
\(807\) | 4.22754 | 0.148816 | ||||||||
\(808\) | −1.72628 | −0.0607305 | ||||||||
\(809\) | 8.67442 | 0.304976 | 0.152488 | − | 0.988305i | \(-0.451271\pi\) | ||||
0.152488 | + | 0.988305i | \(0.451271\pi\) | |||||||
\(810\) | 0.290697 | 0.0102141 | ||||||||
\(811\) | −26.7302 | −0.938623 | −0.469312 | − | 0.883033i | \(-0.655498\pi\) | ||||
−0.469312 | + | 0.883033i | \(0.655498\pi\) | |||||||
\(812\) | −2.57823 | −0.0904780 | ||||||||
\(813\) | 31.1471 | 1.09238 | ||||||||
\(814\) | 9.82093 | 0.344223 | ||||||||
\(815\) | 14.1756 | 0.496551 | ||||||||
\(816\) | −11.9550 | −0.418509 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.95906 | 0.0684968 | ||||||||
\(819\) | −1.20990 | −0.0422775 | ||||||||
\(820\) | 4.94465 | 0.172675 | ||||||||
\(821\) | −9.44863 | −0.329759 | −0.164880 | − | 0.986314i | \(-0.552724\pi\) | ||||
−0.164880 | + | 0.986314i | \(0.552724\pi\) | |||||||
\(822\) | 1.91406 | 0.0667607 | ||||||||
\(823\) | −19.4668 | −0.678570 | −0.339285 | − | 0.940684i | \(-0.610185\pi\) | ||||
−0.339285 | + | 0.940684i | \(0.610185\pi\) | |||||||
\(824\) | −10.4202 | −0.363004 | ||||||||
\(825\) | 5.34764 | 0.186181 | ||||||||
\(826\) | 1.80105 | 0.0626667 | ||||||||
\(827\) | 37.0018 | 1.28668 | 0.643340 | − | 0.765581i | \(-0.277548\pi\) | ||||
0.643340 | + | 0.765581i | \(0.277548\pi\) | |||||||
\(828\) | −12.2829 | −0.426860 | ||||||||
\(829\) | −20.5418 | −0.713448 | −0.356724 | − | 0.934210i | \(-0.616106\pi\) | ||||
−0.356724 | + | 0.934210i | \(0.616106\pi\) | |||||||
\(830\) | −1.70379 | −0.0591396 | ||||||||
\(831\) | 1.05393 | 0.0365603 | ||||||||
\(832\) | −15.0256 | −0.520919 | ||||||||
\(833\) | 23.1006 | 0.800388 | ||||||||
\(834\) | 0.0679523 | 0.00235299 | ||||||||
\(835\) | −12.5563 | −0.434530 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.83099 | −0.166983 | ||||||||
\(838\) | 7.67661 | 0.265184 | ||||||||
\(839\) | 47.7891 | 1.64986 | 0.824932 | − | 0.565233i | \(-0.191214\pi\) | ||||
0.824932 | + | 0.565233i | \(0.191214\pi\) | |||||||
\(840\) | 0.553831 | 0.0191090 | ||||||||
\(841\) | −21.3479 | −0.736134 | ||||||||
\(842\) | −11.0144 | −0.379580 | ||||||||
\(843\) | −25.6354 | −0.882928 | ||||||||
\(844\) | −17.5394 | −0.603730 | ||||||||
\(845\) | −6.81695 | −0.234510 | ||||||||
\(846\) | 3.22984 | 0.111044 | ||||||||
\(847\) | −8.56237 | −0.294206 | ||||||||
\(848\) | −10.4891 | −0.360196 | ||||||||
\(849\) | 29.4112 | 1.00939 | ||||||||
\(850\) | −0.992907 | −0.0340564 | ||||||||
\(851\) | 40.5107 | 1.38869 | ||||||||
\(852\) | −19.0190 | −0.651581 | ||||||||
\(853\) | 11.4326 | 0.391446 | 0.195723 | − | 0.980659i | \(-0.437295\pi\) | ||||
0.195723 | + | 0.980659i | \(0.437295\pi\) | |||||||
\(854\) | −1.67682 | −0.0573795 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.158141 | 0.00540513 | ||||||||
\(857\) | −5.57043 | −0.190282 | −0.0951412 | − | 0.995464i | \(-0.530330\pi\) | ||||
−0.0951412 | + | 0.995464i | \(0.530330\pi\) | |||||||
\(858\) | 3.86549 | 0.131966 | ||||||||
\(859\) | −17.0142 | −0.580517 | −0.290258 | − | 0.956948i | \(-0.593741\pi\) | ||||
−0.290258 | + | 0.956948i | \(0.593741\pi\) | |||||||
\(860\) | 4.76302 | 0.162418 | ||||||||
\(861\) | 1.25604 | 0.0428058 | ||||||||
\(862\) | 5.58304 | 0.190159 | ||||||||
\(863\) | −46.8850 | −1.59598 | −0.797992 | − | 0.602668i | \(-0.794104\pi\) | ||||
−0.797992 | + | 0.602668i | \(0.794104\pi\) | |||||||
\(864\) | 3.29392 | 0.112061 | ||||||||
\(865\) | −2.18964 | −0.0744500 | ||||||||
\(866\) | −4.92768 | −0.167449 | ||||||||
\(867\) | −5.33363 | −0.181140 | ||||||||
\(868\) | −4.50263 | −0.152829 | ||||||||
\(869\) | −43.4908 | −1.47532 | ||||||||
\(870\) | −0.804139 | −0.0272629 | ||||||||
\(871\) | 37.7348 | 1.27859 | ||||||||
\(872\) | −17.9042 | −0.606313 | ||||||||
\(873\) | −2.00000 | −0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.486575 | −0.0164492 | ||||||||
\(876\) | 21.0950 | 0.712735 | ||||||||
\(877\) | 29.7844 | 1.00575 | 0.502873 | − | 0.864360i | \(-0.332276\pi\) | ||||
0.502873 | + | 0.864360i | \(0.332276\pi\) | |||||||
\(878\) | −3.22757 | −0.108925 | ||||||||
\(879\) | 10.8548 | 0.366125 | ||||||||
\(880\) | 18.7173 | 0.630961 | ||||||||
\(881\) | −20.4884 | −0.690271 | −0.345135 | − | 0.938553i | \(-0.612167\pi\) | ||||
−0.345135 | + | 0.938553i | \(0.612167\pi\) | |||||||
\(882\) | −1.96606 | −0.0662006 | ||||||||
\(883\) | 31.4804 | 1.05940 | 0.529699 | − | 0.848186i | \(-0.322305\pi\) | ||||
0.529699 | + | 0.848186i | \(0.322305\pi\) | |||||||
\(884\) | 16.2686 | 0.547173 | ||||||||
\(885\) | −12.7332 | −0.428021 | ||||||||
\(886\) | −4.03900 | −0.135693 | ||||||||
\(887\) | 33.6103 | 1.12852 | 0.564262 | − | 0.825596i | \(-0.309161\pi\) | ||||
0.564262 | + | 0.825596i | \(0.309161\pi\) | |||||||
\(888\) | −7.19080 | −0.241307 | ||||||||
\(889\) | −4.78351 | −0.160434 | ||||||||
\(890\) | 1.89256 | 0.0634389 | ||||||||
\(891\) | 5.34764 | 0.179153 | ||||||||
\(892\) | 20.8742 | 0.698919 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.777031 | −0.0259878 | ||||||||
\(895\) | −7.50421 | −0.250838 | ||||||||
\(896\) | 4.06019 | 0.135641 | ||||||||
\(897\) | 15.9449 | 0.532384 | ||||||||
\(898\) | −8.10099 | −0.270334 | ||||||||
\(899\) | 13.3637 | 0.445704 | ||||||||
\(900\) | −1.91550 | −0.0638498 | ||||||||
\(901\) | 10.2358 | 0.341004 | ||||||||
\(902\) | −4.01289 | −0.133615 | ||||||||
\(903\) | 1.20990 | 0.0402631 | ||||||||
\(904\) | 16.8470 | 0.560323 | ||||||||
\(905\) | 12.6652 | 0.421006 | ||||||||
\(906\) | −1.73042 | −0.0574894 | ||||||||
\(907\) | −21.9494 | −0.728819 | −0.364410 | − | 0.931239i | \(-0.618729\pi\) | ||||
−0.364410 | + | 0.931239i | \(0.618729\pi\) | |||||||
\(908\) | −47.1885 | −1.56600 | ||||||||
\(909\) | 1.51665 | 0.0503040 | ||||||||
\(910\) | −0.351716 | −0.0116593 | ||||||||
\(911\) | −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 | ||||||||
\(914\) | −10.6296 | −0.351597 | ||||||||
\(915\) | 11.8548 | 0.391909 | ||||||||
\(916\) | −32.8845 | −1.08653 | ||||||||
\(917\) | −6.92356 | −0.228636 | ||||||||
\(918\) | −0.992907 | −0.0327708 | ||||||||
\(919\) | −2.61948 | −0.0864087 | −0.0432043 | − | 0.999066i | \(-0.513757\pi\) | ||||
−0.0432043 | + | 0.999066i | \(0.513757\pi\) | |||||||
\(920\) | −7.29873 | −0.240632 | ||||||||
\(921\) | −33.6891 | −1.11009 | ||||||||
\(922\) | 6.37151 | 0.209834 | ||||||||
\(923\) | 24.6893 | 0.812658 | ||||||||
\(924\) | 4.98417 | 0.163967 | ||||||||
\(925\) | 6.31756 | 0.207720 | ||||||||
\(926\) | −4.07718 | −0.133984 | ||||||||
\(927\) | 9.15478 | 0.300682 | ||||||||
\(928\) | −9.11178 | −0.299109 | ||||||||
\(929\) | 3.82474 | 0.125486 | 0.0627428 | − | 0.998030i | \(-0.480015\pi\) | ||||
0.0627428 | + | 0.998030i | \(0.480015\pi\) | |||||||
\(930\) | −1.40436 | −0.0460506 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −54.5210 | −1.78589 | ||||||||
\(933\) | −11.7221 | −0.383765 | ||||||||
\(934\) | 9.86319 | 0.322733 | ||||||||
\(935\) | −18.2654 | −0.597343 | ||||||||
\(936\) | −2.83028 | −0.0925105 | ||||||||
\(937\) | −7.39167 | −0.241475 | −0.120738 | − | 0.992684i | \(-0.538526\pi\) | ||||
−0.120738 | + | 0.992684i | \(0.538526\pi\) | |||||||
\(938\) | −2.14650 | −0.0700856 | ||||||||
\(939\) | 4.47856 | 0.146152 | ||||||||
\(940\) | −21.2824 | −0.694156 | ||||||||
\(941\) | −48.6115 | −1.58469 | −0.792344 | − | 0.610075i | \(-0.791139\pi\) | ||||
−0.792344 | + | 0.610075i | \(0.791139\pi\) | |||||||
\(942\) | −2.09548 | −0.0682746 | ||||||||
\(943\) | −16.5529 | −0.539036 | ||||||||
\(944\) | −44.5675 | −1.45055 | ||||||||
\(945\) | −0.486575 | −0.0158283 | ||||||||
\(946\) | −3.86549 | −0.125678 | ||||||||
\(947\) | −36.0207 | −1.17051 | −0.585257 | − | 0.810848i | \(-0.699006\pi\) | ||||
−0.585257 | + | 0.810848i | \(0.699006\pi\) | |||||||
\(948\) | 15.5782 | 0.505956 | ||||||||
\(949\) | −27.3843 | −0.888930 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.3873 | −0.401687 | ||||||||
\(952\) | −1.89167 | −0.0613093 | ||||||||
\(953\) | −11.2121 | −0.363196 | −0.181598 | − | 0.983373i | \(-0.558127\pi\) | ||||
−0.181598 | + | 0.983373i | \(0.558127\pi\) | |||||||
\(954\) | −0.871155 | −0.0282047 | ||||||||
\(955\) | 8.15777 | 0.263979 | ||||||||
\(956\) | −7.81026 | −0.252602 | ||||||||
\(957\) | −14.7929 | −0.478186 | ||||||||
\(958\) | 9.28769 | 0.300072 | ||||||||
\(959\) | −3.20380 | −0.103456 | ||||||||
\(960\) | −6.04269 | −0.195027 | ||||||||
\(961\) | −7.66153 | −0.247146 | ||||||||
\(962\) | 4.56659 | 0.147233 | ||||||||
\(963\) | −0.138936 | −0.00447716 | ||||||||
\(964\) | −24.2663 | −0.781565 | ||||||||
\(965\) | 3.36505 | 0.108325 | ||||||||
\(966\) | −0.907005 | −0.0291824 | ||||||||
\(967\) | −10.0461 | −0.323062 | −0.161531 | − | 0.986868i | \(-0.551643\pi\) | ||||
−0.161531 | + | 0.986868i | \(0.551643\pi\) | |||||||
\(968\) | −20.0296 | −0.643775 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.581394 | −0.0186674 | ||||||||
\(971\) | 37.8989 | 1.21623 | 0.608117 | − | 0.793847i | \(-0.291925\pi\) | ||||
0.608117 | + | 0.793847i | \(0.291925\pi\) | |||||||
\(972\) | −1.91550 | −0.0614395 | ||||||||
\(973\) | −0.113740 | −0.00364633 | ||||||||
\(974\) | −10.9369 | −0.350440 | ||||||||
\(975\) | 2.48657 | 0.0796341 | ||||||||
\(976\) | 41.4933 | 1.32817 | ||||||||
\(977\) | −44.6435 | −1.42827 | −0.714135 | − | 0.700008i | \(-0.753180\pi\) | ||||
−0.714135 | + | 0.700008i | \(0.753180\pi\) | |||||||
\(978\) | 4.12082 | 0.131769 | ||||||||
\(979\) | 34.8154 | 1.11271 | ||||||||
\(980\) | 12.9550 | 0.413831 | ||||||||
\(981\) | 15.7299 | 0.502219 | ||||||||
\(982\) | −11.6524 | −0.371842 | ||||||||
\(983\) | 12.5091 | 0.398978 | 0.199489 | − | 0.979900i | \(-0.436072\pi\) | ||||
0.199489 | + | 0.979900i | \(0.436072\pi\) | |||||||
\(984\) | 2.93820 | 0.0936665 | ||||||||
\(985\) | 3.83399 | 0.122161 | ||||||||
\(986\) | 2.74662 | 0.0874703 | ||||||||
\(987\) | −5.40616 | −0.172080 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.9449 | −0.507017 | ||||||||
\(990\) | 1.55454 | 0.0494066 | ||||||||
\(991\) | −50.3007 | −1.59785 | −0.798927 | − | 0.601428i | \(-0.794599\pi\) | ||||
−0.798927 | + | 0.601428i | \(0.794599\pi\) | |||||||
\(992\) | −15.9129 | −0.505235 | ||||||||
\(993\) | −24.5058 | −0.777667 | ||||||||
\(994\) | −1.40442 | −0.0445455 | ||||||||
\(995\) | 12.6985 | 0.402569 | ||||||||
\(996\) | 11.2268 | 0.355736 | ||||||||
\(997\) | 12.9375 | 0.409735 | 0.204867 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204867 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(998\) | −8.81007 | −0.278878 | ||||||||
\(999\) | 6.31756 | 0.199879 |
(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 | 5415.2.a.z.1.3 | 5 | ||
19.8 | odd | 6 | 285.2.i.f.121.3 | yes | 10 | ||
19.12 | odd | 6 | 285.2.i.f.106.3 | ✓ | 10 | ||
19.18 | odd | 2 | 5415.2.a.y.1.3 | 5 | |||
57.8 | even | 6 | 855.2.k.i.406.3 | 10 | |||
57.50 | even | 6 | 855.2.k.i.676.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.i.f.106.3 | ✓ | 10 | 19.12 | odd | 6 | ||
285.2.i.f.121.3 | yes | 10 | 19.8 | odd | 6 | ||
855.2.k.i.406.3 | 10 | 57.8 | even | 6 | |||
855.2.k.i.676.3 | 10 | 57.50 | even | 6 | |||
5415.2.a.y.1.3 | 5 | 19.18 | odd | 2 | |||
5415.2.a.z.1.3 | 5 | 1.1 | even | 1 | trivial |