Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} + \cdots + 113 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.21182\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.320182 | −0.184857 | −0.0924285 | − | 0.995719i | \(-0.529463\pi\) | ||||
−0.0924285 | + | 0.995719i | \(0.529463\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.73221 | −1.66909 | −0.834547 | − | 0.550937i | \(-0.814271\pi\) | ||||
−0.834547 | + | 0.550937i | \(0.814271\pi\) | |||||||
\(6\) | 0.320182 | 0.130714 | ||||||||
\(7\) | 2.93372 | 1.10884 | 0.554421 | − | 0.832236i | \(-0.312940\pi\) | ||||
0.554421 | + | 0.832236i | \(0.312940\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.89748 | −0.965828 | ||||||||
\(10\) | 3.73221 | 1.18023 | ||||||||
\(11\) | 4.47132 | 1.34815 | 0.674076 | − | 0.738662i | \(-0.264542\pi\) | ||||
0.674076 | + | 0.738662i | \(0.264542\pi\) | |||||||
\(12\) | −0.320182 | −0.0924285 | ||||||||
\(13\) | 5.74629 | 1.59373 | 0.796867 | − | 0.604155i | \(-0.206489\pi\) | ||||
0.796867 | + | 0.604155i | \(0.206489\pi\) | |||||||
\(14\) | −2.93372 | −0.784070 | ||||||||
\(15\) | 1.19499 | 0.308544 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.67759 | −0.649411 | −0.324706 | − | 0.945815i | \(-0.605265\pi\) | ||||
−0.324706 | + | 0.945815i | \(0.605265\pi\) | |||||||
\(18\) | 2.89748 | 0.682943 | ||||||||
\(19\) | 5.14247 | 1.17976 | 0.589882 | − | 0.807490i | \(-0.299174\pi\) | ||||
0.589882 | + | 0.807490i | \(0.299174\pi\) | |||||||
\(20\) | −3.73221 | −0.834547 | ||||||||
\(21\) | −0.939325 | −0.204977 | ||||||||
\(22\) | −4.47132 | −0.953288 | ||||||||
\(23\) | −0.733776 | −0.153003 | −0.0765014 | − | 0.997069i | \(-0.524375\pi\) | ||||
−0.0765014 | + | 0.997069i | \(0.524375\pi\) | |||||||
\(24\) | 0.320182 | 0.0653568 | ||||||||
\(25\) | 8.92938 | 1.78588 | ||||||||
\(26\) | −5.74629 | −1.12694 | ||||||||
\(27\) | 1.88827 | 0.363397 | ||||||||
\(28\) | 2.93372 | 0.554421 | ||||||||
\(29\) | −3.89230 | −0.722782 | −0.361391 | − | 0.932414i | \(-0.617698\pi\) | ||||
−0.361391 | + | 0.932414i | \(0.617698\pi\) | |||||||
\(30\) | −1.19499 | −0.218173 | ||||||||
\(31\) | −7.74468 | −1.39098 | −0.695492 | − | 0.718533i | \(-0.744814\pi\) | ||||
−0.695492 | + | 0.718533i | \(0.744814\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.43163 | −0.249216 | ||||||||
\(34\) | 2.67759 | 0.459203 | ||||||||
\(35\) | −10.9493 | −1.85076 | ||||||||
\(36\) | −2.89748 | −0.482914 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | −5.14247 | −0.834219 | ||||||||
\(39\) | −1.83986 | −0.294613 | ||||||||
\(40\) | 3.73221 | 0.590114 | ||||||||
\(41\) | −1.26590 | −0.197700 | −0.0988501 | − | 0.995102i | \(-0.531516\pi\) | ||||
−0.0988501 | + | 0.995102i | \(0.531516\pi\) | |||||||
\(42\) | 0.939325 | 0.144941 | ||||||||
\(43\) | −5.70174 | −0.869507 | −0.434753 | − | 0.900550i | \(-0.643164\pi\) | ||||
−0.434753 | + | 0.900550i | \(0.643164\pi\) | |||||||
\(44\) | 4.47132 | 0.674076 | ||||||||
\(45\) | 10.8140 | 1.61206 | ||||||||
\(46\) | 0.733776 | 0.108189 | ||||||||
\(47\) | 3.65985 | 0.533844 | 0.266922 | − | 0.963718i | \(-0.413993\pi\) | ||||
0.266922 | + | 0.963718i | \(0.413993\pi\) | |||||||
\(48\) | −0.320182 | −0.0462143 | ||||||||
\(49\) | 1.60673 | 0.229532 | ||||||||
\(50\) | −8.92938 | −1.26280 | ||||||||
\(51\) | 0.857316 | 0.120048 | ||||||||
\(52\) | 5.74629 | 0.796867 | ||||||||
\(53\) | −2.28501 | −0.313871 | −0.156935 | − | 0.987609i | \(-0.550161\pi\) | ||||
−0.156935 | + | 0.987609i | \(0.550161\pi\) | |||||||
\(54\) | −1.88827 | −0.256961 | ||||||||
\(55\) | −16.6879 | −2.25019 | ||||||||
\(56\) | −2.93372 | −0.392035 | ||||||||
\(57\) | −1.64653 | −0.218088 | ||||||||
\(58\) | 3.89230 | 0.511084 | ||||||||
\(59\) | 4.77466 | 0.621608 | 0.310804 | − | 0.950474i | \(-0.399402\pi\) | ||||
0.310804 | + | 0.950474i | \(0.399402\pi\) | |||||||
\(60\) | 1.19499 | 0.154272 | ||||||||
\(61\) | 3.67128 | 0.470059 | 0.235030 | − | 0.971988i | \(-0.424481\pi\) | ||||
0.235030 | + | 0.971988i | \(0.424481\pi\) | |||||||
\(62\) | 7.74468 | 0.983575 | ||||||||
\(63\) | −8.50041 | −1.07095 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −21.4463 | −2.66009 | ||||||||
\(66\) | 1.43163 | 0.176222 | ||||||||
\(67\) | −5.10474 | −0.623643 | −0.311822 | − | 0.950141i | \(-0.600939\pi\) | ||||
−0.311822 | + | 0.950141i | \(0.600939\pi\) | |||||||
\(68\) | −2.67759 | −0.324706 | ||||||||
\(69\) | 0.234942 | 0.0282837 | ||||||||
\(70\) | 10.9493 | 1.30869 | ||||||||
\(71\) | 0.0947712 | 0.0112473 | 0.00562364 | − | 0.999984i | \(-0.498210\pi\) | ||||
0.00562364 | + | 0.999984i | \(0.498210\pi\) | |||||||
\(72\) | 2.89748 | 0.341472 | ||||||||
\(73\) | −0.442146 | −0.0517493 | −0.0258746 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258746 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.85902 | −0.330132 | ||||||||
\(76\) | 5.14247 | 0.589882 | ||||||||
\(77\) | 13.1176 | 1.49489 | ||||||||
\(78\) | 1.83986 | 0.208323 | ||||||||
\(79\) | 14.4805 | 1.62918 | 0.814592 | − | 0.580035i | \(-0.196961\pi\) | ||||
0.814592 | + | 0.580035i | \(0.196961\pi\) | |||||||
\(80\) | −3.73221 | −0.417274 | ||||||||
\(81\) | 8.08786 | 0.898651 | ||||||||
\(82\) | 1.26590 | 0.139795 | ||||||||
\(83\) | 0.0724002 | 0.00794696 | 0.00397348 | − | 0.999992i | \(-0.498735\pi\) | ||||
0.00397348 | + | 0.999992i | \(0.498735\pi\) | |||||||
\(84\) | −0.939325 | −0.102489 | ||||||||
\(85\) | 9.99333 | 1.08393 | ||||||||
\(86\) | 5.70174 | 0.614834 | ||||||||
\(87\) | 1.24624 | 0.133611 | ||||||||
\(88\) | −4.47132 | −0.476644 | ||||||||
\(89\) | −5.63322 | −0.597120 | −0.298560 | − | 0.954391i | \(-0.596506\pi\) | ||||
−0.298560 | + | 0.954391i | \(0.596506\pi\) | |||||||
\(90\) | −10.8140 | −1.13990 | ||||||||
\(91\) | 16.8580 | 1.76720 | ||||||||
\(92\) | −0.733776 | −0.0765014 | ||||||||
\(93\) | 2.47970 | 0.257133 | ||||||||
\(94\) | −3.65985 | −0.377485 | ||||||||
\(95\) | −19.1928 | −1.96914 | ||||||||
\(96\) | 0.320182 | 0.0326784 | ||||||||
\(97\) | 19.0908 | 1.93838 | 0.969190 | − | 0.246313i | \(-0.0792191\pi\) | ||||
0.969190 | + | 0.246313i | \(0.0792191\pi\) | |||||||
\(98\) | −1.60673 | −0.162304 | ||||||||
\(99\) | −12.9556 | −1.30208 | ||||||||
\(100\) | 8.92938 | 0.892938 | ||||||||
\(101\) | 14.4410 | 1.43694 | 0.718468 | − | 0.695560i | \(-0.244843\pi\) | ||||
0.718468 | + | 0.695560i | \(0.244843\pi\) | |||||||
\(102\) | −0.857316 | −0.0848869 | ||||||||
\(103\) | 4.35741 | 0.429348 | 0.214674 | − | 0.976686i | \(-0.431131\pi\) | ||||
0.214674 | + | 0.976686i | \(0.431131\pi\) | |||||||
\(104\) | −5.74629 | −0.563470 | ||||||||
\(105\) | 3.50575 | 0.342127 | ||||||||
\(106\) | 2.28501 | 0.221940 | ||||||||
\(107\) | 12.1421 | 1.17382 | 0.586911 | − | 0.809652i | \(-0.300344\pi\) | ||||
0.586911 | + | 0.809652i | \(0.300344\pi\) | |||||||
\(108\) | 1.88827 | 0.181699 | ||||||||
\(109\) | 15.0753 | 1.44396 | 0.721978 | − | 0.691916i | \(-0.243233\pi\) | ||||
0.721978 | + | 0.691916i | \(0.243233\pi\) | |||||||
\(110\) | 16.6879 | 1.59113 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.93372 | 0.277211 | ||||||||
\(113\) | −0.406240 | −0.0382159 | −0.0191079 | − | 0.999817i | \(-0.506083\pi\) | ||||
−0.0191079 | + | 0.999817i | \(0.506083\pi\) | |||||||
\(114\) | 1.64653 | 0.154211 | ||||||||
\(115\) | 2.73860 | 0.255376 | ||||||||
\(116\) | −3.89230 | −0.361391 | ||||||||
\(117\) | −16.6498 | −1.53927 | ||||||||
\(118\) | −4.77466 | −0.439543 | ||||||||
\(119\) | −7.85531 | −0.720095 | ||||||||
\(120\) | −1.19499 | −0.109087 | ||||||||
\(121\) | 8.99267 | 0.817516 | ||||||||
\(122\) | −3.67128 | −0.332382 | ||||||||
\(123\) | 0.405318 | 0.0365463 | ||||||||
\(124\) | −7.74468 | −0.695492 | ||||||||
\(125\) | −14.6653 | −1.31170 | ||||||||
\(126\) | 8.50041 | 0.757277 | ||||||||
\(127\) | −11.1969 | −0.993568 | −0.496784 | − | 0.867874i | \(-0.665486\pi\) | ||||
−0.496784 | + | 0.867874i | \(0.665486\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.82559 | 0.160734 | ||||||||
\(130\) | 21.4463 | 1.88097 | ||||||||
\(131\) | −17.0888 | −1.49306 | −0.746528 | − | 0.665354i | \(-0.768280\pi\) | ||||
−0.746528 | + | 0.665354i | \(0.768280\pi\) | |||||||
\(132\) | −1.43163 | −0.124608 | ||||||||
\(133\) | 15.0866 | 1.30817 | ||||||||
\(134\) | 5.10474 | 0.440982 | ||||||||
\(135\) | −7.04741 | −0.606544 | ||||||||
\(136\) | 2.67759 | 0.229601 | ||||||||
\(137\) | 0.00968616 | 0.000827545 0 | 0.000413772 | − | 1.00000i | \(-0.499868\pi\) | ||||
0.000413772 | 1.00000i | \(0.499868\pi\) | ||||||||
\(138\) | −0.234942 | −0.0199996 | ||||||||
\(139\) | −2.38206 | −0.202044 | −0.101022 | − | 0.994884i | \(-0.532211\pi\) | ||||
−0.101022 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(140\) | −10.9493 | −0.925382 | ||||||||
\(141\) | −1.17182 | −0.0986848 | ||||||||
\(142\) | −0.0947712 | −0.00795302 | ||||||||
\(143\) | 25.6935 | 2.14860 | ||||||||
\(144\) | −2.89748 | −0.241457 | ||||||||
\(145\) | 14.5269 | 1.20639 | ||||||||
\(146\) | 0.442146 | 0.0365923 | ||||||||
\(147\) | −0.514445 | −0.0424307 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.7900 | 1.37549 | 0.687747 | − | 0.725950i | \(-0.258600\pi\) | ||||
0.687747 | + | 0.725950i | \(0.258600\pi\) | |||||||
\(150\) | 2.85902 | 0.233438 | ||||||||
\(151\) | −10.1575 | −0.826604 | −0.413302 | − | 0.910594i | \(-0.635625\pi\) | ||||
−0.413302 | + | 0.910594i | \(0.635625\pi\) | |||||||
\(152\) | −5.14247 | −0.417109 | ||||||||
\(153\) | 7.75827 | 0.627219 | ||||||||
\(154\) | −13.1176 | −1.05705 | ||||||||
\(155\) | 28.9047 | 2.32168 | ||||||||
\(156\) | −1.83986 | −0.147306 | ||||||||
\(157\) | 2.28147 | 0.182081 | 0.0910404 | − | 0.995847i | \(-0.470981\pi\) | ||||
0.0910404 | + | 0.995847i | \(0.470981\pi\) | |||||||
\(158\) | −14.4805 | −1.15201 | ||||||||
\(159\) | 0.731620 | 0.0580212 | ||||||||
\(160\) | 3.73221 | 0.295057 | ||||||||
\(161\) | −2.15270 | −0.169656 | ||||||||
\(162\) | −8.08786 | −0.635442 | ||||||||
\(163\) | 3.99005 | 0.312525 | 0.156263 | − | 0.987716i | \(-0.450055\pi\) | ||||
0.156263 | + | 0.987716i | \(0.450055\pi\) | |||||||
\(164\) | −1.26590 | −0.0988501 | ||||||||
\(165\) | 5.34316 | 0.415964 | ||||||||
\(166\) | −0.0724002 | −0.00561935 | ||||||||
\(167\) | −12.4588 | −0.964091 | −0.482046 | − | 0.876146i | \(-0.660106\pi\) | ||||
−0.482046 | + | 0.876146i | \(0.660106\pi\) | |||||||
\(168\) | 0.939325 | 0.0724705 | ||||||||
\(169\) | 20.0198 | 1.53998 | ||||||||
\(170\) | −9.99333 | −0.766453 | ||||||||
\(171\) | −14.9002 | −1.13945 | ||||||||
\(172\) | −5.70174 | −0.434753 | ||||||||
\(173\) | 18.3709 | 1.39671 | 0.698357 | − | 0.715750i | \(-0.253915\pi\) | ||||
0.698357 | + | 0.715750i | \(0.253915\pi\) | |||||||
\(174\) | −1.24624 | −0.0944775 | ||||||||
\(175\) | 26.1963 | 1.98026 | ||||||||
\(176\) | 4.47132 | 0.337038 | ||||||||
\(177\) | −1.52876 | −0.114909 | ||||||||
\(178\) | 5.63322 | 0.422228 | ||||||||
\(179\) | 20.6620 | 1.54435 | 0.772175 | − | 0.635410i | \(-0.219169\pi\) | ||||
0.772175 | + | 0.635410i | \(0.219169\pi\) | |||||||
\(180\) | 10.8140 | 0.806029 | ||||||||
\(181\) | 3.77241 | 0.280401 | 0.140201 | − | 0.990123i | \(-0.455225\pi\) | ||||
0.140201 | + | 0.990123i | \(0.455225\pi\) | |||||||
\(182\) | −16.8580 | −1.24960 | ||||||||
\(183\) | −1.17548 | −0.0868937 | ||||||||
\(184\) | 0.733776 | 0.0540947 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.47970 | −0.181821 | ||||||||
\(187\) | −11.9724 | −0.875505 | ||||||||
\(188\) | 3.65985 | 0.266922 | ||||||||
\(189\) | 5.53965 | 0.402950 | ||||||||
\(190\) | 19.1928 | 1.39239 | ||||||||
\(191\) | 15.2024 | 1.10001 | 0.550005 | − | 0.835161i | \(-0.314626\pi\) | ||||
0.550005 | + | 0.835161i | \(0.314626\pi\) | |||||||
\(192\) | −0.320182 | −0.0231071 | ||||||||
\(193\) | 21.6678 | 1.55969 | 0.779843 | − | 0.625976i | \(-0.215299\pi\) | ||||
0.779843 | + | 0.625976i | \(0.215299\pi\) | |||||||
\(194\) | −19.0908 | −1.37064 | ||||||||
\(195\) | 6.86673 | 0.491737 | ||||||||
\(196\) | 1.60673 | 0.114766 | ||||||||
\(197\) | −13.7395 | −0.978898 | −0.489449 | − | 0.872032i | \(-0.662802\pi\) | ||||
−0.489449 | + | 0.872032i | \(0.662802\pi\) | |||||||
\(198\) | 12.9556 | 0.920712 | ||||||||
\(199\) | 5.63105 | 0.399174 | 0.199587 | − | 0.979880i | \(-0.436040\pi\) | ||||
0.199587 | + | 0.979880i | \(0.436040\pi\) | |||||||
\(200\) | −8.92938 | −0.631402 | ||||||||
\(201\) | 1.63444 | 0.115285 | ||||||||
\(202\) | −14.4410 | −1.01607 | ||||||||
\(203\) | −11.4189 | −0.801452 | ||||||||
\(204\) | 0.857316 | 0.0600241 | ||||||||
\(205\) | 4.72460 | 0.329980 | ||||||||
\(206\) | −4.35741 | −0.303595 | ||||||||
\(207\) | 2.12610 | 0.147774 | ||||||||
\(208\) | 5.74629 | 0.398433 | ||||||||
\(209\) | 22.9936 | 1.59050 | ||||||||
\(210\) | −3.50575 | −0.241920 | ||||||||
\(211\) | −23.0510 | −1.58689 | −0.793447 | − | 0.608639i | \(-0.791716\pi\) | ||||
−0.793447 | + | 0.608639i | \(0.791716\pi\) | |||||||
\(212\) | −2.28501 | −0.156935 | ||||||||
\(213\) | −0.0303440 | −0.00207914 | ||||||||
\(214\) | −12.1421 | −0.830017 | ||||||||
\(215\) | 21.2801 | 1.45129 | ||||||||
\(216\) | −1.88827 | −0.128480 | ||||||||
\(217\) | −22.7207 | −1.54238 | ||||||||
\(218\) | −15.0753 | −1.02103 | ||||||||
\(219\) | 0.141567 | 0.00956622 | ||||||||
\(220\) | −16.6879 | −1.12510 | ||||||||
\(221\) | −15.3862 | −1.03499 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.2412 | −1.02062 | −0.510312 | − | 0.859989i | \(-0.670470\pi\) | ||||
−0.510312 | + | 0.859989i | \(0.670470\pi\) | |||||||
\(224\) | −2.93372 | −0.196018 | ||||||||
\(225\) | −25.8727 | −1.72485 | ||||||||
\(226\) | 0.406240 | 0.0270227 | ||||||||
\(227\) | −12.8314 | −0.851648 | −0.425824 | − | 0.904806i | \(-0.640016\pi\) | ||||
−0.425824 | + | 0.904806i | \(0.640016\pi\) | |||||||
\(228\) | −1.64653 | −0.109044 | ||||||||
\(229\) | −20.2815 | −1.34024 | −0.670120 | − | 0.742253i | \(-0.733757\pi\) | ||||
−0.670120 | + | 0.742253i | \(0.733757\pi\) | |||||||
\(230\) | −2.73860 | −0.180578 | ||||||||
\(231\) | −4.20002 | −0.276341 | ||||||||
\(232\) | 3.89230 | 0.255542 | ||||||||
\(233\) | 20.2108 | 1.32405 | 0.662027 | − | 0.749480i | \(-0.269696\pi\) | ||||
0.662027 | + | 0.749480i | \(0.269696\pi\) | |||||||
\(234\) | 16.6498 | 1.08843 | ||||||||
\(235\) | −13.6593 | −0.891036 | ||||||||
\(236\) | 4.77466 | 0.310804 | ||||||||
\(237\) | −4.63639 | −0.301166 | ||||||||
\(238\) | 7.85531 | 0.509184 | ||||||||
\(239\) | 6.87306 | 0.444582 | 0.222291 | − | 0.974980i | \(-0.428647\pi\) | ||||
0.222291 | + | 0.974980i | \(0.428647\pi\) | |||||||
\(240\) | 1.19499 | 0.0771360 | ||||||||
\(241\) | −14.1313 | −0.910279 | −0.455140 | − | 0.890420i | \(-0.650411\pi\) | ||||
−0.455140 | + | 0.890420i | \(0.650411\pi\) | |||||||
\(242\) | −8.99267 | −0.578071 | ||||||||
\(243\) | −8.25439 | −0.529519 | ||||||||
\(244\) | 3.67128 | 0.235030 | ||||||||
\(245\) | −5.99664 | −0.383111 | ||||||||
\(246\) | −0.405318 | −0.0258421 | ||||||||
\(247\) | 29.5501 | 1.88023 | ||||||||
\(248\) | 7.74468 | 0.491787 | ||||||||
\(249\) | −0.0231812 | −0.00146905 | ||||||||
\(250\) | 14.6653 | 0.927512 | ||||||||
\(251\) | −21.4139 | −1.35163 | −0.675816 | − | 0.737070i | \(-0.736209\pi\) | ||||
−0.675816 | + | 0.737070i | \(0.736209\pi\) | |||||||
\(252\) | −8.50041 | −0.535476 | ||||||||
\(253\) | −3.28095 | −0.206271 | ||||||||
\(254\) | 11.1969 | 0.702559 | ||||||||
\(255\) | −3.19968 | −0.200372 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.281256 | −0.0175443 | −0.00877214 | − | 0.999962i | \(-0.502792\pi\) | ||||
−0.00877214 | + | 0.999962i | \(0.502792\pi\) | |||||||
\(258\) | −1.82559 | −0.113656 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −21.4463 | −1.33005 | ||||||||
\(261\) | 11.2779 | 0.698083 | ||||||||
\(262\) | 17.0888 | 1.05575 | ||||||||
\(263\) | 12.8063 | 0.789669 | 0.394834 | − | 0.918752i | \(-0.370802\pi\) | ||||
0.394834 | + | 0.918752i | \(0.370802\pi\) | |||||||
\(264\) | 1.43163 | 0.0881110 | ||||||||
\(265\) | 8.52814 | 0.523880 | ||||||||
\(266\) | −15.0866 | −0.925018 | ||||||||
\(267\) | 1.80366 | 0.110382 | ||||||||
\(268\) | −5.10474 | −0.311822 | ||||||||
\(269\) | 11.7216 | 0.714677 | 0.357338 | − | 0.933975i | \(-0.383684\pi\) | ||||
0.357338 | + | 0.933975i | \(0.383684\pi\) | |||||||
\(270\) | 7.04741 | 0.428891 | ||||||||
\(271\) | 5.46425 | 0.331930 | 0.165965 | − | 0.986132i | \(-0.446926\pi\) | ||||
0.165965 | + | 0.986132i | \(0.446926\pi\) | |||||||
\(272\) | −2.67759 | −0.162353 | ||||||||
\(273\) | −5.39763 | −0.326679 | ||||||||
\(274\) | −0.00968616 | −0.000585162 0 | ||||||||
\(275\) | 39.9261 | 2.40763 | ||||||||
\(276\) | 0.234942 | 0.0141418 | ||||||||
\(277\) | 6.34878 | 0.381461 | 0.190731 | − | 0.981642i | \(-0.438914\pi\) | ||||
0.190731 | + | 0.981642i | \(0.438914\pi\) | |||||||
\(278\) | 2.38206 | 0.142867 | ||||||||
\(279\) | 22.4401 | 1.34345 | ||||||||
\(280\) | 10.9493 | 0.654344 | ||||||||
\(281\) | 7.35463 | 0.438741 | 0.219370 | − | 0.975642i | \(-0.429600\pi\) | ||||
0.219370 | + | 0.975642i | \(0.429600\pi\) | |||||||
\(282\) | 1.17182 | 0.0697807 | ||||||||
\(283\) | 26.3239 | 1.56479 | 0.782395 | − | 0.622782i | \(-0.213998\pi\) | ||||
0.782395 | + | 0.622782i | \(0.213998\pi\) | |||||||
\(284\) | 0.0947712 | 0.00562364 | ||||||||
\(285\) | 6.14518 | 0.364009 | ||||||||
\(286\) | −25.6935 | −1.51929 | ||||||||
\(287\) | −3.71380 | −0.219218 | ||||||||
\(288\) | 2.89748 | 0.170736 | ||||||||
\(289\) | −9.83051 | −0.578265 | ||||||||
\(290\) | −14.5269 | −0.853048 | ||||||||
\(291\) | −6.11254 | −0.358323 | ||||||||
\(292\) | −0.442146 | −0.0258746 | ||||||||
\(293\) | −20.7874 | −1.21441 | −0.607207 | − | 0.794543i | \(-0.707710\pi\) | ||||
−0.607207 | + | 0.794543i | \(0.707710\pi\) | |||||||
\(294\) | 0.514445 | 0.0300030 | ||||||||
\(295\) | −17.8200 | −1.03752 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.44304 | 0.489915 | ||||||||
\(298\) | −16.7900 | −0.972621 | ||||||||
\(299\) | −4.21649 | −0.243846 | ||||||||
\(300\) | −2.85902 | −0.165066 | ||||||||
\(301\) | −16.7273 | −0.964146 | ||||||||
\(302\) | 10.1575 | 0.584497 | ||||||||
\(303\) | −4.62376 | −0.265628 | ||||||||
\(304\) | 5.14247 | 0.294941 | ||||||||
\(305\) | −13.7020 | −0.784573 | ||||||||
\(306\) | −7.75827 | −0.443511 | ||||||||
\(307\) | 7.73062 | 0.441210 | 0.220605 | − | 0.975363i | \(-0.429197\pi\) | ||||
0.220605 | + | 0.975363i | \(0.429197\pi\) | |||||||
\(308\) | 13.1176 | 0.747445 | ||||||||
\(309\) | −1.39516 | −0.0793680 | ||||||||
\(310\) | −28.9047 | −1.64168 | ||||||||
\(311\) | 27.6312 | 1.56682 | 0.783411 | − | 0.621504i | \(-0.213478\pi\) | ||||
0.783411 | + | 0.621504i | \(0.213478\pi\) | |||||||
\(312\) | 1.83986 | 0.104161 | ||||||||
\(313\) | −12.3333 | −0.697119 | −0.348559 | − | 0.937287i | \(-0.613329\pi\) | ||||
−0.348559 | + | 0.937287i | \(0.613329\pi\) | |||||||
\(314\) | −2.28147 | −0.128751 | ||||||||
\(315\) | 31.7253 | 1.78752 | ||||||||
\(316\) | 14.4805 | 0.814592 | ||||||||
\(317\) | −0.315766 | −0.0177352 | −0.00886760 | − | 0.999961i | \(-0.502823\pi\) | ||||
−0.00886760 | + | 0.999961i | \(0.502823\pi\) | |||||||
\(318\) | −0.731620 | −0.0410272 | ||||||||
\(319\) | −17.4037 | −0.974421 | ||||||||
\(320\) | −3.73221 | −0.208637 | ||||||||
\(321\) | −3.88768 | −0.216989 | ||||||||
\(322\) | 2.15270 | 0.119965 | ||||||||
\(323\) | −13.7694 | −0.766152 | ||||||||
\(324\) | 8.08786 | 0.449326 | ||||||||
\(325\) | 51.3108 | 2.84621 | ||||||||
\(326\) | −3.99005 | −0.220989 | ||||||||
\(327\) | −4.82685 | −0.266926 | ||||||||
\(328\) | 1.26590 | 0.0698976 | ||||||||
\(329\) | 10.7370 | 0.591949 | ||||||||
\(330\) | −5.34316 | −0.294131 | ||||||||
\(331\) | 16.9231 | 0.930179 | 0.465089 | − | 0.885264i | \(-0.346022\pi\) | ||||
0.465089 | + | 0.885264i | \(0.346022\pi\) | |||||||
\(332\) | 0.0724002 | 0.00397348 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4588 | 0.681715 | ||||||||
\(335\) | 19.0519 | 1.04092 | ||||||||
\(336\) | −0.939325 | −0.0512444 | ||||||||
\(337\) | 15.5319 | 0.846075 | 0.423037 | − | 0.906112i | \(-0.360964\pi\) | ||||
0.423037 | + | 0.906112i | \(0.360964\pi\) | |||||||
\(338\) | −20.0198 | −1.08893 | ||||||||
\(339\) | 0.130071 | 0.00706447 | ||||||||
\(340\) | 9.99333 | 0.541964 | ||||||||
\(341\) | −34.6289 | −1.87526 | ||||||||
\(342\) | 14.9002 | 0.805712 | ||||||||
\(343\) | −15.8224 | −0.854327 | ||||||||
\(344\) | 5.70174 | 0.307417 | ||||||||
\(345\) | −0.876851 | −0.0472081 | ||||||||
\(346\) | −18.3709 | −0.987625 | ||||||||
\(347\) | 23.8773 | 1.28180 | 0.640900 | − | 0.767624i | \(-0.278561\pi\) | ||||
0.640900 | + | 0.767624i | \(0.278561\pi\) | |||||||
\(348\) | 1.24624 | 0.0668057 | ||||||||
\(349\) | 18.8292 | 1.00790 | 0.503951 | − | 0.863732i | \(-0.331879\pi\) | ||||
0.503951 | + | 0.863732i | \(0.331879\pi\) | |||||||
\(350\) | −26.1963 | −1.40025 | ||||||||
\(351\) | 10.8505 | 0.579158 | ||||||||
\(352\) | −4.47132 | −0.238322 | ||||||||
\(353\) | −2.49614 | −0.132856 | −0.0664280 | − | 0.997791i | \(-0.521160\pi\) | ||||
−0.0664280 | + | 0.997791i | \(0.521160\pi\) | |||||||
\(354\) | 1.52876 | 0.0812527 | ||||||||
\(355\) | −0.353706 | −0.0187728 | ||||||||
\(356\) | −5.63322 | −0.298560 | ||||||||
\(357\) | 2.51513 | 0.133115 | ||||||||
\(358\) | −20.6620 | −1.09202 | ||||||||
\(359\) | 12.0536 | 0.636164 | 0.318082 | − | 0.948063i | \(-0.396961\pi\) | ||||
0.318082 | + | 0.948063i | \(0.396961\pi\) | |||||||
\(360\) | −10.8140 | −0.569948 | ||||||||
\(361\) | 7.44500 | 0.391842 | ||||||||
\(362\) | −3.77241 | −0.198274 | ||||||||
\(363\) | −2.87929 | −0.151124 | ||||||||
\(364\) | 16.8580 | 0.883600 | ||||||||
\(365\) | 1.65018 | 0.0863744 | ||||||||
\(366\) | 1.17548 | 0.0614431 | ||||||||
\(367\) | 37.0543 | 1.93422 | 0.967111 | − | 0.254356i | \(-0.0818636\pi\) | ||||
0.967111 | + | 0.254356i | \(0.0818636\pi\) | |||||||
\(368\) | −0.733776 | −0.0382507 | ||||||||
\(369\) | 3.66792 | 0.190944 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.70359 | −0.348033 | ||||||||
\(372\) | 2.47970 | 0.128567 | ||||||||
\(373\) | −5.38668 | −0.278912 | −0.139456 | − | 0.990228i | \(-0.544535\pi\) | ||||
−0.139456 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(374\) | 11.9724 | 0.619076 | ||||||||
\(375\) | 4.69555 | 0.242477 | ||||||||
\(376\) | −3.65985 | −0.188742 | ||||||||
\(377\) | −22.3663 | −1.15192 | ||||||||
\(378\) | −5.53965 | −0.284929 | ||||||||
\(379\) | 21.6224 | 1.11067 | 0.555335 | − | 0.831627i | \(-0.312590\pi\) | ||||
0.555335 | + | 0.831627i | \(0.312590\pi\) | |||||||
\(380\) | −19.1928 | −0.984568 | ||||||||
\(381\) | 3.58506 | 0.183668 | ||||||||
\(382\) | −15.2024 | −0.777825 | ||||||||
\(383\) | 37.0449 | 1.89290 | 0.946452 | − | 0.322845i | \(-0.104639\pi\) | ||||
0.946452 | + | 0.322845i | \(0.104639\pi\) | |||||||
\(384\) | 0.320182 | 0.0163392 | ||||||||
\(385\) | −48.9576 | −2.49511 | ||||||||
\(386\) | −21.6678 | −1.10286 | ||||||||
\(387\) | 16.5207 | 0.839794 | ||||||||
\(388\) | 19.0908 | 0.969190 | ||||||||
\(389\) | −22.5262 | −1.14212 | −0.571062 | − | 0.820907i | \(-0.693468\pi\) | ||||
−0.571062 | + | 0.820907i | \(0.693468\pi\) | |||||||
\(390\) | −6.86673 | −0.347710 | ||||||||
\(391\) | 1.96475 | 0.0993618 | ||||||||
\(392\) | −1.60673 | −0.0811520 | ||||||||
\(393\) | 5.47152 | 0.276002 | ||||||||
\(394\) | 13.7395 | 0.692185 | ||||||||
\(395\) | −54.0442 | −2.71926 | ||||||||
\(396\) | −12.9556 | −0.651042 | ||||||||
\(397\) | 17.0296 | 0.854689 | 0.427344 | − | 0.904089i | \(-0.359449\pi\) | ||||
0.427344 | + | 0.904089i | \(0.359449\pi\) | |||||||
\(398\) | −5.63105 | −0.282259 | ||||||||
\(399\) | −4.83045 | −0.241825 | ||||||||
\(400\) | 8.92938 | 0.446469 | ||||||||
\(401\) | −20.7727 | −1.03734 | −0.518671 | − | 0.854974i | \(-0.673573\pi\) | ||||
−0.518671 | + | 0.854974i | \(0.673573\pi\) | |||||||
\(402\) | −1.63444 | −0.0815187 | ||||||||
\(403\) | −44.5031 | −2.21686 | ||||||||
\(404\) | 14.4410 | 0.718468 | ||||||||
\(405\) | −30.1856 | −1.49993 | ||||||||
\(406\) | 11.4189 | 0.566712 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.857316 | −0.0424435 | ||||||||
\(409\) | 0.949968 | 0.0469729 | 0.0234865 | − | 0.999724i | \(-0.492523\pi\) | ||||
0.0234865 | + | 0.999724i | \(0.492523\pi\) | |||||||
\(410\) | −4.72460 | −0.233331 | ||||||||
\(411\) | −0.00310133 | −0.000152977 0 | ||||||||
\(412\) | 4.35741 | 0.214674 | ||||||||
\(413\) | 14.0075 | 0.689266 | ||||||||
\(414\) | −2.12610 | −0.104492 | ||||||||
\(415\) | −0.270213 | −0.0132642 | ||||||||
\(416\) | −5.74629 | −0.281735 | ||||||||
\(417\) | 0.762694 | 0.0373493 | ||||||||
\(418\) | −22.9936 | −1.12465 | ||||||||
\(419\) | −30.2920 | −1.47986 | −0.739930 | − | 0.672684i | \(-0.765141\pi\) | ||||
−0.739930 | + | 0.672684i | \(0.765141\pi\) | |||||||
\(420\) | 3.50575 | 0.171063 | ||||||||
\(421\) | −19.7724 | −0.963649 | −0.481824 | − | 0.876268i | \(-0.660026\pi\) | ||||
−0.481824 | + | 0.876268i | \(0.660026\pi\) | |||||||
\(422\) | 23.0510 | 1.12210 | ||||||||
\(423\) | −10.6044 | −0.515601 | ||||||||
\(424\) | 2.28501 | 0.110970 | ||||||||
\(425\) | −23.9092 | −1.15977 | ||||||||
\(426\) | 0.0303440 | 0.00147017 | ||||||||
\(427\) | 10.7705 | 0.521222 | ||||||||
\(428\) | 12.1421 | 0.586911 | ||||||||
\(429\) | −8.22658 | −0.397183 | ||||||||
\(430\) | −21.2801 | −1.02622 | ||||||||
\(431\) | −5.15897 | −0.248499 | −0.124249 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124249 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(432\) | 1.88827 | 0.0908493 | ||||||||
\(433\) | 16.4459 | 0.790339 | 0.395170 | − | 0.918608i | \(-0.370686\pi\) | ||||
0.395170 | + | 0.918608i | \(0.370686\pi\) | |||||||
\(434\) | 22.7207 | 1.09063 | ||||||||
\(435\) | −4.65124 | −0.223010 | ||||||||
\(436\) | 15.0753 | 0.721978 | ||||||||
\(437\) | −3.77342 | −0.180507 | ||||||||
\(438\) | −0.141567 | −0.00676434 | ||||||||
\(439\) | 8.72749 | 0.416540 | 0.208270 | − | 0.978071i | \(-0.433217\pi\) | ||||
0.208270 | + | 0.978071i | \(0.433217\pi\) | |||||||
\(440\) | 16.6879 | 0.795564 | ||||||||
\(441\) | −4.65547 | −0.221689 | ||||||||
\(442\) | 15.3862 | 0.731847 | ||||||||
\(443\) | 20.5472 | 0.976225 | 0.488112 | − | 0.872781i | \(-0.337686\pi\) | ||||
0.488112 | + | 0.872781i | \(0.337686\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.0244 | 0.996650 | ||||||||
\(446\) | 15.2412 | 0.721690 | ||||||||
\(447\) | −5.37587 | −0.254270 | ||||||||
\(448\) | 2.93372 | 0.138605 | ||||||||
\(449\) | 4.84047 | 0.228436 | 0.114218 | − | 0.993456i | \(-0.463564\pi\) | ||||
0.114218 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(450\) | 25.8727 | 1.21965 | ||||||||
\(451\) | −5.66023 | −0.266530 | ||||||||
\(452\) | −0.406240 | −0.0191079 | ||||||||
\(453\) | 3.25224 | 0.152804 | ||||||||
\(454\) | 12.8314 | 0.602206 | ||||||||
\(455\) | −62.9176 | −2.94962 | ||||||||
\(456\) | 1.64653 | 0.0771056 | ||||||||
\(457\) | 28.5767 | 1.33676 | 0.668380 | − | 0.743820i | \(-0.266988\pi\) | ||||
0.668380 | + | 0.743820i | \(0.266988\pi\) | |||||||
\(458\) | 20.2815 | 0.947692 | ||||||||
\(459\) | −5.05601 | −0.235994 | ||||||||
\(460\) | 2.73860 | 0.127688 | ||||||||
\(461\) | 41.8146 | 1.94750 | 0.973749 | − | 0.227625i | \(-0.0730960\pi\) | ||||
0.973749 | + | 0.227625i | \(0.0730960\pi\) | |||||||
\(462\) | 4.20002 | 0.195403 | ||||||||
\(463\) | −24.6079 | −1.14363 | −0.571814 | − | 0.820383i | \(-0.693760\pi\) | ||||
−0.571814 | + | 0.820383i | \(0.693760\pi\) | |||||||
\(464\) | −3.89230 | −0.180696 | ||||||||
\(465\) | −9.25477 | −0.429180 | ||||||||
\(466\) | −20.2108 | −0.936248 | ||||||||
\(467\) | 8.21176 | 0.379995 | 0.189998 | − | 0.981785i | \(-0.439152\pi\) | ||||
0.189998 | + | 0.981785i | \(0.439152\pi\) | |||||||
\(468\) | −16.6498 | −0.769636 | ||||||||
\(469\) | −14.9759 | −0.691522 | ||||||||
\(470\) | 13.6593 | 0.630058 | ||||||||
\(471\) | −0.730484 | −0.0336589 | ||||||||
\(472\) | −4.77466 | −0.219772 | ||||||||
\(473\) | −25.4943 | −1.17223 | ||||||||
\(474\) | 4.63639 | 0.212957 | ||||||||
\(475\) | 45.9191 | 2.10691 | ||||||||
\(476\) | −7.85531 | −0.360047 | ||||||||
\(477\) | 6.62079 | 0.303145 | ||||||||
\(478\) | −6.87306 | −0.314367 | ||||||||
\(479\) | 1.46099 | 0.0667546 | 0.0333773 | − | 0.999443i | \(-0.489374\pi\) | ||||
0.0333773 | + | 0.999443i | \(0.489374\pi\) | |||||||
\(480\) | −1.19499 | −0.0545434 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.1313 | 0.643665 | ||||||||
\(483\) | 0.689254 | 0.0313621 | ||||||||
\(484\) | 8.99267 | 0.408758 | ||||||||
\(485\) | −71.2510 | −3.23534 | ||||||||
\(486\) | 8.25439 | 0.374427 | ||||||||
\(487\) | −3.63728 | −0.164821 | −0.0824103 | − | 0.996598i | \(-0.526262\pi\) | ||||
−0.0824103 | + | 0.996598i | \(0.526262\pi\) | |||||||
\(488\) | −3.67128 | −0.166191 | ||||||||
\(489\) | −1.27754 | −0.0577725 | ||||||||
\(490\) | 5.99664 | 0.270901 | ||||||||
\(491\) | −22.2913 | −1.00599 | −0.502996 | − | 0.864289i | \(-0.667769\pi\) | ||||
−0.502996 | + | 0.864289i | \(0.667769\pi\) | |||||||
\(492\) | 0.405318 | 0.0182731 | ||||||||
\(493\) | 10.4220 | 0.469383 | ||||||||
\(494\) | −29.5501 | −1.32952 | ||||||||
\(495\) | 48.3529 | 2.17330 | ||||||||
\(496\) | −7.74468 | −0.347746 | ||||||||
\(497\) | 0.278032 | 0.0124715 | ||||||||
\(498\) | 0.0231812 | 0.00103878 | ||||||||
\(499\) | 26.3887 | 1.18132 | 0.590660 | − | 0.806921i | \(-0.298867\pi\) | ||||
0.590660 | + | 0.806921i | \(0.298867\pi\) | |||||||
\(500\) | −14.6653 | −0.655850 | ||||||||
\(501\) | 3.98908 | 0.178219 | ||||||||
\(502\) | 21.4139 | 0.955748 | ||||||||
\(503\) | 27.9428 | 1.24591 | 0.622954 | − | 0.782258i | \(-0.285932\pi\) | ||||
0.622954 | + | 0.782258i | \(0.285932\pi\) | |||||||
\(504\) | 8.50041 | 0.378638 | ||||||||
\(505\) | −53.8970 | −2.39838 | ||||||||
\(506\) | 3.28095 | 0.145856 | ||||||||
\(507\) | −6.40998 | −0.284677 | ||||||||
\(508\) | −11.1969 | −0.496784 | ||||||||
\(509\) | 18.5327 | 0.821449 | 0.410724 | − | 0.911760i | \(-0.365276\pi\) | ||||
0.410724 | + | 0.911760i | \(0.365276\pi\) | |||||||
\(510\) | 3.19968 | 0.141684 | ||||||||
\(511\) | −1.29713 | −0.0573818 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 9.71036 | 0.428723 | ||||||||
\(514\) | 0.281256 | 0.0124057 | ||||||||
\(515\) | −16.2628 | −0.716623 | ||||||||
\(516\) | 1.82559 | 0.0803672 | ||||||||
\(517\) | 16.3643 | 0.719703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.88203 | −0.258192 | ||||||||
\(520\) | 21.4463 | 0.940484 | ||||||||
\(521\) | 5.19140 | 0.227439 | 0.113720 | − | 0.993513i | \(-0.463723\pi\) | ||||
0.113720 | + | 0.993513i | \(0.463723\pi\) | |||||||
\(522\) | −11.2779 | −0.493619 | ||||||||
\(523\) | −1.80007 | −0.0787117 | −0.0393558 | − | 0.999225i | \(-0.512531\pi\) | ||||
−0.0393558 | + | 0.999225i | \(0.512531\pi\) | |||||||
\(524\) | −17.0888 | −0.746528 | ||||||||
\(525\) | −8.38758 | −0.366064 | ||||||||
\(526\) | −12.8063 | −0.558380 | ||||||||
\(527\) | 20.7371 | 0.903321 | ||||||||
\(528\) | −1.43163 | −0.0623039 | ||||||||
\(529\) | −22.4616 | −0.976590 | ||||||||
\(530\) | −8.52814 | −0.370439 | ||||||||
\(531\) | −13.8345 | −0.600367 | ||||||||
\(532\) | 15.0866 | 0.654086 | ||||||||
\(533\) | −7.27422 | −0.315081 | ||||||||
\(534\) | −1.80366 | −0.0780518 | ||||||||
\(535\) | −45.3169 | −1.95922 | ||||||||
\(536\) | 5.10474 | 0.220491 | ||||||||
\(537\) | −6.61560 | −0.285484 | ||||||||
\(538\) | −11.7216 | −0.505353 | ||||||||
\(539\) | 7.18419 | 0.309445 | ||||||||
\(540\) | −7.04741 | −0.303272 | ||||||||
\(541\) | −9.30927 | −0.400237 | −0.200118 | − | 0.979772i | \(-0.564133\pi\) | ||||
−0.200118 | + | 0.979772i | \(0.564133\pi\) | |||||||
\(542\) | −5.46425 | −0.234710 | ||||||||
\(543\) | −1.20786 | −0.0518342 | ||||||||
\(544\) | 2.67759 | 0.114801 | ||||||||
\(545\) | −56.2643 | −2.41010 | ||||||||
\(546\) | 5.39763 | 0.230997 | ||||||||
\(547\) | 34.3737 | 1.46971 | 0.734857 | − | 0.678222i | \(-0.237249\pi\) | ||||
0.734857 | + | 0.678222i | \(0.237249\pi\) | |||||||
\(548\) | 0.00968616 | 0.000413772 0 | ||||||||
\(549\) | −10.6375 | −0.453996 | ||||||||
\(550\) | −39.9261 | −1.70245 | ||||||||
\(551\) | −20.0160 | −0.852712 | ||||||||
\(552\) | −0.234942 | −0.00999978 | ||||||||
\(553\) | 42.4818 | 1.80651 | ||||||||
\(554\) | −6.34878 | −0.269734 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.38206 | −0.101022 | ||||||||
\(557\) | −24.6868 | −1.04601 | −0.523007 | − | 0.852328i | \(-0.675190\pi\) | ||||
−0.523007 | + | 0.852328i | \(0.675190\pi\) | |||||||
\(558\) | −22.4401 | −0.949964 | ||||||||
\(559\) | −32.7638 | −1.38576 | ||||||||
\(560\) | −10.9493 | −0.462691 | ||||||||
\(561\) | 3.83333 | 0.161843 | ||||||||
\(562\) | −7.35463 | −0.310236 | ||||||||
\(563\) | 32.7573 | 1.38056 | 0.690279 | − | 0.723544i | \(-0.257488\pi\) | ||||
0.690279 | + | 0.723544i | \(0.257488\pi\) | |||||||
\(564\) | −1.17182 | −0.0493424 | ||||||||
\(565\) | 1.51617 | 0.0637859 | ||||||||
\(566\) | −26.3239 | −1.10647 | ||||||||
\(567\) | 23.7275 | 0.996463 | ||||||||
\(568\) | −0.0947712 | −0.00397651 | ||||||||
\(569\) | 34.7114 | 1.45518 | 0.727589 | − | 0.686013i | \(-0.240641\pi\) | ||||
0.727589 | + | 0.686013i | \(0.240641\pi\) | |||||||
\(570\) | −6.14518 | −0.257393 | ||||||||
\(571\) | −45.0052 | −1.88341 | −0.941704 | − | 0.336442i | \(-0.890777\pi\) | ||||
−0.941704 | + | 0.336442i | \(0.890777\pi\) | |||||||
\(572\) | 25.6935 | 1.07430 | ||||||||
\(573\) | −4.86755 | −0.203345 | ||||||||
\(574\) | 3.71380 | 0.155011 | ||||||||
\(575\) | −6.55216 | −0.273244 | ||||||||
\(576\) | −2.89748 | −0.120728 | ||||||||
\(577\) | −18.2468 | −0.759625 | −0.379813 | − | 0.925063i | \(-0.624012\pi\) | ||||
−0.379813 | + | 0.925063i | \(0.624012\pi\) | |||||||
\(578\) | 9.83051 | 0.408895 | ||||||||
\(579\) | −6.93765 | −0.288319 | ||||||||
\(580\) | 14.5269 | 0.603196 | ||||||||
\(581\) | 0.212402 | 0.00881193 | ||||||||
\(582\) | 6.11254 | 0.253373 | ||||||||
\(583\) | −10.2170 | −0.423146 | ||||||||
\(584\) | 0.442146 | 0.0182961 | ||||||||
\(585\) | 62.1404 | 2.56919 | ||||||||
\(586\) | 20.7874 | 0.858721 | ||||||||
\(587\) | −29.7791 | −1.22911 | −0.614557 | − | 0.788872i | \(-0.710665\pi\) | ||||
−0.614557 | + | 0.788872i | \(0.710665\pi\) | |||||||
\(588\) | −0.514445 | −0.0212153 | ||||||||
\(589\) | −39.8268 | −1.64103 | ||||||||
\(590\) | 17.8200 | 0.733639 | ||||||||
\(591\) | 4.39913 | 0.180956 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.5120 | 0.883392 | 0.441696 | − | 0.897165i | \(-0.354377\pi\) | ||||
0.441696 | + | 0.897165i | \(0.354377\pi\) | |||||||
\(594\) | −8.44304 | −0.346422 | ||||||||
\(595\) | 29.3176 | 1.20191 | ||||||||
\(596\) | 16.7900 | 0.687747 | ||||||||
\(597\) | −1.80296 | −0.0737902 | ||||||||
\(598\) | 4.21649 | 0.172425 | ||||||||
\(599\) | −1.94068 | −0.0792940 | −0.0396470 | − | 0.999214i | \(-0.512623\pi\) | ||||
−0.0396470 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(600\) | 2.85902 | 0.116719 | ||||||||
\(601\) | −4.10385 | −0.167400 | −0.0836998 | − | 0.996491i | \(-0.526674\pi\) | ||||
−0.0836998 | + | 0.996491i | \(0.526674\pi\) | |||||||
\(602\) | 16.7273 | 0.681754 | ||||||||
\(603\) | 14.7909 | 0.602332 | ||||||||
\(604\) | −10.1575 | −0.413302 | ||||||||
\(605\) | −33.5625 | −1.36451 | ||||||||
\(606\) | 4.62376 | 0.187827 | ||||||||
\(607\) | −5.19962 | −0.211046 | −0.105523 | − | 0.994417i | \(-0.533652\pi\) | ||||
−0.105523 | + | 0.994417i | \(0.533652\pi\) | |||||||
\(608\) | −5.14247 | −0.208555 | ||||||||
\(609\) | 3.65613 | 0.148154 | ||||||||
\(610\) | 13.7020 | 0.554777 | ||||||||
\(611\) | 21.0305 | 0.850805 | ||||||||
\(612\) | 7.75827 | 0.313610 | ||||||||
\(613\) | −18.0439 | −0.728787 | −0.364394 | − | 0.931245i | \(-0.618724\pi\) | ||||
−0.364394 | + | 0.931245i | \(0.618724\pi\) | |||||||
\(614\) | −7.73062 | −0.311982 | ||||||||
\(615\) | −1.51273 | −0.0609992 | ||||||||
\(616\) | −13.1176 | −0.528523 | ||||||||
\(617\) | −49.2054 | −1.98093 | −0.990467 | − | 0.137751i | \(-0.956013\pi\) | ||||
−0.990467 | + | 0.137751i | \(0.956013\pi\) | |||||||
\(618\) | 1.39516 | 0.0561217 | ||||||||
\(619\) | −25.8553 | −1.03921 | −0.519606 | − | 0.854406i | \(-0.673921\pi\) | ||||
−0.519606 | + | 0.854406i | \(0.673921\pi\) | |||||||
\(620\) | 28.9047 | 1.16084 | ||||||||
\(621\) | −1.38557 | −0.0556008 | ||||||||
\(622\) | −27.6312 | −1.10791 | ||||||||
\(623\) | −16.5263 | −0.662113 | ||||||||
\(624\) | −1.83986 | −0.0736532 | ||||||||
\(625\) | 10.0869 | 0.403476 | ||||||||
\(626\) | 12.3333 | 0.492937 | ||||||||
\(627\) | −7.36214 | −0.294015 | ||||||||
\(628\) | 2.28147 | 0.0910404 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −31.7253 | −1.26397 | ||||||||
\(631\) | −31.1715 | −1.24092 | −0.620460 | − | 0.784238i | \(-0.713054\pi\) | ||||
−0.620460 | + | 0.784238i | \(0.713054\pi\) | |||||||
\(632\) | −14.4805 | −0.576003 | ||||||||
\(633\) | 7.38050 | 0.293349 | ||||||||
\(634\) | 0.315766 | 0.0125407 | ||||||||
\(635\) | 41.7893 | 1.65836 | ||||||||
\(636\) | 0.731620 | 0.0290106 | ||||||||
\(637\) | 9.23271 | 0.365813 | ||||||||
\(638\) | 17.4037 | 0.689019 | ||||||||
\(639\) | −0.274598 | −0.0108629 | ||||||||
\(640\) | 3.73221 | 0.147528 | ||||||||
\(641\) | 13.0685 | 0.516175 | 0.258088 | − | 0.966121i | \(-0.416908\pi\) | ||||
0.258088 | + | 0.966121i | \(0.416908\pi\) | |||||||
\(642\) | 3.88768 | 0.153435 | ||||||||
\(643\) | 9.93462 | 0.391783 | 0.195892 | − | 0.980626i | \(-0.437240\pi\) | ||||
0.195892 | + | 0.980626i | \(0.437240\pi\) | |||||||
\(644\) | −2.15270 | −0.0848281 | ||||||||
\(645\) | −6.81349 | −0.268281 | ||||||||
\(646\) | 13.7694 | 0.541751 | ||||||||
\(647\) | 15.3932 | 0.605168 | 0.302584 | − | 0.953123i | \(-0.402151\pi\) | ||||
0.302584 | + | 0.953123i | \(0.402151\pi\) | |||||||
\(648\) | −8.08786 | −0.317721 | ||||||||
\(649\) | 21.3490 | 0.838023 | ||||||||
\(650\) | −51.3108 | −2.01257 | ||||||||
\(651\) | 7.27476 | 0.285120 | ||||||||
\(652\) | 3.99005 | 0.156263 | ||||||||
\(653\) | −36.4160 | −1.42507 | −0.712534 | − | 0.701638i | \(-0.752452\pi\) | ||||
−0.712534 | + | 0.701638i | \(0.752452\pi\) | |||||||
\(654\) | 4.82685 | 0.188745 | ||||||||
\(655\) | 63.7790 | 2.49205 | ||||||||
\(656\) | −1.26590 | −0.0494250 | ||||||||
\(657\) | 1.28111 | 0.0499809 | ||||||||
\(658\) | −10.7370 | −0.418571 | ||||||||
\(659\) | −27.5451 | −1.07300 | −0.536502 | − | 0.843899i | \(-0.680255\pi\) | ||||
−0.536502 | + | 0.843899i | \(0.680255\pi\) | |||||||
\(660\) | 5.34316 | 0.207982 | ||||||||
\(661\) | −46.4292 | −1.80589 | −0.902943 | − | 0.429759i | \(-0.858598\pi\) | ||||
−0.902943 | + | 0.429759i | \(0.858598\pi\) | |||||||
\(662\) | −16.9231 | −0.657736 | ||||||||
\(663\) | 4.92638 | 0.191325 | ||||||||
\(664\) | −0.0724002 | −0.00280967 | ||||||||
\(665\) | −56.3063 | −2.18346 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.85608 | 0.110588 | ||||||||
\(668\) | −12.4588 | −0.482046 | ||||||||
\(669\) | 4.87994 | 0.188670 | ||||||||
\(670\) | −19.0519 | −0.736041 | ||||||||
\(671\) | 16.4154 | 0.633711 | ||||||||
\(672\) | 0.939325 | 0.0362352 | ||||||||
\(673\) | 19.1950 | 0.739914 | 0.369957 | − | 0.929049i | \(-0.379372\pi\) | ||||
0.369957 | + | 0.929049i | \(0.379372\pi\) | |||||||
\(674\) | −15.5319 | −0.598265 | ||||||||
\(675\) | 16.8610 | 0.648982 | ||||||||
\(676\) | 20.0198 | 0.769992 | ||||||||
\(677\) | 21.8139 | 0.838376 | 0.419188 | − | 0.907899i | \(-0.362315\pi\) | ||||
0.419188 | + | 0.907899i | \(0.362315\pi\) | |||||||
\(678\) | −0.130071 | −0.00499534 | ||||||||
\(679\) | 56.0072 | 2.14936 | ||||||||
\(680\) | −9.99333 | −0.383227 | ||||||||
\(681\) | 4.10837 | 0.157433 | ||||||||
\(682\) | 34.6289 | 1.32601 | ||||||||
\(683\) | −21.1418 | −0.808968 | −0.404484 | − | 0.914545i | \(-0.632549\pi\) | ||||
−0.404484 | + | 0.914545i | \(0.632549\pi\) | |||||||
\(684\) | −14.9002 | −0.569724 | ||||||||
\(685\) | −0.0361508 | −0.00138125 | ||||||||
\(686\) | 15.8224 | 0.604101 | ||||||||
\(687\) | 6.49377 | 0.247753 | ||||||||
\(688\) | −5.70174 | −0.217377 | ||||||||
\(689\) | −13.1303 | −0.500226 | ||||||||
\(690\) | 0.876851 | 0.0333812 | ||||||||
\(691\) | 42.4308 | 1.61414 | 0.807072 | − | 0.590453i | \(-0.201051\pi\) | ||||
0.807072 | + | 0.590453i | \(0.201051\pi\) | |||||||
\(692\) | 18.3709 | 0.698357 | ||||||||
\(693\) | −38.0080 | −1.44381 | ||||||||
\(694\) | −23.8773 | −0.906370 | ||||||||
\(695\) | 8.89036 | 0.337231 | ||||||||
\(696\) | −1.24624 | −0.0472388 | ||||||||
\(697\) | 3.38956 | 0.128389 | ||||||||
\(698\) | −18.8292 | −0.712695 | ||||||||
\(699\) | −6.47114 | −0.244761 | ||||||||
\(700\) | 26.1963 | 0.990128 | ||||||||
\(701\) | −2.56487 | −0.0968738 | −0.0484369 | − | 0.998826i | \(-0.515424\pi\) | ||||
−0.0484369 | + | 0.998826i | \(0.515424\pi\) | |||||||
\(702\) | −10.8505 | −0.409527 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.47132 | 0.168519 | ||||||||
\(705\) | 4.37347 | 0.164714 | ||||||||
\(706\) | 2.49614 | 0.0939434 | ||||||||
\(707\) | 42.3660 | 1.59334 | ||||||||
\(708\) | −1.52876 | −0.0574543 | ||||||||
\(709\) | −11.5917 | −0.435334 | −0.217667 | − | 0.976023i | \(-0.569845\pi\) | ||||
−0.217667 | + | 0.976023i | \(0.569845\pi\) | |||||||
\(710\) | 0.353706 | 0.0132743 | ||||||||
\(711\) | −41.9570 | −1.57351 | ||||||||
\(712\) | 5.63322 | 0.211114 | ||||||||
\(713\) | 5.68286 | 0.212825 | ||||||||
\(714\) | −2.51513 | −0.0941262 | ||||||||
\(715\) | −95.8934 | −3.58621 | ||||||||
\(716\) | 20.6620 | 0.772175 | ||||||||
\(717\) | −2.20063 | −0.0821840 | ||||||||
\(718\) | −12.0536 | −0.449836 | ||||||||
\(719\) | −2.58903 | −0.0965546 | −0.0482773 | − | 0.998834i | \(-0.515373\pi\) | ||||
−0.0482773 | + | 0.998834i | \(0.515373\pi\) | |||||||
\(720\) | 10.8140 | 0.403014 | ||||||||
\(721\) | 12.7834 | 0.476080 | ||||||||
\(722\) | −7.44500 | −0.277074 | ||||||||
\(723\) | 4.52460 | 0.168272 | ||||||||
\(724\) | 3.77241 | 0.140201 | ||||||||
\(725\) | −34.7558 | −1.29080 | ||||||||
\(726\) | 2.87929 | 0.106861 | ||||||||
\(727\) | 24.2191 | 0.898235 | 0.449117 | − | 0.893473i | \(-0.351738\pi\) | ||||
0.449117 | + | 0.893473i | \(0.351738\pi\) | |||||||
\(728\) | −16.8580 | −0.624799 | ||||||||
\(729\) | −21.6207 | −0.800766 | ||||||||
\(730\) | −1.65018 | −0.0610759 | ||||||||
\(731\) | 15.2669 | 0.564667 | ||||||||
\(732\) | −1.17548 | −0.0434469 | ||||||||
\(733\) | 7.45122 | 0.275217 | 0.137609 | − | 0.990487i | \(-0.456058\pi\) | ||||
0.137609 | + | 0.990487i | \(0.456058\pi\) | |||||||
\(734\) | −37.0543 | −1.36770 | ||||||||
\(735\) | 1.92002 | 0.0708208 | ||||||||
\(736\) | 0.733776 | 0.0270473 | ||||||||
\(737\) | −22.8249 | −0.840766 | ||||||||
\(738\) | −3.66792 | −0.135018 | ||||||||
\(739\) | 16.4721 | 0.605937 | 0.302968 | − | 0.953001i | \(-0.402022\pi\) | ||||
0.302968 | + | 0.953001i | \(0.402022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.46141 | −0.347573 | ||||||||
\(742\) | 6.70359 | 0.246097 | ||||||||
\(743\) | 17.0926 | 0.627068 | 0.313534 | − | 0.949577i | \(-0.398487\pi\) | ||||
0.313534 | + | 0.949577i | \(0.398487\pi\) | |||||||
\(744\) | −2.47970 | −0.0909104 | ||||||||
\(745\) | −62.6640 | −2.29583 | ||||||||
\(746\) | 5.38668 | 0.197220 | ||||||||
\(747\) | −0.209779 | −0.00767540 | ||||||||
\(748\) | −11.9724 | −0.437753 | ||||||||
\(749\) | 35.6216 | 1.30158 | ||||||||
\(750\) | −4.69555 | −0.171457 | ||||||||
\(751\) | −48.2150 | −1.75939 | −0.879695 | − | 0.475539i | \(-0.842253\pi\) | ||||
−0.879695 | + | 0.475539i | \(0.842253\pi\) | |||||||
\(752\) | 3.65985 | 0.133461 | ||||||||
\(753\) | 6.85633 | 0.249859 | ||||||||
\(754\) | 22.3663 | 0.814532 | ||||||||
\(755\) | 37.9098 | 1.37968 | ||||||||
\(756\) | 5.53965 | 0.201475 | ||||||||
\(757\) | −47.1168 | −1.71249 | −0.856244 | − | 0.516572i | \(-0.827208\pi\) | ||||
−0.856244 | + | 0.516572i | \(0.827208\pi\) | |||||||
\(758\) | −21.6224 | −0.785363 | ||||||||
\(759\) | 1.05050 | 0.0381307 | ||||||||
\(760\) | 19.1928 | 0.696195 | ||||||||
\(761\) | 14.4394 | 0.523427 | 0.261713 | − | 0.965146i | \(-0.415712\pi\) | ||||
0.261713 | + | 0.965146i | \(0.415712\pi\) | |||||||
\(762\) | −3.58506 | −0.129873 | ||||||||
\(763\) | 44.2269 | 1.60112 | ||||||||
\(764\) | 15.2024 | 0.550005 | ||||||||
\(765\) | −28.9555 | −1.04689 | ||||||||
\(766\) | −37.0449 | −1.33849 | ||||||||
\(767\) | 27.4366 | 0.990678 | ||||||||
\(768\) | −0.320182 | −0.0115536 | ||||||||
\(769\) | 0.332592 | 0.0119936 | 0.00599678 | − | 0.999982i | \(-0.498091\pi\) | ||||
0.00599678 | + | 0.999982i | \(0.498091\pi\) | |||||||
\(770\) | 48.9576 | 1.76431 | ||||||||
\(771\) | 0.0900531 | 0.00324318 | ||||||||
\(772\) | 21.6678 | 0.779843 | ||||||||
\(773\) | −9.73329 | −0.350082 | −0.175041 | − | 0.984561i | \(-0.556006\pi\) | ||||
−0.175041 | + | 0.984561i | \(0.556006\pi\) | |||||||
\(774\) | −16.5207 | −0.593824 | ||||||||
\(775\) | −69.1551 | −2.48413 | ||||||||
\(776\) | −19.0908 | −0.685321 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.5262 | 0.807604 | ||||||||
\(779\) | −6.50985 | −0.233239 | ||||||||
\(780\) | 6.86673 | 0.245868 | ||||||||
\(781\) | 0.423752 | 0.0151630 | ||||||||
\(782\) | −1.96475 | −0.0702594 | ||||||||
\(783\) | −7.34970 | −0.262657 | ||||||||
\(784\) | 1.60673 | 0.0573831 | ||||||||
\(785\) | −8.51491 | −0.303910 | ||||||||
\(786\) | −5.47152 | −0.195163 | ||||||||
\(787\) | −43.8694 | −1.56377 | −0.781887 | − | 0.623420i | \(-0.785743\pi\) | ||||
−0.781887 | + | 0.623420i | \(0.785743\pi\) | |||||||
\(788\) | −13.7395 | −0.489449 | ||||||||
\(789\) | −4.10034 | −0.145976 | ||||||||
\(790\) | 54.0442 | 1.92281 | ||||||||
\(791\) | −1.19180 | −0.0423754 | ||||||||
\(792\) | 12.9556 | 0.460356 | ||||||||
\(793\) | 21.0962 | 0.749149 | ||||||||
\(794\) | −17.0296 | −0.604356 | ||||||||
\(795\) | −2.73056 | −0.0968429 | ||||||||
\(796\) | 5.63105 | 0.199587 | ||||||||
\(797\) | 45.6572 | 1.61726 | 0.808630 | − | 0.588317i | \(-0.200209\pi\) | ||||
0.808630 | + | 0.588317i | \(0.200209\pi\) | |||||||
\(798\) | 4.83045 | 0.170996 | ||||||||
\(799\) | −9.79958 | −0.346684 | ||||||||
\(800\) | −8.92938 | −0.315701 | ||||||||
\(801\) | 16.3222 | 0.576715 | ||||||||
\(802\) | 20.7727 | 0.733511 | ||||||||
\(803\) | −1.97697 | −0.0697659 | ||||||||
\(804\) | 1.63444 | 0.0576424 | ||||||||
\(805\) | 8.03431 | 0.283172 | ||||||||
\(806\) | 44.5031 | 1.56756 | ||||||||
\(807\) | −3.75303 | −0.132113 | ||||||||
\(808\) | −14.4410 | −0.508034 | ||||||||
\(809\) | 6.66702 | 0.234400 | 0.117200 | − | 0.993108i | \(-0.462608\pi\) | ||||
0.117200 | + | 0.993108i | \(0.462608\pi\) | |||||||
\(810\) | 30.1856 | 1.06061 | ||||||||
\(811\) | 24.9303 | 0.875421 | 0.437711 | − | 0.899116i | \(-0.355789\pi\) | ||||
0.437711 | + | 0.899116i | \(0.355789\pi\) | |||||||
\(812\) | −11.4189 | −0.400726 | ||||||||
\(813\) | −1.74955 | −0.0613596 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8917 | −0.521634 | ||||||||
\(816\) | 0.857316 | 0.0300121 | ||||||||
\(817\) | −29.3210 | −1.02581 | ||||||||
\(818\) | −0.949968 | −0.0332149 | ||||||||
\(819\) | −48.8458 | −1.70681 | ||||||||
\(820\) | 4.72460 | 0.164990 | ||||||||
\(821\) | 36.1645 | 1.26215 | 0.631074 | − | 0.775722i | \(-0.282614\pi\) | ||||
0.631074 | + | 0.775722i | \(0.282614\pi\) | |||||||
\(822\) | 0.00310133 | 0.000108171 0 | ||||||||
\(823\) | −23.7373 | −0.827430 | −0.413715 | − | 0.910406i | \(-0.635769\pi\) | ||||
−0.413715 | + | 0.910406i | \(0.635769\pi\) | |||||||
\(824\) | −4.35741 | −0.151797 | ||||||||
\(825\) | −12.7836 | −0.445068 | ||||||||
\(826\) | −14.0075 | −0.487385 | ||||||||
\(827\) | −37.0497 | −1.28834 | −0.644172 | − | 0.764881i | \(-0.722798\pi\) | ||||
−0.644172 | + | 0.764881i | \(0.722798\pi\) | |||||||
\(828\) | 2.12610 | 0.0738872 | ||||||||
\(829\) | −22.0397 | −0.765469 | −0.382735 | − | 0.923858i | \(-0.625018\pi\) | ||||
−0.382735 | + | 0.923858i | \(0.625018\pi\) | |||||||
\(830\) | 0.270213 | 0.00937922 | ||||||||
\(831\) | −2.03276 | −0.0705158 | ||||||||
\(832\) | 5.74629 | 0.199217 | ||||||||
\(833\) | −4.30216 | −0.149061 | ||||||||
\(834\) | −0.762694 | −0.0264099 | ||||||||
\(835\) | 46.4988 | 1.60916 | ||||||||
\(836\) | 22.9936 | 0.795251 | ||||||||
\(837\) | −14.6240 | −0.505480 | ||||||||
\(838\) | 30.2920 | 1.04642 | ||||||||
\(839\) | 40.4379 | 1.39607 | 0.698035 | − | 0.716063i | \(-0.254058\pi\) | ||||
0.698035 | + | 0.716063i | \(0.254058\pi\) | |||||||
\(840\) | −3.50575 | −0.120960 | ||||||||
\(841\) | −13.8500 | −0.477586 | ||||||||
\(842\) | 19.7724 | 0.681403 | ||||||||
\(843\) | −2.35482 | −0.0811043 | ||||||||
\(844\) | −23.0510 | −0.793447 | ||||||||
\(845\) | −74.7181 | −2.57038 | ||||||||
\(846\) | 10.6044 | 0.364585 | ||||||||
\(847\) | 26.3820 | 0.906497 | ||||||||
\(848\) | −2.28501 | −0.0784677 | ||||||||
\(849\) | −8.42842 | −0.289263 | ||||||||
\(850\) | 23.9092 | 0.820079 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.0303440 | −0.00103957 | ||||||||
\(853\) | 32.5765 | 1.11540 | 0.557699 | − | 0.830043i | \(-0.311684\pi\) | ||||
0.557699 | + | 0.830043i | \(0.311684\pi\) | |||||||
\(854\) | −10.7705 | −0.368559 | ||||||||
\(855\) | 55.6107 | 1.90185 | ||||||||
\(856\) | −12.1421 | −0.415009 | ||||||||
\(857\) | −19.1790 | −0.655143 | −0.327572 | − | 0.944826i | \(-0.606230\pi\) | ||||
−0.327572 | + | 0.944826i | \(0.606230\pi\) | |||||||
\(858\) | 8.22658 | 0.280851 | ||||||||
\(859\) | 0.252055 | 0.00859999 | 0.00429999 | − | 0.999991i | \(-0.498631\pi\) | ||||
0.00429999 | + | 0.999991i | \(0.498631\pi\) | |||||||
\(860\) | 21.2801 | 0.725644 | ||||||||
\(861\) | 1.18909 | 0.0405241 | ||||||||
\(862\) | 5.15897 | 0.175715 | ||||||||
\(863\) | 7.81387 | 0.265987 | 0.132994 | − | 0.991117i | \(-0.457541\pi\) | ||||
0.132994 | + | 0.991117i | \(0.457541\pi\) | |||||||
\(864\) | −1.88827 | −0.0642401 | ||||||||
\(865\) | −68.5640 | −2.33125 | ||||||||
\(866\) | −16.4459 | −0.558854 | ||||||||
\(867\) | 3.14755 | 0.106896 | ||||||||
\(868\) | −22.7207 | −0.771192 | ||||||||
\(869\) | 64.7469 | 2.19639 | ||||||||
\(870\) | 4.65124 | 0.157692 | ||||||||
\(871\) | −29.3333 | −0.993921 | ||||||||
\(872\) | −15.0753 | −0.510516 | ||||||||
\(873\) | −55.3154 | −1.87214 | ||||||||
\(874\) | 3.77342 | 0.127638 | ||||||||
\(875\) | −43.0238 | −1.45447 | ||||||||
\(876\) | 0.141567 | 0.00478311 | ||||||||
\(877\) | −30.9298 | −1.04443 | −0.522213 | − | 0.852815i | \(-0.674893\pi\) | ||||
−0.522213 | + | 0.852815i | \(0.674893\pi\) | |||||||
\(878\) | −8.72749 | −0.294538 | ||||||||
\(879\) | 6.65576 | 0.224493 | ||||||||
\(880\) | −16.6879 | −0.562548 | ||||||||
\(881\) | −40.7550 | −1.37307 | −0.686535 | − | 0.727096i | \(-0.740869\pi\) | ||||
−0.686535 | + | 0.727096i | \(0.740869\pi\) | |||||||
\(882\) | 4.65547 | 0.156758 | ||||||||
\(883\) | −19.9199 | −0.670359 | −0.335180 | − | 0.942154i | \(-0.608797\pi\) | ||||
−0.335180 | + | 0.942154i | \(0.608797\pi\) | |||||||
\(884\) | −15.3862 | −0.517494 | ||||||||
\(885\) | 5.70565 | 0.191793 | ||||||||
\(886\) | −20.5472 | −0.690295 | ||||||||
\(887\) | 16.2717 | 0.546350 | 0.273175 | − | 0.961964i | \(-0.411926\pi\) | ||||
0.273175 | + | 0.961964i | \(0.411926\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.8487 | −1.10171 | ||||||||
\(890\) | −21.0244 | −0.704738 | ||||||||
\(891\) | 36.1634 | 1.21152 | ||||||||
\(892\) | −15.2412 | −0.510312 | ||||||||
\(893\) | 18.8207 | 0.629810 | ||||||||
\(894\) | 5.37587 | 0.179796 | ||||||||
\(895\) | −77.1149 | −2.57767 | ||||||||
\(896\) | −2.93372 | −0.0980088 | ||||||||
\(897\) | 1.35004 | 0.0450766 | ||||||||
\(898\) | −4.84047 | −0.161529 | ||||||||
\(899\) | 30.1446 | 1.00538 | ||||||||
\(900\) | −25.8727 | −0.862424 | ||||||||
\(901\) | 6.11833 | 0.203831 | ||||||||
\(902\) | 5.66023 | 0.188465 | ||||||||
\(903\) | 5.35578 | 0.178229 | ||||||||
\(904\) | 0.406240 | 0.0135114 | ||||||||
\(905\) | −14.0794 | −0.468016 | ||||||||
\(906\) | −3.25224 | −0.108048 | ||||||||
\(907\) | −21.9857 | −0.730025 | −0.365012 | − | 0.931003i | \(-0.618935\pi\) | ||||
−0.365012 | + | 0.931003i | \(0.618935\pi\) | |||||||
\(908\) | −12.8314 | −0.425824 | ||||||||
\(909\) | −41.8427 | −1.38783 | ||||||||
\(910\) | 62.9176 | 2.08570 | ||||||||
\(911\) | −56.0393 | −1.85667 | −0.928333 | − | 0.371750i | \(-0.878758\pi\) | ||||
−0.928333 | + | 0.371750i | \(0.878758\pi\) | |||||||
\(912\) | −1.64653 | −0.0545219 | ||||||||
\(913\) | 0.323724 | 0.0107137 | ||||||||
\(914\) | −28.5767 | −0.945233 | ||||||||
\(915\) | 4.38712 | 0.145034 | ||||||||
\(916\) | −20.2815 | −0.670120 | ||||||||
\(917\) | −50.1338 | −1.65556 | ||||||||
\(918\) | 5.05601 | 0.166873 | ||||||||
\(919\) | 9.19098 | 0.303183 | 0.151591 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151591 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(920\) | −2.73860 | −0.0902891 | ||||||||
\(921\) | −2.47520 | −0.0815608 | ||||||||
\(922\) | −41.8146 | −1.37709 | ||||||||
\(923\) | 0.544583 | 0.0179252 | ||||||||
\(924\) | −4.20002 | −0.138170 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24.6079 | 0.808667 | ||||||||
\(927\) | −12.6255 | −0.414676 | ||||||||
\(928\) | 3.89230 | 0.127771 | ||||||||
\(929\) | −16.7411 | −0.549257 | −0.274629 | − | 0.961550i | \(-0.588555\pi\) | ||||
−0.274629 | + | 0.961550i | \(0.588555\pi\) | |||||||
\(930\) | 9.25477 | 0.303476 | ||||||||
\(931\) | 8.26255 | 0.270794 | ||||||||
\(932\) | 20.2108 | 0.662027 | ||||||||
\(933\) | −8.84701 | −0.289638 | ||||||||
\(934\) | −8.21176 | −0.268697 | ||||||||
\(935\) | 44.6833 | 1.46130 | ||||||||
\(936\) | 16.6498 | 0.544215 | ||||||||
\(937\) | 52.7728 | 1.72401 | 0.862006 | − | 0.506898i | \(-0.169208\pi\) | ||||
0.862006 | + | 0.506898i | \(0.169208\pi\) | |||||||
\(938\) | 14.9759 | 0.488980 | ||||||||
\(939\) | 3.94890 | 0.128867 | ||||||||
\(940\) | −13.6593 | −0.445518 | ||||||||
\(941\) | −6.39927 | −0.208610 | −0.104305 | − | 0.994545i | \(-0.533262\pi\) | ||||
−0.104305 | + | 0.994545i | \(0.533262\pi\) | |||||||
\(942\) | 0.730484 | 0.0238005 | ||||||||
\(943\) | 0.928886 | 0.0302487 | ||||||||
\(944\) | 4.77466 | 0.155402 | ||||||||
\(945\) | −20.6751 | −0.672562 | ||||||||
\(946\) | 25.4943 | 0.828890 | ||||||||
\(947\) | −12.8938 | −0.418992 | −0.209496 | − | 0.977810i | \(-0.567182\pi\) | ||||
−0.209496 | + | 0.977810i | \(0.567182\pi\) | |||||||
\(948\) | −4.63639 | −0.150583 | ||||||||
\(949\) | −2.54070 | −0.0824745 | ||||||||
\(950\) | −45.9191 | −1.48981 | ||||||||
\(951\) | 0.101103 | 0.00327848 | ||||||||
\(952\) | 7.85531 | 0.254592 | ||||||||
\(953\) | −32.6387 | −1.05727 | −0.528635 | − | 0.848849i | \(-0.677296\pi\) | ||||
−0.528635 | + | 0.848849i | \(0.677296\pi\) | |||||||
\(954\) | −6.62079 | −0.214356 | ||||||||
\(955\) | −56.7387 | −1.83602 | ||||||||
\(956\) | 6.87306 | 0.222291 | ||||||||
\(957\) | 5.57235 | 0.180129 | ||||||||
\(958\) | −1.46099 | −0.0472026 | ||||||||
\(959\) | 0.0284165 | 0.000917617 0 | ||||||||
\(960\) | 1.19499 | 0.0385680 | ||||||||
\(961\) | 28.9800 | 0.934839 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.1816 | −1.13371 | ||||||||
\(964\) | −14.1313 | −0.455140 | ||||||||
\(965\) | −80.8689 | −2.60326 | ||||||||
\(966\) | −0.689254 | −0.0221764 | ||||||||
\(967\) | 58.4647 | 1.88010 | 0.940050 | − | 0.341038i | \(-0.110778\pi\) | ||||
0.940050 | + | 0.341038i | \(0.110778\pi\) | |||||||
\(968\) | −8.99267 | −0.289035 | ||||||||
\(969\) | 4.40872 | 0.141629 | ||||||||
\(970\) | 71.2510 | 2.28773 | ||||||||
\(971\) | −4.47224 | −0.143521 | −0.0717606 | − | 0.997422i | \(-0.522862\pi\) | ||||
−0.0717606 | + | 0.997422i | \(0.522862\pi\) | |||||||
\(972\) | −8.25439 | −0.264760 | ||||||||
\(973\) | −6.98832 | −0.224035 | ||||||||
\(974\) | 3.63728 | 0.116546 | ||||||||
\(975\) | −16.4288 | −0.526142 | ||||||||
\(976\) | 3.67128 | 0.117515 | ||||||||
\(977\) | 42.1220 | 1.34760 | 0.673802 | − | 0.738912i | \(-0.264660\pi\) | ||||
0.673802 | + | 0.738912i | \(0.264660\pi\) | |||||||
\(978\) | 1.27754 | 0.0408513 | ||||||||
\(979\) | −25.1879 | −0.805009 | ||||||||
\(980\) | −5.99664 | −0.191556 | ||||||||
\(981\) | −43.6806 | −1.39461 | ||||||||
\(982\) | 22.2913 | 0.711343 | ||||||||
\(983\) | 15.0374 | 0.479618 | 0.239809 | − | 0.970820i | \(-0.422915\pi\) | ||||
0.239809 | + | 0.970820i | \(0.422915\pi\) | |||||||
\(984\) | −0.405318 | −0.0129211 | ||||||||
\(985\) | 51.2786 | 1.63387 | ||||||||
\(986\) | −10.4220 | −0.331904 | ||||||||
\(987\) | −3.43779 | −0.109426 | ||||||||
\(988\) | 29.5501 | 0.940114 | ||||||||
\(989\) | 4.18380 | 0.133037 | ||||||||
\(990\) | −48.3529 | −1.53676 | ||||||||
\(991\) | 36.1371 | 1.14793 | 0.573966 | − | 0.818879i | \(-0.305404\pi\) | ||||
0.573966 | + | 0.818879i | \(0.305404\pi\) | |||||||
\(992\) | 7.74468 | 0.245894 | ||||||||
\(993\) | −5.41847 | −0.171950 | ||||||||
\(994\) | −0.278032 | −0.00881865 | ||||||||
\(995\) | −21.0162 | −0.666260 | ||||||||
\(996\) | −0.0231812 | −0.000734526 0 | ||||||||
\(997\) | 31.5891 | 1.00044 | 0.500218 | − | 0.865899i | \(-0.333253\pi\) | ||||
0.500218 | + | 0.865899i | \(0.333253\pi\) | |||||||
\(998\) | −26.3887 | −0.835319 | ||||||||
\(999\) | 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 | 2738.2.a.w.1.8 | ✓ | 18 | |
37.36 | even | 2 | 2738.2.a.x.1.8 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2738.2.a.w.1.8 | ✓ | 18 | 1.1 | even | 1 | trivial | |
2738.2.a.x.1.8 | yes | 18 | 37.36 | even | 2 |