Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70820 | −1.91499 | −0.957495 | − | 0.288451i | \(-0.906860\pi\) | ||||
−0.957495 | + | 0.288451i | \(0.906860\pi\) | |||||||
\(3\) | 2.96568 | 1.71224 | 0.856118 | − | 0.516780i | \(-0.172870\pi\) | ||||
0.856118 | + | 0.516780i | \(0.172870\pi\) | |||||||
\(4\) | 5.33437 | 2.66718 | ||||||||
\(5\) | −1.26109 | −0.563977 | −0.281989 | − | 0.959418i | \(-0.590994\pi\) | ||||
−0.281989 | + | 0.959418i | \(0.590994\pi\) | |||||||
\(6\) | −8.03167 | −3.27891 | ||||||||
\(7\) | 1.85077 | 0.699526 | 0.349763 | − | 0.936838i | \(-0.386262\pi\) | ||||
0.349763 | + | 0.936838i | \(0.386262\pi\) | |||||||
\(8\) | −9.03015 | −3.19264 | ||||||||
\(9\) | 5.79526 | 1.93175 | ||||||||
\(10\) | 3.41529 | 1.08001 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 15.8200 | 4.56685 | ||||||||
\(13\) | −5.34816 | −1.48331 | −0.741657 | − | 0.670780i | \(-0.765960\pi\) | ||||
−0.741657 | + | 0.670780i | \(0.765960\pi\) | |||||||
\(14\) | −5.01227 | −1.33958 | ||||||||
\(15\) | −3.73999 | −0.965662 | ||||||||
\(16\) | 13.7868 | 3.44669 | ||||||||
\(17\) | 3.21050 | 0.778661 | 0.389330 | − | 0.921098i | \(-0.372706\pi\) | ||||
0.389330 | + | 0.921098i | \(0.372706\pi\) | |||||||
\(18\) | −15.6947 | −3.69929 | ||||||||
\(19\) | −7.60704 | −1.74517 | −0.872587 | − | 0.488459i | \(-0.837559\pi\) | ||||
−0.872587 | + | 0.488459i | \(0.837559\pi\) | |||||||
\(20\) | −6.72713 | −1.50423 | ||||||||
\(21\) | 5.48880 | 1.19775 | ||||||||
\(22\) | −2.70820 | −0.577391 | ||||||||
\(23\) | −3.07950 | −0.642120 | −0.321060 | − | 0.947059i | \(-0.604039\pi\) | ||||
−0.321060 | + | 0.947059i | \(0.604039\pi\) | |||||||
\(24\) | −26.7805 | −5.46655 | ||||||||
\(25\) | −3.40965 | −0.681930 | ||||||||
\(26\) | 14.4839 | 2.84053 | ||||||||
\(27\) | 8.28984 | 1.59538 | ||||||||
\(28\) | 9.87270 | 1.86576 | ||||||||
\(29\) | −0.603421 | −0.112053 | −0.0560263 | − | 0.998429i | \(-0.517843\pi\) | ||||
−0.0560263 | + | 0.998429i | \(0.517843\pi\) | |||||||
\(30\) | 10.1287 | 1.84923 | ||||||||
\(31\) | 3.99164 | 0.716920 | 0.358460 | − | 0.933545i | \(-0.383302\pi\) | ||||
0.358460 | + | 0.933545i | \(0.383302\pi\) | |||||||
\(32\) | −19.2770 | −3.40773 | ||||||||
\(33\) | 2.96568 | 0.516259 | ||||||||
\(34\) | −8.69469 | −1.49113 | ||||||||
\(35\) | −2.33399 | −0.394517 | ||||||||
\(36\) | 30.9140 | 5.15234 | ||||||||
\(37\) | −0.667363 | −0.109714 | −0.0548569 | − | 0.998494i | \(-0.517470\pi\) | ||||
−0.0548569 | + | 0.998494i | \(0.517470\pi\) | |||||||
\(38\) | 20.6014 | 3.34199 | ||||||||
\(39\) | −15.8609 | −2.53978 | ||||||||
\(40\) | 11.3878 | 1.80058 | ||||||||
\(41\) | 0.907812 | 0.141776 | 0.0708882 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708882 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(42\) | −14.8648 | −2.29369 | ||||||||
\(43\) | −7.50474 | −1.14446 | −0.572231 | − | 0.820093i | \(-0.693922\pi\) | ||||
−0.572231 | + | 0.820093i | \(0.693922\pi\) | |||||||
\(44\) | 5.33437 | 0.804186 | ||||||||
\(45\) | −7.30835 | −1.08946 | ||||||||
\(46\) | 8.33991 | 1.22965 | ||||||||
\(47\) | 2.39940 | 0.349989 | 0.174994 | − | 0.984569i | \(-0.444009\pi\) | ||||
0.174994 | + | 0.984569i | \(0.444009\pi\) | |||||||
\(48\) | 40.8871 | 5.90154 | ||||||||
\(49\) | −3.57465 | −0.510664 | ||||||||
\(50\) | 9.23402 | 1.30589 | ||||||||
\(51\) | 9.52132 | 1.33325 | ||||||||
\(52\) | −28.5291 | −3.95627 | ||||||||
\(53\) | 11.9695 | 1.64414 | 0.822070 | − | 0.569386i | \(-0.192819\pi\) | ||||
0.822070 | + | 0.569386i | \(0.192819\pi\) | |||||||
\(54\) | −22.4506 | −3.05514 | ||||||||
\(55\) | −1.26109 | −0.170046 | ||||||||
\(56\) | −16.7127 | −2.23333 | ||||||||
\(57\) | −22.5600 | −2.98815 | ||||||||
\(58\) | 1.63419 | 0.214579 | ||||||||
\(59\) | 2.90667 | 0.378416 | 0.189208 | − | 0.981937i | \(-0.439408\pi\) | ||||
0.189208 | + | 0.981937i | \(0.439408\pi\) | |||||||
\(60\) | −19.9505 | −2.57560 | ||||||||
\(61\) | 0.749237 | 0.0959299 | 0.0479650 | − | 0.998849i | \(-0.484726\pi\) | ||||
0.0479650 | + | 0.998849i | \(0.484726\pi\) | |||||||
\(62\) | −10.8102 | −1.37290 | ||||||||
\(63\) | 10.7257 | 1.35131 | ||||||||
\(64\) | 24.6326 | 3.07908 | ||||||||
\(65\) | 6.74452 | 0.836555 | ||||||||
\(66\) | −8.03167 | −0.988630 | ||||||||
\(67\) | −6.13031 | −0.748937 | −0.374468 | − | 0.927240i | \(-0.622175\pi\) | ||||
−0.374468 | + | 0.927240i | \(0.622175\pi\) | |||||||
\(68\) | 17.1260 | 2.07683 | ||||||||
\(69\) | −9.13281 | −1.09946 | ||||||||
\(70\) | 6.32093 | 0.755495 | ||||||||
\(71\) | −11.1018 | −1.31754 | −0.658770 | − | 0.752344i | \(-0.728923\pi\) | ||||
−0.658770 | + | 0.752344i | \(0.728923\pi\) | |||||||
\(72\) | −52.3321 | −6.16739 | ||||||||
\(73\) | 2.46272 | 0.288239 | 0.144120 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144120 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(74\) | 1.80736 | 0.210101 | ||||||||
\(75\) | −10.1119 | −1.16762 | ||||||||
\(76\) | −40.5787 | −4.65470 | ||||||||
\(77\) | 1.85077 | 0.210915 | ||||||||
\(78\) | 42.9547 | 4.86366 | ||||||||
\(79\) | −11.2992 | −1.27125 | −0.635627 | − | 0.771996i | \(-0.719258\pi\) | ||||
−0.635627 | + | 0.771996i | \(0.719258\pi\) | |||||||
\(80\) | −17.3864 | −1.94385 | ||||||||
\(81\) | 7.19924 | 0.799916 | ||||||||
\(82\) | −2.45854 | −0.271500 | ||||||||
\(83\) | −7.98386 | −0.876343 | −0.438171 | − | 0.898891i | \(-0.644374\pi\) | ||||
−0.438171 | + | 0.898891i | \(0.644374\pi\) | |||||||
\(84\) | 29.2793 | 3.19463 | ||||||||
\(85\) | −4.04874 | −0.439147 | ||||||||
\(86\) | 20.3244 | 2.19163 | ||||||||
\(87\) | −1.78955 | −0.191860 | ||||||||
\(88\) | −9.03015 | −0.962617 | ||||||||
\(89\) | 3.27238 | 0.346872 | 0.173436 | − | 0.984845i | \(-0.444513\pi\) | ||||
0.173436 | + | 0.984845i | \(0.444513\pi\) | |||||||
\(90\) | 19.7925 | 2.08631 | ||||||||
\(91\) | −9.89823 | −1.03762 | ||||||||
\(92\) | −16.4272 | −1.71265 | ||||||||
\(93\) | 11.8379 | 1.22754 | ||||||||
\(94\) | −6.49807 | −0.670225 | ||||||||
\(95\) | 9.59317 | 0.984239 | ||||||||
\(96\) | −57.1695 | −5.83484 | ||||||||
\(97\) | −4.16250 | −0.422638 | −0.211319 | − | 0.977417i | \(-0.567776\pi\) | ||||
−0.211319 | + | 0.977417i | \(0.567776\pi\) | |||||||
\(98\) | 9.68087 | 0.977915 | ||||||||
\(99\) | 5.79526 | 0.582445 | ||||||||
\(100\) | −18.1883 | −1.81883 | ||||||||
\(101\) | 5.79334 | 0.576459 | 0.288230 | − | 0.957561i | \(-0.406933\pi\) | ||||
0.288230 | + | 0.957561i | \(0.406933\pi\) | |||||||
\(102\) | −25.7857 | −2.55316 | ||||||||
\(103\) | −9.57292 | −0.943248 | −0.471624 | − | 0.881800i | \(-0.656332\pi\) | ||||
−0.471624 | + | 0.881800i | \(0.656332\pi\) | |||||||
\(104\) | 48.2947 | 4.73569 | ||||||||
\(105\) | −6.92188 | −0.675506 | ||||||||
\(106\) | −32.4159 | −3.14851 | ||||||||
\(107\) | −14.5234 | −1.40403 | −0.702016 | − | 0.712161i | \(-0.747716\pi\) | ||||
−0.702016 | + | 0.712161i | \(0.747716\pi\) | |||||||
\(108\) | 44.2211 | 4.25517 | ||||||||
\(109\) | −2.66667 | −0.255421 | −0.127711 | − | 0.991811i | \(-0.540763\pi\) | ||||
−0.127711 | + | 0.991811i | \(0.540763\pi\) | |||||||
\(110\) | 3.41529 | 0.325635 | ||||||||
\(111\) | −1.97919 | −0.187856 | ||||||||
\(112\) | 25.5161 | 2.41105 | ||||||||
\(113\) | 11.9363 | 1.12287 | 0.561434 | − | 0.827521i | \(-0.310250\pi\) | ||||
0.561434 | + | 0.827521i | \(0.310250\pi\) | |||||||
\(114\) | 61.0972 | 5.72227 | ||||||||
\(115\) | 3.88353 | 0.362141 | ||||||||
\(116\) | −3.21887 | −0.298865 | ||||||||
\(117\) | −30.9940 | −2.86540 | ||||||||
\(118\) | −7.87186 | −0.724663 | ||||||||
\(119\) | 5.94190 | 0.544693 | ||||||||
\(120\) | 33.7727 | 3.08301 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.02909 | −0.183705 | ||||||||
\(123\) | 2.69228 | 0.242755 | ||||||||
\(124\) | 21.2929 | 1.91216 | ||||||||
\(125\) | 10.6053 | 0.948570 | ||||||||
\(126\) | −29.0474 | −2.58775 | ||||||||
\(127\) | 16.0814 | 1.42700 | 0.713499 | − | 0.700657i | \(-0.247109\pi\) | ||||
0.713499 | + | 0.700657i | \(0.247109\pi\) | |||||||
\(128\) | −28.1561 | −2.48867 | ||||||||
\(129\) | −22.2566 | −1.95959 | ||||||||
\(130\) | −18.2655 | −1.60199 | ||||||||
\(131\) | 14.0716 | 1.22944 | 0.614722 | − | 0.788744i | \(-0.289268\pi\) | ||||
0.614722 | + | 0.788744i | \(0.289268\pi\) | |||||||
\(132\) | 15.8200 | 1.37696 | ||||||||
\(133\) | −14.0789 | −1.22079 | ||||||||
\(134\) | 16.6021 | 1.43421 | ||||||||
\(135\) | −10.4543 | −0.899759 | ||||||||
\(136\) | −28.9913 | −2.48598 | ||||||||
\(137\) | −11.9734 | −1.02295 | −0.511477 | − | 0.859297i | \(-0.670902\pi\) | ||||
−0.511477 | + | 0.859297i | \(0.670902\pi\) | |||||||
\(138\) | 24.7335 | 2.10546 | ||||||||
\(139\) | −1.75295 | −0.148684 | −0.0743418 | − | 0.997233i | \(-0.523686\pi\) | ||||
−0.0743418 | + | 0.997233i | \(0.523686\pi\) | |||||||
\(140\) | −12.4504 | −1.05225 | ||||||||
\(141\) | 7.11586 | 0.599264 | ||||||||
\(142\) | 30.0659 | 2.52308 | ||||||||
\(143\) | −5.34816 | −0.447236 | ||||||||
\(144\) | 79.8978 | 6.65815 | ||||||||
\(145\) | 0.760970 | 0.0631951 | ||||||||
\(146\) | −6.66954 | −0.551975 | ||||||||
\(147\) | −10.6013 | −0.874377 | ||||||||
\(148\) | −3.55996 | −0.292627 | ||||||||
\(149\) | 3.31700 | 0.271739 | 0.135870 | − | 0.990727i | \(-0.456617\pi\) | ||||
0.135870 | + | 0.990727i | \(0.456617\pi\) | |||||||
\(150\) | 27.3852 | 2.23599 | ||||||||
\(151\) | −15.4234 | −1.25514 | −0.627570 | − | 0.778561i | \(-0.715950\pi\) | ||||
−0.627570 | + | 0.778561i | \(0.715950\pi\) | |||||||
\(152\) | 68.6927 | 5.57171 | ||||||||
\(153\) | 18.6057 | 1.50418 | ||||||||
\(154\) | −5.01227 | −0.403900 | ||||||||
\(155\) | −5.03383 | −0.404327 | ||||||||
\(156\) | −84.6081 | −6.77407 | ||||||||
\(157\) | −10.9000 | −0.869917 | −0.434958 | − | 0.900451i | \(-0.643237\pi\) | ||||
−0.434958 | + | 0.900451i | \(0.643237\pi\) | |||||||
\(158\) | 30.6004 | 2.43444 | ||||||||
\(159\) | 35.4978 | 2.81516 | ||||||||
\(160\) | 24.3101 | 1.92188 | ||||||||
\(161\) | −5.69945 | −0.449179 | ||||||||
\(162\) | −19.4970 | −1.53183 | ||||||||
\(163\) | −0.449109 | −0.0351769 | −0.0175885 | − | 0.999845i | \(-0.505599\pi\) | ||||
−0.0175885 | + | 0.999845i | \(0.505599\pi\) | |||||||
\(164\) | 4.84260 | 0.378144 | ||||||||
\(165\) | −3.73999 | −0.291158 | ||||||||
\(166\) | 21.6219 | 1.67819 | ||||||||
\(167\) | −21.3714 | −1.65377 | −0.826885 | − | 0.562371i | \(-0.809889\pi\) | ||||
−0.826885 | + | 0.562371i | \(0.809889\pi\) | |||||||
\(168\) | −49.5647 | −3.82400 | ||||||||
\(169\) | 15.6028 | 1.20022 | ||||||||
\(170\) | 10.9648 | 0.840962 | ||||||||
\(171\) | −44.0847 | −3.37124 | ||||||||
\(172\) | −40.0330 | −3.05249 | ||||||||
\(173\) | 15.3758 | 1.16900 | 0.584499 | − | 0.811394i | \(-0.301291\pi\) | ||||
0.584499 | + | 0.811394i | \(0.301291\pi\) | |||||||
\(174\) | 4.84648 | 0.367411 | ||||||||
\(175\) | −6.31048 | −0.477027 | ||||||||
\(176\) | 13.7868 | 1.03922 | ||||||||
\(177\) | 8.62026 | 0.647938 | ||||||||
\(178\) | −8.86229 | −0.664256 | ||||||||
\(179\) | −16.8159 | −1.25688 | −0.628438 | − | 0.777860i | \(-0.716305\pi\) | ||||
−0.628438 | + | 0.777860i | \(0.716305\pi\) | |||||||
\(180\) | −38.9854 | −2.90580 | ||||||||
\(181\) | −1.97496 | −0.146798 | −0.0733988 | − | 0.997303i | \(-0.523385\pi\) | ||||
−0.0733988 | + | 0.997303i | \(0.523385\pi\) | |||||||
\(182\) | 26.8064 | 1.98702 | ||||||||
\(183\) | 2.22200 | 0.164255 | ||||||||
\(184\) | 27.8083 | 2.05006 | ||||||||
\(185\) | 0.841606 | 0.0618761 | ||||||||
\(186\) | −32.0596 | −2.35072 | ||||||||
\(187\) | 3.21050 | 0.234775 | ||||||||
\(188\) | 12.7993 | 0.933485 | ||||||||
\(189\) | 15.3426 | 1.11601 | ||||||||
\(190\) | −25.9803 | −1.88481 | ||||||||
\(191\) | −14.6931 | −1.06315 | −0.531577 | − | 0.847010i | \(-0.678400\pi\) | ||||
−0.531577 | + | 0.847010i | \(0.678400\pi\) | |||||||
\(192\) | 73.0525 | 5.27211 | ||||||||
\(193\) | −0.662869 | −0.0477143 | −0.0238572 | − | 0.999715i | \(-0.507595\pi\) | ||||
−0.0238572 | + | 0.999715i | \(0.507595\pi\) | |||||||
\(194\) | 11.2729 | 0.809347 | ||||||||
\(195\) | 20.0021 | 1.43238 | ||||||||
\(196\) | −19.0685 | −1.36203 | ||||||||
\(197\) | −16.1645 | −1.15167 | −0.575837 | − | 0.817564i | \(-0.695324\pi\) | ||||
−0.575837 | + | 0.817564i | \(0.695324\pi\) | |||||||
\(198\) | −15.6947 | −1.11538 | ||||||||
\(199\) | −20.0997 | −1.42483 | −0.712413 | − | 0.701760i | \(-0.752398\pi\) | ||||
−0.712413 | + | 0.701760i | \(0.752398\pi\) | |||||||
\(200\) | 30.7896 | 2.17716 | ||||||||
\(201\) | −18.1805 | −1.28236 | ||||||||
\(202\) | −15.6896 | −1.10391 | ||||||||
\(203\) | −1.11679 | −0.0783836 | ||||||||
\(204\) | 50.7902 | 3.55603 | ||||||||
\(205\) | −1.14483 | −0.0799587 | ||||||||
\(206\) | 25.9254 | 1.80631 | ||||||||
\(207\) | −17.8465 | −1.24042 | ||||||||
\(208\) | −73.7338 | −5.11252 | ||||||||
\(209\) | −7.60704 | −0.526190 | ||||||||
\(210\) | 18.7459 | 1.29359 | ||||||||
\(211\) | 22.3700 | 1.54001 | 0.770006 | − | 0.638036i | \(-0.220253\pi\) | ||||
0.770006 | + | 0.638036i | \(0.220253\pi\) | |||||||
\(212\) | 63.8498 | 4.38523 | ||||||||
\(213\) | −32.9244 | −2.25594 | ||||||||
\(214\) | 39.3324 | 2.68871 | ||||||||
\(215\) | 9.46416 | 0.645450 | ||||||||
\(216\) | −74.8585 | −5.09348 | ||||||||
\(217\) | 7.38762 | 0.501504 | ||||||||
\(218\) | 7.22190 | 0.489129 | ||||||||
\(219\) | 7.30363 | 0.493534 | ||||||||
\(220\) | −6.72713 | −0.453543 | ||||||||
\(221\) | −17.1703 | −1.15500 | ||||||||
\(222\) | 5.36004 | 0.359742 | ||||||||
\(223\) | −27.0966 | −1.81452 | −0.907262 | − | 0.420567i | \(-0.861831\pi\) | ||||
−0.907262 | + | 0.420567i | \(0.861831\pi\) | |||||||
\(224\) | −35.6774 | −2.38380 | ||||||||
\(225\) | −19.7598 | −1.31732 | ||||||||
\(226\) | −32.3258 | −2.15028 | ||||||||
\(227\) | −27.6172 | −1.83302 | −0.916509 | − | 0.400013i | \(-0.869005\pi\) | ||||
−0.916509 | + | 0.400013i | \(0.869005\pi\) | |||||||
\(228\) | −120.344 | −7.96995 | ||||||||
\(229\) | 10.4911 | 0.693269 | 0.346634 | − | 0.938000i | \(-0.387324\pi\) | ||||
0.346634 | + | 0.938000i | \(0.387324\pi\) | |||||||
\(230\) | −10.5174 | −0.693496 | ||||||||
\(231\) | 5.48880 | 0.361136 | ||||||||
\(232\) | 5.44898 | 0.357743 | ||||||||
\(233\) | −18.5041 | −1.21224 | −0.606121 | − | 0.795372i | \(-0.707275\pi\) | ||||
−0.606121 | + | 0.795372i | \(0.707275\pi\) | |||||||
\(234\) | 83.9380 | 5.48720 | ||||||||
\(235\) | −3.02587 | −0.197386 | ||||||||
\(236\) | 15.5053 | 1.00931 | ||||||||
\(237\) | −33.5097 | −2.17669 | ||||||||
\(238\) | −16.0919 | −1.04308 | ||||||||
\(239\) | −25.5943 | −1.65556 | −0.827779 | − | 0.561054i | \(-0.810396\pi\) | ||||
−0.827779 | + | 0.561054i | \(0.810396\pi\) | |||||||
\(240\) | −51.5624 | −3.32834 | ||||||||
\(241\) | −12.0435 | −0.775792 | −0.387896 | − | 0.921703i | \(-0.626798\pi\) | ||||
−0.387896 | + | 0.921703i | \(0.626798\pi\) | |||||||
\(242\) | −2.70820 | −0.174090 | ||||||||
\(243\) | −3.51887 | −0.225736 | ||||||||
\(244\) | 3.99671 | 0.255863 | ||||||||
\(245\) | 4.50796 | 0.288003 | ||||||||
\(246\) | −7.29124 | −0.464873 | ||||||||
\(247\) | 40.6837 | 2.58864 | ||||||||
\(248\) | −36.0451 | −2.28887 | ||||||||
\(249\) | −23.6776 | −1.50051 | ||||||||
\(250\) | −28.7214 | −1.81650 | ||||||||
\(251\) | 18.6971 | 1.18015 | 0.590075 | − | 0.807348i | \(-0.299098\pi\) | ||||
0.590075 | + | 0.807348i | \(0.299098\pi\) | |||||||
\(252\) | 57.2148 | 3.60420 | ||||||||
\(253\) | −3.07950 | −0.193606 | ||||||||
\(254\) | −43.5518 | −2.73268 | ||||||||
\(255\) | −12.0073 | −0.751924 | ||||||||
\(256\) | 26.9873 | 1.68670 | ||||||||
\(257\) | 2.23407 | 0.139357 | 0.0696786 | − | 0.997569i | \(-0.477803\pi\) | ||||
0.0696786 | + | 0.997569i | \(0.477803\pi\) | |||||||
\(258\) | 60.2755 | 3.75259 | ||||||||
\(259\) | −1.23514 | −0.0767477 | ||||||||
\(260\) | 35.9778 | 2.23125 | ||||||||
\(261\) | −3.49698 | −0.216458 | ||||||||
\(262\) | −38.1089 | −2.35437 | ||||||||
\(263\) | 18.3853 | 1.13369 | 0.566843 | − | 0.823826i | \(-0.308165\pi\) | ||||
0.566843 | + | 0.823826i | \(0.308165\pi\) | |||||||
\(264\) | −26.7805 | −1.64823 | ||||||||
\(265\) | −15.0947 | −0.927258 | ||||||||
\(266\) | 38.1285 | 2.33781 | ||||||||
\(267\) | 9.70485 | 0.593927 | ||||||||
\(268\) | −32.7013 | −1.99755 | ||||||||
\(269\) | 28.4063 | 1.73196 | 0.865981 | − | 0.500078i | \(-0.166695\pi\) | ||||
0.865981 | + | 0.500078i | \(0.166695\pi\) | |||||||
\(270\) | 28.3122 | 1.72303 | ||||||||
\(271\) | −10.7111 | −0.650654 | −0.325327 | − | 0.945602i | \(-0.605474\pi\) | ||||
−0.325327 | + | 0.945602i | \(0.605474\pi\) | |||||||
\(272\) | 44.2624 | 2.68380 | ||||||||
\(273\) | −29.3550 | −1.77664 | ||||||||
\(274\) | 32.4264 | 1.95895 | ||||||||
\(275\) | −3.40965 | −0.205609 | ||||||||
\(276\) | −48.7177 | −2.93246 | ||||||||
\(277\) | −3.22663 | −0.193869 | −0.0969346 | − | 0.995291i | \(-0.530904\pi\) | ||||
−0.0969346 | + | 0.995291i | \(0.530904\pi\) | |||||||
\(278\) | 4.74736 | 0.284728 | ||||||||
\(279\) | 23.1326 | 1.38491 | ||||||||
\(280\) | 21.0763 | 1.25955 | ||||||||
\(281\) | 32.7063 | 1.95109 | 0.975547 | − | 0.219791i | \(-0.0705376\pi\) | ||||
0.975547 | + | 0.219791i | \(0.0705376\pi\) | |||||||
\(282\) | −19.2712 | −1.14758 | ||||||||
\(283\) | 25.4567 | 1.51324 | 0.756622 | − | 0.653853i | \(-0.226849\pi\) | ||||
0.756622 | + | 0.653853i | \(0.226849\pi\) | |||||||
\(284\) | −59.2211 | −3.51412 | ||||||||
\(285\) | 28.4503 | 1.68525 | ||||||||
\(286\) | 14.4839 | 0.856452 | ||||||||
\(287\) | 1.68015 | 0.0991763 | ||||||||
\(288\) | −111.715 | −6.58289 | ||||||||
\(289\) | −6.69268 | −0.393687 | ||||||||
\(290\) | −2.06086 | −0.121018 | ||||||||
\(291\) | −12.3446 | −0.723656 | ||||||||
\(292\) | 13.1370 | 0.768787 | ||||||||
\(293\) | −17.5954 | −1.02794 | −0.513968 | − | 0.857809i | \(-0.671825\pi\) | ||||
−0.513968 | + | 0.857809i | \(0.671825\pi\) | |||||||
\(294\) | 28.7104 | 1.67442 | ||||||||
\(295\) | −3.66558 | −0.213418 | ||||||||
\(296\) | 6.02639 | 0.350277 | ||||||||
\(297\) | 8.28984 | 0.481025 | ||||||||
\(298\) | −8.98311 | −0.520378 | ||||||||
\(299\) | 16.4697 | 0.952465 | ||||||||
\(300\) | −53.9407 | −3.11427 | ||||||||
\(301\) | −13.8896 | −0.800581 | ||||||||
\(302\) | 41.7697 | 2.40358 | ||||||||
\(303\) | 17.1812 | 0.987034 | ||||||||
\(304\) | −104.876 | −6.01507 | ||||||||
\(305\) | −0.944856 | −0.0541023 | ||||||||
\(306\) | −50.3880 | −2.88049 | ||||||||
\(307\) | −18.9693 | −1.08264 | −0.541318 | − | 0.840818i | \(-0.682074\pi\) | ||||
−0.541318 | + | 0.840818i | \(0.682074\pi\) | |||||||
\(308\) | 9.87270 | 0.562549 | ||||||||
\(309\) | −28.3902 | −1.61506 | ||||||||
\(310\) | 13.6326 | 0.774282 | ||||||||
\(311\) | −9.47818 | −0.537458 | −0.268729 | − | 0.963216i | \(-0.586604\pi\) | ||||
−0.268729 | + | 0.963216i | \(0.586604\pi\) | |||||||
\(312\) | 143.227 | 8.10861 | ||||||||
\(313\) | 24.2524 | 1.37083 | 0.685414 | − | 0.728153i | \(-0.259621\pi\) | ||||
0.685414 | + | 0.728153i | \(0.259621\pi\) | |||||||
\(314\) | 29.5195 | 1.66588 | ||||||||
\(315\) | −13.5261 | −0.762109 | ||||||||
\(316\) | −60.2739 | −3.39067 | ||||||||
\(317\) | 23.9063 | 1.34271 | 0.671355 | − | 0.741136i | \(-0.265713\pi\) | ||||
0.671355 | + | 0.741136i | \(0.265713\pi\) | |||||||
\(318\) | −96.1352 | −5.39100 | ||||||||
\(319\) | −0.603421 | −0.0337851 | ||||||||
\(320\) | −31.0640 | −1.73653 | ||||||||
\(321\) | −43.0718 | −2.40403 | ||||||||
\(322\) | 15.4353 | 0.860174 | ||||||||
\(323\) | −24.4224 | −1.35890 | ||||||||
\(324\) | 38.4034 | 2.13352 | ||||||||
\(325\) | 18.2354 | 1.01152 | ||||||||
\(326\) | 1.21628 | 0.0673635 | ||||||||
\(327\) | −7.90850 | −0.437341 | ||||||||
\(328\) | −8.19768 | −0.452641 | ||||||||
\(329\) | 4.44075 | 0.244826 | ||||||||
\(330\) | 10.1287 | 0.557565 | ||||||||
\(331\) | 1.13048 | 0.0621370 | 0.0310685 | − | 0.999517i | \(-0.490109\pi\) | ||||
0.0310685 | + | 0.999517i | \(0.490109\pi\) | |||||||
\(332\) | −42.5889 | −2.33737 | ||||||||
\(333\) | −3.86754 | −0.211940 | ||||||||
\(334\) | 57.8782 | 3.16695 | ||||||||
\(335\) | 7.73089 | 0.422383 | ||||||||
\(336\) | 75.6727 | 4.12828 | ||||||||
\(337\) | 26.7203 | 1.45555 | 0.727775 | − | 0.685816i | \(-0.240555\pi\) | ||||
0.727775 | + | 0.685816i | \(0.240555\pi\) | |||||||
\(338\) | −42.2557 | −2.29841 | ||||||||
\(339\) | 35.3991 | 1.92262 | ||||||||
\(340\) | −21.5975 | −1.17129 | ||||||||
\(341\) | 3.99164 | 0.216160 | ||||||||
\(342\) | 119.390 | 6.45590 | ||||||||
\(343\) | −19.5713 | −1.05675 | ||||||||
\(344\) | 67.7689 | 3.65385 | ||||||||
\(345\) | 11.5173 | 0.620071 | ||||||||
\(346\) | −41.6407 | −2.23862 | ||||||||
\(347\) | −13.3911 | −0.718871 | −0.359435 | − | 0.933170i | \(-0.617031\pi\) | ||||
−0.359435 | + | 0.933170i | \(0.617031\pi\) | |||||||
\(348\) | −9.54614 | −0.511727 | ||||||||
\(349\) | 4.38597 | 0.234776 | 0.117388 | − | 0.993086i | \(-0.462548\pi\) | ||||
0.117388 | + | 0.993086i | \(0.462548\pi\) | |||||||
\(350\) | 17.0901 | 0.913502 | ||||||||
\(351\) | −44.3354 | −2.36645 | ||||||||
\(352\) | −19.2770 | −1.02747 | ||||||||
\(353\) | 2.18438 | 0.116263 | 0.0581313 | − | 0.998309i | \(-0.481486\pi\) | ||||
0.0581313 | + | 0.998309i | \(0.481486\pi\) | |||||||
\(354\) | −23.3454 | −1.24080 | ||||||||
\(355\) | 14.0004 | 0.743063 | ||||||||
\(356\) | 17.4561 | 0.925172 | ||||||||
\(357\) | 17.6218 | 0.932644 | ||||||||
\(358\) | 45.5408 | 2.40690 | ||||||||
\(359\) | 2.27025 | 0.119819 | 0.0599096 | − | 0.998204i | \(-0.480919\pi\) | ||||
0.0599096 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(360\) | 65.9955 | 3.47827 | ||||||||
\(361\) | 38.8670 | 2.04563 | ||||||||
\(362\) | 5.34859 | 0.281116 | ||||||||
\(363\) | 2.96568 | 0.155658 | ||||||||
\(364\) | −52.8008 | −2.76751 | ||||||||
\(365\) | −3.10571 | −0.162560 | ||||||||
\(366\) | −6.01762 | −0.314546 | ||||||||
\(367\) | −10.7058 | −0.558841 | −0.279420 | − | 0.960169i | \(-0.590142\pi\) | ||||
−0.279420 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(368\) | −42.4563 | −2.21319 | ||||||||
\(369\) | 5.26101 | 0.273877 | ||||||||
\(370\) | −2.27924 | −0.118492 | ||||||||
\(371\) | 22.1529 | 1.15012 | ||||||||
\(372\) | 63.1479 | 3.27407 | ||||||||
\(373\) | −4.26136 | −0.220645 | −0.110322 | − | 0.993896i | \(-0.535188\pi\) | ||||
−0.110322 | + | 0.993896i | \(0.535188\pi\) | |||||||
\(374\) | −8.69469 | −0.449592 | ||||||||
\(375\) | 31.4520 | 1.62418 | ||||||||
\(376\) | −21.6670 | −1.11739 | ||||||||
\(377\) | 3.22720 | 0.166209 | ||||||||
\(378\) | −41.5509 | −2.13715 | ||||||||
\(379\) | 36.3236 | 1.86582 | 0.932910 | − | 0.360110i | \(-0.117261\pi\) | ||||
0.932910 | + | 0.360110i | \(0.117261\pi\) | |||||||
\(380\) | 51.1735 | 2.62515 | ||||||||
\(381\) | 47.6924 | 2.44336 | ||||||||
\(382\) | 39.7919 | 2.03593 | ||||||||
\(383\) | −21.7319 | −1.11045 | −0.555224 | − | 0.831701i | \(-0.687368\pi\) | ||||
−0.555224 | + | 0.831701i | \(0.687368\pi\) | |||||||
\(384\) | −83.5021 | −4.26120 | ||||||||
\(385\) | −2.33399 | −0.118951 | ||||||||
\(386\) | 1.79518 | 0.0913724 | ||||||||
\(387\) | −43.4919 | −2.21082 | ||||||||
\(388\) | −22.2043 | −1.12725 | ||||||||
\(389\) | −11.2709 | −0.571460 | −0.285730 | − | 0.958310i | \(-0.592236\pi\) | ||||
−0.285730 | + | 0.958310i | \(0.592236\pi\) | |||||||
\(390\) | −54.1698 | −2.74299 | ||||||||
\(391\) | −9.88673 | −0.499993 | ||||||||
\(392\) | 32.2796 | 1.63037 | ||||||||
\(393\) | 41.7320 | 2.10510 | ||||||||
\(394\) | 43.7768 | 2.20544 | ||||||||
\(395\) | 14.2493 | 0.716959 | ||||||||
\(396\) | 30.9140 | 1.55349 | ||||||||
\(397\) | 10.1721 | 0.510522 | 0.255261 | − | 0.966872i | \(-0.417839\pi\) | ||||
0.255261 | + | 0.966872i | \(0.417839\pi\) | |||||||
\(398\) | 54.4340 | 2.72853 | ||||||||
\(399\) | −41.7535 | −2.09029 | ||||||||
\(400\) | −47.0080 | −2.35040 | ||||||||
\(401\) | 22.6399 | 1.13058 | 0.565292 | − | 0.824891i | \(-0.308764\pi\) | ||||
0.565292 | + | 0.824891i | \(0.308764\pi\) | |||||||
\(402\) | 49.2366 | 2.45570 | ||||||||
\(403\) | −21.3480 | −1.06342 | ||||||||
\(404\) | 30.9038 | 1.53752 | ||||||||
\(405\) | −9.07891 | −0.451134 | ||||||||
\(406\) | 3.02451 | 0.150104 | ||||||||
\(407\) | −0.667363 | −0.0330800 | ||||||||
\(408\) | −85.9789 | −4.25659 | ||||||||
\(409\) | −15.6624 | −0.774454 | −0.387227 | − | 0.921984i | \(-0.626567\pi\) | ||||
−0.387227 | + | 0.921984i | \(0.626567\pi\) | |||||||
\(410\) | 3.10045 | 0.153120 | ||||||||
\(411\) | −35.5092 | −1.75154 | ||||||||
\(412\) | −51.0655 | −2.51582 | ||||||||
\(413\) | 5.37959 | 0.264712 | ||||||||
\(414\) | 48.3319 | 2.37538 | ||||||||
\(415\) | 10.0684 | 0.494237 | ||||||||
\(416\) | 103.097 | 5.05473 | ||||||||
\(417\) | −5.19870 | −0.254582 | ||||||||
\(418\) | 20.6014 | 1.00765 | ||||||||
\(419\) | −16.9011 | −0.825673 | −0.412836 | − | 0.910805i | \(-0.635462\pi\) | ||||
−0.412836 | + | 0.910805i | \(0.635462\pi\) | |||||||
\(420\) | −36.9238 | −1.80170 | ||||||||
\(421\) | −9.78715 | −0.476996 | −0.238498 | − | 0.971143i | \(-0.576655\pi\) | ||||
−0.238498 | + | 0.971143i | \(0.576655\pi\) | |||||||
\(422\) | −60.5824 | −2.94911 | ||||||||
\(423\) | 13.9052 | 0.676092 | ||||||||
\(424\) | −108.087 | −5.24915 | ||||||||
\(425\) | −10.9467 | −0.530992 | ||||||||
\(426\) | 89.1659 | 4.32010 | ||||||||
\(427\) | 1.38667 | 0.0671055 | ||||||||
\(428\) | −77.4732 | −3.74481 | ||||||||
\(429\) | −15.8609 | −0.765773 | ||||||||
\(430\) | −25.6309 | −1.23603 | ||||||||
\(431\) | 0.102479 | 0.00493624 | 0.00246812 | − | 0.999997i | \(-0.499214\pi\) | ||||
0.00246812 | + | 0.999997i | \(0.499214\pi\) | |||||||
\(432\) | 114.290 | 5.49878 | ||||||||
\(433\) | 17.3195 | 0.832323 | 0.416161 | − | 0.909291i | \(-0.363375\pi\) | ||||
0.416161 | + | 0.909291i | \(0.363375\pi\) | |||||||
\(434\) | −20.0072 | −0.960376 | ||||||||
\(435\) | 2.25679 | 0.108205 | ||||||||
\(436\) | −14.2250 | −0.681255 | ||||||||
\(437\) | 23.4259 | 1.12061 | ||||||||
\(438\) | −19.7797 | −0.945112 | ||||||||
\(439\) | 0.0191838 | 0.000915595 0 | 0.000457797 | − | 1.00000i | \(-0.499854\pi\) | ||||
0.000457797 | 1.00000i | \(0.499854\pi\) | ||||||||
\(440\) | 11.3878 | 0.542894 | ||||||||
\(441\) | −20.7160 | −0.986476 | ||||||||
\(442\) | 46.5006 | 2.21181 | ||||||||
\(443\) | 20.2494 | 0.962077 | 0.481038 | − | 0.876700i | \(-0.340260\pi\) | ||||
0.481038 | + | 0.876700i | \(0.340260\pi\) | |||||||
\(444\) | −10.5577 | −0.501047 | ||||||||
\(445\) | −4.12678 | −0.195628 | ||||||||
\(446\) | 73.3831 | 3.47479 | ||||||||
\(447\) | 9.83716 | 0.465282 | ||||||||
\(448\) | 45.5894 | 2.15390 | ||||||||
\(449\) | 11.8043 | 0.557077 | 0.278539 | − | 0.960425i | \(-0.410150\pi\) | ||||
0.278539 | + | 0.960425i | \(0.410150\pi\) | |||||||
\(450\) | 53.5135 | 2.52265 | ||||||||
\(451\) | 0.907812 | 0.0427472 | ||||||||
\(452\) | 63.6724 | 2.99490 | ||||||||
\(453\) | −45.7409 | −2.14909 | ||||||||
\(454\) | 74.7930 | 3.51021 | ||||||||
\(455\) | 12.4826 | 0.585192 | ||||||||
\(456\) | 203.721 | 9.54009 | ||||||||
\(457\) | 29.4288 | 1.37662 | 0.688310 | − | 0.725416i | \(-0.258353\pi\) | ||||
0.688310 | + | 0.725416i | \(0.258353\pi\) | |||||||
\(458\) | −28.4119 | −1.32760 | ||||||||
\(459\) | 26.6145 | 1.24226 | ||||||||
\(460\) | 20.7162 | 0.965897 | ||||||||
\(461\) | 29.6630 | 1.38154 | 0.690771 | − | 0.723074i | \(-0.257271\pi\) | ||||
0.690771 | + | 0.723074i | \(0.257271\pi\) | |||||||
\(462\) | −14.8648 | −0.691572 | ||||||||
\(463\) | −3.98757 | −0.185318 | −0.0926591 | − | 0.995698i | \(-0.529537\pi\) | ||||
−0.0926591 | + | 0.995698i | \(0.529537\pi\) | |||||||
\(464\) | −8.31922 | −0.386210 | ||||||||
\(465\) | −14.9287 | −0.692303 | ||||||||
\(466\) | 50.1128 | 2.32143 | ||||||||
\(467\) | −41.2377 | −1.90825 | −0.954127 | − | 0.299402i | \(-0.903213\pi\) | ||||
−0.954127 | + | 0.299402i | \(0.903213\pi\) | |||||||
\(468\) | −165.333 | −7.64254 | ||||||||
\(469\) | −11.3458 | −0.523901 | ||||||||
\(470\) | 8.19467 | 0.377992 | ||||||||
\(471\) | −32.3260 | −1.48950 | ||||||||
\(472\) | −26.2477 | −1.20815 | ||||||||
\(473\) | −7.50474 | −0.345068 | ||||||||
\(474\) | 90.7510 | 4.16833 | ||||||||
\(475\) | 25.9373 | 1.19009 | ||||||||
\(476\) | 31.6963 | 1.45280 | ||||||||
\(477\) | 69.3665 | 3.17607 | ||||||||
\(478\) | 69.3146 | 3.17038 | ||||||||
\(479\) | −3.12730 | −0.142890 | −0.0714449 | − | 0.997445i | \(-0.522761\pi\) | ||||
−0.0714449 | + | 0.997445i | \(0.522761\pi\) | |||||||
\(480\) | 72.0960 | 3.29072 | ||||||||
\(481\) | 3.56917 | 0.162740 | ||||||||
\(482\) | 32.6164 | 1.48563 | ||||||||
\(483\) | −16.9027 | −0.769101 | ||||||||
\(484\) | 5.33437 | 0.242471 | ||||||||
\(485\) | 5.24929 | 0.238358 | ||||||||
\(486\) | 9.52982 | 0.432282 | ||||||||
\(487\) | −5.68093 | −0.257427 | −0.128714 | − | 0.991682i | \(-0.541085\pi\) | ||||
−0.128714 | + | 0.991682i | \(0.541085\pi\) | |||||||
\(488\) | −6.76572 | −0.306270 | ||||||||
\(489\) | −1.33191 | −0.0602312 | ||||||||
\(490\) | −12.2085 | −0.551522 | ||||||||
\(491\) | 28.0152 | 1.26431 | 0.632155 | − | 0.774842i | \(-0.282171\pi\) | ||||
0.632155 | + | 0.774842i | \(0.282171\pi\) | |||||||
\(492\) | 14.3616 | 0.647472 | ||||||||
\(493\) | −1.93728 | −0.0872509 | ||||||||
\(494\) | −110.180 | −4.95722 | ||||||||
\(495\) | −7.30835 | −0.328486 | ||||||||
\(496\) | 55.0318 | 2.47100 | ||||||||
\(497\) | −20.5469 | −0.921654 | ||||||||
\(498\) | 64.1237 | 2.87345 | ||||||||
\(499\) | 29.8915 | 1.33813 | 0.669063 | − | 0.743206i | \(-0.266696\pi\) | ||||
0.669063 | + | 0.743206i | \(0.266696\pi\) | |||||||
\(500\) | 56.5728 | 2.53001 | ||||||||
\(501\) | −63.3808 | −2.83164 | ||||||||
\(502\) | −50.6355 | −2.25997 | ||||||||
\(503\) | 17.1935 | 0.766619 | 0.383310 | − | 0.923620i | \(-0.374784\pi\) | ||||
0.383310 | + | 0.923620i | \(0.374784\pi\) | |||||||
\(504\) | −96.8547 | −4.31425 | ||||||||
\(505\) | −7.30594 | −0.325110 | ||||||||
\(506\) | 8.33991 | 0.370754 | ||||||||
\(507\) | 46.2731 | 2.05506 | ||||||||
\(508\) | 85.7844 | 3.80607 | ||||||||
\(509\) | −11.4147 | −0.505949 | −0.252975 | − | 0.967473i | \(-0.581409\pi\) | ||||
−0.252975 | + | 0.967473i | \(0.581409\pi\) | |||||||
\(510\) | 32.5181 | 1.43993 | ||||||||
\(511\) | 4.55793 | 0.201631 | ||||||||
\(512\) | −16.7748 | −0.741348 | ||||||||
\(513\) | −63.0611 | −2.78422 | ||||||||
\(514\) | −6.05031 | −0.266868 | ||||||||
\(515\) | 12.0723 | 0.531970 | ||||||||
\(516\) | −118.725 | −5.22658 | ||||||||
\(517\) | 2.39940 | 0.105526 | ||||||||
\(518\) | 3.34500 | 0.146971 | ||||||||
\(519\) | 45.5996 | 2.00160 | ||||||||
\(520\) | −60.9041 | −2.67082 | ||||||||
\(521\) | 38.0825 | 1.66843 | 0.834213 | − | 0.551442i | \(-0.185922\pi\) | ||||
0.834213 | + | 0.551442i | \(0.185922\pi\) | |||||||
\(522\) | 9.47054 | 0.414514 | ||||||||
\(523\) | −6.71485 | −0.293620 | −0.146810 | − | 0.989165i | \(-0.546901\pi\) | ||||
−0.146810 | + | 0.989165i | \(0.546901\pi\) | |||||||
\(524\) | 75.0633 | 3.27916 | ||||||||
\(525\) | −18.7149 | −0.816783 | ||||||||
\(526\) | −49.7911 | −2.17100 | ||||||||
\(527\) | 12.8152 | 0.558238 | ||||||||
\(528\) | 40.8871 | 1.77938 | ||||||||
\(529\) | −13.5167 | −0.587682 | ||||||||
\(530\) | 40.8794 | 1.77569 | ||||||||
\(531\) | 16.8449 | 0.731007 | ||||||||
\(532\) | −75.1020 | −3.25608 | ||||||||
\(533\) | −4.85513 | −0.210299 | ||||||||
\(534\) | −26.2827 | −1.13736 | ||||||||
\(535\) | 18.3154 | 0.791842 | ||||||||
\(536\) | 55.3576 | 2.39109 | ||||||||
\(537\) | −49.8704 | −2.15207 | ||||||||
\(538\) | −76.9300 | −3.31669 | ||||||||
\(539\) | −3.57465 | −0.153971 | ||||||||
\(540\) | −55.7668 | −2.39982 | ||||||||
\(541\) | −36.0432 | −1.54962 | −0.774810 | − | 0.632194i | \(-0.782154\pi\) | ||||
−0.774810 | + | 0.632194i | \(0.782154\pi\) | |||||||
\(542\) | 29.0079 | 1.24600 | ||||||||
\(543\) | −5.85710 | −0.251352 | ||||||||
\(544\) | −61.8889 | −2.65347 | ||||||||
\(545\) | 3.36292 | 0.144052 | ||||||||
\(546\) | 79.4993 | 3.40225 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | −63.8704 | −2.72841 | ||||||||
\(549\) | 4.34202 | 0.185313 | ||||||||
\(550\) | 9.23402 | 0.393740 | ||||||||
\(551\) | 4.59025 | 0.195551 | ||||||||
\(552\) | 82.4706 | 3.51018 | ||||||||
\(553\) | −20.9122 | −0.889275 | ||||||||
\(554\) | 8.73836 | 0.371258 | ||||||||
\(555\) | 2.49594 | 0.105947 | ||||||||
\(556\) | −9.35091 | −0.396567 | ||||||||
\(557\) | −15.7749 | −0.668404 | −0.334202 | − | 0.942501i | \(-0.608467\pi\) | ||||
−0.334202 | + | 0.942501i | \(0.608467\pi\) | |||||||
\(558\) | −62.6478 | −2.65209 | ||||||||
\(559\) | 40.1366 | 1.69760 | ||||||||
\(560\) | −32.1782 | −1.35978 | ||||||||
\(561\) | 9.52132 | 0.401990 | ||||||||
\(562\) | −88.5753 | −3.73632 | ||||||||
\(563\) | 9.12226 | 0.384458 | 0.192229 | − | 0.981350i | \(-0.438428\pi\) | ||||
0.192229 | + | 0.981350i | \(0.438428\pi\) | |||||||
\(564\) | 37.9586 | 1.59835 | ||||||||
\(565\) | −15.0527 | −0.633272 | ||||||||
\(566\) | −68.9419 | −2.89784 | ||||||||
\(567\) | 13.3242 | 0.559562 | ||||||||
\(568\) | 100.251 | 4.20643 | ||||||||
\(569\) | 11.6914 | 0.490130 | 0.245065 | − | 0.969507i | \(-0.421191\pi\) | ||||
0.245065 | + | 0.969507i | \(0.421191\pi\) | |||||||
\(570\) | −77.0491 | −3.22723 | ||||||||
\(571\) | 3.59023 | 0.150246 | 0.0751231 | − | 0.997174i | \(-0.476065\pi\) | ||||
0.0751231 | + | 0.997174i | \(0.476065\pi\) | |||||||
\(572\) | −28.5291 | −1.19286 | ||||||||
\(573\) | −43.5750 | −1.82037 | ||||||||
\(574\) | −4.55020 | −0.189922 | ||||||||
\(575\) | 10.5000 | 0.437880 | ||||||||
\(576\) | 142.752 | 5.94802 | ||||||||
\(577\) | −39.3583 | −1.63851 | −0.819255 | − | 0.573430i | \(-0.805613\pi\) | ||||
−0.819255 | + | 0.573430i | \(0.805613\pi\) | |||||||
\(578\) | 18.1252 | 0.753907 | ||||||||
\(579\) | −1.96586 | −0.0816982 | ||||||||
\(580\) | 4.05929 | 0.168553 | ||||||||
\(581\) | −14.7763 | −0.613024 | ||||||||
\(582\) | 33.4318 | 1.38579 | ||||||||
\(583\) | 11.9695 | 0.495727 | ||||||||
\(584\) | −22.2387 | −0.920244 | ||||||||
\(585\) | 39.0863 | 1.61602 | ||||||||
\(586\) | 47.6520 | 1.96849 | ||||||||
\(587\) | −30.1683 | −1.24518 | −0.622590 | − | 0.782548i | \(-0.713920\pi\) | ||||
−0.622590 | + | 0.782548i | \(0.713920\pi\) | |||||||
\(588\) | −56.5510 | −2.33212 | ||||||||
\(589\) | −30.3646 | −1.25115 | ||||||||
\(590\) | 9.92714 | 0.408694 | ||||||||
\(591\) | −47.9388 | −1.97194 | ||||||||
\(592\) | −9.20077 | −0.378149 | ||||||||
\(593\) | 5.38500 | 0.221136 | 0.110568 | − | 0.993869i | \(-0.464733\pi\) | ||||
0.110568 | + | 0.993869i | \(0.464733\pi\) | |||||||
\(594\) | −22.4506 | −0.921159 | ||||||||
\(595\) | −7.49329 | −0.307195 | ||||||||
\(596\) | 17.6941 | 0.724779 | ||||||||
\(597\) | −59.6092 | −2.43964 | ||||||||
\(598\) | −44.6032 | −1.82396 | ||||||||
\(599\) | 8.98567 | 0.367145 | 0.183572 | − | 0.983006i | \(-0.441234\pi\) | ||||
0.183572 | + | 0.983006i | \(0.441234\pi\) | |||||||
\(600\) | 91.3122 | 3.72780 | ||||||||
\(601\) | −1.08029 | −0.0440660 | −0.0220330 | − | 0.999757i | \(-0.507014\pi\) | ||||
−0.0220330 | + | 0.999757i | \(0.507014\pi\) | |||||||
\(602\) | 37.6157 | 1.53310 | ||||||||
\(603\) | −35.5267 | −1.44676 | ||||||||
\(604\) | −82.2741 | −3.34769 | ||||||||
\(605\) | −1.26109 | −0.0512707 | ||||||||
\(606\) | −46.5302 | −1.89016 | ||||||||
\(607\) | −22.1977 | −0.900978 | −0.450489 | − | 0.892782i | \(-0.648750\pi\) | ||||
−0.450489 | + | 0.892782i | \(0.648750\pi\) | |||||||
\(608\) | 146.641 | 5.94708 | ||||||||
\(609\) | −3.31206 | −0.134211 | ||||||||
\(610\) | 2.55886 | 0.103605 | ||||||||
\(611\) | −12.8324 | −0.519143 | ||||||||
\(612\) | 99.2496 | 4.01193 | ||||||||
\(613\) | −28.9653 | −1.16990 | −0.584949 | − | 0.811070i | \(-0.698885\pi\) | ||||
−0.584949 | + | 0.811070i | \(0.698885\pi\) | |||||||
\(614\) | 51.3727 | 2.07323 | ||||||||
\(615\) | −3.39521 | −0.136908 | ||||||||
\(616\) | −16.7127 | −0.673376 | ||||||||
\(617\) | 16.1433 | 0.649905 | 0.324953 | − | 0.945730i | \(-0.394652\pi\) | ||||
0.324953 | + | 0.945730i | \(0.394652\pi\) | |||||||
\(618\) | 76.8865 | 3.09283 | ||||||||
\(619\) | −41.7313 | −1.67732 | −0.838660 | − | 0.544655i | \(-0.816661\pi\) | ||||
−0.838660 | + | 0.544655i | \(0.816661\pi\) | |||||||
\(620\) | −26.8523 | −1.07841 | ||||||||
\(621\) | −25.5285 | −1.02443 | ||||||||
\(622\) | 25.6688 | 1.02923 | ||||||||
\(623\) | 6.05644 | 0.242646 | ||||||||
\(624\) | −218.671 | −8.75384 | ||||||||
\(625\) | 3.67393 | 0.146957 | ||||||||
\(626\) | −65.6805 | −2.62512 | ||||||||
\(627\) | −22.5600 | −0.900961 | ||||||||
\(628\) | −58.1448 | −2.32023 | ||||||||
\(629\) | −2.14257 | −0.0854299 | ||||||||
\(630\) | 36.6314 | 1.45943 | ||||||||
\(631\) | −21.3161 | −0.848582 | −0.424291 | − | 0.905526i | \(-0.639477\pi\) | ||||
−0.424291 | + | 0.905526i | \(0.639477\pi\) | |||||||
\(632\) | 102.033 | 4.05866 | ||||||||
\(633\) | 66.3422 | 2.63686 | ||||||||
\(634\) | −64.7430 | −2.57127 | ||||||||
\(635\) | −20.2802 | −0.804794 | ||||||||
\(636\) | 189.358 | 7.50854 | ||||||||
\(637\) | 19.1178 | 0.757474 | ||||||||
\(638\) | 1.63419 | 0.0646981 | ||||||||
\(639\) | −64.3378 | −2.54516 | ||||||||
\(640\) | 35.5075 | 1.40356 | ||||||||
\(641\) | −10.1135 | −0.399457 | −0.199729 | − | 0.979851i | \(-0.564006\pi\) | ||||
−0.199729 | + | 0.979851i | \(0.564006\pi\) | |||||||
\(642\) | 116.647 | 4.60370 | ||||||||
\(643\) | −26.2851 | −1.03658 | −0.518292 | − | 0.855204i | \(-0.673432\pi\) | ||||
−0.518292 | + | 0.855204i | \(0.673432\pi\) | |||||||
\(644\) | −30.4029 | −1.19804 | ||||||||
\(645\) | 28.0677 | 1.10516 | ||||||||
\(646\) | 66.1408 | 2.60228 | ||||||||
\(647\) | −13.8508 | −0.544530 | −0.272265 | − | 0.962222i | \(-0.587773\pi\) | ||||
−0.272265 | + | 0.962222i | \(0.587773\pi\) | |||||||
\(648\) | −65.0102 | −2.55384 | ||||||||
\(649\) | 2.90667 | 0.114097 | ||||||||
\(650\) | −49.3850 | −1.93704 | ||||||||
\(651\) | 21.9093 | 0.858694 | ||||||||
\(652\) | −2.39571 | −0.0938234 | ||||||||
\(653\) | −30.5105 | −1.19397 | −0.596985 | − | 0.802253i | \(-0.703635\pi\) | ||||
−0.596985 | + | 0.802253i | \(0.703635\pi\) | |||||||
\(654\) | 21.4178 | 0.837504 | ||||||||
\(655\) | −17.7456 | −0.693379 | ||||||||
\(656\) | 12.5158 | 0.488659 | ||||||||
\(657\) | 14.2721 | 0.556807 | ||||||||
\(658\) | −12.0264 | −0.468840 | ||||||||
\(659\) | 37.8830 | 1.47571 | 0.737855 | − | 0.674959i | \(-0.235839\pi\) | ||||
0.737855 | + | 0.674959i | \(0.235839\pi\) | |||||||
\(660\) | −19.9505 | −0.776573 | ||||||||
\(661\) | 41.1371 | 1.60005 | 0.800023 | − | 0.599969i | \(-0.204820\pi\) | ||||
0.800023 | + | 0.599969i | \(0.204820\pi\) | |||||||
\(662\) | −3.06158 | −0.118992 | ||||||||
\(663\) | −50.9216 | −1.97763 | ||||||||
\(664\) | 72.0955 | 2.79785 | ||||||||
\(665\) | 17.7548 | 0.688500 | ||||||||
\(666\) | 10.4741 | 0.405863 | ||||||||
\(667\) | 1.85823 | 0.0719511 | ||||||||
\(668\) | −114.003 | −4.41091 | ||||||||
\(669\) | −80.3599 | −3.10689 | ||||||||
\(670\) | −20.9368 | −0.808860 | ||||||||
\(671\) | 0.749237 | 0.0289240 | ||||||||
\(672\) | −105.808 | −4.08162 | ||||||||
\(673\) | 40.9094 | 1.57694 | 0.788471 | − | 0.615072i | \(-0.210873\pi\) | ||||
0.788471 | + | 0.615072i | \(0.210873\pi\) | |||||||
\(674\) | −72.3641 | −2.78736 | ||||||||
\(675\) | −28.2654 | −1.08794 | ||||||||
\(676\) | 83.2313 | 3.20121 | ||||||||
\(677\) | 0.586737 | 0.0225501 | 0.0112751 | − | 0.999936i | \(-0.496411\pi\) | ||||
0.0112751 | + | 0.999936i | \(0.496411\pi\) | |||||||
\(678\) | −95.8680 | −3.68179 | ||||||||
\(679\) | −7.70383 | −0.295646 | ||||||||
\(680\) | 36.5607 | 1.40204 | ||||||||
\(681\) | −81.9038 | −3.13856 | ||||||||
\(682\) | −10.8102 | −0.413943 | ||||||||
\(683\) | 6.99564 | 0.267681 | 0.133840 | − | 0.991003i | \(-0.457269\pi\) | ||||
0.133840 | + | 0.991003i | \(0.457269\pi\) | |||||||
\(684\) | −235.164 | −8.99173 | ||||||||
\(685\) | 15.0995 | 0.576923 | ||||||||
\(686\) | 53.0029 | 2.02366 | ||||||||
\(687\) | 31.1131 | 1.18704 | ||||||||
\(688\) | −103.466 | −3.94460 | ||||||||
\(689\) | −64.0150 | −2.43878 | ||||||||
\(690\) | −31.1912 | −1.18743 | ||||||||
\(691\) | 40.5622 | 1.54306 | 0.771530 | − | 0.636193i | \(-0.219492\pi\) | ||||
0.771530 | + | 0.636193i | \(0.219492\pi\) | |||||||
\(692\) | 82.0200 | 3.11793 | ||||||||
\(693\) | 10.7257 | 0.407436 | ||||||||
\(694\) | 36.2658 | 1.37663 | ||||||||
\(695\) | 2.21064 | 0.0838542 | ||||||||
\(696\) | 16.1599 | 0.612541 | ||||||||
\(697\) | 2.91453 | 0.110396 | ||||||||
\(698\) | −11.8781 | −0.449593 | ||||||||
\(699\) | −54.8772 | −2.07565 | ||||||||
\(700\) | −33.6624 | −1.27232 | ||||||||
\(701\) | −11.9868 | −0.452736 | −0.226368 | − | 0.974042i | \(-0.572685\pi\) | ||||
−0.226368 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(702\) | 120.069 | 4.53173 | ||||||||
\(703\) | 5.07666 | 0.191470 | ||||||||
\(704\) | 24.6326 | 0.928377 | ||||||||
\(705\) | −8.97376 | −0.337971 | ||||||||
\(706\) | −5.91574 | −0.222642 | ||||||||
\(707\) | 10.7222 | 0.403248 | ||||||||
\(708\) | 45.9836 | 1.72817 | ||||||||
\(709\) | −28.1864 | −1.05856 | −0.529281 | − | 0.848447i | \(-0.677538\pi\) | ||||
−0.529281 | + | 0.848447i | \(0.677538\pi\) | |||||||
\(710\) | −37.9159 | −1.42296 | ||||||||
\(711\) | −65.4815 | −2.45575 | ||||||||
\(712\) | −29.5501 | −1.10744 | ||||||||
\(713\) | −12.2923 | −0.460349 | ||||||||
\(714\) | −47.7234 | −1.78600 | ||||||||
\(715\) | 6.74452 | 0.252231 | ||||||||
\(716\) | −89.7020 | −3.35232 | ||||||||
\(717\) | −75.9046 | −2.83471 | ||||||||
\(718\) | −6.14829 | −0.229452 | ||||||||
\(719\) | −28.2604 | −1.05393 | −0.526967 | − | 0.849886i | \(-0.676671\pi\) | ||||
−0.526967 | + | 0.849886i | \(0.676671\pi\) | |||||||
\(720\) | −100.758 | −3.75505 | ||||||||
\(721\) | −17.7173 | −0.659826 | ||||||||
\(722\) | −105.260 | −3.91736 | ||||||||
\(723\) | −35.7173 | −1.32834 | ||||||||
\(724\) | −10.5352 | −0.391536 | ||||||||
\(725\) | 2.05745 | 0.0764119 | ||||||||
\(726\) | −8.03167 | −0.298083 | ||||||||
\(727\) | −0.523961 | −0.0194326 | −0.00971632 | − | 0.999953i | \(-0.503093\pi\) | ||||
−0.00971632 | + | 0.999953i | \(0.503093\pi\) | |||||||
\(728\) | 89.3825 | 3.31273 | ||||||||
\(729\) | −32.0336 | −1.18643 | ||||||||
\(730\) | 8.41090 | 0.311302 | ||||||||
\(731\) | −24.0940 | −0.891148 | ||||||||
\(732\) | 11.8529 | 0.438098 | ||||||||
\(733\) | 1.22762 | 0.0453433 | 0.0226716 | − | 0.999743i | \(-0.492783\pi\) | ||||
0.0226716 | + | 0.999743i | \(0.492783\pi\) | |||||||
\(734\) | 28.9936 | 1.07017 | ||||||||
\(735\) | 13.3692 | 0.493129 | ||||||||
\(736\) | 59.3636 | 2.18817 | ||||||||
\(737\) | −6.13031 | −0.225813 | ||||||||
\(738\) | −14.2479 | −0.524472 | ||||||||
\(739\) | 8.01240 | 0.294741 | 0.147370 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147370 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(740\) | 4.48944 | 0.165035 | ||||||||
\(741\) | 120.655 | 4.43236 | ||||||||
\(742\) | −59.9944 | −2.20247 | ||||||||
\(743\) | 17.6933 | 0.649104 | 0.324552 | − | 0.945868i | \(-0.394786\pi\) | ||||
0.324552 | + | 0.945868i | \(0.394786\pi\) | |||||||
\(744\) | −106.898 | −3.91908 | ||||||||
\(745\) | −4.18304 | −0.153255 | ||||||||
\(746\) | 11.5406 | 0.422532 | ||||||||
\(747\) | −46.2685 | −1.69288 | ||||||||
\(748\) | 17.1260 | 0.626188 | ||||||||
\(749\) | −26.8795 | −0.982156 | ||||||||
\(750\) | −85.1785 | −3.11028 | ||||||||
\(751\) | −6.38702 | −0.233066 | −0.116533 | − | 0.993187i | \(-0.537178\pi\) | ||||
−0.116533 | + | 0.993187i | \(0.537178\pi\) | |||||||
\(752\) | 33.0800 | 1.20630 | ||||||||
\(753\) | 55.4496 | 2.02070 | ||||||||
\(754\) | −8.73990 | −0.318288 | ||||||||
\(755\) | 19.4503 | 0.707870 | ||||||||
\(756\) | 81.8431 | 2.97660 | ||||||||
\(757\) | 41.2391 | 1.49886 | 0.749430 | − | 0.662084i | \(-0.230328\pi\) | ||||
0.749430 | + | 0.662084i | \(0.230328\pi\) | |||||||
\(758\) | −98.3718 | −3.57303 | ||||||||
\(759\) | −9.13281 | −0.331500 | ||||||||
\(760\) | −86.6278 | −3.14232 | ||||||||
\(761\) | 23.6428 | 0.857051 | 0.428525 | − | 0.903530i | \(-0.359033\pi\) | ||||
0.428525 | + | 0.903530i | \(0.359033\pi\) | |||||||
\(762\) | −129.161 | −4.67900 | ||||||||
\(763\) | −4.93540 | −0.178674 | ||||||||
\(764\) | −78.3783 | −2.83563 | ||||||||
\(765\) | −23.4635 | −0.848324 | ||||||||
\(766\) | 58.8544 | 2.12650 | ||||||||
\(767\) | −15.5454 | −0.561310 | ||||||||
\(768\) | 80.0356 | 2.88804 | ||||||||
\(769\) | 15.5818 | 0.561894 | 0.280947 | − | 0.959723i | \(-0.409351\pi\) | ||||
0.280947 | + | 0.959723i | \(0.409351\pi\) | |||||||
\(770\) | 6.32093 | 0.227790 | ||||||||
\(771\) | 6.62552 | 0.238612 | ||||||||
\(772\) | −3.53599 | −0.127263 | ||||||||
\(773\) | 43.2206 | 1.55454 | 0.777268 | − | 0.629170i | \(-0.216605\pi\) | ||||
0.777268 | + | 0.629170i | \(0.216605\pi\) | |||||||
\(774\) | 117.785 | 4.23369 | ||||||||
\(775\) | −13.6101 | −0.488889 | ||||||||
\(776\) | 37.5880 | 1.34933 | ||||||||
\(777\) | −3.66302 | −0.131410 | ||||||||
\(778\) | 30.5240 | 1.09434 | ||||||||
\(779\) | −6.90576 | −0.247425 | ||||||||
\(780\) | 106.699 | 3.82042 | ||||||||
\(781\) | −11.1018 | −0.397253 | ||||||||
\(782\) | 26.7753 | 0.957482 | ||||||||
\(783\) | −5.00227 | −0.178766 | ||||||||
\(784\) | −49.2827 | −1.76010 | ||||||||
\(785\) | 13.7459 | 0.490613 | ||||||||
\(786\) | −113.019 | −4.03124 | ||||||||
\(787\) | 36.7308 | 1.30931 | 0.654655 | − | 0.755927i | \(-0.272814\pi\) | ||||
0.654655 | + | 0.755927i | \(0.272814\pi\) | |||||||
\(788\) | −86.2275 | −3.07173 | ||||||||
\(789\) | 54.5249 | 1.94114 | ||||||||
\(790\) | −38.5899 | −1.37297 | ||||||||
\(791\) | 22.0913 | 0.785475 | ||||||||
\(792\) | −52.3321 | −1.85954 | ||||||||
\(793\) | −4.00704 | −0.142294 | ||||||||
\(794\) | −27.5480 | −0.977643 | ||||||||
\(795\) | −44.7660 | −1.58768 | ||||||||
\(796\) | −107.219 | −3.80028 | ||||||||
\(797\) | −29.4984 | −1.04489 | −0.522443 | − | 0.852674i | \(-0.674979\pi\) | ||||
−0.522443 | + | 0.852674i | \(0.674979\pi\) | |||||||
\(798\) | 113.077 | 4.00288 | ||||||||
\(799\) | 7.70329 | 0.272523 | ||||||||
\(800\) | 65.7279 | 2.32383 | ||||||||
\(801\) | 18.9643 | 0.670071 | ||||||||
\(802\) | −61.3135 | −2.16506 | ||||||||
\(803\) | 2.46272 | 0.0869074 | ||||||||
\(804\) | −96.9817 | −3.42028 | ||||||||
\(805\) | 7.18753 | 0.253327 | ||||||||
\(806\) | 57.8146 | 2.03643 | ||||||||
\(807\) | 84.2439 | 2.96553 | ||||||||
\(808\) | −52.3148 | −1.84043 | ||||||||
\(809\) | 45.9270 | 1.61471 | 0.807354 | − | 0.590067i | \(-0.200899\pi\) | ||||
0.807354 | + | 0.590067i | \(0.200899\pi\) | |||||||
\(810\) | 24.5875 | 0.863918 | ||||||||
\(811\) | 20.9065 | 0.734127 | 0.367063 | − | 0.930196i | \(-0.380363\pi\) | ||||
0.367063 | + | 0.930196i | \(0.380363\pi\) | |||||||
\(812\) | −5.95740 | −0.209064 | ||||||||
\(813\) | −31.7658 | −1.11407 | ||||||||
\(814\) | 1.80736 | 0.0633478 | ||||||||
\(815\) | 0.566368 | 0.0198390 | ||||||||
\(816\) | 131.268 | 4.59530 | ||||||||
\(817\) | 57.0888 | 1.99728 | ||||||||
\(818\) | 42.4169 | 1.48307 | ||||||||
\(819\) | −57.3628 | −2.00442 | ||||||||
\(820\) | −6.10697 | −0.213265 | ||||||||
\(821\) | −12.5474 | −0.437906 | −0.218953 | − | 0.975735i | \(-0.570264\pi\) | ||||
−0.218953 | + | 0.975735i | \(0.570264\pi\) | |||||||
\(822\) | 96.1662 | 3.35418 | ||||||||
\(823\) | −38.7451 | −1.35057 | −0.675284 | − | 0.737558i | \(-0.735979\pi\) | ||||
−0.675284 | + | 0.737558i | \(0.735979\pi\) | |||||||
\(824\) | 86.4449 | 3.01145 | ||||||||
\(825\) | −10.1119 | −0.352052 | ||||||||
\(826\) | −14.5690 | −0.506921 | ||||||||
\(827\) | −33.6839 | −1.17130 | −0.585652 | − | 0.810562i | \(-0.699162\pi\) | ||||
−0.585652 | + | 0.810562i | \(0.699162\pi\) | |||||||
\(828\) | −95.1997 | −3.30842 | ||||||||
\(829\) | 35.6829 | 1.23932 | 0.619659 | − | 0.784871i | \(-0.287271\pi\) | ||||
0.619659 | + | 0.784871i | \(0.287271\pi\) | |||||||
\(830\) | −27.2672 | −0.946459 | ||||||||
\(831\) | −9.56914 | −0.331950 | ||||||||
\(832\) | −131.739 | −4.56724 | ||||||||
\(833\) | −11.4764 | −0.397634 | ||||||||
\(834\) | 14.0791 | 0.487521 | ||||||||
\(835\) | 26.9513 | 0.932689 | ||||||||
\(836\) | −40.5787 | −1.40344 | ||||||||
\(837\) | 33.0901 | 1.14376 | ||||||||
\(838\) | 45.7716 | 1.58115 | ||||||||
\(839\) | 22.7138 | 0.784166 | 0.392083 | − | 0.919930i | \(-0.371755\pi\) | ||||
0.392083 | + | 0.919930i | \(0.371755\pi\) | |||||||
\(840\) | 62.5056 | 2.15665 | ||||||||
\(841\) | −28.6359 | −0.987444 | ||||||||
\(842\) | 26.5056 | 0.913443 | ||||||||
\(843\) | 96.9964 | 3.34073 | ||||||||
\(844\) | 119.330 | 4.10750 | ||||||||
\(845\) | −19.6766 | −0.676896 | ||||||||
\(846\) | −37.6580 | −1.29471 | ||||||||
\(847\) | 1.85077 | 0.0635933 | ||||||||
\(848\) | 165.021 | 5.66684 | ||||||||
\(849\) | 75.4964 | 2.59103 | ||||||||
\(850\) | 29.6458 | 1.01684 | ||||||||
\(851\) | 2.05514 | 0.0704494 | ||||||||
\(852\) | −175.631 | −6.01701 | ||||||||
\(853\) | 12.5561 | 0.429912 | 0.214956 | − | 0.976624i | \(-0.431039\pi\) | ||||
0.214956 | + | 0.976624i | \(0.431039\pi\) | |||||||
\(854\) | −3.75537 | −0.128506 | ||||||||
\(855\) | 55.5949 | 1.90131 | ||||||||
\(856\) | 131.149 | 4.48257 | ||||||||
\(857\) | −5.87810 | −0.200792 | −0.100396 | − | 0.994948i | \(-0.532011\pi\) | ||||
−0.100396 | + | 0.994948i | \(0.532011\pi\) | |||||||
\(858\) | 42.9547 | 1.46645 | ||||||||
\(859\) | 44.7161 | 1.52569 | 0.762847 | − | 0.646579i | \(-0.223801\pi\) | ||||
0.762847 | + | 0.646579i | \(0.223801\pi\) | |||||||
\(860\) | 50.4853 | 1.72154 | ||||||||
\(861\) | 4.98280 | 0.169813 | ||||||||
\(862\) | −0.277534 | −0.00945286 | ||||||||
\(863\) | −34.9347 | −1.18919 | −0.594595 | − | 0.804026i | \(-0.702688\pi\) | ||||
−0.594595 | + | 0.804026i | \(0.702688\pi\) | |||||||
\(864\) | −159.804 | −5.43663 | ||||||||
\(865\) | −19.3903 | −0.659289 | ||||||||
\(866\) | −46.9048 | −1.59389 | ||||||||
\(867\) | −19.8484 | −0.674086 | ||||||||
\(868\) | 39.4083 | 1.33760 | ||||||||
\(869\) | −11.2992 | −0.383298 | ||||||||
\(870\) | −6.11185 | −0.207211 | ||||||||
\(871\) | 32.7859 | 1.11091 | ||||||||
\(872\) | 24.0805 | 0.815467 | ||||||||
\(873\) | −24.1228 | −0.816432 | ||||||||
\(874\) | −63.4420 | −2.14596 | ||||||||
\(875\) | 19.6281 | 0.663549 | ||||||||
\(876\) | 38.9603 | 1.31635 | ||||||||
\(877\) | −45.9861 | −1.55284 | −0.776421 | − | 0.630215i | \(-0.782967\pi\) | ||||
−0.776421 | + | 0.630215i | \(0.782967\pi\) | |||||||
\(878\) | −0.0519538 | −0.00175335 | ||||||||
\(879\) | −52.1824 | −1.76007 | ||||||||
\(880\) | −17.3864 | −0.586094 | ||||||||
\(881\) | −2.04730 | −0.0689753 | −0.0344876 | − | 0.999405i | \(-0.510980\pi\) | ||||
−0.0344876 | + | 0.999405i | \(0.510980\pi\) | |||||||
\(882\) | 56.1031 | 1.88909 | ||||||||
\(883\) | 15.5665 | 0.523853 | 0.261926 | − | 0.965088i | \(-0.415642\pi\) | ||||
0.261926 | + | 0.965088i | \(0.415642\pi\) | |||||||
\(884\) | −91.5926 | −3.08059 | ||||||||
\(885\) | −10.8709 | −0.365423 | ||||||||
\(886\) | −54.8394 | −1.84237 | ||||||||
\(887\) | 5.24540 | 0.176123 | 0.0880616 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880616 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(888\) | 17.8723 | 0.599757 | ||||||||
\(889\) | 29.7631 | 0.998222 | ||||||||
\(890\) | 11.1762 | 0.374626 | ||||||||
\(891\) | 7.19924 | 0.241184 | ||||||||
\(892\) | −144.543 | −4.83967 | ||||||||
\(893\) | −18.2523 | −0.610792 | ||||||||
\(894\) | −26.6410 | −0.891010 | ||||||||
\(895\) | 21.2063 | 0.708850 | ||||||||
\(896\) | −52.1106 | −1.74089 | ||||||||
\(897\) | 48.8437 | 1.63084 | ||||||||
\(898\) | −31.9683 | −1.06680 | ||||||||
\(899\) | −2.40864 | −0.0803327 | ||||||||
\(900\) | −105.406 | −3.51353 | ||||||||
\(901\) | 38.4282 | 1.28023 | ||||||||
\(902\) | −2.45854 | −0.0818604 | ||||||||
\(903\) | −41.1920 | −1.37078 | ||||||||
\(904\) | −107.786 | −3.58491 | ||||||||
\(905\) | 2.49060 | 0.0827905 | ||||||||
\(906\) | 123.876 | 4.11549 | ||||||||
\(907\) | 21.4012 | 0.710617 | 0.355308 | − | 0.934749i | \(-0.384376\pi\) | ||||
0.355308 | + | 0.934749i | \(0.384376\pi\) | |||||||
\(908\) | −147.320 | −4.88900 | ||||||||
\(909\) | 33.5739 | 1.11358 | ||||||||
\(910\) | −33.8054 | −1.12064 | ||||||||
\(911\) | 8.09467 | 0.268189 | 0.134094 | − | 0.990969i | \(-0.457188\pi\) | ||||
0.134094 | + | 0.990969i | \(0.457188\pi\) | |||||||
\(912\) | −311.030 | −10.2992 | ||||||||
\(913\) | −7.98386 | −0.264227 | ||||||||
\(914\) | −79.6992 | −2.63621 | ||||||||
\(915\) | −2.80214 | −0.0926359 | ||||||||
\(916\) | 55.9632 | 1.84908 | ||||||||
\(917\) | 26.0434 | 0.860028 | ||||||||
\(918\) | −72.0776 | −2.37892 | ||||||||
\(919\) | 22.2669 | 0.734517 | 0.367258 | − | 0.930119i | \(-0.380297\pi\) | ||||
0.367258 | + | 0.930119i | \(0.380297\pi\) | |||||||
\(920\) | −35.0689 | −1.15619 | ||||||||
\(921\) | −56.2569 | −1.85373 | ||||||||
\(922\) | −80.3333 | −2.64564 | ||||||||
\(923\) | 59.3742 | 1.95433 | ||||||||
\(924\) | 29.2793 | 0.963217 | ||||||||
\(925\) | 2.27547 | 0.0748171 | ||||||||
\(926\) | 10.7992 | 0.354883 | ||||||||
\(927\) | −55.4775 | −1.82212 | ||||||||
\(928\) | 11.6322 | 0.381845 | ||||||||
\(929\) | −55.4811 | −1.82028 | −0.910138 | − | 0.414305i | \(-0.864025\pi\) | ||||
−0.910138 | + | 0.414305i | \(0.864025\pi\) | |||||||
\(930\) | 40.4300 | 1.32575 | ||||||||
\(931\) | 27.1925 | 0.891197 | ||||||||
\(932\) | −98.7076 | −3.23328 | ||||||||
\(933\) | −28.1093 | −0.920256 | ||||||||
\(934\) | 111.680 | 3.65429 | ||||||||
\(935\) | −4.04874 | −0.132408 | ||||||||
\(936\) | 279.880 | 9.14818 | ||||||||
\(937\) | −25.5277 | −0.833953 | −0.416976 | − | 0.908917i | \(-0.636910\pi\) | ||||
−0.416976 | + | 0.908917i | \(0.636910\pi\) | |||||||
\(938\) | 30.7268 | 1.00326 | ||||||||
\(939\) | 71.9250 | 2.34718 | ||||||||
\(940\) | −16.1411 | −0.526464 | ||||||||
\(941\) | 1.17540 | 0.0383169 | 0.0191584 | − | 0.999816i | \(-0.493901\pi\) | ||||
0.0191584 | + | 0.999816i | \(0.493901\pi\) | |||||||
\(942\) | 87.5454 | 2.85238 | ||||||||
\(943\) | −2.79561 | −0.0910374 | ||||||||
\(944\) | 40.0736 | 1.30428 | ||||||||
\(945\) | −19.3484 | −0.629404 | ||||||||
\(946\) | 20.3244 | 0.660802 | ||||||||
\(947\) | 50.2495 | 1.63289 | 0.816444 | − | 0.577424i | \(-0.195942\pi\) | ||||
0.816444 | + | 0.577424i | \(0.195942\pi\) | |||||||
\(948\) | −178.753 | −5.80563 | ||||||||
\(949\) | −13.1710 | −0.427549 | ||||||||
\(950\) | −70.2435 | −2.27900 | ||||||||
\(951\) | 70.8983 | 2.29904 | ||||||||
\(952\) | −53.6563 | −1.73901 | ||||||||
\(953\) | −43.3113 | −1.40299 | −0.701495 | − | 0.712675i | \(-0.747484\pi\) | ||||
−0.701495 | + | 0.712675i | \(0.747484\pi\) | |||||||
\(954\) | −187.859 | −6.08215 | ||||||||
\(955\) | 18.5293 | 0.599595 | ||||||||
\(956\) | −136.530 | −4.41568 | ||||||||
\(957\) | −1.78955 | −0.0578481 | ||||||||
\(958\) | 8.46936 | 0.273633 | ||||||||
\(959\) | −22.1600 | −0.715583 | ||||||||
\(960\) | −92.1259 | −2.97335 | ||||||||
\(961\) | −15.0668 | −0.486025 | ||||||||
\(962\) | −9.66604 | −0.311645 | ||||||||
\(963\) | −84.1669 | −2.71224 | ||||||||
\(964\) | −64.2447 | −2.06918 | ||||||||
\(965\) | 0.835938 | 0.0269098 | ||||||||
\(966\) | 45.7761 | 1.47282 | ||||||||
\(967\) | 6.88835 | 0.221514 | 0.110757 | − | 0.993847i | \(-0.464672\pi\) | ||||
0.110757 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(968\) | −9.03015 | −0.290240 | ||||||||
\(969\) | −72.4290 | −2.32676 | ||||||||
\(970\) | −14.2162 | −0.456453 | ||||||||
\(971\) | −39.6340 | −1.27192 | −0.635958 | − | 0.771723i | \(-0.719395\pi\) | ||||
−0.635958 | + | 0.771723i | \(0.719395\pi\) | |||||||
\(972\) | −18.7710 | −0.602079 | ||||||||
\(973\) | −3.24432 | −0.104008 | ||||||||
\(974\) | 15.3851 | 0.492971 | ||||||||
\(975\) | 54.0802 | 1.73195 | ||||||||
\(976\) | 10.3295 | 0.330641 | ||||||||
\(977\) | −28.0212 | −0.896479 | −0.448240 | − | 0.893914i | \(-0.647949\pi\) | ||||
−0.448240 | + | 0.893914i | \(0.647949\pi\) | |||||||
\(978\) | 3.60710 | 0.115342 | ||||||||
\(979\) | 3.27238 | 0.104586 | ||||||||
\(980\) | 24.0471 | 0.768156 | ||||||||
\(981\) | −15.4541 | −0.493410 | ||||||||
\(982\) | −75.8710 | −2.42114 | ||||||||
\(983\) | 55.6586 | 1.77523 | 0.887617 | − | 0.460582i | \(-0.152359\pi\) | ||||
0.887617 | + | 0.460582i | \(0.152359\pi\) | |||||||
\(984\) | −24.3117 | −0.775029 | ||||||||
\(985\) | 20.3849 | 0.649518 | ||||||||
\(986\) | 5.24656 | 0.167085 | ||||||||
\(987\) | 13.1698 | 0.419200 | ||||||||
\(988\) | 217.022 | 6.90438 | ||||||||
\(989\) | 23.1108 | 0.734881 | ||||||||
\(990\) | 19.7925 | 0.629047 | ||||||||
\(991\) | −56.2914 | −1.78816 | −0.894078 | − | 0.447912i | \(-0.852168\pi\) | ||||
−0.894078 | + | 0.447912i | \(0.852168\pi\) | |||||||
\(992\) | −76.9471 | −2.44307 | ||||||||
\(993\) | 3.35265 | 0.106393 | ||||||||
\(994\) | 55.6452 | 1.76496 | ||||||||
\(995\) | 25.3475 | 0.803570 | ||||||||
\(996\) | −126.305 | −4.00213 | ||||||||
\(997\) | −11.5970 | −0.367279 | −0.183640 | − | 0.982994i | \(-0.558788\pi\) | ||||
−0.183640 | + | 0.982994i | \(0.558788\pi\) | |||||||
\(998\) | −80.9522 | −2.56250 | ||||||||
\(999\) | −5.53234 | −0.175035 |
(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 | 6017.2.a.c.1.4 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.4 | ✓ | 106 | 1.1 | even | 1 | trivial |