Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.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: | \(32.1797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 8x^{7} + 39x^{6} + 13x^{5} - 106x^{4} + 9x^{3} + 74x^{2} - 3x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.27701\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-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 | ||||||||
\(3\) | 0.574493 | 0.331684 | 0.165842 | − | 0.986152i | \(-0.446966\pi\) | ||||
0.165842 | + | 0.986152i | \(0.446966\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.574493 | 0.234536 | ||||||||
\(7\) | 2.65097 | 1.00197 | 0.500986 | − | 0.865455i | \(-0.332971\pi\) | ||||
0.500986 | + | 0.865455i | \(0.332971\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.66996 | −0.889986 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 5.46180 | 1.64680 | 0.823398 | − | 0.567465i | \(-0.192076\pi\) | ||||
0.823398 | + | 0.567465i | \(0.192076\pi\) | |||||||
\(12\) | 0.574493 | 0.165842 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.65097 | 0.708502 | ||||||||
\(15\) | 0.574493 | 0.148334 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.09419 | 1.47806 | 0.739030 | − | 0.673673i | \(-0.235284\pi\) | ||||
0.739030 | + | 0.673673i | \(0.235284\pi\) | |||||||
\(18\) | −2.66996 | −0.629315 | ||||||||
\(19\) | −2.11241 | −0.484619 | −0.242310 | − | 0.970199i | \(-0.577905\pi\) | ||||
−0.242310 | + | 0.970199i | \(0.577905\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.52296 | 0.332338 | ||||||||
\(22\) | 5.46180 | 1.16446 | ||||||||
\(23\) | 1.90759 | 0.397761 | 0.198880 | − | 0.980024i | \(-0.436269\pi\) | ||||
0.198880 | + | 0.980024i | \(0.436269\pi\) | |||||||
\(24\) | 0.574493 | 0.117268 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −3.25735 | −0.626878 | ||||||||
\(28\) | 2.65097 | 0.500986 | ||||||||
\(29\) | −1.58086 | −0.293559 | −0.146779 | − | 0.989169i | \(-0.546891\pi\) | ||||
−0.146779 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(30\) | 0.574493 | 0.104888 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.13777 | 0.546215 | ||||||||
\(34\) | 6.09419 | 1.04515 | ||||||||
\(35\) | 2.65097 | 0.448096 | ||||||||
\(36\) | −2.66996 | −0.444993 | ||||||||
\(37\) | −1.86832 | −0.307150 | −0.153575 | − | 0.988137i | \(-0.549079\pi\) | ||||
−0.153575 | + | 0.988137i | \(0.549079\pi\) | |||||||
\(38\) | −2.11241 | −0.342678 | ||||||||
\(39\) | 0.574493 | 0.0919926 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.18624 | −0.341433 | −0.170716 | − | 0.985320i | \(-0.554608\pi\) | ||||
−0.170716 | + | 0.985320i | \(0.554608\pi\) | |||||||
\(42\) | 1.52296 | 0.234999 | ||||||||
\(43\) | 3.93884 | 0.600667 | 0.300333 | − | 0.953834i | \(-0.402902\pi\) | ||||
0.300333 | + | 0.953834i | \(0.402902\pi\) | |||||||
\(44\) | 5.46180 | 0.823398 | ||||||||
\(45\) | −2.66996 | −0.398014 | ||||||||
\(46\) | 1.90759 | 0.281259 | ||||||||
\(47\) | −9.99497 | −1.45792 | −0.728958 | − | 0.684558i | \(-0.759995\pi\) | ||||
−0.728958 | + | 0.684558i | \(0.759995\pi\) | |||||||
\(48\) | 0.574493 | 0.0829210 | ||||||||
\(49\) | 0.0276456 | 0.00394938 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 3.50107 | 0.490248 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −9.86129 | −1.35455 | −0.677276 | − | 0.735729i | \(-0.736840\pi\) | ||||
−0.677276 | + | 0.735729i | \(0.736840\pi\) | |||||||
\(54\) | −3.25735 | −0.443270 | ||||||||
\(55\) | 5.46180 | 0.736469 | ||||||||
\(56\) | 2.65097 | 0.354251 | ||||||||
\(57\) | −1.21356 | −0.160740 | ||||||||
\(58\) | −1.58086 | −0.207578 | ||||||||
\(59\) | −6.85309 | −0.892196 | −0.446098 | − | 0.894984i | \(-0.647187\pi\) | ||||
−0.446098 | + | 0.894984i | \(0.647187\pi\) | |||||||
\(60\) | 0.574493 | 0.0741668 | ||||||||
\(61\) | 8.66537 | 1.10949 | 0.554744 | − | 0.832021i | \(-0.312816\pi\) | ||||
0.554744 | + | 0.832021i | \(0.312816\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | −7.07798 | −0.891742 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 3.13777 | 0.386233 | ||||||||
\(67\) | −4.42904 | −0.541093 | −0.270546 | − | 0.962707i | \(-0.587204\pi\) | ||||
−0.270546 | + | 0.962707i | \(0.587204\pi\) | |||||||
\(68\) | 6.09419 | 0.739030 | ||||||||
\(69\) | 1.09590 | 0.131931 | ||||||||
\(70\) | 2.65097 | 0.316852 | ||||||||
\(71\) | 11.8069 | 1.40122 | 0.700612 | − | 0.713543i | \(-0.252911\pi\) | ||||
0.700612 | + | 0.713543i | \(0.252911\pi\) | |||||||
\(72\) | −2.66996 | −0.314658 | ||||||||
\(73\) | −1.85312 | −0.216891 | −0.108446 | − | 0.994102i | \(-0.534587\pi\) | ||||
−0.108446 | + | 0.994102i | \(0.534587\pi\) | |||||||
\(74\) | −1.86832 | −0.217188 | ||||||||
\(75\) | 0.574493 | 0.0663368 | ||||||||
\(76\) | −2.11241 | −0.242310 | ||||||||
\(77\) | 14.4791 | 1.65004 | ||||||||
\(78\) | 0.574493 | 0.0650486 | ||||||||
\(79\) | 2.76301 | 0.310863 | 0.155432 | − | 0.987847i | \(-0.450323\pi\) | ||||
0.155432 | + | 0.987847i | \(0.450323\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 6.13855 | 0.682061 | ||||||||
\(82\) | −2.18624 | −0.241429 | ||||||||
\(83\) | 10.8906 | 1.19540 | 0.597699 | − | 0.801721i | \(-0.296082\pi\) | ||||
0.597699 | + | 0.801721i | \(0.296082\pi\) | |||||||
\(84\) | 1.52296 | 0.166169 | ||||||||
\(85\) | 6.09419 | 0.661008 | ||||||||
\(86\) | 3.93884 | 0.424736 | ||||||||
\(87\) | −0.908195 | −0.0973688 | ||||||||
\(88\) | 5.46180 | 0.582230 | ||||||||
\(89\) | −5.71941 | −0.606257 | −0.303128 | − | 0.952950i | \(-0.598031\pi\) | ||||
−0.303128 | + | 0.952950i | \(0.598031\pi\) | |||||||
\(90\) | −2.66996 | −0.281438 | ||||||||
\(91\) | 2.65097 | 0.277897 | ||||||||
\(92\) | 1.90759 | 0.198880 | ||||||||
\(93\) | −0.574493 | −0.0595722 | ||||||||
\(94\) | −9.99497 | −1.03090 | ||||||||
\(95\) | −2.11241 | −0.216728 | ||||||||
\(96\) | 0.574493 | 0.0586340 | ||||||||
\(97\) | −1.55602 | −0.157990 | −0.0789949 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789949 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(98\) | 0.0276456 | 0.00279263 | ||||||||
\(99\) | −14.5828 | −1.46562 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 15.1649 | 1.50897 | 0.754483 | − | 0.656320i | \(-0.227888\pi\) | ||||
0.754483 | + | 0.656320i | \(0.227888\pi\) | |||||||
\(102\) | 3.50107 | 0.346658 | ||||||||
\(103\) | −14.4472 | −1.42353 | −0.711764 | − | 0.702418i | \(-0.752104\pi\) | ||||
−0.711764 | + | 0.702418i | \(0.752104\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 1.52296 | 0.148626 | ||||||||
\(106\) | −9.86129 | −0.957813 | ||||||||
\(107\) | −6.75721 | −0.653244 | −0.326622 | − | 0.945155i | \(-0.605910\pi\) | ||||
−0.326622 | + | 0.945155i | \(0.605910\pi\) | |||||||
\(108\) | −3.25735 | −0.313439 | ||||||||
\(109\) | 3.05614 | 0.292726 | 0.146363 | − | 0.989231i | \(-0.453243\pi\) | ||||
0.146363 | + | 0.989231i | \(0.453243\pi\) | |||||||
\(110\) | 5.46180 | 0.520762 | ||||||||
\(111\) | −1.07334 | −0.101877 | ||||||||
\(112\) | 2.65097 | 0.250493 | ||||||||
\(113\) | −5.39957 | −0.507949 | −0.253974 | − | 0.967211i | \(-0.581738\pi\) | ||||
−0.253974 | + | 0.967211i | \(0.581738\pi\) | |||||||
\(114\) | −1.21356 | −0.113661 | ||||||||
\(115\) | 1.90759 | 0.177884 | ||||||||
\(116\) | −1.58086 | −0.146779 | ||||||||
\(117\) | −2.66996 | −0.246838 | ||||||||
\(118\) | −6.85309 | −0.630878 | ||||||||
\(119\) | 16.1555 | 1.48097 | ||||||||
\(120\) | 0.574493 | 0.0524438 | ||||||||
\(121\) | 18.8313 | 1.71193 | ||||||||
\(122\) | 8.66537 | 0.784526 | ||||||||
\(123\) | −1.25598 | −0.113248 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.07798 | −0.630556 | ||||||||
\(127\) | 9.99185 | 0.886634 | 0.443317 | − | 0.896365i | \(-0.353802\pi\) | ||||
0.443317 | + | 0.896365i | \(0.353802\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.26284 | 0.199232 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | −15.5104 | −1.35515 | −0.677573 | − | 0.735455i | \(-0.736968\pi\) | ||||
−0.677573 | + | 0.735455i | \(0.736968\pi\) | |||||||
\(132\) | 3.13777 | 0.273108 | ||||||||
\(133\) | −5.59993 | −0.485576 | ||||||||
\(134\) | −4.42904 | −0.382610 | ||||||||
\(135\) | −3.25735 | −0.280348 | ||||||||
\(136\) | 6.09419 | 0.522573 | ||||||||
\(137\) | 9.64959 | 0.824421 | 0.412210 | − | 0.911089i | \(-0.364757\pi\) | ||||
0.412210 | + | 0.911089i | \(0.364757\pi\) | |||||||
\(138\) | 1.09590 | 0.0932892 | ||||||||
\(139\) | −1.22773 | −0.104134 | −0.0520671 | − | 0.998644i | \(-0.516581\pi\) | ||||
−0.0520671 | + | 0.998644i | \(0.516581\pi\) | |||||||
\(140\) | 2.65097 | 0.224048 | ||||||||
\(141\) | −5.74205 | −0.483568 | ||||||||
\(142\) | 11.8069 | 0.990815 | ||||||||
\(143\) | 5.46180 | 0.456739 | ||||||||
\(144\) | −2.66996 | −0.222496 | ||||||||
\(145\) | −1.58086 | −0.131284 | ||||||||
\(146\) | −1.85312 | −0.153365 | ||||||||
\(147\) | 0.0158822 | 0.00130994 | ||||||||
\(148\) | −1.86832 | −0.153575 | ||||||||
\(149\) | −12.1152 | −0.992518 | −0.496259 | − | 0.868174i | \(-0.665293\pi\) | ||||
−0.496259 | + | 0.868174i | \(0.665293\pi\) | |||||||
\(150\) | 0.574493 | 0.0469072 | ||||||||
\(151\) | 16.3675 | 1.33197 | 0.665986 | − | 0.745964i | \(-0.268011\pi\) | ||||
0.665986 | + | 0.745964i | \(0.268011\pi\) | |||||||
\(152\) | −2.11241 | −0.171339 | ||||||||
\(153\) | −16.2712 | −1.31545 | ||||||||
\(154\) | 14.4791 | 1.16676 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0.574493 | 0.0459963 | ||||||||
\(157\) | 3.69050 | 0.294534 | 0.147267 | − | 0.989097i | \(-0.452952\pi\) | ||||
0.147267 | + | 0.989097i | \(0.452952\pi\) | |||||||
\(158\) | 2.76301 | 0.219814 | ||||||||
\(159\) | −5.66525 | −0.449283 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.05697 | 0.398545 | ||||||||
\(162\) | 6.13855 | 0.482290 | ||||||||
\(163\) | 23.7389 | 1.85938 | 0.929688 | − | 0.368348i | \(-0.120077\pi\) | ||||
0.929688 | + | 0.368348i | \(0.120077\pi\) | |||||||
\(164\) | −2.18624 | −0.170716 | ||||||||
\(165\) | 3.13777 | 0.244275 | ||||||||
\(166\) | 10.8906 | 0.845274 | ||||||||
\(167\) | −14.5857 | −1.12867 | −0.564337 | − | 0.825545i | \(-0.690868\pi\) | ||||
−0.564337 | + | 0.825545i | \(0.690868\pi\) | |||||||
\(168\) | 1.52296 | 0.117499 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.09419 | 0.467403 | ||||||||
\(171\) | 5.64004 | 0.431304 | ||||||||
\(172\) | 3.93884 | 0.300333 | ||||||||
\(173\) | 1.63786 | 0.124524 | 0.0622622 | − | 0.998060i | \(-0.480169\pi\) | ||||
0.0622622 | + | 0.998060i | \(0.480169\pi\) | |||||||
\(174\) | −0.908195 | −0.0688501 | ||||||||
\(175\) | 2.65097 | 0.200395 | ||||||||
\(176\) | 5.46180 | 0.411699 | ||||||||
\(177\) | −3.93705 | −0.295927 | ||||||||
\(178\) | −5.71941 | −0.428688 | ||||||||
\(179\) | 13.0508 | 0.975465 | 0.487733 | − | 0.872993i | \(-0.337824\pi\) | ||||
0.487733 | + | 0.872993i | \(0.337824\pi\) | |||||||
\(180\) | −2.66996 | −0.199007 | ||||||||
\(181\) | 6.55122 | 0.486948 | 0.243474 | − | 0.969907i | \(-0.421713\pi\) | ||||
0.243474 | + | 0.969907i | \(0.421713\pi\) | |||||||
\(182\) | 2.65097 | 0.196503 | ||||||||
\(183\) | 4.97820 | 0.367999 | ||||||||
\(184\) | 1.90759 | 0.140630 | ||||||||
\(185\) | −1.86832 | −0.137362 | ||||||||
\(186\) | −0.574493 | −0.0421239 | ||||||||
\(187\) | 33.2853 | 2.43406 | ||||||||
\(188\) | −9.99497 | −0.728958 | ||||||||
\(189\) | −8.63515 | −0.628114 | ||||||||
\(190\) | −2.11241 | −0.153250 | ||||||||
\(191\) | −25.1493 | −1.81974 | −0.909870 | − | 0.414894i | \(-0.863819\pi\) | ||||
−0.909870 | + | 0.414894i | \(0.863819\pi\) | |||||||
\(192\) | 0.574493 | 0.0414605 | ||||||||
\(193\) | −0.569528 | −0.0409955 | −0.0204978 | − | 0.999790i | \(-0.506525\pi\) | ||||
−0.0204978 | + | 0.999790i | \(0.506525\pi\) | |||||||
\(194\) | −1.55602 | −0.111716 | ||||||||
\(195\) | 0.574493 | 0.0411403 | ||||||||
\(196\) | 0.0276456 | 0.00197469 | ||||||||
\(197\) | −16.6544 | −1.18658 | −0.593289 | − | 0.804990i | \(-0.702171\pi\) | ||||
−0.593289 | + | 0.804990i | \(0.702171\pi\) | |||||||
\(198\) | −14.5828 | −1.03635 | ||||||||
\(199\) | −17.6114 | −1.24844 | −0.624219 | − | 0.781249i | \(-0.714583\pi\) | ||||
−0.624219 | + | 0.781249i | \(0.714583\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.54445 | −0.179472 | ||||||||
\(202\) | 15.1649 | 1.06700 | ||||||||
\(203\) | −4.19082 | −0.294138 | ||||||||
\(204\) | 3.50107 | 0.245124 | ||||||||
\(205\) | −2.18624 | −0.152693 | ||||||||
\(206\) | −14.4472 | −1.00659 | ||||||||
\(207\) | −5.09319 | −0.354001 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −11.5375 | −0.798069 | ||||||||
\(210\) | 1.52296 | 0.105095 | ||||||||
\(211\) | −20.3142 | −1.39849 | −0.699243 | − | 0.714884i | \(-0.746480\pi\) | ||||
−0.699243 | + | 0.714884i | \(0.746480\pi\) | |||||||
\(212\) | −9.86129 | −0.677276 | ||||||||
\(213\) | 6.78300 | 0.464763 | ||||||||
\(214\) | −6.75721 | −0.461913 | ||||||||
\(215\) | 3.93884 | 0.268626 | ||||||||
\(216\) | −3.25735 | −0.221635 | ||||||||
\(217\) | −2.65097 | −0.179960 | ||||||||
\(218\) | 3.05614 | 0.206988 | ||||||||
\(219\) | −1.06461 | −0.0719394 | ||||||||
\(220\) | 5.46180 | 0.368235 | ||||||||
\(221\) | 6.09419 | 0.409940 | ||||||||
\(222\) | −1.07334 | −0.0720377 | ||||||||
\(223\) | 18.0022 | 1.20552 | 0.602759 | − | 0.797923i | \(-0.294068\pi\) | ||||
0.602759 | + | 0.797923i | \(0.294068\pi\) | |||||||
\(224\) | 2.65097 | 0.177125 | ||||||||
\(225\) | −2.66996 | −0.177997 | ||||||||
\(226\) | −5.39957 | −0.359174 | ||||||||
\(227\) | −4.23392 | −0.281015 | −0.140508 | − | 0.990080i | \(-0.544873\pi\) | ||||
−0.140508 | + | 0.990080i | \(0.544873\pi\) | |||||||
\(228\) | −1.21356 | −0.0803702 | ||||||||
\(229\) | 11.2182 | 0.741318 | 0.370659 | − | 0.928769i | \(-0.379132\pi\) | ||||
0.370659 | + | 0.928769i | \(0.379132\pi\) | |||||||
\(230\) | 1.90759 | 0.125783 | ||||||||
\(231\) | 8.31813 | 0.547293 | ||||||||
\(232\) | −1.58086 | −0.103789 | ||||||||
\(233\) | 19.0696 | 1.24929 | 0.624646 | − | 0.780908i | \(-0.285243\pi\) | ||||
0.624646 | + | 0.780908i | \(0.285243\pi\) | |||||||
\(234\) | −2.66996 | −0.174541 | ||||||||
\(235\) | −9.99497 | −0.652000 | ||||||||
\(236\) | −6.85309 | −0.446098 | ||||||||
\(237\) | 1.58733 | 0.103108 | ||||||||
\(238\) | 16.1555 | 1.04721 | ||||||||
\(239\) | −4.55128 | −0.294398 | −0.147199 | − | 0.989107i | \(-0.547026\pi\) | ||||
−0.147199 | + | 0.989107i | \(0.547026\pi\) | |||||||
\(240\) | 0.574493 | 0.0370834 | ||||||||
\(241\) | 15.8198 | 1.01904 | 0.509522 | − | 0.860458i | \(-0.329822\pi\) | ||||
0.509522 | + | 0.860458i | \(0.329822\pi\) | |||||||
\(242\) | 18.8313 | 1.21052 | ||||||||
\(243\) | 13.2986 | 0.853106 | ||||||||
\(244\) | 8.66537 | 0.554744 | ||||||||
\(245\) | 0.0276456 | 0.00176621 | ||||||||
\(246\) | −1.25598 | −0.0800782 | ||||||||
\(247\) | −2.11241 | −0.134409 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 6.25657 | 0.396494 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −16.7453 | −1.05695 | −0.528477 | − | 0.848948i | \(-0.677237\pi\) | ||||
−0.528477 | + | 0.848948i | \(0.677237\pi\) | |||||||
\(252\) | −7.07798 | −0.445871 | ||||||||
\(253\) | 10.4189 | 0.655030 | ||||||||
\(254\) | 9.99185 | 0.626945 | ||||||||
\(255\) | 3.50107 | 0.219246 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.59139 | 0.161646 | 0.0808231 | − | 0.996728i | \(-0.474245\pi\) | ||||
0.0808231 | + | 0.996728i | \(0.474245\pi\) | |||||||
\(258\) | 2.26284 | 0.140878 | ||||||||
\(259\) | −4.95287 | −0.307756 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 4.22084 | 0.261263 | ||||||||
\(262\) | −15.5104 | −0.958233 | ||||||||
\(263\) | −13.3832 | −0.825246 | −0.412623 | − | 0.910902i | \(-0.635387\pi\) | ||||
−0.412623 | + | 0.910902i | \(0.635387\pi\) | |||||||
\(264\) | 3.13777 | 0.193116 | ||||||||
\(265\) | −9.86129 | −0.605774 | ||||||||
\(266\) | −5.59993 | −0.343354 | ||||||||
\(267\) | −3.28577 | −0.201086 | ||||||||
\(268\) | −4.42904 | −0.270546 | ||||||||
\(269\) | 11.4529 | 0.698297 | 0.349149 | − | 0.937067i | \(-0.386471\pi\) | ||||
0.349149 | + | 0.937067i | \(0.386471\pi\) | |||||||
\(270\) | −3.25735 | −0.198236 | ||||||||
\(271\) | −5.81599 | −0.353296 | −0.176648 | − | 0.984274i | \(-0.556525\pi\) | ||||
−0.176648 | + | 0.984274i | \(0.556525\pi\) | |||||||
\(272\) | 6.09419 | 0.369515 | ||||||||
\(273\) | 1.52296 | 0.0921740 | ||||||||
\(274\) | 9.64959 | 0.582953 | ||||||||
\(275\) | 5.46180 | 0.329359 | ||||||||
\(276\) | 1.09590 | 0.0659654 | ||||||||
\(277\) | −28.3232 | −1.70177 | −0.850887 | − | 0.525349i | \(-0.823935\pi\) | ||||
−0.850887 | + | 0.525349i | \(0.823935\pi\) | |||||||
\(278\) | −1.22773 | −0.0736341 | ||||||||
\(279\) | 2.66996 | 0.159846 | ||||||||
\(280\) | 2.65097 | 0.158426 | ||||||||
\(281\) | −13.6691 | −0.815429 | −0.407715 | − | 0.913109i | \(-0.633674\pi\) | ||||
−0.407715 | + | 0.913109i | \(0.633674\pi\) | |||||||
\(282\) | −5.74205 | −0.341934 | ||||||||
\(283\) | −31.5935 | −1.87804 | −0.939018 | − | 0.343868i | \(-0.888263\pi\) | ||||
−0.939018 | + | 0.343868i | \(0.888263\pi\) | |||||||
\(284\) | 11.8069 | 0.700612 | ||||||||
\(285\) | −1.21356 | −0.0718853 | ||||||||
\(286\) | 5.46180 | 0.322963 | ||||||||
\(287\) | −5.79565 | −0.342106 | ||||||||
\(288\) | −2.66996 | −0.157329 | ||||||||
\(289\) | 20.1392 | 1.18466 | ||||||||
\(290\) | −1.58086 | −0.0928315 | ||||||||
\(291\) | −0.893922 | −0.0524027 | ||||||||
\(292\) | −1.85312 | −0.108446 | ||||||||
\(293\) | 9.09822 | 0.531524 | 0.265762 | − | 0.964039i | \(-0.414376\pi\) | ||||
0.265762 | + | 0.964039i | \(0.414376\pi\) | |||||||
\(294\) | 0.0158822 | 0.000926270 0 | ||||||||
\(295\) | −6.85309 | −0.399002 | ||||||||
\(296\) | −1.86832 | −0.108594 | ||||||||
\(297\) | −17.7910 | −1.03234 | ||||||||
\(298\) | −12.1152 | −0.701816 | ||||||||
\(299\) | 1.90759 | 0.110319 | ||||||||
\(300\) | 0.574493 | 0.0331684 | ||||||||
\(301\) | 10.4417 | 0.601852 | ||||||||
\(302\) | 16.3675 | 0.941846 | ||||||||
\(303\) | 8.71214 | 0.500499 | ||||||||
\(304\) | −2.11241 | −0.121155 | ||||||||
\(305\) | 8.66537 | 0.496178 | ||||||||
\(306\) | −16.2712 | −0.930165 | ||||||||
\(307\) | −18.9973 | −1.08423 | −0.542116 | − | 0.840304i | \(-0.682376\pi\) | ||||
−0.542116 | + | 0.840304i | \(0.682376\pi\) | |||||||
\(308\) | 14.4791 | 0.825022 | ||||||||
\(309\) | −8.29984 | −0.472161 | ||||||||
\(310\) | −1.00000 | −0.0567962 | ||||||||
\(311\) | 27.7546 | 1.57382 | 0.786909 | − | 0.617068i | \(-0.211680\pi\) | ||||
0.786909 | + | 0.617068i | \(0.211680\pi\) | |||||||
\(312\) | 0.574493 | 0.0325243 | ||||||||
\(313\) | 2.64737 | 0.149638 | 0.0748192 | − | 0.997197i | \(-0.476162\pi\) | ||||
0.0748192 | + | 0.997197i | \(0.476162\pi\) | |||||||
\(314\) | 3.69050 | 0.208267 | ||||||||
\(315\) | −7.07798 | −0.398799 | ||||||||
\(316\) | 2.76301 | 0.155432 | ||||||||
\(317\) | 21.8541 | 1.22745 | 0.613724 | − | 0.789521i | \(-0.289671\pi\) | ||||
0.613724 | + | 0.789521i | \(0.289671\pi\) | |||||||
\(318\) | −5.66525 | −0.317691 | ||||||||
\(319\) | −8.63436 | −0.483431 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.88197 | −0.216671 | ||||||||
\(322\) | 5.05697 | 0.281814 | ||||||||
\(323\) | −12.8734 | −0.716296 | ||||||||
\(324\) | 6.13855 | 0.341030 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 23.7389 | 1.31478 | ||||||||
\(327\) | 1.75573 | 0.0970923 | ||||||||
\(328\) | −2.18624 | −0.120715 | ||||||||
\(329\) | −26.4964 | −1.46079 | ||||||||
\(330\) | 3.13777 | 0.172728 | ||||||||
\(331\) | −20.5451 | −1.12926 | −0.564631 | − | 0.825343i | \(-0.690982\pi\) | ||||
−0.564631 | + | 0.825343i | \(0.690982\pi\) | |||||||
\(332\) | 10.8906 | 0.597699 | ||||||||
\(333\) | 4.98834 | 0.273359 | ||||||||
\(334\) | −14.5857 | −0.798093 | ||||||||
\(335\) | −4.42904 | −0.241984 | ||||||||
\(336\) | 1.52296 | 0.0830845 | ||||||||
\(337\) | −12.6765 | −0.690530 | −0.345265 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345265 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −3.10202 | −0.168478 | ||||||||
\(340\) | 6.09419 | 0.330504 | ||||||||
\(341\) | −5.46180 | −0.295773 | ||||||||
\(342\) | 5.64004 | 0.304978 | ||||||||
\(343\) | −18.4835 | −0.998016 | ||||||||
\(344\) | 3.93884 | 0.212368 | ||||||||
\(345\) | 1.09590 | 0.0590012 | ||||||||
\(346\) | 1.63786 | 0.0880520 | ||||||||
\(347\) | −1.24387 | −0.0667747 | −0.0333873 | − | 0.999442i | \(-0.510629\pi\) | ||||
−0.0333873 | + | 0.999442i | \(0.510629\pi\) | |||||||
\(348\) | −0.908195 | −0.0486844 | ||||||||
\(349\) | 11.1025 | 0.594305 | 0.297153 | − | 0.954830i | \(-0.403963\pi\) | ||||
0.297153 | + | 0.954830i | \(0.403963\pi\) | |||||||
\(350\) | 2.65097 | 0.141700 | ||||||||
\(351\) | −3.25735 | −0.173865 | ||||||||
\(352\) | 5.46180 | 0.291115 | ||||||||
\(353\) | 5.79077 | 0.308212 | 0.154106 | − | 0.988054i | \(-0.450750\pi\) | ||||
0.154106 | + | 0.988054i | \(0.450750\pi\) | |||||||
\(354\) | −3.93705 | −0.209252 | ||||||||
\(355\) | 11.8069 | 0.626646 | ||||||||
\(356\) | −5.71941 | −0.303128 | ||||||||
\(357\) | 9.28124 | 0.491215 | ||||||||
\(358\) | 13.0508 | 0.689758 | ||||||||
\(359\) | −2.07598 | −0.109566 | −0.0547829 | − | 0.998498i | \(-0.517447\pi\) | ||||
−0.0547829 | + | 0.998498i | \(0.517447\pi\) | |||||||
\(360\) | −2.66996 | −0.140719 | ||||||||
\(361\) | −14.5377 | −0.765144 | ||||||||
\(362\) | 6.55122 | 0.344324 | ||||||||
\(363\) | 10.8184 | 0.567821 | ||||||||
\(364\) | 2.65097 | 0.138949 | ||||||||
\(365\) | −1.85312 | −0.0969968 | ||||||||
\(366\) | 4.97820 | 0.260215 | ||||||||
\(367\) | 17.6437 | 0.920994 | 0.460497 | − | 0.887661i | \(-0.347671\pi\) | ||||
0.460497 | + | 0.887661i | \(0.347671\pi\) | |||||||
\(368\) | 1.90759 | 0.0994402 | ||||||||
\(369\) | 5.83716 | 0.303870 | ||||||||
\(370\) | −1.86832 | −0.0971294 | ||||||||
\(371\) | −26.1420 | −1.35722 | ||||||||
\(372\) | −0.574493 | −0.0297861 | ||||||||
\(373\) | −7.66397 | −0.396825 | −0.198413 | − | 0.980119i | \(-0.563579\pi\) | ||||
−0.198413 | + | 0.980119i | \(0.563579\pi\) | |||||||
\(374\) | 33.2853 | 1.72114 | ||||||||
\(375\) | 0.574493 | 0.0296667 | ||||||||
\(376\) | −9.99497 | −0.515451 | ||||||||
\(377\) | −1.58086 | −0.0814186 | ||||||||
\(378\) | −8.63515 | −0.444144 | ||||||||
\(379\) | 3.68946 | 0.189515 | 0.0947574 | − | 0.995500i | \(-0.469792\pi\) | ||||
0.0947574 | + | 0.995500i | \(0.469792\pi\) | |||||||
\(380\) | −2.11241 | −0.108364 | ||||||||
\(381\) | 5.74025 | 0.294082 | ||||||||
\(382\) | −25.1493 | −1.28675 | ||||||||
\(383\) | 7.99773 | 0.408665 | 0.204332 | − | 0.978902i | \(-0.434498\pi\) | ||||
0.204332 | + | 0.978902i | \(0.434498\pi\) | |||||||
\(384\) | 0.574493 | 0.0293170 | ||||||||
\(385\) | 14.4791 | 0.737922 | ||||||||
\(386\) | −0.569528 | −0.0289882 | ||||||||
\(387\) | −10.5165 | −0.534585 | ||||||||
\(388\) | −1.55602 | −0.0789949 | ||||||||
\(389\) | 20.7990 | 1.05455 | 0.527277 | − | 0.849694i | \(-0.323213\pi\) | ||||
0.527277 | + | 0.849694i | \(0.323213\pi\) | |||||||
\(390\) | 0.574493 | 0.0290906 | ||||||||
\(391\) | 11.6252 | 0.587914 | ||||||||
\(392\) | 0.0276456 | 0.00139632 | ||||||||
\(393\) | −8.91060 | −0.449480 | ||||||||
\(394\) | −16.6544 | −0.839037 | ||||||||
\(395\) | 2.76301 | 0.139022 | ||||||||
\(396\) | −14.5828 | −0.732812 | ||||||||
\(397\) | 4.85991 | 0.243912 | 0.121956 | − | 0.992536i | \(-0.461083\pi\) | ||||
0.121956 | + | 0.992536i | \(0.461083\pi\) | |||||||
\(398\) | −17.6114 | −0.882779 | ||||||||
\(399\) | −3.21712 | −0.161058 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.50310 | −0.0750612 | −0.0375306 | − | 0.999295i | \(-0.511949\pi\) | ||||
−0.0375306 | + | 0.999295i | \(0.511949\pi\) | |||||||
\(402\) | −2.54445 | −0.126906 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | 15.1649 | 0.754483 | ||||||||
\(405\) | 6.13855 | 0.305027 | ||||||||
\(406\) | −4.19082 | −0.207987 | ||||||||
\(407\) | −10.2044 | −0.505813 | ||||||||
\(408\) | 3.50107 | 0.173329 | ||||||||
\(409\) | −30.8261 | −1.52425 | −0.762125 | − | 0.647430i | \(-0.775844\pi\) | ||||
−0.762125 | + | 0.647430i | \(0.775844\pi\) | |||||||
\(410\) | −2.18624 | −0.107970 | ||||||||
\(411\) | 5.54363 | 0.273447 | ||||||||
\(412\) | −14.4472 | −0.711764 | ||||||||
\(413\) | −18.1673 | −0.893956 | ||||||||
\(414\) | −5.09319 | −0.250317 | ||||||||
\(415\) | 10.8906 | 0.534598 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −0.705320 | −0.0345397 | ||||||||
\(418\) | −11.5375 | −0.564320 | ||||||||
\(419\) | 21.3064 | 1.04088 | 0.520442 | − | 0.853897i | \(-0.325767\pi\) | ||||
0.520442 | + | 0.853897i | \(0.325767\pi\) | |||||||
\(420\) | 1.52296 | 0.0743131 | ||||||||
\(421\) | 11.1970 | 0.545708 | 0.272854 | − | 0.962055i | \(-0.412032\pi\) | ||||
0.272854 | + | 0.962055i | \(0.412032\pi\) | |||||||
\(422\) | −20.3142 | −0.988879 | ||||||||
\(423\) | 26.6862 | 1.29753 | ||||||||
\(424\) | −9.86129 | −0.478907 | ||||||||
\(425\) | 6.09419 | 0.295612 | ||||||||
\(426\) | 6.78300 | 0.328637 | ||||||||
\(427\) | 22.9717 | 1.11168 | ||||||||
\(428\) | −6.75721 | −0.326622 | ||||||||
\(429\) | 3.13777 | 0.151493 | ||||||||
\(430\) | 3.93884 | 0.189948 | ||||||||
\(431\) | 36.1462 | 1.74110 | 0.870549 | − | 0.492081i | \(-0.163764\pi\) | ||||
0.870549 | + | 0.492081i | \(0.163764\pi\) | |||||||
\(432\) | −3.25735 | −0.156719 | ||||||||
\(433\) | −25.2596 | −1.21390 | −0.606949 | − | 0.794740i | \(-0.707607\pi\) | ||||
−0.606949 | + | 0.794740i | \(0.707607\pi\) | |||||||
\(434\) | −2.65097 | −0.127251 | ||||||||
\(435\) | −0.908195 | −0.0435446 | ||||||||
\(436\) | 3.05614 | 0.146363 | ||||||||
\(437\) | −4.02961 | −0.192763 | ||||||||
\(438\) | −1.06461 | −0.0508688 | ||||||||
\(439\) | −4.22167 | −0.201489 | −0.100745 | − | 0.994912i | \(-0.532122\pi\) | ||||
−0.100745 | + | 0.994912i | \(0.532122\pi\) | |||||||
\(440\) | 5.46180 | 0.260381 | ||||||||
\(441\) | −0.0738126 | −0.00351489 | ||||||||
\(442\) | 6.09419 | 0.289871 | ||||||||
\(443\) | 7.90570 | 0.375611 | 0.187806 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187806 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(444\) | −1.07334 | −0.0509384 | ||||||||
\(445\) | −5.71941 | −0.271126 | ||||||||
\(446\) | 18.0022 | 0.852430 | ||||||||
\(447\) | −6.96012 | −0.329202 | ||||||||
\(448\) | 2.65097 | 0.125247 | ||||||||
\(449\) | −5.10945 | −0.241130 | −0.120565 | − | 0.992705i | \(-0.538471\pi\) | ||||
−0.120565 | + | 0.992705i | \(0.538471\pi\) | |||||||
\(450\) | −2.66996 | −0.125863 | ||||||||
\(451\) | −11.9408 | −0.562270 | ||||||||
\(452\) | −5.39957 | −0.253974 | ||||||||
\(453\) | 9.40304 | 0.441794 | ||||||||
\(454\) | −4.23392 | −0.198708 | ||||||||
\(455\) | 2.65097 | 0.124279 | ||||||||
\(456\) | −1.21356 | −0.0568303 | ||||||||
\(457\) | −25.9473 | −1.21376 | −0.606881 | − | 0.794793i | \(-0.707580\pi\) | ||||
−0.606881 | + | 0.794793i | \(0.707580\pi\) | |||||||
\(458\) | 11.2182 | 0.524191 | ||||||||
\(459\) | −19.8509 | −0.926562 | ||||||||
\(460\) | 1.90759 | 0.0889420 | ||||||||
\(461\) | −16.4812 | −0.767605 | −0.383803 | − | 0.923415i | \(-0.625386\pi\) | ||||
−0.383803 | + | 0.923415i | \(0.625386\pi\) | |||||||
\(462\) | 8.31813 | 0.386995 | ||||||||
\(463\) | −36.8600 | −1.71303 | −0.856515 | − | 0.516122i | \(-0.827375\pi\) | ||||
−0.856515 | + | 0.516122i | \(0.827375\pi\) | |||||||
\(464\) | −1.58086 | −0.0733897 | ||||||||
\(465\) | −0.574493 | −0.0266415 | ||||||||
\(466\) | 19.0696 | 0.883383 | ||||||||
\(467\) | −0.401555 | −0.0185818 | −0.00929088 | − | 0.999957i | \(-0.502957\pi\) | ||||
−0.00929088 | + | 0.999957i | \(0.502957\pi\) | |||||||
\(468\) | −2.66996 | −0.123419 | ||||||||
\(469\) | −11.7412 | −0.542160 | ||||||||
\(470\) | −9.99497 | −0.461034 | ||||||||
\(471\) | 2.12017 | 0.0976921 | ||||||||
\(472\) | −6.85309 | −0.315439 | ||||||||
\(473\) | 21.5131 | 0.989175 | ||||||||
\(474\) | 1.58733 | 0.0729086 | ||||||||
\(475\) | −2.11241 | −0.0969239 | ||||||||
\(476\) | 16.1555 | 0.740487 | ||||||||
\(477\) | 26.3292 | 1.20553 | ||||||||
\(478\) | −4.55128 | −0.208171 | ||||||||
\(479\) | −35.6527 | −1.62901 | −0.814507 | − | 0.580154i | \(-0.802992\pi\) | ||||
−0.814507 | + | 0.580154i | \(0.802992\pi\) | |||||||
\(480\) | 0.574493 | 0.0262219 | ||||||||
\(481\) | −1.86832 | −0.0851881 | ||||||||
\(482\) | 15.8198 | 0.720573 | ||||||||
\(483\) | 2.90520 | 0.132191 | ||||||||
\(484\) | 18.8313 | 0.855967 | ||||||||
\(485\) | −1.55602 | −0.0706552 | ||||||||
\(486\) | 13.2986 | 0.603237 | ||||||||
\(487\) | 32.5500 | 1.47498 | 0.737490 | − | 0.675358i | \(-0.236011\pi\) | ||||
0.737490 | + | 0.675358i | \(0.236011\pi\) | |||||||
\(488\) | 8.66537 | 0.392263 | ||||||||
\(489\) | 13.6378 | 0.616725 | ||||||||
\(490\) | 0.0276456 | 0.00124890 | ||||||||
\(491\) | 21.6706 | 0.977979 | 0.488990 | − | 0.872290i | \(-0.337366\pi\) | ||||
0.488990 | + | 0.872290i | \(0.337366\pi\) | |||||||
\(492\) | −1.25598 | −0.0566238 | ||||||||
\(493\) | −9.63409 | −0.433897 | ||||||||
\(494\) | −2.11241 | −0.0950417 | ||||||||
\(495\) | −14.5828 | −0.655447 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 31.2998 | 1.40399 | ||||||||
\(498\) | 6.25657 | 0.280364 | ||||||||
\(499\) | −7.01650 | −0.314102 | −0.157051 | − | 0.987591i | \(-0.550199\pi\) | ||||
−0.157051 | + | 0.987591i | \(0.550199\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.37937 | −0.374363 | ||||||||
\(502\) | −16.7453 | −0.747379 | ||||||||
\(503\) | 10.1133 | 0.450931 | 0.225466 | − | 0.974251i | \(-0.427610\pi\) | ||||
0.225466 | + | 0.974251i | \(0.427610\pi\) | |||||||
\(504\) | −7.07798 | −0.315278 | ||||||||
\(505\) | 15.1649 | 0.674830 | ||||||||
\(506\) | 10.4189 | 0.463176 | ||||||||
\(507\) | 0.574493 | 0.0255141 | ||||||||
\(508\) | 9.99185 | 0.443317 | ||||||||
\(509\) | −28.0381 | −1.24277 | −0.621383 | − | 0.783507i | \(-0.713429\pi\) | ||||
−0.621383 | + | 0.783507i | \(0.713429\pi\) | |||||||
\(510\) | 3.50107 | 0.155030 | ||||||||
\(511\) | −4.91257 | −0.217319 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.88086 | 0.303797 | ||||||||
\(514\) | 2.59139 | 0.114301 | ||||||||
\(515\) | −14.4472 | −0.636621 | ||||||||
\(516\) | 2.26284 | 0.0996158 | ||||||||
\(517\) | −54.5906 | −2.40089 | ||||||||
\(518\) | −4.95287 | −0.217616 | ||||||||
\(519\) | 0.940941 | 0.0413027 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −14.6391 | −0.641352 | −0.320676 | − | 0.947189i | \(-0.603910\pi\) | ||||
−0.320676 | + | 0.947189i | \(0.603910\pi\) | |||||||
\(522\) | 4.22084 | 0.184741 | ||||||||
\(523\) | 41.5429 | 1.81654 | 0.908271 | − | 0.418381i | \(-0.137402\pi\) | ||||
0.908271 | + | 0.418381i | \(0.137402\pi\) | |||||||
\(524\) | −15.5104 | −0.677573 | ||||||||
\(525\) | 1.52296 | 0.0664676 | ||||||||
\(526\) | −13.3832 | −0.583537 | ||||||||
\(527\) | −6.09419 | −0.265467 | ||||||||
\(528\) | 3.13777 | 0.136554 | ||||||||
\(529\) | −19.3611 | −0.841786 | ||||||||
\(530\) | −9.86129 | −0.428347 | ||||||||
\(531\) | 18.2975 | 0.794042 | ||||||||
\(532\) | −5.59993 | −0.242788 | ||||||||
\(533\) | −2.18624 | −0.0946964 | ||||||||
\(534\) | −3.28577 | −0.142189 | ||||||||
\(535\) | −6.75721 | −0.292140 | ||||||||
\(536\) | −4.42904 | −0.191305 | ||||||||
\(537\) | 7.49762 | 0.323546 | ||||||||
\(538\) | 11.4529 | 0.493771 | ||||||||
\(539\) | 0.150995 | 0.00650381 | ||||||||
\(540\) | −3.25735 | −0.140174 | ||||||||
\(541\) | −21.8516 | −0.939475 | −0.469738 | − | 0.882806i | \(-0.655651\pi\) | ||||
−0.469738 | + | 0.882806i | \(0.655651\pi\) | |||||||
\(542\) | −5.81599 | −0.249818 | ||||||||
\(543\) | 3.76363 | 0.161513 | ||||||||
\(544\) | 6.09419 | 0.261286 | ||||||||
\(545\) | 3.05614 | 0.130911 | ||||||||
\(546\) | 1.52296 | 0.0651769 | ||||||||
\(547\) | 19.7480 | 0.844365 | 0.422182 | − | 0.906511i | \(-0.361264\pi\) | ||||
0.422182 | + | 0.906511i | \(0.361264\pi\) | |||||||
\(548\) | 9.64959 | 0.412210 | ||||||||
\(549\) | −23.1362 | −0.987428 | ||||||||
\(550\) | 5.46180 | 0.232892 | ||||||||
\(551\) | 3.33943 | 0.142264 | ||||||||
\(552\) | 1.09590 | 0.0466446 | ||||||||
\(553\) | 7.32467 | 0.311477 | ||||||||
\(554\) | −28.3232 | −1.20334 | ||||||||
\(555\) | −1.07334 | −0.0455607 | ||||||||
\(556\) | −1.22773 | −0.0520671 | ||||||||
\(557\) | 21.6809 | 0.918647 | 0.459324 | − | 0.888269i | \(-0.348092\pi\) | ||||
0.459324 | + | 0.888269i | \(0.348092\pi\) | |||||||
\(558\) | 2.66996 | 0.113028 | ||||||||
\(559\) | 3.93884 | 0.166595 | ||||||||
\(560\) | 2.65097 | 0.112024 | ||||||||
\(561\) | 19.1222 | 0.807339 | ||||||||
\(562\) | −13.6691 | −0.576596 | ||||||||
\(563\) | −1.00319 | −0.0422794 | −0.0211397 | − | 0.999777i | \(-0.506729\pi\) | ||||
−0.0211397 | + | 0.999777i | \(0.506729\pi\) | |||||||
\(564\) | −5.74205 | −0.241784 | ||||||||
\(565\) | −5.39957 | −0.227162 | ||||||||
\(566\) | −31.5935 | −1.32797 | ||||||||
\(567\) | 16.2731 | 0.683406 | ||||||||
\(568\) | 11.8069 | 0.495407 | ||||||||
\(569\) | −13.4489 | −0.563807 | −0.281903 | − | 0.959443i | \(-0.590966\pi\) | ||||
−0.281903 | + | 0.959443i | \(0.590966\pi\) | |||||||
\(570\) | −1.21356 | −0.0508306 | ||||||||
\(571\) | −0.213456 | −0.00893286 | −0.00446643 | − | 0.999990i | \(-0.501422\pi\) | ||||
−0.00446643 | + | 0.999990i | \(0.501422\pi\) | |||||||
\(572\) | 5.46180 | 0.228369 | ||||||||
\(573\) | −14.4481 | −0.603578 | ||||||||
\(574\) | −5.79565 | −0.241906 | ||||||||
\(575\) | 1.90759 | 0.0795521 | ||||||||
\(576\) | −2.66996 | −0.111248 | ||||||||
\(577\) | 23.8040 | 0.990972 | 0.495486 | − | 0.868616i | \(-0.334990\pi\) | ||||
0.495486 | + | 0.868616i | \(0.334990\pi\) | |||||||
\(578\) | 20.1392 | 0.837680 | ||||||||
\(579\) | −0.327190 | −0.0135975 | ||||||||
\(580\) | −1.58086 | −0.0656418 | ||||||||
\(581\) | 28.8706 | 1.19776 | ||||||||
\(582\) | −0.893922 | −0.0370543 | ||||||||
\(583\) | −53.8604 | −2.23067 | ||||||||
\(584\) | −1.85312 | −0.0766827 | ||||||||
\(585\) | −2.66996 | −0.110389 | ||||||||
\(586\) | 9.09822 | 0.375844 | ||||||||
\(587\) | 3.46568 | 0.143044 | 0.0715220 | − | 0.997439i | \(-0.477214\pi\) | ||||
0.0715220 | + | 0.997439i | \(0.477214\pi\) | |||||||
\(588\) | 0.0158822 | 0.000654972 0 | ||||||||
\(589\) | 2.11241 | 0.0870402 | ||||||||
\(590\) | −6.85309 | −0.282137 | ||||||||
\(591\) | −9.56785 | −0.393569 | ||||||||
\(592\) | −1.86832 | −0.0767875 | ||||||||
\(593\) | −16.3183 | −0.670113 | −0.335056 | − | 0.942198i | \(-0.608755\pi\) | ||||
−0.335056 | + | 0.942198i | \(0.608755\pi\) | |||||||
\(594\) | −17.7910 | −0.729974 | ||||||||
\(595\) | 16.1555 | 0.662312 | ||||||||
\(596\) | −12.1152 | −0.496259 | ||||||||
\(597\) | −10.1176 | −0.414087 | ||||||||
\(598\) | 1.90759 | 0.0780073 | ||||||||
\(599\) | −12.9927 | −0.530865 | −0.265433 | − | 0.964129i | \(-0.585515\pi\) | ||||
−0.265433 | + | 0.964129i | \(0.585515\pi\) | |||||||
\(600\) | 0.574493 | 0.0234536 | ||||||||
\(601\) | −31.0785 | −1.26772 | −0.633859 | − | 0.773449i | \(-0.718530\pi\) | ||||
−0.633859 | + | 0.773449i | \(0.718530\pi\) | |||||||
\(602\) | 10.4417 | 0.425574 | ||||||||
\(603\) | 11.8253 | 0.481565 | ||||||||
\(604\) | 16.3675 | 0.665986 | ||||||||
\(605\) | 18.8313 | 0.765600 | ||||||||
\(606\) | 8.71214 | 0.353907 | ||||||||
\(607\) | −13.6270 | −0.553101 | −0.276551 | − | 0.960999i | \(-0.589191\pi\) | ||||
−0.276551 | + | 0.960999i | \(0.589191\pi\) | |||||||
\(608\) | −2.11241 | −0.0856694 | ||||||||
\(609\) | −2.40760 | −0.0975609 | ||||||||
\(610\) | 8.66537 | 0.350851 | ||||||||
\(611\) | −9.99497 | −0.404353 | ||||||||
\(612\) | −16.2712 | −0.657726 | ||||||||
\(613\) | −12.0228 | −0.485597 | −0.242798 | − | 0.970077i | \(-0.578065\pi\) | ||||
−0.242798 | + | 0.970077i | \(0.578065\pi\) | |||||||
\(614\) | −18.9973 | −0.766667 | ||||||||
\(615\) | −1.25598 | −0.0506459 | ||||||||
\(616\) | 14.4791 | 0.583379 | ||||||||
\(617\) | 9.88752 | 0.398057 | 0.199028 | − | 0.979994i | \(-0.436221\pi\) | ||||
0.199028 | + | 0.979994i | \(0.436221\pi\) | |||||||
\(618\) | −8.29984 | −0.333869 | ||||||||
\(619\) | 23.9439 | 0.962385 | 0.481192 | − | 0.876615i | \(-0.340204\pi\) | ||||
0.481192 | + | 0.876615i | \(0.340204\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | −6.21370 | −0.249347 | ||||||||
\(622\) | 27.7546 | 1.11286 | ||||||||
\(623\) | −15.1620 | −0.607453 | ||||||||
\(624\) | 0.574493 | 0.0229981 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.64737 | 0.105810 | ||||||||
\(627\) | −6.62825 | −0.264707 | ||||||||
\(628\) | 3.69050 | 0.147267 | ||||||||
\(629\) | −11.3859 | −0.453986 | ||||||||
\(630\) | −7.07798 | −0.281993 | ||||||||
\(631\) | 32.4434 | 1.29155 | 0.645776 | − | 0.763527i | \(-0.276534\pi\) | ||||
0.645776 | + | 0.763527i | \(0.276534\pi\) | |||||||
\(632\) | 2.76301 | 0.109907 | ||||||||
\(633\) | −11.6704 | −0.463855 | ||||||||
\(634\) | 21.8541 | 0.867937 | ||||||||
\(635\) | 9.99185 | 0.396515 | ||||||||
\(636\) | −5.66525 | −0.224642 | ||||||||
\(637\) | 0.0276456 | 0.00109536 | ||||||||
\(638\) | −8.63436 | −0.341838 | ||||||||
\(639\) | −31.5240 | −1.24707 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 11.7690 | 0.464846 | 0.232423 | − | 0.972615i | \(-0.425335\pi\) | ||||
0.232423 | + | 0.972615i | \(0.425335\pi\) | |||||||
\(642\) | −3.88197 | −0.153209 | ||||||||
\(643\) | −25.5912 | −1.00922 | −0.504608 | − | 0.863348i | \(-0.668363\pi\) | ||||
−0.504608 | + | 0.863348i | \(0.668363\pi\) | |||||||
\(644\) | 5.05697 | 0.199273 | ||||||||
\(645\) | 2.26284 | 0.0890991 | ||||||||
\(646\) | −12.8734 | −0.506498 | ||||||||
\(647\) | 10.3291 | 0.406079 | 0.203040 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203040 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(648\) | 6.13855 | 0.241145 | ||||||||
\(649\) | −37.4302 | −1.46926 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | −1.52296 | −0.0596897 | ||||||||
\(652\) | 23.7389 | 0.929688 | ||||||||
\(653\) | −35.6050 | −1.39333 | −0.696665 | − | 0.717396i | \(-0.745334\pi\) | ||||
−0.696665 | + | 0.717396i | \(0.745334\pi\) | |||||||
\(654\) | 1.75573 | 0.0686547 | ||||||||
\(655\) | −15.5104 | −0.606040 | ||||||||
\(656\) | −2.18624 | −0.0853581 | ||||||||
\(657\) | 4.94776 | 0.193030 | ||||||||
\(658\) | −26.4964 | −1.03294 | ||||||||
\(659\) | 5.17288 | 0.201507 | 0.100753 | − | 0.994911i | \(-0.467875\pi\) | ||||
0.100753 | + | 0.994911i | \(0.467875\pi\) | |||||||
\(660\) | 3.13777 | 0.122137 | ||||||||
\(661\) | −29.0936 | −1.13161 | −0.565804 | − | 0.824540i | \(-0.691434\pi\) | ||||
−0.565804 | + | 0.824540i | \(0.691434\pi\) | |||||||
\(662\) | −20.5451 | −0.798509 | ||||||||
\(663\) | 3.50107 | 0.135970 | ||||||||
\(664\) | 10.8906 | 0.422637 | ||||||||
\(665\) | −5.59993 | −0.217156 | ||||||||
\(666\) | 4.98834 | 0.193294 | ||||||||
\(667\) | −3.01564 | −0.116766 | ||||||||
\(668\) | −14.5857 | −0.564337 | ||||||||
\(669\) | 10.3422 | 0.399851 | ||||||||
\(670\) | −4.42904 | −0.171109 | ||||||||
\(671\) | 47.3286 | 1.82710 | ||||||||
\(672\) | 1.52296 | 0.0587496 | ||||||||
\(673\) | 2.96957 | 0.114468 | 0.0572342 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572342 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(674\) | −12.6765 | −0.488279 | ||||||||
\(675\) | −3.25735 | −0.125376 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −5.40749 | −0.207827 | −0.103913 | − | 0.994586i | \(-0.533136\pi\) | ||||
−0.103913 | + | 0.994586i | \(0.533136\pi\) | |||||||
\(678\) | −3.10202 | −0.119132 | ||||||||
\(679\) | −4.12496 | −0.158301 | ||||||||
\(680\) | 6.09419 | 0.233702 | ||||||||
\(681\) | −2.43236 | −0.0932083 | ||||||||
\(682\) | −5.46180 | −0.209143 | ||||||||
\(683\) | 19.5993 | 0.749946 | 0.374973 | − | 0.927036i | \(-0.377652\pi\) | ||||
0.374973 | + | 0.927036i | \(0.377652\pi\) | |||||||
\(684\) | 5.64004 | 0.215652 | ||||||||
\(685\) | 9.64959 | 0.368692 | ||||||||
\(686\) | −18.4835 | −0.705704 | ||||||||
\(687\) | 6.44476 | 0.245883 | ||||||||
\(688\) | 3.93884 | 0.150167 | ||||||||
\(689\) | −9.86129 | −0.375685 | ||||||||
\(690\) | 1.09590 | 0.0417202 | ||||||||
\(691\) | −35.2005 | −1.33909 | −0.669545 | − | 0.742771i | \(-0.733511\pi\) | ||||
−0.669545 | + | 0.742771i | \(0.733511\pi\) | |||||||
\(692\) | 1.63786 | 0.0622622 | ||||||||
\(693\) | −38.6585 | −1.46852 | ||||||||
\(694\) | −1.24387 | −0.0472168 | ||||||||
\(695\) | −1.22773 | −0.0465703 | ||||||||
\(696\) | −0.908195 | −0.0344251 | ||||||||
\(697\) | −13.3233 | −0.504658 | ||||||||
\(698\) | 11.1025 | 0.420237 | ||||||||
\(699\) | 10.9554 | 0.414370 | ||||||||
\(700\) | 2.65097 | 0.100197 | ||||||||
\(701\) | −33.0743 | −1.24920 | −0.624599 | − | 0.780946i | \(-0.714737\pi\) | ||||
−0.624599 | + | 0.780946i | \(0.714737\pi\) | |||||||
\(702\) | −3.25735 | −0.122941 | ||||||||
\(703\) | 3.94666 | 0.148851 | ||||||||
\(704\) | 5.46180 | 0.205849 | ||||||||
\(705\) | −5.74205 | −0.216258 | ||||||||
\(706\) | 5.79077 | 0.217938 | ||||||||
\(707\) | 40.2017 | 1.51194 | ||||||||
\(708\) | −3.93705 | −0.147964 | ||||||||
\(709\) | −5.67506 | −0.213132 | −0.106566 | − | 0.994306i | \(-0.533985\pi\) | ||||
−0.106566 | + | 0.994306i | \(0.533985\pi\) | |||||||
\(710\) | 11.8069 | 0.443106 | ||||||||
\(711\) | −7.37713 | −0.276664 | ||||||||
\(712\) | −5.71941 | −0.214344 | ||||||||
\(713\) | −1.90759 | −0.0714399 | ||||||||
\(714\) | 9.28124 | 0.347342 | ||||||||
\(715\) | 5.46180 | 0.204260 | ||||||||
\(716\) | 13.0508 | 0.487733 | ||||||||
\(717\) | −2.61468 | −0.0976470 | ||||||||
\(718\) | −2.07598 | −0.0774748 | ||||||||
\(719\) | −28.6757 | −1.06942 | −0.534712 | − | 0.845034i | \(-0.679580\pi\) | ||||
−0.534712 | + | 0.845034i | \(0.679580\pi\) | |||||||
\(720\) | −2.66996 | −0.0995034 | ||||||||
\(721\) | −38.2992 | −1.42634 | ||||||||
\(722\) | −14.5377 | −0.541038 | ||||||||
\(723\) | 9.08838 | 0.338000 | ||||||||
\(724\) | 6.55122 | 0.243474 | ||||||||
\(725\) | −1.58086 | −0.0587118 | ||||||||
\(726\) | 10.8184 | 0.401510 | ||||||||
\(727\) | −6.09449 | −0.226032 | −0.113016 | − | 0.993593i | \(-0.536051\pi\) | ||||
−0.113016 | + | 0.993593i | \(0.536051\pi\) | |||||||
\(728\) | 2.65097 | 0.0982515 | ||||||||
\(729\) | −10.7757 | −0.399099 | ||||||||
\(730\) | −1.85312 | −0.0685871 | ||||||||
\(731\) | 24.0040 | 0.887821 | ||||||||
\(732\) | 4.97820 | 0.184000 | ||||||||
\(733\) | −26.7358 | −0.987509 | −0.493754 | − | 0.869601i | \(-0.664376\pi\) | ||||
−0.493754 | + | 0.869601i | \(0.664376\pi\) | |||||||
\(734\) | 17.6437 | 0.651241 | ||||||||
\(735\) | 0.0158822 | 0.000585825 0 | ||||||||
\(736\) | 1.90759 | 0.0703148 | ||||||||
\(737\) | −24.1905 | −0.891069 | ||||||||
\(738\) | 5.83716 | 0.214869 | ||||||||
\(739\) | 3.79203 | 0.139492 | 0.0697460 | − | 0.997565i | \(-0.477781\pi\) | ||||
0.0697460 | + | 0.997565i | \(0.477781\pi\) | |||||||
\(740\) | −1.86832 | −0.0686809 | ||||||||
\(741\) | −1.21356 | −0.0445814 | ||||||||
\(742\) | −26.1420 | −0.959703 | ||||||||
\(743\) | 31.2853 | 1.14775 | 0.573873 | − | 0.818944i | \(-0.305440\pi\) | ||||
0.573873 | + | 0.818944i | \(0.305440\pi\) | |||||||
\(744\) | −0.574493 | −0.0210619 | ||||||||
\(745\) | −12.1152 | −0.443868 | ||||||||
\(746\) | −7.66397 | −0.280598 | ||||||||
\(747\) | −29.0774 | −1.06389 | ||||||||
\(748\) | 33.2853 | 1.21703 | ||||||||
\(749\) | −17.9132 | −0.654533 | ||||||||
\(750\) | 0.574493 | 0.0209775 | ||||||||
\(751\) | −7.11777 | −0.259731 | −0.129866 | − | 0.991532i | \(-0.541455\pi\) | ||||
−0.129866 | + | 0.991532i | \(0.541455\pi\) | |||||||
\(752\) | −9.99497 | −0.364479 | ||||||||
\(753\) | −9.62006 | −0.350574 | ||||||||
\(754\) | −1.58086 | −0.0575717 | ||||||||
\(755\) | 16.3675 | 0.595676 | ||||||||
\(756\) | −8.63515 | −0.314057 | ||||||||
\(757\) | −30.0722 | −1.09299 | −0.546496 | − | 0.837462i | \(-0.684039\pi\) | ||||
−0.546496 | + | 0.837462i | \(0.684039\pi\) | |||||||
\(758\) | 3.68946 | 0.134007 | ||||||||
\(759\) | 5.98559 | 0.217263 | ||||||||
\(760\) | −2.11241 | −0.0766251 | ||||||||
\(761\) | −32.1167 | −1.16423 | −0.582114 | − | 0.813107i | \(-0.697774\pi\) | ||||
−0.582114 | + | 0.813107i | \(0.697774\pi\) | |||||||
\(762\) | 5.74025 | 0.207947 | ||||||||
\(763\) | 8.10175 | 0.293303 | ||||||||
\(764\) | −25.1493 | −0.909870 | ||||||||
\(765\) | −16.2712 | −0.588288 | ||||||||
\(766\) | 7.99773 | 0.288970 | ||||||||
\(767\) | −6.85309 | −0.247451 | ||||||||
\(768\) | 0.574493 | 0.0207302 | ||||||||
\(769\) | 35.4075 | 1.27683 | 0.638414 | − | 0.769693i | \(-0.279591\pi\) | ||||
0.638414 | + | 0.769693i | \(0.279591\pi\) | |||||||
\(770\) | 14.4791 | 0.521790 | ||||||||
\(771\) | 1.48873 | 0.0536154 | ||||||||
\(772\) | −0.569528 | −0.0204978 | ||||||||
\(773\) | 16.6930 | 0.600407 | 0.300204 | − | 0.953875i | \(-0.402945\pi\) | ||||
0.300204 | + | 0.953875i | \(0.402945\pi\) | |||||||
\(774\) | −10.5165 | −0.378009 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | −1.55602 | −0.0558578 | ||||||||
\(777\) | −2.84539 | −0.102078 | ||||||||
\(778\) | 20.7990 | 0.745682 | ||||||||
\(779\) | 4.61822 | 0.165465 | ||||||||
\(780\) | 0.574493 | 0.0205702 | ||||||||
\(781\) | 64.4871 | 2.30753 | ||||||||
\(782\) | 11.6252 | 0.415718 | ||||||||
\(783\) | 5.14943 | 0.184026 | ||||||||
\(784\) | 0.0276456 | 0.000987344 0 | ||||||||
\(785\) | 3.69050 | 0.131720 | ||||||||
\(786\) | −8.91060 | −0.317831 | ||||||||
\(787\) | 14.7485 | 0.525729 | 0.262864 | − | 0.964833i | \(-0.415333\pi\) | ||||
0.262864 | + | 0.964833i | \(0.415333\pi\) | |||||||
\(788\) | −16.6544 | −0.593289 | ||||||||
\(789\) | −7.68858 | −0.273721 | ||||||||
\(790\) | 2.76301 | 0.0983036 | ||||||||
\(791\) | −14.3141 | −0.508951 | ||||||||
\(792\) | −14.5828 | −0.518176 | ||||||||
\(793\) | 8.66537 | 0.307716 | ||||||||
\(794\) | 4.85991 | 0.172472 | ||||||||
\(795\) | −5.66525 | −0.200926 | ||||||||
\(796\) | −17.6114 | −0.624219 | ||||||||
\(797\) | −44.4794 | −1.57554 | −0.787771 | − | 0.615969i | \(-0.788765\pi\) | ||||
−0.787771 | + | 0.615969i | \(0.788765\pi\) | |||||||
\(798\) | −3.21712 | −0.113885 | ||||||||
\(799\) | −60.9113 | −2.15489 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 15.2706 | 0.539560 | ||||||||
\(802\) | −1.50310 | −0.0530763 | ||||||||
\(803\) | −10.1214 | −0.357176 | ||||||||
\(804\) | −2.54445 | −0.0897359 | ||||||||
\(805\) | 5.05697 | 0.178235 | ||||||||
\(806\) | −1.00000 | −0.0352235 | ||||||||
\(807\) | 6.57963 | 0.231614 | ||||||||
\(808\) | 15.1649 | 0.533500 | ||||||||
\(809\) | 21.8448 | 0.768023 | 0.384012 | − | 0.923328i | \(-0.374542\pi\) | ||||
0.384012 | + | 0.923328i | \(0.374542\pi\) | |||||||
\(810\) | 6.13855 | 0.215686 | ||||||||
\(811\) | −6.53612 | −0.229514 | −0.114757 | − | 0.993394i | \(-0.536609\pi\) | ||||
−0.114757 | + | 0.993394i | \(0.536609\pi\) | |||||||
\(812\) | −4.19082 | −0.147069 | ||||||||
\(813\) | −3.34125 | −0.117183 | ||||||||
\(814\) | −10.2044 | −0.357664 | ||||||||
\(815\) | 23.7389 | 0.831538 | ||||||||
\(816\) | 3.50107 | 0.122562 | ||||||||
\(817\) | −8.32043 | −0.291095 | ||||||||
\(818\) | −30.8261 | −1.07781 | ||||||||
\(819\) | −7.07798 | −0.247325 | ||||||||
\(820\) | −2.18624 | −0.0763466 | ||||||||
\(821\) | 12.1753 | 0.424920 | 0.212460 | − | 0.977170i | \(-0.431853\pi\) | ||||
0.212460 | + | 0.977170i | \(0.431853\pi\) | |||||||
\(822\) | 5.54363 | 0.193356 | ||||||||
\(823\) | 30.0875 | 1.04878 | 0.524392 | − | 0.851477i | \(-0.324293\pi\) | ||||
0.524392 | + | 0.851477i | \(0.324293\pi\) | |||||||
\(824\) | −14.4472 | −0.503293 | ||||||||
\(825\) | 3.13777 | 0.109243 | ||||||||
\(826\) | −18.1673 | −0.632122 | ||||||||
\(827\) | 20.2642 | 0.704655 | 0.352328 | − | 0.935877i | \(-0.385390\pi\) | ||||
0.352328 | + | 0.935877i | \(0.385390\pi\) | |||||||
\(828\) | −5.09319 | −0.177001 | ||||||||
\(829\) | −26.0892 | −0.906116 | −0.453058 | − | 0.891481i | \(-0.649667\pi\) | ||||
−0.453058 | + | 0.891481i | \(0.649667\pi\) | |||||||
\(830\) | 10.8906 | 0.378018 | ||||||||
\(831\) | −16.2715 | −0.564451 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0.168478 | 0.00583741 | ||||||||
\(834\) | −0.705320 | −0.0244232 | ||||||||
\(835\) | −14.5857 | −0.504758 | ||||||||
\(836\) | −11.5375 | −0.399035 | ||||||||
\(837\) | 3.25735 | 0.112591 | ||||||||
\(838\) | 21.3064 | 0.736016 | ||||||||
\(839\) | 51.7662 | 1.78717 | 0.893583 | − | 0.448897i | \(-0.148183\pi\) | ||||
0.893583 | + | 0.448897i | \(0.148183\pi\) | |||||||
\(840\) | 1.52296 | 0.0525473 | ||||||||
\(841\) | −26.5009 | −0.913823 | ||||||||
\(842\) | 11.1970 | 0.385874 | ||||||||
\(843\) | −7.85280 | −0.270465 | ||||||||
\(844\) | −20.3142 | −0.699243 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 26.6862 | 0.917489 | ||||||||
\(847\) | 49.9212 | 1.71531 | ||||||||
\(848\) | −9.86129 | −0.338638 | ||||||||
\(849\) | −18.1502 | −0.622914 | ||||||||
\(850\) | 6.09419 | 0.209029 | ||||||||
\(851\) | −3.56400 | −0.122172 | ||||||||
\(852\) | 6.78300 | 0.232382 | ||||||||
\(853\) | −41.7393 | −1.42913 | −0.714564 | − | 0.699570i | \(-0.753375\pi\) | ||||
−0.714564 | + | 0.699570i | \(0.753375\pi\) | |||||||
\(854\) | 22.9717 | 0.786074 | ||||||||
\(855\) | 5.64004 | 0.192885 | ||||||||
\(856\) | −6.75721 | −0.230957 | ||||||||
\(857\) | 5.96129 | 0.203634 | 0.101817 | − | 0.994803i | \(-0.467534\pi\) | ||||
0.101817 | + | 0.994803i | \(0.467534\pi\) | |||||||
\(858\) | 3.13777 | 0.107122 | ||||||||
\(859\) | 13.6214 | 0.464756 | 0.232378 | − | 0.972626i | \(-0.425349\pi\) | ||||
0.232378 | + | 0.972626i | \(0.425349\pi\) | |||||||
\(860\) | 3.93884 | 0.134313 | ||||||||
\(861\) | −3.32956 | −0.113471 | ||||||||
\(862\) | 36.1462 | 1.23114 | ||||||||
\(863\) | −10.0963 | −0.343683 | −0.171842 | − | 0.985125i | \(-0.554972\pi\) | ||||
−0.171842 | + | 0.985125i | \(0.554972\pi\) | |||||||
\(864\) | −3.25735 | −0.110817 | ||||||||
\(865\) | 1.63786 | 0.0556890 | ||||||||
\(866\) | −25.2596 | −0.858356 | ||||||||
\(867\) | 11.5698 | 0.392932 | ||||||||
\(868\) | −2.65097 | −0.0899798 | ||||||||
\(869\) | 15.0910 | 0.511928 | ||||||||
\(870\) | −0.908195 | −0.0307907 | ||||||||
\(871\) | −4.42904 | −0.150072 | ||||||||
\(872\) | 3.05614 | 0.103494 | ||||||||
\(873\) | 4.15450 | 0.140609 | ||||||||
\(874\) | −4.02961 | −0.136304 | ||||||||
\(875\) | 2.65097 | 0.0896192 | ||||||||
\(876\) | −1.06461 | −0.0359697 | ||||||||
\(877\) | 30.3366 | 1.02439 | 0.512197 | − | 0.858868i | \(-0.328832\pi\) | ||||
0.512197 | + | 0.858868i | \(0.328832\pi\) | |||||||
\(878\) | −4.22167 | −0.142474 | ||||||||
\(879\) | 5.22687 | 0.176298 | ||||||||
\(880\) | 5.46180 | 0.184117 | ||||||||
\(881\) | 11.2613 | 0.379402 | 0.189701 | − | 0.981842i | \(-0.439248\pi\) | ||||
0.189701 | + | 0.981842i | \(0.439248\pi\) | |||||||
\(882\) | −0.0738126 | −0.00248540 | ||||||||
\(883\) | −36.0314 | −1.21255 | −0.606277 | − | 0.795253i | \(-0.707338\pi\) | ||||
−0.606277 | + | 0.795253i | \(0.707338\pi\) | |||||||
\(884\) | 6.09419 | 0.204970 | ||||||||
\(885\) | −3.93705 | −0.132343 | ||||||||
\(886\) | 7.90570 | 0.265597 | ||||||||
\(887\) | 32.8651 | 1.10350 | 0.551751 | − | 0.834009i | \(-0.313960\pi\) | ||||
0.551751 | + | 0.834009i | \(0.313960\pi\) | |||||||
\(888\) | −1.07334 | −0.0360189 | ||||||||
\(889\) | 26.4881 | 0.888383 | ||||||||
\(890\) | −5.71941 | −0.191715 | ||||||||
\(891\) | 33.5275 | 1.12321 | ||||||||
\(892\) | 18.0022 | 0.602759 | ||||||||
\(893\) | 21.1135 | 0.706535 | ||||||||
\(894\) | −6.96012 | −0.232781 | ||||||||
\(895\) | 13.0508 | 0.436241 | ||||||||
\(896\) | 2.65097 | 0.0885627 | ||||||||
\(897\) | 1.09590 | 0.0365910 | ||||||||
\(898\) | −5.10945 | −0.170505 | ||||||||
\(899\) | 1.58086 | 0.0527247 | ||||||||
\(900\) | −2.66996 | −0.0889986 | ||||||||
\(901\) | −60.0966 | −2.00211 | ||||||||
\(902\) | −11.9408 | −0.397585 | ||||||||
\(903\) | 5.99871 | 0.199625 | ||||||||
\(904\) | −5.39957 | −0.179587 | ||||||||
\(905\) | 6.55122 | 0.217770 | ||||||||
\(906\) | 9.40304 | 0.312395 | ||||||||
\(907\) | 34.3636 | 1.14103 | 0.570513 | − | 0.821289i | \(-0.306744\pi\) | ||||
0.570513 | + | 0.821289i | \(0.306744\pi\) | |||||||
\(908\) | −4.23392 | −0.140508 | ||||||||
\(909\) | −40.4897 | −1.34296 | ||||||||
\(910\) | 2.65097 | 0.0878788 | ||||||||
\(911\) | 13.0274 | 0.431618 | 0.215809 | − | 0.976436i | \(-0.430761\pi\) | ||||
0.215809 | + | 0.976436i | \(0.430761\pi\) | |||||||
\(912\) | −1.21356 | −0.0401851 | ||||||||
\(913\) | 59.4822 | 1.96857 | ||||||||
\(914\) | −25.9473 | −0.858259 | ||||||||
\(915\) | 4.97820 | 0.164574 | ||||||||
\(916\) | 11.2182 | 0.370659 | ||||||||
\(917\) | −41.1175 | −1.35782 | ||||||||
\(918\) | −19.8509 | −0.655179 | ||||||||
\(919\) | −39.8232 | −1.31365 | −0.656823 | − | 0.754045i | \(-0.728100\pi\) | ||||
−0.656823 | + | 0.754045i | \(0.728100\pi\) | |||||||
\(920\) | 1.90759 | 0.0628915 | ||||||||
\(921\) | −10.9138 | −0.359622 | ||||||||
\(922\) | −16.4812 | −0.542779 | ||||||||
\(923\) | 11.8069 | 0.388629 | ||||||||
\(924\) | 8.31813 | 0.273646 | ||||||||
\(925\) | −1.86832 | −0.0614300 | ||||||||
\(926\) | −36.8600 | −1.21130 | ||||||||
\(927\) | 38.5735 | 1.26692 | ||||||||
\(928\) | −1.58086 | −0.0518944 | ||||||||
\(929\) | −13.8021 | −0.452833 | −0.226416 | − | 0.974031i | \(-0.572701\pi\) | ||||
−0.226416 | + | 0.974031i | \(0.572701\pi\) | |||||||
\(930\) | −0.574493 | −0.0188384 | ||||||||
\(931\) | −0.0583988 | −0.00191394 | ||||||||
\(932\) | 19.0696 | 0.624646 | ||||||||
\(933\) | 15.9448 | 0.522010 | ||||||||
\(934\) | −0.401555 | −0.0131393 | ||||||||
\(935\) | 33.2853 | 1.08854 | ||||||||
\(936\) | −2.66996 | −0.0872703 | ||||||||
\(937\) | 50.0929 | 1.63646 | 0.818232 | − | 0.574888i | \(-0.194954\pi\) | ||||
0.818232 | + | 0.574888i | \(0.194954\pi\) | |||||||
\(938\) | −11.7412 | −0.383365 | ||||||||
\(939\) | 1.52090 | 0.0496327 | ||||||||
\(940\) | −9.99497 | −0.326000 | ||||||||
\(941\) | −41.0898 | −1.33949 | −0.669745 | − | 0.742591i | \(-0.733597\pi\) | ||||
−0.669745 | + | 0.742591i | \(0.733597\pi\) | |||||||
\(942\) | 2.12017 | 0.0690788 | ||||||||
\(943\) | −4.17045 | −0.135808 | ||||||||
\(944\) | −6.85309 | −0.223049 | ||||||||
\(945\) | −8.63515 | −0.280901 | ||||||||
\(946\) | 21.5131 | 0.699453 | ||||||||
\(947\) | 11.2480 | 0.365510 | 0.182755 | − | 0.983158i | \(-0.441498\pi\) | ||||
0.182755 | + | 0.983158i | \(0.441498\pi\) | |||||||
\(948\) | 1.58733 | 0.0515542 | ||||||||
\(949\) | −1.85312 | −0.0601549 | ||||||||
\(950\) | −2.11241 | −0.0685355 | ||||||||
\(951\) | 12.5550 | 0.407125 | ||||||||
\(952\) | 16.1555 | 0.523604 | ||||||||
\(953\) | −22.2592 | −0.721045 | −0.360522 | − | 0.932751i | \(-0.617402\pi\) | ||||
−0.360522 | + | 0.932751i | \(0.617402\pi\) | |||||||
\(954\) | 26.3292 | 0.852440 | ||||||||
\(955\) | −25.1493 | −0.813812 | ||||||||
\(956\) | −4.55128 | −0.147199 | ||||||||
\(957\) | −4.96038 | −0.160346 | ||||||||
\(958\) | −35.6527 | −1.15189 | ||||||||
\(959\) | 25.5808 | 0.826047 | ||||||||
\(960\) | 0.574493 | 0.0185417 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −1.86832 | −0.0602371 | ||||||||
\(963\) | 18.0415 | 0.581378 | ||||||||
\(964\) | 15.8198 | 0.509522 | ||||||||
\(965\) | −0.569528 | −0.0183337 | ||||||||
\(966\) | 2.90520 | 0.0934732 | ||||||||
\(967\) | 34.3610 | 1.10498 | 0.552488 | − | 0.833521i | \(-0.313679\pi\) | ||||
0.552488 | + | 0.833521i | \(0.313679\pi\) | |||||||
\(968\) | 18.8313 | 0.605260 | ||||||||
\(969\) | −7.39569 | −0.237584 | ||||||||
\(970\) | −1.55602 | −0.0499607 | ||||||||
\(971\) | 15.1132 | 0.485005 | 0.242503 | − | 0.970151i | \(-0.422032\pi\) | ||||
0.242503 | + | 0.970151i | \(0.422032\pi\) | |||||||
\(972\) | 13.2986 | 0.426553 | ||||||||
\(973\) | −3.25466 | −0.104340 | ||||||||
\(974\) | 32.5500 | 1.04297 | ||||||||
\(975\) | 0.574493 | 0.0183985 | ||||||||
\(976\) | 8.66537 | 0.277372 | ||||||||
\(977\) | −16.6835 | −0.533751 | −0.266876 | − | 0.963731i | \(-0.585991\pi\) | ||||
−0.266876 | + | 0.963731i | \(0.585991\pi\) | |||||||
\(978\) | 13.6378 | 0.436090 | ||||||||
\(979\) | −31.2383 | −0.998381 | ||||||||
\(980\) | 0.0276456 | 0.000883107 0 | ||||||||
\(981\) | −8.15978 | −0.260522 | ||||||||
\(982\) | 21.6706 | 0.691536 | ||||||||
\(983\) | −22.4386 | −0.715681 | −0.357841 | − | 0.933783i | \(-0.616487\pi\) | ||||
−0.357841 | + | 0.933783i | \(0.616487\pi\) | |||||||
\(984\) | −1.25598 | −0.0400391 | ||||||||
\(985\) | −16.6544 | −0.530654 | ||||||||
\(986\) | −9.63409 | −0.306812 | ||||||||
\(987\) | −15.2220 | −0.484521 | ||||||||
\(988\) | −2.11241 | −0.0672046 | ||||||||
\(989\) | 7.51370 | 0.238922 | ||||||||
\(990\) | −14.5828 | −0.463471 | ||||||||
\(991\) | 23.2263 | 0.737807 | 0.368903 | − | 0.929468i | \(-0.379733\pi\) | ||||
0.368903 | + | 0.929468i | \(0.379733\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | −11.8030 | −0.374558 | ||||||||
\(994\) | 31.2998 | 0.992769 | ||||||||
\(995\) | −17.6114 | −0.558318 | ||||||||
\(996\) | 6.25657 | 0.198247 | ||||||||
\(997\) | −6.59004 | −0.208709 | −0.104354 | − | 0.994540i | \(-0.533278\pi\) | ||||
−0.104354 | + | 0.994540i | \(0.533278\pi\) | |||||||
\(998\) | −7.01650 | −0.222103 | ||||||||
\(999\) | 6.08578 | 0.192546 |
(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 | 4030.2.a.r.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.r.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |