Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.312617.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.762877\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.79920 | −1.27223 | −0.636113 | − | 0.771596i | \(-0.719459\pi\) | ||||
−0.636113 | + | 0.771596i | \(0.719459\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.23712 | 0.618562 | ||||||||
\(5\) | −2.60753 | −1.16612 | −0.583061 | − | 0.812428i | \(-0.698145\pi\) | ||||
−0.583061 | + | 0.812428i | \(0.698145\pi\) | |||||||
\(6\) | 1.79920 | 0.734521 | ||||||||
\(7\) | 1.37040 | 0.517964 | 0.258982 | − | 0.965882i | \(-0.416613\pi\) | ||||
0.258982 | + | 0.965882i | \(0.416613\pi\) | |||||||
\(8\) | 1.37257 | 0.485276 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.69147 | 1.48357 | ||||||||
\(11\) | −5.21722 | −1.57305 | −0.786525 | − | 0.617558i | \(-0.788122\pi\) | ||||
−0.786525 | + | 0.617558i | \(0.788122\pi\) | |||||||
\(12\) | −1.23712 | −0.357127 | ||||||||
\(13\) | −0.609692 | −0.169098 | −0.0845490 | − | 0.996419i | \(-0.526945\pi\) | ||||
−0.0845490 | + | 0.996419i | \(0.526945\pi\) | |||||||
\(14\) | −2.46563 | −0.658968 | ||||||||
\(15\) | 2.60753 | 0.673261 | ||||||||
\(16\) | −4.94377 | −1.23594 | ||||||||
\(17\) | 0.762877 | 0.185025 | 0.0925124 | − | 0.995712i | \(-0.470510\pi\) | ||||
0.0925124 | + | 0.995712i | \(0.470510\pi\) | |||||||
\(18\) | −1.79920 | −0.424076 | ||||||||
\(19\) | 5.43444 | 1.24675 | 0.623373 | − | 0.781925i | \(-0.285762\pi\) | ||||
0.623373 | + | 0.781925i | \(0.285762\pi\) | |||||||
\(20\) | −3.22583 | −0.721318 | ||||||||
\(21\) | −1.37040 | −0.299047 | ||||||||
\(22\) | 9.38682 | 2.00128 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.37257 | −0.280174 | ||||||||
\(25\) | 1.79920 | 0.359840 | ||||||||
\(26\) | 1.09696 | 0.215131 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.69536 | 0.320393 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −4.69147 | −0.856541 | ||||||||
\(31\) | 3.96881 | 0.712819 | 0.356409 | − | 0.934330i | \(-0.384001\pi\) | ||||
0.356409 | + | 0.934330i | \(0.384001\pi\) | |||||||
\(32\) | 6.14970 | 1.08712 | ||||||||
\(33\) | 5.21722 | 0.908201 | ||||||||
\(34\) | −1.37257 | −0.235394 | ||||||||
\(35\) | −3.57337 | −0.604009 | ||||||||
\(36\) | 1.23712 | 0.206187 | ||||||||
\(37\) | −3.31418 | −0.544847 | −0.272424 | − | 0.962177i | \(-0.587825\pi\) | ||||
−0.272424 | + | 0.962177i | \(0.587825\pi\) | |||||||
\(38\) | −9.77765 | −1.58614 | ||||||||
\(39\) | 0.609692 | 0.0976288 | ||||||||
\(40\) | −3.57901 | −0.565891 | ||||||||
\(41\) | −1.10557 | −0.172661 | −0.0863306 | − | 0.996267i | \(-0.527514\pi\) | ||||
−0.0863306 | + | 0.996267i | \(0.527514\pi\) | |||||||
\(42\) | 2.46563 | 0.380455 | ||||||||
\(43\) | 7.23148 | 1.10279 | 0.551395 | − | 0.834244i | \(-0.314096\pi\) | ||||
0.551395 | + | 0.834244i | \(0.314096\pi\) | |||||||
\(44\) | −6.45434 | −0.973029 | ||||||||
\(45\) | −2.60753 | −0.388707 | ||||||||
\(46\) | −1.79920 | −0.265278 | ||||||||
\(47\) | −12.9585 | −1.89020 | −0.945099 | − | 0.326785i | \(-0.894035\pi\) | ||||
−0.945099 | + | 0.326785i | \(0.894035\pi\) | |||||||
\(48\) | 4.94377 | 0.713572 | ||||||||
\(49\) | −5.12199 | −0.731713 | ||||||||
\(50\) | −3.23712 | −0.457798 | ||||||||
\(51\) | −0.762877 | −0.106824 | ||||||||
\(52\) | −0.754264 | −0.104598 | ||||||||
\(53\) | 4.97097 | 0.682815 | 0.341408 | − | 0.939915i | \(-0.389096\pi\) | ||||
0.341408 | + | 0.939915i | \(0.389096\pi\) | |||||||
\(54\) | 1.79920 | 0.244840 | ||||||||
\(55\) | 13.6040 | 1.83437 | ||||||||
\(56\) | 1.88097 | 0.251356 | ||||||||
\(57\) | −5.43444 | −0.719809 | ||||||||
\(58\) | −1.79920 | −0.236247 | ||||||||
\(59\) | 14.3220 | 1.86456 | 0.932282 | − | 0.361733i | \(-0.117815\pi\) | ||||
0.932282 | + | 0.361733i | \(0.117815\pi\) | |||||||
\(60\) | 3.22583 | 0.416453 | ||||||||
\(61\) | 14.4747 | 1.85329 | 0.926645 | − | 0.375938i | \(-0.122679\pi\) | ||||
0.926645 | + | 0.375938i | \(0.122679\pi\) | |||||||
\(62\) | −7.14068 | −0.906867 | ||||||||
\(63\) | 1.37040 | 0.172655 | ||||||||
\(64\) | −1.17700 | −0.147125 | ||||||||
\(65\) | 1.58979 | 0.197189 | ||||||||
\(66\) | −9.38682 | −1.15544 | ||||||||
\(67\) | 12.1060 | 1.47898 | 0.739492 | − | 0.673166i | \(-0.235066\pi\) | ||||
0.739492 | + | 0.673166i | \(0.235066\pi\) | |||||||
\(68\) | 0.943773 | 0.114449 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 6.42921 | 0.768437 | ||||||||
\(71\) | 2.20809 | 0.262052 | 0.131026 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131026 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(72\) | 1.37257 | 0.161759 | ||||||||
\(73\) | 3.58894 | 0.420054 | 0.210027 | − | 0.977696i | \(-0.432645\pi\) | ||||
0.210027 | + | 0.977696i | \(0.432645\pi\) | |||||||
\(74\) | 5.96287 | 0.693170 | ||||||||
\(75\) | −1.79920 | −0.207754 | ||||||||
\(76\) | 6.72307 | 0.771189 | ||||||||
\(77\) | −7.14970 | −0.814784 | ||||||||
\(78\) | −1.09696 | −0.124206 | ||||||||
\(79\) | −7.27909 | −0.818962 | −0.409481 | − | 0.912319i | \(-0.634290\pi\) | ||||
−0.409481 | + | 0.912319i | \(0.634290\pi\) | |||||||
\(80\) | 12.8910 | 1.44126 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.98914 | 0.219664 | ||||||||
\(83\) | −3.93854 | −0.432311 | −0.216155 | − | 0.976359i | \(-0.569352\pi\) | ||||
−0.216155 | + | 0.976359i | \(0.569352\pi\) | |||||||
\(84\) | −1.69536 | −0.184979 | ||||||||
\(85\) | −1.98922 | −0.215761 | ||||||||
\(86\) | −13.0109 | −1.40300 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −7.16099 | −0.763364 | ||||||||
\(89\) | −1.67033 | −0.177054 | −0.0885271 | − | 0.996074i | \(-0.528216\pi\) | ||||
−0.0885271 | + | 0.996074i | \(0.528216\pi\) | |||||||
\(90\) | 4.69147 | 0.494524 | ||||||||
\(91\) | −0.835524 | −0.0875868 | ||||||||
\(92\) | 1.23712 | 0.128979 | ||||||||
\(93\) | −3.96881 | −0.411546 | ||||||||
\(94\) | 23.3150 | 2.40476 | ||||||||
\(95\) | −14.1704 | −1.45386 | ||||||||
\(96\) | −6.14970 | −0.627651 | ||||||||
\(97\) | −18.5166 | −1.88008 | −0.940039 | − | 0.341067i | \(-0.889212\pi\) | ||||
−0.940039 | + | 0.341067i | \(0.889212\pi\) | |||||||
\(98\) | 9.21549 | 0.930905 | ||||||||
\(99\) | −5.21722 | −0.524350 | ||||||||
\(100\) | 2.22583 | 0.222583 | ||||||||
\(101\) | −1.06925 | −0.106394 | −0.0531970 | − | 0.998584i | \(-0.516941\pi\) | ||||
−0.0531970 | + | 0.998584i | \(0.516941\pi\) | |||||||
\(102\) | 1.37257 | 0.135905 | ||||||||
\(103\) | −15.5989 | −1.53701 | −0.768503 | − | 0.639846i | \(-0.778998\pi\) | ||||
−0.768503 | + | 0.639846i | \(0.778998\pi\) | |||||||
\(104\) | −0.836844 | −0.0820593 | ||||||||
\(105\) | 3.57337 | 0.348725 | ||||||||
\(106\) | −8.94377 | −0.868696 | ||||||||
\(107\) | −7.81735 | −0.755732 | −0.377866 | − | 0.925860i | \(-0.623342\pi\) | ||||
−0.377866 | + | 0.925860i | \(0.623342\pi\) | |||||||
\(108\) | −1.23712 | −0.119042 | ||||||||
\(109\) | −1.85985 | −0.178142 | −0.0890709 | − | 0.996025i | \(-0.528390\pi\) | ||||
−0.0890709 | + | 0.996025i | \(0.528390\pi\) | |||||||
\(110\) | −24.4764 | −2.33373 | ||||||||
\(111\) | 3.31418 | 0.314568 | ||||||||
\(112\) | −6.77497 | −0.640174 | ||||||||
\(113\) | 12.2467 | 1.15207 | 0.576035 | − | 0.817425i | \(-0.304599\pi\) | ||||
0.576035 | + | 0.817425i | \(0.304599\pi\) | |||||||
\(114\) | 9.77765 | 0.915760 | ||||||||
\(115\) | −2.60753 | −0.243153 | ||||||||
\(116\) | 1.23712 | 0.114864 | ||||||||
\(117\) | −0.609692 | −0.0563660 | ||||||||
\(118\) | −25.7681 | −2.37215 | ||||||||
\(119\) | 1.04545 | 0.0958363 | ||||||||
\(120\) | 3.57901 | 0.326717 | ||||||||
\(121\) | 16.2194 | 1.47449 | ||||||||
\(122\) | −26.0428 | −2.35781 | ||||||||
\(123\) | 1.10557 | 0.0996860 | ||||||||
\(124\) | 4.90990 | 0.440922 | ||||||||
\(125\) | 8.34617 | 0.746504 | ||||||||
\(126\) | −2.46563 | −0.219656 | ||||||||
\(127\) | 7.53521 | 0.668642 | 0.334321 | − | 0.942459i | \(-0.391493\pi\) | ||||
0.334321 | + | 0.942459i | \(0.391493\pi\) | |||||||
\(128\) | −10.1817 | −0.899947 | ||||||||
\(129\) | −7.23148 | −0.636696 | ||||||||
\(130\) | −2.86035 | −0.250869 | ||||||||
\(131\) | −3.77922 | −0.330192 | −0.165096 | − | 0.986278i | \(-0.552793\pi\) | ||||
−0.165096 | + | 0.986278i | \(0.552793\pi\) | |||||||
\(132\) | 6.45434 | 0.561778 | ||||||||
\(133\) | 7.44738 | 0.645770 | ||||||||
\(134\) | −21.7811 | −1.88160 | ||||||||
\(135\) | 2.60753 | 0.224420 | ||||||||
\(136\) | 1.04710 | 0.0897882 | ||||||||
\(137\) | −7.73550 | −0.660888 | −0.330444 | − | 0.943826i | \(-0.607199\pi\) | ||||
−0.330444 | + | 0.943826i | \(0.607199\pi\) | |||||||
\(138\) | 1.79920 | 0.153158 | ||||||||
\(139\) | −12.3033 | −1.04355 | −0.521777 | − | 0.853082i | \(-0.674731\pi\) | ||||
−0.521777 | + | 0.853082i | \(0.674731\pi\) | |||||||
\(140\) | −4.42070 | −0.373617 | ||||||||
\(141\) | 12.9585 | 1.09131 | ||||||||
\(142\) | −3.97280 | −0.333390 | ||||||||
\(143\) | 3.18090 | 0.266000 | ||||||||
\(144\) | −4.94377 | −0.411981 | ||||||||
\(145\) | −2.60753 | −0.216543 | ||||||||
\(146\) | −6.45723 | −0.534404 | ||||||||
\(147\) | 5.12199 | 0.422455 | ||||||||
\(148\) | −4.10005 | −0.337022 | ||||||||
\(149\) | −13.5656 | −1.11133 | −0.555667 | − | 0.831405i | \(-0.687537\pi\) | ||||
−0.555667 | + | 0.831405i | \(0.687537\pi\) | |||||||
\(150\) | 3.23712 | 0.264310 | ||||||||
\(151\) | −7.82160 | −0.636513 | −0.318256 | − | 0.948005i | \(-0.603097\pi\) | ||||
−0.318256 | + | 0.948005i | \(0.603097\pi\) | |||||||
\(152\) | 7.45914 | 0.605016 | ||||||||
\(153\) | 0.762877 | 0.0616749 | ||||||||
\(154\) | 12.8637 | 1.03659 | ||||||||
\(155\) | −10.3488 | −0.831233 | ||||||||
\(156\) | 0.754264 | 0.0603894 | ||||||||
\(157\) | −3.37164 | −0.269086 | −0.134543 | − | 0.990908i | \(-0.542957\pi\) | ||||
−0.134543 | + | 0.990908i | \(0.542957\pi\) | |||||||
\(158\) | 13.0965 | 1.04191 | ||||||||
\(159\) | −4.97097 | −0.394224 | ||||||||
\(160\) | −16.0355 | −1.26772 | ||||||||
\(161\) | 1.37040 | 0.108003 | ||||||||
\(162\) | −1.79920 | −0.141359 | ||||||||
\(163\) | 1.25282 | 0.0981285 | 0.0490642 | − | 0.998796i | \(-0.484376\pi\) | ||||
0.0490642 | + | 0.998796i | \(0.484376\pi\) | |||||||
\(164\) | −1.36773 | −0.106802 | ||||||||
\(165\) | −13.6040 | −1.05907 | ||||||||
\(166\) | 7.08622 | 0.549998 | ||||||||
\(167\) | −16.6491 | −1.28834 | −0.644171 | − | 0.764881i | \(-0.722798\pi\) | ||||
−0.644171 | + | 0.764881i | \(0.722798\pi\) | |||||||
\(168\) | −1.88097 | −0.145120 | ||||||||
\(169\) | −12.6283 | −0.971406 | ||||||||
\(170\) | 3.57901 | 0.274498 | ||||||||
\(171\) | 5.43444 | 0.415582 | ||||||||
\(172\) | 8.94623 | 0.682143 | ||||||||
\(173\) | −8.21773 | −0.624783 | −0.312391 | − | 0.949954i | \(-0.601130\pi\) | ||||
−0.312391 | + | 0.949954i | \(0.601130\pi\) | |||||||
\(174\) | 1.79920 | 0.136397 | ||||||||
\(175\) | 2.46563 | 0.186384 | ||||||||
\(176\) | 25.7927 | 1.94420 | ||||||||
\(177\) | −14.3220 | −1.07651 | ||||||||
\(178\) | 3.00525 | 0.225253 | ||||||||
\(179\) | −18.3073 | −1.36835 | −0.684176 | − | 0.729317i | \(-0.739838\pi\) | ||||
−0.684176 | + | 0.729317i | \(0.739838\pi\) | |||||||
\(180\) | −3.22583 | −0.240439 | ||||||||
\(181\) | −17.8131 | −1.32403 | −0.662017 | − | 0.749489i | \(-0.730299\pi\) | ||||
−0.662017 | + | 0.749489i | \(0.730299\pi\) | |||||||
\(182\) | 1.50328 | 0.111430 | ||||||||
\(183\) | −14.4747 | −1.07000 | ||||||||
\(184\) | 1.37257 | 0.101187 | ||||||||
\(185\) | 8.64181 | 0.635358 | ||||||||
\(186\) | 7.14068 | 0.523580 | ||||||||
\(187\) | −3.98010 | −0.291053 | ||||||||
\(188\) | −16.0313 | −1.16920 | ||||||||
\(189\) | −1.37040 | −0.0996823 | ||||||||
\(190\) | 25.4955 | 1.84964 | ||||||||
\(191\) | −26.5437 | −1.92064 | −0.960319 | − | 0.278904i | \(-0.910029\pi\) | ||||
−0.960319 | + | 0.278904i | \(0.910029\pi\) | |||||||
\(192\) | 1.17700 | 0.0849428 | ||||||||
\(193\) | 22.4928 | 1.61907 | 0.809535 | − | 0.587072i | \(-0.199720\pi\) | ||||
0.809535 | + | 0.587072i | \(0.199720\pi\) | |||||||
\(194\) | 33.3151 | 2.39189 | ||||||||
\(195\) | −1.58979 | −0.113847 | ||||||||
\(196\) | −6.33653 | −0.452610 | ||||||||
\(197\) | 8.10815 | 0.577681 | 0.288841 | − | 0.957377i | \(-0.406730\pi\) | ||||
0.288841 | + | 0.957377i | \(0.406730\pi\) | |||||||
\(198\) | 9.38682 | 0.667093 | ||||||||
\(199\) | −3.13145 | −0.221983 | −0.110991 | − | 0.993821i | \(-0.535403\pi\) | ||||
−0.110991 | + | 0.993821i | \(0.535403\pi\) | |||||||
\(200\) | 2.46953 | 0.174622 | ||||||||
\(201\) | −12.1060 | −0.853891 | ||||||||
\(202\) | 1.92379 | 0.135357 | ||||||||
\(203\) | 1.37040 | 0.0961835 | ||||||||
\(204\) | −0.943773 | −0.0660773 | ||||||||
\(205\) | 2.88281 | 0.201344 | ||||||||
\(206\) | 28.0656 | 1.95542 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 3.01418 | 0.208996 | ||||||||
\(209\) | −28.3527 | −1.96119 | ||||||||
\(210\) | −6.42921 | −0.443657 | ||||||||
\(211\) | −1.93803 | −0.133419 | −0.0667096 | − | 0.997772i | \(-0.521250\pi\) | ||||
−0.0667096 | + | 0.997772i | \(0.521250\pi\) | |||||||
\(212\) | 6.14970 | 0.422363 | ||||||||
\(213\) | −2.20809 | −0.151296 | ||||||||
\(214\) | 14.0650 | 0.961462 | ||||||||
\(215\) | −18.8563 | −1.28599 | ||||||||
\(216\) | −1.37257 | −0.0933915 | ||||||||
\(217\) | 5.43887 | 0.369215 | ||||||||
\(218\) | 3.34625 | 0.226637 | ||||||||
\(219\) | −3.58894 | −0.242518 | ||||||||
\(220\) | 16.8299 | 1.13467 | ||||||||
\(221\) | −0.465120 | −0.0312873 | ||||||||
\(222\) | −5.96287 | −0.400202 | ||||||||
\(223\) | 23.5288 | 1.57560 | 0.787801 | − | 0.615930i | \(-0.211219\pi\) | ||||
0.787801 | + | 0.615930i | \(0.211219\pi\) | |||||||
\(224\) | 8.42758 | 0.563091 | ||||||||
\(225\) | 1.79920 | 0.119947 | ||||||||
\(226\) | −22.0342 | −1.46570 | ||||||||
\(227\) | 16.2471 | 1.07836 | 0.539179 | − | 0.842191i | \(-0.318735\pi\) | ||||
0.539179 | + | 0.842191i | \(0.318735\pi\) | |||||||
\(228\) | −6.72307 | −0.445246 | ||||||||
\(229\) | −13.5040 | −0.892371 | −0.446185 | − | 0.894941i | \(-0.647218\pi\) | ||||
−0.446185 | + | 0.894941i | \(0.647218\pi\) | |||||||
\(230\) | 4.69147 | 0.309346 | ||||||||
\(231\) | 7.14970 | 0.470416 | ||||||||
\(232\) | 1.37257 | 0.0901135 | ||||||||
\(233\) | −12.4171 | −0.813471 | −0.406735 | − | 0.913546i | \(-0.633333\pi\) | ||||
−0.406735 | + | 0.913546i | \(0.633333\pi\) | |||||||
\(234\) | 1.09696 | 0.0717104 | ||||||||
\(235\) | 33.7898 | 2.20420 | ||||||||
\(236\) | 17.7181 | 1.15335 | ||||||||
\(237\) | 7.27909 | 0.472828 | ||||||||
\(238\) | −1.88097 | −0.121925 | ||||||||
\(239\) | 6.13547 | 0.396870 | 0.198435 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198435 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(240\) | −12.8910 | −0.832112 | ||||||||
\(241\) | −21.1558 | −1.36276 | −0.681382 | − | 0.731928i | \(-0.738621\pi\) | ||||
−0.681382 | + | 0.731928i | \(0.738621\pi\) | |||||||
\(242\) | −29.1819 | −1.87588 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 17.9069 | 1.14637 | ||||||||
\(245\) | 13.3557 | 0.853267 | ||||||||
\(246\) | −1.98914 | −0.126823 | ||||||||
\(247\) | −3.31333 | −0.210822 | ||||||||
\(248\) | 5.44746 | 0.345914 | ||||||||
\(249\) | 3.93854 | 0.249595 | ||||||||
\(250\) | −15.0164 | −0.949723 | ||||||||
\(251\) | −25.5336 | −1.61166 | −0.805832 | − | 0.592144i | \(-0.798282\pi\) | ||||
−0.805832 | + | 0.592144i | \(0.798282\pi\) | |||||||
\(252\) | 1.69536 | 0.106798 | ||||||||
\(253\) | −5.21722 | −0.328004 | ||||||||
\(254\) | −13.5574 | −0.850664 | ||||||||
\(255\) | 1.98922 | 0.124570 | ||||||||
\(256\) | 20.6730 | 1.29206 | ||||||||
\(257\) | 24.1304 | 1.50521 | 0.752607 | − | 0.658470i | \(-0.228796\pi\) | ||||
0.752607 | + | 0.658470i | \(0.228796\pi\) | |||||||
\(258\) | 13.0109 | 0.810022 | ||||||||
\(259\) | −4.54176 | −0.282211 | ||||||||
\(260\) | 1.96676 | 0.121973 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 6.79957 | 0.420079 | ||||||||
\(263\) | 16.0047 | 0.986892 | 0.493446 | − | 0.869776i | \(-0.335737\pi\) | ||||
0.493446 | + | 0.869776i | \(0.335737\pi\) | |||||||
\(264\) | 7.16099 | 0.440729 | ||||||||
\(265\) | −12.9619 | −0.796246 | ||||||||
\(266\) | −13.3993 | −0.821566 | ||||||||
\(267\) | 1.67033 | 0.102222 | ||||||||
\(268\) | 14.9766 | 0.914842 | ||||||||
\(269\) | 8.58719 | 0.523570 | 0.261785 | − | 0.965126i | \(-0.415689\pi\) | ||||
0.261785 | + | 0.965126i | \(0.415689\pi\) | |||||||
\(270\) | −4.69147 | −0.285514 | ||||||||
\(271\) | −5.11668 | −0.310816 | −0.155408 | − | 0.987850i | \(-0.549669\pi\) | ||||
−0.155408 | + | 0.987850i | \(0.549669\pi\) | |||||||
\(272\) | −3.77149 | −0.228680 | ||||||||
\(273\) | 0.835524 | 0.0505682 | ||||||||
\(274\) | 13.9177 | 0.840800 | ||||||||
\(275\) | −9.38682 | −0.566047 | ||||||||
\(276\) | −1.23712 | −0.0744661 | ||||||||
\(277\) | −27.1069 | −1.62870 | −0.814348 | − | 0.580377i | \(-0.802905\pi\) | ||||
−0.814348 | + | 0.580377i | \(0.802905\pi\) | |||||||
\(278\) | 22.1361 | 1.32764 | ||||||||
\(279\) | 3.96881 | 0.237606 | ||||||||
\(280\) | −4.90469 | −0.293111 | ||||||||
\(281\) | −27.2727 | −1.62695 | −0.813477 | − | 0.581597i | \(-0.802428\pi\) | ||||
−0.813477 | + | 0.581597i | \(0.802428\pi\) | |||||||
\(282\) | −23.3150 | −1.38839 | ||||||||
\(283\) | −26.2431 | −1.55999 | −0.779995 | − | 0.625786i | \(-0.784778\pi\) | ||||
−0.779995 | + | 0.625786i | \(0.784778\pi\) | |||||||
\(284\) | 2.73168 | 0.162096 | ||||||||
\(285\) | 14.1704 | 0.839385 | ||||||||
\(286\) | −5.72307 | −0.338412 | ||||||||
\(287\) | −1.51508 | −0.0894323 | ||||||||
\(288\) | 6.14970 | 0.362375 | ||||||||
\(289\) | −16.4180 | −0.965766 | ||||||||
\(290\) | 4.69147 | 0.275492 | ||||||||
\(291\) | 18.5166 | 1.08546 | ||||||||
\(292\) | 4.43996 | 0.259829 | ||||||||
\(293\) | 24.4461 | 1.42815 | 0.714077 | − | 0.700067i | \(-0.246847\pi\) | ||||
0.714077 | + | 0.700067i | \(0.246847\pi\) | |||||||
\(294\) | −9.21549 | −0.537458 | ||||||||
\(295\) | −37.3450 | −2.17431 | ||||||||
\(296\) | −4.54894 | −0.264402 | ||||||||
\(297\) | 5.21722 | 0.302734 | ||||||||
\(298\) | 24.4072 | 1.41387 | ||||||||
\(299\) | −0.609692 | −0.0352594 | ||||||||
\(300\) | −2.22583 | −0.128509 | ||||||||
\(301\) | 9.91005 | 0.571206 | ||||||||
\(302\) | 14.0726 | 0.809789 | ||||||||
\(303\) | 1.06925 | 0.0614267 | ||||||||
\(304\) | −26.8666 | −1.54091 | ||||||||
\(305\) | −37.7431 | −2.16116 | ||||||||
\(306\) | −1.37257 | −0.0784645 | ||||||||
\(307\) | 21.4171 | 1.22234 | 0.611170 | − | 0.791500i | \(-0.290699\pi\) | ||||
0.611170 | + | 0.791500i | \(0.290699\pi\) | |||||||
\(308\) | −8.84506 | −0.503994 | ||||||||
\(309\) | 15.5989 | 0.887391 | ||||||||
\(310\) | 18.6195 | 1.05752 | ||||||||
\(311\) | −3.00084 | −0.170162 | −0.0850811 | − | 0.996374i | \(-0.527115\pi\) | ||||
−0.0850811 | + | 0.996374i | \(0.527115\pi\) | |||||||
\(312\) | 0.836844 | 0.0473770 | ||||||||
\(313\) | 28.8668 | 1.63165 | 0.815825 | − | 0.578299i | \(-0.196283\pi\) | ||||
0.815825 | + | 0.578299i | \(0.196283\pi\) | |||||||
\(314\) | 6.06626 | 0.342339 | ||||||||
\(315\) | −3.57337 | −0.201336 | ||||||||
\(316\) | −9.00513 | −0.506578 | ||||||||
\(317\) | 7.14197 | 0.401133 | 0.200567 | − | 0.979680i | \(-0.435722\pi\) | ||||
0.200567 | + | 0.979680i | \(0.435722\pi\) | |||||||
\(318\) | 8.94377 | 0.501542 | ||||||||
\(319\) | −5.21722 | −0.292108 | ||||||||
\(320\) | 3.06907 | 0.171566 | ||||||||
\(321\) | 7.81735 | 0.436322 | ||||||||
\(322\) | −2.46563 | −0.137404 | ||||||||
\(323\) | 4.14581 | 0.230679 | ||||||||
\(324\) | 1.23712 | 0.0687291 | ||||||||
\(325\) | −1.09696 | −0.0608483 | ||||||||
\(326\) | −2.25407 | −0.124842 | ||||||||
\(327\) | 1.85985 | 0.102850 | ||||||||
\(328\) | −1.51747 | −0.0837884 | ||||||||
\(329\) | −17.7584 | −0.979055 | ||||||||
\(330\) | 24.4764 | 1.34738 | ||||||||
\(331\) | 2.92127 | 0.160568 | 0.0802838 | − | 0.996772i | \(-0.474417\pi\) | ||||
0.0802838 | + | 0.996772i | \(0.474417\pi\) | |||||||
\(332\) | −4.87246 | −0.267411 | ||||||||
\(333\) | −3.31418 | −0.181616 | ||||||||
\(334\) | 29.9550 | 1.63906 | ||||||||
\(335\) | −31.5667 | −1.72467 | ||||||||
\(336\) | 6.77497 | 0.369605 | ||||||||
\(337\) | −18.1590 | −0.989184 | −0.494592 | − | 0.869125i | \(-0.664683\pi\) | ||||
−0.494592 | + | 0.869125i | \(0.664683\pi\) | |||||||
\(338\) | 22.7208 | 1.23585 | ||||||||
\(339\) | −12.2467 | −0.665148 | ||||||||
\(340\) | −2.46091 | −0.133462 | ||||||||
\(341\) | −20.7061 | −1.12130 | ||||||||
\(342\) | −9.77765 | −0.528715 | ||||||||
\(343\) | −16.6120 | −0.896965 | ||||||||
\(344\) | 9.92570 | 0.535158 | ||||||||
\(345\) | 2.60753 | 0.140385 | ||||||||
\(346\) | 14.7854 | 0.794865 | ||||||||
\(347\) | 19.3473 | 1.03862 | 0.519310 | − | 0.854586i | \(-0.326189\pi\) | ||||
0.519310 | + | 0.854586i | \(0.326189\pi\) | |||||||
\(348\) | −1.23712 | −0.0663168 | ||||||||
\(349\) | 15.1619 | 0.811598 | 0.405799 | − | 0.913962i | \(-0.366993\pi\) | ||||
0.405799 | + | 0.913962i | \(0.366993\pi\) | |||||||
\(350\) | −4.43617 | −0.237123 | ||||||||
\(351\) | 0.609692 | 0.0325429 | ||||||||
\(352\) | −32.0843 | −1.71010 | ||||||||
\(353\) | −32.7282 | −1.74195 | −0.870973 | − | 0.491331i | \(-0.836511\pi\) | ||||
−0.870973 | + | 0.491331i | \(0.836511\pi\) | |||||||
\(354\) | 25.7681 | 1.36956 | ||||||||
\(355\) | −5.75766 | −0.305585 | ||||||||
\(356\) | −2.06640 | −0.109519 | ||||||||
\(357\) | −1.04545 | −0.0553311 | ||||||||
\(358\) | 32.9385 | 1.74085 | ||||||||
\(359\) | −13.2280 | −0.698148 | −0.349074 | − | 0.937095i | \(-0.613504\pi\) | ||||
−0.349074 | + | 0.937095i | \(0.613504\pi\) | |||||||
\(360\) | −3.57901 | −0.188630 | ||||||||
\(361\) | 10.5331 | 0.554375 | ||||||||
\(362\) | 32.0493 | 1.68447 | ||||||||
\(363\) | −16.2194 | −0.851297 | ||||||||
\(364\) | −1.03365 | −0.0541778 | ||||||||
\(365\) | −9.35827 | −0.489834 | ||||||||
\(366\) | 26.0428 | 1.36128 | ||||||||
\(367\) | 2.98259 | 0.155690 | 0.0778450 | − | 0.996965i | \(-0.475196\pi\) | ||||
0.0778450 | + | 0.996965i | \(0.475196\pi\) | |||||||
\(368\) | −4.94377 | −0.257712 | ||||||||
\(369\) | −1.10557 | −0.0575537 | ||||||||
\(370\) | −15.5483 | −0.808320 | ||||||||
\(371\) | 6.81224 | 0.353674 | ||||||||
\(372\) | −4.90990 | −0.254567 | ||||||||
\(373\) | −5.90327 | −0.305660 | −0.152830 | − | 0.988253i | \(-0.548839\pi\) | ||||
−0.152830 | + | 0.988253i | \(0.548839\pi\) | |||||||
\(374\) | 7.16099 | 0.370286 | ||||||||
\(375\) | −8.34617 | −0.430995 | ||||||||
\(376\) | −17.7865 | −0.917268 | ||||||||
\(377\) | −0.609692 | −0.0314007 | ||||||||
\(378\) | 2.46563 | 0.126818 | ||||||||
\(379\) | 3.75455 | 0.192858 | 0.0964292 | − | 0.995340i | \(-0.469258\pi\) | ||||
0.0964292 | + | 0.995340i | \(0.469258\pi\) | |||||||
\(380\) | −17.5306 | −0.899300 | ||||||||
\(381\) | −7.53521 | −0.386041 | ||||||||
\(382\) | 47.7575 | 2.44349 | ||||||||
\(383\) | 7.76452 | 0.396749 | 0.198374 | − | 0.980126i | \(-0.436434\pi\) | ||||
0.198374 | + | 0.980126i | \(0.436434\pi\) | |||||||
\(384\) | 10.1817 | 0.519585 | ||||||||
\(385\) | 18.6430 | 0.950138 | ||||||||
\(386\) | −40.4691 | −2.05982 | ||||||||
\(387\) | 7.23148 | 0.367597 | ||||||||
\(388\) | −22.9073 | −1.16294 | ||||||||
\(389\) | 18.8378 | 0.955116 | 0.477558 | − | 0.878600i | \(-0.341522\pi\) | ||||
0.477558 | + | 0.878600i | \(0.341522\pi\) | |||||||
\(390\) | 2.86035 | 0.144839 | ||||||||
\(391\) | 0.762877 | 0.0385803 | ||||||||
\(392\) | −7.03028 | −0.355083 | ||||||||
\(393\) | 3.77922 | 0.190636 | ||||||||
\(394\) | −14.5882 | −0.734942 | ||||||||
\(395\) | 18.9804 | 0.955009 | ||||||||
\(396\) | −6.45434 | −0.324343 | ||||||||
\(397\) | 8.72995 | 0.438144 | 0.219072 | − | 0.975709i | \(-0.429697\pi\) | ||||
0.219072 | + | 0.975709i | \(0.429697\pi\) | |||||||
\(398\) | 5.63411 | 0.282412 | ||||||||
\(399\) | −7.44738 | −0.372835 | ||||||||
\(400\) | −8.89484 | −0.444742 | ||||||||
\(401\) | 9.57017 | 0.477912 | 0.238956 | − | 0.971030i | \(-0.423195\pi\) | ||||
0.238956 | + | 0.971030i | \(0.423195\pi\) | |||||||
\(402\) | 21.7811 | 1.08634 | ||||||||
\(403\) | −2.41975 | −0.120536 | ||||||||
\(404\) | −1.32279 | −0.0658113 | ||||||||
\(405\) | −2.60753 | −0.129569 | ||||||||
\(406\) | −2.46563 | −0.122367 | ||||||||
\(407\) | 17.2908 | 0.857073 | ||||||||
\(408\) | −1.04710 | −0.0518392 | ||||||||
\(409\) | −8.16414 | −0.403691 | −0.201845 | − | 0.979417i | \(-0.564694\pi\) | ||||
−0.201845 | + | 0.979417i | \(0.564694\pi\) | |||||||
\(410\) | −5.18675 | −0.256155 | ||||||||
\(411\) | 7.73550 | 0.381564 | ||||||||
\(412\) | −19.2978 | −0.950733 | ||||||||
\(413\) | 19.6269 | 0.965777 | ||||||||
\(414\) | −1.79920 | −0.0884259 | ||||||||
\(415\) | 10.2699 | 0.504127 | ||||||||
\(416\) | −3.74942 | −0.183831 | ||||||||
\(417\) | 12.3033 | 0.602496 | ||||||||
\(418\) | 51.0121 | 2.49508 | ||||||||
\(419\) | 20.4469 | 0.998895 | 0.499447 | − | 0.866344i | \(-0.333536\pi\) | ||||
0.499447 | + | 0.866344i | \(0.333536\pi\) | |||||||
\(420\) | 4.42070 | 0.215708 | ||||||||
\(421\) | 17.2632 | 0.841356 | 0.420678 | − | 0.907210i | \(-0.361792\pi\) | ||||
0.420678 | + | 0.907210i | \(0.361792\pi\) | |||||||
\(422\) | 3.48690 | 0.169740 | ||||||||
\(423\) | −12.9585 | −0.630066 | ||||||||
\(424\) | 6.82300 | 0.331354 | ||||||||
\(425\) | 1.37257 | 0.0665794 | ||||||||
\(426\) | 3.97280 | 0.192483 | ||||||||
\(427\) | 19.8361 | 0.959938 | ||||||||
\(428\) | −9.67102 | −0.467467 | ||||||||
\(429\) | −3.18090 | −0.153575 | ||||||||
\(430\) | 33.9262 | 1.63607 | ||||||||
\(431\) | −2.96320 | −0.142732 | −0.0713661 | − | 0.997450i | \(-0.522736\pi\) | ||||
−0.0713661 | + | 0.997450i | \(0.522736\pi\) | |||||||
\(432\) | 4.94377 | 0.237857 | ||||||||
\(433\) | 21.8920 | 1.05206 | 0.526032 | − | 0.850465i | \(-0.323679\pi\) | ||||
0.526032 | + | 0.850465i | \(0.323679\pi\) | |||||||
\(434\) | −9.78562 | −0.469725 | ||||||||
\(435\) | 2.60753 | 0.125021 | ||||||||
\(436\) | −2.30087 | −0.110192 | ||||||||
\(437\) | 5.43444 | 0.259964 | ||||||||
\(438\) | 6.45723 | 0.308538 | ||||||||
\(439\) | −29.4328 | −1.40475 | −0.702375 | − | 0.711807i | \(-0.747877\pi\) | ||||
−0.702375 | + | 0.711807i | \(0.747877\pi\) | |||||||
\(440\) | 18.6725 | 0.890176 | ||||||||
\(441\) | −5.12199 | −0.243904 | ||||||||
\(442\) | 0.836844 | 0.0398046 | ||||||||
\(443\) | −13.9192 | −0.661320 | −0.330660 | − | 0.943750i | \(-0.607271\pi\) | ||||
−0.330660 | + | 0.943750i | \(0.607271\pi\) | |||||||
\(444\) | 4.10005 | 0.194580 | ||||||||
\(445\) | 4.35542 | 0.206467 | ||||||||
\(446\) | −42.3330 | −2.00452 | ||||||||
\(447\) | 13.5656 | 0.641629 | ||||||||
\(448\) | −1.61297 | −0.0762056 | ||||||||
\(449\) | 17.3235 | 0.817544 | 0.408772 | − | 0.912636i | \(-0.365957\pi\) | ||||
0.408772 | + | 0.912636i | \(0.365957\pi\) | |||||||
\(450\) | −3.23712 | −0.152599 | ||||||||
\(451\) | 5.76801 | 0.271605 | ||||||||
\(452\) | 15.1506 | 0.712627 | ||||||||
\(453\) | 7.82160 | 0.367491 | ||||||||
\(454\) | −29.2318 | −1.37192 | ||||||||
\(455\) | 2.17865 | 0.102137 | ||||||||
\(456\) | −7.45914 | −0.349306 | ||||||||
\(457\) | −13.5547 | −0.634062 | −0.317031 | − | 0.948415i | \(-0.602686\pi\) | ||||
−0.317031 | + | 0.948415i | \(0.602686\pi\) | |||||||
\(458\) | 24.2964 | 1.13530 | ||||||||
\(459\) | −0.762877 | −0.0356080 | ||||||||
\(460\) | −3.22583 | −0.150405 | ||||||||
\(461\) | −13.5638 | −0.631731 | −0.315866 | − | 0.948804i | \(-0.602295\pi\) | ||||
−0.315866 | + | 0.948804i | \(0.602295\pi\) | |||||||
\(462\) | −12.8637 | −0.598476 | ||||||||
\(463\) | −27.0376 | −1.25654 | −0.628272 | − | 0.777994i | \(-0.716237\pi\) | ||||
−0.628272 | + | 0.777994i | \(0.716237\pi\) | |||||||
\(464\) | −4.94377 | −0.229509 | ||||||||
\(465\) | 10.3488 | 0.479913 | ||||||||
\(466\) | 22.3408 | 1.03492 | ||||||||
\(467\) | 28.2895 | 1.30908 | 0.654540 | − | 0.756027i | \(-0.272862\pi\) | ||||
0.654540 | + | 0.756027i | \(0.272862\pi\) | |||||||
\(468\) | −0.754264 | −0.0348659 | ||||||||
\(469\) | 16.5901 | 0.766061 | ||||||||
\(470\) | −60.7946 | −2.80424 | ||||||||
\(471\) | 3.37164 | 0.155357 | ||||||||
\(472\) | 19.6579 | 0.904829 | ||||||||
\(473\) | −37.7282 | −1.73474 | ||||||||
\(474\) | −13.0965 | −0.601544 | ||||||||
\(475\) | 9.77765 | 0.448629 | ||||||||
\(476\) | 1.29335 | 0.0592806 | ||||||||
\(477\) | 4.97097 | 0.227605 | ||||||||
\(478\) | −11.0389 | −0.504909 | ||||||||
\(479\) | 1.22365 | 0.0559099 | 0.0279550 | − | 0.999609i | \(-0.491100\pi\) | ||||
0.0279550 | + | 0.999609i | \(0.491100\pi\) | |||||||
\(480\) | 16.0355 | 0.731918 | ||||||||
\(481\) | 2.02063 | 0.0921326 | ||||||||
\(482\) | 38.0635 | 1.73374 | ||||||||
\(483\) | −1.37040 | −0.0623556 | ||||||||
\(484\) | 20.0654 | 0.912062 | ||||||||
\(485\) | 48.2826 | 2.19240 | ||||||||
\(486\) | 1.79920 | 0.0816134 | ||||||||
\(487\) | −28.8149 | −1.30573 | −0.652864 | − | 0.757475i | \(-0.726433\pi\) | ||||
−0.652864 | + | 0.757475i | \(0.726433\pi\) | |||||||
\(488\) | 19.8675 | 0.899358 | ||||||||
\(489\) | −1.25282 | −0.0566545 | ||||||||
\(490\) | −24.0296 | −1.08555 | ||||||||
\(491\) | −28.8091 | −1.30014 | −0.650068 | − | 0.759876i | \(-0.725259\pi\) | ||||
−0.650068 | + | 0.759876i | \(0.725259\pi\) | |||||||
\(492\) | 1.36773 | 0.0616619 | ||||||||
\(493\) | 0.762877 | 0.0343582 | ||||||||
\(494\) | 5.96135 | 0.268214 | ||||||||
\(495\) | 13.6040 | 0.611456 | ||||||||
\(496\) | −19.6209 | −0.881003 | ||||||||
\(497\) | 3.02598 | 0.135734 | ||||||||
\(498\) | −7.08622 | −0.317541 | ||||||||
\(499\) | −8.61789 | −0.385790 | −0.192895 | − | 0.981219i | \(-0.561788\pi\) | ||||
−0.192895 | + | 0.981219i | \(0.561788\pi\) | |||||||
\(500\) | 10.3252 | 0.461759 | ||||||||
\(501\) | 16.6491 | 0.743825 | ||||||||
\(502\) | 45.9400 | 2.05040 | ||||||||
\(503\) | −42.6447 | −1.90143 | −0.950717 | − | 0.310059i | \(-0.899651\pi\) | ||||
−0.950717 | + | 0.310059i | \(0.899651\pi\) | |||||||
\(504\) | 1.88097 | 0.0837853 | ||||||||
\(505\) | 2.78809 | 0.124068 | ||||||||
\(506\) | 9.38682 | 0.417295 | ||||||||
\(507\) | 12.6283 | 0.560841 | ||||||||
\(508\) | 9.32198 | 0.413596 | ||||||||
\(509\) | 15.6150 | 0.692123 | 0.346061 | − | 0.938212i | \(-0.387519\pi\) | ||||
0.346061 | + | 0.938212i | \(0.387519\pi\) | |||||||
\(510\) | −3.57901 | −0.158481 | ||||||||
\(511\) | 4.91830 | 0.217573 | ||||||||
\(512\) | −16.8314 | −0.743849 | ||||||||
\(513\) | −5.43444 | −0.239936 | ||||||||
\(514\) | −43.4154 | −1.91497 | ||||||||
\(515\) | 40.6746 | 1.79234 | ||||||||
\(516\) | −8.94623 | −0.393836 | ||||||||
\(517\) | 67.6076 | 2.97338 | ||||||||
\(518\) | 8.17154 | 0.359037 | ||||||||
\(519\) | 8.21773 | 0.360718 | ||||||||
\(520\) | 2.18209 | 0.0956911 | ||||||||
\(521\) | 26.8010 | 1.17417 | 0.587086 | − | 0.809525i | \(-0.300275\pi\) | ||||
0.587086 | + | 0.809525i | \(0.300275\pi\) | |||||||
\(522\) | −1.79920 | −0.0787489 | ||||||||
\(523\) | −39.2125 | −1.71464 | −0.857321 | − | 0.514783i | \(-0.827873\pi\) | ||||
−0.857321 | + | 0.514783i | \(0.827873\pi\) | |||||||
\(524\) | −4.67536 | −0.204244 | ||||||||
\(525\) | −2.46563 | −0.107609 | ||||||||
\(526\) | −28.7957 | −1.25555 | ||||||||
\(527\) | 3.02771 | 0.131889 | ||||||||
\(528\) | −25.7927 | −1.12249 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 23.3211 | 1.01301 | ||||||||
\(531\) | 14.3220 | 0.621521 | ||||||||
\(532\) | 9.21333 | 0.399448 | ||||||||
\(533\) | 0.674058 | 0.0291967 | ||||||||
\(534\) | −3.00525 | −0.130050 | ||||||||
\(535\) | 20.3840 | 0.881275 | ||||||||
\(536\) | 16.6163 | 0.717716 | ||||||||
\(537\) | 18.3073 | 0.790018 | ||||||||
\(538\) | −15.4501 | −0.666100 | ||||||||
\(539\) | 26.7226 | 1.15102 | ||||||||
\(540\) | 3.22583 | 0.138818 | ||||||||
\(541\) | −1.11216 | −0.0478156 | −0.0239078 | − | 0.999714i | \(-0.507611\pi\) | ||||
−0.0239078 | + | 0.999714i | \(0.507611\pi\) | |||||||
\(542\) | 9.20593 | 0.395429 | ||||||||
\(543\) | 17.8131 | 0.764432 | ||||||||
\(544\) | 4.69147 | 0.201145 | ||||||||
\(545\) | 4.84962 | 0.207735 | ||||||||
\(546\) | −1.50328 | −0.0643343 | ||||||||
\(547\) | 22.3385 | 0.955125 | 0.477563 | − | 0.878598i | \(-0.341520\pi\) | ||||
0.477563 | + | 0.878598i | \(0.341520\pi\) | |||||||
\(548\) | −9.56976 | −0.408800 | ||||||||
\(549\) | 14.4747 | 0.617763 | ||||||||
\(550\) | 16.8888 | 0.720140 | ||||||||
\(551\) | 5.43444 | 0.231515 | ||||||||
\(552\) | −1.37257 | −0.0584204 | ||||||||
\(553\) | −9.97530 | −0.424193 | ||||||||
\(554\) | 48.7708 | 2.07207 | ||||||||
\(555\) | −8.64181 | −0.366824 | ||||||||
\(556\) | −15.2207 | −0.645502 | ||||||||
\(557\) | 4.70470 | 0.199344 | 0.0996722 | − | 0.995020i | \(-0.468221\pi\) | ||||
0.0996722 | + | 0.995020i | \(0.468221\pi\) | |||||||
\(558\) | −7.14068 | −0.302289 | ||||||||
\(559\) | −4.40897 | −0.186480 | ||||||||
\(560\) | 17.6659 | 0.746521 | ||||||||
\(561\) | 3.98010 | 0.168040 | ||||||||
\(562\) | 49.0691 | 2.06985 | ||||||||
\(563\) | 17.7092 | 0.746355 | 0.373177 | − | 0.927760i | \(-0.378268\pi\) | ||||
0.373177 | + | 0.927760i | \(0.378268\pi\) | |||||||
\(564\) | 16.0313 | 0.675040 | ||||||||
\(565\) | −31.9336 | −1.34345 | ||||||||
\(566\) | 47.2166 | 1.98466 | ||||||||
\(567\) | 1.37040 | 0.0575516 | ||||||||
\(568\) | 3.03076 | 0.127168 | ||||||||
\(569\) | 24.6412 | 1.03301 | 0.516506 | − | 0.856284i | \(-0.327232\pi\) | ||||
0.516506 | + | 0.856284i | \(0.327232\pi\) | |||||||
\(570\) | −25.4955 | −1.06789 | ||||||||
\(571\) | −1.47211 | −0.0616057 | −0.0308029 | − | 0.999525i | \(-0.509806\pi\) | ||||
−0.0308029 | + | 0.999525i | \(0.509806\pi\) | |||||||
\(572\) | 3.93516 | 0.164537 | ||||||||
\(573\) | 26.5437 | 1.10888 | ||||||||
\(574\) | 2.72593 | 0.113778 | ||||||||
\(575\) | 1.79920 | 0.0750319 | ||||||||
\(576\) | −1.17700 | −0.0490418 | ||||||||
\(577\) | −32.6363 | −1.35867 | −0.679333 | − | 0.733830i | \(-0.737731\pi\) | ||||
−0.679333 | + | 0.733830i | \(0.737731\pi\) | |||||||
\(578\) | 29.5393 | 1.22867 | ||||||||
\(579\) | −22.4928 | −0.934770 | ||||||||
\(580\) | −3.22583 | −0.133945 | ||||||||
\(581\) | −5.39739 | −0.223922 | ||||||||
\(582\) | −33.3151 | −1.38096 | ||||||||
\(583\) | −25.9346 | −1.07410 | ||||||||
\(584\) | 4.92607 | 0.203842 | ||||||||
\(585\) | 1.58979 | 0.0657297 | ||||||||
\(586\) | −43.9834 | −1.81694 | ||||||||
\(587\) | 4.74693 | 0.195927 | 0.0979633 | − | 0.995190i | \(-0.468767\pi\) | ||||
0.0979633 | + | 0.995190i | \(0.468767\pi\) | |||||||
\(588\) | 6.33653 | 0.261314 | ||||||||
\(589\) | 21.5682 | 0.888704 | ||||||||
\(590\) | 67.1911 | 2.76621 | ||||||||
\(591\) | −8.10815 | −0.333525 | ||||||||
\(592\) | 16.3845 | 0.673400 | ||||||||
\(593\) | −29.1757 | −1.19810 | −0.599051 | − | 0.800711i | \(-0.704455\pi\) | ||||
−0.599051 | + | 0.800711i | \(0.704455\pi\) | |||||||
\(594\) | −9.38682 | −0.385146 | ||||||||
\(595\) | −2.72604 | −0.111757 | ||||||||
\(596\) | −16.7823 | −0.687428 | ||||||||
\(597\) | 3.13145 | 0.128162 | ||||||||
\(598\) | 1.09696 | 0.0448579 | ||||||||
\(599\) | −2.07025 | −0.0845883 | −0.0422942 | − | 0.999105i | \(-0.513467\pi\) | ||||
−0.0422942 | + | 0.999105i | \(0.513467\pi\) | |||||||
\(600\) | −2.46953 | −0.100818 | ||||||||
\(601\) | −16.5876 | −0.676622 | −0.338311 | − | 0.941034i | \(-0.609856\pi\) | ||||
−0.338311 | + | 0.941034i | \(0.609856\pi\) | |||||||
\(602\) | −17.8302 | −0.726703 | ||||||||
\(603\) | 12.1060 | 0.492994 | ||||||||
\(604\) | −9.67628 | −0.393722 | ||||||||
\(605\) | −42.2925 | −1.71943 | ||||||||
\(606\) | −1.92379 | −0.0781486 | ||||||||
\(607\) | 1.22240 | 0.0496156 | 0.0248078 | − | 0.999692i | \(-0.492103\pi\) | ||||
0.0248078 | + | 0.999692i | \(0.492103\pi\) | |||||||
\(608\) | 33.4202 | 1.35537 | ||||||||
\(609\) | −1.37040 | −0.0555316 | ||||||||
\(610\) | 67.9074 | 2.74949 | ||||||||
\(611\) | 7.90072 | 0.319629 | ||||||||
\(612\) | 0.943773 | 0.0381497 | ||||||||
\(613\) | 14.7569 | 0.596025 | 0.298013 | − | 0.954562i | \(-0.403676\pi\) | ||||
0.298013 | + | 0.954562i | \(0.403676\pi\) | |||||||
\(614\) | −38.5337 | −1.55509 | ||||||||
\(615\) | −2.88281 | −0.116246 | ||||||||
\(616\) | −9.81346 | −0.395395 | ||||||||
\(617\) | 40.4655 | 1.62908 | 0.814540 | − | 0.580107i | \(-0.196989\pi\) | ||||
0.814540 | + | 0.580107i | \(0.196989\pi\) | |||||||
\(618\) | −28.0656 | −1.12896 | ||||||||
\(619\) | −11.2915 | −0.453842 | −0.226921 | − | 0.973913i | \(-0.572866\pi\) | ||||
−0.226921 | + | 0.973913i | \(0.572866\pi\) | |||||||
\(620\) | −12.8027 | −0.514169 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 5.39912 | 0.216485 | ||||||||
\(623\) | −2.28902 | −0.0917077 | ||||||||
\(624\) | −3.01418 | −0.120664 | ||||||||
\(625\) | −30.7589 | −1.23036 | ||||||||
\(626\) | −51.9372 | −2.07583 | ||||||||
\(627\) | 28.3527 | 1.13230 | ||||||||
\(628\) | −4.17113 | −0.166446 | ||||||||
\(629\) | −2.52831 | −0.100810 | ||||||||
\(630\) | 6.42921 | 0.256146 | ||||||||
\(631\) | 12.7883 | 0.509095 | 0.254547 | − | 0.967060i | \(-0.418074\pi\) | ||||
0.254547 | + | 0.967060i | \(0.418074\pi\) | |||||||
\(632\) | −9.99105 | −0.397423 | ||||||||
\(633\) | 1.93803 | 0.0770296 | ||||||||
\(634\) | −12.8498 | −0.510332 | ||||||||
\(635\) | −19.6483 | −0.779718 | ||||||||
\(636\) | −6.14970 | −0.243852 | ||||||||
\(637\) | 3.12284 | 0.123731 | ||||||||
\(638\) | 9.38682 | 0.371628 | ||||||||
\(639\) | 2.20809 | 0.0873508 | ||||||||
\(640\) | 26.5492 | 1.04945 | ||||||||
\(641\) | 20.0048 | 0.790144 | 0.395072 | − | 0.918650i | \(-0.370720\pi\) | ||||
0.395072 | + | 0.918650i | \(0.370720\pi\) | |||||||
\(642\) | −14.0650 | −0.555101 | ||||||||
\(643\) | −19.5252 | −0.769998 | −0.384999 | − | 0.922917i | \(-0.625798\pi\) | ||||
−0.384999 | + | 0.922917i | \(0.625798\pi\) | |||||||
\(644\) | 1.69536 | 0.0668065 | ||||||||
\(645\) | 18.8563 | 0.742465 | ||||||||
\(646\) | −7.45914 | −0.293476 | ||||||||
\(647\) | 5.45125 | 0.214311 | 0.107155 | − | 0.994242i | \(-0.465826\pi\) | ||||
0.107155 | + | 0.994242i | \(0.465826\pi\) | |||||||
\(648\) | 1.37257 | 0.0539196 | ||||||||
\(649\) | −74.7209 | −2.93305 | ||||||||
\(650\) | 1.97365 | 0.0774128 | ||||||||
\(651\) | −5.43887 | −0.213166 | ||||||||
\(652\) | 1.54989 | 0.0606985 | ||||||||
\(653\) | −29.8135 | −1.16669 | −0.583346 | − | 0.812224i | \(-0.698257\pi\) | ||||
−0.583346 | + | 0.812224i | \(0.698257\pi\) | |||||||
\(654\) | −3.34625 | −0.130849 | ||||||||
\(655\) | 9.85442 | 0.385044 | ||||||||
\(656\) | 5.46569 | 0.213399 | ||||||||
\(657\) | 3.58894 | 0.140018 | ||||||||
\(658\) | 31.9510 | 1.24558 | ||||||||
\(659\) | −5.57380 | −0.217124 | −0.108562 | − | 0.994090i | \(-0.534625\pi\) | ||||
−0.108562 | + | 0.994090i | \(0.534625\pi\) | |||||||
\(660\) | −16.8299 | −0.655102 | ||||||||
\(661\) | −22.8573 | −0.889046 | −0.444523 | − | 0.895768i | \(-0.646627\pi\) | ||||
−0.444523 | + | 0.895768i | \(0.646627\pi\) | |||||||
\(662\) | −5.25595 | −0.204278 | ||||||||
\(663\) | 0.465120 | 0.0180638 | ||||||||
\(664\) | −5.40592 | −0.209790 | ||||||||
\(665\) | −19.4193 | −0.753046 | ||||||||
\(666\) | 5.96287 | 0.231057 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −20.5969 | −0.796919 | ||||||||
\(669\) | −23.5288 | −0.909674 | ||||||||
\(670\) | 56.7949 | 2.19418 | ||||||||
\(671\) | −75.5175 | −2.91532 | ||||||||
\(672\) | −8.42758 | −0.325101 | ||||||||
\(673\) | 27.5285 | 1.06115 | 0.530573 | − | 0.847639i | \(-0.321977\pi\) | ||||
0.530573 | + | 0.847639i | \(0.321977\pi\) | |||||||
\(674\) | 32.6717 | 1.25847 | ||||||||
\(675\) | −1.79920 | −0.0692513 | ||||||||
\(676\) | −15.6227 | −0.600874 | ||||||||
\(677\) | −20.7318 | −0.796789 | −0.398394 | − | 0.917214i | \(-0.630432\pi\) | ||||
−0.398394 | + | 0.917214i | \(0.630432\pi\) | |||||||
\(678\) | 22.0342 | 0.846220 | ||||||||
\(679\) | −25.3753 | −0.973813 | ||||||||
\(680\) | −2.73034 | −0.104704 | ||||||||
\(681\) | −16.2471 | −0.622590 | ||||||||
\(682\) | 37.2545 | 1.42655 | ||||||||
\(683\) | 8.54864 | 0.327105 | 0.163552 | − | 0.986535i | \(-0.447705\pi\) | ||||
0.163552 | + | 0.986535i | \(0.447705\pi\) | |||||||
\(684\) | 6.72307 | 0.257063 | ||||||||
\(685\) | 20.1705 | 0.770676 | ||||||||
\(686\) | 29.8884 | 1.14114 | ||||||||
\(687\) | 13.5040 | 0.515210 | ||||||||
\(688\) | −35.7508 | −1.36299 | ||||||||
\(689\) | −3.03076 | −0.115463 | ||||||||
\(690\) | −4.69147 | −0.178601 | ||||||||
\(691\) | −46.0282 | −1.75100 | −0.875498 | − | 0.483223i | \(-0.839466\pi\) | ||||
−0.875498 | + | 0.483223i | \(0.839466\pi\) | |||||||
\(692\) | −10.1663 | −0.386467 | ||||||||
\(693\) | −7.14970 | −0.271595 | ||||||||
\(694\) | −34.8098 | −1.32136 | ||||||||
\(695\) | 32.0813 | 1.21691 | ||||||||
\(696\) | −1.37257 | −0.0520271 | ||||||||
\(697\) | −0.843415 | −0.0319466 | ||||||||
\(698\) | −27.2793 | −1.03254 | ||||||||
\(699\) | 12.4171 | 0.469658 | ||||||||
\(700\) | 3.05029 | 0.115290 | ||||||||
\(701\) | 20.3401 | 0.768234 | 0.384117 | − | 0.923284i | \(-0.374506\pi\) | ||||
0.384117 | + | 0.923284i | \(0.374506\pi\) | |||||||
\(702\) | −1.09696 | −0.0414020 | ||||||||
\(703\) | −18.0107 | −0.679286 | ||||||||
\(704\) | 6.14068 | 0.231436 | ||||||||
\(705\) | −33.7898 | −1.27260 | ||||||||
\(706\) | 58.8846 | 2.21615 | ||||||||
\(707\) | −1.46530 | −0.0551083 | ||||||||
\(708\) | −17.7181 | −0.665885 | ||||||||
\(709\) | −31.7725 | −1.19324 | −0.596620 | − | 0.802524i | \(-0.703490\pi\) | ||||
−0.596620 | + | 0.802524i | \(0.703490\pi\) | |||||||
\(710\) | 10.3592 | 0.388774 | ||||||||
\(711\) | −7.27909 | −0.272987 | ||||||||
\(712\) | −2.29264 | −0.0859202 | ||||||||
\(713\) | 3.96881 | 0.148633 | ||||||||
\(714\) | 1.88097 | 0.0703937 | ||||||||
\(715\) | −8.29427 | −0.310188 | ||||||||
\(716\) | −22.6484 | −0.846410 | ||||||||
\(717\) | −6.13547 | −0.229133 | ||||||||
\(718\) | 23.7998 | 0.888202 | ||||||||
\(719\) | 2.96699 | 0.110650 | 0.0553251 | − | 0.998468i | \(-0.482380\pi\) | ||||
0.0553251 | + | 0.998468i | \(0.482380\pi\) | |||||||
\(720\) | 12.8910 | 0.480420 | ||||||||
\(721\) | −21.3768 | −0.796115 | ||||||||
\(722\) | −18.9512 | −0.705291 | ||||||||
\(723\) | 21.1558 | 0.786792 | ||||||||
\(724\) | −22.0370 | −0.818997 | ||||||||
\(725\) | 1.79920 | 0.0668206 | ||||||||
\(726\) | 29.1819 | 1.08304 | ||||||||
\(727\) | 52.8858 | 1.96143 | 0.980713 | − | 0.195452i | \(-0.0626172\pi\) | ||||
0.980713 | + | 0.195452i | \(0.0626172\pi\) | |||||||
\(728\) | −1.14681 | −0.0425038 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.8374 | 0.623180 | ||||||||
\(731\) | 5.51673 | 0.204043 | ||||||||
\(732\) | −17.9069 | −0.661859 | ||||||||
\(733\) | 49.9915 | 1.84648 | 0.923239 | − | 0.384227i | \(-0.125532\pi\) | ||||
0.923239 | + | 0.384227i | \(0.125532\pi\) | |||||||
\(734\) | −5.36628 | −0.198073 | ||||||||
\(735\) | −13.3557 | −0.492634 | ||||||||
\(736\) | 6.14970 | 0.226681 | ||||||||
\(737\) | −63.1597 | −2.32652 | ||||||||
\(738\) | 1.98914 | 0.0732214 | ||||||||
\(739\) | −4.91398 | −0.180764 | −0.0903819 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903819 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(740\) | 10.6910 | 0.393008 | ||||||||
\(741\) | 3.31333 | 0.121718 | ||||||||
\(742\) | −12.2566 | −0.449953 | ||||||||
\(743\) | 0.172797 | 0.00633930 | 0.00316965 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00316965 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(744\) | −5.44746 | −0.199714 | ||||||||
\(745\) | 35.3726 | 1.29595 | ||||||||
\(746\) | 10.6212 | 0.388869 | ||||||||
\(747\) | −3.93854 | −0.144104 | ||||||||
\(748\) | −4.92387 | −0.180034 | ||||||||
\(749\) | −10.7129 | −0.391442 | ||||||||
\(750\) | 15.0164 | 0.548323 | ||||||||
\(751\) | −20.1407 | −0.734944 | −0.367472 | − | 0.930035i | \(-0.619777\pi\) | ||||
−0.367472 | + | 0.930035i | \(0.619777\pi\) | |||||||
\(752\) | 64.0641 | 2.33618 | ||||||||
\(753\) | 25.5336 | 0.930495 | ||||||||
\(754\) | 1.09696 | 0.0399488 | ||||||||
\(755\) | 20.3950 | 0.742251 | ||||||||
\(756\) | −1.69536 | −0.0616596 | ||||||||
\(757\) | 51.7908 | 1.88237 | 0.941184 | − | 0.337895i | \(-0.109715\pi\) | ||||
0.941184 | + | 0.337895i | \(0.109715\pi\) | |||||||
\(758\) | −6.75519 | −0.245360 | ||||||||
\(759\) | 5.21722 | 0.189373 | ||||||||
\(760\) | −19.4499 | −0.705523 | ||||||||
\(761\) | 0.526341 | 0.0190798 | 0.00953992 | − | 0.999954i | \(-0.496963\pi\) | ||||
0.00953992 | + | 0.999954i | \(0.496963\pi\) | |||||||
\(762\) | 13.5574 | 0.491131 | ||||||||
\(763\) | −2.54875 | −0.0922711 | ||||||||
\(764\) | −32.8379 | −1.18803 | ||||||||
\(765\) | −1.98922 | −0.0719205 | ||||||||
\(766\) | −13.9699 | −0.504754 | ||||||||
\(767\) | −8.73200 | −0.315294 | ||||||||
\(768\) | −20.6730 | −0.745973 | ||||||||
\(769\) | −31.9202 | −1.15107 | −0.575536 | − | 0.817777i | \(-0.695207\pi\) | ||||
−0.575536 | + | 0.817777i | \(0.695207\pi\) | |||||||
\(770\) | −33.5426 | −1.20879 | ||||||||
\(771\) | −24.1304 | −0.869035 | ||||||||
\(772\) | 27.8264 | 1.00149 | ||||||||
\(773\) | 19.6213 | 0.705731 | 0.352865 | − | 0.935674i | \(-0.385207\pi\) | ||||
0.352865 | + | 0.935674i | \(0.385207\pi\) | |||||||
\(774\) | −13.0109 | −0.467666 | ||||||||
\(775\) | 7.14068 | 0.256501 | ||||||||
\(776\) | −25.4153 | −0.912357 | ||||||||
\(777\) | 4.54176 | 0.162935 | ||||||||
\(778\) | −33.8930 | −1.21512 | ||||||||
\(779\) | −6.00816 | −0.215265 | ||||||||
\(780\) | −1.96676 | −0.0704214 | ||||||||
\(781\) | −11.5201 | −0.412222 | ||||||||
\(782\) | −1.37257 | −0.0490830 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 25.3220 | 0.904356 | ||||||||
\(785\) | 8.79165 | 0.313787 | ||||||||
\(786\) | −6.79957 | −0.242533 | ||||||||
\(787\) | −9.96730 | −0.355296 | −0.177648 | − | 0.984094i | \(-0.556849\pi\) | ||||
−0.177648 | + | 0.984094i | \(0.556849\pi\) | |||||||
\(788\) | 10.0308 | 0.357332 | ||||||||
\(789\) | −16.0047 | −0.569782 | ||||||||
\(790\) | −34.1496 | −1.21499 | ||||||||
\(791\) | 16.7829 | 0.596731 | ||||||||
\(792\) | −7.16099 | −0.254455 | ||||||||
\(793\) | −8.82508 | −0.313388 | ||||||||
\(794\) | −15.7069 | −0.557418 | ||||||||
\(795\) | 12.9619 | 0.459713 | ||||||||
\(796\) | −3.87399 | −0.137310 | ||||||||
\(797\) | −6.13728 | −0.217394 | −0.108697 | − | 0.994075i | \(-0.534668\pi\) | ||||
−0.108697 | + | 0.994075i | \(0.534668\pi\) | |||||||
\(798\) | 13.3993 | 0.474331 | ||||||||
\(799\) | −9.88577 | −0.349733 | ||||||||
\(800\) | 11.0645 | 0.391191 | ||||||||
\(801\) | −1.67033 | −0.0590181 | ||||||||
\(802\) | −17.2187 | −0.608012 | ||||||||
\(803\) | −18.7243 | −0.660766 | ||||||||
\(804\) | −14.9766 | −0.528184 | ||||||||
\(805\) | −3.57337 | −0.125945 | ||||||||
\(806\) | 4.35361 | 0.153349 | ||||||||
\(807\) | −8.58719 | −0.302283 | ||||||||
\(808\) | −1.46762 | −0.0516305 | ||||||||
\(809\) | 28.6740 | 1.00812 | 0.504062 | − | 0.863668i | \(-0.331838\pi\) | ||||
0.504062 | + | 0.863668i | \(0.331838\pi\) | |||||||
\(810\) | 4.69147 | 0.164841 | ||||||||
\(811\) | 10.4813 | 0.368048 | 0.184024 | − | 0.982922i | \(-0.441088\pi\) | ||||
0.184024 | + | 0.982922i | \(0.441088\pi\) | |||||||
\(812\) | 1.69536 | 0.0594954 | ||||||||
\(813\) | 5.11668 | 0.179450 | ||||||||
\(814\) | −31.1096 | −1.09039 | ||||||||
\(815\) | −3.26676 | −0.114430 | ||||||||
\(816\) | 3.77149 | 0.132029 | ||||||||
\(817\) | 39.2990 | 1.37490 | ||||||||
\(818\) | 14.6889 | 0.513586 | ||||||||
\(819\) | −0.835524 | −0.0291956 | ||||||||
\(820\) | 3.56639 | 0.124544 | ||||||||
\(821\) | −21.2833 | −0.742793 | −0.371397 | − | 0.928474i | \(-0.621121\pi\) | ||||
−0.371397 | + | 0.928474i | \(0.621121\pi\) | |||||||
\(822\) | −13.9177 | −0.485436 | ||||||||
\(823\) | −49.6720 | −1.73146 | −0.865729 | − | 0.500513i | \(-0.833145\pi\) | ||||
−0.865729 | + | 0.500513i | \(0.833145\pi\) | |||||||
\(824\) | −21.4106 | −0.745873 | ||||||||
\(825\) | 9.38682 | 0.326807 | ||||||||
\(826\) | −35.3128 | −1.22869 | ||||||||
\(827\) | −34.0143 | −1.18279 | −0.591397 | − | 0.806381i | \(-0.701423\pi\) | ||||
−0.591397 | + | 0.806381i | \(0.701423\pi\) | |||||||
\(828\) | 1.23712 | 0.0429930 | ||||||||
\(829\) | 46.4099 | 1.61188 | 0.805942 | − | 0.591995i | \(-0.201660\pi\) | ||||
0.805942 | + | 0.591995i | \(0.201660\pi\) | |||||||
\(830\) | −18.4775 | −0.641364 | ||||||||
\(831\) | 27.1069 | 0.940328 | ||||||||
\(832\) | 0.717608 | 0.0248786 | ||||||||
\(833\) | −3.90745 | −0.135385 | ||||||||
\(834\) | −22.1361 | −0.766512 | ||||||||
\(835\) | 43.4129 | 1.50236 | ||||||||
\(836\) | −35.0757 | −1.21312 | ||||||||
\(837\) | −3.96881 | −0.137182 | ||||||||
\(838\) | −36.7880 | −1.27082 | ||||||||
\(839\) | 23.8343 | 0.822851 | 0.411426 | − | 0.911443i | \(-0.365031\pi\) | ||||
0.411426 | + | 0.911443i | \(0.365031\pi\) | |||||||
\(840\) | 4.90469 | 0.169228 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −31.0599 | −1.07040 | ||||||||
\(843\) | 27.2727 | 0.939322 | ||||||||
\(844\) | −2.39758 | −0.0825280 | ||||||||
\(845\) | 32.9286 | 1.13278 | ||||||||
\(846\) | 23.3150 | 0.801587 | ||||||||
\(847\) | 22.2271 | 0.763733 | ||||||||
\(848\) | −24.5753 | −0.843921 | ||||||||
\(849\) | 26.2431 | 0.900661 | ||||||||
\(850\) | −2.46953 | −0.0847041 | ||||||||
\(851\) | −3.31418 | −0.113609 | ||||||||
\(852\) | −2.73168 | −0.0935859 | ||||||||
\(853\) | −44.3491 | −1.51848 | −0.759242 | − | 0.650809i | \(-0.774430\pi\) | ||||
−0.759242 | + | 0.650809i | \(0.774430\pi\) | |||||||
\(854\) | −35.6892 | −1.22126 | ||||||||
\(855\) | −14.1704 | −0.484619 | ||||||||
\(856\) | −10.7299 | −0.366739 | ||||||||
\(857\) | −45.1503 | −1.54231 | −0.771153 | − | 0.636650i | \(-0.780319\pi\) | ||||
−0.771153 | + | 0.636650i | \(0.780319\pi\) | |||||||
\(858\) | 5.72307 | 0.195382 | ||||||||
\(859\) | −14.2349 | −0.485687 | −0.242844 | − | 0.970065i | \(-0.578080\pi\) | ||||
−0.242844 | + | 0.970065i | \(0.578080\pi\) | |||||||
\(860\) | −23.3275 | −0.795462 | ||||||||
\(861\) | 1.51508 | 0.0516338 | ||||||||
\(862\) | 5.33139 | 0.181588 | ||||||||
\(863\) | −19.9095 | −0.677727 | −0.338864 | − | 0.940835i | \(-0.610043\pi\) | ||||
−0.338864 | + | 0.940835i | \(0.610043\pi\) | |||||||
\(864\) | −6.14970 | −0.209217 | ||||||||
\(865\) | 21.4280 | 0.728573 | ||||||||
\(866\) | −39.3882 | −1.33846 | ||||||||
\(867\) | 16.4180 | 0.557585 | ||||||||
\(868\) | 6.72855 | 0.228382 | ||||||||
\(869\) | 37.9766 | 1.28827 | ||||||||
\(870\) | −4.69147 | −0.159056 | ||||||||
\(871\) | −7.38093 | −0.250093 | ||||||||
\(872\) | −2.55278 | −0.0864480 | ||||||||
\(873\) | −18.5166 | −0.626693 | ||||||||
\(874\) | −9.77765 | −0.330734 | ||||||||
\(875\) | 11.4376 | 0.386663 | ||||||||
\(876\) | −4.43996 | −0.150013 | ||||||||
\(877\) | −13.7071 | −0.462857 | −0.231429 | − | 0.972852i | \(-0.574340\pi\) | ||||
−0.231429 | + | 0.972852i | \(0.574340\pi\) | |||||||
\(878\) | 52.9555 | 1.78716 | ||||||||
\(879\) | −24.4461 | −0.824545 | ||||||||
\(880\) | −67.2553 | −2.26718 | ||||||||
\(881\) | −12.2371 | −0.412278 | −0.206139 | − | 0.978523i | \(-0.566090\pi\) | ||||
−0.206139 | + | 0.978523i | \(0.566090\pi\) | |||||||
\(882\) | 9.21549 | 0.310302 | ||||||||
\(883\) | −42.7294 | −1.43796 | −0.718979 | − | 0.695032i | \(-0.755390\pi\) | ||||
−0.718979 | + | 0.695032i | \(0.755390\pi\) | |||||||
\(884\) | −0.575410 | −0.0193531 | ||||||||
\(885\) | 37.3450 | 1.25534 | ||||||||
\(886\) | 25.0434 | 0.841349 | ||||||||
\(887\) | −42.5741 | −1.42950 | −0.714750 | − | 0.699380i | \(-0.753459\pi\) | ||||
−0.714750 | + | 0.699380i | \(0.753459\pi\) | |||||||
\(888\) | 4.54894 | 0.152652 | ||||||||
\(889\) | 10.3263 | 0.346333 | ||||||||
\(890\) | −7.83628 | −0.262673 | ||||||||
\(891\) | −5.21722 | −0.174783 | ||||||||
\(892\) | 29.1080 | 0.974607 | ||||||||
\(893\) | −70.4224 | −2.35660 | ||||||||
\(894\) | −24.4072 | −0.816297 | ||||||||
\(895\) | 47.7368 | 1.59566 | ||||||||
\(896\) | −13.9531 | −0.466140 | ||||||||
\(897\) | 0.609692 | 0.0203570 | ||||||||
\(898\) | −31.1684 | −1.04010 | ||||||||
\(899\) | 3.96881 | 0.132367 | ||||||||
\(900\) | 2.22583 | 0.0741944 | ||||||||
\(901\) | 3.79224 | 0.126338 | ||||||||
\(902\) | −10.3778 | −0.345543 | ||||||||
\(903\) | −9.91005 | −0.329786 | ||||||||
\(904\) | 16.8094 | 0.559073 | ||||||||
\(905\) | 46.4481 | 1.54399 | ||||||||
\(906\) | −14.0726 | −0.467532 | ||||||||
\(907\) | −41.7581 | −1.38656 | −0.693278 | − | 0.720671i | \(-0.743834\pi\) | ||||
−0.693278 | + | 0.720671i | \(0.743834\pi\) | |||||||
\(908\) | 20.0996 | 0.667030 | ||||||||
\(909\) | −1.06925 | −0.0354647 | ||||||||
\(910\) | −3.91983 | −0.129941 | ||||||||
\(911\) | 15.8964 | 0.526671 | 0.263335 | − | 0.964704i | \(-0.415177\pi\) | ||||
0.263335 | + | 0.964704i | \(0.415177\pi\) | |||||||
\(912\) | 26.8666 | 0.889643 | ||||||||
\(913\) | 20.5482 | 0.680047 | ||||||||
\(914\) | 24.3876 | 0.806671 | ||||||||
\(915\) | 37.7431 | 1.24775 | ||||||||
\(916\) | −16.7061 | −0.551986 | ||||||||
\(917\) | −5.17906 | −0.171028 | ||||||||
\(918\) | 1.37257 | 0.0453015 | ||||||||
\(919\) | −15.4175 | −0.508576 | −0.254288 | − | 0.967129i | \(-0.581841\pi\) | ||||
−0.254288 | + | 0.967129i | \(0.581841\pi\) | |||||||
\(920\) | −3.57901 | −0.117996 | ||||||||
\(921\) | −21.4171 | −0.705718 | ||||||||
\(922\) | 24.4041 | 0.803706 | ||||||||
\(923\) | −1.34626 | −0.0443126 | ||||||||
\(924\) | 8.84506 | 0.290981 | ||||||||
\(925\) | −5.96287 | −0.196058 | ||||||||
\(926\) | 48.6461 | 1.59861 | ||||||||
\(927\) | −15.5989 | −0.512336 | ||||||||
\(928\) | 6.14970 | 0.201874 | ||||||||
\(929\) | −9.48569 | −0.311215 | −0.155608 | − | 0.987819i | \(-0.549734\pi\) | ||||
−0.155608 | + | 0.987819i | \(0.549734\pi\) | |||||||
\(930\) | −18.6195 | −0.610558 | ||||||||
\(931\) | −27.8351 | −0.912260 | ||||||||
\(932\) | −15.3615 | −0.503182 | ||||||||
\(933\) | 3.00084 | 0.0982432 | ||||||||
\(934\) | −50.8984 | −1.66545 | ||||||||
\(935\) | 10.3782 | 0.339404 | ||||||||
\(936\) | −0.836844 | −0.0273531 | ||||||||
\(937\) | 42.0624 | 1.37412 | 0.687060 | − | 0.726601i | \(-0.258901\pi\) | ||||
0.687060 | + | 0.726601i | \(0.258901\pi\) | |||||||
\(938\) | −29.8490 | −0.974603 | ||||||||
\(939\) | −28.8668 | −0.942034 | ||||||||
\(940\) | 41.8021 | 1.36343 | ||||||||
\(941\) | 9.80889 | 0.319761 | 0.159880 | − | 0.987136i | \(-0.448889\pi\) | ||||
0.159880 | + | 0.987136i | \(0.448889\pi\) | |||||||
\(942\) | −6.06626 | −0.197649 | ||||||||
\(943\) | −1.10557 | −0.0360023 | ||||||||
\(944\) | −70.8046 | −2.30449 | ||||||||
\(945\) | 3.57337 | 0.116242 | ||||||||
\(946\) | 67.8806 | 2.20699 | ||||||||
\(947\) | 26.0436 | 0.846303 | 0.423152 | − | 0.906059i | \(-0.360924\pi\) | ||||
0.423152 | + | 0.906059i | \(0.360924\pi\) | |||||||
\(948\) | 9.00513 | 0.292473 | ||||||||
\(949\) | −2.18815 | −0.0710303 | ||||||||
\(950\) | −17.5919 | −0.570758 | ||||||||
\(951\) | −7.14197 | −0.231594 | ||||||||
\(952\) | 1.43495 | 0.0465071 | ||||||||
\(953\) | 1.85061 | 0.0599470 | 0.0299735 | − | 0.999551i | \(-0.490458\pi\) | ||||
0.0299735 | + | 0.999551i | \(0.490458\pi\) | |||||||
\(954\) | −8.94377 | −0.289565 | ||||||||
\(955\) | 69.2135 | 2.23970 | ||||||||
\(956\) | 7.59033 | 0.245489 | ||||||||
\(957\) | 5.21722 | 0.168649 | ||||||||
\(958\) | −2.20159 | −0.0711301 | ||||||||
\(959\) | −10.6008 | −0.342316 | ||||||||
\(960\) | −3.06907 | −0.0990537 | ||||||||
\(961\) | −15.2486 | −0.491890 | ||||||||
\(962\) | −3.63551 | −0.117214 | ||||||||
\(963\) | −7.81735 | −0.251911 | ||||||||
\(964\) | −26.1723 | −0.842953 | ||||||||
\(965\) | −58.6507 | −1.88803 | ||||||||
\(966\) | 2.46563 | 0.0793304 | ||||||||
\(967\) | −54.5680 | −1.75479 | −0.877395 | − | 0.479769i | \(-0.840721\pi\) | ||||
−0.877395 | + | 0.479769i | \(0.840721\pi\) | |||||||
\(968\) | 22.2622 | 0.715535 | ||||||||
\(969\) | −4.14581 | −0.133183 | ||||||||
\(970\) | −86.8701 | −2.78923 | ||||||||
\(971\) | −18.6434 | −0.598295 | −0.299148 | − | 0.954207i | \(-0.596702\pi\) | ||||
−0.299148 | + | 0.954207i | \(0.596702\pi\) | |||||||
\(972\) | −1.23712 | −0.0396807 | ||||||||
\(973\) | −16.8605 | −0.540524 | ||||||||
\(974\) | 51.8438 | 1.66118 | ||||||||
\(975\) | 1.09696 | 0.0351308 | ||||||||
\(976\) | −71.5594 | −2.29056 | ||||||||
\(977\) | −3.74771 | −0.119900 | −0.0599499 | − | 0.998201i | \(-0.519094\pi\) | ||||
−0.0599499 | + | 0.998201i | \(0.519094\pi\) | |||||||
\(978\) | 2.25407 | 0.0720774 | ||||||||
\(979\) | 8.71446 | 0.278515 | ||||||||
\(980\) | 16.5227 | 0.527798 | ||||||||
\(981\) | −1.85985 | −0.0593806 | ||||||||
\(982\) | 51.8333 | 1.65407 | ||||||||
\(983\) | 56.5888 | 1.80490 | 0.902451 | − | 0.430792i | \(-0.141766\pi\) | ||||
0.902451 | + | 0.430792i | \(0.141766\pi\) | |||||||
\(984\) | 1.51747 | 0.0483752 | ||||||||
\(985\) | −21.1422 | −0.673647 | ||||||||
\(986\) | −1.37257 | −0.0437115 | ||||||||
\(987\) | 17.7584 | 0.565258 | ||||||||
\(988\) | −4.09900 | −0.130407 | ||||||||
\(989\) | 7.23148 | 0.229948 | ||||||||
\(990\) | −24.4764 | −0.777911 | ||||||||
\(991\) | −37.9225 | −1.20465 | −0.602324 | − | 0.798251i | \(-0.705759\pi\) | ||||
−0.602324 | + | 0.798251i | \(0.705759\pi\) | |||||||
\(992\) | 24.4070 | 0.774922 | ||||||||
\(993\) | −2.92127 | −0.0927037 | ||||||||
\(994\) | −5.44435 | −0.172684 | ||||||||
\(995\) | 8.16534 | 0.258859 | ||||||||
\(996\) | 4.87246 | 0.154390 | ||||||||
\(997\) | −44.4838 | −1.40882 | −0.704408 | − | 0.709795i | \(-0.748788\pi\) | ||||
−0.704408 | + | 0.709795i | \(0.748788\pi\) | |||||||
\(998\) | 15.5053 | 0.490812 | ||||||||
\(999\) | 3.31418 | 0.104856 |
(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 | 2001.2.a.h.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 6003.2.a.h.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.h.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6003.2.a.h.1.4 | 5 | 3.2 | odd | 2 |