Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, 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("1470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.24264 | 0.676182 | 0.338091 | − | 0.941113i | \(-0.390219\pi\) | ||||
0.338091 | + | 0.941113i | \(0.390219\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.58579 | 0.627145 | 0.313573 | − | 0.949564i | \(-0.398474\pi\) | ||||
0.313573 | + | 0.949564i | \(0.398474\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.82843 | −1.56655 | −0.783274 | − | 0.621676i | \(-0.786452\pi\) | ||||
−0.783274 | + | 0.621676i | \(0.786452\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.24264 | −0.478133 | ||||||||
\(23\) | 3.17157 | 0.661319 | 0.330659 | − | 0.943750i | \(-0.392729\pi\) | ||||
0.330659 | + | 0.943750i | \(0.392729\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.65685 | −1.10940 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58579 | 0.480168 | 0.240084 | − | 0.970752i | \(-0.422825\pi\) | ||||
0.240084 | + | 0.970752i | \(0.422825\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −10.2426 | −1.83963 | −0.919816 | − | 0.392349i | \(-0.871662\pi\) | ||||
−0.919816 | + | 0.392349i | \(0.871662\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.24264 | −0.390394 | ||||||||
\(34\) | −2.58579 | −0.443459 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.242641 | −0.0398899 | −0.0199449 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199449 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(38\) | 6.82843 | 1.10772 | ||||||||
\(39\) | −5.65685 | −0.905822 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 10.4853 | 1.63753 | 0.818763 | − | 0.574132i | \(-0.194660\pi\) | ||||
0.818763 | + | 0.574132i | \(0.194660\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.07107 | 1.38332 | 0.691662 | − | 0.722221i | \(-0.256879\pi\) | ||||
0.691662 | + | 0.722221i | \(0.256879\pi\) | |||||||
\(44\) | 2.24264 | 0.338091 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −3.17157 | −0.467623 | ||||||||
\(47\) | −2.24264 | −0.327123 | −0.163561 | − | 0.986533i | \(-0.552298\pi\) | ||||
−0.163561 | + | 0.986533i | \(0.552298\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.58579 | −0.362083 | ||||||||
\(52\) | 5.65685 | 0.784465 | ||||||||
\(53\) | 0.343146 | 0.0471347 | 0.0235673 | − | 0.999722i | \(-0.492498\pi\) | ||||
0.0235673 | + | 0.999722i | \(0.492498\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.24264 | 0.302398 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.82843 | 0.904447 | ||||||||
\(58\) | −2.58579 | −0.339530 | ||||||||
\(59\) | −3.17157 | −0.412904 | −0.206452 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206452 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −11.6569 | −1.49251 | −0.746254 | − | 0.665662i | \(-0.768149\pi\) | ||||
−0.746254 | + | 0.665662i | \(0.768149\pi\) | |||||||
\(62\) | 10.2426 | 1.30082 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.65685 | 0.701646 | ||||||||
\(66\) | 2.24264 | 0.276050 | ||||||||
\(67\) | 9.07107 | 1.10821 | 0.554104 | − | 0.832448i | \(-0.313061\pi\) | ||||
0.554104 | + | 0.832448i | \(0.313061\pi\) | |||||||
\(68\) | 2.58579 | 0.313573 | ||||||||
\(69\) | −3.17157 | −0.381813 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48528 | −0.532305 | −0.266152 | − | 0.963931i | \(-0.585752\pi\) | ||||
−0.266152 | + | 0.963931i | \(0.585752\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0.242641 | 0.0282064 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −6.82843 | −0.783274 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.65685 | 0.640513 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.4853 | −1.15791 | ||||||||
\(83\) | 5.17157 | 0.567654 | 0.283827 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | 0.280468 | ||||||||
\(86\) | −9.07107 | −0.978158 | ||||||||
\(87\) | −2.58579 | −0.277225 | ||||||||
\(88\) | −2.24264 | −0.239066 | ||||||||
\(89\) | −0.828427 | −0.0878131 | −0.0439065 | − | 0.999036i | \(-0.513980\pi\) | ||||
−0.0439065 | + | 0.999036i | \(0.513980\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.17157 | 0.330659 | ||||||||
\(93\) | 10.2426 | 1.06211 | ||||||||
\(94\) | 2.24264 | 0.231311 | ||||||||
\(95\) | −6.82843 | −0.700582 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.48528 | −0.658481 | −0.329240 | − | 0.944246i | \(-0.606793\pi\) | ||||
−0.329240 | + | 0.944246i | \(0.606793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.24264 | 0.225394 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 17.6569 | 1.75692 | 0.878461 | − | 0.477813i | \(-0.158571\pi\) | ||||
0.878461 | + | 0.477813i | \(0.158571\pi\) | |||||||
\(102\) | 2.58579 | 0.256031 | ||||||||
\(103\) | 14.8284 | 1.46109 | 0.730544 | − | 0.682865i | \(-0.239266\pi\) | ||||
0.730544 | + | 0.682865i | \(0.239266\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.343146 | −0.0333293 | ||||||||
\(107\) | 9.65685 | 0.933563 | 0.466782 | − | 0.884373i | \(-0.345413\pi\) | ||||
0.466782 | + | 0.884373i | \(0.345413\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −3.65685 | −0.350263 | −0.175132 | − | 0.984545i | \(-0.556035\pi\) | ||||
−0.175132 | + | 0.984545i | \(0.556035\pi\) | |||||||
\(110\) | −2.24264 | −0.213827 | ||||||||
\(111\) | 0.242641 | 0.0230304 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | −6.82843 | −0.639541 | ||||||||
\(115\) | 3.17157 | 0.295751 | ||||||||
\(116\) | 2.58579 | 0.240084 | ||||||||
\(117\) | 5.65685 | 0.522976 | ||||||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −5.97056 | −0.542778 | ||||||||
\(122\) | 11.6569 | 1.05536 | ||||||||
\(123\) | −10.4853 | −0.945426 | ||||||||
\(124\) | −10.2426 | −0.919816 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −9.07107 | −0.798663 | ||||||||
\(130\) | −5.65685 | −0.496139 | ||||||||
\(131\) | −3.17157 | −0.277102 | −0.138551 | − | 0.990355i | \(-0.544244\pi\) | ||||
−0.138551 | + | 0.990355i | \(0.544244\pi\) | |||||||
\(132\) | −2.24264 | −0.195197 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.07107 | −0.783621 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −2.58579 | −0.221729 | ||||||||
\(137\) | 13.6569 | 1.16678 | 0.583392 | − | 0.812191i | \(-0.301725\pi\) | ||||
0.583392 | + | 0.812191i | \(0.301725\pi\) | |||||||
\(138\) | 3.17157 | 0.269982 | ||||||||
\(139\) | −2.34315 | −0.198743 | −0.0993715 | − | 0.995050i | \(-0.531683\pi\) | ||||
−0.0993715 | + | 0.995050i | \(0.531683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.24264 | 0.188864 | ||||||||
\(142\) | 4.48528 | 0.376396 | ||||||||
\(143\) | 12.6863 | 1.06088 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.58579 | 0.214738 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.242641 | −0.0199449 | ||||||||
\(149\) | 22.3848 | 1.83383 | 0.916916 | − | 0.399080i | \(-0.130670\pi\) | ||||
0.916916 | + | 0.399080i | \(0.130670\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 20.1421 | 1.63914 | 0.819572 | − | 0.572976i | \(-0.194211\pi\) | ||||
0.819572 | + | 0.572976i | \(0.194211\pi\) | |||||||
\(152\) | 6.82843 | 0.553859 | ||||||||
\(153\) | 2.58579 | 0.209048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2426 | −0.822709 | ||||||||
\(156\) | −5.65685 | −0.452911 | ||||||||
\(157\) | −8.34315 | −0.665856 | −0.332928 | − | 0.942952i | \(-0.608037\pi\) | ||||
−0.332928 | + | 0.942952i | \(0.608037\pi\) | |||||||
\(158\) | −8.00000 | −0.636446 | ||||||||
\(159\) | −0.343146 | −0.0272132 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −17.0711 | −1.33711 | −0.668555 | − | 0.743663i | \(-0.733087\pi\) | ||||
−0.668555 | + | 0.743663i | \(0.733087\pi\) | |||||||
\(164\) | 10.4853 | 0.818763 | ||||||||
\(165\) | −2.24264 | −0.174589 | ||||||||
\(166\) | −5.17157 | −0.401392 | ||||||||
\(167\) | 2.24264 | 0.173541 | 0.0867704 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867704 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | −2.58579 | −0.198321 | ||||||||
\(171\) | −6.82843 | −0.522183 | ||||||||
\(172\) | 9.07107 | 0.691662 | ||||||||
\(173\) | 20.8284 | 1.58356 | 0.791778 | − | 0.610809i | \(-0.209156\pi\) | ||||
0.791778 | + | 0.610809i | \(0.209156\pi\) | |||||||
\(174\) | 2.58579 | 0.196028 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.24264 | 0.169045 | ||||||||
\(177\) | 3.17157 | 0.238390 | ||||||||
\(178\) | 0.828427 | 0.0620932 | ||||||||
\(179\) | 26.2426 | 1.96147 | 0.980734 | − | 0.195350i | \(-0.0625844\pi\) | ||||
0.980734 | + | 0.195350i | \(0.0625844\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 18.4853 | 1.37400 | 0.687000 | − | 0.726657i | \(-0.258927\pi\) | ||||
0.687000 | + | 0.726657i | \(0.258927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6569 | 0.861699 | ||||||||
\(184\) | −3.17157 | −0.233811 | ||||||||
\(185\) | −0.242641 | −0.0178393 | ||||||||
\(186\) | −10.2426 | −0.751027 | ||||||||
\(187\) | 5.79899 | 0.424064 | ||||||||
\(188\) | −2.24264 | −0.163561 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.82843 | 0.495386 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −4.82843 | −0.347558 | −0.173779 | − | 0.984785i | \(-0.555598\pi\) | ||||
−0.173779 | + | 0.984785i | \(0.555598\pi\) | |||||||
\(194\) | 6.48528 | 0.465616 | ||||||||
\(195\) | −5.65685 | −0.405096 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.7990 | −1.83810 | −0.919051 | − | 0.394139i | \(-0.871043\pi\) | ||||
−0.919051 | + | 0.394139i | \(0.871043\pi\) | |||||||
\(198\) | −2.24264 | −0.159378 | ||||||||
\(199\) | −5.75736 | −0.408128 | −0.204064 | − | 0.978958i | \(-0.565415\pi\) | ||||
−0.204064 | + | 0.978958i | \(0.565415\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −9.07107 | −0.639824 | ||||||||
\(202\) | −17.6569 | −1.24233 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.58579 | −0.181041 | ||||||||
\(205\) | 10.4853 | 0.732324 | ||||||||
\(206\) | −14.8284 | −1.03315 | ||||||||
\(207\) | 3.17157 | 0.220440 | ||||||||
\(208\) | 5.65685 | 0.392232 | ||||||||
\(209\) | −15.3137 | −1.05927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3137 | −1.60498 | −0.802491 | − | 0.596664i | \(-0.796492\pi\) | ||||
−0.802491 | + | 0.596664i | \(0.796492\pi\) | |||||||
\(212\) | 0.343146 | 0.0235673 | ||||||||
\(213\) | 4.48528 | 0.307326 | ||||||||
\(214\) | −9.65685 | −0.660129 | ||||||||
\(215\) | 9.07107 | 0.618642 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.65685 | 0.247673 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 2.24264 | 0.151199 | ||||||||
\(221\) | 14.6274 | 0.983947 | ||||||||
\(222\) | −0.242641 | −0.0162850 | ||||||||
\(223\) | −7.31371 | −0.489762 | −0.244881 | − | 0.969553i | \(-0.578749\pi\) | ||||
−0.244881 | + | 0.969553i | \(0.578749\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | −24.9706 | −1.65735 | −0.828677 | − | 0.559727i | \(-0.810906\pi\) | ||||
−0.828677 | + | 0.559727i | \(0.810906\pi\) | |||||||
\(228\) | 6.82843 | 0.452224 | ||||||||
\(229\) | −16.1421 | −1.06670 | −0.533351 | − | 0.845894i | \(-0.679068\pi\) | ||||
−0.533351 | + | 0.845894i | \(0.679068\pi\) | |||||||
\(230\) | −3.17157 | −0.209127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.58579 | −0.169765 | ||||||||
\(233\) | 18.9706 | 1.24280 | 0.621401 | − | 0.783492i | \(-0.286564\pi\) | ||||
0.621401 | + | 0.783492i | \(0.286564\pi\) | |||||||
\(234\) | −5.65685 | −0.369800 | ||||||||
\(235\) | −2.24264 | −0.146294 | ||||||||
\(236\) | −3.17157 | −0.206452 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3137 | −1.24930 | −0.624650 | − | 0.780905i | \(-0.714758\pi\) | ||||
−0.624650 | + | 0.780905i | \(0.714758\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −19.5563 | −1.25974 | −0.629868 | − | 0.776703i | \(-0.716891\pi\) | ||||
−0.629868 | + | 0.776703i | \(0.716891\pi\) | |||||||
\(242\) | 5.97056 | 0.383802 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.6569 | −0.746254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.4853 | 0.668517 | ||||||||
\(247\) | −38.6274 | −2.45780 | ||||||||
\(248\) | 10.2426 | 0.650408 | ||||||||
\(249\) | −5.17157 | −0.327735 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.9706 | −0.818695 | −0.409347 | − | 0.912379i | \(-0.634244\pi\) | ||||
−0.409347 | + | 0.912379i | \(0.634244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.11270 | 0.447172 | ||||||||
\(254\) | −2.82843 | −0.177471 | ||||||||
\(255\) | −2.58579 | −0.161928 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.5858 | −1.15935 | −0.579675 | − | 0.814848i | \(-0.696820\pi\) | ||||
−0.579675 | + | 0.814848i | \(0.696820\pi\) | |||||||
\(258\) | 9.07107 | 0.564740 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.65685 | 0.350823 | ||||||||
\(261\) | 2.58579 | 0.160056 | ||||||||
\(262\) | 3.17157 | 0.195940 | ||||||||
\(263\) | −12.1421 | −0.748716 | −0.374358 | − | 0.927284i | \(-0.622137\pi\) | ||||
−0.374358 | + | 0.927284i | \(0.622137\pi\) | |||||||
\(264\) | 2.24264 | 0.138025 | ||||||||
\(265\) | 0.343146 | 0.0210793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.828427 | 0.0506989 | ||||||||
\(268\) | 9.07107 | 0.554104 | ||||||||
\(269\) | 12.3431 | 0.752575 | 0.376287 | − | 0.926503i | \(-0.377201\pi\) | ||||
0.376287 | + | 0.926503i | \(0.377201\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 31.6985 | 1.92555 | 0.962773 | − | 0.270312i | \(-0.0871267\pi\) | ||||
0.962773 | + | 0.270312i | \(0.0871267\pi\) | |||||||
\(272\) | 2.58579 | 0.156786 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6569 | −0.825041 | ||||||||
\(275\) | 2.24264 | 0.135236 | ||||||||
\(276\) | −3.17157 | −0.190906 | ||||||||
\(277\) | −15.5563 | −0.934690 | −0.467345 | − | 0.884075i | \(-0.654789\pi\) | ||||
−0.467345 | + | 0.884075i | \(0.654789\pi\) | |||||||
\(278\) | 2.34315 | 0.140533 | ||||||||
\(279\) | −10.2426 | −0.613211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.4558 | −1.39926 | −0.699629 | − | 0.714506i | \(-0.746651\pi\) | ||||
−0.699629 | + | 0.714506i | \(0.746651\pi\) | |||||||
\(282\) | −2.24264 | −0.133547 | ||||||||
\(283\) | 9.51472 | 0.565591 | 0.282796 | − | 0.959180i | \(-0.408738\pi\) | ||||
0.282796 | + | 0.959180i | \(0.408738\pi\) | |||||||
\(284\) | −4.48528 | −0.266152 | ||||||||
\(285\) | 6.82843 | 0.404481 | ||||||||
\(286\) | −12.6863 | −0.750156 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −10.3137 | −0.606689 | ||||||||
\(290\) | −2.58579 | −0.151843 | ||||||||
\(291\) | 6.48528 | 0.380174 | ||||||||
\(292\) | −2.00000 | −0.117041 | ||||||||
\(293\) | 21.3137 | 1.24516 | 0.622580 | − | 0.782556i | \(-0.286084\pi\) | ||||
0.622580 | + | 0.782556i | \(0.286084\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.17157 | −0.184656 | ||||||||
\(296\) | 0.242641 | 0.0141032 | ||||||||
\(297\) | −2.24264 | −0.130131 | ||||||||
\(298\) | −22.3848 | −1.29672 | ||||||||
\(299\) | 17.9411 | 1.03756 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.1421 | −1.15905 | ||||||||
\(303\) | −17.6569 | −1.01436 | ||||||||
\(304\) | −6.82843 | −0.391637 | ||||||||
\(305\) | −11.6569 | −0.667470 | ||||||||
\(306\) | −2.58579 | −0.147820 | ||||||||
\(307\) | −7.31371 | −0.417415 | −0.208708 | − | 0.977978i | \(-0.566926\pi\) | ||||
−0.208708 | + | 0.977978i | \(0.566926\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.8284 | −0.843560 | ||||||||
\(310\) | 10.2426 | 0.581743 | ||||||||
\(311\) | −10.8284 | −0.614024 | −0.307012 | − | 0.951706i | \(-0.599329\pi\) | ||||
−0.307012 | + | 0.951706i | \(0.599329\pi\) | |||||||
\(312\) | 5.65685 | 0.320256 | ||||||||
\(313\) | 30.4853 | 1.72313 | 0.861565 | − | 0.507647i | \(-0.169485\pi\) | ||||
0.861565 | + | 0.507647i | \(0.169485\pi\) | |||||||
\(314\) | 8.34315 | 0.470831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −25.3137 | −1.42176 | −0.710880 | − | 0.703314i | \(-0.751703\pi\) | ||||
−0.710880 | + | 0.703314i | \(0.751703\pi\) | |||||||
\(318\) | 0.343146 | 0.0192427 | ||||||||
\(319\) | 5.79899 | 0.324681 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −9.65685 | −0.538993 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.6569 | −0.982454 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.65685 | 0.313786 | ||||||||
\(326\) | 17.0711 | 0.945479 | ||||||||
\(327\) | 3.65685 | 0.202225 | ||||||||
\(328\) | −10.4853 | −0.578953 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.24264 | 0.123453 | ||||||||
\(331\) | −6.34315 | −0.348651 | −0.174325 | − | 0.984688i | \(-0.555774\pi\) | ||||
−0.174325 | + | 0.984688i | \(0.555774\pi\) | |||||||
\(332\) | 5.17157 | 0.283827 | ||||||||
\(333\) | −0.242641 | −0.0132966 | ||||||||
\(334\) | −2.24264 | −0.122712 | ||||||||
\(335\) | 9.07107 | 0.495605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.1127 | 1.80376 | 0.901882 | − | 0.431983i | \(-0.142186\pi\) | ||||
0.901882 | + | 0.431983i | \(0.142186\pi\) | |||||||
\(338\) | −19.0000 | −1.03346 | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 2.58579 | 0.140234 | ||||||||
\(341\) | −22.9706 | −1.24393 | ||||||||
\(342\) | 6.82843 | 0.369239 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.07107 | −0.489079 | ||||||||
\(345\) | −3.17157 | −0.170752 | ||||||||
\(346\) | −20.8284 | −1.11974 | ||||||||
\(347\) | −22.3431 | −1.19944 | −0.599721 | − | 0.800209i | \(-0.704722\pi\) | ||||
−0.599721 | + | 0.800209i | \(0.704722\pi\) | |||||||
\(348\) | −2.58579 | −0.138613 | ||||||||
\(349\) | 23.4558 | 1.25556 | 0.627781 | − | 0.778390i | \(-0.283963\pi\) | ||||
0.627781 | + | 0.778390i | \(0.283963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | −2.24264 | −0.119533 | ||||||||
\(353\) | 16.0416 | 0.853810 | 0.426905 | − | 0.904297i | \(-0.359604\pi\) | ||||
0.426905 | + | 0.904297i | \(0.359604\pi\) | |||||||
\(354\) | −3.17157 | −0.168567 | ||||||||
\(355\) | −4.48528 | −0.238054 | ||||||||
\(356\) | −0.828427 | −0.0439065 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.2426 | −1.38697 | ||||||||
\(359\) | −28.4853 | −1.50340 | −0.751698 | − | 0.659508i | \(-0.770765\pi\) | ||||
−0.751698 | + | 0.659508i | \(0.770765\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | −18.4853 | −0.971565 | ||||||||
\(363\) | 5.97056 | 0.313373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | −11.6569 | −0.609314 | ||||||||
\(367\) | −10.8284 | −0.565239 | −0.282620 | − | 0.959232i | \(-0.591203\pi\) | ||||
−0.282620 | + | 0.959232i | \(0.591203\pi\) | |||||||
\(368\) | 3.17157 | 0.165330 | ||||||||
\(369\) | 10.4853 | 0.545842 | ||||||||
\(370\) | 0.242641 | 0.0126143 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.2426 | 0.531056 | ||||||||
\(373\) | 6.58579 | 0.340999 | 0.170500 | − | 0.985358i | \(-0.445462\pi\) | ||||
0.170500 | + | 0.985358i | \(0.445462\pi\) | |||||||
\(374\) | −5.79899 | −0.299859 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 2.24264 | 0.115655 | ||||||||
\(377\) | 14.6274 | 0.753350 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.485281 | 0.0249272 | 0.0124636 | − | 0.999922i | \(-0.496033\pi\) | ||||
0.0124636 | + | 0.999922i | \(0.496033\pi\) | |||||||
\(380\) | −6.82843 | −0.350291 | ||||||||
\(381\) | −2.82843 | −0.144905 | ||||||||
\(382\) | −4.00000 | −0.204658 | ||||||||
\(383\) | 19.4142 | 0.992020 | 0.496010 | − | 0.868317i | \(-0.334798\pi\) | ||||
0.496010 | + | 0.868317i | \(0.334798\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.82843 | 0.245760 | ||||||||
\(387\) | 9.07107 | 0.461108 | ||||||||
\(388\) | −6.48528 | −0.329240 | ||||||||
\(389\) | −29.8995 | −1.51596 | −0.757982 | − | 0.652275i | \(-0.773815\pi\) | ||||
−0.757982 | + | 0.652275i | \(0.773815\pi\) | |||||||
\(390\) | 5.65685 | 0.286446 | ||||||||
\(391\) | 8.20101 | 0.414743 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.17157 | 0.159985 | ||||||||
\(394\) | 25.7990 | 1.29973 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 2.24264 | 0.112697 | ||||||||
\(397\) | 6.68629 | 0.335575 | 0.167788 | − | 0.985823i | \(-0.446338\pi\) | ||||
0.167788 | + | 0.985823i | \(0.446338\pi\) | |||||||
\(398\) | 5.75736 | 0.288590 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 9.07107 | 0.452424 | ||||||||
\(403\) | −57.9411 | −2.88625 | ||||||||
\(404\) | 17.6569 | 0.878461 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.544156 | −0.0269728 | ||||||||
\(408\) | 2.58579 | 0.128016 | ||||||||
\(409\) | 4.24264 | 0.209785 | 0.104893 | − | 0.994484i | \(-0.466550\pi\) | ||||
0.104893 | + | 0.994484i | \(0.466550\pi\) | |||||||
\(410\) | −10.4853 | −0.517831 | ||||||||
\(411\) | −13.6569 | −0.673643 | ||||||||
\(412\) | 14.8284 | 0.730544 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.17157 | −0.155874 | ||||||||
\(415\) | 5.17157 | 0.253863 | ||||||||
\(416\) | −5.65685 | −0.277350 | ||||||||
\(417\) | 2.34315 | 0.114744 | ||||||||
\(418\) | 15.3137 | 0.749018 | ||||||||
\(419\) | −36.9706 | −1.80613 | −0.903065 | − | 0.429504i | \(-0.858689\pi\) | ||||
−0.903065 | + | 0.429504i | \(0.858689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.65685 | −0.178224 | −0.0891121 | − | 0.996022i | \(-0.528403\pi\) | ||||
−0.0891121 | + | 0.996022i | \(0.528403\pi\) | |||||||
\(422\) | 23.3137 | 1.13489 | ||||||||
\(423\) | −2.24264 | −0.109041 | ||||||||
\(424\) | −0.343146 | −0.0166646 | ||||||||
\(425\) | 2.58579 | 0.125429 | ||||||||
\(426\) | −4.48528 | −0.217313 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.65685 | 0.466782 | ||||||||
\(429\) | −12.6863 | −0.612500 | ||||||||
\(430\) | −9.07107 | −0.437446 | ||||||||
\(431\) | 13.4558 | 0.648145 | 0.324073 | − | 0.946032i | \(-0.394948\pi\) | ||||
0.324073 | + | 0.946032i | \(0.394948\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −17.7990 | −0.855365 | −0.427682 | − | 0.903929i | \(-0.640670\pi\) | ||||
−0.427682 | + | 0.903929i | \(0.640670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.58579 | −0.123979 | ||||||||
\(436\) | −3.65685 | −0.175132 | ||||||||
\(437\) | −21.6569 | −1.03599 | ||||||||
\(438\) | −2.00000 | −0.0955637 | ||||||||
\(439\) | −23.6985 | −1.13107 | −0.565533 | − | 0.824725i | \(-0.691330\pi\) | ||||
−0.565533 | + | 0.824725i | \(0.691330\pi\) | |||||||
\(440\) | −2.24264 | −0.106914 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.6274 | −0.695755 | ||||||||
\(443\) | 36.2843 | 1.72392 | 0.861959 | − | 0.506978i | \(-0.169238\pi\) | ||||
0.861959 | + | 0.506978i | \(0.169238\pi\) | |||||||
\(444\) | 0.242641 | 0.0115152 | ||||||||
\(445\) | −0.828427 | −0.0392712 | ||||||||
\(446\) | 7.31371 | 0.346314 | ||||||||
\(447\) | −22.3848 | −1.05876 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4853 | −0.494831 | −0.247416 | − | 0.968909i | \(-0.579581\pi\) | ||||
−0.247416 | + | 0.968909i | \(0.579581\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 23.5147 | 1.10726 | ||||||||
\(452\) | 10.0000 | 0.470360 | ||||||||
\(453\) | −20.1421 | −0.946360 | ||||||||
\(454\) | 24.9706 | 1.17193 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.82843 | −0.319770 | ||||||||
\(457\) | 2.48528 | 0.116257 | 0.0581283 | − | 0.998309i | \(-0.481487\pi\) | ||||
0.0581283 | + | 0.998309i | \(0.481487\pi\) | |||||||
\(458\) | 16.1421 | 0.754272 | ||||||||
\(459\) | −2.58579 | −0.120694 | ||||||||
\(460\) | 3.17157 | 0.147875 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6569 | −1.19238 | −0.596188 | − | 0.802845i | \(-0.703319\pi\) | ||||
−0.596188 | + | 0.802845i | \(0.703319\pi\) | |||||||
\(464\) | 2.58579 | 0.120042 | ||||||||
\(465\) | 10.2426 | 0.474991 | ||||||||
\(466\) | −18.9706 | −0.878794 | ||||||||
\(467\) | 12.4853 | 0.577750 | 0.288875 | − | 0.957367i | \(-0.406719\pi\) | ||||
0.288875 | + | 0.957367i | \(0.406719\pi\) | |||||||
\(468\) | 5.65685 | 0.261488 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.24264 | 0.103445 | ||||||||
\(471\) | 8.34315 | 0.384432 | ||||||||
\(472\) | 3.17157 | 0.145983 | ||||||||
\(473\) | 20.3431 | 0.935379 | ||||||||
\(474\) | 8.00000 | 0.367452 | ||||||||
\(475\) | −6.82843 | −0.313310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.343146 | 0.0157116 | ||||||||
\(478\) | 19.3137 | 0.883388 | ||||||||
\(479\) | −8.48528 | −0.387702 | −0.193851 | − | 0.981031i | \(-0.562098\pi\) | ||||
−0.193851 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −1.37258 | −0.0625844 | ||||||||
\(482\) | 19.5563 | 0.890767 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.97056 | −0.271389 | ||||||||
\(485\) | −6.48528 | −0.294481 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 10.8284 | 0.490683 | 0.245341 | − | 0.969437i | \(-0.421100\pi\) | ||||
0.245341 | + | 0.969437i | \(0.421100\pi\) | |||||||
\(488\) | 11.6569 | 0.527681 | ||||||||
\(489\) | 17.0711 | 0.771980 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.0711 | −0.770407 | −0.385203 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385203 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(492\) | −10.4853 | −0.472713 | ||||||||
\(493\) | 6.68629 | 0.301135 | ||||||||
\(494\) | 38.6274 | 1.73793 | ||||||||
\(495\) | 2.24264 | 0.100799 | ||||||||
\(496\) | −10.2426 | −0.459908 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.17157 | 0.231744 | ||||||||
\(499\) | 6.82843 | 0.305682 | 0.152841 | − | 0.988251i | \(-0.451158\pi\) | ||||
0.152841 | + | 0.988251i | \(0.451158\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −2.24264 | −0.100194 | ||||||||
\(502\) | 12.9706 | 0.578905 | ||||||||
\(503\) | −4.58579 | −0.204470 | −0.102235 | − | 0.994760i | \(-0.532599\pi\) | ||||
−0.102235 | + | 0.994760i | \(0.532599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.6569 | 0.785720 | ||||||||
\(506\) | −7.11270 | −0.316198 | ||||||||
\(507\) | −19.0000 | −0.843820 | ||||||||
\(508\) | 2.82843 | 0.125491 | ||||||||
\(509\) | −16.9706 | −0.752207 | −0.376103 | − | 0.926578i | \(-0.622736\pi\) | ||||
−0.376103 | + | 0.926578i | \(0.622736\pi\) | |||||||
\(510\) | 2.58579 | 0.114501 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.82843 | 0.301482 | ||||||||
\(514\) | 18.5858 | 0.819784 | ||||||||
\(515\) | 14.8284 | 0.653419 | ||||||||
\(516\) | −9.07107 | −0.399331 | ||||||||
\(517\) | −5.02944 | −0.221194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8284 | −0.914266 | ||||||||
\(520\) | −5.65685 | −0.248069 | ||||||||
\(521\) | 38.7696 | 1.69852 | 0.849262 | − | 0.527971i | \(-0.177047\pi\) | ||||
0.849262 | + | 0.527971i | \(0.177047\pi\) | |||||||
\(522\) | −2.58579 | −0.113177 | ||||||||
\(523\) | 41.7990 | 1.82774 | 0.913871 | − | 0.406004i | \(-0.133078\pi\) | ||||
0.913871 | + | 0.406004i | \(0.133078\pi\) | |||||||
\(524\) | −3.17157 | −0.138551 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.1421 | 0.529422 | ||||||||
\(527\) | −26.4853 | −1.15372 | ||||||||
\(528\) | −2.24264 | −0.0975984 | ||||||||
\(529\) | −12.9411 | −0.562658 | ||||||||
\(530\) | −0.343146 | −0.0149053 | ||||||||
\(531\) | −3.17157 | −0.137635 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 59.3137 | 2.56916 | ||||||||
\(534\) | −0.828427 | −0.0358495 | ||||||||
\(535\) | 9.65685 | 0.417502 | ||||||||
\(536\) | −9.07107 | −0.391810 | ||||||||
\(537\) | −26.2426 | −1.13245 | ||||||||
\(538\) | −12.3431 | −0.532151 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −29.7990 | −1.28116 | −0.640579 | − | 0.767892i | \(-0.721306\pi\) | ||||
−0.640579 | + | 0.767892i | \(0.721306\pi\) | |||||||
\(542\) | −31.6985 | −1.36157 | ||||||||
\(543\) | −18.4853 | −0.793279 | ||||||||
\(544\) | −2.58579 | −0.110865 | ||||||||
\(545\) | −3.65685 | −0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.3848 | −1.21365 | −0.606823 | − | 0.794837i | \(-0.707556\pi\) | ||||
−0.606823 | + | 0.794837i | \(0.707556\pi\) | |||||||
\(548\) | 13.6569 | 0.583392 | ||||||||
\(549\) | −11.6569 | −0.497502 | ||||||||
\(550\) | −2.24264 | −0.0956265 | ||||||||
\(551\) | −17.6569 | −0.752207 | ||||||||
\(552\) | 3.17157 | 0.134991 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.5563 | 0.660926 | ||||||||
\(555\) | 0.242641 | 0.0102995 | ||||||||
\(556\) | −2.34315 | −0.0993715 | ||||||||
\(557\) | −38.0000 | −1.61011 | −0.805056 | − | 0.593199i | \(-0.797865\pi\) | ||||
−0.805056 | + | 0.593199i | \(0.797865\pi\) | |||||||
\(558\) | 10.2426 | 0.433606 | ||||||||
\(559\) | 51.3137 | 2.17034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.79899 | −0.244834 | ||||||||
\(562\) | 23.4558 | 0.989425 | ||||||||
\(563\) | −20.4853 | −0.863352 | −0.431676 | − | 0.902029i | \(-0.642078\pi\) | ||||
−0.431676 | + | 0.902029i | \(0.642078\pi\) | |||||||
\(564\) | 2.24264 | 0.0944322 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | −9.51472 | −0.399933 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.48528 | 0.188198 | ||||||||
\(569\) | 9.02944 | 0.378534 | 0.189267 | − | 0.981926i | \(-0.439389\pi\) | ||||
0.189267 | + | 0.981926i | \(0.439389\pi\) | |||||||
\(570\) | −6.82843 | −0.286011 | ||||||||
\(571\) | 4.68629 | 0.196115 | 0.0980576 | − | 0.995181i | \(-0.468737\pi\) | ||||
0.0980576 | + | 0.995181i | \(0.468737\pi\) | |||||||
\(572\) | 12.6863 | 0.530440 | ||||||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.17157 | 0.132264 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −3.85786 | −0.160605 | −0.0803025 | − | 0.996771i | \(-0.525589\pi\) | ||||
−0.0803025 | + | 0.996771i | \(0.525589\pi\) | |||||||
\(578\) | 10.3137 | 0.428994 | ||||||||
\(579\) | 4.82843 | 0.200663 | ||||||||
\(580\) | 2.58579 | 0.107369 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.48528 | −0.268824 | ||||||||
\(583\) | 0.769553 | 0.0318716 | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 5.65685 | 0.233882 | ||||||||
\(586\) | −21.3137 | −0.880461 | ||||||||
\(587\) | −5.17157 | −0.213454 | −0.106727 | − | 0.994288i | \(-0.534037\pi\) | ||||
−0.106727 | + | 0.994288i | \(0.534037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 69.9411 | 2.88187 | ||||||||
\(590\) | 3.17157 | 0.130572 | ||||||||
\(591\) | 25.7990 | 1.06123 | ||||||||
\(592\) | −0.242641 | −0.00997247 | ||||||||
\(593\) | −41.2132 | −1.69242 | −0.846212 | − | 0.532847i | \(-0.821122\pi\) | ||||
−0.846212 | + | 0.532847i | \(0.821122\pi\) | |||||||
\(594\) | 2.24264 | 0.0920167 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3848 | 0.916916 | ||||||||
\(597\) | 5.75736 | 0.235633 | ||||||||
\(598\) | −17.9411 | −0.733667 | ||||||||
\(599\) | 4.00000 | 0.163436 | 0.0817178 | − | 0.996656i | \(-0.473959\pi\) | ||||
0.0817178 | + | 0.996656i | \(0.473959\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −31.7574 | −1.29541 | −0.647705 | − | 0.761891i | \(-0.724271\pi\) | ||||
−0.647705 | + | 0.761891i | \(0.724271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.07107 | 0.369402 | ||||||||
\(604\) | 20.1421 | 0.819572 | ||||||||
\(605\) | −5.97056 | −0.242738 | ||||||||
\(606\) | 17.6569 | 0.717261 | ||||||||
\(607\) | 4.00000 | 0.162355 | 0.0811775 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811775 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(608\) | 6.82843 | 0.276929 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.6569 | 0.471972 | ||||||||
\(611\) | −12.6863 | −0.513232 | ||||||||
\(612\) | 2.58579 | 0.104524 | ||||||||
\(613\) | −11.0711 | −0.447156 | −0.223578 | − | 0.974686i | \(-0.571774\pi\) | ||||
−0.223578 | + | 0.974686i | \(0.571774\pi\) | |||||||
\(614\) | 7.31371 | 0.295157 | ||||||||
\(615\) | −10.4853 | −0.422807 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9411 | 1.36642 | 0.683209 | − | 0.730223i | \(-0.260584\pi\) | ||||
0.683209 | + | 0.730223i | \(0.260584\pi\) | |||||||
\(618\) | 14.8284 | 0.596487 | ||||||||
\(619\) | 19.1127 | 0.768204 | 0.384102 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384102 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(620\) | −10.2426 | −0.411354 | ||||||||
\(621\) | −3.17157 | −0.127271 | ||||||||
\(622\) | 10.8284 | 0.434180 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.65685 | −0.226455 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −30.4853 | −1.21844 | ||||||||
\(627\) | 15.3137 | 0.611571 | ||||||||
\(628\) | −8.34315 | −0.332928 | ||||||||
\(629\) | −0.627417 | −0.0250168 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.14214 | −0.324133 | −0.162067 | − | 0.986780i | \(-0.551816\pi\) | ||||
−0.162067 | + | 0.986780i | \(0.551816\pi\) | |||||||
\(632\) | −8.00000 | −0.318223 | ||||||||
\(633\) | 23.3137 | 0.926637 | ||||||||
\(634\) | 25.3137 | 1.00534 | ||||||||
\(635\) | 2.82843 | 0.112243 | ||||||||
\(636\) | −0.343146 | −0.0136066 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.79899 | −0.229584 | ||||||||
\(639\) | −4.48528 | −0.177435 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 26.0000 | 1.02694 | 0.513469 | − | 0.858108i | \(-0.328360\pi\) | ||||
0.513469 | + | 0.858108i | \(0.328360\pi\) | |||||||
\(642\) | 9.65685 | 0.381126 | ||||||||
\(643\) | 28.8284 | 1.13688 | 0.568441 | − | 0.822724i | \(-0.307547\pi\) | ||||
0.568441 | + | 0.822724i | \(0.307547\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.07107 | −0.357173 | ||||||||
\(646\) | 17.6569 | 0.694700 | ||||||||
\(647\) | 8.87006 | 0.348718 | 0.174359 | − | 0.984682i | \(-0.444215\pi\) | ||||
0.174359 | + | 0.984682i | \(0.444215\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −7.11270 | −0.279198 | ||||||||
\(650\) | −5.65685 | −0.221880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0711 | −0.668555 | ||||||||
\(653\) | −1.79899 | −0.0703999 | −0.0352000 | − | 0.999380i | \(-0.511207\pi\) | ||||
−0.0352000 | + | 0.999380i | \(0.511207\pi\) | |||||||
\(654\) | −3.65685 | −0.142994 | ||||||||
\(655\) | −3.17157 | −0.123924 | ||||||||
\(656\) | 10.4853 | 0.409381 | ||||||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3848 | 0.794078 | 0.397039 | − | 0.917802i | \(-0.370038\pi\) | ||||
0.397039 | + | 0.917802i | \(0.370038\pi\) | |||||||
\(660\) | −2.24264 | −0.0872947 | ||||||||
\(661\) | −5.02944 | −0.195622 | −0.0978112 | − | 0.995205i | \(-0.531184\pi\) | ||||
−0.0978112 | + | 0.995205i | \(0.531184\pi\) | |||||||
\(662\) | 6.34315 | 0.246533 | ||||||||
\(663\) | −14.6274 | −0.568082 | ||||||||
\(664\) | −5.17157 | −0.200696 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.242641 | 0.00940214 | ||||||||
\(667\) | 8.20101 | 0.317544 | ||||||||
\(668\) | 2.24264 | 0.0867704 | ||||||||
\(669\) | 7.31371 | 0.282764 | ||||||||
\(670\) | −9.07107 | −0.350446 | ||||||||
\(671\) | −26.1421 | −1.00921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2843 | −1.01318 | −0.506592 | − | 0.862186i | \(-0.669095\pi\) | ||||
−0.506592 | + | 0.862186i | \(0.669095\pi\) | |||||||
\(674\) | −33.1127 | −1.27545 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 19.0000 | 0.730769 | ||||||||
\(677\) | −44.4264 | −1.70745 | −0.853723 | − | 0.520728i | \(-0.825661\pi\) | ||||
−0.853723 | + | 0.520728i | \(0.825661\pi\) | |||||||
\(678\) | 10.0000 | 0.384048 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.58579 | −0.0991604 | ||||||||
\(681\) | 24.9706 | 0.956874 | ||||||||
\(682\) | 22.9706 | 0.879588 | ||||||||
\(683\) | −31.7990 | −1.21675 | −0.608377 | − | 0.793648i | \(-0.708179\pi\) | ||||
−0.608377 | + | 0.793648i | \(0.708179\pi\) | |||||||
\(684\) | −6.82843 | −0.261091 | ||||||||
\(685\) | 13.6569 | 0.521802 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.1421 | 0.615861 | ||||||||
\(688\) | 9.07107 | 0.345831 | ||||||||
\(689\) | 1.94113 | 0.0739510 | ||||||||
\(690\) | 3.17157 | 0.120740 | ||||||||
\(691\) | 3.02944 | 0.115245 | 0.0576226 | − | 0.998338i | \(-0.481648\pi\) | ||||
0.0576226 | + | 0.998338i | \(0.481648\pi\) | |||||||
\(692\) | 20.8284 | 0.791778 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.3431 | 0.848134 | ||||||||
\(695\) | −2.34315 | −0.0888806 | ||||||||
\(696\) | 2.58579 | 0.0980140 | ||||||||
\(697\) | 27.1127 | 1.02697 | ||||||||
\(698\) | −23.4558 | −0.887817 | ||||||||
\(699\) | −18.9706 | −0.717533 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2132 | −0.650134 | −0.325067 | − | 0.945691i | \(-0.605387\pi\) | ||||
−0.325067 | + | 0.945691i | \(0.605387\pi\) | |||||||
\(702\) | 5.65685 | 0.213504 | ||||||||
\(703\) | 1.65685 | 0.0624894 | ||||||||
\(704\) | 2.24264 | 0.0845227 | ||||||||
\(705\) | 2.24264 | 0.0844627 | ||||||||
\(706\) | −16.0416 | −0.603735 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.17157 | 0.119195 | ||||||||
\(709\) | 11.8579 | 0.445331 | 0.222666 | − | 0.974895i | \(-0.428524\pi\) | ||||
0.222666 | + | 0.974895i | \(0.428524\pi\) | |||||||
\(710\) | 4.48528 | 0.168330 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 0.828427 | 0.0310466 | ||||||||
\(713\) | −32.4853 | −1.21658 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.6863 | 0.474440 | ||||||||
\(716\) | 26.2426 | 0.980734 | ||||||||
\(717\) | 19.3137 | 0.721284 | ||||||||
\(718\) | 28.4853 | 1.06306 | ||||||||
\(719\) | 17.9411 | 0.669091 | 0.334546 | − | 0.942380i | \(-0.391417\pi\) | ||||
0.334546 | + | 0.942380i | \(0.391417\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −27.6274 | −1.02819 | ||||||||
\(723\) | 19.5563 | 0.727308 | ||||||||
\(724\) | 18.4853 | 0.687000 | ||||||||
\(725\) | 2.58579 | 0.0960337 | ||||||||
\(726\) | −5.97056 | −0.221588 | ||||||||
\(727\) | −30.6274 | −1.13591 | −0.567954 | − | 0.823060i | \(-0.692265\pi\) | ||||
−0.567954 | + | 0.823060i | \(0.692265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.00000 | 0.0740233 | ||||||||
\(731\) | 23.4558 | 0.867546 | ||||||||
\(732\) | 11.6569 | 0.430850 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 10.8284 | 0.399685 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.17157 | −0.116906 | ||||||||
\(737\) | 20.3431 | 0.749349 | ||||||||
\(738\) | −10.4853 | −0.385969 | ||||||||
\(739\) | 11.1127 | 0.408787 | 0.204394 | − | 0.978889i | \(-0.434478\pi\) | ||||
0.204394 | + | 0.978889i | \(0.434478\pi\) | |||||||
\(740\) | −0.242641 | −0.00891965 | ||||||||
\(741\) | 38.6274 | 1.41901 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2843 | 1.03765 | 0.518825 | − | 0.854881i | \(-0.326370\pi\) | ||||
0.518825 | + | 0.854881i | \(0.326370\pi\) | |||||||
\(744\) | −10.2426 | −0.375513 | ||||||||
\(745\) | 22.3848 | 0.820115 | ||||||||
\(746\) | −6.58579 | −0.241123 | ||||||||
\(747\) | 5.17157 | 0.189218 | ||||||||
\(748\) | 5.79899 | 0.212032 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 21.7990 | 0.795456 | 0.397728 | − | 0.917503i | \(-0.369799\pi\) | ||||
0.397728 | + | 0.917503i | \(0.369799\pi\) | |||||||
\(752\) | −2.24264 | −0.0817807 | ||||||||
\(753\) | 12.9706 | 0.472674 | ||||||||
\(754\) | −14.6274 | −0.532699 | ||||||||
\(755\) | 20.1421 | 0.733047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.8995 | 0.941333 | 0.470667 | − | 0.882311i | \(-0.344013\pi\) | ||||
0.470667 | + | 0.882311i | \(0.344013\pi\) | |||||||
\(758\) | −0.485281 | −0.0176262 | ||||||||
\(759\) | −7.11270 | −0.258175 | ||||||||
\(760\) | 6.82843 | 0.247693 | ||||||||
\(761\) | −26.9706 | −0.977682 | −0.488841 | − | 0.872373i | \(-0.662580\pi\) | ||||
−0.488841 | + | 0.872373i | \(0.662580\pi\) | |||||||
\(762\) | 2.82843 | 0.102463 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.00000 | 0.144715 | ||||||||
\(765\) | 2.58579 | 0.0934893 | ||||||||
\(766\) | −19.4142 | −0.701464 | ||||||||
\(767\) | −17.9411 | −0.647816 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 4.72792 | 0.170493 | 0.0852466 | − | 0.996360i | \(-0.472832\pi\) | ||||
0.0852466 | + | 0.996360i | \(0.472832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.5858 | 0.669351 | ||||||||
\(772\) | −4.82843 | −0.173779 | ||||||||
\(773\) | −22.9706 | −0.826194 | −0.413097 | − | 0.910687i | \(-0.635553\pi\) | ||||
−0.413097 | + | 0.910687i | \(0.635553\pi\) | |||||||
\(774\) | −9.07107 | −0.326053 | ||||||||
\(775\) | −10.2426 | −0.367927 | ||||||||
\(776\) | 6.48528 | 0.232808 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.8995 | 1.07195 | ||||||||
\(779\) | −71.5980 | −2.56526 | ||||||||
\(780\) | −5.65685 | −0.202548 | ||||||||
\(781\) | −10.0589 | −0.359935 | ||||||||
\(782\) | −8.20101 | −0.293268 | ||||||||
\(783\) | −2.58579 | −0.0924085 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.34315 | −0.297780 | ||||||||
\(786\) | −3.17157 | −0.113126 | ||||||||
\(787\) | 38.3431 | 1.36679 | 0.683393 | − | 0.730051i | \(-0.260504\pi\) | ||||
0.683393 | + | 0.730051i | \(0.260504\pi\) | |||||||
\(788\) | −25.7990 | −0.919051 | ||||||||
\(789\) | 12.1421 | 0.432271 | ||||||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.24264 | −0.0796888 | ||||||||
\(793\) | −65.9411 | −2.34164 | ||||||||
\(794\) | −6.68629 | −0.237288 | ||||||||
\(795\) | −0.343146 | −0.0121701 | ||||||||
\(796\) | −5.75736 | −0.204064 | ||||||||
\(797\) | 0.142136 | 0.00503470 | 0.00251735 | − | 0.999997i | \(-0.499199\pi\) | ||||
0.00251735 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.79899 | −0.205154 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −0.828427 | −0.0292710 | ||||||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | −4.48528 | −0.158282 | ||||||||
\(804\) | −9.07107 | −0.319912 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 57.9411 | 2.04089 | ||||||||
\(807\) | −12.3431 | −0.434499 | ||||||||
\(808\) | −17.6569 | −0.621166 | ||||||||
\(809\) | 34.4853 | 1.21244 | 0.606219 | − | 0.795298i | \(-0.292686\pi\) | ||||
0.606219 | + | 0.795298i | \(0.292686\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 10.3431 | 0.363197 | 0.181598 | − | 0.983373i | \(-0.441873\pi\) | ||||
0.181598 | + | 0.983373i | \(0.441873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.6985 | −1.11171 | ||||||||
\(814\) | 0.544156 | 0.0190727 | ||||||||
\(815\) | −17.0711 | −0.597973 | ||||||||
\(816\) | −2.58579 | −0.0905206 | ||||||||
\(817\) | −61.9411 | −2.16705 | ||||||||
\(818\) | −4.24264 | −0.148340 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4853 | 0.366162 | ||||||||
\(821\) | 1.21320 | 0.0423411 | 0.0211705 | − | 0.999776i | \(-0.493261\pi\) | ||||
0.0211705 | + | 0.999776i | \(0.493261\pi\) | |||||||
\(822\) | 13.6569 | 0.476337 | ||||||||
\(823\) | 28.9706 | 1.00985 | 0.504925 | − | 0.863163i | \(-0.331520\pi\) | ||||
0.504925 | + | 0.863163i | \(0.331520\pi\) | |||||||
\(824\) | −14.8284 | −0.516573 | ||||||||
\(825\) | −2.24264 | −0.0780787 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.5147 | 1.23497 | 0.617484 | − | 0.786584i | \(-0.288152\pi\) | ||||
0.617484 | + | 0.786584i | \(0.288152\pi\) | |||||||
\(828\) | 3.17157 | 0.110220 | ||||||||
\(829\) | 33.3137 | 1.15703 | 0.578516 | − | 0.815671i | \(-0.303632\pi\) | ||||
0.578516 | + | 0.815671i | \(0.303632\pi\) | |||||||
\(830\) | −5.17157 | −0.179508 | ||||||||
\(831\) | 15.5563 | 0.539644 | ||||||||
\(832\) | 5.65685 | 0.196116 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.34315 | −0.0811365 | ||||||||
\(835\) | 2.24264 | 0.0776098 | ||||||||
\(836\) | −15.3137 | −0.529636 | ||||||||
\(837\) | 10.2426 | 0.354037 | ||||||||
\(838\) | 36.9706 | 1.27713 | ||||||||
\(839\) | 8.48528 | 0.292944 | 0.146472 | − | 0.989215i | \(-0.453208\pi\) | ||||
0.146472 | + | 0.989215i | \(0.453208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3137 | −0.769438 | ||||||||
\(842\) | 3.65685 | 0.126024 | ||||||||
\(843\) | 23.4558 | 0.807862 | ||||||||
\(844\) | −23.3137 | −0.802491 | ||||||||
\(845\) | 19.0000 | 0.653620 | ||||||||
\(846\) | 2.24264 | 0.0771036 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.343146 | 0.0117837 | ||||||||
\(849\) | −9.51472 | −0.326544 | ||||||||
\(850\) | −2.58579 | −0.0886917 | ||||||||
\(851\) | −0.769553 | −0.0263799 | ||||||||
\(852\) | 4.48528 | 0.153663 | ||||||||
\(853\) | −40.6274 | −1.39106 | −0.695528 | − | 0.718499i | \(-0.744830\pi\) | ||||
−0.695528 | + | 0.718499i | \(0.744830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.82843 | −0.233527 | ||||||||
\(856\) | −9.65685 | −0.330064 | ||||||||
\(857\) | 24.7279 | 0.844690 | 0.422345 | − | 0.906435i | \(-0.361207\pi\) | ||||
0.422345 | + | 0.906435i | \(0.361207\pi\) | |||||||
\(858\) | 12.6863 | 0.433103 | ||||||||
\(859\) | −35.5980 | −1.21459 | −0.607294 | − | 0.794477i | \(-0.707745\pi\) | ||||
−0.607294 | + | 0.794477i | \(0.707745\pi\) | |||||||
\(860\) | 9.07107 | 0.309321 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.4558 | −0.458308 | ||||||||
\(863\) | 45.6569 | 1.55418 | 0.777089 | − | 0.629391i | \(-0.216696\pi\) | ||||
0.777089 | + | 0.629391i | \(0.216696\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 20.8284 | 0.708188 | ||||||||
\(866\) | 17.7990 | 0.604834 | ||||||||
\(867\) | 10.3137 | 0.350272 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.9411 | 0.608611 | ||||||||
\(870\) | 2.58579 | 0.0876664 | ||||||||
\(871\) | 51.3137 | 1.73870 | ||||||||
\(872\) | 3.65685 | 0.123837 | ||||||||
\(873\) | −6.48528 | −0.219494 | ||||||||
\(874\) | 21.6569 | 0.732554 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | 4.24264 | 0.143264 | 0.0716319 | − | 0.997431i | \(-0.477179\pi\) | ||||
0.0716319 | + | 0.997431i | \(0.477179\pi\) | |||||||
\(878\) | 23.6985 | 0.799785 | ||||||||
\(879\) | −21.3137 | −0.718894 | ||||||||
\(880\) | 2.24264 | 0.0755994 | ||||||||
\(881\) | 26.0000 | 0.875962 | 0.437981 | − | 0.898984i | \(-0.355694\pi\) | ||||
0.437981 | + | 0.898984i | \(0.355694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.2426 | −1.15236 | −0.576178 | − | 0.817324i | \(-0.695457\pi\) | ||||
−0.576178 | + | 0.817324i | \(0.695457\pi\) | |||||||
\(884\) | 14.6274 | 0.491973 | ||||||||
\(885\) | 3.17157 | 0.106611 | ||||||||
\(886\) | −36.2843 | −1.21899 | ||||||||
\(887\) | −32.8701 | −1.10367 | −0.551834 | − | 0.833954i | \(-0.686072\pi\) | ||||
−0.551834 | + | 0.833954i | \(0.686072\pi\) | |||||||
\(888\) | −0.242641 | −0.00814249 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.828427 | 0.0277689 | ||||||||
\(891\) | 2.24264 | 0.0751313 | ||||||||
\(892\) | −7.31371 | −0.244881 | ||||||||
\(893\) | 15.3137 | 0.512454 | ||||||||
\(894\) | 22.3848 | 0.748659 | ||||||||
\(895\) | 26.2426 | 0.877195 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.9411 | −0.599037 | ||||||||
\(898\) | 10.4853 | 0.349898 | ||||||||
\(899\) | −26.4853 | −0.883334 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0.887302 | 0.0295603 | ||||||||
\(902\) | −23.5147 | −0.782954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.0000 | −0.332595 | ||||||||
\(905\) | 18.4853 | 0.614472 | ||||||||
\(906\) | 20.1421 | 0.669178 | ||||||||
\(907\) | −16.8701 | −0.560161 | −0.280081 | − | 0.959977i | \(-0.590361\pi\) | ||||
−0.280081 | + | 0.959977i | \(0.590361\pi\) | |||||||
\(908\) | −24.9706 | −0.828677 | ||||||||
\(909\) | 17.6569 | 0.585641 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.9706 | 1.48994 | 0.744971 | − | 0.667097i | \(-0.232463\pi\) | ||||
0.744971 | + | 0.667097i | \(0.232463\pi\) | |||||||
\(912\) | 6.82843 | 0.226112 | ||||||||
\(913\) | 11.5980 | 0.383837 | ||||||||
\(914\) | −2.48528 | −0.0822058 | ||||||||
\(915\) | 11.6569 | 0.385364 | ||||||||
\(916\) | −16.1421 | −0.533351 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.58579 | 0.0853437 | ||||||||
\(919\) | −30.7696 | −1.01499 | −0.507497 | − | 0.861654i | \(-0.669429\pi\) | ||||
−0.507497 | + | 0.861654i | \(0.669429\pi\) | |||||||
\(920\) | −3.17157 | −0.104564 | ||||||||
\(921\) | 7.31371 | 0.240995 | ||||||||
\(922\) | −2.00000 | −0.0658665 | ||||||||
\(923\) | −25.3726 | −0.835149 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.242641 | −0.00797798 | ||||||||
\(926\) | 25.6569 | 0.843137 | ||||||||
\(927\) | 14.8284 | 0.487029 | ||||||||
\(928\) | −2.58579 | −0.0848826 | ||||||||
\(929\) | 55.6569 | 1.82604 | 0.913021 | − | 0.407912i | \(-0.133743\pi\) | ||||
0.913021 | + | 0.407912i | \(0.133743\pi\) | |||||||
\(930\) | −10.2426 | −0.335869 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.9706 | 0.621401 | ||||||||
\(933\) | 10.8284 | 0.354507 | ||||||||
\(934\) | −12.4853 | −0.408531 | ||||||||
\(935\) | 5.79899 | 0.189647 | ||||||||
\(936\) | −5.65685 | −0.184900 | ||||||||
\(937\) | 36.3431 | 1.18728 | 0.593639 | − | 0.804731i | \(-0.297691\pi\) | ||||
0.593639 | + | 0.804731i | \(0.297691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.4853 | −0.994850 | ||||||||
\(940\) | −2.24264 | −0.0731469 | ||||||||
\(941\) | −28.2843 | −0.922041 | −0.461020 | − | 0.887390i | \(-0.652517\pi\) | ||||
−0.461020 | + | 0.887390i | \(0.652517\pi\) | |||||||
\(942\) | −8.34315 | −0.271834 | ||||||||
\(943\) | 33.2548 | 1.08293 | ||||||||
\(944\) | −3.17157 | −0.103226 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.3431 | −0.661413 | ||||||||
\(947\) | −9.17157 | −0.298036 | −0.149018 | − | 0.988834i | \(-0.547611\pi\) | ||||
−0.149018 | + | 0.988834i | \(0.547611\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | −11.3137 | −0.367259 | ||||||||
\(950\) | 6.82843 | 0.221543 | ||||||||
\(951\) | 25.3137 | 0.820853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.68629 | 0.151804 | 0.0759019 | − | 0.997115i | \(-0.475816\pi\) | ||||
0.0759019 | + | 0.997115i | \(0.475816\pi\) | |||||||
\(954\) | −0.343146 | −0.0111098 | ||||||||
\(955\) | 4.00000 | 0.129437 | ||||||||
\(956\) | −19.3137 | −0.624650 | ||||||||
\(957\) | −5.79899 | −0.187455 | ||||||||
\(958\) | 8.48528 | 0.274147 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | 1.37258 | 0.0442539 | ||||||||
\(963\) | 9.65685 | 0.311188 | ||||||||
\(964\) | −19.5563 | −0.629868 | ||||||||
\(965\) | −4.82843 | −0.155433 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3431 | −0.332613 | −0.166307 | − | 0.986074i | \(-0.553184\pi\) | ||||
−0.166307 | + | 0.986074i | \(0.553184\pi\) | |||||||
\(968\) | 5.97056 | 0.191901 | ||||||||
\(969\) | 17.6569 | 0.567220 | ||||||||
\(970\) | 6.48528 | 0.208230 | ||||||||
\(971\) | −4.97056 | −0.159513 | −0.0797565 | − | 0.996814i | \(-0.525414\pi\) | ||||
−0.0797565 | + | 0.996814i | \(0.525414\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.8284 | −0.346965 | ||||||||
\(975\) | −5.65685 | −0.181164 | ||||||||
\(976\) | −11.6569 | −0.373127 | ||||||||
\(977\) | −29.3137 | −0.937829 | −0.468914 | − | 0.883244i | \(-0.655355\pi\) | ||||
−0.468914 | + | 0.883244i | \(0.655355\pi\) | |||||||
\(978\) | −17.0711 | −0.545873 | ||||||||
\(979\) | −1.85786 | −0.0593776 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65685 | −0.116754 | ||||||||
\(982\) | 17.0711 | 0.544760 | ||||||||
\(983\) | −17.0711 | −0.544483 | −0.272241 | − | 0.962229i | \(-0.587765\pi\) | ||||
−0.272241 | + | 0.962229i | \(0.587765\pi\) | |||||||
\(984\) | 10.4853 | 0.334259 | ||||||||
\(985\) | −25.7990 | −0.822024 | ||||||||
\(986\) | −6.68629 | −0.212935 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.6274 | −1.22890 | ||||||||
\(989\) | 28.7696 | 0.914819 | ||||||||
\(990\) | −2.24264 | −0.0712758 | ||||||||
\(991\) | −10.2010 | −0.324046 | −0.162023 | − | 0.986787i | \(-0.551802\pi\) | ||||
−0.162023 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(992\) | 10.2426 | 0.325204 | ||||||||
\(993\) | 6.34315 | 0.201294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.75736 | −0.182521 | ||||||||
\(996\) | −5.17157 | −0.163868 | ||||||||
\(997\) | −56.6274 | −1.79341 | −0.896704 | − | 0.442630i | \(-0.854045\pi\) | ||||
−0.896704 | + | 0.442630i | \(0.854045\pi\) | |||||||
\(998\) | −6.82843 | −0.216150 | ||||||||
\(999\) | 0.242641 | 0.00767681 |
(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 | 1470.2.a.s.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 4410.2.a.bw.1.1 | 2 | |||
5.4 | even | 2 | 7350.2.a.dl.1.2 | 2 | |||
7.2 | even | 3 | 1470.2.i.x.361.1 | 4 | |||
7.3 | odd | 6 | 1470.2.i.w.961.1 | 4 | |||
7.4 | even | 3 | 1470.2.i.x.961.1 | 4 | |||
7.5 | odd | 6 | 1470.2.i.w.361.1 | 4 | |||
7.6 | odd | 2 | 1470.2.a.t.1.2 | yes | 2 | ||
21.20 | even | 2 | 4410.2.a.bz.1.1 | 2 | |||
35.34 | odd | 2 | 7350.2.a.dh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.a.s.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1470.2.a.t.1.2 | yes | 2 | 7.6 | odd | 2 | ||
1470.2.i.w.361.1 | 4 | 7.5 | odd | 6 | |||
1470.2.i.w.961.1 | 4 | 7.3 | odd | 6 | |||
1470.2.i.x.361.1 | 4 | 7.2 | even | 3 | |||
1470.2.i.x.961.1 | 4 | 7.4 | even | 3 | |||
4410.2.a.bw.1.1 | 2 | 3.2 | odd | 2 | |||
4410.2.a.bz.1.1 | 2 | 21.20 | even | 2 | |||
7350.2.a.dh.1.2 | 2 | 35.34 | odd | 2 | |||
7350.2.a.dl.1.2 | 2 | 5.4 | even | 2 |