Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.316645497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 24x^{3} + 13x^{2} - 24x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.28714\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 | ||||||||
\(3\) | −3.28714 | −1.89783 | −0.948915 | − | 0.315533i | \(-0.897817\pi\) | ||||
−0.948915 | + | 0.315533i | \(0.897817\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.88198 | 1.28886 | 0.644431 | − | 0.764662i | \(-0.277094\pi\) | ||||
0.644431 | + | 0.764662i | \(0.277094\pi\) | |||||||
\(6\) | −3.28714 | −1.34197 | ||||||||
\(7\) | 3.02408 | 1.14299 | 0.571497 | − | 0.820604i | \(-0.306363\pi\) | ||||
0.571497 | + | 0.820604i | \(0.306363\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.80527 | 2.60176 | ||||||||
\(10\) | 2.88198 | 0.911364 | ||||||||
\(11\) | 2.88198 | 0.868951 | 0.434476 | − | 0.900684i | \(-0.356934\pi\) | ||||
0.434476 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(12\) | −3.28714 | −0.948915 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.02408 | 0.808219 | ||||||||
\(15\) | −9.47348 | −2.44604 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0993160 | 0.0240877 | 0.0120438 | − | 0.999927i | \(-0.496166\pi\) | ||||
0.0120438 | + | 0.999927i | \(0.496166\pi\) | |||||||
\(18\) | 7.80527 | 1.83972 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.88198 | 0.644431 | ||||||||
\(21\) | −9.94055 | −2.16921 | ||||||||
\(22\) | 2.88198 | 0.614441 | ||||||||
\(23\) | 7.51133 | 1.56622 | 0.783110 | − | 0.621883i | \(-0.213632\pi\) | ||||
0.783110 | + | 0.621883i | \(0.213632\pi\) | |||||||
\(24\) | −3.28714 | −0.670984 | ||||||||
\(25\) | 3.30584 | 0.661167 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.7956 | −3.03986 | ||||||||
\(28\) | 3.02408 | 0.571497 | ||||||||
\(29\) | 3.34220 | 0.620632 | 0.310316 | − | 0.950633i | \(-0.399565\pi\) | ||||
0.310316 | + | 0.950633i | \(0.399565\pi\) | |||||||
\(30\) | −9.47348 | −1.72961 | ||||||||
\(31\) | 5.90708 | 1.06094 | 0.530472 | − | 0.847703i | \(-0.322015\pi\) | ||||
0.530472 | + | 0.847703i | \(0.322015\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −9.47348 | −1.64912 | ||||||||
\(34\) | 0.0993160 | 0.0170326 | ||||||||
\(35\) | 8.71534 | 1.47316 | ||||||||
\(36\) | 7.80527 | 1.30088 | ||||||||
\(37\) | −6.88543 | −1.13196 | −0.565979 | − | 0.824420i | \(-0.691502\pi\) | ||||
−0.565979 | + | 0.824420i | \(0.691502\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.88198 | 0.455682 | ||||||||
\(41\) | 6.94736 | 1.08500 | 0.542498 | − | 0.840057i | \(-0.317479\pi\) | ||||
0.542498 | + | 0.840057i | \(0.317479\pi\) | |||||||
\(42\) | −9.94055 | −1.53386 | ||||||||
\(43\) | 6.08702 | 0.928263 | 0.464131 | − | 0.885766i | \(-0.346367\pi\) | ||||
0.464131 | + | 0.885766i | \(0.346367\pi\) | |||||||
\(44\) | 2.88198 | 0.434476 | ||||||||
\(45\) | 22.4947 | 3.35331 | ||||||||
\(46\) | 7.51133 | 1.10748 | ||||||||
\(47\) | 5.88198 | 0.857976 | 0.428988 | − | 0.903310i | \(-0.358870\pi\) | ||||
0.428988 | + | 0.903310i | \(0.358870\pi\) | |||||||
\(48\) | −3.28714 | −0.474457 | ||||||||
\(49\) | 2.14504 | 0.306435 | ||||||||
\(50\) | 3.30584 | 0.467516 | ||||||||
\(51\) | −0.326465 | −0.0457143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.17556 | 1.26036 | 0.630180 | − | 0.776449i | \(-0.282981\pi\) | ||||
0.630180 | + | 0.776449i | \(0.282981\pi\) | |||||||
\(54\) | −15.7956 | −2.14950 | ||||||||
\(55\) | 8.30584 | 1.11996 | ||||||||
\(56\) | 3.02408 | 0.404109 | ||||||||
\(57\) | 3.28714 | 0.435392 | ||||||||
\(58\) | 3.34220 | 0.438853 | ||||||||
\(59\) | 0.856427 | 0.111497 | 0.0557487 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557487 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(60\) | −9.47348 | −1.22302 | ||||||||
\(61\) | −12.0129 | −1.53809 | −0.769047 | − | 0.639192i | \(-0.779269\pi\) | ||||
−0.769047 | + | 0.639192i | \(0.779269\pi\) | |||||||
\(62\) | 5.90708 | 0.750200 | ||||||||
\(63\) | 23.6037 | 2.97379 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.47348 | −1.16610 | ||||||||
\(67\) | −11.4641 | −1.40056 | −0.700280 | − | 0.713868i | \(-0.746942\pi\) | ||||
−0.700280 | + | 0.713868i | \(0.746942\pi\) | |||||||
\(68\) | 0.0993160 | 0.0120438 | ||||||||
\(69\) | −24.6908 | −2.97242 | ||||||||
\(70\) | 8.71534 | 1.04168 | ||||||||
\(71\) | 8.97303 | 1.06490 | 0.532451 | − | 0.846461i | \(-0.321271\pi\) | ||||
0.532451 | + | 0.846461i | \(0.321271\pi\) | |||||||
\(72\) | 7.80527 | 0.919859 | ||||||||
\(73\) | −0.646560 | −0.0756742 | −0.0378371 | − | 0.999284i | \(-0.512047\pi\) | ||||
−0.0378371 | + | 0.999284i | \(0.512047\pi\) | |||||||
\(74\) | −6.88543 | −0.800415 | ||||||||
\(75\) | −10.8667 | −1.25478 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 8.71534 | 0.993206 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0089 | −1.57612 | −0.788061 | − | 0.615597i | \(-0.788915\pi\) | ||||
−0.788061 | + | 0.615597i | \(0.788915\pi\) | |||||||
\(80\) | 2.88198 | 0.322216 | ||||||||
\(81\) | 28.5064 | 3.16738 | ||||||||
\(82\) | 6.94736 | 0.767207 | ||||||||
\(83\) | 10.0518 | 1.10332 | 0.551662 | − | 0.834068i | \(-0.313994\pi\) | ||||
0.551662 | + | 0.834068i | \(0.313994\pi\) | |||||||
\(84\) | −9.94055 | −1.08460 | ||||||||
\(85\) | 0.286227 | 0.0310457 | ||||||||
\(86\) | 6.08702 | 0.656381 | ||||||||
\(87\) | −10.9863 | −1.17785 | ||||||||
\(88\) | 2.88198 | 0.307221 | ||||||||
\(89\) | −0.951375 | −0.100846 | −0.0504228 | − | 0.998728i | \(-0.516057\pi\) | ||||
−0.0504228 | + | 0.998728i | \(0.516057\pi\) | |||||||
\(90\) | 22.4947 | 2.37115 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.51133 | 0.783110 | ||||||||
\(93\) | −19.4174 | −2.01349 | ||||||||
\(94\) | 5.88198 | 0.606680 | ||||||||
\(95\) | −2.88198 | −0.295685 | ||||||||
\(96\) | −3.28714 | −0.335492 | ||||||||
\(97\) | −16.4426 | −1.66949 | −0.834746 | − | 0.550636i | \(-0.814385\pi\) | ||||
−0.834746 | + | 0.550636i | \(0.814385\pi\) | |||||||
\(98\) | 2.14504 | 0.216682 | ||||||||
\(99\) | 22.4947 | 2.26080 | ||||||||
\(100\) | 3.30584 | 0.330584 | ||||||||
\(101\) | −9.72510 | −0.967684 | −0.483842 | − | 0.875155i | \(-0.660759\pi\) | ||||
−0.483842 | + | 0.875155i | \(0.660759\pi\) | |||||||
\(102\) | −0.326465 | −0.0323249 | ||||||||
\(103\) | −13.0880 | −1.28960 | −0.644801 | − | 0.764351i | \(-0.723060\pi\) | ||||
−0.644801 | + | 0.764351i | \(0.723060\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −28.6485 | −2.79581 | ||||||||
\(106\) | 9.17556 | 0.891210 | ||||||||
\(107\) | 8.21201 | 0.793885 | 0.396942 | − | 0.917844i | \(-0.370071\pi\) | ||||
0.396942 | + | 0.917844i | \(0.370071\pi\) | |||||||
\(108\) | −15.7956 | −1.51993 | ||||||||
\(109\) | −6.16653 | −0.590646 | −0.295323 | − | 0.955397i | \(-0.595427\pi\) | ||||
−0.295323 | + | 0.955397i | \(0.595427\pi\) | |||||||
\(110\) | 8.30584 | 0.791930 | ||||||||
\(111\) | 22.6334 | 2.14826 | ||||||||
\(112\) | 3.02408 | 0.285748 | ||||||||
\(113\) | −15.9957 | −1.50475 | −0.752373 | − | 0.658737i | \(-0.771091\pi\) | ||||
−0.752373 | + | 0.658737i | \(0.771091\pi\) | |||||||
\(114\) | 3.28714 | 0.307869 | ||||||||
\(115\) | 21.6475 | 2.01864 | ||||||||
\(116\) | 3.34220 | 0.310316 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.856427 | 0.0788405 | ||||||||
\(119\) | 0.300339 | 0.0275321 | ||||||||
\(120\) | −9.47348 | −0.864806 | ||||||||
\(121\) | −2.69416 | −0.244924 | ||||||||
\(122\) | −12.0129 | −1.08760 | ||||||||
\(123\) | −22.8369 | −2.05914 | ||||||||
\(124\) | 5.90708 | 0.530472 | ||||||||
\(125\) | −4.88256 | −0.436709 | ||||||||
\(126\) | 23.6037 | 2.10279 | ||||||||
\(127\) | 1.15297 | 0.102309 | 0.0511546 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511546 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −20.0089 | −1.76168 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.25910 | −0.808971 | −0.404486 | − | 0.914544i | \(-0.632549\pi\) | ||||
−0.404486 | + | 0.914544i | \(0.632549\pi\) | |||||||
\(132\) | −9.47348 | −0.824560 | ||||||||
\(133\) | −3.02408 | −0.262221 | ||||||||
\(134\) | −11.4641 | −0.990346 | ||||||||
\(135\) | −45.5226 | −3.91796 | ||||||||
\(136\) | 0.0993160 | 0.00851628 | ||||||||
\(137\) | 6.17416 | 0.527494 | 0.263747 | − | 0.964592i | \(-0.415042\pi\) | ||||
0.263747 | + | 0.964592i | \(0.415042\pi\) | |||||||
\(138\) | −24.6908 | −2.10182 | ||||||||
\(139\) | −6.61882 | −0.561401 | −0.280700 | − | 0.959795i | \(-0.590567\pi\) | ||||
−0.280700 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(140\) | 8.71534 | 0.736581 | ||||||||
\(141\) | −19.3349 | −1.62829 | ||||||||
\(142\) | 8.97303 | 0.753000 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.80527 | 0.650439 | ||||||||
\(145\) | 9.63218 | 0.799909 | ||||||||
\(146\) | −0.646560 | −0.0535097 | ||||||||
\(147\) | −7.05105 | −0.581561 | ||||||||
\(148\) | −6.88543 | −0.565979 | ||||||||
\(149\) | −2.91053 | −0.238440 | −0.119220 | − | 0.992868i | \(-0.538039\pi\) | ||||
−0.119220 | + | 0.992868i | \(0.538039\pi\) | |||||||
\(150\) | −10.8667 | −0.887265 | ||||||||
\(151\) | −3.38645 | −0.275586 | −0.137793 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137793 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0.775188 | 0.0626702 | ||||||||
\(154\) | 8.71534 | 0.702302 | ||||||||
\(155\) | 17.0241 | 1.36741 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.59018 | 0.765380 | 0.382690 | − | 0.923877i | \(-0.374998\pi\) | ||||
0.382690 | + | 0.923877i | \(0.374998\pi\) | |||||||
\(158\) | −14.0089 | −1.11449 | ||||||||
\(159\) | −30.1613 | −2.39195 | ||||||||
\(160\) | 2.88198 | 0.227841 | ||||||||
\(161\) | 22.7148 | 1.79018 | ||||||||
\(162\) | 28.5064 | 2.23967 | ||||||||
\(163\) | 4.35938 | 0.341453 | 0.170726 | − | 0.985318i | \(-0.445389\pi\) | ||||
0.170726 | + | 0.985318i | \(0.445389\pi\) | |||||||
\(164\) | 6.94736 | 0.542498 | ||||||||
\(165\) | −27.3024 | −2.12549 | ||||||||
\(166\) | 10.0518 | 0.780168 | ||||||||
\(167\) | 19.9405 | 1.54305 | 0.771523 | − | 0.636202i | \(-0.219495\pi\) | ||||
0.771523 | + | 0.636202i | \(0.219495\pi\) | |||||||
\(168\) | −9.94055 | −0.766930 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.286227 | 0.0219526 | ||||||||
\(171\) | −7.80527 | −0.596884 | ||||||||
\(172\) | 6.08702 | 0.464131 | ||||||||
\(173\) | −4.85829 | −0.369369 | −0.184685 | − | 0.982798i | \(-0.559126\pi\) | ||||
−0.184685 | + | 0.982798i | \(0.559126\pi\) | |||||||
\(174\) | −10.9863 | −0.832868 | ||||||||
\(175\) | 9.99710 | 0.755710 | ||||||||
\(176\) | 2.88198 | 0.217238 | ||||||||
\(177\) | −2.81519 | −0.211603 | ||||||||
\(178\) | −0.951375 | −0.0713086 | ||||||||
\(179\) | −12.5379 | −0.937126 | −0.468563 | − | 0.883430i | \(-0.655228\pi\) | ||||
−0.468563 | + | 0.883430i | \(0.655228\pi\) | |||||||
\(180\) | 22.4947 | 1.67665 | ||||||||
\(181\) | −21.6396 | −1.60846 | −0.804229 | − | 0.594319i | \(-0.797421\pi\) | ||||
−0.804229 | + | 0.594319i | \(0.797421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 39.4880 | 2.91904 | ||||||||
\(184\) | 7.51133 | 0.553742 | ||||||||
\(185\) | −19.8437 | −1.45894 | ||||||||
\(186\) | −19.4174 | −1.42375 | ||||||||
\(187\) | 0.286227 | 0.0209310 | ||||||||
\(188\) | 5.88198 | 0.428988 | ||||||||
\(189\) | −47.7670 | −3.47454 | ||||||||
\(190\) | −2.88198 | −0.209081 | ||||||||
\(191\) | −10.2866 | −0.744310 | −0.372155 | − | 0.928171i | \(-0.621381\pi\) | ||||
−0.372155 | + | 0.928171i | \(0.621381\pi\) | |||||||
\(192\) | −3.28714 | −0.237229 | ||||||||
\(193\) | 22.5115 | 1.62041 | 0.810206 | − | 0.586146i | \(-0.199355\pi\) | ||||
0.810206 | + | 0.586146i | \(0.199355\pi\) | |||||||
\(194\) | −16.4426 | −1.18051 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.14504 | 0.153217 | ||||||||
\(197\) | −7.05750 | −0.502826 | −0.251413 | − | 0.967880i | \(-0.580895\pi\) | ||||
−0.251413 | + | 0.967880i | \(0.580895\pi\) | |||||||
\(198\) | 22.4947 | 1.59863 | ||||||||
\(199\) | 26.2412 | 1.86019 | 0.930096 | − | 0.367317i | \(-0.119724\pi\) | ||||
0.930096 | + | 0.367317i | \(0.119724\pi\) | |||||||
\(200\) | 3.30584 | 0.233758 | ||||||||
\(201\) | 37.6840 | 2.65802 | ||||||||
\(202\) | −9.72510 | −0.684256 | ||||||||
\(203\) | 10.1071 | 0.709378 | ||||||||
\(204\) | −0.326465 | −0.0228571 | ||||||||
\(205\) | 20.0222 | 1.39841 | ||||||||
\(206\) | −13.0880 | −0.911886 | ||||||||
\(207\) | 58.6279 | 4.07492 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.88198 | −0.199351 | ||||||||
\(210\) | −28.6485 | −1.97694 | ||||||||
\(211\) | 11.2897 | 0.777217 | 0.388608 | − | 0.921403i | \(-0.372956\pi\) | ||||
0.388608 | + | 0.921403i | \(0.372956\pi\) | |||||||
\(212\) | 9.17556 | 0.630180 | ||||||||
\(213\) | −29.4956 | −2.02100 | ||||||||
\(214\) | 8.21201 | 0.561361 | ||||||||
\(215\) | 17.5427 | 1.19640 | ||||||||
\(216\) | −15.7956 | −1.07475 | ||||||||
\(217\) | 17.8635 | 1.21265 | ||||||||
\(218\) | −6.16653 | −0.417650 | ||||||||
\(219\) | 2.12533 | 0.143617 | ||||||||
\(220\) | 8.30584 | 0.559979 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 22.6334 | 1.51905 | ||||||||
\(223\) | 7.80973 | 0.522979 | 0.261489 | − | 0.965206i | \(-0.415786\pi\) | ||||
0.261489 | + | 0.965206i | \(0.415786\pi\) | |||||||
\(224\) | 3.02408 | 0.202055 | ||||||||
\(225\) | 25.8029 | 1.72020 | ||||||||
\(226\) | −15.9957 | −1.06402 | ||||||||
\(227\) | −6.31625 | −0.419224 | −0.209612 | − | 0.977785i | \(-0.567220\pi\) | ||||
−0.209612 | + | 0.977785i | \(0.567220\pi\) | |||||||
\(228\) | 3.28714 | 0.217696 | ||||||||
\(229\) | −6.89920 | −0.455912 | −0.227956 | − | 0.973671i | \(-0.573204\pi\) | ||||
−0.227956 | + | 0.973671i | \(0.573204\pi\) | |||||||
\(230\) | 21.6475 | 1.42740 | ||||||||
\(231\) | −28.6485 | −1.88493 | ||||||||
\(232\) | 3.34220 | 0.219426 | ||||||||
\(233\) | −2.39251 | −0.156739 | −0.0783693 | − | 0.996924i | \(-0.524971\pi\) | ||||
−0.0783693 | + | 0.996924i | \(0.524971\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9518 | 1.10581 | ||||||||
\(236\) | 0.856427 | 0.0557487 | ||||||||
\(237\) | 46.0491 | 2.99121 | ||||||||
\(238\) | 0.300339 | 0.0194681 | ||||||||
\(239\) | 21.5847 | 1.39620 | 0.698100 | − | 0.716000i | \(-0.254029\pi\) | ||||
0.698100 | + | 0.716000i | \(0.254029\pi\) | |||||||
\(240\) | −9.47348 | −0.611510 | ||||||||
\(241\) | −16.4075 | −1.05690 | −0.528451 | − | 0.848964i | \(-0.677227\pi\) | ||||
−0.528451 | + | 0.848964i | \(0.677227\pi\) | |||||||
\(242\) | −2.69416 | −0.173187 | ||||||||
\(243\) | −46.3177 | −2.97128 | ||||||||
\(244\) | −12.0129 | −0.769047 | ||||||||
\(245\) | 6.18198 | 0.394952 | ||||||||
\(246\) | −22.8369 | −1.45603 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.90708 | 0.375100 | ||||||||
\(249\) | −33.0415 | −2.09392 | ||||||||
\(250\) | −4.88256 | −0.308800 | ||||||||
\(251\) | −18.5904 | −1.17342 | −0.586709 | − | 0.809798i | \(-0.699577\pi\) | ||||
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(252\) | 23.6037 | 1.48690 | ||||||||
\(253\) | 21.6475 | 1.36097 | ||||||||
\(254\) | 1.15297 | 0.0723436 | ||||||||
\(255\) | −0.940868 | −0.0589194 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.96066 | 0.434194 | 0.217097 | − | 0.976150i | \(-0.430341\pi\) | ||||
0.217097 | + | 0.976150i | \(0.430341\pi\) | |||||||
\(258\) | −20.0089 | −1.24570 | ||||||||
\(259\) | −20.8221 | −1.29382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.0868 | 1.61473 | ||||||||
\(262\) | −9.25910 | −0.572029 | ||||||||
\(263\) | 1.68874 | 0.104132 | 0.0520661 | − | 0.998644i | \(-0.483419\pi\) | ||||
0.0520661 | + | 0.998644i | \(0.483419\pi\) | |||||||
\(264\) | −9.47348 | −0.583052 | ||||||||
\(265\) | 26.4438 | 1.62443 | ||||||||
\(266\) | −3.02408 | −0.185418 | ||||||||
\(267\) | 3.12730 | 0.191388 | ||||||||
\(268\) | −11.4641 | −0.700280 | ||||||||
\(269\) | 28.3668 | 1.72956 | 0.864778 | − | 0.502154i | \(-0.167459\pi\) | ||||
0.864778 | + | 0.502154i | \(0.167459\pi\) | |||||||
\(270\) | −45.5226 | −2.77042 | ||||||||
\(271\) | −14.0040 | −0.850680 | −0.425340 | − | 0.905034i | \(-0.639845\pi\) | ||||
−0.425340 | + | 0.905034i | \(0.639845\pi\) | |||||||
\(272\) | 0.0993160 | 0.00602192 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.17416 | 0.372995 | ||||||||
\(275\) | 9.52737 | 0.574522 | ||||||||
\(276\) | −24.6908 | −1.48621 | ||||||||
\(277\) | 9.57854 | 0.575519 | 0.287759 | − | 0.957703i | \(-0.407090\pi\) | ||||
0.287759 | + | 0.957703i | \(0.407090\pi\) | |||||||
\(278\) | −6.61882 | −0.396970 | ||||||||
\(279\) | 46.1064 | 2.76032 | ||||||||
\(280\) | 8.71534 | 0.520841 | ||||||||
\(281\) | 0.150742 | 0.00899250 | 0.00449625 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449625 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(282\) | −19.3349 | −1.15138 | ||||||||
\(283\) | −29.5322 | −1.75551 | −0.877755 | − | 0.479110i | \(-0.840959\pi\) | ||||
−0.877755 | + | 0.479110i | \(0.840959\pi\) | |||||||
\(284\) | 8.97303 | 0.532451 | ||||||||
\(285\) | 9.47348 | 0.561160 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.0094 | 1.24014 | ||||||||
\(288\) | 7.80527 | 0.459930 | ||||||||
\(289\) | −16.9901 | −0.999420 | ||||||||
\(290\) | 9.63218 | 0.565621 | ||||||||
\(291\) | 54.0490 | 3.16841 | ||||||||
\(292\) | −0.646560 | −0.0378371 | ||||||||
\(293\) | 3.94681 | 0.230575 | 0.115287 | − | 0.993332i | \(-0.463221\pi\) | ||||
0.115287 | + | 0.993332i | \(0.463221\pi\) | |||||||
\(294\) | −7.05105 | −0.411226 | ||||||||
\(295\) | 2.46821 | 0.143705 | ||||||||
\(296\) | −6.88543 | −0.400208 | ||||||||
\(297\) | −45.5226 | −2.64149 | ||||||||
\(298\) | −2.91053 | −0.168603 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −10.8667 | −0.627391 | ||||||||
\(301\) | 18.4076 | 1.06100 | ||||||||
\(302\) | −3.38645 | −0.194868 | ||||||||
\(303\) | 31.9677 | 1.83650 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −34.6210 | −1.98239 | ||||||||
\(306\) | 0.775188 | 0.0443145 | ||||||||
\(307\) | −0.213487 | −0.0121844 | −0.00609219 | − | 0.999981i | \(-0.501939\pi\) | ||||
−0.00609219 | + | 0.999981i | \(0.501939\pi\) | |||||||
\(308\) | 8.71534 | 0.496603 | ||||||||
\(309\) | 43.0221 | 2.44744 | ||||||||
\(310\) | 17.0241 | 0.966905 | ||||||||
\(311\) | −30.1703 | −1.71080 | −0.855399 | − | 0.517969i | \(-0.826688\pi\) | ||||
−0.855399 | + | 0.517969i | \(0.826688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5575 | −1.10545 | −0.552727 | − | 0.833362i | \(-0.686413\pi\) | ||||
−0.552727 | + | 0.833362i | \(0.686413\pi\) | |||||||
\(314\) | 9.59018 | 0.541205 | ||||||||
\(315\) | 68.0256 | 3.83281 | ||||||||
\(316\) | −14.0089 | −0.788061 | ||||||||
\(317\) | −6.31782 | −0.354844 | −0.177422 | − | 0.984135i | \(-0.556776\pi\) | ||||
−0.177422 | + | 0.984135i | \(0.556776\pi\) | |||||||
\(318\) | −30.1613 | −1.69136 | ||||||||
\(319\) | 9.63218 | 0.539299 | ||||||||
\(320\) | 2.88198 | 0.161108 | ||||||||
\(321\) | −26.9940 | −1.50666 | ||||||||
\(322\) | 22.7148 | 1.26585 | ||||||||
\(323\) | −0.0993160 | −0.00552609 | ||||||||
\(324\) | 28.5064 | 1.58369 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.35938 | 0.241444 | ||||||||
\(327\) | 20.2702 | 1.12095 | ||||||||
\(328\) | 6.94736 | 0.383604 | ||||||||
\(329\) | 17.7876 | 0.980661 | ||||||||
\(330\) | −27.3024 | −1.50295 | ||||||||
\(331\) | 7.47193 | 0.410695 | 0.205347 | − | 0.978689i | \(-0.434168\pi\) | ||||
0.205347 | + | 0.978689i | \(0.434168\pi\) | |||||||
\(332\) | 10.0518 | 0.551662 | ||||||||
\(333\) | −53.7426 | −2.94508 | ||||||||
\(334\) | 19.9405 | 1.09110 | ||||||||
\(335\) | −33.0393 | −1.80513 | ||||||||
\(336\) | −9.94055 | −0.542302 | ||||||||
\(337\) | −3.39531 | −0.184955 | −0.0924773 | − | 0.995715i | \(-0.529479\pi\) | ||||
−0.0924773 | + | 0.995715i | \(0.529479\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 52.5800 | 2.85575 | ||||||||
\(340\) | 0.286227 | 0.0155228 | ||||||||
\(341\) | 17.0241 | 0.921908 | ||||||||
\(342\) | −7.80527 | −0.422060 | ||||||||
\(343\) | −14.6818 | −0.792741 | ||||||||
\(344\) | 6.08702 | 0.328190 | ||||||||
\(345\) | −71.1584 | −3.83104 | ||||||||
\(346\) | −4.85829 | −0.261183 | ||||||||
\(347\) | 1.90912 | 0.102487 | 0.0512436 | − | 0.998686i | \(-0.483682\pi\) | ||||
0.0512436 | + | 0.998686i | \(0.483682\pi\) | |||||||
\(348\) | −10.9863 | −0.588927 | ||||||||
\(349\) | −26.1257 | −1.39848 | −0.699239 | − | 0.714888i | \(-0.746478\pi\) | ||||
−0.699239 | + | 0.714888i | \(0.746478\pi\) | |||||||
\(350\) | 9.99710 | 0.534368 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.88198 | 0.153610 | ||||||||
\(353\) | −11.5915 | −0.616951 | −0.308475 | − | 0.951232i | \(-0.599819\pi\) | ||||
−0.308475 | + | 0.951232i | \(0.599819\pi\) | |||||||
\(354\) | −2.81519 | −0.149626 | ||||||||
\(355\) | 25.8601 | 1.37251 | ||||||||
\(356\) | −0.951375 | −0.0504228 | ||||||||
\(357\) | −0.987256 | −0.0522511 | ||||||||
\(358\) | −12.5379 | −0.662648 | ||||||||
\(359\) | 4.12940 | 0.217941 | 0.108971 | − | 0.994045i | \(-0.465245\pi\) | ||||
0.108971 | + | 0.994045i | \(0.465245\pi\) | |||||||
\(360\) | 22.4947 | 1.18557 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −21.6396 | −1.13735 | ||||||||
\(363\) | 8.85609 | 0.464824 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.86338 | −0.0975336 | ||||||||
\(366\) | 39.4880 | 2.06407 | ||||||||
\(367\) | 22.0476 | 1.15087 | 0.575437 | − | 0.817846i | \(-0.304832\pi\) | ||||
0.575437 | + | 0.817846i | \(0.304832\pi\) | |||||||
\(368\) | 7.51133 | 0.391555 | ||||||||
\(369\) | 54.2260 | 2.82289 | ||||||||
\(370\) | −19.8437 | −1.03163 | ||||||||
\(371\) | 27.7476 | 1.44058 | ||||||||
\(372\) | −19.4174 | −1.00674 | ||||||||
\(373\) | 22.9777 | 1.18974 | 0.594870 | − | 0.803822i | \(-0.297203\pi\) | ||||
0.594870 | + | 0.803822i | \(0.297203\pi\) | |||||||
\(374\) | 0.286227 | 0.0148005 | ||||||||
\(375\) | 16.0496 | 0.828799 | ||||||||
\(376\) | 5.88198 | 0.303340 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −47.7670 | −2.45687 | ||||||||
\(379\) | −10.1844 | −0.523138 | −0.261569 | − | 0.965185i | \(-0.584240\pi\) | ||||
−0.261569 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(380\) | −2.88198 | −0.147843 | ||||||||
\(381\) | −3.78996 | −0.194166 | ||||||||
\(382\) | −10.2866 | −0.526307 | ||||||||
\(383\) | 34.1328 | 1.74410 | 0.872052 | − | 0.489413i | \(-0.162789\pi\) | ||||
0.872052 | + | 0.489413i | \(0.162789\pi\) | |||||||
\(384\) | −3.28714 | −0.167746 | ||||||||
\(385\) | 25.1175 | 1.28011 | ||||||||
\(386\) | 22.5115 | 1.14580 | ||||||||
\(387\) | 47.5108 | 2.41511 | ||||||||
\(388\) | −16.4426 | −0.834746 | ||||||||
\(389\) | −11.1658 | −0.566127 | −0.283063 | − | 0.959101i | \(-0.591351\pi\) | ||||
−0.283063 | + | 0.959101i | \(0.591351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.745995 | 0.0377266 | ||||||||
\(392\) | 2.14504 | 0.108341 | ||||||||
\(393\) | 30.4359 | 1.53529 | ||||||||
\(394\) | −7.05750 | −0.355551 | ||||||||
\(395\) | −40.3734 | −2.03141 | ||||||||
\(396\) | 22.4947 | 1.13040 | ||||||||
\(397\) | 1.89726 | 0.0952209 | 0.0476104 | − | 0.998866i | \(-0.484839\pi\) | ||||
0.0476104 | + | 0.998866i | \(0.484839\pi\) | |||||||
\(398\) | 26.2412 | 1.31535 | ||||||||
\(399\) | 9.94055 | 0.497650 | ||||||||
\(400\) | 3.30584 | 0.165292 | ||||||||
\(401\) | 30.7695 | 1.53656 | 0.768278 | − | 0.640117i | \(-0.221114\pi\) | ||||
0.768278 | + | 0.640117i | \(0.221114\pi\) | |||||||
\(402\) | 37.6840 | 1.87951 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −9.72510 | −0.483842 | ||||||||
\(405\) | 82.1550 | 4.08231 | ||||||||
\(406\) | 10.1071 | 0.501606 | ||||||||
\(407\) | −19.8437 | −0.983616 | ||||||||
\(408\) | −0.326465 | −0.0161624 | ||||||||
\(409\) | −13.5808 | −0.671525 | −0.335763 | − | 0.941947i | \(-0.608994\pi\) | ||||
−0.335763 | + | 0.941947i | \(0.608994\pi\) | |||||||
\(410\) | 20.0222 | 0.988825 | ||||||||
\(411\) | −20.2953 | −1.00109 | ||||||||
\(412\) | −13.0880 | −0.644801 | ||||||||
\(413\) | 2.58990 | 0.127441 | ||||||||
\(414\) | 58.6279 | 2.88140 | ||||||||
\(415\) | 28.9690 | 1.42203 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.7570 | 1.06544 | ||||||||
\(418\) | −2.88198 | −0.140962 | ||||||||
\(419\) | 11.5178 | 0.562684 | 0.281342 | − | 0.959608i | \(-0.409221\pi\) | ||||
0.281342 | + | 0.959608i | \(0.409221\pi\) | |||||||
\(420\) | −28.6485 | −1.39790 | ||||||||
\(421\) | −14.7578 | −0.719249 | −0.359625 | − | 0.933097i | \(-0.617095\pi\) | ||||
−0.359625 | + | 0.933097i | \(0.617095\pi\) | |||||||
\(422\) | 11.2897 | 0.549575 | ||||||||
\(423\) | 45.9105 | 2.23224 | ||||||||
\(424\) | 9.17556 | 0.445605 | ||||||||
\(425\) | 0.328322 | 0.0159260 | ||||||||
\(426\) | −29.4956 | −1.42906 | ||||||||
\(427\) | −36.3279 | −1.75803 | ||||||||
\(428\) | 8.21201 | 0.396942 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.5427 | 0.845985 | ||||||||
\(431\) | 0.0489741 | 0.00235900 | 0.00117950 | − | 0.999999i | \(-0.499625\pi\) | ||||
0.00117950 | + | 0.999999i | \(0.499625\pi\) | |||||||
\(432\) | −15.7956 | −0.759964 | ||||||||
\(433\) | 15.4388 | 0.741941 | 0.370970 | − | 0.928645i | \(-0.379025\pi\) | ||||
0.370970 | + | 0.928645i | \(0.379025\pi\) | |||||||
\(434\) | 17.8635 | 0.857474 | ||||||||
\(435\) | −31.6623 | −1.51809 | ||||||||
\(436\) | −6.16653 | −0.295323 | ||||||||
\(437\) | −7.51133 | −0.359315 | ||||||||
\(438\) | 2.12533 | 0.101552 | ||||||||
\(439\) | 23.4821 | 1.12074 | 0.560370 | − | 0.828243i | \(-0.310659\pi\) | ||||
0.560370 | + | 0.828243i | \(0.310659\pi\) | |||||||
\(440\) | 8.30584 | 0.395965 | ||||||||
\(441\) | 16.7426 | 0.797268 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.851887 | −0.0404744 | −0.0202372 | − | 0.999795i | \(-0.506442\pi\) | ||||
−0.0202372 | + | 0.999795i | \(0.506442\pi\) | |||||||
\(444\) | 22.6334 | 1.07413 | ||||||||
\(445\) | −2.74185 | −0.129976 | ||||||||
\(446\) | 7.80973 | 0.369802 | ||||||||
\(447\) | 9.56731 | 0.452518 | ||||||||
\(448\) | 3.02408 | 0.142874 | ||||||||
\(449\) | 37.3624 | 1.76324 | 0.881620 | − | 0.471959i | \(-0.156453\pi\) | ||||
0.881620 | + | 0.471959i | \(0.156453\pi\) | |||||||
\(450\) | 25.8029 | 1.21636 | ||||||||
\(451\) | 20.0222 | 0.942808 | ||||||||
\(452\) | −15.9957 | −0.752373 | ||||||||
\(453\) | 11.1317 | 0.523014 | ||||||||
\(454\) | −6.31625 | −0.296436 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.28714 | 0.153934 | ||||||||
\(457\) | −18.0321 | −0.843505 | −0.421753 | − | 0.906711i | \(-0.638585\pi\) | ||||
−0.421753 | + | 0.906711i | \(0.638585\pi\) | |||||||
\(458\) | −6.89920 | −0.322379 | ||||||||
\(459\) | −1.56875 | −0.0732231 | ||||||||
\(460\) | 21.6475 | 1.00932 | ||||||||
\(461\) | −20.5994 | −0.959410 | −0.479705 | − | 0.877430i | \(-0.659256\pi\) | ||||
−0.479705 | + | 0.877430i | \(0.659256\pi\) | |||||||
\(462\) | −28.6485 | −1.33285 | ||||||||
\(463\) | 0.835400 | 0.0388243 | 0.0194122 | − | 0.999812i | \(-0.493821\pi\) | ||||
0.0194122 | + | 0.999812i | \(0.493821\pi\) | |||||||
\(464\) | 3.34220 | 0.155158 | ||||||||
\(465\) | −55.9606 | −2.59511 | ||||||||
\(466\) | −2.39251 | −0.110831 | ||||||||
\(467\) | 4.94829 | 0.228979 | 0.114490 | − | 0.993424i | \(-0.463477\pi\) | ||||
0.114490 | + | 0.993424i | \(0.463477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.6683 | −1.60083 | ||||||||
\(470\) | 16.9518 | 0.781928 | ||||||||
\(471\) | −31.5242 | −1.45256 | ||||||||
\(472\) | 0.856427 | 0.0394203 | ||||||||
\(473\) | 17.5427 | 0.806615 | ||||||||
\(474\) | 46.0491 | 2.11511 | ||||||||
\(475\) | −3.30584 | −0.151682 | ||||||||
\(476\) | 0.300339 | 0.0137660 | ||||||||
\(477\) | 71.6177 | 3.27915 | ||||||||
\(478\) | 21.5847 | 0.987263 | ||||||||
\(479\) | 3.05994 | 0.139812 | 0.0699062 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699062 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(480\) | −9.47348 | −0.432403 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.4075 | −0.747343 | ||||||||
\(483\) | −74.6667 | −3.39745 | ||||||||
\(484\) | −2.69416 | −0.122462 | ||||||||
\(485\) | −47.3873 | −2.15175 | ||||||||
\(486\) | −46.3177 | −2.10101 | ||||||||
\(487\) | −12.8479 | −0.582192 | −0.291096 | − | 0.956694i | \(-0.594020\pi\) | ||||
−0.291096 | + | 0.956694i | \(0.594020\pi\) | |||||||
\(488\) | −12.0129 | −0.543798 | ||||||||
\(489\) | −14.3299 | −0.648019 | ||||||||
\(490\) | 6.18198 | 0.279274 | ||||||||
\(491\) | 12.0690 | 0.544665 | 0.272332 | − | 0.962203i | \(-0.412205\pi\) | ||||
0.272332 | + | 0.962203i | \(0.412205\pi\) | |||||||
\(492\) | −22.8369 | −1.02957 | ||||||||
\(493\) | 0.331934 | 0.0149496 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 64.8293 | 2.91386 | ||||||||
\(496\) | 5.90708 | 0.265236 | ||||||||
\(497\) | 27.1351 | 1.21718 | ||||||||
\(498\) | −33.0415 | −1.48063 | ||||||||
\(499\) | 35.1067 | 1.57159 | 0.785796 | − | 0.618485i | \(-0.212253\pi\) | ||||
0.785796 | + | 0.618485i | \(0.212253\pi\) | |||||||
\(500\) | −4.88256 | −0.218355 | ||||||||
\(501\) | −65.5473 | −2.92844 | ||||||||
\(502\) | −18.5904 | −0.829732 | ||||||||
\(503\) | −6.31482 | −0.281564 | −0.140782 | − | 0.990041i | \(-0.544962\pi\) | ||||
−0.140782 | + | 0.990041i | \(0.544962\pi\) | |||||||
\(504\) | 23.6037 | 1.05139 | ||||||||
\(505\) | −28.0276 | −1.24721 | ||||||||
\(506\) | 21.6475 | 0.962350 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.15297 | 0.0511546 | ||||||||
\(509\) | −30.7506 | −1.36300 | −0.681498 | − | 0.731820i | \(-0.738671\pi\) | ||||
−0.681498 | + | 0.731820i | \(0.738671\pi\) | |||||||
\(510\) | −0.940868 | −0.0416623 | ||||||||
\(511\) | −1.95525 | −0.0864951 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.7956 | 0.697391 | ||||||||
\(514\) | 6.96066 | 0.307022 | ||||||||
\(515\) | −37.7195 | −1.66212 | ||||||||
\(516\) | −20.0089 | −0.880842 | ||||||||
\(517\) | 16.9518 | 0.745539 | ||||||||
\(518\) | −20.8221 | −0.914870 | ||||||||
\(519\) | 15.9699 | 0.700999 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.8734 | 1.44021 | 0.720105 | − | 0.693865i | \(-0.244094\pi\) | ||||
0.720105 | + | 0.693865i | \(0.244094\pi\) | |||||||
\(522\) | 26.0868 | 1.14179 | ||||||||
\(523\) | 39.3400 | 1.72022 | 0.860108 | − | 0.510112i | \(-0.170396\pi\) | ||||
0.860108 | + | 0.510112i | \(0.170396\pi\) | |||||||
\(524\) | −9.25910 | −0.404486 | ||||||||
\(525\) | −32.8618 | −1.43421 | ||||||||
\(526\) | 1.68874 | 0.0736326 | ||||||||
\(527\) | 0.586668 | 0.0255557 | ||||||||
\(528\) | −9.47348 | −0.412280 | ||||||||
\(529\) | 33.4200 | 1.45304 | ||||||||
\(530\) | 26.4438 | 1.14865 | ||||||||
\(531\) | 6.68464 | 0.290089 | ||||||||
\(532\) | −3.02408 | −0.131110 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.12730 | 0.135332 | ||||||||
\(535\) | 23.6669 | 1.02321 | ||||||||
\(536\) | −11.4641 | −0.495173 | ||||||||
\(537\) | 41.2138 | 1.77851 | ||||||||
\(538\) | 28.3668 | 1.22298 | ||||||||
\(539\) | 6.18198 | 0.266277 | ||||||||
\(540\) | −45.5226 | −1.95898 | ||||||||
\(541\) | 19.8357 | 0.852802 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(542\) | −14.0040 | −0.601521 | ||||||||
\(543\) | 71.1323 | 3.05258 | ||||||||
\(544\) | 0.0993160 | 0.00425814 | ||||||||
\(545\) | −17.7718 | −0.761262 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.35779 | −0.314596 | −0.157298 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157298 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(548\) | 6.17416 | 0.263747 | ||||||||
\(549\) | −93.7639 | −4.00174 | ||||||||
\(550\) | 9.52737 | 0.406248 | ||||||||
\(551\) | −3.34220 | −0.142383 | ||||||||
\(552\) | −24.6908 | −1.05091 | ||||||||
\(553\) | −42.3639 | −1.80150 | ||||||||
\(554\) | 9.57854 | 0.406953 | ||||||||
\(555\) | 65.2290 | 2.76882 | ||||||||
\(556\) | −6.61882 | −0.280700 | ||||||||
\(557\) | 13.4915 | 0.571654 | 0.285827 | − | 0.958281i | \(-0.407732\pi\) | ||||
0.285827 | + | 0.958281i | \(0.407732\pi\) | |||||||
\(558\) | 46.1064 | 1.95184 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.71534 | 0.368291 | ||||||||
\(561\) | −0.940868 | −0.0397235 | ||||||||
\(562\) | 0.150742 | 0.00635866 | ||||||||
\(563\) | −25.5347 | −1.07616 | −0.538079 | − | 0.842894i | \(-0.680850\pi\) | ||||
−0.538079 | + | 0.842894i | \(0.680850\pi\) | |||||||
\(564\) | −19.3349 | −0.814146 | ||||||||
\(565\) | −46.0993 | −1.93941 | ||||||||
\(566\) | −29.5322 | −1.24133 | ||||||||
\(567\) | 86.2055 | 3.62029 | ||||||||
\(568\) | 8.97303 | 0.376500 | ||||||||
\(569\) | −3.68679 | −0.154558 | −0.0772792 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772792 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(570\) | 9.47348 | 0.396800 | ||||||||
\(571\) | −2.85909 | −0.119649 | −0.0598246 | − | 0.998209i | \(-0.519054\pi\) | ||||
−0.0598246 | + | 0.998209i | \(0.519054\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.8134 | 1.41257 | ||||||||
\(574\) | 21.0094 | 0.876913 | ||||||||
\(575\) | 24.8312 | 1.03553 | ||||||||
\(576\) | 7.80527 | 0.325219 | ||||||||
\(577\) | −1.98920 | −0.0828114 | −0.0414057 | − | 0.999142i | \(-0.513184\pi\) | ||||
−0.0414057 | + | 0.999142i | \(0.513184\pi\) | |||||||
\(578\) | −16.9901 | −0.706697 | ||||||||
\(579\) | −73.9983 | −3.07526 | ||||||||
\(580\) | 9.63218 | 0.399955 | ||||||||
\(581\) | 30.3973 | 1.26109 | ||||||||
\(582\) | 54.0490 | 2.24040 | ||||||||
\(583\) | 26.4438 | 1.09519 | ||||||||
\(584\) | −0.646560 | −0.0267549 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.94681 | 0.163041 | ||||||||
\(587\) | 22.4820 | 0.927933 | 0.463967 | − | 0.885853i | \(-0.346426\pi\) | ||||
0.463967 | + | 0.885853i | \(0.346426\pi\) | |||||||
\(588\) | −7.05105 | −0.290780 | ||||||||
\(589\) | −5.90708 | −0.243397 | ||||||||
\(590\) | 2.46821 | 0.101615 | ||||||||
\(591\) | 23.1989 | 0.954277 | ||||||||
\(592\) | −6.88543 | −0.282990 | ||||||||
\(593\) | −20.4746 | −0.840789 | −0.420395 | − | 0.907341i | \(-0.638108\pi\) | ||||
−0.420395 | + | 0.907341i | \(0.638108\pi\) | |||||||
\(594\) | −45.5226 | −1.86781 | ||||||||
\(595\) | 0.865573 | 0.0354850 | ||||||||
\(596\) | −2.91053 | −0.119220 | ||||||||
\(597\) | −86.2585 | −3.53033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.90709 | −0.323075 | −0.161538 | − | 0.986867i | \(-0.551645\pi\) | ||||
−0.161538 | + | 0.986867i | \(0.551645\pi\) | |||||||
\(600\) | −10.8667 | −0.443633 | ||||||||
\(601\) | −5.32201 | −0.217089 | −0.108545 | − | 0.994092i | \(-0.534619\pi\) | ||||
−0.108545 | + | 0.994092i | \(0.534619\pi\) | |||||||
\(602\) | 18.4076 | 0.750239 | ||||||||
\(603\) | −89.4802 | −3.64392 | ||||||||
\(604\) | −3.38645 | −0.137793 | ||||||||
\(605\) | −7.76454 | −0.315673 | ||||||||
\(606\) | 31.9677 | 1.29860 | ||||||||
\(607\) | 19.0936 | 0.774985 | 0.387493 | − | 0.921873i | \(-0.373341\pi\) | ||||
0.387493 | + | 0.921873i | \(0.373341\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −33.2234 | −1.34628 | ||||||||
\(610\) | −34.6210 | −1.40176 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.775188 | 0.0313351 | ||||||||
\(613\) | 46.5932 | 1.88188 | 0.940941 | − | 0.338571i | \(-0.109943\pi\) | ||||
0.940941 | + | 0.338571i | \(0.109943\pi\) | |||||||
\(614\) | −0.213487 | −0.00861565 | ||||||||
\(615\) | −65.8156 | −2.65394 | ||||||||
\(616\) | 8.71534 | 0.351151 | ||||||||
\(617\) | 37.8493 | 1.52376 | 0.761878 | − | 0.647720i | \(-0.224278\pi\) | ||||
0.761878 | + | 0.647720i | \(0.224278\pi\) | |||||||
\(618\) | 43.0221 | 1.73060 | ||||||||
\(619\) | 25.6498 | 1.03095 | 0.515477 | − | 0.856904i | \(-0.327615\pi\) | ||||
0.515477 | + | 0.856904i | \(0.327615\pi\) | |||||||
\(620\) | 17.0241 | 0.683705 | ||||||||
\(621\) | −118.646 | −4.76109 | ||||||||
\(622\) | −30.1703 | −1.20972 | ||||||||
\(623\) | −2.87703 | −0.115266 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6006 | −1.22403 | ||||||||
\(626\) | −19.5575 | −0.781675 | ||||||||
\(627\) | 9.47348 | 0.378334 | ||||||||
\(628\) | 9.59018 | 0.382690 | ||||||||
\(629\) | −0.683834 | −0.0272662 | ||||||||
\(630\) | 68.0256 | 2.71020 | ||||||||
\(631\) | −37.2968 | −1.48476 | −0.742380 | − | 0.669979i | \(-0.766303\pi\) | ||||
−0.742380 | + | 0.669979i | \(0.766303\pi\) | |||||||
\(632\) | −14.0089 | −0.557243 | ||||||||
\(633\) | −37.1109 | −1.47502 | ||||||||
\(634\) | −6.31782 | −0.250913 | ||||||||
\(635\) | 3.32283 | 0.131863 | ||||||||
\(636\) | −30.1613 | −1.19597 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.63218 | 0.381342 | ||||||||
\(639\) | 70.0369 | 2.77062 | ||||||||
\(640\) | 2.88198 | 0.113920 | ||||||||
\(641\) | 17.1654 | 0.677991 | 0.338995 | − | 0.940788i | \(-0.389913\pi\) | ||||
0.338995 | + | 0.940788i | \(0.389913\pi\) | |||||||
\(642\) | −26.9940 | −1.06537 | ||||||||
\(643\) | −30.6064 | −1.20700 | −0.603500 | − | 0.797363i | \(-0.706228\pi\) | ||||
−0.603500 | + | 0.797363i | \(0.706228\pi\) | |||||||
\(644\) | 22.7148 | 0.895090 | ||||||||
\(645\) | −57.6653 | −2.27057 | ||||||||
\(646\) | −0.0993160 | −0.00390754 | ||||||||
\(647\) | −4.87167 | −0.191525 | −0.0957626 | − | 0.995404i | \(-0.530529\pi\) | ||||
−0.0957626 | + | 0.995404i | \(0.530529\pi\) | |||||||
\(648\) | 28.5064 | 1.11984 | ||||||||
\(649\) | 2.46821 | 0.0968857 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −58.7197 | −2.30141 | ||||||||
\(652\) | 4.35938 | 0.170726 | ||||||||
\(653\) | −12.0799 | −0.472725 | −0.236362 | − | 0.971665i | \(-0.575955\pi\) | ||||
−0.236362 | + | 0.971665i | \(0.575955\pi\) | |||||||
\(654\) | 20.2702 | 0.792629 | ||||||||
\(655\) | −26.6846 | −1.04265 | ||||||||
\(656\) | 6.94736 | 0.271249 | ||||||||
\(657\) | −5.04658 | −0.196886 | ||||||||
\(658\) | 17.7876 | 0.693432 | ||||||||
\(659\) | 33.0823 | 1.28870 | 0.644351 | − | 0.764730i | \(-0.277128\pi\) | ||||
0.644351 | + | 0.764730i | \(0.277128\pi\) | |||||||
\(660\) | −27.3024 | −1.06275 | ||||||||
\(661\) | −38.7512 | −1.50725 | −0.753624 | − | 0.657305i | \(-0.771696\pi\) | ||||
−0.753624 | + | 0.657305i | \(0.771696\pi\) | |||||||
\(662\) | 7.47193 | 0.290405 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.0518 | 0.390084 | ||||||||
\(665\) | −8.71534 | −0.337967 | ||||||||
\(666\) | −53.7426 | −2.08248 | ||||||||
\(667\) | 25.1044 | 0.972046 | ||||||||
\(668\) | 19.9405 | 0.771523 | ||||||||
\(669\) | −25.6717 | −0.992524 | ||||||||
\(670\) | −33.0393 | −1.27642 | ||||||||
\(671\) | −34.6210 | −1.33653 | ||||||||
\(672\) | −9.94055 | −0.383465 | ||||||||
\(673\) | 14.3390 | 0.552729 | 0.276365 | − | 0.961053i | \(-0.410870\pi\) | ||||
0.276365 | + | 0.961053i | \(0.410870\pi\) | |||||||
\(674\) | −3.39531 | −0.130783 | ||||||||
\(675\) | −52.2175 | −2.00985 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.46495 | −0.248468 | −0.124234 | − | 0.992253i | \(-0.539647\pi\) | ||||
−0.124234 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(678\) | 52.5800 | 2.01932 | ||||||||
\(679\) | −49.7236 | −1.90822 | ||||||||
\(680\) | 0.286227 | 0.0109763 | ||||||||
\(681\) | 20.7624 | 0.795616 | ||||||||
\(682\) | 17.0241 | 0.651887 | ||||||||
\(683\) | 17.8309 | 0.682280 | 0.341140 | − | 0.940012i | \(-0.389187\pi\) | ||||
0.341140 | + | 0.940012i | \(0.389187\pi\) | |||||||
\(684\) | −7.80527 | −0.298442 | ||||||||
\(685\) | 17.7938 | 0.679867 | ||||||||
\(686\) | −14.6818 | −0.560552 | ||||||||
\(687\) | 22.6786 | 0.865244 | ||||||||
\(688\) | 6.08702 | 0.232066 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −71.1584 | −2.70895 | ||||||||
\(691\) | 26.5402 | 1.00964 | 0.504819 | − | 0.863225i | \(-0.331559\pi\) | ||||
0.504819 | + | 0.863225i | \(0.331559\pi\) | |||||||
\(692\) | −4.85829 | −0.184685 | ||||||||
\(693\) | 68.0256 | 2.58408 | ||||||||
\(694\) | 1.90912 | 0.0724694 | ||||||||
\(695\) | −19.0753 | −0.723568 | ||||||||
\(696\) | −10.9863 | −0.416434 | ||||||||
\(697\) | 0.689984 | 0.0261350 | ||||||||
\(698\) | −26.1257 | −0.988874 | ||||||||
\(699\) | 7.86451 | 0.297463 | ||||||||
\(700\) | 9.99710 | 0.377855 | ||||||||
\(701\) | −30.9001 | −1.16708 | −0.583541 | − | 0.812083i | \(-0.698333\pi\) | ||||
−0.583541 | + | 0.812083i | \(0.698333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.88543 | 0.259689 | ||||||||
\(704\) | 2.88198 | 0.108619 | ||||||||
\(705\) | −55.7228 | −2.09864 | ||||||||
\(706\) | −11.5915 | −0.436250 | ||||||||
\(707\) | −29.4095 | −1.10606 | ||||||||
\(708\) | −2.81519 | −0.105801 | ||||||||
\(709\) | 31.0370 | 1.16562 | 0.582809 | − | 0.812609i | \(-0.301954\pi\) | ||||
0.582809 | + | 0.812609i | \(0.301954\pi\) | |||||||
\(710\) | 25.8601 | 0.970513 | ||||||||
\(711\) | −109.343 | −4.10068 | ||||||||
\(712\) | −0.951375 | −0.0356543 | ||||||||
\(713\) | 44.3700 | 1.66167 | ||||||||
\(714\) | −0.987256 | −0.0369471 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.5379 | −0.468563 | ||||||||
\(717\) | −70.9520 | −2.64975 | ||||||||
\(718\) | 4.12940 | 0.154108 | ||||||||
\(719\) | −21.3270 | −0.795362 | −0.397681 | − | 0.917524i | \(-0.630185\pi\) | ||||
−0.397681 | + | 0.917524i | \(0.630185\pi\) | |||||||
\(720\) | 22.4947 | 0.838326 | ||||||||
\(721\) | −39.5792 | −1.47401 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 53.9338 | 2.00582 | ||||||||
\(724\) | −21.6396 | −0.804229 | ||||||||
\(725\) | 11.0488 | 0.410341 | ||||||||
\(726\) | 8.85609 | 0.328680 | ||||||||
\(727\) | −2.45044 | −0.0908817 | −0.0454409 | − | 0.998967i | \(-0.514469\pi\) | ||||
−0.0454409 | + | 0.998967i | \(0.514469\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 66.7333 | 2.47161 | ||||||||
\(730\) | −1.86338 | −0.0689667 | ||||||||
\(731\) | 0.604539 | 0.0223597 | ||||||||
\(732\) | 39.4880 | 1.45952 | ||||||||
\(733\) | 14.7075 | 0.543235 | 0.271618 | − | 0.962405i | \(-0.412441\pi\) | ||||
0.271618 | + | 0.962405i | \(0.412441\pi\) | |||||||
\(734\) | 22.0476 | 0.813791 | ||||||||
\(735\) | −20.3210 | −0.749552 | ||||||||
\(736\) | 7.51133 | 0.276871 | ||||||||
\(737\) | −33.0393 | −1.21702 | ||||||||
\(738\) | 54.2260 | 1.99609 | ||||||||
\(739\) | −9.86821 | −0.363008 | −0.181504 | − | 0.983390i | \(-0.558097\pi\) | ||||
−0.181504 | + | 0.983390i | \(0.558097\pi\) | |||||||
\(740\) | −19.8437 | −0.729469 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.7476 | 1.01865 | ||||||||
\(743\) | −38.6841 | −1.41918 | −0.709591 | − | 0.704614i | \(-0.751120\pi\) | ||||
−0.709591 | + | 0.704614i | \(0.751120\pi\) | |||||||
\(744\) | −19.4174 | −0.711876 | ||||||||
\(745\) | −8.38811 | −0.307316 | ||||||||
\(746\) | 22.9777 | 0.841273 | ||||||||
\(747\) | 78.4567 | 2.87058 | ||||||||
\(748\) | 0.286227 | 0.0104655 | ||||||||
\(749\) | 24.8337 | 0.907405 | ||||||||
\(750\) | 16.0496 | 0.586049 | ||||||||
\(751\) | −22.6420 | −0.826217 | −0.413108 | − | 0.910682i | \(-0.635557\pi\) | ||||
−0.413108 | + | 0.910682i | \(0.635557\pi\) | |||||||
\(752\) | 5.88198 | 0.214494 | ||||||||
\(753\) | 61.1093 | 2.22695 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.75970 | −0.355192 | ||||||||
\(756\) | −47.7670 | −1.73727 | ||||||||
\(757\) | −13.1303 | −0.477229 | −0.238614 | − | 0.971114i | \(-0.576693\pi\) | ||||
−0.238614 | + | 0.971114i | \(0.576693\pi\) | |||||||
\(758\) | −10.1844 | −0.369915 | ||||||||
\(759\) | −71.1584 | −2.58289 | ||||||||
\(760\) | −2.88198 | −0.104541 | ||||||||
\(761\) | 16.9767 | 0.615407 | 0.307703 | − | 0.951482i | \(-0.400440\pi\) | ||||
0.307703 | + | 0.951482i | \(0.400440\pi\) | |||||||
\(762\) | −3.78996 | −0.137296 | ||||||||
\(763\) | −18.6481 | −0.675105 | ||||||||
\(764\) | −10.2866 | −0.372155 | ||||||||
\(765\) | 2.23408 | 0.0807733 | ||||||||
\(766\) | 34.1328 | 1.23327 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.28714 | −0.118614 | ||||||||
\(769\) | 5.94960 | 0.214548 | 0.107274 | − | 0.994230i | \(-0.465788\pi\) | ||||
0.107274 | + | 0.994230i | \(0.465788\pi\) | |||||||
\(770\) | 25.1175 | 0.905171 | ||||||||
\(771\) | −22.8806 | −0.824026 | ||||||||
\(772\) | 22.5115 | 0.810206 | ||||||||
\(773\) | −54.6636 | −1.96611 | −0.983056 | − | 0.183305i | \(-0.941320\pi\) | ||||
−0.983056 | + | 0.183305i | \(0.941320\pi\) | |||||||
\(774\) | 47.5108 | 1.70774 | ||||||||
\(775\) | 19.5278 | 0.701461 | ||||||||
\(776\) | −16.4426 | −0.590254 | ||||||||
\(777\) | 68.4450 | 2.45545 | ||||||||
\(778\) | −11.1658 | −0.400312 | ||||||||
\(779\) | −6.94736 | −0.248915 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8601 | 0.925348 | ||||||||
\(782\) | 0.745995 | 0.0266767 | ||||||||
\(783\) | −52.7920 | −1.88663 | ||||||||
\(784\) | 2.14504 | 0.0766087 | ||||||||
\(785\) | 27.6388 | 0.986470 | ||||||||
\(786\) | 30.4359 | 1.08561 | ||||||||
\(787\) | −39.4329 | −1.40563 | −0.702816 | − | 0.711372i | \(-0.748074\pi\) | ||||
−0.702816 | + | 0.711372i | \(0.748074\pi\) | |||||||
\(788\) | −7.05750 | −0.251413 | ||||||||
\(789\) | −5.55112 | −0.197625 | ||||||||
\(790\) | −40.3734 | −1.43642 | ||||||||
\(791\) | −48.3722 | −1.71992 | ||||||||
\(792\) | 22.4947 | 0.799313 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.89726 | 0.0673313 | ||||||||
\(795\) | −86.9245 | −3.08289 | ||||||||
\(796\) | 26.2412 | 0.930096 | ||||||||
\(797\) | −39.0593 | −1.38355 | −0.691776 | − | 0.722112i | \(-0.743171\pi\) | ||||
−0.691776 | + | 0.722112i | \(0.743171\pi\) | |||||||
\(798\) | 9.94055 | 0.351892 | ||||||||
\(799\) | 0.584175 | 0.0206666 | ||||||||
\(800\) | 3.30584 | 0.116879 | ||||||||
\(801\) | −7.42574 | −0.262376 | ||||||||
\(802\) | 30.7695 | 1.08651 | ||||||||
\(803\) | −1.86338 | −0.0657572 | ||||||||
\(804\) | 37.6840 | 1.32901 | ||||||||
\(805\) | 65.4638 | 2.30730 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −93.2456 | −3.28240 | ||||||||
\(808\) | −9.72510 | −0.342128 | ||||||||
\(809\) | 6.72501 | 0.236439 | 0.118219 | − | 0.992988i | \(-0.462281\pi\) | ||||
0.118219 | + | 0.992988i | \(0.462281\pi\) | |||||||
\(810\) | 82.1550 | 2.88663 | ||||||||
\(811\) | −18.0290 | −0.633083 | −0.316542 | − | 0.948579i | \(-0.602522\pi\) | ||||
−0.316542 | + | 0.948579i | \(0.602522\pi\) | |||||||
\(812\) | 10.1071 | 0.354689 | ||||||||
\(813\) | 46.0329 | 1.61444 | ||||||||
\(814\) | −19.8437 | −0.695522 | ||||||||
\(815\) | 12.5637 | 0.440086 | ||||||||
\(816\) | −0.326465 | −0.0114286 | ||||||||
\(817\) | −6.08702 | −0.212958 | ||||||||
\(818\) | −13.5808 | −0.474840 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0222 | 0.699205 | ||||||||
\(821\) | −41.6151 | −1.45238 | −0.726188 | − | 0.687496i | \(-0.758710\pi\) | ||||
−0.726188 | + | 0.687496i | \(0.758710\pi\) | |||||||
\(822\) | −20.2953 | −0.707880 | ||||||||
\(823\) | −21.2485 | −0.740678 | −0.370339 | − | 0.928897i | \(-0.620758\pi\) | ||||
−0.370339 | + | 0.928897i | \(0.620758\pi\) | |||||||
\(824\) | −13.0880 | −0.455943 | ||||||||
\(825\) | −31.3178 | −1.09034 | ||||||||
\(826\) | 2.58990 | 0.0901142 | ||||||||
\(827\) | 18.1628 | 0.631581 | 0.315791 | − | 0.948829i | \(-0.397730\pi\) | ||||
0.315791 | + | 0.948829i | \(0.397730\pi\) | |||||||
\(828\) | 58.6279 | 2.03746 | ||||||||
\(829\) | 5.54733 | 0.192667 | 0.0963334 | − | 0.995349i | \(-0.469288\pi\) | ||||
0.0963334 | + | 0.995349i | \(0.469288\pi\) | |||||||
\(830\) | 28.9690 | 1.00553 | ||||||||
\(831\) | −31.4860 | −1.09224 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.213037 | 0.00738130 | ||||||||
\(834\) | 21.7570 | 0.753382 | ||||||||
\(835\) | 57.4683 | 1.98877 | ||||||||
\(836\) | −2.88198 | −0.0996755 | ||||||||
\(837\) | −93.3057 | −3.22512 | ||||||||
\(838\) | 11.5178 | 0.397877 | ||||||||
\(839\) | −12.1478 | −0.419389 | −0.209695 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209695 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(840\) | −28.6485 | −0.988468 | ||||||||
\(841\) | −17.8297 | −0.614816 | ||||||||
\(842\) | −14.7578 | −0.508586 | ||||||||
\(843\) | −0.495509 | −0.0170662 | ||||||||
\(844\) | 11.2897 | 0.388608 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 45.9105 | 1.57843 | ||||||||
\(847\) | −8.14736 | −0.279947 | ||||||||
\(848\) | 9.17556 | 0.315090 | ||||||||
\(849\) | 97.0765 | 3.33166 | ||||||||
\(850\) | 0.328322 | 0.0112614 | ||||||||
\(851\) | −51.7187 | −1.77290 | ||||||||
\(852\) | −29.4956 | −1.01050 | ||||||||
\(853\) | 17.4434 | 0.597250 | 0.298625 | − | 0.954371i | \(-0.403472\pi\) | ||||
0.298625 | + | 0.954371i | \(0.403472\pi\) | |||||||
\(854\) | −36.3279 | −1.24312 | ||||||||
\(855\) | −22.4947 | −0.769301 | ||||||||
\(856\) | 8.21201 | 0.280681 | ||||||||
\(857\) | 2.87797 | 0.0983095 | 0.0491548 | − | 0.998791i | \(-0.484347\pi\) | ||||
0.0491548 | + | 0.998791i | \(0.484347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.4295 | −1.44767 | −0.723837 | − | 0.689971i | \(-0.757623\pi\) | ||||
−0.723837 | + | 0.689971i | \(0.757623\pi\) | |||||||
\(860\) | 17.5427 | 0.598201 | ||||||||
\(861\) | −69.0606 | −2.35358 | ||||||||
\(862\) | 0.0489741 | 0.00166807 | ||||||||
\(863\) | 36.3443 | 1.23717 | 0.618587 | − | 0.785716i | \(-0.287706\pi\) | ||||
0.618587 | + | 0.785716i | \(0.287706\pi\) | |||||||
\(864\) | −15.7956 | −0.537376 | ||||||||
\(865\) | −14.0015 | −0.476066 | ||||||||
\(866\) | 15.4388 | 0.524631 | ||||||||
\(867\) | 55.8489 | 1.89673 | ||||||||
\(868\) | 17.8635 | 0.606326 | ||||||||
\(869\) | −40.3734 | −1.36957 | ||||||||
\(870\) | −31.6623 | −1.07345 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.16653 | −0.208825 | ||||||||
\(873\) | −128.339 | −4.34361 | ||||||||
\(874\) | −7.51133 | −0.254074 | ||||||||
\(875\) | −14.7652 | −0.499156 | ||||||||
\(876\) | 2.12533 | 0.0718083 | ||||||||
\(877\) | 55.0880 | 1.86019 | 0.930094 | − | 0.367321i | \(-0.119725\pi\) | ||||
0.930094 | + | 0.367321i | \(0.119725\pi\) | |||||||
\(878\) | 23.4821 | 0.792482 | ||||||||
\(879\) | −12.9737 | −0.437592 | ||||||||
\(880\) | 8.30584 | 0.279990 | ||||||||
\(881\) | −43.6793 | −1.47159 | −0.735797 | − | 0.677202i | \(-0.763192\pi\) | ||||
−0.735797 | + | 0.677202i | \(0.763192\pi\) | |||||||
\(882\) | 16.7426 | 0.563754 | ||||||||
\(883\) | −11.2873 | −0.379849 | −0.189925 | − | 0.981799i | \(-0.560824\pi\) | ||||
−0.189925 | + | 0.981799i | \(0.560824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.11335 | −0.272727 | ||||||||
\(886\) | −0.851887 | −0.0286197 | ||||||||
\(887\) | 50.8257 | 1.70656 | 0.853280 | − | 0.521453i | \(-0.174610\pi\) | ||||
0.853280 | + | 0.521453i | \(0.174610\pi\) | |||||||
\(888\) | 22.6334 | 0.759526 | ||||||||
\(889\) | 3.48666 | 0.116939 | ||||||||
\(890\) | −2.74185 | −0.0919070 | ||||||||
\(891\) | 82.1550 | 2.75229 | ||||||||
\(892\) | 7.80973 | 0.261489 | ||||||||
\(893\) | −5.88198 | −0.196833 | ||||||||
\(894\) | 9.56731 | 0.319979 | ||||||||
\(895\) | −36.1340 | −1.20783 | ||||||||
\(896\) | 3.02408 | 0.101027 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.3624 | 1.24680 | ||||||||
\(899\) | 19.7427 | 0.658455 | ||||||||
\(900\) | 25.8029 | 0.860098 | ||||||||
\(901\) | 0.911280 | 0.0303592 | ||||||||
\(902\) | 20.0222 | 0.666666 | ||||||||
\(903\) | −60.5084 | −2.01359 | ||||||||
\(904\) | −15.9957 | −0.532008 | ||||||||
\(905\) | −62.3650 | −2.07308 | ||||||||
\(906\) | 11.1317 | 0.369827 | ||||||||
\(907\) | 7.63723 | 0.253590 | 0.126795 | − | 0.991929i | \(-0.459531\pi\) | ||||
0.126795 | + | 0.991929i | \(0.459531\pi\) | |||||||
\(908\) | −6.31625 | −0.209612 | ||||||||
\(909\) | −75.9070 | −2.51768 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.2286 | 0.338889 | 0.169445 | − | 0.985540i | \(-0.445803\pi\) | ||||
0.169445 | + | 0.985540i | \(0.445803\pi\) | |||||||
\(912\) | 3.28714 | 0.108848 | ||||||||
\(913\) | 28.9690 | 0.958735 | ||||||||
\(914\) | −18.0321 | −0.596448 | ||||||||
\(915\) | 113.804 | 3.76224 | ||||||||
\(916\) | −6.89920 | −0.227956 | ||||||||
\(917\) | −28.0002 | −0.924649 | ||||||||
\(918\) | −1.56875 | −0.0517765 | ||||||||
\(919\) | 36.6393 | 1.20862 | 0.604310 | − | 0.796749i | \(-0.293449\pi\) | ||||
0.604310 | + | 0.796749i | \(0.293449\pi\) | |||||||
\(920\) | 21.6475 | 0.713698 | ||||||||
\(921\) | 0.701762 | 0.0231239 | ||||||||
\(922\) | −20.5994 | −0.678406 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −28.6485 | −0.942467 | ||||||||
\(925\) | −22.7621 | −0.748414 | ||||||||
\(926\) | 0.835400 | 0.0274529 | ||||||||
\(927\) | −102.156 | −3.35523 | ||||||||
\(928\) | 3.34220 | 0.109713 | ||||||||
\(929\) | 2.79520 | 0.0917076 | 0.0458538 | − | 0.998948i | \(-0.485399\pi\) | ||||
0.0458538 | + | 0.998948i | \(0.485399\pi\) | |||||||
\(930\) | −55.9606 | −1.83502 | ||||||||
\(931\) | −2.14504 | −0.0703010 | ||||||||
\(932\) | −2.39251 | −0.0783693 | ||||||||
\(933\) | 99.1738 | 3.24680 | ||||||||
\(934\) | 4.94829 | 0.161913 | ||||||||
\(935\) | 0.824902 | 0.0269772 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0454 | 0.752862 | 0.376431 | − | 0.926445i | \(-0.377151\pi\) | ||||
0.376431 | + | 0.926445i | \(0.377151\pi\) | |||||||
\(938\) | −34.6683 | −1.13196 | ||||||||
\(939\) | 64.2882 | 2.09796 | ||||||||
\(940\) | 16.9518 | 0.552906 | ||||||||
\(941\) | 2.39612 | 0.0781114 | 0.0390557 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390557 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(942\) | −31.5242 | −1.02712 | ||||||||
\(943\) | 52.1839 | 1.69934 | ||||||||
\(944\) | 0.856427 | 0.0278743 | ||||||||
\(945\) | −137.664 | −4.47820 | ||||||||
\(946\) | 17.5427 | 0.570363 | ||||||||
\(947\) | 41.5019 | 1.34863 | 0.674315 | − | 0.738444i | \(-0.264439\pi\) | ||||
0.674315 | + | 0.738444i | \(0.264439\pi\) | |||||||
\(948\) | 46.0491 | 1.49561 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.30584 | −0.107255 | ||||||||
\(951\) | 20.7675 | 0.673434 | ||||||||
\(952\) | 0.300339 | 0.00973405 | ||||||||
\(953\) | 13.9965 | 0.453390 | 0.226695 | − | 0.973966i | \(-0.427208\pi\) | ||||
0.226695 | + | 0.973966i | \(0.427208\pi\) | |||||||
\(954\) | 71.6177 | 2.31871 | ||||||||
\(955\) | −29.6457 | −0.959313 | ||||||||
\(956\) | 21.5847 | 0.698100 | ||||||||
\(957\) | −31.6623 | −1.02350 | ||||||||
\(958\) | 3.05994 | 0.0988622 | ||||||||
\(959\) | 18.6711 | 0.602922 | ||||||||
\(960\) | −9.47348 | −0.305755 | ||||||||
\(961\) | 3.89363 | 0.125601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 64.0969 | 2.06549 | ||||||||
\(964\) | −16.4075 | −0.528451 | ||||||||
\(965\) | 64.8777 | 2.08849 | ||||||||
\(966\) | −74.6667 | −2.40236 | ||||||||
\(967\) | 5.30132 | 0.170479 | 0.0852394 | − | 0.996360i | \(-0.472834\pi\) | ||||
0.0852394 | + | 0.996360i | \(0.472834\pi\) | |||||||
\(968\) | −2.69416 | −0.0865937 | ||||||||
\(969\) | 0.326465 | 0.0104876 | ||||||||
\(970\) | −47.3873 | −1.52151 | ||||||||
\(971\) | 42.2763 | 1.35671 | 0.678355 | − | 0.734734i | \(-0.262693\pi\) | ||||
0.678355 | + | 0.734734i | \(0.262693\pi\) | |||||||
\(972\) | −46.3177 | −1.48564 | ||||||||
\(973\) | −20.0158 | −0.641677 | ||||||||
\(974\) | −12.8479 | −0.411672 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0129 | −0.384523 | ||||||||
\(977\) | −15.7624 | −0.504282 | −0.252141 | − | 0.967690i | \(-0.581135\pi\) | ||||
−0.252141 | + | 0.967690i | \(0.581135\pi\) | |||||||
\(978\) | −14.3299 | −0.458219 | ||||||||
\(979\) | −2.74185 | −0.0876299 | ||||||||
\(980\) | 6.18198 | 0.197476 | ||||||||
\(981\) | −48.1314 | −1.53672 | ||||||||
\(982\) | 12.0690 | 0.385136 | ||||||||
\(983\) | −23.2214 | −0.740647 | −0.370324 | − | 0.928903i | \(-0.620753\pi\) | ||||
−0.370324 | + | 0.928903i | \(0.620753\pi\) | |||||||
\(984\) | −22.8369 | −0.728014 | ||||||||
\(985\) | −20.3396 | −0.648073 | ||||||||
\(986\) | 0.331934 | 0.0105709 | ||||||||
\(987\) | −58.4702 | −1.86113 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.7216 | 1.45386 | ||||||||
\(990\) | 64.8293 | 2.06041 | ||||||||
\(991\) | 4.63538 | 0.147248 | 0.0736239 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736239 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(992\) | 5.90708 | 0.187550 | ||||||||
\(993\) | −24.5613 | −0.779428 | ||||||||
\(994\) | 27.1351 | 0.860674 | ||||||||
\(995\) | 75.6268 | 2.39753 | ||||||||
\(996\) | −33.0415 | −1.04696 | ||||||||
\(997\) | −11.7982 | −0.373652 | −0.186826 | − | 0.982393i | \(-0.559820\pi\) | ||||
−0.186826 | + | 0.982393i | \(0.559820\pi\) | |||||||
\(998\) | 35.1067 | 1.11128 | ||||||||
\(999\) | 108.759 | 3.44099 |
(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 | 6422.2.a.bd.1.1 | 6 | ||
13.3 | even | 3 | 494.2.g.f.191.6 | ✓ | 12 | ||
13.9 | even | 3 | 494.2.g.f.419.6 | yes | 12 | ||
13.12 | even | 2 | 6422.2.a.bc.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.g.f.191.6 | ✓ | 12 | 13.3 | even | 3 | ||
494.2.g.f.419.6 | yes | 12 | 13.9 | even | 3 | ||
6422.2.a.bc.1.1 | 6 | 13.12 | even | 2 | |||
6422.2.a.bd.1.1 | 6 | 1.1 | even | 1 | trivial |