Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1449,2,Mod(1,1449)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1449, 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("1449.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1449 = 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1449.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: | \(11.5703232529\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.24197.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 6x^{2} - x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.509552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1449.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.509552 | 0.360308 | 0.180154 | − | 0.983638i | \(-0.442340\pi\) | ||||
0.180154 | + | 0.983638i | \(0.442340\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.74036 | −0.870178 | ||||||||
\(5\) | −4.41546 | −1.97465 | −0.987327 | − | 0.158699i | \(-0.949270\pi\) | ||||
−0.987327 | + | 0.158699i | \(0.949270\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.90591 | −0.673840 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.24991 | −0.711484 | ||||||||
\(11\) | 1.67510 | 0.505063 | 0.252531 | − | 0.967589i | \(-0.418737\pi\) | ||||
0.252531 | + | 0.967589i | \(0.418737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.66537 | −1.29394 | −0.646970 | − | 0.762515i | \(-0.723964\pi\) | ||||
−0.646970 | + | 0.762515i | \(0.723964\pi\) | |||||||
\(14\) | 0.509552 | 0.136184 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50955 | 0.627388 | ||||||||
\(17\) | −6.24991 | −1.51583 | −0.757913 | − | 0.652356i | \(-0.773781\pi\) | ||||
−0.757913 | + | 0.652356i | \(0.773781\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.694209 | −0.159262 | −0.0796312 | − | 0.996824i | \(-0.525374\pi\) | ||||
−0.0796312 | + | 0.996824i | \(0.525374\pi\) | |||||||
\(20\) | 7.68447 | 1.71830 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.853553 | 0.181978 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.4963 | 2.89926 | ||||||||
\(26\) | −2.37725 | −0.466217 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.74036 | −0.328896 | ||||||||
\(29\) | −5.60012 | −1.03992 | −0.519958 | − | 0.854192i | \(-0.674052\pi\) | ||||
−0.519958 | + | 0.854192i | \(0.674052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.24991 | 0.763306 | 0.381653 | − | 0.924306i | \(-0.375355\pi\) | ||||
0.381653 | + | 0.924306i | \(0.375355\pi\) | |||||||
\(32\) | 5.09056 | 0.899893 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.18466 | −0.546164 | ||||||||
\(35\) | −4.41546 | −0.746349 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.26901 | 1.52382 | 0.761908 | − | 0.647685i | \(-0.224263\pi\) | ||||
0.761908 | + | 0.647685i | \(0.224263\pi\) | |||||||
\(38\) | −0.353736 | −0.0573835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.41546 | 1.33060 | ||||||||
\(41\) | 5.15582 | 0.805203 | 0.402602 | − | 0.915375i | \(-0.368106\pi\) | ||||
0.402602 | + | 0.915375i | \(0.368106\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.20376 | 0.641068 | 0.320534 | − | 0.947237i | \(-0.396138\pi\) | ||||
0.320534 | + | 0.947237i | \(0.396138\pi\) | |||||||
\(44\) | −2.91528 | −0.439495 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.509552 | 0.0751294 | ||||||||
\(47\) | 1.92501 | 0.280792 | 0.140396 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140396 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.38662 | 1.04463 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.11940 | 1.12596 | ||||||||
\(53\) | 1.84066 | 0.252833 | 0.126417 | − | 0.991977i | \(-0.459652\pi\) | ||||
0.126417 | + | 0.991977i | \(0.459652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.39636 | −0.997324 | ||||||||
\(56\) | −1.90591 | −0.254688 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.85355 | −0.374690 | ||||||||
\(59\) | −9.39779 | −1.22349 | −0.611744 | − | 0.791056i | \(-0.709532\pi\) | ||||
−0.611744 | + | 0.791056i | \(0.709532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.72125 | 0.988605 | 0.494302 | − | 0.869290i | \(-0.335424\pi\) | ||||
0.494302 | + | 0.869290i | \(0.335424\pi\) | |||||||
\(62\) | 2.16555 | 0.275025 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.42520 | −0.303149 | ||||||||
\(65\) | 20.5998 | 2.55508 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.22728 | −1.00512 | −0.502561 | − | 0.864542i | \(-0.667609\pi\) | ||||
−0.502561 | + | 0.864542i | \(0.667609\pi\) | |||||||
\(68\) | 10.8771 | 1.31904 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.24991 | −0.268916 | ||||||||
\(71\) | 10.6654 | 1.26575 | 0.632873 | − | 0.774255i | \(-0.281875\pi\) | ||||
0.632873 | + | 0.774255i | \(0.281875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9117 | −1.39416 | −0.697082 | − | 0.716991i | \(-0.745519\pi\) | ||||
−0.697082 | + | 0.716991i | \(0.745519\pi\) | |||||||
\(74\) | 4.72305 | 0.549043 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.20817 | 0.138587 | ||||||||
\(77\) | 1.67510 | 0.190896 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.581012 | 0.0653689 | 0.0326845 | − | 0.999466i | \(-0.489594\pi\) | ||||
0.0326845 | + | 0.999466i | \(0.489594\pi\) | |||||||
\(80\) | −11.0808 | −1.23887 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.62716 | 0.290121 | ||||||||
\(83\) | −6.95032 | −0.762897 | −0.381449 | − | 0.924390i | \(-0.624575\pi\) | ||||
−0.381449 | + | 0.924390i | \(0.624575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 27.5962 | 2.99323 | ||||||||
\(86\) | 2.14204 | 0.230982 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.19259 | −0.340332 | ||||||||
\(89\) | 13.4963 | 1.43060 | 0.715302 | − | 0.698816i | \(-0.246289\pi\) | ||||
0.715302 | + | 0.698816i | \(0.246289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.66537 | −0.489064 | ||||||||
\(92\) | −1.74036 | −0.181445 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.980895 | 0.101172 | ||||||||
\(95\) | 3.06525 | 0.314488 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0999 | 1.02549 | 0.512746 | − | 0.858540i | \(-0.328628\pi\) | ||||
0.512746 | + | 0.858540i | \(0.328628\pi\) | |||||||
\(98\) | 0.509552 | 0.0514726 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.2287 | −2.52287 | ||||||||
\(101\) | 13.7830 | 1.37146 | 0.685729 | − | 0.727857i | \(-0.259484\pi\) | ||||
0.685729 | + | 0.727857i | \(0.259484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5553 | 1.63125 | 0.815623 | − | 0.578584i | \(-0.196395\pi\) | ||||
0.815623 | + | 0.578584i | \(0.196395\pi\) | |||||||
\(104\) | 8.89176 | 0.871909 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.937911 | 0.0910979 | ||||||||
\(107\) | 1.33463 | 0.129024 | 0.0645118 | − | 0.997917i | \(-0.479451\pi\) | ||||
0.0645118 | + | 0.997917i | \(0.479451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00794 | 0.383891 | 0.191945 | − | 0.981406i | \(-0.438520\pi\) | ||||
0.191945 | + | 0.981406i | \(0.438520\pi\) | |||||||
\(110\) | −3.76883 | −0.359344 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.50955 | 0.237130 | ||||||||
\(113\) | 9.06525 | 0.852787 | 0.426394 | − | 0.904538i | \(-0.359784\pi\) | ||||
0.426394 | + | 0.904538i | \(0.359784\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.41546 | −0.411744 | ||||||||
\(116\) | 9.74620 | 0.904912 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.78867 | −0.440832 | ||||||||
\(119\) | −6.24991 | −0.572928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.19403 | −0.744911 | ||||||||
\(122\) | 3.93438 | 0.356202 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.39636 | −0.664212 | ||||||||
\(125\) | −41.9305 | −3.75038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.4977 | −1.90761 | −0.953807 | − | 0.300419i | \(-0.902873\pi\) | ||||
−0.953807 | + | 0.300419i | \(0.902873\pi\) | |||||||
\(128\) | −11.4169 | −1.00912 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.4967 | 0.920618 | ||||||||
\(131\) | −1.17529 | −0.102685 | −0.0513426 | − | 0.998681i | \(-0.516350\pi\) | ||||
−0.0513426 | + | 0.998681i | \(0.516350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.694209 | −0.0601956 | ||||||||
\(134\) | −4.19223 | −0.362153 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.9117 | 1.02142 | ||||||||
\(137\) | −15.8562 | −1.35469 | −0.677345 | − | 0.735666i | \(-0.736869\pi\) | ||||
−0.677345 | + | 0.735666i | \(0.736869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.93438 | −0.164072 | −0.0820361 | − | 0.996629i | \(-0.526142\pi\) | ||||
−0.0820361 | + | 0.996629i | \(0.526142\pi\) | |||||||
\(140\) | 7.68447 | 0.649457 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.43457 | 0.456059 | ||||||||
\(143\) | −7.81498 | −0.653521 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.7271 | 2.05347 | ||||||||
\(146\) | −6.06966 | −0.502329 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.1314 | −1.32599 | ||||||||
\(149\) | −2.61301 | −0.214067 | −0.107033 | − | 0.994255i | \(-0.534135\pi\) | ||||
−0.107033 | + | 0.994255i | \(0.534135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.26281 | −0.753797 | −0.376898 | − | 0.926255i | \(-0.623009\pi\) | ||||
−0.376898 | + | 0.926255i | \(0.623009\pi\) | |||||||
\(152\) | 1.32310 | 0.107317 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.853553 | 0.0687813 | ||||||||
\(155\) | −18.7653 | −1.50727 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.77504 | −0.620516 | −0.310258 | − | 0.950652i | \(-0.600415\pi\) | ||||
−0.310258 | + | 0.950652i | \(0.600415\pi\) | |||||||
\(158\) | 0.296056 | 0.0235530 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −22.4772 | −1.77698 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.12077 | −0.557742 | −0.278871 | − | 0.960329i | \(-0.589960\pi\) | ||||
−0.278871 | + | 0.960329i | \(0.589960\pi\) | |||||||
\(164\) | −8.97296 | −0.700670 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.54156 | −0.274878 | ||||||||
\(167\) | 11.9867 | 0.927562 | 0.463781 | − | 0.885950i | \(-0.346493\pi\) | ||||
0.463781 | + | 0.885950i | \(0.346493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.76567 | 0.674282 | ||||||||
\(170\) | 14.0617 | 1.07849 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.31604 | −0.557843 | ||||||||
\(173\) | 2.09993 | 0.159655 | 0.0798275 | − | 0.996809i | \(-0.474563\pi\) | ||||
0.0798275 | + | 0.996809i | \(0.474563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.4963 | 1.09582 | ||||||||
\(176\) | 4.20376 | 0.316870 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.87707 | 0.515458 | ||||||||
\(179\) | 15.9726 | 1.19385 | 0.596924 | − | 0.802298i | \(-0.296389\pi\) | ||||
0.596924 | + | 0.802298i | \(0.296389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.89970 | −0.215533 | −0.107767 | − | 0.994176i | \(-0.534370\pi\) | ||||
−0.107767 | + | 0.994176i | \(0.534370\pi\) | |||||||
\(182\) | −2.37725 | −0.176214 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.90591 | −0.140505 | ||||||||
\(185\) | −40.9270 | −3.00901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4692 | −0.765587 | ||||||||
\(188\) | −3.35021 | −0.244339 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.56191 | 0.113313 | ||||||||
\(191\) | 21.5486 | 1.55921 | 0.779603 | − | 0.626275i | \(-0.215421\pi\) | ||||
0.779603 | + | 0.626275i | \(0.215421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.58722 | 0.330195 | 0.165098 | − | 0.986277i | \(-0.447206\pi\) | ||||
0.165098 | + | 0.986277i | \(0.447206\pi\) | |||||||
\(194\) | 5.14645 | 0.369493 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.74036 | −0.124311 | ||||||||
\(197\) | 11.8656 | 0.845389 | 0.422695 | − | 0.906272i | \(-0.361084\pi\) | ||||
0.422695 | + | 0.906272i | \(0.361084\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.52866 | −0.179252 | −0.0896259 | − | 0.995976i | \(-0.528567\pi\) | ||||
−0.0896259 | + | 0.995976i | \(0.528567\pi\) | |||||||
\(200\) | −27.6286 | −1.95364 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.02315 | 0.494147 | ||||||||
\(203\) | −5.60012 | −0.393051 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.7653 | −1.59000 | ||||||||
\(206\) | 8.43581 | 0.587751 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.7080 | −0.811803 | ||||||||
\(209\) | −1.16287 | −0.0804376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.9797 | −1.51314 | −0.756572 | − | 0.653911i | \(-0.773127\pi\) | ||||
−0.756572 | + | 0.653911i | \(0.773127\pi\) | |||||||
\(212\) | −3.20340 | −0.220010 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.680065 | 0.0464883 | ||||||||
\(215\) | −18.5615 | −1.26589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.24991 | 0.288503 | ||||||||
\(218\) | 2.04225 | 0.138319 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.8723 | 0.867850 | ||||||||
\(221\) | 29.1581 | 1.96139 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0302726 | 0.00202720 | 0.00101360 | − | 0.999999i | \(-0.499677\pi\) | ||||
0.00101360 | + | 0.999999i | \(0.499677\pi\) | |||||||
\(224\) | 5.09056 | 0.340128 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.61922 | 0.307266 | ||||||||
\(227\) | −21.2393 | −1.40970 | −0.704852 | − | 0.709355i | \(-0.748986\pi\) | ||||
−0.704852 | + | 0.709355i | \(0.748986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.4360 | 1.15220 | 0.576102 | − | 0.817378i | \(-0.304573\pi\) | ||||
0.576102 | + | 0.817378i | \(0.304573\pi\) | |||||||
\(230\) | −2.24991 | −0.148355 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.6733 | 0.700737 | ||||||||
\(233\) | 11.2082 | 0.734272 | 0.367136 | − | 0.930167i | \(-0.380338\pi\) | ||||
0.367136 | + | 0.930167i | \(0.380338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.49982 | −0.554467 | ||||||||
\(236\) | 16.3555 | 1.06465 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.18466 | −0.206431 | ||||||||
\(239\) | 18.5654 | 1.20090 | 0.600449 | − | 0.799663i | \(-0.294989\pi\) | ||||
0.600449 | + | 0.799663i | \(0.294989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6556 | −0.879637 | −0.439818 | − | 0.898087i | \(-0.644957\pi\) | ||||
−0.439818 | + | 0.898087i | \(0.644957\pi\) | |||||||
\(242\) | −4.17529 | −0.268398 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.4377 | −0.860262 | ||||||||
\(245\) | −4.41546 | −0.282093 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.23874 | 0.206076 | ||||||||
\(248\) | −8.09993 | −0.514346 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.3658 | −1.35129 | ||||||||
\(251\) | −0.604526 | −0.0381574 | −0.0190787 | − | 0.999818i | \(-0.506073\pi\) | ||||
−0.0190787 | + | 0.999818i | \(0.506073\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.67510 | 0.105313 | ||||||||
\(254\) | −10.9542 | −0.687329 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.967116 | −0.0604447 | ||||||||
\(257\) | −14.1602 | −0.883291 | −0.441645 | − | 0.897190i | \(-0.645605\pi\) | ||||
−0.441645 | + | 0.897190i | \(0.645605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.26901 | 0.575948 | ||||||||
\(260\) | −35.8509 | −2.22338 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.598870 | −0.0369983 | ||||||||
\(263\) | −20.5788 | −1.26895 | −0.634473 | − | 0.772945i | \(-0.718783\pi\) | ||||
−0.634473 | + | 0.772945i | \(0.718783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.12734 | −0.499259 | ||||||||
\(266\) | −0.353736 | −0.0216889 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.3184 | 0.874635 | ||||||||
\(269\) | 0.496655 | 0.0302816 | 0.0151408 | − | 0.999885i | \(-0.495180\pi\) | ||||
0.0151408 | + | 0.999885i | \(0.495180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0547 | 1.46122 | 0.730609 | − | 0.682797i | \(-0.239236\pi\) | ||||
0.730609 | + | 0.682797i | \(0.239236\pi\) | |||||||
\(272\) | −15.6845 | −0.951011 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.07958 | −0.488105 | ||||||||
\(275\) | 24.2828 | 1.46431 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.2402 | 1.39637 | 0.698183 | − | 0.715919i | \(-0.253992\pi\) | ||||
0.698183 | + | 0.715919i | \(0.253992\pi\) | |||||||
\(278\) | −0.985670 | −0.0591165 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.41546 | 0.502920 | ||||||||
\(281\) | 15.0697 | 0.898985 | 0.449492 | − | 0.893284i | \(-0.351605\pi\) | ||||
0.449492 | + | 0.893284i | \(0.351605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.22691 | 0.548483 | 0.274241 | − | 0.961661i | \(-0.411573\pi\) | ||||
0.274241 | + | 0.961661i | \(0.411573\pi\) | |||||||
\(284\) | −18.5615 | −1.10142 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.98214 | −0.235469 | ||||||||
\(287\) | 5.15582 | 0.304338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.0614 | 1.29773 | ||||||||
\(290\) | 12.5998 | 0.739883 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.7307 | 1.21317 | ||||||||
\(293\) | 12.3881 | 0.723718 | 0.361859 | − | 0.932233i | \(-0.382142\pi\) | ||||
0.361859 | + | 0.932233i | \(0.382142\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.4956 | 2.41596 | ||||||||
\(296\) | −17.6659 | −1.02681 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.33147 | −0.0771299 | ||||||||
\(299\) | −4.66537 | −0.269805 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.20376 | 0.242301 | ||||||||
\(302\) | −4.71989 | −0.271599 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.74215 | −0.0999194 | ||||||||
\(305\) | −34.0929 | −1.95215 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.823281 | 0.0469871 | 0.0234936 | − | 0.999724i | \(-0.492521\pi\) | ||||
0.0234936 | + | 0.999724i | \(0.492521\pi\) | |||||||
\(308\) | −2.91528 | −0.166113 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.56191 | −0.543080 | ||||||||
\(311\) | 30.6632 | 1.73875 | 0.869375 | − | 0.494152i | \(-0.164521\pi\) | ||||
0.869375 | + | 0.494152i | \(0.164521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1323 | 0.742282 | 0.371141 | − | 0.928577i | \(-0.378967\pi\) | ||||
0.371141 | + | 0.928577i | \(0.378967\pi\) | |||||||
\(314\) | −3.96179 | −0.223577 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.01117 | −0.0568826 | ||||||||
\(317\) | 15.2269 | 0.855229 | 0.427614 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427614 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.38078 | −0.525223 | ||||||||
\(320\) | 10.7084 | 0.598615 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.509552 | 0.0283962 | ||||||||
\(323\) | 4.33874 | 0.241414 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −67.6305 | −3.75147 | ||||||||
\(326\) | −3.62841 | −0.200959 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.82651 | −0.542578 | ||||||||
\(329\) | 1.92501 | 0.106129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.5674 | 1.40531 | 0.702655 | − | 0.711530i | \(-0.251998\pi\) | ||||
0.702655 | + | 0.711530i | \(0.251998\pi\) | |||||||
\(332\) | 12.0960 | 0.663857 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.10787 | 0.334208 | ||||||||
\(335\) | 36.3272 | 1.98477 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.2890 | 0.887318 | 0.443659 | − | 0.896196i | \(-0.353680\pi\) | ||||
0.443659 | + | 0.896196i | \(0.353680\pi\) | |||||||
\(338\) | 4.46657 | 0.242949 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −48.0273 | −2.60464 | ||||||||
\(341\) | 7.11904 | 0.385518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.01198 | −0.431977 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.07003 | 0.0575250 | ||||||||
\(347\) | −21.6729 | −1.16346 | −0.581732 | − | 0.813380i | \(-0.697625\pi\) | ||||
−0.581732 | + | 0.813380i | \(0.697625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.5198 | −1.15193 | −0.575964 | − | 0.817475i | \(-0.695373\pi\) | ||||
−0.575964 | + | 0.817475i | \(0.695373\pi\) | |||||||
\(350\) | 7.38662 | 0.394831 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.52722 | 0.454503 | ||||||||
\(353\) | 20.1852 | 1.07435 | 0.537174 | − | 0.843471i | \(-0.319492\pi\) | ||||
0.537174 | + | 0.843471i | \(0.319492\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −47.0925 | −2.49941 | ||||||||
\(356\) | −23.4884 | −1.24488 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.13887 | 0.430153 | ||||||||
\(359\) | −23.2492 | −1.22705 | −0.613524 | − | 0.789676i | \(-0.710249\pi\) | ||||
−0.613524 | + | 0.789676i | \(0.710249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5181 | −0.974635 | ||||||||
\(362\) | −1.47755 | −0.0776583 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.11940 | 0.425572 | ||||||||
\(365\) | 52.5959 | 2.75299 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7171 | 1.44682 | 0.723409 | − | 0.690419i | \(-0.242574\pi\) | ||||
0.723409 | + | 0.690419i | \(0.242574\pi\) | |||||||
\(368\) | 2.50955 | 0.130819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −20.8544 | −1.08417 | ||||||||
\(371\) | 1.84066 | 0.0955621 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.7303 | −1.28048 | −0.640242 | − | 0.768173i | \(-0.721166\pi\) | ||||
−0.640242 | + | 0.768173i | \(0.721166\pi\) | |||||||
\(374\) | −5.33463 | −0.275847 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.66890 | −0.189209 | ||||||||
\(377\) | 26.1266 | 1.34559 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.11140 | −0.159822 | −0.0799109 | − | 0.996802i | \(-0.525464\pi\) | ||||
−0.0799109 | + | 0.996802i | \(0.525464\pi\) | |||||||
\(380\) | −5.33463 | −0.273661 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.9802 | 0.561794 | ||||||||
\(383\) | 18.9503 | 0.968316 | 0.484158 | − | 0.874980i | \(-0.339126\pi\) | ||||
0.484158 | + | 0.874980i | \(0.339126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.39636 | −0.376953 | ||||||||
\(386\) | 2.33743 | 0.118972 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.5775 | −0.892362 | ||||||||
\(389\) | 20.1693 | 1.02262 | 0.511312 | − | 0.859395i | \(-0.329160\pi\) | ||||
0.511312 | + | 0.859395i | \(0.329160\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.24991 | −0.316071 | ||||||||
\(392\) | −1.90591 | −0.0962629 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.04615 | 0.304600 | ||||||||
\(395\) | −2.56543 | −0.129081 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.41634 | 0.422404 | 0.211202 | − | 0.977442i | \(-0.432262\pi\) | ||||
0.211202 | + | 0.977442i | \(0.432262\pi\) | |||||||
\(398\) | −1.28848 | −0.0645859 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 36.3792 | 1.81896 | ||||||||
\(401\) | 5.86329 | 0.292799 | 0.146399 | − | 0.989226i | \(-0.453232\pi\) | ||||
0.146399 | + | 0.989226i | \(0.453232\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.8274 | −0.987673 | ||||||||
\(404\) | −23.9873 | −1.19341 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.85355 | −0.141619 | ||||||||
\(407\) | 15.5266 | 0.769623 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.2686 | −1.29890 | −0.649451 | − | 0.760404i | \(-0.725001\pi\) | ||||
−0.649451 | + | 0.760404i | \(0.725001\pi\) | |||||||
\(410\) | −11.6001 | −0.572889 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.8122 | −1.41947 | ||||||||
\(413\) | −9.39779 | −0.462435 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.6889 | 1.50646 | ||||||||
\(416\) | −23.7494 | −1.16441 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.592544 | −0.0289823 | ||||||||
\(419\) | 0.800648 | 0.0391142 | 0.0195571 | − | 0.999809i | \(-0.493774\pi\) | ||||
0.0195571 | + | 0.999809i | \(0.493774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3845 | 1.13969 | 0.569846 | − | 0.821751i | \(-0.307003\pi\) | ||||
0.569846 | + | 0.821751i | \(0.307003\pi\) | |||||||
\(422\) | −11.1998 | −0.545198 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.50812 | −0.170369 | ||||||||
\(425\) | −90.6005 | −4.39477 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.72125 | 0.373658 | ||||||||
\(428\) | −2.32273 | −0.112274 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.45808 | −0.456109 | ||||||||
\(431\) | 33.4853 | 1.61293 | 0.806465 | − | 0.591281i | \(-0.201378\pi\) | ||||
0.806465 | + | 0.591281i | \(0.201378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1373 | 1.15996 | 0.579982 | − | 0.814629i | \(-0.303059\pi\) | ||||
0.579982 | + | 0.814629i | \(0.303059\pi\) | |||||||
\(434\) | 2.16555 | 0.103950 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.97524 | −0.334053 | ||||||||
\(437\) | −0.694209 | −0.0332085 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.4469 | −0.784968 | −0.392484 | − | 0.919759i | \(-0.628384\pi\) | ||||
−0.392484 | + | 0.919759i | \(0.628384\pi\) | |||||||
\(440\) | 14.0968 | 0.672037 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.8576 | 0.706704 | ||||||||
\(443\) | −9.58542 | −0.455417 | −0.227709 | − | 0.973729i | \(-0.573123\pi\) | ||||
−0.227709 | + | 0.973729i | \(0.573123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −59.5923 | −2.82495 | ||||||||
\(446\) | 0.0154255 | 0.000730417 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.42520 | −0.114580 | ||||||||
\(449\) | −4.17319 | −0.196945 | −0.0984725 | − | 0.995140i | \(-0.531396\pi\) | ||||
−0.0984725 | + | 0.995140i | \(0.531396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.63653 | 0.406678 | ||||||||
\(452\) | −15.7768 | −0.742077 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.8226 | −0.507927 | ||||||||
\(455\) | 20.5998 | 0.965731 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.02668 | 0.375472 | 0.187736 | − | 0.982220i | \(-0.439885\pi\) | ||||
0.187736 | + | 0.982220i | \(0.439885\pi\) | |||||||
\(458\) | 8.88456 | 0.415148 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.68447 | 0.358290 | ||||||||
\(461\) | −11.6192 | −0.541158 | −0.270579 | − | 0.962698i | \(-0.587215\pi\) | ||||
−0.270579 | + | 0.962698i | \(0.587215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.8714 | −1.66708 | −0.833542 | − | 0.552456i | \(-0.813691\pi\) | ||||
−0.833542 | + | 0.552456i | \(0.813691\pi\) | |||||||
\(464\) | −14.0538 | −0.652431 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.71115 | 0.264564 | ||||||||
\(467\) | 13.1731 | 0.609579 | 0.304790 | − | 0.952420i | \(-0.401414\pi\) | ||||
0.304790 | + | 0.952420i | \(0.401414\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.22728 | −0.379900 | ||||||||
\(470\) | −4.33110 | −0.199779 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.9113 | 0.824435 | ||||||||
\(473\) | 7.04174 | 0.323779 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0635 | −0.461743 | ||||||||
\(476\) | 10.8771 | 0.498550 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.46006 | 0.432693 | ||||||||
\(479\) | −5.23080 | −0.239002 | −0.119501 | − | 0.992834i | \(-0.538129\pi\) | ||||
−0.119501 | + | 0.992834i | \(0.538129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.2434 | −1.97173 | ||||||||
\(482\) | −6.95826 | −0.316940 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.2605 | 0.648206 | ||||||||
\(485\) | −44.5959 | −2.02499 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9779 | 1.31311 | 0.656557 | − | 0.754277i | \(-0.272012\pi\) | ||||
0.656557 | + | 0.754277i | \(0.272012\pi\) | |||||||
\(488\) | −14.7160 | −0.666162 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.24991 | −0.101641 | ||||||||
\(491\) | 16.6912 | 0.753262 | 0.376631 | − | 0.926363i | \(-0.377083\pi\) | ||||
0.376631 | + | 0.926363i | \(0.377083\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.0002 | 1.57633 | ||||||||
\(494\) | 1.65031 | 0.0742509 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.6654 | 0.478889 | ||||||||
\(497\) | 10.6654 | 0.478407 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.57213 | 0.428507 | 0.214254 | − | 0.976778i | \(-0.431268\pi\) | ||||
0.214254 | + | 0.976778i | \(0.431268\pi\) | |||||||
\(500\) | 72.9740 | 3.26350 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.308038 | −0.0137484 | ||||||||
\(503\) | 20.6348 | 0.920060 | 0.460030 | − | 0.887903i | \(-0.347839\pi\) | ||||
0.460030 | + | 0.887903i | \(0.347839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −60.8582 | −2.70815 | ||||||||
\(506\) | 0.853553 | 0.0379451 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 37.4137 | 1.65996 | ||||||||
\(509\) | −6.23665 | −0.276434 | −0.138217 | − | 0.990402i | \(-0.544137\pi\) | ||||
−0.138217 | + | 0.990402i | \(0.544137\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9117 | −0.526945 | ||||||||
\(512\) | 22.3410 | 0.987342 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.21538 | −0.318257 | ||||||||
\(515\) | −73.0994 | −3.22115 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.22460 | 0.141818 | ||||||||
\(518\) | 4.72305 | 0.207519 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.2612 | −1.72172 | ||||||||
\(521\) | −12.6615 | −0.554709 | −0.277355 | − | 0.960768i | \(-0.589458\pi\) | ||||
−0.277355 | + | 0.960768i | \(0.589458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.3446 | 1.89533 | 0.947663 | − | 0.319272i | \(-0.103438\pi\) | ||||
0.947663 | + | 0.319272i | \(0.103438\pi\) | |||||||
\(524\) | 2.04542 | 0.0893545 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.4860 | −0.457211 | ||||||||
\(527\) | −26.5615 | −1.15704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.14131 | −0.179887 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.20817 | 0.0523809 | ||||||||
\(533\) | −24.0538 | −1.04189 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.89301 | −0.254777 | ||||||||
\(536\) | 15.6804 | 0.677291 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.253072 | 0.0109107 | ||||||||
\(539\) | 1.67510 | 0.0721518 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.87439 | 0.252560 | 0.126280 | − | 0.991995i | \(-0.459696\pi\) | ||||
0.126280 | + | 0.991995i | \(0.459696\pi\) | |||||||
\(542\) | 12.2571 | 0.526488 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −31.8156 | −1.36408 | ||||||||
\(545\) | −17.6969 | −0.758051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8580 | 0.592524 | 0.296262 | − | 0.955107i | \(-0.404260\pi\) | ||||
0.296262 | + | 0.955107i | \(0.404260\pi\) | |||||||
\(548\) | 27.5955 | 1.17882 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.3734 | 0.527602 | ||||||||
\(551\) | 3.88765 | 0.165620 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.581012 | 0.0247071 | ||||||||
\(554\) | 11.8421 | 0.503122 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.36652 | 0.142772 | ||||||||
\(557\) | 18.5921 | 0.787773 | 0.393887 | − | 0.919159i | \(-0.371130\pi\) | ||||
0.393887 | + | 0.919159i | \(0.371130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.6121 | −0.829503 | ||||||||
\(560\) | −11.0808 | −0.468251 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.67882 | 0.323911 | ||||||||
\(563\) | −5.09582 | −0.214763 | −0.107382 | − | 0.994218i | \(-0.534247\pi\) | ||||
−0.107382 | + | 0.994218i | \(0.534247\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.0273 | −1.68396 | ||||||||
\(566\) | 4.70160 | 0.197623 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.3272 | −0.852911 | ||||||||
\(569\) | 29.3028 | 1.22844 | 0.614218 | − | 0.789136i | \(-0.289471\pi\) | ||||
0.614218 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.10736 | −0.213736 | −0.106868 | − | 0.994273i | \(-0.534082\pi\) | ||||
−0.106868 | + | 0.994273i | \(0.534082\pi\) | |||||||
\(572\) | 13.6008 | 0.568680 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.62716 | 0.109656 | ||||||||
\(575\) | 14.4963 | 0.604537 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7379 | 1.02985 | 0.514926 | − | 0.857235i | \(-0.327819\pi\) | ||||
0.514926 | + | 0.857235i | \(0.327819\pi\) | |||||||
\(578\) | 11.2414 | 0.467581 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −43.0340 | −1.78689 | ||||||||
\(581\) | −6.95032 | −0.288348 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.08329 | 0.127697 | ||||||||
\(584\) | 22.7027 | 0.939444 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.31236 | 0.260761 | ||||||||
\(587\) | −38.8319 | −1.60276 | −0.801382 | − | 0.598152i | \(-0.795902\pi\) | ||||
−0.801382 | + | 0.598152i | \(0.795902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.95032 | −0.121566 | ||||||||
\(590\) | 21.1442 | 0.870492 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.2611 | 0.956024 | ||||||||
\(593\) | −36.9162 | −1.51596 | −0.757982 | − | 0.652275i | \(-0.773815\pi\) | ||||
−0.757982 | + | 0.652275i | \(0.773815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.5962 | 1.13133 | ||||||||
\(596\) | 4.54758 | 0.186276 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.37725 | −0.0972130 | ||||||||
\(599\) | −40.4224 | −1.65161 | −0.825807 | − | 0.563953i | \(-0.809280\pi\) | ||||
−0.825807 | + | 0.563953i | \(0.809280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.98464 | 0.121746 | 0.0608730 | − | 0.998146i | \(-0.480612\pi\) | ||||
0.0608730 | + | 0.998146i | \(0.480612\pi\) | |||||||
\(602\) | 2.14204 | 0.0873029 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.1206 | 0.655937 | ||||||||
\(605\) | 36.1804 | 1.47094 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.1893 | −1.18476 | −0.592378 | − | 0.805660i | \(-0.701811\pi\) | ||||
−0.592378 | + | 0.805660i | \(0.701811\pi\) | |||||||
\(608\) | −3.53392 | −0.143319 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.3721 | −0.703376 | ||||||||
\(611\) | −8.98090 | −0.363328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.88595 | −0.237731 | −0.118866 | − | 0.992910i | \(-0.537926\pi\) | ||||
−0.118866 | + | 0.992910i | \(0.537926\pi\) | |||||||
\(614\) | 0.419505 | 0.0169298 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.19259 | −0.128633 | ||||||||
\(617\) | 8.07326 | 0.325017 | 0.162509 | − | 0.986707i | \(-0.448041\pi\) | ||||
0.162509 | + | 0.986707i | \(0.448041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8589 | 0.436457 | 0.218228 | − | 0.975898i | \(-0.429972\pi\) | ||||
0.218228 | + | 0.975898i | \(0.429972\pi\) | |||||||
\(620\) | 32.6583 | 1.31159 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.6245 | 0.626486 | ||||||||
\(623\) | 13.4963 | 0.540717 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 112.661 | 4.50644 | ||||||||
\(626\) | 6.69160 | 0.267450 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5313 | 0.539959 | ||||||||
\(629\) | −57.9305 | −2.30984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1891 | 0.923145 | 0.461572 | − | 0.887103i | \(-0.347285\pi\) | ||||
0.461572 | + | 0.887103i | \(0.347285\pi\) | |||||||
\(632\) | −1.10736 | −0.0440482 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.75891 | 0.308146 | ||||||||
\(635\) | 94.9223 | 3.76688 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.66537 | −0.184849 | ||||||||
\(638\) | −4.78000 | −0.189242 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50.4108 | 1.99266 | ||||||||
\(641\) | 46.7138 | 1.84509 | 0.922543 | − | 0.385895i | \(-0.126107\pi\) | ||||
0.922543 | + | 0.385895i | \(0.126107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.7524 | 1.33106 | 0.665532 | − | 0.746369i | \(-0.268205\pi\) | ||||
0.665532 | + | 0.746369i | \(0.268205\pi\) | |||||||
\(644\) | −1.74036 | −0.0685796 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.21082 | 0.0869834 | ||||||||
\(647\) | −18.9277 | −0.744124 | −0.372062 | − | 0.928208i | \(-0.621349\pi\) | ||||
−0.372062 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.7423 | −0.617938 | ||||||||
\(650\) | −34.4613 | −1.35168 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.3927 | 0.485335 | ||||||||
\(653\) | 10.1696 | 0.397967 | 0.198984 | − | 0.980003i | \(-0.436236\pi\) | ||||
0.198984 | + | 0.980003i | \(0.436236\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.18943 | 0.202768 | ||||||||
\(656\) | 12.9388 | 0.505175 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.980895 | 0.0382393 | ||||||||
\(659\) | 4.60754 | 0.179484 | 0.0897421 | − | 0.995965i | \(-0.471396\pi\) | ||||
0.0897421 | + | 0.995965i | \(0.471396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1205 | −1.21045 | −0.605223 | − | 0.796056i | \(-0.706916\pi\) | ||||
−0.605223 | + | 0.796056i | \(0.706916\pi\) | |||||||
\(662\) | 13.0279 | 0.506345 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.2467 | 0.514071 | ||||||||
\(665\) | 3.06525 | 0.118865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.60012 | −0.216837 | ||||||||
\(668\) | −20.8612 | −0.807144 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.5106 | 0.715128 | ||||||||
\(671\) | 12.9339 | 0.499308 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.9447 | −1.42411 | −0.712057 | − | 0.702122i | \(-0.752236\pi\) | ||||
−0.712057 | + | 0.702122i | \(0.752236\pi\) | |||||||
\(674\) | 8.30010 | 0.319708 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.2554 | −0.586746 | ||||||||
\(677\) | −0.331401 | −0.0127368 | −0.00636838 | − | 0.999980i | \(-0.502027\pi\) | ||||
−0.00636838 | + | 0.999980i | \(0.502027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.0999 | 0.387600 | ||||||||
\(680\) | −52.5959 | −2.01696 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.62752 | 0.138905 | ||||||||
\(683\) | 16.8856 | 0.646109 | 0.323055 | − | 0.946380i | \(-0.395290\pi\) | ||||
0.323055 | + | 0.946380i | \(0.395290\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 70.0126 | 2.67504 | ||||||||
\(686\) | 0.509552 | 0.0194548 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.5496 | 0.402198 | ||||||||
\(689\) | −8.58734 | −0.327152 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1963 | −0.425929 | −0.212964 | − | 0.977060i | \(-0.568312\pi\) | ||||
−0.212964 | + | 0.977060i | \(0.568312\pi\) | |||||||
\(692\) | −3.65463 | −0.138928 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.0435 | −0.419206 | ||||||||
\(695\) | 8.54119 | 0.323986 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.2234 | −1.22055 | ||||||||
\(698\) | −10.9655 | −0.415049 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −25.2287 | −0.953556 | ||||||||
\(701\) | −9.50609 | −0.359040 | −0.179520 | − | 0.983754i | \(-0.557454\pi\) | ||||
−0.179520 | + | 0.983754i | \(0.557454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.43463 | −0.242687 | ||||||||
\(704\) | −4.06245 | −0.153110 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.2854 | 0.387096 | ||||||||
\(707\) | 13.7830 | 0.518362 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.2890 | 1.36286 | 0.681431 | − | 0.731882i | \(-0.261358\pi\) | ||||
0.681431 | + | 0.731882i | \(0.261358\pi\) | |||||||
\(710\) | −23.9961 | −0.900558 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.7227 | −0.963998 | ||||||||
\(713\) | 4.24991 | 0.159160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.5067 | 1.29048 | ||||||||
\(716\) | −27.7980 | −1.03886 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.8467 | −0.442115 | ||||||||
\(719\) | 33.5772 | 1.25222 | 0.626109 | − | 0.779736i | \(-0.284647\pi\) | ||||
0.626109 | + | 0.779736i | \(0.284647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.5553 | 0.616553 | ||||||||
\(722\) | −9.43593 | −0.351169 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.04651 | 0.187552 | ||||||||
\(725\) | −81.1809 | −3.01498 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5410 | 1.39232 | 0.696159 | − | 0.717887i | \(-0.254891\pi\) | ||||
0.696159 | + | 0.717887i | \(0.254891\pi\) | |||||||
\(728\) | 8.89176 | 0.329551 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.8004 | 0.991925 | ||||||||
\(731\) | −26.2731 | −0.971747 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2222 | 0.894668 | 0.447334 | − | 0.894367i | \(-0.352374\pi\) | ||||
0.447334 | + | 0.894367i | \(0.352374\pi\) | |||||||
\(734\) | 14.1233 | 0.521300 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.09056 | 0.187641 | ||||||||
\(737\) | −13.7815 | −0.507650 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.4377 | −0.715028 | −0.357514 | − | 0.933908i | \(-0.616376\pi\) | ||||
−0.357514 | + | 0.933908i | \(0.616376\pi\) | |||||||
\(740\) | 71.2275 | 2.61837 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.937911 | 0.0344318 | ||||||||
\(743\) | −35.7282 | −1.31074 | −0.655370 | − | 0.755308i | \(-0.727487\pi\) | ||||
−0.655370 | + | 0.755308i | \(0.727487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.5377 | 0.422707 | ||||||||
\(746\) | −12.6014 | −0.461369 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.2202 | 0.666197 | ||||||||
\(749\) | 1.33463 | 0.0487664 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.4795 | 0.528363 | 0.264182 | − | 0.964473i | \(-0.414898\pi\) | ||||
0.264182 | + | 0.964473i | \(0.414898\pi\) | |||||||
\(752\) | 4.83092 | 0.176166 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.3129 | 0.484826 | ||||||||
\(755\) | 40.8996 | 1.48849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8034 | 0.792460 | 0.396230 | − | 0.918151i | \(-0.370318\pi\) | ||||
0.396230 | + | 0.918151i | \(0.370318\pi\) | |||||||
\(758\) | −1.58542 | −0.0575851 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.84209 | −0.211915 | ||||||||
\(761\) | 5.98196 | 0.216846 | 0.108423 | − | 0.994105i | \(-0.465420\pi\) | ||||
0.108423 | + | 0.994105i | \(0.465420\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.00794 | 0.145097 | ||||||||
\(764\) | −37.5023 | −1.35679 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.65619 | 0.348892 | ||||||||
\(767\) | 43.8441 | 1.58312 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0694 | −0.579476 | −0.289738 | − | 0.957106i | \(-0.593568\pi\) | ||||
−0.289738 | + | 0.957106i | \(0.593568\pi\) | |||||||
\(770\) | −3.76883 | −0.135819 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.98340 | −0.287329 | ||||||||
\(773\) | −36.5039 | −1.31295 | −0.656476 | − | 0.754347i | \(-0.727954\pi\) | ||||
−0.656476 | + | 0.754347i | \(0.727954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 61.6079 | 2.21302 | ||||||||
\(776\) | −19.2495 | −0.691018 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2773 | 0.368460 | ||||||||
\(779\) | −3.57921 | −0.128239 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8656 | 0.639282 | ||||||||
\(782\) | −3.18466 | −0.113883 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.50955 | 0.0896269 | ||||||||
\(785\) | 34.3304 | 1.22530 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.7402 | −1.59482 | −0.797408 | − | 0.603440i | \(-0.793796\pi\) | ||||
−0.797408 | + | 0.603440i | \(0.793796\pi\) | |||||||
\(788\) | −20.6504 | −0.735639 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.30722 | −0.0465089 | ||||||||
\(791\) | 9.06525 | 0.322323 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0225 | −1.27920 | ||||||||
\(794\) | 4.28857 | 0.152196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.40076 | 0.155981 | ||||||||
\(797\) | 11.3919 | 0.403521 | 0.201761 | − | 0.979435i | \(-0.435334\pi\) | ||||
0.201761 | + | 0.979435i | \(0.435334\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0312 | −0.425632 | ||||||||
\(800\) | 73.7943 | 2.60902 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.98765 | 0.105498 | ||||||||
\(803\) | −19.9534 | −0.704141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.41546 | −0.155625 | ||||||||
\(806\) | −10.1031 | −0.355866 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −26.2691 | −0.924143 | ||||||||
\(809\) | 23.4803 | 0.825523 | 0.412761 | − | 0.910839i | \(-0.364564\pi\) | ||||
0.412761 | + | 0.910839i | \(0.364564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.320003 | −0.0112368 | −0.00561841 | − | 0.999984i | \(-0.501788\pi\) | ||||
−0.00561841 | + | 0.999984i | \(0.501788\pi\) | |||||||
\(812\) | 9.74620 | 0.342025 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.91160 | 0.277301 | ||||||||
\(815\) | 31.4415 | 1.10135 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.91829 | −0.102098 | ||||||||
\(818\) | −13.3853 | −0.468004 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 39.6197 | 1.38358 | ||||||||
\(821\) | −50.4892 | −1.76208 | −0.881042 | − | 0.473038i | \(-0.843157\pi\) | ||||
−0.881042 | + | 0.473038i | \(0.843157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.6259 | −1.03270 | −0.516348 | − | 0.856379i | \(-0.672709\pi\) | ||||
−0.516348 | + | 0.856379i | \(0.672709\pi\) | |||||||
\(824\) | −31.5529 | −1.09920 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.78867 | −0.166619 | ||||||||
\(827\) | 3.13318 | 0.108951 | 0.0544757 | − | 0.998515i | \(-0.482651\pi\) | ||||
0.0544757 | + | 0.998515i | \(0.482651\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1070 | −0.698345 | −0.349172 | − | 0.937059i | \(-0.613537\pi\) | ||||
−0.349172 | + | 0.937059i | \(0.613537\pi\) | |||||||
\(830\) | 15.6376 | 0.542789 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.3144 | 0.392257 | ||||||||
\(833\) | −6.24991 | −0.216547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.9270 | −1.83161 | ||||||||
\(836\) | 2.02381 | 0.0699950 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.407972 | 0.0140932 | ||||||||
\(839\) | 6.63075 | 0.228919 | 0.114460 | − | 0.993428i | \(-0.463486\pi\) | ||||
0.114460 | + | 0.993428i | \(0.463486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.36131 | 0.0814244 | ||||||||
\(842\) | 11.9156 | 0.410640 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 38.2525 | 1.31670 | ||||||||
\(845\) | −38.7045 | −1.33147 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.19403 | −0.281550 | ||||||||
\(848\) | 4.61922 | 0.158625 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −46.1657 | −1.58347 | ||||||||
\(851\) | 9.26901 | 0.317738 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.1804 | −1.23879 | −0.619397 | − | 0.785078i | \(-0.712623\pi\) | ||||
−0.619397 | + | 0.785078i | \(0.712623\pi\) | |||||||
\(854\) | 3.93438 | 0.134632 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.54368 | −0.0869413 | ||||||||
\(857\) | −12.6983 | −0.433764 | −0.216882 | − | 0.976198i | \(-0.569589\pi\) | ||||
−0.216882 | + | 0.976198i | \(0.569589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.2759 | 1.68127 | 0.840636 | − | 0.541600i | \(-0.182181\pi\) | ||||
0.840636 | + | 0.541600i | \(0.182181\pi\) | |||||||
\(860\) | 32.3037 | 1.10155 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.0625 | 0.581152 | ||||||||
\(863\) | 3.28011 | 0.111656 | 0.0558282 | − | 0.998440i | \(-0.482220\pi\) | ||||
0.0558282 | + | 0.998440i | \(0.482220\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.27218 | −0.315263 | ||||||||
\(866\) | 12.2992 | 0.417944 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.39636 | −0.251049 | ||||||||
\(869\) | 0.973255 | 0.0330154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.3833 | 1.30057 | ||||||||
\(872\) | −7.63876 | −0.258681 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.353736 | −0.0119653 | ||||||||
\(875\) | −41.9305 | −1.41751 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.64380 | 0.258113 | 0.129056 | − | 0.991637i | \(-0.458805\pi\) | ||||
0.129056 | + | 0.991637i | \(0.458805\pi\) | |||||||
\(878\) | −8.38056 | −0.282830 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.5615 | −0.625709 | ||||||||
\(881\) | −5.21611 | −0.175735 | −0.0878676 | − | 0.996132i | \(-0.528005\pi\) | ||||
−0.0878676 | + | 0.996132i | \(0.528005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.2052 | −1.52127 | −0.760637 | − | 0.649177i | \(-0.775113\pi\) | ||||
−0.760637 | + | 0.649177i | \(0.775113\pi\) | |||||||
\(884\) | −50.7455 | −1.70676 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.88428 | −0.164090 | ||||||||
\(887\) | 8.59600 | 0.288626 | 0.144313 | − | 0.989532i | \(-0.453903\pi\) | ||||
0.144313 | + | 0.989532i | \(0.453903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.4977 | −0.721010 | ||||||||
\(890\) | −30.3654 | −1.01785 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.0526851 | −0.00176403 | ||||||||
\(893\) | −1.33636 | −0.0447196 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −70.5263 | −2.35744 | ||||||||
\(896\) | −11.4169 | −0.381412 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.12646 | −0.0709609 | ||||||||
\(899\) | −23.8000 | −0.793774 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.5039 | −0.383251 | ||||||||
\(902\) | 4.40076 | 0.146529 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.2775 | −0.574642 | ||||||||
\(905\) | 12.8035 | 0.425603 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.50429 | 0.0831537 | 0.0415769 | − | 0.999135i | \(-0.486762\pi\) | ||||
0.0415769 | + | 0.999135i | \(0.486762\pi\) | |||||||
\(908\) | 36.9640 | 1.22669 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.4967 | 0.347961 | ||||||||
\(911\) | −29.5776 | −0.979951 | −0.489975 | − | 0.871736i | \(-0.662994\pi\) | ||||
−0.489975 | + | 0.871736i | \(0.662994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6425 | −0.385311 | ||||||||
\(914\) | 4.09001 | 0.135286 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.3448 | −1.00262 | ||||||||
\(917\) | −1.17529 | −0.0388114 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.5583 | 0.777117 | 0.388558 | − | 0.921424i | \(-0.372973\pi\) | ||||
0.388558 | + | 0.921424i | \(0.372973\pi\) | |||||||
\(920\) | 8.41546 | 0.277450 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.92057 | −0.194984 | ||||||||
\(923\) | −49.7579 | −1.63780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 134.366 | 4.41794 | ||||||||
\(926\) | −18.2783 | −0.600664 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.5078 | −0.935813 | ||||||||
\(929\) | 37.9337 | 1.24456 | 0.622281 | − | 0.782794i | \(-0.286206\pi\) | ||||
0.622281 | + | 0.782794i | \(0.286206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.694209 | −0.0227518 | ||||||||
\(932\) | −19.5062 | −0.638947 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.71240 | 0.219636 | ||||||||
\(935\) | 46.2265 | 1.51177 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.3490 | −1.38348 | −0.691741 | − | 0.722146i | \(-0.743156\pi\) | ||||
−0.691741 | + | 0.722146i | \(0.743156\pi\) | |||||||
\(938\) | −4.19223 | −0.136881 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.7927 | 0.482485 | ||||||||
\(941\) | 33.9735 | 1.10750 | 0.553752 | − | 0.832682i | \(-0.313196\pi\) | ||||
0.553752 | + | 0.832682i | \(0.313196\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.15582 | 0.167896 | ||||||||
\(944\) | −23.5842 | −0.767602 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.58813 | 0.116660 | ||||||||
\(947\) | 27.7471 | 0.901659 | 0.450829 | − | 0.892610i | \(-0.351128\pi\) | ||||
0.450829 | + | 0.892610i | \(0.351128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.5727 | 1.80397 | ||||||||
\(950\) | −5.12786 | −0.166370 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.9117 | 0.386062 | ||||||||
\(953\) | 6.25582 | 0.202646 | 0.101323 | − | 0.994854i | \(-0.467692\pi\) | ||||
0.101323 | + | 0.994854i | \(0.467692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −95.1472 | −3.07889 | ||||||||
\(956\) | −32.3105 | −1.04500 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.66537 | −0.0861142 | ||||||||
\(959\) | −15.8562 | −0.512024 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9383 | −0.417364 | ||||||||
\(962\) | −22.0348 | −0.710429 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.7657 | 0.765441 | ||||||||
\(965\) | −20.2547 | −0.652021 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1613 | 1.38797 | 0.693987 | − | 0.719988i | \(-0.255853\pi\) | ||||
0.693987 | + | 0.719988i | \(0.255853\pi\) | |||||||
\(968\) | 15.6171 | 0.501951 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.7239 | −0.729621 | ||||||||
\(971\) | −6.69189 | −0.214753 | −0.107377 | − | 0.994218i | \(-0.534245\pi\) | ||||
−0.107377 | + | 0.994218i | \(0.534245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.93438 | −0.0620135 | ||||||||
\(974\) | 14.7658 | 0.473125 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.3769 | 0.620239 | ||||||||
\(977\) | 47.1871 | 1.50965 | 0.754825 | − | 0.655926i | \(-0.227722\pi\) | ||||
0.754825 | + | 0.655926i | \(0.227722\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.6077 | 0.722545 | ||||||||
\(980\) | 7.68447 | 0.245472 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.50502 | 0.271406 | ||||||||
\(983\) | −18.4505 | −0.588480 | −0.294240 | − | 0.955732i | \(-0.595066\pi\) | ||||
−0.294240 | + | 0.955732i | \(0.595066\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.3921 | −1.66935 | ||||||||
\(986\) | 17.8344 | 0.567965 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.63656 | −0.179323 | ||||||||
\(989\) | 4.20376 | 0.133672 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.3764 | −0.774342 | −0.387171 | − | 0.922008i | \(-0.626548\pi\) | ||||
−0.387171 | + | 0.922008i | \(0.626548\pi\) | |||||||
\(992\) | 21.6344 | 0.686894 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.43457 | 0.172374 | ||||||||
\(995\) | 11.1652 | 0.353960 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.5570 | 1.88619 | 0.943094 | − | 0.332525i | \(-0.107901\pi\) | ||||
0.943094 | + | 0.332525i | \(0.107901\pi\) | |||||||
\(998\) | 4.87750 | 0.154395 | ||||||||
\(999\) | 0 | 0 |
(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 | 1449.2.a.p.1.3 | 4 | ||
3.2 | odd | 2 | 483.2.a.i.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 7728.2.a.cd.1.4 | 4 | |||
21.20 | even | 2 | 3381.2.a.w.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.i.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
1449.2.a.p.1.3 | 4 | 1.1 | even | 1 | trivial | ||
3381.2.a.w.1.2 | 4 | 21.20 | even | 2 | |||
7728.2.a.cd.1.4 | 4 | 12.11 | even | 2 |