Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(1,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, 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("575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 12x^{5} + 9x^{4} + 43x^{3} - 14x^{2} - 49x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.69496\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.69496 | 1.19852 | 0.599260 | − | 0.800555i | \(-0.295462\pi\) | ||||
0.599260 | + | 0.800555i | \(0.295462\pi\) | |||||||
\(3\) | −3.30905 | −1.91048 | −0.955241 | − | 0.295829i | \(-0.904404\pi\) | ||||
−0.955241 | + | 0.295829i | \(0.904404\pi\) | |||||||
\(4\) | 0.872898 | 0.436449 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.60872 | −2.28975 | ||||||||
\(7\) | −0.852729 | −0.322301 | −0.161151 | − | 0.986930i | \(-0.551520\pi\) | ||||
−0.161151 | + | 0.986930i | \(0.551520\pi\) | |||||||
\(8\) | −1.91040 | −0.675427 | ||||||||
\(9\) | 7.94982 | 2.64994 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.80793 | 0.545112 | 0.272556 | − | 0.962140i | \(-0.412131\pi\) | ||||
0.272556 | + | 0.962140i | \(0.412131\pi\) | |||||||
\(12\) | −2.88846 | −0.833827 | ||||||||
\(13\) | 2.70717 | 0.750833 | 0.375417 | − | 0.926856i | \(-0.377500\pi\) | ||||
0.375417 | + | 0.926856i | \(0.377500\pi\) | |||||||
\(14\) | −1.44534 | −0.386284 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98384 | −1.24596 | ||||||||
\(17\) | 4.05059 | 0.982411 | 0.491206 | − | 0.871044i | \(-0.336556\pi\) | ||||
0.491206 | + | 0.871044i | \(0.336556\pi\) | |||||||
\(18\) | 13.4746 | 3.17601 | ||||||||
\(19\) | 7.19786 | 1.65130 | 0.825651 | − | 0.564182i | \(-0.190808\pi\) | ||||
0.825651 | + | 0.564182i | \(0.190808\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82172 | 0.615750 | ||||||||
\(22\) | 3.06438 | 0.653327 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 6.32160 | 1.29039 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.58855 | 0.899888 | ||||||||
\(27\) | −16.3792 | −3.15218 | ||||||||
\(28\) | −0.744345 | −0.140668 | ||||||||
\(29\) | −3.76202 | −0.698589 | −0.349294 | − | 0.937013i | \(-0.613579\pi\) | ||||
−0.349294 | + | 0.937013i | \(0.613579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00336 | 0.719025 | 0.359512 | − | 0.933140i | \(-0.382943\pi\) | ||||
0.359512 | + | 0.933140i | \(0.382943\pi\) | |||||||
\(32\) | −4.62664 | −0.817882 | ||||||||
\(33\) | −5.98254 | −1.04143 | ||||||||
\(34\) | 6.86559 | 1.17744 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.93938 | 1.15656 | ||||||||
\(37\) | 11.4649 | 1.88482 | 0.942411 | − | 0.334458i | \(-0.108553\pi\) | ||||
0.942411 | + | 0.334458i | \(0.108553\pi\) | |||||||
\(38\) | 12.2001 | 1.97912 | ||||||||
\(39\) | −8.95816 | −1.43445 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.09373 | 0.951681 | 0.475841 | − | 0.879531i | \(-0.342144\pi\) | ||||
0.475841 | + | 0.879531i | \(0.342144\pi\) | |||||||
\(42\) | 4.78271 | 0.737989 | ||||||||
\(43\) | −11.4095 | −1.73993 | −0.869967 | − | 0.493111i | \(-0.835860\pi\) | ||||
−0.869967 | + | 0.493111i | \(0.835860\pi\) | |||||||
\(44\) | 1.57814 | 0.237913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.69496 | 0.249909 | ||||||||
\(47\) | 7.31241 | 1.06662 | 0.533312 | − | 0.845918i | \(-0.320947\pi\) | ||||
0.533312 | + | 0.845918i | \(0.320947\pi\) | |||||||
\(48\) | 16.4918 | 2.38039 | ||||||||
\(49\) | −6.27285 | −0.896122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.4036 | −1.87688 | ||||||||
\(52\) | 2.36308 | 0.327700 | ||||||||
\(53\) | 0.406455 | 0.0558309 | 0.0279155 | − | 0.999610i | \(-0.491113\pi\) | ||||
0.0279155 | + | 0.999610i | \(0.491113\pi\) | |||||||
\(54\) | −27.7622 | −3.77795 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.62905 | 0.217691 | ||||||||
\(57\) | −23.8181 | −3.15478 | ||||||||
\(58\) | −6.37647 | −0.837272 | ||||||||
\(59\) | −4.83620 | −0.629619 | −0.314810 | − | 0.949155i | \(-0.601941\pi\) | ||||
−0.314810 | + | 0.949155i | \(0.601941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.22818 | 1.18155 | 0.590774 | − | 0.806837i | \(-0.298823\pi\) | ||||
0.590774 | + | 0.806837i | \(0.298823\pi\) | |||||||
\(62\) | 6.78554 | 0.861765 | ||||||||
\(63\) | −6.77904 | −0.854079 | ||||||||
\(64\) | 2.12571 | 0.265714 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.1402 | −1.24817 | ||||||||
\(67\) | −9.64544 | −1.17838 | −0.589189 | − | 0.807995i | \(-0.700553\pi\) | ||||
−0.589189 | + | 0.807995i | \(0.700553\pi\) | |||||||
\(68\) | 3.53575 | 0.428772 | ||||||||
\(69\) | −3.30905 | −0.398363 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.31241 | −0.867823 | −0.433912 | − | 0.900955i | \(-0.642867\pi\) | ||||
−0.433912 | + | 0.900955i | \(0.642867\pi\) | |||||||
\(72\) | −15.1873 | −1.78984 | ||||||||
\(73\) | 5.46747 | 0.639919 | 0.319960 | − | 0.947431i | \(-0.396331\pi\) | ||||
0.319960 | + | 0.947431i | \(0.396331\pi\) | |||||||
\(74\) | 19.4326 | 2.25900 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.28299 | 0.720709 | ||||||||
\(77\) | −1.54168 | −0.175690 | ||||||||
\(78\) | −15.1837 | −1.71922 | ||||||||
\(79\) | 8.60655 | 0.968313 | 0.484156 | − | 0.874982i | \(-0.339127\pi\) | ||||
0.484156 | + | 0.874982i | \(0.339127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.3502 | 3.37224 | ||||||||
\(82\) | 10.3287 | 1.14061 | ||||||||
\(83\) | 2.49686 | 0.274066 | 0.137033 | − | 0.990566i | \(-0.456243\pi\) | ||||
0.137033 | + | 0.990566i | \(0.456243\pi\) | |||||||
\(84\) | 2.46307 | 0.268744 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.3387 | −2.08534 | ||||||||
\(87\) | 12.4487 | 1.33464 | ||||||||
\(88\) | −3.45387 | −0.368183 | ||||||||
\(89\) | −5.41541 | −0.574033 | −0.287016 | − | 0.957926i | \(-0.592663\pi\) | ||||
−0.287016 | + | 0.957926i | \(0.592663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.30848 | −0.241994 | ||||||||
\(92\) | 0.872898 | 0.0910059 | ||||||||
\(93\) | −13.2473 | −1.37368 | ||||||||
\(94\) | 12.3943 | 1.27837 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.3098 | 1.56255 | ||||||||
\(97\) | 8.41317 | 0.854228 | 0.427114 | − | 0.904198i | \(-0.359530\pi\) | ||||
0.427114 | + | 0.904198i | \(0.359530\pi\) | |||||||
\(98\) | −10.6323 | −1.07402 | ||||||||
\(99\) | 14.3727 | 1.44451 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.87714 | −0.186783 | −0.0933913 | − | 0.995629i | \(-0.529771\pi\) | ||||
−0.0933913 | + | 0.995629i | \(0.529771\pi\) | |||||||
\(102\) | −22.7186 | −2.24948 | ||||||||
\(103\) | −7.10693 | −0.700267 | −0.350133 | − | 0.936700i | \(-0.613864\pi\) | ||||
−0.350133 | + | 0.936700i | \(0.613864\pi\) | |||||||
\(104\) | −5.17176 | −0.507133 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.688927 | 0.0669145 | ||||||||
\(107\) | −0.543106 | −0.0525040 | −0.0262520 | − | 0.999655i | \(-0.508357\pi\) | ||||
−0.0262520 | + | 0.999655i | \(0.508357\pi\) | |||||||
\(108\) | −14.2974 | −1.37577 | ||||||||
\(109\) | 4.33841 | 0.415544 | 0.207772 | − | 0.978177i | \(-0.433379\pi\) | ||||
0.207772 | + | 0.978177i | \(0.433379\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −37.9380 | −3.60092 | ||||||||
\(112\) | 4.24987 | 0.401575 | ||||||||
\(113\) | 19.1171 | 1.79838 | 0.899192 | − | 0.437555i | \(-0.144155\pi\) | ||||
0.899192 | + | 0.437555i | \(0.144155\pi\) | |||||||
\(114\) | −40.3707 | −3.78107 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.28385 | −0.304898 | ||||||||
\(117\) | 21.5215 | 1.98966 | ||||||||
\(118\) | −8.19717 | −0.754611 | ||||||||
\(119\) | −3.45405 | −0.316632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.73138 | −0.702853 | ||||||||
\(122\) | 15.6414 | 1.41611 | ||||||||
\(123\) | −20.1645 | −1.81817 | ||||||||
\(124\) | 3.49452 | 0.313817 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.4902 | −1.02363 | ||||||||
\(127\) | −4.12091 | −0.365672 | −0.182836 | − | 0.983143i | \(-0.558528\pi\) | ||||
−0.182836 | + | 0.983143i | \(0.558528\pi\) | |||||||
\(128\) | 12.8563 | 1.13635 | ||||||||
\(129\) | 37.7546 | 3.32411 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.60359 | 0.140107 | 0.0700533 | − | 0.997543i | \(-0.477683\pi\) | ||||
0.0700533 | + | 0.997543i | \(0.477683\pi\) | |||||||
\(132\) | −5.22214 | −0.454529 | ||||||||
\(133\) | −6.13782 | −0.532216 | ||||||||
\(134\) | −16.3487 | −1.41231 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.73822 | −0.663547 | ||||||||
\(137\) | 0.497378 | 0.0424939 | 0.0212470 | − | 0.999774i | \(-0.493236\pi\) | ||||
0.0212470 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(138\) | −5.60872 | −0.477446 | ||||||||
\(139\) | −9.53966 | −0.809143 | −0.404572 | − | 0.914506i | \(-0.632579\pi\) | ||||
−0.404572 | + | 0.914506i | \(0.632579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.1971 | −2.03777 | ||||||||
\(142\) | −12.3943 | −1.04010 | ||||||||
\(143\) | 4.89438 | 0.409288 | ||||||||
\(144\) | −39.6207 | −3.30172 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.26716 | 0.766956 | ||||||||
\(147\) | 20.7572 | 1.71202 | ||||||||
\(148\) | 10.0077 | 0.822628 | ||||||||
\(149\) | −20.4990 | −1.67934 | −0.839671 | − | 0.543096i | \(-0.817252\pi\) | ||||
−0.839671 | + | 0.543096i | \(0.817252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.11088 | 0.741433 | 0.370717 | − | 0.928746i | \(-0.379112\pi\) | ||||
0.370717 | + | 0.928746i | \(0.379112\pi\) | |||||||
\(152\) | −13.7508 | −1.11533 | ||||||||
\(153\) | 32.2014 | 2.60333 | ||||||||
\(154\) | −2.61308 | −0.210568 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.81956 | −0.626066 | ||||||||
\(157\) | 9.67657 | 0.772274 | 0.386137 | − | 0.922441i | \(-0.373809\pi\) | ||||
0.386137 | + | 0.922441i | \(0.373809\pi\) | |||||||
\(158\) | 14.5878 | 1.16054 | ||||||||
\(159\) | −1.34498 | −0.106664 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.852729 | −0.0672044 | ||||||||
\(162\) | 51.4425 | 4.04170 | ||||||||
\(163\) | 8.10453 | 0.634796 | 0.317398 | − | 0.948292i | \(-0.397191\pi\) | ||||
0.317398 | + | 0.948292i | \(0.397191\pi\) | |||||||
\(164\) | 5.31921 | 0.415360 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.23208 | 0.328473 | ||||||||
\(167\) | 12.7841 | 0.989267 | 0.494633 | − | 0.869102i | \(-0.335302\pi\) | ||||
0.494633 | + | 0.869102i | \(0.335302\pi\) | |||||||
\(168\) | −5.39061 | −0.415894 | ||||||||
\(169\) | −5.67124 | −0.436249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 57.2217 | 4.37585 | ||||||||
\(172\) | −9.95933 | −0.759392 | ||||||||
\(173\) | 0.922225 | 0.0701155 | 0.0350577 | − | 0.999385i | \(-0.488838\pi\) | ||||
0.0350577 | + | 0.999385i | \(0.488838\pi\) | |||||||
\(174\) | 21.1001 | 1.59959 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.01045 | −0.679188 | ||||||||
\(177\) | 16.0032 | 1.20288 | ||||||||
\(178\) | −9.17892 | −0.687989 | ||||||||
\(179\) | −2.90586 | −0.217194 | −0.108597 | − | 0.994086i | \(-0.534636\pi\) | ||||
−0.108597 | + | 0.994086i | \(0.534636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.82751 | −0.433155 | −0.216578 | − | 0.976265i | \(-0.569489\pi\) | ||||
−0.216578 | + | 0.976265i | \(0.569489\pi\) | |||||||
\(182\) | −3.91279 | −0.290035 | ||||||||
\(183\) | −30.5365 | −2.25732 | ||||||||
\(184\) | −1.91040 | −0.140836 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −22.4537 | −1.64639 | ||||||||
\(187\) | 7.32318 | 0.535524 | ||||||||
\(188\) | 6.38299 | 0.465527 | ||||||||
\(189\) | 13.9670 | 1.01595 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.0996100 | 0.00720753 | 0.00360376 | − | 0.999994i | \(-0.498853\pi\) | ||||
0.00360376 | + | 0.999994i | \(0.498853\pi\) | |||||||
\(192\) | −7.03410 | −0.507642 | ||||||||
\(193\) | 8.18136 | 0.588907 | 0.294454 | − | 0.955666i | \(-0.404862\pi\) | ||||
0.294454 | + | 0.955666i | \(0.404862\pi\) | |||||||
\(194\) | 14.2600 | 1.02381 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.47556 | −0.391111 | ||||||||
\(197\) | −8.79695 | −0.626757 | −0.313378 | − | 0.949628i | \(-0.601461\pi\) | ||||
−0.313378 | + | 0.949628i | \(0.601461\pi\) | |||||||
\(198\) | 24.3612 | 1.73128 | ||||||||
\(199\) | 19.6838 | 1.39535 | 0.697673 | − | 0.716416i | \(-0.254219\pi\) | ||||
0.697673 | + | 0.716416i | \(0.254219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.9173 | 2.25127 | ||||||||
\(202\) | −3.18168 | −0.223862 | ||||||||
\(203\) | 3.20798 | 0.225156 | ||||||||
\(204\) | −11.7000 | −0.819161 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.0460 | −0.839284 | ||||||||
\(207\) | 7.94982 | 0.552551 | ||||||||
\(208\) | −13.4921 | −0.935509 | ||||||||
\(209\) | 13.0132 | 0.900144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.781526 | 0.0538025 | 0.0269012 | − | 0.999638i | \(-0.491436\pi\) | ||||
0.0269012 | + | 0.999638i | \(0.491436\pi\) | |||||||
\(212\) | 0.354794 | 0.0243673 | ||||||||
\(213\) | 24.1971 | 1.65796 | ||||||||
\(214\) | −0.920544 | −0.0629271 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 31.2908 | 2.12907 | ||||||||
\(217\) | −3.41378 | −0.231742 | ||||||||
\(218\) | 7.35344 | 0.498038 | ||||||||
\(219\) | −18.0921 | −1.22255 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.9656 | 0.737627 | ||||||||
\(222\) | −64.3035 | −4.31577 | ||||||||
\(223\) | 15.5265 | 1.03973 | 0.519864 | − | 0.854249i | \(-0.325983\pi\) | ||||
0.519864 | + | 0.854249i | \(0.325983\pi\) | |||||||
\(224\) | 3.94527 | 0.263604 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 32.4027 | 2.15540 | ||||||||
\(227\) | −0.373394 | −0.0247830 | −0.0123915 | − | 0.999923i | \(-0.503944\pi\) | ||||
−0.0123915 | + | 0.999923i | \(0.503944\pi\) | |||||||
\(228\) | −20.7907 | −1.37690 | ||||||||
\(229\) | −6.50408 | −0.429802 | −0.214901 | − | 0.976636i | \(-0.568943\pi\) | ||||
−0.214901 | + | 0.976636i | \(0.568943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.10148 | 0.335653 | ||||||||
\(232\) | 7.18694 | 0.471846 | ||||||||
\(233\) | 21.6113 | 1.41580 | 0.707901 | − | 0.706311i | \(-0.249642\pi\) | ||||
0.707901 | + | 0.706311i | \(0.249642\pi\) | |||||||
\(234\) | 36.4781 | 2.38465 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.22151 | −0.274797 | ||||||||
\(237\) | −28.4795 | −1.84994 | ||||||||
\(238\) | −5.85448 | −0.379490 | ||||||||
\(239\) | −11.4088 | −0.737973 | −0.368987 | − | 0.929435i | \(-0.620295\pi\) | ||||
−0.368987 | + | 0.929435i | \(0.620295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7415 | −0.691919 | −0.345959 | − | 0.938250i | \(-0.612446\pi\) | ||||
−0.345959 | + | 0.938250i | \(0.612446\pi\) | |||||||
\(242\) | −13.1044 | −0.842383 | ||||||||
\(243\) | −51.2927 | −3.29043 | ||||||||
\(244\) | 8.05525 | 0.515685 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −34.1780 | −2.17911 | ||||||||
\(247\) | 19.4858 | 1.23985 | ||||||||
\(248\) | −7.64800 | −0.485649 | ||||||||
\(249\) | −8.26223 | −0.523598 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.37284 | 0.149772 | 0.0748860 | − | 0.997192i | \(-0.476141\pi\) | ||||
0.0748860 | + | 0.997192i | \(0.476141\pi\) | |||||||
\(252\) | −5.91741 | −0.372762 | ||||||||
\(253\) | 1.80793 | 0.113664 | ||||||||
\(254\) | −6.98479 | −0.438265 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.5395 | 1.09622 | ||||||||
\(257\) | −9.76254 | −0.608971 | −0.304485 | − | 0.952517i | \(-0.598484\pi\) | ||||
−0.304485 | + | 0.952517i | \(0.598484\pi\) | |||||||
\(258\) | 63.9927 | 3.98401 | ||||||||
\(259\) | −9.77647 | −0.607480 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.9074 | −1.85122 | ||||||||
\(262\) | 2.71803 | 0.167921 | ||||||||
\(263\) | −22.8169 | −1.40695 | −0.703476 | − | 0.710719i | \(-0.748370\pi\) | ||||
−0.703476 | + | 0.710719i | \(0.748370\pi\) | |||||||
\(264\) | 11.4290 | 0.703408 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.4034 | −0.637872 | ||||||||
\(267\) | 17.9199 | 1.09668 | ||||||||
\(268\) | −8.41948 | −0.514302 | ||||||||
\(269\) | −32.2387 | −1.96563 | −0.982815 | − | 0.184593i | \(-0.940903\pi\) | ||||
−0.982815 | + | 0.184593i | \(0.940903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.6883 | −1.31747 | −0.658734 | − | 0.752376i | \(-0.728908\pi\) | ||||
−0.658734 | + | 0.752376i | \(0.728908\pi\) | |||||||
\(272\) | −20.1875 | −1.22405 | ||||||||
\(273\) | 7.63888 | 0.462326 | ||||||||
\(274\) | 0.843038 | 0.0509298 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.88846 | −0.173865 | ||||||||
\(277\) | −7.52661 | −0.452230 | −0.226115 | − | 0.974101i | \(-0.572603\pi\) | ||||
−0.226115 | + | 0.974101i | \(0.572603\pi\) | |||||||
\(278\) | −16.1694 | −0.969774 | ||||||||
\(279\) | 31.8260 | 1.90537 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.71112 | 0.400352 | 0.200176 | − | 0.979760i | \(-0.435849\pi\) | ||||
0.200176 | + | 0.979760i | \(0.435849\pi\) | |||||||
\(282\) | −41.0132 | −2.44230 | ||||||||
\(283\) | −5.64413 | −0.335509 | −0.167754 | − | 0.985829i | \(-0.553652\pi\) | ||||
−0.167754 | + | 0.985829i | \(0.553652\pi\) | |||||||
\(284\) | −6.38299 | −0.378761 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.29578 | 0.490540 | ||||||||
\(287\) | −5.19630 | −0.306728 | ||||||||
\(288\) | −36.7809 | −2.16734 | ||||||||
\(289\) | −0.592760 | −0.0348683 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.8396 | −1.63199 | ||||||||
\(292\) | 4.77254 | 0.279292 | ||||||||
\(293\) | −19.3764 | −1.13198 | −0.565990 | − | 0.824412i | \(-0.691506\pi\) | ||||
−0.565990 | + | 0.824412i | \(0.691506\pi\) | |||||||
\(294\) | 35.1827 | 2.05189 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.9025 | −1.27306 | ||||||||
\(297\) | −29.6125 | −1.71829 | ||||||||
\(298\) | −34.7450 | −2.01272 | ||||||||
\(299\) | 2.70717 | 0.156560 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.72921 | 0.560782 | ||||||||
\(302\) | 15.4426 | 0.888622 | ||||||||
\(303\) | 6.21156 | 0.356845 | ||||||||
\(304\) | −35.8730 | −2.05746 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 54.5802 | 3.12014 | ||||||||
\(307\) | 26.9822 | 1.53995 | 0.769977 | − | 0.638071i | \(-0.220267\pi\) | ||||
0.769977 | + | 0.638071i | \(0.220267\pi\) | |||||||
\(308\) | −1.34572 | −0.0766798 | ||||||||
\(309\) | 23.5172 | 1.33785 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0972 | 1.47984 | 0.739918 | − | 0.672697i | \(-0.234864\pi\) | ||||
0.739918 | + | 0.672697i | \(0.234864\pi\) | |||||||
\(312\) | 17.1136 | 0.968869 | ||||||||
\(313\) | −21.8861 | −1.23708 | −0.618538 | − | 0.785755i | \(-0.712275\pi\) | ||||
−0.618538 | + | 0.785755i | \(0.712275\pi\) | |||||||
\(314\) | 16.4014 | 0.925586 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.51264 | 0.422619 | ||||||||
\(317\) | −27.0750 | −1.52069 | −0.760343 | − | 0.649522i | \(-0.774969\pi\) | ||||
−0.760343 | + | 0.649522i | \(0.774969\pi\) | |||||||
\(318\) | −2.27969 | −0.127839 | ||||||||
\(319\) | −6.80147 | −0.380809 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.79716 | 0.100308 | ||||||||
\(322\) | −1.44534 | −0.0805458 | ||||||||
\(323\) | 29.1555 | 1.62226 | ||||||||
\(324\) | 26.4926 | 1.47181 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.7369 | 0.760815 | ||||||||
\(327\) | −14.3560 | −0.793890 | ||||||||
\(328\) | −11.6414 | −0.642791 | ||||||||
\(329\) | −6.23550 | −0.343774 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5646 | 1.18530 | 0.592650 | − | 0.805460i | \(-0.298082\pi\) | ||||
0.592650 | + | 0.805460i | \(0.298082\pi\) | |||||||
\(332\) | 2.17950 | 0.119616 | ||||||||
\(333\) | 91.1441 | 4.99467 | ||||||||
\(334\) | 21.6686 | 1.18566 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.0630 | −0.767201 | ||||||||
\(337\) | −12.9476 | −0.705302 | −0.352651 | − | 0.935755i | \(-0.614720\pi\) | ||||
−0.352651 | + | 0.935755i | \(0.614720\pi\) | |||||||
\(338\) | −9.61254 | −0.522853 | ||||||||
\(339\) | −63.2594 | −3.43578 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.23780 | 0.391949 | ||||||||
\(342\) | 96.9886 | 5.24454 | ||||||||
\(343\) | 11.3181 | 0.611122 | ||||||||
\(344\) | 21.7967 | 1.17520 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.56314 | 0.0840347 | ||||||||
\(347\) | −28.4938 | −1.52963 | −0.764815 | − | 0.644250i | \(-0.777170\pi\) | ||||
−0.764815 | + | 0.644250i | \(0.777170\pi\) | |||||||
\(348\) | 10.8664 | 0.582502 | ||||||||
\(349\) | −0.394806 | −0.0211335 | −0.0105667 | − | 0.999944i | \(-0.503364\pi\) | ||||
−0.0105667 | + | 0.999944i | \(0.503364\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −44.3413 | −2.36676 | ||||||||
\(352\) | −8.36464 | −0.445837 | ||||||||
\(353\) | −8.83611 | −0.470299 | −0.235149 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235149 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(354\) | 27.1249 | 1.44167 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.72710 | −0.250536 | ||||||||
\(357\) | 11.4296 | 0.604920 | ||||||||
\(358\) | −4.92533 | −0.260312 | ||||||||
\(359\) | 24.6984 | 1.30353 | 0.651766 | − | 0.758421i | \(-0.274029\pi\) | ||||
0.651766 | + | 0.758421i | \(0.274029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.8091 | 1.72680 | ||||||||
\(362\) | −9.87741 | −0.519145 | ||||||||
\(363\) | 25.5835 | 1.34279 | ||||||||
\(364\) | −2.01507 | −0.105618 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −51.7582 | −2.70545 | ||||||||
\(367\) | −27.8223 | −1.45231 | −0.726156 | − | 0.687530i | \(-0.758695\pi\) | ||||
−0.726156 | + | 0.687530i | \(0.758695\pi\) | |||||||
\(368\) | −4.98384 | −0.259801 | ||||||||
\(369\) | 48.4441 | 2.52190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.346596 | −0.0179944 | ||||||||
\(372\) | −11.5636 | −0.599542 | ||||||||
\(373\) | −10.2143 | −0.528876 | −0.264438 | − | 0.964403i | \(-0.585186\pi\) | ||||
−0.264438 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(374\) | 12.4125 | 0.641836 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.9696 | −0.720427 | ||||||||
\(377\) | −10.1844 | −0.524524 | ||||||||
\(378\) | 23.6736 | 1.21764 | ||||||||
\(379\) | −2.10451 | −0.108101 | −0.0540507 | − | 0.998538i | \(-0.517213\pi\) | ||||
−0.0540507 | + | 0.998538i | \(0.517213\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6363 | 0.698610 | ||||||||
\(382\) | 0.168835 | 0.00863836 | ||||||||
\(383\) | −30.0460 | −1.53528 | −0.767639 | − | 0.640882i | \(-0.778569\pi\) | ||||
−0.767639 | + | 0.640882i | \(0.778569\pi\) | |||||||
\(384\) | −42.5421 | −2.17097 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.8671 | 0.705817 | ||||||||
\(387\) | −90.7035 | −4.61072 | ||||||||
\(388\) | 7.34384 | 0.372827 | ||||||||
\(389\) | −28.5252 | −1.44629 | −0.723143 | − | 0.690698i | \(-0.757303\pi\) | ||||
−0.723143 | + | 0.690698i | \(0.757303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.05059 | 0.204847 | ||||||||
\(392\) | 11.9836 | 0.605265 | ||||||||
\(393\) | −5.30638 | −0.267671 | ||||||||
\(394\) | −14.9105 | −0.751180 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.5459 | 0.630456 | ||||||||
\(397\) | 3.05896 | 0.153525 | 0.0767624 | − | 0.997049i | \(-0.475542\pi\) | ||||
0.0767624 | + | 0.997049i | \(0.475542\pi\) | |||||||
\(398\) | 33.3633 | 1.67235 | ||||||||
\(399\) | 20.3104 | 1.01679 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4768 | −1.27225 | −0.636125 | − | 0.771586i | \(-0.719464\pi\) | ||||
−0.636125 | + | 0.771586i | \(0.719464\pi\) | |||||||
\(402\) | 54.0985 | 2.69819 | ||||||||
\(403\) | 10.8378 | 0.539868 | ||||||||
\(404\) | −1.63855 | −0.0815210 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.43740 | 0.269854 | ||||||||
\(407\) | 20.7278 | 1.02744 | ||||||||
\(408\) | 25.6062 | 1.26769 | ||||||||
\(409\) | 36.3411 | 1.79695 | 0.898477 | − | 0.439021i | \(-0.144675\pi\) | ||||
0.898477 | + | 0.439021i | \(0.144675\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.64585 | −0.0811838 | ||||||||
\(412\) | −6.20362 | −0.305631 | ||||||||
\(413\) | 4.12396 | 0.202927 | ||||||||
\(414\) | 13.4746 | 0.662243 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.5251 | −0.614093 | ||||||||
\(417\) | 31.5672 | 1.54585 | ||||||||
\(418\) | 22.0569 | 1.07884 | ||||||||
\(419\) | −22.3222 | −1.09051 | −0.545254 | − | 0.838271i | \(-0.683567\pi\) | ||||
−0.545254 | + | 0.838271i | \(0.683567\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.7755 | 1.01254 | 0.506268 | − | 0.862376i | \(-0.331025\pi\) | ||||
0.506268 | + | 0.862376i | \(0.331025\pi\) | |||||||
\(422\) | 1.32466 | 0.0644833 | ||||||||
\(423\) | 58.1324 | 2.82649 | ||||||||
\(424\) | −0.776491 | −0.0377097 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 41.0132 | 1.98710 | ||||||||
\(427\) | −7.86913 | −0.380814 | ||||||||
\(428\) | −0.474076 | −0.0229153 | ||||||||
\(429\) | −16.1957 | −0.781938 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.4694 | −0.985975 | −0.492988 | − | 0.870036i | \(-0.664095\pi\) | ||||
−0.492988 | + | 0.870036i | \(0.664095\pi\) | |||||||
\(432\) | 81.6315 | 3.92750 | ||||||||
\(433\) | 5.00423 | 0.240488 | 0.120244 | − | 0.992744i | \(-0.461632\pi\) | ||||
0.120244 | + | 0.992744i | \(0.461632\pi\) | |||||||
\(434\) | −5.78623 | −0.277748 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.78699 | 0.181364 | ||||||||
\(437\) | 7.19786 | 0.344320 | ||||||||
\(438\) | −30.6655 | −1.46525 | ||||||||
\(439\) | −5.59393 | −0.266984 | −0.133492 | − | 0.991050i | \(-0.542619\pi\) | ||||
−0.133492 | + | 0.991050i | \(0.542619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49.8681 | −2.37467 | ||||||||
\(442\) | 18.5863 | 0.884061 | ||||||||
\(443\) | −14.7055 | −0.698680 | −0.349340 | − | 0.936996i | \(-0.613594\pi\) | ||||
−0.349340 | + | 0.936996i | \(0.613594\pi\) | |||||||
\(444\) | −33.1160 | −1.57162 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.3168 | 1.24613 | ||||||||
\(447\) | 67.8322 | 3.20835 | ||||||||
\(448\) | −1.81266 | −0.0856400 | ||||||||
\(449\) | 8.27733 | 0.390632 | 0.195316 | − | 0.980740i | \(-0.437427\pi\) | ||||
0.195316 | + | 0.980740i | \(0.437427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.0171 | 0.518773 | ||||||||
\(452\) | 16.6873 | 0.784902 | ||||||||
\(453\) | −30.1484 | −1.41649 | ||||||||
\(454\) | −0.632889 | −0.0297030 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 45.5020 | 2.13082 | ||||||||
\(457\) | −11.4431 | −0.535287 | −0.267643 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267643 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(458\) | −11.0242 | −0.515125 | ||||||||
\(459\) | −66.3454 | −3.09674 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.32589 | −0.341201 | −0.170600 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170600 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(462\) | 8.64682 | 0.402286 | ||||||||
\(463\) | 30.3031 | 1.40830 | 0.704152 | − | 0.710050i | \(-0.251328\pi\) | ||||
0.704152 | + | 0.710050i | \(0.251328\pi\) | |||||||
\(464\) | 18.7493 | 0.870414 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.6303 | 1.69687 | ||||||||
\(467\) | −19.1376 | −0.885583 | −0.442791 | − | 0.896625i | \(-0.646012\pi\) | ||||
−0.442791 | + | 0.896625i | \(0.646012\pi\) | |||||||
\(468\) | 18.7861 | 0.868386 | ||||||||
\(469\) | 8.22494 | 0.379793 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.0203 | −1.47542 | ||||||||
\(472\) | 9.23905 | 0.425262 | ||||||||
\(473\) | −20.6276 | −0.948458 | ||||||||
\(474\) | −48.2717 | −2.21719 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.01503 | −0.138194 | ||||||||
\(477\) | 3.23125 | 0.147949 | ||||||||
\(478\) | −19.3375 | −0.884475 | ||||||||
\(479\) | −19.7035 | −0.900275 | −0.450138 | − | 0.892959i | \(-0.648625\pi\) | ||||
−0.450138 | + | 0.892959i | \(0.648625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.0375 | 1.41519 | ||||||||
\(482\) | −18.2064 | −0.829278 | ||||||||
\(483\) | 2.82172 | 0.128393 | ||||||||
\(484\) | −6.74871 | −0.306759 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −86.9393 | −3.94365 | ||||||||
\(487\) | 31.3608 | 1.42110 | 0.710548 | − | 0.703649i | \(-0.248447\pi\) | ||||
0.710548 | + | 0.703649i | \(0.248447\pi\) | |||||||
\(488\) | −17.6295 | −0.798049 | ||||||||
\(489\) | −26.8183 | −1.21277 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.15290 | 0.277677 | 0.138838 | − | 0.990315i | \(-0.455663\pi\) | ||||
0.138838 | + | 0.990315i | \(0.455663\pi\) | |||||||
\(492\) | −17.6015 | −0.793538 | ||||||||
\(493\) | −15.2384 | −0.686301 | ||||||||
\(494\) | 33.0277 | 1.48599 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.9521 | −0.895877 | ||||||||
\(497\) | 6.23550 | 0.279700 | ||||||||
\(498\) | −14.0042 | −0.627542 | ||||||||
\(499\) | 32.4872 | 1.45433 | 0.727164 | − | 0.686464i | \(-0.240838\pi\) | ||||
0.727164 | + | 0.686464i | \(0.240838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.3034 | −1.88998 | ||||||||
\(502\) | 4.02187 | 0.179505 | ||||||||
\(503\) | −25.0323 | −1.11614 | −0.558068 | − | 0.829795i | \(-0.688457\pi\) | ||||
−0.558068 | + | 0.829795i | \(0.688457\pi\) | |||||||
\(504\) | 12.9507 | 0.576868 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.06438 | 0.136228 | ||||||||
\(507\) | 18.7664 | 0.833446 | ||||||||
\(508\) | −3.59714 | −0.159597 | ||||||||
\(509\) | −7.57178 | −0.335613 | −0.167807 | − | 0.985820i | \(-0.553668\pi\) | ||||
−0.167807 | + | 0.985820i | \(0.553668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.66227 | −0.206247 | ||||||||
\(512\) | 4.01621 | 0.177493 | ||||||||
\(513\) | −117.895 | −5.20520 | ||||||||
\(514\) | −16.5471 | −0.729863 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 32.9559 | 1.45080 | ||||||||
\(517\) | 13.2203 | 0.581430 | ||||||||
\(518\) | −16.5707 | −0.728077 | ||||||||
\(519\) | −3.05169 | −0.133954 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.1231 | 1.45115 | 0.725575 | − | 0.688143i | \(-0.241574\pi\) | ||||
0.725575 | + | 0.688143i | \(0.241574\pi\) | |||||||
\(522\) | −50.6918 | −2.21872 | ||||||||
\(523\) | 12.1651 | 0.531943 | 0.265972 | − | 0.963981i | \(-0.414307\pi\) | ||||
0.265972 | + | 0.963981i | \(0.414307\pi\) | |||||||
\(524\) | 1.39977 | 0.0611494 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −38.6738 | −1.68626 | ||||||||
\(527\) | 16.2159 | 0.706378 | ||||||||
\(528\) | 29.8160 | 1.29758 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −38.4469 | −1.66845 | ||||||||
\(532\) | −5.35769 | −0.232285 | ||||||||
\(533\) | 16.4968 | 0.714554 | ||||||||
\(534\) | 30.3735 | 1.31439 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.4266 | 0.795908 | ||||||||
\(537\) | 9.61565 | 0.414946 | ||||||||
\(538\) | −54.6434 | −2.35585 | ||||||||
\(539\) | −11.3409 | −0.488487 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.74714 | −0.419062 | −0.209531 | − | 0.977802i | \(-0.567194\pi\) | ||||
−0.209531 | + | 0.977802i | \(0.567194\pi\) | |||||||
\(542\) | −36.7608 | −1.57901 | ||||||||
\(543\) | 19.2835 | 0.827536 | ||||||||
\(544\) | −18.7406 | −0.803496 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.9476 | 0.554107 | ||||||||
\(547\) | −24.0053 | −1.02639 | −0.513196 | − | 0.858271i | \(-0.671539\pi\) | ||||
−0.513196 | + | 0.858271i | \(0.671539\pi\) | |||||||
\(548\) | 0.434160 | 0.0185464 | ||||||||
\(549\) | 73.3624 | 3.13103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.0784 | −1.15358 | ||||||||
\(552\) | 6.32160 | 0.269065 | ||||||||
\(553\) | −7.33905 | −0.312088 | ||||||||
\(554\) | −12.7573 | −0.542007 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.32714 | −0.353150 | ||||||||
\(557\) | −39.6594 | −1.68042 | −0.840211 | − | 0.542259i | \(-0.817569\pi\) | ||||
−0.840211 | + | 0.542259i | \(0.817569\pi\) | |||||||
\(558\) | 53.9439 | 2.28363 | ||||||||
\(559\) | −30.8875 | −1.30640 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.2328 | −1.02311 | ||||||||
\(562\) | 11.3751 | 0.479829 | ||||||||
\(563\) | −11.5311 | −0.485980 | −0.242990 | − | 0.970029i | \(-0.578128\pi\) | ||||
−0.242990 | + | 0.970029i | \(0.578128\pi\) | |||||||
\(564\) | −21.1216 | −0.889381 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.56659 | −0.402114 | ||||||||
\(567\) | −25.8805 | −1.08688 | ||||||||
\(568\) | 13.9696 | 0.586151 | ||||||||
\(569\) | 19.6982 | 0.825792 | 0.412896 | − | 0.910778i | \(-0.364517\pi\) | ||||
0.412896 | + | 0.910778i | \(0.364517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0271 | −0.461470 | −0.230735 | − | 0.973017i | \(-0.574113\pi\) | ||||
−0.230735 | + | 0.973017i | \(0.574113\pi\) | |||||||
\(572\) | 4.27229 | 0.178633 | ||||||||
\(573\) | −0.329615 | −0.0137698 | ||||||||
\(574\) | −8.80754 | −0.367619 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 16.8990 | 0.704127 | ||||||||
\(577\) | −1.72708 | −0.0718992 | −0.0359496 | − | 0.999354i | \(-0.511446\pi\) | ||||
−0.0359496 | + | 0.999354i | \(0.511446\pi\) | |||||||
\(578\) | −1.00471 | −0.0417903 | ||||||||
\(579\) | −27.0725 | −1.12510 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.12914 | −0.0883317 | ||||||||
\(582\) | −47.1871 | −1.95597 | ||||||||
\(583\) | 0.734844 | 0.0304341 | ||||||||
\(584\) | −10.4450 | −0.432219 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.8422 | −1.35670 | ||||||||
\(587\) | 24.9467 | 1.02966 | 0.514829 | − | 0.857293i | \(-0.327855\pi\) | ||||
0.514829 | + | 0.857293i | \(0.327855\pi\) | |||||||
\(588\) | 18.1189 | 0.747211 | ||||||||
\(589\) | 28.8156 | 1.18733 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.1096 | 1.19741 | ||||||||
\(592\) | −57.1394 | −2.34841 | ||||||||
\(593\) | 15.4113 | 0.632865 | 0.316433 | − | 0.948615i | \(-0.397515\pi\) | ||||
0.316433 | + | 0.948615i | \(0.397515\pi\) | |||||||
\(594\) | −50.1921 | −2.05941 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.8935 | −0.732947 | ||||||||
\(597\) | −65.1347 | −2.66578 | ||||||||
\(598\) | 4.58855 | 0.187640 | ||||||||
\(599\) | 0.251631 | 0.0102814 | 0.00514069 | − | 0.999987i | \(-0.498364\pi\) | ||||
0.00514069 | + | 0.999987i | \(0.498364\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.0537 | 1.30750 | 0.653749 | − | 0.756711i | \(-0.273195\pi\) | ||||
0.653749 | + | 0.756711i | \(0.273195\pi\) | |||||||
\(602\) | 16.4906 | 0.672109 | ||||||||
\(603\) | −76.6795 | −3.12263 | ||||||||
\(604\) | 7.95287 | 0.323598 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.5284 | 0.427685 | ||||||||
\(607\) | −4.85762 | −0.197165 | −0.0985825 | − | 0.995129i | \(-0.531431\pi\) | ||||
−0.0985825 | + | 0.995129i | \(0.531431\pi\) | |||||||
\(608\) | −33.3019 | −1.35057 | ||||||||
\(609\) | −10.6154 | −0.430156 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.7959 | 0.800858 | ||||||||
\(612\) | 28.1085 | 1.13622 | ||||||||
\(613\) | 36.1790 | 1.46126 | 0.730628 | − | 0.682776i | \(-0.239227\pi\) | ||||
0.730628 | + | 0.682776i | \(0.239227\pi\) | |||||||
\(614\) | 45.7338 | 1.84567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.94521 | 0.118666 | ||||||||
\(617\) | 20.9998 | 0.845421 | 0.422710 | − | 0.906265i | \(-0.361079\pi\) | ||||
0.422710 | + | 0.906265i | \(0.361079\pi\) | |||||||
\(618\) | 39.8608 | 1.60344 | ||||||||
\(619\) | 23.9554 | 0.962849 | 0.481424 | − | 0.876488i | \(-0.340120\pi\) | ||||
0.481424 | + | 0.876488i | \(0.340120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.3792 | −0.657275 | ||||||||
\(622\) | 44.2338 | 1.77361 | ||||||||
\(623\) | 4.61788 | 0.185011 | ||||||||
\(624\) | 44.6461 | 1.78727 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −37.0962 | −1.48266 | ||||||||
\(627\) | −43.0615 | −1.71971 | ||||||||
\(628\) | 8.44665 | 0.337058 | ||||||||
\(629\) | 46.4396 | 1.85167 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.1439 | −0.881533 | −0.440767 | − | 0.897622i | \(-0.645293\pi\) | ||||
−0.440767 | + | 0.897622i | \(0.645293\pi\) | |||||||
\(632\) | −16.4419 | −0.654025 | ||||||||
\(633\) | −2.58611 | −0.102789 | ||||||||
\(634\) | −45.8912 | −1.82257 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.17403 | −0.0465534 | ||||||||
\(637\) | −16.9817 | −0.672838 | ||||||||
\(638\) | −11.5282 | −0.456407 | ||||||||
\(639\) | −58.1324 | −2.29968 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.05308 | 0.120589 | 0.0602947 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602947 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(642\) | 3.04613 | 0.120221 | ||||||||
\(643\) | 0.865731 | 0.0341411 | 0.0170705 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170705 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(644\) | −0.744345 | −0.0293313 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 49.4175 | 1.94431 | ||||||||
\(647\) | 34.7042 | 1.36436 | 0.682181 | − | 0.731184i | \(-0.261032\pi\) | ||||
0.682181 | + | 0.731184i | \(0.261032\pi\) | |||||||
\(648\) | −57.9809 | −2.27771 | ||||||||
\(649\) | −8.74352 | −0.343213 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.2964 | 0.442740 | ||||||||
\(652\) | 7.07442 | 0.277056 | ||||||||
\(653\) | −49.4368 | −1.93461 | −0.967305 | − | 0.253614i | \(-0.918381\pi\) | ||||
−0.967305 | + | 0.253614i | \(0.918381\pi\) | |||||||
\(654\) | −24.3329 | −0.951492 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −30.3702 | −1.18576 | ||||||||
\(657\) | 43.4654 | 1.69575 | ||||||||
\(658\) | −10.5689 | −0.412020 | ||||||||
\(659\) | 3.55117 | 0.138334 | 0.0691670 | − | 0.997605i | \(-0.477966\pi\) | ||||
0.0691670 | + | 0.997605i | \(0.477966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8273 | 0.926776 | 0.463388 | − | 0.886156i | \(-0.346634\pi\) | ||||
0.463388 | + | 0.886156i | \(0.346634\pi\) | |||||||
\(662\) | 36.5512 | 1.42060 | ||||||||
\(663\) | −36.2858 | −1.40922 | ||||||||
\(664\) | −4.76999 | −0.185111 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 154.486 | 5.98620 | ||||||||
\(667\) | −3.76202 | −0.145666 | ||||||||
\(668\) | 11.1592 | 0.431764 | ||||||||
\(669\) | −51.3778 | −1.98638 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.6839 | 0.644075 | ||||||||
\(672\) | −13.0551 | −0.503611 | ||||||||
\(673\) | −16.7319 | −0.644969 | −0.322484 | − | 0.946575i | \(-0.604518\pi\) | ||||
−0.322484 | + | 0.946575i | \(0.604518\pi\) | |||||||
\(674\) | −21.9457 | −0.845319 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.95041 | −0.190400 | ||||||||
\(677\) | −44.3491 | −1.70447 | −0.852237 | − | 0.523155i | \(-0.824755\pi\) | ||||
−0.852237 | + | 0.523155i | \(0.824755\pi\) | |||||||
\(678\) | −107.222 | −4.11785 | ||||||||
\(679\) | −7.17415 | −0.275319 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.23558 | 0.0473476 | ||||||||
\(682\) | 12.2678 | 0.469758 | ||||||||
\(683\) | 14.6621 | 0.561028 | 0.280514 | − | 0.959850i | \(-0.409495\pi\) | ||||
0.280514 | + | 0.959850i | \(0.409495\pi\) | |||||||
\(684\) | 49.9487 | 1.90983 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.1838 | 0.732442 | ||||||||
\(687\) | 21.5223 | 0.821128 | ||||||||
\(688\) | 56.8632 | 2.16789 | ||||||||
\(689\) | 1.10034 | 0.0419197 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.76181 | −0.219189 | −0.109595 | − | 0.993976i | \(-0.534955\pi\) | ||||
−0.109595 | + | 0.993976i | \(0.534955\pi\) | |||||||
\(692\) | 0.805008 | 0.0306018 | ||||||||
\(693\) | −12.2560 | −0.465569 | ||||||||
\(694\) | −48.2960 | −1.83329 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −23.7820 | −0.901453 | ||||||||
\(697\) | 24.6832 | 0.934942 | ||||||||
\(698\) | −0.669182 | −0.0253289 | ||||||||
\(699\) | −71.5129 | −2.70487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.8653 | −1.01469 | −0.507344 | − | 0.861744i | \(-0.669373\pi\) | ||||
−0.507344 | + | 0.861744i | \(0.669373\pi\) | |||||||
\(702\) | −75.1568 | −2.83661 | ||||||||
\(703\) | 82.5229 | 3.11241 | ||||||||
\(704\) | 3.84315 | 0.144844 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.9769 | −0.563662 | ||||||||
\(707\) | 1.60069 | 0.0602002 | ||||||||
\(708\) | 13.9692 | 0.524994 | ||||||||
\(709\) | −9.88754 | −0.371334 | −0.185667 | − | 0.982613i | \(-0.559445\pi\) | ||||
−0.185667 | + | 0.982613i | \(0.559445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 68.4206 | 2.56597 | ||||||||
\(712\) | 10.3456 | 0.387717 | ||||||||
\(713\) | 4.00336 | 0.149927 | ||||||||
\(714\) | 19.3728 | 0.725008 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.53652 | −0.0947943 | ||||||||
\(717\) | 37.7523 | 1.40988 | ||||||||
\(718\) | 41.8628 | 1.56231 | ||||||||
\(719\) | 34.3363 | 1.28053 | 0.640264 | − | 0.768155i | \(-0.278825\pi\) | ||||
0.640264 | + | 0.768155i | \(0.278825\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.06029 | 0.225697 | ||||||||
\(722\) | 55.6103 | 2.06960 | ||||||||
\(723\) | 35.5441 | 1.32190 | ||||||||
\(724\) | −5.08682 | −0.189050 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 43.3631 | 1.60936 | ||||||||
\(727\) | 5.69413 | 0.211184 | 0.105592 | − | 0.994410i | \(-0.466326\pi\) | ||||
0.105592 | + | 0.994410i | \(0.466326\pi\) | |||||||
\(728\) | 4.41011 | 0.163450 | ||||||||
\(729\) | 78.6797 | 2.91406 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.2152 | −1.70933 | ||||||||
\(732\) | −26.6553 | −0.985206 | ||||||||
\(733\) | 33.8318 | 1.24961 | 0.624803 | − | 0.780783i | \(-0.285179\pi\) | ||||
0.624803 | + | 0.780783i | \(0.285179\pi\) | |||||||
\(734\) | −47.1577 | −1.74062 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.62664 | −0.170540 | ||||||||
\(737\) | −17.4383 | −0.642348 | ||||||||
\(738\) | 82.1109 | 3.02255 | ||||||||
\(739\) | 31.2203 | 1.14846 | 0.574228 | − | 0.818695i | \(-0.305302\pi\) | ||||
0.574228 | + | 0.818695i | \(0.305302\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −64.4796 | −2.36872 | ||||||||
\(742\) | −0.587467 | −0.0215666 | ||||||||
\(743\) | 37.2922 | 1.36812 | 0.684059 | − | 0.729426i | \(-0.260213\pi\) | ||||
0.684059 | + | 0.729426i | \(0.260213\pi\) | |||||||
\(744\) | 25.3076 | 0.927823 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.3128 | −0.633868 | ||||||||
\(747\) | 19.8496 | 0.726258 | ||||||||
\(748\) | 6.39239 | 0.233729 | ||||||||
\(749\) | 0.463122 | 0.0169221 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8983 | −0.981534 | −0.490767 | − | 0.871291i | \(-0.663283\pi\) | ||||
−0.490767 | + | 0.871291i | \(0.663283\pi\) | |||||||
\(752\) | −36.4439 | −1.32897 | ||||||||
\(753\) | −7.85184 | −0.286137 | ||||||||
\(754\) | −17.2622 | −0.628652 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 12.1918 | 0.443411 | ||||||||
\(757\) | 20.7947 | 0.755795 | 0.377897 | − | 0.925847i | \(-0.376647\pi\) | ||||
0.377897 | + | 0.925847i | \(0.376647\pi\) | |||||||
\(758\) | −3.56707 | −0.129562 | ||||||||
\(759\) | −5.98254 | −0.217152 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3499 | 0.483934 | 0.241967 | − | 0.970284i | \(-0.422207\pi\) | ||||
0.241967 | + | 0.970284i | \(0.422207\pi\) | |||||||
\(762\) | 23.1130 | 0.837297 | ||||||||
\(763\) | −3.69949 | −0.133930 | ||||||||
\(764\) | 0.0869493 | 0.00314572 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −50.9268 | −1.84006 | ||||||||
\(767\) | −13.0924 | −0.472739 | ||||||||
\(768\) | −58.0391 | −2.09430 | ||||||||
\(769\) | 14.4273 | 0.520262 | 0.260131 | − | 0.965573i | \(-0.416234\pi\) | ||||
0.260131 | + | 0.965573i | \(0.416234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.3048 | 1.16343 | ||||||||
\(772\) | 7.14149 | 0.257028 | ||||||||
\(773\) | −34.9789 | −1.25811 | −0.629053 | − | 0.777363i | \(-0.716557\pi\) | ||||
−0.629053 | + | 0.777363i | \(0.716557\pi\) | |||||||
\(774\) | −153.739 | −5.52604 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.0725 | −0.576969 | ||||||||
\(777\) | 32.3508 | 1.16058 | ||||||||
\(778\) | −48.3492 | −1.73340 | ||||||||
\(779\) | 43.8618 | 1.57151 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2203 | −0.473061 | ||||||||
\(782\) | 6.86559 | 0.245513 | ||||||||
\(783\) | 61.6189 | 2.20208 | ||||||||
\(784\) | 31.2629 | 1.11653 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.99411 | −0.320809 | ||||||||
\(787\) | 4.21165 | 0.150129 | 0.0750646 | − | 0.997179i | \(-0.476084\pi\) | ||||
0.0750646 | + | 0.997179i | \(0.476084\pi\) | |||||||
\(788\) | −7.67884 | −0.273547 | ||||||||
\(789\) | 75.5023 | 2.68795 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.3017 | −0.579621 | ||||||||
\(792\) | −27.4576 | −0.975664 | ||||||||
\(793\) | 24.9822 | 0.887145 | ||||||||
\(794\) | 5.18482 | 0.184003 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.1819 | 0.608997 | ||||||||
\(797\) | −29.6417 | −1.04996 | −0.524982 | − | 0.851114i | \(-0.675928\pi\) | ||||
−0.524982 | + | 0.851114i | \(0.675928\pi\) | |||||||
\(798\) | 34.4253 | 1.21864 | ||||||||
\(799\) | 29.6195 | 1.04786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43.0516 | −1.52115 | ||||||||
\(802\) | −43.1822 | −1.52482 | ||||||||
\(803\) | 9.88482 | 0.348828 | ||||||||
\(804\) | 27.8605 | 0.982564 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.3696 | 0.647042 | ||||||||
\(807\) | 106.680 | 3.75530 | ||||||||
\(808\) | 3.58608 | 0.126158 | ||||||||
\(809\) | −48.5282 | −1.70616 | −0.853080 | − | 0.521780i | \(-0.825268\pi\) | ||||
−0.853080 | + | 0.521780i | \(0.825268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.13032 | −0.320609 | −0.160304 | − | 0.987068i | \(-0.551248\pi\) | ||||
−0.160304 | + | 0.987068i | \(0.551248\pi\) | |||||||
\(812\) | 2.80024 | 0.0982690 | ||||||||
\(813\) | 71.7676 | 2.51700 | ||||||||
\(814\) | 35.1328 | 1.23141 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 66.8014 | 2.33852 | ||||||||
\(817\) | −82.1240 | −2.87315 | ||||||||
\(818\) | 61.5969 | 2.15368 | ||||||||
\(819\) | −18.3520 | −0.641271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.78799 | −0.167102 | −0.0835511 | − | 0.996503i | \(-0.526626\pi\) | ||||
−0.0835511 | + | 0.996503i | \(0.526626\pi\) | |||||||
\(822\) | −2.78966 | −0.0973004 | ||||||||
\(823\) | −17.8317 | −0.621572 | −0.310786 | − | 0.950480i | \(-0.600592\pi\) | ||||
−0.310786 | + | 0.950480i | \(0.600592\pi\) | |||||||
\(824\) | 13.5771 | 0.472979 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.98996 | 0.243212 | ||||||||
\(827\) | −3.79532 | −0.131976 | −0.0659881 | − | 0.997820i | \(-0.521020\pi\) | ||||
−0.0659881 | + | 0.997820i | \(0.521020\pi\) | |||||||
\(828\) | 6.93938 | 0.241160 | ||||||||
\(829\) | 29.5865 | 1.02758 | 0.513790 | − | 0.857916i | \(-0.328241\pi\) | ||||
0.513790 | + | 0.857916i | \(0.328241\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.9059 | 0.863977 | ||||||||
\(832\) | 5.75467 | 0.199507 | ||||||||
\(833\) | −25.4087 | −0.880360 | ||||||||
\(834\) | 53.5053 | 1.85274 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.3592 | 0.392867 | ||||||||
\(837\) | −65.5719 | −2.26650 | ||||||||
\(838\) | −37.8352 | −1.30700 | ||||||||
\(839\) | −11.3505 | −0.391863 | −0.195931 | − | 0.980618i | \(-0.562773\pi\) | ||||
−0.195931 | + | 0.980618i | \(0.562773\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8472 | −0.511974 | ||||||||
\(842\) | 35.2137 | 1.21354 | ||||||||
\(843\) | −22.2074 | −0.764865 | ||||||||
\(844\) | 0.682192 | 0.0234820 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 98.5322 | 3.38761 | ||||||||
\(847\) | 6.59277 | 0.226530 | ||||||||
\(848\) | −2.02571 | −0.0695632 | ||||||||
\(849\) | 18.6767 | 0.640983 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4649 | 0.393012 | ||||||||
\(852\) | 21.1216 | 0.723615 | ||||||||
\(853\) | 13.7072 | 0.469325 | 0.234663 | − | 0.972077i | \(-0.424602\pi\) | ||||
0.234663 | + | 0.972077i | \(0.424602\pi\) | |||||||
\(854\) | −13.3379 | −0.456413 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.03755 | 0.0354626 | ||||||||
\(857\) | 4.99347 | 0.170574 | 0.0852869 | − | 0.996356i | \(-0.472819\pi\) | ||||
0.0852869 | + | 0.996356i | \(0.472819\pi\) | |||||||
\(858\) | −27.4512 | −0.937168 | ||||||||
\(859\) | −36.7762 | −1.25479 | −0.627395 | − | 0.778701i | \(-0.715879\pi\) | ||||
−0.627395 | + | 0.778701i | \(0.715879\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.1948 | 0.585998 | ||||||||
\(862\) | −34.6948 | −1.18171 | ||||||||
\(863\) | 1.37292 | 0.0467349 | 0.0233674 | − | 0.999727i | \(-0.492561\pi\) | ||||
0.0233674 | + | 0.999727i | \(0.492561\pi\) | |||||||
\(864\) | 75.7807 | 2.57811 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.48199 | 0.288230 | ||||||||
\(867\) | 1.96147 | 0.0666152 | ||||||||
\(868\) | −2.97988 | −0.101144 | ||||||||
\(869\) | 15.5601 | 0.527839 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.1118 | −0.884766 | ||||||||
\(872\) | −8.28808 | −0.280670 | ||||||||
\(873\) | 66.8832 | 2.26365 | ||||||||
\(874\) | 12.2001 | 0.412674 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.7926 | −0.533582 | ||||||||
\(877\) | 21.0051 | 0.709293 | 0.354646 | − | 0.935000i | \(-0.384601\pi\) | ||||
0.354646 | + | 0.935000i | \(0.384601\pi\) | |||||||
\(878\) | −9.48150 | −0.319985 | ||||||||
\(879\) | 64.1175 | 2.16263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4448 | −0.823567 | −0.411783 | − | 0.911282i | \(-0.635094\pi\) | ||||
−0.411783 | + | 0.911282i | \(0.635094\pi\) | |||||||
\(882\) | −84.5245 | −2.84609 | ||||||||
\(883\) | 23.7703 | 0.799935 | 0.399967 | − | 0.916529i | \(-0.369021\pi\) | ||||
0.399967 | + | 0.916529i | \(0.369021\pi\) | |||||||
\(884\) | 9.57186 | 0.321936 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.9253 | −0.837381 | ||||||||
\(887\) | 34.6784 | 1.16439 | 0.582193 | − | 0.813051i | \(-0.302195\pi\) | ||||
0.582193 | + | 0.813051i | \(0.302195\pi\) | |||||||
\(888\) | 72.4766 | 2.43216 | ||||||||
\(889\) | 3.51402 | 0.117856 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.8711 | 1.83825 | ||||||||
\(892\) | 13.5530 | 0.453788 | ||||||||
\(893\) | 52.6337 | 1.76132 | ||||||||
\(894\) | 114.973 | 3.84527 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.9629 | −0.366245 | ||||||||
\(897\) | −8.95816 | −0.299104 | ||||||||
\(898\) | 14.0298 | 0.468179 | ||||||||
\(899\) | −15.0607 | −0.502302 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.64638 | 0.0548489 | ||||||||
\(902\) | 18.6735 | 0.621759 | ||||||||
\(903\) | −32.1945 | −1.07136 | ||||||||
\(904\) | −36.5212 | −1.21468 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −51.1004 | −1.69770 | ||||||||
\(907\) | −1.14030 | −0.0378632 | −0.0189316 | − | 0.999821i | \(-0.506026\pi\) | ||||
−0.0189316 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(908\) | −0.325935 | −0.0108165 | ||||||||
\(909\) | −14.9229 | −0.494963 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.8882 | 0.890847 | 0.445424 | − | 0.895320i | \(-0.353053\pi\) | ||||
0.445424 | + | 0.895320i | \(0.353053\pi\) | |||||||
\(912\) | 118.706 | 3.93074 | ||||||||
\(913\) | 4.51415 | 0.149397 | ||||||||
\(914\) | −19.3957 | −0.641552 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.67739 | −0.187586 | ||||||||
\(917\) | −1.36743 | −0.0451565 | ||||||||
\(918\) | −112.453 | −3.71150 | ||||||||
\(919\) | 44.6052 | 1.47139 | 0.735695 | − | 0.677312i | \(-0.236855\pi\) | ||||
0.735695 | + | 0.677312i | \(0.236855\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −89.2855 | −2.94206 | ||||||||
\(922\) | −12.4171 | −0.408936 | ||||||||
\(923\) | −19.7959 | −0.651591 | ||||||||
\(924\) | 4.45307 | 0.146495 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.3626 | 1.68788 | ||||||||
\(927\) | −56.4989 | −1.85567 | ||||||||
\(928\) | 17.4055 | 0.571363 | ||||||||
\(929\) | 11.7066 | 0.384081 | 0.192040 | − | 0.981387i | \(-0.438490\pi\) | ||||
0.192040 | + | 0.981387i | \(0.438490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.1511 | −1.47977 | ||||||||
\(932\) | 18.8644 | 0.617925 | ||||||||
\(933\) | −86.3569 | −2.82720 | ||||||||
\(934\) | −32.4375 | −1.06139 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −41.1146 | −1.34387 | ||||||||
\(937\) | −10.7665 | −0.351726 | −0.175863 | − | 0.984415i | \(-0.556272\pi\) | ||||
−0.175863 | + | 0.984415i | \(0.556272\pi\) | |||||||
\(938\) | 13.9410 | 0.455189 | ||||||||
\(939\) | 72.4223 | 2.36341 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.0936 | −1.01362 | −0.506812 | − | 0.862057i | \(-0.669176\pi\) | ||||
−0.506812 | + | 0.862057i | \(0.669176\pi\) | |||||||
\(942\) | −54.2732 | −1.76831 | ||||||||
\(943\) | 6.09373 | 0.198439 | ||||||||
\(944\) | 24.1029 | 0.784481 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.9630 | −1.13675 | ||||||||
\(947\) | −31.9699 | −1.03888 | −0.519442 | − | 0.854506i | \(-0.673860\pi\) | ||||
−0.519442 | + | 0.854506i | \(0.673860\pi\) | |||||||
\(948\) | −24.8597 | −0.807406 | ||||||||
\(949\) | 14.8014 | 0.480473 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 89.5927 | 2.90524 | ||||||||
\(952\) | 6.59860 | 0.213862 | ||||||||
\(953\) | −44.4559 | −1.44007 | −0.720033 | − | 0.693940i | \(-0.755873\pi\) | ||||
−0.720033 | + | 0.693940i | \(0.755873\pi\) | |||||||
\(954\) | 5.47684 | 0.177319 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.95870 | −0.322087 | ||||||||
\(957\) | 22.5064 | 0.727529 | ||||||||
\(958\) | −33.3967 | −1.07900 | ||||||||
\(959\) | −0.424129 | −0.0136958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9731 | −0.483004 | ||||||||
\(962\) | 52.6074 | 1.69613 | ||||||||
\(963\) | −4.31759 | −0.139132 | ||||||||
\(964\) | −9.37620 | −0.301987 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.78271 | 0.153881 | ||||||||
\(967\) | −37.7617 | −1.21434 | −0.607168 | − | 0.794574i | \(-0.707694\pi\) | ||||
−0.607168 | + | 0.794574i | \(0.707694\pi\) | |||||||
\(968\) | 14.7700 | 0.474726 | ||||||||
\(969\) | −96.4772 | −3.09929 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.7081 | 1.11384 | 0.556918 | − | 0.830568i | \(-0.311984\pi\) | ||||
0.556918 | + | 0.830568i | \(0.311984\pi\) | |||||||
\(972\) | −44.7733 | −1.43610 | ||||||||
\(973\) | 8.13474 | 0.260788 | ||||||||
\(974\) | 53.1554 | 1.70321 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −45.9918 | −1.47216 | ||||||||
\(977\) | 4.66906 | 0.149376 | 0.0746882 | − | 0.997207i | \(-0.476204\pi\) | ||||
0.0746882 | + | 0.997207i | \(0.476204\pi\) | |||||||
\(978\) | −45.4560 | −1.45352 | ||||||||
\(979\) | −9.79070 | −0.312912 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.4896 | 1.10117 | ||||||||
\(982\) | 10.4289 | 0.332801 | ||||||||
\(983\) | −28.9130 | −0.922182 | −0.461091 | − | 0.887353i | \(-0.652542\pi\) | ||||
−0.461091 | + | 0.887353i | \(0.652542\pi\) | |||||||
\(984\) | 38.5221 | 1.22804 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25.8285 | −0.822545 | ||||||||
\(987\) | 20.6336 | 0.656775 | ||||||||
\(988\) | 17.0091 | 0.541132 | ||||||||
\(989\) | −11.4095 | −0.362801 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.9545 | −1.45979 | −0.729896 | − | 0.683558i | \(-0.760432\pi\) | ||||
−0.729896 | + | 0.683558i | \(0.760432\pi\) | |||||||
\(992\) | −18.5221 | −0.588077 | ||||||||
\(993\) | −71.3585 | −2.26449 | ||||||||
\(994\) | 10.5689 | 0.335226 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.21208 | −0.228524 | ||||||||
\(997\) | −32.8384 | −1.04000 | −0.520002 | − | 0.854165i | \(-0.674069\pi\) | ||||
−0.520002 | + | 0.854165i | \(0.674069\pi\) | |||||||
\(998\) | 55.0646 | 1.74304 | ||||||||
\(999\) | −187.786 | −5.94130 |
(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 | 575.2.a.l.1.5 | yes | 7 | |
3.2 | odd | 2 | 5175.2.a.cb.1.3 | 7 | |||
4.3 | odd | 2 | 9200.2.a.db.1.7 | 7 | |||
5.2 | odd | 4 | 575.2.b.f.24.11 | 14 | |||
5.3 | odd | 4 | 575.2.b.f.24.4 | 14 | |||
5.4 | even | 2 | 575.2.a.k.1.3 | ✓ | 7 | ||
15.14 | odd | 2 | 5175.2.a.cg.1.5 | 7 | |||
20.19 | odd | 2 | 9200.2.a.da.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
575.2.a.k.1.3 | ✓ | 7 | 5.4 | even | 2 | ||
575.2.a.l.1.5 | yes | 7 | 1.1 | even | 1 | trivial | |
575.2.b.f.24.4 | 14 | 5.3 | odd | 4 | |||
575.2.b.f.24.11 | 14 | 5.2 | odd | 4 | |||
5175.2.a.cb.1.3 | 7 | 3.2 | odd | 2 | |||
5175.2.a.cg.1.5 | 7 | 15.14 | odd | 2 | |||
9200.2.a.da.1.1 | 7 | 20.19 | odd | 2 | |||
9200.2.a.db.1.7 | 7 | 4.3 | odd | 2 |