Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.74369 | −1.58407 | −0.792034 | − | 0.610477i | \(-0.790978\pi\) | ||||
−0.792034 | + | 0.610477i | \(0.790978\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0184852 | 0.00826685 | 0.00413342 | − | 0.999991i | \(-0.498684\pi\) | ||||
0.00413342 | + | 0.999991i | \(0.498684\pi\) | |||||||
\(6\) | −2.74369 | −1.12011 | ||||||||
\(7\) | 0.788378 | 0.297979 | 0.148989 | − | 0.988839i | \(-0.452398\pi\) | ||||
0.148989 | + | 0.988839i | \(0.452398\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.52782 | 1.50927 | ||||||||
\(10\) | 0.0184852 | 0.00584554 | ||||||||
\(11\) | −2.48763 | −0.750048 | −0.375024 | − | 0.927015i | \(-0.622366\pi\) | ||||
−0.375024 | + | 0.927015i | \(0.622366\pi\) | |||||||
\(12\) | −2.74369 | −0.792034 | ||||||||
\(13\) | 1.53915 | 0.426885 | 0.213442 | − | 0.976956i | \(-0.431532\pi\) | ||||
0.213442 | + | 0.976956i | \(0.431532\pi\) | |||||||
\(14\) | 0.788378 | 0.210703 | ||||||||
\(15\) | −0.0507177 | −0.0130953 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.82077 | 1.16921 | 0.584604 | − | 0.811318i | \(-0.301250\pi\) | ||||
0.584604 | + | 0.811318i | \(0.301250\pi\) | |||||||
\(18\) | 4.52782 | 1.06722 | ||||||||
\(19\) | 1.27873 | 0.293360 | 0.146680 | − | 0.989184i | \(-0.453141\pi\) | ||||
0.146680 | + | 0.989184i | \(0.453141\pi\) | |||||||
\(20\) | 0.0184852 | 0.00413342 | ||||||||
\(21\) | −2.16306 | −0.472019 | ||||||||
\(22\) | −2.48763 | −0.530364 | ||||||||
\(23\) | 8.09086 | 1.68706 | 0.843531 | − | 0.537081i | \(-0.180473\pi\) | ||||
0.843531 | + | 0.537081i | \(0.180473\pi\) | |||||||
\(24\) | −2.74369 | −0.560053 | ||||||||
\(25\) | −4.99966 | −0.999932 | ||||||||
\(26\) | 1.53915 | 0.301853 | ||||||||
\(27\) | −4.19186 | −0.806724 | ||||||||
\(28\) | 0.788378 | 0.148989 | ||||||||
\(29\) | −3.75967 | −0.698153 | −0.349076 | − | 0.937094i | \(-0.613505\pi\) | ||||
−0.349076 | + | 0.937094i | \(0.613505\pi\) | |||||||
\(30\) | −0.0507177 | −0.00925974 | ||||||||
\(31\) | −0.0360307 | −0.00647130 | −0.00323565 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323565 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.82528 | 1.18813 | ||||||||
\(34\) | 4.82077 | 0.826755 | ||||||||
\(35\) | 0.0145734 | 0.00246335 | ||||||||
\(36\) | 4.52782 | 0.754637 | ||||||||
\(37\) | −1.48010 | −0.243326 | −0.121663 | − | 0.992571i | \(-0.538823\pi\) | ||||
−0.121663 | + | 0.992571i | \(0.538823\pi\) | |||||||
\(38\) | 1.27873 | 0.207437 | ||||||||
\(39\) | −4.22296 | −0.676214 | ||||||||
\(40\) | 0.0184852 | 0.00292277 | ||||||||
\(41\) | −2.01682 | −0.314975 | −0.157487 | − | 0.987521i | \(-0.550339\pi\) | ||||
−0.157487 | + | 0.987521i | \(0.550339\pi\) | |||||||
\(42\) | −2.16306 | −0.333768 | ||||||||
\(43\) | 6.31722 | 0.963366 | 0.481683 | − | 0.876345i | \(-0.340026\pi\) | ||||
0.481683 | + | 0.876345i | \(0.340026\pi\) | |||||||
\(44\) | −2.48763 | −0.375024 | ||||||||
\(45\) | 0.0836978 | 0.0124769 | ||||||||
\(46\) | 8.09086 | 1.19293 | ||||||||
\(47\) | −4.15993 | −0.606788 | −0.303394 | − | 0.952865i | \(-0.598120\pi\) | ||||
−0.303394 | + | 0.952865i | \(0.598120\pi\) | |||||||
\(48\) | −2.74369 | −0.396017 | ||||||||
\(49\) | −6.37846 | −0.911209 | ||||||||
\(50\) | −4.99966 | −0.707058 | ||||||||
\(51\) | −13.2267 | −1.85211 | ||||||||
\(52\) | 1.53915 | 0.213442 | ||||||||
\(53\) | 11.3059 | 1.55299 | 0.776494 | − | 0.630125i | \(-0.216996\pi\) | ||||
0.776494 | + | 0.630125i | \(0.216996\pi\) | |||||||
\(54\) | −4.19186 | −0.570440 | ||||||||
\(55\) | −0.0459844 | −0.00620053 | ||||||||
\(56\) | 0.788378 | 0.105351 | ||||||||
\(57\) | −3.50843 | −0.464703 | ||||||||
\(58\) | −3.75967 | −0.493669 | ||||||||
\(59\) | 2.97362 | 0.387133 | 0.193566 | − | 0.981087i | \(-0.437995\pi\) | ||||
0.193566 | + | 0.981087i | \(0.437995\pi\) | |||||||
\(60\) | −0.0507177 | −0.00654763 | ||||||||
\(61\) | −10.5034 | −1.34482 | −0.672410 | − | 0.740179i | \(-0.734741\pi\) | ||||
−0.672410 | + | 0.740179i | \(0.734741\pi\) | |||||||
\(62\) | −0.0360307 | −0.00457590 | ||||||||
\(63\) | 3.56963 | 0.449732 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0284516 | 0.00352899 | ||||||||
\(66\) | 6.82528 | 0.840133 | ||||||||
\(67\) | 4.34181 | 0.530437 | 0.265218 | − | 0.964188i | \(-0.414556\pi\) | ||||
0.265218 | + | 0.964188i | \(0.414556\pi\) | |||||||
\(68\) | 4.82077 | 0.584604 | ||||||||
\(69\) | −22.1988 | −2.67242 | ||||||||
\(70\) | 0.0145734 | 0.00174185 | ||||||||
\(71\) | −7.99641 | −0.949000 | −0.474500 | − | 0.880256i | \(-0.657371\pi\) | ||||
−0.474500 | + | 0.880256i | \(0.657371\pi\) | |||||||
\(72\) | 4.52782 | 0.533609 | ||||||||
\(73\) | 7.78804 | 0.911521 | 0.455760 | − | 0.890102i | \(-0.349367\pi\) | ||||
0.455760 | + | 0.890102i | \(0.349367\pi\) | |||||||
\(74\) | −1.48010 | −0.172058 | ||||||||
\(75\) | 13.7175 | 1.58396 | ||||||||
\(76\) | 1.27873 | 0.146680 | ||||||||
\(77\) | −1.96119 | −0.223499 | ||||||||
\(78\) | −4.22296 | −0.478156 | ||||||||
\(79\) | 2.65372 | 0.298566 | 0.149283 | − | 0.988794i | \(-0.452303\pi\) | ||||
0.149283 | + | 0.988794i | \(0.452303\pi\) | |||||||
\(80\) | 0.0184852 | 0.00206671 | ||||||||
\(81\) | −2.08230 | −0.231367 | ||||||||
\(82\) | −2.01682 | −0.222721 | ||||||||
\(83\) | 1.27427 | 0.139870 | 0.0699349 | − | 0.997552i | \(-0.477721\pi\) | ||||
0.0699349 | + | 0.997552i | \(0.477721\pi\) | |||||||
\(84\) | −2.16306 | −0.236010 | ||||||||
\(85\) | 0.0891131 | 0.00966567 | ||||||||
\(86\) | 6.31722 | 0.681203 | ||||||||
\(87\) | 10.3154 | 1.10592 | ||||||||
\(88\) | −2.48763 | −0.265182 | ||||||||
\(89\) | −15.1053 | −1.60116 | −0.800579 | − | 0.599227i | \(-0.795475\pi\) | ||||
−0.800579 | + | 0.599227i | \(0.795475\pi\) | |||||||
\(90\) | 0.0836978 | 0.00882252 | ||||||||
\(91\) | 1.21344 | 0.127203 | ||||||||
\(92\) | 8.09086 | 0.843531 | ||||||||
\(93\) | 0.0988570 | 0.0102510 | ||||||||
\(94\) | −4.15993 | −0.429064 | ||||||||
\(95\) | 0.0236376 | 0.00242516 | ||||||||
\(96\) | −2.74369 | −0.280026 | ||||||||
\(97\) | 2.52670 | 0.256548 | 0.128274 | − | 0.991739i | \(-0.459056\pi\) | ||||
0.128274 | + | 0.991739i | \(0.459056\pi\) | |||||||
\(98\) | −6.37846 | −0.644322 | ||||||||
\(99\) | −11.2635 | −1.13203 | ||||||||
\(100\) | −4.99966 | −0.499966 | ||||||||
\(101\) | 7.37414 | 0.733755 | 0.366877 | − | 0.930269i | \(-0.380427\pi\) | ||||
0.366877 | + | 0.930269i | \(0.380427\pi\) | |||||||
\(102\) | −13.2267 | −1.30964 | ||||||||
\(103\) | 12.0562 | 1.18793 | 0.593965 | − | 0.804491i | \(-0.297562\pi\) | ||||
0.593965 | + | 0.804491i | \(0.297562\pi\) | |||||||
\(104\) | 1.53915 | 0.150926 | ||||||||
\(105\) | −0.0399847 | −0.00390211 | ||||||||
\(106\) | 11.3059 | 1.09813 | ||||||||
\(107\) | 8.88659 | 0.859099 | 0.429549 | − | 0.903043i | \(-0.358672\pi\) | ||||
0.429549 | + | 0.903043i | \(0.358672\pi\) | |||||||
\(108\) | −4.19186 | −0.403362 | ||||||||
\(109\) | 16.8778 | 1.61660 | 0.808300 | − | 0.588771i | \(-0.200388\pi\) | ||||
0.808300 | + | 0.588771i | \(0.200388\pi\) | |||||||
\(110\) | −0.0459844 | −0.00438444 | ||||||||
\(111\) | 4.06092 | 0.385446 | ||||||||
\(112\) | 0.788378 | 0.0744947 | ||||||||
\(113\) | 4.93298 | 0.464056 | 0.232028 | − | 0.972709i | \(-0.425464\pi\) | ||||
0.232028 | + | 0.972709i | \(0.425464\pi\) | |||||||
\(114\) | −3.50843 | −0.328594 | ||||||||
\(115\) | 0.149561 | 0.0139467 | ||||||||
\(116\) | −3.75967 | −0.349076 | ||||||||
\(117\) | 6.96901 | 0.644286 | ||||||||
\(118\) | 2.97362 | 0.273744 | ||||||||
\(119\) | 3.80059 | 0.348400 | ||||||||
\(120\) | −0.0507177 | −0.00462987 | ||||||||
\(121\) | −4.81170 | −0.437428 | ||||||||
\(122\) | −10.5034 | −0.950931 | ||||||||
\(123\) | 5.53353 | 0.498942 | ||||||||
\(124\) | −0.0360307 | −0.00323565 | ||||||||
\(125\) | −0.184846 | −0.0165331 | ||||||||
\(126\) | 3.56963 | 0.318008 | ||||||||
\(127\) | −12.1590 | −1.07894 | −0.539469 | − | 0.842006i | \(-0.681375\pi\) | ||||
−0.539469 | + | 0.842006i | \(0.681375\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −17.3325 | −1.52604 | ||||||||
\(130\) | 0.0284516 | 0.00249537 | ||||||||
\(131\) | 0.824810 | 0.0720640 | 0.0360320 | − | 0.999351i | \(-0.488528\pi\) | ||||
0.0360320 | + | 0.999351i | \(0.488528\pi\) | |||||||
\(132\) | 6.82528 | 0.594064 | ||||||||
\(133\) | 1.00812 | 0.0874151 | ||||||||
\(134\) | 4.34181 | 0.375076 | ||||||||
\(135\) | −0.0774875 | −0.00666907 | ||||||||
\(136\) | 4.82077 | 0.413378 | ||||||||
\(137\) | −23.0088 | −1.96578 | −0.982889 | − | 0.184201i | \(-0.941030\pi\) | ||||
−0.982889 | + | 0.184201i | \(0.941030\pi\) | |||||||
\(138\) | −22.1988 | −1.88969 | ||||||||
\(139\) | 22.1663 | 1.88012 | 0.940059 | − | 0.341011i | \(-0.110769\pi\) | ||||
0.940059 | + | 0.341011i | \(0.110769\pi\) | |||||||
\(140\) | 0.0145734 | 0.00123167 | ||||||||
\(141\) | 11.4135 | 0.961194 | ||||||||
\(142\) | −7.99641 | −0.671044 | ||||||||
\(143\) | −3.82884 | −0.320184 | ||||||||
\(144\) | 4.52782 | 0.377318 | ||||||||
\(145\) | −0.0694983 | −0.00577152 | ||||||||
\(146\) | 7.78804 | 0.644543 | ||||||||
\(147\) | 17.5005 | 1.44342 | ||||||||
\(148\) | −1.48010 | −0.121663 | ||||||||
\(149\) | −4.23945 | −0.347310 | −0.173655 | − | 0.984807i | \(-0.555558\pi\) | ||||
−0.173655 | + | 0.984807i | \(0.555558\pi\) | |||||||
\(150\) | 13.7175 | 1.12003 | ||||||||
\(151\) | −12.3953 | −1.00871 | −0.504356 | − | 0.863496i | \(-0.668270\pi\) | ||||
−0.504356 | + | 0.863496i | \(0.668270\pi\) | |||||||
\(152\) | 1.27873 | 0.103718 | ||||||||
\(153\) | 21.8276 | 1.76466 | ||||||||
\(154\) | −1.96119 | −0.158037 | ||||||||
\(155\) | −0.000666036 0 | −5.34973e−5 0 | ||||||||
\(156\) | −4.22296 | −0.338107 | ||||||||
\(157\) | 14.4011 | 1.14933 | 0.574666 | − | 0.818388i | \(-0.305132\pi\) | ||||
0.574666 | + | 0.818388i | \(0.305132\pi\) | |||||||
\(158\) | 2.65372 | 0.211118 | ||||||||
\(159\) | −31.0199 | −2.46004 | ||||||||
\(160\) | 0.0184852 | 0.00146139 | ||||||||
\(161\) | 6.37866 | 0.502709 | ||||||||
\(162\) | −2.08230 | −0.163601 | ||||||||
\(163\) | 12.9831 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(164\) | −2.01682 | −0.157487 | ||||||||
\(165\) | 0.126167 | 0.00982207 | ||||||||
\(166\) | 1.27427 | 0.0989029 | ||||||||
\(167\) | 6.79378 | 0.525719 | 0.262859 | − | 0.964834i | \(-0.415334\pi\) | ||||
0.262859 | + | 0.964834i | \(0.415334\pi\) | |||||||
\(168\) | −2.16306 | −0.166884 | ||||||||
\(169\) | −10.6310 | −0.817770 | ||||||||
\(170\) | 0.0891131 | 0.00683466 | ||||||||
\(171\) | 5.78985 | 0.442761 | ||||||||
\(172\) | 6.31722 | 0.481683 | ||||||||
\(173\) | −14.6890 | −1.11679 | −0.558394 | − | 0.829576i | \(-0.688582\pi\) | ||||
−0.558394 | + | 0.829576i | \(0.688582\pi\) | |||||||
\(174\) | 10.3154 | 0.782005 | ||||||||
\(175\) | −3.94162 | −0.297959 | ||||||||
\(176\) | −2.48763 | −0.187512 | ||||||||
\(177\) | −8.15869 | −0.613245 | ||||||||
\(178\) | −15.1053 | −1.13219 | ||||||||
\(179\) | 10.5999 | 0.792273 | 0.396137 | − | 0.918192i | \(-0.370351\pi\) | ||||
0.396137 | + | 0.918192i | \(0.370351\pi\) | |||||||
\(180\) | 0.0836978 | 0.00623847 | ||||||||
\(181\) | −11.7055 | −0.870060 | −0.435030 | − | 0.900416i | \(-0.643262\pi\) | ||||
−0.435030 | + | 0.900416i | \(0.643262\pi\) | |||||||
\(182\) | 1.21344 | 0.0899458 | ||||||||
\(183\) | 28.8180 | 2.13029 | ||||||||
\(184\) | 8.09086 | 0.596466 | ||||||||
\(185\) | −0.0273599 | −0.00201154 | ||||||||
\(186\) | 0.0988570 | 0.00724854 | ||||||||
\(187\) | −11.9923 | −0.876963 | ||||||||
\(188\) | −4.15993 | −0.303394 | ||||||||
\(189\) | −3.30477 | −0.240387 | ||||||||
\(190\) | 0.0236376 | 0.00171485 | ||||||||
\(191\) | 22.1834 | 1.60513 | 0.802566 | − | 0.596563i | \(-0.203468\pi\) | ||||
0.802566 | + | 0.596563i | \(0.203468\pi\) | |||||||
\(192\) | −2.74369 | −0.198009 | ||||||||
\(193\) | 4.63212 | 0.333427 | 0.166714 | − | 0.986005i | \(-0.446685\pi\) | ||||
0.166714 | + | 0.986005i | \(0.446685\pi\) | |||||||
\(194\) | 2.52670 | 0.181407 | ||||||||
\(195\) | −0.0780624 | −0.00559016 | ||||||||
\(196\) | −6.37846 | −0.455604 | ||||||||
\(197\) | 3.87619 | 0.276167 | 0.138084 | − | 0.990421i | \(-0.455906\pi\) | ||||
0.138084 | + | 0.990421i | \(0.455906\pi\) | |||||||
\(198\) | −11.2635 | −0.800465 | ||||||||
\(199\) | −2.00985 | −0.142475 | −0.0712374 | − | 0.997459i | \(-0.522695\pi\) | ||||
−0.0712374 | + | 0.997459i | \(0.522695\pi\) | |||||||
\(200\) | −4.99966 | −0.353529 | ||||||||
\(201\) | −11.9126 | −0.840249 | ||||||||
\(202\) | 7.37414 | 0.518843 | ||||||||
\(203\) | −2.96404 | −0.208035 | ||||||||
\(204\) | −13.2267 | −0.926054 | ||||||||
\(205\) | −0.0372814 | −0.00260385 | ||||||||
\(206\) | 12.0562 | 0.839993 | ||||||||
\(207\) | 36.6340 | 2.54624 | ||||||||
\(208\) | 1.53915 | 0.106721 | ||||||||
\(209\) | −3.18100 | −0.220034 | ||||||||
\(210\) | −0.0399847 | −0.00275921 | ||||||||
\(211\) | 25.9771 | 1.78834 | 0.894168 | − | 0.447731i | \(-0.147768\pi\) | ||||
0.894168 | + | 0.447731i | \(0.147768\pi\) | |||||||
\(212\) | 11.3059 | 0.776494 | ||||||||
\(213\) | 21.9397 | 1.50328 | ||||||||
\(214\) | 8.88659 | 0.607475 | ||||||||
\(215\) | 0.116775 | 0.00796400 | ||||||||
\(216\) | −4.19186 | −0.285220 | ||||||||
\(217\) | −0.0284058 | −0.00192831 | ||||||||
\(218\) | 16.8778 | 1.14311 | ||||||||
\(219\) | −21.3679 | −1.44391 | ||||||||
\(220\) | −0.0459844 | −0.00310027 | ||||||||
\(221\) | 7.41991 | 0.499117 | ||||||||
\(222\) | 4.06092 | 0.272551 | ||||||||
\(223\) | 13.6461 | 0.913811 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(224\) | 0.788378 | 0.0526757 | ||||||||
\(225\) | −22.6376 | −1.50917 | ||||||||
\(226\) | 4.93298 | 0.328137 | ||||||||
\(227\) | −20.5680 | −1.36515 | −0.682575 | − | 0.730816i | \(-0.739140\pi\) | ||||
−0.682575 | + | 0.730816i | \(0.739140\pi\) | |||||||
\(228\) | −3.50843 | −0.232351 | ||||||||
\(229\) | 3.11471 | 0.205826 | 0.102913 | − | 0.994690i | \(-0.467184\pi\) | ||||
0.102913 | + | 0.994690i | \(0.467184\pi\) | |||||||
\(230\) | 0.149561 | 0.00986179 | ||||||||
\(231\) | 5.38090 | 0.354037 | ||||||||
\(232\) | −3.75967 | −0.246834 | ||||||||
\(233\) | −3.85654 | −0.252651 | −0.126325 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126325 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(234\) | 6.96901 | 0.455579 | ||||||||
\(235\) | −0.0768972 | −0.00501622 | ||||||||
\(236\) | 2.97362 | 0.193566 | ||||||||
\(237\) | −7.28097 | −0.472950 | ||||||||
\(238\) | 3.80059 | 0.246356 | ||||||||
\(239\) | 17.2722 | 1.11724 | 0.558622 | − | 0.829422i | \(-0.311330\pi\) | ||||
0.558622 | + | 0.829422i | \(0.311330\pi\) | |||||||
\(240\) | −0.0507177 | −0.00327381 | ||||||||
\(241\) | 25.5288 | 1.64446 | 0.822229 | − | 0.569157i | \(-0.192730\pi\) | ||||
0.822229 | + | 0.569157i | \(0.192730\pi\) | |||||||
\(242\) | −4.81170 | −0.309308 | ||||||||
\(243\) | 18.2888 | 1.17323 | ||||||||
\(244\) | −10.5034 | −0.672410 | ||||||||
\(245\) | −0.117907 | −0.00753282 | ||||||||
\(246\) | 5.53353 | 0.352805 | ||||||||
\(247\) | 1.96816 | 0.125231 | ||||||||
\(248\) | −0.0360307 | −0.00228795 | ||||||||
\(249\) | −3.49621 | −0.221563 | ||||||||
\(250\) | −0.184846 | −0.0116907 | ||||||||
\(251\) | 11.9515 | 0.754371 | 0.377186 | − | 0.926138i | \(-0.376892\pi\) | ||||
0.377186 | + | 0.926138i | \(0.376892\pi\) | |||||||
\(252\) | 3.56963 | 0.224866 | ||||||||
\(253\) | −20.1271 | −1.26538 | ||||||||
\(254\) | −12.1590 | −0.762924 | ||||||||
\(255\) | −0.244498 | −0.0153111 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.0935 | 0.879128 | 0.439564 | − | 0.898211i | \(-0.355133\pi\) | ||||
0.439564 | + | 0.898211i | \(0.355133\pi\) | |||||||
\(258\) | −17.3325 | −1.07907 | ||||||||
\(259\) | −1.16688 | −0.0725061 | ||||||||
\(260\) | 0.0284516 | 0.00176449 | ||||||||
\(261\) | −17.0231 | −1.05370 | ||||||||
\(262\) | 0.824810 | 0.0509569 | ||||||||
\(263\) | 18.4311 | 1.13651 | 0.568256 | − | 0.822851i | \(-0.307618\pi\) | ||||
0.568256 | + | 0.822851i | \(0.307618\pi\) | |||||||
\(264\) | 6.82528 | 0.420067 | ||||||||
\(265\) | 0.208993 | 0.0128383 | ||||||||
\(266\) | 1.00812 | 0.0618118 | ||||||||
\(267\) | 41.4442 | 2.53635 | ||||||||
\(268\) | 4.34181 | 0.265218 | ||||||||
\(269\) | 0.809822 | 0.0493757 | 0.0246879 | − | 0.999695i | \(-0.492141\pi\) | ||||
0.0246879 | + | 0.999695i | \(0.492141\pi\) | |||||||
\(270\) | −0.0774875 | −0.00471574 | ||||||||
\(271\) | −8.62338 | −0.523833 | −0.261917 | − | 0.965091i | \(-0.584355\pi\) | ||||
−0.261917 | + | 0.965091i | \(0.584355\pi\) | |||||||
\(272\) | 4.82077 | 0.292302 | ||||||||
\(273\) | −3.32929 | −0.201498 | ||||||||
\(274\) | −23.0088 | −1.39001 | ||||||||
\(275\) | 12.4373 | 0.749997 | ||||||||
\(276\) | −22.1988 | −1.33621 | ||||||||
\(277\) | 32.1168 | 1.92971 | 0.964856 | − | 0.262779i | \(-0.0846390\pi\) | ||||
0.964856 | + | 0.262779i | \(0.0846390\pi\) | |||||||
\(278\) | 22.1663 | 1.32944 | ||||||||
\(279\) | −0.163141 | −0.00976697 | ||||||||
\(280\) | 0.0145734 | 0.000870924 0 | ||||||||
\(281\) | 7.35716 | 0.438892 | 0.219446 | − | 0.975625i | \(-0.429575\pi\) | ||||
0.219446 | + | 0.975625i | \(0.429575\pi\) | |||||||
\(282\) | 11.4135 | 0.679667 | ||||||||
\(283\) | −15.1597 | −0.901148 | −0.450574 | − | 0.892739i | \(-0.648781\pi\) | ||||
−0.450574 | + | 0.892739i | \(0.648781\pi\) | |||||||
\(284\) | −7.99641 | −0.474500 | ||||||||
\(285\) | −0.0648541 | −0.00384162 | ||||||||
\(286\) | −3.82884 | −0.226404 | ||||||||
\(287\) | −1.59002 | −0.0938558 | ||||||||
\(288\) | 4.52782 | 0.266804 | ||||||||
\(289\) | 6.23984 | 0.367049 | ||||||||
\(290\) | −0.0694983 | −0.00408108 | ||||||||
\(291\) | −6.93248 | −0.406389 | ||||||||
\(292\) | 7.78804 | 0.455760 | ||||||||
\(293\) | 29.0382 | 1.69643 | 0.848214 | − | 0.529653i | \(-0.177678\pi\) | ||||
0.848214 | + | 0.529653i | \(0.177678\pi\) | |||||||
\(294\) | 17.5005 | 1.02065 | ||||||||
\(295\) | 0.0549681 | 0.00320037 | ||||||||
\(296\) | −1.48010 | −0.0860288 | ||||||||
\(297\) | 10.4278 | 0.605082 | ||||||||
\(298\) | −4.23945 | −0.245585 | ||||||||
\(299\) | 12.4531 | 0.720181 | ||||||||
\(300\) | 13.7175 | 0.791980 | ||||||||
\(301\) | 4.98036 | 0.287063 | ||||||||
\(302\) | −12.3953 | −0.713267 | ||||||||
\(303\) | −20.2323 | −1.16232 | ||||||||
\(304\) | 1.27873 | 0.0733400 | ||||||||
\(305\) | −0.194157 | −0.0111174 | ||||||||
\(306\) | 21.8276 | 1.24780 | ||||||||
\(307\) | 9.33714 | 0.532899 | 0.266449 | − | 0.963849i | \(-0.414149\pi\) | ||||
0.266449 | + | 0.963849i | \(0.414149\pi\) | |||||||
\(308\) | −1.96119 | −0.111749 | ||||||||
\(309\) | −33.0784 | −1.88176 | ||||||||
\(310\) | −0.000666036 0 | −3.78283e−5 0 | ||||||||
\(311\) | −13.9792 | −0.792689 | −0.396344 | − | 0.918102i | \(-0.629721\pi\) | ||||
−0.396344 | + | 0.918102i | \(0.629721\pi\) | |||||||
\(312\) | −4.22296 | −0.239078 | ||||||||
\(313\) | 5.19525 | 0.293653 | 0.146826 | − | 0.989162i | \(-0.453094\pi\) | ||||
0.146826 | + | 0.989162i | \(0.453094\pi\) | |||||||
\(314\) | 14.4011 | 0.812700 | ||||||||
\(315\) | 0.0659855 | 0.00371786 | ||||||||
\(316\) | 2.65372 | 0.149283 | ||||||||
\(317\) | −7.35207 | −0.412934 | −0.206467 | − | 0.978454i | \(-0.566197\pi\) | ||||
−0.206467 | + | 0.978454i | \(0.566197\pi\) | |||||||
\(318\) | −31.0199 | −1.73951 | ||||||||
\(319\) | 9.35266 | 0.523648 | ||||||||
\(320\) | 0.0184852 | 0.00103336 | ||||||||
\(321\) | −24.3820 | −1.36087 | ||||||||
\(322\) | 6.37866 | 0.355469 | ||||||||
\(323\) | 6.16445 | 0.342999 | ||||||||
\(324\) | −2.08230 | −0.115683 | ||||||||
\(325\) | −7.69525 | −0.426855 | ||||||||
\(326\) | 12.9831 | 0.719066 | ||||||||
\(327\) | −46.3074 | −2.56081 | ||||||||
\(328\) | −2.01682 | −0.111360 | ||||||||
\(329\) | −3.27960 | −0.180810 | ||||||||
\(330\) | 0.126167 | 0.00694525 | ||||||||
\(331\) | −2.03960 | −0.112106 | −0.0560532 | − | 0.998428i | \(-0.517852\pi\) | ||||
−0.0560532 | + | 0.998428i | \(0.517852\pi\) | |||||||
\(332\) | 1.27427 | 0.0699349 | ||||||||
\(333\) | −6.70161 | −0.367246 | ||||||||
\(334\) | 6.79378 | 0.371739 | ||||||||
\(335\) | 0.0802594 | 0.00438504 | ||||||||
\(336\) | −2.16306 | −0.118005 | ||||||||
\(337\) | 15.4529 | 0.841772 | 0.420886 | − | 0.907114i | \(-0.361719\pi\) | ||||
0.420886 | + | 0.907114i | \(0.361719\pi\) | |||||||
\(338\) | −10.6310 | −0.578250 | ||||||||
\(339\) | −13.5346 | −0.735096 | ||||||||
\(340\) | 0.0891131 | 0.00483283 | ||||||||
\(341\) | 0.0896310 | 0.00485379 | ||||||||
\(342\) | 5.78985 | 0.313079 | ||||||||
\(343\) | −10.5473 | −0.569500 | ||||||||
\(344\) | 6.31722 | 0.340601 | ||||||||
\(345\) | −0.410350 | −0.0220925 | ||||||||
\(346\) | −14.6890 | −0.789688 | ||||||||
\(347\) | 6.31059 | 0.338770 | 0.169385 | − | 0.985550i | \(-0.445822\pi\) | ||||
0.169385 | + | 0.985550i | \(0.445822\pi\) | |||||||
\(348\) | 10.3154 | 0.552961 | ||||||||
\(349\) | 14.4514 | 0.773568 | 0.386784 | − | 0.922170i | \(-0.373586\pi\) | ||||
0.386784 | + | 0.922170i | \(0.373586\pi\) | |||||||
\(350\) | −3.94162 | −0.210689 | ||||||||
\(351\) | −6.45192 | −0.344378 | ||||||||
\(352\) | −2.48763 | −0.132591 | ||||||||
\(353\) | −11.9084 | −0.633822 | −0.316911 | − | 0.948455i | \(-0.602646\pi\) | ||||
−0.316911 | + | 0.948455i | \(0.602646\pi\) | |||||||
\(354\) | −8.15869 | −0.433629 | ||||||||
\(355\) | −0.147816 | −0.00784524 | ||||||||
\(356\) | −15.1053 | −0.800579 | ||||||||
\(357\) | −10.4276 | −0.551889 | ||||||||
\(358\) | 10.5999 | 0.560222 | ||||||||
\(359\) | −1.32615 | −0.0699917 | −0.0349958 | − | 0.999387i | \(-0.511142\pi\) | ||||
−0.0349958 | + | 0.999387i | \(0.511142\pi\) | |||||||
\(360\) | 0.0836978 | 0.00441126 | ||||||||
\(361\) | −17.3649 | −0.913940 | ||||||||
\(362\) | −11.7055 | −0.615225 | ||||||||
\(363\) | 13.2018 | 0.692915 | ||||||||
\(364\) | 1.21344 | 0.0636013 | ||||||||
\(365\) | 0.143964 | 0.00753540 | ||||||||
\(366\) | 28.8180 | 1.50634 | ||||||||
\(367\) | −6.64307 | −0.346765 | −0.173383 | − | 0.984855i | \(-0.555470\pi\) | ||||
−0.173383 | + | 0.984855i | \(0.555470\pi\) | |||||||
\(368\) | 8.09086 | 0.421765 | ||||||||
\(369\) | −9.13181 | −0.475383 | ||||||||
\(370\) | −0.0273599 | −0.00142237 | ||||||||
\(371\) | 8.91334 | 0.462758 | ||||||||
\(372\) | 0.0988570 | 0.00512550 | ||||||||
\(373\) | 21.9878 | 1.13848 | 0.569241 | − | 0.822170i | \(-0.307237\pi\) | ||||
0.569241 | + | 0.822170i | \(0.307237\pi\) | |||||||
\(374\) | −11.9923 | −0.620107 | ||||||||
\(375\) | 0.507160 | 0.0261896 | ||||||||
\(376\) | −4.15993 | −0.214532 | ||||||||
\(377\) | −5.78671 | −0.298031 | ||||||||
\(378\) | −3.30477 | −0.169979 | ||||||||
\(379\) | −12.0688 | −0.619933 | −0.309967 | − | 0.950747i | \(-0.600318\pi\) | ||||
−0.309967 | + | 0.950747i | \(0.600318\pi\) | |||||||
\(380\) | 0.0236376 | 0.00121258 | ||||||||
\(381\) | 33.3605 | 1.70911 | ||||||||
\(382\) | 22.1834 | 1.13500 | ||||||||
\(383\) | −28.9615 | −1.47986 | −0.739931 | − | 0.672683i | \(-0.765142\pi\) | ||||
−0.739931 | + | 0.672683i | \(0.765142\pi\) | |||||||
\(384\) | −2.74369 | −0.140013 | ||||||||
\(385\) | −0.0362531 | −0.00184763 | ||||||||
\(386\) | 4.63212 | 0.235768 | ||||||||
\(387\) | 28.6032 | 1.45398 | ||||||||
\(388\) | 2.52670 | 0.128274 | ||||||||
\(389\) | −3.08570 | −0.156451 | −0.0782255 | − | 0.996936i | \(-0.524925\pi\) | ||||
−0.0782255 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(390\) | −0.0780624 | −0.00395284 | ||||||||
\(391\) | 39.0042 | 1.97253 | ||||||||
\(392\) | −6.37846 | −0.322161 | ||||||||
\(393\) | −2.26302 | −0.114154 | ||||||||
\(394\) | 3.87619 | 0.195280 | ||||||||
\(395\) | 0.0490546 | 0.00246820 | ||||||||
\(396\) | −11.2635 | −0.566014 | ||||||||
\(397\) | 7.76995 | 0.389963 | 0.194981 | − | 0.980807i | \(-0.437535\pi\) | ||||
0.194981 | + | 0.980807i | \(0.437535\pi\) | |||||||
\(398\) | −2.00985 | −0.100745 | ||||||||
\(399\) | −2.76597 | −0.138472 | ||||||||
\(400\) | −4.99966 | −0.249983 | ||||||||
\(401\) | 34.9117 | 1.74341 | 0.871705 | − | 0.490032i | \(-0.163015\pi\) | ||||
0.871705 | + | 0.490032i | \(0.163015\pi\) | |||||||
\(402\) | −11.9126 | −0.594146 | ||||||||
\(403\) | −0.0554568 | −0.00276250 | ||||||||
\(404\) | 7.37414 | 0.366877 | ||||||||
\(405\) | −0.0384918 | −0.00191267 | ||||||||
\(406\) | −2.96404 | −0.147103 | ||||||||
\(407\) | 3.68193 | 0.182506 | ||||||||
\(408\) | −13.2267 | −0.654819 | ||||||||
\(409\) | −34.9325 | −1.72730 | −0.863650 | − | 0.504092i | \(-0.831827\pi\) | ||||
−0.863650 | + | 0.504092i | \(0.831827\pi\) | |||||||
\(410\) | −0.0372814 | −0.00184120 | ||||||||
\(411\) | 63.1290 | 3.11393 | ||||||||
\(412\) | 12.0562 | 0.593965 | ||||||||
\(413\) | 2.34434 | 0.115357 | ||||||||
\(414\) | 36.6340 | 1.80046 | ||||||||
\(415\) | 0.0235553 | 0.00115628 | ||||||||
\(416\) | 1.53915 | 0.0754632 | ||||||||
\(417\) | −60.8173 | −2.97824 | ||||||||
\(418\) | −3.18100 | −0.155588 | ||||||||
\(419\) | 30.3730 | 1.48382 | 0.741909 | − | 0.670501i | \(-0.233921\pi\) | ||||
0.741909 | + | 0.670501i | \(0.233921\pi\) | |||||||
\(420\) | −0.0399847 | −0.00195105 | ||||||||
\(421\) | 23.0913 | 1.12540 | 0.562700 | − | 0.826661i | \(-0.309763\pi\) | ||||
0.562700 | + | 0.826661i | \(0.309763\pi\) | |||||||
\(422\) | 25.9771 | 1.26454 | ||||||||
\(423\) | −18.8354 | −0.915809 | ||||||||
\(424\) | 11.3059 | 0.549064 | ||||||||
\(425\) | −24.1022 | −1.16913 | ||||||||
\(426\) | 21.9397 | 1.06298 | ||||||||
\(427\) | −8.28064 | −0.400728 | ||||||||
\(428\) | 8.88659 | 0.429549 | ||||||||
\(429\) | 10.5052 | 0.507194 | ||||||||
\(430\) | 0.116775 | 0.00563140 | ||||||||
\(431\) | 10.3071 | 0.496478 | 0.248239 | − | 0.968699i | \(-0.420148\pi\) | ||||
0.248239 | + | 0.968699i | \(0.420148\pi\) | |||||||
\(432\) | −4.19186 | −0.201681 | ||||||||
\(433\) | −39.1152 | −1.87976 | −0.939878 | − | 0.341509i | \(-0.889062\pi\) | ||||
−0.939878 | + | 0.341509i | \(0.889062\pi\) | |||||||
\(434\) | −0.0284058 | −0.00136352 | ||||||||
\(435\) | 0.190682 | 0.00914249 | ||||||||
\(436\) | 16.8778 | 0.808300 | ||||||||
\(437\) | 10.3460 | 0.494917 | ||||||||
\(438\) | −21.3679 | −1.02100 | ||||||||
\(439\) | 6.05495 | 0.288987 | 0.144493 | − | 0.989506i | \(-0.453845\pi\) | ||||
0.144493 | + | 0.989506i | \(0.453845\pi\) | |||||||
\(440\) | −0.0459844 | −0.00219222 | ||||||||
\(441\) | −28.8805 | −1.37526 | ||||||||
\(442\) | 7.41991 | 0.352929 | ||||||||
\(443\) | 31.4493 | 1.49420 | 0.747100 | − | 0.664712i | \(-0.231446\pi\) | ||||
0.747100 | + | 0.664712i | \(0.231446\pi\) | |||||||
\(444\) | 4.06092 | 0.192723 | ||||||||
\(445\) | −0.279225 | −0.0132365 | ||||||||
\(446\) | 13.6461 | 0.646162 | ||||||||
\(447\) | 11.6317 | 0.550162 | ||||||||
\(448\) | 0.788378 | 0.0372474 | ||||||||
\(449\) | 14.3148 | 0.675557 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(450\) | −22.6376 | −1.06714 | ||||||||
\(451\) | 5.01711 | 0.236246 | ||||||||
\(452\) | 4.93298 | 0.232028 | ||||||||
\(453\) | 34.0087 | 1.59787 | ||||||||
\(454\) | −20.5680 | −0.965306 | ||||||||
\(455\) | 0.0224306 | 0.00105156 | ||||||||
\(456\) | −3.50843 | −0.164297 | ||||||||
\(457\) | −12.6993 | −0.594050 | −0.297025 | − | 0.954870i | \(-0.595994\pi\) | ||||
−0.297025 | + | 0.954870i | \(0.595994\pi\) | |||||||
\(458\) | 3.11471 | 0.145541 | ||||||||
\(459\) | −20.2080 | −0.943229 | ||||||||
\(460\) | 0.149561 | 0.00697334 | ||||||||
\(461\) | 14.6325 | 0.681503 | 0.340751 | − | 0.940153i | \(-0.389319\pi\) | ||||
0.340751 | + | 0.940153i | \(0.389319\pi\) | |||||||
\(462\) | 5.38090 | 0.250342 | ||||||||
\(463\) | −3.91048 | −0.181735 | −0.0908676 | − | 0.995863i | \(-0.528964\pi\) | ||||
−0.0908676 | + | 0.995863i | \(0.528964\pi\) | |||||||
\(464\) | −3.75967 | −0.174538 | ||||||||
\(465\) | 0.00182739 | 8.47434e−5 0 | ||||||||
\(466\) | −3.85654 | −0.178651 | ||||||||
\(467\) | 37.7693 | 1.74775 | 0.873877 | − | 0.486148i | \(-0.161598\pi\) | ||||
0.873877 | + | 0.486148i | \(0.161598\pi\) | |||||||
\(468\) | 6.96901 | 0.322143 | ||||||||
\(469\) | 3.42299 | 0.158059 | ||||||||
\(470\) | −0.0768972 | −0.00354700 | ||||||||
\(471\) | −39.5121 | −1.82062 | ||||||||
\(472\) | 2.97362 | 0.136872 | ||||||||
\(473\) | −15.7149 | −0.722571 | ||||||||
\(474\) | −7.28097 | −0.334426 | ||||||||
\(475\) | −6.39320 | −0.293340 | ||||||||
\(476\) | 3.80059 | 0.174200 | ||||||||
\(477\) | 51.1912 | 2.34388 | ||||||||
\(478\) | 17.2722 | 0.790011 | ||||||||
\(479\) | 2.74746 | 0.125535 | 0.0627673 | − | 0.998028i | \(-0.480007\pi\) | ||||
0.0627673 | + | 0.998028i | \(0.480007\pi\) | |||||||
\(480\) | −0.0507177 | −0.00231494 | ||||||||
\(481\) | −2.27810 | −0.103872 | ||||||||
\(482\) | 25.5288 | 1.16281 | ||||||||
\(483\) | −17.5010 | −0.796325 | ||||||||
\(484\) | −4.81170 | −0.218714 | ||||||||
\(485\) | 0.0467067 | 0.00212084 | ||||||||
\(486\) | 18.2888 | 0.829596 | ||||||||
\(487\) | −2.34055 | −0.106061 | −0.0530303 | − | 0.998593i | \(-0.516888\pi\) | ||||
−0.0530303 | + | 0.998593i | \(0.516888\pi\) | |||||||
\(488\) | −10.5034 | −0.475466 | ||||||||
\(489\) | −35.6215 | −1.61086 | ||||||||
\(490\) | −0.117907 | −0.00532651 | ||||||||
\(491\) | 0.808608 | 0.0364920 | 0.0182460 | − | 0.999834i | \(-0.494192\pi\) | ||||
0.0182460 | + | 0.999834i | \(0.494192\pi\) | |||||||
\(492\) | 5.53353 | 0.249471 | ||||||||
\(493\) | −18.1245 | −0.816286 | ||||||||
\(494\) | 1.96816 | 0.0885516 | ||||||||
\(495\) | −0.208209 | −0.00935830 | ||||||||
\(496\) | −0.0360307 | −0.00161783 | ||||||||
\(497\) | −6.30420 | −0.282782 | ||||||||
\(498\) | −3.49621 | −0.156669 | ||||||||
\(499\) | −4.23519 | −0.189593 | −0.0947967 | − | 0.995497i | \(-0.530220\pi\) | ||||
−0.0947967 | + | 0.995497i | \(0.530220\pi\) | |||||||
\(500\) | −0.184846 | −0.00826656 | ||||||||
\(501\) | −18.6400 | −0.832775 | ||||||||
\(502\) | 11.9515 | 0.533421 | ||||||||
\(503\) | 37.5604 | 1.67474 | 0.837369 | − | 0.546639i | \(-0.184093\pi\) | ||||
0.837369 | + | 0.546639i | \(0.184093\pi\) | |||||||
\(504\) | 3.56963 | 0.159004 | ||||||||
\(505\) | 0.136313 | 0.00606584 | ||||||||
\(506\) | −20.1271 | −0.894757 | ||||||||
\(507\) | 29.1682 | 1.29540 | ||||||||
\(508\) | −12.1590 | −0.539469 | ||||||||
\(509\) | −8.28309 | −0.367142 | −0.183571 | − | 0.983006i | \(-0.558766\pi\) | ||||
−0.183571 | + | 0.983006i | \(0.558766\pi\) | |||||||
\(510\) | −0.244498 | −0.0108266 | ||||||||
\(511\) | 6.13992 | 0.271614 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.36025 | −0.236661 | ||||||||
\(514\) | 14.0935 | 0.621637 | ||||||||
\(515\) | 0.222861 | 0.00982043 | ||||||||
\(516\) | −17.3325 | −0.763019 | ||||||||
\(517\) | 10.3484 | 0.455120 | ||||||||
\(518\) | −1.16688 | −0.0512696 | ||||||||
\(519\) | 40.3021 | 1.76907 | ||||||||
\(520\) | 0.0284516 | 0.00124769 | ||||||||
\(521\) | −15.8685 | −0.695210 | −0.347605 | − | 0.937641i | \(-0.613005\pi\) | ||||
−0.347605 | + | 0.937641i | \(0.613005\pi\) | |||||||
\(522\) | −17.0231 | −0.745081 | ||||||||
\(523\) | −14.0288 | −0.613435 | −0.306718 | − | 0.951801i | \(-0.599231\pi\) | ||||
−0.306718 | + | 0.951801i | \(0.599231\pi\) | |||||||
\(524\) | 0.824810 | 0.0360320 | ||||||||
\(525\) | 10.8146 | 0.471987 | ||||||||
\(526\) | 18.4311 | 0.803636 | ||||||||
\(527\) | −0.173696 | −0.00756631 | ||||||||
\(528\) | 6.82528 | 0.297032 | ||||||||
\(529\) | 42.4621 | 1.84618 | ||||||||
\(530\) | 0.208993 | 0.00907806 | ||||||||
\(531\) | 13.4640 | 0.584289 | ||||||||
\(532\) | 1.00812 | 0.0437076 | ||||||||
\(533\) | −3.10420 | −0.134458 | ||||||||
\(534\) | 41.4442 | 1.79347 | ||||||||
\(535\) | 0.164271 | 0.00710204 | ||||||||
\(536\) | 4.34181 | 0.187538 | ||||||||
\(537\) | −29.0828 | −1.25502 | ||||||||
\(538\) | 0.809822 | 0.0349139 | ||||||||
\(539\) | 15.8672 | 0.683450 | ||||||||
\(540\) | −0.0774875 | −0.00333453 | ||||||||
\(541\) | −6.00812 | −0.258309 | −0.129155 | − | 0.991624i | \(-0.541226\pi\) | ||||
−0.129155 | + | 0.991624i | \(0.541226\pi\) | |||||||
\(542\) | −8.62338 | −0.370406 | ||||||||
\(543\) | 32.1161 | 1.37823 | ||||||||
\(544\) | 4.82077 | 0.206689 | ||||||||
\(545\) | 0.311990 | 0.0133642 | ||||||||
\(546\) | −3.32929 | −0.142480 | ||||||||
\(547\) | −0.0147045 | −0.000628719 0 | −0.000314360 | − | 1.00000i | \(-0.500100\pi\) | ||||
−0.000314360 | 1.00000i | \(0.500100\pi\) | ||||||||
\(548\) | −23.0088 | −0.982889 | ||||||||
\(549\) | −47.5574 | −2.02970 | ||||||||
\(550\) | 12.4373 | 0.530328 | ||||||||
\(551\) | −4.80759 | −0.204810 | ||||||||
\(552\) | −22.1988 | −0.944844 | ||||||||
\(553\) | 2.09213 | 0.0889665 | ||||||||
\(554\) | 32.1168 | 1.36451 | ||||||||
\(555\) | 0.0750671 | 0.00318642 | ||||||||
\(556\) | 22.1663 | 0.940059 | ||||||||
\(557\) | −13.7665 | −0.583304 | −0.291652 | − | 0.956524i | \(-0.594205\pi\) | ||||
−0.291652 | + | 0.956524i | \(0.594205\pi\) | |||||||
\(558\) | −0.163141 | −0.00690629 | ||||||||
\(559\) | 9.72317 | 0.411246 | ||||||||
\(560\) | 0.0145734 | 0.000615837 0 | ||||||||
\(561\) | 32.9031 | 1.38917 | ||||||||
\(562\) | 7.35716 | 0.310343 | ||||||||
\(563\) | 39.9870 | 1.68525 | 0.842626 | − | 0.538500i | \(-0.181009\pi\) | ||||
0.842626 | + | 0.538500i | \(0.181009\pi\) | |||||||
\(564\) | 11.4135 | 0.480597 | ||||||||
\(565\) | 0.0911872 | 0.00383628 | ||||||||
\(566\) | −15.1597 | −0.637208 | ||||||||
\(567\) | −1.64164 | −0.0689424 | ||||||||
\(568\) | −7.99641 | −0.335522 | ||||||||
\(569\) | 28.5605 | 1.19732 | 0.598659 | − | 0.801004i | \(-0.295701\pi\) | ||||
0.598659 | + | 0.801004i | \(0.295701\pi\) | |||||||
\(570\) | −0.0648541 | −0.00271644 | ||||||||
\(571\) | 9.63595 | 0.403252 | 0.201626 | − | 0.979463i | \(-0.435377\pi\) | ||||
0.201626 | + | 0.979463i | \(0.435377\pi\) | |||||||
\(572\) | −3.82884 | −0.160092 | ||||||||
\(573\) | −60.8642 | −2.54264 | ||||||||
\(574\) | −1.59002 | −0.0663661 | ||||||||
\(575\) | −40.4516 | −1.68695 | ||||||||
\(576\) | 4.52782 | 0.188659 | ||||||||
\(577\) | −13.7790 | −0.573627 | −0.286813 | − | 0.957986i | \(-0.592596\pi\) | ||||
−0.286813 | + | 0.957986i | \(0.592596\pi\) | |||||||
\(578\) | 6.23984 | 0.259543 | ||||||||
\(579\) | −12.7091 | −0.528171 | ||||||||
\(580\) | −0.0694983 | −0.00288576 | ||||||||
\(581\) | 1.00461 | 0.0416782 | ||||||||
\(582\) | −6.93248 | −0.287361 | ||||||||
\(583\) | −28.1249 | −1.16482 | ||||||||
\(584\) | 7.78804 | 0.322271 | ||||||||
\(585\) | 0.128824 | 0.00532621 | ||||||||
\(586\) | 29.0382 | 1.19956 | ||||||||
\(587\) | 8.39657 | 0.346564 | 0.173282 | − | 0.984872i | \(-0.444563\pi\) | ||||
0.173282 | + | 0.984872i | \(0.444563\pi\) | |||||||
\(588\) | 17.5005 | 0.721708 | ||||||||
\(589\) | −0.0460734 | −0.00189842 | ||||||||
\(590\) | 0.0549681 | 0.00226300 | ||||||||
\(591\) | −10.6351 | −0.437468 | ||||||||
\(592\) | −1.48010 | −0.0608316 | ||||||||
\(593\) | 0.968410 | 0.0397679 | 0.0198839 | − | 0.999802i | \(-0.493670\pi\) | ||||
0.0198839 | + | 0.999802i | \(0.493670\pi\) | |||||||
\(594\) | 10.4278 | 0.427858 | ||||||||
\(595\) | 0.0702548 | 0.00288017 | ||||||||
\(596\) | −4.23945 | −0.173655 | ||||||||
\(597\) | 5.51441 | 0.225690 | ||||||||
\(598\) | 12.4531 | 0.509245 | ||||||||
\(599\) | 25.2843 | 1.03309 | 0.516544 | − | 0.856260i | \(-0.327218\pi\) | ||||
0.516544 | + | 0.856260i | \(0.327218\pi\) | |||||||
\(600\) | 13.7175 | 0.560015 | ||||||||
\(601\) | −17.2252 | −0.702630 | −0.351315 | − | 0.936257i | \(-0.614265\pi\) | ||||
−0.351315 | + | 0.936257i | \(0.614265\pi\) | |||||||
\(602\) | 4.98036 | 0.202984 | ||||||||
\(603\) | 19.6590 | 0.800575 | ||||||||
\(604\) | −12.3953 | −0.504356 | ||||||||
\(605\) | −0.0889454 | −0.00361615 | ||||||||
\(606\) | −20.2323 | −0.821883 | ||||||||
\(607\) | −30.4396 | −1.23551 | −0.617753 | − | 0.786372i | \(-0.711957\pi\) | ||||
−0.617753 | + | 0.786372i | \(0.711957\pi\) | |||||||
\(608\) | 1.27873 | 0.0518592 | ||||||||
\(609\) | 8.13240 | 0.329541 | ||||||||
\(610\) | −0.194157 | −0.00786120 | ||||||||
\(611\) | −6.40277 | −0.259028 | ||||||||
\(612\) | 21.8276 | 0.882328 | ||||||||
\(613\) | −32.8020 | −1.32486 | −0.662430 | − | 0.749123i | \(-0.730475\pi\) | ||||
−0.662430 | + | 0.749123i | \(0.730475\pi\) | |||||||
\(614\) | 9.33714 | 0.376816 | ||||||||
\(615\) | 0.102289 | 0.00412467 | ||||||||
\(616\) | −1.96119 | −0.0790187 | ||||||||
\(617\) | −5.77642 | −0.232550 | −0.116275 | − | 0.993217i | \(-0.537095\pi\) | ||||
−0.116275 | + | 0.993217i | \(0.537095\pi\) | |||||||
\(618\) | −33.0784 | −1.33061 | ||||||||
\(619\) | 20.4060 | 0.820186 | 0.410093 | − | 0.912044i | \(-0.365496\pi\) | ||||
0.410093 | + | 0.912044i | \(0.365496\pi\) | |||||||
\(620\) | −0.000666036 0 | −2.67486e−5 0 | ||||||||
\(621\) | −33.9158 | −1.36099 | ||||||||
\(622\) | −13.9792 | −0.560516 | ||||||||
\(623\) | −11.9087 | −0.477112 | ||||||||
\(624\) | −4.22296 | −0.169054 | ||||||||
\(625\) | 24.9949 | 0.999795 | ||||||||
\(626\) | 5.19525 | 0.207644 | ||||||||
\(627\) | 8.72767 | 0.348549 | ||||||||
\(628\) | 14.4011 | 0.574666 | ||||||||
\(629\) | −7.13520 | −0.284499 | ||||||||
\(630\) | 0.0659855 | 0.00262893 | ||||||||
\(631\) | 1.05713 | 0.0420836 | 0.0210418 | − | 0.999779i | \(-0.493302\pi\) | ||||
0.0210418 | + | 0.999779i | \(0.493302\pi\) | |||||||
\(632\) | 2.65372 | 0.105559 | ||||||||
\(633\) | −71.2730 | −2.83285 | ||||||||
\(634\) | −7.35207 | −0.291988 | ||||||||
\(635\) | −0.224762 | −0.00891941 | ||||||||
\(636\) | −31.0199 | −1.23002 | ||||||||
\(637\) | −9.81743 | −0.388981 | ||||||||
\(638\) | 9.35266 | 0.370275 | ||||||||
\(639\) | −36.2063 | −1.43230 | ||||||||
\(640\) | 0.0184852 | 0.000730693 0 | ||||||||
\(641\) | 12.5999 | 0.497668 | 0.248834 | − | 0.968546i | \(-0.419953\pi\) | ||||
0.248834 | + | 0.968546i | \(0.419953\pi\) | |||||||
\(642\) | −24.3820 | −0.962281 | ||||||||
\(643\) | −49.2429 | −1.94195 | −0.970975 | − | 0.239182i | \(-0.923121\pi\) | ||||
−0.970975 | + | 0.239182i | \(0.923121\pi\) | |||||||
\(644\) | 6.37866 | 0.251354 | ||||||||
\(645\) | −0.320395 | −0.0126155 | ||||||||
\(646\) | 6.16445 | 0.242537 | ||||||||
\(647\) | −46.3985 | −1.82411 | −0.912056 | − | 0.410065i | \(-0.865506\pi\) | ||||
−0.912056 | + | 0.410065i | \(0.865506\pi\) | |||||||
\(648\) | −2.08230 | −0.0818005 | ||||||||
\(649\) | −7.39727 | −0.290368 | ||||||||
\(650\) | −7.69525 | −0.301832 | ||||||||
\(651\) | 0.0779367 | 0.00305458 | ||||||||
\(652\) | 12.9831 | 0.508456 | ||||||||
\(653\) | −15.7993 | −0.618275 | −0.309137 | − | 0.951017i | \(-0.600040\pi\) | ||||
−0.309137 | + | 0.951017i | \(0.600040\pi\) | |||||||
\(654\) | −46.3074 | −1.81076 | ||||||||
\(655\) | 0.0152468 | 0.000595742 0 | ||||||||
\(656\) | −2.01682 | −0.0787437 | ||||||||
\(657\) | 35.2628 | 1.37573 | ||||||||
\(658\) | −3.27960 | −0.127852 | ||||||||
\(659\) | 24.6396 | 0.959822 | 0.479911 | − | 0.877317i | \(-0.340669\pi\) | ||||
0.479911 | + | 0.877317i | \(0.340669\pi\) | |||||||
\(660\) | 0.126167 | 0.00491104 | ||||||||
\(661\) | −16.1127 | −0.626710 | −0.313355 | − | 0.949636i | \(-0.601453\pi\) | ||||
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(662\) | −2.03960 | −0.0792713 | ||||||||
\(663\) | −20.3579 | −0.790636 | ||||||||
\(664\) | 1.27427 | 0.0494514 | ||||||||
\(665\) | 0.0186353 | 0.000722647 0 | ||||||||
\(666\) | −6.70161 | −0.259682 | ||||||||
\(667\) | −30.4190 | −1.17783 | ||||||||
\(668\) | 6.79378 | 0.262859 | ||||||||
\(669\) | −37.4407 | −1.44754 | ||||||||
\(670\) | 0.0802594 | 0.00310069 | ||||||||
\(671\) | 26.1285 | 1.00868 | ||||||||
\(672\) | −2.16306 | −0.0834420 | ||||||||
\(673\) | 33.7196 | 1.29979 | 0.649897 | − | 0.760022i | \(-0.274812\pi\) | ||||
0.649897 | + | 0.760022i | \(0.274812\pi\) | |||||||
\(674\) | 15.4529 | 0.595223 | ||||||||
\(675\) | 20.9579 | 0.806669 | ||||||||
\(676\) | −10.6310 | −0.408885 | ||||||||
\(677\) | −2.36642 | −0.0909491 | −0.0454745 | − | 0.998965i | \(-0.514480\pi\) | ||||
−0.0454745 | + | 0.998965i | \(0.514480\pi\) | |||||||
\(678\) | −13.5346 | −0.519791 | ||||||||
\(679\) | 1.99200 | 0.0764458 | ||||||||
\(680\) | 0.0891131 | 0.00341733 | ||||||||
\(681\) | 56.4323 | 2.16249 | ||||||||
\(682\) | 0.0896310 | 0.00343215 | ||||||||
\(683\) | −25.3441 | −0.969765 | −0.484883 | − | 0.874579i | \(-0.661138\pi\) | ||||
−0.484883 | + | 0.874579i | \(0.661138\pi\) | |||||||
\(684\) | 5.78985 | 0.221380 | ||||||||
\(685\) | −0.425324 | −0.0162508 | ||||||||
\(686\) | −10.5473 | −0.402697 | ||||||||
\(687\) | −8.54579 | −0.326042 | ||||||||
\(688\) | 6.31722 | 0.240842 | ||||||||
\(689\) | 17.4016 | 0.662947 | ||||||||
\(690\) | −0.410350 | −0.0156218 | ||||||||
\(691\) | −43.1346 | −1.64092 | −0.820458 | − | 0.571707i | \(-0.806281\pi\) | ||||
−0.820458 | + | 0.571707i | \(0.806281\pi\) | |||||||
\(692\) | −14.6890 | −0.558394 | ||||||||
\(693\) | −8.87993 | −0.337321 | ||||||||
\(694\) | 6.31059 | 0.239547 | ||||||||
\(695\) | 0.409749 | 0.0155427 | ||||||||
\(696\) | 10.3154 | 0.391002 | ||||||||
\(697\) | −9.72264 | −0.368271 | ||||||||
\(698\) | 14.4514 | 0.546995 | ||||||||
\(699\) | 10.5811 | 0.400216 | ||||||||
\(700\) | −3.94162 | −0.148979 | ||||||||
\(701\) | −33.6047 | −1.26923 | −0.634615 | − | 0.772828i | \(-0.718841\pi\) | ||||
−0.634615 | + | 0.772828i | \(0.718841\pi\) | |||||||
\(702\) | −6.45192 | −0.243512 | ||||||||
\(703\) | −1.89264 | −0.0713822 | ||||||||
\(704\) | −2.48763 | −0.0937560 | ||||||||
\(705\) | 0.210982 | 0.00794604 | ||||||||
\(706\) | −11.9084 | −0.448180 | ||||||||
\(707\) | 5.81361 | 0.218643 | ||||||||
\(708\) | −8.15869 | −0.306622 | ||||||||
\(709\) | −44.9350 | −1.68757 | −0.843784 | − | 0.536682i | \(-0.819677\pi\) | ||||
−0.843784 | + | 0.536682i | \(0.819677\pi\) | |||||||
\(710\) | −0.147816 | −0.00554742 | ||||||||
\(711\) | 12.0156 | 0.450618 | ||||||||
\(712\) | −15.1053 | −0.566095 | ||||||||
\(713\) | −0.291519 | −0.0109175 | ||||||||
\(714\) | −10.4276 | −0.390244 | ||||||||
\(715\) | −0.0707771 | −0.00264691 | ||||||||
\(716\) | 10.5999 | 0.396137 | ||||||||
\(717\) | −47.3895 | −1.76979 | ||||||||
\(718\) | −1.32615 | −0.0494916 | ||||||||
\(719\) | −7.55784 | −0.281860 | −0.140930 | − | 0.990020i | \(-0.545009\pi\) | ||||
−0.140930 | + | 0.990020i | \(0.545009\pi\) | |||||||
\(720\) | 0.0836978 | 0.00311923 | ||||||||
\(721\) | 9.50482 | 0.353978 | ||||||||
\(722\) | −17.3649 | −0.646253 | ||||||||
\(723\) | −70.0432 | −2.60493 | ||||||||
\(724\) | −11.7055 | −0.435030 | ||||||||
\(725\) | 18.7971 | 0.698105 | ||||||||
\(726\) | 13.2018 | 0.489965 | ||||||||
\(727\) | 19.0693 | 0.707241 | 0.353621 | − | 0.935389i | \(-0.384950\pi\) | ||||
0.353621 | + | 0.935389i | \(0.384950\pi\) | |||||||
\(728\) | 1.21344 | 0.0449729 | ||||||||
\(729\) | −43.9318 | −1.62710 | ||||||||
\(730\) | 0.143964 | 0.00532833 | ||||||||
\(731\) | 30.4539 | 1.12638 | ||||||||
\(732\) | 28.8180 | 1.06514 | ||||||||
\(733\) | −39.2998 | −1.45157 | −0.725786 | − | 0.687921i | \(-0.758524\pi\) | ||||
−0.725786 | + | 0.687921i | \(0.758524\pi\) | |||||||
\(734\) | −6.64307 | −0.245200 | ||||||||
\(735\) | 0.323501 | 0.0119325 | ||||||||
\(736\) | 8.09086 | 0.298233 | ||||||||
\(737\) | −10.8008 | −0.397853 | ||||||||
\(738\) | −9.13181 | −0.336147 | ||||||||
\(739\) | 16.1536 | 0.594219 | 0.297110 | − | 0.954843i | \(-0.403977\pi\) | ||||
0.297110 | + | 0.954843i | \(0.403977\pi\) | |||||||
\(740\) | −0.0273599 | −0.00100577 | ||||||||
\(741\) | −5.40001 | −0.198374 | ||||||||
\(742\) | 8.91334 | 0.327219 | ||||||||
\(743\) | −7.02866 | −0.257856 | −0.128928 | − | 0.991654i | \(-0.541154\pi\) | ||||
−0.128928 | + | 0.991654i | \(0.541154\pi\) | |||||||
\(744\) | 0.0988570 | 0.00362427 | ||||||||
\(745\) | −0.0783673 | −0.00287116 | ||||||||
\(746\) | 21.9878 | 0.805029 | ||||||||
\(747\) | 5.76969 | 0.211102 | ||||||||
\(748\) | −11.9923 | −0.438482 | ||||||||
\(749\) | 7.00599 | 0.255993 | ||||||||
\(750\) | 0.507160 | 0.0185189 | ||||||||
\(751\) | 22.0628 | 0.805083 | 0.402541 | − | 0.915402i | \(-0.368127\pi\) | ||||
0.402541 | + | 0.915402i | \(0.368127\pi\) | |||||||
\(752\) | −4.15993 | −0.151697 | ||||||||
\(753\) | −32.7912 | −1.19498 | ||||||||
\(754\) | −5.78671 | −0.210739 | ||||||||
\(755\) | −0.229129 | −0.00833886 | ||||||||
\(756\) | −3.30477 | −0.120193 | ||||||||
\(757\) | 26.7813 | 0.973384 | 0.486692 | − | 0.873574i | \(-0.338203\pi\) | ||||
0.486692 | + | 0.873574i | \(0.338203\pi\) | |||||||
\(758\) | −12.0688 | −0.438359 | ||||||||
\(759\) | 55.2224 | 2.00445 | ||||||||
\(760\) | 0.0236376 | 0.000857425 0 | ||||||||
\(761\) | 40.3205 | 1.46162 | 0.730809 | − | 0.682582i | \(-0.239143\pi\) | ||||
0.730809 | + | 0.682582i | \(0.239143\pi\) | |||||||
\(762\) | 33.3605 | 1.20852 | ||||||||
\(763\) | 13.3061 | 0.481713 | ||||||||
\(764\) | 22.1834 | 0.802566 | ||||||||
\(765\) | 0.403488 | 0.0145881 | ||||||||
\(766\) | −28.9615 | −1.04642 | ||||||||
\(767\) | 4.57686 | 0.165261 | ||||||||
\(768\) | −2.74369 | −0.0990043 | ||||||||
\(769\) | −44.8943 | −1.61893 | −0.809465 | − | 0.587168i | \(-0.800243\pi\) | ||||
−0.809465 | + | 0.587168i | \(0.800243\pi\) | |||||||
\(770\) | −0.0362531 | −0.00130647 | ||||||||
\(771\) | −38.6681 | −1.39260 | ||||||||
\(772\) | 4.63212 | 0.166714 | ||||||||
\(773\) | −31.4851 | −1.13244 | −0.566221 | − | 0.824254i | \(-0.691595\pi\) | ||||
−0.566221 | + | 0.824254i | \(0.691595\pi\) | |||||||
\(774\) | 28.6032 | 1.02812 | ||||||||
\(775\) | 0.180141 | 0.00647086 | ||||||||
\(776\) | 2.52670 | 0.0907033 | ||||||||
\(777\) | 3.20154 | 0.114855 | ||||||||
\(778\) | −3.08570 | −0.110628 | ||||||||
\(779\) | −2.57897 | −0.0924010 | ||||||||
\(780\) | −0.0780624 | −0.00279508 | ||||||||
\(781\) | 19.8921 | 0.711796 | ||||||||
\(782\) | 39.0042 | 1.39479 | ||||||||
\(783\) | 15.7600 | 0.563217 | ||||||||
\(784\) | −6.37846 | −0.227802 | ||||||||
\(785\) | 0.266207 | 0.00950135 | ||||||||
\(786\) | −2.26302 | −0.0807193 | ||||||||
\(787\) | −34.6110 | −1.23375 | −0.616874 | − | 0.787062i | \(-0.711601\pi\) | ||||
−0.616874 | + | 0.787062i | \(0.711601\pi\) | |||||||
\(788\) | 3.87619 | 0.138084 | ||||||||
\(789\) | −50.5693 | −1.80031 | ||||||||
\(790\) | 0.0490546 | 0.00174528 | ||||||||
\(791\) | 3.88905 | 0.138279 | ||||||||
\(792\) | −11.2635 | −0.400232 | ||||||||
\(793\) | −16.1663 | −0.574083 | ||||||||
\(794\) | 7.76995 | 0.275745 | ||||||||
\(795\) | −0.573410 | −0.0203368 | ||||||||
\(796\) | −2.00985 | −0.0712374 | ||||||||
\(797\) | 34.8024 | 1.23276 | 0.616382 | − | 0.787447i | \(-0.288598\pi\) | ||||
0.616382 | + | 0.787447i | \(0.288598\pi\) | |||||||
\(798\) | −2.76597 | −0.0979142 | ||||||||
\(799\) | −20.0541 | −0.709462 | ||||||||
\(800\) | −4.99966 | −0.176765 | ||||||||
\(801\) | −68.3941 | −2.41659 | ||||||||
\(802\) | 34.9117 | 1.23278 | ||||||||
\(803\) | −19.3737 | −0.683685 | ||||||||
\(804\) | −11.9126 | −0.420124 | ||||||||
\(805\) | 0.117911 | 0.00415582 | ||||||||
\(806\) | −0.0554568 | −0.00195338 | ||||||||
\(807\) | −2.22190 | −0.0782145 | ||||||||
\(808\) | 7.37414 | 0.259421 | ||||||||
\(809\) | 40.0745 | 1.40894 | 0.704471 | − | 0.709732i | \(-0.251184\pi\) | ||||
0.704471 | + | 0.709732i | \(0.251184\pi\) | |||||||
\(810\) | −0.0384918 | −0.00135246 | ||||||||
\(811\) | −47.9594 | −1.68408 | −0.842041 | − | 0.539414i | \(-0.818646\pi\) | ||||
−0.842041 | + | 0.539414i | \(0.818646\pi\) | |||||||
\(812\) | −2.96404 | −0.104017 | ||||||||
\(813\) | 23.6599 | 0.829788 | ||||||||
\(814\) | 3.68193 | 0.129052 | ||||||||
\(815\) | 0.239995 | 0.00840666 | ||||||||
\(816\) | −13.2267 | −0.463027 | ||||||||
\(817\) | 8.07800 | 0.282613 | ||||||||
\(818\) | −34.9325 | −1.22139 | ||||||||
\(819\) | 5.49422 | 0.191984 | ||||||||
\(820\) | −0.0372814 | −0.00130192 | ||||||||
\(821\) | 23.1030 | 0.806299 | 0.403149 | − | 0.915134i | \(-0.367916\pi\) | ||||
0.403149 | + | 0.915134i | \(0.367916\pi\) | |||||||
\(822\) | 63.1290 | 2.20188 | ||||||||
\(823\) | −22.1407 | −0.771776 | −0.385888 | − | 0.922546i | \(-0.626105\pi\) | ||||
−0.385888 | + | 0.922546i | \(0.626105\pi\) | |||||||
\(824\) | 12.0562 | 0.419996 | ||||||||
\(825\) | −34.1240 | −1.18805 | ||||||||
\(826\) | 2.34434 | 0.0815700 | ||||||||
\(827\) | 31.4763 | 1.09454 | 0.547270 | − | 0.836956i | \(-0.315667\pi\) | ||||
0.547270 | + | 0.836956i | \(0.315667\pi\) | |||||||
\(828\) | 36.6340 | 1.27312 | ||||||||
\(829\) | −20.9745 | −0.728474 | −0.364237 | − | 0.931306i | \(-0.618670\pi\) | ||||
−0.364237 | + | 0.931306i | \(0.618670\pi\) | |||||||
\(830\) | 0.0235553 | 0.000817615 0 | ||||||||
\(831\) | −88.1185 | −3.05680 | ||||||||
\(832\) | 1.53915 | 0.0533606 | ||||||||
\(833\) | −30.7491 | −1.06539 | ||||||||
\(834\) | −60.8173 | −2.10593 | ||||||||
\(835\) | 0.125585 | 0.00434604 | ||||||||
\(836\) | −3.18100 | −0.110017 | ||||||||
\(837\) | 0.151036 | 0.00522056 | ||||||||
\(838\) | 30.3730 | 1.04922 | ||||||||
\(839\) | 20.0722 | 0.692970 | 0.346485 | − | 0.938055i | \(-0.387375\pi\) | ||||
0.346485 | + | 0.938055i | \(0.387375\pi\) | |||||||
\(840\) | −0.0399847 | −0.00137960 | ||||||||
\(841\) | −14.8649 | −0.512583 | ||||||||
\(842\) | 23.0913 | 0.795778 | ||||||||
\(843\) | −20.1858 | −0.695235 | ||||||||
\(844\) | 25.9771 | 0.894168 | ||||||||
\(845\) | −0.196517 | −0.00676038 | ||||||||
\(846\) | −18.8354 | −0.647575 | ||||||||
\(847\) | −3.79344 | −0.130344 | ||||||||
\(848\) | 11.3059 | 0.388247 | ||||||||
\(849\) | 41.5934 | 1.42748 | ||||||||
\(850\) | −24.1022 | −0.826699 | ||||||||
\(851\) | −11.9753 | −0.410506 | ||||||||
\(852\) | 21.9397 | 0.751640 | ||||||||
\(853\) | 24.7291 | 0.846708 | 0.423354 | − | 0.905964i | \(-0.360853\pi\) | ||||
0.423354 | + | 0.905964i | \(0.360853\pi\) | |||||||
\(854\) | −8.28064 | −0.283358 | ||||||||
\(855\) | 0.107027 | 0.00366023 | ||||||||
\(856\) | 8.88659 | 0.303737 | ||||||||
\(857\) | −48.0887 | −1.64268 | −0.821339 | − | 0.570440i | \(-0.806773\pi\) | ||||
−0.821339 | + | 0.570440i | \(0.806773\pi\) | |||||||
\(858\) | 10.5052 | 0.358640 | ||||||||
\(859\) | −13.3622 | −0.455912 | −0.227956 | − | 0.973671i | \(-0.573204\pi\) | ||||
−0.227956 | + | 0.973671i | \(0.573204\pi\) | |||||||
\(860\) | 0.116775 | 0.00398200 | ||||||||
\(861\) | 4.36251 | 0.148674 | ||||||||
\(862\) | 10.3071 | 0.351063 | ||||||||
\(863\) | −13.8921 | −0.472893 | −0.236447 | − | 0.971644i | \(-0.575983\pi\) | ||||
−0.236447 | + | 0.971644i | \(0.575983\pi\) | |||||||
\(864\) | −4.19186 | −0.142610 | ||||||||
\(865\) | −0.271530 | −0.00923231 | ||||||||
\(866\) | −39.1152 | −1.32919 | ||||||||
\(867\) | −17.1202 | −0.581431 | ||||||||
\(868\) | −0.0284058 | −0.000964156 0 | ||||||||
\(869\) | −6.60146 | −0.223939 | ||||||||
\(870\) | 0.190682 | 0.00646471 | ||||||||
\(871\) | 6.68272 | 0.226435 | ||||||||
\(872\) | 16.8778 | 0.571554 | ||||||||
\(873\) | 11.4405 | 0.387201 | ||||||||
\(874\) | 10.3460 | 0.349959 | ||||||||
\(875\) | −0.145729 | −0.00492652 | ||||||||
\(876\) | −21.3679 | −0.721956 | ||||||||
\(877\) | 43.3498 | 1.46382 | 0.731910 | − | 0.681401i | \(-0.238629\pi\) | ||||
0.731910 | + | 0.681401i | \(0.238629\pi\) | |||||||
\(878\) | 6.05495 | 0.204345 | ||||||||
\(879\) | −79.6717 | −2.68726 | ||||||||
\(880\) | −0.0459844 | −0.00155013 | ||||||||
\(881\) | −23.1256 | −0.779122 | −0.389561 | − | 0.921001i | \(-0.627373\pi\) | ||||
−0.389561 | + | 0.921001i | \(0.627373\pi\) | |||||||
\(882\) | −28.8805 | −0.972458 | ||||||||
\(883\) | −40.1517 | −1.35121 | −0.675605 | − | 0.737263i | \(-0.736118\pi\) | ||||
−0.675605 | + | 0.737263i | \(0.736118\pi\) | |||||||
\(884\) | 7.41991 | 0.249559 | ||||||||
\(885\) | −0.150815 | −0.00506960 | ||||||||
\(886\) | 31.4493 | 1.05656 | ||||||||
\(887\) | 2.84685 | 0.0955880 | 0.0477940 | − | 0.998857i | \(-0.484781\pi\) | ||||
0.0477940 | + | 0.998857i | \(0.484781\pi\) | |||||||
\(888\) | 4.06092 | 0.136276 | ||||||||
\(889\) | −9.58589 | −0.321500 | ||||||||
\(890\) | −0.279225 | −0.00935964 | ||||||||
\(891\) | 5.17999 | 0.173536 | ||||||||
\(892\) | 13.6461 | 0.456906 | ||||||||
\(893\) | −5.31941 | −0.178007 | ||||||||
\(894\) | 11.6317 | 0.389023 | ||||||||
\(895\) | 0.195942 | 0.00654960 | ||||||||
\(896\) | 0.788378 | 0.0263379 | ||||||||
\(897\) | −34.1674 | −1.14082 | ||||||||
\(898\) | 14.3148 | 0.477691 | ||||||||
\(899\) | 0.135463 | 0.00451796 | ||||||||
\(900\) | −22.6376 | −0.754585 | ||||||||
\(901\) | 54.5033 | 1.81577 | ||||||||
\(902\) | 5.01711 | 0.167051 | ||||||||
\(903\) | −13.6645 | −0.454727 | ||||||||
\(904\) | 4.93298 | 0.164068 | ||||||||
\(905\) | −0.216378 | −0.00719265 | ||||||||
\(906\) | 34.0087 | 1.12986 | ||||||||
\(907\) | 33.0557 | 1.09760 | 0.548798 | − | 0.835955i | \(-0.315086\pi\) | ||||
0.548798 | + | 0.835955i | \(0.315086\pi\) | |||||||
\(908\) | −20.5680 | −0.682575 | ||||||||
\(909\) | 33.3888 | 1.10744 | ||||||||
\(910\) | 0.0224306 | 0.000743568 0 | ||||||||
\(911\) | −40.3586 | −1.33714 | −0.668570 | − | 0.743649i | \(-0.733093\pi\) | ||||
−0.668570 | + | 0.743649i | \(0.733093\pi\) | |||||||
\(912\) | −3.50843 | −0.116176 | ||||||||
\(913\) | −3.16992 | −0.104909 | ||||||||
\(914\) | −12.6993 | −0.420057 | ||||||||
\(915\) | 0.532707 | 0.0176108 | ||||||||
\(916\) | 3.11471 | 0.102913 | ||||||||
\(917\) | 0.650262 | 0.0214735 | ||||||||
\(918\) | −20.2080 | −0.666964 | ||||||||
\(919\) | 38.4416 | 1.26807 | 0.634035 | − | 0.773304i | \(-0.281398\pi\) | ||||
0.634035 | + | 0.773304i | \(0.281398\pi\) | |||||||
\(920\) | 0.149561 | 0.00493090 | ||||||||
\(921\) | −25.6182 | −0.844148 | ||||||||
\(922\) | 14.6325 | 0.481895 | ||||||||
\(923\) | −12.3077 | −0.405113 | ||||||||
\(924\) | 5.38090 | 0.177019 | ||||||||
\(925\) | 7.39997 | 0.243310 | ||||||||
\(926\) | −3.91048 | −0.128506 | ||||||||
\(927\) | 54.5882 | 1.79291 | ||||||||
\(928\) | −3.75967 | −0.123417 | ||||||||
\(929\) | 34.6265 | 1.13606 | 0.568030 | − | 0.823008i | \(-0.307706\pi\) | ||||
0.568030 | + | 0.823008i | \(0.307706\pi\) | |||||||
\(930\) | 0.00182739 | 5.99226e−5 0 | ||||||||
\(931\) | −8.15631 | −0.267312 | ||||||||
\(932\) | −3.85654 | −0.126325 | ||||||||
\(933\) | 38.3546 | 1.25567 | ||||||||
\(934\) | 37.7693 | 1.23585 | ||||||||
\(935\) | −0.221680 | −0.00724972 | ||||||||
\(936\) | 6.96901 | 0.227789 | ||||||||
\(937\) | 23.4427 | 0.765838 | 0.382919 | − | 0.923782i | \(-0.374919\pi\) | ||||
0.382919 | + | 0.923782i | \(0.374919\pi\) | |||||||
\(938\) | 3.42299 | 0.111765 | ||||||||
\(939\) | −14.2541 | −0.465166 | ||||||||
\(940\) | −0.0768972 | −0.00250811 | ||||||||
\(941\) | 16.0696 | 0.523852 | 0.261926 | − | 0.965088i | \(-0.415642\pi\) | ||||
0.261926 | + | 0.965088i | \(0.415642\pi\) | |||||||
\(942\) | −39.5121 | −1.28737 | ||||||||
\(943\) | −16.3178 | −0.531382 | ||||||||
\(944\) | 2.97362 | 0.0967831 | ||||||||
\(945\) | −0.0610895 | −0.00198724 | ||||||||
\(946\) | −15.7149 | −0.510935 | ||||||||
\(947\) | 57.3229 | 1.86274 | 0.931371 | − | 0.364071i | \(-0.118613\pi\) | ||||
0.931371 | + | 0.364071i | \(0.118613\pi\) | |||||||
\(948\) | −7.28097 | −0.236475 | ||||||||
\(949\) | 11.9870 | 0.389114 | ||||||||
\(950\) | −6.39320 | −0.207423 | ||||||||
\(951\) | 20.1718 | 0.654115 | ||||||||
\(952\) | 3.80059 | 0.123178 | ||||||||
\(953\) | −15.8131 | −0.512237 | −0.256118 | − | 0.966645i | \(-0.582444\pi\) | ||||
−0.256118 | + | 0.966645i | \(0.582444\pi\) | |||||||
\(954\) | 51.1912 | 1.65738 | ||||||||
\(955\) | 0.410065 | 0.0132694 | ||||||||
\(956\) | 17.2722 | 0.558622 | ||||||||
\(957\) | −25.6608 | −0.829495 | ||||||||
\(958\) | 2.74746 | 0.0887663 | ||||||||
\(959\) | −18.1397 | −0.585760 | ||||||||
\(960\) | −0.0507177 | −0.00163691 | ||||||||
\(961\) | −30.9987 | −0.999958 | ||||||||
\(962\) | −2.27810 | −0.0734488 | ||||||||
\(963\) | 40.2369 | 1.29662 | ||||||||
\(964\) | 25.5288 | 0.822229 | ||||||||
\(965\) | 0.0856257 | 0.00275639 | ||||||||
\(966\) | −17.5010 | −0.563087 | ||||||||
\(967\) | −19.7814 | −0.636126 | −0.318063 | − | 0.948070i | \(-0.603032\pi\) | ||||
−0.318063 | + | 0.948070i | \(0.603032\pi\) | |||||||
\(968\) | −4.81170 | −0.154654 | ||||||||
\(969\) | −16.9133 | −0.543334 | ||||||||
\(970\) | 0.0467067 | 0.00149966 | ||||||||
\(971\) | −48.6621 | −1.56164 | −0.780821 | − | 0.624755i | \(-0.785199\pi\) | ||||
−0.780821 | + | 0.624755i | \(0.785199\pi\) | |||||||
\(972\) | 18.2888 | 0.586613 | ||||||||
\(973\) | 17.4754 | 0.560236 | ||||||||
\(974\) | −2.34055 | −0.0749962 | ||||||||
\(975\) | 21.1133 | 0.676168 | ||||||||
\(976\) | −10.5034 | −0.336205 | ||||||||
\(977\) | −42.1880 | −1.34971 | −0.674856 | − | 0.737949i | \(-0.735794\pi\) | ||||
−0.674856 | + | 0.737949i | \(0.735794\pi\) | |||||||
\(978\) | −35.6215 | −1.13905 | ||||||||
\(979\) | 37.5764 | 1.20095 | ||||||||
\(980\) | −0.117907 | −0.00376641 | ||||||||
\(981\) | 76.4197 | 2.43989 | ||||||||
\(982\) | 0.808608 | 0.0258037 | ||||||||
\(983\) | −34.4412 | −1.09850 | −0.549251 | − | 0.835657i | \(-0.685087\pi\) | ||||
−0.549251 | + | 0.835657i | \(0.685087\pi\) | |||||||
\(984\) | 5.53353 | 0.176403 | ||||||||
\(985\) | 0.0716523 | 0.00228303 | ||||||||
\(986\) | −18.1245 | −0.577202 | ||||||||
\(987\) | 8.99819 | 0.286415 | ||||||||
\(988\) | 1.96816 | 0.0626155 | ||||||||
\(989\) | 51.1117 | 1.62526 | ||||||||
\(990\) | −0.208209 | −0.00661732 | ||||||||
\(991\) | −40.3170 | −1.28071 | −0.640355 | − | 0.768079i | \(-0.721213\pi\) | ||||
−0.640355 | + | 0.768079i | \(0.721213\pi\) | |||||||
\(992\) | −0.0360307 | −0.00114398 | ||||||||
\(993\) | 5.59602 | 0.177584 | ||||||||
\(994\) | −6.30420 | −0.199957 | ||||||||
\(995\) | −0.0371526 | −0.00117782 | ||||||||
\(996\) | −3.49621 | −0.110782 | ||||||||
\(997\) | −6.90638 | −0.218727 | −0.109364 | − | 0.994002i | \(-0.534881\pi\) | ||||
−0.109364 | + | 0.994002i | \(0.534881\pi\) | |||||||
\(998\) | −4.23519 | −0.134063 | ||||||||
\(999\) | 6.20436 | 0.196297 |
(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 | 6046.2.a.f.1.6 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.f.1.6 | ✓ | 67 | 1.1 | even | 1 | trivial |