Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3750,2,Mod(1,3750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3750, 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("3750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3750.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: | \(29.9439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3750.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.381966 | −0.144370 | −0.0721848 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721848 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.38197 | 0.416678 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.47214 | −0.685647 | −0.342824 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342824 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(14\) | 0.381966 | 0.102085 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.23607 | 0.784862 | 0.392431 | − | 0.919781i | \(-0.371634\pi\) | ||||
0.392431 | + | 0.919781i | \(0.371634\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.70820 | 1.76838 | 0.884192 | − | 0.467124i | \(-0.154710\pi\) | ||||
0.884192 | + | 0.467124i | \(0.154710\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.381966 | −0.0833518 | ||||||||
\(22\) | −1.38197 | −0.294636 | ||||||||
\(23\) | 4.47214 | 0.932505 | 0.466252 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.47214 | 0.484826 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.381966 | −0.0721848 | ||||||||
\(29\) | −0.472136 | −0.0876734 | −0.0438367 | − | 0.999039i | \(-0.513958\pi\) | ||||
−0.0438367 | + | 0.999039i | \(0.513958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.38197 | 0.787024 | 0.393512 | − | 0.919319i | \(-0.371260\pi\) | ||||
0.393512 | + | 0.919319i | \(0.371260\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.38197 | 0.240569 | ||||||||
\(34\) | −3.23607 | −0.554981 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | −7.70820 | −1.25044 | ||||||||
\(39\) | −2.47214 | −0.395859 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.70820 | −1.20382 | −0.601910 | − | 0.798564i | \(-0.705593\pi\) | ||||
−0.601910 | + | 0.798564i | \(0.705593\pi\) | |||||||
\(42\) | 0.381966 | 0.0589386 | ||||||||
\(43\) | −5.70820 | −0.870493 | −0.435246 | − | 0.900311i | \(-0.643339\pi\) | ||||
−0.435246 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(44\) | 1.38197 | 0.208339 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.47214 | −0.659380 | ||||||||
\(47\) | 11.7082 | 1.70782 | 0.853909 | − | 0.520423i | \(-0.174226\pi\) | ||||
0.853909 | + | 0.520423i | \(0.174226\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.23607 | 0.453140 | ||||||||
\(52\) | −2.47214 | −0.342824 | ||||||||
\(53\) | −9.09017 | −1.24863 | −0.624315 | − | 0.781172i | \(-0.714622\pi\) | ||||
−0.624315 | + | 0.781172i | \(0.714622\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.381966 | 0.0510424 | ||||||||
\(57\) | 7.70820 | 1.02098 | ||||||||
\(58\) | 0.472136 | 0.0619945 | ||||||||
\(59\) | −1.38197 | −0.179917 | −0.0899583 | − | 0.995946i | \(-0.528673\pi\) | ||||
−0.0899583 | + | 0.995946i | \(0.528673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.23607 | 0.926484 | 0.463242 | − | 0.886232i | \(-0.346686\pi\) | ||||
0.463242 | + | 0.886232i | \(0.346686\pi\) | |||||||
\(62\) | −4.38197 | −0.556510 | ||||||||
\(63\) | −0.381966 | −0.0481232 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.38197 | −0.170108 | ||||||||
\(67\) | 10.4721 | 1.27938 | 0.639688 | − | 0.768635i | \(-0.279064\pi\) | ||||
0.639688 | + | 0.768635i | \(0.279064\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | 4.47214 | 0.538382 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4721 | 1.71753 | 0.858763 | − | 0.512373i | \(-0.171233\pi\) | ||||
0.858763 | + | 0.512373i | \(0.171233\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −12.4721 | −1.45975 | −0.729877 | − | 0.683579i | \(-0.760422\pi\) | ||||
−0.729877 | + | 0.683579i | \(0.760422\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.70820 | 0.884192 | ||||||||
\(77\) | −0.527864 | −0.0601557 | ||||||||
\(78\) | 2.47214 | 0.279914 | ||||||||
\(79\) | −3.38197 | −0.380501 | −0.190250 | − | 0.981736i | \(-0.560930\pi\) | ||||
−0.190250 | + | 0.981736i | \(0.560930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.70820 | 0.851229 | ||||||||
\(83\) | −8.85410 | −0.971864 | −0.485932 | − | 0.873997i | \(-0.661520\pi\) | ||||
−0.485932 | + | 0.873997i | \(0.661520\pi\) | |||||||
\(84\) | −0.381966 | −0.0416759 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.70820 | 0.615531 | ||||||||
\(87\) | −0.472136 | −0.0506183 | ||||||||
\(88\) | −1.38197 | −0.147318 | ||||||||
\(89\) | 12.4721 | 1.32204 | 0.661022 | − | 0.750367i | \(-0.270123\pi\) | ||||
0.661022 | + | 0.750367i | \(0.270123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.944272 | 0.0989866 | ||||||||
\(92\) | 4.47214 | 0.466252 | ||||||||
\(93\) | 4.38197 | 0.454389 | ||||||||
\(94\) | −11.7082 | −1.20761 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.61803 | 0.570425 | 0.285212 | − | 0.958464i | \(-0.407936\pi\) | ||||
0.285212 | + | 0.958464i | \(0.407936\pi\) | |||||||
\(98\) | 6.85410 | 0.692369 | ||||||||
\(99\) | 1.38197 | 0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.61803 | 0.658519 | 0.329259 | − | 0.944239i | \(-0.393201\pi\) | ||||
0.329259 | + | 0.944239i | \(0.393201\pi\) | |||||||
\(102\) | −3.23607 | −0.320418 | ||||||||
\(103\) | 1.32624 | 0.130678 | 0.0653391 | − | 0.997863i | \(-0.479187\pi\) | ||||
0.0653391 | + | 0.997863i | \(0.479187\pi\) | |||||||
\(104\) | 2.47214 | 0.242413 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.09017 | 0.882915 | ||||||||
\(107\) | 9.38197 | 0.906989 | 0.453494 | − | 0.891259i | \(-0.350177\pi\) | ||||
0.453494 | + | 0.891259i | \(0.350177\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 12.7639 | 1.22256 | 0.611281 | − | 0.791413i | \(-0.290654\pi\) | ||||
0.611281 | + | 0.791413i | \(0.290654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | −0.381966 | −0.0360924 | ||||||||
\(113\) | 14.7639 | 1.38887 | 0.694437 | − | 0.719554i | \(-0.255654\pi\) | ||||
0.694437 | + | 0.719554i | \(0.255654\pi\) | |||||||
\(114\) | −7.70820 | −0.721939 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.472136 | −0.0438367 | ||||||||
\(117\) | −2.47214 | −0.228549 | ||||||||
\(118\) | 1.38197 | 0.127220 | ||||||||
\(119\) | −1.23607 | −0.113310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.09017 | −0.826379 | ||||||||
\(122\) | −7.23607 | −0.655123 | ||||||||
\(123\) | −7.70820 | −0.695025 | ||||||||
\(124\) | 4.38197 | 0.393512 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.381966 | 0.0340282 | ||||||||
\(127\) | −11.3820 | −1.00999 | −0.504993 | − | 0.863123i | \(-0.668505\pi\) | ||||
−0.504993 | + | 0.863123i | \(0.668505\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.70820 | −0.502579 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8885 | 1.56293 | 0.781465 | − | 0.623949i | \(-0.214473\pi\) | ||||
0.781465 | + | 0.623949i | \(0.214473\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | −2.94427 | −0.255301 | ||||||||
\(134\) | −10.4721 | −0.904655 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.23607 | −0.277491 | ||||||||
\(137\) | −10.1803 | −0.869765 | −0.434883 | − | 0.900487i | \(-0.643210\pi\) | ||||
−0.434883 | + | 0.900487i | \(0.643210\pi\) | |||||||
\(138\) | −4.47214 | −0.380693 | ||||||||
\(139\) | 1.52786 | 0.129592 | 0.0647959 | − | 0.997899i | \(-0.479360\pi\) | ||||
0.0647959 | + | 0.997899i | \(0.479360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.7082 | 0.986009 | ||||||||
\(142\) | −14.4721 | −1.21447 | ||||||||
\(143\) | −3.41641 | −0.285694 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.4721 | 1.03220 | ||||||||
\(147\) | −6.85410 | −0.565317 | ||||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | 10.9098 | 0.893768 | 0.446884 | − | 0.894592i | \(-0.352534\pi\) | ||||
0.446884 | + | 0.894592i | \(0.352534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.67376 | 0.217588 | 0.108794 | − | 0.994064i | \(-0.465301\pi\) | ||||
0.108794 | + | 0.994064i | \(0.465301\pi\) | |||||||
\(152\) | −7.70820 | −0.625218 | ||||||||
\(153\) | 3.23607 | 0.261621 | ||||||||
\(154\) | 0.527864 | 0.0425365 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.47214 | −0.197929 | ||||||||
\(157\) | 22.6525 | 1.80786 | 0.903932 | − | 0.427676i | \(-0.140668\pi\) | ||||
0.903932 | + | 0.427676i | \(0.140668\pi\) | |||||||
\(158\) | 3.38197 | 0.269055 | ||||||||
\(159\) | −9.09017 | −0.720897 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.70820 | −0.134625 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.47214 | −0.663589 | −0.331794 | − | 0.943352i | \(-0.607654\pi\) | ||||
−0.331794 | + | 0.943352i | \(0.607654\pi\) | |||||||
\(164\) | −7.70820 | −0.601910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.85410 | 0.687212 | ||||||||
\(167\) | 1.70820 | 0.132185 | 0.0660924 | − | 0.997814i | \(-0.478947\pi\) | ||||
0.0660924 | + | 0.997814i | \(0.478947\pi\) | |||||||
\(168\) | 0.381966 | 0.0294693 | ||||||||
\(169\) | −6.88854 | −0.529888 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.70820 | 0.589461 | ||||||||
\(172\) | −5.70820 | −0.435246 | ||||||||
\(173\) | 6.09017 | 0.463027 | 0.231514 | − | 0.972832i | \(-0.425632\pi\) | ||||
0.231514 | + | 0.972832i | \(0.425632\pi\) | |||||||
\(174\) | 0.472136 | 0.0357925 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.38197 | 0.104170 | ||||||||
\(177\) | −1.38197 | −0.103875 | ||||||||
\(178\) | −12.4721 | −0.934826 | ||||||||
\(179\) | 3.14590 | 0.235135 | 0.117568 | − | 0.993065i | \(-0.462490\pi\) | ||||
0.117568 | + | 0.993065i | \(0.462490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6525 | 1.83240 | 0.916202 | − | 0.400717i | \(-0.131239\pi\) | ||||
0.916202 | + | 0.400717i | \(0.131239\pi\) | |||||||
\(182\) | −0.944272 | −0.0699941 | ||||||||
\(183\) | 7.23607 | 0.534906 | ||||||||
\(184\) | −4.47214 | −0.329690 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.38197 | −0.321301 | ||||||||
\(187\) | 4.47214 | 0.327035 | ||||||||
\(188\) | 11.7082 | 0.853909 | ||||||||
\(189\) | −0.381966 | −0.0277839 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.7082 | 1.28132 | 0.640660 | − | 0.767824i | \(-0.278661\pi\) | ||||
0.640660 | + | 0.767824i | \(0.278661\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −11.1459 | −0.802299 | −0.401150 | − | 0.916013i | \(-0.631389\pi\) | ||||
−0.401150 | + | 0.916013i | \(0.631389\pi\) | |||||||
\(194\) | −5.61803 | −0.403351 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.85410 | −0.489579 | ||||||||
\(197\) | 5.90983 | 0.421058 | 0.210529 | − | 0.977588i | \(-0.432481\pi\) | ||||
0.210529 | + | 0.977588i | \(0.432481\pi\) | |||||||
\(198\) | −1.38197 | −0.0982120 | ||||||||
\(199\) | −18.5066 | −1.31190 | −0.655948 | − | 0.754806i | \(-0.727731\pi\) | ||||
−0.655948 | + | 0.754806i | \(0.727731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.4721 | 0.738648 | ||||||||
\(202\) | −6.61803 | −0.465643 | ||||||||
\(203\) | 0.180340 | 0.0126574 | ||||||||
\(204\) | 3.23607 | 0.226570 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.32624 | −0.0924034 | ||||||||
\(207\) | 4.47214 | 0.310835 | ||||||||
\(208\) | −2.47214 | −0.171412 | ||||||||
\(209\) | 10.6525 | 0.736847 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.4164 | 1.61205 | 0.806026 | − | 0.591880i | \(-0.201614\pi\) | ||||
0.806026 | + | 0.591880i | \(0.201614\pi\) | |||||||
\(212\) | −9.09017 | −0.624315 | ||||||||
\(213\) | 14.4721 | 0.991614 | ||||||||
\(214\) | −9.38197 | −0.641338 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.67376 | −0.113622 | ||||||||
\(218\) | −12.7639 | −0.864483 | ||||||||
\(219\) | −12.4721 | −0.842789 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 8.00000 | 0.536925 | ||||||||
\(223\) | −3.09017 | −0.206933 | −0.103467 | − | 0.994633i | \(-0.532993\pi\) | ||||
−0.103467 | + | 0.994633i | \(0.532993\pi\) | |||||||
\(224\) | 0.381966 | 0.0255212 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.7639 | −0.982082 | ||||||||
\(227\) | −11.2705 | −0.748050 | −0.374025 | − | 0.927419i | \(-0.622023\pi\) | ||||
−0.374025 | + | 0.927419i | \(0.622023\pi\) | |||||||
\(228\) | 7.70820 | 0.510488 | ||||||||
\(229\) | −14.4721 | −0.956346 | −0.478173 | − | 0.878266i | \(-0.658701\pi\) | ||||
−0.478173 | + | 0.878266i | \(0.658701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.527864 | −0.0347309 | ||||||||
\(232\) | 0.472136 | 0.0309972 | ||||||||
\(233\) | 12.6525 | 0.828891 | 0.414446 | − | 0.910074i | \(-0.363976\pi\) | ||||
0.414446 | + | 0.910074i | \(0.363976\pi\) | |||||||
\(234\) | 2.47214 | 0.161609 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.38197 | −0.0899583 | ||||||||
\(237\) | −3.38197 | −0.219682 | ||||||||
\(238\) | 1.23607 | 0.0801224 | ||||||||
\(239\) | 25.7082 | 1.66293 | 0.831463 | − | 0.555581i | \(-0.187504\pi\) | ||||
0.831463 | + | 0.555581i | \(0.187504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5623 | −0.680378 | −0.340189 | − | 0.940357i | \(-0.610491\pi\) | ||||
−0.340189 | + | 0.940357i | \(0.610491\pi\) | |||||||
\(242\) | 9.09017 | 0.584338 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.23607 | 0.463242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.70820 | 0.491457 | ||||||||
\(247\) | −19.0557 | −1.21249 | ||||||||
\(248\) | −4.38197 | −0.278255 | ||||||||
\(249\) | −8.85410 | −0.561106 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.56231 | −0.414209 | −0.207105 | − | 0.978319i | \(-0.566404\pi\) | ||||
−0.207105 | + | 0.978319i | \(0.566404\pi\) | |||||||
\(252\) | −0.381966 | −0.0240616 | ||||||||
\(253\) | 6.18034 | 0.388555 | ||||||||
\(254\) | 11.3820 | 0.714168 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | 5.70820 | 0.355377 | ||||||||
\(259\) | 3.05573 | 0.189874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.472136 | −0.0292245 | ||||||||
\(262\) | −17.8885 | −1.10516 | ||||||||
\(263\) | −1.70820 | −0.105332 | −0.0526662 | − | 0.998612i | \(-0.516772\pi\) | ||||
−0.0526662 | + | 0.998612i | \(0.516772\pi\) | |||||||
\(264\) | −1.38197 | −0.0850541 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.94427 | 0.180525 | ||||||||
\(267\) | 12.4721 | 0.763282 | ||||||||
\(268\) | 10.4721 | 0.639688 | ||||||||
\(269\) | 2.09017 | 0.127440 | 0.0637200 | − | 0.997968i | \(-0.479704\pi\) | ||||
0.0637200 | + | 0.997968i | \(0.479704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0344 | 0.670295 | 0.335147 | − | 0.942166i | \(-0.391214\pi\) | ||||
0.335147 | + | 0.942166i | \(0.391214\pi\) | |||||||
\(272\) | 3.23607 | 0.196215 | ||||||||
\(273\) | 0.944272 | 0.0571499 | ||||||||
\(274\) | 10.1803 | 0.615017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.47214 | 0.269191 | ||||||||
\(277\) | 0.944272 | 0.0567358 | 0.0283679 | − | 0.999598i | \(-0.490969\pi\) | ||||
0.0283679 | + | 0.999598i | \(0.490969\pi\) | |||||||
\(278\) | −1.52786 | −0.0916352 | ||||||||
\(279\) | 4.38197 | 0.262341 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.8885 | −1.78300 | −0.891501 | − | 0.453020i | \(-0.850347\pi\) | ||||
−0.891501 | + | 0.453020i | \(0.850347\pi\) | |||||||
\(282\) | −11.7082 | −0.697213 | ||||||||
\(283\) | −31.4164 | −1.86751 | −0.933756 | − | 0.357911i | \(-0.883489\pi\) | ||||
−0.933756 | + | 0.357911i | \(0.883489\pi\) | |||||||
\(284\) | 14.4721 | 0.858763 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.41641 | 0.202016 | ||||||||
\(287\) | 2.94427 | 0.173795 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.61803 | 0.329335 | ||||||||
\(292\) | −12.4721 | −0.729877 | ||||||||
\(293\) | 10.9098 | 0.637359 | 0.318680 | − | 0.947863i | \(-0.396761\pi\) | ||||
0.318680 | + | 0.947863i | \(0.396761\pi\) | |||||||
\(294\) | 6.85410 | 0.399739 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.00000 | 0.464991 | ||||||||
\(297\) | 1.38197 | 0.0801898 | ||||||||
\(298\) | −10.9098 | −0.631989 | ||||||||
\(299\) | −11.0557 | −0.639369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18034 | 0.125673 | ||||||||
\(302\) | −2.67376 | −0.153858 | ||||||||
\(303\) | 6.61803 | 0.380196 | ||||||||
\(304\) | 7.70820 | 0.442096 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.23607 | −0.184994 | ||||||||
\(307\) | −10.0000 | −0.570730 | −0.285365 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285365 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(308\) | −0.527864 | −0.0300778 | ||||||||
\(309\) | 1.32624 | 0.0754470 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.9443 | −1.07423 | −0.537116 | − | 0.843509i | \(-0.680486\pi\) | ||||
−0.537116 | + | 0.843509i | \(0.680486\pi\) | |||||||
\(312\) | 2.47214 | 0.139957 | ||||||||
\(313\) | −17.2705 | −0.976187 | −0.488093 | − | 0.872791i | \(-0.662307\pi\) | ||||
−0.488093 | + | 0.872791i | \(0.662307\pi\) | |||||||
\(314\) | −22.6525 | −1.27835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.38197 | −0.190250 | ||||||||
\(317\) | 0.437694 | 0.0245833 | 0.0122917 | − | 0.999924i | \(-0.496087\pi\) | ||||
0.0122917 | + | 0.999924i | \(0.496087\pi\) | |||||||
\(318\) | 9.09017 | 0.509751 | ||||||||
\(319\) | −0.652476 | −0.0365316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.38197 | 0.523650 | ||||||||
\(322\) | 1.70820 | 0.0951945 | ||||||||
\(323\) | 24.9443 | 1.38794 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.47214 | 0.469228 | ||||||||
\(327\) | 12.7639 | 0.705847 | ||||||||
\(328\) | 7.70820 | 0.425614 | ||||||||
\(329\) | −4.47214 | −0.246557 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0000 | −0.989369 | −0.494685 | − | 0.869072i | \(-0.664716\pi\) | ||||
−0.494685 | + | 0.869072i | \(0.664716\pi\) | |||||||
\(332\) | −8.85410 | −0.485932 | ||||||||
\(333\) | −8.00000 | −0.438397 | ||||||||
\(334\) | −1.70820 | −0.0934688 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.381966 | −0.0208380 | ||||||||
\(337\) | −12.0902 | −0.658594 | −0.329297 | − | 0.944226i | \(-0.606812\pi\) | ||||
−0.329297 | + | 0.944226i | \(0.606812\pi\) | |||||||
\(338\) | 6.88854 | 0.374687 | ||||||||
\(339\) | 14.7639 | 0.801867 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.05573 | 0.327936 | ||||||||
\(342\) | −7.70820 | −0.416812 | ||||||||
\(343\) | 5.29180 | 0.285730 | ||||||||
\(344\) | 5.70820 | 0.307766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.09017 | −0.327410 | ||||||||
\(347\) | −0.437694 | −0.0234967 | −0.0117483 | − | 0.999931i | \(-0.503740\pi\) | ||||
−0.0117483 | + | 0.999931i | \(0.503740\pi\) | |||||||
\(348\) | −0.472136 | −0.0253091 | ||||||||
\(349\) | 7.88854 | 0.422264 | 0.211132 | − | 0.977458i | \(-0.432285\pi\) | ||||
0.211132 | + | 0.977458i | \(0.432285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.47214 | −0.131953 | ||||||||
\(352\) | −1.38197 | −0.0736590 | ||||||||
\(353\) | 8.76393 | 0.466457 | 0.233229 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233229 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(354\) | 1.38197 | 0.0734507 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.4721 | 0.661022 | ||||||||
\(357\) | −1.23607 | −0.0654197 | ||||||||
\(358\) | −3.14590 | −0.166266 | ||||||||
\(359\) | −0.180340 | −0.00951798 | −0.00475899 | − | 0.999989i | \(-0.501515\pi\) | ||||
−0.00475899 | + | 0.999989i | \(0.501515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.4164 | 2.12718 | ||||||||
\(362\) | −24.6525 | −1.29571 | ||||||||
\(363\) | −9.09017 | −0.477110 | ||||||||
\(364\) | 0.944272 | 0.0494933 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.23607 | −0.378235 | ||||||||
\(367\) | 28.3820 | 1.48153 | 0.740763 | − | 0.671766i | \(-0.234464\pi\) | ||||
0.740763 | + | 0.671766i | \(0.234464\pi\) | |||||||
\(368\) | 4.47214 | 0.233126 | ||||||||
\(369\) | −7.70820 | −0.401273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.47214 | 0.180264 | ||||||||
\(372\) | 4.38197 | 0.227194 | ||||||||
\(373\) | 20.4721 | 1.06001 | 0.530004 | − | 0.847995i | \(-0.322191\pi\) | ||||
0.530004 | + | 0.847995i | \(0.322191\pi\) | |||||||
\(374\) | −4.47214 | −0.231249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.7082 | −0.603805 | ||||||||
\(377\) | 1.16718 | 0.0601130 | ||||||||
\(378\) | 0.381966 | 0.0196462 | ||||||||
\(379\) | 2.18034 | 0.111997 | 0.0559983 | − | 0.998431i | \(-0.482166\pi\) | ||||
0.0559983 | + | 0.998431i | \(0.482166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3820 | −0.583116 | ||||||||
\(382\) | −17.7082 | −0.906031 | ||||||||
\(383\) | 20.0000 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.1459 | 0.567311 | ||||||||
\(387\) | −5.70820 | −0.290164 | ||||||||
\(388\) | 5.61803 | 0.285212 | ||||||||
\(389\) | −14.6180 | −0.741164 | −0.370582 | − | 0.928800i | \(-0.620842\pi\) | ||||
−0.370582 | + | 0.928800i | \(0.620842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4721 | 0.731887 | ||||||||
\(392\) | 6.85410 | 0.346184 | ||||||||
\(393\) | 17.8885 | 0.902358 | ||||||||
\(394\) | −5.90983 | −0.297733 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.38197 | 0.0694464 | ||||||||
\(397\) | 35.2361 | 1.76845 | 0.884224 | − | 0.467063i | \(-0.154688\pi\) | ||||
0.884224 | + | 0.467063i | \(0.154688\pi\) | |||||||
\(398\) | 18.5066 | 0.927651 | ||||||||
\(399\) | −2.94427 | −0.147398 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2918 | 0.613823 | 0.306912 | − | 0.951738i | \(-0.400704\pi\) | ||||
0.306912 | + | 0.951738i | \(0.400704\pi\) | |||||||
\(402\) | −10.4721 | −0.522303 | ||||||||
\(403\) | −10.8328 | −0.539621 | ||||||||
\(404\) | 6.61803 | 0.329259 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.180340 | −0.00895012 | ||||||||
\(407\) | −11.0557 | −0.548012 | ||||||||
\(408\) | −3.23607 | −0.160209 | ||||||||
\(409\) | −18.7984 | −0.929520 | −0.464760 | − | 0.885437i | \(-0.653859\pi\) | ||||
−0.464760 | + | 0.885437i | \(0.653859\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1803 | −0.502159 | ||||||||
\(412\) | 1.32624 | 0.0653391 | ||||||||
\(413\) | 0.527864 | 0.0259745 | ||||||||
\(414\) | −4.47214 | −0.219793 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.47214 | 0.121206 | ||||||||
\(417\) | 1.52786 | 0.0748198 | ||||||||
\(418\) | −10.6525 | −0.521030 | ||||||||
\(419\) | 8.09017 | 0.395231 | 0.197615 | − | 0.980280i | \(-0.436680\pi\) | ||||
0.197615 | + | 0.980280i | \(0.436680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.2361 | −1.32740 | −0.663702 | − | 0.747997i | \(-0.731016\pi\) | ||||
−0.663702 | + | 0.747997i | \(0.731016\pi\) | |||||||
\(422\) | −23.4164 | −1.13989 | ||||||||
\(423\) | 11.7082 | 0.569272 | ||||||||
\(424\) | 9.09017 | 0.441458 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4721 | −0.701177 | ||||||||
\(427\) | −2.76393 | −0.133756 | ||||||||
\(428\) | 9.38197 | 0.453494 | ||||||||
\(429\) | −3.41641 | −0.164946 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.8328 | −1.77417 | −0.887087 | − | 0.461602i | \(-0.847275\pi\) | ||||
−0.887087 | + | 0.461602i | \(0.847275\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 22.5066 | 1.08160 | 0.540799 | − | 0.841152i | \(-0.318122\pi\) | ||||
0.540799 | + | 0.841152i | \(0.318122\pi\) | |||||||
\(434\) | 1.67376 | 0.0803432 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.7639 | 0.611281 | ||||||||
\(437\) | 34.4721 | 1.64903 | ||||||||
\(438\) | 12.4721 | 0.595942 | ||||||||
\(439\) | 14.5066 | 0.692361 | 0.346181 | − | 0.938168i | \(-0.387478\pi\) | ||||
0.346181 | + | 0.938168i | \(0.387478\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.85410 | −0.326386 | ||||||||
\(442\) | 8.00000 | 0.380521 | ||||||||
\(443\) | −14.3820 | −0.683308 | −0.341654 | − | 0.939826i | \(-0.610987\pi\) | ||||
−0.341654 | + | 0.939826i | \(0.610987\pi\) | |||||||
\(444\) | −8.00000 | −0.379663 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.09017 | 0.146324 | ||||||||
\(447\) | 10.9098 | 0.516017 | ||||||||
\(448\) | −0.381966 | −0.0180462 | ||||||||
\(449\) | −14.2918 | −0.674472 | −0.337236 | − | 0.941420i | \(-0.609492\pi\) | ||||
−0.337236 | + | 0.941420i | \(0.609492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6525 | −0.501605 | ||||||||
\(452\) | 14.7639 | 0.694437 | ||||||||
\(453\) | 2.67376 | 0.125624 | ||||||||
\(454\) | 11.2705 | 0.528951 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.70820 | −0.360970 | ||||||||
\(457\) | −7.09017 | −0.331664 | −0.165832 | − | 0.986154i | \(-0.553031\pi\) | ||||
−0.165832 | + | 0.986154i | \(0.553031\pi\) | |||||||
\(458\) | 14.4721 | 0.676239 | ||||||||
\(459\) | 3.23607 | 0.151047 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5623 | −0.585085 | −0.292542 | − | 0.956253i | \(-0.594501\pi\) | ||||
−0.292542 | + | 0.956253i | \(0.594501\pi\) | |||||||
\(462\) | 0.527864 | 0.0245585 | ||||||||
\(463\) | −30.8328 | −1.43292 | −0.716461 | − | 0.697627i | \(-0.754239\pi\) | ||||
−0.716461 | + | 0.697627i | \(0.754239\pi\) | |||||||
\(464\) | −0.472136 | −0.0219184 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.6525 | −0.586115 | ||||||||
\(467\) | −26.3262 | −1.21823 | −0.609117 | − | 0.793081i | \(-0.708476\pi\) | ||||
−0.609117 | + | 0.793081i | \(0.708476\pi\) | |||||||
\(468\) | −2.47214 | −0.114275 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.6525 | 1.04377 | ||||||||
\(472\) | 1.38197 | 0.0636101 | ||||||||
\(473\) | −7.88854 | −0.362716 | ||||||||
\(474\) | 3.38197 | 0.155339 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.23607 | −0.0566551 | ||||||||
\(477\) | −9.09017 | −0.416210 | ||||||||
\(478\) | −25.7082 | −1.17587 | ||||||||
\(479\) | 11.1246 | 0.508296 | 0.254148 | − | 0.967165i | \(-0.418205\pi\) | ||||
0.254148 | + | 0.967165i | \(0.418205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.7771 | 0.901758 | ||||||||
\(482\) | 10.5623 | 0.481100 | ||||||||
\(483\) | −1.70820 | −0.0777260 | ||||||||
\(484\) | −9.09017 | −0.413190 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 6.79837 | 0.308064 | 0.154032 | − | 0.988066i | \(-0.450774\pi\) | ||||
0.154032 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(488\) | −7.23607 | −0.327561 | ||||||||
\(489\) | −8.47214 | −0.383123 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.27051 | 0.373243 | 0.186621 | − | 0.982432i | \(-0.440246\pi\) | ||||
0.186621 | + | 0.982432i | \(0.440246\pi\) | |||||||
\(492\) | −7.70820 | −0.347513 | ||||||||
\(493\) | −1.52786 | −0.0688115 | ||||||||
\(494\) | 19.0557 | 0.857358 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.38197 | 0.196756 | ||||||||
\(497\) | −5.52786 | −0.247959 | ||||||||
\(498\) | 8.85410 | 0.396762 | ||||||||
\(499\) | −13.5967 | −0.608674 | −0.304337 | − | 0.952564i | \(-0.598435\pi\) | ||||
−0.304337 | + | 0.952564i | \(0.598435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.70820 | 0.0763169 | ||||||||
\(502\) | 6.56231 | 0.292890 | ||||||||
\(503\) | 11.8885 | 0.530084 | 0.265042 | − | 0.964237i | \(-0.414614\pi\) | ||||
0.265042 | + | 0.964237i | \(0.414614\pi\) | |||||||
\(504\) | 0.381966 | 0.0170141 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.18034 | −0.274750 | ||||||||
\(507\) | −6.88854 | −0.305931 | ||||||||
\(508\) | −11.3820 | −0.504993 | ||||||||
\(509\) | 20.5066 | 0.908938 | 0.454469 | − | 0.890763i | \(-0.349829\pi\) | ||||
0.454469 | + | 0.890763i | \(0.349829\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.76393 | 0.210744 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.70820 | 0.340326 | ||||||||
\(514\) | −22.0000 | −0.970378 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.70820 | −0.251290 | ||||||||
\(517\) | 16.1803 | 0.711611 | ||||||||
\(518\) | −3.05573 | −0.134261 | ||||||||
\(519\) | 6.09017 | 0.267329 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.18034 | −0.358387 | −0.179194 | − | 0.983814i | \(-0.557349\pi\) | ||||
−0.179194 | + | 0.983814i | \(0.557349\pi\) | |||||||
\(522\) | 0.472136 | 0.0206648 | ||||||||
\(523\) | −28.9443 | −1.26564 | −0.632822 | − | 0.774297i | \(-0.718104\pi\) | ||||
−0.632822 | + | 0.774297i | \(0.718104\pi\) | |||||||
\(524\) | 17.8885 | 0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.70820 | 0.0744812 | ||||||||
\(527\) | 14.1803 | 0.617705 | ||||||||
\(528\) | 1.38197 | 0.0601424 | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.38197 | −0.0599722 | ||||||||
\(532\) | −2.94427 | −0.127650 | ||||||||
\(533\) | 19.0557 | 0.825395 | ||||||||
\(534\) | −12.4721 | −0.539722 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.4721 | −0.452327 | ||||||||
\(537\) | 3.14590 | 0.135756 | ||||||||
\(538\) | −2.09017 | −0.0901136 | ||||||||
\(539\) | −9.47214 | −0.407994 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.81966 | −0.164220 | −0.0821100 | − | 0.996623i | \(-0.526166\pi\) | ||||
−0.0821100 | + | 0.996623i | \(0.526166\pi\) | |||||||
\(542\) | −11.0344 | −0.473970 | ||||||||
\(543\) | 24.6525 | 1.05794 | ||||||||
\(544\) | −3.23607 | −0.138745 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.944272 | −0.0404111 | ||||||||
\(547\) | 3.70820 | 0.158551 | 0.0792757 | − | 0.996853i | \(-0.474739\pi\) | ||||
0.0792757 | + | 0.996853i | \(0.474739\pi\) | |||||||
\(548\) | −10.1803 | −0.434883 | ||||||||
\(549\) | 7.23607 | 0.308828 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.63932 | −0.155040 | ||||||||
\(552\) | −4.47214 | −0.190347 | ||||||||
\(553\) | 1.29180 | 0.0549328 | ||||||||
\(554\) | −0.944272 | −0.0401183 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.52786 | 0.0647959 | ||||||||
\(557\) | 2.67376 | 0.113291 | 0.0566455 | − | 0.998394i | \(-0.481960\pi\) | ||||
0.0566455 | + | 0.998394i | \(0.481960\pi\) | |||||||
\(558\) | −4.38197 | −0.185503 | ||||||||
\(559\) | 14.1115 | 0.596851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.47214 | 0.188814 | ||||||||
\(562\) | 29.8885 | 1.26077 | ||||||||
\(563\) | 12.2705 | 0.517140 | 0.258570 | − | 0.965992i | \(-0.416749\pi\) | ||||
0.258570 | + | 0.965992i | \(0.416749\pi\) | |||||||
\(564\) | 11.7082 | 0.493004 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 31.4164 | 1.32053 | ||||||||
\(567\) | −0.381966 | −0.0160411 | ||||||||
\(568\) | −14.4721 | −0.607237 | ||||||||
\(569\) | 43.7771 | 1.83523 | 0.917615 | − | 0.397469i | \(-0.130111\pi\) | ||||
0.917615 | + | 0.397469i | \(0.130111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.8885 | −1.16710 | −0.583550 | − | 0.812077i | \(-0.698337\pi\) | ||||
−0.583550 | + | 0.812077i | \(0.698337\pi\) | |||||||
\(572\) | −3.41641 | −0.142847 | ||||||||
\(573\) | 17.7082 | 0.739771 | ||||||||
\(574\) | −2.94427 | −0.122892 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 37.9787 | 1.58107 | 0.790537 | − | 0.612414i | \(-0.209801\pi\) | ||||
0.790537 | + | 0.612414i | \(0.209801\pi\) | |||||||
\(578\) | 6.52786 | 0.271523 | ||||||||
\(579\) | −11.1459 | −0.463208 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.38197 | 0.140308 | ||||||||
\(582\) | −5.61803 | −0.232875 | ||||||||
\(583\) | −12.5623 | −0.520278 | ||||||||
\(584\) | 12.4721 | 0.516101 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.9098 | −0.450681 | ||||||||
\(587\) | 30.0344 | 1.23965 | 0.619827 | − | 0.784738i | \(-0.287203\pi\) | ||||
0.619827 | + | 0.784738i | \(0.287203\pi\) | |||||||
\(588\) | −6.85410 | −0.282658 | ||||||||
\(589\) | 33.7771 | 1.39176 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.90983 | 0.243098 | ||||||||
\(592\) | −8.00000 | −0.328798 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | −1.38197 | −0.0567028 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.9098 | 0.446884 | ||||||||
\(597\) | −18.5066 | −0.757424 | ||||||||
\(598\) | 11.0557 | 0.452102 | ||||||||
\(599\) | −8.47214 | −0.346162 | −0.173081 | − | 0.984908i | \(-0.555372\pi\) | ||||
−0.173081 | + | 0.984908i | \(0.555372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2705 | −1.68346 | −0.841730 | − | 0.539899i | \(-0.818462\pi\) | ||||
−0.841730 | + | 0.539899i | \(0.818462\pi\) | |||||||
\(602\) | −2.18034 | −0.0888640 | ||||||||
\(603\) | 10.4721 | 0.426458 | ||||||||
\(604\) | 2.67376 | 0.108794 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.61803 | −0.268839 | ||||||||
\(607\) | 13.5623 | 0.550477 | 0.275239 | − | 0.961376i | \(-0.411243\pi\) | ||||
0.275239 | + | 0.961376i | \(0.411243\pi\) | |||||||
\(608\) | −7.70820 | −0.312609 | ||||||||
\(609\) | 0.180340 | 0.00730774 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.9443 | −1.17096 | ||||||||
\(612\) | 3.23607 | 0.130810 | ||||||||
\(613\) | 32.2492 | 1.30253 | 0.651267 | − | 0.758849i | \(-0.274238\pi\) | ||||
0.651267 | + | 0.758849i | \(0.274238\pi\) | |||||||
\(614\) | 10.0000 | 0.403567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.527864 | 0.0212682 | ||||||||
\(617\) | −37.8885 | −1.52534 | −0.762668 | − | 0.646791i | \(-0.776111\pi\) | ||||
−0.762668 | + | 0.646791i | \(0.776111\pi\) | |||||||
\(618\) | −1.32624 | −0.0533491 | ||||||||
\(619\) | 17.4164 | 0.700025 | 0.350012 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350012 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.47214 | 0.179461 | ||||||||
\(622\) | 18.9443 | 0.759596 | ||||||||
\(623\) | −4.76393 | −0.190863 | ||||||||
\(624\) | −2.47214 | −0.0989646 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2705 | 0.690268 | ||||||||
\(627\) | 10.6525 | 0.425419 | ||||||||
\(628\) | 22.6525 | 0.903932 | ||||||||
\(629\) | −25.8885 | −1.03224 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.5279 | 1.49396 | 0.746980 | − | 0.664846i | \(-0.231503\pi\) | ||||
0.746980 | + | 0.664846i | \(0.231503\pi\) | |||||||
\(632\) | 3.38197 | 0.134527 | ||||||||
\(633\) | 23.4164 | 0.930719 | ||||||||
\(634\) | −0.437694 | −0.0173831 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.09017 | −0.360449 | ||||||||
\(637\) | 16.9443 | 0.671356 | ||||||||
\(638\) | 0.652476 | 0.0258318 | ||||||||
\(639\) | 14.4721 | 0.572509 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.1803 | −1.42904 | −0.714519 | − | 0.699616i | \(-0.753354\pi\) | ||||
−0.714519 | + | 0.699616i | \(0.753354\pi\) | |||||||
\(642\) | −9.38197 | −0.370277 | ||||||||
\(643\) | 13.8885 | 0.547711 | 0.273855 | − | 0.961771i | \(-0.411701\pi\) | ||||
0.273855 | + | 0.961771i | \(0.411701\pi\) | |||||||
\(644\) | −1.70820 | −0.0673127 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.9443 | −0.981419 | ||||||||
\(647\) | 5.05573 | 0.198761 | 0.0993806 | − | 0.995049i | \(-0.468314\pi\) | ||||
0.0993806 | + | 0.995049i | \(0.468314\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.90983 | −0.0749674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.67376 | −0.0655999 | ||||||||
\(652\) | −8.47214 | −0.331794 | ||||||||
\(653\) | −2.85410 | −0.111690 | −0.0558448 | − | 0.998439i | \(-0.517785\pi\) | ||||
−0.0558448 | + | 0.998439i | \(0.517785\pi\) | |||||||
\(654\) | −12.7639 | −0.499109 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.70820 | −0.300955 | ||||||||
\(657\) | −12.4721 | −0.486584 | ||||||||
\(658\) | 4.47214 | 0.174342 | ||||||||
\(659\) | −18.3820 | −0.716060 | −0.358030 | − | 0.933710i | \(-0.616551\pi\) | ||||
−0.358030 | + | 0.933710i | \(0.616551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.5279 | −0.837337 | −0.418668 | − | 0.908139i | \(-0.637503\pi\) | ||||
−0.418668 | + | 0.908139i | \(0.637503\pi\) | |||||||
\(662\) | 18.0000 | 0.699590 | ||||||||
\(663\) | −8.00000 | −0.310694 | ||||||||
\(664\) | 8.85410 | 0.343606 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.00000 | 0.309994 | ||||||||
\(667\) | −2.11146 | −0.0817559 | ||||||||
\(668\) | 1.70820 | 0.0660924 | ||||||||
\(669\) | −3.09017 | −0.119473 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | 0.381966 | 0.0147347 | ||||||||
\(673\) | −24.4508 | −0.942511 | −0.471255 | − | 0.881997i | \(-0.656199\pi\) | ||||
−0.471255 | + | 0.881997i | \(0.656199\pi\) | |||||||
\(674\) | 12.0902 | 0.465696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.88854 | −0.264944 | ||||||||
\(677\) | −17.9098 | −0.688331 | −0.344165 | − | 0.938909i | \(-0.611838\pi\) | ||||
−0.344165 | + | 0.938909i | \(0.611838\pi\) | |||||||
\(678\) | −14.7639 | −0.567005 | ||||||||
\(679\) | −2.14590 | −0.0823520 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2705 | −0.431887 | ||||||||
\(682\) | −6.05573 | −0.231886 | ||||||||
\(683\) | 4.50658 | 0.172439 | 0.0862197 | − | 0.996276i | \(-0.472521\pi\) | ||||
0.0862197 | + | 0.996276i | \(0.472521\pi\) | |||||||
\(684\) | 7.70820 | 0.294731 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.29180 | −0.202042 | ||||||||
\(687\) | −14.4721 | −0.552146 | ||||||||
\(688\) | −5.70820 | −0.217623 | ||||||||
\(689\) | 22.4721 | 0.856120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.76393 | 0.257312 | 0.128656 | − | 0.991689i | \(-0.458934\pi\) | ||||
0.128656 | + | 0.991689i | \(0.458934\pi\) | |||||||
\(692\) | 6.09017 | 0.231514 | ||||||||
\(693\) | −0.527864 | −0.0200519 | ||||||||
\(694\) | 0.437694 | 0.0166146 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.472136 | 0.0178963 | ||||||||
\(697\) | −24.9443 | −0.944832 | ||||||||
\(698\) | −7.88854 | −0.298586 | ||||||||
\(699\) | 12.6525 | 0.478561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.8328 | −0.484689 | −0.242344 | − | 0.970190i | \(-0.577916\pi\) | ||||
−0.242344 | + | 0.970190i | \(0.577916\pi\) | |||||||
\(702\) | 2.47214 | 0.0933048 | ||||||||
\(703\) | −61.6656 | −2.32576 | ||||||||
\(704\) | 1.38197 | 0.0520848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.76393 | −0.329835 | ||||||||
\(707\) | −2.52786 | −0.0950701 | ||||||||
\(708\) | −1.38197 | −0.0519375 | ||||||||
\(709\) | −30.2918 | −1.13763 | −0.568816 | − | 0.822465i | \(-0.692598\pi\) | ||||
−0.568816 | + | 0.822465i | \(0.692598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.38197 | −0.126834 | ||||||||
\(712\) | −12.4721 | −0.467413 | ||||||||
\(713\) | 19.5967 | 0.733904 | ||||||||
\(714\) | 1.23607 | 0.0462587 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.14590 | 0.117568 | ||||||||
\(717\) | 25.7082 | 0.960090 | ||||||||
\(718\) | 0.180340 | 0.00673022 | ||||||||
\(719\) | −43.4164 | −1.61916 | −0.809579 | − | 0.587010i | \(-0.800305\pi\) | ||||
−0.809579 | + | 0.587010i | \(0.800305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.506578 | −0.0188659 | ||||||||
\(722\) | −40.4164 | −1.50414 | ||||||||
\(723\) | −10.5623 | −0.392816 | ||||||||
\(724\) | 24.6525 | 0.916202 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.09017 | 0.337368 | ||||||||
\(727\) | 35.4164 | 1.31352 | 0.656761 | − | 0.754099i | \(-0.271926\pi\) | ||||
0.656761 | + | 0.754099i | \(0.271926\pi\) | |||||||
\(728\) | −0.944272 | −0.0349970 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.4721 | −0.683217 | ||||||||
\(732\) | 7.23607 | 0.267453 | ||||||||
\(733\) | 0.111456 | 0.00411673 | 0.00205836 | − | 0.999998i | \(-0.499345\pi\) | ||||
0.00205836 | + | 0.999998i | \(0.499345\pi\) | |||||||
\(734\) | −28.3820 | −1.04760 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.47214 | −0.164845 | ||||||||
\(737\) | 14.4721 | 0.533088 | ||||||||
\(738\) | 7.70820 | 0.283743 | ||||||||
\(739\) | −25.8197 | −0.949792 | −0.474896 | − | 0.880042i | \(-0.657514\pi\) | ||||
−0.474896 | + | 0.880042i | \(0.657514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.0557 | −0.700030 | ||||||||
\(742\) | −3.47214 | −0.127466 | ||||||||
\(743\) | −37.0132 | −1.35788 | −0.678940 | − | 0.734193i | \(-0.737561\pi\) | ||||
−0.678940 | + | 0.734193i | \(0.737561\pi\) | |||||||
\(744\) | −4.38197 | −0.160651 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.4721 | −0.749538 | ||||||||
\(747\) | −8.85410 | −0.323955 | ||||||||
\(748\) | 4.47214 | 0.163517 | ||||||||
\(749\) | −3.58359 | −0.130942 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.201626 | 0.00735744 | 0.00367872 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367872 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(752\) | 11.7082 | 0.426954 | ||||||||
\(753\) | −6.56231 | −0.239144 | ||||||||
\(754\) | −1.16718 | −0.0425063 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.381966 | −0.0138920 | ||||||||
\(757\) | −23.1246 | −0.840478 | −0.420239 | − | 0.907413i | \(-0.638054\pi\) | ||||
−0.420239 | + | 0.907413i | \(0.638054\pi\) | |||||||
\(758\) | −2.18034 | −0.0791935 | ||||||||
\(759\) | 6.18034 | 0.224332 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.4164 | −0.921344 | −0.460672 | − | 0.887570i | \(-0.652392\pi\) | ||||
−0.460672 | + | 0.887570i | \(0.652392\pi\) | |||||||
\(762\) | 11.3820 | 0.412325 | ||||||||
\(763\) | −4.87539 | −0.176501 | ||||||||
\(764\) | 17.7082 | 0.640660 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.0000 | −0.722629 | ||||||||
\(767\) | 3.41641 | 0.123359 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −35.6869 | −1.28690 | −0.643452 | − | 0.765487i | \(-0.722498\pi\) | ||||
−0.643452 | + | 0.765487i | \(0.722498\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | 0.792311 | ||||||||
\(772\) | −11.1459 | −0.401150 | ||||||||
\(773\) | 7.85410 | 0.282492 | 0.141246 | − | 0.989974i | \(-0.454889\pi\) | ||||
0.141246 | + | 0.989974i | \(0.454889\pi\) | |||||||
\(774\) | 5.70820 | 0.205177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.61803 | −0.201676 | ||||||||
\(777\) | 3.05573 | 0.109624 | ||||||||
\(778\) | 14.6180 | 0.524082 | ||||||||
\(779\) | −59.4164 | −2.12881 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0000 | 0.715656 | ||||||||
\(782\) | −14.4721 | −0.517523 | ||||||||
\(783\) | −0.472136 | −0.0168728 | ||||||||
\(784\) | −6.85410 | −0.244789 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.8885 | −0.638063 | ||||||||
\(787\) | 30.0689 | 1.07184 | 0.535920 | − | 0.844269i | \(-0.319965\pi\) | ||||
0.535920 | + | 0.844269i | \(0.319965\pi\) | |||||||
\(788\) | 5.90983 | 0.210529 | ||||||||
\(789\) | −1.70820 | −0.0608137 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.63932 | −0.200511 | ||||||||
\(792\) | −1.38197 | −0.0491060 | ||||||||
\(793\) | −17.8885 | −0.635241 | ||||||||
\(794\) | −35.2361 | −1.25048 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.5066 | −0.655948 | ||||||||
\(797\) | 36.5066 | 1.29313 | 0.646565 | − | 0.762859i | \(-0.276205\pi\) | ||||
0.646565 | + | 0.762859i | \(0.276205\pi\) | |||||||
\(798\) | 2.94427 | 0.104226 | ||||||||
\(799\) | 37.8885 | 1.34040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.4721 | 0.440681 | ||||||||
\(802\) | −12.2918 | −0.434038 | ||||||||
\(803\) | −17.2361 | −0.608248 | ||||||||
\(804\) | 10.4721 | 0.369324 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.8328 | 0.381570 | ||||||||
\(807\) | 2.09017 | 0.0735775 | ||||||||
\(808\) | −6.61803 | −0.232822 | ||||||||
\(809\) | 22.8328 | 0.802759 | 0.401380 | − | 0.915912i | \(-0.368531\pi\) | ||||
0.401380 | + | 0.915912i | \(0.368531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.70820 | 0.270672 | 0.135336 | − | 0.990800i | \(-0.456789\pi\) | ||||
0.135336 | + | 0.990800i | \(0.456789\pi\) | |||||||
\(812\) | 0.180340 | 0.00632869 | ||||||||
\(813\) | 11.0344 | 0.386995 | ||||||||
\(814\) | 11.0557 | 0.387503 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.23607 | 0.113285 | ||||||||
\(817\) | −44.0000 | −1.53937 | ||||||||
\(818\) | 18.7984 | 0.657270 | ||||||||
\(819\) | 0.944272 | 0.0329955 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.9098 | −1.18346 | −0.591731 | − | 0.806136i | \(-0.701555\pi\) | ||||
−0.591731 | + | 0.806136i | \(0.701555\pi\) | |||||||
\(822\) | 10.1803 | 0.355080 | ||||||||
\(823\) | −32.0344 | −1.11665 | −0.558325 | − | 0.829622i | \(-0.688556\pi\) | ||||
−0.558325 | + | 0.829622i | \(0.688556\pi\) | |||||||
\(824\) | −1.32624 | −0.0462017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.527864 | −0.0183667 | ||||||||
\(827\) | 43.1033 | 1.49885 | 0.749425 | − | 0.662090i | \(-0.230330\pi\) | ||||
0.749425 | + | 0.662090i | \(0.230330\pi\) | |||||||
\(828\) | 4.47214 | 0.155417 | ||||||||
\(829\) | −9.88854 | −0.343443 | −0.171722 | − | 0.985146i | \(-0.554933\pi\) | ||||
−0.171722 | + | 0.985146i | \(0.554933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.944272 | 0.0327564 | ||||||||
\(832\) | −2.47214 | −0.0857059 | ||||||||
\(833\) | −22.1803 | −0.768503 | ||||||||
\(834\) | −1.52786 | −0.0529056 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.6525 | 0.368424 | ||||||||
\(837\) | 4.38197 | 0.151463 | ||||||||
\(838\) | −8.09017 | −0.279470 | ||||||||
\(839\) | −38.3607 | −1.32436 | −0.662179 | − | 0.749346i | \(-0.730368\pi\) | ||||
−0.662179 | + | 0.749346i | \(0.730368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | 27.2361 | 0.938617 | ||||||||
\(843\) | −29.8885 | −1.02942 | ||||||||
\(844\) | 23.4164 | 0.806026 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.7082 | −0.402536 | ||||||||
\(847\) | 3.47214 | 0.119304 | ||||||||
\(848\) | −9.09017 | −0.312158 | ||||||||
\(849\) | −31.4164 | −1.07821 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.7771 | −1.22642 | ||||||||
\(852\) | 14.4721 | 0.495807 | ||||||||
\(853\) | −5.59675 | −0.191629 | −0.0958145 | − | 0.995399i | \(-0.530546\pi\) | ||||
−0.0958145 | + | 0.995399i | \(0.530546\pi\) | |||||||
\(854\) | 2.76393 | 0.0945798 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.38197 | −0.320669 | ||||||||
\(857\) | −42.0689 | −1.43705 | −0.718523 | − | 0.695503i | \(-0.755181\pi\) | ||||
−0.718523 | + | 0.695503i | \(0.755181\pi\) | |||||||
\(858\) | 3.41641 | 0.116634 | ||||||||
\(859\) | −15.7082 | −0.535957 | −0.267979 | − | 0.963425i | \(-0.586356\pi\) | ||||
−0.267979 | + | 0.963425i | \(0.586356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.94427 | 0.100341 | ||||||||
\(862\) | 36.8328 | 1.25453 | ||||||||
\(863\) | −12.1803 | −0.414624 | −0.207312 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207312 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −22.5066 | −0.764805 | ||||||||
\(867\) | −6.52786 | −0.221698 | ||||||||
\(868\) | −1.67376 | −0.0568112 | ||||||||
\(869\) | −4.67376 | −0.158547 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.8885 | −0.877200 | ||||||||
\(872\) | −12.7639 | −0.432241 | ||||||||
\(873\) | 5.61803 | 0.190142 | ||||||||
\(874\) | −34.4721 | −1.16604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.4721 | −0.421394 | ||||||||
\(877\) | −3.12461 | −0.105511 | −0.0527553 | − | 0.998607i | \(-0.516800\pi\) | ||||
−0.0527553 | + | 0.998607i | \(0.516800\pi\) | |||||||
\(878\) | −14.5066 | −0.489573 | ||||||||
\(879\) | 10.9098 | 0.367979 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5967 | 0.862376 | 0.431188 | − | 0.902262i | \(-0.358095\pi\) | ||||
0.431188 | + | 0.902262i | \(0.358095\pi\) | |||||||
\(882\) | 6.85410 | 0.230790 | ||||||||
\(883\) | −28.0689 | −0.944593 | −0.472297 | − | 0.881440i | \(-0.656575\pi\) | ||||
−0.472297 | + | 0.881440i | \(0.656575\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.3820 | 0.483172 | ||||||||
\(887\) | 3.41641 | 0.114712 | 0.0573559 | − | 0.998354i | \(-0.481733\pi\) | ||||
0.0573559 | + | 0.998354i | \(0.481733\pi\) | |||||||
\(888\) | 8.00000 | 0.268462 | ||||||||
\(889\) | 4.34752 | 0.145811 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.38197 | 0.0462976 | ||||||||
\(892\) | −3.09017 | −0.103467 | ||||||||
\(893\) | 90.2492 | 3.02008 | ||||||||
\(894\) | −10.9098 | −0.364879 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.381966 | 0.0127606 | ||||||||
\(897\) | −11.0557 | −0.369140 | ||||||||
\(898\) | 14.2918 | 0.476923 | ||||||||
\(899\) | −2.06888 | −0.0690011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.4164 | −0.980003 | ||||||||
\(902\) | 10.6525 | 0.354689 | ||||||||
\(903\) | 2.18034 | 0.0725572 | ||||||||
\(904\) | −14.7639 | −0.491041 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.67376 | −0.0888298 | ||||||||
\(907\) | −21.5279 | −0.714821 | −0.357410 | − | 0.933947i | \(-0.616340\pi\) | ||||
−0.357410 | + | 0.933947i | \(0.616340\pi\) | |||||||
\(908\) | −11.2705 | −0.374025 | ||||||||
\(909\) | 6.61803 | 0.219506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.18034 | −0.138501 | −0.0692504 | − | 0.997599i | \(-0.522061\pi\) | ||||
−0.0692504 | + | 0.997599i | \(0.522061\pi\) | |||||||
\(912\) | 7.70820 | 0.255244 | ||||||||
\(913\) | −12.2361 | −0.404955 | ||||||||
\(914\) | 7.09017 | 0.234522 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.4721 | −0.478173 | ||||||||
\(917\) | −6.83282 | −0.225639 | ||||||||
\(918\) | −3.23607 | −0.106806 | ||||||||
\(919\) | 48.7214 | 1.60717 | 0.803585 | − | 0.595190i | \(-0.202923\pi\) | ||||
0.803585 | + | 0.595190i | \(0.202923\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | −0.329511 | ||||||||
\(922\) | 12.5623 | 0.413718 | ||||||||
\(923\) | −35.7771 | −1.17762 | ||||||||
\(924\) | −0.527864 | −0.0173655 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.8328 | 1.01323 | ||||||||
\(927\) | 1.32624 | 0.0435594 | ||||||||
\(928\) | 0.472136 | 0.0154986 | ||||||||
\(929\) | 57.0132 | 1.87054 | 0.935270 | − | 0.353934i | \(-0.115156\pi\) | ||||
0.935270 | + | 0.353934i | \(0.115156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.8328 | −1.73153 | ||||||||
\(932\) | 12.6525 | 0.414446 | ||||||||
\(933\) | −18.9443 | −0.620208 | ||||||||
\(934\) | 26.3262 | 0.861421 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.47214 | 0.0808043 | ||||||||
\(937\) | −51.6869 | −1.68854 | −0.844269 | − | 0.535920i | \(-0.819965\pi\) | ||||
−0.844269 | + | 0.535920i | \(0.819965\pi\) | |||||||
\(938\) | 4.00000 | 0.130605 | ||||||||
\(939\) | −17.2705 | −0.563602 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.5623 | −0.800708 | −0.400354 | − | 0.916360i | \(-0.631113\pi\) | ||||
−0.400354 | + | 0.916360i | \(0.631113\pi\) | |||||||
\(942\) | −22.6525 | −0.738058 | ||||||||
\(943\) | −34.4721 | −1.12257 | ||||||||
\(944\) | −1.38197 | −0.0449792 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.88854 | 0.256479 | ||||||||
\(947\) | 13.4377 | 0.436666 | 0.218333 | − | 0.975874i | \(-0.429938\pi\) | ||||
0.218333 | + | 0.975874i | \(0.429938\pi\) | |||||||
\(948\) | −3.38197 | −0.109841 | ||||||||
\(949\) | 30.8328 | 1.00088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.437694 | 0.0141932 | ||||||||
\(952\) | 1.23607 | 0.0400612 | ||||||||
\(953\) | 57.3050 | 1.85629 | 0.928145 | − | 0.372219i | \(-0.121403\pi\) | ||||
0.928145 | + | 0.372219i | \(0.121403\pi\) | |||||||
\(954\) | 9.09017 | 0.294305 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.7082 | 0.831463 | ||||||||
\(957\) | −0.652476 | −0.0210915 | ||||||||
\(958\) | −11.1246 | −0.359420 | ||||||||
\(959\) | 3.88854 | 0.125568 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.7984 | −0.380593 | ||||||||
\(962\) | −19.7771 | −0.637639 | ||||||||
\(963\) | 9.38197 | 0.302330 | ||||||||
\(964\) | −10.5623 | −0.340189 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.70820 | 0.0549606 | ||||||||
\(967\) | −22.0902 | −0.710372 | −0.355186 | − | 0.934796i | \(-0.615582\pi\) | ||||
−0.355186 | + | 0.934796i | \(0.615582\pi\) | |||||||
\(968\) | 9.09017 | 0.292169 | ||||||||
\(969\) | 24.9443 | 0.801325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.2148 | 1.19428 | 0.597140 | − | 0.802137i | \(-0.296304\pi\) | ||||
0.597140 | + | 0.802137i | \(0.296304\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −0.583592 | −0.0187091 | ||||||||
\(974\) | −6.79837 | −0.217834 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.23607 | 0.231621 | ||||||||
\(977\) | 5.23607 | 0.167517 | 0.0837583 | − | 0.996486i | \(-0.473308\pi\) | ||||
0.0837583 | + | 0.996486i | \(0.473308\pi\) | |||||||
\(978\) | 8.47214 | 0.270909 | ||||||||
\(979\) | 17.2361 | 0.550867 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7639 | 0.407521 | ||||||||
\(982\) | −8.27051 | −0.263923 | ||||||||
\(983\) | −17.8197 | −0.568359 | −0.284179 | − | 0.958771i | \(-0.591721\pi\) | ||||
−0.284179 | + | 0.958771i | \(0.591721\pi\) | |||||||
\(984\) | 7.70820 | 0.245729 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.52786 | 0.0486571 | ||||||||
\(987\) | −4.47214 | −0.142350 | ||||||||
\(988\) | −19.0557 | −0.606243 | ||||||||
\(989\) | −25.5279 | −0.811739 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.4508 | −0.840239 | −0.420119 | − | 0.907469i | \(-0.638012\pi\) | ||||
−0.420119 | + | 0.907469i | \(0.638012\pi\) | |||||||
\(992\) | −4.38197 | −0.139128 | ||||||||
\(993\) | −18.0000 | −0.571213 | ||||||||
\(994\) | 5.52786 | 0.175333 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.85410 | −0.280553 | ||||||||
\(997\) | −43.5967 | −1.38072 | −0.690361 | − | 0.723465i | \(-0.742548\pi\) | ||||
−0.690361 | + | 0.723465i | \(0.742548\pi\) | |||||||
\(998\) | 13.5967 | 0.430398 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(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 | 3750.2.a.d.1.2 | 2 | ||
5.2 | odd | 4 | 3750.2.c.b.1249.2 | 4 | |||
5.3 | odd | 4 | 3750.2.c.b.1249.3 | 4 | |||
5.4 | even | 2 | 3750.2.a.f.1.1 | 2 | |||
25.2 | odd | 20 | 750.2.h.b.649.1 | 8 | |||
25.9 | even | 10 | 150.2.g.a.31.1 | ✓ | 4 | ||
25.11 | even | 5 | 750.2.g.b.601.1 | 4 | |||
25.12 | odd | 20 | 750.2.h.b.349.2 | 8 | |||
25.13 | odd | 20 | 750.2.h.b.349.1 | 8 | |||
25.14 | even | 10 | 150.2.g.a.121.1 | yes | 4 | ||
25.16 | even | 5 | 750.2.g.b.151.1 | 4 | |||
25.23 | odd | 20 | 750.2.h.b.649.2 | 8 | |||
75.14 | odd | 10 | 450.2.h.c.271.1 | 4 | |||
75.59 | odd | 10 | 450.2.h.c.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.31.1 | ✓ | 4 | 25.9 | even | 10 | ||
150.2.g.a.121.1 | yes | 4 | 25.14 | even | 10 | ||
450.2.h.c.181.1 | 4 | 75.59 | odd | 10 | |||
450.2.h.c.271.1 | 4 | 75.14 | odd | 10 | |||
750.2.g.b.151.1 | 4 | 25.16 | even | 5 | |||
750.2.g.b.601.1 | 4 | 25.11 | even | 5 | |||
750.2.h.b.349.1 | 8 | 25.13 | odd | 20 | |||
750.2.h.b.349.2 | 8 | 25.12 | odd | 20 | |||
750.2.h.b.649.1 | 8 | 25.2 | odd | 20 | |||
750.2.h.b.649.2 | 8 | 25.23 | odd | 20 | |||
3750.2.a.d.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3750.2.a.f.1.1 | 2 | 5.4 | even | 2 | |||
3750.2.c.b.1249.2 | 4 | 5.2 | odd | 4 | |||
3750.2.c.b.1249.3 | 4 | 5.3 | odd | 4 |