Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1471,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.i (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32x^{14} + 400x^{12} - 2398x^{10} + 7128x^{8} - 9200x^{6} + 4705x^{4} + 2696x^{2} + 784 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.3 | ||
Root | \(-3.23546 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1471 |
Dual form | 1840.2.i.a.1471.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.36943i | − | 1.36799i | −0.729485 | − | 0.683996i | \(-0.760240\pi\) | ||
0.729485 | − | 0.683996i | \(-0.239760\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.10148 | 1.55022 | 0.775108 | − | 0.631829i | \(-0.217696\pi\) | ||||
0.775108 | + | 0.631829i | \(0.217696\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61421 | −0.871405 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.58230 | 0.477080 | 0.238540 | − | 0.971133i | \(-0.423331\pi\) | ||||
0.238540 | + | 0.971133i | \(0.423331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.61421 | 0.447702 | 0.223851 | − | 0.974623i | \(-0.428137\pi\) | ||||
0.223851 | + | 0.974623i | \(0.428137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.36943 | −0.611785 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.614214i | − | 0.148969i | −0.997222 | − | 0.0744843i | \(-0.976269\pi\) | ||
0.997222 | − | 0.0744843i | \(-0.0237311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.28353 | 0.753293 | 0.376647 | − | 0.926357i | \(-0.377077\pi\) | ||||
0.376647 | + | 0.926357i | \(0.377077\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 9.71819i | − | 2.12068i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.21968 | + | 4.25124i | 0.462835 | + | 0.886444i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.914095i | − | 0.175918i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.48977 | 1.76221 | 0.881103 | − | 0.472925i | \(-0.156802\pi\) | ||||
0.881103 | + | 0.472925i | \(0.156802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.91336i | 0.702861i | 0.936214 | + | 0.351430i | \(0.114305\pi\) | ||||
−0.936214 | + | 0.351430i | \(0.885695\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.74915i | − | 0.652643i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.10148i | − | 0.693277i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.87360i | − | 0.636815i | −0.947954 | − | 0.318408i | \(-0.896852\pi\) | ||
0.947954 | − | 0.318408i | \(-0.103148\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.82477i | − | 0.612454i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.45881 | 0.540175 | 0.270088 | − | 0.962836i | \(-0.412947\pi\) | ||||
0.270088 | + | 0.962836i | \(0.412947\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.20297 | −1.25094 | −0.625470 | − | 0.780248i | \(-0.715093\pi\) | ||||
−0.625470 | + | 0.780248i | \(0.715093\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.61421i | 0.389704i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.487628i | − | 0.0711279i | −0.999367 | − | 0.0355640i | \(-0.988677\pi\) | ||
0.999367 | − | 0.0355640i | \(-0.0113227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.82217 | 1.40317 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.45534 | −0.203788 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.645168i | 0.0886206i | 0.999018 | + | 0.0443103i | \(0.0141090\pi\) | ||||
−0.999018 | + | 0.0443103i | \(0.985891\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.58230i | − | 0.213357i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.78010i | − | 1.03050i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.3132i | 1.86342i | 0.363201 | + | 0.931711i | \(0.381684\pi\) | ||||
−0.363201 | + | 0.931711i | \(0.618316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.94858i | − | 0.889674i | −0.895612 | − | 0.444837i | \(-0.853262\pi\) | ||
0.895612 | − | 0.444837i | \(-0.146738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.7222 | −1.35086 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.61421i | − | 0.200219i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.87386 | 1.20628 | 0.603142 | − | 0.797634i | \(-0.293915\pi\) | ||||
0.603142 | + | 0.797634i | \(0.293915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.0730 | − | 5.25938i | 1.21265 | − | 0.633155i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.75445i | 1.15764i | 0.815455 | + | 0.578820i | \(0.196487\pi\) | ||||
−0.815455 | + | 0.578820i | \(0.803513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5918 | −1.23967 | −0.619837 | − | 0.784730i | \(-0.712801\pi\) | ||||
−0.619837 | + | 0.784730i | \(0.712801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.36943i | 0.273599i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.48977 | 0.739577 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.7302 | −1.76978 | −0.884892 | − | 0.465796i | \(-0.845768\pi\) | ||||
−0.884892 | + | 0.465796i | \(0.845768\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0085 | −1.11206 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.87386 | −1.08380 | −0.541898 | − | 0.840444i | \(-0.682294\pi\) | ||||
−0.541898 | + | 0.840444i | \(0.682294\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.614214 | −0.0666208 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 22.4854i | − | 2.41068i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.22843i | 0.554212i | 0.960839 | + | 0.277106i | \(0.0893753\pi\) | ||||
−0.960839 | + | 0.277106i | \(0.910625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.62067 | 0.694035 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.27245 | 0.961509 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 3.28353i | − | 0.336883i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.6958i | − | 1.28906i | −0.764579 | − | 0.644530i | \(-0.777053\pi\) | ||
0.764579 | − | 0.644530i | \(-0.222947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.13646 | −0.415730 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.56279 | −0.752526 | −0.376263 | − | 0.926513i | \(-0.622791\pi\) | ||||
−0.376263 | + | 0.926513i | \(0.622791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.98476 | −0.491163 | −0.245581 | − | 0.969376i | \(-0.578979\pi\) | ||||
−0.245581 | + | 0.969376i | \(0.578979\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.71819 | −0.948398 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.64615 | −0.255813 | −0.127906 | − | 0.991786i | \(-0.540826\pi\) | ||||
−0.127906 | + | 0.991786i | \(0.540826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.97757i | − | 0.668330i | −0.942515 | − | 0.334165i | \(-0.891546\pi\) | ||
0.942515 | − | 0.334165i | \(-0.108454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.17822 | −0.871159 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.33436i | 0.595887i | 0.954584 | + | 0.297943i | \(0.0963006\pi\) | ||||
−0.954584 | + | 0.297943i | \(0.903699\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.25124 | − | 2.21968i | 0.396430 | − | 0.206986i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.21990 | −0.390130 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.51919i | − | 0.230934i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.49634 | −0.772394 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.19542i | − | 0.738956i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.6188i | − | 1.38594i | −0.720964 | − | 0.692972i | \(-0.756301\pi\) | ||
0.720964 | − | 0.692972i | \(-0.243699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.4364i | 1.71128i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.25124i | − | 0.371432i | −0.982603 | − | 0.185716i | \(-0.940539\pi\) | ||
0.982603 | − | 0.185716i | \(-0.0594605\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.4673 | 1.16777 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.914095 | −0.0786728 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.6668i | 0.911323i | 0.890153 | + | 0.455662i | \(0.150597\pi\) | ||||
−0.890153 | + | 0.455662i | \(0.849403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.49492i | − | 0.296435i | −0.988955 | − | 0.148218i | \(-0.952646\pi\) | ||
0.988955 | − | 0.148218i | \(-0.0473536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.15540 | −0.0973025 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.55417 | 0.213590 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.48977i | − | 0.788082i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 23.2730i | − | 1.91952i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 15.8952i | − | 1.30219i | −0.758998 | − | 0.651093i | \(-0.774311\pi\) | ||
0.758998 | − | 0.651093i | \(-0.225689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.46945i | 0.607855i | 0.952695 | + | 0.303927i | \(0.0982980\pi\) | ||||
−0.952695 | + | 0.303927i | \(0.901702\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.60569i | 0.129812i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.91336 | 0.314329 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.334362i | 0.0266850i | 0.999911 | + | 0.0133425i | \(0.00424718\pi\) | ||||
−0.999911 | + | 0.0133425i | \(0.995753\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.52868 | 0.121232 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.10398 | + | 17.4364i | 0.717494 | + | 1.37418i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.52114i | 0.119145i | 0.998224 | + | 0.0595723i | \(0.0189737\pi\) | ||||
−0.998224 | + | 0.0595723i | \(0.981026\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.74915 | −0.291871 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.42721i | 0.187823i | 0.995581 | + | 0.0939114i | \(0.0299371\pi\) | ||||
−0.995581 | + | 0.0939114i | \(0.970063\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3943 | −0.799563 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.58384 | −0.656423 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.72015 | −0.586952 | −0.293476 | − | 0.955966i | \(-0.594812\pi\) | ||||
−0.293476 | + | 0.955966i | \(0.594812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.10148 | −0.310043 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33.9142 | 2.54915 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1547i | 0.908485i | 0.890878 | + | 0.454242i | \(0.150090\pi\) | ||||
−0.890878 | + | 0.454242i | \(0.849910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.9571i | − | 1.33474i | −0.744726 | − | 0.667371i | \(-0.767420\pi\) | ||
0.744726 | − | 0.667371i | \(-0.232580\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.4642 | −1.21707 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.87360 | −0.284792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.971868i | − | 0.0710700i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.74915i | − | 0.272710i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.9084 | −1.80231 | −0.901155 | − | 0.433498i | \(-0.857279\pi\) | ||||
−0.901155 | + | 0.433498i | \(0.857279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.383830 | −0.0276287 | −0.0138143 | − | 0.999905i | \(-0.504397\pi\) | ||||
−0.0138143 | + | 0.999905i | \(0.504397\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.82477 | −0.273898 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.7932 | −1.83769 | −0.918844 | − | 0.394622i | \(-0.870876\pi\) | ||||
−0.918844 | + | 0.394622i | \(0.870876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.4307 | −1.09385 | −0.546926 | − | 0.837181i | \(-0.684202\pi\) | ||||
−0.546926 | + | 0.837181i | \(0.684202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 23.3954i | − | 1.65019i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 38.9221 | 2.73180 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.45881i | − | 0.241574i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.80272 | − | 11.1136i | −0.403317 | − | 0.772452i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.19552 | 0.359381 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5880i | 1.07312i | 0.843862 | + | 0.536560i | \(0.180277\pi\) | ||||
−0.843862 | + | 0.536560i | \(0.819723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.1125 | 1.58364 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.20297i | 0.559438i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0506i | 1.08959i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.0965i | 1.69587i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.991472i | − | 0.0666936i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.975257i | − | 0.0653080i | −0.999467 | − | 0.0326540i | \(-0.989604\pi\) | ||
0.999467 | − | 0.0326540i | \(-0.0103959\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.61421 | 0.174281 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.62870 | 0.439962 | 0.219981 | − | 0.975504i | \(-0.429400\pi\) | ||||
0.219981 | + | 0.975504i | \(0.429400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.97953i | 0.593384i | 0.954973 | + | 0.296692i | \(0.0958835\pi\) | ||||
−0.954973 | + | 0.296692i | \(0.904117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 15.3771i | − | 1.01174i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.88212 | 0.385351 | 0.192675 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192675 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.487628 | −0.0318094 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 37.2716i | 2.42105i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.19541i | 0.206694i | 0.994645 | + | 0.103347i | \(0.0329552\pi\) | ||||
−0.994645 | + | 0.103347i | \(0.967045\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.17043i | − | 0.461888i | −0.972967 | − | 0.230944i | \(-0.925819\pi\) | ||
0.972967 | − | 0.230944i | \(-0.0741814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.9723i | 1.34537i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9.82217i | − | 0.627515i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.30032 | 0.337251 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.3954i | 1.48263i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6055 | 1.55309 | 0.776543 | − | 0.630064i | \(-0.216971\pi\) | ||||
0.776543 | + | 0.630064i | \(0.216971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.51219 | + | 6.72672i | 0.220810 | + | 0.422905i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.45534i | 0.0911368i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.38383 | 0.398212 | 0.199106 | − | 0.979978i | \(-0.436196\pi\) | ||||
0.199106 | + | 0.979978i | \(0.436196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.8875i | − | 0.987200i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.8083 | −1.53559 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3668 | 0.885897 | 0.442948 | − | 0.896547i | \(-0.353933\pi\) | ||||
0.442948 | + | 0.896547i | \(0.353933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.645168 | 0.0396324 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.3884 | 0.758158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.00853 | 0.488289 | 0.244144 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244144 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.92430i | − | 0.238384i | −0.992871 | − | 0.119192i | \(-0.961970\pi\) | ||
0.992871 | − | 0.119192i | \(-0.0380304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 15.6872i | − | 0.949435i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.58230 | −0.0954161 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.67417 | 0.461096 | 0.230548 | − | 0.973061i | \(-0.425948\pi\) | ||||
0.230548 | + | 0.973061i | \(0.425948\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 10.2304i | − | 0.612476i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0619i | 0.838863i | 0.907787 | + | 0.419432i | \(0.137771\pi\) | ||||
−0.907787 | + | 0.419432i | \(0.862229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9570 | 1.84020 | 0.920102 | − | 0.391679i | \(-0.128106\pi\) | ||||
0.920102 | + | 0.391679i | \(0.128106\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.78010 | −0.460853 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1863 | 0.837388 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6227 | 0.977808 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.0818 | −1.76342 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 25.2520i | − | 1.47524i | −0.675218 | − | 0.737618i | \(-0.735950\pi\) | ||
0.675218 | − | 0.737618i | \(-0.264050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3132 | 0.833348 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.44637i | − | 0.0839269i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.58304 | + | 6.86241i | 0.207212 | + | 0.396863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.6443 | −1.93923 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.9195i | 1.02945i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.94858 | −0.397874 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.4053i | 1.56410i | 0.623214 | + | 0.782051i | \(0.285826\pi\) | ||||
−0.623214 | + | 0.782051i | \(0.714174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.8111i | 0.671907i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.0844i | 1.30900i | 0.756064 | + | 0.654498i | \(0.227120\pi\) | ||||
−0.756064 | + | 0.654498i | \(0.772880\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.9972i | 1.29988i | 0.759986 | + | 0.649940i | \(0.225206\pi\) | ||||
−0.759986 | + | 0.649940i | \(0.774794\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.7222i | 0.604125i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.312762 | 0.0175665 | 0.00878324 | − | 0.999961i | \(-0.497204\pi\) | ||||
0.00878324 | + | 0.999961i | \(0.497204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0156 | 0.840714 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.26987i | 0.349950i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.01679i | − | 0.112217i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.61421 | −0.0895405 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.5329 | −0.914271 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.00000i | − | 0.110264i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9669i | 1.20741i | 0.797207 | + | 0.603705i | \(0.206310\pi\) | ||||
−0.797207 | + | 0.603705i | \(0.793690\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1264i | 0.554924i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.87386i | − | 0.539466i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.12362i | − | 0.496995i | −0.968632 | − | 0.248498i | \(-0.920063\pi\) | ||
0.968632 | − | 0.248498i | \(-0.0799368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0088 | 0.815169 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.19210i | 0.335321i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5751 | 0.624996 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.25938 | − | 10.0730i | −0.283156 | − | 0.542313i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 21.0761i | − | 1.13142i | −0.824603 | − | 0.565712i | \(-0.808601\pi\) | ||
0.824603 | − | 0.565712i | \(-0.191399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4279 | −0.611719 | −0.305860 | − | 0.952077i | \(-0.598944\pi\) | ||||
−0.305860 | + | 0.952077i | \(0.598944\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.47554i | − | 0.0787588i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.2435 | −0.704878 | −0.352439 | − | 0.935835i | \(-0.614648\pi\) | ||||
−0.352439 | + | 0.935835i | \(0.614648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.75445 | 0.517712 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.96905 | −0.315915 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.5609 | 1.61294 | 0.806471 | − | 0.591273i | \(-0.201375\pi\) | ||||
0.806471 | + | 0.591273i | \(0.201375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.21844 | −0.432550 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.1315i | 1.05663i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5918i | 0.554399i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7046 | 1.28957 | 0.644784 | − | 0.764365i | \(-0.276947\pi\) | ||||
0.644784 | + | 0.764365i | \(0.276947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.04207 | −0.470711 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.64615i | 0.137381i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 23.8972i | − | 1.23735i | −0.785648 | − | 0.618674i | \(-0.787670\pi\) | ||
0.785648 | − | 0.618674i | \(-0.212330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.36943 | 0.122357 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.3185 | 0.788943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5130 | −1.10505 | −0.552525 | − | 0.833496i | \(-0.686336\pi\) | ||||
−0.552525 | + | 0.833496i | \(0.686336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.0077 | −1.89596 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5952 | −0.541389 | −0.270695 | − | 0.962665i | \(-0.587253\pi\) | ||||
−0.270695 | + | 0.962665i | \(0.587253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 6.48977i | − | 0.330749i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.4443 | 1.09008 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.63386i | 0.133542i | 0.997768 | + | 0.0667709i | \(0.0212697\pi\) | ||||
−0.997768 | + | 0.0667709i | \(0.978730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61117 | − | 1.36336i | 0.132052 | − | 0.0689479i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.0730 | −0.508117 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.7302i | 0.791472i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.1433 | 1.61322 | 0.806612 | − | 0.591081i | \(-0.201299\pi\) | ||||
0.806612 | + | 0.591081i | \(0.201299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 31.9100i | − | 1.59750i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.28642i | 0.164116i | 0.996628 | + | 0.0820581i | \(0.0261493\pi\) | ||||
−0.996628 | + | 0.0820581i | \(0.973851\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.31700i | 0.314672i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.0085i | 0.497328i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.12918i | − | 0.303812i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.9242 | 1.13353 | 0.566764 | − | 0.823880i | \(-0.308195\pi\) | ||||
0.566764 | + | 0.823880i | \(0.308195\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.2742 | 1.24668 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 58.7054i | 2.88871i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.87386i | 0.484689i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.28098 | −0.405521 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.52574 | −0.172244 | −0.0861218 | − | 0.996285i | \(-0.527447\pi\) | ||||
−0.0861218 | + | 0.996285i | \(0.527447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.7491i | 1.15746i | 0.815518 | + | 0.578731i | \(0.196452\pi\) | ||||
−0.815518 | + | 0.578731i | \(0.803548\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.27476i | 0.0619812i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.614214i | 0.0297937i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 28.4995i | − | 1.37919i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.05192i | − | 0.292190i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.2812 | −0.591564 | −0.295782 | − | 0.955256i | \(-0.595580\pi\) | ||||
−0.295782 | + | 0.955256i | \(0.595580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.5984i | − | 1.27824i | −0.769109 | − | 0.639118i | \(-0.779300\pi\) | ||
0.769109 | − | 0.639118i | \(-0.220700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.4854 | −1.07809 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.28838 | + | 13.9591i | 0.348650 | + | 0.667752i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.24247i | − | 0.107027i | −0.998567 | − | 0.0535137i | \(-0.982958\pi\) | ||
0.998567 | − | 0.0535137i | \(-0.0170421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.6773 | −1.22273 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 34.8704i | − | 1.65674i | −0.560180 | − | 0.828371i | \(-0.689268\pi\) | ||
0.560180 | − | 0.828371i | \(-0.310732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.22843 | 0.247851 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.6626 | −1.78138 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7069 | −0.930025 | −0.465013 | − | 0.885304i | \(-0.653950\pi\) | ||||
−0.465013 | + | 0.885304i | \(0.653950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.47287 | 0.257707 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.6984 | 0.831541 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 6.62067i | − | 0.310382i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 23.3719i | − | 1.09329i | −0.837364 | − | 0.546645i | \(-0.815905\pi\) | ||
0.837364 | − | 0.546645i | \(-0.184095\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.561450 | −0.0262062 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.0730 | −0.934894 | −0.467447 | − | 0.884021i | \(-0.654826\pi\) | ||||
−0.467447 | + | 0.884021i | \(0.654826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.3958i | − | 1.08729i | −0.839314 | − | 0.543647i | \(-0.817043\pi\) | ||
0.839314 | − | 0.543647i | \(-0.182957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 9.27245i | − | 0.430000i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.70683 | 0.125257 | 0.0626286 | − | 0.998037i | \(-0.480052\pi\) | ||||
0.0626286 | + | 0.998037i | \(0.480052\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.4975 | 1.87000 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.792249 | 0.0365049 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.9795 | −0.596799 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.28353 | −0.150659 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.68661i | − | 0.0772244i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.9119 | 1.73224 | 0.866119 | − | 0.499838i | \(-0.166607\pi\) | ||||
0.866119 | + | 0.499838i | \(0.166607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.25281i | − | 0.285104i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 41.3143 | − | 21.5713i | 1.87987 | − | 0.981527i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.6958 | −0.576485 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4903i | 1.33633i | 0.744012 | + | 0.668167i | \(0.232921\pi\) | ||||
−0.744012 | + | 0.668167i | \(0.767079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.60423 | 0.162989 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4432i | 1.23849i | 0.785197 | + | 0.619246i | \(0.212562\pi\) | ||||
−0.785197 | + | 0.619246i | \(0.787438\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.82874i | − | 0.262513i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.13646i | 0.185920i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.0077i | 1.79459i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 22.4504i | − | 1.00502i | −0.864572 | − | 0.502509i | \(-0.832410\pi\) | ||
0.864572 | − | 0.502509i | \(-0.167590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.75110 | 0.256940 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.9555 | −0.622243 | −0.311122 | − | 0.950370i | \(-0.600705\pi\) | ||||
−0.311122 | + | 0.950370i | \(0.600705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.56279i | 0.336540i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.6286i | 1.09380i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.9702 | −1.15111 | −0.575554 | − | 0.817764i | \(-0.695214\pi\) | ||||
−0.575554 | + | 0.817764i | \(0.695214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43.4420 | −1.92176 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.00146i | − | 0.132518i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.98476i | 0.219655i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.771573i | − | 0.0339337i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.2924i | 0.802946i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14.1500i | − | 0.619921i | −0.950749 | − | 0.309961i | \(-0.899684\pi\) | ||
0.950749 | − | 0.309961i | \(-0.100316\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5089 | −0.853064 | −0.426532 | − | 0.904472i | \(-0.640265\pi\) | ||||
−0.426532 | + | 0.904472i | \(0.640265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.71819i | 0.424137i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.40364 | 0.104704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.1460 | + | 18.8728i | −0.571567 | + | 0.820555i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 37.4178i | − | 1.62379i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.58326 | 0.241838 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.64615i | 0.114403i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.7997 | 1.24280 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5416 | 0.669424 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.2191 | 0.697312 | 0.348656 | − | 0.937251i | \(-0.386638\pi\) | ||||
0.348656 | + | 0.937251i | \(0.386638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −42.5482 | −1.82592 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.97757 | −0.298886 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.6301i | 1.30965i | 0.755782 | + | 0.654824i | \(0.227257\pi\) | ||||
−0.755782 | + | 0.654824i | \(0.772743\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.1651i | 0.775266i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.1599 | 1.32746 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −64.5171 | −2.74355 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.17822i | 0.389594i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.4167i | 1.16168i | 0.814016 | + | 0.580842i | \(0.197277\pi\) | ||||
−0.814016 | + | 0.580842i | \(0.802723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.2413 | −0.560049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.30278 | −0.0972233 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7424 | 1.08491 | 0.542457 | − | 0.840084i | \(-0.317494\pi\) | ||||
0.542457 | + | 0.840084i | \(0.317494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.33436 | 0.266489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41.0498 | −1.72393 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.0414i | 1.13364i | 0.823843 | + | 0.566818i | \(0.191826\pi\) | ||||
−0.823843 | + | 0.566818i | \(0.808174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.72458 | −0.406961 | −0.203481 | − | 0.979079i | \(-0.565225\pi\) | ||||
−0.203481 | + | 0.979079i | \(0.565225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 59.0188i | 2.46555i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.21968 | − | 4.25124i | −0.0925670 | − | 0.177289i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.6969 | 1.52771 | 0.763856 | − | 0.645387i | \(-0.223304\pi\) | ||||
0.763856 | + | 0.645387i | \(0.223304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.909460i | 0.0377959i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.4975 | −1.68012 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.02085i | 0.0422792i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.21990i | 0.174471i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.91027i | 0.243943i | 0.992534 | + | 0.121971i | \(0.0389216\pi\) | ||||
−0.992534 | + | 0.121971i | \(0.961078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8496i | 0.529460i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 61.1152i | 2.51394i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.62552 | 0.107817 | 0.0539087 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539087 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.51919 | −0.103277 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.5620i | 1.49638i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 44.2263i | − | 1.80704i | −0.428550 | − | 0.903518i | \(-0.640975\pi\) | ||
0.428550 | − | 0.903518i | \(-0.359025\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.6378 | 0.882623 | 0.441312 | − | 0.897354i | \(-0.354513\pi\) | ||||
0.441312 | + | 0.897354i | \(0.354513\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.8124 | −1.05116 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.49634i | 0.345425i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11.7278i | − | 0.476015i | −0.971263 | − | 0.238007i | \(-0.923506\pi\) | ||
0.971263 | − | 0.238007i | \(-0.0764943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 92.2234i | − | 3.73708i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.787136i | − | 0.0318441i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5636i | 0.749777i | 0.927070 | + | 0.374889i | \(0.122319\pi\) | ||||
−0.927070 | + | 0.374889i | \(0.877681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.19542 | −0.330471 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.5040i | 1.75141i | 0.482850 | + | 0.875703i | \(0.339602\pi\) | ||||
−0.482850 | + | 0.875703i | \(0.660398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.64467 | 0.146492 | 0.0732459 | − | 0.997314i | \(-0.476664\pi\) | ||||
0.0732459 | + | 0.997314i | \(0.476664\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.88604 | − | 2.02900i | 0.155941 | − | 0.0814209i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.4443i | 0.859148i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 12.3104i | − | 0.491631i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.37921 | −0.0948655 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.9799 | −1.94986 | −0.974930 | − | 0.222511i | \(-0.928575\pi\) | ||||
−0.974930 | + | 0.222511i | \(0.928575\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.9347 | 1.46802 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.6188 | −0.619813 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8551 | 0.628201 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 25.5002i | − | 1.00877i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 19.0637i | − | 0.752970i | −0.926423 | − | 0.376485i | \(-0.877133\pi\) | ||
0.926423 | − | 0.376485i | \(-0.122867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.3231 | −1.51132 | −0.755658 | − | 0.654967i | \(-0.772683\pi\) | ||||
−0.755658 | + | 0.654967i | \(0.772683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.4364 | 0.765307 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.7426i | 0.776162i | 0.921625 | + | 0.388081i | \(0.126862\pi\) | ||||
−0.921625 | + | 0.388081i | \(0.873138\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.6478i | 0.889002i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.0308 | 1.49055 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.3858 | −0.406427 | −0.203214 | − | 0.979134i | \(-0.565139\pi\) | ||||
−0.203214 | + | 0.979134i | \(0.565139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.25124 | −0.166110 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.6892 | 1.08026 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.77870 | −0.147197 | −0.0735987 | − | 0.997288i | \(-0.523448\pi\) | ||||
−0.0735987 | + | 0.997288i | \(0.523448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 42.7970i | − | 1.66461i | −0.554319 | − | 0.832304i | \(-0.687021\pi\) | ||
0.554319 | − | 0.832304i | \(-0.312979\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.34923 | −0.0912364 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 13.4673i | − | 0.522241i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.0642 | + | 40.3432i | 0.815610 | + | 1.56210i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.31081 | −0.0893409 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 10.9947i | − | 0.424446i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3877 | −0.785890 | −0.392945 | − | 0.919562i | \(-0.628544\pi\) | ||||
−0.392945 | + | 0.919562i | \(0.628544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.914095i | 0.0351835i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 10.1844i | − | 0.391418i | −0.980662 | − | 0.195709i | \(-0.937299\pi\) | ||
0.980662 | − | 0.195709i | \(-0.0627009\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 52.0715i | − | 1.99832i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.7063i | − | 0.601865i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26.4295i | − | 1.01130i | −0.862739 | − | 0.505649i | \(-0.831253\pi\) | ||
0.862739 | − | 0.505649i | \(-0.168747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6668 | 0.407556 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.2764 | 0.811745 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.04144i | 0.0396757i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.46410i | − | 0.131781i | −0.997827 | − | 0.0658903i | \(-0.979011\pi\) | ||
0.997827 | − | 0.0658903i | \(-0.0209887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.9656 | −0.644471 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.49492 | −0.132570 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.12445i | − | 0.0804692i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 13.9373i | − | 0.527157i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.6219i | − | 1.91196i | −0.293426 | − | 0.955982i | \(-0.594796\pi\) | ||
0.293426 | − | 0.955982i | \(-0.405204\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.7191i | − | 0.479708i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.15540i | 0.0435150i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.0187 | −1.16658 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.1958i | 1.92270i | 0.275330 | + | 0.961350i | \(0.411213\pi\) | ||||
−0.275330 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.1221 | 1.54220 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.6366 | + | 8.68641i | −0.623047 | + | 0.325309i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.55417i | − | 0.0955204i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.57132 | 0.282756 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 11.8826i | − | 0.443147i | −0.975144 | − | 0.221573i | \(-0.928881\pi\) | ||
0.975144 | − | 0.221573i | \(-0.0711193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.4449 | −0.761408 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.9899 | −0.631860 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.48977 | −0.352441 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.4203 | 0.720259 | 0.360130 | − | 0.932902i | \(-0.382733\pi\) | ||||
0.360130 | + | 0.932902i | \(0.382733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.6668 | 0.728399 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.03837i | 0.186351i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 50.5014i | − | 1.86531i | −0.360768 | − | 0.932656i | \(-0.617485\pi\) | ||
0.360768 | − | 0.932656i | \(-0.382515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23.2730 | −0.858437 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.6234 | 0.575494 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.9655i | 1.02873i | 0.857573 | + | 0.514363i | \(0.171972\pi\) | ||||
−0.857573 | + | 0.514363i | \(0.828028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 12.5587i | − | 0.461357i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.1088 | 0.627661 | 0.313830 | − | 0.949479i | \(-0.398388\pi\) | ||||
0.313830 | + | 0.949479i | \(0.398388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8952 | −0.582355 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.8124 | 0.944425 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8531 | −0.396565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.859711 | −0.0313713 | −0.0156856 | − | 0.999877i | \(-0.504993\pi\) | ||||
−0.0156856 | + | 0.999877i | \(0.504993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 58.3011i | − | 2.12461i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.46945 | 0.271841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.7707i | − | 1.08204i | −0.841011 | − | 0.541018i | \(-0.818039\pi\) | ||
0.841011 | − | 0.541018i | \(-0.181961\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.9385 | − | 8.32190i | 0.578531 | − | 0.302066i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.6509 | −0.494845 | −0.247423 | − | 0.968908i | \(-0.579584\pi\) | ||||
−0.247423 | + | 0.968908i | \(0.579584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 28.6184i | − | 1.03606i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.60569 | 0.0580537 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.1046i | 0.834258i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.9625i | 0.467439i | 0.972304 | + | 0.233719i | \(0.0750897\pi\) | ||||
−0.972304 | + | 0.233719i | \(0.924910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.1261i | − | 0.544752i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.18749i | 0.258516i | 0.991611 | + | 0.129258i | \(0.0412595\pi\) | ||||
−0.991611 | + | 0.129258i | \(0.958740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.91336i | − | 0.140572i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −37.6443 | −1.35048 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3571 | 0.406910 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.4344i | 0.552287i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 8.67455i | − | 0.310003i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.334362 | 0.0119339 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.7181 | −0.774167 | −0.387084 | − | 0.922045i | \(-0.626517\pi\) | ||||
−0.387084 | + | 0.922045i | \(0.626517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 34.0412i | − | 1.21190i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.9803i | 0.923753i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11.2165i | − | 0.398309i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 1.52868i | − | 0.0542168i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 30.8963i | − | 1.09440i | −0.837001 | − | 0.547202i | \(-0.815693\pi\) | ||
0.837001 | − | 0.547202i | \(-0.184307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.299508 | −0.0105958 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.6682i | − | 0.482943i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.7594 | −0.591425 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.4364 | − | 9.10398i | 0.614552 | − | 0.320873i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 18.9757i | − | 0.667975i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.3034 | 0.432565 | 0.216282 | − | 0.976331i | \(-0.430607\pi\) | ||||
0.216282 | + | 0.976331i | \(0.430607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0232i | 0.703109i | 0.936167 | + | 0.351554i | \(0.114347\pi\) | ||||
−0.936167 | + | 0.351554i | \(0.885653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.29836 | −0.326108 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.52114 | 0.0532830 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.9347 | −0.942325 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.3078 | −0.604785 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2682 | −1.33557 | −0.667785 | − | 0.744354i | \(-0.732757\pi\) | ||||
−0.667785 | + | 0.744354i | \(0.732757\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.7368i | − | 0.653125i | −0.945176 | − | 0.326563i | \(-0.894110\pi\) | ||
0.945176 | − | 0.326563i | \(-0.105890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.74915i | 0.130529i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.1370 | −0.839326 | −0.419663 | − | 0.907680i | \(-0.637852\pi\) | ||||
−0.419663 | + | 0.907680i | \(0.637852\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.7912 | −0.999960 | −0.499980 | − | 0.866037i | \(-0.666659\pi\) | ||||
−0.499980 | + | 0.866037i | \(0.666659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 18.1834i | − | 0.630776i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.03291i | − | 0.209028i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.42721 | 0.0839969 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.57719 | 0.123646 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.6881 | 0.990422 | 0.495211 | − | 0.868773i | \(-0.335091\pi\) | ||||
0.495211 | + | 0.868773i | \(0.335091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.0556 | 2.10537 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.3188 | 1.14756 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3943i | 0.357575i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.8476 | −1.19738 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 73.3506i | − | 2.51739i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.4676 | − | 8.59814i | 0.564501 | − | 0.294740i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.8952 | 1.84534 | 0.922668 | − | 0.385595i | \(-0.126004\pi\) | ||||
0.922668 | + | 0.385595i | \(0.126004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.58384i | 0.293561i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.2532 | 1.92157 | 0.960786 | − | 0.277291i | \(-0.0894365\pi\) | ||||
0.960786 | + | 0.277291i | \(0.0894365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.58572i | − | 0.156463i | −0.996935 | − | 0.0782314i | \(-0.975073\pi\) | ||
0.996935 | − | 0.0782314i | \(-0.0249273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 33.6134i | − | 1.14554i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21.6941i | − | 0.738475i | −0.929335 | − | 0.369237i | \(-0.879619\pi\) | ||
0.929335 | − | 0.369237i | \(-0.120381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.72015i | 0.262493i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 39.3865i | − | 1.33763i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.8898 | −0.844329 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.9385 | 0.540056 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.1894i | 1.12329i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.10148i | 0.138655i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7201 | 0.665902 | 0.332951 | − | 0.942944i | \(-0.391956\pi\) | ||||
0.332951 | + | 0.942944i | \(0.391956\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −59.8329 | −2.01811 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.2755i | 1.32323i | 0.749845 | + | 0.661613i | \(0.230128\pi\) | ||||
−0.749845 | + | 0.661613i | \(0.769872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.2498i | − | 1.55643i | −0.627997 | − | 0.778215i | \(-0.716125\pi\) | ||
0.627997 | − | 0.778215i | \(-0.283875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 33.9142i | − | 1.14001i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.78957i | − | 0.160818i | −0.996762 | − | 0.0804090i | \(-0.974377\pi\) | ||
0.996762 | − | 0.0804090i | \(-0.0256226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 64.0603i | − | 2.14851i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.8365 | −0.530541 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.60114i | − | 0.0535802i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.1547 | 0.406287 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.2600 | − | 8.48977i | 0.542906 | − | 0.283465i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.1369i | 1.23858i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.396271 | 0.0132017 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 79.7180i | 2.65285i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.9571 | −0.596914 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.61899 | 0.319393 | 0.159697 | − | 0.987166i | \(-0.448948\pi\) | ||||
0.159697 | + | 0.987166i | \(0.448948\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.7707 | 0.655754 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.7144 | 1.34893 | 0.674464 | − | 0.738308i | \(-0.264375\pi\) | ||||
0.674464 | + | 0.738308i | \(0.264375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.6234 | −0.517058 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.4642i | 0.544289i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 17.4364i | − | 0.575800i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.61898 | −0.284314 | −0.142157 | − | 0.989844i | \(-0.545404\pi\) | ||||
−0.142157 | + | 0.989844i | \(0.545404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 64.9350 | 2.13968 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.7458i | 0.518278i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.87360i | 0.127363i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0312 | 0.428002 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.57214 | −0.0843893 | −0.0421946 | − | 0.999109i | \(-0.513435\pi\) | ||||
−0.0421946 | + | 0.999109i | \(0.513435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.2514 | 1.05700 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.6969 | 1.79070 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.971868 | −0.0317835 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 37.8055i | − | 1.23505i | −0.786551 | − | 0.617526i | \(-0.788135\pi\) | ||
0.786551 | − | 0.617526i | \(-0.211865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.4904 | 1.77823 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.1941i | 1.31029i | 0.755504 | + | 0.655144i | \(0.227392\pi\) | ||||
−0.755504 | + | 0.655144i | \(0.772608\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.67745 | + | 14.7042i | 0.250012 | + | 0.478836i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.74915 | −0.121960 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 18.5480i | − | 0.602728i | −0.953509 | − | 0.301364i | \(-0.902558\pi\) | ||
0.953509 | − | 0.301364i | \(-0.0974419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.0974 | −0.555005 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 0.741069i | − | 0.0240308i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.5741i | 0.374922i | 0.982272 | + | 0.187461i | \(0.0600258\pi\) | ||||
−0.982272 | + | 0.187461i | \(0.939974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.9084i | 0.806017i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 35.5785i | − | 1.15009i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.7496i | 1.41275i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.6856 | 0.505987 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.91759 | 0.222916 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.383830i | 0.0123559i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9423i | 1.31661i | 0.752749 | + | 0.658307i | \(0.228727\pi\) | ||||
−0.752749 | + | 0.658307i | \(0.771273\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.77864 | −0.153512 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.0340 | −1.09220 | −0.546101 | − | 0.837719i | \(-0.683889\pi\) | ||||
−0.546101 | + | 0.837719i | \(0.683889\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.3344i | − | 0.459539i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.82477i | 0.122491i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.4336i | 0.781700i | 0.920454 | + | 0.390850i | \(0.127819\pi\) | ||||
−0.920454 | + | 0.390850i | \(0.872181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.27292i | 0.264404i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2409i | 0.582386i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.76928 | −0.247801 | −0.123901 | − | 0.992295i | \(-0.539540\pi\) | ||||
−0.123901 | + | 0.992295i | \(0.539540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.7932i | 0.821839i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.73887 | −0.150840 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.2080 | − | 34.8728i | −0.578979 | − | 1.10889i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.2428i | 0.960693i | 0.877079 | + | 0.480346i | \(0.159489\pi\) | ||||
−0.877079 | + | 0.480346i | \(0.840511\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 52.0491 | 1.65173 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.4307i | 0.489185i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.2040 | 0.513187 | 0.256594 | − | 0.966519i | \(-0.417400\pi\) | ||||
0.256594 | + | 0.966519i | \(0.417400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.54083 | −0.112027 |
(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 | 1840.2.i.a.1471.3 | ✓ | 16 | |
4.3 | odd | 2 | inner | 1840.2.i.a.1471.13 | yes | 16 | |
23.22 | odd | 2 | inner | 1840.2.i.a.1471.4 | yes | 16 | |
92.91 | even | 2 | inner | 1840.2.i.a.1471.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.i.a.1471.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1840.2.i.a.1471.4 | yes | 16 | 23.22 | odd | 2 | inner | |
1840.2.i.a.1471.13 | yes | 16 | 4.3 | odd | 2 | inner | |
1840.2.i.a.1471.14 | yes | 16 | 92.91 | even | 2 | inner |