Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(197,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.m (of order \(4\), degree \(2\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.323 |
Dual form | 630.2.m.b.197.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.707107 | + | 2.12132i | 0.223607 | + | 0.670820i | ||||
\(11\) | − | 0.585786i | − | 0.176621i | −0.996093 | − | 0.0883106i | \(-0.971853\pi\) | ||
0.996093 | − | 0.0883106i | \(-0.0281468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | + | 4.00000i | 1.10940 | + | 1.10940i | 0.993229 | + | 0.116171i | \(0.0370621\pi\) |
0.116171 | + | 0.993229i | \(0.462938\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.585786 | − | 0.585786i | −0.142074 | − | 0.142074i | 0.632492 | − | 0.774567i | \(-0.282032\pi\) |
−0.774567 | + | 0.632492i | \(0.782032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | −1.00000 | + | 2.00000i | −0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.414214 | − | 0.414214i | 0.0883106 | − | 0.0883106i | ||||
\(23\) | −4.82843 | + | 4.82843i | −1.00680 | + | 1.00680i | −0.00681991 | + | 0.999977i | \(0.502171\pi\) |
−0.999977 | + | 0.00681991i | \(0.997829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 5.65685i | 1.10940i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | − | 0.707107i | −0.133631 | − | 0.133631i | ||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.75736 | 0.315631 | 0.157816 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157816 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.828427i | − | 0.142074i | ||||||
\(35\) | −2.12132 | + | 0.707107i | −0.358569 | + | 0.119523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.24264 | − | 6.24264i | 1.02628 | − | 1.02628i | 0.0266387 | − | 0.999645i | \(-0.491520\pi\) |
0.999645 | − | 0.0266387i | \(-0.00848036\pi\) | |||||||
\(38\) | 2.00000 | − | 2.00000i | 0.324443 | − | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.12132 | + | 0.707107i | −0.335410 | + | 0.111803i | ||||
\(41\) | 3.17157i | 0.495316i | 0.968847 | + | 0.247658i | \(0.0796610\pi\) | ||||
−0.968847 | + | 0.247658i | \(0.920339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.07107 | + | 6.07107i | 0.925829 | + | 0.925829i | 0.997433 | − | 0.0716040i | \(-0.0228118\pi\) |
−0.0716040 | + | 0.997433i | \(0.522812\pi\) | |||||||
\(44\) | 0.585786 | 0.0883106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.82843 | −1.00680 | ||||||||
\(47\) | −9.24264 | − | 9.24264i | −1.34818 | − | 1.34818i | −0.887640 | − | 0.460537i | \(-0.847657\pi\) |
−0.460537 | − | 0.887640i | \(-0.652343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −0.707107 | + | 4.94975i | −0.100000 | + | 0.700000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | + | 4.00000i | −0.554700 | + | 0.554700i | ||||
\(53\) | 2.58579 | − | 2.58579i | 0.355185 | − | 0.355185i | −0.506849 | − | 0.862035i | \(-0.669190\pi\) |
0.862035 | + | 0.506849i | \(0.169190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.585786 | − | 1.17157i | 0.0789874 | − | 0.157975i | ||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.585786 | − | 0.585786i | −0.0769175 | − | 0.0769175i | ||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.89949 | −1.26750 | −0.633750 | − | 0.773538i | \(-0.718485\pi\) | ||||
−0.633750 | + | 0.773538i | \(0.718485\pi\) | |||||||
\(62\) | 1.24264 | + | 1.24264i | 0.157816 | + | 0.157816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 4.00000 | + | 12.0000i | 0.496139 | + | 1.48842i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.41421 | − | 8.41421i | 1.02796 | − | 1.02796i | 0.0283621 | − | 0.999598i | \(-0.490971\pi\) |
0.999598 | − | 0.0283621i | \(-0.00902914\pi\) | |||||||
\(68\) | 0.585786 | − | 0.585786i | 0.0710370 | − | 0.0710370i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | − | 1.00000i | −0.239046 | − | 0.119523i | ||||
\(71\) | − | 1.17157i | − | 0.139040i | −0.997581 | − | 0.0695201i | \(-0.977853\pi\) | ||
0.997581 | − | 0.0695201i | \(-0.0221468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.07107 | + | 7.07107i | 0.827606 | + | 0.827606i | 0.987185 | − | 0.159579i | \(-0.0510137\pi\) |
−0.159579 | + | 0.987185i | \(0.551014\pi\) | |||||||
\(74\) | 8.82843 | 1.02628 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.82843 | 0.324443 | ||||||||
\(77\) | 0.414214 | + | 0.414214i | 0.0472040 | + | 0.0472040i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.65685i | − | 0.636446i | −0.948016 | − | 0.318223i | \(-0.896914\pi\) | ||
0.948016 | − | 0.318223i | \(-0.103086\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.24264 | + | 2.24264i | −0.247658 | + | 0.247658i | ||||
\(83\) | 0.828427 | − | 0.828427i | 0.0909317 | − | 0.0909317i | −0.660178 | − | 0.751109i | \(-0.729519\pi\) |
0.751109 | + | 0.660178i | \(0.229519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.585786 | − | 1.75736i | −0.0635375 | − | 0.190612i | ||||
\(86\) | 8.58579i | 0.925829i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.414214 | + | 0.414214i | 0.0441553 | + | 0.0441553i | ||||
\(89\) | −3.17157 | −0.336186 | −0.168093 | − | 0.985771i | \(-0.553761\pi\) | ||||
−0.168093 | + | 0.985771i | \(0.553761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.65685 | −0.592999 | ||||||||
\(92\) | −4.82843 | − | 4.82843i | −0.503398 | − | 0.503398i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 13.0711i | − | 1.34818i | ||||||
\(95\) | 2.82843 | − | 5.65685i | 0.290191 | − | 0.580381i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.58579 | + | 4.58579i | −0.465616 | + | 0.465616i | −0.900491 | − | 0.434875i | \(-0.856793\pi\) |
0.434875 | + | 0.900491i | \(0.356793\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.00000 | + | 3.00000i | −0.400000 | + | 0.300000i | ||||
\(101\) | − | 17.6569i | − | 1.75692i | −0.477813 | − | 0.878461i | \(-0.658571\pi\) | ||
0.477813 | − | 0.878461i | \(-0.341429\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.41421 | − | 7.41421i | −0.730544 | − | 0.730544i | 0.240183 | − | 0.970728i | \(-0.422792\pi\) |
−0.970728 | + | 0.240183i | \(0.922792\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.65685 | 0.355185 | ||||||||
\(107\) | 5.17157 | + | 5.17157i | 0.499955 | + | 0.499955i | 0.911424 | − | 0.411469i | \(-0.134984\pi\) |
−0.411469 | + | 0.911424i | \(0.634984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.31371i | − | 0.892091i | −0.895010 | − | 0.446046i | \(-0.852832\pi\) | ||
0.895010 | − | 0.446046i | \(-0.147168\pi\) | |||||||
\(110\) | 1.24264 | − | 0.414214i | 0.118481 | − | 0.0394937i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | 11.3137 | − | 11.3137i | 1.06430 | − | 1.06430i | 0.0665190 | − | 0.997785i | \(-0.478811\pi\) |
0.997785 | − | 0.0665190i | \(-0.0211893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.4853 | + | 4.82843i | −1.35076 | + | 0.450253i | ||||
\(116\) | − | 0.828427i | − | 0.0769175i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | − | 2.00000i | −0.184115 | − | 0.184115i | ||||
\(119\) | 0.828427 | 0.0759418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6569 | 0.968805 | ||||||||
\(122\) | −7.00000 | − | 7.00000i | −0.633750 | − | 0.633750i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.75736i | 0.157816i | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.65685 | − | 7.65685i | 0.679436 | − | 0.679436i | −0.280437 | − | 0.959873i | \(-0.590479\pi\) |
0.959873 | + | 0.280437i | \(0.0904792\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.65685 | + | 11.3137i | −0.496139 | + | 0.992278i | ||||
\(131\) | − | 16.4853i | − | 1.44033i | −0.693805 | − | 0.720163i | \(-0.744067\pi\) | ||
0.693805 | − | 0.720163i | \(-0.255933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000 | + | 2.00000i | 0.173422 | + | 0.173422i | ||||
\(134\) | 11.8995 | 1.02796 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.828427 | 0.0710370 | ||||||||
\(137\) | −12.0000 | − | 12.0000i | −1.02523 | − | 1.02523i | −0.999673 | − | 0.0255558i | \(-0.991864\pi\) |
−0.0255558 | − | 0.999673i | \(-0.508136\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.6569i | − | 1.49763i | −0.662776 | − | 0.748817i | \(-0.730622\pi\) | ||
0.662776 | − | 0.748817i | \(-0.269378\pi\) | |||||||
\(140\) | −0.707107 | − | 2.12132i | −0.0597614 | − | 0.179284i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.828427 | − | 0.828427i | 0.0695201 | − | 0.0695201i | ||||
\(143\) | 2.34315 | − | 2.34315i | 0.195944 | − | 0.195944i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.65685 | − | 0.828427i | −0.137594 | − | 0.0687971i | ||||
\(146\) | 10.0000i | 0.827606i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.24264 | + | 6.24264i | 0.513142 | + | 0.513142i | ||||
\(149\) | 8.14214 | 0.667030 | 0.333515 | − | 0.942745i | \(-0.391765\pi\) | ||||
0.333515 | + | 0.942745i | \(0.391765\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.8284 | −1.53224 | −0.766118 | − | 0.642700i | \(-0.777814\pi\) | ||||
−0.766118 | + | 0.642700i | \(0.777814\pi\) | |||||||
\(152\) | 2.00000 | + | 2.00000i | 0.162221 | + | 0.162221i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.585786i | 0.0472040i | ||||||||
\(155\) | 3.51472 | + | 1.75736i | 0.282309 | + | 0.141154i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.65685 | + | 9.65685i | −0.770701 | + | 0.770701i | −0.978229 | − | 0.207528i | \(-0.933458\pi\) |
0.207528 | + | 0.978229i | \(0.433458\pi\) | |||||||
\(158\) | 4.00000 | − | 4.00000i | 0.318223 | − | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.707107 | − | 2.12132i | −0.0559017 | − | 0.167705i | ||||
\(161\) | − | 6.82843i | − | 0.538155i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7279 | + | 11.7279i | 0.918602 | + | 0.918602i | 0.996928 | − | 0.0783260i | \(-0.0249575\pi\) |
−0.0783260 | + | 0.996928i | \(0.524958\pi\) | |||||||
\(164\) | −3.17157 | −0.247658 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.17157 | 0.0909317 | ||||||||
\(167\) | 7.58579 | + | 7.58579i | 0.587006 | + | 0.587006i | 0.936819 | − | 0.349814i | \(-0.113755\pi\) |
−0.349814 | + | 0.936819i | \(0.613755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000i | 1.46154i | ||||||||
\(170\) | 0.828427 | − | 1.65685i | 0.0635375 | − | 0.127075i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.07107 | + | 6.07107i | −0.462915 | + | 0.462915i | ||||
\(173\) | 11.4853 | − | 11.4853i | 0.873210 | − | 0.873210i | −0.119611 | − | 0.992821i | \(-0.538165\pi\) |
0.992821 | + | 0.119611i | \(0.0381648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.94975 | − | 0.707107i | −0.374166 | − | 0.0534522i | ||||
\(176\) | 0.585786i | 0.0441553i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.24264 | − | 2.24264i | −0.168093 | − | 0.168093i | ||||
\(179\) | −16.5858 | −1.23968 | −0.619840 | − | 0.784728i | \(-0.712802\pi\) | ||||
−0.619840 | + | 0.784728i | \(0.712802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0711 | −1.41754 | −0.708771 | − | 0.705439i | \(-0.750750\pi\) | ||||
−0.708771 | + | 0.705439i | \(0.750750\pi\) | |||||||
\(182\) | −4.00000 | − | 4.00000i | −0.296500 | − | 0.296500i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.82843i | − | 0.503398i | ||||||
\(185\) | 18.7279 | − | 6.24264i | 1.37690 | − | 0.458968i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.343146 | + | 0.343146i | −0.0250933 | + | 0.0250933i | ||||
\(188\) | 9.24264 | − | 9.24264i | 0.674089 | − | 0.674089i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 2.00000i | 0.435286 | − | 0.145095i | ||||
\(191\) | 14.3431i | 1.03783i | 0.854825 | + | 0.518917i | \(0.173665\pi\) | ||||
−0.854825 | + | 0.518917i | \(0.826335\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4853 | + | 13.4853i | 0.970692 | + | 0.970692i | 0.999583 | − | 0.0288908i | \(-0.00919750\pi\) |
−0.0288908 | + | 0.999583i | \(0.509198\pi\) | |||||||
\(194\) | −6.48528 | −0.465616 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.2426 | + | 10.2426i | 0.729758 | + | 0.729758i | 0.970571 | − | 0.240813i | \(-0.0774142\pi\) |
−0.240813 | + | 0.970571i | \(0.577414\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.10051i | − | 0.290677i | −0.989382 | − | 0.145339i | \(-0.953573\pi\) | ||
0.989382 | − | 0.145339i | \(-0.0464271\pi\) | |||||||
\(200\) | −4.94975 | − | 0.707107i | −0.350000 | − | 0.0500000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.4853 | − | 12.4853i | 0.878461 | − | 0.878461i | ||||
\(203\) | 0.585786 | − | 0.585786i | 0.0411141 | − | 0.0411141i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.17157 | + | 6.34315i | −0.221512 | + | 0.443025i | ||||
\(206\) | − | 10.4853i | − | 0.730544i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | − | 4.00000i | −0.277350 | − | 0.277350i | ||||
\(209\) | −1.65685 | −0.114607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 2.58579 | + | 2.58579i | 0.177593 | + | 0.177593i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.31371i | 0.499955i | ||||||||
\(215\) | 6.07107 | + | 18.2132i | 0.414043 | + | 1.24213i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24264 | + | 1.24264i | −0.0843559 | + | 0.0843559i | ||||
\(218\) | 6.58579 | − | 6.58579i | 0.446046 | − | 0.446046i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.17157 | + | 0.585786i | 0.0789874 | + | 0.0394937i | ||||
\(221\) | − | 4.68629i | − | 0.315234i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.31371 | + | 7.31371i | 0.489762 | + | 0.489762i | 0.908231 | − | 0.418469i | \(-0.137433\pi\) |
−0.418469 | + | 0.908231i | \(0.637433\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | −1.17157 | − | 1.17157i | −0.0777600 | − | 0.0777600i | 0.667157 | − | 0.744917i | \(-0.267511\pi\) |
−0.744917 | + | 0.667157i | \(0.767511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.24264i | 0.544689i | 0.962200 | + | 0.272345i | \(0.0877990\pi\) | ||||
−0.962200 | + | 0.272345i | \(0.912201\pi\) | |||||||
\(230\) | −13.6569 | − | 6.82843i | −0.900506 | − | 0.450253i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.585786 | − | 0.585786i | 0.0384588 | − | 0.0384588i | ||||
\(233\) | −14.8284 | + | 14.8284i | −0.971443 | + | 0.971443i | −0.999603 | − | 0.0281608i | \(-0.991035\pi\) |
0.0281608 | + | 0.999603i | \(0.491035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.24264 | − | 27.7279i | −0.602923 | − | 1.80877i | ||||
\(236\) | − | 2.82843i | − | 0.184115i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.585786 | + | 0.585786i | 0.0379709 | + | 0.0379709i | ||||
\(239\) | −13.6569 | −0.883388 | −0.441694 | − | 0.897166i | \(-0.645622\pi\) | ||||
−0.441694 | + | 0.897166i | \(0.645622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.14214 | −0.266818 | −0.133409 | − | 0.991061i | \(-0.542592\pi\) | ||||
−0.133409 | + | 0.991061i | \(0.542592\pi\) | |||||||
\(242\) | 7.53553 | + | 7.53553i | 0.484402 | + | 0.484402i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.89949i | − | 0.633750i | ||||||
\(245\) | 1.00000 | − | 2.00000i | 0.0638877 | − | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3137 | − | 11.3137i | 0.719874 | − | 0.719874i | ||||
\(248\) | −1.24264 | + | 1.24264i | −0.0789078 | + | 0.0789078i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.36396 | + | 9.19239i | −0.402492 | + | 0.581378i | ||||
\(251\) | 26.6274i | 1.68071i | 0.542038 | + | 0.840354i | \(0.317653\pi\) | ||||
−0.542038 | + | 0.840354i | \(0.682347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82843 | + | 2.82843i | 0.177822 | + | 0.177822i | ||||
\(254\) | 10.8284 | 0.679436 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.58579 | − | 8.58579i | −0.535567 | − | 0.535567i | 0.386657 | − | 0.922224i | \(-0.373630\pi\) |
−0.922224 | + | 0.386657i | \(0.873630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.82843i | 0.548572i | ||||||||
\(260\) | −12.0000 | + | 4.00000i | −0.744208 | + | 0.248069i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.6569 | − | 11.6569i | 0.720163 | − | 0.720163i | ||||
\(263\) | −7.65685 | + | 7.65685i | −0.472142 | + | 0.472142i | −0.902607 | − | 0.430465i | \(-0.858349\pi\) |
0.430465 | + | 0.902607i | \(0.358349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.75736 | − | 2.58579i | 0.476531 | − | 0.158844i | ||||
\(266\) | 2.82843i | 0.173422i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.41421 | + | 8.41421i | 0.513980 | + | 0.513980i | ||||
\(269\) | −5.65685 | −0.344904 | −0.172452 | − | 0.985018i | \(-0.555169\pi\) | ||||
−0.172452 | + | 0.985018i | \(0.555169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.10051 | 0.249088 | 0.124544 | − | 0.992214i | \(-0.460253\pi\) | ||||
0.124544 | + | 0.992214i | \(0.460253\pi\) | |||||||
\(272\) | 0.585786 | + | 0.585786i | 0.0355185 | + | 0.0355185i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.9706i | − | 1.02523i | ||||||
\(275\) | 2.34315 | − | 1.75736i | 0.141297 | − | 0.105973i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.10051 | + | 2.10051i | −0.126207 | + | 0.126207i | −0.767389 | − | 0.641182i | \(-0.778444\pi\) |
0.641182 | + | 0.767389i | \(0.278444\pi\) | |||||||
\(278\) | 12.4853 | − | 12.4853i | 0.748817 | − | 0.748817i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | − | 2.00000i | 0.0597614 | − | 0.119523i | ||||
\(281\) | 19.0711i | 1.13768i | 0.822447 | + | 0.568842i | \(0.192609\pi\) | ||||
−0.822447 | + | 0.568842i | \(0.807391\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3137 | − | 21.3137i | −1.26697 | − | 1.26697i | −0.947646 | − | 0.319322i | \(-0.896545\pi\) |
−0.319322 | − | 0.947646i | \(-0.603455\pi\) | |||||||
\(284\) | 1.17157 | 0.0695201 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.31371 | 0.195944 | ||||||||
\(287\) | −2.24264 | − | 2.24264i | −0.132379 | − | 0.132379i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.3137i | − | 0.959630i | ||||||
\(290\) | −0.585786 | − | 1.75736i | −0.0343986 | − | 0.103196i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.07107 | + | 7.07107i | −0.413803 | + | 0.413803i | ||||
\(293\) | −8.65685 | + | 8.65685i | −0.505739 | + | 0.505739i | −0.913216 | − | 0.407477i | \(-0.866409\pi\) |
0.407477 | + | 0.913216i | \(0.366409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.65685 | − | 2.82843i | −0.329355 | − | 0.164677i | ||||
\(296\) | 8.82843i | 0.513142i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.75736 | + | 5.75736i | 0.333515 | + | 0.333515i | ||||
\(299\) | −38.6274 | −2.23388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.58579 | −0.494877 | ||||||||
\(302\) | −13.3137 | − | 13.3137i | −0.766118 | − | 0.766118i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.82843i | 0.162221i | ||||||||
\(305\) | −19.7990 | − | 9.89949i | −1.13369 | − | 0.566843i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | −0.414214 | + | 0.414214i | −0.0236020 | + | 0.0236020i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.24264 | + | 3.72792i | 0.0705772 | + | 0.211732i | ||||
\(311\) | 4.82843i | 0.273795i | 0.990585 | + | 0.136897i | \(0.0437131\pi\) | ||||
−0.990585 | + | 0.136897i | \(0.956287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.24264 | + | 2.24264i | 0.126762 | + | 0.126762i | 0.767641 | − | 0.640880i | \(-0.221430\pi\) |
−0.640880 | + | 0.767641i | \(0.721430\pi\) | |||||||
\(314\) | −13.6569 | −0.770701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.65685 | 0.318223 | ||||||||
\(317\) | 24.7279 | + | 24.7279i | 1.38886 | + | 1.38886i | 0.827726 | + | 0.561132i | \(0.189634\pi\) |
0.561132 | + | 0.827726i | \(0.310366\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.485281i | 0.0271705i | ||||||||
\(320\) | 1.00000 | − | 2.00000i | 0.0559017 | − | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.82843 | − | 4.82843i | 0.269078 | − | 0.269078i | ||||
\(323\) | −1.65685 | + | 1.65685i | −0.0921898 | + | 0.0921898i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | + | 28.0000i | −0.221880 | + | 1.55316i | ||||
\(326\) | 16.5858i | 0.918602i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.24264 | − | 2.24264i | −0.123829 | − | 0.123829i | ||||
\(329\) | 13.0711 | 0.720631 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6274 | 1.02386 | 0.511928 | − | 0.859029i | \(-0.328932\pi\) | ||||
0.511928 | + | 0.859029i | \(0.328932\pi\) | |||||||
\(332\) | 0.828427 | + | 0.828427i | 0.0454658 | + | 0.0454658i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.7279i | 0.587006i | ||||||||
\(335\) | 25.2426 | − | 8.41421i | 1.37915 | − | 0.459718i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1716 | − | 10.1716i | 0.554081 | − | 0.554081i | −0.373535 | − | 0.927616i | \(-0.621854\pi\) |
0.927616 | + | 0.373535i | \(0.121854\pi\) | |||||||
\(338\) | −13.4350 | + | 13.4350i | −0.730769 | + | 0.730769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.75736 | − | 0.585786i | 0.0953062 | − | 0.0317687i | ||||
\(341\) | − | 1.02944i | − | 0.0557472i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −8.58579 | −0.462915 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.2426 | 0.873210 | ||||||||
\(347\) | 8.48528 | + | 8.48528i | 0.455514 | + | 0.455514i | 0.897180 | − | 0.441666i | \(-0.145612\pi\) |
−0.441666 | + | 0.897180i | \(0.645612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.7279i | 1.75189i | 0.482415 | + | 0.875943i | \(0.339760\pi\) | ||||
−0.482415 | + | 0.875943i | \(0.660240\pi\) | |||||||
\(350\) | −3.00000 | − | 4.00000i | −0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.414214 | + | 0.414214i | −0.0220777 | + | 0.0220777i | ||||
\(353\) | −18.3848 | + | 18.3848i | −0.978523 | + | 0.978523i | −0.999774 | − | 0.0212513i | \(-0.993235\pi\) |
0.0212513 | + | 0.999774i | \(0.493235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.17157 | − | 2.34315i | 0.0621806 | − | 0.124361i | ||||
\(356\) | − | 3.17157i | − | 0.168093i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.7279 | − | 11.7279i | −0.619840 | − | 0.619840i | ||||
\(359\) | −23.7990 | −1.25606 | −0.628031 | − | 0.778188i | \(-0.716139\pi\) | ||||
−0.628031 | + | 0.778188i | \(0.716139\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | −13.4853 | − | 13.4853i | −0.708771 | − | 0.708771i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 5.65685i | − | 0.296500i | ||||||
\(365\) | 7.07107 | + | 21.2132i | 0.370117 | + | 1.11035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2426 | + | 10.2426i | −0.534661 | + | 0.534661i | −0.921956 | − | 0.387295i | \(-0.873410\pi\) |
0.387295 | + | 0.921956i | \(0.373410\pi\) | |||||||
\(368\) | 4.82843 | − | 4.82843i | 0.251699 | − | 0.251699i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.6569 | + | 8.82843i | 0.917936 | + | 0.458968i | ||||
\(371\) | 3.65685i | 0.189854i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0711 | − | 11.0711i | −0.573238 | − | 0.573238i | 0.359794 | − | 0.933032i | \(-0.382847\pi\) |
−0.933032 | + | 0.359794i | \(0.882847\pi\) | |||||||
\(374\) | −0.485281 | −0.0250933 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.0711 | 0.674089 | ||||||||
\(377\) | −3.31371 | − | 3.31371i | −0.170665 | − | 0.170665i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.7990i | 1.32521i | 0.748971 | + | 0.662603i | \(0.230548\pi\) | ||||
−0.748971 | + | 0.662603i | \(0.769452\pi\) | |||||||
\(380\) | 5.65685 | + | 2.82843i | 0.290191 | + | 0.145095i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.1421 | + | 10.1421i | −0.518917 | + | 0.518917i | ||||
\(383\) | −4.41421 | + | 4.41421i | −0.225556 | + | 0.225556i | −0.810833 | − | 0.585277i | \(-0.800986\pi\) |
0.585277 | + | 0.810833i | \(0.300986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.414214 | + | 1.24264i | 0.0211103 | + | 0.0633308i | ||||
\(386\) | 19.0711i | 0.970692i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.58579 | − | 4.58579i | −0.232808 | − | 0.232808i | ||||
\(389\) | 9.79899 | 0.496829 | 0.248414 | − | 0.968654i | \(-0.420091\pi\) | ||||
0.248414 | + | 0.968654i | \(0.420091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65685 | 0.286079 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.4853i | 0.729758i | ||||||||
\(395\) | 5.65685 | − | 11.3137i | 0.284627 | − | 0.569254i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.928932 | + | 0.928932i | −0.0466218 | + | 0.0466218i | −0.730033 | − | 0.683412i | \(-0.760495\pi\) |
0.683412 | + | 0.730033i | \(0.260495\pi\) | |||||||
\(398\) | 2.89949 | − | 2.89949i | 0.145339 | − | 0.145339i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | − | 26.8701i | − | 1.34183i | −0.741536 | − | 0.670913i | \(-0.765902\pi\) | ||
0.741536 | − | 0.670913i | \(-0.234098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.02944 | + | 7.02944i | 0.350161 | + | 0.350161i | ||||
\(404\) | 17.6569 | 0.878461 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.828427 | 0.0411141 | ||||||||
\(407\) | −3.65685 | − | 3.65685i | −0.181264 | − | 0.181264i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.0000i | − | 0.494468i | −0.968956 | − | 0.247234i | \(-0.920478\pi\) | ||
0.968956 | − | 0.247234i | \(-0.0795217\pi\) | |||||||
\(410\) | −6.72792 | + | 2.24264i | −0.332268 | + | 0.110756i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.41421 | − | 7.41421i | 0.365272 | − | 0.365272i | ||||
\(413\) | 2.00000 | − | 2.00000i | 0.0984136 | − | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.48528 | − | 0.828427i | 0.121998 | − | 0.0406659i | ||||
\(416\) | − | 5.65685i | − | 0.277350i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.17157 | − | 1.17157i | −0.0573035 | − | 0.0573035i | ||||
\(419\) | 18.6274 | 0.910009 | 0.455004 | − | 0.890489i | \(-0.349638\pi\) | ||||
0.455004 | + | 0.890489i | \(0.349638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.6274 | −1.98006 | −0.990030 | − | 0.140860i | \(-0.955013\pi\) | ||||
−0.990030 | + | 0.140860i | \(0.955013\pi\) | |||||||
\(422\) | −2.82843 | − | 2.82843i | −0.137686 | − | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.65685i | 0.177593i | ||||||||
\(425\) | 0.585786 | − | 4.10051i | 0.0284148 | − | 0.198904i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.00000 | − | 7.00000i | 0.338754 | − | 0.338754i | ||||
\(428\) | −5.17157 | + | 5.17157i | −0.249977 | + | 0.249977i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.58579 | + | 17.1716i | −0.414043 | + | 0.828087i | ||||
\(431\) | − | 26.1421i | − | 1.25922i | −0.776910 | − | 0.629611i | \(-0.783214\pi\) | ||
0.776910 | − | 0.629611i | \(-0.216786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.2426 | + | 18.2426i | 0.876685 | + | 0.876685i | 0.993190 | − | 0.116505i | \(-0.0371690\pi\) |
−0.116505 | + | 0.993190i | \(0.537169\pi\) | |||||||
\(434\) | −1.75736 | −0.0843559 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.31371 | 0.446046 | ||||||||
\(437\) | 13.6569 | + | 13.6569i | 0.653296 | + | 0.653296i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 3.89949i | − | 0.186113i | −0.995661 | − | 0.0930564i | \(-0.970336\pi\) | ||
0.995661 | − | 0.0930564i | \(-0.0296637\pi\) | |||||||
\(440\) | 0.414214 | + | 1.24264i | 0.0197469 | + | 0.0592406i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.31371 | − | 3.31371i | 0.157617 | − | 0.157617i | ||||
\(443\) | 3.51472 | − | 3.51472i | 0.166989 | − | 0.166989i | −0.618665 | − | 0.785655i | \(-0.712326\pi\) |
0.785655 | + | 0.618665i | \(0.212326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.34315 | − | 3.17157i | −0.300694 | − | 0.150347i | ||||
\(446\) | 10.3431i | 0.489762i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | + | 0.707107i | 0.0334077 | + | 0.0334077i | ||||
\(449\) | 16.7279 | 0.789439 | 0.394720 | − | 0.918802i | \(-0.370842\pi\) | ||||
0.394720 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85786 | 0.0874834 | ||||||||
\(452\) | 11.3137 | + | 11.3137i | 0.532152 | + | 0.532152i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 1.65685i | − | 0.0777600i | ||||||
\(455\) | −11.3137 | − | 5.65685i | −0.530395 | − | 0.265197i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.17157 | − | 2.17157i | 0.101582 | − | 0.101582i | −0.654489 | − | 0.756071i | \(-0.727116\pi\) |
0.756071 | + | 0.654489i | \(0.227116\pi\) | |||||||
\(458\) | −5.82843 | + | 5.82843i | −0.272345 | + | 0.272345i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.82843 | − | 14.4853i | −0.225127 | − | 0.675380i | ||||
\(461\) | 5.31371i | 0.247484i | 0.992314 | + | 0.123742i | \(0.0394895\pi\) | ||||
−0.992314 | + | 0.123742i | \(0.960510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.7990 | − | 19.7990i | −0.920137 | − | 0.920137i | 0.0769016 | − | 0.997039i | \(-0.475497\pi\) |
−0.997039 | + | 0.0769016i | \(0.975497\pi\) | |||||||
\(464\) | 0.828427 | 0.0384588 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.9706 | −0.971443 | ||||||||
\(467\) | 14.0000 | + | 14.0000i | 0.647843 | + | 0.647843i | 0.952471 | − | 0.304629i | \(-0.0985323\pi\) |
−0.304629 | + | 0.952471i | \(0.598532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8995i | 0.549468i | ||||||||
\(470\) | 13.0711 | − | 26.1421i | 0.602923 | − | 1.20585i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | − | 2.00000i | 0.0920575 | − | 0.0920575i | ||||
\(473\) | 3.55635 | − | 3.55635i | 0.163521 | − | 0.163521i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.3137 | − | 8.48528i | 0.519109 | − | 0.389331i | ||||
\(476\) | 0.828427i | 0.0379709i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.65685 | − | 9.65685i | −0.441694 | − | 0.441694i | ||||
\(479\) | −19.1716 | −0.875972 | −0.437986 | − | 0.898982i | \(-0.644308\pi\) | ||||
−0.437986 | + | 0.898982i | \(0.644308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.9411 | 2.27712 | ||||||||
\(482\) | −2.92893 | − | 2.92893i | −0.133409 | − | 0.133409i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.6569i | 0.484402i | ||||||||
\(485\) | −13.7574 | + | 4.58579i | −0.624690 | + | 0.208230i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.9706 | − | 18.9706i | 0.859638 | − | 0.859638i | −0.131657 | − | 0.991295i | \(-0.542030\pi\) |
0.991295 | + | 0.131657i | \(0.0420298\pi\) | |||||||
\(488\) | 7.00000 | − | 7.00000i | 0.316875 | − | 0.316875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.12132 | − | 0.707107i | 0.0958315 | − | 0.0319438i | ||||
\(491\) | 26.7279i | 1.20621i | 0.797660 | + | 0.603107i | \(0.206071\pi\) | ||||
−0.797660 | + | 0.603107i | \(0.793929\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.485281 | + | 0.485281i | 0.0218560 | + | 0.0218560i | ||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.75736 | −0.0789078 | ||||||||
\(497\) | 0.828427 | + | 0.828427i | 0.0371600 | + | 0.0371600i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.4558i | 1.05003i | 0.851094 | + | 0.525014i | \(0.175940\pi\) | ||||
−0.851094 | + | 0.525014i | \(0.824060\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.8284 | + | 18.8284i | −0.840354 | + | 0.840354i | ||||
\(503\) | 16.5563 | − | 16.5563i | 0.738211 | − | 0.738211i | −0.234021 | − | 0.972232i | \(-0.575188\pi\) |
0.972232 | + | 0.234021i | \(0.0751883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.6569 | − | 35.3137i | 0.785720 | − | 1.57144i | ||||
\(506\) | 4.00000i | 0.177822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.65685 | + | 7.65685i | 0.339718 | + | 0.339718i | ||||
\(509\) | 18.3431 | 0.813046 | 0.406523 | − | 0.913641i | \(-0.366741\pi\) | ||||
0.406523 | + | 0.913641i | \(0.366741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 12.1421i | − | 0.535567i | ||||||
\(515\) | −7.41421 | − | 22.2426i | −0.326709 | − | 0.980128i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.41421 | + | 5.41421i | −0.238117 | + | 0.238117i | ||||
\(518\) | −6.24264 | + | 6.24264i | −0.274286 | + | 0.274286i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.3137 | − | 5.65685i | −0.496139 | − | 0.248069i | ||||
\(521\) | − | 42.7696i | − | 1.87377i | −0.349640 | − | 0.936884i | \(-0.613696\pi\) | ||
0.349640 | − | 0.936884i | \(-0.386304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.3137 | − | 25.3137i | −1.10689 | − | 1.10689i | −0.993557 | − | 0.113334i | \(-0.963847\pi\) |
−0.113334 | − | 0.993557i | \(-0.536153\pi\) | |||||||
\(524\) | 16.4853 | 0.720163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.8284 | −0.472142 | ||||||||
\(527\) | −1.02944 | − | 1.02944i | −0.0448430 | − | 0.0448430i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 23.6274i | − | 1.02728i | ||||||
\(530\) | 7.31371 | + | 3.65685i | 0.317687 | + | 0.158844i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | + | 2.00000i | −0.0867110 | + | 0.0867110i | ||||
\(533\) | −12.6863 | + | 12.6863i | −0.549504 | + | 0.549504i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.17157 | + | 15.5147i | 0.223587 | + | 0.670760i | ||||
\(536\) | 11.8995i | 0.513980i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.00000 | − | 4.00000i | −0.172452 | − | 0.172452i | ||||
\(539\) | −0.585786 | −0.0252316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.1127 | −1.25165 | −0.625826 | − | 0.779962i | \(-0.715238\pi\) | ||||
−0.625826 | + | 0.779962i | \(0.715238\pi\) | |||||||
\(542\) | 2.89949 | + | 2.89949i | 0.124544 | + | 0.124544i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.828427i | 0.0355185i | ||||||||
\(545\) | 9.31371 | − | 18.6274i | 0.398955 | − | 0.797911i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5563 | + | 12.5563i | −0.536871 | + | 0.536871i | −0.922608 | − | 0.385738i | \(-0.873947\pi\) |
0.385738 | + | 0.922608i | \(0.373947\pi\) | |||||||
\(548\) | 12.0000 | − | 12.0000i | 0.512615 | − | 0.512615i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.89949 | + | 0.414214i | 0.123635 | + | 0.0176621i | ||||
\(551\) | 2.34315i | 0.0998214i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | + | 4.00000i | 0.170097 | + | 0.170097i | ||||
\(554\) | −2.97056 | −0.126207 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.6569 | 0.748817 | ||||||||
\(557\) | −7.55635 | − | 7.55635i | −0.320173 | − | 0.320173i | 0.528661 | − | 0.848833i | \(-0.322694\pi\) |
−0.848833 | + | 0.528661i | \(0.822694\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.5685i | 2.05423i | ||||||||
\(560\) | 2.12132 | − | 0.707107i | 0.0896421 | − | 0.0298807i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.4853 | + | 13.4853i | −0.568842 | + | 0.568842i | ||||
\(563\) | −6.68629 | + | 6.68629i | −0.281794 | + | 0.281794i | −0.833824 | − | 0.552030i | \(-0.813853\pi\) |
0.552030 | + | 0.833824i | \(0.313853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.9411 | − | 11.3137i | 1.42791 | − | 0.475971i | ||||
\(566\) | − | 30.1421i | − | 1.26697i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.828427 | + | 0.828427i | 0.0347600 | + | 0.0347600i | ||||
\(569\) | 14.1005 | 0.591124 | 0.295562 | − | 0.955324i | \(-0.404493\pi\) | ||||
0.295562 | + | 0.955324i | \(0.404493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0294 | −0.461568 | −0.230784 | − | 0.973005i | \(-0.574129\pi\) | ||||
−0.230784 | + | 0.973005i | \(0.574129\pi\) | |||||||
\(572\) | 2.34315 | + | 2.34315i | 0.0979718 | + | 0.0979718i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 3.17157i | − | 0.132379i | ||||||
\(575\) | −33.7990 | − | 4.82843i | −1.40952 | − | 0.201359i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.7279 | + | 10.7279i | −0.446609 | + | 0.446609i | −0.894226 | − | 0.447616i | \(-0.852273\pi\) |
0.447616 | + | 0.894226i | \(0.352273\pi\) | |||||||
\(578\) | 11.5355 | − | 11.5355i | 0.479815 | − | 0.479815i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.828427 | − | 1.65685i | 0.0343986 | − | 0.0687971i | ||||
\(581\) | 1.17157i | 0.0486050i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.51472 | − | 1.51472i | −0.0627332 | − | 0.0627332i | ||||
\(584\) | −10.0000 | −0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.2426 | −0.505739 | ||||||||
\(587\) | −17.7990 | − | 17.7990i | −0.734643 | − | 0.734643i | 0.236893 | − | 0.971536i | \(-0.423871\pi\) |
−0.971536 | + | 0.236893i | \(0.923871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.97056i | − | 0.204808i | ||||||
\(590\) | −2.00000 | − | 6.00000i | −0.0823387 | − | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.24264 | + | 6.24264i | −0.256571 | + | 0.256571i | ||||
\(593\) | 16.3848 | − | 16.3848i | 0.672842 | − | 0.672842i | −0.285528 | − | 0.958370i | \(-0.592169\pi\) |
0.958370 | + | 0.285528i | \(0.0921690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.65685 | + | 0.828427i | 0.0679244 | + | 0.0339622i | ||||
\(596\) | 8.14214i | 0.333515i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.3137 | − | 27.3137i | −1.11694 | − | 1.11694i | ||||
\(599\) | 15.3137 | 0.625701 | 0.312851 | − | 0.949802i | \(-0.398716\pi\) | ||||
0.312851 | + | 0.949802i | \(0.398716\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.14214 | −0.168961 | −0.0844806 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844806 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(602\) | −6.07107 | − | 6.07107i | −0.247438 | − | 0.247438i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 18.8284i | − | 0.766118i | ||||||
\(605\) | 21.3137 | + | 10.6569i | 0.866525 | + | 0.433263i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.31371 | + | 7.31371i | −0.296854 | + | 0.296854i | −0.839780 | − | 0.542926i | \(-0.817316\pi\) |
0.542926 | + | 0.839780i | \(0.317316\pi\) | |||||||
\(608\) | −2.00000 | + | 2.00000i | −0.0811107 | + | 0.0811107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.00000 | − | 21.0000i | −0.283422 | − | 0.850265i | ||||
\(611\) | − | 73.9411i | − | 2.99134i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.07107 | − | 9.07107i | −0.366377 | − | 0.366377i | 0.499777 | − | 0.866154i | \(-0.333415\pi\) |
−0.866154 | + | 0.499777i | \(0.833415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.585786 | −0.0236020 | ||||||||
\(617\) | −24.0416 | − | 24.0416i | −0.967880 | − | 0.967880i | 0.0316203 | − | 0.999500i | \(-0.489933\pi\) |
−0.999500 | + | 0.0316203i | \(0.989933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.8579i | − | 0.717768i | −0.933382 | − | 0.358884i | \(-0.883157\pi\) | ||
0.933382 | − | 0.358884i | \(-0.116843\pi\) | |||||||
\(620\) | −1.75736 | + | 3.51472i | −0.0705772 | + | 0.141154i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.41421 | + | 3.41421i | −0.136897 | + | 0.136897i | ||||
\(623\) | 2.24264 | − | 2.24264i | 0.0898495 | − | 0.0898495i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 3.17157i | 0.126762i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.65685 | − | 9.65685i | −0.385350 | − | 0.385350i | ||||
\(629\) | −7.31371 | −0.291617 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.201010 | −0.00800209 | −0.00400104 | − | 0.999992i | \(-0.501274\pi\) | ||||
−0.00400104 | + | 0.999992i | \(0.501274\pi\) | |||||||
\(632\) | 4.00000 | + | 4.00000i | 0.159111 | + | 0.159111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 34.9706i | 1.38886i | ||||||||
\(635\) | 22.9706 | − | 7.65685i | 0.911559 | − | 0.303853i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | − | 4.00000i | 0.158486 | − | 0.158486i | ||||
\(638\) | −0.343146 | + | 0.343146i | −0.0135853 | + | 0.0135853i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | − | 0.707107i | 0.0838525 | − | 0.0279508i | ||||
\(641\) | 21.2132i | 0.837871i | 0.908016 | + | 0.418936i | \(0.137597\pi\) | ||||
−0.908016 | + | 0.418936i | \(0.862403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9706 | − | 10.9706i | −0.432637 | − | 0.432637i | 0.456888 | − | 0.889524i | \(-0.348964\pi\) |
−0.889524 | + | 0.456888i | \(0.848964\pi\) | |||||||
\(644\) | 6.82843 | 0.269078 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.34315 | −0.0921898 | ||||||||
\(647\) | 33.2426 | + | 33.2426i | 1.30690 | + | 1.30690i | 0.923639 | + | 0.383264i | \(0.125200\pi\) |
0.383264 | + | 0.923639i | \(0.374800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.65685i | 0.0650372i | ||||||||
\(650\) | −22.6274 | + | 16.9706i | −0.887520 | + | 0.665640i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.7279 | + | 11.7279i | −0.459301 | + | 0.459301i | ||||
\(653\) | −14.2426 | + | 14.2426i | −0.557358 | + | 0.557358i | −0.928554 | − | 0.371197i | \(-0.878948\pi\) |
0.371197 | + | 0.928554i | \(0.378948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.4853 | − | 32.9706i | 0.644133 | − | 1.28827i | ||||
\(656\) | − | 3.17157i | − | 0.123829i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.24264 | + | 9.24264i | 0.360316 | + | 0.360316i | ||||
\(659\) | 26.7279 | 1.04117 | 0.520586 | − | 0.853809i | \(-0.325714\pi\) | ||||
0.520586 | + | 0.853809i | \(0.325714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0416 | 1.55744 | 0.778719 | − | 0.627372i | \(-0.215870\pi\) | ||||
0.778719 | + | 0.627372i | \(0.215870\pi\) | |||||||
\(662\) | 13.1716 | + | 13.1716i | 0.511928 | + | 0.511928i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.17157i | 0.0454658i | ||||||||
\(665\) | 2.00000 | + | 6.00000i | 0.0775567 | + | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000 | − | 4.00000i | 0.154881 | − | 0.154881i | ||||
\(668\) | −7.58579 | + | 7.58579i | −0.293503 | + | 0.293503i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.7990 | + | 11.8995i | 0.919435 | + | 0.459718i | ||||
\(671\) | 5.79899i | 0.223868i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.34315 | + | 3.34315i | 0.128869 | + | 0.128869i | 0.768599 | − | 0.639731i | \(-0.220954\pi\) |
−0.639731 | + | 0.768599i | \(0.720954\pi\) | |||||||
\(674\) | 14.3848 | 0.554081 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.0000 | −0.730769 | ||||||||
\(677\) | −15.8284 | − | 15.8284i | −0.608336 | − | 0.608336i | 0.334175 | − | 0.942511i | \(-0.391542\pi\) |
−0.942511 | + | 0.334175i | \(0.891542\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.48528i | − | 0.248882i | ||||||
\(680\) | 1.65685 | + | 0.828427i | 0.0635375 | + | 0.0317687i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.727922 | − | 0.727922i | 0.0278736 | − | 0.0278736i | ||||
\(683\) | −24.3848 | + | 24.3848i | −0.933058 | + | 0.933058i | −0.997896 | − | 0.0648383i | \(-0.979347\pi\) |
0.0648383 | + | 0.997896i | \(0.479347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | − | 36.0000i | −0.458496 | − | 1.37549i | ||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.07107 | − | 6.07107i | −0.231457 | − | 0.231457i | ||||
\(689\) | 20.6863 | 0.788085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 11.4853 | + | 11.4853i | 0.436605 | + | 0.436605i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000i | 0.455514i | ||||||||
\(695\) | 17.6569 | − | 35.3137i | 0.669763 | − | 1.33953i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.85786 | − | 1.85786i | 0.0703716 | − | 0.0703716i | ||||
\(698\) | −23.1421 | + | 23.1421i | −0.875943 | + | 0.875943i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.707107 | − | 4.94975i | 0.0267261 | − | 0.187083i | ||||
\(701\) | − | 40.8284i | − | 1.54207i | −0.636794 | − | 0.771034i | \(-0.719740\pi\) | ||
0.636794 | − | 0.771034i | \(-0.280260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.6569 | − | 17.6569i | −0.665941 | − | 0.665941i | ||||
\(704\) | −0.585786 | −0.0220777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | 12.4853 | + | 12.4853i | 0.469557 | + | 0.469557i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 40.8284i | − | 1.53334i | −0.642039 | − | 0.766672i | \(-0.721911\pi\) | ||
0.642039 | − | 0.766672i | \(-0.278089\pi\) | |||||||
\(710\) | 2.48528 | − | 0.828427i | 0.0932709 | − | 0.0310903i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.24264 | − | 2.24264i | 0.0840465 | − | 0.0840465i | ||||
\(713\) | −8.48528 | + | 8.48528i | −0.317776 | + | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.02944 | − | 2.34315i | 0.262886 | − | 0.0876287i | ||||
\(716\) | − | 16.5858i | − | 0.619840i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.8284 | − | 16.8284i | −0.628031 | − | 0.628031i | ||||
\(719\) | −38.6274 | −1.44056 | −0.720280 | − | 0.693684i | \(-0.755987\pi\) | ||||
−0.720280 | + | 0.693684i | \(0.755987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4853 | 0.390492 | ||||||||
\(722\) | 7.77817 | + | 7.77817i | 0.289474 | + | 0.289474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 19.0711i | − | 0.708771i | ||||||
\(725\) | −2.48528 | − | 3.31371i | −0.0923010 | − | 0.123068i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6274 | + | 22.6274i | −0.839204 | + | 0.839204i | −0.988754 | − | 0.149550i | \(-0.952218\pi\) |
0.149550 | + | 0.988754i | \(0.452218\pi\) | |||||||
\(728\) | 4.00000 | − | 4.00000i | 0.148250 | − | 0.148250i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.0000 | + | 20.0000i | −0.370117 | + | 0.740233i | ||||
\(731\) | − | 7.11270i | − | 0.263073i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.443651 | − | 0.443651i | −0.0163866 | − | 0.0163866i | 0.698866 | − | 0.715253i | \(-0.253688\pi\) |
−0.715253 | + | 0.698866i | \(0.753688\pi\) | |||||||
\(734\) | −14.4853 | −0.534661 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.82843 | 0.251699 | ||||||||
\(737\) | −4.92893 | − | 4.92893i | −0.181560 | − | 0.181560i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 7.45584i | − | 0.274268i | −0.990553 | − | 0.137134i | \(-0.956211\pi\) | ||
0.990553 | − | 0.137134i | \(-0.0437890\pi\) | |||||||
\(740\) | 6.24264 | + | 18.7279i | 0.229484 | + | 0.688452i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.58579 | + | 2.58579i | −0.0949272 | + | 0.0949272i | ||||
\(743\) | 31.1127 | − | 31.1127i | 1.14141 | − | 1.14141i | 0.153222 | − | 0.988192i | \(-0.451035\pi\) |
0.988192 | − | 0.153222i | \(-0.0489651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.2843 | + | 8.14214i | 0.596610 | + | 0.298305i | ||||
\(746\) | − | 15.6569i | − | 0.573238i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.343146 | − | 0.343146i | −0.0125467 | − | 0.0125467i | ||||
\(749\) | −7.31371 | −0.267237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4853 | 1.76925 | 0.884627 | − | 0.466300i | \(-0.154413\pi\) | ||||
0.884627 | + | 0.466300i | \(0.154413\pi\) | |||||||
\(752\) | 9.24264 | + | 9.24264i | 0.337044 | + | 0.337044i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 4.68629i | − | 0.170665i | ||||||
\(755\) | −37.6569 | − | 18.8284i | −1.37047 | − | 0.685237i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.5563 | + | 23.5563i | −0.856170 | + | 0.856170i | −0.990884 | − | 0.134714i | \(-0.956988\pi\) |
0.134714 | + | 0.990884i | \(0.456988\pi\) | |||||||
\(758\) | −18.2426 | + | 18.2426i | −0.662603 | + | 0.662603i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.00000 | + | 6.00000i | 0.0725476 | + | 0.217643i | ||||
\(761\) | − | 18.9706i | − | 0.687682i | −0.939028 | − | 0.343841i | \(-0.888272\pi\) | ||
0.939028 | − | 0.343841i | \(-0.111728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.58579 | + | 6.58579i | 0.238421 | + | 0.238421i | ||||
\(764\) | −14.3431 | −0.518917 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.24264 | −0.225556 | ||||||||
\(767\) | −11.3137 | − | 11.3137i | −0.408514 | − | 0.408514i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 41.5980i | − | 1.50006i | −0.661403 | − | 0.750031i | \(-0.730039\pi\) | ||
0.661403 | − | 0.750031i | \(-0.269961\pi\) | |||||||
\(770\) | −0.585786 | + | 1.17157i | −0.0211103 | + | 0.0422206i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.4853 | + | 13.4853i | −0.485346 | + | 0.485346i | ||||
\(773\) | −34.9411 | + | 34.9411i | −1.25674 | + | 1.25674i | −0.304107 | + | 0.952638i | \(0.598358\pi\) |
−0.952638 | + | 0.304107i | \(0.901642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.27208 | + | 7.02944i | 0.189379 | + | 0.252505i | ||||
\(776\) | − | 6.48528i | − | 0.232808i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.92893 | + | 6.92893i | 0.248414 | + | 0.248414i | ||||
\(779\) | 8.97056 | 0.321404 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.686292 | −0.0245574 | ||||||||
\(782\) | 4.00000 | + | 4.00000i | 0.143040 | + | 0.143040i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | −28.9706 | + | 9.65685i | −1.03400 | + | 0.344668i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5147 | + | 15.5147i | −0.553040 | + | 0.553040i | −0.927317 | − | 0.374277i | \(-0.877891\pi\) |
0.374277 | + | 0.927317i | \(0.377891\pi\) | |||||||
\(788\) | −10.2426 | + | 10.2426i | −0.364879 | + | 0.364879i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.0000 | − | 4.00000i | 0.426941 | − | 0.142314i | ||||
\(791\) | 16.0000i | 0.568895i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.5980 | − | 39.5980i | −1.40617 | − | 1.40617i | ||||
\(794\) | −1.31371 | −0.0466218 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.10051 | 0.145339 | ||||||||
\(797\) | −20.1716 | − | 20.1716i | −0.714514 | − | 0.714514i | 0.252962 | − | 0.967476i | \(-0.418595\pi\) |
−0.967476 | + | 0.252962i | \(0.918595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8284i | 0.383082i | ||||||||
\(800\) | 0.707107 | − | 4.94975i | 0.0250000 | − | 0.175000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.0000 | − | 19.0000i | 0.670913 | − | 0.670913i | ||||
\(803\) | 4.14214 | − | 4.14214i | 0.146173 | − | 0.146173i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.82843 | − | 13.6569i | 0.240670 | − | 0.481341i | ||||
\(806\) | 9.94113i | 0.350161i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.4853 | + | 12.4853i | 0.439231 | + | 0.439231i | ||||
\(809\) | 46.3848 | 1.63080 | 0.815401 | − | 0.578897i | \(-0.196517\pi\) | ||||
0.815401 | + | 0.578897i | \(0.196517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.9706 | 1.01729 | 0.508647 | − | 0.860975i | \(-0.330146\pi\) | ||||
0.508647 | + | 0.860975i | \(0.330146\pi\) | |||||||
\(812\) | 0.585786 | + | 0.585786i | 0.0205571 | + | 0.0205571i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 5.17157i | − | 0.181264i | ||||||
\(815\) | 11.7279 | + | 35.1838i | 0.410811 | + | 1.23243i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.1716 | − | 17.1716i | 0.600757 | − | 0.600757i | ||||
\(818\) | 7.07107 | − | 7.07107i | 0.247234 | − | 0.247234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.34315 | − | 3.17157i | −0.221512 | − | 0.110756i | ||||
\(821\) | 9.79899i | 0.341987i | 0.985272 | + | 0.170994i | \(0.0546977\pi\) | ||||
−0.985272 | + | 0.170994i | \(0.945302\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.4853 | + | 28.4853i | 0.992934 | + | 0.992934i | 0.999975 | − | 0.00704072i | \(-0.00224115\pi\) |
−0.00704072 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(824\) | 10.4853 | 0.365272 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.82843 | 0.0984136 | ||||||||
\(827\) | 14.2426 | + | 14.2426i | 0.495265 | + | 0.495265i | 0.909960 | − | 0.414695i | \(-0.136112\pi\) |
−0.414695 | + | 0.909960i | \(0.636112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11.7574i | − | 0.408350i | −0.978934 | − | 0.204175i | \(-0.934549\pi\) | ||
0.978934 | − | 0.204175i | \(-0.0654512\pi\) | |||||||
\(830\) | 2.34315 | + | 1.17157i | 0.0813318 | + | 0.0406659i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.00000 | − | 4.00000i | 0.138675 | − | 0.138675i | ||||
\(833\) | −0.585786 | + | 0.585786i | −0.0202963 | + | 0.0202963i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.58579 | + | 22.7574i | 0.262517 | + | 0.787551i | ||||
\(836\) | − | 1.65685i | − | 0.0573035i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.1716 | + | 13.1716i | 0.455004 | + | 0.455004i | ||||
\(839\) | 30.4853 | 1.05247 | 0.526234 | − | 0.850340i | \(-0.323603\pi\) | ||||
0.526234 | + | 0.850340i | \(0.323603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | −28.7279 | − | 28.7279i | −0.990030 | − | 0.990030i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.00000i | − | 0.137686i | ||||||
\(845\) | −19.0000 | + | 38.0000i | −0.653620 | + | 1.30724i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.53553 | + | 7.53553i | −0.258924 | + | 0.258924i | ||||
\(848\) | −2.58579 | + | 2.58579i | −0.0887963 | + | 0.0887963i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.31371 | − | 2.48528i | 0.113659 | − | 0.0852444i | ||||
\(851\) | 60.2843i | 2.06652i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0711 | − | 15.0711i | −0.516024 | − | 0.516024i | 0.400342 | − | 0.916366i | \(-0.368891\pi\) |
−0.916366 | + | 0.400342i | \(0.868891\pi\) | |||||||
\(854\) | 9.89949 | 0.338754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.31371 | −0.249977 | ||||||||
\(857\) | −6.44365 | − | 6.44365i | −0.220111 | − | 0.220111i | 0.588434 | − | 0.808545i | \(-0.299745\pi\) |
−0.808545 | + | 0.588434i | \(0.799745\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000i | 1.36478i | 0.730987 | + | 0.682391i | \(0.239060\pi\) | ||||
−0.730987 | + | 0.682391i | \(0.760940\pi\) | |||||||
\(860\) | −18.2132 | + | 6.07107i | −0.621065 | + | 0.207022i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.4853 | − | 18.4853i | 0.629611 | − | 0.629611i | ||||
\(863\) | 21.1716 | − | 21.1716i | 0.720689 | − | 0.720689i | −0.248057 | − | 0.968745i | \(-0.579792\pi\) |
0.968745 | + | 0.248057i | \(0.0797920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.4558 | − | 11.4853i | 1.17153 | − | 0.390511i | ||||
\(866\) | 25.7990i | 0.876685i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.24264 | − | 1.24264i | −0.0421780 | − | 0.0421780i | ||||
\(869\) | −3.31371 | −0.112410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67.3137 | 2.28084 | ||||||||
\(872\) | 6.58579 | + | 6.58579i | 0.223023 | + | 0.223023i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.3137i | 0.653296i | ||||||||
\(875\) | −9.19239 | − | 6.36396i | −0.310759 | − | 0.215141i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.6985 | + | 37.6985i | −1.27299 | + | 1.27299i | −0.328475 | + | 0.944513i | \(0.606535\pi\) |
−0.944513 | + | 0.328475i | \(0.893465\pi\) | |||||||
\(878\) | 2.75736 | − | 2.75736i | 0.0930564 | − | 0.0930564i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.585786 | + | 1.17157i | −0.0197469 | + | 0.0394937i | ||||
\(881\) | 8.62742i | 0.290665i | 0.989383 | + | 0.145333i | \(0.0464252\pi\) | ||||
−0.989383 | + | 0.145333i | \(0.953575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.3848 | + | 37.3848i | 1.25810 | + | 1.25810i | 0.952000 | + | 0.306098i | \(0.0990235\pi\) |
0.306098 | + | 0.952000i | \(0.400977\pi\) | |||||||
\(884\) | 4.68629 | 0.157617 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.97056 | 0.166989 | ||||||||
\(887\) | 39.7279 | + | 39.7279i | 1.33393 | + | 1.33393i | 0.901819 | + | 0.432114i | \(0.142232\pi\) |
0.432114 | + | 0.901819i | \(0.357768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.8284i | 0.363174i | ||||||||
\(890\) | −2.24264 | − | 6.72792i | −0.0751735 | − | 0.225520i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.31371 | + | 7.31371i | −0.244881 | + | 0.244881i | ||||
\(893\) | −26.1421 | + | 26.1421i | −0.874813 | + | 0.874813i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.1716 | − | 16.5858i | −1.10880 | − | 0.554402i | ||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.8284 | + | 11.8284i | 0.394720 | + | 0.394720i | ||||
\(899\) | −1.45584 | −0.0485551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.02944 | −0.100925 | ||||||||
\(902\) | 1.31371 | + | 1.31371i | 0.0437417 | + | 0.0437417i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.0000i | 0.532152i | ||||||||
\(905\) | −38.1421 | − | 19.0711i | −1.26789 | − | 0.633944i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.5858 | − | 19.5858i | 0.650335 | − | 0.650335i | −0.302738 | − | 0.953074i | \(-0.597901\pi\) |
0.953074 | + | 0.302738i | \(0.0979008\pi\) | |||||||
\(908\) | 1.17157 | − | 1.17157i | 0.0388800 | − | 0.0388800i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | − | 12.0000i | −0.132599 | − | 0.397796i | ||||
\(911\) | − | 4.00000i | − | 0.132526i | −0.997802 | − | 0.0662630i | \(-0.978892\pi\) | ||
0.997802 | − | 0.0662630i | \(-0.0211076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.485281 | − | 0.485281i | −0.0160605 | − | 0.0160605i | ||||
\(914\) | 3.07107 | 0.101582 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.24264 | −0.272345 | ||||||||
\(917\) | 11.6569 | + | 11.6569i | 0.384943 | + | 0.384943i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.7990i | 1.84064i | 0.391168 | + | 0.920319i | \(0.372071\pi\) | ||||
−0.391168 | + | 0.920319i | \(0.627929\pi\) | |||||||
\(920\) | 6.82843 | − | 13.6569i | 0.225127 | − | 0.450253i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.75736 | + | 3.75736i | −0.123742 | + | 0.123742i | ||||
\(923\) | 4.68629 | − | 4.68629i | 0.154251 | − | 0.154251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.6985 | + | 6.24264i | 1.43680 | + | 0.205257i | ||||
\(926\) | − | 28.0000i | − | 0.920137i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.585786 | + | 0.585786i | 0.0192294 | + | 0.0192294i | ||||
\(929\) | 13.0294 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | −14.8284 | − | 14.8284i | −0.485721 | − | 0.485721i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.7990i | 0.647843i | ||||||||
\(935\) | −1.02944 | + | 0.343146i | −0.0336662 | + | 0.0112221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.2132 | + | 29.2132i | −0.954354 | + | 0.954354i | −0.999003 | − | 0.0446490i | \(-0.985783\pi\) |
0.0446490 | + | 0.999003i | \(0.485783\pi\) | |||||||
\(938\) | −8.41421 | + | 8.41421i | −0.274734 | + | 0.274734i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 27.7279 | − | 9.24264i | 0.904385 | − | 0.301462i | ||||
\(941\) | − | 10.2843i | − | 0.335258i | −0.985850 | − | 0.167629i | \(-0.946389\pi\) | ||
0.985850 | − | 0.167629i | \(-0.0536110\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.3137 | − | 15.3137i | −0.498683 | − | 0.498683i | ||||
\(944\) | 2.82843 | 0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.02944 | 0.163521 | ||||||||
\(947\) | −9.75736 | − | 9.75736i | −0.317072 | − | 0.317072i | 0.530570 | − | 0.847641i | \(-0.321978\pi\) |
−0.847641 | + | 0.530570i | \(0.821978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.5685i | 1.83629i | ||||||||
\(950\) | 14.0000 | + | 2.00000i | 0.454220 | + | 0.0648886i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.585786 | + | 0.585786i | −0.0189854 | + | 0.0189854i | ||||
\(953\) | 27.7574 | − | 27.7574i | 0.899149 | − | 0.899149i | −0.0962118 | − | 0.995361i | \(-0.530673\pi\) |
0.995361 | + | 0.0962118i | \(0.0306726\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.3431 | + | 28.6863i | −0.464133 | + | 0.928267i | ||||
\(956\) | − | 13.6569i | − | 0.441694i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.5563 | − | 13.5563i | −0.437986 | − | 0.437986i | ||||
\(959\) | 16.9706 | 0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.9117 | −0.900377 | ||||||||
\(962\) | 35.3137 | + | 35.3137i | 1.13856 | + | 1.13856i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 4.14214i | − | 0.133409i | ||||||
\(965\) | 13.4853 | + | 40.4558i | 0.434107 | + | 1.30232i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.2843 | − | 20.2843i | 0.652298 | − | 0.652298i | −0.301248 | − | 0.953546i | \(-0.597403\pi\) |
0.953546 | + | 0.301248i | \(0.0974031\pi\) | |||||||
\(968\) | −7.53553 | + | 7.53553i | −0.242201 | + | 0.242201i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.9706 | − | 6.48528i | −0.416460 | − | 0.208230i | ||||
\(971\) | 36.0000i | 1.15529i | 0.816286 | + | 0.577647i | \(0.196029\pi\) | ||||
−0.816286 | + | 0.577647i | \(0.803971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.4853 | + | 12.4853i | 0.400260 | + | 0.400260i | ||||
\(974\) | 26.8284 | 0.859638 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.89949 | 0.316875 | ||||||||
\(977\) | −32.9706 | − | 32.9706i | −1.05482 | − | 1.05482i | −0.998407 | − | 0.0564143i | \(-0.982033\pi\) |
−0.0564143 | − | 0.998407i | \(-0.517967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.85786i | 0.0593776i | ||||||||
\(980\) | 2.00000 | + | 1.00000i | 0.0638877 | + | 0.0319438i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.8995 | + | 18.8995i | −0.603107 | + | 0.603107i | ||||
\(983\) | −40.5563 | + | 40.5563i | −1.29355 | + | 1.29355i | −0.360969 | + | 0.932578i | \(0.617554\pi\) |
−0.932578 | + | 0.360969i | \(0.882446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.2426 | + | 30.7279i | 0.326358 | + | 0.979073i | ||||
\(986\) | 0.686292i | 0.0218560i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.3137 | + | 11.3137i | 0.359937 | + | 0.359937i | ||||
\(989\) | −58.6274 | −1.86424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.1421 | −0.957496 | −0.478748 | − | 0.877952i | \(-0.658909\pi\) | ||||
−0.478748 | + | 0.877952i | \(0.658909\pi\) | |||||||
\(992\) | −1.24264 | − | 1.24264i | −0.0394539 | − | 0.0394539i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.17157i | 0.0371600i | ||||||||
\(995\) | 4.10051 | − | 8.20101i | 0.129995 | − | 0.259989i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.89949 | − | 1.89949i | 0.0601576 | − | 0.0601576i | −0.676388 | − | 0.736546i | \(-0.736456\pi\) |
0.736546 | + | 0.676388i | \(0.236456\pi\) | |||||||
\(998\) | −16.5858 | + | 16.5858i | −0.525014 | + | 0.525014i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.2.m.b.323.2 | yes | 4 | |
3.2 | odd | 2 | 630.2.m.a.323.1 | yes | 4 | ||
5.2 | odd | 4 | 630.2.m.a.197.1 | ✓ | 4 | ||
5.3 | odd | 4 | 3150.2.m.b.1457.2 | 4 | |||
5.4 | even | 2 | 3150.2.m.a.2843.1 | 4 | |||
15.2 | even | 4 | inner | 630.2.m.b.197.2 | yes | 4 | |
15.8 | even | 4 | 3150.2.m.a.1457.1 | 4 | |||
15.14 | odd | 2 | 3150.2.m.b.2843.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.a.197.1 | ✓ | 4 | 5.2 | odd | 4 | ||
630.2.m.a.323.1 | yes | 4 | 3.2 | odd | 2 | ||
630.2.m.b.197.2 | yes | 4 | 15.2 | even | 4 | inner | |
630.2.m.b.323.2 | yes | 4 | 1.1 | even | 1 | trivial | |
3150.2.m.a.1457.1 | 4 | 15.8 | even | 4 | |||
3150.2.m.a.2843.1 | 4 | 5.4 | even | 2 | |||
3150.2.m.b.1457.2 | 4 | 5.3 | odd | 4 | |||
3150.2.m.b.2843.2 | 4 | 15.14 | odd | 2 |