Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, 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("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.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: | \(25.1528766367\) |
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: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1457 |
Dual form | 3150.2.m.a.2843.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 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 | 0 | ||||||||
\(11\) | 0.585786i | 0.176621i | 0.996093 | + | 0.0883106i | \(0.0281468\pi\) | ||||
−0.996093 | + | 0.0883106i | \(0.971853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | + | 4.00000i | −1.10940 | + | 1.10940i | −0.116171 | + | 0.993229i | \(0.537062\pi\) |
−0.993229 | + | 0.116171i | \(0.962938\pi\) | |||||||
\(14\) | −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 | \(-0.717968\pi\) |
0.774567 | + | 0.632492i | \(0.217968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.414214 | − | 0.414214i | −0.0883106 | − | 0.0883106i | ||||
\(23\) | 4.82843 | + | 4.82843i | 1.00680 | + | 1.00680i | 0.999977 | + | 0.00681991i | \(0.00217086\pi\) |
0.00681991 | + | 0.999977i | \(0.497829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.24264 | − | 6.24264i | −1.02628 | − | 1.02628i | −0.999645 | − | 0.0266387i | \(-0.991520\pi\) |
−0.0266387 | − | 0.999645i | \(-0.508480\pi\) | |||||||
\(38\) | −2.00000 | − | 2.00000i | −0.324443 | − | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.17157i | − | 0.495316i | −0.968847 | − | 0.247658i | \(-0.920339\pi\) | ||
0.968847 | − | 0.247658i | \(-0.0796610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.07107 | + | 6.07107i | −0.925829 | + | 0.925829i | −0.997433 | − | 0.0716040i | \(-0.977188\pi\) |
0.0716040 | + | 0.997433i | \(0.477188\pi\) | |||||||
\(44\) | 0.585786 | 0.0883106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.82843 | −1.00680 | ||||||||
\(47\) | 9.24264 | − | 9.24264i | 1.34818 | − | 1.34818i | 0.460537 | − | 0.887640i | \(-0.347657\pi\) |
0.887640 | − | 0.460537i | \(-0.152343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | + | 4.00000i | 0.554700 | + | 0.554700i | ||||
\(53\) | −2.58579 | − | 2.58579i | −0.355185 | − | 0.355185i | 0.506849 | − | 0.862035i | \(-0.330810\pi\) |
−0.862035 | + | 0.506849i | \(0.830810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.41421 | − | 8.41421i | −1.02796 | − | 1.02796i | −0.999598 | − | 0.0283621i | \(-0.990971\pi\) |
−0.0283621 | − | 0.999598i | \(-0.509029\pi\) | |||||||
\(68\) | −0.585786 | − | 0.585786i | −0.0710370 | − | 0.0710370i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.17157i | 0.139040i | 0.997581 | + | 0.0695201i | \(0.0221468\pi\) | ||||
−0.997581 | + | 0.0695201i | \(0.977853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.07107 | + | 7.07107i | −0.827606 | + | 0.827606i | −0.987185 | − | 0.159579i | \(-0.948986\pi\) |
0.159579 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(74\) | 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 | \(0.103086\pi\) | ||||
−0.948016 | + | 0.318223i | \(0.896914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.24264 | + | 2.24264i | 0.247658 | + | 0.247658i | ||||
\(83\) | −0.828427 | − | 0.828427i | −0.0909317 | − | 0.0909317i | 0.660178 | − | 0.751109i | \(-0.270481\pi\) |
−0.751109 | + | 0.660178i | \(0.770481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 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 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.58579 | + | 4.58579i | 0.465616 | + | 0.465616i | 0.900491 | − | 0.434875i | \(-0.143207\pi\) |
−0.434875 | + | 0.900491i | \(0.643207\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.6569i | 1.75692i | 0.477813 | + | 0.878461i | \(0.341429\pi\) | ||||
−0.477813 | + | 0.878461i | \(0.658571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.41421 | − | 7.41421i | 0.730544 | − | 0.730544i | −0.240183 | − | 0.970728i | \(-0.577208\pi\) |
0.970728 | + | 0.240183i | \(0.0772076\pi\) | |||||||
\(104\) | −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 | \(-0.865016\pi\) |
0.411469 | + | 0.911424i | \(0.365016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.31371i | 0.892091i | 0.895010 | + | 0.446046i | \(0.147168\pi\) | ||||
−0.895010 | + | 0.446046i | \(0.852832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | −11.3137 | − | 11.3137i | −1.06430 | − | 1.06430i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) |
−0.0665190 | − | 0.997785i | \(-0.521189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.65685 | − | 7.65685i | −0.679436 | − | 0.679436i | 0.280437 | − | 0.959873i | \(-0.409521\pi\) |
−0.959873 | + | 0.280437i | \(0.909521\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4853i | 1.44033i | 0.693805 | + | 0.720163i | \(0.255933\pi\) | ||||
−0.693805 | + | 0.720163i | \(0.744067\pi\) | |||||||
\(132\) | 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 | 0.0255558 | − | 0.999673i | \(-0.491864\pi\) |
0.999673 | − | 0.0255558i | \(-0.00813555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6569i | 1.49763i | 0.662776 | + | 0.748817i | \(0.269378\pi\) | ||||
−0.662776 | + | 0.748817i | \(0.730622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.828427 | − | 0.828427i | −0.0695201 | − | 0.0695201i | ||||
\(143\) | −2.34315 | − | 2.34315i | −0.195944 | − | 0.195944i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 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 | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.65685 | + | 9.65685i | 0.770701 | + | 0.770701i | 0.978229 | − | 0.207528i | \(-0.0665419\pi\) |
−0.207528 | + | 0.978229i | \(0.566542\pi\) | |||||||
\(158\) | −4.00000 | − | 4.00000i | −0.318223 | − | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.82843i | 0.538155i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7279 | + | 11.7279i | −0.918602 | + | 0.918602i | −0.996928 | − | 0.0783260i | \(-0.975042\pi\) |
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −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 | \(-0.886245\pi\) |
0.349814 | + | 0.936819i | \(0.386245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19.0000i | − | 1.46154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.07107 | + | 6.07107i | 0.462915 | + | 0.462915i | ||||
\(173\) | −11.4853 | − | 11.4853i | −0.873210 | − | 0.873210i | 0.119611 | − | 0.992821i | \(-0.461835\pi\) |
−0.992821 | + | 0.119611i | \(0.961835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.343146 | + | 0.343146i | 0.0250933 | + | 0.0250933i | ||||
\(188\) | −9.24264 | − | 9.24264i | −0.674089 | − | 0.674089i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 14.3431i | − | 1.03783i | −0.854825 | − | 0.518917i | \(-0.826335\pi\) | ||
0.854825 | − | 0.518917i | \(-0.173665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.4853 | + | 13.4853i | −0.970692 | + | 0.970692i | −0.999583 | − | 0.0288908i | \(-0.990802\pi\) |
0.0288908 | + | 0.999583i | \(0.490802\pi\) | |||||||
\(194\) | −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 | \(-0.922586\pi\) |
0.240813 | + | 0.970571i | \(0.422586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.10051i | 0.290677i | 0.989382 | + | 0.145339i | \(0.0464271\pi\) | ||||
−0.989382 | + | 0.145339i | \(0.953573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.4853 | − | 12.4853i | −0.878461 | − | 0.878461i | ||||
\(203\) | −0.585786 | − | 0.585786i | −0.0411141 | − | 0.0411141i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.24264 | + | 1.24264i | 0.0843559 | + | 0.0843559i | ||||
\(218\) | −6.58579 | − | 6.58579i | −0.446046 | − | 0.446046i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.68629i | 0.315234i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.31371 | + | 7.31371i | −0.489762 | + | 0.489762i | −0.908231 | − | 0.418469i | \(-0.862567\pi\) |
0.418469 | + | 0.908231i | \(0.362567\pi\) | |||||||
\(224\) | 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 | \(-0.732489\pi\) |
0.744917 | + | 0.667157i | \(0.232489\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.24264i | − | 0.544689i | −0.962200 | − | 0.272345i | \(-0.912201\pi\) | ||
0.962200 | − | 0.272345i | \(-0.0877990\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.585786 | − | 0.585786i | −0.0384588 | − | 0.0384588i | ||||
\(233\) | 14.8284 | + | 14.8284i | 0.971443 | + | 0.971443i | 0.999603 | − | 0.0281608i | \(-0.00896506\pi\) |
−0.0281608 | + | 0.999603i | \(0.508965\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.3137 | − | 11.3137i | −0.719874 | − | 0.719874i | ||||
\(248\) | 1.24264 | + | 1.24264i | 0.0789078 | + | 0.0789078i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.6274i | − | 1.68071i | −0.542038 | − | 0.840354i | \(-0.682347\pi\) | ||
0.542038 | − | 0.840354i | \(-0.317653\pi\) | |||||||
\(252\) | 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 | \(-0.626370\pi\) |
0.922224 | + | 0.386657i | \(0.126370\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.82843i | − | 0.548572i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.6569 | − | 11.6569i | −0.720163 | − | 0.720163i | ||||
\(263\) | 7.65685 | + | 7.65685i | 0.472142 | + | 0.472142i | 0.902607 | − | 0.430465i | \(-0.141651\pi\) |
−0.430465 | + | 0.902607i | \(0.641651\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 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 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.10051 | + | 2.10051i | 0.126207 | + | 0.126207i | 0.767389 | − | 0.641182i | \(-0.221556\pi\) |
−0.641182 | + | 0.767389i | \(0.721556\pi\) | |||||||
\(278\) | −12.4853 | − | 12.4853i | −0.748817 | − | 0.748817i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.0711i | − | 1.13768i | −0.822447 | − | 0.568842i | \(-0.807391\pi\) | ||
0.822447 | − | 0.568842i | \(-0.192609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.3137 | − | 21.3137i | 1.26697 | − | 1.26697i | 0.319322 | − | 0.947646i | \(-0.396545\pi\) |
0.947646 | − | 0.319322i | \(-0.103455\pi\) | |||||||
\(284\) | 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 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.07107 | + | 7.07107i | 0.413803 | + | 0.413803i | ||||
\(293\) | 8.65685 | + | 8.65685i | 0.505739 | + | 0.505739i | 0.913216 | − | 0.407477i | \(-0.133591\pi\) |
−0.407477 | + | 0.913216i | \(0.633591\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 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 | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0.414214 | + | 0.414214i | 0.0236020 | + | 0.0236020i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 4.82843i | − | 0.273795i | −0.990585 | − | 0.136897i | \(-0.956287\pi\) | ||
0.990585 | − | 0.136897i | \(-0.0437131\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.24264 | + | 2.24264i | −0.126762 | + | 0.126762i | −0.767641 | − | 0.640880i | \(-0.778570\pi\) |
0.640880 | + | 0.767641i | \(0.278570\pi\) | |||||||
\(314\) | −13.6569 | −0.770701 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.65685 | 0.318223 | ||||||||
\(317\) | −24.7279 | + | 24.7279i | −1.38886 | + | 1.38886i | −0.561132 | + | 0.827726i | \(0.689634\pi\) |
−0.827726 | + | 0.561132i | \(0.810366\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.485281i | − | 0.0271705i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.82843 | − | 4.82843i | −0.269078 | − | 0.269078i | ||||
\(323\) | 1.65685 | + | 1.65685i | 0.0921898 | + | 0.0921898i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 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 | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1716 | − | 10.1716i | −0.554081 | − | 0.554081i | 0.373535 | − | 0.927616i | \(-0.378146\pi\) |
−0.927616 | + | 0.373535i | \(0.878146\pi\) | |||||||
\(338\) | 13.4350 | + | 13.4350i | 0.730769 | + | 0.730769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 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 | \(-0.854388\pi\) |
0.441666 | + | 0.897180i | \(0.354388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32.7279i | − | 1.75189i | −0.482415 | − | 0.875943i | \(-0.660240\pi\) | ||
0.482415 | − | 0.875943i | \(-0.339760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.414214 | + | 0.414214i | 0.0220777 | + | 0.0220777i | ||||
\(353\) | 18.3848 | + | 18.3848i | 0.978523 | + | 0.978523i | 0.999774 | − | 0.0212513i | \(-0.00676499\pi\) |
−0.0212513 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2426 | + | 10.2426i | 0.534661 | + | 0.534661i | 0.921956 | − | 0.387295i | \(-0.126590\pi\) |
−0.387295 | + | 0.921956i | \(0.626590\pi\) | |||||||
\(368\) | −4.82843 | − | 4.82843i | −0.251699 | − | 0.251699i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.65685i | − | 0.189854i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0711 | − | 11.0711i | 0.573238 | − | 0.573238i | −0.359794 | − | 0.933032i | \(-0.617153\pi\) |
0.933032 | + | 0.359794i | \(0.117153\pi\) | |||||||
\(374\) | −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 | \(-0.769452\pi\) | ||
0.748971 | − | 0.662603i | \(-0.230548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.1421 | + | 10.1421i | 0.518917 | + | 0.518917i | ||||
\(383\) | 4.41421 | + | 4.41421i | 0.225556 | + | 0.225556i | 0.810833 | − | 0.585277i | \(-0.199014\pi\) |
−0.585277 | + | 0.810833i | \(0.699014\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 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 | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.928932 | + | 0.928932i | 0.0466218 | + | 0.0466218i | 0.730033 | − | 0.683412i | \(-0.239505\pi\) |
−0.683412 | + | 0.730033i | \(0.739505\pi\) | |||||||
\(398\) | −2.89949 | − | 2.89949i | −0.145339 | − | 0.145339i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 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 | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.41421 | − | 7.41421i | −0.365272 | − | 0.365272i | ||||
\(413\) | −2.00000 | − | 2.00000i | −0.0984136 | − | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 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 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | − | 7.00000i | −0.338754 | − | 0.338754i | ||||
\(428\) | 5.17157 | + | 5.17157i | 0.249977 | + | 0.249977i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1421i | 1.25922i | 0.776910 | + | 0.629611i | \(0.216786\pi\) | ||||
−0.776910 | + | 0.629611i | \(0.783214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2426 | + | 18.2426i | −0.876685 | + | 0.876685i | −0.993190 | − | 0.116505i | \(-0.962831\pi\) |
0.116505 | + | 0.993190i | \(0.462831\pi\) | |||||||
\(434\) | −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 | \(0.0296637\pi\) | ||||
−0.995661 | + | 0.0930564i | \(0.970336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.31371 | − | 3.31371i | −0.157617 | − | 0.157617i | ||||
\(443\) | −3.51472 | − | 3.51472i | −0.166989 | − | 0.166989i | 0.618665 | − | 0.785655i | \(-0.287674\pi\) |
−0.785655 | + | 0.618665i | \(0.787674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.17157 | − | 2.17157i | −0.101582 | − | 0.101582i | 0.654489 | − | 0.756071i | \(-0.272884\pi\) |
−0.756071 | + | 0.654489i | \(0.772884\pi\) | |||||||
\(458\) | 5.82843 | + | 5.82843i | 0.272345 | + | 0.272345i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.31371i | − | 0.247484i | −0.992314 | − | 0.123742i | \(-0.960510\pi\) | ||
0.992314 | − | 0.123742i | \(-0.0394895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.7990 | − | 19.7990i | 0.920137 | − | 0.920137i | −0.0769016 | − | 0.997039i | \(-0.524503\pi\) |
0.997039 | + | 0.0769016i | \(0.0245027\pi\) | |||||||
\(464\) | 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 | \(-0.901468\pi\) |
0.304629 | + | 0.952471i | \(0.401468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.8995i | − | 0.549468i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | − | 2.00000i | −0.0920575 | − | 0.0920575i | ||||
\(473\) | −3.55635 | − | 3.55635i | −0.163521 | − | 0.163521i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 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 | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.9706 | − | 18.9706i | −0.859638 | − | 0.859638i | 0.131657 | − | 0.991295i | \(-0.457970\pi\) |
−0.991295 | + | 0.131657i | \(0.957970\pi\) | |||||||
\(488\) | −7.00000 | − | 7.00000i | −0.316875 | − | 0.316875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.7279i | − | 1.20621i | −0.797660 | − | 0.603107i | \(-0.793929\pi\) | ||
0.797660 | − | 0.603107i | \(-0.206071\pi\) | |||||||
\(492\) | 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 | \(-0.824060\pi\) | ||
0.851094 | − | 0.525014i | \(-0.175940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.8284 | + | 18.8284i | 0.840354 | + | 0.840354i | ||||
\(503\) | −16.5563 | − | 16.5563i | −0.738211 | − | 0.738211i | 0.234021 | − | 0.972232i | \(-0.424812\pi\) |
−0.972232 | + | 0.234021i | \(0.924812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 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 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.41421 | + | 5.41421i | 0.238117 | + | 0.238117i | ||||
\(518\) | 6.24264 | + | 6.24264i | 0.274286 | + | 0.274286i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.7696i | 1.87377i | 0.349640 | + | 0.936884i | \(0.386304\pi\) | ||||
−0.349640 | + | 0.936884i | \(0.613696\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.3137 | − | 25.3137i | 1.10689 | − | 1.10689i | 0.113334 | − | 0.993557i | \(-0.463847\pi\) |
0.993557 | − | 0.113334i | \(-0.0361531\pi\) | |||||||
\(524\) | 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 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | + | 2.00000i | 0.0867110 | + | 0.0867110i | ||||
\(533\) | 12.6863 | + | 12.6863i | 0.549504 | + | 0.549504i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 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 | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.5563 | + | 12.5563i | 0.536871 | + | 0.536871i | 0.922608 | − | 0.385738i | \(-0.126053\pi\) |
−0.385738 | + | 0.922608i | \(0.626053\pi\) | |||||||
\(548\) | −12.0000 | − | 12.0000i | −0.512615 | − | 0.512615i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 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 | \(-0.677306\pi\) |
0.848833 | + | 0.528661i | \(0.177306\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.5685i | − | 2.05423i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.4853 | + | 13.4853i | 0.568842 | + | 0.568842i | ||||
\(563\) | 6.68629 | + | 6.68629i | 0.281794 | + | 0.281794i | 0.833824 | − | 0.552030i | \(-0.186147\pi\) |
−0.552030 | + | 0.833824i | \(0.686147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.7279 | + | 10.7279i | 0.446609 | + | 0.446609i | 0.894226 | − | 0.447616i | \(-0.147727\pi\) |
−0.447616 | + | 0.894226i | \(0.647727\pi\) | |||||||
\(578\) | −11.5355 | − | 11.5355i | −0.479815 | − | 0.479815i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 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 | \(-0.576129\pi\) |
0.971536 | + | 0.236893i | \(0.0761290\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.97056i | 0.204808i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.24264 | + | 6.24264i | 0.256571 | + | 0.256571i | ||||
\(593\) | −16.3848 | − | 16.3848i | −0.672842 | − | 0.672842i | 0.285528 | − | 0.958370i | \(-0.407831\pi\) |
−0.958370 | + | 0.285528i | \(0.907831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.31371 | + | 7.31371i | 0.296854 | + | 0.296854i | 0.839780 | − | 0.542926i | \(-0.182684\pi\) |
−0.542926 | + | 0.839780i | \(0.682684\pi\) | |||||||
\(608\) | 2.00000 | + | 2.00000i | 0.0811107 | + | 0.0811107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 73.9411i | 2.99134i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.07107 | − | 9.07107i | 0.366377 | − | 0.366377i | −0.499777 | − | 0.866154i | \(-0.666585\pi\) |
0.866154 | + | 0.499777i | \(0.166585\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.585786 | −0.0236020 | ||||||||
\(617\) | 24.0416 | − | 24.0416i | 0.967880 | − | 0.967880i | −0.0316203 | − | 0.999500i | \(-0.510067\pi\) |
0.999500 | + | 0.0316203i | \(0.0100667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.8579i | 0.717768i | 0.933382 | + | 0.358884i | \(0.116843\pi\) | ||||
−0.933382 | + | 0.358884i | \(0.883157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.41421 | + | 3.41421i | 0.136897 | + | 0.136897i | ||||
\(623\) | −2.24264 | − | 2.24264i | −0.0898495 | − | 0.0898495i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 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 | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | − | 4.00000i | −0.158486 | − | 0.158486i | ||||
\(638\) | 0.343146 | + | 0.343146i | 0.0135853 | + | 0.0135853i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 21.2132i | − | 0.837871i | −0.908016 | − | 0.418936i | \(-0.862403\pi\) | ||
0.908016 | − | 0.418936i | \(-0.137597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9706 | − | 10.9706i | 0.432637 | − | 0.432637i | −0.456888 | − | 0.889524i | \(-0.651036\pi\) |
0.889524 | + | 0.456888i | \(0.151036\pi\) | |||||||
\(644\) | 6.82843 | 0.269078 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.34315 | −0.0921898 | ||||||||
\(647\) | −33.2426 | + | 33.2426i | −1.30690 | + | 1.30690i | −0.383264 | + | 0.923639i | \(0.625200\pi\) |
−0.923639 | + | 0.383264i | \(0.874800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.65685i | − | 0.0650372i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.7279 | + | 11.7279i | 0.459301 | + | 0.459301i | ||||
\(653\) | 14.2426 | + | 14.2426i | 0.557358 | + | 0.557358i | 0.928554 | − | 0.371197i | \(-0.121052\pi\) |
−0.371197 | + | 0.928554i | \(0.621052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | − | 4.00000i | −0.154881 | − | 0.154881i | ||||
\(668\) | 7.58579 | + | 7.58579i | 0.293503 | + | 0.293503i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.79899i | − | 0.223868i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.34315 | + | 3.34315i | −0.128869 | + | 0.128869i | −0.768599 | − | 0.639731i | \(-0.779046\pi\) |
0.639731 | + | 0.768599i | \(0.279046\pi\) | |||||||
\(674\) | 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 | \(-0.608458\pi\) |
0.942511 | + | 0.334175i | \(0.108458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.48528i | 0.248882i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.727922 | − | 0.727922i | −0.0278736 | − | 0.0278736i | ||||
\(683\) | 24.3848 | + | 24.3848i | 0.933058 | + | 0.933058i | 0.997896 | − | 0.0648383i | \(-0.0206531\pi\) |
−0.0648383 | + | 0.997896i | \(0.520653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 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 | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 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 | 0 | ||||||||
\(701\) | 40.8284i | 1.54207i | 0.636794 | + | 0.771034i | \(0.280260\pi\) | ||||
−0.636794 | + | 0.771034i | \(0.719740\pi\) | |||||||
\(702\) | 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 | \(0.278089\pi\) | ||||
−0.642039 | + | 0.766672i | \(0.721911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.24264 | − | 2.24264i | −0.0840465 | − | 0.0840465i | ||||
\(713\) | 8.48528 | + | 8.48528i | 0.317776 | + | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6274 | + | 22.6274i | 0.839204 | + | 0.839204i | 0.988754 | − | 0.149550i | \(-0.0477824\pi\) |
−0.149550 | + | 0.988754i | \(0.547782\pi\) | |||||||
\(728\) | −4.00000 | − | 4.00000i | −0.148250 | − | 0.148250i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.11270i | 0.263073i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.443651 | − | 0.443651i | 0.0163866 | − | 0.0163866i | −0.698866 | − | 0.715253i | \(-0.746312\pi\) |
0.715253 | + | 0.698866i | \(0.246312\pi\) | |||||||
\(734\) | −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 | \(0.0437890\pi\) | ||||
−0.990553 | + | 0.137134i | \(0.956211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.58579 | + | 2.58579i | 0.0949272 | + | 0.0949272i | ||||
\(743\) | −31.1127 | − | 31.1127i | −1.14141 | − | 1.14141i | −0.988192 | − | 0.153222i | \(-0.951035\pi\) |
−0.153222 | − | 0.988192i | \(-0.548965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5563 | + | 23.5563i | 0.856170 | + | 0.856170i | 0.990884 | − | 0.134714i | \(-0.0430117\pi\) |
−0.134714 | + | 0.990884i | \(0.543012\pi\) | |||||||
\(758\) | 18.2426 | + | 18.2426i | 0.662603 | + | 0.662603i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.9706i | 0.687682i | 0.939028 | + | 0.343841i | \(0.111728\pi\) | ||||
−0.939028 | + | 0.343841i | \(0.888272\pi\) | |||||||
\(762\) | 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 | \(0.269961\pi\) | ||||
−0.661403 | + | 0.750031i | \(0.730039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.4853 | + | 13.4853i | 0.485346 | + | 0.485346i | ||||
\(773\) | 34.9411 | + | 34.9411i | 1.25674 | + | 1.25674i | 0.952638 | + | 0.304107i | \(0.0983581\pi\) |
0.304107 | + | 0.952638i | \(0.401642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 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 | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5147 | + | 15.5147i | 0.553040 | + | 0.553040i | 0.927317 | − | 0.374277i | \(-0.122109\pi\) |
−0.374277 | + | 0.927317i | \(0.622109\pi\) | |||||||
\(788\) | 10.2426 | + | 10.2426i | 0.364879 | + | 0.364879i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 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 | \(-0.581405\pi\) |
0.967476 | + | 0.252962i | \(0.0814049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.8284i | − | 0.383082i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.0000 | − | 19.0000i | −0.670913 | − | 0.670913i | ||||
\(803\) | −4.14214 | − | 4.14214i | −0.146173 | − | 0.146173i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1716 | − | 17.1716i | −0.600757 | − | 0.600757i | ||||
\(818\) | −7.07107 | − | 7.07107i | −0.247234 | − | 0.247234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.79899i | − | 0.341987i | −0.985272 | − | 0.170994i | \(-0.945302\pi\) | ||
0.985272 | − | 0.170994i | \(-0.0546977\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.4853 | + | 28.4853i | −0.992934 | + | 0.992934i | −0.999975 | − | 0.00704072i | \(-0.997759\pi\) |
0.00704072 | + | 0.999975i | \(0.497759\pi\) | |||||||
\(824\) | 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 | \(-0.863888\pi\) |
0.414695 | + | 0.909960i | \(0.363888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7574i | 0.408350i | 0.978934 | + | 0.204175i | \(0.0654512\pi\) | ||||
−0.978934 | + | 0.204175i | \(0.934549\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | − | 4.00000i | −0.138675 | − | 0.138675i | ||||
\(833\) | 0.585786 | + | 0.585786i | 0.0202963 | + | 0.0202963i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.53553 | + | 7.53553i | 0.258924 | + | 0.258924i | ||||
\(848\) | 2.58579 | + | 2.58579i | 0.0887963 | + | 0.0887963i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 60.2843i | − | 2.06652i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0711 | − | 15.0711i | 0.516024 | − | 0.516024i | −0.400342 | − | 0.916366i | \(-0.631109\pi\) |
0.916366 | + | 0.400342i | \(0.131109\pi\) | |||||||
\(854\) | 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 | \(-0.700255\pi\) |
0.808545 | + | 0.588434i | \(0.200255\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.0000i | − | 1.36478i | −0.730987 | − | 0.682391i | \(-0.760940\pi\) | ||
0.730987 | − | 0.682391i | \(-0.239060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.4853 | − | 18.4853i | −0.629611 | − | 0.629611i | ||||
\(863\) | −21.1716 | − | 21.1716i | −0.720689 | − | 0.720689i | 0.248057 | − | 0.968745i | \(-0.420208\pi\) |
−0.968745 | + | 0.248057i | \(0.920208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 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 | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.6985 | + | 37.6985i | 1.27299 | + | 1.27299i | 0.944513 | + | 0.328475i | \(0.106535\pi\) |
0.328475 | + | 0.944513i | \(0.393465\pi\) | |||||||
\(878\) | −2.75736 | − | 2.75736i | −0.0930564 | − | 0.0930564i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 8.62742i | − | 0.290665i | −0.989383 | − | 0.145333i | \(-0.953575\pi\) | ||
0.989383 | − | 0.145333i | \(-0.0464252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.3848 | + | 37.3848i | −1.25810 | + | 1.25810i | −0.306098 | + | 0.952000i | \(0.599023\pi\) |
−0.952000 | + | 0.306098i | \(0.900977\pi\) | |||||||
\(884\) | 4.68629 | 0.157617 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.97056 | 0.166989 | ||||||||
\(887\) | −39.7279 | + | 39.7279i | −1.33393 | + | 1.33393i | −0.432114 | + | 0.901819i | \(0.642232\pi\) |
−0.901819 | + | 0.432114i | \(0.857768\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 10.8284i | − | 0.363174i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.31371 | + | 7.31371i | 0.244881 | + | 0.244881i | ||||
\(893\) | 26.1421 | + | 26.1421i | 0.874813 | + | 0.874813i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 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 | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5858 | − | 19.5858i | −0.650335 | − | 0.650335i | 0.302738 | − | 0.953074i | \(-0.402099\pi\) |
−0.953074 | + | 0.302738i | \(0.902099\pi\) | |||||||
\(908\) | −1.17157 | − | 1.17157i | −0.0388800 | − | 0.0388800i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.00000i | 0.132526i | 0.997802 | + | 0.0662630i | \(0.0211076\pi\) | ||||
−0.997802 | + | 0.0662630i | \(0.978892\pi\) | |||||||
\(912\) | 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 | \(-0.627929\pi\) | ||
0.391168 | − | 0.920319i | \(-0.372071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.75736 | + | 3.75736i | 0.123742 | + | 0.123742i | ||||
\(923\) | −4.68629 | − | 4.68629i | −0.154251 | − | 0.154251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 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 | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.2132 | + | 29.2132i | 0.954354 | + | 0.954354i | 0.999003 | − | 0.0446490i | \(-0.0142169\pi\) |
−0.0446490 | + | 0.999003i | \(0.514217\pi\) | |||||||
\(938\) | 8.41421 | + | 8.41421i | 0.274734 | + | 0.274734i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.2843i | 0.335258i | 0.985850 | + | 0.167629i | \(0.0536110\pi\) | ||||
−0.985850 | + | 0.167629i | \(0.946389\pi\) | |||||||
\(942\) | 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 | \(-0.678022\pi\) |
0.847641 | + | 0.530570i | \(0.178022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 56.5685i | − | 1.83629i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.585786 | + | 0.585786i | 0.0189854 | + | 0.0189854i | ||||
\(953\) | −27.7574 | − | 27.7574i | −0.899149 | − | 0.899149i | 0.0962118 | − | 0.995361i | \(-0.469327\pi\) |
−0.995361 | + | 0.0962118i | \(0.969327\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.2843 | − | 20.2843i | −0.652298 | − | 0.652298i | 0.301248 | − | 0.953546i | \(-0.402597\pi\) |
−0.953546 | + | 0.301248i | \(0.902597\pi\) | |||||||
\(968\) | 7.53553 | + | 7.53553i | 0.242201 | + | 0.242201i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 36.0000i | − | 1.15529i | −0.816286 | − | 0.577647i | \(-0.803971\pi\) | ||
0.816286 | − | 0.577647i | \(-0.196029\pi\) | |||||||
\(972\) | 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 | 0.0564143 | − | 0.998407i | \(-0.482033\pi\) |
0.998407 | − | 0.0564143i | \(-0.0179668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.85786i | − | 0.0593776i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.8995 | + | 18.8995i | 0.603107 | + | 0.603107i | ||||
\(983\) | 40.5563 | + | 40.5563i | 1.29355 | + | 1.29355i | 0.932578 | + | 0.360969i | \(0.117554\pi\) |
0.360969 | + | 0.932578i | \(0.382446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 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 | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.89949 | − | 1.89949i | −0.0601576 | − | 0.0601576i | 0.676388 | − | 0.736546i | \(-0.263544\pi\) |
−0.736546 | + | 0.676388i | \(0.763544\pi\) | |||||||
\(998\) | 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 | 3150.2.m.a.1457.1 | 4 | ||
3.2 | odd | 2 | 3150.2.m.b.1457.2 | 4 | |||
5.2 | odd | 4 | 630.2.m.a.323.1 | yes | 4 | ||
5.3 | odd | 4 | 3150.2.m.b.2843.2 | 4 | |||
5.4 | even | 2 | 630.2.m.b.197.2 | yes | 4 | ||
15.2 | even | 4 | 630.2.m.b.323.2 | yes | 4 | ||
15.8 | even | 4 | inner | 3150.2.m.a.2843.1 | 4 | ||
15.14 | odd | 2 | 630.2.m.a.197.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.a.197.1 | ✓ | 4 | 15.14 | odd | 2 | ||
630.2.m.a.323.1 | yes | 4 | 5.2 | odd | 4 | ||
630.2.m.b.197.2 | yes | 4 | 5.4 | even | 2 | ||
630.2.m.b.323.2 | yes | 4 | 15.2 | even | 4 | ||
3150.2.m.a.1457.1 | 4 | 1.1 | even | 1 | trivial | ||
3150.2.m.a.2843.1 | 4 | 15.8 | even | 4 | inner | ||
3150.2.m.b.1457.2 | 4 | 3.2 | odd | 2 | |||
3150.2.m.b.2843.2 | 4 | 5.3 | odd | 4 |