Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.a.694.2 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.00000 | + | 2.00000i | −0.316228 | + | 0.632456i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.00000 | + | 2.00000i | −0.258199 | + | 0.516398i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 2.00000 | + | 1.00000i | 0.365148 | + | 0.182574i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −1.00000 | + | 2.00000i | −0.169031 | + | 0.338062i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | −3.00000 | + | 6.00000i | −0.474342 | + | 0.948683i | ||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 2.00000 | + | 1.00000i | 0.298142 | + | 0.149071i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | − | 4.00000i | − | 0.554700i | ||||||
\(53\) | − | 6.00000i | − | 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.00000 | + | 1.00000i | 0.269680 | + | 0.134840i | ||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000i | 0.525226i | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | −1.00000 | + | 2.00000i | −0.129099 | + | 0.258199i | ||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | − | 2.00000i | − | 0.254000i | ||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | −4.00000 | + | 8.00000i | −0.496139 | + | 0.992278i | ||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 2.00000 | + | 1.00000i | 0.239046 | + | 0.119523i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 4.00000 | − | 3.00000i | 0.461880 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 4.00000i | 0.452911i | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 2.00000 | + | 1.00000i | 0.223607 | + | 0.111803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.0000i | 1.10432i | ||||||||
\(83\) | − | 14.0000i | − | 1.53670i | −0.640030 | − | 0.768350i | \(-0.721078\pi\) | ||
0.640030 | − | 0.768350i | \(-0.278922\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −2.00000 | + | 4.00000i | −0.216930 | + | 0.433861i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 4.00000i | 0.428845i | ||||||||
\(88\) | 3.00000i | 0.319801i | ||||||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 1.00000 | − | 2.00000i | 0.105409 | − | 0.210819i | ||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.00000 | −0.510310 | ||||||||
\(97\) | − | 14.0000i | − | 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 2.00000i | 0.198030i | ||||||||
\(103\) | − | 8.00000i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | −12.0000 | −1.17670 | ||||||||
\(105\) | 2.00000 | + | 1.00000i | 0.195180 | + | 0.0975900i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 8.00000i | − | 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 1.00000 | − | 2.00000i | 0.0953463 | − | 0.190693i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | − | 12.0000i | 0.559503 | − | 1.11901i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | 4.00000i | 0.369800i | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 6.00000 | + | 3.00000i | 0.547723 | + | 0.273861i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.00000i | 0.181071i | ||||||||
\(123\) | 10.0000i | 0.901670i | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | − | 3.00000i | − | 0.265165i | ||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 8.00000 | + | 4.00000i | 0.701646 | + | 0.350823i | ||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 1.00000i | 0.0870388i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 1.00000 | − | 2.00000i | 0.0860663 | − | 0.172133i | ||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | 18.0000i | 1.53784i | 0.639343 | + | 0.768922i | \(0.279207\pi\) | ||||
−0.639343 | + | 0.768922i | \(0.720793\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | −1.00000 | + | 2.00000i | −0.0845154 | + | 0.169031i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000i | 0.671345i | ||||||||
\(143\) | 4.00000i | 0.334497i | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.00000 | + | 4.00000i | 0.664364 | + | 0.332182i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | 20.0000 | 1.63846 | 0.819232 | − | 0.573462i | \(-0.194400\pi\) | ||||
0.819232 | + | 0.573462i | \(0.194400\pi\) | |||||||
\(150\) | −3.00000 | − | 4.00000i | −0.244949 | − | 0.326599i | ||||
\(151\) | 2.00000 | 0.162758 | 0.0813788 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813788 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −4.00000 | − | 2.00000i | −0.321288 | − | 0.160644i | ||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | − | 6.00000i | − | 0.478852i | −0.970915 | − | 0.239426i | \(-0.923041\pi\) | ||
0.970915 | − | 0.239426i | \(-0.0769593\pi\) | |||||||
\(158\) | − | 14.0000i | − | 1.11378i | ||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | −5.00000 | + | 10.0000i | −0.395285 | + | 0.790569i | ||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | −10.0000 | −0.780869 | ||||||||
\(165\) | 1.00000 | − | 2.00000i | 0.0778499 | − | 0.155700i | ||||
\(166\) | −14.0000 | −1.08661 | ||||||||
\(167\) | − | 6.00000i | − | 0.464294i | −0.972681 | − | 0.232147i | \(-0.925425\pi\) | ||
0.972681 | − | 0.232147i | \(-0.0745750\pi\) | |||||||
\(168\) | 3.00000i | 0.231455i | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 4.00000 | + | 2.00000i | 0.306786 | + | 0.153393i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 4.00000 | 0.303239 | ||||||||
\(175\) | 4.00000 | − | 3.00000i | 0.302372 | − | 0.226779i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 4.00000i | 0.300658i | ||||||||
\(178\) | − | 12.0000i | − | 0.899438i | ||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | 2.00000 | + | 1.00000i | 0.149071 | + | 0.0745356i | ||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 2.00000i | 0.147844i | ||||||||
\(184\) | 18.0000 | 1.32698 | ||||||||
\(185\) | −4.00000 | + | 8.00000i | −0.294086 | + | 0.588172i | ||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | 2.00000i | 0.146254i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 7.00000i | 0.505181i | ||||||||
\(193\) | − | 10.0000i | − | 0.719816i | −0.932988 | − | 0.359908i | \(-0.882808\pi\) | ||
0.932988 | − | 0.359908i | \(-0.117192\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 8.00000 | + | 4.00000i | 0.572892 | + | 0.286446i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | − | 22.0000i | − | 1.56744i | −0.621117 | − | 0.783718i | \(-0.713321\pi\) | ||
0.621117 | − | 0.783718i | \(-0.286679\pi\) | |||||||
\(198\) | − | 1.00000i | − | 0.0710669i | ||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 12.0000 | − | 9.00000i | 0.848528 | − | 0.636396i | ||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | − | 6.00000i | − | 0.422159i | ||||||
\(203\) | 4.00000i | 0.280745i | ||||||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 20.0000 | + | 10.0000i | 1.39686 | + | 0.698430i | ||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.00000 | − | 2.00000i | 0.0690066 | − | 0.138013i | ||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | −8.00000 | −0.546869 | ||||||||
\(215\) | 4.00000 | − | 8.00000i | 0.272798 | − | 0.545595i | ||||
\(216\) | 3.00000 | 0.204124 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | 14.0000i | 0.948200i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.00000 | + | 1.00000i | 0.134840 | + | 0.0674200i | ||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 4.00000i | 0.268462i | ||||||||
\(223\) | − | 24.0000i | − | 1.60716i | −0.595198 | − | 0.803579i | \(-0.702926\pi\) | ||
0.595198 | − | 0.803579i | \(-0.297074\pi\) | |||||||
\(224\) | −5.00000 | −0.334077 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | − | 10.0000i | − | 0.663723i | −0.943328 | − | 0.331862i | \(-0.892323\pi\) | ||
0.943328 | − | 0.331862i | \(-0.107677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | −12.0000 | − | 6.00000i | −0.791257 | − | 0.395628i | ||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 12.0000i | 0.787839i | ||||||||
\(233\) | − | 10.0000i | − | 0.655122i | −0.944830 | − | 0.327561i | \(-0.893773\pi\) | ||
0.944830 | − | 0.327561i | \(-0.106227\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.00000 | −0.260378 | ||||||||
\(237\) | − | 14.0000i | − | 0.909398i | ||||||
\(238\) | 2.00000i | 0.129641i | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 1.00000 | − | 2.00000i | 0.0645497 | − | 0.129099i | ||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | − | 1.00000i | − | 0.0642824i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 2.00000 | + | 1.00000i | 0.127775 | + | 0.0638877i | ||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 6.00000i | − | 0.381000i | ||||||
\(249\) | −14.0000 | −0.887214 | ||||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | −24.0000 | −1.51487 | −0.757433 | − | 0.652913i | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | 4.00000 | + | 2.00000i | 0.250490 | + | 0.125245i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 2.00000i | − | 0.124757i | −0.998053 | − | 0.0623783i | \(-0.980131\pi\) | ||
0.998053 | − | 0.0623783i | \(-0.0198685\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | −4.00000 | + | 8.00000i | −0.248069 | + | 0.496139i | ||||
\(261\) | 4.00000 | 0.247594 | ||||||||
\(262\) | − | 4.00000i | − | 0.247121i | ||||||
\(263\) | − | 12.0000i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(264\) | 3.00000 | 0.184637 | ||||||||
\(265\) | −6.00000 | + | 12.0000i | −0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.0000i | − | 0.734388i | ||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 32.0000 | 1.95107 | 0.975537 | − | 0.219834i | \(-0.0705517\pi\) | ||||
0.975537 | + | 0.219834i | \(0.0705517\pi\) | |||||||
\(270\) | −2.00000 | − | 1.00000i | −0.121716 | − | 0.0608581i | ||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 4.00000i | 0.242091i | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | −3.00000 | − | 4.00000i | −0.180907 | − | 0.241209i | ||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | − | 22.0000i | − | 1.32185i | −0.750451 | − | 0.660926i | \(-0.770164\pi\) | ||
0.750451 | − | 0.660926i | \(-0.229836\pi\) | |||||||
\(278\) | − | 16.0000i | − | 0.959616i | ||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 6.00000 | + | 3.00000i | 0.358569 | + | 0.179284i | ||||
\(281\) | 4.00000 | 0.238620 | 0.119310 | − | 0.992857i | \(-0.461932\pi\) | ||||
0.119310 | + | 0.992857i | \(0.461932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.0000i | − | 1.18888i | −0.804141 | − | 0.594438i | \(-0.797374\pi\) | ||
0.804141 | − | 0.594438i | \(-0.202626\pi\) | |||||||
\(284\) | −8.00000 | −0.474713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 10.0000i | 0.590281i | ||||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 4.00000 | − | 8.00000i | 0.234888 | − | 0.469776i | ||||
\(291\) | −14.0000 | −0.820695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 8.00000 | + | 4.00000i | 0.465778 | + | 0.232889i | ||||
\(296\) | −12.0000 | −0.697486 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | − | 20.0000i | − | 1.15857i | ||||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 4.00000 | − | 3.00000i | 0.230940 | − | 0.173205i | ||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | − | 2.00000i | − | 0.115087i | ||||||
\(303\) | − | 6.00000i | − | 0.344691i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.00000 | + | 2.00000i | 0.229039 | + | 0.114520i | ||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | − | 20.0000i | − | 1.14146i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) | ||
0.821138 | − | 0.570730i | \(-0.193340\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | −2.00000 | + | 4.00000i | −0.113592 | + | 0.227185i | ||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 12.0000i | 0.679366i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | −6.00000 | −0.338600 | ||||||||
\(315\) | 1.00000 | − | 2.00000i | 0.0563436 | − | 0.112687i | ||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 6.00000i | 0.336463i | ||||||||
\(319\) | 4.00000 | 0.223957 | ||||||||
\(320\) | 14.0000 | + | 7.00000i | 0.782624 | + | 0.391312i | ||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | − | 6.00000i | − | 0.334367i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 16.0000 | − | 12.0000i | 0.887520 | − | 0.665640i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 14.0000i | 0.774202i | ||||||||
\(328\) | 30.0000i | 1.65647i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00000 | − | 1.00000i | −0.110096 | − | 0.0550482i | ||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | − | 14.0000i | − | 0.768350i | ||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | −6.00000 | −0.328305 | ||||||||
\(335\) | 8.00000 | − | 16.0000i | 0.437087 | − | 0.874173i | ||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 30.0000i | 1.63420i | 0.576493 | + | 0.817102i | \(0.304421\pi\) | ||||
−0.576493 | + | 0.817102i | \(0.695579\pi\) | |||||||
\(338\) | 3.00000i | 0.163178i | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | −2.00000 | + | 4.00000i | −0.108465 | + | 0.216930i | ||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | −12.0000 | − | 6.00000i | −0.646058 | − | 0.323029i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | − | 24.0000i | − | 1.28839i | −0.764862 | − | 0.644194i | \(-0.777193\pi\) | ||
0.764862 | − | 0.644194i | \(-0.222807\pi\) | |||||||
\(348\) | 4.00000i | 0.214423i | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | −3.00000 | − | 4.00000i | −0.160357 | − | 0.213809i | ||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 5.00000i | 0.266501i | ||||||||
\(353\) | 22.0000i | 1.17094i | 0.810693 | + | 0.585471i | \(0.199090\pi\) | ||||
−0.810693 | + | 0.585471i | \(0.800910\pi\) | |||||||
\(354\) | 4.00000 | 0.212598 | ||||||||
\(355\) | 16.0000 | + | 8.00000i | 0.849192 | + | 0.424596i | ||||
\(356\) | 12.0000 | 0.635999 | ||||||||
\(357\) | 2.00000i | 0.105851i | ||||||||
\(358\) | 4.00000i | 0.211407i | ||||||||
\(359\) | 20.0000 | 1.05556 | 0.527780 | − | 0.849381i | \(-0.323025\pi\) | ||||
0.527780 | + | 0.849381i | \(0.323025\pi\) | |||||||
\(360\) | 3.00000 | − | 6.00000i | 0.158114 | − | 0.316228i | ||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 18.0000i | 0.946059i | ||||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | −4.00000 | −0.209657 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 24.0000i | 1.25279i | 0.779506 | + | 0.626395i | \(0.215470\pi\) | ||||
−0.779506 | + | 0.626395i | \(0.784530\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 8.00000 | + | 4.00000i | 0.415900 | + | 0.207950i | ||||
\(371\) | −6.00000 | −0.311504 | ||||||||
\(372\) | − | 2.00000i | − | 0.103695i | ||||||
\(373\) | 18.0000i | 0.932005i | 0.884783 | + | 0.466002i | \(0.154306\pi\) | ||||
−0.884783 | + | 0.466002i | \(0.845694\pi\) | |||||||
\(374\) | 2.00000 | 0.103418 | ||||||||
\(375\) | −11.0000 | + | 2.00000i | −0.568038 | + | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0000i | 0.824042i | ||||||||
\(378\) | − | 1.00000i | − | 0.0514344i | ||||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.0000i | − | 0.817562i | −0.912633 | − | 0.408781i | \(-0.865954\pi\) | ||
0.912633 | − | 0.408781i | \(-0.134046\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 1.00000 | − | 2.00000i | 0.0509647 | − | 0.101929i | ||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | − | 14.0000i | − | 0.710742i | ||||||
\(389\) | 34.0000 | 1.72387 | 0.861934 | − | 0.507020i | \(-0.169253\pi\) | ||||
0.861934 | + | 0.507020i | \(0.169253\pi\) | |||||||
\(390\) | 4.00000 | − | 8.00000i | 0.202548 | − | 0.405096i | ||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | −22.0000 | −1.10834 | ||||||||
\(395\) | −28.0000 | − | 14.0000i | −1.40883 | − | 0.704416i | ||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 22.0000i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186163\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813837\pi\) | |||||||
\(398\) | 2.00000i | 0.100251i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | − | 8.00000i | − | 0.399004i | ||||||
\(403\) | − | 8.00000i | − | 0.398508i | ||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | −2.00000 | − | 1.00000i | −0.0993808 | − | 0.0496904i | ||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | 4.00000i | 0.198273i | ||||||||
\(408\) | 6.00000i | 0.297044i | ||||||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 10.0000 | − | 20.0000i | 0.493865 | − | 0.987730i | ||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | −14.0000 | + | 28.0000i | −0.687233 | + | 1.37447i | ||||
\(416\) | −20.0000 | −0.980581 | ||||||||
\(417\) | − | 16.0000i | − | 0.783523i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 2.00000 | + | 1.00000i | 0.0975900 | + | 0.0487950i | ||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | − | 2.00000i | − | 0.0973585i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18.0000 | −0.874157 | ||||||||
\(425\) | 8.00000 | − | 6.00000i | 0.388057 | − | 0.291043i | ||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | −8.00000 | − | 4.00000i | −0.385794 | − | 0.192897i | ||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 4.00000 | − | 8.00000i | 0.191785 | − | 0.383571i | ||||
\(436\) | −14.0000 | −0.670478 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.0000 | −1.71819 | −0.859093 | − | 0.511819i | \(-0.828972\pi\) | ||||
−0.859093 | + | 0.511819i | \(0.828972\pi\) | |||||||
\(440\) | 3.00000 | − | 6.00000i | 0.143019 | − | 0.286039i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | 34.0000i | 1.61539i | 0.589601 | + | 0.807694i | \(0.299285\pi\) | ||||
−0.589601 | + | 0.807694i | \(0.700715\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | −24.0000 | − | 12.0000i | −1.13771 | − | 0.568855i | ||||
\(446\) | −24.0000 | −1.13643 | ||||||||
\(447\) | − | 20.0000i | − | 0.945968i | ||||||
\(448\) | 7.00000i | 0.330719i | ||||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | −4.00000 | + | 3.00000i | −0.188562 | + | 0.141421i | ||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | 6.00000i | 0.282216i | ||||||||
\(453\) | − | 2.00000i | − | 0.0939682i | ||||||
\(454\) | −10.0000 | −0.469323 | ||||||||
\(455\) | 8.00000 | + | 4.00000i | 0.375046 | + | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000i | 1.02912i | 0.857455 | + | 0.514558i | \(0.172044\pi\) | ||||
−0.857455 | + | 0.514558i | \(0.827956\pi\) | |||||||
\(458\) | − | 22.0000i | − | 1.02799i | ||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 6.00000 | − | 12.0000i | 0.279751 | − | 0.559503i | ||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | − | 1.00000i | − | 0.0465242i | ||||||
\(463\) | 24.0000i | 1.11537i | 0.830051 | + | 0.557687i | \(0.188311\pi\) | ||||
−0.830051 | + | 0.557687i | \(0.811689\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | −2.00000 | + | 4.00000i | −0.0927478 | + | 0.185496i | ||||
\(466\) | −10.0000 | −0.463241 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 4.00000i | 0.184900i | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.00000 | −0.276465 | ||||||||
\(472\) | 12.0000i | 0.552345i | ||||||||
\(473\) | − | 4.00000i | − | 0.183920i | ||||||
\(474\) | −14.0000 | −0.643041 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | − | 24.0000i | − | 1.09773i | ||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 10.0000 | + | 5.00000i | 0.456435 | + | 0.228218i | ||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | 2.00000i | 0.0910975i | ||||||||
\(483\) | − | 6.00000i | − | 0.273009i | ||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −14.0000 | + | 28.0000i | −0.635707 | + | 1.27141i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − | 24.0000i | − | 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | 6.00000i | 0.271607i | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 1.00000 | − | 2.00000i | 0.0451754 | − | 0.0903508i | ||||
\(491\) | 28.0000 | 1.26362 | 0.631811 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631811 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(492\) | 10.0000i | 0.450835i | ||||||||
\(493\) | 8.00000i | 0.360302i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | − | 1.00000i | −0.0898933 | − | 0.0449467i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 14.0000i | 0.627355i | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 24.0000i | 1.07117i | ||||||||
\(503\) | − | 6.00000i | − | 0.267527i | −0.991013 | − | 0.133763i | \(-0.957294\pi\) | ||
0.991013 | − | 0.133763i | \(-0.0427062\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | −12.0000 | − | 6.00000i | −0.533993 | − | 0.266996i | ||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | 3.00000i | 0.133235i | ||||||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | 24.0000 | 1.06378 | 0.531891 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(510\) | 2.00000 | − | 4.00000i | 0.0885615 | − | 0.177123i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.00000 | −0.0882162 | ||||||||
\(515\) | −8.00000 | + | 16.0000i | −0.352522 | + | 0.705044i | ||||
\(516\) | 4.00000 | 0.176090 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.00000i | 0.175750i | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 24.0000 | + | 12.0000i | 1.05247 | + | 0.526235i | ||||
\(521\) | −28.0000 | −1.22670 | −0.613351 | − | 0.789810i | \(-0.710179\pi\) | ||||
−0.613351 | + | 0.789810i | \(0.710179\pi\) | |||||||
\(522\) | − | 4.00000i | − | 0.175075i | ||||||
\(523\) | − | 8.00000i | − | 0.349816i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) | ||
0.984585 | − | 0.174908i | \(-0.0559627\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | −3.00000 | − | 4.00000i | −0.130931 | − | 0.174574i | ||||
\(526\) | −12.0000 | −0.523225 | ||||||||
\(527\) | − | 4.00000i | − | 0.174243i | ||||||
\(528\) | − | 1.00000i | − | 0.0435194i | ||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 12.0000 | + | 6.00000i | 0.521247 | + | 0.260623i | ||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.0000i | 1.73259i | ||||||||
\(534\) | −12.0000 | −0.519291 | ||||||||
\(535\) | −8.00000 | + | 16.0000i | −0.345870 | + | 0.691740i | ||||
\(536\) | 24.0000 | 1.03664 | ||||||||
\(537\) | 4.00000i | 0.172613i | ||||||||
\(538\) | − | 32.0000i | − | 1.37962i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 1.00000 | − | 2.00000i | 0.0430331 | − | 0.0860663i | ||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 8.00000i | 0.343629i | ||||||||
\(543\) | 18.0000i | 0.772454i | ||||||||
\(544\) | −10.0000 | −0.428746 | ||||||||
\(545\) | 28.0000 | + | 14.0000i | 1.19939 | + | 0.599694i | ||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | − | 4.00000i | − | 0.171028i | −0.996337 | − | 0.0855138i | \(-0.972747\pi\) | ||
0.996337 | − | 0.0855138i | \(-0.0272532\pi\) | |||||||
\(548\) | 18.0000i | 0.768922i | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −4.00000 | + | 3.00000i | −0.170561 | + | 0.127920i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 18.0000i | − | 0.766131i | ||||||
\(553\) | − | 14.0000i | − | 0.595341i | ||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 8.00000 | + | 4.00000i | 0.339581 | + | 0.169791i | ||||
\(556\) | 16.0000 | 0.678551 | ||||||||
\(557\) | 14.0000i | 0.593199i | 0.955002 | + | 0.296600i | \(0.0958526\pi\) | ||||
−0.955002 | + | 0.296600i | \(0.904147\pi\) | |||||||
\(558\) | 2.00000i | 0.0846668i | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 1.00000 | − | 2.00000i | 0.0422577 | − | 0.0845154i | ||||
\(561\) | 2.00000 | 0.0844401 | ||||||||
\(562\) | − | 4.00000i | − | 0.168730i | ||||||
\(563\) | 42.0000i | 1.77009i | 0.465506 | + | 0.885044i | \(0.345872\pi\) | ||||
−0.465506 | + | 0.885044i | \(0.654128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | − | 12.0000i | 0.252422 | − | 0.504844i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 24.0000i | 1.00702i | ||||||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.0000 | 1.75765 | 0.878823 | − | 0.477149i | \(-0.158330\pi\) | ||||
0.878823 | + | 0.477149i | \(0.158330\pi\) | |||||||
\(572\) | 4.00000i | 0.167248i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.0000 | 0.417392 | ||||||||
\(575\) | −24.0000 | + | 18.0000i | −1.00087 | + | 0.750652i | ||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | − | 10.0000i | − | 0.416305i | −0.978096 | − | 0.208153i | \(-0.933255\pi\) | ||
0.978096 | − | 0.208153i | \(-0.0667451\pi\) | |||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | −10.0000 | −0.415586 | ||||||||
\(580\) | 8.00000 | + | 4.00000i | 0.332182 | + | 0.166091i | ||||
\(581\) | −14.0000 | −0.580818 | ||||||||
\(582\) | 14.0000i | 0.580319i | ||||||||
\(583\) | 6.00000i | 0.248495i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000 | − | 8.00000i | 0.165380 | − | 0.330759i | ||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 1.00000i | 0.0412393i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.00000 | − | 8.00000i | 0.164677 | − | 0.329355i | ||||
\(591\) | −22.0000 | −0.904959 | ||||||||
\(592\) | 4.00000i | 0.164399i | ||||||||
\(593\) | 46.0000i | 1.88899i | 0.328521 | + | 0.944497i | \(0.393450\pi\) | ||||
−0.328521 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 4.00000 | + | 2.00000i | 0.163984 | + | 0.0819920i | ||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | 2.00000i | 0.0818546i | ||||||||
\(598\) | − | 24.0000i | − | 0.981433i | ||||||
\(599\) | 32.0000 | 1.30748 | 0.653742 | − | 0.756717i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(600\) | −9.00000 | − | 12.0000i | −0.367423 | − | 0.489898i | ||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | − | 4.00000i | − | 0.163028i | ||||||
\(603\) | − | 8.00000i | − | 0.325785i | ||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | −2.00000 | − | 1.00000i | −0.0813116 | − | 0.0406558i | ||||
\(606\) | −6.00000 | −0.243733 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.00000 | 0.162088 | ||||||||
\(610\) | 2.00000 | − | 4.00000i | 0.0809776 | − | 0.161955i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00000i | 0.0808452i | ||||||||
\(613\) | − | 34.0000i | − | 1.37325i | −0.727013 | − | 0.686624i | \(-0.759092\pi\) | ||
0.727013 | − | 0.686624i | \(-0.240908\pi\) | |||||||
\(614\) | −20.0000 | −0.807134 | ||||||||
\(615\) | 10.0000 | − | 20.0000i | 0.403239 | − | 0.806478i | ||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 8.00000i | 0.321807i | ||||||||
\(619\) | 38.0000 | 1.52735 | 0.763674 | − | 0.645601i | \(-0.223393\pi\) | ||||
0.763674 | + | 0.645601i | \(0.223393\pi\) | |||||||
\(620\) | −4.00000 | − | 2.00000i | −0.160644 | − | 0.0803219i | ||||
\(621\) | −6.00000 | −0.240772 | ||||||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | − | 12.0000i | − | 0.480770i | ||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 6.00000 | 0.239808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 6.00000i | − | 0.239426i | ||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | −2.00000 | − | 1.00000i | −0.0796819 | − | 0.0398410i | ||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | − | 42.0000i | − | 1.67067i | ||||||
\(633\) | − | 2.00000i | − | 0.0794929i | ||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 8.00000 | − | 16.0000i | 0.317470 | − | 0.634941i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 4.00000i | 0.158486i | ||||||||
\(638\) | − | 4.00000i | − | 0.158362i | ||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | −3.00000 | + | 6.00000i | −0.118585 | + | 0.237171i | ||||
\(641\) | 10.0000 | 0.394976 | 0.197488 | − | 0.980305i | \(-0.436722\pi\) | ||||
0.197488 | + | 0.980305i | \(0.436722\pi\) | |||||||
\(642\) | 8.00000i | 0.315735i | ||||||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 6.00000 | 0.236433 | ||||||||
\(645\) | −8.00000 | − | 4.00000i | −0.315000 | − | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.0000i | 1.10079i | 0.834903 | + | 0.550397i | \(0.185524\pi\) | ||||
−0.834903 | + | 0.550397i | \(0.814476\pi\) | |||||||
\(648\) | − | 3.00000i | − | 0.117851i | ||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | −12.0000 | − | 16.0000i | −0.470679 | − | 0.627572i | ||||
\(651\) | −2.00000 | −0.0783862 | ||||||||
\(652\) | − | 4.00000i | − | 0.156652i | ||||||
\(653\) | 34.0000i | 1.33052i | 0.746611 | + | 0.665261i | \(0.231680\pi\) | ||||
−0.746611 | + | 0.665261i | \(0.768320\pi\) | |||||||
\(654\) | 14.0000 | 0.547443 | ||||||||
\(655\) | −8.00000 | − | 4.00000i | −0.312586 | − | 0.156293i | ||||
\(656\) | 10.0000 | 0.390434 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 1.00000 | − | 2.00000i | 0.0389249 | − | 0.0778499i | ||||
\(661\) | −42.0000 | −1.63361 | −0.816805 | − | 0.576913i | \(-0.804257\pi\) | ||||
−0.816805 | + | 0.576913i | \(0.804257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.00000i | 0.310694i | ||||||||
\(664\) | −42.0000 | −1.62992 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | − | 24.0000i | − | 0.929284i | ||||||
\(668\) | − | 6.00000i | − | 0.232147i | ||||||
\(669\) | −24.0000 | −0.927894 | ||||||||
\(670\) | −16.0000 | − | 8.00000i | −0.618134 | − | 0.309067i | ||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 5.00000i | 0.192879i | ||||||||
\(673\) | − | 6.00000i | − | 0.231283i | −0.993291 | − | 0.115642i | \(-0.963108\pi\) | ||
0.993291 | − | 0.115642i | \(-0.0368924\pi\) | |||||||
\(674\) | 30.0000 | 1.15556 | ||||||||
\(675\) | −4.00000 | + | 3.00000i | −0.153960 | + | 0.115470i | ||||
\(676\) | −3.00000 | −0.115385 | ||||||||
\(677\) | 14.0000i | 0.538064i | 0.963131 | + | 0.269032i | \(0.0867037\pi\) | ||||
−0.963131 | + | 0.269032i | \(0.913296\pi\) | |||||||
\(678\) | − | 6.00000i | − | 0.230429i | ||||||
\(679\) | −14.0000 | −0.537271 | ||||||||
\(680\) | 12.0000 | + | 6.00000i | 0.460179 | + | 0.230089i | ||||
\(681\) | −10.0000 | −0.383201 | ||||||||
\(682\) | 2.00000i | 0.0765840i | ||||||||
\(683\) | 26.0000i | 0.994862i | 0.867503 | + | 0.497431i | \(0.165723\pi\) | ||||
−0.867503 | + | 0.497431i | \(0.834277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | − | 36.0000i | 0.687745 | − | 1.37549i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | − | 22.0000i | − | 0.839352i | ||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | −24.0000 | −0.914327 | ||||||||
\(690\) | −6.00000 | + | 12.0000i | −0.228416 | + | 0.456832i | ||||
\(691\) | −14.0000 | −0.532585 | −0.266293 | − | 0.963892i | \(-0.585799\pi\) | ||||
−0.266293 | + | 0.963892i | \(0.585799\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | −24.0000 | −0.911028 | ||||||||
\(695\) | −32.0000 | − | 16.0000i | −1.21383 | − | 0.606915i | ||||
\(696\) | 12.0000 | 0.454859 | ||||||||
\(697\) | 20.0000i | 0.757554i | ||||||||
\(698\) | 10.0000i | 0.378506i | ||||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 4.00000 | − | 3.00000i | 0.151186 | − | 0.113389i | ||||
\(701\) | 8.00000 | 0.302156 | 0.151078 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151078 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(702\) | − | 4.00000i | − | 0.150970i | ||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 7.00000 | 0.263822 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.0000 | 0.827981 | ||||||||
\(707\) | − | 6.00000i | − | 0.225653i | ||||||
\(708\) | 4.00000i | 0.150329i | ||||||||
\(709\) | −26.0000 | −0.976450 | −0.488225 | − | 0.872718i | \(-0.662356\pi\) | ||||
−0.488225 | + | 0.872718i | \(0.662356\pi\) | |||||||
\(710\) | 8.00000 | − | 16.0000i | 0.300235 | − | 0.600469i | ||||
\(711\) | −14.0000 | −0.525041 | ||||||||
\(712\) | − | 36.0000i | − | 1.34916i | ||||||
\(713\) | 12.0000i | 0.449404i | ||||||||
\(714\) | 2.00000 | 0.0748481 | ||||||||
\(715\) | 4.00000 | − | 8.00000i | 0.149592 | − | 0.299183i | ||||
\(716\) | −4.00000 | −0.149487 | ||||||||
\(717\) | − | 24.0000i | − | 0.896296i | ||||||
\(718\) | − | 20.0000i | − | 0.746393i | ||||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 19.0000i | 0.707107i | ||||||||
\(723\) | 2.00000i | 0.0743808i | ||||||||
\(724\) | −18.0000 | −0.668965 | ||||||||
\(725\) | −12.0000 | − | 16.0000i | −0.445669 | − | 0.594225i | ||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | − | 16.0000i | − | 0.593407i | −0.954970 | − | 0.296704i | \(-0.904113\pi\) | ||
0.954970 | − | 0.296704i | \(-0.0958873\pi\) | |||||||
\(728\) | 12.0000i | 0.444750i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 2.00000i | 0.0739221i | ||||||||
\(733\) | − | 40.0000i | − | 1.47743i | −0.674016 | − | 0.738717i | \(-0.735432\pi\) | ||
0.674016 | − | 0.738717i | \(-0.264568\pi\) | |||||||
\(734\) | 24.0000 | 0.885856 | ||||||||
\(735\) | 1.00000 | − | 2.00000i | 0.0368856 | − | 0.0737711i | ||||
\(736\) | 30.0000 | 1.10581 | ||||||||
\(737\) | − | 8.00000i | − | 0.294684i | ||||||
\(738\) | − | 10.0000i | − | 0.368105i | ||||||
\(739\) | −34.0000 | −1.25071 | −0.625355 | − | 0.780340i | \(-0.715046\pi\) | ||||
−0.625355 | + | 0.780340i | \(0.715046\pi\) | |||||||
\(740\) | −4.00000 | + | 8.00000i | −0.147043 | + | 0.294086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000i | 0.220267i | ||||||||
\(743\) | − | 4.00000i | − | 0.146746i | −0.997305 | − | 0.0733729i | \(-0.976624\pi\) | ||
0.997305 | − | 0.0733729i | \(-0.0233763\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | −40.0000 | − | 20.0000i | −1.46549 | − | 0.732743i | ||||
\(746\) | 18.0000 | 0.659027 | ||||||||
\(747\) | 14.0000i | 0.512233i | ||||||||
\(748\) | 2.00000i | 0.0731272i | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 2.00000 | + | 11.0000i | 0.0730297 | + | 0.401663i | ||||
\(751\) | 12.0000 | 0.437886 | 0.218943 | − | 0.975738i | \(-0.429739\pi\) | ||||
0.218943 | + | 0.975738i | \(0.429739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.0000i | 0.874609i | ||||||||
\(754\) | 16.0000 | 0.582686 | ||||||||
\(755\) | −4.00000 | − | 2.00000i | −0.145575 | − | 0.0727875i | ||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | − | 4.00000i | − | 0.145382i | −0.997354 | − | 0.0726912i | \(-0.976841\pi\) | ||
0.997354 | − | 0.0726912i | \(-0.0231588\pi\) | |||||||
\(758\) | 8.00000i | 0.290573i | ||||||||
\(759\) | −6.00000 | −0.217786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0000 | 1.37750 | 0.688749 | − | 0.724999i | \(-0.258160\pi\) | ||||
0.688749 | + | 0.724999i | \(0.258160\pi\) | |||||||
\(762\) | − | 8.00000i | − | 0.289809i | ||||||
\(763\) | 14.0000i | 0.506834i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | − | 4.00000i | 0.0723102 | − | 0.144620i | ||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 16.0000i | 0.577727i | ||||||||
\(768\) | 17.0000i | 0.613435i | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | −2.00000 | − | 1.00000i | −0.0720750 | − | 0.0360375i | ||||
\(771\) | −2.00000 | −0.0720282 | ||||||||
\(772\) | − | 10.0000i | − | 0.359908i | ||||||
\(773\) | 30.0000i | 1.07903i | 0.841978 | + | 0.539513i | \(0.181391\pi\) | ||||
−0.841978 | + | 0.539513i | \(0.818609\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | 6.00000 | + | 8.00000i | 0.215526 | + | 0.287368i | ||||
\(776\) | −42.0000 | −1.50771 | ||||||||
\(777\) | 4.00000i | 0.143499i | ||||||||
\(778\) | − | 34.0000i | − | 1.21896i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 8.00000 | + | 4.00000i | 0.286446 | + | 0.143223i | ||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | − | 12.0000i | − | 0.429119i | ||||||
\(783\) | − | 4.00000i | − | 0.142948i | ||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −6.00000 | + | 12.0000i | −0.214149 | + | 0.428298i | ||||
\(786\) | −4.00000 | −0.142675 | ||||||||
\(787\) | 44.0000i | 1.56843i | 0.620489 | + | 0.784215i | \(0.286934\pi\) | ||||
−0.620489 | + | 0.784215i | \(0.713066\pi\) | |||||||
\(788\) | − | 22.0000i | − | 0.783718i | ||||||
\(789\) | −12.0000 | −0.427211 | ||||||||
\(790\) | −14.0000 | + | 28.0000i | −0.498098 | + | 0.996195i | ||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | − | 3.00000i | − | 0.106600i | ||||||
\(793\) | 8.00000i | 0.284088i | ||||||||
\(794\) | 22.0000 | 0.780751 | ||||||||
\(795\) | 12.0000 | + | 6.00000i | 0.425596 | + | 0.212798i | ||||
\(796\) | −2.00000 | −0.0708881 | ||||||||
\(797\) | 2.00000i | 0.0708436i | 0.999372 | + | 0.0354218i | \(0.0112775\pi\) | ||||
−0.999372 | + | 0.0354218i | \(0.988723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 20.0000 | − | 15.0000i | 0.707107 | − | 0.530330i | ||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | 30.0000i | 1.05934i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −12.0000 | − | 6.00000i | −0.422944 | − | 0.211472i | ||||
\(806\) | −8.00000 | −0.281788 | ||||||||
\(807\) | − | 32.0000i | − | 1.12645i | ||||||
\(808\) | − | 18.0000i | − | 0.633238i | ||||||
\(809\) | 36.0000 | 1.26569 | 0.632846 | − | 0.774277i | \(-0.281886\pi\) | ||||
0.632846 | + | 0.774277i | \(0.281886\pi\) | |||||||
\(810\) | −1.00000 | + | 2.00000i | −0.0351364 | + | 0.0702728i | ||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 4.00000i | 0.140372i | ||||||||
\(813\) | 8.00000i | 0.280572i | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | −4.00000 | + | 8.00000i | −0.140114 | + | 0.280228i | ||||
\(816\) | 2.00000 | 0.0700140 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | 20.0000 | + | 10.0000i | 0.698430 | + | 0.349215i | ||||
\(821\) | 40.0000 | 1.39601 | 0.698005 | − | 0.716093i | \(-0.254071\pi\) | ||||
0.698005 | + | 0.716093i | \(0.254071\pi\) | |||||||
\(822\) | − | 18.0000i | − | 0.627822i | ||||||
\(823\) | 4.00000i | 0.139431i | 0.997567 | + | 0.0697156i | \(0.0222092\pi\) | ||||
−0.997567 | + | 0.0697156i | \(0.977791\pi\) | |||||||
\(824\) | −24.0000 | −0.836080 | ||||||||
\(825\) | −4.00000 | + | 3.00000i | −0.139262 | + | 0.104447i | ||||
\(826\) | 4.00000 | 0.139178 | ||||||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | − | 6.00000i | − | 0.208514i | ||||||
\(829\) | −54.0000 | −1.87550 | −0.937749 | − | 0.347314i | \(-0.887094\pi\) | ||||
−0.937749 | + | 0.347314i | \(0.887094\pi\) | |||||||
\(830\) | 28.0000 | + | 14.0000i | 0.971894 | + | 0.485947i | ||||
\(831\) | −22.0000 | −0.763172 | ||||||||
\(832\) | 28.0000i | 0.970725i | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | −16.0000 | −0.554035 | ||||||||
\(835\) | −6.00000 | + | 12.0000i | −0.207639 | + | 0.415277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.0000 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(840\) | 3.00000 | − | 6.00000i | 0.103510 | − | 0.207020i | ||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 6.00000i | 0.206774i | ||||||||
\(843\) | − | 4.00000i | − | 0.137767i | ||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | 6.00000 | + | 3.00000i | 0.206406 | + | 0.103203i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −20.0000 | −0.686398 | ||||||||
\(850\) | −6.00000 | − | 8.00000i | −0.205798 | − | 0.274398i | ||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 8.00000i | 0.274075i | ||||||||
\(853\) | 24.0000i | 0.821744i | 0.911693 | + | 0.410872i | \(0.134776\pi\) | ||||
−0.911693 | + | 0.410872i | \(0.865224\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.0000 | −0.820303 | ||||||||
\(857\) | 54.0000i | 1.84460i | 0.386469 | + | 0.922302i | \(0.373695\pi\) | ||||
−0.386469 | + | 0.922302i | \(0.626305\pi\) | |||||||
\(858\) | − | 4.00000i | − | 0.136558i | ||||||
\(859\) | 38.0000 | 1.29654 | 0.648272 | − | 0.761409i | \(-0.275492\pi\) | ||||
0.648272 | + | 0.761409i | \(0.275492\pi\) | |||||||
\(860\) | 4.00000 | − | 8.00000i | 0.136399 | − | 0.272798i | ||||
\(861\) | 10.0000 | 0.340799 | ||||||||
\(862\) | − | 16.0000i | − | 0.544962i | ||||||
\(863\) | 18.0000i | 0.612727i | 0.951915 | + | 0.306364i | \(0.0991123\pi\) | ||||
−0.951915 | + | 0.306364i | \(0.900888\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 6.00000 | − | 12.0000i | 0.204006 | − | 0.408012i | ||||
\(866\) | −14.0000 | −0.475739 | ||||||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | − | 2.00000i | − | 0.0678844i | ||||||
\(869\) | −14.0000 | −0.474917 | ||||||||
\(870\) | −8.00000 | − | 4.00000i | −0.271225 | − | 0.135613i | ||||
\(871\) | 32.0000 | 1.08428 | ||||||||
\(872\) | 42.0000i | 1.42230i | ||||||||
\(873\) | 14.0000i | 0.473828i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0000 | + | 2.00000i | −0.371868 | + | 0.0676123i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0000i | 0.877958i | 0.898497 | + | 0.438979i | \(0.144660\pi\) | ||||
−0.898497 | + | 0.438979i | \(0.855340\pi\) | |||||||
\(878\) | 36.0000i | 1.21494i | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | −2.00000 | − | 1.00000i | −0.0674200 | − | 0.0337100i | ||||
\(881\) | −52.0000 | −1.75192 | −0.875962 | − | 0.482380i | \(-0.839773\pi\) | ||||
−0.875962 | + | 0.482380i | \(0.839773\pi\) | |||||||
\(882\) | − | 1.00000i | − | 0.0336718i | ||||||
\(883\) | − | 48.0000i | − | 1.61533i | −0.589643 | − | 0.807664i | \(-0.700731\pi\) | ||
0.589643 | − | 0.807664i | \(-0.299269\pi\) | |||||||
\(884\) | −8.00000 | −0.269069 | ||||||||
\(885\) | 4.00000 | − | 8.00000i | 0.134459 | − | 0.268917i | ||||
\(886\) | 34.0000 | 1.14225 | ||||||||
\(887\) | − | 22.0000i | − | 0.738688i | −0.929293 | − | 0.369344i | \(-0.879582\pi\) | ||
0.929293 | − | 0.369344i | \(-0.120418\pi\) | |||||||
\(888\) | 12.0000i | 0.402694i | ||||||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | −12.0000 | + | 24.0000i | −0.402241 | + | 0.804482i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | − | 24.0000i | − | 0.803579i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −20.0000 | −0.668900 | ||||||||
\(895\) | 8.00000 | + | 4.00000i | 0.267411 | + | 0.133705i | ||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | − | 24.0000i | − | 0.801337i | ||||||
\(898\) | 34.0000i | 1.13459i | ||||||||
\(899\) | −8.00000 | −0.266815 | ||||||||
\(900\) | −3.00000 | − | 4.00000i | −0.100000 | − | 0.133333i | ||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | − | 10.0000i | − | 0.332964i | ||||||
\(903\) | − | 4.00000i | − | 0.133112i | ||||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | 36.0000 | + | 18.0000i | 1.19668 | + | 0.598340i | ||||
\(906\) | −2.00000 | −0.0664455 | ||||||||
\(907\) | 16.0000i | 0.531271i | 0.964073 | + | 0.265636i | \(0.0855818\pi\) | ||||
−0.964073 | + | 0.265636i | \(0.914418\pi\) | |||||||
\(908\) | − | 10.0000i | − | 0.331862i | ||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 4.00000 | − | 8.00000i | 0.132599 | − | 0.265197i | ||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0000i | 0.463332i | ||||||||
\(914\) | 22.0000 | 0.727695 | ||||||||
\(915\) | 2.00000 | − | 4.00000i | 0.0661180 | − | 0.132236i | ||||
\(916\) | 22.0000 | 0.726900 | ||||||||
\(917\) | − | 4.00000i | − | 0.132092i | ||||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | 50.0000 | 1.64935 | 0.824674 | − | 0.565608i | \(-0.191359\pi\) | ||||
0.824674 | + | 0.565608i | \(0.191359\pi\) | |||||||
\(920\) | −36.0000 | − | 18.0000i | −1.18688 | − | 0.593442i | ||||
\(921\) | −20.0000 | −0.659022 | ||||||||
\(922\) | 30.0000i | 0.987997i | ||||||||
\(923\) | 32.0000i | 1.05329i | ||||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | 16.0000 | − | 12.0000i | 0.526077 | − | 0.394558i | ||||
\(926\) | 24.0000 | 0.788689 | ||||||||
\(927\) | 8.00000i | 0.262754i | ||||||||
\(928\) | 20.0000i | 0.656532i | ||||||||
\(929\) | −16.0000 | −0.524943 | −0.262471 | − | 0.964940i | \(-0.584538\pi\) | ||||
−0.262471 | + | 0.964940i | \(0.584538\pi\) | |||||||
\(930\) | 4.00000 | + | 2.00000i | 0.131165 | + | 0.0655826i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 10.0000i | − | 0.327561i | ||||||
\(933\) | − | 12.0000i | − | 0.392862i | ||||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 2.00000 | − | 4.00000i | 0.0654070 | − | 0.130814i | ||||
\(936\) | 12.0000 | 0.392232 | ||||||||
\(937\) | − | 52.0000i | − | 1.69877i | −0.527777 | − | 0.849383i | \(-0.676974\pi\) | ||
0.527777 | − | 0.849383i | \(-0.323026\pi\) | |||||||
\(938\) | − | 8.00000i | − | 0.261209i | ||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 6.00000i | 0.195491i | ||||||||
\(943\) | − | 60.0000i | − | 1.95387i | ||||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | −2.00000 | − | 1.00000i | −0.0650600 | − | 0.0325300i | ||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | − | 30.0000i | − | 0.974869i | −0.873160 | − | 0.487435i | \(-0.837933\pi\) | ||
0.873160 | − | 0.487435i | \(-0.162067\pi\) | |||||||
\(948\) | − | 14.0000i | − | 0.454699i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 6.00000i | 0.194461i | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | − | 4.00000i | − | 0.129302i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.0000 | 0.581250 | ||||||||
\(960\) | 7.00000 | − | 14.0000i | 0.225924 | − | 0.451848i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 16.0000i | 0.515861i | ||||||||
\(963\) | 8.00000i | 0.257796i | ||||||||
\(964\) | −2.00000 | −0.0644157 | ||||||||
\(965\) | −10.0000 | + | 20.0000i | −0.321911 | + | 0.643823i | ||||
\(966\) | −6.00000 | −0.193047 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | − | 3.00000i | − | 0.0964237i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28.0000 | + | 14.0000i | 0.899026 | + | 0.449513i | ||||
\(971\) | −20.0000 | −0.641831 | −0.320915 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 16.0000i | − | 0.512936i | ||||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | −12.0000 | − | 16.0000i | −0.384308 | − | 0.512410i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | − | 42.0000i | − | 1.34370i | −0.740688 | − | 0.671850i | \(-0.765500\pi\) | ||
0.740688 | − | 0.671850i | \(-0.234500\pi\) | |||||||
\(978\) | 4.00000i | 0.127906i | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | 2.00000 | + | 1.00000i | 0.0638877 | + | 0.0319438i | ||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | − | 28.0000i | − | 0.893516i | ||||||
\(983\) | − | 12.0000i | − | 0.382741i | −0.981518 | − | 0.191370i | \(-0.938707\pi\) | ||
0.981518 | − | 0.191370i | \(-0.0612931\pi\) | |||||||
\(984\) | 30.0000 | 0.956365 | ||||||||
\(985\) | −22.0000 | + | 44.0000i | −0.700978 | + | 1.40196i | ||||
\(986\) | 8.00000 | 0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | −1.00000 | + | 2.00000i | −0.0317821 | + | 0.0635642i | ||||
\(991\) | −56.0000 | −1.77890 | −0.889449 | − | 0.457034i | \(-0.848912\pi\) | ||||
−0.889449 | + | 0.457034i | \(0.848912\pi\) | |||||||
\(992\) | − | 10.0000i | − | 0.317500i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | 4.00000 | + | 2.00000i | 0.126809 | + | 0.0634043i | ||||
\(996\) | −14.0000 | −0.443607 | ||||||||
\(997\) | − | 16.0000i | − | 0.506725i | −0.967371 | − | 0.253363i | \(-0.918463\pi\) | ||
0.967371 | − | 0.253363i | \(-0.0815366\pi\) | |||||||
\(998\) | 4.00000i | 0.126618i | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 1155.2.c.a.694.1 | ✓ | 2 | |
5.2 | odd | 4 | 5775.2.a.s.1.1 | 1 | |||
5.3 | odd | 4 | 5775.2.a.h.1.1 | 1 | |||
5.4 | even | 2 | inner | 1155.2.c.a.694.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.a.694.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1155.2.c.a.694.2 | yes | 2 | 5.4 | even | 2 | inner | |
5775.2.a.h.1.1 | 1 | 5.3 | odd | 4 | |||
5775.2.a.s.1.1 | 1 | 5.2 | odd | 4 |